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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1805.144', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.45153335831088937, 0.892254238618394], 'a3': [0.7541066097768963, 0.6567520240477344], 'a4': [-0.59223525266498, -0.8057651056609781], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9264940672148018, 0.3763093719478355], 'a7': [0.4016954246529695, 0.9157733266550574], 'a8': [0.9863613034027223, -0.1645945902807339], 'a9': [0.13735355781840816, 0.9905220846375032], 'algebraic': True, 'analytic_conductor': 8.382384759716732, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '1805.144', 'coeff_info': ['x^114 - 1', '0.998481516433316 + 0.0550877603558654*I', '\\\\zeta_{114}'], 'conductor': 1805, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_1805.539', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 'a^13', 'a^74', 0, 'a^50', 'a^21', 'a^111', 'a^26', 0, 'a^12', 'a^87', 'a^89', 'a^58', 0, 'a^34', 'a^97', 'a^63', 0, 0, 'a^34', 'a^49', 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'2.22372586075', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.14864175549', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.382384759716732, 'bad_primes': [5, 19], 'central_character': '1805.144', 'conductor': 1805, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1805/144'], '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': '1-1805-1805.144-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': '1-1805-1805.144-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.382384759716732, 'root_angle': 0.3010156971375808, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05384281468', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1805.144', 'Lhash_array': ['dirichlet_L_1805.144'], 'label': '1-1805-1805.144-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1805/144'}