LMFDB - Embedded newform 1.80.a.a.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1,80,Mod(1,1)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1.1"); S:= CuspForms(chi, 80); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 80, names="a")

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 80 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$39.5237048722$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 76\!\cdots\!88 $ x^6 - 3x^5 - 4493465009931118088598x^4 - 13617827867154853888266546820774x^3 + 5183423914918797826459016270129188352477541x^2 + 36020237378286283561256608380952541686850032723239033*x - 768426424275848216319978876834525014212769442584294247793970688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{54}\cdot 3^{24}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 13^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$9.55147e9$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.26554e11 q^{2} +2.57159e18 q^{3} -5.53136e23 q^{4} -2.99197e27 q^{5} +5.82605e29 q^{6} -6.95219e31 q^{7} -2.62259e35 q^{8} -4.26565e37 q^{9} -6.77842e38 q^{10} -1.05363e41 q^{11} -1.42244e42 q^{12} +1.30142e44 q^{13} -1.57505e43 q^{14} -7.69412e45 q^{15} +2.74934e47 q^{16} -1.86211e48 q^{17} -9.66401e48 q^{18} +1.08010e50 q^{19} +1.65496e51 q^{20} -1.78782e50 q^{21} -2.38704e52 q^{22} +5.47579e53 q^{23} -6.74423e53 q^{24} -7.59175e54 q^{25} +2.94841e55 q^{26} -2.36397e56 q^{27} +3.84551e55 q^{28} +4.52983e57 q^{29} -1.74314e57 q^{30} -5.21486e58 q^{31} +2.20813e59 q^{32} -2.70951e59 q^{33} -4.21868e59 q^{34} +2.08007e59 q^{35} +2.35949e61 q^{36} +4.17558e61 q^{37} +2.44702e61 q^{38} +3.34671e62 q^{39} +7.84670e62 q^{40} +8.70655e63 q^{41} -4.05038e61 q^{42} +6.17573e64 q^{43} +5.82800e64 q^{44} +1.27627e65 q^{45} +1.24056e65 q^{46} +9.80346e65 q^{47} +7.07020e65 q^{48} -5.78605e66 q^{49} -1.71994e66 q^{50} -4.78859e66 q^{51} -7.19860e67 q^{52} -1.69065e68 q^{53} -5.35566e67 q^{54} +3.15242e68 q^{55} +1.82327e67 q^{56} +2.77759e68 q^{57} +1.02625e69 q^{58} +1.06669e70 q^{59} +4.25590e69 q^{60} +2.41593e70 q^{61} -1.18145e70 q^{62} +2.96556e69 q^{63} -1.16162e71 q^{64} -3.89379e71 q^{65} -6.13850e70 q^{66} -1.72200e72 q^{67} +1.03000e72 q^{68} +1.40815e72 q^{69} +4.71249e70 q^{70} +8.22517e72 q^{71} +1.11870e73 q^{72} +2.63298e73 q^{73} +9.45996e72 q^{74} -1.95229e73 q^{75} -5.97444e73 q^{76} +7.32503e72 q^{77} +7.58212e73 q^{78} -1.78991e75 q^{79} -8.22595e74 q^{80} +1.49375e75 q^{81} +1.97251e75 q^{82} +3.77264e75 q^{83} +9.88908e73 q^{84} +5.57137e75 q^{85} +1.39914e76 q^{86} +1.16489e76 q^{87} +2.76324e76 q^{88} -1.69258e77 q^{89} +2.89144e76 q^{90} -9.04769e75 q^{91} -3.02885e77 q^{92} -1.34105e77 q^{93} +2.22102e77 q^{94} -3.23163e77 q^{95} +5.67842e77 q^{96} +4.19042e78 q^{97} -1.31085e78 q^{98} +4.49441e78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3} + 15\!\cdots\!88 q^{4} + 60\!\cdots\!40 q^{5} - 22\!\cdots\!28 q^{6} - 20\!\cdots\!00 q^{7} + 54\!\cdots\!60 q^{8} + 98\!\cdots\!22 q^{9} + 27\!\cdots\!40 q^{10}+ \cdots + 12\!\cdots\!24 q^{99}+O(q^{100}) $ 6 * q - 16086577320 * q^2 + 1942174928281180680 * q^3 + 1549737362258405903681088 * q^4 + 6092984858773763455723827540 * q^5 - 2227106590325939088404927087328 * q^6 - 204133057837186288371299604423600 * q^7 + 542570064661378776298915601390568960 * q^8 + 98496326492153316059886441015309696222 * q^9 + 2720626696366658228219065452729623532240 * q^10 + 326182707503353434196853598345012484552152 * q^11 + 3662741799314627362069151990938777789858560 * q^12 - 249286867791526696387831019648013646893106140 * q^13 + 1866634067474695788912841823339193553138295616 * q^14 + 53939724989186019570794541522119517534771796080 * q^15 - 681627631644510368706137880459644753465449181184 * q^16 + 829554518710324966978506506427078451803483469740 * q^17 + 20783419681388619276512545895581772264264550807480 * q^18 - 50727940848110344442361931427855575819428647228760 * q^19 - 1467030065046629207751264576643706806587735144958080 * q^20 + 11440846038310308150487768012211089482880511198926272 * q^21 + 36817507512313772519930542191150104222671820963556960 * q^22 - 1046924887201563380993656359631631933258453525094738960 * q^23 + 4647998047182641817986339484942489649049309172966328320 * q^24 + 10836995626543537474051791335153252813979338793331307850 * q^25 - 165657588130323625805363235243378873928973276983585168368 * q^26 + 452244485424938477892504860024752019079362449583874943440 * q^27 + 1004680642640065837930850364413184139977872155405489282560 * q^28 - 7120822866262655112931363073018274881104708247497947521340 * q^29 - 1093089132342530488188112356341250721972394415479943059520 * q^30 + 134345039550847531062964315804153164343444264343589333172032 * q^31 - 367680407387361126658464447414461787802285956837455133573120 * q^32 + 694937277679484430969386562214930563011269531321798125315360 * q^33 + 3154306959722239121253159757854043021326472297974364404980016 * q^34 + 9191056770903655504272784196241783249847740561191433159558240 * q^35 + 19880287065959074647932230862843896929437344679866234828597056 * q^36 + 200218543091040103155222783880989961642213560574664429550198420 * q^37 + 866365883974611161836395390925862263352921297032838009795060640 * q^38 + 1846928010477803855453412626793191219191424716227436821180804144 * q^39 + 9116669264447274408945009430906339427674431802850195585057510400 * q^40 + 19216804901837266991242147464997667315402616992351385711235458972 * q^41 + 112315174478490788723912174839938916243710780267342081630678531840 * q^42 + 108832931910908864051094641347526853298463718485111641638401400600 * q^43 + 495514650695382135238363336424200091081783038631873261666636656896 * q^44 + 1089311173064980984859644147008913582964905804089164802662670706980 * q^45 + 2339423217798161589056888023635021837153755261863446723443331974592 * q^46 + 766732507168785220421816169748850175208159379232549271592508353760 * q^47 - 1227537570851109157458973684400646232156423736031048093315900456960 * q^48 + 3801016219812200810689187746878210669081675204402752707309154018358 * q^49 - 50723521315108078882353551947661611720805543300108849711322864485400 * q^50 - 139865466375558864334882784640098531626186142446280524443365433199728 * q^51 - 279692249004488191323071540832092417841619330373410063262542264310400 * q^52 - 312193237964710957330604375297544855480450344577449082153802391971020 * q^53 - 996221038973994559873624494431619704350011373216284617130312268666560 * q^54 - 861958222068919393142591787960630586871784969446963670182827020790320 * q^55 + 1123629643438673418216699268533992018915072902064015953839024305295360 * q^56 + 7795598779799587371741461301046795526293245245773998812837273820000480 * q^57 + 16584702356914156466182151363602691995360915944935914137385742159510160 * q^58 + 24289171784532714189639095038219795042285164994033400426178461238907320 * q^59 + 73025956047571458013400417312791668535879728806786116560639243534051840 * q^60 + 80560570425826852880081093564684385117241348668836108242495308815618052 * q^61 + 59777568713863815377707698536571620658579394379949737090862924510332160 * q^62 - 276708678056196744256455115102015383166989187390931876478468368856762480 * q^63 - 719203226636338274682481908236724651863342420498670194455988567598170112 * q^64 - 1007462919483461647300380829039677154191109543250817689988654733030592520 * q^65 - 3347562853423538991999694027669961627986534585541581689746575315495214976 * q^66 - 1851521876973893932513297183455714100127257334040085257904842903903517560 * q^67 - 5899582938115809421316043854246769288699297144820927766700932855979726720 * q^68 - 1427672735602453311144050658084524391331260046448660152415370050225171136 * q^69 + 31159148342952686307596185437939815723517531766889921556924090292621741440 * q^70 + 38507401093845789827495210229167852070939724868887506542264571604541264592 * q^71 + 87904411000641647434917578390462554629488250565124366592415232306933521920 * q^72 + 61123654206386061400310438862981106227383729069503080628162601940159787740 * q^73 + 136513352063977853606694381822259496818965955504365628093794971441921163216 * q^74 + 113188706706427317048365034543759604727098826077328333023878456326260918200 * q^75 - 249903768766885839664688587580825575582546834454828556400015599314274074880 * q^76 - 1195099252106099653800449972868194220235362175583181442486256041652274244800 * q^77 - 3022231856978250782599441544561070134871217051487771942772538597436408443200 * q^78 - 188234723479363903277484397100590307076741783512190126828886315155446684640 * q^79 - 2750248132852209015421484068233717972689944891189322073844459755369097666560 * q^80 - 4202996734890713231427597758184507891641102417282671988811370042535012566794 * q^81 + 3834792966214046709977047126406184257851543195738078433637414913324683717360 * q^82 + 14506845760765784842493952470927474286413727909244314121162679395439622145320 * q^83 + 48942789227023150657016145376829988370028655394086238910889917134273615865856 * q^84 + 38946066828627954832778050727572362568084538101228336437758435671222134267240 * q^85 + 66363633323077708072616297459993363454350669286030390599179655949306835458912 * q^86 - 12188467007600920252987005731487987332580129454574096199578444638747687628880 * q^87 - 68086553439664359269830684533538140843829745277114000504065479672707840583680 * q^88 + 88790169947368466670673875396871954428202115924137373286785364937730407494780 * q^89 - 678121360108159288271315537216087664710338266311311066150921870820864233179120 * q^90 - 1105665330428280782729905276805137770501582996765091919549546053816493845198368 * q^91 - 581852119074779563003978084378550280950528927013853021971971412987670782543360 * q^92 - 724063571132401087495277238269757837179269218308363767014177350097338957840640 * q^93 - 342394004508386413823498343959337212855421843329465021317054652742559913721984 * q^94 + 4133010515441143062055572903340407460351722715065934937506390604234109634359600 * q^95 + 4500277093535091993817003185543220432802869972147132801867826645045331188908032 * q^96 + 2053881285944963905800936410853289740689894385863240159901124624782493905690060 * q^97 + 21591608457226642856925919189308208713047358263642522360137695155926522503830040 * q^98 + 12210721611676619111412804269965201185505307365258823385190308559518832844781624 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.26554e11	0.291398	0.145699	−	0.989329i	$-0.453457\pi$
$2$	2.26554e11	0.291398	0.145699	+	0.989329i	$0.453457\pi$
$3$	2.57159e18	0.366364	0.183182	−	0.983079i	$-0.441360\pi$
$3$	2.57159e18	0.366364	0.183182	+	0.983079i	$0.441360\pi$
$4$	−5.53136e23	−0.915087
$5$	−2.99197e27	−0.735600	−0.367800	−	0.929905i	$-0.619889\pi$
$5$	−2.99197e27	−0.735600	−0.367800	+	0.929905i	$0.619889\pi$
$6$	5.82605e29	0.106758
$7$	−6.95219e31	−0.0288901	−0.0144450	−	0.999896i	$-0.504598\pi$
$7$	−6.95219e31	−0.0288901	−0.0144450	+	0.999896i	$0.504598\pi$
$8$	−2.62259e35	−0.558053
$9$	−4.26565e37	−0.865777
$10$	−6.77842e38	−0.214353
$11$	−1.05363e41	−0.772106	−0.386053	−	0.922477i	$-0.626162\pi$
$11$	−1.05363e41	−0.772106	−0.386053	+	0.922477i	$0.626162\pi$
$12$	−1.42244e42	−0.335255
$13$	1.30142e44	1.29913	0.649567	−	0.760305i	$-0.274950\pi$
$13$	1.30142e44	1.29913	0.649567	+	0.760305i	$0.274950\pi$
$14$	−1.57505e43	−0.00841853
$15$	−7.69412e45	−0.269497
$16$	2.74934e47	0.752471
$17$	−1.86211e48	−0.464807	−0.232403	−	0.972619i	$-0.574659\pi$
$17$	−1.86211e48	−0.464807	−0.232403	+	0.972619i	$0.574659\pi$
$18$	−9.66401e48	−0.252286
$19$	1.08010e50	0.333195	0.166597	−	0.986025i	$-0.446722\pi$
$19$	1.08010e50	0.333195	0.166597	+	0.986025i	$0.446722\pi$
$20$	1.65496e51	0.673138
$21$	−1.78782e50	−0.0105843
$22$	−2.38704e52	−0.224990
$23$	5.47579e53	0.891655	0.445828	−	0.895119i	$-0.352909\pi$
$23$	5.47579e53	0.891655	0.445828	+	0.895119i	$0.352909\pi$
$24$	−6.74423e53	−0.204451
$25$	−7.59175e54	−0.458893
$26$	2.94841e55	0.378565
$27$	−2.36397e56	−0.683554
$28$	3.84551e55	0.0264369
$29$	4.52983e57	0.778684	0.389342	−	0.921093i	$-0.372702\pi$
$29$	4.52983e57	0.778684	0.389342	+	0.921093i	$0.372702\pi$
$30$	−1.74314e57	−0.0785311
$31$	−5.21486e58	−0.643362	−0.321681	−	0.946848i	$-0.604248\pi$
$31$	−5.21486e58	−0.643362	−0.321681	+	0.946848i	$0.604248\pi$
$32$	2.20813e59	0.777322
$33$	−2.70951e59	−0.282872
$34$	−4.21868e59	−0.135444
$35$	2.08007e59	0.0212515
$36$	2.35949e61	0.792262
$37$	4.17558e61	0.475061	0.237530	−	0.971380i	$-0.423662\pi$
$37$	4.17558e61	0.475061	0.237530	+	0.971380i	$0.423662\pi$
$38$	2.44702e61	0.0970924
$39$	3.34671e62	0.475956
$40$	7.84670e62	0.410504
$41$	8.70655e63	1.71745	0.858725	−	0.512437i	$-0.171257\pi$
$41$	8.70655e63	1.71745	0.858725	+	0.512437i	$0.171257\pi$
$42$	−4.05038e61	−0.00308425
$43$	6.17573e64	1.85645	0.928227	−	0.372015i	$-0.121333\pi$
$43$	6.17573e64	1.85645	0.928227	+	0.372015i	$0.121333\pi$
$44$	5.82800e64	0.706544
$45$	1.27627e65	0.636866
$46$	1.24056e65	0.259827
$47$	9.80346e65	0.878040	0.439020	−	0.898477i	$-0.355326\pi$
$47$	9.80346e65	0.878040	0.439020	+	0.898477i	$0.355326\pi$
$48$	7.07020e65	0.275678
$49$	−5.78605e66	−0.999165
$50$	−1.71994e66	−0.133721
$51$	−4.78859e66	−0.170289
$52$	−7.19860e67	−1.18882
$53$	−1.69065e68	−1.31570	−0.657850	−	0.753149i	$-0.728534\pi$
$53$	−1.69065e68	−1.31570	−0.657850	+	0.753149i	$0.728534\pi$
$54$	−5.35566e67	−0.199186
$55$	3.15242e68	0.567961
$56$	1.82327e67	0.0161222
$57$	2.77759e68	0.122071
$58$	1.02625e69	0.226907
$59$	1.06669e70	1.20056	0.600282	−	0.799788i	$-0.295055\pi$
$59$	1.06669e70	1.20056	0.600282	+	0.799788i	$0.295055\pi$
$60$	4.25590e69	0.246613
$61$	2.41593e70	0.728713	0.364356	−	0.931260i	$-0.381289\pi$
$61$	2.41593e70	0.728713	0.364356	+	0.931260i	$0.381289\pi$
$62$	−1.18145e70	−0.187475
$63$	2.96556e69	0.0250124
$64$	−1.16162e71	−0.525961
$65$	−3.89379e71	−0.955642
$66$	−6.13850e70	−0.0824284
$67$	−1.72200e72	−1.27667	−0.638335	−	0.769758i	$-0.720377\pi$
$67$	−1.72200e72	−1.27667	−0.638335	+	0.769758i	$0.720377\pi$
$68$	1.03000e72	0.425339
$69$	1.40815e72	0.326670
$70$	4.71249e70	0.00619267
$71$	8.22517e72	0.617220	0.308610	−	0.951189i	$-0.400136\pi$
$71$	8.22517e72	0.617220	0.308610	+	0.951189i	$0.400136\pi$
$72$	1.11870e73	0.483150
$73$	2.63298e73	0.659470	0.329735	−	0.944074i	$-0.393041\pi$
$73$	2.63298e73	0.659470	0.329735	+	0.944074i	$0.393041\pi$
$74$	9.45996e72	0.138432
$75$	−1.95229e73	−0.168122
$76$	−5.97444e73	−0.304902
$77$	7.32503e72	0.0223062
$78$	7.58212e73	0.138693
$79$	−1.78991e75	−1.97953	−0.989764	−	0.142713i	$-0.954417\pi$
$79$	−1.78991e75	−1.97953	−0.989764	+	0.142713i	$0.954417\pi$
$80$	−8.22595e74	−0.553518
$81$	1.49375e75	0.615348
$82$	1.97251e75	0.500462
$83$	3.77264e75	0.593008	0.296504	−	0.955032i	$-0.404179\pi$
$83$	3.77264e75	0.593008	0.296504	+	0.955032i	$0.404179\pi$
$84$	9.88908e73	0.00968555
$85$	5.57137e75	0.341912
$86$	1.39914e76	0.540968
$87$	1.16489e76	0.285282
$88$	2.76324e76	0.430876
$89$	−1.69258e77	−1.68906	−0.844530	−	0.535509i	$-0.820120\pi$
$89$	−1.69258e77	−1.68906	−0.844530	+	0.535509i	$0.820120\pi$
$90$	2.89144e76	0.185582
$91$	−9.04769e75	−0.0375321
$92$	−3.02885e77	−0.815942
$93$	−1.34105e77	−0.235705
$94$	2.22102e77	0.255859
$95$	−3.23163e77	−0.245098
$96$	5.67842e77	0.284783
$97$	4.19042e78	1.39564	0.697821	−	0.716272i	$-0.254153\pi$
$97$	4.19042e78	1.39564	0.697821	+	0.716272i	$0.254153\pi$
$98$	−1.31085e78	−0.291155
$99$	4.49441e78	0.668472
$100$	4.19927e78	0.419927
$101$	−1.14008e79	−0.769555	−0.384777	−	0.923009i	$-0.625722\pi$
$101$	−1.14008e79	−0.769555	−0.384777	+	0.923009i	$0.625722\pi$
$102$	−1.08487e78	−0.0496218
$103$	−2.23381e79	−0.694987	−0.347493	−	0.937682i	$-0.612967\pi$
$103$	−2.23381e79	−0.694987	−0.347493	+	0.937682i	$0.612967\pi$
$104$	−3.41308e79	−0.724985
$105$	5.34910e77	0.00778580
$106$	−3.83024e79	−0.383393
$107$	3.98038e79	0.274957	0.137479	−	0.990505i	$-0.456100\pi$
$107$	3.98038e79	0.274957	0.137479	+	0.990505i	$0.456100\pi$
$108$	1.30760e80	0.625511
$109$	6.10347e79	0.202876	0.101438	−	0.994842i	$-0.467656\pi$
$109$	6.10347e79	0.202876	0.101438	+	0.994842i	$0.467656\pi$
$110$	7.14194e79	0.165503
$111$	1.07379e80	0.174045
$112$	−1.91140e79	−0.0217390
$113$	1.38832e81	1.11145	0.555725	−	0.831366i	$-0.312441\pi$
