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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1089.335', 'a10': [-0.6548607339452851, -0.7557495743542583], 'a2': [-0.009519833939576644, -0.9999546853541729], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9998187455235258, 0.019038805103346677], 'a5': [0.7619494932706709, -0.647636448715302], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.0665905319833038, -0.9977803871845651], 'a8': [0.028556050793696254, 0.9995921928281892], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 117.02930310134664, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '1089.335', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 1089, 'conductor_radical': 33, 'conjugate': 'dirichlet_L_1089.1076', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^247', 0, 'a^164', 'a^293', 0, 'a^244', 'a^81', 0, 'a^210', 0, 0, 'a^32', 'a^161', 0, 'a^328', 'a^3', 0, 'a^96', 'a^127', 0, 0, 'a^185', 0, 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00280073461892', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.932297652495816232831276127554-0.507798871926272765689003339814*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.20367076618', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.43800301351', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.83058404075', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 117.02930310134664, 'bad_primes': [3, 11], 'central_character': '1089.335', 'conductor': 1089, 'conductor_radical': 33, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1089/335'], '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': '1-33e2-1089.335-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': '1-33e2-1089.335-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 117.02930310134664, 'root_angle': 0.0028007346189164377, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20367076618', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1089.335', 'Lhash_array': ['dirichlet_L_1089.335'], 'label': '1-33e2-1089.335-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1089/335'}