LMFDB - Embedded newform 2.82.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,82,Mod(1,2)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 82, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 82);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 82 $
Character orbit:	$[\chi]$	$=$	2.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:	$83.1002571076$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 215736607049989005852988854472x + 10253113298782277175624314846636353390456960 $ x^3 - x^2 - 215736607049989005852988854472*x + 10253113298782277175624314846636353390456960
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.38588e14$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.09951e12 q^{2} +2.69378e19 q^{3} +1.20893e24 q^{4} +1.65593e28 q^{5} -2.96185e31 q^{6} +2.15367e33 q^{7} -1.32923e36 q^{8} +2.82220e38 q^{9} +O(q^{10})$	\(q-1.09951e12 q^{2} +2.69378e19 q^{3} +1.20893e24 q^{4} +1.65593e28 q^{5} -2.96185e31 q^{6} +2.15367e33 q^{7} -1.32923e36 q^{8} +2.82220e38 q^{9} -1.82071e40 q^{10} -3.85124e40 q^{11} +3.25658e43 q^{12} -8.46841e43 q^{13} -2.36798e45 q^{14} +4.46071e47 q^{15} +1.46150e48 q^{16} -7.68035e49 q^{17} -3.10304e50 q^{18} -7.37973e51 q^{19} +2.00189e52 q^{20} +5.80152e52 q^{21} +4.23448e52 q^{22} -1.05342e55 q^{23} -3.58065e55 q^{24} -1.39380e56 q^{25} +9.31111e55 q^{26} -4.34255e57 q^{27} +2.60363e57 q^{28} -1.79362e59 q^{29} -4.90461e59 q^{30} -4.86617e60 q^{31} -1.60694e60 q^{32} -1.03744e60 q^{33} +8.44463e61 q^{34} +3.56632e61 q^{35} +3.41183e62 q^{36} +2.30511e63 q^{37} +8.11410e63 q^{38} -2.28121e63 q^{39} -2.20111e64 q^{40} -1.35802e65 q^{41} -6.37884e64 q^{42} +2.10516e66 q^{43} -4.65586e64 q^{44} +4.67337e66 q^{45} +1.15824e67 q^{46} +1.03746e68 q^{47} +3.93697e67 q^{48} -2.79115e68 q^{49} +1.53250e68 q^{50} -2.06892e69 q^{51} -1.02377e68 q^{52} +2.99301e69 q^{53} +4.77468e69 q^{54} -6.37737e68 q^{55} -2.86272e69 q^{56} -1.98794e71 q^{57} +1.97211e71 q^{58} -5.68737e71 q^{59} +5.39267e71 q^{60} +5.44662e71 q^{61} +5.35041e72 q^{62} +6.07809e71 q^{63} +1.76685e72 q^{64} -1.40231e72 q^{65} +1.14068e72 q^{66} -5.75193e73 q^{67} -9.28497e73 q^{68} -2.83767e74 q^{69} -3.92121e73 q^{70} +4.64836e74 q^{71} -3.75135e74 q^{72} +4.70398e75 q^{73} -2.53449e75 q^{74} -3.75460e75 q^{75} -8.92155e75 q^{76} -8.29429e73 q^{77} +2.50821e75 q^{78} -4.20695e76 q^{79} +2.42014e76 q^{80} -2.42123e77 q^{81} +1.49315e77 q^{82} -7.46283e77 q^{83} +7.01361e76 q^{84} -1.27181e78 q^{85} -2.31465e78 q^{86} -4.83163e78 q^{87} +5.11917e76 q^{88} +5.59868e78 q^{89} -5.13842e78 q^{90} -1.82382e77 q^{91} -1.27350e79 q^{92} -1.31084e80 q^{93} -1.14070e80 q^{94} -1.22203e80 q^{95} -4.32874e79 q^{96} -1.28380e80 q^{97} +3.06890e80 q^{98} -1.08690e79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3298534883328 q^{2} + 12\!\cdots\!88 q^{3}+ \cdots - 11\!\cdots\!61 q^{9}+O(q^{10}) $ 3 * q - 3298534883328 * q^2 + 12604360672390214988 * q^3 + 3626777458843887524118528 * q^4 - 20983063979496004028435775150 * q^5 - 13858641119975563142110472306688 * q^6 - 552766607526265634132821897861224 * q^7 - 3987683987354747618711421180841033728 * q^8 - 117787926384549736709174105715608001561 * q^9	$ 3 q - 3298534883328 q^{2} + 12\!\cdots\!88 q^{3}+ \cdots - 54\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q - 3298534883328 * q^2 + 12604360672390214988 * q^3 + 3626777458843887524118528 * q^4 - 20983063979496004028435775150 * q^5 - 13858641119975563142110472306688 * q^6 - 552766607526265634132821897861224 * q^7 - 3987683987354747618711421180841033728 * q^8 - 117787926384549736709174105715608001561 * q^9 + 23071122831823603677392872526248830566400 * q^10 + 1280703554832406814772038626747672506628836 * q^11 + 15237737056587739139724154617942692371365888 * q^12 - 203053213213228262252289604826178427009253142 * q^13 + 607773312421421660059947871105692013191757824 * q^14 + 258521148569780014125709880112718518230943462600 * q^15 + 4384504911992708754611054498148849058967797628928 * q^16 + 13707915509793004617532214813228047814831020392246 * q^17 + 129509194671435939545936242487957259125865458958336 * q^18 + 4795253838113603708371668796877035230312394724136060 * q^19 - 25366967819438409173828536843196320983278888052326400 * q^20 - 519561242096418127707719252363204767758340529227929504 * q^21 - 1408148450272289287785839512865281090582833620620148736 * q^22 - 30160326897246150414676624400786632753521325735600143672 * q^23 - 16754069074711460085681771147599677065524525007359705088 * q^24 + 280923310225904394201067316034822697319282719805054788125 * q^25 + 223259368985223798004862759385395227818359125574462472192 * q^26 - 625732627028059848123157770721822016131959245230905824520 * q^27 - 668253824059288729544577409501125262363392110293023719424 * q^28 + 21426901075097725646400095068279905894982750657375381771290 * q^29 - 284247008878479957653591543774260948340603378455551777177600 * q^30 - 3860912612203425210987573972171722804903899142052351141235104 * q^31 - 4820814132776970826625886277023487807566608981348378505904128 * q^32 + 8168133227004704222278627528558820550230283855880259452058256 * q^33 - 15072012495588383375840729817410870669983615065857449468624896 * q^34 + 796090962825005181029369759037285415121243766103175607760525200 * q^35 - 142396865445149395381460288303846938058595761644053336724340736 * q^36 - 962488012673974734154716715779071426226206694726253291815438414 * q^37 - 5272437353143400002601123557255816511393680180123473805899202560 * q^38 + 36399394236397559852249384794748301006956973683053277402364624168 * q^39 + 27891276078892134524892145882383175355059555080188678327658086400 * q^40 + 315729621076478275418732734280056694539166286076338101303285961726 * q^41 + 571263627026753110335028642726281008965977037891914073465216303104 * q^42 + 909989621545075850999251035125487926201005781380826452677677267268 * q^43 + 1548275594709136585239376117673204105702523898770639375302588891136 * q^44 + 18726742363164362961210285095677755369767013044398376551081888987050 * q^45 + 33161630121047390334190832695565871193686149855479234561060185833472 * q^46 + 163450219955907571723000348929623433672676106405825241782972369095056 * q^47 + 18421293760207539636329616625228032485526805502091287721258189324288 * q^48 + 84812568823216657456965826417651253151115010649007120996812564086571 * q^49 - 308878446106706366749766699689999329829075494845604303484181544960000 * q^50 - 772668114968744140818526844449587165078736038177006698750562111292584 * q^51 - 245476272209186027435979673735318928259666399417721223896051054804992 * q^52 - 9024153738612400417538776640914507257088387728526558953119104505855262 * q^53 + 688000299296174776837040539007613919441804640939925628100944613867520 * q^54 - 47582265107476429230871013599303461307138199609079326757133914456997800 * q^55 + 734752849858965262954329330674619565324848328021238234080860149121024 * q^56 - 216617828008754172617635723539247550424408451696387193425209932869178640 * q^57 - 23559126879276024743748830323085589194984582286732740071220506043351040 * q^58 + 173083732030804573367247232387536299255274355093160491876857331837886580 * q^59 + 312532891422436622416291987827866414001366266719668703388792623045017600 * q^60 + 3682273674088882162766525675671573547949650573236627272535804184395569786 * q^61 + 4245118310944676295775623698651741067018146620927310456707340474152648704 * q^62 + 9705799226705237716648578379561491511812293162477695944136214255847932088 * q^63 + 5300541194335152988749892502228755547482451690626856874364818603877859328 * q^64 - 44151816740799940959026445433284813207449285152198691890526681479556208900 * q^65 - 8980957460315174060246993877740912710546379374029437859477782888139718656 * q^66 - 45459418332173895471620473386340508364570599523844133604129556114327113204 * q^67 + 16571852992884595424446978834061245676151100304309921706423425641318711296 * q^68 - 381439114954192945191386382600395171642161070159132929461545170926869452512 * q^69 - 875311270393484550029235899022474573456262617665795224851553160648667955200 * q^70 - 663360175811055431998373202697213154081787807552643411579641705598806018984 * q^71 + 