LMFDB - Embedded newform 297.2.t.a.206.9

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			206.9
Character	$\chi$	$=$	297.206
Dual form			297.2.t.a.62.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.79897 + 0.800953i) q^{2} +(1.25651 + 1.39549i) q^{4} +(0.804185 + 1.80623i) q^{5} +(0.0659410 + 0.310228i) q^{7} +(-0.0743474 - 0.228818i) q^{8} +3.89347i q^{10} +(2.31445 + 2.37557i) q^{11} +(-1.91314 + 0.201079i) q^{13} +(-0.129852 + 0.610907i) q^{14} +(0.442095 - 4.20626i) q^{16} +(-2.02504 - 1.47127i) q^{17} +(4.44962 - 1.44577i) q^{19} +(-1.51012 + 3.39178i) q^{20} +(2.26090 + 6.12735i) q^{22} +(-4.68148 - 2.70286i) q^{23} +(0.729903 - 0.810640i) q^{25} +(-3.60274 - 1.17060i) q^{26} +(-0.350066 + 0.481825i) q^{28} +(-8.72180 + 1.85388i) q^{29} +(0.0348605 + 0.331676i) q^{31} +(3.92374 - 6.79612i) q^{32} +(-2.46456 - 4.26874i) q^{34} +(-0.507314 + 0.368585i) q^{35} +(2.37275 - 7.30257i) q^{37} +(9.16273 + 0.963042i) q^{38} +(0.353508 - 0.318300i) q^{40} +(9.78937 + 2.08079i) q^{41} +(-7.95160 + 4.59086i) q^{43} +(-0.406974 + 6.21472i) q^{44} +(-6.25699 - 8.61201i) q^{46} +(-6.33820 - 5.70694i) q^{47} +(6.30292 - 2.80624i) q^{49} +(1.96236 - 0.873699i) q^{50} +(-2.68448 - 2.41712i) q^{52} +(-1.05383 - 1.45047i) q^{53} +(-2.42958 + 6.09082i) q^{55} +(0.0660832 - 0.0381531i) q^{56} +(-17.1751 - 3.65069i) q^{58} +(-5.77236 + 5.19746i) q^{59} +(2.45876 + 0.258426i) q^{61} +(-0.202944 + 0.624596i) q^{62} +(5.65871 - 4.11130i) q^{64} +(-1.90171 - 3.29387i) q^{65} +(-5.40401 + 9.36002i) q^{67} +(-0.491320 - 4.67459i) q^{68} +(-1.20786 + 0.256739i) q^{70} +(6.99647 - 9.62982i) q^{71} +(0.116476 + 0.0378454i) q^{73} +(10.1175 - 11.2367i) q^{74} +(7.60855 + 4.39280i) q^{76} +(-0.584352 + 0.874654i) q^{77} +(-5.07900 + 11.4076i) q^{79} +(7.95299 - 2.58408i) q^{80} +(15.9442 + 11.5841i) q^{82} +(0.0451069 - 0.429164i) q^{83} +(1.02896 - 4.84085i) q^{85} +(-17.9818 + 1.88996i) q^{86} +(0.371500 - 0.706204i) q^{88} +8.15328i q^{89} +(-0.188535 - 0.580251i) q^{91} +(-2.11051 - 9.92915i) q^{92} +(-6.83124 - 15.3432i) q^{94} +(6.18971 + 6.87437i) q^{95} +(7.89676 + 3.51587i) q^{97} +13.5864 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.79897	+	0.800953i	1.27206	+	0.566360i	0.927998	−	0.372586i	$-0.121529\pi$
$2$	1.79897	+	0.800953i	1.27206	+	0.566360i	0.344067	+	0.938945i	$0.388195\pi$
$3$		0			0
$3$		0			0
$4$	1.25651	+	1.39549i	0.628254	+	0.697747i
$5$	0.804185	+	1.80623i	0.359642	+	0.807770i	0.999237	+	0.0390577i	$0.0124356\pi$
$5$	0.804185	+	1.80623i	0.359642	+	0.807770i	−0.639594	+	0.768712i	$0.720898\pi$
$6$		0			0
$7$	0.0659410	+	0.310228i	0.0249234	+	0.117255i	0.988851	−	0.148910i	$-0.0475766\pi$
$7$	0.0659410	+	0.310228i	0.0249234	+	0.117255i	−0.963927	+	0.266166i	$0.914243\pi$
$8$	−0.0743474	−	0.228818i	−0.0262858	−	0.0808993i
$9$		0			0
$10$			3.89347i			1.23122i
$11$	2.31445	+	2.37557i	0.697832	+	0.716262i
$11$	2.31445	+	2.37557i	0.697832	+	0.716262i
$12$		0			0
$13$	−1.91314	+	0.201079i	−0.530610	+	0.0557694i	−0.366045	−	0.930597i	$-0.619289\pi$
$13$	−1.91314	+	0.201079i	−0.530610	+	0.0557694i	−0.164565	+	0.986366i	$0.552622\pi$
$14$	−0.129852	+	0.610907i	−0.0347045	+	0.163272i
$15$		0			0
$16$	0.442095	−	4.20626i	0.110524	−	1.05156i
$17$	−2.02504	−	1.47127i	−0.491143	−	0.356836i	0.314481	−	0.949264i	$-0.398170\pi$
$17$	−2.02504	−	1.47127i	−0.491143	−	0.356836i	−0.805624	+	0.592427i	$0.798170\pi$
$18$		0			0
$19$	4.44962	−	1.44577i	1.02081	−	0.331682i	0.249661	−	0.968333i	$-0.419681\pi$
$19$	4.44962	−	1.44577i	1.02081	−	0.331682i	0.771152	+	0.636651i	$0.219681\pi$
$20$	−1.51012	+	3.39178i	−0.337672	+	0.758425i
$21$		0			0
$22$	2.26090	+	6.12735i	0.482025	+	1.30635i
$23$	−4.68148	−	2.70286i	−0.976157	−	0.563584i	−0.0750491	−	0.997180i	$-0.523911\pi$
$23$	−4.68148	−	2.70286i	−0.976157	−	0.563584i	−0.901108	+	0.433595i	$0.857245\pi$
$24$		0			0
$25$	0.729903	−	0.810640i	0.145981	−	0.162128i
$26$	−3.60274	−	1.17060i	−0.706556	−	0.229574i
$27$		0			0
$28$	−0.350066	+	0.481825i	−0.0661563	+	0.0910563i
$29$	−8.72180	+	1.85388i	−1.61960	+	0.344256i	−0.926414	−	0.376506i	$-0.877126\pi$
$29$	−8.72180	+	1.85388i	−1.61960	+	0.344256i	−0.693183	+	0.720762i	$0.743792\pi$
$30$		0			0
$31$	0.0348605	+	0.331676i	0.00626113	+	0.0595707i	0.997206	−	0.0746962i	$-0.0237987\pi$
$31$	0.0348605	+	0.331676i	0.00626113	+	0.0595707i	−0.990945	+	0.134267i	$0.957132\pi$
$32$	3.92374	−	6.79612i	0.693626	−	1.20140i
$33$		0			0
$34$	−2.46456	−	4.26874i	−0.422668	−	0.732083i
$35$	−0.507314	+	0.368585i	−0.0857518	+	0.0623023i
$36$		0			0
$37$	2.37275	−	7.30257i	0.390078	−	1.20054i	−0.542652	−	0.839958i	$-0.682580\pi$
$37$	2.37275	−	7.30257i	0.390078	−	1.20054i	0.932729	−	0.360577i	$-0.117420\pi$
$38$	9.16273	+	0.963042i	1.48639	+	0.156226i
$39$		0			0
$40$	0.353508	−	0.318300i	0.0558946	−	0.0503277i
$41$	9.78937	+	2.08079i	1.52884	+	0.324965i	0.894139	−	0.447790i	$-0.147789\pi$
$41$	9.78937	+	2.08079i	1.52884	+	0.324965i	0.634704	+	0.772756i	$0.281122\pi$
$42$		0			0
$43$	−7.95160	+	4.59086i	−1.21261	+	0.700100i	−0.963327	−	0.268331i	$-0.913528\pi$
$43$	−7.95160	+	4.59086i	−1.21261	+	0.700100i	−0.249281	+	0.968431i	$0.580194\pi$
$44$	−0.406974	+	6.21472i	−0.0613536	+	0.936905i
$45$		0			0
$46$	−6.25699	−	8.61201i	−0.922543	−	1.26977i
$47$	−6.33820	−	5.70694i	−0.924521	−	0.832443i	0.0616625	−	0.998097i	$-0.480360\pi$
$47$	−6.33820	−	5.70694i	−0.924521	−	0.832443i	−0.986184	+	0.165654i	$0.947026\pi$
$48$		0			0
$49$	6.30292	−	2.80624i	0.900418	−	0.400892i
$50$	1.96236	−	0.873699i	0.277519	−	0.123560i
$51$		0			0
$52$	−2.68448	−	2.41712i	−0.372271	−	0.335194i
$53$	−1.05383	−	1.45047i	−0.144754	−	0.199237i	0.730483	−	0.682931i	$-0.239295\pi$
$53$	−1.05383	−	1.45047i	−0.144754	−	0.199237i	−0.875238	+	0.483693i	$0.839295\pi$
$54$		0			0
$55$	−2.42958	+	6.09082i	−0.327605	+	0.821286i
$56$	0.0660832	−	0.0381531i	0.00883074	−	0.00509843i
$57$		0			0
$58$	−17.1751	−	3.65069i	−2.25520	−	0.479359i
$59$	−5.77236	+	5.19746i	−0.751498	+	0.676652i	−0.953046	−	0.302827i	$-0.902070\pi$
$59$	−5.77236	+	5.19746i	−0.751498	+	0.676652i	0.201548	+	0.979479i	$0.435403\pi$
$60$		0			0
$61$	2.45876	+	0.258426i	0.314811	+	0.0330880i	0.260617	−	0.965442i	$-0.416074\pi$
$61$	2.45876	+	0.258426i	0.314811	+	0.0330880i	0.0541948	+	0.998530i	$0.482741\pi$
$62$	−0.202944	+	0.624596i	−0.0257739	+	0.0793238i
$63$		0			0
$64$	5.65871	−	4.11130i	0.707339	−	0.513912i
$65$	−1.90171	−	3.29387i	−0.235879	−	0.408554i
$66$		0			0
$67$	−5.40401	+	9.36002i	−0.660205	+	1.14351i	0.320357	+	0.947297i	$0.396197\pi$
$67$	−5.40401	+	9.36002i	−0.660205	+	1.14351i	−0.980562	+	0.196211i	$0.937136\pi$
$68$	−0.491320	−	4.67459i	−0.0595813	−	0.566878i
$69$		0			0
$70$	−1.20786	+	0.256739i	−0.144367	+	0.0306862i
$71$	6.99647	−	9.62982i	0.830329	−	1.14285i	−0.157533	−	0.987514i	$-0.550354\pi$
$71$	6.99647	−	9.62982i	0.830329	−	1.14285i	0.987862	−	0.155336i	$-0.0496459\pi$
$72$		0			0
$73$	0.116476	+	0.0378454i	0.0136325	+	0.00442947i	0.315825	−	0.948817i	$-0.397719\pi$
$73$	0.116476	+	0.0378454i	0.0136325	+	0.00442947i	−0.302193	+	0.953247i	$0.597719\pi$
$74$	10.1175	−	11.2367i	1.17614	−	1.30623i
$75$		0			0
$76$	7.60855	+	4.39280i	0.872761	+	0.503889i
$77$	−0.584352	+	0.874654i	−0.0665931	+	0.0996761i
$78$		0			0
$79$	−5.07900	+	11.4076i	−0.571433	+	1.28346i	0.364475	+	0.931213i	$0.381248\pi$
$79$	−5.07900	+	11.4076i	−0.571433	+	1.28346i	−0.935908	+	0.352245i	$0.885418\pi$
$80$	7.95299	−	2.58408i	0.889171	−	0.288909i
$81$		0			0
$82$	15.9442	+	11.5841i	1.76074	+	1.27925i
$83$	0.0451069	−	0.429164i	0.00495113	−	0.0471068i	−0.991767	−	0.128053i	$-0.959127\pi$
