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lfunc_lfunctions • Show schema
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{'Lhash': '2486378730943598369625372628431', 'a10': [2.4892885718100786, 0.0], 'a2': [2.4892885718100786, 0.0], 'a3': [0.0, 0.0], 'a4': [4.196557593744262, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.1965575937442616, 0.0], 'a8': [5.467865715430237, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.1', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '2486378730943598369625372628431', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.4892885718100786, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.1965575937442616, 0], [7.0, 0]], [[1.0, 0], [-1.1965575937442616, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [6.175134737364419, 0], [17.0, 0]], 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[[1.0, 0], [-8.393115187488524, 0], [109.0, 0]], [[1.0, 0], [7.957154287240315, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-585-1.1-c1-0-14', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/585/2/a/n/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [4.042476810427294, 4.050409982581838, 4.070713138454124, 4.093514555421713, 4.104205103314049, 4.08560775894739, 4.020213219954183, 3.8922164281350673, 3.689271175074728, 3.4039557500521984, 3.0349317030716314, 2.58773411268946, 2.075095737421304, 1.5166980771853222, 0.9382644394645899, 0.369961166625576, -0.15585296304204554, -0.6074013995739176, -0.9565704194043975, -1.1819976437649948, -1.271814944366679, -1.2256740388043104, -1.055712340805505, -0.7861983386709173, 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'6.01428354362857075115516384799116', '6.64833433437964352001168506391944', '7.64317386362695216035855708317823', '9.106966165072204819750037331353761', '9.949136806755564029889054996514375', '11.28947496160790155345587643500982'], 'prelabel': '2-585-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96140697641443756608236313913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.15847293670893930892454280812', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08345915782330000823802932237', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/a/n/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': '2-585-1.1-c1-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-585-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96140697641443756608236313913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2486378730943598369625372628431', 'Lhash_array': ['2486378730943598369625372628431'], 'label': '2-585-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/n/1/3'}