-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '716130602330829199226080623071,1341816237464445923679997926403', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2482.695136051794, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 1]], [5, [1, 2, 1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '6240.1', 'coefficient_field': '1.1.1.1', 'conductor': 38937600, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1, -2, 1], [1, 2, 1], [1, 0, 6, 0, 49], [1, 0, 14, 0, 121], [1, -2, 1], [1, -4, 6, -68, 289], [1, -8, 46, -152, 361], [1, 8, 62, 184, 529], [1, 4, 30, 116, 841], [1, -8, 70, -248, 961], [1, 4, 78, 148, 1369], [1, 4, 86, 164, 1681], [1, -8, 70, -344, 1849], [1, -8, 102, -376, 2209], [1, 4, 110, 212, 2809], [1, 0, 46, 0, 3481], [1, -12, 158, -732, 3721], [1, 0, 126, 0, 4489], [1, 16, 198, 1136, 5041], [1, -20, 214, -1460, 5329], [1, 16, 190, 1264, 6241], [1, -8, 174, -664, 6889], [1, -12, 86, -1068, 7921], [1, -4, 166, -388, 9409], [1, 4, 174, 404, 10201], [1, -8, 190, -824, 10609], [1, -8, 102, -856, 11449], [1, 20, 286, 2180, 11881], [1, 12, 230, 1356, 12769]], 'euler_factors_factorization': [[1], [[[1, -1], 2]], [[[1, 1], 2]], [[[1, 0, 6, 0, 49], 1]], [[[1, 0, 14, 0, 121], 1]], [[[1, -1], 2]], [[[1, -4, 6, -68, 289], 1]], [[[1, -8, 46, -152, 361], 1]], [[[1, 4, 23], 2]], [[[1, 4, 30, 116, 841], 1]], [[[1, -8, 70, -248, 961], 1]], [[[1, 2, 37], 2]], [[[1, 2, 41], 2]], [[[1, -8, 70, -344, 1849], 1]], [[[1, -8, 102, -376, 2209], 1]], [[[1, 2, 53], 2]], [[[1, 0, 46, 0, 3481], 1]], [[[1, -6, 61], 2]], [[[1, 0, 126, 0, 4489], 1]], [[[1, 16, 198, 1136, 5041], 1]], [[[1, -20, 214, -1460, 5329], 1]], [[[1, 16, 190, 1264, 6241], 1]], [[[1, -8, 174, -664, 6889], 1]], [[[1, -12, 86, -1068, 7921], 1]], [[[1, -4, 166, -388, 9409], 1]], [[[1, 4, 174, 404, 10201], 1]], [[[1, -8, 190, -824, 10609], 1]], [[[1, -8, 102, -856, 11449], 1]], [[[1, 20, 286, 2180, 11881], 1]], [[[1, 12, 230, 1356, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 3, 'label': '4-6240e2-1.1-c1e2-0-3', 'leading_term': '4.59611012782371927185398175581216606421624468441648570268880000000000000000000000000000000', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/6240/2/a/br', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0234375', 'prec': 30}, 'plot_values': [4.596110127823719, 4.581755017861182, 4.554107925863393, 4.50279870361344, 4.428828265554028, 4.33532326818303, 4.222496739674019, 4.090142454742258, 3.938964372189023, 3.7699220201546777, 3.583894599608484, 3.3818548023965747, 3.1649761109929306, 2.934576424007611, 2.6921176682015533, 2.4391963987343286, 2.177575440354377, 1.9091480382581099, 1.6359625224137935, 1.3601792664753711, 1.0840946585300562, 0.8100872369705052, 0.5406359004632609, 0.2782585365319844, 0.025522737771861728, -0.21502057349398646, -0.44083557179770133, -0.649469432923448, -0.8385603431376207, -1.005903178040936, -1.1494663616583323, -1.2674514180306875, -1.3583166580881991, -1.4208268748533683, -1.4540806076115935, -1.4575467335212817, -1.431091001997702, -1.3749970820101807, -1.2899872985779788, -1.1772268066050684, -1.0383331024948756, -0.8753633662109798, -0.6908074463646069, -0.4875599651734544, -0.26889213114540395, -0.038411829893371774, 0.19998919413664634, 0.4421824665236672, 0.6838820220548149, 0.9206925928988496, 1.148215012758373, 1.3620882973817365, 1.5581186893432284, 1.732307960164462, 1.8810012775240628, 2.000894174480175, 2.0891923265180483, 2.143590443684869, 2.162435383244696, 2.1446717414832586, 2.089998717201662, 1.9987793596860757, 1.872181417155431, 1.712049910691235, 1.5210229640702235, 1.3023704239267102, 1.060077402248883, 0.798654793572628, 0.5231858989809741, 0.23911760254396922, -0.04773118765554751, -0.33138656436403846, -0.6057468029715153, -0.864794904288312, -1.102654907329722, -1.3137868051370498, -1.4930618588573572, -1.6359275275800946, -1.7384887226927728, -1.7976324784359823, -1.8111002397642997, -1.7775653059656888, -1.6966807843830853, -1.5691071452763907, -1.3965215745224118, -1.1815979321293753, -0.9279659203234802, -0.6401508807425498, -0.32347530632261723, 