-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2147508523873244700358015781013', 'a10': 0, 'a2': 0, 'a3': 34, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 106, 'a8': 0, 'a9': -1031, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.47700509682438, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '200.1', 'coefficient_field': '1.1.1.1', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, -34, 2187], [1], [1, -106, 823543], [1, 1324, 19487171], [1, -8828, 62748517], [1, 24000, 410338673], [1, 4876, 893871739], [1, -46646, 3404825447], [1, 110902, 17249876309], [1, 247680, 27512614111], [1, -360092, 94931877133], [1, -104402, 194754273881], [1, 713622, 271818611107], [1, -156882, 506623120463], [1, 1066268, 1174711139837], [1, -832572, 2488651484819], [1, -529070, 3142742836021], [1, 4174418, 6060711605323], [1, -5176568, 9095120158391], [1, -237976, 11047398519097], [1, 3742736, 19203908986159], [1, 7861886, 27136050989627], [1, -4300854, 44231334895529], [1, 1147792, 80798284478113], [1, 10605714, 107213535210701], [1, 20054042, 122987386542487], [1, -8801350, 160578147647843], [1, 3555294, 182803912081669], [1, 27997648, 235260548044817]], 'euler_factors_factorization': [[1], [[[1, -34, 2187], 1]], [1], [[[1, -106, 823543], 1]], [[[1, 1324, 19487171], 1]], [[[1, -8828, 62748517], 1]], [[[1, 24000, 410338673], 1]], [[[1, 4876, 893871739], 1]], [[[1, -46646, 3404825447], 1]], [[[1, 110902, 17249876309], 1]], [[[1, 247680, 27512614111], 1]], [[[1, -360092, 94931877133], 1]], [[[1, -104402, 194754273881], 1]], [[[1, 713622, 271818611107], 1]], [[[1, -156882, 506623120463], 1]], [[[1, 1066268, 1174711139837], 1]], [[[1, -832572, 2488651484819], 1]], [[[1, -529070, 3142742836021], 1]], [[[1, 4174418, 6060711605323], 1]], [[[1, -5176568, 9095120158391], 1]], [[[1, -237976, 11047398519097], 1]], [[[1, 3742736, 19203908986159], 1]], [[[1, 7861886, 27136050989627], 1]], [[[1, -4300854, 44231334895529], 1]], [[[1, 1147792, 80798284478113], 1]], [[[1, 10605714, 107213535210701], 1]], [[[1, 20054042, 122987386542487], 1]], [[[1, -8801350, 160578147647843], 1]], [[[1, 3555294, 182803912081669], 1]], [[[1, 27997648, 235260548044817], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-200-1.1-c7-0-28', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/200/8/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [-2.1537466938222545e-60, 0.3082503448032538, 0.6120697235284711, 0.9070923922869356, 1.1890822565451975, 1.4539957117879958, 1.6980421134915362, 1.9177411036649235, 2.1099760373939493, 2.272042774462542, 2.4016931290837658, 2.497172305972133, 2.557249694390401, 2.5812424443443156, 2.569031311640188, 2.521068331793961, 2.4383759673309497, 2.3225374691463103, 2.1756783003196536, 2.0004385897688137, 1.799936712688182, 1.577724233742531, 1.3377325959498918, 1.0842120911268893, 0.8216638042996146, 0.554765381806259, 0.28829162776164907, 0.027031082616745607, -0.2243001230407431, -0.46114572049500036, -0.6791965336376858, -0.8744758749473003, -1.043421432509019, -1.1829619425489695, -1.2905869433906396, -1.3644079438045558, -1.4032094136762248, -1.4064881192874403, -1.3744794799699684, -1.3081698171771245, -1.209293599824209, -1.0803150586749297, -0.9243938440674259, -0.7453347307090431, -0.5475217248341517, -0.33583729586288, -0.11556782900004808, 0.10770323168916708, 0.32821271763651266, 0.5401433732785427, 0.737755310669949, 0.9155205238825815, 1.0682574848543929, 1.1912626807805893, 1.2804358593067202, 1.332395728790019, 1.3445829223483357, 1.3153471801522922, 1.2440159362526415, 1.1309418137573215, 0.9775269325748187, 0.7862224119186003, 0.5605019974828364, 0.30480935031285933, 