-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1077699426260079394165425513717,2233562367300867318905389137486,2427619738104058915695276448129,3765229156015716436833622544082', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3955029613605165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2, 0, 1]], [5, [1, 0, 8, 0, 25]], [17, [1, 0, 2, 0, 289]]], 'bad_primes': [2, 5, 17], 'central_character': '170.1', 'coefficient_field': '1.1.1.1', 'conductor': 835210000, 'conductor_radical': 170, 'degree': 8, 'euler_factors': [[1, 0, 2, 0, 1], [1, 0, -4, 0, 22, 0, -36, 0, 81], [1, 0, 8, 0, 25], [1, 0, -8, 0, 114, 0, -392, 0, 2401], [1, 0, -44, 0, 726, 0, -5324, 0, 14641], [1, 0, 20, 0, 438, 0, 3380, 0, 28561], [1, 0, 2, 0, 289], [1, -8, 100, -488, 3094, -9272, 36100, -54872, 130321], [1, 0, 88, 0, 2994, 0, 46552, 0, 279841], [1, 0, -80, 0, 3282, 0, -67280, 0, 707281], [1, 0, -88, 0, 3858, 0, -84568, 0, 923521], [1, 0, 112, 0, 5874, 0, 153328, 0, 1874161], [1, 0, -20, 0, 3462, 0, -33620, 0, 2825761], [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], [1, 0, -188, 0, 13254, 0, -415292, 0, 4879681], [1, 0, -140, 0, 10518, 0, -393260, 0, 7890481], [1, 48, 1100, 15408, 143574, 909072, 3829100, 9858192, 12117361], [1, 0, -208, 0, 18258, 0, -773968, 0, 13845841], [1, 0, 20, 0, 9078, 0, 89780, 0, 20151121], [1, 0, -248, 0, 25458, 0, -1250168, 0, 25411681], [1, 0, 148, 0, 16134, 0, 788692, 0, 28398241], [1, 0, -280, 0, 32082, 0, -1747480, 0, 38950081], [1, 0, -260, 0, 30678, 0, -1791140, 0, 47458321], [1, -48, 1220, -19728, 222054, -1755792, 9663620, -33838512, 62742241], [1, 0, 388, 0, 56454, 0, 3650692, 0, 88529281], [1, -24, 620, -8136, 106134, -821736, 6324620, -24727224, 104060401], [1, 0, -124, 0, 25062, 0, -1315516, 0, 112550881], [1, 0, 364, 0, 56022, 0, 4167436, 0, 131079601], [1, 0, -400, 0, 63762, 0, -4752400, 0, 141158161], [1, 0, 52, 0, 26214, 0, 663988, 0, 163047361]], 'euler_factors_factorization': [[[[1, 0, 1], 2]], [[[1, 0, -2, 0, 9], 2]], [[[1, 0, 8, 0, 25], 1]], [[[1, 0, -4, 0, 49], 2]], [[[1, 0, -11], 4]], [[[1, -4, 13], 2], [[1, 4, 13], 2]], [[[1, 0, 2, 0, 289], 1]], [[[1, -2, 19], 4]], [[[1, 0, 44, 0, 529], 2]], [[[1, 0, -40, 0, 841], 2]], [[[1, 0, -44, 0, 961], 2]], [[[1, 0, 56, 0, 1369], 2]], [[[1, 0, -10, 0, 1681], 2]], [[[1, 0, -50, 0, 1849], 2]], [[[1, 0, -47], 4]], [[[1, 0, -70, 0, 2809], 2]], [[[1, 12, 59], 4]], [[[1, 0, -104, 0, 3721], 2]], [[[1, 0, 10, 0, 4489], 2]], [[[1, 0, -124, 0, 5041], 2]], [[[1, 0, 74, 0, 5329], 2]], [[[1, 0, -140, 0, 6241], 2]], [[[1, 0, -130, 0, 6889], 2]], [[[1, -12, 89], 4]], [[[1, 0, 97], 4]], [[[1, -6, 101], 4]], [[[1, 0, -62, 0, 10609], 2]], [[[1, 0, 182, 0, 11449], 2]], [[[1, 0, -200, 0, 11881], 2]], [[[1, 0, 26, 0, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '8-170e4-1.1-c1e4-0-1', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/170/2/d/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [1.182230878513483, 1.1830275486792492, 1.1829859013030024, 1.182359462503832, 1.18138036960857, 1.1801554642752623, 1.1783696596945643, 1.1755845732100094, 1.1713374766910205, 1.1651419658769708, 1.1564871762593618, 1.1448345065155658, 1.12961733437949, 1.110224988056019, 1.085956722150591, 1.0560829558740432, 1.0198710690567083, 0.9765907302473498, 0.9255132781201908, 0.8659438198027154, 0.79724410305681, 0.7188526429755612, 0.6303098019831743, 0.5312857982191616, 0.4216072972649778, 0.3012898246461005, 0.17058150140844383, 