LMFDB - Embedded newform 1.80.a.a.1.2

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			1.2
Root			$-3.49960e10$ 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)

$f(q)$	$=$	\(q-8.42585e11 q^{2} +1.18388e19 q^{3} +1.05486e23 q^{4} +5.37236e27 q^{5} -9.97521e30 q^{6} -2.88361e33 q^{7} +4.20430e35 q^{8} +9.08882e37 q^{9} -4.52667e39 q^{10} +1.27714e41 q^{11} +1.24883e42 q^{12} +8.81976e43 q^{13} +2.42968e45 q^{14} +6.36024e46 q^{15} -4.18010e47 q^{16} -2.88942e47 q^{17} -7.65810e49 q^{18} +2.48242e50 q^{19} +5.66707e50 q^{20} -3.41385e52 q^{21} -1.07609e53 q^{22} -9.54744e53 q^{23} +4.97740e54 q^{24} +1.23186e55 q^{25} -7.43139e55 q^{26} +4.92715e56 q^{27} -3.04179e56 q^{28} +2.62380e57 q^{29} -5.35904e58 q^{30} +5.35966e58 q^{31} +9.80745e58 q^{32} +1.51198e60 q^{33} +2.43458e59 q^{34} -1.54918e61 q^{35} +9.58741e60 q^{36} +1.24508e62 q^{37} -2.09165e62 q^{38} +1.04416e63 q^{39} +2.25870e63 q^{40} +4.32605e62 q^{41} +2.87646e64 q^{42} -2.59673e64 q^{43} +1.34720e64 q^{44} +4.88284e65 q^{45} +8.04453e65 q^{46} +1.81584e65 q^{47} -4.94875e66 q^{48} +2.52430e66 q^{49} -1.03795e67 q^{50} -3.42074e66 q^{51} +9.30359e66 q^{52} -1.64629e68 q^{53} -4.15154e68 q^{54} +6.86123e68 q^{55} -1.21236e69 q^{56} +2.93890e69 q^{57} -2.21077e69 q^{58} +1.72621e70 q^{59} +6.70915e69 q^{60} +3.55854e70 q^{61} -4.51596e70 q^{62} -2.62086e71 q^{63} +1.70036e71 q^{64} +4.73829e71 q^{65} -1.27397e72 q^{66} +1.15292e71 q^{67} -3.04793e70 q^{68} -1.13031e73 q^{69} +1.30531e73 q^{70} +1.64661e73 q^{71} +3.82122e73 q^{72} -2.56980e72 q^{73} -1.04908e74 q^{74} +1.45838e74 q^{75} +2.61860e73 q^{76} -3.68276e74 q^{77} -8.79790e74 q^{78} +1.45007e75 q^{79} -2.24570e75 q^{80} +1.35514e75 q^{81} -3.64507e74 q^{82} +5.44189e75 q^{83} -3.60113e75 q^{84} -1.55230e75 q^{85} +2.18797e76 q^{86} +3.10627e76 q^{87} +5.36947e76 q^{88} +1.18618e76 q^{89} -4.11420e77 q^{90} -2.54327e77 q^{91} -1.00712e77 q^{92} +6.34521e77 q^{93} -1.53000e77 q^{94} +1.33365e78 q^{95} +1.16109e78 q^{96} -2.81055e78 q^{97} -2.12694e78 q^{98} +1.16077e79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.42585e11	−1.08375	−0.541874	−	0.840459i	$-0.682285\pi$
$2$	−8.42585e11	−1.08375	−0.541874	+	0.840459i	$0.682285\pi$
$3$	1.18388e19	1.68663	0.843314	−	0.537422i	$-0.180602\pi$
$3$	1.18388e19	1.68663	0.843314	+	0.537422i	$0.180602\pi$
$4$	1.05486e23	0.174512
$5$	5.37236e27	1.32084	0.660419	−	0.750897i	$-0.270379\pi$
$5$	5.37236e27	1.32084	0.660419	+	0.750897i	$0.270379\pi$
$6$	−9.97521e30	−1.82788
$7$	−2.88361e33	−1.19829	−0.599147	−	0.800639i	$-0.704494\pi$
$7$	−2.88361e33	−1.19829	−0.599147	+	0.800639i	$0.704494\pi$
$8$	4.20430e35	0.894622
$9$	9.08882e37	1.84471
$10$	−4.52667e39	−1.43146
$11$	1.27714e41	0.935892	0.467946	−	0.883757i	$-0.344994\pi$
$11$	1.27714e41	0.935892	0.467946	+	0.883757i	$0.344994\pi$
$12$	1.24883e42	0.294336
$13$	8.81976e43	0.880429	0.440214	−	0.897893i	$-0.354902\pi$
$13$	8.81976e43	0.880429	0.440214	+	0.897893i	$0.354902\pi$
$14$	2.42968e45	1.29865
$15$	6.36024e46	2.22776
$16$	−4.18010e47	−1.14406
$17$	−2.88942e47	−0.0721238	−0.0360619	−	0.999350i	$-0.511481\pi$
$17$	−2.88942e47	−0.0721238	−0.0360619	+	0.999350i	$0.511481\pi$
$18$	−7.65810e49	−1.99920
$19$	2.48242e50	0.765789	0.382894	−	0.923792i	$-0.374927\pi$
$19$	2.48242e50	0.765789	0.382894	+	0.923792i	$0.374927\pi$
$20$	5.66707e50	0.230502
$21$	−3.41385e52	−2.02108
$22$	−1.07609e53	−1.01427
$23$	−9.54744e53	−1.55467	−0.777334	−	0.629088i	$-0.783428\pi$
$23$	−9.54744e53	−1.55467	−0.777334	+	0.629088i	$0.783428\pi$
$24$	4.97740e54	1.50889
$25$	1.23186e55	0.744615
$26$	−7.43139e55	−0.954164
$27$	4.92715e56	1.42471
$28$	−3.04179e56	−0.209116
$29$	2.62380e57	0.451034	0.225517	−	0.974239i	$-0.427593\pi$
$29$	2.62380e57	0.451034	0.225517	+	0.974239i	$0.427593\pi$
$30$	−5.35904e58	−2.41433
$31$	5.35966e58	0.661226	0.330613	−	0.943766i	$-0.392744\pi$
$31$	5.35966e58	0.661226	0.330613	+	0.943766i	$0.392744\pi$
$32$	9.80745e58	0.345249
$33$	1.51198e60	1.57850
$34$	2.43458e59	0.0781641
$35$	−1.54918e61	−1.58275
$36$	9.58741e60	0.321923
$37$	1.24508e62	1.41654	0.708268	−	0.705944i	$-0.249477\pi$
$37$	1.24508e62	1.41654	0.708268	+	0.705944i	$0.249477\pi$
$38$	−2.09165e62	−0.829922
$39$	1.04416e63	1.48496
$40$	2.25870e63	1.18165
$41$	4.32605e62	0.0853355	0.0426677	−	0.999089i	$-0.486414\pi$
$41$	4.32605e62	0.0853355	0.0426677	+	0.999089i	$0.486414\pi$
$42$	2.87646e64	2.19034
$43$	−2.59673e64	−0.780590	−0.390295	−	0.920690i	$-0.627627\pi$
$43$	−2.59673e64	−0.780590	−0.390295	+	0.920690i	$0.627627\pi$
$44$	1.34720e64	0.163324
$45$	4.88284e65	2.43657
$46$	8.04453e65	1.68487
$47$	1.81584e65	0.162634	0.0813170	−	0.996688i	$-0.474087\pi$
$47$	1.81584e65	0.162634	0.0813170	+	0.996688i	$0.474087\pi$
$48$	−4.94875e66	−1.92960
$49$	2.52430e66	0.435909
$50$	−1.03795e67	−0.806976
$51$	−3.42074e66	−0.121646
$52$	9.30359e66	0.153645
$53$	−1.64629e68	−1.28117	−0.640587	−	0.767885i	$-0.721309\pi$
$53$	−1.64629e68	−1.28117	−0.640587	+	0.767885i	$0.721309\pi$
$54$	−4.15154e68	−1.54403
$55$	6.86123e68	1.23616
$56$	−1.21236e69	−1.07202
$57$	2.93890e69	1.29160
$58$	−2.21077e69	−0.488808
$59$	1.72621e70	1.94285	0.971424	−	0.237352i	$-0.0762795\pi$
$59$	1.72621e70	1.94285	0.971424	+	0.237352i	$0.0762795\pi$
$60$	6.70915e69	0.388770
$61$	3.55854e70	1.07335	0.536677	−	0.843788i	$-0.319679\pi$
$61$	3.55854e70	1.07335	0.536677	+	0.843788i	$0.319679\pi$
$62$	−4.51596e70	−0.716603
$63$	−2.62086e71	−2.21051
$64$	1.70036e71	0.769895
$65$	4.73829e71	1.16290
$66$	−1.27397e72	−1.71070
$67$	1.15292e71	0.0854762	0.0427381	−	0.999086i	$-0.486392\pi$
$67$	1.15292e71	0.0854762	0.0427381	+	0.999086i	$0.486392\pi$
$68$	−3.04793e70	−0.0125864
$69$	−1.13031e73	−2.62214
$70$	1.30531e73	1.71531
$71$	1.64661e73	1.23562	0.617812	−	0.786326i	$-0.288019\pi$
$71$	1.64661e73	1.23562	0.617812	+	0.786326i	$0.288019\pi$
$72$	3.82122e73	1.65032
$73$	−2.56980e72	−0.0643645	−0.0321822	−	0.999482i	$-0.510246\pi$
$73$	−2.56980e72	−0.0643645	−0.0321822	+	0.999482i	$0.510246\pi$
$74$	−1.04908e74	−1.53517
$75$	1.45838e74	1.25589
$76$	2.61860e73	0.133639
$77$	−3.68276e74	−1.12147
