LMFDB - Embedded newform 2.74.a.b.1.1

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			1.1
Root			$2.29885e14$ 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)

$f(q)$	$=$	\(q+6.87195e10 q^{2} -3.65112e17 q^{3} +4.72237e21 q^{4} -6.80519e24 q^{5} -2.50903e28 q^{6} +6.19950e30 q^{7} +3.24519e32 q^{8} +6.57217e34 q^{9} -4.67649e35 q^{10} +3.23190e37 q^{11} -1.72419e39 q^{12} -6.31056e40 q^{13} +4.26026e41 q^{14} +2.48466e42 q^{15} +2.23007e43 q^{16} -4.49909e44 q^{17} +4.51636e45 q^{18} +3.27330e46 q^{19} -3.21366e46 q^{20} -2.26351e48 q^{21} +2.22095e48 q^{22} -8.46773e49 q^{23} -1.18486e50 q^{24} -1.01248e51 q^{25} -4.33658e51 q^{26} +6.80388e50 q^{27} +2.92763e52 q^{28} +7.55802e51 q^{29} +1.70744e53 q^{30} +5.30479e54 q^{31} +1.53250e54 q^{32} -1.18001e55 q^{33} -3.09175e55 q^{34} -4.21888e55 q^{35} +3.10362e56 q^{36} +1.75519e57 q^{37} +2.24940e57 q^{38} +2.30406e58 q^{39} -2.20841e57 q^{40} -4.90971e58 q^{41} -1.55547e59 q^{42} -7.94351e58 q^{43} +1.52622e59 q^{44} -4.47249e59 q^{45} -5.81898e60 q^{46} +1.68814e61 q^{47} -8.14227e60 q^{48} -1.07880e61 q^{49} -6.95771e61 q^{50} +1.64267e62 q^{51} -2.98008e62 q^{52} +1.52771e63 q^{53} +4.67559e61 q^{54} -2.19937e62 q^{55} +2.01185e63 q^{56} -1.19512e64 q^{57} +5.19383e62 q^{58} -5.86986e64 q^{59} +1.17335e64 q^{60} +1.23093e65 q^{61} +3.64543e65 q^{62} +4.07442e65 q^{63} +1.05312e65 q^{64} +4.29445e65 q^{65} -8.10895e65 q^{66} +4.29028e64 q^{67} -2.12463e66 q^{68} +3.09167e67 q^{69} -2.89919e66 q^{70} +3.23078e67 q^{71} +2.13279e67 q^{72} +5.08128e67 q^{73} +1.20615e68 q^{74} +3.69669e68 q^{75} +1.54577e68 q^{76} +2.00362e68 q^{77} +1.58334e69 q^{78} +2.74338e69 q^{79} -1.51761e68 q^{80} -4.69023e69 q^{81} -3.37393e69 q^{82} +6.35075e69 q^{83} -1.06891e70 q^{84} +3.06171e69 q^{85} -5.45874e69 q^{86} -2.75952e69 q^{87} +1.04881e70 q^{88} -4.25484e70 q^{89} -3.07347e70 q^{90} -3.91223e71 q^{91} -3.99877e71 q^{92} -1.93685e72 q^{93} +1.16008e72 q^{94} -2.22754e71 q^{95} -5.59533e71 q^{96} +6.06774e72 q^{97} -7.41343e71 q^{98} +2.12406e72 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.65112e17	−1.40443	−0.702216	−	0.711964i	$-0.747806\pi$
$3$	−3.65112e17	−1.40443	−0.702216	+	0.711964i	$0.747806\pi$
$4$	4.72237e21	0.500000
$5$	−6.80519e24	−0.209139	−0.104570	−	0.994518i	$-0.533346\pi$
$5$	−6.80519e24	−0.209139	−0.104570	+	0.994518i	$0.533346\pi$
$6$	−2.50903e28	−0.993083
$7$	6.19950e30	0.883646	0.441823	−	0.897102i	$-0.354332\pi$
$7$	6.19950e30	0.883646	0.441823	+	0.897102i	$0.354332\pi$
$8$	3.24519e32	0.353553
$9$	6.57217e34	0.972427
$10$	−4.67649e35	−0.147884
$11$	3.23190e37	0.315228	0.157614	−	0.987501i	$-0.449620\pi$
$11$	3.23190e37	0.315228	0.157614	+	0.987501i	$0.449620\pi$
$12$	−1.72419e39	−0.702216
$13$	−6.31056e40	−1.38400	−0.691999	−	0.721899i	$-0.743270\pi$
$13$	−6.31056e40	−1.38400	−0.691999	+	0.721899i	$0.743270\pi$
$14$	4.26026e41	0.624832
$15$	2.48466e42	0.293721
$16$	2.23007e43	0.250000
$17$	−4.49909e44	−0.551746	−0.275873	−	0.961194i	$-0.588967\pi$
$17$	−4.49909e44	−0.551746	−0.275873	+	0.961194i	$0.588967\pi$
$18$	4.51636e45	0.687610
$19$	3.27330e46	0.692596	0.346298	−	0.938125i	$-0.387439\pi$
$19$	3.27330e46	0.692596	0.346298	+	0.938125i	$0.387439\pi$
$20$	−3.21366e46	−0.104570
$21$	−2.26351e48	−1.24102
$22$	2.22095e48	0.222900
$23$	−8.46773e49	−1.67765	−0.838824	−	0.544403i	$-0.816756\pi$
$23$	−8.46773e49	−1.67765	−0.838824	+	0.544403i	$0.816756\pi$
$24$	−1.18486e50	−0.496541
$25$	−1.01248e51	−0.956261
$26$	−4.33658e51	−0.978634
$27$	6.80388e50	0.0387239
$28$	2.92763e52	0.441823
$29$	7.55802e51	0.0316870	0.0158435	−	0.999874i	$-0.494957\pi$
$29$	7.55802e51	0.0316870	0.0158435	+	0.999874i	$0.494957\pi$
$30$	1.70744e53	0.207692
$31$	5.30479e54	1.94970	0.974848	−	0.222872i	$-0.0715432\pi$
$31$	5.30479e54	1.94970	0.974848	+	0.222872i	$0.0715432\pi$
$32$	1.53250e54	0.176777
$33$	−1.18001e55	−0.442717
$34$	−3.09175e55	−0.390143
$35$	−4.21888e55	−0.184805
$36$	3.10362e56	0.486214
$37$	1.75519e57	1.01149	0.505743	−	0.862684i	$-0.331218\pi$
$37$	1.75519e57	1.01149	0.505743	+	0.862684i	$0.331218\pi$
$38$	2.24940e57	0.489739
$39$	2.30406e58	1.94373
$40$	−2.20841e57	−0.0739418
$41$	−4.90971e58	−0.667491	−0.333745	−	0.942663i	$-0.608313\pi$
$41$	−4.90971e58	−0.667491	−0.333745	+	0.942663i	$0.608313\pi$
$42$	−1.55547e59	−0.877533
$43$	−7.94351e58	−0.189852	−0.0949258	−	0.995484i	$-0.530261\pi$
$43$	−7.94351e58	−0.189852	−0.0949258	+	0.995484i	$0.530261\pi$
$44$	1.52622e59	0.157614
$45$	−4.47249e59	−0.203373
$46$	−5.81898e60	−1.18628
$47$	1.68814e61	1.56978	0.784888	−	0.619638i	$-0.212720\pi$
$47$	1.68814e61	1.56978	0.784888	+	0.619638i	$0.212720\pi$
$48$	−8.14227e60	−0.351108
$49$	−1.07880e61	−0.219171
$50$	−6.95771e61	−0.676179
$51$	1.64267e62	0.774889
$52$	−2.98008e62	−0.691999
$53$	1.52771e63	1.76999	0.884996	−	0.465599i	$-0.154161\pi$
$53$	1.52771e63	1.76999	0.884996	+	0.465599i	$0.154161\pi$
$54$	4.67559e61	0.0273819
$55$	−2.19937e62	−0.0659266
$56$	2.01185e63	0.312416
$57$	−1.19512e64	−0.972703
$58$	5.19383e62	0.0224061
$59$	−5.86986e64	−1.35684	−0.678422	−	0.734673i	$-0.737336\pi$
$59$	−5.86986e64	−1.35684	−0.678422	+	0.734673i	$0.737336\pi$
$60$	1.17335e64	0.146861
$61$	1.23093e65	0.842741	0.421371	−	0.906889i	$-0.361549\pi$
$61$	1.23093e65	0.842741	0.421371	+	0.906889i	$0.361549\pi$
$62$	3.64543e65	1.37864
$63$	4.07442e65	0.859281
$64$	1.05312e65	0.125000
$65$	4.29445e65	0.289448
$66$	−8.10895e65	−0.313048
$67$	4.29028e64	0.00956654	0.00478327	−	0.999989i	$-0.498477\pi$
$67$	4.29028e64	0.00956654	0.00478327	+	0.999989i	$0.498477\pi$
$68$	−2.12463e66	−0.275873
$69$	3.09167e67	2.35614
$70$	−2.89919e66	−0.130677
$71$	3.23078e67	0.867715	0.433858	−	0.900981i	$-0.357152\pi$
$71$	3.23078e67	0.867715	0.433858	+	0.900981i	$0.357152\pi$
$72$	2.13279e67	0.343805
$73$	5.08128e67	0.495095	0.247547	−	0.968876i	$-0.420375\pi$
$73$	5.08128e67	0.495095	0.247547	+	0.968876i	$0.420375\pi$
$74$	1.20615e68	0.715229
$75$	3.69669e68	1.34300
$76$	1.54577e68	0.346298
$77$	2.00362e68	0.278550
$78$	1.58334e69	1.37442
$79$	2.74338e69	1.49588	0.747940	−	0.663767i	$-0.231043\pi$
