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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_847.24', 'a10': [0.23575893550942723, 0.9718115683235417], 'a2': [0.5326077245747999, 0.8463622225284244], 'a3': [0.9781476007338057, -0.20791169081775934], 'a4': [-0.4326580234465083, 0.9015581150138691], 'a5': [0.9480716290349995, 0.3180568914815749], 'a6': [0.6969375686552934, 0.7171318047589635], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9934817353485502, 0.11399140989054063], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.24', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.600', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^53', 'a^319', 'a^106', 'a^17', 'a^42', 0, 'a^159', 'a^308', 'a^70', 0, 'a^95', 'a^18', 0, 'a^6', 'a^212', 'a^232', 'a^31', 'a^164', 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'data': '0.237941548095', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.83000192640241129109063023141+1.03063600631619770897113143095*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.55340252042', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.6718518909', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.46452474943', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.24', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/24'], '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': '1-847-847.24-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': '1-847-847.24-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.23794154809526843, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55340252042', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.24', 'Lhash_array': ['dirichlet_L_847.24'], 'label': '1-847-847.24-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/24'}