LMFDB - Embedded newform 1638.2.cm.a.341.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(269,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1638.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.cm (of order $6$, degree $2$, minimal)

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:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.11
Character	$\chi$	$=$	1638.341
Dual form			1638.2.cm.a.269.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-0.967738 + 1.67617i) q^{5} +(1.05411 - 2.42670i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.967738 + 1.67617i) q^{5} +(1.05411 - 2.42670i) q^{7} -1.00000i q^{8} +(-1.67617 - 0.967738i) q^{10} +(0.194016 + 0.112015i) q^{11} +(-3.42443 - 1.12839i) q^{13} +(2.42670 + 1.05411i) q^{14} +1.00000 q^{16} +6.84527 q^{17} +(-6.28540 + 3.62888i) q^{19} +(0.967738 - 1.67617i) q^{20} +(-0.112015 + 0.194016i) q^{22} +1.42842i q^{23} +(0.626968 + 1.08594i) q^{25} +(1.12839 - 3.42443i) q^{26} +(-1.05411 + 2.42670i) q^{28} +(-8.07070 + 4.65962i) q^{29} +(-5.72173 + 3.30344i) q^{31} +1.00000i q^{32} +6.84527i q^{34} +(3.04746 + 4.11527i) q^{35} -6.95504 q^{37} +(-3.62888 - 6.28540i) q^{38} +(1.67617 + 0.967738i) q^{40} +(-2.78373 - 4.82157i) q^{41} +(5.05283 - 8.75176i) q^{43} +(-0.194016 - 0.112015i) q^{44} -1.42842 q^{46} +(-3.56427 + 6.17349i) q^{47} +(-4.77771 - 5.11601i) q^{49} +(-1.08594 + 0.626968i) q^{50} +(3.42443 + 1.12839i) q^{52} +(2.20736 - 1.27442i) q^{53} +(-0.375514 + 0.216803i) q^{55} +(-2.42670 - 1.05411i) q^{56} +(-4.65962 - 8.07070i) q^{58} -8.27164 q^{59} +(-10.7151 + 6.18639i) q^{61} +(-3.30344 - 5.72173i) q^{62} -1.00000 q^{64} +(5.20533 - 4.64794i) q^{65} +(-1.20910 + 2.09421i) q^{67} -6.84527 q^{68} +(-4.11527 + 3.04746i) q^{70} +(6.17036 + 3.56246i) q^{71} +(10.3059 - 5.95012i) q^{73} -6.95504i q^{74} +(6.28540 - 3.62888i) q^{76} +(0.476341 - 0.352742i) q^{77} +(-2.95621 + 5.12031i) q^{79} +(-0.967738 + 1.67617i) q^{80} +(4.82157 - 2.78373i) q^{82} +9.37902 q^{83} +(-6.62442 + 11.4738i) q^{85} +(8.75176 + 5.05283i) q^{86} +(0.112015 - 0.194016i) q^{88} -9.12512 q^{89} +(-6.34799 + 7.12060i) q^{91} -1.42842i q^{92} +(-6.17349 - 3.56427i) q^{94} -14.0472i q^{95} +(-7.01412 - 4.04961i) q^{97} +(5.11601 - 4.77771i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) $ 72 * q - 72 * q^4 - 4 * q^7	$ 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) $ 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.967738	+	1.67617i	−0.432785	+	0.749606i	−0.997112	−	0.0759454i	$-0.975803\pi$
$5$	−0.967738	+	1.67617i	−0.432785	+	0.749606i	0.564327	+	0.825552i	$0.309136\pi$
$6$		0			0
$7$	1.05411	−	2.42670i	0.398416	−	0.917205i
$7$	1.05411	−	2.42670i	0.398416	−	0.917205i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.67617	−	0.967738i	−0.530052	−	0.306025i
$11$	0.194016	+	0.112015i	0.0584981	+	0.0337739i	0.528964	−	0.848644i	$-0.322581\pi$
$11$	0.194016	+	0.112015i	0.0584981	+	0.0337739i	−0.470466	+	0.882418i	$0.655914\pi$
$12$		0			0
$13$	−3.42443	−	1.12839i	−0.949766	−	0.312960i
$13$	−3.42443	−	1.12839i	−0.949766	−	0.312960i
$14$	2.42670	+	1.05411i	0.648562	+	0.281723i
$15$		0			0
$16$	1.00000			0.250000
$17$	6.84527			1.66022			0.830110	−	0.557599i	$-0.188277\pi$
$17$	6.84527			1.66022			0.830110	+	0.557599i	$0.188277\pi$
$18$		0			0
$19$	−6.28540	+	3.62888i	−1.44197	+	0.832521i	−0.997981	−	0.0635114i	$-0.979770\pi$
$19$	−6.28540	+	3.62888i	−1.44197	+	0.832521i	−0.443988	+	0.896033i	$0.646437\pi$
$20$	0.967738	−	1.67617i	0.216393	−	0.374803i
$21$		0			0
$22$	−0.112015	+	0.194016i	−0.0238817	+	0.0413644i
$23$			1.42842i			0.297846i	0.988849	+	0.148923i	$0.0475807\pi$
$23$			1.42842i			0.297846i	−0.988849	+	0.148923i	$0.952419\pi$
$24$		0			0
$25$	0.626968	+	1.08594i	0.125394	+	0.217188i
$26$	1.12839	−	3.42443i	0.221296	−	0.671586i
$27$		0			0
$28$	−1.05411	+	2.42670i	−0.199208	+	0.458602i
$29$	−8.07070	+	4.65962i	−1.49869	+	0.865270i	−0.999999	−	0.00150900i	$-0.999520\pi$
$29$	−8.07070	+	4.65962i	−1.49869	+	0.865270i	−0.498693	+	0.866779i	$0.666186\pi$
$30$		0			0
$31$	−5.72173	+	3.30344i	−1.02765	+	0.593316i	−0.916312	−	0.400466i	$-0.868848\pi$
$31$	−5.72173	+	3.30344i	−1.02765	+	0.593316i	−0.111342	+	0.993782i	$0.535515\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$			6.84527i			1.17395i
$35$	3.04746	+	4.11527i	0.515114	+	0.695608i
$36$		0			0
$37$	−6.95504			−1.14340			−0.571700	−	0.820462i	$-0.693716\pi$
$37$	−6.95504			−1.14340			−0.571700	+	0.820462i	$0.693716\pi$
$38$	−3.62888	−	6.28540i	−0.588681	−	1.01963i
$39$		0			0
$40$	1.67617	+	0.967738i	0.265026	+	0.153013i
$41$	−2.78373	−	4.82157i	−0.434746	−	0.753003i	0.562529	−	0.826778i	$-0.309829\pi$
$41$	−2.78373	−	4.82157i	−0.434746	−	0.753003i	−0.997275	+	0.0737751i	$0.976495\pi$
$42$		0			0
$43$	5.05283	−	8.75176i	0.770549	−	1.33463i	−0.166713	−	0.986005i	$-0.553315\pi$
$43$	5.05283	−	8.75176i	0.770549	−	1.33463i	0.937262	−	0.348625i	$-0.113351\pi$
$44$	−0.194016	−	0.112015i	−0.0292490	−	0.0168869i
$45$		0			0
$46$	−1.42842			−0.210609
$47$	−3.56427	+	6.17349i	−0.519902	+	0.900496i	0.479831	+	0.877361i	$0.340698\pi$
$47$	−3.56427	+	6.17349i	−0.519902	+	0.900496i	−0.999732	+	0.0231348i	$0.992635\pi$
$48$		0			0
$49$	−4.77771	−	5.11601i	−0.682530	−	0.730858i
$50$	−1.08594	+	0.626968i	−0.153575	+	0.0886667i
$51$		0			0
$52$	3.42443	+	1.12839i	0.474883	+	0.156480i
$53$	2.20736	−	1.27442i	0.303204	−	0.175055i	−0.340677	−	0.940180i	$-0.610656\pi$
$53$	2.20736	−	1.27442i	0.303204	−	0.175055i	0.643881	+	0.765125i	$0.277323\pi$
$54$		0			0
$55$	−0.375514	+	0.216803i	−0.0506342	+	0.0292337i
$56$	−2.42670	−	1.05411i	−0.324281	−	0.140861i
$57$		0			0
$58$	−4.65962	−	8.07070i	−0.611838	−	1.05973i
$59$	−8.27164			−1.07688			−0.538438	−	0.842665i	$-0.680985\pi$
$59$	−8.27164			−1.07688			−0.538438	+	0.842665i	$0.680985\pi$
$60$		0			0
$61$	−10.7151	+	6.18639i	−1.37193	+	0.792086i	−0.991171	−	0.132587i	$-0.957672\pi$
$61$	−10.7151	+	6.18639i	−1.37193	+	0.792086i	−0.380762	+	0.924673i	$0.624338\pi$
$62$	−3.30344	−	5.72173i	−0.419538	−	0.726661i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	5.20533	−	4.64794i	0.645642	−	0.576506i
$66$		0			0
$67$	−1.20910	+	2.09421i	−0.147714	+	0.255849i	−0.930382	−	0.366591i	$-0.880525\pi$
$67$	−1.20910	+	2.09421i	−0.147714	+	0.255849i	0.782668	+	0.622440i	$0.213858\pi$
$68$	−6.84527			−0.830110
$69$		0			0
$70$	−4.11527	+	3.04746i	−0.491869	+	0.364241i
$71$	6.17036	+	3.56246i	0.732288	+	0.422786i	0.819258	−	0.573424i	$-0.194385\pi$
$71$	6.17036	+	3.56246i	0.732288	+	0.422786i	−0.0869709	+	0.996211i	$0.527719\pi$
$72$		0			0
$73$	10.3059	−	5.95012i	1.20622	−	0.696409i	0.244286	−	0.969703i	$-0.421447\pi$
$73$	10.3059	−	5.95012i	1.20622	−	0.696409i	0.961931	+	0.273294i	$0.0881132\pi$
$74$		−	6.95504i		−	0.808507i
$75$		0			0
$76$	6.28540	−	3.62888i	0.720985	−	0.416261i
$77$	0.476341	−	0.352742i	0.0542841	−	0.0401987i
$78$		0			0
$79$	−2.95621	+	5.12031i	−0.332600	+	0.576080i	−0.983021	−	0.183494i	$-0.941259\pi$
$79$	−2.95621	+	5.12031i	−0.332600	+	0.576080i	0.650421	+	0.759574i	$0.274593\pi$
$80$	−0.967738	+	1.67617i	−0.108196	+	0.187402i
