LMFDB - Embedded newform 2.74.a.b.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,74,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2.1"); S:= CuspForms(chi, 74); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 74, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 74 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$67.4967947474$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2 x^{3} + \cdots + 21\!\cdots\!44 $ x^4 - 2x^3 - 50110216549679282411939889123x^2 - 1553419798812705152849518883586567702011976*x + 212476488708962349290223416738491633360102623610323343644
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{14}\cdot 5^{5}\cdot 7^{2}\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-9.26366e13$ 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)

$f(q)$	$=$	\(q+6.87195e10 q^{2} +2.54129e17 q^{3} +4.72237e21 q^{4} +6.33389e25 q^{5} +1.74636e28 q^{6} +7.98841e30 q^{7} +3.24519e32 q^{8} -3.00372e33 q^{9} +4.35262e36 q^{10} +7.13848e37 q^{11} +1.20009e39 q^{12} +4.11677e40 q^{13} +5.48959e41 q^{14} +1.60963e43 q^{15} +2.23007e43 q^{16} -4.48307e43 q^{17} -2.06414e44 q^{18} -2.90679e46 q^{19} +2.99110e47 q^{20} +2.03009e48 q^{21} +4.90553e48 q^{22} -7.33502e49 q^{23} +8.24695e49 q^{24} +2.95303e51 q^{25} +2.82902e51 q^{26} -1.79387e52 q^{27} +3.77242e52 q^{28} -3.82926e53 q^{29} +1.10613e54 q^{30} -2.83221e54 q^{31} +1.53250e54 q^{32} +1.81409e55 q^{33} -3.08074e54 q^{34} +5.05978e56 q^{35} -1.41847e55 q^{36} +1.25071e56 q^{37} -1.99753e57 q^{38} +1.04619e58 q^{39} +2.05547e58 q^{40} -6.14755e58 q^{41} +1.39506e59 q^{42} -2.13671e59 q^{43} +3.37105e59 q^{44} -1.90252e59 q^{45} -5.04058e60 q^{46} -1.57986e61 q^{47} +5.66726e60 q^{48} +1.45930e61 q^{49} +2.02931e62 q^{50} -1.13928e61 q^{51} +1.94409e62 q^{52} -9.46633e62 q^{53} -1.23274e63 q^{54} +4.52144e63 q^{55} +2.59239e63 q^{56} -7.38698e63 q^{57} -2.63145e64 q^{58} +4.99698e63 q^{59} +7.60124e64 q^{60} +1.28364e65 q^{61} -1.94628e65 q^{62} -2.39949e64 q^{63} +1.05312e65 q^{64} +2.60752e66 q^{65} +1.24664e66 q^{66} +4.85072e66 q^{67} -2.11707e65 q^{68} -1.86404e67 q^{69} +3.47705e67 q^{70} +9.31876e66 q^{71} -9.74762e65 q^{72} +1.98507e68 q^{73} +8.59483e66 q^{74} +7.50450e68 q^{75} -1.37269e68 q^{76} +5.70251e68 q^{77} +7.18937e68 q^{78} +2.37050e68 q^{79} +1.41251e69 q^{80} -4.35573e69 q^{81} -4.22457e69 q^{82} +1.57736e70 q^{83} +9.58681e69 q^{84} -2.83953e69 q^{85} -1.46833e70 q^{86} -9.73125e70 q^{87} +2.31657e70 q^{88} -2.10023e71 q^{89} -1.30740e70 q^{90} +3.28865e71 q^{91} -3.46386e71 q^{92} -7.19747e71 q^{93} -1.08567e72 q^{94} -1.84113e72 q^{95} +3.89451e71 q^{96} +3.81990e72 q^{97} +1.00282e72 q^{98} -2.14420e71 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 274877906944 q^{2} + 30\!\cdots\!76 q^{3} + 18\!\cdots\!84 q^{4} - 78\!\cdots\!60 q^{5} + 20\!\cdots\!36 q^{6} + 36\!\cdots\!12 q^{7} + 12\!\cdots\!24 q^{8} + 12\!\cdots\!52 q^{9} - 53\!\cdots\!60 q^{10}+ \cdots + 28\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q + 274877906944 * q^2 + 305066325723244176 * q^3 + 18889465931478580854784 * q^4 - 7846962293700032321337960 * q^5 + 20963998273475476527079489536 * q^6 + 3636364966558861993065799361312 * q^7 + 1298074214633706907132624082305024 * q^8 + 122378175810775448230425774569321652 * q^9 - 539239142790188570468632018613698560 * q^10 + 52775218805667734867535256611889929648 * q^11 + 1440634991647642175069153055191907434496 * q^12 + 1355651207894098513401138234675081313976 * q^13 + 249889097723047134707119792526923642437632 * q^14 - 7830535738800097006518186191927965043233440 * q^15 + 89202980794122492566142873090593446023921664 * q^16 + 954348456154904658262187917015529592600353352 * q^17 + 8409764205622701352790716382891279683915087872 * q^18 + 95454725025342640211946932212410556121580424400 * q^19 - 37056231728110945597372254620868777164836700160 * q^20 + 663014063083061571146153755002330860310806732928 * q^21 + 3626685420953393611175405108400560201438412668928 * q^22 - 67417603669907011086030463893163498895122860076704 * q^23 + 98999682793597700758917102567483606960313315885056 * q^24 + 3460631286066960520802994294848553614203197326799100 * q^25 + 93159641643008802343361703153674358874682043662336 * q^26 + 12084377134756095104629255763677919783130973382555040 * q^27 + 17172248037558968144537376756119075900141234554929152 * q^28 - 408828336209279227379368505274385966779755922402879240 * q^29 - 538110318532889838793969736377110224776301614297251840 * q^30 + 3799789752719913567257037059011407543542506417455406208 * q^31 + 6129982163463555433433388108601236734474956488734408704 * q^32 + 62216718136234720076912175436040395811344879605468165312 * q^33 + 65582326530774486675746452751808984389419539918143619072 * q^34 + 431767153301184553170750885645944283201771950341035990720 * q^35 + 577914595683534746006577363150871362656072314419299745792 * q^36 + 6801183386761815205425784377566670372797473237706983459352 * q^37 + 6559598755720310574473705317437316221877768362108806758400 * q^38 + 11327031655330197070885706025461449402448174139265298802144 * q^39 - 2546484854163745203205584274150660432487763653884127477760 * q^40 + 56874804657516327155642316307646742627510460774170204545448 * q^41 + 45561979483677286074033721822761719180903349012837861163008 * q^42 - 195612042326640270143679332399870892198183174704527897687504 * q^43 + 249223924413997099203419280962107854932114473139165366059008 * q^44 - 7974393496061748311007765969419683838885297239373320672939080 * q^45 - 4632902446991043071609764558093537051767757086902843703558144 * q^46 - 26837344299723692260252514346441012876376468762050649660269888 * q^47 + 6803206398606016687045493374438715598570618586234125042057216 * q^48 + 49288467772056748491478921994228369389621400119046767962459108 * q^49 + 237812771154752254447551810483985904734485337875788141795737600 * q^50 + 462279018098899407813413748964859585061118118125593850879008288 * q^51 + 6401881826620840209677866843902262937608427838850834991415296 * q^52 + 45487338963145722322030598089193311856717264520906215815881816 * q^53 + 830432073380921814576773627357058722333743090603526299519549440 * q^54 - 2050760578084075114386836605813651219506186672252469754486193120 * q^55 + 1180067899521855165636701347474591981965573827111773174992207872 * q^56 - 3592025896576963719316420752340210472238227670222328115746257600 * q^57 - 28094469339151150293224568244574259740806305945322881152597360640 * q^58 - 36211351257280450133792917437500801540590596428487702560293076880 * q^59 - 36978659515822472927852993596054879014422789587819242807613194240 * q^60 + 355926993234389260836197952322967108098379440839658027389943954808 * q^61 + 261119563513727293109050729509024279847084176781457491228085977088 * q^62 + 1354878537917418371717449932688191098150383285998373405919969463456 * q^63 + 421249166674228746791672110734681729275580381602196445017243910144 * q^64 + 5535868819575966258563337770064603238403854822937797912179994113360 * q^65 + 4275500314553251124960838370592128635913946298920690444546586181632 * q^66 + 2491990477133118795215059534264173871640752538756993508607055683472 * q^67 + 4506783162324312925176300335312460684664503237948693775125149908992 * q^68 + 36011984923282423612732885710686669353728819466689401794442606346624 * q^69 + 29670812846649697502859970521797864502236363135438170030421751889920 * q^70 + 61369373660787623297444370825513800920470177886238250167413906103328 * q^71 + 39713988613469511996446662010030528264172580579870746230364057894912 * q^72 + 456671534259044615009379581820843089057568686566115963985790726852136 * q^73 + 467373763523848250382388250508745044972436409398187647819676565635072 * q^74 + 2274484745358414989035084574628142288008132133113498093192382898732400 * q^75 + 450772194091216429445240588005353147247604717195532969934588372582400 * q^76 + 