Formats: - HTML - YAML - JSON - 2026-05-02T20:54:52.872747
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -5, 'Lhash': '636542129197126536669216133034', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.6666666666666667, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.806954898944674, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '640000.1', 'coefficient_field': '1.1.1.1', 'conductor': 640000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 0, 5, 0, 9], [1], [1, 0, 14, 0, 49], [1, 0, -19, 0, 121], [1, 0, 10, 0, 169], [1, 0, 31, 0, 289], [1, 0, -11, 0, 361], [1, 0, -2, 0, 529], [1, 0, -10, 0, 841], [1, 8, 78, 248, 961], [1, 0, 10, 0, 1369], [1, 6, 91, 246, 1681], [1, 0, 22, 0, 1849], [1, 0, 46, 0, 2209], [1, 0, -38, 0, 2809], [1, 0, -10, 0, 3481], [1, 0, -122, 0, 3721], [1, 0, 85, 0, 4489], [1, -24, 286, -1704, 5041], [1, 0, 71, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, -59, 0, 6889], [1, 6, 187, 534, 7921], [1, 0, 194, 0, 9409], [1, 0, -10, 0, 10201], [1, 0, 158, 0, 10609], [1, 0, 205, 0, 11449], [1, 0, -26, 0, 11881], [1, 0, 79, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'id': 9505174, 'index': 3, 'label': '4-800e2-1.1-c1e2-0-3', 'leading_term': '1.07579999677', '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/2.2.40.1/400.1/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [1.0757999967746568, 1.0664041622766804, 1.0380870018887882, 0.9904722143890716, 0.9229744849983345, 0.8348609366369131, 0.7253344754308747, 0.5936362876813628, 0.4391638972602477, 0.2616003227938539, 0.061049006059747245, -0.16183164679527268, -0.4057010117641646, -0.668423775228014, -0.9469801130903518, -1.2374064726596221, -1.5347746262219084, -1.8332159506345174, -2.125996689032989, -2.4056482382939333, -2.6641542770045126, -2.893193835700298, -3.0844362857738057, -3.229880799610926, -3.322229268366439, -3.355278150830251, -3.324311495350697, -3.22647467768939, -3.0611064907904915, -2.8300063595220006, -2.537613858813532, -2.191079563330363, -1.800209657761789, -1.3772717072612175, -0.9366554411691277, -0.4943901378081764, -0.06752889195908982, 0.3265807379387515, 0.6711110083419535, 0.9506159389416651, 1.1518964126939195, 1.26481861327906, 1.283033276759829, 1.2045436356749035, 1.0320738178552256, 0.7731970006442134, 0.44019374428330066, 0.0496252967131028, -0.3783763441578505, -0.8210810972342543, -1.2543563509093578, -1.6540269424393443, -1.9973246254268295, -2.264339177943251, -2.4393753002688525, -2.5121174724065387, -2.4785097773648945, -2.3412697052096783, -2.109973982347904, -1.8006798084985483, -1.4350752510085807, -1.0391861334134314, -0.6417013090952626, -0.2720111667586429, 0.04191713000299047, 0.275682445598322, 0.41045285019813077, 0.43467016521642615, 0.3453077418553695, 0.14855664384522058, -0.1401496288575245, -0.4968169161380086, -0.8902718172321578, -1.2841805475248638, -1.639588457882946, -1.9178141971248956, -2.083493068145573, -2.1075385592988223, -1.9697825367009023, -1.6610651828090848, -1.1845760133826888, -0.5562961020231986, 0.19554380123505105, 1.0319986336087097, 1.9058656384462238, 2.764909389116422, 3.5556297831185746, 4.2272898916606225, 4.735883810986455, 5.047713455904169, 5.142260179937727, 5.014082451208514, 4.6735422438179715, 4.146255466693266, 3.4712685197909856, 2.6980750493806602, 1.8826942247173037, 1.0831242472563758, 0.3545529655736238, -0.2552562483716914, -0.7099858937782043, -0.9878150648041836, -1.0831981814856277, -1.007178696648025, -0.786175910363979, -0.45932553371537616, -0.0745952243923773, 0.3159788489861528, 0.6614922778976625, 0.9173109062836643, 1.049639512377219, 1.039053407267025, 0.8826148172729534, 0.5943266279741792, 0.20383693989149085, -0.2465161721247689, -0.7060567056775443, -1.1211033892233837, -1.4407507763290321, -1.622501613212298, -1.6371484145151118, -1.472360553607317, -1.1345514495211748, -0.6487686934531288, -0.056552450966251215, 