$83$	0.0451069	−	0.429164i	0.00495113	−	0.0471068i	0.996719	+	0.0809457i	$0.0257940\pi$
$84$		0			0
$85$	1.02896	−	4.84085i	0.111606	−	0.525064i
$86$	−17.9818	+	1.88996i	−1.93902	+	0.203800i
$87$		0			0
$88$	0.371500	−	0.706204i	0.0396020	−	0.0752816i
$89$			8.15328i			0.864246i	0.901815	+	0.432123i	$0.142235\pi$
$89$			8.15328i			0.864246i	−0.901815	+	0.432123i	$0.857765\pi$
$90$		0			0
$91$	−0.188535	−	0.580251i	−0.0197638	−	0.0608268i
$92$	−2.11051	−	9.92915i	−0.220035	−	1.03519i
$93$		0			0
$94$	−6.83124	−	15.3432i	−0.704589	−	1.58253i
$95$	6.18971	+	6.87437i	0.635051	+	0.705295i
$96$		0			0
$97$	7.89676	+	3.51587i	0.801795	+	0.356982i	0.766377	−	0.642391i	$-0.222057\pi$
$97$	7.89676	+	3.51587i	0.801795	+	0.356982i	0.0354174	+	0.999373i	$0.488724\pi$
$98$	13.5864			1.37244
$99$		0			0
$100$	2.04837			0.204837
$101$	−1.51058	−	0.672555i	−0.150309	−	0.0669217i	0.330204	−	0.943910i	$-0.392883\pi$
$101$	−1.51058	−	0.672555i	−0.150309	−	0.0669217i	−0.480512	+	0.876988i	$0.659549\pi$
$102$		0			0
$103$	4.13083	+	4.58775i	0.407023	+	0.452045i	0.911451	−	0.411409i	$-0.134963\pi$
$103$	4.13083	+	4.58775i	0.407023	+	0.452045i	−0.504428	+	0.863454i	$0.668297\pi$
$104$	0.188248	+	0.422811i	0.0184592	+	0.0414600i
$105$		0			0
$106$	−0.734048	−	3.45342i	−0.0712970	−	0.335426i
$107$	3.66316	+	11.2740i	0.354131	+	1.08990i	0.956512	+	0.291694i	$0.0942188\pi$
$107$	3.66316	+	11.2740i	0.354131	+	1.08990i	−0.602381	+	0.798209i	$0.705781\pi$
$108$		0			0
$109$		−	3.30028i		−	0.316109i	−0.987430	−	0.158055i	$-0.949478\pi$
$109$		−	3.30028i		−	0.316109i	0.987430	−	0.158055i	$-0.0505222\pi$
$110$	−9.24921	+	9.01122i	−0.881878	+	0.859186i
$111$		0			0
$112$	1.33405	−	0.140215i	0.126056	−	0.0132490i
$113$	1.07633	−	5.06373i	0.101253	−	0.476356i	−0.898080	−	0.439832i	$-0.855038\pi$
$113$	1.07633	−	5.06373i	0.101253	−	0.476356i	0.999333	−	0.0365240i	$-0.0116285\pi$
$114$		0			0
$115$	1.11720	−	10.6294i	0.104179	−	0.991199i
$116$	−13.5461	−	9.84181i	−1.25772	−	0.913789i
$117$		0			0
$118$	−14.5472	+	4.72668i	−1.33918	+	0.435127i
$119$	0.322898	−	0.725240i	0.0296000	−	0.0664827i
$120$		0			0
$121$	−0.286676	+	10.9963i	−0.0260615	+	0.999660i
$122$	4.21624	+	2.43425i	0.381721	+	0.220387i
$123$		0			0
$124$	−0.419049	+	0.465401i	−0.0376317	+	0.0417942i
$125$	11.4532	+	3.72135i	1.02440	+	0.332848i
$126$		0			0
$127$	−2.22013	+	3.05575i	−0.197005	+	0.271154i	−0.896078	−	0.443896i	$-0.853596\pi$
$127$	−2.22013	+	3.05575i	−0.197005	+	0.271154i	0.699073	+	0.715050i	$0.253596\pi$
$128$	−1.87917	+	0.399431i	−0.166097	+	0.0353050i
$129$		0			0
$130$	−0.782896	−	7.44876i	−0.0686645	−	0.653299i
$131$	−4.45993	+	7.72483i	−0.389666	+	0.674921i	−0.992405	−	0.123017i	$-0.960743\pi$
$131$	−4.45993	+	7.72483i	−0.389666	+	0.674921i	0.602738	+	0.797939i	$0.294076\pi$
$132$		0			0
$133$	0.741931	+	1.28506i	0.0643336	+	0.111429i
$134$	−17.2186	+	12.5100i	−1.48746	+	1.08070i
$135$		0			0
$136$	−0.186098	+	0.572750i	−0.0159577	+	0.0491129i
$137$	4.79687	+	0.504171i	0.409824	+	0.0430743i	0.307198	−	0.951646i	$-0.400609\pi$
$137$	4.79687	+	0.504171i	0.409824	+	0.0430743i	0.102626	+	0.994720i	$0.467275\pi$
$138$		0			0
$139$	−5.34940	+	4.81662i	−0.453730	+	0.408540i	−0.864054	−	0.503399i	$-0.832082\pi$
$139$	−5.34940	+	4.81662i	−0.453730	+	0.408540i	0.410324	+	0.911940i	$0.365416\pi$
$140$	−1.15180	−	0.244823i	−0.0973452	−	0.0206914i
$141$		0			0
$142$	20.2995	−	11.7199i	1.70350	−	0.983514i
$143$	−4.90554	−	4.07942i	−0.410222	−	0.341138i
$144$		0			0
$145$	−10.3625	−	14.2627i	−0.860556	−	1.18445i
$146$	0.179225	+	0.161375i	0.0148328	+	0.0133555i
$147$		0			0
$148$	13.1721	−	5.86459i	1.08274	−	0.482066i
$149$	−3.10216	+	1.38117i	−0.254139	+	0.113150i	−0.529852	−	0.848090i	$-0.677753\pi$
$149$	−3.10216	+	1.38117i	−0.254139	+	0.113150i	0.275713	+	0.961240i	$0.411086\pi$
$150$		0			0
$151$	−6.31260	−	5.68389i	−0.513712	−	0.462549i	0.371035	−	0.928619i	$-0.379003\pi$
$151$	−6.31260	−	5.68389i	−0.513712	−	0.462549i	−0.884748	+	0.466070i	$0.845670\pi$
$152$	−0.661635	−	0.910663i	−0.0536657	−	0.0738645i
$153$		0			0
$154$	−1.75179	+	1.10544i	−0.141163	+	0.0890788i
$155$	−0.571048	+	0.329695i	−0.0458677	+	0.0264817i
$156$		0			0
$157$	18.0930	+	3.84578i	1.44398	+	0.306927i	0.862261	−	0.506465i	$-0.169048\pi$
$157$	18.0930	+	3.84578i	1.44398	+	0.306927i	0.581717	+	0.813391i	$0.302381\pi$
$158$	−18.2740	+	16.4539i	−1.45380	+	1.30901i
$159$		0			0
$160$	15.4308	+	1.62184i	1.21991	+	0.128218i
$161$	0.529800	−	1.63056i	0.0417541	−	0.128506i
$162$		0			0
$163$	−15.0169	+	10.9104i	−1.17622	+	0.854572i	−0.991740	−	0.128265i	$-0.959059\pi$
$163$	−15.0169	+	10.9104i	−1.17622	+	0.854572i	−0.184478	+	0.982837i	$0.559059\pi$
$164$	9.39669	+	16.2755i	0.733758	+	1.27091i
$165$		0			0
$166$	0.424886	−	0.735925i	0.0329776	−	0.0571188i
$167$	−1.43137	−	13.6185i	−0.110762	−	1.05383i	−0.898846	−	0.438265i	$-0.855593\pi$
$167$	−1.43137	−	13.6185i	−0.110762	−	1.05383i	0.788083	−	0.615569i	$-0.211074\pi$
$168$		0			0
$169$	−9.09624	+	1.93347i	−0.699711	+	0.148728i
$170$	5.72836	−	7.88441i	0.439345	−	0.604707i
$171$		0			0
$172$	−16.3978	−	5.32796i	−1.25032	−	0.406253i
$173$	−8.85187	+	9.83099i	−0.672995	+	0.747437i	−0.978836	−	0.204646i	$-0.934396\pi$
$173$	−8.85187	+	9.83099i	−0.672995	+	0.747437i	0.305841	+	0.952083i	$0.401062\pi$
$174$		0			0
$175$	0.299614	+	0.172982i	0.0226487	+	0.0130762i
$176$	11.0155	−	8.68493i	0.830322	−	0.654651i
$177$		0			0
$178$	−6.53040	+	14.6675i	−0.489474	+	1.09938i
$179$	−5.38656	+	1.75020i	−0.402611	+	0.130816i	−0.503321	−	0.864100i	$-0.667889\pi$
$179$	−5.38656	+	1.75020i	−0.402611	+	0.130816i	0.100710	+	0.994916i	$0.467889\pi$
$180$		0			0
$181$	8.30217	+	6.03188i	0.617096	+	0.448346i	0.851906	−	0.523695i	$-0.175447\pi$
$181$	8.30217	+	6.03188i	0.617096	+	0.448346i	−0.234810	+	0.972041i	$0.575447\pi$
$182$	0.125585	−	1.19486i	0.00930899	−	0.0885691i
$183$		0			0
$184$	−0.270405	+	1.27216i	−0.0199345	+	0.0937847i
$185$	15.0982	−	1.58689i	1.11004	−	0.116670i
$186$		0			0
$187$	−1.19172	−	8.21580i	−0.0871471	−	0.600799i
$188$		−	16.0157i		−	1.16807i
$189$		0			0
$190$	5.62906	+	17.3245i	0.408375	+	1.25685i
$191$	1.17503	+	5.52810i	0.0850225	+	0.400000i	0.999994	−	0.00351939i	$-0.00112026\pi$
$191$	1.17503	+	5.52810i	0.0850225	+	0.400000i	−0.914971	+	0.403519i	$0.867787\pi$
$192$		0			0
$193$	−7.30850	−	16.4152i	−0.526078	−	1.18159i	−0.959836	−	0.280561i	$-0.909480\pi$
$193$	−7.30850	−	16.4152i	−0.526078	−	1.18159i	0.433759	−	0.901029i	$-0.357187\pi$
$194$	11.3900	+	12.6499i	0.817755	+	0.908208i
$195$		0			0
$196$	11.8358	+	5.26963i	0.845413	+	0.376402i
$197$	2.51065			0.178877			0.0894383	−	0.995992i	$-0.471493\pi$
$197$	2.51065			0.178877			0.0894383	+	0.995992i	$0.471493\pi$
$198$		0			0
$199$	12.2300			0.866959			0.433479	−	0.901163i	$-0.357286\pi$
$199$	12.2300			0.866959			0.433479	+	0.901163i	$0.357286\pi$
$200$	−0.239755	−	0.106746i	−0.0169532	−	0.00754807i
$201$		0			0
$202$	−2.17881	−	2.41981i	−0.153300	−	0.170257i
$203$	−1.15025	−	2.58350i	−0.0807316	−	0.181326i
$204$		0			0
$205$	4.11407	+	19.3552i	0.287339	+	1.35182i
$206$	3.75667	+	11.5618i	0.261739	+	0.805551i
$207$		0			0
$208$			8.13606i			0.564134i
$209$	13.7329	+	7.22423i	0.949927	+	0.499711i
$210$		0			0
$211$	25.1315	−	2.64142i	1.73012	−	0.181843i	0.813490	−	0.581579i	$-0.197565\pi$
$211$	25.1315	−	2.64142i	1.73012	−	0.181843i	0.916630	+	0.399736i	$0.130898\pi$
$212$	0.699979	−	3.29314i	0.0480747	−	0.226174i
$213$		0			0
$214$	−2.44007	+	23.2157i	−0.166800	+	1.58699i
$215$	−14.6867	−	10.6705i	−1.00162	−	0.727723i
$216$		0			0
