LMFDB - Embedded newform 891.2.k.a.161.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(161,891)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("891.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.17
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.59313 + 1.15748i) q^{2} +(0.580279 + 1.78592i) q^{4} +(-1.16215 - 1.59956i) q^{5} +(-0.301636 + 0.0980075i) q^{7} +(0.0743474 - 0.228818i) q^{8} -3.89347i q^{10} +(3.21453 + 0.816584i) q^{11} +(1.13071 - 1.55629i) q^{13} +(-0.593987 - 0.192998i) q^{14} +(3.42168 - 2.48599i) q^{16} +(2.02504 - 1.47127i) q^{17} +(4.44962 + 1.44577i) q^{19} +(2.18231 - 3.00369i) q^{20} +(4.17599 + 5.02167i) q^{22} +5.40571i q^{23} +(0.337083 - 1.03743i) q^{25} +(3.60274 - 1.17060i) q^{26} +(-0.350066 - 0.481825i) q^{28} +(-2.75540 - 8.48024i) q^{29} +(0.269809 + 0.196028i) q^{31} +7.84748 q^{32} +4.92912 q^{34} +(0.507314 + 0.368585i) q^{35} +(2.37275 + 7.30257i) q^{37} +(5.41539 + 7.45364i) q^{38} +(-0.452410 + 0.146997i) q^{40} +(3.09266 - 9.51824i) q^{41} +9.18172i q^{43} +(0.406974 + 6.21472i) q^{44} +(-6.25699 + 8.61201i) q^{46} +(-8.11146 - 2.63557i) q^{47} +(-5.58174 + 4.05537i) q^{49} +(1.73782 - 1.26260i) q^{50} +(3.43553 + 1.11627i) q^{52} +(1.05383 - 1.45047i) q^{53} +(-2.42958 - 6.09082i) q^{55} +0.0763063i q^{56} +(5.42598 - 16.6994i) q^{58} +(-7.38731 + 2.40028i) q^{59} +(-1.45318 - 2.00013i) q^{61} +(0.202944 + 0.624596i) q^{62} +(5.65871 + 4.11130i) q^{64} -3.80343 q^{65} +10.8080 q^{67} +(3.80266 + 2.76279i) q^{68} +(0.381589 + 1.17441i) q^{70} +(-6.99647 - 9.62982i) q^{71} +(0.116476 - 0.0378454i) q^{73} +(-4.67246 + 14.3804i) q^{74} +8.78560i q^{76} +(-1.04965 + 0.0687367i) q^{77} +(-7.33980 + 10.1024i) q^{79} +(-7.95299 - 2.58408i) q^{80} +(15.9442 - 11.5841i) q^{82} +(-0.349113 + 0.253646i) q^{83} +(-4.70678 - 1.52933i) q^{85} +(-10.6276 + 14.6277i) q^{86} +(0.425841 - 0.674830i) q^{88} +8.15328i q^{89} +(-0.188535 + 0.580251i) q^{91} +(-9.65415 + 3.13682i) q^{92} +(-9.87200 - 13.5876i) q^{94} +(-2.85852 - 8.79763i) q^{95} +(-6.99321 - 5.08086i) q^{97} -13.5864 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.59313	+	1.15748i	1.12651	+	0.818460i	0.985184	−	0.171502i	$-0.0548620\pi$
$2$	1.59313	+	1.15748i	1.12651	+	0.818460i	0.141330	+	0.989962i	$0.454862\pi$
$3$		0			0
$3$		0			0
$4$	0.580279	+	1.78592i	0.290140	+	0.892958i
$5$	−1.16215	−	1.59956i	−0.519728	−	0.715345i	0.465794	−	0.884893i	$-0.345769\pi$
$5$	−1.16215	−	1.59956i	−0.519728	−	0.715345i	−0.985522	+	0.169549i	$0.945769\pi$
$6$		0			0
$7$	−0.301636	+	0.0980075i	−0.114008	+	0.0370433i	−0.365465	−	0.930825i	$-0.619090\pi$
$7$	−0.301636	+	0.0980075i	−0.114008	+	0.0370433i	0.251458	+	0.967868i	$0.419090\pi$
$8$	0.0743474	−	0.228818i	0.0262858	−	0.0808993i
$9$		0			0
$10$		−	3.89347i		−	1.23122i
$11$	3.21453	+	0.816584i	0.969217	+	0.246209i
$11$	3.21453	+	0.816584i	0.969217	+	0.246209i
$12$		0			0
$13$	1.13071	−	1.55629i	0.313603	−	0.431637i	−0.622898	−	0.782303i	$-0.714045\pi$
$13$	1.13071	−	1.55629i	0.313603	−	0.431637i	0.936501	+	0.350666i	$0.114045\pi$
$14$	−0.593987	−	0.192998i	−0.158750	−	0.0515809i
$15$		0			0
$16$	3.42168	−	2.48599i	0.855420	−	0.621499i
$17$	2.02504	−	1.47127i	0.491143	−	0.356836i	−0.314481	−	0.949264i	$-0.601830\pi$
$17$	2.02504	−	1.47127i	0.491143	−	0.356836i	0.805624	+	0.592427i	$0.201830\pi$
$18$		0			0
$19$	4.44962	+	1.44577i	1.02081	+	0.331682i	0.771152	−	0.636651i	$-0.219681\pi$
$19$	4.44962	+	1.44577i	1.02081	+	0.331682i	0.249661	+	0.968333i	$0.419681\pi$
$20$	2.18231	−	3.00369i	0.487979	−	0.671645i
$21$		0			0
$22$	4.17599	+	5.02167i	0.890324	+	1.07062i
$23$			5.40571i			1.12717i	0.826059	+	0.563584i	$0.190578\pi$
$23$			5.40571i			1.12717i	−0.826059	+	0.563584i	$0.809422\pi$
$24$		0			0
$25$	0.337083	−	1.03743i	0.0674166	−	0.207487i
$26$	3.60274	−	1.17060i	0.706556	−	0.229574i
$27$		0			0
$28$	−0.350066	−	0.481825i	−0.0661563	−	0.0910563i
$29$	−2.75540	−	8.48024i	−0.511664	−	1.57474i	−0.789271	−	0.614045i	$-0.789541\pi$
$29$	−2.75540	−	8.48024i	−0.511664	−	1.57474i	0.277607	−	0.960695i	$-0.410459\pi$
$30$		0			0
$31$	0.269809	+	0.196028i	0.0484592	+	0.0352077i	0.611751	−	0.791050i	$-0.290465\pi$
$31$	0.269809	+	0.196028i	0.0484592	+	0.0352077i	−0.563292	+	0.826258i	$0.690465\pi$
$32$	7.84748			1.38725
