LMFDB - Embedded newform 2.74.a.b.1.4

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			1.4
Root			$-1.89813e14$ 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)

$f(q)$	$=$	\(q+6.87195e10 q^{2} +4.40707e17 q^{3} +4.72237e21 q^{4} -6.01656e25 q^{5} +3.02852e28 q^{6} +1.36725e30 q^{7} +3.24519e32 q^{8} +1.26637e35 q^{9} -4.13455e36 q^{10} +1.17371e38 q^{11} +2.08118e39 q^{12} -4.64177e40 q^{13} +9.39565e40 q^{14} -2.65154e43 q^{15} +2.23007e43 q^{16} +7.41645e44 q^{17} +8.70246e45 q^{18} +3.86997e46 q^{19} -2.84124e47 q^{20} +6.02555e47 q^{21} +8.06565e48 q^{22} +5.58055e49 q^{23} +1.43018e50 q^{24} +2.56110e51 q^{25} -3.18980e51 q^{26} +2.60247e52 q^{27} +6.45664e51 q^{28} -1.18607e53 q^{29} -1.82212e54 q^{30} +2.47658e52 q^{31} +1.53250e54 q^{32} +5.17260e55 q^{33} +5.09655e55 q^{34} -8.22612e55 q^{35} +5.98028e56 q^{36} +2.03375e57 q^{37} +2.65942e57 q^{38} -2.04566e58 q^{39} -1.95248e58 q^{40} +1.41862e59 q^{41} +4.14073e58 q^{42} +2.36476e59 q^{43} +5.54267e59 q^{44} -7.61921e60 q^{45} +3.83492e60 q^{46} -7.61861e60 q^{47} +9.82809e60 q^{48} -4.73524e61 q^{49} +1.75998e62 q^{50} +3.26848e62 q^{51} -2.19201e62 q^{52} -6.20840e62 q^{53} +1.78841e63 q^{54} -7.06167e63 q^{55} +4.43697e62 q^{56} +1.70552e64 q^{57} -8.15063e63 q^{58} +4.74332e64 q^{59} -1.25215e65 q^{60} +6.52682e64 q^{61} +1.70189e63 q^{62} +1.73145e65 q^{63} +1.05312e65 q^{64} +2.79275e66 q^{65} +3.55459e66 q^{66} -7.25393e66 q^{67} +3.50232e66 q^{68} +2.45939e67 q^{69} -5.65294e66 q^{70} -2.81253e67 q^{71} +4.10962e67 q^{72} +5.22665e67 q^{73} +1.39758e68 q^{74} +1.12870e69 q^{75} +1.82754e68 q^{76} +1.60475e68 q^{77} -1.40577e69 q^{78} +6.42026e68 q^{79} -1.34174e69 q^{80} +2.91046e69 q^{81} +9.74871e69 q^{82} +1.58123e69 q^{83} +2.84549e69 q^{84} -4.46215e70 q^{85} +1.62505e70 q^{86} -5.22711e70 q^{87} +3.80889e70 q^{88} +4.25333e69 q^{89} -5.23588e71 q^{90} -6.34644e70 q^{91} +2.63534e71 q^{92} +1.09144e70 q^{93} -5.23547e71 q^{94} -2.32839e72 q^{95} +6.75381e71 q^{96} -2.34394e72 q^{97} -3.25403e72 q^{98} +1.48635e73 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	4.40707e17	1.69521	0.847606	−	0.530626i	$-0.178043\pi$
$3$	4.40707e17	1.69521	0.847606	+	0.530626i	$0.178043\pi$
$4$	4.72237e21	0.500000
$5$	−6.01656e25	−1.84903	−0.924513	−	0.381151i	$-0.875528\pi$
$5$	−6.01656e25	−1.84903	−0.924513	+	0.381151i	$0.875528\pi$
$6$	3.02852e28	1.19870
$7$	1.36725e30	0.194880	0.0974402	−	0.995241i	$-0.468935\pi$
$7$	1.36725e30	0.194880	0.0974402	+	0.995241i	$0.468935\pi$
$8$	3.24519e32	0.353553
$9$	1.26637e35	1.87374
$10$	−4.13455e36	−1.30746
$11$	1.17371e38	1.14479	0.572396	−	0.819978i	$-0.306014\pi$
$11$	1.17371e38	1.14479	0.572396	+	0.819978i	$0.306014\pi$
$12$	2.08118e39	0.847606
$13$	−4.64177e40	−1.01801	−0.509004	−	0.860764i	$-0.669986\pi$
$13$	−4.64177e40	−1.01801	−0.509004	+	0.860764i	$0.669986\pi$
$14$	9.39565e40	0.137801
$15$	−2.65154e43	−3.13449
$16$	2.23007e43	0.250000
$17$	7.41645e44	0.909517	0.454758	−	0.890615i	$-0.349726\pi$
$17$	7.41645e44	0.909517	0.454758	+	0.890615i	$0.349726\pi$
$18$	8.70246e45	1.32494
$19$	3.86997e46	0.818844	0.409422	−	0.912345i	$-0.365730\pi$
$19$	3.86997e46	0.818844	0.409422	+	0.912345i	$0.365730\pi$
$20$	−2.84124e47	−0.924513
$21$	6.02555e47	0.330364
$22$	8.06565e48	0.809490
$23$	5.58055e49	1.10563	0.552816	−	0.833303i	$-0.313553\pi$
$23$	5.58055e49	1.10563	0.552816	+	0.833303i	$0.313553\pi$
$24$	1.43018e50	0.599348
$25$	2.56110e51	2.41889
$26$	−3.18980e51	−0.719840
$27$	2.60247e52	1.48118
$28$	6.45664e51	0.0974402
$29$	−1.18607e53	−0.497261	−0.248631	−	0.968598i	$-0.579981\pi$
$29$	−1.18607e53	−0.497261	−0.248631	+	0.968598i	$0.579981\pi$
$30$	−1.82212e54	−2.21642
$31$	2.47658e52	0.00910227	0.00455114	−	0.999990i	$-0.498551\pi$
$31$	2.47658e52	0.00910227	0.00455114	+	0.999990i	$0.498551\pi$
$32$	1.53250e54	0.176777
$33$	5.17260e55	1.94066
$34$	5.09655e55	0.643125
$35$	−8.22612e55	−0.360339
$36$	5.98028e56	0.936872
$37$	2.03375e57	1.17202	0.586010	−	0.810303i	$-0.300698\pi$
$37$	2.03375e57	1.17202	0.586010	+	0.810303i	$0.300698\pi$
$38$	2.65942e57	0.579010
$39$	−2.04566e58	−1.72574
$40$	−1.95248e58	−0.653729
$41$	1.41862e59	1.92866	0.964332	−	0.264696i	$-0.0852717\pi$
$41$	1.41862e59	1.92866	0.964332	+	0.264696i	$0.0852717\pi$
$42$	4.14073e58	0.233602
$43$	2.36476e59	0.565182	0.282591	−	0.959241i	$-0.408806\pi$
$43$	2.36476e59	0.565182	0.282591	+	0.959241i	$0.408806\pi$
$44$	5.54267e59	0.572396
$45$	−7.61921e60	−3.46460
$46$	3.83492e60	0.781800
$47$	−7.61861e60	−0.708441	−0.354221	−	0.935162i	$-0.615254\pi$
$47$	−7.61861e60	−0.708441	−0.354221	+	0.935162i	$0.615254\pi$
$48$	9.82809e60	0.423803
$49$	−4.73524e61	−0.962022
$50$	1.75998e62	1.71042
$51$	3.26848e62	1.54182
$52$	−2.19201e62	−0.509004
$53$	−6.20840e62	−0.719300	−0.359650	−	0.933087i	$-0.617104\pi$
$53$	−6.20840e62	−0.719300	−0.359650	+	0.933087i	$0.617104\pi$
$54$	1.78841e63	1.04735
$55$	−7.06167e63	−2.11675
$56$	4.43697e62	0.0689007
$57$	1.70552e64	1.38812
$58$	−8.15063e63	−0.351617
$59$	4.74332e64	1.09644	0.548219	−	0.836335i	$-0.315306\pi$
$59$	4.74332e64	1.09644	0.548219	+	0.836335i	$0.315306\pi$
$60$	−1.25215e65	−1.56725
$61$	6.52682e64	0.446851	0.223425	−	0.974721i	$-0.428276\pi$
$61$	6.52682e64	0.446851	0.223425	+	0.974721i	$0.428276\pi$
$62$	1.70189e63	0.00643628
$63$	1.73145e65	0.365156
$64$	1.05312e65	0.125000
$65$	2.79275e66	1.88232
$66$	3.55459e66	1.37226
$67$	−7.25393e66	−1.61750	−0.808748	−	0.588156i	$-0.799854\pi$
$67$	−7.25393e66	−1.61750	−0.808748	+	0.588156i	$0.799854\pi$
$68$	3.50232e66	0.454758
$69$	2.45939e67	1.87428
$70$	−5.65294e66	−0.254798
$71$	−2.81253e67	−0.755385	−0.377692	−	0.925931i	$-0.623282\pi$
$71$	−2.81253e67	−0.755385	−0.377692	+	0.925931i	$0.623282\pi$
$72$	4.10962e67	0.662469
$73$	5.22665e67	0.509260	0.254630	−	0.967039i	$-0.418046\pi$
$73$	5.22665e67	0.509260	0.254630	+	0.967039i	$0.418046\pi$
$74$	1.39758e68	0.828744
$75$	1.12870e69	4.10054
$76$	1.82754e68	0.409422
$77$	1.60475e68	0.223098
$78$	−1.40577e69	−1.22028
$79$	6.42026e68	0.350077	0.175039	−	0.984562i	$-0.443995\pi$
