{ "Index":74, "Name":"9_39", "RolfsenName":"9_39", "DTname":"9a_32", "TunnelNumber":2, "BridgeNumber":"Not implemented", "Hyperbolic":true, "Diagram":{ "Scode":"{-12, 16, -10, -18, -14, -2, -6, 4, -8}", "Acode":"{-7, 9, -6, -1, -8, -2, -4, 3, -5}", "PDcode":[ "{1, 12, 2, 13}", "{3, 17, 4, 16}", "{5, 10, 6, 11}", "{7, 18, 8, 1}", "{9, 14, 10, 15}", "{11, 2, 12, 3}", "{13, 6, 14, 7}", "{15, 5, 16, 4}", "{17, 8, 18, 9}" ], "CBtype":"{3, 0}", "ParabolicReps":{ "SolvingSeq":[ "{1, 7, 4}", [], [ "{1, -7, 2, 1}", "{4, -1, 5, 1}", "{7, -4, 8, 1}", "{7, -2, 6, 2}", "{4, -6, 3, 2}", "{1, -5, 9, 2}" ], "{2, 5}", "{8}", 8 ], "SolvingSeqIdx":1, "Comps":{ "u":{ "CheckEq":[ "1 - a + b^2 + a*b^3 + b^4 + u^2 + a*u^2 + b*u^2 + 2*a*b*u^2 + 2*b^2*u^2 + a^2*b^2*u^2 + 2*a*b^3*u^2 + b^4*u^2 + a*u^4", "-b + b^4 - u^2 - a*u^2 - b*u^2 + b^2*u^2 + a*b^3*u^2 + b^4*u^2 - 2*a*u^4 - b*u^4 - a*u^6", "a + b + u - a^3*u^2 - a^2*b*u^2 - a^3*b^2*u^2", "b - u - a*u^2 - b*u^2 - a^2*b*u^2 - 2*a*b^2*u^2 - a^2*b^3*u^2 - u^3" ], "TimingForPrimaryIdeals":0.122954 }, "v":{ "CheckEq":[ "-b + b^4", "1 - 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90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20", "1 + 10*u + 55*u^2 + 210*u^3 + 615*u^4 + 1452*u^5 + 2850*u^6 + 4740*u^7 + 6765*u^8 + 8350*u^9 + 8953*u^10 + 8350*u^11 + 6765*u^12 + 4740*u^13 + 2850*u^14 + 1452*u^15 + 615*u^16 + 210*u^17 + 55*u^18 + 10*u^19 + u^20", "1 + 4*u + 10*u^2 + 24*u^3 + 47*u^4 + 80*u^5 + 126*u^6 + 176*u^7 + 227*u^8 + 268*u^9 + 288*u^10 + 288*u^11 + 260*u^12 + 216*u^13 + 162*u^14 + 108*u^15 + 65*u^16 + 32*u^17 + 14*u^18 + 4*u^19 + u^20", "7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20" ], "uPolys":[ "7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20", "(1 + u + u^2 + 2*u^3 + u^4 + u^5)^4", "1 + 2*u + 8*u^2 + 29*u^3 + 65*u^4 + 137*u^5 + 283*u^6 + 476*u^7 + 639*u^8 + 736*u^9 + 754*u^10 + 659*u^11 + 497*u^12 + 328*u^13 + 193*u^14 + 97*u^15 + 48*u^16 + 27*u^17 + 14*u^18 + 5*u^19 + u^20", "7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20", "1 + 2*u + 8*u^2 + 29*u^3 + 65*u^4 + 137*u^5 + 283*u^6 + 476*u^7 + 639*u^8 + 736*u^9 + 754*u^10 + 659*u^11 + 497*u^12 + 328*u^13 + 193*u^14 + 97*u^15 + 48*u^16 + 27*u^17 + 14*u^18 + 5*u^19 + u^20", "7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20", "(1 + u + u^2)^10", "(1 + u + u^2 + 2*u^3 + u^4 + u^5)^4", "7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20" ], "aCuspShape":"5 + (11020313801 - 22381283924*u + 61136122368*u^2 - 91942801820*u^3 + 50630799424*u^4 - 111156813556*u^5 + 31156659684*u^6 - 27289514848*u^7 + 14951107100*u^8 + 59148654176*u^9 - 21786653480*u^10 + 49376741736*u^11 - 31866081816*u^12 - 1617237388*u^13 - 13288181028*u^14 - 17395957744*u^15 - 1613129576*u^16 - 8309758644*u^17 - 100220208*u^18 - 1402773924*u^19)\/2996962805", "RepresentationsN":[ [ "u->-0.590252 + 0.825819 I", "a->0.407671 - 0.896841 I", "b->0.070663 + 0.512466 I" ], [ "u->-0.590252 - 0.825819 I", "a->0.407671 + 0.896841 I", "b->0.070663 - 0.512466 I" ], [ "u->0.067213 + 1.0723 I", "a->0.833585 - 0.414037 I", "b->-0.38849 - 1.61565 I" ], [ "u->0.067213 - 1.0723 I", "a->0.833585 + 0.414037 I", "b->-0.38849 + 1.61565 I" ], [ "u->-0.13082 + 1.15333 I", "a->-0.789899 - 0.343929 I", "b->0.739688 - 0.098744 I" ], [ "u->-0.13082 - 1.15333 I", "a->-0.789899 + 0.343929 I", "b->0.739688 + 0.098744 I" ], [ "u->0.387179 + 1.14799 I", "a->0.809229 - 0.162618 I", "b->-1.28637 - 0.02887 I" ], [ "u->0.387179 - 1.14799 I", "a->0.809229 + 0.162618 I", "b->-1.28637 + 0.02887 I" ], [ "u->0.739688 + 0.098744 I", "a->0.817684 + 1.06164 I", "b->-0.13082 - 1.15333 I" ], [ "u->0.739688 - 0.098744 I", "a->0.817684 - 1.06164 I", "b->-0.13082 + 1.15333 I" ], [ "u->-1.28637 + 0.02887 I", "a->-0.403596 + 0.664172 I", "b->0.387179 - 1.14799 I" ], [ "u->-1.28637 - 0.02887 I", "a->-0.403596 - 0.664172 I", "b->0.387179 + 1.14799 I" ], [ "u->-0.133857 + 1.34163 I", "a->-0.675959 - 0.30524 I", "b->0.76505 - 1.34819 I" ], [ "u->-0.133857 - 1.34163 I", "a->-0.675959 + 0.30524 I", "b->0.76505 + 1.34819 I" ], [ "u->0.070663 + 0.512466 I", "a->1.79041 - 0.7288 I", "b->-0.590252 + 0.825819 I" ], [ "u->0.070663 - 0.512466 I", "a->1.79041 + 0.7288 I", "b->-0.590252 - 0.825819 I" ], [ "u->0.76505 + 1.34819 I", "a->0.645088 - 0.004802 I", "b->-0.133857 - 1.34163 I" ], [ "u->0.76505 - 1.34819 I", "a->0.645088 + 0.004802 I", "b->-0.133857 + 1.34163 I" ], [ "u->-0.38849 + 1.61565 I", "a->-0.577071 - 0.170713 I", "b->0.067213 - 1.0723 I" ], [ "u->-0.38849 - 1.61565 I", "a->-0.577071 + 0.170713 I", "b->0.067213 + 1.0723 I" ] ], "Epsilon":0.854924, "uPolys_ij_N":[ "7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20", "49 + 468*u + 1454*u^2 + 681*u^3 - 4951*u^4 - 10575*u^5 - 4099*u^6 + 17070*u^7 + 36725*u^8 + 35766*u^9 + 15022*u^10 - 6171*u^11 - 13131*u^12 - 8406*u^13 - 2063*u^14 + 765*u^15 + 904*u^16 + 399*u^17 + 102*u^18 + 15*u^19 + u^20", "7 - 20*u + 48*u^2 + 135*u^3 + 851*u^4 + 2261*u^5 + 4447*u^6 + 448*u^7 - 5177*u^8 - 6350*u^9 - 1672*u^10 + 3639*u^11 + 3279*u^12 + 580*u^13 - 737*u^14 - 533*u^15 + 188*u^16 + 49*u^17 - 10*u^18 - 5*u^19 + u^20", "49 + 468*u + 1454*u^2 + 681*u^3 - 4951*u^4 - 10575*u^5 - 4099*u^6 + 17070*u^7 + 36725*u^8 + 35766*u^9 + 15022*u^10 - 6171*u^11 - 13131*u^12 - 8406*u^13 - 2063*u^14 + 765*u^15 + 904*u^16 + 399*u^17 + 102*u^18 + 15*u^19 + u^20", "181 - 560*u + 1340*u^2 - 2167*u^3 + 5625*u^4 - 6719*u^5 + 6813*u^6 - 3934*u^7 + 4503*u^8 - 2198*u^9 + 814*u^10 + 1195*u^11 + 175*u^12 + 14*u^13 - 193*u^14 + 65*u^15 + 14*u^16 - 13*u^17 + u^19 + u^20", "1 + 2*u + 8*u^2 + 29*u^3 + 65*u^4 + 137*u^5 + 283*u^6 + 476*u^7 + 639*u^8 + 736*u^9 + 754*u^10 + 659*u^11 + 497*u^12 + 328*u^13 + 193*u^14 + 97*u^15 + 48*u^16 + 27*u^17 + 14*u^18 + 5*u^19 + u^20", "1 + 12*u + 74*u^2 + 320*u^3 + 1079*u^4 + 2968*u^5 + 6854*u^6 + 13512*u^7 + 22915*u^8 + 33564*u^9 + 42424*u^10 + 45984*u^11 + 42324*u^12 + 32536*u^13 + 20346*u^14 + 10004*u^15 + 3721*u^16 + 1000*u^17 + 182*u^18 + 20*u^19 + u^20", "49 - 300*u + 734*u^2 - 923*u^3 + 851*u^4 - 1059*u^5 + 1535*u^6 - 1972*u^7 + 2365*u^8 - 2376*u^9 + 2158*u^10 - 1289*u^11 + 885*u^12 - 304*u^13 + 201*u^14 - 3*u^15 + 54*u^16 + 11*u^17 + 12*u^18 + u^19 + u^20", "1 + 12*u + 78*u^2 + 217*u^3 + 181*u^4 - 799*u^5 + 469*u^6 + 258*u^7 + 2229*u^8 + 6130*u^9 + 8918*u^10 + 8005*u^11 + 5289*u^12 + 2750*u^13 + 773*u^14 + 241*u^15 + 184*u^16 + 31*u^17 + 22*u^18 + 3*u^19 + u^20", "1 + 16*u + 132*u^2 + 657*u^3 + 2201*u^4 + 5353*u^5 + 9959*u^6 + 14448*u^7 + 16461*u^8 + 15164*u^9 + 11624*u^10 + 7507*u^11 + 4325*u^12 + 2166*u^13 + 1033*u^14 + 407*u^15 + 166*u^16 + 47*u^17 + 16*u^18 + 3*u^19 + u^20", "7 - 72*u + 244*u^2 - 369*u^3 + 655*u^4 - 1137*u^5 + 55*u^6 + 2454*u^7 - 2265*u^8 - 1020*u^9 + 2374*u^10 - 477*u^11 - 1021*u^12 + 564*u^13 + 185*u^14 - 213*u^15 + 8*u^16 + 39*u^17 - 8*u^18 - 3*u^19 + u^20", "7 - 20*u + 48*u^2 + 135*u^3 + 851*u^4 + 2261*u^5 + 4447*u^6 + 448*u^7 - 5177*u^8 - 6350*u^9 - 1672*u^10 + 3639*u^11 + 3279*u^12 + 580*u^13 - 737*u^14 - 533*u^15 + 188*u^16 + 49*u^17 - 10*u^18 - 5*u^19 + u^20", "2887 + 17388*u + 50616*u^2 + 91029*u^3 + 116935*u^4 + 121731*u^5 + 117485*u^6 + 113994*u^7 + 107551*u^8 + 88878*u^9 + 60852*u^10 + 34665*u^11 + 17149*u^12 + 7548*u^13 + 2965*u^14 + 867*u^15 + 230*u^16 + 87*u^17 + 36*u^18 + 9*u^19 + u^20", "7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20", "1 + 10*u + 55*u^2 + 210*u^3 + 615*u^4 + 1452*u^5 + 2850*u^6 + 4740*u^7 + 6765*u^8 + 8350*u^9 + 8953*u^10 + 8350*u^11 + 6765*u^12 + 4740*u^13 + 2850*u^14 + 1452*u^15 + 615*u^16 + 210*u^17 + 55*u^18 + 10*u^19 + u^20", "1 + 4*u + 10*u^2 + 24*u^3 + 47*u^4 + 80*u^5 + 126*u^6 + 176*u^7 + 227*u^8 + 268*u^9 + 288*u^10 + 288*u^11 + 260*u^12 + 216*u^13 + 162*u^14 + 108*u^15 + 65*u^16 + 32*u^17 + 14*u^18 + 4*u^19 + u^20", "1 + 16*u + 132*u^2 + 657*u^3 + 2201*u^4 + 5353*u^5 + 9959*u^6 + 14448*u^7 + 16461*u^8 + 15164*u^9 + 11624*u^10 + 7507*u^11 + 4325*u^12 + 2166*u^13 + 1033*u^14 + 407*u^15 + 166*u^16 + 47*u^17 + 16*u^18 + 3*u^19 + u^20", "1 + 4*u + 10*u^2 + 8*u^3 - 9*u^4 - 40*u^5 - 34*u^6 + 24*u^7 + 83*u^8 + 44*u^9 - 72*u^10 - 88*u^11 + 12*u^12 + 88*u^13 + 18*u^14 - 60*u^15 - 7*u^16 + 24*u^17 - 2*u^18 - 4*u^19 + u^20", "1 + 2*u + 8*u^2 + 29*u^3 + 65*u^4 + 137*u^5 + 283*u^6 + 476*u^7 + 639*u^8 + 736*u^9 + 754*u^10 + 659*u^11 + 497*u^12 + 328*u^13 + 193*u^14 + 97*u^15 + 48*u^16 + 27*u^17 + 14*u^18 + 5*u^19 + u^20", "1 + 10*u + 55*u^2 + 210*u^3 + 615*u^4 + 1452*u^5 + 2850*u^6 + 4740*u^7 + 6765*u^8 + 8350*u^9 + 8953*u^10 + 8350*u^11 + 6765*u^12 + 4740*u^13 + 2850*u^14 + 1452*u^15 + 615*u^16 + 210*u^17 + 55*u^18 + 10*u^19 + u^20", "7 - 72*u + 244*u^2 - 369*u^3 + 655*u^4 - 1137*u^5 + 55*u^6 + 2454*u^7 - 2265*u^8 - 1020*u^9 + 2374*u^10 - 477*u^11 - 1021*u^12 + 564*u^13 + 185*u^14 - 213*u^15 + 8*u^16 + 39*u^17 - 8*u^18 - 3*u^19 + u^20", "1 - 4*u + 2*u^2 + 24*u^3 - 65*u^4 + 32*u^5 + 166*u^6 - 392*u^7 + 267*u^8 + 372*u^9 - 1048*u^10 + 1024*u^11 - 164*u^12 - 864*u^13 + 1330*u^14 - 1124*u^15 + 641*u^16 - 256*u^17 + 70*u^18 - 12*u^19 + u^20", "49 - 300*u + 734*u^2 - 923*u^3 + 851*u^4 - 1059*u^5 + 1535*u^6 - 1972*u^7 + 2365*u^8 - 2376*u^9 + 2158*u^10 - 1289*u^11 + 885*u^12 - 304*u^13 + 201*u^14 - 3*u^15 + 54*u^16 + 11*u^17 + 12*u^18 + u^19 + u^20", "1 + 12*u + 78*u^2 + 217*u^3 + 181*u^4 - 799*u^5 + 469*u^6 + 258*u^7 + 2229*u^8 + 6130*u^9 + 8918*u^10 + 8005*u^11 + 5289*u^12 + 2750*u^13 + 773*u^14 + 241*u^15 + 184*u^16 + 31*u^17 + 22*u^18 + 3*u^19 + u^20" ], "GeometricComponent":0, "Multiplicity":1, "MinRepresentationVolume":[ "{3, 4, 19, 20}", 0.4993 ], "ij_list":[ [ "{1, 7}", "{2, 6}", "{2, 7}" ], [ "{1, 2}", "{6, 7}" ], [ "{1, 6}" ], [ "{1, 9}", "{4, 5}" ], [ "{3, 7}" ], [ "{3, 6}", "{4, 6}" ], [ "{5, 7}" ], [ "{7, 9}" ], [ "{5, 6}" ], [ "{3, 5}" ], [ "{1, 8}" ], [ "{4, 9}" ], [ "{1, 3}" ], [ "{1, 4}", "{1, 5}", "{5, 9}" ], [ "{4, 7}", "{4, 8}" ], [ "{2, 9}", "{3, 8}", "{3, 9}" ], [ "{6, 9}" ], [ "{2, 8}" ], [ "{5, 8}", "{6, 8}" ], [ "{7, 8}" ], [ "{2, 4}" ], [ "{2, 3}", "{8, 9}" ], [ "{2, 5}" ], [ "{3, 4}" ] ], "SortedReprnIndices":"{7, 12, 8, 11, 14, 17, 13, 18, 2, 16, 1, 15, 6, 9, 5, 10, 3, 20, 4, 19}", "aCuspShapeN":[ "4.7443136184177284761`5.150503525887063 + 0.0344842269665930817`3.0119506307995954*I", "4.7443136184177284761`5.150503525887063 - 0.0344842269665930817`3.0119506307995954*I", "0.5151149374602366447`4.822908898075614 + 0.9665466830036797311`5.096227588963372*I", "0.5151149374602366447`4.822908898075614 - 0.9665466830036797311`5.096227588963372*I", "1.4811428882440697608`4.74506285561614 + 3.464101615137754578`5.114056521008323*I", "1.4811428882440697608`4.74506285561614 - 3.464101615137754578`5.114056521008323*I", "4.7443136184177284867`4.901097360240306 - 6.9626874572421022515`5.067700871204248*I", "4.7443136184177284867`4.901097360240306 + 6.9626874572421022515`5.067700871204248*I", "1.4811428882440697647`4.74506285561614 - 3.464101615137754587`5.114056521008323*I", "1.4811428882440697647`4.74506285561614 + 3.464101615137754587`5.114056521008323*I", "4.7443136184177284708`4.901097360240306 + 6.9626874572421022659`5.067700871204248*I", "4.7443136184177284708`4.901097360240306 - 6.9626874572421022659`5.067700871204248*I", "0.5151149374602366959`3.9641582716490635 + 7.8947499132791889134`5.149592504937719*I", "0.5151149374602366959`3.9641582716490635 - 7.8947499132791889134`5.149592504937719*I", "4.744313618417728476`5.150503525887063 + 0.0344842269665930832`3.0119506307995954*I", "4.744313618417728476`5.150503525887063 - 0.0344842269665930832`3.0119506307995954*I", "0.5151149374602368279`3.9641582716490635 - 7.894749913279189024`5.149592504937719*I", "0.5151149374602368279`3.9641582716490635 + 7.894749913279189024`5.149592504937719*I", "0.5151149374602363729`4.822908898075614 - 0.9665466830036799635`5.096227588963372*I", "0.5151149374602363729`4.822908898075614 + 0.9665466830036799635`5.096227588963372*I" ], "Abelian":false }, { "IdealName":"J9_39_2", "Generators":[ "b + u", "a - 2*u - u^2 - u^3", "1 - u + 2*u^2 + u^4" ], "VariableOrder":[ "b", "a", "u" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":true, "IdealDimension":0, "Timings":{ "TimingGroebner":5.9258e-2, "TimingZeroDimVars":4.9882e-2, "TimingmagmaVCompNormalize":5.1129e-2, "TimingNumberOfSols":5.2065e-2, "TimingIsRadical":2.2530000000000002e-3, "TimingArcColoring":4.8544000000000004e-2, "TimingObstruction":3.32e-3, "TimingComplexVolumeN":3.391601, "TimingaCuspShapeN":2.0265000000000005e-2, "TiminguValues":0.578003, "TiminguPolysN":1.2150000000000004e-3, "TiminguPolys":0.725032, "TimingaCuspShape":9.785500000000001e-2, "TimingRepresentationsN":5.1694000000000004e-2, "TiminguValues_ij":0.113976, "TiminguPoly_ij":1.224804, "TiminguPolys_ij_N":2.146e-3 }, "ZeroDimensionalVars":[ "b", "a", "u" ], "NumberOfSols":4, "IsRadical":true, "ArcColoring":[ "{1, 0}", [ 1, "-u^2" ], [ "3*u + u^2 + 2*u^3", "-u - u^2" ], [ "2*u + u^2 + u^3", "-u" ], [ "u + u^2 + u^3", "-u" ], [ "-u", "u + u^3" ], [ 0, "u" ], [ "-1 - 2*u - u^2 - u^3", "1 + u + u^2" ], [ "2 - u + u^2 - u^3", "u^2" ] ], "Obstruction":1, "ComplexVolumeN":[ "1.13814 + 3.38562*I", "1.13814 - 3.38562*I", "-4.42801 - 2.37936*I", "-4.42801 + 2.37936*I" ], "uPolysN":[ "1 - u + 2*u^2 + u^4", "1 + 2*u^2 + u^3 + u^4", "1 + u + u^4", "1 - u + 2*u^2 + u^4", "1 + u + u^4", "1 + u + 2*u^2 + u^4", "1 - u^3 + u^4", "1 + 2*u^2 - u^3 + u^4", "1 + u + 2*u^2 + u^4" ], "uPolys":[ "1 - u + 2*u^2 + u^4", "1 + 2*u^2 + u^3 + u^4", "1 + u + u^4", "1 - u + 2*u^2 + u^4", "1 + u + u^4", "1 + u + 2*u^2 + u^4", "1 - u^3 + u^4", "1 + 2*u^2 - u^3 + u^4", "1 + u + 2*u^2 + u^4" ], "aCuspShape":"8 - 11*u - 2*u^2 - 7*u^3", "RepresentationsN":[ [ "u->0.343815 + 0.625358 I", "a->0.05204 + 1.65794 I", "b->-0.343815 - 0.625358 I" ], [ "u->0.343815 - 0.625358 I", "a->0.05204 - 1.65794 I", "b->-0.343815 + 0.625358 I" ], [ "u->-0.343815 + 1.35844 I", "a->-0.552038 - 0.242275 