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lfunc_lfunctions • Show schema
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{'Lhash': '1726702376982099586855306695115', 'a10': [-2.128194303265508, -0.6861406616345072], 'a2': [-0.25881904510252074, -0.9659258262890683], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, 0.5], 'a5': [1.2135782029036426, -1.8780915700351688], 'a6': [0.0, 0.0], 'a7': [0.5760282378465621, 2.582284157331138], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.2135782029036426, 1.8780915700351688]]], [7, [[1.0, 0], [-0.5760282378465621, -2.582284157331138]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '630.107', 'coefficient_field': 'CDF', 'conductor': 630, 'conductor_radical': 210, 'conjugate': '1429258816599934921034128321095', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.25881904510252074, 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'7.85187096439866552252295132106408', '9.156336013817355654427795672378646', '9.742958872700809732658912228048687', '10.74220607391459228645567819775030'], 'prelabel': '2-630-105.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.3622795624985555, 'root_number': '0.41928854879622773 + 0.9078530238140716*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.181139781249', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36212800015337185863234031829', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13262799847267522665959711624', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30162326566505535652095389031', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.030575327340666, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.2', 'conductor': 630, 'conductor_radical': 210, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/630/2/ce/b/107/2'], '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': '2-630-105.2-c1-0-9', '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': '2-630-105.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.18113978124927774, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36212800015337185863234031829', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1726702376982099586855306695115', 'Lhash_array': ['1726702376982099586855306695115'], 'label': '2-630-105.2-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/630/2/ce/b/107/2'}