$217$	−0.100596	+	0.0326858i	−0.00682893	+	0.00221885i
$218$	2.64337	−	5.93711i	0.179032	−	0.402112i
$219$		0			0
$220$	−11.5525	+	4.26270i	−0.778869	+	0.287391i
$221$	4.17002	+	2.40756i	0.280506	+	0.161950i
$222$		0			0
$223$	9.42718	−	10.4699i	0.631290	−	0.701119i	−0.339620	−	0.940563i	$-0.610298\pi$
$223$	9.42718	−	10.4699i	0.631290	−	0.701119i	0.970910	+	0.239444i	$0.0769651\pi$
$224$	2.36708	+	0.769112i	0.158157	+	0.0513884i
$225$		0			0
$226$	5.99210	−	8.24741i	0.398588	−	0.548610i
$227$	15.2425	−	3.23990i	1.01168	−	0.215040i	0.327890	−	0.944716i	$-0.393663\pi$
$227$	15.2425	−	3.23990i	1.01168	−	0.215040i	0.683793	+	0.729676i	$0.260329\pi$
$228$		0			0
$229$	−2.15145	−	20.4697i	−0.142172	−	1.35268i	−0.800223	−	0.599702i	$-0.795286\pi$
$229$	−2.15145	−	20.4697i	−0.142172	−	1.35268i	0.658051	−	0.752973i	$-0.271381\pi$
$230$	10.5235	−	18.2272i	0.693898	−	1.20187i
$231$		0			0
$232$	1.07264	+	1.85787i	0.0704224	+	0.121975i
$233$	−2.11851	+	1.53918i	−0.138788	+	0.100835i	−0.655013	−	0.755618i	$-0.727337\pi$
$233$	−2.11851	+	1.53918i	−0.138788	+	0.100835i	0.516225	+	0.856453i	$0.327337\pi$
$234$		0			0
$235$	5.21096	−	16.0377i	0.339925	−	1.04618i
$236$	−14.5061	−	1.52465i	−0.944264	−	0.0992461i
$237$		0			0
$238$	1.16177	−	1.04606i	0.0753062	−	0.0678060i
$239$	−21.7827	−	4.63006i	−1.40901	−	0.299494i	−0.560271	−	0.828310i	$-0.689303\pi$
$239$	−21.7827	−	4.63006i	−1.40901	−	0.299494i	−0.848736	+	0.528816i	$0.822636\pi$
$240$		0			0
$241$	−21.2923	+	12.2931i	−1.37156	+	0.791870i	−0.991124	−	0.132938i	$-0.957559\pi$
$241$	−21.2923	+	12.2931i	−1.37156	+	0.791870i	−0.380434	+	0.924808i	$0.624225\pi$
$242$	−9.32322	+	19.5523i	−0.599319	+	1.25687i
$243$		0			0
$244$	2.72882	+	3.75589i	0.174695	+	0.240447i
$245$	10.1374	+	9.12779i	0.647657	+	0.583153i
$246$		0			0
$247$	−8.22204	+	3.66069i	−0.523156	+	0.232924i
$248$	0.0733015	−	0.0326359i	0.00465465	−	0.00207238i
$249$		0			0
$250$	17.6233	+	15.8680i	1.11459	+	1.00358i
$251$	−7.34629	−	10.1113i	−0.463694	−	0.638220i	0.511576	−	0.859238i	$-0.329062\pi$
$251$	−7.34629	−	10.1113i	−0.463694	−	0.638220i	−0.975270	+	0.221018i	$0.929062\pi$
$252$		0			0
$253$	−4.41422	−	17.3768i	−0.277519	−	1.09247i
$254$	−6.44147	+	3.71898i	−0.404174	+	0.233350i
$255$		0			0
$256$	−17.3839	−	3.69506i	−1.08649	−	0.230942i
$257$	9.11426	−	8.20652i	0.568532	−	0.511908i	−0.333976	−	0.942582i	$-0.608390\pi$
$257$	9.11426	−	8.20652i	0.568532	−	0.511908i	0.902508	+	0.430673i	$0.141724\pi$
$258$		0			0
$259$	2.42192	+	0.254555i	0.150491	+	0.0158172i
$260$	2.20705	−	6.79261i	0.136876	−	0.421259i
$261$		0			0
$262$	−14.2105	+	10.3245i	−0.877929	+	0.637853i
$263$	−4.64521	−	8.04575i	−0.286436	−	0.496122i	0.686520	−	0.727111i	$-0.259137\pi$
$263$	−4.64521	−	8.04575i	−0.286436	−	0.496122i	−0.972956	+	0.230989i	$0.925804\pi$
$264$		0			0
$265$	1.77241	−	3.06990i	0.108878	−	0.188583i
$266$	0.305437	+	2.90604i	0.0187276	+	0.178181i
$267$		0			0
$268$	−19.8520	+	4.21968i	−1.21266	+	0.257758i
$269$	12.5983	−	17.3401i	0.768131	−	1.05724i	−0.228363	−	0.973576i	$-0.573337\pi$
$269$	12.5983	−	17.3401i	0.768131	−	1.05724i	0.996494	−	0.0836659i	$-0.0266629\pi$
$270$		0			0
$271$	−7.87807	−	2.55974i	−0.478559	−	0.155493i	0.0597976	−	0.998211i	$-0.480954\pi$
$271$	−7.87807	−	2.55974i	−0.478559	−	0.155493i	−0.538356	+	0.842717i	$0.680954\pi$
$272$	−7.08382	+	7.86738i	−0.429520	+	0.477030i
$273$		0			0
$274$	8.22561	+	4.74906i	0.496927	+	0.286901i
$275$	3.61505	−	0.142245i	0.217996	−	0.00857769i
$276$		0			0
$277$	4.69723	−	10.5502i	0.282229	−	0.633898i	−0.715687	−	0.698421i	$-0.753886\pi$
$277$	4.69723	−	10.5502i	0.282229	−	0.633898i	0.997916	+	0.0645238i	$0.0205528\pi$
$278$	−13.4813	+	4.38034i	−0.808555	+	0.262715i
$279$		0			0
$280$	0.122056	+	0.0886792i	0.00729427	+	0.00529959i
$281$	0.135394	−	1.28818i	0.00807691	−	0.0768467i	−0.989741	−	0.142874i	$-0.954366\pi$
$281$	0.135394	−	1.28818i	0.00807691	−	0.0768467i	0.997818	+	0.0660271i	$0.0210324\pi$
$282$		0			0
$283$	−1.37490	+	6.46839i	−0.0817293	+	0.384506i	−0.999933	−	0.0116032i	$-0.996307\pi$
$283$	−1.37490	+	6.46839i	−0.0817293	+	0.384506i	0.918203	+	0.396109i	$0.129640\pi$
$284$	22.2295	−	2.33641i	1.31908	−	0.138641i
$285$		0			0
$286$	−5.55750	−	11.2679i	−0.328622	−	0.666283i
$287$			3.17415i			0.187364i
$288$		0			0
$289$	−3.31717	−	10.2092i	−0.195128	−	0.600541i
$290$	−7.21800	−	33.9580i	−0.423856	−	1.99408i
$291$		0			0
$292$	0.0935403	+	0.210095i	0.00547403	+	0.0122949i
$293$	−4.62215	−	5.13342i	−0.270029	−	0.299897i	0.592845	−	0.805316i	$-0.298005\pi$
$293$	−4.62215	−	5.13342i	−0.270029	−	0.299897i	−0.862874	+	0.505419i	$0.831338\pi$
$294$		0			0
$295$	−14.0299	−	6.24649i	−0.816850	−	0.363685i
$296$	−1.84737			−0.107376
$297$		0			0
$298$	−6.68695			−0.387365
$299$	9.49983	+	4.22960i	0.549389	+	0.244604i
$300$		0			0
$301$	−1.94855	−	2.16409i	−0.112313	−	0.124736i
$302$	−6.80366	−	15.2813i	−0.391506	−	0.879338i
$303$		0			0
$304$	−4.11412	−	19.3554i	−0.235961	−	1.11011i
$305$	1.51052	+	4.64890i	0.0864921	+	0.266195i
$306$		0			0
$307$			11.5549i			0.659473i	0.944073	+	0.329737i	$0.106960\pi$
$307$			11.5549i			0.659473i	−0.944073	+	0.329737i	$0.893040\pi$
$308$	−1.95482	+	0.283550i	−0.111386	+	0.0161568i
$309$		0			0
$310$	−1.29137	+	0.135728i	−0.0733448	+	0.00770885i
$311$	−1.45143	+	6.82843i	−0.0823029	+	0.387205i	−0.999948	−	0.0101961i	$-0.996754\pi$
$311$	−1.45143	+	6.82843i	−0.0823029	+	0.387205i	0.917645	+	0.397401i	$0.130088\pi$
$312$		0			0
$313$	2.99774	−	28.5216i	0.169442	−	1.61214i	−0.497798	−	0.867293i	$-0.665858\pi$
$313$	2.99774	−	28.5216i	0.169442	−	1.61214i	0.667240	−	0.744843i	$-0.267475\pi$
$314$	29.4685	+	21.4101i	1.66300	+	1.20824i
$315$		0			0
$316$	−22.3011	+	7.24607i	−1.25453	+	0.407623i
$317$	12.2046	−	27.4120i	0.685478	−	1.53961i	−0.149161	−	0.988813i	$-0.547657\pi$
$317$	12.2046	−	27.4120i	0.685478	−	1.53961i	0.834639	−	0.550797i	$-0.185676\pi$
$318$		0			0
$319$	−24.5901	−	16.4286i	−1.37678	−	0.919823i
$320$	11.9766	+	6.91469i	0.669512	+	0.386543i
$321$		0			0
$322$	2.25910	−	2.50898i	0.125894	−	0.139820i
$323$	−11.1378	−	3.61888i	−0.619722	−	0.201360i
$324$		0			0
$325$	−1.23341	+	1.69764i	−0.0684170	+	0.0941679i
$326$	−35.7538	+	7.59970i	−1.98022	+	0.420909i
$327$		0			0
$328$	−0.251691	−	2.39468i	−0.0138973	−	0.132224i
$329$	1.35251	−	2.34261i	0.0745661	−	0.129152i
$330$		0			0
$331$	−4.26661	−	7.38998i	−0.234514	−	0.406190i	0.724617	−	0.689151i	$-0.242017\pi$
$331$	−4.26661	−	7.38998i	−0.234514	−	0.406190i	−0.959131	+	0.282961i	$0.908683\pi$
$332$	0.655573	−	0.476302i	0.0359792	−	0.0261404i
$333$		0			0
$334$	8.33283	−	25.6458i	0.455952	−	1.40328i
$335$	−21.2522	−	2.23369i	−1.16113	−	0.122040i
$336$		0			0
$337$	−8.87505	+	7.99113i	−0.483455	+	0.435304i	−0.874470	−	0.485080i	$-0.838791\pi$
$337$	−8.87505	+	7.99113i	−0.483455	+	0.435304i	0.391015	+	0.920384i	$0.372124\pi$
$338$	−17.9125	−	3.80742i	−0.974311	−	0.207096i
$339$		0			0
$340$	8.04828	−	4.64667i	0.436479	−	0.252001i
$341$	−0.707236	+	0.850459i	−0.0382990	+	0.0460549i
$342$		0			0
$343$	2.59115	+	3.56641i	0.139909	+	0.192568i
$344$	1.64165	+	1.47815i	0.0885119	+	0.0796965i
$345$		0			0
$346$	−23.7984	+	10.5957i	−1.27941	+	0.569631i
$347$	−13.1923	+	5.87358i	−0.708199	+	0.315310i	−0.729039	−	0.684472i	$-0.760033\pi$
$347$	−13.1923	+	5.87358i	−0.708199	+	0.315310i	0.0208399	+	0.999783i	$0.493366\pi$
$348$		0			0
$349$	23.9844	+	21.5956i	1.28385	+	1.15599i	0.979061	+	0.203568i	$0.0652539\pi$
$349$	23.9844	+	21.5956i	1.28385	+	1.15599i	0.304793	+	0.952419i	$0.401413\pi$
$350$	0.400446	+	0.551167i	0.0214047	+	0.0294611i
