LMFDB - Embedded newform 1.100.a.a.1.3

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			1.3
Root			$-9.79932e12$ 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)

$f(q)$	$=$	$q-7.31556e14 q^{2} -2.11461e23 q^{3} -9.86512e28 q^{4} +5.46163e34 q^{5} +1.54696e38 q^{6} -9.42405e41 q^{7} +5.35848e44 q^{8} -1.27077e47 q^{9} +O(q^{10})$	\(q-7.31556e14 q^{2} -2.11461e23 q^{3} -9.86512e28 q^{4} +5.46163e34 q^{5} +1.54696e38 q^{6} -9.42405e41 q^{7} +5.35848e44 q^{8} -1.27077e47 q^{9} -3.99548e49 q^{10} +6.80844e51 q^{11} +2.08609e52 q^{12} +1.27244e55 q^{13} +6.89422e56 q^{14} -1.15492e58 q^{15} -3.29475e59 q^{16} +1.40992e60 q^{17} +9.29638e61 q^{18} -1.83028e63 q^{19} -5.38796e63 q^{20} +1.99282e65 q^{21} -4.98075e66 q^{22} +7.80909e66 q^{23} -1.13311e68 q^{24} +1.40521e69 q^{25} -9.30860e69 q^{26} +6.31992e70 q^{27} +9.29694e70 q^{28} -4.49461e72 q^{29} +8.44889e72 q^{30} -6.78211e73 q^{31} -9.86044e73 q^{32} -1.43972e75 q^{33} -1.03144e75 q^{34} -5.14706e76 q^{35} +1.25363e76 q^{36} +1.72780e77 q^{37} +1.33895e78 q^{38} -2.69071e78 q^{39} +2.92660e79 q^{40} -3.13802e78 q^{41} -1.45786e80 q^{42} +1.67273e80 q^{43} -6.71660e80 q^{44} -6.94046e81 q^{45} -5.71278e81 q^{46} +5.53499e82 q^{47} +6.96711e82 q^{48} +4.26060e83 q^{49} -1.02799e84 q^{50} -2.98144e83 q^{51} -1.25527e84 q^{52} -9.83283e84 q^{53} -4.62337e85 q^{54} +3.71851e86 q^{55} -5.04986e86 q^{56} +3.87034e86 q^{57} +3.28806e87 q^{58} -2.85418e87 q^{59} +1.13934e87 q^{60} -7.36889e87 q^{61} +4.96150e88 q^{62} +1.19758e89 q^{63} +2.80964e89 q^{64} +6.94958e89 q^{65} +1.05324e90 q^{66} +2.22058e90 q^{67} -1.39091e89 q^{68} -1.65132e90 q^{69} +3.76537e91 q^{70} +7.03212e91 q^{71} -6.80938e91 q^{72} +1.65280e92 q^{73} -1.26398e92 q^{74} -2.97148e92 q^{75} +1.80560e92 q^{76} -6.41631e93 q^{77} +1.96841e93 q^{78} -2.18798e93 q^{79} -1.79947e94 q^{80} +8.46667e93 q^{81} +2.29564e93 q^{82} -6.95611e94 q^{83} -1.96594e94 q^{84} +7.70048e94 q^{85} -1.22369e95 q^{86} +9.50434e95 q^{87} +3.64828e96 q^{88} +8.71787e95 q^{89} +5.07733e96 q^{90} -1.19915e97 q^{91} -7.70375e95 q^{92} +1.43415e97 q^{93} -4.04915e97 q^{94} -9.99632e97 q^{95} +2.08510e97 q^{96} +1.85375e98 q^{97} -3.11686e98 q^{98} -8.65194e98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.31556e14	−0.918888	−0.459444	−	0.888207i	$-0.651951\pi$
$2$	−7.31556e14	−0.918888	−0.459444	+	0.888207i	$0.651951\pi$
$3$	−2.11461e23	−0.510186	−0.255093	−	0.966917i	$-0.582106\pi$
$3$	−2.11461e23	−0.510186	−0.255093	+	0.966917i	$0.582106\pi$
$4$	−9.86512e28	−0.155644
$5$	5.46163e34	1.37501	0.687506	−	0.726178i	$-0.258705\pi$
$5$	5.46163e34	1.37501	0.687506	+	0.726178i	$0.258705\pi$
$6$	1.54696e38	0.468804
$7$	−9.42405e41	−1.38639	−0.693194	−	0.720751i	$-0.743797\pi$
$7$	−9.42405e41	−1.38639	−0.693194	+	0.720751i	$0.743797\pi$
$8$	5.35848e44	1.06191
$9$	−1.27077e47	−0.739711
$10$	−3.99548e49	−1.26348
$11$	6.80844e51	1.92358	0.961788	−	0.273794i	$-0.0882787\pi$
$11$	6.80844e51	1.92358	0.961788	+	0.273794i	$0.0882787\pi$
$12$	2.08609e52	0.0794074
$13$	1.27244e55	0.921384	0.460692	−	0.887560i	$-0.347601\pi$
$13$	1.27244e55	0.921384	0.460692	+	0.887560i	$0.347601\pi$
$14$	6.89422e56	1.27394
$15$	−1.15492e58	−0.701512
$16$	−3.29475e59	−0.820131
$17$	1.40992e60	0.174572	0.0872860	−	0.996183i	$-0.472181\pi$
$17$	1.40992e60	0.174572	0.0872860	+	0.996183i	$0.472181\pi$
$18$	9.29638e61	0.679712
$19$	−1.83028e63	−0.920906	−0.460453	−	0.887684i	$-0.652313\pi$
$19$	−1.83028e63	−0.920906	−0.460453	+	0.887684i	$0.652313\pi$
$20$	−5.38796e63	−0.214013
$21$	1.99282e65	0.707315
$22$	−4.98075e66	−1.76755
$23$	7.80909e66	0.306953	0.153477	−	0.988152i	$-0.450953\pi$
$23$	7.80909e66	0.306953	0.153477	+	0.988152i	$0.450953\pi$
$24$	−1.13311e68	−0.541770
$25$	1.40521e69	0.890660
$26$	−9.30860e69	−0.846649
$27$	6.31992e70	0.887575
$28$	9.29694e70	0.215783
$29$	−4.49461e72	−1.83650	−0.918250	−	0.396001i	$-0.870398\pi$
$29$	−4.49461e72	−1.83650	−0.918250	+	0.396001i	$0.870398\pi$
$30$	8.44889e72	0.644611
$31$	−6.78211e73	−1.02085	−0.510424	−	0.859923i	$-0.670512\pi$
$31$	−6.78211e73	−1.02085	−0.510424	+	0.859923i	$0.670512\pi$
$32$	−9.86044e73	−0.308299
$33$	−1.43972e75	−0.981381
$34$	−1.03144e75	−0.160412
$35$	−5.14706e76	−1.90630
$36$	1.25363e76	0.115132
$37$	1.72780e77	0.408797	0.204399	−	0.978888i	$-0.434476\pi$
$37$	1.72780e77	0.408797	0.204399	+	0.978888i	$0.434476\pi$
$38$	1.33895e78	0.846209
$39$	−2.69071e78	−0.470077
$40$	2.92660e79	1.46014
$41$	−3.13802e78	−0.0461164	−0.0230582	−	0.999734i	$-0.507340\pi$
$41$	−3.13802e78	−0.0461164	−0.0230582	+	0.999734i	$0.507340\pi$
$42$	−1.45786e80	−0.649944
$43$	1.67273e80	0.232668	0.116334	−	0.993210i	$-0.462886\pi$
$43$	1.67273e80	0.232668	0.116334	+	0.993210i	$0.462886\pi$
$44$	−6.71660e80	−0.299393
$45$	−6.94046e81	−1.01711
$46$	−5.71278e81	−0.282056
$47$	5.53499e82	0.942481	0.471241	−	0.882005i	$-0.343806\pi$
$47$	5.53499e82	0.942481	0.471241	+	0.882005i	$0.343806\pi$
$48$	6.96711e82	0.418419
$49$	4.26060e83	0.922071
$50$	−1.02799e84	−0.818417
$51$	−2.98144e83	−0.0890641
$52$	−1.25527e84	−0.143408
$53$	−9.83283e84	−0.437545	−0.218773	−	0.975776i	$-0.570205\pi$
$53$	−9.83283e84	−0.437545	−0.218773	+	0.975776i	$0.570205\pi$
$54$	−4.62337e85	−0.815583
$55$	3.71851e86	2.64494
$56$	−5.04986e86	−1.47222
$57$	3.87034e86	0.469833
$58$	3.28806e87	1.68754
$59$	−2.85418e87	−0.628503	−0.314251	−	0.949340i	$-0.601753\pi$
$59$	−2.85418e87	−0.628503	−0.314251	+	0.949340i	$0.601753\pi$
$60$	1.13934e87	0.109186
$61$	−7.36889e87	−0.311584	−0.155792	−	0.987790i	$-0.549793\pi$
$61$	−7.36889e87	−0.311584	−0.155792	+	0.987790i	$0.549793\pi$
$62$	4.96150e88	0.938046
$63$	1.19758e89	1.02553
$64$	2.80964e89	1.10342
$65$	6.94958e89	1.26691
$66$	1.05324e90	0.901780
$67$	2.22058e90	0.903159	0.451580	−	0.892231i	$-0.350861\pi$
$67$	2.22058e90	0.903159	0.451580	+	0.892231i	$0.350861\pi$
$68$	−1.39091e89	−0.0271711
$69$	−1.65132e90	−0.156603
$70$	3.76537e91	1.75168
$71$	7.03212e91	1.62106	0.810528	−	0.585699i	$-0.199180\pi$
$71$	7.03212e91	1.62106	0.810528	+	0.585699i	$0.199180\pi$
$72$	−6.80938e91	−0.785505
$73$	1.65280e92	0.963250	0.481625	−	0.876377i	$-0.340047\pi$
$73$	1.65280e92	0.963250	0.481625	+	0.876377i	$0.340047\pi$
