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lfunc_lfunctions • Show schema
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{'Lhash': '2484903112791426310486369421997', 'a10': [1.2262733111085773, 0.590542102350959], 'a2': [0.25875637789378664, 0.3244702349960709], 'a3': [-2.072939230106338, 0.9982749195496317], 'a4': [0.4067157976149354, -1.7819383388797891], 'a5': [2.9547828346923968, -1.4229484172760198], 'a6': [-0.8602967445132036, -0.41429707680030387], 'a7': [2.3915254272613526, -1.1316386926764235], 'a8': [1.4312538574797435, -0.6892555308326124], 'a9': [1.4300548311358334, -1.7932320389272705], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-2.3915254272613526, 1.1316386926764235]]], [13, [[1.0, 0], [0.6234898018587335, 0.7818314824680298]]]], 'bad_primes': [7, 13], 'central_character': '637.547', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '1008610934412003375669992226387', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'z1': {'__RealLiteral__': 0, 'data': '1.96024291894315455876234568330', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51151077142178764436661513729', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.52623160188865338216542570259', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '49.8', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/w/a/547/17'], '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': '2-637-49.8-c1-0-42', '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': '2-637-49.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.1960518989161109, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96024291894315455876234568330', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2484903112791426310486369421997', 'Lhash_array': ['2484903112791426310486369421997'], 'label': '2-637-49.8-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/w/a/547/17'}