-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '740204244676807311278321584606', 'a10': [0.0, 0.0], 'a2': [0.766044443118978, 0.6427876096865394], 'a3': [-0.32635182233306964, 0.11878234922776941], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [0.0, 0.0], 'a6': [-0.32635182233306964, -0.11878234922776941], 'a7': [0.0, 0.0], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.6736481776669303, 0.565257937423568], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8964470480054092, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.766044443118978, -0.6427876096865394]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0.9396926207859084, 0.3420201433256687]]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.1251', 'coefficient_field': 'CDF', 'conductor': 3800, 'conductor_radical': 190, 'conjugate': '2335277947070267298514749765281', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0.32635182233306964, -0.11878234922776941], [0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.17364817766693036, -0.3007674663608706], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [-1.532088886237956, -1.2855752193730787], [0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4396926207859084, -0.5240052604587699], [0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0.17364817766693036, -0.984807753012208], [-0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [1.4396926207859084, 1.2080455471101075], [0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [-1.1736481776669303, 0.984807753012208], [0.17364817766693036, -0.984807753012208]], [[1.0, 0], [0, 0], [0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [1.4396926207859084, -0.5240052604587699], [0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0, 0], [-0.766044443118978, 0.6427876096865394]], [[1.0, 0], [-0.9396926207859084, -1.6275953626987474], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.9396926207859084, -0.3420201433256687], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [-0.266044443118978, -0.22323779409789932], [0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [-1.532088886237956, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3800-152.35-c0-0-1', 'leading_term': '1.3344754237142536570394502769340', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3800/1/cv/b/1251/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.3344754237142538, 1.2243407574784755, 1.1220247516587276, 1.0240967563815742, 0.9271137085138189, 0.827890812082529, 0.7237069353621957, 0.6124339350384795, 0.4925982738449543, 0.36339239163147813, 0.22465384400495148, 0.07682627265191608, -0.07908875512457034, -0.24158426331263747, -0.40870290054170594, -0.5780943547884932, -0.7470758082298734, -0.9126962901395089, -1.0718056311275803, -1.2211283757436764, -1.357342574113509, -1.4771629085342761, -1.5774271553235442, -1.6551845595009471, -1.7077843264587989, -1.7329621230974124, -1.7289222412338554, -1.6944129172405162, -1.628792231286329, -1.5320820331481484, -1.4050074633443181, -1.2490198600242761, -1.0663011626339656, -0.8597483388332408, -0.6329368641424149, -0.39006286358364006, -0.1358641669639852, 0.12447878307430567, 0.3854605190399427, 0.6413842678257607, 0.8865087463255272, 1.1152043382927919, 1.3221143934746216, 1.5023169287617857, 1.6514816768230856, 1.7660172422630418, 1.8432031068821695, 1.881301387546056, 1.8796436002929358, 1.838688224066229, 1.7600455813333324, 1.6464674480224195, 1.5017998514490345, 1.3308986847726705, 1.1395090258546654, 0.9341103570913163, 0.7217311959533782, 0.5097379152153075, 0.30560370703295725, 0.11666467597665679, -0.050129115304241356, -0.18845922202248439, -0.29287226144225736, -0.3589924488191394, -0.3837047500471934, -0.36530081082780036, -0.3035807867600482, -0.1999054761715307, -0.05719471741200449, 0.1201301887868563, 0.3262602892260827, 0.5541671791977939, 0.7958216137015822, 1.0424564494959492, 1.2848658661759291, 1.5137310538103894, 1.7199610878437734, 1.8950366140733474, 2.0313433020979903, 2.122481845318782, 2.1635416230590128, 2.1513260099772014, 2.0845187127917084, 1.963782405327578, 1.7917832686008828, 1.5731377501187884, 1.31428084312458, 1.023258342540242, 0.7094487369739435, 0.3832235137064852, 0.05555755075994914, -0.26239618631145484, -0.5597513608020278, -0.8263346385509449, -1.0531151722955423, -1.2325986098507131, -1.3591677885334459, -1.4293538234943484, -1.4420236111146516, -1.3984727876436993, -1.3024168108971794, -1.1598769404768685, -0.9789623232098402, -0.7695539666280296, -0.5429009100624173, -0.31114317836221617, -0.0867799263694439, 0.11789563788627733, 0.291370598569977, 0.42347058754879296, 0.5058762528182709, 