LMFDB - Embedded newform 1.100.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,100,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, 100, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 100);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 100 $
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:	$62.0676682981$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + \cdots + 23\!\cdots\!00 $ x^8 - x^7 - 765795356833478153590815019x^6 - 847018239936508469063593510315947812341x^5 + 166266085475297433798436838383182406675010433940631891x^4 + 383003540937606521762330014068972951053203782113187882011683494365x^3 - 11669647006531450010063357990045396397379108481887224639799570451704082949635225x^2 - 23238142613948580473684129972228711535824919000337506052734804657134844164338957751998110375x + 236649725056018508613975268945421267815761184396120868241489878887556709696071978474081515546520542830000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{109}\cdot 3^{44}\cdot 5^{13}\cdot 7^{9}\cdot 11^{3}\cdot 13\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$8.50040e12$ 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)

$f(q)$	$=$	$q+5.86024e14 q^{2} -4.40976e23 q^{3} -2.90401e29 q^{4} +2.74639e34 q^{5} -2.58422e38 q^{6} +3.47138e41 q^{7} -5.41619e44 q^{8} +2.26671e46 q^{9} +O(q^{10})$	\(q+5.86024e14 q^{2} -4.40976e23 q^{3} -2.90401e29 q^{4} +2.74639e34 q^{5} -2.58422e38 q^{6} +3.47138e41 q^{7} -5.41619e44 q^{8} +2.26671e46 q^{9} +1.60945e49 q^{10} -4.95910e51 q^{11} +1.28060e53 q^{12} +1.21492e55 q^{13} +2.03431e56 q^{14} -1.21109e58 q^{15} -1.33338e59 q^{16} -3.97916e60 q^{17} +1.32834e61 q^{18} -4.47251e62 q^{19} -7.97554e63 q^{20} -1.53079e65 q^{21} -2.90615e66 q^{22} -4.53817e67 q^{23} +2.38841e68 q^{24} -8.23457e68 q^{25} +7.11971e69 q^{26} +6.57607e70 q^{27} -1.00809e71 q^{28} -5.62741e71 q^{29} -7.09728e72 q^{30} +7.11109e73 q^{31} +2.65152e74 q^{32} +2.18684e75 q^{33} -2.33189e75 q^{34} +9.53375e75 q^{35} -6.58255e75 q^{36} +3.44683e77 q^{37} -2.62100e77 q^{38} -5.35749e78 q^{39} -1.48750e79 q^{40} +2.52241e78 q^{41} -8.97081e79 q^{42} +8.67636e80 q^{43} +1.44013e81 q^{44} +6.22526e80 q^{45} -2.65948e82 q^{46} +3.44728e82 q^{47} +5.87988e82 q^{48} -3.41563e83 q^{49} -4.82566e83 q^{50} +1.75471e84 q^{51} -3.52813e84 q^{52} +2.95920e85 q^{53} +3.85373e85 q^{54} -1.36196e86 q^{55} -1.88016e86 q^{56} +1.97227e86 q^{57} -3.29780e86 q^{58} +7.60447e87 q^{59} +3.51702e87 q^{60} +8.96058e87 q^{61} +4.16727e88 q^{62} +7.86860e87 q^{63} +2.39899e89 q^{64} +3.33663e89 q^{65} +1.28154e90 q^{66} +2.62496e90 q^{67} +1.15555e90 q^{68} +2.00122e91 q^{69} +5.58700e90 q^{70} +6.35730e91 q^{71} -1.22769e91 q^{72} -3.15102e92 q^{73} +2.01993e92 q^{74} +3.63125e92 q^{75} +1.29882e92 q^{76} -1.72149e93 q^{77} -3.13962e93 q^{78} -1.44064e94 q^{79} -3.66198e93 q^{80} -3.28929e94 q^{81} +1.47819e93 q^{82} +6.97978e94 q^{83} +4.44544e94 q^{84} -1.09283e95 q^{85} +5.08455e95 q^{86} +2.48155e95 q^{87} +2.68594e96 q^{88} -1.17382e96 q^{89} +3.64815e95 q^{90} +4.21744e96 q^{91} +1.31789e97 q^{92} -3.13582e97 q^{93} +2.02019e97 q^{94} -1.22833e97 q^{95} -1.16926e98 q^{96} -3.50742e98 q^{97} -2.00164e98 q^{98} -1.12408e98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots + 15\!\cdots\!76 q^{9}+O(q^{10}) $ 8 * q - 208040616902520 * q^2 - 282956306495420632223520 * q^3 + 2874573971021731526732655093824 * q^4 - 48829879146635109942685521105004560 * q^5 - 77942153094234171155671704171199405344 * q^6 - 56830940560713017104682273454607970657600 * q^7 + 592603013041539183163433278232078795937538560 * q^8 + 15585042525631880727258151421002821416820695976 * q^9	$ 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots - 13\!\cdots\!08 q^{99}+O(q^{100}) $ 8 * q - 208040616902520 * q^2 - 282956306495420632223520 * q^3 + 2874573971021731526732655093824 * q^4 - 48829879146635109942685521105004560 * q^5 - 77942153094234171155671704171199405344 * q^6 - 56830940560713017104682273454607970657600 * q^7 + 592603013041539183163433278232078795937538560 * q^8 + 15585042525631880727258151421002821416820695976 * q^9 - 20961738819400631174675750189416259674325116377360 * q^10 + 668605620058921294359176615672652323197376366725536 * q^11 - 260751428362765138428103958747533086169389679507011840 * q^12 - 5313129021153651674083973849295770678848247690376073040 * q^13 - 275891262636795191856274681125121829106120036919920873792 * q^14 + 39601076201132911228470767893146157937452742673766616546880 * q^15 + 1686978001168411473373901309719868789822314791151035737182208 * q^16 + 29870581004484716934093126001838988402381517134653878061066640 * q^17 + 104619592562318909205389831941745992324800916717508145002954280 * q^18 - 2584541347057387315132230533073883085094549482599567538462153120 * q^19 - 87020910945991395973478129409062640628123700866757624264022986880 * q^20 + 720725986617461186277876616197863336884455731162862159407836416 * q^21 + 6448630494375222037284713151002631218361976067562272720681828806560 * q^22 - 591705231800483702926418342143069697446663268741979110571049882560 * q^23 - 786094952626208255303024343193893163353569305701641632350239286773760 * q^24 + 716804381062067209680195080749365299641535704320602348503400092268600 * q^25 + 34654632463607194325743429354208471986051789816879940147342898057153456 * q^26 + 13869683363495491009982193176608883185849831807068440771218044677979840 * q^27 - 1135994339501291724748966539673012720374432727977564592829456188165859840 * q^28 - 439009994693767454184499584774890376667926937141064013921655743937571280 * q^29 + 23517293722912668382363618879896733566643340714874843272431473003480521280 * q^30 - 42796079732631926995692344425065773646038440365668203549397431930127162624 * q^31 - 284044778854068845159282113651411076631875258269403845301648101866131128320 * q^32 - 1184428676639946519273358190717309258531732537332484528437733831641965671040 * q^33 + 11470334814206853457708153296668381286712583035391282441563479133450208961168 * q^34 - 13317873075112713679215664096634074386516466958921311305188860496632195839360 * q^35 - 224326234591498863152148578877455893579609783196337897663675145770615318305472 * q^36 + 7013041648409278763731742859978750449729753703775477297667583228204170683120 * q^37 + 4097267709666535974097951231260487171744232792996835026005028682857459985875040 * q^38 + 3086772337289173445407063166797596998267422181270693039748051240117483908526912 * q^39 - 61154477845927513224255221208858320971333500267390856556166248662272460823577600 * q^40 + 16836611518887404247693904661111767446154336367366992887095255319045118001938896 * q^41 + 586782577486516292654880709693602500520055556295982039518980517393750164948778240 * q^42 - 115479509651193412125043402629710680178430977878852566804453976757651553792322400 * q^43 - 4823674089938931277708865059630293953738849935605913988972972769383583829463937792 * q^44 - 4204225762790416656941382640299001599040327829208847740401216426127468587838672720 * q^45 + 41220575732227465405339930795314328162570779910219577393801310430729179103724398656 * q^46 + 28878226575287510694522520507929237505491250714878620920990009419290436045018975360 * q^47 - 270645616492149970234041108687889002599221246648694105429287982543953957103033794560 * q^48 - 14382803175556111227730750647629461517090856222687609645964147941666232976982659256 * q^49 + 2538900041031429584911497444199766832786695308479217204477072876574482801521012636600 * q^50 - 1711868817156841452117007804086601271536721152787522351736690290031659132307369497664 * q^51 - 199691168563235615231272208715487263769590246824861808533841002609282642680495606400 * q^52 - 30091820242734525213832735040802634061423162425240717202059443809754039115425881976720 * q^53 + 136432908322968282680263912195201284966825652472631606906205576348979246713807692108480 * q^54 + 226099583633880167546966079422139027647924161654010953637858494806538127768993139084480 * q^55 + 323037227302956226932352973051969540564093713359973342312103259763994205180305378488320 * q^56 - 273423384330404631781757518792671605280054294102341216713398337934356290096852147342720 * q^57 + 5713973478801321937231450378714667908258440100056694714036585358012358074567853731219760 * q^58 + 14607245332654695346837714400351649175544087130678579822473040904252509022932739720811040 * q^59 + 53008257791762983739773607116394245193846456713938833829846630209166818928009302295114240 * q^60 + 38323682921378832161349805479389921828014992489778724538462200957929376165086831637164336 * q^61 + 201697385927609334439920541372343666252345396922224455072723131310512431934088015943381760 * q^62 + 659857333915856699600072965534847901170546674796116288100652182111732663513752207410870720 * q^63 + 2567569508313686836352267062189989701299823975229681223291764819542997452948800142018084864 * q^64 + 2649617703605055039617798586548537725956903247199823944158672914229112797191302156162117280 * q^65 + 7971156345834212651621212324655177899942634890685144307138793590710555397223588657590125952 * q^66 + 11538024122310165476577023936338470394129524138300592332780359783942082451772953721242543840 * q^67 + 56045208748154976002290739488865109707859265886693431912946708486067523902076046154608254080 * q^68 + 54550768708090409722131753417710688638608175085564682877064185400954540597503860451967981312 * q^69 + 143889269423962258520958611175254488367329101991613194841590826662727327088381209016536883840 * q^70 + 52677154721705052088453955375369863850612862186345822027042426779160256515633503076296638656 * q^71 + 365038759307175377119135471724071125896012767600977654405238165616233444129512164397555141120 * q^72 + 506688790556979736999516532365405438114465768501506115275379047447697188620686370699300754640 * q^73 - 399134575097952393052355140371514479012153174980660646654807435656154590439317636650100727312 * q^74 - 2324004895287993423141911565246677610480036000604538705092119528699965986086154360593593272800 * q^75 - 6633935918720327036715040118664821987731317587536782451991725427750234686044104260504536239360 * q^76 - 6461585481973245548189356793856436395182994379442713381123224045549509062132894968864516460800 * q^77 - 28556176219359102115465270938556084350909705495286117230117205751412922131522017940137826091200 * q^78 - 30611582035787076807516826687485094690084083072098723290730859803828786802497884290624307556480 * q^79 - 127732467855339073698199167907855646502900419187610712488908375947950612344972404753625834332160 * q^80 - 105098591020590401711840147132548556253048052082258241572206720930835350937368467193794679663032 * q^81 - 68830371209738349493630432122952083611773652840970378016560437888326646942049769865516365685040 * q^82 + 22938542661502254568160041367746263129225779762371870743525183586562110235427022830971680103520 * q^83 + 361795660381091268015394970465025503071664436510904020432798379164529165144740663778138523854848 * q^84 - 65747002822668948096103688317539312015762969670721483634214688263171509401935169398146161091360 * q^85 + 2926007787385729535219437868096352598169987790407590983846487590337872781868895638215544350378656 * q^86 + 4145530857628120059159343787991300967686349677839106320836691853415365479077514876503669002112320 * q^87 + 13379567436970727806886279611606134975535418870618956336086465570267315661188646758052286051051520 * q^88 + 13262749235321210784149676214189766161707478948372569815117556700615668825668004121877579168519760 * q^89 + 18562789747759155399933926620841126049267839227249440162668332587565567838001478928890860138613680 * q^90 - 6466499581384229905399040912443724309264614193875257390824803270602537852945701184143169943974784 * q^91 - 3605940592933441273788896348672120936868261799818064643016984038777885904937799268971010435816960 * q^92 - 6218230725998946523812046145774116878209214952116357458146814759754757343477151669356631201623040 * q^93 - 111501057917354496628976353847689989005658650697758014190949880350502870630016419857891186452986752 * q^94 - 310841228909329722722502224651860795134807193058850708412373586195233672473563873013656113819102400 * q^95 - 967769551108604066125272773812882212494392412979843145463542262778370585211900025491604732868952064 * q^96 - 870148289336425543686683480565613230312583210673688585087479722135977346731183581578056793848665840 * q^97 - 1259902767579045380431363502561233259244081818944281851461225234703715688976807437199140410707221560 * q^98 - 137018494226539733211453518241879004188470623376815926515879377141376994388427950391858832640432608 * 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 $

$2$	5.86024e14	0.736089	0.368045	−	0.929808i	$-0.380027\pi$
$2$	5.86024e14	0.736089	0.368045	+	0.929808i	$0.380027\pi$
$3$	−4.40976e23	−1.06393	−0.531964	−	0.846767i	$-0.678546\pi$
$3$	−4.40976e23	−1.06393	−0.531964	+	0.846767i	$0.678546\pi$
$4$	−2.90401e29	−0.458172
$5$	2.74639e34	0.691427	0.345714	−	0.938340i	$-0.387637\pi$
$5$	2.74639e34	0.691427	0.345714	+	0.938340i	$0.387637\pi$
$6$	−2.58422e38	−0.783147
$7$	3.47138e41	0.510680	0.255340	−	0.966851i	$-0.417813\pi$
$7$	3.47138e41	0.510680	0.255340	+	0.966851i	$0.417813\pi$
$8$	−5.41619e44	−1.07335
$9$	2.26671e46	0.131944
$10$	1.60945e49	0.508952
$11$	−4.95910e51	−1.40109	−0.700543	−	0.713611i	$-0.747059\pi$
$11$	−4.95910e51	−1.40109	−0.700543	+	0.713611i	$0.747059\pi$
$12$	1.28060e53	0.487463
$13$	1.21492e55	0.879733	0.439866	−	0.898063i	$-0.355026\pi$
$13$	1.21492e55	0.879733	0.439866	+	0.898063i	$0.355026\pi$
$14$	2.03431e56	0.375906
$15$	−1.21109e58	−0.735630
$16$	−1.33338e59	−0.331906
$17$	−3.97916e60	−0.492686	−0.246343	−	0.969183i	$-0.579229\pi$
$17$	−3.97916e60	−0.492686	−0.246343	+	0.969183i	$0.579229\pi$
$18$	1.32834e61	0.0971229
$19$	−4.47251e62	−0.225034	−0.112517	−	0.993650i	$-0.535891\pi$
$19$	−4.47251e62	−0.225034	−0.112517	+	0.993650i	$0.535891\pi$
$20$	−7.97554e63	−0.316793
$21$	−1.53079e65	−0.543327
$22$	−2.90615e66	−1.03132
$23$	−4.53817e67	−1.78383	−0.891914	−	0.452205i	$-0.850637\pi$
$23$	−4.53817e67	−1.78383	−0.891914	+	0.452205i	$0.850637\pi$
$24$	2.38841e68	1.14196
$25$	−8.23457e68	−0.521928
$26$	7.11971e69	0.647562
$27$	6.57607e70	0.923549
$28$	−1.00809e71	−0.233979
$29$	−5.62741e71	−0.229936	−0.114968	−	0.993369i	$-0.536677\pi$
$29$	−5.62741e71	−0.229936	−0.114968	+	0.993369i	$0.536677\pi$
$30$	−7.09728e72	−0.541489
$31$	7.11109e73	1.07037	0.535183	−	0.844736i	$-0.320243\pi$
$31$	7.11109e73	1.07037	0.535183	+	0.844736i	$0.320243\pi$
$32$	2.65152e74	0.829033
$33$	2.18684e75	1.49065
$34$	−2.33189e75	−0.362661
$35$	9.53375e75	0.353098
$36$	−6.58255e75	−0.0604533
$37$	3.44683e77	0.815520	0.407760	−	0.913089i	$-0.366310\pi$
$37$	3.44683e77	0.815520	0.407760	+	0.913089i	$0.366310\pi$
$38$	−2.62100e77	−0.165645
$39$	−5.35749e78	−0.935973
$40$	−1.48750e79	−0.742140
$41$	2.52241e78	0.0370693	0.0185346	−	0.999828i	$-0.494100\pi$
$41$	2.52241e78	0.0370693	0.0185346	+	0.999828i	$0.494100\pi$
$42$	−8.97081e79	−0.399937
$43$	8.67636e80	1.20684	0.603419	−	0.797425i	$-0.293805\pi$
$43$	8.67636e80	1.20684	0.603419	+	0.797425i	$0.293805\pi$
$44$	1.44013e81	0.641939
$45$	6.22526e80	0.0912300
$46$	−2.65948e82	−1.31306
$47$	3.44728e82	0.586992	0.293496	−	0.955960i	$-0.405181\pi$
$47$	3.44728e82	0.586992	0.293496	+	0.955960i	$0.405181\pi$
$48$	5.87988e82	0.353124
$49$	−3.41563e83	−0.739206
$50$	−4.82566e83	−0.384186
$51$	1.75471e84	0.524183
$52$	−3.52813e84	−0.403069
$53$	2.95920e85	1.31680	0.658399	−	0.752669i	$-0.271234\pi$
$53$	2.95920e85	1.31680	0.658399	+	0.752669i	$0.271234\pi$
$54$	3.85373e85	0.679815
$55$	−1.36196e86	−0.968749
$56$	−1.88016e86	−0.548136
$57$	1.97227e86	0.239420
$58$	−3.29780e86	−0.169254
$59$	7.60447e87	1.67454	0.837268	−	0.546792i	$-0.184151\pi$
$59$	7.60447e87	1.67454	0.837268	+	0.546792i	$0.184151\pi$
$60$	3.51702e87	0.337045
$61$	8.96058e87	0.378887	0.189443	−	0.981892i	$-0.439332\pi$
$61$	8.96058e87	0.378887	0.189443	+	0.981892i	$0.439332\pi$
$62$	4.16727e88	0.787885
$63$	7.86860e87	0.0673814
$64$	2.39899e89	0.942148
$65$	3.33663e89	0.608271
$66$	1.28154e90	1.09726
$67$	2.62496e90	1.06763	0.533813	−	0.845602i	$-0.320759\pi$
$67$	2.62496e90	1.06763	0.533813	+	0.845602i	$0.320759\pi$
$68$	1.15555e90	0.225735
$69$	2.00122e91	1.89787
$70$	5.58700e90	0.259912
$71$	6.35730e91	1.46550	0.732748	−	0.680501i	$-0.238238\pi$
$71$	6.35730e91	1.46550	0.732748	+	0.680501i	$0.238238\pi$
$72$	−1.22769e91	−0.141622
$73$	−3.15102e92	−1.83641	−0.918205	−	0.396105i	$-0.870362\pi$
$73$	−3.15102e92	−1.83641	−0.918205	+	0.396105i	$0.870362\pi$
$74$	2.01993e92	0.600296
$75$	3.63125e92	0.555294
$76$	1.29882e92	0.103104
$77$	−1.72149e93	−0.715506
$78$	−3.13962e93	−0.688960
$79$	−1.44064e94	−1.68273	−0.841365	−	0.540468i	$-0.818247\pi$
$79$	−1.44064e94	−1.68273	−0.841365	+	0.540468i	$0.818247\pi$
$80$	−3.66198e93	−0.229489
$81$	−3.28929e94	−1.11454
$82$	1.47819e93	0.0272863
$83$	6.97978e94	0.707093	0.353546	−	0.935417i	$-0.384976\pi$
$83$	6.97978e94	0.707093	0.353546	+	0.935417i	$0.384976\pi$
$84$	4.44544e94	0.248937
$85$	−1.09283e95	−0.340657
$86$	5.08455e95	0.888340
$87$	2.48155e95	0.244636
$88$	2.68594e96	1.50385
$89$	−1.17382e96	−0.375660	−0.187830	−	0.982202i	$-0.560145\pi$
$89$	−1.17382e96	−0.375660	−0.187830	+	0.982202i	$0.560145\pi$
$90$	3.64815e95	0.0671535
