{"author":"Ismail Hammoudeh","acknowledgement":"Developed with extensive use of ChatGPT.","scope":"Every finite single-vertex motion with proper triangle endpoints. Distinct collinear crossings follow by continuity; coincidence-crossing paths by endpoint approximation. No value at an exactly coincident input is asserted.","records":[{"X":18236,"method":"Exact positive coefficients after a=v+w,b=w+u,c=u+v; Jxx,Jyy and determinant cleared by positive denominators.","tests":{"Jxx":{"passed":false,"degree":16,"terms":87,"negative_terms":11,"minimum_coefficient":"-49664","coefficients":[]},"Jyy":{"passed":true,"degree":16,"terms":95,"negative_terms":0,"minimum_coefficient":"512","coefficients":[{"powers":[0,6,10],"coefficient":"512"},{"powers":[0,7,9],"coefficient":"2560"},{"powers":[0,8,8],"coefficient":"5120"},{"powers":[0,9,7],"coefficient":"5120"},{"powers":[0,10,6],"coefficient":"2560"},{"powers":[0,11,5],"coefficient":"512"},{"powers":[1,5,10],"coefficient":"3072"},{"powers":[1,6,9],"coefficient":"11264"},{"powers":[1,7,8],"coefficient":"18432"},{"powers":[1,8,7],"coefficient":"19456"},{"powers":[1,9,6],"coefficient":"14336"},{"powers":[1,10,5],"coefficient":"6144"},{"powers":[1,11,4],"coefficient":"1024"},{"powers":[2,4,10],"coefficient":"7680"},{"powers":[2,5,9],"coefficient":"26624"},{"powers":[2,6,8],"coefficient":"38912"},{"powers":[2,7,7],"coefficient":"48640"},{"powers":[2,8,6],"coefficient":"60416"},{"powers":[2,9,5],"coefficient":"45568"},{"powers":[2,10,4],"coefficient":"15872"},{"powers":[2,11,3],"coefficient":"2048"},{"powers":[3,3,10],"coefficient":"10240"},{"powers":[3,4,9],"coefficient":"41472"},{"powers":[3,5,8],"coefficient":"71680"},{"powers":[3,6,7],"coefficient":"87552"},{"powers":[3,7,6],"coefficient":"90112"},{"powers":[3,8,5],"coefficient":"87552"},{"powers":[3,9,4],"coefficient":"64512"},{"powers":[3,10,3],"coefficient":"23040"},{"powers":[3,11,2],"coefficient":"3072"},{"powers":[4,2,10],"coefficient":"7680"},{"powers":[4,3,9],"coefficient":"41472"},{"powers":[4,4,8],"coefficient":"92160"},{"powers":[4,5,7],"coefficient":"109568"},{"powers":[4,6,6],"coefficient":"145920"},{"powers":[4,7,5],"coefficient":"154624"},{"powers":[4,8,4],"coefficient":"143360"},{"powers":[4,9,3],"coefficient":"79872"},{"powers":[4,10,2],"coefficient":"18432"},{"powers":[4,11,1],"coefficient":"1536"},{"powers":[5,1,10],"coefficient":"3072"},{"powers":[5,2,9],"coefficient":"26624"},{"powers":[5,3,8],"coefficient":"71680"},{"powers":[5,4,7],"coefficient":"109568"},{"powers":[5,5,6],"coefficient":"208896"},{"powers":[5,6,5],"coefficient":"295424"},{"powers":[5,7,4],"coefficient":"221184"},{"powers":[5,8,3],"coefficient":"134144"},{"powers":[5,9,2],"coefficient":"48128"},{"powers":[5,10,1],"coefficient":"7680"},{"powers":[6,0,10],"coefficient":"512"},{"powers":[6,1,9],"coefficient":"11264"},{"powers":[6,2,8],"coefficient":"38912"},{"powers":[6,3,7],"coefficient":"87552"},{"powers":[6,4,6],"coefficient":"145920"},{"powers":[6,5,5],"coefficient":"295424"},{"powers":[6,6,4],"coefficient":"254976"},{"powers":[6,7,3],"coefficient":"145920"},{"powers":[6,8,2],"coefficient":"75776"},{"powers":[6,9,1],"coefficient":"16896"},{"powers":[7,0,9],"coefficient":"2560"},{"powers":[7,1,8],"coefficient":"18432"},{"powers":[7,2,7],"coefficient":"48640"},{"powers":[7,3,6],"coefficient":"90112"},{"powers":[7,4,5],"coefficient":"154624"},{"powers":[7,5,4],"coefficient":"221184"},{"powers":[7,6,3],"coefficient":"145920"},{"powers":[7,7,2],"coefficient":"86016"},{"powers":[7,8,1],"coefficient":"23040"},{"powers":[8,0,8],"coefficient":"5120"},{"powers":[8,1,7],"coefficient":"19456"},{"powers":[8,2,6],"coefficient":"60416"},{"powers":[8,3,5],"coefficient":"87552"},{"powers":[8,4,4],"coefficient":"143360"},{"powers":[8,5,3],"coefficient":"134144"},{"powers":[8,6,2],"coefficient":"75776"},{"powers":[8,7,1],"coefficient":"23040"},{"powers":[9,0,7],"coefficient":"5120"},{"powers":[9,1,6],"coefficient":"14336"},{"powers":[9,2,5],"coefficient":"45568"},{"powers":[9,3,4],"coefficient":"64512"},{"powers":[9,4,3],"coefficient":"79872"},{"powers":[9,5,2],"coefficient":"48128"},{"powers":[9,6,1],"coefficient":"16896"},{"powers":[10,0,6],"coefficient":"2560"},{"powers":[10,1,5],"coefficient":"6144"},{"powers":[10,2,4],"coefficient":"15872"},{"powers":[10,3,3],"coefficient":"23040"},{"powers":[10,4,2],"coefficient":"18432"},{"powers":[10,5,1],"coefficient":"7680"},{"powers":[11,0,5],"coefficient":"512"},{"powers":[11,1,4],"coefficient":"1024"},{"powers":[11,2,3],"coefficient":"2048"},{"powers":[11,3,2],"coefficient":"3072"},{"powers":[11,4,1],"coefficient":"1536"}]},"determinant":{"passed":true,"degree":34,"terms":363,"negative_terms":0,"minimum_coefficient":"1048576","coefficients":[{"powers":[0,14,20],"coefficient":"1048576"},{"powers":[0,15,19],"coefficient":"10485760"},{"powers":[0,16,18],"coefficient":"47185920"},{"powers":[0,17,17],"coefficient":"125829120"},{"powers":[0,18,16],"coefficient":"220200960"},{"powers":[0,19,15],"coefficient":"264241152"},{"powers":[0,20,14],"coefficient":"220200960"},{"powers":[0,21,13],"coefficient":"125829120"},{"powers":[0,22,12],"coefficient":"47185920"},{"powers":[0,23,11],"coefficient":"10485760"},{"powers":[0,24,10],"coefficient":"1048576"},{"powers":[1,13,20],"coefficient":"14680064"},{"powers":[1,14,19],"coefficient":"133169152"},{"powers":[1,15,18],"coefficient":"551550976"},{"powers":[1,16,17],"coefficient":"1387266048"},{"powers":[1,17,16],"coefficient":"2378170368"},{"powers":[1,18,15],"coefficient":"2950692864"},{"powers":[1,19,14],"coefficient":"2730491904"},{"powers":[1,20,13],"coefficient":"1893728256"},{"powers":[1,21,12],"coefficient":"962592768"},{"powers":[1,22,11],"coefficient":"338690048"},{"powers":[1,