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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_196.191', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.36534102436639504, -0.9308737486442042], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9888308262251285, -0.14904226617617444], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7330518718298263, 0.6801727377709194], 'algebraic': True, 'analytic_conductor': 21.063125259746503, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '196.191', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 196, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_196.39', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^29', 0, 'a^22', 0, 0, 0, 'a^16', 0, 'a^47', 0, 'a^12', 0, 'a^51', 0, 'a^32', 0, 'a^49', 0, 0, 0, 'a^31', 0, 'a^2', 0, 'a^45', 0, 'a^18', 0, 'a^35', 0, 'a^34', 0, 0, 0, 'a^4', 0, 'a^41', 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'190.61613337713962350582445791559', '191.088601888088834349978479315088', '191.894122983154912333509695535572', '192.79150793246132382403194303081', '193.5769843143310918334750947667', '194.39331437304737790026071774711', '195.20337445983139308380302368545', '195.65358816988446113737016806572', '195.96172680376890754341619393445', '197.04803897037402179061754721121', '197.900081049783691015926263663092', '198.44044129367991426917695240034', '199.52436230856251271393308693086'], 'prelabel': '1-14e2-196.191-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': -0.14965986394557826, 'root_number': '0.891491135545289584096248464203-0.453038138840616943309900146760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0748299319728', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.827300150336454951731217978375-0.181184072159306181455289609206*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.78805029536', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.22057845429', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.89581752767', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.063125259746503, 'bad_primes': [2, 7], 'central_character': '196.191', 'conductor': 196, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/196/191'], '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': '1-14e2-196.191-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': '1-14e2-196.191-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': -0.07482993197278913, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78805029536', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_196.191', 'Lhash_array': ['dirichlet_L_196.191'], 'label': '1-14e2-196.191-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/196/191'}