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lfunc_lfunctions • Show schema
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{'Lhash': '1230095294924909568505132016855', 'a10': [0.0, 0.0], 'a2': [-10.046030464104044, 0.0], 'a3': [-9.0, 0.0], 'a4': [68.92272808570651, 0.0], 'a5': [0.0, 0.0], 'a6': [90.41427417693639, 0.0], 'a7': [29.05242273620507, 0.0], 'a8': [-370.92685116683754, 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], [10.046030464104044, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-29.05242273620507, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [1023.5129932558245, 0], [371293.0, 0]], [[1.0, 0], [-1509.6860487378192, 0], [1419857.0, 0]], [[1.0, 0], 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['0.970374087862571651213944914098340', '1.93389099870098101383101916391504', '3.12245203968317520079696524476507', '4.76957189283136033481948035706557', '5.78965211775070673157921535766187', '6.82436348068163103312596629268914', '7.60735179604719338816571931994452', '8.050742227031890438222820570905044', '9.368062234102189195438552596940338'], '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': '0.970374087862571651213944914098', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.93389099870098101383101916392', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12245203968317520079696524477', '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': 86, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/v/1/2'], '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-c5-0-86', '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': '0.970374087862571651213944914098', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1230095294924909568505132016855', 'Lhash_array': ['1230095294924909568505132016855'], 'label': '2-825-1.1-c5-0-86', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/v/1/2'}