LMFDB - Embedded newform 351.2.i.b.242.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(161,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.i (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 184x^{12} + 600x^{10} + 894x^{8} + 600x^{6} + 184x^{4} + 24x^{2} + 1 $ x^16 + 24x^14 + 184x^12 + 600x^10 + 894x^8 + 600x^6 + 184x^4 + 24*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			242.6
Root			$1.68741i$ of defining polynomial
Character	$\chi$	$=$	351.242
Dual form			351.2.i.b.161.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14002 - 1.14002i) q^{2} -0.599280i q^{4} +(-2.84492 + 2.84492i) q^{5} +(-2.82684 + 2.82684i) q^{7} +(1.59685 + 1.59685i) q^{8} +6.48652i q^{10} +(-2.08263 - 2.08263i) q^{11} +(3.59030 + 0.331331i) q^{13} +6.44529i q^{14} +4.83942 q^{16} -3.94914 q^{17} +(2.32235 + 2.32235i) q^{19} +(1.70490 + 1.70490i) q^{20} -4.74846 q^{22} +0.755446 q^{23} -11.1872i q^{25} +(4.47072 - 3.71528i) q^{26} +(1.69407 + 1.69407i) q^{28} -3.40981i q^{29} +(6.39174 + 6.39174i) q^{31} +(2.32334 - 2.32334i) q^{32} +(-4.50208 + 4.50208i) q^{34} -16.0843i q^{35} +(-2.85824 + 2.85824i) q^{37} +5.29503 q^{38} -9.08580 q^{40} +(2.08263 - 2.08263i) q^{41} -0.526914i q^{43} +(-1.24808 + 1.24808i) q^{44} +(0.861221 - 0.861221i) q^{46} +(3.18684 + 3.18684i) q^{47} -8.98203i q^{49} +(-12.7536 - 12.7536i) q^{50} +(0.198560 - 2.15159i) q^{52} +10.3944i q^{53} +11.8498 q^{55} -9.02805 q^{56} +(-3.88724 - 3.88724i) q^{58} +(7.20759 + 7.20759i) q^{59} +2.91264 q^{61} +14.5734 q^{62} +4.38156i q^{64} +(-11.1567 + 9.27150i) q^{65} +(-5.13277 - 5.13277i) q^{67} +2.36664i q^{68} +(-18.3364 - 18.3364i) q^{70} +(-2.08948 + 2.08948i) q^{71} +(-3.56787 + 3.56787i) q^{73} +6.51690i q^{74} +(1.39174 - 1.39174i) q^{76} +11.7745 q^{77} +5.79246 q^{79} +(-13.7678 + 13.7678i) q^{80} -4.74846i q^{82} +(7.18887 - 7.18887i) q^{83} +(11.2350 - 11.2350i) q^{85} +(-0.600691 - 0.600691i) q^{86} -6.65127i q^{88} +(-1.51774 - 1.51774i) q^{89} +(-11.0858 + 9.21257i) q^{91} -0.452723i q^{92} +7.26611 q^{94} -13.2138 q^{95} +(2.07237 + 2.07237i) q^{97} +(-10.2397 - 10.2397i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 16 q^{13} - 8 q^{16} - 32 q^{19} + 8 q^{22} + 40 q^{28} + 16 q^{31} + 24 q^{34} - 32 q^{37} - 72 q^{40} + 48 q^{46} + 48 q^{52} + 32 q^{55} + 56 q^{58} - 64 q^{61} - 32 q^{67} - 40 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 16 * q^13 - 8 * q^16 - 32 * q^19 + 8 * q^22 + 40 * q^28 + 16 * q^31 + 24 * q^34 - 32 * q^37 - 72 * q^40 + 48 * q^46 + 48 * q^52 + 32 * q^55 + 56 * q^58 - 64 * q^61 - 32 * q^67 - 40 * q^70 - 56 * q^73 - 64 * q^76 - 16 * q^79 - 104 * q^91 - 64 * q^94 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.14002	−	1.14002i	0.806114	−	0.806114i	−0.177929	−	0.984043i	$-0.556940\pi$
$2$	1.14002	−	1.14002i	0.806114	−	0.806114i	0.984043	+	0.177929i	$0.0569398\pi$
$3$		0			0
$3$		0			0
$4$		−	0.599280i		−	0.299640i
$5$	−2.84492	+	2.84492i	−1.27229	+	1.27229i	−0.327403	+	0.944885i	$0.606174\pi$
$5$	−2.84492	+	2.84492i	−1.27229	+	1.27229i	−0.944885	+	0.327403i	$0.893826\pi$
$6$		0			0
$7$	−2.82684	+	2.82684i	−1.06844	+	1.06844i	−0.0709657	+	0.997479i	$0.522608\pi$
$7$	−2.82684	+	2.82684i	−1.06844	+	1.06844i	−0.997479	+	0.0709657i	$0.977392\pi$
$8$	1.59685	+	1.59685i	0.564570	+	0.564570i
$9$		0			0
$10$			6.48652i			2.05122i
$11$	−2.08263	−	2.08263i	−0.627936	−	0.627936i	0.319612	−	0.947548i	$-0.396447\pi$
$11$	−2.08263	−	2.08263i	−0.627936	−	0.627936i	−0.947548	+	0.319612i	$0.896447\pi$
$12$		0			0
$13$	3.59030	+	0.331331i	0.995769	+	0.0918946i
$13$	3.59030	+	0.331331i	0.995769	+	0.0918946i
$14$			6.44529i			1.72258i
$15$		0			0
$16$	4.83942			1.20986
$17$	−3.94914			−0.957806			−0.478903	−	0.877868i	$-0.658965\pi$
$17$	−3.94914			−0.957806			−0.478903	+	0.877868i	$0.658965\pi$
$18$		0			0
$19$	2.32235	+	2.32235i	0.532783	+	0.532783i	0.921399	−	0.388617i	$-0.127047\pi$
$19$	2.32235	+	2.32235i	0.532783	+	0.532783i	−0.388617	+	0.921399i	$0.627047\pi$
$20$	1.70490	+	1.70490i	0.381228	+	0.381228i
$21$		0			0
$22$	−4.74846			−1.01238
$23$	0.755446			0.157521			0.0787607	−	0.996894i	$-0.474904\pi$
$23$	0.755446			0.157521			0.0787607	+	0.996894i	$0.474904\pi$
$24$		0			0
$25$		−	11.1872i		−	2.23743i
$26$	4.47072	−	3.71528i	0.876781	−	0.728626i
$27$		0			0
$28$	1.69407	+	1.69407i	0.320149	+	0.320149i
$29$		−	3.40981i		−	0.633186i	−0.948562	−	0.316593i	$-0.897461\pi$
$29$		−	3.40981i		−	0.633186i	0.948562	−	0.316593i	$-0.102539\pi$
$30$		0			0
$31$	6.39174	+	6.39174i	1.14799	+	1.14799i	0.986948	+	0.161042i	$0.0514855\pi$
$31$	6.39174	+	6.39174i	1.14799	+	1.14799i	0.161042	+	0.986948i	$0.448515\pi$
$32$	2.32334	−	2.32334i	0.410712	−	0.410712i
$33$		0			0
$34$	−4.50208	+	4.50208i	−0.772101	+	0.772101i
$35$		−	16.0843i		−	2.71874i
$36$		0			0
$37$	−2.85824	+	2.85824i	−0.469892	+	0.469892i	−0.901880	−	0.431987i	$-0.857813\pi$
$37$	−2.85824	+	2.85824i	−0.469892	+	0.469892i	0.431987	+	0.901880i	$0.357813\pi$
$38$	5.29503			0.858967
$39$		0			0
$40$	−9.08580			−1.43659
$41$	2.08263	−	2.08263i	0.325252	−	0.325252i	−0.525526	−	0.850778i	$-0.676131\pi$
$41$	2.08263	−	2.08263i	0.325252	−	0.325252i	0.850778	+	0.525526i	$0.176131\pi$
$42$		0			0
$43$		−	0.526914i		−	0.0803536i	−0.999193	−	0.0401768i	$-0.987208\pi$
$43$		−	0.526914i		−	0.0803536i	0.999193	−	0.0401768i	$-0.0127921\pi$
$44$	−1.24808	+	1.24808i	−0.188155	+	0.188155i
$45$		0			0
$46$	0.861221	−	0.861221i	0.126980	−	0.126980i
$47$	3.18684	+	3.18684i	0.464849	+	0.464849i	0.900241	−	0.435392i	$-0.143390\pi$
$47$	3.18684	+	3.18684i	0.464849	+	0.464849i	−0.435392	+	0.900241i	$0.643390\pi$
$48$		0			0
$49$		−	8.98203i		−	1.28315i
$50$	−12.7536	−	12.7536i	−1.80363	−	1.80363i
$51$		0			0
$52$	0.198560	−	2.15159i	0.0275353	−	0.298372i
$53$			10.3944i			1.42778i	0.700256	+	0.713892i	$0.253069\pi$
$53$			10.3944i			1.42778i	−0.700256	+	0.713892i	$0.746931\pi$
$54$		0			0
$55$	11.8498			1.59783
$56$	−9.02805			−1.20642
$57$		0			0
$58$	−3.88724	−	3.88724i	−0.510420	−	0.510420i
$59$	7.20759	+	7.20759i	0.938348	+	0.938348i	0.998207	−	0.0598591i	$-0.0190652\pi$
$59$	7.20759	+	7.20759i	0.938348	+	0.938348i	−0.0598591	+	0.998207i	$0.519065\pi$
$60$		0			0
$61$	2.91264			0.372926			0.186463	−	0.982462i	$-0.440298\pi$
$61$	2.91264			0.372926			0.186463	+	0.982462i	$0.440298\pi$
$62$	14.5734			1.85082
$63$		0			0
$64$			4.38156i			0.547695i
$65$	−11.1567	+	9.27150i	−1.38382	+	1.14999i
$66$		0			0
$67$	−5.13277	−	5.13277i	−0.627068	−	0.627068i	0.320261	−	0.947329i	$-0.396229\pi$
$67$	−5.13277	−	5.13277i	−0.627068	−	0.627068i	−0.947329	+	0.320261i	$0.896229\pi$
$68$			2.36664i			0.286997i
$69$		0			0
$70$	−18.3364	−	18.3364i	−2.19161	−	2.19161i