$91$	4.21744e96	0.449262
$92$	1.31789e97	0.817301
$93$	−3.13582e97	−1.13879
$94$	2.02019e97	0.432079
$95$	−1.22833e97	−0.155595
$96$	−1.16926e98	−0.882032
$97$	−3.50742e98	−1.58412	−0.792059	−	0.610445i	$-0.790991\pi$
$97$	−3.50742e98	−1.58412	−0.792059	+	0.610445i	$0.790991\pi$
$98$	−2.00164e98	−0.544122
$99$	−1.12408e98	−0.184865
$100$	2.39133e98	0.239133
$101$	1.73608e99	1.06087	0.530433	−	0.847727i	$-0.322029\pi$
$101$	1.73608e99	1.06087	0.530433	+	0.847727i	$0.322029\pi$
$102$	1.02830e99	0.385845
$103$	4.78555e99	1.10787	0.553935	−	0.832560i	$-0.313125\pi$
$103$	4.78555e99	1.10787	0.553935	+	0.832560i	$0.313125\pi$
$104$	−6.58022e99	−0.944257
$105$	−4.20415e99	−0.375671
$106$	1.73416e100	0.969281
$107$	3.65346e100	1.28294	0.641472	−	0.767147i	$-0.278324\pi$
$107$	3.65346e100	1.28294	0.641472	+	0.767147i	$0.278324\pi$
$108$	−1.90970e100	−0.423145
$109$	3.21241e100	0.451045	0.225523	−	0.974238i	$-0.427591\pi$
$109$	3.21241e100	0.451045	0.225523	+	0.974238i	$0.427591\pi$
$110$	−7.98141e100	−0.713086
$111$	−1.51997e101	−0.867656
$112$	−4.62866e100	−0.169498
$113$	−2.90167e101	−0.684328	−0.342164	−	0.939640i	$-0.611160\pi$
$113$	−2.90167e101	−0.684328	−0.342164	+	0.939640i	$0.611160\pi$
$114$	1.15580e101	0.176235
$115$	−1.24636e102	−1.23339
$116$	1.63421e101	0.105350
$117$	2.75386e101	0.116076
$118$	4.45640e102	1.23261
$119$	−1.38132e102	−0.251605
$120$	6.55949e102	0.789584
$121$	1.20648e103	0.963040
$122$	5.25111e102	0.278894
$123$	−1.11232e102	−0.0394391
$124$	−2.06507e103	−0.490412
$125$	−6.59457e103	−1.05230
$126$	4.61119e102	0.0495987
$127$	1.08452e104	0.788778	0.394389	−	0.918944i	$-0.370956\pi$
$127$	1.08452e104	0.788778	0.394389	+	0.918944i	$0.370956\pi$
$128$	−2.74740e103	−0.135528
$129$	−3.82606e104	−1.28399
$130$	1.95535e104	0.447742
$131$	−4.99285e104	−0.782383	−0.391191	−	0.920309i	$-0.627937\pi$
$131$	−4.99285e104	−0.782383	−0.391191	+	0.920309i	$0.627937\pi$
$132$	−6.35061e104	−0.682977
$133$	−1.55258e104	−0.114920
$134$	1.53829e105	0.785869
$135$	1.80604e105	0.638567
$136$	2.15519e105	0.528822
$137$	6.93572e105	1.18420	0.592098	−	0.805866i	$-0.298300\pi$
$137$	6.93572e105	1.18420	0.592098	+	0.805866i	$0.298300\pi$
$138$	1.17276e106	1.39700
$139$	−2.29477e106	−1.91208	−0.956041	−	0.293233i	$-0.905269\pi$
$139$	−2.29477e106	−1.91208	−0.956041	+	0.293233i	$0.905269\pi$
$140$	−2.76861e105	−0.161780
$141$	−1.52017e106	−0.624518
$142$	3.72553e106	1.07874
$143$	−6.02489e106	−1.23258
$144$	−3.02238e105	−0.0437931
$145$	−1.54550e106	−0.158984
$146$	−1.84657e107	−1.35176
$147$	1.50621e107	0.786463
$148$	−1.00096e107	−0.373649
$149$	2.14718e107	0.574313	0.287157	−	0.957884i	$-0.407290\pi$
$149$	2.14718e107	0.574313	0.287157	+	0.957884i	$0.407290\pi$
$150$	2.12800e107	0.408746
$151$	3.79732e107	0.524950	0.262475	−	0.964939i	$-0.415461\pi$
$151$	3.79732e107	0.524950	0.262475	+	0.964939i	$0.415461\pi$
$152$	2.42240e107	0.241539
$153$	−9.01960e106	−0.0650072
$154$	−1.00883e108	−0.526677
$155$	1.95298e108	0.740080
$156$	1.55582e108	0.428837
$157$	6.42622e108	1.29099	0.645495	−	0.763765i	$-0.276651\pi$
$157$	6.42622e108	1.29099	0.645495	+	0.763765i	$0.276651\pi$
$158$	−8.44249e108	−1.23864
$159$	−1.30494e109	−1.40098
$160$	7.28211e108	0.573216
$161$	−1.57537e109	−0.910965
$162$	−1.92760e109	−0.820398
$163$	−1.44977e109	−0.455001	−0.227500	−	0.973778i	$-0.573055\pi$
$163$	−1.44977e109	−0.455001	−0.227500	+	0.973778i	$0.573055\pi$
$164$	−7.32510e107	−0.0169841
$165$	6.00591e109	1.03068
$166$	4.09032e109	0.520483
$167$	1.01965e110	0.963802	0.481901	−	0.876226i	$-0.339947\pi$
$167$	1.01965e110	0.963802	0.481901	+	0.876226i	$0.339947\pi$
$168$	8.29106e109	0.583178
$169$	−4.31157e109	−0.226070
$170$	−6.40426e109	−0.250754
$171$	−1.01379e109	−0.0296920
$172$	−2.51962e110	−0.552940
$173$	2.83264e110	0.466563	0.233281	−	0.972409i	$-0.425054\pi$
$173$	2.83264e110	0.466563	0.233281	+	0.972409i	$0.425054\pi$
$174$	1.45425e110	0.180074
$175$	−2.85853e110	−0.266538
$176$	6.61236e110	0.465028
$177$	−3.35339e111	−1.78159
$178$	−6.87884e110	−0.276519
$179$	9.74438e110	0.296845	0.148422	−	0.988924i	$-0.452581\pi$
$179$	9.74438e110	0.296845	0.148422	+	0.988924i	$0.452581\pi$
$180$	−1.80782e110	−0.0417991
$181$	−2.50040e111	−0.439461	−0.219731	−	0.975561i	$-0.570518\pi$
$181$	−2.50040e111	−0.439461	−0.219731	+	0.975561i	$0.570518\pi$
$182$	2.47152e111	0.330697
$183$	−3.95140e111	−0.403108
$184$	2.45796e112	1.91466
$185$	9.46634e111	0.563873
$186$	−1.83766e112	−0.838253
$187$	1.97331e112	0.690295
$188$	−1.00109e112	−0.268944
$189$	2.28280e112	0.471638
$190$	−7.19828e111	−0.114532
$191$	4.15309e112	0.509589	0.254794	−	0.966995i	$-0.417992\pi$
$191$	4.15309e112	0.509589	0.254794	+	0.966995i	$0.417992\pi$
$192$	−1.05790e113	−1.00238
$193$	−1.18499e113	−0.868218	−0.434109	−	0.900860i	$-0.642937\pi$
$193$	−1.18499e113	−0.868218	−0.434109	+	0.900860i	$0.642937\pi$
$194$	−2.05543e113	−1.16605
$195$	−1.47137e113	−0.647157
$196$	9.91905e112	0.338684
$197$	3.77075e113	1.00080	0.500402	−	0.865793i	$-0.333185\pi$
$197$	3.77075e113	1.00080	0.500402	+	0.865793i	$0.333185\pi$
$198$	−6.58739e112	−0.136078
$199$	7.97917e113	1.28449	0.642244	−	0.766500i	$-0.278003\pi$
$199$	7.97917e113	1.28449	0.642244	+	0.766500i	$0.278003\pi$
$200$	4.46000e113	0.560209
$201$	−1.15754e114	−1.13588
$202$	1.01738e114	0.780892
$203$	−1.95349e113	−0.117424
$204$	−5.09571e113	−0.240166
$205$	6.92751e112	0.0256307
$206$	2.80445e114	0.815492
$207$	−1.02867e114	−0.235366
$208$	−1.61995e114	−0.291988
$209$	2.21796e114	0.315292
$210$	−2.46373e114	−0.276528
$211$	−7.80452e114	−0.692412	−0.346206	−	0.938158i	$-0.612530\pi$
$211$	−7.80452e114	−0.692412	−0.346206	+	0.938158i	$0.612530\pi$
$212$	−8.59356e114	−0.603321
$213$	−2.80341e115	−1.55918
$214$	2.14102e115	0.944361
$215$	2.38286e115	0.834440
$216$	−3.56172e115	−0.991287
$217$	2.46853e115	0.546614
$218$	1.88255e115	0.332010
$219$	1.38952e116	1.95381
$220$	3.95515e115	0.443854
$221$	−4.83435e115	−0.433432
$222$	−8.90738e115	−0.638672
$223$	−4.52991e115	−0.260015	−0.130008	−	0.991513i	$-0.541500\pi$
$223$	−4.52991e115	−0.260015	−0.130008	+	0.991513i	$0.541500\pi$
$224$	9.20444e115	0.423371
$225$	−1.86654e115	−0.0688655
$226$	−1.70045e116	−0.503727
$227$	−8.61274e115	−0.205051	−0.102525	−	0.994730i	$-0.532692\pi$
$227$	−8.61274e115	−0.205051	−0.102525	+	0.994730i	$0.532692\pi$
$228$	−5.72749e115	−0.109696
$229$	−7.05746e116	−1.08841	−0.544204	−	0.838953i	$-0.683168\pi$
$229$	−7.05746e116	−1.08841	−0.544204	+	0.838953i	$0.683168\pi$
$230$	−7.30395e116	−0.907883
$231$	7.59135e116	0.761248
$232$	3.04791e116	0.246801
$233$	1.12126e117	0.733818	0.366909	−	0.930257i	$-0.380416\pi$
$233$	1.12126e117	0.733818	0.366909	+	0.930257i	$0.380416\pi$
$234$	1.61383e116	0.0854422
$235$	9.46756e116	0.405862
$236$	−2.20835e117	−0.767226
$237$	6.35287e117	1.79030
$238$	−8.09485e116	−0.185204
$239$	−5.10013e117	−0.948168	−0.474084	−	0.880480i	$-0.657221\pi$
$239$	−5.10013e117	−0.948168	−0.474084	+	0.880480i	$0.657221\pi$
$240$	1.61484e117	0.244160
$241$	−2.12044e117	−0.260965	−0.130482	−	0.991451i	$-0.541653\pi$
$241$	−2.12044e117	−0.260965	−0.130482	+	0.991451i	$0.541653\pi$
$242$	7.07026e117	0.708883
$243$	3.20778e117	0.262237
$244$	−2.60216e117	−0.173595
$245$	−9.38066e117	−0.511107
$246$	−6.51846e116	−0.0290307
$247$	−5.43373e117	−0.197970
$248$	−3.85150e118	−1.14887
$249$	−3.07791e118	−0.752296
$250$	−3.86458e118	−0.774589
$251$	3.91161e118	0.643438	0.321719	−	0.946835i	$-0.395739\pi$
$251$	3.91161e118	0.643438	0.321719	+	0.946835i	$0.395739\pi$
$252$	−2.28505e117	−0.0308723
$253$	2.25052e119	2.49929
$254$	6.35557e118	0.580611
$255$	4.81913e118	0.362434
$256$	−1.68154e119	−1.04191
$257$	2.03371e119	1.03896	0.519482	−	0.854482i	$-0.326125\pi$
$257$	2.03371e119	1.03896	0.519482	+	0.854482i	$0.326125\pi$
$258$	−2.24216e119	−0.945131
$259$	1.19653e119	0.416470
$260$	−9.68962e118	−0.278693
$261$	−1.27557e118	−0.0303388
$262$	−2.92593e119	−0.575904
$263$	1.73244e118	0.0282390	0.0141195	−	0.999900i	$-0.495505\pi$
$263$	1.73244e118	0.0282390	0.0141195	+	0.999900i	$0.495505\pi$
$264$	−1.18443e120	−1.59999
$265$	8.12712e119	0.910470
$266$	−9.09848e118	−0.0845917
$267$	5.17624e119	0.399675
$268$	−7.62290e119	−0.489157
$269$	−1.30868e120	−0.698385	−0.349192	−	0.937051i	$-0.613544\pi$
$269$	−1.30868e120	−0.698385	−0.349192	+	0.937051i	$0.613544\pi$
$270$	1.05838e120	0.470043
$271$	2.20037e120	0.813795	0.406898	−	0.913474i	$-0.366611\pi$
$271$	2.20037e120	0.813795	0.406898	+	0.913474i	$0.366611\pi$
$272$	5.30574e119	0.163525
$273$	−1.85979e120	−0.477983
$274$	4.06450e120	0.871674
$275$	4.08360e120	0.731266
$276$	−5.81158e120	−0.869550
