LMFDB - Embedded newform 1.102.a.a.1.3

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			1.3
Root			$1.78363e13$ 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)

$f(q)$	$=$	$q-1.76666e15 q^{2} -3.81746e23 q^{3} +5.85773e29 q^{4} -3.44135e35 q^{5} +6.74413e38 q^{6} -5.35995e42 q^{7} +3.44415e45 q^{8} -1.40040e48 q^{9} +O(q^{10})$	\(q-1.76666e15 q^{2} -3.81746e23 q^{3} +5.85773e29 q^{4} -3.44135e35 q^{5} +6.74413e38 q^{6} -5.35995e42 q^{7} +3.44415e45 q^{8} -1.40040e48 q^{9} +6.07967e50 q^{10} -3.44385e52 q^{11} -2.23616e53 q^{12} +3.09748e56 q^{13} +9.46918e57 q^{14} +1.31372e59 q^{15} -7.56973e60 q^{16} -1.06203e62 q^{17} +2.47403e63 q^{18} -6.11425e63 q^{19} -2.01585e65 q^{20} +2.04614e66 q^{21} +6.08410e67 q^{22} -3.47561e68 q^{23} -1.31479e69 q^{24} +7.89855e70 q^{25} -5.47219e71 q^{26} +1.12483e72 q^{27} -3.13971e72 q^{28} +5.28104e73 q^{29} -2.32089e74 q^{30} +2.84133e75 q^{31} +4.64116e75 q^{32} +1.31468e76 q^{33} +1.87624e77 q^{34} +1.84454e78 q^{35} -8.20318e77 q^{36} +1.90109e79 q^{37} +1.08018e79 q^{38} -1.18245e80 q^{39} -1.18525e81 q^{40} +6.25482e80 q^{41} -3.61482e81 q^{42} -1.65073e82 q^{43} -2.01731e82 q^{44} +4.81927e83 q^{45} +6.14021e83 q^{46} -1.59905e84 q^{47} +2.88971e84 q^{48} +6.08770e84 q^{49} -1.39540e86 q^{50} +4.05425e85 q^{51} +1.81442e86 q^{52} +9.26087e86 q^{53} -1.98718e87 q^{54} +1.18515e88 q^{55} -1.84604e88 q^{56} +2.33409e87 q^{57} -9.32978e88 q^{58} -2.36767e89 q^{59} +7.69540e88 q^{60} +8.85775e89 q^{61} -5.01965e90 q^{62} +7.50609e90 q^{63} +1.09922e91 q^{64} -1.06595e92 q^{65} -2.32258e91 q^{66} -3.21574e92 q^{67} -6.22108e91 q^{68} +1.32680e92 q^{69} -3.25867e93 q^{70} +1.94954e93 q^{71} -4.82319e93 q^{72} -1.32770e94 q^{73} -3.35857e94 q^{74} -3.01524e94 q^{75} -3.58156e93 q^{76} +1.84589e95 q^{77} +2.08898e95 q^{78} -3.38956e95 q^{79} +2.60501e96 q^{80} +1.73581e96 q^{81} -1.10501e96 q^{82} -8.23897e95 q^{83} +1.19857e96 q^{84} +3.65481e97 q^{85} +2.91628e97 q^{86} -2.01601e97 q^{87} -1.18611e98 q^{88} +2.68359e98 q^{89} -8.51399e98 q^{90} -1.66023e99 q^{91} -2.03592e98 q^{92} -1.08467e99 q^{93} +2.82498e99 q^{94} +2.10412e99 q^{95} -1.77174e99 q^{96} +1.33729e100 q^{97} -1.07549e100 q^{98} +4.82278e100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.76666e15	−1.10953	−0.554763	−	0.832009i	$-0.687191\pi$
$2$	−1.76666e15	−1.10953	−0.554763	+	0.832009i	$0.687191\pi$
$3$	−3.81746e23	−0.307009	−0.153504	−	0.988148i	$-0.549056\pi$
$3$	−3.81746e23	−0.307009	−0.153504	+	0.988148i	$0.549056\pi$
$4$	5.85773e29	0.231047
$5$	−3.44135e35	−1.73278	−0.866389	−	0.499369i	$-0.833565\pi$
$5$	−3.44135e35	−1.73278	−0.866389	+	0.499369i	$0.833565\pi$
$6$	6.74413e38	0.340634
$7$	−5.35995e42	−1.12644	−0.563222	−	0.826306i	$-0.690438\pi$
$7$	−5.35995e42	−1.12644	−0.563222	+	0.826306i	$0.690438\pi$
$8$	3.44415e45	0.853173
$9$	−1.40040e48	−0.905746
$10$	6.07967e50	1.92256
$11$	−3.44385e52	−0.884533	−0.442267	−	0.896884i	$-0.645825\pi$
$11$	−3.44385e52	−0.884533	−0.442267	+	0.896884i	$0.645825\pi$
$12$	−2.23616e53	−0.0709333
$13$	3.09748e56	1.72532	0.862660	−	0.505785i	$-0.168797\pi$
$13$	3.09748e56	1.72532	0.862660	+	0.505785i	$0.168797\pi$
$14$	9.46918e57	1.24982
$15$	1.31372e59	0.531978
$16$	−7.56973e60	−1.17766
$17$	−1.06203e62	−0.773510	−0.386755	−	0.922182i	$-0.626404\pi$
$17$	−1.06203e62	−0.773510	−0.386755	+	0.922182i	$0.626404\pi$
$18$	2.47403e63	1.00495
$19$	−6.11425e63	−0.161915	−0.0809574	−	0.996718i	$-0.525798\pi$
$19$	−6.11425e63	−0.161915	−0.0809574	+	0.996718i	$0.525798\pi$
$20$	−2.01585e65	−0.400352
$21$	2.04614e66	0.345828
$22$	6.08410e67	0.981412
$23$	−3.47561e68	−0.593985	−0.296992	−	0.954880i	$-0.595984\pi$
$23$	−3.47561e68	−0.593985	−0.296992	+	0.954880i	$0.595984\pi$
$24$	−1.31479e69	−0.261932
$25$	7.89855e70	2.00252
$26$	−5.47219e71	−1.91429
$27$	1.12483e72	0.585081
$28$	−3.13971e72	−0.260261
$29$	5.28104e73	0.744082	0.372041	−	0.928216i	$-0.378658\pi$
$29$	5.28104e73	0.744082	0.372041	+	0.928216i	$0.378658\pi$
$30$	−2.32089e74	−0.590243
$31$	2.84133e75	1.37961	0.689805	−	0.723996i	$-0.257696\pi$
$31$	2.84133e75	1.37961	0.689805	+	0.723996i	$0.257696\pi$
$32$	4.64116e75	0.453475
$33$	1.31468e76	0.271559
$34$	1.87624e77	0.858229
$35$	1.84454e78	1.95188
$36$	−8.20318e77	−0.209269
$37$	1.90109e79	1.21567	0.607834	−	0.794064i	$-0.292039\pi$
$37$	1.90109e79	1.21567	0.607834	+	0.794064i	$0.292039\pi$
$38$	1.08018e79	0.179649
$39$	−1.18245e80	−0.529688
$40$	−1.18525e81	−1.47836
$41$	6.25482e80	0.224197	0.112099	−	0.993697i	$-0.464243\pi$
$41$	6.25482e80	0.224197	0.112099	+	0.993697i	$0.464243\pi$
$42$	−3.61482e81	−0.383705
$43$	−1.65073e82	−0.533974	−0.266987	−	0.963700i	$-0.586028\pi$
$43$	−1.65073e82	−0.533974	−0.266987	+	0.963700i	$0.586028\pi$
$44$	−2.01731e82	−0.204368
$45$	4.81927e83	1.56946
$46$	6.14021e83	0.659041
$47$	−1.59905e84	−0.579323	−0.289662	−	0.957129i	$-0.593543\pi$
$47$	−1.59905e84	−0.579323	−0.289662	+	0.957129i	$0.593543\pi$
$48$	2.88971e84	0.361553
$49$	6.08770e84	0.268876
$50$	−1.39540e86	−2.22185
$51$	4.05425e85	0.237474
$52$	1.81442e86	0.398629
$53$	9.26087e86	0.777536	0.388768	−	0.921336i	$-0.372901\pi$
$53$	9.26087e86	0.777536	0.388768	+	0.921336i	$0.372901\pi$
$54$	−1.98718e87	−0.649162
$55$	1.18515e88	1.53270
$56$	−1.84604e88	−0.961052
$57$	2.33409e87	0.0497092
$58$	−9.32978e88	−0.825578
$59$	−2.36767e89	−0.883681	−0.441840	−	0.897094i	$-0.645674\pi$
$59$	−2.36767e89	−0.883681	−0.441840	+	0.897094i	$0.645674\pi$
$60$	7.69540e88	0.122912
$61$	8.85775e89	0.613998	0.306999	−	0.951710i	$-0.400675\pi$
$61$	8.85775e89	0.613998	0.306999	+	0.951710i	$0.400675\pi$
$62$	−5.01965e90	−1.53071
$63$	7.50609e90	1.02027
$64$	1.09922e91	0.674522
$65$	−1.06595e92	−2.98960
$66$	−2.32258e91	−0.301302
$67$	−3.21574e92	−1.95210	−0.976052	−	0.217537i	$-0.930198\pi$
$67$	−3.21574e92	−1.95210	−0.976052	+	0.217537i	$0.930198\pi$
$68$	−6.22108e91	−0.178717
$69$	1.32680e92	0.182358
$70$	−3.25867e93	−2.16566
$71$	1.94954e93	0.632974	0.316487	−	0.948597i	$-0.397497\pi$
$71$	1.94954e93	0.632974	0.316487	+	0.948597i	$0.397497\pi$
$72$	−4.82319e93	−0.772758
$73$	−1.32770e94	−1.05998	−0.529988	−	0.848005i	$-0.677804\pi$
$73$	−1.32770e94	−1.05998	−0.529988	+	0.848005i	$0.677804\pi$
