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lfunc_lfunctions • Show schema
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{'Lhash': '785989143719951550223285105821', 'a10': [0.0, 0.0], 'a2': [5.640178748749575, 0.0], 'a3': [9.0, 0.0], 'a4': [-0.18838368215367451, 0.0], 'a5': [0.0, 0.0], 'a6': [50.761608738746176, 0.0], 'a7': [-145.02127770455604, 0.0], 'a8': [-181.54823760068075, 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], [-5.640178748749575, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [145.02127770455604, 0], [16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [-69.90674337895739, 0], [371293.0, 0]], [[1.0, 0], [-500.49527769911316, 0], [1419857.0, 0]], [[1.0, 0], 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-1.078912440138994, -1.3973154192576887, -1.6713244524028839], 'positive_zeros': ['0.62003610740880892615285872975003', '2.36846396987066372542909394937025', '3.21085468562664707665454223681859', '3.94079489210083763665820737705278', '4.89775317683149519071407058269941', '5.97113568836800681539075944419466', '6.59681478688753380727396214218790', '7.76528065066203192817561623946894', '8.694128891843557596694585803001718', '9.509466977606516008424136571652369'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62003610740880892615285872975', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36846396987066372542909394937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21085468562664707665454223682', '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': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/h/1/3'], '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-c5-0-36', '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': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62003610740880892615285872975', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '785989143719951550223285105821', 'Lhash_array': ['785989143719951550223285105821'], 'label': '2-825-1.1-c5-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/h/1/3'}