-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '847990927317935227487850855828', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 333.29080413713064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -4, 5]], [11, [1, 2, 11]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '5227200.1', 'coefficient_field': '1.1.1.1', 'conductor': 5227200, 'conductor_radical': 330, 'degree': 4, 'euler_factors': [[1], [1, -1], [1, -4, 5], [1, 0, -8, 0, 49], [1, 2, 11], [1, 0, -8, 0, 169], [1, 0, 8, 0, 289], [1, 0, 18, 0, 361], [1, 6, 46, 138, 529], [1, 0, -10, 0, 841], [1, 8, 42, 248, 961], [1, -2, 50, -74, 1369], [1, 0, -38, 0, 1681], [1, 0, 16, 0, 1849], [1, 2, 46, 94, 2209], [1, -14, 130, -742, 2809], [1, -8, 70, -472, 3481], [1, 0, -34, 0, 3721], [1, -14, 174, -938, 4489], [1, 0, 142, 0, 5041], [1, 0, -64, 0, 5329], [1, 0, -54, 0, 6241], [1, 0, -24, 0, 6889], [1, 8, 178, 712, 7921], [1, 18, 274, 1746, 9409], [1, 0, -38, 0, 10201], [1, -10, 110, -1030, 10609], [1, 0, -152, 0, 11449], [1, 0, -62, 0, 11881], [1, -10, 130, -1130, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 29, 'label': '4-5227200-1.1-c1e2-0-29', 'leading_term': '4.29050460626', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/2.0.11.1/43200.7/bb', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.04296875', 'prec': 34}, 'plot_values': [4.290504606261569, 4.271380501492206, 4.213960829197384, 4.118122354908358, 3.983721455338301, 3.8106831904550518, 3.59911895015887, 3.349465867411186, 3.062639603349388, 2.740190803698944, 2.3844545703598525, 1.9986817583869139, 1.5871408642512888, 1.155179775403298, 0.7092377485142148, 0.2567996981644894, -0.1937127946502136, -0.6331164415967996, -1.0517064585344613, -1.4395575306247828, -1.7868770275972008, -2.0843979404578508, -2.3237951985611027, -2.4981056839233236, -2.6021296556983, -2.6327896933173847, -2.5894228979963985, -2.473983149277605, -2.291132819643945, -2.0482075440565324, -1.755043359153374, -1.4236625932195164, -1.0678230109615117, -0.7024434922372886, -0.3429284473790184, -0.00442166266329822, 0.29897229874774545, 0.55495527516907, 0.7537439440387913, 0.8886715338330723, 0.9566373170503542, 0.9583642236774015, 0.8984340515245623, 0.7850819089310467, 0.6297461689328056, 0.4463865579713341, 0.25060004556873927, 0.05858077643368723, -0.1140148712658747, -0.2532251831997373, -0.3478814043693473, -0.3905644292578643, -0.37834033714645243, -0.3132049056461119, -0.20218302708694916, -0.05705024543717426, 0.10633067536191358, 0.2690367080206044, 0.41042417186975066, 0.5097020132996125, 0.5476353080363019, 0.5082569846570325, 0.3804551467893354, 0.159302252382336, -0.15299825274741183, -0.5466522572850473, -1.004376681528121, -1.5020985133884166, -2.010242603016042, -2.495552095394418, -2.923338466603674, -3.260015738551308, -3.475739444000959, -3.546948802011679, -3.4586031534332395, -3.2059128108578863, -2.795390670969231, -2.2450933940209086, -1.583977399926763, -0.8503617102318048, -0.08956194950954038, 0.6491680779353532, 1.316185016422673, 1.865239113750097, 2.257200548947219, 2.463423992526964, 2.4684576605726942, 2.271839847361935, 1.8887867172315436, 1.349656339804464, 0.6981698465727538, -0.01152623323326629, -0.7187704790791879, -1.360992283043325, -1.8786623532595779, -2.22019129218088, -2.346365228971216, -2.233928276668738, -1.877977526295383, -1.2929242548500741, -0.5118887855638556, 0.41547294072662244, 1.4265765230437772, 2.4506851562956142, 3.4144778884535834, 4.247951004529062, 4.890149466669905, 5.29422545077369, 5.431367083391676, 5.293230078346586, 4.892631426452227, 4.26241710449658, 3.4525814448115804, 2.525879021255174, 1.5523149265626597, 