$74$	−1.26398e92	−0.375639
$75$	−2.97148e92	−0.454402
$76$	1.80560e92	0.143334
$77$	−6.41631e93	−2.66682
$78$	1.96841e93	0.431948
$79$	−2.18798e93	−0.255566	−0.127783	−	0.991802i	$-0.540786\pi$
$79$	−2.18798e93	−0.255566	−0.127783	+	0.991802i	$0.540786\pi$
$80$	−1.79947e94	−1.12769
$81$	8.46667e93	0.286882
$82$	2.29564e93	0.0423758
$83$	−6.95611e94	−0.704695	−0.352347	−	0.935869i	$-0.614616\pi$
$83$	−6.95611e94	−0.704695	−0.352347	+	0.935869i	$0.614616\pi$
$84$	−1.96594e94	−0.110089
$85$	7.70048e94	0.240039
$86$	−1.22369e95	−0.213796
$87$	9.50434e95	0.936956
$88$	3.64828e96	2.04266
$89$	8.71787e95	0.279000	0.139500	−	0.990222i	$-0.455450\pi$
$89$	8.71787e95	0.279000	0.139500	+	0.990222i	$0.455450\pi$
$90$	5.07733e96	0.934612
$91$	−1.19915e97	−1.27740
$92$	−7.70375e95	−0.0477755
$93$	1.43415e97	0.520822
$94$	−4.04915e97	−0.866035
$95$	−9.99632e97	−1.26626
$96$	2.08510e97	0.157290
$97$	1.85375e98	0.837239	0.418620	−	0.908162i	$-0.362514\pi$
$97$	1.85375e98	0.837239	0.418620	+	0.908162i	$0.362514\pi$
$98$	−3.11686e98	−0.847280
$99$	−8.65194e98	−1.42289
$100$	−1.38626e98	−0.138626
$101$	1.68468e99	1.02946	0.514730	−	0.857353i	$-0.327892\pi$
$101$	1.68468e99	1.02946	0.514730	+	0.857353i	$0.327892\pi$
$102$	2.18109e98	0.0818400
$103$	−1.52597e99	−0.353267	−0.176633	−	0.984277i	$-0.556521\pi$
$103$	−1.52597e99	−0.353267	−0.176633	+	0.984277i	$0.556521\pi$
$104$	6.81833e99	0.978425
$105$	1.08840e100	0.972567
$106$	7.19326e99	0.402055
$107$	2.57114e100	0.902878	0.451439	−	0.892302i	$-0.350911\pi$
$107$	2.57114e100	0.902878	0.451439	+	0.892302i	$0.350911\pi$
$108$	−6.23467e99	−0.138146
$109$	2.02085e98	0.00283741	0.00141870	−	0.999999i	$-0.499548\pi$
$109$	2.02085e98	0.00283741	0.00141870	+	0.999999i	$0.499548\pi$
$110$	−2.72030e101	−2.43041
$111$	−3.65362e100	−0.208563
$112$	3.10499e101	1.13702
$113$	−4.90442e101	−1.15666	−0.578329	−	0.815804i	$-0.696295\pi$
$113$	−4.90442e101	−1.15666	−0.578329	+	0.815804i	$0.696295\pi$
$114$	−2.83137e101	−0.431724
$115$	4.26503e101	0.422065
$116$	4.43398e101	0.285840
$117$	−1.61697e102	−0.681558
$118$	2.08799e102	0.577524
$119$	−1.32872e102	−0.242024
$120$	−6.18862e102	−0.744941
$121$	3.38270e103	2.70015
$122$	5.39075e102	0.286311
$123$	6.63569e101	0.0235279
$124$	6.69063e102	0.158889
$125$	−9.42174e102	−0.150344
$126$	−8.76095e103	−0.942344
$127$	−4.46955e103	−0.325072	−0.162536	−	0.986703i	$-0.551967\pi$
$127$	−4.46955e103	−0.325072	−0.162536	+	0.986703i	$0.551967\pi$
$128$	−1.43043e104	−0.705624
$129$	−3.53717e103	−0.118704
$130$	−5.08401e104	−1.16415
$131$	2.41669e104	0.378697	0.189348	−	0.981910i	$-0.439362\pi$
$131$	2.41669e104	0.378697	0.189348	+	0.981910i	$0.439362\pi$
$132$	1.42030e104	0.152746
$133$	1.72487e105	1.27673
$134$	−1.62448e105	−0.829903
$135$	3.45170e105	1.22043
$136$	7.55505e104	0.185379
$137$	−2.42346e105	−0.413778	−0.206889	−	0.978364i	$-0.566334\pi$
$137$	−2.42346e105	−0.413778	−0.206889	+	0.978364i	$0.566334\pi$
$138$	1.20803e105	0.143901
$139$	8.76713e105	0.730508	0.365254	−	0.930908i	$-0.380982\pi$
$139$	8.76713e105	0.730508	0.365254	+	0.930908i	$0.380982\pi$
$140$	5.07764e105	0.296704
$141$	−1.17043e106	−0.480840
$142$	−5.14439e106	−1.48957
$143$	8.66331e106	1.77235
$144$	4.18686e106	0.606660
$145$	−2.45479e107	−2.52521
$146$	−1.20912e107	−0.885119
$147$	−9.00950e106	−0.470427
$148$	−1.70450e106	−0.0636269
$149$	4.85752e107	1.29926	0.649628	−	0.760252i	$-0.274925\pi$
$149$	4.85752e107	1.29926	0.649628	+	0.760252i	$0.274925\pi$
$150$	2.17380e107	0.417545
$151$	1.15800e108	1.60084	0.800422	−	0.599437i	$-0.204609\pi$
$151$	1.15800e108	1.60084	0.800422	+	0.599437i	$0.204609\pi$
$152$	−9.80753e107	−0.977917
$153$	−1.79169e107	−0.129133
$154$	4.69389e108	2.45051
$155$	−3.70414e108	−1.40368
$156$	2.65442e107	0.0731647
$157$	−6.69272e108	−1.34453	−0.672264	−	0.740312i	$-0.734678\pi$
$157$	−6.69272e108	−1.34453	−0.672264	+	0.740312i	$0.734678\pi$
$158$	1.60063e108	0.234836
$159$	2.07926e108	0.223229
$160$	−5.38540e108	−0.423915
$161$	−7.35932e108	−0.425556
$162$	−6.19384e108	−0.263613
$163$	1.42458e109	0.447097	0.223548	−	0.974693i	$-0.428236\pi$
$163$	1.42458e109	0.447097	0.223548	+	0.974693i	$0.428236\pi$
$164$	3.09569e107	0.00717774
$165$	−7.86321e109	−1.34941
$166$	5.08878e109	0.647536
$167$	9.67468e109	0.914473	0.457237	−	0.889345i	$-0.348839\pi$
$167$	9.67468e109	0.914473	0.457237	+	0.889345i	$0.348839\pi$
$168$	1.06785e110	0.751103
$169$	−2.88082e109	−0.151051
$170$	−5.63333e109	−0.220569
$171$	2.32586e110	0.681204
$172$	−1.65017e109	−0.0362134
$173$	1.01986e111	1.67981	0.839905	−	0.542734i	$-0.182611\pi$
$173$	1.01986e111	1.67981	0.839905	+	0.542734i	$0.182611\pi$
$174$	−6.95296e110	−0.860958
$175$	−1.32428e111	−1.23480
$176$	−2.24321e111	−1.57758
$177$	6.03548e110	0.320653
$178$	−6.37761e110	−0.256370
$179$	−1.78728e111	−0.544463	−0.272232	−	0.962232i	$-0.587762\pi$
$179$	−1.78728e111	−0.544463	−0.272232	+	0.962232i	$0.587762\pi$
$180$	6.84684e110	0.158307
$181$	1.57402e111	0.276643	0.138322	−	0.990387i	$-0.455829\pi$
$181$	1.57402e111	0.276643	0.138322	+	0.990387i	$0.455829\pi$
$182$	8.77247e111	1.17378
$183$	1.55823e111	0.158966
$184$	4.18448e111	0.325956
$185$	9.43660e111	0.562102
$186$	−1.04916e112	−0.478577
$187$	9.59939e111	0.335802
$188$	−5.46033e111	−0.146692
$189$	−5.95593e112	−1.23052
$190$	7.31287e112	1.16355
$191$	2.95228e112	0.362248	0.181124	−	0.983460i	$-0.442027\pi$
$191$	2.95228e112	0.362248	0.181124	+	0.983460i	$0.442027\pi$
$192$	−5.94130e112	−0.562951
$193$	1.95641e112	0.143342	0.0716709	−	0.997428i	$-0.477167\pi$
$193$	1.95641e112	0.143342	0.0716709	+	0.997428i	$0.477167\pi$
$194$	−1.35612e113	−0.769330
$195$	−1.46957e113	−0.646362
$196$	−4.20313e112	−0.143515
$197$	−5.55253e113	−1.47371	−0.736856	−	0.676050i	$-0.763691\pi$
$197$	−5.55253e113	−1.47371	−0.736856	+	0.676050i	$0.763691\pi$
$198$	6.32938e113	1.30748
$199$	3.07478e113	0.494979	0.247489	−	0.968891i	$-0.420394\pi$
$199$	3.07478e113	0.494979	0.247489	+	0.968891i	$0.420394\pi$
$200$	7.52980e113	0.945799
$201$	−4.69567e113	−0.460779
$202$	−1.23244e114	−0.945958
$203$	4.23574e114	2.54610
$204$	2.94123e112	0.0138623
$205$	−1.71387e113	−0.0634106