$81$		0			0
$82$	4.82157	−	2.78373i	0.532453	−	0.307412i
$83$	9.37902			1.02948			0.514740	−	0.857346i	$-0.327888\pi$
$83$	9.37902			1.02948			0.514740	+	0.857346i	$0.327888\pi$
$84$		0			0
$85$	−6.62442	+	11.4738i	−0.718519	+	1.24451i
$86$	8.75176	+	5.05283i	0.943726	+	0.544861i
$87$		0			0
$88$	0.112015	−	0.194016i	0.0119409	−	0.0206822i
$89$	−9.12512			−0.967261			−0.483631	−	0.875272i	$-0.660682\pi$
$89$	−9.12512			−0.967261			−0.483631	+	0.875272i	$0.660682\pi$
$90$		0			0
$91$	−6.34799	+	7.12060i	−0.665451	+	0.746442i
$92$		−	1.42842i		−	0.148923i
$93$		0			0
$94$	−6.17349	−	3.56427i	−0.636747	−	0.367626i
$95$		−	14.0472i		−	1.44121i
$96$		0			0
$97$	−7.01412	−	4.04961i	−0.712176	−	0.411175i	0.0996900	−	0.995019i	$-0.468215\pi$
$97$	−7.01412	−	4.04961i	−0.712176	−	0.411175i	−0.811866	+	0.583843i	$0.801548\pi$
$98$	5.11601	−	4.77771i	0.516795	−	0.482621i
$99$		0			0
$100$	−0.626968	−	1.08594i	−0.0626968	−	0.108594i
$101$	7.58190	−	13.1322i	0.754427	−	1.30671i	−0.191231	−	0.981545i	$-0.561248\pi$
$101$	7.58190	−	13.1322i	0.754427	−	1.30671i	0.945658	−	0.325162i	$-0.105419\pi$
$102$		0			0
$103$	−6.95345	−	4.01457i	−0.685143	−	0.395568i	0.116647	−	0.993173i	$-0.462785\pi$
$103$	−6.95345	−	4.01457i	−0.685143	−	0.395568i	−0.801790	+	0.597606i	$0.796119\pi$
$104$	−1.12839	+	3.42443i	−0.110648	+	0.335793i
$105$		0			0
$106$	1.27442	+	2.20736i	0.123783	+	0.214398i
$107$			0.247828i			0.0239584i	0.999928	+	0.0119792i	$0.00381319\pi$
$107$			0.247828i			0.0239584i	−0.999928	+	0.0119792i	$0.996187\pi$
$108$		0			0
$109$	−4.70394	−	8.14746i	−0.450555	−	0.780385i	0.547865	−	0.836567i	$-0.315441\pi$
$109$	−4.70394	−	8.14746i	−0.450555	−	0.780385i	−0.998421	+	0.0561818i	$0.982107\pi$
$110$	−0.216803	−	0.375514i	−0.0206713	−	0.0358038i
$111$		0			0
$112$	1.05411	−	2.42670i	0.0996040	−	0.229301i
$113$	−1.42007	−	0.819879i	−0.133589	−	0.0771277i	0.431716	−	0.902010i	$-0.357908\pi$
$113$	−1.42007	−	0.819879i	−0.133589	−	0.0771277i	−0.565305	+	0.824882i	$0.691242\pi$
$114$		0			0
$115$	−2.39428	−	1.38234i	−0.223267	−	0.128903i
$116$	8.07070	−	4.65962i	0.749346	−	0.432635i
$117$		0			0
$118$		−	8.27164i		−	0.761466i
$119$	7.21566	−	16.6114i	0.661458	−	1.52276i
$120$		0			0
$121$	−5.47491	−	9.48281i	−0.497719	−	0.862074i
$122$	−6.18639	−	10.7151i	−0.560089	−	0.970103i
$123$		0			0
$124$	5.72173	−	3.30344i	0.513827	−	0.296658i
$125$	−12.1043			−1.08264
$126$		0			0
$127$	10.5988	+	18.3577i	0.940494	+	1.62898i	0.764531	+	0.644587i	$0.222971\pi$
$127$	10.5988	+	18.3577i	0.940494	+	1.62898i	0.175964	+	0.984397i	$0.443696\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	4.64794	+	5.20533i	0.407651	+	0.456538i
$131$	−5.75920	+	9.97522i	−0.503183	+	0.871539i	0.496810	+	0.867859i	$0.334505\pi$
$131$	−5.75920	+	9.97522i	−0.503183	+	0.871539i	−0.999993	+	0.00367964i	$0.998829\pi$
$132$		0			0
$133$	2.18068	+	19.0780i	0.189089	+	1.65427i
$134$	−2.09421	−	1.20910i	−0.180913	−	0.104450i
$135$		0			0
$136$		−	6.84527i		−	0.586977i
$137$			6.96539i			0.595094i	0.954707	+	0.297547i	$0.0961684\pi$
$137$			6.96539i			0.595094i	−0.954707	+	0.297547i	$0.903832\pi$
$138$		0			0
$139$	2.75339	+	1.58967i	0.233539	+	0.134834i	0.612204	−	0.790700i	$-0.290283\pi$
$139$	2.75339	+	1.58967i	0.233539	+	0.134834i	−0.378665	+	0.925534i	$0.623617\pi$
$140$	−3.04746	−	4.11527i	−0.257557	−	0.347804i
$141$		0			0
$142$	−3.56246	+	6.17036i	−0.298955	+	0.517806i
$143$	−0.537998	−	0.602516i	−0.0449896	−	0.0503849i
$144$		0			0
$145$		−	18.0372i		−	1.49790i
$146$	5.95012	+	10.3059i	0.492436	+	0.852924i
$147$		0			0
$148$	6.95504			0.571700
$149$	−12.2823	+	7.09118i	−1.00620	+	0.580932i	−0.910078	−	0.414437i	$-0.863979\pi$
$149$	−12.2823	+	7.09118i	−1.00620	+	0.580932i	−0.0961261	+	0.995369i	$0.530645\pi$
$150$		0			0
$151$	−5.93638	−	10.2821i	−0.483096	−	0.836747i	0.516716	−	0.856157i	$-0.327154\pi$
$151$	−5.93638	−	10.2821i	−0.483096	−	0.836747i	−0.999812	+	0.0194104i	$0.993821\pi$
$152$	3.62888	+	6.28540i	0.294341	+	0.509813i
$153$		0			0
$154$	0.352742	+	0.476341i	0.0284248	+	0.0383847i
$155$		−	12.7875i		−	1.02711i
$156$		0			0
$157$	−20.2256	+	11.6773i	−1.61418	+	0.931948i	−0.625794	+	0.779988i	$0.715225\pi$
$157$	−20.2256	+	11.6773i	−1.61418	+	0.931948i	−0.988387	+	0.151960i	$0.951442\pi$
$158$	−5.12031	−	2.95621i	−0.407350	−	0.235184i
$159$		0			0
$160$	−1.67617	−	0.967738i	−0.132513	−	0.0765064i
$161$	3.46634	+	1.50571i	0.273186	+	0.118667i
$162$		0			0
$163$	−9.69822	−	16.7978i	−0.759623	−	1.31571i	−0.943043	−	0.332671i	$-0.892050\pi$
$163$	−9.69822	−	16.7978i	−0.759623	−	1.31571i	0.183420	−	0.983035i	$-0.441283\pi$
$164$	2.78373	+	4.82157i	0.217373	+	0.376501i
$165$		0			0
$166$			9.37902i			0.727953i
$167$	7.24188	+	12.5433i	0.560394	+	0.970630i	0.997462	+	0.0712018i	$0.0226834\pi$
$167$	7.24188	+	12.5433i	0.560394	+	0.970630i	−0.437068	+	0.899428i	$0.643983\pi$
$168$		0			0
$169$	10.4535	+	7.72822i	0.804112	+	0.594478i
$170$	−11.4738	−	6.62442i	−0.880003	−	0.508070i
$171$		0			0
$172$	−5.05283	+	8.75176i	−0.385275	+	0.667315i
$173$	4.30098	+	7.44952i	0.326997	+	0.566376i	0.981915	−	0.189324i	$-0.0606298\pi$
$173$	4.30098	+	7.44952i	0.326997	+	0.566376i	−0.654917	+	0.755701i	$0.727296\pi$
$174$		0			0
$175$	3.29614	−	0.376761i	0.249165	−	0.0284805i
$176$	0.194016	+	0.112015i	0.0146245	+	0.00844347i
$177$		0			0
$178$		−	9.12512i		−	0.683957i
$179$	16.5969	+	9.58221i	1.24051	+	0.716208i	0.969198	−	0.246284i	$-0.0792096\pi$
$179$	16.5969	+	9.58221i	1.24051	+	0.716208i	0.271311	+	0.962492i	$0.412543\pi$
$180$		0			0
$181$			4.92120i			0.365790i	0.983132	+	0.182895i	$0.0585468\pi$
$181$			4.92120i			0.365790i	−0.983132	+	0.182895i	$0.941453\pi$
$182$	−7.12060	−	6.34799i	−0.527814	−	0.470545i
$183$		0			0
$184$	1.42842			0.105305
$185$	6.73065	−	11.6578i	0.494847	−	0.857100i
$186$		0			0
$187$	1.32809	+	0.766775i	0.0971198	+	0.0560721i
$188$	3.56427	−	6.17349i	0.259951	−	0.450248i
$189$		0			0
$190$	14.0472			1.01909
$191$	6.99433	−	4.03818i	0.506092	−	0.292192i	−0.225134	−	0.974328i	$-0.572282\pi$
$191$	6.99433	−	4.03818i	0.506092	−	0.292192i	0.731226	+	0.682136i	$0.238949\pi$
$192$		0			0
$193$	5.94575	−	10.2983i	0.427985	−	0.741291i	−0.568709	−	0.822539i	$-0.692557\pi$
$193$	5.94575	−	10.2983i	0.427985	−	0.741291i	0.996694	+	0.0812475i	$0.0258904\pi$
$194$	4.04961	−	7.01412i	0.290745	−	0.503585i
$195$		0			0
$196$	4.77771	+	5.11601i	0.341265	+	0.365429i
$197$	−7.59842	+	4.38695i	−0.541365	+	0.312557i	−0.745632	−	0.666358i	$-0.767852\pi$
$197$	−7.59842	+	4.38695i	−0.541365	+	0.312557i	0.204267	+	0.978915i	$0.434519\pi$
$198$		0			0
$199$			1.86218i			0.132006i	0.997819	+	0.0660031i	$0.0210247\pi$
$199$			1.86218i			0.132006i	−0.997819	+	0.0660031i	$0.978975\pi$
$200$	1.08594	−	0.626968i	0.0767876	−	0.0443333i
$201$		0			0
$202$	13.1322	+	7.58190i	0.923981	+	0.533461i
$203$	2.80008	+	24.4969i	0.196527	+	1.71934i
$204$		0			0
$205$	10.7757			0.752607
$206$	4.01457	−	6.95345i	0.279709	−	0.484470i
$207$		0			0
$208$	−3.42443	−	1.12839i	−0.237442	−	0.0782401i
$209$	−1.62596			−0.112470
$210$		0			0
$211$	−7.81359	−	13.5335i	−0.537909	−	0.931686i	−0.999016	−	0.0443419i	$-0.985881\pi$