$71$	−2.08948	+	2.08948i	−0.247975	+	0.247975i	−0.820139	−	0.572164i	$-0.806104\pi$
$71$	−2.08948	+	2.08948i	−0.247975	+	0.247975i	0.572164	+	0.820139i	$0.306104\pi$
$72$		0			0
$73$	−3.56787	+	3.56787i	−0.417588	+	0.417588i	−0.884372	−	0.466784i	$-0.845413\pi$
$73$	−3.56787	+	3.56787i	−0.417588	+	0.417588i	0.466784	+	0.884372i	$0.345413\pi$
$74$			6.51690i			0.757574i
$75$		0			0
$76$	1.39174	−	1.39174i	0.159643	−	0.159643i
$77$	11.7745			1.34183
$78$		0			0
$79$	5.79246			0.651702			0.325851	−	0.945421i	$-0.394349\pi$
$79$	5.79246			0.651702			0.325851	+	0.945421i	$0.394349\pi$
$80$	−13.7678	+	13.7678i	−1.53929	+	1.53929i
$81$		0			0
$82$		−	4.74846i		−	0.524380i
$83$	7.18887	−	7.18887i	0.789081	−	0.789081i	−0.192262	−	0.981344i	$-0.561582\pi$
$83$	7.18887	−	7.18887i	0.789081	−	0.789081i	0.981344	+	0.192262i	$0.0615824\pi$
$84$		0			0
$85$	11.2350	−	11.2350i	1.21861	−	1.21861i
$86$	−0.600691	−	0.600691i	−0.0647742	−	0.0647742i
$87$		0			0
$88$		−	6.65127i		−	0.709028i
$89$	−1.51774	−	1.51774i	−0.160880	−	0.160880i	0.622076	−	0.782957i	$-0.286289\pi$
$89$	−1.51774	−	1.51774i	−0.160880	−	0.160880i	−0.782957	+	0.622076i	$0.786289\pi$
$90$		0			0
$91$	−11.0858	+	9.21257i	−1.16211	+	0.965739i
$92$		−	0.452723i		−	0.0471997i
$93$		0			0
$94$	7.26611			0.749442
$95$	−13.2138			−1.35571
$96$		0			0
$97$	2.07237	+	2.07237i	0.210417	+	0.210417i	0.804445	−	0.594028i	$-0.202463\pi$
$97$	2.07237	+	2.07237i	0.210417	+	0.210417i	−0.594028	+	0.804445i	$0.702463\pi$
$98$	−10.2397	−	10.2397i	−1.03436	−	1.03436i
$99$		0			0
$100$	−6.70425			−0.670425
$101$	−9.92671			−0.987744			−0.493872	−	0.869535i	$-0.664419\pi$
$101$	−9.92671			−0.987744			−0.493872	+	0.869535i	$0.664419\pi$
$102$		0			0
$103$		−	8.93719i		−	0.880607i	−0.897849	−	0.440304i	$-0.854871\pi$
$103$		−	8.93719i		−	0.880607i	0.897849	−	0.440304i	$-0.145129\pi$
$104$	5.20406	+	6.26223i	0.510300	+	0.614062i
$105$		0			0
$106$	11.8498	+	11.8498i	1.15096	+	1.15096i
$107$			12.3513i			1.19404i	0.802226	+	0.597020i	$0.203649\pi$
$107$			12.3513i			1.19404i	−0.802226	+	0.597020i	$0.796351\pi$
$108$		0			0
$109$	−8.62828	−	8.62828i	−0.826439	−	0.826439i	0.160583	−	0.987022i	$-0.448663\pi$
$109$	−8.62828	−	8.62828i	−0.826439	−	0.826439i	−0.987022	+	0.160583i	$0.948663\pi$
$110$	13.5090	−	13.5090i	1.28803	−	1.28803i
$111$		0			0
$112$	−13.6803	+	13.6803i	−1.29266	+	1.29266i
$113$		−	10.9338i		−	1.02856i	−0.857622	−	0.514281i	$-0.828059\pi$
$113$		−	10.9338i		−	1.02856i	0.857622	−	0.514281i	$-0.171941\pi$
$114$		0			0
$115$	−2.14918	+	2.14918i	−0.200412	+	0.200412i
$116$	−2.04343			−0.189728
$117$		0			0
$118$	16.4335			1.51283
$119$	11.1636	−	11.1636i	1.02336	−	1.02336i
$120$		0			0
$121$		−	2.32532i		−	0.211393i
$122$	3.32046	−	3.32046i	0.300621	−	0.300621i
$123$		0			0
$124$	3.83044	−	3.83044i	0.343984	−	0.343984i
$125$	17.6020	+	17.6020i	1.57437	+	1.57437i
$126$		0			0
$127$		−	6.58429i		−	0.584261i	−0.956378	−	0.292131i	$-0.905636\pi$
$127$		−	6.58429i		−	0.584261i	0.956378	−	0.292131i	$-0.0943642\pi$
$128$	9.64173	+	9.64173i	0.852216	+	0.852216i
$129$		0			0
$130$	−2.14918	+	23.2885i	−0.188496	+	2.04254i
$131$			1.84780i			0.161443i	0.996737	+	0.0807214i	$0.0257224\pi$
$131$			1.84780i			0.161443i	−0.996737	+	0.0807214i	$0.974278\pi$
$132$		0			0
$133$	−13.1298			−1.13850
$134$	−11.7029			−1.01098
$135$		0			0
$136$	−6.30616	−	6.30616i	−0.540749	−	0.540749i
$137$	0.932368	+	0.932368i	0.0796575	+	0.0796575i	0.745813	−	0.666155i	$-0.232061\pi$
$137$	0.932368	+	0.932368i	0.0796575	+	0.0796575i	−0.666155	+	0.745813i	$0.732061\pi$
$138$		0			0
$139$	−1.59985			−0.135697			−0.0678487	−	0.997696i	$-0.521614\pi$
$139$	−1.59985			−0.135697			−0.0678487	+	0.997696i	$0.521614\pi$
$140$	−9.63898			−0.814643
$141$		0			0
$142$			4.76408i			0.399793i
$143$	−6.78721	−	8.16729i	−0.567575	−	0.682983i
$144$		0			0
$145$	9.70064	+	9.70064i	0.805595	+	0.805595i
$146$			8.13488i			0.673247i
$147$		0			0
$148$	1.71289	+	1.71289i	0.140799	+	0.140799i
$149$	10.6174	−	10.6174i	0.869811	−	0.869811i	−0.122640	−	0.992451i	$-0.539136\pi$
$149$	10.6174	−	10.6174i	0.869811	−	0.869811i	0.992451	+	0.122640i	$0.0391361\pi$
$150$		0			0
$151$	−4.67908	+	4.67908i	−0.380778	+	0.380778i	−0.871382	−	0.490605i	$-0.836776\pi$
$151$	−4.67908	+	4.67908i	−0.380778	+	0.380778i	0.490605	+	0.871382i	$0.336776\pi$
$152$			7.41686i			0.601586i
$153$		0			0
$154$	13.4231	−	13.4231i	1.08167	−	1.08167i
$155$	−36.3680			−2.92115
$156$		0			0
$157$	−4.46410			−0.356274			−0.178137	−	0.984006i	$-0.557007\pi$
$157$	−4.46410			−0.356274			−0.178137	+	0.984006i	$0.557007\pi$
$158$	6.60350	−	6.60350i	0.525346	−	0.525346i
$159$		0			0
$160$			13.2194i			1.04509i
$161$	−2.13552	+	2.13552i	−0.168303	+	0.168303i
$162$		0			0
$163$	5.14776	−	5.14776i	0.403204	−	0.403204i	−0.476157	−	0.879361i	$-0.657970\pi$
$163$	5.14776	−	5.14776i	0.403204	−	0.403204i	0.879361	+	0.476157i	$0.157970\pi$
$164$	−1.24808	−	1.24808i	−0.0974584	−	0.0974584i
$165$		0			0
$166$		−	16.3909i		−	1.27218i
$167$	6.61536	+	6.61536i	0.511912	+	0.511912i	0.915112	−	0.403200i	$-0.132102\pi$
$167$	6.61536	+	6.61536i	0.511912	+	0.511912i	−0.403200	+	0.915112i	$0.632102\pi$
$168$		0			0
$169$	12.7804	+	2.37915i	0.983111	+	0.183012i
$170$		−	25.6162i		−	1.96467i
$171$		0			0
$172$	−0.315769			−0.0240771
$173$	5.15052			0.391587			0.195793	−	0.980645i	$-0.437272\pi$
$173$	5.15052			0.391587			0.195793	+	0.980645i	$0.437272\pi$
$174$		0			0
$175$	31.6243	+	31.6243i	2.39057	+	2.39057i
$176$	−10.0787	−	10.0787i	−0.759712	−	0.759712i
$177$		0			0
$178$	−3.46050			−0.259376
$179$	24.9678			1.86618			0.933091	−	0.359641i	$-0.117101\pi$
$179$	24.9678			1.86618			0.933091	+	0.359641i	$0.117101\pi$
$180$		0			0
$181$		−	12.9012i		−	0.958942i	−0.877558	−	0.479471i	$-0.840829\pi$
$181$		−	12.9012i		−	0.958942i	0.877558	−	0.479471i	$-0.159171\pi$
$182$	−2.13552	+	23.1405i	−0.158295	+	1.71529i
$183$		0			0
$184$	1.20633	+	1.20633i	0.0889318	+	0.0889318i
$185$		−	16.2630i		−	1.19568i
$186$		0			0
$187$	8.22458	+	8.22458i	0.601441	+	0.601441i
$188$	1.90981	−	1.90981i	0.139287	−	0.139287i
$189$		0			0
$190$	−15.0640	+	15.0640i	−1.09285	+	1.09285i
$191$			4.73877i			0.342885i	0.985194	+	0.171443i	$0.0548428\pi$
$191$			4.73877i			0.342885i	−0.985194	+	0.171443i	$0.945157\pi$
$192$		0			0
$193$	−13.2715	+	13.2715i	−0.955307	+	0.955307i	−0.999043	−	0.0437361i	$-0.986074\pi$
$193$	−13.2715	+	13.2715i	−0.955307	+	0.955307i	0.0437361	+	0.999043i	$0.486074\pi$
$194$	4.72507			0.339240
$195$		0			0
$196$	−5.38275			−0.384482
$197$	11.3728	−	11.3728i	0.810281	−	0.810281i	−0.174395	−	0.984676i	$-0.555797\pi$
$197$	11.3728	−	11.3728i	0.810281	−	0.810281i	0.984676	+	0.174395i	$0.0557968\pi$
$198$		0			0
$199$			3.44854i			0.244460i	0.992502	+	0.122230i	$0.0390046\pi$
