LMFDB - Embedded newform 1.102.a.a.1.4

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			1.4
Root			$2.10926e12$ 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)

$f(q)$	$=$	$q-2.56863e14 q^{2} -3.45553e23 q^{3} -2.46932e30 q^{4} +1.16158e35 q^{5} +8.87596e37 q^{6} +2.79663e42 q^{7} +1.28550e45 q^{8} -1.42673e48 q^{9} +O(q^{10})$	\(q-2.56863e14 q^{2} -3.45553e23 q^{3} -2.46932e30 q^{4} +1.16158e35 q^{5} +8.87596e37 q^{6} +2.79663e42 q^{7} +1.28550e45 q^{8} -1.42673e48 q^{9} -2.98366e49 q^{10} -9.95717e51 q^{11} +8.53281e53 q^{12} -1.44350e56 q^{13} -7.18350e56 q^{14} -4.01386e58 q^{15} +5.93028e60 q^{16} +1.59801e62 q^{17} +3.66473e62 q^{18} +1.62028e64 q^{19} -2.86831e65 q^{20} -9.66383e65 q^{21} +2.55763e66 q^{22} +7.65727e68 q^{23} -4.44208e68 q^{24} -2.59504e70 q^{25} +3.70781e70 q^{26} +1.02728e72 q^{27} -6.90578e72 q^{28} -7.16454e72 q^{29} +1.03101e73 q^{30} +1.90510e75 q^{31} -4.78240e75 q^{32} +3.44073e75 q^{33} -4.10469e76 q^{34} +3.24850e77 q^{35} +3.52305e78 q^{36} -1.10721e79 q^{37} -4.16190e78 q^{38} +4.98805e79 q^{39} +1.49321e80 q^{40} -1.87777e81 q^{41} +2.48228e80 q^{42} +9.41841e81 q^{43} +2.45875e82 q^{44} -1.65725e83 q^{45} -1.96687e83 q^{46} +3.14875e84 q^{47} -2.04922e84 q^{48} -1.48202e85 q^{49} +6.66570e84 q^{50} -5.52197e85 q^{51} +3.56447e86 q^{52} -4.00521e86 q^{53} -2.63870e86 q^{54} -1.15660e87 q^{55} +3.59507e87 q^{56} -5.59893e87 q^{57} +1.84030e87 q^{58} -2.34450e89 q^{59} +9.91152e88 q^{60} -4.02186e89 q^{61} -4.89350e89 q^{62} -3.99002e90 q^{63} -1.38066e91 q^{64} -1.67674e91 q^{65} -8.83794e89 q^{66} -3.05726e92 q^{67} -3.94600e92 q^{68} -2.64599e92 q^{69} -8.34418e91 q^{70} -5.37677e93 q^{71} -1.83406e93 q^{72} -2.11035e94 q^{73} +2.84401e93 q^{74} +8.96724e93 q^{75} -4.00100e94 q^{76} -2.78465e94 q^{77} -1.28124e94 q^{78} +8.91772e95 q^{79} +6.88848e95 q^{80} +1.85093e96 q^{81} +4.82328e95 q^{82} +7.50442e96 q^{83} +2.38631e96 q^{84} +1.85621e97 q^{85} -2.41924e96 q^{86} +2.47573e96 q^{87} -1.28000e97 q^{88} -3.83813e98 q^{89} +4.25686e97 q^{90} -4.03693e98 q^{91} -1.89083e99 q^{92} -6.58314e98 q^{93} -8.08797e98 q^{94} +1.88208e99 q^{95} +1.65257e99 q^{96} +1.03291e100 q^{97} +3.80676e99 q^{98} +1.42062e100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.56863e14	−0.161319	−0.0806596	−	0.996742i	$-0.525703\pi$
$2$	−2.56863e14	−0.161319	−0.0806596	+	0.996742i	$0.525703\pi$
$3$	−3.45553e23	−0.277902	−0.138951	−	0.990299i	$-0.544373\pi$
$3$	−3.45553e23	−0.277902	−0.138951	+	0.990299i	$0.544373\pi$
$4$	−2.46932e30	−0.973976
$5$	1.16158e35	0.584875	0.292437	−	0.956285i	$-0.405534\pi$
$5$	1.16158e35	0.584875	0.292437	+	0.956285i	$0.405534\pi$
$6$	8.87596e37	0.0448309
$7$	2.79663e42	0.587738	0.293869	−	0.955846i	$-0.405057\pi$
$7$	2.79663e42	0.587738	0.293869	+	0.955846i	$0.405057\pi$
$8$	1.28550e45	0.318440
$9$	−1.42673e48	−0.922771
$10$	−2.98366e49	−0.0943515
$11$	−9.95717e51	−0.255744	−0.127872	−	0.991791i	$-0.540815\pi$
$11$	−9.95717e51	−0.255744	−0.127872	+	0.991791i	$0.540815\pi$
$12$	8.53281e53	0.270669
$13$	−1.44350e56	−0.804039	−0.402020	−	0.915631i	$-0.631692\pi$
$13$	−1.44350e56	−0.804039	−0.402020	+	0.915631i	$0.631692\pi$
$14$	−7.18350e56	−0.0948135
$15$	−4.01386e58	−0.162538
$16$	5.93028e60	0.922606
$17$	1.59801e62	1.16388	0.581941	−	0.813231i	$-0.302293\pi$
$17$	1.59801e62	1.16388	0.581941	+	0.813231i	$0.302293\pi$
$18$	3.66473e62	0.148861
$19$	1.62028e64	0.429076	0.214538	−	0.976716i	$-0.431175\pi$
$19$	1.62028e64	0.429076	0.214538	+	0.976716i	$0.431175\pi$
$20$	−2.86831e65	−0.569654
$21$	−9.66383e65	−0.163333
$22$	2.55763e66	0.0412564
$23$	7.65727e68	1.30863	0.654317	−	0.756220i	$-0.272956\pi$
$23$	7.65727e68	1.30863	0.654317	+	0.756220i	$0.272956\pi$
$24$	−4.44208e68	−0.0884951
$25$	−2.59504e70	−0.657922
$26$	3.70781e70	0.129707
$27$	1.02728e72	0.534341
$28$	−6.90578e72	−0.572443
$29$	−7.16454e72	−0.100946	−0.0504730	−	0.998725i	$-0.516073\pi$
$29$	−7.16454e72	−0.100946	−0.0504730	+	0.998725i	$0.516073\pi$
$30$	1.03101e73	0.0262204
$31$	1.90510e75	0.925024	0.462512	−	0.886613i	$-0.346948\pi$
$31$	1.90510e75	0.925024	0.462512	+	0.886613i	$0.346948\pi$
$32$	−4.78240e75	−0.467274
$33$	3.44073e75	0.0710716
$34$	−4.10469e76	−0.187757
$35$	3.24850e77	0.343753
$36$	3.52305e78	0.898757
$37$	−1.10721e79	−0.708017	−0.354009	−	0.935242i	$-0.615182\pi$
$37$	−1.10721e79	−0.708017	−0.354009	+	0.935242i	$0.615182\pi$
$38$	−4.16190e78	−0.0692182
$39$	4.98805e79	0.223444
$40$	1.49321e80	0.186248
$41$	−1.87777e81	−0.673064	−0.336532	−	0.941672i	$-0.609254\pi$
$41$	−1.87777e81	−0.673064	−0.336532	+	0.941672i	$0.609254\pi$
$42$	2.48228e80	0.0263488
$43$	9.41841e81	0.304664	0.152332	−	0.988329i	$-0.451322\pi$
$43$	9.41841e81	0.304664	0.152332	+	0.988329i	$0.451322\pi$
$44$	2.45875e82	0.249088
$45$	−1.65725e83	−0.539705
$46$	−1.96687e83	−0.211108
$47$	3.14875e84	1.14077	0.570383	−	0.821379i	$-0.306795\pi$
$47$	3.14875e84	1.14077	0.570383	+	0.821379i	$0.306795\pi$
$48$	−2.04922e84	−0.256393
$49$	−1.48202e85	−0.654564
$50$	6.66570e84	0.106135
$51$	−5.52197e85	−0.323445
$52$	3.56447e86	0.783115
$53$	−4.00521e86	−0.336275	−0.168137	−	0.985764i	$-0.553775\pi$
$53$	−4.00521e86	−0.336275	−0.168137	+	0.985764i	$0.553775\pi$
$54$	−2.63870e86	−0.0861995
$55$	−1.15660e87	−0.149578
$56$	3.59507e87	0.187160
$57$	−5.59893e87	−0.119241
$58$	1.84030e87	0.0162846
$59$	−2.34450e89	−0.875031	−0.437516	−	0.899211i	$-0.644142\pi$
$59$	−2.34450e89	−0.875031	−0.437516	+	0.899211i	$0.644142\pi$
$60$	9.91152e88	0.158308
$61$	−4.02186e89	−0.278785	−0.139393	−	0.990237i	$-0.544515\pi$
$61$	−4.02186e89	−0.278785	−0.139393	+	0.990237i	$0.544515\pi$
$62$	−4.89350e89	−0.149224
$63$	−3.99002e90	−0.542348
$64$	−1.38066e91	−0.847225
$65$	−1.67674e91	−0.470262
$66$	−8.83794e89	−0.0114652
$67$	−3.05726e92	−1.85590	−0.927951	−	0.372702i	$-0.878432\pi$
$67$	−3.05726e92	−1.85590	−0.927951	+	0.372702i	$0.878432\pi$
$68$	−3.94600e92	−1.13359
$69$	−2.64599e92	−0.363672
$70$	−8.34418e91	−0.0554540
$71$	−5.37677e93	−1.74572	−0.872861	−	0.487968i	$-0.837738\pi$
$71$	−5.37677e93	−1.74572	−0.872861	+	0.487968i	$0.837738\pi$
$72$	−1.83406e93	−0.293847
$73$	−2.11035e94	−1.68480	−0.842402	−	0.538850i	$-0.818859\pi$
$73$	−2.11035e94	−1.68480	−0.842402	+	0.538850i	$0.818859\pi$