$211$	−7.81359	−	13.5335i	−0.537909	−	0.931686i	0.461107	−	0.887345i	$-0.347452\pi$
$212$	−2.20736	+	1.27442i	−0.151602	+	0.0875275i
$213$		0			0
$214$	−0.247828			−0.0169412
$215$	9.77963	+	16.9388i	0.666965	+	1.15522i
$216$		0			0
$217$	1.98512	+	17.3671i	0.134759	+	1.17896i
$218$	8.14746	−	4.70394i	0.551815	−	0.318591i
$219$		0			0
$220$	0.375514	−	0.216803i	0.0253171	−	0.0146168i
$221$	−23.4411	−	7.72416i	−1.57682	−	0.519583i
$222$		0			0
$223$	3.19762	−	1.84615i	0.214128	−	0.123627i	−0.389100	−	0.921195i	$-0.627214\pi$
$223$	3.19762	−	1.84615i	0.214128	−	0.123627i	0.603229	+	0.797568i	$0.293881\pi$
$224$	2.42670	+	1.05411i	0.162140	+	0.0704306i
$225$		0			0
$226$	0.819879	−	1.42007i	0.0545375	−	0.0944618i
$227$	−19.0034			−1.26130			−0.630650	−	0.776068i	$-0.717211\pi$
$227$	−19.0034			−1.26130			−0.630650	+	0.776068i	$0.717211\pi$
$228$		0			0
$229$	20.5951	+	11.8906i	1.36096	+	0.785753i	0.989752	−	0.142795i	$-0.0456088\pi$
$229$	20.5951	+	11.8906i	1.36096	+	0.785753i	0.371212	+	0.928548i	$0.378942\pi$
$230$	1.38234	−	2.39428i	0.0911485	−	0.157874i
$231$		0			0
$232$	4.65962	+	8.07070i	0.305919	+	0.529867i
$233$	−8.51390	−	4.91550i	−0.557764	−	0.322025i	0.194484	−	0.980906i	$-0.437697\pi$
$233$	−8.51390	−	4.91550i	−0.557764	−	0.322025i	−0.752247	+	0.658881i	$0.771030\pi$
$234$		0			0
$235$	−6.89855	−	11.9486i	−0.450012	−	0.779443i
$236$	8.27164			0.538438
$237$		0			0
$238$	16.6114	+	7.21566i	1.07676	+	0.467722i
$239$			11.4665i			0.741708i	0.928691	+	0.370854i	$0.120935\pi$
$239$			11.4665i			0.741708i	−0.928691	+	0.370854i	$0.879065\pi$
$240$		0			0
$241$			5.21381i			0.335851i	0.985800	+	0.167925i	$0.0537068\pi$
$241$			5.21381i			0.335851i	−0.985800	+	0.167925i	$0.946293\pi$
$242$	9.48281	−	5.47491i	0.609578	−	0.351940i
$243$		0			0
$244$	10.7151	−	6.18639i	0.685967	−	0.396043i
$245$	13.1989	−	3.05730i	0.843245	−	0.195324i
$246$		0			0
$247$	25.6187	−	5.33443i	1.63008	−	0.339421i
$248$	3.30344	+	5.72173i	0.209769	+	0.363330i
$249$		0			0
$250$		−	12.1043i		−	0.765546i
$251$	−14.4634	+	25.0514i	−0.912922	+	1.58123i	−0.103007	+	0.994681i	$0.532846\pi$
$251$	−14.4634	+	25.0514i	−0.912922	+	1.58123i	−0.809915	+	0.586547i	$0.800487\pi$
$252$		0			0
$253$	−0.160005	+	0.277137i	−0.0100594	+	0.0174234i
$254$	−18.3577	+	10.5988i	−1.15187	+	0.665030i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−13.8934			−0.866649			−0.433325	−	0.901238i	$-0.642660\pi$
$257$	−13.8934			−0.866649			−0.433325	+	0.901238i	$0.642660\pi$
$258$		0			0
$259$	−7.33137	+	16.8778i	−0.455549	+	1.04873i
$260$	−5.20533	+	4.64794i	−0.322821	+	0.288253i
$261$		0			0
$262$	−9.97522	−	5.75920i	−0.616271	−	0.355804i
$263$	24.0993	+	13.9137i	1.48603	+	0.857958i	0.999873	−	0.0159146i	$-0.00506599\pi$
$263$	24.0993	+	13.9137i	1.48603	+	0.857958i	0.486154	+	0.873873i	$0.338399\pi$
$264$		0			0
$265$			4.93321i			0.303045i
$266$	−19.0780	+	2.18068i	−1.16975	+	0.133706i
$267$		0			0
$268$	1.20910	−	2.09421i	0.0738572	−	0.127925i
$269$	6.17002			0.376192			0.188096	−	0.982151i	$-0.439768\pi$
$269$	6.17002			0.376192			0.188096	+	0.982151i	$0.439768\pi$
$270$		0			0
$271$			20.3203i			1.23437i	0.786819	+	0.617184i	$0.211727\pi$
$271$			20.3203i			1.23437i	−0.786819	+	0.617184i	$0.788273\pi$
$272$	6.84527			0.415055
$273$		0			0
$274$	−6.96539			−0.420795
$275$			0.280920i			0.0169401i
$276$		0			0
$277$	30.4294			1.82833			0.914163	−	0.405347i	$-0.132849\pi$
$277$	30.4294			1.82833			0.914163	+	0.405347i	$0.132849\pi$
$278$	−1.58967	+	2.75339i	−0.0953419	+	0.165137i
$279$		0			0
$280$	4.11527	−	3.04746i	0.245935	−	0.182120i
$281$		−	19.6770i		−	1.17383i	−0.809647	−	0.586917i	$-0.800341\pi$
$281$		−	19.6770i		−	1.17383i	0.809647	−	0.586917i	$-0.199659\pi$
$282$		0			0
$283$	−7.27518	−	4.20033i	−0.432464	−	0.249683i	0.267932	−	0.963438i	$-0.413660\pi$
$283$	−7.27518	−	4.20033i	−0.432464	−	0.249683i	−0.700396	+	0.713754i	$0.746993\pi$
$284$	−6.17036	−	3.56246i	−0.366144	−	0.211393i
$285$		0			0
$286$	0.602516	−	0.537998i	0.0356275	−	0.0318125i
$287$	−14.6348	+	1.67282i	−0.863868	+	0.0987433i
$288$		0			0
$289$	29.8577			1.75633
$290$	18.0372			1.05918
$291$		0			0
$292$	−10.3059	+	5.95012i	−0.603108	+	0.348205i
$293$	12.9505	−	22.4309i	0.756577	−	1.31043i	−0.188010	−	0.982167i	$-0.560204\pi$
$293$	12.9505	−	22.4309i	0.756577	−	1.31043i	0.944587	−	0.328262i	$-0.106463\pi$
$294$		0			0
$295$	8.00477	−	13.8647i	0.466056	−	0.807233i
$296$			6.95504i			0.404253i
$297$		0			0
$298$	−7.09118	−	12.2823i	−0.410781	−	0.711494i
$299$	1.61182	−	4.89153i	0.0932140	−	0.282884i
$300$		0			0
$301$	−15.9116	−	21.4870i	−0.917131	−	1.23849i
$302$	10.2821	−	5.93638i	0.591669	−	0.341600i
$303$		0			0
$304$	−6.28540	+	3.62888i	−0.360492	+	0.208130i
$305$		−	23.9472i		−	1.37121i
$306$		0			0
$307$		−	18.9300i		−	1.08039i	−0.841540	−	0.540195i	$-0.818350\pi$
$307$		−	18.9300i		−	1.08039i	0.841540	−	0.540195i	$-0.181650\pi$
$308$	−0.476341	+	0.352742i	−0.0271421	+	0.0200993i
$309$		0			0
$310$	12.7875			0.726279
$311$	−5.25637	−	9.10430i	−0.298061	−	0.516258i	0.677631	−	0.735402i	$-0.263007\pi$
$311$	−5.25637	−	9.10430i	−0.298061	−	0.516258i	−0.975692	+	0.219145i	$0.929673\pi$
$312$		0			0
$313$	−3.63388	−	2.09802i	−0.205399	−	0.118587i	0.393772	−	0.919208i	$-0.371170\pi$
$313$	−3.63388	−	2.09802i	−0.205399	−	0.118587i	−0.599171	+	0.800621i	$0.704503\pi$
$314$	−11.6773	−	20.2256i	−0.658987	−	1.14140i
$315$		0			0
$316$	2.95621	−	5.12031i	0.166300	−	0.288040i
$317$	18.0322	+	10.4109i	1.01279	+	0.584735i	0.912007	−	0.410174i	$-0.134532\pi$
$317$	18.0322	+	10.4109i	1.01279	+	0.584735i	0.100783	+	0.994908i	$0.467865\pi$
$318$		0			0
$319$	−2.08780			−0.116894
$320$	0.967738	−	1.67617i	0.0540982	−	0.0937008i
$321$		0			0
$322$	−1.50571	+	3.46634i	−0.0839100	+	0.193172i
$323$	−43.0252	+	24.8406i	−2.39399	+	1.38217i
$324$		0			0
$325$	−0.921640	−	4.42620i	−0.0511234	−	0.245521i
$326$	16.7978	−	9.69822i	0.930344	−	0.537135i
$327$		0			0
$328$	−4.82157	+	2.78373i	−0.266227	+	0.153706i
$329$	11.2241	+	15.1569i	0.618802	+	0.835628i
$330$		0			0
$331$	3.58458	+	6.20867i	0.197026	+	0.341259i	0.947563	−	0.319569i	$-0.103538\pi$
$331$	3.58458	+	6.20867i	0.197026	+	0.341259i	−0.750537	+	0.660829i	$0.770205\pi$
$332$	−9.37902			−0.514740
$333$		0			0
$334$	−12.5433	+	7.24188i	−0.686339	+	0.396258i
$335$	−2.34017	−	4.05330i	−0.127857	−	0.221455i
$336$		0			0
$337$	9.27518			0.505251			0.252626	−	0.967564i	$-0.418706\pi$
$337$	9.27518			0.505251			0.252626	+	0.967564i	$0.418706\pi$
$338$	−7.72822	+	10.4535i	−0.420360	+	0.568593i
$339$		0			0
$340$	6.62442	−	11.4738i	0.359260	−	0.622256i
$341$	−1.48015			−0.0801544
$342$		0			0
$343$	−17.4512	+	6.20122i	−0.942277	+	0.334834i
$344$	−8.75176	−	5.05283i	−0.471863	−	0.272430i
$345$		0			0
$346$	−7.44952	+	4.30098i	−0.400488	+	0.231222i
$347$			31.3426i			1.68256i	0.540602	+	0.841278i	$0.318196\pi$
$347$			31.3426i			1.68256i	−0.540602	+	0.841278i	$0.681804\pi$
$348$		0			0
$349$	14.7905	−	8.53929i	0.791716	−	0.457098i	−0.0488502	−	0.998806i	$-0.515556\pi$
$349$	14.7905	−	8.53929i	0.791716	−	0.457098i	0.840566	+	0.541709i	$0.182222\pi$
