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lfunc_lfunctions • Show schema
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{'Lhash': '1769884105383337202206170923404', 'a10': [0.0, -1.0], 'a2': [1.0, 0.0], 'a3': [1.0, 1.4142135623730951], 'a4': [1.0, 0.0], 'a5': [0.0, -1.0], 'a6': [1.0, 1.4142135623730951], 'a7': [0.585786437626905, 0.0], 'a8': [1.0, 0.0], 'a9': [-1.0, 2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.551472915212984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, -1.4142135623730951]]], [5, [[1.0, 0], [0, 1.0]]], [19, [[1.0, 0], [-4.242640687119285, 1.0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '570.341', 'coefficient_field': 'CDF', 'conductor': 570, 'conductor_radical': 570, 'conjugate': '2518342389872559191474849871927', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, -1.4142135623730951]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-0.585786437626905, 0], [7.0, 0]], [[1.0, 0], [0, -5.414213562373095], [-11.0, 0]], [[1.0, 0], [0, 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'3.51427677932967976688097641075422', '5.13496602190129717167897367181579', '6.15120139300849228076225475643594', '6.93632721454390896411354400546656', '7.82139138698658946244817395543935', '8.683228756300927528409459671252449', '9.676950236032948983858772177976919', '10.96389387510736316835769717218383'], 'prelabel': '2-570-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.133418129484463, 'root_angle': -0.26959480939477504, 'root_number': '0.6622661785325219 - 0.7492686492653552*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.134797404697', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39619237750898003875282140663', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94739214611423107813885716974', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51427677932967976688097641075', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.551472915212984, 'bad_primes': [2, 3, 5, 19], 'central_character': '57.56', 'conductor': 570, 'conductor_radical': 570, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/570/2/f/b/341/3'], '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': '2-570-57.56-c1-0-10', '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': '2-570-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.133418129484463, 'root_angle': -0.13479740469738752, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39619237750898003875282140663', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1769884105383337202206170923404', 'Lhash_array': ['1769884105383337202206170923404'], 'label': '2-570-57.56-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/570/2/f/b/341/3'}