Formats: - HTML - YAML - JSON - 2026-07-22T11:55:29.481544
  • lfunc_lfunctions • Show schema
    {'Lhash': '1093229355286107653762984266122,1327245258341076220278288842239,1346636485796298859986968238152,1644623668992629598160271605811,1808663330119967319332154795515,2313837214140112856876679482186', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49951001001.787384, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [19, [1, -6, 15, -20, 15, -6, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '7600.1', 'coefficient_field': '1.1.1.1', 'conductor': 192699928576000000000000, 'conductor_radical': 190, 'degree': 12, 'euler_factors': [[1], [1, 2, 8, 14, 30, 50, 87, 150, 270, 378, 648, 486, 729], [1], [1, 2, 12, 22, 118, 126, 779, 882, 5782, 7546, 28812, 33614, 117649], [1, 3, 26, 26, 65, -749, -2288, -8239, 7865, 34606, 380666, 483153, 1771561], [1, 1, 13, 50, 38, -516, 1813, -6708, 6422, 109850, 371293, 371293, 4826809], [1, 14, 124, 848, 4842, 24018, 105929, 408306, 1399338, 4166224, 10356604, 19877998, 24137569], [1, -6, 15, -20, 15, -6, 1], [1, 12, 112, 778, 4884, 25856, 128015, 594688, 2583636, 9465926, 31342192, 77236116, 148035889], [1, -9, 107, -600, 5158, -26640, 189919, -772560, 4337878, -14633400, 75679067, -184600341, 594823321], [1, 5, 50, 176, 771, 5843, 22284, 181133, 740931, 5243216, 46176050, 143145755, 887503681], [1, 8, 132, 743, 7797, 33802, 309503, 1250674, 10674093, 37635179, 247389252, 554751656, 2565726409], [1, -3, 66, -146, 4087, -5943, 137612, -243663, 6870247, -10062466, 186500226, -347568603, 4750104241], [1, 15, 271, 2530, 26829, 185919, 1470270, 7994517, 49606821, 201152710, 926495071, 2205126645, 6321363049], [1, 4, 230, 749, 23811, 63544, 1431531, 2986568, 52598499, 77763427, 1122326630, 917380028, 10779215329], [1, -13, 126, -1554, 12921, -108347, 968797, -5742391, 36295089, -231354858, 994200606, -5436541409, 22164361129], [1, 0, 161, -255, 12605, -44407, 744938, -2620013, 43878005, -52371645, 1950895121, 0, 42180533641], [1, -9, 234, -2302, 30205, -236741, 2409968, -14441201, 112392805, -522510262, 3239926794, -7601366709, 51520374361], [1, -3, 203, -820, 23862, -100928, 1840467, -6762176, 107116518, -246625660, 4090677563, -4050375321, 90458382169], [1, 19, 351, 3254, 31709, 169223, 1652142, 12014833, 159845069, 1164642394, 8919500031, 34280357669, 128100283921], [1, -3, 133, -274, 18744, -31092, 1356111, -2269716, 99886776, -106590658, 3776966053, -6219214779, 151334226289], [1, -16, 189, -1815, 19499, -139691, 1154286, -11035589, 121693259, -894865785, 7361565309, -49232902384, 243087455521], [1, 31, 824, 13802, 205891, 2327315, 23897248, 193167145, 1418383099, 7891804174, 39105656504, 122110259933, 326940373369], [1, -14, 467, -5503, 93933, -916667, 10735038, -81583363, 744043293, -3879444407, 29300626547, -78176832286, 496981290961], [1, 11, 374, 3862, 74175, 650639, 8888572, 63111983, 697912575, 3524743126, 33109951094, 94460742827, 832972004929], [1, -12, 425, -5263, 90347, -967617, 11622638, -97729317, 921629747, -5422474163, 44225670425, -126121206012, 1061520150601], [1, 10, 425, 3177, 86075, 553367, 11135246, 56996801, 913169675, 3471593679, 47834124425, 115927407430, 1194052296529], [1, -8, 472, -4302, 102944, -916844, 13663255, -98102308, 1178605856, -5270134986, 61869571672, -112204138456, 1500730351849], [1, -17, 401, -3410, 54288, -317402, 5799063, -34596818, 644995728, -4416048890, 56604422561, -261566072333, 1677100110841], [1, 14, 501, 7073, 120649, 1494305, 17336834, 168856465, 1540567081, 10205610481, 81686727861, 257940925102, 2081951752609]], 'euler_factors_factorization': [[1], [[[1, 2, 8, 14, 30, 50, 87, 150, 270, 378, 648, 486, 729], 1]], [1], [[[1, 2, 12, 22, 118, 126, 779, 882, 5782, 7546, 28812, 33614, 117649], 1]], [[[1, 3, 26, 26, 65, -749, -2288, -8239, 7865, 34606, 380666, 483153, 1771561], 1]], [[[1, 1, 13, 50, 38, -516, 1813, -6708, 6422, 109850, 371293, 371293, 4826809], 1]], [[[1, 14, 124, 848, 4842, 24018, 105929, 408306, 1399338, 4166224, 10356604, 19877998, 24137569], 1]], [[[1, -1], 6]], [[[1, 12, 112, 778, 4884, 25856, 128015, 594688, 2583636, 9465926, 31342192, 77236116, 148035889], 1]], [[[1, -9, 107, -600, 5158, -26640, 189919, -772560, 4337878, -14633400, 75679067, -184600341, 594823321], 1]], [[[1, 5, 50, 176, 771, 5843, 22284, 181133, 740931, 5243216, 46176050, 143145755, 887503681], 1]], [[[1, 8, 132, 743, 7797, 33802, 309503, 1250674, 10674093, 37635179, 247389252, 554751656, 2565726409], 1]], [[[1, -3, 66, -146, 4087, -5943, 137612, -243663, 6870247, -10062466, 186500226, -347568603, 4750104241], 1]], [[[1, 15, 271, 2530, 26829, 185919, 1470270, 7994517, 49606821, 201152710, 926495071, 2205126645, 6321363049], 1]], [[[1, 4, 230, 749, 23811, 63544, 1431531, 2986568, 52598499, 77763427, 1122326630, 917380028, 10779215329], 1]], [[[1, -13, 126, -1554, 12921, -108347, 968797, -5742391, 36295089, -231354858, 994200606, -5436541409, 22164361129], 1]], [[[1, 0, 161, -255, 12605, -44407, 744938, -2620013, 43878005, -52371645, 1950895121, 0, 42180533641], 1]], [[[1, -9, 234, -2302, 30205, -236741, 2409968, -14441201, 112392805, -522510262, 3239926794, -7601366709, 51520374361], 1]], [[[1, -3, 203, -820, 23862, -100928, 1840467, -6762176, 107116518, -246625660, 4090677563, -4050375321, 90458382169], 1]], [[[1, 19, 351, 3254, 31709, 169223, 1652142, 12014833, 159845069, 1164642394, 8919500031, 34280357669, 128100283921], 1]], [[[1, -3, 133, -274, 18744, -31092, 1356111, -2269716, 99886776, -106590658, 3776966053, -6219214779, 151334226289], 1]], [[[1, -16, 189, -1815, 19499, -139691, 1154286, -11035589, 121693259, -894865785, 7361565309, -49232902384, 243087455521], 1]], [[[1, 31, 824, 13802, 205891, 2327315, 23897248, 193167145, 1418383099, 7891804174, 39105656504, 122110259933, 326940373369], 1]], [[[1, -14, 467, -5503, 93933, -916667, 10735038, -81583363, 744043293, -3879444407, 29300626547, -78176832286, 496981290961], 1]], [[[1, 11, 374, 3862, 74175, 650639, 8888572, 63111983, 