LMFDB - Embedded newform 1.102.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,102,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, 102, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 102);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 102 $
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:	$64.6006978936$
Analytic rank:	$1$
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 + 14\!\cdots\!00 $ x^8 - x^7 - 1587875693797102871013870264x^6 - 1330672377046512025083958312008691941376x^5 + 791445357227345439680707260473135602197341722594809856x^4 + 1619878418527606484256994450085468366256752280708006567605868625920x^3 - 123437551313054499723143526216928211228510769023293658451121904309621876706508800x^2 - 461414543589146449205827365849494496729755778377708510322901762861807152038306434693201920000x + 1491743821439154656522591042817873299711189313438184985174364653060384818799349544894763946517463040000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{119}\cdot 3^{37}\cdot 5^{14}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-6.74954e12$ 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)

$f(q)$	$=$	$q+5.93582e14 q^{2} +2.15060e24 q^{3} -2.18296e30 q^{4} +2.07725e34 q^{5} +1.27656e39 q^{6} -6.15512e42 q^{7} -2.80068e45 q^{8} +3.07894e48 q^{9} +O(q^{10})$	\(q+5.93582e14 q^{2} +2.15060e24 q^{3} -2.18296e30 q^{4} +2.07725e34 q^{5} +1.27656e39 q^{6} -6.15512e42 q^{7} -2.80068e45 q^{8} +3.07894e48 q^{9} +1.23302e49 q^{10} -1.93541e51 q^{11} -4.69467e54 q^{12} +2.07990e56 q^{13} -3.65357e57 q^{14} +4.46732e58 q^{15} +3.87203e60 q^{16} +9.51139e61 q^{17} +1.82761e63 q^{18} -2.07479e64 q^{19} -4.53455e64 q^{20} -1.32372e67 q^{21} -1.14883e66 q^{22} -1.01002e69 q^{23} -6.02314e69 q^{24} -3.90116e70 q^{25} +1.23459e71 q^{26} +3.29646e72 q^{27} +1.34364e73 q^{28} -1.12007e74 q^{29} +2.65172e73 q^{30} -3.39166e75 q^{31} +9.39893e75 q^{32} -4.16230e75 q^{33} +5.64580e76 q^{34} -1.27857e77 q^{35} -6.72122e78 q^{36} -2.80250e78 q^{37} -1.23156e79 q^{38} +4.47304e80 q^{39} -5.81770e79 q^{40} -2.18595e81 q^{41} -7.85736e81 q^{42} +4.27840e82 q^{43} +4.22493e81 q^{44} +6.39572e82 q^{45} -5.99533e83 q^{46} -4.06463e84 q^{47} +8.32719e84 q^{48} +1.52441e85 q^{49} -2.31566e85 q^{50} +2.04552e86 q^{51} -4.54035e86 q^{52} -1.28592e87 q^{53} +1.95672e87 q^{54} -4.02033e85 q^{55} +1.72385e88 q^{56} -4.46205e88 q^{57} -6.64855e88 q^{58} +2.29239e88 q^{59} -9.75199e88 q^{60} +1.48144e90 q^{61} -2.01323e90 q^{62} -1.89513e91 q^{63} -4.23772e90 q^{64} +4.32047e90 q^{65} -2.47067e90 q^{66} -1.12651e92 q^{67} -2.07630e92 q^{68} -2.17216e93 q^{69} -7.58936e91 q^{70} -1.07138e93 q^{71} -8.62313e93 q^{72} +8.88946e92 q^{73} -1.66351e93 q^{74} -8.38982e94 q^{75} +4.52919e94 q^{76} +1.19127e94 q^{77} +2.65512e95 q^{78} +3.94018e95 q^{79} +8.04316e94 q^{80} +2.32892e96 q^{81} -1.29754e96 q^{82} +7.91760e96 q^{83} +2.88963e97 q^{84} +1.97575e96 q^{85} +2.53958e97 q^{86} -2.40883e98 q^{87} +5.42047e96 q^{88} +1.56456e98 q^{89} +3.79639e97 q^{90} -1.28020e99 q^{91} +2.20484e99 q^{92} -7.29409e99 q^{93} -2.41269e99 q^{94} -4.30986e98 q^{95} +2.02133e100 q^{96} +6.75748e99 q^{97} +9.04864e99 q^{98} -5.95903e99 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 52\!\cdots\!84 q^{9}+O(q^{10}) $ 8 * q - 434989091795040 * q^2 - 1209375896611771518910560 * q^3 + 9008967123164113911511576503296 * q^4 + 38238791540232828026421308589217200 * q^5 + 2477260046146272006672820535971480695936 * q^6 - 5786789720778120168956257648884421874283200 * q^7 - 6101688461407407841888405145259998920458731520 * q^8 + 5273640617280587177839635242070674204864681879784 * q^9	$ 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 22\!\cdots\!08 q^{99}+O(q^{100}) $ 8 * q - 434989091795040 * q^2 - 1209375896611771518910560 * q^3 + 9008967123164113911511576503296 * q^4 + 38238791540232828026421308589217200 * q^5 + 2477260046146272006672820535971480695936 * q^6 - 5786789720778120168956257648884421874283200 * q^7 - 6101688461407407841888405145259998920458731520 * q^8 + 5273640617280587177839635242070674204864681879784 * q^9 - 376167658847177398692429835067300112512860198593600 * q^10 + 4622006661480385115355021397632645270205791478300896 * q^11 - 7273290781506553143908216801865849714958844187989422080 * q^12 + 250316830865150221699601352256397536965043294984328650480 * q^13 - 4856789037716039923353321450215036970203737520869624889088 * q^14 - 296460708185002952419818874947342543917521978696100167156800 * q^15 - 10662656154906175558835021484824464714661655552497093859868672 * q^16 - 397968518694853312322660892941326449007299986932512193696587120 * q^17 - 7270968925217398747066352706388703938040714138623386028515252960 * q^18 - 21387776045417165942123954421061470474744368808488511816400717280 * q^19 + 1745002690168409059221421019241581897927614179506161156200285542400 * q^20 + 4030935126807879780648600654579655736182360851489572706466859540736 * q^21 + 61357881995862711169740037407631980426480577127973320405539739944320 * q^22 - 1366243345208606848425464574347748611753917469593153677393324561698880 * q^23 + 10457354719000260635321058863018299052737315743164922361342586480885760 * q^24 + 77471873089568593564333770877949420045843582630742632687744142562715000 * q^25 - 97549630676937426518340388130407212490384846814009484188479115327886144 * q^26 - 5951874968930013487417142282111771144801435961988629201748805497863184320 * q^27 + 9217624035174751886516129105576165061663773766415040330328487084880404480 * q^28 + 15465799862710125255662370242568323665682807414567501281109138719156160880 * q^29 + 1101689156065505631051293671607641382064945196508526428823375711603202118400 * q^30 - 6594370386043135339784923725045360443937393326734068279132668478779615001344 * q^31 + 12265519409733718324179959581296851912742484455832107241543734281342036213760 * q^32 + 43813172582105581329585760338258562815639759809845990212191452867766348215680 * q^33 + 9531455444774917507766540524882635666895777953789094347547215472626183995712 * q^34 - 1122850631208004175280217132184898888977788452428069383882586628450512616297600 * q^35 + 1966242586607976986737003826554029255087710066072863106322127653222050407339008 * q^36 + 39729696767983511833540209209183332457877293383323859312175998401968644864715440 * q^37 - 70873740526925065519455012686645778106113298999572267198467188879790467046148480 * q^38 - 269289195198196884798470270521708844679404215685249767615656452740889673105306432 * q^39 - 763642761360299050617237751714968411270996317577517686387843428508400019349504000 * q^40 + 5607291724825101314952096252772109505395882457063737303656079003304969203257094736 * q^41 + 3008066923831569706716293907931878334959183836053498604235677758281531565332526080 * q^42 - 28642921955044714117801359306021921736063108483729021321044095944585527287681223200 * q^43 - 207838425393205175674959052733026300855796348257745356716186803699782799277851086848 * q^44 + 712633045382921242540931880134776511927082560144290402835715503414563529286220047600 * q^45 + 1088094260619851586903932234100844276278561023621942541398958535856528393570339218176 * q^46 - 4595399220200007631460417274797048154524720407021496316223236391731855709593438718080 * q^47 - 58354182581817955899154335674671016574355963424701638945735582725996041826866298880 * q^48 + 12068461406676719302337658501270392621238416595305390197216228129207599916872005856456 * q^49 - 40493179837482260394665357435432250163405353367416857829233726008281167215503492420000 * q^50 + 117646730044094759803745147399491979694134742922341911657750530682089815486256248611136 * q^51 - 736020167800817028850658909331852777746165402605863935107936992324104798352324258252800 * q^52 + 131026696145917691346168139299202731343660174597285772716290345361212508775951813313840 * q^53 + 6803608957095266771149163140167539716357850176039815317805755392633822625226741503089920 * q^54 - 14585157967675450217148723878599628333971210001615112897255333178063634767400530051473600 * q^55 - 23665562342657326400415121984960944704012341384928617813498515591030351969339927087022080 * q^56 - 66899487754306674554237314096607510056291565049587799982155034523058479948455991635655040 * q^57 + 29173417521771002425120779628349939892591335515731485644911210555324770598093888308326080 * q^58 + 212583149562022564923669670483574922097682552074321909615339251529169016840977455874187360 * q^59 - 3455800135608334392541843481344001808338357411235959344412061781382196941870275476295065600 * q^60 - 3390796423636162146406492296389682436951029380958058095674208836333532599894943317230895504 * q^61 - 5878859817222970028213836429448832127296537243368792127423103234889716583457526212133370880 * q^62 - 20171938924061808002384576493874339158887341995607670819297079343133751793255425885494984640 * q^63 - 74870090698021647967203019932764377907062372989513317693678846896652408519412785858115272704 * q^64 - 161067075283368767182138254547148962244907084326790507487294907612770451283405321317426536800 * q^65 - 745278055170676259198413344675313071673593040227005461838089798951153726758412015071955911168 * q^66 - 618774503558862942537948810466095132313460919373052732511642097824837019429997681150398682720 * q^67 - 2182412150351293808121583165511486752102068977919329447376923905220322529537335456462676162560 * q^68 - 5393950442083315109606578094475120918497802785657891521452512469623636760248087300551286537472 * q^69 - 12923520657540473465038555822652190723092643731233782501675276653712048411292540691873715571200 * q^70 - 15797470289857673806303846655911576507977904169297655042639265226995032204172380517793831135424 * q^71 - 55126715113590704564504537983251285080485074916503283789364546398928839504287032847376708239360 * q^72 - 20462651635605668591994589976366754984142669867347912050159975933828495442291952971923777071280 * q^73 - 142953411935712165334538916257020870493984381200782662943456748743148514063783881306064429441088 * q^74 - 204312291750914950304829914412770260373631281822544572731633720960361618548975517964814619460000 * q^75 + 64556217054886497186737063238064337992823205997653378371004031509089422583081356800943896432640 * q^76 + 250231448169383959900618348975396989794902211753647918986458150866408618577007907131029306438400 * q^77 + 1260981709052401111398092363772739439414079820346824747462408082793911096042108256417770344646400 * q^78 + 1474556321278768744579716979675929750918930811984805387023357390321899878561204701118206999166080 * q^79 + 6033438037435277941170744030808192554572458649979375320464765273747209092446481051552234550067200 * q^80 + 14613214105102112111129469132612601529386527627758931132459526147171392070559192290643105065182408 * q^81 + 30083863369214129982421840097969977845328701273986110579467106900080547794123383776302929686086720 * q^82 + 33762254529254022439253159341806143692643909652777369725086142424861011401680843403961249425712160 * q^83 + 57799153837692447414380568170128797835929379783304235587752969314531310322308849537769529417695232 * q^84 + 17314966267116570951109803841412092095679328201414316724042066880549149931729490643535478494114400 * q^85 + 67989564188024628582959760637462873453376851598916319417912395832044408164663357850732592560556416 * q^86 + 2586434133428712948881772736535019341274237946379240114707154003676967765014837223291966941531840 * q^87 - 363099602372059077387783242048689913608334478213970275423791339756517232974574737922754584123146240 * q^88 - 620007165949691950044675276484549383308720953973642955804615855186521697520022438525123333812557360 * q^89 - 4716676146177962028099989697458384454375488041754925418224025761569034561814581975790426208019028800 * q^90 - 3685711793015793225308940042728501386995879977832891226647110522985454537354035281338855172828873344 * q^91 - 4618779932089713137770970202224414792688843158843334085630908366025929325979388063902511470793400320 * q^92 - 3975022445092224432029728046757042348886229630318622378634497589784647142077875089398179428115102720 * q^93 - 17371370943540992303713705925513939673302729250250795188383540356993592041601425149438637190677682688 * q^94 - 2642077700832720169247174948884057845373174576960370774287679094739730873649398763127258995555528000 * q^95 + 4679875418673156206717240026356824763600126819048403120235276936002238426687957733980747642601209856 * q^96 + 64020476116668335744724892375903667651900818166631138467214326399663196857065619648203365824701173520 * q^97 + 202971561788470754768820264959327860776947519106194867162872422213964707447467488105939520314595817120 * q^98 + 225914901454627435116272921386700923755368861971179328902362103653753469396751969300619190223813523808 * 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 $

$2$	5.93582e14	0.372792	0.186396	−	0.982475i	$-0.440319\pi$
$2$	5.93582e14	0.372792	0.186396	+	0.982475i	$0.440319\pi$
$3$	2.15060e24	1.72956	0.864781	−	0.502149i	$-0.167457\pi$
$3$	2.15060e24	1.72956	0.864781	+	0.502149i	$0.167457\pi$
$4$	−2.18296e30	−0.861026
$5$	2.07725e34	0.104593	0.0522965	−	0.998632i	$-0.483346\pi$
$5$	2.07725e34	0.104593	0.0522965	+	0.998632i	$0.483346\pi$
$6$	1.27656e39	0.644766
$7$	−6.15512e42	−1.29356	−0.646778	−	0.762678i	$-0.723884\pi$
$7$	−6.15512e42	−1.29356	−0.646778	+	0.762678i	$0.723884\pi$
$8$	−2.80068e45	−0.693775
$9$	3.07894e48	1.99138
$10$	1.23302e49	0.0389914
$11$	−1.93541e51	−0.0497099	−0.0248550	−	0.999691i	$-0.507912\pi$
$11$	−1.93541e51	−0.0497099	−0.0248550	+	0.999691i	$0.507912\pi$
$12$	−4.69467e54	−1.48920
$13$	2.07990e56	1.15852	0.579260	−	0.815143i	$-0.303341\pi$
$13$	2.07990e56	1.15852	0.579260	+	0.815143i	$0.303341\pi$
$14$	−3.65357e57	−0.482227
$15$	4.46732e58	0.180900
$16$	3.87203e60	0.602393
$17$	9.51139e61	0.692745	0.346373	−	0.938097i	$-0.387413\pi$
$17$	9.51139e61	0.692745	0.346373	+	0.938097i	$0.387413\pi$
$18$	1.82761e63	0.742372
$19$	−2.07479e64	−0.549437	−0.274719	−	0.961525i	$-0.588585\pi$
$19$	−2.07479e64	−0.549437	−0.274719	+	0.961525i	$0.588585\pi$
$20$	−4.53455e64	−0.0900573
$21$	−1.32372e67	−2.23729
$22$	−1.14883e66	−0.0185314
$23$	−1.01002e69	−1.72614	−0.863070	−	0.505084i	$-0.831461\pi$
$23$	−1.01002e69	−1.72614	−0.863070	+	0.505084i	$0.831461\pi$
$24$	−6.02314e69	−1.19993
$25$	−3.90116e70	−0.989060
$26$	1.23459e71	0.431887
$27$	3.29646e72	1.71466
$28$	1.34364e73	1.11379
$29$	−1.12007e74	−1.57815	−0.789073	−	0.614299i	$-0.789439\pi$
$29$	−1.12007e74	−1.57815	−0.789073	+	0.614299i	$0.789439\pi$
$30$	2.65172e73	0.0674381
$31$	−3.39166e75	−1.64682	−0.823410	−	0.567447i	$-0.807931\pi$
$31$	−3.39166e75	−1.64682	−0.823410	+	0.567447i	$0.807931\pi$
$32$	9.39893e75	0.918342
$33$	−4.16230e75	−0.0859764
$34$	5.64580e76	0.258250
$35$	−1.27857e77	−0.135297
$36$	−6.72122e78	−1.71463
$37$	−2.80250e78	−0.179208	−0.0896041	−	0.995977i	$-0.528560\pi$
$37$	−2.80250e78	−0.179208	−0.0896041	+	0.995977i	$0.528560\pi$
$38$	−1.23156e79	−0.204826
$39$	4.47304e80	2.00373
$40$	−5.81770e79	−0.0725640
$41$	−2.18595e81	−0.783531	−0.391765	−	0.920065i	$-0.628136\pi$
$41$	−2.18595e81	−0.783531	−0.391765	+	0.920065i	$0.628136\pi$
$42$	−7.85736e81	−0.834042
$43$	4.27840e82	1.38396	0.691981	−	0.721916i	$-0.256738\pi$
$43$	4.27840e82	1.38396	0.691981	+	0.721916i	$0.256738\pi$
$44$	4.22493e81	0.0428015
$45$	6.39572e82	0.208285
$46$	−5.99533e83	−0.643491
$47$	−4.06463e84	−1.47258	−0.736291	−	0.676665i	$-0.763424\pi$
$47$	−4.06463e84	−1.47258	−0.736291	+	0.676665i	$0.763424\pi$
$48$	8.32719e84	1.04188
$49$	1.52441e85	0.673287
$50$	−2.31566e85	−0.368714
$51$	2.04552e86	1.19815
$52$	−4.54035e86	−0.997517
$53$	−1.28592e87	−1.07965	−0.539824	−	0.841778i	$-0.681509\pi$
$53$	−1.28592e87	−1.07965	−0.539824	+	0.841778i	$0.681509\pi$
$54$	1.95672e87	0.639212
$55$	−4.02033e85	−0.00519931
$56$	1.72385e88	0.897437
$57$	−4.46205e88	−0.950286
$58$	−6.64855e88	−0.588320
$59$	2.29239e88	0.0855583	0.0427792	−	0.999085i	$-0.486379\pi$
$59$	2.29239e88	0.0855583	0.0427792	+	0.999085i	$0.486379\pi$
$60$	−9.75199e88	−0.155760
$61$	1.48144e90	1.02690	0.513451	−	0.858119i	$-0.328367\pi$
$61$	1.48144e90	1.02690	0.513451	+	0.858119i	$0.328367\pi$
$62$	−2.01323e90	−0.613921
$63$	−1.89513e91	−2.57597
$64$	−4.23772e90	−0.260042
$65$	4.32047e90	0.121173
$66$	−2.47067e90	−0.0320513
$67$	−1.12651e92	−0.683844	−0.341922	−	0.939728i	$-0.611078\pi$
$67$	−1.12651e92	−0.683844	−0.341922	+	0.939728i	$0.611078\pi$
$68$	−2.07630e92	−0.596472
$69$	−2.17216e93	−2.98547
$70$	−7.58936e91	−0.0504376
$71$	−1.07138e93	−0.347852	−0.173926	−	0.984759i	$-0.555645\pi$
$71$	−1.07138e93	−0.347852	−0.173926	+	0.984759i	$0.555645\pi$
$72$	−8.62313e93	−1.38157
$73$	8.88946e92	0.0709694	0.0354847	−	0.999370i	$-0.488703\pi$
$73$	8.88946e92	0.0709694	0.0354847	+	0.999370i	$0.488703\pi$
$74$	−1.66351e93	−0.0668074
$75$	−8.38982e94	−1.71064
$76$	4.52919e94	0.473080
$77$	1.19127e94	0.0643026
$78$	2.65512e95	0.746975
$79$	3.94018e95	0.582570	0.291285	−	0.956636i	$-0.405917\pi$
$79$	3.94018e95	0.582570	0.291285	+	0.956636i	$0.405917\pi$
$80$	8.04316e94	0.0630060
$81$	2.32892e96	0.974228
$82$	−1.29754e96	−0.292094
$83$	7.91760e96	0.966385	0.483192	−	0.875514i	$-0.339477\pi$
$83$	7.91760e96	0.966385	0.483192	+	0.875514i	$0.339477\pi$
$84$	2.88963e97	1.92636
$85$	1.97575e96	0.0724563
$86$	2.53958e97	0.515930
$87$	−2.40883e98	−2.72950
$88$	5.42047e96	0.0344875
$89$	1.56456e98	0.562596	0.281298	−	0.959620i	$-0.409235\pi$