2937010629095569814915333560530816478733805597591112398546851047158144 * q^77 + 778387688326399048011025618131633095876378404208918525166023274921984 * q^78 + 2026656030798125727242892609149209096074932883431594515097100420626240 * q^79 - 174993106694281841226317741152783755749378573017756654247586677391360 * q^80 - 1690644062388676955190899758084885673044542109854601078388778076183836 * q^81 + 3908406815526737691512327206640483748897384622767229920965275290697728 * q^82 + 15812009999547814415856750888845542429811781646082575448908590281393616 * q^83 + 3130995389174670552096177120478769476523452667952199965531326159781888 * q^84 - 47381303711757475901026713604519693996172406037229330915853699493216080 * q^85 - 13442357191947003357179327260296938825816612575574428538999419325906944 * q^86 - 154442588212957708624899011736533281049174301414639814817610904676124960 * q^87 + 17126537675822296091480855409729418434530303396175771263348924259237888 * q^88 - 244126894674274014119641875856417639495708996405247140614177242434617240 * q^89 - 547996148336325020677785466250868450986753355813559933203104972805242880 * q^90 - 956695923071478195873919348809058005807314877434919486549850807547281472 * q^91 - 318370631926158457559861197620346139940908410808319098178907957031337984 * q^92 - 2677792907975102091334715599122289169140096674655183648095758982803701248 * q^93 - 1844248257260884481506445917115759428754429189071570338982602871897325568 * q^94 - 4616055418633200363736062249001551807751077321632189313148700192365581600 * q^95 + 467512783839212506555050574518383453633693938789845165676965876492926976 * q^96 + 5819977544840824809887571543683857252285947538686838060303213522914493832 * q^97 + 3387077714414939478831988874216735156541302325328582001492198793557311488 * q^98 + 28045365238060746865970778341472050511805413521238694500165502185235671024 * q^99

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 $

$2$	6.87195e10	0.707107
$2$	6.87195e10	0.707107
$3$	2.54129e17	0.977526	0.488763	−	0.872417i	$-0.337448\pi$
$3$	2.54129e17	0.977526	0.488763	+	0.872417i	$0.337448\pi$
$4$	4.72237e21	0.500000
$5$	6.33389e25	1.94655	0.973275	−	0.229641i	$-0.0737554\pi$
$5$	6.33389e25	1.94655	0.973275	+	0.229641i	$0.0737554\pi$
$6$	1.74636e28	0.691215
$7$	7.98841e30	1.13863	0.569314	−	0.822120i	$-0.307209\pi$
$7$	7.98841e30	1.13863	0.569314	+	0.822120i	$0.307209\pi$
$8$	3.24519e32	0.353553
$9$	−3.00372e33	−0.0444434
$10$	4.35262e36	1.37642
$11$	7.13848e37	0.696262	0.348131	−	0.937446i	$-0.386816\pi$
$11$	7.13848e37	0.696262	0.348131	+	0.937446i	$0.386816\pi$
$12$	1.20009e39	0.488763
$13$	4.11677e40	0.902868	0.451434	−	0.892304i	$-0.350913\pi$
$13$	4.11677e40	0.902868	0.451434	+	0.892304i	$0.350913\pi$
$14$	5.48959e41	0.805132
$15$	1.60963e43	1.90280
$16$	2.23007e43	0.250000
$17$	−4.48307e43	−0.0549781	−0.0274890	−	0.999622i	$-0.508751\pi$
$17$	−4.48307e43	−0.0549781	−0.0274890	+	0.999622i	$0.508751\pi$
$18$	−2.06414e44	−0.0314263
$19$	−2.90679e46	−0.615045	−0.307522	−	0.951541i	$-0.599500\pi$
$19$	−2.90679e46	−0.615045	−0.307522	+	0.951541i	$0.599500\pi$
$20$	2.99110e47	0.973275
$21$	2.03009e48	1.11304
$22$	4.90553e48	0.492332
$23$	−7.33502e49	−1.45323	−0.726616	−	0.687044i	$-0.758908\pi$
$23$	−7.33502e49	−1.45323	−0.726616	+	0.687044i	$0.758908\pi$
$24$	8.24695e49	0.345608
$25$	2.95303e51	2.78906
$26$	2.82902e51	0.638424
$27$	−1.79387e52	−1.02097
$28$	3.77242e52	0.569314
$29$	−3.82926e53	−1.60542	−0.802708	−	0.596372i	$-0.796608\pi$
$29$	−3.82926e53	−1.60542	−0.802708	+	0.596372i	$0.796608\pi$
$30$	1.10613e54	1.34549
$31$	−2.83221e54	−1.04094	−0.520468	−	0.853881i	$-0.674243\pi$
$31$	−2.83221e54	−1.04094	−0.520468	+	0.853881i	$0.674243\pi$
$32$	1.53250e54	0.176777
$33$	1.81409e55	0.680614
$34$	−3.08074e54	−0.0388754
$35$	5.05978e56	2.21640
$36$	−1.41847e55	−0.0222217
$37$	1.25071e56	0.0720767	0.0360383	−	0.999350i	$-0.488526\pi$
$37$	1.25071e56	0.0720767	0.0360383	+	0.999350i	$0.488526\pi$
$38$	−1.99753e57	−0.434902
$39$	1.04619e58	0.882577
$40$	2.05547e58	0.688210
$41$	−6.14755e58	−0.835779	−0.417890	−	0.908498i	$-0.637230\pi$
$41$	−6.14755e58	−0.835779	−0.417890	+	0.908498i	$0.637230\pi$
$42$	1.39506e59	0.787037
$43$	−2.13671e59	−0.510677	−0.255338	−	0.966852i	$-0.582187\pi$
$43$	−2.13671e59	−0.510677	−0.255338	+	0.966852i	$0.582187\pi$
$44$	3.37105e59	0.348131
$45$	−1.90252e59	−0.0865114
$46$	−5.04058e60	−1.02759
$47$	−1.57986e61	−1.46908	−0.734540	−	0.678565i	$-0.762602\pi$
$47$	−1.57986e61	−1.46908	−0.734540	+	0.678565i	$0.762602\pi$
$48$	5.66726e60	0.244381
$49$	1.45930e61	0.296474
$50$	2.02931e62	1.97216
$51$	−1.13928e61	−0.0537425
$52$	1.94409e62	0.451434
$53$	−9.46633e62	−1.09676	−0.548381	−	0.836229i	$-0.684756\pi$
$53$	−9.46633e62	−1.09676	−0.548381	+	0.836229i	$0.684756\pi$
$54$	−1.23274e63	−0.721935
$55$	4.52144e63	1.35531
$56$	2.59239e63	0.402566
$57$	−7.38698e63	−0.601222
$58$	−2.63145e64	−1.13520
$59$	4.99698e63	0.115507	0.0577536	−	0.998331i	$-0.481606\pi$
$59$	4.99698e63	0.115507	0.0577536	+	0.998331i	$0.481606\pi$
$60$	7.60124e64	0.951402
$61$	1.28364e65	0.878832	0.439416	−	0.898284i	$-0.355185\pi$
$61$	1.28364e65	0.878832	0.439416	+	0.898284i	$0.355185\pi$
$62$	−1.94628e65	−0.736053
$63$	−2.39949e64	−0.0506045
$64$	1.05312e65	0.125000
$65$	2.60752e66	1.75748
$66$	1.24664e66	0.481267
$67$	4.85072e66	1.08162	0.540811	−	0.841144i	$-0.318117\pi$
$67$	4.85072e66	1.08162	0.540811	+	0.841144i	$0.318117\pi$
$68$	−2.11707e65	−0.0274890
$69$	−1.86404e67	−1.42057
$70$	3.47705e67	1.56723
$71$	9.31876e66	0.250281	0.125141	−	0.992139i	$-0.460062\pi$
$71$	9.31876e66	0.250281	0.125141	+	0.992139i	$0.460062\pi$
$72$	−9.74762e65	−0.0157131
$73$	1.98507e68	1.93416	0.967078	−	0.254482i	$-0.0819049\pi$
$73$	1.98507e68	1.93416	0.967078	+	0.254482i	$0.0819049\pi$
$74$	8.59483e66	0.0509659
$75$	7.50450e68	2.72638
$76$	−1.37269e68	−0.307522
$77$	5.70251e68	0.792784
$78$	7.18937e68	0.624076
$79$	2.37050e68	0.129256	0.0646280	−	0.997909i	$-0.479414\pi$
$79$	2.37050e68	0.129256	0.0646280	+	0.997909i	$0.479414\pi$
$80$	1.41251e69	0.486638
$81$	−4.35573e69	−0.953581
$82$	−4.22457e69	−0.590985
$83$	1.57736e70	1.41768	0.708842	−	0.705367i	$-0.249218\pi$
$83$	1.57736e70	1.41768	0.708842	+	0.705367i	$0.249218\pi$
$84$	9.58681e69	0.556519
$85$	−2.83953e69	−0.107018
$86$	−1.46833e70	−0.361103
$87$	−9.73125e70	−1.56934
$88$	2.31657e70	0.246166
$89$	−2.10023e71	−1.47752	−0.738759	−	0.673970i	$-0.764588\pi$
$89$	−2.10023e71	−1.47752	−0.738759	+	0.673970i	$0.764588\pi$
$90$	−1.30740e70	−0.0611728
$91$	3.28865e71	1.02803
$92$	−3.46386e71	−0.726616
$93$	−7.19747e71	−1.01754
$94$	−1.08567e72	−1.03880
$95$	−1.84113e72	−1.19722
$96$	3.89451e71	0.172804
$97$	3.81990e72	1.16114	0.580569	−	0.814211i	$-0.302830\pi$
$97$	3.81990e72	1.16114	0.580569	+	0.814211i	$0.302830\pi$
$98$	1.00282e72	0.209639
$99$	−2.14420e71	−0.0309443
$100$	1.39453e73	1.39453
$101$	9.50398e72	0.660960	0.330480	−	0.943813i	$-0.392789\pi$
$101$	9.50398e72	0.660960	0.330480	+	0.943813i	$0.392789\pi$
$102$	−7.82905e71	−0.0380017
$103$	−7.80324e72	−0.265287	−0.132644	−	0.991164i	$-0.542347\pi$
$103$	−7.80324e72	−0.265287	−0.132644	+	0.991164i	$0.542347\pi$
$104$	1.33597e73	0.319212
$105$	1.28583e74	2.16659
$106$	−6.50521e73	−0.775528
$107$	−1.01149e74	−0.855963	−0.427982	−	0.903787i	$-0.640775\pi$
$107$	−1.01149e74	−0.855963	−0.427982	+	0.903787i	$0.640775\pi$
$108$	−8.47130e73	−0.510485
$109$	5.05336e73	0.217527	0.108764	−	0.994068i	$-0.465311\pi$
$109$	5.05336e73	0.217527	0.108764	+	0.994068i	$0.465311\pi$
$110$	3.10711e74	0.958348
$111$	3.17842e73	0.0704568
$112$	1.78148e74	0.284657
$113$	3.71187e74	0.428775	0.214387	−	0.976749i	$-0.431225\pi$
$113$	3.71187e74	0.428775	0.214387	+	0.976749i	$0.431225\pi$
$114$	−5.07630e74	−0.425128
$115$	−4.64592e75	−2.82879
$116$	−1.80832e75	−0.802708
$117$	−1.23656e74	−0.0401266
$118$	3.43390e74	0.0816759
$119$	−3.58126e74	−0.0625996
$120$	5.22353e75	0.672743