$277$	1.31707e121	1.64763	0.823815	−	0.566859i	$-0.191842\pi$
$277$	1.31707e121	1.64763	0.823815	+	0.566859i	$0.191842\pi$
$278$	−1.34479e121	−1.40746
$279$	1.61188e120	0.141229
$280$	−5.16366e120	−0.378996
$281$	5.75758e120	0.354223	0.177112	−	0.984191i	$-0.443325\pi$
$281$	5.75758e120	0.354223	0.177112	+	0.984191i	$0.443325\pi$
$282$	−8.90854e120	−0.459701
$283$	−1.56708e119	−0.00678678	−0.00339339	−	0.999994i	$-0.501080\pi$
$283$	−1.56708e119	−0.00678678	−0.00339339	+	0.999994i	$0.501080\pi$
$284$	−1.84617e121	−0.671449
$285$	5.41662e120	0.165542
$286$	−3.53073e121	−0.907289
$287$	8.75623e119	0.0189305
$288$	6.01023e120	0.109386
$289$	−4.93956e121	−0.757261
$290$	−9.05703e120	−0.117027
$291$	1.54669e122	1.68539
$292$	9.15060e121	0.841392
$293$	5.55330e121	0.431125	0.215563	−	0.976490i	$-0.430841\pi$
$293$	5.55330e121	0.431125	0.215563	+	0.976490i	$0.430841\pi$
$294$	8.82676e121	0.578907
$295$	2.08848e122	1.15782
$296$	−1.86687e122	−0.875335
$297$	−3.26114e122	−1.29397
$298$	1.25830e122	0.422746
$299$	−5.51350e122	−1.56929
$300$	−1.05452e122	−0.254421
$301$	3.01189e122	0.616308
$302$	2.22532e122	0.386410
$303$	−7.65567e122	−1.12869
$304$	5.96356e121	0.0746901
$305$	2.46092e122	0.261973
$306$	−5.28570e121	−0.0478511
$307$	8.42818e122	0.649209	0.324604	−	0.945850i	$-0.394769\pi$
$307$	8.42818e122	0.649209	0.324604	+	0.945850i	$0.394769\pi$
$308$	4.99923e122	0.327825
$309$	−2.11031e123	−1.17870
$310$	1.14449e123	0.544765
$311$	−3.17716e123	−1.28943	−0.644717	−	0.764421i	$-0.723025\pi$
$311$	−3.17716e123	−1.28943	−0.644717	+	0.764421i	$0.723025\pi$
$312$	2.90172e123	1.00462
$313$	3.30714e123	0.977256	0.488628	−	0.872492i	$-0.337498\pi$
$313$	3.30714e123	0.977256	0.488628	+	0.872492i	$0.337498\pi$
$314$	3.76592e123	0.950284
$315$	2.16102e122	0.0465893
$316$	4.18363e123	0.770980
$317$	−5.69941e123	−0.898249	−0.449125	−	0.893469i	$-0.648264\pi$
$317$	−5.69941e123	−0.898249	−0.449125	+	0.893469i	$0.648264\pi$
$318$	−7.64724e123	−1.03125
$319$	2.79069e123	0.322160
$320$	6.58855e123	0.651427
$321$	−1.61109e124	−1.36496
$322$	−9.23205e123	−0.670552
$323$	1.77969e123	0.110871
$324$	9.55214e123	0.510649
$325$	−1.00043e124	−0.459157
$326$	−8.49599e123	−0.334921
$327$	−1.41660e124	−0.479880
$328$	−1.36618e123	−0.0397881
$329$	1.19668e124	0.299765
$330$	3.51961e124	0.758672
$331$	6.54340e124	1.21428	0.607139	−	0.794596i	$-0.292317\pi$
$331$	6.54340e124	1.21428	0.607139	+	0.794596i	$0.292317\pi$
$332$	−2.02694e124	−0.323970
$333$	7.81296e123	0.107603
$334$	5.97542e124	0.709444
$335$	7.20915e124	0.738186
$336$	2.04113e124	0.180333
$337$	−2.31249e125	−1.76360	−0.881798	−	0.471627i	$-0.843667\pi$
$337$	−2.31249e125	−1.76360	−0.881798	+	0.471627i	$0.843667\pi$
$338$	−2.52668e124	−0.166408
$339$	1.27956e125	0.728077
$340$	3.17360e124	0.156079
$341$	−3.52646e125	−1.49967
$342$	−5.94104e123	−0.0218560
$343$	−2.78971e125	−0.888178
$344$	−4.69928e125	−1.29535
$345$	5.49613e125	1.31224
$346$	1.66000e125	0.343432
$347$	9.66068e125	1.73260	0.866301	−	0.499523i	$-0.166491\pi$
$347$	9.66068e125	1.73260	0.866301	+	0.499523i	$0.166491\pi$
$348$	−7.20646e124	−0.112085
$349$	−7.11768e125	−0.960462	−0.480231	−	0.877142i	$-0.659447\pi$
$349$	−7.11768e125	−0.960462	−0.480231	+	0.877142i	$0.659447\pi$
$350$	−1.67517e125	−0.196196
$351$	7.98938e125	0.812476
$352$	−1.31492e126	−1.16155
$353$	1.98320e126	1.52237	0.761183	−	0.648537i	$-0.224619\pi$
$353$	1.98320e126	1.52237	0.761183	+	0.648537i	$0.224619\pi$
$354$	−1.96517e126	−1.31141
$355$	1.74596e126	1.01328
$356$	3.40878e125	0.172117
$357$	6.09128e125	0.267690
$358$	5.71044e125	0.218504
$359$	2.78440e126	0.928017	0.464009	−	0.885831i	$-0.346411\pi$
$359$	2.78440e126	0.928017	0.464009	+	0.885831i	$0.346411\pi$
$360$	−3.37172e125	−0.0979213
$361$	−3.75005e126	−0.949360
$362$	−1.46530e126	−0.323483
$363$	−5.32028e126	−1.02461
$364$	−1.22475e126	−0.205839
$365$	−8.65392e126	−1.26974
$366$	−2.31561e126	−0.296724
$367$	5.16692e126	0.578444	0.289222	−	0.957262i	$-0.406603\pi$
$367$	5.16692e126	0.578444	0.289222	+	0.957262i	$0.406603\pi$
$368$	6.05111e126	0.592063
$369$	5.71756e124	0.00489109
$370$	5.54750e126	0.415061
$371$	1.02725e127	0.672462
$372$	9.10645e126	0.521763
$373$	−1.15989e127	−0.581875	−0.290937	−	0.956742i	$-0.593967\pi$
$373$	−1.15989e127	−0.581875	−0.290937	+	0.956742i	$0.593967\pi$
$374$	1.15640e127	0.508119
$375$	2.90804e127	1.11958
$376$	−1.86711e127	−0.630045
$377$	−6.83684e126	−0.202283
$378$	1.33778e127	0.347168
$379$	−5.08000e126	−0.115671	−0.0578353	−	0.998326i	$-0.518420\pi$
$379$	−5.08000e126	−0.115671	−0.0578353	+	0.998326i	$0.518420\pi$
$380$	3.56707e126	0.0712892
$381$	−4.78249e127	−0.839204
$382$	2.43381e127	0.375103
$383$	−7.74698e127	−1.04904	−0.524521	−	0.851397i	$-0.675756\pi$
$383$	−7.74698e127	−1.04904	−0.524521	+	0.851397i	$0.675756\pi$
$384$	1.21154e127	0.144192
$385$	−4.72788e127	−0.494721
$386$	−6.94434e127	−0.639086
$387$	1.96668e127	0.159236
$388$	1.01856e128	0.725799
$389$	−1.01568e128	−0.637166	−0.318583	−	0.947895i	$-0.603207\pi$
$389$	−1.01568e128	−0.637166	−0.318583	+	0.947895i	$0.603207\pi$
$390$	−8.62261e127	−0.476366
$391$	1.80581e128	0.878867
$392$	1.84997e128	0.793423
$393$	2.20172e128	0.832400
$394$	2.20975e128	0.736682
$395$	−3.95655e128	−1.16349
$396$	3.26435e127	0.0847002
$397$	−5.30344e128	−1.21458	−0.607292	−	0.794479i	$-0.707744\pi$
$397$	−5.30344e128	−1.21458	−0.607292	+	0.794479i	$0.707744\pi$
$398$	4.67598e128	0.945499
$399$	6.84649e127	0.122267
$400$	1.09798e128	0.173231
$401$	6.20267e128	0.864833	0.432416	−	0.901674i	$-0.357661\pi$
$401$	6.20267e128	0.864833	0.432416	+	0.901674i	$0.357661\pi$
$402$	−6.78347e128	−0.836108
$403$	8.63938e128	0.941635
$404$	−5.04158e128	−0.486060
$405$	−9.03367e128	−0.770620
$406$	−1.14479e128	−0.0864345
$407$	−1.70932e129	−1.14261
$408$	−9.50387e128	−0.562629
$409$	2.12452e129	1.11418	0.557091	−	0.830452i	$-0.311917\pi$
$409$	2.12452e129	1.11418	0.557091	+	0.830452i	$0.311917\pi$
$410$	4.05968e127	0.0188665
$411$	−3.05849e129	−1.25990
$412$	−1.38973e129	−0.507596
$413$	2.63980e129	0.855152
$414$	−6.02826e128	−0.173251
$415$	1.91692e129	0.488903
$416$	3.22138e129	0.729327
$417$	1.01194e130	2.03432
$418$	1.29978e129	0.232083
$419$	−1.17297e129	−0.186078	−0.0930389	−	0.995662i	$-0.529658\pi$
$419$	−1.17297e129	−0.186078	−0.0930389	+	0.995662i	$0.529658\pi$
$420$	1.22089e129	0.172122
$421$	−2.90272e129	−0.363782	−0.181891	−	0.983319i	$-0.558222\pi$
$421$	−2.90272e129	−0.363782	−0.181891	+	0.983319i	$0.558222\pi$
$422$	−4.57364e129	−0.509677
$423$	7.81397e128	0.0774504
$424$	−1.60276e130	−1.41338
$425$	3.27667e129	0.257147
$426$	−1.64287e130	−1.14770
$427$	3.11056e129	0.193490
$428$	−1.06097e130	−0.587809
$429$	2.65683e130	1.31138
$430$	1.39641e130	0.614223
$431$	−1.14931e130	−0.450621	−0.225310	−	0.974287i	$-0.572340\pi$
$431$	−1.14931e130	−0.450621	−0.225310	+	0.974287i	$0.572340\pi$
$432$	−8.76840e129	−0.306531
$433$	−3.56146e130	−1.11039	−0.555197	−	0.831719i	$-0.687357\pi$
$433$	−3.56146e130	−1.11039	−0.555197	+	0.831719i	$0.687357\pi$
$434$	1.44662e130	0.402357
$435$	6.81530e129	0.169148
$436$	−9.32889e129	−0.206656
$437$	2.02970e130	0.401422
$438$	8.14294e130	1.43818
$439$	−4.79640e130	−0.756697	−0.378348	−	0.925663i	$-0.623508\pi$
$439$	−4.79640e130	−0.756697	−0.378348	+	0.925663i	$0.623508\pi$
$440$	7.37663e130	1.03980
$441$	−7.74224e129	−0.0975341
$442$	−2.83305e130	−0.319045
$443$	2.90550e130	0.292575	0.146287	−	0.989242i	$-0.453268\pi$
$443$	2.90550e130	0.292575	0.146287	+	0.989242i	$0.453268\pi$
$444$	4.41401e130	0.397536
$445$	−3.22375e130	−0.259741
$446$	−2.65464e130	−0.191395
$447$	−9.46856e130	−0.611028
$448$	8.32779e130	0.481136
$449$	−2.00616e131	−1.03794	−0.518969	−	0.854793i	$-0.673684\pi$
$449$	−2.00616e131	−1.03794	−0.518969	+	0.854793i	$0.673684\pi$
$450$	−1.09384e130	−0.0506912
$451$	−1.25089e130	−0.0519372
$452$	8.42647e130	0.313540
$453$	−1.67452e131	−0.558510
$454$	−5.04727e130	−0.150936
$455$	1.15827e131	0.310632
$456$	−1.06822e131	−0.256981
$457$	1.84843e130	0.0398980	0.0199490	−	0.999801i	$-0.493650\pi$
$457$	1.84843e130	0.0398980	0.0199490	+	0.999801i	$0.493650\pi$
$458$	−4.13584e131	−0.801166
$459$	−2.61673e131	−0.455020
$460$	3.61944e131	0.565104
$461$	6.75015e131	0.946493	0.473247	−	0.880930i	$-0.343082\pi$
$461$	6.75015e131	0.946493	0.473247	+	0.880930i	$0.343082\pi$
$462$	4.44871e131	0.560346
$463$	1.42500e132	1.61271	0.806354	−	0.591433i	$-0.201438\pi$
$463$	1.42500e132	1.61271	0.806354	+	0.591433i	$0.201438\pi$
$464$	7.50348e130	0.0763172
$465$	−8.61217e131	−0.787392
$466$	6.57085e131	0.540155
$467$	−2.11125e131	−0.156083	−0.0780414	−	0.996950i	$-0.524867\pi$
