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lfunc_lfunctions • Show schema
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{'Lhash': '1719086495584536713702763679448', 'a10': [0.0, 0.0], 'a2': [-0.7330518718298263, 0.6801727377709194], 'a3': [1.9555728057861408, -0.2947551744109042], 'a4': [0.07473009358642425, -0.9972037971811801], 'a5': [0.0, 0.0], 'a6': [-1.2330518718298262, 1.546198141555358], 'a7': [0.6234898018587335, 0.7818314824680298], 'a8': [0.6234898018587335, 0.7818314824680298], 'a9': [2.7818115801021355, -0.8580752324745262], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7330518718298263, -0.6801727377709194]]], [7, [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]]], [17, [[1.0, 0], [-0.8262387743159949, 0.5633200580636221]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1971', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1954370889001834133254355881034', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'2.23748452126035914842930989058018', '3.05841681744816473345643522185573', '3.70606342822045487934250674999741', '4.41558787284496910939108645033472', '5.51001513911989508036411613555306', '7.32497587525810460632487716127816', '7.58955916229801554869883680724607', '8.105517268152289020637854959101652', '8.536747489391904120441557406183306'], 'prelabel': '2-3332-3332.1971-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.20408163265306123, 'root_number': '0.80141362186795665978698328953346 - 0.59811053049121596205926635490525*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10204081632653061', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35612012906003454602534806278', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23748452126035914842930989058', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05841681744816473345643522186', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '3332.1971', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/cc/b/1971/1'], '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': '2-3332-3332.1971-c0-0-1', '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': '2-3332-3332.1971-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.10204081632653061, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35612012906003454602534806278', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1719086495584536713702763679448', 'Lhash_array': ['1719086495584536713702763679448'], 'label': '2-3332-3332.1971-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/cc/b/1971/1'}