0.024479188176910218, -0.27436684422448093, -0.5849479994422514, -0.8999736721601346, -1.2118111172041863, -1.5126680624748636, -1.7947860714664923, -2.0506400261701803, -2.273138719158607, -2.455821280351647, -2.593044033772683, -2.6801523939216483, -2.713632578038407, -2.6912382332870703, -2.6120875561022827, -2.4767271092398344, -2.2871593102541636, -2.0468314581252405, -1.7605851628277343, -1.434566121655533, -1.0760953180734631, -0.6935038725030236, -0.29593491603422184, 0.10688304767829417, 0.5048858159112407, 0.8879398264509443, 1.2461180527435054, 1.5699777850426322, 1.8508322773852102, 2.0810081192107273, 2.254080313909364, 2.3650774223747435, 2.410649757866222, 2.3891944910988263, 2.300932625060012, 2.147934102899609, 1.934088786730473, 1.6650226504275178, 1.3479602193199822, 0.99153601273609, 0.605559446749014, 0.20073927730211003, -0.21162484883936364, -0.6199748713150054, -1.0128409030805294, -1.3791912415790097, -1.7087746772179437, -1.9924438845038224, -2.2224489648930508, -2.3926908710597834, -2.498925472562103, -2.5389104023053912, -2.5124885181231034, -2.421603778013862, -2.2702475033503697, -2.0643353239536593, -1.8115174864922476, -1.520927581706384, -1.202877021946383, -0.8685046938471308, -0.5293930400437041, -0.19716331321081626, 0.11693617087521234, 0.402434331291622, 0.650019597446573, 0.8518859875983726, 1.00202974196916, 1.0964847001874602, 1.1334865286184732, 1.1135582429003832, 1.0395121629801076, 0.9163663943385412, 0.7511770486898508, 0.5527905888656807, 0.33152378817665057, 0.09878171454646015, -0.13337323312437016, -0.35268600474090445, -0.5471903706197248, -0.7056891618445407, -0.8182148140961745, -0.8764520034895034, -0.8741051265886625, -0.8071950368389283, -0.6742717649522715, -0.47653285283747304, -0.2178403253504291, 0.095366905585806, 0.45426440026571446, 0.8479324112148682, 1.2637360336110606, 1.6877825613996986, 2.105439922115772, 2.50189720197399, 2.8627460842802437, 3.174560618171439, 3.425452192703167, 3.6055769626595704, 3.7075742709019246, 3.7269168139257354, 3.6621563410643168, 3.5150524653059523, 3.290576562911026, 2.996787588207203, 2.644581743421225, 2.2473231184354696, 1.8203674400349672, 1.3804957320558113, 0.9452787827306006, 0.5323966565850804, 0.15893991437528293, -0.15927941184396463, -0.4083787879171698, -0.5769907094495638, -0.6567575001949305, -0.6427132769150696, -0.533535182449699, -0.33165104520161737, -0.04319634223275148, 0.32218050157684297, 0.7516591059710338, 1.2297227893831277, 1.7387513501840195, 2.259708152664165, 2.772894267581365, 3.2587390627466593, 3.698594530096435, 4.075499894045921, 4.3748837368242715, 4.585173003700283, 4.6982817548392495, 4.709957288679152, 4.619967092895508, 4.4321167494109455, 4.154096152138423, 3.7971588806098646, 3.3756469805566978, 2.9063804003120755, 2.4079365962862216, 1.8998510536994486, 1.4017734118228722, 0.9326163302969864, 0.5097350422306739, 0.14817464000238245, -0.13998046282098126, -0.34612467039308736, -0.46549239778630924, -0.4973446715808536, -0.44497131836412324, -0.3155073313862615, -0.11957061698461312, 0.12926326346622632, 0.41512592210049465, 0.720630266990224, 1.027718116924092, 1.3185415871605233, 1.5763364275132996, 1.7862453549075163, 1.936051286243338, 2.0167841938666964, 2.023170930008417, 1.9539045626797504, 1.8117182169313093, 1.6032577374281993, 1.3387572454208543, 1.0315313889358575, 0.6973073040127382, 0.353427555863849, 0.017962187859910297, -0.29122689193028967, -0.5574228991183696, -0.7659454273824006, -0.9049503610957018, -0.9660966350675699, -0.9450439807669543, -0.8417536508187197, -0.6605735154903756, -0.4100994386254687, -0.10281596287696321, 0.24546947980339062, 0.6163739270382705, 0.9898332641052336, 1.3451009785779766, 1.6618025493461366, 1.920992971056267, 2.1061637400332236, 2.20414714802402, 2.20586992481328, 2.1069149826063787, 1.9078589551344578, 1.6143639837938168, 1.2370142710094771, 0.7909007085578449], 