LMFDB - Embedded newform 297.2.t.a.35.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			35.9
Character	$\chi$	$=$	297.35
Dual form			297.2.t.a.17.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.65440 + 1.83740i) q^{2} +(-0.429934 + 4.09055i) q^{4} +(1.51955 + 1.36821i) q^{5} +(-0.441031 - 0.990572i) q^{7} +(-4.22672 + 3.07089i) q^{8} +5.05558i q^{10} +(-1.28919 - 3.05581i) q^{11} +(-0.231169 - 1.08757i) q^{13} +(1.09043 - 2.44916i) q^{14} +(-4.58875 - 0.975370i) q^{16} +(2.03372 + 6.25916i) q^{17} +(-4.19112 - 5.76858i) q^{19} +(-6.25003 + 5.62755i) q^{20} +(3.48191 - 7.42429i) q^{22} +(4.70965 - 2.71912i) q^{23} +(-0.0856067 - 0.814494i) q^{25} +(1.61585 - 2.22402i) q^{26} +(4.24160 - 1.37818i) q^{28} +(-6.76852 + 3.01354i) q^{29} +(1.16034 - 0.246638i) q^{31} +(-0.574983 - 0.995900i) q^{32} +(-8.13598 + 14.0919i) q^{34} +(0.685140 - 2.10865i) q^{35} +(0.780793 + 0.567279i) q^{37} +(3.66539 - 17.2443i) q^{38} +(-10.6243 - 1.11666i) q^{40} +(1.00893 + 0.449206i) q^{41} +(4.42893 + 2.55705i) q^{43} +(13.0542 - 3.95969i) q^{44} +(12.7877 + 4.15499i) q^{46} +(4.27162 - 0.448965i) q^{47} +(3.89719 - 4.32827i) q^{49} +(1.35492 - 1.50479i) q^{50} +(4.54813 - 0.478028i) q^{52} +(-10.3556 - 3.36474i) q^{53} +(2.22200 - 6.40733i) q^{55} +(4.90606 + 2.83251i) q^{56} +(-16.7349 - 7.45086i) q^{58} +(2.19385 + 0.230582i) q^{59} +(1.20666 - 5.67690i) q^{61} +(2.37284 + 1.72397i) q^{62} +(-2.02075 + 6.21923i) q^{64} +(1.13674 - 1.96890i) q^{65} +(0.496739 + 0.860378i) q^{67} +(-26.4778 + 5.62802i) q^{68} +(5.00792 - 2.22967i) q^{70} +(-6.12170 + 1.98906i) q^{71} +(-0.486222 + 0.669227i) q^{73} +(0.249427 + 2.37314i) q^{74} +(25.3986 - 14.6639i) q^{76} +(-2.45843 + 2.62474i) q^{77} +(-4.53104 + 4.07977i) q^{79} +(-5.63833 - 7.76049i) q^{80} +(0.843809 + 2.59698i) q^{82} +(-2.14558 - 0.456058i) q^{83} +(-5.47349 + 12.2937i) q^{85} +(2.62892 + 12.3681i) q^{86} +(14.8331 + 8.95712i) q^{88} +6.19738i q^{89} +(-0.975360 + 0.708641i) q^{91} +(9.09784 + 20.4341i) q^{92} +(7.89190 + 7.10590i) q^{94} +(1.52401 - 14.5000i) q^{95} +(-6.37180 - 7.07660i) q^{97} +14.4003 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

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

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	1.65440	+	1.83740i	1.16984	+	1.29924i	0.945834	+	0.324649i	$0.105246\pi$
$2$	1.65440	+	1.83740i	1.16984	+	1.29924i	0.224004	+	0.974588i	$0.428087\pi$
$3$		0			0
$3$		0			0
$4$	−0.429934	+	4.09055i	−0.214967	+	2.04527i
$5$	1.51955	+	1.36821i	0.679563	+	0.611881i	0.934875	−	0.354978i	$-0.115512\pi$
$5$	1.51955	+	1.36821i	0.679563	+	0.611881i	−0.255312	+	0.966859i	$0.582178\pi$
$6$		0			0
$7$	−0.441031	−	0.990572i	−0.166694	−	0.374401i	0.810812	−	0.585306i	$-0.199026\pi$
$7$	−0.441031	−	0.990572i	−0.166694	−	0.374401i	−0.977507	+	0.210905i	$0.932359\pi$
$8$	−4.22672	+	3.07089i	−1.49437	+	1.08572i
$9$		0			0
$10$			5.05558i			1.59872i
$11$	−1.28919	−	3.05581i	−0.388705	−	0.921362i
$11$	−1.28919	−	3.05581i	−0.388705	−	0.921362i
$12$		0			0
$13$	−0.231169	−	1.08757i	−0.0641148	−	0.301637i	0.934393	−	0.356244i	$-0.115943\pi$
$13$	−0.231169	−	1.08757i	−0.0641148	−	0.301637i	−0.998508	+	0.0546071i	$0.982609\pi$
$14$	1.09043	−	2.44916i	0.291431	−	0.654564i
$15$		0			0
$16$	−4.58875	−	0.975370i	−1.14719	−	0.243842i
$17$	2.03372	+	6.25916i	0.493251	+	1.51807i	0.819665	+	0.572843i	$0.194159\pi$
$17$	2.03372	+	6.25916i	0.493251	+	1.51807i	−0.326415	+	0.945227i	$0.605841\pi$
$18$		0			0
$19$	−4.19112	−	5.76858i	−0.961508	−	1.32340i	−0.946221	−	0.323520i	$-0.895134\pi$
$19$	−4.19112	−	5.76858i	−0.961508	−	1.32340i	−0.0152869	−	0.999883i	$-0.504866\pi$
$20$	−6.25003	+	5.62755i	−1.39755	+	1.25836i
$21$		0			0
$22$	3.48191	−	7.42429i	0.742347	−	1.58287i
$23$	4.70965	−	2.71912i	0.982029	−	0.566975i	0.0791471	−	0.996863i	$-0.474780\pi$
$23$	4.70965	−	2.71912i	0.982029	−	0.566975i	0.902882	+	0.429888i	$0.141447\pi$
$24$		0			0
$25$	−0.0856067	−	0.814494i	−0.0171213	−	0.162899i
$26$	1.61585	−	2.22402i	0.316894	−	0.436166i
$27$		0			0
$28$	4.24160	−	1.37818i	0.801587	−	0.260451i
$29$	−6.76852	+	3.01354i	−1.25688	+	0.559600i	−0.923647	−	0.383244i	$-0.874807\pi$
$29$	−6.76852	+	3.01354i	−1.25688	+	0.559600i	−0.333235	+	0.942844i	$0.608140\pi$
$30$		0			0
$31$	1.16034	−	0.246638i	0.208404	−	0.0442975i	−0.102527	−	0.994730i	$-0.532693\pi$
$31$	1.16034	−	0.246638i	0.208404	−	0.0442975i	0.310930	+	0.950433i	$0.399359\pi$
$32$	−0.574983	−	0.995900i	−0.101644	−	0.176052i
$33$		0			0
$34$	−8.13598	+	14.0919i	−1.39531	+	2.41675i
$35$	0.685140	−	2.10865i	0.115810	−	0.356426i
$36$		0			0
$37$	0.780793	+	0.567279i	0.128362	+	0.0932602i	0.650114	−	0.759837i	$-0.274721\pi$
$37$	0.780793	+	0.567279i	0.128362	+	0.0932602i	−0.521752	+	0.853097i	$0.674721\pi$
$38$	3.66539	−	17.2443i	0.594605	−	2.79740i
$39$		0			0
$40$	−10.6243	−	1.11666i	−1.67985	−	0.176560i
$41$	1.00893	+	0.449206i	0.157569	+	0.0701541i	0.484006	−	0.875065i	$-0.339181\pi$
$41$	1.00893	+	0.449206i	0.157569	+	0.0701541i	−0.326437	+	0.945219i	$0.605848\pi$
$42$		0			0
$43$	4.42893	+	2.55705i	0.675406	+	0.389946i	0.798122	−	0.602496i	$-0.205827\pi$
$43$	4.42893	+	2.55705i	0.675406	+	0.389946i	−0.122716	+	0.992442i	$0.539160\pi$
$44$	13.0542	−	3.95969i	1.96800	−	0.596945i
$45$		0			0
$46$	12.7877	+	4.15499i	1.88545	+	0.612620i
$47$	4.27162	−	0.448965i	0.623080	−	0.0654883i	0.212273	−	0.977211i	$-0.431914\pi$
$47$	4.27162	−	0.448965i	0.623080	−	0.0654883i	0.410807	+	0.911722i	$0.365247\pi$
$48$		0			0
$49$	3.89719	−	4.32827i	0.556741	−	0.618324i
$50$	1.35492	−	1.50479i	0.191615	−	0.212810i
$51$		0			0
$52$	4.54813	−	0.478028i	0.630712	−	0.0662905i
$53$	−10.3556	−	3.36474i	−1.42245	−	0.462183i	−0.506072	−	0.862491i	$-0.668903\pi$
$53$	−10.3556	−	3.36474i	−1.42245	−	0.462183i	−0.916380	+	0.400308i	$0.868903\pi$
$54$		0			0
$55$	2.22200	−	6.40733i	0.299615	−	0.863965i
$56$	4.90606	+	2.83251i	0.655600	+	0.378511i
$57$		0			0
$58$	−16.7349	−	7.45086i	−2.19740	−	0.978346i
$59$	2.19385	+	0.230582i	0.285614	+	0.0300193i	0.246252	−	0.969206i	$-0.420801\pi$
$59$	2.19385	+	0.230582i	0.285614	+	0.0300193i	0.0393620	+	0.999225i	$0.487467\pi$
$60$		0			0
$61$	1.20666	−	5.67690i	0.154497	−	0.726853i	−0.830878	−	0.556455i	$-0.812161\pi$
$61$	1.20666	−	5.67690i	0.154497	−	0.726853i	0.985375	−	0.170398i	$-0.0545054\pi$
$62$	2.37284	+	1.72397i	0.301352	+	0.218945i
$63$		0			0
$64$	−2.02075	+	6.21923i	−0.252594	+	0.777404i
$65$	1.13674	−	1.96890i	0.140996	−	0.244212i
$66$		0			0
$67$	0.496739	+	0.860378i	0.0606864	+	0.105112i	0.894772	−	0.446523i	$-0.147338\pi$
$67$	0.496739	+	0.860378i	0.0606864	+	0.105112i	−0.834086	+	0.551634i	$0.814004\pi$
$68$	−26.4778	+	5.62802i	−3.21090	+	0.682498i
$69$		0			0
$70$	5.00792	−	2.22967i	0.598561	−	0.266497i
$71$	−6.12170	+	1.98906i	−0.726512	+	0.236058i	−0.648844	−	0.760921i	$-0.724747\pi$
$71$	−6.12170	+	1.98906i	−0.726512	+	0.236058i	−0.0776676	+	0.996979i	$0.524747\pi$
$72$		0			0
$73$	−0.486222	+	0.669227i	−0.0569080	+	0.0783271i	−0.836523	−	0.547933i	$-0.815415\pi$
$73$	−0.486222	+	0.669227i	−0.0569080	+	0.0783271i	0.779615	+	0.626260i	$0.215415\pi$
$74$	0.249427	+	2.37314i	0.0289953	+	0.275872i
$75$		0			0
$76$	25.3986	−	14.6639i	2.91341	−	1.68206i
$77$	−2.45843	+	2.62474i	−0.280164	+	0.299117i
$78$		0			0
$79$	−4.53104	+	4.07977i	−0.509782	+	0.459010i	−0.883432	−	0.468560i	$-0.844773\pi$
$79$	−4.53104	+	4.07977i	−0.509782	+	0.459010i	0.373650	+	0.927570i	$0.378106\pi$
$80$	−5.63833	−	7.76049i	−0.630384	−	0.867649i
$81$		0			0
$82$	0.843809	+	2.59698i	0.0931831	+	0.286788i