156567009315796258559371618044865000947560071154027590172344122439825883136 * q^72 + 2875774114961093540042489135457037118623579706430287895576809293063724624478 * q^73 + 1058266761530049278342349439594403567843746419708291471605671028744219787264 * q^74 + 10375259783421120323437883415423908867929791104823014714965332849751129672500 * q^75 + 5797106176501684687211043996484842348086442945206709564991930078125946306560 * q^76 - 30868237386271625806706807506325457951957257249868500448028258335470666673888 * q^77 - 40021557206921833579421107130768288096369682034648702942405604830436149690368 * q^78 - 161970107563907182248111919540000364532077003546202035586261450715135988178960 * q^79 - 30666782362252501426187331709976780976797178163640583917249396059633247846400 * q^80 - 299082334358425446166064721339785324689357638880155921207411342332373570690837 * q^81 - 347148389606898305991152076671360411666324733389734989961305134834963894501376 * q^82 - 1551644647158271447807906137086282123739475283733105818013885940684527133830852 * q^83 - 628111000441407059444538271675557174582977063534777274464062826341812041416704 * q^84 - 5282756950234547173621607909805842177285468672028854473129976993442919157706300 * q^85 - 1000544170044292549089574941787678182163502426454419285939792765992630084435968 * q^86 - 5562608887098194592587989531458685107064636512216475421164235996460442752999960 * q^87 - 1702347019384497220096060609753563967878468415968847544815229284239878217793536 * q^88 - 8621118410314024378389076217632288587702101272330766532155222306149385764271730 * q^89 - 20590270978664625661714404112581680708566453290315884360291836574024273284300800 * q^90 - 58818429441931738974494712027943381122004094832556221941814570900274994185170864 * q^91 - 36461597914098448064383011084918512893601406801264240344797801790065853985718272 * q^92 - 240404744478319194110331229870238328818799091224439431760300521618055178727456384 * q^93 - 179715417404065173132559582630226240824158475728290692441384718063336098633875456 * q^94 - 433274751899148074134278380777280708876242908949531972946158534560456001105919000 * q^95 - 20254426688025663721128815841682505745347385078485744734548553502718284412223488 * q^96 - 533678667972555021629681531571524475991025351825819428841423661701166265694104794 * q^97 - 93252405602678975820826304474476792170868714668077393805420770046393998792196096 * q^98 - 542180767943235177708947795218783507805362281402610542195265148391971885481633132 * 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 $

$2$	−1.09951e12	−0.707107
$2$	−1.09951e12	−0.707107
$3$	2.69378e19	1.27924	0.639620	−	0.768692i	$-0.279092\pi$
$3$	2.69378e19	1.27924	0.639620	+	0.768692i	$0.279092\pi$
$4$	1.20893e24	0.500000
$5$	1.65593e28	0.814247	0.407124	−	0.913373i	$-0.366532\pi$
$5$	1.65593e28	0.814247	0.407124	+	0.913373i	$0.366532\pi$
$6$	−2.96185e31	−0.904559
$7$	2.15367e33	0.127852	0.0639261	−	0.997955i	$-0.479638\pi$
$7$	2.15367e33	0.127852	0.0639261	+	0.997955i	$0.479638\pi$
$8$	−1.32923e36	−0.353553
$9$	2.82220e38	0.636453
$10$	−1.82071e40	−0.575760
$11$	−3.85124e40	−0.0256564	−0.0128282	−	0.999918i	$-0.504083\pi$
$11$	−3.85124e40	−0.0256564	−0.0128282	+	0.999918i	$0.504083\pi$
$12$	3.25658e43	0.639620
$13$	−8.46841e43	−0.0650273	−0.0325137	−	0.999471i	$-0.510351\pi$
$13$	−8.46841e43	−0.0650273	−0.0325137	+	0.999471i	$0.510351\pi$
$14$	−2.36798e45	−0.0904052
$15$	4.46071e47	1.04162
$16$	1.46150e48	0.250000
$17$	−7.68035e49	−1.12772	−0.563858	−	0.825872i	$-0.690683\pi$
$17$	−7.68035e49	−1.12772	−0.563858	+	0.825872i	$0.690683\pi$
$18$	−3.10304e50	−0.450041
$19$	−7.37973e51	−1.19817	−0.599087	−	0.800684i	$-0.704469\pi$
$19$	−7.37973e51	−1.19817	−0.599087	+	0.800684i	$0.704469\pi$
$20$	2.00189e52	0.407124
$21$	5.80152e52	0.163554
$22$	4.23448e52	0.0181418
$23$	−1.05342e55	−0.745800	−0.372900	−	0.927872i	$-0.621637\pi$
$23$	−1.05342e55	−0.745800	−0.372900	+	0.927872i	$0.621637\pi$
$24$	−3.58065e55	−0.452279
$25$	−1.39380e56	−0.337001
$26$	9.31111e55	0.0459813
$27$	−4.34255e57	−0.465063
$28$	2.60363e57	0.0639261
$29$	−1.79362e59	−1.06319	−0.531597	−	0.846998i	$-0.678408\pi$
$29$	−1.79362e59	−1.06319	−0.531597	+	0.846998i	$0.678408\pi$
$30$	−4.90461e59	−0.736535
$31$	−4.86617e60	−1.93659	−0.968297	−	0.249800i	$-0.919635\pi$
$31$	−4.86617e60	−1.93659	−0.968297	+	0.249800i	$0.919635\pi$
$32$	−1.60694e60	−0.176777
$33$	−1.03744e60	−0.0328207
$34$	8.44463e61	0.797416
$35$	3.56632e61	0.104103
$36$	3.41183e62	0.318227
$37$	2.30511e63	0.708796	0.354398	−	0.935095i	$-0.384686\pi$
$37$	2.30511e63	0.708796	0.354398	+	0.935095i	$0.384686\pi$
$38$	8.11410e63	0.847236
$39$	−2.28121e63	−0.0831855
$40$	−2.20111e64	−0.287880
$41$	−1.35802e65	−0.653369	−0.326684	−	0.945133i	$-0.605931\pi$
$41$	−1.35802e65	−0.653369	−0.326684	+	0.945133i	$0.605931\pi$
$42$	−6.37884e64	−0.115650
$43$	2.10516e66	1.47168	0.735838	−	0.677158i	$-0.236788\pi$
$43$	2.10516e66	1.47168	0.735838	+	0.677158i	$0.236788\pi$
$44$	−4.65586e64	−0.0128282
$45$	4.67337e66	0.518231
$46$	1.15824e67	0.527360
$47$	1.03746e68	1.97700	0.988501	−	0.151212i	$-0.0483177\pi$
$47$	1.03746e68	1.97700	0.988501	+	0.151212i	$0.0483177\pi$
$48$	3.93697e67	0.319810
$49$	−2.79115e68	−0.983654
$50$	1.53250e68	0.238296
$51$	−2.06892e69	−1.44262
$52$	−1.02377e68	−0.0325137
$53$	2.99301e69	0.439476	0.219738	−	0.975559i	$-0.429480\pi$
$53$	2.99301e69	0.439476	0.219738	+	0.975559i	$0.429480\pi$
$54$	4.77468e69	0.328849
$55$	−6.37737e68	−0.0208907
$56$	−2.86272e69	−0.0452026
$57$	−1.98794e71	−1.53275
$58$	1.97211e71	0.751791
$59$	−5.68737e71	−1.08494	−0.542469	−	0.840076i	$-0.682510\pi$
$59$	−5.68737e71	−1.08494	−0.542469	+	0.840076i	$0.682510\pi$
$60$	5.39267e71	0.520809
$61$	5.44662e71	0.269320	0.134660	−	0.990892i	$-0.457006\pi$
$61$	5.44662e71	0.269320	0.134660	+	0.990892i	$0.457006\pi$
$62$	5.35041e72	1.36938
$63$	6.07809e71	0.0813720
$64$	1.76685e72	0.125000
$65$	−1.40231e72	−0.0529484
$66$	1.14068e72	0.0232078
$67$	−5.75193e73	−0.636479	−0.318240	−	0.948010i	$-0.603092\pi$
$67$	−5.75193e73	−0.636479	−0.318240	+	0.948010i	$0.603092\pi$
$68$	−9.28497e73	−0.563858
$69$	−2.83767e74	−0.954057
$70$	−3.92121e73	−0.0736122
$71$	4.64836e74	0.491289	0.245644	−	0.969360i	$-0.421000\pi$
$71$	4.64836e74	0.491289	0.245644	+	0.969360i	$0.421000\pi$
$72$	−3.75135e74	−0.225020
$73$	4.70398e75	1.61395	0.806974	−	0.590587i	$-0.201104\pi$
$73$	4.70398e75	1.61395	0.806974	+	0.590587i	$0.201104\pi$
$74$	−2.53449e75	−0.501195
$75$	−3.75460e75	−0.431105
$76$	−8.92155e75	−0.599087
$77$	−8.29429e73	−0.00328023
$78$	2.50821e75	0.0588211
$79$	−4.20695e76	−0.588939	−0.294469	−	0.955661i	$-0.595143\pi$
$79$	−4.20695e76	−0.588939	−0.294469	+	0.955661i	$0.595143\pi$
$80$	2.42014e76	0.203562
$81$	−2.42123e77	−1.23138
$82$	1.49315e77	0.462002
$83$	−7.46283e77	−1.41332	−0.706661	−	0.707552i	$-0.749799\pi$
$83$	−7.46283e77	−1.41332	−0.706661	+	0.707552i	$0.749799\pi$
$84$	7.01361e76	0.0817768
$85$	−1.27181e78	−0.918240
$86$	−2.31465e78	−1.04063
$87$	−4.83163e78	−1.36008
$88$	5.11917e76	0.00907092
$89$	5.59868e78	0.627755	0.313878	−	0.949463i	$-0.398372\pi$
$89$	5.59868e78	0.627755	0.313878	+	0.949463i	$0.398372\pi$
$90$	−5.13842e78	−0.366444
$91$	−1.82382e77	−0.00831389
$92$	−1.27350e79	−0.372900
$93$	−1.31084e80	−2.47737
$94$	−1.14070e80	−1.39795
$95$	−1.22203e80	−0.975610
$96$	−4.32874e79	−0.226140
$97$	−1.28380e80	−0.440800	−0.220400	−	0.975410i	$-0.570736\pi$
$97$	−1.28380e80	−0.440800	−0.220400	+	0.975410i	$0.570736\pi$
$98$	3.06890e80	0.695548
$99$	−1.08690e79	−0.0163291
$100$	−1.68501e80	−0.168501
$101$	−7.72319e79	−0.0516156	−0.0258078	−	0.999667i	$-0.508216\pi$
$101$	−7.72319e79	−0.0516156	−0.0258078	+	0.999667i	$0.508216\pi$
$102$	2.27480e81	1.02009
$103$	−3.15136e80	−0.0951897	−0.0475948	−	0.998867i	$-0.515156\pi$
$103$	−3.15136e80	−0.0951897	−0.0475948	+	0.998867i	$0.515156\pi$
$104$	1.12564e80	0.0229906
$105$	9.60690e80	0.133173
$106$	−3.29085e81	−0.310757
$107$	1.69471e82	1.09409	0.547045	−	0.837103i	$-0.315753\pi$
$107$	1.69471e82	1.09409	0.547045	+	0.837103i	$0.315753\pi$
$108$	−5.24982e81	−0.232532
$109$	4.82859e82	1.47247	0.736236	−	0.676725i	$-0.236601\pi$
$109$	4.82859e82	1.47247	0.736236	+	0.676725i	$0.236601\pi$
$110$	7.01199e80	0.0147719