I", "b->0.343815 - 1.35844 I" ], [ "u->-0.343815 - 1.35844 I", "a->-0.552038 + 0.242275 I", "b->0.343815 + 1.35844 I" ] ], "Epsilon":2.44871, "uPolys_ij":[ "1 + u + 2*u^2 + u^4", "1 - u + 2*u^2 + u^4", "1 - 3*u + 6*u^2 - 4*u^3 + u^4", "1 + 3*u + 6*u^2 + 4*u^3 + u^4", "1 + u + u^4", "3 - 2*u - u^2 + u^4", "5 - 4*u + 5*u^2 - 4*u^3 + u^4", "3 + 2*u - u^2 + u^4", "1 + 5*u^2 - 4*u^3 + u^4", "1 + 4*u + 6*u^2 + 3*u^3 + u^4", "5 + 7*u + 7*u^2 + 3*u^3 + u^4", "3 - 2*u + 4*u^2 - u^3 + u^4", "1 + u^3 + u^4", "1 - u + 3*u^2 - 3*u^3 + u^4", "1 + 2*u^2 + u^3 + u^4", "3 + 5*u - u^2 - 3*u^3 + u^4", "9 + 5*u + u^2 + u^3 + u^4" ], "GeometricComponent":0, "uPolys_ij_N":[ "1 + u + 2*u^2 + u^4", "1 - u + 2*u^2 + u^4", "1 - 3*u + 6*u^2 - 4*u^3 + u^4", "1 + 3*u + 6*u^2 + 4*u^3 + u^4", "1 + u + u^4", "3 - 2*u - u^2 + u^4", "5 - 4*u + 5*u^2 - 4*u^3 + u^4", "3 + 2*u - u^2 + u^4", "1 + 5*u^2 - 4*u^3 + u^4", "1 + 4*u + 6*u^2 + 3*u^3 + u^4", "5 + 7*u + 7*u^2 + 3*u^3 + u^4", "3 - 2*u + 4*u^2 - u^3 + u^4", "1 + u^3 + u^4", "1 - u + 3*u^2 - 3*u^3 + u^4", "1 + 2*u^2 + u^3 + u^4", "3 + 5*u - u^2 - 3*u^3 + u^4", "9 + 5*u + u^2 + u^3 + u^4" ], "Multiplicity":1, "MinRepresentationVolume":[ "{3, 4}", 2.37936 ], "ij_list":[ [ "{1, 4}", "{1, 5}", "{3, 4}", "{5, 6}" ], [ "{1, 7}", "{2, 6}", "{2, 7}", "{5, 9}" ], [ "{1, 2}", "{4, 5}", "{6, 7}" ], [ "{1, 9}" ], [ "{3, 6}", "{4, 6}", "{5, 8}", "{6, 8}" ], [ "{2, 4}" ], [ "{1, 3}" ], [ "{1, 8}" ], [ "{2, 8}" ], [ "{2, 3}", "{8, 9}" ], [ "{2, 5}", "{7, 9}" ], [ "{3, 5}", "{6, 9}" ], [ "{4, 7}", "{4, 8}" ], [ "{1, 6}", "{4, 9}" ], [ "{2, 9}", "{3, 8}", "{3, 9}", "{7, 8}" ], [ "{5, 7}" ], [ "{3, 7}" ] ], "SortedReprnIndices":"{1, 2, 4, 3}", "aCuspShapeN":[ "7.3028590029077891701`4.9917785597166615 - 7.5794177637803294557`5.007921489215894*I", "7.3028590029077891701`4.9917785597166615 + 7.5794177637803294557`5.007921489215894*I", "2.1971409970922108297`5.101889220602329 + 1.1007290945304811855`4.801711738737424*I", "2.1971409970922108297`5.101889220602329 - 1.1007290945304811855`4.801711738737424*I" ], "Abelian":false }, { "IdealName":"abJ9_39_3", "Generators":[ "b", "-1 + a", "-1 + v" ], "VariableOrder":[ "b", "a", "v" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":true, "IdealDimension":0, "Timings":{ "TimingGroebner":5.5569e-2, "TimingZeroDimVars":4.5793e-2, "TimingmagmaVCompNormalize":4.7022000000000015e-2, "TimingNumberOfSols":2.2532e-2, "TimingIsRadical":1.408e-3, "TimingArcColoring":4.7985e-2, "TimingObstruction":3.8500000000000003e-4, "TimingComplexVolumeN":0.245994, "TimingaCuspShapeN":4.476e-3, "TiminguValues":0.56809, "TiminguPolysN":6.7e-5, "TiminguPolys":0.721483, "TimingaCuspShape":9.1828e-2, "TimingRepresentationsN":2.1867e-2, "TiminguValues_ij":0.107545, "TiminguPoly_ij":0.122423, "TiminguPolys_ij_N":2.8e-5 }, "ZeroDimensionalVars":[ "b", "a", "v" ], "NumberOfSols":1, "IsRadical":true, "ArcColoring":[ "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}" ], "Obstruction":1, "ComplexVolumeN":"{0}", "uPolysN":[ "u", "u", "u", "u", "u", "u", "u", "u", "u" ], "uPolys":[ "u", "u", "u", "u", "u", "u", "u", "u", "u" ], "aCuspShape":0, "RepresentationsN":[ [ "v->1.", "a->1.", "b->0" ] ], "Epsilon":"Infinity", "uPolys_ij":[ "u" ], "GeometricComponent":0, "uPolys_ij_N":[ "u" ], "Multiplicity":1, "ij_list":[ [ "{1, 2}", "{1, 3}", "{1, 4}", "{1, 5}", "{1, 6}", "{1, 7}", "{1, 8}", "{1, 9}", "{2, 3}", "{2, 4}", "{2, 5}", "{2, 6}", "{2, 7}", "{2, 8}", "{2, 9}", "{3, 4}", "{3, 5}", "{3, 6}", "{3, 7}", "{3, 8}", "{3, 9}", "{4, 5}", "{4, 6}", "{4, 7}", "{4, 8}", "{4, 9}", "{5, 6}", "{5, 7}", "{5, 8}", "{5, 9}", "{6, 7}", "{6, 8}", "{6, 9}", "{7, 8}", "{7, 9}", "{8, 9}" ] ], "SortedReprnIndices":"{1}", "aCuspShapeN":"{0}", "Abelian":true } ] }, "uPolyC":[ "(1 - u + 2*u^2 + u^4)*(-1 + u + u^2 + u^3 + 3*u^4 + 4*u^5 + 3*u^6 + 7*u^7 + u^8 + 4*u^9 + u^11)*(7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20)", "(1 + 2*u^2 + u^3 + u^4)*(1 + u + u^2 + 2*u^3 + u^4 + u^5)^4*(-4 + 26*u - 69*u^2 + 123*u^3 - 163*u^4 + 169*u^5 - 141*u^6 + 95*u^7 - 51*u^8 + 21*u^9 - 6*u^10 + u^11)", "(1 + u + u^4)*(-1 - u + 5*u^2 + 5*u^3 - 9*u^4 - 4*u^5 + 3*u^6 + 7*u^7 - 3*u^8 - 2*u^9 + u^11)*(1 + 2*u + 8*u^2 + 29*u^3 + 65*u^4 + 137*u^5 + 283*u^6 + 476*u^7 + 639*u^8 + 736*u^9 + 754*u^10 + 659*u^11 + 497*u^12 + 328*u^13 + 193*u^14 + 97*u^15 + 48*u^16 + 27*u^17 + 14*u^18 + 5*u^19 + u^20)", "(1 - u + 2*u^2 + u^4)*(-1 + u + u^2 + u^3 + 3*u^4 + 4*u^5 + 3*u^6 + 7*u^7 + u^8 + 4*u^9 + u^11)*(7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20)", "(1 + u + u^4)*(-1 - u + 5*u^2 + 5*u^3 - 9*u^4 - 4*u^5 + 3*u^6 + 7*u^7 - 3*u^8 - 2*u^9 + u^11)*(1 + 2*u + 8*u^2 + 29*u^3 + 65*u^4 + 137*u^5 + 283*u^6 + 476*u^7 + 639*u^8 + 736*u^9 + 754*u^10 + 659*u^11 + 497*u^12 + 328*u^13 + 193*u^14 + 97*u^15 + 48*u^16 + 27*u^17 + 14*u^18 + 5*u^19 + u^20)", "(1 + u + 2*u^2 + u^4)*(-1 + u + u^2 + u^3 + 3*u^4 + 4*u^5 + 3*u^6 + 7*u^7 + u^8 + 4*u^9 + u^11)*(7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20)", "(1 + u + u^2)^10*(1 - u^3 + u^4)*(-32 + 176*u - 456*u^2 + 768*u^3 - 950*u^4 + 905*u^5 - 669*u^6 + 381*u^7 - 163*u^8 + 50*u^9 - 10*u^10 + u^11)", "(1 + 2*u^2 - u^3 + u^4)*(1 + u + u^2 + 2*u^3 + u^4 + u^5)^4*(-4 + 26*u - 69*u^2 + 123*u^3 - 163*u^4 + 169*u^5 - 141*u^6 + 95*u^7 - 51*u^8 + 21*u^9 - 6*u^10 + u^11)", "(1 + u + 2*u^2 + u^4)*(-1 + u + u^2 + u^3 + 3*u^4 + 4*u^5 + 3*u^6 + 7*u^7 + u^8 + 4*u^9 + u^11)*(7 + 8*u + 38*u^2 + 37*u^3 + 43*u^4 + 77*u^5 + u^6 + 64*u^7 - 11*u^8 - 28*u^9 + 28*u^10 - 103*u^11 + 61*u^12 - 90*u^13 + 55*u^14 - 39*u^15 + 