$199$			3.44854i			0.244460i	−0.992502	+	0.122230i	$0.960995\pi$
$200$	17.8642	−	17.8642i	1.26319	−	1.26319i
$201$		0			0
$202$	−11.3166	+	11.3166i	−0.796235	+	0.796235i
$203$	9.63898	+	9.63898i	0.676524	+	0.676524i
$204$		0			0
$205$			11.8498i			0.827628i
$206$	−10.1886	−	10.1886i	−0.709870	−	0.709870i
$207$		0			0
$208$	17.3750	+	1.60345i	1.20474	+	0.111179i
$209$		−	9.67316i		−	0.669107i
$210$		0			0
$211$	11.4485			0.788150			0.394075	−	0.919078i	$-0.371065\pi$
$211$	11.4485			0.788150			0.394075	+	0.919078i	$0.371065\pi$
$212$	6.22917			0.427821
$213$		0			0
$214$	14.0806	+	14.0806i	0.962533	+	0.962533i
$215$	1.49903	+	1.49903i	0.102233	+	0.102233i
$216$		0			0
$217$	−36.1368			−2.45313
$218$	−19.6728			−1.33241
$219$		0			0
$220$		−	7.10136i		−	0.478774i
$221$	−14.1786	−	1.30847i	−0.953754	−	0.0880172i
$222$		0			0
$223$	4.29695	+	4.29695i	0.287745	+	0.287745i	0.836188	−	0.548443i	$-0.184779\pi$
$223$	4.29695	+	4.29695i	0.287745	+	0.287745i	−0.548443	+	0.836188i	$0.684779\pi$
$224$			13.1354i			0.877645i
$225$		0			0
$226$	−12.4647	−	12.4647i	−0.829138	−	0.829138i
$227$	−0.709400	+	0.709400i	−0.0470845	+	0.0470845i	−0.730257	−	0.683173i	$-0.760600\pi$
$227$	−0.709400	+	0.709400i	−0.0470845	+	0.0470845i	0.683173	+	0.730257i	$0.260600\pi$
$228$		0			0
$229$	13.7455	−	13.7455i	0.908327	−	0.908327i	−0.0878099	−	0.996137i	$-0.527987\pi$
$229$	13.7455	−	13.7455i	0.908327	−	0.908327i	0.996137	+	0.0878099i	$0.0279868\pi$
$230$			4.90022i			0.323111i
$231$		0			0
$232$	5.44494	−	5.44494i	0.357478	−	0.357478i
$233$	−23.6593			−1.54997			−0.774987	−	0.631977i	$-0.782244\pi$
$233$	−23.6593			−1.54997			−0.774987	+	0.631977i	$0.782244\pi$
$234$		0			0
$235$	−18.1326			−1.18284
$236$	4.31936	−	4.31936i	0.281166	−	0.281166i
$237$		0			0
$238$		−	25.4533i		−	1.64989i
$239$	−10.6634	+	10.6634i	−0.689761	+	0.689761i	−0.962179	−	0.272418i	$-0.912177\pi$
$239$	−10.6634	+	10.6634i	−0.689761	+	0.689761i	0.272418	+	0.962179i	$0.412177\pi$
$240$		0			0
$241$	−13.1118	+	13.1118i	−0.844607	+	0.844607i	−0.989454	−	0.144847i	$-0.953731\pi$
$241$	−13.1118	+	13.1118i	−0.844607	+	0.844607i	0.144847	+	0.989454i	$0.453731\pi$
$242$	−2.65091	−	2.65091i	−0.170407	−	0.170407i
$243$		0			0
$244$		−	1.74549i		−	0.111743i
$245$	25.5532	+	25.5532i	1.63253	+	1.63253i
$246$		0			0
$247$	7.56844	+	9.10737i	0.481569	+	0.579488i
$248$			20.4132i			1.29624i
$249$		0			0
$250$	40.1332			2.53825
$251$	19.9605			1.25990			0.629948	−	0.776637i	$-0.283076\pi$
$251$	19.9605			1.25990			0.629948	+	0.776637i	$0.283076\pi$
$252$		0			0
$253$	−1.57331	−	1.57331i	−0.0989133	−	0.0989133i
$254$	−7.50620	−	7.50620i	−0.470981	−	0.470981i
$255$		0			0
$256$	13.2204			0.826272
$257$	−3.84205			−0.239660			−0.119830	−	0.992794i	$-0.538235\pi$
$257$	−3.84205			−0.239660			−0.119830	+	0.992794i	$0.538235\pi$
$258$		0			0
$259$		−	16.1596i		−	1.00411i
$260$	5.55622	+	6.68600i	0.344582	+	0.414648i
$261$		0			0
$262$	2.10652	+	2.10652i	0.130141	+	0.130141i
$263$			16.9250i			1.04364i	0.853055	+	0.521821i	$0.174747\pi$
$263$			16.9250i			1.04364i	−0.853055	+	0.521821i	$0.825253\pi$
$264$		0			0
$265$	−29.5713	−	29.5713i	−1.81655	−	1.81655i
$266$	−14.9682	+	14.9682i	−0.917759	+	0.917759i
$267$		0			0
$268$	−3.07597	+	3.07597i	−0.187895	+	0.187895i
$269$		−	13.1409i		−	0.801214i	−0.916250	−	0.400607i	$-0.868799\pi$
$269$		−	13.1409i		−	0.801214i	0.916250	−	0.400607i	$-0.131201\pi$
$270$		0			0
$271$	3.45455	−	3.45455i	0.209849	−	0.209849i	−0.594354	−	0.804203i	$-0.702592\pi$
$271$	3.45455	−	3.45455i	0.209849	−	0.209849i	0.804203	+	0.594354i	$0.202592\pi$
$272$	−19.1115			−1.15881
$273$		0			0
$274$	2.12583			0.128426
$275$	−23.2987	+	23.2987i	−1.40496	+	1.40496i
$276$		0			0
$277$		−	2.38332i		−	0.143200i	−0.997433	−	0.0715999i	$-0.977190\pi$
$277$		−	2.38332i		−	0.143200i	0.997433	−	0.0715999i	$-0.0228105\pi$
$278$	−1.82386	+	1.82386i	−0.109388	+	0.109388i
$279$		0			0
$280$	25.6841	−	25.6841i	1.53492	−	1.53492i
$281$	−20.8144	−	20.8144i	−1.24168	−	1.24168i	−0.959302	−	0.282382i	$-0.908875\pi$
$281$	−20.8144	−	20.8144i	−1.24168	−	1.24168i	−0.282382	−	0.959302i	$-0.591125\pi$
$282$		0			0
$283$			29.2051i			1.73606i	0.496511	+	0.868030i	$0.334614\pi$
$283$			29.2051i			1.73606i	−0.496511	+	0.868030i	$0.665386\pi$
$284$	1.25218	+	1.25218i	0.0743033	+	0.0743033i
$285$		0			0
$286$	−17.0484	−	1.57331i	−1.00809	−	0.0930319i
$287$			11.7745i			0.695027i
$288$		0			0
$289$	−1.40432			−0.0826071
$290$	22.1178			1.29880
$291$		0			0
$292$	2.13816	+	2.13816i	0.125126	+	0.125126i
$293$	23.6406	+	23.6406i	1.38110	+	1.38110i	0.842670	+	0.538430i	$0.180982\pi$
$293$	23.6406	+	23.6406i	1.38110	+	1.38110i	0.538430	+	0.842670i	$0.319018\pi$
$294$		0			0
$295$	−41.0100			−2.38770
$296$	−9.12835			−0.530575
$297$		0			0
$298$		−	24.2080i		−	1.40233i
$299$	2.71227	+	0.250302i	0.156855	+	0.0144754i
$300$		0			0
$301$	1.48950	+	1.48950i	0.0858533	+	0.0858533i
$302$			10.6685i			0.613901i
$303$		0			0
$304$	11.2388	+	11.2388i	0.644590	+	0.644590i
$305$	−8.28624	+	8.28624i	−0.474469	+	0.474469i
$306$		0			0
$307$	−10.5089	+	10.5089i	−0.599777	+	0.599777i	−0.940253	−	0.340476i	$-0.889412\pi$
$307$	−10.5089	+	10.5089i	−0.599777	+	0.599777i	0.340476	+	0.940253i	$0.389412\pi$
$308$		−	7.05622i		−	0.402066i
$309$		0			0
$310$	−41.4601	+	41.4601i	−2.35478	+	2.35478i
$311$	4.95488			0.280966			0.140483	−	0.990083i	$-0.455135\pi$
$311$	4.95488			0.280966			0.140483	+	0.990083i	$0.455135\pi$
$312$		0			0
$313$	4.30078			0.243094			0.121547	−	0.992586i	$-0.461214\pi$
$313$	4.30078			0.243094			0.121547	+	0.992586i	$0.461214\pi$
$314$	−5.08915	+	5.08915i	−0.287198	+	0.287198i
$315$		0			0
$316$		−	3.47130i		−	0.195276i
$317$	18.9565	−	18.9565i	1.06470	−	1.06470i	0.0669483	−	0.997756i	$-0.478674\pi$
$317$	18.9565	−	18.9565i	1.06470	−	1.06470i	0.997756	−	0.0669483i	$-0.0213263\pi$
$318$		0			0
$319$	−7.10136	+	7.10136i	−0.397600	+	0.397600i
$320$	−12.4652	−	12.4652i	−0.696825	−	0.696825i
$321$		0			0
$322$			4.86907i			0.271343i
$323$	−9.17126	−	9.17126i	−0.510303	−	0.510303i
$324$		0			0
$325$	3.70665	−	40.1652i	0.205608	−	2.22797i
$326$		−	11.7371i		−	0.650057i
$327$		0			0
$328$	6.65127			0.367255
$329$	−18.0174			−0.993330
$330$		0			0
$331$	−21.1471	−	21.1471i	−1.16235	−	1.16235i	−0.983960	−	0.178387i	$-0.942912\pi$
$331$	−21.1471	−	21.1471i	−1.16235	−	1.16235i	−0.178387	−	0.983960i	$-0.557088\pi$
$332$	−4.30815	−	4.30815i	−0.236440	−	0.236440i
$333$		0			0
$334$	15.0833			0.825319
$335$	29.2047			1.59562
$336$		0			0
$337$		−	26.3468i		−	1.43520i	−0.696456	−	0.717600i	$-0.745241\pi$
$337$		−	26.3468i		−	1.43520i	0.696456	−	0.717600i	$-0.254759\pi$
$338$	17.2822	−	11.8577i	0.940028	−	0.644971i