23,10],"coefficient":"73400320"},{"powers":[1,24,9],"coefficient":"7340032"},{"powers":[2,12,20],"coefficient":"95420416"},{"powers":[2,13,19],"coefficient":"787480576"},{"powers":[2,14,18],"coefficient":"3009413120"},{"powers":[2,15,17],"coefficient":"7164919808"},{"powers":[2,16,16],"coefficient":"12080644096"},{"powers":[2,17,15],"coefficient":"15472787456"},{"powers":[2,18,14],"coefficient":"15575547904"},{"powers":[2,19,13],"coefficient":"12389974016"},{"powers":[2,20,12],"coefficient":"7657750528"},{"powers":[2,21,11],"coefficient":"3545235456"},{"powers":[2,22,10],"coefficient":"1153433600"},{"powers":[2,23,9],"coefficient":"233832448"},{"powers":[2,24,8],"coefficient":"22020096"},{"powers":[3,11,20],"coefficient":"381681664"},{"powers":[3,12,19],"coefficient":"2889875456"},{"powers":[3,13,18],"coefficient":"10252976128"},{"powers":[3,14,17],"coefficient":"23222812672"},{"powers":[3,15,16],"coefficient":"38645268480"},{"powers":[3,16,15],"coefficient":"50990153728"},{"powers":[3,17,14],"coefficient":"55125737472"},{"powers":[3,18,13],"coefficient":"48981082112"},{"powers":[3,19,12],"coefficient":"35217473536"},{"powers":[3,20,11],"coefficient":"19870515200"},{"powers":[3,21,10],"coefficient":"8382316544"},{"powers":[3,22,9],"coefficient":"2454716416"},{"powers":[3,23,8],"coefficient":"439353344"},{"powers":[3,24,7],"coefficient":"35651584"},{"powers":[4,10,20],"coefficient":"1049624576"},{"powers":[4,11,19],"coefficient":"7415529472"},{"powers":[4,12,18],"coefficient":"24704450560"},{"powers":[4,13,17],"coefficient":"53579087872"},{"powers":[4,14,16],"coefficient":"88282759168"},{"powers":[4,15,15],"coefficient":"119942414336"},{"powers":[4,16,14],"coefficient":"138332340224"},{"powers":[4,17,13],"coefficient":"135182417920"},{"powers":[4,18,12],"coefficient":"110071119872"},{"powers":[4,19,11],"coefficient":"72592916480"},{"powers":[4,20,10],"coefficient":"37212913664"},{"powers":[4,21,9],"coefficient":"13991149568"},{"powers":[4,22,8],"coefficient":"3537895424"},{"powers":[4,23,7],"coefficient":"520093696"},{"powers":[4,24,6],"coefficient":"32505856"},{"powers":[5,9,20],"coefficient":"2099249152"},{"powers":[5,10,19],"coefficient":"14244904960"},{"powers":[5,11,18],"coefficient":"45388660736"},{"powers":[5,12,17],"coefficient":"95046074368"},{"powers":[5,13,16],"coefficient":"155724021760"},{"powers":[5,14,15],"coefficient":"218481295360"},{"powers":[5,15,14],"coefficient":"267759124480"},{"powers":[5,16,13],"coefficient":"283666022400"},{"powers":[5,17,12],"coefficient":"255756075008"},{"powers":[5,18,11],"coefficient":"191541280768"},{"powers":[5,19,10],"coefficient":"114702680064"},{"powers":[5,20,9],"coefficient":"52176093184"},{"powers":[5,21,8],"coefficient":"16829644800"},{"powers":[5,22,7],"coefficient":"3469737984"},{"powers":[5,23,6],"coefficient":"381681664"},{"powers":[5,24,5],"coefficient":"15728640"},{"powers":[6,8,20],"coefficient":"3148873728"},{"powers":[6,9,19],"coefficient":"21442330624"},{"powers":[6,10,18],"coefficient":"67152904192"},{"powers":[6,11,17],"coefficient":"137372893184"},{"powers":[6,12,16],"coefficient":"225388265472"},{"powers":[6,13,15],"coefficient":"328535638016"},{"powers":[6,14,14],"coefficient":"425367437312"},{"powers":[6,15,13],"coefficient":"479342886912"},{"powers":[6,16,12],"coefficient":"467522289664"},{"powers":[6,17,11],"coefficient":"387815833600"},{"powers":[6,18,10],"coefficient":"263297433600"},{"powers":[6,19,9],"coefficient":"139591680000"},{"powers":[6,20,8],"coefficient":"54558457856"},{"powers":[6,21,7],"coefficient":"14406385664"},{"powers":[6,22,6],"coefficient":"2227175424"},{"powers":[6,23,5],"coefficient":"158334976"},{"powers":[6,24,4],"coefficient":"3145728"},{"powers":[7,7,20],"coefficient":"3598712832"},{"powers":[7,8,19],"coefficient":"26090668032"},{"powers":[7,9,18],"coefficient":"83393249280"},{"powers":[7,10,17],"coefficient":"169796960256"},{"powers":[7,11,16],"coefficient":"281883443200"},{"powers":[7,12,15],"coefficient":"429389774848"},{"powers":[7,13,14],"coefficient":"581262376960"},{"powers":[7,14,13],"coefficient":"679599931392"},{"powers":[7,15,12],"coefficient":"698146095104"},{"powers":[7,16,11],"coefficient":"626352193536"},{"powers":[7,17,10],"coefficient":"470400630784"},{"powers":[7,18,9],"coefficient":"282571309056"},{"powers":[7,19,8],"coefficient":"129411055616"},{"powers":[7,20,7],"coefficient":"42010148864"},{"powers":[7,21,6],"coefficient":"8545894400"},{"powers":[7,22,5],"coefficient":"858783744"},{"powers":[7,23,4],"coefficient":"28311552"},{"powers":[8,6,20],"coefficient":"3148873728"},{"powers":[8,7,19],"coefficient":"26090668032"},{"powers":[8,8,18],"coefficient":"89344966656"},{"powers":[8,9,17],"coefficient":"186614022144"},{"powers":[8,10,16],"coefficient":"317199482880"},{"powers":[8,11,15],"coefficient":"505602375680"},{"powers":[8,12,14],"coefficient":"707346300928"},{"powers":[8,13,13],"coefficient":"835569319936"},{"powers":[8,14,12],"coefficient":"876734316544"},{"powers":[8,15,11],"coefficient":"830281351168"},{"powers":[8,16,10],"coefficient":"675181232128"},{"powers":[8,17,9],"coefficient":"448997097472"},{"powers":[8,18,8],"coefficient":"235086544896"},{"powers":[8,19,7],"coefficient":"91607793664"},{"powers":[8,20,6],"coefficient":"23937941504"},{"powers":[8,21,5],"coefficient":"3381657600"},{"powers":[8,22,4],"coefficient":"164626432"},{"powers":[9,5,20],"coefficient":"2099249152"},{"powers":[9,6,19],"coefficient":"21442330624"},{"powers":[9,7,18],"coefficient":"83393249280"},{"powers":[9,8,17],"coefficient":"186614022144"},{"powers":[9,9,16],"coefficient":"329080897536"},{"powers":[9,10,15],"coefficient":"546721234944"},{"powers":[9,11,14],"coefficient":"786413125632"},{"powers":[9,12,13],"coefficient