LMFDB - Embedded newform 1.80.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,80,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 80, names="a")

//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);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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			1.1
Root			$-5.13988e10$ 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)

$f(q)$	$=$	$q-1.23625e12 q^{2} -2.24416e18 q^{3} +9.23858e23 q^{4} -5.14707e27 q^{5} +2.77435e30 q^{6} +4.93307e32 q^{7} -3.94854e35 q^{8} -4.42334e37 q^{9} +O(q^{10})$	\(q-1.23625e12 q^{2} -2.24416e18 q^{3} +9.23858e23 q^{4} -5.14707e27 q^{5} +2.77435e30 q^{6} +4.93307e32 q^{7} -3.94854e35 q^{8} -4.42334e37 q^{9} +6.36308e39 q^{10} +1.90215e41 q^{11} -2.07328e42 q^{12} -7.98386e43 q^{13} -6.09852e44 q^{14} +1.15508e46 q^{15} -7.02992e46 q^{16} -4.22775e48 q^{17} +5.46836e49 q^{18} -5.43469e50 q^{19} -4.75516e51 q^{20} -1.10706e51 q^{21} -2.35154e53 q^{22} -6.81154e53 q^{23} +8.86114e53 q^{24} +9.94869e54 q^{25} +9.87007e55 q^{26} +2.09835e56 q^{27} +4.55746e56 q^{28} -1.01743e58 q^{29} -1.42797e58 q^{30} +1.25251e58 q^{31} +3.25582e59 q^{32} -4.26873e59 q^{33} +5.22657e60 q^{34} -2.53908e60 q^{35} -4.08654e61 q^{36} -6.27648e61 q^{37} +6.71865e62 q^{38} +1.79170e62 q^{39} +2.03234e63 q^{40} +6.35773e63 q^{41} +1.36860e63 q^{42} -1.89548e64 q^{43} +1.75732e65 q^{44} +2.27672e65 q^{45} +8.42078e65 q^{46} -6.42119e65 q^{47} +1.57762e65 q^{48} -5.54754e66 q^{49} -1.22991e67 q^{50} +9.48774e66 q^{51} -7.37595e67 q^{52} +1.33588e68 q^{53} -2.59410e68 q^{54} -9.79052e68 q^{55} -1.94784e68 q^{56} +1.21963e69 q^{57} +1.25780e70 q^{58} -2.01169e69 q^{59} +1.06713e70 q^{60} +1.94595e69 q^{61} -1.54842e70 q^{62} -2.18206e70 q^{63} -3.60008e71 q^{64} +4.10935e71 q^{65} +5.27724e71 q^{66} -1.81247e72 q^{67} -3.90584e72 q^{68} +1.52862e72 q^{69} +3.13895e72 q^{70} +1.18133e73 q^{71} +1.74657e73 q^{72} +2.44514e73 q^{73} +7.75932e73 q^{74} -2.23264e73 q^{75} -5.02088e74 q^{76} +9.38346e73 q^{77} -2.21500e74 q^{78} +1.60756e74 q^{79} +3.61835e74 q^{80} +1.70846e75 q^{81} -7.85977e75 q^{82} +4.26218e75 q^{83} -1.02277e75 q^{84} +2.17605e76 q^{85} +2.34329e76 q^{86} +2.28327e76 q^{87} -7.51073e76 q^{88} +1.07359e77 q^{89} -2.81460e77 q^{90} -3.93849e76 q^{91} -6.29290e77 q^{92} -2.81083e76 q^{93} +7.93822e77 q^{94} +2.79727e78 q^{95} -7.30657e77 q^{96} -3.66274e78 q^{97} +6.85816e78 q^{98} -8.41387e78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3}+ \cdots + 98\!\cdots\!22 q^{9}+O(q^{10}) $ 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	$ 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3}+ \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

Display 100 coefficients 10 coefficients

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 $

$2$	−1.23625e12	−1.59009	−0.795046	−	0.606549i	$-0.792554\pi$
$2$	−1.23625e12	−1.59009	−0.795046	+	0.606549i	$0.792554\pi$
$3$	−2.24416e18	−0.319716	−0.159858	−	0.987140i	$-0.551104\pi$
$3$	−2.24416e18	−0.319716	−0.159858	+	0.987140i	$0.551104\pi$
$4$	9.23858e23	1.52840
$5$	−5.14707e27	−1.26545	−0.632725	−	0.774377i	$-0.718063\pi$
$5$	−5.14707e27	−1.26545	−0.632725	+	0.774377i	$0.718063\pi$
$6$	2.77435e30	0.508377
$7$	4.93307e32	0.204996	0.102498	−	0.994733i	$-0.467317\pi$
$7$	4.93307e32	0.204996	0.102498	+	0.994733i	$0.467317\pi$
$8$	−3.94854e35	−0.840198
$9$	−4.42334e37	−0.897782
$10$	6.36308e39	2.01218
$11$	1.90215e41	1.39391	0.696955	−	0.717115i	$-0.254538\pi$
$11$	1.90215e41	1.39391	0.696955	+	0.717115i	$0.254538\pi$
$12$	−2.07328e42	−0.488652
$13$	−7.98386e43	−0.796985	−0.398493	−	0.917171i	$-0.630467\pi$
$13$	−7.98386e43	−0.796985	−0.398493	+	0.917171i	$0.630467\pi$
$14$	−6.09852e44	−0.325962
$15$	1.15508e46	0.404584
$16$	−7.02992e46	−0.192403
$17$	−4.22775e48	−1.05530	−0.527651	−	0.849461i	$-0.676927\pi$
$17$	−4.22775e48	−1.05530	−0.527651	+	0.849461i	$0.676927\pi$
$18$	5.46836e49	1.42756
$19$	−5.43469e50	−1.67651	−0.838257	−	0.545275i	$-0.816425\pi$
$19$	−5.43469e50	−1.67651	−0.838257	+	0.545275i	$0.816425\pi$
$20$	−4.75516e51	−1.93411
$21$	−1.10706e51	−0.0655403
$22$	−2.35154e53	−2.21645
$23$	−6.81154e53	−1.10916	−0.554582	−	0.832129i	$-0.687122\pi$
$23$	−6.81154e53	−1.10916	−0.554582	+	0.832129i	$0.687122\pi$
$24$	8.86114e53	0.268624
$25$	9.94869e54	0.601361
$26$	9.87007e55	1.26728
$27$	2.09835e56	0.606750
$28$	4.55746e56	0.313314
$29$	−1.01743e58	−1.74897	−0.874486	−	0.485050i	$-0.838801\pi$
$29$	−1.01743e58	−1.74897	−0.874486	+	0.485050i	$0.838801\pi$
$30$	−1.42797e58	−0.643326
$31$	1.25251e58	0.154523	0.0772616	−	0.997011i	$-0.475382\pi$
$31$	1.25251e58	0.154523	0.0772616	+	0.997011i	$0.475382\pi$
$32$	3.25582e59	1.14614
$33$	−4.26873e59	−0.445655
$34$	5.22657e60	1.67803
$35$	−2.53908e60	−0.259411
$36$	−4.08654e61	−1.37217
$37$	−6.27648e61	−0.714082	−0.357041	−	0.934089i	$-0.616214\pi$
$37$	−6.27648e61	−0.714082	−0.357041	+	0.934089i	$0.616214\pi$
$38$	6.71865e62	2.66581
$39$	1.79170e62	0.254809
$40$	2.03234e63	1.06323
$41$	6.35773e63	1.25412	0.627061	−	0.778970i	$-0.284258\pi$
$41$	6.35773e63	1.25412	0.627061	+	0.778970i	$0.284258\pi$
$42$	1.36860e63	0.104215
$43$	−1.89548e64	−0.569791	−0.284895	−	0.958559i	$-0.591959\pi$
$43$	−1.89548e64	−0.569791	−0.284895	+	0.958559i	$0.591959\pi$
$44$	1.75732e65	2.13045
$45$	2.27672e65	1.13610
$46$	8.42078e65	1.76367
$47$	−6.42119e65	−0.575109	−0.287554	−	0.957764i	$-0.592842\pi$
$47$	−6.42119e65	−0.575109	−0.287554	+	0.957764i	$0.592842\pi$
$48$	1.57762e65	0.0615141
$49$	−5.54754e66	−0.957977
$50$	−1.22991e67	−0.956220
$51$	9.48774e66	0.337397
$52$	−7.37595e67	−1.21811
$53$	1.33588e68	1.03961	0.519804	−	0.854285i	$-0.326005\pi$
$53$	1.33588e68	1.03961	0.519804	+	0.854285i	$0.326005\pi$
$54$	−2.59410e68	−0.964790
$55$	−9.79052e68	−1.76392
$56$	−1.94784e68	−0.172237
$57$	1.21963e69	0.536008
$58$	1.25780e70	2.78103
$59$	−2.01169e69	−0.226416	−0.113208	−	0.993571i	$-0.536113\pi$
$59$	−2.01169e69	−0.226416	−0.113208	+	0.993571i	$0.536113\pi$
$60$	1.06713e70	0.618364
$61$	1.94595e69	0.0586952	0.0293476	−	0.999569i	$-0.490657\pi$
$61$	1.94595e69	0.0586952	0.0293476	+	0.999569i	$0.490657\pi$
$62$	−1.54842e70	−0.245706
$63$	−2.18206e70	−0.184041
$64$	−3.60008e71	−1.63006
