Formats: - HTML - YAML - JSON - 2026-03-10T11:18:35.583784
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '2341239366490173256261476279073', 'a10': [0.5896101138664923, 1.4742440134039323], 'a2': [-1.3434516260986231, -0.44174396241823777], 'a3': [1.7317863678756165, -0.03026509607088658], 'a4': [1.609724543334069, 1.1869232892600612], 'a5': [-0.721675529145276, -0.8600594045462102], 'a6': [-2.3399406354392474, -0.7243464796767991], 'a7': [1.3179259951947067, -0.4796858332165353], 'a8': [-1.638270858428791, -2.3056601211850354], 'a9': [2.99816804791964, -0.10482536159601452], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7247686836596572, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3434516260986231, 0.44174396241823777]]], [3, [[1.0, 0], [-1.7317863678756165, 0.03026509607088658]]]], 'bad_primes': [2, 3], 'central_character': '216.133', 'coefficient_field': 'CDF', 'conductor': 216, 'conductor_radical': 6, 'conjugate': '1900468864378019983441873690036', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3434516260986231, 0.44174396241823777]], [[1.0, 0], [-1.7317863678756165, 0.03026509607088658]], [[1.0, 0], [0.721675529145276, 0.8600594045462102], [-0.8682408883346517, 4.924038765061041]], [[1.0, 0], [-1.3179259951947067, 0.4796858332165353], [5.362311101832846, -4.499513267805775]], [[1.0, 0], [-1.058158696987159, 1.2610644286692547], [-1.9101299543362338, -10.832885283134289]], [[1.0, 0], [0.6710769719656189, -0.11832897628967678], [12.216004070216808, -4.446261863233693]], [[1.0, 0], [-0.9074431142879434, -1.5717375789252495], [-8.5, 14.722431864335457]], [[1.0, 0], [-2.9677687397937733, -1.7134420808124915], [9.5, 16.454482671904334]], [[1.0, 0], [3.6227764898770825, 1.318582807714652], [17.619022191736494, 14.784115022790404]], [[1.0, 0], [-3.9239465581275415, -0.6918976490560025], [27.251086002791343, 9.918584156444393]], [[1.0, 0], [6.214683406064264, 2.2619597751954905], [23.747377736688318, 19.92641590028272]], [[1.0, 0], [-3.8353170585138074, 2.2143213361605105], [18.5, -32.04293994002423]], [[1.0, 0], [-0.9522169993985836, -5.400290957020115], [-38.527397452222246, 14.022825876352417]], [[1.0, 0], [7.2601725920982725, -8.652336769487134], [-7.466871639678005, -42.34673337952495]], [[1.0, 0], [11.546905910932631, -4.202730049451946], [36.00408882659197, -30.211017655267348]], [[1.0, 0], [0, -6.897410969477711], [-53.0, 0]], [[1.0, 0], [6.789207631428473, 8.09106258562291], [-10.24524248234889, 58.10365742772028]], [[1.0, 0], [-1.2408359225061196, -3.4091686783337094], [-46.728711030257664, 39.2100441908789]], [[1.0, 0], [11.942498336100497, -2.1057846737204673], [62.95940559265586, -22.915349602819806]], [[1.0, 0], [-6.803546104196448, -11.784087524105546], [-35.5, 61.48780366869514]], [[1.0, 0], [-4.738225878235825, 8.206847958842113], [-36.5, -63.21985447626402]], [[1.0, 0], [-1.5929021915221369, 9.033797239208702], [-74.23571704208676, -27.01959132272783]], [[1.0, 0], [-1.2985286386211403, -0.2289656342115391], [77.9944875252304, 28.387671896030504]], [[1.0, 0], [3.5233927083646277, -6.102695185905247], [-44.5, -77.07626093681505]], [[1.0, 0], [6.332749132635892, 5.313807461533017], [16.843873233692243, 95.52635204218419]], [[1.0, 0], [-6.041369296569847, -16.59852572491211], [-77.37048875501678, 64.92154857834048]], [[1.0, 0], [2.9803834416011052, -2.5008386466143597], [17.885762299693827, -101.43519856025743]], [[1.0, 0], [0, 4.164093895229031], [-107.0, 0]], [[1.0, 0], [0, 20.608205226822403], [-109.0, 0]], [[1.0, 0], [-2.032053769858704, 1.7050955688208398], [19.62224407636313, -111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9685062, 'index': 21, 'label': '2-6e3-216.133-c1-0-21', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/216/2/t/a/133/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1273321787253168, 1.1593870344032957, 1.195830059023818, 1.234394101576198, 1.2709208724749885, 1.2997985551017481, 1.3144686496639826, 1.3079394231804202, 1.2732958640821228, 1.2042220706435276, 1.095551322580982, 0.9438435756667212, 0.7479702611696188, 0.5096678462137372, 0.23400717852358602, -0.07028357410896068, -0.3907076685687069, -0.7111616030103116, -1.0124198160916342, -1.2729725047322207, -1.4702195573389565, -1.5819898823597167, -1.5883173738479817, -1.4733655301426716, -1.2273563104831857, -0.8483297339800623, -0.3435437139844523, 0.26967697284468667, 0.9638144864482217, 1.7018856286644857, 2.439092618992218, 3.125385840428703, 3.708834507576326, 4.139603740479409, 4.374244735476533, 4.379929969273255, 4.138218982819462, 3.6479321447546296, 2.926746820672156, 2.0112151723853344, 0.9550325799300665, -0.17444832481935924, -1.30127533592534, -2.347153387815185, -3.238357802080186, -3.912635021488685, -4.325359365555421, -4.454231505551569, -4.301908382033059, -3.8961421499770883, -3.287263104854677, -2.543143206481346, -1.7420886952252417, -0.964392977343402, -0.2834944870158667, 0.24220638602048963, 0.5758365048277929, 0.7059678226868195, 0.6473726665962011, 