LMFDB - Embedded newform 1176.2.p.a.979.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1176,2,Mod(979,1176)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1176, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1176.979"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.p (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.30
Character	$\chi$	$=$	1176.979
Dual form			1176.2.p.a.979.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41258 - 0.0679787i) q^{2} -1.00000i q^{3} +(1.99076 - 0.192050i) q^{4} +3.22796 q^{5} +(-0.0679787 - 1.41258i) q^{6} +(2.79905 - 0.406616i) q^{8} -1.00000 q^{9} +(4.55975 - 0.219433i) q^{10} +2.21319 q^{11} +(-0.192050 - 1.99076i) q^{12} -5.08369 q^{13} -3.22796i q^{15} +(3.92623 - 0.764652i) q^{16} -3.15923i q^{17} +(-1.41258 + 0.0679787i) q^{18} -3.38981i q^{19} +(6.42609 - 0.619932i) q^{20} +(3.12631 - 0.150450i) q^{22} +3.06401i q^{23} +(-0.406616 - 2.79905i) q^{24} +5.41974 q^{25} +(-7.18112 + 0.345583i) q^{26} +1.00000i q^{27} +9.88340i q^{29} +(-0.219433 - 4.55975i) q^{30} -2.02805 q^{31} +(5.49413 - 1.34703i) q^{32} -2.21319i q^{33} +(-0.214760 - 4.46266i) q^{34} +(-1.99076 + 0.192050i) q^{36} -0.921883i q^{37} +(-0.230435 - 4.78837i) q^{38} +5.08369i q^{39} +(9.03522 - 1.31254i) q^{40} +5.96303i q^{41} -6.68790 q^{43} +(4.40593 - 0.425045i) q^{44} -3.22796 q^{45} +(0.208287 + 4.32815i) q^{46} +2.12226 q^{47} +(-0.764652 - 3.92623i) q^{48} +(7.65581 - 0.368427i) q^{50} -3.15923 q^{51} +(-10.1204 + 0.976326i) q^{52} +3.60913i q^{53} +(0.0679787 + 1.41258i) q^{54} +7.14411 q^{55} -3.38981 q^{57} +(0.671861 + 13.9611i) q^{58} -12.2803i q^{59} +(-0.619932 - 6.42609i) q^{60} -12.6823 q^{61} +(-2.86477 + 0.137864i) q^{62} +(7.66933 - 2.27627i) q^{64} -16.4100 q^{65} +(-0.150450 - 3.12631i) q^{66} +8.81440 q^{67} +(-0.606731 - 6.28926i) q^{68} +3.06401 q^{69} -11.7036i q^{71} +(-2.79905 + 0.406616i) q^{72} +9.03055i q^{73} +(-0.0626684 - 1.30223i) q^{74} -5.41974i q^{75} +(-0.651014 - 6.74828i) q^{76} +(0.345583 + 7.18112i) q^{78} -11.0863i q^{79} +(12.6737 - 2.46827i) q^{80} +1.00000 q^{81} +(0.405359 + 8.42325i) q^{82} +3.57322i q^{83} -10.1979i q^{85} +(-9.44719 + 0.454635i) q^{86} +9.88340 q^{87} +(6.19484 - 0.899919i) q^{88} +7.30063i q^{89} +(-4.55975 + 0.219433i) q^{90} +(0.588444 + 6.09969i) q^{92} +2.02805i q^{93} +(2.99786 - 0.144268i) q^{94} -10.9422i q^{95} +(-1.34703 - 5.49413i) q^{96} +15.2238i q^{97} -2.21319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 4 q^{4} + 16 q^{8} - 32 q^{9} - 16 q^{11} - 12 q^{16} - 4 q^{18} - 20 q^{22} + 32 q^{25} + 16 q^{30} + 24 q^{32} - 4 q^{36} - 16 q^{43} - 48 q^{44} - 16 q^{46} + 76 q^{50} + 16 q^{57} + 12 q^{58}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 4 * q^4 + 16 * q^8 - 32 * q^9 - 16 * q^11 - 12 * q^16 - 4 * q^18 - 20 * q^22 + 32 * q^25 + 16 * q^30 + 24 * q^32 - 4 * q^36 - 16 * q^43 - 48 * q^44 - 16 * q^46 + 76 * q^50 + 16 * q^57 + 12 * q^58 + 4 * q^60 + 76 * q^64 + 64 * q^67 - 16 * q^72 + 68 * q^74 - 12 * q^78 + 32 * q^81 - 100 * q^86 + 28 * q^88 - 128 * q^92 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	1.41258	−	0.0679787i	0.998844	−	0.0480682i
$2$	1.41258	−	0.0679787i	0.998844	−	0.0480682i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.99076	−	0.192050i	0.995379	−	0.0960252i
$5$	3.22796			1.44359			0.721794	−	0.692108i	$-0.243318\pi$
$5$	3.22796			1.44359			0.721794	+	0.692108i	$0.243318\pi$
$6$	−0.0679787	−	1.41258i	−0.0277522	−	0.576683i
$7$		0			0
$7$		0			0
$8$	2.79905	−	0.406616i	0.989613	−	0.143760i
$9$	−1.00000			−0.333333
$10$	4.55975	−	0.219433i	1.44192	−	0.0693907i
$11$	2.21319			0.667303			0.333652	−	0.942696i	$-0.391719\pi$
$11$	2.21319			0.667303			0.333652	+	0.942696i	$0.391719\pi$
$12$	−0.192050	−	1.99076i	−0.0554402	−	0.574682i
$13$	−5.08369			−1.40996			−0.704981	−	0.709226i	$-0.749045\pi$
$13$	−5.08369			−1.40996			−0.704981	+	0.709226i	$0.749045\pi$
$14$		0			0
$15$		−	3.22796i		−	0.833456i
$16$	3.92623	−	0.764652i	0.981558	−	0.191163i
$17$		−	3.15923i		−	0.766226i	−0.923702	−	0.383113i	$-0.874852\pi$
$17$		−	3.15923i		−	0.766226i	0.923702	−	0.383113i	$-0.125148\pi$
$18$	−1.41258	+	0.0679787i	−0.332948	+	0.0160227i
$19$		−	3.38981i		−	0.777675i	−0.921306	−	0.388838i	$-0.872877\pi$
$19$		−	3.38981i		−	0.777675i	0.921306	−	0.388838i	$-0.127123\pi$
$20$	6.42609	−	0.619932i	1.43692	−	0.138621i
$21$		0			0
$22$	3.12631	−	0.150450i	0.666532	−	0.0320761i
$23$			3.06401i			0.638889i	0.947605	+	0.319445i	$0.103496\pi$
$23$			3.06401i			0.638889i	−0.947605	+	0.319445i	$0.896504\pi$
$24$	−0.406616	−	2.79905i	−0.0830000	−	0.571353i
$25$	5.41974			1.08395
$26$	−7.18112	+	0.345583i	−1.40833	+	0.0677743i
$27$			1.00000i			0.192450i
$28$		0			0
$29$			9.88340i			1.83530i	0.397387	+	0.917651i	$0.369917\pi$
$29$			9.88340i			1.83530i	−0.397387	+	0.917651i	$0.630083\pi$
$30$	−0.219433	−	4.55975i	−0.0400627	−	0.832493i
$31$	−2.02805			−0.364248			−0.182124	−	0.983276i	$-0.558297\pi$
$31$	−2.02805			−0.364248			−0.182124	+	0.983276i	$0.558297\pi$
$32$	5.49413	−	1.34703i	0.971235	−	0.238124i
$33$		−	2.21319i		−	0.385268i
$34$	−0.214760	−	4.46266i	−0.0368311	−	0.765340i
$35$		0			0
$36$	−1.99076	+	0.192050i	−0.331793	+	0.0320084i
$37$		−	0.921883i		−	0.151557i	−0.997125	−	0.0757783i	$-0.975856\pi$
$37$		−	0.921883i		−	0.151557i	0.997125	−	0.0757783i	$-0.0241441\pi$
$38$	−0.230435	−	4.78837i	−0.0373814	−	0.776776i
$39$			5.08369i			0.814042i
$40$	9.03522	−	1.31254i	1.42859	−	0.207531i
$41$			5.96303i			0.931269i	0.884977	+	0.465635i	$0.154174\pi$
$41$			5.96303i			0.931269i	−0.884977	+	0.465635i	$0.845826\pi$
$42$		0			0
$43$	−6.68790			−1.01990			−0.509948	−	0.860205i	$-0.670335\pi$
$43$	−6.68790			−1.01990			−0.509948	+	0.860205i	$0.670335\pi$
$44$	4.40593	−	0.425045i	0.664220	−	0.0640780i
$45$	−3.22796			−0.481196
$46$	0.208287	+	4.32815i	0.0307102	+	0.638151i
$47$	2.12226			0.309564			0.154782	−	0.987949i	$-0.450533\pi$
$47$	2.12226			0.309564			0.154782	+	0.987949i	$0.450533\pi$
$48$	−0.764652	−	3.92623i	−0.110368	−	0.566703i
$49$		0			0
$50$	7.65581	−	0.368427i	1.08269	−	0.0521034i
$51$	−3.15923			−0.442381
$52$	−10.1204	+	0.976326i	−1.40345	+	0.135392i
$53$			3.60913i			0.495753i	0.968792	+	0.247876i	$0.0797326\pi$
$53$			3.60913i			0.495753i	−0.968792	+	0.247876i	$0.920267\pi$
$54$	0.0679787	+	1.41258i	0.00925073	+	0.192228i
$55$	7.14411			0.963311
$56$		0			0
$57$	−3.38981			−0.448991
$58$	0.671861	+	13.9611i	0.0882196	+	1.83318i
$59$		−	12.2803i		−	1.59876i	−0.600827	−	0.799379i	$-0.705162\pi$
$59$		−	12.2803i		−	1.59876i	0.600827	−	0.799379i	$-0.294838\pi$
$60$	−0.619932	−	6.42609i	−0.0800328	−	0.829605i
$61$	−12.6823			−1.62380			−0.811901	−	0.583795i	$-0.801567\pi$
$61$	−12.6823			−1.62380			−0.811901	+	0.583795i	$0.801567\pi$
$62$	−2.86477	+	0.137864i	−0.363827	+	0.0175087i
$63$		0			0
$64$	7.66933	−	2.27627i	0.958666	−	0.284534i
$65$	−16.4100			−2.03541
$66$	−0.150450	−	3.12631i	−0.0185191	−	0.384822i
$67$	8.81440			1.07685			0.538425	−	0.842673i	$-0.319019\pi$
$67$	8.81440			1.07685			0.538425	+	0.842673i	$0.319019\pi$
$68$	−0.606731	−	6.28926i	−0.0735770	−	0.762685i
$69$	3.06401			0.368863
$70$		0			0
$71$		−	11.7036i		−	1.38896i	−0.719512	−	0.694480i	$-0.755634\pi$
$71$		−	11.7036i		−	1.38896i	0.719512	−	0.694480i	$-0.244366\pi$
$72$	−2.79905	+	0.406616i	−0.329871	+	0.0479201i
$73$			9.03055i			1.05695i	0.848950	+	0.528473i	$0.177235\pi$
$73$			9.03055i			1.05695i	−0.848950	+	0.528473i	$0.822765\pi$