$78$	−8.79790e74	−1.60932
$79$	1.45007e75	1.60369	0.801844	−	0.597533i	$-0.203852\pi$
$79$	1.45007e75	1.60369	0.801844	+	0.597533i	$0.203852\pi$
$80$	−2.24570e75	−1.51112
$81$	1.35514e75	0.558247
$82$	−3.64507e74	−0.0924822
$83$	5.44189e75	0.855391	0.427696	−	0.903923i	$-0.359326\pi$
$83$	5.44189e75	0.855391	0.427696	+	0.903923i	$0.359326\pi$
$84$	−3.60113e75	−0.352701
$85$	−1.55230e75	−0.0952639
$86$	2.18797e76	0.845964
$87$	3.10627e76	0.760726
$88$	5.36947e76	0.837270
$89$	1.18618e76	0.118371	0.0591856	−	0.998247i	$-0.481150\pi$
$89$	1.18618e76	0.118371	0.0591856	+	0.998247i	$0.481150\pi$
$90$	−4.11420e77	−2.64063
$91$	−2.54327e77	−1.05501
$92$	−1.00712e77	−0.271307
$93$	6.34521e77	1.11524
$94$	−1.53000e77	−0.176254
$95$	1.33365e78	1.01148
$96$	1.16109e78	0.582306
$97$	−2.81055e78	−0.936068	−0.468034	−	0.883711i	$-0.655037\pi$
$97$	−2.81055e78	−0.936068	−0.468034	+	0.883711i	$0.655037\pi$
$98$	−2.12694e78	−0.472416
$99$	1.16077e79	1.72645
$100$	1.29944e78	0.129944
$101$	−5.67731e78	−0.383220	−0.191610	−	0.981471i	$-0.561371\pi$
$101$	−5.67731e78	−0.383220	−0.191610	+	0.981471i	$0.561371\pi$
$102$	2.88226e78	0.131834
$103$	−3.45707e79	−1.07557	−0.537784	−	0.843082i	$-0.680739\pi$
$103$	−3.45707e79	−1.07557	−0.537784	+	0.843082i	$0.680739\pi$
$104$	3.70810e79	0.787651
$105$	−1.83404e80	−2.66951
$106$	1.38713e80	1.38847
$107$	−3.03063e79	−0.209350	−0.104675	−	0.994506i	$-0.533380\pi$
$107$	−3.03063e79	−0.209350	−0.104675	+	0.994506i	$0.533380\pi$
$108$	5.19744e79	0.248629
$109$	1.29743e80	0.431259	0.215629	−	0.976475i	$-0.430820\pi$
$109$	1.29743e80	0.431259	0.215629	+	0.976475i	$0.430820\pi$
$110$	−5.78116e80	−1.33969
$111$	1.47402e81	2.38917
$112$	1.20538e81	1.37092
$113$	1.61408e80	0.129219	0.0646094	−	0.997911i	$-0.479420\pi$
$113$	1.61408e80	0.129219	0.0646094	+	0.997911i	$0.479420\pi$
$114$	−2.47627e81	−1.39977
$115$	−5.12923e81	−2.05347
$116$	2.76773e80	0.0787106
$117$	8.01612e81	1.62414
$118$	−1.45448e82	−2.10556
$119$	8.33196e80	0.0864256
$120$	2.67404e82	1.99301
$121$	−2.31107e81	−0.124106
$122$	−2.99837e82	−1.16325
$123$	5.12154e81	0.143929
$124$	5.65368e81	0.115392
$125$	−2.26982e82	−0.337322
$126$	2.20829e83	2.39563
$127$	1.29381e83	1.02713	0.513564	−	0.858051i	$-0.328325\pi$
$127$	1.29381e83	1.02713	0.513564	+	0.858051i	$0.328325\pi$
$128$	−2.02552e83	−1.17962
$129$	−3.07423e83	−1.31656
$130$	−3.99241e83	−1.26030
$131$	1.27969e83	0.298461	0.149230	−	0.988802i	$-0.452320\pi$
$131$	1.27969e83	0.298461	0.149230	+	0.988802i	$0.452320\pi$
$132$	1.59492e83	0.275467
$133$	−7.15834e83	−0.917640
$134$	−9.71434e82	−0.0926347
$135$	2.64704e84	1.88181
$136$	−1.21480e83	−0.0645236
$137$	−3.69646e84	−1.47002	−0.735010	−	0.678056i	$-0.762823\pi$
$137$	−3.69646e84	−1.47002	−0.735010	+	0.678056i	$0.762823\pi$
$138$	9.52378e84	2.84175
$139$	−1.99076e84	−0.446615	−0.223307	−	0.974748i	$-0.571685\pi$
$139$	−1.99076e84	−0.446615	−0.223307	+	0.974748i	$0.571685\pi$
$140$	−1.63416e84	−0.276209
$141$	2.14974e84	0.274303
$142$	−1.38741e85	−1.33911
$143$	1.12640e85	0.823987
$144$	−3.79922e85	−2.11045
$145$	1.40960e85	0.595743
$146$	2.16527e84	0.0697549
$147$	2.98848e85	0.735216
$148$	1.31338e85	0.247202
$149$	−1.34763e85	−0.194408	−0.0972041	−	0.995264i	$-0.530990\pi$
$149$	−1.34763e85	−0.194408	−0.0972041	+	0.995264i	$0.530990\pi$
$150$	−1.22881e86	−1.36107
$151$	7.89611e85	0.672704	0.336352	−	0.941736i	$-0.390807\pi$
$151$	7.89611e85	0.672704	0.336352	+	0.941736i	$0.390807\pi$
$152$	1.04369e86	0.685091
$153$	−2.62614e85	−0.133048
$154$	3.10303e86	1.21540
$155$	2.87940e86	0.873373
$156$	1.10144e86	0.259142
$157$	−4.59639e86	−0.840196	−0.420098	−	0.907479i	$-0.638004\pi$
$157$	−4.59639e86	−0.840196	−0.420098	+	0.907479i	$0.638004\pi$
$158$	−1.22181e87	−1.73800
$159$	−1.94901e87	−2.16086
$160$	5.26891e86	0.456018
$161$	2.75311e87	1.86295
$162$	−1.14182e87	−0.605000
$163$	4.82420e84	0.00200454	0.00100227	−	0.999999i	$-0.499681\pi$
$163$	4.82420e84	0.00200454	0.00100227	+	0.999999i	$0.499681\pi$
$164$	4.56337e85	0.0148920
$165$	8.12289e87	2.08495
$166$	−4.58525e87	−0.927029
$167$	8.96603e87	1.42988	0.714940	−	0.699186i	$-0.246454\pi$
$167$	8.96603e87	1.42988	0.714940	+	0.699186i	$0.246454\pi$
$168$	−1.43529e88	−1.80810
$169$	−2.25636e87	−0.224845
$170$	1.30795e87	0.103242
$171$	2.25623e88	1.41266
$172$	−2.73918e87	−0.136222
$173$	−2.37720e88	−0.940255	−0.470127	−	0.882599i	$-0.655792\pi$
$173$	−2.37720e88	−0.940255	−0.470127	+	0.882599i	$0.655792\pi$
$174$	−2.61729e88	−0.824436
$175$	−3.55221e88	−0.892268
$176$	−5.33856e88	−1.07071
$177$	2.04363e89	3.27686
$178$	−9.99459e87	−0.128285
$179$	−1.10473e89	−1.13648	−0.568241	−	0.822862i	$-0.692376\pi$
$179$	−1.10473e89	−1.13648	−0.568241	+	0.822862i	$0.692376\pi$
$180$	5.15070e88	0.425209
$181$	−1.73036e89	−1.14771	−0.573856	−	0.818956i	$-0.694553\pi$
$181$	−1.73036e89	−1.14771	−0.573856	+	0.818956i	$0.694553\pi$
$182$	2.14292e89	1.14337
$183$	4.21289e89	1.81035
$184$	−4.01404e89	−1.39084
$185$	6.68899e89	1.87102
$186$	−5.34637e89	−1.20864
$187$	−3.69018e88	−0.0675001
$188$	1.91545e88	0.0283815
$189$	−1.42080e90	−1.70722
$190$	−1.12371e90	−1.09619
$191$	−5.36614e89	−0.425445	−0.212723	−	0.977113i	$-0.568233\pi$
$191$	−5.36614e89	−0.425445	−0.212723	+	0.977113i	$0.568233\pi$
$192$	2.01302e90	1.29852
$193$	−1.08896e90	−0.572134	−0.286067	−	0.958210i	$-0.592348\pi$
$193$	−1.08896e90	−0.572134	−0.286067	+	0.958210i	$0.592348\pi$
$194$	2.36812e90	1.01446
$195$	5.60958e90	1.96139
$196$	2.66278e89	0.0760712
$197$	2.43944e90	0.569999	0.285000	−	0.958528i	$-0.408007\pi$
$197$	2.43944e90	0.569999	0.285000	+	0.958528i	$0.408007\pi$
$198$	−9.78043e90	−1.87104
$199$	−4.75368e90	−0.745304	−0.372652	−	0.927971i	$-0.621551\pi$
$199$	−4.75368e90	−0.745304	−0.372652	+	0.927971i	$0.621551\pi$
$200$	5.17912e90	0.666149
$201$	1.36492e90	0.144166
$202$	4.78362e90	0.415315
$203$	−7.56600e90	−0.540472
$204$	−3.60839e89	−0.0212286
$205$	2.32411e90	0.112714
$206$	2.91288e91	1.16565
$207$	−8.67750e91	−2.86791
$208$	−3.68675e91	−1.00726
$209$	3.17039e91	0.716696
$210$	1.54534e92	2.89308
$211$	−1.15316e92	−1.78950	−0.894750	−	0.446568i	$-0.852646\pi$
