LMFDB - Embedded newform 531.8.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 $ x^18 - 6x^17 - 1798x^16 + 11087x^15 + 1326765x^14 - 8403720x^13 - 518334228x^12 + 3375594921x^11 + 115310342333x^10 - 774932111214x^9 - 14600047830166x^8 + 102185027148481x^7 + 988557475638619x^6 - 7379206238519716x^5 - 30152342836849520x^4 + 260578770749067175x^3 + 182609347488069978x^2 - 3481290425710753600*x + 5164646074739714048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$15.9283$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.9283 q^{2} +158.568 q^{4} +421.077 q^{5} -62.1753 q^{7} -517.469 q^{8} +O(q^{10})$	\(q-16.9283 q^{2} +158.568 q^{4} +421.077 q^{5} -62.1753 q^{7} -517.469 q^{8} -7128.13 q^{10} -8422.53 q^{11} +11389.2 q^{13} +1052.52 q^{14} -11536.9 q^{16} -1307.83 q^{17} -7903.89 q^{19} +66769.4 q^{20} +142579. q^{22} +2032.53 q^{23} +99180.7 q^{25} -192800. q^{26} -9859.03 q^{28} -64202.2 q^{29} +320926. q^{31} +261536. q^{32} +22139.4 q^{34} -26180.6 q^{35} -143662. q^{37} +133800. q^{38} -217894. q^{40} -577414. q^{41} +817246. q^{43} -1.33555e6 q^{44} -34407.3 q^{46} -264964. q^{47} -819677. q^{49} -1.67896e6 q^{50} +1.80597e6 q^{52} -1.60310e6 q^{53} -3.54653e6 q^{55} +32173.8 q^{56} +1.08684e6 q^{58} -205379. q^{59} -274208. q^{61} -5.43273e6 q^{62} -2.95064e6 q^{64} +4.79573e6 q^{65} -1.66313e6 q^{67} -207381. q^{68} +443194. q^{70} +2.97718e6 q^{71} -2.72516e6 q^{73} +2.43196e6 q^{74} -1.25331e6 q^{76} +523673. q^{77} +1.33414e6 q^{79} -4.85790e6 q^{80} +9.77465e6 q^{82} -8.00004e6 q^{83} -550698. q^{85} -1.38346e7 q^{86} +4.35840e6 q^{88} +1.07983e7 q^{89} -708128. q^{91} +322295. q^{92} +4.48540e6 q^{94} -3.32814e6 q^{95} -1.36112e7 q^{97} +1.38758e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8}+O(q^{10}) $ 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8	\( 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8} + 3609 q^{10} - 15070 q^{11} + 13662 q^{13} - 20861 q^{14} + 60482 q^{16} - 71919 q^{17} + 56231 q^{19} - 143053 q^{20} + 274198 q^{22} - 150029 q^{23} + 399672 q^{25} - 182846 q^{26} + 434150 q^{28} - 591285 q^{29} + 426733 q^{31} - 1205630 q^{32} + 403548 q^{34} - 912879 q^{35} + 7703 q^{37} + 417859 q^{38} + 618020 q^{40} - 770959 q^{41} + 793050 q^{43} - 2591274 q^{44} - 4068019 q^{46} - 1410373 q^{47} + 1637427 q^{49} - 1021549 q^{50} - 3749190 q^{52} - 1037934 q^{53} + 331974 q^{55} + 391748 q^{56} + 653724 q^{58} - 3696822 q^{59} - 1374623 q^{61} - 5251718 q^{62} + 5077197 q^{64} - 3257170 q^{65} - 2436904 q^{67} - 14119909 q^{68} + 5185580 q^{70} - 14289172 q^{71} + 5482515 q^{73} - 14934154 q^{74} + 3822912 q^{76} - 23157109 q^{77} + 19786414 q^{79} - 31978143 q^{80} + 9749509 q^{82} - 30227337 q^{83} + 9946981 q^{85} - 44295864 q^{86} + 39970897 q^{88} - 31061677 q^{89} + 26377785 q^{91} - 4719698 q^{92} + 44488296 q^{94} - 15534599 q^{95} + 12084118 q^{97} - 42274744 q^{98}+O(q^{100}) \) 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8 + 3609 * q^10 - 15070 * q^11 + 13662 * q^13 - 20861 * q^14 + 60482 * q^16 - 71919 * q^17 + 56231 * q^19 - 143053 * q^20 + 274198 * q^22 - 150029 * q^23 + 399672 * q^25 - 182846 * q^26 + 434150 * q^28 - 591285 * q^29 + 426733 * q^31 - 1205630 * q^32 + 403548 * q^34 - 912879 * q^35 + 7703 * q^37 + 417859 * q^38 + 618020 * q^40 - 770959 * q^41 + 793050 * q^43 - 2591274 * q^44 - 4068019 * q^46 - 1410373 * q^47 + 1637427 * q^49 - 1021549 * q^50 - 3749190 * q^52 - 1037934 * q^53 + 331974 * q^55 + 391748 * q^56 + 653724 * q^58 - 3696822 * q^59 - 1374623 * q^61 - 5251718 * q^62 + 5077197 * q^64 - 3257170 * q^65 - 2436904 * q^67 - 14119909 * q^68 + 5185580 * q^70 - 14289172 * q^71 + 5482515 * q^73 - 14934154 * q^74 + 3822912 * q^76 - 23157109 * q^77 + 19786414 * q^79 - 31978143 * q^80 + 9749509 * q^82 - 30227337 * q^83 + 9946981 * q^85 - 44295864 * q^86 + 39970897 * q^88 - 31061677 * q^89 + 26377785 * q^91 - 4719698 * q^92 + 44488296 * q^94 - 15534599 * q^95 + 12084118 * q^97 - 42274744 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−16.9283	−1.49627	−0.748133	−	0.663548i	$-0.769050\pi$
$2$	−16.9283	−1.49627	−0.748133	+	0.663548i	$0.769050\pi$
$3$	0	0
$3$	0	0
$4$	158.568	1.23881
$5$	421.077	1.50649	0.753245	−	0.657740i	$-0.228487\pi$
$5$	421.077	1.50649	0.753245	+	0.657740i	$0.228487\pi$
$6$	0	0
$7$	−62.1753	−0.0685133	−0.0342567	−	0.999413i	$-0.510906\pi$
$7$	−62.1753	−0.0685133	−0.0342567	+	0.999413i	$0.510906\pi$
$8$	−517.469	−0.357330
$9$	0	0
$10$	−7128.13	−2.25411
$11$	−8422.53	−1.90795	−0.953977	−	0.299878i	$-0.903054\pi$
$11$	−8422.53	−1.90795	−0.953977	+	0.299878i	$0.903054\pi$
$12$	0	0
$13$	11389.2	1.43778	0.718889	−	0.695125i	$-0.244651\pi$
$13$	11389.2	1.43778	0.718889	+	0.695125i	$0.244651\pi$
$14$	1052.52	0.102514
$15$	0	0
$16$	−11536.9	−0.704154
$17$	−1307.83	−0.0645626	−0.0322813	−	0.999479i	$-0.510277\pi$
$17$	−1307.83	−0.0645626	−0.0322813	+	0.999479i	$0.510277\pi$
$18$	0	0
$19$	−7903.89	−0.264365	−0.132182	−	0.991225i	$-0.542198\pi$
$19$	−7903.89	−0.264365	−0.132182	+	0.991225i	$0.542198\pi$
$20$	66769.4	1.86626
$21$	0	0
$22$	142579.	2.85481
$23$	2032.53	0.0348329	0.0174164	−	0.999848i	$-0.494456\pi$
$23$	2032.53	0.0348329	0.0174164	+	0.999848i	$0.494456\pi$
$24$	0	0
$25$	99180.7	1.26951
$26$	−192800.	−2.15130
$27$	0	0
$28$	−9859.03	−0.0848753
$29$	−64202.2	−0.488829	−0.244414	−	0.969671i	$-0.578596\pi$
$29$	−64202.2	−0.488829	−0.244414	+	0.969671i	$0.578596\pi$
$30$	0	0
$31$	320926.	1.93481	0.967405	−	0.253233i	$-0.0814939\pi$
$31$	320926.	1.93481	0.967405	+	0.253233i	$0.0814939\pi$
$32$	261536.	1.41093
$33$	0	0
$34$	22139.4	0.0966029