$350$	0.376761	+	3.29614i	0.0201387	+	0.176186i
$351$		0			0
$352$	−0.112015	+	0.194016i	−0.00597044	+	0.0103411i
$353$	−0.789015	+	1.36661i	−0.0419950	+	0.0727375i	−0.886259	−	0.463190i	$-0.846705\pi$
$353$	−0.789015	+	1.36661i	−0.0419950	+	0.0727375i	0.844264	+	0.535928i	$0.180038\pi$
$354$		0			0
$355$	−11.9426	+	6.89506i	−0.633847	+	0.365952i
$356$	9.12512			0.483631
$357$		0			0
$358$	−9.58221	+	16.5969i	−0.506435	+	0.877172i
$359$	−5.52884	−	3.19207i	−0.291801	−	0.168471i	0.346953	−	0.937883i	$-0.387216\pi$
$359$	−5.52884	−	3.19207i	−0.291801	−	0.168471i	−0.638754	+	0.769411i	$0.720550\pi$
$360$		0			0
$361$	16.8375	−	29.1634i	0.886183	−	1.53491i
$362$	−4.92120			−0.258652
$363$		0			0
$364$	6.34799	−	7.12060i	0.332725	−	0.373221i
$365$			23.0326i			1.20558i
$366$		0			0
$367$	−5.36640	−	3.09829i	−0.280124	−	0.161730i	0.353356	−	0.935489i	$-0.385041\pi$
$367$	−5.36640	−	3.09829i	−0.280124	−	0.161730i	−0.633480	+	0.773759i	$0.718374\pi$
$368$			1.42842i			0.0744615i
$369$		0			0
$370$	11.6578	+	6.73065i	0.606062	+	0.349910i
$371$	−0.765831	−	6.69997i	−0.0397600	−	0.347845i
$372$		0			0
$373$	−10.2007	−	17.6682i	−0.528174	−	0.914824i	−0.999460	−	0.0328439i	$-0.989544\pi$
$373$	−10.2007	−	17.6682i	−0.528174	−	0.914824i	0.471287	−	0.881980i	$-0.343790\pi$
$374$	−0.766775	+	1.32809i	−0.0396490	+	0.0686740i
$375$		0			0
$376$	6.17349	+	3.56427i	0.318373	+	0.183813i
$377$	32.8954	−	6.84962i	1.69420	−	0.352773i
$378$		0			0
$379$	−1.42478	−	2.46779i	−0.0731859	−	0.126762i	0.827110	−	0.562040i	$-0.189983\pi$
$379$	−1.42478	−	2.46779i	−0.0731859	−	0.126762i	−0.900296	+	0.435278i	$0.856650\pi$
$380$			14.0472i			0.720606i
$381$		0			0
$382$	4.03818	+	6.99433i	0.206611	+	0.357861i
$383$	11.5853	+	20.0664i	0.591983	+	1.02534i	0.993965	+	0.109697i	$0.0349880\pi$
$383$	11.5853	+	20.0664i	0.591983	+	1.02534i	−0.401982	+	0.915647i	$0.631679\pi$
$384$		0			0
$385$	0.130282	+	1.13979i	0.00663980	+	0.0580891i
$386$	10.2983	+	5.94575i	0.524172	+	0.302631i
$387$		0			0
$388$	7.01412	+	4.04961i	0.356088	+	0.205588i
$389$	33.4771	−	19.3280i	1.69735	−	0.979968i	0.749100	−	0.662457i	$-0.230486\pi$
$389$	33.4771	−	19.3280i	1.69735	−	0.979968i	0.948255	−	0.317511i	$-0.102847\pi$
$390$		0			0
$391$			9.77792i			0.494490i
$392$	−5.11601	+	4.77771i	−0.258397	+	0.241311i
$393$		0			0
$394$	−4.38695	−	7.59842i	−0.221011	−	0.382803i
$395$	−5.72168	−	9.91024i	−0.287889	−	0.498638i
$396$		0			0
$397$	4.15762	−	2.40040i	0.208665	−	0.120473i	−0.392026	−	0.919954i	$-0.628226\pi$
$397$	4.15762	−	2.40040i	0.208665	−	0.120473i	0.600691	+	0.799481i	$0.294892\pi$
$398$	−1.86218			−0.0933425
$399$		0			0
$400$	0.626968	+	1.08594i	0.0313484	+	0.0542970i
$401$			5.70246i			0.284767i	0.989812	+	0.142384i	$0.0454767\pi$
$401$			5.70246i			0.284767i	−0.989812	+	0.142384i	$0.954523\pi$
$402$		0			0
$403$	23.3213	−	4.85604i	1.16172	−	0.241897i
$404$	−7.58190	+	13.1322i	−0.377214	+	0.653353i
$405$		0			0
$406$	−24.4969	+	2.80008i	−1.21576	+	0.138966i
$407$	−1.34939	−	0.779071i	−0.0668868	−	0.0386171i
$408$		0			0
$409$			8.24506i			0.407692i	0.979003	+	0.203846i	$0.0653442\pi$
$409$			8.24506i			0.407692i	−0.979003	+	0.203846i	$0.934656\pi$
$410$			10.7757i			0.532174i
$411$		0			0
$412$	6.95345	+	4.01457i	0.342572	+	0.197784i
$413$	−8.71921	+	20.0728i	−0.429044	+	0.987716i
$414$		0			0
$415$	−9.07643	+	15.7208i	−0.445544	+	0.771705i
$416$	1.12839	−	3.42443i	0.0553241	−	0.167897i
$417$		0			0
$418$		−	1.62596i		−	0.0795282i
$419$	13.0751	+	22.6468i	0.638762	+	1.10637i	0.985705	+	0.168482i	$0.0538865\pi$
$419$	13.0751	+	22.6468i	0.638762	+	1.10637i	−0.346943	+	0.937886i	$0.612780\pi$
$420$		0			0
$421$	−1.13645			−0.0553872			−0.0276936	−	0.999616i	$-0.508816\pi$
$421$	−1.13645			−0.0553872			−0.0276936	+	0.999616i	$0.508816\pi$
$422$	13.5335	−	7.81359i	0.658802	−	0.380359i
$423$		0			0
$424$	−1.27442	−	2.20736i	−0.0618913	−	0.107199i
$425$	4.29176	+	7.43355i	0.208181	+	0.360580i
$426$		0			0
$427$	3.71756	+	32.5235i	0.179905	+	1.57392i
$428$		−	0.247828i		−	0.0119792i
$429$		0			0
$430$	−16.9388	+	9.77963i	−0.816862	+	0.471615i
$431$	12.7531	+	7.36299i	0.614294	+	0.354663i	0.774644	−	0.632397i	$-0.217929\pi$
$431$	12.7531	+	7.36299i	0.614294	+	0.354663i	−0.160350	+	0.987060i	$0.551262\pi$
$432$		0			0
$433$	2.98079	+	1.72096i	0.143247	+	0.0827040i	0.569911	−	0.821707i	$-0.306978\pi$
$433$	2.98079	+	1.72096i	0.143247	+	0.0827040i	−0.426663	+	0.904411i	$0.640311\pi$
$434$	−17.3671	+	1.98512i	−0.833648	+	0.0952890i
$435$		0			0
$436$	4.70394	+	8.14746i	0.225278	+	0.390192i
$437$	−5.18356	−	8.97819i	−0.247963	−	0.429485i
$438$		0			0
$439$			5.06111i			0.241553i	0.992680	+	0.120777i	$0.0385385\pi$
$439$			5.06111i			0.241553i	−0.992680	+	0.120777i	$0.961461\pi$
$440$	0.216803	+	0.375514i	0.0103357	+	0.0179019i
$441$		0			0
$442$	7.72416	−	23.4411i	0.367401	−	1.11498i
$443$	−14.6889	−	8.48064i	−0.697891	−	0.402927i	0.108671	−	0.994078i	$-0.465341\pi$
$443$	−14.6889	−	8.48064i	−0.697891	−	0.402927i	−0.806561	+	0.591150i	$0.798674\pi$
$444$		0			0
$445$	8.83073	−	15.2953i	0.418617	−	0.725065i
$446$	1.84615	+	3.19762i	0.0874175	+	0.151412i
$447$		0			0
$448$	−1.05411	+	2.42670i	−0.0498020	+	0.114651i
$449$	−6.33282	−	3.65625i	−0.298864	−	0.172549i	0.343068	−	0.939310i	$-0.388534\pi$
$449$	−6.33282	−	3.65625i	−0.298864	−	0.172549i	−0.641933	+	0.766761i	$0.721867\pi$
$450$		0			0
$451$		−	1.24728i		−	0.0587323i
$452$	1.42007	+	0.819879i	0.0667946	+	0.0385639i
$453$		0			0
$454$		−	19.0034i		−	0.891873i
$455$	−5.79215	−	17.5312i	−0.271540	−	0.821875i
$456$		0			0
$457$	37.8232			1.76929			0.884647	−	0.466262i	$-0.154399\pi$
$457$	37.8232			1.76929			0.884647	+	0.466262i	$0.154399\pi$
$458$	−11.8906	+	20.5951i	−0.555612	+	0.962347i
$459$		0			0
$460$	2.39428	+	1.38234i	0.111634	+	0.0644517i
$461$	−16.7657	+	29.0391i	−0.780857	+	1.35248i	0.150586	+	0.988597i	$0.451884\pi$
$461$	−16.7657	+	29.0391i	−0.780857	+	1.35248i	−0.931443	+	0.363887i	$0.881449\pi$
$462$		0			0
$463$	9.05246			0.420704			0.210352	−	0.977626i	$-0.432539\pi$
$463$	9.05246			0.420704			0.210352	+	0.977626i	$0.432539\pi$
$464$	−8.07070	+	4.65962i	−0.374673	+	0.216317i
$465$		0			0
$466$	4.91550	−	8.51390i	0.227706	−	0.394399i
$467$	9.08764	−	15.7403i	0.420526	−	0.728372i	−0.575465	−	0.817826i	$-0.695179\pi$
$467$	9.08764	−	15.7403i	0.420526	−	0.728372i	0.995991	+	0.0894543i	$0.0285123\pi$
$468$		0			0
$469$	3.80750	+	5.14164i	0.175814	+	0.237419i
$470$	11.9486	−	6.89855i	0.551149	−	0.318206i
$471$		0			0
$472$			8.27164i			0.380733i
$473$	1.96066	−	1.13199i	0.0901513	−	0.0520489i
$474$		0			0
$475$	−7.88149	−	4.55038i	−0.361628	−	0.208786i
$476$	−7.21566	+	16.6114i	−0.330729	+	0.761381i
$477$		0			0
$478$	−11.4665			−0.524467
$479$	−14.0816	+	24.3900i	−0.643402	+	1.11441i	0.341266	+	0.939967i	$0.389144\pi$
$479$	−14.0816	+	24.3900i	−0.643402	+	1.11441i	−0.984668	+	0.174439i	$0.944189\pi$
$480$		0			0
$481$	23.8170	+	7.84802i	1.08596	+	0.357839i
$482$	−5.21381			−0.237482
$483$		0			0
$484$	5.47491	+	9.48281i	0.248859	+	0.431037i
$485$	13.5757	−	7.83791i	0.616439	−	0.355901i