$113$	1.38832e81	1.11145	0.555725	+	0.831366i	$0.312441\pi$
$114$	6.29274e79	0.0355712
$115$	−1.63834e81	−0.655901
$116$	−2.50561e81	−0.712563
$117$	−5.55139e81	−1.12476
$118$	2.41664e81	0.349842
$119$	1.29457e80	0.0134283
$120$	2.01785e81	0.150394
$121$	−7.52048e81	−0.403853
$122$	5.47340e81	0.212346
$123$	2.23897e82	0.629212
$124$	2.88453e82	0.588732
$125$	7.22122e82	1.07316
$126$	6.71860e80	0.00728857
$127$	−1.06797e83	−0.847834	−0.423917	−	0.905701i	$-0.639345\pi$
$127$	−1.06797e83	−0.847834	−0.423917	+	0.905701i	$0.639345\pi$
$128$	−1.59790e83	−0.930586
$129$	1.58815e83	0.680138
$130$	−8.82155e82	−0.278473
$131$	−4.67202e83	−1.08965	−0.544827	−	0.838549i	$-0.683405\pi$
$131$	−4.67202e83	−1.08965	−0.544827	+	0.838549i	$0.683405\pi$
$132$	1.49873e83	0.258852
$133$	−7.50908e81	−0.00962602
$134$	−3.90127e83	−0.372020
$135$	7.07291e83	0.502822
$136$	4.88354e83	0.259387
$137$	1.42666e84	0.567359	0.283680	−	0.958919i	$-0.408445\pi$
$137$	1.42666e84	0.567359	0.283680	+	0.958919i	$0.408445\pi$
$138$	3.19022e83	0.0951912
$139$	1.85162e84	0.415402	0.207701	−	0.978192i	$-0.433402\pi$
$139$	1.85162e84	0.415402	0.207701	+	0.978192i	$0.433402\pi$
$140$	−1.15056e83	−0.0194470
$141$	2.52105e84	0.321682
$142$	1.86345e84	0.179857
$143$	−1.37121e85	−1.00307
$144$	−1.17277e85	−0.651473
$145$	−1.35531e85	−0.572800
$146$	5.96513e84	0.192168
$147$	−1.48794e85	−0.366058
$148$	−2.30967e85	−0.434722
$149$	1.10625e86	1.59586	0.797930	−	0.602750i	$-0.205928\pi$
$149$	1.10625e86	1.59586	0.797930	+	0.602750i	$0.205928\pi$
$150$	−4.42299e84	−0.0489905
$151$	5.89617e85	0.502320	0.251160	−	0.967946i	$-0.419188\pi$
$151$	5.89617e85	0.502320	0.251160	+	0.967946i	$0.419188\pi$
$152$	−2.83267e85	−0.185940
$153$	7.94311e85	0.402419
$154$	1.65952e84	0.00649999
$155$	1.56027e86	0.473257
$156$	−1.85119e86	−0.435541
$157$	−1.43336e86	−0.262010	−0.131005	−	0.991382i	$-0.541820\pi$
$157$	−1.43336e86	−0.262010	−0.131005	+	0.991382i	$0.541820\pi$
$158$	−4.05512e86	−0.576831
$159$	−4.34767e86	−0.482026
$160$	−6.60666e86	−0.571798
$161$	−3.80687e85	−0.0257600
$162$	3.38416e86	0.179311
$163$	4.34490e87	1.80538	0.902692	−	0.430287i	$-0.141588\pi$
$163$	4.34490e87	1.80538	0.902692	+	0.430287i	$0.141588\pi$
$164$	−4.81591e87	−1.57162
$165$	8.10675e86	0.208080
$166$	8.54706e86	0.172801
$167$	6.91793e87	1.10325	0.551627	−	0.834091i	$-0.314007\pi$
$167$	6.91793e87	1.10325	0.551627	+	0.834091i	$0.314007\pi$
$168$	4.68872e85	0.00590660
$169$	6.90166e87	0.687747
$170$	1.26222e87	0.0996326
$171$	−4.60734e87	−0.288472
$172$	−3.41602e88	−1.69882
$173$	−5.12084e87	−0.202544	−0.101272	−	0.994859i	$-0.532291\pi$
$173$	−5.12084e87	−0.202544	−0.101272	+	0.994859i	$0.532291\pi$
$174$	2.63910e87	0.0831307
$175$	5.27793e86	0.0132575
$176$	−2.89679e88	−0.580987
$177$	2.74310e88	0.439844
$178$	−3.83462e88	−0.492189
$179$	1.19247e89	1.22674	0.613371	−	0.789795i	$-0.289813\pi$
$179$	1.19247e89	1.22674	0.613371	+	0.789795i	$0.289813\pi$
$180$	−7.05950e88	−0.582787
$181$	2.27641e89	1.50989	0.754947	−	0.655786i	$-0.227663\pi$
$181$	2.27641e89	1.50989	0.754947	+	0.655786i	$0.227663\pi$
$182$	−2.04979e87	−0.0109368
$183$	6.21280e88	0.266974
$184$	−1.43607e89	−0.497591
$185$	−1.24932e89	−0.349454
$186$	−3.03820e88	−0.0686840
$187$	1.96197e89	0.358880
$188$	−5.42265e89	−0.803483
$189$	1.64347e88	0.0197479
$190$	−7.32140e88	−0.0714211
$191$	−1.30499e90	−1.03464	−0.517321	−	0.855791i	$-0.673071\pi$
$191$	−1.30499e90	−1.03464	−0.517321	+	0.855791i	$0.673071\pi$
$192$	−2.98720e89	−0.192693
$193$	1.36353e90	0.716390	0.358195	−	0.933647i	$-0.383392\pi$
$193$	1.36353e90	0.716390	0.358195	+	0.933647i	$0.383392\pi$
$194$	9.49357e89	0.406688
$195$	−1.00133e90	−0.350113
$196$	3.20048e90	0.914323
$197$	2.11090e90	0.493233	0.246616	−	0.969113i	$-0.420681\pi$
$197$	2.11090e90	0.493233	0.246616	+	0.969113i	$0.420681\pi$
$198$	1.01823e90	0.194792
$199$	−6.95730e89	−0.109080	−0.0545399	−	0.998512i	$-0.517369\pi$
$199$	−6.95730e89	−0.109080	−0.0545399	+	0.998512i	$0.517369\pi$
$200$	1.99100e90	0.256087
$201$	−4.42829e90	−0.467726
$202$	−2.58289e90	−0.224247
$203$	−3.14922e89	−0.0224962
$204$	2.64874e90	0.155829
$205$	−2.60497e91	−1.26336
$206$	−5.06080e90	−0.202518
$207$	−2.33578e91	−0.771975
$208$	3.57804e91	0.977560
$209$	−1.13803e91	−0.257261
$210$	1.21186e89	0.00226877
$211$	5.48819e91	0.851672	0.425836	−	0.904800i	$-0.359980\pi$
$211$	5.48819e91	0.851672	0.425836	+	0.904800i	$0.359980\pi$
$212$	9.35160e91	1.20398
$213$	2.11518e91	0.226127
$214$	9.01772e90	0.0801221
$215$	−1.84776e92	−1.36561
$216$	6.19971e91	0.381459
$217$	3.62547e90	0.0185868
$218$	1.38277e91	0.0591177
$219$	6.77096e91	0.241606
$220$	−1.74372e92	−0.519733
$221$	−2.42338e92	−0.603846
$222$	2.43272e91	0.0507165
$223$	−5.44004e92	−0.949643	−0.474822	−	0.880082i	$-0.657487\pi$
$223$	−5.44004e92	−0.949643	−0.474822	+	0.880082i	$0.657487\pi$
$224$	−1.53514e91	−0.0224569
$225$	3.23837e92	0.397299
$226$	3.14529e92	0.323875
$227$	7.29949e92	0.631352	0.315676	−	0.948867i	$-0.397769\pi$
$227$	7.29949e92	0.631352	0.315676	+	0.948867i	$0.397769\pi$
$228$	−1.53638e92	−0.111705
$229$	1.36338e93	0.833905	0.416952	−	0.908928i	$-0.363098\pi$
$229$	1.36338e93	0.833905	0.416952	+	0.908928i	$0.363098\pi$
$230$	−3.71172e92	−0.191129
$231$	1.88370e91	0.00817219
$232$	−1.18799e93	−0.434547
$233$	5.61899e93	1.73420	0.867100	−	0.498134i	$-0.165981\pi$
$233$	5.61899e93	1.73420	0.867100	+	0.498134i	$0.165981\pi$
$234$	−1.25769e93	−0.327753
$235$	−2.93316e93	−0.645886
$236$	−5.90027e93	−1.09862
$237$	−4.60293e93	−0.725228
$238$	2.93291e91	0.00391299
$239$	6.03063e92	0.0681782	0.0340891	−	0.999419i	$-0.489147\pi$
$239$	6.03063e92	0.0681782	0.0340891	+	0.999419i	$0.489147\pi$
$240$	−2.11538e93	−0.202789
$241$	3.90428e93	0.317591	0.158795	−	0.987312i	$-0.449239\pi$
$241$	3.90428e93	0.317591	0.158795	+	0.987312i	$0.449239\pi$
$242$	−1.70380e93	−0.117682
$243$	1.54885e94	0.908995
$244$	−1.33634e94	−0.666836
$245$	1.73117e94	0.734986
$246$	5.07248e93	0.183351
$247$	1.40566e94	0.432864
$248$	1.36764e94	0.359030
$249$	9.70169e93	0.217257
$250$	1.63600e94	0.312717
$251$	−7.98962e94	−1.30441	−0.652205	−	0.758043i	$-0.726156\pi$
$251$	−7.98962e94	−1.30441	−0.652205	+	0.758043i	$0.726156\pi$
$252$	−1.64036e93	−0.0228885
$253$	−5.76945e94	−0.688452
$254$	−2.41952e94	−0.247057
$255$	1.43273e94	0.125264
$256$	3.40142e94	0.254789
$257$	−1.08122e95	−0.694314	−0.347157	−	0.937807i	$-0.612853\pi$
$257$	−1.08122e95	−0.694314	−0.347157	+	0.937807i	$0.612853\pi$
$258$	3.59801e94	0.198191
$259$	−2.90294e93	−0.0137245
$260$	2.15380e95	0.874496
$261$	−1.93227e95	−0.674167
$262$	−1.05847e95	−0.317523
$263$	3.84204e95	0.991538	0.495769	−	0.868454i	$-0.334886\pi$
$263$	3.84204e95	0.991538	0.495769	+	0.868454i	$0.334886\pi$
$264$	7.10592e94	0.157857
$265$	5.05837e95	0.967829
$266$	−1.70121e93	−0.00280501
$267$	−4.35264e95	−0.618811
$268$	9.52501e95	1.16826
$269$	−7.25523e95	−0.768133	−0.384066	−	0.923305i	$-0.625477\pi$
$269$	−7.25523e95	−0.768133	−0.384066	+	0.923305i	$0.625477\pi$
$270$	1.60240e95	0.146522
$271$	−2.43216e96	−1.92179	−0.960894	−	0.276917i	$-0.910687\pi$
$271$	−2.43216e96	−1.92179	−0.960894	+	0.276917i	$0.910687\pi$
$272$	−5.11958e95	−0.349754
$273$	−2.32670e94	−0.0137504
$274$	3.23216e95	0.165328
$275$	7.99889e95	0.354314
$276$	−7.78899e95	−0.298932
$277$	6.71709e95	0.223476	0.111738	−	0.993738i	$-0.464358\pi$
$277$	6.71709e95	0.223476	0.111738	+	0.993738i	$0.464358\pi$
$278$	4.19493e95	0.121047
$279$	2.22448e96	0.557009
$280$	−5.45517e94	−0.0118595
$281$	4.85898e95	0.0917583	0.0458792	−	0.998947i	$-0.485391\pi$
$281$	4.85898e95	0.0917583	0.0458792	+	0.998947i	$0.485391\pi$
$282$	5.71155e95	0.0937377
$283$	1.13183e97	1.61516	0.807580	−	0.589758i	$-0.200777\pi$
$283$	1.13183e97	1.61516	0.807580	+	0.589758i	$0.200777\pi$
$284$	−4.54964e96	−0.564810
$285$	−8.31045e95	−0.0897951
$286$	−3.10653e96	−0.292292
$287$	−6.05296e95	−0.0496173
$288$	−9.41912e96	−0.672988
$289$	−1.25822e97	−0.783954
$290$	−3.07051e96	−0.166913
$291$	1.07761e97	0.511313
$292$	−1.45640e97	−0.603472
$293$	2.29109e97	0.829413	0.414706	−	0.909955i	$-0.363884\pi$