$79$	6.42026e68	0.350077	0.175039	+	0.984562i	$0.443995\pi$
$80$	−1.34174e69	−0.462256
$81$	2.91046e69	0.637175
$82$	9.74871e69	1.36377
$83$	1.58123e69	0.142117	0.0710584	−	0.997472i	$-0.477362\pi$
$83$	1.58123e69	0.142117	0.0710584	+	0.997472i	$0.477362\pi$
$84$	2.84549e69	0.165182
$85$	−4.46215e70	−1.68172
$86$	1.62505e70	0.399644
$87$	−5.22711e70	−0.842963
$88$	3.80889e70	0.404745
$89$	4.25333e69	0.0299222	0.0149611	−	0.999888i	$-0.495238\pi$
$89$	4.25333e69	0.0299222	0.0149611	+	0.999888i	$0.495238\pi$
$90$	−5.23588e71	−2.44984
$91$	−6.34644e70	−0.198390
$92$	2.63534e71	0.552816
$93$	1.09144e70	0.0154303
$94$	−5.23547e71	−0.500944
$95$	−2.32839e72	−1.51406
$96$	6.75381e71	0.299674
$97$	−2.34394e72	−0.712490	−0.356245	−	0.934393i	$-0.615943\pi$
$97$	−2.34394e72	−0.712490	−0.356245	+	0.934393i	$0.615943\pi$
$98$	−3.25403e72	−0.680252
$99$	1.48635e73	2.14505
$100$	1.20945e73	1.20945
$101$	5.56733e72	0.387183	0.193592	−	0.981082i	$-0.437986\pi$
$101$	5.56733e72	0.387183	0.193592	+	0.981082i	$0.437986\pi$
$102$	2.24608e73	1.09023
$103$	7.78162e72	0.264552	0.132276	−	0.991213i	$-0.457771\pi$
$103$	7.78162e72	0.264552	0.132276	+	0.991213i	$0.457771\pi$
$104$	−1.50634e73	−0.359920
$105$	−3.62531e73	−0.610851
$106$	−4.26638e73	−0.508622
$107$	1.02093e74	0.863947	0.431974	−	0.901886i	$-0.357817\pi$
$107$	1.02093e74	0.863947	0.431974	+	0.901886i	$0.357817\pi$
$108$	1.22898e74	0.740591
$109$	4.14598e73	0.178468	0.0892340	−	0.996011i	$-0.471558\pi$
$109$	4.14598e73	0.178468	0.0892340	+	0.996011i	$0.471558\pi$
$110$	−4.85274e74	−1.49677
$111$	8.96289e74	1.98682
$112$	3.04906e73	0.0487201
$113$	−1.34444e75	−1.55303	−0.776515	−	0.630099i	$-0.783014\pi$
$113$	−1.34444e75	−1.55303	−0.776515	+	0.630099i	$0.783014\pi$
$114$	1.17203e75	0.981546
$115$	−3.35757e75	−2.04434
$116$	−5.60107e74	−0.248631
$117$	−5.87822e75	−1.90749
$118$	3.25959e75	0.775299
$119$	1.01401e75	0.177247
$120$	−8.60473e75	−1.10821
$121$	3.26433e75	0.310547
$122$	4.48520e75	0.315971
$123$	6.25197e76	3.26949
$124$	1.16953e74	0.00455114
$125$	−9.03875e76	−2.62357
$126$	1.18984e76	0.258205
$127$	6.87081e76	1.11731	0.558653	−	0.829401i	$-0.311318\pi$
$127$	6.87081e76	1.11731	0.558653	+	0.829401i	$0.311318\pi$
$128$	7.23701e75	0.0883883
$129$	1.04217e77	0.958103
$130$	1.91916e77	1.33100
$131$	−1.63020e77	−0.854747	−0.427373	−	0.904075i	$-0.640561\pi$
$131$	−1.63020e77	−0.854747	−0.427373	+	0.904075i	$0.640561\pi$
$132$	2.44269e77	0.970332
$133$	5.29121e76	0.159577
$134$	−4.98486e77	−1.14374
$135$	−1.56579e78	−2.73874
$136$	2.40678e77	0.321563
$137$	−3.23319e77	−0.330621	−0.165311	−	0.986242i	$-0.552863\pi$
$137$	−3.23319e77	−0.330621	−0.165311	+	0.986242i	$0.552863\pi$
$138$	1.69008e78	1.32532
$139$	1.33914e78	0.806838	0.403419	−	0.915015i	$-0.367822\pi$
$139$	1.33914e78	0.806838	0.403419	+	0.915015i	$0.367822\pi$
$140$	−3.88467e77	−0.180169
$141$	−3.35757e78	−1.20096
$142$	−1.93276e78	−0.534138
$143$	−5.44807e78	−1.16541
$144$	2.82411e78	0.468436
$145$	7.13608e78	0.919448
$146$	3.59173e78	0.360101
$147$	−2.08685e79	−1.63083
$148$	9.60413e78	0.586010
$149$	−1.70860e79	−0.815347	−0.407674	−	0.913128i	$-0.633660\pi$
$149$	−1.70860e79	−0.815347	−0.407674	+	0.913128i	$0.633660\pi$
$150$	7.75634e79	2.89952
$151$	5.81417e78	0.170541	0.0852705	−	0.996358i	$-0.472825\pi$
$151$	5.81417e78	0.170541	0.0852705	+	0.996358i	$0.472825\pi$
$152$	1.25588e79	0.289505
$153$	9.39200e79	1.70420
$154$	1.10277e79	0.157754
$155$	−1.49005e78	−0.0168303
$156$	−9.66036e79	−0.862870
$157$	−2.65451e80	−1.87779	−0.938895	−	0.344204i	$-0.888149\pi$
$157$	−2.65451e80	−1.87779	−0.938895	+	0.344204i	$0.888149\pi$
$158$	4.41197e79	0.247542
$159$	−2.73608e80	−1.21937
$160$	−9.22035e79	−0.326865
$161$	7.62998e79	0.215466
$162$	2.00005e80	0.450551
$163$	5.19219e80	0.934335	0.467168	−	0.884169i	$-0.345274\pi$
$163$	5.19219e80	0.934335	0.467168	+	0.884169i	$0.345274\pi$
$164$	6.69926e80	0.964332
$165$	−3.11213e81	−3.58834
$166$	1.08661e80	0.100492
$167$	1.52156e81	1.13015	0.565076	−	0.825039i	$-0.308847\pi$
$167$	1.52156e81	1.13015	0.565076	+	0.825039i	$0.308847\pi$
$168$	1.95540e80	0.116801
$169$	7.55530e79	0.0363402
$170$	−3.06637e81	−1.18916
$171$	4.90083e81	1.53431
$172$	1.11673e81	0.282591
$173$	1.82325e81	0.373391	0.186695	−	0.982418i	$-0.440222\pi$
$173$	1.82325e81	0.373391	0.186695	+	0.982418i	$0.440222\pi$
$174$	−3.59204e81	−0.596065
$175$	3.50166e81	0.471395
$176$	2.61745e81	0.286198
$177$	2.09042e82	1.85870
$178$	2.92287e80	0.0211582
$179$	−9.69849e80	−0.0572227	−0.0286114	−	0.999591i	$-0.509109\pi$
$179$	−9.69849e80	−0.0572227	−0.0286114	+	0.999591i	$0.509109\pi$
$180$	−3.59807e82	−1.73230
$181$	−4.27027e81	−0.167953	−0.0839765	−	0.996468i	$-0.526762\pi$
$181$	−4.27027e81	−0.167953	−0.0839765	+	0.996468i	$0.526762\pi$
$182$	−4.36124e81	−0.140283
$183$	2.87641e82	0.757507
$184$	1.81099e82	0.390900
$185$	−1.22362e83	−2.16710
$186$	7.50035e80	0.0109109
$187$	8.70474e82	1.04121
$188$	−3.59779e82	−0.354221
$189$	3.55822e82	0.288654
$190$	−1.60006e83	−1.07061
$191$	−2.67648e83	−1.47859	−0.739293	−	0.673384i	$-0.764840\pi$
$191$	−2.67648e83	−1.47859	−0.739293	+	0.673384i	$0.764840\pi$
$192$	4.64119e82	0.211902
$193$	−1.63168e83	−0.616300	−0.308150	−	0.951338i	$-0.599710\pi$
$193$	−1.63168e83	−0.616300	−0.308150	+	0.951338i	$0.599710\pi$
$194$	−1.61075e83	−0.503806
$195$	1.23078e84	3.19094
$196$	−2.23615e83	−0.481011
$197$	4.78478e83	0.854761	0.427380	−	0.904072i	$-0.359436\pi$
$197$	4.78478e83	0.854761	0.427380	+	0.904072i	$0.359436\pi$
$198$	1.02141e84	1.51678
$199$	7.72352e83	0.954285	0.477143	−	0.878826i	$-0.341673\pi$
$199$	7.72352e83	0.954285	0.477143	+	0.878826i	$0.341673\pi$
$200$	8.31126e83	0.855208
$201$	−3.19686e84	−2.74200
$202$	3.82584e83	0.273780
$203$	−1.62165e83	−0.0969065
$204$	1.54350e84	0.770912
$205$	−8.53523e84	−3.56615
$206$	5.34749e83	0.187067
$207$	7.06706e84	2.07167
$208$	−1.03515e84	−0.254502
$209$	4.54221e84	0.937406
$210$	−2.49129e84	−0.431937
$211$	−2.41050e84	−0.351397	−0.175698	−	0.984444i	$-0.556218\pi$
$211$	−2.41050e84	−0.351397	−0.175698	+	0.984444i	$0.556218\pi$