$89$	1.56456e98	0.562596	0.281298	+	0.959620i	$0.409235\pi$
$90$	3.79639e97	0.0776469
$91$	−1.28020e99	−1.49861
$92$	2.20484e99	1.48625
$93$	−7.29409e99	−2.84828
$94$	−2.41269e99	−0.548966
$95$	−4.30986e98	−0.0574673
$96$	2.02133e100	1.58833
$97$	6.75748e99	0.314639	0.157319	−	0.987548i	$-0.449715\pi$
$97$	6.75748e99	0.314639	0.157319	+	0.987548i	$0.449715\pi$
$98$	9.04864e99	0.250996
$99$	−5.95903e99	−0.0989916
$100$	8.51607e100	0.851607
$101$	6.91980e100	0.418663	0.209331	−	0.977845i	$-0.432871\pi$
$101$	6.91980e100	0.418663	0.209331	+	0.977845i	$0.432871\pi$
$102$	1.21418e101	0.446659
$103$	3.86032e101	0.867647	0.433823	−	0.900998i	$-0.357164\pi$
$103$	3.86032e101	0.867647	0.433823	+	0.900998i	$0.357164\pi$
$104$	−5.82514e101	−0.803753
$105$	−2.74969e101	−0.234004
$106$	−7.63299e101	−0.402484
$107$	−2.00326e102	−0.657441	−0.328720	−	0.944427i	$-0.606617\pi$
$107$	−2.00326e102	−0.657441	−0.328720	+	0.944427i	$0.606617\pi$
$108$	−7.19605e102	−1.47637
$109$	7.50780e102	0.967107	0.483553	−	0.875315i	$-0.339346\pi$
$109$	7.50780e102	0.967107	0.483553	+	0.875315i	$0.339346\pi$
$110$	−2.38640e100	−0.00193826
$111$	−6.02705e102	−0.309952
$112$	−2.38328e103	−0.779229
$113$	2.79242e103	0.582800	0.291400	−	0.956601i	$-0.405879\pi$
$113$	2.79242e103	0.582800	0.291400	+	0.956601i	$0.405879\pi$
$114$	−2.64860e103	−0.354259
$115$	−2.09807e103	−0.180542
$116$	2.44507e104	1.35883
$117$	6.40391e104	2.30706
$118$	1.36072e103	0.0318954
$119$	−5.85437e104	−0.896105
$120$	−1.25115e104	−0.125504
$121$	−1.51212e105	−0.997529
$122$	8.79360e104	0.382820
$123$	−4.70111e105	−1.35517
$124$	7.40385e105	1.41796
$125$	−1.62969e105	−0.208042
$126$	−1.12491e106	−0.960299
$127$	−2.25447e106	−1.29109	−0.645544	−	0.763723i	$-0.723369\pi$
$127$	−2.25447e106	−1.29109	−0.645544	+	0.763723i	$0.723369\pi$
$128$	−2.63446e106	−1.01528
$129$	9.20112e106	2.39365
$130$	2.56456e105	0.0451724
$131$	4.52448e106	0.541213	0.270606	−	0.962690i	$-0.412776\pi$
$131$	4.52448e106	0.541213	0.270606	+	0.962690i	$0.412776\pi$
$132$	9.08613e105	0.0740279
$133$	1.27706e107	0.710728
$134$	−6.68676e106	−0.254931
$135$	6.84757e106	0.179342
$136$	−2.66383e107	−0.480610
$137$	1.30756e108	1.62957	0.814787	−	0.579761i	$-0.196854\pi$
$137$	1.30756e108	1.62957	0.814787	+	0.579761i	$0.196854\pi$
$138$	−1.28935e108	−1.11296
$139$	−1.97428e107	−0.118348	−0.0591742	−	0.998248i	$-0.518847\pi$
$139$	−1.97428e107	−0.118348	−0.0591742	+	0.998248i	$0.518847\pi$
$140$	2.79107e107	0.116494
$141$	−8.74139e108	−2.54692
$142$	−6.35950e107	−0.129677
$143$	−4.02547e107	−0.0575900
$144$	1.19218e109	1.19960
$145$	−2.32667e108	−0.165063
$146$	5.27663e107	0.0264568
$147$	3.27840e109	1.16449
$148$	6.11774e108	0.154303
$149$	3.36638e109	0.604305	0.302153	−	0.953260i	$-0.402295\pi$
$149$	3.36638e109	0.604305	0.302153	+	0.953260i	$0.402295\pi$
$150$	−4.98005e109	−0.637713
$151$	−7.09829e109	−0.649857	−0.324929	−	0.945739i	$-0.605340\pi$
$151$	−7.09829e109	−0.649857	−0.324929	+	0.945739i	$0.605340\pi$
$152$	5.81083e109	0.381186
$153$	2.92851e110	1.37952
$154$	7.07116e108	0.0239715
$155$	−7.04530e109	−0.172246
$156$	−9.76447e110	−1.72527
$157$	−3.72274e110	−0.476354	−0.238177	−	0.971222i	$-0.576550\pi$
$157$	−3.72274e110	−0.476354	−0.238177	+	0.971222i	$0.576550\pi$
$158$	2.33882e110	0.217177
$159$	−2.76550e111	−1.86732
$160$	1.95239e110	0.0960522
$161$	6.21682e111	2.23286
$162$	1.38240e111	0.363184
$163$	−4.16933e111	−0.802771	−0.401386	−	0.915909i	$-0.631471\pi$
$163$	−4.16933e111	−0.802771	−0.401386	+	0.915909i	$0.631471\pi$
$164$	4.77185e111	0.674641
$165$	−8.64611e109	−0.00899253
$166$	4.69975e111	0.360260
$167$	−9.93308e111	−0.562215	−0.281107	−	0.959676i	$-0.590702\pi$
$167$	−9.93308e111	−0.562215	−0.281107	+	0.959676i	$0.590702\pi$
$168$	3.70731e112	1.55217
$169$	1.10286e112	0.342171
$170$	1.17277e111	0.0270111
$171$	−6.38818e112	−1.09414
$172$	−9.33958e112	−1.19163
$173$	−5.87533e112	−0.559377	−0.279688	−	0.960091i	$-0.590231\pi$
$173$	−5.87533e112	−0.559377	−0.279688	+	0.960091i	$0.590231\pi$
$174$	−1.42984e113	−1.01754
$175$	2.40121e113	1.27940
$176$	−7.49398e111	−0.0299449
$177$	4.93002e112	0.147978
$178$	9.28695e112	0.209731
$179$	2.72675e113	0.464053	0.232027	−	0.972709i	$-0.425464\pi$
$179$	2.72675e113	0.464053	0.232027	+	0.972709i	$0.425464\pi$
$180$	−1.39616e113	−0.179339
$181$	−4.92080e113	−0.477823	−0.238912	−	0.971041i	$-0.576791\pi$
$181$	−4.92080e113	−0.477823	−0.238912	+	0.971041i	$0.576791\pi$
$182$	−7.59907e113	−0.558670
$183$	3.18599e114	1.77609
$184$	2.82875e114	1.19755
$185$	−5.82147e112	−0.0187439
$186$	−4.32964e114	−1.06181
$187$	−1.84085e113	−0.0344363
$188$	8.87293e114	1.26793
$189$	−2.02901e115	−2.21801
$190$	−2.55826e113	−0.0214233
$191$	−2.75631e115	−1.77069	−0.885346	−	0.464933i	$-0.846079\pi$
$191$	−2.75631e115	−1.77069	−0.885346	+	0.464933i	$0.846079\pi$
$192$	−9.11364e114	−0.449759
$193$	4.98329e115	1.89179	0.945893	−	0.324479i	$-0.105189\pi$
$193$	4.98329e115	1.89179	0.945893	+	0.324479i	$0.105189\pi$
$194$	4.01112e114	0.117295
$195$	9.29160e114	0.209577
$196$	−3.32773e115	−0.579718
$197$	7.76102e115	1.04562	0.522810	−	0.852449i	$-0.324884\pi$
$197$	7.76102e115	1.04562	0.522810	+	0.852449i	$0.324884\pi$
$198$	−3.53718e114	−0.0369032
$199$	3.53197e115	0.285717	0.142859	−	0.989743i	$-0.454371\pi$
$199$	3.53197e115	0.285717	0.142859	+	0.989743i	$0.454371\pi$
$200$	1.09259e116	0.686186
$201$	−2.42267e116	−1.18275
$202$	4.10747e115	0.156074
$203$	6.89418e116	2.04142
$204$	−4.46529e116	−1.03164
$205$	−4.54076e115	−0.0819518
$206$	2.29142e116	0.323452
$207$	−3.10981e117	−3.43741
$208$	8.05345e116	0.697884
$209$	4.01558e115	0.0273125
$210$	−1.63217e116	−0.0872349
$211$	2.23121e117	0.938158	0.469079	−	0.883156i	$-0.344586\pi$
$211$	2.23121e117	0.938158	0.469079	+	0.883156i	$0.344586\pi$
$212$	2.80711e117	0.929606
$213$	−2.30410e117	−0.601632
$214$	−1.18910e117	−0.245088
$215$	8.88728e116	0.144753
$216$	−9.23233e117	−1.18959
$217$	2.08760e118	2.13025
$218$	4.45650e117	0.360529
$219$	1.91177e117	0.122746
$220$	8.77622e115	0.00447674
$221$	1.97828e118	0.802560
$222$	−3.57755e117	−0.115547
$223$	−3.91127e118	−1.00675	−0.503376	−	0.864068i	$-0.667909\pi$
$223$	−3.91127e118	−1.00675	−0.503376	+	0.864068i	$0.667909\pi$
$224$	−5.78515e118	−1.18793
$225$	−1.20114e119	−1.96960
$226$	1.65753e118	0.217263
$227$	7.18962e118	0.754050	0.377025	−	0.926203i	$-0.376947\pi$
$227$	7.18962e118	0.754050	0.377025	+	0.926203i	$0.376947\pi$
$228$	9.74048e118	0.818221
$229$	2.25539e118	0.151890	0.0759452	−	0.997112i	$-0.475803\pi$
$229$	2.25539e118	0.151890	0.0759452	+	0.997112i	$0.475803\pi$
$230$	−1.24538e118	−0.0673046
$231$	2.56194e118	0.111215
$232$	3.13696e119	1.09488
$233$	−4.34636e119	−1.22082	−0.610410	−	0.792085i	$-0.708995\pi$
$233$	−4.34636e119	−1.22082	−0.610410	+	0.792085i	$0.708995\pi$
$234$	3.80125e119	0.860053
$235$	−8.44324e118	−0.154022
$236$	−5.00420e118	−0.0736680
$237$	8.47375e119	1.00759
$238$	−3.47505e119	−0.334061
$239$	5.86452e119	0.456183	0.228091	−	0.973640i	$-0.426752\pi$
$239$	5.86452e119	0.456183	0.228091	+	0.973640i	$0.426752\pi$
$240$	1.72976e119	0.108973
$241$	−2.33319e120	−1.19149	−0.595743	−	0.803175i	$-0.703142\pi$
$241$	−2.33319e120	−1.19149	−0.595743	+	0.803175i	$0.703142\pi$
$242$	−8.97569e119	−0.371871
$243$	−8.82029e118	−0.0296733
$244$	−3.23394e120	−0.884189
$245$	3.16658e119	0.0704211
$246$	−2.79050e120	−0.505194
$247$	−4.31537e120	−0.636535
$248$	9.49893e120	1.14252
$249$	1.70276e121	1.67142
$250$	−9.67358e119	−0.0775563
$251$	−2.88476e121	−1.89055	−0.945273	−	0.326280i	$-0.894205\pi$
$251$	−2.88476e121	−1.89055	−0.945273	+	0.326280i	$0.894205\pi$
$252$	4.13699e121	2.21798
$253$	1.95481e120	0.0858063
$254$	−1.33821e121	−0.481307
$255$	4.24905e120	0.125318
$256$	−4.89376e120	−0.118447
$257$	1.22979e120	0.0244461	0.0122230	−	0.999925i	$-0.496109\pi$
$257$	1.22979e120	0.0244461	0.0122230	+	0.999925i	$0.496109\pi$
$258$	5.46162e121	0.892332
$259$	1.72497e121	0.231816
$260$	−9.43142e120	−0.104333
$261$	−3.44864e122	−3.14270
$262$	2.68565e121	0.201760
$263$	−3.92088e121	−0.243006	−0.121503	−	0.992591i	$-0.538771\pi$
$263$	−3.92088e121	−0.243006	−0.121503	+	0.992591i	$0.538771\pi$
$264$	1.16573e121	0.0596483
$265$	−2.67117e121	−0.112924
$266$	7.58040e121	0.264954
$267$	3.36474e122	0.973045
$268$	2.45912e122	0.588808
$269$	4.57510e122	0.907634	0.453817	−	0.891095i	$-0.350062\pi$
$269$	4.57510e122	0.907634	0.453817	+	0.891095i	$0.350062\pi$
$270$	4.06459e121	0.0668570
$271$	−1.82542e122	−0.249123	−0.124562	−	0.992212i	$-0.539752\pi$
$271$	−1.82542e122	−0.249123	−0.124562	+	0.992212i	$0.539752\pi$
$272$	3.68284e122	0.417305
$273$	−2.75321e123	−2.59194
$274$	7.76146e122	0.607492
$275$	7.55035e121	0.0491661