$467$	−2.11125e131	−0.156083	−0.0780414	+	0.996950i	$0.524867\pi$
$468$	−7.99725e130	−0.0531828
$469$	9.11221e131	0.545215
$470$	5.54822e131	0.298751
$471$	−2.83381e132	−1.37352
$472$	−4.11873e132	−1.79736
$473$	−4.30269e132	−1.69088
$474$	3.72293e132	1.31782
$475$	3.68292e131	0.117452
$476$	4.01136e131	0.115278
$477$	6.70765e131	0.173744
$478$	−2.98880e132	−0.697937
$479$	7.96883e132	1.67798	0.838990	−	0.544147i	$-0.183147\pi$
$479$	7.96883e132	1.67798	0.838990	+	0.544147i	$0.183147\pi$
$480$	−3.21124e132	−0.609861
$481$	4.18762e132	0.717440
$482$	−1.24263e132	−0.192093
$483$	6.94700e132	0.969202
$484$	−3.50363e132	−0.441238
$485$	−9.63275e132	−1.09530
$486$	1.87983e132	0.193030
$487$	1.43717e133	1.33298	0.666492	−	0.745512i	$-0.267795\pi$
$487$	1.43717e133	1.33298	0.666492	+	0.745512i	$0.267795\pi$
$488$	−4.85322e132	−0.406676
$489$	6.39313e132	0.484088
$490$	−5.49729e132	−0.376221
$491$	1.85917e132	0.115023	0.0575115	−	0.998345i	$-0.481683\pi$
$491$	1.85917e132	0.115023	0.0575115	+	0.998345i	$0.481683\pi$
$492$	3.23019e131	0.0180699
$493$	2.23924e132	0.113286
$494$	−3.18430e132	−0.145723
$495$	−3.08716e132	−0.127821
$496$	−9.48178e132	−0.355260
$497$	2.20686e133	0.748399
$498$	−1.80373e133	−0.553757
$499$	−5.27233e133	−1.46563	−0.732817	−	0.680426i	$-0.761795\pi$
$499$	−5.27233e133	−1.46563	−0.732817	+	0.680426i	$0.761795\pi$
$500$	1.91507e133	0.482136
$501$	−4.49643e133	−1.02542
$502$	2.29230e133	0.473628
$503$	−6.27760e133	−1.17538	−0.587690	−	0.809086i	$-0.699963\pi$
$503$	−6.27760e133	−1.17538	−0.587690	+	0.809086i	$0.699963\pi$
$504$	−4.26178e132	−0.0723235
$505$	4.76794e133	0.733512
$506$	1.31886e134	1.83970
$507$	1.90130e133	0.240523
$508$	−3.14947e133	−0.361396
$509$	1.23227e134	1.28285	0.641426	−	0.767185i	$-0.278343\pi$
$509$	1.23227e134	1.28285	0.641426	+	0.767185i	$0.278343\pi$
$510$	2.82412e133	0.266784
$511$	−1.09384e134	−0.937818
$512$	−8.11287e133	−0.631410
$513$	−2.94116e133	−0.207830
$514$	1.19180e134	0.764770
$515$	1.31430e134	0.766012
$516$	1.11109e134	0.588288
$517$	−1.70954e134	−0.822426
$518$	7.01193e133	0.306559
$519$	−1.24913e134	−0.496390
$520$	−1.80718e134	−0.652885
$521$	−2.37521e134	−0.780251	−0.390126	−	0.920762i	$-0.627568\pi$
$521$	−2.37521e134	−0.780251	−0.390126	+	0.920762i	$0.627568\pi$
$522$	−7.47514e132	−0.0223321
$523$	−5.70779e134	−1.55108	−0.775541	−	0.631297i	$-0.782523\pi$
$523$	−5.70779e134	−1.55108	−0.775541	+	0.631297i	$0.782523\pi$
$524$	1.44993e134	0.358466
$525$	1.26054e134	0.283578
$526$	1.01525e133	0.0207864
$527$	−2.82962e134	−0.527354
$528$	−2.91589e134	−0.494757
$529$	1.41227e135	2.18204
$530$	4.76269e134	0.670188
$531$	1.72371e134	0.220946
$532$	4.50870e133	0.0526533
$533$	3.06452e133	0.0326111
$534$	3.03340e134	0.294197
$535$	1.00338e135	0.887062
$536$	−1.42173e135	−1.14593
$537$	−4.29704e134	−0.315822
$538$	−7.66916e134	−0.514074
$539$	1.69385e135	1.03569
$540$	−5.24477e134	−0.292574
$541$	−2.45114e135	−1.24768	−0.623840	−	0.781552i	$-0.714428\pi$
$541$	−2.45114e135	−1.24768	−0.623840	+	0.781552i	$0.714428\pi$
$542$	1.28947e135	0.599026
$543$	1.10262e135	0.467555
$544$	−1.05509e135	−0.408453
$545$	8.82254e134	0.311865
$546$	−1.08988e135	−0.351838
$547$	1.90796e134	0.0562597	0.0281298	−	0.999604i	$-0.491045\pi$
$547$	1.90796e134	0.0562597	0.0281298	+	0.999604i	$0.491045\pi$
$548$	−2.01414e135	−0.542566
$549$	2.03110e134	0.0499920
$550$	2.39309e135	0.538277
$551$	2.51687e134	0.0517435
$552$	−1.08390e136	−2.03707
$553$	−5.00100e135	−0.859336
$554$	7.71833e135	1.21280
$555$	−4.17442e135	−0.599921
$556$	6.66404e135	0.876063
$557$	1.13600e136	1.36630	0.683150	−	0.730278i	$-0.260610\pi$
$557$	1.13600e136	1.36630	0.683150	+	0.730278i	$0.260610\pi$
$558$	9.44597e134	0.103957
$559$	1.05411e136	1.06169
$560$	−1.27121e135	−0.117195
$561$	−8.70180e135	−0.734425
$562$	3.37408e135	0.260740
$563$	1.65637e136	1.17217	0.586085	−	0.810250i	$-0.300668\pi$
$563$	1.65637e136	1.17217	0.586085	+	0.810250i	$0.300668\pi$
$564$	4.41458e135	0.286137
$565$	−7.96910e135	−0.473163
$566$	−9.18349e133	−0.00499568
$567$	−1.14184e136	−0.569171
$568$	−3.44323e136	−1.57298
$569$	3.17509e135	0.132953	0.0664765	−	0.997788i	$-0.478824\pi$
$569$	3.17509e135	0.132953	0.0664765	+	0.997788i	$0.478824\pi$
$570$	3.17427e135	0.121854
$571$	−3.78940e136	−1.33378	−0.666889	−	0.745157i	$-0.732374\pi$
$571$	−3.78940e136	−1.33378	−0.666889	+	0.745157i	$0.732374\pi$
$572$	1.74964e136	0.564734
$573$	−1.83141e136	−0.542166
$574$	5.13136e134	0.0139346
$575$	3.73699e136	0.931030
$576$	5.43780e135	0.124311
$577$	−3.37277e136	−0.707595	−0.353797	−	0.935322i	$-0.615110\pi$
$577$	−3.37277e136	−0.707595	−0.353797	+	0.935322i	$0.615110\pi$
$578$	−2.89470e136	−0.557411
$579$	5.22553e136	0.923722
$580$	4.48817e135	0.0728422
$581$	2.42295e136	0.361098
$582$	9.06397e136	1.24060
$583$	−1.46750e137	−1.84495
$584$	1.70665e137	1.97110
$585$	7.56317e135	0.0802580
$586$	3.25436e136	0.317347
$587$	−2.18802e136	−0.196094	−0.0980470	−	0.995182i	$-0.531260\pi$
$587$	−2.18802e136	−0.196094	−0.0980470	+	0.995182i	$0.531260\pi$
$588$	−4.37406e136	−0.360335
$589$	−3.18044e136	−0.240869
$590$	1.22390e137	0.852259
$591$	−1.66281e137	−1.06478
$592$	−4.59594e136	−0.270676
$593$	2.12353e137	1.15040	0.575202	−	0.818011i	$-0.304923\pi$
$593$	2.12353e137	1.15040	0.575202	+	0.818011i	$0.304923\pi$
$594$	−1.91110e137	−0.952479
$595$	−3.79363e136	−0.173966
$596$	−6.23545e136	−0.263134
$597$	−3.51862e137	−1.36660
$598$	−3.23104e137	−1.15514
$599$	5.17821e137	1.70432	0.852162	−	0.523278i	$-0.175291\pi$
$599$	5.17821e137	1.70432	0.852162	+	0.523278i	$0.175291\pi$
$600$	−1.96675e137	−0.596023
$601$	3.68650e137	1.02879	0.514397	−	0.857552i	$-0.328016\pi$
$601$	3.68650e137	1.02879	0.514397	+	0.857552i	$0.328016\pi$
$602$	1.76504e137	0.453658
$603$	5.95001e136	0.140867
$604$	−1.10275e137	−0.240518
$605$	3.31346e137	0.665872
$606$	−4.48641e137	−0.830814
$607$	−3.33790e137	−0.569682	−0.284841	−	0.958575i	$-0.591941\pi$
$607$	−3.33790e137	−0.569682	−0.284841	+	0.958575i	$0.591941\pi$
$608$	−1.18590e137	−0.186561
$609$	8.61440e136	0.124931
$610$	1.44216e137	0.192835
$611$	4.18816e137	0.516396
$612$	2.61930e136	0.0297845
$613$	7.62260e137	0.799484	0.399742	−	0.916628i	$-0.369100\pi$
$613$	7.62260e137	0.799484	0.399742	+	0.916628i	$0.369100\pi$
$614$	4.93912e137	0.477876
$615$	−3.05486e136	−0.0272693
$616$	9.32391e137	0.767985
$617$	2.19162e138	1.66590	0.832950	−	0.553348i	$-0.186650\pi$
$617$	2.19162e138	1.66590	0.832950	+	0.553348i	$0.186650\pi$
$618$	−1.23669e138	−0.867625
$619$	−1.77432e138	−1.14907	−0.574533	−	0.818481i	$-0.694816\pi$
$619$	−1.77432e138	−1.14907	−0.574533	+	0.818481i	$0.694816\pi$
$620$	−5.67148e137	−0.339084
$621$	−2.98433e138	−1.64745
$622$	−1.86189e138	−0.949139
$623$	−4.07476e137	−0.191842
$624$	7.14357e137	0.310655
$625$	−5.11937e137	−0.205663
$626$	1.93806e138	0.719348
$627$	−9.78067e137	−0.335448
$628$	−1.86618e138	−0.591496
$629$	−1.37155e138	−0.401795
$630$	1.26641e137	0.0342939
$631$	2.15180e138	0.538702	0.269351	−	0.963042i	$-0.413191\pi$
$631$	2.15180e138	0.538702	0.269351	+	0.963042i	$0.413191\pi$
$632$	7.80277e138	1.80615
$633$	3.44160e138	0.736677
$634$	−3.33999e138	−0.661192
$635$	2.97852e138	0.545383
$636$	3.78955e138	0.641890
$637$	−4.14971e138	−0.650304
$638$	1.63541e138	0.237139
$639$	1.44101e138	0.193364
$640$	−7.54542e137	−0.0937075
$641$	−2.79316e138	−0.321088	−0.160544	−	0.987029i	$-0.551325\pi$
$641$	−2.79316e138	−0.321088	−0.160544	+	0.987029i	$0.551325\pi$
$642$	−9.44136e138	−1.00473
$643$	4.84615e138	0.477479	0.238739	−	0.971084i	$-0.423266\pi$
$643$	4.84615e138	0.477479	0.238739	+	0.971084i	$0.423266\pi$
$644$	4.57489e138	0.417379
$645$	−1.05078e139	−0.887785
$646$	1.04294e138	0.0816111
$647$	7.87068e138	0.570493	0.285247	−	0.958454i	$-0.407925\pi$
$647$	7.87068e138	0.570493	0.285247	+	0.958454i	$0.407925\pi$
$648$	1.78154e139	1.19628
$649$	−3.77113e139	−2.34617
$650$	−5.86277e138	−0.337981
$651$	−1.08856e139	−0.581559
$652$	4.21014e138	0.208469
$653$	2.55074e139	1.17075	0.585375	−	0.810762i	$-0.300947\pi$
$653$	2.55074e139	1.17075	0.585375	+	0.810762i	$0.300947\pi$
$654$	−8.30160e138	−0.353234
$655$	−1.37123e139	−0.540961
$656$	−3.36333e137	−0.0123035
$657$	−7.14244e138	−0.242304
$658$	7.01283e138	0.220654
$659$	2.07729e139	0.606273	0.303137	−	0.952947i	$-0.401966\pi$
$659$	2.07729e139	0.606273	0.303137	+	0.952947i	$0.401966\pi$
$660$	−1.74412e139	−0.472229
$661$	3.61394e139	0.907838	0.453919	−	0.891043i	$-0.350026\pi$
$661$	3.61394e139	0.907838	0.453919	+	0.891043i	$0.350026\pi$
$662$	3.83459e139	0.893817
$663$	2.13183e139	0.461141
$664$	−3.78038e139	−0.758955
$665$	−4.26398e138	−0.0794591