$212$	−2.93183e84	−0.359650
$213$	−1.23950e85	−1.28054
$214$	7.01576e84	0.610903
$215$	−1.42277e85	−1.04504
$216$	8.44551e84	0.523677
$217$	3.38609e82	0.00177386
$218$	2.84910e84	0.126196
$219$	2.30342e85	0.863303
$220$	−3.33478e85	−1.05837
$221$	−3.44255e85	−0.925895
$222$	6.15925e85	1.40490
$223$	2.03817e84	0.0394560	0.0197280	−	0.999805i	$-0.493720\pi$
$223$	2.03817e84	0.0394560	0.0197280	+	0.999805i	$0.493720\pi$
$224$	2.09530e84	0.0344503
$225$	3.24332e86	4.53239
$226$	−9.23895e85	−1.09816
$227$	−1.34214e86	−1.35786	−0.678929	−	0.734204i	$-0.737556\pi$
$227$	−1.34214e86	−1.35786	−0.678929	+	0.734204i	$0.737556\pi$
$228$	8.05411e85	0.694058
$229$	−2.03245e85	−0.149288	−0.0746438	−	0.997210i	$-0.523782\pi$
$229$	−2.03245e85	−0.149288	−0.0746438	+	0.997210i	$0.523782\pi$
$230$	−2.30730e86	−1.44557
$231$	7.07223e85	0.378198
$232$	−3.84903e85	−0.175808
$233$	−2.65619e86	−1.03698	−0.518488	−	0.855085i	$-0.673505\pi$
$233$	−2.65619e86	−1.03698	−0.518488	+	0.855085i	$0.673505\pi$
$234$	−4.03948e86	−1.34880
$235$	4.58378e86	1.30993
$236$	2.23997e86	0.548219
$237$	2.82945e86	0.593455
$238$	6.96824e85	0.125333
$239$	−1.21129e87	−1.86950	−0.934752	−	0.355301i	$-0.884378\pi$
$239$	−1.21129e87	−1.86950	−0.934752	+	0.355301i	$0.884378\pi$
$240$	−5.91313e86	−0.783623
$241$	−5.87394e86	−0.668817	−0.334409	−	0.942428i	$-0.608537\pi$
$241$	−5.87394e86	−0.668817	−0.334409	+	0.942428i	$0.608537\pi$
$242$	2.24323e86	0.219590
$243$	−4.76226e86	−0.401036
$244$	3.08220e86	0.223425
$245$	2.84898e87	1.77880
$246$	4.29632e87	2.31188
$247$	−1.79635e87	−0.833590
$248$	8.03695e84	0.00321814
$249$	6.96860e86	0.240918
$250$	−6.21138e87	−1.85515
$251$	6.83827e87	1.76545	0.882726	−	0.469889i	$-0.155706\pi$
$251$	6.83827e87	1.76545	0.882726	+	0.469889i	$0.155706\pi$
$252$	8.17652e86	0.182578
$253$	6.54992e87	1.26572
$254$	4.72159e87	0.790055
$255$	−1.96650e88	−2.85087
$256$	4.97323e86	0.0625000
$257$	−1.37152e88	−1.49501	−0.747504	−	0.664257i	$-0.768748\pi$
$257$	−1.37152e88	−1.49501	−0.747504	+	0.664257i	$0.768748\pi$
$258$	7.16171e87	0.677481
$259$	2.78064e87	0.228404
$260$	1.31884e88	0.941161
$261$	−1.50201e88	−0.931740
$262$	−1.12026e88	−0.604397
$263$	−1.37975e88	−0.647763	−0.323881	−	0.946098i	$-0.604988\pi$
$263$	−1.37975e88	−0.647763	−0.323881	+	0.946098i	$0.604988\pi$
$264$	1.67861e88	0.686128
$265$	3.73532e88	1.33000
$266$	3.63609e87	0.112838
$267$	1.87447e87	0.0507245
$268$	−3.42557e88	−0.808748
$269$	−5.70510e88	−1.17572	−0.587862	−	0.808962i	$-0.700030\pi$
$269$	−5.70510e88	−1.17572	−0.587862	+	0.808962i	$0.700030\pi$
$270$	−1.07600e89	−1.93658
$271$	5.21634e88	0.820326	0.410163	−	0.912012i	$-0.365472\pi$
$271$	5.21634e88	0.820326	0.410163	+	0.912012i	$0.365472\pi$
$272$	1.65392e88	0.227379
$273$	−2.79692e88	−0.336313
$274$	−2.22183e88	−0.233785
$275$	3.00598e89	2.76913
$276$	1.16141e89	0.937141
$277$	1.77935e89	1.25820	0.629100	−	0.777324i	$-0.283424\pi$
$277$	1.77935e89	1.25820	0.629100	+	0.777324i	$0.283424\pi$
$278$	9.20251e88	0.570521
$279$	3.13627e87	0.0170553
$280$	−2.66953e88	−0.127399
$281$	−3.49527e89	−1.46453	−0.732267	−	0.681017i	$-0.761538\pi$
$281$	−3.49527e89	−1.46453	−0.732267	+	0.681017i	$0.761538\pi$
$282$	−2.30731e89	−0.849206
$283$	5.88769e89	1.90432	0.952160	−	0.305600i	$-0.0988571\pi$
$283$	5.88769e89	1.90432	0.952160	+	0.305600i	$0.0988571\pi$
$284$	−1.32818e89	−0.377692
$285$	−1.02614e90	−2.56666
$286$	−3.74389e89	−0.824067
$287$	1.93961e89	0.375859
$288$	1.94071e89	0.331234
$289$	−1.14885e89	−0.172780
$290$	4.90387e89	0.650148
$291$	−1.03299e90	−1.20782
$292$	2.46822e89	0.254630
$293$	2.14538e90	1.95361	0.976803	−	0.214141i	$-0.0686953\pi$
$293$	2.14538e90	1.95361	0.976803	+	0.214141i	$0.0686953\pi$
$294$	−1.43407e90	−1.15317
$295$	−2.85385e90	−2.02734
$296$	6.59991e89	0.414372
$297$	3.05454e90	1.69565
$298$	−1.17414e90	−0.576538
$299$	−2.59036e90	−1.12554
$300$	5.33012e90	2.05027
$301$	3.23321e89	0.110143
$302$	3.99547e89	0.120591
$303$	2.45356e90	0.656358
$304$	8.63033e89	0.204711
$305$	−3.92690e90	−0.826239
$306$	6.45414e90	1.20505
$307$	−5.86814e90	−0.972635	−0.486317	−	0.873782i	$-0.661660\pi$
$307$	−5.86814e90	−0.972635	−0.486317	+	0.873782i	$0.661660\pi$
$308$	7.57820e89	0.111549
$309$	3.42941e90	0.448472
$310$	−1.02395e89	−0.0119008
$311$	7.44177e90	0.768993	0.384496	−	0.923127i	$-0.374375\pi$
$311$	7.44177e90	0.768993	0.384496	+	0.923127i	$0.374375\pi$
$312$	−6.63855e90	−0.610141
$313$	6.11264e89	0.0499874	0.0249937	−	0.999688i	$-0.492043\pi$
$313$	6.11264e89	0.0499874	0.0249937	+	0.999688i	$0.492043\pi$
$314$	−1.82417e91	−1.32780
$315$	−1.04173e91	−0.675183
$316$	3.03188e90	0.175039
$317$	4.50179e90	0.231591	0.115796	−	0.993273i	$-0.463058\pi$
$317$	4.50179e90	0.231591	0.115796	+	0.993273i	$0.463058\pi$
$318$	−1.88022e91	−0.862223
$319$	−1.39210e91	−0.569260
$320$	−6.33617e90	−0.231128
$321$	4.49930e91	1.46457
$322$	5.24328e90	0.152358
$323$	2.87015e91	0.744753
$324$	1.37443e91	0.318587
$325$	−1.18881e92	−2.46245
$326$	3.56804e91	0.660675
$327$	1.82716e91	0.302541
$328$	4.60370e91	0.681886
$329$	−1.04165e91	−0.138061
$330$	−2.13864e92	−2.53734
$331$	4.58554e91	0.487157	0.243578	−	0.969881i	$-0.421679\pi$
$331$	4.58554e91	0.487157	0.243578	+	0.969881i	$0.421679\pi$
$332$	7.46716e90	0.0710584
$333$	2.57549e92	2.19607
$334$	1.04561e92	0.799138
$335$	4.36437e92	2.99079
$336$	1.34374e91	0.0825910
$337$	−5.44105e91	−0.300049	−0.150024	−	0.988682i	$-0.547935\pi$
$337$	−5.44105e91	−0.300049	−0.150024	+	0.988682i	$0.547935\pi$
$338$	5.19196e90	0.0256964
$339$	−5.92506e92	−2.63272
$340$	−2.10719e92	−0.840860
$341$	2.90677e90	0.0104202
$342$	3.36783e92	1.08492
$343$	−1.32041e92	−0.382360
$344$	7.67408e91	0.199822
$345$	−1.47970e93	−3.46559
$346$	1.25293e92	0.264027
$347$	4.82676e92	0.915439	0.457720	−	0.889097i	$-0.348666\pi$
$347$	4.82676e92	0.915439	0.457720	+	0.889097i	$0.348666\pi$
$348$	−2.46843e92	−0.421482
$349$	2.26931e92	0.348951	0.174476	−	0.984661i	$-0.444177\pi$
$349$	2.26931e92	0.348951	0.174476	+	0.984661i	$0.444177\pi$
$350$	2.40632e92	0.333327
$351$	−1.20801e93	−1.50786