$206$	1.11633e114	0.324613
$207$	−9.92353e113	−0.227057
$208$	−4.19236e114	−0.755655
$209$	−1.24614e115	−1.77143
$210$	−7.96228e114	−0.893681
$211$	1.95393e115	1.73352	0.866758	−	0.498730i	$-0.166200\pi$
$211$	1.95393e115	1.73352	0.866758	+	0.498730i	$0.166200\pi$
$212$	9.70020e113	0.0681013
$213$	−1.48702e115	−0.827040
$214$	−1.88093e115	−0.829644
$215$	9.13581e114	0.319921
$216$	3.38651e115	0.942523
$217$	6.39150e115	1.41529
$218$	−1.47836e113	−0.00260726
$219$	−3.49503e115	−0.491436
$220$	−3.66836e115	−0.411670
$221$	1.79404e115	0.160848
$222$	2.67283e115	0.191646
$223$	3.84088e115	0.220465	0.110233	−	0.993906i	$-0.464840\pi$
$223$	3.84088e115	0.220465	0.110233	+	0.993906i	$0.464840\pi$
$224$	9.29253e115	0.427422
$225$	−1.78570e116	−0.658831
$226$	3.58786e116	1.06284
$227$	−2.68414e116	−0.639036	−0.319518	−	0.947580i	$-0.603521\pi$
$227$	−2.68414e116	−0.639036	−0.319518	+	0.947580i	$0.603521\pi$
$228$	−3.81813e115	−0.0731267
$229$	−1.28789e117	−1.98619	−0.993095	−	0.117312i	$-0.962572\pi$
$229$	−1.28789e117	−1.98619	−0.993095	+	0.117312i	$0.962572\pi$
$230$	−3.12011e116	−0.387830
$231$	1.35680e117	1.36057
$232$	−2.40842e117	−1.95019
$233$	8.81640e116	0.576997	0.288498	−	0.957480i	$-0.406844\pi$
$233$	8.81640e116	0.576997	0.288498	+	0.957480i	$0.406844\pi$
$234$	1.18291e117	0.626275
$235$	3.02300e117	1.29592
$236$	2.81568e116	0.0978228
$237$	4.62673e116	0.130386
$238$	9.72034e116	0.222393
$239$	3.99091e117	0.741952	0.370976	−	0.928642i	$-0.379023\pi$
$239$	3.99091e117	0.741952	0.370976	+	0.928642i	$0.379023\pi$
$240$	3.80517e117	0.575331
$241$	4.49958e117	0.553769	0.276884	−	0.960903i	$-0.410698\pi$
$241$	4.49958e117	0.553769	0.276884	+	0.960903i	$0.410698\pi$
$242$	−2.47463e118	−2.48113
$243$	−1.26475e118	−1.03394
$244$	7.26949e116	0.0484962
$245$	2.32698e118	1.26786
$246$	−4.85438e116	−0.0216195
$247$	−2.32892e118	−0.848508
$248$	−3.63418e118	−1.08405
$249$	1.47095e118	0.359525
$250$	6.89253e117	0.138149
$251$	4.93146e118	0.811197	0.405599	−	0.914051i	$-0.367063\pi$
$251$	4.93146e118	0.811197	0.405599	+	0.914051i	$0.367063\pi$
$252$	−1.18142e118	−0.159617
$253$	5.31677e118	0.590448
$254$	3.26973e118	0.298705
$255$	−1.62835e118	−0.122464
$256$	−7.34382e118	−0.455034
$257$	1.76024e119	0.899256	0.449628	−	0.893216i	$-0.351557\pi$
$257$	1.76024e119	0.899256	0.449628	+	0.893216i	$0.351557\pi$
$258$	2.58764e118	0.109076
$259$	−1.62829e119	−0.566752
$260$	−6.85584e118	−0.197188
$261$	5.71160e119	1.35848
$262$	−1.76794e119	−0.347980
$263$	8.39054e118	0.136767	0.0683834	−	0.997659i	$-0.478216\pi$
$263$	8.39054e118	0.136767	0.0683834	+	0.997659i	$0.478216\pi$
$264$	−7.71470e119	−1.04214
$265$	−5.37032e119	−0.601630
$266$	−1.26184e120	−1.17317
$267$	−1.84349e119	−0.142342
$268$	−2.19063e119	−0.140571
$269$	2.54624e120	1.35882	0.679410	−	0.733759i	$-0.262236\pi$
$269$	2.54624e120	1.35882	0.679410	+	0.733759i	$0.262236\pi$
$270$	−2.52511e120	−1.12144
$271$	3.10717e120	1.14917	0.574587	−	0.818444i	$-0.305163\pi$
$271$	3.10717e120	1.14917	0.574587	+	0.818444i	$0.305163\pi$
$272$	−4.64535e119	−0.143172
$273$	2.53574e120	0.651709
$274$	1.77289e120	0.380215
$275$	9.56731e120	1.71325
$276$	1.62904e119	0.0243744
$277$	−5.18719e120	−0.648909	−0.324454	−	0.945901i	$-0.605181\pi$
$277$	−5.18719e120	−0.648909	−0.324454	+	0.945901i	$0.605181\pi$
$278$	−6.41365e120	−0.671255
$279$	8.61849e120	0.755132
$280$	−2.75804e121	−2.02432
$281$	−2.03299e121	−1.25075	−0.625377	−	0.780323i	$-0.715055\pi$
$281$	−2.03299e121	−1.25075	−0.625377	+	0.780323i	$0.715055\pi$
$282$	8.56238e120	0.441839
$283$	3.13687e121	1.35853	0.679264	−	0.733894i	$-0.262299\pi$
$283$	3.13687e121	1.35853	0.679264	+	0.733894i	$0.262299\pi$
$284$	−6.93727e120	−0.252308
$285$	2.11383e121	0.646026
$286$	−6.33770e121	−1.62859
$287$	2.95729e120	0.0639351
$288$	1.25303e121	0.228052
$289$	−6.32415e121	−0.969525
$290$	1.79581e122	2.32039
$291$	−3.91995e121	−0.427148
$292$	−1.63051e121	−0.149924
$293$	4.12897e121	0.320549	0.160275	−	0.987072i	$-0.448762\pi$
$293$	4.12897e121	0.320549	0.160275	+	0.987072i	$0.448762\pi$
$294$	6.59095e121	0.432270
$295$	−1.55885e122	−0.864199
$296$	9.25838e121	0.434105
$297$	4.30288e122	1.70732
$298$	−3.55355e122	−1.19387
$299$	9.93658e121	0.282822
$300$	2.93140e121	0.0707250
$301$	−1.57639e122	−0.322568
$302$	−8.47141e122	−1.47100
$303$	−3.56244e122	−0.525215
$304$	6.03032e122	0.755263
$305$	−4.02461e122	−0.428432
$306$	1.31072e122	0.118659
$307$	−1.79941e123	−1.38606	−0.693029	−	0.720909i	$-0.743724\pi$
$307$	−1.79941e123	−1.38606	−0.693029	+	0.720909i	$0.743724\pi$
$308$	6.32976e122	0.415075
$309$	3.22683e122	0.180232
$310$	2.70978e123	1.28982
$311$	3.27772e123	1.33025	0.665123	−	0.746733i	$-0.268379\pi$
$311$	3.27772e123	1.33025	0.665123	+	0.746733i	$0.268379\pi$
$312$	−1.44181e123	−0.499178
$313$	−3.03613e123	−0.897171	−0.448586	−	0.893740i	$-0.648072\pi$
$313$	−3.03613e123	−0.897171	−0.448586	+	0.893740i	$0.648072\pi$
$314$	4.89610e123	1.23547
$315$	6.54072e123	1.41011
$316$	2.15847e122	0.0397773
$317$	−4.26809e123	−0.672667	−0.336334	−	0.941743i	$-0.609187\pi$
$317$	−4.26809e123	−0.672667	−0.336334	+	0.941743i	$0.609187\pi$
$318$	−1.52110e123	−0.205123
$319$	−3.06013e124	−3.53265
$320$	1.53452e124	1.51722
$321$	−5.43696e123	−0.460636
$322$	5.38376e123	0.391039
$323$	−2.58056e123	−0.160764
$324$	−8.35246e122	−0.0446516
$325$	1.78805e124	0.820640
$326$	−1.04216e124	−0.410832
$327$	−4.27330e121	−0.00144760
$328$	−1.68150e123	−0.0489713
$329$	−5.21620e124	−1.30664
$330$	5.75238e124	1.23996
$331$	5.61983e124	1.04289	0.521443	−	0.853286i	$-0.325394\pi$
$331$	5.61983e124	1.04289	0.521443	+	0.853286i	$0.325394\pi$
$332$	6.86228e123	0.109682
$333$	−2.19563e124	−0.302392
$334$	−7.07757e124	−0.840299
$335$	1.21280e125	1.24186
$336$	−6.56584e124	−0.580091
$337$	1.23831e125	0.944388	0.472194	−	0.881495i	$-0.343462\pi$
$337$	1.23831e125	0.944388	0.472194	+	0.881495i	$0.343462\pi$
$338$	2.10748e124	0.138799
$339$	1.03709e125	0.590110
$340$	−7.59662e123	−0.0373606
$341$	−4.61756e125	−1.96368
$342$	−1.70150e125	−0.625950
$343$	3.39346e124	0.108040
$344$	8.96327e124	0.247072
$345$	−9.01888e124	−0.215331
$346$	−7.46087e125	−1.54356
