-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1001939175017515154219020786088', 'a10': [7.807764064044151, 0.0], 'a2': [-1.5615528128088303, 0.0], 'a3': [3.0, 0.0], 'a4': [-5.56155281280883, 0.0], 'a5': [-5.0, 0.0], 'a6': [-4.68465843842649, 0.0], 'a7': [10.246211251235321, 0.0], 'a8': [21.177080940897135, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 107.08846666041927, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [5.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '1815.1', 'coefficient_field': 'CDF', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5615528128088303, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-10.246211251235321, 0], [343.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-40.87689437438234, 0], [2197.0, 0]], [[1.0, 0], [-98.70832376358854, 0], [4913.0, 0]], [[1.0, 0], [-39.64583811820573, 0], [6859.0, 0]], [[1.0, 0], [-61.693168768529816, 0], [12167.0, 0]], [[1.0, 0], [-149.09279563550024, 0], [24389.0, 0]], [[1.0, 0], [-54.73863375370596, 0], [29791.0, 0]], [[1.0, 0], [-44.89391503458899, 0], [50653.0, 0]], [[1.0, 0], [336.47913317255984, 0], [68921.0, 0]], [[1.0, 0], [-2.367451211705046, 0], [79507.0, 0]], [[1.0, 0], [333.29540756670735, 0], [103823.0, 0]], [[1.0, 0], [-640.0643513105307, 0], [148877.0, 0]], [[1.0, 0], [370.77267507411926, 0], [205379.0, 0]], [[1.0, 0], [-714.4052238624142, 0], [226981.0, 0]], [[1.0, 0], [404.9848450049413, 0], [300763.0, 0]], [[1.0, 0], [-939.2916762364115, 0], [357911.0, 0]], [[1.0, 0], [-362.57006314291215, 0], [389017.0, 0]], [[1.0, 0], [951.835160719502, 0], [493039.0, 0]], [[1.0, 0], [735.2214982565617, 0], [571787.0, 0]], [[1.0, 0], [-385.8787600395303, 0], [704969.0, 0]], [[1.0, 0], [966.3446038821794, 0], [912673.0, 0]], [[1.0, 0], [348.60037313302956, 0], [1030301.0, 0]], [[1.0, 0], [1536.3786452025927, 0], [1092727.0, 0]], [[1.0, 0], [-779.1799942755566, 0], [1225043.0, 0]], [[1.0, 0], [-1501.791561399474, 0], [1295029.0, 0]], [[1.0, 0], [-170.0, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 79, 'label': '2-1815-1.1-c3-0-79', 'leading_term': '2.0036154458663726474014260025926', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1815/4/a/n/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.0036154458663726, 1.9922544157390198, 1.95833412711273, 1.9023420029112854, 1.8250870950739488, 1.727694949908039, 1.6116001186241207, 1.478536033936871, 1.3305219240431108, 1.169846406611999, 0.9990474004653563, 0.8208880132651103, 0.6383281106292116, 0.4544913455087486, 0.27262752520634004, 0.0960703149609035, -0.07180958146904645, -0.22765546616579324, -0.3681794491017843, -0.49022036499072547, -0.5908039855852185, -0.6672045366953165, -0.7170063690564085, -0.7381644894285623, -0.7290625390334646, -0.6885667164357354, -0.6160740866294364, -0.5115537021758716, -0.37557898976395615, -0.20934992960138274, -0.014703677568841778, 0.20588754818737395, 0.4493322742254862, 0.711949963548656, 0.9895159737113618, 1.2773213156800907, 1.5702468698151268, 1.8628513147811516, 2.1494716117560437, 2.424334470861128, 2.681676821144492, 2.915872922290517, 3.1215654084752797, 3.2937972554383856, 3.428141423523904, 3.5208247639857935, 3.568842693851286, 3.5700611550123673, 3.523302482801485, 3.4284120224507406, 3.2863026500558346, 3.098974776381841, 2.869509932162607, 2.6020366441429355, 2.3016680002463596, 1.9744110548484848, 1.627049023019283, 1.2669980348281331, 0.9021410441433917, 0.5406422858392959, 0.19074642493534436, -0.13943278535594084, -0.44212894814674447, -0.7101387360859024, -0.9370307422240303, -1.1173412072436064, -1.2467504131182345, -1.322233776052444, -1.342182110103498, -1.3064861654953597, -1.2165813642066168, -1.0754496452959288, -0.8875764724569589, -0.6588623190686769, -0.39648929839409025, -0.10874501045616893, 0.19519290967157482, 0.5055066799010077, 0.8120165379403214, 1.104479862841474, 1.37290293459177, 1.6078562380813017, 1.8007836935140649, 1.9442959544392808, 2.032437979910498, 2.060921472619983, 2.027313483918718, 1.9311735123448148, 1.7741327464101124, 1.5599106955387338, 1.2942662750516252, 0.9848824118301321, 0.6411853579074738, 0.2741020737190262, -0.10423880012251724, -0.480854798044371, -0.8422968277945105, -1.1750645670817046, -1.4660375594120318, -1.7029085219428333, -1.8746048066632959, -1.9716838388990252, -1.9866887173813934, -1.9144510053893637, -1.7523290633033195, -1.5003720424561227, -1.1614018343400818, -0.7410077875159485, -0.24745179149160362, 0.3085157059583529, 