$74$	2.84401e93	0.114217
$75$	8.96724e93	0.182837
$76$	−4.00100e94	−0.417910
$77$	−2.78465e94	−0.150310
$78$	−1.28124e94	−0.0360458
$79$	8.91772e95	1.31852	0.659259	−	0.751916i	$-0.270870\pi$
$79$	8.91772e95	1.31852	0.659259	+	0.751916i	$0.270870\pi$
$80$	6.88848e95	0.539608
$81$	1.85093e96	0.774277
$82$	4.82328e95	0.108578
$83$	7.50442e96	0.915954	0.457977	−	0.888964i	$-0.348574\pi$
$83$	7.50442e96	0.915954	0.457977	+	0.888964i	$0.348574\pi$
$84$	2.38631e96	0.159083
$85$	1.85621e97	0.680725
$86$	−2.41924e96	−0.0491481
$87$	2.47573e96	0.0280531
$88$	−1.28000e97	−0.0814392
$89$	−3.83813e98	−1.38014	−0.690072	−	0.723741i	$-0.742421\pi$
$89$	−3.83813e98	−1.38014	−0.690072	+	0.723741i	$0.742421\pi$
$90$	4.25686e97	0.0870648
$91$	−4.03693e98	−0.472565
$92$	−1.89083e99	−1.27458
$93$	−6.58314e98	−0.257066
$94$	−8.08797e98	−0.184028
$95$	1.88208e99	0.250956
$96$	1.65257e99	0.129856
$97$	1.03291e100	0.480937	0.240469	−	0.970657i	$-0.422699\pi$
$97$	1.03291e100	0.480937	0.240469	+	0.970657i	$0.422699\pi$
$98$	3.80676e99	0.105594
$99$	1.42062e100	0.235993
$100$	6.40800e100	0.640800
$101$	2.39177e101	1.44707	0.723535	−	0.690288i	$-0.242516\pi$
$101$	2.39177e101	1.44707	0.723535	+	0.690288i	$0.242516\pi$
$102$	1.41839e100	0.0521778
$103$	−1.67545e101	−0.376575	−0.188288	−	0.982114i	$-0.560294\pi$
$103$	−1.67545e101	−0.376575	−0.188288	+	0.982114i	$0.560294\pi$
$104$	−1.85562e101	−0.256039
$105$	−1.12253e101	−0.0955295
$106$	1.02879e101	0.0542476
$107$	−9.91379e101	−0.325356	−0.162678	−	0.986679i	$-0.552013\pi$
$107$	−9.91379e101	−0.325356	−0.162678	+	0.986679i	$0.552013\pi$
$108$	−2.53668e102	−0.520435
$109$	−1.40368e103	−1.80814	−0.904068	−	0.427390i	$-0.859433\pi$
$109$	−1.40368e103	−1.80814	−0.904068	+	0.427390i	$0.859433\pi$
$110$	2.97088e101	0.0241298
$111$	3.82600e102	0.196759
$112$	1.65848e103	0.542251
$113$	1.51940e102	0.0317110	0.0158555	−	0.999874i	$-0.494953\pi$
$113$	1.51940e102	0.0317110	0.0158555	+	0.999874i	$0.494953\pi$
$114$	1.43816e102	0.0192358
$115$	8.89451e103	0.765387
$116$	1.76916e103	0.0983191
$117$	2.05948e104	0.741944
$118$	6.02215e103	0.141159
$119$	4.46904e104	0.684058
$120$	−5.15982e103	−0.0517585
$121$	−1.41672e105	−0.934595
$122$	1.03306e104	0.0449734
$123$	6.48867e104	0.187046
$124$	−4.70432e105	−0.900952
$125$	−7.59596e105	−0.969676
$126$	1.02489e105	0.0874911
$127$	−1.19794e106	−0.686034	−0.343017	−	0.939329i	$-0.611449\pi$
$127$	−1.19794e106	−0.686034	−0.343017	+	0.939329i	$0.611449\pi$
$128$	1.56712e106	0.603948
$129$	−3.25456e105	−0.0846665
$130$	4.30691e105	0.0758623
$131$	1.15584e107	1.38261	0.691304	−	0.722564i	$-0.257037\pi$
$131$	1.15584e107	1.38261	0.691304	+	0.722564i	$0.257037\pi$
$132$	−8.49627e105	−0.0692221
$133$	4.53133e106	0.252184
$134$	7.85297e106	0.299393
$135$	1.19326e107	0.312522
$136$	2.05424e107	0.370627
$137$	−3.40012e107	−0.423746	−0.211873	−	0.977297i	$-0.567956\pi$
$137$	−3.40012e107	−0.423746	−0.211873	+	0.977297i	$0.567956\pi$
$138$	6.79657e106	0.0586672
$139$	−2.26071e108	−1.35518	−0.677592	−	0.735438i	$-0.736976\pi$
$139$	−2.26071e108	−1.35518	−0.677592	+	0.735438i	$0.736976\pi$
$140$	−8.02159e107	−0.334807
$141$	−1.08806e108	−0.317021
$142$	1.38109e108	0.281619
$143$	1.43732e108	0.205628
$144$	−8.46088e108	−0.851353
$145$	−8.32217e107	−0.0590408
$146$	5.42069e108	0.271791
$147$	5.12116e108	0.181904
$148$	2.73406e109	0.689592
$149$	8.38640e109	1.50546	0.752730	−	0.658330i	$-0.228737\pi$
$149$	8.38640e109	1.50546	0.752730	+	0.658330i	$0.228737\pi$
$150$	−2.30335e108	−0.0294952
$151$	−9.80255e108	−0.0897436	−0.0448718	−	0.998993i	$-0.514288\pi$
$151$	−9.80255e108	−0.0897436	−0.0448718	+	0.998993i	$0.514288\pi$
$152$	2.08288e109	0.136635
$153$	−2.27992e110	−1.07400
$154$	7.15273e108	0.0242480
$155$	2.21292e110	0.541023
$156$	−1.23171e110	−0.217629
$157$	−1.27999e111	−1.63785	−0.818923	−	0.573903i	$-0.805429\pi$
$157$	−1.27999e111	−1.63785	−0.818923	+	0.573903i	$0.805429\pi$
$158$	−2.29063e110	−0.212702
$159$	1.38401e110	0.0934512
$160$	−5.55513e110	−0.273297
$161$	2.14146e111	0.769135
$162$	−4.75434e110	−0.124906
$163$	1.59995e111	0.308058	0.154029	−	0.988066i	$-0.450775\pi$
$163$	1.59995e111	0.308058	0.154029	+	0.988066i	$0.450775\pi$
$164$	4.63681e111	0.655548
$165$	3.99667e110	0.0415680
$166$	−1.92761e111	−0.147761
$167$	2.33044e112	1.31904	0.659518	−	0.751689i	$-0.270761\pi$
$167$	2.33044e112	1.31904	0.659518	+	0.751689i	$0.270761\pi$
$168$	−1.24229e111	−0.0520119
$169$	−1.13945e112	−0.353521
$170$	−4.76791e111	−0.109814
$171$	−2.31170e112	−0.395939
$172$	−2.32571e112	−0.296735
$173$	−8.33103e112	−0.793178	−0.396589	−	0.917996i	$-0.629806\pi$
$173$	−8.33103e112	−0.793178	−0.396589	+	0.917996i	$0.629806\pi$
$174$	−6.35922e110	−0.00452550
$175$	−7.25738e112	−0.386686
$176$	−5.90488e112	−0.235951
$177$	8.10148e112	0.243173
$178$	9.85873e112	0.222644
$179$	−3.61084e113	−0.614512	−0.307256	−	0.951627i	$-0.599411\pi$
$179$	−3.61084e113	−0.614512	−0.307256	+	0.951627i	$0.599411\pi$
$180$	4.09229e113	0.525660
$181$	1.67890e114	1.63026	0.815132	−	0.579275i	$-0.196664\pi$
$181$	1.67890e114	1.63026	0.815132	+	0.579275i	$0.196664\pi$
$182$	1.03694e113	0.0762338
$183$	1.38976e113	0.0774748
$184$	9.84344e113	0.416722
$185$	−1.28611e114	−0.414101
$186$	1.69096e113	0.0414697
$187$	−1.59117e114	−0.297656
$188$	−7.77529e114	−1.11108
$189$	2.87292e114	0.314053
$190$	−4.83437e113	−0.0404840
$191$	−2.24809e114	−0.144421	−0.0722103	−	0.997389i	$-0.523005\pi$
$191$	−2.24809e114	−0.144421	−0.0722103	+	0.997389i	$0.523005\pi$
$192$	4.77092e114	0.235445
$193$	−3.98577e115	−1.51310	−0.756551	−	0.653934i	$-0.773117\pi$
$193$	−3.98577e115	−1.51310	−0.756551	+	0.653934i	$0.773117\pi$
$194$	−2.65315e114	−0.0775844
$195$	5.79400e114	0.130687
$196$	3.65959e115	0.637529
$197$	9.87434e115	1.33034	0.665171	−	0.746691i	$-0.268358\pi$
$197$	9.87434e115	1.33034	0.665171	+	0.746691i	$0.268358\pi$
$198$	−3.64903e114	−0.0380702
$199$	4.01699e115	0.324953	0.162476	−	0.986712i	$-0.448052\pi$
$199$	4.01699e115	0.324953	0.162476	+	0.986712i	$0.448052\pi$
$200$	−3.33593e115	−0.209509
$201$	1.05645e116	0.515758
$202$	−6.14356e115	−0.233440
$203$	−2.00366e115	−0.0593299
$204$	1.36355e116	0.315027
$205$	−2.18117e116	−0.393658
