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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1974481513362628161', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '235200.1', 'coefficient_field': '1.1.1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1], [1, -2, 11], [1, -1, 13], [1, 0, 17], [1, 3, 19], [1, 0, 23], [1, 0, 29], [1, 9, 31], [1, -3, 37], [1, -2, 41], [1, -3, 43], [1, -6, 47], [1, 0, 53], [1, -4, 59], [1, 2, 61], [1, -5, 67], [1, -14, 71], [1, 1, 73], [1, -9, 79], [1, 6, 83], [1, 4, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 474, 'label': '2-235200-1.1-c1-0-474', 'leading_term': '6.48048139536', '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': 1, 'origin': 'EllipticCurve/Q/235200/kf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.387445699817797, 1.557327034636569, 0.2441329765403342, -1.243840005362951, -1.026118679072731, 0.9824472714973579, 2.351035441113893, 1.021269939797725, -1.380255945972976, -1.035745414063581, 2.642723342250558, 5.363266150048991, 3.614873470271935, -0.1259513351012989, -1.059620638799515, 0.5801812008202935, 0.4056776945667782, -2.258518579121284, -3.078382792969033, -0.543152956705275, 1.07838998887651, -0.625295709156143, -1.94875893921964, -0.3352862652029343, 0.715790211412791, -1.139135783824541, -2.059609668667912, 0.09820194189643806, 0.691150959859435, -2.462939584671982, -3.580614104257677, 0.1559585700939218, 2.178710852748611, -1.201641283177729, -3.41395004545611, -0.4647263326921104, 1.56125052074287, -0.4691007793065201, -0.382425417594698, 3.724831281342501, 4.890669418914666, 1.476501108934972, -0.123511189663901, 0.7525811024933478, -0.8283540796143323, -2.956752761826692, -1.124208237007791, 0.781563918606113, -1.117277828853943, -1.763992866879768, 0.9799963354914533, 0.9799972936117904, -1.41945298133973, 1.036337246234459, 5.390511973226847, 3.283597570992693, -0.9581440614602048, 0.2162980473845916, 1.2794052628372, -2.659168687308879, -4.031805963038841, -0.2563873461460601, 0.2967035288867175, -2.555098225733352, -1.319863713298799, 1.497610526557417, 0.3734925146600797, -0.3156556712650743, 1.455407935912423, 0.004578685177338475, -2.790815561269435, -0.9809978171255892, 0.6270369002610375, -1.900485490201517, -1.649251588826189, 1.460771347160618, -0.7208041469477787, -4.170503094917026, -1.250748247482491, 0.9189601614160442, -2.148918806998594, -1.097728078275726, 4.045185103419546, 2.879383177176616, -1.24967766746513, -0.202745947471399, 0.4899503234575885, -2.204476458096382, -1.345428939250089, 1.258687633356536, -0.05588136342820017, 0.03805093409145474, 3.182094279057903, 2.162631853758169, -0.5214169868139455, 0.4401427871084092, -1.097604907643346, -5.211160305316379, -2.861694980095118, 1.330713853124168, -0.6133228381737137, -1.054758363321092, 2.166645947701787, -0.5207785359716107, -4.295088744738908, 0.1455589453650482, 3.50663304143452, -0.04371706227159804, -0.9707578935226665, 0.6795202204841077, -1.222151095527282, -1.240016409490029, 1.523417149132155, 0.05669560058475951, -1.113544611179717, 2.211727327566732, 2.099738475125661, -0.644055253629385, 0.6509990849755602, 0.09837010647649061], 'positive_zeros': ['0.7849479947612411', '1.390657172013036', '2.097227719074964', '2.586113307588891', '3.489364531521449', '3.914197208786037', '4.296878097580145', '5.048020434033692', '5.434526817675010', '6.039777690678569', '6.376479299939824', '6.989893696285204', '7.323544711458383', '7.991043854038467', '8.431102266872363', '9.030972145475529', '9.451438102718324', '9.780654738209112', '10.65144517951262', '10.79523140616766', '11.17220622771598', '11.84641949241366', '12.14029411704811', '12.66404793210337', '13.08856740958357', '13.44502615601254', '14.16717891662097', '14.48105570163901', '14.85386886967786', '15.51921306596705', '15.77811138658461', '16.34273282864388', '16.79683435550709', '17.05114529914146', '17.50033157382228', '18.08148024196732', '18.33592376624034', '18.86584110961519', '19.21048081813365', '19.82453452293617'], 'prelabel': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1974481513362628161, 'z1': {'__RealLiteral__': 0, 'data': '0.7849479947612411', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.390657172013036', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.097227719074964', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -9, 0, -2, 0, 0, 0, 3, 0, -1, 0, 2, 0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 14, 0, -1, 0, 0, 0, 0, 0, 9, 0, 1, 0, -6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 9, 0, 0, 0, 14, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, -1, 13], 'euler17': [1, 0, 17], 'euler19': [1, 3, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, 9, 31], 'euler37': [1, -3, 37], 'euler41': [1, -2, 41], 'euler43': [1, -3, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -5, 67], 'euler7': [1, 0, 0], 'euler71': [1, -14, 71], 'euler73': [1, 1, 73], 'euler79': [1, -9, 79], 'euler83': [1, 6, 83], 'euler89': [1, 4, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, -2, 11], [1, -1, 13], [1, 0, 17], [1, 3, 19], [1, 0, 23], [1, 0, 29], [1, 9, 31], [1, -3, 37], [1, -2, 41], [1, -3, 43], [1, -6, 47], [1, 0, 53], [1, -4, 59], [1, 2, 61], [1, -5, 67], [1, -14, 71], [1, 1, 73], [1, -9, 79], [1, 6, 83], [1, 4, 89], [1, -14, 97]], 'index': 474, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/235200/kf'], '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': '2-235200-1.1-c1-0-474', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1974481513362628161, 'z1': {'__RealLiteral__': 0, 'data': '0.7849479947612411', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1974481513362628161', 'Lhash_array': ['1974481513362628161'], 'label': '2-235200-1.1-c1-0-474', 'type': 'ECQ', 'url': 'EllipticCurve/Q/235200/kf'}