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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_91.72', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [-0.8660254037844386, -0.5], 'a3': [1.0, 0.0], 'a4': [0.5, 0.8660254037844386], 'a5': [0.8660254037844386, -0.5], 'a6': [-0.8660254037844386, -0.5], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 9.779308156310877, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '91.72', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 91, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_91.67', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^0', 'a^2', 'a^11', 'a^7', 0, 'a^9', 'a^0', 'a^6', 'a^9', 'a^2', 0, 0, 'a^11', 'a^4', 'a^2', 'a^7', 'a^3', 'a^1', 0, 'a^4', 'a^10', 'a^9', 'a^10', 0, 'a^0', 0, 'a^8', 'a^6', 'a^7', 'a^11', 'a^9', 'a^9', 0, 'a^2', 'a^1', 'a^10', 0, 'a^8', 'a^11', 0, 'a^10', 'a^11', 'a^11', 'a^5', 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'185.66054056752638687205834298838', '186.792410043813756007758836116121', '187.60169631758144361063947489477', '188.71743274954910339666227293658', '189.34026320771141013541655794465', '190.02510793411412195305532398387', '190.85823149173168375762919919706', '191.65747447888382315100031075919', '192.36544808724616890068747306380', '192.684174071590838128314128362469', '193.69363701926146099244558838831', '194.39403785501308087036893780806', '195.82435486212561499497707044392', '196.60354995869420031446631127185', '197.35157364055322930819445589628', '197.69985417814532694464846578440', '198.71104768943979831409181363447', '199.489981930865174729886261973056'], 'prelabel': '1-91-91.72-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.779308156310877, 'root_angle': -0.30495114409978785, 'root_number': '0.575130819255122667847389389328-0.818061452913490736323913136790*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15247557205', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.17923088035389332704149493171-0.378667347254204819975612201763*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.20840109054', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.4935830224', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.89501226271', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.779308156310877, 'bad_primes': [7, 13], 'central_character': '91.72', 'conductor': 91, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/91/72'], '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': '1-91-91.72-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': '1-91-91.72-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.779308156310877, 'root_angle': -0.15247557204989393, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20840109054', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_91.72', 'Lhash_array': ['dirichlet_L_91.72'], 'label': '1-91-91.72-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/91/72'}
Lfunction data - 1-91-91.72-r1-0-0