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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_2209.31', 'a10': [-0.9858275205874054, 0.16776203280983681], 'a2': [-0.8110619300975102, -0.584960293991397], 'a3': [-0.8467794156288633, 0.531944189992936], 'a4': [0.3156429089069967, 0.9488780501501388], 'a5': [0.7014330435578273, -0.7127353543954468], 'a6': [0.997956776972071, 0.06389265447229593], 'a7': [0.9999324331840109, 0.01162450285834163], 'a8': [0.29905003625810744, -0.9542374315724701], 'a9': [0.4340707574655184, -0.9008787806987748], 'algebraic': True, 'analytic_conductor': 237.39001887132667, 'analytic_normalization': 0, 'bad_lfactors': [[47, [1]]], 'bad_primes': [47], 'central_character': '2209.31', 'coeff_info': ['x^2162 - 1', '0.999995777029417 + 0.00290618707798714*I', '\\\\zeta_{2162}'], 'conductor': 2209, 'conductor_radical': 47, 'conjugate': 'dirichlet_L_2209.1924', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1296', 'a^888', 'a^430', 'a^1889', 'a^22', 'a^4', 'a^1726', 'a^1776', 'a^1023', 'a^1677', 'a^1318', 'a^79', 'a^1300', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 237.39001887132667, 'root_angle': -0.42446414864093535, 'root_number': '-0.889472957537538816120267689107-0.456987809256903121338522697098*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.424464148641', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(2162)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.673221662177776481348434926288-0.246388809209763914376815316377*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.276802667354', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.16617647212', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.72746465071', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 237.39001887132667, 'bad_primes': [47], 'central_character': '2209.31', 'conductor': 2209, 'conductor_radical': 47, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2209/31'], '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': '1-47e2-2209.31-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': '1-47e2-2209.31-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 237.39001887132667, 'root_angle': -0.42446414864093535, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.276802667354', 'prec': 47}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_2209.31', 'Lhash_array': ['dirichlet_L_2209.31'], 'factors': ['1-47e2-2209.31-r1-0-0'], 'label': '1-47e2-2209.31-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2209/31'}