0.01602928575859149, 0.3717807580937879, 0.7367462516746218, 1.1036569371282547, 1.4651010056564182, 1.8137853507852084, 2.142602231996603, 2.4449232536717136, 2.71462156271303, 2.9463795396518924, 3.13565172273792, 3.2789654780984123, 3.3738150229809443, 3.418934368086838, 3.41411941127223, 3.3604547885357694, 3.260068395062481, 3.116298319329005, 2.9333915445005845, 2.7166034770308154, 2.4718591459414347, 2.205785329936366, 1.9253574923058716, 1.6378723276251992, 1.3506062635724443, 1.07074345908993, 0.8050715137031413, 0.5598856331760288, 0.34074405443939815, 0.1523724601450276, -0.0015042598327949003, -0.11823276896081385, -0.19631466999710356, -0.23543046261410036, -0.23643903610624922, -0.20133837333138818, -0.13319187900676002, -0.03601727982575707, 0.08534060472646893, 0.225391947873706, 0.3781562605762725, 0.537404969071162, 0.6968126099728151, 0.8502407031561628, 0.991855360534302, 1.1164267602887101, 1.2193864264042285, 1.2971133349328843, 1.3469113978577865, 1.3672538214647947, 1.3576714166164827, 1.3189314354627937, 1.2528390378826293, 1.1623350585643013, 1.0512248023067474, 0.9241901062596912, 0.7864700209627461, 0.6437947542908768, 0.5020502268042769, 0.36715335234049756, 0.24473575492758012, 0.13998962402110895, 0.05740436452616547, 0.0006184034141292061, -0.027763837489468566, -0.026277460349726098, 0.005316975371090458, 0.06600334742914808, 0.15352431744428166, 0.2644502604445914, 0.3942823010302736, 0.5376306143618289, 0.6883806555813617, 0.8399753678223325, 0.9856081457544009, 1.11858732379158, 1.2325131777083698, 1.3216889221704196, 1.3812387562952593, 1.4075197476804984, 1.398143991940848, 1.35234202384146, 1.2708641004581769, 1.1562492249988137, 1.012596985373648, 0.8457069916633987, 0.6627314458341442, 0.4721667975826698, 0.28341562143162435, 0.10663359279608076, -0.04775550485080372, -0.16933158610893673, -0.24815675793610895, -0.27511896026977317, -0.24234862853780334, -0.1435711644327917, 0.025587070319671668, 0.26730875159356515, 0.5814244782308685, 0.9652552283452255, 1.4136091631139742, 1.9188150565690358, 2.47086504088358, 3.057676775578346, 3.665344788160383, 4.2786414567901305, 4.881317696567105, 5.456821722969816, 5.988574989282174, 6.460857465110821, 6.85897975119981, 7.1702587125201065, 7.384013118819997, 7.4925379012357025, 7.490868426482406, 7.377658277467492, 7.154684592093036, 6.827544363847008, 6.4049068202663575, 5.898966145734367, 5.324482119504176, 4.6989602817621225, 4.041553897570898, 3.372981638595864, 2.714387439586856, 2.087045326313994, 1.5112848478995156, 1.0060669211640378, 0.5880788014776357, 0.27128836526415834, 0.06629363134406763, -0.02002830689480993, 0.015135484326099825, 0.17038551738049207, 0.44008488250153793, 0.8144973881476908, 1.2800463167634517, 1.8197843474416782, 2.4138588823779497, 3.040312325121514, 3.6756433115591918, 4.295887147721134, 4.8771434639190385, 5.396843145962523, 5.834112295050969, 6.171100630917863, 6.393070131834763, 6.4896459482157605, 6.454553817036509, 6.286660894989306, 5.989334384651285, 5.571166304486055, 5.0449799899307495, 4.428176493312401, 3.7414677887159886, 3.0088373184044097, 2.2561208583049783, 1.510631822713586, 0.7997360574907368, 0.1502451856514449, -0.4128643893595857, -0.8671477683570958, -1.193696718092855, -1.3777642451584207, -1.409401559227122, -1.2838541681699347, -1.0017928110184975, -0.5693524982904912, 0.0020185116791391028, 0.6959571052289057, 1.4916342593215732, 2.364609856183638, 3.287446831199089, 4.230975868135352, 5.164912489092368, 6.059425339314026, 6.88558868632692, 7.6171032918163215, 8.230437247558216, 8.706525864059234, 9.030497429825877, 9.193181896003377, 9.190378748312762, 9.024033297786772, 8.701072317614043, 8.23415717030806, 7.640178647415678, 6.940560236299152, 6.15955637062765, 5.324146870842755, 4.4623140951385265, 3.6026303068187926, 2.7726938114820125, 1.9985550926955804, 1.3034689181012606, 0.7073255588203191, 0.22582846150771957, -0.1299094447449524, -0.3537172144066427, -0.44447638413717927, -0.40602732068455716, -0.24691049144310193, 