697912575, 3524743126, 33109951094, 94460742827, 832972004929], 1]], [[[1, -12, 425, -5263, 90347, -967617, 11622638, -97729317, 921629747, -5422474163, 44225670425, -126121206012, 1061520150601], 1]], [[[1, 10, 425, 3177, 86075, 553367, 11135246, 56996801, 913169675, 3471593679, 47834124425, 115927407430, 1194052296529], 1]], [[[1, -8, 472, -4302, 102944, -916844, 13663255, -98102308, 1178605856, -5270134986, 61869571672, -112204138456, 1500730351849], 1]], [[[1, -17, 401, -3410, 54288, -317402, 5799063, -34596818, 644995728, -4416048890, 56604422561, -261566072333, 1677100110841], 1]], [[[1, 14, 501, 7073, 120649, 1494305, 17336834, 168856465, 1540567081, 10205610481, 81686727861, 257940925102, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 7, 'label': '12-7600e6-1.1-c1e6-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 6, 'origin': 'ModularForm/GL2/Q/holomorphic/7600/2/a/ch', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0078125', 'prec': 30}, 'plot_values': [0.0, 5.471306655175725e-10, 3.499040882412593e-08, 3.980702945557379e-07, 2.232751734038048e-06, 8.498329619418732e-06, 2.530688075185884e-05, 6.360931482808201e-05, 0.00014120682884215295, 0.0002850588339694142, 0.0005338537131099974, 0.0009408042886722883, 0.0015766258910631828, 0.00253264913181753, 0.0039240087730253925, 0.005892867736121612, 0.008611617082419667, 0.012285992781124919, 0.01715805165077302, 0.02350892851587743, 0.03166125429349801, 0.0419813078090941, 0.05488077630222235, 0.07081805586434056, 0.09029904822874063, 0.11387732044325152, 0.14215336425514588, 0.17577353935294882, 0.2154282842875995, 0.26184953404202543, 0.3158073752481968, 0.3781056871954236, 0.44957623322097223, 0.5310730493004101, 0.6234658890322792, 0.7276327104692445, 0.8444514083752658, 0.9747903474774495, 1.1194967890816083, 1.2793871477796062, 1.4552363119624845, 1.647766128886055, 1.857633532937197, 2.0854176834240854, 2.3316049138845245, 2.5965775892217824, 2.8806023532048504, 3.1838180459130405, 3.506224054269766, 3.8476684950998963, 4.2078351790686055, 4.5862356490405665, 4.982201419068119, 5.394876822950666, 5.823213283799457, 6.265965014678892, 6.721686124378871, 7.188730455203014, 7.6652531862380116, 8.14921440984763, 8.638384913488052, 9.13035575681526, 9.622553854604767, 10.112251352986915, 10.596579454512362, 11.072545929580105, 11.5370549119034, 11.98693335672061, 12.418969789629399, 12.829929144111421, 13.216576209029125, 13.575704715487477, 13.904167715645695, 14.198917501786584, 14.457064723313206, 14.675887611353605, 14.85285562961042, 14.985660871600583, 15.072248751967225, 15.110860561420875, 15.10010110990378, 15.03892658641016, 14.926654096727946, 14.762981195930275, 14.548002392155063, 14.282238891995085, 13.966696644432382, 13.60281876293366, 13.192467515318368, 12.737918730883099, 12.24185171416241, 11.707352800239372, 11.13794676131644, 10.537510045538099, 9.910220682547788, 9.26052312903102, 8.593089194374173, 7.912792325518363, 7.2247058376636994, 6.533990337115602, 5.845822223368355, 5.165339338533969, 4.4975857270447515, 3.8474691199478617, 3.2197363182667638, 2.618865131015868, 2.0489972043043982, 1.5138889815307943, 1.0168663057574834, 0.5607907215886403, 0.14803725595792402, -0.21957194082859186, -0.5407990792501245, -0.8150055600511728, -1.042159416735902, -1.2228330668397867, -1.3581950854039146, -1.45000878500782, -1.5006075221211543, -1.5128582416381247, -1.490117324147682, -1.436180555724241, -1.355231468352397, -1.2517748235224846, -1.1305617829756183, -0.9965114158764228, -0.8546289949253798, -0.7099242625493214, -0.5673318519435524, -0.4316170971629654, -0.30728783447408176, -0.1985118171817595, -0.10903885351664785, -0.042129579416701576, -0.00049002689444537, 0.01379171769933537, -0.0007061344117198832, -0.04470319534663833, -0.1181929859793313, -0.22043035616749854, -0.3499274320119984, -0.5044698455873727, -0.6811483075971674, -0.8764033988707143, -1.0860838119712175, -1.3055154599105445, -1.5295789229331664, -1.7528110346293586, -1.9695134322817662, -2.17386741940305, -2.360055240539773, -2.5223851171727745, -2.6554196495413747, -2.7541118522647965, -2.813935013891032, -2.831006708883951, -2.8022058990294125, -2.725282252779212, -2.59895957951175, -2.4230193954413273, -2.1983672176033893, -1.9270817721777063, -1.6124449525992164, -1.2589539980621576, -0.8723185271722869, -0.459419163174014, -0.028246358740603775, 0.4121809737395436, 0.851918743684647, 1.2802200161252786, 1.6856747909313348, 2.056381407650178, 2.3801290417935705, 2.6445914098088243, 2.8375309924866787, 2.9470108681370895, 2.9616134453874556, 2.870661065964139, 2.664430751198169, 2.3343616084546075, 1.8732515289735305, 1.275440109680627, 0.5369748752953024, -0.34424790533877037, -1.3683662980064795, -2.533462580836348, -3.835502874608934, -5.268312448120277, -6.823596706046626, -8.490976838688047, -10.25806162312476, -12.11055627834604, -14.032404810864008, -16.005979074242408, -18.012334914469157, -20.031414026467136, -22.04228644027861, -24.023426062296874, -25.953002991759654, -27.809216415168837, -29.570696905261237, -31.216744183146496, -32.7276063594154, -34.08477792048039, -35.27128537068991, -36.27199352545424, -37.07396139583231, -37.66653631030367, -38.04149327572793, -38.19317924064544, -38.118621286111036, -37.81763324109427, -37.29293770422338, -36.55000677687504, -35.59695693674872, -34.444445356403286, -33.10552807362973, -31.595504045088965, -29.931740100394375, -28.133306829892618, -26.22067608682583, -24.21542782914165, -22.139941153591295, -20.017072216867536, -17.869789908698813, -15.72080176737949, -13.592234621503584, -11.505333883171398, -9.4801795101467, -7.535396210760427, -5.687812311469716, -3.9522990987209563, -2.3416337353152397, -0.866377682643695, 0.4652079816106697, 1.6472516853243877, 2.6764126076421233, 3.551725589951759, 4.27447441502906, 4.84807133113197, 5.27790605183295, 5.571210681926366, 5.736976334606122, 5.785574993251787, 5.728462953273485, 5.577922001329029, 