$352$	1.79870e92	0.202372
$353$	3.79349e92	0.384824	0.192412	−	0.981314i	$-0.438369\pi$
$353$	3.79349e92	0.384824	0.192412	+	0.981314i	$0.438369\pi$
$354$	1.43652e93	1.31430
$355$	1.69218e93	1.39673
$356$	2.00858e91	0.0149611
$357$	4.46882e92	0.300471
$358$	−6.66475e91	−0.0404626
$359$	4.26527e92	0.233883	0.116942	−	0.993139i	$-0.462691\pi$
$359$	4.26527e92	0.233883	0.116942	+	0.993139i	$0.462691\pi$
$360$	−2.47258e93	−1.22492
$361$	−7.35970e92	−0.329494
$362$	−2.93451e92	−0.118761
$363$	1.43861e93	0.526444
$364$	−2.99702e92	−0.0991949
$365$	−3.14465e93	−0.941634
$366$	1.97666e93	0.535638
$367$	1.28566e93	0.315365	0.157683	−	0.987490i	$-0.449598\pi$
$367$	1.28566e93	0.315365	0.157683	+	0.987490i	$0.449598\pi$
$368$	1.24450e93	0.276408
$369$	1.79651e94	3.61382
$370$	−8.40865e93	−1.53237
$371$	−8.48841e92	−0.140178
$372$	5.15420e91	0.00771514
$373$	−5.43996e93	−0.738284	−0.369142	−	0.929373i	$-0.620348\pi$
$373$	−5.43996e93	−0.738284	−0.369142	+	0.929373i	$0.620348\pi$
$374$	5.98185e93	0.736244
$375$	−3.98344e94	−4.44751
$376$	−2.47238e93	−0.250472
$377$	5.50548e93	0.506216
$378$	2.44519e93	0.204109
$379$	5.07066e93	0.384356	0.192178	−	0.981360i	$-0.438445\pi$
$379$	5.07066e93	0.384356	0.192178	+	0.981360i	$0.438445\pi$
$380$	−1.09955e94	−0.757032
$381$	3.02802e94	1.89407
$382$	−1.83927e94	−1.04552
$383$	1.73605e94	0.897032	0.448516	−	0.893775i	$-0.351953\pi$
$383$	1.73605e94	0.897032	0.448516	+	0.893775i	$0.351953\pi$
$384$	3.18940e93	0.149837
$385$	−9.65504e93	−0.412513
$386$	−1.12128e94	−0.435790
$387$	2.99467e94	1.05901
$388$	−1.10690e94	−0.356245
$389$	−5.19087e94	−1.52083	−0.760414	−	0.649439i	$-0.775004\pi$
$389$	−5.19087e94	−1.52083	−0.760414	+	0.649439i	$0.775004\pi$
$390$	8.45788e94	2.25633
$391$	4.13879e94	1.00559
$392$	−1.53667e94	−0.340126
$393$	−7.18439e94	−1.44898
$394$	3.28808e94	0.604407
$395$	−3.86279e94	−0.647302
$396$	7.01909e94	1.07252
$397$	9.79236e94	1.36469	0.682345	−	0.731030i	$-0.260960\pi$
$397$	9.79236e94	1.36469	0.682345	+	0.731030i	$0.260960\pi$
$398$	5.30757e94	0.674782
$399$	2.33187e94	0.270517
$400$	5.71145e94	0.604724
$401$	−1.67677e95	−1.62071	−0.810354	−	0.585941i	$-0.800725\pi$
$401$	−1.67677e95	−1.62071	−0.810354	+	0.585941i	$0.800725\pi$
$402$	−2.19686e95	−1.93889
$403$	−1.14957e93	−0.00926619
$404$	2.62910e94	0.193592
$405$	−1.75110e95	−1.17815
$406$	−1.11439e94	−0.0685232
$407$	2.38703e95	1.34172
$408$	1.06068e95	0.545117
$409$	−1.70027e95	−0.799127	−0.399564	−	0.916705i	$-0.630838\pi$
$409$	−1.70027e95	−0.799127	−0.399564	+	0.916705i	$0.630838\pi$
$410$	−5.86537e95	−2.52165
$411$	−1.42489e95	−0.560473
$412$	3.67476e94	0.132276
$413$	6.48529e94	0.213674
$414$	4.85645e95	1.46489
$415$	−9.51357e94	−0.262777
$416$	−7.11349e94	−0.179960
$417$	5.90169e95	1.36776
$418$	3.12138e95	0.662846
$419$	4.66273e95	0.907463	0.453731	−	0.891138i	$-0.350093\pi$
$419$	4.66273e95	0.907463	0.453731	+	0.891138i	$0.350093\pi$
$420$	−1.71200e95	−0.305426
$421$	6.58342e95	1.07685	0.538425	−	0.842674i	$-0.319020\pi$
$421$	6.58342e95	1.07685	0.538425	+	0.842674i	$0.319020\pi$
$422$	−1.65648e95	−0.248475
$423$	−9.64801e95	−1.32744
$424$	−2.01474e95	−0.254311
$425$	1.89943e96	2.20002
$426$	−8.51780e95	−0.905477
$427$	8.92377e94	0.0870825
$428$	4.82120e95	0.431974
$429$	−2.40100e96	−1.97561
$430$	−9.77720e95	−0.738951
$431$	−1.71148e96	−1.18837	−0.594184	−	0.804329i	$-0.702525\pi$
$431$	−1.71148e96	−1.18837	−0.594184	+	0.804329i	$0.702525\pi$
$432$	5.80371e95	0.370296
$433$	2.15999e96	1.26661	0.633306	−	0.773901i	$-0.281697\pi$
$433$	2.15999e96	1.26661	0.633306	+	0.773901i	$0.281697\pi$
$434$	2.32690e93	0.00125431
$435$	3.14492e96	1.55866
$436$	1.95789e95	0.0892340
$437$	2.15966e96	0.905341
$438$	1.58290e96	0.610448
$439$	−3.71212e96	−1.31725	−0.658624	−	0.752472i	$-0.728861\pi$
$439$	−3.71212e96	−1.31725	−0.658624	+	0.752472i	$0.728861\pi$
$440$	−2.29164e96	−0.748383
$441$	−5.99658e96	−1.80258
$442$	−2.36570e96	−0.654707
$443$	−2.95072e96	−0.751956	−0.375978	−	0.926629i	$-0.622693\pi$
$443$	−2.95072e96	−0.751956	−0.375978	+	0.926629i	$0.622693\pi$
$444$	4.23261e96	0.993412
$445$	−2.55904e95	−0.0553270
$446$	1.40062e95	0.0278996
$447$	−7.52994e96	−1.38219
$448$	1.43988e95	0.0243601
$449$	−7.64002e96	−1.19153	−0.595763	−	0.803161i	$-0.703150\pi$
$449$	−7.64002e96	−1.19153	−0.595763	+	0.803161i	$0.703150\pi$
$450$	2.22879e97	3.20488
$451$	1.66505e97	2.20792
$452$	−6.34896e96	−0.776515
$453$	2.56234e96	0.289103
$454$	−9.22313e96	−0.960151
$455$	3.81837e96	0.366828
$456$	5.53474e96	0.490773
$457$	5.24571e96	0.429401	0.214700	−	0.976680i	$-0.431122\pi$
$457$	5.24571e96	0.429401	0.214700	+	0.976680i	$0.431122\pi$
$458$	−1.39669e96	−0.105562
$459$	1.93011e97	1.34716
$460$	−1.58557e97	−1.02217
$461$	1.20990e97	0.720550	0.360275	−	0.932846i	$-0.382683\pi$
$461$	1.20990e97	0.720550	0.360275	+	0.932846i	$0.382683\pi$
$462$	4.86000e96	0.267426
$463$	−2.83398e97	−1.44109	−0.720544	−	0.693409i	$-0.756108\pi$
$463$	−2.83398e97	−1.44109	−0.720544	+	0.693409i	$0.756108\pi$
$464$	−2.64503e96	−0.124315
$465$	−6.56674e95	−0.0285310
$466$	−1.82532e97	−0.733252
$467$	2.09309e97	0.777537	0.388768	−	0.921336i	$-0.372901\pi$
$467$	2.09309e97	0.777537	0.388768	+	0.921336i	$0.372901\pi$
$468$	−2.77591e97	−0.953744
$469$	−9.91791e96	−0.315218
$470$	3.14995e97	0.926258
$471$	−1.16986e98	−3.18325
$472$	1.53930e97	0.387650
$473$	2.77553e97	0.647015
$474$	1.94439e97	0.419636
$475$	9.91140e97	1.98070
$476$	4.78854e96	0.0886235
$477$	−7.86215e97	−1.34779
$478$	−8.32395e97	−1.32194
$479$	9.84743e97	1.44903	0.724514	−	0.689260i	$-0.242064\pi$
$479$	9.84743e97	1.44903	0.724514	+	0.689260i	$0.242064\pi$
$480$	−4.06347e97	−0.554105
$481$	−9.44021e97	−1.19313
$482$	−4.03654e97	−0.472925
$483$	3.36259e97	0.365261
$484$	1.54154e97	0.155274
$485$	1.41025e98	1.31741
$486$	−3.27260e97	−0.283576
$487$	1.79002e98	1.43897	0.719485	−	0.694508i	$-0.244378\pi$
$487$	1.79002e98	1.43897	0.719485	+	0.694508i	$0.244378\pi$
$488$	2.11807e97	0.157986
$489$	2.28823e98	1.58390
$490$	1.95781e98	1.25780
$491$	−1.44665e98	−0.862761	−0.431380	−	0.902170i	$-0.641973\pi$