$351$		0			0
$352$	25.2259	−	6.40813i	1.34455	−	0.341554i
$353$	−5.61311	+	3.24073i	−0.298756	+	0.172487i	−0.641884	−	0.766802i	$-0.721847\pi$
$353$	−5.61311	+	3.24073i	−0.298756	+	0.172487i	0.343128	+	0.939289i	$0.388513\pi$
$354$		0			0
$355$	23.0201	+	4.89308i	1.22178	+	0.259698i
$356$	−11.3779	+	10.2447i	−0.603026	+	0.542967i
$357$		0			0
$358$	−11.0921	−	1.16583i	−0.586236	−	0.0616159i
$359$	−2.95299	+	9.08837i	−0.155853	+	0.479666i	−0.998246	−	0.0591972i	$-0.981146\pi$
$359$	−2.95299	+	9.08837i	−0.155853	+	0.479666i	0.842393	+	0.538863i	$0.181146\pi$
$360$		0			0
$361$	2.33755	−	1.69833i	0.123029	−	0.0893858i
$362$	10.1041	+	17.5008i	0.531060	+	0.919824i
$363$		0			0
$364$	0.572841	−	0.992190i	0.0300250	−	0.0520049i
$365$	0.0253109	+	0.240817i	0.00132483	+	0.0126050i
$366$		0			0
$367$	7.89325	−	1.67776i	0.412024	−	0.0875785i	0.00276405	−	0.999996i	$-0.499120\pi$
$367$	7.89325	−	1.67776i	0.412024	−	0.0875785i	0.409260	+	0.912418i	$0.365787\pi$
$368$	−13.4386	+	18.4966i	−0.700534	+	0.964202i
$369$		0			0
$370$	28.4323	+	9.23822i	1.47813	+	0.480272i
$371$	0.380486	−	0.422573i	0.0197539	−	0.0219389i
$372$		0			0
$373$	−0.603037	−	0.348164i	−0.0312241	−	0.0180272i	0.484307	−	0.874898i	$-0.339072\pi$
$373$	−0.603037	−	0.348164i	−0.0312241	−	0.0180272i	−0.515531	+	0.856871i	$0.672405\pi$
$374$	4.43661	−	15.7345i	0.229411	−	0.813612i
$375$		0			0
$376$	−0.834621	+	1.87459i	−0.0430423	+	0.0966745i
$377$	16.3133	−	5.30050i	0.840175	−	0.272990i
$378$		0			0
$379$	2.08014	+	1.51131i	0.106850	+	0.0776308i	0.639927	−	0.768436i	$-0.278965\pi$
$379$	2.08014	+	1.51131i	0.106850	+	0.0776308i	−0.533077	+	0.846066i	$0.678965\pi$
$380$	−1.81572	+	17.2754i	−0.0931444	+	0.886210i
$381$		0			0
$382$	−2.31390	+	10.8860i	−0.118389	+	0.556979i
$383$	6.20139	−	0.651793i	0.316876	−	0.0333050i	0.0552447	−	0.998473i	$-0.482406\pi$
$383$	6.20139	−	0.651793i	0.316876	−	0.0333050i	0.261632	+	0.965168i	$0.415739\pi$
$384$		0			0
$385$	−2.04975	−	0.352090i	−0.104465	−	0.0179442i
$386$		−	35.3842i		−	1.80101i
$387$		0			0
$388$	5.01598	+	15.4376i	0.254648	+	0.783726i
$389$	−5.71286	−	26.8769i	−0.289653	−	1.36271i	−0.846629	−	0.532183i	$-0.821372\pi$
$389$	−5.71286	−	26.8769i	−0.289653	−	1.36271i	0.556976	−	0.830528i	$-0.311961\pi$
$390$		0			0
$391$	5.50353	+	12.3611i	0.278325	+	0.625129i
$392$	−1.11072	−	1.23358i	−0.0561001	−	0.0623054i
$393$		0			0
$394$	4.51659	+	2.01092i	0.227543	+	0.101308i
$395$	−24.6893			−1.24225
$396$		0			0
$397$	7.45945			0.374379			0.187190	−	0.982324i	$-0.440062\pi$
$397$	7.45945			0.374379			0.187190	+	0.982324i	$0.440062\pi$
$398$	22.0013	+	9.79563i	1.10283	+	0.491010i
$399$		0			0
$400$	−3.08707	−	3.42854i	−0.154354	−	0.171427i
$401$	1.01221	+	2.27346i	0.0505474	+	0.113531i	0.937054	−	0.349185i	$-0.113542\pi$
$401$	1.01221	+	2.27346i	0.0505474	+	0.113531i	−0.886506	+	0.462716i	$0.846875\pi$
$402$		0			0
$403$	−0.133386	−	0.627533i	−0.00664444	−	0.0312596i
$404$	−0.959514	−	2.95308i	−0.0477376	−	0.146921i
$405$		0			0
$406$		−	5.56894i		−	0.276382i
$407$	22.8394	−	11.2648i	1.13211	−	0.558374i
$408$		0			0
$409$	29.4555	−	3.09590i	1.45648	−	0.153082i	0.657054	−	0.753844i	$-0.271802\pi$
$409$	29.4555	−	3.09590i	1.45648	−	0.153082i	0.799429	+	0.600761i	$0.205136\pi$
$410$	−8.10151	+	38.1146i	−0.400105	+	1.88235i
$411$		0			0
$412$	−1.21176	+	11.5291i	−0.0596990	+	0.567998i
$413$	−1.99303	−	1.44802i	−0.0980708	−	0.0712526i
$414$		0			0
$415$	0.811442	−	0.263654i	0.0398321	−	0.0129422i
$416$	−6.14011	+	13.7909i	−0.301044	+	0.676155i
$417$		0			0
$418$	18.9189	+	23.9956i	0.925353	+	1.17366i
$419$	7.83379	+	4.52284i	0.382706	+	0.220955i	0.678995	−	0.734143i	$-0.262416\pi$
$419$	7.83379	+	4.52284i	0.382706	+	0.220955i	−0.296289	+	0.955098i	$0.595749\pi$
$420$		0			0
$421$	−14.5427	+	16.1513i	−0.708770	+	0.787169i	−0.984746	−	0.173996i	$-0.944332\pi$
$421$	−14.5427	+	16.1513i	−0.708770	+	0.787169i	0.275977	+	0.961164i	$0.410999\pi$
$422$	47.3264	+	15.3773i	2.30381	+	0.748554i
$423$		0			0
$424$	−0.253544	+	0.348973i	−0.0123132	+	0.0169476i
$425$	−2.67075	+	0.567686i	−0.129551	+	0.0275368i
$426$		0			0
$427$	0.0819620	+	0.779816i	0.00396642	+	0.0377380i
$428$	−11.1301	+	19.2778i	−0.537992	+	0.931830i
$429$		0			0
$430$	−17.8744	−	30.9593i	−0.861979	−	1.49299i
$431$	14.2119	−	10.3256i	0.684565	−	0.497366i	−0.190304	−	0.981725i	$-0.560947\pi$
$431$	14.2119	−	10.3256i	0.684565	−	0.497366i	0.874869	+	0.484359i	$0.160947\pi$
$432$		0			0
$433$	−4.84981	+	14.9262i	−0.233067	+	0.717306i	0.764305	+	0.644855i	$0.223082\pi$
$433$	−4.84981	+	14.9262i	−0.233067	+	0.717306i	−0.997372	+	0.0724515i	$0.976918\pi$
$434$	−0.207150	−	0.0217723i	−0.00994351	−	0.00104510i
$435$		0			0
$436$	4.60552	−	4.14683i	0.220565	−	0.198597i
$437$	−24.7385	−	5.25834i	−1.18340	−	0.251540i
$438$		0			0
$439$	−10.3281	+	5.96296i	−0.492936	+	0.284597i	−0.725792	−	0.687915i	$-0.758526\pi$
$439$	−10.3281	+	5.96296i	−0.492936	+	0.284597i	0.232856	+	0.972511i	$0.425193\pi$
$440$	1.57432	+	0.103095i	0.0750528	+	0.00491487i
$441$		0			0
$442$	5.57340	+	7.67113i	0.265100	+	0.364878i
$443$	11.4755	+	10.3326i	0.545219	+	0.490917i	0.895093	−	0.445879i	$-0.147109\pi$
$443$	11.4755	+	10.3326i	0.545219	+	0.490917i	−0.349874	+	0.936797i	$0.613776\pi$
$444$		0			0
$445$	−14.7267	+	6.55675i	−0.698112	+	0.310820i
$446$	25.3452	−	11.2844i	1.20013	−	0.534331i
$447$		0			0
$448$	1.64858	+	1.48439i	0.0778881	+	0.0701308i
$449$	13.6969	+	18.8521i	0.646395	+	0.889687i	0.998936	−	0.0461094i	$-0.0146823\pi$
$449$	13.6969	+	18.8521i	0.646395	+	0.889687i	−0.352541	+	0.935796i	$0.614682\pi$
$450$		0			0
$451$	17.7139	+	28.0712i	0.834115	+	1.32182i
$452$	8.41882	−	4.86061i	0.395988	−	0.228624i
$453$		0			0
$454$	30.0159	+	6.38007i	1.40872	+	0.299432i
$455$	0.896449	−	0.807167i	0.0420262	−	0.0378406i
$456$		0			0
$457$	−0.614944	−	0.0646333i	−0.0287659	−	0.00302342i	0.0901346	−	0.995930i	$-0.471270\pi$
$457$	−0.614944	−	0.0646333i	−0.0287659	−	0.00302342i	−0.118900	+	0.992906i	$0.537937\pi$
$458$	12.5249	−	38.5476i	0.585249	−	1.80121i
$459$		0			0
$460$	16.2371	−	11.7969i	0.757058	−	0.550035i
$461$	11.3787	+	19.7085i	0.529959	+	0.917915i	0.999389	+	0.0349460i	$0.0111259\pi$
$461$	11.3787	+	19.7085i	0.529959	+	0.917915i	−0.469430	+	0.882969i	$0.655541\pi$
$462$		0			0
$463$	−3.54426	+	6.13884i	−0.164716	+	0.285296i	−0.936554	−	0.350523i	$-0.886004\pi$
$463$	−3.54426	+	6.13884i	−0.164716	+	0.285296i	0.771839	+	0.635818i	$0.219337\pi$
$464$	3.94201	+	37.5057i	0.183003	+	1.74116i
$465$		0			0
$466$	−5.04395	+	1.07212i	−0.233656	+	0.0496652i
$467$	−3.50195	+	4.82002i	−0.162051	+	0.223044i	−0.882319	−	0.470652i	$-0.844019\pi$
$467$	−3.50195	+	4.82002i	−0.162051	+	0.223044i	0.720268	+	0.693696i	$0.244019\pi$
$468$		0			0
$469$	−3.26009	−	1.05927i	−0.150537	−	0.0489124i
$470$	22.2198	−	24.6776i	1.02492	−	1.13829i
$471$		0			0
$472$	1.61843	+	0.934402i	0.0744944	+	0.0430093i
$473$	−29.3095	−	8.26430i	−1.34765	−	0.379993i
$474$		0			0
$475$	2.07579	−	4.66231i	0.0952440	−	0.213921i
$476$	1.41779	−	0.460669i	0.0649844	−	0.0211147i
$477$		0			0
$478$	−35.4780	−	25.7763i	−1.62273	−	1.17898i
$479$	−0.184201	+	1.75255i	−0.00841635	+	0.0800762i	−0.997924	−	0.0644056i	$-0.979485\pi$
$479$	−0.184201	+	1.75255i	−0.00841635	+	0.0800762i	0.989507	+	0.144482i	$0.0461515\pi$
$480$		0			0
$481$	−3.07101	+	14.4480i	−0.140026	+	0.658770i
$482$	−48.1505	+	5.06082i	−2.19319	+	0.230514i
$483$		0			0
$484$	−15.7054	+	13.4168i	−0.713883	+	0.609857i
$485$			17.0908i			0.776052i
$486$		0			0
$487$	−5.37983	−	16.5574i	−0.243783	−	0.750288i	−0.995834	−	0.0911829i	$-0.970935\pi$