$111$	6.20946e82	0.906720
$112$	3.14759e81	0.0319631
$113$	7.06228e82	0.500343	0.250172	−	0.968202i	$-0.419513\pi$
$113$	7.06228e82	0.500343	0.250172	+	0.968202i	$0.419513\pi$
$114$	2.18576e83	1.08382
$115$	−1.74438e83	−0.607266
$116$	−2.16836e83	−0.531597
$117$	−2.38996e82	−0.0413869
$118$	6.25333e83	0.767167
$119$	−1.65409e83	−0.144181
$120$	−5.92930e83	−0.368267
$121$	−2.25176e84	−0.999342
$122$	−5.98862e83	−0.190438
$123$	−3.65820e84	−0.835815
$124$	−5.88284e84	−0.968297
$125$	−9.15680e84	−1.08865
$126$	−6.68293e83	−0.0575387
$127$	−1.77729e84	−0.111098	−0.0555491	−	0.998456i	$-0.517691\pi$
$127$	−1.77729e84	−0.111098	−0.0555491	+	0.998456i	$0.517691\pi$
$128$	−1.94267e84	−0.0883883
$129$	5.67084e85	1.88263
$130$	1.54185e84	0.0374401
$131$	−2.55142e85	−0.454250	−0.227125	−	0.973866i	$-0.572933\pi$
$131$	−2.55142e85	−0.454250	−0.227125	+	0.973866i	$0.572933\pi$
$132$	−1.25419e84	−0.0164104
$133$	−1.58935e85	−0.153189
$134$	6.32432e85	0.450059
$135$	−7.19095e85	−0.378676
$136$	1.02089e86	0.398708
$137$	−6.97596e85	−0.202498	−0.101249	−	0.994861i	$-0.532284\pi$
$137$	−6.97596e85	−0.202498	−0.101249	+	0.994861i	$0.532284\pi$
$138$	3.12005e86	0.674620
$139$	4.07982e86	0.658478	0.329239	−	0.944247i	$-0.393208\pi$
$139$	4.07982e86	0.658478	0.329239	+	0.944247i	$0.393208\pi$
$140$	4.31142e85	0.0520517
$141$	2.79469e87	2.52906
$142$	−5.11093e86	−0.347394
$143$	3.26138e84	0.00166837
$144$	4.12465e86	0.159113
$145$	−2.97011e87	−0.865703
$146$	−5.17208e87	−1.14123
$147$	−7.51876e87	−1.25833
$148$	2.78670e87	0.354398
$149$	−4.93272e87	−0.477576	−0.238788	−	0.971072i	$-0.576750\pi$
$149$	−4.93272e87	−0.477576	−0.238788	+	0.971072i	$0.576750\pi$
$150$	4.12823e87	0.304837
$151$	−1.01232e88	−0.571152	−0.285576	−	0.958356i	$-0.592185\pi$
$151$	−1.01232e88	−0.571152	−0.285576	+	0.958356i	$0.592185\pi$
$152$	9.80934e87	0.423618
$153$	−2.16755e88	−0.717739
$154$	9.11967e85	0.00231948
$155$	−8.05803e88	−1.57687
$156$	−2.75781e87	−0.0415928
$157$	1.17061e89	1.36294	0.681471	−	0.731845i	$-0.261340\pi$
$157$	1.17061e89	1.36294	0.681471	+	0.731845i	$0.261340\pi$
$158$	4.62559e88	0.416442
$159$	8.06252e88	0.562195
$160$	−2.66097e88	−0.143940
$161$	−2.26871e88	−0.0953522
$162$	2.66217e89	0.870717
$163$	1.93542e89	0.493375	0.246687	−	0.969095i	$-0.420658\pi$
$163$	1.93542e89	0.493375	0.246687	+	0.969095i	$0.420658\pi$
$164$	−1.64174e89	−0.326684
$165$	−1.71793e88	−0.0267242
$166$	8.20547e89	0.999369
$167$	2.65462e89	0.253505	0.126752	−	0.991934i	$-0.459545\pi$
$167$	2.65462e89	0.253505	0.126752	+	0.991934i	$0.459545\pi$
$168$	−7.71154e88	−0.0578250
$169$	−1.68877e90	−0.995771
$170$	1.39837e90	0.649294
$171$	−2.08271e90	−0.762581
$172$	2.54498e90	0.735838
$173$	−4.22319e90	−0.965547	−0.482773	−	0.875745i	$-0.660371\pi$
$173$	−4.22319e90	−0.965547	−0.482773	+	0.875745i	$0.660371\pi$
$174$	5.31244e90	0.961721
$175$	−3.00179e89	−0.0430863
$176$	−5.62859e88	−0.00641411
$177$	−1.53205e91	−1.38790
$178$	−6.15581e90	−0.443890
$179$	−2.47654e91	−1.42330	−0.711652	−	0.702532i	$-0.752053\pi$
$179$	−2.47654e91	−1.42330	−0.711652	+	0.702532i	$0.752053\pi$
$180$	5.64975e90	0.259115
$181$	−2.31583e91	−0.848643	−0.424321	−	0.905512i	$-0.639487\pi$
$181$	−2.31583e91	−0.848643	−0.424321	+	0.905512i	$0.639487\pi$
$182$	2.00531e89	0.00587881
$183$	1.46720e91	0.344525
$184$	1.40023e91	0.263680
$185$	3.81709e91	0.577135
$186$	1.44128e92	1.75176
$187$	2.95788e90	0.0289332
$188$	1.25421e92	0.988501
$189$	−9.35241e90	−0.0594594
$190$	1.34364e92	0.689860
$191$	−1.10964e92	−0.460607	−0.230304	−	0.973119i	$-0.573972\pi$
$191$	−1.10964e92	−0.460607	−0.230304	+	0.973119i	$0.573972\pi$
$192$	4.75950e91	0.159905
$193$	−5.11836e92	−1.39335	−0.696675	−	0.717387i	$-0.745338\pi$
$193$	−5.11836e92	−1.39335	−0.696675	+	0.717387i	$0.745338\pi$
$194$	1.41155e92	0.311692
$195$	−3.77751e91	−0.0677336
$196$	−3.37430e92	−0.491827
$197$	1.19905e93	1.42218	0.711092	−	0.703099i	$-0.248201\pi$
$197$	1.19905e93	1.42218	0.711092	+	0.703099i	$0.248201\pi$
$198$	1.19506e91	0.0115464
$199$	−8.67630e92	−0.683573	−0.341786	−	0.939778i	$-0.611032\pi$
$199$	−8.67630e92	−0.683573	−0.341786	+	0.939778i	$0.611032\pi$
$200$	1.85268e92	0.119148
$201$	−1.54945e93	−0.814209
$202$	8.49173e91	0.0364977
$203$	−3.86287e92	−0.135932
$204$	−2.50117e93	−0.721309
$205$	−2.24878e93	−0.532004
$206$	3.46495e92	0.0673093
$207$	−2.97295e93	−0.474667
$208$	−1.23766e92	−0.0162568
$209$	2.84211e92	0.0307409
$210$	−1.05629e93	−0.0941676
$211$	1.56322e94	1.14969	0.574845	−	0.818262i	$-0.305062\pi$
$211$	1.56322e94	1.14969	0.574845	+	0.818262i	$0.305062\pi$
$212$	3.61833e93	0.219738
$213$	1.25217e94	0.628476
$214$	−1.86336e94	−0.773639
$215$	3.48599e94	1.19831
$216$	5.77223e93	0.164425
$217$	−1.04801e94	−0.247598
$218$	−5.30909e94	−1.04119
$219$	1.26715e95	2.06463
$220$	−7.70977e92	−0.0104453
$221$	6.50403e93	0.0733324
$222$	−6.82737e94	−0.641148
$223$	1.51413e95	1.18527	0.592633	−	0.805472i	$-0.298088\pi$
$223$	1.51413e95	1.18527	0.592633	+	0.805472i	$0.298088\pi$
$224$	−3.46081e93	−0.0226013
$225$	−3.93360e94	−0.214485
$226$	−7.76506e94	−0.353796
$227$	−3.54890e95	−1.35222	−0.676109	−	0.736801i	$-0.736335\pi$
$227$	−3.54890e95	−1.35222	−0.676109	+	0.736801i	$0.736335\pi$
$228$	−2.40327e95	−0.766375
$229$	−7.16704e95	−1.91427	−0.957133	−	0.289647i	$-0.906462\pi$
$229$	−7.16704e95	−1.91427	−0.957133	+	0.289647i	$0.906462\pi$
$230$	1.91797e95	0.429402
$231$	−2.23430e93	−0.00419620
$232$	2.38413e95	0.375896
$233$	−1.74206e94	−0.0230754	−0.0115377	−	0.999933i	$-0.503673\pi$
$233$	−1.74206e94	−0.0230754	−0.0115377	+	0.999933i	$0.503673\pi$
$234$	2.62779e94	0.0292649
$235$	1.71796e96	1.60977
$236$	−6.87561e95	−0.542469
$237$	−1.13326e96	−0.753393
$238$	1.81870e95	0.101951
$239$	2.85641e96	1.35116	0.675579	−	0.737288i	$-0.263894\pi$
$239$	2.85641e96	1.35116	0.675579	+	0.737288i	$0.263894\pi$
$240$	6.51934e95	0.260404
$241$	1.64482e96	0.555174	0.277587	−	0.960700i	$-0.410465\pi$
$241$	1.64482e96	0.555174	0.277587	+	0.960700i	$0.410465\pi$
$242$	2.47583e96	0.706641
$243$	−4.59666e96	−1.11017
$244$	6.58456e95	0.134660
$245$	−4.62195e96	−0.800938
$246$	4.02223e96	0.591011
$247$	6.24946e95	0.0779140
$248$	6.46825e96	0.684690
$249$	−2.01033e97	−1.80798
$250$	1.00680e97	0.769792
$251$	2.49036e97	1.61986	0.809928	−	0.586530i	$-0.199506\pi$
$251$	2.49036e97	1.61986	0.809928	+	0.586530i	$0.199506\pi$
$252$	7.34796e95	0.0406860
$253$	4.05695e95	0.0191346
$254$	1.95415e96	0.0785583
$255$	−3.42598e97	−1.17465
$256$	2.13599e96	0.0625000
$257$	−6.39309e97	−1.59742	−0.798710	−	0.601716i	$-0.794484\pi$
$257$	−6.39309e97	−1.59742	−0.798710	+	0.601716i	$0.794484\pi$
$258$	−6.23515e97	−1.33122
$259$	4.96444e96	0.0906212
$260$	−1.69529e96	−0.0264742
$261$	−5.06197e97	−0.676673
$262$	2.80532e97	0.321203
$263$	1.31373e98	1.28914	0.644569	−	0.764546i	$-0.277037\pi$
$263$	1.31373e98	1.28914	0.644569	+	0.764546i	$0.277037\pi$
$264$	1.37899e96	0.0116039
$265$	4.95621e97	0.357842
$266$	1.74751e97	0.108321
$267$	1.50816e98	0.803049
$268$	−6.95366e97	−0.318240
$269$	1.34185e98	0.528126	0.264063	−	0.964505i	$-0.414937\pi$
$269$	1.34185e98	0.528126	0.264063	+	0.964505i	$0.414937\pi$
$270$	7.90653e97	0.267765
$271$	2.31481e98	0.674930	0.337465	−	0.941338i	$-0.390431\pi$
$271$	2.31481e98	0.674930	0.337465	+	0.941338i	$0.390431\pi$
$272$	−1.12248e98	−0.281929
$273$	−4.91296e96	−0.0106355
$274$	7.67015e97	0.143188
$275$	5.36787e96	0.00864624
$276$	−3.43054e98	−0.477028
$277$	1.19697e99	1.43765	0.718827	−	0.695189i	$-0.244680\pi$
$277$	1.19697e99	1.43765	0.718827	+	0.695189i	$0.244680\pi$
$278$	−4.48581e98	−0.465615
$279$	−1.37333e99	−1.23255
$280$	−4.74046e97	−0.0368061
$281$	2.35229e99	1.58083	0.790415	−	0.612571i	$-0.209865\pi$
$281$	2.35229e99	1.58083	0.790415	+	0.612571i	$0.209865\pi$
$282$	−3.07279e99	−1.78832
$283$	−1.76801e99	−0.891524	−0.445762	−	0.895152i	$-0.647067\pi$
$283$	−1.76801e99	−0.891524	−0.445762	+	0.895152i	$0.647067\pi$
$284$	5.61952e98	0.245644
$285$	−3.29189e99	−1.24804
$286$	−3.58593e96	−0.00117972
$287$	−2.92472e98	−0.0835347
$288$	−4.53511e98	−0.112510
$289$	1.26044e99	0.271743
$290$	3.26567e99	0.612144
$291$	−3.45827e99	−0.563888
$292$	5.68676e99	0.806974
$293$	7.41514e99	0.916180	0.458090	−	0.888906i	$-0.348534\pi$