0.02997486355752263, -0.11977363744784927, -0.2776134191491422, -0.44215969273113837, -0.6117105257058771, -0.7842511800456076, -0.9574495864260326, -1.128653506075752, -1.2949515183606055, -1.453219363512901, -1.60016579638433, -1.7323995978006166, -1.8465357765030592, -1.9392883314039473, -2.007575019641396, -2.048663606894216, -2.06029318670102, -2.040786356589193, -1.9891847390826742, -1.9054346749445652, -1.790454631666491, -1.6462014485426524, -1.4757638986023147, -1.2834916857050618, -1.0749200544078057, -0.8567065193262233, -0.6365887430779928, -0.42333861664984757, -0.22648857394686533, -0.056090246195525904, 0.07751704020240087, 0.16398702325516296, 0.19339230646089353, 0.15659174649852375, 0.045591441886299565, -0.14602852190886295, -0.4227167305204007, -0.7866366619299198, -1.2373778344212099, -1.771646656091321, -2.383151099991976, -3.062581571481364, -3.797660870985851, -4.573283025576985, -5.37183836526476, -6.173626824072013, -6.9573958676181915, -7.701092954493898, -8.38250293047946, -8.979953866870423, -9.473188162085627, -9.844511138629834, -10.079278393760694, -10.166451863602214, -10.099327911811583, -9.876485688757878, -9.501559129241205, -8.983136422456743, -8.334809960238188, -7.575289469136394, -6.727241780669532, -5.816379356508661, -4.870674277277212, -3.9194809031204674, -2.991928878373961, -2.115680741226251, -1.315799774164423, -0.6134866849885714, -0.02507380892094332, 0.43863129297273473, 0.7729231348125867, 0.9798125794050965, 1.0675509323632781, 1.0500429472349901, 0.9462747092747615, 0.7796567686625202, 0.5762050763232678, 0.3630113454429866, 0.16688586119089208, 0.012903498652586855, -0.07743615352196073, -0.08744032574208646, -0.006159364634960309, 0.1706919944787437, 0.4404369908748912, 0.7937067690856834, 1.2149456304593194, 1.683013830921619, 2.1727893898585395, 2.6568852107584164, 3.1073171146766216, 3.497161571478969, 3.802629743363135, 4.004705293425091, 4.090408812169464, 4.053812680835094, 3.896533519069195, 3.627617977599625, 3.263005437380566, 2.824661474858338, 2.338879756033337, 1.8343912538140827, 1.34041038776743, 0.8846401714897362, 0.4910890040773265, 0.1783393173700982, -0.04175490936802317, -0.16497469034112472, -0.19499536956658997, -0.14296606767292316, -0.026553673556514747, 0.13144616515839141, 0.30517682745726643, 0.4680012430131153, 0.5948119562355422, 0.6641345137724877, 0.660199918402527, 0.5745315406393278, 0.4068532993163221, 0.1649512996644291, -0.13570729190615552, -0.47301032602350057, -0.8201193283262873, -1.1485957494962369, -1.4305973447182045, -1.6412151018040477, -1.7611898794038856, -1.7800475543574925, -1.6966831266518947, -1.5196252920768782, -1.2671155902340927, -0.9667108439724998, -0.6522811452767693, -0.3610586482840269, -0.13066855476020567, 0.004212093638453034, 0.01577582602265184, -0.11396938669607555, -0.39103217266331103, -0.8079397320989479, -1.3435302280428043, -1.9640355423180273, -2.6253318529938707, -3.2764500244890313, -3.863495791397704, -4.33401595013031, -4.641836348817444, -4.752250381454425, -4.6446596896409185, -4.314696071576001, -3.7757623543982874, -3.0593707569652855, -2.2117929063808073, -1.2905585412269607, -0.36031394146794143, 0.5128099042104152, 1.2674537312995413, 1.852017145267762, 2.229284201275901, 2.3811677029700844, 2.3096749999332538, 2.0362337624956086, 1.6001978383014597, 1.0563992598808933, 0.4683480701100188, -0.0983208312483158, -0.5819893215581384, -0.9311735088009552, -1.111094334646775, -1.1076891707095262, -0.9295911013520011, -0.6082981316916817, -0.19575248031512002, 0.24039697635757606, 0.6231524781631277, 0.8739743597200753, 0.9211698232178361, 0.7077614283084156, 0.1984274988338337, -0.6149835412465233, -1.711020613669709, -3.0386833347169215, -4.520152713145187, -6.056865347065497, -7.537255295615873, -8.845637558265004, -9.872469102172325, -10.52602721190983, -10.739530619551232, -10.476976375552441, -9.737741488147392, -8.558883733166182, -7.010413969251292, -5.189640660667515, -3.2138051943317545, -1.2094453471257312, 