$74$	−0.0626684	−	1.30223i	−0.00728505	−	0.151381i
$75$		−	5.41974i		−	0.625817i
$76$	−0.651014	−	6.74828i	−0.0746764	−	0.774081i
$77$		0			0
$78$	0.345583	+	7.18112i	0.0391295	+	0.813101i
$79$		−	11.0863i		−	1.24731i	−0.781699	−	0.623655i	$-0.785647\pi$
$79$		−	11.0863i		−	1.24731i	0.781699	−	0.623655i	$-0.214353\pi$
$80$	12.6737	−	2.46827i	1.41697	−	0.275961i
$81$	1.00000			0.111111
$82$	0.405359	+	8.42325i	0.0447644	+	0.930193i
$83$			3.57322i			0.392212i	0.980583	+	0.196106i	$0.0628297\pi$
$83$			3.57322i			0.392212i	−0.980583	+	0.196106i	$0.937170\pi$
$84$		0			0
$85$		−	10.1979i		−	1.10611i
$86$	−9.44719	+	0.454635i	−1.01872	+	0.0490245i
$87$	9.88340			1.05961
$88$	6.19484	−	0.899919i	0.660372	−	0.0959317i
$89$			7.30063i			0.773865i	0.922108	+	0.386933i	$0.126465\pi$
$89$			7.30063i			0.773865i	−0.922108	+	0.386933i	$0.873535\pi$
$90$	−4.55975	+	0.219433i	−0.480640	+	0.0231302i
$91$		0			0
$92$	0.588444	+	6.09969i	0.0613495	+	0.635937i
$93$			2.02805i			0.210299i
$94$	2.99786	−	0.144268i	0.309206	−	0.0148802i
$95$		−	10.9422i		−	1.12264i
$96$	−1.34703	−	5.49413i	−0.137481	−	0.560743i
$97$			15.2238i			1.54574i	0.634566	+	0.772869i	$0.281179\pi$
$97$			15.2238i			1.54574i	−0.634566	+	0.772869i	$0.718821\pi$
$98$		0			0
$99$	−2.21319			−0.222434
$100$	10.7894	−	1.04086i	1.07894	−	0.104086i
$101$	9.84247			0.979362			0.489681	−	0.871902i	$-0.337113\pi$
$101$	9.84247			0.979362			0.489681	+	0.871902i	$0.337113\pi$
$102$	−4.46266	+	0.214760i	−0.441869	+	0.0212644i
$103$	1.98452			0.195540			0.0977701	−	0.995209i	$-0.468829\pi$
$103$	1.98452			0.195540			0.0977701	+	0.995209i	$0.468829\pi$
$104$	−14.2295	+	2.06711i	−1.39532	+	0.202697i
$105$		0			0
$106$	0.245344	+	5.09818i	0.0238299	+	0.495179i
$107$	−3.23611			−0.312846			−0.156423	−	0.987690i	$-0.549996\pi$
$107$	−3.23611			−0.312846			−0.156423	+	0.987690i	$0.549996\pi$
$108$	0.192050	+	1.99076i	0.0184801	+	0.191561i
$109$		−	4.19152i		−	0.401475i	−0.979645	−	0.200738i	$-0.935666\pi$
$109$		−	4.19152i		−	0.401475i	0.979645	−	0.200738i	$-0.0643339\pi$
$110$	10.0916	−	0.485647i	0.962198	−	0.0463046i
$111$	−0.921883			−0.0875012
$112$		0			0
$113$	−2.84651			−0.267777			−0.133889	−	0.990996i	$-0.542746\pi$
$113$	−2.84651			−0.267777			−0.133889	+	0.990996i	$0.542746\pi$
$114$	−4.78837	+	0.230435i	−0.448472	+	0.0215822i
$115$			9.89049i			0.922293i
$116$	1.89811	+	19.6755i	0.176235	+	1.82682i
$117$	5.08369			0.469987
$118$	−0.834798	−	17.3469i	−0.0768494	−	1.59691i
$119$		0			0
$120$	−1.31254	−	9.03522i	−0.119818	−	0.824799i
$121$	−6.10177			−0.554706
$122$	−17.9148	+	0.862126i	−1.62193	+	0.0780533i
$123$	5.96303			0.537668
$124$	−4.03735	+	0.389487i	−0.362565	+	0.0349770i
$125$	1.35490			0.121186
$126$		0			0
$127$			21.0058i			1.86396i	0.362506	+	0.931981i	$0.381921\pi$
$127$			21.0058i			1.86396i	−0.362506	+	0.931981i	$0.618079\pi$
$128$	10.6788	−	3.73676i	0.943881	−	0.330286i
$129$			6.68790i			0.588837i
$130$	−23.1804	+	1.11553i	−2.03305	+	0.0978382i
$131$			0.570937i			0.0498830i	0.999689	+	0.0249415i	$0.00793994\pi$
$131$			0.570937i			0.0498830i	−0.999689	+	0.0249415i	$0.992060\pi$
$132$	−0.425045	−	4.40593i	−0.0369954	−	0.383487i
$133$		0			0
$134$	12.4510	−	0.599191i	1.07561	−	0.0517623i
$135$			3.22796i			0.277819i
$136$	−1.28459	−	8.84283i	−0.110153	−	0.758266i
$137$	−13.1563			−1.12402			−0.562008	−	0.827132i	$-0.689971\pi$
$137$	−13.1563			−1.12402			−0.562008	+	0.827132i	$0.689971\pi$
$138$	4.32815	−	0.208287i	0.368436	−	0.0177306i
$139$		−	9.54821i		−	0.809869i	−0.914346	−	0.404934i	$-0.867294\pi$
$139$		−	9.54821i		−	0.809869i	0.914346	−	0.404934i	$-0.132706\pi$
$140$		0			0
$141$		−	2.12226i		−	0.178727i
$142$	−0.795594	−	16.5322i	−0.0667648	−	1.38735i
$143$	−11.2512			−0.940873
$144$	−3.92623	+	0.764652i	−0.327186	+	0.0637210i
$145$			31.9032i			2.64942i
$146$	0.613885	+	12.7564i	0.0508055	+	1.05572i
$147$		0			0
$148$	−0.177048	−	1.83524i	−0.0145533	−	0.150856i
$149$		−	10.5961i		−	0.868068i	−0.900896	−	0.434034i	$-0.857090\pi$
$149$		−	10.5961i		−	0.868068i	0.900896	−	0.434034i	$-0.142910\pi$
$150$	−0.368427	−	7.65581i	−0.0300819	−	0.625094i
$151$			1.21610i			0.0989651i	0.998775	+	0.0494826i	$0.0157572\pi$
$151$			1.21610i			0.0989651i	−0.998775	+	0.0494826i	$0.984243\pi$
$152$	−1.37835	−	9.48823i	−0.111799	−	0.769597i
$153$			3.15923i			0.255409i
$154$		0			0
$155$	−6.54645			−0.525824
$156$	0.976326	+	10.1204i	0.0781686	+	0.810280i
$157$	3.62504			0.289310			0.144655	−	0.989482i	$-0.453793\pi$
$157$	3.62504			0.289310			0.144655	+	0.989482i	$0.453793\pi$
$158$	−0.753635	−	15.6603i	−0.0599560	−	1.24587i
$159$	3.60913			0.286223
$160$	17.7349	−	4.34817i	1.40206	−	0.343753i
$161$		0			0
$162$	1.41258	−	0.0679787i	0.110983	−	0.00534091i
$163$	19.8314			1.55332			0.776659	−	0.629921i	$-0.216913\pi$
$163$	19.8314			1.55332			0.776659	+	0.629921i	$0.216913\pi$
$164$	1.14520	+	11.8710i	0.0894253	+	0.926966i
$165$		−	7.14411i		−	0.556168i
$166$	0.242903	+	5.04746i	0.0188529	+	0.391759i
$167$	−12.3971			−0.959317			−0.479659	−	0.877455i	$-0.659240\pi$
$167$	−12.3971			−0.959317			−0.479659	+	0.877455i	$0.659240\pi$
$168$		0			0
$169$	12.8439			0.987994
$170$	−0.693238	−	14.4053i	−0.0531689	−	1.10484i
$171$			3.38981i			0.259225i
$172$	−13.3140	+	1.28441i	−1.01518	+	0.0979357i
$173$	−1.03865			−0.0789672			−0.0394836	−	0.999220i	$-0.512571\pi$
$173$	−1.03865			−0.0789672			−0.0394836	+	0.999220i	$0.512571\pi$
$174$	13.9611	−	0.671861i	1.05839	−	0.0509336i
$175$		0			0
$176$	8.68952	−	1.69232i	0.654997	−	0.127564i
$177$	−12.2803			−0.923044
$178$	0.496287	+	10.3127i	0.0371983	+	0.772971i
$179$	−2.52607			−0.188808			−0.0944038	−	0.995534i	$-0.530094\pi$
$179$	−2.52607			−0.188808			−0.0944038	+	0.995534i	$0.530094\pi$
$180$	−6.42609	+	0.619932i	−0.478972	+	0.0462070i
$181$	8.29867			0.616835			0.308418	−	0.951251i	$-0.400201\pi$
$181$	8.29867			0.616835			0.308418	+	0.951251i	$0.400201\pi$
$182$		0			0
$183$			12.6823i			0.937503i
$184$	1.24587	+	8.57629i	0.0918469	+	0.632253i
$185$		−	2.97580i		−	0.218785i
$186$	0.137864	+	2.86477i	0.0101087	+	0.210055i
$187$		−	6.99199i		−	0.511305i
$188$	4.22491	−	0.407581i	0.308133	−	0.0297259i
$189$		0			0
$190$	−0.743834	−	15.4567i	−0.0539634	−	1.12134i
$191$			6.07541i			0.439601i	0.975545	+	0.219801i	$0.0705407\pi$
$191$			6.07541i			0.439601i	−0.975545	+	0.219801i	$0.929459\pi$
$192$	−2.27627	−	7.66933i	−0.164276	−	0.553486i
$193$	−9.18679			−0.661280			−0.330640	−	0.943757i	$-0.607265\pi$
$193$	−9.18679			−0.661280			−0.330640	+	0.943757i	$0.607265\pi$
$194$	1.03489	+	21.5048i	0.0743008	+	1.54395i
$195$			16.4100i			1.17514i
$196$		0			0
$197$		−	20.2764i		−	1.44463i	−0.691563	−	0.722316i	$-0.743078\pi$
$197$		−	20.2764i		−	1.44463i	0.691563	−	0.722316i	$-0.256922\pi$
$198$	−3.12631	+	0.150450i	−0.222177	+	0.0106920i
$199$	−3.28711			−0.233017			−0.116508	−	0.993190i	$-0.537170\pi$
$199$	−3.28711			−0.233017			−0.116508	+	0.993190i	$0.537170\pi$
$200$	15.1701	−	2.20375i	1.07269	−	0.155829i
$201$		−	8.81440i		−	0.621720i
$202$	13.9033	−	0.669078i	0.978230	−	0.0470762i
$203$		0			0
$204$	−6.28926	+	0.606731i	−0.440336	+	0.0424797i
$205$			19.2484i			1.34437i
$206$	2.80329	−	0.134905i	0.195314	−	0.00939926i
$207$		−	3.06401i		−	0.212963i
$208$	−19.9598	+	3.88726i	−1.38396	+	0.269533i
$209$		−	7.50230i		−	0.518945i
$210$		0			0
$211$	−21.6901			−1.49320			−0.746602	−	0.665271i	$-0.768316\pi$