$35$	−26180.6	−0.103215
$36$	0	0
$37$	−143662.	−0.466269	−0.233135	−	0.972444i	$-0.574898\pi$
$37$	−143662.	−0.466269	−0.233135	+	0.972444i	$0.574898\pi$
$38$	133800.	0.395560
$39$	0	0
$40$	−217894.	−0.538314
$41$	−577414.	−1.30841	−0.654205	−	0.756318i	$-0.726996\pi$
$41$	−577414.	−1.30841	−0.654205	+	0.756318i	$0.726996\pi$
$42$	0	0
$43$	817246.	1.56752	0.783760	−	0.621064i	$-0.213299\pi$
$43$	817246.	1.56752	0.783760	+	0.621064i	$0.213299\pi$
$44$	−1.33555e6	−2.36360
$45$	0	0
$46$	−34407.3	−0.0521193
$47$	−264964.	−0.372259	−0.186129	−	0.982525i	$-0.559594\pi$
$47$	−264964.	−0.372259	−0.186129	+	0.982525i	$0.559594\pi$
$48$	0	0
$49$	−819677.	−0.995306
$50$	−1.67896e6	−1.89953
$51$	0	0
$52$	1.80597e6	1.78114
$53$	−1.60310e6	−1.47909	−0.739545	−	0.673107i	$-0.764959\pi$
$53$	−1.60310e6	−1.47909	−0.739545	+	0.673107i	$0.764959\pi$
$54$	0	0
$55$	−3.54653e6	−2.87432
$56$	32173.8	0.0244818
$57$	0	0
$58$	1.08684e6	0.731418
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	−274208.	−0.154677	−0.0773386	−	0.997005i	$-0.524642\pi$
$61$	−274208.	−0.154677	−0.0773386	+	0.997005i	$0.524642\pi$
$62$	−5.43273e6	−2.89499
$63$	0	0
$64$	−2.95064e6	−1.40698
$65$	4.79573e6	2.16600
$66$	0	0
$67$	−1.66313e6	−0.675562	−0.337781	−	0.941225i	$-0.609676\pi$
$67$	−1.66313e6	−0.675562	−0.337781	+	0.941225i	$0.609676\pi$
$68$	−207381.	−0.0799811
$69$	0	0
$70$	443194.	0.154437
$71$	2.97718e6	0.987190	0.493595	−	0.869692i	$-0.335683\pi$
$71$	2.97718e6	0.987190	0.493595	+	0.869692i	$0.335683\pi$
$72$	0	0
$73$	−2.72516e6	−0.819904	−0.409952	−	0.912107i	$-0.634454\pi$
$73$	−2.72516e6	−0.819904	−0.409952	+	0.912107i	$0.634454\pi$
$74$	2.43196e6	0.697663
$75$	0	0
$76$	−1.25331e6	−0.327499
$77$	523673.	0.130720
$78$	0	0
$79$	1.33414e6	0.304442	0.152221	−	0.988346i	$-0.451357\pi$
$79$	1.33414e6	0.304442	0.152221	+	0.988346i	$0.451357\pi$
$80$	−4.85790e6	−1.06080
$81$	0	0
$82$	9.77465e6	1.95773
$83$	−8.00004e6	−1.53574	−0.767872	−	0.640603i	$-0.778684\pi$
$83$	−8.00004e6	−1.53574	−0.767872	+	0.640603i	$0.778684\pi$
$84$	0	0
$85$	−550698.	−0.0972629
$86$	−1.38346e7	−2.34543
$87$	0	0
$88$	4.35840e6	0.681769
$89$	1.07983e7	1.62365	0.811825	−	0.583901i	$-0.198474\pi$
$89$	1.07983e7	1.62365	0.811825	+	0.583901i	$0.198474\pi$
$90$	0	0
$91$	−708128.	−0.0985069
$92$	322295.	0.0431515
$93$	0	0
$94$	4.48540e6	0.556998
$95$	−3.32814e6	−0.398263
$96$	0	0
$97$	−1.36112e7	−1.51425	−0.757124	−	0.653272i	$-0.773396\pi$
$97$	−1.36112e7	−1.51425	−0.757124	+	0.653272i	$0.773396\pi$
$98$	1.38758e7	1.48924
$99$	0	0
$100$	1.57269e7	1.57269
$101$	8.15059e6	0.787162	0.393581	−	0.919290i	$-0.371236\pi$
$101$	8.15059e6	0.787162	0.393581	+	0.919290i	$0.371236\pi$
$102$	0	0
$103$	−5.09641e6	−0.459551	−0.229776	−	0.973244i	$-0.573799\pi$
$103$	−5.09641e6	−0.459551	−0.229776	+	0.973244i	$0.573799\pi$
$104$	−5.89356e6	−0.513761
$105$	0	0
$106$	2.71378e7	2.21311
$107$	2.19007e7	1.72828	0.864140	−	0.503251i	$-0.167863\pi$
$107$	2.19007e7	1.72828	0.864140	+	0.503251i	$0.167863\pi$
$108$	0	0
$109$	19486.8	0.00144128	0.000720639	−	1.00000i	$-0.499771\pi$
$109$	19486.8	0.00144128	0.000720639		1.00000i	$0.499771\pi$
$110$	6.00368e7	4.30074
$111$	0	0
$112$	717307.	0.0482439
$113$	−7.14160e6	−0.465608	−0.232804	−	0.972524i	$-0.574790\pi$
$113$	−7.14160e6	−0.465608	−0.232804	+	0.972524i	$0.574790\pi$
$114$	0	0
$115$	855851.	0.0524754
$116$	−1.01804e7	−0.605568
$117$	0	0
$118$	3.47672e6	0.194797
$119$	81314.9	0.00442340
$120$	0	0
$121$	5.14518e7	2.64029
$122$	4.64189e6	0.231438
$123$	0	0
$124$	5.08886e7	2.39687
$125$	8.86607e6	0.406019
$126$	0	0
$127$	−3.64410e7	−1.57862	−0.789308	−	0.613997i	$-0.789561\pi$
$127$	−3.64410e7	−1.57862	−0.789308	+	0.613997i	$0.789561\pi$
$128$	1.64729e7	0.694280
$129$	0	0
$130$	−8.11837e7	−3.24091
$131$	−1.30081e7	−0.505549	−0.252774	−	0.967525i	$-0.581343\pi$
$131$	−1.30081e7	−0.505549	−0.252774	+	0.967525i	$0.581343\pi$
$132$	0	0
$133$	491427.	0.0181125
$134$	2.81541e7	1.01082
$135$	0	0
$136$	676763.	0.0230701
$137$	1.31043e7	0.435404	0.217702	−	0.976015i	$-0.430144\pi$
$137$	1.31043e7	0.435404	0.217702	+	0.976015i	$0.430144\pi$
$138$	0	0
$139$	8.55786e6	0.270280	0.135140	−	0.990827i	$-0.456852\pi$
$139$	8.55786e6	0.270280	0.135140	+	0.990827i	$0.456852\pi$
$140$	−4.15141e6	−0.127864
$141$	0	0
$142$	−5.03986e7	−1.47710
$143$	−9.59260e7	−2.74322
$144$	0	0
$145$	−2.70340e7	−0.736416
$146$	4.61325e7	1.22679
$147$	0	0
$148$	−2.27803e7	−0.577621
$149$	−8.02680e7	−1.98788	−0.993941	−	0.109916i	$-0.964942\pi$
$149$	−8.02680e7	−1.98788	−0.993941	+	0.109916i	$0.964942\pi$
$150$	0	0
$151$	606581.	0.0143374	0.00716869	−	0.999974i	$-0.497718\pi$
$151$	606581.	0.0143374	0.00716869	+	0.999974i	$0.497718\pi$
$152$	4.09002e6	0.0944653
$153$	0	0
$154$	−8.86492e6	−0.195592
$155$	1.35134e8	2.91477
$156$	0	0
$157$	6.17847e7	1.27418	0.637092	−	0.770788i	$-0.280137\pi$
$157$	6.17847e7	1.27418	0.637092	+	0.770788i	$0.280137\pi$
$158$	−2.25847e7	−0.455527
$159$	0	0
$160$	1.10127e8	2.12555
$161$	−126373.	−0.00238652
$162$	0	0
$163$	−1.21598e6	−0.0219922	−0.0109961	−	0.999940i	$-0.503500\pi$
$163$	−1.21598e6	−0.0219922	−0.0109961	+	0.999940i	$0.503500\pi$
$164$	−9.15595e7	−1.62088
$165$	0	0
$166$	1.35427e8	2.29788
$167$	−1.21038e7	−0.201102	−0.100551	−	0.994932i	$-0.532060\pi$
$167$	−1.21038e7	−0.201102	−0.100551	+	0.994932i	$0.532060\pi$
$168$	0	0
$169$	6.69656e7	1.06721
$170$	9.32240e6	0.145531
$171$	0	0
$172$	1.29589e8	1.94187
$173$	1.01126e8	1.48492	0.742460	−	0.669890i	$-0.233659\pi$
$173$	1.01126e8	1.48492	0.742460	+	0.669890i	$0.233659\pi$
$174$	0	0
$175$	−6.16659e6	−0.0869785
$176$	9.71695e7	1.34349
$177$	0	0
