-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1388867016591995277824969499112', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -11.98301511285953], 'a6': [0, 0], 'a7': [26.46242100385972, 15.278085889987617], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.61289388268662, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-33.975192978711, -32.290652858982995]]]], 'bad_primes': [2, 3, 13], 'central_character': '468.361', 'coefficient_field': 'CDF', 'conductor': 468, 'conductor_radical': 78, 'conjugate': '1389770425710126389211481008192', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 11.98301511285953], [-125.0, 0]], [[1.0, 0], [-26.46242100385972, -15.278085889987617], [171.5, 297.04671349806245]], [[1.0, 0], [-36.83580715192059, 21.267163174978496], [665.5, -1152.6798124370878]], [[1.0, 0], [-33.975192978711, -32.290652858982995]], [[1.0, 0], [26.333987766486718, -45.61180477745226], [-2456.5, -4254.782808792947]], [[1.0, 0], [111.7443215867575, 64.51561414852655], [3429.5, 5940.068244557465]], [[1.0, 0], [-54.25948352978323, -93.98018226603125], [-6083.5, 10536.931087845265]], [[1.0, 0], [-44.18066433498823, -76.52315534034585], [-12194.5, 21121.493572898675]], [[1.0, 0], [0, -32.18255825436183], [-29791.0, 0]], [[1.0, 0], [-300.0713007210293, 173.2462462473674], [25326.5, -43866.78477789317]], [[1.0, 0], [157.56429060842856, -90.96978559744866], [34460.5, -59687.336854227295]], [[1.0, 0], [-37.82722209903095, 65.51867058471383], [-39753.5, -68855.08177868936]], [[1.0, 0], [0, 307.3736364293033], [-103823.0, 0]], [[1.0, 0], [-693.0925433724841, 0], [148877.0, 0]], [[1.0, 0], [314.3007834617211, 181.46164193813493], [102689.5, 177863.43140384424]], [[1.0, 0], [-214.6718051138898, 371.8224734097815], [-113490.5, -196571.31217639567]], [[1.0, 0], [169.92035193215202, -98.10356092882391], [150381.5, -260468.39851841913]], [[1.0, 0], [-907.3850045926492, -523.8789766601959], [178955.5, 309960.0182938922]], [[1.0, 0], [0, 234.4415772323946], [-389017.0, 0]], [[1.0, 0], [-409.7897913526146, 0], [493039.0, 0]], [[1.0, 0], [0, -13.181331977803136], [-571787.0, 0]], [[1.0, 0], [552.9531776743717, -319.24766597955744], [352484.5, -610521.062880512]], [[1.0, 0], [1060.4146599499136, 612.230689374708], [456336.5, 790398.003348155]], [[1.0, 0], [387.8743889453594, 671.8181486080946], [-515150.5, 892266.8395445109]], [[1.0, 0], [-432.8177769527231, 0], [1092727.0, 0]], [[1.0, 0], [63.41341059487716, 109.8352490315538], [-612521.5, 1060918.3587283]], [[1.0, 0], [0, -1393.6575714068092], [-1295029.0, 0]], [[1.0, 0], [-1041.0612033164457, 1803.1708979328769], [-721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-468-13.10-c3-0-10', 'leading_term': '2.505731380980395891007467826885981598911296137860724993', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/468/4/t/g/361/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [2.505731380980396, 2.5094731039743694, 2.4924567064996177, 2.454613131566461, 2.3960267891002447, 2.316942645965763, 2.2177755338189695, 2.0991211749331877, 1.9617682838814932, 1.8067109835990023, 1.635160681792234, 1.4485564907649582, 1.248573242352451, 1.0371261507597398, 0.8163712098686413, 0.5887004775456937, 0.3567314966326277, 0.12329022913610879, -0.10861296529738655, -0.33581459565230276, -0.5550366373255958, -0.7629323270433763, -0.9561387846662243, -1.1313358458758538, -1.2853102396455771, -1.4150239962540319, -1.5176857323481403, -1.5908232367079715, -1.6323555818454767, -1.6406628205405622, -1.614651201029523, -1.5538117576718598, -1.4582701127961961, -1.3288253664070528, -1.1669760586080826, -0.9749313684643477, -0.7556059641890764, -0.5125972424259021, -0.2501440860261021, 0.026933275463185868, 0.31331220860269915, 0.6032647743109613, 0.890771749276886, 1.1696517390878285, 1.4337029556770973, 1.6768546585647517, 1.89332472979873, 2.0777793877679795, 2.2254906662444016, 2.3324870122582113, 2.3956922081054026, 2.4130478147227565, 2.3836144782388446, 2.307647746939477, 2.18664451553102, 2.023356845365013, 1.821770695257966, 1.5870480236449453, 1.3254317688371082, 1.0441143539418198, 0.7510715648497615, 0.45486487704964773, 0.1644165194332859, -0.1112372825174217, -0.36320839031521224, -0.583026764732436, -0.7629102942120823, -0.8960258412497024, -0.9767326853744387, -1.0007996071861187, -0.9655872307051971, -0.8701879290057378, -0.7155165975789213, -0.5043468961315981, -0.24128912540680475, 0.06729229808510752, 0.41342183046634706, 0.7877142182133222, 1.17963016747183, 1.5777799706058417, 1.9702667867623682, 2.345059453901314, 2.6903831598062524, 2.995115093768093, 3.2491714051301717, 3.443871464188315, 3.572265594835533, 3.629413149312766, 3.6125990265950696, 3.5214784796511576, 3.3581422739813984, 3.127096890151944, 2.8351574260503347, 2.4912540517141997, 2.1061561870346632, 1.6921218851398563, 1.2624830795529878, 0.8311802570945042, 0.41226262030931926, 