LMFDB - Embedded newform 2.74.a.b.1.2

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			1.2
Root			$5.25645e13$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+6.87195e10 q^{2} -2.46573e16 q^{3} +4.72237e21 q^{4} -4.21515e24 q^{5} -1.69444e27 q^{6} -1.19188e31 q^{7} +3.24519e32 q^{8} -6.69772e34 q^{9} -2.89663e35 q^{10} -1.68299e38 q^{11} -1.16441e38 q^{12} +6.97112e40 q^{13} -8.19053e41 q^{14} +1.03934e41 q^{15} +2.23007e43 q^{16} +7.07443e44 q^{17} -4.60264e45 q^{18} +5.30898e46 q^{19} -1.99055e46 q^{20} +2.93885e47 q^{21} -1.15654e49 q^{22} +3.48043e49 q^{23} -8.00176e48 q^{24} -1.04102e51 q^{25} +4.79052e51 q^{26} +3.31795e51 q^{27} -5.62849e52 q^{28} +8.51468e52 q^{29} +7.14232e51 q^{30} +1.30244e54 q^{31} +1.53250e54 q^{32} +4.14981e54 q^{33} +4.86151e55 q^{34} +5.02395e55 q^{35} -3.16291e56 q^{36} +2.88717e57 q^{37} +3.64831e57 q^{38} -1.71889e57 q^{39} -1.36790e57 q^{40} +2.55851e58 q^{41} +2.01957e58 q^{42} -1.38982e59 q^{43} -7.94771e59 q^{44} +2.82319e59 q^{45} +2.39174e60 q^{46} -2.03016e61 q^{47} -5.49877e59 q^{48} +9.28358e61 q^{49} -7.15386e61 q^{50} -1.74436e61 q^{51} +3.29202e62 q^{52} +8.52520e61 q^{53} +2.28008e62 q^{54} +7.09407e62 q^{55} -3.86787e63 q^{56} -1.30905e63 q^{57} +5.85124e63 q^{58} -2.99429e64 q^{59} +4.90816e62 q^{60} +3.92014e64 q^{61} +8.95032e64 q^{62} +7.98287e65 q^{63} +1.05312e65 q^{64} -2.93843e65 q^{65} +2.85173e65 q^{66} +4.85230e66 q^{67} +3.34080e66 q^{68} -8.58182e65 q^{69} +3.45243e66 q^{70} +4.78682e67 q^{71} -2.17353e67 q^{72} +1.55085e68 q^{73} +1.98405e68 q^{74} +2.56689e67 q^{75} +2.50710e68 q^{76} +2.00592e69 q^{77} -1.18121e68 q^{78} -1.59580e69 q^{79} -9.40011e67 q^{80} +4.44486e69 q^{81} +1.75819e69 q^{82} -7.89354e69 q^{83} +1.38783e69 q^{84} -2.98198e69 q^{85} -9.55078e69 q^{86} -2.09949e69 q^{87} -5.46162e70 q^{88} +4.19168e69 q^{89} +1.94008e70 q^{90} -8.30873e71 q^{91} +1.64359e71 q^{92} -3.21148e70 q^{93} -1.39512e72 q^{94} -2.23782e71 q^{95} -3.77872e70 q^{96} -1.72372e72 q^{97} +6.37963e72 q^{98} +1.12722e73 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 274877906944 q^{2} + 30\!\cdots\!76 q^{3} + 18\!\cdots\!84 q^{4} - 78\!\cdots\!60 q^{5} + 20\!\cdots\!36 q^{6} + 36\!\cdots\!12 q^{7} + 12\!\cdots\!24 q^{8} + 12\!\cdots\!52 q^{9} - 53\!\cdots\!60 q^{10}+ \cdots + 28\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q + 274877906944 * q^2 + 305066325723244176 * q^3 + 18889465931478580854784 * q^4 - 7846962293700032321337960 * q^5 + 20963998273475476527079489536 * q^6 + 3636364966558861993065799361312 * q^7 + 1298074214633706907132624082305024 * q^8 + 122378175810775448230425774569321652 * q^9 - 539239142790188570468632018613698560 * q^10 + 52775218805667734867535256611889929648 * q^11 + 1440634991647642175069153055191907434496 * q^12 + 1355651207894098513401138234675081313976 * q^13 + 249889097723047134707119792526923642437632 * q^14 - 7830535738800097006518186191927965043233440 * q^15 + 89202980794122492566142873090593446023921664 * q^16 + 954348456154904658262187917015529592600353352 * q^17 + 8409764205622701352790716382891279683915087872 * q^18 + 95454725025342640211946932212410556121580424400 * q^19 - 37056231728110945597372254620868777164836700160 * q^20 + 663014063083061571146153755002330860310806732928 * q^21 + 3626685420953393611175405108400560201438412668928 * q^22 - 67417603669907011086030463893163498895122860076704 * q^23 + 98999682793597700758917102567483606960313315885056 * q^24 + 3460631286066960520802994294848553614203197326799100 * q^25 + 93159641643008802343361703153674358874682043662336 * q^26 + 12084377134756095104629255763677919783130973382555040 * q^27 + 17172248037558968144537376756119075900141234554929152 * q^28 - 408828336209279227379368505274385966779755922402879240 * q^29 - 538110318532889838793969736377110224776301614297251840 * q^30 + 3799789752719913567257037059011407543542506417455406208 * q^31 + 6129982163463555433433388108601236734474956488734408704 * q^32 + 62216718136234720076912175436040395811344879605468165312 * q^33 + 65582326530774486675746452751808984389419539918143619072 * q^34 + 431767153301184553170750885645944283201771950341035990720 * q^35 + 577914595683534746006577363150871362656072314419299745792 * q^36 + 6801183386761815205425784377566670372797473237706983459352 * q^37 + 6559598755720310574473705317437316221877768362108806758400 * q^38 + 11327031655330197070885706025461449402448174139265298802144 * q^39 - 2546484854163745203205584274150660432487763653884127477760 * q^40 + 56874804657516327155642316307646742627510460774170204545448 * q^41 + 45561979483677286074033721822761719180903349012837861163008 * q^42 - 195612042326640270143679332399870892198183174704527897687504 * q^43 + 249223924413997099203419280962107854932114473139165366059008 * q^44 - 7974393496061748311007765969419683838885297239373320672939080 * q^45 - 4632902446991043071609764558093537051767757086902843703558144 * q^46 - 26837344299723692260252514346441012876376468762050649660269888 * q^47 + 6803206398606016687045493374438715598570618586234125042057216 * q^48 + 49288467772056748491478921994228369389621400119046767962459108 * q^49 + 237812771154752254447551810483985904734485337875788141795737600 * q^50 + 462279018098899407813413748964859585061118118125593850879008288 * q^51 + 6401881826620840209677866843902262937608427838850834991415296 * q^52 + 45487338963145722322030598089193311856717264520906215815881816 * q^53 + 830432073380921814576773627357058722333743090603526299519549440 * q^54 - 2050760578084075114386836605813651219506186672252469754486193120 * q^55 + 1180067899521855165636701347474591981965573827111773174992207872 * q^56 - 3592025896576963719316420752340210472238227670222328115746257600 * q^57 - 28094469339151150293224568244574259740806305945322881152597360640 * q^58 - 36211351257280450133792917437500801540590596428487702560293076880 * q^59 - 36978659515822472927852993596054879014422789587819242807613194240 * q^60 + 355926993234389260836197952322967108098379440839658027389943954808 * q^61 + 261119563513727293109050729509024279847084176781457491228085977088 * q^62 + 1354878537917418371717449932688191098150383285998373405919969463456 * q^63 + 421249166674228746791672110734681729275580381602196445017243910144 * q^64 + 5535868819575966258563337770064603238403854822937797912179994113360 * q^65 + 4275500314553251124960838370592128635913946298920690444546586181632 * q^66 + 2491990477133118795215059534264173871640752538756993508607055683472 * q^67 + 4506783162324312925176300335312460684664503237948693775125149908992 * q^68 + 36011984923282423612732885710686669353728819466689401794442606346624 * q^69 + 29670812846649697502859970521797864502236363135438170030421751889920 * q^70 + 61369373660787623297444370825513800920470177886238250167413906103328 * q^71 + 39713988613469511996446662010030528264172580579870746230364057894912 * q^72 + 456671534259044615009379581820843089057568686566115963985790726852136 * q^73 + 