$487$	−5.37983	−	16.5574i	−0.243783	−	0.750288i	0.752051	−	0.659105i	$-0.229065\pi$
$488$	−0.123670	−	0.581820i	−0.00559827	−	0.0263378i
$489$		0			0
$490$	10.9260	+	24.5402i	0.493587	+	1.10861i
$491$	22.4852	+	24.9723i	1.01474	+	1.12698i	0.991871	+	0.127245i	$0.0406135\pi$
$491$	22.4852	+	24.9723i	1.01474	+	1.12698i	0.0228695	+	0.999738i	$0.492720\pi$
$492$		0			0
$493$	20.3895	+	9.07799i	0.918297	+	0.408852i
$494$	−17.7233			−0.797407
$495$		0			0
$496$	1.41052			0.0633344
$497$	3.44880	+	1.53550i	0.154700	+	0.0688767i
$498$		0			0
$499$	13.0633	+	14.5082i	0.584791	+	0.649477i	0.960834	−	0.277126i	$-0.0893819\pi$
$499$	13.0633	+	14.5082i	0.584791	+	0.649477i	−0.376042	+	0.926603i	$0.622715\pi$
$500$	9.19786	+	20.6587i	0.411341	+	0.923886i
$501$		0			0
$502$	−5.11708	−	24.0740i	−0.228386	−	1.07447i
$503$	7.43631	+	22.8866i	0.331569	+	1.02046i	0.968388	+	0.249450i	$0.0802499\pi$
$503$	7.43631	+	22.8866i	0.331569	+	1.02046i	−0.636819	+	0.771013i	$0.719750\pi$
$504$		0			0
$505$		−	3.26932i		−	0.145483i
$506$	5.97697	−	34.7960i	0.265709	−	1.54687i
$507$		0			0
$508$	−7.05390	+	0.741395i	−0.312966	+	0.0328941i
$509$	3.64390	−	17.1432i	0.161513	−	0.759859i	−0.820590	−	0.571517i	$-0.806355\pi$
$509$	3.64390	−	17.1432i	0.161513	−	0.759859i	0.982103	−	0.188342i	$-0.0603114\pi$
$510$		0			0
$511$	−0.00406015	+	0.0386298i	−0.000179611	+	0.00170888i
$512$	−25.2051	−	18.3126i	−1.11392	−	0.809309i
$513$		0			0
$514$	22.9693	−	7.46319i	1.01313	−	0.329187i
$515$	−4.96458	+	11.1506i	−0.218765	+	0.491355i
$516$		0			0
$517$	−1.11218	−	28.2653i	−0.0489136	−	1.24310i
$518$	4.15309	+	2.39779i	0.182476	+	0.105353i
$519$		0			0
$520$	−0.612308	+	0.680037i	−0.0268515	+	0.0298216i
$521$	−7.32063	−	2.37862i	−0.320723	−	0.104209i	0.144231	−	0.989544i	$-0.453929\pi$
$521$	−7.32063	−	2.37862i	−0.320723	−	0.104209i	−0.464954	+	0.885335i	$0.653929\pi$
$522$		0			0
$523$	−7.75187	+	10.6695i	−0.338966	+	0.466546i	−0.944139	−	0.329547i	$-0.893104\pi$
$523$	−7.75187	+	10.6695i	−0.338966	+	0.466546i	0.605173	+	0.796094i	$0.293104\pi$
$524$	−16.3839	+	3.48251i	−0.715734	+	0.152134i
$525$		0			0
$526$	−1.91234	−	18.1947i	−0.0833818	−	0.793325i
$527$	0.417392	−	0.722944i	0.0181819	−	0.0314919i
$528$		0			0
$529$	3.11086	+	5.38816i	0.135255	+	0.234268i
$530$	5.64736	−	4.10305i	0.245306	−	0.178225i
$531$		0			0
$532$	−0.861054	+	2.65005i	−0.0373314	+	0.114894i
$533$	−19.1468	−	2.01242i	−0.829342	−	0.0871674i
$534$		0			0
$535$	−17.4176	+	15.6829i	−0.753030	+	0.678031i
$536$	2.54351	+	0.540640i	0.109863	+	0.0233521i
$537$		0			0
$538$	36.5525	−	21.1036i	1.57589	−	0.909842i
$539$	21.2542	+	8.47815i	0.915484	+	0.365180i
$540$		0			0
$541$	−8.36941	−	11.5195i	−0.359829	−	0.495262i	0.590272	−	0.807204i	$-0.299021\pi$
$541$	−8.36941	−	11.5195i	−0.359829	−	0.495262i	−0.950101	+	0.311942i	$0.899021\pi$
$542$	−12.1222	−	10.9149i	−0.520692	−	0.468834i
$543$		0			0
$544$	−17.9447	+	7.98948i	−0.769371	+	0.342546i
$545$	5.96106	−	2.65404i	0.255344	−	0.113686i
$546$		0			0
$547$	−28.1019	−	25.3030i	−1.20155	−	1.08188i	−0.994627	−	0.103523i	$-0.966988\pi$
$547$	−28.1019	−	25.3030i	−1.20155	−	1.08188i	−0.206923	−	0.978357i	$-0.566345\pi$
$548$	5.32374	+	7.32750i	0.227419	+	0.313015i
$549$		0			0
$550$	6.61731	+	2.63960i	0.282163	+	0.112553i
$551$	−36.1284	+	20.8588i	−1.53912	+	0.888613i
$552$		0			0
$553$	−3.87388	−	0.823419i	−0.164734	−	0.0350154i
$554$	16.9004	−	15.2172i	0.718028	−	0.646515i
$555$		0			0
$556$	−13.4431	−	1.41293i	−0.570116	−	0.0599216i
$557$	−4.83577	+	14.8830i	−0.204898	+	0.630612i	0.794819	+	0.606846i	$0.207566\pi$
$557$	−4.83577	+	14.8830i	−0.204898	+	0.630612i	−0.999718	+	0.0237660i	$0.992434\pi$
$558$		0			0
$559$	14.2894	−	10.3819i	0.604378	−	0.439106i
$560$	1.32608	+	2.29684i	0.0560373	+	0.0970594i
$561$		0			0
$562$	1.27535	−	2.20896i	0.0537972	−	0.0931795i
$563$	−1.68479	−	16.0297i	−0.0710056	−	0.675573i	−0.970903	−	0.239472i	$-0.923026\pi$
$563$	−1.68479	−	16.0297i	−0.0710056	−	0.675573i	0.899898	−	0.436101i	$-0.143641\pi$
$564$		0			0
$565$	10.0118	−	2.12808i	0.421201	−	0.0895289i
$566$	−7.65428	+	10.5352i	−0.321734	+	0.442828i
$567$		0			0
$568$	−2.72364	−	0.884966i	−0.114282	−	0.0371323i
$569$	16.2341	−	18.0298i	0.680569	−	0.755848i	−0.299589	−	0.954068i	$-0.596849\pi$
$569$	16.2341	−	18.0298i	0.680569	−	0.755848i	0.980157	+	0.198220i	$0.0635161\pi$
$570$		0			0
$571$	−14.5377	−	8.39334i	−0.608384	−	0.351250i	0.163949	−	0.986469i	$-0.447577\pi$
$571$	−14.5377	−	8.39334i	−0.608384	−	0.351250i	−0.772333	+	0.635218i	$0.780910\pi$
$572$	−0.471053	−	11.9715i	−0.0196957	−	0.500553i
$573$		0			0
$574$	−2.54234	+	5.71020i	−0.106115	+	0.238339i
$575$	−5.60807	+	1.82217i	−0.233873	+	0.0759899i
$576$		0			0
$577$	5.58119	+	4.05497i	0.232348	+	0.168811i	0.697867	−	0.716227i	$-0.254132\pi$
$577$	5.58119	+	4.05497i	0.232348	+	0.168811i	−0.465519	+	0.885038i	$0.654132\pi$
$578$	2.20960	−	21.0229i	0.0919073	−	0.874439i
$579$		0			0
$580$	6.88300	−	32.3820i	0.285801	−	1.34459i
$581$	0.136113	−	0.0143061i	0.00564692	−	0.000593515i
$582$		0			0
$583$	1.00667	−	5.86048i	0.0416919	−	0.242716i
$584$		−	0.0294655i		−	0.00121929i
$585$		0			0
$586$	−4.20349	−	12.9370i	−0.173644	−	0.534422i
$587$	5.11090	+	24.0449i	0.210949	+	0.992439i	0.948409	+	0.317048i	$0.102692\pi$
$587$	5.11090	+	24.0449i	0.210949	+	0.992439i	−0.737460	+	0.675391i	$0.763975\pi$
$588$		0			0
$589$	0.634643	+	1.42543i	0.0261500	+	0.0587338i
$590$	−20.2361	−	22.4745i	−0.833109	−	0.925261i
$591$		0			0
$592$	−29.6675	−	13.2088i	−1.21933	−	0.542879i
$593$	−25.3400			−1.04059			−0.520295	−	0.853987i	$-0.674178\pi$
$593$	−25.3400			−1.04059			−0.520295	+	0.853987i	$0.674178\pi$
$594$		0			0
$595$	1.56962			0.0643481
$596$	−5.82531	−	2.59359i	−0.238614	−	0.106238i
$597$		0			0
$598$	13.7022	+	15.2178i	0.560325	+	0.622304i
$599$	−8.83839	−	19.8513i	−0.361127	−	0.811104i	−0.999155	−	0.0410913i	$-0.986917\pi$
$599$	−8.83839	−	19.8513i	−0.361127	−	0.811104i	0.638029	−	0.770013i	$-0.279750\pi$
$600$		0			0
$601$	3.90498	+	18.3715i	0.159288	+	0.749389i	0.983179	+	0.182642i	$0.0584650\pi$
$601$	3.90498	+	18.3715i	0.159288	+	0.749389i	−0.823892	+	0.566747i	$0.808202\pi$
$602$	−1.77206	−	5.45383i	−0.0722236	−	0.222281i
$603$		0			0
$604$		−	15.9511i		−	0.649040i
$605$	−20.0923	+	8.32523i	−0.816869	+	0.338469i
$606$		0			0
$607$	−47.7631	+	5.02011i	−1.93865	+	0.203760i	−0.992704	−	0.120576i	$-0.961526\pi$
$607$	−47.7631	+	5.02011i	−1.93865	+	0.203760i	−0.945942	+	0.324336i	$0.894859\pi$
$608$	7.63354	−	35.9130i	0.309581	−	1.45646i
$609$		0			0
$610$	−1.00617	+	9.57309i	−0.0407387	+	0.387603i
$611$	13.2734	+	9.64370i	0.536985	+	0.390142i
$612$		0			0
$613$	1.96455	−	0.638321i	0.0793474	−	0.0257815i	−0.269074	−	0.963119i	$-0.586718\pi$
$613$	1.96455	−	0.638321i	0.0793474	−	0.0257815i	0.348422	+	0.937338i	$0.386718\pi$
$614$	−9.25494	+	20.7869i	−0.373499	+	0.838893i
$615$		0			0
$616$	0.243581	+	0.0686819i	0.00981418	+	0.00276727i
$617$	29.9543	+	17.2941i	1.20591	+	0.696235i	0.961864	−	0.273527i	$-0.0881904\pi$
$617$	29.9543	+	17.2941i	1.20591	+	0.696235i	0.244050	+	0.969763i	$0.421524\pi$
$618$		0			0
$619$	18.3552	−	20.3855i	0.737756	−	0.819362i	−0.251143	−	0.967950i	$-0.580806\pi$
$619$	18.3552	−	20.3855i	0.737756	−	0.819362i	0.988899	+	0.148589i	$0.0474730\pi$
$620$	−1.17761	−	0.382630i	−0.0472941	−	0.0153668i
$621$		0			0
$622$	−8.08033	+	11.1216i	−0.323992	+	0.445936i
$623$	−2.52938	+	0.537636i	−0.101337	+	0.0215399i
$624$		0			0
$625$	1.91872	+	18.2554i	0.0767489	+	0.730217i
$626$	28.2373	−	48.9085i	1.12859	−	1.95478i
$627$		0			0