$293$	7.41514e99	0.916180	0.458090	+	0.888906i	$0.348534\pi$
$294$	8.26696e99	0.889773
$295$	−9.41788e99	−0.883408
$296$	−3.06401e99	−0.250597
$297$	1.67242e98	0.0119319
$298$	5.42358e99	0.337697
$299$	8.92075e98	0.0484974
$300$	−4.53904e99	−0.215552
$301$	4.53381e99	0.188157
$302$	1.11306e100	0.403866
$303$	−2.08046e99	−0.0660287
$304$	−1.07855e100	−0.299543
$305$	9.01921e99	0.219293
$306$	2.38325e100	0.507518
$307$	3.35912e100	0.626789	0.313395	−	0.949623i	$-0.398534\pi$
$307$	3.35912e100	0.626789	0.313395	+	0.949623i	$0.398534\pi$
$308$	−1.00272e98	−0.00164012
$309$	−8.48907e99	−0.121770
$310$	8.85990e100	1.11501
$311$	−1.52457e101	−1.68404	−0.842019	−	0.539448i	$-0.818633\pi$
$311$	−1.52457e101	−1.68404	−0.842019	+	0.539448i	$0.818633\pi$
$312$	3.03224e99	0.0294105
$313$	−1.80423e101	−1.53726	−0.768628	−	0.639696i	$-0.779060\pi$
$313$	−1.80423e101	−1.53726	−0.768628	+	0.639696i	$0.779060\pi$
$314$	−1.28710e101	−0.963746
$315$	1.00649e100	0.0662570
$316$	−5.08589e100	−0.294469
$317$	−9.83506e100	−0.501045	−0.250523	−	0.968111i	$-0.580602\pi$
$317$	−9.83506e100	−0.501045	−0.250523	+	0.968111i	$0.580602\pi$
$318$	−8.86483e100	−0.397532
$319$	6.90767e99	0.0272778
$320$	2.92577e100	0.101781
$321$	4.56519e101	1.39960
$322$	2.49447e100	0.0674242
$323$	5.66789e101	1.35120
$324$	−2.92708e101	−0.615690
$325$	1.18033e100	0.0219143
$326$	−2.12802e101	−0.348869
$327$	1.30072e102	1.88364
$328$	1.80511e101	0.231001
$329$	2.23434e101	0.252764
$330$	1.88888e100	0.0188969
$331$	−7.65599e99	−0.00677591	−0.00338795	−	0.999994i	$-0.501078\pi$
$331$	−7.65599e99	−0.00677591	−0.00338795	+	0.999994i	$0.501078\pi$
$332$	−9.02201e101	−0.706661
$333$	6.50548e101	0.451116
$334$	−2.91879e101	−0.179255
$335$	−9.52479e101	−0.518252
$336$	8.47893e100	0.0408884
$337$	−4.29366e102	−1.83576	−0.917881	−	0.396856i	$-0.870101\pi$
$337$	−4.29366e102	−1.83576	−0.917881	+	0.396856i	$0.870101\pi$
$338$	1.85683e102	0.704117
$339$	1.90242e102	0.640059
$340$	−1.53753e102	−0.459120
$341$	1.87408e101	0.0496861
$342$	2.28996e102	0.539226
$343$	−1.21223e102	−0.253615
$344$	−2.79823e102	−0.520316
$345$	−4.69898e102	−0.776838
$346$	4.64344e102	0.682745
$347$	1.89134e101	0.0247415	0.0123708	−	0.999923i	$-0.496062\pi$
$347$	1.89134e101	0.0247415	0.0123708	+	0.999923i	$0.496062\pi$
$348$	−5.84109e102	−0.680040
$349$	−1.37592e103	−1.42614	−0.713070	−	0.701093i	$-0.752696\pi$
$349$	−1.37592e103	−1.42614	−0.713070	+	0.701093i	$0.752696\pi$
$350$	3.30051e101	0.0304666
$351$	3.67745e101	0.0302418
$352$	6.18870e100	0.00453546
$353$	2.78332e103	1.81839	0.909195	−	0.416371i	$-0.136698\pi$
$353$	2.78332e103	1.81839	0.909195	+	0.416371i	$0.136698\pi$
$354$	1.68451e103	0.981390
$355$	7.69735e102	0.400031
$356$	6.76839e102	0.313878
$357$	−4.45577e102	−0.184442
$358$	2.72298e103	1.00643
$359$	−5.09879e103	−1.68322	−0.841612	−	0.540082i	$-0.818393\pi$
$359$	−5.09879e103	−1.68322	−0.841612	+	0.540082i	$0.818393\pi$
$360$	−6.21197e102	−0.183222
$361$	1.65253e103	0.435619
$362$	2.54629e103	0.600081
$363$	−6.06575e103	−1.27840
$364$	−2.20486e101	−0.00415695
$365$	7.78946e103	1.31415
$366$	−1.61320e103	−0.243616
$367$	7.65169e103	1.03462	0.517311	−	0.855798i	$-0.326933\pi$
$367$	7.65169e103	1.03462	0.517311	+	0.855798i	$0.326933\pi$
$368$	−1.53957e103	−0.186450
$369$	−3.83260e103	−0.415839
$370$	−4.19694e103	−0.408096
$371$	6.44595e102	0.0561880
$372$	−1.58471e104	−1.23868
$373$	1.10313e104	0.773430	0.386715	−	0.922199i	$-0.373610\pi$
$373$	1.10313e104	0.773430	0.386715	+	0.922199i	$0.373610\pi$
$374$	−3.25223e102	−0.0204588
$375$	−2.46664e104	−1.39264
$376$	−1.37902e104	−0.698976
$377$	1.51891e103	0.0691367
$378$	1.02831e103	0.0420441
$379$	−2.28475e104	−0.839365	−0.419682	−	0.907671i	$-0.637859\pi$
$379$	−2.28475e104	−0.839365	−0.419682	+	0.907671i	$0.637859\pi$
$380$	−1.47734e104	−0.487805
$381$	−4.78763e103	−0.142121
$382$	1.22006e104	0.325699
$383$	7.62871e104	1.83189	0.915947	−	0.401298i	$-0.131441\pi$
$383$	7.62871e104	1.83189	0.915947	+	0.401298i	$0.131441\pi$
$384$	−5.23313e103	−0.113070
$385$	−1.37347e102	−0.00267092
$386$	5.62770e104	0.985247
$387$	5.94118e104	0.936653
$388$	−1.55202e104	−0.220400
$389$	6.74768e104	0.863368	0.431684	−	0.902025i	$-0.357920\pi$
$389$	6.74768e104	0.863368	0.431684	+	0.902025i	$0.357920\pi$
$390$	4.15342e103	0.0478949
$391$	8.09060e104	0.841051
$392$	3.71008e104	0.347774
$393$	−6.87298e104	−0.581094
$394$	−1.31837e105	−1.00564
$395$	−6.96641e104	−0.479542
$396$	−1.31398e103	−0.00816456
$397$	−2.50030e105	−1.40274	−0.701368	−	0.712799i	$-0.747427\pi$
$397$	−2.50030e105	−1.40274	−0.701368	+	0.712799i	$0.747427\pi$
$398$	9.53969e104	0.483359
$399$	−4.28136e104	−0.195966
$400$	−2.03705e104	−0.0842503
$401$	7.15970e103	0.0267638	0.0133819	−	0.999910i	$-0.495740\pi$
$401$	7.15970e103	0.0267638	0.0133819	+	0.999910i	$0.495740\pi$
$402$	1.70363e105	0.575733
$403$	4.12087e104	0.125932
$404$	−9.33676e103	−0.0258078
$405$	−4.00938e105	−1.00265
$406$	4.24727e104	0.0961182
$407$	−8.87751e103	−0.0181852
$408$	2.75007e105	0.510043
$409$	−5.18525e105	−0.870914	−0.435457	−	0.900209i	$-0.643413\pi$
$409$	−5.18525e105	−0.870914	−0.435457	+	0.900209i	$0.643413\pi$
$410$	2.47256e105	0.376184
$411$	−1.87917e105	−0.259044
$412$	−3.80976e104	−0.0475948
$413$	−1.22487e105	−0.138712
$414$	3.26880e105	0.335640
$415$	−1.23579e106	−1.15079
$416$	1.36082e104	0.0114953
$417$	1.09901e106	0.842351
$418$	−3.12493e104	−0.0217371
$419$	1.13062e106	0.713919	0.356960	−	0.934120i	$-0.383813\pi$
$419$	1.13062e106	0.713919	0.356960	+	0.934120i	$0.383813\pi$
$420$	1.16140e105	0.0665866
$421$	2.52430e106	1.31437	0.657183	−	0.753731i	$-0.271748\pi$
$421$	2.52430e106	1.31437	0.657183	+	0.753731i	$0.271748\pi$
$422$	−1.71878e106	−0.812953
$423$	2.92792e106	1.25827
$424$	−3.97839e105	−0.155378
$425$	1.07049e106	0.380041
$426$	−1.37677e106	−0.444400
$427$	1.17302e105	0.0344332
$428$	2.04878e106	0.547045
$429$	8.78546e103	0.00213424
$430$	−3.83289e106	−0.847332
$431$	2.23744e105	0.0450217	0.0225108	−	0.999747i	$-0.492834\pi$
$431$	2.23744e105	0.0450217	0.0225108	+	0.999747i	$0.492834\pi$
$432$	−6.34664e105	−0.116266
$433$	−4.63717e106	−0.773559	−0.386780	−	0.922172i	$-0.626413\pi$
$433$	−4.63717e106	−0.773559	−0.386780	+	0.922172i	$0.626413\pi$
$434$	1.15230e106	0.175078
$435$	−8.00084e106	−1.10744
$436$	5.83740e106	0.736236
$437$	7.77392e106	0.893598
$438$	−1.39325e107	−1.45991
$439$	−8.66735e106	−0.828082	−0.414041	−	0.910258i	$-0.635883\pi$
$439$	−8.66735e106	−0.828082	−0.414041	+	0.910258i	$0.635883\pi$
$440$	8.47698e104	0.00738597
$441$	−7.87720e106	−0.626050
$442$	−7.15126e105	−0.0518538
$443$	9.95720e106	0.658850	0.329425	−	0.944182i	$-0.393145\pi$
$443$	9.95720e106	0.658850	0.329425	+	0.944182i	$0.393145\pi$
$444$	7.50678e106	0.453360
$445$	9.27101e106	0.511148
$446$	−1.66480e107	−0.838110
$447$	−1.32877e107	−0.610934
$448$	3.80520e105	0.0159815
$449$	3.96267e107	1.52059	0.760294	−	0.649579i	$-0.225055\pi$
$449$	3.96267e107	1.52059	0.760294	+	0.649579i	$0.225055\pi$
$450$	4.32504e106	0.151664
$451$	5.23004e105	0.0167631
$452$	8.53777e106	0.250172
$453$	−2.72697e107	−0.730641
$454$	3.90206e107	0.956163
$455$	−3.02011e105	−0.00676957
$456$	2.64242e107	0.541909
$457$	4.31708e107	0.810184	0.405092	−	0.914276i	$-0.367240\pi$
$457$	4.31708e107	0.810184	0.405092	+	0.914276i	$0.367240\pi$
$458$	7.88024e107	1.35359
$459$	3.33523e107	0.524459
$460$	−2.10883e107	−0.303633
$461$	−8.16084e107	−1.07609	−0.538043	−	0.842917i	$-0.680836\pi$
$461$	−8.16084e107	−1.07609	−0.538043	+	0.842917i	$0.680836\pi$
$462$	2.45664e105	0.00296716
$463$	−6.62658e107	−0.733262	−0.366631	−	0.930366i	$-0.619489\pi$
$463$	−6.62658e107	−0.733262	−0.366631	+	0.930366i	$0.619489\pi$
$464$	−2.62138e107	−0.265798
$465$	−2.17066e108	−2.01719
$466$	1.91542e106	0.0163167
$467$	−8.07914e107	−0.631003	−0.315502	−	0.948925i	$-0.602173\pi$
$467$	−8.07914e107	−0.631003	−0.315502	+	0.948925i	$0.602173\pi$
$468$	−2.88928e106	−0.0206934
$469$	−1.23878e107	−0.0813753
$470$	−1.88891e108	−1.13828
$471$	3.15338e108	1.74353
$472$	7.55981e107	0.383584
$473$	−8.10746e106	−0.0377580
$474$	1.24603e108	0.532730
$475$	1.02859e108	0.403786
$476$	−1.99968e107	−0.0720905
$477$	8.44688e107	0.279706
$478$	−3.14066e108	−0.955413