5.346797934357811, 5.048273360502432, 4.695691488154063, 4.302180296242308, 3.8803866445653745, 3.4422696970976885, 2.9989195482180313, 2.5604202078748672, 2.1357566822271075, 1.7326406979733788, 1.357434122796698, 1.0151271435960654, 0.7093481262112686, 0.4424078203487282, 0.21536910709403004, 0.028110631756874654, -0.120557552309393, -0.2327532646691305, -0.31136857520281197, -0.3599087909154028, -0.38233236314318186, -0.3828837782424817, -0.36592611740968595, -0.335783760317531, -0.2965990143108488, -0.25220728808442733, -0.20603370546160243, -0.16100124339995256, -0.11946649380129559, -0.08318220030399366, -0.05328481035453311, -0.030306471529569057, -0.014209267978530378, -0.004437948835251472, 6.514693266657752e-06, 0.00047787041850277343, -0.0014155676586030466, -0.003918125313021997, -0.005237185351210208, -0.003652968081044177, 0.0023772643352996635, 0.014124852103899034, 0.032508921221429024, 0.05803202140791647, 0.09073407546839646, 0.13016944742273515, 0.17540728567247083, 0.2250554207484255, 0.2773077603345821, 0.330013921968608, 0.3807691119831455, 0.4270235517762174, 0.4662064077794323, 0.4958604297417259, 0.5137830983876452, 0.5181695952014947, 0.5077524495751218, 0.4819318703512982, 0.4408929702061218, 0.385704777815587, 0.31839635672699534, 0.24200567501966858, 0.16059699257518015, 0.07924724588679401, 0.003998916254891612, -0.058222215433410426, -0.09972424400727073, -0.1122002551697057, -0.0869082195169437, -0.014873315957911503, 0.11288466550109705, 0.3051048452931301, 0.570025738070047, 0.9151250053732034, 1.346885477716173, 1.8705476303497546, 2.4898736339837706, 3.2069353404035783, 4.021929395181391, 4.933051016118856, 5.9364875628183675, 7.0263311540639295, 8.194548603593955, 9.431017127748179, 10.723608783249318, 12.05838362406315, 13.419991542082375, 14.7917928138696, 16.156074598945974, 17.49434983555287, 18.78768407545972, 20.017144509787812, 21.1645006517889, 22.21234733890968, 23.144358618027, 23.945618633086617, 24.6029322749476, 25.10523946091971, 25.444268660017126, 25.61435633443914, 25.612444255014786, 25.438152706026592, 25.093801728319537, 24.58451523420004, 23.918521137315278, 23.106550099325514, 22.16147330033304, 21.098038988247318, 19.9325739464651, 18.68276826635752, 17.36761349971598, 16.006607884775867, 14.619247350477872, 13.224649196241403, 11.841193093445773, 10.486258198829631, 9.176080398892513, 7.925181204240266, 6.746071254497808, 5.649092682464009, 4.642317185452007, 3.7315327410070283, 2.92031111912156, 2.2099164025747013, 1.5994011070844358, 1.0857935259827833, 0.6643262664345607, 0.32870638198947644, 0.07140901245756945, -0.11606397071022792, -0.24286500991941753, -0.3184723372476201, -0.3523749877059671, -0.3537805234210832, -0.33135673659273773, -0.29300589615310413, -0.24567505789487595, -0.19521600653048427, -0.14629835902594104, -0.10237731704860302, -0.06571470540745761, -0.037445872475414504, -0.017696995642365952, -0.005745521769938341, -0.0002153730378728621, 0.0007016893726633304, -0.0009919283145651628, -0.0033449507684955647, -0.004699510687599357, -0.003919067668794616, -0.0005917685616214134, 0.004800017897351342, 0.010752234894869416, 0.014661579595579724, 0.01280312575727996, 0.00036643368647525017, -0.028448435042382245, -0.08027560644207339, -0.16237105170338736, -0.2823488790550759, -0.44787341625990684, -0.6663158583294383, -0.9443860928433657, -1.2877533486780814, -1.7006732860644298, -2.1856217746273816, -2.742956167006176, -3.3706185516643035, -4.063892892961751, -4.815237945219907, -5.6142245447139585, -6.447503874462997, -7.2988724233096836, -8.14943797132896, -8.97788033958567, -9.760827932783942, -10.47337097328341, -11.089517371605506, -11.582749529401733, -11.92665891755189, -12.095624141423846, -12.065539791615471, -11.814576169104793, -11.323756168172306, -10.57756844115862, -9.564561911177998, -8.27787708688087, -6.715687472219613, -4.881453844688564, -2.7840588181704873, -0.43789268488416366, 2.137174754416199, 4.9159462084436365, 7.868260774677696, 10.95976330727627, 14.152358954982247, 17.40478321726522, 20.673317051923284, 23.912574008684604, 27.07653043150897, 30.120071766369662, 32.99949796686276, 35.673211872080124, 38.10253307124648, 40.25246198148101, 42.0926436270292, 43.598829435675185, 44.75263838488259, 45.541618407816564, 45.95943619353166, 46.00594245126541, 45.68739820185451, 45.01711653851237, 44.01419717699361, 42.70272943802666, 41.11119387986362, 39.27178712655946, 37.21992492349372, 34.99408356835609, 32.63408629862813, 30.179990379993527, 27.671263766766717, 25.146008581936783, 22.64040008254552, 20.188398919843163, 17.82055927717368, 15.563419179411683, 13.439191084694444, 11.465574422814996, 9.655759309432202, 8.018609388704496, 6.55849230949216, 5.27549393855542, 4.1658161839124785, 3.222249772622212, 2.434724751750558, 1.790905471547998, 1.2766742405893117, 0.8767280756137704, 0.575185480045975, 0.35615414067476586, 0.2042464071802154, 0.10502433721596104, 0.045353785978041745, 0.013694344849493879, 0.0002990750493461397, -0.0026819248247627408, -0.0011913748013028553, 0.0006578886141246993, 0.00042764180402912424, -0.0028691802695407402, -0.009047449139350752, -0.01706854973473152, -0.02538199633384022, -0.0322729940635096, -0.03619885444481895, -0.03609732407465219, -0.031651693030154006, -0.023499601991672715, -0.013375065019809139, -0.004175782357239924, 4.9942778165225335e-05, -0.005803591035823289, -0.027728447903516813, -0.07235986504937744, -0.14667008536807086, -0.2576123454908167, -0.4117294031987532, -0.6147424384948299, -0.8711383052493475, -1.183773776944667, -1.5535201185333942, -1.9789783332470703, -2.4562456549774825, -2.978766540003172, -3.537282839563264, -4.119889377474978, -4.712216589693719, -5.297767633137121, -5.858272572230296, -6.37415607247666, -6.825107327631515, -7.190725370099829, -7.451246814124975, -7.588350984763018, -7.585813647007492, -7.430194855983195, -7.111515844392111, -6.623876449549945, -5.9659977145821905, -5.141628331193109, -4.159725962706011, -3.0345683040401945, -1.7857347324862245, -0.43793300732761464, 