$74$	−3.35857e94	−1.34881
$75$	−3.01524e94	−0.614791
$76$	−3.58156e93	−0.0374098
$77$	1.84589e95	0.996377
$78$	2.08898e95	0.587702
$79$	−3.38956e95	−0.501158	−0.250579	−	0.968096i	$-0.580621\pi$
$79$	−3.38956e95	−0.501158	−0.250579	+	0.968096i	$0.580621\pi$
$80$	2.60501e96	2.04063
$81$	1.73581e96	0.726121
$82$	−1.10501e96	−0.248752
$83$	−8.23897e95	−0.100561	−0.0502805	−	0.998735i	$-0.516012\pi$
$83$	−8.23897e95	−0.100561	−0.0502805	+	0.998735i	$0.516012\pi$
$84$	1.19857e96	0.0799024
$85$	3.65481e97	1.34032
$86$	2.91628e97	0.592458
$87$	−2.01601e97	−0.228440
$88$	−1.18611e98	−0.754660
$89$	2.68359e98	0.964985	0.482492	−	0.875900i	$-0.339732\pi$
$89$	2.68359e98	0.964985	0.482492	+	0.875900i	$0.339732\pi$
$90$	−8.51399e98	−1.74135
$91$	−1.66023e99	−1.94348
$92$	−2.03592e98	−0.137238
$93$	−1.08467e99	−0.423552
$94$	2.82498e99	0.642774
$95$	2.10412e99	0.280562
$96$	−1.77174e99	−0.139221
$97$	1.33729e100	0.622664	0.311332	−	0.950301i	$-0.399225\pi$
$97$	1.33729e100	0.622664	0.311332	+	0.950301i	$0.399225\pi$
$98$	−1.07549e100	−0.298324
$99$	4.82278e100	0.801162
$100$	4.62676e100	0.462676
$101$	3.34535e100	0.202401	0.101200	−	0.994866i	$-0.467732\pi$
$101$	3.34535e100	0.202401	0.101200	+	0.994866i	$0.467732\pi$
$102$	−7.16247e100	−0.263484
$103$	3.42996e101	0.770919	0.385459	−	0.922725i	$-0.374043\pi$
$103$	3.42996e101	0.770919	0.385459	+	0.922725i	$0.374043\pi$
$104$	1.06682e102	1.47200
$105$	−7.04146e101	−0.599243
$106$	−1.63608e102	−0.862696
$107$	−5.39428e102	−1.77032	−0.885162	−	0.465284i	$-0.845952\pi$
$107$	−5.39428e102	−1.77032	−0.885162	+	0.465284i	$0.845952\pi$
$108$	6.58893e101	0.135181
$109$	1.02335e102	0.131822	0.0659108	−	0.997826i	$-0.479005\pi$
$109$	1.02335e102	0.131822	0.0659108	+	0.997826i	$0.479005\pi$
$110$	−2.09375e103	−1.70057
$111$	−7.25732e102	−0.373221
$112$	4.05734e103	1.32657
$113$	3.86042e103	0.805699	0.402850	−	0.915266i	$-0.368020\pi$
$113$	3.86042e103	0.805699	0.402850	+	0.915266i	$0.368020\pi$
$114$	−4.12353e102	−0.0551537
$115$	1.19608e104	1.02924
$116$	3.09349e103	0.171918
$117$	−4.33772e104	−1.56270
$118$	4.18287e104	0.980466
$119$	5.69242e104	0.871316
$120$	4.52464e104	0.453870
$121$	−3.29855e104	−0.217601
$122$	−1.56486e105	−0.681246
$123$	−2.38775e104	−0.0688305
$124$	1.66437e105	0.318754
$125$	−1.36079e106	−1.73715
$126$	−1.32607e106	−1.13202
$127$	1.39229e106	0.797339	0.398670	−	0.917095i	$-0.369472\pi$
$127$	1.39229e106	0.797339	0.398670	+	0.917095i	$0.369472\pi$
$128$	−3.11862e106	−1.20187
$129$	6.30160e105	0.163935
$130$	1.88317e107	3.31703
$131$	−9.77949e106	−1.16981	−0.584905	−	0.811102i	$-0.698868\pi$
$131$	−9.77949e106	−1.16981	−0.584905	+	0.811102i	$0.698868\pi$
$132$	7.70101e105	0.0627429
$133$	3.27721e106	0.182388
$134$	5.68110e107	2.16591
$135$	−3.87092e107	−1.01381
$136$	−3.65778e107	−0.659938
$137$	−4.26131e107	−0.531073	−0.265537	−	0.964101i	$-0.585549\pi$
$137$	−4.26131e107	−0.531073	−0.265537	+	0.964101i	$0.585549\pi$
$138$	−2.34400e107	−0.202331
$139$	−1.67295e107	−0.100285	−0.0501425	−	0.998742i	$-0.515968\pi$
$139$	−1.67295e107	−0.100285	−0.0501425	+	0.998742i	$0.515968\pi$
$140$	1.08048e108	0.450975
$141$	6.10432e107	0.177857
$142$	−3.44417e108	−0.702301
$143$	−1.06673e109	−1.52610
$144$	1.06007e109	1.06666
$145$	−1.81739e109	−1.28933
$146$	2.34559e109	1.17607
$147$	−2.32395e108	−0.0825471
$148$	1.11360e109	0.280876
$149$	7.26079e109	1.30340	0.651700	−	0.758477i	$-0.274056\pi$
$149$	7.26079e109	1.30340	0.651700	+	0.758477i	$0.274056\pi$
$150$	5.32689e109	0.682127
$151$	2.69592e109	0.246815	0.123408	−	0.992356i	$-0.460618\pi$
$151$	2.69592e109	0.246815	0.123408	+	0.992356i	$0.460618\pi$
$152$	−2.10584e109	−0.138141
$153$	1.48727e110	0.700603
$154$	−3.26105e110	−1.10551
$155$	−9.77800e110	−2.39056
$156$	−6.92647e109	−0.122383
$157$	4.68140e110	0.599023	0.299511	−	0.954093i	$-0.403176\pi$
$157$	4.68140e110	0.599023	0.299511	+	0.954093i	$0.403176\pi$
$158$	5.98818e110	0.556048
$159$	−3.53530e110	−0.238710
$160$	−1.59719e111	−0.785771
$161$	1.86291e111	0.669090
$162$	−3.06658e111	−0.805649
$163$	9.76956e111	1.88105	0.940526	−	0.339721i	$-0.110333\pi$
$163$	9.76956e111	1.88105	0.940526	+	0.339721i	$0.110333\pi$
$164$	3.66390e110	0.0518000
$165$	−4.52425e111	−0.470552
$166$	1.45554e111	0.111575
$167$	−2.19092e111	−0.124007	−0.0620034	−	0.998076i	$-0.519749\pi$
$167$	−2.19092e111	−0.124007	−0.0620034	+	0.998076i	$0.519749\pi$
$168$	7.04719e111	0.295051
$169$	6.37126e112	1.97673
$170$	−6.45679e112	−1.48712
$171$	8.56241e111	0.146654
$172$	−9.66955e111	−0.123373
$173$	−1.20621e113	−1.14840	−0.574202	−	0.818714i	$-0.694688\pi$
$173$	−1.20621e113	−1.14840	−0.574202	+	0.818714i	$0.694688\pi$
$174$	3.56160e112	0.253460
$175$	−4.23358e113	−2.25573
$176$	2.60691e113	1.04168
$177$	9.03850e112	0.271298
$178$	−4.74098e113	−1.07068
$179$	7.66204e113	1.30397	0.651983	−	0.758234i	$-0.273937\pi$
$179$	7.66204e113	1.30397	0.651983	+	0.758234i	$0.273937\pi$
$180$	2.82300e113	0.362617
$181$	5.31499e113	0.516101	0.258051	−	0.966131i	$-0.416920\pi$
$181$	5.31499e113	0.516101	0.258051	+	0.966131i	$0.416920\pi$
$182$	2.93306e114	2.15633
$183$	−3.38141e113	−0.188503
$184$	−1.19705e114	−0.506772
$185$	−6.54230e114	−2.10648
$186$	1.91623e114	0.469942
$187$	3.65747e114	0.684195
$188$	−9.36682e113	−0.133851
$189$	−6.02901e114	−0.659060
$190$	−3.71727e114	−0.311291
$191$	8.28574e113	0.0532288	0.0266144	−	0.999646i	$-0.491527\pi$
$191$	8.28574e113	0.0532288	0.0266144	+	0.999646i	$0.491527\pi$
$192$	−4.19623e114	−0.207084
$193$	3.05207e114	0.115865	0.0579323	−	0.998321i	$-0.481549\pi$
$193$	3.05207e114	0.115865	0.0579323	+	0.998321i	$0.481549\pi$
$194$	−2.36254e115	−0.690861
$195$	4.06922e115	0.917832
$196$	3.56601e114	0.0621228
$197$	−4.98888e115	−0.672139	−0.336069	−	0.941837i	$-0.609098\pi$
$197$	−4.98888e115	−0.672139	−0.336069	+	0.941837i	$0.609098\pi$
$198$	−8.52020e115	−0.888910
$199$	1.87907e116	1.52006	0.760032	−	0.649885i	$-0.225183\pi$
$199$	1.87907e116	1.52006	0.760032	+	0.649885i	$0.225183\pi$
$200$	2.72038e116	1.70850
$201$	1.22759e116	0.599313
$202$	−5.91008e115	−0.224569
$203$	−2.83061e116	−0.838166
$204$	2.37487e115	0.0548676
$205$	−2.15250e116	−0.388484