467373763523848250382388250508745044972436409398187647819676565635072 * q^74 + 2274484745358414989035084574628142288008132133113498093192382898732400 * q^75 + 450772194091216429445240588005353147247604717195532969934588372582400 * q^76 + 2937010629095569814915333560530816478733805597591112398546851047158144 * q^77 + 778387688326399048011025618131633095876378404208918525166023274921984 * q^78 + 2026656030798125727242892609149209096074932883431594515097100420626240 * q^79 - 174993106694281841226317741152783755749378573017756654247586677391360 * q^80 - 1690644062388676955190899758084885673044542109854601078388778076183836 * q^81 + 3908406815526737691512327206640483748897384622767229920965275290697728 * q^82 + 15812009999547814415856750888845542429811781646082575448908590281393616 * q^83 + 3130995389174670552096177120478769476523452667952199965531326159781888 * q^84 - 47381303711757475901026713604519693996172406037229330915853699493216080 * q^85 - 13442357191947003357179327260296938825816612575574428538999419325906944 * q^86 - 154442588212957708624899011736533281049174301414639814817610904676124960 * q^87 + 17126537675822296091480855409729418434530303396175771263348924259237888 * q^88 - 244126894674274014119641875856417639495708996405247140614177242434617240 * q^89 - 547996148336325020677785466250868450986753355813559933203104972805242880 * q^90 - 956695923071478195873919348809058005807314877434919486549850807547281472 * q^91 - 318370631926158457559861197620346139940908410808319098178907957031337984 * q^92 - 2677792907975102091334715599122289169140096674655183648095758982803701248 * q^93 - 1844248257260884481506445917115759428754429189071570338982602871897325568 * q^94 - 4616055418633200363736062249001551807751077321632189313148700192365581600 * q^95 + 467512783839212506555050574518383453633693938789845165676965876492926976 * q^96 + 5819977544840824809887571543683857252285947538686838060303213522914493832 * q^97 + 3387077714414939478831988874216735156541302325328582001492198793557311488 * q^98 + 28045365238060746865970778341472050511805413521238694500165502185235671024 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	6.87195e10	0.707107
$2$	6.87195e10	0.707107
$3$	−2.46573e16	−0.0948462	−0.0474231	−	0.998875i	$-0.515101\pi$
$3$	−2.46573e16	−0.0948462	−0.0474231	+	0.998875i	$0.515101\pi$
$4$	4.72237e21	0.500000
$5$	−4.21515e24	−0.129541	−0.0647707	−	0.997900i	$-0.520632\pi$
$5$	−4.21515e24	−0.129541	−0.0647707	+	0.997900i	$0.520632\pi$
$6$	−1.69444e27	−0.0670664
$7$	−1.19188e31	−1.69884	−0.849422	−	0.527713i	$-0.823049\pi$
$7$	−1.19188e31	−1.69884	−0.849422	+	0.527713i	$0.823049\pi$
$8$	3.24519e32	0.353553
$9$	−6.69772e34	−0.991004
$10$	−2.89663e35	−0.0915995
$11$	−1.68299e38	−1.64153	−0.820766	−	0.571265i	$-0.806453\pi$
$11$	−1.68299e38	−1.64153	−0.820766	+	0.571265i	$0.806453\pi$
$12$	−1.16441e38	−0.0474231
$13$	6.97112e40	1.52887	0.764434	−	0.644702i	$-0.223018\pi$
$13$	6.97112e40	1.52887	0.764434	+	0.644702i	$0.223018\pi$
$14$	−8.19053e41	−1.20126
$15$	1.03934e41	0.0122865
$16$	2.23007e43	0.250000
$17$	7.07443e44	0.867572	0.433786	−	0.901016i	$-0.357177\pi$
$17$	7.07443e44	0.867572	0.433786	+	0.901016i	$0.357177\pi$
$18$	−4.60264e45	−0.700746
$19$	5.30898e46	1.12332	0.561662	−	0.827367i	$-0.310162\pi$
$19$	5.30898e46	1.12332	0.561662	+	0.827367i	$0.310162\pi$
$20$	−1.99055e46	−0.0647707
$21$	2.93885e47	0.161129
$22$	−1.15654e49	−1.16074
$23$	3.48043e49	0.689553	0.344776	−	0.938685i	$-0.387955\pi$
$23$	3.48043e49	0.689553	0.344776	+	0.938685i	$0.387955\pi$
$24$	−8.00176e48	−0.0335332
$25$	−1.04102e51	−0.983219
$26$	4.79052e51	1.08107
$27$	3.31795e51	0.188839
$28$	−5.62849e52	−0.849422
$29$	8.51468e52	0.356978	0.178489	−	0.983942i	$-0.442879\pi$
$29$	8.51468e52	0.356978	0.178489	+	0.983942i	$0.442879\pi$
$30$	7.14232e51	0.00868787
$31$	1.30244e54	0.478693	0.239346	−	0.970934i	$-0.423067\pi$
$31$	1.30244e54	0.478693	0.239346	+	0.970934i	$0.423067\pi$
$32$	1.53250e54	0.176777
$33$	4.14981e54	0.155693
$34$	4.86151e55	0.613466
$35$	5.02395e55	0.220071
$36$	−3.16291e56	−0.495502
$37$	2.88717e57	1.66383	0.831917	−	0.554900i	$-0.187244\pi$
$37$	2.88717e57	1.66383	0.831917	+	0.554900i	$0.187244\pi$
$38$	3.64831e57	0.794310
$39$	−1.71889e57	−0.145007
$40$	−1.36790e57	−0.0457998
$41$	2.55851e58	0.347837	0.173919	−	0.984760i	$-0.444357\pi$
$41$	2.55851e58	0.347837	0.173919	+	0.984760i	$0.444357\pi$
$42$	2.01957e58	0.113935
$43$	−1.38982e59	−0.332170	−0.166085	−	0.986111i	$-0.553113\pi$
$43$	−1.38982e59	−0.332170	−0.166085	+	0.986111i	$0.553113\pi$
$44$	−7.94771e59	−0.820766
$45$	2.82319e59	0.128376
$46$	2.39174e60	0.487587
$47$	−2.03016e61	−1.88781	−0.943906	−	0.330214i	$-0.892879\pi$
$47$	−2.03016e61	−1.88781	−0.943906	+	0.330214i	$0.892879\pi$
$48$	−5.49877e59	−0.0237116
$49$	9.28358e61	1.88607
$50$	−7.15386e61	−0.695241
$51$	−1.74436e61	−0.0822859
$52$	3.29202e62	0.764434
$53$	8.52520e61	0.0987724	0.0493862	−	0.998780i	$-0.484273\pi$
$53$	8.52520e61	0.0987724	0.0493862	+	0.998780i	$0.484273\pi$
$54$	2.28008e62	0.133530
$55$	7.09407e62	0.212646
$56$	−3.86787e63	−0.600632
$57$	−1.30905e63	−0.106543
$58$	5.85124e63	0.252422
$59$	−2.99429e64	−0.692143	−0.346071	−	0.938208i	$-0.612484\pi$
$59$	−2.99429e64	−0.692143	−0.346071	+	0.938208i	$0.612484\pi$
$60$	4.90816e62	0.00614325
$61$	3.92014e64	0.268388	0.134194	−	0.990955i	$-0.457156\pi$
$61$	3.92014e64	0.268388	0.134194	+	0.990955i	$0.457156\pi$
$62$	8.95032e64	0.338487
$63$	7.98287e65	1.68356
$64$	1.05312e65	0.125000
$65$	−2.93843e65	−0.198052
$66$	2.85173e65	0.110092
$67$	4.85230e66	1.08198	0.540988	−	0.841030i	$-0.318050\pi$
$67$	4.85230e66	1.08198	0.540988	+	0.841030i	$0.318050\pi$
$68$	3.34080e66	0.433786
$69$	−8.58182e65	−0.0654015
$70$	3.45243e66	0.155613
$71$	4.78682e67	1.28563	0.642817	−	0.766020i	$-0.277766\pi$
$71$	4.78682e67	1.28563	0.642817	+	0.766020i	$0.277766\pi$
$72$	−2.17353e67	−0.350373
$73$	1.55085e68	1.51108	0.755538	−	0.655105i	$-0.227376\pi$
$73$	1.55085e68	1.51108	0.755538	+	0.655105i	$0.227376\pi$
$74$	1.98405e68	1.17651
$75$	2.56689e67	0.0932546
$76$	2.50710e68	0.561662
$77$	2.00592e69	2.78871
$78$	−1.18121e68	−0.102536
$79$	−1.59580e69	−0.870139	−0.435070	−	0.900397i	$-0.643276\pi$
$79$	−1.59580e69	−0.870139	−0.435070	+	0.900397i	$0.643276\pi$
$80$	−9.40011e67	−0.0323853
$81$	4.44486e69	0.973093
$82$	1.75819e69	0.245958
$83$	−7.89354e69	−0.709449	−0.354725	−	0.934971i	$-0.615425\pi$
$83$	−7.89354e69	−0.709449	−0.354725	+	0.934971i	$0.615425\pi$
$84$	1.38783e69	0.0805645
$85$	−2.98198e69	−0.112386
$86$	−9.55078e69	−0.234880
$87$	−2.09949e69	−0.0338580
$88$	−5.46162e70	−0.580369
$89$	4.19168e69	0.0294885	0.0147443	−	0.999891i	$-0.495307\pi$
$89$	4.19168e69	0.0294885	0.0147443	+	0.999891i	$0.495307\pi$
$90$	1.94008e70	0.0907755
$91$	−8.30873e71	−2.59731
$92$	1.64359e71	0.344776
$93$	−3.21148e70	−0.0454022
$94$	−1.39512e72	−1.33488
$95$	−2.23782e71	−0.145517
$96$	−3.77872e70	−0.0167666
$97$	−1.72372e72	−0.523961	−0.261980	−	0.965073i	$-0.584376\pi$
