Formats: - HTML - YAML - JSON - 2026-10-12T15:34:29.170603
  • lfunc_lfunctions • Show schema
    {'Lhash': '1890429685146062083198017055892', 'a10': 0, 'a2': 0, 'a3': 57, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -1174, 'a8': 0, 'a9': 1062, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 124.95401019364876, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '400.1', 'coefficient_field': '1.1.1.1', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, -57, 2187], [1], [1, 1174, 823543], [1, -7563, 19487171], [1, 5372, 62748517], [1, 24021, 410338673], [1, -51235, 893871739], [1, 57618, 3404825447], [1, -47040, 17249876309], [1, -192358, 27512614111], [1, 197066, 94931877133], [1, 237723, 194754273881], [1, -653012, 271818611107], [1, 826884, 506623120463], [1, 569022, 1174711139837], [1, 1501080, 2488651484819], [1, 2068918, 3142742836021], [1, 3444349, 6060711605323], [1, 4121052, 9095120158391], [1, -83653, 11047398519097], [1, 1454030, 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1]], [[[1, -6004335, 44231334895529], 1]], [[[1, 3411746, 80798284478113], 1]], [[[1, 3955578, 107213535210701], 1]], [[[1, -1750892, 122987386542487], 1]], [[[1, -8833941, 160578147647843], 1]], [[[1, 12216130, 182803912081669], 1]], [[[1, 20783607, 235260548044817], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 54, 'label': '2-20e2-1.1-c7-0-54', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/400/8/a/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [-2.1877788086230576e-60, 0.3755002280267043, 0.744797086679392, 1.1017958935324723, 1.4406175595482347, 1.7557019563366485, 2.041906029256555, 2.2945950069417407, 2.5097251452623905, 2.683916552957466, 2.814514777023096, 2.8996399780808706, 2.9382226988215625, 2.9300254213841157, 2.8756493210012826, 2.7765258518332208, 2.6348930445753034, 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'2.75839247292413006825940906518691', '3.45612518344335536132975703899761', '4.44503658309887931829091930761235', '6.09750803551509174001512348022400', '6.86161453262520336080479060495680', '7.84332414668275423454674602928195', '9.052704081688684217724689738600189', '9.346985481556482486584067294502829'], 'prelabel': '2-20e2-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.17828297162175, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c7-0', 'trace_hash': 960538344335056766, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49128607268099486985582980060', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.75839247292413006825940906519', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.45612518344335536132975703900', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 124.95401019364876, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, 57, 0, 0, 0, -1174, 0, 1062, 0, 7563, 0, -5372, 0, 0, 0, -24021, 0, 51235, 0, -66918, 0, -57618, 0, 0, 0, -64125, 0, 47040, 0, 192358, 0, 431091, 0, 0, 0, -197066, 0, -306204, 0, -237723, 0, 653012, 0, 0, 0, -826884, 0, 554733, 0, -1369197, 0, -569022, 0, 0, 0, 2920395, 0, -1501080, 0, -2068918, 0, -1246788, 0, 0, 0, -3444349, 0, -3284226, 0, -4121052, 0, 83653, 0, 0, 0, -8878962, 0, -1454030, 0, -5977719, 0, 1626567, 0, 0, 0, 2681280, 0, 6004335, 0, 6306728, 0, 10964406, 0, 0, 0, -3411746, 0, 8031906, 0], 'euler11': [1, -7563, 19487171], 'euler13': [1, 5372, 62748517], 'euler17': [1, 24021, 410338673], 'euler19': [1, -51235, 893871739], 'euler2': [1, 0, 0], 'euler23': [1, 57618, 3404825447], 'euler29': [1, -47040, 17249876309], 'euler3': [1, -57, 2187], 'euler31': [1, -192358, 27512614111], 'euler37': [1, 197066, 94931877133], 'euler41': [1, 237723, 194754273881], 'euler43': [1, -653012, 271818611107], 'euler47': [1, 826884, 506623120463], 'euler5': [1, 0, 0], 'euler53': [1, 569022, 1174711139837], 'euler59': [1, 1501080, 2488651484819], 'euler61': [1, 2068918, 3142742836021], 'euler67': [1, 3444349, 6060711605323], 'euler7': [1, 1174, 823543], 'euler71': [1, 4121052, 9095120158391], 'euler73': [1, -83653, 11047398519097], 'euler79': [1, 1454030, 19203908986159], 'euler83': [1, -1626567, 27136050989627], 'euler89': [1, -6004335, 44231334895529], 'euler97': [1, 3411746, 80798284478113], 'euler_factors': [[1, 0, 0], [1, -57, 2187], [1, 0, 0], [1, 1174, 823543], [1, -7563, 19487171], [1, 5372, 62748517], [1, 24021, 410338673], [1, -51235, 893871739], [1, 57618, 3404825447], [1, -47040, 17249876309], [1, -192358, 27512614111], [1, 197066, 94931877133], [1, 237723, 194754273881], [1, -653012, 271818611107], [1, 826884, 506623120463], [1, 569022, 1174711139837], [1, 1501080, 2488651484819], [1, 2068918, 3142742836021], [1, 3444349, 6060711605323], [1, 4121052, 9095120158391], [1, -83653, 11047398519097], [1, 1454030, 19203908986159], [1, -1626567, 27136050989627], [1, -6004335, 44231334895529], [1, 3411746, 80798284478113]], 'index': 54, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/8/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/400/8/a/q'], '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': '2-20e2-1.1-c7-0-54', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-20e2-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.17828297162175, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 960538344335056766, 'z1': {'__RealLiteral__': 0, 'data': '1.49128607268099486985582980060', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 20890423
      {'Lhash': '1890429685146062083198017055892', 'Lhash_array': ['1890429685146062083198017055892'], 'factors': ['2-20e2-1.1-c7-0-54'], 'label': '2-20e2-1.1-c7-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/8/a/q'}
    • id: 24592950
      {'Lhash': '1890429685146062083198017055892', 'Lhash_array': ['1890429685146062083198017055892'], 'factors': ['2-20e2-1.1-c7-0-54'], 'label': '2-20e2-1.1-c7-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/8/a/q/1/1'}