$339$		0			0
$340$	−6.73290	−	6.73290i	−0.365143	−	0.365143i
$341$		−	26.6232i		−	1.44173i
$342$		0			0
$343$	5.60288	+	5.60288i	0.302527	+	0.302527i
$344$	0.841400	−	0.841400i	0.0453652	−	0.0453652i
$345$		0			0
$346$	5.87168	−	5.87168i	0.315664	−	0.315664i
$347$			0.164998i			0.00885753i	0.999990	+	0.00442877i	$0.00140972\pi$
$347$			0.164998i			0.00885753i	−0.999990	+	0.00442877i	$0.998590\pi$
$348$		0			0
$349$	25.4287	−	25.4287i	1.36117	−	1.36117i	0.488739	−	0.872430i	$-0.337457\pi$
$349$	25.4287	−	25.4287i	1.36117	−	1.36117i	0.872430	−	0.488739i	$-0.162543\pi$
$350$	72.1045			3.85415
$351$		0			0
$352$	−9.67729			−0.515801
$353$	8.52107	−	8.52107i	0.453531	−	0.453531i	−0.442994	−	0.896525i	$-0.646084\pi$
$353$	8.52107	−	8.52107i	0.453531	−	0.453531i	0.896525	+	0.442994i	$0.146084\pi$
$354$		0			0
$355$		−	11.8888i		−	0.630992i
$356$	−0.909551	+	0.909551i	−0.0482061	+	0.0482061i
$357$		0			0
$358$	28.4637	−	28.4637i	1.50436	−	1.50436i
$359$	−20.2377	−	20.2377i	−1.06810	−	1.06810i	−0.997505	−	0.0705983i	$-0.977509\pi$
$359$	−20.2377	−	20.2377i	−1.06810	−	1.06810i	−0.0705983	−	0.997505i	$-0.522491\pi$
$360$		0			0
$361$		−	8.21342i		−	0.432285i
$362$	−14.7077	−	14.7077i	−0.773017	−	0.773017i
$363$		0			0
$364$	5.52091	+	6.64350i	0.289374	+	0.348214i
$365$		−	20.3006i		−	1.06258i
$366$		0			0
$367$	−6.88506			−0.359397			−0.179699	−	0.983722i	$-0.557512\pi$
$367$	−6.88506			−0.359397			−0.179699	+	0.983722i	$0.557512\pi$
$368$	3.65592			0.190578
$369$		0			0
$370$	−18.5401	−	18.5401i	−0.963852	−	0.963852i
$371$	−29.3834	−	29.3834i	−1.52551	−	1.52551i
$372$		0			0
$373$	32.1812			1.66628			0.833140	−	0.553062i	$-0.186541\pi$
$373$	32.1812			1.66628			0.833140	+	0.553062i	$0.186541\pi$
$374$	18.7523			0.969660
$375$		0			0
$376$			10.1778i			0.524879i
$377$	1.12977	−	12.2422i	0.0581864	−	0.630507i
$378$		0			0
$379$	14.4969	+	14.4969i	0.744657	+	0.744657i	0.973470	−	0.228813i	$-0.0734845\pi$
$379$	14.4969	+	14.4969i	0.744657	+	0.744657i	−0.228813	+	0.973470i	$0.573484\pi$
$380$			7.91876i			0.406224i
$381$		0			0
$382$	5.40228	+	5.40228i	0.276404	+	0.276404i
$383$	−19.6199	+	19.6199i	−1.00253	+	1.00253i	−0.00253237	+	0.999997i	$0.500806\pi$
$383$	−19.6199	+	19.6199i	−1.00253	+	1.00253i	−0.999997	+	0.00253237i	$0.999194\pi$
$384$		0			0
$385$	−33.4976	+	33.4976i	−1.70719	+	1.70719i
$386$			30.2596i			1.54017i
$387$		0			0
$388$	1.24193	−	1.24193i	0.0630493	−	0.0630493i
$389$	5.17424			0.262345			0.131172	−	0.991360i	$-0.458126\pi$
$389$	5.17424			0.262345			0.131172	+	0.991360i	$0.458126\pi$
$390$		0			0
$391$	−2.98336			−0.150875
$392$	14.3429	−	14.3429i	0.724427	−	0.724427i
$393$		0			0
$394$		−	25.9305i		−	1.30636i
$395$	−16.4791	+	16.4791i	−0.829153	+	0.829153i
$396$		0			0
$397$	−26.9826	+	26.9826i	−1.35422	+	1.35422i	−0.473336	+	0.880882i	$0.656950\pi$
$397$	−26.9826	+	26.9826i	−1.35422	+	1.35422i	−0.880882	+	0.473336i	$0.843050\pi$
$398$	3.93140	+	3.93140i	0.197063	+	0.197063i
$399$		0			0
$400$		−	54.1394i		−	2.70697i
$401$	−11.4444	−	11.4444i	−0.571508	−	0.571508i	0.361041	−	0.932550i	$-0.382421\pi$
$401$	−11.4444	−	11.4444i	−0.571508	−	0.571508i	−0.932550	+	0.361041i	$0.882421\pi$
$402$		0			0
$403$	20.8304	+	25.0660i	1.03764	+	1.24863i
$404$			5.94888i			0.295968i
$405$		0			0
$406$	21.9772			1.09071
$407$	11.9053			0.590125
$408$		0			0
$409$	−16.7065	−	16.7065i	−0.826084	−	0.826084i	0.160888	−	0.986973i	$-0.448564\pi$
$409$	−16.7065	−	16.7065i	−0.826084	−	0.826084i	−0.986973	+	0.160888i	$0.948564\pi$
$410$	13.5090	+	13.5090i	0.667163	+	0.667163i
$411$		0			0
$412$	−5.35588			−0.263865
$413$	−40.7494			−2.00514
$414$		0			0
$415$			40.9036i			2.00788i
$416$	9.11126	−	7.57167i	0.446716	−	0.371232i
$417$		0			0
$418$	−11.0276	−	11.0276i	−0.539376	−	0.539376i
$419$		−	39.8507i		−	1.94683i	−0.229040	−	0.973417i	$-0.573559\pi$
$419$		−	39.8507i		−	1.94683i	0.229040	−	0.973417i	$-0.426441\pi$
$420$		0			0
$421$	−1.73565	−	1.73565i	−0.0845905	−	0.0845905i	0.663545	−	0.748136i	$-0.269051\pi$
$421$	−1.73565	−	1.73565i	−0.0845905	−	0.0845905i	−0.748136	+	0.663545i	$0.769051\pi$
$422$	13.0515	−	13.0515i	0.635339	−	0.635339i
$423$		0			0
$424$	−16.5983	+	16.5983i	−0.806084	+	0.806084i
$425$			44.1797i			2.14303i
$426$		0			0
$427$	−8.23357	+	8.23357i	−0.398450	+	0.398450i
$428$	7.40186			0.357782
$429$		0			0
$430$	3.41784			0.164823
$431$	−5.07206	+	5.07206i	−0.244313	+	0.244313i	−0.818632	−	0.574319i	$-0.805267\pi$
$431$	−5.07206	+	5.07206i	−0.244313	+	0.244313i	0.574319	+	0.818632i	$0.305267\pi$
$432$		0			0
$433$			10.4803i			0.503650i	0.967773	+	0.251825i	$0.0810308\pi$
$433$			10.4803i			0.503650i	−0.967773	+	0.251825i	$0.918969\pi$
$434$	−41.1966	+	41.1966i	−1.97750	+	1.97750i
$435$		0			0
$436$	−5.17075	+	5.17075i	−0.247634	+	0.247634i
$437$	1.75441	+	1.75441i	0.0839246	+	0.0839246i
$438$		0			0
$439$			2.71763i			0.129705i	0.997895	+	0.0648526i	$0.0206577\pi$
$439$			2.71763i			0.129705i	−0.997895	+	0.0648526i	$0.979342\pi$
$440$	18.9223	+	18.9223i	0.902087	+	0.902087i
$441$		0			0
$442$	−17.6555	+	14.6721i	−0.839786	+	0.697882i
$443$			4.55328i			0.216333i	0.994133	+	0.108166i	$0.0344980\pi$
$443$			4.55328i			0.216333i	−0.994133	+	0.108166i	$0.965502\pi$
$444$		0			0
$445$	8.63571			0.409372
$446$	9.79719			0.463910
$447$		0			0
$448$	−12.3860	−	12.3860i	−0.585181	−	0.585181i
$449$	28.2655	+	28.2655i	1.33393	+	1.33393i	0.901822	+	0.432107i	$0.142230\pi$
$449$	28.2655	+	28.2655i	1.33393	+	1.33393i	0.432107	+	0.901822i	$0.357770\pi$
$450$		0			0
$451$	−8.67468			−0.408475
$452$	−6.55238			−0.308198
$453$		0			0
$454$			1.61746i			0.0759110i
$455$	5.32921	−	57.7473i	0.249837	−	2.70723i
$456$		0			0
$457$	6.20457	+	6.20457i	0.290237	+	0.290237i	0.837174	−	0.546937i	$-0.184206\pi$
$457$	6.20457	+	6.20457i	0.290237	+	0.290237i	−0.546937	+	0.837174i	$0.684206\pi$
$458$		−	31.3402i		−	1.46443i
$459$		0			0
$460$	1.28796	+	1.28796i	0.0600516	+	0.0600516i
$461$	−24.9610	+	24.9610i	−1.16255	+	1.16255i	−0.178632	+	0.983916i	$0.557167\pi$
$461$	−24.9610	+	24.9610i	−1.16255	+	1.16255i	−0.983916	+	0.178632i	$0.942833\pi$
$462$		0			0
$463$	−0.184419	+	0.184419i	−0.00857068	+	0.00857068i	−0.711379	−	0.702808i	$-0.751929\pi$
$463$	−0.184419	+	0.184419i	−0.00857068	+	0.00857068i	0.702808	+	0.711379i	$0.251929\pi$
$464$		−	16.5015i		−	0.766064i
$465$		0			0
$466$	−26.9721	+	26.9721i	−1.24946	+	1.24946i
$467$	−3.26530			−0.151100			−0.0755500	−	0.997142i	$-0.524071\pi$
$467$	−3.26530			−0.151100			−0.0755500	+	0.997142i	$0.524071\pi$
$468$		0			0
$469$	29.0190			1.33997
$470$	−20.6715	+	20.6715i	−0.953506	+	0.953506i
$471$		0			0
$472$			23.0188i			1.05953i
$473$	−1.09737	+	1.09737i	−0.0504569	+	0.0504569i
$474$		0			0