$33$		0			0
$34$	4.92912			0.845336
$35$	0.507314	+	0.368585i	0.0857518	+	0.0623023i
$36$		0			0
$37$	2.37275	+	7.30257i	0.390078	+	1.20054i	0.932729	+	0.360577i	$0.117420\pi$
$37$	2.37275	+	7.30257i	0.390078	+	1.20054i	−0.542652	+	0.839958i	$0.682580\pi$
$38$	5.41539	+	7.45364i	0.878491	+	1.20914i
$39$		0			0
$40$	−0.452410	+	0.146997i	−0.0715323	+	0.0232423i
$41$	3.09266	−	9.51824i	0.482993	−	1.48650i	−0.351874	−	0.936047i	$-0.614455\pi$
$41$	3.09266	−	9.51824i	0.482993	−	1.48650i	0.834867	−	0.550452i	$-0.185545\pi$
$42$		0			0
$43$			9.18172i			1.40020i	0.714045	+	0.700100i	$0.246861\pi$
$43$			9.18172i			1.40020i	−0.714045	+	0.700100i	$0.753139\pi$
$44$	0.406974	+	6.21472i	0.0613536	+	0.936905i
$45$		0			0
$46$	−6.25699	+	8.61201i	−0.922543	+	1.26977i
$47$	−8.11146	−	2.63557i	−1.18318	−	0.384438i	−0.349631	−	0.936887i	$-0.613693\pi$
$47$	−8.11146	−	2.63557i	−1.18318	−	0.384438i	−0.833546	+	0.552450i	$0.813693\pi$
$48$		0			0
$49$	−5.58174	+	4.05537i	−0.797391	+	0.579339i
$50$	1.73782	−	1.26260i	0.245766	−	0.178559i
$51$		0			0
$52$	3.43553	+	1.11627i	0.476422	+	0.154799i
$53$	1.05383	−	1.45047i	0.144754	−	0.199237i	−0.730483	−	0.682931i	$-0.760705\pi$
$53$	1.05383	−	1.45047i	0.144754	−	0.199237i	0.875238	+	0.483693i	$0.160705\pi$
$54$		0			0
$55$	−2.42958	−	6.09082i	−0.327605	−	0.821286i
$56$			0.0763063i			0.0101969i
$57$		0			0
$58$	5.42598	−	16.6994i	0.712466	−	2.19274i
$59$	−7.38731	+	2.40028i	−0.961746	+	0.312490i	−0.747480	−	0.664285i	$-0.768736\pi$
$59$	−7.38731	+	2.40028i	−0.961746	+	0.312490i	−0.214267	+	0.976775i	$0.568736\pi$
$60$		0			0
$61$	−1.45318	−	2.00013i	−0.186061	−	0.256091i	0.705789	−	0.708422i	$-0.250593\pi$
$61$	−1.45318	−	2.00013i	−0.186061	−	0.256091i	−0.891850	+	0.452331i	$0.850593\pi$
$62$	0.202944	+	0.624596i	0.0257739	+	0.0793238i
$63$		0			0
$64$	5.65871	+	4.11130i	0.707339	+	0.513912i
$65$	−3.80343			−0.471757
$66$		0			0
$67$	10.8080			1.32041			0.660205	−	0.751086i	$-0.270469\pi$
$67$	10.8080			1.32041			0.660205	+	0.751086i	$0.270469\pi$
$68$	3.80266	+	2.76279i	0.461140	+	0.335038i
$69$		0			0
$70$	0.381589	+	1.17441i	0.0456086	+	0.140369i
$71$	−6.99647	−	9.62982i	−0.830329	−	1.14285i	−0.987862	−	0.155336i	$-0.950354\pi$
$71$	−6.99647	−	9.62982i	−0.830329	−	1.14285i	0.157533	−	0.987514i	$-0.449646\pi$
$72$		0			0
$73$	0.116476	−	0.0378454i	0.0136325	−	0.00442947i	−0.302193	−	0.953247i	$-0.597719\pi$
$73$	0.116476	−	0.0378454i	0.0136325	−	0.00442947i	0.315825	+	0.948817i	$0.397719\pi$
$74$	−4.67246	+	14.3804i	−0.543163	+	1.67168i
$75$		0			0
$76$			8.78560i			1.00778i
$77$	−1.04965	+	0.0687367i	−0.119619	+	0.00783328i
$78$		0			0
$79$	−7.33980	+	10.1024i	−0.825792	+	1.13660i	0.162900	+	0.986643i	$0.447915\pi$
$79$	−7.33980	+	10.1024i	−0.825792	+	1.13660i	−0.988692	+	0.149962i	$0.952085\pi$
$80$	−7.95299	−	2.58408i	−0.889171	−	0.288909i
$81$		0			0
$82$	15.9442	−	11.5841i	1.76074	−	1.27925i
$83$	−0.349113	+	0.253646i	−0.0383202	+	0.0278412i	−0.606780	−	0.794869i	$-0.707539\pi$
$83$	−0.349113	+	0.253646i	−0.0383202	+	0.0278412i	0.568460	+	0.822711i	$0.307539\pi$
$84$		0			0
$85$	−4.70678	−	1.52933i	−0.510522	−	0.165879i
$86$	−10.6276	+	14.6277i	−1.14601	+	1.57734i
$87$		0			0
$88$	0.425841	−	0.674830i	0.0453948	−	0.0719372i
$89$			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
$92$	−9.65415	+	3.13682i	−1.00651	+	0.327036i
$93$		0			0
$94$	−9.87200	−	13.5876i	−1.01822	−	1.40146i
$95$	−2.85852	−	8.79763i	−0.293278	−	0.902618i
$96$		0			0
$97$	−6.99321	−	5.08086i	−0.710053	−	0.515884i	0.173138	−	0.984898i	$-0.444609\pi$
$97$	−6.99321	−	5.08086i	−0.710053	−	0.515884i	−0.883191	+	0.469014i	$0.844609\pi$
$98$	−13.5864			−1.37244
$99$		0			0
$100$	2.04837			0.204837
$101$	−1.33774	−	0.971925i	−0.133110	−	0.0967102i	0.519238	−	0.854630i	$-0.326216\pi$
$101$	−1.33774	−	0.971925i	−0.133110	−	0.0967102i	−0.652348	+	0.757920i	$0.726216\pi$
$102$		0			0
$103$	1.90769	+	5.87128i	0.187971	+	0.578514i	0.999987	−	0.00512061i	$-0.00162995\pi$
$103$	1.90769	+	5.87128i	0.187971	+	0.578514i	−0.812016	+	0.583635i	$0.801630\pi$
$104$	−0.272041	−	0.374433i	−0.0266758	−	0.0367162i
$105$		0			0
$106$	3.35778	−	1.09101i	0.326136	−	0.105968i
$107$	−3.66316	+	11.2740i	−0.354131	+	1.08990i	0.602381	+	0.798209i	$0.294219\pi$