0.5325730362392861, 0.5002113004632102, 0.4083569047488367, 0.2596164198238073, 0.05962615638810011, -0.1831001235682597, -0.4574637638119273, -0.7502065837060118, -1.0464552520867931, -1.3303648483541448, -1.5858364205242732, -1.797278885216527, -1.9503823034891496, -2.032867612472701, -2.035177446110662, -1.9510738265964391, -1.7781112692083334, -1.5179581613254054, -1.1765450209943011, -0.7640252091044143, -0.29454159384953366, 0.2141987776360698, 0.7415311256106669, 1.2646009394175168, 1.7592658231231075, 2.201096262641102, 2.5664344903243816, 2.833466356879326, 2.9832587525515253, 3.000714834403402, 2.8754012084611227, 2.602205280427513, 2.1817871201736705, 1.6207981756735879, 0.9318487183416578, 0.1332166160581671, -0.7516985447797351, -1.695160338648733, -2.6660924363225953, -3.631250226068497, -4.556520712739907, -5.40829710458162, -6.154869566254536, -6.767771237962932, -7.2230189844799, -7.5021915093531275, -7.593293381517445, -7.491361973577158, -7.1987849749555615, -6.725308574825852, -6.087730067233626, -5.309282897680078, -4.418736383756076, -3.44924582395065, -2.4370007977872645, -1.4197295468182256, -0.4351248816669164, 0.4807383323734519, 1.2949226832197371, 1.9790152736158089, 2.5103182182904376, 2.872786918222042, 3.057671697389754, 3.063831915940746, 2.8977068641847463, 2.572943876455522, 2.1097004039955856, 1.533652450161158, 0.8747560153302858, 0.16582029650183003, -0.5590392928212788, -1.2659941736843496, -1.923065191212646, -2.5015795691308957, -2.9774521697900873, -3.3322296489138123, -3.553847872528068, -3.637067299360428, -3.5835672135866212, -3.4016969035426428, -3.105899241701992, -2.715838731468106, -2.2552810778651122, -1.7507839184058935, -1.2302678426986091, -0.7215427169431597, -0.25086628134949024, 0.15839011920440413, 0.48689988554214325, 0.7203045441462131, 0.8498559915803892, 0.8727467935426318, 0.7921147297414198, 0.6167255026462546, 0.36035501379476664, 0.040908894466573205, -0.3206688439222928, -0.7016348923456797, -1.0787625630949873, -1.4296598754761265, -1.73401556456663, -1.9747033820049562, -2.138683607770463, -2.2176527041491543, -2.208406841545327, -2.112901770018836, -1.9380092419779051, -1.694987887944105, -1.3987030808280605, -1.0666449209329314, -0.7178051716249424, -0.37148207509630365, -0.04608598571341179, 0.24198158070309536, 0.47930757022579457, 0.6562465522745469, 0.767452647774601, 0.8121326790807066, 0.7940061851487464, 0.7209760676696737, 0.6045315952215932, 0.4589221967975614, 0.30015489197796097, 0.14487942936010467, 0.009232519269186027, -0.09228453595652897, -0.14782221370173046, -0.14902680881163155, -0.09165628630137483, 0.024073802793151463, 0.19343921942744213, 0.4074569975556587, 0.6534234825377608, 0.9157088204590027, 1.1767594062679145, 1.4182457966241955, 1.622283380593055, 1.7726473801782643, 1.8559029542745036, 1.8623754319393433, 1.7868948152601405, 1.6292621691953502, 1.394402571270066, 1.0921889026360188, 0.7369417177067816, 0.3466314182696036], 'positive_zeros': ['0.58391819050418152457507952929315', '1.85470866296079420774986080169624', '3.03076114885464023737334460882962', '3.47054503241654298779352632800875', '4.57902630061509221961705527342670', '5.40358468396883439418968532946926', '5.85309521639287561963078924282282', '6.68209315383449728255707631903953', '7.42199575729730029518229857722213', '8.504005184735619740129174072947418'], 'prelabel': '2-3800-152.35-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3771154809983834, 'root_angle': -0.8937122133900252, 'root_number': '-0.94476714678654826902355529713894 - 0.32774233530748626303273412761898*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4468561066950126', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58391819050418152457507952929', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85470866296079420774986080170', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03076114885464023737334460883', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.8964470480054092, 'bad_primes': [2, 5, 19], 'central_character': '152.35', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/1/cv/b/1251/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-3800-152.35-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3800-152.35-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3771154809983834, 'root_angle': -0.4468561066950126, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58391819050418152457507952929', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '740204244676807311278321584606', 'Lhash_array': ['740204244676807311278321584606'], 'label': '2-3800-152.35-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/1/cv/b/1251/1'}