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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2667.1049', 'a10': [-0.9009688679024191, -0.4338837391175581], 'a2': [0.9009688679024191, -0.4338837391175581], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [-0.6234898018587335, -0.7818314824680298], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.2225209339563144, -0.9749279121818236], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 286.6089544272649, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [127, [1]]], 'bad_primes': [3, 7, 127], 'central_character': '2667.1049', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 2667, 'conductor_radical': 2667, 'conjugate': 'dirichlet_L_2667.839', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^39', 0, 'a^36', 'a^27', 0, 0, 'a^33', 0, 'a^24', 'a^31', 0, 'a^41', 0, 0, 'a^30', 'a^34', 0, 'a^21', 'a^21', 0, 'a^28', 'a^32', 0, 'a^12', 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'-0.664956693372992935862391670326+0.746881915658998569499278221814*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.365775008648', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.13508685737459108109533480413-1.10042773538055435366028339029*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.360963439555', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.893261734849', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '2.03197783792', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 286.6089544272649, 'bad_primes': [3, 7, 127], 'central_character': '2667.1049', 'conductor': 2667, 'conductor_radical': 2667, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2667/1049'], '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': '1-2667-2667.1049-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': '1-2667-2667.1049-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 286.6089544272649, 'root_angle': 0.3657750086475992, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.360963439555', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2667.1049', 'Lhash_array': ['dirichlet_L_2667.1049'], 'factors': ['1-2667-2667.1049-r1-0-0'], 'label': '1-2667-2667.1049-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2667/1049'}
Lfunction data - 1-2667-2667.1049-r1-0-0