$178$	−1.82798e8	−2.42941
$179$	7.67192e7	0.999813	0.499906	−	0.866079i	$-0.333368\pi$
$179$	7.67192e7	0.999813	0.499906	+	0.866079i	$0.333368\pi$
$180$	0	0
$181$	4.41123e7	0.552949	0.276474	−	0.961021i	$-0.410834\pi$
$181$	4.41123e7	0.552949	0.276474	+	0.961021i	$0.410834\pi$
$182$	1.19874e7	0.147393
$183$	0	0
$184$	−1.05177e6	−0.0124468
$185$	−6.04929e7	−0.702430
$186$	0	0
$187$	1.10153e7	0.123183
$188$	−4.20149e7	−0.461159
$189$	0	0
$190$	5.63399e7	0.595907
$191$	−3.96720e7	−0.411972	−0.205986	−	0.978555i	$-0.566040\pi$
$191$	−3.96720e7	−0.411972	−0.205986	+	0.978555i	$0.566040\pi$
$192$	0	0
$193$	−6.49743e7	−0.650565	−0.325283	−	0.945617i	$-0.605459\pi$
$193$	−6.49743e7	−0.650565	−0.325283	+	0.945617i	$0.605459\pi$
$194$	2.30416e8	2.26572
$195$	0	0
$196$	−1.29975e8	−1.23300
$197$	−1.60147e8	−1.49241	−0.746204	−	0.665717i	$-0.768126\pi$
$197$	−1.60147e8	−1.49241	−0.746204	+	0.665717i	$0.768126\pi$
$198$	0	0
$199$	3.62822e7	0.326368	0.163184	−	0.986596i	$-0.447824\pi$
$199$	3.62822e7	0.326368	0.163184	+	0.986596i	$0.447824\pi$
$200$	−5.13229e7	−0.453635
$201$	0	0
$202$	−1.37976e8	−1.17780
$203$	3.99179e6	0.0334913
$204$	0	0
$205$	−2.43136e8	−1.97111
$206$	8.62737e7	0.687611
$207$	0	0
$208$	−1.31396e8	−1.01242
$209$	6.65707e7	0.504396
$210$	0	0
$211$	−2.00331e8	−1.46811	−0.734056	−	0.679089i	$-0.762375\pi$
$211$	−2.00331e8	−1.46811	−0.734056	+	0.679089i	$0.762375\pi$
$212$	−2.54200e8	−1.83232
$213$	0	0
$214$	−3.70742e8	−2.58597
$215$	3.44123e8	2.36145
$216$	0	0
$217$	−1.99537e7	−0.132560
$218$	−329879.	−0.00215654
$219$	0	0
$220$	−5.62367e8	−3.56074
$221$	−1.48952e7	−0.0928267
$222$	0	0
$223$	1.92870e8	1.16465	0.582327	−	0.812955i	$-0.302142\pi$
$223$	1.92870e8	1.16465	0.582327	+	0.812955i	$0.302142\pi$
$224$	−1.62611e7	−0.0966676
$225$	0	0
$226$	1.20895e8	0.696674
$227$	3.48084e7	0.197512	0.0987560	−	0.995112i	$-0.468514\pi$
$227$	3.48084e7	0.197512	0.0987560	+	0.995112i	$0.468514\pi$
$228$	0	0
$229$	−2.38784e8	−1.31396	−0.656978	−	0.753910i	$-0.728165\pi$
$229$	−2.38784e8	−1.31396	−0.656978	+	0.753910i	$0.728165\pi$
$230$	−1.44881e7	−0.0785172
$231$	0	0
$232$	3.32226e7	0.174673
$233$	−3.17570e8	−1.64473	−0.822364	−	0.568962i	$-0.807345\pi$
$233$	−3.17570e8	−1.64473	−0.822364	+	0.568962i	$0.807345\pi$
$234$	0	0
$235$	−1.11570e8	−0.560804
$236$	−3.25666e7	−0.161280
$237$	0	0
$238$	−1.37653e6	−0.00661858
$239$	1.63040e8	0.772505	0.386252	−	0.922393i	$-0.373769\pi$
$239$	1.63040e8	0.772505	0.386252	+	0.922393i	$0.373769\pi$
$240$	0	0
$241$	9.18889e7	0.422867	0.211433	−	0.977392i	$-0.432187\pi$
$241$	9.18889e7	0.422867	0.211433	+	0.977392i	$0.432187\pi$
$242$	−8.70993e8	−3.95058
$243$	0	0
$244$	−4.34808e7	−0.191616
$245$	−3.45147e8	−1.49942
$246$	0	0
$247$	−9.00191e7	−0.380098
$248$	−1.66069e8	−0.691366
$249$	0	0
$250$	−1.50088e8	−0.607513
$251$	1.98730e7	0.0793242	0.0396621	−	0.999213i	$-0.487372\pi$
$251$	1.98730e7	0.0793242	0.0396621	+	0.999213i	$0.487372\pi$
$252$	0	0
$253$	−1.71190e7	−0.0664596
$254$	6.16884e8	2.36203
$255$	0	0
$256$	9.88239e7	0.368148
$257$	−5.09658e8	−1.87289	−0.936447	−	0.350810i	$-0.885906\pi$
$257$	−5.09658e8	−1.87289	−0.936447	+	0.350810i	$0.885906\pi$
$258$	0	0
$259$	8.93225e6	0.0319456
$260$	7.60451e8	2.68327
$261$	0	0
$262$	2.20205e8	0.756436
$263$	1.92628e8	0.652941	0.326471	−	0.945207i	$-0.394141\pi$
$263$	1.92628e8	0.652941	0.326471	+	0.945207i	$0.394141\pi$
$264$	0	0
$265$	−6.75028e8	−2.22823
$266$	−8.31903e6	−0.0271011
$267$	0	0
$268$	−2.63720e8	−0.836896
$269$	−4.06864e8	−1.27443	−0.637215	−	0.770686i	$-0.719914\pi$
$269$	−4.06864e8	−1.27443	−0.637215	+	0.770686i	$0.719914\pi$
$270$	0	0
$271$	−1.77838e8	−0.542789	−0.271395	−	0.962468i	$-0.587485\pi$
$271$	−1.77838e8	−0.542789	−0.271395	+	0.962468i	$0.587485\pi$
$272$	1.50883e7	0.0454620
$273$	0	0
$274$	−2.21834e8	−0.651481
$275$	−8.35352e8	−2.42217
$276$	0	0
$277$	−5.24499e8	−1.48274	−0.741371	−	0.671095i	$-0.765824\pi$
$277$	−5.24499e8	−1.48274	−0.741371	+	0.671095i	$0.765824\pi$
$278$	−1.44870e8	−0.404411
$279$	0	0
$280$	1.35476e7	0.0368817
$281$	9.91059e7	0.266457	0.133229	−	0.991085i	$-0.457466\pi$
$281$	9.91059e7	0.266457	0.133229	+	0.991085i	$0.457466\pi$
$282$	0	0
$283$	3.36868e8	0.883502	0.441751	−	0.897138i	$-0.354357\pi$
$283$	3.36868e8	0.883502	0.441751	+	0.897138i	$0.354357\pi$
$284$	4.72086e8	1.22294
$285$	0	0
$286$	1.62387e9	4.10458
$287$	3.59009e7	0.0896434
$288$	0	0
$289$	−4.08628e8	−0.995832
$290$	4.57641e8	1.10187
$291$	0	0
$292$	−4.32125e8	−1.01571
$293$	−1.54762e8	−0.359441	−0.179720	−	0.983718i	$-0.557519\pi$
$293$	−1.54762e8	−0.359441	−0.179720	+	0.983718i	$0.557519\pi$
$294$	0	0
$295$	−8.64803e7	−0.196128
$296$	7.43407e7	0.166612
$297$	0	0
$298$	1.35880e9	2.97440
$299$	2.31489e7	0.0500819
$300$	0	0
$301$	−5.08125e7	−0.107396
$302$	−1.02684e7	−0.0214525
$303$	0	0
$304$	9.11860e7	0.186153
$305$	−1.15463e8	−0.233020
$306$	0	0
$307$	1.34130e8	0.264570	0.132285	−	0.991212i	$-0.457769\pi$
$307$	1.34130e8	0.264570	0.132285	+	0.991212i	$0.457769\pi$
$308$	8.30380e7	0.161938
$309$	0	0
$310$	−2.28760e9	−4.36128
$311$	1.66463e8	0.313802	0.156901	−	0.987614i	$-0.449850\pi$
$311$	1.66463e8	0.313802	0.156901	+	0.987614i	$0.449850\pi$
$312$	0	0
$313$	4.01885e8	0.740793	0.370396	−	0.928874i	$-0.379222\pi$
$313$	4.01885e8	0.740793	0.370396	+	0.928874i	$0.379222\pi$
$314$	−1.04591e9	−1.90652
$315$	0	0
$316$	2.11551e8	0.377147
$317$	−1.50022e8	−0.264513	−0.132257	−	0.991216i	$-0.542222\pi$
$317$	−1.50022e8	−0.264513	−0.132257	+	0.991216i	$0.542222\pi$
$318$	0	0
$319$	5.40745e8	0.932663
$320$	−1.24245e9	−2.11960
$321$	0	0
$322$	2.13929e6	0.00357086
$323$	1.03370e7	0.0170681