$347$	−1.38039e124	−0.0247567	−0.0123784	−	0.999923i	$-0.503940\pi$
$347$	−1.38039e124	−0.0247567	−0.0123784	+	0.999923i	$0.503940\pi$
$348$	−9.37615e124	−0.145832
$349$	1.26018e126	1.70049	0.850244	−	0.526388i	$-0.176454\pi$
$349$	1.26018e126	1.70049	0.850244	+	0.526388i	$0.176454\pi$
$350$	9.68786e125	1.13464
$351$	8.04171e125	0.817798
$352$	−6.71342e125	−0.593037
$353$	−1.32876e126	−1.02000	−0.509999	−	0.860175i	$-0.670354\pi$
$353$	−1.32876e126	−1.02000	−0.509999	+	0.860175i	$0.670354\pi$
$354$	−4.41529e125	−0.294644
$355$	3.84068e126	2.22897
$356$	−8.60028e124	−0.0434248
$357$	2.80973e125	0.123477
$358$	1.30750e126	0.500301
$359$	−3.79958e126	−1.26637	−0.633184	−	0.774001i	$-0.718252\pi$
$359$	−3.79958e126	−1.26637	−0.633184	+	0.774001i	$0.718252\pi$
$360$	−3.71903e126	−1.08008
$361$	−6.00148e125	−0.151933
$362$	−1.15148e126	−0.254204
$363$	−7.15309e126	−1.37758
$364$	1.18298e126	0.198819
$365$	9.02698e126	1.32448
$366$	−1.13993e126	−0.146072
$367$	3.60030e126	0.403059	0.201529	−	0.979482i	$-0.435409\pi$
$367$	3.60030e126	0.403059	0.201529	+	0.979482i	$0.435409\pi$
$368$	−2.57290e126	−0.251742
$369$	3.98770e125	0.0341128
$370$	−6.90340e126	−0.516509
$371$	9.26651e126	0.606607
$372$	−1.41481e126	−0.0810629
$373$	1.78308e127	0.894504	0.447252	−	0.894408i	$-0.352403\pi$
$373$	1.78308e127	0.894504	0.447252	+	0.894408i	$0.352403\pi$
$374$	−7.02249e126	−0.308565
$375$	1.99233e126	0.0767032
$376$	2.96591e127	1.00083
$377$	−5.71911e127	−1.69212
$378$	4.35709e127	1.13071
$379$	−9.09562e126	−0.207105	−0.103553	−	0.994624i	$-0.533021\pi$
$379$	−9.09562e126	−0.207105	−0.103553	+	0.994624i	$0.533021\pi$
$380$	9.86149e126	0.197085
$381$	9.45136e126	0.165847
$382$	−2.15976e127	−0.332865
$383$	9.32015e127	1.26207	0.631035	−	0.775754i	$-0.282630\pi$
$383$	9.32015e127	1.26207	0.631035	+	0.775754i	$0.282630\pi$
$384$	3.02480e127	0.359999
$385$	−3.50435e128	−3.66692
$386$	−1.43122e127	−0.131715
$387$	−2.12565e127	−0.172107
$388$	−1.82874e127	−0.130311
$389$	−4.49313e126	−0.0281866	−0.0140933	−	0.999901i	$-0.504486\pi$
$389$	−4.49313e126	−0.0281866	−0.0140933	+	0.999901i	$0.504486\pi$
$390$	1.07507e128	0.593934
$391$	1.10102e127	0.0535854
$392$	2.28303e128	0.979154
$393$	−5.11036e127	−0.193206
$394$	4.06199e128	1.35418
$395$	−1.19499e128	−0.351406
$396$	8.53524e127	0.221464
$397$	6.57051e128	1.50477	0.752383	−	0.658726i	$-0.228904\pi$
$397$	6.57051e128	1.50477	0.752383	+	0.658726i	$0.228904\pi$
$398$	−2.24937e128	−0.454830
$399$	−3.64742e128	−0.651370
$400$	−4.62983e128	−0.730458
$401$	1.75015e128	0.244021	0.122011	−	0.992529i	$-0.461066\pi$
$401$	1.75015e128	0.244021	0.122011	+	0.992529i	$0.461066\pi$
$402$	3.43514e128	0.423404
$403$	−8.62982e128	−0.940593
$404$	−1.66196e128	−0.160229
$405$	4.62418e128	0.394467
$406$	−3.09868e129	−2.33958
$407$	1.17636e129	0.786353
$408$	−1.59760e128	−0.0945779
$409$	8.41409e128	0.441269	0.220635	−	0.975357i	$-0.429187\pi$
$409$	8.41409e128	0.441269	0.220635	+	0.975357i	$0.429187\pi$
$410$	1.25379e128	0.0582672
$411$	5.12466e128	0.211103
$412$	1.50539e128	0.0549839
$413$	2.68980e129	0.871349
$414$	7.25962e128	0.208640
$415$	−3.79917e129	−0.968964
$416$	−1.25468e129	−0.284062
$417$	−1.85391e129	−0.372695
$418$	9.11619e129	1.62775
$419$	4.04316e129	0.641397	0.320699	−	0.947181i	$-0.396082\pi$
$419$	4.04316e129	0.641397	0.320699	+	0.947181i	$0.396082\pi$
$420$	−1.07372e129	−0.151374
$421$	1.07790e130	1.35088	0.675439	−	0.737416i	$-0.263954\pi$
$421$	1.07790e130	1.35088	0.675439	+	0.737416i	$0.263954\pi$
$422$	−1.42941e130	−1.59291
$423$	−7.03368e129	−0.697163
$424$	−5.26890e129	−0.464633
$425$	1.98125e129	0.155484
$426$	1.08784e130	0.759957
$427$	6.94448e129	0.431976
$428$	−2.53646e129	−0.140528
$429$	−1.83195e130	−0.904229
$430$	−6.68336e129	−0.293972
$431$	−1.40330e130	−0.550206	−0.275103	−	0.961415i	$-0.588712\pi$
$431$	−1.40330e130	−0.550206	−0.275103	+	0.961415i	$0.588712\pi$
$432$	−2.08225e130	−0.727928
$433$	1.62667e130	0.507165	0.253583	−	0.967314i	$-0.418391\pi$
$433$	1.62667e130	0.507165	0.253583	+	0.967314i	$0.418391\pi$
$434$	−4.67574e130	−1.30049
$435$	5.19092e130	1.28833
$436$	−1.99359e127	−0.000441626 0
$437$	−1.42928e130	−0.282675
$438$	2.55681e130	0.451575
$439$	5.92513e130	0.934769	0.467385	−	0.884054i	$-0.345196\pi$
$439$	5.92513e130	0.934769	0.467385	+	0.884054i	$0.345196\pi$
$440$	1.99256e131	2.80869
$441$	−5.41423e130	−0.682066
$442$	−1.31244e130	−0.147801
$443$	−8.59362e130	−0.865350	−0.432675	−	0.901550i	$-0.642430\pi$
$443$	−8.59362e130	−0.865350	−0.432675	+	0.901550i	$0.642430\pi$
$444$	3.60434e129	0.0324615
$445$	4.76137e130	0.383629
$446$	−2.80982e130	−0.202583
$447$	−1.02718e131	−0.662862
$448$	−2.64782e131	−1.52977
$449$	−4.65840e130	−0.241014	−0.120507	−	0.992712i	$-0.538452\pi$
$449$	−4.65840e130	−0.241014	−0.120507	+	0.992712i	$0.538452\pi$
$450$	1.30634e131	0.605392
$451$	−2.13650e130	−0.0887083
$452$	4.83827e130	0.180027
$453$	−2.44872e131	−0.816728
$454$	1.96360e131	0.587203
$455$	−6.54932e131	−1.75644
$456$	2.07391e131	0.498919
$457$	6.36535e131	1.37395	0.686974	−	0.726682i	$-0.258939\pi$
$457$	6.36535e131	1.37395	0.686974	+	0.726682i	$0.258939\pi$
$458$	9.42160e131	1.82509
$459$	8.91061e130	0.154946
$460$	−4.20750e130	−0.0656919
$461$	−1.06429e132	−1.49233	−0.746167	−	0.665759i	$-0.768108\pi$
$461$	−1.06429e132	−1.49233	−0.746167	+	0.665759i	$0.768108\pi$
$462$	−9.92574e131	−1.25022
$463$	7.81359e130	0.0884283	0.0442142	−	0.999022i	$-0.485922\pi$
$463$	7.81359e130	0.0884283	0.0442142	+	0.999022i	$0.485922\pi$
$464$	1.48086e132	1.50617
$465$	7.83280e131	0.716137
$466$	−6.44969e131	−0.530196
$467$	2.28637e132	1.69029	0.845143	−	0.534541i	$-0.179515\pi$
$467$	2.28637e132	1.69029	0.845143	+	0.534541i	$0.179515\pi$
$468$	1.59516e131	0.106080
$469$	−2.09269e132	−1.25213
$470$	−2.21150e132	−1.19081
$471$	1.41525e132	0.685958
$472$	−1.52941e132	−0.667412
$473$	1.13887e132	0.447555
$474$	−3.38471e131	−0.119810
$475$	−2.57194e132	−0.820214
$476$	1.31080e131	0.0376697
$477$	1.24952e132	0.323657
$478$	−2.91957e132	−0.681771
$479$	−1.65589e132	−0.348678	−0.174339	−	0.984686i	$-0.555779\pi$
$479$	−1.65589e132	−0.348678	−0.174339	+	0.984686i	$0.555779\pi$
$480$	1.13880e132	0.216276
$481$	2.19852e132	0.376660
