LMFDB - Embedded newform 980.2.s.e.619.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(19,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,6,6,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.11
Character	$\chi$	$=$	980.619
Dual form			980.2.s.e.19.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.674125 - 1.24320i) q^{2} +(-0.634715 - 0.366453i) q^{3} +(-1.09111 - 1.67615i) q^{4} +(-1.51934 - 1.64061i) q^{5} +(-0.883452 + 0.542044i) q^{6} +(-2.81934 + 0.226536i) q^{8} +(-1.23142 - 2.13289i) q^{9} +(-3.06384 + 0.782877i) q^{10} +(-2.33007 - 1.34527i) q^{11} +(0.0783137 + 1.46372i) q^{12} +3.95118 q^{13} +(0.363144 + 1.59809i) q^{15} +(-1.61896 + 3.65773i) q^{16} +(0.709509 - 1.22891i) q^{17} +(-3.48175 + 0.0930760i) q^{18} +(-1.61265 - 2.79319i) q^{19} +(-1.09214 + 4.33673i) q^{20} +(-3.24320 + 1.98987i) q^{22} +(2.45620 + 4.25426i) q^{23} +(1.87249 + 0.889369i) q^{24} +(-0.383193 + 4.98529i) q^{25} +(2.66359 - 4.91212i) q^{26} +4.00375i q^{27} -5.17926 q^{29} +(2.23155 + 0.625848i) q^{30} +(-3.81745 + 6.61201i) q^{31} +(3.45592 + 4.47846i) q^{32} +(0.985953 + 1.70772i) q^{33} +(-1.04948 - 1.71050i) q^{34} +(-2.23142 + 4.39127i) q^{36} +(3.87963 - 2.23990i) q^{37} +(-4.55962 + 0.121890i) q^{38} +(-2.50787 - 1.44792i) q^{39} +(4.65520 + 4.28125i) q^{40} +0.325509i q^{41} -9.28165 q^{43} +(0.287494 + 5.37338i) q^{44} +(-1.62828 + 5.26088i) q^{45} +(6.94469 - 0.185649i) q^{46} +(5.68610 - 3.28287i) q^{47} +(2.36796 - 1.72834i) q^{48} +(5.93942 + 3.83710i) q^{50} +(-0.900672 + 0.520003i) q^{51} +(-4.31117 - 6.62277i) q^{52} +(-1.39942 - 0.807955i) q^{53} +(4.97748 + 2.69903i) q^{54} +(1.33312 + 5.86665i) q^{55} +2.36383i q^{57} +(-3.49147 + 6.43888i) q^{58} +(3.81745 - 6.61201i) q^{59} +(2.28240 - 2.35237i) q^{60} +(-12.3842 + 7.15003i) q^{61} +(5.64664 + 9.20319i) q^{62} +(7.89736 - 1.27737i) q^{64} +(-6.00319 - 6.48234i) q^{65} +(2.78770 - 0.0745223i) q^{66} +(1.51329 - 2.62109i) q^{67} +(-2.83398 + 0.151627i) q^{68} -3.60032i q^{69} -15.4089i q^{71} +(3.95498 + 5.73438i) q^{72} +(-0.709509 + 1.22891i) q^{73} +(-0.169301 - 6.33314i) q^{74} +(2.07009 - 3.02382i) q^{75} +(-2.92222 + 5.75071i) q^{76} +(-3.49068 + 2.14171i) q^{78} +(10.5765 - 6.10637i) q^{79} +(8.46065 - 2.90127i) q^{80} +(-2.22709 + 3.85743i) q^{81} +(0.404674 + 0.219434i) q^{82} -5.26172i q^{83} +(-3.09414 + 0.703103i) q^{85} +(-6.25699 + 11.5390i) q^{86} +(3.28735 + 1.89795i) q^{87} +(6.87401 + 3.26492i) q^{88} +(-4.10930 + 2.37250i) q^{89} +(5.44268 + 5.57078i) q^{90} +(4.45079 - 8.75882i) q^{92} +(4.84598 - 2.79783i) q^{93} +(-0.248133 - 9.28205i) q^{94} +(-2.13236 + 6.88953i) q^{95} +(-0.552378 - 4.10898i) q^{96} -8.35134 q^{97} +6.62638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{4} + 6 q^{5} + 4 q^{9} + 12 q^{10} + 18 q^{16} + 48 q^{24} - 26 q^{25} + 18 q^{26} - 26 q^{30} - 28 q^{36} - 42 q^{40} - 26 q^{44} - 36 q^{45} - 22 q^{46} + 36 q^{50} - 48 q^{54} + 4 q^{60}+ \cdots - 60 q^{96}+O(q^{100}) $ 32 * q + 6 * q^4 + 6 * q^5 + 4 * q^9 + 12 * q^10 + 18 * q^16 + 48 * q^24 - 26 * q^25 + 18 * q^26 - 26 * q^30 - 28 * q^36 - 42 * q^40 - 26 * q^44 - 36 * q^45 - 22 * q^46 + 36 * q^50 - 48 * q^54 + 4 * q^60 - 36 * q^61 + 36 * q^64 - 4 * q^65 + 24 * q^66 + 14 * q^74 - 72 * q^80 + 72 * q^81 + 20 * q^85 + 8 * q^86 + 108 * q^89 - 30 * q^94 - 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	0.674125	−	1.24320i	0.476679	−	0.879078i
$2$	0.674125	−	1.24320i	0.476679	−	0.879078i
$3$	−0.634715	−	0.366453i	−0.366453	−	0.211572i	0.305455	−	0.952207i	$-0.401191\pi$
$3$	−0.634715	−	0.366453i	−0.366453	−	0.211572i	−0.671908	+	0.740635i	$0.734525\pi$
$4$	−1.09111	−	1.67615i	−0.545555	−	0.838075i
$5$	−1.51934	−	1.64061i	−0.679471	−	0.733702i
$5$	−1.51934	−	1.64061i	−0.679471	−	0.733702i
$6$	−0.883452	+	0.542044i	−0.360668	+	0.221289i
$7$		0			0
$7$		0			0
$8$	−2.81934	+	0.226536i	−0.996787	+	0.0800926i
$9$	−1.23142	−	2.13289i	−0.410475	−	0.710964i
$10$	−3.06384	+	0.782877i	−0.968871	+	0.247567i
$11$	−2.33007	−	1.34527i	−0.702542	−	0.405613i	0.105751	−	0.994393i	$-0.466275\pi$
$11$	−2.33007	−	1.34527i	−0.702542	−	0.405613i	−0.808294	+	0.588780i	$0.799609\pi$
$12$	0.0783137	+	1.46372i	0.0226072	+	0.422539i
$13$	3.95118			1.09586			0.547930	−	0.836524i	$-0.315416\pi$
$13$	3.95118			1.09586			0.547930	+	0.836524i	$0.315416\pi$
$14$		0			0
$15$	0.363144	+	1.59809i	0.0937633	+	0.412624i
$16$	−1.61896	+	3.65773i	−0.404740	+	0.914432i
$17$	0.709509	−	1.22891i	0.172081	−	0.298053i	−0.767066	−	0.641568i	$-0.778284\pi$
$17$	0.709509	−	1.22891i	0.172081	−	0.298053i	0.939147	+	0.343515i	$0.111618\pi$
$18$	−3.48175	+	0.0930760i	−0.820657	+	0.0219382i
$19$	−1.61265	−	2.79319i	−0.369966	−	0.640801i	0.619593	−	0.784923i	$-0.287297\pi$
$19$	−1.61265	−	2.79319i	−0.369966	−	0.640801i	−0.989560	+	0.144122i	$0.953964\pi$
$20$	−1.09214	+	4.33673i	−0.244209	+	0.969723i
$21$		0			0
$22$	−3.24320	+	1.98987i	−0.691452	+	0.424242i
$23$	2.45620	+	4.25426i	0.512152	+	0.887074i	0.999901	+	0.0140897i	$0.00448504\pi$
$23$	2.45620	+	4.25426i	0.512152	+	0.887074i	−0.487748	+	0.872984i	$0.662182\pi$
$24$	1.87249	+	0.889369i	0.382221	+	0.181542i
$25$	−0.383193	+	4.98529i	−0.0766386	+	0.997059i
$26$	2.66359	−	4.91212i	0.522373	−	0.963345i
$27$			4.00375i			0.770522i
$28$		0			0
$29$	−5.17926			−0.961765			−0.480882	−	0.876785i	$-0.659684\pi$
$29$	−5.17926			−0.961765			−0.480882	+	0.876785i	$0.659684\pi$
$30$	2.23155	+	0.625848i	0.407423	+	0.114264i
$31$	−3.81745	+	6.61201i	−0.685634	+	1.18755i	0.287603	+	0.957750i	$0.407142\pi$
$31$	−3.81745	+	6.61201i	−0.685634	+	1.18755i	−0.973237	+	0.229803i	$0.926192\pi$
$32$	3.45592	+	4.47846i	0.610926	+	0.791688i
$33$	0.985953	+	1.70772i	0.171632	+	0.297276i
$34$	−1.04948	−	1.71050i	−0.179985	−	0.293349i
$35$		0			0
$36$	−2.23142	+	4.39127i	−0.371904	+	0.731878i
$37$	3.87963	−	2.23990i	0.637806	−	0.368238i	−0.145963	−	0.989290i	$-0.546628\pi$
$37$	3.87963	−	2.23990i	0.637806	−	0.368238i	0.783769	+	0.621052i	$0.213295\pi$
$38$	−4.55962	+	0.121890i	−0.739669	+	0.0197732i
$39$	−2.50787	−	1.44792i	−0.401581	−	0.231853i
$40$	4.65520	+	4.28125i	0.736052	+	0.676925i
$41$			0.325509i			0.0508359i	0.999677	+	0.0254180i	$0.00809166\pi$
$41$			0.325509i			0.0508359i	−0.999677	+	0.0254180i	$0.991908\pi$
$42$		0			0
$43$	−9.28165			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$43$	−9.28165			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$44$	0.287494	+	5.37338i	0.0433413	+	0.810067i
$45$	−1.62828	+	5.26088i	−0.242730	+	0.784246i
$46$	6.94469	−	0.185649i	1.02394	−	0.0273725i
$47$	5.68610	−	3.28287i	0.829403	−	0.478856i	−0.0242453	−	0.999706i	$-0.507718\pi$
$47$	5.68610	−	3.28287i	0.829403	−	0.478856i	0.853648	+	0.520850i	$0.174385\pi$
$48$	2.36796	−	1.72834i	0.341786	−	0.249465i
$49$		0			0
$50$	5.93942	+	3.83710i	0.839960	+	0.542648i
$51$	−0.900672	+	0.520003i	−0.126119	+	0.0728150i
$52$	−4.31117	−	6.62277i	−0.597851	−	0.918412i
$53$	−1.39942	−	0.807955i	−0.192225	−	0.110981i	0.400799	−	0.916166i	$-0.368733\pi$
$53$	−1.39942	−	0.807955i	−0.192225	−	0.110981i	−0.593024	+	0.805185i	$0.702066\pi$
$54$	4.97748	+	2.69903i	0.677349	+	0.367292i
$55$	1.33312	+	5.86665i	0.179758	+	0.791059i
$56$		0			0
$57$			2.36383i			0.313097i
$58$	−3.49147	+	6.43888i	−0.458453	+	0.845466i
$59$	3.81745	−	6.61201i	0.496989	−	0.860811i	−0.503005	−	0.864284i	$-0.667772\pi$
$59$	3.81745	−	6.61201i	0.496989	−	0.860811i	0.999994	+	0.00347297i	$0.00110548\pi$
$60$	2.28240	−	2.35237i	0.294657	−	0.303690i
$61$	−12.3842	+	7.15003i	−1.58564	+	0.915467i	−0.591622	+	0.806215i	$0.701512\pi$
$61$	−12.3842	+	7.15003i	−1.58564	+	0.915467i	−0.994014	+	0.109252i	$0.965154\pi$
$62$	5.64664	+	9.20319i	0.717124	+	1.16881i
$63$		0			0
$64$	7.89736	−	1.27737i	0.987170	−	0.159671i
$65$	−6.00319	−	6.48234i	−0.744605	−	0.804035i
$66$	2.78770	−	0.0745223i	0.343142	−	0.00917306i
$67$	1.51329	−	2.62109i	0.184878	−	0.320218i	−0.758658	−	0.651490i	$-0.774144\pi$
$67$	1.51329	−	2.62109i	0.184878	−	0.320218i	0.943535	+	0.331272i	$0.107478\pi$
$68$	−2.83398	+	0.151627i	−0.343671	+	0.0183875i
$69$		−	3.60032i		−	0.433427i
$70$		0			0
$71$		−	15.4089i		−	1.82870i	−0.404922	−	0.914351i	$-0.632701\pi$
$71$		−	15.4089i		−	1.82870i	0.404922	−	0.914351i	$-0.367299\pi$
$72$	3.95498	+	5.73438i	0.466099	+	0.675803i
$73$	−0.709509	+	1.22891i	−0.0830418	+	0.143833i	−0.904555	−	0.426357i	$-0.859797\pi$
$73$	−0.709509	+	1.22891i	−0.0830418	+	0.143833i	0.821513	+	0.570189i	$0.193130\pi$
$74$	−0.169301	−	6.33314i	−0.0196808	−	0.736212i
$75$	2.07009	−	3.02382i	0.239034	−	0.349160i
$76$	−2.92222	+	5.75071i	−0.335202	+	0.659652i