0.9793750061692876, 2.4326651345666868, 3.884998598324697, 5.296773968710009, 6.626614057363895, 7.832345800105333, 8.87215566937407, 9.706055049853083, 10.29675342424825, 10.610605773697655, 10.618595676679405, 10.297241337927082, 9.629530914834842, 8.605975891182878, 7.224670725696669, 5.4914247350938785, 3.419849914265543, 1.0312696658897178, -1.6454638457550077, -4.574258109196066, -7.712887701060928, -11.01395544412357, -14.425864238681687, -17.893887946735504, -21.361328394846492, -24.770890913396006, -28.066128358829893, -31.192669469091257, -34.099362649393086, -36.739334495877216, -39.071054292948084, -41.05961334207182, -42.67722975907685, -43.903605626625584, -44.72618344004613, -45.1402187926916, -45.14883681434167, -44.763281448172265, -44.002007475789355, -42.88985225112714, -41.45723334863145, -39.739247358873456, -37.77484081234354, -35.60619577102642, -33.27718241909341, -30.83213034451668, -28.314796066544922, -25.767403083528716, -23.22986152400556, -20.739221393890293, -18.328696418387345, -16.02706994806357, -13.858350016262822, -11.841576590863179, -9.990807809670603, -8.315276360513502, -6.8194691395081755, -5.503437603345389, -4.363245098008261, -3.3914907186808785, -2.5778917647334287, -1.9098991529769838, -1.373297223932474, -0.9528159097430143, -0.6327182485019748, -0.39733970365712057, -0.23156387419056135, -0.121224718659023, -0.05343422544323318, -0.016817369228120393, -0.0016589267679488992, 3.3309101881332834e-05, -0.005457058412707763, -0.013472392566785674, -0.02083759535435835, -0.025668861669528253, -0.027151185438926192, -0.02529860197377387, -0.020710920957796895, -0.014339284832253682, -0.00727159166246158, -0.0005511312300923291, 0.0049652307743244225, 0.008704695903924873, 0.010429595398473069, 0.010241712381901134, 0.008541238326028369, 0.005947406143901455, 0.003188037828665707, 0.0009665426329375157, -0.0001837827942797816, -4.7111582847818386e-05, 0.0011379320301411458, 0.002561134561835942, 0.0027524482995600792, -0.00046921129506814356, -0.010002981722157571, -0.02942330343049313, -0.06289200329909268, -0.11502360439731153, -0.1907059973403868, -0.29488179254168984, -0.43229901148339694, -0.607251397121414, -0.8233122725252076, -1.0830679054232204, -1.387865020011251, -1.737583844047546, -2.1304637964263664, -2.5630384521108414, -3.030064933056049, -3.5245140358655735, -4.0376351806966495, -4.5590881321522065, -5.077185923586111, -5.579335313508092, -6.052299091474758, -6.482527977086488, -6.856556999421414, -7.161420334545774, -7.385147127616241, -7.51743257747336, -7.549847643838642, -7.476095012174071, -7.292275885447445, -6.997092568235578, -6.592062748245682, -6.081820782172248, -5.473814009548569, -4.778064233950674, -4.006932595212912, -3.174812894001684, -2.2978233094751292, -1.3935337246365436, -0.48024852226512155, 0.4235725906104053, 1.2998273733606103, 2.1312694142089947, 2.9019539824118756, 3.597634142066689, 4.206265705617299, 4.718333124552956, 5.127058267451961, 5.4285197662117275, 5.621686341962041, 5.708391301078581, 5.693195543157745, 5.583139139790166, 5.387420285291496, 5.117015503271589, 4.7842673911268045, 4.402468149390867, 3.985357569354843, 3.5466423902413036, 3.099549683877381, 2.656419078853885, 2.228352111538257, 1.8249306330990072, 1.45397538433956, 1.121398258764252, 0.8311416112466907, 0.5851980200528256, 0.38370631420200146, 0.2251171565338269, 0.1064199447569564, 0.023416579829812528, -0.02897110135296211, -0.056374495625805404, -0.0646469280841247, -0.059541608522414725, -0.046416254536285804, -0.02997882903574535, -0.01408159581919982, -0.0015714371568871163, 0.005797811226007144, 0.007386270484990243, 0.0036220881783381245, -0.00410195253664216, -0.013584642543808638, -0.02201776827354996, -0.02622330256512469, -0.022912466587267616, -0.008943299355802058, 0.01842695818509395, 0.06130684767466579, 0.12096576445316104, 0.19767558204057273, 0.2906292418256628, 0.3979001962315263, 0.5164555385439962, 0.6422309845850153, 0.7702638720782, 0.8949017375317049, 1.0101216706468081, 1.1097706823315483, 1.1878376009210272, 1.2387498833311563, 1.2576669638824864, 1.2407922212786688, 1.1857293817042027, 1.0915790235615592, 0.9590305184277209, 0.790425449239412, 0.5897557589884426, 0.36262413953145484, 0.1161743427591054, -0.14125057402498958, -0.4004252759930819, -0.6515687678476957, -0.8847035198997517, -1.0900263628927929, -1.258300149271821, -1.3813087144677556, -1.4522178936156211, -1.465875407462216, -1.4190545659879024, -1.3106422719353226, -1.1417860358130292, -0.9158980681809573, -0.6385623124417112, -0.3173653700545554, 0.03834800128591623, 0.4177771222305284, 0.8090189267333694, 1.1995410887512044, 1.576654745925372, 1.9279823125313624, 2.2419142107092243, 2.5080427437884274, 2.717582853811853, 2.863720838934092, 2.94186776038968, 2.9498268617038113, 2.8878696505527373, 2.7587318889976533, 2.5675516055605376, 2.3216389457951467, 2.0301728177857608, 1.703838900294052, 1.3544133638199976, 0.9943171879499056, 0.6361630142340656, 0.2922458698277266, -0.025929370875284272, -0.30807428467395803, -0.5454890726931919, -0.7313661218822477, -0.861014407506354, -0.9319988192908026, -0.9441843993625826, -0.8996870100222976, -0.8027343968854347, -0.6594421844808279, -0.4775066635917856, -0.26584975089334256, -0.03422716440305877, 0.20718954083683588, 0.44823867612568097, 0.6791943153133291, 0.891186883264041, 1.0765134062674888, 1.2289026158143512, 1.3437219743070115, 1.4181096315957764, 1.4510382304469354, 1.443310755906306, 1.3973989635693462, 1.3172474167222632, 1.2080329049976348, 1.0758770421116957, 0.9275289560280564, 0.7700251749057545, 0.6103218659069882, 0.45497201104586227, 0.30983978701925713, 0.17985741357817756, 0.06883308377290709, -0.020682593752601244, -0.08744508312436428, -0.13149509019123276, -0.1540757056946836, -0.15749129624740954, -0.14491327699643877, -0.12013145544753355, -0.08728523778824436, -0.05059314760984333, -0.014086850637594399, 