$79$	2.74338e69	1.49588	0.747940	+	0.663767i	$0.231043\pi$
$80$	−1.51761e68	−0.0522848
$81$	−4.69023e69	−1.02681
$82$	−3.37393e69	−0.471987
$83$	6.35075e69	0.570787	0.285394	−	0.958410i	$-0.407876\pi$
$83$	6.35075e69	0.570787	0.285394	+	0.958410i	$0.407876\pi$
$84$	−1.06891e70	−0.620510
$85$	3.06171e69	0.115392
$86$	−5.45874e69	−0.134245
$87$	−2.75952e69	−0.0445022
$88$	1.04881e70	0.111450
$89$	−4.25484e70	−0.299329	−0.149664	−	0.988737i	$-0.547819\pi$
$89$	−4.25484e70	−0.299329	−0.149664	+	0.988737i	$0.547819\pi$
$90$	−3.07347e70	−0.143806
$91$	−3.91223e71	−1.22296
$92$	−3.99877e71	−0.838824
$93$	−1.93685e72	−2.73821
$94$	1.16008e72	1.11000
$95$	−2.22754e71	−0.144849
$96$	−5.59533e71	−0.248271
$97$	6.06774e72	1.84442	0.922208	−	0.386694i	$-0.126383\pi$
$97$	6.06774e72	1.84442	0.922208	+	0.386694i	$0.126383\pi$
$98$	−7.41343e71	−0.154977
$99$	2.12406e72	0.306537
$100$	−4.78130e72	−0.478130
$101$	1.11331e73	0.774255	0.387128	−	0.922026i	$-0.373467\pi$
$101$	1.11331e73	0.774255	0.387128	+	0.922026i	$0.373467\pi$
$102$	1.12884e73	0.547929
$103$	1.61632e73	0.549502	0.274751	−	0.961515i	$-0.411405\pi$
$103$	1.61632e73	0.549502	0.274751	+	0.961515i	$0.411405\pi$
$104$	−2.04789e73	−0.489317
$105$	1.54036e73	0.259546
$106$	1.04983e74	1.25157
$107$	8.46135e73	0.716031	0.358015	−	0.933716i	$-0.383454\pi$
$107$	8.46135e73	0.716031	0.358015	+	0.933716i	$0.383454\pi$
$108$	3.21304e72	0.0193620
$109$	−1.73263e74	−0.745828	−0.372914	−	0.927866i	$-0.621641\pi$
$109$	−1.73263e74	−0.745828	−0.372914	+	0.927866i	$0.621641\pi$
$110$	−1.51140e73	−0.0466171
$111$	−6.40840e74	−1.42056
$112$	1.38253e74	0.220911
$113$	5.79341e74	0.669223	0.334611	−	0.942356i	$-0.391395\pi$
$113$	5.79341e74	0.669223	0.334611	+	0.942356i	$0.391395\pi$
$114$	−8.21282e74	−0.687805
$115$	5.76245e74	0.350862
$116$	3.56917e73	0.0158435
$117$	−4.14741e75	−1.34584
$118$	−4.03374e75	−0.959433
$119$	−2.78921e75	−0.487547
$120$	8.06318e74	0.103846
$121$	−9.46701e75	−0.900631
$122$	8.45888e75	0.595908
$123$	1.79260e76	0.937445
$124$	2.50512e76	0.974848
$125$	1.40954e76	0.409131
$126$	2.79992e76	0.607603
$127$	4.55552e76	0.740802	0.370401	−	0.928872i	$-0.379220\pi$
$127$	4.55552e76	0.740802	0.370401	+	0.928872i	$0.379220\pi$
$128$	7.23701e75	0.0883883
$129$	2.90027e76	0.266633
$130$	2.95113e76	0.204671
$131$	−2.83392e77	−1.48589	−0.742943	−	0.669355i	$-0.766571\pi$
$131$	−2.83392e77	−1.48589	−0.742943	+	0.669355i	$0.766571\pi$
$132$	−5.57243e76	−0.221358
$133$	2.02928e77	0.612009
$134$	2.94826e75	0.00676457
$135$	−4.63017e75	−0.00809868
$136$	−1.46004e77	−0.195072
$137$	−5.93749e77	−0.607158	−0.303579	−	0.952806i	$-0.598182\pi$
$137$	−5.93749e77	−0.607158	−0.303579	+	0.952806i	$0.598182\pi$
$138$	2.12458e78	1.66604
$139$	−2.47728e78	−1.49257	−0.746284	−	0.665627i	$-0.768164\pi$
$139$	−2.47728e78	−1.49257	−0.746284	+	0.665627i	$0.768164\pi$
$140$	−1.99231e77	−0.0924024
$141$	−6.16362e78	−2.20464
$142$	2.22017e78	0.613567
$143$	−2.03951e78	−0.436275
$144$	1.46564e78	0.243107
$145$	−5.14337e76	−0.00662699
$146$	3.49183e78	0.350085
$147$	3.93881e78	0.307810
$148$	8.28863e78	0.505743
$149$	1.12793e79	0.538248	0.269124	−	0.963106i	$-0.413266\pi$
$149$	1.12793e79	0.538248	0.269124	+	0.963106i	$0.413266\pi$
$150$	2.54035e79	0.949646
$151$	2.13431e78	0.0626036	0.0313018	−	0.999510i	$-0.490035\pi$
$151$	2.13431e78	0.0626036	0.0313018	+	0.999510i	$0.490035\pi$
$152$	1.06225e79	0.244870
$153$	−2.95688e79	−0.536532
$154$	1.37688e79	0.196965
$155$	−3.61001e79	−0.407757
$156$	1.08806e80	0.971865
$157$	8.40883e79	0.594837	0.297419	−	0.954747i	$-0.403874\pi$
$157$	8.40883e79	0.594837	0.297419	+	0.954747i	$0.403874\pi$
$158$	1.88523e80	1.05775
$159$	−5.57785e80	−2.48583
$160$	−1.04289e79	−0.0369709
$161$	−5.24957e80	−1.48245
$162$	−3.22310e80	−0.726066
$163$	1.13703e80	0.204608	0.102304	−	0.994753i	$-0.467378\pi$
$163$	1.13703e80	0.204608	0.102304	+	0.994753i	$0.467378\pi$
$164$	−2.31855e80	−0.333745
$165$	8.03017e79	0.0925893
$166$	4.36420e80	0.403608
$167$	6.33317e80	0.470403	0.235202	−	0.971947i	$-0.424425\pi$
$167$	6.33317e80	0.470403	0.235202	+	0.971947i	$0.424425\pi$
$168$	−7.34552e80	−0.438767
$169$	1.90327e81	0.915450
$170$	2.10399e80	0.0815941
$171$	2.15127e81	0.673499
$172$	−3.75122e80	−0.0949258
$173$	−2.16055e81	−0.442468	−0.221234	−	0.975221i	$-0.571009\pi$
$173$	−2.16055e81	−0.442468	−0.221234	+	0.975221i	$0.571009\pi$
$174$	−1.89633e80	−0.0314678
$175$	−6.27687e81	−0.844996
$176$	7.20738e80	0.0788071
$177$	2.14316e82	1.90559
$178$	−2.92391e81	−0.211657
$179$	1.27274e82	0.750936	0.375468	−	0.926835i	$-0.377482\pi$
$179$	1.27274e82	0.750936	0.375468	+	0.926835i	$0.377482\pi$
$180$	−2.11207e81	−0.101686
$181$	4.19463e82	1.64978	0.824888	−	0.565296i	$-0.191238\pi$
$181$	4.19463e82	1.64978	0.824888	+	0.565296i	$0.191238\pi$
$182$	−2.68846e82	−0.864766
$183$	−4.49427e82	−1.18357
$184$	−2.74793e82	−0.593138
$185$	−1.19444e82	−0.211541
$186$	−1.33099e83	−1.93621
$187$	−1.45406e82	−0.173926
$188$	7.97203e82	0.784888
$189$	4.21806e81	0.0342182
$190$	−1.53076e82	−0.102424
$191$	−2.37720e83	−1.31325	−0.656627	−	0.754216i	$-0.728017\pi$
$191$	−2.37720e83	−1.31325	−0.656627	+	0.754216i	$0.728017\pi$
$192$	−3.84508e82	−0.175554
$193$	4.02354e83	1.51973	0.759865	−	0.650081i	$-0.225265\pi$
$193$	4.02354e83	1.51973	0.759865	+	0.650081i	$0.225265\pi$
$194$	4.16972e83	1.30420
$195$	−1.56796e83	−0.406510
$196$	−5.09447e82	−0.109585
$197$	6.77095e83	1.20957	0.604787	−	0.796387i	$-0.293258\pi$
$197$	6.77095e83	1.20957	0.604787	+	0.796387i	$0.293258\pi$
$198$	1.45964e83	0.216754
$199$	−2.88518e83	−0.356480	−0.178240	−	0.983987i	$-0.557040\pi$
$199$	−2.88518e83	−0.356480	−0.178240	+	0.983987i	$0.557040\pi$
$200$	−3.28569e83	−0.338089
$201$	−1.56643e82	−0.0134356
$202$	7.65058e83	0.547481
$203$	4.68559e82	0.0280001
$204$	7.75730e83	0.387444
$205$	3.34115e83	0.139598
$206$	1.11073e84	0.388556
$207$	−5.56513e84	−1.63139
$208$	−1.40730e84	−0.345999
$209$	1.05790e84	0.218326
$210$	1.05853e84	0.183526
$211$	−1.26798e85	−1.84842	−0.924212	−	0.381879i	$-0.875277\pi$