":"922637828096"},{"powers":[9,13,12],"coefficient":"958220206080"},{"powers":[9,14,11],"coefficient":"930417213440"},{"powers":[9,15,10],"coefficient":"800425246720"},{"powers":[9,16,9],"coefficient":"577882816512"},{"powers":[9,17,8],"coefficient":"340327923712"},{"powers":[9,18,7],"coefficient":"156434956288"},{"powers":[9,19,6],"coefficient":"51733594112"},{"powers":[9,20,5],"coefficient":"10365173760"},{"powers":[9,21,4],"coefficient":"830472192"},{"powers":[9,22,3],"coefficient":"8388608"},{"powers":[10,4,20],"coefficient":"1049624576"},{"powers":[10,5,19],"coefficient":"14244904960"},{"powers":[10,6,18],"coefficient":"67152904192"},{"powers":[10,7,17],"coefficient":"169796960256"},{"powers":[10,8,16],"coefficient":"317199482880"},{"powers":[10,9,15],"coefficient":"546721234944"},{"powers":[10,10,14],"coefficient":"812898058240"},{"powers":[10,11,13],"coefficient":"953560334336"},{"powers":[10,12,12],"coefficient":"962476376064"},{"powers":[10,13,11],"coefficient":"924373221376"},{"powers":[10,14,10],"coefficient":"812797394944"},{"powers":[10,15,9],"coefficient":"623663644672"},{"powers":[10,16,8],"coefficient":"410424180736"},{"powers":[10,17,7],"coefficient":"220066742272"},{"powers":[10,18,6],"coefficient":"90200604672"},{"powers":[10,19,5],"coefficient":"24961351680"},{"powers":[10,20,4],"coefficient":"3290431488"},{"powers":[10,21,3],"coefficient":"100663296"},{"powers":[11,3,20],"coefficient":"381681664"},{"powers":[11,4,19],"coefficient":"7415529472"},{"powers":[11,5,18],"coefficient":"45388660736"},{"powers":[11,6,17],"coefficient":"137372893184"},{"powers":[11,7,16],"coefficient":"281883443200"},{"powers":[11,8,15],"coefficient":"505602375680"},{"powers":[11,9,14],"coefficient":"786413125632"},{"powers":[11,10,13],"coefficient":"953560334336"},{"powers":[11,11,12],"coefficient":"952413192192"},{"powers":[11,12,11],"coefficient":"883353976832"},{"powers":[11,13,10],"coefficient":"757794340864"},{"powers":[11,14,9],"coefficient":"595551322112"},{"powers":[11,15,8],"coefficient":"435491438592"},{"powers":[11,16,7],"coefficient":"270975107072"},{"powers":[11,17,6],"coefficient":"132952096768"},{"powers":[11,18,5],"coefficient":"47874834432"},{"powers":[11,19,4],"coefficient":"9550430208"},{"powers":[11,20,3],"coefficient":"562036736"},{"powers":[12,2,20],"coefficient":"95420416"},{"powers":[12,3,19],"coefficient":"2889875456"},{"powers":[12,4,18],"coefficient":"24704450560"},{"powers":[12,5,17],"coefficient":"95046074368"},{"powers":[12,6,16],"coefficient":"225388265472"},{"powers":[12,7,15],"coefficient":"429389774848"},{"powers":[12,8,14],"coefficient":"707346300928"},{"powers":[12,9,13],"coefficient":"922637828096"},{"powers":[12,10,12],"coefficient":"962476376064"},{"powers":[12,11,11],"coefficient":"883353976832"},{"powers":[12,12,10],"coefficient":"724270317568"},{"powers":[12,13,9],"coefficient":"552823947264"},{"powers":[12,14,8],"coefficient":"433463492608"},{"powers":[12,15,7],"coefficient":"307916439552"},{"powers":[12,16,6],"coefficient":"172851462144"},{"powers":[12,17,5],"coefficient":"75116838912"},{"powers":[12,18,4],"coefficient":"20516438016"},{"powers":[12,19,3],"coefficient":"1937768448"},{"powers":[13,1,20],"coefficient":"14680064"},{"powers":[13,2,19],"coefficient":"787480576"},{"powers":[13,3,18],"coefficient":"10252976128"},{"powers":[13,4,17],"coefficient":"53579087872"},{"powers":[13,5,16],"coefficient":"155724021760"},{"powers":[13,6,15],"coefficient":"328535638016"},{"powers":[13,7,14],"coefficient":"581262376960"},{"powers":[13,8,13],"coefficient":"835569319936"},{"powers":[13,9,12],"coefficient":"958220206080"},{"powers":[13,10,11],"coefficient":"924373221376"},{"powers":[13,11,10],"coefficient":"757794340864"},{"powers":[13,12,9],"coefficient":"552823947264"},{"powers":[13,13,8],"coefficient":"429186351104"},{"powers":[13,14,7],"coefficient":"329223503872"},{"powers":[13,15,6],"coefficient":"202597466112"},{"powers":[13,16,5],"coefficient":"99411296256"},{"powers":[13,17,4],"coefficient":"33864810496"},{"powers":[13,18,3],"coefficient":"4613734400"},{"powers":[14,0,20],"coefficient":"1048576"},{"powers":[14,1,19],"coefficient":"133169152"},{"powers":[14,2,18],"coefficient":"3009413120"},{"powers":[14,3,17],"coefficient":"23222812672"},{"powers":[14,4,16],"coefficient":"88282759168"},{"powers":[14,5,15],"coefficient":"218481295360"},{"powers":[14,6,14],"coefficient":"425367437312"},{"powers":[14,7,13],"coefficient":"679599931392"},{"powers":[14,8,12],"coefficient":"876734316544"},{"powers":[14,9,11],"coefficient":"930417213440"},{"powers":[14,10,10],"coefficient":"812797394944"},{"powers":[14,11,9],"coefficient":"595551322112"},{"powers":[14,12,8],"coefficient":"433463492608"},{"powers":[14,13,7],"coefficient":"329223503872"},{"powers":[14,14,6],"coefficient":"213922086912"},{"powers":[14,15,5],"coefficient":"113665638400"},{"powers":[14,16,4],"coefficient":"44744835072"},{"powers":[14,17,3],"coefficient":"8027897856"},{"powers":[15,0,19],"coefficient":"10485760"},{"powers":[15,1,18],"coefficient":"551550976"},{"powers":[15,2,17],"coefficient":"7164919808"},{"powers":[15,3,16],"coefficient":"38645268480"},{"powers":[15,4,15],"coefficient":"119942414336"},{"powers":[15,5,14],"coefficient":"267759124480"},{"powers":[15,6,13],"coefficient":"479342886912"},{"powers":[15,7,12],"coefficient":"698146095104"},{"powers":[15,8,11],"coefficient":"830281351168"},{"powers":[15,9,10],"coefficient":"800425246720"},{"powers":[15,10,9],"coefficient":"623663644672"},{"powers":[15,11,8],"coefficient":"435491438592"},{"powers":[15,12,7],"coefficient":"307916439552"},{"powers":[15,13,6],"coefficient":"202597466112"},{"powers":[15,14,5],"coefficient":"113665638400"},{"powers":[15,15,4],"coefficient