28*u^16 - 9*u^17 + 8*u^18 - u^19 + u^20)" ], "RileyPolyC":[ "(1 + 3*y + 6*y^2 + 4*y^3 + y^4)*(-1 + 3*y + 7*y^2 + 9*y^3 + 9*y^4 + 18*y^5 + 51*y^6 + 77*y^7 + 63*y^8 + 30*y^9 + 8*y^10 + y^11)*(49 + 468*y + 1454*y^2 + 681*y^3 - 4951*y^4 - 10575*y^5 - 4099*y^6 + 17070*y^7 + 36725*y^8 + 35766*y^9 + 15022*y^10 - 6171*y^11 - 13131*y^12 - 8406*y^13 - 2063*y^14 + 765*y^15 + 904*y^16 + 399*y^17 + 102*y^18 + 15*y^19 + y^20)", "(1 + 4*y + 6*y^2 + 3*y^3 + y^4)*(-1 - y + y^2 + 4*y^3 + 3*y^4 + y^5)^4*(-16 + 124*y + 331*y^2 + 295*y^3 + 79*y^4 - 29*y^5 - 7*y^6 + 31*y^7 + 35*y^8 + 19*y^9 + 6*y^10 + y^11)", "(1 - y + 2*y^2 + y^4)*(-1 + 11*y - 53*y^2 + 129*y^3 - 171*y^4 + 174*y^5 - 141*y^6 + 93*y^7 - 45*y^8 + 18*y^9 - 4*y^10 + y^11)*(1 + 12*y + 78*y^2 + 217*y^3 + 181*y^4 - 799*y^5 + 469*y^6 + 258*y^7 + 2229*y^8 + 6130*y^9 + 8918*y^10 + 8005*y^11 + 5289*y^12 + 2750*y^13 + 773*y^14 + 241*y^15 + 184*y^16 + 31*y^17 + 22*y^18 + 3*y^19 + y^20)", "(1 + 3*y + 6*y^2 + 4*y^3 + y^4)*(-1 + 3*y + 7*y^2 + 9*y^3 + 9*y^4 + 18*y^5 + 51*y^6 + 77*y^7 + 63*y^8 + 30*y^9 + 8*y^10 + y^11)*(49 + 468*y + 1454*y^2 + 681*y^3 - 4951*y^4 - 10575*y^5 - 4099*y^6 + 17070*y^7 + 36725*y^8 + 35766*y^9 + 15022*y^10 - 6171*y^11 - 13131*y^12 - 8406*y^13 - 2063*y^14 + 765*y^15 + 904*y^16 + 399*y^17 + 102*y^18 + 15*y^19 + y^20)", "(1 - y + 2*y^2 + y^4)*(-1 + 11*y - 53*y^2 + 129*y^3 - 171*y^4 + 174*y^5 - 141*y^6 + 93*y^7 - 45*y^8 + 18*y^9 - 4*y^10 + y^11)*(1 + 12*y + 78*y^2 + 217*y^3 + 181*y^4 - 799*y^5 + 469*y^6 + 258*y^7 + 2229*y^8 + 6130*y^9 + 8918*y^10 + 8005*y^11 + 5289*y^12 + 2750*y^13 + 773*y^14 + 241*y^15 + 184*y^16 + 31*y^17 + 22*y^18 + 3*y^19 + y^20)", "(1 + 3*y + 6*y^2 + 4*y^3 + y^4)*(-1 + 3*y + 7*y^2 + 9*y^3 + 9*y^4 + 18*y^5 + 51*y^6 + 77*y^7 + 63*y^8 + 30*y^9 + 8*y^10 + y^11)*(49 + 468*y + 1454*y^2 + 681*y^3 - 4951*y^4 - 10575*y^5 - 4099*y^6 + 17070*y^7 + 36725*y^8 + 35766*y^9 + 15022*y^10 - 6171*y^11 - 13131*y^12 - 8406*y^13 - 2063*y^14 + 765*y^15 + 904*y^16 + 399*y^17 + 102*y^18 + 15*y^19 + y^20)", "(1 + y + y^2)^10*(1 + 2*y^2 - y^3 + y^4)*(-1024 + 1792*y + 1600*y^2 - 832*y^3 + 1132*y^4 + 1445*y^5 + 381*y^6 + 103*y^7 - 39*y^8 + 2*y^9 + y^11)", "(1 + 4*y + 6*y^2 + 3*y^3 + y^4)*(-1 - y + y^2 + 4*y^3 + 3*y^4 + y^5)^4*(-16 + 124*y + 331*y^2 + 295*y^3 + 79*y^4 - 29*y^5 - 7*y^6 + 31*y^7 + 35*y^8 + 19*y^9 + 6*y^10 + y^11)", "(1 + 3*y + 6*y^2 + 4*y^3 + y^4)*(-1 + 3*y + 7*y^2 + 9*y^3 + 9*y^4 + 18*y^5 + 51*y^6 + 77*y^7 + 63*y^8 + 30*y^9 + 8*y^10 + y^11)*(49 + 468*y + 1454*y^2 + 681*y^3 - 4951*y^4 - 10575*y^5 - 4099*y^6 + 17070*y^7 + 36725*y^8 + 35766*y^9 + 15022*y^10 - 6171*y^11 - 13131*y^12 - 8406*y^13 - 2063*y^14 + 765*y^15 + 904*y^16 + 399*y^17 + 102*y^18 + 15*y^19 + y^20)" ] }, "GeometricRepresentation":[ 1.2810299999999998e1, [ "J9_39_0", 1, "{9, 10}" ] ] } }