$211$	−1.15316e92	−1.78950	−0.894750	+	0.446568i	$0.852646\pi$
$212$	−1.73660e91	−0.223580
$213$	1.94939e92	2.08404
$214$	2.55356e91	0.226883
$215$	−1.39506e92	−1.03103
$216$	2.07152e92	1.27458
$217$	−1.54551e92	−0.792344
$218$	−1.09320e92	−0.467376
$219$	−3.04234e91	−0.108559
$220$	7.23762e91	0.215725
$221$	−2.54840e91	−0.0634999
$222$	−1.24199e93	−2.58926
$223$	5.04592e92	0.880843	0.440421	−	0.897791i	$-0.354829\pi$
$223$	5.04592e92	0.880843	0.440421	+	0.897791i	$0.354829\pi$
$224$	−2.82808e92	−0.413709
$225$	1.11962e93	1.37360
$226$	−1.36000e92	−0.140041
$227$	−6.12932e92	−0.530141	−0.265070	−	0.964229i	$-0.585395\pi$
$227$	−6.12932e92	−0.530141	−0.265070	+	0.964229i	$0.585395\pi$
$228$	3.10012e92	0.225399
$229$	3.04419e93	1.86196	0.930979	−	0.365074i	$-0.118956\pi$
$229$	3.04419e93	1.86196	0.930979	+	0.365074i	$0.118956\pi$
$230$	4.32181e93	2.22544
$231$	−4.35995e93	−1.89151
$232$	1.10312e93	0.403505
$233$	−5.71081e93	−1.76254	−0.881270	−	0.472613i	$-0.843311\pi$
$233$	−5.71081e93	−1.76254	−0.881270	+	0.472613i	$0.843311\pi$
$234$	−6.75426e93	−1.76016
$235$	9.75532e92	0.214813
$236$	1.82090e93	0.339049
$237$	1.71672e94	2.70482
$238$	−7.02038e92	−0.0936636
$239$	−7.27019e93	−0.821919	−0.410959	−	0.911654i	$-0.634806\pi$
$239$	−7.27019e93	−0.821919	−0.410959	+	0.911654i	$0.634806\pi$
$240$	−2.65865e94	−2.54869
$241$	1.42766e94	1.16132	0.580660	−	0.814146i	$-0.302795\pi$
$241$	1.42766e94	1.16132	0.580660	+	0.814146i	$0.302795\pi$
$242$	1.94728e93	0.134499
$243$	−8.23259e93	−0.483157
$244$	3.75375e93	0.187313
$245$	1.35615e94	0.575766
$246$	−4.31533e93	−0.155983
$247$	2.18944e94	0.674222
$248$	2.25336e94	0.591548
$249$	6.44255e94	1.44273
$250$	1.91251e94	0.365573
$251$	−7.23508e94	−1.18122	−0.590611	−	0.806957i	$-0.701113\pi$
$251$	−7.23508e94	−1.18122	−0.590611	+	0.806957i	$0.701113\pi$
$252$	−2.76463e94	−0.385759
$253$	−1.21934e95	−1.45500
$254$	−1.09015e95	−1.11315
$255$	−1.83774e94	−0.160675
$256$	6.78868e94	0.508518
$257$	4.59411e94	0.295014	0.147507	−	0.989061i	$-0.452875\pi$
$257$	4.59411e94	0.295014	0.147507	+	0.989061i	$0.452875\pi$
$258$	2.59030e95	1.42683
$259$	−3.59031e95	−1.69743
$260$	4.99822e94	0.202940
$261$	2.38472e95	0.832027
$262$	−1.07824e95	−0.323456
$263$	3.48081e95	0.898313	0.449157	−	0.893453i	$-0.351725\pi$
$263$	3.48081e95	0.898313	0.449157	+	0.893453i	$0.351725\pi$
$264$	6.35682e95	1.41216
$265$	−8.84444e95	−1.69223
$266$	6.03150e95	0.994491
$267$	1.40430e95	0.199648
$268$	1.21617e94	0.0149166
$269$	−6.17619e95	−0.653891	−0.326946	−	0.945043i	$-0.606019\pi$
$269$	−6.17619e95	−0.653891	−0.326946	+	0.945043i	$0.606019\pi$
$270$	−2.23036e96	−2.03941
$271$	1.31525e96	1.03925	0.519626	−	0.854394i	$-0.326071\pi$
$271$	1.31525e96	1.03925	0.519626	+	0.854394i	$0.326071\pi$
$272$	1.20781e95	0.0825138
$273$	−3.01094e96	−1.77941
$274$	3.11458e96	1.59313
$275$	1.57325e96	0.696879
$276$	−1.19231e96	−0.457595
$277$	−2.08593e96	−0.693982	−0.346991	−	0.937868i	$-0.612797\pi$
$277$	−2.08593e96	−0.693982	−0.346991	+	0.937868i	$0.612797\pi$
$278$	1.67738e96	0.484018
$279$	4.87130e96	1.21977
$280$	−6.51321e96	−1.41597
$281$	−8.38622e95	−0.158368	−0.0791838	−	0.996860i	$-0.525231\pi$
$281$	−8.38622e95	−0.158368	−0.0791838	+	0.996860i	$0.525231\pi$
$282$	−1.81134e96	−0.297275
$283$	9.06369e96	1.29342	0.646712	−	0.762734i	$-0.276144\pi$
$283$	9.06369e96	1.29342	0.646712	+	0.762734i	$0.276144\pi$
$284$	1.73694e96	0.215631
$285$	1.57888e97	1.70599
$286$	−9.49089e96	−0.892995
$287$	−1.24746e96	−0.102257
$288$	8.91381e96	0.636884
$289$	−1.59661e97	−0.994798
$290$	−1.18771e97	−0.645636
$291$	−3.32736e97	−1.57880
$292$	−2.71077e95	−0.0112323
$293$	−4.12037e97	−1.49164	−0.745821	−	0.666146i	$-0.767943\pi$
$293$	−4.12037e97	−1.49164	−0.745821	+	0.666146i	$0.767943\pi$
$294$	−2.51804e97	−0.796790
$295$	9.27381e97	2.56619
$296$	5.23467e97	1.26726
$297$	6.29264e97	1.33338
$298$	1.13550e97	0.210690
$299$	−8.42062e97	−1.36877
$300$	1.53838e97	0.219167
$301$	7.48795e97	0.935377
$302$	−6.65314e97	−0.729042
$303$	−6.72127e97	−0.646350
$304$	−1.03768e98	−0.876106
$305$	1.91177e98	1.41773
$306$	2.21275e97	0.144190
$307$	2.87152e97	0.164492	0.0822462	−	0.996612i	$-0.473791\pi$
$307$	2.87152e97	0.164492	0.0822462	+	0.996612i	$0.473791\pi$
$308$	−3.88478e97	−0.195710
$309$	−4.09277e98	−1.81408
$310$	−2.42614e98	−0.946517
$311$	1.34411e98	0.461741	0.230870	−	0.972985i	$-0.425843\pi$
$311$	1.34411e98	0.461741	0.230870	+	0.972985i	$0.425843\pi$
$312$	4.38995e98	1.32847
$313$	1.81703e98	0.484574	0.242287	−	0.970205i	$-0.422102\pi$
$313$	1.81703e98	0.484574	0.242287	+	0.970205i	$0.422102\pi$
$314$	3.87285e98	0.910561
$315$	−1.40802e99	−2.91972
$316$	1.52962e98	0.279862
$317$	−1.07040e98	−0.172864	−0.0864319	−	0.996258i	$-0.527546\pi$
$317$	−1.07040e98	−0.172864	−0.0864319	+	0.996258i	$0.527546\pi$
$318$	1.64220e99	2.34183
$319$	3.35094e98	0.422119
$320$	9.13493e98	1.01691
$321$	−3.58791e98	−0.353096
$322$	−2.31973e99	−2.01897
$323$	−7.17278e97	−0.0552316
$324$	1.42948e98	0.0974206
$325$	1.08647e99	0.655581
$326$	−4.06480e96	−0.00217242
$327$	1.53601e99	0.727373
$328$	1.81880e98	0.0763430
$329$	−5.23616e98	−0.194883
$330$	−6.84422e99	−2.25956
$331$	−6.59239e99	−1.93124	−0.965622	−	0.259951i	$-0.916294\pi$
$331$	−6.59239e99	−1.93124	−0.965622	+	0.259951i	$0.916294\pi$
$332$	5.74042e98	0.149276
$333$	1.13163e100	2.61310
$334$	−7.55464e99	−1.54963
$335$	6.19391e98	0.112900
$336$	1.42703e100	2.31223
$337$	4.54396e99	0.654716	0.327358	−	0.944900i	$-0.393842\pi$
$337$	4.54396e99	0.654716	0.327358	+	0.944900i	$0.393842\pi$
$338$	1.90117e99	0.243675
$339$	1.91088e99	0.217944
$340$	−1.63746e98	−0.0166247
$341$	6.84501e99	0.618837
$342$	−1.90107e100	−1.53097
$343$	9.41955e99	0.675947
$344$	−1.09175e100	−0.698333
$345$	−6.07240e100	−3.46343
$346$	2.00300e100	1.01900
$347$	3.55374e100	1.61314	0.806569	−	0.591140i	$-0.201322\pi$
$347$	3.55374e100	1.61314	0.806569	+	0.591140i	$0.201322\pi$
$348$	3.27667e99	0.132756
$349$	−4.60202e100	−1.66473	−0.832366	−	0.554227i	$-0.813014\pi$
$349$	−4.60202e100	−1.66473	−0.832366	+	0.554227i	$0.813014\pi$