$77$		0			0
$78$	−3.49068	+	2.14171i	−0.395241	+	0.242501i
$79$	10.5765	−	6.10637i	1.18995	−	0.687021i	0.231659	−	0.972797i	$-0.425585\pi$
$79$	10.5765	−	6.10637i	1.18995	−	0.687021i	0.958296	+	0.285776i	$0.0922515\pi$
$80$	8.46065	−	2.90127i	0.945930	−	0.324371i
$81$	−2.22709	+	3.85743i	−0.247454	+	0.428604i
$82$	0.404674	+	0.219434i	0.0446887	+	0.0242324i
$83$		−	5.26172i		−	0.577549i	−0.957397	−	0.288774i	$-0.906752\pi$
$83$		−	5.26172i		−	0.577549i	0.957397	−	0.288774i	$-0.0932477\pi$
$84$		0			0
$85$	−3.09414	+	0.703103i	−0.335607	+	0.0762622i
$86$	−6.25699	+	11.5390i	−0.674709	+	1.24428i
$87$	3.28735	+	1.89795i	0.352441	+	0.203482i
$88$	6.87401	+	3.26492i	0.732772	+	0.348041i
$89$	−4.10930	+	2.37250i	−0.435585	+	0.251485i	−0.701723	−	0.712450i	$-0.747586\pi$
$89$	−4.10930	+	2.37250i	−0.435585	+	0.251485i	0.266138	+	0.963935i	$0.414252\pi$
$90$	5.44268	+	5.57078i	0.573709	+	0.587212i
$91$		0			0
$92$	4.45079	−	8.75882i	0.464027	−	0.913170i
$93$	4.84598	−	2.79783i	0.502505	−	0.290121i
$94$	−0.248133	−	9.28205i	−0.0255929	−	0.957370i
$95$	−2.13236	+	6.88953i	−0.218776	+	0.706851i
$96$	−0.552378	−	4.10898i	−0.0563768	−	0.419371i
$97$	−8.35134			−0.847950			−0.423975	−	0.905674i	$-0.639366\pi$
$97$	−8.35134			−0.847950			−0.423975	+	0.905674i	$0.639366\pi$
$98$		0			0
$99$			6.62638i			0.665976i
$100$	8.77421	−	4.79721i	0.877421	−	0.479721i
$101$	0.241927	+	0.139677i	0.0240727	+	0.0138984i	0.511988	−	0.858993i	$-0.328909\pi$
$101$	0.241927	+	0.139677i	0.0240727	+	0.0138984i	−0.487915	+	0.872891i	$0.662243\pi$
$102$	0.0393039	+	1.47027i	0.00389167	+	0.145578i
$103$	−11.6053	+	6.70030i	−1.14350	+	0.660200i	−0.947295	−	0.320362i	$-0.896195\pi$
$103$	−11.6053	+	6.70030i	−1.14350	+	0.660200i	−0.196206	+	0.980563i	$0.562862\pi$
$104$	−11.1397	+	0.895084i	−1.09234	+	0.0877703i
$105$		0			0
$106$	−1.94784	+	1.19510i	−0.189191	+	0.116078i
$107$	2.71447	+	4.70160i	0.262418	+	0.454521i	0.966884	−	0.255217i	$-0.0821468\pi$
$107$	2.71447	+	4.70160i	0.262418	+	0.454521i	−0.704466	+	0.709738i	$0.748813\pi$
$108$	6.71089	−	4.36853i	0.645756	−	0.420362i
$109$	−4.45851	+	7.72237i	−0.427048	+	0.739669i	−0.996609	−	0.0822798i	$-0.973780\pi$
$109$	−4.45851	+	7.72237i	−0.427048	+	0.739669i	0.569561	+	0.821949i	$0.307113\pi$
$110$	8.19213	+	2.29752i	0.781089	+	0.219060i
$111$	−3.28327			−0.311634
$112$		0			0
$113$			1.05161i			0.0989268i	0.998776	+	0.0494634i	$0.0157511\pi$
$113$			1.05161i			0.0989268i	−0.998776	+	0.0494634i	$0.984249\pi$
$114$	2.93873	+	1.59352i	0.275237	+	0.149247i
$115$	3.24777	−	10.4933i	0.302856	−	0.978508i
$116$	5.65114	+	8.68122i	0.524695	+	0.806031i
$117$	−4.86558	−	8.42743i	−0.449823	−	0.779116i
$118$	−5.64664	−	9.20319i	−0.519815	−	0.847222i
$119$		0			0
$120$	−1.38585	−	4.42328i	−0.126510	−	0.403789i
$121$	−1.88052	−	3.25715i	−0.170956	−	0.296105i
$122$	0.540428	+	20.2161i	0.0489280	+	1.83028i
$123$	0.119284	−	0.206605i	0.0107554	−	0.0186290i
$124$	15.2480	−	0.815817i	1.36931	−	0.0732626i
$125$	8.76112	−	6.94570i	0.783618	−	0.621243i
$126$		0			0
$127$	1.71773			0.152424			0.0762121	−	0.997092i	$-0.475717\pi$
$127$	1.71773			0.152424			0.0762121	+	0.997092i	$0.475717\pi$
$128$	3.73579	−	10.6791i	0.330200	−	0.943911i
$129$	5.89120	+	3.40128i	0.518691	+	0.299466i
$130$	−12.1058	+	3.09328i	−1.06175	+	0.271299i
$131$	−7.07173	−	12.2486i	−0.617860	−	1.07016i	−0.989876	−	0.141938i	$-0.954667\pi$
$131$	−7.07173	−	12.2486i	−0.617860	−	1.07016i	0.372016	−	0.928226i	$-0.378667\pi$
$132$	1.78661	−	3.51591i	0.155505	−	0.306021i
$133$		0			0
$134$	−2.23841	−	3.64827i	−0.193369	−	0.315163i
$135$	6.56859	−	6.08307i	0.565334	−	0.523547i
$136$	−1.72196	+	3.62543i	−0.147657	+	0.310878i
$137$	−12.8787	−	7.43551i	−1.10030	−	0.635259i	−0.164000	−	0.986460i	$-0.552440\pi$
$137$	−12.8787	−	7.43551i	−1.10030	−	0.635259i	−0.936300	+	0.351202i	$0.885773\pi$
$138$	−4.47593	−	2.42707i	−0.381016	−	0.206606i
$139$	7.06762			0.599468			0.299734	−	0.954023i	$-0.403102\pi$
$139$	7.06762			0.599468			0.299734	+	0.954023i	$0.403102\pi$
$140$		0			0
$141$	−4.81207			−0.405249
$142$	−19.1564	−	10.3875i	−1.60757	−	0.871703i
$143$	−9.20652	−	5.31538i	−0.769888	−	0.444495i
$144$	9.79516	−	1.05116i	0.816263	−	0.0875963i
$145$	7.86908	+	8.49714i	0.653491	+	0.705649i
$146$	1.04948	+	1.71050i	0.0868557	+	0.141562i
$147$		0			0
$148$	−7.98751	−	4.05885i	−0.656569	−	0.333636i
$149$	−4.39289	−	7.60870i	−0.359879	−	0.623329i	0.628061	−	0.778164i	$-0.283849\pi$
$149$	−4.39289	−	7.60870i	−0.359879	−	0.623329i	−0.987940	+	0.154835i	$0.950515\pi$
$150$	−2.36372	−	4.61198i	−0.192997	−	0.376566i
$151$	0.260095	+	0.150166i	0.0211663	+	0.0122204i	0.510546	−	0.859851i	$-0.329443\pi$
$151$	0.260095	+	0.150166i	0.0211663	+	0.0122204i	−0.489380	+	0.872071i	$0.662777\pi$
$152$	5.17936	+	7.50962i	0.420101	+	0.609110i
$153$	−3.49483			−0.282540
$154$		0			0
$155$	16.6477	−	3.78298i	1.33718	−	0.303856i
$156$	0.309431	+	5.78341i	0.0247743	+	0.463043i
$157$	9.61742	−	16.6579i	0.767553	−	1.32944i	−0.171333	−	0.985213i	$-0.554807\pi$
$157$	9.61742	−	16.6579i	0.767553	−	1.32944i	0.938886	−	0.344228i	$-0.111859\pi$
$158$	−0.461544	−	17.2653i	−0.0367185	−	1.37355i
$159$	0.592155	+	1.02564i	0.0469609	+	0.0813387i
$160$	2.09668	−	12.4741i	0.165757	−	0.986167i
$161$		0			0
$162$	3.29424	+	5.36912i	0.258820	+	0.421838i
$163$	−5.35958	−	9.28306i	−0.419795	−	0.727105i	0.576124	−	0.817362i	$-0.304565\pi$
$163$	−5.35958	−	9.28306i	−0.419795	−	0.727105i	−0.995919	+	0.0902569i	$0.971231\pi$
$164$	0.545602	−	0.355166i	0.0426043	−	0.0277338i
$165$	1.30370	−	4.21218i	0.101493	−	0.327917i
$166$	−6.54139	−	3.54706i	−0.507710	−	0.275305i
$167$		−	13.2256i		−	1.02343i	−0.859155	−	0.511715i	$-0.829010\pi$
$167$		−	13.2256i		−	1.02343i	0.859155	−	0.511715i	$-0.170990\pi$
$168$		0			0
$169$	2.61180			0.200908
$170$	−1.21174	+	4.32063i	−0.0929362	+	0.331377i
$171$	−3.97171	+	6.87920i	−0.303724	+	0.526065i
$172$	10.1273	+	15.5574i	0.772199	+	1.18624i
$173$	−5.62704	−	9.74632i	−0.427816	−	0.740999i	0.568863	−	0.822432i	$-0.307384\pi$
$173$	−5.62704	−	9.74632i	−0.427816	−	0.740999i	−0.996679	+	0.0814335i	$0.974050\pi$
$174$	4.57563	−	2.80739i	0.346878	−	0.212828i
$175$		0			0
$176$	8.69290	−	6.34483i	0.655252	−	0.478259i
$177$	−4.84598	+	2.79783i	−0.364246	+	0.210298i
$178$	0.179323	+	6.70806i	0.0134409	+	0.502790i
$179$	−0.697992	−	0.402986i	−0.0521703	−	0.0301206i	0.473688	−	0.880693i	$-0.342922\pi$
$179$	−0.697992	−	0.402986i	−0.0521703	−	0.0301206i	−0.525858	+	0.850572i	$0.676256\pi$
$180$	10.5947	−	3.01095i	0.789679	−	0.224423i
$181$		−	0.0667108i		−	0.00495857i	−0.999997	−	0.00247929i	$-0.999211\pi$
$181$		−	0.0667108i		−	0.00495857i	0.999997	−	0.00247929i	$-0.000789182\pi$
$182$		0			0
$183$	10.4806			0.774747
$184$	−7.88860	−	11.4378i	−0.581555	−	0.843205i
$185$	−9.56929	−	2.96177i	−0.703548	−	0.217753i
$186$	−0.211471	−	7.91062i	−0.0155058	−	0.580035i
$187$	−3.30641	+	1.90896i	−0.241789	+	0.139597i
$188$	−11.7067	−	5.94878i	−0.853802	−	0.433860i
$189$		0			0
$190$	7.12761	+	7.29536i	0.517091	+	0.529261i
$191$	−15.1210	+	8.73010i	−1.09412	+	0.631688i	−0.934669	−	0.355519i	$-0.884304\pi$
$191$	−15.1210	+	8.73010i	−1.09412	+	0.631688i	−0.159446	+	0.987207i	$0.550971\pi$
$192$	−5.48067	−	2.08325i	−0.395533	−	0.150345i
$193$	14.8928	+	8.59835i	1.07201	+	0.618923i	0.928729	−	0.370760i	$-0.120903\pi$
$193$	14.8928	+	8.59835i	1.07201	+	0.618923i	0.143277	+	0.989683i	$0.454236\pi$
$194$	−5.62985	+	10.3824i	−0.404200	+	0.745414i
$195$	1.43485	+	6.31432i	0.102751	+	0.452178i
$196$		0			0
$197$		−	11.9392i		−	0.850635i	−0.905044	−	0.425318i	$-0.860162\pi$
$197$		−	11.9392i		−	0.850635i	0.905044	−	0.425318i	$-0.139838\pi$
$198$	8.23793	+	4.46701i	0.585445	+	0.317457i
$199$	−7.76016	+	13.4410i	−0.550103	+	0.952807i	0.448163	+	0.893952i	$0.352078\pi$
$199$	−7.76016	+	13.4410i	−0.550103	+	0.952807i	−0.998267	+	0.0588552i	$0.981255\pi$
$200$	−0.0489975	−	14.1421i	−0.00346465	−	0.999994i
$201$	−1.92101	+	1.10910i	−0.135498	+	0.0782297i
$202$	0.336736	−	0.206605i	0.0236927	−	0.0145367i
$203$		0			0
$204$	1.85433	+	0.942281i	0.129829	+	0.0659728i
$205$	0.534033	−	0.494560i	0.0372985	−	0.0345415i
$206$	0.506436	+	18.9445i	0.0352850	+	1.31993i
$207$	6.04924	−	10.4776i	0.420452	−	0.728243i
$208$	−6.39679	+	14.4523i	−0.443538	+	1.00209i
$209$			8.67775i			0.600253i
$210$		0			0
$211$			14.1636i			0.975063i	0.873105	+	0.487531i	$0.162103\pi$
$211$			14.1636i			0.975063i	−0.873105	+	0.487531i	$0.837897\pi$
$212$	0.172666	+	3.22720i	0.0118588	+	0.221645i
$213$	−5.64664	+	9.78027i	−0.386901	+	0.670133i
