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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2000.691', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.6845471059286887, -0.7289686274214116], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8090169943749475, 0.5877852522924731], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.06279051952931337, 0.9980267284282716], 'algebraic': True, 'analytic_conductor': 214.92984958925004, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '2000.691', 'coeff_info': ['x^100 - 1', '0.998026728428272 + 0.0627905195293134*I', '\\\\zeta_{100}'], 'conductor': 2000, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_2000.411', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^163', 0, 0, 0, 'a^40', 0, 'a^126', 0, 'a^109', 0, 'a^101', 0, 0, 0, 'a^32', 0, 'a^87', 0, 'a^103', 0, 'a^4', 0, 0, 0, 'a^89', 0, 'a^33', 0, 'a^82', 0, 'a^72', 0, 0, 0, 'a^111', 0, 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'196.06194602439346241332828140875', '196.729391620329098644405820789852', '197.12602531858458252150457668719', '197.648747158695409798525491910680', '198.4428946469970303926413420053', '199.38462828049871236810873419437', '199.59849230849326379993884378080', '199.89957367190339281049660064864'], 'prelabel': '1-2000-2000.691-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 214.92984958925004, 'root_angle': 0.0785, 'root_number': '0.880808114923003601007048512329+0.473473404412312140072823657456*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0785', 'prec': 20}, 'spectral_label': 'r1-0', 'st_group': 'mu(100)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.940463020068096527117045328271+0.0161632569759550411606216089439*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.756857270733', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.55998484658', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.55316970986', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 214.92984958925004, 'bad_primes': [2, 5], 'central_character': '2000.691', 'conductor': 2000, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2000/691'], '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': '1-2000-2000.691-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': '1-2000-2000.691-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 214.92984958925004, 'root_angle': 0.0785, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.756857270733', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2000.691', 'Lhash_array': ['dirichlet_L_2000.691'], 'factors': ['1-2000-2000.691-r1-0-0'], 'label': '1-2000-2000.691-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2000/691'}
Lfunction data - 1-2000-2000.691-r1-0-0