$350$	2.99303e100	0.966994
$351$	4.34563e100	1.25436
$352$	1.25254e100	0.323115
$353$	1.55847e100	0.359416	0.179708	−	0.983720i	$-0.442485\pi$
$353$	1.55847e100	0.359416	0.179708	+	0.983720i	$0.442485\pi$
$354$	−1.72193e101	−3.55129
$355$	8.84618e100	1.63206
$356$	1.25125e99	0.0206571
$357$	9.86406e99	0.145768
$358$	9.30831e100	1.23166
$359$	−1.48242e101	−1.75687	−0.878436	−	0.477859i	$-0.841413\pi$
$359$	−1.48242e101	−1.75687	−0.878436	+	0.477859i	$0.841413\pi$
$360$	2.05289e101	2.17981
$361$	−4.34592e100	−0.413568
$362$	1.45798e101	1.24383
$363$	−2.73604e100	−0.209320
$364$	−2.68279e100	−0.184112
$365$	−1.38059e100	−0.0850151
$366$	−3.54972e101	−1.96196
$367$	−3.28023e101	−1.62777	−0.813887	−	0.581023i	$-0.802653\pi$
$367$	−3.28023e101	−1.62777	−0.813887	+	0.581023i	$0.802653\pi$
$368$	3.99093e101	1.77863
$369$	3.93187e100	0.157419
$370$	−5.63604e101	−2.02771
$371$	4.74724e101	1.53522
$372$	6.69329e100	0.194623
$373$	−4.44406e100	−0.116220	−0.0581100	−	0.998310i	$-0.518507\pi$
$373$	−4.44406e100	−0.116220	−0.0581100	+	0.998310i	$0.518507\pi$
$374$	3.10929e100	0.0731532
$375$	−2.68720e101	−0.568937
$376$	7.63433e100	0.145496
$377$	2.31413e101	0.397103
$378$	1.19714e102	1.85020
$379$	−8.31944e101	−1.15836	−0.579182	−	0.815198i	$-0.696628\pi$
$379$	−8.31944e101	−1.15836	−0.579182	+	0.815198i	$0.696628\pi$
$380$	1.40681e101	0.176515
$381$	1.53172e102	1.73238
$382$	4.52143e101	0.461076
$383$	3.50121e101	0.322008	0.161004	−	0.986954i	$-0.448527\pi$
$383$	3.50121e101	0.322008	0.161004	+	0.986954i	$0.448527\pi$
$384$	−2.39798e102	−1.98958
$385$	−1.97851e102	−1.48129
$386$	9.17539e101	0.620049
$387$	−2.36012e102	−1.43996
$388$	−2.96473e101	−0.163355
$389$	3.91980e102	1.95099	0.975495	−	0.220020i	$-0.0706123\pi$
$389$	3.91980e102	1.95099	0.975495	+	0.220020i	$0.0706123\pi$
$390$	−4.72655e102	−2.12565
$391$	2.75866e101	0.112129
$392$	1.06129e102	0.389974
$393$	1.51500e102	0.503392
$394$	−2.05543e102	−0.617736
$395$	7.79032e102	2.11821
$396$	1.22444e102	0.301286
$397$	9.85040e101	0.219396	0.109698	−	0.993965i	$-0.465012\pi$
$397$	9.85040e101	0.219396	0.109698	+	0.993965i	$0.465012\pi$
$398$	4.00537e102	0.807722
$399$	−8.47463e102	−1.54772
$400$	−5.14931e102	−0.851882
$401$	−1.90633e102	−0.285757	−0.142878	−	0.989740i	$-0.545636\pi$
$401$	−1.90633e102	−0.285757	−0.142878	+	0.989740i	$0.545636\pi$
$402$	−1.15006e102	−0.156240
$403$	4.72709e102	0.582163
$404$	−5.98876e101	−0.0668764
$405$	7.28031e102	0.737354
$406$	6.37499e102	0.585735
$407$	1.59013e103	1.32572
$408$	−1.43818e102	−0.108827
$409$	−2.16826e103	−1.48950	−0.744751	−	0.667342i	$-0.767432\pi$
$409$	−2.16826e103	−1.48950	−0.744751	+	0.667342i	$0.767432\pi$
$410$	−1.95826e102	−0.122154
$411$	−4.37617e103	−2.47938
$412$	−3.64672e102	−0.187699
$413$	−4.97771e103	−2.32810
$414$	7.31153e103	3.10810
$415$	2.92358e103	1.12983
$416$	8.64993e102	0.303967
$417$	−2.35682e103	−0.753273
$418$	−2.67132e103	−0.776718
$419$	4.16825e103	1.10281	0.551404	−	0.834238i	$-0.314092\pi$
$419$	4.16825e103	1.10281	0.551404	+	0.834238i	$0.314092\pi$
$420$	−1.93465e103	−0.465861
$421$	7.48726e103	1.64127	0.820635	−	0.571452i	$-0.193620\pi$
$421$	7.48726e103	1.64127	0.820635	+	0.571452i	$0.193620\pi$
$422$	9.71632e103	1.93937
$423$	1.65038e103	0.300013
$424$	−6.92149e103	−1.14617
$425$	−3.55937e102	−0.0537045
$426$	−1.64253e104	−2.25857
$427$	−1.02614e104	−1.28619
$428$	−3.19688e102	−0.0365341
$429$	1.33353e104	1.38976
$430$	1.17545e104	1.11738
$431$	5.01983e102	0.0435348	0.0217674	−	0.999763i	$-0.493071\pi$
$431$	5.01983e102	0.0435348	0.0217674	+	0.999763i	$0.493071\pi$
$432$	−2.05960e104	−1.62995
$433$	−2.28973e104	−1.65391	−0.826957	−	0.562265i	$-0.809930\pi$
$433$	−2.28973e104	−1.65391	−0.826957	+	0.562265i	$0.809930\pi$
$434$	1.30223e104	0.858702
$435$	1.66880e104	1.00480
$436$	1.36861e103	0.0752596
$437$	−2.37008e104	−1.19055
$438$	2.56343e103	0.117651
$439$	1.98050e104	0.830664	0.415332	−	0.909670i	$-0.363665\pi$
$439$	1.98050e104	0.830664	0.415332	+	0.909670i	$0.363665\pi$
$440$	2.88467e104	1.10590
$441$	2.29429e104	0.804126
$442$	2.14724e103	0.0688180
$443$	−1.06558e104	−0.312347	−0.156174	−	0.987730i	$-0.549916\pi$
$443$	−1.06558e104	−0.312347	−0.156174	+	0.987730i	$0.549916\pi$
$444$	1.55488e104	0.416937
$445$	6.37259e103	0.156349
$446$	−4.25161e104	−0.954612
$447$	−1.59544e104	−0.327894
$448$	−4.90316e104	−0.922560
$449$	6.69918e104	1.15423	0.577113	−	0.816664i	$-0.304179\pi$
$449$	6.69918e104	1.15423	0.577113	+	0.816664i	$0.304179\pi$
$450$	−9.43372e104	−1.48864
$451$	5.52496e103	0.0798648
$452$	1.70262e103	0.0225502
$453$	9.34807e104	1.13460
$454$	5.16447e104	0.574540
$455$	−1.36634e105	−1.39350
$456$	1.23560e105	1.15549
$457$	1.78653e104	0.153222	0.0766108	−	0.997061i	$-0.475590\pi$
$457$	1.78653e104	0.153222	0.0766108	+	0.997061i	$0.475590\pi$
$458$	−2.56498e105	−2.01789
$459$	−1.42366e104	−0.102756
$460$	−5.41061e104	−0.358353
$461$	−1.12025e105	−0.680971	−0.340486	−	0.940250i	$-0.610591\pi$
$461$	−1.12025e105	−0.680971	−0.340486	+	0.940250i	$0.610591\pi$
$462$	3.67363e105	2.04992
$463$	−8.78634e104	−0.450152	−0.225076	−	0.974341i	$-0.572263\pi$
$463$	−8.78634e104	−0.450152	−0.225076	+	0.974341i	$0.572263\pi$
$464$	−1.09677e105	−0.516009
$465$	3.40887e105	1.47306
$466$	4.81184e105	1.91015
$467$	−7.04870e104	−0.257094	−0.128547	−	0.991703i	$-0.541031\pi$
$467$	−7.04870e104	−0.257094	−0.128547	+	0.991703i	$0.541031\pi$
$468$	8.45586e104	0.283431
$469$	−3.32457e104	−0.102426
$470$	−8.21969e104	−0.232804
$471$	−5.44158e105	−1.41710
$472$	7.25750e105	1.73811
$473$	−3.31638e105	−0.730548
$474$	−1.44648e106	−2.93135
$475$	3.05801e105	0.570218
$476$	8.78903e103	0.0150823
$477$	−1.49628e106	−2.36340
$478$	6.12575e105	0.890753
$479$	2.95510e105	0.395658	0.197829	−	0.980237i	$-0.436611\pi$
$479$	2.95510e105	0.395658	0.197829	+	0.980237i	$0.436611\pi$
$480$	6.23777e105	0.769132
$481$	1.09813e106	1.24716
$482$	−1.20292e106	−1.25858
$483$	3.25936e106	3.14210
$484$	−2.43785e104	−0.0216579
$485$	−1.50993e106	−1.23639
$486$	6.93665e105	0.523621
$487$	−2.60640e106	−1.81404	−0.907020	−	0.421087i	$-0.861649\pi$
