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lfunc_lfunctions • Show schema
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{'Lhash': '977659849376646958671814358841', 'a10': [-3.061424304747892, -1.3271423457045886], 'a2': [-1.0551599679415151, -1.0551599679415151], 'a3': [0.0, 0.0], 'a4': [0.0, 0.22672511589267844], 'a5': [2.0795740853465206, -0.821809968031042], 'a6': [0.0, 0.0], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [-1.8710886698661753, 1.8710886698661753], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.545862991011, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0795740853465206, 0.821809968031042]]], [7, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [3, 5, 7], 'central_character': '945.323', 'coefficient_field': 'CDF', 'conductor': 945, 'conductor_radical': 105, 'conjugate': '2012203866749467756980476867847', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0551599679415151, 1.0551599679415151], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'0.0282067812776', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77123763377749977407263642941', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64008186631101626895721755085', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51337746287465761832465600851', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.545862991011, 'bad_primes': [3, 5, 7], 'central_character': '15.8', 'conductor': 945, 'conductor_radical': 105, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/945/2/m/a/323/7'], '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': '2-945-15.8-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': '2-945-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.746973423790445, 'root_angle': 0.02820678127764311, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77123763377749977407263642941', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '977659849376646958671814358841', 'Lhash_array': ['977659849376646958671814358841'], 'label': '2-945-15.8-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/945/2/m/a/323/7'}