$121$	−5.41574e75	−0.515219
$122$	8.82114e75	0.621428
$123$	−1.56227e76	−0.816996
$124$	−1.33748e76	−0.520468
$125$	1.19979e77	3.48249
$126$	−1.64892e75	−0.0357828
$127$	−2.75505e76	−0.448016	−0.224008	−	0.974587i	$-0.571914\pi$
$127$	−2.75505e76	−0.448016	−0.224008	+	0.974587i	$0.571914\pi$
$128$	7.23701e75	0.0883883
$129$	−5.42999e76	−0.499200
$130$	1.79187e77	1.24273
$131$	2.79084e76	0.146330	0.0731649	−	0.997320i	$-0.476690\pi$
$131$	2.79084e76	0.146330	0.0731649	+	0.997320i	$0.476690\pi$
$132$	8.56682e76	0.340307
$133$	−2.32206e77	−0.700307
$134$	3.33339e77	0.764822
$135$	−1.13622e78	−1.98737
$136$	−1.45484e76	−0.0194377
$137$	−2.06327e76	−0.0210987	−0.0105494	−	0.999944i	$-0.503358\pi$
$137$	−2.06327e76	−0.0210987	−0.0105494	+	0.999944i	$0.503358\pi$
$138$	−1.28096e78	−1.00450
$139$	6.56975e77	0.395830	0.197915	−	0.980219i	$-0.436583\pi$
$139$	6.56975e77	0.395830	0.197915	+	0.980219i	$0.436583\pi$
$140$	2.38941e78	1.10820
$141$	−4.01487e78	−1.43606
$142$	6.40381e77	0.176976
$143$	2.93875e78	0.628633
$144$	−6.69852e76	−0.0111109
$145$	−2.42541e79	−3.12502
$146$	1.36413e79	1.36765
$147$	3.70849e78	0.289811
$148$	5.90632e77	0.0360383
$149$	4.27961e78	0.204224	0.102112	−	0.994773i	$-0.467440\pi$
$149$	4.27961e78	0.204224	0.102112	+	0.994773i	$0.467440\pi$
$150$	5.15706e79	1.92784
$151$	5.40575e79	1.58561	0.792807	−	0.609472i	$-0.208619\pi$
$151$	5.40575e79	1.58561	0.792807	+	0.609472i	$0.208619\pi$
$152$	−9.43306e78	−0.217451
$153$	1.34659e77	0.00244341
$154$	3.91874e79	0.560583
$155$	−1.79389e80	−2.02624
$156$	4.94050e79	0.441289
$157$	7.32470e79	0.518147	0.259073	−	0.965858i	$-0.416583\pi$
$157$	7.32470e79	0.518147	0.259073	+	0.965858i	$0.416583\pi$
$158$	1.62899e79	0.0913978
$159$	−2.40567e80	−1.07211
$160$	9.70667e79	0.344105
$161$	−5.85951e80	−1.65469
$162$	−2.99323e80	−0.674284
$163$	6.71357e79	0.120811	0.0604055	−	0.998174i	$-0.480761\pi$
$163$	6.71357e79	0.120811	0.0604055	+	0.998174i	$0.480761\pi$
$164$	−2.90310e80	−0.417890
$165$	1.14903e81	1.32485
$166$	1.08395e81	1.00245
$167$	−2.11352e81	−1.56984	−0.784919	−	0.619598i	$-0.787296\pi$
$167$	−2.11352e81	−1.56984	−0.784919	+	0.619598i	$0.787296\pi$
$168$	6.58800e80	0.393518
$169$	−3.84268e80	−0.184829
$170$	−1.95131e80	−0.0756729
$171$	8.73117e79	0.0273347
$172$	−1.00903e81	−0.255338
$173$	4.41850e81	0.904883	0.452441	−	0.891794i	$-0.350553\pi$
$173$	4.41850e81	0.904883	0.452441	+	0.891794i	$0.350553\pi$
$174$	−6.68726e81	−1.10969
$175$	2.35900e82	3.17570
$176$	1.59193e81	0.174066
$177$	1.26988e81	0.112911
$178$	−1.44327e82	−1.04476
$179$	4.89767e81	0.288971	0.144485	−	0.989507i	$-0.453847\pi$
$179$	4.89767e81	0.288971	0.144485	+	0.989507i	$0.453847\pi$
$180$	−8.98441e80	−0.0432557
$181$	−4.10029e82	−1.61267	−0.806337	−	0.591456i	$-0.798553\pi$
$181$	−4.10029e82	−1.61267	−0.806337	+	0.591456i	$0.798553\pi$
$182$	2.25994e82	0.726928
$183$	3.26211e82	0.859081
$184$	−2.38035e82	−0.513795
$185$	7.92188e81	0.140301
$186$	−4.94607e82	−0.719511
$187$	−3.20023e81	−0.0382792
$188$	−7.46066e82	−0.734540
$189$	−1.43302e83	−1.16251
$190$	−1.26521e83	−0.846559
$191$	1.02818e83	0.568003	0.284002	−	0.958824i	$-0.408338\pi$
$191$	1.02818e83	0.568003	0.284002	+	0.958824i	$0.408338\pi$
$192$	2.67629e82	0.122191
$193$	−3.17855e82	−0.120057	−0.0600284	−	0.998197i	$-0.519119\pi$
$193$	−3.17855e82	−0.120057	−0.0600284	+	0.998197i	$0.519119\pi$
$194$	2.62501e83	0.821048
$195$	6.62646e83	1.71798
$196$	6.89134e82	0.148237
$197$	−4.23384e83	−0.756340	−0.378170	−	0.925736i	$-0.623446\pi$
$197$	−4.23384e83	−0.756340	−0.378170	+	0.925736i	$0.623446\pi$
$198$	−1.47348e82	−0.0218809
$199$	5.68804e83	0.702790	0.351395	−	0.936227i	$-0.385707\pi$
$199$	5.68804e83	0.702790	0.351395	+	0.936227i	$0.385707\pi$
$200$	9.58313e83	0.986081
$201$	1.23271e84	1.05731
$202$	6.53108e83	0.467369
$203$	−3.05897e84	−1.82797
$204$	−5.38008e82	−0.0268712
$205$	−3.89380e84	−1.62689
$206$	−5.36235e83	−0.187586
$207$	2.20323e83	0.0645866
$208$	9.18071e83	0.225717
$209$	−2.07500e84	−0.428232
$210$	8.83619e84	1.53201
$211$	−8.12038e83	−0.118377	−0.0591884	−	0.998247i	$-0.518851\pi$
$211$	−8.12038e83	−0.118377	−0.0591884	+	0.998247i	$0.518851\pi$
$212$	−4.47035e84	−0.548381
$213$	2.36817e84	0.244657
$214$	−6.95093e84	−0.605257
$215$	−1.35337e85	−0.994058
$216$	−5.82143e84	−0.360968
$217$	−2.26249e85	−1.18524
$218$	3.47264e84	0.153815
$219$	5.04463e85	1.89069
$220$	2.13519e85	0.677655
$221$	−1.84558e84	−0.0496380
$222$	2.18420e84	0.0498205
$223$	1.71384e85	0.331774	0.165887	−	0.986145i	$-0.446951\pi$
$223$	1.71384e85	0.331774	0.165887	+	0.986145i	$0.446951\pi$
$224$	1.22422e85	0.201283
$225$	−8.87007e84	−0.123955
$226$	2.55078e85	0.303189
$227$	1.57773e86	1.59621	0.798103	−	0.602521i	$-0.205837\pi$
$227$	1.57773e86	1.59621	0.798103	+	0.602521i	$0.205837\pi$
$228$	−3.48840e85	−0.300611
$229$	4.54203e85	0.333622	0.166811	−	0.985989i	$-0.446653\pi$
$229$	4.54203e85	0.333622	0.166811	+	0.985989i	$0.446653\pi$
$230$	−3.19265e86	−2.00026
$231$	1.44917e86	0.774966
$232$	−1.24267e86	−0.567600
$233$	2.89599e86	1.13059	0.565296	−	0.824888i	$-0.308762\pi$
$233$	2.89599e86	1.13059	0.565296	+	0.824888i	$0.308762\pi$
$234$	−8.49759e84	−0.0283738
$235$	−1.00066e87	−2.85964
$236$	2.35976e85	0.0577536
$237$	6.02412e85	0.126351
$238$	−2.46102e85	−0.0442646
$239$	−7.49799e86	−1.15723	−0.578617	−	0.815599i	$-0.696407\pi$
$239$	−7.49799e86	−1.15723	−0.578617	+	0.815599i	$0.696407\pi$
$240$	3.58958e86	0.475701
$241$	9.85047e86	1.12159	0.560796	−	0.827954i	$-0.310495\pi$
$241$	9.85047e86	1.12159	0.560796	+	0.827954i	$0.310495\pi$
$242$	−3.72167e86	−0.364315
$243$	1.05473e86	0.0888200
$244$	6.06184e86	0.439416
$245$	9.24303e86	0.577102
$246$	−1.07358e87	−0.577703
$247$	−1.19666e87	−0.555305
$248$	−9.19106e86	−0.368027
$249$	4.00852e87	1.38582
$250$	8.24491e87	2.46250
$251$	4.43294e86	0.114446	0.0572231	−	0.998361i	$-0.481775\pi$
$251$	4.43294e86	0.114446	0.0572231	+	0.998361i	$0.481775\pi$
$252$	−1.13313e86	−0.0253023
$253$	−5.23609e87	−1.01183
$254$	−1.89326e87	−0.316795
$255$	−7.21606e86	−0.104612
$256$	4.97323e86	0.0625000
$257$	−1.69641e88	−1.84914	−0.924572	−	0.381008i	$-0.875577\pi$
$257$	−1.69641e88	−1.84914	−0.924572	+	0.381008i	$0.875577\pi$
$258$	−3.73146e87	−0.352987
$259$	9.99121e86	0.0820685
$260$	1.23137e88	0.878740
$261$	1.15020e87	0.0713502
$262$	1.91785e87	0.103471
$263$	3.03790e88	1.42623	0.713114	−	0.701048i	$-0.247284\pi$
$263$	3.03790e88	1.42623	0.713114	+	0.701048i	$0.247284\pi$
$264$	5.88707e87	0.240633
$265$	−5.99587e88	−2.13490
$266$	−1.59571e88	−0.495192
$267$	−5.33730e88	−1.44431
$268$	2.29069e88	0.540811
$269$	6.34199e88	1.30697	0.653487	−	0.756937i	$-0.273305\pi$
$269$	6.34199e88	1.30697	0.653487	+	0.756937i	$0.273305\pi$
$270$	−7.80803e88	−1.40528
$271$	4.97003e87	0.0781591	0.0390796	−	0.999236i	$-0.487557\pi$
$271$	4.97003e87	0.0781591	0.0390796	+	0.999236i	$0.487557\pi$
$272$	−9.99757e86	−0.0137445
$273$	8.35740e88	1.00493
$274$	−1.41787e87	−0.0149190
$275$	2.10802e89	1.94192
$276$	−8.80268e88	−0.710286
$277$	8.71778e88	0.616445	0.308223	−	0.951314i	$-0.400266\pi$
$277$	8.71778e88	0.616445	0.308223	+	0.951314i	$0.400266\pi$
$278$	4.51470e88	0.279894
$279$	8.50717e87	0.0462628
$280$	1.64199e89	0.783615
$281$	1.12322e89	0.470636	0.235318	−	0.971918i	$-0.424387\pi$
$281$	1.12322e89	0.470636	0.235318	+	0.971918i	$0.424387\pi$
$282$	−2.75900e89	−1.01545
$283$	−3.69227e88	−0.119423	−0.0597116	−	0.998216i	$-0.519018\pi$
$283$	−3.69227e88	−0.119423	−0.0597116	+	0.998216i	$0.519018\pi$
$284$	4.40066e88	0.125141
$285$	−4.67884e89	−1.17031
$286$	2.01949e89	0.444511
$287$	−4.91092e89	−0.951642
$288$	−4.60318e87	−0.00785656
$289$	−6.62913e89	−0.996977
$290$	−1.66673e90	−2.20973
$291$	9.70747e89	1.13504
$292$	9.37422e89	0.967078
$293$	7.71205e89	0.702266	0.351133	−	0.936326i	$-0.385796\pi$
$293$	7.71205e89	0.702266	0.351133	+	0.936326i	$0.385796\pi$
$294$	2.54846e89	0.204927
$295$	3.16503e89	0.224841