0.698673558058171, 2.3969056196161818, 3.7920384321389107, 4.821475654574159, 5.454773749470832, 5.69318395209389, 5.568716983013979, 5.142438260880825, 4.492999652536729, 3.707050487140604, 2.871512902657182, 2.0666201299758327, 1.3559498237616512, 0.7816648609396585, 0.36328657044510293, 0.09868830069828753, -0.033267111466648, -0.06686826111870033, -0.042438848877778, 0.0009336935819671161, 0.03214125867626762, 0.033303444468279396, 0.00273217526811077, -0.04471241109958977, -0.08008634880405069, -0.0652796806043632, 0.040223597140256244, 0.2717752670123006, 0.6520538297290503, 1.1844787194034438, 1.8488047203415765, 2.600863916514079, 3.3740678235953707, 4.083556503756578, 4.63423411616665, 4.93391075130992, 4.901776102371315, 4.4771224526636315, 3.629168101247901, 2.367100829330904, 0.7380815041808452, -1.1757322552374563, -3.261285088306479, -5.382248551347629, -7.394503031903071, -9.159065051736674, -10.554130827072104, -11.488403006724134, -11.90967284266762, -11.80801394977646, -11.216145439255637, -10.208027696967621, -8.887977063248051, -7.378208041870423, -5.806532186305333, -4.294565603193692, -2.9440316763749963, -1.8274237965308728, -0.9829619227992806, -0.4136714365463167, -0.09040311318496164, 0.04132962485843865, 0.051721557293803545, 0.015402117688629653, 0.0005390623781236303, 0.059501250687475374, 0.2218688435937526, 0.49168120534326853, 0.8484114410486869, 1.250593231329271, 1.6427910800443435, 1.9672329453230724, 2.1719428529245177, 2.217684897292415, 2.0849293278880277, 1.7807931461683486, 1.3353233934726163, 0.7964218789617687, 0.22439485803694909, -0.3146716425120413, -0.7609349900212986, -1.0692971068710027, -1.2149862776810771, -1.1970154784908784, -1.0382227868485578, -0.781048427358652, -0.4807566962227627, -0.19688651687759837, 0.01688860655199532, 0.12135629721152516, 0.09806446723497372, -0.047227391363683265, -0.2853098175811276, -0.568089201258406, -0.8362158608341544, -1.0294395654041568, -1.0969094255992444, -1.0060651579195548, -0.7496682180991948, -0.35016185000711175, 0.14334471942254498, 0.6614687603426538, 1.12357110151575, 1.449501006061361, 1.5737908114844543, 1.4567637592041038, 1.0924449460025023, 0.5134513632748201, -0.21138446347525378, -0.9854435080900468, -1.6965090031885657, -2.230014690562527, -2.487495489813671, -2.403348589486596, -1.9564896199401534, -1.1722064702491817, -0.12419317097170884, 1.0706831691104879, 2.2668572202668607, 3.3160910342696375, 4.083661350127103, 4.465349826728077, 4.405380486750354, 3.9136566763864917, 3.0627167945076894, 1.9794558090740522, 0.831857857947486, -0.1896798646775678, -0.8990133863120615, -1.1404800990408, -0.8121375633540212, 0.11963753497966417, 1.6132918068854851, 3.5511046525255603, 5.750082945203209, 7.992848196232855, 10.048470260291936, 11.693968175329854, 12.7445140140624, 13.094900187322807, 12.716429432529553, 11.653352650305594, 10.023650241784662, 8.018919031829686, 5.8606496321622, 3.769694564958733, 1.9454012683698632, 0.5460784606730833, -0.33859768957018116, -0.6939752452315021, -0.5752519044754826, -0.09743568184613753, 0.5839939891593983, 1.2992579124951367, 1.889991555956305, 2.2309039568957165, 2.2474812116209386, 1.9250412675956954, 1.308254190774105, 0.49056515089565483, -0.4031196874192918, -1.2364640245772591, -1.883761345470301, -2.252851808564, -2.2968139213585923, -2.018423757612308, -1.4695104441527302, -0.7445302218465695, 0.04029478186627514, 0.766903404901544, 1.3327915026892552, 1.6660905859686017, 1.738707944777201, 1.5685092114522472, 1.2134119571852844, 0.7593203420611849, 