$206$	4.30361e115	0.0607489
$207$	−1.09248e117	−1.20757
$208$	−8.56035e116	−0.741811
$209$	−1.61334e116	−0.109734
$210$	2.88336e115	0.0154108
$211$	4.53257e116	0.190581	0.0952907	−	0.995449i	$-0.469622\pi$
$211$	4.53257e116	0.190581	0.0952907	+	0.995449i	$0.469622\pi$
$212$	9.89016e116	0.327523
$213$	1.85796e117	0.485139
$214$	2.54648e116	0.0524862
$215$	1.09402e117	0.178190
$216$	1.32057e117	0.170156
$217$	5.32787e117	0.543672
$218$	3.60554e117	0.291687
$219$	7.29236e117	0.468209
$220$	2.85602e117	0.145685
$221$	−2.30673e118	−0.935807
$222$	−9.82757e116	−0.0317410
$223$	−3.52241e118	−0.906660	−0.453330	−	0.891343i	$-0.649764\pi$
$223$	−3.52241e118	−0.906660	−0.453330	+	0.891343i	$0.649764\pi$
$224$	−1.33746e118	−0.274635
$225$	3.70242e118	0.607111
$226$	−3.90276e116	−0.00511559
$227$	−1.25414e119	−1.31535	−0.657674	−	0.753302i	$-0.728460\pi$
$227$	−1.25414e119	−1.31535	−0.657674	+	0.753302i	$0.728460\pi$
$228$	1.38256e118	0.116138
$229$	5.60999e118	0.377807	0.188904	−	0.981996i	$-0.439507\pi$
$229$	5.60999e118	0.377807	0.188904	+	0.981996i	$0.439507\pi$
$230$	−2.28467e118	−0.123472
$231$	9.62244e117	0.0417715
$232$	−9.21003e117	−0.0321453
$233$	4.54576e119	1.27683	0.638415	−	0.769693i	$-0.279591\pi$
$233$	4.54576e119	1.27683	0.638415	+	0.769693i	$0.279591\pi$
$234$	−5.29003e118	−0.119690
$235$	3.65752e119	0.667205
$236$	5.78933e119	0.852260
$237$	−3.08154e119	−0.366418
$238$	−1.14793e119	−0.110352
$239$	−1.02709e120	−0.798939	−0.399469	−	0.916747i	$-0.630806\pi$
$239$	−1.02709e120	−0.798939	−0.399469	+	0.916747i	$0.630806\pi$
$240$	−2.38033e119	−0.149958
$241$	−8.90997e119	−0.455005	−0.227502	−	0.973778i	$-0.573056\pi$
$241$	−8.90997e119	−0.455005	−0.227502	+	0.973778i	$0.573056\pi$
$242$	3.63903e119	0.150768
$243$	−2.22790e120	−0.749514
$244$	9.93126e119	0.271530
$245$	−1.72148e120	−0.382838
$246$	−1.66670e119	−0.0301741
$247$	−2.33888e120	−0.344994
$248$	2.44901e120	0.294565
$249$	−2.59317e120	−0.254545
$250$	1.95112e120	0.156427
$251$	2.54170e121	1.66572	0.832860	−	0.553484i	$-0.186702\pi$
$251$	2.54170e121	1.66572	0.832860	+	0.553484i	$0.186702\pi$
$252$	9.85266e120	0.528234
$253$	−7.62448e120	−0.334675
$254$	3.07705e120	0.110671
$255$	−6.41419e120	−0.189174
$256$	3.09786e121	0.749797
$257$	−6.07536e121	−1.20767	−0.603836	−	0.797108i	$-0.706362\pi$
$257$	−6.07536e121	−1.20767	−0.603836	+	0.797108i	$0.706362\pi$
$258$	8.35974e119	0.0136583
$259$	−3.09646e121	−0.416129
$260$	4.14040e121	0.458024
$261$	1.02218e121	0.0931501
$262$	−2.96893e121	−0.223041
$263$	−2.58199e122	−1.60026	−0.800128	−	0.599829i	$-0.795235\pi$
$263$	−2.58199e122	−1.60026	−0.800128	+	0.599829i	$0.795235\pi$
$264$	4.42306e120	0.0226321
$265$	−4.65236e121	−0.196678
$266$	−1.16393e121	−0.0406822
$267$	1.32628e122	0.383544
$268$	7.54937e122	1.80760
$269$	−2.19706e122	−0.435865	−0.217932	−	0.975964i	$-0.569931\pi$
$269$	−2.19706e122	−0.435865	−0.217932	+	0.975964i	$0.569931\pi$
$270$	−3.06505e121	−0.0504159
$271$	−2.27556e122	−0.310555	−0.155278	−	0.987871i	$-0.549627\pi$
$271$	−2.27556e122	−0.310555	−0.155278	+	0.987871i	$0.549627\pi$
$272$	9.47664e122	1.07380
$273$	1.39497e122	0.131326
$274$	8.73363e121	0.0683583
$275$	2.58393e122	0.168259
$276$	6.53381e122	0.354207
$277$	−2.83013e123	−1.27814	−0.639070	−	0.769148i	$-0.720681\pi$
$277$	−2.83013e123	−1.27814	−0.639070	+	0.769148i	$0.720681\pi$
$278$	5.80693e122	0.218617
$279$	−2.71806e123	−0.853586
$280$	4.17595e122	0.109465
$281$	−5.27048e123	−1.15393	−0.576967	−	0.816768i	$-0.695764\pi$
$281$	−5.27048e123	−1.15393	−0.576967	+	0.816768i	$0.695764\pi$
$282$	2.79482e122	0.0511416
$283$	−4.08346e123	−0.624904	−0.312452	−	0.949934i	$-0.601150\pi$
$283$	−4.08346e123	−0.624904	−0.312452	+	0.949934i	$0.601150\pi$
$284$	1.32770e124	1.70029
$285$	−6.50359e122	−0.0697409
$286$	−3.69193e122	−0.0331718
$287$	−5.25141e123	−0.395586
$288$	6.82317e123	0.431187
$289$	6.68506e123	0.354621
$290$	2.13765e122	0.00952442
$291$	−3.56924e123	−0.133653
$292$	5.21112e124	1.64096
$293$	−6.02275e123	−0.159580	−0.0797902	−	0.996812i	$-0.525425\pi$
$293$	−6.02275e123	−0.159580	−0.0797902	+	0.996812i	$0.525425\pi$
$294$	−1.31543e123	−0.0293447
$295$	−2.72332e124	−0.511784
$296$	−1.42332e124	−0.225461
$297$	−1.02288e124	−0.136654
$298$	−2.15415e124	−0.242860
$299$	−1.10533e125	−1.05219
$300$	−2.21430e124	−0.178079
$301$	2.63398e124	0.179062
$302$	2.51791e123	0.0144774
$303$	−8.26481e124	−0.402143
$304$	9.60873e124	0.395868
$305$	−4.67169e124	−0.163054
$306$	5.85627e124	0.173256
$307$	2.01247e125	0.504943	0.252471	−	0.967604i	$-0.418757\pi$
$307$	2.01247e125	0.504943	0.252471	+	0.967604i	$0.418757\pi$
$308$	6.87620e124	0.146399
$309$	5.78957e124	0.104651
$310$	−5.68418e124	−0.0872775
$311$	9.00803e125	1.17552	0.587760	−	0.809035i	$-0.300010\pi$
$311$	9.00803e125	1.17552	0.587760	+	0.809035i	$0.300010\pi$
$312$	6.41214e124	0.0711535
$313$	4.50650e125	0.425452	0.212726	−	0.977112i	$-0.431766\pi$
$313$	4.50650e125	0.425452	0.212726	+	0.977112i	$0.431766\pi$
$314$	3.28781e125	0.264216
$315$	−4.63472e125	−0.317205
$316$	−2.20207e126	−1.28420
$317$	−1.39121e126	−0.691671	−0.345835	−	0.938295i	$-0.612404\pi$
$317$	−1.39121e126	−0.691671	−0.345835	+	0.938295i	$0.612404\pi$
$318$	−3.55501e124	−0.0150755
$319$	7.13386e124	0.0258163
$320$	−1.60375e126	−0.495520
$321$	3.42574e125	0.0904170
$322$	−5.50060e125	−0.124076
$323$	2.58923e126	0.499394
$324$	−4.57054e126	−0.754127
$325$	3.74594e126	0.528995
$326$	−4.10968e125	−0.0496957
$327$	4.85046e126	0.502484
$328$	−2.41387e126	−0.214331
$329$	8.80590e126	0.670472
$330$	−1.02660e125	−0.00670572
$331$	2.75350e127	1.54373	0.771864	−	0.635788i	$-0.219325\pi$
$331$	2.75350e127	1.54373	0.771864	+	0.635788i	$0.219325\pi$
$332$	−1.85308e127	−0.892117
$333$	1.57969e127	0.653337
$334$	−5.98604e126	−0.212786
$335$	−3.55124e127	−1.08547
$336$	−5.73092e126	−0.150692
$337$	7.77367e126	0.175920	0.0879602	−	0.996124i	$-0.471965\pi$
$337$	7.77367e126	0.175920	0.0879602	+	0.996124i	$0.471965\pi$
$338$	2.92681e126	0.0570297
$339$	−5.25031e125	−0.00881252
$340$	−4.58358e127	−0.663010
$341$	−1.89694e127	−0.236569
$342$	5.93789e126	0.0638725
$343$	−1.04766e128	−0.972450
$344$	1.21074e127	0.0970172
$345$	−3.07352e127	−0.212702
