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lfunc_lfunctions • Show schema
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{'Lhash': '1483770373975483926382772361119', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.36602540378443865, -0.36602540378443865], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.660888362042632, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 13], 'central_character': '3328.1025', 'coefficient_field': 'CDF', 'conductor': 3328, 'conductor_radical': 26, 'conjugate': '1227379961768272714783478105348', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.36602540378443865, 0.36602540378443865], [0, 1.0]], [[1.0, 0], [0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], 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-2.1462646554596487, -1.6294167241585644], 'positive_zeros': ['1.17048844035441946714802455680569', '2.45292755576224510062924665726816', '3.33281082882583115050541068870584', '4.14765001669613203585249659149744', '5.17613042039331570527716168283052', '5.69182023675411015620143268965706', '6.81268683773220191033946512110648', '7.42963887633839981628674184318608', '8.029462050504810331328612279167123', '8.720337304884890578986721770788483'], 'prelabel': '2-3328-13.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2887545778939573, 'root_angle': 0.07718776385096696, 'root_number': '0.88468193107510709723517360596756 + 0.46619511025880511198384571672197*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07718776385096694', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17048844035441946714802455681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45292755576224510062924665727', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33281082882583115050541068871', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.660888362042632, 'bad_primes': [2, 13], 'central_character': '13.11', 'conductor': 3328, 'conductor_radical': 26, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3328/1/bl/b/1025/1'], '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': '2-3328-13.11-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3328-13.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2887545778939573, 'root_angle': 0.07718776385096696, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17048844035441946714802455681', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1483770373975483926382772361119', 'Lhash_array': ['1483770373975483926382772361119'], 'factors': ['2-3328-13.11-c0-0-0'], 'label': '2-3328-13.11-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3328/1/bl/b/1025/1'}