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lfunc_lfunctions • Show schema
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{'Lhash': '2156814586487558461780903572488', 'a10': [2.423000033901225, 0.0], 'a2': [2.423000033901225, 0.0], 'a3': [-1.0, 0.0], 'a4': [3.8709291642853367, 0.0], 'a5': [1.0, 0.0], 'a6': [-2.423000033901225, 0.0], 'a7': [0.0, 0.0], 'a8': [4.533261428490161, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.55905003420523, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '8085.1', 'coefficient_field': 'CDF', 'conductor': 8085, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.423000033901225, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [6.703393814070392, 0], [13.0, 0]], [[1.0, 0], [5.7418583285706735, 0], [17.0, 0]], [[1.0, 0], [-1.8396193290499656, 0], [19.0, 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[13.563871551213664, 0], [109.0, 0]], [[1.0, 0], [4.2382993207416595, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 261, 'label': '2-8085-1.1-c1-0-261', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/8085/2/a/ce/1/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.2716436629536082e-60, 0.42634463044994564, 0.8514065575155014, 1.2738239042743638, 1.692081560434716, 2.1044469779718136, 2.508919869020124, 2.9031989217826384, 3.2846675899003484, 3.6503999273554197, 3.9971864233250876, 4.321578900612384, 4.619952808478102, 4.888584670900418, 5.1237420310412105, 5.3217829387123095, 5.479261834339345, 5.593038567832724, 5.660387237452696, 5.679101532673593, 5.647593313003911, 5.5649812533637375, 5.431166540690774, 5.246892821957205, 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'4.72291734608468666208301481405517', '5.31163840756353874478137218879412', '5.79011498133138028759051142023450', '6.67691270465215480559769885620273', '7.14105698017991575232700330271206'], 'prelabel': '2-8085-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.034864655624588, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70142670709045762509885758487', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52461915802333247091974256599', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09683991314522185413939748337', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.55905003420523, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 8085, 'conductor_radical': 1155, 'degree': 2, 'index': 261, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8085/2/a/ce/1/8'], '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': '2-8085-1.1-c1-0-261', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8085-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.034864655624588, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70142670709045762509885758487', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2156814586487558461780903572488', 'Lhash_array': ['2156814586487558461780903572488'], 'label': '2-8085-1.1-c1-0-261', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8085/2/a/ce/1/8'}