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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1312.1123', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.8910065241883679, -0.4539904997395468], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5877852522924731, -0.8090169943749475], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 140.99398133054802, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [41, [1]]], 'bad_primes': [2, 41], 'central_character': '1312.1123', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 1312, 'conductor_radical': 82, 'conjugate': 'dirichlet_L_1312.715', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^25', 0, 'a^23', 0, 'a^26', 0, 'a^10', 0, 'a^47', 0, 'a^49', 0, 'a^8', 0, 'a^52', 0, 'a^21', 0, 'a^51', 0, 'a^54', 0, 'a^46', 0, 'a^35', 0, 'a^13', 0, 'a^52', 0, 'a^32', 0, 'a^49', 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140.99398133054802, 'root_angle': -0.8438806860907269, 'root_number': '-0.882114727819028537765733725372-0.471034613340422362146501195077*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.421940343045', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(40)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.560356605216368839371820495402-0.0458597734228391220847722071127*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.26697627741', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.97194926061', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.66952862344', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 140.99398133054802, 'bad_primes': [2, 41], 'central_character': '1312.1123', 'conductor': 1312, 'conductor_radical': 82, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1312/1123'], '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': '1-1312-1312.1123-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': '1-1312-1312.1123-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 140.99398133054802, 'root_angle': -0.42194034304536343, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26697627741', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1312.1123', 'Lhash_array': ['dirichlet_L_1312.1123'], 'label': '1-1312-1312.1123-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1312/1123'}