0.020080137952336232, 0.3785375869740664, 0.8090981120564203, 1.290411653251999, 1.7998368110953769, 2.3146350625597356, 2.812533793916067, 3.2730025957177626, 3.677541573992579, 4.010887167160816, 4.260933637873156, 4.419731076022949, 4.483012784144122, 4.450886377726574, 4.327007705312004, 4.118920180569023, 3.8369754327894054, 3.494336409297656, 3.1057861408968255, 2.687465935783192, 2.2557297082229852, 1.826729868251943, 1.4154632542877827, 1.035336932175269, 0.6975153713826835, 0.4105931341778606, 0.1802983998641311, 0.00937086965793997, -0.10238591291315313, -0.15796944206950106, -0.1628440981483637, -0.12455178610685692, -0.052208428951278724, 0.044083661689003246, 0.15377257248772896, 0.266545905529916, 0.37276698282065096, 0.4641479385710043, 0.5339785660517578, 0.5776692335288427, 0.5927119717792166, 0.5790058660458254, 0.5385464455394284, 0.47549120600713607, 0.3956288479695415, 0.30619690645117686, 0.215226061851798, 0.13117466235760525, 0.0622666890284349, 0.016048557003291695, -0.001162175369464817, 0.015327601399328612, 0.06823711528084579, 0.15808384773317358, 0.28308185180715706, 0.4391718243539892, 0.6201577359941316, 0.8180358517074877, 1.0233060712143918, 1.2255818524127597, 1.413970877516075, 1.5778905963015428, 1.7073923284151944, 1.794063380960553, 1.8311742234998758, 1.8145271514173684, 1.7423372808809485, 1.615894543995028, 1.439140258962954, 1.2190434458636852, 0.9648957107353432, 0.6883585283352074, 0.4025578670809126, 0.12182574335049272, -0.13927979797074988, -0.36645092747469865, -0.5465390546238049, -0.6681114349064593, -0.7221527648524599, -0.7025408521337637, -0.6064420836869615, -0.4345523813738381, -0.19114755155007843, 0.11602568735410435, 0.47601306881118655, 0.8751638786464953, 1.297609444378206, 1.7261528350835154, 2.142813722979804, 2.5299994160374997, 2.870945097034617, 3.1510119996613013, 3.3578633958982653, 3.4827075844388986, 3.520094078485611, 3.468926307022139, 3.3318317080365496, 3.115811347974602, 2.831219119900455, 2.491985484985793, 2.1143188002736046, 1.7165248588836075, 1.317601738173633, 0.9367591694246005, 0.5921047339522367, 0.3000306030139515, 0.07417691562245188, -0.07511537392110595, -0.14142751629620223, -0.12255375104106637, -0.02065253563434474, 0.15786161780474764, 0.40260458203382, 0.6997938980362642, 1.0328504802404948, 1.3834031235096427, 1.7320167617135374, 2.059509371282948, 2.3475878495766183, 2.5802875332164072, 2.7443099158706503, 2.830363037002284, 2.833050509355946, 2.7519040354186726, 2.590760671503433, 2.358335718309433, 2.0671280088970043, 1.7334723255036293, 1.376110229439077, 1.0157685284302083, 0.6736055639333538, 0.37046455757561586, 0.12543660775393994, -0.04498637381822887, -0.12800829638933006, -0.11521897001390577, -0.003191337392806035, 0.2062237345977682, 0.5058586230548461, 0.8834986162419992, 1.322344362799466, 1.8019080713791553, 2.2988112709156114, 2.788244935675078, 3.244857715672678, 3.6445999447697695, 3.9654260000691472, 4.189256334960822, 4.302241789666257, 4.296542510805739, 4.169979014648148, 3.9273514897117807, 3.57941839417437, 3.1435617507188383, 2.6421666909717128, 2.102563735933979, 1.5550053793531704, 1.0319614805548967, 0.5659761554427478, 0.1885288943289763, -0.07191250877018963, -0.19115234608458403, -0.15073325710339422, 0.06103712585873792, 0.44829507365154164, 1.0071574561958172, 1.7256665039265695, 2.584128498894248, 3.5557038947306103, 4.607646416893068, 5.70230934055605, 6.799220150134723, 7.856176157892645, 8.831935108390011, 9.687037917328484, 10.386779886225566, 10.901434332503898, 11.209115784952878, 11.295180667879203, 11.154614326491304, 10.790535169124666, 10.215828413723628, 9.450849488317795, 8.524171624035658, 7.469739607552021, 6.326767539238935, 5.136704056205032, 3.9424772143190454, 2.7856743662061003, 1.7054511824992837, 0.7362940495040851, -0.09303427072442855, -0.7608885577288388, -1.2534063733381289, -1.5649547314135812, -1.69814488793151, -1.6634057134147262, -1.4782298045129993, -1.1661096128779422, -0.7550619591432232, -0.2762772183516648, 