$666$	4.57858e138	0.0792057
$667$	2.55381e139	0.410167
$668$	−2.96109e139	−0.441587
$669$	1.99758e139	0.276638
$670$	4.22473e139	0.543371
$671$	−4.44364e139	−0.530853
$672$	−4.05894e139	−0.450436
$673$	1.34479e140	1.38647	0.693234	−	0.720713i	$-0.256185\pi$
$673$	1.34479e140	1.38647	0.693234	+	0.720713i	$0.256185\pi$
$674$	−1.35517e140	−1.29816
$675$	−5.41511e139	−0.482026
$676$	1.25209e139	0.103579
$677$	−1.06781e140	−0.821019	−0.410509	−	0.911856i	$-0.634649\pi$
$677$	−1.06781e140	−0.821019	−0.410509	+	0.911856i	$0.634649\pi$
$678$	7.49855e139	0.535930
$679$	−1.21756e140	−0.808977
$680$	5.91899e139	0.365642
$681$	3.79801e139	0.218159
$682$	−2.06659e140	−1.10389
$683$	−1.17467e140	−0.583570	−0.291785	−	0.956484i	$-0.594249\pi$
$683$	−1.17467e140	−0.583570	−0.291785	+	0.956484i	$0.594249\pi$
$684$	2.94405e138	0.0136041
$685$	1.90482e140	0.818786
$686$	−1.63484e140	−0.653778
$687$	3.11217e140	1.15799
$688$	−1.15689e140	−0.400556
$689$	3.59519e140	1.15843
$690$	3.22087e140	0.965923
$691$	4.07613e140	1.13785	0.568925	−	0.822389i	$-0.307360\pi$
$691$	4.07613e140	1.13785	0.568925	+	0.822389i	$0.307360\pi$
$692$	−8.22604e139	−0.213766
$693$	−3.90211e139	−0.0944071
$694$	5.66139e140	1.27535
$695$	−6.30233e140	−1.32207
$696$	−1.34406e140	−0.262579
$697$	−1.00371e139	−0.0182635
$698$	−4.17113e140	−0.706986
$699$	−4.94448e140	−0.780730
$700$	8.30121e139	0.122120
$701$	−8.03658e140	−1.10161	−0.550807	−	0.834633i	$-0.685680\pi$
$701$	−8.03658e140	−1.10161	−0.550807	+	0.834633i	$0.685680\pi$
$702$	4.68197e140	0.598055
$703$	−1.54160e140	−0.183520
$704$	−1.18968e141	−1.32003
$705$	−4.17496e140	−0.431809
$706$	1.16220e141	1.12060
$707$	6.02657e140	0.541763
$708$	9.73828e140	0.816274
$709$	−2.61948e140	−0.204751	−0.102375	−	0.994746i	$-0.532644\pi$
$709$	−2.61948e140	−0.204751	−0.102375	+	0.994746i	$0.532644\pi$
$710$	1.02317e141	0.745867
$711$	−3.26551e140	−0.222027
$712$	6.35761e140	0.403213
$713$	−3.22713e141	−1.90935
$714$	3.56963e140	0.197044
$715$	−1.65467e141	−0.852240
$716$	−2.82978e140	−0.136006
$717$	2.24904e141	1.00878
$718$	1.63172e141	0.683104
$719$	3.26481e141	1.27579	0.637894	−	0.770125i	$-0.279806\pi$
$719$	3.26481e141	1.27579	0.637894	+	0.770125i	$0.279806\pi$
$720$	−8.30063e139	−0.0302798
$721$	1.66124e141	0.565767
$722$	−2.19762e141	−0.698814
$723$	9.35061e140	0.277648
$724$	7.26120e140	0.201349
$725$	4.63393e140	0.120010
$726$	−3.11781e141	−0.754202
$727$	−2.32668e140	−0.0525756	−0.0262878	−	0.999654i	$-0.508369\pi$
$727$	−2.32668e140	−0.0525756	−0.0262878	+	0.999654i	$0.508369\pi$
$728$	−2.28424e141	−0.482213
$729$	4.23620e141	0.835534
$730$	−5.07141e141	−0.934645
$731$	−3.45246e141	−0.594592
$732$	1.14749e141	0.184693
$733$	−2.70840e141	−0.407442	−0.203721	−	0.979029i	$-0.565304\pi$
$733$	−2.70840e141	−0.407442	−0.203721	+	0.979029i	$0.565304\pi$
$734$	3.02794e141	0.425787
$735$	4.13664e141	0.543782
$736$	−1.20331e142	−1.47885
$737$	−1.30174e142	−1.49584
$738$	3.35063e139	0.00360028
$739$	1.71766e142	1.72599	0.862994	−	0.505215i	$-0.168587\pi$
$739$	1.71766e142	1.72599	0.862994	+	0.505215i	$0.168587\pi$
$740$	−2.74904e141	−0.258351
$741$	2.39614e141	0.210626
$742$	6.01994e141	0.494993
$743$	−4.70285e141	−0.361755	−0.180878	−	0.983506i	$-0.557894\pi$
$743$	−4.70285e141	−0.361755	−0.180878	+	0.983506i	$0.557894\pi$
$744$	1.69842e142	1.22232
$745$	5.89700e141	0.397096
$746$	−6.79723e141	−0.428312
$747$	1.58211e141	0.0932970
$748$	−5.73050e141	−0.316274
$749$	1.26825e142	0.655173
$750$	1.70418e142	0.824108
$751$	6.67448e141	0.302163	0.151081	−	0.988521i	$-0.451724\pi$
$751$	6.67448e141	0.302163	0.151081	+	0.988521i	$0.451724\pi$
$752$	−4.59653e141	−0.194826
$753$	−1.72493e142	−0.684572
$754$	−4.00655e141	−0.148898
$755$	1.04289e142	0.362965
$756$	−6.62928e141	−0.216092
$757$	2.32174e142	0.708872	0.354436	−	0.935080i	$-0.384673\pi$
$757$	2.32174e142	0.708872	0.354436	+	0.935080i	$0.384673\pi$
$758$	−2.97700e141	−0.0851439
$759$	−9.92426e142	−2.65907
$760$	6.65284e141	0.167007
$761$	−1.90091e142	−0.447116	−0.223558	−	0.974691i	$-0.571767\pi$
$761$	−1.90091e142	−0.447116	−0.223558	+	0.974691i	$0.571767\pi$
$762$	−2.80265e142	−0.617729
$763$	1.11515e142	0.230340
$764$	−1.20606e142	−0.233479
$765$	−2.47713e141	−0.0449478
$766$	−4.53991e142	−0.772189
$767$	9.23881e142	1.47314
$768$	7.41520e142	1.10852
$769$	7.64363e142	1.07139	0.535693	−	0.844413i	$-0.320050\pi$
$769$	7.64363e142	1.07139	0.535693	+	0.844413i	$0.320050\pi$
$770$	−2.77065e142	−0.364159
$771$	−8.96818e142	−1.10538
$772$	3.44123e142	0.397794
$773$	6.36354e142	0.689944	0.344972	−	0.938613i	$-0.387888\pi$
$773$	6.36354e142	0.689944	0.344972	+	0.938613i	$0.387888\pi$
$774$	1.15252e142	0.117212
$775$	−5.85568e142	−0.558654
$776$	1.89969e143	1.70031
$777$	−5.27639e142	−0.443094
$778$	−5.95214e142	−0.469011
$779$	−1.12815e141	−0.00834185
$780$	4.27289e142	0.296510
$781$	−3.15265e143	−2.05328
$782$	1.05825e143	0.646925
$783$	−3.70062e142	−0.212358
$784$	4.55434e142	0.245347
$785$	1.76489e143	0.892626
$786$	1.29026e143	0.612720
$787$	1.25919e138	5.61491e−6 0	2.80746e−6	−	1.00000i	$-0.499999\pi$
$787$	1.25919e138	5.61491e−6 0	2.80746e−6		1.00000i	$0.499999\pi$
$788$	−1.09503e143	−0.458541
$789$	−7.63965e141	−0.0300443
$790$	−2.31864e143	−0.856429
$791$	−1.00728e143	−0.349473
$792$	6.08824e142	0.198424
$793$	1.08864e143	0.333319
$794$	−3.10794e143	−0.894043
$795$	−3.58386e143	−0.968676
$796$	−2.31716e143	−0.588517
$797$	3.51754e143	0.839561	0.419780	−	0.907626i	$-0.362107\pi$
$797$	3.51754e143	0.839561	0.419780	+	0.907626i	$0.362107\pi$
$798$	4.01221e142	0.0899995
$799$	−1.37173e143	−0.289203
$800$	−2.18342e143	−0.432696
$801$	−2.66070e142	−0.0495662
$802$	3.63491e143	0.636594
$803$	1.56262e144	2.57297
$804$	3.36152e143	0.520428
$805$	−4.32658e143	−0.629866
$806$	5.06288e143	0.693128
$807$	5.77095e143	0.743032
$808$	−9.40291e143	−1.13868
$809$	7.13853e143	0.813124	0.406562	−	0.913623i	$-0.366727\pi$
$809$	7.13853e143	0.813124	0.406562	+	0.913623i	$0.366727\pi$
$810$	−5.29394e143	−0.567245
$811$	1.39702e143	0.140822	0.0704110	−	0.997518i	$-0.477569\pi$
$811$	1.39702e143	0.140822	0.0704110	+	0.997518i	$0.477569\pi$
$812$	5.67295e142	0.0538004
$813$	−9.70308e143	−0.865820
$814$	−1.00170e144	−0.841066
$815$	−3.98162e143	−0.314600
$816$	−2.33970e143	−0.173979
$817$	−3.88051e143	−0.271580
$818$	1.24502e144	0.820137
$819$	9.55969e142	0.0592776
$820$	−2.01176e142	−0.0117433
$821$	−1.28163e144	−0.704332	−0.352166	−	0.935937i	$-0.614555\pi$
$821$	−1.28163e144	−0.704332	−0.352166	+	0.935937i	$0.614555\pi$
$822$	−1.79235e144	−0.927399
$823$	2.12695e144	1.03625	0.518125	−	0.855305i	$-0.326630\pi$
$823$	2.12695e144	1.03625	0.518125	+	0.855305i	$0.326630\pi$
$824$	−2.59194e144	−1.18913
$825$	−1.80077e144	−0.778015
$826$	1.54699e144	0.629469
$827$	3.02565e144	1.15957	0.579784	−	0.814770i	$-0.303137\pi$
$827$	3.02565e144	1.15957	0.579784	+	0.814770i	$0.303137\pi$
$828$	2.98727e143	0.107838
$829$	1.14336e144	0.388806	0.194403	−	0.980922i	$-0.437723\pi$
$829$	1.14336e144	0.388806	0.194403	+	0.980922i	$0.437723\pi$
$830$	1.12336e144	0.359876
$831$	−5.80795e144	−1.75296
$832$	2.91457e144	0.828839
$833$	1.35914e144	0.364196
$834$	5.93020e144	1.49744
$835$	2.80037e144	0.666399
$836$	−6.44099e143	−0.144458
$837$	4.67630e144	0.988535
$838$	−6.87391e143	−0.136970
$839$	−8.57600e144	−1.61090	−0.805448	−	0.592666i	$-0.798075\pi$
$839$	−8.57600e144	−1.61090	−0.805448	+	0.592666i	$0.798075\pi$
$840$	2.27705e144	0.403225
$841$	−5.67298e144	−0.947129
$842$	−1.70106e144	−0.267776
$843$	−2.53895e144	−0.376868
$844$	2.26644e144	0.317244
$845$	−1.18412e144	−0.156311
$846$	4.57917e143	0.0570104
$847$	4.18815e144	0.491805
$848$	−3.94574e144	−0.437053
$849$	6.91046e142	0.00722065
$850$	1.92021e144	0.189283
$851$	−1.56423e145	−1.45475
$852$	8.14115e144	0.714374
$853$	−2.36436e144	−0.195766	−0.0978829	−	0.995198i	$-0.531207\pi$
$853$	−2.36436e144	−0.195766	−0.0978829	+	0.995198i	$0.531207\pi$
$854$	1.82286e144	0.142426
$855$	−2.78425e143	−0.0205299
$856$	−1.97878e145	−1.37704
$857$	9.43233e144	0.619538	0.309769	−	0.950812i	$-0.399748\pi$
$857$	9.43233e144	0.619538	0.309769	+	0.950812i	$0.399748\pi$
$858$	1.55697e145	0.965291
$859$	1.77899e145	1.04115	0.520573	−	0.853817i	$-0.325718\pi$
$859$	1.77899e145	1.04115	0.520573	+	0.853817i	$0.325718\pi$
$860$	−6.91986e144	−0.382318
$861$	−3.86128e143	−0.0201407
$862$	−6.73522e144	−0.331697
$863$	−2.61032e145	−1.21384	−0.606918	−	0.794764i	$-0.707594\pi$
$863$	−2.61032e145	−1.21384	−0.606918	+	0.794764i	$0.707594\pi$
$864$	1.74366e145	0.765653
$865$	7.77954e144	0.322594
$866$	−2.08710e145	−0.817350
$867$	2.17823e145	0.805671
$868$	−7.16863e144	−0.250444
