LMFDB - Embedded newform 297.2.k.a.134.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(107,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			134.4
Character	$\chi$	$=$	297.134
Dual form			297.2.k.a.215.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.191808 + 0.590323i) q^{2} +(1.30634 + 0.949113i) q^{4} +(-3.55080 + 1.15372i) q^{5} +(-1.30394 + 1.79472i) q^{7} +(-1.81517 + 1.31880i) q^{8} -2.31741i q^{10} +(0.692107 - 3.24361i) q^{11} +(-5.86699 - 1.90630i) q^{13} +(-0.809360 - 1.11399i) q^{14} +(0.567603 + 1.74690i) q^{16} +(0.0962825 + 0.296327i) q^{17} +(1.44540 + 1.98943i) q^{19} +(-5.73357 - 1.86295i) q^{20} +(1.78203 + 1.03072i) q^{22} +8.92408i q^{23} +(7.23200 - 5.25435i) q^{25} +(2.25067 - 3.09778i) q^{26} +(-3.40679 + 1.10693i) q^{28} +(5.34066 + 3.88022i) q^{29} +(-0.333193 + 1.02546i) q^{31} -5.62745 q^{32} -0.193397 q^{34} +(2.55942 - 7.87708i) q^{35} +(-3.01593 - 2.19120i) q^{37} +(-1.45165 + 0.471668i) q^{38} +(4.92377 - 6.77699i) q^{40} +(-3.38021 + 2.45587i) q^{41} +4.75812i q^{43} +(3.98268 - 3.58037i) q^{44} +(-5.26809 - 1.71171i) q^{46} +(0.846838 + 1.16557i) q^{47} +(0.642357 + 1.97697i) q^{49} +(1.71462 + 5.27704i) q^{50} +(-5.85501 - 8.05873i) q^{52} +(5.61052 + 1.82297i) q^{53} +(1.28469 + 12.3159i) q^{55} -4.97736i q^{56} +(-3.31496 + 2.40846i) q^{58} +(3.28830 - 4.52596i) q^{59} +(-1.43139 + 0.465088i) q^{61} +(-0.541446 - 0.393383i) q^{62} +(-0.0558176 + 0.171789i) q^{64} +23.0319 q^{65} +2.79751 q^{67} +(-0.155470 + 0.478488i) q^{68} +(4.15911 + 3.02177i) q^{70} +(6.47873 - 2.10507i) q^{71} +(5.66251 - 7.79378i) q^{73} +(1.87199 - 1.36008i) q^{74} +3.97073i q^{76} +(4.91890 + 5.47161i) q^{77} +(-4.73172 - 1.53743i) q^{79} +(-4.03089 - 5.54804i) q^{80} +(-0.801405 - 2.46647i) q^{82} +(-4.13920 - 12.7392i) q^{83} +(-0.683759 - 0.941114i) q^{85} +(-2.80883 - 0.912645i) q^{86} +(3.02137 + 6.80044i) q^{88} +3.05090i q^{89} +(11.0715 - 8.04392i) q^{91} +(-8.46996 + 11.6579i) q^{92} +(-0.850495 + 0.276342i) q^{94} +(-7.42759 - 5.39646i) q^{95} +(-4.54792 + 13.9971i) q^{97} -1.29026 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{4} - 4 q^{16} + 36 q^{22} + 8 q^{25} - 100 q^{28} + 8 q^{31} - 64 q^{34} - 12 q^{37} - 60 q^{40} - 20 q^{46} + 100 q^{52} + 8 q^{55} + 24 q^{58} + 60 q^{61} + 36 q^{64} - 24 q^{67} + 8 q^{70}+ \cdots - 24 q^{97}+O(q^{100}) $ 32 * q - 8 * q^4 - 4 * q^16 + 36 * q^22 + 8 * q^25 - 100 * q^28 + 8 * q^31 - 64 * q^34 - 12 * q^37 - 60 * q^40 - 20 * q^46 + 100 * q^52 + 8 * q^55 + 24 * q^58 + 60 * q^61 + 36 * q^64 - 24 * q^67 + 8 * q^70 + 80 * q^73 - 60 * q^79 + 72 * q^82 - 20 * q^85 - 24 * q^88 + 24 * q^91 + 20 * q^94 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.191808	+	0.590323i	−0.135629	+	0.417422i	−0.995687	−	0.0927733i	$-0.970427\pi$
$2$	−0.191808	+	0.590323i	−0.135629	+	0.417422i	0.860059	+	0.510195i	$0.170427\pi$
$3$		0			0
$3$		0			0
$4$	1.30634	+	0.949113i	0.653171	+	0.474557i
$5$	−3.55080	+	1.15372i	−1.58796	+	0.515961i	−0.964093	−	0.265565i	$-0.914441\pi$
$5$	−3.55080	+	1.15372i	−1.58796	+	0.515961i	−0.623872	+	0.781526i	$0.714441\pi$
$6$		0			0
$7$	−1.30394	+	1.79472i	−0.492844	+	0.678341i	−0.980909	−	0.194466i	$-0.937703\pi$
$7$	−1.30394	+	1.79472i	−0.492844	+	0.678341i	0.488066	+	0.872807i	$0.337703\pi$
$8$	−1.81517	+	1.31880i	−0.641759	+	0.466265i
$9$		0			0
$10$		−	2.31741i		−	0.732830i
$11$	0.692107	−	3.24361i	0.208678	−	0.977984i
$11$	0.692107	−	3.24361i	0.208678	−	0.977984i
$12$		0			0
$13$	−5.86699	−	1.90630i	−1.62721	−	0.528713i	−0.653584	−	0.756854i	$-0.726735\pi$
$13$	−5.86699	−	1.90630i	−1.62721	−	0.528713i	−0.973628	+	0.228141i	$0.926735\pi$
$14$	−0.809360	−	1.11399i	−0.216311	−	0.297726i
$15$		0			0
$16$	0.567603	+	1.74690i	0.141901	+	0.436726i
$17$	0.0962825	+	0.296327i	0.0233519	+	0.0718699i	0.962053	−	0.272861i	$-0.0879700\pi$
$17$	0.0962825	+	0.296327i	0.0233519	+	0.0718699i	−0.938701	+	0.344731i	$0.887970\pi$
$18$		0			0
$19$	1.44540	+	1.98943i	0.331598	+	0.456406i	0.941964	−	0.335714i	$-0.108977\pi$
$19$	1.44540	+	1.98943i	0.331598	+	0.456406i	−0.610366	+	0.792120i	$0.708977\pi$
$20$	−5.73357	−	1.86295i	−1.28207	−	0.416568i
$21$		0			0
$22$	1.78203	+	1.03072i	0.379929	+	0.219749i
$23$			8.92408i			1.86080i	0.366548	+	0.930399i	$0.380540\pi$
$23$			8.92408i			1.86080i	−0.366548	+	0.930399i	$0.619460\pi$
$24$		0			0
$25$	7.23200	−	5.25435i	1.44640	−	1.05087i
$26$	2.25067	−	3.09778i	0.441393	−	0.607525i
$27$		0			0
$28$	−3.40679	+	1.10693i	−0.643822	+	0.209191i
$29$	5.34066	+	3.88022i	0.991736	+	0.720538i	0.960300	−	0.278968i	$-0.0899922\pi$
$29$	5.34066	+	3.88022i	0.991736	+	0.720538i	0.0314351	+	0.999506i	$0.489992\pi$
$30$		0			0
$31$	−0.333193	+	1.02546i	−0.0598433	+	0.184179i	−0.976509	−	0.215476i	$-0.930870\pi$
$31$	−0.333193	+	1.02546i	−0.0598433	+	0.184179i	0.916666	+	0.399654i	$0.130870\pi$
$32$	−5.62745			−0.994802
$33$		0			0
$34$	−0.193397			−0.0331672
$35$	2.55942	−	7.87708i	0.432621	−	1.33147i
$36$		0			0
$37$	−3.01593	−	2.19120i	−0.495815	−	0.360231i	0.311601	−	0.950213i	$-0.399135\pi$
$37$	−3.01593	−	2.19120i	−0.495815	−	0.360231i	−0.807416	+	0.589982i	$0.799135\pi$
$38$	−1.45165	+	0.471668i	−0.235488	+	0.0765147i
$39$		0			0
$40$	4.92377	−	6.77699i	0.778516	−	1.07154i
$41$	−3.38021	+	2.45587i	−0.527900	+	0.383542i	−0.819572	−	0.572977i	$-0.805789\pi$
$41$	−3.38021	+	2.45587i	−0.527900	+	0.383542i	0.291672	+	0.956519i	$0.405789\pi$
$42$		0			0
$43$			4.75812i			0.725607i	0.931866	+	0.362803i	$0.118180\pi$
$43$			4.75812i			0.725607i	−0.931866	+	0.362803i	$0.881820\pi$
$44$	3.98268	−	3.58037i	0.600412	−	0.539762i
$45$		0			0
$46$	−5.26809	−	1.71171i	−0.776738	−	0.252377i
$47$	0.846838	+	1.16557i	0.123524	+	0.170016i	0.866300	−	0.499523i	$-0.166491\pi$
$47$	0.846838	+	1.16557i	0.123524	+	0.170016i	−0.742776	+	0.669539i	$0.766491\pi$
$48$		0			0
$49$	0.642357	+	1.97697i	0.0917653	+	0.282425i
$50$	1.71462	+	5.27704i	0.242483	+	0.746287i
$51$		0			0
$52$	−5.85501	−	8.05873i	−0.811943	−	1.11754i
$53$	5.61052	+	1.82297i	0.770664	+	0.250404i	0.667849	−	0.744297i	$-0.267215\pi$
$53$	5.61052	+	1.82297i	0.770664	+	0.250404i	0.102815	+	0.994701i	$0.467215\pi$
$54$		0			0
$55$	1.28469	+	12.3159i	0.173228	+	1.66067i
$56$		−	4.97736i		−	0.665127i
$57$		0			0
$58$	−3.31496	+	2.40846i	−0.435276	+	0.316246i
$59$	3.28830	−	4.52596i	0.428101	−	0.589230i	−0.539415	−	0.842040i	$-0.681355\pi$
$59$	3.28830	−	4.52596i	0.428101	−	0.589230i	0.967516	+	0.252810i	$0.0813547\pi$
$60$		0			0
$61$	−1.43139	+	0.465088i	−0.183271	+	0.0595484i	−0.399215	−	0.916857i	$-0.630717\pi$
$61$	−1.43139	+	0.465088i	−0.183271	+	0.0595484i	0.215944	+	0.976406i	$0.430717\pi$
$62$	−0.541446	−	0.393383i	−0.0687637	−	0.0499597i
$63$		0			0
$64$	−0.0558176	+	0.171789i	−0.00697720	+	0.0214736i
$65$	23.0319			2.85675
$66$		0			0
$67$	2.79751			0.341770			0.170885	−	0.985291i	$-0.445337\pi$
$67$	2.79751			0.341770			0.170885	+	0.985291i	$0.445337\pi$
$68$	−0.155470	+	0.478488i	−0.0188535	+	0.0580251i
$69$		0			0
$70$	4.15911	+	3.02177i	0.497109	+	0.361171i
$71$	6.47873	−	2.10507i	0.768884	−	0.249826i	0.101797	−	0.994805i	$-0.467541\pi$
$71$	6.47873	−	2.10507i	0.768884	−	0.249826i	0.667087	+	0.744980i	$0.267541\pi$
$72$		0			0
$73$	5.66251	−	7.79378i	0.662747	−	0.912193i	−0.336821	−	0.941569i	$-0.609352\pi$
$73$	5.66251	−	7.79378i	0.662747	−	0.912193i	0.999568	+	0.0293753i	$0.00935180\pi$
$74$	1.87199	−	1.36008i	0.217615	−	0.158107i
$75$		0			0