":"48890904576"},{"powers":[15,16,3],"coefficient":"10519314432"},{"powers":[16,0,18],"coefficient":"47185920"},{"powers":[16,1,17],"coefficient":"1387266048"},{"powers":[16,2,16],"coefficient":"12080644096"},{"powers":[16,3,15],"coefficient":"50990153728"},{"powers":[16,4,14],"coefficient":"138332340224"},{"powers":[16,5,13],"coefficient":"283666022400"},{"powers":[16,6,12],"coefficient":"467522289664"},{"powers":[16,7,11],"coefficient":"626352193536"},{"powers":[16,8,10],"coefficient":"675181232128"},{"powers":[16,9,9],"coefficient":"577882816512"},{"powers":[16,10,8],"coefficient":"410424180736"},{"powers":[16,11,7],"coefficient":"270975107072"},{"powers":[16,12,6],"coefficient":"172851462144"},{"powers":[16,13,5],"coefficient":"99411296256"},{"powers":[16,14,4],"coefficient":"44744835072"},{"powers":[16,15,3],"coefficient":"10519314432"},{"powers":[17,0,17],"coefficient":"125829120"},{"powers":[17,1,16],"coefficient":"2378170368"},{"powers":[17,2,15],"coefficient":"15472787456"},{"powers":[17,3,14],"coefficient":"55125737472"},{"powers":[17,4,13],"coefficient":"135182417920"},{"powers":[17,5,12],"coefficient":"255756075008"},{"powers":[17,6,11],"coefficient":"387815833600"},{"powers":[17,7,10],"coefficient":"470400630784"},{"powers":[17,8,9],"coefficient":"448997097472"},{"powers":[17,9,8],"coefficient":"340327923712"},{"powers":[17,10,7],"coefficient":"220066742272"},{"powers":[17,11,6],"coefficient":"132952096768"},{"powers":[17,12,5],"coefficient":"75116838912"},{"powers":[17,13,4],"coefficient":"33864810496"},{"powers":[17,14,3],"coefficient":"8027897856"},{"powers":[18,0,16],"coefficient":"220200960"},{"powers":[18,1,15],"coefficient":"2950692864"},{"powers":[18,2,14],"coefficient":"15575547904"},{"powers":[18,3,13],"coefficient":"48981082112"},{"powers":[18,4,12],"coefficient":"110071119872"},{"powers":[18,5,11],"coefficient":"191541280768"},{"powers":[18,6,10],"coefficient":"263297433600"},{"powers":[18,7,9],"coefficient":"282571309056"},{"powers":[18,8,8],"coefficient":"235086544896"},{"powers":[18,9,7],"coefficient":"156434956288"},{"powers":[18,10,6],"coefficient":"90200604672"},{"powers":[18,11,5],"coefficient":"47874834432"},{"powers":[18,12,4],"coefficient":"20516438016"},{"powers":[18,13,3],"coefficient":"4613734400"},{"powers":[19,0,15],"coefficient":"264241152"},{"powers":[19,1,14],"coefficient":"2730491904"},{"powers":[19,2,13],"coefficient":"12389974016"},{"powers":[19,3,12],"coefficient":"35217473536"},{"powers":[19,4,11],"coefficient":"72592916480"},{"powers":[19,5,10],"coefficient":"114702680064"},{"powers":[19,6,9],"coefficient":"139591680000"},{"powers":[19,7,8],"coefficient":"129411055616"},{"powers":[19,8,7],"coefficient":"91607793664"},{"powers":[19,9,6],"coefficient":"51733594112"},{"powers":[19,10,5],"coefficient":"24961351680"},{"powers":[19,11,4],"coefficient":"9550430208"},{"powers":[19,12,3],"coefficient":"1937768448"},{"powers":[20,0,14],"coefficient":"220200960"},{"powers":[20,1,13],"coefficient":"1893728256"},{"powers":[20,2,12],"coefficient":"7657750528"},{"powers":[20,3,11],"coefficient":"19870515200"},{"powers":[20,4,10],"coefficient":"37212913664"},{"powers":[20,5,9],"coefficient":"52176093184"},{"powers":[20,6,8],"coefficient":"54558457856"},{"powers":[20,7,7],"coefficient":"42010148864"},{"powers":[20,8,6],"coefficient":"23937941504"},{"powers":[20,9,5],"coefficient":"10365173760"},{"powers":[20,10,4],"coefficient":"3290431488"},{"powers":[20,11,3],"coefficient":"562036736"},{"powers":[21,0,13],"coefficient":"125829120"},{"powers":[21,1,12],"coefficient":"962592768"},{"powers":[21,2,11],"coefficient":"3545235456"},{"powers":[21,3,10],"coefficient":"8382316544"},{"powers":[21,4,9],"coefficient":"13991149568"},{"powers":[21,5,8],"coefficient":"16829644800"},{"powers":[21,6,7],"coefficient":"14406385664"},{"powers":[21,7,6],"coefficient":"8545894400"},{"powers":[21,8,5],"coefficient":"3381657600"},{"powers":[21,9,4],"coefficient":"830472192"},{"powers":[21,10,3],"coefficient":"100663296"},{"powers":[22,0,12],"coefficient":"47185920"},{"powers":[22,1,11],"coefficient":"338690048"},{"powers":[22,2,10],"coefficient":"1153433600"},{"powers":[22,3,9],"coefficient":"2454716416"},{"powers":[22,4,8],"coefficient":"3537895424"},{"powers":[22,5,7],"coefficient":"3469737984"},{"powers":[22,6,6],"coefficient":"2227175424"},{"powers":[22,7,5],"coefficient":"858783744"},{"powers":[22,8,4],"coefficient":"164626432"},{"powers":[22,9,3],"coefficient":"8388608"},{"powers":[23,0,11],"coefficient":"10485760"},{"powers":[23,1,10],"coefficient":"73400320"},{"powers":[23,2,9],"coefficient":"233832448"},{"powers":[23,3,8],"coefficient":"439353344"},{"powers":[23,4,7],"coefficient":"520093696"},{"powers":[23,5,6],"coefficient":"381681664"},{"powers":[23,6,5],"coefficient":"158334976"},{"powers":[23,7,4],"coefficient":"28311552"},{"powers":[24,0,10],"coefficient":"1048576"},{"powers":[24,1,9],"coefficient":"7340032"},{"powers":[24,2,8],"coefficient":"22020096"},{"powers":[24,3,7],"coefficient":"35651584"},{"powers":[24,4,6],"coefficient":"32505856"},{"powers":[24,5,5],"coefficient":"15728640"},{"powers":[24,6,4],"coefficient":"3145728"}]},"weight_sum_squared":{"passed":true,"degree":12,"terms":61,"negative_terms":0,"minimum_coefficient":"256","coefficients":[{"powers":[0,4,8],"coefficient":"256"},{"powers":[0,5,7],"coefficient":"1024"},{"powers":[0,6,6],"coefficient":"1536"},{"powers":[0,7,5],"coefficient":"1024"},{"powers":[0,8,4],"coefficient":"256"},{"powers":[1,3,8],"coefficient":"1024"},{"powers":[1,4,7],"coefficient":"2560"},{"powers":[1,5,6],"coefficient":"2560"},{"powers":[1,6,5],"coefficient":"2560"},{"powers":[1,7,4],"coefficient":"2560"},{"powers":[1,8,3],"coefficient":"1024"},{"powers":[2,2