$475$	25.9805	−	25.9805i	1.19207	−	1.19207i
$476$	−6.69010	−	6.69010i	−0.306640	−	0.306640i
$477$		0			0
$478$			24.3130i			1.11205i
$479$	15.2846	+	15.2846i	0.698369	+	0.698369i	0.964059	−	0.265690i	$-0.0855996\pi$
$479$	15.2846	+	15.2846i	0.698369	+	0.698369i	−0.265690	+	0.964059i	$0.585600\pi$
$480$		0			0
$481$	−11.2090	+	9.31492i	−0.511085	+	0.424724i
$482$			29.8954i			1.36170i
$483$		0			0
$484$	−1.39352			−0.0633418
$485$	−11.7914			−0.535422
$486$		0			0
$487$	11.7321	+	11.7321i	0.531630	+	0.531630i	0.921057	−	0.389427i	$-0.127327\pi$
$487$	11.7321	+	11.7321i	0.531630	+	0.531630i	−0.389427	+	0.921057i	$0.627327\pi$
$488$	4.65104	+	4.65104i	0.210543	+	0.210543i
$489$		0			0
$490$	58.2621			2.63202
$491$	25.7233			1.16087			0.580437	−	0.814305i	$-0.302882\pi$
$491$	25.7233			1.16087			0.580437	+	0.814305i	$0.302882\pi$
$492$		0			0
$493$			13.4658i			0.606469i
$494$	19.0107	+	1.75441i	0.855333	+	0.0789345i
$495$		0			0
$496$	30.9323	+	30.9323i	1.38890	+	1.38890i
$497$		−	11.8132i		−	0.529896i
$498$		0			0
$499$	16.0744	+	16.0744i	0.719589	+	0.719589i	0.968521	−	0.248932i	$-0.0800794\pi$
$499$	16.0744	+	16.0744i	0.719589	+	0.719589i	−0.248932	+	0.968521i	$0.580079\pi$
$500$	10.5485	−	10.5485i	0.471745	−	0.471745i
$501$		0			0
$502$	22.7553	−	22.7553i	1.01562	−	1.01562i
$503$		−	18.0242i		−	0.803658i	−0.915715	−	0.401829i	$-0.868375\pi$
$503$		−	18.0242i		−	0.803658i	0.915715	−	0.401829i	$-0.131625\pi$
$504$		0			0
$505$	28.2407	−	28.2407i	1.25670	−	1.25670i
$506$	−3.58721			−0.159471
$507$		0			0
$508$	−3.94583			−0.175068
$509$	−22.7730	+	22.7730i	−1.00940	+	1.00940i	−0.00944076	+	0.999955i	$0.503005\pi$
$509$	−22.7730	+	22.7730i	−1.00940	+	1.00940i	−0.999955	+	0.00944076i	$0.996995\pi$
$510$		0			0
$511$		−	20.1716i		−	0.892339i
$512$	−4.21201	+	4.21201i	−0.186146	+	0.186146i
$513$		0			0
$514$	−4.38000	+	4.38000i	−0.193194	+	0.193194i
$515$	25.4256	+	25.4256i	1.12039	+	1.12039i
$516$		0			0
$517$		−	13.2740i		−	0.583790i
$518$	−18.4222	−	18.4222i	−0.809426	−	0.809426i
$519$		0			0
$520$	−32.6207	−	3.01041i	−1.43051	−	0.132015i
$521$			34.8024i			1.52472i	0.647152	+	0.762361i	$0.275960\pi$
$521$			34.8024i			1.52472i	−0.647152	+	0.762361i	$0.724040\pi$
$522$		0			0
$523$	−0.671646			−0.0293690			−0.0146845	−	0.999892i	$-0.504674\pi$
$523$	−0.671646			−0.0293690			−0.0146845	+	0.999892i	$0.504674\pi$
$524$	1.10735			0.0483747
$525$		0			0
$526$	19.2948	+	19.2948i	0.841294	+	0.841294i
$527$	−25.2418	−	25.2418i	−1.09955	−	1.09955i
$528$		0			0
$529$	−22.4293			−0.975187
$530$	−67.4237			−2.92870
$531$		0			0
$532$			7.86842i			0.341139i
$533$	8.16729	−	6.78721i	0.353764	−	0.293987i
$534$		0			0
$535$	−35.1384	−	35.1384i	−1.51916	−	1.51916i
$536$		−	16.3925i		−	0.708047i
$537$		0			0
$538$	−14.9808	−	14.9808i	−0.645870	−	0.645870i
$539$	−18.7062	+	18.7062i	−0.805734	+	0.805734i
$540$		0			0
$541$	23.7311	−	23.7311i	1.02028	−	1.02028i	0.0204881	−	0.999790i	$-0.493478\pi$
$541$	23.7311	−	23.7311i	1.02028	−	1.02028i	0.999790	−	0.0204881i	$-0.00652201\pi$
$542$		−	7.87649i		−	0.338324i
$543$		0			0
$544$	−9.17517	+	9.17517i	−0.393382	+	0.393382i
$545$	49.0936			2.10294
$546$		0			0
$547$	−12.5878			−0.538217			−0.269108	−	0.963110i	$-0.586729\pi$
$547$	−12.5878			−0.538217			−0.269108	+	0.963110i	$0.586729\pi$
$548$	0.558749	−	0.558749i	0.0238686	−	0.0238686i
$549$		0			0
$550$			53.1219i			2.26512i
$551$	7.91876	−	7.91876i	0.337350	−	0.337350i
$552$		0			0
$553$	−16.3743	+	16.3743i	−0.696308	+	0.696308i
$554$	−2.71703	−	2.71703i	−0.115435	−	0.115435i
$555$		0			0
$556$			0.958758i			0.0406604i
$557$	9.28336	+	9.28336i	0.393349	+	0.393349i	0.875879	−	0.482530i	$-0.160282\pi$
$557$	9.28336	+	9.28336i	0.393349	+	0.393349i	−0.482530	+	0.875879i	$0.660282\pi$
$558$		0			0
$559$	0.174583	−	1.89178i	0.00738406	−	0.0800136i
$560$		−	77.8386i		−	3.28928i
$561$		0			0
$562$	−47.4576			−2.00188
$563$	24.7006			1.04100			0.520502	−	0.853860i	$-0.325745\pi$
$563$	24.7006			1.04100			0.520502	+	0.853860i	$0.325745\pi$
$564$		0			0
$565$	31.1057	+	31.1057i	1.30863	+	1.30863i
$566$	33.2943	+	33.2943i	1.39946	+	1.39946i
$567$		0			0
$568$	−6.67314			−0.279999
$569$	11.6163			0.486980			0.243490	−	0.969903i	$-0.421708\pi$
$569$	11.6163			0.486980			0.243490	+	0.969903i	$0.421708\pi$
$570$		0			0
$571$			4.79069i			0.200484i	0.994963	+	0.100242i	$0.0319617\pi$
$571$			4.79069i			0.200484i	−0.994963	+	0.100242i	$0.968038\pi$
$572$	−4.89449	+	4.06744i	−0.204649	+	0.170068i
$573$		0			0
$574$	13.4231	+	13.4231i	0.560271	+	0.560271i
$575$		−	8.45130i		−	0.352443i
$576$		0			0
$577$	−10.9082	−	10.9082i	−0.454116	−	0.454116i	0.442602	−	0.896718i	$-0.354055\pi$
$577$	−10.9082	−	10.9082i	−0.454116	−	0.454116i	−0.896718	+	0.442602i	$0.854055\pi$
$578$	−1.60095	+	1.60095i	−0.0665907	+	0.0665907i
$579$		0			0
$580$	5.81340	−	5.81340i	0.241388	−	0.241388i
$581$			40.6436i			1.68618i
$582$		0			0
$583$	21.6477	−	21.6477i	0.896557	−	0.896557i
$584$	−11.3947			−0.471515
$585$		0			0
$586$	53.9015			2.22665
$587$	−21.9578	+	21.9578i	−0.906296	+	0.906296i	−0.995971	−	0.0896746i	$-0.971417\pi$
$587$	−21.9578	+	21.9578i	−0.906296	+	0.906296i	0.0896746	+	0.995971i	$0.471417\pi$
$588$		0			0
$589$			29.6876i			1.22326i
$590$	−46.7522	+	46.7522i	−1.92476	+	1.92476i
$591$		0			0
$592$	−13.8323	+	13.8323i	−0.568502	+	0.568502i
$593$	−24.5051	−	24.5051i	−1.00630	−	1.00630i	−0.999980	−	0.00632392i	$-0.997987\pi$
$593$	−24.5051	−	24.5051i	−1.00630	−	1.00630i	−0.00632392	−	0.999980i	$-0.502013\pi$
$594$		0			0
$595$			63.5190i			2.60402i
$596$	−6.36279	−	6.36279i	−0.260630	−	0.260630i
$597$		0			0
$598$	3.37739	−	2.80669i	0.138112	−	0.114774i
$599$		−	23.0963i		−	0.943689i	−0.881682	−	0.471844i	$-0.843588\pi$
$599$		−	23.0963i		−	0.943689i	0.881682	−	0.471844i	$-0.156412\pi$
$600$		0			0
$601$	18.0484			0.736209			0.368105	−	0.929784i	$-0.380007\pi$
$601$	18.0484			0.736209			0.368105	+	0.929784i	$0.380007\pi$
$602$	3.39611			0.138415
$603$		0			0
$604$	2.80408	+	2.80408i	0.114096	+	0.114096i
$605$	6.61536	+	6.61536i	0.268953	+	0.268953i
$606$		0			0
$607$	−5.55379			−0.225421			−0.112711	−	0.993628i	$-0.535953\pi$
$607$	−5.55379			−0.225421			−0.112711	+	0.993628i	$0.535953\pi$
$608$	10.7912			0.437640
$609$		0			0
$610$			18.8929i			0.764952i
$611$	10.3858	+	12.4976i	0.420165	+	0.505599i
$612$		0			0
$613$	−15.8678	−	15.8678i	−0.640894	−	0.640894i	0.309881	−	0.950775i	$-0.399711\pi$
$613$	−15.8678	−	15.8678i	−0.640894	−	0.640894i	−0.950775	+	0.309881i	$0.899711\pi$
$614$			23.9608i			0.966978i
$615$		0			0
$616$	18.8021	+	18.8021i	0.757557	+	0.757557i
$617$	−15.6265	+	15.6265i	−0.629098	+	0.629098i	−0.947841	−	0.318743i	$-0.896739\pi$
