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lfunc_lfunctions • Show schema
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{'Lhash': '826133011806862787611641321768', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.4062206595281426, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.3379041817654933, 0.0], 'a8': [0.0, 0.0], 'a9': [8.602339181396335, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.989435883192783, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 13], 'central_character': '3380.1', 'coefficient_field': 'CDF', 'conductor': 3380, 'conductor_radical': 130, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.4062206595281426, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.3379041817654933, 0], [7.0, 0]], [[1.0, 0], [-6.165648776590792, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.0751951644271376, 0], [17.0, 0]], [[1.0, 0], [-0.09026807516670605, 0], [19.0, 0]], [[1.0, 0], [-4.819541550124347, 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'5.71885275653110581456076763227723', '6.37869982901242399345846756467842', '6.89886167555757737212228960119002', '7.42742584525047477961042060176160', '8.797975555858564994521396781085552'], 'prelabel': '2-3380-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.195135790640393, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65170403552692261229580577739', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.49609864538553886379069701153', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38911233934669049877242905290', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.989435883192783, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 3380, 'conductor_radical': 130, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3380/2/a/r/1/1'], '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': '2-3380-1.1-c1-0-7', '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': '2-3380-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.195135790640393, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65170403552692261229580577739', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '826133011806862787611641321768', 'Lhash_array': ['826133011806862787611641321768'], 'label': '2-3380-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3380/2/a/r/1/1'}