$276$	4.74173e123	2.57056
$277$	1.06562e123	0.481256	0.240628	−	0.970617i	$-0.422647\pi$
$277$	1.06562e123	0.481256	0.240628	+	0.970617i	$0.422647\pi$
$278$	−1.17190e122	−0.0441193
$279$	−1.04427e124	−3.27945
$280$	3.58086e122	0.0938656
$281$	3.52617e123	0.772029	0.386015	−	0.922493i	$-0.373851\pi$
$281$	3.52617e123	0.772029	0.386015	+	0.922493i	$0.373851\pi$
$282$	−5.18874e123	−0.949471
$283$	−5.45476e123	−0.834758	−0.417379	−	0.908732i	$-0.637051\pi$
$283$	−5.45476e123	−0.834758	−0.417379	+	0.908732i	$0.637051\pi$
$284$	2.33877e123	0.299510
$285$	−9.26877e122	−0.0993933
$286$	−2.38945e122	−0.0214691
$287$	1.34548e124	1.01354
$288$	2.89388e124	1.82877
$289$	−9.80463e123	−0.520104
$290$	−1.38107e123	−0.0615341
$291$	1.45326e124	0.544187
$292$	−1.94053e123	−0.0611065
$293$	−3.35595e124	−0.889203	−0.444601	−	0.895729i	$-0.646655\pi$
$293$	−3.35595e124	−0.889203	−0.444601	+	0.895729i	$0.646655\pi$
$294$	1.94600e124	0.434113
$295$	4.76186e122	0.00894880
$296$	7.84889e123	0.124330
$297$	−6.38002e123	−0.0852357
$298$	1.99822e124	0.225280
$299$	−2.10075e125	−1.99977
$300$	1.83147e125	1.47291
$301$	−2.63340e125	−1.79023
$302$	−4.21342e124	−0.242261
$303$	1.48817e125	0.724103
$304$	−8.03367e124	−0.330977
$305$	3.07732e124	0.107407
$306$	1.73831e125	0.514275
$307$	7.02970e124	0.176380	0.0881900	−	0.996104i	$-0.471892\pi$
$307$	7.02970e124	0.176380	0.0881900	+	0.996104i	$0.471892\pi$
$308$	−2.60049e124	−0.0553662
$309$	8.30199e125	1.50065
$310$	−4.18197e124	−0.0642118
$311$	1.14224e126	1.49058	0.745291	−	0.666739i	$-0.232310\pi$
$311$	1.14224e126	1.49058	0.745291	+	0.666739i	$0.232310\pi$
$312$	−1.25275e126	−1.39014
$313$	−6.45867e125	−0.609753	−0.304876	−	0.952392i	$-0.598615\pi$
$313$	−6.45867e125	−0.609753	−0.304876	+	0.952392i	$0.598615\pi$
$314$	−2.20975e125	−0.177581
$315$	−3.93664e125	−0.269428
$316$	−8.60126e125	−0.501608
$317$	2.85359e126	1.41873	0.709364	−	0.704843i	$-0.248982\pi$
$317$	2.85359e126	1.41873	0.709364	+	0.704843i	$0.248982\pi$
$318$	−1.64155e126	−0.696121
$319$	2.16780e125	0.0784495
$320$	−8.80279e124	−0.0271986
$321$	−4.30821e126	−1.13708
$322$	3.69019e126	0.832391
$323$	−1.97342e126	−0.380620
$324$	−5.08394e126	−0.838836
$325$	−8.11403e126	−1.14585
$326$	−2.47484e126	−0.299266
$327$	1.61463e127	1.67267
$328$	6.12215e126	0.543594
$329$	2.50183e127	1.90487
$330$	−5.13218e124	−0.00335234
$331$	1.94587e127	1.09094	0.545469	−	0.838131i	$-0.316351\pi$
$331$	1.94587e127	1.09094	0.545469	+	0.838131i	$0.316351\pi$
$332$	−1.72838e127	−0.832083
$333$	−8.62873e126	−0.356873
$334$	−5.89610e126	−0.209589
$335$	−2.34004e126	−0.0715253
$336$	−5.12548e127	−1.34772
$337$	−3.84815e127	−0.870848	−0.435424	−	0.900225i	$-0.643402\pi$
$337$	−3.84815e127	−0.870848	−0.435424	+	0.900225i	$0.643402\pi$
$338$	6.54640e126	0.127558
$339$	6.00537e127	1.00799
$340$	−4.31298e126	−0.0623868
$341$	6.56425e126	0.0818633
$342$	−3.79191e127	−0.407887
$343$	4.55307e127	0.422621
$344$	−1.19824e128	−0.960159
$345$	−4.51210e127	−0.312259
$346$	−3.48749e127	−0.208531
$347$	−5.10458e127	−0.263828	−0.131914	−	0.991261i	$-0.542112\pi$
$347$	−5.10458e127	−0.263828	−0.131914	+	0.991261i	$0.542112\pi$
$348$	5.25838e128	2.35017
$349$	−2.94005e128	−1.13677	−0.568383	−	0.822764i	$-0.692431\pi$
$349$	−2.94005e128	−1.13677	−0.568383	+	0.822764i	$0.692431\pi$
$350$	1.42531e128	0.476952
$351$	6.85633e128	1.98647
$352$	−1.81908e127	−0.0456507
$353$	−3.11192e128	−0.676714	−0.338357	−	0.941018i	$-0.609871\pi$
$353$	−3.11192e128	−0.676714	−0.338357	+	0.941018i	$0.609871\pi$
$354$	2.92637e127	0.0551651
$355$	−2.22551e127	−0.0363829
$356$	−3.41537e128	−0.484410
$357$	−1.25904e129	−1.54987
$358$	1.61855e128	0.172995
$359$	1.27605e129	1.18467	0.592336	−	0.805691i	$-0.298206\pi$
$359$	1.27605e129	1.18467	0.592336	+	0.805691i	$0.298206\pi$
$360$	−1.79124e128	−0.144503
$361$	−9.95504e128	−0.698119
$362$	−2.92090e128	−0.178129
$363$	−3.25197e129	−1.72529
$364$	2.79464e129	1.29034
$365$	1.84656e127	0.00742290
$366$	1.89115e129	0.662112
$367$	3.07513e129	0.938052	0.469026	−	0.883184i	$-0.344605\pi$
$367$	3.07513e129	0.938052	0.469026	+	0.883184i	$0.344605\pi$
$368$	−3.91084e129	−1.03981
$369$	−6.73043e129	−1.56031
$370$	−3.45552e127	−0.00698758
$371$	7.91499e129	1.39659
$372$	1.59227e130	2.45244
$373$	−9.10110e128	−0.122405	−0.0612023	−	0.998125i	$-0.519493\pi$
$373$	−9.10110e128	−0.122405	−0.0612023	+	0.998125i	$0.519493\pi$
$374$	−1.09269e128	−0.0128376
$375$	−3.50482e129	−0.359821
$376$	1.13837e130	1.02164
$377$	−2.32964e130	−1.82832
$378$	−1.20439e130	−0.826856
$379$	1.67118e130	1.00402	0.502011	−	0.864861i	$-0.332594\pi$
$379$	1.67118e130	1.00402	0.502011	+	0.864861i	$0.332594\pi$
$380$	9.40825e128	0.0494809
$381$	−4.84845e130	−2.23302
$382$	−1.63610e130	−0.660099
$383$	4.34816e130	1.53733	0.768666	−	0.639650i	$-0.220921\pi$
$383$	4.34816e130	1.53733	0.768666	+	0.639650i	$0.220921\pi$
$384$	−5.66566e130	−1.75600
$385$	2.47456e128	0.00672560
$386$	2.95799e130	0.705242
$387$	1.31730e131	2.75600
$388$	−1.47513e130	−0.270912
$389$	−2.46326e130	−0.397242	−0.198621	−	0.980076i	$-0.563646\pi$
$389$	−2.46326e130	−0.397242	−0.198621	+	0.980076i	$0.563646\pi$
$390$	5.51533e129	0.0781284
$391$	−9.60674e130	−1.19578
$392$	−4.26939e130	−0.467110
$393$	9.73034e130	0.936061
$394$	4.60680e130	0.389799
$395$	8.18472e129	0.0609327
$396$	1.30083e130	0.0852343
$397$	1.12850e131	0.651001	0.325500	−	0.945542i	$-0.394467\pi$
$397$	1.12850e131	0.651001	0.325500	+	0.945542i	$0.394467\pi$
$398$	2.09651e130	0.106513
$399$	2.74644e131	1.22925
$400$	−1.51054e131	−0.595803
$401$	−2.71882e131	−0.945343	−0.472672	−	0.881239i	$-0.656710\pi$
$401$	−2.71882e131	−0.945343	−0.472672	+	0.881239i	$0.656710\pi$
$402$	−1.43805e131	−0.440920
$403$	−7.05431e131	−1.90788
$404$	−1.51057e131	−0.360480
$405$	4.83773e130	0.101897
$406$	4.09226e131	0.761025
$407$	5.42399e129	0.00890843
$408$	−5.72884e131	−0.831244
$409$	4.67974e131	0.600059	0.300030	−	0.953930i	$-0.403003\pi$
$409$	4.67974e131	0.600059	0.300030	+	0.953930i	$0.403003\pi$
$410$	−2.69532e130	−0.0305510
$411$	2.81204e132	2.81845
$412$	−8.42692e131	−0.747067
$413$	−1.41099e131	−0.110674
$414$	−1.84593e132	−1.28144
$415$	1.64468e131	0.101077
$416$	1.95489e132	1.06392
$417$	−4.24589e131	−0.204691
$418$	2.38358e130	0.0101819
$419$	1.77543e132	0.672194	0.336097	−	0.941827i	$-0.390893\pi$
$419$	1.77543e132	0.672194	0.336097	+	0.941827i	$0.390893\pi$
$420$	6.00246e131	0.201484
$421$	2.58058e132	0.768194	0.384097	−	0.923293i	$-0.374513\pi$
$421$	2.58058e132	0.768194	0.384097	+	0.923293i	$0.374513\pi$
$422$	1.32441e132	0.349738
$423$	−1.25148e133	−2.93248
$424$	3.60145e132	0.749034
$425$	−3.71054e132	−0.685167
$426$	−1.36767e132	−0.224284
$427$	−9.11847e132	−1.32835
$428$	4.37304e132	0.566074
$429$	−8.65718e131	−0.0996054
$430$	5.27534e131	0.0539626
$431$	−6.70076e132	−0.609568	−0.304784	−	0.952422i	$-0.598584\pi$
$431$	−6.70076e132	−0.609568	−0.304784	+	0.952422i	$0.598584\pi$
$432$	1.27640e133	1.03290
$433$	2.06034e133	1.48354	0.741771	−	0.670653i	$-0.233986\pi$
$433$	2.06034e133	1.48354	0.741771	+	0.670653i	$0.233986\pi$
$434$	1.23916e133	0.794141
$435$	−5.00373e132	−0.285487
$436$	−1.63892e133	−0.832704
$437$	2.09559e133	0.948406
$438$	1.13479e132	0.0457587
$439$	−2.98273e133	−1.07190	−0.535952	−	0.844249i	$-0.680047\pi$
$439$	−2.98273e133	−1.07190	−0.535952	+	0.844249i	$0.680047\pi$
$440$	1.12596e131	0.00360715
$441$	4.69358e133	1.34077
$442$	1.17427e133	0.299188
$443$	−8.60604e133	−1.95621	−0.978105	−	0.208113i	$-0.933268\pi$
$443$	−8.60604e133	−1.95621	−0.978105	+	0.208113i	$0.933268\pi$
$444$	1.31568e133	0.266877
$445$	3.24997e132	0.0588436
$446$	−2.32166e133	−0.375308
$447$	7.23973e133	1.04518
$448$	2.60837e133	0.336379
$449$	−7.10386e133	−0.818567	−0.409283	−	0.912407i	$-0.634221\pi$
$449$	−7.10386e133	−0.818567	−0.409283	+	0.912407i	$0.634221\pi$
$450$	−7.12978e133	−0.734250
$451$	4.23072e132	0.0389493
$452$	−6.09574e133	−0.501806
$453$	−1.52656e134	−1.12397
$454$	4.26763e133	0.281104
$455$	−2.65930e133	−0.156744
$456$	1.24968e134	0.659285
$457$	1.42058e134	0.670962	0.335481	−	0.942047i	$-0.391101\pi$
$457$	1.42058e134	0.670962	0.335481	+	0.942047i	$0.391101\pi$
$458$	1.33876e133	0.0566235
$459$	3.13540e134	1.18782
$460$	4.58000e133	0.155452
$461$	6.35945e134	1.93430	0.967148	−	0.254214i	$-0.0818168\pi$
$461$	6.35945e134	1.93430	0.967148	+	0.254214i	$0.0818168\pi$
$462$	1.52072e133	0.0414601
$463$	−4.26577e134	−1.04270	−0.521348	−	0.853344i	$-0.674571\pi$
$463$	−4.26577e134	−1.04270	−0.521348	+	0.853344i	$0.674571\pi$
$464$	−4.33696e134	−0.950664
$465$	−1.51516e134	−0.297910
$466$	−2.57992e134	−0.455112
$467$	7.39973e134	1.17142	0.585711	−	0.810520i	$-0.300815\pi$
$467$	7.39973e134	1.17142	0.585711	+	0.810520i	$0.300815\pi$