0.018637005325568615, 0.044641993354645776, 0.0618493124777276, 0.06913082545035508, 0.06634973042489539, 0.05434604372152284, 0.03486073988305903, 0.010403858379532421, -0.015939368661622003, -0.04077282094742675, -0.06066040717436849, -0.07240392647099449, -0.07331894212629907, -0.06150228620110227, -0.036093372671607615, 0.00255779443992598, 0.052788360735274896, 0.11158435815388182, 0.1746154725157819, 0.23633687795216748, 0.29016231710628265, 0.3287683638126897, 0.3444347825040881, 0.32941756620194207, 0.27634736725300285, 0.17864239727223333, 0.030947985217367253, -0.17047370051911034, -0.42742710569933245, -0.739538276527646, -1.1040961972307837, -1.5159748595009483, -1.9676161318774326, -2.4492141282832245, -2.9489986769129892, -3.4536054032058154, -3.9485315975355877, -4.4186532964643765, -4.848782466947888, -5.224303794340521, -5.531791201334636, -5.759586509905453, -5.898322476885909, -5.941373906427646, -5.885226997818743, -5.729682177291689, -5.477931606319466, -5.136502717144392, -4.715060082692839, -4.22608011480628, -3.6844071735103334, -3.106636533633406, -2.51044896402902, -1.9139024072893618, -1.3346990030596215, -0.789455460656029, -0.29299320012265184, 0.14227593233824756, 0.5068424503085347, 0.7944637637407038, 1.0023806515345033, 1.1313840123059575, 1.1857313179477875, 1.1728118529841778, 1.1026804222916096, 0.987467140397092, 0.8406744715313148, 0.676396124507826, 0.5084846572380878, 0.349673973414603, 0.21077127153601216, 0.09993441639264881, 0.022063299449447023, -0.02166156675321735, -0.034062163849139605, -0.022030143830671325, 0.0036217017307610556, 0.028520572605833, 0.03530225602854055, 0.00437695079682093, -0.08512236377018344, -0.25428789863070544, -0.5233087637430298, -0.9103048577614697, -1.4301736481035567, -2.093505633459184, -2.9056666209361133, -3.866077528570074, -4.967689045855754, -6.196700233524571, -7.532547574856207, -8.948242817946872, -10.411230868164944, -11.88425475265084, -13.3264647159239, -14.694777799888032, -15.945406647418471, -17.0356566723244, -17.926179648876065, -18.582371514656817, -18.975801870349432, -19.085603789117997, -18.899644197547726, -18.41561366153863, -17.642176970645775, -16.59855497205612, -15.314040758487055, -13.827316293214515, -12.185397207823035, -10.442369143994853, -8.657980664995483, -6.8950243644359315, -5.216937271317579, -3.685472290475005, -2.3583601708385546, -1.287079024763658, -0.5147344584262118, -0.07389794286151172, 0.014961362520893874, -0.25542351692196347, -0.878465823786597, -1.8335324503212513, -3.086188795648435, -4.5890979231771745, -6.283442527764944, -8.100774493928451, -9.965241516973045, -11.79612561166492, -13.510679577300083, -15.02710874735113, -16.267518702203922, -17.160759920558057, -17.645071278500364, -17.67047974452147, -17.200962216928218, -16.21585448353014, -14.710770558820174, -12.698001455085135, -10.206336042182818, -7.280335890954752, -3.979086036334704, -0.37424072074415266, 3.4522817249929383, 7.410925283736578, 11.407384729200675, 15.345704025384933, 19.131555120500632, 22.675156084777495, 25.894051991190658, 28.715666237170776, 31.07949367990703, 32.93894426796235, 34.262804221462396, 35.03558880248918, 35.25757526949893, 34.944397852288624, 34.12613039845295, 32.84591765408541, 31.15812005689548, 29.12591149019189, 26.818869427124856, 24.310473143067327, 21.675547607251506, 18.987675708345666, 16.31654934243443, 13.725971246957862, 11.27215557253899, 9.002321629876056, 6.953668588724384, 5.152669464837359, 3.614679836695683, 2.3445825441782655, 1.3375719900047942, 0.5801518572988174, 0.05139541153197065, -0.2756071229747808, -0.4320759197535486, -0.4516136574383884, -0.36853197112534175, -0.2163257612465481, -0.026299913025126773, 0.17366186406414943, 0.36025945793971936, 0.5153241040890391, 0.6260566015581558, 0.6850268347211086, 0.6899162744347297, 0.6430969286073416, 0.5511154014987215, 0.42357326806338075, 0.27206679824966457, 0.10917525951288612, -0.05252091099555006, -0.2013167064828751, -0.32713342755876235, -0.42230908314162513, -0.4820530355808236, -0.5046448122348408, -0.49141829952627336, -0.44654143294693605, -0.3766234380691625, -0.29015862839989437, -0.19681384460049756, -0.10664312215528216, -0.029284621319850167, 0.026810840615416102, 0.055078607037005345, 0.05142351722853828, 0.014627265544807295, -0.053443124199778966, -0.14783965666382828, -0.26075487583036216, -0.381961952037174, -0.49946311361924584, -0.600299539994597, -0.67148170959288, -0.7009921022603554, -0.6788139348946315, -0.5979490798707527, -0.4553047503169969, -0.25242367024670864, 0.00398462859894997, 0.3017554215260725, 0.6232477223681635, 0.9456042686486692, 1.2413343639647068, 1.479171197211698, 1.625181655491862, 1.644094908402023, 1.5007973849797862, 1.1619091043227783, 0.5973857597223118, -0.21789512379726578, -1.3026471133693585, -2.667858105327452, -4.315769250358182, -6.239366021572001, -8.421935514916266, -10.836972981397563, -13.448497637462523, -16.211743781969837, -19.074420086682544, -21.978852186188384, -24.86326222790191, -27.663431922333324, -30.31467674114763, -32.75389670003052, -34.921990764432465, -36.76696840480931, -38.2447036335277, -39.320014515615995, -39.96780208129118, -40.17386844576437, -39.935786457978544, -39.26408148648986, -38.18043306906514, -36.716432407637065, -34.91246148125269, -32.8163076047322, -30.48186255929099, -27.968032081429076, -25.335559213200185, -22.644788219573456, -19.953871451536813, -17.31711902664029, -14.78368107962266, -12.396555757276916, -10.190953317426228, -8.193598143695896, -6.422546634382247, -4.8873177546142905, -3.5893466224668678, -2.522691863991577, -1.6747828525320463, -1.0275659162851782, -0.5588068886545221, -0.24343593815725467, -0.054884488493242116, 0.03362787682195891, 0.047935091696832854, 