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lfunc_lfunctions • Show schema
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{'Lhash': '718328128769109480311543017899', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.6457513110645907, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.49537367319314, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '4320.1', 'coefficient_field': 'CDF', 'conductor': 4320, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.6457513110645907, 0], [7.0, 0]], [[1.0, 0], [3.6457513110645907, 0], [11.0, 0]], [[1.0, 0], [1.6457513110645905, 0], [13.0, 0]], [[1.0, 0], [0.6457513110645906, 0], [17.0, 0]], [[1.0, 0], [2.6457513110645907, 0], [19.0, 0]], [[1.0, 0], [6.291502622129181, 0], [23.0, 0]], [[1.0, 0], 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'GL2', 'index': 5, 'label': '2-4320-1.1-c1-0-5', 'leading_term': '1.144362068000066032094647205007', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4320/2/a/z/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.1443620680000661, 1.1353580473235578, 1.1083013993533286, 1.0630659077529254, 0.9994658332240326, 0.9172910924362477, 0.8163531946990714, 0.6965390314848843, 0.5578692792657608, 0.4005580858529254, 0.22507082252493466, 0.03217694189303391, -0.1770046724331283, -0.40097009077593365, -0.6378062862821305, -0.8851800872358582, -1.1403411936887127, -1.400139948229618, -1.6610601795311035, -1.9192670582036377, -2.170669511907846, -2.4109963387081836, -2.6358847365972546, -2.840979539424307, -3.0220410252762333, -3.1750587558645513, -3.2963685300748335, 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'6.06214530184113424180862402953770', '6.87555070510443013174835379715210', '7.63401025837079178462894069045948', '8.342509921805721901857345501756976'], 'prelabel': '2-4320-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.87327622994127, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56666097790651523729993303139', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27403980351110964475763902809', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70905632307146620253206277415', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.49537367319314, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 4320, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4320/2/a/z/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': '2-4320-1.1-c1-0-5', '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': '2-4320-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.87327622994127, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56666097790651523729993303139', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '718328128769109480311543017899', 'Lhash_array': ['718328128769109480311543017899'], 'label': '2-4320-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4320/2/a/z/1/1'}