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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_163.41', 'a10': [0.323733942058321, -0.9461481568757504], 'a2': [0.996992941167792, -0.07749242067193095], 'a3': [0.019391331771824373, -0.9998119704485015], 'a4': [0.987989849476809, -0.15451879280784048], 'a5': [0.39607976603915684, -0.918216106880274], 'a6': [-0.05814482891047583, -0.9983081582712682], 'a7': [0.8135520702629676, 0.5814920712880267], 'a8': [0.9730448705798238, -0.23061587074244017], 'a9': [-0.99924795250423, -0.03877537125681671], 'algebraic': True, 'analytic_conductor': 0.7569688176364694, 'analytic_normalization': 0, 'bad_lfactors': [[163, [1]]], 'bad_primes': [163], 'central_character': '163.41', 'coeff_info': ['x^81 - 1', '0.996992941167792 + 0.0774924206719309*I', '\\\\zeta_{81}'], 'conductor': 163, 'conductor_radical': 163, 'conjugate': 'dirichlet_L_163.4', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^80', 'a^61', 'a^79', 'a^66', 'a^60', 'a^8', 'a^78', 'a^41', 'a^65', 'a^34', 'a^59', 'a^30', 'a^7', 'a^46', 'a^77', 'a^24', 'a^40', 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'unitary', 'types': ['DIR'], 'values': [[1, '1.74541650499670775654519143502-0.726359445147720658250304360671*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.72674823216', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.3837293445', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.48925505642', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7569688176364694, 'bad_primes': [163], 'central_character': '163.41', 'conductor': 163, 'conductor_radical': 163, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/163/41'], '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': '1-163-163.41-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': '1-163-163.41-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7569688176364694, 'root_angle': -0.18238049232784836, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72674823216', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_163.41', 'Lhash_array': ['dirichlet_L_163.41'], 'factors': ['1-163-163.41-r0-0-0'], 'label': '1-163-163.41-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/163/41'}