$486$		0			0
$487$	−35.3211			−1.60055			−0.800275	−	0.599633i	$-0.795313\pi$
$487$	−35.3211			−1.60055			−0.800275	+	0.599633i	$0.795313\pi$
$488$	6.18639	+	10.7151i	0.280045	+	0.485052i
$489$		0			0
$490$	3.05730	+	13.1989i	0.138115	+	0.596264i
$491$	−9.34266	+	5.39399i	−0.421629	+	0.243427i	−0.695774	−	0.718261i	$-0.744938\pi$
$491$	−9.34266	+	5.39399i	−0.421629	+	0.243427i	0.274145	+	0.961688i	$0.411605\pi$
$492$		0			0
$493$	−55.2461	+	31.8963i	−2.48816	+	1.43654i
$494$	5.33443	+	25.6187i	0.240007	+	1.15264i
$495$		0			0
$496$	−5.72173	+	3.30344i	−0.256913	+	0.148329i
$497$	15.1493	−	11.2184i	0.679537	−	0.503213i
$498$		0			0
$499$	0.366130	−	0.634156i	0.0163902	−	0.0283887i	−0.857714	−	0.514127i	$-0.828116\pi$
$499$	0.366130	−	0.634156i	0.0163902	−	0.0283887i	0.874104	+	0.485738i	$0.161449\pi$
$500$	12.1043			0.541322
$501$		0			0
$502$	−25.0514	−	14.4634i	−1.11810	−	0.645533i
$503$	−4.79756	+	8.30962i	−0.213913	+	0.370508i	−0.952936	−	0.303173i	$-0.901954\pi$
$503$	−4.79756	+	8.30962i	−0.213913	+	0.370508i	0.739023	+	0.673680i	$0.235287\pi$
$504$		0			0
$505$	14.6746	+	25.4171i	0.653010	+	1.13105i
$506$	−0.277137	−	0.160005i	−0.0123202	−	0.00711309i
$507$		0			0
$508$	−10.5988	−	18.3577i	−0.470247	−	0.814492i
$509$	−5.50661			−0.244076			−0.122038	−	0.992525i	$-0.538943\pi$
$509$	−5.50661			−0.244076			−0.122038	+	0.992525i	$0.538943\pi$
$510$		0			0
$511$	−3.57558	−	31.2814i	−0.158174	−	1.38381i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	13.8934i		−	0.612814i
$515$	13.4582	−	7.77011i	0.593040	−	0.342392i
$516$		0			0
$517$	−1.38305	+	0.798505i	−0.0608265	+	0.0351182i
$518$	−16.8778	−	7.33137i	−0.741566	−	0.322122i
$519$		0			0
$520$	−4.64794	−	5.20533i	−0.203826	−	0.228269i
$521$	−6.18410	−	10.7112i	−0.270930	−	0.469265i	0.698170	−	0.715932i	$-0.253998\pi$
$521$	−6.18410	−	10.7112i	−0.270930	−	0.469265i	−0.969100	+	0.246667i	$0.920665\pi$
$522$		0			0
$523$		−	19.5053i		−	0.852907i	−0.904509	−	0.426454i	$-0.859763\pi$
$523$		−	19.5053i		−	0.852907i	0.904509	−	0.426454i	$-0.140237\pi$
$524$	5.75920	−	9.97522i	0.251592	−	0.435770i
$525$		0			0
$526$	−13.9137	+	24.0993i	−0.606668	+	1.05078i
$527$	−39.1668	+	22.6130i	−1.70613	+	0.985036i
$528$		0			0
$529$	20.9596			0.911288
$530$	−4.93321			−0.214285
$531$		0			0
$532$	−2.18068	−	19.0780i	−0.0945446	−	0.827135i
$533$	4.09207	+	19.6523i	0.177247	+	0.851235i
$534$		0			0
$535$	−0.415402	−	0.239832i	−0.0179594	−	0.0103689i
$536$	2.09421	+	1.20910i	0.0904563	+	0.0522250i
$537$		0			0
$538$			6.17002i			0.266008i
$539$	−0.353882	−	1.52776i	−0.0152428	−	0.0658055i
$540$		0			0
$541$	2.79274	−	4.83716i	0.120069	−	0.207966i	−0.799726	−	0.600366i	$-0.795022\pi$
$541$	2.79274	−	4.83716i	0.120069	−	0.207966i	0.919795	+	0.392400i	$0.128355\pi$
$542$	−20.3203			−0.872830
$543$		0			0
$544$			6.84527i			0.293488i
$545$	18.2087			0.779975
$546$		0			0
$547$	2.96145			0.126622			0.0633112	−	0.997994i	$-0.479834\pi$
$547$	2.96145			0.126622			0.0633112	+	0.997994i	$0.479834\pi$
$548$		−	6.96539i		−	0.297547i
$549$		0			0
$550$	−0.280920			−0.0119785
$551$	33.8184	−	58.5751i	1.44071	−	2.49539i
$552$		0			0
$553$	9.30927	+	12.5712i	0.395870	+	0.534582i
$554$			30.4294i			1.29282i
$555$		0			0
$556$	−2.75339	−	1.58967i	−0.116770	−	0.0674169i
$557$	−11.8743	−	6.85566i	−0.503132	−	0.290484i	0.226874	−	0.973924i	$-0.427149\pi$
$557$	−11.8743	−	6.85566i	−0.503132	−	0.290484i	−0.730006	+	0.683441i	$0.760483\pi$
$558$		0			0
$559$	−27.1785	+	24.2682i	−1.14953	+	1.02644i
$560$	3.04746	+	4.11527i	0.128778	+	0.173902i
$561$		0			0
$562$	19.6770			0.830026
$563$	9.03631			0.380835			0.190418	−	0.981703i	$-0.439016\pi$
$563$	9.03631			0.380835			0.190418	+	0.981703i	$0.439016\pi$
$564$		0			0
$565$	2.74851	−	1.58686i	0.115631	−	0.0667595i
$566$	4.20033	−	7.27518i	0.176553	−	0.305799i
$567$		0			0
$568$	3.56246	−	6.17036i	0.149478	−	0.258903i
$569$		−	9.37636i		−	0.393078i	−0.980496	−	0.196539i	$-0.937030\pi$
$569$		−	9.37636i		−	0.393078i	0.980496	−	0.196539i	$-0.0629702\pi$
$570$		0			0
$571$	11.2933	+	19.5605i	0.472609	+	0.818583i	0.999509	−	0.0313444i	$-0.00997887\pi$
$571$	11.2933	+	19.5605i	0.472609	+	0.818583i	−0.526899	+	0.849928i	$0.676646\pi$
$572$	0.537998	+	0.602516i	0.0224948	+	0.0251924i
$573$		0			0
$574$	−1.67282	−	14.6348i	−0.0698220	−	0.610847i
$575$	−1.55118	+	0.895574i	−0.0646887	+	0.0373480i
$576$		0			0
$577$	−28.7868	+	16.6201i	−1.19841	+	0.691903i	−0.960201	−	0.279311i	$-0.909894\pi$
$577$	−28.7868	+	16.6201i	−1.19841	+	0.691903i	−0.238210	+	0.971214i	$0.576561\pi$
$578$			29.8577i			1.24192i
$579$		0			0
$580$			18.0372i			0.748952i
$581$	9.88651	−	22.7600i	0.410161	−	0.944245i
$582$		0			0
$583$	0.571018			0.0236492
$584$	−5.95012	−	10.3059i	−0.246218	−	0.426462i
$585$		0			0
$586$	22.4309	+	12.9505i	0.926614	+	0.534981i
$587$	7.64647	+	13.2441i	0.315604	+	0.546642i	0.979566	−	0.201125i	$-0.0644597\pi$
$587$	7.64647	+	13.2441i	0.315604	+	0.546642i	−0.663962	+	0.747766i	$0.731126\pi$
$588$		0			0
$589$	23.9756	−	41.5269i	0.987897	−	1.71109i
$590$	13.8647	+	8.00477i	0.570800	+	0.329551i
$591$		0			0
$592$	−6.95504			−0.285850
$593$	−17.0042	+	29.4521i	−0.698279	+	1.20945i	0.270784	+	0.962640i	$0.412717\pi$
$593$	−17.0042	+	29.4521i	−0.698279	+	1.20945i	−0.969063	+	0.246814i	$0.920616\pi$
$594$		0			0
$595$	20.8606	+	28.1701i	0.855203	+	1.15486i
$596$	12.2823	−	7.09118i	0.503102	−	0.290466i
$597$		0			0
$598$	4.89153	+	1.61182i	0.200029	+	0.0659123i
$599$	11.8739	−	6.85538i	0.485153	−	0.280103i	−0.237408	−	0.971410i	$-0.576298\pi$
$599$	11.8739	−	6.85538i	0.485153	−	0.280103i	0.722562	+	0.691307i	$0.242965\pi$
$600$		0			0
$601$	−12.8578	+	7.42343i	−0.524479	+	0.302808i	−0.738765	−	0.673963i	$-0.764591\pi$
$601$	−12.8578	+	7.42343i	−0.524479	+	0.302808i	0.214286	+	0.976771i	$0.431257\pi$
$602$	21.4870	−	15.9116i	0.875744	−	0.648509i
$603$		0			0
$604$	5.93638	+	10.2821i	0.241548	+	0.418373i
$605$	21.1931			0.861621
$606$		0			0
$607$	10.6831	−	6.16790i	0.433614	−	0.250347i	−0.267271	−	0.963621i	$-0.586122\pi$
$607$	10.6831	−	6.16790i	0.433614	−	0.250347i	0.700885	+	0.713274i	$0.252789\pi$
$608$	−3.62888	−	6.28540i	−0.147170	−	0.254907i
$609$		0			0
$610$	23.9472			0.969594
$611$	19.1717	−	17.1188i	0.775604	−	0.692552i
$612$		0			0
$613$	6.99525	−	12.1161i	0.282535	−	0.489366i	−0.689473	−	0.724311i	$-0.742158\pi$
$613$	6.99525	−	12.1161i	0.282535	−	0.489366i	0.972009	+	0.234946i	$0.0754912\pi$
$614$	18.9300			0.763951
$615$		0			0
$616$	−0.352742	−	0.476341i	−0.0142124	−	0.0191923i
$617$	−8.53585	−	4.92818i	−0.343640	−	0.198401i	0.318240	−	0.948010i	$-0.396908\pi$
$617$	−8.53585	−	4.92818i	−0.343640	−	0.198401i	−0.661881	+	0.749609i	$0.730241\pi$
$618$		0			0
$619$	−12.5602	+	7.25165i	−0.504838	+	0.291468i	−0.730709	−	0.682689i	$-0.760811\pi$
$619$	−12.5602	+	7.25165i	−0.504838	+	0.291468i	0.225871	+	0.974157i	$0.427477\pi$
$620$			12.7875i			0.513557i
$621$		0			0
$622$	9.10430	−	5.25637i	0.365049	−	0.210761i
$623$	−9.61888	+	22.1439i	−0.385372	+	0.887177i
$624$		0			0
$625$	8.57898	−	14.8592i	0.343159	−	0.594369i
$626$	2.09802	−	3.63388i	0.0838539	−	0.145239i