$107$	−3.66316	+	11.2740i	−0.354131	+	1.08990i	−0.956512	+	0.291694i	$0.905781\pi$
$108$		0			0
$109$			3.30028i			0.316109i	0.987430	+	0.158055i	$0.0505222\pi$
$109$			3.30028i			0.316109i	−0.987430	+	0.158055i	$0.949478\pi$
$110$	3.17934	−	12.5157i	0.303138	−	1.19332i
$111$		0			0
$112$	−0.788455	+	1.08522i	−0.0745020	+	0.102543i
$113$	4.92348	+	1.59974i	0.463162	+	0.150491i	0.531297	−	0.847186i	$-0.321705\pi$
$113$	4.92348	+	1.59974i	0.463162	+	0.150491i	−0.0681348	+	0.997676i	$0.521705\pi$
$114$		0			0
$115$	8.64676	−	6.28224i	0.806314	−	0.585821i
$116$	13.5461	−	9.84181i	1.25772	−	0.913789i
$117$		0			0
$118$	−14.5472	−	4.72668i	−1.33918	−	0.435127i
$119$	−0.466628	+	0.642258i	−0.0427757	+	0.0588757i
$120$		0			0
$121$	9.66638	+	5.24986i	0.878762	+	0.477260i
$122$		−	4.86850i		−	0.440773i
$123$		0			0
$124$	−0.193525	+	0.595608i	−0.0173790	+	0.0534871i
$125$	−11.4532	+	3.72135i	−1.02440	+	0.332848i
$126$		0			0
$127$	−2.22013	−	3.05575i	−0.197005	−	0.271154i	0.699073	−	0.715050i	$-0.253596\pi$
$127$	−2.22013	−	3.05575i	−0.197005	−	0.271154i	−0.896078	+	0.443896i	$0.853596\pi$
$128$	−0.593669	−	1.82713i	−0.0524735	−	0.161497i
$129$		0			0
$130$	−6.05936	−	4.40239i	−0.531441	−	0.386115i
$131$	−8.91986			−0.779332			−0.389666	−	0.920956i	$-0.627410\pi$
$131$	−8.91986			−0.779332			−0.389666	+	0.920956i	$0.627410\pi$
$132$		0			0
$133$	−1.48386			−0.128667
$134$	17.2186	+	12.5100i	1.48746	+	1.08070i
$135$		0			0
$136$	−0.186098	−	0.572750i	−0.0159577	−	0.0491129i
$137$	2.83506	+	3.90213i	0.242216	+	0.333381i	0.912766	−	0.408483i	$-0.133942\pi$
$137$	2.83506	+	3.90213i	0.242216	+	0.333381i	−0.670550	+	0.741864i	$0.733942\pi$
$138$		0			0
$139$	6.84602	−	2.22441i	0.580672	−	0.188672i	−0.00392986	−	0.999992i	$-0.501251\pi$
$139$	6.84602	−	2.22441i	0.580672	−	0.188672i	0.584601	+	0.811321i	$0.301251\pi$
$140$	−0.363879	+	1.11990i	−0.0307534	+	0.0946491i
$141$		0			0
$142$		−	23.4398i		−	1.96703i
$143$	4.90554	−	4.07942i	0.410222	−	0.341138i
$144$		0			0
$145$	−10.3625	+	14.2627i	−0.860556	+	1.18445i
$146$	0.229367	+	0.0745259i	0.0189826	+	0.00616781i
$147$		0			0
$148$	−11.6649	+	8.47506i	−0.958850	+	0.696646i
$149$	−2.74721	+	1.99596i	−0.225060	+	0.163516i	−0.694601	−	0.719395i	$-0.744419\pi$
$149$	−2.74721	+	1.99596i	−0.225060	+	0.163516i	0.469541	+	0.882910i	$0.344419\pi$
$150$		0			0
$151$	8.07870	+	2.62493i	0.657435	+	0.213614i	0.618690	−	0.785635i	$-0.287664\pi$
$151$	8.07870	+	2.62493i	0.657435	+	0.213614i	0.0387455	+	0.999249i	$0.487664\pi$
$152$	0.661635	−	0.910663i	0.0536657	−	0.0738645i
$153$		0			0
$154$	−1.75179	−	1.10544i	−0.141163	−	0.0890788i
$155$		−	0.659389i		−	0.0529634i
$156$		0			0
$157$	−5.71595	+	17.5919i	−0.456182	+	1.40398i	0.413559	+	0.910477i	$0.364285\pi$
$157$	−5.71595	+	17.5919i	−0.456182	+	1.40398i	−0.869742	+	0.493507i	$0.835715\pi$
$158$	−23.3865	+	7.59874i	−1.86053	+	0.604523i
$159$		0			0
$160$	−9.11993	−	12.5525i	−0.720994	−	0.992363i
$161$	−0.529800	−	1.63056i	−0.0417541	−	0.128506i
$162$		0			0
$163$	−15.0169	−	10.9104i	−1.17622	−	0.854572i	−0.184478	−	0.982837i	$-0.559059\pi$
$163$	−15.0169	−	10.9104i	−1.17622	−	0.854572i	−0.991740	+	0.128265i	$0.959059\pi$
$164$	18.7934			1.46752
$165$		0			0
$166$	−0.849772			−0.0659551
$167$	11.0783	+	8.04887i	0.857266	+	0.622840i	0.927140	−	0.374716i	$-0.122260\pi$
$167$	11.0783	+	8.04887i	0.857266	+	0.622840i	−0.0698740	+	0.997556i	$0.522260\pi$
$168$		0			0
$169$	2.87369	+	8.84431i	0.221053	+	0.680331i
$170$	−5.72836	−	7.88441i	−0.439345	−	0.604707i
$171$		0			0
$172$	−16.3978	+	5.32796i	−1.25032	+	0.406253i
$173$	4.08796	−	12.5814i	0.310802	−	0.956549i	−0.666647	−	0.745374i	$-0.732271\pi$
$173$	4.08796	−	12.5814i	0.310802	−	0.956549i	0.977448	−	0.211175i	$-0.0677290\pi$
$174$		0			0
$175$			0.345964i			0.0261524i
$176$	13.0291	−	5.19721i	0.982106	−	0.391755i
$177$		0			0
$178$	−9.43725	+	12.9893i	−0.707351	+	0.973586i
$179$	5.38656	+	1.75020i	0.402611	+	0.130816i	0.503321	−	0.864100i	$-0.332111\pi$
$179$	5.38656	+	1.75020i	0.402611	+	0.130816i	−0.100710	+	0.994916i	$0.532111\pi$
$180$		0			0
$181$	8.30217	−	6.03188i	0.617096	−	0.448346i	−0.234810	−	0.972041i	$-0.575447\pi$
$181$	8.30217	−	6.03188i	0.617096	−	0.448346i	0.851906	+	0.523695i	$0.175447\pi$
$182$	−0.971989	+	0.706191i	−0.0720486	+	0.0523464i
$183$		0			0