$211$	−21.6901			−1.49320			−0.746602	+	0.665271i	$0.768316\pi$
$212$	0.693136	+	7.18491i	0.0476048	+	0.493462i
$213$	−11.7036			−0.801916
$214$	−4.57125	+	0.219986i	−0.312485	+	0.0150379i
$215$	−21.5883			−1.47231
$216$	0.406616	+	2.79905i	0.0276667	+	0.190451i
$217$		0			0
$218$	−0.284934	−	5.92086i	−0.0192982	−	0.401011i
$219$	9.03055			0.610228
$220$	14.2222	−	1.37203i	0.958860	−	0.0925022i
$221$			16.0605i			1.08035i
$222$	−1.30223	+	0.0626684i	−0.0874001	+	0.00420603i
$223$	−19.3266			−1.29420			−0.647102	−	0.762404i	$-0.724019\pi$
$223$	−19.3266			−1.29420			−0.647102	+	0.762404i	$0.724019\pi$
$224$		0			0
$225$	−5.41974			−0.361316
$226$	−4.02092	+	0.193502i	−0.267468	+	0.0128716i
$227$		−	0.539061i		−	0.0357788i	−0.999840	−	0.0178894i	$-0.994305\pi$
$227$		−	0.539061i		−	0.0357788i	0.999840	−	0.0178894i	$-0.00569467\pi$
$228$	−6.74828	+	0.651014i	−0.446916	+	0.0431145i
$229$	22.8623			1.51078			0.755392	−	0.655274i	$-0.227447\pi$
$229$	22.8623			1.51078			0.755392	+	0.655274i	$0.227447\pi$
$230$	0.672343	+	13.9711i	0.0443330	+	0.921227i
$231$		0			0
$232$	4.01875	+	27.6641i	0.263844	+	1.81624i
$233$	−3.00490			−0.196857			−0.0984287	−	0.995144i	$-0.531382\pi$
$233$	−3.00490			−0.196857			−0.0984287	+	0.995144i	$0.531382\pi$
$234$	7.18112	−	0.345583i	0.469444	−	0.0225914i
$235$	6.85058			0.446882
$236$	−2.35844	−	24.4471i	−0.153521	−	1.59137i
$237$	−11.0863			−0.720135
$238$		0			0
$239$			11.2699i			0.728988i	0.931206	+	0.364494i	$0.118758\pi$
$239$			11.2699i			0.728988i	−0.931206	+	0.364494i	$0.881242\pi$
$240$	−2.46827	−	12.6737i	−0.159326	−	0.818086i
$241$			11.2731i			0.726162i	0.931758	+	0.363081i	$0.118275\pi$
$241$			11.2731i			0.726162i	−0.931758	+	0.363081i	$0.881725\pi$
$242$	−8.61923	+	0.414790i	−0.554065	+	0.0266637i
$243$		−	1.00000i		−	0.0641500i
$244$	−25.2474	+	2.43564i	−1.61630	+	0.155926i
$245$		0			0
$246$	8.42325	−	0.405359i	0.537047	−	0.0258447i
$247$			17.2327i			1.09649i
$248$	−5.67659	+	0.824635i	−0.360464	+	0.0523644i
$249$	3.57322			0.226444
$250$	1.91390	−	0.0921040i	0.121045	−	0.00582517i
$251$		−	3.26625i		−	0.206164i	−0.994673	−	0.103082i	$-0.967130\pi$
$251$		−	3.26625i		−	0.206164i	0.994673	−	0.103082i	$-0.0328704\pi$
$252$		0			0
$253$			6.78124i			0.426333i
$254$	1.42795	+	29.6723i	0.0895973	+	1.86181i
$255$	−10.1979			−0.638615
$256$	14.8306	−	6.00440i	0.926913	−	0.375275i
$257$			12.0704i			0.752933i	0.926430	+	0.376467i	$0.122861\pi$
$257$			12.0704i			0.752933i	−0.926430	+	0.376467i	$0.877139\pi$
$258$	0.454635	+	9.44719i	0.0283043	+	0.588156i
$259$		0			0
$260$	−32.6683	+	3.15154i	−2.02600	+	0.195450i
$261$		−	9.88340i		−	0.611767i
$262$	0.0388115	+	0.806493i	0.00239778	+	0.0498253i
$263$			16.3807i			1.01008i	0.863097	+	0.505038i	$0.168522\pi$
$263$			16.3807i			1.01008i	−0.863097	+	0.505038i	$0.831478\pi$
$264$	−0.899919	−	6.19484i	−0.0553862	−	0.381266i
$265$			11.6501i			0.715663i
$266$		0			0
$267$	7.30063			0.446791
$268$	17.5473	−	1.69281i	1.07187	−	0.103405i
$269$	−7.47144			−0.455542			−0.227771	−	0.973715i	$-0.573144\pi$
$269$	−7.47144			−0.455542			−0.227771	+	0.973715i	$0.573144\pi$
$270$	0.219433	+	4.55975i	0.0133542	+	0.277498i
$271$	8.97234			0.545031			0.272515	−	0.962151i	$-0.412144\pi$
$271$	8.97234			0.545031			0.272515	+	0.962151i	$0.412144\pi$
$272$	−2.41571	−	12.4039i	−0.146474	−	0.752095i
$273$		0			0
$274$	−18.5843	+	0.894345i	−1.12272	+	0.0540294i
$275$	11.9949			0.723322
$276$	6.09969	−	0.588444i	0.367158	−	0.0354201i
$277$		−	6.13883i		−	0.368847i	−0.982847	−	0.184423i	$-0.940958\pi$
$277$		−	6.13883i		−	0.368847i	0.982847	−	0.184423i	$-0.0590417\pi$
$278$	−0.649075	−	13.4876i	−0.0389289	−	0.808933i
$279$	2.02805			0.121416
$280$		0			0
$281$	−19.2936			−1.15096			−0.575480	−	0.817816i	$-0.695185\pi$
$281$	−19.2936			−1.15096			−0.575480	+	0.817816i	$0.695185\pi$
$282$	−0.144268	−	2.99786i	−0.00859106	−	0.178520i
$283$			22.3435i			1.32818i	0.747651	+	0.664092i	$0.231182\pi$
$283$			22.3435i			1.32818i	−0.747651	+	0.664092i	$0.768818\pi$
$284$	−2.24768	−	23.2990i	−0.133375	−	1.38254i
$285$	−10.9422			−0.648158
$286$	−15.8932	+	0.764842i	−0.939785	+	0.0452260i
$287$		0			0
$288$	−5.49413	+	1.34703i	−0.323745	+	0.0793746i
$289$	7.01927			0.412898
$290$	2.16874	+	45.0658i	0.127353	+	2.64636i
$291$	15.2238			0.892432
$292$	1.73432	+	17.9776i	0.101493	+	1.05206i
$293$	14.0707			0.822018			0.411009	−	0.911631i	$-0.365176\pi$
$293$	14.0707			0.822018			0.411009	+	0.911631i	$0.365176\pi$
$294$		0			0
$295$		−	39.6403i		−	2.30795i
$296$	−0.374852	−	2.58039i	−0.0217878	−	0.149982i
$297$			2.21319i			0.128423i
$298$	−0.720311	−	14.9679i	−0.0417265	−	0.867065i
$299$		−	15.5765i		−	0.900810i
$300$	−1.04086	−	10.7894i	−0.0600943	−	0.622925i
$301$		0			0
$302$	0.0826691	+	1.71784i	0.00475707	+	0.0988507i
$303$		−	9.84247i		−	0.565435i
$304$	−2.59202	−	13.3092i	−0.148663	−	0.763333i
$305$	−40.9380			−2.34410
$306$	0.214760	+	4.46266i	0.0122770	+	0.255113i
$307$		−	9.61787i		−	0.548921i	−0.961598	−	0.274460i	$-0.911501\pi$
$307$		−	9.61787i		−	0.548921i	0.961598	−	0.274460i	$-0.0884992\pi$
$308$		0			0
$309$		−	1.98452i		−	0.112895i
$310$	−9.24738	+	0.445019i	−0.525216	+	0.0252754i
$311$	21.6970			1.23032			0.615162	−	0.788401i	$-0.289091\pi$
$311$	21.6970			1.23032			0.615162	+	0.788401i	$0.289091\pi$
$312$	2.06711	+	14.2295i	0.117027	+	0.805586i
$313$			10.9294i			0.617766i	0.951100	+	0.308883i	$0.0999552\pi$
$313$			10.9294i			0.617766i	−0.951100	+	0.308883i	$0.900045\pi$
$314$	5.12065	−	0.246425i	0.288975	−	0.0139066i
$315$		0			0
$316$	−2.12914	−	22.0702i	−0.119773	−	1.24155i
$317$		−	7.09278i		−	0.398370i	−0.979962	−	0.199185i	$-0.936171\pi$
$317$		−	7.09278i		−	0.398370i	0.979962	−	0.199185i	$-0.0638295\pi$
$318$	5.09818	−	0.245344i	0.285892	−	0.0137582i
$319$			21.8739i			1.22470i
$320$	24.7563	−	7.34772i	1.38392	−	0.410750i
$321$			3.23611i			0.180622i
$322$		0			0
$323$	−10.7092			−0.595874
$324$	1.99076	−	0.192050i	0.110598	−	0.0106695i
$325$	−27.5523			−1.52833
$326$	28.0135	−	1.34811i	1.55152	−	0.0746652i
$327$	−4.19152			−0.231792
$328$	2.42466	+	16.6908i	0.133880	+	0.921595i
$329$		0			0
$330$	−0.485647	−	10.0916i	−0.0267340	−	0.555525i
$331$	11.7240			0.644411			0.322206	−	0.946670i	$-0.395576\pi$
$331$	11.7240			0.644411			0.322206	+	0.946670i	$0.395576\pi$
$332$	0.686239	+	7.11342i	0.0376623	+	0.390400i
$333$			0.921883i			0.0505189i
$334$	−17.5119	+	0.842739i	−0.958208	+	0.0461126i
$335$	28.4526			1.55453
$336$		0			0
$337$	23.5287			1.28169			0.640846	−	0.767670i	$-0.278584\pi$
$337$	23.5287			1.28169			0.640846	+	0.767670i	$0.278584\pi$
$338$	18.1431	−	0.873113i	0.986852	−	0.0474911i
$339$			2.84651i			0.154601i
$340$	−1.95851	−	20.3015i	−0.106215	−	1.10100i
$341$	−4.48846			−0.243064
$342$	0.230435	+	4.78837i	0.0124605	+	0.258925i
$343$		0			0
$344$	−18.7197	+	2.71940i	−1.00930	+	0.146620i
$345$	9.89049			0.532486
$346$	−1.46718	+	0.0706062i	−0.0788759	+	0.00379581i
$347$	−10.3426			−0.555222			−0.277611	−	0.960694i	$-0.589543\pi$
$347$	−10.3426			−0.555222			−0.277611	+	0.960694i	$0.589543\pi$
$348$	19.6755	−	1.89811i	1.05472	−	0.101749i
$349$	−0.830301			−0.0444450			−0.0222225	−	0.999753i	$-0.507074\pi$
$349$	−0.830301			−0.0444450			−0.0222225	+	0.999753i	$0.507074\pi$
$350$		0			0
$351$		−	5.08369i		−	0.271347i
$352$	12.1596	−	2.98124i	0.648108	−	0.158901i
$353$		−	4.86336i		−	0.258850i	−0.991589	−	0.129425i	$-0.958687\pi$