$487$	−2.60640e106	−1.81404	−0.907020	+	0.421087i	$0.861649\pi$
$488$	1.49612e106	0.960246
$489$	5.71129e103	0.00338092
$490$	−1.14267e106	−0.623985
$491$	2.32180e106	1.16979	0.584893	−	0.811111i	$-0.301137\pi$
$491$	2.32180e106	1.16979	0.584893	+	0.811111i	$0.301137\pi$
$492$	5.40249e104	0.0251173
$493$	−7.58126e104	−0.0325303
$494$	−1.84479e106	−0.730688
$495$	6.23605e106	2.28036
$496$	−2.24039e106	−0.756481
$497$	−4.74818e106	−1.48064
$498$	−5.42840e106	−1.56355
$499$	−4.48706e106	−1.19396	−0.596981	−	0.802256i	$-0.703633\pi$
$499$	−4.48706e106	−1.19396	−0.596981	+	0.802256i	$0.703633\pi$
$500$	−2.39433e105	−0.0588667
$501$	1.06147e107	2.41167
$502$	6.09617e106	1.28015
$503$	−1.36594e106	−0.265152	−0.132576	−	0.991173i	$-0.542325\pi$
$503$	−1.36594e106	−0.265152	−0.132576	+	0.991173i	$0.542325\pi$
$504$	−1.10189e107	−1.97757
$505$	−3.05006e106	−0.506172
$506$	1.02740e107	1.57686
$507$	−2.67126e106	−0.379229
$508$	1.36479e106	0.179246
$509$	1.91849e106	0.233135	0.116568	−	0.993183i	$-0.462811\pi$
$509$	1.91849e106	0.233135	0.116568	+	0.993183i	$0.462811\pi$
$510$	1.54845e106	0.174131
$511$	7.41029e105	0.0771276
$512$	6.52347e106	0.628515
$513$	1.22313e107	1.09103
$514$	−3.87092e106	−0.319721
$515$	−1.85726e107	−1.42065
$516$	−3.24287e106	−0.229756
$517$	2.31907e106	0.152208
$518$	3.02514e107	1.83958
$519$	−2.81433e107	−1.58586
$520$	1.99212e107	1.04036
$521$	3.81999e106	0.184915	0.0924575	−	0.995717i	$-0.470528\pi$
$521$	3.81999e106	0.184915	0.0924575	+	0.995717i	$0.470528\pi$
$522$	−2.00933e107	−0.901709
$523$	−2.09703e107	−0.872546	−0.436273	−	0.899814i	$-0.643702\pi$
$523$	−2.09703e107	−0.872546	−0.436273	+	0.899814i	$0.643702\pi$
$524$	1.34989e106	0.0520848
$525$	−4.20540e107	−1.50492
$526$	−2.93287e107	−0.973546
$527$	−1.54863e106	−0.0476902
$528$	−6.32023e107	−1.80590
$529$	5.34400e107	1.41699
$530$	7.45219e107	1.83395
$531$	1.56892e108	3.58399
$532$	−7.55103e106	−0.160139
$533$	3.81548e106	0.0751318
$534$	−1.18324e107	−0.216368
$535$	−1.62816e107	−0.276518
$536$	4.84723e106	0.0764689
$537$	−1.30787e108	−1.91682
$538$	5.20396e107	0.708654
$539$	3.22387e107	0.407964
$540$	2.79225e107	0.328398
$541$	−2.74852e107	−0.300475	−0.150237	−	0.988650i	$-0.548004\pi$
$541$	−2.74852e107	−0.300475	−0.150237	+	0.988650i	$0.548004\pi$
$542$	−1.10821e108	−1.12629
$543$	−2.04855e108	−1.93576
$544$	−2.83379e106	−0.0249006
$545$	6.97027e107	0.569623
$546$	2.53697e108	1.92844
$547$	−1.01588e108	−0.718363	−0.359181	−	0.933268i	$-0.616944\pi$
$547$	−1.01588e108	−0.718363	−0.359181	+	0.933268i	$0.616944\pi$
$548$	−3.89924e107	−0.256535
$549$	3.23429e108	1.98003
$550$	−1.32560e108	−0.755242
$551$	6.51338e107	0.345397
$552$	−4.75215e108	−2.34583
$553$	−4.18144e108	−1.92169
$554$	1.75757e108	0.752103
$555$	7.91898e108	3.15570
$556$	−2.09996e107	−0.0779395
$557$	6.78169e107	0.234454	0.117227	−	0.993105i	$-0.462599\pi$
$557$	6.78169e107	0.234454	0.117227	+	0.993105i	$0.462599\pi$
$558$	−4.10448e108	−1.32193
$559$	−2.29026e108	−0.687254
$560$	6.47572e108	1.81076
$561$	−4.36874e107	−0.113848
$562$	7.06610e107	0.171631
$563$	6.00806e108	1.36036	0.680178	−	0.733047i	$-0.261903\pi$
$563$	6.00806e108	1.36036	0.680178	+	0.733047i	$0.261903\pi$
$564$	2.26767e107	0.0478690
$565$	8.67140e107	0.170677
$566$	−7.63692e108	−1.40175
$567$	−3.90770e108	−0.668944
$568$	6.92285e108	1.10542
$569$	−1.02026e109	−1.51976	−0.759881	−	0.650062i	$-0.774743\pi$
$569$	−1.02026e109	−1.51976	−0.759881	+	0.650062i	$0.774743\pi$
$570$	−1.33034e109	−1.84887
$571$	1.13551e109	1.47253	0.736264	−	0.676694i	$-0.236588\pi$
$571$	1.13551e109	1.47253	0.736264	+	0.676694i	$0.236588\pi$
$572$	1.18819e108	0.143795
$573$	−6.35288e108	−0.717568
$574$	1.05109e108	0.110821
$575$	−1.17611e109	−1.15763
$576$	1.54542e109	1.42023
$577$	2.13763e108	0.183438	0.0917189	−	0.995785i	$-0.470764\pi$
$577$	2.13763e108	0.183438	0.0917189	+	0.995785i	$0.470764\pi$
$578$	1.34528e109	1.07811
$579$	−1.28920e109	−0.964976
$580$	1.48692e108	0.103964
$581$	−1.56923e109	−1.02501
$582$	2.80358e109	1.71102
$583$	−2.10253e109	−1.19904
$584$	−1.08042e108	−0.0575819
$585$	4.30655e109	2.14522
$586$	3.47176e109	1.61657
$587$	−4.78489e108	−0.208289	−0.104145	−	0.994562i	$-0.533211\pi$
$587$	−4.78489e108	−0.208289	−0.104145	+	0.994562i	$0.533211\pi$
$588$	3.15242e108	0.128304
$589$	1.33049e109	0.506360
$590$	−7.81397e109	−2.78110
$591$	2.88801e109	0.961376
$592$	−5.20454e109	−1.62060
$593$	−1.37706e108	−0.0401137	−0.0200568	−	0.999799i	$-0.506385\pi$
$593$	−1.37706e108	−0.0401137	−0.0200568	+	0.999799i	$0.506385\pi$
$594$	−5.30208e109	−1.44505
$595$	4.47623e108	0.114154
$596$	−1.42156e108	−0.0339265
$597$	−5.62780e109	−1.25705
$598$	7.09508e109	1.48341
$599$	1.69678e108	0.0332097	0.0166049	−	0.999862i	$-0.494714\pi$
$599$	1.69678e108	0.0332097	0.0166049	+	0.999862i	$0.494714\pi$
$600$	6.13147e109	1.12355
$601$	5.53355e109	0.949428	0.474714	−	0.880140i	$-0.342551\pi$
$601$	5.53355e109	0.949428	0.474714	+	0.880140i	$0.342551\pi$
$602$	−6.30923e109	−1.01371
$603$	1.04787e109	0.157679
$604$	8.32928e108	0.117395
$605$	−1.24159e109	−0.163924
$606$	5.66324e109	0.700481
$607$	8.72796e109	1.01148	0.505742	−	0.862684i	$-0.331219\pi$
$607$	8.72796e109	1.01148	0.505742	+	0.862684i	$0.331219\pi$
$608$	2.43463e109	0.264387
$609$	−8.95725e109	−0.911574
$610$	−1.61083e110	−1.53646
$611$	1.60152e109	0.143188
$612$	−2.77021e108	−0.0232183
$613$	9.62870e109	0.756622	0.378311	−	0.925679i	$-0.376505\pi$
$613$	9.62870e109	0.756622	0.378311	+	0.925679i	$0.376505\pi$
$614$	−2.41950e109	−0.178269
$615$	2.75147e109	0.190107
$616$	−1.54834e110	−1.00330
$617$	1.93190e110	1.17414	0.587071	−	0.809536i	$-0.300281\pi$
$617$	1.93190e110	1.17414	0.587071	+	0.809536i	$0.300281\pi$
$618$	3.44850e110	1.96601
$619$	4.62898e109	0.247574	0.123787	−	0.992309i	$-0.460496\pi$
$619$	4.62898e109	0.247574	0.123787	+	0.992309i	$0.460496\pi$
$620$	3.03736e109	0.152414
$621$	−4.70417e110	−2.21495
$622$	−1.13252e110	−0.500411
$623$	−3.42048e109	−0.141844
$624$	−4.36468e110	−1.69887
$625$	−3.25737e110	−1.19016
$626$	−1.53100e110	−0.525157
$627$	3.75337e110	1.20880
$628$	−4.84853e109	−0.146624
