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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_837.313', 'a10': [0.30901699437494745, -0.9510565162951535], 'a2': [0.9902680687415704, 0.13917310096006544], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9612616959383189, 0.27563735581699916], 'a5': [0.17364817766693036, -0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9975640502598242, 0.0697564737441253], 'a8': [0.9135454576426009, 0.4067366430758002], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 89.94814205310114, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.313', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.238', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 'a^70', 0, 'a^44', 'a^6', 0, 'a^72', 'a^59', 0, 'a^13', 'a^46', 0, 'a^8', 'a^51', 0, 'a^72', 'a^74', 0, 'a^61', 'a^31', 0, 'a^50', 'a^15', 0, 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'193.44381503322735384825371927043', '194.14308568757439822583257937531', '194.57036896551087119474001173890', '195.32109753991190377469813177858', '195.939087671550645122269613271952', '196.44638206211963283830230372147', '197.03239072543618357051463552471', '197.5304144124237605811201595234', '197.89443625444934480534786420573', '199.29560680342366605094196813226', '199.52026146274496887388867749408'], 'prelabel': '1-837-837.313-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': 0.9805471383123302, 'root_number': '-0.998133183732812753409113171795+0.0610749337404393608444118850850*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.490273569156', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.43259075112195126566086207840-0.159983846239884005911998391732*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.062922412747', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.49733331038', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.6691972747', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.94814205310114, 'bad_primes': [3, 31], 'central_character': '837.313', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/313'], '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': '1-837-837.313-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': '1-837-837.313-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': 0.4902735691561651, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.062922412747', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_837.313', 'Lhash_array': ['dirichlet_L_837.313'], 'label': '1-837-837.313-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/313'}