$296$	4.05879e88	0.0254829
$297$	−1.28055e90	−0.710863
$298$	2.94093e89	0.144408
$299$	−3.01966e90	−1.31208
$300$	3.54390e90	1.36319
$301$	−1.70689e90	−0.581471
$302$	3.71481e90	1.12120
$303$	2.41523e90	0.646105
$304$	−6.48235e89	−0.153761
$305$	8.13047e90	1.71069
$306$	9.25367e87	0.00172776
$307$	−4.30897e90	−0.714204	−0.357102	−	0.934065i	$-0.616235\pi$
$307$	−4.30897e90	−0.714204	−0.357102	+	0.934065i	$0.616235\pi$
$308$	2.69293e90	0.396392
$309$	−1.98303e90	−0.259325
$310$	−1.23276e91	−1.43277
$311$	−2.84482e90	−0.293969	−0.146984	−	0.989139i	$-0.546957\pi$
$311$	−2.84482e90	−0.293969	−0.146984	+	0.989139i	$0.546957\pi$
$312$	3.39508e90	0.312038
$313$	−5.87161e90	−0.480163	−0.240082	−	0.970753i	$-0.577174\pi$
$313$	−5.87161e90	−0.480163	−0.240082	+	0.970753i	$0.577174\pi$
$314$	5.03350e90	0.366385
$315$	−1.51981e90	−0.0985043
$316$	1.11944e90	0.0646280
$317$	2.64007e91	1.35817	0.679083	−	0.734061i	$-0.262377\pi$
$317$	2.64007e91	1.35817	0.679083	+	0.734061i	$0.262377\pi$
$318$	−1.65316e91	−0.758098
$319$	−2.73351e91	−1.11779
$320$	6.67037e90	0.243319
$321$	−2.57050e91	−0.836726
$322$	−4.02663e91	−1.17004
$323$	1.30313e90	0.0338140
$324$	−2.05694e91	−0.476791
$325$	1.21570e92	2.51815
$326$	4.61353e90	0.0854262
$327$	1.28421e91	0.212638
$328$	−1.99500e91	−0.295493
$329$	−1.26205e92	−1.67274
$330$	7.89606e91	0.936810
$331$	7.39087e91	0.785188	0.392594	−	0.919712i	$-0.371578\pi$
$331$	7.39087e91	0.785188	0.392594	+	0.919712i	$0.371578\pi$
$332$	7.44886e91	0.708842
$333$	−3.75679e89	−0.00320333
$334$	−1.45240e92	−1.11004
$335$	3.07239e92	2.10543
$336$	4.52724e91	0.278260
$337$	4.29570e91	0.236888	0.118444	−	0.992961i	$-0.462209\pi$
$337$	4.29570e91	0.236888	0.118444	+	0.992961i	$0.462209\pi$
$338$	−2.64067e91	−0.130694
$339$	9.43292e91	0.419138
$340$	−1.34093e91	−0.0535088
$341$	−2.02177e92	−0.724765
$342$	6.00001e90	0.0193286
$343$	−2.76629e92	−0.801054
$344$	−6.93401e91	−0.180552
$345$	−1.18066e93	−2.76522
$346$	3.03637e92	0.639849
$347$	−2.82414e92	−0.535625	−0.267812	−	0.963471i	$-0.586301\pi$
$347$	−2.82414e92	−0.535625	−0.267812	+	0.963471i	$0.586301\pi$
$348$	−4.59545e92	−0.784668
$349$	−2.09174e92	−0.321648	−0.160824	−	0.986983i	$-0.551415\pi$
$349$	−2.09174e92	−0.321648	−0.160824	+	0.986983i	$0.551415\pi$
$350$	1.62109e93	2.24556
$351$	−7.38495e92	−0.921802
$352$	1.09397e92	0.123083
$353$	1.90983e93	1.93739	0.968696	−	0.248248i	$-0.0798549\pi$
$353$	1.90983e93	1.93739	0.968696	+	0.248248i	$0.0798549\pi$
$354$	8.72652e91	0.0798403
$355$	5.90241e92	0.487185
$356$	−9.91808e92	−0.738759
$357$	−9.10101e91	−0.0611927
$358$	3.36566e92	0.204333
$359$	7.58659e92	0.416006	0.208003	−	0.978128i	$-0.433304\pi$
$359$	7.58659e92	0.416006	0.208003	+	0.978128i	$0.433304\pi$
$360$	−6.17404e91	−0.0305864
$361$	−1.38870e93	−0.621720
$362$	−2.81770e93	−1.14033
$363$	−1.37630e93	−0.503640
$364$	1.55302e93	0.514016
$365$	1.25732e94	3.76493
$366$	2.24171e93	0.607462
$367$	−5.68661e93	−1.39490	−0.697448	−	0.716635i	$-0.745681\pi$
$367$	−5.68661e93	−1.39490	−0.697448	+	0.716635i	$0.745681\pi$
$368$	−1.63576e93	−0.363308
$369$	1.84655e92	0.0371449
$370$	5.44388e92	0.0992077
$371$	−7.56209e93	−1.24880
$372$	−3.39891e93	−0.508771
$373$	−1.02511e94	−1.39122	−0.695612	−	0.718418i	$-0.744867\pi$
$373$	−1.02511e94	−1.39122	−0.695612	+	0.718418i	$0.744867\pi$
$374$	−2.19918e92	−0.0270675
$375$	3.04902e94	3.40423
$376$	−5.12693e93	−0.519398
$377$	−1.57642e94	−1.44948
$378$	−9.84761e93	−0.822016
$379$	5.42139e93	0.410941	0.205471	−	0.978663i	$-0.434127\pi$
$379$	5.42139e93	0.410941	0.205471	+	0.978663i	$0.434127\pi$
$380$	−8.69448e93	−0.598608
$381$	−7.00138e93	−0.437948
$382$	7.06559e93	0.401639
$383$	−2.37119e94	−1.22521	−0.612606	−	0.790389i	$-0.709879\pi$
$383$	−2.37119e94	−1.22521	−0.612606	+	0.790389i	$0.709879\pi$
$384$	1.83913e93	0.0864019
$385$	3.61191e94	1.54319
$386$	−2.18428e93	−0.0848930
$387$	6.41806e92	0.0226962
$388$	1.80390e94	0.580569
$389$	−7.87942e93	−0.230852	−0.115426	−	0.993316i	$-0.536823\pi$
$389$	−7.87942e93	−0.230852	−0.115426	+	0.993316i	$0.536823\pi$
$390$	4.55367e94	1.21480
$391$	3.28834e93	0.0798959
$392$	4.73569e93	0.104819
$393$	7.09233e93	0.143041
$394$	−2.90947e94	−0.534813
$395$	1.50145e94	0.251603
$396$	−1.01257e93	−0.0154721
$397$	2.28259e94	0.318108	0.159054	−	0.987270i	$-0.449156\pi$
$397$	2.28259e94	0.318108	0.159054	+	0.987270i	$0.449156\pi$
$398$	3.90879e94	0.496947
$399$	−5.90103e94	−0.684568
$400$	6.58548e94	0.697265
$401$	8.52612e93	0.0824103	0.0412052	−	0.999151i	$-0.486880\pi$
$401$	8.52612e93	0.0824103	0.0412052	+	0.999151i	$0.486880\pi$
$402$	8.47110e94	0.747633
$403$	−1.16596e95	−0.939829
$404$	4.48813e94	0.330480
$405$	−2.75887e95	−1.85619
$406$	−2.10211e95	−1.29257
$407$	8.92819e93	0.0501842
$408$	−3.69716e93	−0.0190008
$409$	−1.63013e94	−0.0766163	−0.0383081	−	0.999266i	$-0.512197\pi$
$409$	−1.63013e94	−0.0766163	−0.0383081	+	0.999266i	$0.512197\pi$
$410$	−2.67580e95	−1.15038
$411$	−5.24337e93	−0.0206245
$412$	−3.68498e94	−0.132644
$413$	3.99179e94	0.131520
$414$	1.51405e94	0.0456696
$415$	9.99081e95	2.75959
$416$	6.30893e94	0.159606
$417$	1.66956e95	0.386934
$418$	−1.42593e95	−0.302806
$419$	−3.55345e95	−0.691573	−0.345787	−	0.938313i	$-0.612388\pi$
$419$	−3.55345e95	−0.691573	−0.345787	+	0.938313i	$0.612388\pi$
$420$	6.07218e95	1.08329
$421$	−6.22478e94	−0.101819	−0.0509094	−	0.998703i	$-0.516212\pi$
$421$	−6.22478e94	−0.101819	−0.0509094	+	0.998703i	$0.516212\pi$
$422$	−5.58028e94	−0.0837050
$423$	4.74544e94	0.0652910
$424$	−3.07200e95	−0.387764
$425$	−1.32386e95	−0.153337
$426$	1.62739e95	0.172998
$427$	1.02543e96	1.00066
$428$	−4.77664e95	−0.427982
$429$	7.46821e95	0.614505
$430$	−9.30027e95	−0.702905
$431$	−7.99882e94	−0.0555400	−0.0277700	−	0.999614i	$-0.508841\pi$
$431$	−7.99882e94	−0.0555400	−0.0277700	+	0.999614i	$0.508841\pi$
$432$	−4.00046e95	−0.255243
$433$	2.16260e96	1.26814	0.634070	−	0.773276i	$-0.281383\pi$
$433$	2.16260e96	1.26814	0.634070	+	0.773276i	$0.281383\pi$
$434$	−1.55477e96	−0.838091
$435$	−6.16367e96	−3.05479
$436$	2.38638e95	0.108764
$437$	2.13213e96	0.893803
$438$	3.46665e96	1.33692
$439$	1.16601e96	0.413759	0.206880	−	0.978366i	$-0.433669\pi$
$439$	1.16601e96	0.413759	0.206880	+	0.978366i	$0.433669\pi$
$440$	1.46729e96	0.479174
$441$	−4.38332e94	−0.0131763
$442$	−1.26827e95	−0.0350993
$443$	−4.77553e96	−1.21699	−0.608493	−	0.793560i	$-0.708225\pi$
$443$	−4.77553e96	−1.21699	−0.608493	+	0.793560i	$0.708225\pi$
$444$	1.50097e95	0.0352284
$445$	−1.33027e97	−2.87606
$446$	1.17774e96	0.234600
$447$	1.08757e96	0.199634
$448$	8.41278e95	0.142329
$449$	5.42765e96	0.846487	0.423243	−	0.906016i	$-0.360892\pi$
$449$	5.42765e96	0.846487	0.423243	+	0.906016i	$0.360892\pi$
$450$	−6.09547e95	−0.0876497
$451$	−4.38842e96	−0.581921
$452$	1.75288e96	0.214387
$453$	1.37376e97	1.54998
$454$	1.08421e97	1.12869
$455$	2.08299e97	2.00112
$456$	−2.39721e96	−0.212564
$457$	−4.92935e96	−0.403504	−0.201752	−	0.979437i	$-0.564664\pi$
$457$	−4.92935e96	−0.403504	−0.201752	+	0.979437i	$0.564664\pi$
$458$	3.12126e96	0.235906
$459$	8.04203e95	0.0561310
$460$	−2.19397e97	−1.41439
$461$	−8.23547e96	−0.490461	−0.245230	−	0.969465i	$-0.578864\pi$
$461$	−8.23547e96	−0.490461	−0.245230	+	0.969465i	$0.578864\pi$
$462$	9.95864e96	0.547984
$463$	1.42358e97	0.723894	0.361947	−	0.932199i	$-0.382112\pi$
$463$	1.42358e97	0.723894	0.361947	+	0.932199i	$0.382112\pi$
$464$	−8.53953e96	−0.401354
$465$	−4.55880e97	−1.98070
$466$	1.99011e97	0.799449
$467$	3.19912e95	0.0118841	0.00594203	−	0.999982i	$-0.498109\pi$
$467$	3.19912e95	0.0118841	0.00594203	+	0.999982i	$0.498109\pi$
$468$	−5.83950e95	−0.0200633
$469$	3.87495e97	1.23157
$470$	−6.87651e97	−2.02207
$471$	1.86142e97	0.506502
$472$	1.62161e96	0.0408380
$473$	−1.52528e97	−0.355565
$474$	4.13974e96	0.0893437
$475$	−8.58383e97	−1.71540
$476$	−1.69120e96	−0.0312998
$477$	2.84342e96	0.0487439
$478$	−5.15258e97	−0.818288