'positive_zeros': ['1.69408551811248665560918015891389', '2.90735454392952570004171269716521', '4.00524961612221556689217980578357', '5.42090826644910419518029140180259', '6.59295971425392925325302747647965', '7.85116942402493317781855190963521', '8.713883415628370643768806774572806', '9.419490761930170309008579285033787', '10.90468652471678823326020103225043'], 'prelabel': '2-200-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.90423969125585, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'trace_hash': 8737160699931485, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69408551811248665560918015891', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90735454392952570004171269717', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00524961612221556689217980578', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 62.47700509682438, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, 34, 0, 0, 0, 106, 0, -1031, 0, -1324, 0, 8828, 0, 0, 0, -24000, 0, -4876, 0, 3604, 0, 46646, 0, 0, 0, -109412, 0, -110902, 0, -247680, 0, -45016, 0, 0, 0, 360092, 0, 300152, 0, 104402, 0, -713622, 0, 0, 0, 156882, 0, -812307, 0, -816000, 0, -1066268, 0, 0, 0, -165784, 0, 832572, 0, 529070, 0, -109286, 0, 0, 0, -4174418, 0, 1585964, 0, 5176568, 0, 237976, 0, 0, 0, -140344, 0, -3742736, 0, -1465211, 0, -7861886, 0, 0, 0, -3770668, 0, 4300854, 0, 935768, 0, -8421120, 0, 0, 0, -1147792, 0, 1365044, 0], 'euler11': [1, 1324, 19487171], 'euler13': [1, -8828, 62748517], 'euler17': [1, 24000, 410338673], 'euler19': [1, 4876, 893871739], 'euler2': [1, 0, 0], 'euler23': [1, -46646, 3404825447], 'euler29': [1, 110902, 17249876309], 'euler3': [1, -34, 2187], 'euler31': [1, 247680, 27512614111], 'euler37': [1, -360092, 94931877133], 'euler41': [1, -104402, 194754273881], 'euler43': [1, 713622, 271818611107], 'euler47': [1, -156882, 506623120463], 'euler5': [1, 0, 0], 'euler53': [1, 1066268, 1174711139837], 'euler59': [1, -832572, 2488651484819], 'euler61': [1, -529070, 3142742836021], 'euler67': [1, 4174418, 6060711605323], 'euler7': [1, -106, 823543], 'euler71': [1, -5176568, 9095120158391], 'euler73': [1, -237976, 11047398519097], 'euler79': [1, 3742736, 19203908986159], 'euler83': [1, 7861886, 27136050989627], 'euler89': [1, -4300854, 44231334895529], 'euler97': [1, 1147792, 80798284478113], 'euler_factors': [[1, 0, 0], [1, -34, 2187], [1, 0, 0], [1, -106, 823543], [1, 1324, 19487171], [1, -8828, 62748517], [1, 24000, 410338673], [1, 4876, 893871739], [1, -46646, 3404825447], [1, 110902, 17249876309], [1, 247680, 27512614111], [1, -360092, 94931877133], [1, -104402, 194754273881], [1, 713622, 271818611107], [1, -156882, 506623120463], [1, 1066268, 1174711139837], [1, -832572, 2488651484819], [1, -529070, 3142742836021], [1, 4174418, 6060711605323], [1, -5176568, 9095120158391], [1, -237976, 11047398519097], [1, 3742736, 19203908986159], [1, 7861886, 27136050989627], [1, -4300854, 44231334895529], [1, 1147792, 80798284478113]], 'index': 28, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/200/8/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/200/8/a/f'], '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': '2-200-1.1-c7-0-28', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-200-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.90423969125585, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 8737160699931485, 'z1': {'__RealLiteral__': 0, 'data': '1.69408551811248665560918015891', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20278200
{'Lhash': '2147508523873244700358015781013', 'Lhash_array': ['2147508523873244700358015781013'], 'label': '2-200-1.1-c7-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/8/a/f'}
-
id: 24581327
{'Lhash': '2147508523873244700358015781013', 'Lhash_array': ['2147508523873244700358015781013'], 'label': '2-200-1.1-c7-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/8/a/f/1/1'}