$97$	−1.72372e72	−0.523961	−0.261980	+	0.965073i	$0.584376\pi$
$98$	6.37963e72	1.33366
$99$	1.12722e73	1.62676
$100$	−4.91610e72	−0.491610
$101$	−3.97103e71	−0.0276168	−0.0138084	−	0.999905i	$-0.504395\pi$
$101$	−3.97103e71	−0.0276168	−0.0138084	+	0.999905i	$0.504395\pi$
$102$	−1.19872e72	−0.0581850
$103$	3.91865e73	1.33222	0.666112	−	0.745852i	$-0.267957\pi$
$103$	3.91865e73	1.33222	0.666112	+	0.745852i	$0.267957\pi$
$104$	2.26226e73	0.540537
$105$	−1.23877e72	−0.0208729
$106$	5.85847e72	0.0698426
$107$	−2.83117e73	−0.239584	−0.119792	−	0.992799i	$-0.538223\pi$
$107$	−2.83117e73	−0.239584	−0.119792	+	0.992799i	$0.538223\pi$
$108$	1.56686e73	0.0944196
$109$	1.01633e74	0.437489	0.218745	−	0.975782i	$-0.429804\pi$
$109$	1.01633e74	0.437489	0.218745	+	0.975782i	$0.429804\pi$
$110$	4.87501e73	0.150364
$111$	−7.11900e73	−0.157808
$112$	−2.65798e74	−0.424711
$113$	−5.40833e74	−0.624741	−0.312371	−	0.949960i	$-0.601123\pi$
$113$	−5.40833e74	−0.624741	−0.312371	+	0.949960i	$0.601123\pi$
$114$	−8.99575e73	−0.0753373
$115$	−1.46706e74	−0.0893256
$116$	4.02094e74	0.178489
$117$	−4.66906e75	−1.51512
$118$	−2.05766e75	−0.489419
$119$	−8.43186e75	−1.47387
$120$	3.37286e73	0.00434394
$121$	1.78131e76	1.69462
$122$	2.69390e75	0.189779
$123$	−6.30860e74	−0.0329911
$124$	6.15061e75	0.239346
$125$	8.85104e75	0.256909
$126$	5.48579e76	1.19046
$127$	3.23151e76	0.525497	0.262748	−	0.964864i	$-0.415371\pi$
$127$	3.23151e76	0.525497	0.262748	+	0.964864i	$0.415371\pi$
$128$	7.23701e75	0.0883883
$129$	3.42693e75	0.0315051
$130$	−2.01928e76	−0.140044
$131$	1.41984e77	0.744452	0.372226	−	0.928142i	$-0.378595\pi$
$131$	1.41984e77	0.744452	0.372226	+	0.928142i	$0.378595\pi$
$132$	1.95969e76	0.0778465
$133$	−6.32767e77	−1.90835
$134$	3.33448e77	0.765072
$135$	−1.39857e76	−0.0244625
$136$	2.29578e77	0.306733
$137$	−9.06516e77	−0.926990	−0.463495	−	0.886100i	$-0.653405\pi$
$137$	−9.06516e77	−0.926990	−0.463495	+	0.886100i	$0.653405\pi$
$138$	−5.89738e76	−0.0462458
$139$	−1.26307e78	−0.761002	−0.380501	−	0.924781i	$-0.624248\pi$
$139$	−1.26307e78	−0.761002	−0.380501	+	0.924781i	$0.624248\pi$
$140$	2.37250e77	0.110035
$141$	5.00583e77	0.179052
$142$	3.28948e78	0.909080
$143$	−1.17323e79	−2.50969
$144$	−1.49364e78	−0.247751
$145$	−3.58907e77	−0.0462434
$146$	1.06574e79	1.06849
$147$	−2.28908e78	−0.178887
$148$	1.36343e79	0.831917
$149$	1.62808e79	0.776919	0.388460	−	0.921466i	$-0.373007\pi$
$149$	1.62808e79	0.776919	0.388460	+	0.921466i	$0.373007\pi$
$150$	1.76395e78	0.0659410
$151$	1.91503e79	0.561715	0.280858	−	0.959749i	$-0.409381\pi$
$151$	1.91503e79	0.561715	0.280858	+	0.959749i	$0.409381\pi$
$152$	1.72286e79	0.397155
$153$	−4.73825e79	−0.859768
$154$	1.37846e80	1.97191
$155$	−5.49000e78	−0.0620105
$156$	−8.11724e78	−0.0725037
$157$	−1.60355e80	−1.13435	−0.567174	−	0.823598i	$-0.691963\pi$
$157$	−1.60355e80	−1.13435	−0.567174	+	0.823598i	$0.691963\pi$
$158$	−1.09662e80	−0.615281
$159$	−2.10209e78	−0.00936819
$160$	−6.45971e78	−0.0228999
$161$	−4.14826e80	−1.17144
$162$	3.05448e80	0.688081
$163$	−7.66920e80	−1.38007	−0.690037	−	0.723774i	$-0.742406\pi$
$163$	−7.66920e80	−1.38007	−0.690037	+	0.723774i	$0.742406\pi$
$164$	1.20822e80	0.173919
$165$	−1.74921e79	−0.0201687
$166$	−5.42440e80	−0.501656
$167$	1.01721e81	0.755542	0.377771	−	0.925899i	$-0.376691\pi$
$167$	1.01721e81	0.755542	0.377771	+	0.925899i	$0.376691\pi$
$168$	9.53713e79	0.0569677
$169$	2.78060e81	1.33744
$170$	−2.04920e80	−0.0794692
$171$	−3.55581e81	−1.11322
$172$	−6.56324e80	−0.166085
$173$	2.48040e81	0.507971	0.253986	−	0.967208i	$-0.418258\pi$
$173$	2.48040e81	0.507971	0.253986	+	0.967208i	$0.418258\pi$
$174$	−1.44276e80	−0.0239412
$175$	1.24077e82	1.67034
$176$	−3.75320e81	−0.410383
$177$	7.38312e80	0.0656471
$178$	2.88050e80	0.0208515
$179$	1.17175e82	0.691354	0.345677	−	0.938353i	$-0.387649\pi$
$179$	1.17175e82	0.691354	0.345677	+	0.938353i	$0.387649\pi$
$180$	1.33322e81	0.0641880
$181$	2.01741e82	0.793462	0.396731	−	0.917935i	$-0.370145\pi$
$181$	2.01741e82	0.793462	0.396731	+	0.917935i	$0.370145\pi$
$182$	−5.70972e82	−1.83658
$183$	−9.66601e80	−0.0254556
$184$	1.12947e82	0.243794
$185$	−1.21699e82	−0.215535
$186$	−2.20691e81	−0.0321042
$187$	−1.19062e83	−1.42415
$188$	−9.58717e82	−0.943906
$189$	−3.95459e82	−0.320809
$190$	−1.53782e82	−0.102896
$191$	3.02289e83	1.66995	0.834976	−	0.550286i	$-0.185481\pi$
$191$	3.02289e83	1.66995	0.834976	+	0.550286i	$0.185481\pi$
$192$	−2.59672e81	−0.0118558
$193$	−2.11997e83	−0.800734	−0.400367	−	0.916355i	$-0.631117\pi$
$193$	−2.11997e83	−0.800734	−0.400367	+	0.916355i	$0.631117\pi$
$194$	−1.18453e83	−0.370496
$195$	7.24539e81	0.0187845
$196$	4.38405e83	0.943037
$197$	1.09618e84	1.95823	0.979114	−	0.203314i	$-0.0651713\pi$
$197$	1.09618e84	1.95823	0.979114	+	0.203314i	$0.0651713\pi$
$198$	7.74621e83	1.15030
$199$	−5.35149e83	−0.661207	−0.330603	−	0.943770i	$-0.607252\pi$
$199$	−5.35149e83	−0.661207	−0.330603	+	0.943770i	$0.607252\pi$
$200$	−3.37831e83	−0.347620
$201$	−1.19645e83	−0.102621
$202$	−2.72887e82	−0.0195280
$203$	−1.01485e84	−0.606450
$204$	−8.23753e82	−0.0411430
$205$	−1.07845e83	−0.0450593
$206$	2.69287e84	0.942025
$207$	−2.33110e84	−0.683350
$208$	1.55461e84	0.382217
$209$	−8.93498e84	−1.84397
$210$	−8.51278e82	−0.0147593
$211$	1.53995e84	0.224490	0.112245	−	0.993681i	$-0.464196\pi$
$211$	1.53995e84	0.224490	0.112245	+	0.993681i	$0.464196\pi$
$212$	4.02591e83	0.0493862
$213$	−1.18030e84	−0.121938
$214$	−1.94556e84	−0.169411
$215$	5.85831e83	0.0430297
$216$	1.07674e84	0.0667648
$217$	−1.55235e85	−0.813225
$218$	6.98416e84	0.309352
$219$	−3.82399e84	−0.143320
$220$	3.35008e84	0.106323
$221$	4.93167e85	1.32640
$222$	−4.89214e84	−0.111587
$223$	1.13513e85	0.219744	0.109872	−	0.993946i	$-0.464956\pi$
$223$	1.13513e85	0.219744	0.109872	+	0.993946i	$0.464956\pi$
$224$	−1.82655e85	−0.300316
$225$	6.97249e85	0.974374
$226$	−3.71658e85	−0.441759
$227$	6.57006e85	0.664700	0.332350	−	0.943156i	$-0.392159\pi$
$227$	6.57006e85	0.664700	0.332350	+	0.943156i	$0.392159\pi$
$228$	−6.18183e84	−0.0532715
$229$	1.69600e86	1.24575	0.622876	−	0.782321i	$-0.285964\pi$
$229$	1.69600e86	1.24575	0.622876	+	0.782321i	$0.285964\pi$
$230$	−1.00815e85	−0.0631627
$231$	−4.94607e85	−0.264498
$232$	2.76317e85	0.126211
$233$	−4.48858e86	−1.75234	−0.876168	−	0.482006i	$-0.839908\pi$
$233$	−4.48858e86	−1.75234	−0.876168	+	0.482006i	$0.839908\pi$
$234$	−3.20856e86	−1.07135
$235$	8.55744e85	0.244550
$236$	−1.41401e86	−0.346071
$237$	3.93481e85	0.0825294
$238$	−5.79433e86	−1.04218
$239$	−8.90705e85	−0.137471	−0.0687354	−	0.997635i	$-0.521896\pi$
$239$	−8.90705e85	−0.137471	−0.0687354	+	0.997635i	$0.521896\pi$
$240$	2.31781e84	0.00307163
$241$	1.83299e86	0.208708	0.104354	−	0.994540i	$-0.466723\pi$
$241$	1.83299e86	0.208708	0.104354	+	0.994540i	$0.466723\pi$
$242$	1.22411e87	1.19828
$243$	−3.33842e86	−0.281134
$244$	1.85123e86	0.134194
$245$	−3.91317e86	−0.244325
$246$	−4.33524e85	−0.0233282
$247$	3.70096e87	1.71741
$248$	4.22667e86	0.169244