$491$	−1.44665e98	−0.862761	−0.431380	+	0.902170i	$0.641973\pi$
$492$	2.95241e98	1.63475
$493$	−8.79646e97	−0.452267
$494$	−1.23444e98	−0.589437
$495$	−8.94272e98	−3.96625
$496$	5.52295e95	0.00227557
$497$	−3.84543e97	−0.147210
$498$	4.78879e97	0.170355
$499$	2.56109e97	0.0846749	0.0423374	−	0.999103i	$-0.486520\pi$
$499$	2.56109e97	0.0846749	0.0423374	+	0.999103i	$0.486520\pi$
$500$	−4.26843e98	−1.31179
$501$	6.70560e98	1.91585
$502$	4.69923e98	1.24836
$503$	−5.69558e98	−1.40704	−0.703520	−	0.710675i	$-0.748389\pi$
$503$	−5.69558e98	−1.40704	−0.703520	+	0.710675i	$0.748389\pi$
$504$	5.61886e97	0.129102
$505$	−3.34961e98	−0.715912
$506$	4.50107e98	0.894998
$507$	3.32967e97	0.0616043
$508$	3.24465e98	0.558653
$509$	−1.31519e97	−0.0210761	−0.0105381	−	0.999944i	$-0.503354\pi$
$509$	−1.31519e97	−0.0210761	−0.0105381	+	0.999944i	$0.503354\pi$
$510$	−1.35137e99	−2.01587
$511$	7.14612e97	0.0992448
$512$	3.41758e97	0.0441942
$513$	1.00715e99	1.21286
$514$	−9.42503e98	−1.05713
$515$	−4.68185e98	−0.489163
$516$	4.92149e98	0.479051
$517$	−8.94201e98	−0.811018
$518$	1.91084e98	0.161506
$519$	8.03520e98	0.632977
$520$	9.06298e98	0.665501
$521$	9.33703e98	0.639193	0.319596	−	0.947554i	$-0.396453\pi$
$521$	9.33703e98	0.639193	0.319596	+	0.947554i	$0.396453\pi$
$522$	−1.03217e99	−0.658840
$523$	1.72766e99	1.02837	0.514183	−	0.857681i	$-0.328095\pi$
$523$	1.72766e99	1.02837	0.514183	+	0.857681i	$0.328095\pi$
$524$	−7.69838e98	−0.427373
$525$	1.54321e99	0.799115
$526$	−9.48158e98	−0.458038
$527$	1.83674e97	0.00827867
$528$	1.15353e99	0.485166
$529$	5.66646e98	0.222423
$530$	2.56689e99	0.940455
$531$	6.00682e99	2.05445
$532$	2.49870e98	0.0797884
$533$	−6.58492e99	−1.96339
$534$	1.28813e98	0.0358677
$535$	−6.14247e99	−1.59746
$536$	−2.35403e99	−0.571871
$537$	−4.27419e98	−0.0970047
$538$	−3.92052e99	−0.831362
$539$	−5.55778e99	−1.10131
$540$	−7.39424e99	−1.36937
$541$	5.02383e99	0.869631	0.434816	−	0.900520i	$-0.356814\pi$
$541$	5.02383e99	0.869631	0.434816	+	0.900520i	$0.356814\pi$
$542$	3.58464e99	0.580058
$543$	−1.88194e99	−0.284716
$544$	1.13657e99	0.160781
$545$	−2.49446e99	−0.329992
$546$	−1.92203e99	−0.237809
$547$	7.38676e99	0.854902	0.427451	−	0.904038i	$-0.359412\pi$
$547$	7.38676e99	0.854902	0.427451	+	0.904038i	$0.359412\pi$
$548$	−1.52683e99	−0.165311
$549$	8.26540e99	0.837285
$550$	2.06570e100	1.95807
$551$	−4.59007e99	−0.407180
$552$	7.98116e99	0.662659
$553$	8.77808e98	0.0682233
$554$	1.22276e100	0.889682
$555$	−5.39258e100	−3.67369
$556$	6.32392e99	0.403419
$557$	2.60182e100	1.55440	0.777200	−	0.629254i	$-0.216639\pi$
$557$	2.60182e100	1.55440	0.777200	+	0.629254i	$0.216639\pi$
$558$	2.15523e98	0.0120599
$559$	−1.09767e100	−0.575359
$560$	−1.83449e99	−0.0900847
$561$	3.83624e100	1.76507
$562$	−2.40193e100	−1.03558
$563$	−3.27071e100	−1.32156	−0.660778	−	0.750582i	$-0.729773\pi$
$563$	−3.27071e100	−1.32156	−0.660778	+	0.750582i	$0.729773\pi$
$564$	−1.58557e100	−0.600479
$565$	8.08893e100	2.87159
$566$	4.04599e100	1.34656
$567$	3.97932e99	0.124173
$568$	−9.12720e99	−0.267069
$569$	1.42662e100	0.391480	0.195740	−	0.980656i	$-0.437289\pi$
$569$	1.42662e100	0.391480	0.195740	+	0.980656i	$0.437289\pi$
$570$	−7.05157e100	−1.81490
$571$	−4.71485e100	−1.13828	−0.569141	−	0.822240i	$-0.692724\pi$
$571$	−4.71485e100	−1.13828	−0.569141	+	0.822240i	$0.692724\pi$
$572$	−2.57278e100	−0.582703
$573$	−1.17954e101	−2.50652
$574$	1.33289e100	0.265772
$575$	1.42924e101	2.67441
$576$	1.33365e100	0.234218
$577$	−5.71235e100	−0.941668	−0.470834	−	0.882222i	$-0.656047\pi$
$577$	−5.71235e100	−0.941668	−0.470834	+	0.882222i	$0.656047\pi$
$578$	−7.89484e99	−0.122174
$579$	−7.19091e100	−1.04476
$580$	3.36992e100	0.459724
$581$	2.16193e99	0.0276958
$582$	−7.09867e100	−0.854059
$583$	−7.28683e100	−0.823449
$584$	1.69615e100	0.180050
$585$	3.53666e101	3.52699
$586$	1.47430e101	1.38141
$587$	−1.41978e101	−1.25006	−0.625030	−	0.780601i	$-0.714913\pi$
$587$	−1.41978e101	−1.25006	−0.625030	+	0.780601i	$0.714913\pi$
$588$	−9.85488e100	−0.815415
$589$	9.58428e98	0.00745335
$590$	−1.96115e101	−1.43355
$591$	2.10869e101	1.44900
$592$	4.53542e100	0.293005
$593$	−1.84307e101	−1.11956	−0.559778	−	0.828642i	$-0.689114\pi$
$593$	−1.84307e101	−1.11956	−0.559778	+	0.828642i	$0.689114\pi$
$594$	2.09906e101	1.19900
$595$	−6.10086e100	−0.327734
$596$	−8.06866e100	−0.407674
$597$	3.40381e101	1.61772
$598$	−1.78008e101	−0.795879
$599$	−3.83951e100	−0.161509	−0.0807546	−	0.996734i	$-0.525733\pi$
$599$	−3.83951e100	−0.161509	−0.0807546	+	0.996734i	$0.525733\pi$
$600$	3.66283e101	1.44976
$601$	2.44570e101	0.910929	0.455465	−	0.890254i	$-0.349473\pi$
$601$	2.44570e101	0.910929	0.455465	+	0.890254i	$0.349473\pi$
$602$	2.22184e100	0.0778828
$603$	−9.18619e101	−3.03077
$604$	2.74566e100	0.0852705
$605$	−1.96400e101	−0.574210
$606$	1.68607e101	0.464115
$607$	7.40100e101	1.91824	0.959120	−	0.283000i	$-0.0913297\pi$
$607$	7.40100e101	1.91824	0.959120	+	0.283000i	$0.0913297\pi$
$608$	5.93072e100	0.144753
$609$	−7.14674e100	−0.164277
$610$	−2.69854e101	−0.584239
$611$	3.53638e101	0.721199
$612$	4.43525e101	0.852101
$613$	1.17887e101	0.213382	0.106691	−	0.994292i	$-0.465974\pi$
$613$	1.17887e101	0.213382	0.106691	+	0.994292i	$0.465974\pi$
$614$	−4.03256e101	−0.687757
$615$	−3.76154e102	−6.04538
$616$	5.20770e100	0.0788769
$617$	−8.71142e101	−1.24360	−0.621799	−	0.783177i	$-0.713598\pi$
$617$	−8.71142e101	−1.24360	−0.621799	+	0.783177i	$0.713598\pi$
$618$	2.35667e101	0.317117
$619$	7.46816e101	0.947339	0.473669	−	0.880703i	$-0.342929\pi$
$619$	7.46816e101	0.947339	0.473669	+	0.880703i	$0.342929\pi$
$620$	−7.03654e99	−0.00841517
$621$	1.45232e102	1.63764
$622$	5.11395e101	0.543760
$623$	5.81535e99	0.00583126
$624$	−4.56197e101	−0.431435
$625$	2.72654e102	2.43216
$626$	4.20057e100	0.0353464
$627$	2.00178e102	1.58910
$628$	−1.25356e102	−0.938895
$629$	1.50832e102	1.06597
$630$	−7.15874e101	−0.477427
$631$	1.75887e102	1.10704	0.553518	−	0.832837i	$-0.313285\pi$
$631$	1.75887e102	1.10704	0.553518	+	0.832837i	$0.313285\pi$
$632$	2.08349e101	0.123771