0.9139251326202236, 1.5539360362719956, 2.2122546067875173, 2.871608291768725, 3.5142630153556915, 4.122566643845891, 4.6795009984968745, 5.169223961732956, 5.57758310486761, 5.8925828083671234, 6.104788050808527, 6.207649886447908, 6.197740065306222, 6.074885201566158, 5.842194271474753, 5.505976907253592, 5.07555381958405, 4.562964587826201, 3.9825818579954526, 3.350644536899382, 2.6847257251989904, 2.0031537619614244, 1.324406744495124, 0.6665021474859475, 0.04640362826824747, -0.5205332664352392, -1.0210559877364966, -1.44443198299858, -1.7827720941734713, -2.0312480729953117, -2.188195893019586, -2.255100889768229, -2.236465333552222, -2.1395636554354494, -1.9740950195309723, -1.7517470798604686, -1.4856884017651748, -1.1900100072530426, -0.8791386852767881, -0.5672459863599016, -0.26767712614609374, 0.007576676444811183, 0.24834059280187606, 0.44663410815525806, 0.5969487503521652, 0.696414088537231, 0.7448452014022363, 0.7446699012997389, 0.7007392250608114, 0.6200298402019263, 0.5112518403632826, 0.3843796988251437, 0.25012771467382716, 0.11939395115261003, 0.002698294455424579, -0.09035923876740527, -0.15159448978849124, -0.17466582498516534, -0.15541080843808996, -0.09207614418638195, 0.014571075239120922, 0.1612573712138488, 0.3423428843611235, 0.5500821893791419, 0.7749949117111871, 1.0063297277697711, 1.2326005837383551, 1.4421701214936324, 1.6238525543782782, 1.7675067447819182, 1.8645900995669846, 1.9086451573596852, 1.8956933683640462, 1.8245144724456948, 1.6967949119905952, 1.5171346624992956, 1.2929084671061835, 1.0339844241444271, 0.7523098772265897, 0.4613812621074785, 0.175620645661425, -0.09031315801606304, -0.32224706298058076, -0.5072154259128231, -0.6341457120828148, -0.6944735646888694, -0.682655155023105, -0.5965487333849515, -0.4376428112989903, -0.21111516087666446, 0.07428547267258861, 0.40653472835695625, 0.7707962909792322, 1.1500367206512538, 1.5257665293187792, 1.8788757767255935, 2.1905269853671103, 2.443064336410955, 2.620896137382148, 2.711307595009208, 2.7051630371157103, 2.597460861339918, 2.387710502035454, 2.0801083611097497, 1.6834986187789314, 1.2111147284661667, 0.6801077531290685, 0.1108780301000177, -0.4737635419927066, -1.04956950540934, -1.5919227133596965, -2.0769481692907896, -2.4826186262411594, -2.789801807735166, -2.983198666911563, -3.0521261250628102, -2.9911040880777664, -2.800214975508584, -2.485214150231358, -2.0573810522149074, -1.5331129903415512, -0.9332758557259188, -0.2823378916637893, 0.39267649967994744, 1.0633666669526853, 1.701215885985501, 2.2788736088017796, 2.7713995865432337, 3.1574105541959026, 3.4200739542212384, 3.5478997354984934, 3.5352903204134645, 3.382819983772991, 3.097227617461051, 2.6911205605790167, 2.1824011922133, 1.5934416209781248, 0.9500443765626395, 0.28023786941072026, -0.38703603413554816, -1.0232791367801701, -1.6017727914361184, -2.0988270963568523, -2.4948817455312047, -2.7754037954434843, -2.931537357557671, -2.9604723454786144], 'positive_zeros': ['0.790390644580710781391790215406570', '1.52701016907896674242472741761114', '3.07576153527720861045827526548693', '3.82699095849970679249022270876971', '4.75949872444302853093417180655628', '5.50761729835406809003913038289367', '6.80865577436549044515143411397724', '7.66648913910745085004576431270821', '8.329416802262843097606747714238893', '8.626895943751117484650205134829948'], 'prelabel': '2-1815-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.348355746707748, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.790390644580710781391790215407', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.52701016907896674242472741761', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07576153527720861045827526549', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 107.08846666041927, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'index': 79, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1815/4/a/n/1/1'], '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': '2-1815-1.1-c3-0-79', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1815-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.348355746707748, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.790390644580710781391790215407', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1001939175017515154219020786088', 'Lhash_array': ['1001939175017515154219020786088'], 'label': '2-1815-1.1-c3-0-79', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1815/4/a/n/1/1'}