0.011912466833449683, -0.053333016281452116, -0.13004589459432564, -0.20418439777422964, -0.26558321302090643, -0.3078285144883007, -0.3279438345930567, -0.3259255734717484, -0.3041610554449909, -0.26678194481018247, -0.21899714998228118, -0.1663834481067956, -0.1142642149079379, -0.06719855466729947, -0.028598245803406457, -0.0004912298564849333, 0.016563518251346433, 0.02341091132423165, 0.02207926869732375, 0.015436213988310795, 0.006752730655801412, -0.0007895887874893601, -0.004610582780038025, -0.0032224089823528305, 0.003344687218367202, 0.01321708003943887, 0.022482359431041137, 0.02514605449831421, 0.013255529657825435, -0.022807871402526193, -0.09387752600982718, -0.21140914442008352, -0.3867755080134195, -0.6304922279539795, -0.951442246580681, -1.356091072344464, -1.8477623002639854, -2.4260262496101275, -3.086241357188627, -3.8193395465138362, -4.6119948410304, -5.446753490641748, -6.302423294332227, -7.154727588669975, -7.977166749466423, -8.742192930240089, -9.422840729277558, -9.993633035112369, -10.431661774040224, -10.717741529675257, -10.837459009007574, -10.782247800297773, -10.550578898834969, -10.147685759267594, -9.585374906463425, -8.881729118899038, -8.060510805075877, -7.150421693341269, -6.1842531128495555, -5.19681773844701, -4.22320808860641, -3.2971632159328848, -2.449434199483673, -1.706267701548331, -1.0880111162224448, -0.6075985126334382, -0.2696581236858262, -0.07005411048568928, 0.004189517865903494, -0.02542891616146363, -0.12959144785700974, -0.2723396016248472, -0.4126617013325743, -0.5063615936436197, -0.5081354160149693, -0.37379282117006685, -0.062605283833868, 0.4604547334495593, 1.2226987957968183, 2.2419845577552473, 3.5253352714650705, 5.067944005644525, 6.852588170051136, 8.849839073451104, 11.01876790729799, 13.308132584507257, 15.658039028938228, 18.002029974566582, 20.269641141387122, 22.389241752191992, 24.290907476795795, 25.909281013752846, 27.18631221622751, 28.073854267187297, 28.536185465175933, 28.551599195234232, 28.113484810362184, 27.230880383560272, 25.928404630452423, 24.245661882373113, 22.236224585082773, 19.965427787868297, 17.507845445984884, 14.944474714444338, 12.359645762605599, 9.837811193309077, 7.46032560386065, 5.302115369636168, 3.428734104953999, 1.8938364966575678, 0.7371303042894102, -0.017120514454517802, -0.3609747787597133, -0.3029424637387303, 0.13252981575968895, 0.9062006989420331, 1.9657663128113612, 3.2481398184398387, 4.682274805827659, 6.192157456327864, 7.6999296598603415, 9.129068127331088, 10.407477503718875, 11.470444151068978, 12.263395082231703, 12.743739278830454, 12.882308742724705, 12.66430717801992, 12.0896640211328, 11.172806672497213, 9.941780998785811, 8.436603820292968, 6.707351667115315, 4.811934248481739, 2.8135988551864393, 0.7781801331633355, -1.228961758553426, -3.145409158806473, -4.913968827075306, -6.4847411805339314, -7.816839316722076, -8.879830516333277, -9.654923784767286, -10.134760019018982, -10.32302559440701, -10.233780292997317, -9.890399064517839, -9.32423910004322, -8.572999596787023, -7.678433017307013, -6.68433221057456, -5.634640017663769, -4.571660101859046, -3.534384860328535, -2.5568510298373055, -1.6670748260756656, -0.8864210375082364, -0.2292874412581094, 0.2968823332401578, 0.6913646305602216, 0.9597971499804693, 1.1129983824407406, 1.1657729817975502, 1.1357132325957229, 1.041973211464361, 0.9041221781185648, 0.7411139291021186, 0.5700685850674639, 0.4054440314169829, 0.2585018082845115, 0.13701508309735047, 0.04522114237537705, -0.01601742822829178, -0.04887210248054843, -0.05796356917516714, -0.049642434628145625, -0.03120119144800786, -0.010072392368421489, 0.006939734052092014, 0.014370905331829012, 0.00866924083882111, -0.01140457483532179, -0.044567098896825724, -0.0870000102051172, -0.13253441957073778, -0.17303271197272743, -0.1989346017070198, -0.1999264939070701, -0.16569063387106472, -0.08669018962974674, 0.04504554625733975, 0.23521980495587363, 0.48668596468793474, 0.7990186202017454, 1.168270285332877, 1.586930746763554, 2.044096896888674, 2.5258698075674193, 3.0159373034209906, 3.496317072744191, 3.9482254025624335, 4.353037328997322, 4.693299066067664, 4.953641173853041, 5.121626911346496, 5.188483423160228, 5.149662430249636, 5.005207644053728, 4.7598940670239545, 4.423029821325258, 4.008074517687096, 3.53205500049837, 3.0147855815698974, 2.4779218889168484, 1.9438695869109137, 1.4346700690300205, 0.9709200010284254, 0.5707469030575237, 0.2488918042948373, 0.01593970358797016, -0.12223667831607975, -0.16471289432931174, -0.11553878917911872, 0.016466928846153337, 0.21815919836536765, 0.4727584629859799, 0.7608499951777749, 1.061392829882265, 1.3527816958233099, 1.6139524741203304, 1.8254653607984817, 1.9705782802970926, 2.036332347586029, 2.01405359749611, 1.8997176636024742, 1.6941434235187711, 1.4029504080016046, 1.0363255378567755, 0.6085897806000417, 0.1372285100441991, -0.35807261146349534, -0.8564313861768192, -1.3368209988330877, -1.7791341676367798, -2.16529284727115, -2.480208962333088, -2.7124894708687584, -2.8549371397693997, -2.9048320645584402, -2.8640286392605527, -2.7389202308265537, -2.5398877753232316, -2.280594344637983, -1.9771639129043863, -1.6472505229385166, -1.3090739248189343, -0.9804648505358641, -0.6777573092876621, -0.41488085816930054, -0.20264313413265608, -0.04820365816679179, 0.045236299612928146, 0.07853310148114719, 0.05647000202519355, -0.012641922401940044, -0.11757123827205725, -0.24493893653370336, -0.38010846750081384, -0.5081446246396385, -0.6148130135957519, -0.6875263581157147, -0.7161836789002751, -0.6938561099221018, -0.6172805876013934, -0.48713435843740444, -0.308048904373562, -0.08837333414911412, 0.16030205844784554, 0.4238409043536988, 0.6864407349619787, 0.9316546029260514, 1.1434801598414615, 1.3074650797081897, 1.411769181659943, 1.4481194935458046, 1.4125981027379977, 1.3061970657835187, 1.1351099878176212, 0.9107587443645899, 0.6495282870449783, 0.3722060054183031, 0.10312947064774386, -0.1309210376330551, -0.3019320109942289, -0.3820161548765739, -0.34486200871091854, -0.16719877256916194, 