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lfunc_lfunctions • Show schema
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{'Lhash': '2071009454816547701312713647377', 'a10': [2.0, -0.3360827212213939], 'a2': [0.0, -0.9069676505260347], 'a3': [0.0, 0.0], 'a4': [1.1774096808992847, 0.0], 'a5': [0.3705564592369621, 2.205150314721825], 'a6': [0.0, 0.0], 'a7': [0.0, -2.5963653283915815], 'a8': [0.0, -2.881807793043902], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.8272093728194765, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.3705564592369621, -2.205150314721825]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '855.514', 'coefficient_field': 'CDF', 'conductor': 855, 'conductor_radical': 285, 'conjugate': '1218524463669059170827046170405', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.9069676505260347], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3705564592369621, -2.205150314721825]], [[1.0, 0], [0, 2.5963653283915815], [-7.0, 0]], [[1.0, 0], 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'2.67431927381163926755411113721083', '4.32289491246926012575726101773403', '5.29521076006401585573314191413489', '6.02149632613426477450951275997234', '6.78761352205866707793526320129726', '7.969544884928370259141898104442189', '8.540503832087814769025826280018527', '9.281037133292102684033768338719369', '10.27103432802632473901376876809966'], 'prelabel': '2-855-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.612892912619933, 'root_angle': 0.4470058862091802, 'root_number': '0.16571788647109548 + 0.9861732008646114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.223502943105', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63373839324785596726698187873', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67431927381163926755411113721', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32289491246926012575726101773', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.8272093728194765, 'bad_primes': [3, 5, 19], 'central_character': '5.4', 'conductor': 855, 'conductor_radical': 285, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/855/2/c/d/514/3'], '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': '2-855-5.4-c1-0-30', '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': '2-855-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.612892912619933, 'root_angle': 0.2235029431045901, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63373839324785596726698187873', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2071009454816547701312713647377', 'Lhash_array': ['2071009454816547701312713647377'], 'label': '2-855-5.4-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/855/2/c/d/514/3'}