$83$	−2.14558	−	0.456058i	−0.235508	−	0.0500589i	0.0886454	−	0.996063i	$-0.471746\pi$
$83$	−2.14558	−	0.456058i	−0.235508	−	0.0500589i	−0.324154	+	0.946004i	$0.605080\pi$
$84$		0			0
$85$	−5.47349	+	12.2937i	−0.593683	+	1.33343i
$86$	2.62892	+	12.3681i	0.283484	+	1.33369i
$87$		0			0
$88$	14.8331	+	8.95712i	1.58122	+	0.954832i
$89$			6.19738i			0.656921i	0.944518	+	0.328460i	$0.106530\pi$
$89$			6.19738i			0.656921i	−0.944518	+	0.328460i	$0.893470\pi$
$90$		0			0
$91$	−0.975360	+	0.708641i	−0.102246	+	0.0742857i
$92$	9.09784	+	20.4341i	0.948515	+	2.13040i
$93$		0			0
$94$	7.89190	+	7.10590i	0.813988	+	0.732918i
$95$	1.52401	−	14.5000i	0.156360	−	1.48766i
$96$		0			0
$97$	−6.37180	−	7.07660i	−0.646958	−	0.718520i	0.327056	−	0.945005i	$-0.393943\pi$
$97$	−6.37180	−	7.07660i	−0.646958	−	0.718520i	−0.974015	+	0.226485i	$0.927277\pi$
$98$	14.4003			1.45465
$99$		0			0
$100$	3.36853			0.336853
$101$	−2.38335	−	2.64698i	−0.237152	−	0.263384i	0.612807	−	0.790232i	$-0.290040\pi$
$101$	−2.38335	−	2.64698i	−0.237152	−	0.263384i	−0.849959	+	0.526849i	$0.823374\pi$
$102$		0			0
$103$	−0.550597	+	5.23858i	−0.0542520	+	0.516173i	0.933325	+	0.359034i	$0.116894\pi$
$103$	−0.550597	+	5.23858i	−0.0542520	+	0.516173i	−0.987576	+	0.157139i	$0.949773\pi$
$104$	4.31689	+	3.88694i	0.423306	+	0.381146i
$105$		0			0
$106$	−10.9500	−	24.5940i	−1.06355	−	2.38878i
$107$	−8.88743	+	6.45709i	−0.859180	+	0.624231i	−0.927662	−	0.373422i	$-0.878185\pi$
$107$	−8.88743	+	6.45709i	−0.859180	+	0.624231i	0.0684817	+	0.997652i	$0.478185\pi$
$108$		0			0
$109$			2.65252i			0.254065i	0.991899	+	0.127033i	$0.0405453\pi$
$109$			2.65252i			0.254065i	−0.991899	+	0.127033i	$0.959455\pi$
$110$	15.4489	−	6.51759i	1.47300	−	0.621428i
$111$		0			0
$112$	1.05761	+	4.97566i	0.0999347	+	0.470156i
$113$	−3.76963	+	8.46673i	−0.354617	+	0.796483i	0.644865	+	0.764297i	$0.276914\pi$
$113$	−3.76963	+	8.46673i	−0.354617	+	0.796483i	−0.999482	+	0.0321862i	$0.989753\pi$
$114$		0			0
$115$	10.8769	+	2.31195i	1.01427	+	0.215590i
$116$	−9.41701	−	28.9826i	−0.874347	−	2.69096i
$117$		0			0
$118$	3.20583	+	4.41245i	0.295121	+	0.406199i
$119$	5.30321	−	4.77504i	0.486145	−	0.437727i
$120$		0			0
$121$	−7.67599	+	7.87903i	−0.697817	+	0.716276i
$122$	12.4270	−	7.17476i	1.12509	−	0.649572i
$123$		0			0
$124$	0.510015	+	4.85247i	0.0458007	+	0.435765i
$125$	6.99369	−	9.62600i	0.625535	−	0.860975i
$126$		0			0
$127$	−11.0254	+	3.58238i	−0.978349	+	0.317885i	−0.754182	−	0.656666i	$-0.771966\pi$
$127$	−11.0254	+	3.58238i	−0.978349	+	0.317885i	−0.224167	+	0.974551i	$0.571966\pi$
$128$	−16.8714	+	7.51165i	−1.49124	+	0.663942i
$129$		0			0
$130$	5.49828	−	1.16870i	0.482231	−	0.102501i
$131$	−5.18051	−	8.97291i	−0.452624	−	0.783967i	0.545924	−	0.837834i	$-0.316179\pi$
$131$	−5.18051	−	8.97291i	−0.452624	−	0.783967i	−0.998548	+	0.0538672i	$0.982845\pi$
$132$		0			0
$133$	−3.86578	+	6.69573i	−0.335206	+	0.580593i
$134$	−0.759051	+	2.33612i	−0.0655720	+	0.201810i
$135$		0			0
$136$	−27.8172	−	20.2104i	−2.38531	−	1.73303i
$137$	−0.0609871	+	0.286922i	−0.00521048	+	0.0245134i	−0.980676	−	0.195639i	$-0.937322\pi$
$137$	−0.0609871	+	0.286922i	−0.00521048	+	0.0245134i	0.975466	+	0.220152i	$0.0706554\pi$
$138$		0			0
$139$	−2.07215	−	0.217791i	−0.175757	−	0.0184728i	0.0162410	−	0.999868i	$-0.494830\pi$
$139$	−2.07215	−	0.217791i	−0.175757	−	0.0184728i	−0.191998	+	0.981395i	$0.561497\pi$
$140$	8.33095	+	3.70918i	0.704094	+	0.313483i
$141$		0			0
$142$	−13.7824	−	7.95730i	−1.15660	−	0.667762i
$143$	−3.02538	+	2.10849i	−0.252995	+	0.176321i
$144$		0			0
$145$	−14.4082	−	4.68152i	−1.19654	−	0.388779i
$146$	−2.03404	+	0.213787i	−0.168339	+	0.0176931i
$147$		0			0
$148$	−2.65617	+	2.94998i	−0.218336	+	0.242487i
$149$	−11.2077	+	12.4474i	−0.918171	+	1.01973i	0.0815630	+	0.996668i	$0.474009\pi$
$149$	−11.2077	+	12.4474i	−0.918171	+	1.01973i	−0.999734	+	0.0230640i	$0.992658\pi$
$150$		0			0
$151$	−9.63700	+	1.01289i	−0.784248	+	0.0824278i	−0.488185	−	0.872740i	$-0.662341\pi$
$151$	−9.63700	+	1.01289i	−0.784248	+	0.0824278i	−0.296064	+	0.955168i	$0.595674\pi$
$152$	35.4294	+	11.5117i	2.87370	+	0.933723i
$153$		0			0
$154$	−8.88994	−	0.174742i	−0.716371	−	0.0140811i
$155$	2.10065	+	1.21281i	0.168728	+	0.0974152i
$156$		0			0
$157$	2.69509	+	1.19993i	0.215092	+	0.0957651i	0.511454	−	0.859310i	$-0.329107\pi$
$157$	2.69509	+	1.19993i	0.215092	+	0.0957651i	−0.296362	+	0.955076i	$0.595774\pi$
$158$	−14.9923	−	1.57576i	−1.19273	−	0.125360i
$159$		0			0
$160$	0.488883	−	2.30001i	0.0386496	−	0.181832i
$161$	−4.77058	−	3.46603i	−0.375975	−	0.273162i
$162$		0			0
$163$	6.82701	−	21.0114i	0.534733	−	1.64574i	−0.209493	−	0.977810i	$-0.567181\pi$
$163$	6.82701	−	21.0114i	0.534733	−	1.64574i	0.744226	−	0.667928i	$-0.232819\pi$
$164$	−2.27127	+	3.93396i	−0.177357	+	0.307190i
$165$		0			0
$166$	−2.71170	−	4.69680i	−0.210469	−	0.364542i
$167$	11.3999	−	2.42313i	0.882152	−	0.187507i	0.255503	−	0.966808i	$-0.417759\pi$
$167$	11.3999	−	2.42313i	0.882152	−	0.187507i	0.626650	+	0.779301i	$0.284426\pi$
$168$		0			0
$169$	10.7467	−	4.78475i	0.826672	−	0.368058i
$170$	−31.6437	+	10.2817i	−2.42696	+	0.788567i
$171$		0			0
$172$	−12.3639	+	17.0174i	−0.942736	+	1.29756i
$173$	−1.25808	−	11.9699i	−0.0956503	−	0.910052i	−0.932147	−	0.362080i	$-0.882067\pi$
$173$	−1.25808	−	11.9699i	−0.0956503	−	0.910052i	0.836497	−	0.547972i	$-0.184600\pi$
$174$		0			0
$175$	−0.769060	+	0.444017i	−0.0581354	+	0.0335645i
$176$	2.93522	+	15.2798i	0.221250	+	1.15176i
$177$		0			0
$178$	−11.3871	+	10.2530i	−0.853496	+	0.768491i
$179$	−1.69252	−	2.32955i	−0.126505	−	0.174119i	0.741067	−	0.671431i	$-0.234320\pi$
$179$	−1.69252	−	2.32955i	−0.126505	−	0.174119i	−0.867571	+	0.497313i	$0.834320\pi$
$180$		0			0
$181$	7.23838	+	22.2775i	0.538025	+	1.65587i	0.737021	+	0.675870i	$0.236232\pi$
$181$	7.23838	+	22.2775i	0.538025	+	1.65587i	−0.198996	+	0.980000i	$0.563768\pi$
$182$	−2.91569	−	0.619750i	−0.216126	−	0.0459389i
$183$		0			0
$184$	−11.5563	+	25.9558i	−0.851938	+	1.91349i
$185$	0.410297	+	1.93030i	0.0301656	+	0.141918i
$186$		0			0
$187$	16.5050	−	14.2839i	1.20696	−	1.04454i
$188$			17.6663i			1.28845i
$189$		0			0
$190$	29.1635	−	21.1885i	2.11574	−	1.53718i
$191$	−0.333646	−	0.749382i	−0.0241418	−	0.0542234i	0.901072	−	0.433669i	$-0.142781\pi$
$191$	−0.333646	−	0.749382i	−0.0241418	−	0.0542234i	−0.925214	+	0.379446i	$0.876115\pi$
$192$		0			0
$193$	−10.5813	−	9.52744i	−0.761659	−	0.685800i	0.193762	−	0.981049i	$-0.437931\pi$
$193$	−10.5813	−	9.52744i	−0.761659	−	0.685800i	−0.955421	+	0.295248i	$0.904598\pi$
$194$	2.46102	−	23.4151i	0.176691	−	1.68110i
$195$		0			0
$196$	16.0295	+	17.8025i	1.14496	+	1.27161i
$197$	13.4127			0.955618			0.477809	−	0.878464i	$-0.341431\pi$
$197$	13.4127			0.955618			0.477809	+	0.878464i	$0.341431\pi$
$198$		0			0
$199$	21.2586			1.50698			0.753489	−	0.657460i	$-0.228369\pi$
$199$	21.2586			1.50698			0.753489	+	0.657460i	$0.228369\pi$
$200$	2.86306	+	3.17975i	0.202449	+	0.224842i
$201$		0			0
$202$	0.920537	−	8.75832i	0.0647687	−	0.616233i
$203$	5.97025	+	5.37564i	0.419030	+	0.377296i
$204$		0			0
$205$	0.918515	+	2.06302i	0.0641519	+	0.144087i
$206$	−10.5363	+	7.65505i	−0.734097	+	0.533353i
$207$		0			0
$208$			5.21605i			0.361668i
$209$	−12.2246	+	20.2441i	−0.845591	+	1.40031i
$210$		0			0
$211$	3.10519	+	14.6088i	0.213770	+	1.00571i	0.945878	+	0.324522i	$0.105203\pi$
$211$	3.10519	+	14.6088i	0.213770	+	1.00571i	−0.732108	+	0.681189i	$0.761463\pi$
$212$	18.2159	−	40.9135i	1.25107	−	2.80995i
$213$		0			0
$214$	−26.5676	−	5.64712i	−1.81613	−	0.386030i