$184$	1.23692	+	0.401901i	0.0911872	+	0.0296285i
$185$	8.92341	−	12.2820i	0.656062	−	0.902992i
$186$		0			0
$187$	7.71095	−	3.07584i	0.563881	−	0.224928i
$188$		−	16.0157i		−	1.16807i
$189$		0			0
$190$	5.62906	−	17.3245i	0.408375	−	1.25685i
$191$	5.37500	−	1.74644i	0.388921	−	0.126368i	−0.108028	−	0.994148i	$-0.534454\pi$
$191$	5.37500	−	1.74644i	0.388921	−	0.126368i	0.496949	+	0.867780i	$0.334454\pi$
$192$		0			0
$193$	−10.5617	−	14.5369i	−0.760248	−	1.04639i	−0.997193	−	0.0748686i	$-0.976146\pi$
$193$	−10.5617	−	14.5369i	−0.760248	−	1.04639i	0.236945	−	0.971523i	$-0.423854\pi$
$194$	−5.26012	−	16.1890i	−0.377654	−	1.16230i
$195$		0			0
$196$	−10.4815	−	7.61527i	−0.748680	−	0.543948i
$197$	−2.51065			−0.178877			−0.0894383	−	0.995992i	$-0.528507\pi$
$197$	−2.51065			−0.178877			−0.0894383	+	0.995992i	$0.528507\pi$
$198$		0			0
$199$	12.2300			0.866959			0.433479	−	0.901163i	$-0.357286\pi$
$199$	12.2300			0.866959			0.433479	+	0.901163i	$0.357286\pi$
$200$	−0.212322	−	0.154261i	−0.0150134	−	0.0109079i
$201$		0			0
$202$	−1.00621	−	3.09681i	−0.0707970	−	0.217891i
$203$	1.66225	+	2.28790i	0.116667	+	0.160579i
$204$		0			0
$205$	−18.8191	+	6.11470i	−1.31438	+	0.427069i
$206$	−3.75667	+	11.5618i	−0.261739	+	0.805551i
$207$		0			0
$208$		−	8.13606i		−	0.564134i
$209$	13.1228	+	8.28095i	0.907726	+	0.572806i
$210$		0			0
$211$	−14.8533	+	20.4438i	−1.02254	+	1.40741i	−0.112134	+	0.993693i	$0.535769\pi$
$211$	−14.8533	+	20.4438i	−1.02254	+	1.40741i	−0.910407	+	0.413714i	$0.864231\pi$
$212$	3.20193	+	1.04037i	0.219910	+	0.0714530i
$213$		0			0
$214$	−18.8853	+	13.7210i	−1.29098	+	0.937948i
$215$	14.6867	−	10.6705i	1.00162	−	0.727723i
$216$		0			0
$217$	−0.100596	−	0.0326858i	−0.00682893	−	0.00221885i
$218$	−3.82000	+	5.25778i	−0.258723	+	0.356102i
$219$		0			0
$220$	9.46785	−	7.87341i	0.638323	−	0.530825i
$221$		−	4.81513i		−	0.323900i
$222$		0			0
$223$	4.35365	−	13.3991i	0.291542	−	0.897273i	−0.692819	−	0.721111i	$-0.743632\pi$
$223$	4.35365	−	13.3991i	0.291542	−	0.897273i	0.984361	−	0.176162i	$-0.0563683\pi$
$224$	−2.36708	+	0.769112i	−0.158157	+	0.0513884i
$225$		0			0
$226$	5.99210	+	8.24741i	0.398588	+	0.548610i
$227$	4.81543	+	14.8204i	0.319611	+	0.983663i	0.973815	+	0.227344i	$0.0730041\pi$
$227$	4.81543	+	14.8204i	0.319611	+	0.983663i	−0.654203	+	0.756319i	$0.726996\pi$
$228$		0			0
$229$	−16.6515	−	12.0981i	−1.10037	−	0.799462i	−0.119246	−	0.992865i	$-0.538048\pi$
$229$	−16.6515	−	12.0981i	−1.10037	−	0.799462i	−0.981119	+	0.193403i	$0.938048\pi$
$230$	21.0470			1.38780
$231$		0			0
$232$	−2.14529			−0.140845
$233$	2.11851	+	1.53918i	0.138788	+	0.100835i	0.655013	−	0.755618i	$-0.272663\pi$
$233$	2.11851	+	1.53918i	0.138788	+	0.100835i	−0.516225	+	0.856453i	$0.672663\pi$
$234$		0			0
$235$	5.21096	+	16.0377i	0.339925	+	1.04618i
$236$	−8.57341	−	11.8003i	−0.558081	−	0.768133i
$237$		0			0
$238$	−1.48680	+	0.483090i	−0.0963748	+	0.0313141i
$239$	−6.88161	+	21.1794i	−0.445134	+	1.36998i	0.437202	+	0.899363i	$0.355969\pi$
$239$	−6.88161	+	21.1794i	−0.445134	+	1.36998i	−0.882336	+	0.470619i	$0.844031\pi$
$240$		0			0
$241$			24.5862i			1.58374i	0.610690	+	0.791870i	$0.290892\pi$
$241$			24.5862i			1.58374i	−0.610690	+	0.791870i	$0.709108\pi$
$242$	9.32322	+	19.5523i	0.599319	+	1.25687i
$243$		0			0
$244$	2.72882	−	3.75589i	0.174695	−	0.240447i
$245$	12.9736	+	4.21538i	0.828854	+	0.269311i
$246$		0			0
$247$	7.28127	−	5.29015i	0.463296	−	0.336604i
$248$	0.0649143	−	0.0471630i	0.00412206	−	0.00299485i
$249$		0			0
$250$	−22.5538	−	7.32816i	−1.42643	−	0.463474i
$251$	7.34629	−	10.1113i	0.463694	−	0.638220i	−0.511576	−	0.859238i	$-0.670938\pi$
$251$	7.34629	−	10.1113i	0.463694	−	0.638220i	0.975270	+	0.221018i	$0.0709381\pi$
$252$		0			0
$253$	−4.41422	+	17.3768i	−0.277519	+	1.09247i
$254$		−	7.43797i		−	0.466700i
$255$		0			0
$256$	5.49194	−	16.9024i	0.343246	−	1.05640i
$257$	11.6642	−	3.78992i	0.727592	−	0.236409i	0.0782801	−	0.996931i	$-0.475057\pi$
$257$	11.6642	−	3.78992i	0.727592	−	0.236409i	0.649311	+	0.760523i	$0.275057\pi$
$258$		0			0
$259$	−1.43141	−	1.97017i	−0.0889437	−	0.122420i
$260$	−2.20705	−	6.79261i	−0.136876	−	0.421259i
$261$		0			0
$262$	−14.2105	−	10.3245i	−0.877929	−	0.637853i
$263$	−9.29043			−0.572872			−0.286436	−	0.958099i	$-0.592471\pi$