0.43841256599458345, 0.13529970285249798, -0.19608901215034555, -0.48978943100012823, -0.6894123647837759, -0.7565041758930515, -0.6763373159264453, -0.46017594797695055, -0.14353970136848204, 0.21942858670289683, 0.5647785987181565, 0.8295006794100878, 0.9625746791494008, 0.9345377613209672, 0.7439126504303688, 0.4192368533483576, 0.01606659753010474, -0.3908868567056349, -0.7195118036853032, -0.8942422822903867, -0.8599979721844269, -0.5937469457370782, -0.11152954497427968, 0.5306296792556089, 1.2425933530915805, 1.9123478907247704, 2.4230778808065607, 2.672607523623813, 2.592134926216834, 2.1610520133113513, 1.4150413874712942, 0.44554685939365146, -0.6099873593526289, -1.5862134683630147, -2.3139560545186835, -2.646740772729668, -2.4855934555850974, -1.797934739369237, -0.627110780270089, 0.909551094257317, 2.6344831134359463, 4.333785638423882, 5.787893394007504, 6.804295142008904, 7.247049090142267, 7.058159918456056, 6.2670721564215235, 4.986421569629017, 3.3944697581540377, 1.7069388442431288, 0.14285376168497468, -1.1098663624870468, -1.923182320877076, -2.247096644743429, -2.1140540302759994, -1.6288738037188504, -0.9461300005580793, -0.23921184953894548, 0.33313478130436536, 0.6564834531662932, 0.6810085115853458, 0.4285365947678046, -0.014919471042763702, -0.5195932271906548, -0.9412334489166785, -1.1532775306475371, -1.0753516679134296, -0.6921879074892626, -0.058927054437158635, 0.7084855134198986, 1.456045364607886, 2.0230518003057734, 2.2756840901651603, 2.135799662874235, 1.5988236926009864, 0.7367665141837685, -0.31454396039914734, -1.381615704461222, -2.2875569588834606, -2.887362367602102, -3.096795810060892, -2.908697727778587, -2.393155670648371, -1.6814122168354773, -0.9369139782060265, -0.3197556482518617, 0.04770306401256109, 0.10644460683311213, -0.1280999654315296, -0.5719662061242236, -1.0942734431594316, -1.5496028538856166, -1.813628329892271, -1.8136015684992615, -1.5463376530353512, -1.079148117958115, -0.5331310804511472, -0.052463924661361704, 0.23313573503349067, 0.24367350244775113, -0.02707496484359188, -0.505344940940052, -1.0515628270436528, -1.4926277432033377, -1.6654192173211313, -1.4614788489309212, -0.8618718254457134, 0.04712488868201707, 1.0828823172699604, 1.9996972756687061, 2.5405433922925416, 2.496578959319242, 1.7611467075419172, 0.3653942581800169, -1.513953770026306, -3.5783640652520776, -5.459562440098772, -6.790116279140583, -7.278115754674125, -6.7699654572333, -5.287267438252943, -3.0289699407427544, -0.3372984156019097, 2.366130535980057, 4.66096738540632, 6.208654744795851, 6.815775465336357, 6.4668593037703905, 5.319991873683357, 3.666799255573557, 1.8662491764736402, 0.267395082815851, -0.8616298946019996, -1.3828890054950405, -1.306095609510382, -0.7718027180423466, -0.0059580302503424425, 0.7419941756388211, 1.2618165352938777, 1.4307615254979416, 1.2363568449917128, 0.7694049575489413, 0.19059402028790973, -0.31925938157462874, -0.6114315867976137, -0.6098937254342905, -0.32973642209582205, 0.13087542774863614, 0.6221922011167914, 0.9883811468068512, 1.1138387464737067, 0.9570052659040766, 0.5619672901218257, 0.0444622031698334, -0.44376775642404914, -0.7620161132343342, -0.8252932212336288, -0.6332466267488617, -0.2741190483935857, 0.09849011383685698, 0.3104415611247021, 0.22128693437380878, -0.2275903775290434, -0.9854910092501211, -1.8950087024216515, -2.7261081366783158, -3.234185489066876, -3.227408313577944, -2.6251494329524756, -1.4907275630680261, -0.027786941044686847, 1.4609819367079875, 2.64389011882866, 3.2419306836815314, 3.100996369378311, 2.2351285743098757, 0.8282252938425219, -0.8077631780142794, -2.3085941360405973, -3.348531735424938, -3.722690998657275, -3.399032862245339, -2.5256564978605813, -1.3906470297005826, -0.34438685430263644, 0.295477882862937, 0.3311611438444821, -0.2596419488919019, -1.3151399062992952, -2.530881200788917, -3.5407685514530933, -4.016266370506301, -3.7571455235436813, -2.7490225660220067, -1.1716453591554639, 0.6449234961080901, 2.3049272711422337, 3.449823660904214], 'positive_zeros': ['1.84691220598850628783022992562321', '3.32240870083796185829812174094853', '5.10589054442774434488223181645804', '6.81211494041398387867793564748939', '7.55087413373891202213550619237152', '8.425151418303016439196741954115522', '9.379797282576025705907445944220383', '10.14864434981969769536651644357360', '11.30291930979233041125860578884215', '12.17891110336714584896969872579888'], 'prelabel': '2-6e3-216.133-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3133044900782367, 'root_angle': 0.09703961709082123, 'root_number': '0.8198095932475237 + 0.5726362115857936*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0970396170908', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84691220598850628783022992562', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.32240870083796185829812174095', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.10589054442774434488223181646', 'prec': 103}}