$211$	−1.26798e85	−1.84842	−0.924212	+	0.381879i	$0.875277\pi$
$212$	7.21440e84	0.884996
$213$	−1.17960e85	−1.21865
$214$	5.81459e84	0.506310
$215$	5.40571e83	0.0397054
$216$	2.20799e83	0.0136910
$217$	3.28871e85	1.72284
$218$	−1.19065e85	−0.527380
$219$	−1.85524e85	−0.695327
$220$	−1.03862e84	−0.0329633
$221$	2.83918e85	0.763615
$222$	−4.40382e85	−1.00449
$223$	6.38051e85	1.23517	0.617587	−	0.786503i	$-0.288110\pi$
$223$	6.38051e85	1.23517	0.617587	+	0.786503i	$0.288110\pi$
$224$	9.50070e84	0.156208
$225$	−6.65419e85	−0.929894
$226$	3.98120e85	0.473212
$227$	1.70860e86	1.72860	0.864302	−	0.502973i	$-0.167761\pi$
$227$	1.70860e86	1.72860	0.864302	+	0.502973i	$0.167761\pi$
$228$	−5.64381e85	−0.486351
$229$	1.58156e86	1.16169	0.580846	−	0.814014i	$-0.302722\pi$
$229$	1.58156e86	1.16169	0.580846	+	0.814014i	$0.302722\pi$
$230$	3.95992e85	0.248097
$231$	−7.31545e85	−0.391205
$232$	2.45272e84	0.0112030
$233$	−2.31351e86	−0.903192	−0.451596	−	0.892223i	$-0.649145\pi$
$233$	−2.31351e86	−0.903192	−0.451596	+	0.892223i	$0.649145\pi$
$234$	−2.85008e86	−0.951651
$235$	−1.14881e86	−0.328301
$236$	−2.77197e86	−0.678422
$237$	−1.00164e87	−2.10086
$238$	−1.91673e86	−0.344748
$239$	7.57770e86	1.16954	0.584769	−	0.811200i	$-0.301185\pi$
$239$	7.57770e86	1.16954	0.584769	+	0.811200i	$0.301185\pi$
$240$	5.54097e85	0.0734304
$241$	8.09092e86	0.921246	0.460623	−	0.887596i	$-0.347626\pi$
$241$	8.09092e86	0.921246	0.460623	+	0.887596i	$0.347626\pi$
$242$	−6.50568e86	−0.636842
$243$	1.66648e87	1.40336
$244$	5.81290e86	0.421371
$245$	7.34141e85	0.0458371
$246$	1.23186e87	0.662874
$247$	−2.06564e87	−0.958551
$248$	1.72150e87	0.689321
$249$	−2.31873e87	−0.801632
$250$	9.68628e86	0.289299
$251$	2.18094e87	0.563059	0.281529	−	0.959553i	$-0.409158\pi$
$251$	2.18094e87	0.563059	0.281529	+	0.959553i	$0.409158\pi$
$252$	1.92409e87	0.429641
$253$	−2.73669e87	−0.528842
$254$	3.13053e87	0.523826
$255$	−1.11787e87	−0.162059
$256$	4.97323e86	0.0625000
$257$	−7.57378e87	−0.825569	−0.412785	−	0.910829i	$-0.635444\pi$
$257$	−7.57378e87	−0.825569	−0.412785	+	0.910829i	$0.635444\pi$
$258$	1.99305e87	0.188538
$259$	1.08813e88	0.893796
$260$	2.02800e87	0.144724
$261$	4.96726e86	0.0308133
$262$	−1.94746e88	−1.05068
$263$	−4.19276e88	−1.96841	−0.984205	−	0.177033i	$-0.943350\pi$
$263$	−4.19276e88	−1.96841	−0.984205	+	0.177033i	$0.943350\pi$
$264$	−3.82934e87	−0.156524
$265$	−1.03963e88	−0.370174
$266$	1.39451e88	0.432756
$267$	1.55349e88	0.420386
$268$	2.02603e86	0.00478327
$269$	6.40106e88	1.31915	0.659574	−	0.751640i	$-0.270737\pi$
$269$	6.40106e88	1.31915	0.659574	+	0.751640i	$0.270737\pi$
$270$	−3.18183e86	−0.00572663
$271$	−9.97779e88	−1.56912	−0.784558	−	0.620055i	$-0.787110\pi$
$271$	−9.97779e88	−1.56912	−0.784558	+	0.620055i	$0.787110\pi$
$272$	−1.00333e88	−0.137936
$273$	1.42840e89	1.71757
$274$	−4.08021e88	−0.429326
$275$	−3.27224e88	−0.301441
$276$	1.46000e89	1.17807
$277$	9.16008e88	0.647720	0.323860	−	0.946105i	$-0.395019\pi$
$277$	9.16008e88	0.647720	0.323860	+	0.946105i	$0.395019\pi$
$278$	−1.70237e89	−1.05541
$279$	3.48640e89	1.89594
$280$	−1.36910e88	−0.0653384
$281$	−1.14673e88	−0.0480486	−0.0240243	−	0.999711i	$-0.507648\pi$
$281$	−1.14673e88	−0.0480486	−0.0240243	+	0.999711i	$0.507648\pi$
$282$	−4.23561e89	−1.55892
$283$	1.46679e89	0.474420	0.237210	−	0.971458i	$-0.423767\pi$
$283$	1.46679e89	0.474420	0.237210	+	0.971458i	$0.423767\pi$
$284$	1.52569e89	0.433858
$285$	8.13304e88	0.203430
$286$	−1.40154e89	−0.308493
$287$	−3.04378e89	−0.589825
$288$	1.00718e89	0.171902
$289$	−4.62505e89	−0.695577
$290$	−3.53450e87	−0.00468599
$291$	−2.21541e90	−2.59036
$292$	2.39956e89	0.247547
$293$	−2.04263e89	−0.186004	−0.0930020	−	0.995666i	$-0.529646\pi$
$293$	−2.04263e89	−0.186004	−0.0930020	+	0.995666i	$0.529646\pi$
$294$	2.70673e89	0.217655
$295$	3.99455e89	0.283769
$296$	5.69590e89	0.357615
$297$	2.19895e88	0.0122069
$298$	7.75106e89	0.380599
$299$	5.34361e90	2.32186
$300$	1.74571e90	0.671501
$301$	−4.92458e89	−0.167761
$302$	1.46669e89	0.0442674
$303$	−4.06481e90	−1.08739
$304$	7.29971e89	0.173149
$305$	−8.37671e89	−0.176250
$306$	−2.03195e90	−0.379386
$307$	2.07621e90	0.344129	0.172064	−	0.985086i	$-0.444956\pi$
$307$	2.07621e90	0.344129	0.172064	+	0.985086i	$0.444956\pi$
$308$	9.46182e89	0.139275
$309$	−5.90139e90	−0.771738
$310$	−2.48078e90	−0.288328
$311$	1.27144e91	1.31384	0.656918	−	0.753962i	$-0.271860\pi$
$311$	1.27144e91	1.31384	0.656918	+	0.753962i	$0.271860\pi$
$312$	7.47711e90	0.687212
$313$	−1.63787e91	−1.33940	−0.669699	−	0.742632i	$-0.733577\pi$
$313$	−1.63787e91	−1.33940	−0.669699	+	0.742632i	$0.733577\pi$
$314$	5.77850e90	0.420613
$315$	−2.77272e90	−0.179709
$316$	1.29552e91	0.747940
$317$	7.29724e90	0.375401	0.187701	−	0.982226i	$-0.439897\pi$
$317$	7.29724e90	0.375401	0.187701	+	0.982226i	$0.439897\pi$
$318$	−3.83307e91	−1.75775
$319$	2.44268e89	0.00998864
$320$	−7.16670e89	−0.0261424
$321$	−3.08934e91	−1.00562
$322$	−3.60747e91	−1.04825
$323$	−1.47269e91	−0.382137
$324$	−2.21490e91	−0.513406
$325$	6.38932e91	1.32346
$326$	7.81360e90	0.144680
$327$	6.32604e91	1.04746
$328$	−1.59329e91	−0.235994
$329$	1.04656e92	1.38713
$330$	5.51829e90	0.0654705
$331$	−3.52411e91	−0.374393	−0.187196	−	0.982323i	$-0.559940\pi$
$331$	−3.52411e91	−0.374393	−0.187196	+	0.982323i	$0.559940\pi$
$332$	2.99906e91	0.285394
$333$	1.15354e92	0.983597
$334$	4.35212e91	0.332625
$335$	−2.91962e89	−0.00200074
$336$	−5.04780e91	−0.310255
$337$	−1.52250e92	−0.839589	−0.419794	−	0.907619i	$-0.637898\pi$
$337$	−1.52250e92	−0.839589	−0.419794	+	0.907619i	$0.637898\pi$
$338$	1.30791e92	0.647321
$339$	−2.11524e92	−0.939878
$340$	1.44585e91	0.0576958
$341$	1.71446e92	0.614599
$342$	1.47834e92	0.476236
$343$	−3.72030e92	−1.07731
$344$	−2.57782e91	−0.0671226
$345$	−2.10394e92	−0.492761
$346$	−1.48472e92	−0.312872
$347$	−2.38741e92	−0.452794	−0.226397	−	0.974035i	$-0.572695\pi$
$347$	−2.38741e92	−0.452794	−0.226397	+	0.974035i	$0.572695\pi$
$348$	−1.30315e91	−0.0222511
$349$	−2.35163e92	−0.361610	−0.180805	−	0.983519i	$-0.557870\pi$
$349$	−2.35163e92	−0.361610	−0.180805	+	0.983519i	$0.557870\pi$
