-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': -2, 'A8': 1, 'A9': 1, 'Lhash': '1905209159643037991', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1639.7280055069934, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '205350.1', 'coefficient_field': '1.1.1.1', 'conductor': 205350, 'conductor_radical': 1110, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1], [1, 2, 7], [1, -4, 11], [1, 6, 13], [1, 6, 17], [1, 2, 19], [1, 4, 23], [1, -8, 29], [1, 0, 31], [1], [1, 2, 41], [1, 12, 43], [1, 6, 47], [1, -14, 53], [1, 14, 59], [1, -12, 61], [1, -4, 67], [1, 0, 71], [1, 16, 73], [1, -8, 79], [1, 16, 83], [1, -10, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 10, 'label': '2-205350-1.1-c1-0-10', 'leading_term': '2.13153010119', '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': 0, 'origin': 'EllipticCurve/Q/205350/ds', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.131530101185462, 0.7929221109244078, -2.442748463686231, -5.37441508522244, -5.581155478449091, -2.708965787487559, 0.6828852437180315, 1.595474925594891, 0.007285023679419034, -1.260786694795988, -0.478202160182875, 0.676054021254984, -0.003362704842699762, -1.510566650980323, -1.203271325075708, 0.6532576672221253, 1.197254946116275, 0.003114947381597729, -0.1084241073807281, 1.451566630864508, 1.227704637276556, -1.964920167246403, -3.625773835385727, -0.5939738597879457, 3.098773168588022, 2.681733147422923, 0.3183817066308762, -0.04819115482511889, -0.4765649238316337, -3.765679665341018, -5.72123794877059, -2.159738969464337, 1.733039849736169, -0.305032209413345, -3.835206789823837, -1.955815933019687, 1.494692386373641, -0.1373915844245729, -3.025761335148557, -1.178463987382242, 1.117520517550934, -0.8469220483756628, -0.9077327839956387, 5.349868983331742, 9.48705830819656, 5.192387262965511, -0.001583547305869781, 0.3966713067751981, 1.283322800156261, -0.7563918169703414, -0.9306201528774583, 1.386075423876865, 1.096885692131277, -0.7579349940918998, 0.1831630547991524, 1.279579541612981, -0.5456046778476155, -1.392835082850474, 0.199328346118297, 0.05044124183915015, -0.9495834400121284, 0.8226401701333025, 1.504049333996924, -1.529656705443591, -1.726099237807945, 1.858449643714611, 0.9065563619674954, -2.853874205390588, -0.4353986669805363, 2.934553261287386, -1.133534801870538, -3.146217063359922, 4.072375462014617, 6.624500723871731, -2.544908774598363, -8.116535184256646, -2.998982182995234, 1.089265177714631, 0.08106225176506078, 0.1730232219084225, 0.4214651027330309, -0.2932614751022918, 3.162484550881893, 7.275297332371516, 3.82081305950969, -1.735409810496608, -1.367823892694374, 0.2344879090460059, -0.2337308666974157, 1.027655849880758, 1.489165769866677, -1.425111644726999, -1.205671983869588, 1.832646647566859, -0.6087123124238119, -4.536446109421088, -1.905689897031334, 1.28192016958437, 0.094967406685488, -0.07894498917735641, -0.09166805568020192, -3.12558685998599, -2.841981412472735, 0.4877214220548382, -1.78901327144755, -4.794670128651803, -1.352009039234401, -0.08618753296851143, -2.482897877974782, 1.966632323576868, 6.46821942267455, 0.5479109604617988, -2.138509263805259, 5.974255605079057, 8.033655529627154, 1.000113988418465, -0.4991949187981125, 1.724731257788526, -0.07320349145365031, -0.02382656909804832, 2.106981774781278], 'positive_zeros': ['0.3204932389474585', '1.439041721461618', '2.000929360864695', '2.581191405151636', '2.999459268316674', '3.661814865284420', '4.250679329805656', '4.523234162030302', '5.111172462852346', '5.782902504425397', '6.563870202341898', '6.780727651152016', '6.902164879799988', '7.856993111426086', '8.232174174197975', '8.865309215898354', '9.240690725141011', '9.837096715287038', '10.17361735275669', '10.55254373379223', '11.49983364220111', '11.69755260899705', '12.16771532444380', '12.60115717603378', '13.12488164591805', '13.47678651166544', '13.94150225955787', '14.46609933652259', '14.75879836114508', '15.16510693733969', '15.63648000022654', '16.11869396806731', '16.55207038296002', '17.02113811690662', '17.45136998327117', '17.88005698219777', '18.44143361003104', '19.13281065367027', '19.51830591913462', '19.70376513715038'], 'prelabel': '2-205350-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.49355511074563, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1905209159643037991, 'z1': {'__RealLiteral__': 0, 'data': '0.3204932389474585', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.439041721461618', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.000929360864695', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1639.7280055069934, 'bad_primes': [2, 3, 5, 37], 'central_character': '1.1', 'conductor': 205350, 'conductor_radical': 1110, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, -2, 1, 1, 0, 4, 1, -6, -2, 0, 1, -6, 1, -2, 0, -2, 4, -4, 1, 0, -6, 1, -2, 8, 0, 0, 1, 4, -6, 0, 1, 0, -2, -6, 0, -2, -2, -12, 4, 0, -4, -6, 1, -3, 0, -6, -6, 14, 1, 0, -2, -2, 8, -14, 0, 12, 0, -2, 1, 0, 4, 4, -6, -4, 0, 0, 1, -16, 0, 0, -2, -8, -6, 8, 0, 1, -2, -16, -2, 0, -12, 8, 4, 10, 0, 12, -4, 0, -6, 0, 1, -6, -3, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 6, 13], 'euler17': [1, 6, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -8, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 0, 0], 'euler41': [1, 2, 41], 'euler43': [1, 12, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -14, 53], 'euler59': [1, 14, 59], 'euler61': [1, -12, 61], 'euler67': [1, -4, 67], 'euler7': [1, 2, 7], 'euler71': [1, 0, 71], 'euler73': [1, 16, 73], 'euler79': [1, -8, 79], 'euler83': [1, 16, 83], 'euler89': [1, -10, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 0], [1, 2, 7], [1, -4, 11], [1, 6, 13], [1, 6, 17], [1, 2, 19], [1, 4, 23], [1, -8, 29], [1, 0, 31], [1, 0, 0], [1, 2, 41], [1, 12, 43], [1, 6, 47], [1, -14, 53], [1, 14, 59], [1, -12, 61], [1, -4, 67], [1, 0, 71], [1, 16, 73], [1, -8, 79], [1, 16, 83], [1, -10, 89], [1, 6, 97]], 'index': 10, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/205350/ds'], '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': '2-205350-1.1-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-205350-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.49355511074563, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1905209159643037991, 'z1': {'__RealLiteral__': 0, 'data': '0.3204932389474585', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1905209159643037991', 'Lhash_array': ['1905209159643037991'], 'label': '2-205350-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/205350/ds'}