$479$	4.07310e107	0.113851	0.0569254	−	0.998378i	$-0.481870\pi$
$479$	4.07310e107	0.113851	0.0569254	+	0.998378i	$0.481870\pi$
$480$	−7.16809e107	−0.184134
$481$	−1.95206e107	−0.0460911
$482$	−1.80850e108	−0.392568
$483$	−6.11141e107	−0.121978
$484$	−2.72221e108	−0.499671
$485$	−2.12588e108	−0.358920
$486$	5.05408e108	0.785007
$487$	8.18293e108	1.16946	0.584731	−	0.811227i	$-0.301200\pi$
$487$	8.18293e108	1.16946	0.584731	+	0.811227i	$0.301200\pi$
$488$	−7.23980e107	−0.0952190
$489$	5.21360e108	0.631145
$490$	5.08189e108	0.566348
$491$	−4.58698e107	−0.0470681	−0.0235341	−	0.999723i	$-0.507492\pi$
$491$	−4.58698e107	−0.0470681	−0.0235341	+	0.999723i	$0.507492\pi$
$492$	−4.42249e108	−0.417908
$493$	1.37757e109	1.19898
$494$	−6.87135e107	−0.0550935
$495$	−1.79982e107	−0.0132959
$496$	−7.11192e108	−0.484149
$497$	1.00110e108	0.0628124
$498$	2.21038e109	1.27843
$499$	−1.29605e109	−0.691116	−0.345558	−	0.938397i	$-0.612310\pi$
$499$	−1.29605e109	−0.691116	−0.345558	+	0.938397i	$0.612310\pi$
$500$	−1.10699e109	−0.544325
$501$	7.15098e108	0.324293
$502$	−2.73818e109	−1.14541
$503$	−3.21057e109	−1.23902	−0.619511	−	0.784988i	$-0.712669\pi$
$503$	−3.21057e109	−1.23902	−0.619511	+	0.784988i	$0.712669\pi$
$504$	−8.07917e107	−0.0287694
$505$	−1.27890e108	−0.0420279
$506$	−4.46067e107	−0.0135302
$507$	−4.54919e109	−1.27383
$508$	−2.14861e108	−0.0555491
$509$	−4.21642e109	−1.00664	−0.503319	−	0.864100i	$-0.667888\pi$
$509$	−4.21642e109	−1.00664	−0.503319	+	0.864100i	$0.667888\pi$
$510$	3.76691e109	0.830602
$511$	1.01308e109	0.206347
$512$	−2.34854e108	−0.0441942
$513$	3.20468e109	0.557226
$514$	7.02927e109	1.12955
$515$	−5.21842e108	−0.0775079
$516$	6.85562e109	0.941313
$517$	−3.99549e108	−0.0507228
$518$	−5.45846e108	−0.0640789
$519$	−1.13764e110	−1.23517
$520$	1.86399e108	0.0187201
$521$	6.70105e109	0.622609	0.311304	−	0.950310i	$-0.399234\pi$
$521$	6.70105e109	0.622609	0.311304	+	0.950310i	$0.399234\pi$
$522$	5.56569e109	0.478480
$523$	1.39503e110	1.10986	0.554928	−	0.831898i	$-0.312746\pi$
$523$	1.39503e110	1.10986	0.554928	+	0.831898i	$0.312746\pi$
$524$	−3.08448e109	−0.227125
$525$	−8.08618e108	−0.0551178
$526$	−1.44447e110	−0.911559
$527$	3.73739e110	2.18393
$528$	−1.51622e108	−0.00820518
$529$	−8.85370e109	−0.443782
$530$	−5.44941e109	−0.253033
$531$	−1.60509e110	−0.690513
$532$	−1.92141e109	−0.0765946
$533$	1.15002e109	0.0424869
$534$	−1.65824e110	−0.567842
$535$	2.80632e110	0.890860
$536$	7.64563e109	0.225029
$537$	−6.67126e110	−1.82075
$538$	−1.47538e110	−0.373441
$539$	1.07494e109	0.0252370
$540$	−8.69332e109	−0.189338
$541$	7.78185e109	0.157251	0.0786256	−	0.996904i	$-0.474947\pi$
$541$	7.78185e109	0.157251	0.0786256	+	0.996904i	$0.474947\pi$
$542$	−2.54516e110	−0.477247
$543$	−6.23835e110	−1.08562
$544$	1.23418e110	0.199354
$545$	7.99580e110	1.19896
$546$	5.40186e108	0.00752041
$547$	−2.81651e110	−0.364103	−0.182051	−	0.983289i	$-0.558274\pi$
$547$	−2.81651e110	−0.364103	−0.182051	+	0.983289i	$0.558274\pi$
$548$	−8.43342e109	−0.101249
$549$	1.53715e110	0.171410
$550$	−5.90203e108	−0.00611382
$551$	1.32365e111	1.27389
$552$	3.77191e110	0.337310
$553$	−9.06038e109	−0.0752971
$554$	−1.31609e111	−1.01657
$555$	1.02824e111	0.738294
$556$	4.93220e110	0.329239
$557$	−3.50511e110	−0.217554	−0.108777	−	0.994066i	$-0.534693\pi$
$557$	−3.50511e110	−0.217554	−0.108777	+	0.994066i	$0.534693\pi$
$558$	1.50999e111	0.871546
$559$	−1.78273e110	−0.0956992
$560$	5.21219e109	0.0260258
$561$	7.96790e109	0.0370124
$562$	−2.58637e111	−1.11782
$563$	−2.55312e111	−1.02679	−0.513395	−	0.858152i	$-0.671612\pi$
$563$	−2.55312e111	−1.02679	−0.513395	+	0.858152i	$0.671612\pi$
$564$	3.37857e111	1.26453
$565$	1.16946e111	0.407403
$566$	1.94394e111	0.630403
$567$	−5.21452e110	−0.157435
$568$	−6.17873e110	−0.173697
$569$	2.41238e111	0.631538	0.315769	−	0.948836i	$-0.397738\pi$
$569$	2.41238e111	0.631538	0.315769	+	0.948836i	$0.397738\pi$
$570$	3.61947e111	0.882496
$571$	−4.06873e111	−0.924052	−0.462026	−	0.886866i	$-0.652877\pi$
$571$	−4.06873e111	−0.924052	−0.462026	+	0.886866i	$0.652877\pi$
$572$	3.94277e108	0.000834185 0
$573$	−2.98913e111	−0.589227
$574$	3.21576e110	0.0590680
$575$	1.46825e111	0.251335
$576$	4.98640e110	0.0795567
$577$	−6.19248e111	−0.920967	−0.460484	−	0.887668i	$-0.652324\pi$
$577$	−6.19248e111	−0.920967	−0.460484	+	0.887668i	$0.652324\pi$
$578$	−1.38586e111	−0.192151
$579$	−1.37878e112	−1.78243
$580$	−3.59065e111	−0.432851
$581$	−1.60725e111	−0.180696
$582$	3.80241e111	0.398729
$583$	−1.15268e110	−0.0112754
$584$	−6.25266e111	−0.570617
$585$	−3.95760e110	−0.0336992
$586$	−8.15303e111	−0.647837
$587$	−9.44491e110	−0.0700414	−0.0350207	−	0.999387i	$-0.511150\pi$
$587$	−9.44491e110	−0.0700414	−0.0350207	+	0.999387i	$0.511150\pi$
$588$	−9.08962e111	−0.629164
$589$	3.59110e112	2.32038
$590$	1.03551e112	0.624664
$591$	3.22999e112	1.81931
$592$	3.36892e111	0.177199
$593$	3.51703e112	1.72767	0.863836	−	0.503773i	$-0.168055\pi$
$593$	3.51703e112	1.72767	0.863836	+	0.503773i	$0.168055\pi$
$594$	−1.83884e110	−0.00843710
$595$	−2.73906e111	−0.117399
$596$	−5.96329e111	−0.238788
$597$	−2.33721e112	−0.874453
$598$	−9.80847e110	−0.0342928
$599$	−8.52279e111	−0.278481	−0.139240	−	0.990259i	$-0.544466\pi$
$599$	−8.52279e111	−0.278481	−0.139240	+	0.990259i	$0.544466\pi$
$600$	4.99073e111	0.152419
$601$	−1.13950e112	−0.325312	−0.162656	−	0.986683i	$-0.552006\pi$
$601$	−1.13950e112	−0.325312	−0.162656	+	0.986683i	$0.552006\pi$
$602$	−4.98498e111	−0.133047
$603$	−1.62331e112	−0.405089
$604$	−1.22382e112	−0.285576
$605$	−3.72875e112	−0.813712
$606$	2.28749e111	0.0466893
$607$	5.48765e112	1.04772	0.523859	−	0.851805i	$-0.324492\pi$
$607$	5.48765e112	1.04772	0.523859	+	0.851805i	$0.324492\pi$
$608$	1.18588e112	0.211809
$609$	−1.04057e112	−0.173889
$610$	−9.91673e111	−0.155064
$611$	−8.78562e111	−0.128559
$612$	−2.62041e112	−0.358869
$613$	3.54802e112	0.454817	0.227408	−	0.973799i	$-0.426975\pi$
$613$	3.54802e112	0.454817	0.227408	+	0.973799i	$0.426975\pi$
$614$	−3.69339e112	−0.443207
$615$	−6.05772e112	−0.680561
$616$	1.10250e110	0.00115974
$617$	−9.42261e112	−0.928159	−0.464079	−	0.885794i	$-0.653615\pi$
$617$	−9.42261e112	−0.928159	−0.464079	+	0.885794i	$0.653615\pi$
$618$	9.33383e111	0.0861047
$619$	3.52629e111	0.0304682	0.0152341	−	0.999884i	$-0.495151\pi$
$619$	3.52629e111	0.0304682	0.0152341	+	0.999884i	$0.495151\pi$
$620$	−9.74156e112	−0.788434
$621$	4.57451e112	0.346844
$622$	1.67628e113	1.19079
$623$	1.20577e112	0.0802599
$624$	−3.33399e111	−0.0207964
$625$	−9.39837e112	−0.549429
$626$	1.98377e113	1.08700
$627$	7.65602e111	0.0393249
$628$	1.41519e113	0.681471
$629$	−1.77040e113	−0.799321
$630$	−1.10665e112	−0.0468507
$631$	−1.55289e113	−0.616527	−0.308263	−	0.951301i	$-0.599748\pi$
$631$	−1.55289e113	−0.616527	−0.308263	+	0.951301i	$0.599748\pi$
$632$	5.59199e112	0.208221
$633$	4.21098e113	1.47073
$634$	1.08138e113	0.354293
$635$	−2.94306e112	−0.0904615
$636$	9.74699e112	0.281098
$637$	2.36366e112	0.0639644
$638$	−7.59506e111	−0.0192883
$639$	1.31186e113	0.312682
$640$	−3.21692e112	−0.0719700
$641$	4.55438e113	0.956487	0.478244	−	0.878227i	$-0.341274\pi$
$641$	4.55438e113	0.956487	0.478244	+	0.878227i	$0.341274\pi$
$642$	−5.01948e113	−0.989669
$643$	−8.10226e113	−1.49990	−0.749949	−	0.661496i	$-0.769922\pi$
$643$	−8.10226e113	−1.49990	−0.749949	+	0.661496i	$0.769922\pi$
$644$	−2.74270e112	−0.0476761
$645$	9.39050e113	1.53292
$646$	−6.23191e113	−0.955442
$647$	−7.61202e113	−1.09617	−0.548083	−	0.836424i	$-0.684642\pi$
$647$	−7.61202e113	−1.09617	−0.548083	+	0.836424i	$0.684642\pi$
$648$	3.21836e113	0.435359
$649$	2.19034e112	0.0278356
$650$	−1.29779e112	−0.0154957
$651$	−2.82312e113	−0.316737
$652$	2.33978e113	0.246687
$653$	9.46822e113	0.938176	0.469088	−	0.883151i	$-0.344583\pi$
$653$	9.46822e113	0.938176	0.469088	+	0.883151i	$0.344583\pi$
$654$	−1.43015e114	−1.33194
$655$	−4.22497e113	−0.369872
$656$	−1.98474e113	−0.163342
$657$	1.32756e114	1.02720
$658$	−2.45668e113	−0.178731
$659$	−1.13280e114	−0.774986	−0.387493	−	0.921873i	$-0.626659\pi$
$659$	−1.13280e114	−0.774986	−0.387493	+	0.921873i	$0.626659\pi$
$660$	−2.07684e112	−0.0133621
$661$	−2.33352e114	−1.41206	−0.706029	−	0.708183i	$-0.749515\pi$
