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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_55.47', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9510565162951535, 0.30901699437494745], 'a3': [0.5877852522924731, 0.8090169943749475], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.30901699437494745, 0.9510565162951535], 'a7': [0.5877852522924731, -0.8090169943749475], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [-0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 5.910570863704376, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '55.47', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 55, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_55.48', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^3', 'a^2', 0, 'a^4', 'a^17', 'a^3', 'a^6', 0, 0, 'a^5', 'a^11', 'a^18', 0, 'a^4', 'a^9', 'a^7', 'a^18', 0, 'a^0', 0, 'a^15', 'a^6', 0, 'a^12', 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'197.88263101413424340713282538099', '198.65706077065735912912178449179', '199.3423544044170932768590966143'], 'prelabel': '1-55-55.47-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.910570863704376, 'root_angle': 0.18432035848521997, 'root_number': '0.401063357659432515877325320030+0.916050316927483036117140637859*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.184320358485', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.01050937875845902252203600390+0.874052159200032193072854381541*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.54593204901', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.12435399561', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.08425539169', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 5.910570863704376, 'bad_primes': [5, 11], 'central_character': '55.47', 'conductor': 55, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/55/47'], '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': '1-55-55.47-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': '1-55-55.47-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.910570863704376, 'root_angle': 0.18432035848521997, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.54593204901', 'prec': 44}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_55.47', 'Lhash_array': ['dirichlet_L_55.47'], 'factors': ['1-55-55.47-r1-0-0'], 'label': '1-55-55.47-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/55/47'}