$617$	−15.6265	+	15.6265i	−0.629098	+	0.629098i	0.318743	+	0.947841i	$0.396739\pi$
$618$		0			0
$619$	30.6482	−	30.6482i	1.23185	−	1.23185i	0.268602	−	0.963251i	$-0.413438\pi$
$619$	30.6482	−	30.6482i	1.23185	−	1.23185i	0.963251	−	0.268602i	$-0.0865617\pi$
$620$			21.7946i			0.875292i
$621$		0			0
$622$	5.64866	−	5.64866i	0.226490	−	0.226490i
$623$	8.58081			0.343783
$624$		0			0
$625$	−44.2169			−1.76868
$626$	4.90296	−	4.90296i	0.195962	−	0.195962i
$627$		0			0
$628$			2.67525i			0.106754i
$629$	11.2876	−	11.2876i	0.450066	−	0.450066i
$630$		0			0
$631$	−11.2885	+	11.2885i	−0.449389	+	0.449389i	−0.895151	−	0.445762i	$-0.852933\pi$
$631$	−11.2885	+	11.2885i	−0.449389	+	0.449389i	0.445762	+	0.895151i	$0.352933\pi$
$632$	9.24966	+	9.24966i	0.367932	+	0.367932i
$633$		0			0
$634$		−	43.2216i		−	1.71655i
$635$	18.7318	+	18.7318i	0.743348	+	0.743348i
$636$		0			0
$637$	2.97602	−	32.2481i	0.117914	−	1.27772i
$638$			16.1914i			0.641022i
$639$		0			0
$640$	−54.8599			−2.16853
$641$	20.8879			0.825021			0.412510	−	0.910953i	$-0.364652\pi$
$641$	20.8879			0.825021			0.412510	+	0.910953i	$0.364652\pi$
$642$		0			0
$643$	32.4927	+	32.4927i	1.28139	+	1.28139i	0.939879	+	0.341507i	$0.110937\pi$
$643$	32.4927	+	32.4927i	1.28139	+	1.28139i	0.341507	+	0.939879i	$0.389063\pi$
$644$	1.27978	+	1.27978i	0.0504302	+	0.0504302i
$645$		0			0
$646$	−20.9108			−0.822724
$647$	11.9714			0.470646			0.235323	−	0.971917i	$-0.424385\pi$
$647$	11.9714			0.470646			0.235323	+	0.971917i	$0.424385\pi$
$648$		0			0
$649$		−	30.0214i		−	1.17844i
$650$	−41.5634	−	50.0147i	−1.63025	−	1.96174i
$651$		0			0
$652$	−3.08495	−	3.08495i	−0.120816	−	0.120816i
$653$			9.71059i			0.380005i	0.981784	+	0.190002i	$0.0608496\pi$
$653$			9.71059i			0.380005i	−0.981784	+	0.190002i	$0.939150\pi$
$654$		0			0
$655$	−5.25684	−	5.25684i	−0.205402	−	0.205402i
$656$	10.0787	−	10.0787i	0.393508	−	0.393508i
$657$		0			0
$658$	−20.5401	+	20.5401i	−0.800737	+	0.800737i
$659$		−	29.0022i		−	1.12977i	−0.825171	−	0.564884i	$-0.808921\pi$
$659$		−	29.0022i		−	1.12977i	0.825171	−	0.564884i	$-0.191079\pi$
$660$		0			0
$661$	22.9631	−	22.9631i	0.893160	−	0.893160i	−0.101659	−	0.994819i	$-0.532415\pi$
$661$	22.9631	−	22.9631i	0.893160	−	0.893160i	0.994819	+	0.101659i	$0.0324151\pi$
$662$	−48.2160			−1.87397
$663$		0			0
$664$	22.9590			0.890984
$665$	37.3532	−	37.3532i	1.44850	−	1.44850i
$666$		0			0
$667$		−	2.57593i		−	0.0997403i
$668$	3.96445	−	3.96445i	0.153389	−	0.153389i
$669$		0			0
$670$	33.2938	−	33.2938i	1.28625	−	1.28625i
$671$	−6.06595	−	6.06595i	−0.234173	−	0.234173i
$672$		0			0
$673$			12.5669i			0.484420i	0.970224	+	0.242210i	$0.0778723\pi$
$673$			12.5669i			0.484420i	−0.970224	+	0.242210i	$0.922128\pi$
$674$	−30.0358	−	30.0358i	−1.15693	−	1.15693i
$675$		0			0
$676$	1.42578	−	7.65906i	0.0548376	−	0.294579i
$677$		−	21.1632i		−	0.813367i	−0.913569	−	0.406684i	$-0.866685\pi$
$677$		−	21.1632i		−	0.813367i	0.913569	−	0.406684i	$-0.133315\pi$
$678$		0			0
$679$	−11.7165			−0.449638
$680$	35.8811			1.37598
$681$		0			0
$682$	−30.3509	−	30.3509i	−1.16220	−	1.16220i
$683$	6.59843	+	6.59843i	0.252482	+	0.252482i	0.821987	−	0.569506i	$-0.192865\pi$
$683$	6.59843	+	6.59843i	0.252482	+	0.252482i	−0.569506	+	0.821987i	$0.692865\pi$
$684$		0			0
$685$	−5.30503			−0.202695
$686$	12.7748			0.487743
$687$		0			0
$688$		−	2.54996i		−	0.0972163i
$689$	−3.44399	+	37.3191i	−0.131206	+	1.42174i
$690$		0			0
$691$	−34.7891	−	34.7891i	−1.32344	−	1.32344i	−0.910974	−	0.412465i	$-0.864668\pi$
$691$	−34.7891	−	34.7891i	−1.32344	−	1.32344i	−0.412465	−	0.910974i	$-0.635332\pi$
$692$		−	3.08660i		−	0.117335i
$693$		0			0
$694$	0.188100	+	0.188100i	0.00714018	+	0.00714018i
$695$	4.55145	−	4.55145i	0.172646	−	0.172646i
$696$		0			0
$697$	−8.22458	+	8.22458i	−0.311528	+	0.311528i
$698$		−	57.9784i		−	2.19451i
$699$		0			0
$700$	18.9518	−	18.9518i	0.716311	−	0.716311i
$701$	31.6224			1.19436			0.597181	−	0.802106i	$-0.296287\pi$
$701$	31.6224			1.19436			0.597181	+	0.802106i	$0.296287\pi$
$702$		0			0
$703$	−13.2757			−0.500701
$704$	9.12515	−	9.12515i	0.343917	−	0.343917i
$705$		0			0
$706$		−	19.4283i		−	0.731195i
$707$	28.0612	−	28.0612i	1.05535	−	1.05535i
$708$		0			0
$709$	−7.91321	+	7.91321i	−0.297187	+	0.297187i	−0.839911	−	0.542724i	$-0.817393\pi$
$709$	−7.91321	+	7.91321i	−0.297187	+	0.297187i	0.542724	+	0.839911i	$0.317393\pi$
$710$	−13.5534	−	13.5534i	−0.508652	−	0.508652i
$711$		0			0
$712$		−	4.84719i		−	0.181656i
$713$	4.82861	+	4.82861i	0.180833	+	0.180833i
$714$		0			0
$715$	42.5444	+	3.92621i	1.59107	+	0.146832i
$716$		−	14.9627i		−	0.559183i
$717$		0			0
$718$	−46.1426			−1.72203
$719$	7.86279			0.293233			0.146616	−	0.989193i	$-0.453162\pi$
$719$	7.86279			0.293233			0.146616	+	0.989193i	$0.453162\pi$
$720$		0			0
$721$	25.2640	+	25.2640i	0.940880	+	0.940880i
$722$	−9.36344	−	9.36344i	−0.348471	−	0.348471i
$723$		0			0
$724$	−7.73146			−0.287337
$725$	−38.1461			−1.41671
$726$		0			0
$727$		−	8.92509i		−	0.331013i	−0.986209	−	0.165507i	$-0.947074\pi$
$727$		−	8.92509i		−	0.331013i	0.986209	−	0.165507i	$-0.0529259\pi$
$728$	−32.4134	−	2.99127i	−1.20132	−	0.110864i
$729$		0			0
$730$	−23.1431	−	23.1431i	−0.856564	−	0.856564i
$731$			2.08085i			0.0769632i
$732$		0			0
$733$	13.8333	+	13.8333i	0.510944	+	0.510944i	0.914816	−	0.403872i	$-0.132336\pi$
$733$	13.8333	+	13.8333i	0.510944	+	0.510944i	−0.403872	+	0.914816i	$0.632336\pi$
$734$	−7.84909	+	7.84909i	−0.289715	+	0.289715i
$735$		0			0
$736$	1.75515	−	1.75515i	0.0646959	−	0.0646959i
$737$			21.3793i			0.787517i
$738$		0			0
$739$	10.3041	−	10.3041i	0.379042	−	0.379042i	−0.491714	−	0.870757i	$-0.663630\pi$
$739$	10.3041	−	10.3041i	0.379042	−	0.379042i	0.870757	+	0.491714i	$0.163630\pi$
$740$	−9.74607			−0.358273
$741$		0			0
$742$	−66.9951			−2.45947
$743$	−1.22694	+	1.22694i	−0.0450122	+	0.0450122i	−0.729255	−	0.684242i	$-0.760133\pi$
$743$	−1.22694	+	1.22694i	−0.0450122	+	0.0450122i	0.684242	+	0.729255i	$0.260133\pi$
$744$		0			0
$745$			60.4113i			2.21330i
$746$	36.6871	−	36.6871i	1.34321	−	1.34321i
$747$		0			0
$748$	4.92883	−	4.92883i	0.180216	−	0.180216i
$749$	−34.9150	−	34.9150i	−1.27577	−	1.27577i
$750$		0			0
$751$		−	50.9443i		−	1.85898i	−0.368842	−	0.929492i	$-0.620246\pi$
$751$		−	50.9443i		−	1.85898i	0.368842	−	0.929492i	$-0.379754\pi$
$752$	15.4225	+	15.4225i	0.562400	+	0.562400i
$753$		0			0
$754$	−12.6684	−	15.2443i	−0.461355	−	0.555165i
$755$		−	26.6232i		−	0.968918i
$756$		0			0
$757$	13.7057			0.498143			0.249071	−	0.968485i	$-0.419875\pi$
$757$	13.7057			0.498143			0.249071	+	0.968485i	$0.419875\pi$
$758$	33.0535			1.20056
$759$		0			0
$760$	−21.1004	−	21.1004i	−0.765391	−	0.765391i
$761$	−20.9931	−	20.9931i	−0.761000	−	0.761000i	0.215503	−	0.976503i	$-0.430861\pi$
