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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_287.222', 'a10': [-0.9135454576426009, 0.4067366430758002], 'a2': [0.7431448254773942, 0.6691306063588582], 'a3': [0.25881904510252074, 0.9659258262890683], 'a4': [0.10452846326765347, 0.9945218953682733], 'a5': [-0.4067366430758002, 0.9135454576426009], 'a6': [-0.4539904997395468, 0.8910065241883679], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5877852522924731, 0.8090169943749475], 'a9': [-0.8660254037844386, 0.5], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.222', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.234', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^25', 'a^28', 'a^38', 'a^39', 0, 'a^42', 'a^50', 'a^52', 'a^97', 'a^53', 'a^9', 0, 'a^63', 'a^56', 'a^7', 'a^64', 'a^71', 'a^66', 0, 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'4.23779038595', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.222', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/222'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-287-287.222-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-287-287.222-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.47513297568053203, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63882313763', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_287.222', 'Lhash_array': ['dirichlet_L_287.222'], 'label': '1-287-287.222-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/222'}