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lfunc_lfunctions • Show schema
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{'Lhash': '705964955009809521967694483583', 'a10': [-0.8660254037844386, 0.5], 'a2': [0.8660254037844386, -0.5], 'a3': [0, 0], 'a4': [0.5, -0.8660254037844386], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [1.1610878577258799, 2.3773672384891498], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.1610878577258799, -2.3773672384891498]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1890.1601', 'coefficient_field': 'CDF', 'conductor': 1890, 'conductor_radical': 210, 'conjugate': '1878147098858563348025313291557', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.1610878577258799, -2.3773672384891498]], [[1.0, 0], [0, 1.7179578655253125], [-11.0, 0]], 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'7.33079261812165848048098578070212', '7.934322138531798095755190797085844', '9.041854510872382438482663242673829'], 'prelabel': '2-1890-63.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': -0.3311078279474792, 'root_number': '0.5060426603731041957195856204605348087946826866030766851 - 0.8625084497455727074197711158514080853562669818107487465*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1655539139737396', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55690815346334921264118058431', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29994220733079599644228547936', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30033848755849739137172416998', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.091725982022, 'bad_primes': [2, 3, 5, 7], 'central_character': '63.47', 'conductor': 1890, 'conductor_radical': 210, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1890/2/t/c/1601/15'], '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': '2-1890-63.47-c1-0-5', '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': '2-1890-63.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': -0.1655539139737396, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55690815346334921264118058431', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '705964955009809521967694483583', 'Lhash_array': ['705964955009809521967694483583'], 'label': '2-1890-63.47-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1890/2/t/c/1601/15'}