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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_196.11', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9555728057861407, 0.2947551744109042], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.7330518718298263, -0.6801727377709194], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.8262387743159949, -0.5633200580636221], 'algebraic': True, 'analytic_conductor': 21.063125259746503, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '196.11', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 196, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_196.107', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^61', 0, 'a^26', 0, 0, 0, 'a^38', 0, 'a^25', 0, 'a^18', 0, 'a^45', 0, 'a^34', 0, 'a^35', 0, 0, 0, 'a^29', 0, 'a^10', 0, 'a^57', 0, 'a^6', 0, 'a^49', 0, 'a^2', 0, 0, 0, 'a^20', 0, 'a^37', 0, 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'191.06428334976102802029289086691', '191.40946955995340672839184609034', '192.39439779524624642209783384630', '193.12799885078180605225007120935', '193.64934952307952624033698408505', '194.61197005764441913977430503369', '195.07097192458171075104377060509', '195.782130104820049987872349619138', '196.43356596969512913314382350130', '197.26070118152602452513551590855', '198.454622010382920171465061041152', '198.82434123146163549119391049945', '199.48885281297640055592002932224'], 'prelabel': '1-14e2-196.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': 0.2448979591836735, 'root_number': '0.0320515775716551742335505253458+0.999486216200687867697489397011*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.244897959184', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.586993751800521671391368601084+0.0138084568630833711130080013768*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.91371576073', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.04692971327', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.67473158391', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.063125259746503, 'bad_primes': [2, 7], 'central_character': '196.11', 'conductor': 196, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/196/11'], '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': '1-14e2-196.11-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': '1-14e2-196.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': 0.2448979591836735, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.91371576073', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_196.11', 'Lhash_array': ['dirichlet_L_196.11'], 'factors': ['1-14e2-196.11-r1-0-0'], 'label': '1-14e2-196.11-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/196/11'}
Lfunction data - 1-14e2-196.11-r1-0-0