$65$	4.10935e71	1.00854
$66$	5.27724e71	0.708633
$67$	−1.81247e72	−1.34374	−0.671870	−	0.740669i	$-0.734509\pi$
$67$	−1.81247e72	−1.34374	−0.671870	+	0.740669i	$0.734509\pi$
$68$	−3.90584e72	−1.61292
$69$	1.52862e72	0.354617
$70$	3.13895e72	0.412488
$71$	1.18133e73	0.886477	0.443238	−	0.896404i	$-0.353829\pi$
$71$	1.18133e73	0.886477	0.443238	+	0.896404i	$0.353829\pi$
$72$	1.74657e73	0.754315
$73$	2.44514e73	0.612423	0.306211	−	0.951964i	$-0.400939\pi$
$73$	2.44514e73	0.612423	0.306211	+	0.951964i	$0.400939\pi$
$74$	7.75932e73	1.13546
$75$	−2.23264e73	−0.192265
$76$	−5.02088e74	−2.56238
$77$	9.38346e73	0.285745
$78$	−2.21500e74	−0.405169
$79$	1.60756e74	0.177786	0.0888929	−	0.996041i	$-0.471667\pi$
$79$	1.60756e74	0.177786	0.0888929	+	0.996041i	$0.471667\pi$
$80$	3.61835e74	0.243476
$81$	1.70846e75	0.703794
$82$	−7.85977e75	−1.99417
$83$	4.26218e75	0.669957	0.334979	−	0.942226i	$-0.391271\pi$
$83$	4.26218e75	0.669957	0.334979	+	0.942226i	$0.391271\pi$
$84$	−1.02277e75	−0.100171
$85$	2.17605e76	1.33543
$86$	2.34329e76	0.906020
$87$	2.28327e76	0.559174
$88$	−7.51073e76	−1.17116
$89$	1.07359e77	1.07135	0.535677	−	0.844423i	$-0.320056\pi$
$89$	1.07359e77	1.07135	0.535677	+	0.844423i	$0.320056\pi$
$90$	−2.81460e77	−1.80650
$91$	−3.93849e76	−0.163379
$92$	−6.29290e77	−1.69524
$93$	−2.81083e76	−0.0494035
$94$	7.93822e77	0.914477
$95$	2.79727e78	2.12154
$96$	−7.30657e77	−0.366438
$97$	−3.66274e78	−1.21990	−0.609949	−	0.792441i	$-0.708810\pi$
$97$	−3.66274e78	−1.21990	−0.609949	+	0.792441i	$0.708810\pi$
$98$	6.85816e78	1.52327
$99$	−8.41387e78	−1.25143
$100$	9.19118e78	0.919118
$101$	8.14257e78	0.549626	0.274813	−	0.961498i	$-0.411384\pi$
$101$	8.14257e78	0.549626	0.274813	+	0.961498i	$0.411384\pi$
$102$	−1.17293e79	−0.536492
$103$	−2.90005e79	−0.902266	−0.451133	−	0.892457i	$-0.648980\pi$
$103$	−2.90005e79	−0.902266	−0.451133	+	0.892457i	$0.648980\pi$
$104$	3.15246e79	0.669626
$105$	5.69810e78	0.0829379
$106$	−1.65148e80	−1.65307
$107$	−1.89315e80	−1.30775	−0.653876	−	0.756602i	$-0.726858\pi$
$107$	−1.89315e80	−1.30775	−0.653876	+	0.756602i	$0.726858\pi$
$108$	1.93858e80	0.927355
$109$	7.81535e79	0.259778	0.129889	−	0.991529i	$-0.458538\pi$
$109$	7.81535e79	0.259778	0.129889	+	0.991529i	$0.458538\pi$
$110$	1.21036e81	2.80480
$111$	1.40854e80	0.228303
$112$	−3.46791e79	−0.0394417
$113$	−1.23064e81	−0.985215	−0.492608	−	0.870252i	$-0.663956\pi$
$113$	−1.23064e81	−0.985215	−0.492608	+	0.870252i	$0.663956\pi$
$114$	−1.50777e81	−0.852302
$115$	3.50594e81	1.40359
$116$	−9.39960e81	−2.67312
$117$	3.53153e81	0.715519
$118$	2.48696e81	0.360022
$119$	−2.08558e81	−0.216332
$120$	−4.56089e81	−0.339930
$121$	1.75601e82	0.942985
$122$	−2.40568e81	−0.0933308
$123$	−1.42678e82	−0.400963
$124$	1.15714e82	0.236173
$125$	3.39445e82	0.504457
$126$	2.69758e82	0.292643
$127$	−3.13695e82	−0.249035	−0.124517	−	0.992217i	$-0.539738\pi$
$127$	−3.13695e82	−0.249035	−0.124517	+	0.992217i	$0.539738\pi$
$128$	2.48259e83	1.44581
$129$	4.25376e82	0.182171
$130$	−5.08019e83	−1.60368
$131$	−7.16304e83	−1.67063	−0.835317	−	0.549768i	$-0.814716\pi$
$131$	−7.16304e83	−1.67063	−0.835317	+	0.549768i	$0.814716\pi$
$132$	−3.94371e83	−0.681137
$133$	−2.68097e83	−0.343678
$134$	2.24067e84	2.13667
$135$	−1.08004e84	−0.767812
$136$	1.66934e84	0.886663
$137$	3.33552e84	1.32648	0.663240	−	0.748406i	$-0.269181\pi$
$137$	3.33552e84	1.32648	0.663240	+	0.748406i	$0.269181\pi$
$138$	−1.88976e84	−0.563874
$139$	2.91297e84	0.653508	0.326754	−	0.945109i	$-0.394045\pi$
$139$	2.91297e84	0.653508	0.326754	+	0.945109i	$0.394045\pi$
$140$	−2.34575e84	−0.396483
$141$	1.44102e84	0.183871
$142$	−1.46043e85	−1.40958
$143$	−1.51865e85	−1.11093
$144$	3.10957e84	0.172736
$145$	5.23677e85	2.21324
$146$	−3.02281e85	−0.973809
$147$	1.24495e85	0.306280
$148$	−5.79858e85	−1.09140
$149$	−4.91450e85	−0.708960	−0.354480	−	0.935064i	$-0.615342\pi$
$149$	−4.91450e85	−0.708960	−0.354480	+	0.935064i	$0.615342\pi$
$150$	2.76011e85	0.305719
$151$	3.71789e85	0.316743	0.158372	−	0.987380i	$-0.449376\pi$
$151$	3.71789e85	0.316743	0.158372	+	0.987380i	$0.449376\pi$
$152$	2.14591e86	1.40860
$153$	1.87008e86	0.947432
$154$	−1.16003e86	−0.454362
$155$	−6.44675e85	−0.195541
$156$	1.65528e86	0.389448
$157$	−3.56134e86	−0.650995	−0.325497	−	0.945543i	$-0.605532\pi$
$157$	−3.56134e86	−0.650995	−0.325497	+	0.945543i	$0.605532\pi$
$158$	−1.98735e86	−0.282696
$159$	−2.99792e86	−0.332379
$160$	−1.67579e87	−1.45038
$161$	−3.36018e86	−0.227374
$162$	−2.11208e87	−1.11910
$163$	4.19593e87	1.74348	0.871741	−	0.489966i	$-0.162991\pi$
$163$	4.19593e87	1.74348	0.871741	+	0.489966i	$0.162991\pi$
$164$	5.87365e87	1.91680
$165$	2.19715e87	0.563953
$166$	−5.26913e87	−1.06529
$167$	5.31476e87	0.847584	0.423792	−	0.905759i	$-0.360699\pi$
$167$	5.31476e87	0.847584	0.423792	+	0.905759i	$0.360699\pi$
$168$	4.37126e86	0.0550668
$169$	−3.66097e87	−0.364814
$170$	−2.69015e88	−2.12346
$171$	2.40394e88	1.50514
$172$	−1.75116e88	−0.870866
$173$	3.43466e88	1.35851	0.679255	−	0.733903i	$-0.262303\pi$
$173$	3.43466e88	1.35851	0.679255	+	0.733903i	$0.262303\pi$
$174$	−2.82270e88	−0.889138
$175$	4.90776e87	0.123276
$176$	−1.33720e88	−0.268192
$177$	4.51455e87	0.0723886
$178$	−1.32723e89	−1.70355
$179$	4.58262e88	0.471432	0.235716	−	0.971822i	$-0.424256\pi$
$179$	4.58262e88	0.471432	0.235716	+	0.971822i	$0.424256\pi$
$180$	2.10337e89	1.73641
$181$	−4.98229e88	−0.330465	−0.165232	−	0.986255i	$-0.552837\pi$
$181$	−4.98229e88	−0.330465	−0.165232	+	0.986255i	$0.552837\pi$
$182$	4.86897e88	0.259787
$183$	−4.36701e87	−0.0187658
$184$	2.68956e89	0.931917
$185$	3.23055e89	0.903635
$186$	3.47489e88	0.0785562
$187$	−8.04184e89	−1.47100
$188$	−5.93227e89	−0.878994
$189$	1.03513e89	0.124381
$190$	−3.45813e90	−3.37345
$191$	2.10607e90	1.66976	0.834881	−	0.550430i	$-0.185536\pi$
$191$	2.10607e90	1.66976	0.834881	+	0.550430i	$0.185536\pi$
$192$	8.07916e89	0.521156
$193$	1.17808e90	0.618959	0.309479	−	0.950906i	$-0.399845\pi$
$193$	1.17808e90	0.618959	0.309479	+	0.950906i	$0.399845\pi$
$194$	4.52808e90	1.93975
$195$	−9.22202e89	−0.322447
$196$	−5.12514e90	−1.46417
$197$	1.79248e90	0.418832	0.209416	−	0.977827i	$-0.432844\pi$
$197$	1.79248e90	0.418832	0.209416	+	0.977827i	$0.432844\pi$
$198$	1.04017e91	1.98989