0.3038385921789508, -0.06254389454613203, -0.27387163968592465, -0.3021348022444312, -0.16297253638864678, 0.08604377475671454, 0.3544568703896249, 0.5343338939818475, 0.5195068893818535, 0.22514446568072524, -0.39525923752881437, -1.3399033626355683, -2.5553292817629236, -3.9399404995363834, -5.3565210694400704, -6.656123886103812, -7.69570622895908, -8.355719695483694, -8.558917172324442, -8.288501591253002, -7.582722290999775, -6.526810999178083, -5.24287460444456, -3.87516002290759, -2.5639332077260035, -1.4268644657029348, -0.5458176258669092, 0.042368515365809316, 0.3467899254831224, 0.41499363301048137, 0.3209826398928889, 0.15024137051906097, -0.017886193054462637, -0.12374831043721977, -0.13585389730025135, -0.05369076911723513, 0.09604758039941262, 0.26862894096296774, 0.41362781919329794, 0.48849540474562125, 0.46885551858131574, 0.3544388684429223, 0.16985224831558626, -0.04099048270620311, -0.22652441894816697, -0.340753194578732, -0.3566684432619883, -0.2778501000414038, -0.14266782927175065, -0.021661536838748444, -0.00836979813096719, -0.20315244248725664, -0.6929173880442778, -1.5315641458553086, -2.723416898118133, -4.213972066214798, -5.890374320033307, -7.590264356922736, -9.120786638996927, -10.29117408959097, -10.937810231708738, -10.947080795395285, -10.277860933985858, -8.981728400707713, -7.190087822384231, -5.095844648064621, -2.9315938700381183, -0.9411859053719058, 0.6631726452318776, 1.7313016293680084, 2.1948619988703406, 2.0784978877644793, 1.4952973727234913, 0.6266033665141932, -0.3077186109671687, -1.0843102325410274, -1.5134240543694504, -1.4698908951457148, -0.9137853405996726, 0.10477644825448483, 1.455167617998551, 2.9461023798854544, 4.356721339443149, 5.479674832597771, 6.1503920013209905, 6.269125512447509, 5.818077165058821, 4.870163092792361, 3.5657933712414622, 2.086834813064287, 0.6294792043587395, -0.6266313827579162, -1.5504992831838382, -2.0756533553190737, -2.204637795543552, -2.0047328908819853, -1.587452722071877, -1.081741118952854, -0.6074167169152016, -0.2519725836997208, -0.052733453388988265, 0.007896869669016053, -0.004952985995855112, 0.0039452753419703165, 0.13580424373718167, 0.47169616212481397, 1.0497952164549933, 1.8527014530117338, 2.8052384512372672, 3.782737564862111, 4.631907861128282, 5.205933113105332, 5.389511909767126, 5.120435393388831, 4.408567756955043, 3.347731027136138, 2.0939057917964328, 0.8391074453641612, -0.2172338421310189, -0.9018071149249393, -1.1064500486500528, -0.8091259694155831, -0.07998635235094369, 0.9262640846874106, 1.994410013056812, 2.8855326661654734, 3.3786200807017224, 3.3114152278195137, 2.6108153086820196, 1.3092332441959535, -0.45661828212782873, -2.4679040731336723, -4.4574435528934435, -6.150752639955804, -7.312530697209217, -7.7931098157190535, -7.545720000103009, -6.632002142690978, -5.214936955268084, -3.533539185031152, -1.8553408203165997, -0.4335888417269054, 0.5324677441345995, 0.9327854803102139, 0.7595753268555517, 0.10239641486465885, -0.8697821844398876, -1.9413736604719314, -2.8935746351461518, -3.541617788143529, -3.764991539794158, -3.5297977598237282, -2.8879516243562926, -1.9613692604656012, -0.9161959129484624, 0.07091327866700149, 0.8476219625687581, 1.3126223138760629, 1.4325447550600099, 1.2464707575849627, 0.8496675928837529, 0.37018348644362115, -0.059302464625828145, -0.33185664971302614, -0.39011338823481617, -0.23755739816298316, 0.06160615844463088, 0.39675143634306126, 0.6364503735526787, 0.6556916218055276, 0.3631446346938998, -0.27316984164907054, -1.2190003649642125, -2.378789545087529, -3.609617202664652, -4.745736443677547, -5.630249017735154, -6.141088627506252, -6.211852861825102, -5.847834390384739, -5.118090215874285, -4.138731114961615, -3.0527299894875366, -2.0072861249257397, -1.1224957371207072, -0.47316854715524354, -0.08223251570559917, 