0.6030115250202424, -0.2559828312456001, -0.9693630936399713, -1.4971762495265106, -1.8179260752440098, -1.9298715358787024, -1.8503907070447467, -1.6134730149954573, -1.2655913511545995, -0.8603729208240931, -0.4526157535800915, -0.09227228078009543, 0.18096701417335034, 0.34191118447082086, 0.3824654110674641, 0.31229246548501677, 0.157448337752805, -0.042880611328509864, -0.24120188319372574, -0.3875868620017591, -0.4359440636760821, -0.3499930843517092, -0.10825242735189744, 0.29255351584056283, 0.8361022353730514, 1.4873155127709325, 2.195411134558822, 2.8988883996679577, 3.531944569153577, 4.031641156093003, 4.345031524854021, 4.43543924327138, 4.287145510665302, 3.9078992080280637, 3.32889017556398, 2.6021020128432863, 1.7952554141255734, 0.984833916073514, 0.24791842129150607, -0.3462834625109453, -0.7442632742272994, -0.9144852135254411, -0.851347524686217, -0.5763116485595354, -0.1359862832546575, 0.40270479783486934, 0.9598043972402693, 1.451291253832796, 1.7987588355190558, 1.9387148680628439, 1.830424791545545, 1.4613590163985146, 0.8495533136385616, 0.04252832266813103, -0.8871986358835577, -1.849582209070405, -2.7467158658855833, -3.4836413533450665, -3.979087760230449, -4.174907330499561, -4.04309873224196, -3.589564534699172, -2.8541111959726777, -1.9066266730758537, -0.8398137813014623, 0.24073555034767075, 1.2280180976522324, 2.025345517241026, 2.556969568625733, 2.776370796565383, 2.671237270825635, 2.264541536443351, 1.611580696316457, 0.7933223751021921, -0.0931594999878921, -0.9460248161863757, -1.670433404384391, -2.189334416269154, -2.451994268808045, -2.439254633647529, -2.164913398506988, -1.6730993656368398, -1.0320065553448796, -0.3248043280140159, 0.3611119549667415, 0.9451631178825989, 1.3635258561414751, 1.576723616995966, 1.5739309791124965, 1.3734829714234316, 1.0195753742084441, 0.5756379840336254, 0.11529518913832001, -0.28786015896079253, -0.5703044066724348, -0.6870909388217574, -0.6176999986381994, -0.36846704643185574, 0.02870582886750114, 0.5211426303302918, 1.0429978272895655, 1.5245946969098363, 1.902182805074666, 2.1267445777818463, 2.1706167301115524, 2.0310018766441456, 1.7298871842820471, 1.3103996044243233, 0.8301392728756894, 0.3524712732301064, -0.06294251362042275, -0.3689705701332538, -0.5378802501386091, -0.5652070969094615, -0.47001883937655864, -0.29149950085773674, -0.08233217617644004, 0.1001469170996119, 0.20368969233502734, 0.19026855206625093, 0.043145611864377084, -0.22930538992430874, -0.5937514128416249, -0.9961705372696694, -1.3697575238180895, -1.6454022531657022, -1.763234786083462, -1.6834933029483123, -1.394983984674271, -0.9196738546456376, -0.31246005954151823, 0.34417146838414087, 0.950139064562786, 1.4012342427870967, 1.6043084927598896, 1.4920636260391857, 1.0352629592812395, 0.25042371869550295, -0.7984146429491826, -2.004488853675683, -3.2294267130956267, -4.319525995980987], 'positive_zeros': ['0.66894689054323161210674966401111', '1.50449458536836257081068089116966', '2.03340786319214331073935928918229', '2.37859158699726680228149915056813', '2.73044273296147154407240924695672', '3.44258566124391067400014378658136', '3.90946734191003820640835947157584', '4.32125063493921347349656123491628', '4.97090328020147701564370881997470', '5.42690899293069439365063838653612', '5.66299449995493948247146288710470', '5.90011308306553386127242469516368', '6.59068565317438925155567612096683', '6.84339293447776337810667502250257', '7.22081445821323812185703917018721'], 'prelabel': '4-5227200-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.272733766143977, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1529583277805983942, 'z1': {'__RealLiteral__': 0, 