0.2378775533538921, 0.7551026914560538, 1.245375206141518, 1.681727984244411, 2.042319501170263, 2.310498949988208, 2.4764204389009485, 2.536295787687135, 2.4933274675785904, 2.3562464035772503, 2.1395217432666236, 1.8613520333828266, 1.5431510545244664, 1.2075545791903164, 0.8776830485206633, 0.5747807725525408, 0.3168745498389589, 0.11866936393363058, -0.008679841683038267, -0.06165122988975523], 'positive_zeros': ['0.56492743521116634883363645383918', '1.05850637172645494585055398586219', '1.63672031196530829095024112529266', '2.08485894192586346884349811533768', '2.78880310297802647189884345659179', '2.96053767648405298717827732618672', '3.56283926799386805248613475985734', '3.63002299131087803642245995445398', '4.18758962183782718635967707455942', '4.33294874046153155615714486841683', '5.14687088372028335536484851135206', '5.17551722681849086834980266009901', '5.81837700760266866724089808489175', '6.02336281164342769701599003632258', '6.69353084831137070819910273189503', '6.81880733544531876910030350907427', '7.45470429801986328900002231543055', '7.58357159965533610354586005159217', '7.986670566002030683395853942275247', '7.999009734022219590190478181539692'], 'prelabel': '4-6240e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2131860536179329434, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56492743521116634883363645384', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.05850637172645494585055398586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.63672031196530829095024112529', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2482.695136051794, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 38937600, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, -2, 0, 0, 0, 3, 0, 0, 0, 2, 0, -4, 0, 4, 0, 8, 0, 0, 0, -8, 0, 3, 0, 4, 0, -4, 0, 8, 0, 0, 0, 0, 0, -4, 0, 4, 0, -4, 0, 8, 0, -6, 0, 8, 0, -6, 0, 8, 0, -4, 0, 0, 0, 16, 0, 0, 0, 12, 0, 0, 0, -4, 0, 0, 0, -16, 0, -16, 0, 20, 0, 6, 0, 0, 0, -16, 0, 5, 0, 8, 0, -8, 0, -8, 0, 12, 0, 0, 0, 16, 0, -16, 0, 4, 0, 0, 0], 'euler11': [1, 0, 14, 0, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, -4, 6, -68, 289], 'euler19': [1, -8, 46, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, 4, 30, 116, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, -8, 70, -248, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, -8, 70, -344, 1849], 'euler47': [1, -8, 102, -376, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 0, 46, 0, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 0, 126, 0, 4489], 'euler7': [1, 0, 6, 0, 49], 'euler71': [1, 16, 198, 1136, 5041], 'euler73': [1, -20, 214, -1460, 5329], 'euler79': [1, 16, 190, 1264, 6241], 'euler83': [1, -8, 174, -664, 6889], 'euler89': [1, -12, 86, -1068, 7921], 'euler97': [1, -4, 166, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, 0, 6, 0, 49], [1, 0, 14, 0, 121], [1, -2, 1, 0, 0], [1, -4, 6, -68, 289], [1, -8, 46, -152, 361], [1, 8, 62, 184, 529], [1, 4, 30, 116, 841], [1, -8, 70, -248, 961], [1, 4, 78, 148, 1369], [1, 4, 86, 164, 1681], [1, -8, 70, -344, 1849], [1, -8, 102, -376, 2209], [1, 4, 110, 212, 2809], [1, 0, 46, 0, 3481], [1, -12, 158, -732, 3721], [1, 0, 126, 0, 4489], [1, 16, 198, 1136, 5041], [1, -20, 214, -1460, 5329], [1, 16, 190, 1264, 6241], [1, -8, 174, -664, 6889], [1, -12, 86, -1068, 7921], [1, -4, 166, -388, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6240/2/a/br'], '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': '4-6240e2-1.1-c1e2-0-3', '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': '4-6240e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2131860536179329434, 'z1': {'__RealLiteral__': 0, 'data': '0.56492743521116634883363645384', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '716130602330829199226080623071,1341816237464445923679997926403', 'Lhash_array': ['716130602330829199226080623071', '1341816237464445923679997926403'], 'label': '4-6240e2-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/br'}