$249$	1.94634e86	0.0672886
$250$	6.08239e86	0.181662
$251$	−2.63560e87	−0.680438	−0.340219	−	0.940346i	$-0.610501\pi$
$251$	−2.63560e87	−0.680438	−0.340219	+	0.940346i	$0.610501\pi$
$252$	3.76981e87	0.841781
$253$	−5.85754e87	−1.13192
$254$	2.22068e87	0.371582
$255$	7.35276e85	0.0106594
$256$	4.97323e86	0.0625000
$257$	1.34793e88	1.46930	0.734648	−	0.678448i	$-0.237347\pi$
$257$	1.34793e88	1.46930	0.734648	+	0.678448i	$0.237347\pi$
$258$	2.35497e86	0.0222774
$259$	−3.44116e88	−2.82660
$260$	−1.38764e87	−0.0990258
$261$	−5.70290e87	−0.353767
$262$	9.75706e87	0.526407
$263$	1.66537e88	0.781857	0.390928	−	0.920421i	$-0.372154\pi$
$263$	1.66537e88	0.781857	0.390928	+	0.920421i	$0.372154\pi$
$264$	1.34669e87	0.0550458
$265$	−3.59350e86	−0.0127951
$266$	−4.34834e88	−1.34941
$267$	−1.03356e86	−0.00279687
$268$	2.29143e88	0.540988
$269$	−8.11478e88	−1.67232	−0.836159	−	0.548487i	$-0.815204\pi$
$269$	−8.11478e88	−1.67232	−0.836159	+	0.548487i	$0.815204\pi$
$270$	−9.61088e86	−0.0172976
$271$	7.71353e88	1.21304	0.606519	−	0.795069i	$-0.292566\pi$
$271$	7.71353e88	1.21304	0.606519	+	0.795069i	$0.292566\pi$
$272$	1.57765e88	0.216893
$273$	2.04871e88	0.246345
$274$	−6.22953e88	−0.655481
$275$	1.75203e89	1.61398
$276$	−4.05265e87	−0.0327007
$277$	2.18690e89	1.54639	0.773194	−	0.634170i	$-0.218658\pi$
$277$	2.18690e89	1.54639	0.773194	+	0.634170i	$0.218658\pi$
$278$	−8.67972e88	−0.538109
$279$	−8.72340e88	−0.474387
$280$	1.63037e88	0.0778067
$281$	2.65258e89	1.11144	0.555721	−	0.831369i	$-0.312442\pi$
$281$	2.65258e89	1.11144	0.555721	+	0.831369i	$0.312442\pi$
$282$	3.43998e88	0.126609
$283$	−3.32070e89	−1.07405	−0.537025	−	0.843566i	$-0.680452\pi$
$283$	−3.32070e89	−1.07405	−0.537025	+	0.843566i	$0.680452\pi$
$284$	2.26051e89	0.642817
$285$	5.51786e87	0.0138017
$286$	−8.06240e89	−1.77462
$287$	−3.04943e89	−0.590922
$288$	−1.02642e89	−0.175186
$289$	−1.64448e89	−0.247319
$290$	−2.46639e88	−0.0326990
$291$	4.25023e88	0.0496957
$292$	7.32370e89	0.755538
$293$	−1.70729e90	−1.55468	−0.777339	−	0.629082i	$-0.783431\pi$
$293$	−1.70729e90	−1.55468	−0.777339	+	0.629082i	$0.783431\pi$
$294$	−1.57305e89	−0.126492
$295$	1.26214e89	0.0896611
$296$	9.36941e89	0.588254
$297$	−5.58408e89	−0.309986
$298$	1.11881e90	0.549365
$299$	2.42625e90	1.05424
$300$	1.21218e89	0.0466273
$301$	1.65650e90	0.564305
$302$	1.31600e90	0.397193
$303$	9.79150e87	0.00261935
$304$	1.18394e90	0.280831
$305$	−1.65240e89	−0.0347673
$306$	−3.25610e90	−0.607947
$307$	−8.53783e90	−1.41513	−0.707566	−	0.706648i	$-0.750207\pi$
$307$	−8.53783e90	−1.41513	−0.707566	+	0.706648i	$0.750207\pi$
$308$	9.47270e90	1.39435
$309$	−9.66233e89	−0.126356
$310$	−3.77270e89	−0.0438481
$311$	5.33359e90	0.551145	0.275572	−	0.961280i	$-0.411133\pi$
$311$	5.33359e90	0.551145	0.275572	+	0.961280i	$0.411133\pi$
$312$	−5.57812e89	−0.0512679
$313$	4.68674e90	0.383268	0.191634	−	0.981466i	$-0.438621\pi$
$313$	4.68674e90	0.383268	0.191634	+	0.981466i	$0.438621\pi$
$314$	−1.10195e91	−0.802105
$315$	−3.36490e90	−0.218091
$316$	−7.53594e90	−0.435070
$317$	−2.27814e90	−0.117197	−0.0585986	−	0.998282i	$-0.518663\pi$
$317$	−2.27814e90	−0.117197	−0.0585986	+	0.998282i	$0.518663\pi$
$318$	−1.44454e89	−0.00662431
$319$	−1.43301e91	−0.585990
$320$	−4.43908e89	−0.0161927
$321$	6.98090e89	0.0227236
$322$	−2.85066e91	−0.828335
$323$	3.75580e91	0.974565
$324$	2.09902e91	0.486547
$325$	−7.25710e91	−1.50321
$326$	−5.27023e91	−0.975860
$327$	−2.50600e90	−0.0414942
$328$	8.30284e90	0.122979
$329$	2.41971e92	3.20710
$330$	−1.20205e90	−0.0142614
$331$	1.25174e92	1.32981	0.664907	−	0.746926i	$-0.268471\pi$
$331$	1.25174e92	1.32981	0.664907	+	0.746926i	$0.268471\pi$
$332$	−3.72762e91	−0.354725
$333$	−1.93375e92	−1.64887
$334$	6.99020e91	0.534249
$335$	−2.04532e91	−0.140161
$336$	6.55386e90	0.0402823
$337$	1.95805e92	1.07977	0.539886	−	0.841738i	$-0.318467\pi$
$337$	1.95805e92	1.07977	0.539886	+	0.841738i	$0.318467\pi$
$338$	1.91082e92	0.945713
$339$	1.33355e91	0.0592544
$340$	−1.40820e91	−0.0561932
$341$	−2.19200e92	−0.785789
$342$	−2.44353e92	−0.787165
$343$	−5.19827e92	−1.50530
$344$	−4.51023e91	−0.117440
$345$	3.61737e90	0.00847219
$346$	1.70452e92	0.359190
$347$	−4.37169e92	−0.829131	−0.414565	−	0.910020i	$-0.636066\pi$
$347$	−4.37169e92	−0.829131	−0.414565	+	0.910020i	$0.636066\pi$
$348$	−9.91457e90	−0.0169290
$349$	−9.71678e92	−1.49415	−0.747075	−	0.664740i	$-0.768542\pi$
$349$	−9.71678e92	−1.49415	−0.747075	+	0.664740i	$0.768542\pi$
$350$	8.52654e92	1.18111
$351$	2.31298e92	0.288710
$352$	−2.57918e92	−0.290184
$353$	9.19080e92	0.932345	0.466173	−	0.884694i	$-0.345633\pi$
$353$	9.19080e92	0.932345	0.466173	+	0.884694i	$0.345633\pi$
$354$	5.07364e91	0.0464195
$355$	−2.01772e92	−0.166543
$356$	1.97946e91	0.0147443
$357$	2.07907e92	0.139791
$358$	8.05223e92	0.488861
$359$	1.43837e93	0.788721	0.394360	−	0.918956i	$-0.370966\pi$
$359$	1.43837e93	0.788721	0.394360	+	0.918956i	$0.370966\pi$
$360$	9.16179e91	0.0453878
$361$	5.84893e92	0.261857
$362$	1.38635e93	0.561063
$363$	−4.39223e92	−0.160729
$364$	−3.92369e93	−1.29866
$365$	−6.53709e92	−0.195747
$366$	−6.64243e91	−0.0179998
$367$	5.34425e93	1.31092	0.655459	−	0.755231i	$-0.272475\pi$
$367$	5.34425e93	1.31092	0.655459	+	0.755231i	$0.272475\pi$
$368$	7.76163e92	0.172388
$369$	−1.71362e93	−0.344708
$370$	−8.36308e92	−0.152406
$371$	−1.01610e93	−0.167799
$372$	−1.51658e92	−0.0227011
$373$	1.76265e93	0.239218	0.119609	−	0.992821i	$-0.461836\pi$
$373$	1.76265e93	0.239218	0.119609	+	0.992821i	$0.461836\pi$
$374$	−8.18188e93	−1.00702
$375$	−2.18243e92	−0.0243668
$376$	−6.58825e93	−0.667442
$377$	5.93569e93	0.545772
$378$	−2.71758e93	−0.226846
$379$	−1.02323e94	−0.775608	−0.387804	−	0.921742i	$-0.626766\pi$
$379$	−1.02323e94	−0.775608	−0.387804	+	0.921742i	$0.626766\pi$
$380$	−1.05678e93	−0.0727584
$381$	−7.96805e92	−0.0498414
$382$	2.07731e94	1.18084
$383$	−1.25070e94	−0.646244	−0.323122	−	0.946357i	$-0.604732\pi$
$383$	−1.25070e94	−0.646244	−0.323122	+	0.946357i	$0.604732\pi$
$384$	−1.78445e92	−0.00838330
$385$	−8.45528e93	−0.361253
$386$	−1.45683e94	−0.566205
$387$	9.30863e93	0.329182
$388$	−8.14004e93	−0.261980
$389$	3.49901e94	1.02514	0.512572	−	0.858644i	$-0.328693\pi$
$389$	3.49901e94	1.02514	0.512572	+	0.858644i	$0.328693\pi$
$390$	4.97900e92	0.0132826
$391$	2.46221e94	0.598237
$392$	3.01269e94	0.666828
$393$	−3.50094e93	−0.0706085
$394$	7.53286e94	1.38468
$395$	6.72653e93	0.112719
$396$	5.32315e94	0.813382
$397$	−6.05088e94	−0.843267	−0.421633	−	0.906766i	$-0.638543\pi$
$397$	−6.05088e94	−0.843267	−0.421633	+	0.906766i	$0.638543\pi$
$398$	−3.67752e94	−0.467544
$399$	1.56023e94	0.181000
$400$	−2.32156e94	−0.245805
$401$	−1.35545e95	−1.31013	−0.655066	−	0.755572i	$-0.727359\pi$
$401$	−1.35545e95	−1.31013	−0.655066	+	0.755572i	$0.727359\pi$
$402$	−8.22193e93	−0.0725642
$403$	9.07949e94	0.731859
$404$	−1.87527e93	−0.0138084
$405$	−1.87358e94	−0.126056
$406$	−6.97397e94	−0.428825
$407$	−4.85909e95	−2.73123
$408$	−5.66078e93	−0.0290925
$409$	1.01393e95	0.476551	0.238275	−	0.971198i	$-0.423418\pi$
