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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4725.2246', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.7193398003386512, -0.6946583704589973], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.03489949670250097, -0.9993908270190958], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6691306063588582, -0.7431448254773942], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 21.94280775050502, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '4725.2246', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 4725, 'conductor_radical': 105, 'conjugate': 'dirichlet_L_4725.2981', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^79', 0, 'a^68', 0, 0, 0, 'a^57', 0, 0, 'a^19', 0, 'a^11', 0, 0, 'a^46', 'a^42', 0, 'a^57', 0, 0, 'a^8', 'a^59', 0, 0, 'a^0', 0, 0, 'a^43', 0, 'a^77', 'a^35', 0, 'a^31', 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'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.09780744863', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.94280775050502, 'bad_primes': [3, 5, 7], 'central_character': '4725.2246', 'conductor': 4725, 'conductor_radical': 105, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4725/2246'], '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': '1-4725-4725.2246-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': '1-4725-4725.2246-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.94280775050502, 'root_angle': 0.39925925925925926, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.119153056175', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4725.2246', 'Lhash_array': ['dirichlet_L_4725.2246'], 'label': '1-4725-4725.2246-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4725/2246'}