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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_441.121', 'a10': [0.07473009358642425, -0.9972037971811801], 'a2': [0.6234898018587335, -0.7818314824680298], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.2225209339563144, -0.9749279121818236], 'a5': [0.8262387743159949, -0.5633200580636221], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9009688679024191, -0.4338837391175581], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.047995390047135, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.121', 'coeff_info': ['x^21 - 1', '0.955572805786141 + 0.294755174410904*I', '\\\\zeta_{21}'], 'conductor': 441, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_441.277', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 0, 'a^15', 'a^19', 0, 0, 'a^12', 0, 'a^16', 'a^11', 0, 'a^11', 0, 0, 'a^9', 'a^13', 0, 'a^14', 'a^13', 0, 'a^8', 'a^1', 0, 'a^17', 'a^8', 0, 0, 'a^13', 0, 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'0.965701107857152118771993150378-0.919325934964707051438625041102*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.664213625683', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.23228413377', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.77408361222', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2.047995390047135, 'bad_primes': [3, 7], 'central_character': '441.121', 'conductor': 441, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/441/121'], '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': '1-21e2-441.121-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': '1-21e2-441.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': -0.4467120181405896, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.664213625683', 'prec': 47}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_441.121', 'Lhash_array': ['dirichlet_L_441.121'], 'factors': ['1-21e2-441.121-r0-0-0'], 'label': '1-21e2-441.121-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/441/121'}