$353$		−	4.86336i		−	0.258850i	0.991589	−	0.129425i	$-0.0413132\pi$
$354$	−17.3469	+	0.834798i	−0.921977	+	0.0443690i
$355$		−	37.7787i		−	2.00509i
$356$	1.40209	+	14.5338i	0.0743106	+	0.770289i
$357$		0			0
$358$	−3.56828	+	0.171719i	−0.188589	+	0.00907564i
$359$		−	18.8309i		−	0.993855i	−0.867792	−	0.496928i	$-0.834461\pi$
$359$		−	18.8309i		−	0.993855i	0.867792	−	0.496928i	$-0.165539\pi$
$360$	−9.03522	+	1.31254i	−0.476198	+	0.0691769i
$361$	7.50921			0.395222
$362$	11.7225	−	0.564133i	0.616122	−	0.0296502i
$363$			6.10177i			0.320260i
$364$		0			0
$365$			29.1503i			1.52579i
$366$	0.862126	+	17.9148i	0.0450641	+	0.936419i
$367$	21.4539			1.11989			0.559943	−	0.828531i	$-0.310823\pi$
$367$	21.4539			1.11989			0.559943	+	0.828531i	$0.310823\pi$
$368$	2.34290	+	12.0300i	0.122132	+	0.627107i
$369$		−	5.96303i		−	0.310423i
$370$	−0.202291	−	4.20355i	−0.0105166	−	0.218532i
$371$		0			0
$372$	0.389487	+	4.03735i	0.0201940	+	0.209327i
$373$		−	16.3420i		−	0.846154i	−0.906094	−	0.423077i	$-0.860950\pi$
$373$		−	16.3420i		−	0.846154i	0.906094	−	0.423077i	$-0.139050\pi$
$374$	−0.475306	−	9.87673i	−0.0245775	−	0.510714i
$375$		−	1.35490i		−	0.0699665i
$376$	5.94031	−	0.862944i	0.306348	−	0.0445030i
$377$		−	50.2442i		−	2.58771i
$378$		0			0
$379$	−4.31636			−0.221717			−0.110858	−	0.993836i	$-0.535360\pi$
$379$	−4.31636			−0.221717			−0.110858	+	0.993836i	$0.535360\pi$
$380$	−2.10145	−	21.7832i	−0.107802	−	1.11745i
$381$	21.0058			1.07616
$382$	0.412998	+	8.58200i	0.0211308	+	0.439093i
$383$	20.1897			1.03165			0.515823	−	0.856695i	$-0.327486\pi$
$383$	20.1897			1.03165			0.515823	+	0.856695i	$0.327486\pi$
$384$	−3.73676	−	10.6788i	−0.190691	−	0.544950i
$385$		0			0
$386$	−12.9771	+	0.624506i	−0.660515	+	0.0317865i
$387$	6.68790			0.339965
$388$	2.92373	+	30.3068i	0.148430	+	1.53859i
$389$		−	33.7614i		−	1.71177i	−0.517164	−	0.855886i	$-0.673012\pi$
$389$		−	33.7614i		−	1.71177i	0.517164	−	0.855886i	$-0.326988\pi$
$390$	1.11553	+	23.1804i	0.0564869	+	1.17378i
$391$	9.67989			0.489533
$392$		0			0
$393$	0.570937			0.0287999
$394$	−1.37836	−	28.6420i	−0.0694408	−	1.44296i
$395$		−	35.7863i		−	1.80060i
$396$	−4.40593	+	0.425045i	−0.221407	+	0.0213593i
$397$	0.0882317			0.00442822			0.00221411	−	0.999998i	$-0.499295\pi$
$397$	0.0882317			0.00442822			0.00221411	+	0.999998i	$0.499295\pi$
$398$	−4.64330	+	0.223453i	−0.232748	+	0.0112007i
$399$		0			0
$400$	21.2792	−	4.14421i	1.06396	−	0.207211i
$401$	−25.2075			−1.25880			−0.629400	−	0.777081i	$-0.716699\pi$
$401$	−25.2075			−1.25880			−0.629400	+	0.777081i	$0.716699\pi$
$402$	−0.599191	−	12.4510i	−0.0298850	−	0.621001i
$403$	10.3100			0.513576
$404$	19.5940	−	1.89025i	0.974837	−	0.0940435i
$405$	3.22796			0.160399
$406$		0			0
$407$		−	2.04031i		−	0.101134i
$408$	−8.84283	+	1.28459i	−0.437785	+	0.0635968i
$409$		−	31.0824i		−	1.53692i	−0.639895	−	0.768462i	$-0.721022\pi$
$409$		−	31.0824i		−	1.53692i	0.639895	−	0.768462i	$-0.278978\pi$
$410$	1.30848	+	27.1899i	0.0646214	+	1.34282i
$411$			13.1563i			0.648951i
$412$	3.95069	−	0.381127i	0.194637	−	0.0187768i
$413$		0			0
$414$	−0.208287	−	4.32815i	−0.0102367	−	0.212717i
$415$			11.5342i			0.566193i
$416$	−27.9305	+	6.84789i	−1.36940	+	0.335746i
$417$	−9.54821			−0.467578
$418$	−0.509997	−	10.5976i	−0.0249448	−	0.518345i
$419$		−	22.7655i		−	1.11217i	−0.831126	−	0.556085i	$-0.812303\pi$
$419$		−	22.7655i		−	1.11217i	0.831126	−	0.556085i	$-0.187697\pi$
$420$		0			0
$421$			24.0207i			1.17070i	0.810781	+	0.585349i	$0.199042\pi$
$421$			24.0207i			1.17070i	−0.810781	+	0.585349i	$0.800958\pi$
$422$	−30.6389	+	1.47446i	−1.49148	+	0.0717756i
$423$	−2.12226			−0.103188
$424$	1.46753	+	10.1021i	0.0712695	+	0.490603i
$425$		−	17.1222i		−	0.830548i
$426$	−16.5322	+	0.795594i	−0.800989	+	0.0385467i
$427$		0			0
$428$	−6.44230	+	0.621496i	−0.311400	+	0.0300411i
$429$			11.2512i			0.543213i
$430$	−30.4952	+	1.46754i	−1.47061	+	0.0707712i
$431$		−	32.6078i		−	1.57066i	−0.619077	−	0.785330i	$-0.712493\pi$
$431$		−	32.6078i		−	1.57066i	0.619077	−	0.785330i	$-0.287507\pi$
$432$	0.764652	+	3.92623i	0.0367893	+	0.188901i
$433$			18.4752i			0.887861i	0.896061	+	0.443931i	$0.146416\pi$
$433$			18.4752i			0.887861i	−0.896061	+	0.443931i	$0.853584\pi$
$434$		0			0
$435$	31.9032			1.52964
$436$	−0.804984	−	8.34431i	−0.0385518	−	0.399620i
$437$	10.3864			0.496848
$438$	12.7564	−	0.613885i	0.609522	−	0.0293325i
$439$	−22.4276			−1.07041			−0.535206	−	0.844722i	$-0.679766\pi$
$439$	−22.4276			−1.07041			−0.535206	+	0.844722i	$0.679766\pi$
$440$	19.9967	−	2.90491i	0.953305	−	0.138486i
$441$		0			0
$442$	1.09177	+	22.6868i	0.0519304	+	1.07910i
$443$	9.04336			0.429663			0.214832	−	0.976651i	$-0.431080\pi$
$443$	9.04336			0.429663			0.214832	+	0.976651i	$0.431080\pi$
$444$	−1.83524	+	0.177048i	−0.0870969	+	0.00840233i
$445$			23.5662i			1.11714i
$446$	−27.3003	+	1.31380i	−1.29271	+	0.0622100i
$447$	−10.5961			−0.501179
$448$		0			0
$449$	5.65664			0.266954			0.133477	−	0.991052i	$-0.457386\pi$
$449$	5.65664			0.266954			0.133477	+	0.991052i	$0.457386\pi$
$450$	−7.65581	+	0.368427i	−0.360898	+	0.0173678i
$451$			13.1973i			0.621439i
$452$	−5.66672	+	0.546674i	−0.266540	+	0.0257134i
$453$	1.21610			0.0571375
$454$	−0.0366447	−	0.761467i	−0.00171982	−	0.0357374i
$455$		0			0
$456$	−9.48823	+	1.37835i	−0.444327	+	0.0645471i
$457$	9.37943			0.438751			0.219376	−	0.975640i	$-0.429598\pi$
$457$	9.37943			0.438751			0.219376	+	0.975640i	$0.429598\pi$
$458$	32.2948	−	1.55415i	1.50904	−	0.0726206i
$459$	3.15923			0.147460
$460$	1.89947	+	19.6896i	0.0885634	+	0.918031i
$461$	−31.7960			−1.48089			−0.740444	−	0.672118i	$-0.765385\pi$
$461$	−31.7960			−1.48089			−0.740444	+	0.672118i	$0.765385\pi$
$462$		0			0
$463$		−	8.87505i		−	0.412458i	−0.978504	−	0.206229i	$-0.933881\pi$
$463$		−	8.87505i		−	0.412458i	0.978504	−	0.206229i	$-0.0661193\pi$
$464$	7.55736	+	38.8045i	0.350842	+	1.80146i
$465$			6.54645i			0.303585i
$466$	−4.24465	+	0.204269i	−0.196630	+	0.00946258i
$467$		−	3.12922i		−	0.144803i	−0.997376	−	0.0724015i	$-0.976934\pi$
$467$		−	3.12922i		−	0.144803i	0.997376	−	0.0724015i	$-0.0230663\pi$
$468$	10.1204	−	0.976326i	0.467816	−	0.0451307i
$469$		0			0
$470$	9.67698	−	0.465693i	0.446366	−	0.0214808i
$471$		−	3.62504i		−	0.167033i
$472$	−4.99336	−	34.3731i	−0.229838	−	1.58215i
$473$	−14.8016			−0.680579
$474$	−15.6603	+	0.753635i	−0.719303	+	0.0346156i
$475$		−	18.3719i		−	0.842959i
$476$		0			0
$477$		−	3.60913i		−	0.165251i
$478$	0.766111	+	15.9196i	0.0350411	+	0.728145i
$479$	−16.3903			−0.748894			−0.374447	−	0.927248i	$-0.622167\pi$
$479$	−16.3903			−0.748894			−0.374447	+	0.927248i	$0.622167\pi$
$480$	−4.34817	−	17.7349i	−0.198466	−	0.809482i
$481$			4.68657i			0.213689i
$482$	0.766328	+	15.9241i	0.0349053	+	0.725323i
$483$		0			0
$484$	−12.1471	+	1.17185i	−0.552143	+	0.0532658i
$485$			49.1417i			2.23141i
$486$	−0.0679787	−	1.41258i	−0.00308358	−	0.0640759i
$487$		−	29.3637i		−	1.33060i	−0.746577	−	0.665299i	$-0.768304\pi$
$487$		−	29.3637i		−	1.33060i	0.746577	−	0.665299i	$-0.231696\pi$
$488$	−35.4984	+	5.15682i	−1.60694	+	0.233438i
$489$		−	19.8314i		−	0.896808i
$490$		0			0
$491$	33.8967			1.52974			0.764869	−	0.644186i	$-0.222804\pi$
$491$	33.8967			1.52974			0.764869	+	0.644186i	$0.222804\pi$
$492$	11.8710	−	1.14520i	0.535184	−	0.0516297i
$493$	31.2239			1.40626
$494$	1.17146	+	24.3426i	0.0527064	+	1.09523i
$495$	−7.14411			−0.321104
$496$	−7.96258	+	1.55075i	−0.357530	+	0.0696307i