$628$	17.3672	+	30.0809i	0.693028	+	1.20036i
$629$	−15.5490	+	11.2970i	−0.619979	+	0.450441i
$630$		0			0
$631$	−8.09100	+	24.9015i	−0.322098	+	0.991315i	0.650636	+	0.759390i	$0.274502\pi$
$631$	−8.09100	+	24.9015i	−0.322098	+	0.991315i	−0.972734	+	0.231925i	$0.925498\pi$
$632$	2.98788	+	0.314039i	0.118851	+	0.0124918i
$633$		0			0
$634$	43.9114	−	39.5380i	1.74395	−	1.57026i
$635$	−7.30478	−	1.55268i	−0.289882	−	0.0616162i
$636$		0			0
$637$	−11.4941	+	6.63613i	−0.455413	+	0.262933i
$638$	−31.0784	−	49.2501i	−1.23041	−	1.94983i
$639$		0			0
$640$	−2.23267	−	3.07300i	−0.0882539	−	0.121471i
$641$	4.54375	+	4.09121i	0.179467	+	0.161593i	0.753968	−	0.656911i	$-0.228137\pi$
$641$	4.54375	+	4.09121i	0.179467	+	0.161593i	−0.574501	+	0.818504i	$0.694804\pi$
$642$		0			0
$643$	−0.747639	+	0.332870i	−0.0294840	+	0.0131271i	−0.421426	−	0.906863i	$-0.638470\pi$
$643$	−0.747639	+	0.332870i	−0.0294840	+	0.0131271i	0.391942	+	0.919990i	$0.371803\pi$
$644$	2.94113	−	1.30948i	0.115897	−	0.0516006i
$645$		0			0
$646$	−17.1380	−	15.4311i	−0.674284	−	0.607128i
$647$	3.42533	+	4.71456i	0.134664	+	0.185349i	0.871023	−	0.491242i	$-0.163457\pi$
$647$	3.42533	+	4.71456i	0.134664	+	0.185349i	−0.736360	+	0.676590i	$0.763457\pi$
$648$		0			0
$649$	−25.7068	−	1.68342i	−1.00908	−	0.0660800i
$650$	−3.57859	+	2.06610i	−0.140364	+	0.0810391i
$651$		0			0
$652$	−34.0944	−	7.24699i	−1.33524	−	0.283814i
$653$	1.93524	−	1.74250i	0.0757318	−	0.0681892i	−0.630396	−	0.776274i	$-0.717107\pi$
$653$	1.93524	−	1.74250i	0.0757318	−	0.0681892i	0.706127	+	0.708085i	$0.250441\pi$
$654$		0			0
$655$	−17.5394	−	1.84347i	−0.685322	−	0.0720302i
$656$	13.0802	−	40.2567i	0.510696	−	1.57176i
$657$		0			0
$658$	4.30944	−	3.13099i	0.168000	−	0.122059i
$659$	−11.2518	−	19.4886i	−0.438306	−	0.759169i	0.559253	−	0.828997i	$-0.311088\pi$
$659$	−11.2518	−	19.4886i	−0.438306	−	0.759169i	−0.997559	+	0.0698283i	$0.977755\pi$
$660$		0			0
$661$	3.23287	−	5.59950i	0.125744	−	0.217795i	−0.796279	−	0.604929i	$-0.793201\pi$
$661$	3.23287	−	5.59950i	0.125744	−	0.217795i	0.922024	+	0.387134i	$0.126535\pi$
$662$	−1.75647	−	16.7117i	−0.0682673	−	0.649520i
$663$		0			0
$664$	−0.101554	+	0.0215859i	−0.00394105	+	0.000837697i
$665$	−1.72447	+	2.37353i	−0.0668720	+	0.0920414i
$666$		0			0
$667$	45.8417	+	14.8949i	1.77500	+	0.576732i
$668$	17.2061	−	19.1093i	0.665723	−	0.739360i
$669$		0			0
$670$	−36.4429	−	21.0403i	−1.40791	−	0.812859i
$671$	5.07675	+	6.43906i	0.195986	+	0.248577i
$672$		0			0
$673$	0.144560	−	0.324687i	0.00557238	−	0.0125158i	−0.910738	−	0.412985i	$-0.864486\pi$
$673$	0.144560	−	0.324687i	0.00557238	−	0.0125158i	0.916310	+	0.400469i	$0.131153\pi$
$674$	−22.3665	+	7.26731i	−0.861524	+	0.279926i
$675$		0			0
$676$	−14.1276	−	10.2643i	−0.543371	−	0.394782i
$677$	−3.05705	+	29.0859i	−0.117492	+	1.11786i	0.763854	+	0.645389i	$0.223305\pi$
$677$	−3.05705	+	29.0859i	−0.117492	+	1.11786i	−0.881346	+	0.472471i	$0.843362\pi$
$678$		0			0
$679$	−0.570000	+	2.68164i	−0.0218746	+	0.102912i
$680$	−1.18417	+	0.124462i	−0.0454110	+	0.00477289i
$681$		0			0
$682$	−1.95348	+	0.963488i	−0.0748025	+	0.0368939i
$683$		−	26.1630i		−	1.00110i	−0.865708	−	0.500549i	$-0.833132\pi$
$683$		−	26.1630i		−	1.00110i	0.865708	−	0.500549i	$-0.166868\pi$
$684$		0			0
$685$	2.94692	+	9.06969i	0.112596	+	0.346535i
$686$	1.80487	+	8.49125i	0.0689103	+	0.324197i
$687$		0			0
$688$	15.7950	+	35.4761i	0.602178	+	1.35251i
$689$	2.30778	+	2.56305i	0.0879195	+	0.0976445i
$690$		0			0
$691$	40.7691	+	18.1516i	1.55093	+	0.690518i	0.990478	−	0.137669i	$-0.0439611\pi$
$691$	40.7691	+	18.1516i	1.55093	+	0.690518i	0.560451	+	0.828188i	$0.310628\pi$
$692$	−24.8415			−0.944334
$693$		0			0
$694$	−28.4370			−1.07945
$695$	−13.0018	−	5.78879i	−0.493187	−	0.219581i
$696$		0			0
$697$	−16.7624	−	18.6165i	−0.634921	−	0.705151i
$698$	25.8501	+	58.0602i	0.978440	+	2.19761i
$699$		0			0
$700$	0.135072	+	0.635463i	0.00510524	+	0.0240182i
$701$	−3.87098	−	11.9137i	−0.146205	−	0.449972i	0.850959	−	0.525232i	$-0.176021\pi$
$701$	−3.87098	−	11.9137i	−0.146205	−	0.449972i	−0.997164	+	0.0752595i	$0.976021\pi$
$702$		0			0
$703$		−	35.9241i		−	1.35490i
$704$	22.8635	+	3.92730i	0.861699	+	0.148016i
$705$		0			0
$706$	−12.6935	+	1.33414i	−0.477726	+	0.0502110i
$707$	0.109036	−	0.512974i	0.00410072	−	0.0192924i
$708$		0			0
$709$	1.17524	−	11.1817i	0.0441371	−	0.419937i	−0.950036	−	0.312141i	$-0.898954\pi$
$709$	1.17524	−	11.1817i	0.0441371	−	0.419937i	0.994173	−	0.107796i	$-0.0343794\pi$
$710$	37.4934	+	27.2406i	1.40710	+	1.02232i
$711$		0			0
$712$	1.86562	−	0.606176i	0.0699169	−	0.0227174i
$713$	0.733272	−	1.64696i	0.0274613	−	0.0616790i
$714$		0			0
$715$	3.42340	−	12.1411i	0.128028	−	0.454053i
$716$	−9.21066	−	5.31778i	−0.344219	−	0.198735i
$717$		0			0
$718$	−12.5917	+	13.9845i	−0.469918	+	0.521897i
$719$	8.20360	+	2.66551i	0.305942	+	0.0994067i	0.457965	−	0.888970i	$-0.348579\pi$
$719$	8.20360	+	2.66551i	0.305942	+	0.0994067i	−0.152022	+	0.988377i	$0.548579\pi$
$720$		0			0
$721$	−1.15086	+	1.58402i	−0.0428602	+	0.0589920i
$722$	5.56547	−	1.18298i	0.207125	−	0.0440259i
$723$		0			0
$724$	2.01430	+	19.1648i	0.0748607	+	0.712252i
$725$	−4.86324	+	8.42338i	−0.180616	+	0.312837i
$726$		0			0
$727$	23.7016	+	41.0524i	0.879044	+	1.52255i	0.852391	+	0.522905i	$0.175152\pi$
$727$	23.7016	+	41.0524i	0.879044	+	1.52255i	0.0266533	+	0.999645i	$0.491515\pi$
$728$	−0.118755	+	0.0862803i	−0.00440134	+	0.00319776i
$729$		0			0
$730$	−0.147350	+	0.453496i	−0.00545366	+	0.0167847i
$731$	22.8567	+	2.40234i	0.845385	+	0.0888536i
$732$		0			0
$733$	11.5041	−	10.3583i	0.424913	−	0.382593i	−0.428747	−	0.903425i	$-0.641045\pi$
$733$	11.5041	−	10.3583i	0.424913	−	0.382593i	0.853660	+	0.520831i	$0.174378\pi$
$734$	15.5435	+	3.30388i	0.573722	+	0.121948i
$735$		0			0
$736$	−36.7379	+	21.2106i	−1.35418	+	0.781833i
$737$	−34.7427	+	8.82565i	−1.27976	+	0.325097i
$738$		0			0
$739$	25.0234	+	34.4418i	0.920502	+	1.26696i	0.963451	+	0.267885i	$0.0863246\pi$
$739$	25.0234	+	34.4418i	0.920502	+	1.26696i	−0.0429492	+	0.999077i	$0.513675\pi$
$740$	21.1856	+	19.0756i	0.778797	+	0.701232i
$741$		0			0
$742$	1.02295	−	0.455445i	0.0375535	−	0.0167199i
$743$	44.1108	−	19.6394i	1.61827	−	0.720499i	0.620308	−	0.784358i	$-0.287007\pi$
$743$	44.1108	−	19.6394i	1.61827	−	0.720499i	0.997959	+	0.0638590i	$0.0203408\pi$
$744$		0			0
$745$	−4.98942	−	4.49249i	−0.182798	−	0.164592i
$746$	−0.805983	−	1.10934i	−0.0295091	−	0.0406159i
$747$		0			0
$748$	9.96770	−	11.9863i	0.364455	−	0.438261i
$749$	−3.25597	+	1.87984i	−0.118971	+	0.0686877i
$750$		0			0
$751$	−25.1708	−	5.35021i	−0.918494	−	0.195232i	−0.275676	−	0.961251i	$-0.588902\pi$
$751$	−25.1708	−	5.35021i	−0.918494	−	0.195232i	−0.642818	+	0.766019i	$0.722235\pi$
$752$	−26.8070	+	24.1371i	−0.977549	+	0.880189i
$753$		0			0
$754$	33.5925	+	3.53072i	1.22337	+	0.128581i
$755$	5.18991	−	15.9729i	0.188880	−	0.581314i
$756$		0			0
$757$	−41.1683	+	29.9105i	−1.49629	+	1.08712i	−0.524454	+	0.851439i	$0.675731\pi$
$757$	−41.1683	+	29.9105i	−1.49629	+	1.08712i	−0.971832	+	0.235676i	$0.924269\pi$
$758$	2.53162	+	4.38490i	0.0919527	+	0.159267i
$759$		0			0
$760$	1.11279	−	1.92741i	0.0403651	−	0.0699144i
$761$	−2.23110	−	21.2275i	−0.0808772	−	0.769495i	−0.957523	−	0.288358i	$-0.906891\pi$
$761$	−2.23110	−	21.2275i	−0.0808772	−	0.769495i	0.876645	−	0.481137i	$-0.159776\pi$
$762$		0			0
$763$	1.02384	−	0.217624i	0.0370655	−	0.00787851i
$764$	−6.23800	+	8.58587i	−0.225683	+	0.310626i
$765$		0			0
$766$	11.6782	+	3.79447i	0.421950	+	0.137100i
$767$	9.99825	−	11.1042i	0.361016	−	0.400949i
$768$		0			0