$324$	0	0
$325$	1.12959e9	1.82528
$326$	2.05845e7	0.0329062
$327$	0	0
$328$	2.98794e8	0.467534
$329$	1.64742e7	0.0255047
$330$	0	0
$331$	2.12361e8	0.321867	0.160934	−	0.986965i	$-0.448550\pi$
$331$	2.12361e8	0.321867	0.160934	+	0.986965i	$0.448550\pi$
$332$	−1.26855e9	−1.90250
$333$	0	0
$334$	2.04898e8	0.300902
$335$	−7.00307e8	−1.01773
$336$	0	0
$337$	3.59426e8	0.511570	0.255785	−	0.966734i	$-0.417666\pi$
$337$	3.59426e8	0.511570	0.255785	+	0.966734i	$0.417666\pi$
$338$	−1.13362e9	−1.59682
$339$	0	0
$340$	−8.73232e7	−0.120491
$341$	−2.70301e9	−3.69153
$342$	0	0
$343$	1.02168e8	0.136705
$344$	−4.22899e8	−0.560122
$345$	0	0
$346$	−1.71190e9	−2.22184
$347$	1.80343e8	0.231711	0.115855	−	0.993266i	$-0.463039\pi$
$347$	1.80343e8	0.231711	0.115855	+	0.993266i	$0.463039\pi$
$348$	0	0
$349$	1.08403e9	1.36506	0.682531	−	0.730856i	$-0.260879\pi$
$349$	1.08403e9	1.36506	0.682531	+	0.730856i	$0.260879\pi$
$350$	1.04390e8	0.130143
$351$	0	0
$352$	−2.20279e9	−2.69199
$353$	9.01373e8	1.09067	0.545335	−	0.838218i	$-0.316403\pi$
$353$	9.01373e8	1.09067	0.545335	+	0.838218i	$0.316403\pi$
$354$	0	0
$355$	1.25362e9	1.48719
$356$	1.71227e9	2.01140
$357$	0	0
$358$	−1.29873e9	−1.49599
$359$	4.12758e8	0.470830	0.235415	−	0.971895i	$-0.424355\pi$
$359$	4.12758e8	0.470830	0.235415	+	0.971895i	$0.424355\pi$
$360$	0	0
$361$	−8.31400e8	−0.930111
$362$	−7.46748e8	−0.827359
$363$	0	0
$364$	−1.12287e8	−0.122032
$365$	−1.14750e9	−1.23518
$366$	0	0
$367$	−5.59200e8	−0.590521	−0.295261	−	0.955417i	$-0.595407\pi$
$367$	−5.59200e8	−0.590521	−0.295261	+	0.955417i	$0.595407\pi$
$368$	−2.34490e7	−0.0245277
$369$	0	0
$370$	1.02404e9	1.05102
$371$	9.96732e7	0.101337
$372$	0	0
$373$	7.41533e8	0.739860	0.369930	−	0.929060i	$-0.379382\pi$
$373$	7.41533e8	0.739860	0.369930	+	0.929060i	$0.379382\pi$
$374$	−1.86470e8	−0.184314
$375$	0	0
$376$	1.37111e8	0.133019
$377$	−7.31212e8	−0.702827
$378$	0	0
$379$	−1.84508e9	−1.74091	−0.870457	−	0.492244i	$-0.836177\pi$
$379$	−1.84508e9	−1.74091	−0.870457	+	0.492244i	$0.836177\pi$
$380$	−5.27738e8	−0.493373
$381$	0	0
$382$	6.71581e8	0.616420
$383$	−5.18339e8	−0.471431	−0.235716	−	0.971822i	$-0.575743\pi$
$383$	−5.18339e8	−0.471431	−0.235716	+	0.971822i	$0.575743\pi$
$384$	0	0
$385$	2.20507e8	0.196929
$386$	1.09991e9	0.973419
$387$	0	0
$388$	−2.15831e9	−1.87587
$389$	−1.36832e9	−1.17860	−0.589298	−	0.807916i	$-0.700596\pi$
$389$	−1.36832e9	−1.17860	−0.589298	+	0.807916i	$0.700596\pi$
$390$	0	0
$391$	−2.65821e6	−0.00224890
$392$	4.24157e8	0.355652
$393$	0	0
$394$	2.71102e9	2.23304
$395$	5.61773e8	0.458639
$396$	0	0
$397$	3.13292e8	0.251294	0.125647	−	0.992075i	$-0.459899\pi$
$397$	3.13292e8	0.251294	0.125647	+	0.992075i	$0.459899\pi$
$398$	−6.14196e8	−0.488334
$399$	0	0
$400$	−1.14423e9	−0.893932
$401$	−7.32537e8	−0.567315	−0.283658	−	0.958926i	$-0.591548\pi$
$401$	−7.32537e8	−0.567315	−0.283658	+	0.958926i	$0.591548\pi$
$402$	0	0
$403$	3.65509e9	2.78183
$404$	1.29242e9	0.975148
$405$	0	0
$406$	−6.75743e7	−0.0501119
$407$	1.21000e9	0.889620
$408$	0	0
$409$	−4.52805e8	−0.327250	−0.163625	−	0.986523i	$-0.552319\pi$
$409$	−4.52805e8	−0.327250	−0.163625	+	0.986523i	$0.552319\pi$
$410$	4.11588e9	2.94930
$411$	0	0
$412$	−8.08129e8	−0.569299
$413$	1.27695e7	0.00891967
$414$	0	0
$415$	−3.36863e9	−2.31358
$416$	2.97868e9	2.02861
$417$	0	0
$418$	−1.12693e9	−0.754710
$419$	−2.74019e8	−0.181983	−0.0909916	−	0.995852i	$-0.529004\pi$
$419$	−2.74019e8	−0.181983	−0.0909916	+	0.995852i	$0.529004\pi$
$420$	0	0
$421$	−2.84288e9	−1.85683	−0.928414	−	0.371546i	$-0.878828\pi$
$421$	−2.84288e9	−1.85683	−0.928414	+	0.371546i	$0.878828\pi$
$422$	3.39127e9	2.19669
$423$	0	0
$424$	8.29553e8	0.528523
$425$	−1.29712e8	−0.0819631
$426$	0	0
$427$	1.70490e7	0.0105975
$428$	3.47275e9	2.14102
$429$	0	0
$430$	−5.82543e9	−3.53336
$431$	−1.06285e9	−0.639440	−0.319720	−	0.947512i	$-0.603589\pi$
$431$	−1.06285e9	−0.639440	−0.319720	+	0.947512i	$0.603589\pi$
$432$	0	0
$433$	−1.53055e9	−0.906022	−0.453011	−	0.891505i	$-0.649650\pi$
$433$	−1.53055e9	−0.906022	−0.453011	+	0.891505i	$0.649650\pi$
$434$	3.37782e8	0.198346
$435$	0	0
$436$	3.08999e6	0.00178548
$437$	−1.60649e7	−0.00920858
$438$	0	0
$439$	5.70324e8	0.321733	0.160867	−	0.986976i	$-0.448571\pi$
$439$	5.70324e8	0.321733	0.160867	+	0.986976i	$0.448571\pi$
$440$	1.83522e9	1.02708
$441$	0	0
$442$	2.52151e8	0.138893
$443$	1.53721e9	0.840078	0.420039	−	0.907506i	$-0.362016\pi$
$443$	1.53721e9	0.840078	0.420039	+	0.907506i	$0.362016\pi$
$444$	0	0
$445$	4.54693e9	2.44601
$446$	−3.26496e9	−1.74263
$447$	0	0
$448$	1.83457e8	0.0963966
$449$	3.53047e9	1.84065	0.920323	−	0.391160i	$-0.127926\pi$
$449$	3.53047e9	1.84065	0.920323	+	0.391160i	$0.127926\pi$
$450$	0	0
$451$	4.86328e9	2.49639
$452$	−1.13243e9	−0.576802
$453$	0	0
$454$	−5.89248e8	−0.295531
$455$	−2.98176e8	−0.148400
$456$	0	0
$457$	2.13769e8	0.104770	0.0523850	−	0.998627i	$-0.483318\pi$
$457$	2.13769e8	0.104770	0.0523850	+	0.998627i	$0.483318\pi$
$458$	4.04221e9	1.96603
$459$	0	0
$460$	1.35711e8	0.0650073
$461$	2.72011e9	1.29310	0.646551	−	0.762871i	$-0.276211\pi$
$461$	2.72011e9	1.29310	0.646551	+	0.762871i	$0.276211\pi$
$462$	0	0
$463$	−2.70333e9	−1.26580	−0.632901	−	0.774233i	$-0.718136\pi$
$463$	−2.70333e9	−1.26580	−0.632901	+	0.774233i	$0.718136\pi$
$464$	7.40691e8	0.344210
$465$	0	0
$466$	5.37593e9	2.46095
$467$	−2.43270e9	−1.10530	−0.552650	−	0.833414i	$-0.686383\pi$
$467$	−2.43270e9	−1.10530	−0.552650	+	0.833414i	$0.686383\pi$
$468$	0	0
$469$	1.03406e8	0.0462850
$470$	1.88870e9	0.839112
$471$	0	0
$472$	1.06277e8	0.0465204
$473$	−6.88327e9	−2.99076
$474$	0	0
$475$	−7.83913e8	−0.335614