$214$	7.67494	−	0.205171i	0.524648	−	0.0140252i
$215$	14.1020	+	15.2275i	0.961749	+	1.03851i
$216$	−0.906994	−	11.2879i	−0.0617132	−	0.768047i
$217$		0			0
$218$	6.59488	+	10.7487i	0.446662	+	0.727993i
$219$	0.900672	−	0.520003i	0.0608618	−	0.0351385i
$220$	8.37881	−	8.63567i	0.564899	−	0.582217i
$221$	2.80340	−	4.85563i	0.188577	−	0.326625i
$222$	−2.21334	+	4.08178i	−0.148550	+	0.273951i
$223$		−	3.03443i		−	0.203201i	−0.994825	−	0.101600i	$-0.967604\pi$
$223$		−	3.03443i		−	0.203201i	0.994825	−	0.101600i	$-0.0323963\pi$
$224$		0			0
$225$	11.1050	−	5.32171i	0.740331	−	0.354780i
$226$	1.30736	+	0.708914i	0.0869643	+	0.0471563i
$227$	12.7971	+	7.38839i	0.849371	+	0.490385i	0.860439	−	0.509554i	$-0.170190\pi$
$227$	12.7971	+	7.38839i	0.849371	+	0.490385i	−0.0110676	+	0.999939i	$0.503523\pi$
$228$	3.96214	−	2.57920i	0.262399	−	0.170812i
$229$	5.56933	−	3.21545i	0.368031	−	0.212483i	−0.304567	−	0.952491i	$-0.598512\pi$
$229$	5.56933	−	3.21545i	0.368031	−	0.212483i	0.672598	+	0.740008i	$0.265178\pi$
$230$	−10.8559	−	11.1115i	−0.715820	−	0.732668i
$231$		0			0
$232$	14.6021	−	1.17329i	0.958675	−	0.0770303i
$233$	−15.1300	+	8.73532i	−0.991201	+	0.572270i	−0.905633	−	0.424062i	$-0.860604\pi$
$233$	−15.1300	+	8.73532i	−0.991201	+	0.572270i	−0.0855677	+	0.996332i	$0.527270\pi$
$234$	−13.7570	+	0.367760i	−0.899324	+	0.0240412i
$235$	−14.0250	−	4.34086i	−0.914893	−	0.283166i
$236$	−15.2480	+	0.815817i	−0.992559	+	0.0531052i
$237$	−8.95079			−0.581416
$238$		0			0
$239$			3.22490i			0.208601i	0.994546	+	0.104301i	$0.0332604\pi$
$239$			3.22490i			0.208601i	−0.994546	+	0.104301i	$0.966740\pi$
$240$	−6.43328	−	1.25895i	−0.415266	−	0.0812651i
$241$	17.7424	+	10.2436i	1.14289	+	0.659848i	0.947145	−	0.320807i	$-0.103954\pi$
$241$	17.7424	+	10.2436i	1.14289	+	0.659848i	0.195745	+	0.980655i	$0.437287\pi$
$242$	−5.31701	+	0.142137i	−0.341790	+	0.00913692i
$243$	13.2292	−	7.63787i	0.848653	−	0.489970i
$244$	25.4971	+	12.9563i	1.63228	+	0.829444i
$245$		0			0
$246$	−0.176440	−	0.287572i	−0.0112494	−	0.0183349i
$247$	−6.37185	−	11.0364i	−0.405431	−	0.702227i
$248$	9.26482	−	19.5063i	0.588317	−	1.23865i
$249$	−1.92817	+	3.33969i	−0.122193	+	0.211644i
$250$	−2.72883	−	15.5741i	−0.172586	−	0.984994i
$251$	−15.1647			−0.957189			−0.478594	−	0.878036i	$-0.658854\pi$
$251$	−15.1647			−0.957189			−0.478594	+	0.878036i	$0.658854\pi$
$252$		0			0
$253$		−	13.2170i		−	0.830943i
$254$	1.15797	−	2.13549i	0.0726574	−	0.133993i
$255$	2.22155	+	0.687587i	0.139119	+	0.0430583i
$256$	−10.7579	−	11.8434i	−0.672372	−	0.740214i
$257$	2.36577	+	4.09764i	0.147573	+	0.255604i	0.930330	−	0.366724i	$-0.119521\pi$
$257$	2.36577	+	4.09764i	0.147573	+	0.255604i	−0.782757	+	0.622327i	$0.786187\pi$
$258$	8.19989	−	5.03106i	0.510503	−	0.313220i
$259$		0			0
$260$	−4.31522	+	17.1352i	−0.267619	+	1.06268i
$261$	6.37787	+	11.0468i	0.394780	+	0.683780i
$262$	−19.9947	+	0.534510i	−1.23528	+	0.0330221i
$263$	2.35021	−	4.07068i	0.144920	−	0.251009i	−0.784423	−	0.620226i	$-0.787041\pi$
$263$	2.35021	−	4.07068i	0.144920	−	0.251009i	0.929343	+	0.369217i	$0.120374\pi$
$264$	−3.16660	−	4.59129i	−0.194891	−	0.282574i
$265$	0.800660	+	3.52346i	0.0491842	+	0.216444i
$266$		0			0
$267$	3.47764			0.212828
$268$	−6.04451	+	0.323401i	−0.369227	+	0.0197549i
$269$	−21.2532	−	12.2706i	−1.29583	−	0.748149i	−0.316151	−	0.948709i	$-0.602391\pi$
$269$	−21.2532	−	12.2706i	−1.29583	−	0.748149i	−0.979682	+	0.200559i	$0.935724\pi$
$270$	−3.13444	−	12.2668i	−0.190756	−	0.746537i
$271$	−13.1957	−	22.8556i	−0.801582	−	1.38838i	−0.918574	−	0.395248i	$-0.870659\pi$
$271$	−13.1957	−	22.8556i	−0.801582	−	1.38838i	0.116993	−	0.993133i	$-0.462675\pi$
$272$	3.34634	+	4.58474i	0.202902	+	0.277991i
$273$		0			0
$274$	−17.9257	+	10.9984i	−1.08293	+	0.664435i
$275$	7.59941	−	11.1006i	0.458262	−	0.669390i
$276$	−6.03468	+	3.92834i	−0.363245	+	0.236458i
$277$	−20.8453	−	12.0350i	−1.25247	−	0.723115i	−0.280872	−	0.959745i	$-0.590624\pi$
$277$	−20.8453	−	12.0350i	−1.25247	−	0.723115i	−0.971600	+	0.236630i	$0.923957\pi$
$278$	4.76446	−	8.78649i	0.285753	−	0.526979i
$279$	18.8036			1.12574
$280$		0			0
$281$	−7.78577			−0.464460			−0.232230	−	0.972661i	$-0.574602\pi$
$281$	−7.78577			−0.464460			−0.232230	+	0.972661i	$0.574602\pi$
$282$	−3.24394	+	5.98238i	−0.193174	+	0.356245i
$283$	6.88540	+	3.97529i	0.409294	+	0.236306i	0.690487	−	0.723345i	$-0.257396\pi$
$283$	6.88540	+	3.97529i	0.409294	+	0.236306i	−0.281192	+	0.959651i	$0.590730\pi$
$284$	−25.8277	+	16.8128i	−1.53259	+	0.997657i
$285$	3.87813	−	3.59147i	0.229720	−	0.212741i
$286$	−12.8145	+	7.86234i	−0.757734	+	0.464910i
$287$		0			0
$288$	5.29637	−	12.8860i	0.312091	−	0.759314i
$289$	7.49319	+	12.9786i	0.440776	+	0.763447i
$290$	15.8684	−	4.05472i	0.931826	−	0.238102i
$291$	5.30071	+	3.06037i	0.310733	+	0.179402i
$292$	2.83398	−	0.151627i	0.165846	−	0.00887333i
$293$	2.11501			0.123560			0.0617801	−	0.998090i	$-0.480322\pi$
$293$	2.11501			0.123560			0.0617801	+	0.998090i	$0.480322\pi$
$294$		0			0
$295$	−16.6477	+	3.78298i	−0.969269	+	0.220254i
$296$	−10.4306	+	7.19392i	−0.606264	+	0.418138i
$297$	5.38611	−	9.32902i	0.312534	−	0.541325i
$298$	−12.4205	+	0.332032i	−0.719501	+	0.0192341i
$299$	9.70487	+	16.8093i	0.561247	+	0.972108i
$300$	−7.32707	−	0.170469i	−0.423029	−	0.00984206i
$301$		0			0
$302$	0.362024	−	0.222121i	0.0208321	−	0.0127816i
$303$	−0.102370	−	0.177310i	−0.00588100	−	0.0101862i
$304$	12.8275	−	1.37657i	0.735709	−	0.0789517i
$305$	30.5463	+	9.45430i	1.74907	+	0.541352i
$306$	−2.35595	+	4.34478i	−0.134681	+	0.248375i
$307$		−	18.6560i		−	1.06475i	−0.846508	−	0.532376i	$-0.821299\pi$
$307$		−	18.6560i		−	1.06475i	0.846508	−	0.532376i	$-0.178701\pi$
$308$		0			0
$309$	9.82137			0.558718
$310$	6.51965	−	23.2467i	0.370291	−	1.32033i
$311$	4.09153	−	7.08673i	0.232009	−	0.401852i	−0.726390	−	0.687283i	$-0.758803\pi$
$311$	4.09153	−	7.08673i	0.232009	−	0.401852i	0.958399	+	0.285431i	$0.0921367\pi$
$312$	7.39855	+	3.51405i	0.418860	+	0.198944i
$313$	11.6871	+	20.2427i	0.660597	+	1.14419i	0.980459	+	0.196723i	$0.0630299\pi$
$313$	11.6871	+	20.2427i	0.660597	+	1.14419i	−0.319863	+	0.947464i	$0.603637\pi$
$314$	−14.2258	−	23.1859i	−0.802806	−	1.30846i
$315$		0			0
$316$	−21.7754	−	11.0652i	−1.22496	−	0.622464i
$317$	22.6966	−	13.1039i	1.27477	−	0.735988i	0.298887	−	0.954288i	$-0.403385\pi$
$317$	22.6966	−	13.1039i	1.27477	−	0.735988i	0.975882	+	0.218300i	$0.0700512\pi$
$318$	1.67427	−	0.0447574i	0.0938883	−	0.00250987i
$319$	12.0680	+	6.96749i	0.675680	+	0.390104i
$320$	−14.0945	−	11.0157i	−0.787904	−	0.615798i
$321$		−	3.97890i		−	0.222081i
$322$		0			0
$323$	−4.57675			−0.254657
$324$	8.89563	−	0.475946i	0.494202	−	0.0264414i
$325$	−1.51406	+	19.6978i	−0.0839852	+	1.09264i
$326$	−15.1538	+	0.405098i	−0.839289	+	0.0224363i
$327$	5.65977	−	3.26767i	0.312986	−	0.180702i
$328$	−0.0737395	−	0.917720i	−0.00407158	−	0.0506726i
$329$		0			0
$330$	−4.35773	−	4.46030i	−0.239885	−	0.245531i
$331$	−16.9060	+	9.76067i	−0.929237	+	0.536495i	−0.886570	−	0.462594i	$-0.846919\pi$
$331$	−16.9060	+	9.76067i	−0.929237	+	0.536495i	−0.0426665	+	0.999089i	$0.513585\pi$
$332$	−8.81943	+	5.74111i	−0.484029	+	0.315085i
$333$	−9.55493	−	5.51654i	−0.523607	−	0.302305i
$334$	−16.4422	−	8.91574i	−0.899675	−	0.487848i
$335$	−6.59940	+	1.49963i	−0.360564	+	0.0819333i
$336$		0			0
$337$			31.7520i			1.72964i	0.502082	+	0.864820i	$0.332567\pi$
$337$			31.7520i			1.72964i	−0.502082	+	0.864820i	$0.667433\pi$
$338$	1.76068	−	3.24700i	0.0957684	−	0.176614i
$339$	0.385364	−	0.667470i	0.0209301	−	0.0362520i
$340$	4.55455	+	4.41908i	0.247005	+	0.239658i
$341$	17.7898	−	10.2710i	0.963373	−	0.556204i
$342$	5.87481	+	9.57508i	0.317674	+	0.517761i
$343$		0			0
$344$	26.1681	−	2.10263i	1.41089	−	0.113366i
$345$	−5.90671	+	5.47012i	−0.318007	+	0.294501i
$346$	−15.9100	+	0.425314i	−0.855326	+	0.0228650i
$347$	9.19210	−	15.9212i	0.493458	−	0.854694i	−0.506514	−	0.862232i	$-0.669066\pi$
$347$	9.19210	−	15.9212i	0.493458	−	0.854694i	0.999972	+	0.00753782i	$0.00239938\pi$
$348$	−0.405607	−	7.58097i	−0.0217428	−	0.406383i
$349$		−	2.37390i		−	0.127072i	−0.997980	−	0.0635360i	$-0.979762\pi$
$349$		−	2.37390i		−	0.127072i	0.997980	−	0.0635360i	$-0.0202378\pi$
$350$		0			0
$351$			15.8195i			0.844384i
$352$	−2.02781	−	15.0843i	−0.108082	−	0.803994i
$353$	−1.07710	+	1.86560i	−0.0573284	+	0.0992958i	−0.893265	−	0.449530i	$-0.851592\pi$
$353$	−1.07710	+	1.86560i	−0.0573284	+	0.0992958i	0.835937	+	0.548826i	$0.184925\pi$
$354$	0.211471	+	7.91062i	0.0112396	+	0.420445i
$355$	−25.2800	+	23.4114i	−1.34172	+	1.24255i