$76$			3.97073i			0.455473i
$77$	4.91890	+	5.47161i	0.560561	+	0.623548i
$78$		0			0
$79$	−4.73172	−	1.53743i	−0.532360	−	0.172974i	0.0304872	−	0.999535i	$-0.490294\pi$
$79$	−4.73172	−	1.53743i	−0.532360	−	0.172974i	−0.562847	+	0.826561i	$0.690294\pi$
$80$	−4.03089	−	5.54804i	−0.450667	−	0.620290i
$81$		0			0
$82$	−0.801405	−	2.46647i	−0.0885004	−	0.272376i
$83$	−4.13920	−	12.7392i	−0.454337	−	1.39830i	−0.871912	−	0.489662i	$-0.837120\pi$
$83$	−4.13920	−	12.7392i	−0.454337	−	1.39830i	0.417576	−	0.908642i	$-0.362880\pi$
$84$		0			0
$85$	−0.683759	−	0.941114i	−0.0741641	−	0.102078i
$86$	−2.80883	−	0.912645i	−0.302884	−	0.0984130i
$87$		0			0
$88$	3.02137	+	6.80044i	0.322079	+	0.724930i
$89$			3.05090i			0.323394i	0.986840	+	0.161697i	$0.0516968\pi$
$89$			3.05090i			0.323394i	−0.986840	+	0.161697i	$0.948303\pi$
$90$		0			0
$91$	11.0715	−	8.04392i	1.16061	−	0.843231i
$92$	−8.46996	+	11.6579i	−0.883054	+	1.21542i
$93$		0			0
$94$	−0.850495	+	0.276342i	−0.0877218	+	0.0285026i
$95$	−7.42759	−	5.39646i	−0.762054	−	0.553665i
$96$		0			0
$97$	−4.54792	+	13.9971i	−0.461772	+	1.42119i	0.401226	+	0.915979i	$0.368584\pi$
$97$	−4.54792	+	13.9971i	−0.461772	+	1.42119i	−0.862998	+	0.505208i	$0.831416\pi$
$98$	−1.29026			−0.130336
$99$		0			0
$100$	14.4344			1.44344
$101$	−2.02523	+	6.23302i	−0.201518	+	0.620209i	0.798320	+	0.602233i	$0.205722\pi$
$101$	−2.02523	+	6.23302i	−0.201518	+	0.620209i	−0.999838	+	0.0179758i	$0.994278\pi$
$102$		0			0
$103$	7.08858	+	5.15015i	0.698458	+	0.507460i	0.879430	−	0.476029i	$-0.157924\pi$
$103$	7.08858	+	5.15015i	0.698458	+	0.507460i	−0.180971	+	0.983488i	$0.557924\pi$
$104$	13.1636	−	4.27712i	1.29080	−	0.419406i
$105$		0			0
$106$	−2.15228	+	2.96236i	−0.209048	+	0.287730i
$107$	−0.618545	+	0.449399i	−0.0597970	+	0.0434451i	−0.617282	−	0.786742i	$-0.711766\pi$
$107$	−0.618545	+	0.449399i	−0.0597970	+	0.0434451i	0.557485	+	0.830187i	$0.311766\pi$
$108$		0			0
$109$			4.39272i			0.420746i	0.977621	+	0.210373i	$0.0674678\pi$
$109$			4.39272i			0.420746i	−0.977621	+	0.210373i	$0.932532\pi$
$110$	−7.51677	−	1.60390i	−0.716696	−	0.152926i
$111$		0			0
$112$	−3.87533	−	1.25917i	−0.366184	−	0.118980i
$113$	3.53549	+	4.86618i	0.332591	+	0.457772i	0.942259	−	0.334885i	$-0.108697\pi$
$113$	3.53549	+	4.86618i	0.332591	+	0.457772i	−0.609668	+	0.792657i	$0.708697\pi$
$114$		0			0
$115$	−10.2959	−	31.6876i	−0.960100	−	2.95488i
$116$	3.29397	+	10.1378i	0.305837	+	0.941269i
$117$		0			0
$118$	2.04106	+	2.80928i	0.187895	+	0.258615i
$119$	−0.657371	−	0.213593i	−0.0602611	−	0.0195800i
$120$		0			0
$121$	−10.0420	−	4.48985i	−0.912907	−	0.408168i
$122$		−	0.934192i		−	0.0845778i
$123$		0			0
$124$	−1.40854	+	1.02337i	−0.126491	+	0.0919011i
$125$	−8.64472	+	11.8984i	−0.773207	+	1.06423i
$126$		0			0
$127$	−10.7264	+	3.48521i	−0.951811	+	0.309262i	−0.743451	−	0.668790i	$-0.766813\pi$
$127$	−10.7264	+	3.48521i	−0.951811	+	0.309262i	−0.208360	+	0.978052i	$0.566813\pi$
$128$	−9.19611	−	6.68137i	−0.812829	−	0.590555i
$129$		0			0
$130$	−4.41769	+	13.5962i	−0.387457	+	1.19247i
$131$	−17.1821			−1.50121			−0.750603	−	0.660754i	$-0.770237\pi$
$131$	−17.1821			−1.50121			−0.750603	+	0.660754i	$0.770237\pi$
$132$		0			0
$133$	−5.45519			−0.473025
$134$	−0.536583	+	1.65143i	−0.0463537	+	0.142662i
$135$		0			0
$136$	−0.565564	−	0.410906i	−0.0484967	−	0.0352349i
$137$	−1.29299	+	0.420119i	−0.110468	+	0.0358932i	−0.363729	−	0.931505i	$-0.618497\pi$
$137$	−1.29299	+	0.420119i	−0.110468	+	0.0358932i	0.253261	+	0.967398i	$0.418497\pi$
$138$		0			0
$139$	7.09084	−	9.75970i	0.601437	−	0.827807i	−0.394402	−	0.918938i	$-0.629048\pi$
$139$	7.09084	−	9.75970i	0.601437	−	0.827807i	0.995839	+	0.0911310i	$0.0290482\pi$
$140$	10.8197	−	7.86099i	0.914433	−	0.664375i
$141$		0			0
$142$			4.22832i			0.354833i
$143$	−10.2439	+	17.7109i	−0.856637	+	1.48106i
$144$		0			0
$145$	−23.4403	−	7.61622i	−1.94661	−	0.632492i
$146$	3.51474	+	4.83762i	0.290882	+	0.400365i
$147$		0			0
$148$	−1.86014	−	5.72491i	−0.152902	−	0.470585i
$149$	−4.51772	−	13.9041i	−0.370106	−	1.13907i	−0.946721	−	0.322053i	$-0.895627\pi$
$149$	−4.51772	−	13.9041i	−0.370106	−	1.13907i	0.576616	−	0.817016i	$-0.304373\pi$
$150$		0			0
$151$	−1.63511	−	2.25054i	−0.133064	−	0.183146i	0.737286	−	0.675581i	$-0.236107\pi$
$151$	−1.63511	−	2.25054i	−0.133064	−	0.183146i	−0.870349	+	0.492435i	$0.836107\pi$
$152$	−5.24730	−	1.70495i	−0.425613	−	0.138290i
$153$		0			0
$154$	−4.17351	+	1.85425i	−0.336311	+	0.149419i
$155$		−	4.02562i		−	0.323346i
$156$		0			0
$157$	14.3225	−	10.4059i	1.14306	−	0.830479i	0.155514	−	0.987834i	$-0.450297\pi$
$157$	14.3225	−	10.4059i	1.14306	−	0.830479i	0.987542	+	0.157355i	$0.0502966\pi$
$158$	1.81516	−	2.49836i	0.144406	−	0.198758i
$159$		0			0
$160$	19.9819	−	6.49253i	1.57971	−	0.513279i
$161$	−16.0162	−	11.6365i	−1.26226	−	0.917083i
$162$		0			0
$163$	0.454189	−	1.39785i	0.0355748	−	0.109488i	−0.931692	−	0.363249i	$-0.881668\pi$
$163$	0.454189	−	1.39785i	0.0355748	−	0.109488i	0.967267	+	0.253761i	$0.0816675\pi$
$164$	−6.74661			−0.526822
$165$		0			0
$166$	8.31416			0.645304
$167$	2.77651	−	8.54523i	0.214853	−	0.661250i	−0.784311	−	0.620368i	$-0.786983\pi$
$167$	2.77651	−	8.54523i	0.214853	−	0.661250i	0.999164	−	0.0408818i	$-0.0130167\pi$
$168$		0			0
$169$	20.2704	+	14.7273i	1.55926	+	1.13287i
$170$	0.686712	−	0.223126i	0.0526684	−	0.0171130i
$171$		0			0
$172$	−4.51600	+	6.21574i	−0.344342	+	0.473946i
$173$	−5.33494	+	3.87606i	−0.405608	+	0.294691i	−0.771821	−	0.635840i	$-0.780654\pi$
$173$	−5.33494	+	3.87606i	−0.405608	+	0.294691i	0.366213	+	0.930531i	$0.380654\pi$
$174$		0			0
$175$			19.8308i			1.49907i
$176$	6.05911	−	0.632037i	0.456723	−	0.0476416i
$177$		0			0
$178$	−1.80102	−	0.585185i	−0.134992	−	0.0438615i
$179$	0.750385	+	1.03282i	0.0560864	+	0.0771963i	0.836139	−	0.548518i	$-0.184808\pi$
$179$	0.750385	+	1.03282i	0.0560864	+	0.0771963i	−0.780053	+	0.625714i	$0.784808\pi$
$180$		0			0
$181$	6.39068	+	19.6685i	0.475016	+	1.46195i	0.845937	+	0.533283i	$0.179042\pi$
$181$	6.39068	+	19.6685i	0.475016	+	1.46195i	−0.370921	+	0.928664i	$0.620958\pi$
$182$	2.62491	+	8.07865i	0.194571	+	0.598829i
$183$		0			0
$184$	−11.7690	−	16.1987i	−0.867626	−	1.19418i
$185$	13.2370	+	4.30096i	0.973203	+	0.316213i
$186$		0			0
$187$	1.02781	−	0.107212i	0.0751606	−	0.00784015i
$188$			2.32638i			0.169669i
$189$		0			0
$190$	4.61032	−	3.34960i	0.334468	−	0.243005i
$191$	−3.95575	+	5.44462i	−0.286228	+	0.393959i	−0.927784	−	0.373117i	$-0.878289\pi$
$191$	−3.95575	+	5.44462i	−0.286228	+	0.393959i	0.641556	+	0.767076i	$0.278289\pi$
$192$		0			0
$193$	15.0175	−	4.87948i	1.08098	−	0.351233i	0.286227	−	0.958162i	$-0.407599\pi$
$193$	15.0175	−	4.87948i	1.08098	−	0.351233i	0.794756	+	0.606929i	$0.207599\pi$
$194$	−7.39047	−	5.36949i	−0.530605	−	0.385507i
$195$		0			0
$196$	−1.03723	+	3.19227i	−0.0740880	+	0.228019i
$197$	−2.09103			−0.148980			−0.0744900	−	0.997222i	$-0.523733\pi$
$197$	−2.09103			−0.148980			−0.0744900	+	0.997222i	$0.523733\pi$
$198$		0			0
$199$	−3.76773			−0.267087			−0.133544	−	0.991043i	$-0.542636\pi$
$199$	−3.76773			−0.267087			−0.133544	+	0.991043i	$0.542636\pi$
$200$	−6.19787	+	19.0751i	−0.438256	+	1.34881i
$201$		0			0
$202$	−3.29104	−	2.39108i	−0.231557	−	0.168236i
$203$	−13.9278	+	4.52542i	−0.977541	+	0.317622i
$204$		0			0
$205$	9.16905	−	12.6201i	0.640394	−	0.881427i
$206$	−4.39990	+	3.19671i	−0.306556	+	0.222726i
$207$		0			0