$215$	3.23141	+	9.94525i	0.220380	+	0.678261i
$216$		0			0
$217$	−0.756060	−	1.04063i	−0.0513247	−	0.0706424i
$218$	−4.87373	+	4.38833i	−0.330091	+	0.297215i
$219$		0			0
$220$	25.2542	+	11.8439i	1.70264	+	0.798519i
$221$	6.33712	−	3.65874i	0.426280	−	0.246113i
$222$		0			0
$223$	2.62067	+	24.9340i	0.175493	+	1.66971i	0.628203	+	0.778049i	$0.283791\pi$
$223$	2.62067	+	24.9340i	0.175493	+	1.66971i	−0.452710	+	0.891658i	$0.649543\pi$
$224$	−0.732925	+	1.00879i	−0.0489706	+	0.0674023i
$225$		0			0
$226$	−21.7932	+	7.08105i	−1.44966	+	0.471025i
$227$	−2.66748	+	1.18764i	−0.177047	+	0.0788264i	−0.493346	−	0.869833i	$-0.664226\pi$
$227$	−2.66748	+	1.18764i	−0.177047	+	0.0788264i	0.316299	+	0.948660i	$0.397560\pi$
$228$		0			0
$229$	3.27567	−	0.696264i	0.216462	−	0.0460104i	−0.0984040	−	0.995147i	$-0.531374\pi$
$229$	3.27567	−	0.696264i	0.216462	−	0.0460104i	0.314866	+	0.949136i	$0.398040\pi$
$230$	13.7467	+	23.8100i	0.906432	+	1.56999i
$231$		0			0
$232$	19.3544	−	33.5228i	1.27068	−	2.20088i
$233$	−3.74639	+	11.5302i	−0.245434	+	0.755369i	0.750131	+	0.661290i	$0.229991\pi$
$233$	−3.74639	+	11.5302i	−0.245434	+	0.755369i	−0.995565	+	0.0940790i	$0.970009\pi$
$234$		0			0
$235$	7.10521	+	5.16224i	0.463493	+	0.336747i
$236$	−1.88642	+	8.87490i	−0.122795	+	0.577707i
$237$		0			0
$238$	17.5473	+	1.84429i	1.13742	+	0.119548i
$239$	−6.20840	−	2.76416i	−0.401588	−	0.178798i	0.195996	−	0.980605i	$-0.437206\pi$
$239$	−6.20840	−	2.76416i	−0.401588	−	0.178798i	−0.597584	+	0.801806i	$0.703873\pi$
$240$		0			0
$241$	2.82339	+	1.63009i	0.181871	+	0.105003i	0.588171	−	0.808736i	$-0.299848\pi$
$241$	2.82339	+	1.63009i	0.181871	+	0.105003i	−0.406301	+	0.913739i	$0.633181\pi$
$242$	−27.1761	−	1.06877i	−1.74695	−	0.0687032i
$243$		0			0
$244$	22.7029	+	7.37661i	1.45340	+	0.472239i
$245$	11.8439	−	1.24485i	0.756681	−	0.0795304i
$246$		0			0
$247$	−5.30485	+	5.89164i	−0.337540	+	0.374876i
$248$	−4.14704	+	4.60576i	−0.263337	+	0.292466i
$249$		0			0
$250$	29.2572	−	3.07505i	1.85039	−	0.194483i
$251$	11.6389	+	3.78172i	0.734643	+	0.238700i	0.652360	−	0.757909i	$-0.273779\pi$
$251$	11.6389	+	3.78172i	0.734643	+	0.238700i	0.0822830	+	0.996609i	$0.473779\pi$
$252$		0			0
$253$	−14.3807	−	10.8864i	−0.904109	−	0.684419i
$254$	−24.8227	−	14.3314i	−1.55752	−	0.899233i
$255$		0			0
$256$	−29.7662	−	13.2528i	−1.86039	−	0.828297i
$257$	15.8233	+	1.66310i	0.987033	+	0.103741i	0.584267	−	0.811561i	$-0.301382\pi$
$257$	15.8233	+	1.66310i	0.987033	+	0.103741i	0.402766	+	0.915303i	$0.368049\pi$
$258$		0			0
$259$	0.217577	−	1.02362i	0.0135196	−	0.0636047i
$260$	7.56514	+	5.49640i	0.469170	+	0.340872i
$261$		0			0
$262$	7.91617	−	24.3635i	0.489063	−	1.50518i
$263$	5.95707	−	10.3180i	0.367329	−	0.636232i	−0.621818	−	0.783162i	$-0.713606\pi$
$263$	5.95707	−	10.3180i	0.367329	−	0.636232i	0.989147	+	0.146929i	$0.0469390\pi$
$264$		0			0
$265$	−11.1322	−	19.2815i	−0.683845	−	1.18445i
$266$	−18.6983	+	3.97444i	−1.14647	+	0.243689i
$267$		0			0
$268$	−3.73298	+	1.66203i	−0.228028	+	0.101525i
$269$	24.0428	−	7.81198i	1.46592	−	0.476305i	0.536045	−	0.844190i	$-0.319918\pi$
$269$	24.0428	−	7.81198i	1.46592	−	0.476305i	0.929872	+	0.367884i	$0.119918\pi$
$270$		0			0
$271$	4.66877	−	6.42601i	0.283608	−	0.390352i	−0.643317	−	0.765600i	$-0.722442\pi$
$271$	4.66877	−	6.42601i	0.283608	−	0.390352i	0.926925	+	0.375248i	$0.122442\pi$
$272$	−3.22727	−	30.7054i	−0.195682	−	1.86179i
$273$		0			0
$274$	−0.628087	+	0.362626i	−0.0379441	+	0.0219070i
$275$	−2.37858	+	1.31163i	−0.143434	+	0.0790945i
$276$		0			0
$277$	7.13066	−	6.42047i	0.428440	−	0.385769i	−0.426507	−	0.904484i	$-0.640256\pi$
$277$	7.13066	−	6.42047i	0.428440	−	0.385769i	0.854947	+	0.518715i	$0.173590\pi$
$278$	−3.02799	−	4.16767i	−0.181607	−	0.249960i
$279$		0			0
$280$	3.57953	+	11.0167i	0.213918	+	0.658371i
$281$	17.7500	+	3.77288i	1.05888	+	0.225071i	0.704261	−	0.709941i	$-0.251278\pi$
$281$	17.7500	+	3.77288i	1.05888	+	0.225071i	0.354615	+	0.935012i	$0.384612\pi$
$282$		0			0
$283$	7.89128	−	17.7241i	0.469088	−	1.05359i	−0.511816	−	0.859095i	$-0.671027\pi$
$283$	7.89128	−	17.7241i	0.469088	−	1.05359i	0.980904	−	0.194494i	$-0.0623064\pi$
$284$	−5.50442	−	25.8963i	−0.326627	−	1.53666i
$285$		0			0
$286$	−8.87932	−	2.07054i	−0.525045	−	0.122434i
$287$		−	1.19753i		−	0.0706882i
$288$		0			0
$289$	−21.2878	+	15.4665i	−1.25222	+	0.909792i
$290$	−15.2352	−	34.2188i	−0.894641	−	2.00940i
$291$		0			0
$292$	−2.52846	−	2.27664i	−0.147967	−	0.133230i
$293$	−1.60794	+	15.2985i	−0.0939368	+	0.893749i	0.841501	+	0.540256i	$0.181673\pi$
$293$	−1.60794	+	15.2985i	−0.0939368	+	0.893749i	−0.935437	+	0.353493i	$0.884994\pi$
$294$		0			0
$295$	3.01817	+	3.35202i	0.175725	+	0.195162i
$296$	−5.04225			−0.293075
$297$		0			0
$298$	−41.4129			−2.39899
$299$	−4.04594	−	4.49348i	−0.233983	−	0.259864i
$300$		0			0
$301$	0.579641	−	5.51492i	0.0334100	−	0.317874i
$302$	−17.8046	−	16.0313i	−1.02454	−	0.922498i
$303$		0			0
$304$	13.6055	+	30.5585i	0.780330	+	1.75265i
$305$	9.60077	−	6.97537i	0.549738	−	0.399408i
$306$		0			0
$307$			5.86988i			0.335012i	0.985871	+	0.167506i	$0.0535713\pi$
$307$			5.86988i			0.335012i	−0.985871	+	0.167506i	$0.946429\pi$
$308$	−9.67968	−	11.1848i	−0.551551	−	0.637313i
$309$		0			0
$310$	1.24690	+	5.86620i	0.0708192	+	0.333178i
$311$	−10.7581	+	24.1632i	−0.610038	+	1.37017i	0.299320	+	0.954153i	$0.403240\pi$
$311$	−10.7581	+	24.1632i	−0.610038	+	1.37017i	−0.909358	+	0.416015i	$0.863426\pi$
$312$		0			0
$313$	−7.58871	−	1.61303i	−0.428939	−	0.0911738i	−0.0116171	−	0.999933i	$-0.503698\pi$
$313$	−7.58871	−	1.61303i	−0.428939	−	0.0911738i	−0.417322	+	0.908759i	$0.637031\pi$
$314$	2.25401	+	6.93714i	0.127201	+	0.391485i
$315$		0			0
$316$	−14.7404	−	20.2885i	−0.829214	−	1.14132i
$317$	−4.58523	+	4.12856i	−0.257532	+	0.231883i	−0.787775	−	0.615963i	$-0.788767\pi$
$317$	−4.58523	+	4.12856i	−0.257532	+	0.231883i	0.530243	+	0.847846i	$0.322101\pi$
$318$		0			0
$319$	17.9347	+	16.7983i	1.00415	+	0.940525i
$320$	−11.5798	+	6.68562i	−0.647332	+	0.373738i
$321$		0			0
$322$	−1.52398	−	14.4997i	−0.0849279	−	0.808035i
$323$	27.5829	−	37.9646i	1.53475	−	2.11241i
$324$		0			0
$325$	−0.866026	+	0.281389i	−0.0480385	+	0.0156086i
$326$	49.9009	−	22.2173i	2.76376	−	1.23050i
$327$		0			0
$328$	−5.64394	+	1.19966i	−0.311634	+	0.0662399i
$329$	−2.32865	−	4.03334i	−0.128383	−	0.222365i
$330$		0			0
$331$	8.44643	−	14.6297i	0.464258	−	0.804118i	−0.534910	−	0.844909i	$-0.679654\pi$
$331$	8.44643	−	14.6297i	0.464258	−	0.804118i	0.999168	+	0.0407908i	$0.0129877\pi$
$332$	2.78799	−	8.58054i	0.153011	−	0.470918i
$333$		0			0
$334$	23.3123	+	16.9374i	1.27559	+	0.926772i
$335$	−0.422356	+	1.98703i	−0.0230758	+	0.108563i
$336$		0			0
$337$	30.0047	+	3.15362i	1.63446	+	0.171789i	0.876798	−	0.480860i	$-0.159675\pi$
$337$	30.0047	+	3.15362i	1.63446	+	0.171789i	0.757661	+	0.652648i	$0.226342\pi$
$338$	26.5709	+	11.8301i	1.44527	+	0.643474i
$339$		0			0
$340$	−47.9345	−	27.6750i	−2.59962	−	1.50089i
$341$	−2.24958	−	3.22782i	−0.121822	−	0.174797i
$342$		0			0
$343$	−13.2250	−	4.29705i	−0.714081	−	0.232019i
$344$	−26.5723	+	2.79286i	−1.43268	+	0.150581i
$345$		0			0
$346$	19.9120	−	22.1146i	1.07048	−	1.18889i
$347$	11.8785	−	13.1925i	0.637673	−	0.708208i	−0.334520	−	0.942389i	$-0.608574\pi$
$347$	11.8785	−	13.1925i	0.637673	−	0.708208i	0.972193	+	0.234181i	$0.0752407\pi$
$348$		0			0
$349$	−9.27936	+	0.975300i	−0.496713	+	0.0522066i	−0.349573	−	0.936909i	$-0.613673\pi$
$349$	−9.27936	+	0.975300i	−0.496713	+	0.0522066i	−0.147140	+	0.989116i	$0.547007\pi$