$761$	−20.9931	−	20.9931i	−0.761000	−	0.761000i	−0.976503	+	0.215503i	$0.930861\pi$
$762$		0			0
$763$	48.7815			1.76601
$764$	2.83985			0.102742
$765$		0			0
$766$			44.7340i			1.61631i
$767$	23.4893	+	28.2655i	0.848148	+	1.02061i
$768$		0			0
$769$	−5.06281	−	5.06281i	−0.182570	−	0.182570i	0.609905	−	0.792475i	$-0.291208\pi$
$769$	−5.06281	−	5.06281i	−0.182570	−	0.182570i	−0.792475	+	0.609905i	$0.791208\pi$
$770$			76.3756i			2.75239i
$771$		0			0
$772$	7.95337	+	7.95337i	0.286248	+	0.286248i
$773$	11.2488	−	11.2488i	0.404592	−	0.404592i	−0.475256	−	0.879848i	$-0.657645\pi$
$773$	11.2488	−	11.2488i	0.404592	−	0.404592i	0.879848	+	0.475256i	$0.157645\pi$
$774$		0			0
$775$	71.5054	−	71.5054i	2.56855	−	2.56855i
$776$			6.61850i			0.237590i
$777$		0			0
$778$	5.89873	−	5.89873i	0.211480	−	0.211480i
$779$	9.67316			0.346577
$780$		0			0
$781$	8.70320			0.311425
$782$	−3.40108	+	3.40108i	−0.121622	+	0.121622i
$783$		0			0
$784$		−	43.4678i		−	1.55242i
$785$	12.7000	−	12.7000i	0.453283	−	0.453283i
$786$		0			0
$787$	−16.4021	+	16.4021i	−0.584673	+	0.584673i	−0.936184	−	0.351511i	$-0.885668\pi$
$787$	−16.4021	+	16.4021i	−0.584673	+	0.584673i	0.351511	+	0.936184i	$0.385668\pi$
$788$	−6.81552	−	6.81552i	−0.242793	−	0.242793i
$789$		0			0
$790$			37.5729i			1.33678i
$791$	30.9080	+	30.9080i	1.09896	+	1.09896i
$792$		0			0
$793$	10.4572	+	0.965048i	0.371348	+	0.0342698i
$794$			61.5213i			2.18331i
$795$		0			0
$796$	2.06664			0.0732501
$797$	−51.6968			−1.83119			−0.915597	−	0.402096i	$-0.868282\pi$
$797$	−51.6968			−1.83119			−0.915597	+	0.402096i	$0.868282\pi$
$798$		0			0
$799$	−12.5853	−	12.5853i	−0.445235	−	0.445235i
$800$	−25.9916	−	25.9916i	−0.918940	−	0.918940i
$801$		0			0
$802$	−26.0937			−0.921402
$803$	14.8611			0.524437
$804$		0			0
$805$		−	12.1508i		−	0.428259i
$806$	52.3227	+	4.82861i	1.84299	+	0.170080i
$807$		0			0
$808$	−15.8514	−	15.8514i	−0.557651	−	0.557651i
$809$		−	33.3494i		−	1.17250i	−0.810129	−	0.586252i	$-0.800603\pi$
$809$		−	33.3494i		−	1.17250i	0.810129	−	0.586252i	$-0.199397\pi$
$810$		0			0
$811$	−14.8364	−	14.8364i	−0.520978	−	0.520978i	0.396889	−	0.917867i	$-0.370090\pi$
$811$	−14.8364	−	14.8364i	−0.520978	−	0.520978i	−0.917867	+	0.396889i	$0.870090\pi$
$812$	5.77645	−	5.77645i	0.202714	−	0.202714i
$813$		0			0
$814$	13.5723	−	13.5723i	0.475708	−	0.475708i
$815$			29.2900i			1.02598i
$816$		0			0
$817$	1.22368	−	1.22368i	0.0428110	−	0.0428110i
$818$	−38.0914			−1.33184
$819$		0			0
$820$	7.10136			0.247990
$821$	−19.3172	+	19.3172i	−0.674174	+	0.674174i	−0.958675	−	0.284502i	$-0.908172\pi$
$821$	−19.3172	+	19.3172i	−0.674174	+	0.674174i	0.284502	+	0.958675i	$0.408172\pi$
$822$		0			0
$823$		−	43.3067i		−	1.50958i	−0.655968	−	0.754788i	$-0.727739\pi$
$823$		−	43.3067i		−	1.50958i	0.655968	−	0.754788i	$-0.272261\pi$
$824$	14.2713	−	14.2713i	0.497165	−	0.497165i
$825$		0			0
$826$	−46.4550	+	46.4550i	−1.61638	+	1.61638i
$827$	0.987036	+	0.987036i	0.0343226	+	0.0343226i	0.724060	−	0.689737i	$-0.242274\pi$
$827$	0.987036	+	0.987036i	0.0343226	+	0.0343226i	−0.689737	+	0.724060i	$0.742274\pi$
$828$		0			0
$829$			32.5598i			1.13085i	0.824800	+	0.565424i	$0.191288\pi$
$829$			32.5598i			1.13085i	−0.824800	+	0.565424i	$0.808712\pi$
$830$	46.6308	+	46.6308i	1.61858	+	1.61858i
$831$		0			0
$832$	−1.45174	+	15.7311i	−0.0503302	+	0.545377i
$833$			35.4713i			1.22901i
$834$		0			0
$835$	−37.6404			−1.30260
$836$	−5.79693			−0.200491
$837$		0			0
$838$	−45.4305	−	45.4305i	−1.56937	−	1.56937i
$839$	−22.3969	−	22.3969i	−0.773227	−	0.773227i	0.205442	−	0.978669i	$-0.434137\pi$
$839$	−22.3969	−	22.3969i	−0.773227	−	0.773227i	−0.978669	+	0.205442i	$0.934137\pi$
$840$		0			0
$841$	17.3732			0.599076
$842$	−3.95735			−0.136379
$843$		0			0
$844$		−	6.86088i		−	0.236161i
$845$	−43.1279	+	29.5909i	−1.48364	+	1.01796i
$846$		0			0
$847$	6.57331	+	6.57331i	0.225862	+	0.225862i
$848$			50.3030i			1.72741i
$849$		0			0
$850$	50.3656	+	50.3656i	1.72753	+	1.72753i
$851$	−2.15925	+	2.15925i	−0.0740181	+	0.0740181i
$852$		0			0
$853$	8.37348	−	8.37348i	0.286703	−	0.286703i	−0.549072	−	0.835775i	$-0.685019\pi$
$853$	8.37348	−	8.37348i	0.286703	−	0.286703i	0.835775	+	0.549072i	$0.185019\pi$
$854$			18.7728i			0.642393i
$855$		0			0
$856$	−19.7230	+	19.7230i	−0.674120	+	0.674120i
$857$	−41.8824			−1.43067			−0.715337	−	0.698779i	$-0.753727\pi$
$857$	−41.8824			−1.43067			−0.715337	+	0.698779i	$0.753727\pi$
$858$		0			0
$859$	17.4849			0.596578			0.298289	−	0.954476i	$-0.403584\pi$
$859$	17.4849			0.596578			0.298289	+	0.954476i	$0.403584\pi$
$860$	0.898338	−	0.898338i	0.0306331	−	0.0306331i
$861$		0			0
$862$			11.5645i			0.393888i
$863$	−25.9343	+	25.9343i	−0.882814	+	0.882814i	−0.993820	−	0.111006i	$-0.964593\pi$
$863$	−25.9343	+	25.9343i	−0.882814	+	0.882814i	0.111006	+	0.993820i	$0.464593\pi$
$864$		0			0
$865$	−14.6528	+	14.6528i	−0.498211	+	0.498211i
$866$	11.9477	+	11.9477i	0.406000	+	0.406000i
$867$		0			0
$868$			21.6561i			0.735055i
$869$	−12.0635	−	12.0635i	−0.409227	−	0.409227i
$870$		0			0
$871$	−16.7275	−	20.1288i	−0.566790	−	0.682039i
$872$		−	27.5561i		−	0.933166i
$873$		0			0
$874$	4.00011			0.135306
$875$	−99.5161			−3.36426
$876$		0			0
$877$	−19.4440	−	19.4440i	−0.656576	−	0.656576i	0.297993	−	0.954568i	$-0.403683\pi$
$877$	−19.4440	−	19.4440i	−0.656576	−	0.656576i	−0.954568	+	0.297993i	$0.903683\pi$
$878$	3.09814	+	3.09814i	0.104557	+	0.104557i
$879$		0			0
$880$	57.3463			1.93314
$881$	38.6717			1.30288			0.651442	−	0.758698i	$-0.274164\pi$
$881$	38.6717			1.30288			0.651442	+	0.758698i	$0.274164\pi$
$882$		0			0
$883$		−	32.1536i		−	1.08206i	−0.841005	−	0.541028i	$-0.818035\pi$
$883$		−	32.1536i		−	1.08206i	0.841005	−	0.541028i	$-0.181965\pi$
$884$	−0.784140	+	8.49693i	−0.0263735	+	0.285783i
$885$		0			0
$886$	5.19082	+	5.19082i	0.174389	+	0.174389i
$887$			15.4017i			0.517140i	0.965993	+	0.258570i	$0.0832512\pi$
$887$			15.4017i			0.517140i	−0.965993	+	0.258570i	$0.916749\pi$
$888$		0			0
$889$	18.6127	+	18.6127i	0.624250	+	0.624250i
$890$	9.84486	−	9.84486i	0.330000	−	0.330000i
$891$		0			0
$892$	2.57507	−	2.57507i	0.0862199	−	0.0862199i
$893$			14.8019i			0.495327i
$894$		0			0
$895$	−71.0315	+	71.0315i	−2.37432	+	2.37432i
$896$	−54.5112			−1.82109
$897$		0			0
$898$	64.4462			2.15060
$899$	21.7946	−	21.7946i	0.726891	−	0.726891i
$900$		0			0
$901$		−	41.0490i		−	1.36754i
$902$	−9.88928	+	9.88928i	−0.329277	+	0.329277i
$903$		0			0
$904$	17.4595	−	17.4595i	0.580695	−	0.580695i
$905$	36.7031	+	36.7031i	1.22005	+	1.22005i
$906$		0			0
$907$		−	41.1690i		−	1.36699i	−0.729953	−	0.683497i	$-0.760458\pi$
$907$		−	41.1690i		−	1.36699i	0.729953	−	0.683497i	$-0.239542\pi$
$908$	0.425129	+	0.425129i	0.0141084	+	0.0141084i
