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{'Lhash': 'dirichlet_L_171.49', 'a10': [-0.5, 0.8660254037844386], 'a2': [1.0, 0.0], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, 0.0], 'a5': [-0.5, 0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.7941206614468482, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [19, [1]]], 'bad_primes': [3, 19], 'central_character': '171.49', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 171, 'conductor_radical': 57, 'conjugate': 'dirichlet_L_171.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^0', 0, 'a^0', 'a^1', 0, 'a^1', 'a^0', 0, 'a^1', 'a^1', 0, 'a^0', 'a^1', 0, 'a^0', 'a^2', 0, 0, 'a^1', 0, 'a^1', 'a^0', 0, 'a^2', 'a^0', 0, 'a^1', 'a^2', 0, 'a^2', 'a^0', 0, 'a^2', 'a^2', 0, 'a^0', 0, 0, 'a^1', 'a^1', 0, 'a^0', 'a^1', 0, 'a^0', 'a^2', 0, 'a^2', 'a^2', 0, 'a^0', 'a^1', 0, 'a^2', 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'195.854914295344647163417206007111', '196.81748646977821237414413827520', '197.63776572378719600221163869856', '198.07590227771838003498124439604', '199.24738502594366172035834543873', '199.62212414898990507967103041819'], 'prelabel': '1-171-171.49-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7941206614468482, 'root_angle': 0.289975510284499, 'root_number': '0.612967843766223541301885358512+0.790107854984739768646770667792*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.144987755142', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(3)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.61449245472667851020154512388+0.420897552532349993051733146476*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.28470707798', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.19877118433', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.47838322987', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7941206614468482, 'bad_primes': [3, 19], 'central_character': '171.49', 'conductor': 171, 'conductor_radical': 57, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/171/49'], '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': '1-171-171.49-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-171-171.49-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7941206614468482, 'root_angle': 0.1449877551422495, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.28470707798', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_171.49', 'Lhash_array': ['dirichlet_L_171.49'], 'label': '1-171-171.49-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/171/49'}