$350$	−4.31343e92	−0.597502
$351$	−4.29363e91	−0.0535938
$352$	4.95288e91	0.0557250
$353$	−1.91135e92	−0.193893	−0.0969466	−	0.995290i	$-0.530908\pi$
$353$	−1.91135e92	−0.193893	−0.0969466	+	0.995290i	$0.530908\pi$
$354$	1.47277e93	1.34746
$355$	−2.19861e92	−0.181473
$356$	−2.00929e92	−0.149664
$357$	1.01837e93	0.684727
$358$	8.74618e92	0.530992
$359$	8.27181e92	0.453579	0.226790	−	0.973944i	$-0.427177\pi$
$359$	8.27181e92	0.453579	0.226790	+	0.973944i	$0.427177\pi$
$360$	−1.45140e92	−0.0719030
$361$	−1.16219e93	−0.520311
$362$	2.88252e93	1.16657
$363$	3.45652e93	1.26487
$364$	−1.84750e93	−0.611482
$365$	−3.45790e92	−0.103544
$366$	−3.08844e93	−0.836912
$367$	−1.02598e93	−0.251668	−0.125834	−	0.992051i	$-0.540161\pi$
$367$	−1.02598e93	−0.251668	−0.125834	+	0.992051i	$0.540161\pi$
$368$	−1.88837e93	−0.419412
$369$	−3.22675e93	−0.649086
$370$	−8.20811e92	−0.149582
$371$	9.47102e93	1.56404
$372$	−9.14649e93	−1.36911
$373$	5.02008e93	0.681300	0.340650	−	0.940190i	$-0.389353\pi$
$373$	5.02008e93	0.681300	0.340650	+	0.940190i	$0.389353\pi$
$374$	−9.99224e92	−0.122984
$375$	−5.14640e93	−0.574596
$376$	5.47834e93	0.555000
$377$	−4.76953e92	−0.0438547
$378$	2.89863e92	0.0241959
$379$	2.34857e93	0.178022	0.0890108	−	0.996031i	$-0.471629\pi$
$379$	2.34857e93	0.178022	0.0890108	+	0.996031i	$0.471629\pi$
$380$	−1.05193e93	−0.0724244
$381$	−1.66328e94	−1.04041
$382$	−1.63360e94	−0.928610
$383$	−4.28352e93	−0.221333	−0.110666	−	0.993858i	$-0.535298\pi$
$383$	−4.28352e93	−0.221333	−0.110666	+	0.993858i	$0.535298\pi$
$384$	−2.64232e93	−0.124135
$385$	−1.36350e93	−0.0582557
$386$	2.76495e94	1.07461
$387$	−5.22061e93	−0.184617
$388$	2.86541e94	0.922208
$389$	−3.13280e94	−0.917850	−0.458925	−	0.888475i	$-0.651765\pi$
$389$	−3.13280e94	−0.917850	−0.458925	+	0.888475i	$0.651765\pi$
$390$	−1.07749e94	−0.287446
$391$	3.80970e94	0.925635
$392$	−3.50089e93	−0.0774885
$393$	1.03470e95	2.08682
$394$	4.65296e94	0.855298
$395$	−1.86692e94	−0.312847
$396$	1.00306e94	0.153268
$397$	1.09838e95	1.53074	0.765369	−	0.643592i	$-0.222557\pi$
$397$	1.09838e95	1.53074	0.765369	+	0.643592i	$0.222557\pi$
$398$	−1.98268e94	−0.252069
$399$	−7.40916e94	−0.859525
$400$	−2.25791e94	−0.239065
$401$	−1.82977e95	−1.76859	−0.884296	−	0.466927i	$-0.845361\pi$
$401$	−1.82977e95	−1.76859	−0.884296	+	0.466927i	$0.845361\pi$
$402$	−1.07644e93	−0.00950037
$403$	−3.34762e95	−2.69837
$404$	5.25744e94	0.387128
$405$	3.19179e94	0.214747
$406$	3.21991e93	0.0197990
$407$	5.67259e94	0.318849
$408$	5.33077e94	0.273965
$409$	3.39276e94	0.159460	0.0797301	−	0.996816i	$-0.474594\pi$
$409$	3.39276e94	0.159460	0.0797301	+	0.996816i	$0.474594\pi$
$410$	2.29602e94	0.0987110
$411$	2.16785e95	0.852712
$412$	7.63286e94	0.274751
$413$	−3.63902e95	−1.19897
$414$	−3.82433e95	−1.15357
$415$	−4.32180e94	−0.119374
$416$	−9.67090e94	−0.244659
$417$	9.04484e95	2.09621
$418$	7.26983e94	0.154380
$419$	2.28986e95	0.445654	0.222827	−	0.974858i	$-0.428472\pi$
$419$	2.28986e95	0.445654	0.222827	+	0.974858i	$0.428472\pi$
$420$	7.27416e94	0.129773
$421$	−3.12668e95	−0.511431	−0.255716	−	0.966752i	$-0.582311\pi$
$421$	−3.12668e95	−0.511431	−0.255716	+	0.966752i	$0.582311\pi$
$422$	−8.71347e95	−1.30703
$423$	1.10948e96	1.52649
$424$	4.95770e95	0.625786
$425$	4.55524e95	0.527613
$426$	−8.10612e95	−0.861713
$427$	7.63114e95	0.744684
$428$	3.99576e95	0.358015
$429$	7.44650e95	0.612719
$430$	3.71478e94	0.0280759
$431$	−2.02504e96	−1.40609	−0.703045	−	0.711145i	$-0.748177\pi$
$431$	−2.02504e96	−1.40609	−0.703045	+	0.711145i	$0.748177\pi$
$432$	1.51732e94	0.00968098
$433$	−2.48577e96	−1.45765	−0.728824	−	0.684701i	$-0.759933\pi$
$433$	−2.48577e96	−1.45765	−0.728824	+	0.684701i	$0.759933\pi$
$434$	2.25998e96	1.21823
$435$	1.87791e94	0.00930715
$436$	−8.18211e95	−0.372914
$437$	−2.77174e96	−1.16193
$438$	−1.27491e96	−0.491670
$439$	8.00456e95	0.284042	0.142021	−	0.989864i	$-0.454640\pi$
$439$	8.00456e95	0.284042	0.142021	+	0.989864i	$0.454640\pi$
$440$	−7.13737e94	−0.0233086
$441$	−7.09003e95	−0.213128
$442$	1.95107e96	0.539957
$443$	2.79973e96	0.713479	0.356739	−	0.934204i	$-0.383888\pi$
$443$	2.79973e96	0.713479	0.356739	+	0.934204i	$0.383888\pi$
$444$	−3.02628e96	−0.710282
$445$	2.89550e95	0.0626013
$446$	4.38466e96	0.873400
$447$	−4.11820e96	−0.755932
$448$	6.52883e95	0.110456
$449$	−1.66076e96	−0.259009	−0.129504	−	0.991579i	$-0.541339\pi$
$449$	−1.66076e96	−0.259009	−0.129504	+	0.991579i	$0.541339\pi$
$450$	−4.57273e96	−0.657534
$451$	−1.58677e96	−0.210412
$452$	2.73586e96	0.334611
$453$	−7.79263e95	−0.0879224
$454$	1.17414e97	1.22231
$455$	2.66235e96	0.255769
$456$	−3.87839e96	−0.343902
$457$	8.70589e96	0.712643	0.356321	−	0.934363i	$-0.384031\pi$
$457$	8.70589e96	0.712643	0.356321	+	0.934363i	$0.384031\pi$
$458$	1.08684e97	0.821440
$459$	−3.06113e95	−0.0213657
$460$	2.72124e96	0.175431
$461$	2.15290e97	1.28216	0.641078	−	0.767476i	$-0.278487\pi$
$461$	2.15290e97	1.28216	0.641078	+	0.767476i	$0.278487\pi$
$462$	−5.02714e96	−0.276623
$463$	−1.55171e97	−0.789048	−0.394524	−	0.918886i	$-0.629090\pi$
$463$	−1.55171e97	−0.789048	−0.394524	+	0.918886i	$0.629090\pi$
$464$	1.68549e95	0.00792175
$465$	1.31806e97	0.572667
$466$	−1.58983e97	−0.638653
$467$	−1.90434e97	−0.707420	−0.353710	−	0.935355i	$-0.615080\pi$
$467$	−1.90434e97	−0.707420	−0.353710	+	0.935355i	$0.615080\pi$
$468$	−1.95856e97	−0.672919
$469$	2.65976e95	0.00845343
$470$	−7.89459e96	−0.232144
$471$	−3.07016e97	−0.835408
$472$	−1.90488e97	−0.479717
$473$	−2.56727e96	−0.0598466
$474$	−6.88322e97	−1.48553
$475$	−3.31416e97	−0.662302
$476$	−1.31717e97	−0.243774
$477$	1.00404e98	1.72119
$478$	5.20736e97	0.826988
$479$	6.66159e97	0.980238	0.490119	−	0.871655i	$-0.336953\pi$
$479$	6.66159e97	0.980238	0.490119	+	0.871655i	$0.336953\pi$
$480$	3.80773e96	0.0519231
$481$	−1.10762e98	−1.39990
$482$	5.56003e97	0.651419
$483$	1.91668e98	2.08199
$484$	−4.47067e97	−0.450316
$485$	−4.12921e97	−0.385739
$486$	1.14519e98	0.992328
$487$	−1.71633e97	−0.137973	−0.0689863	−	0.997618i	$-0.521976\pi$
$487$	−1.71633e97	−0.137973	−0.0689863	+	0.997618i	$0.521976\pi$