$199$	−6.84961e90	−1.07391	−0.536957	−	0.843610i	$-0.680426\pi$
$199$	−6.84961e90	−1.07391	−0.536957	+	0.843610i	$0.680426\pi$
$200$	−3.92828e90	−0.505263
$201$	4.06746e90	0.429615
$202$	−1.00663e91	−0.873956
$203$	−5.01904e90	−0.358532
$204$	8.76533e90	0.515676
$205$	−3.27237e91	−1.58703
$206$	3.58519e91	1.43469
$207$	3.01297e91	0.995787
$208$	5.61259e90	0.153342
$209$	−1.03376e92	−2.33691
$210$	−7.04430e90	−0.131879
$211$	−3.66707e91	−0.569066	−0.284533	−	0.958666i	$-0.591839\pi$
$211$	−3.66707e91	−0.569066	−0.284533	+	0.958666i	$0.591839\pi$
$212$	1.23416e92	1.58893
$213$	−2.65110e91	−0.283420
$214$	2.34041e92	2.07945
$215$	9.75617e91	0.721041
$216$	−8.28543e91	−0.509791
$217$	6.17871e90	0.0316766
$218$	−9.66175e91	−0.413070
$219$	−5.48728e91	−0.195801
$220$	−9.04505e92	−2.69597
$221$	3.37538e92	0.841061
$222$	−1.74131e92	−0.363023
$223$	−1.53144e92	−0.267336	−0.133668	−	0.991026i	$-0.542676\pi$
$223$	−1.53144e92	−0.267336	−0.133668	+	0.991026i	$0.542676\pi$
$224$	1.60612e92	0.234953
$225$	−4.40064e92	−0.539891
$226$	1.52138e93	1.56658
$227$	3.98091e92	0.344319	0.172160	−	0.985069i	$-0.444925\pi$
$227$	3.98091e92	0.344319	0.172160	+	0.985069i	$0.444925\pi$
$228$	1.12676e93	0.819232
$229$	2.40501e93	1.47101	0.735504	−	0.677521i	$-0.236946\pi$
$229$	2.40501e93	1.47101	0.735504	+	0.677521i	$0.236946\pi$
$230$	−4.33423e93	−2.23184
$231$	−2.10580e92	−0.0913573
$232$	4.01735e93	1.46948
$233$	−3.73920e93	−1.15404	−0.577018	−	0.816731i	$-0.695784\pi$
$233$	−3.73920e93	−1.15404	−0.577018	+	0.816731i	$0.695784\pi$
$234$	−4.36586e93	−1.13774
$235$	3.30503e93	0.727771
$236$	−1.85852e93	−0.346053
$237$	−3.60762e92	−0.0568409
$238$	2.57830e93	0.343989
$239$	1.57391e93	0.177936	0.0889680	−	0.996034i	$-0.471643\pi$
$239$	1.57391e93	0.177936	0.0889680	+	0.996034i	$0.471643\pi$
$240$	−8.12014e92	−0.0778430
$241$	5.50031e93	0.447418	0.223709	−	0.974656i	$-0.428183\pi$
$241$	5.50031e93	0.447418	0.223709	+	0.974656i	$0.428183\pi$
$242$	−2.17087e94	−1.49943
$243$	−1.41726e94	−0.831764
$244$	1.79778e93	0.0897094
$245$	2.85535e94	1.21227
$246$	1.76386e94	0.637568
$247$	4.33898e94	1.33616
$248$	−4.94558e93	−0.129830
$249$	−9.56500e93	−0.214196
$250$	−4.19640e94	−0.802133
$251$	8.70250e94	1.42080	0.710399	−	0.703799i	$-0.248515\pi$
$251$	8.70250e94	1.42080	0.710399	+	0.703799i	$0.248515\pi$
$252$	−2.01592e94	−0.281288
$253$	−1.29566e95	−1.54607
$254$	3.87806e94	0.395988
$255$	−4.88341e94	−0.426958
$256$	−8.92995e94	−0.668914
$257$	−2.23618e95	−1.43598	−0.717991	−	0.696053i	$-0.754938\pi$
$257$	−2.23618e95	−1.43598	−0.717991	+	0.696053i	$0.754938\pi$
$258$	−5.25872e94	−0.289669
$259$	−3.09623e94	−0.146384
$260$	3.79645e95	1.54145
$261$	4.50043e95	1.57020
$262$	8.85533e95	2.65646
$263$	−6.93935e95	−1.79088	−0.895441	−	0.445180i	$-0.853140\pi$
$263$	−6.93935e95	−1.79088	−0.895441	+	0.445180i	$0.853140\pi$
$264$	1.68553e95	0.374438
$265$	−6.87585e95	−1.31557
$266$	3.31435e95	0.546480
$267$	−2.40930e95	−0.342529
$268$	−1.67446e96	−2.05377
$269$	9.17003e95	0.970858	0.485429	−	0.874276i	$-0.338663\pi$
$269$	9.17003e95	0.970858	0.485429	+	0.874276i	$0.338663\pi$
$270$	1.33520e96	1.22089
$271$	−6.50794e95	−0.514229	−0.257115	−	0.966381i	$-0.582772\pi$
$271$	−6.50794e95	−0.514229	−0.257115	+	0.966381i	$0.582772\pi$
$272$	2.97208e95	0.203043
$273$	8.83860e94	0.0522347
$274$	−4.12354e96	−2.10923
$275$	1.89239e96	0.838244
$276$	1.41223e96	0.541995
$277$	1.72756e96	0.574755	0.287378	−	0.957817i	$-0.407217\pi$
$277$	1.72756e96	0.574755	0.287378	+	0.957817i	$0.407217\pi$
$278$	−3.60116e96	−1.03914
$279$	−5.54027e95	−0.138728
$280$	1.00257e96	0.217957
$281$	5.22950e96	0.987554	0.493777	−	0.869589i	$-0.335616\pi$
$281$	5.22950e96	0.987554	0.493777	+	0.869589i	$0.335616\pi$
$282$	−1.78146e96	−0.292372
$283$	−2.30760e96	−0.329303	−0.164652	−	0.986352i	$-0.552650\pi$
$283$	−2.30760e96	−0.329303	−0.164652	+	0.986352i	$0.552650\pi$
$284$	1.09138e97	1.35489
$285$	−6.27751e96	−0.678290
$286$	1.87744e97	1.76648
$287$	3.13631e96	0.257090
$288$	−1.44016e97	−1.02898
$289$	1.82427e96	0.113664
$290$	−6.47398e97	−3.51925
$291$	8.21978e96	0.390020
$292$	2.25897e97	0.936024
$293$	−2.22907e97	−0.806962	−0.403481	−	0.914988i	$-0.632200\pi$
$293$	−2.22907e97	−0.806962	−0.403481	+	0.914988i	$0.632200\pi$
$294$	−1.53908e97	−0.487014
$295$	1.03543e97	0.286517
$296$	2.47829e97	0.599971
$297$	3.99139e97	0.845756
$298$	6.07557e97	1.12731
$299$	5.43824e97	0.883987
$300$	−2.06265e97	−0.293856
$301$	−9.35054e96	−0.116805
$302$	−4.59626e97	−0.503651
$303$	−1.82732e97	−0.175724
$304$	3.82054e97	0.322566
$305$	−1.00159e97	−0.0742758
$306$	−2.31189e98	−1.50650
$307$	−9.75063e97	−0.558556	−0.279278	−	0.960210i	$-0.590095\pi$
$307$	−9.75063e97	−0.558556	−0.279278	+	0.960210i	$0.590095\pi$
$308$	8.66899e97	0.436732
$309$	6.50816e97	0.288468
$310$	7.96981e97	0.310929
$311$	−1.13796e98	−0.390922	−0.195461	−	0.980712i	$-0.562620\pi$
$311$	−1.13796e98	−0.390922	−0.195461	+	0.980712i	$0.562620\pi$
$312$	−7.07461e97	−0.214090
$313$	−2.65568e97	−0.0708231	−0.0354115	−	0.999373i	$-0.511274\pi$
$313$	−2.65568e97	−0.0708231	−0.0354115	+	0.999373i	$0.511274\pi$
$314$	4.40272e98	1.03514
$315$	1.12312e98	0.232895
$316$	1.48516e98	0.271727
$317$	−7.54881e98	−1.21910	−0.609548	−	0.792749i	$-0.708649\pi$
$317$	−7.54881e98	−1.21910	−0.609548	+	0.792749i	$0.708649\pi$
$318$	3.70619e98	0.528513
$319$	−1.93531e99	−2.43791
$320$	1.85299e99	2.06276
$321$	4.24852e98	0.418108
$322$	4.15403e98	0.361545
$323$	2.29765e99	1.76923
$324$	1.57837e99	1.07568
$325$	−7.94289e98	−0.479276
$326$	−5.18723e99	−2.77230
$327$	−1.75389e98	−0.0830549
$328$	−2.51037e99	−1.05371
$329$	−3.16762e98	−0.117895
$330$	−2.71623e99	−0.896738
$331$	4.77113e98	0.139771	0.0698853	−	0.997555i	$-0.477737\pi$
$331$	4.77113e98	0.139771	0.0698853	+	0.997555i	$0.477737\pi$
$332$	3.93765e99	1.02396
$333$	2.77630e99	0.641090
$334$	−6.57039e99	−1.34774
$335$	9.32889e99	1.70043
$336$	7.78253e97	0.0126101
$337$	−1.15100e99	−0.165843	−0.0829213	−	0.996556i	$-0.526425\pi$
$337$	−1.15100e99	−0.165843	−0.0829213	+	0.996556i	$0.526425\pi$
$338$	4.52589e99	0.580088
$339$	2.76174e99	0.314989
$340$	2.01036e100	2.04107
$341$	2.38247e99	0.215392
$342$	−2.97188e100	−2.39332
$343$	−5.59332e99	−0.401377
