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lfunc_lfunctions • Show schema
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{'Lhash': '1156848744782751585177742166243', 'a10': [39.17026055475932, 0.0], 'a2': [2.0, 0.0], 'a3': [-0.37774353250818543, 0.0], 'a4': [4.0, 0.0], 'a5': [19.58513027737966, 0.0], 'a6': [-0.7554870650163709, 0.0], 'a7': [0.0, 0.0], 'a8': [8.0, 0.0], 'a9': [-26.857309823648237, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.9903051529394, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [7, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [23.0, 0]]]], 'bad_primes': [2, 7, 23], 'central_character': '2254.1', 'coefficient_field': 'CDF', 'conductor': 2254, 'conductor_radical': 322, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [0.37774353250818543, 0], [27.0, 0]], [[1.0, 0], [-19.58513027737966, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-30.953598895633828, 0], [1331.0, 0]], [[1.0, 0], [7.348423702731228, 0], [2197.0, 0]], [[1.0, 0], [20.059915364965736, 0], [4913.0, 0]], [[1.0, 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['0.912592748013112673546226205764452', '2.24686786223198547529609610174959', '2.48797384759666895081631193325509', '3.90717859352312963950814228210856', '4.74177587563572110042045655387070', '5.81034144608028675382151889110689', '6.06720177405040410695779153424476', '6.69309584413035364297088472894365', '7.86387699259925951215615808202545', '8.989546863204920698047909432959187'], 'prelabel': '2-2254-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.532142262083806, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.912592748013112673546226205764', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.24686786223198547529609610175', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.48797384759666895081631193326', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.9903051529394, 'bad_primes': [2, 7, 23], 'central_character': '1.1', 'conductor': 2254, 'conductor_radical': 322, 'degree': 2, 'index': 105, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2254/4/a/x/1/5'], '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': '2-2254-1.1-c3-0-105', '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': '2-2254-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.532142262083806, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.912592748013112673546226205764', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1156848744782751585177742166243', 'Lhash_array': ['1156848744782751585177742166243'], 'factors': ['2-2254-1.1-c3-0-105'], 'label': '2-2254-1.1-c3-0-105', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2254/4/a/x/1/5'}