$468$	−1.39795e135	−1.98644
$469$	6.93379e134	0.884591
$470$	−5.01176e133	−0.0574180
$471$	−8.00612e134	−0.823885
$472$	−6.42025e133	−0.0593582
$473$	−8.28047e133	−0.0687966
$474$	5.02987e134	0.375621
$475$	8.09409e134	0.543427
$476$	1.27799e135	0.771570
$477$	−3.95928e135	−2.15000
$478$	3.48108e134	0.170061
$479$	−7.32367e134	−0.321948	−0.160974	−	0.986959i	$-0.551464\pi$
$479$	−7.32367e134	−0.321948	−0.160974	+	0.986959i	$0.551464\pi$
$480$	4.19881e134	0.166128
$481$	−5.82892e134	−0.207617
$482$	−1.38494e135	−0.444176
$483$	1.33699e136	3.86187
$484$	3.30090e135	0.858899
$485$	1.40369e134	0.0329090
$486$	−5.23557e133	−0.0110620
$487$	−5.67086e135	−1.08003	−0.540016	−	0.841655i	$-0.681582\pi$
$487$	−5.67086e135	−1.08003	−0.540016	+	0.841655i	$0.681582\pi$
$488$	−4.14905e135	−0.712439
$489$	−8.96655e135	−1.38844
$490$	1.87963e134	0.0262524
$491$	1.09683e135	0.138205	0.0691027	−	0.997610i	$-0.477986\pi$
$491$	1.09683e135	0.138205	0.0691027	+	0.997610i	$0.477986\pi$
$492$	1.02623e136	1.16683
$493$	−1.06535e136	−1.09325
$494$	−2.56153e135	−0.237295
$495$	−1.23784e134	−0.0103538
$496$	−1.31326e136	−0.992032
$497$	6.59444e135	0.449967
$498$	1.01073e136	0.623093
$499$	1.68834e136	0.940550	0.470275	−	0.882520i	$-0.344155\pi$
$499$	1.68834e136	0.940550	0.470275	+	0.882520i	$0.344155\pi$
$500$	3.55756e135	0.179129
$501$	−2.13621e136	−0.972385
$502$	−1.71235e136	−0.704780
$503$	−4.59541e136	−1.71057	−0.855285	−	0.518158i	$-0.826618\pi$
$503$	−4.59541e136	−1.71057	−0.855285	+	0.518158i	$0.826618\pi$
$504$	5.30764e136	1.78714
$505$	1.43741e135	0.0437892
$506$	1.16034e135	0.0319879
$507$	2.37181e136	0.591805
$508$	4.92141e136	1.11166
$509$	3.06425e136	0.626724	0.313362	−	0.949634i	$-0.398545\pi$
$509$	3.06425e136	0.626724	0.313362	+	0.949634i	$0.398545\pi$
$510$	2.52216e135	0.0467174
$511$	−5.47157e135	−0.0918029
$512$	6.38865e136	0.971128
$513$	−6.83949e136	−0.942099
$514$	7.29983e134	0.00911329
$515$	8.01882e135	0.0907498
$516$	−2.00857e137	−2.06099
$517$	7.86674e135	0.0732019
$518$	1.02391e136	0.0864191
$519$	−1.26355e137	−0.967476
$520$	−1.21002e136	−0.0840669
$521$	4.01949e136	0.253435	0.126717	−	0.991939i	$-0.459556\pi$
$521$	4.01949e136	0.253435	0.126717	+	0.991939i	$0.459556\pi$
$522$	−2.04705e137	−1.17157
$523$	1.74801e137	0.908256	0.454128	−	0.890937i	$-0.349951\pi$
$523$	1.74801e137	0.908256	0.454128	+	0.890937i	$0.349951\pi$
$524$	−9.87676e136	−0.465999
$525$	5.16403e137	2.21281
$526$	−2.32736e136	−0.0905908
$527$	−3.22594e137	−1.14083
$528$	−1.61165e136	−0.0517915
$529$	6.77766e137	1.97956
$530$	−1.58556e136	−0.0420970
$531$	7.05815e136	0.170379
$532$	−2.78777e137	−0.611956
$533$	−4.54657e137	−0.907737
$534$	1.99725e137	0.362743
$535$	−4.16126e136	−0.0687637
$536$	3.15499e137	0.474434
$537$	5.86415e137	0.802609
$538$	2.71570e137	0.338359
$539$	−2.95037e136	−0.0334691
$540$	−1.49480e137	−0.154418
$541$	−1.25633e138	−1.18207	−0.591034	−	0.806647i	$-0.701280\pi$
$541$	−1.25633e138	−1.18207	−0.591034	+	0.806647i	$0.701280\pi$
$542$	−1.08354e137	−0.0928711
$543$	−1.05827e138	−0.826425
$544$	8.93969e137	0.636177
$545$	1.55955e137	0.101153
$546$	−1.63426e138	−0.966254
$547$	−2.40142e138	−1.29452	−0.647259	−	0.762270i	$-0.724085\pi$
$547$	−2.40142e138	−1.29452	−0.647259	+	0.762270i	$0.724085\pi$
$548$	−2.85436e138	−1.40311
$549$	4.56129e138	2.04496
$550$	4.48175e136	0.0183287
$551$	2.32392e138	0.867093
$552$	6.08351e138	2.07124
$553$	−2.42523e138	−0.753587
$554$	6.32536e137	0.179408
$555$	−1.25197e137	−0.0324188
$556$	4.30979e137	0.101901
$557$	−2.32646e138	−0.502353	−0.251176	−	0.967941i	$-0.580817\pi$
$557$	−2.32646e138	−0.502353	−0.251176	+	0.967941i	$0.580817\pi$
$558$	−6.19861e138	−1.22255
$559$	8.89866e138	1.60335
$560$	−4.95066e137	−0.0815019
$561$	−3.95892e137	−0.0595597
$562$	2.09307e138	0.287806
$563$	−1.12700e139	−1.41661	−0.708306	−	0.705906i	$-0.750540\pi$
$563$	−1.12700e139	−1.41661	−0.708306	+	0.705906i	$0.750540\pi$
$564$	1.90821e139	2.19297
$565$	5.80054e137	0.0609568
$566$	−3.23785e138	−0.311191
$567$	−1.43348e139	−1.26022
$568$	3.00058e138	0.241331
$569$	−6.22965e138	−0.458452	−0.229226	−	0.973373i	$-0.573620\pi$
$569$	−6.22965e138	−0.458452	−0.229226	+	0.973373i	$0.573620\pi$
$570$	−5.50178e137	−0.0370530
$571$	−1.06373e139	−0.655704	−0.327852	−	0.944729i	$-0.606325\pi$
$571$	−1.06373e139	−0.655704	−0.327852	+	0.944729i	$0.606325\pi$
$572$	8.78745e137	0.0495865
$573$	−5.92772e139	−3.06252
$574$	7.98653e138	0.377840
$575$	3.94026e139	1.70726
$576$	−1.30477e139	−0.517844
$577$	3.61142e139	1.31310	0.656552	−	0.754281i	$-0.272014\pi$
$577$	3.61142e139	1.31310	0.656552	+	0.754281i	$0.272014\pi$
$578$	−5.81986e138	−0.193890
$579$	1.07171e140	3.27196
$580$	5.07902e138	0.142124
$581$	−4.87338e139	−1.25007
$582$	8.62632e138	0.202869
$583$	2.48879e138	0.0536692
$584$	−2.48965e138	−0.0492368
$585$	1.33025e139	0.241302
$586$	−1.99203e139	−0.331487
$587$	−9.37398e139	−1.43120	−0.715599	−	0.698511i	$-0.753846\pi$
$587$	−9.37398e139	−1.43120	−0.715599	+	0.698511i	$0.753846\pi$
$588$	−7.15662e139	−1.00266
$589$	7.03699e139	0.904824
$590$	2.82656e137	0.00333604
$591$	1.66908e140	1.80847
$592$	−1.08514e139	−0.107954
$593$	−1.79083e140	−1.63603	−0.818015	−	0.575197i	$-0.804926\pi$
$593$	−1.79083e140	−1.63603	−0.818015	+	0.575197i	$0.804926\pi$
$594$	−3.78707e138	−0.0317751
$595$	−1.21610e139	−0.0937263
$596$	−7.34868e139	−0.520323
$597$	7.59584e139	0.494165
$598$	−1.24697e140	−0.745497
$599$	−8.24207e139	−0.452879	−0.226439	−	0.974025i	$-0.572709\pi$
$599$	−8.24207e139	−0.452879	−0.226439	+	0.974025i	$0.572709\pi$
$600$	2.34972e140	1.18680
$601$	1.29641e140	0.601980	0.300990	−	0.953627i	$-0.402683\pi$
$601$	1.29641e140	0.601980	0.300990	+	0.953627i	$0.402683\pi$
$602$	−1.56314e140	−0.667384
$603$	−3.46846e140	−1.36180
$604$	1.54953e140	0.559544
$605$	−3.14105e139	−0.104335
$606$	8.83353e139	0.269940
$607$	4.97901e140	1.39996	0.699978	−	0.714164i	$-0.253193\pi$
$607$	4.97901e140	1.39996	0.699978	+	0.714164i	$0.253193\pi$
$608$	−1.95008e140	−0.504572
$609$	1.48266e141	3.53076
$610$	1.82665e139	0.0400403
$611$	−8.45404e140	−1.70602
$612$	−6.39281e140	−1.18781
$613$	2.08079e140	0.356019	0.178010	−	0.984029i	$-0.443034\pi$
$613$	2.08079e140	0.356019	0.178010	+	0.984029i	$0.443034\pi$
$614$	4.17271e139	0.0657530
$615$	−9.76536e139	−0.141741
$616$	−3.33636e139	−0.0446115
$617$	−8.92522e140	−1.09956	−0.549779	−	0.835310i	$-0.685288\pi$
$617$	−8.92522e140	−1.09956	−0.549779	+	0.835310i	$0.685288\pi$
$618$	4.92792e140	0.559429
$619$	4.62079e140	0.483436	0.241718	−	0.970347i	$-0.422289\pi$
$619$	4.62079e140	0.483436	0.241718	+	0.970347i	$0.422289\pi$
$620$	1.53796e140	0.148308
$621$	−3.32951e141	−2.95974
$622$	6.78011e140	0.555677
$623$	−9.63005e140	−0.727750
$624$	1.73197e141	1.20703
$625$	1.50488e141	0.967301
$626$	−3.83375e140	−0.227311
$627$	8.63591e139	0.0472386
$628$	8.12660e140	0.410154
$629$	−2.66556e140	−0.124146
$630$	−2.33672e140	−0.100441
$631$	−3.56470e141	−1.41430	−0.707148	−	0.707066i	$-0.750018\pi$
$631$	−3.56470e141	−1.41430	−0.707148	+	0.707066i	$0.750018\pi$
$632$	−1.10352e141	−0.404173
$633$	4.79844e141	1.62260
$634$	1.69384e141	0.528890
$635$	−4.68308e140	−0.135039
$636$	6.03697e141	1.60781
$637$	3.17063e141	0.780017
$638$	1.28677e140	0.0292453
$639$	−3.29871e141	−0.692708
$640$	−5.47241e140	−0.106192
$641$	−1.80821e140	−0.0324278	−0.0162139	−	0.999869i	$-0.505161\pi$
$641$	−1.80821e140	−0.0324278	−0.0162139	+	0.999869i	$0.505161\pi$
$642$	−2.55728e141	−0.423896
$643$	5.93023e140	0.0908693	0.0454347	−	0.998967i	$-0.485533\pi$
$643$	5.93023e140	0.0908693	0.0454347	+	0.998967i	$0.485533\pi$
$644$	−1.35711e142	−1.92255
$645$	1.91130e141	0.250359
$646$	−1.17139e141	−0.141892
$647$	−1.30820e142	−1.46558	−0.732788	−	0.680457i	$-0.761781\pi$
$647$	−1.30820e142	−1.46558	−0.732788	+	0.680457i	$0.761781\pi$
$648$	−6.52255e141	−0.675895
$649$	−4.43672e139	−0.00425310
$650$	−4.81634e141	−0.427162
$651$	4.48960e142	3.68441
$652$	9.10148e141	0.691207
$653$	−2.39043e142	−1.68020	−0.840100	−	0.542431i	$-0.817504\pi$
$653$	−2.39043e142	−1.68020	−0.840100	+	0.542431i	$0.817504\pi$
$654$	9.58414e141	0.623558
$655$	9.39845e140	0.0566071
$656$	−8.46408e141	−0.471993
$657$	2.73702e141	0.141327
$658$	1.48504e142	0.710119
$659$	−2.10277e142	−0.931278	−0.465639	−	0.884975i	$-0.654175\pi$
$659$	−2.10277e142	−0.931278	−0.465639	+	0.884975i	$0.654175\pi$
$660$	1.88741e140	0.00774280
$661$	−1.91977e142	−0.729583	−0.364792	−	0.931089i	$-0.618860\pi$
$661$	−1.91977e142	−0.729583	−0.364792	+	0.931089i	$0.618860\pi$
$662$	1.15503e142	0.406693
$663$	4.25448e142	1.38808
$664$	−2.21747e142	−0.670454
$665$	2.65277e141	0.0743372
$666$	−5.12186e141	−0.133039