$356$	8.46037	+	4.29914i	0.448399	+	0.227854i
$357$		0			0
$358$	−0.971527	+	0.596083i	−0.0513468	+	0.0315039i
$359$	−4.40004	+	2.54037i	−0.232225	+	0.134075i	−0.611598	−	0.791168i	$-0.709473\pi$
$359$	−4.40004	+	2.54037i	−0.232225	+	0.134075i	0.379373	+	0.925244i	$0.376140\pi$
$360$	3.39890	−	15.2011i	0.179138	−	0.801167i
$361$	4.29874	−	7.44564i	0.226250	−	0.391876i
$362$	−0.0829350	−	0.0449714i	−0.00435897	−	0.00236364i
$363$			2.75648i			0.144678i
$364$		0			0
$365$	3.09414	−	0.703103i	0.161955	−	0.0368021i
$366$	7.06523	−	13.0295i	0.369306	−	0.681063i
$367$	11.7306	+	6.77267i	0.612333	+	0.353530i	0.773878	−	0.633335i	$-0.218314\pi$
$367$	11.7306	+	6.77267i	0.612333	+	0.353530i	−0.161545	+	0.986865i	$0.551648\pi$
$368$	−19.5374	+	2.09663i	−1.01846	+	0.109295i
$369$	0.694275	−	0.400840i	0.0361425	−	0.0208669i
$370$	−10.1330	+	9.89997i	−0.526788	+	0.514675i
$371$		0			0
$372$	−9.97707	−	5.06985i	−0.517287	−	0.262860i
$373$	−6.17822	+	3.56700i	−0.319896	+	0.184692i	−0.651346	−	0.758781i	$-0.725795\pi$
$373$	−6.17822	+	3.56700i	−0.319896	+	0.184692i	0.331450	+	0.943473i	$0.392462\pi$
$374$	0.144287	+	5.39742i	0.00746089	+	0.279094i
$375$	−8.10608	+	1.19800i	−0.418596	+	0.0618647i
$376$	−15.2874	+	10.5436i	−0.788386	+	0.543747i
$377$	−20.4642			−1.05396
$378$		0			0
$379$		−	16.2436i		−	0.834379i	−0.908820	−	0.417189i	$-0.863015\pi$
$379$		−	16.2436i		−	0.834379i	0.908820	−	0.417189i	$-0.136985\pi$
$380$	13.8745	−	3.94308i	0.711748	−	0.202275i
$381$	−1.09027	−	0.629468i	−0.0558562	−	0.0322486i
$382$	0.659856	+	24.6836i	0.0337612	+	1.26292i
$383$	−8.56254	+	4.94358i	−0.437525	+	0.252605i	−0.702547	−	0.711637i	$-0.747954\pi$
$383$	−8.56254	+	4.94358i	−0.437525	+	0.252605i	0.265022	+	0.964242i	$0.414621\pi$
$384$	−6.28456	+	5.40921i	−0.320707	+	0.276038i
$385$		0			0
$386$	20.7291	−	12.7184i	1.05508	−	0.647349i
$387$	11.4296	+	19.7967i	0.581002	+	1.00632i
$388$	9.11222	+	13.9981i	0.462603	+	0.710645i
$389$	15.9811	−	27.6802i	0.810276	−	1.40344i	−0.102395	−	0.994744i	$-0.532650\pi$
$389$	15.9811	−	27.6802i	0.810276	−	1.40344i	0.912671	−	0.408696i	$-0.134016\pi$
$390$	8.81725	+	2.47284i	0.446479	+	0.125217i
$391$	6.97078			0.352527
$392$		0			0
$393$			10.3658i			0.522886i
$394$	−14.8429	−	8.04854i	−0.747774	−	0.405480i
$395$	−26.0876	−	8.07430i	−1.31261	−	0.406262i
$396$	11.1068	−	7.23011i	0.558138	−	0.363326i
$397$	−8.73784	−	15.1344i	−0.438539	−	0.759573i	0.559038	−	0.829142i	$-0.311171\pi$
$397$	−8.73784	−	15.1344i	−0.438539	−	0.759573i	−0.997577	+	0.0695697i	$0.977837\pi$
$398$	11.4786	+	18.7084i	0.575369	+	0.937766i
$399$		0			0
$400$	−17.6145	−	9.47260i	−0.880724	−	0.473630i
$401$	8.67926	+	15.0329i	0.433422	+	0.750708i	0.997165	−	0.0752415i	$-0.0239728\pi$
$401$	8.67926	+	15.0329i	0.433422	+	0.750708i	−0.563744	+	0.825950i	$0.690639\pi$
$402$	0.0838301	+	3.13588i	0.00418106	+	0.156404i
$403$	−15.0834	+	26.1252i	−0.751358	+	1.30139i
$404$	−0.0298500	−	0.557909i	−0.00148509	−	0.0277570i
$405$	9.71225	−	2.20698i	0.482606	−	0.109666i
$406$		0			0
$407$	−12.0531			−0.597448
$408$	2.42150	−	1.67010i	0.119882	−	0.0826823i
$409$	−6.32187	−	3.64993i	−0.312596	−	0.180478i	0.335491	−	0.942043i	$-0.391098\pi$
$409$	−6.32187	−	3.64993i	−0.312596	−	0.180478i	−0.648088	+	0.761566i	$0.724431\pi$
$410$	−0.254833	−	0.997306i	−0.0125853	−	0.0492535i
$411$	5.44952	+	9.43885i	0.268805	+	0.465584i
$412$	23.8933	+	12.1414i	1.17714	+	0.598164i
$413$		0			0
$414$	−8.94784	−	14.5837i	−0.439762	−	0.716748i
$415$	−8.63242	+	7.99436i	−0.423749	+	0.392428i
$416$	13.6549	+	17.6952i	0.669489	+	0.867578i
$417$	−4.48592	−	2.58995i	−0.219677	−	0.126830i
$418$	10.7882	+	5.84989i	0.527669	+	0.286128i
$419$	−17.9278			−0.875831			−0.437915	−	0.899016i	$-0.644283\pi$
$419$	−17.9278			−0.875831			−0.437915	+	0.899016i	$0.644283\pi$
$420$		0			0
$421$	12.6334			0.615716			0.307858	−	0.951432i	$-0.400388\pi$
$421$	12.6334			0.615716			0.307858	+	0.951432i	$0.400388\pi$
$422$	17.6082	+	9.54805i	0.857156	+	0.464792i
$423$	−14.0040	−	8.08522i	−0.680898	−	0.393117i
$424$	4.12847	+	1.96088i	0.200496	+	0.0952288i
$425$	5.85458	+	4.00802i	0.283989	+	0.194418i
$426$	8.35232	+	13.6130i	0.404671	+	0.659554i
$427$		0			0
$428$	4.91881	−	9.67983i	0.237759	−	0.467892i
$429$	3.89567	+	6.74750i	0.188085	+	0.325773i
$430$	28.4375	−	7.26638i	1.37138	−	0.350416i
$431$	28.2962	+	16.3368i	1.36298	+	0.786918i	0.990020	−	0.140929i	$-0.0450090\pi$
$431$	28.2962	+	16.3368i	1.36298	+	0.786918i	0.372962	+	0.927847i	$0.378342\pi$
$432$	−14.6446	−	6.48191i	−0.704590	−	0.311861i
$433$	23.5884			1.13359			0.566794	−	0.823860i	$-0.308184\pi$
$433$	23.5884			1.13359			0.566794	+	0.823860i	$0.308184\pi$
$434$		0			0
$435$	−1.88082	−	8.27690i	−0.0901783	−	0.396847i
$436$	17.8086	−	0.952818i	0.852877	−	0.0456317i
$437$	7.92195	−	13.7212i	0.378958	−	0.656375i
$438$	−0.0393039	−	1.47027i	−0.00187801	−	0.0702520i
$439$	9.19501	+	15.9262i	0.438854	+	0.760117i	0.997601	−	0.0692207i	$-0.0220513\pi$
$439$	9.19501	+	15.9262i	0.438854	+	0.760117i	−0.558748	+	0.829338i	$0.688718\pi$
$440$	−5.08753	−	16.2381i	−0.242538	−	0.774121i
$441$		0			0
$442$	−4.14669	−	6.75849i	−0.197238	−	0.321469i
$443$	1.69217	+	2.93092i	0.0803973	+	0.139252i	0.903421	−	0.428755i	$-0.141048\pi$
$443$	1.69217	+	2.93092i	0.0803973	+	0.139252i	−0.823023	+	0.568008i	$0.807714\pi$
$444$	3.58241	+	5.50326i	0.170014	+	0.261173i
$445$	10.1358	+	3.13710i	0.480482	+	0.148713i
$446$	−3.77242	−	2.04559i	−0.178629	−	0.0968614i
$447$			6.43914i			0.304561i
$448$		0			0
$449$	−11.9013			−0.561658			−0.280829	−	0.959758i	$-0.590609\pi$
$449$	−11.9013			−0.561658			−0.280829	+	0.959758i	$0.590609\pi$
$450$	0.870172	−	17.3932i	0.0410203	−	0.819924i
$451$	0.437896	−	0.758458i	0.0206197	−	0.0357144i
$452$	1.76265	−	1.14742i	0.0829081	−	0.0539700i
$453$	−0.110058	−	0.190625i	−0.00517096	−	0.00895636i
$454$	17.8121	−	10.9287i	0.835963	−	0.512907i
$455$		0			0
$456$	−0.535494	−	6.66445i	−0.0250768	−	0.312092i
$457$	−18.2475	+	10.5352i	−0.853582	+	0.492816i	−0.861858	−	0.507150i	$-0.830699\pi$
$457$	−18.2475	+	10.5352i	−0.853582	+	0.492816i	0.00827601	+	0.999966i	$0.497366\pi$
$458$	−0.243037	−	9.09142i	−0.0113564	−	0.424814i
$459$	4.92023	+	2.84070i	0.229657	+	0.132592i
$460$	−21.1321	+	6.00564i	−0.985288	+	0.280014i
$461$			29.6708i			1.38191i	0.722899	+	0.690954i	$0.242809\pi$
$461$			29.6708i			1.38191i	−0.722899	+	0.690954i	$0.757191\pi$
$462$		0			0
$463$	15.0481			0.699342			0.349671	−	0.936873i	$-0.386293\pi$
$463$	15.0481			0.699342			0.349671	+	0.936873i	$0.386293\pi$
$464$	8.38501	−	18.9443i	0.389264	−	0.879468i
$465$	−11.9528	−	3.69950i	−0.554300	−	0.171560i
$466$	0.660251	+	24.6984i	0.0305855	+	1.14413i
$467$	4.45656	−	2.57299i	0.206225	−	0.119064i	−0.393331	−	0.919397i	$-0.628677\pi$
$467$	4.45656	−	2.57299i	0.206225	−	0.119064i	0.599556	+	0.800333i	$0.295344\pi$
$468$	−8.81676	+	17.3507i	−0.407555	+	0.802036i
$469$		0			0
$470$	−14.8512	+	14.5097i	−0.685035	+	0.669283i
$471$	−12.2086	+	7.04865i	−0.562544	+	0.324785i
$472$	−9.26482	+	19.5063i	−0.426448	+	0.897850i
$473$	21.6269	+	12.4863i	0.994405	+	0.574120i
$474$	−6.03395	+	11.1277i	−0.277149	+	0.511110i
$475$	14.5428	−	6.96919i	0.667270	−	0.319768i
$476$		0			0
$477$			3.97974i			0.182220i
$478$	4.00921	+	2.17399i	0.183377	+	0.0994358i
$479$	19.9783	−	34.6035i	0.912834	−	1.58107i	0.102792	−	0.994703i	$-0.467222\pi$
$479$	19.9783	−	34.6035i	0.912834	−	1.58107i	0.810042	−	0.586372i	$-0.199444\pi$
$480$	−5.90197	+	7.14918i	−0.269387	+	0.326314i
$481$	15.3291	−	8.85025i	0.698946	−	0.403537i
$482$	24.6955	−	15.1520i	1.12485	−	0.690153i
$483$		0			0
$484$	−3.40763	+	6.70594i	−0.154892	+	0.304816i
$485$	12.6885	+	13.7013i	0.576157	+	0.622143i
$486$	−0.577301	−	21.5955i	−0.0261869	−	0.979590i
$487$	−6.11246	+	10.5871i	−0.276982	+	0.479747i	−0.970633	−	0.240564i	$-0.922668\pi$
$487$	−6.11246	+	10.5871i	−0.276982	+	0.479747i	0.693651	+	0.720311i	$0.256001\pi$
$488$	33.2956	−	22.9638i	1.50722	−	1.03952i
$489$			7.85613i			0.355266i
$490$		0			0
$491$		−	22.9515i		−	1.03579i	−0.855445	−	0.517894i	$-0.826716\pi$
$491$		−	22.9515i		−	1.03579i	0.855445	−	0.517894i	$-0.173284\pi$
$492$	−0.476453	+	0.0254918i	−0.0214802	+	0.00114926i
$493$	−3.67473	+	6.36483i	−0.165502	+	0.286657i
$494$	−18.0159	+	0.481610i	−0.810573	+	0.0216687i
$495$	10.8713	−	10.0677i	0.488628	−	0.452511i
$496$	−18.0047	−	24.6678i	−0.808433	−	1.10762i
$497$		0			0
$498$	2.85209	+	4.64848i	0.127805	+	0.208303i
$499$	3.64376	−	2.10372i	0.163117	−	0.0941756i	−0.416219	−	0.909264i	$-0.636645\pi$
$499$	3.64376	−	2.10372i	0.163117	−	0.0941756i	0.579336	+	0.815089i	$0.303312\pi$