$208$		−	11.3311i		−	0.785670i
$209$	7.45330	−	3.31142i	0.515555	−	0.229056i
$210$		0			0
$211$	−10.3564	−	3.36499i	−0.712963	−	0.231656i	−0.0699935	−	0.997547i	$-0.522298\pi$
$211$	−10.3564	−	3.36499i	−0.712963	−	0.231656i	−0.642970	+	0.765892i	$0.722298\pi$
$212$	5.59905	+	7.70644i	0.384545	+	0.529280i
$213$		0			0
$214$	−0.146649	−	0.451340i	−0.0100247	−	0.0308530i
$215$	−5.48956	−	16.8951i	−0.374385	−	1.15224i
$216$		0			0
$217$	−1.40596	−	1.93513i	−0.0954425	−	0.131365i
$218$	−2.59312	−	0.842557i	−0.175628	−	0.0570651i
$219$		0			0
$220$	−10.0109	+	17.3081i	−0.674937	+	1.16691i
$221$		−	1.92209i		−	0.129294i
$222$		0			0
$223$	−9.18792	+	6.67541i	−0.615269	+	0.447019i	−0.851266	−	0.524735i	$-0.824164\pi$
$223$	−9.18792	+	6.67541i	−0.615269	+	0.447019i	0.235997	+	0.971754i	$0.424164\pi$
$224$	7.33787	−	10.0997i	0.490282	−	0.674815i
$225$		0			0
$226$	−3.55076	+	1.15371i	−0.236193	+	0.0767437i
$227$	8.66753	+	6.29733i	0.575284	+	0.417968i	0.837021	−	0.547171i	$-0.184295\pi$
$227$	8.66753	+	6.29733i	0.575284	+	0.417968i	−0.261737	+	0.965139i	$0.584295\pi$
$228$		0			0
$229$	−6.07986	+	18.7119i	−0.401769	+	1.23652i	0.521795	+	0.853071i	$0.325263\pi$
$229$	−6.07986	+	18.7119i	−0.401769	+	1.23652i	−0.923563	+	0.383446i	$0.874737\pi$
$230$	20.6808			1.36365
$231$		0			0
$232$	−14.8114			−0.972417
$233$	−6.22888	+	19.1705i	−0.408068	+	1.25590i	0.510238	+	0.860033i	$0.329557\pi$
$233$	−6.22888	+	19.1705i	−0.408068	+	1.25590i	−0.918306	+	0.395871i	$0.870443\pi$
$234$		0			0
$235$	−4.35170	−	3.16169i	−0.283874	−	0.206246i
$236$	8.59130	−	2.79148i	0.559246	−	0.181710i
$237$		0			0
$238$	0.252178	−	0.347093i	0.0163463	−	0.0224987i
$239$	13.9139	−	10.1090i	0.900015	−	0.653899i	−0.0384552	−	0.999260i	$-0.512244\pi$
$239$	13.9139	−	10.1090i	0.900015	−	0.653899i	0.938470	+	0.345361i	$0.112244\pi$
$240$		0			0
$241$			20.5296i			1.32243i	0.750196	+	0.661215i	$0.229959\pi$
$241$			20.5296i			1.32243i	−0.750196	+	0.661215i	$0.770041\pi$
$242$	4.57659	−	5.06683i	0.294194	−	0.325708i
$243$		0			0
$244$	−2.31131	−	0.750990i	−0.147966	−	0.0480772i
$245$	−4.56176	−	6.27872i	−0.291440	−	0.401133i
$246$		0			0
$247$	−4.68773	−	14.4273i	−0.298273	−	0.917990i
$248$	−0.747576	−	2.30080i	−0.0474711	−	0.146101i
$249$		0			0
$250$	−5.36580	−	7.38539i	−0.339363	−	0.467093i
$251$	−6.04667	−	1.96468i	−0.381662	−	0.124010i	0.111901	−	0.993719i	$-0.464306\pi$
$251$	−6.04667	−	1.96468i	−0.381662	−	0.124010i	−0.493563	+	0.869710i	$0.664306\pi$
$252$		0			0
$253$	28.9462	+	6.17642i	1.81983	+	0.388308i
$254$		−	7.00052i		−	0.439252i
$255$		0			0
$256$	5.41579	−	3.93480i	0.338487	−	0.245925i
$257$	8.13615	−	11.1984i	0.507519	−	0.698540i	−0.475979	−	0.879456i	$-0.657906\pi$
$257$	8.13615	−	11.1984i	0.507519	−	0.698540i	0.983498	+	0.180916i	$0.0579063\pi$
$258$		0			0
$259$	7.86519	−	2.55555i	0.488719	−	0.158794i
$260$	30.0875	+	21.8598i	1.86595	+	1.35569i
$261$		0			0
$262$	3.29566	−	10.1430i	0.203606	−	0.626636i
$263$	−15.4355			−0.951791			−0.475896	−	0.879502i	$-0.657876\pi$
$263$	−15.4355			−0.951791			−0.475896	+	0.879502i	$0.657876\pi$
$264$		0			0
$265$	−22.0250			−1.35299
$266$	1.04635	−	3.22033i	0.0641557	−	0.197451i
$267$		0			0
$268$	3.65450	+	2.65515i	0.223234	+	0.162189i
$269$	−5.84229	+	1.89827i	−0.356211	+	0.115740i	−0.481655	−	0.876361i	$-0.659964\pi$
$269$	−5.84229	+	1.89827i	−0.356211	+	0.115740i	0.125445	+	0.992101i	$0.459964\pi$
$270$		0			0
$271$	11.0715	−	15.2386i	0.672546	−	0.925680i	−0.327269	−	0.944931i	$-0.606128\pi$
$271$	11.0715	−	15.2386i	0.672546	−	0.925680i	0.999815	+	0.0192514i	$0.00612829\pi$
$272$	−0.463004	+	0.336392i	−0.0280738	+	0.0203968i
$273$		0			0
$274$		−	0.843867i		−	0.0509798i
$275$	−12.0377	−	27.0943i	−0.725903	−	1.63385i
$276$		0			0
$277$	5.21611	+	1.69482i	0.313405	+	0.101832i	0.461496	−	0.887142i	$-0.347313\pi$
$277$	5.21611	+	1.69482i	0.313405	+	0.101832i	−0.148091	+	0.988974i	$0.547313\pi$
$278$	4.40130	+	6.05787i	0.263973	+	0.363327i
$279$		0			0
$280$	5.74250	+	17.6736i	0.343180	+	1.05620i
$281$	8.06510	+	24.8218i	0.481124	+	1.48075i	0.837518	+	0.546410i	$0.184006\pi$
$281$	8.06510	+	24.8218i	0.481124	+	1.48075i	−0.356394	+	0.934336i	$0.615994\pi$
$282$		0			0
$283$	10.1368	+	13.9521i	0.602571	+	0.829367i	0.995941	−	0.0900130i	$-0.0286908\pi$
$283$	10.1368	+	13.9521i	0.602571	+	0.829367i	−0.393370	+	0.919380i	$0.628691\pi$
$284$	10.4614	+	3.39911i	0.620770	+	0.201700i
$285$		0			0
$286$	−8.49028	−	9.44429i	−0.502041	−	0.558452i
$287$		−	9.26884i		−	0.547122i
$288$		0			0
$289$	13.6747	−	9.93529i	0.804397	−	0.584429i
$290$	8.99206	−	12.3765i	0.528032	−	0.726774i
$291$		0			0
$292$	14.7944	−	4.80698i	0.865775	−	0.281307i
$293$	21.9665	+	15.9596i	1.28330	+	0.932369i	0.999647	−	0.0265597i	$-0.00845521\pi$
$293$	21.9665	+	15.9596i	1.28330	+	0.932369i	0.283648	+	0.958928i	$0.408455\pi$
$294$		0			0
$295$	−6.45439	+	19.8646i	−0.375789	+	1.15656i
$296$	8.36416			0.486157
$297$		0			0
$298$	9.07446			0.525669
$299$	17.0120	−	52.3575i	0.983828	−	3.02791i
$300$		0			0
$301$	−8.53951	−	6.20431i	−0.492209	−	0.357611i
$302$	1.64217	−	0.533574i	0.0944964	−	0.0307037i
$303$		0			0
$304$	−2.65492	+	3.65419i	−0.152270	+	0.209582i
$305$	4.54600	−	3.30286i	0.260303	−	0.189121i
$306$		0			0
$307$		−	14.5585i		−	0.830895i	−0.909617	−	0.415448i	$-0.863625\pi$
$307$		−	14.5585i		−	0.830895i	0.909617	−	0.415448i	$-0.136375\pi$
$308$	1.23259	+	11.8164i	0.0702334	+	0.673302i
$309$		0			0
$310$	2.37642	+	0.772146i	0.134972	+	0.0438549i
$311$	−2.57524	−	3.54451i	−0.146028	−	0.200991i	0.729737	−	0.683728i	$-0.239643\pi$
$311$	−2.57524	−	3.54451i	−0.146028	−	0.200991i	−0.875765	+	0.482737i	$0.839643\pi$
$312$		0			0
$313$	−1.74230	−	5.36224i	−0.0984805	−	0.303092i	0.889665	−	0.456615i	$-0.150938\pi$
$313$	−1.74230	−	5.36224i	−0.0984805	−	0.303092i	−0.988145	+	0.153523i	$0.950938\pi$
$314$	3.39567	+	10.4508i	0.191629	+	0.589773i
$315$		0			0
$316$	−4.72205	−	6.49935i	−0.265636	−	0.365617i
$317$	15.1307	+	4.91625i	0.849823	+	0.276124i	0.701372	−	0.712796i	$-0.252571\pi$
$317$	15.1307	+	4.91625i	0.849823	+	0.276124i	0.148451	+	0.988920i	$0.452571\pi$
$318$		0			0
$319$	16.2822	−	14.6375i	0.911629	−	0.819541i
$320$		−	0.674386i		−	0.0376993i
$321$		0			0
$322$	9.94132	−	7.22279i	0.554008	−	0.402510i
$323$	−0.450354	+	0.619859i	−0.0250584	+	0.0344899i
$324$		0			0
$325$	−52.4465	+	17.0409i	−2.90921	+	0.945259i
$326$	0.738067	+	0.536237i	0.0408777	+	0.0296994i
$327$		0			0
$328$	2.89686	−	8.91562i	0.159952	−	0.492283i
$329$	−3.19610			−0.176207
$330$		0			0
$331$	19.7855			1.08751			0.543755	−	0.839244i	$-0.317002\pi$
$331$	19.7855			1.08751			0.543755	+	0.839244i	$0.317002\pi$
$332$	6.68369	−	20.5703i	0.366815	−	1.12894i
$333$		0			0
$334$	4.51189	+	3.27808i	0.246880	+	0.179369i
$335$	−9.93338	+	3.22755i	−0.542718	+	0.176340i
$336$		0			0
$337$	−14.0306	+	19.3115i	−0.764296	+	1.05196i	0.232548	+	0.972585i	$0.425294\pi$
$337$	−14.0306	+	19.3115i	−0.764296	+	1.05196i	−0.996845	+	0.0793789i	$0.974706\pi$
$338$	−12.5819	+	9.14129i	−0.684365	+	0.497221i
$339$		0			0
$340$		−	1.87838i		−	0.101870i
$341$	3.09559	+	1.79048i	0.167636	+	0.0969598i
$342$		0			0
$343$	−19.1545	−	6.22366i	−1.03424	−	0.336046i
$344$	−6.27500	−	8.63680i	−0.338325	−	0.465665i
$345$		0			0
$346$	−1.26485	−	3.89280i	−0.0679986	−	0.209278i
$347$	5.36202	+	16.5026i	0.287848	+	0.885905i	0.985530	+	0.169498i	$0.0542147\pi$
$347$	5.36202	+	16.5026i	0.287848	+	0.885905i	−0.697682	+	0.716407i	$0.745785\pi$