$409$	1.01393e95	0.476551	0.238275	+	0.971198i	$0.423418\pi$
$410$	−7.41106e93	−0.0318617
$411$	2.23523e94	0.0879215
$412$	1.85053e95	0.666112
$413$	3.56883e95	1.17584
$414$	−1.60192e95	−0.483201
$415$	3.32725e94	0.0919030
$416$	1.06832e95	0.270268
$417$	3.11438e94	0.0721781
$418$	−6.14007e95	−1.30388
$419$	3.47086e95	0.675499	0.337750	−	0.941236i	$-0.390334\pi$
$419$	3.47086e95	0.675499	0.337750	+	0.941236i	$0.390334\pi$
$420$	−5.84994e93	−0.0104364
$421$	5.50175e95	0.899921	0.449960	−	0.893049i	$-0.351438\pi$
$421$	5.50175e95	0.899921	0.449960	+	0.893049i	$0.351438\pi$
$422$	1.05825e95	0.158739
$423$	1.35975e96	1.87083
$424$	2.76659e94	0.0349213
$425$	−7.36464e95	−0.853013
$426$	−8.11097e94	−0.0862228
$427$	−4.67233e95	−0.455949
$428$	−1.33698e95	−0.119792
$429$	2.89288e95	0.238034
$430$	4.02580e94	0.0304266
$431$	−3.59759e95	−0.249799	−0.124900	−	0.992169i	$-0.539861\pi$
$431$	−3.59759e95	−0.249799	−0.124900	+	0.992169i	$0.539861\pi$
$432$	7.39927e94	0.0472098
$433$	−7.04462e95	−0.413094	−0.206547	−	0.978437i	$-0.566223\pi$
$433$	−7.04462e95	−0.413094	−0.206547	+	0.978437i	$0.566223\pi$
$434$	−1.06677e96	−0.575037
$435$	8.84968e93	0.00438601
$436$	4.79948e95	0.218745
$437$	1.84776e96	0.774591
$438$	−2.62782e95	−0.101342
$439$	−1.03055e96	−0.365690	−0.182845	−	0.983142i	$-0.558531\pi$
$439$	−1.03055e96	−0.365690	−0.182845	+	0.983142i	$0.558531\pi$
$440$	2.30216e95	0.0751818
$441$	−6.21789e96	−1.86911
$442$	3.38902e96	0.937909
$443$	−2.58508e96	−0.658776	−0.329388	−	0.944195i	$-0.606842\pi$
$443$	−2.58508e96	−0.658776	−0.329388	+	0.944195i	$0.606842\pi$
$444$	−3.36185e95	−0.0789042
$445$	−1.76686e94	−0.00381998
$446$	7.80052e95	0.155382
$447$	−4.01440e95	−0.0736879
$448$	−1.25520e96	−0.212356
$449$	3.72911e96	0.581585	0.290793	−	0.956786i	$-0.406081\pi$
$449$	3.72911e96	0.581585	0.290793	+	0.956786i	$0.406081\pi$
$450$	4.79146e96	0.688987
$451$	−4.30595e96	−0.570986
$452$	−2.55401e96	−0.312371
$453$	−4.72194e95	−0.0532766
$454$	4.51491e96	0.470014
$455$	3.50226e96	0.336459
$456$	−4.24812e95	−0.0376687
$457$	2.33555e97	1.91183	0.955913	−	0.293649i	$-0.0948696\pi$
$457$	2.33555e97	1.91183	0.955913	+	0.293649i	$0.0948696\pi$
$458$	1.16548e97	0.880879
$459$	2.34726e96	0.163832
$460$	−6.92798e95	−0.0446628
$461$	−1.08470e97	−0.645989	−0.322995	−	0.946401i	$-0.604690\pi$
$461$	−1.08470e97	−0.645989	−0.322995	+	0.946401i	$0.604690\pi$
$462$	−3.39891e96	−0.187029
$463$	−1.10282e97	−0.560789	−0.280395	−	0.959885i	$-0.590465\pi$
$463$	−1.10282e97	−0.560789	−0.280395	+	0.959885i	$0.590465\pi$
$464$	1.89884e96	0.0892445
$465$	1.35369e95	0.00588146
$466$	−3.08453e97	−1.23909
$467$	4.23418e97	1.57291	0.786454	−	0.617649i	$-0.211915\pi$
$467$	4.23418e97	1.57291	0.786454	+	0.617649i	$0.211915\pi$
$468$	−2.20490e97	−0.757558
$469$	−5.78336e97	−1.83811
$470$	5.88063e96	0.172923
$471$	3.95393e96	0.107589
$472$	−9.71703e96	−0.244709
$473$	2.33906e97	0.545267
$474$	2.70398e96	0.0583571
$475$	−5.52678e97	−1.10447
$476$	−3.98183e97	−0.736935
$477$	−5.70994e96	−0.0978838
$478$	−6.12088e96	−0.0972065
$479$	−1.65825e97	−0.244008	−0.122004	−	0.992530i	$-0.538932\pi$
$479$	−1.65825e97	−0.244008	−0.122004	+	0.992530i	$0.538932\pi$
$480$	1.59279e95	0.00217197
$481$	2.01268e98	2.54378
$482$	1.25962e97	0.147579
$483$	1.02285e97	0.111107
$484$	8.41200e97	0.847312
$485$	7.26575e96	0.0678746
$486$	−2.29415e97	−0.198791
$487$	−3.81643e97	−0.306797	−0.153398	−	0.988164i	$-0.549022\pi$
$487$	−3.81643e97	−0.306797	−0.153398	+	0.988164i	$0.549022\pi$
$488$	1.27216e97	0.0948894
$489$	1.89102e97	0.130895
$490$	−2.68911e97	−0.172764
$491$	7.77542e96	0.0463713	0.0231857	−	0.999731i	$-0.492619\pi$
$491$	7.77542e96	0.0463713	0.0231857	+	0.999731i	$0.492619\pi$
$492$	−2.97915e96	−0.0164955
$493$	6.02365e97	0.309704
$494$	2.54328e98	1.21440
$495$	−4.75141e97	−0.210733
$496$	2.90455e97	0.119673
$497$	−5.70531e98	−2.18409
$498$	1.33751e97	0.0475802
$499$	−9.82857e97	−0.324953	−0.162476	−	0.986712i	$-0.551948\pi$
$499$	−9.82857e97	−0.324953	−0.162476	+	0.986712i	$0.551948\pi$
$500$	4.17979e97	0.128454
$501$	−2.50816e97	−0.0716603
$502$	−1.81117e98	−0.481142
$503$	3.97085e98	0.980963	0.490481	−	0.871452i	$-0.336821\pi$
$503$	3.97085e98	0.980963	0.490481	+	0.871452i	$0.336821\pi$
$504$	2.59059e98	0.595229
$505$	1.67385e96	0.00357752
$506$	−4.02527e98	−0.800390
$507$	−6.85622e97	−0.126851
$508$	1.52604e98	0.262748
$509$	−1.48658e98	−0.238227	−0.119113	−	0.992881i	$-0.538005\pi$
$509$	−1.48658e98	−0.238227	−0.119113	+	0.992881i	$0.538005\pi$
$510$	5.05278e96	0.00753736
$511$	−1.84843e99	−2.56708
$512$	3.41758e97	0.0441942
$513$	1.76149e98	0.212128
$514$	9.26293e98	1.03895
$515$	−1.65177e98	−0.172578
$516$	1.61832e97	0.0157525
$517$	3.41675e99	3.09890
$518$	−2.36475e99	−1.99870
$519$	−6.11600e97	−0.0481791
$520$	−9.53577e97	−0.0700218
$521$	6.36978e98	0.436061	0.218031	−	0.975942i	$-0.430037\pi$
$521$	6.36978e98	0.436061	0.218031	+	0.975942i	$0.430037\pi$
$522$	−3.91900e98	−0.250151
$523$	1.48632e99	0.884711	0.442356	−	0.896840i	$-0.354143\pi$
$523$	1.48632e99	0.884711	0.442356	+	0.896840i	$0.354143\pi$
$524$	6.70500e98	0.372226
$525$	−3.05942e98	−0.158425
$526$	1.14444e99	0.552856
$527$	9.21404e98	0.415301
$528$	9.25438e97	0.0389233
$529$	−1.33626e99	−0.524517
$530$	−2.46944e97	−0.00904750
$531$	2.00549e99	0.685916
$532$	−2.98816e99	−0.954177
$533$	1.78357e99	0.531798
$534$	−7.10254e96	−0.00197769
$535$	1.19338e98	0.0310360
$536$	1.57466e99	0.382536
$537$	−2.88923e98	−0.0655724
$538$	−5.57644e99	−1.18251
$539$	−1.56242e100	−3.09605
$540$	−6.60454e97	−0.0122312
$541$	2.17161e99	0.375908	0.187954	−	0.982178i	$-0.439814\pi$
$541$	2.17161e99	0.375908	0.187954	+	0.982178i	$0.439814\pi$
$542$	5.30070e99	0.857747
$543$	−4.97439e98	−0.0752569
$544$	1.08415e99	0.153367
$545$	−4.28399e98	−0.0566729
$546$	1.40786e99	0.174192
$547$	−7.48667e99	−0.866466	−0.433233	−	0.901282i	$-0.642627\pi$
$547$	−7.48667e99	−0.866466	−0.433233	+	0.901282i	$0.642627\pi$
$548$	−4.28090e99	−0.463495
$549$	−2.62560e99	−0.265973
$550$	1.20399e100	1.14126
$551$	4.52043e99	0.401002
$552$	−2.78496e98	−0.0231229
$553$	1.90200e100	1.47823
$554$	1.50283e100	1.09346
$555$	3.00077e98	0.0204427
$556$	−5.96466e99	−0.380501
$557$	9.86873e99	0.589585	0.294793	−	0.955561i	$-0.404749\pi$
$557$	9.86873e99	0.589585	0.294793	+	0.955561i	$0.404749\pi$
$558$	−5.99468e99	−0.335442
$559$	−9.68861e99	−0.507844
$560$	1.12038e99	0.0550177
$561$	2.93575e99	0.135075
$562$	1.82284e100	0.785909
$563$	−1.44052e100	−0.582055	−0.291028	−	0.956715i	$-0.593997\pi$
$563$	−1.44052e100	−0.582055	−0.291028	+	0.956715i	$0.593997\pi$
$564$	2.36394e99	0.0895259
$565$	2.27970e99	0.0809298
$566$	−2.28197e100	−0.759469
$567$	−5.29773e100	−1.65313
$568$	1.55341e100	0.454540
$569$	5.73588e100	1.57399	0.786996	−	0.616958i	$-0.211635\pi$
$569$	5.73588e100	1.57399	0.786996	+	0.616958i	$0.211635\pi$
$570$	3.79185e98	0.00975930
$571$	2.54969e100	0.615560	0.307780	−	0.951458i	$-0.400414\pi$
