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lfunc_lfunctions • Show schema
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{'Lhash': '1187474011658850749096975371124', 'a10': [180.68322619056013, 0.0], 'a2': [-7.227329047622406, 0.0], 'a3': [-15.920927411457358, 0.0], 'a4': [20.234285162606582, 0.0], 'a5': [-25.0, 0.0], 'a6': [115.06578114591355, 0.0], 'a7': [0.0, 0.0], 'a8': [85.03469261033536, 0.0], 'a9': [10.475929640894288, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.294035854180265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [25.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': 'CDF', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'euler_factors': [[[1.0, 0], [7.227329047622406, 0], [32.0, 0]], [[1.0, 0], [15.920927411457358, 0], [243.0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [387.0664557684646, 0], [161051.0, 0]], [[1.0, 0], [920.8226636195164, 0], [371293.0, 0]], [[1.0, 0], [-678.472919788612, 0], [1419857.0, 0]], [[1.0, 0], 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['0.936751823763627328388798543442007', '2.77393816521697384147327131406225', '4.76439962533707293214923117742628', '5.55496298657086659619928415561176', '7.23301421550558077010934328792100', '7.63242626740884179345743680724838', '8.888711862044523054936002580983339', '9.927446489189857789710214167546589', '10.54922614687735474133115350162118'], 'prelabel': '2-245-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.268495501647925, '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': '0.936751823763627328388798543442', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.77393816521697384147327131406', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.76439962533707293214923117743', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.294035854180265, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/6/a/i/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': '2-245-1.1-c5-0-24', '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': '2-245-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.268495501647925, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.936751823763627328388798543442', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1187474011658850749096975371124', 'Lhash_array': ['1187474011658850749096975371124'], 'label': '2-245-1.1-c5-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/6/a/i/1/2'}