$476$	1.28940e7	0.00547977
$477$	0	0
$478$	−2.75999e9	−1.15587
$479$	−3.67141e8	−0.152636	−0.0763182	−	0.997084i	$-0.524316\pi$
$479$	−3.67141e8	−0.152636	−0.0763182	+	0.997084i	$0.524316\pi$
$480$	0	0
$481$	−1.63620e9	−0.670392
$482$	−1.55552e9	−0.632721
$483$	0	0
$484$	8.15862e9	3.27083
$485$	−5.73138e9	−2.28120
$486$	0	0
$487$	−3.04793e9	−1.19579	−0.597894	−	0.801575i	$-0.703996\pi$
$487$	−3.04793e9	−1.19579	−0.597894	+	0.801575i	$0.703996\pi$
$488$	1.41894e8	0.0552708
$489$	0	0
$490$	5.84276e9	2.24353
$491$	4.09474e9	1.56114	0.780568	−	0.625071i	$-0.214930\pi$
$491$	4.09474e9	1.56114	0.780568	+	0.625071i	$0.214930\pi$
$492$	0	0
$493$	8.39657e7	0.0315600
$494$	1.52387e9	0.568727
$495$	0	0
$496$	−3.70247e9	−1.36240
$497$	−1.85107e8	−0.0676356
$498$	0	0
$499$	−3.30636e9	−1.19124	−0.595618	−	0.803268i	$-0.703093\pi$
$499$	−3.30636e9	−1.19124	−0.595618	+	0.803268i	$0.703093\pi$
$500$	1.40588e9	0.502982
$501$	0	0
$502$	−3.36417e8	−0.118690
$503$	4.42202e9	1.54929	0.774645	−	0.632397i	$-0.217929\pi$
$503$	4.42202e9	1.54929	0.774645	+	0.632397i	$0.217929\pi$
$504$	0	0
$505$	3.43202e9	1.18585
$506$	2.89797e8	0.0994412
$507$	0	0
$508$	−5.77838e9	−1.95561
$509$	−3.77691e9	−1.26947	−0.634737	−	0.772728i	$-0.718892\pi$
$509$	−3.77691e9	−1.26947	−0.634737	+	0.772728i	$0.718892\pi$
$510$	0	0
$511$	1.69438e8	0.0561743
$512$	−3.78145e9	−1.24513
$513$	0	0
$514$	8.62766e9	2.80235
$515$	−2.14598e9	−0.692310
$516$	0	0
$517$	2.23167e9	0.710252
$518$	−1.51208e8	−0.0477992
$519$	0	0
$520$	−2.48164e9	−0.773976
$521$	4.54529e9	1.40809	0.704044	−	0.710157i	$-0.251376\pi$
$521$	4.54529e9	1.40809	0.704044	+	0.710157i	$0.251376\pi$
$522$	0	0
$523$	−4.00555e9	−1.22435	−0.612176	−	0.790721i	$-0.709706\pi$
$523$	−4.00555e9	−1.22435	−0.612176	+	0.790721i	$0.709706\pi$
$524$	−2.06267e9	−0.626281
$525$	0	0
$526$	−3.26087e9	−0.976974
$527$	−4.19717e8	−0.124916
$528$	0	0
$529$	−3.40069e9	−0.998787
$530$	1.14271e10	3.33403
$531$	0	0
$532$	7.79247e7	0.0224380
$533$	−6.57629e9	−1.88120
$534$	0	0
$535$	9.22186e9	2.60364
$536$	8.60620e8	0.241399
$537$	0	0
$538$	6.88752e9	1.90689
$539$	6.90376e9	1.89900
$540$	0	0
$541$	−1.98627e9	−0.539320	−0.269660	−	0.962956i	$-0.586911\pi$
$541$	−1.98627e9	−0.539320	−0.269660	+	0.962956i	$0.586911\pi$
$542$	3.01049e9	0.812157
$543$	0	0
$544$	−3.42045e8	−0.0910934
$545$	8.20544e6	0.00217127
$546$	0	0
$547$	−1.31698e9	−0.344052	−0.172026	−	0.985092i	$-0.555031\pi$
$547$	−1.31698e9	−0.344052	−0.172026	+	0.985092i	$0.555031\pi$
$548$	2.07793e9	0.539385
$549$	0	0
$550$	1.41411e10	3.62422
$551$	5.07447e8	0.129229
$552$	0	0
$553$	−8.29503e7	−0.0208584
$554$	8.87889e9	2.21858
$555$	0	0
$556$	1.35700e9	0.334826
$557$	−3.87423e9	−0.949931	−0.474965	−	0.880004i	$-0.657539\pi$
$557$	−3.87423e9	−0.949931	−0.474965	+	0.880004i	$0.657539\pi$
$558$	0	0
$559$	9.30778e9	2.25375
$560$	3.02042e8	0.0726789
$561$	0	0
$562$	−1.67770e9	−0.398691
$563$	5.14028e9	1.21397	0.606984	−	0.794714i	$-0.292379\pi$
$563$	5.14028e9	1.21397	0.606984	+	0.794714i	$0.292379\pi$
$564$	0	0
$565$	−3.00716e9	−0.701435
$566$	−5.70262e9	−1.32196
$567$	0	0
$568$	−1.54060e9	−0.352752
$569$	−5.94344e9	−1.35252	−0.676262	−	0.736661i	$-0.736401\pi$
$569$	−5.94344e9	−1.35252	−0.676262	+	0.736661i	$0.736401\pi$
$570$	0	0
$571$	−6.34028e9	−1.42522	−0.712611	−	0.701560i	$-0.752487\pi$
$571$	−6.34028e9	−1.42522	−0.712611	+	0.701560i	$0.752487\pi$
$572$	−1.52108e10	−3.39833
$573$	0	0
$574$	−6.07742e8	−0.134131
$575$	2.01588e8	0.0442208
$576$	0	0
$577$	2.74120e9	0.594052	0.297026	−	0.954869i	$-0.404005\pi$
$577$	2.74120e9	0.594052	0.297026	+	0.954869i	$0.404005\pi$
$578$	6.91739e9	1.49003
$579$	0	0
$580$	−4.28674e9	−0.912282
$581$	4.97405e8	0.105219
$582$	0	0
$583$	1.35021e10	2.82204
$584$	1.41019e9	0.292976
$585$	0	0
$586$	2.61986e9	0.537819
$587$	7.75794e8	0.158312	0.0791558	−	0.996862i	$-0.474778\pi$
$587$	7.75794e8	0.158312	0.0791558	+	0.996862i	$0.474778\pi$
$588$	0	0
$589$	−2.53656e9	−0.511495
$590$	1.46397e9	0.293460
$591$	0	0
$592$	1.65741e9	0.328325
$593$	−1.63585e9	−0.322145	−0.161072	−	0.986943i	$-0.551495\pi$
$593$	−1.63585e9	−0.322145	−0.161072	+	0.986943i	$0.551495\pi$
$594$	0	0
$595$	3.42398e7	0.00666381
$596$	−1.27280e10	−2.46262
$597$	0	0
$598$	−3.91872e8	−0.0749360
$599$	4.17190e9	0.793121	0.396561	−	0.918009i	$-0.370204\pi$
$599$	4.17190e9	0.793121	0.396561	+	0.918009i	$0.370204\pi$
$600$	0	0
$601$	−4.54954e9	−0.854883	−0.427442	−	0.904043i	$-0.640585\pi$
$601$	−4.54954e9	−0.854883	−0.427442	+	0.904043i	$0.640585\pi$
$602$	8.60171e8	0.160693
$603$	0	0
$604$	9.61845e7	0.0177613
$605$	2.16652e10	3.97757
$606$	0	0
$607$	−5.26426e9	−0.955381	−0.477691	−	0.878528i	$-0.658526\pi$
$607$	−5.26426e9	−0.955381	−0.477691	+	0.878528i	$0.658526\pi$
$608$	−2.06715e9	−0.373000
$609$	0	0
$610$	1.95459e9	0.348660
$611$	−3.01773e9	−0.535225
$612$	0	0
$613$	−1.30761e9	−0.229281	−0.114641	−	0.993407i	$-0.536572\pi$
$613$	−1.30761e9	−0.229281	−0.114641	+	0.993407i	$0.536572\pi$
$614$	−2.27059e9	−0.395867
$615$	0	0
$616$	−2.70985e8	−0.0467103
$617$	5.09050e9	0.872493	0.436247	−	0.899827i	$-0.356308\pi$
$617$	5.09050e9	0.872493	0.436247	+	0.899827i	$0.356308\pi$
$618$	0	0
$619$	8.73085e9	1.47958	0.739792	−	0.672836i	$-0.234924\pi$
$619$	8.73085e9	1.47958	0.739792	+	0.672836i	$0.234924\pi$
$620$	2.14280e10	3.61086
$621$	0	0
$622$	−2.81794e9	−0.469532
$623$	−6.71391e8	−0.111242
$624$	0	0
$625$	−4.01519e9	−0.657850
$626$	−6.80324e9	−1.10842
$627$	0	0
$628$	9.79709e9	1.57848
$629$	1.87886e8	0.0301035
$630$	0	0
$631$	−7.67163e9	−1.21558	−0.607792	−	0.794096i	$-0.707945\pi$
$631$	−7.67163e9	−1.21558	−0.607792	+	0.794096i	$0.707945\pi$