$348$		0			0
$349$	−6.55774	−	9.02596i	−0.351028	−	0.483148i	0.596594	−	0.802543i	$-0.296520\pi$
$349$	−6.55774	−	9.02596i	−0.351028	−	0.483148i	−0.947622	+	0.319395i	$0.896520\pi$
$350$	−11.7066	−	3.80370i	−0.625743	−	0.203316i
$351$		0			0
$352$	−3.89480	+	18.2532i	−0.207594	+	0.972901i
$353$			23.4457i			1.24789i	0.781469	+	0.623944i	$0.214471\pi$
$353$			23.4457i			1.24789i	−0.781469	+	0.623944i	$0.785529\pi$
$354$		0			0
$355$	−20.5760	+	14.9493i	−1.09206	+	0.793429i
$356$	−2.89565	+	3.98551i	−0.153469	+	0.211232i
$357$		0			0
$358$	−0.753625	+	0.244868i	−0.0398303	+	0.0129417i
$359$	14.8582	+	10.7951i	0.784184	+	0.569743i	0.906232	−	0.422781i	$-0.138946\pi$
$359$	14.8582	+	10.7951i	0.784184	+	0.569743i	−0.122048	+	0.992524i	$0.538946\pi$
$360$		0			0
$361$	4.00269	−	12.3190i	0.210668	−	0.648370i
$362$	−12.8366			−0.674674
$363$		0			0
$364$	22.0978			1.15824
$365$	−11.1146	+	34.2071i	−0.581763	+	1.79048i
$366$		0			0
$367$	−10.9221	−	7.93538i	−0.570130	−	0.414223i	0.265023	−	0.964242i	$-0.414621\pi$
$367$	−10.9221	−	7.93538i	−0.570130	−	0.414223i	−0.835152	+	0.550019i	$0.814621\pi$
$368$	−15.5895	+	5.06533i	−0.812659	+	0.264049i
$369$		0			0
$370$	−5.07791	+	6.98915i	−0.263988	+	0.363348i
$371$	−10.5875	+	7.69227i	−0.549676	+	0.399363i
$372$		0			0
$373$		−	28.2829i		−	1.46443i	−0.681073	−	0.732215i	$-0.738486\pi$
$373$		−	28.2829i		−	1.46443i	0.681073	−	0.732215i	$-0.261514\pi$
$374$	−0.133851	+	0.627302i	−0.00692128	+	0.0324370i
$375$		0			0
$376$	−3.07431	−	0.998903i	−0.158545	−	0.0515145i
$377$	−23.9368	−	32.9461i	−1.23281	−	1.69681i
$378$		0			0
$379$	−0.0682032	−	0.209908i	−0.00350336	−	0.0107822i	0.949290	−	0.314403i	$-0.101804\pi$
$379$	−0.0682032	−	0.209908i	−0.00350336	−	0.0107822i	−0.952793	+	0.303621i	$0.901804\pi$
$380$	−4.58112	−	14.0992i	−0.235007	−	0.723276i
$381$		0			0
$382$	−2.45534	−	3.37949i	−0.125626	−	0.172910i
$383$	−36.6998	−	11.9245i	−1.87527	−	0.609313i	−0.989366	−	0.145447i	$-0.953538\pi$
$383$	−36.6998	−	11.9245i	−1.87527	−	0.609313i	−0.885906	−	0.463866i	$-0.846462\pi$
$384$		0			0
$385$	−23.7788	−	13.7535i	−1.21188	−	0.700945i
$386$			9.80110i			0.498863i
$387$		0			0
$388$	−19.2260	+	13.9685i	−0.976050	+	0.709142i
$389$	21.3708	−	29.4144i	1.08354	−	1.49137i	0.227981	−	0.973665i	$-0.426787\pi$
$389$	21.3708	−	29.4144i	1.08354	−	1.49137i	0.855561	−	0.517702i	$-0.173213\pi$
$390$		0			0
$391$	−2.64444	+	0.859232i	−0.133735	+	0.0434532i
$392$	−3.77321	−	2.74140i	−0.190576	−	0.138462i
$393$		0			0
$394$	0.401076	−	1.23439i	0.0202059	−	0.0621875i
$395$	18.5752			0.934617
$396$		0			0
$397$	22.4527			1.12687			0.563434	−	0.826161i	$-0.309480\pi$
$397$	22.4527			1.12687			0.563434	+	0.826161i	$0.309480\pi$
$398$	0.722679	−	2.22418i	0.0362246	−	0.111488i
$399$		0			0
$400$	13.2838	+	9.65121i	0.664188	+	0.482561i
$401$	−26.1789	+	8.50604i	−1.30731	+	0.424772i	−0.878120	−	0.478441i	$-0.841202\pi$
$401$	−26.1789	+	8.50604i	−1.30731	+	0.424772i	−0.429193	+	0.903213i	$0.641202\pi$
$402$		0			0
$403$	3.90968	−	5.38122i	0.194755	−	0.268058i
$404$	−8.56149	+	6.22029i	−0.425950	+	0.309471i
$405$		0			0
$406$		−	9.08993i		−	0.451126i
$407$	−9.19474	+	8.26594i	−0.455766	+	0.409727i
$408$		0			0
$409$	38.0007	+	12.3472i	1.87901	+	0.610529i	0.987519	+	0.157500i	$0.0503434\pi$
$409$	38.0007	+	12.3472i	1.87901	+	0.610529i	0.891496	+	0.453029i	$0.149657\pi$
$410$	5.69125	+	7.83334i	0.281071	+	0.386861i
$411$		0			0
$412$	4.37203	+	13.4557i	0.215395	+	0.662916i
$413$	3.83509	+	11.8032i	0.188712	+	0.580797i
$414$		0			0
$415$	29.3949	+	40.4587i	1.44294	+	1.98604i
$416$	33.0162	+	10.7276i	1.61875	+	0.525965i
$417$		0			0
$418$	0.525212	+	5.03501i	0.0256889	+	0.246271i
$419$		−	25.3455i		−	1.23821i	−0.785308	−	0.619105i	$-0.787495\pi$
$419$		−	25.3455i		−	1.23821i	0.785308	−	0.619105i	$-0.212505\pi$
$420$		0			0
$421$	12.0521	−	8.75640i	0.587386	−	0.426761i	−0.253993	−	0.967206i	$-0.581744\pi$
$421$	12.0521	−	8.75640i	0.587386	−	0.426761i	0.841379	+	0.540445i	$0.181744\pi$
$422$	3.97287	−	5.46819i	0.193396	−	0.266187i
$423$		0			0
$424$	−12.5882	+	4.09014i	−0.611335	+	0.198635i
$425$	2.25332	+	1.63713i	0.109302	+	0.0794127i
$426$		0			0
$427$	1.03175	−	3.17540i	0.0499298	−	0.153668i
$428$	−1.23456			−0.0596748
$429$		0			0
$430$	11.0265			0.531747
$431$	−4.81473	+	14.8182i	−0.231917	+	0.713768i	0.765598	+	0.643319i	$0.222443\pi$
$431$	−4.81473	+	14.8182i	−0.231917	+	0.713768i	−0.997515	+	0.0704489i	$0.977557\pi$
$432$		0			0
$433$	−8.59479	−	6.24448i	−0.413039	−	0.300091i	0.361792	−	0.932259i	$-0.382165\pi$
$433$	−8.59479	−	6.24448i	−0.413039	−	0.300091i	−0.774831	+	0.632168i	$0.782165\pi$
$434$	1.41203	−	0.458796i	0.0677795	−	0.0220229i
$435$		0			0
$436$	−4.16918	+	5.73839i	−0.199668	+	0.274819i
$437$	−17.7538	+	12.8989i	−0.849280	+	0.617038i
$438$		0			0
$439$			17.8131i			0.850171i	0.905153	+	0.425085i	$0.139756\pi$
$439$			17.8131i			0.850171i	−0.905153	+	0.425085i	$0.860244\pi$
$440$	−18.5741	−	20.6612i	−0.885486	−	0.984983i
$441$		0			0
$442$	1.13466	+	0.368672i	0.0539701	+	0.0175359i
$443$	−10.7668	−	14.8192i	−0.511545	−	0.704081i	0.472634	−	0.881259i	$-0.343303\pi$
$443$	−10.7668	−	14.8192i	−0.511545	−	0.704081i	−0.984179	+	0.177178i	$0.943303\pi$
$444$		0			0
$445$	−3.51989	−	10.8331i	−0.166859	−	0.513539i
$446$	−2.17834	−	6.70424i	−0.103147	−	0.317455i
$447$		0			0
$448$	−0.235530	−	0.324180i	−0.0111278	−	0.0153161i
$449$	13.4434	+	4.36802i	0.634433	+	0.206140i	0.608538	−	0.793525i	$-0.291756\pi$
$449$	13.4434	+	4.36802i	0.634433	+	0.206140i	0.0258953	+	0.999665i	$0.491756\pi$
$450$		0			0
$451$	5.62640	+	12.6638i	0.264937	+	0.596315i
$452$			9.71248i			0.456837i
$453$		0			0
$454$	−5.37996	+	3.90877i	−0.252494	+	0.183448i
$455$	−30.0322	+	41.3358i	−1.40793	+	1.93785i
$456$		0			0
$457$	8.23043	−	2.67423i	0.385003	−	0.125095i	−0.110119	−	0.993918i	$-0.535123\pi$
$457$	8.23043	−	2.67423i	0.385003	−	0.125095i	0.495122	+	0.868823i	$0.335123\pi$
$458$	−9.87990	−	7.17817i	−0.461658	−	0.335414i
$459$		0			0
$460$	16.6251	−	51.1668i	0.775150	−	2.38567i
$461$	−36.2682			−1.68918			−0.844590	−	0.535414i	$-0.820155\pi$
$461$	−36.2682			−1.68918			−0.844590	+	0.535414i	$0.820155\pi$
$462$		0			0
$463$	−28.3027			−1.31534			−0.657669	−	0.753307i	$-0.728457\pi$
$463$	−28.3027			−1.31534			−0.657669	+	0.753307i	$0.728457\pi$
$464$	−3.74699	+	11.5320i	−0.173949	+	0.535361i
$465$		0			0
$466$	−10.1221	−	7.35411i	−0.468896	−	0.340673i
$467$	26.4483	−	8.59356i	1.22388	−	0.397662i	0.375386	−	0.926869i	$-0.377510\pi$
$467$	26.4483	−	8.59356i	1.22388	−	0.397662i	0.848493	+	0.529206i	$0.177510\pi$
$468$		0			0
$469$	−3.64778	+	5.02074i	−0.168439	+	0.231836i
$470$	2.70111	−	1.96247i	0.124593	−	0.0905221i
$471$		0			0
$472$			12.5520i			0.577752i
$473$	15.4335	+	3.29313i	0.709632	+	0.151418i
$474$		0			0
$475$	20.9063	+	6.79287i	0.959248	+	0.311678i
$476$	−0.656028	−	0.902945i	−0.0300690	−	0.0413864i
$477$		0			0
$478$	3.29881	+	10.1527i	0.150884	+	0.464373i
$479$	2.29132	+	7.05195i	0.104693	+	0.322212i	0.989658	−	0.143445i	$-0.0458181\pi$
$479$	2.29132	+	7.05195i	0.104693	+	0.322212i	−0.884965	+	0.465657i	$0.845818\pi$
$480$		0			0
$481$	13.5173	+	18.6050i	0.616338	+	0.848316i
$482$	−12.1191	−	3.93774i	−0.552011	−	0.179359i
$483$		0			0
$484$	−8.85688	−	15.3963i	−0.402585	−	0.699830i
$485$		−	54.9478i		−	2.49505i
$486$		0			0
$487$	15.0683	−	10.9477i	0.682808	−	0.496089i	−0.191480	−	0.981496i	$-0.561329\pi$
