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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_179.139', 'a10': [-0.7834010269718525, -0.6215165572528594], 'a2': [-0.26165925596844064, 0.9651603150596496], 'a3': [-0.9499598007429908, -0.31237217701379416], 'a4': [-0.8630688675320841, -0.5050862598575473], 'a5': [-0.39487898637059127, 0.9187331419530561], 'a6': [0.5500550034448413, -0.8351284291564356], 'a7': [0.9603921063437793, -0.2786521165764922], 'a8': [0.7133191714243802, -0.700839325151233], 'a9': [0.8048472460553258, 0.5934820220673563], 'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'analytic_normalization': 0, 'bad_lfactors': [[179, [1]]], 'bad_primes': [179], 'central_character': '179.139', 'coeff_info': ['x^89 - 1', '0.997509025150764 + 0.0705389590423110*I', '\\\\zeta_{89}'], 'conductor': 179, 'conductor_radical': 179, 'conjugate': 'dirichlet_L_179.85', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^49', 'a^52', 'a^28', 'a^75', 'a^85', 'a^78', 'a^9', 'a^54', 'a^34', 'a^12', 'a^27', 'a^22', 'a^77', 'a^15', 'a^44', 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0, 'data': '-0.467561771324', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(89)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.412507581922771101522619417232+0.316237030638266831157500352567*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.87917375137', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.32410958964', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.10378463686', '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': '179.139', 'conductor': 179, 'conductor_radical': 179, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/179/139'], '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': '1-179-179.139-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': '1-179-179.139-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8312725052572271, 'root_angle': -0.4675617713236052, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.87917375137', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_179.139', 'Lhash_array': ['dirichlet_L_179.139'], 'label': '1-179-179.139-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/179/139'}