$632$	−6.90373e8	−0.108786
$633$	0	0
$634$	2.53962e9	0.395782
$635$	−1.53444e10	−2.37817
$636$	0	0
$637$	−9.33548e9	−1.43103
$638$	−9.15390e9	−1.39551
$639$	0	0
$640$	6.93635e9	1.04593
$641$	3.46528e9	0.519679	0.259840	−	0.965652i	$-0.416330\pi$
$641$	3.46528e9	0.519679	0.259840	+	0.965652i	$0.416330\pi$
$642$	0	0
$643$	5.49488e9	0.815117	0.407559	−	0.913179i	$-0.366380\pi$
$643$	5.49488e9	0.815117	0.407559	+	0.913179i	$0.366380\pi$
$644$	−2.00388e7	−0.00295645
$645$	0	0
$646$	−1.74988e8	−0.0255384
$647$	−8.98807e9	−1.30467	−0.652336	−	0.757930i	$-0.726211\pi$
$647$	−8.98807e9	−1.30467	−0.652336	+	0.757930i	$0.726211\pi$
$648$	0	0
$649$	1.72981e9	0.248395
$650$	−1.91221e10	−2.73110
$651$	0	0
$652$	−1.92815e8	−0.0272443
$653$	2.09537e9	0.294486	0.147243	−	0.989100i	$-0.452960\pi$
$653$	2.09537e9	0.294486	0.147243	+	0.989100i	$0.452960\pi$
$654$	0	0
$655$	−5.47739e9	−0.761604
$656$	6.66154e9	0.921321
$657$	0	0
$658$	−2.78881e8	−0.0381618
$659$	−1.34881e10	−1.83591	−0.917953	−	0.396690i	$-0.870159\pi$
$659$	−1.34881e10	−1.83591	−0.917953	+	0.396690i	$0.870159\pi$
$660$	0	0
$661$	−2.15284e9	−0.289939	−0.144969	−	0.989436i	$-0.546308\pi$
$661$	−2.15284e9	−0.289939	−0.144969	+	0.989436i	$0.546308\pi$
$662$	−3.59492e9	−0.481599
$663$	0	0
$664$	4.13977e9	0.548767
$665$	2.06928e8	0.0272863
$666$	0	0
$667$	−1.30493e8	−0.0170273
$668$	−1.91928e9	−0.249127
$669$	0	0
$670$	1.18550e10	1.52279
$671$	2.30953e9	0.295117
$672$	0	0
$673$	−1.17042e10	−1.48010	−0.740048	−	0.672554i	$-0.765197\pi$
$673$	−1.17042e10	−1.48010	−0.740048	+	0.672554i	$0.765197\pi$
$674$	−6.08448e9	−0.765445
$675$	0	0
$676$	1.06186e10	1.32207
$677$	6.54348e9	0.810491	0.405245	−	0.914208i	$-0.367186\pi$
$677$	6.54348e9	0.810491	0.405245	+	0.914208i	$0.367186\pi$
$678$	0	0
$679$	8.46284e8	0.103746
$680$	2.84969e8	0.0347549
$681$	0	0
$682$	4.57574e10	5.52352
$683$	−1.02317e10	−1.22878	−0.614390	−	0.789003i	$-0.710598\pi$
$683$	−1.02317e10	−1.22878	−0.614390	+	0.789003i	$0.710598\pi$
$684$	0	0
$685$	5.51793e9	0.655932
$686$	−1.72953e9	−0.204547
$687$	0	0
$688$	−9.42844e9	−1.10377
$689$	−1.82580e10	−2.12660
$690$	0	0
$691$	−1.10128e10	−1.26977	−0.634887	−	0.772605i	$-0.718953\pi$
$691$	−1.10128e10	−1.26977	−0.634887	+	0.772605i	$0.718953\pi$
$692$	1.60354e10	1.83954
$693$	0	0
$694$	−3.05291e9	−0.346701
$695$	3.60352e9	0.407174
$696$	0	0
$697$	7.55161e8	0.0844743
$698$	−1.83508e10	−2.04250
$699$	0	0
$700$	−9.77826e8	−0.107750
$701$	−5.07374e9	−0.556308	−0.278154	−	0.960536i	$-0.589723\pi$
$701$	−5.07374e9	−0.556308	−0.278154	+	0.960536i	$0.589723\pi$
$702$	0	0
$703$	1.13549e9	0.123265
$704$	2.48519e10	2.68445
$705$	0	0
$706$	−1.52587e10	−1.63193
$707$	−5.06766e8	−0.0539311
$708$	0	0
$709$	−9.55775e8	−0.100715	−0.0503575	−	0.998731i	$-0.516036\pi$
$709$	−9.55775e8	−0.100715	−0.0503575	+	0.998731i	$0.516036\pi$
$710$	−2.12217e10	−2.22524
$711$	0	0
$712$	−5.58781e9	−0.580178
$713$	6.52291e8	0.0673950
$714$	0	0
$715$	−4.03922e10	−4.13263
$716$	1.21652e10	1.23858
$717$	0	0
$718$	−6.98730e9	−0.704488
$719$	−9.39305e9	−0.942444	−0.471222	−	0.882015i	$-0.656187\pi$
$719$	−9.39305e9	−0.942444	−0.471222	+	0.882015i	$0.656187\pi$
$720$	0	0
$721$	3.16871e8	0.0314854
$722$	1.40742e10	1.39169
$723$	0	0
$724$	6.99481e9	0.685001
$725$	−6.36762e9	−0.620574
$726$	0	0
$727$	−1.28780e9	−0.124302	−0.0621508	−	0.998067i	$-0.519796\pi$
$727$	−1.28780e9	−0.124302	−0.0621508	+	0.998067i	$0.519796\pi$
$728$	3.66434e8	0.0351995
$729$	0	0
$730$	1.94253e10	1.84815
$731$	−1.06882e9	−0.101203
$732$	0	0
$733$	6.05304e8	0.0567687	0.0283844	−	0.999597i	$-0.490964\pi$
$733$	6.05304e8	0.0567687	0.0283844	+	0.999597i	$0.490964\pi$
$734$	9.46631e9	0.883578
$735$	0	0
$736$	5.31579e8	0.0491468
$737$	1.40078e10	1.28894
$738$	0	0
$739$	6.67329e9	0.608253	0.304126	−	0.952632i	$-0.401635\pi$
$739$	6.67329e9	0.608253	0.304126	+	0.952632i	$0.401635\pi$
$740$	−9.59224e9	−0.870180
$741$	0	0
$742$	−1.68730e9	−0.151628
$743$	6.01656e9	0.538130	0.269065	−	0.963122i	$-0.413285\pi$
$743$	6.01656e9	0.538130	0.269065	+	0.963122i	$0.413285\pi$
$744$	0	0
$745$	−3.37990e10	−2.99472
$746$	−1.25529e10	−1.10703
$747$	0	0
$748$	1.74667e9	0.152600
$749$	−1.36168e9	−0.118410
$750$	0	0
$751$	6.84419e9	0.589634	0.294817	−	0.955554i	$-0.404741\pi$
$751$	6.84419e9	0.589634	0.294817	+	0.955554i	$0.404741\pi$
$752$	3.05685e9	0.262127
$753$	0	0
$754$	1.23782e10	1.05162
$755$	2.55417e8	0.0215991
$756$	0	0
$757$	4.04396e8	0.0338822	0.0169411	−	0.999856i	$-0.494607\pi$
$757$	4.04396e8	0.0338822	0.0169411	+	0.999856i	$0.494607\pi$
$758$	3.12341e10	2.60487
$759$	0	0
$760$	1.72221e9	0.142311
$761$	−3.58785e9	−0.295112	−0.147556	−	0.989054i	$-0.547141\pi$
$761$	−3.58785e9	−0.295112	−0.147556	+	0.989054i	$0.547141\pi$
$762$	0	0
$763$	−1.21160e6	−9.87467e−5 0
$764$	−6.29072e9	−0.510356
$765$	0	0
$766$	8.77461e9	0.705387
$767$	−2.33910e9	−0.187183
$768$	0	0
$769$	−1.00703e10	−0.798550	−0.399275	−	0.916831i	$-0.630738\pi$
$769$	−1.00703e10	−0.798550	−0.399275	+	0.916831i	$0.630738\pi$
$770$	−3.73281e9	−0.294658
$771$	0	0
$772$	−1.03029e10	−0.805929
$773$	−1.18136e10	−0.919927	−0.459964	−	0.887938i	$-0.652138\pi$
$773$	−1.18136e10	−0.919927	−0.459964	+	0.887938i	$0.652138\pi$
$774$	0	0
$775$	3.18296e10	2.45627
$776$	7.04340e9	0.541086
$777$	0	0
$778$	2.31634e10	1.76349
$779$	4.56381e9	0.345897
$780$	0	0
$781$	−2.50754e10	−1.88351
$782$	4.49990e7	0.00336496
$783$	0	0
$784$	9.45649e9	0.700848
$785$	2.60161e10	1.91955
$786$	0	0
$787$	−1.44585e10	−1.05734	−0.528668	−	0.848829i	$-0.677308\pi$
$787$	−1.44585e10	−1.05734	−0.528668	+	0.848829i	$0.677308\pi$