$571$	2.54969e100	0.615560	0.307780	+	0.951458i	$0.400414\pi$
$572$	−5.54044e100	−1.25484
$573$	−7.45363e99	−0.158389
$574$	−2.09555e100	−0.417845
$575$	−3.62321e100	−0.677981
$576$	−7.05352e99	−0.123876
$577$	−2.33530e100	−0.384969	−0.192484	−	0.981300i	$-0.561654\pi$
$577$	−2.33530e100	−0.384969	−0.192484	+	0.981300i	$0.561654\pi$
$578$	−1.13008e100	−0.174881
$579$	5.22728e99	0.0759466
$580$	−1.69489e99	−0.0231217
$581$	9.40814e100	1.20524
$582$	2.92074e99	0.0351402
$583$	−1.43478e100	−0.162138
$584$	5.03281e100	0.534246
$585$	1.96808e100	0.196270
$586$	−1.17324e101	−1.09932
$587$	−8.91264e100	−0.784722	−0.392361	−	0.919811i	$-0.628342\pi$
$587$	−8.91264e100	−0.784722	−0.392361	+	0.919811i	$0.628342\pi$
$588$	−1.08099e100	−0.0894435
$589$	6.91465e100	0.537727
$590$	8.67336e99	0.0633999
$591$	−2.70288e100	−0.185730
$592$	6.43861e100	0.415958
$593$	2.80777e101	1.70555	0.852777	−	0.522275i	$-0.174917\pi$
$593$	2.80777e101	1.70555	0.852777	+	0.522275i	$0.174917\pi$
$594$	−3.83735e100	−0.219193
$595$	3.55416e100	0.190927
$596$	7.68837e100	0.388460
$597$	1.31953e100	0.0627130
$598$	1.66731e101	0.745457
$599$	−4.19691e101	−1.76543	−0.882716	−	0.469906i	$-0.844288\pi$
$599$	−4.19691e101	−1.76543	−0.882716	+	0.469906i	$0.844288\pi$
$600$	8.33002e99	0.0329705
$601$	3.81035e101	1.41921	0.709605	−	0.704600i	$-0.248873\pi$
$601$	3.81035e101	1.41921	0.709605	+	0.704600i	$0.248873\pi$
$602$	1.13834e101	0.399024
$603$	−3.24994e101	−1.07224
$604$	9.04345e100	0.280858
$605$	−7.50850e100	−0.219524
$606$	6.72867e98	0.00185216
$607$	2.27651e101	0.590040	0.295020	−	0.955491i	$-0.404674\pi$
$607$	2.27651e101	0.590040	0.295020	+	0.955491i	$0.404674\pi$
$608$	8.13600e100	0.198577
$609$	2.50234e100	0.0575195
$610$	−1.13552e100	−0.0245842
$611$	−1.41525e102	−2.88622
$612$	−2.23758e101	−0.429884
$613$	−1.39360e101	−0.252250	−0.126125	−	0.992014i	$-0.540254\pi$
$613$	−1.39360e101	−0.252250	−0.126125	+	0.992014i	$0.540254\pi$
$614$	−5.86715e101	−1.00065
$615$	2.65917e99	0.00427371
$616$	6.50959e101	0.985957
$617$	−2.31583e101	−0.330596	−0.165298	−	0.986244i	$-0.552859\pi$
$617$	−2.31583e101	−0.330596	−0.165298	+	0.986244i	$0.552859\pi$
$618$	−6.63990e100	−0.0893475
$619$	3.89396e101	0.493950	0.246975	−	0.969022i	$-0.420563\pi$
$619$	3.89396e101	0.493950	0.246975	+	0.969022i	$0.420563\pi$
$620$	−2.59258e100	−0.0310053
$621$	1.15479e101	0.130215
$622$	3.66522e101	0.389718
$623$	−4.99597e100	−0.0500964
$624$	−3.83326e100	−0.0362519
$625$	1.06492e102	0.949939
$626$	3.22070e101	0.271011
$627$	2.20313e101	0.174894
$628$	−7.57257e101	−0.567174
$629$	2.04251e102	1.44350
$630$	−2.31234e101	−0.154214
$631$	4.73744e101	0.298176	0.149088	−	0.988824i	$-0.452366\pi$
$631$	4.73744e101	0.298176	0.149088	+	0.988824i	$0.452366\pi$
$632$	−5.17866e101	−0.307641
$633$	−3.79711e100	−0.0212921
$634$	−1.56553e101	−0.0828709
$635$	−1.36213e101	−0.0680736
$636$	−9.92682e99	−0.00468409
$637$	6.47170e102	2.88356
$638$	−9.84760e101	−0.414358
$639$	−3.20608e102	−1.27407
$640$	−3.05051e100	−0.0114499
$641$	−4.78614e102	−1.69694	−0.848472	−	0.529240i	$-0.822477\pi$
$641$	−4.78614e102	−1.69694	−0.848472	+	0.529240i	$0.822477\pi$
$642$	4.79724e100	0.0160680
$643$	−1.43293e102	−0.453445	−0.226722	−	0.973959i	$-0.572801\pi$
$643$	−1.43293e102	−0.453445	−0.226722	+	0.973959i	$0.572801\pi$
$644$	−1.95896e102	−0.585721
$645$	−1.44450e100	−0.00408121
$646$	2.58097e102	0.689121
$647$	−3.12019e102	−0.787363	−0.393682	−	0.919247i	$-0.628799\pi$
$647$	−3.12019e102	−0.787363	−0.393682	+	0.919247i	$0.628799\pi$
$648$	1.44244e102	0.344041
$649$	5.03937e102	1.13617
$650$	−4.98704e102	−1.06293
$651$	3.82769e101	0.0771313
$652$	−3.62168e102	−0.690037
$653$	−1.45141e102	−0.261493	−0.130746	−	0.991416i	$-0.541737\pi$
$653$	−1.45141e102	−0.261493	−0.130746	+	0.991416i	$0.541737\pi$
$654$	−1.72211e101	−0.0293408
$655$	−5.98484e101	−0.0964374
$656$	5.70567e101	0.0869593
$657$	−1.03872e103	−1.49748
$658$	1.66281e103	2.26776
$659$	3.94181e102	0.508601	0.254301	−	0.967125i	$-0.418155\pi$
$659$	3.94181e102	0.508601	0.254301	+	0.967125i	$0.418155\pi$
$660$	−8.26040e100	−0.0100843
$661$	−3.00820e102	−0.347499	−0.173749	−	0.984790i	$-0.555588\pi$
$661$	−3.00820e102	−0.347499	−0.173749	+	0.984790i	$0.555588\pi$
$662$	8.60186e102	0.940320
$663$	−1.21602e102	−0.125804
$664$	−2.56160e102	−0.250828
$665$	2.66721e102	0.247211
$666$	−1.32886e103	−1.16592
$667$	2.96348e102	0.246155
$668$	4.80363e102	0.377771
$669$	−2.79892e101	−0.0208419
$670$	−1.40553e102	−0.0991085
$671$	−6.59756e102	−0.440567
$672$	4.50378e101	0.0284839
$673$	2.58357e103	1.54764	0.773821	−	0.633404i	$-0.218343\pi$
$673$	2.58357e103	1.54764	0.773821	+	0.633404i	$0.218343\pi$
$674$	1.34556e103	0.763514
$675$	−3.45406e102	−0.185670
$676$	1.31310e103	0.668720
$677$	−1.19121e103	−0.574781	−0.287390	−	0.957814i	$-0.592788\pi$
$677$	−1.19121e103	−0.574781	−0.287390	+	0.957814i	$0.592788\pi$
$678$	9.16409e101	0.0418992
$679$	2.05447e103	0.890128
$680$	−9.67708e101	−0.0397346
$681$	−1.62000e102	−0.0630443
$682$	−1.50633e103	−0.555637
$683$	−3.28132e103	−1.14734	−0.573671	−	0.819086i	$-0.694481\pi$
$683$	−3.28132e103	−1.14734	−0.573671	+	0.819086i	$0.694481\pi$
$684$	−1.67918e103	−0.556609
$685$	3.82111e102	0.120083
$686$	−3.57223e103	−1.06441
$687$	−4.18189e102	−0.118155
$688$	−3.09940e102	−0.0830425
$689$	5.94302e102	0.151010
$690$	2.48584e101	0.00599075
$691$	7.58195e103	1.73313	0.866567	−	0.499061i	$-0.166322\pi$
$691$	7.58195e103	1.73313	0.866567	+	0.499061i	$0.166322\pi$
$692$	1.17134e103	0.253986
$693$	−1.34351e104	−2.76362
$694$	−3.00420e103	−0.586284
$695$	5.32402e102	0.0985812
$696$	−6.81324e101	−0.0119706
$697$	1.81000e103	0.301774
$698$	−6.67732e103	−1.05652
$699$	1.10676e103	0.166202
$700$	5.85939e103	0.835168
$701$	4.05230e103	0.548270	0.274135	−	0.961691i	$-0.411609\pi$
$701$	4.05230e103	0.548270	0.274135	+	0.961691i	$0.411609\pi$
$702$	1.58947e103	0.204149
$703$	1.53280e104	1.86902
$704$	−1.77240e103	−0.205191
$705$	−2.11004e102	−0.0231946
$706$	6.31587e103	0.659268
$707$	4.73299e102	0.0469166
$708$	3.48658e102	0.0328236
$709$	−6.63282e103	−0.593077	−0.296538	−	0.955021i	$-0.595832\pi$
$709$	−6.63282e103	−0.593077	−0.296538	+	0.955021i	$0.595832\pi$
$710$	−1.38657e103	−0.117763
$711$	1.06882e104	0.862312
$712$	1.36028e102	0.0104258
$713$	4.53307e103	0.330084
$714$	1.42873e103	0.0988472
$715$	4.94536e103	0.325108
$716$	5.53345e103	0.345677
$717$	2.19624e102	0.0130386
$718$	9.88441e103	0.557710
$719$	−3.21508e104	−1.72420	−0.862098	−	0.506741i	$-0.830850\pi$
$719$	−3.21508e104	−1.72420	−0.862098	+	0.506741i	$0.830850\pi$
$720$	6.29593e102	0.0320940
$721$	−4.67055e104	−2.26324
$722$	4.01936e103	0.185161
$723$	−4.51967e102	−0.0197952
$724$	9.52695e103	0.396731
$725$	−8.86398e103	−0.350988
$726$	−3.01832e103	−0.113652
$727$	2.56403e104	0.918157	0.459078	−	0.888396i	$-0.348180\pi$
$727$	2.56403e104	0.918157	0.459078	+	0.888396i	$0.348180\pi$
$728$	−2.69634e104	−0.918288
$729$	−2.92175e104	−0.946429
$730$	−4.49225e103	−0.138414
$731$	−9.83219e103	−0.288181
