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{'Lhash': 'dirichlet_L_980.919', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.07473009358642425, -0.9972037971811801], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9888308262251285, -0.14904226617617444], 'algebraic': True, 'analytic_conductor': 105.31562629873252, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '980.919', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 980, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_980.739', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^32', 0, 0, 0, 0, 0, 'a^22', 0, 'a^41', 0, 'a^27', 0, 0, 0, 'a^23', 0, 'a^49', 0, 0, 0, 'a^40', 0, 0, 0, 'a^54', 0, 'a^30', 0, 'a^35', 0, 'a^31', 0, 0, 0, 'a^37', 0, 'a^59', 0, 'a^18', 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'192.28383278776599018183752770174', '192.66733863683121559806655496721', '193.63154776644868520233895716899', '194.02017775415988777788104807634', '195.01329268248800815182873197089', '195.16648181474209916500624500883', '195.90232970021138535411594962672', '196.37476160433059360328195147810', '197.13317668847975248029321966509', '197.63232776599511862962522049878', '198.10080917775541770688399494719', '198.979707133741305064753928817155', '199.741534669894205688011923317292'], 'prelabel': '1-980-980.919-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 105.31562629873252, 'root_angle': 0.8299319727891157, 'root_number': '-0.860633218180016254116052688579+0.509225356561423146717766600103*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.414965986395', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.845928525832529819705872177673-0.439642587921324816155454045064*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.180890843477', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.15591029875', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.24122101313', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 105.31562629873252, 'bad_primes': [2, 5, 7], 'central_character': '980.919', 'conductor': 980, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/980/919'], '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': '1-980-980.919-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': '1-980-980.919-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 105.31562629873252, 'root_angle': 0.41496598639455784, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.180890843477', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_980.919', 'Lhash_array': ['dirichlet_L_980.919'], 'label': '1-980-980.919-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/980/919'}