$487$	15.0683	−	10.9477i	0.682808	−	0.496089i	0.874288	+	0.485408i	$0.161329\pi$
$488$	1.98486	−	2.73193i	0.0898505	−	0.123669i
$489$		0			0
$490$	4.58146	−	1.48861i	0.206969	−	0.0672484i
$491$	17.2824	+	12.5564i	0.779944	+	0.566662i	0.904962	−	0.425492i	$-0.139899\pi$
$491$	17.2824	+	12.5564i	0.779944	+	0.566662i	−0.125018	+	0.992154i	$0.539899\pi$
$492$		0			0
$493$	−0.635601	+	1.95618i	−0.0286260	+	0.0881019i
$494$	9.41594			0.423643
$495$		0			0
$496$	−1.98051			−0.0889273
$497$	−4.66988	+	14.3724i	−0.209473	+	0.644691i
$498$		0			0
$499$	−9.66639	−	7.02304i	−0.432727	−	0.314395i	0.350011	−	0.936745i	$-0.386178\pi$
$499$	−9.66639	−	7.02304i	−0.432727	−	0.314395i	−0.782738	+	0.622351i	$0.786178\pi$
$500$	−22.5859	+	7.33861i	−1.01007	+	0.328193i
$501$		0			0
$502$	2.31959	−	3.19265i	0.103529	−	0.142495i
$503$	21.5801	−	15.6789i	0.962210	−	0.699087i	0.00854739	−	0.999963i	$-0.497279\pi$
$503$	21.5801	−	15.6789i	0.962210	−	0.699087i	0.953663	+	0.300877i	$0.0972792\pi$
$504$		0			0
$505$		−	24.4688i		−	1.08885i
$506$	−9.19819	+	15.9029i	−0.408909	+	0.706972i
$507$		0			0
$508$	−17.3202	−	5.62766i	−0.768458	−	0.249687i
$509$	15.2021	+	20.9240i	0.673823	+	0.927438i	0.999839	−	0.0179260i	$-0.00570632\pi$
$509$	15.2021	+	20.9240i	0.673823	+	0.927438i	−0.326016	+	0.945364i	$0.605706\pi$
$510$		0			0
$511$	6.60408	+	20.3253i	0.292147	+	0.899137i
$512$	−5.74119	−	17.6696i	−0.253727	−	0.780892i
$513$		0			0
$514$	5.05013	+	6.95091i	0.222752	+	0.306591i
$515$	−31.1120	−	10.1089i	−1.37096	−	0.445451i
$516$		0			0
$517$	4.36676	−	1.94011i	0.192050	−	0.0853259i
$518$			5.13318i			0.225539i
$519$		0			0
$520$	−41.8067	+	30.3743i	−1.83335	+	1.33200i
$521$	−13.0853	+	18.0103i	−0.573276	+	0.789047i	−0.992938	−	0.118634i	$-0.962149\pi$
$521$	−13.0853	+	18.0103i	−0.573276	+	0.789047i	0.419662	+	0.907680i	$0.362149\pi$
$522$		0			0
$523$	−27.2570	+	8.85633i	−1.19186	+	0.387260i	−0.836762	−	0.547567i	$-0.815554\pi$
$523$	−27.2570	+	8.85633i	−1.19186	+	0.387260i	−0.355103	+	0.934827i	$0.615554\pi$
$524$	−22.4457	−	16.3077i	−0.980544	−	0.712407i
$525$		0			0
$526$	2.96064	−	9.11191i	0.129090	−	0.397298i
$527$	−0.335953			−0.0146343
$528$		0			0
$529$	−56.6391			−2.46257
$530$	4.22457	−	13.0019i	0.183503	−	0.564766i
$531$		0			0
$532$	−7.12635	−	5.17759i	−0.308966	−	0.224477i
$533$	24.5133	−	7.96485i	1.06179	−	0.344996i
$534$		0			0
$535$	1.67785	−	2.30936i	0.0725396	−	0.0998422i
$536$	−5.07795	+	3.68934i	−0.219334	+	0.159355i
$537$		0			0
$538$		−	3.81294i		−	0.164388i
$539$	6.85710	−	0.715277i	0.295356	−	0.0308092i
$540$		0			0
$541$	27.0426	+	8.78666i	1.16265	+	0.377768i	0.825895	−	0.563824i	$-0.190670\pi$
$541$	27.0426	+	8.78666i	1.16265	+	0.377768i	0.336755	+	0.941592i	$0.390670\pi$
$542$	6.87211	+	9.45865i	0.295182	+	0.406284i
$543$		0			0
$544$	−0.541825	−	1.66757i	−0.0232306	−	0.0714963i
$545$	−5.06798	−	15.5976i	−0.217088	−	0.668130i
$546$		0			0
$547$	10.5010	+	14.4534i	0.448991	+	0.617983i	0.972180	−	0.234233i	$-0.0752579\pi$
$547$	10.5010	+	14.4534i	0.448991	+	0.617983i	−0.523189	+	0.852217i	$0.675258\pi$
$548$	−2.08783	−	0.678378i	−0.0891878	−	0.0289789i
$549$		0			0
$550$	18.3034	−	1.90926i	0.780458	−	0.0814110i
$551$			16.2333i			0.691563i
$552$		0			0
$553$	8.92915	−	6.48740i	0.379706	−	0.275872i
$554$	−2.00098	+	2.75411i	−0.0850134	+	0.117011i
$555$		0			0
$556$	18.5261	−	6.01950i	0.785683	−	0.255284i
$557$	−27.7784	−	20.1822i	−1.17701	−	0.855148i	−0.185179	−	0.982705i	$-0.559287\pi$
$557$	−27.7784	−	20.1822i	−1.17701	−	0.855148i	−0.991831	+	0.127556i	$0.959287\pi$
$558$		0			0
$559$	9.07042	−	27.9159i	0.383638	−	1.18072i
$560$	15.2132			0.642876
$561$		0			0
$562$	−16.1999			−0.683350
$563$	0.0303872	−	0.0935222i	0.00128067	−	0.00394149i	−0.950414	−	0.310987i	$-0.899340\pi$
$563$	0.0303872	−	0.0935222i	0.00128067	−	0.00394149i	0.951695	+	0.307046i	$0.0993404\pi$
$564$		0			0
$565$	−18.1680	−	13.1999i	−0.764335	−	0.555322i
$566$	−10.1806	+	3.30787i	−0.427922	+	0.139040i
$567$		0			0
$568$	−8.98384	+	12.3652i	−0.376953	+	0.518832i
$569$	28.2745	−	20.5427i	1.18533	−	0.861193i	0.192568	−	0.981284i	$-0.438318\pi$
$569$	28.2745	−	20.5427i	1.18533	−	0.861193i	0.992763	+	0.120091i	$0.0383185\pi$
$570$		0			0
$571$			8.92780i			0.373617i	0.982396	+	0.186808i	$0.0598144\pi$
$571$			8.92780i			0.373617i	−0.982396	+	0.186808i	$0.940186\pi$
$572$	−30.1916	+	13.4138i	−1.26238	+	0.560861i
$573$		0			0
$574$	5.47161	+	1.77784i	0.228381	+	0.0742054i
$575$	46.8903	+	64.5389i	1.95546	+	2.69146i
$576$		0			0
$577$	−1.57214	−	4.83854i	−0.0654489	−	0.201431i	0.912984	−	0.407995i	$-0.133772\pi$
$577$	−1.57214	−	4.83854i	−0.0654489	−	0.201431i	−0.978433	+	0.206564i	$0.933772\pi$
$578$	3.24211	+	9.97819i	0.134854	+	0.415038i
$579$		0			0
$580$	−23.3924	−	32.1969i	−0.971317	−	1.33690i
$581$	28.2605	+	9.18240i	1.17244	+	0.380950i
$582$		0			0
$583$	9.79607	−	16.9366i	0.405712	−	0.701443i
$584$			21.6147i			0.894424i
$585$		0			0
$586$	−13.6347	+	9.90616i	−0.563242	+	0.409220i
$587$	−2.01322	+	2.77096i	−0.0830945	+	0.114370i	−0.848541	−	0.529130i	$-0.822518\pi$
$587$	−2.01322	+	2.77096i	−0.0830945	+	0.114370i	0.765446	+	0.643500i	$0.222518\pi$
$588$		0			0
$589$	−2.52168	+	0.819344i	−0.103904	+	0.0337605i
$590$	−10.4885	−	7.62036i	−0.431806	−	0.313725i
$591$		0			0
$592$	2.11596	−	6.51226i	0.0869655	−	0.267652i
$593$	−16.6897			−0.685365			−0.342683	−	0.939451i	$-0.611336\pi$
$593$	−16.6897			−0.685365			−0.342683	+	0.939451i	$0.611336\pi$
$594$		0			0
$595$	2.58062			0.105795
$596$	7.29489	−	22.4514i	0.298810	−	0.919643i
$597$		0			0
$598$	27.6448	+	20.0851i	1.13048	+	0.821343i
$599$	45.8771	−	14.9064i	1.87449	−	0.609058i	0.884770	−	0.466029i	$-0.154316\pi$
$599$	45.8771	−	14.9064i	1.87449	−	0.609058i	0.989718	−	0.143029i	$-0.0456843\pi$
$600$		0			0
$601$	11.1155	−	15.2991i	0.453409	−	0.624065i	−0.519716	−	0.854339i	$-0.673962\pi$
$601$	11.1155	−	15.2991i	0.453409	−	0.624065i	0.973126	+	0.230274i	$0.0739624\pi$
$602$	5.30050	−	3.85104i	0.216032	−	0.156956i
$603$		0			0
$604$		−	4.49188i		−	0.182772i
$605$	40.8371	+	4.35688i	1.66026	+	0.177132i
$606$		0			0
$607$	34.0815	+	11.0738i	1.38333	+	0.449470i	0.903762	−	0.428036i	$-0.140794\pi$
$607$	34.0815	+	11.0738i	1.38333	+	0.449470i	0.479565	+	0.877506i	$0.340794\pi$
$608$	−8.13394	−	11.1954i	−0.329875	−	0.454034i
$609$		0			0
$610$	1.07780	+	3.31713i	0.0436388	+	0.134307i
$611$	−2.74646	−	8.45274i	−0.111110	−	0.341961i
$612$		0			0
$613$	−0.393669	−	0.541839i	−0.0159002	−	0.0218847i	0.800993	−	0.598674i	$-0.204305\pi$
$613$	−0.393669	−	0.541839i	−0.0159002	−	0.0218847i	−0.816893	+	0.576789i	$0.804305\pi$
$614$	8.59420	+	2.79243i	0.346834	+	0.112693i
$615$		0			0
$616$	−16.1446	−	3.44487i	−0.650484	−	0.138798i
$617$			10.8544i			0.436981i	0.975839	+	0.218490i	$0.0701132\pi$
$617$			10.8544i			0.436981i	−0.975839	+	0.218490i	$0.929887\pi$
$618$		0			0
$619$	−22.4415	+	16.3047i	−0.901998	+	0.655340i	−0.938978	−	0.343976i	$-0.888226\pi$
$619$	−22.4415	+	16.3047i	−0.901998	+	0.655340i	0.0369803	+	0.999316i	$0.488226\pi$
$620$	3.82077	−	5.25884i	0.153446	−	0.211200i
$621$		0			0
$622$	2.58636	−	0.840360i	0.103704	−	0.0336953i
$623$	−5.47551	−	3.97819i	−0.219372	−	0.159383i
$624$		0			0
$625$	3.15625	−	9.71394i	0.126250	−	0.388557i
$626$	3.49964			0.139874
$627$		0			0
$628$	28.5864			1.14072
$629$	0.358931	−	1.10467i	0.0143115	−	0.0440463i
$630$		0			0
