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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_179.31', 'a10': [-0.8630688675320841, 0.5050862598575473], 'a2': [-0.5791852582395334, 0.815195949841512], 'a3': [-0.7376084637406223, -0.6752286680956305], 'a4': [-0.32908887327600994, -0.9442989534495557], 'a5': [0.9116210382765418, 0.41103172939762184], 'a6': [0.9776556239997144, -0.2102129417084711], 'a7': [-0.9255590665712211, -0.37860324125370337], 'a8': [0.9603921063437793, 0.2786521165764922], 'a9': [0.08813249156360176, 0.9961087610952891], 'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'analytic_normalization': 0, 'bad_lfactors': [[179, [1]]], 'bad_primes': [179], 'central_character': '179.31', 'coeff_info': ['x^89 - 1', '0.997509025150764 + 0.0705389590423110*I', '\\\\zeta_{89}'], 'conductor': 179, 'conductor_radical': 179, 'conjugate': 'dirichlet_L_179.52', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^31', 'a^55', 'a^62', 'a^6', 'a^86', 'a^50', 'a^4', 'a^21', 'a^37', 'a^20', 'a^28', 'a^63', 'a^81', 'a^61', 'a^35', 'a^73', 'a^52', 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0, 'data': '-0.00998582281713', 'prec': 57}, 'spectral_label': 'r0-0', 'st_group': 'mu(89)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.689244595967410660366411081697+0.0601992338639876472621310624044*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.906805195094', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.56074188384', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.96304447628', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'bad_primes': [179], 'central_character': '179.31', 'conductor': 179, 'conductor_radical': 179, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/179/31'], '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': '1-179-179.31-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': '1-179-179.31-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8312725052572271, 'root_angle': -0.009985822817131907, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.906805195094', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_179.31', 'Lhash_array': ['dirichlet_L_179.31'], 'label': '1-179-179.31-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/179/31'}