$263$	−9.29043			−0.572872			−0.286436	+	0.958099i	$0.592471\pi$
$264$		0			0
$265$	−3.54482			−0.217756
$266$	−2.36399	−	1.71754i	−0.144945	−	0.105309i
$267$		0			0
$268$	6.27167	+	19.3022i	0.383103	+	1.17907i
$269$	−12.5983	−	17.3401i	−0.768131	−	1.05724i	−0.996494	−	0.0836659i	$-0.973337\pi$
$269$	−12.5983	−	17.3401i	−0.768131	−	1.05724i	0.228363	−	0.973576i	$-0.426663\pi$
$270$		0			0
$271$	−7.87807	+	2.55974i	−0.478559	+	0.155493i	−0.538356	−	0.842717i	$-0.680954\pi$
$271$	−7.87807	+	2.55974i	−0.478559	+	0.155493i	0.0597976	+	0.998211i	$0.480954\pi$
$272$	3.27144	−	10.0685i	0.198360	−	0.610490i
$273$		0			0
$274$			9.49812i			0.573802i
$275$	1.93071	−	3.05961i	0.116426	−	0.184501i
$276$		0			0
$277$	6.78809	−	9.34300i	0.407857	−	0.561367i	−0.554837	−	0.831959i	$-0.687220\pi$
$277$	6.78809	−	9.34300i	0.407857	−	0.561367i	0.962694	+	0.270592i	$0.0872195\pi$
$278$	13.4813	+	4.38034i	0.808555	+	0.262715i
$279$		0			0
$280$	0.122056	−	0.0886792i	0.00729427	−	0.00529959i
$281$	−1.04790	+	0.761347i	−0.0625127	+	0.0454181i	−0.618603	−	0.785704i	$-0.712301\pi$
$281$	−1.04790	+	0.761347i	−0.0625127	+	0.0454181i	0.556090	+	0.831122i	$0.312301\pi$
$282$		0			0
$283$	6.28924	+	2.04350i	0.373857	+	0.121473i	0.489918	−	0.871769i	$-0.337027\pi$
$283$	6.28924	+	2.04350i	0.373857	+	0.121473i	−0.116061	+	0.993242i	$0.537027\pi$
$284$	13.1381	−	18.0831i	0.779605	−	1.07303i
$285$		0			0
$286$	12.5370	−	0.820992i	0.741329	−	0.0485463i
$287$			3.17415i			0.187364i
$288$		0			0
$289$	−3.31717	+	10.2092i	−0.195128	+	0.600541i
$290$	−33.0175	+	10.7280i	−1.93886	+	0.629973i
$291$		0			0
$292$	0.135177	+	0.186056i	0.00791066	+	0.0108881i
$293$	2.13460	+	6.56961i	0.124704	+	0.383801i	0.993847	−	0.110761i	$-0.0353287\pi$
$293$	2.13460	+	6.56961i	0.124704	+	0.383801i	−0.869143	+	0.494561i	$0.835329\pi$
$294$		0			0
$295$	12.4245	+	9.02696i	0.723385	+	0.525570i
$296$	1.84737			0.107376
$297$		0			0
$298$	−6.68695			−0.387365
$299$	8.41285	+	6.11229i	0.486528	+	0.353483i
$300$		0			0
$301$	−0.899877	−	2.76954i	−0.0518681	−	0.159633i
$302$	9.83213	+	13.5328i	0.565776	+	0.778724i
$303$		0			0
$304$	18.8193	−	6.11478i	1.07936	−	0.350706i
$305$	−1.51052	+	4.64890i	−0.0864921	+	0.266195i
$306$		0			0
$307$		−	11.5549i		−	0.659473i	−0.944073	−	0.329737i	$-0.893040\pi$
$307$		−	11.5549i		−	0.659473i	0.944073	−	0.329737i	$-0.106960\pi$
$308$	−0.731847	−	1.83470i	−0.0417009	−	0.104542i
$309$		0			0
$310$	0.763228	−	1.05049i	0.0433485	−	0.0596640i
$311$	−6.63931	−	2.15724i	−0.376481	−	0.122326i	0.114663	−	0.993404i	$-0.463421\pi$
$311$	−6.63931	−	2.15724i	−0.376481	−	0.122326i	−0.491144	+	0.871078i	$0.663421\pi$
$312$		0			0
$313$	23.2016	−	16.8569i	1.31143	−	0.952809i	0.311433	−	0.950268i	$-0.399191\pi$
$313$	23.2016	−	16.8569i	1.31143	−	0.952809i	0.999997	−	0.00254099i	$-0.000808825\pi$
$314$	−29.4685	+	21.4101i	−1.66300	+	1.20824i
$315$		0			0
$316$	−22.3011	−	7.24607i	−1.25453	−	0.407623i
$317$	−17.6372	+	24.2755i	−0.990602	+	1.36345i	−0.0596841	+	0.998217i	$0.519009\pi$
$317$	−17.6372	+	24.2755i	−0.990602	+	1.36345i	−0.930918	+	0.365229i	$0.880991\pi$
$318$		0			0
$319$	−1.93247	−	29.5100i	−0.108198	−	1.65224i
$320$		−	13.8294i		−	0.773086i
$321$		0			0
$322$	1.04329	−	3.21092i	0.0581404	−	0.178938i
$323$	11.1378	−	3.61888i	0.619722	−	0.201360i
$324$		0			0
$325$	−1.23341	−	1.69764i	−0.0684170	−	0.0941679i
$326$	−11.2954	−	34.7636i	−0.625592	−	1.92538i
$327$		0			0
$328$	−1.94801	−	1.41531i	−0.107561	−	0.0781476i
$329$	2.70501			0.149132
$330$		0			0
$331$	8.53322			0.469028			0.234514	−	0.972113i	$-0.424650\pi$
$331$	8.53322			0.469028			0.234514	+	0.972113i	$0.424650\pi$
$332$	−0.655573	−	0.476302i	−0.0359792	−	0.0261404i
$333$		0			0
$334$	8.33283	+	25.6458i	0.455952	+	1.40328i
$335$	−12.5605	−	17.2881i	−0.686254	−	0.944548i
$336$		0			0
$337$	11.3580	−	3.69045i	0.618712	−	0.201032i	0.0171437	−	0.999853i	$-0.494543\pi$
$337$	11.3580	−	3.69045i	0.618712	−	0.201032i	0.601568	+	0.798821i	$0.294543\pi$
$338$	−5.65893	+	17.4164i	−0.307805	+	0.947326i
$339$		0			0
$340$		−	9.29335i		−	0.504003i
$341$	0.707236	+	0.850459i	0.0382990	+	0.0460549i
$342$		0			0
$343$	2.59115	−	3.56641i	0.139909	−	0.192568i
$344$	2.10094	+	0.682637i	0.113275	+	0.0368053i
$345$		0			0
$346$	21.0754	−	15.3122i	1.13302	−	0.823187i