$346$	2.13993e127	0.127955
$347$	2.37286e128	1.22640	0.613202	−	0.789926i	$-0.289881\pi$
$347$	2.37286e128	1.22640	0.613202	+	0.789926i	$0.289881\pi$
$348$	−6.11337e126	−0.0273230
$349$	3.72904e128	1.44183	0.720913	−	0.693026i	$-0.243723\pi$
$349$	3.72904e128	1.44183	0.720913	+	0.693026i	$0.243723\pi$
$350$	1.86415e127	0.0623799
$351$	−1.48288e128	−0.429631
$352$	4.76192e127	0.119503
$353$	7.61652e126	0.0165628	0.00828140	−	0.999966i	$-0.497364\pi$
$353$	7.61652e126	0.0165628	0.00828140	+	0.999966i	$0.497364\pi$
$354$	−2.08097e127	−0.0392284
$355$	−6.24554e128	−1.02103
$356$	9.47758e128	1.34423
$357$	−1.54429e128	−0.190101
$358$	9.27491e127	0.0991327
$359$	−1.27355e129	−1.18235	−0.591175	−	0.806543i	$-0.701336\pi$
$359$	−1.27355e129	−1.18235	−0.591175	+	0.806543i	$0.701336\pi$
$360$	−2.13040e128	−0.171864
$361$	−1.16345e129	−0.815894
$362$	−4.31248e128	−0.262993
$363$	4.89552e128	0.259725
$364$	9.96849e128	0.460267
$365$	−2.45133e129	−0.985398
$366$	−3.56978e127	−0.0124982
$367$	1.66816e129	0.508863	0.254431	−	0.967091i	$-0.418112\pi$
$367$	1.66816e129	0.508863	0.254431	+	0.967091i	$0.418112\pi$
$368$	4.54098e129	1.20735
$369$	2.67906e129	0.621084
$370$	3.30354e128	0.0668025
$371$	−1.12011e129	−0.197641
$372$	1.62559e129	0.250376
$373$	−3.54244e129	−0.476438	−0.238219	−	0.971211i	$-0.576564\pi$
$373$	−3.54244e129	−0.476438	−0.238219	+	0.971211i	$0.576564\pi$
$374$	4.08711e128	0.0480176
$375$	2.62480e129	0.269475
$376$	4.04773e129	0.363266
$377$	1.03420e129	0.0811646
$378$	−7.37946e128	−0.0506627
$379$	−1.58386e130	−0.951561	−0.475781	−	0.879564i	$-0.657834\pi$
$379$	−1.58386e130	−0.951561	−0.475781	+	0.879564i	$0.657834\pi$
$380$	−4.64747e129	−0.244425
$381$	4.13950e129	0.190650
$382$	5.77451e128	0.0232978
$383$	−3.23739e130	−1.14461	−0.572305	−	0.820041i	$-0.693951\pi$
$383$	−3.23739e130	−1.14461	−0.572305	+	0.820041i	$0.693951\pi$
$384$	−5.41524e129	−0.167838
$385$	−3.23459e129	−0.0879128
$386$	1.02380e130	0.244093
$387$	−1.34375e130	−0.281135
$388$	−2.55058e130	−0.468421
$389$	8.82272e130	1.42281	0.711406	−	0.702781i	$-0.248059\pi$
$389$	8.82272e130	1.42281	0.711406	+	0.702781i	$0.248059\pi$
$390$	−1.48826e129	−0.0210823
$391$	1.22364e131	1.52310
$392$	−1.90514e130	−0.208440
$393$	−3.99405e130	−0.384229
$394$	−2.53635e130	−0.214610
$395$	1.03586e131	0.771167
$396$	−3.50796e130	−0.229852
$397$	5.46354e130	0.315176	0.157588	−	0.987505i	$-0.449628\pi$
$397$	5.46354e130	0.315176	0.157588	+	0.987505i	$0.449628\pi$
$398$	−1.03181e130	−0.0524211
$399$	−1.56581e130	−0.0700824
$400$	−1.53893e131	−0.607002
$401$	1.18778e130	0.0412996	0.0206498	−	0.999787i	$-0.493426\pi$
$401$	1.18778e130	0.0412996	0.0206498	+	0.999787i	$0.493426\pi$
$402$	−2.71361e130	−0.0832017
$403$	−2.75002e131	−0.743756
$404$	−5.90604e131	−1.40941
$405$	2.15000e131	0.452855
$406$	5.14665e129	0.00957105
$407$	1.10247e131	0.181071
$408$	−7.09849e130	−0.102998
$409$	6.47684e131	0.830493	0.415247	−	0.909709i	$-0.363695\pi$
$409$	6.47684e131	0.830493	0.415247	+	0.909709i	$0.363695\pi$
$410$	5.60261e130	0.0635046
$411$	1.17492e131	0.117760
$412$	4.13723e131	0.366775
$413$	−6.55670e131	−0.514289
$414$	2.80618e131	0.194804
$415$	8.71696e131	0.535718
$416$	6.90339e131	0.375707
$417$	7.81196e131	0.376608
$418$	4.14408e130	0.0177021
$419$	3.66872e131	0.138901	0.0694507	−	0.997585i	$-0.477875\pi$
$419$	3.66872e131	0.138901	0.0694507	+	0.997585i	$0.477875\pi$
$420$	2.77188e131	0.0930435
$421$	−1.22752e132	−0.365412	−0.182706	−	0.983168i	$-0.558486\pi$
$421$	−1.22752e132	−0.365412	−0.182706	+	0.983168i	$0.558486\pi$
$422$	−1.16425e131	−0.0307445
$423$	−4.49241e132	−1.05267
$424$	−5.14871e131	−0.107083
$425$	−4.14691e132	−0.765743
$426$	−4.77240e131	−0.0782623
$427$	−1.12476e132	−0.163853
$428$	2.44803e132	0.316889
$429$	−4.96669e131	−0.0571444
$430$	−2.81013e131	−0.0287455
$431$	1.06447e133	0.968344	0.484172	−	0.874973i	$-0.339121\pi$
$431$	1.06447e133	0.968344	0.484172	+	0.874973i	$0.339121\pi$
$432$	6.09205e132	0.492986
$433$	−2.64916e133	−1.90752	−0.953762	−	0.300564i	$-0.902825\pi$
$433$	−2.64916e133	−1.90752	−0.953762	+	0.300564i	$0.902825\pi$
$434$	−1.36853e132	−0.0877048
$435$	2.87575e131	0.0164075
$436$	3.46615e133	1.76108
$437$	1.24070e133	0.561504
$438$	−1.87313e132	−0.0755312
$439$	1.51769e133	0.545411	0.272706	−	0.962098i	$-0.412081\pi$
$439$	1.51769e133	0.545411	0.272706	+	0.962098i	$0.412081\pi$
$440$	−1.48681e132	−0.0476317
$441$	2.11444e133	0.604012
$442$	5.92512e132	0.150964
$443$	−5.30570e133	−1.20602	−0.603010	−	0.797733i	$-0.706032\pi$
$443$	−5.30570e133	−1.20602	−0.603010	+	0.797733i	$0.706032\pi$
$444$	−9.44763e132	−0.191639
$445$	−4.45828e133	−0.807211
$446$	9.04776e132	0.146262
$447$	−2.89794e133	−0.418369
$448$	−3.86120e133	−0.497947
$449$	5.37070e131	0.00618857	0.00309429	−	0.999995i	$-0.499015\pi$
$449$	5.37070e131	0.00618857	0.00309429	+	0.999995i	$0.499015\pi$
$450$	−9.51013e132	−0.0979387
$451$	1.86972e133	0.172132
$452$	−3.75188e132	−0.0308857
$453$	3.38730e132	0.0249399
$454$	3.22142e133	0.212191
$455$	−4.68921e133	−0.276391
$456$	−7.19743e132	−0.0379711
$457$	2.17557e134	1.02755	0.513777	−	0.857924i	$-0.328246\pi$
$457$	2.17557e134	1.02755	0.513777	+	0.857924i	$0.328246\pi$
$458$	−1.44100e133	−0.0609476
$459$	1.64160e134	0.621910
$460$	−2.19634e134	−0.745469
$461$	3.26419e134	0.992838	0.496419	−	0.868083i	$-0.334648\pi$
$461$	3.26419e134	0.992838	0.496419	+	0.868083i	$0.334648\pi$
$462$	−2.47165e132	−0.00673855
$463$	2.23237e134	0.545664	0.272832	−	0.962062i	$-0.412040\pi$
$463$	2.23237e134	0.545664	0.272832	+	0.962062i	$0.412040\pi$
$464$	−4.24877e133	−0.0931334
$465$	−7.64682e133	−0.150351
$466$	−1.16764e134	−0.205977
$467$	1.51582e134	0.239963	0.119982	−	0.992776i	$-0.461716\pi$
$467$	1.51582e134	0.239963	0.119982	+	0.992776i	$0.461716\pi$
$468$	−5.08551e134	−0.722636
$469$	−8.55003e134	−1.09078
$470$	−9.39480e133	−0.107633
$471$	4.42303e134	0.455160
$472$	−3.01386e134	−0.278645
$473$	−9.37807e133	−0.0779158
$474$	7.91533e133	0.0591103
$475$	−4.20471e134	−0.282298
$476$	−1.10355e135	−0.666256
$477$	5.71434e134	0.310304
$478$	2.63820e134	0.128884
$479$	1.07969e135	0.474632	0.237316	−	0.971432i	$-0.423732\pi$
$479$	1.07969e135	0.474632	0.237316	+	0.971432i	$0.423732\pi$
