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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_431.122', 'a10': [-0.2950876062343146, 0.9554702008157565], 'a2': [0.5209403404879303, 0.8535930890373464], 'a3': [0.7447721827437819, 0.6673188112222395], 'a4': [-0.45724232330463854, 0.889342148882519], 'a5': [0.6618597221319832, 0.749627713081216], 'a6': [-0.18163685097943644, 0.9833656768294661], 'a7': [0.979148666789775, 0.20314499335156208], 'a8': [-0.9973322836635516, 0.07299531466090753], 'a9': [0.10937120837787438, 0.9940009752399459], 'algebraic': True, 'analytic_conductor': 2.0015555852841613, 'analytic_normalization': 0, 'bad_lfactors': [[431, [1]]], 'bad_primes': [431], 'central_character': '431.122', 'coeff_info': ['x^215 - 1', '0.999573005862893 + 0.0292199580804198*I', '\\\\zeta_{215}'], 'conductor': 431, 'conductor_radical': 431, 'conjugate': 'dirichlet_L_431.53', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^35', 'a^25', 'a^70', 'a^29', 'a^60', 'a^7', 'a^105', 'a^50', 'a^64', 'a^131', 'a^95', 'a^94', 'a^42', 'a^54', 'a^140', 'a^2', 'a^85', 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2.0015555852841613, 'root_angle': 0.8530871213092537, 'root_number': '-0.895367567950831310282859999393+0.445327877256537215611291719647*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.426543560655', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(215)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.13786293357920170917264431293+1.39736918498310817884452508577*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.3317244533', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.97491293765', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.36767315661', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.0015555852841613, 'bad_primes': [431], 'central_character': '431.122', 'conductor': 431, 'conductor_radical': 431, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/431/122'], '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': '1-431-431.122-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': '1-431-431.122-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0015555852841613, 'root_angle': 0.42654356065462684, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.3317244533', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_431.122', 'Lhash_array': ['dirichlet_L_431.122'], 'label': '1-431-431.122-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/431/122'}
Lfunction data - 1-431-431.122-r0-0-0