0.0767041446409287, 0.06797280637582982, -0.025929545201335953, -0.1254465734356262, -0.17184370047232606, -0.13899737289826333, -0.03551523537676147, 0.1025496768884588, 0.22619863553695055, 0.2906856152661097, 0.27157624235499744, 0.17555212428658692, 0.041847329439891376, -0.06618014553883327, -0.07644657728302251, 0.07143932185279983, 0.4051276448805292, 0.9067745321249798, 1.5093949277116072, 2.104060542400458, 2.5616037117956925, 2.7618684891254364, 2.623459588470415, 2.1305205230623954, 1.3516271966913787, 0.4394171778922814, -0.3865254481076688, -0.8724582632689769, -0.7759192631748504, 0.08942704249259505, 1.8113081243891274, 4.348459841258408, 7.529870465802114, 11.069786979439291, 14.595312310612957, 17.69936310877821, 20.029735577058705, 21.322324300137147, 21.427753785551122, 20.343493297741674, 18.245398780406017, 15.420302385112782, 12.210472388810398, 8.971739077765683, 6.033598147265206, 3.6288694721754227, 1.869183896399863, 0.7496948640290043, 0.17006555380582622, -0.03281977548448907, -0.03720908831462623, 0.008648171214777284, 0.01952475063646476, -0.011646547271167606, -0.020059736059033634, 0.10517405293785446, 0.48231104561721194, 1.194764093239666, 2.253848043790002, 3.57636974885346, 4.991219339147304, 6.260872367206444, 7.117188875602896, 7.314525763535292, 6.699801545464282, 5.240209064358487, 3.0359829119213564, 0.3206816664529074, -2.560209556990808, -5.21932111147123, -7.292808554320502, -8.500844027041312, -8.70554294965416, -7.936944785802065, -6.386094334123894, -4.375512229282714, -2.30930893600184, -0.5923900088340013, 0.441240655634168, 0.584559517420893, -0.20689595318930223, -1.8084087550436994, -3.951596913394517, -6.274877734828612, -8.395046533891044, -9.97299990174041, -10.767936680743246, -10.677079022872656, -9.754438811683613, -8.182688028107975, -6.23143166402589, -4.206727559242679, -2.393782301834055, -1.0052583773219304, -0.15289415112066115, 0.1614263382503292, 0.034014919050507575, -0.3756570166872762, -0.8846668248547167, -1.3259187694179737, -1.5844063052555322, -1.612348605173432, -1.4265564513324926, -1.0945304937927496, -0.7119229298047605, -0.36921825301703026, -0.12768352166067032, -0.007074988019191067, 0.014642286370358906, -0.010851272075101814, -0.024051259856091307, 0.01840526958921868, 0.12392382289408785, 0.25498488739950437, 0.3337942479233992, 0.2600808932451784, -0.06183020462605786, -0.6931062172025578, -1.6342228318719856, -2.8101044687241137, -4.078215385547881, -5.247060159438746, -6.105055878941533, -6.462300074630706, -6.204894776782185, -5.31332826300333, -3.868337521236428, -2.0470981013103, -0.10383727773241967, 1.6867069182411347, 3.079332198995158, 3.899938776765775, 4.079242800097486, 3.6652942857601847, 2.8097220176678337, 1.7357368755454574, 0.693757700968438, -0.09076689814627538, -0.46121326146526714, -0.35866476788593143, 0.17229537796432806, 0.9993202745617972, 1.9321929625098895, 2.765433177701127, 3.3310056499552188, 3.5266716780813017, 3.329528346176389, 2.798302408613279, 2.0608803378407003, 1.2711175006145594, 0.5714221821166287, 0.06394120436669841, -0.20961677594939518, -0.2729899475291043, -0.1989307391665337, -0.08109520362870157, -0.0011270399144699325, 0.002283666849604504, -0.04857317937085285, -0.0699563221793809, 0.06568228455642132, 0.4969610605306667, 1.3324722441594168, 2.6115880834274985, 4.284002651160144, 6.202663899708137, 8.133761952865987, 9.793533012110425, 10.921849063783592, 11.319516713136933, 10.879791201546265, 9.621886508036955, 7.719560851914162, 5.443740505046158, 