$497$		0			0
$498$	5.04746	−	0.242903i	0.226182	−	0.0108847i
$499$	−8.89053			−0.397995			−0.198997	−	0.980000i	$-0.563769\pi$
$499$	−8.89053			−0.397995			−0.198997	+	0.980000i	$0.563769\pi$
$500$	2.69727	−	0.260208i	0.120626	−	0.0116369i
$501$			12.3971i			0.553862i
$502$	−0.222035	−	4.61384i	−0.00990992	−	0.205926i
$503$	−1.51626			−0.0676065			−0.0338032	−	0.999429i	$-0.510762\pi$
$503$	−1.51626			−0.0676065			−0.0338032	+	0.999429i	$0.510762\pi$
$504$		0			0
$505$	31.7711			1.41380
$506$	0.460980	+	9.57904i	0.0204930	+	0.425840i
$507$		−	12.8439i		−	0.570419i
$508$	4.03417	+	41.8174i	0.178987	+	1.85535i
$509$	−7.43439			−0.329524			−0.164762	−	0.986333i	$-0.552686\pi$
$509$	−7.43439			−0.329524			−0.164762	+	0.986333i	$0.552686\pi$
$510$	−14.4053	+	0.693238i	−0.637877	+	0.0306971i
$511$		0			0
$512$	20.5412	−	9.48986i	0.907803	−	0.419397i
$513$	3.38981			0.149664
$514$	0.820532	+	17.0504i	0.0361921	+	0.752063i
$515$	6.40594			0.282280
$516$	1.28441	+	13.3140i	0.0565432	+	0.586116i
$517$	4.69698			0.206573
$518$		0			0
$519$			1.03865i			0.0455917i
$520$	−45.9323	+	6.67255i	−2.01426	+	0.292611i
$521$		−	13.5936i		−	0.595545i	−0.954637	−	0.297772i	$-0.903756\pi$
$521$		−	13.5936i		−	0.595545i	0.954637	−	0.297772i	$-0.0962436\pi$
$522$	−0.671861	−	13.9611i	−0.0294065	−	0.611060i
$523$		−	3.91073i		−	0.171004i	−0.996338	−	0.0855020i	$-0.972751\pi$
$523$		−	3.91073i		−	0.171004i	0.996338	−	0.0855020i	$-0.0272494\pi$
$524$	0.109649	+	1.13660i	0.00479002	+	0.0496524i
$525$		0			0
$526$	1.11354	+	23.1390i	0.0485525	+	1.00891i
$527$			6.40706i			0.279096i
$528$	−1.69232	−	8.68952i	−0.0736489	−	0.378163i
$529$	13.6119			0.591821
$530$	0.791961	+	16.4567i	0.0344006	+	0.714835i
$531$			12.2803i			0.532920i
$532$		0			0
$533$		−	30.3142i		−	1.31305i
$534$	10.3127	−	0.496287i	0.446275	−	0.0214764i
$535$	−10.4460			−0.451621
$536$	24.6719	−	3.58407i	1.06566	−	0.154808i
$537$			2.52607i			0.109008i
$538$	−10.5540	+	0.507899i	−0.455015	+	0.0218971i
$539$		0			0
$540$	0.619932	+	6.42609i	0.0266776	+	0.276535i
$541$		−	33.9327i		−	1.45888i	−0.684045	−	0.729440i	$-0.739781\pi$
$541$		−	33.9327i		−	1.45888i	0.684045	−	0.729440i	$-0.260219\pi$
$542$	12.6741	−	0.609928i	0.544401	−	0.0261986i
$543$		−	8.29867i		−	0.356130i
$544$	−4.25558	−	17.3572i	−0.182456	−	0.744185i
$545$		−	13.5301i		−	0.579565i
$546$		0			0
$547$	19.9416			0.852640			0.426320	−	0.904572i	$-0.359810\pi$
$547$	19.9416			0.852640			0.426320	+	0.904572i	$0.359810\pi$
$548$	−26.1909	+	2.52667i	−1.11882	+	0.107934i
$549$	12.6823			0.541268
$550$	16.9438	−	0.815400i	0.722486	−	0.0347688i
$551$	33.5028			1.42727
$552$	8.57629	−	1.24587i	0.365031	−	0.0530278i
$553$		0			0
$554$	−0.417310	−	8.67158i	−0.0177298	−	0.368420i
$555$	−2.97580			−0.126316
$556$	−1.83374	−	19.0082i	−0.0777678	−	0.806126i
$557$		−	34.1791i		−	1.44821i	−0.689688	−	0.724107i	$-0.742252\pi$
$557$		−	34.1791i		−	1.44821i	0.689688	−	0.724107i	$-0.257748\pi$
$558$	2.86477	−	0.137864i	0.121276	−	0.00583624i
$559$	33.9992			1.43801
$560$		0			0
$561$	−6.99199			−0.295202
$562$	−27.2537	+	1.31155i	−1.14963	+	0.0553245i
$563$			2.25839i			0.0951800i	0.998867	+	0.0475900i	$0.0151541\pi$
$563$			2.25839i			0.0951800i	−0.998867	+	0.0475900i	$0.984846\pi$
$564$	−0.407581	−	4.22491i	−0.0171623	−	0.177901i
$565$	−9.18843			−0.386560
$566$	1.51888	+	31.5620i	0.0638434	+	1.32665i
$567$		0			0
$568$	−4.75886	−	32.7589i	−0.199677	−	1.37453i
$569$	29.1605			1.22247			0.611236	−	0.791448i	$-0.290672\pi$
$569$	29.1605			1.22247			0.611236	+	0.791448i	$0.290672\pi$
$570$	−15.4567	+	0.743834i	−0.647409	+	0.0311558i
$571$	−26.2578			−1.09885			−0.549427	−	0.835541i	$-0.685154\pi$
$571$	−26.2578			−1.09885			−0.549427	+	0.835541i	$0.685154\pi$
$572$	−22.3984	+	2.16080i	−0.936525	+	0.0903475i
$573$	6.07541			0.253804
$574$		0			0
$575$			16.6061i			0.692522i
$576$	−7.66933	+	2.27627i	−0.319555	+	0.0948447i
$577$			0.0540052i			0.00224826i	0.999999	+	0.00112413i	$0.000357822\pi$
$577$			0.0540052i			0.00224826i	−0.999999	+	0.00112413i	$0.999642\pi$
$578$	9.91528	−	0.477161i	0.412421	−	0.0198473i
$579$			9.18679i			0.381790i
$580$	6.12703	+	63.5116i	0.254411	+	2.63718i
$581$		0			0
$582$	21.5048	−	1.03489i	0.891401	−	0.0428976i
$583$			7.98771i			0.330817i
$584$	3.67196	+	25.2769i	0.151947	+	1.04597i
$585$	16.4100			0.678468
$586$	19.8760	−	0.956507i	0.821068	−	0.0395129i
$587$		−	4.75946i		−	0.196444i	−0.995165	−	0.0982219i	$-0.968685\pi$
$587$		−	4.75946i		−	0.196444i	0.995165	−	0.0982219i	$-0.0313155\pi$
$588$		0			0
$589$			6.87468i			0.283266i
$590$	−2.69470	−	55.9951i	−0.110939	−	2.30528i
$591$	−20.2764			−0.834059
$592$	−0.704919	−	3.61953i	−0.0289720	−	0.148762i
$593$			11.8705i			0.487464i	0.969843	+	0.243732i	$0.0783718\pi$
$593$			11.8705i			0.487464i	−0.969843	+	0.243732i	$0.921628\pi$
$594$	0.150450	+	3.12631i	0.00617304	+	0.128274i
$595$		0			0
$596$	−2.03499	−	21.0943i	−0.0833565	−	0.864057i
$597$			3.28711i			0.134532i
$598$	−1.05887	−	22.0030i	−0.0433003	−	0.899769i
$599$			29.6273i			1.21054i	0.796021	+	0.605269i	$0.206934\pi$
$599$			29.6273i			1.21054i	−0.796021	+	0.605269i	$0.793066\pi$
$600$	−2.20375	−	15.1701i	−0.0899677	−	0.619317i
$601$			26.4608i			1.07936i	0.841870	+	0.539680i	$0.181455\pi$
$601$			26.4608i			1.07936i	−0.841870	+	0.539680i	$0.818545\pi$
$602$		0			0
$603$	−8.81440			−0.358950
$604$	0.233553	+	2.42097i	0.00950315	+	0.0985078i
$605$	−19.6963			−0.800768
$606$	−0.669078	−	13.9033i	−0.0271794	−	0.564782i
$607$	15.3842			0.624424			0.312212	−	0.950012i	$-0.398930\pi$
$607$	15.3842			0.624424			0.312212	+	0.950012i	$0.398930\pi$
$608$	−4.56618	−	18.6241i	−0.185183	−	0.755305i
$609$		0			0
$610$	−57.8282	+	2.78291i	−2.34139	+	0.112677i
$611$	−10.7889			−0.436473
$612$	0.606731	+	6.28926i	0.0245257	+	0.254228i
$613$			19.4338i			0.784925i	0.919768	+	0.392463i	$0.128377\pi$
$613$			19.4338i			0.784925i	−0.919768	+	0.392463i	$0.871623\pi$
$614$	−0.653810	−	13.5860i	−0.0263856	−	0.548286i
$615$	19.2484			0.776172
$616$		0			0
$617$	−0.173969			−0.00700371			−0.00350186	−	0.999994i	$-0.501115\pi$
$617$	−0.173969			−0.00700371			−0.00350186	+	0.999994i	$0.501115\pi$
$618$	−0.134905	−	2.80329i	−0.00542667	−	0.112765i
$619$		−	37.9663i		−	1.52600i	−0.646401	−	0.762998i	$-0.723727\pi$
$619$		−	37.9663i		−	1.52600i	0.646401	−	0.762998i	$-0.276273\pi$
$620$	−13.0324	+	1.25725i	−0.523394	+	0.0504924i
$621$	−3.06401			−0.122954
$622$	30.6487	−	1.47493i	1.22890	−	0.0591394i
$623$		0			0
$624$	3.88726	+	19.9598i	0.155615	+	0.799030i
$625$	−22.7251			−0.909005
$626$	0.742966	+	15.4386i	0.0296949	+	0.617052i
$627$	−7.50230			−0.299613
$628$	7.21658	−	0.696191i	0.287973	−	0.0277810i
$629$	−2.91244			−0.116127
$630$		0			0
$631$			26.0140i			1.03560i	0.855501	+	0.517801i	$0.173249\pi$
$631$			26.0140i			1.03560i	−0.855501	+	0.517801i	$0.826751\pi$
$632$	−4.50788	−	31.0312i	−0.179314	−	1.23435i
$633$			21.6901i			0.862102i
$634$	−0.482158	−	10.0191i	−0.0191489	−	0.397910i
$635$			67.8059i			2.69080i
$636$	7.18491	−	0.693136i	0.284900	−	0.0274846i
$637$		0			0
$638$	1.48696	+	30.8986i	0.0588693	+	1.22329i
$639$			11.7036i			0.462987i
$640$	34.4707	−	12.0621i	1.36258	−	0.476798i
$641$	24.9147			0.984070			0.492035	−	0.870575i	$-0.336253\pi$
$641$	24.9147			0.984070			0.492035	+	0.870575i	$0.336253\pi$
$642$	0.219986	+	4.57125i	0.00868216	+	0.180413i
$643$		−	4.80941i		−	0.189665i	−0.995493	−	0.0948323i	$-0.969769\pi$