$480$	1.91959e134	0.0759496
$481$	1.59826e135	0.569273
$482$	2.28864e134	0.0734010
$483$	−7.39986e134	−0.213744
$484$	3.49834e135	0.910273
$485$	1.19980e135	0.281288
$486$	5.72265e134	0.120911
$487$	1.89475e135	0.360861	0.180430	−	0.983588i	$-0.442251\pi$
$487$	1.89475e135	0.360861	0.180430	+	0.983588i	$0.442251\pi$
$488$	−5.17010e134	−0.0887765
$489$	−5.52867e134	−0.0856098
$490$	4.42184e134	0.0617591
$491$	−1.35592e136	−1.70851	−0.854257	−	0.519852i	$-0.825987\pi$
$491$	−1.35592e136	−1.70851	−0.854257	+	0.519852i	$0.825987\pi$
$492$	−1.60226e135	−0.182178
$493$	−1.14490e135	−0.117489
$494$	6.00770e134	0.0556541
$495$	1.65015e135	0.138026
$496$	1.12978e136	0.853433
$497$	−1.50368e136	−1.02603
$498$	6.66089e134	0.0410630
$499$	−3.19004e136	−1.77713	−0.888563	−	0.458755i	$-0.848295\pi$
$499$	−3.19004e136	−1.77713	−0.888563	+	0.458755i	$0.848295\pi$
$500$	1.87569e136	0.944441
$501$	−8.05290e135	−0.366562
$502$	−6.52869e135	−0.268713
$503$	4.79960e136	1.78658	0.893288	−	0.449485i	$-0.148392\pi$
$503$	4.79960e136	1.78658	0.893288	+	0.449485i	$0.148392\pi$
$504$	−5.12918e135	−0.172705
$505$	2.77822e136	0.846354
$506$	1.95844e135	0.0539896
$507$	3.93739e135	0.0982440
$508$	2.95809e136	0.668181
$509$	1.97121e136	0.403167	0.201583	−	0.979471i	$-0.435391\pi$
$509$	1.97121e136	0.403167	0.201583	+	0.979471i	$0.435391\pi$
$510$	1.64757e135	0.0305175
$511$	−5.90185e136	−0.990223
$512$	−4.76885e136	−0.724905
$513$	1.66448e136	0.229273
$514$	1.56053e136	0.194821
$515$	−1.94616e136	−0.220249
$516$	8.03655e135	0.0824631
$517$	−3.13527e136	−0.291744
$518$	7.95366e135	0.0671296
$519$	2.87881e136	0.220425
$520$	−2.15545e136	−0.149750
$521$	−1.89189e137	−1.19286	−0.596430	−	0.802665i	$-0.703415\pi$
$521$	−1.89189e137	−1.19286	−0.596430	+	0.802665i	$0.703415\pi$
$522$	−2.62561e135	−0.0150269
$523$	6.85650e136	0.356260	0.178130	−	0.984007i	$-0.442995\pi$
$523$	6.85650e136	0.356260	0.178130	+	0.984007i	$0.442995\pi$
$524$	−2.85415e137	−1.34663
$525$	2.50781e136	0.107461
$526$	6.63217e136	0.258152
$527$	3.04438e137	1.07662
$528$	2.04045e136	0.0655711
$529$	2.43956e137	0.712525
$530$	1.19502e136	0.0317280
$531$	3.34496e137	0.807453
$532$	−1.11893e137	−0.245621
$533$	2.71055e137	0.541170
$534$	−3.40671e136	−0.0618731
$535$	−1.15156e137	−0.190293
$536$	−3.93011e137	−0.590994
$537$	1.24774e137	0.170774
$538$	5.64342e136	0.0703134
$539$	1.47567e137	0.167401
$540$	−2.94655e137	−0.304389
$541$	−1.17231e137	−0.110301	−0.0551506	−	0.998478i	$-0.517564\pi$
$541$	−1.17231e137	−0.110301	−0.0551506	+	0.998478i	$0.517564\pi$
$542$	5.84506e136	0.0500986
$543$	−5.80150e137	−0.453053
$544$	−7.64232e137	−0.543852
$545$	−1.63049e138	−1.05753
$546$	−3.58317e136	−0.0211855
$547$	−1.71733e136	−0.00925751	−0.00462875	−	0.999989i	$-0.501473\pi$
$547$	−1.71733e136	−0.00925751	−0.00462875	+	0.999989i	$0.501473\pi$
$548$	8.39599e137	0.412718
$549$	5.73808e137	0.257255
$550$	−6.63715e136	−0.0271435
$551$	−1.16086e137	−0.0433135
$552$	−3.40143e137	−0.115808
$553$	2.49396e138	0.774943
$554$	7.26956e137	0.206189
$555$	4.44419e137	0.115079
$556$	5.58243e138	1.31992
$557$	−1.70337e138	−0.367808	−0.183904	−	0.982944i	$-0.558874\pi$
$557$	−1.70337e138	−0.367808	−0.183904	+	0.982944i	$0.558874\pi$
$558$	6.98169e137	0.137700
$559$	−1.35955e138	−0.244961
$560$	1.92645e138	0.317149
$561$	5.49831e137	0.0827190
$562$	1.35379e138	0.186152
$563$	−1.19099e139	−1.49705	−0.748523	−	0.663109i	$-0.769237\pi$
$563$	−1.19099e139	−1.49705	−0.748523	+	0.663109i	$0.769237\pi$
$564$	2.68677e138	0.308771
$565$	1.76489e137	0.0185469
$566$	1.04889e138	0.100809
$567$	5.17636e138	0.455072
$568$	−6.91185e138	−0.555909
$569$	−2.22588e139	−1.63807	−0.819034	−	0.573745i	$-0.805490\pi$
$569$	−2.22588e139	−1.63807	−0.819034	+	0.573745i	$0.805490\pi$
$570$	1.67053e137	0.0112506
$571$	7.96541e138	0.491004	0.245502	−	0.969396i	$-0.421047\pi$
$571$	7.96541e138	0.491004	0.245502	+	0.969396i	$0.421047\pi$
$572$	−3.54920e138	−0.200277
$573$	7.76834e137	0.0401347
$574$	1.34889e138	0.0638156
$575$	−1.98710e139	−0.860979
$576$	1.96983e139	0.781795
$577$	2.07485e139	0.754411	0.377205	−	0.926130i	$-0.376885\pi$
$577$	2.07485e139	0.754411	0.377205	+	0.926130i	$0.376885\pi$
$578$	−1.71714e138	−0.0572072
$579$	1.37729e139	0.420494
$580$	2.05501e138	0.0575043
$581$	2.09871e139	0.538341
$582$	9.16804e137	0.0215608
$583$	3.98806e138	0.0860002
$584$	−2.71285e139	−0.536509
$585$	2.39224e139	0.433944
$586$	1.54702e138	0.0257434
$587$	2.85396e139	0.435736	0.217868	−	0.975978i	$-0.430090\pi$
$587$	2.85396e139	0.435736	0.217868	+	0.975978i	$0.430090\pi$
$588$	−1.26458e139	−0.177170
$589$	3.08681e139	0.396906
$590$	6.99519e138	0.0825606
$591$	−3.41210e139	−0.369704
$592$	−6.56608e139	−0.653220
$593$	−1.04560e140	−0.955220	−0.477610	−	0.878572i	$-0.658497\pi$
$593$	−1.04560e140	−0.955220	−0.477610	+	0.878572i	$0.658497\pi$
$594$	2.62740e138	0.0220450
$595$	5.19113e139	0.400088
$596$	−2.07087e140	−1.46628
$597$	−1.38808e139	−0.0903048
$598$	2.83917e139	0.169739
$599$	−1.21440e140	−0.667277	−0.333639	−	0.942701i	$-0.608277\pi$
$599$	−1.21440e140	−0.667277	−0.333639	+	0.942701i	$0.608277\pi$
$600$	1.15274e139	0.0582228
$601$	2.46874e140	1.14634	0.573171	−	0.819436i	$-0.305713\pi$
$601$	2.46874e140	1.14634	0.573171	+	0.819436i	$0.305713\pi$
$602$	−6.76571e138	−0.0288862
$603$	4.36188e140	1.71257
$604$	2.42057e139	0.0874081
$605$	−1.64563e140	−0.546621
$606$	2.12292e139	0.0648734
$607$	1.09575e140	0.308093	0.154046	−	0.988064i	$-0.450770\pi$
$607$	1.09575e140	0.308093	0.154046	+	0.988064i	$0.450770\pi$
$608$	−7.74884e139	−0.200496
$609$	6.92369e138	0.0164879
$610$	1.19998e139	0.0263038
$611$	−4.54522e140	−0.917221
$612$	5.62986e140	1.04605
$613$	7.23778e140	1.23837	0.619186	−	0.785244i	$-0.287463\pi$
$613$	7.23778e140	1.23837	0.619186	+	0.785244i	$0.287463\pi$
$614$	−5.16929e139	−0.0814570
$615$	7.53709e139	0.109398
$616$	−3.57967e139	−0.0478649
$617$	−1.53781e141	−1.89453	−0.947265	−	0.320452i	$-0.896165\pi$
$617$	−1.53781e141	−1.89453	−0.947265	+	0.320452i	$0.896165\pi$
$618$	−1.48712e139	−0.0168822
$619$	−6.21672e140	−0.650404	−0.325202	−	0.945644i	$-0.605432\pi$
$619$	−6.21672e140	−0.650404	−0.325202	+	0.945644i	$0.605432\pi$
$620$	−5.46443e140	−0.526944