$482$	−3.29169e132	−0.508852
$483$	1.55621e132	0.217113
$484$	−3.33707e132	−0.420262
$485$	1.01245e133	1.15121
$486$	9.25237e132	0.950074
$487$	1.90824e133	1.76991	0.884953	−	0.465680i	$-0.154190\pi$
$487$	1.90824e133	1.76991	0.884953	+	0.465680i	$0.154190\pi$
$488$	−3.94860e132	−0.330874
$489$	−3.01244e132	−0.228102
$490$	−1.70231e133	−1.16502
$491$	9.77870e132	0.604989	0.302494	−	0.953151i	$-0.402181\pi$
$491$	9.77870e132	0.604989	0.302494	+	0.953151i	$0.402181\pi$
$492$	−6.54619e130	−0.00366198
$493$	−6.33706e132	−0.320601
$494$	1.70374e133	0.779684
$495$	−4.72537e133	−1.95649
$496$	2.23454e133	0.837229
$497$	−6.62711e133	−2.24741
$498$	−1.07608e133	−0.330363
$499$	3.90207e133	1.08472	0.542361	−	0.840146i	$-0.317531\pi$
$499$	3.90207e133	1.08472	0.542361	+	0.840146i	$0.317531\pi$
$500$	9.29466e131	0.0234001
$501$	−2.04582e133	−0.466551
$502$	−3.60764e133	−0.745400
$503$	1.53390e133	0.287199	0.143599	−	0.989636i	$-0.454132\pi$
$503$	1.53390e133	0.287199	0.143599	+	0.989636i	$0.454132\pi$
$504$	6.41719e133	1.08901
$505$	9.20108e133	1.41552
$506$	−3.88951e133	−0.542556
$507$	6.09182e132	0.0770642
$508$	4.40926e132	0.0505956
$509$	1.08301e134	1.12747	0.563733	−	0.825957i	$-0.309365\pi$
$509$	1.08301e134	1.12747	0.563733	+	0.825957i	$0.309365\pi$
$510$	1.19123e133	0.112531
$511$	−1.55761e134	−1.33544
$512$	1.44388e134	1.12375
$513$	−1.15672e134	−0.817373
$514$	−1.28772e134	−0.826316
$515$	−8.33427e133	−0.485746
$516$	3.48946e132	0.0184756
$517$	3.76846e134	1.81294
$518$	1.19118e134	0.520782
$519$	−2.15661e134	−0.857014
$520$	3.72392e134	1.34535
$521$	−2.84093e134	−0.933241	−0.466620	−	0.884458i	$-0.654529\pi$
$521$	−2.84093e134	−0.933241	−0.466620	+	0.884458i	$0.654529\pi$
$522$	−4.17836e134	−1.24829
$523$	−5.19576e134	−1.41194	−0.705968	−	0.708243i	$-0.749488\pi$
$523$	−5.19576e134	−1.41194	−0.705968	+	0.708243i	$0.749488\pi$
$524$	−2.38409e133	−0.0589419
$525$	2.80034e134	0.629977
$526$	−6.13815e133	−0.125673
$527$	−9.56227e133	−0.178211
$528$	4.74351e134	0.804861
$529$	−5.86244e134	−0.905780
$530$	3.92869e134	0.552831
$531$	3.62700e134	0.464910
$532$	−1.70160e134	−0.198716
$533$	−3.99294e133	−0.0424909
$534$	1.34862e134	0.130796
$535$	1.40426e135	1.24147
$536$	1.18989e135	0.959072
$537$	3.77941e134	0.277777
$538$	−1.86272e135	−1.24860
$539$	2.90080e135	1.77367
$540$	−3.40515e134	−0.189952
$541$	−2.11746e135	−1.07783	−0.538914	−	0.842361i	$-0.681165\pi$
$541$	−2.11746e135	−1.07783	−0.538914	+	0.842361i	$0.681165\pi$
$542$	−2.27307e135	−1.05596
$543$	−3.32843e134	−0.141139
$544$	−1.39025e134	−0.0538204
$545$	1.10371e133	0.00390147
$546$	−1.85504e135	−0.598848
$547$	−2.44429e135	−0.720742	−0.360371	−	0.932809i	$-0.617350\pi$
$547$	−2.44429e135	−0.720742	−0.360371	+	0.932809i	$0.617350\pi$
$548$	2.39077e134	0.0644020
$549$	9.36414e134	0.230482
$550$	−6.99902e135	−1.57429
$551$	8.22641e135	1.69124
$552$	−8.84854e134	−0.166298
$553$	2.06196e135	0.354313
$554$	3.79472e135	0.596275
$555$	−1.99547e135	−0.286776
$556$	−8.64888e134	−0.113699
$557$	1.00722e136	1.21142	0.605709	−	0.795686i	$-0.292890\pi$
$557$	1.00722e136	1.21142	0.605709	+	0.795686i	$0.292890\pi$
$558$	−6.30491e135	−0.693882
$559$	2.12844e135	0.214377
$560$	1.69583e136	1.56342
$561$	−2.02990e135	−0.171322
$562$	1.48724e136	1.14930
$563$	−2.00101e136	−1.41606	−0.708032	−	0.706180i	$-0.750417\pi$
$563$	−2.00101e136	−1.41606	−0.708032	+	0.706180i	$0.750417\pi$
$564$	1.15465e135	0.0748400
$565$	−2.67861e136	−1.59042
$566$	−2.29480e136	−1.24834
$567$	−7.97903e135	−0.397730
$568$	3.76815e136	1.72141
$569$	3.10088e136	1.29846	0.649229	−	0.760593i	$-0.275092\pi$
$569$	3.10088e136	1.29846	0.649229	+	0.760593i	$0.275092\pi$
$570$	−1.54639e136	−0.593626
$571$	−9.42950e135	−0.331895	−0.165948	−	0.986135i	$-0.553068\pi$
$571$	−9.42950e135	−0.331895	−0.165948	+	0.986135i	$0.553068\pi$
$572$	−8.54646e135	−0.275856
$573$	−6.24292e135	−0.184814
$574$	−2.16342e135	−0.0587493
$575$	1.09734e136	0.273391
$576$	−3.57040e136	−0.816214
$577$	−6.70411e136	−1.40650	−0.703248	−	0.710945i	$-0.748267\pi$
$577$	−6.70411e136	−1.40650	−0.703248	+	0.710945i	$0.748267\pi$
$578$	4.62647e136	0.890885
$579$	−4.13704e135	−0.0731310
$580$	2.42168e136	0.393034
$581$	6.55548e136	0.976980
$582$	2.86767e136	0.392501
$583$	−6.69462e136	−0.841652
$584$	8.85650e136	1.02288
$585$	−8.83130e136	−0.937150
$586$	−3.02058e136	−0.294549
$587$	1.49411e137	1.33905	0.669526	−	0.742789i	$-0.266497\pi$
$587$	1.49411e137	1.33905	0.669526	+	0.742789i	$0.266497\pi$
$588$	8.88797e135	0.0732192
$589$	1.24132e137	0.940105
$590$	1.14038e137	0.794103
$591$	1.17414e137	0.751867
$592$	−5.69267e136	−0.335267
$593$	−3.05977e137	−1.65761	−0.828803	−	0.559540i	$-0.810978\pi$
$593$	−3.05977e137	−1.65761	−0.828803	+	0.559540i	$0.810978\pi$
$594$	−3.14780e137	−1.56884
$595$	−7.25698e136	−0.332787
$596$	−4.79200e136	−0.202221
$597$	−6.50196e136	−0.252531
$598$	−7.26916e136	−0.259882
$599$	8.42963e136	0.277448	0.138724	−	0.990331i	$-0.455700\pi$
$599$	8.42963e136	0.277448	0.138724	+	0.990331i	$0.455700\pi$
$600$	−1.59226e137	−0.482533
$601$	−8.86552e136	−0.247410	−0.123705	−	0.992319i	$-0.539478\pi$
$601$	−8.86552e136	−0.247410	−0.123705	+	0.992319i	$0.539478\pi$
$602$	1.15322e137	0.296404
$603$	−2.82185e137	−0.668077
$604$	−1.14238e137	−0.249162
$605$	1.84750e138	3.71274
$606$	2.60612e137	0.482614
$607$	−7.64526e137	−1.30483	−0.652413	−	0.757864i	$-0.726243\pi$
$607$	−7.64526e137	−1.30483	−0.652413	+	0.757864i	$0.726243\pi$
$608$	1.80474e137	0.283914
$609$	−8.95694e137	−1.29898
$610$	2.94423e137	0.393681
$611$	7.04293e137	0.868387
$612$	1.76752e136	0.0200987
$613$	5.01622e137	0.526118	0.263059	−	0.964780i	$-0.415269\pi$
$613$	5.01622e137	0.526118	0.263059	+	0.964780i	$0.415269\pi$
$614$	1.31637e138	1.27363
$615$	3.62417e136	0.0323512
$616$	−3.43816e138	−2.83192
$617$	8.77003e137	0.666631	0.333315	−	0.942815i	$-0.391833\pi$
$617$	8.77003e137	0.666631	0.333315	+	0.942815i	$0.391833\pi$
$618$	−2.36060e137	−0.165613
$619$	−2.63976e137	−0.170953	−0.0854767	−	0.996340i	$-0.527241\pi$
$619$	−2.63976e137	−0.170953	−0.0854767	+	0.996340i	$0.527241\pi$
$620$	3.65417e137	0.218474
$621$	4.93528e137	0.272444
$622$	−2.39783e138	−1.22235
