-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': -1, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 3, 'A9': 0, 'Lhash': '552601619718995112', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1521.7490365205517, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1, 1]], [11, [1]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '190575.1', 'coefficient_field': '1.1.1.1', 'conductor': 190575, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1], [1, 1], [1], [1, 6, 13], [1, -6, 17], [1, 0, 19], [1, -6, 23], [1, 6, 29], [1, 0, 31], [1, 4, 37], [1, 6, 41], [1, 8, 43], [1, 10, 47], [1, -4, 53], [1, 12, 59], [1, -10, 61], [1, -2, 67], [1, 8, 71], [1, -2, 73], [1, 8, 79], [1, 0, 83], [1, -6, 89], [1, 0, 97]], 'gamma_factors': [[], [0]], 'index': 131, 'label': '2-190575-1.1-c1-0-131', 'leading_term': '8.38064406401', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'origin': 'EllipticCurve/Q/190575/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.4851433692159613, -1.495745667868332, -1.944112092773745, -1.071141119331346, 0.3637482422256678, 0.4365491245595668, -1.570155793870702, -3.516106190861183, -2.507509130297513, 1.028578464164487, 3.094669364469936, 1.298022273401792, -1.375140220338027, -0.5669239581719245, 2.673455194058096, 3.006439884285101, -0.9006271343137313, -3.891424401187858, -2.367807805819361, 0.1189775413467874, -0.4497638905752479, -0.997632205617966, 3.060707881360423, 8.260079301076365, 7.381633734946931, 1.4442910678266, -1.66025944630924, 0.09522321545132299, 1.093409525520317, -0.7593205928087299, -1.289181655996507, 0.4510281996557792, 0.2850421670865626, -2.063680450286524, -2.144399432913043, 0.1620313985382233, 0.6835135737191373, -0.4087544824104351, 0.07688089295797985, 0.8248015659405845, -0.2366101900445849, 0.3033687206866129, 3.793731680703076, 3.897771938143548, -1.419891983674221, -3.727824849327687, 0.3714461997045577, 2.32868859682429, -1.190576374775864, -2.147170931798628, 1.247553954389394, 1.232728062955226, -1.673820342087223, 0.2506018324354961, 3.897248248069074, 1.221545368918992, -2.989260724461501, -1.222111387870511, 1.062163778073103, -0.6768961867735276, 1.23651551224384, 8.346973212884048, 9.417317981650307, 2.559242171561804, -1.152100185401729, 0.5756875029738171, 0.747965631624095, -0.2764760677511304, 0.7385290209497312, 0.3126097197467829, -1.952371668482889, -0.7085529691292457, 2.267567000706984, 1.479497292690824, -0.2356351542030266, 0.2132327696351015, -0.6199832165349968, -1.621033913999228, 1.095828626249623, 2.383927812655742, -0.4611370685571446, 1.408794436170878, 7.941871634789203, 6.825964889284694, 0.006843479106014034, -0.126084137500855, 2.548020606024202, -0.5068832806680214, -2.175859670625368, 1.478334816454947, 1.745871376642622, -0.4486327608315334, 1.730998865307357, 1.233062778705588, -5.564661170685952, -6.282545954230908, 0.06719566005419796, 0.1906614374362412, -3.655272633498795, -1.262611823153141, 1.51783289611863, -0.840101156015951, -0.8571691695892222, 1.858775625736891, 0.7563922097191138, -0.7492010171578538, 0.5771801645566074, -0.01380809206265666, -1.380232968862947, -0.06709586944840436, -0.2672618788216756, -1.560928923783927, 0.8487708498957551, 1.789900617823443, -1.610284786691981, -1.431644336060194, 1.058892362435516, -0.8564297409806643, -0.8254256505885408, 2.329855627387868], 'positive_zeros': ['1.177458367059596', '1.576356772234285', '2.430763118449834', '3.102751293977418', '3.546834735791575', '4.201026024432490', '4.976815438140403', '5.173844442701077', '5.596723699899412', '6.570093083322766', '6.990205031825637', '7.411549890224783', '7.934313556346198', '8.284959601931001', '8.980348277849901', '9.394245949131957', '9.734422302815738', '10.20218212851641', '10.46702341200689', '11.18887195690905', '11.73079151859340', '12.17665308689173', '12.65969079590172', '13.09478800788485', '13.48578808476197', '14.05637790933172', '14.58584310078621', '14.91680710213294', '15.18625937472850', '16.11048258465449', '16.43198544425088', '16.88485669751084', '17.10795862733228', '17.53425091458513', '18.05149298939802', '18.68061894301845', '18.91663016226513', '19.15227799649659', '19.67225692852157'], 'prelabel': '2-190575-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.0096018503208, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 552601619718995112, 'z1': {'__RealLiteral__': 0, 'data': '1.177458367059596', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.576356772234285', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.430763118449834', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1521.7490365205517, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 190575, 'conductor_radical': 1155, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, -1, 3, 0, 0, 0, 0, -6, 1, 0, -1, 6, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 1, -6, 0, 0, -5, 0, -6, 0, 0, -4, 0, 0, 0, -6, 0, -8, 0, 0, -6, -10, 0, 1, 0, 0, 6, 4, 0, 0, -3, 0, 6, -12, 0, 10, 0, 0, 7, 0, 0, 2, -6, 0, 0, -8, 0, 2, 4, 0, 0, 0, 0, -8, 0, 0, 6, 0, 0, 0, 8, 0, 0, 6, 0, 6, -6, 0, 10, 0, 0, 0, -1, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 6, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, -6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, 4, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 0], 'euler53': [1, -4, 53], 'euler59': [1, 12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -2, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -6, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 6, 13], [1, -6, 17], [1, 0, 19], [1, -6, 23], [1, 6, 29], [1, 0, 31], [1, 4, 37], [1, 6, 41], [1, 8, 43], [1, 10, 47], [1, -4, 53], [1, 12, 59], [1, -10, 61], [1, -2, 67], [1, 8, 71], [1, -2, 73], [1, 8, 79], [1, 0, 83], [1, -6, 89], [1, 0, 97]], 'index': 131, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/190575/r'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-190575-1.1-c1-0-131', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-190575-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.0096018503208, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 552601619718995112, 'z1': {'__RealLiteral__': 0, 'data': '1.177458367059596', 'prec': 57}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '552601619718995112', 'Lhash_array': ['552601619718995112'], 'label': '2-190575-1.1-c1-0-131', 'type': 'ECQ', 'url': 'EllipticCurve/Q/190575/r'}