$621$	7.86616e140	0.699257
$622$	−2.31383e140	−0.189634
$623$	−1.07338e141	−0.811164
$624$	2.95805e140	0.206150
$625$	1.41236e140	0.0907829
$626$	−1.15755e140	−0.0686336
$627$	5.57495e139	0.0304951
$628$	3.16070e141	1.59522
$629$	−1.76934e141	−0.824048
$630$	1.19049e140	0.0511713
$631$	1.33263e141	0.528721	0.264360	−	0.964424i	$-0.414839\pi$
$631$	1.33263e141	0.528721	0.264360	+	0.964424i	$0.414839\pi$
$632$	1.14637e141	0.419869
$633$	−1.56624e140	−0.0529629
$634$	3.57349e140	0.111580
$635$	−1.39150e141	−0.401244
$636$	−3.41757e140	−0.0910193
$637$	2.13929e141	0.526295
$638$	−1.83242e139	−0.00416467
$639$	7.67118e141	1.61090
$640$	1.82033e141	0.353234
$641$	−1.00041e142	−1.79410	−0.897049	−	0.441931i	$-0.854294\pi$
$641$	−1.00041e142	−1.79410	−0.897049	+	0.441931i	$0.854294\pi$
$642$	−8.79944e139	−0.0145860
$643$	6.42814e140	0.0984989	0.0492494	−	0.998787i	$-0.484317\pi$
$643$	6.42814e140	0.0984989	0.0492494	+	0.998787i	$0.484317\pi$
$644$	−5.28795e141	−0.749119
$645$	−3.78042e140	−0.0495193
$646$	−6.65076e140	−0.0805618
$647$	−1.06846e142	−1.19699	−0.598496	−	0.801126i	$-0.704235\pi$
$647$	−1.06846e142	−1.19699	−0.598496	+	0.801126i	$0.704235\pi$
$648$	2.37937e141	0.246561
$649$	2.33446e141	0.223784
$650$	−9.62193e140	−0.0853371
$651$	−1.84106e141	−0.151087
$652$	−3.95080e141	−0.300041
$653$	−8.23618e140	−0.0578909	−0.0289454	−	0.999581i	$-0.509215\pi$
$653$	−8.23618e140	−0.0578909	−0.0289454	+	0.999581i	$0.509215\pi$
$654$	−1.24590e141	−0.0810603
$655$	1.34260e142	0.808652
$656$	−1.11357e142	−0.620973
$657$	3.01088e142	1.55469
$658$	−2.26191e141	−0.108160
$659$	−1.12345e142	−0.497556	−0.248778	−	0.968561i	$-0.580029\pi$
$659$	−1.12345e142	−0.497556	−0.248778	+	0.968561i	$0.580029\pi$
$660$	−9.86906e140	−0.0404862
$661$	4.11483e142	1.56379	0.781895	−	0.623410i	$-0.214253\pi$
$661$	4.11483e142	1.56379	0.781895	+	0.623410i	$0.214253\pi$
$662$	−7.07271e141	−0.249033
$663$	7.97095e141	0.260062
$664$	9.64694e141	0.291677
$665$	5.26349e141	0.147496
$666$	−4.05763e141	−0.105396
$667$	−5.48609e141	−0.132102
$668$	−5.75461e142	−1.28471
$669$	1.21718e142	0.251962
$670$	9.12182e141	0.175107
$671$	4.00463e141	0.0712976
$672$	4.62163e141	0.0763215
$673$	−1.14033e143	−1.74691	−0.873456	−	0.486902i	$-0.838127\pi$
$673$	−1.14033e143	−1.74691	−0.873456	+	0.486902i	$0.838127\pi$
$674$	−1.99677e141	−0.0283793
$675$	−2.66583e142	−0.351555
$676$	2.81366e142	0.344321
$677$	−1.56671e142	−0.177935	−0.0889673	−	0.996035i	$-0.528357\pi$
$677$	−1.56671e142	−0.177935	−0.0889673	+	0.996035i	$0.528357\pi$
$678$	1.34861e140	0.00142163
$679$	2.88866e142	0.282665
$680$	2.38616e142	0.216770
$681$	4.33372e142	0.365537
$682$	4.87254e141	0.0381632
$683$	−2.23192e142	−0.162343	−0.0811714	−	0.996700i	$-0.525866\pi$
$683$	−2.23192e142	−0.162343	−0.0811714	+	0.996700i	$0.525866\pi$
$684$	5.70833e142	0.385635
$685$	−3.94950e142	−0.247838
$686$	2.69105e142	0.156875
$687$	−1.93855e142	−0.104993
$688$	5.58538e142	0.281084
$689$	5.78152e142	0.270378
$690$	7.89473e141	0.0343130
$691$	2.36035e143	0.953530	0.476765	−	0.879031i	$-0.341809\pi$
$691$	2.36035e143	0.953530	0.476765	+	0.879031i	$0.341809\pi$
$692$	2.05720e143	0.772537
$693$	3.97293e142	0.138702
$694$	−6.09499e142	−0.197843
$695$	−2.62599e143	−0.792612
$696$	3.18255e141	0.00893323
$697$	−3.00069e143	−0.783367
$698$	−9.57851e142	−0.232594
$699$	−1.57080e143	−0.354833
$700$	1.79208e143	0.376623
$701$	−6.16772e143	−1.20605	−0.603025	−	0.797723i	$-0.706038\pi$
$701$	−6.16772e143	−1.20605	−0.603025	+	0.797723i	$0.706038\pi$
$702$	3.80896e142	0.0693078
$703$	−1.79400e143	−0.303793
$704$	1.37475e143	0.216673
$705$	−1.26387e143	−0.185417
$706$	−1.95640e141	−0.00267190
$707$	6.68888e143	0.850498
$708$	−2.00052e143	−0.236844
$709$	4.62173e143	0.509529	0.254765	−	0.967003i	$-0.418002\pi$
$709$	4.62173e143	0.509529	0.254765	+	0.967003i	$0.418002\pi$
$710$	1.60425e143	0.164712
$711$	−1.27231e144	−1.21669
$712$	−4.93392e143	−0.439494
$713$	1.45879e144	1.21052
$714$	3.96670e142	0.0306669
$715$	1.66955e143	0.120267
$716$	8.91634e143	0.598520
$717$	3.54913e143	0.222026
$718$	3.27127e143	0.190736
$719$	3.09556e144	1.68241	0.841203	−	0.540719i	$-0.181848\pi$
$719$	3.09556e144	1.68241	0.841203	+	0.540719i	$0.181848\pi$
$720$	−9.82797e143	−0.497935
$721$	−4.68562e143	−0.221328
$722$	2.98847e143	0.131619
$723$	3.07887e143	0.126446
$724$	−4.14576e144	−1.58784
$725$	1.85923e143	0.0664146
$726$	−1.25748e143	−0.0418987
$727$	−3.18407e144	−0.989681	−0.494840	−	0.868984i	$-0.664773\pi$
$727$	−3.18407e144	−0.989681	−0.494840	+	0.868984i	$0.664773\pi$
$728$	−5.18948e143	−0.150484
$729$	−2.09192e144	−0.565986
$730$	6.29655e143	0.158964
$731$	1.50507e144	0.354592
$732$	−3.43177e143	−0.0754586
$733$	8.96985e143	0.184092	0.0920459	−	0.995755i	$-0.470659\pi$
$733$	8.96985e143	0.184092	0.0920459	+	0.995755i	$0.470659\pi$
$734$	−4.28487e143	−0.0820894
$735$	5.94862e143	0.106391
$736$	−3.66202e144	−0.611492
$737$	3.04417e144	0.474636
$738$	−6.88150e143	−0.100193
$739$	−1.38916e144	−0.188889	−0.0944445	−	0.995530i	$-0.530107\pi$
$739$	−1.38916e144	−0.188889	−0.0944445	+	0.995530i	$0.530107\pi$
$740$	3.17582e144	0.403325
$741$	8.08205e143	0.0958743
$742$	2.87714e143	0.0318834
$743$	1.30796e145	1.35413	0.677066	−	0.735923i	$-0.263251\pi$
$743$	1.30796e145	1.35413	0.677066	+	0.735923i	$0.263251\pi$
$744$	−8.46263e143	−0.0818601
$745$	9.74145e144	0.880505
$746$	9.09921e143	0.0768587
$747$	−1.07068e145	−0.845215
$748$	3.92910e144	0.289910
$749$	−2.77252e144	−0.191224
$750$	−6.74214e143	−0.0434714
$751$	−1.15451e145	−0.695954	−0.347977	−	0.937503i	$-0.613131\pi$
$751$	−1.15451e145	−0.695954	−0.347977	+	0.937503i	$0.613131\pi$
$752$	1.86730e145	1.05248
$753$	−8.78293e144	−0.462906
$754$	−2.65648e143	−0.0130934
$755$	−1.13864e144	−0.0524887
$756$	−7.09417e144	−0.305880
$757$	−3.83259e145	−1.54579	−0.772896	−	0.634533i	$-0.781193\pi$
$757$	−3.83259e145	−1.54579	−0.772896	+	0.634533i	$0.781193\pi$
$758$	4.06835e144	0.153505
$759$	2.63466e144	0.0930068
$760$	2.41942e144	0.0799144
$761$	2.11377e145	0.653329	0.326665	−	0.945140i	$-0.394075\pi$
$761$	2.11377e145	0.653329	0.326665	+	0.945140i	$0.394075\pi$
$762$	−1.06328e144	−0.0307555
$763$	−3.92558e145	−1.06271
$764$	5.55126e144	0.140662
