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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1380.83', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7557495743542583, 0.6548607339452851], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 6.408693057290354, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [23, [1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.83', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 1380, 'conductor_radical': 690, 'conjugate': 'dirichlet_L_1380.1247', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^61', 0, 0, 0, 'a^26', 0, 'a^27', 0, 0, 0, 'a^41', 0, 'a^58', 0, 0, 0, 0, 0, 0, 0, 0, 0, 'a^8', 0, 'a^54', 0, 0, 0, 0, 0, 'a^35', 0, 0, 0, 'a^42', 0, 'a^23', 0, 0, 0, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0681482614366', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.903406925445750331306347379454+0.0186746080155543992013514055225*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.579636115862', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.09794835708', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.97916369762', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.408693057290354, 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.83', 'conductor': 1380, 'conductor_radical': 690, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1380/83'], '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': '1-1380-1380.83-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': '1-1380-1380.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.408693057290354, 'root_angle': -0.06814826143663137, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.579636115862', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1380.83', 'Lhash_array': ['dirichlet_L_1380.83'], 'label': '1-1380-1380.83-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1380/83'}