$869$	7.14427e145	2.35765
$870$	3.99393e144	0.124508
$871$	3.18910e145	0.939226
$872$	−1.73990e145	−0.484127
$873$	−7.95031e144	−0.209016
$874$	1.18945e145	0.295483
$875$	−2.28922e145	−0.537390
$876$	−4.03519e145	−0.895182
$877$	−4.20512e145	−0.881656	−0.440828	−	0.897592i	$-0.645315\pi$
$877$	−4.20512e145	−0.881656	−0.440828	+	0.897592i	$0.645315\pi$
$878$	−2.81081e145	−0.556997
$879$	−2.44887e145	−0.458687
$880$	1.81601e145	0.321533
$881$	−9.64785e145	−1.61482	−0.807408	−	0.589993i	$-0.799130\pi$
$881$	−9.64785e145	−1.61482	−0.807408	+	0.589993i	$0.799130\pi$
$882$	−4.53714e144	−0.0717939
$883$	4.53533e145	0.678507	0.339254	−	0.940695i	$-0.389826\pi$
$883$	4.53533e145	0.678507	0.339254	+	0.940695i	$0.389826\pi$
$884$	1.40390e145	0.198587
$885$	−9.20970e145	−1.23184
$886$	1.70269e145	0.215361
$887$	4.03648e145	0.482818	0.241409	−	0.970423i	$-0.422390\pi$
$887$	4.03648e145	0.482818	0.241409	+	0.970423i	$0.422390\pi$
$888$	8.23244e145	0.931294
$889$	3.76479e145	0.402813
$890$	−1.88920e145	−0.191193
$891$	1.63119e146	1.56156
$892$	1.31549e145	0.119132
$893$	−1.54180e145	−0.132093
$894$	−5.54880e145	−0.449771
$895$	2.67618e145	0.205247
$896$	−9.53725e144	−0.0692113
$897$	2.43132e146	1.66961
$898$	−1.17566e146	−0.764015
$899$	−4.00170e145	−0.246116
$900$	5.42045e144	0.0315523
$901$	−1.17752e146	−0.648768
$902$	−7.33049e144	−0.0382304
$903$	−1.32817e146	−0.655708
$904$	1.57160e146	0.734521
$905$	−6.86708e145	−0.303856
$906$	−9.81312e145	−0.411113
$907$	1.29462e146	0.513548	0.256774	−	0.966471i	$-0.417340\pi$
$907$	1.29462e146	0.513548	0.256774	+	0.966471i	$0.417340\pi$
$908$	2.50115e145	0.0939486
$909$	3.93517e145	0.139975
$910$	6.78775e145	0.228653
$911$	−3.27662e146	−1.04536	−0.522681	−	0.852528i	$-0.675068\pi$
$911$	−3.27662e146	−1.04536	−0.522681	+	0.852528i	$0.675068\pi$
$912$	−2.62978e145	−0.0794649
$913$	−3.46134e146	−0.990697
$914$	1.08323e145	0.0293685
$915$	−1.08521e146	−0.278720
$916$	2.04949e146	0.498679
$917$	−1.73321e146	−0.399547
$918$	−1.53346e146	−0.334935
$919$	−5.39868e145	−0.111730	−0.0558650	−	0.998438i	$-0.517792\pi$
$919$	−5.39868e145	−0.111730	−0.0558650	+	0.998438i	$0.517792\pi$
$920$	6.75051e146	1.32385
$921$	−3.71662e146	−0.690712
$922$	3.95575e146	0.696704
$923$	7.72359e146	1.28924
$924$	−2.20454e146	−0.348783
$925$	−2.83832e146	−0.425643
$926$	8.35084e146	1.18710
$927$	1.08474e146	0.146177
$928$	−1.49212e146	−0.190625
$929$	−4.98883e146	−0.604256	−0.302128	−	0.953267i	$-0.597697\pi$
$929$	−4.98883e146	−0.604256	−0.302128	+	0.953267i	$0.597697\pi$
$930$	−5.04694e146	−0.579591
$931$	1.52765e146	0.166347
$932$	−3.25615e146	−0.336215
$933$	1.40105e147	1.37187
$934$	−1.23725e146	−0.114891
$935$	5.41946e146	0.477289
$936$	−1.49154e146	−0.124589
$937$	−9.40993e146	−0.745550	−0.372775	−	0.927922i	$-0.621594\pi$
$937$	−9.40993e146	−0.745550	−0.372775	+	0.927922i	$0.621594\pi$
$938$	5.33998e146	0.401327
$939$	−1.45837e147	−1.03973
$940$	−2.74939e146	−0.185955
$941$	2.51488e147	1.61373	0.806866	−	0.590735i	$-0.201162\pi$
$941$	2.51488e147	1.61373	0.806866	+	0.590735i	$0.201162\pi$
$942$	−1.66068e147	−1.01103
$943$	−1.14471e146	−0.0661252
$944$	−1.01397e147	−0.555788
$945$	6.26946e146	0.326104
$946$	−2.52148e147	−1.24464
$947$	2.37499e146	0.111260	0.0556299	−	0.998451i	$-0.482283\pi$
$947$	2.37499e146	0.111260	0.0556299	+	0.998451i	$0.482283\pi$
$948$	−1.84488e147	−0.820268
$949$	−3.82823e147	−1.61555
$950$	2.15828e146	0.0864549
$951$	2.51330e147	0.955673
$952$	7.48148e146	0.270059
$953$	4.61266e147	1.58071	0.790356	−	0.612648i	$-0.209896\pi$
$953$	4.61266e147	1.58071	0.790356	+	0.612648i	$0.209896\pi$
$954$	3.93084e146	0.127891
$955$	1.14060e147	0.352344
$956$	1.48109e147	0.434425
$957$	−1.23063e147	−0.342756
$958$	4.66993e147	1.23514
$959$	2.40765e147	0.604745
$960$	−2.90539e147	−0.693072
$961$	6.43005e146	0.145682
$962$	2.45404e147	0.528100
$963$	8.28133e146	0.169277
$964$	6.15777e146	0.119567
$965$	−3.25445e147	−0.600310
$966$	4.07111e147	0.713419
$967$	−4.90506e147	−0.816645	−0.408323	−	0.912838i	$-0.633886\pi$
$967$	−4.90506e147	−0.816645	−0.408323	+	0.912838i	$0.633886\pi$
$968$	−6.53452e147	−1.03367
$969$	−7.84798e146	−0.117959
$970$	−5.64502e147	−0.806241
$971$	−1.98310e147	−0.269149	−0.134574	−	0.990903i	$-0.542967\pi$
$971$	−1.98310e147	−0.269149	−0.134574	+	0.990903i	$0.542967\pi$
$972$	−9.31542e146	−0.120150
$973$	−7.96601e147	−0.976462
$974$	8.42217e147	0.981195
$975$	4.41166e147	0.488511
$976$	−1.19479e147	−0.125755
$977$	−1.24239e148	−1.24302	−0.621508	−	0.783408i	$-0.713480\pi$
$977$	−1.24239e148	−1.24302	−0.621508	+	0.783408i	$0.713480\pi$
$978$	3.74652e147	0.356332
$979$	5.82107e147	0.526331
$980$	2.72415e147	0.234175
$981$	7.28160e146	0.0595129
$982$	1.08952e147	0.0846673
$983$	5.29380e147	0.391172	0.195586	−	0.980687i	$-0.437339\pi$
$983$	5.29380e147	0.391172	0.195586	+	0.980687i	$0.437339\pi$
$984$	6.02454e146	0.0423317
$985$	1.03559e148	0.691984
$986$	1.31225e147	0.0833889
$987$	−5.27707e147	−0.318929
$988$	1.57796e147	0.0907043
$989$	−3.93748e148	−2.15279
$990$	−1.80915e147	−0.0940877
$991$	3.37469e148	1.66951	0.834754	−	0.550623i	$-0.185610\pi$
$991$	3.37469e148	1.66951	0.834754	+	0.550623i	$0.185610\pi$
$992$	1.88552e148	0.887368
$993$	−2.88548e148	−1.29190
$994$	1.29327e148	0.550889
$995$	2.19139e148	0.888131
$996$	8.93830e147	0.344681
$997$	2.13404e148	0.783055	0.391527	−	0.920166i	$-0.371947\pi$
$997$	2.13404e148	0.783055	0.391527	+	0.920166i	$0.371947\pi$
$998$	−3.08971e148	−1.07884
$999$	2.26666e148	0.753173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.100.a.a.1.6	✓	8
3.2	odd	2		9.100.a.d.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.100.a.a.1.6	✓	8	1.1	even	1	trivial
9.100.a.d.1.3		8	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:	\( k \)	\(=\)	\( 100 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+5.86024e14 q^{2} -4.40976e23 q^{3} -2.90401e29 q^{4} +2.74639e34 q^{5} -2.58422e38 q^{6} +3.47138e41 q^{7} -5.41619e44 q^{8} +2.26671e46 q^{9} +O(q^{10})\)	\(q+5.86024e14 q^{2} -4.40976e23 q^{3} -2.90401e29 q^{4} +2.74639e34 q^{5} -2.58422e38 q^{6} +3.47138e41 q^{7} -5.41619e44 q^{8} +2.26671e46 q^{9} +1.60945e49 q^{10} -4.95910e51 q^{11} +1.28060e53 q^{12} +1.21492e55 q^{13} +2.03431e56 q^{14} -1.21109e58 q^{15} -1.33338e59 q^{16} -3.97916e60 q^{17} +1.32834e61 q^{18} -4.47251e62 q^{19} -7.97554e63 q^{20} -1.53079e65 q^{21} -2.90615e66 q^{22} -4.53817e67 q^{23} +2.38841e68 q^{24} -8.23457e68 q^{25} +7.11971e69 q^{26} +6.57607e70 q^{27} -1.00809e71 q^{28} -5.62741e71 q^{29} -7.09728e72 q^{30} +7.11109e73 q^{31} +2.65152e74 q^{32} +2.18684e75 q^{33} -2.33189e75 q^{34} +9.53375e75 q^{35} -6.58255e75 q^{36} +3.44683e77 q^{37} -2.62100e77 q^{38} -5.35749e78 q^{39} -1.48750e79 q^{40} +2.52241e78 q^{41} -8.97081e79 q^{42} +8.67636e80 q^{43} +1.44013e81 q^{44} +6.22526e80 q^{45} -2.65948e82 q^{46} +3.44728e82 q^{47} +5.87988e82 q^{48} -3.41563e83 q^{49} -4.82566e83 q^{50} +1.75471e84 q^{51} -3.52813e84 q^{52} +2.95920e85 q^{53} +3.85373e85 q^{54} -1.36196e86 q^{55} -1.88016e86 q^{56} +1.97227e86 q^{57} -3.29780e86 q^{58} +7.60447e87 q^{59} +3.51702e87 q^{60} +8.96058e87 q^{61} +4.16727e88 q^{62} +7.86860e87 q^{63} +2.39899e89 q^{64} +3.33663e89 q^{65} +1.28154e90 q^{66} +2.62496e90 q^{67} +1.15555e90 q^{68} +2.00122e91 q^{69} +5.58700e90 q^{70} +6.35730e91 q^{71} -1.22769e91 q^{72} -3.15102e92 q^{73} +2.01993e92 q^{74} +3.63125e92 q^{75} +1.29882e92 q^{76} -1.72149e93 q^{77} -3.13962e93 q^{78} -1.44064e94 q^{79} -3.66198e93 q^{80} -3.28929e94 q^{81} +1.47819e93 q^{82} +6.97978e94 q^{83} +4.44544e94 q^{84} -1.09283e95 q^{85} +5.08455e95 q^{86} +2.48155e95 q^{87} +2.68594e96 q^{88} -1.17382e96 q^{89} +3.64815e95 q^{90} +4.21744e96 q^{91} +1.31789e97 q^{92} -3.13582e97 q^{93} +2.02019e97 q^{94} -1.22833e97 q^{95} -1.16926e98 q^{96} -3.50742e98 q^{97} -2.00164e98 q^{98} -1.12408e98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots + 15\!\cdots\!76 q^{9}+O(q^{10}) \) 8 * q - 208040616902520 * q^2 - 282956306495420632223520 * q^3 + 2874573971021731526732655093824 * q^4 - 48829879146635109942685521105004560 * q^5 - 77942153094234171155671704171199405344 * q^6 - 56830940560713017104682273454607970657600 * q^7 + 592603013041539183163433278232078795937538560 * q^8 + 15585042525631880727258151421002821416820695976 * q^9	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots - 13\!