$344$	7.48437e99	0.478737
$345$	−7.86789e99	−0.448750
$346$	−4.24611e100	−2.16016
$347$	−1.33537e100	−0.606161	−0.303080	−	0.952965i	$-0.598015\pi$
$347$	−1.33537e100	−0.606161	−0.303080	+	0.952965i	$0.598015\pi$
$348$	2.10942e100	0.854639
$349$	4.95536e100	1.79255	0.896275	−	0.443499i	$-0.146263\pi$
$349$	4.95536e100	1.79255	0.896275	+	0.443499i	$0.146263\pi$
$350$	−6.06723e99	−0.196021
$351$	−1.67530e100	−0.483571
$352$	6.19307e100	1.59761
$353$	−5.02605e100	−1.15911	−0.579557	−	0.814932i	$-0.696774\pi$
$353$	−5.02605e100	−1.15911	−0.579557	+	0.814932i	$0.696774\pi$
$354$	−5.58112e99	−0.115105
$355$	−6.08040e100	−1.12179
$356$	9.91845e100	1.63745
$357$	4.68037e99	0.0691649
$358$	−5.66528e100	−0.749621
$359$	4.37275e100	0.518232	0.259116	−	0.965846i	$-0.416569\pi$
$359$	4.37275e100	0.518232	0.259116	+	0.965846i	$0.416569\pi$
$360$	−8.98972e100	−0.954547
$361$	1.90275e101	1.81070
$362$	6.15937e100	0.525470
$363$	−3.94076e100	−0.301487
$364$	−3.63861e100	−0.249707
$365$	−1.25853e101	−0.774990
$366$	5.39873e99	0.0298393
$367$	1.11542e101	0.553514	0.276757	−	0.960940i	$-0.410740\pi$
$367$	1.11542e101	0.553514	0.276757	+	0.960940i	$0.410740\pi$
$368$	4.78846e100	0.213406
$369$	−2.81224e101	−1.12593
$370$	−3.99378e101	−1.43686
$371$	6.58997e100	0.213115
$372$	−2.59681e100	−0.0755081
$373$	−7.12911e101	−1.86439	−0.932194	−	0.361958i	$-0.882108\pi$
$373$	−7.12911e101	−1.86439	−0.932194	+	0.361958i	$0.882108\pi$
$374$	9.94175e101	2.33902
$375$	−7.61769e100	−0.161283
$376$	2.53543e101	0.483205
$377$	8.12300e101	1.39391
$378$	−1.27969e101	−0.197778
$379$	−1.87730e101	−0.261387	−0.130694	−	0.991423i	$-0.541720\pi$
$379$	−1.87730e101	−0.261387	−0.130694	+	0.991423i	$0.541720\pi$
$380$	2.58428e102	3.24256
$381$	7.03980e100	0.0796203
$382$	−2.60364e102	−2.65508
$383$	−1.32118e101	−0.121510	−0.0607550	−	0.998153i	$-0.519351\pi$
$383$	−1.32118e101	−0.121510	−0.0607550	+	0.998153i	$0.519351\pi$
$384$	−5.57133e101	−0.462248
$385$	−4.82973e101	−0.361596
$386$	−1.45641e102	−0.984202
$387$	8.38435e101	0.511548
$388$	−3.38386e102	−1.86449
$389$	5.66265e101	0.281845	0.140923	−	0.990021i	$-0.454993\pi$
$389$	5.66265e101	0.281845	0.140923	+	0.990021i	$0.454993\pi$
$390$	1.14007e102	0.512721
$391$	2.87975e102	1.17050
$392$	2.19046e102	0.804890
$393$	1.60750e102	0.534128
$394$	−2.21596e102	−0.665981
$395$	−8.27422e101	−0.224979
$396$	−7.77323e102	−1.91268
$397$	3.74203e102	0.833454	0.416727	−	0.909032i	$-0.363177\pi$
$397$	3.74203e102	0.833454	0.416727	+	0.909032i	$0.363177\pi$
$398$	8.46785e102	1.70762
$399$	6.01651e101	0.109879
$400$	−6.99385e101	−0.115703
$401$	1.86616e102	0.279735	0.139868	−	0.990170i	$-0.455332\pi$
$401$	1.86616e102	0.279735	0.139868	+	0.990170i	$0.455332\pi$
$402$	−5.02841e102	−0.683127
$403$	−9.99985e101	−0.123153
$404$	7.52258e102	0.840045
$405$	−8.79354e102	−0.890616
$406$	6.20481e102	0.570099
$407$	−1.19388e103	−0.995367
$408$	−3.74627e102	−0.283480
$409$	−2.88894e102	−0.198458	−0.0992288	−	0.995065i	$-0.531638\pi$
$409$	−2.88894e102	−0.198458	−0.0992288	+	0.995065i	$0.531638\pi$
$410$	4.04548e103	2.52352
$411$	−7.48543e102	−0.424097
$412$	−2.67923e103	−1.37902
$413$	−9.92380e101	−0.0464142
$414$	−3.72480e103	−1.58339
$415$	−2.19377e103	−0.847797
$416$	−2.59940e103	−0.913454
$417$	−6.53716e102	−0.208937
$418$	1.27799e104	3.71590
$419$	4.46955e103	1.18252	0.591262	−	0.806479i	$-0.298630\pi$
$419$	4.46955e103	1.18252	0.591262	+	0.806479i	$0.298630\pi$
$420$	5.26424e102	0.126762
$421$	−1.61786e103	−0.354649	−0.177325	−	0.984152i	$-0.556744\pi$
$421$	−1.61786e103	−0.354649	−0.177325	+	0.984152i	$0.556744\pi$
$422$	4.53343e103	0.904868
$423$	2.84031e103	0.516322
$424$	−5.27476e103	−0.873477
$425$	−4.20606e103	−0.634618
$426$	3.27743e103	0.450665
$427$	9.59949e101	0.0120323
$428$	−1.74900e104	−1.99876
$429$	3.40810e103	0.355180
$430$	−1.20611e104	−1.14652
$431$	3.48898e103	0.302584	0.151292	−	0.988489i	$-0.451657\pi$
$431$	3.48898e103	0.302584	0.151292	+	0.988489i	$0.451657\pi$
$432$	−1.47513e103	−0.116740
$433$	−1.55557e103	−0.112362	−0.0561809	−	0.998421i	$-0.517892\pi$
$433$	−1.55557e103	−0.112362	−0.0561809	+	0.998421i	$0.517892\pi$
$434$	−7.63845e102	−0.0503687
$435$	−1.17521e104	−0.707606
$436$	7.22027e103	0.397043
$437$	3.70186e104	1.85953
$438$	6.78367e103	0.311342
$439$	−1.33670e104	−0.560643	−0.280321	−	0.959906i	$-0.590441\pi$
$439$	−1.33670e104	−0.560643	−0.280321	+	0.959906i	$0.590441\pi$
$440$	3.86582e104	1.48204
$441$	2.45386e104	0.860054
$442$	−4.17282e104	−1.33737
$443$	−1.74021e104	−0.510098	−0.255049	−	0.966928i	$-0.582092\pi$
$443$	−1.74021e104	−0.510098	−0.255049	+	0.966928i	$0.582092\pi$
$444$	1.30129e104	0.348938
$445$	−5.52584e104	−1.35574
$446$	1.89325e104	0.425089
$447$	1.10289e104	0.226666
$448$	−1.77595e104	−0.334155
$449$	−2.21627e104	−0.381849	−0.190925	−	0.981605i	$-0.561149\pi$
$449$	−2.21627e104	−0.381849	−0.190925	+	0.981605i	$0.561149\pi$
$450$	5.44030e104	0.858477
$451$	1.20934e105	1.74813
$452$	−1.13693e105	−1.50580
$453$	−8.34354e103	−0.101268
$454$	−4.92142e104	−0.547500
$455$	2.02717e104	0.206747
$456$	−4.81575e104	−0.450353
$457$	7.39074e104	0.633867	0.316934	−	0.948448i	$-0.397347\pi$
$457$	7.39074e104	0.633867	0.316934	+	0.948448i	$0.397347\pi$
$458$	−2.97320e105	−2.33904
$459$	−8.87132e104	−0.640306
$460$	3.23900e105	2.14524
$461$	−9.63460e104	−0.585662	−0.292831	−	0.956164i	$-0.594597\pi$
$461$	−9.63460e104	−0.585662	−0.292831	+	0.956164i	$0.594597\pi$
$462$	2.60330e104	0.145267
$463$	1.71819e105	0.880283	0.440141	−	0.897928i	$-0.354928\pi$
$463$	1.71819e105	0.880283	0.440141	+	0.897928i	$0.354928\pi$
$464$	7.15244e104	0.336507
$465$	1.44675e104	0.0625176
$466$	4.62259e105	1.83502
$467$	−2.59791e105	−0.947562	−0.473781	−	0.880643i	$-0.657111\pi$
$467$	−2.59791e105	−0.947562	−0.473781	+	0.880643i	$0.657111\pi$
$468$	3.26263e105	1.09360
$469$	−8.94102e104	−0.275461
$470$	−4.08585e105	−1.15722
$471$	7.99221e104	0.208133
$472$	7.94322e104	0.190234
$473$	−3.60550e105	−0.794237
$474$	4.45993e104	0.0903823
$475$	−5.40680e105	−1.00819
$476$	−1.92678e105	−0.330642
$477$	−5.90904e105	−0.933342
$478$	−1.94576e105	−0.282935
$479$	6.16363e104	0.0825247	0.0412623	−	0.999148i	$-0.486862\pi$
$479$	6.16363e104	0.0825247	0.0412623	+	0.999148i	$0.486862\pi$