$623$	−8.21576e137	−0.386803
$624$	8.86521e137	0.385525
$625$	−2.73162e138	−1.09738
$626$	2.22110e138	0.824400
$627$	2.63509e138	0.903759
$628$	6.60244e137	0.209268
$629$	2.43607e137	0.0713646
$630$	−4.78490e138	−1.29573
$631$	3.92118e138	0.981666	0.490833	−	0.871254i	$-0.336692\pi$
$631$	3.92118e138	0.981666	0.490833	+	0.871254i	$0.336692\pi$
$632$	−1.17242e138	−0.271387
$633$	−4.13180e138	−0.884415
$634$	3.12235e138	0.618106
$635$	−2.44110e138	−0.446978
$636$	−2.05121e137	−0.0347443
$637$	5.42134e138	0.849581
$638$	2.23865e139	3.24611
$639$	−8.93619e138	−1.19911
$640$	−7.81247e138	−0.970242
$641$	−1.91801e138	−0.220485	−0.110243	−	0.993905i	$-0.535163\pi$
$641$	−1.91801e138	−0.220485	−0.110243	+	0.993905i	$0.535163\pi$
$642$	3.97744e138	0.423273
$643$	−2.67091e138	−0.263158	−0.131579	−	0.991306i	$-0.542005\pi$
$643$	−2.67091e138	−0.263158	−0.131579	+	0.991306i	$0.542005\pi$
$644$	7.26006e137	0.0662353
$645$	−1.93187e138	−0.163219
$646$	1.88783e138	0.147724
$647$	8.99979e138	0.652334	0.326167	−	0.945312i	$-0.394243\pi$
$647$	8.99979e138	0.652334	0.326167	+	0.945312i	$0.394243\pi$
$648$	4.53684e138	0.304643
$649$	−1.94325e139	−1.20897
$650$	−1.30806e139	−0.754077
$651$	−1.35155e139	−0.722061
$652$	−1.40537e138	−0.0695880
$653$	−3.38291e139	−1.55270	−0.776351	−	0.630301i	$-0.782931\pi$
$653$	−3.38291e139	−1.55270	−0.776351	+	0.630301i	$0.782931\pi$
$654$	3.12616e136	0.00133019
$655$	1.31991e139	0.520713
$656$	1.03390e138	0.0378214
$657$	−2.10033e139	−0.712526
$658$	3.81594e139	1.20066
$659$	5.64282e139	1.64690	0.823452	−	0.567386i	$-0.192045\pi$
$659$	5.64282e139	1.64690	0.823452	+	0.567386i	$0.192045\pi$
$660$	7.75714e138	0.210028
$661$	6.31312e139	1.58588	0.792942	−	0.609297i	$-0.208548\pi$
$661$	6.31312e139	1.58588	0.792942	+	0.609297i	$0.208548\pi$
$662$	−4.11122e139	−0.958297
$663$	−3.79370e138	−0.0820622
$664$	−3.72741e139	−0.748321
$665$	9.42059e139	1.75552
$666$	1.60623e139	0.277864
$667$	−3.50988e139	−0.563720
$668$	−9.54418e138	−0.142332
$669$	−8.12196e138	−0.112478
$670$	−8.87231e139	−1.14113
$671$	−5.01706e139	−0.599356
$672$	−1.96501e139	−0.218065
$673$	8.50414e139	0.876768	0.438384	−	0.898788i	$-0.355551\pi$
$673$	8.50414e139	0.876768	0.438384	+	0.898788i	$0.355551\pi$
$674$	−9.05896e139	−0.867787
$675$	8.88084e139	0.790528
$676$	2.84196e138	0.0235103
$677$	−6.55320e139	−0.503865	−0.251933	−	0.967745i	$-0.581066\pi$
$677$	−6.55320e139	−0.503865	−0.251933	+	0.967745i	$0.581066\pi$
$678$	−7.58692e139	−0.542245
$679$	−1.74698e140	−1.16074
$680$	4.12628e139	0.254899
$681$	5.67591e139	0.326027
$682$	3.37800e140	1.80440
$683$	−6.62308e139	−0.329030	−0.164515	−	0.986375i	$-0.552606\pi$
$683$	−6.62308e139	−0.329030	−0.164515	+	0.986375i	$0.552606\pi$
$684$	−2.29449e139	−0.106025
$685$	−1.32360e140	−0.568949
$686$	−2.48251e139	−0.0992766
$687$	2.72338e140	1.01333
$688$	−5.51122e139	−0.190818
$689$	−1.25117e140	−0.403147
$690$	6.59781e139	0.197865
$691$	−3.27423e140	−0.914001	−0.457000	−	0.889467i	$-0.651076\pi$
$691$	−3.27423e140	−0.914001	−0.457000	+	0.889467i	$0.651076\pi$
$692$	−1.00611e140	−0.261452
$693$	8.15363e140	1.97268
$694$	1.00983e139	0.0227487
$695$	4.78828e140	1.00446
$696$	5.09288e140	0.994961
$697$	−4.42437e138	−0.00805062
$698$	−9.21892e140	−1.56256
$699$	−1.86433e140	−0.294375
$700$	1.30642e140	0.192189
$701$	−1.08174e141	−1.48280	−0.741398	−	0.671065i	$-0.765837\pi$
$701$	−1.08174e141	−1.48280	−0.741398	+	0.671065i	$0.765837\pi$
$702$	−5.88296e140	−0.751465
$703$	−3.16236e140	−0.376464
$704$	1.91293e141	2.12252
$705$	−6.39247e140	−0.661162
$706$	9.72064e140	0.937265
$707$	−1.58765e141	−1.42723
$708$	−5.95408e139	−0.0499078
$709$	4.18874e140	0.327412	0.163706	−	0.986509i	$-0.447655\pi$
$709$	4.18874e140	0.327412	0.163706	+	0.986509i	$0.447655\pi$
$710$	−2.80967e141	−2.04818
$711$	2.78041e140	0.189045
$712$	4.67145e140	0.296273
$713$	−5.29621e140	−0.313353
$714$	−2.05547e140	−0.113462
$715$	4.73158e141	2.43701
$716$	1.76318e140	0.0847425
$717$	−8.43922e140	−0.378533
$718$	2.77960e141	1.16365
$719$	−4.49709e140	−0.175732	−0.0878661	−	0.996132i	$-0.528005\pi$
$719$	−4.49709e140	−0.175732	−0.0878661	+	0.996132i	$0.528005\pi$
$720$	2.28671e141	0.834165
$721$	1.43808e141	0.489765
$722$	4.39042e140	0.139609
$723$	−9.51486e140	−0.282525
$724$	−1.55279e140	−0.0430579
$725$	−6.31589e141	−1.63570
$726$	5.23288e141	1.26584
$727$	−2.04219e141	−0.461469	−0.230734	−	0.973017i	$-0.574113\pi$
$727$	−2.04219e141	−0.461469	−0.230734	+	0.973017i	$0.574113\pi$
$728$	−6.42563e141	−1.35648
$729$	1.21995e141	0.240618
$730$	−6.60374e141	−1.21705
$731$	2.35842e140	0.0406173
$732$	−1.53721e140	−0.0247421
$733$	2.28504e141	0.343754	0.171877	−	0.985118i	$-0.445017\pi$
$733$	2.28504e141	0.343754	0.171877	+	0.985118i	$0.445017\pi$
$734$	−2.63382e141	−0.370366
$735$	−4.92065e141	−0.646844
$736$	−7.70010e140	−0.0946335
$737$	1.51187e142	1.73730
$738$	−2.91722e140	−0.0313458
$739$	−1.32577e141	−0.133220	−0.0666100	−	0.997779i	$-0.521218\pi$
$739$	−1.32577e141	−0.133220	−0.0666100	+	0.997779i	$0.521218\pi$
$740$	−9.30931e140	−0.0874878
$741$	4.92476e141	0.432896
$742$	−6.77897e141	−0.557404
$743$	−2.29644e141	−0.176648	−0.0883241	−	0.996092i	$-0.528151\pi$
$743$	−2.29644e141	−0.176648	−0.0883241	+	0.996092i	$0.528151\pi$
$744$	7.68487e141	0.553065
$745$	2.65300e142	1.78649
$746$	−1.30442e142	−0.821950
$747$	8.83960e141	0.521270
$748$	−9.46991e140	−0.0522657
$749$	−2.42306e142	−1.25174
$750$	−1.45750e141	−0.0704817
$751$	3.65587e141	0.165506	0.0827529	−	0.996570i	$-0.473629\pi$
$751$	3.65587e141	0.165506	0.0827529	+	0.996570i	$0.473629\pi$
$752$	−1.82364e142	−0.772958
$753$	−1.04281e142	−0.413861
$754$	4.18385e142	1.55487
$755$	6.32455e142	2.20118
$756$	5.87559e141	0.191524
$757$	−6.03767e142	−1.84342	−0.921708	−	0.387884i	$-0.873206\pi$
$757$	−6.03767e142	−1.84342	−0.921708	+	0.387884i	$0.873206\pi$
$758$	6.65395e141	0.190307
$759$	−1.12429e142	−0.301238
$760$	−5.35651e142	−1.34465
$761$	7.48167e140	0.0175978	0.00879890	−	0.999961i	$-0.497199\pi$
$761$	7.48167e140	0.0175978	0.00879890	+	0.999961i	$0.497199\pi$
$762$	−6.91420e141	−0.152395
$763$	−1.90446e140	−0.00393375
$764$	−2.91246e141	−0.0563817
$765$	−9.78552e141	−0.177559