\cdots\!08 q^{99}+O(q^{100}) \) 8 * q - 208040616902520 * q^2 - 282956306495420632223520 * q^3 + 2874573971021731526732655093824 * q^4 - 48829879146635109942685521105004560 * q^5 - 77942153094234171155671704171199405344 * q^6 - 56830940560713017104682273454607970657600 * q^7 + 592603013041539183163433278232078795937538560 * q^8 + 15585042525631880727258151421002821416820695976 * q^9 - 20961738819400631174675750189416259674325116377360 * q^10 + 668605620058921294359176615672652323197376366725536 * q^11 - 260751428362765138428103958747533086169389679507011840 * q^12 - 5313129021153651674083973849295770678848247690376073040 * q^13 - 275891262636795191856274681125121829106120036919920873792 * q^14 + 39601076201132911228470767893146157937452742673766616546880 * q^15 + 1686978001168411473373901309719868789822314791151035737182208 * q^16 + 29870581004484716934093126001838988402381517134653878061066640 * q^17 + 104619592562318909205389831941745992324800916717508145002954280 * q^18 - 2584541347057387315132230533073883085094549482599567538462153120 * q^19 - 87020910945991395973478129409062640628123700866757624264022986880 * q^20 + 720725986617461186277876616197863336884455731162862159407836416 * q^21 + 6448630494375222037284713151002631218361976067562272720681828806560 * q^22 - 591705231800483702926418342143069697446663268741979110571049882560 * q^23 - 786094952626208255303024343193893163353569305701641632350239286773760 * q^24 + 716804381062067209680195080749365299641535704320602348503400092268600 * q^25 + 34654632463607194325743429354208471986051789816879940147342898057153456 * q^26 + 13869683363495491009982193176608883185849831807068440771218044677979840 * q^27 - 1135994339501291724748966539673012720374432727977564592829456188165859840 * q^28 - 439009994693767454184499584774890376667926937141064013921655743937571280 * q^29 + 23517293722912668382363618879896733566643340714874843272431473003480521280 * q^30 - 42796079732631926995692344425065773646038440365668203549397431930127162624 * q^31 - 284044778854068845159282113651411076631875258269403845301648101866131128320 * q^32 - 1184428676639946519273358190717309258531732537332484528437733831641965671040 * q^33 + 11470334814206853457708153296668381286712583035391282441563479133450208961168 * q^34 - 13317873075112713679215664096634074386516466958921311305188860496632195839360 * q^35 - 224326234591498863152148578877455893579609783196337897663675145770615318305472 * q^36 + 7013041648409278763731742859978750449729753703775477297667583228204170683120 * q^37 + 4097267709666535974097951231260487171744232792996835026005028682857459985875040 * q^38 + 3086772337289173445407063166797596998267422181270693039748051240117483908526912 * q^39 - 61154477845927513224255221208858320971333500267390856556166248662272460823577600 * q^40 + 16836611518887404247693904661111767446154336367366992887095255319045118001938896 * q^41 + 586782577486516292654880709693602500520055556295982039518980517393750164948778240 * q^42 - 115479509651193412125043402629710680178430977878852566804453976757651553792322400 * q^43 - 4823674089938931277708865059630293953738849935605913988972972769383583829463937792 * q^44 - 4204225762790416656941382640299001599040327829208847740401216426127468587838672720 * q^45 + 41220575732227465405339930795314328162570779910219577393801310430729179103724398656 * q^46 + 28878226575287510694522520507929237505491250714878620920990009419290436045018975360 * q^47 - 270645616492149970234041108687889002599221246648694105429287982543953957103033794560 * q^48 - 14382803175556111227730750647629461517090856222687609645964147941666232976982659256 * q^49 + 2538900041031429584911497444199766832786695308479217204477072876574482801521012636600 * q^50 - 1711868817156841452117007804086601271536721152787522351736690290031659132307369497664 * q^51 - 199691168563235615231272208715487263769590246824861808533841002609282642680495606400 * q^52 - 30091820242734525213832735040802634061423162425240717202059443809754039115425881976720 * q^53 + 136432908322968282680263912195201284966825652472631606906205576348979246713807692108480 * q^54 + 226099583633880167546966079422139027647924161654010953637858494806538127768993139084480 * q^55 + 323037227302956226932352973051969540564093713359973342312103259763994205180305378488320 * q^56 - 273423384330404631781757518792671605280054294102341216713398337934356290096852147342720 * q^57 + 5713973478801321937231450378714667908258440100056694714036585358012358074567853731219760 * q^58 + 14607245332654695346837714400351649175544087130678579822473040904252509022932739720811040 * q^59 + 53008257791762983739773607116394245193846456713938833829846630209166818928009302295114240 * q^60 + 38323682921378832161349805479389921828014992489778724538462200957929376165086831637164336 * q^61 + 201697385927609334439920541372343666252345396922224455072723131310512431934088015943381760 * q^62 + 659857333915856699600072965534847901170546674796116288100652182111732663513752207410870720 * q^63 + 2567569508313686836352267062189989701299823975229681223291764819542997452948800142018084864 * q^64 + 2649617703605055039617798586548537725956903247199823944158672914229112797191302156162117280 * q^65 + 7971156345834212651621212324655177899942634890685144307138793590710555397223588657590125952 * q^66 + 11538024122310165476577023936338470394129524138300592332780359783942082451772953721242543840 * q^67 + 56045208748154976002290739488865109707859265886693431912946708486067523902076046154608254080 * q^68 + 54550768708090409722131753417710688638608175085564682877064185400954540597503860451967981312 * q^69 + 143889269423962258520958611175254488367329101991613194841590826662727327088381209016536883840 * q^70 + 52677154721705052088453955375369863850612862186345822027042426779160256515633503076296638656 * q^71 + 365038759307175377119135471724071125896012767600977654405238165616233444129512164397555141120 * q^72 + 506688790556979736999516532365405438114465768501506115275379047447697188620686370699300754640 * q^73 - 399134575097952393052355140371514479012153174980660646654807435656154590439317636650100727312 * q^74 - 2324004895287993423141911565246677610480036000604538705092119528699965986086154360593593272800 * q^75 - 6633935918720327036715040118664821987731317587536782451991725427750234686044104260504536239360 * q^76 - 6461585481973245548189356793856436395182994379442713381123224045549509062132894968864516460800 * q^77 - 28556176219359102115465270938556084350909705495286117230117205751412922131522017940137826091200 * q^78 - 30611582035787076807516826687485094690084083072098723290730859803828786802497884290624307556480 * q^79 - 127732467855339073698199167907855646502900419187610712488908375947950612344972404753625834332160 * q^80 - 105098591020590401711840147132548556253048052082258241572206720930835350937368467193794679663032 * q^81 - 68830371209738349493630432122952083611773652840970378016560437888326646942049769865516365685040 * q^82 + 22938542661502254568160041367746263129225779762371870743525183586562110235427022830971680103520 * q^83 + 361795660381091268015394970465025503071664436510904020432798379164529165144740663778138523854848 * q^84 - 65747002822668948096103688317539312015762969670721483634214688263171509401935169398146161091360 * q^85 + 2926007787385729535219437868096352598169987790407590983846487590337872781868895638215544350378656 * q^86 + 4145530857628120059159343787991300967686349677839106320836691853415365479077514876503669002112320 * q^87 + 13379567436970727806886279611606134975535418870618956336086465570267315661188646758052286051051520 * q^88 + 13262749235321210784149676214189766161707478948372569815117556700615668825668004121877579168519760 * q^89 + 18562789747759155399933926620841126049267839227249440162668332587565567838001478928890860138613680 * q^90 - 6466499581384229905399040912443724309264614193875257390824803270602537852945701184143169943974784 * q^91 - 3605940592933441273788896348672120936868261799818064643016984038777885904937799268971010435816960 * q^92 - 6218230725998946523812046145774116878209214952116357458146814759754757343477151669356631201623040 * q^93 - 111501057917354496628976353847689989005658650697758014190949880350502870630016419857891186452986752 * q^94 - 310841228909329722722502224651860795134807193058850708412373586195233672473563873013656113819102400 * q^95 - 967769551108604066125272773812882212494392412979843145463542262778370585211900025491604732868952064 * q^96 - 870148289336425543686683480565613230312583210673688585087479722135977346731183581578056793848665840 * q^97 - 1259902767579045380431363502561233259244081818944281851461225234703715688976807437199140410707221560 * q^98 - 137018494226539733211453518241879004188470623376815926515879377141376994388427950391858832640432608 * q^99

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