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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_153.5', 'a10': [0.9238795325112867, -0.3826834323650898], 'a2': [0.25881904510252074, 0.9659258262890683], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8660254037844386, 0.5], 'a5': [-0.1305261922200516, -0.9914448613738104], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.1305261922200516, -0.9914448613738104], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.7105290128734958, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '153.5', 'coeff_info': ['x^48 - 1', '0.991444861373810 + 0.130526192220052*I', '\\\\zeta_{48}'], 'conductor': 153, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_153.92', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 0, 'a^20', 'a^35', 0, 'a^37', 'a^30', 0, 'a^45', 'a^1', 0, 'a^44', 'a^47', 0, 'a^40', 0, 0, 'a^18', 'a^7', 0, 'a^11', 'a^41', 0, 'a^22', 'a^6', 0, 'a^9', 'a^43', 0, 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'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7105290128734958, 'bad_primes': [3, 17], 'central_character': '153.5', 'conductor': 153, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/153/5'], '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': '1-153-153.5-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': '1-153-153.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7105290128734958, 'root_angle': 0.02242405787013343, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06008812936', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_153.5', 'Lhash_array': ['dirichlet_L_153.5'], 'label': '1-153-153.5-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/153/5'}