$350$	−2.08817	−	0.678487i	−0.111617	−	0.0362667i
$351$		0			0
$352$	−2.30202	+	3.04094i	−0.122698	+	0.162083i
$353$	−12.6509	−	7.30399i	−0.673339	−	0.388752i	0.124002	−	0.992282i	$-0.460427\pi$
$353$	−12.6509	−	7.30399i	−0.673339	−	0.388752i	−0.797341	+	0.603530i	$0.793761\pi$
$354$		0			0
$355$	−12.0237	−	5.35328i	−0.638150	−	0.284123i
$356$	−25.3507	−	2.66446i	−1.34358	−	0.141216i
$357$		0			0
$358$	1.48021	−	6.96384i	0.0782315	−	0.368050i
$359$	−13.4671	−	9.78443i	−0.710767	−	0.516402i	0.172654	−	0.984983i	$-0.444766\pi$
$359$	−13.4671	−	9.78443i	−0.710767	−	0.516402i	−0.883421	+	0.468580i	$0.844766\pi$
$360$		0			0
$361$	−9.83971	+	30.2835i	−0.517880	+	1.59387i
$362$	−28.9574	+	50.1557i	−1.52197	+	2.63612i
$363$		0			0
$364$	−2.47939	−	4.29443i	−0.129955	−	0.225089i
$365$	−1.65448	+	0.351671i	−0.0865995	+	0.0184073i
$366$		0			0
$367$	26.9769	−	12.0109i	1.40818	−	0.626963i	0.444930	−	0.895565i	$-0.353228\pi$
$367$	26.9769	−	12.0109i	1.40818	−	0.626963i	0.963251	+	0.268602i	$0.0865617\pi$
$368$	−24.2636	+	7.88371i	−1.26483	+	0.410967i
$369$		0			0
$370$	−2.86793	+	3.94736i	−0.149096	+	0.205214i
$371$	1.23413	+	11.7419i	0.0640727	+	0.609611i
$372$		0			0
$373$	−6.04790	+	3.49176i	−0.313148	+	0.180796i	−0.648334	−	0.761356i	$-0.724534\pi$
$373$	−6.04790	+	3.49176i	−0.313148	+	0.180796i	0.335186	+	0.942152i	$0.391201\pi$
$374$	53.5511	+	6.69489i	2.76906	+	0.346185i
$375$		0			0
$376$	−16.6762	+	15.0153i	−0.860011	+	0.774357i
$377$	4.84209	+	6.66457i	0.249381	+	0.343243i
$378$		0			0
$379$	−10.0677	−	30.9850i	−0.517140	−	1.59159i	−0.779353	−	0.626585i	$-0.784452\pi$
$379$	−10.0677	−	30.9850i	−0.517140	−	1.59159i	0.262213	−	0.965010i	$-0.415548\pi$
$380$	58.6575	+	12.4680i	3.00907	+	0.639597i
$381$		0			0
$382$	0.824929	−	1.85282i	0.0422070	−	0.0947986i
$383$	−5.10003	−	23.9938i	−0.260600	−	1.22602i	−0.892526	−	0.450996i	$-0.851069\pi$
$383$	−5.10003	−	23.9938i	−0.260600	−	1.22602i	0.631926	−	0.775028i	$-0.282264\pi$
$384$		0			0
$385$	−7.32690	+	0.624778i	−0.373413	+	0.0318417i
$386$		−	35.2043i		−	1.79185i
$387$		0			0
$388$	31.6866	−	23.0217i	1.60864	−	1.16875i
$389$	11.1419	+	25.0252i	0.564918	+	1.26883i	0.939791	+	0.341750i	$0.111020\pi$
$389$	11.1419	+	25.0252i	0.564918	+	1.26883i	−0.374873	+	0.927076i	$0.622314\pi$
$390$		0			0
$391$	26.5975	+	23.9485i	1.34509	+	1.21113i
$392$	−3.18069	+	30.2622i	−0.160649	+	1.52847i
$393$		0			0
$394$	22.1901	+	24.6446i	1.11792	+	1.24158i
$395$	−12.4671			−0.627288
$396$		0			0
$397$	20.5147			1.02960			0.514801	−	0.857310i	$-0.327866\pi$
$397$	20.5147			1.02960			0.514801	+	0.857310i	$0.327866\pi$
$398$	35.1702	+	39.0604i	1.76292	+	1.95792i
$399$		0			0
$400$	−0.401604	+	3.82101i	−0.0200802	+	0.191050i
$401$	7.43411	+	6.69370i	0.371242	+	0.334267i	0.833542	−	0.552456i	$-0.186309\pi$
$401$	7.43411	+	6.69370i	0.371242	+	0.334267i	−0.462301	+	0.886723i	$0.652976\pi$
$402$		0			0
$403$	−0.536471	−	1.20493i	−0.0267235	−	0.0600220i
$404$	11.8523	−	8.61117i	0.589672	−	0.428422i
$405$		0			0
$406$			19.8632i			0.985795i
$407$	0.726911	−	3.11729i	0.0360316	−	0.154518i
$408$		0			0
$409$	−1.69115	−	7.95624i	−0.0836220	−	0.393411i	0.916354	−	0.400369i	$-0.131118\pi$
$409$	−1.69115	−	7.95624i	−0.0836220	−	0.393411i	−0.999976	+	0.00695894i	$0.997785\pi$
$410$	−2.27100	+	5.10074i	−0.112156	+	0.251908i
$411$		0			0
$412$	−21.1920	−	4.50449i	−1.04405	−	0.221920i
$413$	−0.739146	−	2.27486i	−0.0363710	−	0.111938i
$414$		0			0
$415$	−2.63634	−	3.62861i	−0.129413	−	0.178121i
$416$	−0.950188	+	0.855553i	−0.0465868	+	0.0419470i
$417$		0			0
$418$	−57.4207	+	11.0304i	−2.80854	+	0.539514i
$419$	−22.7014	+	13.1067i	−1.10904	+	0.640302i	−0.938579	−	0.345064i	$-0.887857\pi$
$419$	−22.7014	+	13.1067i	−1.10904	+	0.640302i	−0.170456	+	0.985365i	$0.554524\pi$
$420$		0			0
$421$	3.91539	+	37.2524i	0.190824	+	1.81557i	0.501611	+	0.865093i	$0.332741\pi$
$421$	3.91539	+	37.2524i	0.190824	+	1.81557i	−0.310787	+	0.950480i	$0.600593\pi$
$422$	−21.7049	+	29.8743i	−1.05658	+	1.45426i
$423$		0			0
$424$	54.1031	−	17.5791i	2.62748	−	0.853719i
$425$	4.92394	−	2.19228i	0.238846	−	0.106341i
$426$		0			0
$427$	−6.15556	+	1.30840i	−0.297888	+	0.0633181i
$428$	−22.5920	−	39.1306i	−1.09203	−	1.89145i
$429$		0			0
$430$	−12.9274	+	22.3908i	−0.623412	+	1.07978i
$431$	−7.37759	+	22.7059i	−0.355366	+	1.09370i	0.600431	+	0.799677i	$0.294996\pi$
$431$	−7.37759	+	22.7059i	−0.355366	+	1.09370i	−0.955797	+	0.294027i	$0.905004\pi$
$432$		0			0
$433$	17.3812	+	12.6282i	0.835286	+	0.606871i	0.921050	−	0.389445i	$-0.127333\pi$
$433$	17.3812	+	12.6282i	0.835286	+	0.606871i	−0.0857640	+	0.996315i	$0.527333\pi$
$434$	0.661221	−	3.11080i	0.0317396	−	0.149323i
$435$		0			0
$436$	−10.8502	−	1.14041i	−0.519633	−	0.0546156i
$437$	−35.4241	−	15.7718i	−1.69457	−	0.754469i
$438$		0			0
$439$	8.94708	+	5.16560i	0.427021	+	0.246541i	0.698077	−	0.716023i	$-0.254039\pi$
$439$	8.94708	+	5.16560i	0.427021	+	0.246541i	−0.271056	+	0.962564i	$0.587373\pi$
$440$	10.2844	+	33.9056i	0.490292	+	1.61638i
$441$		0			0
$442$	17.2067	+	5.59079i	0.818439	+	0.265927i
$443$	−31.5603	+	3.31712i	−1.49948	+	0.157601i	−0.818416	−	0.574627i	$-0.805147\pi$
$443$	−31.5603	+	3.31712i	−1.49948	+	0.157601i	−0.681060	+	0.732228i	$0.738481\pi$
$444$		0			0
$445$	−8.47930	+	9.41722i	−0.401957	+	0.446419i
$446$	−41.4782	+	46.0662i	−1.96405	+	2.18130i
$447$		0			0
$448$	7.05182	−	0.741176i	0.333167	−	0.0350173i
$449$	−8.43287	−	2.74001i	−0.397972	−	0.129309i	0.103192	−	0.994661i	$-0.467094\pi$
$449$	−8.43287	−	2.74001i	−0.397972	−	0.129309i	−0.501163	+	0.865353i	$0.667094\pi$
$450$		0			0
$451$	0.0719854	−	3.66222i	0.00338966	−	0.172447i
$452$	−33.0129	−	19.0600i	−1.55279	−	0.896507i
$453$		0			0
$454$	−6.59525	−	2.93640i	−0.309531	−	0.137812i
$455$	−2.45167	−	0.257681i	−0.114936	−	0.0120803i
$456$		0			0
$457$	−3.49450	+	16.4403i	−0.163466	+	0.769046i	0.817664	+	0.575696i	$0.195269\pi$
$457$	−3.49450	+	16.4403i	−0.163466	+	0.769046i	−0.981130	+	0.193350i	$0.938065\pi$
$458$	6.69858	+	4.86681i	0.313004	+	0.227411i
$459$		0			0
$460$	−14.1335	+	43.4983i	−0.658976	+	2.02812i
$461$	−4.98284	+	8.63053i	−0.232074	+	0.401964i	−0.958418	−	0.285367i	$-0.907884\pi$
$461$	−4.98284	+	8.63053i	−0.232074	+	0.401964i	0.726344	+	0.687331i	$0.241218\pi$
$462$		0			0
$463$	−17.6360	−	30.5465i	−0.819616	−	1.41962i	−0.905966	−	0.423352i	$-0.860854\pi$
$463$	−17.6360	−	30.5465i	−0.819616	−	1.41962i	0.0863496	−	0.996265i	$-0.472480\pi$
$464$	33.9984	−	7.22658i	1.57833	−	0.335485i
$465$		0			0
$466$	−27.3836	+	12.1920i	−1.26852	+	0.564782i
$467$	3.77750	−	1.22739i	0.174802	−	0.0567966i	−0.220308	−	0.975430i	$-0.570706\pi$
$467$	3.77750	−	1.22739i	0.174802	−	0.0567966i	0.395110	+	0.918634i	$0.370706\pi$
$468$		0			0
$469$	0.633189	−	0.871510i	0.0292379	−	0.0402426i
$470$	2.26978	+	21.5955i	0.104697	+	0.996127i
$471$		0			0
$472$	−9.98087	+	5.76246i	−0.459407	+	0.265239i
$473$	2.10413	−	16.8305i	0.0967479	−	0.773867i
$474$		0			0
$475$	−4.33968	+	3.90747i	−0.199118	+	0.179287i
$476$	17.2525	+	23.7460i	0.790766	+	1.08840i
$477$		0			0
$478$	−5.19232	−	15.9803i	−0.237491	−	0.730923i
$479$	33.0561	+	7.02630i	1.51037	+	0.321040i	0.887325	−	0.461144i	$-0.152561\pi$
$479$	33.0561	+	7.02630i	1.51037	+	0.321040i	0.623048	+	0.782184i	$0.285894\pi$
$480$		0			0
$481$	0.436458	−	0.980302i	0.0199008	−	0.0446979i
$482$	1.67591	+	7.88451i	0.0763354	+	0.359130i
$483$		0			0
$484$	−28.9294	−	34.7865i	−1.31497	−	1.58120i
$485$		−	19.4712i		−	0.884141i
$486$		0			0
$487$	12.5920	−	9.14862i	0.570598	−	0.414563i	−0.264725	−	0.964324i	$-0.585281\pi$