$661$	−2.33352e114	−1.41206	−0.706029	+	0.708183i	$0.749515\pi$
$662$	8.41785e111	0.00479129
$663$	1.75205e113	0.0938097
$664$	9.91981e113	0.499685
$665$	−2.63185e113	−0.124734
$666$	−7.15285e113	−0.318987
$667$	1.88943e114	0.792930
$668$	3.20924e113	0.126752
$669$	4.07874e114	1.51624
$670$	1.04726e114	0.366459
$671$	−2.09762e112	−0.00690979
$672$	−9.32268e112	−0.0289125
$673$	3.04730e114	0.889827	0.444914	−	0.895573i	$-0.353234\pi$
$673$	3.04730e114	0.889827	0.444914	+	0.895573i	$0.353234\pi$
$674$	4.72092e114	1.29808
$675$	6.05266e113	0.156727
$676$	−2.04160e114	−0.497886
$677$	1.93415e114	0.444272	0.222136	−	0.975016i	$-0.428697\pi$
$677$	1.93415e114	0.444272	0.222136	+	0.975016i	$0.428697\pi$
$678$	−2.09174e114	−0.452590
$679$	−2.76488e113	−0.0563572
$680$	1.69053e114	0.324647
$681$	−9.55998e114	−1.72981
$682$	−2.06057e113	−0.0351334
$683$	3.94780e114	0.634331	0.317166	−	0.948370i	$-0.397269\pi$
$683$	3.94780e114	0.634331	0.317166	+	0.948370i	$0.397269\pi$
$684$	−2.51784e114	−0.381291
$685$	−1.15517e114	−0.164884
$686$	1.33286e114	0.179333
$687$	−1.93064e115	−2.44881
$688$	3.07669e114	0.367919
$689$	−2.53460e113	−0.0285780
$690$	5.16659e114	0.549308
$691$	−1.75270e115	−1.75730	−0.878649	−	0.477468i	$-0.841555\pi$
$691$	−1.75270e115	−1.75730	−0.878649	+	0.477468i	$0.841555\pi$
$692$	−5.10552e114	−0.482773
$693$	−2.34082e112	−0.00208772
$694$	−2.07955e113	−0.0174949
$695$	6.75589e114	0.536164
$696$	6.42234e114	0.480861
$697$	1.04300e115	0.736815
$698$	1.51284e115	1.00843
$699$	−4.69273e113	−0.0295189
$700$	−3.62894e113	−0.0215432
$701$	6.82707e114	0.382521	0.191260	−	0.981539i	$-0.438743\pi$
$701$	6.82707e114	0.382521	0.191260	+	0.981539i	$0.438743\pi$
$702$	−4.04339e113	−0.0213842
$703$	−1.70111e115	−0.849261
$704$	−6.80454e112	−0.00320705
$705$	4.62780e115	2.05928
$706$	−3.06029e115	−1.28580
$707$	−1.66332e113	−0.00659917
$708$	−1.85214e115	−0.693948
$709$	2.03694e114	0.0720783	0.0360392	−	0.999350i	$-0.488526\pi$
$709$	2.03694e114	0.0720783	0.0360392	+	0.999350i	$0.488526\pi$
$710$	−8.46333e114	−0.282864
$711$	−1.18729e115	−0.374832
$712$	−7.44192e114	−0.221945
$713$	5.12610e115	1.44431
$714$	4.89917e114	0.130420
$715$	5.40062e112	0.00135847
$716$	−2.99395e115	−0.711652
$717$	7.69456e115	1.72845
$718$	5.60618e115	1.19022
$719$	−5.76168e115	−1.15619	−0.578095	−	0.815969i	$-0.696204\pi$
$719$	−5.76168e115	−1.15619	−0.578095	+	0.815969i	$0.696204\pi$
$720$	6.83013e114	0.129558
$721$	−6.78698e113	−0.0121702
$722$	−1.81697e115	−0.308029
$723$	4.43080e115	0.710201
$724$	−2.79967e115	−0.424321
$725$	2.49996e115	0.358297
$726$	6.66936e115	0.903963
$727$	−1.53192e116	−1.96378	−0.981889	−	0.189456i	$-0.939328\pi$
$727$	−1.53192e116	−1.96378	−0.981889	+	0.189456i	$0.939328\pi$
$728$	2.42427e113	0.00293941
$729$	−1.64605e115	−0.188789
$730$	−8.56460e115	−0.929247
$731$	−1.61683e116	−1.65963
$732$	1.77374e115	0.172262
$733$	1.27965e116	1.17592	0.587961	−	0.808889i	$-0.299931\pi$
$733$	1.27965e116	1.17592	0.587961	+	0.808889i	$0.299931\pi$
$734$	−8.41312e115	−0.731588
$735$	−1.24505e116	−1.02459
$736$	1.69277e115	0.131840
$737$	2.21520e114	0.0163298
$738$	4.21398e115	0.294042
$739$	3.22829e115	0.213242	0.106621	−	0.994300i	$-0.465997\pi$
$739$	3.22829e115	0.213242	0.106621	+	0.994300i	$0.465997\pi$
$740$	4.61458e115	0.288568
$741$	1.68347e115	0.0996707
$742$	−7.08740e114	−0.0397309
$743$	2.55795e116	1.35783	0.678913	−	0.734219i	$-0.262451\pi$
$743$	2.55795e116	1.35783	0.678913	+	0.734219i	$0.262451\pi$
$744$	1.74241e116	0.875882
$745$	−8.16823e115	−0.388865
$746$	−1.21291e116	−0.546897
$747$	−2.10616e116	−0.899513
$748$	3.57586e114	0.0144666
$749$	3.64985e115	0.139882
$750$	2.71210e116	0.984748
$751$	−3.19459e116	−1.09900	−0.549499	−	0.835494i	$-0.685182\pi$
$751$	−3.19459e116	−1.09900	−0.549499	+	0.835494i	$0.685182\pi$
$752$	1.51625e116	0.494251
$753$	6.70849e116	2.07218
$754$	−1.67006e115	−0.0488870
$755$	−1.67633e116	−0.465059
$756$	−1.13064e115	−0.0297297
$757$	−2.48299e116	−0.618860	−0.309430	−	0.950922i	$-0.600138\pi$
$757$	−2.48299e116	−0.618860	−0.309430	+	0.950922i	$0.600138\pi$
$758$	2.51211e116	0.593520
$759$	1.09285e115	0.0244777
$760$	1.62436e116	0.344930
$761$	6.23857e116	1.25605	0.628025	−	0.778194i	$-0.283864\pi$
$761$	6.23857e116	1.25605	0.628025	+	0.778194i	$0.283864\pi$
$762$	5.26405e115	0.100495
$763$	1.03992e116	0.188259
$764$	−1.34147e116	−0.230304
$765$	−3.58931e116	−0.584417
$766$	−8.38785e116	−1.29535
$767$	4.81630e115	0.0705507
$768$	5.75389e115	0.0799525
$769$	−8.17099e116	−1.07710	−0.538552	−	0.842592i	$-0.681029\pi$
$769$	−8.17099e116	−1.07710	−0.538552	+	0.842592i	$0.681029\pi$
$770$	1.51015e114	0.00188863
$771$	−1.72216e117	−2.04348
$772$	−6.18772e116	−0.696675
$773$	1.05233e117	1.12431	0.562153	−	0.827033i	$-0.309973\pi$
$773$	1.05233e117	1.12431	0.562153	+	0.827033i	$0.309973\pi$
$774$	−6.53240e116	−0.662314
$775$	6.78249e116	0.652634
$776$	1.70646e116	0.155846
$777$	1.33731e116	0.115926
$778$	−7.41915e116	−0.610493
$779$	1.00218e117	0.782849
$780$	−4.56673e115	−0.0338668
$781$	−1.79019e115	−0.0126047
$782$	−8.89571e116	−0.594713
$783$	7.78889e116	0.494452
$784$	−4.07927e116	−0.245913
$785$	1.93845e117	1.10977
$786$	7.55692e116	0.410896
$787$	−2.70781e117	−1.39843	−0.699216	−	0.714910i	$-0.746468\pi$
$787$	−2.70781e117	−1.39843	−0.699216	+	0.714910i	$0.746468\pi$
$788$	1.44957e117	0.711092
$789$	3.53892e117	1.64912
$790$	7.65964e116	0.339087
$791$	1.52098e116	0.0639700
$792$	1.44473e115	0.00577322
$793$	−4.61242e115	−0.0175132
$794$	2.74911e117	0.991885
$795$	1.33510e117	0.457766
$796$	−1.04890e117	−0.341786
$797$	−2.00940e117	−0.622306	−0.311153	−	0.950360i	$-0.600715\pi$
$797$	−2.00940e117	−0.622306	−0.311153	+	0.950360i	$0.600715\pi$
$798$	4.70741e116	0.138569
$799$	−7.96804e117	−2.22950
$800$	2.23976e116	0.0595739
$801$	1.58006e117	0.399537
$802$	−7.87217e115	−0.0189249
$803$	−1.81161e116	−0.0414082
$804$	−1.87317e117	−0.407105
$805$	−3.75682e116	−0.0776403
$806$	−4.53095e116	−0.0890471
$807$	3.61466e117	0.675599
$808$	1.02659e116	0.0182489
$809$	6.39070e117	1.08052	0.540261	−	0.841498i	$-0.318326\pi$
$809$	6.39070e117	1.08052	0.540261	+	0.841498i	$0.318326\pi$
$810$	4.40836e117	0.708980
$811$	−1.12578e118	−1.72230	−0.861151	−	0.508350i	$-0.830256\pi$
$811$	−1.12578e118	−1.72230	−0.861151	+	0.508350i	$0.830256\pi$
$812$	−4.66993e116	−0.0679659
$813$	6.23559e117	0.863397
$814$	9.76093e115	0.0128589
$815$	3.20492e117	0.401729
$816$	−3.02373e117	−0.360655
$817$	−1.55355e118	−1.76332
$818$	5.70124e117	0.615829
$819$	−5.14718e115	−0.00529141
$820$	−2.71860e117	−0.266002
$821$	−1.95190e118	−1.81785	−0.908927	−	0.416955i	$-0.863097\pi$
$821$	−1.95190e118	−1.81785	−0.908927	+	0.416955i	$0.863097\pi$
$822$	2.06617e117	0.183171
$823$	−7.18378e117	−0.606261	−0.303131	−	0.952949i	$-0.598032\pi$
$823$	−7.18378e117	−0.606261	−0.303131	+	0.952949i	$0.598032\pi$
$824$	4.18887e116	0.0336546
$825$	1.44599e116	0.0110606
$826$	1.34676e117	0.0980841
$827$	1.72528e118	1.19643	0.598214	−	0.801336i	$-0.295877\pi$
$827$	1.72528e118	1.19643	0.598214	+	0.801336i	$0.295877\pi$
$828$	−3.59408e117	−0.237333
$829$	−2.41901e118	−1.52118	−0.760589	−	0.649234i	$-0.775090\pi$
$829$	−2.41901e118	−1.52118	−0.760589	+	0.649234i	$0.775090\pi$
$830$	1.35877e118	0.813734
$831$	3.22439e118	1.83910
$832$	−1.49624e116	−0.00812842
$833$	2.14370e118	1.10928
$834$	−1.20838e118	−0.595632
$835$	4.39587e117	0.206416
$836$	3.43590e116	0.0153704
$837$	2.11316e118	0.900639
$838$	−1.24313e118	−0.504817
$839$	3.03813e118	1.17556	0.587782	−	0.809019i	$-0.300001\pi$
$839$	3.03813e118	1.17556	0.587782	+	0.809019i	$0.300001\pi$
$840$	−1.27698e117	−0.0470838
$841$	3.71065e117	0.130380
$842$	−2.77550e118	−0.929397
$843$	6.33657e118	2.02226
$844$	1.88982e118	0.574845
$845$	−2.79649e118	−0.810804
$846$	−3.21928e118	−0.889731
$847$	−4.84954e117	−0.127768
$848$	4.37429e117	0.109869
$849$	−4.76262e118	−1.14047
$850$	−1.17702e118	−0.268730
$851$	−2.42824e118	−0.528620
$852$	1.51378e118	0.314238
$853$	−6.30022e118	−1.24715	−0.623577	−	0.781762i	$-0.714321\pi$
$853$	−6.30022e118	−1.24715	−0.623577	+	0.781762i	$0.714321\pi$
$854$	−1.28975e117	−0.0243479
$855$	−3.44882e118	−0.620930
$856$	−2.25266e118	−0.386819
$857$	3.80553e118	0.623292	0.311646	−	0.950198i	$-0.399120\pi$
$857$	3.80553e118	0.623292	0.311646	+	0.950198i	$0.399120\pi$
$858$	−9.65972e115	−0.00150914
$859$	2.11862e118	0.315740	0.157870	−	0.987460i	$-0.449537\pi$
$859$	2.11862e118	0.315740	0.157870	+	0.987460i	$0.449537\pi$
$860$	4.21430e118	0.599154
$861$	−7.87855e117	−0.106861
$862$	−2.46009e117	−0.0318351
$863$	−5.31849e118	−0.656676	−0.328338	−	0.944560i	$-0.606489\pi$
$863$	−5.31849e118	−0.656676	−0.328338	+	0.944560i	$0.606489\pi$
$864$	6.97820e117	0.0822123
$865$	−6.99330e118	−0.786194
$866$	5.09863e118	0.546989
$867$	3.39534e118	0.347624
$868$	−1.26697e118	−0.123799
$869$	1.62019e117	0.0151101
$870$	8.79701e118	0.783079
$871$	4.87097e117	0.0413886
$872$	−6.41829e118	−0.520597
$873$	−3.62314e118	−0.280548
$874$	−8.54752e118	−0.631869
$875$	−1.97207e118	−0.139186
$876$	1.53189e119	1.03231
$877$	−5.34719e118	−0.344066	−0.172033	−	0.985091i	$-0.555034\pi$
$877$	−5.34719e118	−0.344066	−0.172033	+	0.985091i	$0.555034\pi$
$878$	9.52985e118	0.585542
$879$	1.99748e119	1.17201
$880$	−9.32054e116	−0.00522267
$881$	3.52621e119	1.88705	0.943527	−	0.331296i	$-0.107486\pi$
$881$	3.52621e119	1.88705	0.943527	+	0.331296i	$0.107486\pi$
$882$	8.66107e118	0.442684
$883$	3.55834e118	0.173716	0.0868578	−	0.996221i	$-0.472317\pi$
$883$	3.55834e118	0.173716	0.0868578	+	0.996221i	$0.472317\pi$
$884$	7.86289e117	0.0366662
$885$	−2.53697e119	−1.13009
$886$	−1.09481e119	−0.465877
$887$	1.29338e119	0.525801	0.262900	−	0.964823i	$-0.415321\pi$
$887$	1.29338e119	0.525801	0.262900	+	0.964823i	$0.415321\pi$
$888$	−8.25379e118	−0.320574
$889$	−3.82769e117	−0.0142042
$890$	−1.01936e119	−0.361436
$891$	9.32472e117	0.0315928
$892$	1.83047e119	0.592633
$893$	−7.65616e119	−2.36879
$894$	1.46100e119	0.431996
$895$	−4.10097e119	−1.15892
$896$	−4.18387e117	−0.0113007
$897$	2.40306e118	0.0620398
$898$	−4.35701e119	−1.07522
$899$	8.72808e119	2.05898
$900$	−4.75543e118	−0.107243
$901$	−2.29874e119	−0.495604
$902$	−5.75049e117	−0.0118533
$903$	1.22131e119	0.240698
$904$	−9.38738e118	−0.176898
$905$	−3.83485e119	−0.691005
$906$	2.99834e119	0.516641
$907$	4.19243e119	0.690830	0.345415	−	0.938450i	$-0.387738\pi$
$907$	4.19243e119	0.690830	0.345415	+	0.938450i	$0.387738\pi$
$908$	−4.29036e119	−0.676109
$909$	−2.17964e118	−0.0328509
$910$	3.32064e117	0.00478681
$911$	9.31240e119	1.28401	0.642003	−	0.766702i	$-0.278104\pi$
$911$	9.31240e119	1.28401	0.642003	+	0.766702i	$0.278104\pi$
$912$	−2.90538e119	−0.383188
$913$	2.87411e118	0.0362608
$914$	−4.74667e119	−0.572886
$915$	2.42958e119	0.280528
$916$	−8.66441e119	−0.957133
$917$	−5.49492e118	−0.0580769
$918$	−3.66712e119	−0.370849
$919$	−6.05994e119	−0.586395	−0.293197	−	0.956052i	$-0.594719\pi$
$919$	−6.05994e119	−0.586395	−0.293197	+	0.956052i	$0.594719\pi$
$920$	2.31868e119	0.214701
$921$	9.04874e119	0.801813
$922$	8.97293e119	0.760908
$923$	−3.93642e118	−0.0319472
$924$	−2.70110e117	−0.00209810
$925$	−3.21287e119	−0.238865
$926$	7.28600e119	0.518494
$927$	−8.89376e118	−0.0605838
$928$	2.88224e119	0.187948
$929$	1.78670e120	1.11536	0.557681	−	0.830055i	$-0.311691\pi$
$929$	1.78670e120	1.11536	0.557681	+	0.830055i	$0.311691\pi$
$930$	2.38666e120	1.42637
$931$	2.05979e120	1.17859
$932$	−2.10602e118	−0.0115377
$933$	−4.10686e120	−2.15429
$934$	8.88311e119	0.446187
$935$	4.89804e118	0.0235588
$936$	3.17680e118	0.0146325
$937$	9.18961e119	0.405363	0.202681	−	0.979245i	$-0.435034\pi$
$937$	9.18961e119	0.405363	0.202681	+	0.979245i	$0.435034\pi$
$938$	1.36205e119	0.0575410
$939$	−4.86020e120	−1.96652
$940$	2.07688e120	0.804885
$941$	8.77906e118	0.0325888	0.0162944	−	0.999867i	$-0.494813\pi$
$941$	8.77906e118	0.0325888	0.0162944	+	0.999867i	$0.494813\pi$
$942$	−3.46718e120	−1.23286
$943$	1.43055e120	0.487283
$944$	−8.31210e119	−0.271235
$945$	−1.54869e119	−0.0484147
$946$	8.91424e118	0.0266989
$947$	−5.56825e120	−1.59788	−0.798941	−	0.601409i	$-0.794606\pi$
$947$	−5.56825e120	−1.59788	−0.798941	+	0.601409i	$0.794606\pi$
$948$	−1.37003e120	−0.376697
$949$	−3.98352e119	−0.104951
$950$	−1.13095e120	−0.285520
$951$	−2.64935e120	−0.640957
$952$	2.19867e119	0.0509757
$953$	4.55605e119	0.101234	0.0506169	−	0.998718i	$-0.483881\pi$
$953$	4.55605e119	0.101234	0.0506169	+	0.998718i	$0.483881\pi$
$954$	−9.28744e119	−0.197782
$955$	−1.83749e120	−0.375048
$956$	3.45319e120	0.675579
$957$	1.86078e119	0.0348948
$958$	−4.47842e119	−0.0805047
$959$	−1.50239e119	−0.0258898
$960$	7.88140e119	0.130202
$961$	1.73657e121	2.75040
$962$	2.14631e119	0.0325914
$963$	4.78282e120	0.696338
$964$	1.98847e120	0.277587
$965$	−8.47564e120	−1.13453
$966$	6.71957e119	0.0862517
$967$	5.91369e120	0.727924	0.363962	−	0.931414i	$-0.381424\pi$
$967$	5.91369e120	0.727924	0.363962	+	0.931414i	$0.381424\pi$
$968$	2.99310e120	0.353321
$969$	1.52681e121	1.72851
$970$	2.33743e120	0.253795
$971$	−1.75570e121	−1.82840	−0.914202	−	0.405258i	$-0.867182\pi$
$971$	−1.75570e121	−1.82840	−0.914202	+	0.405258i	$0.867182\pi$
$972$	−5.55702e120	−0.555084
$973$	8.78658e119	0.0841880
$974$	−8.99723e120	−0.826934
$975$	3.17955e119	0.0280336
$976$	7.96024e119	0.0673300
$977$	3.67319e120	0.298067	0.149034	−	0.988832i	$-0.452384\pi$
$977$	3.67319e120	0.298067	0.149034	+	0.988832i	$0.452384\pi$
$978$	−5.73241e120	−0.446287
$979$	−2.15618e119	−0.0161060
$980$	−5.58759e120	−0.400469
$981$	1.36273e121	0.937160
$982$	5.04344e119	0.0332822
$983$	−6.03863e120	−0.382403	−0.191201	−	0.981551i	$-0.561238\pi$
$983$	−6.03863e120	−0.382403	−0.191201	+	0.981551i	$0.561238\pi$
$984$	4.86258e120	0.295505
$985$	1.98554e121	1.15801
$986$	−1.51465e121	−0.847807
$987$	6.01883e120	0.323346
$988$	7.55513e119	0.0389570
$989$	−2.21761e121	−1.09758
$990$	1.97893e119	0.00940166
$991$	−1.08669e121	−0.495591	−0.247796	−	0.968812i	$-0.579706\pi$
$991$	−1.08669e121	−0.495591	−0.247796	+	0.968812i	$0.579706\pi$
$992$	7.81964e120	0.342345
$993$	−2.06236e119	−0.00866801
$994$	−1.10072e120	−0.0444151
$995$	−1.43673e121	−0.556597
$996$	−2.43033e121	−0.903988
$997$	−3.79923e121	−1.35688	−0.678441	−	0.734655i	$-0.737344\pi$
$997$	−3.79923e121	−1.35688	−0.678441	+	0.734655i	$0.737344\pi$
$998$	1.42503e121	0.488693
$999$	−1.00100e121	−0.329635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.82.a.a.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.82.a.a.1.3	✓	3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 82 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-1.09951e12 q^{2} +2.69378e19 q^{3} +1.20893e24 q^{4} +1.65593e28 q^{5} -2.96185e31 q^{6} +2.15367e33 q^{7} -1.32923e36 q^{8} +2.82220e38 q^{9} +O(q^{10})\)	\(q-1.09951e12 q^{2} +2.69378e19 q^{3} +1.20893e24 q^{4} +1.65593e28 q^{5} -2.96185e31 q^{6} +2.15367e33 q^{7} -1.32923e36 q^{8} +2.82220e38 q^{9} -1.82071e40 q^{10} -3.85124e40 q^{11} +3.25658e43 q^{12} -8.46841e43 q^{13} -2.36798e45 q^{14} +4.46071e47 q^{15} +1.46150e48 q^{16} -7.68035e49 q^{17} -3.10304e50 q^{18} -7.37973e51 q^{19} +2.00189e52 q^{20} +5.80152e52 q^{21} +4.23448e52 q^{22} -1.05342e55 q^{23} -3.58065e55 q^{24} -1.39380e56 q^{25} +9.31111e55 q^{26} -4.34255e57 q^{27} +2.60363e57 q^{28} -1.79362e59 q^{29} -4.90461e59 q^{30} -4.86617e60 q^{31} -1.60694e60 q^{32} -1.03744e60 q^{33} +8.44463e61 q^{34} +3.56632e61 q^{35} +3.41183e62 q^{36} +2.30511e63 q^{37} +8.11410e63 q^{38} -2.28121e63 q^{39} -2.20111e64 q^{40} -1.35802e65 q^{41} -6.37884e64 q^{42} +2.10516e66 q^{43} -4.65586e64 q^{44} +4.67337e66 q^{45} +1.15824e67 q^{46} +1.03746e68 q^{47} +3.93697e67 q^{48} -2.79115e68 q^{49} +1.53250e68 q^{50} -2.06892e69 q^{51} -1.02377e68 q^{52} +2.99301e69 q^{53} +4.77468e69 q^{54} -6.37737e68 q^{55} -2.86272e69 q^{56} -1.98794e71 q^{57} +1.97211e71 q^{58} -5.68737e71 q^{59} +5.39267e71 q^{60} +5.44662e71 q^{61} +5.35041e72 q^{62} +6.07809e71 q^{63} +1.76685e72 q^{64} -1.40231e72 q^{65} +1.14068e72 q^{66} -5.75193e73 q^{67} -9.28497e73 q^{68} -2.83767e74 q^{69} -3.92121e73 q^{70} +4.64836e74 q^{71} -3.75135e74 q^{72} +4.70398e75 q^{73} -2.53449e75 q^{74} -3.75460e75 q^{75} -8.92155e75 q^{76} -8.29429e73 q^{77} +2.50821e75 q^{78} -4.20695e76 q^{79} +2.42014e76 q^{80} -2.42123e77 q^{81} +1.49315e77 q^{82} -7.46283e77 q^{83} +7.01361e76 q^{84} -1.27181e78 q^{85} -2.31465e78 q^{86} -4.83163e78 q^{87} +5.11917e76 q^{88} +5.59868e78 q^{89} -5.13842e78 q^{90} -1.82382e77 q^{91} -1.27350e79 q^{92} -1.31084e80 q^{93} -1.14070e80 q^{94} -1.22203e80 q^{95} -4.32874e79 q^{96} -1.28380e80 q^{97} +3.06890e80 q^{98} -1.08690e79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3298534883328 q^{2} + 12\!