$347$	−11.6828	+	8.48806i	−0.627166	+	0.455663i	−0.855417	−	0.517939i	$-0.826699\pi$
$347$	−11.6828	+	8.48806i	−0.627166	+	0.455663i	0.228251	+	0.973602i	$0.426699\pi$
$348$		0			0
$349$	−30.6945	−	9.97326i	−1.64304	−	0.533856i	−0.665826	−	0.746107i	$-0.731921\pi$
$349$	−30.6945	−	9.97326i	−1.64304	−	0.533856i	−0.977215	+	0.212251i	$0.931921\pi$
$350$	−0.400446	+	0.551167i	−0.0214047	+	0.0294611i
$351$		0			0
$352$	25.2259	+	6.40813i	1.34455	+	0.341554i
$353$		−	6.48146i		−	0.344973i	−0.985012	−	0.172487i	$-0.944820\pi$
$353$		−	6.48146i		−	0.344973i	0.985012	−	0.172487i	$-0.0551802\pi$
$354$		0			0
$355$	−7.27253	+	22.3825i	−0.385986	+	1.18794i
$356$	−14.5611	+	4.73118i	−0.771736	+	0.250752i
$357$		0			0
$358$	6.55569	+	9.02313i	0.346479	+	0.476887i
$359$	2.95299	+	9.08837i	0.155853	+	0.479666i	0.998246	−	0.0591972i	$-0.0188541\pi$
$359$	2.95299	+	9.08837i	0.155853	+	0.479666i	−0.842393	+	0.538863i	$0.818854\pi$
$360$		0			0
$361$	2.33755	+	1.69833i	0.123029	+	0.0893858i
$362$	20.2082			1.06212
$363$		0			0
$364$	−1.14568			−0.0600501
$365$	−0.195899	−	0.142329i	−0.0102538	−	0.00744982i
$366$		0			0
$367$	−2.49364	−	7.67463i	−0.130167	−	0.400613i	0.864640	−	0.502392i	$-0.167546\pi$
$367$	−2.49364	−	7.67463i	−0.130167	−	0.400613i	−0.994807	+	0.101779i	$0.967546\pi$
$368$	13.4386	+	18.4966i	0.700534	+	0.964202i
$369$		0			0
$370$	28.4323	−	9.23822i	1.47813	−	0.480272i
$371$	−0.175716	+	0.540797i	−0.00912270	+	0.0280768i
$372$		0			0
$373$		−	0.696327i		−	0.0360545i	−0.999837	−	0.0180272i	$-0.994261\pi$
$373$		−	0.696327i		−	0.0360545i	0.999837	−	0.0180272i	$-0.00573856\pi$
$374$	15.8448	+	4.02504i	0.819314	+	0.208130i
$375$		0			0
$376$	−1.20613	+	1.66010i	−0.0622015	+	0.0856130i
$377$	−16.3133	−	5.30050i	−0.840175	−	0.272990i
$378$		0			0
$379$	2.08014	−	1.51131i	0.106850	−	0.0776308i	−0.533077	−	0.846066i	$-0.678965\pi$
$379$	2.08014	−	1.51131i	0.106850	−	0.0776308i	0.639927	+	0.768436i	$0.278965\pi$
$380$	14.0531	−	10.2102i	0.720908	−	0.523770i
$381$		0			0
$382$	10.5845	+	3.43913i	0.541552	+	0.175961i
$383$	3.66517	−	5.04467i	0.187281	−	0.257770i	−0.705044	−	0.709164i	$-0.749073\pi$
$383$	3.66517	−	5.04467i	0.187281	−	0.257770i	0.892325	+	0.451393i	$0.149073\pi$
$384$		0			0
$385$	1.32980	+	1.59909i	0.0677727	+	0.0814973i
$386$		−	35.3842i		−	1.80101i
$387$		0			0
$388$	5.01598	−	15.4376i	0.254648	−	0.783726i
$389$	−26.1325	+	8.49096i	−1.32497	+	0.430509i	−0.884199	−	0.467111i	$-0.845295\pi$
$389$	−26.1325	+	8.49096i	−1.32497	+	0.430509i	−0.440771	+	0.897620i	$0.645295\pi$
$390$		0			0
$391$	7.95328	+	10.9468i	0.402215	+	0.553601i
$392$	0.512953	+	1.57871i	0.0259081	+	0.0797368i
$393$		0			0
$394$	−3.99980	−	2.90602i	−0.201507	−	0.146403i
$395$	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	$0.440062\pi$
$398$	19.4839	+	14.1559i	0.976641	+	0.709571i
$399$		0			0
$400$	−1.42567	−	4.38775i	−0.0712834	−	0.219388i
$401$	−1.46277	−	2.01333i	−0.0730473	−	0.100541i	0.770930	−	0.636920i	$-0.219792\pi$
$401$	−1.46277	−	2.01333i	−0.0730473	−	0.100541i	−0.843977	+	0.536379i	$0.819792\pi$
$402$		0			0
$403$	0.610152	−	0.198251i	0.0303939	−	0.00987556i
$404$	0.959514	−	2.95308i	0.0477376	−	0.146921i
$405$		0			0
$406$			5.56894i			0.276382i
$407$	1.66411	+	25.4119i	0.0824867	+	1.25962i
$408$		0			0
$409$	−17.4089	+	23.9613i	−0.860815	+	1.18481i	0.120560	+	0.992706i	$0.461531\pi$
$409$	−17.4089	+	23.9613i	−0.860815	+	1.18481i	−0.981375	+	0.192104i	$0.938469\pi$
$410$	−37.0590	−	12.0412i	−1.83021	−	0.594672i
$411$		0			0
$412$	−9.37861	+	6.81396i	−0.462051	+	0.335700i
$413$	1.99303	−	1.44802i	0.0980708	−	0.0712526i
$414$		0			0
$415$	0.811442	+	0.263654i	0.0398321	+	0.0129422i
$416$	8.87323	−	12.2130i	0.435046	−	0.598789i
$417$		0			0
$418$	11.3214	+	28.3820i	0.553747	+	1.38821i
$419$		−	9.04569i		−	0.441911i	−0.975284	−	0.220955i	$-0.929082\pi$
$419$		−	9.04569i		−	0.441911i	0.975284	−	0.220955i	$-0.0709175\pi$
$420$		0			0
$421$	−6.71611	+	20.6701i	−0.327323	+	1.00740i	0.643058	+	0.765818i	$0.277665\pi$
$421$	−6.71611	+	20.6701i	−0.327323	+	1.00740i	−0.970381	+	0.241579i	$0.922335\pi$
$422$	−47.3264	+	15.3773i	−2.30381	+	0.748554i
$423$		0			0
$424$	−0.253544	−	0.348973i	−0.0123132	−	0.0169476i
$425$	−0.843746	−	2.59678i	−0.0409277	−	0.125962i
$426$		0			0
$427$	0.634360	+	0.460889i	0.0306988	+	0.0223040i