$500$	−21.2014	−	7.10643i	−0.948155	−	0.317809i
$501$	−4.84657	+	8.39451i	−0.216529	+	0.375039i
$502$	−10.2229	+	18.8528i	−0.456272	+	0.841443i
$503$			43.1904i			1.92576i	0.269924	+	0.962882i	$0.413001\pi$
$503$			43.1904i			1.92576i	−0.269924	+	0.962882i	$0.586999\pi$
$504$		0			0
$505$	−0.138416	−	0.609125i	−0.00615942	−	0.0271057i
$506$	−16.4314	−	8.90988i	−0.730463	−	0.396093i
$507$	−1.65775	−	0.957101i	−0.0736232	−	0.0425064i
$508$	−1.87424	−	2.87918i	−0.0831558	−	0.127743i
$509$	32.3532	−	18.6791i	1.43403	−	0.827937i	0.436604	−	0.899654i	$-0.356181\pi$
$509$	32.3532	−	18.6791i	1.43403	−	0.827937i	0.997425	+	0.0717169i	$0.0228478\pi$
$510$	2.35241	−	2.29832i	0.104167	−	0.101771i
$511$		0			0
$512$	−21.9760	+	5.39037i	−0.971211	+	0.238223i
$513$	11.1832	−	6.45664i	0.493751	−	0.285067i
$514$	6.68903	−	0.178815i	0.295040	−	0.00788717i
$515$	28.6249	+	8.85964i	1.26137	+	0.390402i
$516$	−0.726880	−	13.5857i	−0.0319991	−	0.598077i
$517$	−17.6653			−0.776921
$518$		0			0
$519$			8.24817i			0.362055i
$520$	18.3935	+	16.9160i	0.806610	+	0.741814i
$521$	−13.9610	−	8.06040i	−0.611643	−	0.353132i	0.161965	−	0.986796i	$-0.448217\pi$
$521$	−13.9610	−	8.06040i	−0.611643	−	0.353132i	−0.773608	+	0.633664i	$0.781550\pi$
$522$	18.0329	−	0.482065i	0.789279	−	0.0210994i
$523$	13.8279	−	7.98356i	0.604653	−	0.349097i	−0.166217	−	0.986089i	$-0.553155\pi$
$523$	13.8279	−	7.98356i	0.604653	−	0.349097i	0.770870	+	0.636993i	$0.219822\pi$
$524$	−12.8145	+	25.2178i	−0.559802	+	1.10165i
$525$		0			0
$526$	−3.47635	−	5.66594i	−0.151576	−	0.247047i
$527$	5.41703	+	9.38257i	0.235969	+	0.408711i
$528$	−7.84259	+	0.841618i	−0.341305	+	0.0366267i
$529$	−0.565805	+	0.980002i	−0.0246002	+	0.0426088i
$530$	4.92012	+	1.37987i	0.213717	+	0.0599378i
$531$	−18.8036			−0.816007
$532$		0			0
$533$			1.28614i			0.0557090i
$534$	2.34437	−	4.32342i	0.101451	−	0.187092i
$535$	3.58928	−	11.5967i	0.155178	−	0.501371i
$536$	−3.67271	+	7.73257i	−0.158637	+	0.333996i
$537$	0.295350	+	0.511562i	0.0127453	+	0.0220755i
$538$	−29.5822	+	18.1502i	−1.27538	+	0.782511i
$539$		0			0
$540$	−17.3632	−	4.37264i	−0.747193	−	0.188169i
$541$	7.31686	+	12.6732i	0.314576	+	0.544862i	0.979347	−	0.202185i	$-0.0648042\pi$
$541$	7.31686	+	12.6732i	0.314576	+	0.544862i	−0.664771	+	0.747047i	$0.731471\pi$
$542$	−37.3098	+	0.997384i	−1.60259	+	0.0428413i
$543$	−0.0244463	+	0.0423423i	−0.00104909	+	0.00181708i
$544$	7.95562	−	1.06949i	0.341094	−	0.0458540i
$545$	19.4434	−	4.41826i	0.832864	−	0.189257i
$546$		0			0
$547$	−16.5936			−0.709493			−0.354747	−	0.934963i	$-0.615433\pi$
$547$	−16.5936			−0.709493			−0.354747	+	0.934963i	$0.615433\pi$
$548$	1.58902	+	29.6996i	0.0678798	+	1.26870i
$549$	30.5005	+	17.6094i	1.30173	+	0.751553i
$550$	−8.67733	−	16.9308i	−0.370002	−	0.721932i
$551$	8.35232	+	14.4666i	0.355821	+	0.616300i
$552$	0.815602	+	10.1505i	0.0347143	+	0.432035i
$553$		0			0
$554$	−29.0143	+	17.8018i	−1.23270	+	0.756327i
$555$	4.98842	+	5.38657i	0.211747	+	0.228647i
$556$	−7.71155	−	11.8464i	−0.327043	−	0.502399i
$557$	−21.4562	−	12.3878i	−0.909129	−	0.524886i	−0.0289782	−	0.999580i	$-0.509225\pi$
$557$	−21.4562	−	12.3878i	−0.909129	−	0.524886i	−0.880151	+	0.474694i	$0.842559\pi$
$558$	12.6760	−	23.3767i	0.536617	−	0.989615i
$559$	−36.6734			−1.55112
$560$		0			0
$561$	2.79817			0.118139
$562$	−5.24859	+	9.67930i	−0.221398	+	0.408296i
$563$	20.7434	+	11.9762i	0.874230	+	0.504737i	0.868751	−	0.495248i	$-0.164923\pi$
$563$	20.7434	+	11.9762i	0.874230	+	0.504737i	0.00547814	+	0.999985i	$0.498256\pi$
$564$	5.25049	+	8.06575i	0.221086	+	0.339629i
$565$	1.72527	−	1.59775i	0.0725828	−	0.0672179i
$566$	9.58371	−	5.88011i	0.402833	−	0.247159i
$567$		0			0
$568$	3.49068	+	43.4430i	0.146466	+	1.82283i
$569$	−4.58078	−	7.93415i	−0.192036	−	0.332617i	0.753889	−	0.657002i	$-0.228176\pi$
$569$	−4.58078	−	7.93415i	−0.192036	−	0.332617i	−0.945925	+	0.324385i	$0.894843\pi$
$570$	−1.85059	−	7.24240i	−0.0775127	−	0.303351i
$571$	−21.4132	−	12.3629i	−0.896114	−	0.517372i	−0.0201768	−	0.999796i	$-0.506423\pi$
$571$	−21.4132	−	12.3629i	−0.896114	−	0.517372i	−0.875938	+	0.482425i	$0.839756\pi$
$572$	1.13594	+	21.2312i	0.0474959	+	0.887720i
$573$	12.7967			0.534589
$574$		0			0
$575$	−22.1499	+	10.6147i	−0.923716	+	0.442662i
$576$	−12.4495	−	15.2712i	−0.518729	−	0.636301i
$577$	4.75184	−	8.23042i	0.197822	−	0.342637i	−0.750000	−	0.661438i	$-0.769947\pi$
$577$	4.75184	−	8.23042i	0.197822	−	0.342637i	0.947822	+	0.318801i	$0.103280\pi$
$578$	21.1864	−	0.566366i	0.881237	−	0.0235577i
$579$	−6.30178	−	10.9150i	−0.261893	−	0.453612i
$580$	5.65646	−	22.4611i	0.234872	−	0.932645i
$581$		0			0
$582$	7.37801	−	4.52679i	0.305828	−	0.187642i
$583$	2.17383	+	3.76518i	0.0900308	+	0.155938i
$584$	1.72196	−	3.62543i	0.0712551	−	0.150022i
$585$	−6.43363	+	20.7867i	−0.265998	+	0.859423i
$586$	1.42578	−	2.62939i	0.0588985	−	0.108619i
$587$			14.2100i			0.586508i	0.956035	+	0.293254i	$0.0947382\pi$
$587$			14.2100i			0.586508i	−0.956035	+	0.293254i	$0.905262\pi$
$588$		0			0
$589$	24.6248			1.01465
$590$	−6.51965	+	23.2467i	−0.268410	+	0.957053i
$591$	−4.37516	+	7.57801i	−0.179970	+	0.311717i
$592$	1.91200	+	17.8169i	0.0785828	+	0.732271i
$593$	8.87854	+	15.3781i	0.364598	+	0.631502i	0.988712	−	0.149831i	$-0.0478731\pi$
$593$	8.87854	+	15.3781i	0.364598	+	0.631502i	−0.624114	+	0.781334i	$0.714540\pi$
$594$	−7.96695	−	12.9850i	−0.326888	−	0.532779i
$595$		0			0
$596$	−7.96020	+	15.6651i	−0.326063	+	0.641666i
$597$	9.85098	−	5.68746i	0.403174	−	0.232772i
$598$	27.4397	−	0.733533i	1.12209	−	0.0299964i
$599$	−18.1537	−	10.4811i	−0.741741	−	0.428244i	0.0809612	−	0.996717i	$-0.474201\pi$
$599$	−18.1537	−	10.4811i	−0.741741	−	0.428244i	−0.822702	+	0.568473i	$0.807534\pi$
$600$	−5.15129	+	8.99412i	−0.210301	+	0.367183i
$601$		−	20.7196i		−	0.845169i	−0.906324	−	0.422585i	$-0.861123\pi$
$601$		−	20.7196i		−	0.845169i	0.906324	−	0.422585i	$-0.138877\pi$
$602$		0			0
$603$	−7.45401			−0.303551
$604$	−0.0320917	−	0.599807i	−0.00130579	−	0.0244058i
$605$	−2.48656	+	8.03393i	−0.101093	+	0.326626i
$606$	−0.289442	+	0.00773753i	−0.0117578	+	0.000314316i
$607$	2.77584	−	1.60263i	0.112668	−	0.0650487i	−0.442607	−	0.896716i	$-0.645946\pi$
$607$	2.77584	−	1.60263i	0.112668	−	0.0650487i	0.555275	+	0.831667i	$0.312613\pi$
$608$	6.93600	−	16.8752i	0.281292	−	0.684380i
$609$		0			0
$610$	32.3456	−	31.6018i	1.30964	−	1.27952i
$611$	22.4668	−	12.9712i	0.908909	−	0.524759i
$612$	3.81324	+	5.85786i	0.154141	+	0.236790i
$613$	4.15308	+	2.39778i	0.167741	+	0.0968454i	0.581520	−	0.813532i	$-0.302458\pi$
$613$	4.15308	+	2.39778i	0.167741	+	0.0968454i	−0.413779	+	0.910377i	$0.635791\pi$
$614$	−23.1932	−	12.5765i	−0.936000	−	0.507545i
$615$	−0.520191	+	0.118207i	−0.0209761	+	0.00476655i
$616$		0			0
$617$		−	8.95961i		−	0.360700i	−0.983602	−	0.180350i	$-0.942277\pi$
$617$		−	8.95961i		−	0.360700i	0.983602	−	0.180350i	$-0.0577231\pi$
$618$	6.62084	−	12.2100i	0.266329	−	0.491157i
$619$	−12.8347	+	22.2303i	−0.515868	+	0.893510i	0.483962	+	0.875089i	$0.339197\pi$
$619$	−12.8347	+	22.2303i	−0.515868	+	0.893510i	−0.999830	+	0.0184212i	$0.994136\pi$
$620$	−24.5054	−	23.7765i	−0.984159	−	0.954886i
$621$	−17.0330	+	9.83400i	−0.683510	+	0.394625i
$622$	−6.05205	−	9.86394i	−0.242665	−	0.395508i
$623$		0			0
$624$	9.35623	−	6.82898i	0.374549	−	0.273378i
$625$	−24.7063	−	3.82066i	−0.988253	−	0.152826i
$626$	33.0444	−	0.883361i	1.32072	−	0.0353062i
$627$	3.17999	−	5.50790i	0.126996	−	0.219964i
$628$	−38.4147	+	2.05531i	−1.53291	+	0.0820160i
$629$		−	6.35693i		−	0.253467i
$630$		0			0
$631$			1.75095i			0.0697043i	0.999392	+	0.0348521i	$0.0110960\pi$
$631$			1.75095i			0.0697043i	−0.999392	+	0.0348521i	$0.988904\pi$
$632$	−28.4356	+	19.6119i	−1.13111	+	0.780120i
$633$	5.19029	−	8.98985i	0.206296	−	0.357314i
$634$	−0.990445	−	37.0502i	−0.0393356	−	1.47145i
$635$	−2.60983	−	2.81813i	−0.103568	−	0.111834i
$636$	1.07302	−	2.11163i	0.0425482	−	0.0837315i
$637$		0			0
$638$	16.7974	−	10.3061i	0.665014	−	0.408021i
$639$	−32.8655	+	18.9749i	−1.30014	+	0.750636i
$640$	−23.1962	+	10.0963i	−0.916911	+	0.399091i
$641$	20.3887	−	35.3143i	0.805306	−	1.39483i	−0.110778	−	0.993845i	$-0.535334\pi$
$641$	20.3887	−	35.3143i	0.805306	−	1.39483i	0.916084	−	0.400986i	$-0.131332\pi$
$642$	−4.94658	−	2.68228i	−0.195226	−	0.105861i
$643$			35.0077i			1.38057i	0.723538	+	0.690285i	$0.242515\pi$
$643$			35.0077i			1.38057i	−0.723538	+	0.690285i	$0.757485\pi$
$644$		0			0
$645$	−3.37057	−	14.8329i	−0.132716	−	0.584043i
$646$	−3.08530	+	5.68983i	−0.121390	+	0.223863i
