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lfunc_lfunctions • Show schema
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{'Lhash': '1307225291427764143754335482509', 'a10': [27.031852930309064, 0.0], 'a2': [-1.0812741172123626, 0.0], 'a3': [0.0, 0.0], 'a4': [-30.830846283446625, 0.0], 'a5': [-25.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-139.5079775171979, 0.0], 'a8': [67.9373678488394, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 79.38999080742543, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [25.0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '495.1', 'coefficient_field': 'CDF', 'conductor': 495, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0812741172123626, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [139.5079775171979, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [646.3312427219229, 0], [371293.0, 0]], [[1.0, 0], [-1378.3172140704316, 0], [1419857.0, 0]], [[1.0, 0], 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'positive_zeros': ['1.03121892672350698630691836067201', '2.94257371112952454596774972604975', '3.80870189604633262763517229754887', '4.91520514685328850814074401651229', '5.87178833177433471847123245909646', '7.17678415380728784425510634180926', '7.86838214065113783636151243362413', '8.970359519836336292430568783601874', '9.786933515172844498396175787467572'], 'prelabel': '2-495-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.910106105284349, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03121892672350698630691836067', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94257371112952454596774972605', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80870189604633262763517229755', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 79.38999080742543, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 495, 'conductor_radical': 165, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/495/6/a/c/1/2'], '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': '2-495-1.1-c5-0-43', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-495-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.910106105284349, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03121892672350698630691836067', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1307225291427764143754335482509', 'Lhash_array': ['1307225291427764143754335482509'], 'label': '2-495-1.1-c5-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/495/6/a/c/1/2'}