$765$	−2.64830e145	−0.628153
$766$	8.31566e144	0.184648
$767$	3.38428e145	0.703560
$768$	−1.07047e145	−0.208370
$769$	9.71643e144	0.177103	0.0885516	−	0.996072i	$-0.471776\pi$
$769$	9.71643e144	0.177103	0.0885516	+	0.996072i	$0.471776\pi$
$770$	8.30845e143	0.0141820
$771$	2.09936e145	0.335614
$772$	9.84216e145	1.47373
$773$	5.12373e145	0.718657	0.359328	−	0.933211i	$-0.383006\pi$
$773$	5.12373e145	0.718657	0.359328	+	0.933211i	$0.383006\pi$
$774$	3.45159e144	0.0453524
$775$	−4.94383e145	−0.608594
$776$	1.32780e145	0.153150
$777$	1.06999e145	0.115643
$778$	−2.26623e145	−0.229527
$779$	−3.04251e145	−0.288796
$780$	−1.43073e145	−0.127286
$781$	5.35375e145	0.446458
$782$	−3.14307e145	−0.245705
$783$	−7.35999e144	−0.0539396
$784$	−8.78879e145	−0.603904
$785$	−1.48680e146	−0.957935
$786$	1.02592e145	0.0619835
$787$	1.01267e146	0.573778	0.286889	−	0.957964i	$-0.407379\pi$
$787$	1.01267e146	0.573778	0.286889	+	0.957964i	$0.407379\pi$
$788$	−2.43829e146	−1.29572
$789$	8.92214e145	0.444714
$790$	−2.66074e145	−0.124404
$791$	4.24919e144	0.0186377
$792$	1.82620e145	0.0751497
$793$	5.80554e145	0.224154
$794$	−1.40338e145	−0.0508440
$795$	1.60764e145	0.0546573
$796$	−9.91924e145	−0.316496
$797$	−2.74405e146	−0.821764	−0.410882	−	0.911688i	$-0.634779\pi$
$797$	−2.74405e146	−0.821764	−0.410882	+	0.911688i	$0.634779\pi$
$798$	4.02199e144	0.0113056
$799$	5.03174e146	1.32772
$800$	1.24105e146	0.307430
$801$	5.47596e146	1.27356
$802$	−3.05097e144	−0.00666242
$803$	2.10131e146	0.430878
$804$	−2.60870e146	−0.502336
$805$	2.48747e146	0.449847
$806$	7.06377e145	0.119982
$807$	7.59200e145	0.121127
$808$	3.07462e146	0.460805
$809$	−7.66386e146	−1.07906	−0.539532	−	0.841965i	$-0.681399\pi$
$809$	−7.66386e146	−1.07906	−0.539532	+	0.841965i	$0.681399\pi$
$810$	−5.52254e145	−0.0730542
$811$	−1.19038e147	−1.47956	−0.739781	−	0.672848i	$-0.765071\pi$
$811$	−1.19038e147	−1.47956	−0.739781	+	0.672848i	$0.765071\pi$
$812$	4.94768e145	0.0577859
$813$	7.86326e145	0.0863038
$814$	−2.83183e145	−0.0292103
$815$	1.85847e146	0.180175
$816$	−3.27468e146	−0.298412
$817$	1.52605e146	0.130724
$818$	−1.66366e146	−0.133975
$819$	5.75960e146	0.436069
$820$	5.38601e146	0.383414
$821$	−1.88359e147	−1.26083	−0.630414	−	0.776259i	$-0.717115\pi$
$821$	−1.88359e147	−1.26083	−0.630414	+	0.776259i	$0.717115\pi$
$822$	−3.01793e145	−0.0189969
$823$	−4.64333e146	−0.274876	−0.137438	−	0.990510i	$-0.543887\pi$
$823$	−4.64333e146	−0.274876	−0.137438	+	0.990510i	$0.543887\pi$
$824$	−2.15379e146	−0.119917
$825$	−8.92884e145	−0.0467596
$826$	1.68417e146	0.0829648
$827$	−2.44457e147	−1.13285	−0.566427	−	0.824112i	$-0.691675\pi$
$827$	−2.44457e147	−1.13285	−0.566427	+	0.824112i	$0.691675\pi$
$828$	2.69769e147	1.17614
$829$	4.20030e147	1.72297	0.861483	−	0.507786i	$-0.169536\pi$
$829$	4.20030e147	1.72297	0.861483	+	0.507786i	$0.169536\pi$
$830$	−2.23906e146	−0.0864216
$831$	9.77960e146	0.355197
$832$	1.99299e147	0.681202
$833$	−2.36828e147	−0.761835
$834$	−2.00660e146	−0.0607541
$835$	2.70699e147	0.771470
$836$	3.98387e146	0.106878
$837$	1.95707e147	0.494278
$838$	−9.42358e145	−0.0224075
$839$	−4.27111e147	−0.956228	−0.478114	−	0.878298i	$-0.658679\pi$
$839$	−4.27111e147	−0.956228	−0.478114	+	0.878298i	$0.658679\pi$
$840$	−1.44301e146	−0.0304205
$841$	−4.98597e147	−0.989810
$842$	3.15304e146	0.0589480
$843$	1.82123e147	0.320680
$844$	−1.11924e147	−0.185622
$845$	−1.32355e147	−0.206765
$846$	1.15393e147	0.169815
$847$	−3.96205e147	−0.549297
$848$	−2.37520e147	−0.310249
$849$	1.41105e147	0.173662
$850$	1.06519e147	0.123529
$851$	−8.47823e147	−0.926536
$852$	−4.58790e147	−0.472514
$853$	1.65370e147	0.160521	0.0802604	−	0.996774i	$-0.474425\pi$
$853$	1.65370e147	0.160521	0.0802604	+	0.996774i	$0.474425\pi$
$854$	2.88910e146	0.0264326
$855$	−2.68522e147	−0.231574
$856$	−1.27442e147	−0.103607
$857$	2.26666e148	1.73722	0.868610	−	0.495497i	$-0.165014\pi$
$857$	2.26666e148	1.73722	0.868610	+	0.495497i	$0.165014\pi$
$858$	1.27576e146	0.00921849
$859$	1.45946e148	0.994344	0.497172	−	0.867652i	$-0.334372\pi$
$859$	1.45946e148	0.994344	0.497172	+	0.867652i	$0.334372\pi$
$860$	−2.70149e147	−0.173553
$861$	1.81464e147	0.109934
$862$	−2.73422e147	−0.156213
$863$	1.99479e148	1.07486	0.537430	−	0.843308i	$-0.319395\pi$
$863$	1.99479e148	1.07486	0.537430	+	0.843308i	$0.319395\pi$
$864$	−4.91286e147	−0.249684
$865$	−9.67714e147	−0.463910
$866$	6.80471e147	0.307720
$867$	−2.31004e147	−0.0985497
$868$	−1.31562e148	−0.529524
$869$	−8.87953e147	−0.337203
$870$	−7.38672e145	−0.00264685
$871$	4.41316e148	1.49222
$872$	−1.80444e148	−0.575783
$873$	−1.47367e148	−0.443795
$874$	−3.18688e147	−0.0905813
$875$	−2.12431e148	−0.569916
$876$	−1.80072e148	−0.456025
$877$	−9.73527e147	−0.232739	−0.116369	−	0.993206i	$-0.537126\pi$
$877$	−9.73527e147	−0.232739	−0.116369	+	0.993206i	$0.537126\pi$
$878$	−3.89837e147	−0.0879854
$879$	2.08118e147	0.0443477
$880$	−6.85897e147	−0.138002
$881$	6.24527e147	0.118650	0.0593250	−	0.998239i	$-0.481105\pi$
$881$	6.24527e147	0.118650	0.0593250	+	0.998239i	$0.481105\pi$
$882$	−5.43120e147	−0.0974388
$883$	−1.09918e149	−1.86232	−0.931159	−	0.364615i	$-0.881201\pi$
$883$	−1.09918e149	−1.86232	−0.931159	+	0.364615i	$0.881201\pi$
$884$	5.69605e148	0.911453
$885$	9.41050e147	0.142225
$886$	1.36284e148	0.194554
$887$	1.10849e149	1.49481	0.747407	−	0.664366i	$-0.231298\pi$
$887$	1.10849e149	1.49481	0.747407	+	0.664366i	$0.231298\pi$
$888$	4.91833e147	0.0626560
$889$	−3.35018e148	−0.403209
$890$	1.14517e148	0.130219
$891$	−1.84300e148	−0.198017
$892$	8.69797e148	0.883065
$893$	5.10187e148	0.489475
$894$	7.44373e147	0.0674910
$895$	−4.19427e148	−0.359413
$896$	4.38266e148	0.354963
$897$	3.81949e148	0.292406
$898$	−1.37953e146	−0.000998336 0
$899$	−1.36492e148	−0.0933776
$900$	−9.14246e148	−0.591312
$901$	−6.40037e148	−0.391384
$902$	−4.80262e147	−0.0277682
$903$	−9.10179e147	−0.0497617
$904$	1.95318e147	0.0100981
$905$	1.95018e149	0.953500
$906$	−8.70071e146	−0.00402328
$907$	−3.76928e149	−1.64851	−0.824253	−	0.566221i	$-0.808405\pi$
$907$	−3.76928e149	−1.64851	−0.824253	+	0.566221i	$0.808405\pi$
$908$	3.09688e149	1.28112
$909$	−3.41239e149	−1.33531
$910$	1.20448e148	0.0445872
$911$	−2.36013e149	−0.826528	−0.413264	−	0.910611i	$-0.635611\pi$