$428$	−22.2601			−1.07598
$429$		0			0
$430$	35.7487			1.72396
$431$	−14.2119	−	10.3256i	−0.684565	−	0.497366i	0.190304	−	0.981725i	$-0.439053\pi$
$431$	−14.2119	−	10.3256i	−0.684565	−	0.497366i	−0.874869	+	0.484359i	$0.839053\pi$
$432$		0			0
$433$	−4.84981	−	14.9262i	−0.233067	−	0.717306i	−0.997372	−	0.0724515i	$-0.976918\pi$
$433$	−4.84981	−	14.9262i	−0.233067	−	0.717306i	0.764305	−	0.644855i	$-0.223082\pi$
$434$	−0.122430	−	0.168511i	−0.00587684	−	0.00808878i
$435$		0			0
$436$	−5.89402	+	1.91508i	−0.282272	+	0.0917159i
$437$	−7.81541	+	24.0534i	−0.373862	+	1.15063i
$438$		0			0
$439$			11.9259i			0.569193i	0.958647	+	0.284597i	$0.0918596\pi$
$439$			11.9259i			0.569193i	−0.958647	+	0.284597i	$0.908140\pi$
$440$	−1.57432	+	0.103095i	−0.0750528	+	0.00491487i
$441$		0			0
$442$	5.57340	−	7.67113i	0.265100	−	0.364878i
$443$	14.6861	+	4.77179i	0.697756	+	0.226715i	0.636353	−	0.771398i	$-0.280442\pi$
$443$	14.6861	+	4.77179i	0.697756	+	0.226715i	0.0614036	+	0.998113i	$0.480442\pi$
$444$		0			0
$445$	13.0417	−	9.47532i	0.618234	−	0.449173i
$446$	22.4451	−	16.3074i	1.06281	−	0.772175i
$447$		0			0
$448$	−2.10981	−	0.685519i	−0.0996791	−	0.0323877i
$449$	−13.6969	+	18.8521i	−0.646395	+	0.889687i	−0.998936	−	0.0461094i	$-0.985318\pi$
$449$	−13.6969	+	18.8521i	−0.646395	+	0.889687i	0.352541	+	0.935796i	$0.385318\pi$
$450$		0			0
$451$	17.7139	−	28.0712i	0.834115	−	1.32182i
$452$			9.72122i			0.457248i
$453$		0			0
$454$	−9.48264	+	29.1846i	−0.445042	+	1.36970i
$455$	1.14725	−	0.372765i	0.0537840	−	0.0174755i
$456$		0			0
$457$	0.363446	+	0.500241i	0.0170013	+	0.0234003i	0.817433	−	0.576024i	$-0.195396\pi$
$457$	0.363446	+	0.500241i	0.0170013	+	0.0234003i	−0.800432	+	0.599424i	$0.795396\pi$
$458$	−12.5249	−	38.5476i	−0.585249	−	1.80121i
$459$		0			0
$460$	16.2371	+	11.7969i	0.757058	+	0.550035i
$461$	22.7574			1.05992			0.529959	−	0.848023i	$-0.322207\pi$
$461$	22.7574			1.05992			0.529959	+	0.848023i	$0.322207\pi$
$462$		0			0
$463$	7.08852			0.329431			0.164716	−	0.986341i	$-0.447329\pi$
$463$	7.08852			0.329431			0.164716	+	0.986341i	$0.447329\pi$
$464$	−30.5099	−	22.1667i	−1.41639	−	1.02907i
$465$		0			0
$466$	1.59349	+	4.90425i	0.0738169	+	0.227185i
$467$	3.50195	+	4.82002i	0.162051	+	0.223044i	0.882319	−	0.470652i	$-0.155981\pi$
$467$	3.50195	+	4.82002i	0.162051	+	0.223044i	−0.720268	+	0.693696i	$0.755981\pi$
$468$		0			0
$469$	−3.26009	+	1.05927i	−0.150537	+	0.0489124i
$470$	−10.2615	+	31.5817i	−0.473328	+	1.45675i
$471$		0			0
$472$			1.86880i			0.0860187i
$473$	−7.49764	+	29.5149i	−0.344742	+	1.35710i
$474$		0			0
$475$	2.99978	−	4.12885i	0.137639	−	0.189444i
$476$	−1.41779	−	0.460669i	−0.0649844	−	0.0211147i
$477$		0			0
$478$	−35.4780	+	25.7763i	−1.62273	+	1.17898i
$479$	1.42565	−	1.03580i	0.0651398	−	0.0473269i	−0.554739	−	0.832025i	$-0.687182\pi$
$479$	1.42565	−	1.03580i	0.0651398	−	0.0473269i	0.619879	+	0.784698i	$0.287182\pi$
$480$		0			0
$481$	14.0478	+	4.56441i	0.640525	+	0.208119i
$482$	−28.4580	+	39.1691i	−1.29623	+	1.78410i
$483$		0			0
$484$	−3.76661	+	20.3097i	−0.171210	+	0.923170i
$485$			17.0908i			0.776052i
$486$		0			0
$487$	−5.37983	+	16.5574i	−0.243783	+	0.750288i	0.752051	+	0.659105i	$0.229065\pi$
$487$	−5.37983	+	16.5574i	−0.243783	+	0.750288i	−0.995834	+	0.0911829i	$0.970935\pi$
$488$	−0.565706	+	0.183809i	−0.0256083	+	0.00832065i
$489$		0			0
$490$	15.7895	+	21.7323i	0.713295	+	0.981767i
$491$	−10.3841	−	31.9589i	−0.468626	−	1.44228i	−0.854364	−	0.519675i	$-0.826053\pi$
$491$	−10.3841	−	31.9589i	−0.468626	−	1.44228i	0.385738	−	0.922608i	$-0.373947\pi$
$492$		0			0
$493$	−18.0565	−	13.1188i	−0.813225	−	0.590843i
$494$	17.7233			0.797407
$495$		0			0
$496$	1.41052			0.0633344
$497$	3.05418	+	2.21899i	0.136999	+	0.0995355i
$498$		0			0
$499$	6.03285	+	18.5672i	0.270068	+	0.831183i	0.990482	+	0.137639i	$0.0439514\pi$
$499$	6.03285	+	18.5672i	0.270068	+	0.831183i	−0.720415	+	0.693543i	$0.756049\pi$
$500$	−13.2921	−	18.2949i	−0.594439	−	0.818175i
$501$		0			0
$502$	23.4072	−	7.60546i	1.04471	−	0.339448i
$503$	−7.43631	+	22.8866i	−0.331569	+	1.02046i	0.636819	+	0.771013i	$0.280250\pi$
$503$	−7.43631	+	22.8866i	−0.331569	+	1.02046i	−0.968388	+	0.249450i	$0.919750\pi$
$504$		0			0
$505$			3.26932i			0.145483i
$506$	−27.1457	+	22.5742i	−1.20677	+	1.00355i