$631$	−35.5496	−	25.8283i	−1.41521	−	1.02821i	−0.992540	−	0.121923i	$-0.961094\pi$
$631$	−35.5496	−	25.8283i	−1.41521	−	1.02821i	−0.422667	−	0.906285i	$-0.638906\pi$
$632$	10.6164	−	3.44949i	0.422299	−	0.137213i
$633$		0			0
$634$	−5.80436	+	7.98901i	−0.230520	+	0.317284i
$635$	34.0662	−	24.7505i	1.35188	−	0.982195i
$636$		0			0
$637$		−	12.8234i		−	0.508082i
$638$	5.51779	+	12.4193i	0.218451	+	0.491687i
$639$		0			0
$640$	40.3620	+	13.1144i	1.59545	+	0.518392i
$641$	−8.28166	−	11.3987i	−0.327106	−	0.450223i	0.613514	−	0.789684i	$-0.289755\pi$
$641$	−8.28166	−	11.3987i	−0.327106	−	0.450223i	−0.940620	+	0.339461i	$0.889755\pi$
$642$		0			0
$643$	9.04036	+	27.8234i	0.356517	+	1.09725i	0.955125	+	0.296204i	$0.0957209\pi$
$643$	9.04036	+	27.8234i	0.356517	+	1.09725i	−0.598608	+	0.801042i	$0.704279\pi$
$644$	−9.87835	−	30.4024i	−0.389262	−	1.19802i
$645$		0			0
$646$	−0.279536	−	0.384748i	−0.0109982	−	0.0151377i
$647$	39.3432	+	12.7834i	1.54674	+	0.502566i	0.953226	−	0.302258i	$-0.0977405\pi$
$647$	39.3432	+	12.7834i	1.54674	+	0.502566i	0.593513	+	0.804824i	$0.297740\pi$
$648$		0			0
$649$	−12.4046	−	13.7984i	−0.486923	−	0.541635i
$650$		−	34.2290i		−	1.34257i
$651$		0			0
$652$	1.92004	−	1.39499i	0.0751947	−	0.0546322i
$653$	16.0547	−	22.0973i	0.628267	−	0.864735i	−0.369655	−	0.929169i	$-0.620524\pi$
$653$	16.0547	−	22.0973i	0.628267	−	0.864735i	0.997922	+	0.0644337i	$0.0205241\pi$
$654$		0			0
$655$	61.0101	−	19.8234i	2.38386	−	0.774564i
$656$	−6.20878	−	4.51094i	−0.242412	−	0.176123i
$657$		0			0
$658$	0.613038	−	1.88674i	0.0238987	−	0.0735526i
$659$	−0.641792			−0.0250007			−0.0125003	−	0.999922i	$-0.503979\pi$
$659$	−0.641792			−0.0250007			−0.0125003	+	0.999922i	$0.503979\pi$
$660$		0			0
$661$	−8.24156			−0.320559			−0.160280	−	0.987072i	$-0.551240\pi$
$661$	−8.24156			−0.320559			−0.160280	+	0.987072i	$0.551240\pi$
$662$	−3.79501	+	11.6798i	−0.147497	+	0.453950i
$663$		0			0
$664$	24.3137	+	17.6650i	0.943555	+	0.685533i
$665$	19.3703	−	6.29378i	0.751147	−	0.244063i
$666$		0			0
$667$	−34.6273	+	47.6604i	−1.34078	+	1.84542i
$668$	11.7375	−	8.52777i	0.454136	−	0.329949i
$669$		0			0
$670$		−	6.48298i		−	0.250459i
$671$	0.517884	+	4.96476i	0.0199927	+	0.191663i
$672$		0			0
$673$	14.0956	+	4.57995i	0.543346	+	0.176544i	0.567814	−	0.823157i	$-0.307789\pi$
$673$	14.0956	+	4.57995i	0.543346	+	0.176544i	−0.0244679	+	0.999701i	$0.507789\pi$
$674$	−8.70884	−	11.9867i	−0.335452	−	0.461710i
$675$		0			0
$676$	12.5022	+	38.4778i	0.480854	+	1.47992i
$677$	1.94580	+	5.98854i	0.0747830	+	0.230158i	0.981460	−	0.191667i	$-0.0613894\pi$
$677$	1.94580	+	5.98854i	0.0747830	+	0.230158i	−0.906677	+	0.421826i	$0.861389\pi$
$678$		0			0
$679$	−19.1906	−	26.4136i	−0.736468	−	1.01366i
$680$	2.48228	+	0.806541i	0.0951910	+	0.0309294i
$681$		0			0
$682$	−1.65072	+	1.48397i	−0.0632093	+	0.0568243i
$683$			14.1497i			0.541422i	0.962661	+	0.270711i	$0.0872588\pi$
$683$			14.1497i			0.541422i	−0.962661	+	0.270711i	$0.912741\pi$
$684$		0			0
$685$	4.10646	−	2.98352i	0.156900	−	0.113994i
$686$	7.34795	−	10.1136i	0.280546	−	0.386138i
$687$		0			0
$688$	−8.31198	+	2.70073i	−0.316891	+	0.102964i
$689$	−29.4417	−	21.3907i	−1.12164	−	0.814920i
$690$		0			0
$691$	−7.95871	+	24.4944i	−0.302764	+	0.931811i	0.677739	+	0.735303i	$0.262960\pi$
$691$	−7.95871	+	24.4944i	−0.302764	+	0.931811i	−0.980502	+	0.196508i	$0.937040\pi$
$692$	−10.6481			−0.404779
$693$		0			0
$694$	−10.7703			−0.408837
$695$	−13.9181	+	42.8356i	−0.527945	+	1.62485i
$696$		0			0
$697$	−1.05319	−	0.765191i	−0.0398926	−	0.0289837i
$698$	6.58606	−	2.13994i	0.249286	−	0.0809979i
$699$		0			0
$700$	−18.8217	+	25.9058i	−0.711392	+	0.979148i
$701$	−8.55571	+	6.21609i	−0.323145	+	0.234778i	−0.737516	−	0.675329i	$-0.764001\pi$
$701$	−8.55571	+	6.21609i	−0.323145	+	0.234778i	0.414371	+	0.910108i	$0.364001\pi$
$702$		0			0
$703$		−	9.16714i		−	0.345745i
$704$	0.518584	+	0.299947i	0.0195449	+	0.0113047i
$705$		0			0
$706$	−13.8405	−	4.49706i	−0.520896	−	0.169249i
$707$	−8.54575	−	11.7622i	−0.321396	−	0.442364i
$708$		0			0
$709$	−8.05868	−	24.8021i	−0.302650	−	0.931461i	−0.980544	−	0.196301i	$-0.937107\pi$
$709$	−8.05868	−	24.8021i	−0.302650	−	0.931461i	0.677894	−	0.735160i	$-0.262893\pi$
$710$	−4.87831	−	15.0139i	−0.183080	−	0.563462i
$711$		0			0
$712$	−4.02351	−	5.53789i	−0.150788	−	0.207541i
$713$	−9.15131	−	2.97344i	−0.342719	−	0.111356i
$714$		0			0
$715$	15.9405	−	74.7063i	0.596142	−	2.79386i
$716$			2.06141i			0.0770386i
$717$		0			0
$718$	−9.22251	+	6.70055i	−0.344181	+	0.250062i
$719$	−8.91625	+	12.2722i	−0.332520	+	0.457675i	−0.942238	−	0.334944i	$-0.891283\pi$
$719$	−8.91625	+	12.2722i	−0.332520	+	0.457675i	0.609718	+	0.792618i	$0.291283\pi$
$720$		0			0
$721$	−18.4862	+	6.00653i	−0.688461	+	0.223695i
$722$	6.50446	+	4.72577i	0.242071	+	0.175875i
$723$		0			0
$724$	−10.3192	+	31.7593i	−0.383510	+	1.18032i
$725$	59.0117			2.19164
$726$		0			0
$727$	−16.5646			−0.614347			−0.307174	−	0.951653i	$-0.599383\pi$
$727$	−16.5646			−0.614347			−0.307174	+	0.951653i	$0.599383\pi$
$728$	−9.48835	+	29.2021i	−0.351662	+	1.08230i
$729$		0			0
$730$	−18.0614	−	13.1224i	−0.668483	−	0.485681i
$731$	−1.40996	+	0.458124i	−0.0521493	+	0.0169443i
$732$		0			0
$733$	−13.2990	+	18.3045i	−0.491209	+	0.676092i	−0.980610	−	0.195967i	$-0.937215\pi$
$733$	−13.2990	+	18.3045i	−0.491209	+	0.676092i	0.489401	+	0.872059i	$0.337215\pi$
$734$	6.77939	−	4.92551i	0.250232	−	0.181804i
$735$		0			0
$736$		−	50.2198i		−	1.85113i
$737$	1.93618	−	9.07401i	0.0713199	−	0.334245i
$738$		0			0
$739$	−29.5613	−	9.60506i	−1.08743	−	0.353328i	−0.290178	−	0.956973i	$-0.593714\pi$
$739$	−29.5613	−	9.60506i	−1.08743	−	0.353328i	−0.797253	+	0.603645i	$0.793714\pi$
$740$	13.2099	+	18.1819i	0.485607	+	0.668381i
$741$		0			0
$742$	−2.51016	−	7.72549i	−0.0921510	−	0.283612i
$743$	14.5400	+	44.7495i	0.533420	+	1.64170i	0.747037	+	0.664782i	$0.231476\pi$
$743$	14.5400	+	44.7495i	0.533420	+	1.64170i	−0.213617	+	0.976917i	$0.568524\pi$
$744$		0			0
$745$	32.0830	+	44.1585i	1.17543	+	1.61784i
$746$	16.6960	+	5.42487i	0.611285	+	0.198619i
$747$		0			0
$748$	1.44442	+	0.835448i	0.0528134	+	0.0305470i
$749$		−	1.69611i		−	0.0619744i
$750$		0			0
$751$	−29.5479	+	21.4678i	−1.07822	+	0.783373i	−0.977372	−	0.211529i	$-0.932156\pi$
$751$	−29.5479	+	21.4678i	−1.07822	+	0.783373i	−0.100848	+	0.994902i	$0.532156\pi$
$752$	−1.55547	+	2.14093i	−0.0567223	+	0.0780715i
$753$		0			0
$754$	24.0401	−	7.81111i	0.875490	−	0.284464i
$755$	8.40245	+	6.10474i	0.305796	+	0.222174i
$756$		0			0
$757$	−8.52322	+	26.2318i	−0.309782	+	0.953409i	0.668068	+	0.744100i	$0.267122\pi$
$757$	−8.52322	+	26.2318i	−0.309782	+	0.953409i	−0.977849	+	0.209309i	$0.932878\pi$
$758$	0.136995			0.00497590
$759$		0			0
$760$	20.5992			0.747210
$761$	16.2865	−	50.1246i	0.590384	−	1.81701i	0.0139037	−	0.999903i	$-0.495574\pi$
$761$	16.2865	−	50.1246i	0.590384	−	1.81701i	0.576480	−	0.817111i	$-0.304426\pi$
$762$		0			0
$763$	−7.88370	−	5.72784i	−0.285409	−	0.207362i
$764$	−10.3351	+	3.35808i	−0.373912	+	0.121491i
$765$		0			0
$766$	14.0786	−	19.3775i	0.508681	−	0.700139i
$767$	−27.9203	+	20.2853i	−1.00814	+	0.732460i
$768$		0			0
$769$			18.1315i			0.653839i	0.945052	+	0.326919i	$0.106011\pi$
$769$			18.1315i			0.653839i	−0.945052	+	0.326919i	$0.893989\pi$
$770$	12.6800	−	11.3991i	0.456955	−	0.410796i
$771$		0			0
$772$	24.2492	+	7.87903i	0.872746	+	0.283573i