$627$		0			0
$628$	20.2256	−	11.6773i	0.807091	−	0.465974i
$629$	−47.6091			−1.89830
$630$		0			0
$631$	13.3769	−	23.1694i	0.532525	−	0.922361i	−0.466754	−	0.884387i	$-0.654577\pi$
$631$	13.3769	−	23.1694i	0.532525	−	0.922361i	0.999279	−	0.0379732i	$-0.0120902\pi$
$632$	5.12031	+	2.95621i	0.203675	+	0.117592i
$633$		0			0
$634$	−10.4109	+	18.0322i	−0.413470	+	0.716151i
$635$	−41.0276			−1.62813
$636$		0			0
$637$	10.5881	+	22.9105i	0.419514	+	0.907749i
$638$		−	2.08780i		−	0.0826566i
$639$		0			0
$640$	1.67617	+	0.967738i	0.0662565	+	0.0382532i
$641$		−	10.9769i		−	0.433561i	−0.976220	−	0.216781i	$-0.930444\pi$
$641$		−	10.9769i		−	0.433561i	0.976220	−	0.216781i	$-0.0695557\pi$
$642$		0			0
$643$	−13.4718	−	7.77797i	−0.531277	−	0.306733i	0.210259	−	0.977646i	$-0.432569\pi$
$643$	−13.4718	−	7.77797i	−0.531277	−	0.306733i	−0.741536	+	0.670913i	$0.765903\pi$
$644$	−3.46634	−	1.50571i	−0.136593	−	0.0593333i
$645$		0			0
$646$	−24.8406	−	43.0252i	−0.977341	−	1.69280i
$647$	−12.2196	+	21.1650i	−0.480403	+	0.832082i	−0.999747	−	0.0224830i	$-0.992843\pi$
$647$	−12.2196	+	21.1650i	−0.480403	+	0.832082i	0.519344	+	0.854565i	$0.326176\pi$
$648$		0			0
$649$	−1.60483	−	0.926550i	−0.0629952	−	0.0363703i
$650$	4.42620	−	0.921640i	0.173610	−	0.0361497i
$651$		0			0
$652$	9.69822	+	16.7978i	0.379812	+	0.657853i
$653$		−	43.1792i		−	1.68973i	−0.534979	−	0.844866i	$-0.679680\pi$
$653$		−	43.1792i		−	1.68973i	0.534979	−	0.844866i	$-0.320320\pi$
$654$		0			0
$655$	−11.1468	−	19.3068i	−0.435541	−	0.754379i
$656$	−2.78373	−	4.82157i	−0.108687	−	0.188251i
$657$		0			0
$658$	−15.1569	+	11.2241i	−0.590878	+	0.437559i
$659$	15.3813	+	8.88038i	0.599169	+	0.345931i	0.768715	−	0.639592i	$-0.220897\pi$
$659$	15.3813	+	8.88038i	0.599169	+	0.345931i	−0.169545	+	0.985522i	$0.554230\pi$
$660$		0			0
$661$	8.83354	+	5.10005i	0.343585	+	0.198369i	0.661856	−	0.749631i	$-0.269769\pi$
$661$	8.83354	+	5.10005i	0.343585	+	0.198369i	−0.318271	+	0.948000i	$0.603102\pi$
$662$	−6.20867	+	3.58458i	−0.241307	+	0.139319i
$663$		0			0
$664$		−	9.37902i		−	0.363976i
$665$	−34.0883	−	14.8073i	−1.32189	−	0.574202i
$666$		0			0
$667$	−6.65590	−	11.5284i	−0.257717	−	0.446380i
$668$	−7.24188	−	12.5433i	−0.280197	−	0.485315i
$669$		0			0
$670$	4.05330	−	2.34017i	0.156593	−	0.0904088i
$671$	−2.77188			−0.107007
$672$		0			0
$673$	10.1274	+	17.5413i	0.390384	+	0.676166i	0.992500	−	0.122243i	$-0.0390087\pi$
$673$	10.1274	+	17.5413i	0.390384	+	0.676166i	−0.602116	+	0.798409i	$0.705675\pi$
$674$			9.27518i			0.357267i
$675$		0			0
$676$	−10.4535	−	7.72822i	−0.402056	−	0.297239i
$677$	20.6703	−	35.8020i	0.794425	−	1.37598i	−0.128779	−	0.991673i	$-0.541106\pi$
$677$	20.6703	−	35.8020i	0.794425	−	1.37598i	0.923204	−	0.384311i	$-0.125561\pi$
$678$		0			0
$679$	−17.2208	+	12.7524i	−0.660874	+	0.489393i
$680$	11.4738	+	6.62442i	0.440001	+	0.254035i
$681$		0			0
$682$		−	1.48015i		−	0.0566777i
$683$		−	48.9733i		−	1.87391i	−0.349446	−	0.936956i	$-0.613630\pi$
$683$		−	48.9733i		−	1.87391i	0.349446	−	0.936956i	$-0.386370\pi$
$684$		0			0
$685$	−11.6752	−	6.74067i	−0.446086	−	0.257548i
$686$	−6.20122	−	17.4512i	−0.236764	−	0.666290i
$687$		0			0
$688$	5.05283	−	8.75176i	0.192637	−	0.333658i
$689$	−8.99700	+	1.87339i	−0.342758	+	0.0713705i
$690$		0			0
$691$		−	6.03675i		−	0.229649i	−0.993386	−	0.114824i	$-0.963369\pi$
$691$		−	6.03675i		−	0.229649i	0.993386	−	0.114824i	$-0.0366305\pi$
$692$	−4.30098	−	7.44952i	−0.163499	−	0.283188i
$693$		0			0
$694$	−31.3426			−1.18975
$695$	−5.32911	+	3.07676i	−0.202145	+	0.116708i
$696$		0			0
$697$	−19.0554	−	33.0049i	−0.721775	−	1.25015i
$698$	8.53929	+	14.7905i	0.323217	+	0.559828i
$699$		0			0
$700$	−3.29614	+	0.376761i	−0.124582	+	0.0142402i
$701$		−	18.3879i		−	0.694502i	−0.937772	−	0.347251i	$-0.887115\pi$
$701$		−	18.3879i		−	0.694502i	0.937772	−	0.347251i	$-0.112885\pi$
$702$		0			0
$703$	43.7152	−	25.2390i	1.64875	−	0.951906i
$704$	−0.194016	−	0.112015i	−0.00731226	−	0.00422174i
$705$		0			0
$706$	−1.36661	−	0.789015i	−0.0514332	−	0.0296950i
$707$	−23.8758	−	32.2418i	−0.897942	−	1.21258i
$708$		0			0
$709$	12.6890	+	21.9780i	0.476546	+	0.825401i	0.999639	−	0.0268742i	$-0.00855535\pi$
$709$	12.6890	+	21.9780i	0.476546	+	0.825401i	−0.523093	+	0.852276i	$0.675222\pi$
$710$	−6.89506	−	11.9426i	−0.258767	−	0.448197i
$711$		0			0
$712$			9.12512i			0.341978i
$713$	−4.71871	−	8.17304i	−0.176717	−	0.306083i
$714$		0			0
$715$	1.53056	−	0.318699i	0.0572397	−	0.0119187i
$716$	−16.5969	−	9.58221i	−0.620254	−	0.358104i
$717$		0			0
$718$	3.19207	−	5.52884i	0.119127	−	0.206334i
$719$	−12.2659	−	21.2452i	−0.457442	−	0.792312i	0.541383	−	0.840776i	$-0.317901\pi$
$719$	−12.2659	−	21.2452i	−0.457442	−	0.792312i	−0.998825	+	0.0484635i	$0.984568\pi$
$720$		0			0
$721$	−17.0718	+	12.6421i	−0.635789	+	0.470816i
$722$	29.1634	+	16.8375i	1.08535	+	0.626626i
$723$		0			0
$724$		−	4.92120i		−	0.182895i
$725$	−10.1201	−	5.84287i	−0.375853	−	0.216999i
$726$		0			0
$727$		−	7.84230i		−	0.290855i	−0.989369	−	0.145427i	$-0.953544\pi$
$727$		−	7.84230i		−	0.290855i	0.989369	−	0.145427i	$-0.0464557\pi$
$728$	7.12060	+	6.34799i	0.263907	+	0.235272i
$729$		0			0
$730$	−23.0326			−0.852476
$731$	34.5880	−	59.9081i	1.27928	−	2.21578i
$732$		0			0
$733$	−11.9213	−	6.88276i	−0.440323	−	0.254220i	0.263412	−	0.964683i	$-0.415152\pi$
$733$	−11.9213	−	6.88276i	−0.440323	−	0.254220i	−0.703734	+	0.710463i	$0.748486\pi$
$734$	3.09829	−	5.36640i	0.114360	−	0.198078i
$735$		0			0
$736$	−1.42842			−0.0526523
$737$	−0.469168	+	0.270874i	−0.0172820	+	0.00997779i
$738$		0			0
$739$	0.478412	−	0.828633i	0.0175987	−	0.0304818i	−0.857092	−	0.515163i	$-0.827731\pi$
$739$	0.478412	−	0.828633i	0.0175987	−	0.0304818i	0.874691	+	0.484682i	$0.161065\pi$
$740$	−6.73065	+	11.6578i	−0.247424	+	0.428550i
$741$		0			0
$742$	6.69997	−	0.765831i	0.245964	−	0.0281145i
$743$	−32.8468	+	18.9641i	−1.20503	+	0.695726i	−0.961670	−	0.274209i	$-0.911584\pi$
$743$	−32.8468	+	18.9641i	−1.20503	+	0.695726i	−0.243363	+	0.969935i	$0.578251\pi$
$744$		0			0
$745$		−	27.4496i		−	1.00568i
$746$	17.6682	−	10.2007i	0.646878	−	0.373475i
$747$		0			0
$748$	−1.32809	−	0.766775i	−0.0485599	−	0.0280361i
$749$	0.601403	+	0.261238i	0.0219748	+	0.00954541i
$750$		0			0
$751$	−9.65995			−0.352497			−0.176248	−	0.984346i	$-0.556396\pi$
$751$	−9.65995			−0.352497			−0.176248	+	0.984346i	$0.556396\pi$
$752$	−3.56427	+	6.17349i	−0.129975	+	0.225124i
$753$		0			0
$754$	6.84962	+	32.8954i	0.249448	+	1.19798i
$755$	22.9794			0.836307
$756$		0			0
$757$	−15.1209	−	26.1902i	−0.549578	−	0.951898i	−0.998303	−	0.0582278i	$-0.981455\pi$
$757$	−15.1209	−	26.1902i	−0.549578	−	0.951898i	0.448725	−	0.893670i	$-0.351878\pi$
$758$	2.46779	−	1.42478i	0.0896341	−	0.0517503i
$759$		0			0
$760$	−14.0472			−0.509545
$761$	−2.11982	−	3.67164i	−0.0768436	−	0.133097i	0.825043	−	0.565070i	$-0.191151\pi$
$761$	−2.11982	−	3.67164i	−0.0768436	−	0.133097i	−0.901886	+	0.431973i	$0.857818\pi$
$762$		0			0
$763$	−24.7299	+	2.82671i	−0.895281	+	0.102334i
$764$	−6.99433	+	4.03818i	−0.253046	+	0.146096i
$765$		0			0