$633$	−1.06232e102	−0.595692
$634$	3.09360e101	0.163760
$635$	−4.13386e102	−2.06593
$636$	−1.29208e102	−0.609683
$637$	2.19799e102	0.979346
$638$	−9.56645e101	−0.402528
$639$	−3.56172e102	−1.41540
$640$	−4.35419e101	−0.163432
$641$	5.11680e102	1.81418	0.907091	−	0.420935i	$-0.138298\pi$
$641$	5.11680e102	1.81418	0.907091	+	0.420935i	$0.138298\pi$
$642$	3.09190e102	1.03561
$643$	−2.35088e101	−0.0743925	−0.0371963	−	0.999308i	$-0.511843\pi$
$643$	−2.35088e101	−0.0743925	−0.0371963	+	0.999308i	$0.511843\pi$
$644$	3.60316e101	0.107733
$645$	−6.27025e102	−1.77156
$646$	1.97235e102	0.526620
$647$	−5.13307e102	−1.29530	−0.647651	−	0.761937i	$-0.724249\pi$
$647$	−5.13307e102	−1.29530	−0.647651	+	0.761937i	$0.724249\pi$
$648$	9.44499e101	0.225275
$649$	5.56727e102	1.25519
$650$	−8.16941e102	−1.74122
$651$	1.49227e100	0.00300706
$652$	2.45194e102	0.467168
$653$	−1.01178e103	−1.82286	−0.911430	−	0.411454i	$-0.865021\pi$
$653$	−1.01178e103	−1.82286	−0.911430	+	0.411454i	$0.865021\pi$
$654$	1.25562e102	0.213929
$655$	9.80816e102	1.58045
$656$	3.16364e102	0.482166
$657$	6.61890e102	0.954223
$658$	−7.15818e101	−0.0976241
$659$	1.89029e102	0.243900	0.121950	−	0.992536i	$-0.461085\pi$
$659$	1.89029e102	0.243900	0.121950	+	0.992536i	$0.461085\pi$
$660$	−1.46966e103	−1.79417
$661$	9.13646e100	0.0105542	0.00527709	−	0.999986i	$-0.498320\pi$
$661$	9.13646e100	0.0105542	0.00527709	+	0.999986i	$0.498320\pi$
$662$	3.15116e102	0.344472
$663$	−1.51715e103	−1.56959
$664$	5.13139e101	0.0502459
$665$	−3.18348e102	−0.295062
$666$	1.76987e103	1.55285
$667$	−6.61894e102	−0.549788
$668$	7.18535e102	0.565076
$669$	8.98236e101	0.0668863
$670$	2.99917e103	2.11481
$671$	7.66057e102	0.511551
$672$	9.23413e101	0.0584006
$673$	−2.13125e103	−1.27669	−0.638344	−	0.769751i	$-0.720380\pi$
$673$	−2.13125e103	−1.27669	−0.638344	+	0.769751i	$0.720380\pi$
$674$	−3.73906e102	−0.212166
$675$	6.66520e103	3.58283
$676$	3.56789e101	0.0181701
$677$	−5.31475e102	−0.256446	−0.128223	−	0.991745i	$-0.540927\pi$
$677$	−5.31475e102	−0.256446	−0.128223	+	0.991745i	$0.540927\pi$
$678$	−4.07167e103	−1.86161
$679$	−3.20475e102	−0.138850
$680$	−1.44805e103	−0.594578
$681$	−5.91491e103	−2.30186
$682$	1.99752e101	0.00736820
$683$	−5.72510e102	−0.200183	−0.100092	−	0.994978i	$-0.531914\pi$
$683$	−5.72510e102	−0.200183	−0.100092	+	0.994978i	$0.531914\pi$
$684$	2.31435e103	0.767153
$685$	1.94527e103	0.611327
$686$	−9.07376e102	−0.270369
$687$	−8.95713e102	−0.253074
$688$	5.27359e102	0.141295
$689$	2.88179e103	0.732254
$690$	−1.01684e104	−2.45055
$691$	4.29996e103	0.982914	0.491457	−	0.870902i	$-0.336464\pi$
$691$	4.29996e103	0.982914	0.491457	+	0.870902i	$0.336464\pi$
$692$	8.61006e102	0.186695
$693$	2.03221e103	0.418028
$694$	3.31692e103	0.647313
$695$	−8.05702e103	−1.49186
$696$	−1.69629e103	−0.298032
$697$	1.05212e104	1.75415
$698$	1.55946e103	0.246746
$699$	−1.17060e104	−1.75789
$700$	1.65361e103	0.235698
$701$	−1.07964e104	−1.46074	−0.730369	−	0.683053i	$-0.760652\pi$
$701$	−1.07964e104	−1.46074	−0.730369	+	0.683053i	$0.760652\pi$
$702$	−8.30136e103	−1.06622
$703$	7.87057e103	0.959703
$704$	1.23606e103	0.143099
$705$	2.02010e104	2.22060
$706$	2.60687e103	0.272112
$707$	7.61191e102	0.0754545
$708$	9.87171e103	0.929348
$709$	−4.86603e103	−0.435098	−0.217549	−	0.976049i	$-0.569806\pi$
$709$	−4.86603e103	−0.435098	−0.217549	+	0.976049i	$0.569806\pi$
$710$	1.16286e104	0.987634
$711$	8.13046e103	0.655956
$712$	1.38028e102	0.0105791
$713$	1.38207e102	0.0100638
$714$	3.07095e103	0.212465
$715$	3.27786e104	2.15487
$716$	−4.57998e102	−0.0286114
$717$	−5.33826e104	−3.16921
$718$	2.93107e103	0.165381
$719$	−2.92832e103	−0.157041	−0.0785207	−	0.996912i	$-0.525020\pi$
$719$	−2.92832e103	−0.157041	−0.0785207	+	0.996912i	$0.525020\pi$
$720$	−1.69914e104	−0.866150
$721$	1.06394e103	0.0515560
$722$	−5.05755e103	−0.232987
$723$	−2.58869e104	−1.13379
$724$	−2.01658e103	−0.0839765
$725$	−3.03766e104	−1.20282
$726$	9.88607e103	0.372252
$727$	2.53306e104	0.907069	0.453534	−	0.891239i	$-0.350163\pi$
$727$	2.53306e104	0.907069	0.453534	+	0.891239i	$0.350163\pi$
$728$	−2.05954e103	−0.0701414
$729$	−4.06580e104	−1.31702
$730$	−2.16098e104	−0.665836
$731$	1.75381e104	0.514042
$732$	1.35835e104	0.378754
$733$	−9.16740e103	−0.243193	−0.121596	−	0.992580i	$-0.538801\pi$
$733$	−9.16740e103	−0.243193	−0.121596	+	0.992580i	$0.538801\pi$
$734$	8.83497e103	0.222997
$735$	1.25557e105	3.01545
$736$	8.55216e103	0.195450
$737$	−8.51398e104	−1.85169
$738$	1.23455e105	2.55536
$739$	−5.93173e104	−1.16858	−0.584292	−	0.811544i	$-0.698628\pi$
$739$	−5.93173e104	−1.16858	−0.584292	+	0.811544i	$0.698628\pi$
$740$	−5.77838e104	−1.08355
$741$	−7.91665e104	−1.41311
$742$	−5.83319e103	−0.0991205
$743$	1.03004e105	1.66633	0.833167	−	0.553021i	$-0.186525\pi$
$743$	1.03004e105	1.66633	0.833167	+	0.553021i	$0.186525\pi$
$744$	3.54194e102	0.00545543
$745$	1.02799e105	1.50760
$746$	−3.73831e104	−0.522046
$747$	2.00243e104	0.266291
$748$	4.11070e104	0.520603
$749$	1.39586e104	0.168366
$750$	−2.73740e105	−3.14487
$751$	−1.02419e105	−1.12078	−0.560392	−	0.828228i	$-0.689349\pi$
$751$	−1.02419e105	−1.12078	−0.560392	+	0.828228i	$0.689349\pi$
$752$	−1.69901e104	−0.177110
$753$	3.01368e105	2.99281
$754$	3.78334e104	0.357949
$755$	−3.49813e104	−0.315335
$756$	1.68032e104	0.144327
$757$	−1.34912e104	−0.110421	−0.0552103	−	0.998475i	$-0.517583\pi$
$757$	−1.34912e104	−0.110421	−0.0552103	+	0.998475i	$0.517583\pi$
$758$	3.48453e104	0.271781
$759$	2.88660e105	2.14566
$760$	−7.55606e104	−0.535303
$761$	1.84315e104	0.124458	0.0622288	−	0.998062i	$-0.480179\pi$
$761$	1.84315e104	0.124458	0.0622288	+	0.998062i	$0.480179\pi$
$762$	2.08084e105	1.33931
$763$	5.66858e103	0.0347799
$764$	−1.26393e105	−0.739293
$765$	−5.65075e105	−3.15111
$766$	1.19301e105	0.634298
$767$	−2.20174e105	−1.11618
$768$	2.19174e104	0.105951
$769$	1.37771e104	0.0635107	0.0317554	−	0.999496i	$-0.489890\pi$
$769$	1.37771e104	0.0635107	0.0317554	+	0.999496i	$0.489890\pi$
$770$	−6.63489e104	−0.291691
$771$	−6.04439e105	−2.53436
$772$	−7.70537e104	−0.308150
