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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1441.1009', 'a10': [-0.970941817426052, -0.23931566428755777], 'a2': [-0.9988322268323266, 0.048313379525507065], 'a3': [0.024163745236132288, 0.9997080140801929], 'a4': [0.9953316347176486, -0.09651392091451512], 'a5': [0.9582458291091662, 0.2859456783986893], 'a6': [-0.07243480016176236, -0.9973731496914912], 'a7': [-0.9261746489577765, -0.37709484168832047], 'a8': [-0.9895063994510511, 0.14448904956922132], 'a9': [-0.9988322268323266, 0.048313379525507065], 'algebraic': True, 'analytic_conductor': 6.691975866344493, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.1009', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.964', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^64', 'a^32', 'a^128', 'a^6', 'a^96', 'a^73', 'a^62', 'a^64', 'a^70', 0, 'a^30', 'a^99', 'a^7', 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[1, 'a^89']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1441-1441.1009-r0-0-0', 'leading_term': '0.579596774978108729575592617199-0.267801968914219354006252801225*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1441/1009', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6384749925559783, 0.07829568032210772, -0.9448738206782041, -2.1022972964674778, -2.469634073948266, -1.4166345472220383, 0.6214792048320092, 2.260483224230888, 2.290802339699545, 0.9171640751894917, -0.1703102655057771, 0.7254223588693312, 3.4904263668313753, 5.92005455906572, 5.592005750981051, 2.2803451025203136, -1.5731251684003846, -3.0729647255974553, -1.6798806234110402, 0.338877813018527, 0.41534016443792454, -1.5100430567984584, -3.0005122428682633, -1.983825201722511, 0.7988548742495125, 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'3.0324078072', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.691975866344493, 'bad_primes': [11, 131], 'central_character': '1441.1009', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/1009'], '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': '1-1441-1441.1009-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': '1-1441-1441.1009-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': -0.13777355101701122, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.343204666591', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1441.1009', 'Lhash_array': ['dirichlet_L_1441.1009'], 'label': '1-1441-1441.1009-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/1009'}