0.16982871812135303, 0.6796080485305815, 1.3691293909386588, 2.238237414342502, 3.279168749577312, 4.476395385660721, 5.806978667425054, 7.241846056319386, 8.746451214415659, 10.28174080640466, 11.805460552380111, 13.273625113659655, 14.642467031881568, 15.871334686933139, 16.92340788871971, 17.766707399009654, 18.37525459356724, 18.730021721162593, 18.820077991657705, 18.644306800016363, 18.210049211100326, 17.53226854390928, 16.632892177846255, 15.539924338691181, 14.286704779134643, 12.91149153694992, 11.454703255992904, 9.957064591306224, 8.458194105193083, 6.995301473819552, 5.602189790588741, 4.308547850419265, 3.138412051242377, 2.1095304558858454, 1.2332089213728292, 0.5144196451911245, -0.04782915344320666, -0.4599650354975262, -0.7332930706036352, -0.8830645512599684, -0.9274156866875525, -0.8862799280132468, -0.780338923319238, -0.6300778522634345, -0.4548394539932629, -0.27202113099060304, -0.09646285694014575, 0.05997122755850844, 0.18861021834606284, 0.2840057501531881, 0.34382481951292465, 0.3685633839405205, 0.36112648887509896, 0.32631762461565417, 0.27027561143930234, 0.19989741071908962, 0.12227346225084272, 0.04417339938839183, -0.028390777066385996, -0.0905050097234347, -0.13858551909716602, -0.1704983977534159, -0.18555947902542158, -0.18443456379729536, -0.1689549529037497, -0.1418665252886766, -0.10653467963013191, -0.06662633386469666, -0.02579522538030643, 0.012600272814088589, 0.04573367266237739, 0.07148818720315304, 0.08856742945056276, 0.0965337939629892, 0.09576730797384655, 0.08736437038600801, 0.07298665290855169, 0.05467290191778613, 0.03462882555558775, 0.01501032247030246, -0.002272577143156932, -0.01571900166783634, -0.024358798819200403, -0.027823570248747934, -0.02636239061112895, -0.020797700805895127, -0.01242563414613766, -0.0028797143505246894, 0.006033723596778509, 0.012515997422475727, 0.014959951990713963, 0.012122817562030578, 0.0032524519239748744, -0.011826959894609076, -0.03267613419724708, -0.05825462018822, -0.08699011858721309, -0.11691211606119986, -0.1458219027781717, -0.1714801420502431, -0.19180437102247672, -0.20506081749505187, -0.2100433194181371, -0.206235757078882, -0.1938679117658052, -0.17391362559831228, -0.1480290116369525, -0.11842458330515646, -0.08768239470483165, -0.05852480077564566, -0.033503452224968464, -0.014696404205509477, -0.003424778727876609, -4.697735903194484e-06, -0.0035563752393781936, -0.011890404021553055, -0.021499630526566452, -0.02766722861415742, -0.024686122978828363, -0.006183669120060643, 0.0344635917099135, 0.10363179833012506, 0.20685662413131636, 0.34822382159507514, 0.5297799446332927, 0.7510023151791424, 1.008402503760407, 1.295512139748728, 1.6031192186206868, 1.9196329777612897, 2.231644180411678], 'positive_zeros': ['0.862405898825182011215777121633208', '1.04701189594523705657282763502149', '1.06230887718891052529893363417437', '1.29737931626942746944142033685614', '1.42678379183848712607059082936654', '1.82529571928063356520382359159003', '2.04039875632863891560039312445053', '2.18747725391138967077014601062759', '2.19803017826799435681990141822338', '2.23200998671857837340803908898727', '2.42232386141092767121161833591959', '2.46207099836660768785245629664866', '2.92454298028065355397106180435081', '3.04749440188583651494434610164916', '3.05883331486150828370753259193762', '3.09474303984619965388238504575972', '3.13295763112600551633933995688298', '3.40762663573411455041373874920417', '3.83628037580636372920698586051306', '3.85596890245412095532682002163062', '3.86882505245860189016958756184233', '3.96023836069807826518508487374041', '3.96180573318158933165713647039144', '4.22119685744969334121500885387854', '4.36248026131235495478560677017667', '4.77590696491682074753368837203190', '4.78134136706409467267573833676356', '4.86007096735683766411280911245048', '4.92759447807509492493891228916475', '4.93797269619618200559932629368319', '4.96809267323638294905636588760714', '5.27756970455463084589818072248534', '5.51862176116546650657856552970146', '5.57938931447306457922472683939474', '5.60560089207558285777111872585515', '5.65148248393494759839495314965664', '5.83167818007367399627663333722844', '5.95231137339679489208669064878760', '6.12433239040089232249503817298495', '6.21986885398983613234626340056902', '6.38863326200938573989075656353572', '6.46414666547436515032788821761587', '6.52653575300142848291434774009671', '6.58549392205802183016046747501494', '6.67322849468142290359539151814074', '6.91137251861527237451378541924176', '7.03446551605195146612841303297257', '7.06148627034610560416369034643336', '7.08651896670988547755996044065318', '7.38566461407741513358092845294053', '7.39164841862591292596287336783527', '7.57109400360368819232640665556708', '7.82910337621629357278985768466668', '7.87602809844224312852933399617898'], 'prelabel': '12-7600e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.79014156072745, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e6-0', 'trace_hash': 2025538793433305976, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.862405898825182011215777121633', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.04701189594523705657282763502', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.06230887718891052529893363417', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 49951001001.787384, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 192699928576000000000000, 'conductor_radical': 190, 'degree': 12, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, -2, 0, -4, 0, -3, 0, -1, 0, 0, 0, -14, 0, 6, 0, 4, 0, -12, 0, 0, 0, 10, 0, 9, 0, -5, 0, 6, 0, 0, 0, -8, 0, 2, 0, 3, 0, -15, 0, 0, 0, -4, 0, -8, 0, 28, 0, 13, 0, 0, 0, -12, 0, 0, 0, 9, 0, 8, 0, 0, 0, 3, 0, 24, 0, -19, 0, 3, 0, 0, 0, 6, 0, 16, 0, 10, 0, -31, 0, 0, 0, -18, 0, 14, 0, 2, 0, 10, 0, 0, 0, -11, 0, 12, 0], 'euler11': [1, 3, 26, 26, 65, -749, -2288, -8239, 7865, 34606, 380666, 483153, 1771561], 'euler13': [1, 1, 13, 50, 38, -516, 1813, -6708, 6422, 109850, 371293, 