$647$	20.9951	+	12.1215i	0.825404	+	0.476547i	0.852276	−	0.523092i	$-0.175221\pi$
$647$	20.9951	+	12.1215i	0.825404	+	0.476547i	−0.0268724	+	0.999639i	$0.508555\pi$
$648$	5.40508	−	11.3799i	0.212331	−	0.447046i
$649$	−17.7898	+	10.2710i	−0.698312	+	0.403171i
$650$	23.4677	+	15.1611i	0.920478	+	0.594666i
$651$		0			0
$652$	−9.71192	+	19.1123i	−0.380348	+	0.748495i
$653$	37.4046	−	21.5956i	1.46376	−	0.845100i	0.464574	−	0.885534i	$-0.346208\pi$
$653$	37.4046	−	21.5956i	1.46376	−	0.845100i	0.999182	+	0.0404346i	$0.0128742\pi$
$654$	−0.246984	−	9.23906i	−0.00965782	−	0.361276i
$655$	−9.35077	+	30.2118i	−0.365365	+	1.18047i
$656$	−1.19062	−	0.526985i	−0.0464860	−	0.0205753i
$657$	3.49483			0.136346
$658$		0			0
$659$			11.6398i			0.453422i	0.973962	+	0.226711i	$0.0727973\pi$
$659$			11.6398i			0.453422i	−0.973962	+	0.226711i	$0.927203\pi$
$660$	−8.48272	+	2.41075i	−0.330189	+	0.0938383i
$661$	−14.8021	−	8.54599i	−0.575735	−	0.332400i	0.183702	−	0.982982i	$-0.441192\pi$
$661$	−14.8021	−	8.54599i	−0.575735	−	0.332400i	−0.759436	+	0.650582i	$0.774525\pi$
$662$	0.737751	+	27.5975i	0.0286735	+	1.07261i
$663$	−3.55871	+	2.05462i	−0.138209	+	0.0797950i
$664$	1.19197	+	14.8346i	0.0462574	+	0.575693i
$665$		0			0
$666$	−13.2994	+	8.15989i	−0.515342	+	0.316189i
$667$	−12.7213	−	22.0339i	−0.492570	−	0.853157i
$668$	−22.1682	+	14.4306i	−0.857712	+	0.558338i
$669$	−1.11198	+	1.92600i	−0.0429915	+	0.0744634i
$670$	−2.58448	+	9.21533i	−0.0998472	+	0.356019i
$671$	38.4748			1.48530
$672$		0			0
$673$			3.77972i			0.145697i	0.997343	+	0.0728487i	$0.0232090\pi$
$673$			3.77972i			0.145697i	−0.997343	+	0.0728487i	$0.976791\pi$
$674$	39.4742	+	21.4048i	1.52049	+	0.824482i
$675$	−19.9599	−	1.53421i	−0.768256	−	0.0590518i
$676$	−2.84976	−	4.37777i	−0.109606	−	0.168376i
$677$	−13.8872	−	24.0534i	−0.533729	−	0.924446i	−0.999224	−	0.0393956i	$-0.987457\pi$
$677$	−13.8872	−	24.0534i	−0.533729	−	0.924446i	0.465494	−	0.885051i	$-0.345877\pi$
$678$	−0.570017	−	0.929044i	−0.0218914	−	0.0356797i
$679$		0			0
$680$	8.56416	−	2.68322i	0.328421	−	0.102897i
$681$	−5.41499	−	9.37904i	−0.207503	−	0.359405i
$682$	−0.776321	−	29.0403i	−0.0297269	−	1.11201i
$683$	−5.58652	+	9.67614i	−0.213762	+	0.370247i	−0.952889	−	0.303319i	$-0.901905\pi$
$683$	−5.58652	+	9.67614i	−0.213762	+	0.370247i	0.739127	+	0.673567i	$0.235239\pi$
$684$	15.8641	−	0.848783i	0.606580	−	0.0324540i
$685$	7.36837	+	32.4260i	0.281531	+	1.23893i
$686$		0			0
$687$	−4.71324			−0.179821
$688$	15.0266	−	33.9497i	0.572884	−	1.29432i
$689$	−5.52935	−	3.19237i	−0.210652	−	0.121620i
$690$	2.81861	+	11.0308i	0.107302	+	0.419935i
$691$	17.7057	+	30.6672i	0.673556	+	1.16663i	0.976889	+	0.213749i	$0.0685675\pi$
$691$	17.7057	+	30.6672i	0.673556	+	1.16663i	−0.303332	+	0.952885i	$0.598099\pi$
$692$	−10.1966	+	20.0661i	−0.387616	+	0.762797i
$693$		0			0
$694$	−13.5966	−	22.1605i	−0.516122	−	0.841202i
$695$	−10.7381	−	11.5952i	−0.407321	−	0.439831i
$696$	−9.69812	−	4.60627i	−0.367606	−	0.174600i
$697$	0.400020	+	0.230952i	0.0151518	+	0.00874791i
$698$	−2.95124	−	1.60031i	−0.111706	−	0.0605725i
$699$	12.8043			0.484304
$700$		0			0
$701$	2.24955			0.0849643			0.0424821	−	0.999097i	$-0.486473\pi$
$701$	2.24955			0.0849643			0.0424821	+	0.999097i	$0.486473\pi$
$702$	19.6669	+	10.6643i	0.742279	+	0.402500i
$703$	−12.5129	−	7.22434i	−0.471934	−	0.272471i
$704$	−20.1198	−	7.64771i	−0.758293	−	0.288234i
$705$	7.31118	+	7.89472i	0.275355	+	0.297332i
$706$	1.59321	+	2.59671i	0.0599614	+	0.0977283i
$707$		0			0
$708$	9.97707	+	5.06985i	0.374961	+	0.190537i
$709$	7.94601	+	13.7629i	0.298418	+	0.516876i	0.975774	−	0.218780i	$-0.0702076\pi$
$709$	7.94601	+	13.7629i	0.298418	+	0.516876i	−0.677356	+	0.735656i	$0.736874\pi$
$710$	12.0633	+	47.2104i	0.452727	+	1.77178i
$711$	−26.0485	−	15.0391i	−0.976893	−	0.564010i
$712$	11.0480	−	7.61980i	0.414043	−	0.285564i
$713$	−37.5056			−1.40460
$714$		0			0
$715$	5.26739	+	23.1802i	0.196989	+	0.866890i
$716$	0.0861211	+	1.60964i	0.00321850	+	0.0601551i
$717$	1.18177	−	2.04689i	0.0441341	−	0.0764425i
$718$	0.192011	+	7.18267i	0.00716579	+	0.268055i
$719$	−18.0142	−	31.2015i	−0.671817	−	1.16362i	−0.977388	−	0.211452i	$-0.932181\pi$
$719$	−18.0142	−	31.2015i	−0.671817	−	1.16362i	0.305572	−	0.952169i	$-0.401152\pi$
$720$	−16.6067	−	14.4730i	−0.618897	−	0.539375i
$721$		0			0
$722$	−6.35856	−	10.3635i	−0.236641	−	0.385690i
$723$	−7.50758	−	13.0035i	−0.279210	−	0.483606i
$724$	−0.111817	+	0.0727888i	−0.00415565	+	0.00270517i
$725$	1.98466	−	25.8201i	0.0737083	−	0.958936i
$726$	3.42687	+	1.85822i	0.127183	+	0.0689648i
$727$		−	51.4779i		−	1.90921i	−0.297878	−	0.954604i	$-0.596279\pi$
$727$		−	51.4779i		−	1.90921i	0.297878	−	0.954604i	$-0.403721\pi$
$728$		0			0
$729$	2.16686			0.0802541
$730$	1.21174	−	4.32063i	0.0448485	−	0.159914i
$731$	−6.58541	+	11.4063i	−0.243570	+	0.421876i
$732$	−11.4355	−	17.5670i	−0.422667	−	0.649296i
$733$	−17.9717	−	31.1280i	−0.663801	−	1.14974i	−0.979609	−	0.200914i	$-0.935609\pi$
$733$	−17.9717	−	31.1280i	−0.663801	−	1.14974i	0.315807	−	0.948823i	$-0.397725\pi$
$734$	16.3277	−	10.0179i	0.602667	−	0.369768i
$735$		0			0
$736$	−10.5641	+	25.7024i	−0.389398	+	0.947401i
$737$	−7.05214	+	4.07155i	−0.259769	+	0.149978i
$738$	−0.0302971	−	1.13334i	−0.00111525	−	0.0417189i
$739$	−15.7903	−	9.11653i	−0.580855	−	0.335357i	0.180618	−	0.983553i	$-0.442190\pi$
$739$	−15.7903	−	9.11653i	−0.580855	−	0.335357i	−0.761473	+	0.648196i	$0.775524\pi$
$740$	5.47678	+	19.2712i	0.201330	+	0.708422i
$741$			9.33993i			0.343111i
$742$		0			0
$743$	29.1171			1.06820			0.534102	−	0.845420i	$-0.320650\pi$
$743$	29.1171			1.06820			0.534102	+	0.845420i	$0.320650\pi$
$744$	−13.0287	+	8.98582i	−0.477654	+	0.329436i
$745$	−5.80860	+	18.7672i	−0.212811	+	0.687578i
$746$	0.269608	+	10.0854i	0.00987105	+	0.369252i
$747$	−11.2227	+	6.47941i	−0.410616	+	0.237069i
$748$	6.80736	+	3.45916i	0.248902	+	0.126479i
$749$		0			0
$750$	−3.97515	+	10.8851i	−0.145152	+	0.397468i
$751$	37.2703	−	21.5180i	1.36001	−	0.785203i	0.370386	−	0.928878i	$-0.379225\pi$
$751$	37.2703	−	21.5180i	1.36001	−	0.785203i	0.989625	+	0.143675i	$0.0458921\pi$
$752$	2.80229	+	26.1130i	0.102189	+	0.952245i
$753$	9.62527	+	5.55715i	0.350764	+	0.202514i
$754$	−13.7954	+	25.4411i	−0.502400	+	0.926512i
$755$	−0.148810	−	0.654869i	−0.00541576	−	0.0238331i
$756$		0			0
$757$		−	10.6531i		−	0.387193i	−0.981081	−	0.193597i	$-0.937985\pi$
$757$		−	10.6531i		−	0.387193i	0.981081	−	0.193597i	$-0.0620153\pi$
$758$	−20.1941	−	10.9502i	−0.733484	−	0.397730i
$759$	−4.84339	+	8.38899i	−0.175804	+	0.304501i
$760$	4.45112	−	19.9070i	0.161459	−	0.722102i
$761$	−12.3298	+	7.11864i	−0.446956	+	0.258050i	−0.706544	−	0.707669i	$-0.749747\pi$
$761$	−12.3298	+	7.11864i	−0.446956	+	0.258050i	0.259588	+	0.965720i	$0.416413\pi$
$762$	−1.51754	+	0.931088i	−0.0549745	+	0.0337297i
$763$		0			0
$764$	31.1316	+	15.8195i	1.12630	+	0.572331i
$765$	5.30984	+	5.73365i	0.191978	+	0.207300i
$766$	0.373656	+	13.9776i	0.0135007	+	0.505030i
$767$	15.0834	−	26.1252i	0.544630	−	0.943327i
$768$	2.48817	+	11.4595i	0.0897842	+	0.413508i
$769$		−	35.5770i		−	1.28294i	−0.767149	−	0.641469i	$-0.778325\pi$
$769$		−	35.5770i		−	1.28294i	0.767149	−	0.641469i	$-0.221675\pi$
$770$		0			0
$771$		−	3.46777i		−	0.124889i
$772$	−1.83753	−	34.3443i	−0.0661342	−	1.23608i
$773$	−5.94268	+	10.2930i	−0.213743	+	0.370214i	−0.952883	−	0.303338i	$-0.901899\pi$
$773$	−5.94268	+	10.2930i	−0.213743	+	0.370214i	0.739140	+	0.673552i	$0.235232\pi$
$774$	32.3164	−	0.863899i	1.16159	−	0.0310522i
$775$	−31.5000	−	21.5648i	−1.13151	−	0.774630i
$776$	23.5453	−	1.89188i	0.845226	−	0.0679145i
$777$		0			0
$778$	−23.6388	−	38.5277i	−0.847491	−	1.38129i
$779$	0.909207	−	0.524931i	0.0325757	−	0.0188076i
$780$	9.01817	−	9.29463i	0.322902	−	0.332801i
$781$	−20.7291	+	35.9038i	−0.741745	+	1.28474i
$782$	4.69918	−	8.66609i	0.168042	−	0.309899i
$783$		−	20.7365i		−	0.741061i
$784$		0			0
$785$	−41.9412	+	9.53058i	−1.49694	+	0.340161i
$786$	12.8868	+	6.98786i	0.459658	+	0.249249i
$787$	−40.1645	−	23.1890i	−1.43171	−	0.826597i	−0.434457	−	0.900692i	$-0.643060\pi$
$787$	−40.1645	−	23.1890i	−1.43171	−	0.826597i	−0.997251	+	0.0740951i	$0.976393\pi$
$788$	−20.0119	+	13.0270i	−0.712896	+	0.464068i
$789$	−2.98342	+	1.72248i	−0.106213	+	0.0613219i
$790$	−27.6243	+	26.9891i	−0.982828	+	0.960228i
$791$		0			0
$792$	−1.50111	−	18.6820i	−0.0533398	−	0.663836i
$793$	−48.9322	+	28.2510i	−1.73763	+	1.00322i
$794$	−24.7055	+	0.660441i	−0.876766	+	0.0234382i
$795$	0.782991	−	2.52980i	0.0277698	−	0.0897226i
$796$	30.9963	−	1.65841i	1.09864	−	0.0587806i