$206$	−6.05955e116	−0.855354
$207$	4.86725e116	0.537999
$208$	−2.34471e117	−2.03185
$209$	2.10566e116	0.143219
$210$	1.24398e117	0.664876
$211$	−1.37595e117	−0.578548	−0.289274	−	0.957246i	$-0.593414\pi$
$211$	−1.37595e117	−0.578548	−0.289274	+	0.957246i	$0.593414\pi$
$212$	5.42477e116	0.179647
$213$	−7.44229e116	−0.194329
$214$	9.52984e117	1.96422
$215$	5.68075e117	0.925258
$216$	3.87407e117	0.499175
$217$	−1.52294e118	−1.55405
$218$	−1.80791e117	−0.146259
$219$	5.06845e117	0.325422
$220$	6.94228e117	0.354125
$221$	−3.28962e118	−1.33455
$222$	1.28212e118	0.414098
$223$	6.07548e118	1.56381	0.781907	−	0.623396i	$-0.214247\pi$
$223$	6.07548e118	1.56381	0.781907	+	0.623396i	$0.214247\pi$
$224$	−2.48764e118	−0.510814
$225$	−1.10612e119	−1.81377
$226$	−6.82003e118	−0.893944
$227$	1.61334e119	1.69207	0.846037	−	0.533124i	$-0.178982\pi$
$227$	1.61334e119	1.69207	0.846037	+	0.533124i	$0.178982\pi$
$228$	1.36725e117	0.0114851
$229$	−7.19765e118	−0.484729	−0.242364	−	0.970185i	$-0.577923\pi$
$229$	−7.19765e118	−0.484729	−0.242364	+	0.970185i	$0.577923\pi$
$230$	−2.11306e119	−1.14197
$231$	−7.04659e118	−0.305896
$232$	1.81887e119	0.634831
$233$	1.46080e119	0.410314	0.205157	−	0.978729i	$-0.434230\pi$
$233$	1.46080e119	0.410314	0.205157	+	0.978729i	$0.434230\pi$
$234$	7.66326e119	1.73386
$235$	5.50289e119	1.00384
$236$	−1.38692e119	−0.204171
$237$	1.29395e119	0.153860
$238$	−1.00566e120	−0.966747
$239$	7.43010e119	0.577964	0.288982	−	0.957334i	$-0.406683\pi$
$239$	7.43010e119	0.577964	0.288982	+	0.957334i	$0.406683\pi$
$240$	−9.94450e119	−0.626491
$241$	−2.53445e120	−1.29427	−0.647133	−	0.762377i	$-0.724032\pi$
$241$	−2.53445e120	−1.29427	−0.647133	+	0.762377i	$0.724032\pi$
$242$	5.82740e119	0.241434
$243$	−2.40177e120	−0.808006
$244$	5.18863e119	0.141862
$245$	−2.09499e120	−0.465902
$246$	4.21833e119	0.0763691
$247$	−1.89388e120	−0.279355
$248$	9.78596e120	1.17705
$249$	3.14519e119	0.0308731
$250$	2.40405e121	1.92741
$251$	−2.12075e121	−1.38985	−0.694923	−	0.719084i	$-0.744562\pi$
$251$	−2.12075e121	−1.38985	−0.694923	+	0.719084i	$0.744562\pi$
$252$	4.39686e120	0.235730
$253$	1.19695e121	0.525399
$254$	−2.45971e121	−0.884668
$255$	−1.39521e121	−0.411490
$256$	2.72267e121	0.658988
$257$	7.82104e121	1.55468	0.777341	−	0.629079i	$-0.216568\pi$
$257$	7.82104e121	1.55468	0.777341	+	0.629079i	$0.216568\pi$
$258$	−1.11328e121	−0.181890
$259$	−1.01897e122	−1.36938
$260$	−6.24405e121	−0.690736
$261$	−7.39559e121	−0.673949
$262$	1.72770e122	1.29793
$263$	−4.46862e121	−0.276954	−0.138477	−	0.990366i	$-0.544221\pi$
$263$	−4.46862e121	−0.276954	−0.138477	+	0.990366i	$0.544221\pi$
$264$	4.52794e121	0.231687
$265$	−3.18699e122	−1.34730
$266$	−5.78970e121	−0.202364
$267$	−1.02445e122	−0.296259
$268$	−1.88369e122	−0.451027
$269$	6.09483e122	1.20913	0.604563	−	0.796557i	$-0.293348\pi$
$269$	6.09483e122	1.20913	0.604563	+	0.796557i	$0.293348\pi$
$270$	6.83858e122	1.12485
$271$	2.88488e122	0.393712	0.196856	−	0.980432i	$-0.436927\pi$
$271$	2.88488e122	0.393712	0.196856	+	0.980432i	$0.436927\pi$
$272$	8.03928e122	0.910935
$273$	6.33787e122	0.596664
$274$	7.52827e122	0.589239
$275$	−2.72015e123	−1.77130
$276$	7.77202e121	0.0421333
$277$	−2.29440e123	−1.03619	−0.518097	−	0.855322i	$-0.673359\pi$
$277$	−2.29440e123	−1.03619	−0.518097	+	0.855322i	$0.673359\pi$
$278$	2.95553e122	0.111269
$279$	−3.97901e123	−1.24958
$280$	6.35288e123	1.66529
$281$	−8.87210e123	−1.94248	−0.971242	−	0.238095i	$-0.923477\pi$
$281$	−8.87210e123	−1.94248	−0.971242	+	0.238095i	$0.923477\pi$
$282$	−1.07842e123	−0.197337
$283$	3.63420e123	0.556152	0.278076	−	0.960559i	$-0.410303\pi$
$283$	3.63420e123	0.556152	0.278076	+	0.960559i	$0.410303\pi$
$284$	1.14199e123	0.146247
$285$	−8.03241e122	−0.0861351
$286$	1.88454e124	1.69325
$287$	−3.35255e123	−0.252545
$288$	−6.49950e123	−0.410733
$289$	−7.57223e123	−0.401682
$290$	3.21070e124	1.43054
$291$	−5.10505e123	−0.191163
$292$	−7.77732e123	−0.244904
$293$	−3.97733e124	−1.05384	−0.526922	−	0.849913i	$-0.676654\pi$
$293$	−3.97733e124	−1.05384	−0.526922	+	0.849913i	$0.676654\pi$
$294$	4.10563e123	0.0915881
$295$	8.14799e124	1.53122
$296$	6.54762e124	1.03718
$297$	−3.87374e124	−0.517523
$298$	−1.28273e125	−1.44615
$299$	−1.07656e125	−1.02481
$300$	−1.76624e124	−0.142045
$301$	8.84785e124	0.601492
$302$	−4.76277e124	−0.273848
$303$	−1.27707e124	−0.0621388
$304$	4.62832e124	0.190681
$305$	−3.04826e125	−1.06392
$306$	−2.62749e125	−0.777337
$307$	6.37866e125	1.60045	0.800223	−	0.599702i	$-0.204714\pi$
$307$	6.37866e125	1.60045	0.800223	+	0.599702i	$0.204714\pi$
$308$	1.08127e125	0.230209
$309$	−1.30937e125	−0.236679
$310$	1.72744e126	2.65238
$311$	4.16169e124	0.0543088	0.0271544	−	0.999631i	$-0.491355\pi$
$311$	4.16169e124	0.0543088	0.0271544	+	0.999631i	$0.491355\pi$
$312$	−4.07253e125	−0.451916
$313$	9.78296e125	0.923594	0.461797	−	0.886986i	$-0.347205\pi$
$313$	9.78296e125	0.923594	0.461797	+	0.886986i	$0.347205\pi$
$314$	−8.27042e125	−0.664631
$315$	−2.58310e126	−1.76790
$316$	−1.98551e125	−0.115791
$317$	1.90344e125	0.0946336	0.0473168	−	0.998880i	$-0.484933\pi$
$317$	1.90344e125	0.0946336	0.0473168	+	0.998880i	$0.484933\pi$
$318$	6.24566e125	0.264855
$319$	−1.81871e126	−0.658165
$320$	−3.78280e126	−1.16880
$321$	2.05924e126	0.543505
$322$	−3.29112e126	−0.742373
$323$	6.49351e125	0.125243
$324$	1.01679e126	0.167768
$325$	2.44656e127	3.45499
$326$	−1.72594e127	−2.08708
$327$	−3.90660e125	−0.0404704
$328$	2.15425e126	0.191279
$329$	8.57084e126	0.652575
$330$	7.99280e126	0.522090
$331$	−1.95148e127	−1.09409	−0.547043	−	0.837105i	$-0.684247\pi$
$331$	−1.95148e127	−1.09409	−0.547043	+	0.837105i	$0.684247\pi$
$332$	−4.82616e125	−0.0232343
$333$	−2.66229e127	−1.10109
$334$	3.87061e126	0.137589
$335$	1.10665e128	3.38256
$336$	−1.54887e127	−0.407269
$337$	−1.63331e126	−0.0369623	−0.0184811	−	0.999829i	$-0.505883\pi$
$337$	−1.63331e126	−0.0369623	−0.0184811	+	0.999829i	$0.505883\pi$
$338$	−1.12558e128	−2.19323
$339$	−1.47370e127	−0.247357
$340$	2.14089e127	0.309677
$341$	−9.78512e127	−1.22031
$342$	−1.51268e127	−0.162716
$343$	8.87266e127	0.823571
$344$	−5.68537e127	−0.455572
$345$	−4.56597e127	−0.315987
$346$	2.13096e128	1.27418