$667$	1.13130e143	2.72410
$668$	2.16835e142	0.484082
$669$	−8.41157e142	−1.74124
$670$	−1.38900e141	−0.0266640
$671$	−2.86721e141	−0.0510472
$672$	−1.24415e143	−2.05459
$673$	5.63386e142	0.863069	0.431534	−	0.902096i	$-0.357972\pi$
$673$	5.63386e142	0.863069	0.431534	+	0.902096i	$0.357972\pi$
$674$	−2.28420e142	−0.324645
$675$	−1.28600e143	−1.69590
$676$	−2.40751e142	−0.294618
$677$	6.51705e141	0.0740157	0.0370078	−	0.999315i	$-0.488217\pi$
$677$	6.51705e141	0.0740157	0.0370078	+	0.999315i	$0.488217\pi$
$678$	3.56469e142	0.375770
$679$	−4.15931e142	−0.407003
$680$	−5.53344e141	−0.0502684
$681$	1.54620e143	1.30418
$682$	3.89643e141	0.0305180
$683$	1.77465e142	0.129083	0.0645413	−	0.997915i	$-0.479442\pi$
$683$	1.77465e142	0.129083	0.0645413	+	0.997915i	$0.479442\pi$
$684$	1.39451e143	0.942084
$685$	2.71613e142	0.170442
$686$	2.70262e142	0.157550
$687$	4.85045e142	0.262704
$688$	1.65661e143	0.833689
$689$	−2.67459e143	−1.25080
$690$	−2.67831e142	−0.116408
$691$	−7.60623e142	−0.307275	−0.153638	−	0.988127i	$-0.549099\pi$
$691$	−7.60623e142	−0.307275	−0.153638	+	0.988127i	$0.549099\pi$
$692$	1.28256e143	0.481638
$693$	3.66785e142	0.128051
$694$	−3.02999e142	−0.0983530
$695$	−4.10107e141	−0.0123784
$696$	6.74635e143	1.89366
$697$	−2.07915e143	−0.542787
$698$	−1.74516e143	−0.423777
$699$	−9.34728e143	−2.11148
$700$	−5.24174e143	−1.10160
$701$	2.53234e143	0.495179	0.247590	−	0.968865i	$-0.420362\pi$
$701$	2.53234e143	0.495179	0.247590	+	0.968865i	$0.420362\pi$
$702$	4.06980e143	0.740540
$703$	5.81460e142	0.0984637
$704$	8.20174e141	0.0129267
$705$	−1.81580e143	−0.266390
$706$	−1.84718e143	−0.252274
$707$	−4.25922e143	−0.541564
$708$	−1.07620e143	−0.127413
$709$	−4.79369e143	−0.528488	−0.264244	−	0.964456i	$-0.585122\pi$
$709$	−4.79369e143	−0.528488	−0.264244	+	0.964456i	$0.585122\pi$
$710$	−1.32102e142	−0.0135633
$711$	1.21316e144	1.16012
$712$	−4.38183e143	−0.390315
$713$	3.42565e144	2.84264
$714$	−7.47345e143	−0.577778
$715$	−8.36189e141	−0.00602351
$716$	−5.95240e143	−0.399562
$717$	1.26122e144	0.788996
$718$	7.57440e143	0.441636
$719$	2.96453e143	0.161119	0.0805595	−	0.996750i	$-0.474329\pi$
$719$	2.96453e143	0.161119	0.0805595	+	0.996750i	$0.474329\pi$
$720$	2.47644e143	0.125469
$721$	−2.37607e144	−1.12235
$722$	−5.90914e143	−0.260253
$723$	−5.01775e144	−2.06075
$724$	1.07419e144	0.411418
$725$	4.36958e144	1.56088
$726$	−1.93031e144	−0.643173
$727$	−5.04268e143	−0.156738	−0.0783689	−	0.996924i	$-0.524971\pi$
$727$	−5.04268e143	−0.156738	−0.0783689	+	0.996924i	$0.524971\pi$
$728$	3.58544e144	1.03970
$729$	−3.79050e144	−1.02555
$730$	1.09609e142	0.00276720
$731$	4.06935e144	0.958733
$732$	−6.95490e144	−1.52926
$733$	1.13594e144	0.233134	0.116567	−	0.993183i	$-0.462811\pi$
$733$	1.13594e144	0.233134	0.116567	+	0.993183i	$0.462811\pi$
$734$	1.82534e144	0.349698
$735$	6.81004e143	0.121798
$736$	−9.49315e144	−1.58519
$737$	2.18026e143	0.0339938
$738$	−3.99507e144	−0.581671
$739$	9.39645e144	1.27767	0.638836	−	0.769343i	$-0.279416\pi$
$739$	9.39645e144	1.27767	0.638836	+	0.769343i	$0.279416\pi$
$740$	1.27080e143	0.0161390
$741$	−9.28063e144	−1.10093
$742$	4.69820e144	0.520636
$743$	3.87882e144	0.401574	0.200787	−	0.979635i	$-0.435650\pi$
$743$	3.87882e144	0.401574	0.200787	+	0.979635i	$0.435650\pi$
$744$	2.04284e145	1.97606
$745$	6.99280e143	0.0632061
$746$	−5.40226e143	−0.0456315
$747$	2.43779e145	1.92444
$748$	4.01850e143	0.0296506
$749$	1.23303e145	0.850436
$750$	−2.08040e144	−0.134138
$751$	−1.87721e145	−1.13161	−0.565804	−	0.824540i	$-0.691434\pi$
$751$	−1.87721e145	−1.13161	−0.565804	+	0.824540i	$0.691434\pi$
$752$	−1.57384e145	−0.887072
$753$	−6.20397e145	−3.26982
$754$	−1.38284e145	−0.681581
$755$	−1.47449e144	−0.0679705
$756$	4.42925e145	1.90977
$757$	−6.72388e144	−0.271193	−0.135596	−	0.990764i	$-0.543295\pi$
$757$	−6.72388e144	−0.271193	−0.135596	+	0.990764i	$0.543295\pi$
$758$	9.91984e144	0.374291
$759$	4.20402e144	0.148407
$760$	1.20705e144	0.0398694
$761$	2.75168e144	0.0850496	0.0425248	−	0.999095i	$-0.486460\pi$
$761$	2.75168e144	0.0850496	0.0425248	+	0.999095i	$0.486460\pi$
$762$	−2.87796e145	−0.832450
$763$	−4.62114e145	−1.25101
$764$	6.01692e145	1.52461
$765$	6.08322e144	0.144288
$766$	2.58099e145	0.573105
$767$	4.76795e144	0.0991211
$768$	−1.05245e145	−0.204862
$769$	−8.90258e144	−0.162269	−0.0811345	−	0.996703i	$-0.525854\pi$
$769$	−8.90258e144	−0.162269	−0.0811345	+	0.996703i	$0.525854\pi$
$770$	1.46885e143	0.00250725
$771$	2.64479e144	0.0422810
$772$	−1.08783e146	−1.62888
$773$	6.30125e145	0.883816	0.441908	−	0.897060i	$-0.354302\pi$
$773$	6.30125e145	0.883816	0.441908	+	0.897060i	$0.354302\pi$
$774$	7.81923e145	1.02741
$775$	1.32314e146	1.62880
$776$	−1.89255e145	−0.218289
$777$	3.70972e145	0.400940
$778$	−1.46215e145	−0.148088
$779$	4.53540e145	0.430501
$780$	−2.02832e145	−0.180451
$781$	2.07355e144	0.0172917
$782$	−5.70239e145	−0.445775
$783$	−3.69228e146	−2.70599
$784$	5.90257e145	0.405583
$785$	−7.73304e144	−0.0498233
$786$	5.77576e145	0.348956
$787$	1.04521e146	0.592216	0.296108	−	0.955154i	$-0.404311\pi$
$787$	1.04521e146	0.592216	0.296108	+	0.955154i	$0.404311\pi$
$788$	−1.69420e146	−0.900307
$789$	−8.43223e145	−0.420295
$790$	4.85831e144	0.0227152
$791$	−1.71877e146	−0.753884
$792$	1.66893e145	0.0686779
$793$	3.08126e146	1.18969
$794$	6.69859e145	0.242688
$795$	−5.74462e145	−0.195309
$796$	−7.71014e145	−0.246010
$797$	4.25964e146	1.27564	0.637820	−	0.770186i	$-0.279836\pi$
$797$	4.25964e146	1.27564	0.637820	+	0.770186i	$0.279836\pi$
$798$	1.63024e146	0.458254
$799$	−3.86603e146	−1.02012
$800$	−3.66667e146	−0.908296
$801$	4.81719e146	1.12035
$802$	−1.61384e146	−0.352416
$803$	−1.72048e144	−0.00352788
$804$	5.28859e146	1.01838
$805$	1.29139e146	0.233541
$806$	−4.18732e146	−0.711240
$807$	9.83922e146	1.56981
$808$	−1.93801e146	−0.290458
$809$	−3.72784e146	−0.524877	−0.262438	−	0.964949i	$-0.584527\pi$
$809$	−3.72784e146	−0.524877	−0.262438	+	0.964949i	$0.584527\pi$
$810$	2.87159e145	0.0379865
$811$	1.18387e147	1.47147	0.735735	−	0.677270i	$-0.236837\pi$
$811$	1.18387e147	1.47147	0.735735	+	0.677270i	$0.236837\pi$
$812$	−1.50497e147	−1.75772
$813$	−3.92575e146	−0.430874
$814$	3.21958e144	0.00332099
$815$	−8.66071e145	−0.0839642
$816$	7.92031e146	0.721754
$817$	−8.87680e146	−0.760401
$818$	2.77781e146	0.223697
$819$	−3.94168e147	−2.98431
$820$	9.91231e145	0.0705627
$821$	−1.48927e147	−0.996885	−0.498442	−	0.866923i	$-0.666094\pi$
$821$	−1.48927e147	−0.996885	−0.498442	+	0.866923i	$0.666094\pi$
$822$	1.66918e147	1.05069
$823$	2.78199e147	1.64689	0.823443	−	0.567399i	$-0.192050\pi$
$823$	2.78199e147	1.64689	0.823443	+	0.567399i	$0.192050\pi$
$824$	−1.08115e147	−0.601952
$825$	1.62378e146	0.0850358
$826$	−8.37541e145	−0.0412585
$827$	−2.17061e147	−1.00590	−0.502950	−	0.864316i	$-0.667752\pi$
$827$	−2.17061e147	−1.00590	−0.502950	+	0.864316i	$0.667752\pi$
$828$	6.78859e147	2.95970
$829$	1.19927e147	0.491941	0.245970	−	0.969277i	$-0.420893\pi$
$829$	1.19927e147	0.491941	0.245970	+	0.969277i	$0.420893\pi$
$830$	9.76254e145	0.0376807
$831$	2.29173e147	0.832361
$832$	−8.81405e146	−0.301264
$833$	1.44993e147	0.466417
$834$	−2.52029e146	−0.0763071
$835$	−2.06335e146	−0.0588037
$836$	−8.76586e145	−0.0235168
$837$	−1.11805e148	−2.82374
$838$	1.05386e147	0.250588
$839$	−4.40608e147	−0.986445	−0.493223	−	0.869903i	$-0.664181\pi$
$839$	−4.40608e147	−0.986445	−0.493223	+	0.869903i	$0.664181\pi$
$840$	7.70099e146	0.162346
$841$	7.50833e147	1.49055
$842$	1.53179e147	0.286377
$843$	7.58338e147	1.33527
$844$	−4.87064e147	−0.807779
$845$	2.29092e146	0.0357886
$846$	−7.42855e147	−1.09320
$847$	9.30728e147	1.29036
$848$	−4.97912e147	−0.650372
$849$	−1.17310e148	−1.44377
$850$	−2.20251e147	−0.255425
$851$	2.83059e147	0.309339
$852$	5.02976e147	0.518021
$853$	−1.23230e148	−1.19616	−0.598082	−	0.801435i	$-0.704070\pi$
$853$	−1.23230e148	−1.19616	−0.598082	+	0.801435i	$0.704070\pi$
$854$	−5.41256e147	−0.495200
$855$	−1.32698e147	−0.114439
$856$	5.61049e147	0.456116
$857$	9.78619e147	0.750036	0.375018	−	0.927018i	$-0.377637\pi$
$857$	9.78619e147	0.750036	0.375018	+	0.927018i	$0.377637\pi$
$858$	−5.13875e146	−0.0371321
$859$	1.54130e147	0.105010	0.0525052	−	0.998621i	$-0.483279\pi$
$859$	1.54130e147	0.105010	0.0525052	+	0.998621i	$0.483279\pi$
$860$	−1.94006e147	−0.124636
$861$	2.89359e148	1.75298
$862$	−3.97746e147	−0.227242
$863$	1.29970e148	0.700321	0.350160	−	0.936690i	$-0.386127\pi$
$863$	1.29970e148	0.700321	0.350160	+	0.936690i	$0.386127\pi$
$864$	3.09832e148	1.57465
$865$	−1.22045e147	−0.0585069
$866$	1.22298e148	0.553053
$867$	−2.10858e148	−0.899552
$868$	−4.55716e148	−1.83420
$869$	−7.62588e146	−0.0289595
$870$	−2.97012e147	−0.106427
$871$	−2.34303e148	−0.792248