$293$	2.29109e97	0.829413	0.414706	+	0.909955i	$0.363884\pi$
$294$	−3.37099e96	−0.106669
$295$	−3.19151e97	−0.883135
$296$	−1.09508e97	−0.265109
$297$	2.49074e97	0.527776
$298$	2.50625e97	0.465031
$299$	7.12627e97	1.15838
$300$	1.07988e97	0.153846
$301$	−4.29348e96	−0.0536331
$302$	1.33580e97	0.146375
$303$	−2.93181e97	−0.281937
$304$	2.96958e97	0.250719
$305$	−7.22839e97	−0.536041
$306$	1.79954e97	0.117264
$307$	−8.03429e97	−0.460237	−0.230119	−	0.973163i	$-0.573911\pi$
$307$	−8.03429e97	−0.460237	−0.230119	+	0.973163i	$0.573911\pi$
$308$	−4.05174e96	−0.0204121
$309$	−5.74446e97	−0.254618
$310$	3.53485e97	0.137906
$311$	−2.82915e98	−0.971898	−0.485949	−	0.873987i	$-0.661526\pi$
$311$	−2.82915e98	−0.971898	−0.485949	+	0.873987i	$0.661526\pi$
$312$	−8.77705e97	−0.265609
$313$	−1.36197e98	−0.363216	−0.181608	−	0.983371i	$-0.558130\pi$
$313$	−1.36197e98	−0.363216	−0.181608	+	0.983371i	$0.558130\pi$
$314$	−3.24733e97	−0.0763494
$315$	−8.87286e96	−0.0183991
$316$	9.90065e98	1.81144
$317$	7.41767e98	1.19792	0.598958	−	0.800780i	$-0.295582\pi$
$317$	7.41767e98	1.19792	0.598958	+	0.800780i	$0.295582\pi$
$318$	−9.84982e97	−0.140461
$319$	−4.77276e98	−0.601226
$320$	3.47551e98	0.386897
$321$	1.02359e98	0.100735
$322$	−8.62462e96	−0.00750642
$323$	−2.01127e98	−0.154871
$324$	−8.26249e98	−0.563097
$325$	−9.88002e98	−0.596163
$326$	9.84355e98	0.526086
$327$	1.56957e98	0.0743264
$328$	−2.28337e99	−0.958428
$329$	−6.81555e97	−0.0253666
$330$	1.83662e98	0.0606343
$331$	4.81935e98	0.141183	0.0705916	−	0.997505i	$-0.477511\pi$
$331$	4.81935e98	0.141183	0.0705916	+	0.997505i	$0.477511\pi$
$332$	−2.08678e99	−0.542653
$333$	−1.78116e99	−0.411297
$334$	1.56728e99	0.321486
$335$	5.15217e99	0.939119
$336$	−4.91533e97	−0.00796437
$337$	3.87502e99	0.558333	0.279166	−	0.960243i	$-0.409942\pi$
$337$	3.87502e99	0.558333	0.279166	+	0.960243i	$0.409942\pi$
$338$	1.56360e99	0.200408
$339$	3.57019e99	0.407196
$340$	−3.08172e99	−0.312879
$341$	5.49453e99	0.496744
$342$	−1.04381e99	−0.0840604
$343$	8.04851e98	0.0577561
$344$	−1.61964e100	−1.03600
$345$	−4.21314e99	−0.240299
$346$	−1.16015e99	−0.0590211
$347$	1.23307e100	0.559724	0.279862	−	0.960040i	$-0.409711\pi$
$347$	1.23307e100	0.559724	0.279862	+	0.960040i	$0.409711\pi$
$348$	−6.44342e99	−0.261058
$349$	−2.11739e100	−0.765942	−0.382971	−	0.923760i	$-0.625099\pi$
$349$	−2.11739e100	−0.765942	−0.382971	+	0.923760i	$0.625099\pi$
$350$	1.19574e98	0.00386320
$351$	−3.07650e100	−0.888027
$352$	−2.32655e100	−0.600175
$353$	6.07664e100	1.40140	0.700701	−	0.713456i	$-0.252871\pi$
$353$	6.07664e100	1.40140	0.700701	+	0.713456i	$0.252871\pi$
$354$	6.21461e99	0.128170
$355$	−2.46094e100	−0.454027
$356$	9.36229e100	1.54564
$357$	3.32912e98	0.00491965
$358$	2.70159e100	0.357470
$359$	6.79992e100	0.805885	0.402942	−	0.915225i	$-0.367988\pi$
$359$	6.79992e100	0.805885	0.402942	+	0.915225i	$0.367988\pi$
$360$	−3.34713e100	−0.355405
$361$	−9.34173e100	−0.888981
$362$	5.15730e100	0.439981
$363$	−1.93396e100	−0.147957
$364$	5.00460e99	0.0343451
$365$	−7.87779e100	−0.485106
$366$	1.40754e100	0.0777959
$367$	−1.85720e101	−0.921614	−0.460807	−	0.887500i	$-0.652440\pi$
$367$	−1.85720e101	−0.921614	−0.460807	+	0.887500i	$0.652440\pi$
$368$	1.50548e101	0.670945
$369$	−3.71391e101	−1.48693
$370$	−2.83039e100	−0.101830
$371$	1.17537e100	0.0380107
$372$	7.41783e100	0.215690
$373$	3.75252e101	0.981350	0.490675	−	0.871343i	$-0.336750\pi$
$373$	3.75252e101	0.981350	0.490675	+	0.871343i	$0.336750\pi$
$374$	4.44493e100	0.104577
$375$	1.85700e101	0.393168
$376$	−2.57104e101	−0.489993
$377$	5.89519e101	1.01161
$378$	3.72336e99	0.00575452
$379$	−3.86263e101	−0.537816	−0.268908	−	0.963166i	$-0.586663\pi$
$379$	−3.86263e101	−0.537816	−0.268908	+	0.963166i	$0.586663\pi$
$380$	1.78753e101	0.224286
$381$	−2.74638e101	−0.310616
$382$	−2.95652e101	−0.301493
$383$	2.01420e102	1.85247	0.926236	−	0.376945i	$-0.123025\pi$
$383$	2.01420e102	1.85247	0.926236	+	0.376945i	$0.123025\pi$
$384$	−4.10916e101	−0.340933
$385$	−2.19162e100	−0.0164084
$386$	3.08912e101	0.208755
$387$	−2.63435e102	−1.60728
$388$	−2.31787e102	−1.27713
$389$	7.65356e101	0.380938	0.190469	−	0.981693i	$-0.438999\pi$
$389$	7.65356e101	0.380938	0.190469	+	0.981693i	$0.438999\pi$
$390$	−2.26854e101	−0.102022
$391$	−1.01965e102	−0.414448
$392$	1.51744e102	0.557587
$393$	−1.20145e102	−0.399210
$394$	4.78233e101	0.143727
$395$	5.35536e102	1.45614
$396$	−2.48602e102	−0.611710
$397$	3.14882e102	0.701331	0.350665	−	0.936501i	$-0.385955\pi$
$397$	3.14882e102	0.701331	0.350665	+	0.936501i	$0.385955\pi$
$398$	−1.57621e101	−0.0317857
$399$	−1.93103e100	−0.00352663
$400$	−2.08723e102	−0.345304
$401$	1.04073e103	1.56004	0.780022	−	0.625753i	$-0.215208\pi$
$401$	1.04073e103	1.56004	0.780022	+	0.625753i	$0.215208\pi$
$402$	−1.00325e102	−0.136295
$403$	−6.78670e102	−0.835813
$404$	6.30617e102	0.704209
$405$	−4.46926e102	−0.452650
$406$	−7.13470e100	−0.00655537
$407$	−4.39952e102	−0.366797
$408$	1.25585e102	0.0950301
$409$	−2.52838e103	−1.73689	−0.868443	−	0.495789i	$-0.834879\pi$
$409$	−2.52838e103	−1.73689	−0.868443	+	0.495789i	$0.834879\pi$
$410$	−5.90167e102	−0.368140
$411$	3.66879e102	0.207860
$412$	1.23560e103	0.635973
$413$	−7.41586e101	−0.0346844
$414$	−5.29180e102	−0.224952
$415$	−1.12876e103	−0.436216
$416$	2.87370e103	1.00984
$417$	4.76163e102	0.152188
$418$	−2.57825e102	−0.0749656
$419$	6.42522e103	1.69994	0.849971	−	0.526830i	$-0.176619\pi$
$419$	6.42522e103	1.69994	0.849971	+	0.526830i	$0.176619\pi$
$420$	−2.95878e101	−0.00712469
$421$	−4.22922e103	−0.927081	−0.463541	−	0.886076i	$-0.653421\pi$
$421$	−4.22922e103	−0.927081	−0.463541	+	0.886076i	$0.653421\pi$
$422$	1.24337e103	0.248176
$423$	−4.18182e103	−0.760187
$424$	4.43388e103	0.734231
$425$	1.41367e103	0.213297
$426$	4.79203e102	0.0658931
$427$	−1.67960e102	−0.0210526
$428$	−2.20169e103	−0.251610
$429$	−3.52619e103	−0.367488
$430$	−4.18617e103	−0.397936
$431$	−5.19481e103	−0.450524	−0.225262	−	0.974298i	$-0.572324\pi$
$431$	−5.19481e103	−0.450524	−0.225262	+	0.974298i	$0.572324\pi$
$432$	−6.49936e103	−0.514355
$433$	3.00705e103	0.217205	0.108602	−	0.994085i	$-0.465362\pi$
$433$	3.00705e103	0.217205	0.108602	+	0.994085i	$0.465362\pi$
$434$	8.21365e101	0.00541616
$435$	−3.48531e103	−0.209853
$436$	−3.37605e103	−0.185649
$437$	5.91441e103	0.297095
$438$	1.53399e103	0.0704036
$439$	2.10236e104	0.881779	0.440889	−	0.897561i	$-0.354663\pi$
$439$	2.10236e104	0.881779	0.440889	+	0.897561i	$0.354663\pi$
$440$	−8.26751e103	−0.316952
$441$	2.46813e104	0.865055
$442$	−5.49026e103	−0.175960
$443$	1.34279e103	0.0393605	0.0196802	−	0.999806i	$-0.493735\pi$
$443$	1.34279e103	0.0393605	0.0196802	+	0.999806i	$0.493735\pi$
$444$	−5.93952e103	−0.159266
$445$	5.06415e104	1.24247
$446$	−1.23246e104	−0.276724
$447$	2.84482e104	0.584666
$448$	8.07577e102	0.0151951
$449$	−6.23910e104	−1.07496	−0.537479	−	0.843277i	$-0.680623\pi$
$449$	−6.23910e104	−1.07496	−0.537479	+	0.843277i	$0.680623\pi$
$450$	7.33667e103	0.115772
$451$	−9.17348e104	−1.32605
$452$	−7.67928e104	−1.01707
$453$	1.51625e104	0.184032
$454$	1.65373e104	0.183975
$455$	2.70704e103	0.0276086
$456$	−7.28447e103	−0.0681219
$457$	4.17343e104	0.357934	0.178967	−	0.983855i	$-0.442724\pi$
$457$	4.17343e104	0.357934	0.178967	+	0.983855i	$0.442724\pi$
$458$	3.08880e104	0.242998
$459$	4.40196e104	0.317721
$460$	9.06223e104	0.600207
$461$	−1.78885e105	−1.08740	−0.543699	−	0.839281i	$-0.682977\pi$
$461$	−1.78885e105	−1.08740	−0.543699	+	0.839281i	$0.682977\pi$
$462$	4.26760e102	0.00238136
$463$	9.88800e104	0.506593	0.253297	−	0.967389i	$-0.418485\pi$
$463$	9.88800e104	0.506593	0.253297	+	0.967389i	$0.418485\pi$
$464$	1.24541e105	0.585937
$465$	4.01238e104	0.173384
$466$	1.27300e105	0.505343
$467$	−1.45775e105	−0.531700	−0.265850	−	0.964014i	$-0.585653\pi$
$467$	−1.45775e105	−0.531700	−0.265850	+	0.964014i	$0.585653\pi$
$468$	3.07067e105	1.02925
$469$	1.19717e104	0.0368831
$470$	−6.64520e104	−0.188210
$471$	−3.68602e104	−0.0959912
$472$	−2.79750e105	−0.669979
$473$	−6.50693e105	−1.43338
$474$	−1.04281e105	−0.211330
$475$	−8.19987e104	−0.152901
$476$	−7.16075e103	−0.0122881
$477$	7.21173e105	1.13910