$347$	−2.36944e128	−1.22464	−0.612319	−	0.790611i	$-0.709763\pi$
$347$	−2.36944e128	−1.22464	−0.612319	+	0.790611i	$0.709763\pi$
$348$	−1.18093e127	−0.0527802
$349$	−7.03918e126	−0.0272169	−0.0136084	−	0.999907i	$-0.504332\pi$
$349$	−7.03918e126	−0.0272169	−0.0136084	+	0.999907i	$0.504332\pi$
$350$	7.47928e128	2.50279
$351$	3.48413e128	1.00945
$352$	−1.59835e128	−0.401113
$353$	2.29284e128	0.498599	0.249299	−	0.968426i	$-0.419800\pi$
$353$	2.29284e128	0.498599	0.249299	+	0.968426i	$0.419800\pi$
$354$	−1.59679e128	−0.301012
$355$	−6.70905e128	−1.09680
$356$	1.57197e128	0.222956
$357$	−2.17306e128	−0.267502
$358$	−1.35362e129	−1.44678
$359$	−5.85822e128	−0.543871	−0.271935	−	0.962316i	$-0.587664\pi$
$359$	−5.85822e128	−0.543871	−0.271935	+	0.962316i	$0.587664\pi$
$360$	1.65983e129	1.33902
$361$	−1.38860e129	−0.973784
$362$	−9.38977e128	−0.572627
$363$	1.25921e128	0.0668055
$364$	−9.72520e128	−0.449033
$365$	4.56908e129	1.83671
$366$	5.97378e128	0.209148
$367$	−3.80604e129	−1.16101	−0.580506	−	0.814256i	$-0.697145\pi$
$367$	−3.80604e129	−1.16101	−0.580506	+	0.814256i	$0.697145\pi$
$368$	2.63094e129	0.699514
$369$	−8.75927e128	−0.203066
$370$	1.15580e130	2.33720
$371$	−4.96378e129	−0.875851
$372$	−6.35367e128	−0.0978602
$373$	−4.09983e129	−0.551404	−0.275702	−	0.961243i	$-0.588910\pi$
$373$	−4.09983e129	−0.551404	−0.275702	+	0.961243i	$0.588910\pi$
$374$	−6.46150e129	−0.759132
$375$	5.19477e129	0.533319
$376$	−5.50737e129	−0.494263
$377$	1.63579e130	1.28378
$378$	1.06512e130	0.731244
$379$	−1.69783e130	−1.02004	−0.510018	−	0.860164i	$-0.670361\pi$
$379$	−1.69783e130	−1.02004	−0.510018	+	0.860164i	$0.670361\pi$
$380$	1.23254e129	0.0648230
$381$	−5.31502e129	−0.244790
$382$	−1.46381e129	−0.0590587
$383$	−2.79558e130	−0.988403	−0.494201	−	0.869347i	$-0.664539\pi$
$383$	−2.79558e130	−0.988403	−0.494201	+	0.869347i	$0.664539\pi$
$384$	1.19052e130	0.368986
$385$	−6.35234e130	−1.72650
$386$	−5.39196e129	−0.128555
$387$	2.31169e130	0.483645
$388$	7.83349e129	0.143864
$389$	1.02053e131	1.64577	0.822886	−	0.568206i	$-0.192362\pi$
$389$	1.02053e131	1.64577	0.822886	+	0.568206i	$0.192362\pi$
$390$	−7.18891e130	−1.01836
$391$	3.69120e130	0.459453
$392$	2.09669e130	0.229397
$393$	3.73328e130	0.359142
$394$	8.81364e130	0.745755
$395$	1.16646e131	0.868396
$396$	2.82505e130	0.185106
$397$	2.41789e131	1.39481	0.697406	−	0.716676i	$-0.254337\pi$
$397$	2.41789e131	1.39481	0.697406	+	0.716676i	$0.254337\pi$
$398$	−3.31967e131	−1.68655
$399$	−1.25106e130	−0.0559947
$400$	−5.97899e131	−2.35830
$401$	−3.05800e131	−1.06328	−0.531638	−	0.846972i	$-0.678423\pi$
$401$	−3.05800e131	−1.06328	−0.531638	+	0.846972i	$0.678423\pi$
$402$	−2.16874e131	−0.664953
$403$	8.80097e131	2.38027
$404$	1.95961e130	0.0467640
$405$	−5.97352e131	−1.25821
$406$	5.00072e131	0.929967
$407$	−6.54706e131	−1.07530
$408$	1.39634e131	0.202607
$409$	2.88971e131	0.370533	0.185267	−	0.982688i	$-0.440685\pi$
$409$	2.88971e131	0.370533	0.185267	+	0.982688i	$0.440685\pi$
$410$	3.80273e131	0.431033
$411$	1.62674e131	0.163044
$412$	2.00917e131	0.178118
$413$	1.26906e132	0.995417
$414$	−8.59876e131	−0.596924
$415$	2.83531e131	0.174250
$416$	1.43759e132	0.782389
$417$	6.38642e130	0.0307884
$418$	−3.71997e131	−0.158905
$419$	−4.10257e132	−1.55327	−0.776637	−	0.629948i	$-0.783076\pi$
$419$	−4.10257e132	−1.55327	−0.776637	+	0.629948i	$0.783076\pi$
$420$	−4.12470e131	−0.138453
$421$	9.23486e131	0.274906	0.137453	−	0.990508i	$-0.456108\pi$
$421$	9.23486e131	0.274906	0.137453	+	0.990508i	$0.456108\pi$
$422$	2.43083e132	0.641913
$423$	2.23932e132	0.524720
$424$	3.18958e132	0.663373
$425$	−8.38849e132	−1.54897
$426$	1.31480e132	0.215613
$427$	−4.74771e132	−0.691634
$428$	−3.15982e132	−0.409027
$429$	4.07219e132	0.468527
$430$	−1.00359e133	−1.02660
$431$	−4.45061e132	−0.404872	−0.202436	−	0.979295i	$-0.564886\pi$
$431$	−4.45061e132	−0.404872	−0.202436	+	0.979295i	$0.564886\pi$
$432$	−8.51464e132	−0.689028
$433$	1.12944e133	0.813252	0.406626	−	0.913595i	$-0.366705\pi$
$433$	1.12944e133	0.813252	0.406626	+	0.913595i	$0.366705\pi$
$434$	2.69051e133	1.72426
$435$	6.93780e132	0.395835
$436$	5.99451e131	0.0304569
$437$	2.12507e132	0.0961749
$438$	−8.95420e132	−0.361064
$439$	−8.84001e130	−0.00317683	−0.00158842	−	0.999999i	$-0.500506\pi$
$439$	−8.84001e130	−0.00317683	−0.00158842	+	0.999999i	$0.500506\pi$
$440$	4.08183e133	1.30766
$441$	−8.52523e132	−0.243533
$442$	5.81162e133	1.48072
$443$	−1.19259e133	−0.271082	−0.135541	−	0.990772i	$-0.543277\pi$
$443$	−1.19259e133	−0.271082	−0.135541	+	0.990772i	$0.543277\pi$
$444$	−4.25114e132	−0.0862313
$445$	−9.23515e133	−1.67210
$446$	−1.07333e134	−1.73509
$447$	−2.77178e133	−0.400155
$448$	−5.89177e133	−0.759811
$449$	−3.96128e133	−0.456452	−0.228226	−	0.973608i	$-0.573293\pi$
$449$	−3.96128e133	−0.456452	−0.228226	+	0.973608i	$0.573293\pi$
$450$	1.95413e134	2.01243
$451$	−2.15407e133	−0.198310
$452$	2.26133e133	0.186154
$453$	−1.02916e133	−0.0757744
$454$	−2.85021e134	−1.87740
$455$	5.71344e134	3.36761
$456$	8.03894e132	0.0424106
$457$	−1.35379e134	−0.639414	−0.319707	−	0.947516i	$-0.603585\pi$
$457$	−1.35379e134	−0.639414	−0.319707	+	0.947516i	$0.603585\pi$
$458$	1.27158e134	0.537819
$459$	−1.19460e134	−0.452566
$460$	7.00629e133	0.237803
$461$	−6.86709e133	−0.208870	−0.104435	−	0.994532i	$-0.533303\pi$
$461$	−6.86709e133	−0.208870	−0.104435	+	0.994532i	$0.533303\pi$
$462$	1.24489e134	0.339400
$463$	2.52099e134	0.616213	0.308107	−	0.951352i	$-0.400305\pi$
$463$	2.52099e134	0.616213	0.308107	+	0.951352i	$0.400305\pi$
$464$	−3.99761e134	−0.876278
$465$	3.73271e134	0.733922
$466$	−2.58073e134	−0.455253
$467$	−6.60220e134	−1.04517	−0.522584	−	0.852588i	$-0.675032\pi$
$467$	−6.60220e134	−1.04517	−0.522584	+	0.852588i	$0.675032\pi$
$468$	−2.54092e134	−0.361057
$469$	1.72362e135	2.19894
$470$	−9.72172e134	−1.11378
$471$	−1.78710e134	−0.183905
$472$	−8.15462e134	−0.753933
$473$	5.68489e134	0.472318
$474$	−2.28596e134	−0.170712
$475$	−4.82937e134	−0.324238
$476$	3.33446e134	0.201314
$477$	−1.29690e135	−0.704250
$478$	−1.31264e135	−0.641266
$479$	−1.49265e135	−0.656166	−0.328083	−	0.944649i	$-0.606403\pi$
$479$	−1.49265e135	−0.656166	−0.328083	+	0.944649i	$0.606403\pi$