$629$	−3.59755e109	−0.102166
$630$	1.18637e111	3.16425
$631$	2.31441e110	0.579804	0.289902	−	0.957056i	$-0.406377\pi$
$631$	2.31441e110	0.579804	0.289902	+	0.957056i	$0.406377\pi$
$632$	6.09655e110	1.43470
$633$	−1.36520e111	−3.01822
$634$	9.01900e109	0.187341
$635$	6.95083e110	1.35667
$636$	−2.05593e110	−0.377096
$637$	2.22637e110	0.383787
$638$	−2.82345e110	−0.457471
$639$	1.49657e111	2.27937
$640$	−1.08818e111	−1.55809
$641$	−3.59419e110	−0.483848	−0.241924	−	0.970295i	$-0.577778\pi$
$641$	−3.59419e110	−0.483848	−0.241924	+	0.970295i	$0.577778\pi$
$642$	3.02312e110	0.382668
$643$	−8.26218e110	−0.983470	−0.491735	−	0.870745i	$-0.663637\pi$
$643$	−8.26218e110	−0.983470	−0.491735	+	0.870745i	$0.663637\pi$
$644$	2.90414e110	0.325106
$645$	−1.65158e111	−1.73897
$646$	6.04367e109	0.0598572
$647$	−1.00058e111	−0.932253	−0.466127	−	0.884718i	$-0.654351\pi$
$647$	−1.00058e111	−0.932253	−0.466127	+	0.884718i	$0.654351\pi$
$648$	5.69743e110	0.499420
$649$	2.20460e111	1.81830
$650$	−9.15445e110	−0.710485
$651$	−1.82971e111	−1.33639
$652$	5.08885e107	0.000349816 0
$653$	2.19401e111	1.41961	0.709803	−	0.704400i	$-0.248784\pi$
$653$	2.19401e111	1.41961	0.709803	+	0.704400i	$0.248784\pi$
$654$	−1.29422e111	−0.788289
$655$	6.87493e110	0.394218
$656$	−1.80834e110	−0.0976287
$657$	−2.33564e110	−0.118734
$658$	4.41191e110	0.211205
$659$	2.97784e111	1.34254	0.671271	−	0.741212i	$-0.265749\pi$
$659$	2.97784e111	1.34254	0.671271	+	0.741212i	$0.265749\pi$
$660$	8.56849e110	0.363847
$661$	−1.56534e111	−0.626110	−0.313055	−	0.949735i	$-0.601352\pi$
$661$	−1.56534e111	−0.626110	−0.313055	+	0.949735i	$0.601352\pi$
$662$	5.55464e111	2.09298
$663$	−3.01701e110	−0.107101
$664$	2.28793e111	0.765252
$665$	−3.84572e111	−1.21205
$666$	−9.53491e111	−2.83194
$667$	−2.50506e111	−0.701208
$668$	9.45788e110	0.249531
$669$	5.97378e111	1.48565
$670$	−5.21889e110	−0.122356
$671$	4.54473e111	1.00454
$672$	−3.34812e111	−0.697773
$673$	−5.99621e111	−1.17837	−0.589185	−	0.807998i	$-0.700551\pi$
$673$	−5.99621e111	−1.17837	−0.589185	+	0.807998i	$0.700551\pi$
$674$	−3.82867e111	−0.709548
$675$	6.06957e111	1.06086
$676$	−2.38013e110	−0.0392380
$677$	3.39075e111	0.527282	0.263641	−	0.964621i	$-0.415077\pi$
$677$	3.39075e111	0.527282	0.263641	+	0.964621i	$0.415077\pi$
$678$	−1.61008e111	−0.236197
$679$	8.10451e111	1.12168
$680$	−6.52635e110	−0.0852252
$681$	−7.25640e111	−0.894150
$682$	−5.76750e111	−0.670663
$683$	−5.01990e111	−0.550905	−0.275453	−	0.961315i	$-0.588828\pi$
$683$	−5.01990e111	−0.550905	−0.275453	+	0.961315i	$0.588828\pi$
$684$	2.38000e111	0.246525
$685$	−1.98587e112	−1.94166
$686$	−7.93677e111	−0.732557
$687$	3.60396e112	3.14043
$688$	1.08546e112	0.893040
$689$	−1.45198e112	−1.12798
$690$	5.11651e112	3.75349
$691$	2.42401e112	1.67939	0.839696	−	0.543057i	$-0.182733\pi$
$691$	2.42401e112	1.67939	0.839696	+	0.543057i	$0.182733\pi$
$692$	−2.50761e111	−0.164085
$693$	−3.34719e112	−2.06880
$694$	−2.99433e112	−1.74824
$695$	−1.06951e112	−0.589906
$696$	1.30597e112	0.680563
$697$	−1.24998e110	−0.00615472
$698$	3.87759e112	1.80415
$699$	−6.76093e112	−2.97275
$700$	−3.74707e111	−0.155711
$701$	−3.79533e112	−1.49069	−0.745346	−	0.666678i	$-0.767716\pi$
$701$	−3.79533e112	−1.49069	−0.745346	+	0.666678i	$0.767716\pi$
$702$	−3.66156e112	−1.35941
$703$	3.09081e112	1.08477
$704$	2.17159e112	0.720538
$705$	1.15492e112	0.362310
$706$	−1.31314e112	−0.389517
$707$	1.63711e112	0.459211
$708$	2.15574e112	0.571850
$709$	4.39351e112	1.10226	0.551131	−	0.834419i	$-0.314196\pi$
$709$	4.39351e112	1.10226	0.551131	+	0.834419i	$0.314196\pi$
$710$	−7.45366e112	−1.76874
$711$	1.31795e113	2.95834
$712$	4.98707e111	0.105898
$713$	−5.11710e112	−1.02799
$714$	−8.31131e111	−0.157976
$715$	6.05144e112	1.08835
$716$	−1.16534e112	−0.198329
$717$	−8.60706e112	−1.38627
$718$	1.24906e113	1.90401
$719$	−8.57228e112	−1.23682	−0.618408	−	0.785857i	$-0.712222\pi$
$719$	−8.57228e112	−1.23682	−0.618408	+	0.785857i	$0.712222\pi$
$720$	−2.04108e113	−2.78757
$721$	9.96884e112	1.28885
$722$	3.66180e112	0.448204
$723$	1.69018e113	1.95871
$724$	−1.82529e112	−0.200289
$725$	3.23216e112	0.335847
$726$	2.30535e112	0.226850
$727$	−1.80771e113	−1.68469	−0.842344	−	0.538940i	$-0.818825\pi$
$727$	−1.80771e113	−1.68469	−0.842344	+	0.538940i	$0.818825\pi$
$728$	−1.06927e113	−0.943838
$729$	−1.64231e113	−1.37315
$730$	1.16326e112	0.0921350
$731$	7.50306e111	0.0562992
$732$	4.44400e112	0.315927
$733$	−1.18515e113	−0.798300	−0.399150	−	0.916886i	$-0.630695\pi$
$733$	−1.18515e113	−0.798300	−0.399150	+	0.916886i	$0.630695\pi$
$734$	2.76387e113	1.76410
$735$	1.60552e113	0.971102
$736$	−9.36361e112	−0.536747
$737$	1.47244e112	0.0799965
$738$	−3.31293e112	−0.170603
$739$	1.08752e113	0.530865	0.265432	−	0.964130i	$-0.414485\pi$
$739$	1.08752e113	0.530865	0.265432	+	0.964130i	$0.414485\pi$
$740$	7.05593e112	0.326514
$741$	2.59204e113	1.13716
$742$	−3.99995e113	−1.66380
$743$	−3.36935e113	−1.32889	−0.664443	−	0.747339i	$-0.731331\pi$
$743$	−3.36935e113	−1.32889	−0.664443	+	0.747339i	$0.731331\pi$
$744$	2.66772e113	0.997720
$745$	−7.23998e112	−0.256782
$746$	3.74449e112	0.125953
$747$	4.94603e113	1.57795
$748$	−3.89262e111	−0.0117796
$749$	8.73915e112	0.250863
$750$	2.26419e113	0.616585
$751$	−1.70764e112	−0.0441184	−0.0220592	−	0.999757i	$-0.507022\pi$
$751$	−1.70764e112	−0.0441184	−0.0220592	+	0.999757i	$0.507022\pi$
$752$	−7.59039e112	−0.186063
$753$	−8.56549e113	−1.99228
$754$	−1.94985e113	−0.430360
$755$	4.24208e113	0.888533
$756$	−1.49874e113	−0.297930
$757$	−3.22054e113	−0.607634	−0.303817	−	0.952730i	$-0.598261\pi$
$757$	−3.22054e113	−0.607634	−0.303817	+	0.952730i	$0.598261\pi$
$758$	7.00983e113	1.25538
$759$	−1.44355e114	−2.45404
$760$	5.60706e113	0.904895
$761$	5.35481e113	0.820446	0.410223	−	0.911985i	$-0.365451\pi$
$761$	5.35481e113	0.820446	0.410223	+	0.911985i	$0.365451\pi$
$762$	−1.29061e114	−1.87747
$763$	−3.74128e113	−0.516775
$764$	−5.66051e112	−0.0742451
$765$	−1.41086e113	−0.175734
$766$	−2.95007e113	−0.348976
$767$	1.52247e114	1.71054
$768$	8.03700e113	0.857681
$769$	1.38510e114	1.40408	0.702039	−	0.712138i	$-0.252273\pi$