$732$	−4.56465e102	−0.0127278
$733$	5.34357e104	1.41754	0.708772	−	0.705437i	$-0.249249\pi$
$733$	5.34357e104	1.41754	0.708772	+	0.705437i	$0.249249\pi$
$734$	3.67254e104	0.926959
$735$	9.64884e102	0.0231733
$736$	5.33375e103	0.121897
$737$	−8.16639e104	−1.77610
$738$	−1.17759e104	−0.243746
$739$	7.86633e104	1.54971	0.774855	−	0.632140i	$-0.217823\pi$
$739$	7.86633e104	1.54971	0.774855	+	0.632140i	$0.217823\pi$
$740$	−5.74706e103	−0.107768
$741$	−9.12557e103	−0.162890
$742$	−6.98259e103	−0.118652
$743$	2.23895e104	0.362204	0.181102	−	0.983464i	$-0.442034\pi$
$743$	2.23895e104	0.362204	0.181102	+	0.983464i	$0.442034\pi$
$744$	−1.04218e103	−0.0160521
$745$	−6.86259e103	−0.100643
$746$	1.21128e104	0.169152
$747$	5.28687e104	0.703067
$748$	−5.62255e104	−0.712073
$749$	3.37441e104	0.407016
$750$	−1.49975e103	−0.0172300
$751$	1.46053e105	1.59828	0.799139	−	0.601146i	$-0.205289\pi$
$751$	1.46053e105	1.59828	0.799139	+	0.601146i	$0.205289\pi$
$752$	−4.52741e104	−0.471953
$753$	6.49868e103	0.0645370
$754$	4.07897e104	0.385919
$755$	−8.07213e103	−0.0727653
$756$	−1.86750e104	−0.160404
$757$	−1.39006e105	−1.13772	−0.568858	−	0.822436i	$-0.692615\pi$
$757$	−1.39006e105	−1.13772	−0.568858	+	0.822436i	$0.692615\pi$
$758$	−7.03159e104	−0.548438
$759$	1.44431e104	0.107359
$760$	−7.26214e103	−0.0514480
$761$	2.40591e105	1.62457	0.812287	−	0.583258i	$-0.198222\pi$
$761$	2.40591e105	1.62457	0.812287	+	0.583258i	$0.198222\pi$
$762$	−5.47560e103	−0.0352432
$763$	−1.21134e105	−0.743226
$764$	1.42752e105	0.834976
$765$	1.99725e104	0.111375
$766$	−8.59471e104	−0.456963
$767$	−2.08736e105	−1.05820
$768$	−1.22627e103	−0.00592789
$769$	−2.83446e105	−1.30665	−0.653324	−	0.757078i	$-0.726626\pi$
$769$	−2.83446e105	−1.30665	−0.653324	+	0.757078i	$0.726626\pi$
$770$	−5.81042e104	−0.255444
$771$	−3.32364e104	−0.139357
$772$	−1.00113e105	−0.400367
$773$	1.66230e105	0.634099	0.317050	−	0.948409i	$-0.397308\pi$
$773$	1.66230e105	0.634099	0.317050	+	0.948409i	$0.397308\pi$
$774$	6.39684e104	0.232767
$775$	−1.35587e105	−0.470660
$776$	−5.59379e104	−0.185248
$777$	8.48498e104	0.268092
$778$	2.40450e105	0.724886
$779$	1.35831e105	0.390734
$780$	3.42154e103	0.00939223
$781$	−8.05618e105	−2.11041
$782$	1.69202e105	0.423017
$783$	2.82513e104	0.0674114
$784$	2.07031e105	0.471518
$785$	6.75922e104	0.146945
$786$	−2.40583e104	−0.0499278
$787$	4.95321e105	0.981316	0.490658	−	0.871352i	$-0.336756\pi$
$787$	4.95321e105	0.981316	0.490658	+	0.871352i	$0.336756\pi$
$788$	5.17655e105	0.979114
$789$	−4.10637e104	−0.0741561
$790$	4.62244e104	0.0797044
$791$	6.44608e105	1.06134
$792$	3.65804e105	0.575148
$793$	2.73278e105	0.410329
$794$	−4.15813e105	−0.596279
$795$	8.86062e102	0.00121357
$796$	−2.52717e105	−0.330603
$797$	1.50414e106	1.87958	0.939790	−	0.341752i	$-0.111020\pi$
$797$	1.50414e106	1.87958	0.939790	+	0.341752i	$0.111020\pi$
$798$	1.07218e105	0.127986
$799$	−1.43622e106	−1.63781
$800$	−1.59536e105	−0.173810
$801$	−2.80747e104	−0.0292232
$802$	−9.31460e105	−0.926403
$803$	−2.61007e106	−2.48048
$804$	−5.65006e104	−0.0513107
$805$	1.74855e105	0.151750
$806$	6.23938e105	0.517502
$807$	2.00089e105	0.158613
$808$	−1.28867e104	−0.00976401
$809$	2.21112e106	1.60137	0.800684	−	0.599087i	$-0.204469\pi$
$809$	2.21112e106	1.60137	0.800684	+	0.599087i	$0.204469\pi$
$810$	−1.28751e105	−0.0891349
$811$	−1.89100e106	−1.25150	−0.625751	−	0.780023i	$-0.715207\pi$
$811$	−1.89100e106	−1.25150	−0.625751	+	0.780023i	$0.715207\pi$
$812$	−4.79248e105	−0.303225
$813$	−1.90195e105	−0.115052
$814$	−3.33914e106	−1.93127
$815$	3.23269e105	0.178777
$816$	−3.89006e104	−0.0205715
$817$	−7.37854e105	−0.373134
$818$	6.96771e105	0.336972
$819$	5.56496e106	2.57395
$820$	−5.09284e104	−0.0225297
$821$	1.08139e105	0.0457569	0.0228784	−	0.999738i	$-0.492717\pi$
$821$	1.08139e105	0.0457569	0.0228784	+	0.999738i	$0.492717\pi$
$822$	1.53604e105	0.0621699
$823$	4.93448e104	0.0191050	0.00955251	−	0.999954i	$-0.496959\pi$
$823$	4.93448e104	0.0191050	0.00955251	+	0.999954i	$0.496959\pi$
$824$	1.27167e106	0.471012
$825$	−4.32005e105	−0.153080
$826$	2.45248e106	0.831446
$827$	−5.68244e106	−1.84325	−0.921625	−	0.388082i	$-0.873138\pi$
$827$	−5.68244e106	−1.84325	−0.921625	+	0.388082i	$0.873138\pi$
$828$	−1.10083e106	−0.341675
$829$	3.75142e106	1.11418	0.557091	−	0.830452i	$-0.311918\pi$
$829$	3.75142e106	1.11418	0.557091	+	0.830452i	$0.311918\pi$
$830$	2.28647e105	0.0649852
$831$	−5.39232e105	−0.146669
$832$	7.34145e105	0.191109
$833$	6.56760e106	1.63631
$834$	2.14019e105	0.0510377
$835$	−4.28769e105	−0.0978739
$836$	−4.21942e106	−0.921986
$837$	4.32144e105	0.0903960
$838$	2.38515e106	0.477650
$839$	−7.53290e105	−0.144428	−0.0722139	−	0.997389i	$-0.523006\pi$
$839$	−7.53290e105	−0.144428	−0.0722139	+	0.997389i	$0.523006\pi$
$840$	−4.02005e104	−0.00737967
$841$	−4.96424e106	−0.872567
$842$	3.78077e106	0.636340
$843$	−6.54054e105	−0.105416
$844$	7.27222e105	0.112245
$845$	−1.17207e106	−0.173254
$846$	9.34410e106	1.32288
$847$	−2.12311e107	−2.87890
$848$	1.90118e105	0.0246931
$849$	8.18796e105	0.101870
$850$	−5.06095e106	−0.603172
$851$	1.00486e107	1.14730
$852$	−5.57381e105	−0.0609688
$853$	7.00405e106	0.734023	0.367012	−	0.930216i	$-0.380381\pi$
$853$	7.00405e106	0.734023	0.367012	+	0.930216i	$0.380381\pi$
$854$	−3.21080e106	−0.322405
$855$	1.49883e106	0.144208
$856$	−9.18766e105	−0.0847057
$857$	−1.15321e107	−1.01884	−0.509422	−	0.860517i	$-0.670141\pi$
$857$	−1.15321e107	−1.01884	−0.509422	+	0.860517i	$0.670141\pi$
$858$	1.98797e106	0.168316
$859$	−1.07933e107	−0.875800	−0.437900	−	0.899024i	$-0.644278\pi$
$859$	−1.07933e107	−0.875800	−0.437900	+	0.899024i	$0.644278\pi$
$860$	2.76651e105	0.0215149
$861$	7.51909e105	0.0560467
$862$	−2.47224e106	−0.176635
$863$	−6.63854e106	−0.454651	−0.227326	−	0.973819i	$-0.572998\pi$
$863$	−6.63854e106	−0.454651	−0.227326	+	0.973819i	$0.572998\pi$
$864$	5.08474e105	0.0333824
$865$	−1.04553e106	−0.0658032
$866$	−4.84102e106	−0.292102
$867$	4.05484e105	0.0234572
$868$	−7.33079e106	−0.406613
$869$	2.68571e107	1.42836
$870$	6.08146e104	0.00310138
$871$	3.38260e107	1.65420
$872$	3.29818e106	0.154676
$873$	1.15450e107	0.519247
$874$	1.26977e107	0.547719
$875$	−1.05494e107	−0.436448
$876$	−1.80583e106	−0.0716599
$877$	7.36036e106	0.280165	0.140083	−	0.990140i	$-0.455263\pi$
$877$	7.36036e106	0.280165	0.140083	+	0.990140i	$0.455263\pi$
$878$	−7.08187e106	−0.258582
$879$	4.20973e106	0.147455
$880$	1.58203e106	0.0531615
$881$	6.48457e106	0.209055	0.104527	−	0.994522i	$-0.466667\pi$
$881$	6.48457e106	0.209055	0.104527	+	0.994522i	$0.466667\pi$
$882$	−4.27290e107	−1.32166
$883$	3.77643e107	1.12077	0.560384	−	0.828233i	$-0.310654\pi$
$883$	3.77643e107	1.12077	0.560384	+	0.828233i	$0.310654\pi$
$884$	2.32891e107	0.663202
$885$	−3.11210e105	−0.00850401
$886$	−1.77645e107	−0.465825
$887$	5.30998e107	1.33623	0.668115	−	0.744058i	$-0.267102\pi$
$887$	5.30998e107	1.33623	0.668115	+	0.744058i	$0.267102\pi$
$888$	−2.31025e106	−0.0557937
$889$	−3.85157e107	−0.892738
$890$	−1.21418e105	−0.00270113
