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lfunc_lfunctions • Show schema
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{'Lhash': '1024447075655318555817599792986', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.8740320488976422, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.23606797749979, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.126696990427405, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '4900.1', 'coefficient_field': 'CDF', 'conductor': 4900, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.8740320488976422, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.4721359549995796, 0], [11.0, 0]], [[1.0, 0], [2.288245611270737, 0], [13.0, 0]], [[1.0, 0], [-1.7480640977952844, 0], [17.0, 0]], [[1.0, 0], [-0.33385053542218923, 0], [19.0, 0]], [[1.0, 0], [-5.47213595499958, 0], [23.0, 0]], [[1.0, 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-70e2-1.1-c1-0-21', 'leading_term': '2.2615472370803756816331509303454', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4900/2/a/bi/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.2615472370803755, 2.2527031715691317, 2.22611170203464, 2.181603761002051, 2.118926123032892, 2.037782141231683, 1.9378848251138994, 1.8190188061597414, 1.6811073550460813, 1.5242805294063015, 1.3489406909309065, 1.1558219656013116, 0.9460406605429142, 0.721134137570191, 0.48308613768412373, 0.2343370319945673, -0.022222062741731254, -0.2832719173342633, -0.5451047426583131, -0.8036803859309904, -1.0546984399383144, -1.2936850681423318, -1.5160928747452227, -1.717411675485135, -1.8932875645536507, 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'4.46672060887746376130340083552758', '5.43718188702745864673866994585314', '6.00091304033578855017683975695358', '7.04839199255493739819120014507606', '7.42303270964194617777325899026950', '8.457214888589752125887916277075847'], 'prelabel': '2-70e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.25513365088448, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.808146247452472961744912424162', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.03109353934158492908520839028', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89969950553206809920443604195', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.126696990427405, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 4900, 'conductor_radical': 70, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4900/2/a/bi/1/3'], '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': '2-70e2-1.1-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-70e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.25513365088448, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.808146247452472961744912424162', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1024447075655318555817599792986', 'Lhash_array': ['1024447075655318555817599792986'], 'factors': ['2-70e2-1.1-c1-0-21'], 'label': '2-70e2-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4900/2/a/bi/1/3'}