$480$	6.09718e134	0.241239
$481$	5.88858e135	2.09741
$482$	4.47751e135	1.43602
$483$	−7.11157e134	−0.205417
$484$	−1.93220e134	−0.0502760
$485$	−4.60208e135	−1.07894
$486$	4.24310e135	0.896503
$487$	1.65892e135	0.315946	0.157973	−	0.987443i	$-0.449504\pi$
$487$	1.65892e135	0.315946	0.157973	+	0.987443i	$0.449504\pi$
$488$	3.05074e135	0.523847
$489$	−3.72949e135	−0.577499
$490$	3.70112e135	0.516930
$491$	−5.07962e135	−0.640053	−0.320027	−	0.947409i	$-0.603692\pi$
$491$	−5.07962e135	−0.640053	−0.320027	+	0.947409i	$0.603692\pi$
$492$	−1.39868e134	−0.0159030
$493$	−5.60862e135	−0.575555
$494$	3.34583e135	0.309951
$495$	−1.65969e136	−1.38824
$496$	−2.15081e136	−1.62472
$497$	−1.04494e136	−0.713010
$498$	−5.55647e134	−0.0342545
$499$	3.25310e136	1.81226	0.906130	−	0.422999i	$-0.139023\pi$
$499$	3.25310e136	1.81226	0.906130	+	0.422999i	$0.139023\pi$
$500$	−7.97115e135	−0.401362
$501$	8.36375e134	0.0380712
$502$	3.74664e136	1.54207
$503$	2.14382e136	0.798006	0.399003	−	0.916950i	$-0.369356\pi$
$503$	2.14382e136	0.798006	0.399003	+	0.916950i	$0.369356\pi$
$504$	2.58521e136	0.870468
$505$	−1.15125e136	−0.350716
$506$	−2.11460e136	−0.582944
$507$	−2.43220e136	−0.606872
$508$	8.15568e135	0.184222
$509$	−2.39037e136	−0.488897	−0.244448	−	0.969662i	$-0.578607\pi$
$509$	−2.39037e136	−0.488897	−0.244448	+	0.969662i	$0.578607\pi$
$510$	2.46485e136	0.456559
$511$	7.11642e136	1.19400
$512$	3.09661e136	0.470711
$513$	−6.87748e135	−0.0947332
$514$	−1.38171e137	−1.72496
$515$	−1.18037e137	−1.33583
$516$	3.69131e135	0.0378765
$517$	5.50691e136	0.512431
$518$	1.80017e137	1.51936
$519$	4.60465e136	0.352570
$520$	−3.67129e137	−2.55064
$521$	1.68827e137	1.06448	0.532239	−	0.846594i	$-0.321351\pi$
$521$	1.68827e137	1.06448	0.532239	+	0.846594i	$0.321351\pi$
$522$	1.30655e137	0.747763
$523$	−2.56145e137	−1.33091	−0.665457	−	0.746436i	$-0.731763\pi$
$523$	−2.56145e137	−1.33091	−0.665457	+	0.746436i	$0.731763\pi$
$524$	−5.72855e136	−0.270281
$525$	1.61615e137	0.692528
$526$	7.89452e136	0.307288
$527$	−3.01758e137	−1.06714
$528$	−9.95175e136	−0.319806
$529$	−2.21584e137	−0.647182
$530$	5.63031e137	1.49486
$531$	3.31570e137	0.800390
$532$	1.91970e136	0.0421401
$533$	1.93742e137	0.386812
$534$	1.80985e137	0.328707
$535$	1.85636e138	3.06758
$536$	−1.10755e138	−1.66548
$537$	−2.92495e137	−0.400329
$538$	−1.07675e138	−1.34156
$539$	−2.09652e137	−0.237829
$540$	−2.26748e137	−0.234238
$541$	5.13635e137	0.483273	0.241636	−	0.970367i	$-0.422316\pi$
$541$	5.13635e137	0.483273	0.241636	+	0.970367i	$0.422316\pi$
$542$	−5.09659e137	−0.436833
$543$	−2.02898e137	−0.158448
$544$	−4.92905e137	−0.350767
$545$	−3.52171e137	−0.228418
$546$	−1.11968e138	−0.662014
$547$	−1.51606e138	−0.817251	−0.408626	−	0.912702i	$-0.633992\pi$
$547$	−1.51606e138	−0.817251	−0.408626	+	0.912702i	$0.633992\pi$
$548$	−2.49616e137	−0.122703
$549$	−1.24044e138	−0.556126
$550$	4.80556e138	1.96530
$551$	−3.22896e137	−0.120478
$552$	4.56969e137	0.155583
$553$	1.81679e138	0.564527
$554$	4.05342e138	1.14968
$555$	2.49749e138	0.646709
$556$	−9.79969e136	−0.0231705
$557$	−2.27470e138	−0.491175	−0.245588	−	0.969374i	$-0.578981\pi$
$557$	−2.27470e138	−0.491175	−0.245588	+	0.969374i	$0.578981\pi$
$558$	7.02954e138	1.38644
$559$	−5.11312e138	−0.921276
$560$	−1.39627e139	−2.29866
$561$	−1.39622e138	−0.210054
$562$	1.56740e139	2.15523
$563$	2.50855e138	0.315318	0.157659	−	0.987494i	$-0.449605\pi$
$563$	2.50855e138	0.315318	0.157659	+	0.987494i	$0.449605\pi$
$564$	3.57574e137	0.0410933
$565$	−1.32850e139	−1.39610
$566$	−6.42038e138	−0.617065
$567$	−9.30385e138	−0.817934
$568$	6.71451e138	0.540037
$569$	−5.91124e138	−0.435020	−0.217510	−	0.976058i	$-0.569793\pi$
$569$	−5.91124e138	−0.435020	−0.217510	+	0.976058i	$0.569793\pi$
$570$	1.41905e138	0.0955691
$571$	2.25293e139	1.38875	0.694375	−	0.719613i	$-0.255681\pi$
$571$	2.25293e139	1.38875	0.694375	+	0.719613i	$0.255681\pi$
$572$	−6.24860e138	−0.352601
$573$	−3.16305e137	−0.0163417
$574$	5.92280e138	0.280206
$575$	−2.74523e139	−1.18947
$576$	−1.53935e139	−0.610946
$577$	2.94565e139	1.07103	0.535517	−	0.844525i	$-0.320117\pi$
$577$	2.94565e139	1.07103	0.535517	+	0.844525i	$0.320117\pi$
$578$	1.33775e139	0.445677
$579$	−1.16512e138	−0.0355715
$580$	−1.06458e139	−0.297895
$581$	4.41605e138	0.113276
$582$	9.01887e138	0.212100
$583$	−3.18931e139	−0.687756
$584$	−4.57280e139	−0.904344
$585$	1.49276e140	2.70781
$586$	7.02657e139	1.16927
$587$	4.14398e139	0.632694	0.316347	−	0.948644i	$-0.397544\pi$
$587$	4.14398e139	0.632694	0.316347	+	0.948644i	$0.397544\pi$
$588$	−1.36131e138	−0.0190722
$589$	−1.73726e139	−0.223379
$590$	−1.43947e140	−1.69893
$591$	1.90448e139	0.206352
$592$	−1.43907e140	−1.43165
$593$	−4.72697e139	−0.431838	−0.215919	−	0.976411i	$-0.569275\pi$
$593$	−4.72697e139	−0.431838	−0.215919	+	0.976411i	$0.569275\pi$
$594$	6.84357e139	0.574205
$595$	−1.95896e140	−1.50980
$596$	4.25317e139	0.301146
$597$	−7.17326e139	−0.466673
$598$	1.90192e140	1.13706
$599$	−1.54853e139	−0.0850875	−0.0425438	−	0.999095i	$-0.513546\pi$
$599$	−1.54853e139	−0.0850875	−0.0425438	+	0.999095i	$0.513546\pi$
$600$	−1.03849e140	−0.524524
$601$	−7.43424e139	−0.345204	−0.172602	−	0.984992i	$-0.555217\pi$
$601$	−7.43424e139	−0.345204	−0.172602	+	0.984992i	$0.555217\pi$
$602$	−1.56311e140	−0.667370
$603$	4.50333e140	1.76811
$604$	1.57920e139	0.0570258
$605$	1.13514e140	0.377055
$606$	2.25615e139	0.0689445
$607$	6.16048e140	1.73215	0.866076	−	0.499913i	$-0.166635\pi$
$607$	6.16048e140	1.73215	0.866076	+	0.499913i	$0.166635\pi$
$608$	−2.83772e139	−0.0734243
$609$	1.08057e140	0.257324
$610$	5.38522e140	1.18045
$611$	−4.95304e140	−0.999518
$612$	8.71201e139	0.161872
$613$	−9.19299e140	−1.57291	−0.786453	−	0.617650i	$-0.788085\pi$
$613$	−9.19299e140	−1.57291	−0.786453	+	0.617650i	$0.788085\pi$
$614$	−1.12689e141	−1.77574
$615$	8.21707e139	0.119268
$616$	6.35751e140	0.850082
$617$	−1.54803e140	−0.190712	−0.0953560	−	0.995443i	$-0.530399\pi$
$617$	−1.54803e140	−0.190712	−0.0953560	+	0.995443i	$0.530399\pi$
$618$	2.31321e140	0.262601
$619$	5.82380e140	0.609297	0.304648	−	0.952465i	$-0.401461\pi$
$619$	5.82380e140	0.609297	0.304648	+	0.952465i	$0.401461\pi$
$620$	−5.72768e140	−0.552330