$773$	1.82843e105	0.697472	0.348736	−	0.937221i	$-0.386611\pi$
$773$	1.82843e105	0.697472	0.348736	+	0.937221i	$0.386611\pi$
$774$	2.05792e105	0.748830
$775$	6.34277e103	0.0220174
$776$	−7.60653e104	−0.251903
$777$	1.22545e105	0.387193
$778$	−3.56714e105	−1.07539
$779$	5.49004e105	1.57928
$780$	5.81221e105	1.59547
$781$	−3.30109e105	−0.864758
$782$	2.84415e105	0.711060
$783$	−3.08672e105	−0.736535
$784$	−1.05599e105	−0.240505
$785$	1.59710e106	3.47208
$786$	−4.93707e105	−1.02458
$787$	−3.90064e105	−0.772784	−0.386392	−	0.922335i	$-0.626279\pi$
$787$	−3.90064e105	−0.772784	−0.386392	+	0.922335i	$0.626279\pi$
$788$	2.25955e105	0.427380
$789$	−6.08066e105	−1.09810
$790$	−2.65449e105	−0.457712
$791$	−1.83819e105	−0.302655
$792$	4.82348e105	0.758389
$793$	−3.02960e105	−0.454898
$794$	6.72926e105	0.964981
$795$	1.64618e106	2.25464
$796$	3.64733e105	0.477143
$797$	−8.67794e105	−1.08440	−0.542198	−	0.840251i	$-0.682408\pi$
$797$	−8.67794e105	−1.08440	−0.542198	+	0.840251i	$0.682408\pi$
$798$	1.60245e105	0.191284
$799$	−5.65031e105	−0.644339
$800$	3.92488e105	0.427604
$801$	5.38631e104	0.0560666
$802$	−1.15227e106	−1.14601
$803$	6.13455e105	0.582996
$804$	−1.50967e106	−1.37100
$805$	−4.59062e105	−0.398402
$806$	−7.89978e103	−0.00655218
$807$	−2.51428e106	−1.99310
$808$	1.80670e105	0.136890
$809$	1.18602e106	0.858955	0.429478	−	0.903077i	$-0.358698\pi$
$809$	1.18602e106	0.858955	0.429478	+	0.903077i	$0.358698\pi$
$810$	−1.20334e106	−0.833079
$811$	1.04206e106	0.689653	0.344826	−	0.938666i	$-0.387938\pi$
$811$	1.04206e106	0.689653	0.344826	+	0.938666i	$0.387938\pi$
$812$	−7.65805e104	−0.0484532
$813$	2.29888e106	1.39063
$814$	1.64035e106	0.948739
$815$	−3.12391e106	−1.72761
$816$	7.28896e105	0.385456
$817$	9.15155e105	0.462796
$818$	−1.16841e106	−0.565068
$819$	−8.03697e105	−0.371732
$820$	−4.03065e106	−1.78307
$821$	−3.06697e106	−1.29773	−0.648864	−	0.760904i	$-0.724756\pi$
$821$	−3.06697e106	−1.29773	−0.648864	+	0.760904i	$0.724756\pi$
$822$	−9.79177e105	−0.396315
$823$	−6.90406e105	−0.267307	−0.133654	−	0.991028i	$-0.542671\pi$
$823$	−6.90406e105	−0.267307	−0.133654	+	0.991028i	$0.542671\pi$
$824$	2.52528e105	0.0935333
$825$	1.32476e107	4.69426
$826$	4.45666e105	0.151091
$827$	4.71629e106	1.52985	0.764926	−	0.644119i	$-0.222776\pi$
$827$	4.71629e106	1.52985	0.764926	+	0.644119i	$0.222776\pi$
$828$	3.33733e106	1.03584
$829$	−6.66879e106	−1.98065	−0.990323	−	0.138781i	$-0.955682\pi$
$829$	−6.66879e106	−1.98065	−0.990323	+	0.138781i	$0.955682\pi$
$830$	−6.53768e105	−0.185812
$831$	7.84172e106	2.13292
$832$	−4.88835e105	−0.127251
$833$	−3.51187e106	−0.874975
$834$	4.05561e106	0.967154
$835$	−9.15453e106	−2.08968
$836$	2.14500e106	0.468703
$837$	6.44522e104	0.0134821
$838$	3.20421e106	0.641673
$839$	−3.53926e106	−0.678579	−0.339290	−	0.940682i	$-0.610187\pi$
$839$	−3.53926e106	−0.678579	−0.339290	+	0.940682i	$0.610187\pi$
$840$	−1.17648e106	−0.215968
$841$	−4.28247e106	−0.752731
$842$	4.52409e106	0.761447
$843$	−1.54039e107	−2.48270
$844$	−1.13833e106	−0.175698
$845$	−4.54569e105	−0.0671939
$846$	−6.63006e106	−0.938641
$847$	4.46314e105	0.0605196
$848$	−1.38452e106	−0.179825
$849$	2.59474e107	3.22823
$850$	1.30528e107	1.55565
$851$	1.13495e107	1.29582
$852$	−5.85339e106	−0.640269
$853$	−9.52082e105	−0.0997780	−0.0498890	−	0.998755i	$-0.515887\pi$
$853$	−9.52082e105	−0.0997780	−0.0498890	+	0.998755i	$0.515887\pi$
$854$	6.13237e105	0.0615766
$855$	−2.94861e107	−2.83697
$856$	3.31310e106	0.305452
$857$	6.55956e106	0.579529	0.289764	−	0.957098i	$-0.406423\pi$
$857$	6.55956e106	0.579529	0.289764	+	0.957098i	$0.406423\pi$
$858$	−1.64996e107	−1.39697
$859$	−1.41476e107	−1.14798	−0.573989	−	0.818863i	$-0.694605\pi$
$859$	−1.41476e107	−1.14798	−0.573989	+	0.818863i	$0.694605\pi$
$860$	−6.71884e106	−0.522518
$861$	8.54799e106	0.637161
$862$	−1.17612e107	−0.840304
$863$	4.99653e105	0.0342195	0.0171098	−	0.999854i	$-0.494554\pi$
$863$	4.99653e105	0.0342195	0.0171098	+	0.999854i	$0.494554\pi$
$864$	3.98828e106	0.261839
$865$	−1.09697e107	−0.690409
$866$	1.48434e107	0.895631
$867$	−5.06306e106	−0.292898
$868$	1.59904e104	0.000886928 0
$869$	7.53550e106	0.400766
$870$	2.16117e107	1.10214
$871$	3.36711e107	1.64662
$872$	1.34545e106	0.0630980
$873$	−2.96831e107	−1.33502
$874$	1.48410e107	0.640173
$875$	−1.23582e107	−0.511283
$876$	1.08776e107	0.431652
$877$	2.87704e107	1.09512	0.547558	−	0.836767i	$-0.315557\pi$
$877$	2.87704e107	1.09512	0.547558	+	0.836767i	$0.315557\pi$
$878$	−2.55095e107	−0.931435
$879$	9.45486e107	3.31178
$880$	−1.57480e107	−0.529187
$881$	5.29762e107	1.70789	0.853946	−	0.520362i	$-0.174203\pi$
$881$	5.29762e107	1.70789	0.853946	+	0.520362i	$0.174203\pi$
$882$	−4.12082e107	−1.27462
$883$	5.20945e107	1.54606	0.773030	−	0.634369i	$-0.218740\pi$
$883$	5.20945e107	1.54606	0.773030	+	0.634369i	$0.218740\pi$
$884$	−1.62570e107	−0.462948
$885$	−1.25771e108	−3.43678
$886$	−2.02772e107	−0.531713
$887$	−6.50483e107	−1.63691	−0.818453	−	0.574574i	$-0.805168\pi$
$887$	−6.50483e107	−1.63691	−0.818453	+	0.574574i	$0.805168\pi$
$888$	2.90863e107	0.702448
$889$	9.39410e106	0.217741
$890$	−1.75856e106	−0.0391221
$891$	3.41603e107	0.729432
$892$	9.62499e105	0.0197280
$893$	−2.94838e107	−0.580103
$894$	−5.17453e107	−0.977354
$895$	5.83515e106	0.105806
$896$	9.89477e105	0.0172252
$897$	−1.14159e108	−1.90803
$898$	−5.25018e107	−0.842535
$899$	−2.93740e105	−0.00452621
$900$	1.53161e108	2.26620
$901$	−4.60443e107	−0.654216
$902$	1.14421e108	1.56123
$903$	1.42490e107	0.186716
$904$	−4.36297e107	−0.549079
$905$	2.56924e107	0.310549
$906$	1.76083e107	0.204427
$907$	−5.23703e107	−0.584008	−0.292004	−	0.956417i	$-0.594322\pi$
$907$	−5.23703e107	−0.584008	−0.292004	+	0.956417i	$0.594322\pi$
$908$	−6.33809e107	−0.678929
$909$	7.05032e107	0.725483
$910$	2.62397e107	0.259387
$911$	6.95039e107	0.660067	0.330034	−	0.943969i	$-0.392940\pi$
$911$	6.95039e107	0.660067	0.330034	+	0.943969i	$0.392940\pi$
$912$	3.80344e107	0.347029
$913$	1.85590e107	0.162694
$914$	3.60482e107	0.303632
$915$	−1.73061e108	−1.40065
$916$	−9.59795e106	−0.0746438