$487$	12.5920	−	9.14862i	0.570598	−	0.414563i	0.835322	+	0.549761i	$0.185281\pi$
$488$	12.3329	+	27.7002i	0.558286	+	1.25393i
$489$		0			0
$490$	21.8819	+	19.7026i	0.988524	+	0.890071i
$491$	−0.872254	+	8.29894i	−0.0393643	+	0.374526i	0.957050	+	0.289922i	$0.0936293\pi$
$491$	−0.872254	+	8.29894i	−0.0393643	+	0.374526i	−0.996415	+	0.0846043i	$0.973037\pi$
$492$		0			0
$493$	−32.6275	−	36.2365i	−1.46947	−	1.63201i
$494$	−19.6016			−0.881920
$495$		0			0
$496$	−5.56509			−0.249880
$497$	4.67017	+	5.18675i	0.209486	+	0.232657i
$498$		0			0
$499$	0.0190581	−	0.181325i	0.000853156	−	0.00811723i	−0.994087	−	0.108586i	$-0.965368\pi$
$499$	0.0190581	−	0.181325i	0.000853156	−	0.00811723i	0.994940	+	0.100469i	$0.0320343\pi$
$500$	36.3688	+	32.7466i	1.62646	+	1.46447i
$501$		0			0
$502$	12.3070	+	27.6419i	0.549286	+	1.23372i
$503$	11.2333	−	8.16148i	0.500869	−	0.363902i	−0.308480	−	0.951231i	$-0.599820\pi$
$503$	11.2333	−	8.16148i	0.500869	−	0.363902i	0.809349	+	0.587328i	$0.199820\pi$
$504$		0			0
$505$		−	7.28312i		−	0.324095i
$506$	−3.78893	−	44.4335i	−0.168439	−	1.97531i
$507$		0			0
$508$	−9.91369	−	46.6402i	−0.439849	−	2.06933i
$509$	10.4443	−	23.4583i	0.462935	−	1.03977i	−0.519722	−	0.854336i	$-0.673964\pi$
$509$	10.4443	−	23.4583i	0.462935	−	1.03977i	0.982657	−	0.185434i	$-0.0593689\pi$
$510$		0			0
$511$	0.877357	+	0.186488i	0.0388120	+	0.00824975i
$512$	−13.4807	−	41.4893i	−0.595768	−	1.83359i
$513$		0			0
$514$	23.1224	+	31.8252i	1.01988	+	1.40375i
$515$	−8.00413	+	7.20695i	−0.352704	+	0.317576i
$516$		0			0
$517$	−6.87887	−	12.4745i	−0.302533	−	0.548627i
$518$	2.24076	−	1.29370i	0.0984533	−	0.0568420i
$519$		0			0
$520$	1.24158	+	11.8128i	0.0544467	+	0.518026i
$521$	−23.3218	+	32.0997i	−1.02175	+	1.40631i	−0.110774	+	0.993846i	$0.535333\pi$
$521$	−23.3218	+	32.0997i	−1.02175	+	1.40631i	−0.910972	+	0.412468i	$0.864667\pi$
$522$		0			0
$523$	3.90330	−	1.26826i	0.170679	−	0.0554571i	−0.222431	−	0.974949i	$-0.571399\pi$
$523$	3.90330	−	1.26826i	0.170679	−	0.0554571i	0.393110	+	0.919491i	$0.371399\pi$
$524$	38.9314	−	17.3334i	1.70073	−	0.757212i
$525$		0			0
$526$	28.8136	−	6.12452i	1.25633	−	0.267042i
$527$	3.90356	+	6.76117i	0.170042	+	0.294521i
$528$		0			0
$529$	3.28719	−	5.69357i	0.142921	−	0.247547i
$530$	17.0107	−	52.3536i	0.738899	−	2.27410i
$531$		0			0
$532$	−25.7272	−	18.6919i	−1.11541	−	0.810396i
$533$	0.255307	−	1.20112i	0.0110586	−	0.0520264i
$534$		0			0
$535$	−22.3395	−	2.34798i	−0.965822	−	0.101512i
$536$	−4.74171	−	2.11114i	−0.204811	−	0.0911875i
$537$		0			0
$538$	54.1302	+	31.2521i	2.33372	+	1.34737i
$539$	−18.2506	−	6.32913i	−0.786108	−	0.272615i
$540$		0			0
$541$	23.5956	+	7.66668i	1.01445	+	0.329616i	0.768627	−	0.639697i	$-0.220940\pi$
$541$	23.5956	+	7.66668i	1.01445	+	0.329616i	0.245828	+	0.969314i	$0.420940\pi$
$542$	19.5312	−	2.05281i	0.838936	−	0.0881757i
$543$		0			0
$544$	5.06414	−	5.62429i	0.217123	−	0.241140i
$545$	−3.62919	+	4.03063i	−0.155458	+	0.172653i
$546$		0			0
$547$	−38.9111	+	4.08972i	−1.66372	+	0.174864i	−0.889146	−	0.457623i	$-0.848701\pi$
$547$	−38.9111	+	4.08972i	−1.66372	+	0.174864i	−0.774571	+	0.632487i	$0.782034\pi$
$548$	−1.14745	−	0.372828i	−0.0490165	−	0.0159264i
$549$		0			0
$550$	−6.34512	−	2.20043i	−0.270557	−	0.0938265i
$551$	45.7515	+	26.4146i	1.94908	+	1.12530i
$552$		0			0
$553$	6.03964	+	2.68902i	0.256831	+	0.114349i
$554$	23.5939	+	2.47982i	1.00241	+	0.105358i
$555$		0			0
$556$	1.78177	−	8.38258i	0.0755639	−	0.355500i
$557$	−4.19799	−	3.05002i	−0.177874	−	0.129233i	0.495285	−	0.868730i	$-0.335063\pi$
$557$	−4.19799	−	3.05002i	−0.177874	−	0.129233i	−0.673160	+	0.739497i	$0.735063\pi$
$558$		0			0
$559$	1.75712	−	5.40787i	0.0743184	−	0.228728i
$560$	−5.20065	+	9.00779i	−0.219768	+	0.380649i
$561$		0			0
$562$	22.4333	+	38.8557i	0.946294	+	1.63903i
$563$	−7.87812	+	1.67455i	−0.332023	+	0.0705737i	−0.370907	−	0.928670i	$-0.620953\pi$
$563$	−7.87812	+	1.67455i	−0.332023	+	0.0705737i	0.0388838	+	0.999244i	$0.487620\pi$
$564$		0			0
$565$	−17.3124	+	7.70797i	−0.728337	+	0.324277i
$566$	45.6216	−	14.8234i	1.91762	−	0.623072i
$567$		0			0
$568$	19.7665	−	27.2063i	0.829385	−	1.14155i
$569$	−3.17482	−	30.2064i	−0.133096	−	1.26632i	−0.833478	−	0.552552i	$-0.813654\pi$
$569$	−3.17482	−	30.2064i	−0.133096	−	1.26632i	0.700383	−	0.713767i	$-0.253013\pi$
$570$		0			0
$571$	−33.4911	+	19.3361i	−1.40156	+	0.809190i	−0.994553	−	0.104236i	$-0.966760\pi$
$571$	−33.4911	+	19.3361i	−1.40156	+	0.809190i	−0.407005	+	0.913426i	$0.633427\pi$
$572$	−7.32416	−	13.2820i	−0.306238	−	0.555347i
$573$		0			0
$574$	2.20035	−	1.98120i	0.0918408	−	0.0826938i
$575$	−2.61788	−	3.60320i	−0.109173	−	0.150264i
$576$		0			0
$577$	5.09511	+	15.6811i	0.212112	+	0.652815i	0.999346	+	0.0361598i	$0.0115125\pi$
$577$	5.09511	+	15.6811i	0.212112	+	0.652815i	−0.787234	+	0.616655i	$0.788487\pi$
$578$	−63.6366	−	13.5264i	−2.64693	−	0.562623i
$579$		0			0
$580$	25.3446	−	56.9248i	1.05238	−	2.36368i
$581$	0.494511	+	2.32649i	0.0205158	+	0.0965192i
$582$		0			0
$583$	3.06830	+	35.9826i	0.127076	+	1.49025i
$584$		−	4.32178i		−	0.178836i
$585$		0			0
$586$	−30.7697	+	22.3555i	−1.27108	+	0.923496i
$587$	−18.4063	−	41.3412i	−0.759709	−	1.70633i	−0.706460	−	0.707753i	$-0.749709\pi$
$587$	−18.4063	−	41.3412i	−0.759709	−	1.70633i	−0.0532493	−	0.998581i	$-0.516958\pi$
$588$		0			0
$589$	−6.28588	−	5.65983i	−0.259005	−	0.233209i
$590$	−1.16573	+	11.0912i	−0.0479923	+	0.456616i
$591$		0			0
$592$	−3.02956	−	3.36467i	−0.124514	−	0.138287i
$593$	4.03343			0.165633			0.0828166	−	0.996565i	$-0.473608\pi$
$593$	4.03343			0.165633			0.0828166	+	0.996565i	$0.473608\pi$
$594$		0			0
$595$	14.5917			0.598203
$596$	−46.0982	−	51.1972i	−1.88826	−	2.09712i
$597$		0			0
$598$	1.56269	−	14.8680i	0.0639033	−	0.607999i
$599$	4.60639	+	4.14761i	0.188212	+	0.169467i	0.757850	−	0.652429i	$-0.226250\pi$
$599$	4.60639	+	4.14761i	0.188212	+	0.169467i	−0.569638	+	0.821896i	$0.692917\pi$
$600$		0			0
$601$	−19.3713	−	43.5087i	−0.790174	−	1.77476i	−0.612165	−	0.790730i	$-0.709701\pi$
$601$	−19.3713	−	43.5087i	−0.790174	−	1.77476i	−0.178008	−	0.984029i	$-0.556965\pi$
$602$	11.0921	−	8.05885i	0.452079	−	0.328454i
$603$		0			0
$604$		−	39.8561i		−	1.62172i
$605$	−22.4442	+	1.47023i	−0.912486	+	0.0597732i
$606$		0			0
$607$	1.72601	+	8.12026i	0.0700568	+	0.329591i	0.999194	−	0.0401441i	$-0.0127817\pi$
$607$	1.72601	+	8.12026i	0.0700568	+	0.329591i	−0.929137	+	0.369735i	$0.879448\pi$
$608$	−3.33510	+	7.49077i	−0.135256	+	0.303791i
$609$		0			0
$610$	28.7001	+	6.10039i	1.16203	+	0.246997i
$611$	−1.47575	−	4.54188i	−0.0597023	−	0.183745i
$612$		0			0
$613$	−13.0470	−	17.9576i	−0.526962	−	0.725301i	0.459702	−	0.888073i	$-0.347956\pi$
$613$	−13.0470	−	17.9576i	−0.526962	−	0.725301i	−0.986664	+	0.162773i	$0.947956\pi$
$614$	−10.7853	+	9.71114i	−0.435260	+	0.391910i
$615$		0			0
$616$	2.33080	−	18.6436i	0.0939108	−	0.751174i
$617$	2.63944	−	1.52388i	0.106260	−	0.0613492i	−0.445928	−	0.895069i	$-0.647126\pi$
$617$	2.63944	−	1.52388i	0.106260	−	0.0613492i	0.552188	+	0.833720i	$0.313793\pi$
$618$		0			0
$619$	−2.58526	−	24.5971i	−0.103910	−	0.988642i	−0.914927	−	0.403619i	$-0.867752\pi$
$619$	−2.58526	−	24.5971i	−0.103910	−	0.988642i	0.811017	−	0.585023i	$-0.198915\pi$
$620$	−5.86420	+	8.07137i	−0.235512	+	0.324154i
$621$		0			0
$622$	−62.1957	+	20.2086i	−2.49382	+	0.810291i
$623$	6.13895	−	2.73324i	0.245952	−	0.109505i
$624$		0			0
$625$	19.7922	−	4.20696i	0.791688	−	0.168278i
$626$	−9.59099	−	16.6121i	−0.383333	−	0.663952i
$627$		0			0