$621$	−3.90946e140	−0.347529
$622$	−7.35228e139	−0.0602570
$623$	−1.43839e141	−1.08700
$624$	8.95083e140	0.623795
$625$	1.56753e141	1.00757
$626$	−1.72831e141	−1.02475
$627$	−8.03826e139	−0.0439695
$628$	2.74224e140	0.138402
$629$	−2.01901e141	−0.940331
$630$	4.56345e141	1.96153
$631$	2.40604e141	0.954597	0.477298	−	0.878741i	$-0.341616\pi$
$631$	2.40604e141	0.954597	0.477298	+	0.878741i	$0.341616\pi$
$632$	−1.16741e141	−0.427575
$633$	5.25263e140	0.177619
$634$	−3.36272e140	−0.104998
$635$	−4.79137e141	−1.38161
$636$	−2.07088e140	−0.0551532
$637$	1.88565e141	0.463896
$638$	3.21304e141	0.730251
$639$	−2.73014e141	−0.573314
$640$	1.07322e142	2.08258
$641$	8.62217e140	0.154627	0.0773136	−	0.997007i	$-0.475366\pi$
$641$	8.62217e140	0.154627	0.0773136	+	0.997007i	$0.475366\pi$
$642$	−3.63797e141	−0.603032
$643$	−4.65858e141	−0.713838	−0.356919	−	0.934135i	$-0.616173\pi$
$643$	−4.65858e141	−0.713838	−0.356919	+	0.934135i	$0.616173\pi$
$644$	1.09124e141	0.154591
$645$	−2.16860e141	−0.284062
$646$	−1.14718e141	−0.138960
$647$	−1.01951e142	−1.14216	−0.571078	−	0.820896i	$-0.693474\pi$
$647$	−1.01951e142	−1.14216	−0.571078	+	0.820896i	$0.693474\pi$
$648$	5.97839e141	0.619507
$649$	8.15393e141	0.781645
$650$	−4.32223e142	−3.83340
$651$	5.81375e141	0.477108
$652$	5.72274e141	0.434611
$653$	−6.34673e141	−0.446102	−0.223051	−	0.974807i	$-0.571602\pi$
$653$	−6.34673e141	−0.446102	−0.223051	+	0.974807i	$0.571602\pi$
$654$	6.90162e140	0.0449029
$655$	3.36546e142	2.02702
$656$	−4.73473e141	−0.264029
$657$	1.85932e142	0.960069
$658$	−1.51417e142	−0.724049
$659$	2.68625e142	1.18969	0.594844	−	0.803841i	$-0.297214\pi$
$659$	2.68625e142	1.18969	0.594844	+	0.803841i	$0.297214\pi$
$660$	−2.65018e141	−0.108719
$661$	−1.00522e142	−0.382021	−0.191010	−	0.981588i	$-0.561176\pi$
$661$	−1.00522e142	−0.382021	−0.191010	+	0.981588i	$0.561176\pi$
$662$	3.44760e142	1.21392
$663$	1.25580e142	0.409719
$664$	−2.83762e141	−0.0857959
$665$	−1.12780e142	−0.316038
$666$	4.70335e142	1.22168
$667$	−1.83548e142	−0.441973
$668$	−1.28338e141	−0.0286513
$669$	−2.31929e142	−0.480104
$670$	−1.95506e143	−3.75304
$671$	−3.05048e142	−0.543101
$672$	9.49646e141	0.156824
$673$	8.39160e142	1.28554	0.642768	−	0.766061i	$-0.277786\pi$
$673$	8.39160e142	1.28554	0.642768	+	0.766061i	$0.277786\pi$
$674$	2.88550e141	0.0410106
$675$	8.88451e142	1.17164
$676$	3.73211e142	0.456716
$677$	−1.31642e143	−1.49509	−0.747546	−	0.664210i	$-0.768768\pi$
$677$	−1.31642e143	−1.49509	−0.747546	+	0.664210i	$0.768768\pi$
$678$	2.60352e142	0.274449
$679$	−7.16781e142	−0.701396
$680$	1.25877e143	1.14353
$681$	−6.15885e142	−0.519482
$682$	1.72869e143	1.35396
$683$	−1.72479e143	−1.25456	−0.627278	−	0.778795i	$-0.715831\pi$
$683$	−1.72479e143	−1.25456	−0.627278	+	0.778795i	$0.715831\pi$
$684$	5.01563e141	0.0338838
$685$	1.46646e143	0.920232
$686$	−1.56749e143	−0.913772
$687$	2.74767e142	0.148816
$688$	1.24956e143	0.628842
$689$	2.86854e143	1.34150
$690$	8.06650e142	0.350595
$691$	−2.96283e143	−1.19692	−0.598461	−	0.801152i	$-0.704221\pi$
$691$	−2.96283e143	−1.19692	−0.598461	+	0.801152i	$0.704221\pi$
$692$	−7.06565e142	−0.265335
$693$	−2.58499e143	−0.902464
$694$	4.18599e143	1.35877
$695$	5.75720e142	0.173772
$696$	−6.94345e142	−0.194899
$697$	−6.64280e142	−0.173419
$698$	1.24358e142	0.0301978
$699$	−5.57653e142	−0.125970
$700$	−2.47992e143	−0.521178
$701$	6.60750e143	1.29204	0.646022	−	0.763319i	$-0.276432\pi$
$701$	6.60750e143	1.29204	0.646022	+	0.763319i	$0.276432\pi$
$702$	−6.15526e143	−1.12001
$703$	−1.16237e143	−0.196835
$704$	−3.78556e143	−0.596637
$705$	−2.10071e143	−0.308187
$706$	−4.05066e143	−0.553208
$707$	−1.79309e143	−0.227993
$708$	5.29450e142	0.0626824
$709$	−1.19409e144	−1.31644	−0.658221	−	0.752825i	$-0.728691\pi$
$709$	−1.19409e144	−1.31644	−0.658221	+	0.752825i	$0.728691\pi$
$710$	1.18526e144	1.21693
$711$	4.74675e143	0.453922
$712$	9.24267e143	0.823299
$713$	−9.87535e143	−0.819467
$714$	3.83904e143	0.296800
$715$	3.67098e144	2.64440
$716$	4.48821e143	0.301277
$717$	−2.83641e143	−0.177440
$718$	1.03495e144	0.603438
$719$	−1.73333e143	−0.0942047	−0.0471023	−	0.998890i	$-0.514999\pi$
$719$	−1.73333e143	−0.0942047	−0.0471023	+	0.998890i	$0.514999\pi$
$720$	−3.64806e144	−1.84829
$721$	−1.83844e144	−0.868397
$722$	2.45317e144	1.08044
$723$	9.67517e143	0.397351
$724$	3.11338e143	0.119243
$725$	4.17126e144	1.49004
$726$	−2.22458e143	−0.0741224
$727$	−5.44264e144	−1.69169	−0.845847	−	0.533425i	$-0.820905\pi$
$727$	−5.44264e144	−1.69169	−0.845847	+	0.533425i	$0.820905\pi$
$728$	−5.71809e144	−1.65812
$729$	−1.76693e144	−0.478056
$730$	−8.07200e144	−2.03787
$731$	1.75313e144	0.413034
$732$	−1.98074e143	−0.0435529
$733$	3.16959e144	0.650508	0.325254	−	0.945627i	$-0.394550\pi$
$733$	3.16959e144	0.650508	0.325254	+	0.945627i	$0.394550\pi$
$734$	6.72396e144	1.28817
$735$	7.99753e143	0.143036
$736$	−1.61309e144	−0.269357
$737$	1.10745e145	1.72670
$738$	1.54746e144	0.225306
$739$	−3.13110e144	−0.425748	−0.212874	−	0.977080i	$-0.568282\pi$
$739$	−3.13110e144	−0.425748	−0.212874	+	0.977080i	$0.568282\pi$
$740$	−3.83230e144	−0.486696
$741$	7.22980e143	0.0857643
$742$	8.76929e144	0.971779
$743$	5.48983e144	0.568361	0.284180	−	0.958771i	$-0.408279\pi$
$743$	5.48983e144	0.568361	0.284180	+	0.958771i	$0.408279\pi$
$744$	−3.73575e144	−0.361363
$745$	−2.49869e145	−2.25850
$746$	7.24299e144	0.611797
$747$	1.15379e144	0.0910826
$748$	2.14245e144	0.158081
$749$	2.89131e145	1.99417
$750$	−9.17737e144	−0.591731
$751$	−1.26915e145	−0.765061	−0.382531	−	0.923943i	$-0.624947\pi$
$751$	−1.26915e145	−0.765061	−0.382531	+	0.923943i	$0.624947\pi$
$752$	1.21044e145	0.682248
$753$	8.09588e144	0.426695
$754$	−2.88988e145	−1.42439
$755$	−9.27760e144	−0.427676
$756$	−3.53163e144	−0.152274
$757$	−4.29701e144	−0.173310	−0.0866552	−	0.996238i	$-0.527618\pi$
$757$	−4.29701e144	−0.173310	−0.0866552	+	0.996238i	$0.527618\pi$
$758$	2.99949e145	1.13176
$759$	−4.56930e144	−0.161302
$760$	7.24691e144	0.239368
$761$	−4.62573e145	−1.42973	−0.714866	−	0.699261i	$-0.753512\pi$
$761$	−4.62573e145	−1.42973	−0.714866	+	0.699261i	$0.753512\pi$
$762$	9.38982e144	0.271601
$763$	−5.48511e144	−0.148490
$764$	4.85356e143	0.0122983