$479$	1.03818e98	1.52765	0.763827	−	0.645421i	$-0.223318\pi$
$479$	1.03818e98	1.52765	0.763827	+	0.645421i	$0.223318\pi$
$480$	2.46674e97	0.336371
$481$	5.14890e96	0.0650757
$482$	6.76919e97	0.793085
$483$	−1.48907e98	−1.61750
$484$	−2.55751e97	−0.257610
$485$	2.41948e98	2.26021
$486$	7.24803e96	0.0628052
$487$	1.87478e98	1.50711	0.753554	−	0.657386i	$-0.228338\pi$
$487$	1.87478e98	1.50711	0.753554	+	0.657386i	$0.228338\pi$
$488$	4.16567e97	0.310714
$489$	1.70611e97	0.118096
$490$	6.35176e97	0.408073
$491$	−2.51169e98	−1.49793	−0.748964	−	0.662611i	$-0.769448\pi$
$491$	−2.51169e98	−1.49793	−0.748964	+	0.662611i	$0.769448\pi$
$492$	−7.37762e97	−0.408498
$493$	1.71668e97	0.0882627
$494$	−8.22337e97	−0.392660
$495$	−1.35811e97	−0.0602346
$496$	−6.31605e97	−0.260234
$497$	7.44421e97	0.284977
$498$	2.75463e98	0.979925
$499$	−3.71751e98	−1.22909	−0.614543	−	0.788884i	$-0.710659\pi$
$499$	−3.71751e98	−1.22909	−0.614543	+	0.788884i	$0.710659\pi$
$500$	5.66586e98	1.74125
$501$	−5.37106e98	−1.53456
$502$	3.04630e97	0.0809257
$503$	−6.92235e98	−1.71010	−0.855051	−	0.518544i	$-0.826474\pi$
$503$	−6.92235e98	−1.71010	−0.855051	+	0.518544i	$0.826474\pi$
$504$	−7.78680e96	−0.0178914
$505$	6.01972e98	1.28659
$506$	−3.59821e98	−0.715472
$507$	−9.76535e97	−0.180675
$508$	−1.30104e98	−0.224008
$509$	−3.70821e98	−0.594245	−0.297123	−	0.954839i	$-0.596027\pi$
$509$	−3.70821e98	−0.594245	−0.297123	+	0.954839i	$0.596027\pi$
$510$	−4.95884e97	−0.0739722
$511$	1.58575e99	2.20228
$512$	3.41758e97	0.0441942
$513$	5.21439e98	0.627942
$514$	−1.16576e99	−1.30754
$515$	−4.94249e98	−0.516395
$516$	−2.56424e98	−0.249600
$517$	−1.12778e99	−1.02287
$518$	6.86591e97	0.0580312
$519$	1.12287e99	0.884546
$520$	8.46189e98	0.621363
$521$	−1.03002e99	−0.705127	−0.352564	−	0.935788i	$-0.614690\pi$
$521$	−1.03002e99	−0.705127	−0.352564	+	0.935788i	$0.614690\pi$
$522$	7.90412e97	0.0504522
$523$	−7.18306e98	−0.427561	−0.213780	−	0.976882i	$-0.568578\pi$
$523$	−7.18306e98	−0.427561	−0.213780	+	0.976882i	$0.568578\pi$
$524$	1.31794e98	0.0731649
$525$	5.99491e99	3.10433
$526$	2.08763e99	1.00850
$527$	1.26970e98	0.0572287
$528$	4.04556e98	0.170154
$529$	2.83264e99	1.11188
$530$	−4.12033e99	−1.50960
$531$	−1.50095e97	−0.00513354
$532$	−1.09656e99	−0.350154
$533$	−2.53081e99	−0.754599
$534$	−3.66777e99	−1.02128
$535$	−6.40669e99	−1.66618
$536$	1.57415e99	0.382411
$537$	1.24464e99	0.282477
$538$	4.35818e99	0.924171
$539$	1.04172e99	0.206424
$540$	−5.36563e99	−0.993685
$541$	−2.53521e99	−0.438847	−0.219424	−	0.975630i	$-0.570418\pi$
$541$	−2.53521e99	−0.438847	−0.219424	+	0.975630i	$0.570418\pi$
$542$	3.41538e98	0.0552668
$543$	−1.04200e100	−1.57643
$544$	−6.87028e97	−0.00971884
$545$	3.20075e99	0.423427
$546$	5.74316e99	0.710591
$547$	−5.50907e99	−0.637589	−0.318795	−	0.947824i	$-0.603278\pi$
$547$	−5.50907e99	−0.637589	−0.318795	+	0.947824i	$0.603278\pi$
$548$	−9.74353e97	−0.0105494
$549$	−3.85571e98	−0.0390583
$550$	1.44862e100	1.37314
$551$	1.11308e100	0.987403
$552$	−6.04915e99	−0.502248
$553$	1.89365e99	0.147175
$554$	5.99081e99	0.435893
$555$	2.01318e99	0.137148
$556$	3.10248e99	0.197915
$557$	1.00702e100	0.601623	0.300811	−	0.953684i	$-0.402743\pi$
$557$	1.00702e100	0.601623	0.300811	+	0.953684i	$0.402743\pi$
$558$	5.84609e98	0.0327127
$559$	−8.79633e99	−0.461074
$560$	1.12837e100	0.554099
$561$	−8.13270e98	−0.0374189
$562$	7.71872e99	0.332790
$563$	−2.96665e100	−1.19870	−0.599349	−	0.800488i	$-0.704574\pi$
$563$	−2.96665e100	−1.19870	−0.599349	+	0.800488i	$0.704574\pi$
$564$	−1.89597e100	−0.718032
$565$	2.35106e100	0.834632
$566$	−2.53731e99	−0.0844450
$567$	−3.47954e100	−1.08577
$568$	3.02411e99	0.0884878
$569$	5.01542e100	1.37629	0.688144	−	0.725574i	$-0.258426\pi$
$569$	5.01542e100	1.37629	0.688144	+	0.725574i	$0.258426\pi$
$570$	−3.21527e100	−0.827534
$571$	6.93604e100	1.67453	0.837266	−	0.546795i	$-0.184152\pi$
$571$	6.93604e100	1.67453	0.837266	+	0.546795i	$0.184152\pi$
$572$	1.38779e100	0.314317
$573$	2.61290e100	0.555238
$574$	−3.37476e100	−0.672912
$575$	−2.16605e101	−4.05315
$576$	−3.16328e98	−0.00555543
$577$	5.93643e100	0.978607	0.489304	−	0.872113i	$-0.337251\pi$
$577$	5.93643e100	0.978607	0.489304	+	0.872113i	$0.337251\pi$
$578$	−4.55550e100	−0.704969
$579$	−8.07761e99	−0.117359
$580$	−1.14537e101	−1.56251
$581$	1.26006e101	1.61422
$582$	6.67092e100	0.802596
$583$	−6.75752e100	−0.763634
$584$	6.44192e100	0.683827
$585$	−7.83226e99	−0.0781084
$586$	5.29968e100	0.496577
$587$	1.36789e101	1.20437	0.602186	−	0.798356i	$-0.294297\pi$
$587$	1.36789e101	1.20437	0.602186	+	0.798356i	$0.294297\pi$
$588$	1.75129e100	0.144906
$589$	8.23264e100	0.640223
$590$	2.17499e100	0.158986
$591$	−1.07594e101	−0.739341
$592$	2.78918e99	0.0180192
$593$	−1.97672e101	−1.20074	−0.600371	−	0.799722i	$-0.704980\pi$
$593$	−1.97672e101	−1.20074	−0.600371	+	0.799722i	$0.704980\pi$
$594$	−8.79987e100	−0.502656
$595$	−2.26833e100	−0.121853
$596$	2.02099e100	0.102112
$597$	1.44550e101	0.686995
$598$	−2.07509e101	−0.927779
$599$	3.40427e101	1.43201	0.716004	−	0.698097i	$-0.245969\pi$
$599$	3.40427e101	1.43201	0.716004	+	0.698097i	$0.245969\pi$
$600$	2.43535e101	0.963920
$601$	4.26797e101	1.58966	0.794828	−	0.606835i	$-0.207561\pi$
$601$	4.26797e101	1.58966	0.794828	+	0.606835i	$0.207561\pi$
$602$	−1.17296e101	−0.411162
$603$	−1.45702e100	−0.0480710
$604$	2.55280e101	0.792807
$605$	−3.43027e101	−1.00290
$606$	1.65974e101	0.456866
$607$	−4.95613e101	−1.28456	−0.642282	−	0.766468i	$-0.722012\pi$
$607$	−4.95613e101	−1.28456	−0.642282	+	0.766468i	$0.722012\pi$
$608$	−4.45464e100	−0.108726
$609$	−7.77372e101	−1.78689
$610$	5.58722e101	1.20964
$611$	−6.50391e101	−1.32639
$612$	6.35908e98	0.00122171
$613$	1.08093e101	0.195655	0.0978276	−	0.995203i	$-0.468811\pi$
$613$	1.08093e101	0.195655	0.0978276	+	0.995203i	$0.468811\pi$
$614$	−2.96110e101	−0.505019
$615$	−9.89526e101	−1.59032
$616$	1.85057e101	0.280291
$617$	6.89839e101	0.984780	0.492390	−	0.870375i	$-0.336123\pi$
$617$	6.89839e101	0.984780	0.492390	+	0.870375i	$0.336123\pi$
$618$	−1.36273e101	−0.183371
$619$	−1.61138e101	−0.204404	−0.102202	−	0.994764i	$-0.532589\pi$
$619$	−1.61138e101	−0.204404	−0.102202	+	0.994764i	$0.532589\pi$
$620$	−8.47143e101	−1.01312
$621$	1.31581e102	1.48371
$622$	−1.95495e101	−0.207867
$623$	−1.67775e102	−1.68234
$624$	2.33308e101	0.220644
$625$	4.47271e102	3.98979
$626$	−4.03494e101	−0.339527
$627$	−5.27318e101	−0.418608
$628$	3.45899e101	0.259073
$629$	−5.60703e99	−0.00396264
$630$	−1.04441e101	−0.0696531
$631$	2.29550e102	1.44480	0.722398	−	0.691478i	$-0.243040\pi$
$631$	2.29550e102	1.44480	0.722398	+	0.691478i	$0.243040\pi$
$632$	7.69270e100	0.0456989
$633$	−2.06362e101	−0.115716
$634$	1.81425e102	0.960369
$635$	−1.74502e102	−0.872086
$636$	−1.13604e102	−0.536056
$637$	6.00759e101	0.267677
$638$	−1.87845e102	−0.790397
$639$	−2.79909e100	−0.0111234
$640$	4.58384e101	0.172052
$641$	8.93579e101	0.316822	0.158411	−	0.987373i	$-0.449363\pi$
$641$	8.93579e101	0.316822	0.158411	+	0.987373i	$0.449363\pi$
$642$	−1.76643e102	−0.591655
$643$	−1.95870e102	−0.619822	−0.309911	−	0.950766i	$-0.600299\pi$
$643$	−1.95870e102	−0.619822	−0.309911	+	0.950766i	$0.600299\pi$
$644$	−2.76708e102	−0.827346
$645$	−3.43930e102	−0.971717
$646$	8.95505e100	0.0239101
$647$	4.22171e102	1.06532	0.532662	−	0.846328i	$-0.321192\pi$
$647$	4.22171e102	1.06532	0.532662	+	0.846328i	$0.321192\pi$
$648$	−1.41352e102	−0.337142
$649$	3.56708e101	0.0804233
$650$	8.35420e102	1.78060
$651$	−5.74964e102	−1.15860
$652$	3.17040e101	0.0604055
$653$	−1.06443e102	−0.191772	−0.0958860	−	0.995392i	$-0.530568\pi$
$653$	−1.06443e102	−0.191772	−0.0958860	+	0.995392i	$0.530568\pi$
$654$	8.82499e101	0.150358
$655$	1.76769e102	0.284838
$656$	−1.37095e102	−0.208945
$657$	−5.96259e101	−0.0859605
$658$	−8.67277e102	−1.18280
$659$	−7.83423e102	−1.01083	−0.505415	−	0.862876i	$-0.668661\pi$
$659$	−7.83423e102	−1.01083	−0.505415	+	0.862876i	$0.668661\pi$
