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lfunc_lfunctions • Show schema
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{'Lhash': '3791082860209497353818338744255', 'a10': [0.0, -3.4641016151377544], 'a2': [1.0, 0.0], 'a3': [-1.5, -0.8660254037844386], 'a4': [1.0, 0.0], 'a5': [0.0, -3.4641016151377544], 'a6': [-1.5, -0.8660254037844386], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.5, 0.8660254037844386]]], [19, [[1.0, 0], [4.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.113', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '2083634513329348070736626838973', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.5, 0.8660254037844386]], [[1.0, 0], [0, 3.4641016151377544], [-5.0, 0]], [[1.0, 0], [-1.0, 0], [7.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-11.0, 0]], [[1.0, 0], [0, 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'11.43843241121292595298890662751771', '12.61561510748546313828220353693467', '13.93865406482178534730604431979094'], 'prelabel': '2-114-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.2967401358131697, 'root_number': '0.5960395606792696 + 0.8029550685469663*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.148370067907', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.99063705687272663952860070260', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.36832954540764876987581180628', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.99522944989182225075727631750', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '57.56', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/b/c/113/1'], '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': '2-114-57.56-c1-0-6', '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': '2-114-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.14837006790658486, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.99063705687272663952860070260', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3791082860209497353818338744255', 'Lhash_array': ['3791082860209497353818338744255'], 'label': '2-114-57.56-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/b/c/113/1'}