0.5880759940469187, 1.2241258065715712, 1.7901021400898844, 2.2307551194684803, 2.503385167190898, 2.5829979686993045, 2.4657008629839585, 2.16990160991476, 1.7350947537888648, 1.2182777765362822, 0.6883018576523382, 0.21870141800760737, -0.12026489053054337, -0.2695146149112004, -0.1881115890775716, 0.14149446546477548, 0.7105953259304483, 1.484114283175309, 2.4033605769568207, 3.391434458641872, 4.360766782666861, 5.222022893129933, 5.893425335085354, 6.309476399697655, 6.428101629353054, 6.235388344468986, 5.7473450276962685, 5.008431987607013, 4.086975645821119, 3.067936951828293, 2.0438167764261013, 1.1047096354987362, 0.3286324359581976, -0.22675964457603637, -0.5301042648698412, -0.579207975736126, -0.4005179673345065, -0.04524165854341202, 0.41743111929430643, 0.9091937673142816, 1.3525043003125317, 1.6802746029497495, 1.8441704121680957, 1.820484159172152, 1.6128342606305217, 1.2513346563905487, 0.7883205602069779, 0.29115585083605716, -0.16697157991573708, -0.5170878648948006, -0.703999646066625, -0.6941236735716747, -0.4805187083163369, -0.08440602926167044, 0.4470869192767436, 1.0467316930430681, 1.6358493927292843, 2.1347088125613114, 2.4733152808506076, 2.601147350201735, 2.4945020627078502, 2.160394299326334, 1.636389151715158, 0.9862749911580828, 0.2920412588372387, -0.35686453306446525, -0.8756311915535179, -1.195937268006777, -1.275955265988093, -1.10709796015595, -0.7164929225025065, -0.16471411298435643, 0.4610784511598545, 1.0578197900534414, 1.5197361403569463, 1.7523761703170522, 1.68563801495436, 1.2840364280868573, 0.5527758638307572, -0.4612823334119194, -1.6740127420345556, -2.9733254503545004, -4.232256950097404, -5.324210718508797, -6.138390419891832, -6.593411405432548, -6.647290251993105, -6.302473484714882, -5.605216716660947, -4.639378181598287, -3.5154439817822296, -2.356252151497463, -1.2813371282564063, -0.392009340384069, 0.24081419894718115, 0.5843930963430158, 0.6465378425651488, 0.47231274012950447, 0.13560697937324398, -0.27315726427456133, -0.6613594199722502, -0.948445575016721, -1.0780246040125026, -1.0260153152623026, -0.8036474302038132, -0.45488337612624297, -0.04866303574571694, 0.3328429131092643, 0.6081708195752632, 0.7105413157803983, 0.5996927673864814, 0.2696862679610079, -0.24861289221617125, -0.8908753732645087, -1.568079813296483, -2.1794810731062646, -2.627864324408697, -2.8347774123539957, -2.753380891757089, -2.376862217702951, -1.7409893492566502, -0.9202412103252605, -0.017922064448112743, 0.8484015333636581, 1.5640521546348225, 2.0344421375391923, 2.199710653705213, 2.0445077049255778, 1.6013161066877775, 0.9466450101754487, 0.19049523264327176, -0.5394724410984147], 'positive_zeros': ['0.50214320024975548831087623862485', '1.76584322210679783680166776157462', '2.30075939793565868913691142543792', '3.11777778252421033443591535342612', '3.39596266268224950048168817989912', '3.99182667831283863365527453643124', '4.81215981119790443785594662350046', '5.18496433514385854159986925342025', '5.58899525120293222298727729519102', '6.05906706107540846561151799389111', '6.66925180190664287671492954194377', '6.81912952132796605113592459464162', '7.69226238293556567279711329602497', '7.915327623218048963038712631795704', '8.428486400747804793151703529999984'], 'prelabel': '4-800e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.527455669582047, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2285102114230750619, 'z1': {'__RealLiteral__': 0, 'data': '0.50214320024975548831087623862485', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.76584322210679783680166776157462', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.30075939793565868913691142543792', 'prec': 113}}