$660$	5.42613e102	0.662425
$661$	2.34548e102	0.270943	0.135471	−	0.990781i	$-0.456745\pi$
$661$	2.34548e102	0.270943	0.135471	+	0.990781i	$0.456745\pi$
$662$	5.07897e102	0.555212
$663$	−4.69014e101	−0.0485224
$664$	5.11882e102	0.501227
$665$	−1.47077e103	−1.36318
$666$	−2.58165e100	−0.00226510
$667$	2.80877e103	2.33304
$668$	−9.98081e102	−0.784919
$669$	4.35536e102	0.324318
$670$	2.11133e103	1.48877
$671$	9.16327e102	0.611897
$672$	3.11110e102	0.196759
$673$	1.32429e103	0.793294	0.396647	−	0.917971i	$-0.370174\pi$
$673$	1.32429e103	0.793294	0.396647	+	0.917971i	$0.370174\pi$
$674$	2.95198e102	0.167505
$675$	−5.29735e103	−2.84755
$676$	−1.81465e102	−0.0924143
$677$	−2.72914e103	−1.31686	−0.658429	−	0.752643i	$-0.728779\pi$
$677$	−2.72914e103	−1.31686	−0.658429	+	0.752643i	$0.728779\pi$
$678$	6.48226e102	0.296376
$679$	3.05149e103	1.32210
$680$	−9.21479e101	−0.0378364
$681$	4.00947e103	1.56033
$682$	−1.38935e103	−0.512486
$683$	−1.63395e103	−0.571325	−0.285662	−	0.958330i	$-0.592214\pi$
$683$	−1.63395e103	−0.571325	−0.285662	+	0.958330i	$0.592214\pi$
$684$	4.12318e101	0.0136674
$685$	−1.30686e102	−0.0410697
$686$	−1.90098e103	−0.566431
$687$	1.15426e103	0.326124
$688$	−4.76501e102	−0.127669
$689$	−3.89707e103	−0.990232
$690$	−8.11345e103	−1.95530
$691$	−2.88815e102	−0.0660193	−0.0330096	−	0.999455i	$-0.510509\pi$
$691$	−2.88815e102	−0.0660193	−0.0330096	+	0.999455i	$0.510509\pi$
$692$	2.08658e103	0.452441
$693$	−1.71287e102	−0.0352340
$694$	−1.94074e103	−0.378744
$695$	4.16121e103	0.770503
$696$	−3.15797e103	−0.554844
$697$	2.75599e102	0.0459495
$698$	−1.43743e103	−0.227439
$699$	7.35954e103	1.10518
$700$	1.11401e104	1.58785
$701$	2.28101e103	0.308617	0.154309	−	0.988023i	$-0.450685\pi$
$701$	2.28101e103	0.308617	0.154309	+	0.988023i	$0.450685\pi$
$702$	−5.07490e103	−0.651812
$703$	−3.63556e102	−0.0443304
$704$	7.51770e102	0.0870328
$705$	−2.54298e104	−2.79537
$706$	1.31242e104	1.36994
$707$	7.59217e103	0.752588
$708$	5.99682e102	0.0564556
$709$	1.52766e104	1.36596	0.682980	−	0.730437i	$-0.260684\pi$
$709$	1.52766e104	1.36596	0.682980	+	0.730437i	$0.260684\pi$
$710$	4.05610e103	0.344492
$711$	−7.12031e101	−0.00574458
$712$	−6.81565e103	−0.522381
$713$	2.07743e104	1.51272
$714$	−6.25417e102	−0.0432698
$715$	1.86137e104	1.22367
$716$	2.31286e103	0.144485
$717$	−1.90546e104	−1.13123
$718$	5.21346e103	0.294160
$719$	−2.20224e104	−1.18103	−0.590514	−	0.807027i	$-0.701075\pi$
$719$	−2.20224e104	−1.18103	−0.590514	+	0.807027i	$0.701075\pi$
$720$	−4.24277e102	−0.0216278
$721$	−6.23355e103	−0.302063
$722$	−9.54306e103	−0.439622
$723$	2.50329e104	1.09639
$724$	−1.93631e104	−0.806337
$725$	−1.13079e105	−4.47760
$726$	−9.45784e103	−0.356127
$727$	−2.04174e104	−0.731131	−0.365565	−	0.930786i	$-0.619124\pi$
$727$	−2.04174e104	−0.731131	−0.365565	+	0.930786i	$0.619124\pi$
$728$	1.06723e104	0.363464
$729$	3.21187e104	1.04041
$730$	8.64025e104	2.66221
$731$	9.57900e102	0.0280760
$732$	1.54049e104	0.429540
$733$	−5.14427e103	−0.136467	−0.0682336	−	0.997669i	$-0.521736\pi$
$733$	−5.14427e103	−0.136467	−0.0682336	+	0.997669i	$0.521736\pi$
$734$	−3.90781e104	−0.986340
$735$	2.34892e104	0.564132
$736$	−1.12409e104	−0.256898
$737$	3.46267e104	0.753092
$738$	1.26894e103	0.0262654
$739$	4.57596e104	0.901488	0.450744	−	0.892653i	$-0.351159\pi$
$739$	4.57596e104	0.901488	0.450744	+	0.892653i	$0.351159\pi$
$740$	3.74100e103	0.0701504
$741$	−3.04105e104	−0.542824
$742$	−5.19663e104	−0.883038
$743$	1.90777e104	0.308627	0.154313	−	0.988022i	$-0.450683\pi$
$743$	1.90777e104	0.308627	0.154313	+	0.988022i	$0.450683\pi$
$744$	−2.33571e104	−0.359756
$745$	2.71066e104	0.397531
$746$	−7.04449e104	−0.983744
$747$	−4.73794e103	−0.0630068
$748$	−1.51127e103	−0.0191396
$749$	−8.08022e104	−0.974624
$750$	2.09527e105	2.40715
$751$	1.05420e105	1.15363	0.576813	−	0.816876i	$-0.304296\pi$
$751$	1.05420e105	1.15363	0.576813	+	0.816876i	$0.304296\pi$
$752$	−3.52320e104	−0.367270
$753$	1.12654e104	0.111874
$754$	−1.08331e105	−1.02494
$755$	3.42395e105	3.08648
$756$	−6.76722e104	−0.581253
$757$	−5.61161e104	−0.459291	−0.229645	−	0.973274i	$-0.573757\pi$
$757$	−5.61161e104	−0.459291	−0.229645	+	0.973274i	$0.573757\pi$
$758$	3.72555e104	0.290579
$759$	−1.33064e105	−0.989090
$760$	−5.97480e104	−0.423280
$761$	−1.31808e105	−0.890023	−0.445012	−	0.895525i	$-0.646800\pi$
$761$	−1.31808e105	−0.890023	−0.445012	+	0.895525i	$0.646800\pi$
$762$	−4.81131e104	−0.309676
$763$	4.03683e104	0.247682
$764$	4.85544e104	0.284002
$765$	8.52914e102	0.00475623
$766$	−1.62947e105	−0.866355
$767$	2.05714e104	0.104288
$768$	1.26384e104	0.0610954
$769$	2.38600e105	1.09991	0.549957	−	0.835193i	$-0.314644\pi$
$769$	2.38600e105	1.09991	0.549957	+	0.835193i	$0.314644\pi$
$770$	2.48209e105	1.09120
$771$	−4.31106e105	−1.80759
$772$	−1.50103e104	−0.0600284
$773$	−2.01565e105	−0.768889	−0.384445	−	0.923148i	$-0.625607\pi$
$773$	−2.01565e105	−0.768889	−0.384445	+	0.923148i	$0.625607\pi$
$774$	4.41046e103	0.0160487
$775$	−8.36362e105	−2.90323
$776$	1.23963e105	0.410524
$777$	2.53905e104	0.0802241
$778$	−5.41470e104	−0.163237
$779$	1.78696e105	0.514042
$780$	3.12926e105	0.858991
$781$	6.65218e104	0.174261
$782$	2.25973e104	0.0564949
$783$	6.86918e105	1.63908
$784$	3.25434e104	0.0741185
$785$	4.63939e105	1.00860
$786$	4.87382e104	0.101145
$787$	−4.67954e105	−0.927097	−0.463548	−	0.886072i	$-0.653424\pi$
$787$	−4.67954e105	−0.927097	−0.463548	+	0.886072i	$0.653424\pi$
$788$	−1.99937e105	−0.378170
$789$	7.72019e105	1.39417
$790$	1.03179e105	0.177910
$791$	2.96519e105	0.488215
$792$	−6.95832e103	−0.0109405
$793$	5.28447e105	0.793470
$794$	1.56859e105	0.224936
$795$	−1.52372e106	−2.08692
$796$	2.68610e105	0.351395
$797$	−3.29230e105	−0.411406	−0.205703	−	0.978614i	$-0.565948\pi$
$797$	−3.29230e105	−0.411406	−0.205703	+	0.978614i	$0.565948\pi$
$798$	−4.05515e105	−0.484063
$799$	7.08260e104	0.0807672
$800$	4.52551e105	0.493041
$801$	6.30851e104	0.0656659
$802$	5.85910e104	0.0582729
$803$	1.41704e106	1.34668
$804$	5.82129e105	0.528657
$805$	−3.71135e106	−3.22094
$806$	−8.01240e105	−0.664559
$807$	1.61168e106	1.27760
$808$	3.08422e105	0.233685
$809$	7.80880e105	0.565540	0.282770	−	0.959188i	$-0.408747\pi$
$809$	7.80880e105	0.565540	0.282770	+	0.959188i	$0.408747\pi$
$810$	−1.89588e106	−1.31253
$811$	−1.52623e106	−1.01008	−0.505042	−	0.863095i	$-0.668523\pi$
$811$	−1.52623e106	−1.01008	−0.505042	+	0.863095i	$0.668523\pi$
$812$	−1.44456e106	−0.913986
$813$	1.26303e105	0.0764026
$814$	6.13540e104	0.0354856
$815$	4.25231e105	0.235165
$816$	−2.54067e104	−0.0134356
$817$	6.21095e105	0.314089
$818$	−1.12022e105	−0.0541759
$819$	−9.87817e104	−0.0456892
$820$	−1.83879e106	−0.813443
$821$	3.17885e106	1.34507	0.672536	−	0.740065i	$-0.265205\pi$
$821$	3.17885e106	1.34507	0.672536	+	0.740065i	$0.265205\pi$
$822$	−3.60322e104	−0.0145837
$823$	2.93578e105	0.113666	0.0568329	−	0.998384i	$-0.481900\pi$
$823$	2.93578e105	0.113666	0.0568329	+	0.998384i	$0.481900\pi$
$824$	−2.53230e105	−0.0937932
$825$	5.35708e106	1.89827
$826$	2.74314e105	0.0929985
$827$	−3.03145e106	−0.983332	−0.491666	−	0.870784i	$-0.663612\pi$
$827$	−3.03145e106	−0.983332	−0.491666	+	0.870784i	$0.663612\pi$
$828$	1.04045e105	0.0322933
$829$	2.69889e105	0.0801576	0.0400788	−	0.999197i	$-0.487239\pi$
$829$	2.69889e105	0.0801576	0.0400788	+	0.999197i	$0.487239\pi$
$830$	6.86564e106	1.95133
$831$	2.21544e106	0.602591
$832$	4.33547e105	0.112859
$833$	−6.54213e104	−0.0162996
$834$	1.14732e106	0.273604
$835$	−1.33868e107	−3.05577
$836$	−9.79893e105	−0.214116
$837$	5.08062e106	1.06277
$838$	−2.44191e106	−0.489016
$839$	−7.86508e106	−1.50797	−0.753983	−	0.656894i	$-0.771870\pi$
$839$	−7.86508e106	−1.50797	−0.753983	+	0.656894i	$0.771870\pi$
$840$	4.17277e106	0.766004
$841$	8.97399e106	1.57736
$842$	−4.27764e105	−0.0719967
$843$	2.85443e106	0.460059
$844$	−3.83474e105	−0.0591884
$845$	−2.43391e106	−0.359778
$846$	3.26104e105	0.0461677
$847$	−4.32632e106	−0.586643