,8],"coefficient":"1536"},{"powers":[2,3,7],"coefficient":"2560"},{"powers":[2,4,6],"coefficient":"2816"},{"powers":[2,5,5],"coefficient":"3584"},{"powers":[2,6,4],"coefficient":"2816"},{"powers":[2,7,3],"coefficient":"2560"},{"powers":[2,8,2],"coefficient":"1536"},{"powers":[3,1,8],"coefficient":"1024"},{"powers":[3,2,7],"coefficient":"2560"},{"powers":[3,3,6],"coefficient":"3584"},{"powers":[3,4,5],"coefficient":"5120"},{"powers":[3,5,4],"coefficient":"5120"},{"powers":[3,6,3],"coefficient":"3584"},{"powers":[3,7,2],"coefficient":"2560"},{"powers":[3,8,1],"coefficient":"1024"},{"powers":[4,0,8],"coefficient":"256"},{"powers":[4,1,7],"coefficient":"2560"},{"powers":[4,2,6],"coefficient":"2816"},{"powers":[4,3,5],"coefficient":"5120"},{"powers":[4,4,4],"coefficient":"9216"},{"powers":[4,5,3],"coefficient":"5120"},{"powers":[4,6,2],"coefficient":"2816"},{"powers":[4,7,1],"coefficient":"2560"},{"powers":[4,8,0],"coefficient":"256"},{"powers":[5,0,7],"coefficient":"1024"},{"powers":[5,1,6],"coefficient":"2560"},{"powers":[5,2,5],"coefficient":"3584"},{"powers":[5,3,4],"coefficient":"5120"},{"powers":[5,4,3],"coefficient":"5120"},{"powers":[5,5,2],"coefficient":"3584"},{"powers":[5,6,1],"coefficient":"2560"},{"powers":[5,7,0],"coefficient":"1024"},{"powers":[6,0,6],"coefficient":"1536"},{"powers":[6,1,5],"coefficient":"2560"},{"powers":[6,2,4],"coefficient":"2816"},{"powers":[6,3,3],"coefficient":"3584"},{"powers":[6,4,2],"coefficient":"2816"},{"powers":[6,5,1],"coefficient":"2560"},{"powers":[6,6,0],"coefficient":"1536"},{"powers":[7,0,5],"coefficient":"1024"},{"powers":[7,1,4],"coefficient":"2560"},{"powers":[7,2,3],"coefficient":"2560"},{"powers":[7,3,2],"coefficient":"2560"},{"powers":[7,4,1],"coefficient":"2560"},{"powers":[7,5,0],"coefficient":"1024"},{"powers":[8,0,4],"coefficient":"256"},{"powers":[8,1,3],"coefficient":"1024"},{"powers":[8,2,2],"coefficient":"1536"},{"powers":[8,3,1],"coefficient":"1024"},{"powers":[8,4,0],"coefficient":"256"}]}},"passed":true,"proper_path_certificate":true,"nonzero_on_distinct_collinear_triangles":true,"finite_proper_endpoint_certificate":true},{"X":56203,"method":"Exact positive coefficients after a=v+w,b=w+u,c=u+v; Jxx,Jyy and determinant cleared by positive denominators.","tests":{"Jxx":{"passed":true,"degree":12,"terms":69,"negative_terms":0,"minimum_coefficient":"1008","coefficients":[{"powers":[0,4,8],"coefficient":"3024"},{"powers":[0,5,7],"coefficient":"15120"},{"powers":[0,6,6],"coefficient":"30240"},{"powers":[0,7,5],"coefficient":"30240"},{"powers":[0,8,4],"coefficient":"15120"},{"powers":[0,9,3],"coefficient":"3024"},{"powers":[1,3,8],"coefficient":"12096"},{"powers":[1,4,7],"coefficient":"90000"},{"powers":[1,5,6],"coefficient":"247248"},{"powers":[1,6,5],"coefficient":"333216"},{"powers":[1,7,4],"coefficient":"234720"},{"powers":[1,8,3],"coefficient":"81360"},{"powers":[1,9,2],"coefficient":"10512"},{"powers":[2,2,8],"coefficient":"18144"},{"powers":[2,3,7],"coefficient":"139104"},{"powers":[2,4,6],"coefficient":"474144"},{"powers":[2,5,5],"coefficient":"820704"},{"powers":[2,6,4],"coefficient":"744624"},{"powers":[2,7,3],"coefficient":"338640"},{"powers":[2,8,2],"coefficient":"63120"},{"powers":[2,9,1],"coefficient":"1584"},{"powers":[3,1,8],"coefficient":"12096"},{"powers":[3,2,7],"coefficient":"139104"},{"powers":[3,3,6],"coefficient":"514272"},{"powers":[3,4,5],"coefficient":"1009760"},{"powers":[3,5,4],"coefficient":"1119200"},{"powers":[3,6,3],"coefficient":"667216"},{"powers":[3,7,2],"coefficient":"188560"},{"powers":[3,8,1],"coefficient":"19056"},{"powers":[3,9,0],"coefficient":"1008"},{"powers":[4,0,8],"coefficient":"3024"},{"powers":[4,1,7],"coefficient":"90000"},{"powers":[4,2,6],"coefficient":"474144"},{"powers":[4,3,5],"coefficient":"1009760"},{"powers":[4,4,4],"coefficient":"1188352"},{"powers":[4,5,3],"coefficient":"850752"},{"powers":[4,6,2],"coefficient":"354352"},{"powers":[4,7,1],"coefficient":"73104"},{"powers":[4,8,0],"coefficient":"6048"},{"powers":[5,0,7],"coefficient":"15120"},{"powers":[5,1,6],"coefficient":"247248"},{"powers":[5,2,5],"coefficient":"820704"},{"powers":[5,3,4],"coefficient":"1119200"},{"powers":[5,4,3],"coefficient":"850752"},{"powers":[5,5,2],"coefficient":"436800"},{"powers":[5,6,1],"coefficient":"135120"},{"powers":[5,7,0],"coefficient":"15120"},{"powers":[6,0,6],"coefficient":"30240"},{"powers":[6,1,5],"coefficient":"333216"},{"powers":[6,2,4],"coefficient":"744624"},{"powers":[6,3,3],"coefficient":"667216"},{"powers":[6,4,2],"coefficient":"354352"},{"powers":[6,5,1],"coefficient":"135120"},{"powers":[6,6,0],"coefficient":"20160"},{"powers":[7,0,5],"coefficient":"30240"},{"powers":[7,1,4],"coefficient":"234720"},{"powers":[7,2,3],"coefficient":"338640"},{"powers":[7,3,2],"coefficient":"188560"},{"powers":[7,4,1],"coefficient":"73104"},{"powers":[7,5,0],"coefficient":"15120"},{"powers":[8,0,4],"coefficient":"15120"},{"powers":[8,1,3],"coefficient":"81360"},{"powers":[8,2,2],"coefficient":"63120"},{"powers":[8,3,1],"coefficient":"19056"},{"powers":[8,4,0],"coefficient":"6048"},{"powers":[9,0,3],"coefficient":"3024"},{"powers":[9,1,2],"coefficient":"10512"},{"powers":[9,2,1],"coefficient":"1584"},{"powers":[9,3,0],"coefficient":"1008"}]},"Jyy":{"passed":true,"degree":12,"terms":60,"negative_terms":0,"minimum_coefficient":"3024","coefficients":[{"powers":[0,4,8],"coefficient":"3024"},{"powers":[0,5,7],"coefficient":"16128"},{"powers":[0,6,6],"coefficient":"34272"},{"powers":[0,7,5],"coefficient":"36288"},{"powers":[0,8,4],"coefficient":"19152"},{"powers":[0,9,3],"coefficient":"4032"},{"powers":[1,3,8],"coefficient":"12096"},{"powers":[1,4,7],"coefficient":"72000"},{"powers":[1,5,6],"coefficient":"172560"},{"powers":[1,6,5],"coefficient":"206640"},{"powers":[1,7,4],"coefficient":"123120"},{"powers":[1,8,3],"coefficient":"29136"},{"powers":[2,2,8],"coefficient":"18144"},{"powers":[2,3,7],"coefficient":"190656"},{"powers":[2,4,6],"coefficient":"649056"},{"powers":[2,5,5],"coefficient":"1062128"},{"powers":[2,6,4],"coefficient":"927376"},{"powers":[2,7,3],"coefficient":"432272"},{"powers":[2,8,2],"coefficient":"102576"},{"powers":[2,9,1],"coefficient":"12096"},{"powers":[3,1,8],"coefficient":"12096"},{"powers":[3,2,7],"coefficient":"190656"},{"powers":[3,3,6],"coefficient":"1021536"},{"powers":[3,4,5],"coefficient":"2405152"},{"powers":[3,5,4],"coefficient":"2904784"},{"powers":[3,6,3],"coefficient":"1875248"},{"powers":[3,7,2],"coefficient":"618320"},{"powers":[3,8,1],"coefficient":"85680"},{"powers":[4,0,8],"coefficient":"3024"},{"powers":[4,1,7],"coefficient":"72000"},{"powers":[4,2,6],"coefficient":"649056"},{"powers":[4,3,5],"coefficient":"2405152"},{"powers":[4,4,4],"coefficient":"4162752"},{"powers":[4,5,3],"coefficient":"3632048"},{"powers":[4,6,2],"coefficient":"1550096"},{"powers":[4,7,1],"coefficient":"259056"},{"powers":[5,0,7],"coefficient":"16128"},{"powers":[5,1,6],"coefficient":"172560"},{"powers":[5,2,5],"coefficient":"1062128"},{"powers":[5,3,4],"coefficient":"2904784"},{"powers":[5,4,3],"coefficient":"3632048"},{"powers":[5,5,2],"coefficient":"2068704"},{"powers":[5,6,1],"coefficient":"433440"},{"powers":[6,0,6],"coefficient":"34272"},{"powers":[6,1,5],"coefficient":"206640"},{"powers":[6,2,4],"coefficient":"927376"},{"powers":[6,3,3],"coefficient":"1875248"},{"powers":[6,4,2],"coefficient":"1550096"},{"powers":[6,5,1],"coefficient":"433440"},{"powers":[7,0,5],"coefficient":"36288"},{"powers":[7,1,4],"coefficient":"123120"},{"powers":[7,2,3],"coefficient":"432272"},{"powers":[7,3,2],"coefficient":"618320"},{"powers":[7,4,1],"coefficient":"259056"},{"powers":[8,0,4],"coefficient":"19152"},{"powers":[8,1,3],"coefficient":"29136"},{"powers":[8,2,2],"coefficient":"102576"},{"powers":[8,3,1],"coefficient":"85680"},{"powers":[9,0,3],"coefficient":"4032"},{"powers":[9,2,1],"coefficient":"12096"}]},"determinant":{"passed":true,"degree":26,"terms":266,"negative_terms":0,"minimum_coefficient":"36578304","coefficients":[{"powers":[0,10,16],"coefficient":"36578304"},{"powers":[0,11,15],"coefficient":"377975808"},{"powers":[0,12,14],"coefficient":"1755758592"},{"powers":[0,13,13],"coefficient":"4828336128"},{"powers":[0,14,12],"coefficient":"8705636352"},{"powers":[0,15,11],"coefficient":"10754021376"},{"powers":[0,16,10],"coefficient":"9217732608"},{"powers":[0,17,9],"coefficient":"5413588992"},{"powers":[0,18,8],"coefficient":"2084963328"},{"powers":[0,19,7],"coefficient":"475517952"},{"powers":[0,20,6],"coefficient":"48771072"},{"powers":[1,9,16],"coefficient":"365783040"},{"powers":[1,10,15],"coefficient":"4227406848"},{"powers":[1,11,14],"coefficient":"21850269696"},{"powers":[1,12,13],"coefficient":"66677686272"},{"powers":[1,13,12],"coefficient":"133391453184"},{"powers":[1,14,11],"coefficient":"183423937536"},{"powers":[1,15,10],"coefficient":"176454319104"},{"powers":[1,16,9],"coefficient":"118262301696"},{"powers":[1,17,8],"coefficient":"53746301952"},{"powers":[1,18,7],"coefficient":"15588993024"},{"powers":[1,19,6],"coefficient":"2539662336"},{"powers":[1,20,5],"coefficient":"167463936"},{"powers":[2,8,16],"coefficient":"1646023680"},{"powers":[2,9,15],"coefficient":"21415726080"},{"powers":[2,10,14],"coefficient":"123862929408"},{"powers":[2,11,13],"coefficient":"421380182016"},{"powers":[2,12,12],"coefficient":"938570720256"},{"powers":[2,13,11],"coefficient":"1439221506048"},{"powers":[2,14,10],"coefficient":"1552434951168"},{"powers":[2,15,9],"coefficient":"1180058996736"},{"powers":[2,16,8],"coefficient":"621668653056"},{"powers":[2,17,7],"coefficient":"218137936896"},{"powers":[2,18,6],"coefficient":"47221152768"},{"powers":[2,19,5],"coefficient":"5420003328"},{"powers":[2,20,4],"coefficient":"229920768"},{"powers":[3,7,16],"coefficient":"4389396480"},{"powers":[3,8,15],"coefficient":"64874234880"},{"powers":[3,9,14],"coefficient":"422788958208"},{"powers":[3,10,13],"coefficient":"1612106993664"},{"powers":[3,11,12],"coefficient":"4013510971392"},{"powers":[3,12,11],"coefficient":"6878236032000"},{"powers":[3,13,10],"coefficient":"8317533901824"},{"powers":[3,14,9],"coefficient":"7140831528960"},{"powers":[3,15,8],"coefficient":"4309302767616"},{"powers":[3,16,7],"coefficient":"1777147379712"},{"powers":[3,17,6],"coefficient":"474427468800"},{"powers":[3,18,5],"coefficient":"74202292224"},{"powers":[3,19,4],"coefficient":"5559293952"},{"powers":[3,20,3],"coefficient":"114296832"},{"powers":[4,6,16],"coefficient":"7681443840"},{"powers":[4,7,15],"coefficient":"130584545280"},{"powers":[4,8,14],"coefficient":"967633993728"},{"powers":[4,9,13],"coefficient":"4162908708864"},{"powers":[4,10,12],"coefficient":"11639102211072"},{"powers":[4,11,11],"coefficient":"22358946757632"},{"powers":[4,12,10],"coefficient":"30339841050624"},{"powers":[4,13,9],"coefficient":"29365757174784"},{"powers":[4,14,8],"coefficient":"20174308534272"},{"powers":[4,15,7],"coefficient":"9641609342976"},{"powers":[4,16,6],"coefficient":"3081769273344"},{"powers":[4,17,5],"coefficient":"615897019392"},{"powers":[4,18,4],"coefficient":"69094407168"},{"powers":[4,19,3],"coefficient":"3862066176"},{"powers":[4,20,2],"coefficient":"134701056"},{"powers":[5,5,16],"coefficient":"9217732608"},{"powers":[5,6,15],"coefficient":"183403616256"},{"powers":[5,7,14],"coefficient":"1564192788480"},{"powers":[5,8,13],"coefficient":"7658556936192"},{"powers":[5,9,12],"coefficient":"24193131992064"},{"powers":[5,10,11],"coefficient":"52302173853696"},{"powers":[5,11,10],