$488$	3.99459e97	0.297954
$489$	−4.15143e97	−0.287359
$490$	5.04498e96	0.0324117
$491$	−2.05703e98	−1.22678	−0.613388	−	0.789781i	$-0.710194\pi$
$491$	−2.05703e98	−1.22678	−0.613388	+	0.789781i	$0.710194\pi$
$492$	8.46529e97	0.468722
$493$	−3.40042e96	−0.0174832
$494$	−1.41949e98	−0.677798
$495$	−1.44546e97	−0.0641088
$496$	1.18301e98	0.487424
$497$	2.00292e98	0.766753
$498$	−1.59342e98	−0.566839
$499$	2.56755e98	0.848886	0.424443	−	0.905455i	$-0.360470\pi$
$499$	2.56755e98	0.848886	0.424443	+	0.905455i	$0.360470\pi$
$500$	6.65636e97	0.204565
$501$	−2.31232e98	−0.660649
$502$	1.49873e98	0.398143
$503$	−3.81022e98	−0.941279	−0.470640	−	0.882326i	$-0.655977\pi$
$503$	−3.81022e98	−0.941279	−0.470640	+	0.882326i	$0.655977\pi$
$504$	1.32222e98	0.303802
$505$	−7.57626e97	−0.161927
$506$	−1.88064e98	−0.373948
$507$	−6.94905e98	−1.28569
$508$	2.15128e98	0.370401
$509$	−4.83731e98	−0.775184	−0.387592	−	0.921831i	$-0.626693\pi$
$509$	−4.83731e98	−0.775184	−0.387592	+	0.921831i	$0.626693\pi$
$510$	−7.68194e97	−0.114593
$511$	3.15014e98	0.437488
$512$	3.41758e97	0.0441942
$513$	2.22712e97	0.0268200
$514$	−5.20466e98	−0.583766
$515$	−1.09994e98	−0.114922
$516$	1.36962e98	0.133317
$517$	5.45592e98	0.494838
$518$	7.47755e98	0.632009
$519$	7.88844e98	0.621416
$520$	1.39363e98	0.102335
$521$	2.04685e99	1.40123	0.700613	−	0.713541i	$-0.252910\pi$
$521$	2.04685e99	1.40123	0.700613	+	0.713541i	$0.252910\pi$
$522$	3.41347e97	0.0217883
$523$	7.07713e98	0.421256	0.210628	−	0.977566i	$-0.432449\pi$
$523$	7.07713e98	0.421256	0.210628	+	0.977566i	$0.432449\pi$
$524$	−1.33828e99	−0.742943
$525$	2.29176e99	1.18674
$526$	−2.88125e99	−1.39188
$527$	−2.38667e99	−1.07574
$528$	−2.63150e98	−0.110679
$529$	4.62263e99	1.81450
$530$	−7.14431e98	−0.261753
$531$	−3.85777e99	−1.31943
$532$	9.58302e98	0.306004
$533$	3.09830e99	0.923806
$534$	1.06755e99	0.297258
$535$	−5.75811e98	−0.149750
$536$	1.39227e97	0.00338228
$537$	−4.64692e99	−1.05464
$538$	4.39877e99	0.932779
$539$	−3.48656e98	−0.0690888
$540$	−2.18654e97	−0.00404934
$541$	−6.09127e99	−1.05440	−0.527202	−	0.849740i	$-0.676759\pi$
$541$	−6.09127e99	−1.05440	−0.527202	+	0.849740i	$0.676759\pi$
$542$	−6.85668e99	−1.10953
$543$	−1.53151e100	−2.31700
$544$	−6.89483e98	−0.0975358
$545$	1.17909e99	0.155982
$546$	9.81591e99	1.21450
$547$	1.07778e99	0.124736	0.0623681	−	0.998053i	$-0.480135\pi$
$547$	1.07778e99	0.124736	0.0623681	+	0.998053i	$0.480135\pi$
$548$	−2.80390e99	−0.303579
$549$	8.08988e99	0.819504
$550$	−2.24867e99	−0.213151
$551$	2.47397e98	0.0219463
$552$	1.00330e100	0.833022
$553$	1.70076e100	1.32183
$554$	6.29476e99	0.458007
$555$	4.36104e99	0.297095
$556$	−1.16986e100	−0.746284
$557$	−4.55868e99	−0.272348	−0.136174	−	0.990685i	$-0.543481\pi$
$557$	−4.55868e99	−0.272348	−0.136174	+	0.990685i	$0.543481\pi$
$558$	2.39584e100	1.34063
$559$	5.01280e99	0.262754
$560$	−9.40841e98	−0.0462012
$561$	5.30896e99	0.244267
$562$	−7.88028e98	−0.0339755
$563$	4.14423e99	0.167451	0.0837255	−	0.996489i	$-0.473318\pi$
$563$	4.14423e99	0.167451	0.0837255	+	0.996489i	$0.473318\pi$
$564$	−2.91069e100	−1.10232
$565$	−3.94252e99	−0.139961
$566$	1.00797e100	0.335466
$567$	−2.90771e100	−0.907338
$568$	1.04845e100	0.306784
$569$	−5.61680e100	−1.54131	−0.770657	−	0.637250i	$-0.780072\pi$
$569$	−5.61680e100	−1.54131	−0.770657	+	0.637250i	$0.780072\pi$
$570$	5.58898e99	0.143847
$571$	−6.13398e100	−1.48090	−0.740448	−	0.672113i	$-0.765387\pi$
$571$	−6.13398e100	−1.48090	−0.740448	+	0.672113i	$0.765387\pi$
$572$	−9.63132e99	−0.218138
$573$	8.67946e100	1.84437
$574$	−2.09167e100	−0.417069
$575$	8.57341e100	1.60427
$576$	6.92130e99	0.121553
$577$	7.13815e100	1.17671	0.588354	−	0.808603i	$-0.299776\pi$
$577$	7.13815e100	1.17671	0.588354	+	0.808603i	$0.299776\pi$
$578$	−3.17831e100	−0.491847
$579$	−1.46904e101	−2.13436
$580$	−2.42889e98	−0.00331349
$581$	3.93714e100	0.504374
$582$	−1.52242e101	−1.83166
$583$	4.93740e100	0.557951
$584$	1.64897e100	0.175042
$585$	2.82239e100	0.281467
$586$	−1.40369e100	−0.131525
$587$	−5.83655e100	−0.513885	−0.256942	−	0.966427i	$-0.582715\pi$
$587$	−5.83655e100	−0.513885	−0.256942	+	0.966427i	$0.582715\pi$
$588$	1.86005e100	0.153905
$589$	1.73642e101	1.35035
$590$	2.74504e100	0.200655
$591$	−2.47216e101	−1.69876
$592$	3.91419e100	0.252872
$593$	2.33205e101	1.41658	0.708290	−	0.705922i	$-0.249467\pi$
$593$	2.33205e101	1.41658	0.708290	+	0.705922i	$0.249467\pi$
$594$	1.51111e99	0.00863157
$595$	1.89811e100	0.101965
$596$	5.32649e100	0.269124
$597$	1.05341e101	0.500652
$598$	3.67210e101	1.64180
$599$	−2.51022e101	−1.05593	−0.527963	−	0.849268i	$-0.677044\pi$
$599$	−2.51022e101	−1.05593	−0.527963	+	0.849268i	$0.677044\pi$
$600$	1.19964e101	0.474823
$601$	9.46626e100	0.352582	0.176291	−	0.984338i	$-0.443590\pi$
$601$	9.46626e100	0.352582	0.176291	+	0.984338i	$0.443590\pi$
$602$	−3.38415e100	−0.118625
$603$	2.81964e99	0.00930277
$604$	1.00790e100	0.0313018
$605$	6.44248e100	0.188357
$606$	−2.79332e101	−0.768900
$607$	−6.32704e101	−1.63988	−0.819942	−	0.572446i	$-0.805995\pi$
$607$	−6.32704e101	−1.63988	−0.819942	+	0.572446i	$0.805995\pi$
$608$	5.01632e100	0.122435
$609$	−1.71077e100	−0.0393242
$610$	−5.75643e100	−0.124628
$611$	−1.06531e102	−2.17257
$612$	−1.39635e101	−0.268266
$613$	6.70863e101	1.21430	0.607150	−	0.794587i	$-0.292313\pi$
$613$	6.70863e101	1.21430	0.607150	+	0.794587i	$0.292313\pi$
$614$	1.42676e101	0.243336
$615$	−1.21990e101	−0.196056
$616$	6.50211e100	0.0984823
$617$	−5.79164e101	−0.826785	−0.413393	−	0.910553i	$-0.635656\pi$
$617$	−5.79164e101	−0.826785	−0.413393	+	0.910553i	$0.635656\pi$
$618$	−4.05540e101	−0.545701
$619$	1.13125e102	1.43499	0.717495	−	0.696564i	$-0.245289\pi$
$619$	1.13125e102	1.43499	0.717495	+	0.696564i	$0.245289\pi$
$620$	−1.70478e101	−0.203879
$621$	−5.76134e100	−0.0649651
$622$	8.73726e101	0.929022
$623$	−2.63779e101	−0.264500
$624$	5.13823e101	0.485932
$625$	9.76084e101	0.870696
$626$	−1.12553e102	−0.947098
$627$	−3.86252e101	−0.306624
$628$	3.97096e101	0.297419
$629$	−7.89673e101	−0.558083
$630$	−1.90540e101	−0.127074