$848$	−2.11106e106	−0.274190
$849$	−9.38313e105	−0.116739
$850$	−9.09752e105	−0.108426
$851$	−9.17400e105	−0.104744
$852$	1.11834e106	0.122328
$853$	−1.18855e107	−1.24559	−0.622797	−	0.782383i	$-0.714004\pi$
$853$	−1.18855e107	−1.24559	−0.622797	+	0.782383i	$0.714004\pi$
$854$	7.04669e106	0.707575
$855$	5.53023e105	0.0532084
$856$	−3.28248e106	−0.302629
$857$	−1.29887e106	−0.114754	−0.0573768	−	0.998353i	$-0.518274\pi$
$857$	−1.29887e106	−0.114754	−0.0573768	+	0.998353i	$0.518274\pi$
$858$	5.13212e106	0.434521
$859$	1.45898e107	1.18385	0.591926	−	0.805992i	$-0.298368\pi$
$859$	1.45898e107	1.18385	0.591926	+	0.805992i	$0.298368\pi$
$860$	−6.39110e106	−0.497029
$861$	−1.24801e107	−0.930254
$862$	−5.49675e105	−0.0392727
$863$	−2.41892e107	−1.65664	−0.828318	−	0.560258i	$-0.810702\pi$
$863$	−2.41892e107	−1.65664	−0.828318	+	0.560258i	$0.810702\pi$
$864$	−2.74909e106	−0.180484
$865$	2.79863e107	1.76140
$866$	1.48612e107	0.896710
$867$	−1.68465e107	−0.974571
$868$	−1.06843e107	−0.592620
$869$	1.69217e106	0.0899960
$870$	−4.23564e107	−2.16006
$871$	1.99693e107	0.976562
$872$	1.63991e106	0.0769074
$873$	−1.14739e106	−0.0516049
$874$	1.46519e107	0.632014
$875$	9.58443e107	3.96527
$876$	2.38226e107	0.945343
$877$	−2.46509e107	−0.938314	−0.469157	−	0.883115i	$-0.655442\pi$
$877$	−2.46509e107	−0.938314	−0.469157	+	0.883115i	$0.655442\pi$
$878$	8.01277e106	0.292572
$879$	1.95985e107	0.686483
$880$	1.00831e107	0.338827
$881$	3.02781e107	0.976130	0.488065	−	0.872807i	$-0.337703\pi$
$881$	3.02781e107	0.976130	0.488065	+	0.872807i	$0.337703\pi$
$882$	−3.01219e105	−0.00931707
$883$	−4.63659e107	−1.37605	−0.688023	−	0.725689i	$-0.741521\pi$
$883$	−4.63659e107	−1.37605	−0.688023	+	0.725689i	$0.741521\pi$
$884$	−8.71549e105	−0.0248190
$885$	8.04326e106	0.219787
$886$	−3.28172e107	−0.860538
$887$	−6.36801e107	−1.60248	−0.801238	−	0.598346i	$-0.795825\pi$
$887$	−6.36801e107	−1.60248	−0.801238	+	0.598346i	$0.795825\pi$
$888$	1.03146e106	0.0249102
$889$	−2.20085e107	−0.510124
$890$	−9.14152e107	−2.03368
$891$	−3.10933e107	−0.663943
$892$	8.09337e106	0.165887
$893$	4.59230e107	0.903550
$894$	7.47375e106	0.141162
$895$	3.10213e107	0.562497
$896$	5.78122e106	0.100641
$897$	−7.67382e107	−1.28259
$898$	3.72985e107	0.598556
$899$	1.08453e108	1.67114
$900$	−4.18877e106	−0.0619777
$901$	4.24382e106	0.0602979
$902$	−3.01570e107	−0.411481
$903$	−4.33770e107	−0.568403
$904$	1.20457e107	0.151595
$905$	−2.59708e108	−3.13915
$906$	9.44039e107	1.09600
$907$	−1.81468e106	−0.0202364	−0.0101182	−	0.999949i	$-0.503221\pi$
$907$	−1.81468e106	−0.0202364	−0.0101182	+	0.999949i	$0.503221\pi$
$908$	7.45062e107	0.798103
$909$	−2.85473e106	−0.0293753
$910$	1.43142e108	1.41500
$911$	−7.75069e107	−0.736071	−0.368036	−	0.929812i	$-0.619970\pi$
$911$	−7.75069e107	−0.736071	−0.368036	+	0.929812i	$0.619970\pi$
$912$	−1.64735e107	−0.150306
$913$	1.12599e108	0.987080
$914$	−3.38742e107	−0.285321
$915$	2.06619e108	1.67224
$916$	2.14491e107	0.166811
$917$	2.22944e107	0.166615
$918$	5.52644e106	0.0396906
$919$	1.58396e108	1.09327	0.546635	−	0.837371i	$-0.315909\pi$
$919$	1.58396e108	1.09327	0.546635	+	0.837371i	$0.315909\pi$
$920$	−1.50769e108	−1.00013
$921$	−1.09503e108	−0.698153
$922$	−5.65937e107	−0.346808
$923$	3.83632e107	0.225971
$924$	6.84352e107	0.387483
$925$	3.69339e107	0.201026
$926$	9.78275e107	0.511871
$927$	2.34387e106	0.0117903
$928$	−5.86832e107	−0.283800
$929$	−6.82932e107	−0.317544	−0.158772	−	0.987315i	$-0.550754\pi$
$929$	−6.82932e107	−0.317544	−0.158772	+	0.987315i	$0.550754\pi$
$930$	−3.13279e108	−1.40056
$931$	−4.24187e107	−0.182345
$932$	1.36759e108	0.565296
$933$	−7.22952e107	−0.287362
$934$	2.19842e106	0.00840329
$935$	−2.02699e107	−0.0745123
$936$	−4.01287e106	−0.0141869
$937$	1.99222e108	0.677395	0.338697	−	0.940895i	$-0.390014\pi$
$937$	1.99222e108	0.677395	0.338697	+	0.940895i	$0.390014\pi$
$938$	2.66285e108	0.870848
$939$	−1.49215e108	−0.469372
$940$	−4.72550e108	−1.42982
$941$	−1.80439e108	−0.525182	−0.262591	−	0.964907i	$-0.584577\pi$
$941$	−1.80439e108	−0.525182	−0.262591	+	0.964907i	$0.584577\pi$
$942$	1.27916e108	0.358151
$943$	4.50924e108	1.21458
$944$	1.11436e107	0.0288768
$945$	−9.07657e108	−2.26288
$946$	−1.04817e108	−0.251422
$947$	−5.76718e108	−1.33103	−0.665517	−	0.746383i	$-0.731789\pi$
$947$	−5.76718e108	−1.33103	−0.665517	+	0.746383i	$0.731789\pi$
$948$	2.84481e107	0.0631755
$949$	8.17208e108	1.74629
$950$	−5.89876e108	−1.21297
$951$	6.70919e108	1.32764
$952$	−1.16218e107	−0.0221323
$953$	4.83287e108	0.885757	0.442879	−	0.896582i	$-0.353957\pi$
$953$	4.83287e108	0.885757	0.442879	+	0.896582i	$0.353957\pi$
$954$	1.95398e107	0.0344671
$955$	6.51238e108	1.10565
$956$	−3.54082e108	−0.578617
$957$	−6.94663e108	−1.09267
$958$	7.13430e108	1.08021
$959$	−1.64823e107	−0.0240236
$960$	1.69513e108	0.237850
$961$	6.18508e107	0.0835490
$962$	3.53830e107	0.0460155
$963$	3.03824e107	0.0380419
$964$	4.65175e108	0.560796
$965$	−2.01326e108	−0.233697
$966$	−1.02328e109	−1.14375
$967$	−1.15809e108	−0.124646	−0.0623228	−	0.998056i	$-0.519851\pi$
$967$	−1.15809e108	−0.124646	−0.0623228	+	0.998056i	$0.519851\pi$
$968$	−1.75751e108	−0.182157
$969$	3.31163e107	0.0330540
$970$	1.66266e109	1.59821
$971$	−1.16642e109	−1.07983	−0.539913	−	0.841721i	$-0.681543\pi$
$971$	−1.16642e109	−1.07983	−0.539913	+	0.841721i	$0.681543\pi$
$972$	4.98081e107	0.0444100
$973$	5.24819e108	0.450703
$974$	1.28834e109	1.06569
$975$	3.08943e109	2.46156
$976$	2.86262e108	0.219708
$977$	−1.75136e109	−1.29486	−0.647430	−	0.762125i	$-0.724156\pi$
$977$	−1.75136e109	−1.29486	−0.647430	+	0.762125i	$0.724156\pi$
$978$	1.17243e108	0.0835063
$979$	−1.49925e109	−1.02874
$980$	4.36490e108	0.288551
$981$	−1.51789e107	−0.00966765
$982$	−1.72602e109	−1.05919
$983$	−2.11285e108	−0.124930	−0.0624648	−	0.998047i	$-0.519896\pi$
$983$	−2.11285e108	−0.124930	−0.0624648	+	0.998047i	$0.519896\pi$
$984$	−5.06986e108	−0.288852
$985$	−2.68167e109	−1.47225
$986$	1.17969e108	0.0624112
$987$	−3.20724e109	−1.63514
$988$	−5.65106e108	−0.277652
$989$	1.56728e109	0.742132
$990$	−9.33288e107	−0.0425923
$991$	−4.00038e109	−1.75959	−0.879797	−	0.475350i	$-0.842322\pi$
$991$	−4.00038e109	−1.75959	−0.879797	+	0.475350i	$0.842322\pi$
$992$	−4.34036e108	−0.184013
$993$	1.87823e109	0.767542
$994$	5.11562e108	0.201510
$995$	3.60274e109	1.36802
$996$	1.89297e109	0.692912
$997$	−6.50021e108	−0.229379	−0.114690	−	0.993401i	$-0.536587\pi$
$997$	−6.50021e108	−0.229379	−0.114690	+	0.993401i	$0.536587\pi$
$998$	−2.55465e109	−0.869095
$999$	−2.24361e108	−0.0735881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.74.a.b.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.74.a.b.1.3	✓	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 74 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+6.87195e10 q^{2} +2.54129e17 q^{3} +4.72237e21 q^{4} +6.33389e25 q^{5} +1.74636e28 q^{6} +7.98841e30 q^{7} +3.24519e32 q^{8} -3.00372e33 q^{9} +4.35262e36 q^{10} +7.13848e37 q^{11} +1.20009e39 q^{12} +4.11677e40 q^{13} +5.48959e41 q^{14} +1.60963e43 q^{15} +2.23007e43 q^{16} -4.48307e43 q^{17} -2.06414e44 q^{18} -2.90679e46 q^{19} +2.99110e47 q^{20} +2.03009e48 q^{21} +4.90553e48 q^{22} -7.33502e49 q^{23} +8.24695e49 q^{24} +2.95303e51 q^{25} +2.82902e51 q^{26} -1.79387e52 q^{27} +3.77242e52 q^{28} -3.82926e53 q^{29} +1.10613e54 q^{30} -2.83221e54 q^{31} +1.53250e54 q^{32} +1.81409e55 q^{33} -3.08074e54 q^{34} +5.05978e56 q^{35} -1.41847e55 q^{36} +1.25071e56 q^{37} -1.99753e57 q^{38} +1.04619e58 q^{39} +2.05547e58 q^{40} -6.14755e58 q^{41} +1.39506e59 q^{42} -2.13671e59 q^{43} +3.37105e59 q^{44} -1.90252e59 q^{45} -5.04058e60 q^{46} -1.57986e61 q^{47} +5.66726e60 q^{48} +1.45930e61 q^{49} +2.02931e62 q^{50} -1.13928e61 q^{51} +1.94409e62 q^{52} -9.46633e62 q^{53} -1.23274e63 q^{54} +4.52144e63 q^{55} +2.59239e63 q^{56} -7.38698e63 q^{57} -2.63145e64 q^{58} +4.99698e63 q^{59} +7.60124e64 q^{60} +1.28364e65 q^{61} -1.94628e65 q^{62} -2.39949e64 q^{63} +1.05312e65 q^{64} +2.60752e66 q^{65} +1.24664e66 q^{66} +4.85072e66 q^{67} -2.11707e65 q^{68} -1.86404e67 q^{69} +3.47705e67 q^{70} +9.31876e66 q^{71} -9.74762e65 q^{72} +1.98507e68 q^{73} +8.59483e66 q^{74} +7.50450e68 q^{75} -1.37269e68 q^{76} +5.70251e68 q^{77} +7.18937e68 q^{78} +2.37050e68 q^{79} +1.41251e69 q^{80} -4.35573e69 q^{81} -4.22457e69 q^{82} +1.57736e70 q^{83} +9.58681e69 q^{84} -2.83953e69 q^{85} -1.46833e70 q^{86} -9.73125e70 q^{87} +2.31657e70 q^{88} -2.10023e71 q^{89} -1.30740e70 q^{90} +3.28865e71 q^{91} -3.46386e71 q^{92} -7.19747e71 q^{93} -1.08567e72 q^{94} -1.84113e72 q^{95} +3.89451e71 q^{96} +3.81990e72 q^{97} +1.00282e72 q^{98} -2.14420e71 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 274877906944 q^{2} + 30\!