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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_760.339', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.766044443118978, 0.6427876096865394], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.17364817766693036, -0.984807753012208], 'algebraic': True, 'analytic_conductor': 81.67334284391502, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [19, [1]]], 'bad_primes': [2, 5, 19], 'central_character': '760.339', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 760, 'conductor_radical': 190, 'conjugate': 'dirichlet_L_760.139', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^7', 0, 0, 0, 'a^24', 0, 'a^14', 0, 'a^12', 0, 'a^20', 0, 0, 0, 'a^13', 0, 0, 0, 'a^13', 0, 'a^26', 0, 0, 0, 'a^3', 0, 'a^23', 0, 'a^15', 0, 'a^1', 0, 0, 0, 'a^0', 0, 'a^9', 0, 'a^16', 0, 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'199.52783827971695468789152276958'], 'prelabel': '1-760-760.339-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 81.67334284391502, 'root_angle': 0.671489991167803, 'root_number': '-0.513064910531823770580629790917+0.858349810730433882897933464283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.335744995584', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.721081026452604178408552688129+0.211595929292917810344372921967*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.837446980587', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.45277150587', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.4864585665', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 81.67334284391502, 'bad_primes': [2, 5, 19], 'central_character': '760.339', 'conductor': 760, 'conductor_radical': 190, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/760/339'], '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': '1-760-760.339-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-760-760.339-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 81.67334284391502, 'root_angle': 0.3357449955839015, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.837446980587', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_760.339', 'Lhash_array': ['dirichlet_L_760.339'], 'label': '1-760-760.339-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/760/339'}