$788$	−2.53943e10	−1.84882
$789$	0	0
$790$	−9.50988e9	−0.686247
$791$	4.44031e8	0.0319004
$792$	0	0
$793$	−3.12302e9	−0.222392
$794$	−5.30351e9	−0.376003
$795$	0	0
$796$	5.75320e9	0.404309
$797$	−2.14577e10	−1.50134	−0.750669	−	0.660678i	$-0.770269\pi$
$797$	−2.14577e10	−1.50134	−0.750669	+	0.660678i	$0.770269\pi$
$798$	0	0
$799$	3.46529e8	0.0240340
$800$	2.59393e10	1.79120
$801$	0	0
$802$	1.24006e10	0.848855
$803$	2.29528e10	1.56434
$804$	0	0
$805$	−5.32128e7	−0.00359526
$806$	−6.18745e10	−4.16236
$807$	0	0
$808$	−4.21768e9	−0.281277
$809$	−1.76950e9	−0.117498	−0.0587491	−	0.998273i	$-0.518711\pi$
$809$	−1.76950e9	−0.117498	−0.0587491	+	0.998273i	$0.518711\pi$
$810$	0	0
$811$	−1.15307e10	−0.759074	−0.379537	−	0.925177i	$-0.623917\pi$
$811$	−1.15307e10	−0.759074	−0.379537	+	0.925177i	$0.623917\pi$
$812$	6.32971e8	0.0414895
$813$	0	0
$814$	−2.04833e10	−1.33111
$815$	−5.12020e8	−0.0331311
$816$	0	0
$817$	−6.45942e9	−0.414397
$818$	7.66523e9	0.489653
$819$	0	0
$820$	−3.85536e10	−2.44183
$821$	−1.88474e10	−1.18864	−0.594321	−	0.804228i	$-0.702579\pi$
$821$	−1.88474e10	−1.18864	−0.594321	+	0.804228i	$0.702579\pi$
$822$	0	0
$823$	2.70001e10	1.68836	0.844180	−	0.536059i	$-0.180088\pi$
$823$	2.70001e10	1.68836	0.844180	+	0.536059i	$0.180088\pi$
$824$	2.63723e9	0.164211
$825$	0	0
$826$	−2.16166e8	−0.0133462
$827$	−2.57017e10	−1.58013	−0.790064	−	0.613024i	$-0.789953\pi$
$827$	−2.57017e10	−1.58013	−0.790064	+	0.613024i	$0.789953\pi$
$828$	0	0
$829$	1.20559e10	0.734952	0.367476	−	0.930033i	$-0.380222\pi$
$829$	1.20559e10	0.734952	0.367476	+	0.930033i	$0.380222\pi$
$830$	5.70253e10	3.46174
$831$	0	0
$832$	−3.36055e10	−2.02292
$833$	1.07200e9	0.0642595
$834$	0	0
$835$	−5.09665e9	−0.302958
$836$	1.05560e10	0.624853
$837$	0	0
$838$	4.63868e9	0.272295
$839$	−1.49873e10	−0.876106	−0.438053	−	0.898949i	$-0.644332\pi$
$839$	−1.49873e10	−0.876106	−0.438053	+	0.898949i	$0.644332\pi$
$840$	0	0
$841$	−1.31280e10	−0.761047
$842$	4.81253e10	2.77831
$843$	0	0
$844$	−3.17661e10	−1.81872
$845$	2.81977e10	1.60774
$846$	0	0
$847$	−3.19903e9	−0.180895
$848$	1.84947e10	1.04151
$849$	0	0
$850$	2.19580e9	0.122639
$851$	−2.91998e8	−0.0162415
$852$	0	0
$853$	7.24550e9	0.399712	0.199856	−	0.979825i	$-0.435953\pi$
$853$	7.24550e9	0.399712	0.199856	+	0.979825i	$0.435953\pi$
$854$	−2.88611e8	−0.0158566
$855$	0	0
$856$	−1.13329e10	−0.617566
$857$	−3.25083e10	−1.76426	−0.882128	−	0.471010i	$-0.843890\pi$
$857$	−3.25083e10	−1.76426	−0.882128	+	0.471010i	$0.843890\pi$
$858$	0	0
$859$	−1.44247e10	−0.776480	−0.388240	−	0.921558i	$-0.626917\pi$
$859$	−1.44247e10	−0.776480	−0.388240	+	0.921558i	$0.626917\pi$
$860$	5.45670e10	2.92540
$861$	0	0
$862$	1.79922e10	0.956773
$863$	1.11462e10	0.590324	0.295162	−	0.955447i	$-0.404626\pi$
$863$	1.11462e10	0.590324	0.295162	+	0.955447i	$0.404626\pi$
$864$	0	0
$865$	4.25820e10	2.23702
$866$	2.59096e10	1.35565
$867$	0	0
$868$	−3.16402e9	−0.164218
$869$	−1.12368e10	−0.580862
$870$	0	0
$871$	−1.89418e10	−0.971309
$872$	−1.00838e7	−0.000515012 0
$873$	0	0
$874$	2.71952e8	0.0137785
$875$	−5.51251e8	−0.0278177
$876$	0	0
$877$	−2.20664e10	−1.10467	−0.552334	−	0.833623i	$-0.686263\pi$
$877$	−2.20664e10	−1.10467	−0.552334	+	0.833623i	$0.686263\pi$
$878$	−9.65463e9	−0.481399
$879$	0	0
$880$	4.09158e10	2.02396
$881$	5.78724e9	0.285138	0.142569	−	0.989785i	$-0.454464\pi$
$881$	5.78724e9	0.285138	0.142569	+	0.989785i	$0.454464\pi$
$882$	0	0
$883$	−3.69412e10	−1.80571	−0.902855	−	0.429944i	$-0.858533\pi$
$883$	−3.69412e10	−1.80571	−0.902855	+	0.429944i	$0.858533\pi$
$884$	−2.36190e9	−0.114995
$885$	0	0
$886$	−2.60224e10	−1.25698
$887$	−8.57880e9	−0.412756	−0.206378	−	0.978472i	$-0.566168\pi$
$887$	−8.57880e9	−0.412756	−0.206378	+	0.978472i	$0.566168\pi$
$888$	0	0
$889$	2.26573e9	0.108156
$890$	−7.69720e10	−3.65989
$891$	0	0
$892$	3.05830e10	1.44279
$893$	2.09425e9	0.0984120
$894$	0	0
$895$	3.23047e10	1.50621
$896$	−1.02421e9	−0.0475674
$897$	0	0
$898$	−5.97649e10	−2.75410
$899$	−2.06041e10	−0.945791
$900$	0	0
$901$	2.09658e9	0.0954939
$902$	−8.23273e10	−3.73526
$903$	0	0
$904$	3.69555e9	0.166376
$905$	1.85747e10	0.833012
$906$	0	0
$907$	4.99672e9	0.222362	0.111181	−	0.993800i	$-0.464537\pi$
$907$	4.99672e9	0.222362	0.111181	+	0.993800i	$0.464537\pi$
$908$	5.51951e9	0.244681
$909$	0	0
$910$	5.04762e9	0.222046
$911$	2.67519e10	1.17230	0.586151	−	0.810202i	$-0.300642\pi$
$911$	2.67519e10	1.17230	0.586151	+	0.810202i	$0.300642\pi$
$912$	0	0
$913$	6.73806e10	2.93013
$914$	−3.61875e9	−0.156764
$915$	0	0
$916$	−3.78635e10	−1.62775
$917$	8.08780e8	0.0346368
$918$	0	0
$919$	−1.20296e10	−0.511268	−0.255634	−	0.966774i	$-0.582284\pi$
$919$	−1.20296e10	−0.511268	−0.255634	+	0.966774i	$0.582284\pi$
$920$	−4.42876e8	−0.0187510
$921$	0	0
$922$	−4.60469e10	−1.93483
$923$	3.39077e10	1.41936
$924$	0	0
$925$	−1.42485e10	−0.591935
$926$	4.57629e10	1.89398
$927$	0	0
$928$	−1.67911e10	−0.689704
$929$	−9.92866e9	−0.406290	−0.203145	−	0.979149i	$-0.565116\pi$
$929$	−9.92866e9	−0.406290	−0.203145	+	0.979149i	$0.565116\pi$
$930$	0	0
$931$	6.47864e9	0.263124
$932$	−5.03565e10	−2.03751
$933$	0	0
$934$	4.11816e10	1.65382
$935$	4.63827e9	0.185573
$936$	0	0
$937$	−4.20534e10	−1.66998	−0.834992	−	0.550262i	$-0.814528\pi$
$937$	−4.20534e10	−1.66998	−0.834992	+	0.550262i	$0.814528\pi$
$938$	−1.75049e9	−0.0692547
$939$	0	0
$940$	−1.76915e10	−0.694732
$941$	3.81848e9	0.149392	0.0746960	−	0.997206i	$-0.476201\pi$
$941$	3.81848e9	0.149392	0.0746960	+	0.997206i	$0.476201\pi$
$942$	0	0
$943$	−1.17361e9	−0.0455757
$944$	2.36943e9	0.0916730
$945$	0	0
$946$	1.16522e11	4.47497
$947$	1.89974e10	0.726892	0.363446	−	0.931615i	$-0.381600\pi$