$773$	−8.15106	−	11.2190i	−0.293173	−	0.403518i	0.636868	−	0.770973i	$-0.280229\pi$
$773$	−8.15106	−	11.2190i	−0.293173	−	0.403518i	−0.930042	+	0.367454i	$0.880229\pi$
$774$		0			0
$775$	2.97849	+	9.16686i	0.106991	+	0.329283i
$776$	−10.2040	−	31.4048i	−0.366304	−	1.12737i
$777$		0			0
$778$	13.2649	+	18.2576i	0.475570	+	0.654566i
$779$	−9.77154	−	3.17496i	−0.350102	−	0.113755i
$780$		0			0
$781$	−2.34403	−	22.4714i	−0.0838761	−	0.804090i
$782$		−	1.72589i		−	0.0617175i
$783$		0			0
$784$	−3.08897	+	2.24427i	−0.110320	+	0.0801525i
$785$	−38.8506	+	53.4733i	−1.38664	+	1.90854i
$786$		0			0
$787$	−0.638949	+	0.207607i	−0.0227761	+	0.00740040i	−0.320383	−	0.947288i	$-0.603812\pi$
$787$	−0.638949	+	0.207607i	−0.0227761	+	0.00740040i	0.297607	+	0.954689i	$0.403812\pi$
$788$	−2.73161	−	1.98463i	−0.0973094	−	0.0706994i
$789$		0			0
$790$	−3.56286	+	10.9653i	−0.126761	+	0.390130i
$791$	−13.3435			−0.474441
$792$		0			0
$793$	9.28457			0.329705
$794$	−4.30660	+	13.2544i	−0.152836	+	0.470379i
$795$		0			0
$796$	−4.92194	−	3.57600i	−0.174454	−	0.126748i
$797$	4.99857	−	1.62413i	0.177058	−	0.0575297i	−0.219146	−	0.975692i	$-0.570327\pi$
$797$	4.99857	−	1.62413i	0.177058	−	0.0575297i	0.396204	+	0.918162i	$0.370327\pi$
$798$		0			0
$799$	−0.263855	+	0.363165i	−0.00933452	+	0.0128479i
$800$	−40.6977	+	29.5686i	−1.43888	+	1.04541i
$801$		0			0
$802$		−	17.0856i		−	0.603312i
$803$	−21.3609	−	23.7611i	−0.753810	−	0.838511i
$804$		0			0
$805$	70.2957	+	22.8404i	2.47760	+	0.805020i
$806$	2.42675	+	3.34014i	0.0854787	+	0.117651i
$807$		0			0
$808$	−4.54395	−	13.9849i	−0.159856	−	0.491985i
$809$	8.82483	+	27.1600i	0.310265	+	0.954896i	0.977660	+	0.210193i	$0.0674091\pi$
$809$	8.82483	+	27.1600i	0.310265	+	0.954896i	−0.667395	+	0.744704i	$0.732591\pi$
$810$		0			0
$811$	13.6775	+	18.8255i	0.480283	+	0.661053i	0.978559	−	0.205965i	$-0.0660335\pi$
$811$	13.6775	+	18.8255i	0.480283	+	0.661053i	−0.498276	+	0.867018i	$0.666033\pi$
$812$	−22.4896	−	7.30733i	−0.789231	−	0.256437i
$813$		0			0
$814$	−3.11596	−	7.01334i	−0.109214	−	0.245817i
$815$			5.48749i			0.192218i
$816$		0			0
$817$	−9.46594	+	6.87741i	−0.331171	+	0.240610i
$818$	−14.5777	+	20.0644i	−0.509696	+	0.701536i
$819$		0			0
$820$	23.9558	−	7.78372i	0.836574	−	0.271819i
$821$	−17.3792	−	12.6267i	−0.606539	−	0.440677i	0.241655	−	0.970362i	$-0.422310\pi$
$821$	−17.3792	−	12.6267i	−0.606539	−	0.440677i	−0.848194	+	0.529686i	$0.822310\pi$
$822$		0			0
$823$	14.9710	−	46.0760i	0.521856	−	1.60611i	−0.248593	−	0.968608i	$-0.579968\pi$
$823$	14.9710	−	46.0760i	0.521856	−	1.60611i	0.770450	−	0.637501i	$-0.220032\pi$
$824$	−19.6590			−0.684853
$825$		0			0
$826$	−7.70329			−0.268032
$827$	12.2819	−	37.7998i	0.427084	−	1.31443i	−0.473901	−	0.880578i	$-0.657155\pi$
$827$	12.2819	−	37.7998i	0.427084	−	1.31443i	0.900985	−	0.433851i	$-0.142845\pi$
$828$		0			0
$829$	27.8772	+	20.2540i	0.968215	+	0.703450i	0.955044	−	0.296464i	$-0.0958074\pi$
$829$	27.8772	+	20.2540i	0.968215	+	0.703450i	0.0131712	+	0.999913i	$0.495807\pi$
$830$	−29.5219	+	9.59224i	−1.02472	+	0.332952i
$831$		0			0
$832$	0.654963	−	0.901480i	0.0227068	−	0.0312532i
$833$	−0.523982	+	0.380695i	−0.0181549	+	0.0131903i
$834$		0			0
$835$			33.5457i			1.16090i
$836$	12.8795	+	2.74817i	0.445446	+	0.0950474i
$837$		0			0
$838$	14.9621	+	4.86147i	0.516856	+	0.167937i
$839$	15.4394	+	21.2505i	0.533026	+	0.733647i	0.987588	−	0.157068i	$-0.0502042\pi$
$839$	15.4394	+	21.2505i	0.533026	+	0.733647i	−0.454562	+	0.890715i	$0.650204\pi$
$840$		0			0
$841$	4.50507	+	13.8652i	0.155347	+	0.478110i
$842$	2.85741	+	8.79421i	0.0984729	+	0.303068i
$843$		0			0
$844$	−10.3352	−	14.2252i	−0.355753	−	0.489652i
$845$	−88.9674	−	28.9073i	−3.06057	−	0.994440i
$846$		0			0
$847$	21.1522	−	12.1680i	0.726797	−	0.418099i
$848$			10.8358i			0.372101i
$849$		0			0
$850$	−1.39864	+	1.01617i	−0.0479731	+	0.0348545i
$851$	19.5544	−	26.9144i	0.670317	−	0.922612i
$852$		0			0
$853$	−38.7864	+	12.6025i	−1.32802	+	0.431500i	−0.885242	−	0.465131i	$-0.846007\pi$
$853$	−38.7864	+	12.6025i	−1.32802	+	0.431500i	−0.442779	+	0.896631i	$0.646007\pi$
$854$	1.67661	+	1.21813i	0.0573726	+	0.0416836i
$855$		0			0
$856$	0.530097	−	1.63147i	0.0181183	−	0.0557625i
$857$	45.9406			1.56930			0.784651	−	0.619938i	$-0.212842\pi$
$857$	45.9406			1.56930			0.784651	+	0.619938i	$0.212842\pi$
$858$		0			0
$859$	−18.2550			−0.622853			−0.311427	−	0.950270i	$-0.600807\pi$
$859$	−18.2550			−0.622853			−0.311427	+	0.950270i	$0.600807\pi$
$860$	8.86415	−	27.2810i	0.302265	−	0.930276i
$861$		0			0
$862$	−7.82404	−	5.68449i	−0.266488	−	0.193615i
$863$	−18.5553	+	6.02899i	−0.631631	+	0.205229i	−0.607297	−	0.794475i	$-0.707746\pi$
$863$	−18.5553	+	6.02899i	−0.631631	+	0.205229i	−0.0243334	+	0.999704i	$0.507746\pi$
$864$		0			0
$865$	14.4714	−	19.9181i	0.492042	−	0.677237i
$866$	5.33481	−	3.87597i	0.181284	−	0.131711i
$867$		0			0
$868$		−	3.86236i		−	0.131097i
$869$	−8.26168	+	14.2838i	−0.280258	+	0.484544i
$870$		0			0
$871$	−16.4130	−	5.33289i	−0.556132	−	0.180698i
$872$	−5.79310	−	7.97352i	−0.196179	−	0.270017i
$873$		0			0
$874$	−4.20920	−	12.9546i	−0.142378	−	0.438196i
$875$	−10.0822	−	31.0297i	−0.340840	−	1.04900i
$876$		0			0
$877$	12.0397	+	16.5713i	0.406553	+	0.559572i	0.962373	−	0.271730i	$-0.0875959\pi$
$877$	12.0397	+	16.5713i	0.406553	+	0.559572i	−0.555821	+	0.831302i	$0.687596\pi$
$878$	−10.5155	−	3.41668i	−0.354880	−	0.115307i
$879$		0			0
$880$	−20.7855	+	9.23478i	−0.700678	+	0.311304i
$881$			38.0577i			1.28220i	0.767459	+	0.641099i	$0.221521\pi$
$881$			38.0577i			1.28220i	−0.767459	+	0.641099i	$0.778479\pi$
$882$		0			0
$883$	17.6981	−	12.8584i	0.595590	−	0.432721i	−0.248721	−	0.968575i	$-0.580010\pi$
$883$	17.6981	−	12.8584i	0.595590	−	0.432721i	0.844311	+	0.535854i	$0.180010\pi$
$884$	1.82428	−	2.51091i	0.0613573	−	0.0844511i
$885$		0			0
$886$	10.8133	−	3.51344i	0.363279	−	0.118036i
$887$	27.4074	+	19.9127i	0.920251	+	0.668602i	0.943587	−	0.331126i	$-0.107429\pi$
$887$	27.4074	+	19.9127i	0.920251	+	0.668602i	−0.0233353	+	0.999728i	$0.507429\pi$
$888$		0			0
$889$	7.73158	−	23.7954i	0.259309	−	0.798071i
$890$	7.07018			0.236993
$891$		0			0
$892$	−18.3383			−0.614011
$893$	−1.09480	+	3.36945i	−0.0366361	+	0.112754i
$894$		0			0
$895$	−3.85605	−	2.80158i	−0.128893	−	0.0936466i
$896$	23.9824	−	7.79235i	0.801195	−	0.260324i
$897$		0			0
$898$	−5.15709	+	7.09813i	−0.172094	+	0.236868i
$899$	−5.75849	+	4.18379i	−0.192056	+	0.139537i
$900$		0			0
$901$			1.83807i			0.0612349i
$902$	−8.55492	+	0.892380i	−0.284848	+	0.0297130i
$903$		0			0
$904$	−12.8350	−	4.17035i	−0.426886	−	0.138704i
$905$	−45.3840	−	62.4658i	−1.50862	−	2.07643i
$906$		0			0
$907$	−5.02928	−	15.4785i	−0.166995	−	0.513957i	0.832183	−	0.554501i	$-0.187091\pi$
$907$	−5.02928	−	15.4785i	−0.166995	−	0.513957i	−0.999178	+	0.0405443i	$0.987091\pi$
$908$	5.34588	+	16.4529i	0.177409	+	0.546010i
$909$		0			0
$910$	−18.6411	−	25.6572i	−0.617945	−	0.850529i
$911$	−15.7382	−	5.11364i	−0.521429	−	0.169423i	0.0364648	−	0.999335i	$-0.488390\pi$
$911$	−15.7382	−	5.11364i	−0.521429	−	0.169423i	−0.557894	+	0.829912i	$0.688390\pi$
$912$		0			0
$913$	−44.1856	+	4.60908i	−1.46233	+	0.152538i
$914$			5.37155i			0.177675i
$915$		0			0
$916$	−25.7021	+	18.6737i	−0.849221	+	0.616995i
$917$	22.4044	−	30.8371i	0.739860	−	1.01833i
$918$		0			0
$919$	30.9592	−	10.0592i	1.02125	−	0.331824i	0.249924	−	0.968265i	$-0.419594\pi$