3.1076980263650924, 1.0197719282587332, -0.5642262635239521, -1.5050118359964806, -1.7997708193099995, -1.570789331966513, -1.0334391170121835, -0.446845694626853, -0.05328862070524391, -0.023521733043891702, -0.42093844116065626, -1.1914513570319725, -2.1774114498198656, -3.1558359524394506, -3.899248522489021, -4.224730227093823, -4.0314476633744265, -3.326942554311722, -2.234577865689904, -0.9516170018779924, 0.296700985876733, 1.3016574203174778, 1.9154670217688485, 2.086808220644201, 1.862656807506801, 1.3681274668192847, 0.7730809306135775, 0.24515622740310772, -0.09440117761776617, -0.1988568398114427, -0.10168845334026069, 0.09853001748832121, 0.2719951143108998, 0.3023057942007445, 0.12893946164330772, -0.22849348366569708, -0.6668460977150947, -1.0213163278310824, -1.1151316735730186, -0.8155082442310717, -0.08527888197469667, 0.9772250579741212, 2.1236489596370918, 2.9895027433552297, 3.155247995654839, 2.2261847821021417, -0.0845767242688646, -3.8730812664484224, -8.989443731328981, -15.031899080600473, -21.425357577328107, -27.47953488721927, -32.47186800952078, -35.77200371782016, -37.01218535231596, -36.09065428574961, -33.162837227637304, -28.63186216986772, -23.121290343326976, -17.31656070969462, -11.848642624235024, -7.2129290675882, -3.712021712230271, -1.4251074615097081, -0.23106689199865565, 0.13527195844460627, 0.005170140543807511, -0.3074271171928529, -0.5647865895592704, -0.6407003589290383, -0.5272692452695005, -0.30019110305315205, -0.07033160975773152, 0.06692402986548406, 0.07804773868022652, 0.014772671713285937, 0.0072491916884027795, 0.23543271728161627, 0.8791307982557427, 2.062298177120614, 3.8118617993062185, 6.035612111145571, 8.520828006127637, 10.969789651587988, 13.053954384755928, 14.476195829007654, 15.033376238964932, 14.650305952523077, 13.390237544366876, 11.444226548766961, 9.09862302688166, 6.666223364952422, 4.42928134583054, 2.5968203749408705, 1.2771820117148152, 0.47011585050670207, 0.08846583354922616, -0.005569231288651513, 0.04072852424724952, 0.10794849664047965, 0.12790518950801566, 0.08911363060915085, 0.024873240684080564, -0.010719771507676706, 0.029909580765497486, 0.16502964486857133, 0.37322206131313335, 0.5988030385533291, 0.7692050857566974, 0.8203382401585733, 0.7244027473703729, 0.5050631440943044, 0.2381499961839295, 0.03721136184229815, 0.025153950870034796, 0.29841005880337196, 0.8939754374080181, 1.76842074238055, 2.801564927626958, 3.8150235963158843, 4.603878443622602, 4.983981567109971, 4.850971010997823, 4.196251129564862, 3.109455954137201, 1.7698263738621018, 0.41671776319405995, -0.7169325193867772, -1.4539172626125256, -1.7064479606735021, -1.497062289211783, -0.9502767769615011, -0.25512127705401494, 0.38494168915923255, 0.8039516705223935, 0.9163916252722316, 0.7374855897647045, 0.37587587102784, -0.001600630765712348, -0.22311593013022732, -0.16691349733087102, 0.19257156230631323, 0.7645997440489966, 1.356096003318346, 1.710604620270204, 1.5713874525041023, 0.764257966617478, -0.7511114457215775, -2.854544609549476, -5.2648787117807, -7.581829399671916, -9.373807797726657, -10.26414520877423, -10.012954061815488, -8.59172088422828, -6.193854111639571, -3.200497139990912, -0.11493325433364046, 2.532739476118963, 4.296386343779073, 4.898713741215573, 4.283688722543136, 2.6286957946435026, 0.2938103509668199, -2.2560225119767434, -4.546592764748133, -6.199354470650576, -6.994013925446392, -6.892598839534984, -6.033672579784084, -4.693481135062311, -3.192612034427986, -1.819502144847381, -0.7751554888972961, -0.13975683259959684, 0.12738792040143168, 0.14830480578038574, 0.07028350823147572, 