$766$	−6.81821e142	−1.15970
$767$	−3.63177e142	−0.579093
$768$	1.55293e142	0.232152
$769$	−3.41088e142	−0.478093	−0.239046	−	0.971008i	$-0.576835\pi$
$769$	−3.41088e142	−0.478093	−0.239046	+	0.971008i	$0.576835\pi$
$770$	2.56363e143	3.36949
$771$	−3.72223e142	−0.458788
$772$	−1.93002e141	−0.0223103
$773$	1.15276e142	0.124984	0.0624920	−	0.998045i	$-0.480095\pi$
$773$	1.15276e142	0.124984	0.0624920	+	0.998045i	$0.480095\pi$
$774$	1.55503e142	0.158147
$775$	−9.53032e142	−0.909229
$776$	9.93326e142	0.889071
$777$	3.44319e142	0.289149
$778$	3.28697e141	0.0259004
$779$	5.74347e141	0.0424688
$780$	1.44974e142	0.100602
$781$	4.78778e143	3.11823
$782$	−8.05460e141	−0.0492390
$783$	−2.84056e143	−1.63003
$784$	−1.40376e143	−0.756219
$785$	−3.65531e143	−1.84874
$786$	3.73851e142	0.177534
$787$	−2.59288e143	−1.15620	−0.578101	−	0.815965i	$-0.696206\pi$
$787$	−2.59288e143	−1.15620	−0.578101	+	0.815965i	$0.696206\pi$
$788$	5.47764e142	0.229375
$789$	−1.77427e142	−0.0697764
$790$	8.74204e142	0.322903
$791$	4.62195e143	1.60358
$792$	−4.63612e143	−1.51098
$793$	−9.37645e142	−0.287089
$794$	−4.80669e143	−1.38271
$795$	1.13561e143	0.306943
$796$	−3.03331e142	−0.0770406
$797$	6.36151e143	1.51835	0.759177	−	0.650884i	$-0.225601\pi$
$797$	6.36151e143	1.51835	0.759177	+	0.650884i	$0.225601\pi$
$798$	2.66830e143	0.598537
$799$	7.80392e142	0.164531
$800$	−1.38560e143	−0.274590
$801$	−1.10784e143	−0.206380
$802$	−1.28033e143	−0.224228
$803$	1.12530e144	1.85289
$804$	4.63233e142	0.0717175
$805$	−4.01939e143	−0.585145
$806$	6.31320e143	0.864300
$807$	−5.38431e143	−0.693250
$808$	9.02731e143	1.09319
$809$	−8.12264e143	−0.925221	−0.462610	−	0.886562i	$-0.653087\pi$
$809$	−8.12264e143	−0.925221	−0.462610	+	0.886562i	$0.653087\pi$
$810$	−3.38284e143	−0.362471
$811$	2.12283e143	0.213984	0.106992	−	0.994260i	$-0.465878\pi$
$811$	2.12283e143	0.213984	0.106992	+	0.994260i	$0.465878\pi$
$812$	−4.17861e143	−0.396286
$813$	−6.57046e143	−0.586292
$814$	−8.60575e143	−0.722571
$815$	7.78054e143	0.614764
$816$	9.82310e142	0.0730442
$817$	−3.06157e143	−0.214265
$818$	−6.15538e143	−0.405477
$819$	1.52384e144	0.944903
$820$	1.69075e142	0.00986948
$821$	2.67422e144	1.46964	0.734821	−	0.678261i	$-0.237266\pi$
$821$	2.67422e144	1.46964	0.734821	+	0.678261i	$0.237266\pi$
$822$	−3.74898e143	−0.193980
$823$	−3.19342e144	−1.55584	−0.777918	−	0.628366i	$-0.783724\pi$
$823$	−3.19342e144	−1.55584	−0.777918	+	0.628366i	$0.783724\pi$
$824$	−8.17686e143	−0.375137
$825$	−2.02311e144	−0.874077
$826$	−1.96774e144	−0.800672
$827$	4.42099e142	0.0169432	0.00847162	−	0.999964i	$-0.497303\pi$
$827$	4.42099e142	0.0169432	0.00847162	+	0.999964i	$0.497303\pi$
$828$	9.78968e142	0.0353400
$829$	−6.49360e143	−0.220819	−0.110409	−	0.993886i	$-0.535216\pi$
$829$	−6.49360e143	−0.220819	−0.110409	+	0.993886i	$0.535216\pi$
$830$	2.77930e144	0.890370
$831$	1.09689e144	0.331064
$832$	3.57509e144	1.01668
$833$	6.00712e143	0.160968
$834$	1.35624e144	0.342465
$835$	5.28395e144	1.25741
$836$	1.22933e144	0.275713
$837$	−4.28624e144	−0.906080
$838$	−2.95780e144	−0.589373
$839$	−5.23735e144	−0.983773	−0.491887	−	0.870659i	$-0.663693\pi$
$839$	−5.23735e144	−0.983773	−0.491887	+	0.870659i	$0.663693\pi$
$840$	5.83218e144	1.03278
$841$	1.42118e145	2.37273
$842$	−7.88547e144	−1.24131
$843$	4.29897e144	0.638116
$844$	−1.92758e144	−0.269811
$845$	−1.57340e144	−0.207698
$846$	5.14553e144	0.640615
$847$	−3.18787e145	−3.74345
$848$	3.23967e144	0.358844
$849$	−6.63327e144	−0.693101
$850$	−1.44939e144	−0.142873
$851$	1.34925e144	0.125482
$852$	1.46696e144	0.128724
$853$	−6.81934e144	−0.564632	−0.282316	−	0.959321i	$-0.591103\pi$
$853$	−6.81934e144	−0.564632	−0.282316	+	0.959321i	$0.591103\pi$
$854$	−5.08027e144	−0.396938
$855$	1.27030e145	0.936664
$856$	1.37774e145	0.958774
$857$	−1.46748e145	−0.963875	−0.481937	−	0.876206i	$-0.660067\pi$
$857$	−1.46748e145	−0.963875	−0.481937	+	0.876206i	$0.660067\pi$
$858$	1.34018e145	0.830886
$859$	1.63980e145	0.959689	0.479844	−	0.877354i	$-0.340693\pi$
$859$	1.63980e145	0.959689	0.479844	+	0.877354i	$0.340693\pi$
$860$	−9.01258e143	−0.0497939
$861$	−6.25351e143	−0.0326188
$862$	1.02659e145	0.505578
$863$	−1.95414e145	−0.908700	−0.454350	−	0.890823i	$-0.650128\pi$
$863$	−1.95414e145	−0.908700	−0.454350	+	0.890823i	$0.650128\pi$
$864$	−6.23172e144	−0.273639
$865$	5.57011e145	2.30976
$866$	−1.19000e145	−0.466028
$867$	1.33731e145	0.494638
$868$	−6.30529e144	−0.220282
$869$	−1.48967e145	−0.491600
$870$	−3.79745e145	−1.18383
$871$	2.82556e145	0.832157
$872$	1.08287e143	0.00301306
$873$	−2.35568e145	−0.619315
$874$	1.04560e145	0.259747
$875$	8.87910e144	0.208435
$876$	3.44789e144	0.0764892
$877$	2.40483e145	0.504202	0.252101	−	0.967701i	$-0.418879\pi$
$877$	2.40483e145	0.504202	0.252101	+	0.967701i	$0.418879\pi$
$878$	−4.33457e145	−0.858949
$879$	−8.73117e144	−0.163540
$880$	−1.22516e146	−2.16920
$881$	−4.45913e145	−0.746350	−0.373175	−	0.927761i	$-0.621731\pi$
$881$	−4.45913e145	−0.746350	−0.373175	+	0.927761i	$0.621731\pi$
$882$	3.96081e145	0.626742
$883$	1.07046e146	1.60145	0.800727	−	0.599029i	$-0.204447\pi$
$883$	1.07046e146	1.60145	0.800727	+	0.599029i	$0.204447\pi$
$884$	−1.76984e144	−0.0250350
$885$	3.29636e145	0.440902
$886$	6.28671e145	0.795160
$887$	−1.06549e146	−1.27448	−0.637238	−	0.770667i	$-0.719923\pi$
$887$	−1.06549e146	−1.27448	−0.637238	+	0.770667i	$0.719923\pi$
$888$	−1.95779e145	−0.221474
$889$	4.21213e145	0.450676
$890$	−3.48321e145	−0.352512
$891$	5.76448e145	0.551840
$892$	−3.78907e144	−0.0343141
$893$	−1.01306e146	−0.867936
$894$	7.51437e145	0.609096
$895$	−9.76148e145	−0.748644
$896$	1.34804e146	0.978268
$897$	−2.10120e145	−0.144292
$898$	3.40788e145	0.221465
$899$	3.04829e146	1.87479
$900$	1.76161e145	0.102543
$901$	−1.38636e145	−0.0763831
$902$	1.56297e145	0.0815131
$903$	3.33344e145	0.164570
$904$	−2.62802e146	−1.22826
$905$	8.59669e145	0.380388
$906$	1.79137e146	0.750482
$907$	−4.81892e146	−1.91156	−0.955782	−	0.294078i	$-0.904988\pi$
$907$	−4.81892e146	−1.91156	−0.955782	+	0.294078i	$0.904988\pi$
$908$	2.64794e145	0.0994622
$909$	−2.14083e146	−0.761502
$910$	4.79119e146	1.61397
$911$	−3.97990e145	−0.126973	−0.0634867	−	0.997983i	$-0.520222\pi$