$478$	1.36626e104	0.0198670
$479$	−7.10565e105	−0.951373	−0.475687	−	0.879615i	$-0.657800\pi$
$479$	−7.10565e105	−0.951373	−0.475687	+	0.879615i	$0.657800\pi$
$480$	−1.69896e105	−0.209486
$481$	5.43417e105	0.617167
$482$	8.84531e104	0.0925455
$483$	−9.78972e103	−0.00943754
$484$	4.15985e105	0.369561
$485$	−1.25376e106	−1.02663
$486$	3.50898e105	0.264880
$487$	2.44934e106	1.70473	0.852364	−	0.522949i	$-0.175168\pi$
$487$	2.44934e106	1.70473	0.852364	+	0.522949i	$0.175168\pi$
$488$	−6.33600e105	−0.406661
$489$	1.11733e106	0.661428
$490$	3.92203e105	0.214174
$491$	1.05299e106	0.530524	0.265262	−	0.964176i	$-0.414542\pi$
$491$	1.05299e106	0.530524	0.265262	+	0.964176i	$0.414542\pi$
$492$	−1.23846e106	−0.575783
$493$	−8.43504e105	−0.361938
$494$	3.18459e105	0.126136
$495$	−1.34471e106	−0.491727
$496$	−1.43374e106	−0.484112
$497$	−5.71829e104	−0.0178315
$498$	2.19796e105	0.0633082
$499$	−3.28935e106	−0.875263	−0.437631	−	0.899155i	$-0.644182\pi$
$499$	−3.28935e106	−0.875263	−0.437631	+	0.899155i	$0.644182\pi$
$500$	−3.99432e106	−0.982036
$501$	1.77901e106	0.404192
$502$	−1.81008e106	−0.380103
$503$	3.83098e106	0.743659	0.371830	−	0.928301i	$-0.378731\pi$
$503$	3.83098e106	0.743659	0.371830	+	0.928301i	$0.378731\pi$
$504$	−7.77745e104	−0.0139582
$505$	3.41107e106	0.566084
$506$	−1.30709e106	−0.200614
$507$	1.77483e106	0.251966
$508$	5.90731e106	0.775842
$509$	6.85633e104	0.00833181	0.00416590	−	0.999991i	$-0.498674\pi$
$509$	6.85633e104	0.00833181	0.00416590	+	0.999991i	$0.498674\pi$
$510$	3.24591e105	0.0365018
$511$	−1.83050e105	−0.0190521
$512$	1.04293e107	1.00483
$513$	−2.55333e106	−0.227756
$514$	−2.44955e106	−0.202322
$515$	6.68349e106	0.511232
$516$	−8.78461e106	−0.622385
$517$	−1.03292e107	−0.677939
$518$	−6.57674e104	−0.00399931
$519$	−1.31687e106	−0.0742050
$520$	1.02118e107	0.533299
$521$	−1.93007e107	−0.934295	−0.467148	−	0.884179i	$-0.654718\pi$
$521$	−1.93007e107	−0.934295	−0.467148	+	0.884179i	$0.654718\pi$
$522$	−4.37763e106	−0.196451
$523$	−3.32594e107	−1.38388	−0.691940	−	0.721955i	$-0.743244\pi$
$523$	−3.32594e107	−1.38388	−0.691940	+	0.721955i	$0.743244\pi$
$524$	2.58426e107	0.997128
$525$	1.35727e105	0.00485706
$526$	8.70429e106	0.288933
$527$	9.71063e106	0.299039
$528$	−7.44937e106	−0.212853
$529$	−7.72947e106	−0.204951
$530$	1.14600e107	0.282024
$531$	−4.55014e107	−1.03942
$532$	4.15354e105	0.00880865
$533$	1.13308e108	2.23120
$534$	−9.86108e106	−0.180320
$535$	−1.19092e107	−0.202259
$536$	4.51610e107	0.712450
$537$	3.06655e107	0.449434
$538$	−1.64370e107	−0.223833
$539$	6.09636e107	0.771461
$540$	−3.91228e107	−0.460126
$541$	−1.41074e108	−1.54225	−0.771125	−	0.636684i	$-0.780306\pi$
$541$	−1.41074e108	−1.54225	−0.771125	+	0.636684i	$0.780306\pi$
$542$	−5.51016e107	−0.560006
$543$	5.85400e107	0.553171
$544$	−4.11178e107	−0.361305
$545$	−1.82614e107	−0.149235
$546$	−5.27123e105	−0.00400685
$547$	5.31465e107	0.375816	0.187908	−	0.982187i	$-0.439829\pi$
$547$	5.31465e107	0.375816	0.187908	+	0.982187i	$0.439829\pi$
$548$	−7.89137e107	−0.519183
$549$	−1.03055e108	−0.630903
$550$	1.81218e107	0.103246
$551$	4.89269e107	0.259453
$552$	−3.69300e107	−0.182299
$553$	1.24438e107	0.0571887
$554$	1.52178e107	0.0651204
$555$	−3.21275e107	−0.128028
$556$	−1.02420e108	−0.380129
$557$	2.90432e108	1.00407	0.502036	−	0.864847i	$-0.332585\pi$
$557$	2.90432e108	1.00407	0.502036	+	0.864847i	$0.332585\pi$
$558$	5.03964e107	0.162311
$559$	8.03719e108	2.41178
$560$	5.71883e106	0.0159912
$561$	5.04540e107	0.131481
$562$	1.10082e107	0.0267382
$563$	−6.53853e108	−1.48047	−0.740234	−	0.672350i	$-0.765285\pi$
$563$	−6.53853e108	−1.48047	−0.740234	+	0.672350i	$0.765285\pi$
$564$	−1.39449e108	−0.294367
$565$	−4.15380e108	−0.817583
$566$	2.56420e108	0.470655
$567$	−1.03849e107	−0.0177775
$568$	−2.15712e108	−0.344442
$569$	−3.15030e108	−0.469264	−0.234632	−	0.972084i	$-0.575388\pi$
$569$	−3.15030e108	−0.469264	−0.234632	+	0.972084i	$0.575388\pi$
$570$	−1.88277e107	−0.0261661
$571$	−4.19088e108	−0.543475	−0.271737	−	0.962371i	$-0.587598\pi$
$571$	−4.19088e108	−0.543475	−0.271737	+	0.962371i	$0.587598\pi$
$572$	7.58466e108	0.917894
$573$	−3.35591e108	−0.379056
$574$	−1.37132e107	−0.0144584
$575$	−4.15708e108	−0.409174
$576$	4.95505e108	0.455365
$577$	−2.69716e108	−0.231453	−0.115727	−	0.993281i	$-0.536920\pi$
$577$	−2.69716e108	−0.231453	−0.115727	+	0.993281i	$0.536920\pi$
$578$	−2.85054e108	−0.228443
$579$	3.50643e108	0.262460
$580$	7.49671e108	0.524162
$581$	−2.62281e107	−0.0171320
$582$	2.44136e108	0.148996
$583$	1.78132e109	1.01586
$584$	−6.90523e108	−0.368019
$585$	1.66096e109	0.827373
$586$	5.19055e108	0.241689
$587$	−2.20807e109	−0.961188	−0.480594	−	0.876943i	$-0.659579\pi$
$587$	−2.20807e109	−0.961188	−0.480594	+	0.876943i	$0.659579\pi$
$588$	8.23033e108	0.334975
$589$	−5.63259e108	−0.214365
$590$	−7.23050e108	−0.257344
$591$	5.42838e108	0.180703
$592$	1.14801e109	0.357469
$593$	−2.87189e109	−0.836581	−0.418290	−	0.908313i	$-0.637371\pi$
$593$	−2.87189e109	−0.836581	−0.418290	+	0.908313i	$0.637371\pi$
$594$	5.64288e108	0.153793
$595$	−3.87332e107	−0.00987787
$596$	−6.11906e109	−1.46035
$597$	−1.78914e108	−0.0399629
$598$	1.61449e109	0.337550
$599$	−2.43564e109	−0.476708	−0.238354	−	0.971178i	$-0.576608\pi$
$599$	−2.43564e109	−0.476708	−0.238354	+	0.971178i	$0.576608\pi$
$600$	5.12005e108	0.0938210
$601$	−1.26276e109	−0.216659	−0.108330	−	0.994115i	$-0.534550\pi$
$601$	−1.26276e109	−0.216659	−0.108330	+	0.994115i	$0.534550\pi$
$602$	−9.72706e107	−0.0156286
$603$	7.34546e109	1.10531
$604$	−3.26138e109	−0.459666
$605$	2.25010e109	0.297074
$606$	−6.64214e108	−0.0821560
$607$	9.37912e109	1.08695	0.543474	−	0.839426i	$-0.317109\pi$
$607$	9.37912e109	1.08695	0.543474	+	0.839426i	$0.317109\pi$
$608$	2.38501e109	0.259000
$609$	−8.09853e107	−0.00824182
$610$	−1.63762e109	−0.156201
$611$	1.27584e110	1.14069
$612$	−4.39362e109	−0.368249
$613$	1.02139e109	0.0802605	0.0401302	−	0.999194i	$-0.487223\pi$
$613$	1.02139e109	0.0802605	0.0401302	+	0.999194i	$0.487223\pi$
$614$	−1.82020e109	−0.134112
$615$	−6.69893e109	−0.462848
$616$	−1.92105e108	−0.0124480
$617$	−1.52691e110	−0.928004	−0.464002	−	0.885834i	$-0.653587\pi$
$617$	−1.52691e110	−0.928004	−0.464002	+	0.885834i	$0.653587\pi$
$618$	−1.30143e109	−0.0741953
$619$	8.02231e109	0.429061	0.214530	−	0.976717i	$-0.431178\pi$
$619$	8.02231e109	0.429061	0.214530	+	0.976717i	$0.431178\pi$
$620$	−8.63041e109	−0.433071
$621$	−1.29446e110	−0.609494
$622$	−6.40956e109	−0.283210
$623$	1.17672e109	0.0487971
$624$	9.20127e109	0.358143
$625$	−9.04615e109	−0.330524
$626$	−3.08559e109	−0.105841
$627$	−2.92655e109	−0.0942514
$628$	7.92842e109	0.239762
$629$	−7.77539e109	−0.220811
$630$	−2.01018e108	−0.00536147
$631$	1.86506e110	0.467233	0.233616	−	0.972329i	$-0.424944\pi$
$631$	1.86506e110	0.467233	0.233616	+	0.972329i	$0.424944\pi$
$632$	4.69420e110	1.10468
$633$	1.41134e110	0.312022
$634$	1.68050e110	0.349071
$635$	3.19532e110	0.623666
$636$	2.40485e110	0.441095
$637$	−7.53006e110	−1.29805
$638$	−1.08129e110	−0.175196
$639$	−3.50857e110	−0.534375
$640$	4.78087e110	0.684539
$641$	−8.62439e109	−0.116101	−0.0580505	−	0.998314i	$-0.518488\pi$
$641$	−8.62439e109	−0.116101	−0.0580505	+	0.998314i	$0.518488\pi$
$642$	2.31899e109	0.0293539
$643$	−7.70160e110	−0.916743	−0.458372	−	0.888761i	$-0.651567\pi$
$643$	−7.70160e110	−0.916743	−0.458372	+	0.888761i	$0.651567\pi$
$644$	2.10572e109	0.0235726
$645$	−4.75168e110	−0.500309
$646$	−4.55661e109	−0.0451292
$647$	1.96641e111	1.83212	0.916062	−	0.401037i	$-0.131350\pi$
$647$	1.96641e111	1.83212	0.916062	+	0.401037i	$0.131350\pi$
$648$	−3.91750e110	−0.343397
$649$	−1.12390e111	−0.926962
$650$	−2.23836e110	−0.173721
$651$	9.32323e108	0.00680953
$652$	−2.40332e111	−1.65208
$653$	−6.21599e110	−0.402198	−0.201099	−	0.979571i	$-0.564451\pi$
$653$	−6.21599e110	−0.402198	−0.201099	+	0.979571i	$0.564451\pi$
$654$	3.55591e109	0.0216586
$655$	1.39785e111	0.801549
$656$	2.39373e111	1.29233
$657$	−1.12314e111	−0.570954
$658$	−1.54409e109	−0.00739180
$659$	4.33965e111	1.95650	0.978251	−	0.207423i	$-0.0665078\pi$
$659$	4.33965e111	1.95650	0.978251	+	0.207423i	$0.0665078\pi$
