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lfunc_lfunctions • Show schema
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{'Lhash': '1207820507131552006052439518487', 'a10': [0.0, 0.0], 'a2': [-0.8865593102913535, 0.0], 'a3': [9.0, 0.0], 'a4': [-31.21401258933572, 0.0], 'a5': [0.0, 0.0], 'a6': [-7.9790337926221815, 0.0], 'a7': [224.77356889705902, 0.0], 'a8': [56.04297140195041, 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], [0.8865593102913535, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-224.77356889705902, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-1065.6352280045846, 0], [371293.0, 0]], [[1.0, 0], [1347.7483179814437, 0], [1419857.0, 0]], [[1.0, 0], 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-0.768468316995079, -1.1177463710659081], 'positive_zeros': ['0.952802378600297660443546801840841', '1.56789029136306637902983738139266', '3.07712473589331097144553039460501', '4.29514817200029544740577060906226', '4.71145252455652317400083014598037', '5.86553830453701709960775299520035', '7.12625554045203538088999916812934', '8.129720827124642268803093278393868', '8.702560491630807047413330712704839', '9.023379865764342962666043178095568'], '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': '0.952802378600297660443546801841', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.56789029136306637902983738139', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07712473589331097144553039461', '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': 82, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/y/1/6'], '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-c5-0-82', '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': '0.952802378600297660443546801841', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1207820507131552006052439518487', 'Lhash_array': ['1207820507131552006052439518487'], 'label': '2-825-1.1-c5-0-82', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/y/1/6'}