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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.758', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.3420201433256687, -0.9396926207859084], 'a3': [-0.984807753012208, 0.17364817766693036], 'a4': [-0.766044443118978, -0.6427876096865394], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.17364817766693036, 0.984807753012208], 'a7': [-0.8660254037844386, -0.5], 'a8': [-0.8660254037844386, 0.5], 'a9': [0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.758', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.142', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^17', 'a^22', 0, 'a^10', 'a^21', 'a^15', 'a^34', 0, 0, 'a^3', 'a^19', 'a^14', 0, 'a^8', 'a^29', 'a^27', 0, 0, 'a^2', 0, 'a^13', 'a^32', 0, 'a^12', 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'188.36280499790748083848467633689', '189.18399273032188906593897132392', '189.93366804777143979171477739468', '190.35388564627936378147018159652', '190.99271320197639811684618587172', '191.6603350899075881936294013968', '192.17782595235647195323102176659', '193.036019871529490185841585963906', '193.59045652520700956312720839054', '193.95225080498042617583727603265', '194.21052482371195197303352904448', '195.19294644880912870609641535364', '195.54934031726104785532354487600', '196.14572166339338340619799885558', '196.79617178575486619668376230885', '197.75316910406197318449841569820', '198.39509683489769751614893949164', '198.977823679344321697198612804143', '199.726454804756049429371512694'], 'prelabel': '1-1045-1045.758-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.04098294462829562, 'root_number': '0.991722941139818390941944987139+0.128396292847528535015946231832*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0204914723141', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.554136031701308862848392865490-0.295805344663308114892633399920*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.824233319656', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.09537410689', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.32452880808', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.758', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/758'], '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': '1-1045-1045.758-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': '1-1045-1045.758-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.02049147231414781, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.824233319656', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.758', 'Lhash_array': ['dirichlet_L_1045.758'], 'label': '1-1045-1045.758-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/758'}
Lfunction data - 1-1045-1045.758-r0-0-0