$765$	−5.11821e145	−1.21399
$766$	4.93883e145	1.09666
$767$	−7.33383e145	−1.52463
$768$	−1.03937e145	−0.202315
$769$	5.22254e145	0.951922	0.475961	−	0.879466i	$-0.342100\pi$
$769$	5.22254e145	0.951922	0.475961	+	0.879466i	$0.342100\pi$
$770$	1.12224e146	1.91560
$771$	−2.98565e145	−0.477301
$772$	1.78782e144	0.0267701
$773$	1.02627e145	0.143945	0.0719725	−	0.997407i	$-0.477071\pi$
$773$	1.02627e145	0.143945	0.0719725	+	0.997407i	$0.477071\pi$
$774$	−4.08397e145	−0.536616
$775$	2.24424e146	2.76270
$776$	4.60583e145	0.531240
$777$	3.88988e145	0.420412
$778$	−1.80292e146	−1.82603
$779$	−3.82435e144	−0.0363008
$780$	2.38364e145	0.212062
$781$	−6.71394e145	−0.559887
$782$	−6.52108e145	−0.509775
$783$	5.94026e145	0.435348
$784$	−4.60823e145	−0.316645
$785$	−1.61103e146	−1.03797
$786$	−6.59541e145	−0.398477
$787$	4.14033e145	0.234591	0.117296	−	0.993097i	$-0.462578\pi$
$787$	4.14033e145	0.234591	0.117296	+	0.993097i	$0.462578\pi$
$788$	−2.92235e145	−0.155295
$789$	1.70588e145	0.0850274
$790$	−2.06074e146	−0.963508
$791$	−2.06916e146	−0.907575
$792$	1.66104e146	0.683530
$793$	2.74367e146	1.05934
$794$	−4.27158e146	−1.54758
$795$	1.21662e146	0.413632
$796$	1.10071e146	0.351206
$797$	5.59586e146	1.67580	0.837899	−	0.545825i	$-0.183784\pi$
$797$	5.59586e146	1.67580	0.837899	+	0.545825i	$0.183784\pi$
$798$	2.21019e145	0.0621275
$799$	1.69824e146	0.448113
$800$	3.66585e146	0.908093
$801$	−3.75810e146	−0.874031
$802$	5.40243e146	1.17973
$803$	4.57241e146	0.937585
$804$	7.19091e145	0.138469
$805$	−6.41091e146	−1.15939
$806$	−1.55483e147	−2.64097
$807$	−2.32668e146	−0.371212
$808$	1.15219e146	0.172683
$809$	4.55725e146	0.641657	0.320828	−	0.947137i	$-0.396039\pi$
$809$	4.55725e146	0.641657	0.320828	+	0.947137i	$0.396039\pi$
$810$	1.05532e147	1.39601
$811$	2.45816e146	0.305532	0.152766	−	0.988262i	$-0.451182\pi$
$811$	2.45816e146	0.305532	0.152766	+	0.988262i	$0.451182\pi$
$812$	−1.65809e146	−0.193655
$813$	−1.10129e146	−0.120873
$814$	1.15664e147	1.19307
$815$	−3.36204e147	−3.25945
$816$	−3.06896e146	−0.279665
$817$	1.00930e146	0.0864583
$818$	−5.10512e146	−0.411116
$819$	2.32500e147	1.76029
$820$	−1.26087e146	−0.0897579
$821$	7.99047e146	0.534863	0.267432	−	0.963577i	$-0.413825\pi$
$821$	7.99047e146	0.534863	0.267432	+	0.963577i	$0.413825\pi$
$822$	−2.87388e146	−0.180902
$823$	−3.10849e147	−1.84017	−0.920084	−	0.391721i	$-0.871880\pi$
$823$	−3.10849e147	−1.84017	−0.920084	+	0.391721i	$0.871880\pi$
$824$	1.18133e147	0.657727
$825$	1.03840e147	0.543803
$826$	−2.24199e147	−1.10444
$827$	2.11410e147	0.979709	0.489854	−	0.871804i	$-0.337050\pi$
$827$	2.11410e147	0.979709	0.489854	+	0.871804i	$0.337050\pi$
$828$	2.85110e146	0.124303
$829$	−1.42947e147	−0.586370	−0.293185	−	0.956056i	$-0.594715\pi$
$829$	−1.42947e147	−0.586370	−0.293185	+	0.956056i	$0.594715\pi$
$830$	−5.00903e146	−0.193335
$831$	8.75878e146	0.318121
$832$	3.40482e147	1.16377
$833$	−6.46532e146	−0.207978
$834$	−1.12826e146	−0.0341605
$835$	7.53972e146	0.214876
$836$	1.23344e146	0.0330902
$837$	3.19600e147	0.807183
$838$	7.24784e147	1.72340
$839$	1.47014e145	0.00329138	0.00164569	−	0.999999i	$-0.499476\pi$
$839$	1.47014e145	0.00329138	0.00164569	+	0.999999i	$0.499476\pi$
$840$	−2.42518e147	−0.511259
$841$	−2.24836e147	−0.446342
$842$	−1.63148e147	−0.305016
$843$	3.38689e147	0.596359
$844$	−8.05994e146	−0.133671
$845$	−2.19257e148	−3.42523
$846$	−3.95611e147	−0.582190
$847$	1.76800e147	0.245116
$848$	−7.01023e147	−0.915676
$849$	−1.38734e147	−0.170744
$850$	1.48196e148	1.71862
$851$	−6.60743e147	−0.722088
$852$	−4.35949e146	−0.0448990
$853$	8.51957e147	0.826974	0.413487	−	0.910510i	$-0.364311\pi$
$853$	8.51957e147	0.826974	0.413487	+	0.910510i	$0.364311\pi$
$854$	8.38757e147	0.767385
$855$	−2.94662e147	−0.254118
$856$	−1.85787e148	−1.51039
$857$	2.41123e148	1.84802	0.924010	−	0.382368i	$-0.124891\pi$
$857$	2.41123e148	1.84802	0.924010	+	0.382368i	$0.124891\pi$
$858$	−7.19415e147	−0.519842
$859$	1.06941e148	0.728601	0.364300	−	0.931282i	$-0.381308\pi$
$859$	1.06941e148	0.728601	0.364300	+	0.931282i	$0.381308\pi$
$860$	3.32762e147	0.213778
$861$	1.27982e147	0.0775336
$862$	7.86270e147	0.449216
$863$	−2.26991e147	−0.122310	−0.0611552	−	0.998128i	$-0.519478\pi$
$863$	−2.26991e147	−0.122310	−0.0611552	+	0.998128i	$0.519478\pi$
$864$	5.22051e147	0.265319
$865$	4.15098e148	1.98993
$866$	−1.99533e148	−0.902323
$867$	2.89066e147	0.123320
$868$	−8.92095e147	−0.359058
$869$	1.16731e148	0.443291
$870$	−1.22567e148	−0.439189
$871$	−9.96069e148	−3.36800
$872$	3.52457e147	0.112467
$873$	−1.87275e148	−0.563975
$874$	−3.75428e147	−0.106708
$875$	7.29378e148	1.95680
$876$	2.96896e147	0.0751877
$877$	3.37030e148	0.805728	0.402864	−	0.915260i	$-0.368015\pi$
$877$	3.37030e148	0.805728	0.402864	+	0.915260i	$0.368015\pi$
$878$	1.56173e146	0.00352478
$879$	1.51833e148	0.323540
$880$	−8.97126e148	−1.80501
$881$	−7.25925e148	−1.37914	−0.689570	−	0.724219i	$-0.742201\pi$
$881$	−7.25925e148	−1.37914	−0.689570	+	0.724219i	$0.742201\pi$
$882$	1.50612e148	0.270206
$883$	9.12520e148	1.54606	0.773031	−	0.634368i	$-0.218740\pi$
$883$	9.12520e148	1.54606	0.773031	+	0.634368i	$0.218740\pi$
$884$	−1.92697e148	−0.308344
$885$	−3.11046e148	−0.470099
$886$	2.10689e148	0.300773
$887$	5.96302e148	0.804124	0.402062	−	0.915612i	$-0.368294\pi$
$887$	5.96302e148	0.804124	0.402062	+	0.915612i	$0.368294\pi$
$888$	−2.49953e148	−0.318422
$889$	−7.46262e148	−0.898158
$890$	1.63153e149	1.85524
$891$	−5.97788e148	−0.642278
$892$	3.55885e148	0.361314
$893$	9.77701e147	0.0938010
$894$	4.89677e148	0.443982
$895$	−2.63677e149	−2.25948
$896$	1.67156e149	1.35384
$897$	4.10974e148	0.314627
$898$	6.99822e148	0.506446
$899$	1.50052e149	1.02654
$900$	−6.47932e148	−0.419066
$901$	−9.83532e148	−0.601432
$902$	3.80550e148	0.220030
$903$	−3.37763e148	−0.184663
$904$	1.32958e149	0.687401
$905$	−1.82907e149	−0.894289
$906$	1.81817e148	0.0840736
$907$	2.15967e149	0.944540	0.472270	−	0.881454i	$-0.343435\pi$
$907$	2.15967e149	0.944540	0.472270	+	0.881454i	$0.343435\pi$
$908$	9.45049e148	0.390948
$909$	−4.68484e148	−0.183324
$910$	−1.00937e150	−3.73645
$911$	−3.54148e149	−1.24024	−0.620121	−	0.784506i	$-0.712916\pi$
$911$	−3.54148e149	−1.24024	−0.620121	+	0.784506i	$0.712916\pi$
