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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_260.7', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8660254037844386, -0.5], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, -0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 27.940880446602506, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '260.7', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 260, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_260.223', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^11', 0, 0, 0, 'a^10', 0, 'a^10', 0, 'a^11', 0, 0, 0, 0, 0, 'a^1', 0, 'a^7', 0, 'a^9', 0, 'a^17', 0, 0, 0, 'a^9', 0, 'a^2', 0, 'a^9', 0, 'a^10', 0, 0, 0, 'a^8', 0, 0, 0, 'a^11', 0, 'a^13', 0, 0, 0, 'a^6', 0, 'a^8', 0, 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'184.60617076867641048732925165562', '185.1425376468191946614954054367', '185.82808097459532834160391493126', '186.38657432032402519104458879655', '187.34875149632180401725113379072', '187.84260581979376886837706479290', '188.72457280286194224830946213715', '189.63760804057939611200947555370', '190.07733612717564459715826951412', '190.77329755734616624697237018649', '191.70781331343715059348782705490', '192.02979231789806198863302447447', '192.53731500354418034883310596292', '193.60338684885710426435860554481', '194.55269372945004738358374672534', '194.939851415740193820579477702452', '195.724694993655887505545050236673', '196.49148403952654164675933844232', '197.03277322081523454465902972117', '197.8376801017171487050371818309', '198.31607803787868271073397410296', '198.86275155243931126091260054322'], 'prelabel': '1-260-260.7-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': -0.4822492393122839, 'root_number': '0.0557367604433135539761871572509-0.998445498530232584211066732109*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.241124619656', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.48961293407654772209608103713-0.592817704956371604144305263151*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.846499595512', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.94594469356', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.4609913712', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 27.940880446602506, 'bad_primes': [2, 5, 13], 'central_character': '260.7', 'conductor': 260, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/260/7'], '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': '1-260-260.7-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': '1-260-260.7-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': -0.24112461965614196, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.846499595512', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_260.7', 'Lhash_array': ['dirichlet_L_260.7'], 'label': '1-260-260.7-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/260/7'}
Lfunction data - 1-260-260.7-r1-0-0