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lfunc_lfunctions • Show schema
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{'Lhash': '1543598665366803928589447771980', 'a10': [0.0, 0.0], 'a2': [-0.5253204540001407, 0.0], 'a3': [1.3668253400591948, 0.0], 'a4': [-1.7240384206090862, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.718021308178793, 0.0], 'a7': [-0.4267464462744363, 0.0], 'a8': [1.956313553828332, 0.0], 'a9': [-1.1317884897720663, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.69191546037511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 17], 'central_character': '7225.1', 'coefficient_field': 'CDF', 'conductor': 7225, 'conductor_radical': 85, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5253204540001407, 0], [2.0, 0]], [[1.0, 0], [-1.3668253400591948, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.4267464462744363, 0], [7.0, 0]], [[1.0, 0], [1.0507124005407553, 0], [11.0, 0]], [[1.0, 0], [-2.1948884796860777, 0], [13.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'5.36166543094593516188604721121764', '6.14547610142167226712065189134450', '7.11840717723777282837266243591563', '7.892249338199151823256002647565576'], 'prelabel': '2-85e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.595519433216869, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21768464045920263192847913006', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26501061381781201639981378227', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34726628257653850353601659115', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.69191546037511, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 7225, 'conductor_radical': 85, 'degree': 2, 'index': 289, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7225/2/a/bt/1/7'], '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': '2-85e2-1.1-c1-0-289', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-85e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.595519433216869, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21768464045920263192847913006', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1543598665366803928589447771980', 'Lhash_array': ['1543598665366803928589447771980'], 'label': '2-85e2-1.1-c1-0-289', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7225/2/a/bt/1/7'}