$909$		0			0
$910$	−59.7575	−	71.9083i	−1.98094	−	2.38374i
$911$			18.6022i			0.616319i	0.951335	+	0.308159i	$0.0997130\pi$
$911$			18.6022i			0.616319i	−0.951335	+	0.308159i	$0.900287\pi$
$912$		0			0
$913$	−29.9435			−0.990985
$914$	14.1466			0.467929
$915$		0			0
$916$	−8.23739	−	8.23739i	−0.272171	−	0.272171i
$917$	−5.22342	−	5.22342i	−0.172493	−	0.172493i
$918$		0			0
$919$	−3.42602			−0.113014			−0.0565071	−	0.998402i	$-0.517996\pi$
$919$	−3.42602			−0.113014			−0.0565071	+	0.998402i	$0.517996\pi$
$920$	−6.86383			−0.226294
$921$		0			0
$922$			56.9119i			1.87429i
$923$	−8.19415	+	6.80953i	−0.269714	+	0.224138i
$924$		0			0
$925$	31.9757	+	31.9757i	1.05135	+	1.05135i
$926$			0.420482i			0.0138179i
$927$		0			0
$928$	−7.92214	−	7.92214i	−0.260057	−	0.260057i
$929$	12.4259	−	12.4259i	0.407682	−	0.407682i	−0.473248	−	0.880929i	$-0.656918\pi$
$929$	12.4259	−	12.4259i	0.407682	−	0.407682i	0.880929	+	0.473248i	$0.156918\pi$
$930$		0			0
$931$	20.8594	−	20.8594i	0.683639	−	0.683639i
$932$			14.1786i			0.464434i
$933$		0			0
$934$	−3.72250	+	3.72250i	−0.121804	+	0.121804i
$935$	−46.7966			−1.53041
$936$		0			0
$937$	13.8756			0.453298			0.226649	−	0.973977i	$-0.427223\pi$
$937$	13.8756			0.453298			0.226649	+	0.973977i	$0.427223\pi$
$938$	33.0822	−	33.0822i	1.08017	−	1.08017i
$939$		0			0
$940$			10.8665i			0.354427i
$941$	24.9933	−	24.9933i	0.814759	−	0.814759i	−0.170585	−	0.985343i	$-0.554566\pi$
$941$	24.9933	−	24.9933i	0.814759	−	0.814759i	0.985343	+	0.170585i	$0.0545656\pi$
$942$		0			0
$943$	1.57331	−	1.57331i	0.0512341	−	0.0512341i
$944$	34.8806	+	34.8806i	1.13527	+	1.13527i
$945$		0			0
$946$			2.50203i			0.0813480i
$947$	−42.4253	−	42.4253i	−1.37864	−	1.37864i	−0.846925	−	0.531712i	$-0.821549\pi$
$947$	−42.4253	−	42.4253i	−1.37864	−	1.37864i	−0.531712	−	0.846925i	$-0.678451\pi$
$948$		0			0
$949$	−13.9919	+	11.6276i	−0.454195	+	0.377447i
$950$		−	59.2364i		−	1.92188i
$951$		0			0
$952$	35.6530			1.15552
$953$	49.0629			1.58930			0.794652	−	0.607065i	$-0.207653\pi$
$953$	49.0629			1.58930			0.794652	+	0.607065i	$0.207653\pi$
$954$		0			0
$955$	−13.4814	−	13.4814i	−0.436249	−	0.436249i
$956$	6.39039	+	6.39039i	0.206680	+	0.206680i
$957$		0			0
$958$	34.8493			1.12593
$959$	−5.27130			−0.170219
$960$		0			0
$961$			50.7086i			1.63576i
$962$	−2.15925	+	23.3976i	−0.0696170	+	0.754368i
$963$		0			0
$964$	7.85765	+	7.85765i	0.253078	+	0.253078i
$965$		−	75.5131i		−	2.43085i
$966$		0			0
$967$	23.7884	+	23.7884i	0.764985	+	0.764985i	0.977219	−	0.212234i	$-0.0680740\pi$
$967$	23.7884	+	23.7884i	0.764985	+	0.764985i	−0.212234	+	0.977219i	$0.568074\pi$
$968$	3.71318	−	3.71318i	0.119346	−	0.119346i
$969$		0			0
$970$	−13.4425	+	13.4425i	−0.431611	+	0.431611i
$971$			14.8419i			0.476300i	0.971228	+	0.238150i	$0.0765410\pi$
$971$			14.8419i			0.476300i	−0.971228	+	0.238150i	$0.923459\pi$
$972$		0			0
$973$	4.52252	−	4.52252i	0.144985	−	0.144985i
$974$	26.7495			0.857109
$975$		0			0
$976$	14.0955			0.451186
$977$	29.6113	−	29.6113i	0.947351	−	0.947351i	−0.0513308	−	0.998682i	$-0.516346\pi$
$977$	29.6113	−	29.6113i	0.947351	−	0.947351i	0.998682	+	0.0513308i	$0.0163463\pi$
$978$		0			0
$979$			6.32178i			0.202045i
$980$	15.3135	−	15.3135i	0.489172	−	0.489172i
$981$		0			0
$982$	29.3250	−	29.3250i	0.935797	−	0.935797i
$983$	23.4450	+	23.4450i	0.747779	+	0.747779i	0.974062	−	0.226283i	$-0.0726573\pi$
$983$	23.4450	+	23.4450i	0.747779	+	0.747779i	−0.226283	+	0.974062i	$0.572657\pi$
$984$		0			0
$985$			64.7097i			2.06182i
$986$	15.3513	+	15.3513i	0.488884	+	0.488884i
$987$		0			0
$988$	5.45787	−	4.53562i	0.173638	−	0.144297i
$989$		−	0.398055i		−	0.0126574i
$990$		0			0
$991$	18.6854			0.593560			0.296780	−	0.954946i	$-0.404087\pi$
$991$	18.6854			0.593560			0.296780	+	0.954946i	$0.404087\pi$
$992$	29.7003			0.942986
$993$		0			0
$994$	−13.4673	−	13.4673i	−0.427156	−	0.427156i
$995$	−9.81083	−	9.81083i	−0.311024	−	0.311024i
$996$		0			0
$997$	45.8968			1.45357			0.726783	−	0.686867i	$-0.241014\pi$
$997$	45.8968			1.45357			0.726783	+	0.686867i	$0.241014\pi$
$998$	36.6502			1.16014
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.i.b.242.6	yes	16
3.2	odd	2	inner	351.2.i.b.242.3	yes	16
13.5	odd	4	inner	351.2.i.b.161.3	✓	16
39.5	even	4	inner	351.2.i.b.161.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.i.b.161.3	✓	16	13.5	odd	4	inner
351.2.i.b.161.6	yes	16	39.5	even	4	inner
351.2.i.b.242.3	yes	16	3.2	odd	2	inner
351.2.i.b.242.6	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14002 - 1.14002i) q^{2} -0.599280i q^{4} +(-2.84492 + 2.84492i) q^{5} +(-2.82684 + 2.82684i) q^{7} +(1.59685 + 1.59685i) q^{8} +6.48652i q^{10} +(-2.08263 - 2.08263i) q^{11} +(3.59030 + 0.331331i) q^{13} +6.44529i q^{14} +4.83942 q^{16} -3.94914 q^{17} +(2.32235 + 2.32235i) q^{19} +(1.70490 + 1.70490i) q^{20} -4.74846 q^{22} +0.755446 q^{23} -11.1872i q^{25} +(4.47072 - 3.71528i) q^{26} +(1.69407 + 1.69407i) q^{28} -3.40981i q^{29} +(6.39174 + 6.39174i) q^{31} +(2.32334 - 2.32334i) q^{32} +(-4.50208 + 4.50208i) q^{34} -16.0843i q^{35} +(-2.85824 + 2.85824i) q^{37} +5.29503 q^{38} -9.08580 q^{40} +(2.08263 - 2.08263i) q^{41} -0.526914i q^{43} +(-1.24808 + 1.24808i) q^{44} +(0.861221 - 0.861221i) q^{46} +(3.18684 + 3.18684i) q^{47} -8.98203i q^{49} +(-12.7536 - 12.7536i) q^{50} +(0.198560 - 2.15159i) q^{52} +10.3944i q^{53} +11.8498 q^{55} -9.02805 q^{56} +(-3.88724 - 3.88724i) q^{58} +(7.20759 + 7.20759i) q^{59} +2.91264 q^{61} +14.5734 q^{62} +4.38156i q^{64} +(-11.1567 + 9.27150i) q^{65} +(-5.13277 - 5.13277i) q^{67} +2.36664i q^{68} +(-18.3364 - 18.3364i) q^{70} +(-2.08948 + 2.08948i) q^{71} +(-3.56787 + 3.56787i) q^{73} +6.51690i q^{74} +(1.39174 - 1.39174i) q^{76} +11.7745 q^{77} +5.79246 q^{79} +(-13.7678 + 13.7678i) q^{80} -4.74846i q^{82} +(7.18887 - 7.18887i) q^{83} +(11.2350 - 11.2350i) q^{85} +(-0.600691 - 0.600691i) q^{86} -6.65127i q^{88} +(-1.51774 - 1.51774i) q^{89} +(-11.0858 + 9.21257i) q^{91} -0.452723i q^{92} +7.26611 q^{94} -13.2138 q^{95} +(2.07237 + 2.07237i) q^{97} +(-10.2397 - 10.2397i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 16 q^{13} - 8 q^{16} - 32 q^{19} + 8 q^{22} + 40 q^{28} + 16 q^{31} + 24 q^{34} - 32 q^{37} - 72 q^{40} + 48 q^{46} + 48 q^{52} + 32 q^{55} + 56 q^{58} - 64 q^{61} - 32 q^{67} - 40 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 16 * q^13 - 8 * q^16 - 32 * q^19 + 8 * q^22 + 40 * q^28 + 16 * q^31 + 24 * q^34 - 32 * q^37 - 72 * q^40 + 48 * q^46 + 48 * q^52 + 32 * q^55 + 56 * q^58 - 64 * q^61 - 32 * q^67 - 40 * q^70 - 56 * q^73 - 64 * q^76 - 16 * q^79 - 104 * q^91 - 64 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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