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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_2624.125', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.3826834323650898, 0.9238795325112867], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.996917333733128, 0.07845909572784494], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.15643446504023087, 0.9876883405951378], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 12.185804769804268, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [41, [1]]], 'bad_primes': [2, 41], 'central_character': '2624.125', 'coeff_info': ['x^80 - 1', '0.996917333733128 + 0.0784590957278449*I', '\\\\zeta_{80}'], 'conductor': 2624, 'conductor_radical': 82, 'conjugate': 'dirichlet_L_2624.21', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^105', 0, 'a^39', 0, 'a^98', 0, 'a^50', 0, 'a^151', 0, 'a^77', 0, 'a^64', 0, 'a^56', 0, 'a^93', 0, 'a^43', 0, 'a^82', 0, 'a^78', 0, 'a^75', 0, 'a^49', 0, 'a^56', 0, 'a^96', 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0, 'data': '-0.192555050879', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(80)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.735827772446649430929391089468+0.164683814115637489885671509412*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.221696922057', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.4698580042', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.99025923013', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.185804769804268, 'bad_primes': [2, 41], 'central_character': '2624.125', 'conductor': 2624, 'conductor_radical': 82, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2624/125'], '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': '1-2624-2624.125-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': '1-2624-2624.125-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.185804769804268, 'root_angle': -0.192555050879481, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.221696922057', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2624.125', 'Lhash_array': ['dirichlet_L_2624.125'], 'label': '1-2624-2624.125-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2624/125'}