0.008013707667666042, -0.0014526758358538634, -0.013352764689900456, -0.15695587759334947, -0.5887802198446032, -1.4299948136203517, -2.7061076272462525, -4.306854012304633, -5.985965501547799, -7.394475975323383, -8.144055840276431, -7.895680105490481, -6.45887790903882, -3.8412514745126334, -0.26900395871539984, 3.830972921553935, 7.908833463850656, 11.395735850443195, 13.80073084553587, 14.806803076133969, 14.360523400379753, 12.651105952400627, 10.056988947383989, 7.076395530205717, 4.238366955792964, 1.9748818026582207, 0.5457504190166832, 0.009151632857594834, 0.23137551882465085, 0.9373247421754998, 1.7908501317610457, 2.480265767677716, 2.7920752421005393, 2.6491704040536423, 2.1122914145466476, 1.3478938043657196, 0.5677759202212689, -0.03577419135691407, -0.3418332180748284, -0.3332331884294122, -0.09795336897106818, 0.20908253352040038, 0.41367403637293904, 0.3739706326672971, 0.03108437015061055, -0.5751610829346763, -1.3199368095192752, -2.0253351204222114, -2.507334020980651, -2.6340762649974607, -2.362616490084324, -1.750698376959617, -0.9441236839313659, -0.13689728083240824, 0.4818982816465935, 0.7790379195613311, 0.7123908780014557, 0.3403850322819698, -0.19538978211273028, -0.7114257167097371, -1.0399792262747005, -1.0758316797769847, -0.8061688121603874, -0.3180077583726288, 0.2253577597372452, 0.6358879662047323, 0.7551669327859437, 0.5046754612320368, -0.0797539336069002, -0.8534543828515105, -1.5956339560580608, -2.062192683640423, -2.055578280408801, -1.4855784088116264, -0.40051681144192125, 1.015490235302877, 2.4853192064202116, 3.6970200481663134, 4.3701310311795085, 4.321057807673642, 3.5208538393800617, 2.1194855887345687, 0.41811083113756914, -1.2131390964648054, -2.488678653935845, -3.2634663266852257], 'positive_zeros': ['0.850154944955691292142113475388834', '1.76197003093654825177348797754958', '1.91505430413316352158022021370214', '2.97024208037910435614385931099296', '3.31581171376736480719605291617077', '3.40772590844707343908426910388027', '4.14911131052640219693930101612162', '4.28697831313215297950563479453165', '4.58024683313541212341029973975739', '5.06086884440264440471390678976984', '5.10054656720727117602642902702252', '5.66876859062903956842955748050905', '5.99433283283112592830123563923168', '6.23266659380700618461353091115525', '6.41504184010593481425340639787267', '6.95699127394199851292202224631224', '7.45775701579912025621558633254398', '7.56179581696777197603083861310062', '7.65822435266637210201028614554054', '7.77265927397674281762515943603199', '8.231272092882065147406641620986783', '8.860554645954631556466625401262816', '8.956520327368728494365539279328210', '8.967506047524813963148122237658412', '9.418839338644338202652010668407453', '9.715638839323166305387507512703934', '9.804568842318255675860229131819473', '10.08505581735487839464065369488665', '10.33506300331523678719266673260776', '10.59709115577916658019563288664996', '10.93109742760105470370346470825299', '11.05935331083785229407179087194269', '11.57945730078922605149236699831386', '11.69241471254141501382257160969359', '11.95466595037747718627858757914023', '12.21714819523356411468600912315743', '12.49374556968304931490314759437137', '12.61507320067704743410662341677517', '12.76340090201164043951785380030929', '13.30956120658930436056588348478389'], 'prelabel': '8-170e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1650994954774323, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1275892196604968439, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.850154944955691292142113475389', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.76197003093654825177348797755', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.91505430413316352158022021370', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.3955029613605165, 