$891$	−7.48066e107	−1.59736
$892$	5.36048e106	0.109872
$893$	−1.07781e108	−2.12062
$894$	−2.75867e106	−0.0521052
$895$	−4.93912e106	−0.0895590
$896$	−8.62564e106	−0.150158
$897$	−5.98249e106	−0.0999903
$898$	2.56262e107	0.411243
$899$	1.10899e107	0.170883
$900$	3.29266e107	0.487187
$901$	6.03109e106	0.0856922
$902$	−2.95903e107	−0.403748
$903$	−4.08448e106	−0.0535222
$904$	−1.75510e107	−0.220879
$905$	−8.50370e106	−0.102786
$906$	−3.24489e106	−0.0376722
$907$	−1.83274e107	−0.204378	−0.102189	−	0.994765i	$-0.532585\pi$
$907$	−1.83274e107	−0.204378	−0.102189	+	0.994765i	$0.532585\pi$
$908$	3.10262e107	0.332350
$909$	2.65969e106	0.0273684
$910$	2.40673e107	0.237913
$911$	5.12980e106	0.0487169	0.0243585	−	0.999703i	$-0.492246\pi$
$911$	5.12980e106	0.0487169	0.0243585	+	0.999703i	$0.492246\pi$
$912$	−2.91929e106	−0.0266358
$913$	1.32848e108	1.16458
$914$	1.60498e108	1.35187
$915$	4.07437e105	0.00329755
$916$	8.00914e107	0.622876
$917$	−1.69228e108	−1.26471
$918$	1.61302e107	0.115846
$919$	1.33051e108	0.918337	0.459169	−	0.888349i	$-0.348147\pi$
$919$	1.33051e108	0.918337	0.459169	+	0.888349i	$0.348147\pi$
$920$	−4.76087e106	−0.0315814
$921$	2.10520e107	0.134220
$922$	−7.45399e107	−0.456783
$923$	3.33695e108	1.96557
$924$	−2.33572e107	−0.132249
$925$	−3.00562e108	−1.63591
$926$	−7.57854e107	−0.396538
$927$	−2.62460e108	−1.32024
$928$	1.30487e107	0.0631054
$929$	−2.12965e108	−0.990225	−0.495112	−	0.868829i	$-0.664873\pi$
$929$	−2.12965e108	−0.990225	−0.495112	+	0.868829i	$0.664873\pi$
$930$	9.30247e105	0.00415882
$931$	4.92864e108	2.11867
$932$	−2.11967e108	−0.876168
$933$	−1.31512e107	−0.0522740
$934$	2.90971e108	1.11221
$935$	5.01865e107	0.184486
$936$	−1.51520e108	−0.535674
$937$	9.90660e107	0.336844	0.168422	−	0.985715i	$-0.446133\pi$
$937$	9.90660e107	0.336844	0.168422	+	0.985715i	$0.446133\pi$
$938$	−3.97429e108	−1.29974
$939$	−1.15562e107	−0.0363515
$940$	4.04114e107	0.122275
$941$	−3.43396e108	−0.999480	−0.499740	−	0.866175i	$-0.666571\pi$
$941$	−3.43396e108	−0.999480	−0.499740	+	0.866175i	$0.666571\pi$
$942$	2.71712e107	0.0760766
$943$	8.90472e107	0.239852
$944$	−6.67749e107	−0.173036
$945$	1.66692e107	0.0415580
$946$	1.60739e108	0.385562
$947$	−5.32334e108	−1.22860	−0.614299	−	0.789073i	$-0.710561\pi$
$947$	−5.32334e108	−1.22860	−0.614299	+	0.789073i	$0.710561\pi$
$948$	1.85816e107	0.0412647
$949$	1.08112e109	2.31024
$950$	−3.79797e108	−0.780981
$951$	5.61728e106	0.0111157
$952$	−2.73629e108	−0.521092
$953$	−4.69757e108	−0.860958	−0.430479	−	0.902601i	$-0.641655\pi$
$953$	−4.69757e108	−0.860958	−0.430479	+	0.902601i	$0.641655\pi$
$954$	−3.92384e107	−0.0692143
$955$	−1.27419e108	−0.216328
$956$	−4.20624e107	−0.0687354
$957$	3.53343e107	0.0555790
$958$	−1.13954e108	−0.172540
$959$	1.08046e109	1.57481
$960$	1.09456e106	0.00153581
$961$	−5.70657e108	−0.770853
$962$	1.38311e109	1.79873
$963$	1.89624e108	0.237429
$964$	8.65607e107	0.104354
$965$	8.93601e107	0.103728
$966$	7.02896e107	0.0785645
$967$	3.37585e107	0.0363343	0.0181672	−	0.999835i	$-0.494217\pi$
$967$	3.37585e107	0.0363343	0.0181672	+	0.999835i	$0.494217\pi$
$968$	5.78068e108	0.599140
$969$	−9.26080e107	−0.0924338
$970$	4.99299e107	0.0479946
$971$	−5.40325e108	−0.500211	−0.250105	−	0.968219i	$-0.580465\pi$
$971$	−5.40325e108	−0.500211	−0.250105	+	0.968219i	$0.580465\pi$
$972$	−1.57653e108	−0.140567
$973$	1.50542e109	1.29282
$974$	−2.62263e108	−0.216938
$975$	1.78941e108	0.142574
$976$	8.74220e107	0.0670969
$977$	−1.88340e109	−1.39249	−0.696244	−	0.717805i	$-0.745147\pi$
$977$	−1.88340e109	−1.39249	−0.696244	+	0.717805i	$0.745147\pi$
$978$	1.29950e108	0.0925566
$979$	−7.05456e107	−0.0484063
$980$	−1.84794e108	−0.122162
$981$	−6.80709e108	−0.433554
$982$	5.34323e107	0.0327895
$983$	−1.55920e109	−0.921932	−0.460966	−	0.887418i	$-0.652497\pi$
$983$	−1.55920e109	−0.921932	−0.460966	+	0.887418i	$0.652497\pi$
$984$	−2.04726e107	−0.0116641
$985$	−4.62055e108	−0.253671
$986$	4.13942e108	0.218994
$987$	−5.96635e108	−0.304181
$988$	1.74773e109	0.858707
$989$	−4.83718e108	−0.229049
$990$	−3.26515e108	−0.149011
$991$	−3.07383e109	−1.35205	−0.676023	−	0.736881i	$-0.736298\pi$
$991$	−3.07383e109	−1.35205	−0.676023	+	0.736881i	$0.736298\pi$
$992$	1.99599e108	0.0846218
$993$	−3.08645e108	−0.126128
$994$	−3.92066e109	−1.54439
$995$	2.25574e108	0.0856536
$996$	9.19131e107	0.0336443
$997$	−9.01559e107	−0.0318142	−0.0159071	−	0.999873i	$-0.505064\pi$
$997$	−9.01559e107	−0.0318142	−0.0159071	+	0.999873i	$0.505064\pi$
$998$	−6.75414e108	−0.229776
$999$	9.57949e108	0.314197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.74.a.b.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.74.a.b.1.2	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+6.87195e10 q^{2} -2.46573e16 q^{3} +4.72237e21 q^{4} -4.21515e24 q^{5} -1.69444e27 q^{6} -1.19188e31 q^{7} +3.24519e32 q^{8} -6.69772e34 q^{9} -2.89663e35 q^{10} -1.68299e38 q^{11} -1.16441e38 q^{12} +6.97112e40 q^{13} -8.19053e41 q^{14} +1.03934e41 q^{15} +2.23007e43 q^{16} +7.07443e44 q^{17} -4.60264e45 q^{18} +5.30898e46 q^{19} -1.99055e46 q^{20} +2.93885e47 q^{21} -1.15654e49 q^{22} +3.48043e49 q^{23} -8.00176e48 q^{24} -1.04102e51 q^{25} +4.79052e51 q^{26} +3.31795e51 q^{27} -5.62849e52 q^{28} +8.51468e52 q^{29} +7.14232e51 q^{30} +1.30244e54 q^{31} +1.53250e54 q^{32} +4.14981e54 q^{33} +4.86151e55 q^{34} +5.02395e55 q^{35} -3.16291e56 q^{36} +2.88717e57 q^{37} +3.64831e57 q^{38} -1.71889e57 q^{39} -1.36790e57 q^{40} +2.55851e58 q^{41} +2.01957e58 q^{42} -1.38982e59 q^{43} -7.94771e59 q^{44} +2.82319e59 q^{45} +2.39174e60 q^{46} -2.03016e61 q^{47} -5.49877e59 q^{48} +9.28358e61 q^{49} -7.15386e61 q^{50} -1.74436e61 q^{51} +3.29202e62 q^{52} +8.52520e61 q^{53} +2.28008e62 q^{54} +7.09407e62 q^{55} -3.86787e63 q^{56} -1.30905e63 q^{57} +5.85124e63 q^{58} -2.99429e64 q^{59} +4.90816e62 q^{60} +3.92014e64 q^{61} +8.95032e64 q^{62} +7.98287e65 q^{63} +1.05312e65 q^{64} -2.93843e65 q^{65} +2.85173e65 q^{66} +4.85230e66 q^{67} +3.34080e66 q^{68} -8.58182e65 q^{69} +3.45243e66 q^{70} +4.78682e67 q^{71} -2.17353e67 q^{72} +1.55085e68 q^{73} +1.98405e68 q^{74} +2.56689e67 q^{75} +2.50710e68 q^{76} +2.00592e69 q^{77} -1.18121e68 q^{78} -1.59580e69 q^{79} -9.40011e67 q^{80} +4.44486e69 q^{81} +1.75819e69 q^{82} -7.89354e69 q^{83} +1.38783e69 q^{84} -2.98198e69 q^{85} -9.55078e69 q^{86} -2.09949e69 q^{87} -5.46162e70 q^{88} +4.19168e69 q^{89} +1.94008e70 q^{90} -8.30873e71 q^{91} +1.64359e71 q^{92} -3.21148e70 q^{93} -1.39512e72 q^{94} -2.23782e71 q^{95} -3.77872e70 q^{96} -1.72372e72 q^{97} +6.37963e72 q^{98} +1.12722e73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 274877906944 q^{2} + 30\!\cdots\!76 q^{3} + 18\!\cdots\!84 q^{4} - 78\!\cdots\!60 q^{5} + 20\!\cdots\!36 q^{6} + 36\!\cdots\!12 q^{7} + 12\!\cdots\!24 q^{8} + 12\!\cdots\!52 q^{9} - 53\!\cdots\!60 q^{10}+ \cdots + 28\!\cdots\!24 q^{99}+O(q^{100}) \) 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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