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lfunc_lfunctions • Show schema
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{'Lhash': '470346839632836903952906962561', 'a10': [234.0, 405.2998889711173], 'a2': [3.0, -5.196152422706632], 'a3': [4.5, 7.794228634059948], 'a4': [-2.0, -3.4641016151377544], 'a5': [-39.0, 67.54998149518622], 'a6': [54.0, 0], 'a7': [0, 0], 'a8': [168.0, 0], 'a9': [-40.5, 70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.57642151250816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-4.5, -7.794228634059948]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.79', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'conjugate': '2770746932861826591989487510633', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.0, 5.196152422706632], [-16.0, -27.712812921102035]], [[1.0, 0], [-4.5, -7.794228634059948]], [[1.0, 0], [39.0, -67.54998149518622], [-1562.5, -2706.329386826371]], [[1.0, 0], [0, 0]], [[1.0, 0], [222.0, 384.51527928029077], [-80525.5, 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'root_angle': -0.6263207605587745, 'root_number': '-0.3865135727591552881869185769990697126707082293252108640 - 0.9222837188593069656715137745867251124838836430784361633*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.31316038027938725', 'prec': 67}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37103823368060179196664231475', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12192349625375215475327525950', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39714423639403199621530903871', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.57642151250816, 'bad_primes': [3, 7], 'central_character': '7.2', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/e/j/79/1'], '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': '2-147-7.2-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-147-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': -0.31316038027938725, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37103823368060179196664231475', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '470346839632836903952906962561', 'Lhash_array': ['470346839632836903952906962561'], 'label': '2-147-7.2-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/e/j/79/1'}