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lfunc_lfunctions • Show schema
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{'Lhash': '505426886114135383547131231696', 'a10': [1.629683664318002, -2.822694906863802], 'a2': [-0.5, 0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-3.259367328636004, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.1284163748308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.361', 'coefficient_field': 'CDF', 'conductor': 2646, 'conductor_radical': 42, 'conjugate': '678128505113432237427328794481', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.259367328636004, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.623475382979799, 0], [11.0, 0]], [[1.0, 0], [0.6136160175714132, -1.0628141187717646], [-6.5, -11.258330249197702]], 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True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.319251272144391, 'root_number': '0.5378113372268514492985494615554488372383348584544536651 - 0.8430652202233620006310820415920467405119042550305728707*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1596256360721955', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39871151090303408056122523740', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95029454977668915389949119229', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14307586919654715347231793409', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.1284163748308, 'bad_primes': [2, 3, 7], 'central_character': '63.4', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2646/2/h/r/361/1'], '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': '2-2646-63.4-c1-0-11', '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': '2-2646-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.1596256360721955, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39871151090303408056122523740', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '505426886114135383547131231696', 'Lhash_array': ['505426886114135383547131231696'], 'label': '2-2646-63.4-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/h/r/361/1'}