$912$	−1.76684e148	−0.0585408
$913$	2.83738e148	0.0889495
$914$	2.39168e149	0.709446
$915$	1.16366e149	0.326633
$916$	−4.21618e148	−0.111995
$917$	5.24175e149	1.31773
$918$	2.11045e149	0.502133
$919$	−3.46818e149	−0.781032	−0.390516	−	0.920596i	$-0.627703\pi$
$919$	−3.46818e149	−0.781032	−0.390516	+	0.920596i	$0.627703\pi$
$920$	4.11947e149	0.878123
$921$	−2.43502e149	−0.491351
$922$	1.21318e149	0.231747
$923$	6.03867e149	1.09208
$924$	−4.12770e148	−0.0706763
$925$	1.50158e150	2.43440
$926$	−4.45372e149	−0.683704
$927$	−4.80332e149	−0.698256
$928$	2.45102e149	0.337422
$929$	−1.59274e149	−0.207659	−0.103829	−	0.994595i	$-0.533110\pi$
$929$	−1.59274e149	−0.207659	−0.103829	+	0.994595i	$0.533110\pi$
$930$	−6.59441e149	−0.814305
$931$	−3.72217e148	−0.0435349
$932$	8.55695e148	0.0948015
$933$	−1.58871e148	−0.0166733
$934$	1.16638e150	1.15964
$935$	−1.25866e150	−1.18556
$936$	−1.49398e150	−1.33325
$937$	9.70291e149	0.820451	0.410226	−	0.911984i	$-0.365450\pi$
$937$	9.70291e149	0.820451	0.410226	+	0.911984i	$0.365450\pi$
$938$	−3.04504e150	−2.43977
$939$	−3.73460e149	−0.283552
$940$	3.22344e149	0.231934
$941$	2.18073e149	0.148705	0.0743526	−	0.997232i	$-0.476311\pi$
$941$	2.18073e149	0.148705	0.0743526	+	0.997232i	$0.476311\pi$
$942$	3.15720e149	0.204048
$943$	−2.17393e149	−0.133170
$944$	1.79227e150	1.04068
$945$	2.07479e150	1.14201
$946$	−1.00432e150	−0.524048
$947$	2.56888e150	1.27078	0.635389	−	0.772192i	$-0.280840\pi$
$947$	2.56888e150	1.27078	0.635389	+	0.772192i	$0.280840\pi$
$948$	7.57960e148	0.0355488
$949$	−4.11254e150	−1.82880
$950$	8.53184e149	0.359750
$951$	−7.26628e148	−0.0290533
$952$	1.96055e150	0.743383
$953$	−4.47909e150	−1.61064	−0.805319	−	0.592842i	$-0.798006\pi$
$953$	−4.47909e150	−1.61064	−0.805319	+	0.592842i	$0.798006\pi$
$954$	2.29117e150	0.781383
$955$	−2.85141e149	−0.0922337
$956$	4.35235e149	0.133537
$957$	6.94286e149	0.202062
$958$	2.63699e150	0.728033
$959$	2.28404e150	0.598224
$960$	1.44407e150	0.358831
$961$	3.83154e150	0.903322
$962$	−1.04031e151	−2.32714
$963$	7.55416e150	1.60346
$964$	−1.48461e150	−0.299036
$965$	−1.05032e150	−0.200768
$966$	1.25637e150	0.227915
$967$	−1.06296e151	−1.83012	−0.915060	−	0.403318i	$-0.867857\pi$
$967$	−1.06296e151	−1.83012	−0.915060	+	0.403318i	$0.867857\pi$
$968$	−1.13607e150	−0.185652
$969$	−2.47887e149	−0.0384506
$970$	8.13030e150	1.19711
$971$	2.05230e150	0.286860	0.143430	−	0.989660i	$-0.454187\pi$
$971$	2.05230e150	0.286860	0.143430	+	0.989660i	$0.454187\pi$
$972$	−1.40689e150	−0.186687
$973$	8.96693e149	0.112965
$974$	−2.93074e150	−0.350550
$975$	−9.33965e150	−1.06071
$976$	−6.70508e150	−0.723083
$977$	−1.45556e150	−0.149058	−0.0745289	−	0.997219i	$-0.523745\pi$
$977$	−1.45556e150	−0.149058	−0.0745289	+	0.997219i	$0.523745\pi$
$978$	6.58872e150	0.640750
$979$	−9.24188e150	−0.853561
$980$	−1.22719e150	−0.107645
$981$	−1.43310e150	−0.119397
$982$	8.97394e150	0.710155
$983$	−6.44594e150	−0.484545	−0.242272	−	0.970208i	$-0.577893\pi$
$983$	−6.44594e150	−0.484545	−0.242272	+	0.970208i	$0.577893\pi$
$984$	−8.22376e149	−0.0587243
$985$	1.71685e151	1.16467
$986$	9.90851e150	0.638593
$987$	−3.27188e150	−0.200346
$988$	−1.10938e150	−0.0645439
$989$	5.73731e150	0.317172
$990$	2.93209e151	1.54028
$991$	1.69874e151	0.848024	0.424012	−	0.905656i	$-0.360621\pi$
$991$	1.69874e151	0.848024	0.424012	+	0.905656i	$0.360621\pi$
$992$	1.31871e151	0.625618
$993$	7.44971e150	0.335894
$994$	1.84606e151	0.791103
$995$	−6.46652e151	−2.63394
$996$	1.84237e149	0.00713312
$997$	−9.31202e150	−0.342719	−0.171360	−	0.985209i	$-0.554816\pi$
$997$	−9.31202e150	−0.342719	−0.171360	+	0.985209i	$0.554816\pi$
$998$	−5.74712e151	−2.01075
$999$	2.13839e151	0.711264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.102.a.a.1.3	✓	8
3.2	odd	2		9.102.a.b.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.102.a.a.1.3	✓	8	1.1	even	1	trivial
9.102.a.b.1.6		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 102 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.76666e15 q^{2} -3.81746e23 q^{3} +5.85773e29 q^{4} -3.44135e35 q^{5} +6.74413e38 q^{6} -5.35995e42 q^{7} +3.44415e45 q^{8} -1.40040e48 q^{9} +O(q^{10})\)	\(q-1.76666e15 q^{2} -3.81746e23 q^{3} +5.85773e29 q^{4} -3.44135e35 q^{5} +6.74413e38 q^{6} -5.35995e42 q^{7} +3.44415e45 q^{8} -1.40040e48 q^{9} +6.07967e50 q^{10} -3.44385e52 q^{11} -2.23616e53 q^{12} +3.09748e56 q^{13} +9.46918e57 q^{14} +1.31372e59 q^{15} -7.56973e60 q^{16} -1.06203e62 q^{17} +2.47403e63 q^{18} -6.11425e63 q^{19} -2.01585e65 q^{20} +2.04614e66 q^{21} +6.08410e67 q^{22} -3.47561e68 q^{23} -1.31479e69 q^{24} +7.89855e70 q^{25} -5.47219e71 q^{26} +1.12483e72 q^{27} -3.13971e72 q^{28} +5.28104e73 q^{29} -2.32089e74 q^{30} +2.84133e75 q^{31} +4.64116e75 q^{32} +1.31468e76 q^{33} +1.87624e77 q^{34} +1.84454e78 q^{35} -8.20318e77 q^{36} +1.90109e79 q^{37} +1.08018e79 q^{38} -1.18245e80 q^{39} -1.18525e81 q^{40} +6.25482e80 q^{41} -3.61482e81 q^{42} -1.65073e82 q^{43} -2.01731e82 q^{44} +4.81927e83 q^{45} +6.14021e83 q^{46} -1.59905e84 q^{47} +2.88971e84 q^{48} +6.08770e84 q^{49} -1.39540e86 q^{50} +4.05425e85 q^{51} +1.81442e86 q^{52} +9.26087e86 q^{53} -1.98718e87 q^{54} +1.18515e88 q^{55} -1.84604e88 q^{56} +2.33409e87 q^{57} -9.32978e88 q^{58} -2.36767e89 q^{59} +7.69540e88 q^{60} +8.85775e89 q^{61} -5.01965e90 q^{62} +7.50609e90 q^{63} +1.09922e91 q^{64} -1.06595e92 q^{65} -2.32258e91 q^{66} -3.21574e92 q^{67} -6.22108e91 q^{68} +1.32680e92 q^{69} -3.25867e93 q^{70} +1.94954e93 q^{71} -4.82319e93 q^{72} -1.32770e94 q^{73} -3.35857e94 q^{74} -3.01524e94 q^{75} -3.58156e93 q^{76} +1.84589e95 q^{77} +2.08898e95 q^{78} -3.38956e95 q^{79} +2.60501e96 q^{80} +1.73581e96 q^{81} -1.10501e96 q^{82} -8.23897e95 q^{83} +1.19857e96 q^{84} +3.65481e97 q^{85} +2.91628e97 q^{86} -2.01601e97 q^{87} -1.18611e98 q^{88} +2.68359e98 q^{89} -8.51399e98 q^{90} -1.66023e99 q^{91} -2.03592e98 q^{92} -1.08467e99 q^{93} +2.82498e99 q^{94} +2.10412e99 q^{95} -1.77174e99 q^{96} +1.33729e100 q^{97} -1.07549e100 q^{98} +4.82278e100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 52\!\cdots\!84 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more