$769$	1.38510e114	1.40408	0.702039	+	0.712138i	$0.252273\pi$
$770$	1.66706e114	1.60534
$771$	5.43888e113	0.497579
$772$	−1.14870e113	−0.0998439
$773$	−1.39183e114	−1.14947	−0.574733	−	0.818341i	$-0.694894\pi$
$773$	−1.39183e114	−1.14947	−0.574733	+	0.818341i	$0.694894\pi$
$774$	1.98860e114	1.56056
$775$	6.60236e113	0.492359
$776$	−1.18164e114	−0.837427
$777$	−4.25050e114	−2.86293
$778$	−3.30277e114	−2.11438
$779$	1.07391e113	0.0653489
$780$	5.91731e113	0.342285
$781$	2.10294e114	1.15641
$782$	−2.32440e113	−0.121519
$783$	1.29278e114	0.642594
$784$	−1.05518e114	−0.498705
$785$	−2.46934e114	−1.10976
$786$	−1.27651e114	−0.545550
$787$	4.36246e114	1.77308	0.886542	−	0.462649i	$-0.153101\pi$
$787$	4.36246e114	1.77308	0.886542	+	0.462649i	$0.153101\pi$
$788$	2.57326e113	0.0994715
$789$	4.12087e114	1.51512
$790$	−6.56400e114	−2.29561
$791$	−4.65436e113	−0.154842
$792$	4.88021e114	1.54452
$793$	3.13854e114	0.945012
$794$	−8.29980e113	−0.237770
$795$	−1.04708e115	−2.85415
$796$	−5.01445e113	−0.130064
$797$	4.51588e113	0.111465	0.0557325	−	0.998446i	$-0.482251\pi$
$797$	4.51588e113	0.111465	0.0557325	+	0.998446i	$0.482251\pi$
$798$	7.14059e114	1.67734
$799$	−5.24672e112	−0.0117298
$800$	1.20814e114	0.257077
$801$	1.07810e114	0.218361
$802$	1.60625e114	0.309688
$803$	−3.28198e113	−0.0602382
$804$	1.43980e113	0.0251587
$805$	1.47907e115	2.46066
$806$	−3.98297e114	−0.630918
$807$	−7.31188e114	−1.10287
$808$	−2.38692e114	−0.342838
$809$	−1.13305e114	−0.154982	−0.0774911	−	0.996993i	$-0.524691\pi$
$809$	−1.13305e114	−0.154982	−0.0774911	+	0.996993i	$0.524691\pi$
$810$	−6.13427e114	−0.799107
$811$	−8.23822e114	−1.02214	−0.511069	−	0.859540i	$-0.670750\pi$
$811$	−8.23822e114	−1.02214	−0.511069	+	0.859540i	$0.670750\pi$
$812$	−7.98105e113	−0.0943185
$813$	1.55710e115	1.75283
$814$	−1.33982e115	−1.43675
$815$	2.59174e112	0.00264768
$816$	1.42990e114	0.139170
$817$	−6.44619e114	−0.597767
$818$	1.82694e115	1.61425
$819$	−2.31153e115	−1.94619
$820$	2.45161e113	0.0196700
$821$	−1.83306e115	−1.40159	−0.700795	−	0.713362i	$-0.747171\pi$
$821$	−1.83306e115	−1.40159	−0.700795	+	0.713362i	$0.747171\pi$
$822$	3.68729e115	2.68702
$823$	−1.77225e115	−1.23093	−0.615463	−	0.788166i	$-0.711031\pi$
$823$	−1.77225e115	−1.23093	−0.615463	+	0.788166i	$0.711031\pi$
$824$	−1.45346e115	−0.962228
$825$	1.86255e115	1.17538
$826$	4.19414e115	2.52308
$827$	9.78862e114	0.561376	0.280688	−	0.959799i	$-0.409437\pi$
$827$	9.78862e114	0.561376	0.280688	+	0.959799i	$0.409437\pi$
$828$	−9.15352e114	−0.500484
$829$	4.01341e114	0.209223	0.104612	−	0.994513i	$-0.466640\pi$
$829$	4.01341e114	0.209223	0.104612	+	0.994513i	$0.466640\pi$
$830$	−2.46336e115	−1.22446
$831$	−2.46949e115	−1.17049
$832$	1.49967e115	0.677837
$833$	−7.29377e113	−0.0314394
$834$	1.98582e115	0.816359
$835$	4.81687e115	1.88864
$836$	3.34431e114	0.125072
$837$	2.64078e115	0.942057
$838$	−3.51210e115	−1.19517
$839$	1.59510e115	0.517834	0.258917	−	0.965900i	$-0.416634\pi$
$839$	1.59510e115	0.517834	0.258917	+	0.965900i	$0.416634\pi$
$840$	−7.71088e115	−2.38821
$841$	−2.69566e115	−0.796568
$842$	−6.30865e115	−1.77873
$843$	−9.92830e114	−0.267107
$844$	−1.21642e115	−0.312288
$845$	−1.21220e115	−0.296984
$846$	−1.39059e115	−0.325138
$847$	6.66423e114	0.148715
$848$	6.88165e115	1.46574
$849$	1.07303e116	2.18152
$850$	2.99907e114	0.0582022
$851$	−1.18873e116	−2.20224
$852$	2.05633e115	0.363688
$853$	5.81489e115	0.981871	0.490936	−	0.871196i	$-0.336655\pi$
$853$	5.81489e115	0.981871	0.490936	+	0.871196i	$0.336655\pi$
$854$	8.64611e115	1.39391
$855$	1.21213e116	1.86589
$856$	−1.27417e115	−0.187290
$857$	−8.63740e115	−1.21239	−0.606193	−	0.795318i	$-0.707304\pi$
$857$	−8.63740e115	−1.21239	−0.606193	+	0.795318i	$0.707304\pi$
$858$	−1.12361e116	−1.50615
$859$	−8.23961e114	−0.105482	−0.0527408	−	0.998608i	$-0.516796\pi$
$859$	−8.23961e114	−0.105482	−0.0527408	+	0.998608i	$0.516796\pi$
$860$	−1.47159e115	−0.179927
$861$	−1.47685e115	−0.172469
$862$	−4.22963e114	−0.0471808
$863$	7.93638e115	0.845661	0.422830	−	0.906209i	$-0.361037\pi$
$863$	7.93638e115	0.845661	0.422830	+	0.906209i	$0.361037\pi$
$864$	4.83228e115	0.491880
$865$	−1.27712e116	−1.24192
$866$	1.92929e116	1.79243
$867$	−1.89020e116	−1.67785
$868$	−1.63030e115	−0.138273
$869$	1.85194e116	1.50088
$870$	−1.40610e116	−1.08895
$871$	1.01685e115	0.0752557
$872$	5.45480e115	0.385814
$873$	−2.55445e116	−1.72677
$874$	1.99699e116	1.29025
$875$	6.54526e115	0.404212
$876$	−3.20924e114	−0.0189448
$877$	2.93010e116	1.65348	0.826740	−	0.562584i	$-0.190193\pi$
$877$	2.93010e116	1.65348	0.826740	+	0.562584i	$0.190193\pi$
$878$	−1.66874e116	−0.900232
$879$	−4.87803e116	−2.51584
$880$	−2.86806e116	−1.41424
$881$	1.12747e116	0.531565	0.265783	−	0.964033i	$-0.414370\pi$
$881$	1.12747e116	0.531565	0.265783	+	0.964033i	$0.414370\pi$
$882$	−1.93313e116	−0.871471
$883$	−3.56610e116	−1.53726	−0.768628	−	0.639696i	$-0.779060\pi$
$883$	−3.56610e116	−1.53726	−0.768628	+	0.639696i	$0.779060\pi$
$884$	−2.68820e114	−0.0110815
$885$	1.09791e117	4.32820
$886$	8.97838e115	0.338506
$887$	1.58042e116	0.569889	0.284944	−	0.958544i	$-0.408025\pi$
$887$	1.58042e116	0.569889	0.284944	+	0.958544i	$0.408025\pi$
$888$	6.19724e116	2.13740
$889$	−3.73085e116	−1.23080
$890$	−5.36945e115	−0.169443
$891$	1.73070e116	0.522459
$892$	5.32273e115	0.153717
$893$	4.50768e115	0.124543
$894$	1.34429e116	0.355355
$895$	−5.93502e116	−1.50111
$896$	5.84080e116	1.41353
$897$	−9.96902e116	−2.30861
$898$	−5.64462e116	−1.25089
$899$	1.40627e116	0.298236
$900$	1.18104e116	0.239709
$901$	4.75682e115	0.0924032
$902$	−4.65524e115	−0.0865534
$903$	8.86486e116	1.57763
$904$	6.78607e115	0.115602
$905$	−9.29612e116	−1.51594
$906$	−7.87654e116	−1.22962
$907$	−8.05017e115	−0.120314	−0.0601571	−	0.998189i	$-0.519160\pi$
$907$	−8.05017e115	−0.120314	−0.0601571	+	0.998189i	$0.519160\pi$
$908$	−6.46556e115	−0.0925157
$909$	−5.16001e116	−0.706931
$910$	1.15125e117	1.51021
$911$	1.78870e116	0.224679	0.112339	−	0.993670i	$-0.464166\pi$
$911$	1.78870e116	0.224679	0.112339	+	0.993670i	$0.464166\pi$
$912$	−1.22849e117	−1.47766
$913$	6.95003e116	0.800554