\cdots\!88 q^{3}+ \cdots - 11\!\cdots\!61 q^{9}+O(q^{10}) \) 3 * q - 3298534883328 * q^2 + 12604360672390214988 * q^3 + 3626777458843887524118528 * q^4 - 20983063979496004028435775150 * q^5 - 13858641119975563142110472306688 * q^6 - 552766607526265634132821897861224 * q^7 - 3987683987354747618711421180841033728 * q^8 - 117787926384549736709174105715608001561 * q^9	\( 3 q - 3298534883328 q^{2} + 12\!\cdots\!88 q^{3}+ \cdots - 54\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q - 3298534883328 * q^2 + 12604360672390214988 * q^3 + 3626777458843887524118528 * q^4 - 20983063979496004028435775150 * q^5 - 13858641119975563142110472306688 * q^6 - 552766607526265634132821897861224 * q^7 - 3987683987354747618711421180841033728 * q^8 - 117787926384549736709174105715608001561 * q^9 + 23071122831823603677392872526248830566400 * q^10 + 1280703554832406814772038626747672506628836 * q^11 + 15237737056587739139724154617942692371365888 * q^12 - 203053213213228262252289604826178427009253142 * q^13 + 607773312421421660059947871105692013191757824 * q^14 + 258521148569780014125709880112718518230943462600 * q^15 + 4384504911992708754611054498148849058967797628928 * q^16 + 13707915509793004617532214813228047814831020392246 * q^17 + 129509194671435939545936242487957259125865458958336 * q^18 + 4795253838113603708371668796877035230312394724136060 * q^19 - 25366967819438409173828536843196320983278888052326400 * q^20 - 519561242096418127707719252363204767758340529227929504 * q^21 - 1408148450272289287785839512865281090582833620620148736 * q^22 - 30160326897246150414676624400786632753521325735600143672 * q^23 - 16754069074711460085681771147599677065524525007359705088 * q^24 + 280923310225904394201067316034822697319282719805054788125 * q^25 + 223259368985223798004862759385395227818359125574462472192 * q^26 - 625732627028059848123157770721822016131959245230905824520 * q^27 - 668253824059288729544577409501125262363392110293023719424 * q^28 + 21426901075097725646400095068279905894982750657375381771290 * q^29 - 284247008878479957653591543774260948340603378455551777177600 * q^30 - 3860912612203425210987573972171722804903899142052351141235104 * q^31 - 4820814132776970826625886277023487807566608981348378505904128 * q^32 + 8168133227004704222278627528558820550230283855880259452058256 * q^33 - 15072012495588383375840729817410870669983615065857449468624896 * q^34 + 796090962825005181029369759037285415121243766103175607760525200 * q^35 - 142396865445149395381460288303846938058595761644053336724340736 * q^36 - 962488012673974734154716715779071426226206694726253291815438414 * q^37 - 5272437353143400002601123557255816511393680180123473805899202560 * q^38 + 36399394236397559852249384794748301006956973683053277402364624168 * q^39 + 27891276078892134524892145882383175355059555080188678327658086400 * q^40 + 315729621076478275418732734280056694539166286076338101303285961726 * q^41 + 571263627026753110335028642726281008965977037891914073465216303104 * q^42 + 909989621545075850999251035125487926201005781380826452677677267268 * q^43 + 1548275594709136585239376117673204105702523898770639375302588891136 * q^44 + 18726742363164362961210285095677755369767013044398376551081888987050 * q^45 + 33161630121047390334190832695565871193686149855479234561060185833472 * q^46 + 163450219955907571723000348929623433672676106405825241782972369095056 * q^47 + 18421293760207539636329616625228032485526805502091287721258189324288 * q^48 + 84812568823216657456965826417651253151115010649007120996812564086571 * q^49 - 308878446106706366749766699689999329829075494845604303484181544960000 * q^50 - 772668114968744140818526844449587165078736038177006698750562111292584 * q^51 - 245476272209186027435979673735318928259666399417721223896051054804992 * q^52 - 9024153738612400417538776640914507257088387728526558953119104505855262 * q^53 + 688000299296174776837040539007613919441804640939925628100944613867520 * q^54 - 47582265107476429230871013599303461307138199609079326757133914456997800 * q^55 + 734752849858965262954329330674619565324848328021238234080860149121024 * q^56 - 216617828008754172617635723539247550424408451696387193425209932869178640 * q^57 - 23559126879276024743748830323085589194984582286732740071220506043351040 * q^58 + 173083732030804573367247232387536299255274355093160491876857331837886580 * q^59 + 312532891422436622416291987827866414001366266719668703388792623045017600 * q^60 + 3682273674088882162766525675671573547949650573236627272535804184395569786 * q^61 + 4245118310944676295775623698651741067018146620927310456707340474152648704 * q^62 + 9705799226705237716648578379561491511812293162477695944136214255847932088 * q^63 + 5300541194335152988749892502228755547482451690626856874364818603877859328 * q^64 - 44151816740799940959026445433284813207449285152198691890526681479556208900 * q^65 - 8980957460315174060246993877740912710546379374029437859477782888139718656 * q^66 - 45459418332173895471620473386340508364570599523844133604129556114327113204 * q^67 + 16571852992884595424446978834061245676151100304309921706423425641318711296 * q^68 - 381439114954192945191386382600395171642161070159132929461545170926869452512 * q^69 - 875311270393484550029235899022474573456262617665795224851553160648667955200 * q^70 - 663360175811055431998373202697213154081787807552643411579641705598806018984 * q^71 + 156567009315796258559371618044865000947560071154027590172344122439825883136 * q^72 + 2875774114961093540042489135457037118623579706430287895576809293063724624478 * q^73 + 1058266761530049278342349439594403567843746419708291471605671028744219787264 * q^74 + 10375259783421120323437883415423908867929791104823014714965332849751129672500 * q^75 + 5797106176501684687211043996484842348086442945206709564991930078125946306560 * q^76 - 30868237386271625806706807506325457951957257249868500448028258335470666673888 * q^77 - 40021557206921833579421107130768288096369682034648702942405604830436149690368 * q^78 - 161970107563907182248111919540000364532077003546202035586261450715135988178960 * q^79 - 30666782362252501426187331709976780976797178163640583917249396059633247846400 * q^80 - 299082334358425446166064721339785324689357638880155921207411342332373570690837 * q^81 - 347148389606898305991152076671360411666324733389734989961305134834963894501376 * q^82 - 1551644647158271447807906137086282123739475283733105818013885940684527133830852 * q^83 - 628111000441407059444538271675557174582977063534777274464062826341812041416704 * q^84 - 5282756950234547173621607909805842177285468672028854473129976993442919157706300 * q^85 - 1000544170044292549089574941787678182163502426454419285939792765992630084435968 * q^86 - 5562608887098194592587989531458685107064636512216475421164235996460442752999960 * q^87 - 1702347019384497220096060609753563967878468415968847544815229284239878217793536 * q^88 - 8621118410314024378389076217632288587702101272330766532155222306149385764271730 * q^89 - 20590270978664625661714404112581680708566453290315884360291836574024273284300800 * q^90 - 58818429441931738974494712027943381122004094832556221941814570900274994185170864 * q^91 - 36461597914098448064383011084918512893601406801264240344797801790065853985718272 * q^92 - 240404744478319194110331229870238328818799091224439431760300521618055178727456384 * q^93 - 179715417404065173132559582630226240824158475728290692441384718063336098633875456 * q^94 - 433274751899148074134278380777280708876242908949531972946158534560456001105919000 * q^95 - 20254426688025663721128815841682505745347385078485744734548553502718284412223488 * q^96 - 533678667972555021629681531571524475991025351825819428841423661701166265694104794 * q^97 - 93252405602678975820826304474476792170868714668077393805420770046393998792196096 * q^98 - 542180767943235177708947795218783507805362281402610542195265148391971885481633132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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