$628$	−6.06710	+	10.5085i	−0.242104	+	0.419336i
$629$	−1.96277	+	6.04080i	−0.0782609	+	0.240862i
$630$		0			0
$631$	−15.6052	−	11.3378i	−0.621233	−	0.451352i	0.232119	−	0.972687i	$-0.425434\pi$
$631$	−15.6052	−	11.3378i	−0.621233	−	0.451352i	−0.853352	+	0.521335i	$0.825434\pi$
$632$	6.62292	−	31.1584i	0.263446	−	1.23941i
$633$		0			0
$634$	−15.1716	−	1.59460i	−0.602542	−	0.0633297i
$635$	−21.6551	−	9.64148i	−0.859357	−	0.382610i
$636$		0			0
$637$	−5.60819	−	3.23789i	−0.222204	−	0.128290i
$638$	−1.19400	+	60.7443i	−0.0472711	+	2.40489i
$639$		0			0
$640$	−35.9145	−	11.6693i	−1.41964	−	0.461270i
$641$	0.279901	−	0.0294188i	0.0110554	−	0.00116197i	−0.0989991	−	0.995088i	$-0.531564\pi$
$641$	0.279901	−	0.0294188i	0.0110554	−	0.00116197i	0.110055	+	0.993926i	$0.464897\pi$
$642$		0			0
$643$	8.19973	−	9.10672i	0.323366	−	0.359134i	−0.559441	−	0.828870i	$-0.688984\pi$
$643$	8.19973	−	9.10672i	0.323366	−	0.359134i	0.882807	+	0.469736i	$0.155651\pi$
$644$	16.2290	−	18.0241i	0.639512	−	0.710251i
$645$		0			0
$646$	115.389	−	12.1279i	4.53993	−	0.477166i
$647$	12.4773	+	4.05411i	0.490532	+	0.159383i	0.543830	−	0.839195i	$-0.316974\pi$
$647$	12.4773	+	4.05411i	0.490532	+	0.159383i	−0.0532987	+	0.998579i	$0.516974\pi$
$648$		0			0
$649$	−2.12366	−	7.00125i	−0.0833610	−	0.274823i
$650$	−1.94978	−	1.12571i	−0.0764766	−	0.0441538i
$651$		0			0
$652$	83.0129	+	36.9597i	3.25104	+	1.44745i
$653$	6.95495	+	0.730994i	0.272168	+	0.0286060i	0.239629	−	0.970864i	$-0.422974\pi$
$653$	6.95495	+	0.730994i	0.272168	+	0.0286060i	0.0325388	+	0.999470i	$0.489641\pi$
$654$		0			0
$655$	4.40477	−	20.7228i	0.172108	−	0.809707i
$656$	−4.19160	−	3.04538i	−0.163655	−	0.118902i
$657$		0			0
$658$	3.55833	−	10.9514i	0.138718	−	0.426931i
$659$	−4.59171	+	7.95307i	−0.178868	+	0.309808i	−0.941493	−	0.337033i	$-0.890577\pi$
$659$	−4.59171	+	7.95307i	−0.178868	+	0.309808i	0.762625	+	0.646840i	$0.223910\pi$
$660$		0			0
$661$	6.85052	+	11.8654i	0.266454	+	0.461512i	0.967944	−	0.251168i	$-0.0808145\pi$
$661$	6.85052	+	11.8654i	0.266454	+	0.461512i	−0.701489	+	0.712680i	$0.747481\pi$
$662$	40.8543	−	8.68385i	1.58785	−	0.337507i
$663$		0			0
$664$	10.4693	−	4.66123i	0.406287	−	0.180891i
$665$	−15.0354	+	4.88529i	−0.583047	+	0.189444i
$666$		0			0
$667$	−23.6832	+	32.5971i	−0.917016	+	1.26216i
$668$	5.01071	+	47.6737i	0.193870	+	1.84455i
$669$		0			0
$670$	−4.34971	+	2.51131i	−0.168044	+	0.0970202i
$671$	−18.9032	+	3.63126i	−0.729749	+	0.140183i
$672$		0			0
$673$	13.4171	−	12.0808i	0.517193	−	0.465682i	−0.368716	−	0.929542i	$-0.620202\pi$
$673$	13.4171	−	12.0808i	0.517193	−	0.465682i	0.885909	+	0.463860i	$0.153536\pi$
$674$	43.8453	+	60.3479i	1.68886	+	2.32451i
$675$		0			0
$676$	14.9519	+	46.0171i	0.575072	+	1.76989i
$677$	−25.8410	−	5.49267i	−0.993149	−	0.211100i	−0.317448	−	0.948276i	$-0.602826\pi$
$677$	−25.8410	−	5.49267i	−0.993149	−	0.211100i	−0.675702	+	0.737175i	$0.736159\pi$
$678$		0			0
$679$	−4.19972	+	9.43273i	−0.161171	+	0.361995i
$680$	−14.6176	−	68.7704i	−0.560559	−	2.63722i
$681$		0			0
$682$	2.20910	−	9.47349i	0.0845906	−	0.362759i
$683$			19.4399i			0.743848i	0.928263	+	0.371924i	$0.121302\pi$
$683$			19.4399i			0.743848i	−0.928263	+	0.371924i	$0.878698\pi$
$684$		0			0
$685$	−0.485241	+	0.352548i	−0.0185401	+	0.0134702i
$686$	−13.9840	−	31.4086i	−0.533912	−	1.19919i
$687$		0			0
$688$	−17.8292	−	16.0535i	−0.679733	−	0.612034i
$689$	−1.26548	+	12.0402i	−0.0482109	+	0.458696i
$690$		0			0
$691$	−18.1567	−	20.1651i	−0.690715	−	0.767117i	0.291154	−	0.956676i	$-0.405961\pi$
$691$	−18.1567	−	20.1651i	−0.690715	−	0.767117i	−0.981869	+	0.189559i	$0.939294\pi$
$692$	49.5042			1.88187
$693$		0			0
$694$	43.8917			1.66611
$695$	−2.85074	−	3.16607i	−0.108135	−	0.120096i
$696$		0			0
$697$	−0.759759	+	7.22863i	−0.0287779	+	0.273804i
$698$	−17.1438	−	15.4363i	−0.648902	−	0.584274i
$699$		0			0
$700$	−1.48563	−	3.33677i	−0.0561514	−	0.126118i
$701$	−39.8170	+	28.9287i	−1.50387	+	1.09262i	−0.535058	+	0.844815i	$0.679710\pi$
$701$	−39.8170	+	28.9287i	−1.50387	+	1.09262i	−0.968809	+	0.247808i	$0.920290\pi$
$702$		0			0
$703$		−	6.88160i		−	0.259545i
$704$	21.6099	−	1.84272i	0.814456	−	0.0694501i
$705$		0			0
$706$	−7.50930	−	35.3285i	−0.282616	−	1.32960i
$707$	−1.57089	+	3.52828i	−0.0590794	+	0.132695i
$708$		0			0
$709$	24.4648	+	5.20015i	0.918794	+	0.195296i	0.642951	−	0.765907i	$-0.277710\pi$
$709$	24.4648	+	5.20015i	0.918794	+	0.195296i	0.275843	+	0.961203i	$0.411043\pi$
$710$	−10.0559	−	30.9487i	−0.377390	−	1.16149i
$711$		0			0
$712$	−19.0315	−	26.1946i	−0.713235	−	0.981684i
$713$	4.79416	−	4.31668i	0.179543	−	0.161661i
$714$		0			0
$715$	−7.48206	−	0.935397i	−0.279813	−	0.0349819i
$716$	10.2568	−	5.92177i	0.383315	−	0.221307i
$717$		0			0
$718$	−4.30211	−	40.9318i	−0.160553	−	1.52756i
$719$	2.83956	−	3.90832i	0.105898	−	0.145756i	−0.752779	−	0.658273i	$-0.771287\pi$
$719$	2.83956	−	3.90832i	0.105898	−	0.145756i	0.858677	+	0.512518i	$0.171287\pi$
$720$		0			0
$721$	5.43203	−	1.76497i	0.202299	−	0.0657310i
$722$	−71.9217	+	32.0216i	−2.67665	+	1.19172i
$723$		0			0
$724$	−94.2390	+	20.0311i	−3.50237	+	0.744451i
$725$	3.03394	+	5.25493i	0.112678	+	0.195163i
$726$		0			0
$727$	−26.6643	+	46.1840i	−0.988926	+	1.71287i	−0.365934	+	0.930641i	$0.619250\pi$
$727$	−26.6643	+	46.1840i	−0.988926	+	1.71287i	−0.622991	+	0.782229i	$0.714083\pi$
$728$	1.94642	−	5.99045i	0.0721390	−	0.222021i
$729$		0			0
$730$	−3.38333	−	2.45814i	−0.125223	−	0.0909797i
$731$	−6.99773	+	32.9217i	−0.258820	+	1.21765i
$732$		0			0
$733$	39.8238	+	4.18566i	1.47093	+	0.154601i	0.805826	−	0.592152i	$-0.201722\pi$
$733$	39.8238	+	4.18566i	1.47093	+	0.154601i	0.665101	+	0.746753i	$0.268388\pi$
$734$	66.6994	+	29.6965i	2.46192	+	1.09612i
$735$		0			0
$736$	−5.41593	−	3.12689i	−0.199634	−	0.115259i
$737$	1.98876	−	2.62713i	0.0732570	−	0.0967716i
$738$		0			0
$739$	−6.09069	−	1.97899i	−0.224050	−	0.0727982i	0.194841	−	0.980835i	$-0.437581\pi$
$739$	−6.09069	−	1.97899i	−0.224050	−	0.0727982i	−0.418891	+	0.908037i	$0.637581\pi$
$740$	−8.07237	+	0.848440i	−0.296746	+	0.0311893i
$741$		0			0
$742$	−19.5329	+	21.6935i	−0.717075	+	0.796392i
$743$	12.6164	−	14.0120i	0.462852	−	0.514049i	−0.465856	−	0.884860i	$-0.654254\pi$
$743$	12.6164	−	14.0120i	0.462852	−	0.514049i	0.928708	+	0.370811i	$0.120920\pi$
$744$		0			0
$745$	−34.0613	+	3.57999i	−1.24791	+	0.131161i
$746$	−16.4214	−	5.33564i	−0.601230	−	0.195352i
$747$		0			0
$748$	51.3330	+	73.6555i	1.87692	+	2.69311i
$749$	10.3159	+	5.95586i	0.376933	+	0.217622i
$750$		0			0
$751$	17.6705	+	7.86740i	0.644804	+	0.287085i	0.702968	−	0.711222i	$-0.251858\pi$
$751$	17.6705	+	7.86740i	0.644804	+	0.287085i	−0.0581635	+	0.998307i	$0.518524\pi$
$752$	−20.0393	−	2.10622i	−0.730759	−	0.0768059i
$753$		0			0
$754$	−4.23471	+	19.9227i	−0.154219	+	0.725543i
$755$	−16.0297	−	11.6463i	−0.583382	−	0.423852i
$756$		0			0
$757$	−4.32387	+	13.3075i	−0.157154	+	0.483670i	−0.998373	−	0.0570248i	$-0.981839\pi$
$757$	−4.32387	+	13.3075i	−0.157154	+	0.483670i	0.841219	+	0.540695i	$0.181839\pi$
$758$	40.2760	−	69.7600i	1.46289	−	2.53380i
$759$		0			0
$760$	38.0863	+	65.9674i	1.38153	+	2.39289i
$761$	20.6551	−	4.39039i	0.748749	−	0.159151i	0.182294	−	0.983244i	$-0.441648\pi$
$761$	20.6551	−	4.39039i	0.748749	−	0.159151i	0.566455	+	0.824093i	$0.308315\pi$
$762$		0			0
$763$	2.62751	−	1.16984i	0.0951222	−	0.0423512i
$764$	3.20883	−	1.04261i	0.116091	−	0.0377204i
$765$		0			0
$766$	35.6486	−	49.0661i	1.28804	−	1.77283i
$767$	−0.256376	−	2.43926i	−0.00925720	−	0.0880764i
$768$		0			0