$643$		−	4.80941i		−	0.189665i	0.995493	−	0.0948323i	$-0.0302315\pi$
$644$		0			0
$645$			21.5883i			0.850038i
$646$	−15.1276	+	0.727996i	−0.595186	+	0.0286426i
$647$	−8.54067			−0.335769			−0.167884	−	0.985807i	$-0.553693\pi$
$647$	−8.54067			−0.335769			−0.167884	+	0.985807i	$0.553693\pi$
$648$	2.79905	−	0.406616i	0.109957	−	0.0159734i
$649$		−	27.1787i		−	1.06686i
$650$	−38.9198	+	1.87297i	−1.52656	+	0.0734638i
$651$		0			0
$652$	39.4796	−	3.80864i	1.54614	−	0.149158i
$653$		−	27.9386i		−	1.09332i	−0.837354	−	0.546661i	$-0.815899\pi$
$653$		−	27.9386i		−	1.09332i	0.837354	−	0.546661i	$-0.184101\pi$
$654$	−5.92086	+	0.284934i	−0.231524	+	0.0111418i
$655$			1.84296i			0.0720105i
$656$	4.55964	+	23.4123i	0.178024	+	0.914095i
$657$		−	9.03055i		−	0.352315i
$658$		0			0
$659$	28.0553			1.09288			0.546439	−	0.837499i	$-0.315983\pi$
$659$	28.0553			1.09288			0.546439	+	0.837499i	$0.315983\pi$
$660$	−1.37203	−	14.2222i	−0.0534062	−	0.553598i
$661$	−8.94254			−0.347825			−0.173912	−	0.984761i	$-0.555641\pi$
$661$	−8.94254			−0.347825			−0.173912	+	0.984761i	$0.555641\pi$
$662$	16.5611	−	0.796984i	0.643666	−	0.0309757i
$663$	16.0605			0.623740
$664$	1.45293	+	10.0016i	0.0563846	+	0.388138i
$665$		0			0
$666$	0.0626684	+	1.30223i	0.00242835	+	0.0504605i
$667$	−30.2828			−1.17255
$668$	−24.6796	+	2.38087i	−0.954884	+	0.0921187i
$669$			19.3266i			0.747209i
$670$	40.1915	−	1.93417i	1.55273	−	0.0747234i
$671$	−28.0684			−1.08357
$672$		0			0
$673$	45.4881			1.75344			0.876720	−	0.481002i	$-0.159727\pi$
$673$	45.4881			1.75344			0.876720	+	0.481002i	$0.159727\pi$
$674$	33.2362	−	1.59945i	1.28021	−	0.0616086i
$675$			5.41974i			0.208606i
$676$	25.5691	−	2.46668i	0.983429	−	0.0948724i
$677$	−10.9689			−0.421571			−0.210785	−	0.977532i	$-0.567602\pi$
$677$	−10.9689			−0.421571			−0.210785	+	0.977532i	$0.567602\pi$
$678$	0.193502	+	4.02092i	0.00743141	+	0.154423i
$679$		0			0
$680$	−4.14661	−	28.5443i	−0.159015	−	1.09462i
$681$	−0.539061			−0.0206569
$682$	−6.34030	+	0.305120i	−0.242783	+	0.0116836i
$683$	−28.2074			−1.07933			−0.539663	−	0.841881i	$-0.681448\pi$
$683$	−28.2074			−1.07933			−0.539663	+	0.841881i	$0.681448\pi$
$684$	0.651014	+	6.74828i	0.0248921	+	0.258027i
$685$	−42.4679			−1.62262
$686$		0			0
$687$		−	22.8623i		−	0.872251i
$688$	−26.2583	+	5.11392i	−1.00109	+	0.194966i
$689$		−	18.3477i		−	0.698992i
$690$	13.9711	−	0.672343i	0.531871	−	0.0255956i
$691$		−	9.49222i		−	0.361101i	−0.983566	−	0.180550i	$-0.942212\pi$
$691$		−	9.49222i		−	0.361101i	0.983566	−	0.180550i	$-0.0577879\pi$
$692$	−2.06770	+	0.199474i	−0.0786023	+	0.00758285i
$693$		0			0
$694$	−14.6098	+	0.703079i	−0.554581	+	0.0266885i
$695$		−	30.8213i		−	1.16912i
$696$	27.6641	−	4.01875i	1.04861	−	0.152330i
$697$	18.8386			0.713562
$698$	−1.17287	+	0.0564427i	−0.0443936	+	0.00213639i
$699$			3.00490i			0.113656i
$700$		0			0
$701$		−	14.3589i		−	0.542328i	−0.962533	−	0.271164i	$-0.912591\pi$
$701$		−	14.3589i		−	0.542328i	0.962533	−	0.271164i	$-0.0874085\pi$
$702$	−0.345583	−	7.18112i	−0.0130432	−	0.271034i
$703$	−3.12500			−0.117862
$704$	16.9737	−	5.03783i	0.639721	−	0.189870i
$705$		−	6.85058i		−	0.258008i
$706$	−0.330605	−	6.86988i	−0.0124425	−	0.258551i
$707$		0			0
$708$	−24.4471	+	2.35844i	−0.918778	+	0.0886355i
$709$			10.2787i			0.386024i	0.981196	+	0.193012i	$0.0618257\pi$
$709$			10.2787i			0.386024i	−0.981196	+	0.193012i	$0.938174\pi$
$710$	−2.56815	−	53.3654i	−0.0963809	−	2.00277i
$711$			11.0863i			0.415770i
$712$	2.96855	+	20.4348i	0.111251	+	0.765827i
$713$		−	6.21394i		−	0.232714i
$714$		0			0
$715$	−36.3184			−1.35823
$716$	−5.02880	+	0.485134i	−0.187935	+	0.0181303i
$717$	11.2699			0.420881
$718$	−1.28010	−	26.6001i	−0.0477728	−	0.992706i
$719$	−14.7893			−0.551549			−0.275775	−	0.961222i	$-0.588934\pi$
$719$	−14.7893			−0.551549			−0.275775	+	0.961222i	$0.588934\pi$
$720$	−12.6737	+	2.46827i	−0.472322	+	0.0919869i
$721$		0			0
$722$	10.6074	−	0.510466i	0.394765	−	0.0189976i
$723$	11.2731			0.419250
$724$	16.5206	−	1.59376i	0.613985	−	0.0592318i
$725$			53.5654i			1.98937i
$726$	0.414790	+	8.61923i	0.0153943	+	0.319890i
$727$	−43.5679			−1.61585			−0.807923	−	0.589289i	$-0.799408\pi$
$727$	−43.5679			−1.61585			−0.807923	+	0.589289i	$0.799408\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	1.98160	+	41.1770i	0.0733422	+	1.52403i
$731$			21.1286i			0.781470i
$732$	2.43564	+	25.2474i	0.0900240	+	0.933171i
$733$	−22.6824			−0.837792			−0.418896	−	0.908034i	$-0.637583\pi$
$733$	−22.6824			−0.837792			−0.418896	+	0.908034i	$0.637583\pi$
$734$	30.3054	−	1.45841i	1.11859	−	0.0538309i
$735$		0			0
$736$	4.12731	+	16.8341i	0.152135	+	0.620511i
$737$	19.5080			0.718586
$738$	−0.405359	−	8.42325i	−0.0149215	−	0.310064i
$739$	4.65190			0.171123			0.0855615	−	0.996333i	$-0.472732\pi$
$739$	4.65190			0.171123			0.0855615	+	0.996333i	$0.472732\pi$
$740$	−0.571504	−	5.92410i	−0.0210089	−	0.217774i
$741$	17.2327			0.633060
$742$		0			0
$743$			28.3209i			1.03899i	0.854473	+	0.519496i	$0.173880\pi$
$743$			28.3209i			1.03899i	−0.854473	+	0.519496i	$0.826120\pi$
$744$	0.824635	+	5.67659i	0.0302326	+	0.208114i
$745$		−	34.2039i		−	1.25313i
$746$	−1.11090	−	23.0843i	−0.0406731	−	0.845176i
$747$		−	3.57322i		−	0.130737i
$748$	−1.34281	−	13.9194i	−0.0490982	−	0.508942i
$749$		0			0
$750$	−0.0921040	−	1.91390i	−0.00336316	−	0.0698856i
$751$		−	33.0040i		−	1.20433i	−0.798371	−	0.602166i	$-0.794304\pi$
$751$		−	33.0040i		−	1.20433i	0.798371	−	0.602166i	$-0.205696\pi$
$752$	8.33249	−	1.62279i	0.303855	−	0.0591771i
$753$	−3.26625			−0.119029
$754$	−3.41553	−	70.9739i	−0.124386	−	2.58472i
$755$			3.92554i			0.142865i
$756$		0			0
$757$		−	19.0350i		−	0.691838i	−0.938264	−	0.345919i	$-0.887567\pi$
$757$		−	19.0350i		−	0.691838i	0.938264	−	0.345919i	$-0.112433\pi$
$758$	−6.09720	+	0.293420i	−0.221460	+	0.0106575i
$759$	6.78124			0.246143
$760$	−4.44926	−	30.6276i	−0.161391	−	1.11098i
$761$		−	49.9704i		−	1.81142i	−0.423893	−	0.905712i	$-0.639337\pi$
$761$		−	49.9704i		−	1.81142i	0.423893	−	0.905712i	$-0.360663\pi$
$762$	29.6723	−	1.42795i	1.07492	−	0.0517290i
$763$		0			0
$764$	1.16679	+	12.0947i	0.0422128	+	0.437570i
$765$			10.1979i			0.368705i
$766$	28.5195	−	1.37247i	1.03045	−	0.0495893i
$767$			62.4293i			2.25419i
$768$	−6.00440	−	14.8306i	−0.216665	−	0.535154i
$769$		−	24.2908i		−	0.875949i	−0.898987	−	0.437974i	$-0.855696\pi$
$769$		−	24.2908i		−	0.875949i	0.898987	−	0.437974i	$-0.144304\pi$
$770$		0			0
$771$	12.0704			0.434706
$772$	−18.2887	+	1.76433i	−0.658224	+	0.0634995i
$773$	−16.0322			−0.576640			−0.288320	−	0.957534i	$-0.593097\pi$
$773$	−16.0322			−0.576640			−0.288320	+	0.957534i	$0.593097\pi$
$774$	9.44719	−	0.454635i	0.339572	−	0.0163415i
$775$	−10.9915			−0.394825
$776$	6.19021	+	42.6120i	0.222216	+	1.52968i
$777$		0			0
$778$	−2.29506	−	47.6907i	−0.0822818	−	1.70979i
$779$	20.2135			0.724225
$780$	3.15154	+	32.6683i	0.112843	+	1.16971i
$781$		−	25.9023i		−	0.926858i
$782$	13.6736	−	0.658026i	0.488967	−	0.0235310i
$783$	−9.88340			−0.353204
$784$		0			0
$785$	11.7015			0.417644
$786$	0.806493	−	0.0388115i	0.0287666	−	0.00138436i
$787$		−	10.0646i		−	0.358764i	−0.983780	−	0.179382i	$-0.942590\pi$
$787$		−	10.0646i		−	0.358764i	0.983780	−	0.179382i	$-0.0574097\pi$
$788$	−3.89409	−	40.3653i	−0.138721	−	1.43796i
$789$	16.3807			0.583168
$790$	−2.43270	−	50.5510i	−0.0865517	−	1.79852i
$791$		0			0
$792$	−6.19484	+	0.899919i	−0.220124	+	0.0319772i