$766$	−20.0664	+	11.5853i	−0.725028	+	0.418595i
$767$	28.3257	+	9.33367i	1.02278	+	0.337019i
$768$		0			0
$769$	−1.98250	+	1.14459i	−0.0714906	+	0.0412751i	−0.535319	−	0.844650i	$-0.679809\pi$
$769$	−1.98250	+	1.14459i	−0.0714906	+	0.0412751i	0.463829	+	0.885925i	$0.346475\pi$
$770$	−1.13979	+	0.130282i	−0.0410752	+	0.00469505i
$771$		0			0
$772$	−5.94575	+	10.2983i	−0.213992	+	0.370646i
$773$	3.41739			0.122915			0.0614575	−	0.998110i	$-0.480425\pi$
$773$	3.41739			0.122915			0.0614575	+	0.998110i	$0.480425\pi$
$774$		0			0
$775$	−7.17469	−	4.14231i	−0.257722	−	0.148796i
$776$	−4.04961	+	7.01412i	−0.145372	+	0.251792i
$777$		0			0
$778$	19.3280	+	33.4771i	0.692942	+	1.20021i
$779$	34.9938	+	20.2037i	1.25378	+	0.723871i
$780$		0			0
$781$	0.798101	+	1.38235i	0.0285583	+	0.0494644i
$782$	−9.77792			−0.349658
$783$		0			0
$784$	−4.77771	−	5.11601i	−0.170632	−	0.182714i
$785$		−	45.2021i		−	1.61333i
$786$		0			0
$787$		−	33.8037i		−	1.20497i	−0.798130	−	0.602485i	$-0.794177\pi$
$787$		−	33.8037i		−	1.20497i	0.798130	−	0.602485i	$-0.205823\pi$
$788$	7.59842	−	4.38695i	0.270683	−	0.156279i
$789$		0			0
$790$	9.91024	−	5.72168i	0.352590	−	0.203568i
$791$	−3.48651	+	2.58184i	−0.123966	+	0.0917997i
$792$		0			0
$793$	43.6739	−	9.09396i	1.55091	−	0.322936i
$794$	2.40040	+	4.15762i	0.0851871	+	0.147548i
$795$		0			0
$796$		−	1.86218i		−	0.0660031i
$797$	11.9304	−	20.6641i	0.422597	−	0.731959i	−0.573596	−	0.819138i	$-0.694452\pi$
$797$	11.9304	−	20.6641i	0.422597	−	0.731959i	0.996193	+	0.0871795i	$0.0277854\pi$
$798$		0			0
$799$	−24.3983	+	42.2592i	−0.863151	+	1.49502i
$800$	−1.08594	+	0.626968i	−0.0383938	+	0.0221667i
$801$		0			0
$802$	−5.70246			−0.201361
$803$	2.66602			0.0940818
$804$		0			0
$805$	−5.87834	+	4.35305i	−0.207184	+	0.153425i
$806$	4.85604	+	23.3213i	0.171047	+	0.821457i
$807$		0			0
$808$	−13.1322	−	7.58190i	−0.461991	−	0.266730i
$809$	−1.80829	−	1.04402i	−0.0635762	−	0.0367057i	0.467875	−	0.883795i	$-0.345020\pi$
$809$	−1.80829	−	1.04402i	−0.0635762	−	0.0367057i	−0.531451	+	0.847089i	$0.678353\pi$
$810$		0			0
$811$		−	24.0358i		−	0.844011i	−0.906593	−	0.422005i	$-0.861326\pi$
$811$		−	24.0358i		−	0.844011i	0.906593	−	0.422005i	$-0.138674\pi$
$812$	−2.80008	−	24.4969i	−0.0982637	−	0.859672i
$813$		0			0
$814$	0.779071	−	1.34939i	0.0273064	−	0.0472961i
$815$	37.5413			1.31502
$816$		0			0
$817$			73.3444i			2.56599i
$818$	−8.24506			−0.288282
$819$		0			0
$820$	−10.7757			−0.376304
$821$			0.166105i			0.00579711i	0.999996	+	0.00289855i	$0.000922639\pi$
$821$			0.166105i			0.00579711i	−0.999996	+	0.00289855i	$0.999077\pi$
$822$		0			0
$823$	17.4911			0.609702			0.304851	−	0.952400i	$-0.401393\pi$
$823$	17.4911			0.609702			0.304851	+	0.952400i	$0.401393\pi$
$824$	−4.01457	+	6.95345i	−0.139854	+	0.242235i
$825$		0			0
$826$	−20.0728	−	8.71921i	−0.698420	−	0.303380i
$827$		−	17.4128i		−	0.605502i	−0.953070	−	0.302751i	$-0.902095\pi$
$827$		−	17.4128i		−	0.605502i	0.953070	−	0.302751i	$-0.0979050\pi$
$828$		0			0
$829$	−37.2431	−	21.5023i	−1.29351	−	0.746805i	−0.314231	−	0.949346i	$-0.601747\pi$
$829$	−37.2431	−	21.5023i	−1.29351	−	0.746805i	−0.979274	+	0.202541i	$0.935080\pi$
$830$	−15.7208	−	9.07643i	−0.545678	−	0.315047i
$831$		0			0
$832$	3.42443	+	1.12839i	0.118721	+	0.0391200i
$833$	−32.7047	−	35.0204i	−1.13315	−	1.21339i
$834$		0			0
$835$	−28.0330			−0.970120
$836$	1.62596			0.0562350
$837$		0			0
$838$	−22.6468	+	13.0751i	−0.782321	+	0.451673i
$839$	4.47093	−	7.74388i	0.154354	−	0.267348i	−0.778470	−	0.627682i	$-0.784004\pi$
$839$	4.47093	−	7.74388i	0.154354	−	0.267348i	0.932823	+	0.360334i	$0.117337\pi$
$840$		0			0
$841$	28.9241	−	50.0981i	0.997384	−	1.72752i
$842$		−	1.13645i		−	0.0391647i
$843$		0			0
$844$	7.81359	+	13.5335i	0.268955	+	0.465843i
$845$	−23.0700	+	10.0429i	−0.793632	+	0.345486i
$846$		0			0
$847$	−28.7831	+	3.29001i	−0.988997	+	0.113046i
$848$	2.20736	−	1.27442i	0.0758010	−	0.0437638i
$849$		0			0
$850$	−7.43355	+	4.29176i	−0.254969	+	0.147206i
$851$		−	9.93471i		−	0.340558i
$852$		0			0
$853$			11.6841i			0.400054i	0.979790	+	0.200027i	$0.0641031\pi$
$853$			11.6841i			0.400054i	−0.979790	+	0.200027i	$0.935897\pi$
$854$	−32.5235	+	3.71756i	−1.11293	+	0.127212i
$855$		0			0
$856$	0.247828			0.00847058
$857$	−22.3524	−	38.7154i	−0.763542	−	1.32249i	−0.941014	−	0.338368i	$-0.890125\pi$
$857$	−22.3524	−	38.7154i	−0.763542	−	1.32249i	0.177471	−	0.984126i	$-0.443208\pi$
$858$		0			0
$859$	6.10859	+	3.52680i	0.208423	+	0.120333i	0.600578	−	0.799566i	$-0.294937\pi$
$859$	6.10859	+	3.52680i	0.208423	+	0.120333i	−0.392156	+	0.919899i	$0.628271\pi$
$860$	−9.77963	−	16.9388i	−0.333482	−	0.577609i
$861$		0			0
$862$	−7.36299	+	12.7531i	−0.250785	+	0.434372i
$863$	2.72653	+	1.57416i	0.0928121	+	0.0535851i	0.545688	−	0.837989i	$-0.316269\pi$
$863$	2.72653	+	1.57416i	0.0928121	+	0.0535851i	−0.452876	+	0.891574i	$0.649602\pi$
$864$		0			0
$865$	−16.6489			−0.566079
$866$	−1.72096	+	2.98079i	−0.0584805	+	0.101291i
$867$		0			0
$868$	−1.98512	−	17.3671i	−0.0673795	−	0.589478i
$869$	−1.14711	+	0.662282i	−0.0389129	+	0.0224664i
$870$		0			0
$871$	6.50356	−	5.80716i	0.220365	−	0.196768i
$872$	−8.14746	+	4.70394i	−0.275908	+	0.159295i
$873$		0			0
$874$	8.97819	−	5.18356i	0.303692	−	0.175337i
$875$	−12.7593	+	29.3735i	−0.431343	+	0.993007i
$876$		0			0
$877$	24.4372	+	42.3265i	0.825187	+	1.42927i	0.901777	+	0.432202i	$0.142263\pi$
$877$	24.4372	+	42.3265i	0.825187	+	1.42927i	−0.0765899	+	0.997063i	$0.524403\pi$
$878$	−5.06111			−0.170804
$879$		0			0
$880$	−0.375514	+	0.216803i	−0.0126586	+	0.00730842i
$881$	17.1139	+	29.6421i	0.576581	+	0.998668i	0.995868	+	0.0908138i	$0.0289468\pi$
$881$	17.1139	+	29.6421i	0.576581	+	0.998668i	−0.419287	+	0.907854i	$0.637720\pi$
$882$		0			0
$883$	−2.54522			−0.0856536			−0.0428268	−	0.999083i	$-0.513636\pi$
$883$	−2.54522			−0.0856536			−0.0428268	+	0.999083i	$0.513636\pi$
$884$	23.4411	+	7.72416i	0.788411	+	0.259792i
$885$		0			0
$886$	8.48064	−	14.6889i	0.284913	−	0.493483i
$887$	−45.7929			−1.53758			−0.768788	−	0.639504i	$-0.779140\pi$
$887$	−45.7929			−1.53758			−0.768788	+	0.639504i	$0.779140\pi$
$888$		0			0
$889$	55.7209	−	6.36911i	1.86882	−	0.213613i
$890$	15.2953	+	8.83073i	0.512698	+	0.296007i
$891$		0			0
$892$	−3.19762	+	1.84615i	−0.107064	+	0.0618135i
$893$		−	51.7371i		−	1.73132i
$894$		0			0
$895$	−32.1228	+	18.5461i	−1.07375	+	0.619929i
$896$	−2.42670	−	1.05411i	−0.0810702	−	0.0352153i
$897$		0			0
$898$	3.65625	−	6.33282i	0.122011	−	0.211329i
$899$	30.7856	−	53.3222i	1.02676	−	1.77840i
$900$		0			0
$901$	15.1100	−	8.72374i	0.503386	−	0.290630i
$902$	1.24728			0.0415300
$903$		0			0
$904$	−0.819879	+	1.42007i	−0.0272688	+	0.0472309i
$905$	−8.24876	−	4.76243i	−0.274198	−	0.158308i
$906$		0			0
$907$	−18.3597	+	31.8000i	−0.609625	+	1.05590i	0.381677	+	0.924296i	$0.375347\pi$
$907$	−18.3597	+	31.8000i	−0.609625	+	1.05590i	−0.991302	+	0.131606i	$0.957987\pi$
$908$	19.0034			0.630650
$909$		0			0
$910$	17.5312	−	5.79215i	0.581153	−	0.192008i
$911$			19.3371i			0.640667i	0.947305	+	0.320333i	$0.103795\pi$
$911$			19.3371i			0.640667i	−0.947305	+	0.320333i	$0.896205\pi$