$797$	9.09251			0.322073			0.161037	−	0.986948i	$-0.448516\pi$
$797$	9.09251			0.322073			0.161037	+	0.986948i	$0.448516\pi$
$798$		0			0
$799$		−	9.31691i		−	0.329609i
$800$	−23.6507	+	15.5127i	−0.836180	+	0.548455i
$801$	10.1206	+	5.84312i	0.357593	+	0.206457i
$802$	24.5399	−	0.656013i	0.866534	−	0.0231646i
$803$	3.30641	−	1.90896i	0.116681	−	0.0673656i
$804$	3.95505	+	2.00976i	0.139484	+	0.0708788i
$805$		0			0
$806$	22.3109	+	36.3634i	0.785867	+	1.28085i
$807$	8.99316	+	15.5766i	0.316574	+	0.548323i
$808$	−0.713717	−	0.338991i	−0.0251085	−	0.0119257i
$809$	−8.66128	+	15.0018i	−0.304515	+	0.527435i	−0.977153	−	0.212536i	$-0.931828\pi$
$809$	−8.66128	+	15.0018i	−0.304515	+	0.527435i	0.672639	+	0.739971i	$0.265161\pi$
$810$	3.80355	−	13.5621i	0.133643	−	0.476523i
$811$	16.4459			0.577493			0.288746	−	0.957406i	$-0.406762\pi$
$811$	16.4459			0.577493			0.288746	+	0.957406i	$0.406762\pi$
$812$		0			0
$813$			19.3424i			0.678368i
$814$	−8.12527	+	14.9844i	−0.284791	+	0.525203i
$815$	−7.08683	+	22.8971i	−0.248241	+	0.802051i
$816$	−0.443879	−	4.13628i	−0.0155389	−	0.144799i
$817$	14.9680	+	25.9254i	0.523664	+	0.907013i
$818$	−8.79934	+	5.39886i	−0.307662	+	0.188767i
$819$		0			0
$820$	−1.41164	−	0.355500i	−0.0492968	−	0.0124146i
$821$	−22.4527	−	38.8892i	−0.783603	−	1.35724i	−0.929830	−	0.367990i	$-0.880046\pi$
$821$	−22.4527	−	38.8892i	−0.783603	−	1.35724i	0.146226	−	0.989251i	$-0.453287\pi$
$822$	15.4081	−	0.411897i	0.537418	−	0.0143666i
$823$	11.8546	−	20.5328i	0.413226	−	0.715729i	−0.582014	−	0.813179i	$-0.697735\pi$
$823$	11.8546	−	20.5328i	0.413226	−	0.715729i	0.995240	+	0.0974497i	$0.0310685\pi$
$824$	31.2013	−	21.5194i	1.08695	−	0.749665i
$825$	−8.89130	+	4.26088i	−0.309555	+	0.148345i
$826$		0			0
$827$	8.20536			0.285328			0.142664	−	0.989771i	$-0.454433\pi$
$827$	8.20536			0.285328			0.142664	+	0.989771i	$0.454433\pi$
$828$	−24.1624	+	1.29277i	−0.839702	+	0.0449268i
$829$	19.1548	+	11.0590i	0.665272	+	0.384095i	0.794283	−	0.607548i	$-0.207847\pi$
$829$	19.1548	+	11.0590i	0.665272	+	0.384095i	−0.129011	+	0.991643i	$0.541180\pi$
$830$	4.11928	+	16.1211i	0.142982	+	0.559570i
$831$	8.82054	+	15.2776i	0.305981	+	0.529975i
$832$	31.2039	−	5.04710i	1.08180	−	0.174977i
$833$		0			0
$834$	−6.24391	+	3.83096i	−0.216209	+	0.132655i
$835$	−21.6981	+	20.0943i	−0.750894	+	0.695391i
$836$	14.5452	−	9.46838i	0.503057	−	0.327471i
$837$	−26.4729	−	15.2841i	−0.915036	−	0.528296i
$838$	−12.0856	+	22.2879i	−0.417490	+	0.769923i
$839$	−3.64977			−0.126004			−0.0630020	−	0.998013i	$-0.520067\pi$
$839$	−3.64977			−0.126004			−0.0630020	+	0.998013i	$0.520067\pi$
$840$		0			0
$841$	−2.17525			−0.0750086
$842$	8.51652	−	15.7059i	0.293499	−	0.541262i
$843$	4.94174	+	2.85312i	0.170203	+	0.0982665i
$844$	23.7403	−	15.4541i	0.817176	−	0.531950i
$845$	−3.96822	−	4.28494i	−0.136511	−	0.147407i
$846$	−19.4920	+	11.9594i	−0.670150	+	0.411172i
$847$		0			0
$848$	5.22088	−	3.81065i	0.179286	−	0.130858i
$849$	−2.91351	−	5.04634i	−0.0999913	−	0.173190i
$850$	8.92951	−	4.57652i	0.306280	−	0.156974i
$851$	19.0582	+	11.0033i	0.653308	+	0.377188i
$852$	22.5543	−	1.20673i	0.772697	−	0.0413419i
$853$	−1.03474			−0.0354290			−0.0177145	−	0.999843i	$-0.505639\pi$
$853$	−1.03474			−0.0354290			−0.0177145	+	0.999843i	$0.505639\pi$
$854$		0			0
$855$	17.3205	−	3.93584i	0.592347	−	0.134603i
$856$	−8.71810	−	12.6405i	−0.297979	−	0.432043i
$857$	24.2563	−	42.0132i	0.828581	−	1.43514i	−0.0705709	−	0.997507i	$-0.522482\pi$
$857$	24.2563	−	42.0132i	0.828581	−	1.43514i	0.899152	−	0.437637i	$-0.144185\pi$
$858$	11.0147	−	0.294451i	0.376035	−	0.0100524i
$859$	−12.4674	−	21.5941i	−0.425382	−	0.736783i	0.571074	−	0.820898i	$-0.306527\pi$
$859$	−12.4674	−	21.5941i	−0.425382	−	0.736783i	−0.996456	+	0.0841157i	$0.973193\pi$
$860$	10.1368	−	40.2520i	0.345663	−	1.37258i
$861$		0			0
$862$	39.3852	−	24.1649i	1.34147	−	0.823060i
$863$	2.98354	+	5.16765i	0.101561	+	0.175909i	0.912328	−	0.409460i	$-0.134283\pi$
$863$	2.98354	+	5.16765i	0.101561	+	0.175909i	−0.810767	+	0.585369i	$0.800950\pi$
$864$	−17.9307	+	13.8366i	−0.610013	+	0.470732i
$865$	−7.44049	+	24.0398i	−0.252984	+	0.817377i
$866$	15.9016	−	29.3252i	0.540357	−	0.996511i
$867$		−	10.9836i		−	0.373023i
$868$		0			0
$869$	−32.8588			−1.11466
$870$	−11.5578	−	3.24143i	−0.391845	−	0.109895i
$871$	5.97927	−	10.3564i	0.202600	−	0.350913i
$872$	10.8207	−	22.7820i	0.366434	−	0.771496i
$873$	10.2840	+	17.8125i	0.348062	+	0.602861i
$874$	−11.7179	−	19.0984i	−0.396363	−	0.646014i
$875$		0			0
$876$	−1.85433	−	0.942281i	−0.0626522	−	0.0318367i
$877$	29.2974	−	16.9149i	0.989304	−	0.571175i	0.0842381	−	0.996446i	$-0.473154\pi$
$877$	29.2974	−	16.9149i	0.989304	−	0.571175i	0.905066	+	0.425270i	$0.139821\pi$
$878$	25.9981	−	0.694996i	0.877394	−	0.0234550i
$879$	−1.34243	−	0.775051i	−0.0452789	−	0.0261418i
$880$	−23.6169	−	4.62168i	−0.796125	−	0.155797i
$881$		−	20.9239i		−	0.704944i	−0.935822	−	0.352472i	$-0.885341\pi$
$881$		−	20.9239i		−	0.704944i	0.935822	−	0.352472i	$-0.114659\pi$
$882$		0			0
$883$	14.7876			0.497642			0.248821	−	0.968549i	$-0.419957\pi$
$883$	14.7876			0.497642			0.248821	+	0.968549i	$0.419957\pi$
$884$	−11.1976	+	0.599107i	−0.376615	+	0.0201501i
$885$	11.9528	+	3.69950i	0.401790	+	0.124357i
$886$	4.78446	−	0.127901i	0.160737	−	0.00429691i
$887$	−6.40786	+	3.69958i	−0.215155	+	0.124220i	−0.603705	−	0.797208i	$-0.706309\pi$
$887$	−6.40786	+	3.69958i	−0.215155	+	0.124220i	0.388550	+	0.921428i	$0.372976\pi$
$888$	9.25667	−	0.743780i	0.310633	−	0.0249596i
$889$		0			0
$890$	10.7328	−	10.4860i	0.359766	−	0.351493i
$891$	10.3785	−	5.99206i	0.347694	−	0.200741i
$892$	−5.08617	+	3.31090i	−0.170297	+	0.110857i
$893$	−18.3393	−	10.5882i	−0.613702	−	0.354321i
$894$	8.00516	+	4.34079i	0.267733	+	0.145178i
$895$	0.399347	+	1.75740i	0.0133487	+	0.0587435i
$896$		0			0
$897$		−	14.2255i		−	0.474976i
$898$	−8.02298	+	14.7958i	−0.267730	+	0.493741i
$899$	19.7716	−	34.2453i	0.659418	−	1.14215i
$900$	−21.0367	−	12.8070i	−0.701224	−	0.426901i
$901$	−1.98580	+	1.14650i	−0.0661566	+	0.0381956i
$902$	−0.647721	−	1.05569i	−0.0215668	−	0.0351506i
$903$		0			0
$904$	−0.238227	−	2.96484i	−0.00792331	−	0.0986090i
$905$	−0.109446	+	0.101357i	−0.00363812	+	0.00336920i
$906$	−0.311179	+	0.00831860i	−0.0103382	+	0.000276367i
$907$	9.25608	−	16.0320i	0.307343	−	0.532334i	−0.670437	−	0.741966i	$-0.733893\pi$
$907$	9.25608	−	16.0320i	0.307343	−	0.532334i	0.977780	+	0.209632i	$0.0672268\pi$
$908$	−1.57895	−	29.5113i	−0.0523994	−	0.979368i
$909$		−	0.688006i		−	0.0228197i
$910$		0			0
$911$		−	10.8437i		−	0.359267i	−0.983734	−	0.179634i	$-0.942509\pi$
$911$		−	10.8437i		−	0.359267i	0.983734	−	0.179634i	$-0.0574912\pi$
$912$	−8.64626	−	3.82695i	−0.286306	−	0.126723i
$913$	−7.07841	+	12.2602i	−0.234261	+	0.405752i
$914$	0.796292	+	29.7874i	0.0263390	+	0.985279i
$915$	−15.9236	−	17.1945i	−0.526418	−	0.568434i
$916$	−11.4663	−	5.82661i	−0.378858	−	0.192517i
$917$		0			0
$918$	6.84842	−	4.20187i	0.226032	−	0.138682i
$919$	13.9555	−	8.05723i	0.460351	−	0.265784i	−0.251841	−	0.967769i	$-0.581036\pi$
$919$	13.9555	−	8.05723i	0.460351	−	0.265784i	0.712192	+	0.701985i	$0.247703\pi$
$920$	−6.77944	+	30.3200i	−0.223511	+	0.999621i
$921$	−6.83653	+	11.8412i	−0.225271	+	0.390181i
$922$	36.8869	+	20.0019i	1.21480	+	0.658726i
$923$		−	60.8834i		−	2.00400i
$924$		0			0
$925$	9.67993	+	20.1994i	0.318274	+	0.664152i
$926$	10.1443	−	18.7078i	0.333362	−	0.614776i
$927$	28.5820	+	16.5018i	0.938757	+	0.541991i
$928$	−17.8991	−	23.1951i	−0.587567	−	0.761417i
$929$	−42.7419	+	24.6770i	−1.40232	+	0.809627i	−0.994630	−	0.103495i	$-0.966998\pi$
$929$	−42.7419	+	24.6770i	−1.40232	+	0.809627i	−0.407686	+	0.913122i	$0.633664\pi$
$930$	−12.6569	+	12.3659i	−0.415037	+	0.405494i
$931$		0			0
$932$	31.1502	+	15.8290i	1.02036	+	0.518496i
$933$	−5.19390	+	2.99870i	−0.170041	+	0.0981731i
$934$	−0.194477	−	7.27493i	−0.00636349	−	0.238043i
$935$	8.15542	+	2.52417i	0.266711	+	0.0825490i
$936$	15.6268	+	22.6576i	0.510779	+	0.740586i
$937$	−31.3085			−1.02280			−0.511402	−	0.859342i	$-0.670874\pi$
$937$	−31.3085			−1.02280			−0.511402	+	0.859342i	$0.670874\pi$
$938$		0			0
$939$		−	17.1311i		−	0.559054i
$940$	8.02694	+	28.2444i	0.261810	+	0.921232i
$941$	−37.9492	−	21.9100i	−1.23711	−	0.714245i	−0.268606	−	0.963250i	$-0.586563\pi$
$941$	−37.9492	−	21.9100i	−1.23711	−	0.714245i	−0.968502	+	0.249005i	$0.919896\pi$
$942$	0.532766	+	19.9295i	0.0173584	+	0.649338i
$943$	−1.38480	+	0.799514i	−0.0450952	+	0.0260358i
$944$	18.0047	+	24.6678i	0.586002	+	0.802867i
$945$		0			0
$946$	30.1022	−	18.4693i	0.978708	−	0.600488i
