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lfunc_lfunctions • Show schema
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{'Lhash': '1657389078140902493871311940773', 'a10': [0.0, 0.0], 'a2': [7.398546478150766, 0.0], 'a3': [-9.0, 0.0], 'a4': [22.7384899893571, 0.0], 'a5': [0.0, 0.0], 'a6': [-66.5869183033569, 0.0], 'a7': [-150.85173441848244, 0.0], 'a8': [-68.5217122716001, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-7.398546478150766, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [150.85173441848244, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-868.4262744793441, 0], [371293.0, 0]], [[1.0, 0], [-2317.8718533855185, 0], [1419857.0, 0]], [[1.0, 0], [2655.2436025013694, 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'positive_zeros': ['1.30744944848565061126168142289331', '3.01034552446950475565957711199511', '3.59557991808413660480953148370551', '4.54022993360139095321513018453746', '5.56706614436997597276697925830448', '6.31545483956867836398483689528561', '6.67020539443906456406104992186400', '8.155065759041971791732497605001556', '9.143988326429303449030078250055236'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30744944848565061126168142289', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01034552446950475565957711200', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59557991808413660480953148371', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 131, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/v/1/11'], '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': '2-825-1.1-c5-0-131', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30744944848565061126168142289', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1657389078140902493871311940773', 'Lhash_array': ['1657389078140902493871311940773'], 'label': '2-825-1.1-c5-0-131', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/v/1/11'}