$480$	3.76074e105	0.463708
$481$	5.01106e105	0.569113
$482$	−6.79977e105	−0.711437
$483$	7.54077e104	0.0726949
$484$	1.62230e106	1.44125
$485$	1.88524e106	1.54372
$486$	1.75209e106	1.32258
$487$	−1.15721e105	−0.0805411	−0.0402705	−	0.999189i	$-0.512822\pi$
$487$	−1.15721e105	−0.0805411	−0.0402705	+	0.999189i	$0.512822\pi$
$488$	−7.68364e104	−0.0493156
$489$	−9.41633e105	−0.557419
$490$	−3.52994e106	−1.92762
$491$	−1.49730e106	−0.754378	−0.377189	−	0.926136i	$-0.623109\pi$
$491$	−1.49730e106	−0.754378	−0.377189	+	0.926136i	$0.623109\pi$
$492$	−1.31814e106	−0.612829
$493$	4.30144e106	1.84570
$494$	−5.36407e106	−2.12461
$495$	4.33068e106	1.58362
$496$	−8.80504e104	−0.0297307
$497$	5.82759e105	0.181724
$498$	1.18248e106	0.340591
$499$	−1.06252e106	−0.282726	−0.141363	−	0.989958i	$-0.545148\pi$
$499$	−1.06252e106	−0.282726	−0.141363	+	0.989958i	$0.545148\pi$
$500$	3.13599e106	0.771010
$501$	−1.19272e106	−0.270986
$502$	−1.07585e107	−2.25920
$503$	−5.59385e104	−0.0108586	−0.00542932	−	0.999985i	$-0.501728\pi$
$503$	−5.59385e104	−0.0108586	−0.00542932	+	0.999985i	$0.501728\pi$
$504$	8.61595e105	0.154631
$505$	−4.19103e106	−0.695523
$506$	1.60176e107	2.45840
$507$	8.21580e105	0.116637
$508$	−2.89809e106	−0.380624
$509$	−6.71459e106	−0.815957	−0.407979	−	0.912992i	$-0.633766\pi$
$509$	−6.71459e106	−0.815957	−0.407979	+	0.912992i	$0.633766\pi$
$510$	6.03712e106	0.678904
$511$	1.20621e106	0.125544
$512$	−3.96668e106	−0.382176
$513$	−1.14039e107	−1.01723
$514$	2.76449e107	2.28334
$515$	1.49267e107	1.14177
$516$	3.92987e106	0.278429
$517$	−1.22141e107	−0.801650
$518$	3.82773e106	0.232764
$519$	−7.70792e106	−0.434337
$520$	−1.62259e107	−0.847377
$521$	3.76003e107	1.82012	0.910062	−	0.414472i	$-0.136034\pi$
$521$	3.76003e107	1.82012	0.910062	+	0.414472i	$0.136034\pi$
$522$	−5.56367e107	−2.49676
$523$	−3.48501e107	−1.45006	−0.725031	−	0.688716i	$-0.758175\pi$
$523$	−3.48501e107	−1.45006	−0.725031	+	0.688716i	$0.758175\pi$
$524$	−6.61764e107	−2.55339
$525$	−1.10138e106	−0.0394134
$526$	8.57880e107	2.84767
$527$	−5.29530e106	−0.163069
$528$	3.00089e106	0.0857451
$529$	8.68337e106	0.230244
$530$	8.50029e107	2.09188
$531$	8.89838e106	0.203272
$532$	−2.47683e107	−0.525276
$533$	−5.07592e107	−0.999518
$534$	2.97851e107	0.544652
$535$	9.74416e107	1.65489
$536$	7.15659e107	1.12901
$537$	−1.02841e107	−0.150724
$538$	−1.13365e108	−1.54375
$539$	−1.05523e108	−1.33533
$540$	−9.97801e107	−1.17352
$541$	1.11217e108	1.21584	0.607922	−	0.793997i	$-0.292003\pi$
$541$	1.11217e108	1.21584	0.607922	+	0.793997i	$0.292003\pi$
$542$	8.04546e107	0.817672
$543$	1.11810e107	0.105655
$544$	−1.37648e108	−1.20952
$545$	−4.02261e107	−0.328735
$546$	−1.09267e107	−0.0830580
$547$	−2.64017e108	−1.86695	−0.933473	−	0.358647i	$-0.883238\pi$
$547$	−2.64017e108	−1.86695	−0.933473	+	0.358647i	$0.883238\pi$
$548$	3.08155e108	2.02739
$549$	−8.60758e106	−0.0526955
$550$	−2.33948e108	−1.33289
$551$	5.52940e108	2.93218
$552$	−6.03580e107	−0.297948
$553$	7.93020e106	0.0364453
$554$	−2.13570e108	−0.913914
$555$	−7.24986e107	−0.288906
$556$	2.69117e108	0.998819
$557$	−3.13495e108	−1.08380	−0.541902	−	0.840442i	$-0.682296\pi$
$557$	−3.13495e108	−1.08380	−0.541902	+	0.840442i	$0.682296\pi$
$558$	6.84917e107	0.220591
$559$	1.51332e108	0.454115
$560$	1.78495e107	0.0499114
$561$	1.80472e108	0.470301
$562$	−6.46499e108	−1.57030
$563$	4.38790e108	0.993516	0.496758	−	0.867889i	$-0.334524\pi$
$563$	4.38790e108	0.993516	0.496758	+	0.867889i	$0.334524\pi$
$564$	1.33130e108	0.281028
$565$	6.33417e108	1.24674
$566$	2.85278e108	0.523623
$567$	8.42793e107	0.144275
$568$	−4.66454e108	−0.744816
$569$	−4.37892e108	−0.652278	−0.326139	−	0.945322i	$-0.605748\pi$
$569$	−4.37892e108	−0.652278	−0.326139	+	0.945322i	$0.605748\pi$
$570$	7.76059e108	1.07854
$571$	−1.27872e109	−1.65824	−0.829122	−	0.559068i	$-0.811159\pi$
$571$	−1.27872e109	−1.65824	−0.829122	+	0.559068i	$0.811159\pi$
$572$	−1.40302e109	−1.69793
$573$	−4.72635e108	−0.533849
$574$	−3.87728e108	−0.408796
$575$	−6.77659e108	−0.667008
$576$	1.59244e109	1.46344
$577$	−3.37276e108	−0.289428	−0.144714	−	0.989474i	$-0.546226\pi$
$577$	−3.37276e108	−0.289428	−0.144714	+	0.989474i	$0.546226\pi$
$578$	−2.25526e108	−0.180737
$579$	−2.64380e108	−0.197891
$580$	4.83804e109	3.38270
$581$	2.10256e108	0.137338
$582$	−1.01617e109	−0.620168
$583$	2.54105e109	1.44912
$584$	−9.65473e108	−0.514556
$585$	−1.81770e109	−0.905453
$586$	2.75570e109	1.28314
$587$	−1.99677e109	−0.869208	−0.434604	−	0.900622i	$-0.643112\pi$
$587$	−1.99677e109	−0.869208	−0.434604	+	0.900622i	$0.643112\pi$
$588$	1.15016e109	0.468117
$589$	−6.80699e108	−0.259060
$590$	−1.28005e109	−0.455589
$591$	−4.02262e108	−0.133907
$592$	4.41232e108	0.137391
$593$	−2.38401e109	−0.694461	−0.347231	−	0.937780i	$-0.612878\pi$
$593$	−2.38401e109	−0.694461	−0.347231	+	0.937780i	$0.612878\pi$
$594$	−4.93437e109	−1.34483
$595$	1.07346e109	0.273758
$596$	−4.54030e109	−1.08357
$597$	1.53716e109	0.343347
$598$	−6.72304e109	−1.40562
$599$	8.34636e109	1.63357	0.816785	−	0.576943i	$-0.195754\pi$
$599$	8.34636e109	1.63357	0.816785	+	0.576943i	$0.195754\pi$
$600$	8.81567e108	0.161540
$601$	7.66341e109	1.31486	0.657432	−	0.753514i	$-0.271643\pi$
$601$	7.66341e109	1.31486	0.657432	+	0.753514i	$0.271643\pi$
$602$	1.15596e109	0.185730
$603$	8.01715e109	1.20639
$604$	3.43481e109	0.484109
$605$	−9.03830e109	−1.19330
$606$	2.25903e109	0.279417
$607$	−2.50952e109	−0.290829	−0.145415	−	0.989371i	$-0.546452\pi$
$607$	−2.50952e109	−0.290829	−0.145415	+	0.989371i	$0.546452\pi$
$608$	−1.76944e110	−1.92151
$609$	1.12635e109	0.114628
$610$	1.23822e109	0.118105
$611$	5.12659e109	0.458354
$612$	1.72769e110	1.44805
$613$	−8.49773e109	−0.667750	−0.333875	−	0.942617i	$-0.608356\pi$
$613$	−8.49773e109	−0.667750	−0.333875	+	0.942617i	$0.608356\pi$
$614$	1.20542e110	0.888157
$615$	7.34371e109	0.507398
$616$	−3.70509e109	−0.240083
$617$	1.81863e109	0.110530	0.0552651	−	0.998472i	$-0.482400\pi$
$617$	1.81863e109	0.110530	0.0552651	+	0.998472i	$0.482400\pi$
$618$	−8.04573e109	−0.458692
$619$	−1.85858e110	−0.994033	−0.497016	−	0.867741i	$-0.665571\pi$
$619$	−1.85858e110	−0.994033	−0.497016	+	0.867741i	$0.665571\pi$
$620$	−5.95588e109	−0.298864
