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lfunc_lfunctions • Show schema
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{'Lhash': '2640918816591311104727557051144', 'a10': [0.0, 0.0], 'a2': [5.032509117370184, 0.0], 'a3': [-8.475353951294315, 0.0], 'a4': [17.326148016414027, 0.0], 'a5': [0.0, 0.0], 'a6': [-42.652296032828055, 0.0], 'a7': [-3.818284947749528, 0.0], 'a8': [46.93392492254744, 0.0], 'a9': [44.83162459972016, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.075811752439773, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-17.0, 0]]]], 'bad_primes': [5, 17], 'central_character': '425.1', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.032509117370184, 0], [8.0, 0]], [[1.0, 0], [8.475353951294315, 0], [27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.818284947749528, 0], [343.0, 0]], [[1.0, 0], [52.37199678575484, 0], [1331.0, 0]], [[1.0, 0], [-8.060245264023633, 0], [2197.0, 0]], [[1.0, 0], [-17.0, 0]], [[1.0, 0], 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'3.60327630568298560647343117197106', '4.73122437496075906569633285956535', '5.39660698371921280187530146822368', '6.11544185169223641764041228683083', '6.85672979542525907518217516971436', '8.021778024239753841482710190722357', '10.11571479183306067922846111793907', '10.65582148305419295010878568267296'], 'prelabel': '2-425-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.00757543652013, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08331760827142492881258176376', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.60327630568298560647343117197', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73122437496075906569633285957', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.075811752439773, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 64, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/4/a/g/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': '2-425-1.1-c3-0-64', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-425-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.00757543652013, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08331760827142492881258176376', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2640918816591311104727557051144', 'Lhash_array': ['2640918816591311104727557051144'], 'label': '2-425-1.1-c3-0-64', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/4/a/g/1/3'}