$660$	−4.48414e110	−0.190412
$661$	1.41103e111	0.564389	0.282194	−	0.959357i	$-0.408938\pi$
$661$	1.41103e111	0.564389	0.282194	+	0.959357i	$0.408938\pi$
$662$	1.09184e110	0.0411406
$663$	−6.23194e110	−0.221228
$664$	−9.89407e110	−0.330930
$665$	2.24669e109	0.00708090
$666$	−4.03529e110	−0.119851
$667$	2.48044e111	0.694317
$668$	−3.82656e111	−1.00957
$669$	−1.39896e111	−0.347915
$670$	1.16725e111	0.273658
$671$	−2.54550e111	−0.562643
$672$	−3.94775e109	−0.00822740
$673$	−2.62717e111	−0.516289	−0.258144	−	0.966106i	$-0.583111\pi$
$673$	−2.62717e111	−0.516289	−0.258144	+	0.966106i	$0.583111\pi$
$674$	8.77902e110	0.162697
$675$	1.79466e111	0.313678
$676$	−3.81756e111	−0.629348
$677$	−5.41256e111	−0.841686	−0.420843	−	0.907133i	$-0.638266\pi$
$677$	−5.41256e111	−0.841686	−0.420843	+	0.907133i	$0.638266\pi$
$678$	8.08841e110	0.118656
$679$	−2.91326e110	−0.0403202
$680$	−1.46114e111	−0.190805
$681$	1.87713e111	0.231305
$682$	1.24481e111	0.144750
$683$	1.66576e112	1.82808	0.914039	−	0.405627i	$-0.132947\pi$
$683$	1.66576e112	1.82808	0.914039	+	0.405627i	$0.132947\pi$
$684$	2.54849e111	0.263977
$685$	−4.26852e111	−0.417349
$686$	1.82342e110	0.0168300
$687$	3.50607e111	0.305513
$688$	1.69792e112	1.39693
$689$	−2.20024e112	−1.70927
$690$	−9.54504e110	−0.0700226
$691$	8.58467e111	0.594759	0.297379	−	0.954759i	$-0.403887\pi$
$691$	8.58467e111	0.594759	0.297379	+	0.954759i	$0.403887\pi$
$692$	2.83252e111	0.185346
$693$	−3.12460e110	−0.0193122
$694$	2.79358e111	0.163103
$695$	−5.54000e111	−0.305569
$696$	−3.05502e111	−0.159202
$697$	−1.62125e112	−0.798282
$698$	−4.79703e111	−0.223194
$699$	1.44498e112	0.635349
$700$	−2.91941e110	−0.0121317
$701$	−3.70615e112	−1.45566	−0.727832	−	0.685756i	$-0.759472\pi$
$701$	−3.70615e112	−1.45566	−0.727832	+	0.685756i	$0.759472\pi$
$702$	−6.96995e111	−0.258770
$703$	4.51006e111	0.158288
$704$	1.22391e112	0.406097
$705$	−7.54291e111	−0.236629
$706$	1.37669e112	0.408366
$707$	7.92602e110	0.0222325
$708$	−1.51731e112	−0.402495
$709$	−1.84997e112	−0.464129	−0.232065	−	0.972700i	$-0.574548\pi$
$709$	−1.84997e112	−0.464129	−0.232065	+	0.972700i	$0.574548\pi$
$710$	−5.57537e111	−0.132303
$711$	7.63514e112	1.71383
$712$	4.43895e112	0.942585
$713$	−2.85554e112	−0.573657
$714$	7.54225e109	0.00143358
$715$	4.10261e112	0.737857
$716$	−6.59599e112	−1.12258
$717$	1.55083e111	0.0249781
$718$	1.54055e112	0.234833
$719$	5.69435e112	0.821586	0.410793	−	0.911729i	$-0.365252\pi$
$719$	5.69435e112	0.821586	0.410793	+	0.911729i	$0.365252\pi$
$720$	3.50890e112	0.479223
$721$	1.55299e111	0.0200782
$722$	−2.11641e112	−0.259048
$723$	1.00402e112	0.116354
$724$	−1.25916e113	−1.38168
$725$	−3.43893e112	−0.357333
$726$	−4.38147e111	−0.0431145
$727$	3.14790e112	0.293367	0.146684	−	0.989183i	$-0.453140\pi$
$727$	3.14790e112	0.293367	0.146684	+	0.989183i	$0.453140\pi$
$728$	2.37284e111	0.0209449
$729$	−3.37665e112	−0.282325
$730$	−1.78475e112	−0.141359
$731$	−1.14999e113	−0.862892
$732$	−3.43652e112	−0.244305
$733$	−9.05213e112	−0.609739	−0.304869	−	0.952394i	$-0.598613\pi$
$733$	−9.05213e112	−0.609739	−0.304869	+	0.952394i	$0.598613\pi$
$734$	−4.20756e112	−0.268557
$735$	4.45186e112	0.269272
$736$	1.20913e113	0.693103
$737$	1.81435e113	0.985725
$738$	−8.41402e112	−0.433289
$739$	2.79395e113	1.36384	0.681920	−	0.731427i	$-0.261145\pi$
$739$	2.79395e113	1.36384	0.681920	+	0.731427i	$0.261145\pi$
$740$	6.91044e112	0.319781
$741$	3.61480e112	0.158586
$742$	2.66285e111	0.0110763
$743$	2.07791e113	0.819538	0.409769	−	0.912189i	$-0.365609\pi$
$743$	2.07791e113	0.819538	0.409769	+	0.912189i	$0.365609\pi$
$744$	3.51702e112	0.131536
$745$	−3.30986e113	−1.17391
$746$	8.50149e112	0.285964
$747$	−1.60927e113	−0.513413
$748$	−1.08524e113	−0.328406
$749$	−2.76724e111	−0.00794354
$750$	4.20712e112	0.114568
$751$	−9.72161e112	−0.251166	−0.125583	−	0.992083i	$-0.540080\pi$
$751$	−9.72161e112	−0.251166	−0.125583	+	0.992083i	$0.540080\pi$
$752$	2.69531e113	0.660700
$753$	−2.05461e113	−0.477889
$754$	1.33558e113	0.294783
$755$	−1.76411e113	−0.369506
$756$	−9.09065e111	−0.0180711
$757$	−4.33032e113	−0.817020	−0.408510	−	0.912754i	$-0.633952\pi$
$757$	−4.33032e113	−0.817020	−0.408510	+	0.912754i	$0.633952\pi$
$758$	−8.75094e112	−0.156719
$759$	−1.48367e113	−0.252224
$760$	8.47524e112	0.136778
$761$	−5.63572e113	−0.863486	−0.431743	−	0.901997i	$-0.642101\pi$
$761$	−5.63572e113	−0.863486	−0.431743	+	0.901997i	$0.642101\pi$
$762$	−6.22203e112	−0.0905130
$763$	−4.24325e111	−0.00586110
$764$	7.21839e113	0.946788
$765$	−2.37655e113	−0.296020
$766$	4.56326e113	0.539807
$767$	1.38821e114	1.55969
$768$	8.74707e112	0.0933457
$769$	−1.51146e113	−0.153216	−0.0766081	−	0.997061i	$-0.524409\pi$
$769$	−1.51146e113	−0.153216	−0.0766081	+	0.997061i	$0.524409\pi$
$770$	−4.96521e111	−0.00478139
$771$	−2.78046e113	−0.254372
$772$	−7.54215e113	−0.655559
$773$	1.74194e114	1.43861	0.719307	−	0.694693i	$-0.244460\pi$
$773$	1.74194e114	1.43861	0.719307	+	0.694693i	$0.244460\pi$
$774$	−5.96823e113	−0.468357
$775$	3.95899e113	0.295234
$776$	−1.09897e114	−0.778843
$777$	−7.46519e111	−0.00502818
$778$	1.73395e113	0.111005
$779$	9.40398e113	0.572245
$780$	5.53869e113	0.320384
$781$	−8.66627e113	−0.476559
$782$	−2.31006e113	−0.120769
$783$	−1.07084e114	−0.532272
$784$	−1.59079e114	−0.751843
$785$	4.28856e113	0.192735
$786$	−2.72194e113	−0.116329
$787$	−2.89087e114	−1.17497	−0.587485	−	0.809235i	$-0.699882\pi$
$787$	−2.89087e114	−1.17497	−0.587485	+	0.809235i	$0.699882\pi$
$788$	−1.16762e114	−0.451351
$789$	9.88016e113	0.363264
$790$	1.21328e114	0.424317
$791$	−9.65184e112	−0.0321099
$792$	−1.17870e114	−0.373043
$793$	3.14413e114	0.946695
$794$	7.13378e113	0.204367
$795$	1.30081e114	0.354578
$796$	3.84834e113	0.0998175
$797$	2.27379e114	0.561238	0.280619	−	0.959819i	$-0.409460\pi$
$797$	2.27379e114	0.561238	0.280619	+	0.959819i	$0.409460\pi$
$798$	−4.37483e111	−0.00102765
$799$	−1.82551e114	−0.408119
$800$	−1.67636e114	−0.356708
$801$	7.21997e114	1.46235
$802$	2.35782e114	0.454594
$803$	−2.77419e114	−0.509180
$804$	2.44945e114	0.428010
$805$	1.13900e113	0.0189490
$806$	−1.53755e114	−0.243555
$807$	−1.86575e114	−0.281416
$808$	2.98995e114	0.429452
$809$	−1.13994e115	−1.55925	−0.779624	−	0.626248i	$-0.784590\pi$
$809$	−1.13994e115	−1.55925	−0.779624	+	0.626248i	$0.784590\pi$
$810$	−1.01253e114	−0.131901
$811$	3.37570e114	0.418832	0.209416	−	0.977827i	$-0.432844\pi$
$811$	3.37570e114	0.418832	0.209416	+	0.977827i	$0.432844\pi$
$812$	1.74195e113	0.0205860
$813$	−6.25453e114	−0.704074
$814$	−9.96728e113	−0.106884
$815$	−1.29998e115	−1.32804
$816$	−1.31655e114	−0.128137
$817$	6.67042e114	0.618560
$818$	−5.72814e114	−0.506126
$819$	3.85943e113	0.0324944
$820$	1.44090e115	1.15608
$821$	1.31862e115	1.00825	0.504123	−	0.863632i	$-0.331816\pi$
$821$	1.31862e115	1.00825	0.504123	+	0.863632i	$0.331816\pi$
$822$	8.31180e113	0.0605701
$823$	−1.10044e115	−0.764315	−0.382158	−	0.924097i	$-0.624819\pi$
$823$	−1.10044e115	−0.764315	−0.382158	+	0.924097i	$0.624819\pi$
$824$	5.85837e114	0.387840
$825$	2.05699e114	0.129808
$826$	−1.68009e113	−0.0101070
$827$	−1.56799e115	−0.899240	−0.449620	−	0.893220i	$-0.648441\pi$
$827$	−1.56799e115	−0.899240	−0.449620	+	0.893220i	$0.648441\pi$
$828$	1.29200e115	0.706424
$829$	2.57815e115	1.34402	0.672008	−	0.740544i	$-0.265432\pi$
$829$	2.57815e115	1.34402	0.672008	+	0.740544i	$0.265432\pi$
$830$	−2.55725e114	−0.127113
$831$	1.72736e114	0.0818734
$832$	−1.51174e115	−0.683293
$833$	1.07743e115	0.464419
$834$	1.07877e114	0.0443474
$835$	−2.06982e115	−0.811553
$836$	6.29485e114	0.235417
$837$	1.23278e115	0.439773
$838$	1.45566e115	0.495360
$839$	−1.81002e115	−0.587607	−0.293803	−	0.955866i	$-0.594921\pi$
$839$	−1.81002e115	−0.587607	−0.293803	+	0.955866i	$0.594921\pi$
$840$	−1.40285e113	−0.00434489
$841$	−1.33215e115	−0.393651
$842$	−9.58148e114	−0.270150
$843$	1.24953e114	0.0336169
$844$	−3.03572e115	−0.779354
$845$	−2.06495e115	−0.505907
$846$	−9.47408e114	−0.221517
$847$	5.22838e113	0.0116673
$848$	−4.64818e115	−0.990027
$849$	2.91060e115	0.591737
$850$	3.20272e114	0.0621543
$851$	2.28646e115	0.423590
$852$	−1.16998e115	−0.206926
