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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_147.137', 'a10': [-0.9888308262251285, -0.14904226617617444], 'a2': [-0.9555728057861407, -0.2947551744109042], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8262387743159949, 0.5633200580636221], 'a5': [0.9888308262251285, -0.14904226617617444], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6234898018587335, -0.7818314824680298], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.797343944809878, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.137', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 147, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_147.44', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 0, 'a^4', 'a^41', 0, 0, 'a^27', 0, 'a^22', 'a^37', 0, 'a^30', 0, 0, 'a^8', 'a^31', 0, 'a^14', 'a^3', 0, 'a^18', 'a^11', 0, 'a^40', 'a^11', 0, 0, 'a^3', 0, 'a^28', 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'194.45331349325515651438459885300', '195.78379856175648660458560025177', '196.43927268907866832328452125155', '197.24281724811252488943667266842', '197.89280753072171727247052975036', '198.32021391707878099927120004831', '199.60593843213557936129634213195', '199.87184299572659099688385088551'], 'prelabel': '1-147-147.137-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': -0.2108843537414966, 'root_number': '0.243304086743308689627615364703-0.969950061278416807934283432993*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.210884353741', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.852631179957402389281336487946-0.263949577050247616860039420135*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.740549134086', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.11014056437', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.45336216316', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.797343944809878, 'bad_primes': [3, 7], 'central_character': '147.137', 'conductor': 147, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/147/137'], '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': '1-147-147.137-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': '1-147-147.137-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': -0.2108843537414966, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.740549134086', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_147.137', 'Lhash_array': ['dirichlet_L_147.137'], 'factors': ['1-147-147.137-r1-0-0'], 'label': '1-147-147.137-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/147/137'}
Lfunction data - 1-147-147.137-r1-0-0