$911$	−2.36013e149	−0.826528	−0.413264	+	0.910611i	$0.635611\pi$
$912$	−3.32032e148	−0.110012
$913$	−7.47228e148	−0.234250
$914$	−5.58822e148	−0.165764
$915$	1.61432e148	0.0453131
$916$	−1.38529e149	−0.367975
$917$	3.23247e149	0.812611
$918$	−4.21666e148	−0.100326
$919$	4.61378e149	1.03902	0.519510	−	0.854464i	$-0.326115\pi$
$919$	4.61378e149	1.03902	0.519510	+	0.854464i	$0.326115\pi$
$920$	1.14339e149	0.243730
$921$	−6.95416e148	−0.140324
$922$	−8.38448e148	−0.160164
$923$	7.76137e149	1.40363
$924$	−2.37609e148	−0.0406845
$925$	2.87326e149	0.465820
$926$	−5.73412e148	−0.0880262
$927$	2.39041e149	0.347493
$928$	3.42637e148	0.0471695
$929$	−6.15334e148	−0.0802264	−0.0401132	−	0.999195i	$-0.512772\pi$
$929$	−6.15334e148	−0.0802264	−0.0401132	+	0.999195i	$0.512772\pi$
$930$	1.96418e148	0.0242545
$931$	−2.40129e149	−0.280857
$932$	−1.12250e150	−1.24360
$933$	−3.11275e149	−0.326679
$934$	−3.89358e148	−0.0387107
$935$	−1.84826e149	−0.174091
$936$	2.64746e149	0.236265
$937$	9.87076e149	0.834644	0.417322	−	0.908759i	$-0.362969\pi$
$937$	9.87076e149	0.834644	0.417322	+	0.908759i	$0.362969\pi$
$938$	2.19618e149	0.175965
$939$	−1.55723e149	−0.118234
$940$	−9.03160e149	−0.649842
$941$	−5.12586e149	−0.349535	−0.174768	−	0.984610i	$-0.555917\pi$
$941$	−5.12586e149	−0.349535	−0.174768	+	0.984610i	$0.555917\pi$
$942$	−1.13611e149	−0.0734261
$943$	−1.43786e150	−0.880795
$944$	−1.39035e150	−0.807309
$945$	3.33712e149	0.183681
$946$	2.40888e148	0.0125693
$947$	−7.23652e149	−0.357978	−0.178989	−	0.983851i	$-0.557283\pi$
$947$	−7.23652e149	−0.357978	−0.178989	+	0.983851i	$0.557283\pi$
$948$	7.60932e149	0.356882
$949$	3.04628e150	1.35465
$950$	1.08003e149	0.0455402
$951$	4.80736e149	0.192216
$952$	5.74496e149	0.217832
$953$	1.33924e150	0.481578	0.240789	−	0.970578i	$-0.422594\pi$
$953$	1.33924e150	0.481578	0.240789	+	0.970578i	$0.422594\pi$
$954$	−1.46780e149	−0.0500581
$955$	−2.61133e149	−0.0844679
$956$	2.53621e150	0.778147
$957$	−2.46512e148	−0.00717440
$958$	−2.77333e149	−0.0765673
$959$	−9.50887e149	−0.249052
$960$	5.54179e149	0.137706
$961$	−6.12191e149	−0.144330
$962$	−4.10533e149	−0.0918348
$963$	1.41443e150	0.300229
$964$	2.20016e150	0.443164
$965$	−4.62978e150	−0.884975
$966$	1.90075e149	0.0344810
$967$	3.91457e150	0.673980	0.336990	−	0.941508i	$-0.390591\pi$
$967$	3.91457e150	0.673980	0.336990	+	0.941508i	$0.390591\pi$
$968$	−1.82120e150	−0.297613
$969$	−8.94715e149	−0.138782
$970$	−3.08184e149	−0.0453772
$971$	−1.14003e151	−1.59348	−0.796740	−	0.604322i	$-0.793444\pi$
$971$	−1.14003e151	−1.59348	−0.796740	+	0.604322i	$0.793444\pi$
$972$	5.50141e150	0.730008
$973$	−6.32238e150	−0.796493
$974$	−4.86691e149	−0.0582138
$975$	−1.29442e150	−0.147008
$976$	−2.38507e150	−0.257209
$977$	−9.05921e150	−0.927716	−0.463858	−	0.885910i	$-0.653535\pi$
$977$	−9.05921e150	−0.927716	−0.463858	+	0.885910i	$0.653535\pi$
$978$	1.42011e149	0.0138105
$979$	3.82169e150	0.352964
$980$	4.25089e150	0.372875
$981$	2.00267e151	1.66849
$982$	3.48285e150	0.275616
$983$	−1.35939e151	−1.02186	−0.510930	−	0.859623i	$-0.670699\pi$
$983$	−1.35939e151	−1.02186	−0.510930	+	0.859623i	$0.670699\pi$
$984$	8.34119e149	0.0595629
$985$	1.14698e151	0.778084
$986$	2.94082e149	0.0189533
$987$	−3.04290e150	−0.186325
$988$	5.77544e150	0.336016
$989$	7.21193e150	0.398693
$990$	−4.23863e149	−0.0222663
$991$	1.59255e151	0.795010	0.397505	−	0.917600i	$-0.369876\pi$
$991$	1.59255e151	0.795010	0.397505	+	0.917600i	$0.369876\pi$
$992$	−9.11097e150	−0.432240
$993$	−9.51478e150	−0.429004
$994$	3.86241e150	0.165518
$995$	4.66604e150	0.190057
$996$	6.40338e150	0.247921
$997$	−7.11596e148	−0.00261896	−0.00130948	−	0.999999i	$-0.500417\pi$
$997$	−7.11596e148	−0.00261896	−0.00130948	+	0.999999i	$0.500417\pi$
$998$	8.19401e150	0.286685
$999$	−1.13742e151	−0.378322

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.102.a.a.1.4	✓	8	1.1	even	1	trivial
9.102.a.b.1.5		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)

\(f(q)\)	\(=\)	\(q-2.56863e14 q^{2} -3.45553e23 q^{3} -2.46932e30 q^{4} +1.16158e35 q^{5} +8.87596e37 q^{6} +2.79663e42 q^{7} +1.28550e45 q^{8} -1.42673e48 q^{9} +O(q^{10})\)	\(q-2.56863e14 q^{2} -3.45553e23 q^{3} -2.46932e30 q^{4} +1.16158e35 q^{5} +8.87596e37 q^{6} +2.79663e42 q^{7} +1.28550e45 q^{8} -1.42673e48 q^{9} -2.98366e49 q^{10} -9.95717e51 q^{11} +8.53281e53 q^{12} -1.44350e56 q^{13} -7.18350e56 q^{14} -4.01386e58 q^{15} +5.93028e60 q^{16} +1.59801e62 q^{17} +3.66473e62 q^{18} +1.62028e64 q^{19} -2.86831e65 q^{20} -9.66383e65 q^{21} +2.55763e66 q^{22} +7.65727e68 q^{23} -4.44208e68 q^{24} -2.59504e70 q^{25} +3.70781e70 q^{26} +1.02728e72 q^{27} -6.90578e72 q^{28} -7.16454e72 q^{29} +1.03101e73 q^{30} +1.90510e75 q^{31} -4.78240e75 q^{32} +3.44073e75 q^{33} -4.10469e76 q^{34} +3.24850e77 q^{35} +3.52305e78 q^{36} -1.10721e79 q^{37} -4.16190e78 q^{38} +4.98805e79 q^{39} +1.49321e80 q^{40} -1.87777e81 q^{41} +2.48228e80 q^{42} +9.41841e81 q^{43} +2.45875e82 q^{44} -1.65725e83 q^{45} -1.96687e83 q^{46} +3.14875e84 q^{47} -2.04922e84 q^{48} -1.48202e85 q^{49} +6.66570e84 q^{50} -5.52197e85 q^{51} +3.56447e86 q^{52} -4.00521e86 q^{53} -2.63870e86 q^{54} -1.15660e87 q^{55} +3.59507e87 q^{56} -5.59893e87 q^{57} +1.84030e87 q^{58} -2.34450e89 q^{59} +9.91152e88 q^{60} -4.02186e89 q^{61} -4.89350e89 q^{62} -3.99002e90 q^{63} -1.38066e91 q^{64} -1.67674e91 q^{65} -8.83794e89 q^{66} -3.05726e92 q^{67} -3.94600e92 q^{68} -2.64599e92 q^{69} -8.34418e91 q^{70} -5.37677e93 q^{71} -1.83406e93 q^{72} -2.11035e94 q^{73} +2.84401e93 q^{74} +8.96724e93 q^{75} -4.00100e94 q^{76} -2.78465e94 q^{77} -1.28124e94 q^{78} +8.91772e95 q^{79} +6.88848e95 q^{80} +1.85093e96 q^{81} +4.82328e95 q^{82} +7.50442e96 q^{83} +2.38631e96 q^{84} +1.85621e97 q^{85} -2.41924e96 q^{86} +2.47573e96 q^{87} -1.28000e97 q^{88} -3.83813e98 q^{89} +4.25686e97 q^{90} -4.03693e98 q^{91} -1.89083e99 q^{92} -6.58314e98 q^{93} -8.08797e98 q^{94} +1.88208e99 q^{95} +1.65257e99 q^{96} +1.03291e100 q^{97} +3.80676e99 q^{98} +1.42062e100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 52\!\cdots\!84 q^{9}+O(q^{10}) \) 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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