'bad_primes': [2, 5, 17], 'central_character': '1.1', 'conductor': 835210000, 'conductor_radical': 170, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16], 'euler11': [1, 0, -44, 0, 726, 0, -5324, 0, 14641], 'euler13': [1, 0, 20, 0, 438, 0, 3380, 0, 28561], 'euler17': [1, 0, 2, 0, 289, 0, 0, 0, 0], 'euler19': [1, -8, 100, -488, 3094, -9272, 36100, -54872, 130321], 'euler2': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, 88, 0, 2994, 0, 46552, 0, 279841], 'euler29': [1, 0, -80, 0, 3282, 0, -67280, 0, 707281], 'euler3': [1, 0, -4, 0, 22, 0, -36, 0, 81], 'euler31': [1, 0, -88, 0, 3858, 0, -84568, 0, 923521], 'euler37': [1, 0, 112, 0, 5874, 0, 153328, 0, 1874161], 'euler41': [1, 0, -20, 0, 3462, 0, -33620, 0, 2825761], 'euler43': [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], 'euler47': [1, 0, -188, 0, 13254, 0, -415292, 0, 4879681], 'euler5': [1, 0, 8, 0, 25, 0, 0, 0, 0], 'euler53': [1, 0, -140, 0, 10518, 0, -393260, 0, 7890481], 'euler59': [1, 48, 1100, 15408, 143574, 909072, 3829100, 9858192, 12117361], 'euler61': [1, 0, -208, 0, 18258, 0, -773968, 0, 13845841], 'euler67': [1, 0, 20, 0, 9078, 0, 89780, 0, 20151121], 'euler7': [1, 0, -8, 0, 114, 0, -392, 0, 2401], 'euler71': [1, 0, -248, 0, 25458, 0, -1250168, 0, 25411681], 'euler73': [1, 0, 148, 0, 16134, 0, 788692, 0, 28398241], 'euler79': [1, 0, -280, 0, 32082, 0, -1747480, 0, 38950081], 'euler83': [1, 0, -260, 0, 30678, 0, -1791140, 0, 47458321], 'euler89': [1, -48, 1220, -19728, 222054, -1755792, 9663620, -33838512, 62742241], 'euler97': [1, 0, 388, 0, 56454, 0, 3650692, 0, 88529281], 'euler_factors': [[1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, -4, 0, 22, 0, -36, 0, 81], [1, 0, 8, 0, 25, 0, 0, 0, 0], [1, 0, -8, 0, 114, 0, -392, 0, 2401], [1, 0, -44, 0, 726, 0, -5324, 0, 14641], [1, 0, 20, 0, 438, 0, 3380, 0, 28561], [1, 0, 2, 0, 289, 0, 0, 0, 0], [1, -8, 100, -488, 3094, -9272, 36100, -54872, 130321], [1, 0, 88, 0, 2994, 0, 46552, 0, 279841], [1, 0, -80, 0, 3282, 0, -67280, 0, 707281], [1, 0, -88, 0, 3858, 0, -84568, 0, 923521], [1, 0, 112, 0, 5874, 0, 153328, 0, 1874161], [1, 0, -20, 0, 3462, 0, -33620, 0, 2825761], [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], [1, 0, -188, 0, 13254, 0, -415292, 0, 4879681], [1, 0, -140, 0, 10518, 0, -393260, 0, 7890481], [1, 48, 1100, 15408, 143574, 909072, 3829100, 9858192, 12117361], [1, 0, -208, 0, 18258, 0, -773968, 0, 13845841], [1, 0, 20, 0, 9078, 0, 89780, 0, 20151121], [1, 0, -248, 0, 25458, 0, -1250168, 0, 25411681], [1, 0, 148, 0, 16134, 0, 788692, 0, 28398241], [1, 0, -280, 0, 32082, 0, -1747480, 0, 38950081], [1, 0, -260, 0, 30678, 0, -1791140, 0, 47458321], [1, -48, 1220, -19728, 222054, -1755792, 9663620, -33838512, 62742241], [1, 0, 388, 0, 56454, 0, 3650692, 0, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/170/2/d/c'], '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': '8-170e4-1.1-c1e4-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-170e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1650994954774323, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1275892196604968439, 'z1': {'__RealLiteral__': 0, 'data': '0.850154944955691292142113475389', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1077699426260079394165425513717,2233562367300867318905389137486,2427619738104058915695276448129,3765229156015716436833622544082', 'Lhash_array': ['1077699426260079394165425513717', '2233562367300867318905389137486', '2427619738104058915695276448129', '3765229156015716436833622544082'], 'label': '8-170e4-1.1-c1e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/170/2/d/c'}