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lfunc_lfunctions • Show schema
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{'Lhash': '1537982024213664002482319707128', 'a10': [0.0, 0.0], 'a2': [-0.8953935284393791, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.1982704292288786, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.8953935284393791, 0.0], 'a7': [5.089915275828827, 0.0], 'a8': [2.8637106445305736, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8953935284393791, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.089915275828827, 0], [7.0, 0]], [[1.0, 0], [-2.6430996204366655, 0], [11.0, 0]], [[1.0, 0], [-2.1329529680218404, 0], [13.0, 0]], [[1.0, 0], [-7.750006584442504, 0], [17.0, 0]], [[1.0, 0], [-3.086519062307829, 0], [19.0, 0]], 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'5.09668112670700773956308757739902', '5.89718786427866556198531737915014', '7.51011154255935939872250904603154', '7.75411406212177557789578191270561', '8.424448530129276865303725173228514', '9.109761148014022756293669365841354'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21325389183483508222637168978', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74311898049595940710649393089', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47280216121887770054096542325', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/o/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': '2-1875-1.1-c1-0-36', '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': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21325389183483508222637168978', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1537982024213664002482319707128', 'Lhash_array': ['1537982024213664002482319707128'], 'label': '2-1875-1.1-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/o/1/3'}