371293, 4826809], 'euler17': [1, 14, 124, 848, 4842, 24018, 105929, 408306, 1399338, 4166224, 10356604, 19877998, 24137569], 'euler19': [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 12, 112, 778, 4884, 25856, 128015, 594688, 2583636, 9465926, 31342192, 77236116, 148035889], 'euler29': [1, -9, 107, -600, 5158, -26640, 189919, -772560, 4337878, -14633400, 75679067, -184600341, 594823321], 'euler3': [1, 2, 8, 14, 30, 50, 87, 150, 270, 378, 648, 486, 729], 'euler31': [1, 5, 50, 176, 771, 5843, 22284, 181133, 740931, 5243216, 46176050, 143145755, 887503681], 'euler37': [1, 8, 132, 743, 7797, 33802, 309503, 1250674, 10674093, 37635179, 247389252, 554751656, 2565726409], 'euler41': [1, -3, 66, -146, 4087, -5943, 137612, -243663, 6870247, -10062466, 186500226, -347568603, 4750104241], 'euler43': [1, 15, 271, 2530, 26829, 185919, 1470270, 7994517, 49606821, 201152710, 926495071, 2205126645, 6321363049], 'euler47': [1, 4, 230, 749, 23811, 63544, 1431531, 2986568, 52598499, 77763427, 1122326630, 917380028, 10779215329], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, -13, 126, -1554, 12921, -108347, 968797, -5742391, 36295089, -231354858, 994200606, -5436541409, 22164361129], 'euler59': [1, 0, 161, -255, 12605, -44407, 744938, -2620013, 43878005, -52371645, 1950895121, 0, 42180533641], 'euler61': [1, -9, 234, -2302, 30205, -236741, 2409968, -14441201, 112392805, -522510262, 3239926794, -7601366709, 51520374361], 'euler67': [1, -3, 203, -820, 23862, -100928, 1840467, -6762176, 107116518, -246625660, 4090677563, -4050375321, 90458382169], 'euler7': [1, 2, 12, 22, 118, 126, 779, 882, 5782, 7546, 28812, 33614, 117649], 'euler71': [1, 19, 351, 3254, 31709, 169223, 1652142, 12014833, 159845069, 1164642394, 8919500031, 34280357669, 128100283921], 'euler73': [1, -3, 133, -274, 18744, -31092, 1356111, -2269716, 99886776, -106590658, 3776966053, -6219214779, 151334226289], 'euler79': [1, -16, 189, -1815, 19499, -139691, 1154286, -11035589, 121693259, -894865785, 7361565309, -49232902384, 243087455521], 'euler83': [1, 31, 824, 13802, 205891, 2327315, 23897248, 193167145, 1418383099, 7891804174, 39105656504, 122110259933, 326940373369], 'euler89': [1, -14, 467, -5503, 93933, -916667, 10735038, -81583363, 744043293, -3879444407, 29300626547, -78176832286, 496981290961], 'euler97': [1, 11, 374, 3862, 74175, 650639, 8888572, 63111983, 697912575, 3524743126, 33109951094, 94460742827, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 8, 14, 30, 50, 87, 150, 270, 378, 648, 486, 729], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 12, 22, 118, 126, 779, 882, 5782, 7546, 28812, 33614, 117649], [1, 3, 26, 26, 65, -749, -2288, -8239, 7865, 34606, 380666, 483153, 1771561], [1, 1, 13, 50, 38, -516, 1813, -6708, 6422, 109850, 371293, 371293, 4826809], [1, 14, 124, 848, 4842, 24018, 105929, 408306, 1399338, 4166224, 10356604, 19877998, 24137569], [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], [1, 12, 112, 778, 4884, 25856, 128015, 594688, 2583636, 9465926, 31342192, 77236116, 148035889], [1, -9, 107, -600, 5158, -26640, 189919, -772560, 4337878, -14633400, 75679067, -184600341, 594823321], [1, 5, 50, 176, 771, 5843, 22284, 181133, 740931, 5243216, 46176050, 143145755, 887503681], [1, 8, 132, 743, 7797, 33802, 309503, 1250674, 10674093, 37635179, 247389252, 554751656, 2565726409], [1, -3, 66, -146, 4087, -5943, 137612, -243663, 6870247, -10062466, 186500226, -347568603, 4750104241], [1, 15, 271, 2530, 26829, 185919, 1470270, 7994517, 49606821, 201152710, 926495071, 2205126645, 6321363049], [1, 4, 230, 749, 23811, 63544, 1431531, 2986568, 52598499, 77763427, 1122326630, 917380028, 10779215329], [1, -13, 126, -1554, 12921, -108347, 968797, -5742391, 36295089, -231354858, 994200606, -5436541409, 22164361129], [1, 0, 161, -255, 12605, -44407, 744938, -2620013, 43878005, -52371645, 1950895121, 0, 42180533641], [1, -9, 234, -2302, 30205, -236741, 2409968, -14441201, 112392805, -522510262, 3239926794, -7601366709, 51520374361], [1, -3, 203, -820, 23862, -100928, 1840467, -6762176, 107116518, -246625660, 4090677563, -4050375321, 90458382169], [1, 19, 351, 3254, 31709, 169223, 1652142, 12014833, 159845069, 1164642394, 8919500031, 34280357669, 128100283921], [1, -3, 133, -274, 18744, -31092, 1356111, -2269716, 99886776, -106590658, 3776966053, -6219214779, 151334226289], [1, -16, 189, -1815, 19499, -139691, 1154286, -11035589, 121693259, -894865785, 7361565309, -49232902384, 243087455521], [1, 31, 824, 13802, 205891, 2327315, 23897248, 193167145, 1418383099, 7891804174, 39105656504, 122110259933, 326940373369], [1, -14, 467, -5503, 93933, -916667, 10735038, -81583363, 744043293, -3879444407, 29300626547, -78176832286, 496981290961], [1, 11, 374, 3862, 74175, 650639, 8888572, 63111983, 697912575, 3524743126, 33109951094, 94460742827, 832972004929]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7600/2/a/ch'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-7600e6-1.1-c1e6-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 6, 'prelabel': '12-7600e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.79014156072745, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 2025538793433305976, 'z1': {'__RealLiteral__': 0, 'data': '0.862405898825182011215777121633', 'prec': 107}}
  • lfunc_instances • Show schema
    {'Lhash': '1093229355286107653762984266122,1327245258341076220278288842239,1346636485796298859986968238152,1644623668992629598160271605811,1808663330119967319332154795515,2313837214140112856876679482186', 'Lhash_array': ['1093229355286107653762984266122', '1327245258341076220278288842239', '1346636485796298859986968238152', '1644623668992629598160271605811', '1808663330119967319332154795515', '2313837214140112856876679482186'], 'factors': ['2-7600-1.1-c1-0-68', '2-7600-1.1-c1-0-92', '2-7600-1.1-c1-0-96', '2-7600-1.1-c1-0-132', '2-7600-1.1-c1-0-143', '2-7600-1.1-c1-0-170'], 'label': '12-7600e6-1.1-c1e6-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7600/2/a/ch'}