$621$	−1.42930e110	−0.672986
$622$	1.40680e110	0.621602
$623$	5.29609e109	0.219623
$624$	−1.25955e109	−0.0490259
$625$	−3.39302e110	−1.23973
$626$	3.28309e109	0.112615
$627$	2.31992e110	0.747146
$628$	−3.29018e110	−0.994977
$629$	2.65354e110	0.753573
$630$	−1.38846e110	−0.370325
$631$	−1.57829e110	−0.395390	−0.197695	−	0.980264i	$-0.563346\pi$
$631$	−1.57829e110	−0.395390	−0.197695	+	0.980264i	$0.563346\pi$
$632$	−6.34751e109	−0.149375
$633$	8.22949e109	0.181939
$634$	9.33224e110	1.93848
$635$	1.61461e110	0.315141
$636$	−2.76965e110	−0.508007
$637$	4.42907e110	0.763494
$638$	2.39253e111	3.87650
$639$	−5.22543e110	−0.795863
$640$	−1.27781e111	−1.82960
$641$	−1.24547e111	−1.67664	−0.838322	−	0.545175i	$-0.816463\pi$
$641$	−1.24547e111	−1.67664	−0.838322	+	0.545175i	$0.816463\pi$
$642$	−5.25225e110	−0.664831
$643$	1.14749e111	1.36588	0.682942	−	0.730472i	$-0.260700\pi$
$643$	1.14749e111	1.36588	0.682942	+	0.730472i	$0.260700\pi$
$644$	−3.10433e110	−0.347517
$645$	−2.18944e110	−0.230528
$646$	−2.84048e111	−2.81324
$647$	2.68544e109	0.0250205	0.0125102	−	0.999922i	$-0.496018\pi$
$647$	2.68544e109	0.0250205	0.0125102	+	0.999922i	$0.496018\pi$
$648$	−6.74590e110	−0.591327
$649$	−3.82654e110	−0.315603
$650$	9.81942e110	0.762094
$651$	−1.38660e109	−0.0101275
$652$	3.87644e111	2.66473
$653$	−2.31609e111	−1.49860	−0.749299	−	0.662232i	$-0.769609\pi$
$653$	−2.31609e111	−1.49860	−0.749299	+	0.662232i	$0.769609\pi$
$654$	2.16825e110	0.132065
$655$	3.68687e111	2.11410
$656$	−4.46944e110	−0.241296
$657$	−1.08157e111	−0.549822
$658$	3.91598e110	0.187464
$659$	1.52481e111	0.687453	0.343727	−	0.939070i	$-0.388311\pi$
$659$	1.52481e111	0.687453	0.343727	+	0.939070i	$0.388311\pi$
$660$	2.02985e111	0.861944
$661$	−4.06320e111	−1.62521	−0.812607	−	0.582812i	$-0.801952\pi$
$661$	−4.06320e111	−1.62521	−0.812607	+	0.582812i	$0.801952\pi$
$662$	−5.89833e110	−0.222248
$663$	−7.57488e110	−0.268900
$664$	−1.68294e111	−0.562897
$665$	1.37991e111	0.434907
$666$	−3.43221e111	−1.01939
$667$	6.93025e111	1.93990
$668$	4.91009e111	1.29544
$669$	3.43679e110	0.0854716
$670$	−1.15329e112	−2.70385
$671$	3.70149e110	0.0818158
$672$	−3.60438e110	−0.0751181
$673$	−7.82336e109	−0.0153744	−0.00768720	−	0.999970i	$-0.502447\pi$
$673$	−7.82336e109	−0.0153744	−0.00768720	+	0.999970i	$0.502447\pi$
$674$	1.42293e111	0.263705
$675$	2.08759e111	0.364876
$676$	−3.38222e111	−0.557580
$677$	5.64261e111	0.877461	0.438730	−	0.898619i	$-0.355428\pi$
$677$	5.64261e111	0.877461	0.438730	+	0.898619i	$0.355428\pi$
$678$	−3.41421e111	−0.500861
$679$	−1.80686e111	−0.250074
$680$	−8.59222e111	−1.12203
$681$	−8.93380e110	−0.110084
$682$	−2.94533e111	−0.342493
$683$	5.06491e111	0.555845	0.277923	−	0.960603i	$-0.410354\pi$
$683$	5.06491e111	0.555845	0.277923	+	0.960603i	$0.410354\pi$
$684$	2.22090e112	2.30046
$685$	−1.71681e112	−1.67859
$686$	6.91476e111	0.638226
$687$	−5.39721e111	−0.470304
$688$	1.33251e111	0.109629
$689$	−1.06655e112	−0.828553
$690$	9.72671e111	0.713554
$691$	2.37581e112	1.64600	0.822998	−	0.568044i	$-0.192300\pi$
$691$	2.37581e112	1.64600	0.822998	+	0.568044i	$0.192300\pi$
$692$	3.17314e112	2.07634
$693$	−4.15062e111	−0.256537
$694$	1.65086e112	0.963852
$695$	−1.49932e112	−0.826981
$696$	−9.01557e111	−0.469817
$697$	−2.68789e112	−1.32348
$698$	−6.12608e112	−2.85032
$699$	8.39134e111	0.368963
$700$	4.53407e111	0.188415
$701$	−3.55839e112	−1.39763	−0.698814	−	0.715303i	$-0.746289\pi$
$701$	−3.55839e112	−1.39763	−0.698814	+	0.715303i	$0.746289\pi$
$702$	2.07109e112	0.768923
$703$	3.41107e112	1.19717
$704$	−6.84792e112	−2.27216
$705$	−7.41701e111	−0.232680
$706$	6.21347e112	1.84310
$707$	4.01678e111	0.112671
$708$	4.17080e111	0.110638
$709$	9.60963e111	0.241091	0.120545	−	0.992708i	$-0.461536\pi$
$709$	9.60963e111	0.241091	0.120545	+	0.992708i	$0.461536\pi$
$710$	7.51691e112	1.78375
$711$	−7.11078e111	−0.159613
$712$	−4.23911e112	−0.900150
$713$	−8.53151e111	−0.171392
$714$	−5.78612e111	−0.109979
$715$	7.81661e112	1.40582
$716$	4.23369e112	0.720535
$717$	−3.53211e111	−0.0568889
$718$	−5.40583e112	−0.824037
$719$	1.11637e113	1.61071	0.805357	−	0.592790i	$-0.201974\pi$
$719$	1.11637e113	1.61071	0.805357	+	0.592790i	$0.201974\pi$
$720$	−1.60052e112	−0.218588
$721$	−1.43061e112	−0.184961
$722$	−2.35228e113	−2.87918
$723$	−1.23436e112	−0.143047
$724$	−4.60293e112	−0.505081
$725$	−1.01221e113	−1.05176
$726$	4.87178e112	0.479393
$727$	1.00127e113	0.933128	0.466564	−	0.884487i	$-0.345492\pi$
$727$	1.00127e113	0.933128	0.466564	+	0.884487i	$0.345492\pi$
$728$	1.55513e112	0.137270
$729$	−5.23696e112	−0.437866
$730$	1.55586e113	1.23231
$731$	8.01362e112	0.601302
$732$	−4.03450e111	−0.0286815
$733$	1.89002e113	1.27309	0.636547	−	0.771238i	$-0.280362\pi$
$733$	1.89002e113	1.27309	0.636547	+	0.771238i	$0.280362\pi$
$734$	−1.37894e113	−0.880139
$735$	−6.40786e112	−0.387582
$736$	−2.21771e113	−1.27125
$737$	−3.44759e113	−1.87305
$738$	3.47664e113	1.79033
$739$	−2.24030e113	−1.09358	−0.546791	−	0.837269i	$-0.684151\pi$
$739$	−2.24030e113	−1.09358	−0.546791	+	0.837269i	$0.684151\pi$
$740$	2.98457e113	1.38111
$741$	−9.73735e112	−0.427190
$742$	−8.14688e112	−0.338873
$743$	2.06023e113	0.812564	0.406282	−	0.913748i	$-0.366825\pi$
$743$	2.06023e113	0.812564	0.406282	+	0.913748i	$0.366825\pi$
$744$	1.10987e112	0.0415087
$745$	2.52953e113	0.897153
$746$	8.81338e113	2.96455
$747$	−1.88531e113	−0.601475
$748$	−7.42952e113	−2.24827
$749$	−9.33902e112	−0.268083
$750$	9.41739e112	0.256455
$751$	6.91709e113	1.78709	0.893544	−	0.448975i	$-0.148211\pi$
$751$	6.91709e113	1.78709	0.893544	+	0.448975i	$0.148211\pi$
$752$	4.51404e112	0.110652
$753$	−1.95298e113	−0.454251
$754$	−1.00421e114	−2.21644
$755$	−1.91362e113	−0.400822
$756$	9.56316e112	0.190104
$757$	−5.32072e113	−1.00388	−0.501942	−	0.864901i	$-0.667381\pi$
$757$	−5.32072e113	−1.00388	−0.501942	+	0.864901i	$0.667381\pi$
$758$	2.32082e113	0.415630
$759$	2.90767e113	0.494304
$760$	−1.10451e114	−1.78252
$761$	−1.15443e113	−0.176878	−0.0884390	−	0.996082i	$-0.528188\pi$
$761$	−1.15443e113	−0.176878	−0.0884390	+	0.996082i	$0.528188\pi$
$762$	−8.70297e112	−0.126604
$763$	3.85536e112	0.0532533
$764$	1.94571e114	2.55206
$765$	−9.62541e113	−1.19893
$766$	1.63332e113	0.193212
$767$	1.60610e113	0.180450