$793$	64.4729			2.28950
$794$	0.124634	−	0.00599787i	0.00442310	−	0.000212857i
$795$	11.6501			0.413188
$796$	−6.54384	+	0.631291i	−0.231940	+	0.0223755i
$797$	53.0872			1.88045			0.940223	−	0.340560i	$-0.110617\pi$
$797$	53.0872			1.88045			0.940223	+	0.340560i	$0.110617\pi$
$798$		0			0
$799$		−	6.70471i		−	0.237196i
$800$	29.7768	−	7.30056i	1.05277	−	0.258114i
$801$		−	7.30063i		−	0.257955i
$802$	−35.6075	+	1.71357i	−1.25735	+	0.0605082i
$803$			19.9864i			0.705303i
$804$	−1.69281	−	17.5473i	−0.0597008	−	0.618847i
$805$		0			0
$806$	14.5636	−	0.700857i	0.512982	−	0.0246866i
$807$			7.47144i			0.263007i
$808$	27.5495	−	4.00210i	0.969189	−	0.140793i
$809$	53.9058			1.89523			0.947614	−	0.319418i	$-0.103487\pi$
$809$	53.9058			1.89523			0.947614	+	0.319418i	$0.103487\pi$
$810$	4.55975	−	0.219433i	0.160213	−	0.00771007i
$811$		−	48.2050i		−	1.69271i	−0.532621	−	0.846354i	$-0.678793\pi$
$811$		−	48.2050i		−	1.69271i	0.532621	−	0.846354i	$-0.321207\pi$
$812$		0			0
$813$		−	8.97234i		−	0.314674i
$814$	−0.138697	−	2.88209i	−0.00486134	−	0.101017i
$815$	64.0151			2.24235
$816$	−12.4039	+	2.41571i	−0.434222	+	0.0845668i
$817$			22.6707i			0.793147i
$818$	−2.11294	−	43.9063i	−0.0738771	−	1.53515i
$819$		0			0
$820$	3.69667	+	38.3190i	0.129093	+	1.33816i
$821$			25.8966i			0.903798i	0.892069	+	0.451899i	$0.149253\pi$
$821$			25.8966i			0.903798i	−0.892069	+	0.451899i	$0.850747\pi$
$822$	0.894345	+	18.5843i	0.0311939	+	0.648201i
$823$		−	55.5526i		−	1.93644i	−0.250095	−	0.968221i	$-0.580462\pi$
$823$		−	55.5526i		−	1.93644i	0.250095	−	0.968221i	$-0.419538\pi$
$824$	5.55476	−	0.806935i	0.193509	−	0.0281109i
$825$		−	11.9949i		−	0.417610i
$826$		0			0
$827$	23.2870			0.809770			0.404885	−	0.914368i	$-0.367312\pi$
$827$	23.2870			0.809770			0.404885	+	0.914368i	$0.367312\pi$
$828$	−0.588444	−	6.09969i	−0.0204498	−	0.211979i
$829$	5.17675			0.179796			0.0898980	−	0.995951i	$-0.471346\pi$
$829$	5.17675			0.179796			0.0898980	+	0.995951i	$0.471346\pi$
$830$	0.784082	+	16.2930i	0.0272159	+	0.565539i
$831$	−6.13883			−0.212954
$832$	−38.9885	+	11.5719i	−1.35168	+	0.401182i
$833$		0			0
$834$	−13.4876	+	0.649075i	−0.467037	+	0.0224756i
$835$	−40.0174			−1.38486
$836$	−1.44082	−	14.9353i	−0.0498318	−	0.516547i
$837$		−	2.02805i		−	0.0700995i
$838$	−1.54757	−	32.1581i	−0.0534600	−	1.11088i
$839$	12.7298			0.439480			0.219740	−	0.975558i	$-0.429479\pi$
$839$	12.7298			0.439480			0.219740	+	0.975558i	$0.429479\pi$
$840$		0			0
$841$	−68.6816			−2.36833
$842$	1.63290	+	33.9312i	0.0562733	+	1.16934i
$843$			19.2936i			0.664507i
$844$	−43.1796	+	4.16558i	−1.48630	+	0.143385i
$845$	41.4597			1.42626
$846$	−2.99786	+	0.144268i	−0.103069	+	0.00496005i
$847$		0			0
$848$	2.75973	+	14.1703i	0.0947695	+	0.486610i
$849$	22.3435			0.766827
$850$	−1.16394	−	24.1864i	−0.0399229	−	0.829588i
$851$	2.82465			0.0968279
$852$	−23.2990	+	2.24768i	−0.798211	+	0.0770042i
$853$	47.2928			1.61927			0.809637	−	0.586930i	$-0.199664\pi$
$853$	47.2928			1.61927			0.809637	+	0.586930i	$0.199664\pi$
$854$		0			0
$855$			10.9422i			0.374214i
$856$	−9.05801	+	1.31585i	−0.309596	+	0.0449749i
$857$			52.2530i			1.78493i	0.451120	+	0.892463i	$0.351025\pi$
$857$			52.2530i			1.78493i	−0.451120	+	0.892463i	$0.648975\pi$
$858$	0.764842	+	15.8932i	0.0261113	+	0.542585i
$859$		−	50.4680i		−	1.72195i	−0.508651	−	0.860973i	$-0.669855\pi$
$859$		−	50.4680i		−	1.72195i	0.508651	−	0.860973i	$-0.330145\pi$
$860$	−42.9770	+	4.14604i	−1.46551	+	0.141379i
$861$		0			0
$862$	−2.21663	−	46.0610i	−0.0754988	−	1.56884i
$863$			26.7795i			0.911586i	0.890086	+	0.455793i	$0.150644\pi$
$863$			26.7795i			0.911586i	−0.890086	+	0.455793i	$0.849356\pi$
$864$	1.34703	+	5.49413i	0.0458269	+	0.186914i
$865$	−3.35273			−0.113996
$866$	1.25592	+	26.0977i	0.0426779	+	0.886835i
$867$		−	7.01927i		−	0.238387i
$868$		0			0
$869$		−	24.5362i		−	0.832335i
$870$	45.0658	−	2.16874i	1.52788	−	0.0735272i
$871$	−44.8097			−1.51832
$872$	−1.70434	−	11.7323i	−0.0577162	−	0.397305i
$873$		−	15.2238i		−	0.515246i
$874$	14.6716	−	0.706053i	0.496274	−	0.0238826i
$875$		0			0
$876$	17.9776	−	1.73432i	0.607408	−	0.0585973i
$877$			25.9128i			0.875013i	0.899215	+	0.437506i	$0.144138\pi$
$877$			25.9128i			0.875013i	−0.899215	+	0.437506i	$0.855862\pi$
$878$	−31.6808	+	1.52460i	−1.06917	+	0.0514528i
$879$		−	14.0707i		−	0.474593i
$880$	28.0494	−	5.46276i	0.945546	−	0.184149i
$881$			10.0120i			0.337313i	0.985675	+	0.168657i	$0.0539429\pi$
$881$			10.0120i			0.337313i	−0.985675	+	0.168657i	$0.946057\pi$
$882$		0			0
$883$	−23.6231			−0.794981			−0.397491	−	0.917606i	$-0.630119\pi$
$883$	−23.6231			−0.794981			−0.397491	+	0.917606i	$0.630119\pi$
$884$	3.08444	+	31.9727i	0.103741	+	1.07536i
$885$	−39.6403			−1.33250
$886$	12.7745	−	0.614756i	0.429166	−	0.0206531i
$887$	−18.1625			−0.609835			−0.304918	−	0.952379i	$-0.598629\pi$
$887$	−18.1625			−0.609835			−0.304918	+	0.952379i	$0.598629\pi$
$888$	−2.58039	+	0.374852i	−0.0865923	+	0.0125792i
$889$		0			0
$890$	1.60200	+	33.2891i	0.0536990	+	1.11585i
$891$	2.21319			0.0741448
$892$	−38.4745	+	3.71168i	−1.28822	+	0.124276i
$893$		−	7.19405i		−	0.240740i
$894$	−14.9679	+	0.720311i	−0.500600	+	0.0240908i
$895$	−8.15407			−0.272560
$896$		0			0
$897$	−15.5765			−0.520083
$898$	7.99045	−	0.384531i	0.266645	−	0.0128320i
$899$		−	20.0440i		−	0.668505i
$900$	−10.7894	+	1.04086i	−0.359646	+	0.0346954i
$901$	11.4021			0.379858
$902$	0.897138	+	18.6423i	0.0298714	+	0.620721i
$903$		0			0
$904$	−7.96752	+	1.15744i	−0.264996	+	0.0384958i
$905$	26.7878			0.890456
$906$	1.71784	−	0.0826691i	0.0570715	−	0.00274650i
$907$	−55.4370			−1.84075			−0.920377	−	0.391031i	$-0.872118\pi$
$907$	−55.4370			−1.84075			−0.920377	+	0.391031i	$0.872118\pi$
$908$	−0.103527	−	1.07314i	−0.00343566	−	0.0356134i
$909$	−9.84247			−0.326454
$910$		0			0
$911$		−	18.4722i		−	0.612012i	−0.952030	−	0.306006i	$-0.901007\pi$
$911$		−	18.4722i		−	0.612012i	0.952030	−	0.306006i	$-0.0989928\pi$
$912$	−13.3092	+	2.59202i	−0.440711	+	0.0858304i
$913$			7.90824i			0.261725i
$914$	13.2492	−	0.637601i	0.438244	−	0.0210900i
$915$			40.9380i			1.35337i
$916$	45.5133	−	4.39071i	1.50380	−	0.145073i
$917$		0			0
$918$	4.46266	−	0.214760i	0.147290	−	0.00708814i
$919$			0.166633i			0.00549671i	0.999996	+	0.00274835i	$0.000874829\pi$
$919$			0.166633i			0.00549671i	−0.999996	+	0.00274835i	$0.999125\pi$
$920$	4.02163	+	27.6839i	0.132589	+	0.912713i
$921$	−9.61787			−0.316920
$922$	−44.9144	+	2.16145i	−1.47918	+	0.0711836i
$923$			59.4974i			1.95838i
$924$		0			0
$925$		−	4.99636i		−	0.164279i
$926$	−0.603314	−	12.5367i	−0.0198261	−	0.411982i
$927$	−1.98452			−0.0651801
$928$	13.3133	+	54.3007i	0.437029	+	1.78251i
$929$		−	16.1882i		−	0.531117i	−0.964095	−	0.265559i	$-0.914444\pi$
$929$		−	16.1882i		−	0.531117i	0.964095	−	0.265559i	$-0.0855564\pi$
$930$	0.445019	+	9.24738i	0.0145928	+	0.303234i
$931$		0			0
$932$	−5.98202	+	0.577092i	−0.195948	+	0.0189033i
$933$		−	21.6970i		−	0.710328i
$934$	−0.212720	−	4.42027i	−0.00696041	−	0.144636i
$935$		−	22.5699i		−	0.738114i
$936$	14.2295	−	2.06711i	0.465106	−	0.0675655i
$937$			19.5153i			0.637538i	0.947832	+	0.318769i	$0.103270\pi$
$937$			19.5153i			0.637538i	−0.947832	+	0.318769i	$0.896730\pi$
$938$		0			0
$939$	10.9294			0.356668
$940$	13.6378	−	1.31566i	0.444817	−	0.0429120i
$941$	−24.6402			−0.803248			−0.401624	−	0.915805i	$-0.631554\pi$
$941$	−24.6402			−0.803248			−0.401624	+	0.915805i	$0.631554\pi$
