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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4033.1175', 'a10': [0.23061587074244017, -0.9730448705798238], 'a2': [0.6427876096865394, 0.766044443118978], 'a3': [0.8936326403234123, -0.44879918020046217], 'a4': [-0.17364817766693036, 0.984807753012208], 'a5': [-0.5971585917027862, -0.8021231927550437], 'a6': [0.918216106880274, 0.39607976603915684], 'a7': [0.39607976603915684, -0.918216106880274], 'a8': [-0.8660254037844386, 0.5], 'a9': [0.5971585917027862, -0.8021231927550437], 'algebraic': True, 'analytic_conductor': 433.4060416967227, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.1175', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.1040', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^15', 'a^100', 'a^30', 'a^70', 'a^7', 'a^88', 'a^45', 'a^92', 'a^85', 'a^23', 'a^22', 'a^25', 'a^103', 'a^62', 'a^60', 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'unitary', 'types': ['DIR'], 'values': [[1, '1.51508873790514198978778616824+0.384390561339123625247268234995*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.31229341623', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.8744060469', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.1624130488', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 433.4060416967227, 'bad_primes': [37, 109], 'central_character': '4033.1175', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/1175'], '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': '1-4033-4033.1175-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4033-4033.1175-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 433.4060416967227, 'root_angle': -0.42530233022454983, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31229341623', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4033.1175', 'Lhash_array': ['dirichlet_L_4033.1175'], 'label': '1-4033-4033.1175-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/1175'}