$768$	2.00402e113	0.213862
$769$	1.24929e114	1.26640	0.633202	−	0.773987i	$-0.281740\pi$
$769$	1.24929e114	1.26640	0.633202	+	0.773987i	$0.281740\pi$
$770$	5.97077e113	0.574972
$771$	5.01834e113	0.459106
$772$	1.08838e114	0.946014
$773$	−8.37354e113	−0.691543	−0.345772	−	0.938319i	$-0.612383\pi$
$773$	−8.37354e113	−0.691543	−0.345772	+	0.938319i	$0.612383\pi$
$774$	−1.03652e114	−0.813409
$775$	1.24608e113	0.0929243
$776$	1.44625e114	1.02496
$777$	6.94843e112	0.0468012
$778$	−7.00047e113	−0.448160
$779$	−3.45523e114	−2.10255
$780$	−8.51984e113	−0.492827
$781$	2.24708e114	1.23567
$782$	−3.56010e114	−1.86121
$783$	−2.13493e114	−1.06119
$784$	3.89987e113	0.184317
$785$	1.83305e114	0.823801
$786$	−1.98728e114	−0.849313
$787$	2.39120e114	0.971883	0.485941	−	0.873991i	$-0.338477\pi$
$787$	2.39120e114	0.971883	0.485941	+	0.873991i	$0.338477\pi$
$788$	1.65600e114	0.640140
$789$	1.55730e114	0.572573
$790$	1.02290e114	0.357737
$791$	−6.07081e113	−0.201965
$792$	3.32225e114	1.05145
$793$	−1.55362e113	−0.0467792
$794$	−4.62609e114	−1.32527
$795$	1.54305e114	0.420609
$796$	−6.32807e114	−1.64136
$797$	4.54631e114	1.12216	0.561081	−	0.827761i	$-0.310386\pi$
$797$	4.54631e114	1.12216	0.561081	+	0.827761i	$0.310386\pi$
$798$	−7.43793e113	−0.174718
$799$	2.71472e114	0.606914
$800$	3.23911e114	0.689242
$801$	−4.74885e114	−0.961842
$802$	−2.30705e114	−0.444805
$803$	4.65104e114	0.853662
$804$	3.75776e114	0.656621
$805$	1.72951e114	0.287730
$806$	1.23623e114	0.195824
$807$	−2.05790e114	−0.310398
$808$	−3.21512e114	−0.461794
$809$	−8.95779e113	−0.122528	−0.0612639	−	0.998122i	$-0.519513\pi$
$809$	−8.95779e113	−0.122528	−0.0612639	+	0.998122i	$0.519513\pi$
$810$	1.08710e115	1.41616
$811$	−1.41985e115	−1.76165	−0.880825	−	0.473442i	$-0.843011\pi$
$811$	−1.41985e115	−1.76165	−0.880825	+	0.473442i	$0.843011\pi$
$812$	−4.63689e114	−0.547978
$813$	1.46048e114	0.164407
$814$	1.47594e115	1.58273
$815$	−2.15967e115	−2.20629
$816$	−6.66981e113	−0.0649160
$817$	1.03013e115	0.955262
$818$	3.57146e114	0.315566
$819$	1.74213e114	0.146678
$820$	−3.02321e115	−2.42561
$821$	−2.10652e115	−1.61069	−0.805343	−	0.592809i	$-0.798019\pi$
$821$	−2.10652e115	−1.61069	−0.805343	+	0.592809i	$0.798019\pi$
$822$	9.25388e114	0.674353
$823$	1.23301e115	0.856393	0.428196	−	0.903686i	$-0.359149\pi$
$823$	1.23301e115	0.856393	0.428196	+	0.903686i	$0.359149\pi$
$824$	1.14509e115	0.758082
$825$	−4.24683e114	−0.268000
$826$	1.22683e114	0.0738029
$827$	−2.61045e114	−0.149709	−0.0748544	−	0.997194i	$-0.523849\pi$
$827$	−2.61045e114	−0.149709	−0.0748544	+	0.997194i	$0.523849\pi$
$828$	2.78356e115	1.52196
$829$	2.14085e115	1.11605	0.558023	−	0.829825i	$-0.311560\pi$
$829$	2.14085e115	1.11605	0.558023	+	0.829825i	$0.311560\pi$
$830$	2.71206e115	1.34808
$831$	−3.87692e114	−0.183758
$832$	2.87426e115	1.29913
$833$	2.34536e115	1.01096
$834$	8.08158e114	0.332229
$835$	−2.73554e115	−1.07257
$836$	−9.55049e115	−3.57172
$837$	2.62821e114	0.0937571
$838$	−5.52550e115	−1.88032
$839$	−3.13034e115	−1.01624	−0.508118	−	0.861287i	$-0.669659\pi$
$839$	−3.13034e115	−1.01624	−0.508118	+	0.861287i	$0.669659\pi$
$840$	−2.24992e114	−0.0696842
$841$	6.96752e115	2.05890
$842$	2.00009e115	0.563925
$843$	−1.17358e115	−0.315736
$844$	−3.38786e115	−0.869758
$845$	1.88433e115	0.461654
$846$	−3.51134e115	−0.821001
$847$	8.66252e114	0.193308
$848$	−9.39111e114	−0.200023
$849$	5.17862e114	0.105283
$850$	5.19975e115	1.00910
$851$	4.27525e115	0.792034
$852$	−2.44924e115	−0.433179
$853$	4.15250e115	0.701169	0.350584	−	0.936531i	$-0.385983\pi$
$853$	4.15250e115	0.701169	0.350584	+	0.936531i	$0.385983\pi$
$854$	−1.18674e114	−0.0191324
$855$	−1.23733e116	−1.90468
$856$	7.47516e115	1.09877
$857$	7.73765e115	1.08609	0.543046	−	0.839703i	$-0.317271\pi$
$857$	7.73765e115	1.08609	0.543046	+	0.839703i	$0.317271\pi$
$858$	−4.21327e115	−0.564770
$859$	8.33999e115	1.06767	0.533833	−	0.845590i	$-0.320751\pi$
$859$	8.33999e115	1.06767	0.533833	+	0.845590i	$0.320751\pi$
$860$	9.01332e115	1.10204
$861$	−7.03838e114	−0.0821956
$862$	−4.31326e115	−0.481137
$863$	−1.83088e116	−1.95090	−0.975449	−	0.220226i	$-0.929321\pi$
$863$	−1.83088e116	−1.95090	−0.975449	+	0.220226i	$0.929321\pi$
$864$	6.83186e115	0.695419
$865$	−1.76784e116	−1.71912
$866$	1.92308e115	0.178666
$867$	−4.09395e114	−0.0363403
$868$	5.70825e114	0.0484144
$869$	3.05783e115	0.247817
$870$	1.45286e116	1.12516
$871$	1.44705e116	1.07094
$872$	−3.08592e115	−0.218265
$873$	1.62016e116	1.09520
$874$	−4.57643e116	−2.95682
$875$	1.67451e115	0.103411
$876$	−5.06947e115	−0.299261
$877$	−1.20863e116	−0.682037	−0.341018	−	0.940057i	$-0.610772\pi$
$877$	−1.20863e116	−0.682037	−0.341018	+	0.940057i	$0.610772\pi$
$878$	1.65250e116	0.891474
$879$	5.00239e115	0.257998
$880$	6.88265e115	0.339383
$881$	−4.95295e115	−0.233516	−0.116758	−	0.993160i	$-0.537250\pi$
$881$	−4.95295e115	−0.233516	−0.116758	+	0.993160i	$0.537250\pi$
$882$	−3.03359e116	−1.36757
$883$	−3.29817e116	−1.42175	−0.710877	−	0.703316i	$-0.751702\pi$
$883$	−3.29817e116	−1.42175	−0.710877	+	0.703316i	$0.751702\pi$
$884$	3.11837e116	1.28547
$885$	−2.32367e115	−0.0916041
$886$	2.15133e116	0.811103
$887$	6.41823e115	0.231437	0.115718	−	0.993282i	$-0.463083\pi$
$887$	6.41823e115	0.231437	0.115718	+	0.993282i	$0.463083\pi$
$888$	−5.56168e115	−0.191820
$889$	−1.54748e115	−0.0510510
$890$	6.83133e116	2.15576
$891$	3.24975e116	0.981026
$892$	−1.41483e116	−0.408596
$893$	3.48972e116	0.964178
$894$	−1.36345e116	−0.360419
$895$	−2.35871e116	−0.596573
$896$	1.22468e116	0.296385
$897$	−1.22043e116	−0.282625
$898$	2.73987e116	0.607176
$899$	−1.27434e116	−0.270257
$900$	−4.06557e116	−0.825167
$901$	−5.64776e116	−1.09710
$902$	−1.49505e117	−2.77970
$903$	2.09841e115	0.0373442
$904$	4.85921e116	0.827776
$905$	2.56442e116	0.418187
$906$	1.03147e116	0.161025
$907$	−6.09100e116	−0.910335	−0.455167	−	0.890406i	$-0.650421\pi$
$907$	−6.09100e116	−0.910335	−0.455167	+	0.890406i	$0.650421\pi$
$908$	3.67780e116	0.526256
$909$	−3.60173e116	−0.493444
$910$	−2.50609e116	−0.328747
$911$	1.07066e117	1.34486	0.672430	−	0.740161i	$-0.265251\pi$
$911$	1.07066e117	1.34486	0.672430	+	0.740161i	$0.265251\pi$
$912$	−8.57389e115	−0.103129
$913$	8.10732e116	0.933860
$914$	−9.13683e116	−1.00791
