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lfunc_lfunctions • Show schema
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{'Lhash': '1716742791676747138271559396326', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 3.0], 'a4': [0, 0], 'a5': [0, 2.8284271247461903], 'a6': [0, 0], 'a7': [-14.142135623730951, 0], 'a8': [0, 0], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.656733442204406, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -3.0]]]], 'bad_primes': [2, 3], 'central_character': '384.193', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '323082016134947704601522709547', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.0]], [[1.0, 0], [0, -2.8284271247461903], [-125.0, 0]], [[1.0, 0], [14.142135623730951, 0], [343.0, 0]], [[1.0, 0], [0, -20.0], [-1331.0, 0]], [[1.0, 0], [0, 39.59797974644666], [-2197.0, 0]], [[1.0, 0], [34.0, 0], [4913.0, 0]], [[1.0, 0], [0, 52.0], [-6859.0, 0]], [[1.0, 0], [62.22539674441618, 0], [12167.0, 0]], [[1.0, 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'8.505622132753173292373583581896959', '9.125580676017375478451013815639673', '10.25839028405504696884475520190622', '11.21274302896840530641706007652283'], 'prelabel': '2-384-8.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': 0.5, 'root_number': '0.e-55 + 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35427127267376563876911138928', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83489369265530440013514325255', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08496260060414511643724764386', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.656733442204406, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/4/d/d/193/4'], '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': '2-384-8.5-c3-0-17', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-384-8.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35427127267376563876911138928', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1716742791676747138271559396326', 'Lhash_array': ['1716742791676747138271559396326'], 'label': '2-384-8.5-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/4/d/d/193/4'}