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lfunc_lfunctions • Show schema
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{'Lhash': '47281701913969524895311084020', 'a10': [7.5706377253761366, -3.7742070737882704e-61], 'a2': [-1.228894728748758, -2.128508107346423], 'a3': [0.0, 0.0], 'a4': [-2.020364508692967, 3.499373978865152], 'a5': [-1.5401314588362758, 2.6675859370396044], 'a6': [0.0, 0.0], 'a7': [1.3293335667991255, 2.302473277902841], 'a8': [5.015682264540414, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.244', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2387310956805072325308164825388', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.228894728748758, 2.128508107346423], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5401314588362758, -2.6675859370396044], [-2.5, -4.330127018922194]], [[1.0, 0], [-1.3293335667991255, 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'9.753424925186744719474131461227626'], 'prelabel': '2-3e6-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.6666666666666667, 'root_number': '-0.5000000000000002 - 0.8660254037844385*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.333333333333', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.03729868617224404585428071870', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.52510346913649049204251592041', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24729880946969635843351842243', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '9.4', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/c/d/244/1'], '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': '2-3e6-9.4-c1-0-0', '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': '2-3e6-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.33333333333333337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.03729868617224404585428071870', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '47281701913969524895311084020', 'Lhash_array': ['47281701913969524895311084020'], 'label': '2-3e6-9.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/c/d/244/1'}