$912$		0			0
$913$	1.81968	+	1.05059i	0.0602227	+	0.0347696i
$914$			37.8232i			1.25108i
$915$		0			0
$916$	−20.5951	−	11.8906i	−0.680482	−	0.392877i
$917$	18.1360	+	24.4908i	0.598904	+	0.808757i
$918$		0			0
$919$	27.8170	+	48.1805i	0.917599	+	1.58933i	0.803050	+	0.595911i	$0.203209\pi$
$919$	27.8170	+	48.1805i	0.917599	+	1.58933i	0.114549	+	0.993418i	$0.463458\pi$
$920$	−1.38234	+	2.39428i	−0.0455743	+	0.0789369i
$921$		0			0
$922$	−29.0391	−	16.7657i	−0.956350	−	0.552149i
$923$	−17.1101	−	19.1620i	−0.563187	−	0.630725i
$924$		0			0
$925$	−4.36059	−	7.55276i	−0.143375	−	0.248333i
$926$			9.05246i			0.297482i
$927$		0			0
$928$	−4.65962	−	8.07070i	−0.152960	−	0.264934i
$929$	−5.19416	−	8.99655i	−0.170415	−	0.295167i	0.768150	−	0.640270i	$-0.221177\pi$
$929$	−5.19416	−	8.99655i	−0.170415	−	0.295167i	−0.938565	+	0.345103i	$0.887844\pi$
$930$		0			0
$931$	48.5951	+	14.8184i	1.59264	+	0.485654i
$932$	8.51390	+	4.91550i	0.278882	+	0.161013i
$933$		0			0
$934$	15.7403	+	9.08764i	0.515037	+	0.297357i
$935$	−2.57049	+	1.48407i	−0.0840640	+	0.0485344i
$936$		0			0
$937$			13.6357i			0.445458i	0.974880	+	0.222729i	$0.0714964\pi$
$937$			13.6357i			0.445458i	−0.974880	+	0.222729i	$0.928504\pi$
$938$	−5.14164	+	3.80750i	−0.167880	+	0.124319i
$939$		0			0
$940$	6.89855	+	11.9486i	0.225006	+	0.389721i
$941$	12.4831	+	21.6214i	0.406938	+	0.704838i	0.994545	−	0.104309i	$-0.0332631\pi$
$941$	12.4831	+	21.6214i	0.406938	+	0.704838i	−0.587607	+	0.809147i	$0.699930\pi$
$942$		0			0
$943$	6.88723	−	3.97634i	0.224279	−	0.129488i
$944$	−8.27164			−0.269219
$945$		0			0
$946$	1.13199	+	1.96066i	0.0368041	+	0.0637466i
$947$			34.3107i			1.11495i	0.830194	+	0.557474i	$0.188230\pi$
$947$			34.3107i			1.11495i	−0.830194	+	0.557474i	$0.811770\pi$
$948$		0			0
$949$	−42.0060	+	8.74665i	−1.36357	+	0.283928i
$950$	4.55038	−	7.88149i	0.147634	−	0.255709i
$951$		0			0
$952$	−16.6114	−	7.21566i	−0.538378	−	0.233861i
$953$	15.3469	+	8.86051i	0.497133	+	0.287020i	0.727529	−	0.686077i	$-0.240669\pi$
$953$	15.3469	+	8.86051i	0.497133	+	0.287020i	−0.230396	+	0.973097i	$0.574002\pi$
$954$		0			0
$955$			15.6316i			0.505826i
$956$		−	11.4665i		−	0.370854i
$957$		0			0
$958$	−24.3900	−	14.0816i	−0.788004	−	0.454954i
$959$	16.9029	+	7.34228i	0.545823	+	0.237095i
$960$		0			0
$961$	6.32549	−	10.9561i	0.204048	−	0.353422i
$962$	−7.84802	+	23.8170i	−0.253030	+	0.767892i
$963$		0			0
$964$		−	5.21381i		−	0.167925i
$965$	11.5079	+	19.9322i	0.370451	+	0.641640i
$966$		0			0
$967$	−5.15789			−0.165867			−0.0829333	−	0.996555i	$-0.526429\pi$
$967$	−5.15789			−0.165867			−0.0829333	+	0.996555i	$0.526429\pi$
$968$	−9.48281	+	5.47491i	−0.304789	+	0.175970i
$969$		0			0
$970$	7.83791	+	13.5757i	0.251660	+	0.435888i
$971$	19.4619	+	33.7090i	0.624563	+	1.08177i	0.988625	+	0.150400i	$0.0480561\pi$
$971$	19.4619	+	33.7090i	0.624563	+	1.08177i	−0.364062	+	0.931375i	$0.618611\pi$
$972$		0			0
$973$	6.76001	−	5.00595i	0.216716	−	0.160483i
$974$		−	35.3211i		−	1.13176i
$975$		0			0
$976$	−10.7151	+	6.18639i	−0.342983	+	0.198021i
$977$	5.03805	+	2.90872i	0.161181	+	0.0930582i	0.578421	−	0.815738i	$-0.303669\pi$
$977$	5.03805	+	2.90872i	0.161181	+	0.0930582i	−0.417240	+	0.908797i	$0.637002\pi$
$978$		0			0
$979$	−1.77042	−	1.02215i	−0.0565829	−	0.0326682i
$980$	−13.1989	+	3.05730i	−0.421622	+	0.0976620i
$981$		0			0
$982$	−5.39399	−	9.34266i	−0.172129	−	0.298136i
$983$	−19.2500	−	33.3420i	−0.613980	−	1.06344i	−0.990563	−	0.137062i	$-0.956234\pi$
$983$	−19.2500	−	33.3420i	−0.613980	−	1.06344i	0.376582	−	0.926383i	$-0.377099\pi$
$984$		0			0
$985$		−	16.9817i		−	0.541081i
$986$	−31.8963	−	55.2461i	−1.01579	−	1.75939i
$987$		0			0
$988$	−25.6187	+	5.33443i	−0.815040	+	0.169711i
$989$	12.5012	+	7.21756i	0.397515	+	0.229505i
$990$		0			0
$991$	−23.0490	+	39.9221i	−0.732176	+	1.26817i	0.223775	+	0.974641i	$0.428162\pi$
$991$	−23.0490	+	39.9221i	−0.732176	+	1.26817i	−0.955951	+	0.293525i	$0.905172\pi$
$992$	−3.30344	−	5.72173i	−0.104884	−	0.181665i
$993$		0			0
$994$	11.2184	+	15.1493i	0.355825	+	0.480505i
$995$	−3.12132	−	1.80210i	−0.0989527	−	0.0571303i
$996$		0			0
$997$		−	28.4436i		−	0.900816i	−0.892823	−	0.450408i	$-0.851278\pi$
$997$		−	28.4436i		−	0.900816i	0.892823	−	0.450408i	$-0.148722\pi$
$998$	0.634156	+	0.366130i	0.0200738	+	0.0115896i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.cm.a.341.11	yes	72
3.2	odd	2	inner	1638.2.cm.a.341.26	yes	72
7.3	odd	6		1638.2.bq.a.1277.6	yes	72
13.9	even	3		1638.2.bq.a.971.31	yes	72
21.17	even	6		1638.2.bq.a.1277.31	yes	72
39.35	odd	6		1638.2.bq.a.971.6	✓	72
91.87	odd	6	inner	1638.2.cm.a.269.26	yes	72
273.269	even	6	inner	1638.2.cm.a.269.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bq.a.971.6	✓	72	39.35	odd	6
1638.2.bq.a.971.31	yes	72	13.9	even	3
1638.2.bq.a.1277.6	yes	72	7.3	odd	6
1638.2.bq.a.1277.31	yes	72	21.17	even	6
1638.2.cm.a.269.11	yes	72	273.269	even	6	inner
1638.2.cm.a.269.26	yes	72	91.87	odd	6	inner
1638.2.cm.a.341.11	yes	72	1.1	even	1	trivial
1638.2.cm.a.341.26	yes	72	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.cm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.967738 + 1.67617i) q^{5} +(1.05411 - 2.42670i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.967738 + 1.67617i) q^{5} +(1.05411 - 2.42670i) q^{7} -1.00000i q^{8} +(-1.67617 - 0.967738i) q^{10} +(0.194016 + 0.112015i) q^{11} +(-3.42443 - 1.12839i) q^{13} +(2.42670 + 1.05411i) q^{14} +1.00000 q^{16} +6.84527 q^{17} +(-6.28540 + 3.62888i) q^{19} +(0.967738 - 1.67617i) q^{20} +(-0.112015 + 0.194016i) q^{22} +1.42842i q^{23} +(0.626968 + 1.08594i) q^{25} +(1.12839 - 3.42443i) q^{26} +(-1.05411 + 2.42670i) q^{28} +(-8.07070 + 4.65962i) q^{29} +(-5.72173 + 3.30344i) q^{31} +1.00000i q^{32} +6.84527i q^{34} +(3.04746 + 4.11527i) q^{35} -6.95504 q^{37} +(-3.62888 - 6.28540i) q^{38} +(1.67617 + 0.967738i) q^{40} +(-2.78373 - 4.82157i) q^{41} +(5.05283 - 8.75176i) q^{43} +(-0.194016 - 0.112015i) q^{44} -1.42842 q^{46} +(-3.56427 + 6.17349i) q^{47} +(-4.77771 - 5.11601i) q^{49} +(-1.08594 + 0.626968i) q^{50} +(3.42443 + 1.12839i) q^{52} +(2.20736 - 1.27442i) q^{53} +(-0.375514 + 0.216803i) q^{55} +(-2.42670 - 1.05411i) q^{56} +(-4.65962 - 8.07070i) q^{58} -8.27164 q^{59} +(-10.7151 + 6.18639i) q^{61} +(-3.30344 - 5.72173i) q^{62} -1.00000 q^{64} +(5.20533 - 4.64794i) q^{65} +(-1.20910 + 2.09421i) q^{67} -6.84527 q^{68} +(-4.11527 + 3.04746i) q^{70} +(6.17036 + 3.56246i) q^{71} +(10.3059 - 5.95012i) q^{73} -6.95504i q^{74} +(6.28540 - 3.62888i) q^{76} +(0.476341 - 0.352742i) q^{77} +(-2.95621 + 5.12031i) q^{79} +(-0.967738 + 1.67617i) q^{80} +(4.82157 - 2.78373i) q^{82} +9.37902 q^{83} +(-6.62442 + 11.4738i) q^{85} +(8.75176 + 5.05283i) q^{86} +(0.112015 - 0.194016i) q^{88} -9.12512 q^{89} +(-6.34799 + 7.12060i) q^{91} -1.42842i q^{92} +(-6.17349 - 3.56427i) q^{94} -14.0472i q^{95} +(-7.01412 - 4.04961i) q^{97} +(5.11601 - 4.77771i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) \) 72 * q - 72 * q^4 - 4 * q^7	\( 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) \) 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more