$631$	2.61303e101	0.164465	0.0822325	−	0.996613i	$-0.473795\pi$
$631$	2.61303e101	0.164465	0.0822325	+	0.996613i	$0.473795\pi$
$632$	8.90277e101	0.528873
$633$	4.62954e102	2.59599
$634$	5.01463e101	0.265449
$635$	−3.10012e101	−0.154931
$636$	−2.63406e102	−1.24292
$637$	6.80780e101	0.303332
$638$	1.67860e100	0.00706303
$639$	2.12332e102	0.843790
$640$	−4.92492e100	−0.0184855
$641$	−3.98775e102	−1.41387	−0.706936	−	0.707278i	$-0.749923\pi$
$641$	−3.98775e102	−1.41387	−0.706936	+	0.707278i	$0.749923\pi$
$642$	−2.12298e102	−0.711078
$643$	4.29748e102	1.35992	0.679960	−	0.733250i	$-0.261997\pi$
$643$	4.29748e102	1.35992	0.679960	+	0.733250i	$0.261997\pi$
$644$	−2.47904e102	−0.741223
$645$	−1.97369e101	−0.0557635
$646$	−1.01202e102	−0.270211
$647$	−5.32563e102	−1.34389	−0.671946	−	0.740600i	$-0.734542\pi$
$647$	−5.32563e102	−1.34389	−0.671946	+	0.740600i	$0.734542\pi$
$648$	−1.52207e102	−0.363033
$649$	−1.89708e102	−0.427715
$650$	4.39071e102	0.935830
$651$	−1.20075e103	−2.41961
$652$	5.36946e101	0.102304
$653$	4.80226e102	0.865197	0.432598	−	0.901587i	$-0.357597\pi$
$653$	4.80226e102	0.865197	0.432598	+	0.901587i	$0.357597\pi$
$654$	4.34722e102	0.740669
$655$	1.92854e102	0.310757
$656$	−1.09490e102	−0.166873
$657$	3.33950e102	0.481444
$658$	7.19194e102	0.980846
$659$	−4.43880e102	−0.572727	−0.286363	−	0.958121i	$-0.592446\pi$
$659$	−4.43880e102	−0.572727	−0.286363	+	0.958121i	$0.592446\pi$
$660$	3.79214e101	0.0462947
$661$	1.19501e103	1.38044	0.690222	−	0.723597i	$-0.257513\pi$
$661$	1.19501e103	1.38044	0.690222	+	0.723597i	$0.257513\pi$
$662$	−2.42175e102	−0.264736
$663$	−1.03662e103	−1.07244
$664$	2.06094e102	0.201804
$665$	−1.38097e102	−0.127995
$666$	7.92705e102	0.695508
$667$	−6.39992e101	−0.0531596
$668$	2.99076e102	0.235202
$669$	−2.32960e103	−1.73472
$670$	−2.00634e100	−0.00141474
$671$	3.97824e102	0.265656
$672$	−3.46882e102	−0.219383
$673$	2.75588e103	1.65086	0.825430	−	0.564504i	$-0.190932\pi$
$673$	2.75588e103	1.65086	0.825430	+	0.564504i	$0.190932\pi$
$674$	−1.04626e103	−0.593679
$675$	−6.88880e101	−0.0370302
$676$	8.98792e102	0.457725
$677$	3.22081e103	1.55410	0.777050	−	0.629439i	$-0.216715\pi$
$677$	3.22081e103	1.55410	0.777050	+	0.629439i	$0.216715\pi$
$678$	−1.45358e103	−0.664594
$679$	3.76170e103	1.62981
$680$	9.93583e101	0.0407971
$681$	−6.23829e103	−2.42771
$682$	1.17817e103	0.434587
$683$	2.97295e103	1.03952	0.519760	−	0.854312i	$-0.326021\pi$
$683$	2.97295e103	1.03952	0.519760	+	0.854312i	$0.326021\pi$
$684$	1.01591e103	0.336749
$685$	4.04057e102	0.126981
$686$	−2.55657e103	−0.761776
$687$	−5.77447e103	−1.63152
$688$	−1.77146e102	−0.0474629
$689$	−9.64069e103	−2.44966
$690$	−1.44582e103	−0.348435
$691$	2.23381e103	0.510619	0.255310	−	0.966859i	$-0.417823\pi$
$691$	2.23381e103	0.510619	0.255310	+	0.966859i	$0.417823\pi$
$692$	−1.02029e103	−0.221234
$693$	1.31681e103	0.270870
$694$	−1.64061e103	−0.320174
$695$	1.68583e103	0.312154
$696$	−8.95517e101	−0.0157339
$697$	2.20892e103	0.368285
$698$	−1.61603e103	−0.255697
$699$	8.44690e103	1.26847
$700$	−2.96417e103	−0.422498
$701$	6.41226e102	0.0867568	0.0433784	−	0.999059i	$-0.486188\pi$
$701$	6.41226e102	0.0867568	0.0433784	+	0.999059i	$0.486188\pi$
$702$	−2.95056e102	−0.0378965
$703$	5.74525e103	0.700551
$704$	3.40359e102	0.0394035
$705$	4.19446e103	0.461077
$706$	−1.31347e103	−0.137103
$707$	6.90193e103	0.684167
$708$	1.01208e104	0.952797
$709$	1.09588e104	0.979889	0.489944	−	0.871754i	$-0.337017\pi$
$709$	1.09588e104	0.979889	0.489944	+	0.871754i	$0.337017\pi$
$710$	−1.51087e103	−0.128321
$711$	1.80299e104	1.45463
$712$	−1.38078e103	−0.105829
$713$	−4.49196e104	−3.27090
$714$	6.99821e103	0.484175
$715$	1.38793e103	0.0912422
$716$	6.01033e103	0.375468
$717$	−2.76671e104	−1.64254
$718$	5.68434e103	0.320729
$719$	9.49446e102	0.0509173	0.0254587	−	0.999676i	$-0.491895\pi$
$719$	9.49446e102	0.0509173	0.0254587	+	0.999676i	$0.491895\pi$
$720$	−9.97398e102	−0.0508431
$721$	1.00204e104	0.485565
$722$	−7.98649e103	−0.367916
$723$	−2.95409e104	−1.29383
$724$	1.98086e104	0.824888
$725$	−7.65235e102	−0.0303010
$726$	2.37530e104	0.894401
$727$	2.91800e103	0.104491	0.0522455	−	0.998634i	$-0.483362\pi$
$727$	2.91800e103	0.104491	0.0522455	+	0.998634i	$0.483362\pi$
$728$	−1.26959e104	−0.432383
$729$	−2.91461e104	−0.944115
$730$	−2.37625e103	−0.0732164
$731$	3.57386e103	0.104750
$732$	−2.12236e104	−0.591786
$733$	−6.57120e103	−0.174321	−0.0871604	−	0.996194i	$-0.527779\pi$
$733$	−6.57120e103	−0.174321	−0.0871604	+	0.996194i	$0.527779\pi$
$734$	−7.05048e103	−0.177956
$735$	−2.68044e103	−0.0643751
$736$	−1.29768e104	−0.296569
$737$	1.38658e102	0.00301565
$738$	−2.21740e104	−0.458973
$739$	4.98322e104	0.981721	0.490861	−	0.871238i	$-0.336682\pi$
$739$	4.98322e104	0.981721	0.490861	+	0.871238i	$0.336682\pi$
$740$	−5.64057e103	−0.105771
$741$	7.54189e104	1.34622
$742$	6.50844e104	1.10595
$743$	−2.21775e104	−0.358775	−0.179387	−	0.983779i	$-0.557412\pi$
$743$	−2.21775e104	−0.358775	−0.179387	+	0.983779i	$0.557412\pi$
$744$	−6.28542e104	−0.968105
$745$	−7.67576e103	−0.112569
$746$	3.44978e104	0.481752
$747$	4.17382e104	0.555049
$748$	−6.86661e103	−0.0869629
$749$	5.24561e104	0.632717
$750$	−3.53658e104	−0.406301
$751$	7.02988e104	0.769290	0.384645	−	0.923065i	$-0.374324\pi$
$751$	7.02988e104	0.769290	0.384645	+	0.923065i	$0.374324\pi$
$752$	3.76469e104	0.392444
$753$	−7.96289e104	−0.790778
$754$	−3.27760e103	−0.0310100
$755$	−1.45244e103	−0.0130928
$756$	1.99192e103	0.0171091
$757$	2.99786e104	0.245365	0.122682	−	0.992446i	$-0.460850\pi$
$757$	2.99786e104	0.245365	0.122682	+	0.992446i	$0.460850\pi$
$758$	1.61393e104	0.125880
$759$	9.99198e104	0.742723
$760$	−7.22880e103	−0.0512118
$761$	−2.11804e105	−1.43019	−0.715095	−	0.699027i	$-0.753617\pi$
$761$	−2.11804e105	−1.43019	−0.715095	+	0.699027i	$0.753617\pi$
$762$	−1.14299e105	−0.735678
$763$	−1.07414e105	−0.659047
$764$	−1.12260e105	−0.656627
$765$	2.01221e104	0.112210
$766$	−2.94361e104	−0.156506
$767$	3.70421e105	1.87787
$768$	−1.81579e104	−0.0877770
$769$	−2.30856e105	−1.06422	−0.532108	−	0.846677i	$-0.678600\pi$