0.019371781531572062, -0.3347716209794735, -0.6388583623588672, -0.8834382488505753, -1.0613059917388508, -1.1678081794806483, -1.2010567292433552, -1.1620374446087716, -1.0546061558997655, -0.8853692402947219, -0.6634499506251467, -0.40014674313222365, -0.10849448949060128, 0.19725611574005106, 0.5022216855258651, 0.7915092471365995, 1.0508543005938185, 1.2672473150594474, 1.4295217411179053, 1.5288773532224154, 1.5593146337951223, 1.5179589340877349, 1.4052572106813697, 1.2250351037986438, 0.9844078111335168, 0.69354439482161, 0.3652915833274774, 0.014669516169180453, -0.34174206106556515, -0.6865031971659147, -1.0020702132285253, -1.2715773006493425, -1.4796091661852366, -1.612930006143417, -1.6611350020735707, -1.6171930117399675, -1.477853124838497, -1.2438931329848368, -0.9201945278960052, -0.5156361267469114, -0.042806511963318625, 0.48245619408900936, 1.0416805046221276, 1.6145093152225234, 2.1795480904000644, 2.7152768687195685, 3.200985542399849, 3.617689750257769, 3.9489845722759345, 4.181795100596789, 4.306986859349802, 4.319804829115136, 4.220117278847341, 4.012449406981814, 3.705801555010282, 3.3132570308559113, 2.8513948750027853, 2.3395327110538164, 1.7988336430939118, 1.2513185267616778, 0.7188304389878758, 0.22200147344420143, -0.22072713415508474, -0.5939822079008353, -0.8861880046792591, -1.0901091733108366, -1.203177401424717, -1.2275822682121142, -1.1701184809631142, -1.0417940101498187, -0.8572160331494226, -0.6337834099243953, -0.39072501540214033, -0.14803205758117577, 0.07466099113709104, 0.2591884318254528, 0.3898991185949152, 0.4545790445928589, 0.44519915485142786, 0.3584450225903226, 0.19599574095504965, -0.03546790869892907, -0.32453187489651136, -0.6555849790210218, -1.009599322761645, -1.3651178153629389, -1.6993996685404877, -1.9896650688887927, -2.214373552269133, -2.3544673106744014, -2.3945110250245603, -2.323663910004602, -2.1364273495603956, -1.833122462710471, -1.4200656485562448, -0.9094259306982284, -0.3187649362062922, 0.3297223062644659, 1.0102308322516869, 1.6945833809032045, 2.3536193828830685, 2.95866294057414, 3.482991722500879, 3.9032271877084885, 4.200569444663295, 4.361807268822539, 4.380045042583033, 4.255103094653952, 3.993565346293441, 3.608467389810322, 3.1186380767706776, 2.5477272593044993, 1.9229703837666092, 1.2737561187117201, 0.6300751696804688, 0.020936134302507296, -0.5271628443932959, -0.9916200211803383, -1.354894164480719, -1.6053793090086959, -1.7379385994817493, -1.7540649137698958, -1.6616573646640405, -1.4744251485823259, -1.2109522360627711, -0.8934767745948755, -0.5464565614064689, -0.19500545032237518, 0.13670579457511006, 0.4269875001617642, 0.6580138097281866, 0.8169642736037596, 0.89685202734701, 0.8969844486227715, 0.8230239246877723, 0.6866404225123055, 0.5047725133430239, 0.2985378591701143, 0.09185642205862746, -0.0901315918768333, -0.22275700886560987, -0.2835177742039554, -0.25367336410575003, -0.11963549940797905, 0.12593601408597205, 0.4834068083335617, 0.9458637268223217, 1.4992604642264011, 2.1230132404688313, 2.791018721969495, 3.4730396669200605, 4.1363799432844965, 4.7477511881064896, 5.275219737322066, 5.69011551532569, 5.968784890281392, 6.094077186804333, 6.056469252830129], 'positive_zeros': ['1.09562289194036741743452991968047', '2.43153494763520883815560188094943', '3.91174172212997904210333341156562', '4.67455306284264714812859967926029', '6.19073272634838074832069861345034', '6.95985228656816957434545721159349', '7.87757185205050264806694714304125', '8.692806844116309086830722730783045', '10.03024078404173314466350198287288', '10.79057557818388410270027929271550'], 'prelabel': '2-468-13.10-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.2547972256488285, 'root_angle': 0.039662620906339006, 'root_number': '0.96910816115740190753274037432770452804278580362570351954 + 0.24663611247771306996017420065382328460552141688131280640*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.039662620906339006', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09562289194036741743452991968', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43153494763520883815560188095', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.91174172212997904210333341157', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.61289388268662, 'bad_primes': [2, 3, 13], 'central_character': '13.10', 'conductor': 468, 'conductor_radical': 78, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/468/4/t/g/361/1'], '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': '2-468-13.10-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-468-13.10-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.2547972256488285, 'root_angle': 0.039662620906339006, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09562289194036741743452991968', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1388867016591995277824969499112', 'Lhash_array': ['1388867016591995277824969499112'], 'factors': ['2-468-13.10-c3-0-10'], 'label': '2-468-13.10-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/468/4/t/g/361/1'}