"coefficient":"79794905521152"},{"powers":[5,12,9],"coefficient":"87043463871488"},{"powers":[5,13,8],"coefficient":"67843941320704"},{"powers":[5,14,7],"coefficient":"37266132903936"},{"powers":[5,15,6],"coefficient":"14021396240384"},{"powers":[5,16,5],"coefficient":"3452202993664"},{"powers":[5,17,4],"coefficient":"523769115648"},{"powers":[5,18,3],"coefficient":"47285028864"},{"powers":[5,19,2],"coefficient":"2711190528"},{"powers":[5,20,1],"coefficient":"46697472"},{"powers":[6,4,16],"coefficient":"7681443840"},{"powers":[6,5,15],"coefficient":"183403616256"},{"powers":[6,6,14],"coefficient":"1831158669312"},{"powers":[6,7,13],"coefficient":"10324140761088"},{"powers":[6,8,12],"coefficient":"37148031737856"},{"powers":[6,9,11],"coefficient":"90861528112128"},{"powers":[6,10,10],"coefficient":"156331525721088"},{"powers":[6,11,9],"coefficient":"192339941206016"},{"powers":[6,12,8],"coefficient":"169749880688640"},{"powers":[6,13,7],"coefficient":"106535935410176"},{"powers":[6,14,6],"coefficient":"46579590877184"},{"powers":[6,15,5],"coefficient":"13735056420864"},{"powers":[6,16,4],"coefficient":"2626866636800"},{"powers":[6,17,3],"coefficient":"318077979648"},{"powers":[6,18,2],"coefficient":"24060552192"},{"powers":[6,19,1],"coefficient":"712820736"},{"powers":[7,3,16],"coefficient":"4389396480"},{"powers":[7,4,15],"coefficient":"130584545280"},{"powers":[7,5,14],"coefficient":"1564192788480"},{"powers":[7,6,13],"coefficient":"10324140761088"},{"powers":[7,7,12],"coefficient":"42788751777792"},{"powers":[7,8,11],"coefficient":"119290453782528"},{"powers":[7,9,10],"coefficient":"232502393951232"},{"powers":[7,10,9],"coefficient":"323251211599872"},{"powers":[7,11,8],"coefficient":"322773272571904"},{"powers":[7,12,7],"coefficient":"230450954405888"},{"powers":[7,13,6],"coefficient":"115905739683840"},{"powers":[7,14,5],"coefficient":"40068723773440"},{"powers":[7,15,4],"coefficient":"9235544428544"},{"powers":[7,16,3],"coefficient":"1380531560448"},{"powers":[7,17,2],"coefficient":"127379727360"},{"powers":[7,18,1],"coefficient":"5063897088"},{"powers":[8,2,16],"coefficient":"1646023680"},{"powers":[8,3,15],"coefficient":"64874234880"},{"powers":[8,4,14],"coefficient":"967633993728"},{"powers":[8,5,13],"coefficient":"7658556936192"},{"powers":[8,6,12],"coefficient":"37148031737856"},{"powers":[8,7,11],"coefficient":"119290453782528"},{"powers":[8,8,10],"coefficient":"265116536475648"},{"powers":[8,9,9],"coefficient":"417956644670464"},{"powers":[8,10,8],"coefficient":"472433528794112"},{"powers":[8,11,7],"coefficient":"382672881890304"},{"powers":[8,12,6],"coefficient":"219779316959232"},{"powers":[8,13,5],"coefficient":"87749499893760"},{"powers":[8,14,4],"coefficient":"23709583736832"},{"powers":[8,15,3],"coefficient":"4196128708608"},{"powers":[8,16,2],"coefficient":"454974769152"},{"powers":[8,17,1],"coefficient":"22211324928"},{"powers":[9,1,16],"coefficient":"365783040"},{"powers":[9,2,15],"coefficient":"21415726080"},{"powers":[9,3,14],"coefficient":"422788958208"},{"powers":[9,4,13],"coefficient":"4162908708864"},{"powers":[9,5,12],"coefficient":"24193131992064"},{"powers":[9,6,11],"coefficient":"90861528112128"},{"powers":[9,7,10],"coefficient":"232502393951232"},{"powers":[9,8,9],"coefficient":"417956644670464"},{"powers":[9,9,8],"coefficient":"536002417342464"},{"powers":[9,10,7],"coefficient":"492091103226880"},{"powers":[9,11,6],"coefficient":"321222224812032"},{"powers":[9,12,5],"coefficient":"146682155925504"},{"powers":[9,13,4],"coefficient":"45692926798848"},{"powers":[9,14,3],"coefficient":"9362931084288"},{"powers":[9,15,2],"coefficient":"1169718635520"},{"powers":[9,16,1],"coefficient":"67276624896"},{"powers":[10,0,16],"coefficient":"36578304"},{"powers":[10,1,15],"coefficient":"4227406848"},{"powers":[10,2,14],"coefficient":"123862929408"},{"powers":[10,3,13],"coefficient":"1612106993664"},{"powers":[10,4,12],"coefficient":"11639102211072"},{"powers":[10,5,11],"coefficient":"52302173853696"},{"powers":[10,6,10],"coefficient":"156331525721088"},{"powers":[10,7,9],"coefficient":"323251211599872"},{"powers":[10,8,8],"coefficient":"472433528794112"},{"powers":[10,9,7],"coefficient":"492091103226880"},{"powers":[10,10,6],"coefficient":"364276761667584"},{"powers":[10,11,5],"coefficient":"189156174753792"},{"powers":[10,12,4],"coefficient":"67289731943424"},{"powers":[10,13,3],"coefficient":"15776076349440"},{"powers":[10,14,2],"coefficient":"2247578606592"},{"powers":[10,15,1],"coefficient":"149068947456"},{"powers":[11,0,15],"coefficient":"377975808"},{"powers":[11,1,14],"coefficient":"21850269696"},{"powers":[11,2,13],"coefficient":"421380182016"},{"powers":[11,3,12],"coefficient":"4013510971392"},{"powers":[11,4,11],"coefficient":"22358946757632"},{"powers":[11,5,10],"coefficient":"79794905521152"},{"powers":[11,6,9],"coefficient":"192339941206016"},{"powers":[11,7,8],"coefficient":"322773272571904"},{"powers":[11,8,7],"coefficient":"382672881890304"},{"powers":[11,9,6],"coefficient":"321222224812032"},{"powers":[11,10,5],"coefficient":"189156174753792"},{"powers":[11,11,4],"coefficient":"76475414016000"},{"powers":[11,12,3],"coefficient":"20401830890496"},{"powers":[11,13,2],"coefficient":"3299902239744"},{"powers":[11,14,1],"coefficient":"249626437632"},{"powers":[12,0,14],"coefficient":"1755758592"},{"powers":[12,1,13],"coefficient":"66677686272"},{"powers":[12,2,12],"coefficient":"938570720256"},{"powers":[12,3,11],"coefficient":"6878236032000"},{"powers":[12,4,10],"coefficient":"30339841050624"},{"powers":[12,5,9],"coefficient":"87043463871488"},{"powers":[12,6,8],"coefficient":"169749880688640"},{"powers":[12,7,7],"coefficient":"230450954405888"},{"powers":[12,8,6],"coefficient":"219779316