$911$	−3.97990e145	−0.126973	−0.0634867	+	0.997983i	$0.520222\pi$
$912$	−1.27518e146	−0.385324
$913$	−4.73602e146	−1.35553
$914$	−4.65661e146	−1.26250
$915$	8.51048e145	0.218580
$916$	1.27051e146	0.309139
$917$	−2.27750e146	−0.525021
$918$	−6.51861e145	−0.142378
$919$	−3.58017e146	−0.740945	−0.370473	−	0.928843i	$-0.620804\pi$
$919$	−3.58017e146	−0.740945	−0.370473	+	0.928843i	$0.620804\pi$
$920$	2.28541e146	0.448194
$921$	3.80506e146	0.707147
$922$	7.78591e146	1.37129
$923$	8.94794e146	1.49362
$924$	−1.33850e146	−0.211765
$925$	2.42793e146	0.364100
$926$	−5.71608e145	−0.0812558
$927$	1.93915e146	0.261315
$928$	4.43188e146	0.566192
$929$	1.03312e147	1.25134	0.625668	−	0.780089i	$-0.284826\pi$
$929$	1.03312e147	1.25134	0.625668	+	0.780089i	$0.284826\pi$
$930$	−5.73014e146	−0.658050
$931$	−7.79810e146	−0.849140
$932$	−8.69748e145	−0.0898061
$933$	−6.93109e146	−0.678673
$934$	−1.67260e147	−1.55318
$935$	5.24283e146	0.461733
$936$	−8.66451e146	−0.723751
$937$	4.83974e146	0.383453	0.191727	−	0.981448i	$-0.438591\pi$
$937$	4.83974e146	0.383453	0.191727	+	0.981448i	$0.438591\pi$
$938$	1.53092e147	1.15057
$939$	6.42023e146	0.457724
$940$	−2.98223e146	−0.201703
$941$	−1.32268e147	−0.848730	−0.424365	−	0.905491i	$-0.639503\pi$
$941$	−1.32268e147	−0.848730	−0.424365	+	0.905491i	$0.639503\pi$
$942$	−1.03533e147	−0.630319
$943$	−2.45051e145	−0.0141556
$944$	9.40382e146	0.515455
$945$	−3.25290e147	−1.69199
$946$	−8.33144e146	−0.411253
$947$	1.96481e147	0.920442	0.460221	−	0.887804i	$-0.347770\pi$
$947$	1.96481e147	0.920442	0.460221	+	0.887804i	$0.347770\pi$
$948$	−4.56432e145	−0.0202938
$949$	2.10309e147	0.887523
$950$	1.88152e147	0.753685
$951$	9.02535e146	0.343185
$952$	−7.11992e146	−0.257008
$953$	−4.56786e147	−1.56536	−0.782680	−	0.622424i	$-0.786148\pi$
$953$	−4.56786e147	−1.56536	−0.782680	+	0.622424i	$0.786148\pi$
$954$	−9.14097e146	−0.297405
$955$	1.61242e147	0.498095
$956$	−3.93708e146	−0.115480
$957$	6.47097e147	1.80231
$958$	1.21138e147	0.320396
$959$	2.28388e147	0.573656
$960$	−3.24491e147	−0.774064
$961$	1.85957e146	0.0421312
$962$	−1.60834e147	−0.346108
$963$	−3.26732e147	−0.667869
$964$	−4.43889e146	−0.0861908
$965$	1.06852e147	0.197097
$966$	−1.13845e147	−0.199502
$967$	4.36982e147	0.727534	0.363767	−	0.931490i	$-0.381490\pi$
$967$	4.36982e147	0.727534	0.363767	+	0.931490i	$0.381490\pi$
$968$	1.81261e148	2.86731
$969$	5.45688e146	0.0820196
$970$	−7.40662e147	−1.05784
$971$	−1.07311e148	−1.45644	−0.728221	−	0.685342i	$-0.759653\pi$
$971$	−1.07311e148	−1.45644	−0.728221	+	0.685342i	$0.759653\pi$
$972$	1.24769e147	0.160926
$973$	−8.26219e147	−1.01277
$974$	−1.39599e148	−1.62635
$975$	−3.78102e147	−0.418679
$976$	2.42786e147	0.255540
$977$	3.39054e147	0.339226	0.169613	−	0.985511i	$-0.445748\pi$
$977$	3.39054e147	0.339226	0.169613	+	0.985511i	$0.445748\pi$
$978$	2.20377e147	0.209601
$979$	5.93551e147	0.536679
$980$	−2.29559e147	−0.197335
$981$	−2.56803e145	−0.00209886
$982$	−7.15367e147	−0.555917
$983$	1.53026e148	1.13075	0.565375	−	0.824834i	$-0.308731\pi$
$983$	1.53026e148	1.13075	0.565375	+	0.824834i	$0.308731\pi$
$984$	3.55572e146	0.0249845
$985$	−3.03258e148	−2.02637
$986$	4.63591e147	0.294597
$987$	1.10302e148	0.666631
$988$	2.29751e147	0.132065
$989$	1.30625e147	0.0714182
$990$	3.45687e148	1.79780
$991$	7.81790e145	0.00386763	0.00193381	−	0.999998i	$-0.499384\pi$
$991$	7.81790e145	0.00386763	0.00193381	+	0.999998i	$0.499384\pi$
$992$	6.68746e147	0.314727
$993$	−1.18837e148	−0.532066
$994$	4.84810e148	2.06512
$995$	1.67933e148	0.680602
$996$	−1.45111e147	−0.0559579
$997$	−1.50134e148	−0.550893	−0.275447	−	0.961316i	$-0.588826\pi$
$997$	−1.50134e148	−0.550893	−0.275447	+	0.961316i	$0.588826\pi$
$998$	−2.85458e148	−0.996738
$999$	1.09196e148	0.362839

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.100.a.a.1.3	✓	8	1.1	even	1	trivial
9.100.a.d.1.6		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)

\(f(q)\)	\(=\)	\(q-7.31556e14 q^{2} -2.11461e23 q^{3} -9.86512e28 q^{4} +5.46163e34 q^{5} +1.54696e38 q^{6} -9.42405e41 q^{7} +5.35848e44 q^{8} -1.27077e47 q^{9} +O(q^{10})\)	\(q-7.31556e14 q^{2} -2.11461e23 q^{3} -9.86512e28 q^{4} +5.46163e34 q^{5} +1.54696e38 q^{6} -9.42405e41 q^{7} +5.35848e44 q^{8} -1.27077e47 q^{9} -3.99548e49 q^{10} +6.80844e51 q^{11} +2.08609e52 q^{12} +1.27244e55 q^{13} +6.89422e56 q^{14} -1.15492e58 q^{15} -3.29475e59 q^{16} +1.40992e60 q^{17} +9.29638e61 q^{18} -1.83028e63 q^{19} -5.38796e63 q^{20} +1.99282e65 q^{21} -4.98075e66 q^{22} +7.80909e66 q^{23} -1.13311e68 q^{24} +1.40521e69 q^{25} -9.30860e69 q^{26} +6.31992e70 q^{27} +9.29694e70 q^{28} -4.49461e72 q^{29} +8.44889e72 q^{30} -6.78211e73 q^{31} -9.86044e73 q^{32} -1.43972e75 q^{33} -1.03144e75 q^{34} -5.14706e76 q^{35} +1.25363e76 q^{36} +1.72780e77 q^{37} +1.33895e78 q^{38} -2.69071e78 q^{39} +2.92660e79 q^{40} -3.13802e78 q^{41} -1.45786e80 q^{42} +1.67273e80 q^{43} -6.71660e80 q^{44} -6.94046e81 q^{45} -5.71278e81 q^{46} +5.53499e82 q^{47} +6.96711e82 q^{48} +4.26060e83 q^{49} -1.02799e84 q^{50} -2.98144e83 q^{51} -1.25527e84 q^{52} -9.83283e84 q^{53} -4.62337e85 q^{54} +3.71851e86 q^{55} -5.04986e86 q^{56} +3.87034e86 q^{57} +3.28806e87 q^{58} -2.85418e87 q^{59} +1.13934e87 q^{60} -7.36889e87 q^{61} +4.96150e88 q^{62} +1.19758e89 q^{63} +2.80964e89 q^{64} +6.94958e89 q^{65} +1.05324e90 q^{66} +2.22058e90 q^{67} -1.39091e89 q^{68} -1.65132e90 q^{69} +3.76537e91 q^{70} +7.03212e91 q^{71} -6.80938e91 q^{72} +1.65280e92 q^{73} -1.26398e92 q^{74} -2.97148e92 q^{75} +1.80560e92 q^{76} -6.41631e93 q^{77} +1.96841e93 q^{78} -2.18798e93 q^{79} -1.79947e94 q^{80} +8.46667e93 q^{81} +2.29564e93 q^{82} -6.95611e94 q^{83} -1.96594e94 q^{84} +7.70048e94 q^{85} -1.22369e95 q^{86} +9.50434e95 q^{87} +3.64828e96 q^{88} +8.71787e95 q^{89} +5.07733e96 q^{90} -1.19915e97 q^{91} -7.70375e95 q^{92} +1.43415e97 q^{93} -4.04915e97 q^{94} -9.99632e97 q^{95} +2.08510e97 q^{96} +1.85375e98 q^{97} -3.11686e98 q^{98} -8.65194e98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots + 15\!\cdots\!76 q^{9}+O(q^{10}) \) 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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