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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_31.23', 'a10': [-0.8090169943749475, -0.5877852522924731], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [0.8090169943749475, -0.5877852522924731], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [1.0, 0.0], 'a6': [-1.0, -1.4081532572346456e-30], 'a7': [0.30901699437494745, 0.9510565162951535], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'analytic_normalization': 0, 'bad_lfactors': [[31, [1]]], 'bad_primes': [31], 'central_character': '31.23', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 31, 'conductor_radical': 31, 'conjugate': 'dirichlet_L_31.27', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^9', 'a^2', 'a^0', 'a^5', 'a^2', 'a^8', 'a^8', 'a^6', 'a^7', 'a^1', 'a^9', 'a^8', 'a^9', 'a^4', 'a^3', 'a^4', 'a^6', 'a^2', 'a^1', 'a^3', 'a^3', 'a^7', 'a^0', 'a^5', 'a^7', 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'187.94172629075903417278401869029', '189.370307193835690087867232842915', '189.588846065180627979034074161479', '190.28637062392132901949110054058', '191.549757711614850929656983249790', '192.312176879199929200522271815', '192.740207555904602594651188074582', '193.95476543708006767397665040659', '194.91938803234128379631697353021', '196.57758601551862981906051179608', '196.78373610715809903250994931643', '197.768106719113052146563695100617', '198.78276255561829912035613871185', '199.681985516551894117957026610124'], 'prelabel': '1-31-31.23-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': -0.15836426880119428, 'root_number': '0.544476009580829984496950250466-0.838776415375954603938423790085*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.158364268801', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.05346071726558211144336669163-0.404620636219078106031724744418*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.63373215919', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.02314007771', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.21471622634', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'bad_primes': [31], 'central_character': '31.23', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/23'], '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': '1-31-31.23-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': '1-31-31.23-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': -0.15836426880119428, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63373215919', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_31.23', 'Lhash_array': ['dirichlet_L_31.23'], 'factors': ['1-31-31.23-r1-0-0'], 'label': '1-31-31.23-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/31/23'}