$853$	9.42828e115	1.59201	0.796005	−	0.605290i	$-0.206943\pi$
$853$	9.42828e115	1.59201	0.796005	+	0.605290i	$0.206943\pi$
$854$	−3.80521e113	−0.00613469
$855$	1.37850e115	0.212200
$856$	−1.04389e115	−0.153441
$857$	3.47343e115	0.487547	0.243774	−	0.969832i	$-0.421615\pi$
$857$	3.47343e115	0.487547	0.243774	+	0.969832i	$0.421615\pi$
$858$	−7.98874e114	−0.107085
$859$	−3.35629e115	−0.429665	−0.214832	−	0.976651i	$-0.568921\pi$
$859$	−3.35629e115	−0.429665	−0.214832	+	0.976651i	$0.568921\pi$
$860$	1.02206e116	1.24965
$861$	−1.55658e114	−0.0181780
$862$	−1.17691e115	−0.131282
$863$	−1.83081e115	−0.195082	−0.0975409	−	0.995232i	$-0.531098\pi$
$863$	−1.83081e115	−0.195082	−0.0975409	+	0.995232i	$0.531098\pi$
$864$	−5.21995e115	−0.531341
$865$	1.53214e115	0.148992
$866$	6.81260e114	0.0632931
$867$	−3.23562e115	−0.287213
$868$	−2.00538e114	−0.0170085
$869$	1.88590e116	1.52840
$870$	−7.89611e114	−0.0611509
$871$	−2.24104e116	−1.65857
$872$	−1.60069e115	−0.113216
$873$	−1.78749e116	−1.20832
$874$	1.33993e115	0.0865729
$875$	−5.02033e114	−0.0310037
$876$	−3.74526e115	−0.221091
$877$	−2.55219e116	−1.44022	−0.720110	−	0.693860i	$-0.755909\pi$
$877$	−2.55219e116	−1.44022	−0.720110	+	0.693860i	$0.755909\pi$
$878$	4.76299e115	0.256949
$879$	5.89175e115	0.303867
$880$	8.66710e115	0.427374
$881$	1.70526e116	0.803973	0.401987	−	0.915646i	$-0.368320\pi$
$881$	1.70526e116	0.803973	0.401987	+	0.915646i	$0.368320\pi$
$882$	5.59165e115	0.252076
$883$	2.44942e116	1.05588	0.527941	−	0.849281i	$-0.322964\pi$
$883$	2.44942e116	1.05588	0.527941	+	0.849281i	$0.322964\pi$
$884$	1.34046e116	0.552572
$885$	−8.20728e115	−0.323549
$886$	3.04214e114	0.0114696
$887$	−6.30841e115	−0.227477	−0.113738	−	0.993511i	$-0.536283\pi$
$887$	−6.30841e115	−0.227477	−0.113738	+	0.993511i	$0.536283\pi$
$888$	−2.81611e115	−0.0971265
$889$	7.42470e114	0.0244940
$890$	1.14731e116	0.362054
$891$	−1.57386e116	−0.475113
$892$	3.00909e116	0.869006
$893$	1.05888e116	0.292558
$894$	6.44506e115	0.170371
$895$	−3.56783e116	−0.902391
$896$	1.11089e115	0.0268847
$897$	1.83259e116	0.424388
$898$	−1.41349e116	−0.313241
$899$	−2.36224e116	−0.500976
$900$	−1.79126e116	−0.363563
$901$	3.14818e116	0.611547
$902$	−2.07829e116	−0.386409
$903$	−1.10411e115	−0.0196492
$904$	−3.64098e116	−0.620249
$905$	−6.81094e116	−1.11068
$906$	3.43514e115	0.0536266
$907$	1.49305e116	0.223145	0.111572	−	0.993756i	$-0.464411\pi$
$907$	1.49305e116	0.223145	0.111572	+	0.993756i	$0.464411\pi$
$908$	−4.03761e116	−0.577742
$909$	4.86316e116	0.666263
$910$	6.13291e114	0.00804510
$911$	1.03169e117	1.29591	0.647953	−	0.761680i	$-0.275625\pi$
$911$	1.03169e117	1.29591	0.647953	+	0.761680i	$0.275625\pi$
$912$	7.63655e115	0.0918546
$913$	−3.97496e116	−0.457864
$914$	9.45507e115	0.104301
$915$	−1.85885e116	−0.196386
$916$	−7.54137e116	−0.763095
$917$	3.24808e115	0.0314802
$918$	9.97283e115	0.0925833
$919$	1.91946e117	1.70693	0.853465	−	0.521150i	$-0.174497\pi$
$919$	1.91946e117	1.70693	0.853465	+	0.521150i	$0.174497\pi$
$920$	4.29668e116	0.366028
$921$	−2.06609e116	−0.168614
$922$	−4.05272e116	−0.316866
$923$	1.07044e117	0.801851
$924$	−1.04194e115	−0.00747826
$925$	−3.17000e116	−0.218002
$926$	2.24017e116	0.147620
$927$	9.52867e116	0.601704
$928$	1.00025e117	0.605288
$929$	−2.30453e117	−1.33647	−0.668237	−	0.743948i	$-0.732951\pi$
$929$	−2.30453e117	−1.33647	−0.668237	+	0.743948i	$0.732951\pi$
$930$	9.09020e115	0.0505239
$931$	−6.24954e116	−0.332917
$932$	−3.10807e117	−1.58694
$933$	−7.27543e116	−0.356069
$934$	−3.30259e116	−0.154936
$935$	−5.87015e116	−0.263992
$936$	1.45590e117	0.627676
$937$	−1.07766e117	−0.445416	−0.222708	−	0.974885i	$-0.571490\pi$
$937$	−1.07766e117	−0.445416	−0.222708	+	0.974885i	$0.571490\pi$
$938$	2.71223e115	0.0107477
$939$	−3.50242e116	−0.133069
$940$	1.62244e117	0.591042
$941$	−3.50987e117	−1.22603	−0.613014	−	0.790072i	$-0.710043\pi$
$941$	−3.50987e117	−1.22603	−0.613014	+	0.790072i	$0.710043\pi$
$942$	−8.35082e115	−0.0279717
$943$	4.76752e117	1.53137
$944$	2.93271e117	0.903390
$945$	−4.91722e115	−0.0145266
$946$	−1.47417e117	−0.417684
$947$	−3.03631e117	−0.825130	−0.412565	−	0.910928i	$-0.635367\pi$
$947$	−3.03631e117	−0.825130	−0.412565	+	0.910928i	$0.635367\pi$
$948$	2.54605e117	0.663647
$949$	3.42660e117	0.856739
$950$	−1.85771e116	−0.0445550
$951$	1.90752e117	0.438874
$952$	−3.39513e115	−0.00749372
$953$	−2.65846e117	−0.562939	−0.281469	−	0.959570i	$-0.590822\pi$
$953$	−2.65846e117	−0.562939	−0.281469	+	0.959570i	$0.590822\pi$
$954$	1.63385e117	0.331933
$955$	3.90450e117	0.761083
$956$	−3.33576e116	−0.0623890
$957$	−1.22736e117	−0.220268
$958$	−1.60981e117	−0.277229
$959$	−9.91841e115	−0.0163911
$960$	8.93761e116	0.141745
$961$	−3.85065e117	−0.586085
$962$	1.23113e117	0.179841
$963$	−1.69789e117	−0.238052
$964$	−2.15960e117	−0.290623
$965$	−4.07962e117	−0.526976
$966$	−2.21790e115	−0.00275008
$967$	−1.24040e118	−1.47644	−0.738218	−	0.674562i	$-0.764333\pi$
$967$	−1.24040e118	−1.47644	−0.738218	+	0.674562i	$0.764333\pi$
$968$	1.97231e117	0.225371
$969$	−5.17217e116	−0.0567392
$970$	−2.84044e117	−0.299160
$971$	1.57789e118	1.59558	0.797789	−	0.602937i	$-0.206003\pi$
$971$	1.57789e118	1.59558	0.797789	+	0.602937i	$0.206003\pi$
$972$	−8.56725e117	−0.831810
$973$	−1.28728e116	−0.0120010
$974$	5.54908e117	0.496755
$975$	−2.54074e117	−0.218413
$976$	6.64223e117	0.548335
$977$	−2.24009e116	−0.0177595	−0.00887973	−	0.999961i	$-0.502827\pi$
$977$	−2.24009e116	−0.0177595	−0.00887973	+	0.999961i	$0.502827\pi$
$978$	2.53136e117	0.192739
$979$	1.78336e118	1.30413
$980$	−9.57572e117	−0.672576
$981$	−2.60353e117	−0.175645
$982$	2.38559e117	0.154594
$983$	1.03837e118	0.646383	0.323192	−	0.946334i	$-0.395244\pi$
$983$	1.03837e118	0.646383	0.323192	+	0.946334i	$0.395244\pi$
$984$	−5.87190e117	−0.351134
$985$	−6.31574e117	−0.362822
$986$	−1.91099e117	−0.105468
$987$	−1.75268e116	−0.00929343
$988$	−7.77523e117	−0.396108
$989$	3.38170e118	1.65532
$990$	−3.04650e117	−0.143289
$991$	9.97864e117	0.450985	0.225493	−	0.974245i	$-0.427601\pi$
$991$	9.97864e117	0.450985	0.225493	+	0.974245i	$0.427601\pi$
$992$	−1.15151e118	−0.500100
$993$	1.23934e117	0.0517245
$994$	−1.29550e116	−0.00519608
$995$	2.08160e117	0.0802391
$996$	−5.36635e117	−0.198809
$997$	−5.36356e118	−1.90983	−0.954914	−	0.296883i	$-0.904053\pi$
$997$	−5.36356e118	−1.90983	−0.954914	+	0.296883i	$0.904053\pi$
$998$	−7.45215e117	−0.255050
$999$	−9.87094e117	−0.324729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.80.a.a.1.4	✓	6
3.2	odd	2		9.80.a.b.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.80.a.a.1.4	✓	6	1.1	even	1	trivial
9.80.a.b.1.3		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 80 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.26554e11 q^{2} +2.57159e18 q^{3} -5.53136e23 q^{4} -2.99197e27 q^{5} +5.82605e29 q^{6} -6.95219e31 q^{7} -2.62259e35 q^{8} -4.26565e37 q^{9} -6.77842e38 q^{10} -1.05363e41 q^{11} -1.42244e42 q^{12} +1.30142e44 q^{13} -1.57505e43 q^{14} -7.69412e45 q^{15} +2.74934e47 q^{16} -1.86211e48 q^{17} -9.66401e48 q^{18} +1.08010e50 q^{19} +1.65496e51 q^{20} -1.78782e50 q^{21} -2.38704e52 q^{22} +5.47579e53 q^{23} -6.74423e53 q^{24} -7.59175e54 q^{25} +2.94841e55 q^{26} -2.36397e56 q^{27} +3.84551e55 q^{28} +4.52983e57 q^{29} -1.74314e57 q^{30} -5.21486e58 q^{31} +2.20813e59 q^{32} -2.70951e59 q^{33} -4.21868e59 q^{34} +2.08007e59 q^{35} +2.35949e61 q^{36} +4.17558e61 q^{37} +2.44702e61 q^{38} +3.34671e62 q^{39} +7.84670e62 q^{40} +8.70655e63 q^{41} -4.05038e61 q^{42} +6.17573e64 q^{43} +5.82800e64 q^{44} +1.27627e65 q^{45} +1.24056e65 q^{46} +9.80346e65 q^{47} +7.07020e65 q^{48} -5.78605e66 q^{49} -1.71994e66 q^{50} -4.78859e66 q^{51} -7.19860e67 q^{52} -1.69065e68 q^{53} -5.35566e67 q^{54} +3.15242e68 q^{55} +1.82327e67 q^{56} +2.77759e68 q^{57} +1.02625e69 q^{58} +1.06669e70 q^{59} +4.25590e69 q^{60} +2.41593e70 q^{61} -1.18145e70 q^{62} +2.96556e69 q^{63} -1.16162e71 q^{64} -3.89379e71 q^{65} -6.13850e70 q^{66} -1.72200e72 q^{67} +1.03000e72 q^{68} +1.40815e72 q^{69} +4.71249e70 q^{70} +8.22517e72 q^{71} +1.11870e73 q^{72} +2.63298e73 q^{73} +9.45996e72 q^{74} -1.95229e73 q^{75} -5.97444e73 q^{76} +7.32503e72 q^{77} +7.58212e73 q^{78} -1.78991e75 q^{79} -8.22595e74 q^{80} +1.49375e75 q^{81} +1.97251e75 q^{82} +3.77264e75 q^{83} +9.88908e73 q^{84} +5.57137e75 q^{85} +1.39914e76 q^{86} +1.16489e76 q^{87} +2.76324e76 q^{88} -1.69258e77 q^{89} +2.89144e76 q^{90} -9.04769e75 q^{91} -3.02885e77 q^{92} -1.34105e77 q^{93} +2.22102e77 q^{94} -3.23163e77 q^{95} +5.67842e77 q^{96} +4.19042e78 q^{97} -1.31085e78 q^{98} +4.49441e78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3} + 15\!