$947$	1.89974e10	0.726892	0.363446	+	0.931615i	$0.381600\pi$
$948$	0	0
$949$	−3.10375e10	−1.17884
$950$	1.32703e10	0.502169
$951$	0	0
$952$	−4.20779e7	−0.00158061
$953$	3.31060e10	1.23903	0.619514	−	0.784986i	$-0.287330\pi$
$953$	3.31060e10	1.23903	0.619514	+	0.784986i	$0.287330\pi$
$954$	0	0
$955$	−1.67050e10	−0.620631
$956$	2.58529e10	0.956990
$957$	0	0
$958$	6.21507e9	0.228385
$959$	−8.14766e8	−0.0298310
$960$	0	0
$961$	7.54807e10	2.74349
$962$	2.76981e10	1.00308
$963$	0	0
$964$	1.45707e10	0.523853
$965$	−2.73592e10	−0.980070
$966$	0	0
$967$	4.23227e9	0.150515	0.0752576	−	0.997164i	$-0.476022\pi$
$967$	4.23227e9	0.150515	0.0752576	+	0.997164i	$0.476022\pi$
$968$	−2.66247e10	−0.943455
$969$	0	0
$970$	9.70227e10	3.41328
$971$	−2.31036e10	−0.809866	−0.404933	−	0.914346i	$-0.632705\pi$
$971$	−2.31036e10	−0.809866	−0.404933	+	0.914346i	$0.632705\pi$
$972$	0	0
$973$	−5.32088e8	−0.0185178
$974$	5.15964e10	1.78922
$975$	0	0
$976$	3.16350e9	0.108917
$977$	5.89335e9	0.202177	0.101088	−	0.994877i	$-0.467768\pi$
$977$	5.89335e9	0.202177	0.101088	+	0.994877i	$0.467768\pi$
$978$	0	0
$979$	−9.09494e10	−3.09785
$980$	−5.47294e10	−1.85750
$981$	0	0
$982$	−6.93171e10	−2.33588
$983$	−4.17317e10	−1.40129	−0.700646	−	0.713509i	$-0.747105\pi$
$983$	−4.17317e10	−1.40129	−0.700646	+	0.713509i	$0.747105\pi$
$984$	0	0
$985$	−6.74343e10	−2.24830
$986$	−1.42140e9	−0.0472222
$987$	0	0
$988$	−1.42742e10	−0.470870
$989$	1.66108e9	0.0546012
$990$	0	0
$991$	2.97978e10	0.972583	0.486292	−	0.873797i	$-0.338349\pi$
$991$	2.97978e10	0.972583	0.486292	+	0.873797i	$0.338349\pi$
$992$	8.39335e10	2.72989
$993$	0	0
$994$	3.13355e9	0.101201
$995$	1.52776e10	0.491670
$996$	0	0
$997$	1.92441e10	0.614986	0.307493	−	0.951550i	$-0.400510\pi$
$997$	1.92441e10	0.614986	0.307493	+	0.951550i	$0.400510\pi$
$998$	5.59711e10	1.78241
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.e.1.4		18
3.2	odd	2		177.8.a.d.1.15	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.15	✓	18	3.2	odd	2
531.8.a.e.1.4		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q-16.9283 q^{2} +158.568 q^{4} +421.077 q^{5} -62.1753 q^{7} -517.469 q^{8} +O(q^{10})\)	\(q-16.9283 q^{2} +158.568 q^{4} +421.077 q^{5} -62.1753 q^{7} -517.469 q^{8} -7128.13 q^{10} -8422.53 q^{11} +11389.2 q^{13} +1052.52 q^{14} -11536.9 q^{16} -1307.83 q^{17} -7903.89 q^{19} +66769.4 q^{20} +142579. q^{22} +2032.53 q^{23} +99180.7 q^{25} -192800. q^{26} -9859.03 q^{28} -64202.2 q^{29} +320926. q^{31} +261536. q^{32} +22139.4 q^{34} -26180.6 q^{35} -143662. q^{37} +133800. q^{38} -217894. q^{40} -577414. q^{41} +817246. q^{43} -1.33555e6 q^{44} -34407.3 q^{46} -264964. q^{47} -819677. q^{49} -1.67896e6 q^{50} +1.80597e6 q^{52} -1.60310e6 q^{53} -3.54653e6 q^{55} +32173.8 q^{56} +1.08684e6 q^{58} -205379. q^{59} -274208. q^{61} -5.43273e6 q^{62} -2.95064e6 q^{64} +4.79573e6 q^{65} -1.66313e6 q^{67} -207381. q^{68} +443194. q^{70} +2.97718e6 q^{71} -2.72516e6 q^{73} +2.43196e6 q^{74} -1.25331e6 q^{76} +523673. q^{77} +1.33414e6 q^{79} -4.85790e6 q^{80} +9.77465e6 q^{82} -8.00004e6 q^{83} -550698. q^{85} -1.38346e7 q^{86} +4.35840e6 q^{88} +1.07983e7 q^{89} -708128. q^{91} +322295. q^{92} +4.48540e6 q^{94} -3.32814e6 q^{95} -1.36112e7 q^{97} +1.38758e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8}+O(q^{10}) \) 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8	\( 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8} + 3609 q^{10} - 15070 q^{11} + 13662 q^{13} - 20861 q^{14} + 60482 q^{16} - 71919 q^{17} + 56231 q^{19} - 143053 q^{20} + 274198 q^{22} - 150029 q^{23} + 399672 q^{25} - 182846 q^{26} + 434150 q^{28} - 591285 q^{29} + 426733 q^{31} - 1205630 q^{32} + 403548 q^{34} - 912879 q^{35} + 7703 q^{37} + 417859 q^{38} + 618020 q^{40} - 770959 q^{41} + 793050 q^{43} - 2591274 q^{44} - 4068019 q^{46} - 1410373 q^{47} + 1637427 q^{49} - 1021549 q^{50} - 3749190 q^{52} - 1037934 q^{53} + 331974 q^{55} + 391748 q^{56} + 653724 q^{58} - 3696822 q^{59} - 1374623 q^{61} - 5251718 q^{62} + 5077197 q^{64} - 3257170 q^{65} - 2436904 q^{67} - 14119909 q^{68} + 5185580 q^{70} - 14289172 q^{71} + 5482515 q^{73} - 14934154 q^{74} + 3822912 q^{76} - 23157109 q^{77} + 19786414 q^{79} - 31978143 q^{80} + 9749509 q^{82} - 30227337 q^{83} + 9946981 q^{85} - 44295864 q^{86} + 39970897 q^{88} - 31061677 q^{89} + 26377785 q^{91} - 4719698 q^{92} + 44488296 q^{94} - 15534599 q^{95} + 12084118 q^{97} - 42274744 q^{98}+O(q^{100}) \) 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8 + 3609 * q^10 - 15070 * q^11 + 13662 * q^13 - 20861 * q^14 + 60482 * q^16 - 71919 * q^17 + 56231 * q^19 - 143053 * q^20 + 274198 * q^22 - 150029 * q^23 + 399672 * q^25 - 182846 * q^26 + 434150 * q^28 - 591285 * q^29 + 426733 * q^31 - 1205630 * q^32 + 403548 * q^34 - 912879 * q^35 + 7703 * q^37 + 417859 * q^38 + 618020 * q^40 - 770959 * q^41 + 793050 * q^43 - 2591274 * q^44 - 4068019 * q^46 - 1410373 * q^47 + 1637427 * q^49 - 1021549 * q^50 - 3749190 * q^52 - 1037934 * q^53 + 331974 * q^55 + 391748 * q^56 + 653724 * q^58 - 3696822 * q^59 - 1374623 * q^61 - 5251718 * q^62 + 5077197 * q^64 - 3257170 * q^65 - 2436904 * q^67 - 14119909 * q^68 + 5185580 * q^70 - 14289172 * q^71 + 5482515 * q^73 - 14934154 * q^74 + 3822912 * q^76 - 23157109 * q^77 + 19786414 * q^79 - 31978143 * q^80 + 9749509 * q^82 - 30227337 * q^83 + 9946981 * q^85 - 44295864 * q^86 + 39970897 * q^88 - 31061677 * q^89 + 26377785 * q^91 - 4719698 * q^92 + 44488296 * q^94 - 15534599 * q^95 + 12084118 * q^97 - 42274744 * q^98

Introduction

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