$915$	2.24773e115	0.0237471
$916$	2.22189e117	2.24828
$917$	−3.53358e116	−0.342473
$918$	1.09672e117	1.01815
$919$	9.00461e116	0.800759	0.400380	−	0.916349i	$-0.368878\pi$
$919$	9.00461e116	0.800759	0.400380	+	0.916349i	$0.368878\pi$
$920$	−1.38434e117	−1.17929
$921$	2.18820e116	0.178579
$922$	1.19108e117	0.931257
$923$	−9.43159e116	−0.706509
$924$	−1.94546e116	−0.139630
$925$	−6.24428e116	−0.429422
$926$	−2.12412e117	−1.39973
$927$	1.28279e117	0.810038
$928$	−3.31256e117	−2.00456
$929$	−4.11810e116	−0.238823	−0.119412	−	0.992845i	$-0.538101\pi$
$929$	−4.11810e116	−0.238823	−0.119412	+	0.992845i	$0.538101\pi$
$930$	−1.78855e116	−0.0994088
$931$	3.01491e117	1.60606
$932$	−3.45449e117	−1.76382
$933$	2.55375e116	0.124984
$934$	3.21168e117	1.50671
$935$	4.13919e117	1.86147
$936$	−1.39444e117	−0.601178
$937$	−2.51406e117	−1.03911	−0.519555	−	0.854437i	$-0.673902\pi$
$937$	−2.51406e117	−1.03911	−0.519555	+	0.854437i	$0.673902\pi$
$938$	1.10534e117	0.438008
$939$	5.95977e115	0.0226432
$940$	3.05338e117	1.11232
$941$	−5.47062e117	−1.91094	−0.955469	−	0.295092i	$-0.904650\pi$
$941$	−5.47062e117	−1.91094	−0.955469	+	0.295092i	$0.904650\pi$
$942$	−9.88040e116	−0.330951
$943$	−4.33060e117	−1.39103
$944$	1.41420e116	0.0435629
$945$	−5.32790e116	−0.157398
$946$	4.45731e117	1.26291
$947$	7.07031e115	0.0192138	0.00960692	−	0.999954i	$-0.496942\pi$
$947$	7.07031e115	0.0192138	0.00960692	+	0.999954i	$0.496942\pi$
$948$	−3.33293e116	−0.0868754
$949$	−1.95217e117	−0.488092
$950$	6.68417e117	1.60312
$951$	1.69407e117	0.389764
$952$	8.23498e116	0.181762
$953$	2.62273e117	0.555371	0.277686	−	0.960672i	$-0.410433\pi$
$953$	2.62273e117	0.555371	0.277686	+	0.960672i	$0.410433\pi$
$954$	7.30506e117	1.48410
$955$	−1.08401e118	−2.11300
$956$	1.45407e117	0.271957
$957$	4.34313e117	0.779438
$958$	−7.61981e116	−0.131222
$959$	1.64543e117	0.271923
$960$	−4.15840e117	−0.659496
$961$	−6.41325e117	−0.976123
$962$	−6.19493e117	−0.904943
$963$	8.37403e117	1.17408
$964$	5.08150e117	0.683832
$965$	−6.06367e117	−0.783261
$966$	−9.32230e116	−0.115592
$967$	8.92243e117	1.06203	0.531016	−	0.847362i	$-0.321811\pi$
$967$	8.92243e117	1.06203	0.531016	+	0.847362i	$0.321811\pi$
$968$	−6.93367e117	−0.792294
$969$	−5.15629e117	−0.565650
$970$	−2.33063e118	−2.45465
$971$	5.92187e117	0.598824	0.299412	−	0.954124i	$-0.403209\pi$
$971$	5.92187e117	0.598824	0.299412	+	0.954124i	$0.403209\pi$
$972$	−1.30934e118	−1.27127
$973$	1.43699e117	0.133966
$974$	1.43060e117	0.128068
$975$	1.78251e117	0.153232
$976$	−1.36798e116	−0.0112931
$977$	6.48674e117	0.514270	0.257135	−	0.966376i	$-0.417222\pi$
$977$	6.48674e117	0.514270	0.257135	+	0.966376i	$0.417222\pi$
$978$	1.16410e118	0.886347
$979$	2.04213e118	1.49337
$980$	2.63794e118	1.85283
$981$	−3.45699e117	−0.233224
$982$	1.85104e118	1.19953
$983$	6.70554e117	0.417416	0.208708	−	0.977978i	$-0.433074\pi$
$983$	6.70554e117	0.417416	0.208708	+	0.977978i	$0.433074\pi$
$984$	5.63368e117	0.336888
$985$	−9.22604e117	−0.530010
$986$	−5.31766e118	−2.93483
$987$	7.10863e116	0.0376928
$988$	4.00860e118	2.04218
$989$	1.29111e118	0.631991
$990$	−5.35381e118	−2.51810
$991$	−3.38942e118	−1.53185	−0.765925	−	0.642930i	$-0.777718\pi$
$991$	−3.38942e118	−1.53185	−0.765925	+	0.642930i	$0.777718\pi$
$992$	4.07794e117	0.177105
$993$	−1.07072e117	−0.0446868
$994$	−7.20438e117	−0.288958
$995$	3.52554e118	1.35898
$996$	−8.83671e117	−0.327376
$997$	−2.53786e118	−0.903667	−0.451834	−	0.892102i	$-0.649230\pi$
$997$	−2.53786e118	−0.903667	−0.451834	+	0.892102i	$0.649230\pi$
$998$	1.31354e118	0.449560
$999$	−1.31703e118	−0.433270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.80.a.a.1.1	✓	6
3.2	odd	2		9.80.a.b.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.80.a.a.1.1	✓	6	1.1	even	1	trivial
9.80.a.b.1.6		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.23625e12 q^{2} -2.24416e18 q^{3} +9.23858e23 q^{4} -5.14707e27 q^{5} +2.77435e30 q^{6} +4.93307e32 q^{7} -3.94854e35 q^{8} -4.42334e37 q^{9} +O(q^{10})\)	\(q-1.23625e12 q^{2} -2.24416e18 q^{3} +9.23858e23 q^{4} -5.14707e27 q^{5} +2.77435e30 q^{6} +4.93307e32 q^{7} -3.94854e35 q^{8} -4.42334e37 q^{9} +6.36308e39 q^{10} +1.90215e41 q^{11} -2.07328e42 q^{12} -7.98386e43 q^{13} -6.09852e44 q^{14} +1.15508e46 q^{15} -7.02992e46 q^{16} -4.22775e48 q^{17} +5.46836e49 q^{18} -5.43469e50 q^{19} -4.75516e51 q^{20} -1.10706e51 q^{21} -2.35154e53 q^{22} -6.81154e53 q^{23} +8.86114e53 q^{24} +9.94869e54 q^{25} +9.87007e55 q^{26} +2.09835e56 q^{27} +4.55746e56 q^{28} -1.01743e58 q^{29} -1.42797e58 q^{30} +1.25251e58 q^{31} +3.25582e59 q^{32} -4.26873e59 q^{33} +5.22657e60 q^{34} -2.53908e60 q^{35} -4.08654e61 q^{36} -6.27648e61 q^{37} +6.71865e62 q^{38} +1.79170e62 q^{39} +2.03234e63 q^{40} +6.35773e63 q^{41} +1.36860e63 q^{42} -1.89548e64 q^{43} +1.75732e65 q^{44} +2.27672e65 q^{45} +8.42078e65 q^{46} -6.42119e65 q^{47} +1.57762e65 q^{48} -5.54754e66 q^{49} -1.22991e67 q^{50} +9.48774e66 q^{51} -7.37595e67 q^{52} +1.33588e68 q^{53} -2.59410e68 q^{54} -9.79052e68 q^{55} -1.94784e68 q^{56} +1.21963e69 q^{57} +1.25780e70 q^{58} -2.01169e69 q^{59} +1.06713e70 q^{60} +1.94595e69 q^{61} -1.54842e70 q^{62} -2.18206e70 q^{63} -3.60008e71 q^{64} +4.10935e71 q^{65} +5.27724e71 q^{66} -1.81247e72 q^{67} -3.90584e72 q^{68} +1.52862e72 q^{69} +3.13895e72 q^{70} +1.18133e73 q^{71} +1.74657e73 q^{72} +2.44514e73 q^{73} +7.75932e73 q^{74} -2.23264e73 q^{75} -5.02088e74 q^{76} +9.38346e73 q^{77} -2.21500e74 q^{78} +1.60756e74 q^{79} +3.61835e74 q^{80} +1.70846e75 q^{81} -7.85977e75 q^{82} +4.26218e75 q^{83} -1.02277e75 q^{84} +2.17605e76 q^{85} +2.34329e76 q^{86} +2.28327e76 q^{87} -7.51073e76 q^{88} +1.07359e77 q^{89} -2.81460e77 q^{90} -3.93849e76 q^{91} -6.29290e77 q^{92} -2.81083e76 q^{93} +7.93822e77 q^{94} +2.79727e78 q^{95} -7.30657e77 q^{96} -3.66274e78 q^{97} +6.85816e78 q^{98} -8.41387e78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3}+ \cdots + 98\!\cdots\!22 q^{9}+O(q^{10}) \) 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	\( 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3}+ \cdots + 12\!\cdots\!24 q^{99}+O(q^{100}) \) 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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