\cdots\!88 q^{4} + 60\!\cdots\!40 q^{5} - 22\!\cdots\!28 q^{6} - 20\!\cdots\!00 q^{7} + 54\!\cdots\!60 q^{8} + 98\!\cdots\!22 q^{9} + 27\!\cdots\!40 q^{10}+ \cdots + 12\!\cdots\!24 q^{99}+O(q^{100}) \) 6 * q - 16086577320 * q^2 + 1942174928281180680 * q^3 + 1549737362258405903681088 * q^4 + 6092984858773763455723827540 * q^5 - 2227106590325939088404927087328 * q^6 - 204133057837186288371299604423600 * q^7 + 542570064661378776298915601390568960 * q^8 + 98496326492153316059886441015309696222 * q^9 + 2720626696366658228219065452729623532240 * q^10 + 326182707503353434196853598345012484552152 * q^11 + 3662741799314627362069151990938777789858560 * q^12 - 249286867791526696387831019648013646893106140 * q^13 + 1866634067474695788912841823339193553138295616 * q^14 + 53939724989186019570794541522119517534771796080 * q^15 - 681627631644510368706137880459644753465449181184 * q^16 + 829554518710324966978506506427078451803483469740 * q^17 + 20783419681388619276512545895581772264264550807480 * q^18 - 50727940848110344442361931427855575819428647228760 * q^19 - 1467030065046629207751264576643706806587735144958080 * q^20 + 11440846038310308150487768012211089482880511198926272 * q^21 + 36817507512313772519930542191150104222671820963556960 * q^22 - 1046924887201563380993656359631631933258453525094738960 * q^23 + 4647998047182641817986339484942489649049309172966328320 * q^24 + 10836995626543537474051791335153252813979338793331307850 * q^25 - 165657588130323625805363235243378873928973276983585168368 * q^26 + 452244485424938477892504860024752019079362449583874943440 * q^27 + 1004680642640065837930850364413184139977872155405489282560 * q^28 - 7120822866262655112931363073018274881104708247497947521340 * q^29 - 1093089132342530488188112356341250721972394415479943059520 * q^30 + 134345039550847531062964315804153164343444264343589333172032 * q^31 - 367680407387361126658464447414461787802285956837455133573120 * q^32 + 694937277679484430969386562214930563011269531321798125315360 * q^33 + 3154306959722239121253159757854043021326472297974364404980016 * q^34 + 9191056770903655504272784196241783249847740561191433159558240 * q^35 + 19880287065959074647932230862843896929437344679866234828597056 * q^36 + 200218543091040103155222783880989961642213560574664429550198420 * q^37 + 866365883974611161836395390925862263352921297032838009795060640 * q^38 + 1846928010477803855453412626793191219191424716227436821180804144 * q^39 + 9116669264447274408945009430906339427674431802850195585057510400 * q^40 + 19216804901837266991242147464997667315402616992351385711235458972 * q^41 + 112315174478490788723912174839938916243710780267342081630678531840 * q^42 + 108832931910908864051094641347526853298463718485111641638401400600 * q^43 + 495514650695382135238363336424200091081783038631873261666636656896 * q^44 + 1089311173064980984859644147008913582964905804089164802662670706980 * q^45 + 2339423217798161589056888023635021837153755261863446723443331974592 * q^46 + 766732507168785220421816169748850175208159379232549271592508353760 * q^47 - 1227537570851109157458973684400646232156423736031048093315900456960 * q^48 + 3801016219812200810689187746878210669081675204402752707309154018358 * q^49 - 50723521315108078882353551947661611720805543300108849711322864485400 * q^50 - 139865466375558864334882784640098531626186142446280524443365433199728 * q^51 - 279692249004488191323071540832092417841619330373410063262542264310400 * q^52 - 312193237964710957330604375297544855480450344577449082153802391971020 * q^53 - 996221038973994559873624494431619704350011373216284617130312268666560 * q^54 - 861958222068919393142591787960630586871784969446963670182827020790320 * q^55 + 1123629643438673418216699268533992018915072902064015953839024305295360 * q^56 + 7795598779799587371741461301046795526293245245773998812837273820000480 * q^57 + 16584702356914156466182151363602691995360915944935914137385742159510160 * q^58 + 24289171784532714189639095038219795042285164994033400426178461238907320 * q^59 + 73025956047571458013400417312791668535879728806786116560639243534051840 * q^60 + 80560570425826852880081093564684385117241348668836108242495308815618052 * q^61 + 59777568713863815377707698536571620658579394379949737090862924510332160 * q^62 - 276708678056196744256455115102015383166989187390931876478468368856762480 * q^63 - 719203226636338274682481908236724651863342420498670194455988567598170112 * q^64 - 1007462919483461647300380829039677154191109543250817689988654733030592520 * q^65 - 3347562853423538991999694027669961627986534585541581689746575315495214976 * q^66 - 1851521876973893932513297183455714100127257334040085257904842903903517560 * q^67 - 5899582938115809421316043854246769288699297144820927766700932855979726720 * q^68 - 1427672735602453311144050658084524391331260046448660152415370050225171136 * q^69 + 31159148342952686307596185437939815723517531766889921556924090292621741440 * q^70 + 38507401093845789827495210229167852070939724868887506542264571604541264592 * q^71 + 87904411000641647434917578390462554629488250565124366592415232306933521920 * q^72 + 61123654206386061400310438862981106227383729069503080628162601940159787740 * q^73 + 136513352063977853606694381822259496818965955504365628093794971441921163216 * q^74 + 113188706706427317048365034543759604727098826077328333023878456326260918200 * q^75 - 249903768766885839664688587580825575582546834454828556400015599314274074880 * q^76 - 1195099252106099653800449972868194220235362175583181442486256041652274244800 * q^77 - 3022231856978250782599441544561070134871217051487771942772538597436408443200 * q^78 - 188234723479363903277484397100590307076741783512190126828886315155446684640 * q^79 - 2750248132852209015421484068233717972689944891189322073844459755369097666560 * q^80 - 4202996734890713231427597758184507891641102417282671988811370042535012566794 * q^81 + 3834792966214046709977047126406184257851543195738078433637414913324683717360 * q^82 + 14506845760765784842493952470927474286413727909244314121162679395439622145320 * q^83 + 48942789227023150657016145376829988370028655394086238910889917134273615865856 * q^84 + 38946066828627954832778050727572362568084538101228336437758435671222134267240 * q^85 + 66363633323077708072616297459993363454350669286030390599179655949306835458912 * q^86 - 12188467007600920252987005731487987332580129454574096199578444638747687628880 * q^87 - 68086553439664359269830684533538140843829745277114000504065479672707840583680 * q^88 + 88790169947368466670673875396871954428202115924137373286785364937730407494780 * q^89 - 678121360108159288271315537216087664710338266311311066150921870820864233179120 * q^90 - 1105665330428280782729905276805137770501582996765091919549546053816493845198368 * q^91 - 581852119074779563003978084378550280950528927013853021971971412987670782543360 * q^92 - 724063571132401087495277238269757837179269218308363767014177350097338957840640 * q^93 - 342394004508386413823498343959337212855421843329465021317054652742559913721984 * q^94 + 4133010515441143062055572903340407460351722715065934937506390604234109634359600 * q^95 + 4500277093535091993817003185543220432802869972147132801867826645045331188908032 * q^96 + 2053881285944963905800936410853289740689894385863240159901124624782493905690060 * q^97 + 21591608457226642856925919189308208713047358263642522360137695155926522503830040 * q^98 + 12210721611676619111412804269965201185505307365258823385190308559518832844781624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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