'data': '0.66894689054323161210674966401111', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.50449458536836257081068089116966', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.03340786319214331073935928918229', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 333.29080413713064, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 5227200, 'conductor_radical': 330, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 4, 0, 0, 0, 1, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 11, 0, 1, 0, 0, 0, -8, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 8, 0, 0, 0, 14, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 14, 0, -6, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, -18, 0, -2, 0], 'euler11': [1, 2, 11, 0, 0], 'euler13': [1, 0, -8, 0, 169], 'euler17': [1, 0, 8, 0, 289], 'euler19': [1, 0, 18, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 6, 46, 138, 529], 'euler29': [1, 0, -10, 0, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, 8, 42, 248, 961], 'euler37': [1, -2, 50, -74, 1369], 'euler41': [1, 0, -38, 0, 1681], 'euler43': [1, 0, 16, 0, 1849], 'euler47': [1, 2, 46, 94, 2209], 'euler5': [1, -4, 5, 0, 0], 'euler53': [1, -14, 130, -742, 2809], 'euler59': [1, -8, 70, -472, 3481], 'euler61': [1, 0, -34, 0, 3721], 'euler67': [1, -14, 174, -938, 4489], 'euler7': [1, 0, -8, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, -64, 0, 5329], 'euler79': [1, 0, -54, 0, 6241], 'euler83': [1, 0, -24, 0, 6889], 'euler89': [1, 8, 178, 712, 7921], 'euler97': [1, 18, 274, 1746, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 0, 0, 0], [1, -4, 5, 0, 0], [1, 0, -8, 0, 49], [1, 2, 11, 0, 0], [1, 0, -8, 0, 169], [1, 0, 8, 0, 289], [1, 0, 18, 0, 361], [1, 6, 46, 138, 529], [1, 0, -10, 0, 841], [1, 8, 42, 248, 961], [1, -2, 50, -74, 1369], [1, 0, -38, 0, 1681], [1, 0, 16, 0, 1849], [1, 2, 46, 94, 2209], [1, -14, 130, -742, 2809], [1, -8, 70, -472, 3481], [1, 0, -34, 0, 3721], [1, -14, 174, -938, 4489], [1, 0, 142, 0, 5041], [1, 0, -64, 0, 5329], [1, 0, -54, 0, 6241], [1, 0, -24, 0, 6889], [1, 8, 178, 712, 7921], [1, 18, 274, 1746, 9409]], 'index': 29, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.11.1/43200.6/bb', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/43200.7/bb', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/43200.6/bb', 'EllipticCurve/2.0.11.1/43200.7/bb'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-5227200-1.1-c1e2-0-29', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-5227200-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.272733766143977, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1529583277805983942, 'z1': {'__RealLiteral__': 0, 'data': '0.66894689054323161210674966401111', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9933819
{'Lhash': '847990927317935227487850855828', 'Lhash_array': ['847990927317935227487850855828'], 'factors': ['4-5227200-1.1-c1e2-0-29'], 'label': '4-5227200-1.1-c1e2-0-29', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/43200.7/bb'}
-
id: 9933388
{'Lhash': '847990927317935227487850855828', 'Lhash_array': ['847990927317935227487850855828'], 'factors': ['4-5227200-1.1-c1e2-0-29'], 'label': '4-5227200-1.1-c1e2-0-29', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/43200.6/bb'}
-
id: 9933207
{'Lhash': '847990927317935227487850855828', 'Lhash_array': ['847990927317935227487850855828'], 'factors': ['4-5227200-1.1-c1e2-0-29'], 'label': '4-5227200-1.1-c1e2-0-29', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/43200.7/bb'}
-
id: 9933200
{'Lhash': '847990927317935227487850855828', 'Lhash_array': ['847990927317935227487850855828'], 'factors': ['4-5227200-1.1-c1e2-0-29'], 'label': '4-5227200-1.1-c1e2-0-29', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/43200.6/bb'}