\cdots\!76 q^{3} + 18\!\cdots\!84 q^{4} - 78\!\cdots\!60 q^{5} + 20\!\cdots\!36 q^{6} + 36\!\cdots\!12 q^{7} + 12\!\cdots\!24 q^{8} + 12\!\cdots\!52 q^{9} - 53\!\cdots\!60 q^{10}+ \cdots + 28\!\cdots\!24 q^{99}+O(q^{100}) \) 4 * q + 274877906944 * q^2 + 305066325723244176 * q^3 + 18889465931478580854784 * q^4 - 7846962293700032321337960 * q^5 + 20963998273475476527079489536 * q^6 + 3636364966558861993065799361312 * q^7 + 1298074214633706907132624082305024 * q^8 + 122378175810775448230425774569321652 * q^9 - 539239142790188570468632018613698560 * q^10 + 52775218805667734867535256611889929648 * q^11 + 1440634991647642175069153055191907434496 * q^12 + 1355651207894098513401138234675081313976 * q^13 + 249889097723047134707119792526923642437632 * q^14 - 7830535738800097006518186191927965043233440 * q^15 + 89202980794122492566142873090593446023921664 * q^16 + 954348456154904658262187917015529592600353352 * q^17 + 8409764205622701352790716382891279683915087872 * q^18 + 95454725025342640211946932212410556121580424400 * q^19 - 37056231728110945597372254620868777164836700160 * q^20 + 663014063083061571146153755002330860310806732928 * q^21 + 3626685420953393611175405108400560201438412668928 * q^22 - 67417603669907011086030463893163498895122860076704 * q^23 + 98999682793597700758917102567483606960313315885056 * q^24 + 3460631286066960520802994294848553614203197326799100 * q^25 + 93159641643008802343361703153674358874682043662336 * q^26 + 12084377134756095104629255763677919783130973382555040 * q^27 + 17172248037558968144537376756119075900141234554929152 * q^28 - 408828336209279227379368505274385966779755922402879240 * q^29 - 538110318532889838793969736377110224776301614297251840 * q^30 + 3799789752719913567257037059011407543542506417455406208 * q^31 + 6129982163463555433433388108601236734474956488734408704 * q^32 + 62216718136234720076912175436040395811344879605468165312 * q^33 + 65582326530774486675746452751808984389419539918143619072 * q^34 + 431767153301184553170750885645944283201771950341035990720 * q^35 + 577914595683534746006577363150871362656072314419299745792 * q^36 + 6801183386761815205425784377566670372797473237706983459352 * q^37 + 6559598755720310574473705317437316221877768362108806758400 * q^38 + 11327031655330197070885706025461449402448174139265298802144 * q^39 - 2546484854163745203205584274150660432487763653884127477760 * q^40 + 56874804657516327155642316307646742627510460774170204545448 * q^41 + 45561979483677286074033721822761719180903349012837861163008 * q^42 - 195612042326640270143679332399870892198183174704527897687504 * q^43 + 249223924413997099203419280962107854932114473139165366059008 * q^44 - 7974393496061748311007765969419683838885297239373320672939080 * q^45 - 4632902446991043071609764558093537051767757086902843703558144 * q^46 - 26837344299723692260252514346441012876376468762050649660269888 * q^47 + 6803206398606016687045493374438715598570618586234125042057216 * q^48 + 49288467772056748491478921994228369389621400119046767962459108 * q^49 + 237812771154752254447551810483985904734485337875788141795737600 * q^50 + 462279018098899407813413748964859585061118118125593850879008288 * q^51 + 6401881826620840209677866843902262937608427838850834991415296 * q^52 + 45487338963145722322030598089193311856717264520906215815881816 * q^53 + 830432073380921814576773627357058722333743090603526299519549440 * q^54 - 2050760578084075114386836605813651219506186672252469754486193120 * q^55 + 1180067899521855165636701347474591981965573827111773174992207872 * q^56 - 3592025896576963719316420752340210472238227670222328115746257600 * q^57 - 28094469339151150293224568244574259740806305945322881152597360640 * q^58 - 36211351257280450133792917437500801540590596428487702560293076880 * q^59 - 36978659515822472927852993596054879014422789587819242807613194240 * q^60 + 355926993234389260836197952322967108098379440839658027389943954808 * q^61 + 261119563513727293109050729509024279847084176781457491228085977088 * q^62 + 1354878537917418371717449932688191098150383285998373405919969463456 * q^63 + 421249166674228746791672110734681729275580381602196445017243910144 * q^64 + 5535868819575966258563337770064603238403854822937797912179994113360 * q^65 + 4275500314553251124960838370592128635913946298920690444546586181632 * q^66 + 2491990477133118795215059534264173871640752538756993508607055683472 * q^67 + 4506783162324312925176300335312460684664503237948693775125149908992 * q^68 + 36011984923282423612732885710686669353728819466689401794442606346624 * q^69 + 29670812846649697502859970521797864502236363135438170030421751889920 * q^70 + 61369373660787623297444370825513800920470177886238250167413906103328 * q^71 + 39713988613469511996446662010030528264172580579870746230364057894912 * q^72 + 456671534259044615009379581820843089057568686566115963985790726852136 * q^73 + 467373763523848250382388250508745044972436409398187647819676565635072 * q^74 + 2274484745358414989035084574628142288008132133113498093192382898732400 * q^75 + 450772194091216429445240588005353147247604717195532969934588372582400 * q^76 + 2937010629095569814915333560530816478733805597591112398546851047158144 * q^77 + 778387688326399048011025618131633095876378404208918525166023274921984 * q^78 + 2026656030798125727242892609149209096074932883431594515097100420626240 * q^79 - 174993106694281841226317741152783755749378573017756654247586677391360 * q^80 - 1690644062388676955190899758084885673044542109854601078388778076183836 * q^81 + 3908406815526737691512327206640483748897384622767229920965275290697728 * q^82 + 15812009999547814415856750888845542429811781646082575448908590281393616 * q^83 + 3130995389174670552096177120478769476523452667952199965531326159781888 * q^84 - 47381303711757475901026713604519693996172406037229330915853699493216080 * q^85 - 13442357191947003357179327260296938825816612575574428538999419325906944 * q^86 - 154442588212957708624899011736533281049174301414639814817610904676124960 * q^87 + 17126537675822296091480855409729418434530303396175771263348924259237888 * q^88 - 244126894674274014119641875856417639495708996405247140614177242434617240 * q^89 - 547996148336325020677785466250868450986753355813559933203104972805242880 * q^90 - 956695923071478195873919348809058005807314877434919486549850807547281472 * q^91 - 318370631926158457559861197620346139940908410808319098178907957031337984 * q^92 - 2677792907975102091334715599122289169140096674655183648095758982803701248 * q^93 - 1844248257260884481506445917115759428754429189071570338982602871897325568 * q^94 - 4616055418633200363736062249001551807751077321632189313148700192365581600 * q^95 + 467512783839212506555050574518383453633693938789845165676965876492926976 * q^96 + 5819977544840824809887571543683857252285947538686838060303213522914493832 * q^97 + 3387077714414939478831988874216735156541302325328582001492198793557311488 * q^98 + 28045365238060746865970778341472050511805413521238694500165502185235671024 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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