$769$	18.7124	+	10.8036i	0.674786	+	0.389588i	0.797888	−	0.602806i	$-0.205951\pi$
$769$	18.7124	+	10.8036i	0.674786	+	0.389588i	−0.123102	+	0.992394i	$0.539284\pi$
$770$	−3.40544	−	2.27516i	−0.122723	−	0.0819910i
$771$		0			0
$772$	13.7241	−	30.8248i	0.493940	−	1.10941i
$773$	9.33763	−	3.03398i	0.335851	−	0.109125i	−0.136236	−	0.990676i	$-0.543501\pi$
$773$	9.33763	−	3.03398i	0.335851	−	0.109125i	0.472088	+	0.881552i	$0.343501\pi$
$774$		0			0
$775$	0.294314	+	0.213832i	0.0105721	+	0.00768106i
$776$	0.217389	−	2.06832i	0.00780380	−	0.0742482i
$777$		0			0
$778$	11.2499	−	52.9264i	0.403327	−	1.89750i
$779$	46.5673	−	4.89442i	1.66845	−	0.175361i
$780$		0			0
$781$	39.0693	−	5.66708i	1.39801	−	0.202784i
$782$			26.6454i			0.952837i
$783$		0			0
$784$	−9.01729	−	27.7524i	−0.322046	−	0.991155i
$785$	7.60374	+	35.7728i	0.271389	+	1.27679i
$786$		0			0
$787$	−14.2836	−	32.0814i	−0.509154	−	1.14358i	−0.967053	−	0.254574i	$-0.918065\pi$
$787$	−14.2836	−	32.0814i	−0.509154	−	1.14358i	0.457899	−	0.889004i	$-0.348602\pi$
$788$	3.15466	+	3.50360i	0.112380	+	0.124811i
$789$		0			0
$790$	−44.4152	−	19.7749i	−1.58022	−	0.703561i
$791$	1.64189			0.0583787
$792$		0			0
$793$	−4.75591			−0.168887
$794$	13.4193	+	5.97468i	0.476235	+	0.212033i
$795$		0			0
$796$	15.3671	+	17.0668i	0.544671	+	0.604918i
$797$	19.8012	+	44.4743i	0.701395	+	1.57536i	0.813435	+	0.581656i	$0.197595\pi$
$797$	19.8012	+	44.4743i	0.701395	+	1.57536i	−0.112040	+	0.993704i	$0.535738\pi$
$798$		0			0
$799$	4.43860	+	20.8820i	0.157026	+	0.738752i
$800$	−2.64525	−	8.14125i	−0.0935238	−	0.287837i
$801$		0			0
$802$			4.90063i			0.173047i
$803$	0.179673	+	0.364289i	0.00634054	+	0.0128555i
$804$		0			0
$805$	3.37122	−	0.354329i	0.118820	−	0.0124885i
$806$	0.262667	−	1.23575i	0.00925204	−	0.0435274i
$807$		0			0
$808$	−0.0415846	+	0.395651i	−0.00146294	+	0.0139189i
$809$	−1.95603	−	1.42114i	−0.0687705	−	0.0499647i	0.552869	−	0.833268i	$-0.313533\pi$
$809$	−1.95603	−	1.42114i	−0.0687705	−	0.0499647i	−0.621639	+	0.783304i	$0.713533\pi$
$810$		0			0
$811$	22.4513	−	7.29488i	0.788373	−	0.256158i	0.112962	−	0.993599i	$-0.463966\pi$
$811$	22.4513	−	7.29488i	0.788373	−	0.256158i	0.675411	+	0.737441i	$0.263966\pi$
$812$	2.15996	−	4.85136i	0.0757999	−	0.170249i
$813$		0			0
$814$	50.1099	−	1.97172i	1.75635	−	0.0691089i
$815$	−31.7832	−	18.3500i	−1.11332	−	0.642773i
$816$		0			0
$817$	−28.7443	+	31.9238i	−1.00564	+	1.11687i
$818$	55.4693	+	18.0231i	1.93944	+	0.630162i
$819$		0			0
$820$	−21.8407	+	30.0611i	−0.762710	+	1.04978i
$821$	35.0071	−	7.44099i	1.22176	−	0.259692i	0.448498	−	0.893784i	$-0.351959\pi$
$821$	35.0071	−	7.44099i	1.22176	−	0.259692i	0.773258	+	0.634092i	$0.218626\pi$
$822$		0			0
$823$	3.75180	+	35.6960i	0.130779	+	1.24428i	0.841285	+	0.540591i	$0.181800\pi$
$823$	3.75180	+	35.6960i	0.130779	+	1.24428i	−0.710506	+	0.703691i	$0.751534\pi$
$824$	0.742643	−	1.28629i	0.0258712	−	0.0448102i
$825$		0			0
$826$	−2.42561	−	4.20128i	−0.0843978	−	0.146181i
$827$	11.6799	−	8.48596i	0.406151	−	0.295086i	−0.365891	−	0.930658i	$-0.619236\pi$
$827$	11.6799	−	8.48596i	0.406151	−	0.295086i	0.772042	+	0.635572i	$0.219236\pi$
$828$		0			0
$829$	−16.7616	+	51.5868i	−0.582153	+	1.79168i	0.0282623	+	0.999601i	$0.491003\pi$
$829$	−16.7616	+	51.5868i	−0.582153	+	1.79168i	−0.610415	+	0.792082i	$0.708997\pi$
$830$	1.67094	+	0.175622i	0.0579990	+	0.00609594i
$831$		0			0
$832$	−9.99922	+	9.00334i	−0.346661	+	0.312135i
$833$	−16.8924	−	3.59059i	−0.585287	−	0.124407i
$834$		0			0
$835$	23.4471	−	13.5372i	0.811421	−	0.468474i
$836$	7.17418	+	28.2416i	0.248124	+	0.976754i
$837$		0			0
$838$	10.4702	+	14.4110i	0.361686	+	0.497819i
$839$	−41.3232	−	37.2076i	−1.42664	−	1.28455i	−0.900987	−	0.433847i	$-0.857156\pi$
$839$	−41.3232	−	37.2076i	−1.42664	−	1.28455i	−0.525649	−	0.850702i	$-0.676177\pi$
$840$		0			0
$841$	46.1401	−	20.5429i	1.59104	−	0.708375i
$842$	−39.0984	+	17.4078i	−1.34742	+	0.599911i
$843$		0			0
$844$	35.2640	+	31.7518i	1.21384	+	1.09294i
$845$	−10.8073	−	14.8750i	−0.371784	−	0.511717i
$846$		0			0
$847$	−3.43025	+	0.636170i	−0.117865	+	0.0218591i
$848$	−6.56695	+	3.79143i	−0.225510	+	0.130198i
$849$		0			0
$850$	−5.25930	−	1.11790i	−0.180392	−	0.0383436i
$851$	−30.8458	+	27.7737i	−1.05738	+	0.952069i
$852$		0			0
$853$	−16.0536	−	1.68730i	−0.549665	−	0.0577721i	−0.174374	−	0.984679i	$-0.555790\pi$
$853$	−16.0536	−	1.68730i	−0.549665	−	0.0577721i	−0.375290	+	0.926907i	$0.622457\pi$
$854$	−0.477149	+	1.46851i	−0.0163277	+	0.0502515i
$855$		0			0
$856$	2.30735	−	1.67639i	0.0788637	−	0.0572979i
$857$	−23.6770	−	41.0098i	−0.808792	−	1.40087i	−0.913701	−	0.406387i	$-0.866789\pi$
$857$	−23.6770	−	41.0098i	−0.808792	−	1.40087i	0.104909	−	0.994482i	$-0.466545\pi$
$858$		0			0
$859$	4.16516	−	7.21427i	0.142114	−	0.246148i	−0.786179	−	0.617999i	$-0.787944\pi$
$859$	4.16516	−	7.21427i	0.142114	−	0.246148i	0.928292	+	0.371851i	$0.121277\pi$
$860$	−3.56333	−	33.9028i	−0.121509	−	1.15608i
$861$		0			0
$862$	33.8372	−	7.19232i	1.15250	−	0.244971i
$863$	−3.57452	+	4.91990i	−0.121678	+	0.167475i	−0.865511	−	0.500890i	$-0.833006\pi$
$863$	−3.57452	+	4.91990i	−0.121678	+	0.167475i	0.743833	+	0.668366i	$0.233006\pi$
$864$		0			0
$865$	−24.8756	−	8.08256i	−0.845795	−	0.274815i
$866$	−20.6798	+	22.9673i	−0.702730	+	0.780460i
$867$		0			0
$868$	−0.172013	−	0.0993118i	−0.00583850	−	0.00337086i
$869$	−38.8547	+	14.3368i	−1.31806	+	0.486343i
$870$		0			0
$871$	8.45653	−	18.9937i	0.286539	−	0.643576i
$872$	−0.755163	+	0.245367i	−0.0255730	+	0.00830918i
$873$		0			0
$874$	−40.2922	−	29.2740i	−1.36290	−	0.990208i
$875$	−0.399236	+	3.79848i	−0.0134967	+	0.128412i
$876$		0			0
$877$	2.58745	−	12.1730i	0.0873719	−	0.411053i	−0.912626	−	0.408797i	$-0.865949\pi$
$877$	2.58745	−	12.1730i	0.0873719	−	0.411053i	0.999997	−	0.00225604i	$-0.000718120\pi$
$878$	−23.3561	+	2.45482i	−0.788230	+	0.0828463i
$879$		0			0
$880$	24.5454	+	12.9122i	0.827427	+	0.435269i
$881$		−	59.2385i		−	1.99580i	−0.0647993	−	0.997898i	$-0.520641\pi$
$881$		−	59.2385i		−	1.99580i	0.0647993	−	0.997898i	$-0.479359\pi$
$882$		0			0
$883$	−13.1258	−	40.3970i	−0.441718	−	1.35947i	−0.886043	−	0.463603i	$-0.846556\pi$
$883$	−13.1258	−	40.3970i	−0.441718	−	1.35947i	0.444325	−	0.895866i	$-0.353444\pi$
$884$	1.87993	+	8.84437i	0.0632288	+	0.297468i
$885$		0			0
$886$	12.3682	+	27.7794i	0.415518	+	0.933268i
$887$	−15.3978	−	17.1009i	−0.517006	−	0.574193i	0.426946	−	0.904277i	$-0.359590\pi$
$887$	−15.3978	−	17.1009i	−0.517006	−	0.574193i	−0.943952	+	0.330084i	$0.892923\pi$
$888$		0			0
$889$	−1.09438	−	0.487249i	−0.0367043	−	0.0163418i
$890$	−31.7446			−1.06408
$891$		0			0
$892$	26.4561			0.885815
$893$	−36.4535	−	16.2301i	−1.21987	−	0.543121i
$894$		0			0
$895$	−7.49306	−	8.32188i	−0.250465	−	0.278170i
$896$	−0.247829	−	0.556634i	−0.00827939	−	0.0185958i
$897$		0			0
$898$	9.54060	+	44.8850i	0.318374	+	1.49783i
$899$	−0.918932	−	2.82818i	−0.0306481	−	0.0943251i
$900$		0			0
$901$			4.48773i			0.149508i
$902$	9.38303	+	64.6873i	0.312421	+	2.15385i
$903$		0			0
$904$	−1.23869	+	0.130192i	−0.0411983	+	0.00433012i
$905$	−4.21848	+	19.8464i	−0.140227	+	0.659716i
$906$		0			0
$907$	1.18005	−	11.2274i	0.0391829	−	0.372800i	−0.957306	−	0.289076i	$-0.906652\pi$
$907$	1.18005	−	11.2274i	0.0391829	−	0.372800i	0.996489	−	0.0837239i	$-0.0266814\pi$
$908$	23.6736	+	17.1999i	0.785637	+	0.570799i
$909$		0			0
$910$	2.25919	−	0.734055i	0.0748914	−	0.0243337i
$911$	−9.96223	+	22.3755i	−0.330063	+	0.741335i	−0.999999	−	0.00108422i	$-0.999655\pi$
$911$	−9.96223	+	22.3755i	−0.330063	+	0.741335i	0.669936	+	0.742419i	$0.266322\pi$