$872$	−2.10269e148	−0.670955
$873$	2.08059e148	0.626567
$874$	1.24391e148	0.353558
$875$	1.00310e148	0.269114
$876$	−4.17331e147	−0.105687
$877$	3.62999e148	0.867813	0.433906	−	0.900958i	$-0.357135\pi$
$877$	3.62999e148	0.867813	0.433906	+	0.900958i	$0.357135\pi$
$878$	−1.77050e148	−0.399597
$879$	−7.21731e148	−1.53793
$880$	−1.55668e146	−0.00313203
$881$	3.01535e148	0.572869	0.286434	−	0.958100i	$-0.407530\pi$
$881$	3.01535e148	0.572869	0.286434	+	0.958100i	$0.407530\pi$
$882$	2.78603e148	0.499829
$883$	−5.32283e148	−0.901835	−0.450917	−	0.892566i	$-0.648903\pi$
$883$	−5.32283e148	−0.901835	−0.450917	+	0.892566i	$0.648903\pi$
$884$	−4.31850e148	−0.691025
$885$	1.02409e147	0.0154775
$886$	−5.10840e148	−0.729259
$887$	2.38497e147	0.0321618	0.0160809	−	0.999871i	$-0.494881\pi$
$887$	2.38497e147	0.0321618	0.0160809	+	0.999871i	$0.494881\pi$
$888$	1.68798e148	0.215037
$889$	1.38765e149	1.67009
$890$	1.92913e147	0.0219364
$891$	−4.50742e147	−0.0484288
$892$	8.53815e148	0.866839
$893$	8.43327e148	0.809091
$894$	4.29738e148	0.389636
$895$	5.66414e147	0.0485367
$896$	1.62154e149	1.31333
$897$	−4.51788e149	−3.45872
$898$	−4.21673e148	−0.305155
$899$	3.79890e149	2.59892
$900$	2.62205e149	1.69588
$901$	−1.22309e149	−0.747922
$902$	2.51128e147	0.0145200
$903$	−5.66340e149	−3.09632
$904$	−7.82067e148	−0.404332
$905$	−1.02217e148	−0.0499770
$906$	−9.06138e148	−0.419006
$907$	−1.47830e149	−0.646541	−0.323270	−	0.946307i	$-0.604782\pi$
$907$	−1.47830e149	−0.646541	−0.323270	+	0.946307i	$0.604782\pi$
$908$	−1.56947e149	−0.649257
$909$	2.13057e149	0.833718
$910$	−1.57851e148	−0.0584330
$911$	4.77532e149	1.67234	0.836170	−	0.548470i	$-0.184790\pi$
$911$	4.77532e149	1.67234	0.836170	+	0.548470i	$0.184790\pi$
$912$	−1.72772e149	−0.572445
$913$	−1.53238e148	−0.0480389
$914$	8.43232e148	0.250129
$915$	6.61809e148	0.185767
$916$	−4.92344e148	−0.130782
$917$	−2.78487e149	−0.700089
$918$	1.86112e149	0.442811
$919$	−2.19568e148	−0.0494465	−0.0247232	−	0.999694i	$-0.507870\pi$
$919$	−2.19568e148	−0.0494465	−0.0247232	+	0.999694i	$0.507870\pi$
$920$	5.87601e148	0.125256
$921$	1.51181e149	0.305060
$922$	3.77486e149	0.721090
$923$	−2.22836e149	−0.402994
$924$	−5.59262e148	−0.0957593
$925$	1.09330e149	0.177248
$926$	−2.53209e149	−0.388708
$927$	1.18857e150	1.72782
$928$	−1.05275e150	−1.44928
$929$	−1.54224e149	−0.201076	−0.100538	−	0.994933i	$-0.532056\pi$
$929$	−1.54224e149	−0.201076	−0.100538	+	0.994933i	$0.532056\pi$
$930$	−8.99373e148	−0.111058
$931$	−3.16284e149	−0.369929
$932$	9.48794e149	1.05116
$933$	2.45649e150	2.57805
$934$	4.39235e149	0.436696
$935$	−3.82389e147	−0.00360180
$936$	−1.79353e150	−1.60058
$937$	−2.20649e150	−1.86574	−0.932871	−	0.360210i	$-0.882705\pi$
$937$	−2.20649e150	−1.86574	−0.932871	+	0.360210i	$0.882705\pi$
$938$	4.11578e149	0.329768
$939$	−1.38900e150	−1.05461
$940$	1.84313e149	0.132617
$941$	−2.68784e150	−1.83285	−0.916426	−	0.400205i	$-0.868939\pi$
$941$	−2.68784e150	−1.83285	−0.916426	+	0.400205i	$0.868939\pi$
$942$	−4.75229e149	−0.307137
$943$	2.20787e150	1.35248
$944$	8.87621e148	0.0515397
$945$	−4.21476e149	−0.231988
$946$	−4.91514e148	−0.0256468
$947$	−2.21163e149	−0.109406	−0.0547028	−	0.998503i	$-0.517421\pi$
$947$	−2.21163e149	−0.109406	−0.0547028	+	0.998503i	$0.517421\pi$
$948$	−1.84979e150	−0.867562
$949$	1.84892e149	0.0822195
$950$	4.80451e149	0.202585
$951$	6.13693e150	2.45378
$952$	1.63962e150	0.621695
$953$	4.98371e150	1.79210	0.896048	−	0.443957i	$-0.146426\pi$
$953$	4.98371e150	1.79210	0.896048	+	0.443957i	$0.146426\pi$
$954$	−2.35016e150	−0.801501
$955$	−5.72553e149	−0.185202
$956$	−1.28020e150	−0.392785
$957$	4.66208e149	0.135683
$958$	−4.34720e149	−0.120020
$959$	−8.04820e150	−2.10794
$960$	−1.89313e149	−0.0470417
$961$	7.26171e150	1.71202
$962$	−3.45995e149	−0.0773977
$963$	−6.16793e150	−1.30922
$964$	5.09325e150	1.02590
$965$	1.03515e150	0.197868
$966$	7.93613e150	1.43967
$967$	−6.03489e150	−1.03904	−0.519520	−	0.854458i	$-0.673889\pi$
$967$	−6.03489e150	−1.03904	−0.519520	+	0.854458i	$0.673889\pi$
$968$	4.23497e150	0.692061
$969$	−4.24403e150	−0.658306
$970$	8.33209e148	0.0122682
$971$	−1.06084e151	−1.48278	−0.741392	−	0.671072i	$-0.765834\pi$
$971$	−1.06084e151	−1.48278	−0.741392	+	0.671072i	$0.765834\pi$
$972$	1.92544e149	0.0255495
$973$	1.21520e150	0.153090
$974$	−3.36612e150	−0.402627
$975$	−1.74500e151	−1.98181
$976$	5.73620e150	0.618598
$977$	5.88403e149	0.0602559	0.0301279	−	0.999546i	$-0.490409\pi$
$977$	5.88403e149	0.0602559	0.0301279	+	0.999546i	$0.490409\pi$
$978$	−5.32239e150	−0.517600
$979$	−3.02807e149	−0.0279666
$980$	−6.91252e149	−0.0606344
$981$	2.31161e151	1.92588
$982$	6.51061e149	0.0515218
$983$	−5.74386e150	−0.431769	−0.215884	−	0.976419i	$-0.569263\pi$
$983$	−5.74386e150	−0.431769	−0.215884	+	0.976419i	$0.569263\pi$
$984$	1.31663e151	0.940180
$985$	1.61215e150	0.109365
$986$	−6.32370e150	−0.407556
$987$	5.38043e151	3.29459
$988$	9.42029e150	0.548073
$989$	−4.32129e151	−2.38891
$990$	−7.34758e148	−0.00385982
$991$	−6.60511e150	−0.329731	−0.164866	−	0.986316i	$-0.552719\pi$
$991$	−6.60511e150	−0.329731	−0.164866	+	0.986316i	$0.552719\pi$
$992$	−3.18779e151	−1.51234
$993$	4.18479e151	1.88685
$994$	3.91434e150	0.167744
$995$	7.33676e149	0.0298840
$996$	−3.71706e151	−1.43914
$997$	−6.44459e150	−0.237186	−0.118593	−	0.992943i	$-0.537838\pi$
$997$	−6.44459e150	−0.237186	−0.118593	+	0.992943i	$0.537838\pi$
$998$	1.00217e151	0.350629
$999$	−9.23833e150	−0.307281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.102.a.a.1.5	✓	8
3.2	odd	2		9.102.a.b.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.102.a.a.1.5	✓	8	1.1	even	1	trivial
9.102.a.b.1.4		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:	\( k \)	\(=\)	\( 102 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+5.93582e14 q^{2} +2.15060e24 q^{3} -2.18296e30 q^{4} +2.07725e34 q^{5} +1.27656e39 q^{6} -6.15512e42 q^{7} -2.80068e45 q^{8} +3.07894e48 q^{9} +O(q^{10})\)	\(q+5.93582e14 q^{2} +2.15060e24 q^{3} -2.18296e30 q^{4} +2.07725e34 q^{5} +1.27656e39 q^{6} -6.15512e42 q^{7} -2.80068e45 q^{8} +3.07894e48 q^{9} +1.23302e49 q^{10} -1.93541e51 q^{11} -4.69467e54 q^{12} +2.07990e56 q^{13} -3.65357e57 q^{14} +4.46732e58 q^{15} +3.87203e60 q^{16} +9.51139e61 q^{17} +1.82761e63 q^{18} -2.07479e64 q^{19} -4.53455e64 q^{20} -1.32372e67 q^{21} -1.14883e66 q^{22} -1.01002e69 q^{23} -6.02314e69 q^{24} -3.90116e70 q^{25} +1.23459e71 q^{26} +3.29646e72 q^{27} +1.34364e73 q^{28} -1.12007e74 q^{29} +2.65172e73 q^{30} -3.39166e75 q^{31} +9.39893e75 q^{32} -4.16230e75 q^{33} +5.64580e76 q^{34} -1.27857e77 q^{35} -6.72122e78 q^{36} -2.80250e78 q^{37} -1.23156e79 q^{38} +4.47304e80 q^{39} -5.81770e79 q^{40} -2.18595e81 q^{41} -7.85736e81 q^{42} +4.27840e82 q^{43} +4.22493e81 q^{44} +6.39572e82 q^{45} -5.99533e83 q^{46} -4.06463e84 q^{47} +8.32719e84 q^{48} +1.52441e85 q^{49} -2.31566e85 q^{50} +2.04552e86 q^{51} -4.54035e86 q^{52} -1.28592e87 q^{53} +1.95672e87 q^{54} -4.02033e85 q^{55} +1.72385e88 q^{56} -4.46205e88 q^{57} -6.64855e88 q^{58} +2.29239e88 q^{59} -9.75199e88 q^{60} +1.48144e90 q^{61} -2.01323e90 q^{62} -1.89513e91 q^{63} -4.23772e90 q^{64} +4.32047e90 q^{65} -2.47067e90 q^{66} -1.12651e92 q^{67} -2.07630e92 q^{68} -2.17216e93 q^{69} -7.58936e91 q^{70} -1.07138e93 q^{71} -8.62313e93 q^{72} +8.88946e92 q^{73} -1.66351e93 q^{74} -8.38982e94 q^{75} +4.52919e94 q^{76} +1.19127e94 q^{77} +2.65512e95 q^{78} +3.94018e95 q^{79} +8.04316e94 q^{80} +2.32892e96 q^{81} -1.29754e96 q^{82} +7.91760e96 q^{83} +2.88963e97 q^{84} +1.97575e96 q^{85} +2.53958e97 q^{86} -2.40883e98 q^{87} +5.42047e96 q^{88} +1.56456e98 q^{89} +3.79639e97 q^{90} -1.28020e99 q^{91} +2.20484e99 q^{92} -7.29409e99 q^{93} -2.41269e99 q^{94} -4.30986e98 q^{95} +2.02133e100 q^{96} +6.75748e99 q^{97} +9.04864e99 q^{98} -5.95903e99 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 52\!\cdots\!84 q^{9}+O(q^{10}) \) 8 * q - 434989091795040 * q^2 - 1209375896611771518910560 * q^3 + 9008967123164113911511576503296 * q^4 + 38238791540232828026421308589217200 * q^5 + 2477260046146272006672820535971480695936 * q^6 - 5786789720778120168956257648884421874283200 * q^7 - 6101688461407407841888405145259998920458731520 * q^8 + 5273640617280587177839635242070674204864681879784 * q^9	\( 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 22\!