$769$	36.6834	−	21.1791i	1.32284	−	0.763740i	0.338656	−	0.940910i	$-0.390028\pi$
$769$	36.6834	−	21.1791i	1.32284	−	0.763740i	0.984180	+	0.177171i	$0.0566945\pi$
$770$	−13.2696	−	12.4288i	−0.478203	−	0.447903i
$771$		0			0
$772$	43.5217	−	39.1871i	1.56638	−	1.41038i
$773$	9.77676	+	13.4566i	0.351646	+	0.483999i	0.947797	−	0.318873i	$-0.103304\pi$
$773$	9.77676	+	13.4566i	0.351646	+	0.483999i	−0.596152	+	0.802872i	$0.703304\pi$
$774$		0			0
$775$	−0.300218	−	0.923977i	−0.0107842	−	0.0331902i
$776$	48.6633	+	10.3437i	1.74691	+	0.371317i
$777$		0			0
$778$	−27.5480	+	61.8738i	−0.987644	+	2.21828i
$779$	−1.63728	−	7.70278i	−0.0586615	−	0.275981i
$780$		0			0
$781$	13.9702	+	16.1425i	0.499894	+	0.577624i
$782$			88.4907i			3.16442i
$783$		0			0
$784$	−22.1049	+	16.0602i	−0.789461	+	0.573577i
$785$	2.45357	+	5.51081i	0.0875716	+	0.196689i
$786$		0			0
$787$	−28.1427	−	25.3398i	−1.00318	−	0.903267i	−0.00786598	−	0.999969i	$-0.502504\pi$
$787$	−28.1427	−	25.3398i	−1.00318	−	0.903267i	−0.995313	+	0.0967023i	$0.969171\pi$
$788$	−5.76659	+	54.8655i	−0.205426	+	1.95450i
$789$		0			0
$790$	−20.6256	−	22.9070i	−0.733826	−	0.814996i
$791$	10.0494			0.357317
$792$		0			0
$793$	−6.45295			−0.229151
$794$	33.9395	+	37.6936i	1.20447	+	1.33770i
$795$		0			0
$796$	−9.13977	+	86.9591i	−0.323951	+	3.08219i
$797$	−22.3660	−	20.1385i	−0.792246	−	0.713341i	0.170024	−	0.985440i	$-0.445616\pi$
$797$	−22.3660	−	20.1385i	−0.792246	−	0.713341i	−0.962269	+	0.272099i	$0.912282\pi$
$798$		0			0
$799$	11.4974	+	25.8237i	0.406750	+	0.913576i
$800$	−0.761931	+	0.553576i	−0.0269383	+	0.0195719i
$801$		0			0
$802$			24.7335i			0.873370i
$803$	2.67187	+	0.623044i	0.0942881	+	0.0219868i
$804$		0			0
$805$	−2.50688	−	11.7940i	−0.0883560	−	0.415682i
$806$	1.32640	−	2.97915i	0.0467206	−	0.104936i
$807$		0			0
$808$	18.2023	+	3.86902i	0.640356	+	0.136112i
$809$	−13.7550	−	42.3334i	−0.483599	−	1.48836i	−0.834000	−	0.551765i	$-0.813955\pi$
$809$	−13.7550	−	42.3334i	−0.483599	−	1.48836i	0.350401	−	0.936600i	$-0.386045\pi$
$810$		0			0
$811$	16.8211	+	23.1522i	0.590667	+	0.812984i	0.994814	−	0.101710i	$-0.0324314\pi$
$811$	16.8211	+	23.1522i	0.590667	+	0.812984i	−0.404147	+	0.914694i	$0.632431\pi$
$812$	−24.5561	+	22.1104i	−0.861751	+	0.775925i
$813$		0			0
$814$	6.93031	−	3.82162i	0.242907	−	0.133948i
$815$	39.1219	−	22.5870i	1.37038	−	0.791190i
$816$		0			0
$817$	−3.81166	−	36.2655i	−0.133353	−	1.26877i
$818$	11.8209	−	16.2701i	0.413309	−	0.568872i
$819$		0			0
$820$	−8.83378	+	2.87027i	−0.308489	+	0.100234i
$821$	5.68020	−	2.52899i	0.198240	−	0.0882623i	−0.305215	−	0.952283i	$-0.598728\pi$
$821$	5.68020	−	2.52899i	0.198240	−	0.0882623i	0.503456	+	0.864021i	$0.332062\pi$
$822$		0			0
$823$	31.1819	−	6.62791i	1.08693	−	0.231034i	0.370599	−	0.928793i	$-0.379153\pi$
$823$	31.1819	−	6.62791i	1.08693	−	0.231034i	0.716333	+	0.697759i	$0.245819\pi$
$824$	−13.7599	−	23.8329i	−0.479349	−	0.830257i
$825$		0			0
$826$	2.95698	−	5.12163i	0.102886	−	0.178204i
$827$	3.59606	−	11.0675i	0.125047	−	0.384856i	−0.868862	−	0.495054i	$-0.835148\pi$
$827$	3.59606	−	11.0675i	0.125047	−	0.384856i	0.993910	+	0.110198i	$0.0351484\pi$
$828$		0			0
$829$	32.8784	+	23.8875i	1.14191	+	0.829649i	0.987385	−	0.158340i	$-0.0506141\pi$
$829$	32.8784	+	23.8875i	1.14191	+	0.829649i	0.154529	+	0.987988i	$0.450614\pi$
$830$	2.30564	−	10.8472i	0.0800299	−	0.376511i
$831$		0			0
$832$	7.23096	+	0.760005i	0.250689	+	0.0263484i
$833$	35.0171	+	15.5906i	1.21327	+	0.540183i
$834$		0			0
$835$	20.6381	+	11.9154i	0.714210	+	0.412349i
$836$	−77.5535	−	58.7088i	−2.68225	−	2.03049i
$837$		0			0
$838$	−61.6394	−	20.0278i	−2.12930	−	0.691850i
$839$	−1.99712	+	0.209905i	−0.0689481	+	0.00724674i	−0.138940	−	0.990301i	$-0.544369\pi$
$839$	−1.99712	+	0.209905i	−0.0689481	+	0.00724674i	0.0699916	+	0.997548i	$0.477703\pi$
$840$		0			0
$841$	17.3266	−	19.2432i	0.597469	−	0.663557i
$842$	−61.9700	+	68.8246i	−2.13563	+	2.37185i
$843$		0			0
$844$	−61.0930	+	6.42113i	−2.10291	+	0.221025i
$845$	22.8767	+	7.43309i	0.786983	+	0.255706i
$846$		0			0
$847$	11.1901	+	4.12872i	0.384497	+	0.141865i
$848$	44.2375	+	25.5405i	1.51912	+	0.877065i
$849$		0			0
$850$	12.1743	+	5.42034i	0.417574	+	0.185916i
$851$	5.21976	+	0.548619i	0.178931	+	0.0188064i
$852$		0			0
$853$	−2.06462	+	9.71327i	−0.0706912	+	0.332576i	−0.999255	−	0.0385972i	$-0.987711\pi$
$853$	−2.06462	+	9.71327i	−0.0706912	+	0.332576i	0.928564	+	0.371173i	$0.121044\pi$
$854$	−12.5878	−	9.14560i	−0.430747	−	0.312956i
$855$		0			0
$856$	17.7356	−	54.5847i	0.606192	−	1.86567i
$857$	18.3785	−	31.8325i	0.627797	−	1.08738i	−0.360196	−	0.932877i	$-0.617290\pi$
$857$	18.3785	−	31.8325i	0.627797	−	1.08738i	0.987993	−	0.154500i	$-0.0493765\pi$
$858$		0			0
$859$	−16.6007	−	28.7532i	−0.566407	−	0.981045i	−0.996917	−	0.0784599i	$-0.975000\pi$
$859$	−16.6007	−	28.7532i	−0.566407	−	0.981045i	0.430510	−	0.902586i	$-0.358334\pi$
$860$	−42.0708	+	8.94243i	−1.43460	+	0.304934i
$861$		0			0
$862$	−53.9253	+	24.0091i	−1.83670	+	0.817752i
$863$	−0.486372	+	0.158032i	−0.0165563	+	0.00537947i	−0.317283	−	0.948331i	$-0.602771\pi$
$863$	−0.486372	+	0.158032i	−0.0165563	+	0.00537947i	0.300727	+	0.953710i	$0.402771\pi$
$864$		0			0
$865$	14.4655	−	19.9101i	0.491843	−	0.676964i
$866$	5.55247	+	52.8282i	0.188681	+	1.79518i
$867$		0			0
$868$	4.58179	−	2.64530i	0.155516	−	0.0897873i
$869$	18.3084	+	8.58643i	0.621069	+	0.291275i
$870$		0			0
$871$	0.820887	−	0.739130i	0.0278147	−	0.0250445i
$872$	−8.14560	−	11.2115i	−0.275845	−	0.379668i
$873$		0			0
$874$	−29.6266	−	91.1812i	−1.00213	−	3.08425i
$875$	−12.6197	−	2.68240i	−0.426623	−	0.0906816i
$876$		0			0
$877$	14.6037	−	32.8005i	0.493133	−	1.10759i	−0.479983	−	0.877278i	$-0.659357\pi$
$877$	14.6037	−	32.8005i	0.493133	−	1.10759i	0.973116	−	0.230317i	$-0.0739762\pi$
$878$	5.31080	+	24.9853i	0.179231	+	0.843214i
$879$		0			0
$880$	−16.4458	+	27.2344i	−0.554386	+	0.918072i
$881$		−	6.31663i		−	0.212813i	−0.994323	−	0.106406i	$-0.966066\pi$
$881$		−	6.31663i		−	0.212813i	0.994323	−	0.106406i	$-0.0339345\pi$
$882$		0			0
$883$	−20.5419	+	14.9246i	−0.691290	+	0.502252i	−0.877084	−	0.480337i	$-0.840514\pi$
$883$	−20.5419	+	14.9246i	−0.691290	+	0.502252i	0.185794	+	0.982589i	$0.440514\pi$
$884$	12.2417	+	27.4953i	0.411733	+	0.924767i
$885$		0			0
$886$	−58.3083	−	52.5010i	−1.95891	−	1.76381i
$887$	−4.01725	+	38.2216i	−0.134886	+	1.28336i	0.692375	+	0.721538i	$0.256564\pi$
$887$	−4.01725	+	38.2216i	−0.134886	+	1.28336i	−0.827261	+	0.561818i	$0.810102\pi$
$888$		0			0
$889$	8.41116	+	9.34154i	0.282101	+	0.313305i
$890$	−31.3314			−1.05023
$891$		0			0
$892$	−103.121			−3.45274
$893$	−20.4928	−	22.7595i	−0.685764	−	0.761618i
$894$		0			0
$895$	0.615446	−	5.85558i	0.0205721	−	0.195730i
$896$	14.8817	+	13.3995i	0.497162	+	0.447646i
$897$		0			0
$898$	−8.91687	−	20.0276i	−0.297560	−	0.668330i
$899$	−7.11054	+	5.16611i	−0.237150	+	0.172299i
$900$		0			0
$901$		−	71.6604i		−	2.38735i
$902$	6.84805	−	5.92651i	0.228015	−	0.197331i
$903$		0			0
$904$	−10.0672	−	47.3626i	−0.334831	−	1.57526i
$905$	−19.4811	+	43.7553i	−0.647574	+	1.45448i
$906$		0			0
$907$	25.5735	+	5.43581i	0.849154	+	0.180493i	0.611881	−	0.790950i	$-0.290413\pi$
$907$	25.5735	+	5.43581i	0.849154	+	0.180493i	0.237273	+	0.971443i	$0.423746\pi$
$908$	−3.71125	−	11.4221i	−0.123162	−	0.379055i
$909$		0			0
$910$	−3.58259	−	4.93101i	−0.118762	−	0.163461i
$911$	−24.8117	+	22.3406i	−0.822048	+	0.740176i	−0.968492	−	0.249043i	$-0.919884\pi$
$911$	−24.8117	+	22.3406i	−0.822048	+	0.740176i	0.146444	+	0.989219i	$0.453217\pi$