$914$	−1.50530e116	−0.166054
$915$	2.26332e117	2.39118
$916$	3.21118e116	0.324933
$917$	−3.69011e116	−0.357644
$918$	1.19956e116	0.111361
$919$	9.52514e116	0.847049	0.423525	−	0.905885i	$-0.360793\pi$
$919$	9.52514e116	0.847049	0.423525	+	0.905885i	$0.360793\pi$
$920$	−2.15648e117	−1.83708
$921$	3.39954e116	0.277437
$922$	9.43906e116	0.738002
$923$	1.45227e117	1.08788
$924$	−4.59913e116	−0.330090
$925$	1.53376e117	1.05477
$926$	7.40323e116	0.487851
$927$	−3.14207e117	−1.98411
$928$	2.57328e116	0.155719
$929$	−2.85231e117	−1.65415	−0.827077	−	0.562088i	$-0.809998\pi$
$929$	−2.85231e117	−1.65415	−0.827077	+	0.562088i	$0.809998\pi$
$930$	−2.87226e117	−1.59642
$931$	6.26639e116	0.333814
$932$	−6.02409e116	−0.307584
$933$	1.59126e117	0.778784
$934$	5.93912e116	0.278625
$935$	−1.98250e116	−0.0891568
$936$	3.37022e117	1.45299
$937$	−4.69296e117	−1.93969	−0.969847	−	0.243714i	$-0.921634\pi$
$937$	−4.69296e117	−1.93969	−0.969847	+	0.243714i	$0.921634\pi$
$938$	2.80123e116	0.111004
$939$	2.15115e117	0.817296
$940$	1.02905e116	0.0374874
$941$	2.18384e117	0.762835	0.381418	−	0.924403i	$-0.375436\pi$
$941$	2.18384e117	0.762835	0.381418	+	0.924403i	$0.375436\pi$
$942$	4.58499e117	1.53578
$943$	−4.13028e116	−0.132668
$944$	−7.21573e117	−2.22273
$945$	−7.63303e117	−2.25497
$946$	2.79433e117	0.791731
$947$	6.61338e117	1.79721	0.898606	−	0.438757i	$-0.144581\pi$
$947$	6.61338e117	1.79721	0.898606	+	0.438757i	$0.144581\pi$
$948$	1.81089e117	0.472023
$949$	−2.26650e116	−0.0566684
$950$	−2.57663e117	−0.617973
$951$	−1.26722e117	−0.291557
$952$	3.50301e116	0.0773182
$953$	−4.39619e117	−0.930908	−0.465454	−	0.885072i	$-0.654109\pi$
$953$	−4.39619e117	−0.930908	−0.465454	+	0.885072i	$0.654109\pi$
$954$	1.26074e118	2.56133
$955$	−2.88288e117	−0.561945
$956$	−7.66902e116	−0.143434
$957$	3.96712e117	0.711958
$958$	−2.48992e117	−0.428793
$959$	1.06591e118	1.76152
$960$	1.08147e118	1.71514
$961$	−3.69753e117	−0.562780
$962$	−9.25264e117	−1.35161
$963$	−2.75449e117	−0.386191
$964$	1.50598e117	0.202664
$965$	−5.85027e117	−0.755696
$966$	−2.74628e118	−3.40525
$967$	−8.20710e117	−0.976886	−0.488443	−	0.872596i	$-0.662435\pi$
$967$	−8.20710e117	−0.976886	−0.488443	+	0.872596i	$0.662435\pi$
$968$	−9.71646e116	−0.111028
$969$	−8.49172e116	−0.0931551
$970$	1.27224e118	1.33994
$971$	−9.66918e117	−0.977755	−0.488877	−	0.872353i	$-0.662593\pi$
$971$	−9.66918e117	−0.977755	−0.488877	+	0.872353i	$0.662593\pi$
$972$	−8.68421e116	−0.0843165
$973$	5.74056e117	0.535176
$974$	2.19611e118	1.96596
$975$	1.28626e118	1.10572
$976$	−1.48751e118	−1.22798
$977$	1.35219e118	1.07202	0.536008	−	0.844213i	$-0.319932\pi$
$977$	1.35219e118	1.07202	0.536008	+	0.844213i	$0.319932\pi$
$978$	−4.81225e115	−0.00366406
$979$	1.51491e117	0.110783
$980$	1.43054e117	0.100478
$981$	1.17921e118	0.795548
$982$	−1.95631e118	−1.26775
$983$	1.23625e118	0.769559	0.384780	−	0.923008i	$-0.374277\pi$
$983$	1.23625e118	0.769559	0.384780	+	0.923008i	$0.374277\pi$
$984$	2.15325e117	0.128762
$985$	1.31055e118	0.752877
$986$	6.38785e116	0.0352547
$987$	−6.19900e117	−0.328696
$988$	2.30955e117	0.117660
$989$	2.47922e118	1.21356
$990$	−5.25440e118	−2.47134
$991$	5.32564e117	0.240692	0.120346	−	0.992732i	$-0.461600\pi$
$991$	5.32564e117	0.240692	0.120346	+	0.992732i	$0.461600\pi$
$992$	5.25646e117	0.228287
$993$	−7.80461e118	−3.25729
$994$	4.00074e118	1.60464
$995$	−2.55385e118	−0.984426
$996$	6.79598e117	0.251772
$997$	1.22747e118	0.437071	0.218535	−	0.975829i	$-0.429872\pi$
$997$	1.22747e118	0.437071	0.218535	+	0.975829i	$0.429872\pi$
$998$	3.78073e118	1.29395
$999$	6.13467e118	2.01816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.80.a.a.1.2	✓	6
3.2	odd	2		9.80.a.b.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.80.a.a.1.2	✓	6	1.1	even	1	trivial
9.80.a.b.1.5		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)

\(f(q)\)	\(=\)	\(q-8.42585e11 q^{2} +1.18388e19 q^{3} +1.05486e23 q^{4} +5.37236e27 q^{5} -9.97521e30 q^{6} -2.88361e33 q^{7} +4.20430e35 q^{8} +9.08882e37 q^{9} -4.52667e39 q^{10} +1.27714e41 q^{11} +1.24883e42 q^{12} +8.81976e43 q^{13} +2.42968e45 q^{14} +6.36024e46 q^{15} -4.18010e47 q^{16} -2.88942e47 q^{17} -7.65810e49 q^{18} +2.48242e50 q^{19} +5.66707e50 q^{20} -3.41385e52 q^{21} -1.07609e53 q^{22} -9.54744e53 q^{23} +4.97740e54 q^{24} +1.23186e55 q^{25} -7.43139e55 q^{26} +4.92715e56 q^{27} -3.04179e56 q^{28} +2.62380e57 q^{29} -5.35904e58 q^{30} +5.35966e58 q^{31} +9.80745e58 q^{32} +1.51198e60 q^{33} +2.43458e59 q^{34} -1.54918e61 q^{35} +9.58741e60 q^{36} +1.24508e62 q^{37} -2.09165e62 q^{38} +1.04416e63 q^{39} +2.25870e63 q^{40} +4.32605e62 q^{41} +2.87646e64 q^{42} -2.59673e64 q^{43} +1.34720e64 q^{44} +4.88284e65 q^{45} +8.04453e65 q^{46} +1.81584e65 q^{47} -4.94875e66 q^{48} +2.52430e66 q^{49} -1.03795e67 q^{50} -3.42074e66 q^{51} +9.30359e66 q^{52} -1.64629e68 q^{53} -4.15154e68 q^{54} +6.86123e68 q^{55} -1.21236e69 q^{56} +2.93890e69 q^{57} -2.21077e69 q^{58} +1.72621e70 q^{59} +6.70915e69 q^{60} +3.55854e70 q^{61} -4.51596e70 q^{62} -2.62086e71 q^{63} +1.70036e71 q^{64} +4.73829e71 q^{65} -1.27397e72 q^{66} +1.15292e71 q^{67} -3.04793e70 q^{68} -1.13031e73 q^{69} +1.30531e73 q^{70} +1.64661e73 q^{71} +3.82122e73 q^{72} -2.56980e72 q^{73} -1.04908e74 q^{74} +1.45838e74 q^{75} +2.61860e73 q^{76} -3.68276e74 q^{77} -8.79790e74 q^{78} +1.45007e75 q^{79} -2.24570e75 q^{80} +1.35514e75 q^{81} -3.64507e74 q^{82} +5.44189e75 q^{83} -3.60113e75 q^{84} -1.55230e75 q^{85} +2.18797e76 q^{86} +3.10627e76 q^{87} +5.36947e76 q^{88} +1.18618e76 q^{89} -4.11420e77 q^{90} -2.54327e77 q^{91} -1.00712e77 q^{92} +6.34521e77 q^{93} -1.53000e77 q^{94} +1.33365e78 q^{95} +1.16109e78 q^{96} -2.81055e78 q^{97} -2.12694e78 q^{98} +1.16077e79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3} + 15\!\cdots\!88 q^{4} + 60\!\cdots\!40 q^{5} - 22\!\cdots\!28 q^{6} - 20\!\cdots\!00 q^{7} + 54\!\cdots\!60 q^{8} + 98\!\cdots\!22 q^{9} + 27\!\cdots\!40 q^{10}+ \cdots + 12\!\cdots\!24 q^{99}+O(q^{100}) \) 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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