$917$	−2.22888e107	−0.166573
$918$	1.32636e108	0.952586
$919$	1.60470e108	1.10759	0.553794	−	0.832654i	$-0.313179\pi$
$919$	1.60470e108	1.10759	0.553794	+	0.832654i	$0.313179\pi$
$920$	−1.08959e108	−0.722784
$921$	−2.58613e108	−1.64882
$922$	8.31434e107	0.509506
$923$	1.30551e108	0.768988
$924$	3.33976e107	0.189099
$925$	5.20865e108	2.83500
$926$	−1.94750e108	−1.01900
$927$	9.85444e107	0.495703
$928$	−1.81765e107	−0.0879042
$929$	−1.44798e108	−0.673268	−0.336634	−	0.941635i	$-0.609289\pi$
$929$	−1.44798e108	−0.673268	−0.336634	+	0.941635i	$0.609289\pi$
$930$	−4.51263e106	−0.0201745
$931$	−1.83252e108	−0.787746
$932$	−1.25435e108	−0.518488
$933$	3.27964e108	1.30361
$934$	1.43836e108	0.549802
$935$	−5.23725e108	−1.92522
$936$	−1.90759e108	−0.674399
$937$	−4.06681e108	−1.38280	−0.691400	−	0.722472i	$-0.743006\pi$
$937$	−4.06681e108	−1.38280	−0.691400	+	0.722472i	$0.743006\pi$
$938$	−6.81554e107	−0.222893
$939$	2.69388e107	0.0847392
$940$	2.16463e108	0.654963
$941$	−1.02707e108	−0.298935	−0.149468	−	0.988767i	$-0.547756\pi$
$941$	−1.02707e108	−0.298935	−0.149468	+	0.988767i	$0.547756\pi$
$942$	−8.03922e108	−2.25090
$943$	7.91670e108	2.13239
$944$	1.05780e108	0.274110
$945$	−2.14082e108	−0.533728
$946$	1.90733e108	0.457509
$947$	4.82553e107	0.111371	0.0556853	−	0.998448i	$-0.482266\pi$
$947$	4.82553e107	0.111371	0.0556853	+	0.998448i	$0.482266\pi$
$948$	1.33617e108	0.296728
$949$	−2.42609e108	−0.518430
$950$	6.81106e108	1.40057
$951$	1.98397e108	0.392596
$952$	3.29066e107	0.0626663
$953$	−7.60641e108	−1.39408	−0.697041	−	0.717031i	$-0.745501\pi$
$953$	−7.60641e108	−1.39408	−0.697041	+	0.717031i	$0.745501\pi$
$954$	−5.40283e108	−0.953028
$955$	1.61032e109	2.73394
$956$	−5.72018e108	−0.934752
$957$	−6.13509e108	−0.965017
$958$	6.76710e108	1.02462
$959$	−4.42057e107	−0.0644317
$960$	−2.79240e108	−0.391811
$961$	−7.40232e108	−0.999917
$962$	−6.48727e108	−0.843668
$963$	1.29288e109	1.61882
$964$	−2.77389e108	−0.334409
$965$	9.81707e108	1.13955
$966$	2.31075e108	0.258278
$967$	−2.33112e108	−0.250899	−0.125449	−	0.992100i	$-0.540037\pi$
$967$	−2.33112e108	−0.250899	−0.125449	+	0.992100i	$0.540037\pi$
$968$	1.05933e108	0.109795
$969$	1.26489e109	1.26251
$970$	9.69114e108	0.931551
$971$	3.57624e108	0.331074	0.165537	−	0.986204i	$-0.447064\pi$
$971$	3.57624e108	0.331074	0.165537	+	0.986204i	$0.447064\pi$
$972$	−2.24891e108	−0.200518
$973$	1.83094e108	0.157237
$974$	1.23010e109	1.01751
$975$	−5.23915e109	−4.17438
$976$	1.45553e108	0.111713
$977$	−3.42553e108	−0.253266	−0.126633	−	0.991950i	$-0.540417\pi$
$977$	−3.42553e108	−0.253266	−0.126633	+	0.991950i	$0.540417\pi$
$978$	1.57246e109	1.11998
$979$	4.99216e107	0.0342547
$980$	1.34539e109	0.889401
$981$	5.25037e108	0.334404
$982$	−9.94134e108	−0.610064
$983$	−1.73690e108	−0.102700	−0.0513502	−	0.998681i	$-0.516352\pi$
$983$	−1.73690e108	−0.102700	−0.0513502	+	0.998681i	$0.516352\pi$
$984$	2.02888e109	1.15594
$985$	−2.87879e109	−1.58047
$986$	−6.04488e108	−0.319801
$987$	−4.59063e108	−0.234043
$988$	−8.48303e108	−0.416795
$989$	1.31966e109	0.624883
$990$	−6.14539e109	−2.80456
$991$	−1.78550e109	−0.785363	−0.392682	−	0.919675i	$-0.628453\pi$
$991$	−1.78550e109	−0.785363	−0.392682	+	0.919675i	$0.628453\pi$
$992$	3.79534e106	0.00160907
$993$	2.02088e109	0.825834
$994$	−2.64256e108	−0.104093
$995$	−4.64690e109	−1.76450
$996$	3.29083e108	0.120459
$997$	6.27538e108	0.221446	0.110723	−	0.993851i	$-0.464683\pi$
$997$	6.27538e108	0.221446	0.110723	+	0.993851i	$0.464683\pi$
$998$	1.75997e108	0.0598742
$999$	5.29279e109	1.73598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.74.a.b.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.74.a.b.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+6.87195e10 q^{2} +4.40707e17 q^{3} +4.72237e21 q^{4} -6.01656e25 q^{5} +3.02852e28 q^{6} +1.36725e30 q^{7} +3.24519e32 q^{8} +1.26637e35 q^{9} -4.13455e36 q^{10} +1.17371e38 q^{11} +2.08118e39 q^{12} -4.64177e40 q^{13} +9.39565e40 q^{14} -2.65154e43 q^{15} +2.23007e43 q^{16} +7.41645e44 q^{17} +8.70246e45 q^{18} +3.86997e46 q^{19} -2.84124e47 q^{20} +6.02555e47 q^{21} +8.06565e48 q^{22} +5.58055e49 q^{23} +1.43018e50 q^{24} +2.56110e51 q^{25} -3.18980e51 q^{26} +2.60247e52 q^{27} +6.45664e51 q^{28} -1.18607e53 q^{29} -1.82212e54 q^{30} +2.47658e52 q^{31} +1.53250e54 q^{32} +5.17260e55 q^{33} +5.09655e55 q^{34} -8.22612e55 q^{35} +5.98028e56 q^{36} +2.03375e57 q^{37} +2.65942e57 q^{38} -2.04566e58 q^{39} -1.95248e58 q^{40} +1.41862e59 q^{41} +4.14073e58 q^{42} +2.36476e59 q^{43} +5.54267e59 q^{44} -7.61921e60 q^{45} +3.83492e60 q^{46} -7.61861e60 q^{47} +9.82809e60 q^{48} -4.73524e61 q^{49} +1.75998e62 q^{50} +3.26848e62 q^{51} -2.19201e62 q^{52} -6.20840e62 q^{53} +1.78841e63 q^{54} -7.06167e63 q^{55} +4.43697e62 q^{56} +1.70552e64 q^{57} -8.15063e63 q^{58} +4.74332e64 q^{59} -1.25215e65 q^{60} +6.52682e64 q^{61} +1.70189e63 q^{62} +1.73145e65 q^{63} +1.05312e65 q^{64} +2.79275e66 q^{65} +3.55459e66 q^{66} -7.25393e66 q^{67} +3.50232e66 q^{68} +2.45939e67 q^{69} -5.65294e66 q^{70} -2.81253e67 q^{71} +4.10962e67 q^{72} +5.22665e67 q^{73} +1.39758e68 q^{74} +1.12870e69 q^{75} +1.82754e68 q^{76} +1.60475e68 q^{77} -1.40577e69 q^{78} +6.42026e68 q^{79} -1.34174e69 q^{80} +2.91046e69 q^{81} +9.74871e69 q^{82} +1.58123e69 q^{83} +2.84549e69 q^{84} -4.46215e70 q^{85} +1.62505e70 q^{86} -5.22711e70 q^{87} +3.80889e70 q^{88} +4.25333e69 q^{89} -5.23588e71 q^{90} -6.34644e70 q^{91} +2.63534e71 q^{92} +1.09144e70 q^{93} -5.23547e71 q^{94} -2.32839e72 q^{95} +6.75381e71 q^{96} -2.34394e72 q^{97} -3.25403e72 q^{98} +1.48635e73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 274877906944 q^{2} + 30\!\cdots\!76 q^{3} + 18\!\cdots\!84 q^{4} - 78\!\cdots\!60 q^{5} + 20\!\cdots\!36 q^{6} + 36\!\cdots\!12 q^{7} + 12\!\cdots\!24 q^{8} + 12\!\cdots\!52 q^{9} - 53\!\cdots\!60 q^{10}+ \cdots + 28\!\cdots\!24 q^{99}+O(q^{100}) \) 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

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Groups

Database

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