$912$		0			0
$913$	1.37243	+	7.14445i	0.0454209	+	0.236447i
$914$	−35.9887	+	20.7781i	−1.19040	+	0.687279i
$915$		0			0
$916$	1.43978	+	13.6986i	0.0475718	+	0.452615i
$917$	−6.60355	+	9.08901i	−0.218069	+	0.300146i
$918$		0			0
$919$	−17.6258	+	5.72696i	−0.581420	+	0.188915i	−0.584937	−	0.811079i	$-0.698881\pi$
$919$	−17.6258	+	5.72696i	−0.581420	+	0.188915i	0.00351649	+	0.999994i	$0.498881\pi$
$920$	−53.0732	+	23.6297i	−1.74977	+	0.779048i
$921$		0			0
$922$	−24.1013	+	5.12290i	−0.793735	+	0.168714i
$923$	3.57838	+	6.19794i	0.117784	+	0.204008i
$924$		0			0
$925$	0.395204	−	0.684514i	0.0129942	−	0.0225067i
$926$	26.9490	−	82.9406i	0.885600	−	2.72560i
$927$		0			0
$928$	6.89296	+	5.00803i	0.226273	+	0.164397i
$929$	7.01279	−	32.9926i	0.230082	−	1.08245i	−0.699727	−	0.714410i	$-0.746695\pi$
$929$	7.01279	−	32.9926i	0.230082	−	1.08245i	0.929809	−	0.368042i	$-0.119972\pi$
$930$		0			0
$931$	−41.3015	−	4.34097i	−1.35360	−	0.142269i
$932$	−45.5542	−	20.2820i	−1.49218	−	0.664360i
$933$		0			0
$934$	8.50470	+	4.91019i	0.278282	+	0.160666i
$935$	44.6235	+	0.877128i	1.45934	+	0.0286852i
$936$		0			0
$937$	−5.72211	−	1.85923i	−0.186933	−	0.0607383i	0.214054	−	0.976822i	$-0.431333\pi$
$937$	−5.72211	−	1.85923i	−0.186933	−	0.0607383i	−0.400988	+	0.916083i	$0.631333\pi$
$938$	2.64886	−	0.278406i	0.0864883	−	0.00909029i
$939$		0			0
$940$	−24.1712	+	26.8448i	−0.788376	+	0.875581i
$941$	29.0952	−	32.3135i	0.948477	−	1.05339i	−0.0500286	−	0.998748i	$-0.515931\pi$
$941$	29.0952	−	32.3135i	0.948477	−	1.05339i	0.998506	−	0.0546430i	$-0.0174021\pi$
$942$		0			0
$943$	5.97316	−	0.627804i	0.194513	−	0.0204441i
$944$	−9.84211	−	3.19790i	−0.320334	−	0.104083i
$945$		0			0
$946$	34.4054	−	23.9783i	1.11862	−	0.779601i
$947$	5.19891	+	3.00159i	0.168942	+	0.0975387i	0.582087	−	0.813127i	$-0.302236\pi$
$947$	5.19891	+	3.00159i	0.168942	+	0.0975387i	−0.413145	+	0.910665i	$0.635570\pi$
$948$		0			0
$949$	0.840229	+	0.374094i	0.0272750	+	0.0121436i
$950$	−14.3592	−	1.50921i	−0.465873	−	0.0489652i
$951$		0			0
$952$	−7.75159	+	36.4684i	−0.251230	+	1.18195i
$953$	4.38241	+	3.18400i	0.141960	+	0.103140i	0.656499	−	0.754327i	$-0.272037\pi$
$953$	4.38241	+	3.18400i	0.141960	+	0.103140i	−0.514539	+	0.857467i	$0.672037\pi$
$954$		0			0
$955$	0.518319	−	1.59522i	0.0167724	−	0.0516201i
$956$	13.9761	−	24.2073i	0.452020	−	0.782921i
$957$		0			0
$958$	41.7780	+	72.3616i	1.34979	+	2.33790i
$959$	0.311114	−	0.0661293i	0.0100464	−	0.00213543i
$960$		0			0
$961$	−27.0343	+	12.0365i	−0.872076	+	0.388273i
$962$	2.52328	−	0.819864i	0.0813539	−	0.0264335i
$963$		0			0
$964$	−7.88182	+	10.8484i	−0.253856	+	0.349403i
$965$	−3.04328	−	28.9548i	−0.0979665	−	0.932089i
$966$		0			0
$967$	−30.2152	+	17.4447i	−0.971654	+	0.560985i	−0.899740	−	0.436426i	$-0.856244\pi$
$967$	−30.2152	+	17.4447i	−0.971654	+	0.560985i	−0.0719138	+	0.997411i	$0.522911\pi$
$968$	8.24861	−	56.8746i	0.265120	−	1.82802i
$969$		0			0
$970$	35.7763	−	32.2132i	1.14871	−	1.03430i
$971$	−25.4555	−	35.0365i	−0.816907	−	1.12438i	−0.990221	−	0.139509i	$-0.955447\pi$
$971$	−25.4555	−	35.0365i	−0.816907	−	1.12438i	0.173314	−	0.984867i	$-0.444553\pi$
$972$		0			0
$973$	0.698143	+	2.14866i	0.0223814	+	0.0688830i
$974$	37.6419	+	8.00103i	1.20612	+	0.256369i
$975$		0			0
$976$	−11.0742	+	24.8730i	−0.354475	+	0.796165i
$977$	−6.74631	−	31.7389i	−0.215833	−	1.01542i	−0.943982	−	0.329997i	$-0.892952\pi$
$977$	−6.74631	−	31.7389i	−0.215833	−	1.01542i	0.728149	−	0.685419i	$-0.240381\pi$
$978$		0			0
$979$	18.9380	−	7.98958i	0.605262	−	0.255348i
$980$			48.9834i			1.56472i
$981$		0			0
$982$	−16.6915	+	12.1271i	−0.532648	+	0.386991i
$983$	7.26749	+	16.3230i	0.231797	+	0.520624i	0.991571	−	0.129563i	$-0.0413573\pi$
$983$	7.26749	+	16.3230i	0.231797	+	0.520624i	−0.759774	+	0.650187i	$0.774691\pi$
$984$		0			0
$985$	20.3813	+	18.3514i	0.649403	+	0.584725i
$986$	12.6019	−	119.900i	0.401328	−	3.81838i
$987$		0			0
$988$	−21.8193	−	24.2328i	−0.694164	−	0.770947i
$989$	27.8116			0.884358
$990$		0			0
$991$	21.5914			0.685875			0.342937	−	0.939358i	$-0.388578\pi$
$991$	21.5914			0.685875			0.342937	+	0.939358i	$0.388578\pi$
$992$	−0.912804	−	1.01377i	−0.0289815	−	0.0321873i
$993$		0			0
$994$	−1.80379	+	17.1619i	−0.0572128	+	0.544343i
$995$	32.3034	+	29.0861i	1.02409	+	0.922092i
$996$		0			0
$997$	9.72923	+	21.8522i	0.308128	+	0.692067i	0.999538	−	0.0303960i	$-0.00967684\pi$
$997$	9.72923	+	21.8522i	0.308128	+	0.692067i	−0.691410	+	0.722463i	$0.743010\pi$
$998$	0.364697	−	0.264968i	0.0115443	−	0.00838740i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.35.9		80
3.2	odd	2		99.2.p.a.2.2	✓	80
9.2	odd	6		891.2.k.a.728.2		80
9.4	even	3		99.2.p.a.68.2	yes	80
9.5	odd	6	inner	297.2.t.a.233.9		80
9.7	even	3		891.2.k.a.728.19		80
11.6	odd	10	inner	297.2.t.a.116.9		80
33.17	even	10		99.2.p.a.83.2	yes	80
99.50	even	30	inner	297.2.t.a.17.9		80
99.61	odd	30		891.2.k.a.809.2		80
99.83	even	30		891.2.k.a.809.19		80
99.94	odd	30		99.2.p.a.50.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.2	✓	80	3.2	odd	2
99.2.p.a.50.2	yes	80	99.94	odd	30
99.2.p.a.68.2	yes	80	9.4	even	3
99.2.p.a.83.2	yes	80	33.17	even	10
297.2.t.a.17.9		80	99.50	even	30	inner
297.2.t.a.35.9		80	1.1	even	1	trivial
297.2.t.a.116.9		80	11.6	odd	10	inner
297.2.t.a.233.9		80	9.5	odd	6	inner
891.2.k.a.728.2		80	9.2	odd	6
891.2.k.a.728.19		80	9.7	even	3
891.2.k.a.809.2		80	99.61	odd	30
891.2.k.a.809.19		80	99.83	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.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.65440 + 1.83740i) q^{2} +(-0.429934 + 4.09055i) q^{4} +(1.51955 + 1.36821i) q^{5} +(-0.441031 - 0.990572i) q^{7} +(-4.22672 + 3.07089i) q^{8} +5.05558i q^{10} +(-1.28919 - 3.05581i) q^{11} +(-0.231169 - 1.08757i) q^{13} +(1.09043 - 2.44916i) q^{14} +(-4.58875 - 0.975370i) q^{16} +(2.03372 + 6.25916i) q^{17} +(-4.19112 - 5.76858i) q^{19} +(-6.25003 + 5.62755i) q^{20} +(3.48191 - 7.42429i) q^{22} +(4.70965 - 2.71912i) q^{23} +(-0.0856067 - 0.814494i) q^{25} +(1.61585 - 2.22402i) q^{26} +(4.24160 - 1.37818i) q^{28} +(-6.76852 + 3.01354i) q^{29} +(1.16034 - 0.246638i) q^{31} +(-0.574983 - 0.995900i) q^{32} +(-8.13598 + 14.0919i) q^{34} +(0.685140 - 2.10865i) q^{35} +(0.780793 + 0.567279i) q^{37} +(3.66539 - 17.2443i) q^{38} +(-10.6243 - 1.11666i) q^{40} +(1.00893 + 0.449206i) q^{41} +(4.42893 + 2.55705i) q^{43} +(13.0542 - 3.95969i) q^{44} +(12.7877 + 4.15499i) q^{46} +(4.27162 - 0.448965i) q^{47} +(3.89719 - 4.32827i) q^{49} +(1.35492 - 1.50479i) q^{50} +(4.54813 - 0.478028i) q^{52} +(-10.3556 - 3.36474i) q^{53} +(2.22200 - 6.40733i) q^{55} +(4.90606 + 2.83251i) q^{56} +(-16.7349 - 7.45086i) q^{58} +(2.19385 + 0.230582i) q^{59} +(1.20666 - 5.67690i) q^{61} +(2.37284 + 1.72397i) q^{62} +(-2.02075 + 6.21923i) q^{64} +(1.13674 - 1.96890i) q^{65} +(0.496739 + 0.860378i) q^{67} +(-26.4778 + 5.62802i) q^{68} +(5.00792 - 2.22967i) q^{70} +(-6.12170 + 1.98906i) q^{71} +(-0.486222 + 0.669227i) q^{73} +(0.249427 + 2.37314i) q^{74} +(25.3986 - 14.6639i) q^{76} +(-2.45843 + 2.62474i) q^{77} +(-4.53104 + 4.07977i) q^{79} +(-5.63833 - 7.76049i) q^{80} +(0.843809 + 2.59698i) q^{82} +(-2.14558 - 0.456058i) q^{83} +(-5.47349 + 12.2937i) q^{85} +(2.62892 + 12.3681i) q^{86} +(14.8331 + 8.95712i) q^{88} +6.19738i q^{89} +(-0.975360 + 0.708641i) q^{91} +(9.09784 + 20.4341i) q^{92} +(7.89190 + 7.10590i) q^{94} +(1.52401 - 14.5000i) q^{95} +(-6.37180 - 7.07660i) q^{97} +14.4003 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Introduction

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