$912$		0			0
$913$	1.12391	−	0.886122i	0.0371959	−	0.0293263i
$914$	−1.05450	−	0.608815i	−0.0348797	−	0.0201378i
$915$		0			0
$916$	25.8620	−	28.7227i	0.854505	−	0.949024i
$917$	−2.69055	−	0.874214i	−0.0888499	−	0.0288691i
$918$		0			0
$919$	20.6927	−	28.4811i	0.682590	−	0.939504i	−0.317371	−	0.948301i	$-0.602800\pi$
$919$	20.6927	−	28.4811i	0.682590	−	0.939504i	0.999961	+	0.00879691i	$0.00280018\pi$
$920$	−2.51526	+	0.534636i	−0.0829258	+	0.0176264i
$921$		0			0
$922$	4.68437	+	44.5688i	0.154271	+	1.46779i
$923$	−11.4489	+	19.8301i	−0.376845	+	0.652714i
$924$		0			0
$925$	−4.18788	−	7.25361i	−0.137696	−	0.238497i
$926$	−11.2929	+	8.20480i	−0.371109	+	0.269626i
$927$		0			0
$928$	−21.6229	+	66.5485i	−0.709807	+	2.18456i
$929$	−18.0243	−	1.89443i	−0.591359	−	0.0621543i	−0.195877	−	0.980628i	$-0.562755\pi$
$929$	−18.0243	−	1.89443i	−0.591359	−	0.0621543i	−0.395481	+	0.918474i	$0.629422\pi$
$930$		0			0
$931$	23.9884	−	21.5993i	0.786190	−	0.707888i
$932$	−4.80985	−	1.02236i	−0.157552	−	0.0334887i
$933$		0			0
$934$	−10.1605	+	5.86618i	−0.332462	+	0.191947i
$935$	13.8813	−	8.75954i	0.453966	−	0.286468i
$936$		0			0
$937$	−17.7777	−	24.4689i	−0.580772	−	0.799365i	0.413007	−	0.910728i	$-0.364478\pi$
$937$	−17.7777	−	24.4689i	−0.580772	−	0.799365i	−0.993780	+	0.111363i	$0.964478\pi$
$938$	−5.01638	−	4.51677i	−0.163791	−	0.147478i
$939$		0			0
$940$	28.9281	−	12.8796i	0.943531	−	0.420087i
$941$	−23.9373	+	10.6576i	−0.780333	+	0.347427i	−0.757941	−	0.652323i	$-0.773795\pi$
$941$	−23.9373	+	10.6576i	−0.780333	+	0.347427i	−0.0223916	+	0.999749i	$0.507128\pi$
$942$		0			0
$943$	−40.2047	−	36.2005i	−1.30924	−	1.17885i
$944$	19.3099	+	26.5778i	0.628484	+	0.865035i
$945$		0			0
$946$	−46.1076	−	38.3428i	−1.49909	−	1.24663i
$947$	28.0006	−	16.1662i	0.909897	−	0.525330i	0.0294993	−	0.999565i	$-0.490609\pi$
$947$	28.0006	−	16.1662i	0.909897	−	0.525330i	0.880398	+	0.474235i	$0.157275\pi$
$948$		0			0
$949$	−0.230445	−	0.0489827i	−0.00748057	−	0.00159004i
$950$	7.46859	−	6.72475i	0.242313	−	0.218180i
$951$		0			0
$952$	−0.189955	−	0.0199650i	−0.00615646	−	0.000647070i
$953$	−10.9868	+	33.8138i	−0.355897	+	1.09534i	0.599591	+	0.800306i	$0.295330\pi$
$953$	−10.9868	+	33.8138i	−0.355897	+	1.09534i	−0.955488	+	0.295031i	$0.904670\pi$
$954$		0			0
$955$	−9.04008	+	6.56800i	−0.292530	+	0.212536i
$956$	−20.9090	−	36.2154i	−0.676244	−	1.17129i
$957$		0			0
$958$	−1.73509	+	3.00526i	−0.0560581	+	0.0970954i
$959$	0.159902	+	1.52137i	0.00516352	+	0.0491276i
$960$		0			0
$961$	30.2138	−	6.42214i	0.974638	−	0.207166i
$962$	−17.0968	+	23.5317i	−0.551223	+	0.758693i
$963$		0			0
$964$	−43.9090	−	14.2669i	−1.41421	−	0.459506i
$965$	23.7722	−	26.4017i	0.765253	−	0.849900i
$966$		0			0
$967$	−37.9734	−	21.9240i	−1.22114	−	0.705027i	−0.255981	−	0.966682i	$-0.582398\pi$
$967$	−37.9734	−	21.9240i	−1.22114	−	0.705027i	−0.965161	+	0.261655i	$0.915732\pi$
$968$	2.53745	−	0.751947i	0.0815569	−	0.0241685i
$969$		0			0
$970$	−13.6889	+	30.7458i	−0.439524	+	0.987188i
$971$	24.4501	−	7.94432i	0.784641	−	0.254945i	0.110820	−	0.993840i	$-0.464652\pi$
$971$	24.4501	−	7.94432i	0.784641	−	0.254945i	0.673820	+	0.738895i	$0.264652\pi$
$972$		0			0
$973$	−1.84700	−	1.34192i	−0.0592120	−	0.0430200i
$974$	3.58356	−	34.0953i	0.114825	−	1.09248i
$975$		0			0
$976$	2.17401	−	10.2279i	0.0695884	−	0.327388i
$977$	−16.5029	+	1.73452i	−0.527974	+	0.0554923i	−0.364766	−	0.931099i	$-0.618851\pi$
$977$	−16.5029	+	1.73452i	−0.527974	+	0.0554923i	−0.163208	+	0.986592i	$0.552184\pi$
$978$		0			0
$979$	−19.3687	+	18.8703i	−0.619027	+	0.603099i
$980$			25.6159i			0.818269i
$981$		0			0
$982$	20.4485	+	62.9340i	0.652538	+	2.00830i
$983$	−8.71340	−	40.9933i	−0.277914	−	1.30748i	−0.866552	−	0.499087i	$-0.833669\pi$
$983$	−8.71340	−	40.9933i	−0.277914	−	1.30748i	0.588637	−	0.808397i	$-0.299665\pi$
$984$		0			0
$985$	2.01903	+	4.53481i	0.0643316	+	0.144491i
$986$	29.4091	+	32.6621i	0.936576	+	1.04017i
$987$		0			0
$988$	−15.4395	−	6.87412i	−0.491197	−	0.218695i
$989$	49.6337			1.57826
$990$		0			0
$991$	−21.9883			−0.698482			−0.349241	−	0.937033i	$-0.613561\pi$
$991$	−21.9883			−0.698482			−0.349241	+	0.937033i	$0.613561\pi$
$992$	2.39089	+	1.06449i	0.0759108	+	0.0337977i
$993$		0			0
$994$	4.97442	+	5.52465i	0.157779	+	0.175231i
$995$	9.83515	+	22.0901i	0.311795	+	0.700303i
$996$		0			0
$997$	−9.83942	−	46.2909i	−0.311618	−	1.46605i	−0.803458	−	0.595361i	$-0.797009\pi$
$997$	−9.83942	−	46.2909i	−0.311618	−	1.46605i	0.491841	−	0.870685i	$-0.336324\pi$
$998$	11.8800	+	36.5629i	0.376055	+	1.15738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.206.9		80
3.2	odd	2		99.2.p.a.41.2	yes	80
9.2	odd	6	inner	297.2.t.a.8.9		80
9.4	even	3		891.2.k.a.404.4		80
9.5	odd	6		891.2.k.a.404.17		80
9.7	even	3		99.2.p.a.74.2	yes	80
11.7	odd	10	inner	297.2.t.a.260.9		80
33.29	even	10		99.2.p.a.95.2	yes	80
99.7	odd	30		99.2.p.a.29.2	✓	80
99.29	even	30	inner	297.2.t.a.62.9		80
99.40	odd	30		891.2.k.a.161.17		80
99.95	even	30		891.2.k.a.161.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.2	✓	80	99.7	odd	30
99.2.p.a.41.2	yes	80	3.2	odd	2
99.2.p.a.74.2	yes	80	9.7	even	3
99.2.p.a.95.2	yes	80	33.29	even	10
297.2.t.a.8.9		80	9.2	odd	6	inner
297.2.t.a.62.9		80	99.29	even	30	inner
297.2.t.a.206.9		80	1.1	even	1	trivial
297.2.t.a.260.9		80	11.7	odd	10	inner
891.2.k.a.161.4		80	99.95	even	30
891.2.k.a.161.17		80	99.40	odd	30
891.2.k.a.404.4		80	9.4	even	3
891.2.k.a.404.17		80	9.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(1.79897 + 0.800953i) q^{2} +(1.25651 + 1.39549i) q^{4} +(0.804185 + 1.80623i) q^{5} +(0.0659410 + 0.310228i) q^{7} +(-0.0743474 - 0.228818i) q^{8} +3.89347i q^{10} +(2.31445 + 2.37557i) q^{11} +(-1.91314 + 0.201079i) q^{13} +(-0.129852 + 0.610907i) q^{14} +(0.442095 - 4.20626i) q^{16} +(-2.02504 - 1.47127i) q^{17} +(4.44962 - 1.44577i) q^{19} +(-1.51012 + 3.39178i) q^{20} +(2.26090 + 6.12735i) q^{22} +(-4.68148 - 2.70286i) q^{23} +(0.729903 - 0.810640i) q^{25} +(-3.60274 - 1.17060i) q^{26} +(-0.350066 + 0.481825i) q^{28} +(-8.72180 + 1.85388i) q^{29} +(0.0348605 + 0.331676i) q^{31} +(3.92374 - 6.79612i) q^{32} +(-2.46456 - 4.26874i) q^{34} +(-0.507314 + 0.368585i) q^{35} +(2.37275 - 7.30257i) q^{37} +(9.16273 + 0.963042i) q^{38} +(0.353508 - 0.318300i) q^{40} +(9.78937 + 2.08079i) q^{41} +(-7.95160 + 4.59086i) q^{43} +(-0.406974 + 6.21472i) q^{44} +(-6.25699 - 8.61201i) q^{46} +(-6.33820 - 5.70694i) q^{47} +(6.30292 - 2.80624i) q^{49} +(1.96236 - 0.873699i) q^{50} +(-2.68448 - 2.41712i) q^{52} +(-1.05383 - 1.45047i) q^{53} +(-2.42958 + 6.09082i) q^{55} +(0.0660832 - 0.0381531i) q^{56} +(-17.1751 - 3.65069i) q^{58} +(-5.77236 + 5.19746i) q^{59} +(2.45876 + 0.258426i) q^{61} +(-0.202944 + 0.624596i) q^{62} +(5.65871 - 4.11130i) q^{64} +(-1.90171 - 3.29387i) q^{65} +(-5.40401 + 9.36002i) q^{67} +(-0.491320 - 4.67459i) q^{68} +(-1.20786 + 0.256739i) q^{70} +(6.99647 - 9.62982i) q^{71} +(0.116476 + 0.0378454i) q^{73} +(10.1175 - 11.2367i) q^{74} +(7.60855 + 4.39280i) q^{76} +(-0.584352 + 0.874654i) q^{77} +(-5.07900 + 11.4076i) q^{79} +(7.95299 - 2.58408i) q^{80} +(15.9442 + 11.5841i) q^{82} +(0.0451069 - 0.429164i) q^{83} +(1.02896 - 4.84085i) q^{85} +(-17.9818 + 1.88996i) q^{86} +(0.371500 - 0.706204i) q^{88} +8.15328i q^{89} +(-0.188535 - 0.580251i) q^{91} +(-2.11051 - 9.92915i) q^{92} +(-6.83124 - 15.3432i) q^{94} +(6.18971 + 6.87437i) q^{95} +(7.89676 + 3.51587i) q^{97} +13.5864 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 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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