\cdots\!08 q^{99}+O(q^{100}) \) 8 * q - 434989091795040 * q^2 - 1209375896611771518910560 * q^3 + 9008967123164113911511576503296 * q^4 + 38238791540232828026421308589217200 * q^5 + 2477260046146272006672820535971480695936 * q^6 - 5786789720778120168956257648884421874283200 * q^7 - 6101688461407407841888405145259998920458731520 * q^8 + 5273640617280587177839635242070674204864681879784 * q^9 - 376167658847177398692429835067300112512860198593600 * q^10 + 4622006661480385115355021397632645270205791478300896 * q^11 - 7273290781506553143908216801865849714958844187989422080 * q^12 + 250316830865150221699601352256397536965043294984328650480 * q^13 - 4856789037716039923353321450215036970203737520869624889088 * q^14 - 296460708185002952419818874947342543917521978696100167156800 * q^15 - 10662656154906175558835021484824464714661655552497093859868672 * q^16 - 397968518694853312322660892941326449007299986932512193696587120 * q^17 - 7270968925217398747066352706388703938040714138623386028515252960 * q^18 - 21387776045417165942123954421061470474744368808488511816400717280 * q^19 + 1745002690168409059221421019241581897927614179506161156200285542400 * q^20 + 4030935126807879780648600654579655736182360851489572706466859540736 * q^21 + 61357881995862711169740037407631980426480577127973320405539739944320 * q^22 - 1366243345208606848425464574347748611753917469593153677393324561698880 * q^23 + 10457354719000260635321058863018299052737315743164922361342586480885760 * q^24 + 77471873089568593564333770877949420045843582630742632687744142562715000 * q^25 - 97549630676937426518340388130407212490384846814009484188479115327886144 * q^26 - 5951874968930013487417142282111771144801435961988629201748805497863184320 * q^27 + 9217624035174751886516129105576165061663773766415040330328487084880404480 * q^28 + 15465799862710125255662370242568323665682807414567501281109138719156160880 * q^29 + 1101689156065505631051293671607641382064945196508526428823375711603202118400 * q^30 - 6594370386043135339784923725045360443937393326734068279132668478779615001344 * q^31 + 12265519409733718324179959581296851912742484455832107241543734281342036213760 * q^32 + 43813172582105581329585760338258562815639759809845990212191452867766348215680 * q^33 + 9531455444774917507766540524882635666895777953789094347547215472626183995712 * q^34 - 1122850631208004175280217132184898888977788452428069383882586628450512616297600 * q^35 + 1966242586607976986737003826554029255087710066072863106322127653222050407339008 * q^36 + 39729696767983511833540209209183332457877293383323859312175998401968644864715440 * q^37 - 70873740526925065519455012686645778106113298999572267198467188879790467046148480 * q^38 - 269289195198196884798470270521708844679404215685249767615656452740889673105306432 * q^39 - 763642761360299050617237751714968411270996317577517686387843428508400019349504000 * q^40 + 5607291724825101314952096252772109505395882457063737303656079003304969203257094736 * q^41 + 3008066923831569706716293907931878334959183836053498604235677758281531565332526080 * q^42 - 28642921955044714117801359306021921736063108483729021321044095944585527287681223200 * q^43 - 207838425393205175674959052733026300855796348257745356716186803699782799277851086848 * q^44 + 712633045382921242540931880134776511927082560144290402835715503414563529286220047600 * q^45 + 1088094260619851586903932234100844276278561023621942541398958535856528393570339218176 * q^46 - 4595399220200007631460417274797048154524720407021496316223236391731855709593438718080 * q^47 - 58354182581817955899154335674671016574355963424701638945735582725996041826866298880 * q^48 + 12068461406676719302337658501270392621238416595305390197216228129207599916872005856456 * q^49 - 40493179837482260394665357435432250163405353367416857829233726008281167215503492420000 * q^50 + 117646730044094759803745147399491979694134742922341911657750530682089815486256248611136 * q^51 - 736020167800817028850658909331852777746165402605863935107936992324104798352324258252800 * q^52 + 131026696145917691346168139299202731343660174597285772716290345361212508775951813313840 * q^53 + 6803608957095266771149163140167539716357850176039815317805755392633822625226741503089920 * q^54 - 14585157967675450217148723878599628333971210001615112897255333178063634767400530051473600 * q^55 - 23665562342657326400415121984960944704012341384928617813498515591030351969339927087022080 * q^56 - 66899487754306674554237314096607510056291565049587799982155034523058479948455991635655040 * q^57 + 29173417521771002425120779628349939892591335515731485644911210555324770598093888308326080 * q^58 + 212583149562022564923669670483574922097682552074321909615339251529169016840977455874187360 * q^59 - 3455800135608334392541843481344001808338357411235959344412061781382196941870275476295065600 * q^60 - 3390796423636162146406492296389682436951029380958058095674208836333532599894943317230895504 * q^61 - 5878859817222970028213836429448832127296537243368792127423103234889716583457526212133370880 * q^62 - 20171938924061808002384576493874339158887341995607670819297079343133751793255425885494984640 * q^63 - 74870090698021647967203019932764377907062372989513317693678846896652408519412785858115272704 * q^64 - 161067075283368767182138254547148962244907084326790507487294907612770451283405321317426536800 * q^65 - 745278055170676259198413344675313071673593040227005461838089798951153726758412015071955911168 * q^66 - 618774503558862942537948810466095132313460919373052732511642097824837019429997681150398682720 * q^67 - 2182412150351293808121583165511486752102068977919329447376923905220322529537335456462676162560 * q^68 - 5393950442083315109606578094475120918497802785657891521452512469623636760248087300551286537472 * q^69 - 12923520657540473465038555822652190723092643731233782501675276653712048411292540691873715571200 * q^70 - 15797470289857673806303846655911576507977904169297655042639265226995032204172380517793831135424 * q^71 - 55126715113590704564504537983251285080485074916503283789364546398928839504287032847376708239360 * q^72 - 20462651635605668591994589976366754984142669867347912050159975933828495442291952971923777071280 * q^73 - 142953411935712165334538916257020870493984381200782662943456748743148514063783881306064429441088 * q^74 - 204312291750914950304829914412770260373631281822544572731633720960361618548975517964814619460000 * q^75 + 64556217054886497186737063238064337992823205997653378371004031509089422583081356800943896432640 * q^76 + 250231448169383959900618348975396989794902211753647918986458150866408618577007907131029306438400 * q^77 + 1260981709052401111398092363772739439414079820346824747462408082793911096042108256417770344646400 * q^78 + 1474556321278768744579716979675929750918930811984805387023357390321899878561204701118206999166080 * q^79 + 6033438037435277941170744030808192554572458649979375320464765273747209092446481051552234550067200 * q^80 + 14613214105102112111129469132612601529386527627758931132459526147171392070559192290643105065182408 * q^81 + 30083863369214129982421840097969977845328701273986110579467106900080547794123383776302929686086720 * q^82 + 33762254529254022439253159341806143692643909652777369725086142424861011401680843403961249425712160 * q^83 + 57799153837692447414380568170128797835929379783304235587752969314531310322308849537769529417695232 * q^84 + 17314966267116570951109803841412092095679328201414316724042066880549149931729490643535478494114400 * q^85 + 67989564188024628582959760637462873453376851598916319417912395832044408164663357850732592560556416 * q^86 + 2586434133428712948881772736535019341274237946379240114707154003676967765014837223291966941531840 * q^87 - 363099602372059077387783242048689913608334478213970275423791339756517232974574737922754584123146240 * q^88 - 620007165949691950044675276484549383308720953973642955804615855186521697520022438525123333812557360 * q^89 - 4716676146177962028099989697458384454375488041754925418224025761569034561814581975790426208019028800 * q^90 - 3685711793015793225308940042728501386995879977832891226647110522985454537354035281338855172828873344 * q^91 - 4618779932089713137770970202224414792688843158843334085630908366025929325979388063902511470793400320 * q^92 - 3975022445092224432029728046757042348886229630318622378634497589784647142077875089398179428115102720 * q^93 - 17371370943540992303713705925513939673302729250250795188383540356993592041601425149438637190677682688 * q^94 - 2642077700832720169247174948884057845373174576960370774287679094739730873649398763127258995555528000 * q^95 + 4679875418673156206717240026356824763600126819048403120235276936002238426687957733980747642601209856 * q^96 + 64020476116668335744724892375903667651900818166631138467214326399663196857065619648203365824701173520 * q^97 + 202971561788470754768820264959327860776947519106194867162872422213964707447467488105939520314595817120 * q^98 + 225914901454627435116272921386700923755368861971179328902362103653753469396751969300619190223813523808 * q^99

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