$947$	7.31729	+	12.6739i	0.237780	+	0.411847i	0.960077	−	0.279736i	$-0.0902469\pi$
$947$	7.31729	+	12.6739i	0.237780	+	0.411847i	−0.722297	+	0.691583i	$0.756914\pi$
$948$	9.76629	+	15.0029i	0.317194	+	0.487270i
$949$	−2.80340	+	4.85563i	−0.0910021	+	0.157620i
$950$	1.13956	−	22.7778i	0.0369721	−	0.739009i
$951$	−19.2078			−0.622857
$952$		0			0
$953$		−	28.2044i		−	0.913630i	−0.889562	−	0.456815i	$-0.848990\pi$
$953$		−	28.2044i		−	0.913630i	0.889562	−	0.456815i	$-0.151010\pi$
$954$	4.94763	+	2.68285i	0.160186	+	0.0868604i
$955$	37.2966	+	11.5436i	1.20689	+	0.373542i
$956$	5.40542	−	3.51872i	0.174824	−	0.113804i
$957$	−5.10651	−	8.84473i	−0.165070	−	0.285909i
$958$	−29.5513	−	48.1643i	−0.954759	−	1.55612i
$959$		0			0
$960$	4.90922	+	12.1568i	0.158444	+	0.392359i
$961$	−13.6458	−	23.6352i	−0.440187	−	0.762427i
$962$	−0.668938	−	25.0234i	−0.0215674	−	0.806785i
$963$	6.68534	−	11.5793i	0.215432	−	0.373139i
$964$	−2.18913	−	40.9158i	−0.0705072	−	1.31781i
$965$	−8.52071	−	37.4971i	−0.274291	−	1.20707i
$966$		0			0
$967$	8.88824			0.285827			0.142913	−	0.989735i	$-0.454353\pi$
$967$	8.88824			0.285827			0.142913	+	0.989735i	$0.454353\pi$
$968$	6.03968	+	8.75702i	0.194123	+	0.281461i
$969$	2.90493	+	1.67716i	0.0933198	+	0.0538782i
$970$	25.5871	−	6.53807i	0.821554	−	0.209925i
$971$	−4.37105	−	7.57089i	−0.140274	−	0.242961i	0.787326	−	0.616537i	$-0.211465\pi$
$971$	−4.37105	−	7.57089i	−0.140274	−	0.242961i	−0.927600	+	0.373576i	$0.878132\pi$
$972$	−27.2367	−	13.8403i	−0.873618	−	0.443929i
$973$		0			0
$974$	9.04134	+	14.7360i	0.289703	+	0.472173i
$975$	8.17930	−	11.9476i	0.261947	−	0.382631i
$976$	−6.10333	−	56.8737i	−0.195363	−	1.82048i
$977$	36.3569	+	20.9907i	1.16316	+	0.671551i	0.952059	−	0.305914i	$-0.0989620\pi$
$977$	36.3569	+	20.9907i	1.16316	+	0.671551i	0.211100	+	0.977464i	$0.432295\pi$
$978$	9.76676	+	5.29601i	0.312307	+	0.169348i
$979$	12.7666			0.408022
$980$		0			0
$981$	21.9613			0.701170
$982$	−28.5334	−	15.4722i	−0.910539	−	0.493738i
$983$	−9.53036	−	5.50236i	−0.303971	−	0.175498i	0.340254	−	0.940333i	$-0.389487\pi$
$983$	−9.53036	−	5.50236i	−0.303971	−	0.175498i	−0.644226	+	0.764836i	$0.722820\pi$
$984$	−0.289497	+	0.609513i	−0.00922884	+	0.0194306i
$985$	−19.5876	+	18.1398i	−0.624113	+	0.577982i
$986$	5.43554	+	8.85913i	0.173103	+	0.282132i
$987$		0			0
$988$	−11.5462	+	22.7221i	−0.367334	+	0.722885i
$989$	−22.7975	−	39.4865i	−0.724920	−	1.25560i
$990$	−5.18764	−	20.3021i	−0.164874	−	0.645245i
$991$	−31.6799	−	18.2904i	−1.00634	−	0.581013i	−0.0962255	−	0.995360i	$-0.530677\pi$
$991$	−31.6799	−	18.2904i	−1.00634	−	0.581013i	−0.910119	+	0.414346i	$0.864010\pi$
$992$	−42.8044	+	5.75429i	−1.35904	+	0.182699i
$993$	14.3073			0.454028
$994$		0			0
$995$	33.8418	−	7.69010i	1.07286	−	0.243792i
$996$	7.70167	−	0.412065i	0.244037	−	0.0130568i
$997$	−7.23204	+	12.5263i	−0.229041	+	0.396711i	−0.957524	−	0.288353i	$-0.906892\pi$
$997$	−7.23204	+	12.5263i	−0.229041	+	0.396711i	0.728483	+	0.685064i	$0.240226\pi$
$998$	−0.159008	−	5.94811i	−0.00503331	−	0.188284i
$999$	8.96801	+	15.5331i	0.283735	+	0.491444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.s.e.619.11		32
4.3	odd	2	inner	980.2.s.e.619.16		32
5.4	even	2	inner	980.2.s.e.619.6		32
7.2	even	3		140.2.s.b.19.1	✓	32
7.3	odd	6		980.2.c.d.979.23		32
7.4	even	3		980.2.c.d.979.24		32
7.5	odd	6	inner	980.2.s.e.19.1		32
7.6	odd	2		140.2.s.b.59.11	yes	32
20.19	odd	2	inner	980.2.s.e.619.1		32
28.3	even	6		980.2.c.d.979.12		32
28.11	odd	6		980.2.c.d.979.11		32
28.19	even	6	inner	980.2.s.e.19.6		32
28.23	odd	6		140.2.s.b.19.6	yes	32
28.27	even	2		140.2.s.b.59.16	yes	32
35.2	odd	12		700.2.p.e.551.8		32
35.4	even	6		980.2.c.d.979.9		32
35.9	even	6		140.2.s.b.19.16	yes	32
35.13	even	4		700.2.p.e.451.3		32
35.19	odd	6	inner	980.2.s.e.19.16		32
35.23	odd	12		700.2.p.e.551.9		32
35.24	odd	6		980.2.c.d.979.10		32
35.27	even	4		700.2.p.e.451.14		32
35.34	odd	2		140.2.s.b.59.6	yes	32
140.19	even	6	inner	980.2.s.e.19.11		32
140.23	even	12		700.2.p.e.551.3		32
140.27	odd	4		700.2.p.e.451.8		32
140.39	odd	6		980.2.c.d.979.22		32
140.59	even	6		980.2.c.d.979.21		32
140.79	odd	6		140.2.s.b.19.11	yes	32
140.83	odd	4		700.2.p.e.451.9		32
140.107	even	12		700.2.p.e.551.14		32
140.139	even	2		140.2.s.b.59.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.1	✓	32	7.2	even	3
140.2.s.b.19.6	yes	32	28.23	odd	6
140.2.s.b.19.11	yes	32	140.79	odd	6
140.2.s.b.19.16	yes	32	35.9	even	6
140.2.s.b.59.1	yes	32	140.139	even	2
140.2.s.b.59.6	yes	32	35.34	odd	2
140.2.s.b.59.11	yes	32	7.6	odd	2
140.2.s.b.59.16	yes	32	28.27	even	2
700.2.p.e.451.3		32	35.13	even	4
700.2.p.e.451.8		32	140.27	odd	4
700.2.p.e.451.9		32	140.83	odd	4
700.2.p.e.451.14		32	35.27	even	4
700.2.p.e.551.3		32	140.23	even	12
700.2.p.e.551.8		32	35.2	odd	12
700.2.p.e.551.9		32	35.23	odd	12
700.2.p.e.551.14		32	140.107	even	12
980.2.c.d.979.9		32	35.4	even	6
980.2.c.d.979.10		32	35.24	odd	6
980.2.c.d.979.11		32	28.11	odd	6
980.2.c.d.979.12		32	28.3	even	6
980.2.c.d.979.21		32	140.59	even	6
980.2.c.d.979.22		32	140.39	odd	6
980.2.c.d.979.23		32	7.3	odd	6
980.2.c.d.979.24		32	7.4	even	3
980.2.s.e.19.1		32	7.5	odd	6	inner
980.2.s.e.19.6		32	28.19	even	6	inner
980.2.s.e.19.11		32	140.19	even	6	inner
980.2.s.e.19.16		32	35.19	odd	6	inner
980.2.s.e.619.1		32	20.19	odd	2	inner
980.2.s.e.619.6		32	5.4	even	2	inner
980.2.s.e.619.11		32	1.1	even	1	trivial
980.2.s.e.619.16		32	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.674125 - 1.24320i) q^{2} +(-0.634715 - 0.366453i) q^{3} +(-1.09111 - 1.67615i) q^{4} +(-1.51934 - 1.64061i) q^{5} +(-0.883452 + 0.542044i) q^{6} +(-2.81934 + 0.226536i) q^{8} +(-1.23142 - 2.13289i) q^{9} +(-3.06384 + 0.782877i) q^{10} +(-2.33007 - 1.34527i) q^{11} +(0.0783137 + 1.46372i) q^{12} +3.95118 q^{13} +(0.363144 + 1.59809i) q^{15} +(-1.61896 + 3.65773i) q^{16} +(0.709509 - 1.22891i) q^{17} +(-3.48175 + 0.0930760i) q^{18} +(-1.61265 - 2.79319i) q^{19} +(-1.09214 + 4.33673i) q^{20} +(-3.24320 + 1.98987i) q^{22} +(2.45620 + 4.25426i) q^{23} +(1.87249 + 0.889369i) q^{24} +(-0.383193 + 4.98529i) q^{25} +(2.66359 - 4.91212i) q^{26} +4.00375i q^{27} -5.17926 q^{29} +(2.23155 + 0.625848i) q^{30} +(-3.81745 + 6.61201i) q^{31} +(3.45592 + 4.47846i) q^{32} +(0.985953 + 1.70772i) q^{33} +(-1.04948 - 1.71050i) q^{34} +(-2.23142 + 4.39127i) q^{36} +(3.87963 - 2.23990i) q^{37} +(-4.55962 + 0.121890i) q^{38} +(-2.50787 - 1.44792i) q^{39} +(4.65520 + 4.28125i) q^{40} +0.325509i q^{41} -9.28165 q^{43} +(0.287494 + 5.37338i) q^{44} +(-1.62828 + 5.26088i) q^{45} +(6.94469 - 0.185649i) q^{46} +(5.68610 - 3.28287i) q^{47} +(2.36796 - 1.72834i) q^{48} +(5.93942 + 3.83710i) q^{50} +(-0.900672 + 0.520003i) q^{51} +(-4.31117 - 6.62277i) q^{52} +(-1.39942 - 0.807955i) q^{53} +(4.97748 + 2.69903i) q^{54} +(1.33312 + 5.86665i) q^{55} +2.36383i q^{57} +(-3.49147 + 6.43888i) q^{58} +(3.81745 - 6.61201i) q^{59} +(2.28240 - 2.35237i) q^{60} +(-12.3842 + 7.15003i) q^{61} +(5.64664 + 9.20319i) q^{62} +(7.89736 - 1.27737i) q^{64} +(-6.00319 - 6.48234i) q^{65} +(2.78770 - 0.0745223i) q^{66} +(1.51329 - 2.62109i) q^{67} +(-2.83398 + 0.151627i) q^{68} -3.60032i q^{69} -15.4089i q^{71} +(3.95498 + 5.73438i) q^{72} +(-0.709509 + 1.22891i) q^{73} +(-0.169301 - 6.33314i) q^{74} +(2.07009 - 3.02382i) q^{75} +(-2.92222 + 5.75071i) q^{76} +(-3.49068 + 2.14171i) q^{78} +(10.5765 - 6.10637i) q^{79} +(8.46065 - 2.90127i) q^{80} +(-2.22709 + 3.85743i) q^{81} +(0.404674 + 0.219434i) q^{82} -5.26172i q^{83} +(-3.09414 + 0.703103i) q^{85} +(-6.25699 + 11.5390i) q^{86} +(3.28735 + 1.89795i) q^{87} +(6.87401 + 3.26492i) q^{88} +(-4.10930 + 2.37250i) q^{89} +(5.44268 + 5.57078i) q^{90} +(4.45079 - 8.75882i) q^{92} +(4.84598 - 2.79783i) q^{93} +(-0.248133 - 9.28205i) q^{94} +(-2.13236 + 6.88953i) q^{95} +(-0.552378 - 4.10898i) q^{96} -8.35134 q^{97} +6.62638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{4} + 6 q^{5} + 4 q^{9} + 12 q^{10} + 18 q^{16} + 48 q^{24} - 26 q^{25} + 18 q^{26} - 26 q^{30} - 28 q^{36} - 42 q^{40} - 26 q^{44} - 36 q^{45} - 22 q^{46} + 36 q^{50} - 48 q^{54} + 4 q^{60}+ \cdots - 60 q^{96}+O(q^{100}) \) 32 * q + 6 * q^4 + 6 * q^5 + 4 * q^9 + 12 * q^10 + 18 * q^16 + 48 * q^24 - 26 * q^25 + 18 * q^26 - 26 * q^30 - 28 * q^36 - 42 * q^40 - 26 * q^44 - 36 * q^45 - 22 * q^46 + 36 * q^50 - 48 * q^54 + 4 * q^60 - 36 * q^61 + 36 * q^64 - 4 * q^65 + 24 * q^66 + 14 * q^74 - 72 * q^80 + 72 * q^81 + 20 * q^85 + 8 * q^86 + 108 * q^89 - 30 * q^94 - 60 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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