$919$	30.9592	−	10.0592i	1.02125	−	0.331824i	0.771325	+	0.636441i	$0.219594\pi$
$920$	60.4783	+	43.9401i	1.99391	+	1.44866i
$921$		0			0
$922$	6.95652	−	21.4100i	0.229101	−	0.705100i
$923$	−42.0236			−1.38322
$924$		0			0
$925$	−33.3245			−1.09570
$926$	5.42868	−	16.7078i	0.178397	−	0.549051i
$927$		0			0
$928$	−30.0543	−	21.8357i	−0.986581	−	0.716793i
$929$	−49.3237	+	16.0262i	−1.61826	+	0.525804i	−0.971530	−	0.236917i	$-0.923863\pi$
$929$	−49.3237	+	16.0262i	−1.61826	+	0.525804i	−0.646728	+	0.762721i	$0.723863\pi$
$930$		0			0
$931$	−3.00458	+	4.13545i	−0.0984710	+	0.135534i
$932$	−26.3321	+	19.1314i	−0.862536	+	0.626669i
$933$		0			0
$934$			17.2613i			0.564808i
$935$	−3.52584	+	1.56649i	−0.115307	+	0.0512298i
$936$		0			0
$937$	4.46609	+	1.45112i	0.145901	+	0.0474061i	0.381057	−	0.924552i	$-0.375560\pi$
$937$	4.46609	+	1.45112i	0.145901	+	0.0474061i	−0.235156	+	0.971958i	$0.575560\pi$
$938$	−2.26419	−	3.11639i	−0.0739284	−	0.101754i
$939$		0			0
$940$	−2.68400	−	8.26051i	−0.0875425	−	0.269428i
$941$	−2.78471	−	8.57044i	−0.0907788	−	0.279388i	0.895352	−	0.445360i	$-0.146924\pi$
$941$	−2.78471	−	8.57044i	−0.0907788	−	0.279388i	−0.986131	+	0.165971i	$0.946924\pi$
$942$		0			0
$943$	−21.9163	−	30.1653i	−0.713694	−	0.982316i
$944$	9.77287	+	3.17540i	0.318080	+	0.103350i
$945$		0			0
$946$	−4.90427	+	8.47910i	−0.159452	+	0.275679i
$947$			32.5009i			1.05614i	0.849202	+	0.528068i	$0.177084\pi$
$947$			32.5009i			1.05614i	−0.849202	+	0.528068i	$0.822916\pi$
$948$		0			0
$949$	−48.0792	+	34.9316i	−1.56072	+	1.13393i
$950$	−8.01999	+	11.0386i	−0.260203	+	0.358138i
$951$		0			0
$952$	1.47493	−	0.479232i	0.0478026	−	0.0155320i
$953$	9.17192	+	6.66379i	0.297108	+	0.215861i	0.726345	−	0.687331i	$-0.241218\pi$
$953$	9.17192	+	6.66379i	0.297108	+	0.215861i	−0.429237	+	0.903192i	$0.641218\pi$
$954$		0			0
$955$	7.76447	−	23.8966i	0.251252	−	0.773275i
$956$	27.7709			0.898176
$957$		0			0
$958$	−4.60242			−0.148698
$959$	0.931991	−	2.86837i	0.0300956	−	0.0926246i
$960$		0			0
$961$	24.1390	+	17.5380i	0.778676	+	0.565742i
$962$	−13.5757	+	4.41102i	−0.437699	+	0.142217i
$963$		0			0
$964$	−19.4850	+	26.8187i	−0.627568	+	0.863774i
$965$	−47.6945	+	34.6521i	−1.53534	+	1.11549i
$966$		0			0
$967$			4.91092i			0.157925i	0.996878	+	0.0789623i	$0.0251607\pi$
$967$			4.91092i			0.157925i	−0.996878	+	0.0789623i	$0.974839\pi$
$968$	24.1491	−	5.09349i	0.776181	−	0.163711i
$969$		0			0
$970$	32.4370	+	10.5394i	1.04149	+	0.338400i
$971$	−6.66140	−	9.16863i	−0.213774	−	0.294235i	0.688641	−	0.725103i	$-0.258208\pi$
$971$	−6.66140	−	9.16863i	−0.213774	−	0.294235i	−0.902415	+	0.430867i	$0.858208\pi$
$972$		0			0
$973$	8.26991	+	25.4522i	0.265121	+	0.815959i
$974$	3.57249	+	10.9950i	0.114470	+	0.352303i
$975$		0			0
$976$	−1.62493	−	2.23652i	−0.0520126	−	0.0715892i
$977$	28.4040	+	9.22902i	0.908724	+	0.295262i	0.725833	−	0.687871i	$-0.241454\pi$
$977$	28.4040	+	9.22902i	0.908724	+	0.295262i	0.182891	+	0.983133i	$0.441454\pi$
$978$		0			0
$979$	9.89591	+	2.11155i	0.316275	+	0.0674854i
$980$		−	12.5318i		−	0.400313i
$981$		0			0
$982$	−10.7272	+	7.79379i	−0.342320	+	0.248710i
$983$	3.95270	−	5.44042i	0.126071	−	0.173522i	−0.741316	−	0.671157i	$-0.765798\pi$
$983$	3.95270	−	5.44042i	0.126071	−	0.173522i	0.867387	+	0.497634i	$0.165798\pi$
$984$		0			0
$985$	7.42484	−	2.41248i	0.236575	−	0.0768679i
$986$	−1.03286	−	0.750420i	−0.0328931	−	0.0238983i
$987$		0			0
$988$	7.56940	−	23.2962i	0.240815	−	0.741152i
$989$	−42.4618			−1.35021
$990$		0			0
$991$	−6.33993			−0.201395			−0.100697	−	0.994917i	$-0.532107\pi$
$991$	−6.33993			−0.201395			−0.100697	+	0.994917i	$0.532107\pi$
$992$	1.87503	−	5.77074i	0.0595322	−	0.183221i
$993$		0			0
$994$	−7.58865	−	5.51348i	−0.240697	−	0.174877i
$995$	13.3784	−	4.34692i	0.424125	−	0.137807i
$996$		0			0
$997$	3.96967	−	5.46378i	0.125721	−	0.173040i	−0.741517	−	0.670934i	$-0.765893\pi$
$997$	3.96967	−	5.46378i	0.125721	−	0.173040i	0.867238	+	0.497895i	$0.165893\pi$
$998$	5.99996	−	4.35922i	0.189925	−	0.137989i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.k.a.134.4	✓	32
3.2	odd	2	inner	297.2.k.a.134.5	yes	32
9.2	odd	6		891.2.u.e.134.4		64
9.4	even	3		891.2.u.e.431.4		64
9.5	odd	6		891.2.u.e.431.5		64
9.7	even	3		891.2.u.e.134.5		64
11.6	odd	10	inner	297.2.k.a.215.5	yes	32
33.17	even	10	inner	297.2.k.a.215.4	yes	32
99.50	even	30		891.2.u.e.512.5		64
99.61	odd	30		891.2.u.e.215.5		64
99.83	even	30		891.2.u.e.215.4		64
99.94	odd	30		891.2.u.e.512.4		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.k.a.134.4	✓	32	1.1	even	1	trivial
297.2.k.a.134.5	yes	32	3.2	odd	2	inner
297.2.k.a.215.4	yes	32	33.17	even	10	inner
297.2.k.a.215.5	yes	32	11.6	odd	10	inner
891.2.u.e.134.4		64	9.2	odd	6
891.2.u.e.134.5		64	9.7	even	3
891.2.u.e.215.4		64	99.83	even	30
891.2.u.e.215.5		64	99.61	odd	30
891.2.u.e.431.4		64	9.4	even	3
891.2.u.e.431.5		64	9.5	odd	6
891.2.u.e.512.4		64	99.94	odd	30
891.2.u.e.512.5		64	99.50	even	30

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.191808 + 0.590323i) q^{2} +(1.30634 + 0.949113i) q^{4} +(-3.55080 + 1.15372i) q^{5} +(-1.30394 + 1.79472i) q^{7} +(-1.81517 + 1.31880i) q^{8} -2.31741i q^{10} +(0.692107 - 3.24361i) q^{11} +(-5.86699 - 1.90630i) q^{13} +(-0.809360 - 1.11399i) q^{14} +(0.567603 + 1.74690i) q^{16} +(0.0962825 + 0.296327i) q^{17} +(1.44540 + 1.98943i) q^{19} +(-5.73357 - 1.86295i) q^{20} +(1.78203 + 1.03072i) q^{22} +8.92408i q^{23} +(7.23200 - 5.25435i) q^{25} +(2.25067 - 3.09778i) q^{26} +(-3.40679 + 1.10693i) q^{28} +(5.34066 + 3.88022i) q^{29} +(-0.333193 + 1.02546i) q^{31} -5.62745 q^{32} -0.193397 q^{34} +(2.55942 - 7.87708i) q^{35} +(-3.01593 - 2.19120i) q^{37} +(-1.45165 + 0.471668i) q^{38} +(4.92377 - 6.77699i) q^{40} +(-3.38021 + 2.45587i) q^{41} +4.75812i q^{43} +(3.98268 - 3.58037i) q^{44} +(-5.26809 - 1.71171i) q^{46} +(0.846838 + 1.16557i) q^{47} +(0.642357 + 1.97697i) q^{49} +(1.71462 + 5.27704i) q^{50} +(-5.85501 - 8.05873i) q^{52} +(5.61052 + 1.82297i) q^{53} +(1.28469 + 12.3159i) q^{55} -4.97736i q^{56} +(-3.31496 + 2.40846i) q^{58} +(3.28830 - 4.52596i) q^{59} +(-1.43139 + 0.465088i) q^{61} +(-0.541446 - 0.393383i) q^{62} +(-0.0558176 + 0.171789i) q^{64} +23.0319 q^{65} +2.79751 q^{67} +(-0.155470 + 0.478488i) q^{68} +(4.15911 + 3.02177i) q^{70} +(6.47873 - 2.10507i) q^{71} +(5.66251 - 7.79378i) q^{73} +(1.87199 - 1.36008i) q^{74} +3.97073i q^{76} +(4.91890 + 5.47161i) q^{77} +(-4.73172 - 1.53743i) q^{79} +(-4.03089 - 5.54804i) q^{80} +(-0.801405 - 2.46647i) q^{82} +(-4.13920 - 12.7392i) q^{83} +(-0.683759 - 0.941114i) q^{85} +(-2.80883 - 0.912645i) q^{86} +(3.02137 + 6.80044i) q^{88} +3.05090i q^{89} +(11.0715 - 8.04392i) q^{91} +(-8.46996 + 11.6579i) q^{92} +(-0.850495 + 0.276342i) q^{94} +(-7.42759 - 5.39646i) q^{95} +(-4.54792 + 13.9971i) q^{97} -1.29026 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{4} - 4 q^{16} + 36 q^{22} + 8 q^{25} - 100 q^{28} + 8 q^{31} - 64 q^{34} - 12 q^{37} - 60 q^{40} - 20 q^{46} + 100 q^{52} + 8 q^{55} + 24 q^{58} + 60 q^{61} + 36 q^{64} - 24 q^{67} + 8 q^{70}+ \cdots - 24 q^{97}+O(q^{100}) \) 32 * q - 8 * q^4 - 4 * q^16 + 36 * q^22 + 8 * q^25 - 100 * q^28 + 8 * q^31 - 64 * q^34 - 12 * q^37 - 60 * q^40 - 20 * q^46 + 100 * q^52 + 8 * q^55 + 24 * q^58 + 60 * q^61 + 36 * q^64 - 24 * q^67 + 8 * q^70 + 80 * q^73 - 60 * q^79 + 72 * q^82 - 20 * q^85 - 24 * q^88 + 24 * q^91 + 20 * q^94 - 24 * q^97

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