$769$	−2.30856e105	−1.06422	−0.532108	+	0.846677i	$0.678600\pi$
$770$	−9.36990e103	−0.0411930
$771$	2.76528e105	1.15946
$772$	1.90006e105	0.759865
$773$	−3.96296e104	−0.151171	−0.0755855	−	0.997139i	$-0.524083\pi$
$773$	−3.96296e104	−0.151171	−0.0755855	+	0.997139i	$0.524083\pi$
$774$	−3.58758e104	−0.130544
$775$	−5.37100e105	−1.86442
$776$	1.96909e105	0.652099
$777$	−3.97288e105	−1.25527
$778$	−2.15284e105	−0.649018
$779$	−1.60710e105	−0.462301
$780$	−7.40447e104	−0.203255
$781$	1.04416e105	0.273529
$782$	2.61801e105	0.654523
$783$	5.14238e102	0.00122704
$784$	−2.40580e104	−0.0547927
$785$	−5.72237e104	−0.124404
$786$	7.11040e105	1.47561
$787$	−3.96236e105	−0.785012	−0.392506	−	0.919749i	$-0.628392\pi$
$787$	−3.96236e105	−0.785012	−0.392506	+	0.919749i	$0.628392\pi$
$788$	3.19749e105	0.604787
$789$	1.53083e106	2.76450
$790$	−1.28294e105	−0.221216
$791$	3.59162e105	0.591356
$792$	6.89297e104	0.108377
$793$	−7.76785e105	−1.16635
$794$	7.54804e105	1.08239
$795$	3.79583e105	0.519884
$796$	−1.36249e105	−0.178240
$797$	8.51051e105	1.06347	0.531737	−	0.846909i	$-0.321539\pi$
$797$	8.51051e105	1.06347	0.531737	+	0.846909i	$0.321539\pi$
$798$	−5.09154e105	−0.607776
$799$	−7.59511e105	−0.866117
$800$	−1.55162e105	−0.169045
$801$	−2.79635e105	−0.291075
$802$	−1.25741e106	−1.25058
$803$	1.64222e105	0.156068
$804$	−7.39727e103	−0.00671778
$805$	3.57243e105	0.310037
$806$	−2.30047e106	−1.90804
$807$	−2.33710e106	−1.85265
$808$	3.61288e105	0.273741
$809$	−2.64445e105	−0.191520	−0.0957602	−	0.995404i	$-0.530528\pi$
$809$	−2.64445e105	−0.191520	−0.0957602	+	0.995404i	$0.530528\pi$
$810$	2.19338e105	0.151849
$811$	−5.57507e105	−0.368969	−0.184484	−	0.982835i	$-0.559061\pi$
$811$	−5.57507e105	−0.368969	−0.184484	+	0.982835i	$0.559061\pi$
$812$	2.21271e104	0.0140000
$813$	3.64301e106	2.20372
$814$	3.89817e105	0.225461
$815$	−7.73769e104	−0.0427916
$816$	3.66328e105	0.193722
$817$	−2.60015e105	−0.131490
$818$	2.33149e105	0.112755
$819$	−2.57118e106	−1.18924
$820$	1.57781e105	0.0697992
$821$	2.59339e106	1.09735	0.548673	−	0.836037i	$-0.315133\pi$
$821$	2.59339e106	1.09735	0.548673	+	0.836037i	$0.315133\pi$
$822$	1.48973e106	0.602959
$823$	−3.77001e105	−0.145965	−0.0729824	−	0.997333i	$-0.523252\pi$
$823$	−3.77001e105	−0.145965	−0.0729824	+	0.997333i	$0.523252\pi$
$824$	5.24526e105	0.194278
$825$	1.19473e106	0.423353
$826$	−2.50072e106	−0.847799
$827$	1.56745e106	0.508442	0.254221	−	0.967146i	$-0.418181\pi$
$827$	1.56745e106	0.508442	0.254221	+	0.967146i	$0.418181\pi$
$828$	−2.62806e106	−0.815695
$829$	2.25285e106	0.669100	0.334550	−	0.942378i	$-0.391416\pi$
$829$	2.25285e106	0.669100	0.334550	+	0.942378i	$0.391416\pi$
$830$	−2.96992e105	−0.0844101
$831$	−3.34446e106	−0.909679
$832$	−6.64579e105	−0.173000
$833$	4.85360e105	0.120926
$834$	6.21557e106	1.48224
$835$	−4.30984e105	−0.0983797
$836$	4.99579e105	0.109163
$837$	3.60932e105	0.0754998
$838$	1.57358e106	0.315125
$839$	8.27024e106	1.58565	0.792823	−	0.609452i	$-0.208610\pi$
$839$	8.27024e106	1.58565	0.792823	+	0.609452i	$0.208610\pi$
$840$	4.99876e105	0.0917632
$841$	−5.68352e106	−0.998996
$842$	−2.14864e106	−0.361636
$843$	4.18686e105	0.0674810
$844$	−5.98785e106	−0.924212
$845$	−1.29521e106	−0.191456
$846$	7.62427e106	1.07939
$847$	−5.86907e106	−0.795839
$848$	3.40690e106	0.442498
$849$	−5.35543e106	−0.666291
$850$	3.13034e106	0.373079
$851$	−1.48624e107	−1.69692
$852$	−5.57048e106	−0.609323
$853$	4.93407e106	0.517089	0.258544	−	0.965999i	$-0.416757\pi$
$853$	4.93407e106	0.517089	0.258544	+	0.965999i	$0.416757\pi$
$854$	5.24408e106	0.526571
$855$	−1.46398e106	−0.140855
$856$	2.74586e106	0.253155
$857$	−1.34172e107	−1.18539	−0.592695	−	0.805427i	$-0.701936\pi$
$857$	−1.34172e107	−1.18539	−0.592695	+	0.805427i	$0.701936\pi$
$858$	5.11720e106	0.433258
$859$	−9.86198e106	−0.800228	−0.400114	−	0.916465i	$-0.631030\pi$
$859$	−9.86198e106	−0.800228	−0.400114	+	0.916465i	$0.631030\pi$
$860$	2.55278e105	0.0198527
$861$	1.11132e107	0.828369
$862$	−1.39160e107	−0.994256
$863$	1.07941e107	0.739252	0.369626	−	0.929181i	$-0.379486\pi$
$863$	1.07941e107	0.739252	0.369626	+	0.929181i	$0.379486\pi$
$864$	1.04269e105	0.00684549
$865$	1.47030e106	0.0925374
$866$	−1.70821e107	−1.03071
$867$	1.68866e107	0.976890
$868$	1.55305e107	0.861420
$869$	8.86633e106	0.471544
$870$	1.29049e105	0.00658115
$871$	−2.70740e105	−0.0132401
$872$	−5.62270e106	−0.263690
$873$	3.98782e107	1.79356
$874$	−1.90473e107	−0.821610
$875$	8.73844e106	0.361526
$876$	−8.76110e106	−0.347663
$877$	−1.29026e107	−0.491124	−0.245562	−	0.969381i	$-0.578972\pi$
$877$	−1.29026e107	−0.491124	−0.245562	+	0.969381i	$0.578972\pi$
$878$	5.50069e106	0.200848
$879$	7.45790e106	0.261230
$880$	−4.90476e105	−0.0164816
$881$	2.43115e107	0.783775	0.391887	−	0.920013i	$-0.371822\pi$
$881$	2.43115e107	0.783775	0.391887	+	0.920013i	$0.371822\pi$
$882$	−4.87223e106	−0.150704
$883$	1.86783e107	0.554333	0.277166	−	0.960822i	$-0.410605\pi$
$883$	1.86783e107	0.554333	0.277166	+	0.960822i	$0.410605\pi$
$884$	1.34076e107	0.381807
$885$	−1.45846e107	−0.398534
$886$	1.92396e107	0.504506
$887$	−7.39573e107	−1.86110	−0.930549	−	0.366169i	$-0.880669\pi$
$887$	−7.39573e107	−1.86110	−0.930549	+	0.366169i	$0.880669\pi$
$888$	−2.07964e107	−0.502245
$889$	2.82419e107	0.654607
$890$	1.98977e106	0.0442658
$891$	−1.51584e107	−0.323680
$892$	3.01311e107	0.617587
$893$	5.52581e107	1.08722
$894$	−2.83001e107	−0.534525
$895$	−8.66122e106	−0.157050
$896$	4.48658e106	0.0781040
$897$	−1.95102e108	−3.26089
$898$	−1.14126e107	−0.183147
$899$	4.00937e106	0.0617800
$900$	−3.14235e107	−0.464947
$901$	−6.87329e107	−0.976585
$902$	−1.09042e107	−0.148784
$903$	1.79802e107	0.235609
$904$	1.88007e107	0.236606
$905$	−2.85452e107	−0.345033
$906$	−5.35505e106	−0.0621705
$907$	1.15651e108	1.28969	0.644843	−	0.764315i	$-0.276923\pi$
$907$	1.15651e108	1.28969	0.644843	+	0.764315i	$0.276923\pi$
$908$	8.06862e107	0.864302
$909$	7.31683e107	0.752907
$910$	1.82955e107	0.180856
$911$	9.43725e107	0.896241	0.448121	−	0.893973i	$-0.352094\pi$
$911$	9.43725e107	0.896241	0.448121	+	0.893973i	$0.352094\pi$