959232"},{"powers":[12,9,5],"coefficient":"146682155925504"},{"powers":[12,10,4],"coefficient":"67289731943424"},{"powers":[12,11,3],"coefficient":"20401830890496"},{"powers":[12,12,2],"coefficient":"3745926328320"},{"powers":[12,13,1],"coefficient":"321705686016"},{"powers":[13,0,13],"coefficient":"4828336128"},{"powers":[13,1,12],"coefficient":"133391453184"},{"powers":[13,2,11],"coefficient":"1439221506048"},{"powers":[13,3,10],"coefficient":"8317533901824"},{"powers":[13,4,9],"coefficient":"29365757174784"},{"powers":[13,5,8],"coefficient":"67843941320704"},{"powers":[13,6,7],"coefficient":"106535935410176"},{"powers":[13,7,6],"coefficient":"115905739683840"},{"powers":[13,8,5],"coefficient":"87749499893760"},{"powers":[13,9,4],"coefficient":"45692926798848"},{"powers":[13,10,3],"coefficient":"15776076349440"},{"powers":[13,11,2],"coefficient":"3299902239744"},{"powers":[13,12,1],"coefficient":"321705686016"},{"powers":[14,0,12],"coefficient":"8705636352"},{"powers":[14,1,11],"coefficient":"183423937536"},{"powers":[14,2,10],"coefficient":"1552434951168"},{"powers":[14,3,9],"coefficient":"7140831528960"},{"powers":[14,4,8],"coefficient":"20174308534272"},{"powers":[14,5,7],"coefficient":"37266132903936"},{"powers":[14,6,6],"coefficient":"46579590877184"},{"powers":[14,7,5],"coefficient":"40068723773440"},{"powers":[14,8,4],"coefficient":"23709583736832"},{"powers":[14,9,3],"coefficient":"9362931084288"},{"powers":[14,10,2],"coefficient":"2247578606592"},{"powers":[14,11,1],"coefficient":"249626437632"},{"powers":[15,0,11],"coefficient":"10754021376"},{"powers":[15,1,10],"coefficient":"176454319104"},{"powers":[15,2,9],"coefficient":"1180058996736"},{"powers":[15,3,8],"coefficient":"4309302767616"},{"powers":[15,4,7],"coefficient":"9641609342976"},{"powers":[15,5,6],"coefficient":"14021396240384"},{"powers":[15,6,5],"coefficient":"13735056420864"},{"powers":[15,7,4],"coefficient":"9235544428544"},{"powers":[15,8,3],"coefficient":"4196128708608"},{"powers":[15,9,2],"coefficient":"1169718635520"},{"powers":[15,10,1],"coefficient":"149068947456"},{"powers":[16,0,10],"coefficient":"9217732608"},{"powers":[16,1,9],"coefficient":"118262301696"},{"powers":[16,2,8],"coefficient":"621668653056"},{"powers":[16,3,7],"coefficient":"1777147379712"},{"powers":[16,4,6],"coefficient":"3081769273344"},{"powers":[16,5,5],"coefficient":"3452202993664"},{"powers":[16,6,4],"coefficient":"2626866636800"},{"powers":[16,7,3],"coefficient":"1380531560448"},{"powers":[16,8,2],"coefficient":"454974769152"},{"powers":[16,9,1],"coefficient":"67276624896"},{"powers":[17,0,9],"coefficient":"5413588992"},{"powers":[17,1,8],"coefficient":"53746301952"},{"powers":[17,2,7],"coefficient":"218137936896"},{"powers":[17,3,6],"coefficient":"474427468800"},{"powers":[17,4,5],"coefficient":"615897019392"},{"powers":[17,5,4],"coefficient":"523769115648"},{"powers":[17,6,3],"coefficient":"318077979648"},{"powers":[17,7,2],"coefficient":"127379727360"},{"powers":[17,8,1],"coefficient":"22211324928"},{"powers":[18,0,8],"coefficient":"2084963328"},{"powers":[18,1,7],"coefficient":"15588993024"},{"powers":[18,2,6],"coefficient":"47221152768"},{"powers":[18,3,5],"coefficient":"74202292224"},{"powers":[18,4,4],"coefficient":"69094407168"},{"powers":[18,5,3],"coefficient":"47285028864"},{"powers":[18,6,2],"coefficient":"24060552192"},{"powers":[18,7,1],"coefficient":"5063897088"},{"powers":[19,0,7],"coefficient":"475517952"},{"powers":[19,1,6],"coefficient":"2539662336"},{"powers":[19,2,5],"coefficient":"5420003328"},{"powers":[19,3,4],"coefficient":"5559293952"},{"powers":[19,4,3],"coefficient":"3862066176"},{"powers":[19,5,2],"coefficient":"2711190528"},{"powers":[19,6,1],"coefficient":"712820736"},{"powers":[20,0,6],"coefficient":"48771072"},{"powers":[20,1,5],"coefficient":"167463936"},{"powers":[20,2,4],"coefficient":"229920768"},{"powers":[20,3,3],"coefficient":"114296832"},{"powers":[20,4,2],"coefficient":"134701056"},{"powers":[20,5,1],"coefficient":"46697472"}]},"weight_sum_squared":{"passed":true,"degree":8,"terms":36,"negative_terms":0,"minimum_coefficient":"1764","coefficients":[{"powers":[0,2,6],"coefficient":"1764"},{"powers":[0,3,5],"coefficient":"7056"},{"powers":[0,4,4],"coefficient":"10584"},{"powers":[0,5,3],"coefficient":"7056"},{"powers":[0,6,2],"coefficient":"1764"},{"powers":[1,1,6],"coefficient":"3528"},{"powers":[1,2,5],"coefficient":"26544"},{"powers":[1,3,4],"coefficient":"61992"},{"powers":[1,4,3],"coefficient":"61992"},{"powers":[1,5,2],"coefficient":"26544"},{"powers":[1,6,1],"coefficient":"3528"},{"powers":[2,0,6],"coefficient":"1764"},{"powers":[2,1,5],"coefficient":"26544"},{"powers":[2,2,4],"coefficient":"106912"},{"powers":[2,3,3],"coefficient":"164264"},{"powers":[2,4,2],"coefficient":"106912"},{"powers":[2,5,1],"coefficient":"26544"},{"powers":[2,6,0],"coefficient":"1764"},{"powers":[3,0,5],"coefficient":"7056"},{"powers":[3,1,4],"coefficient":"61992"},{"powers":[3,2,3],"coefficient":"164264"},{"powers":[3,3,2],"coefficient":"164264"},{"powers":[3,4,1],"coefficient":"61992"},{"powers":[3,5,0],"coefficient":"7056"},{"powers":[4,0,4],"coefficient":"10584"},{"powers":[4,1,3],"coefficient":"61992"},{"powers":[4,2,2],"coefficient":"106912"},{"powers":[4,3,1],"coefficient":"61992"},{"powers":[4,4,0],"coefficient":"10584"},{"powers":[5,0,3],"coefficient":"7056"},{"powers":[5,1,2],"coefficient":"26544"},{"powers":[5,2,1],"coefficient":"26544"},{"powers":[5,3,0],"coefficient":"7056"},{"powers":[6,0,2],"coefficient":"1764"},{"powers":[6,1,1],"coefficient":"3528"},{"powers":[6,2,0],"coefficient":"1764"}]}},"passed":true,"proper_path_certificate":true,"nonzero_on_distinct_collinear_triangles":true,"finite_proper_endpoint_certificate":true}]}