$942$	−0.246425	−	5.12065i	−0.00802897	−	0.166840i
$943$	−18.2708			−0.594978
$944$	−9.39015	−	48.2153i	−0.305623	−	1.56927i
$945$		0			0
$946$	−20.9085	+	1.00619i	−0.679793	+	0.0327142i
$947$	−8.61539			−0.279963			−0.139981	−	0.990154i	$-0.544704\pi$
$947$	−8.61539			−0.279963			−0.139981	+	0.990154i	$0.544704\pi$
$948$	−22.0702	+	2.12914i	−0.716808	+	0.0691512i
$949$		−	45.9085i		−	1.49025i
$950$	−1.24889	−	25.9517i	−0.0405195	−	0.841984i
$951$	−7.09278			−0.229999
$952$		0			0
$953$	−27.4982			−0.890755			−0.445378	−	0.895343i	$-0.646931\pi$
$953$	−27.4982			−0.890755			−0.445378	+	0.895343i	$0.646931\pi$
$954$	−0.245344	−	5.09818i	−0.00794331	−	0.165060i
$955$			19.6112i			0.634603i
$956$	2.16439	+	22.4356i	0.0700012	+	0.725619i
$957$	21.8739			0.707083
$958$	−23.1526	+	1.11419i	−0.748028	+	0.0359980i
$959$		0			0
$960$	−7.34772	−	24.7563i	−0.237147	−	0.799006i
$961$	−26.8870			−0.867324
$962$	0.318587	+	6.62015i	0.0102716	+	0.213442i
$963$	3.23611			0.104282
$964$	2.16500	+	22.4419i	0.0697299	+	0.722806i
$965$	−29.6546			−0.954616
$966$		0			0
$967$			21.2591i			0.683647i	0.939764	+	0.341823i	$0.111044\pi$
$967$			21.2591i			0.683647i	−0.939764	+	0.341823i	$0.888956\pi$
$968$	−17.0791	+	2.48107i	−0.548944	+	0.0797447i
$969$			10.7092i			0.344028i
$970$	3.34059	+	69.4165i	0.107260	+	2.22883i
$971$			31.5634i			1.01292i	0.862264	+	0.506459i	$0.169046\pi$
$971$			31.5634i			1.01292i	−0.862264	+	0.506459i	$0.830954\pi$
$972$	−0.192050	−	1.99076i	−0.00616002	−	0.0638536i
$973$		0			0
$974$	−1.99611	−	41.4786i	−0.0639594	−	1.32906i
$975$			27.5523i			0.882379i
$976$	−49.7937	+	9.69755i	−1.59386	+	0.310411i
$977$	−19.5142			−0.624316			−0.312158	−	0.950030i	$-0.601052\pi$
$977$	−19.5142			−0.624316			−0.312158	+	0.950030i	$0.601052\pi$
$978$	−1.34811	−	28.0135i	−0.0431080	−	0.895772i
$979$			16.1577i			0.516403i
$980$		0			0
$981$			4.19152i			0.133825i
$982$	47.8818	−	2.30426i	1.52797	−	0.0735318i
$983$	22.4802			0.717007			0.358503	−	0.933528i	$-0.383287\pi$
$983$	22.4802			0.717007			0.358503	+	0.933528i	$0.383287\pi$
$984$	16.6908	−	2.42466i	0.532083	−	0.0772954i
$985$		−	65.4514i		−	2.08545i
$986$	44.1063	−	2.12256i	1.40463	−	0.0675961i
$987$		0			0
$988$	3.30955	+	34.3062i	0.105291	+	1.09143i
$989$		−	20.4918i		−	0.651600i
$990$	−10.0916	+	0.485647i	−0.320733	+	0.0154349i
$991$			44.9263i			1.42713i	0.700589	+	0.713565i	$0.252921\pi$
$991$			44.9263i			1.42713i	−0.700589	+	0.713565i	$0.747079\pi$
$992$	−11.1424	+	2.73184i	−0.353770	+	0.0867360i
$993$		−	11.7240i		−	0.372051i
$994$		0			0
$995$	−10.6107			−0.336381
$996$	7.11342	−	0.686239i	0.225397	−	0.0217443i
$997$	29.1779			0.924075			0.462037	−	0.886861i	$-0.347119\pi$
$997$	29.1779			0.924075			0.462037	+	0.886861i	$0.347119\pi$
$998$	−12.5586	+	0.604367i	−0.397535	+	0.0191309i
$999$	0.921883			0.0291671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.p.a.979.30		32
4.3	odd	2		4704.2.p.a.3919.10		32
7.4	even	3		168.2.t.a.19.7	yes	32
7.5	odd	6		168.2.t.a.115.5	yes	32
7.6	odd	2	inner	1176.2.p.a.979.29		32
8.3	odd	2	inner	1176.2.p.a.979.31		32
8.5	even	2		4704.2.p.a.3919.20		32
21.5	even	6		504.2.bk.c.451.12		32
21.11	odd	6		504.2.bk.c.19.10		32
28.11	odd	6		672.2.bb.a.271.9		32
28.19	even	6		672.2.bb.a.367.16		32
28.27	even	2		4704.2.p.a.3919.19		32
56.5	odd	6		672.2.bb.a.367.9		32
56.11	odd	6		168.2.t.a.19.5	✓	32
56.13	odd	2		4704.2.p.a.3919.9		32
56.19	even	6		168.2.t.a.115.7	yes	32
56.27	even	2	inner	1176.2.p.a.979.32		32
56.53	even	6		672.2.bb.a.271.16		32
84.11	even	6		2016.2.bs.c.271.15		32
84.47	odd	6		2016.2.bs.c.1711.2		32
168.5	even	6		2016.2.bs.c.1711.15		32
168.11	even	6		504.2.bk.c.19.12		32
168.53	odd	6		2016.2.bs.c.271.2		32
168.131	odd	6		504.2.bk.c.451.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.5	✓	32	56.11	odd	6
168.2.t.a.19.7	yes	32	7.4	even	3
168.2.t.a.115.5	yes	32	7.5	odd	6
168.2.t.a.115.7	yes	32	56.19	even	6
504.2.bk.c.19.10		32	21.11	odd	6
504.2.bk.c.19.12		32	168.11	even	6
504.2.bk.c.451.10		32	168.131	odd	6
504.2.bk.c.451.12		32	21.5	even	6
672.2.bb.a.271.9		32	28.11	odd	6
672.2.bb.a.271.16		32	56.53	even	6
672.2.bb.a.367.9		32	56.5	odd	6
672.2.bb.a.367.16		32	28.19	even	6
1176.2.p.a.979.29		32	7.6	odd	2	inner
1176.2.p.a.979.30		32	1.1	even	1	trivial
1176.2.p.a.979.31		32	8.3	odd	2	inner
1176.2.p.a.979.32		32	56.27	even	2	inner
2016.2.bs.c.271.2		32	168.53	odd	6
2016.2.bs.c.271.15		32	84.11	even	6
2016.2.bs.c.1711.2		32	84.47	odd	6
2016.2.bs.c.1711.15		32	168.5	even	6
4704.2.p.a.3919.9		32	56.13	odd	2
4704.2.p.a.3919.10		32	4.3	odd	2
4704.2.p.a.3919.19		32	28.27	even	2
4704.2.p.a.3919.20		32	8.5	even	2

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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41258 - 0.0679787i) q^{2} -1.00000i q^{3} +(1.99076 - 0.192050i) q^{4} +3.22796 q^{5} +(-0.0679787 - 1.41258i) q^{6} +(2.79905 - 0.406616i) q^{8} -1.00000 q^{9} +(4.55975 - 0.219433i) q^{10} +2.21319 q^{11} +(-0.192050 - 1.99076i) q^{12} -5.08369 q^{13} -3.22796i q^{15} +(3.92623 - 0.764652i) q^{16} -3.15923i q^{17} +(-1.41258 + 0.0679787i) q^{18} -3.38981i q^{19} +(6.42609 - 0.619932i) q^{20} +(3.12631 - 0.150450i) q^{22} +3.06401i q^{23} +(-0.406616 - 2.79905i) q^{24} +5.41974 q^{25} +(-7.18112 + 0.345583i) q^{26} +1.00000i q^{27} +9.88340i q^{29} +(-0.219433 - 4.55975i) q^{30} -2.02805 q^{31} +(5.49413 - 1.34703i) q^{32} -2.21319i q^{33} +(-0.214760 - 4.46266i) q^{34} +(-1.99076 + 0.192050i) q^{36} -0.921883i q^{37} +(-0.230435 - 4.78837i) q^{38} +5.08369i q^{39} +(9.03522 - 1.31254i) q^{40} +5.96303i q^{41} -6.68790 q^{43} +(4.40593 - 0.425045i) q^{44} -3.22796 q^{45} +(0.208287 + 4.32815i) q^{46} +2.12226 q^{47} +(-0.764652 - 3.92623i) q^{48} +(7.65581 - 0.368427i) q^{50} -3.15923 q^{51} +(-10.1204 + 0.976326i) q^{52} +3.60913i q^{53} +(0.0679787 + 1.41258i) q^{54} +7.14411 q^{55} -3.38981 q^{57} +(0.671861 + 13.9611i) q^{58} -12.2803i q^{59} +(-0.619932 - 6.42609i) q^{60} -12.6823 q^{61} +(-2.86477 + 0.137864i) q^{62} +(7.66933 - 2.27627i) q^{64} -16.4100 q^{65} +(-0.150450 - 3.12631i) q^{66} +8.81440 q^{67} +(-0.606731 - 6.28926i) q^{68} +3.06401 q^{69} -11.7036i q^{71} +(-2.79905 + 0.406616i) q^{72} +9.03055i q^{73} +(-0.0626684 - 1.30223i) q^{74} -5.41974i q^{75} +(-0.651014 - 6.74828i) q^{76} +(0.345583 + 7.18112i) q^{78} -11.0863i q^{79} +(12.6737 - 2.46827i) q^{80} +1.00000 q^{81} +(0.405359 + 8.42325i) q^{82} +3.57322i q^{83} -10.1979i q^{85} +(-9.44719 + 0.454635i) q^{86} +9.88340 q^{87} +(6.19484 - 0.899919i) q^{88} +7.30063i q^{89} +(-4.55975 + 0.219433i) q^{90} +(0.588444 + 6.09969i) q^{92} +2.02805i q^{93} +(2.99786 - 0.144268i) q^{94} -10.9422i q^{95} +(-1.34703 - 5.49413i) q^{96} +15.2238i q^{97} -2.21319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 4 q^{4} + 16 q^{8} - 32 q^{9} - 16 q^{11} - 12 q^{16} - 4 q^{18} - 20 q^{22} + 32 q^{25} + 16 q^{30} + 24 q^{32} - 4 q^{36} - 16 q^{43} - 48 q^{44} - 16 q^{46} + 76 q^{50} + 16 q^{57} + 12 q^{58}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 4 * q^4 + 16 * q^8 - 32 * q^9 - 16 * q^11 - 12 * q^16 - 4 * q^18 - 20 * q^22 + 32 * q^25 + 16 * q^30 + 24 * q^32 - 4 * q^36 - 16 * q^43 - 48 * q^44 - 16 * q^46 + 76 * q^50 + 16 * q^57 + 12 * q^58 + 4 * q^60 + 76 * q^64 + 64 * q^67 - 16 * q^72 + 68 * q^74 - 12 * q^78 + 32 * q^81 - 100 * q^86 + 28 * q^88 - 128 * q^92 + 16 * q^99

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