$912$	−2.66521e107	−0.243176
$913$	2.05250e107	0.179928
$914$	5.98264e107	0.503915
$915$	3.05844e107	0.247531
$916$	7.46871e107	0.580846
$917$	−1.75689e108	−1.31300
$918$	−2.10359e106	−0.0151079
$919$	2.59097e108	1.78833	0.894163	−	0.447742i	$-0.147772\pi$
$919$	2.59097e108	1.78833	0.894163	+	0.447742i	$0.147772\pi$
$920$	1.87002e107	0.124048
$921$	−7.58050e107	−0.483305
$922$	1.47946e108	0.906622
$923$	−2.03880e108	−1.20092
$924$	−3.45462e107	−0.195602
$925$	−1.77709e108	−0.967245
$926$	−1.06632e108	−0.557941
$927$	1.06227e108	0.534351
$928$	1.15826e106	0.00560152
$929$	5.78288e107	0.268888	0.134444	−	0.990921i	$-0.457075\pi$
$929$	5.78288e107	0.268888	0.134444	+	0.990921i	$0.457075\pi$
$930$	9.05764e107	0.404937
$931$	−3.53123e107	−0.151797
$932$	−1.09252e108	−0.451596
$933$	−4.64217e108	−1.84519
$934$	−1.30865e108	−0.500222
$935$	9.89517e106	0.0363747
$936$	−1.34591e108	−0.475825
$937$	4.62342e108	1.57206	0.786028	−	0.618191i	$-0.212134\pi$
$937$	4.62342e108	1.57206	0.786028	+	0.618191i	$0.212134\pi$
$938$	1.82777e106	0.00597748
$939$	5.98005e108	1.88109
$940$	−5.42512e107	−0.164151
$941$	−3.22102e107	−0.0937503	−0.0468751	−	0.998901i	$-0.514926\pi$
$941$	−3.22102e107	−0.0937503	−0.0468751	+	0.998901i	$0.514926\pi$
$942$	−2.10980e108	−0.590723
$943$	4.15741e108	1.11981
$944$	−1.30902e108	−0.339211
$945$	−2.87047e106	−0.00715636
$946$	−1.76421e107	−0.0423179
$947$	−3.71646e108	−0.857739	−0.428869	−	0.903367i	$-0.641088\pi$
$947$	−3.71646e108	−0.857739	−0.428869	+	0.903367i	$0.641088\pi$
$948$	−4.73011e108	−1.05043
$949$	−3.20657e108	−0.685210
$950$	−2.27747e108	−0.468318
$951$	−2.66431e108	−0.527225
$952$	−9.05150e107	−0.172374
$953$	−6.51962e108	−1.19490	−0.597450	−	0.801906i	$-0.703819\pi$
$953$	−6.51962e108	−1.19490	−0.597450	+	0.801906i	$0.703819\pi$
$954$	6.89968e108	1.21706
$955$	1.61773e108	0.274653
$956$	3.57847e108	0.584769
$957$	−8.91851e106	−0.0140284
$958$	4.57781e108	0.693133
$959$	−3.68094e108	−0.536513
$960$	2.61665e107	0.0367152
$961$	2.07379e109	2.80131
$962$	−7.61151e108	−0.989875
$963$	5.56094e108	0.696288
$964$	3.82083e108	0.460623
$965$	−2.73809e108	−0.317835
$966$	1.31713e109	1.47219
$967$	−4.57894e108	−0.492832	−0.246416	−	0.969164i	$-0.579253\pi$
$967$	−4.57894e108	−0.492832	−0.246416	+	0.969164i	$0.579253\pi$
$968$	−3.07222e108	−0.318421
$969$	5.37696e108	0.536685
$970$	−2.83757e108	−0.272759
$971$	5.02125e108	0.464847	0.232424	−	0.972615i	$-0.425334\pi$
$971$	5.02125e108	0.464847	0.232424	+	0.972615i	$0.425334\pi$
$972$	7.86971e108	0.701682
$973$	−1.53579e109	−1.31890
$974$	−1.17945e108	−0.0975614
$975$	−2.33282e109	−1.85871
$976$	2.74506e108	0.210685
$977$	1.87265e109	1.38454	0.692270	−	0.721639i	$-0.256611\pi$
$977$	1.87265e109	1.38454	0.692270	+	0.721639i	$0.256611\pi$
$978$	−2.85284e108	−0.203193
$979$	−1.37512e108	−0.0943569
$980$	3.46688e107	0.0229186
$981$	−1.13871e109	−0.725263
$982$	−1.41358e109	−0.867462
$983$	3.33453e108	0.197165	0.0985827	−	0.995129i	$-0.468569\pi$
$983$	3.33453e108	0.197165	0.0985827	+	0.995129i	$0.468569\pi$
$984$	5.81731e108	0.331437
$985$	−4.60776e108	−0.252969
$986$	−2.33675e107	−0.0123625
$987$	−3.82113e109	−1.94812
$988$	−9.75469e108	−0.479275
$989$	6.72635e108	0.318504
$990$	−9.93315e107	−0.0453318
$991$	1.14253e109	0.502552	0.251276	−	0.967916i	$-0.419150\pi$
$991$	1.14253e109	0.502552	0.251276	+	0.967916i	$0.419150\pi$
$992$	8.12957e108	0.344661
$993$	1.28669e109	0.525809
$994$	1.37640e109	0.542176
$995$	1.96342e108	0.0745539
$996$	−1.09499e109	−0.400816
$997$	−2.91782e109	−1.02964	−0.514819	−	0.857299i	$-0.672141\pi$
$997$	−2.91782e109	−1.02964	−0.514819	+	0.857299i	$0.672141\pi$
$998$	1.76441e109	0.600253
$999$	1.19421e108	0.0391687

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.74.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+6.87195e10 q^{2} -3.65112e17 q^{3} +4.72237e21 q^{4} -6.80519e24 q^{5} -2.50903e28 q^{6} +6.19950e30 q^{7} +3.24519e32 q^{8} +6.57217e34 q^{9} -4.67649e35 q^{10} +3.23190e37 q^{11} -1.72419e39 q^{12} -6.31056e40 q^{13} +4.26026e41 q^{14} +2.48466e42 q^{15} +2.23007e43 q^{16} -4.49909e44 q^{17} +4.51636e45 q^{18} +3.27330e46 q^{19} -3.21366e46 q^{20} -2.26351e48 q^{21} +2.22095e48 q^{22} -8.46773e49 q^{23} -1.18486e50 q^{24} -1.01248e51 q^{25} -4.33658e51 q^{26} +6.80388e50 q^{27} +2.92763e52 q^{28} +7.55802e51 q^{29} +1.70744e53 q^{30} +5.30479e54 q^{31} +1.53250e54 q^{32} -1.18001e55 q^{33} -3.09175e55 q^{34} -4.21888e55 q^{35} +3.10362e56 q^{36} +1.75519e57 q^{37} +2.24940e57 q^{38} +2.30406e58 q^{39} -2.20841e57 q^{40} -4.90971e58 q^{41} -1.55547e59 q^{42} -7.94351e58 q^{43} +1.52622e59 q^{44} -4.47249e59 q^{45} -5.81898e60 q^{46} +1.68814e61 q^{47} -8.14227e60 q^{48} -1.07880e61 q^{49} -6.95771e61 q^{50} +1.64267e62 q^{51} -2.98008e62 q^{52} +1.52771e63 q^{53} +4.67559e61 q^{54} -2.19937e62 q^{55} +2.01185e63 q^{56} -1.19512e64 q^{57} +5.19383e62 q^{58} -5.86986e64 q^{59} +1.17335e64 q^{60} +1.23093e65 q^{61} +3.64543e65 q^{62} +4.07442e65 q^{63} +1.05312e65 q^{64} +4.29445e65 q^{65} -8.10895e65 q^{66} +4.29028e64 q^{67} -2.12463e66 q^{68} +3.09167e67 q^{69} -2.89919e66 q^{70} +3.23078e67 q^{71} +2.13279e67 q^{72} +5.08128e67 q^{73} +1.20615e68 q^{74} +3.69669e68 q^{75} +1.54577e68 q^{76} +2.00362e68 q^{77} +1.58334e69 q^{78} +2.74338e69 q^{79} -1.51761e68 q^{80} -4.69023e69 q^{81} -3.37393e69 q^{82} +6.35075e69 q^{83} -1.06891e70 q^{84} +3.06171e69 q^{85} -5.45874e69 q^{86} -2.75952e69 q^{87} +1.04881e70 q^{88} -4.25484e70 q^{89} -3.07347e70 q^{90} -3.91223e71 q^{91} -3.99877e71 q^{92} -1.93685e72 q^{93} +1.16008e72 q^{94} -2.22754e71 q^{95} -5.59533e71 q^{96} +6.06774e72 q^{97} -7.41343e71 q^{98} +2.12406e72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 274877906944 q^{2} + 30\!\cdots\!76 q^{3} + 18\!\cdots\!84 q^{4} - 78\!\cdots\!60 q^{5} + 20\!\cdots\!36 q^{6} + 36\!\cdots\!12 q^{7} + 12\!\cdots\!24 q^{8} + 12\!\cdots\!52 q^{9} - 53\!\cdots\!60 q^{10}+ \cdots + 28\!\cdots\!24 q^{99}+O(q^{100}) \) 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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