$507$		0			0
$508$	4.16902	−	5.73816i	0.184970	−	0.254590i
$509$	16.6684	+	5.41589i	0.738814	+	0.240055i	0.654161	−	0.756355i	$-0.273022\pi$
$509$	16.6684	+	5.41589i	0.738814	+	0.240055i	0.0846527	+	0.996411i	$0.473022\pi$
$510$		0			0
$511$	−0.0314243	+	0.0228311i	−0.00139013	+	0.00100999i
$512$	25.2051	−	18.3126i	1.11392	−	0.809309i
$513$		0			0
$514$	22.9693	+	7.46319i	1.01313	+	0.329187i
$515$	7.17444	−	9.87476i	0.316143	−	0.435134i
$516$		0			0
$517$	−23.9223	−	15.0958i	−1.05210	−	0.663913i
$518$		−	4.79557i		−	0.210705i
$519$		0			0
$520$	−0.282775	+	0.870292i	−0.0124005	+	0.0381648i
$521$	7.32063	−	2.37862i	0.320723	−	0.104209i	−0.144231	−	0.989544i	$-0.546071\pi$
$521$	7.32063	−	2.37862i	0.320723	−	0.104209i	0.464954	+	0.885335i	$0.346071\pi$
$522$		0			0
$523$	−7.75187	−	10.6695i	−0.338966	−	0.466546i	0.605173	−	0.796094i	$-0.293104\pi$
$523$	−7.75187	−	10.6695i	−0.338966	−	0.466546i	−0.944139	+	0.329547i	$0.893104\pi$
$524$	−5.17601	−	15.9301i	−0.226115	−	0.695911i
$525$		0			0
$526$	−14.8009	−	10.7535i	−0.645349	−	0.468873i
$527$	0.834784			0.0363638
$528$		0			0
$529$	−6.22172			−0.270509
$530$	−5.64736	−	4.10305i	−0.245306	−	0.178225i
$531$		0			0
$532$	−0.861054	−	2.65005i	−0.0373314	−	0.114894i
$533$	−11.3162	−	15.5755i	−0.490160	−	0.674648i
$534$		0			0
$535$	22.2906	−	7.24266i	0.963708	−	0.313128i
$536$	0.803548	−	2.47307i	0.0347080	−	0.106820i
$537$		0			0
$538$		−	42.2072i		−	1.81968i
$539$	−21.2542	+	8.47815i	−0.915484	+	0.365180i
$540$		0			0
$541$	−8.36941	+	11.5195i	−0.359829	+	0.495262i	−0.950101	−	0.311942i	$-0.899021\pi$
$541$	−8.36941	+	11.5195i	−0.359829	+	0.495262i	0.590272	+	0.807204i	$0.299021\pi$
$542$	−15.5136	−	5.04069i	−0.666368	−	0.216516i
$543$		0			0
$544$	15.8914	−	11.5458i	0.681339	−	0.495022i
$545$	5.27899	−	3.83541i	0.226127	−	0.164291i
$546$		0			0
$547$	35.9640	+	11.6854i	1.53771	+	0.499632i	0.950744	−	0.309978i	$-0.100322\pi$
$547$	35.9640	+	11.6854i	1.53771	+	0.499632i	0.586967	+	0.809611i	$0.300322\pi$
$548$	−5.32374	+	7.32750i	−0.227419	+	0.313015i
$549$		0			0
$550$	6.61731	−	2.63960i	0.282163	−	0.112553i
$551$		−	41.7175i		−	1.77723i
$552$		0			0
$553$	1.22384	−	3.76659i	0.0520430	−	0.160172i
$554$	21.6286	−	7.02757i	0.918913	−	0.298573i
$555$		0			0
$556$	7.94520	+	10.9356i	0.336952	+	0.463774i
$557$	4.83577	+	14.8830i	0.204898	+	0.630612i	0.999718	+	0.0237660i	$0.00756565\pi$
$557$	4.83577	+	14.8830i	0.204898	+	0.630612i	−0.794819	+	0.606846i	$0.792434\pi$
$558$		0			0
$559$	14.2894	+	10.3819i	0.604378	+	0.439106i
$560$	2.65217			0.112075
$561$		0			0
$562$	−2.55069			−0.107594
$563$	13.0398	+	9.47394i	0.549561	+	0.399279i	0.827623	−	0.561284i	$-0.189692\pi$
$563$	13.0398	+	9.47394i	0.549561	+	0.399279i	−0.278063	+	0.960563i	$0.589692\pi$
$564$		0			0
$565$	−3.16294	−	9.73453i	−0.133066	−	0.409535i
$566$	7.65428	+	10.5352i	0.321734	+	0.442828i
$567$		0			0
$568$	−2.72364	+	0.884966i	−0.114282	+	0.0371323i
$569$	−7.49721	+	23.0740i	−0.314299	+	0.967314i	0.661743	+	0.749731i	$0.269817\pi$
$569$	−7.49721	+	23.0740i	−0.314299	+	0.967314i	−0.976042	+	0.217583i	$0.930183\pi$
$570$		0			0
$571$		−	16.7867i		−	0.702501i	−0.936282	−	0.351250i	$-0.885757\pi$
$571$		−	16.7867i		−	0.702501i	0.936282	−	0.351250i	$-0.114243\pi$
$572$	10.1321	+	6.39368i	0.423643	+	0.267333i
$573$		0			0
$574$	−3.67401	+	5.05683i	−0.153350	+	0.211068i
$575$	5.60807	+	1.82217i	0.233873	+	0.0759899i
$576$		0			0
$577$	5.58119	−	4.05497i	0.232348	−	0.168811i	−0.465519	−	0.885038i	$-0.654132\pi$
$577$	5.58119	−	4.05497i	0.232348	−	0.168811i	0.697867	+	0.716227i	$0.254132\pi$
$578$	−17.1016	+	12.4250i	−0.711333	+	0.516814i
$579$		0			0
$580$	−31.4851	−	10.2301i	−1.30735	−	0.424783i
$581$	0.0804460	−	0.110724i	0.00333746	−	0.00459362i
$582$		0			0
$583$	4.57199	−	3.80204i	0.189353	−	0.157464i
$584$		−	0.0294655i		−	0.00121929i
$585$		0			0
$586$	−4.20349	+	12.9370i	−0.173644	+	0.534422i
$587$	23.3789	−	7.59628i	0.964952	−	0.313532i	0.216176	−	0.976354i	$-0.430642\pi$
$587$	23.3789	−	7.59628i	0.964952	−	0.313532i	0.748777	+	0.662822i	$0.230642\pi$
$588$		0			0
$589$	0.917138	+	1.26233i	0.0377900	+	0.0520135i
$590$	9.34543	+	28.7623i	0.384745	+	1.18412i
$591$		0			0
$592$	26.2729	+	19.0884i	1.07981	+	0.784529i
$593$	25.3400			1.04059			0.520295	−	0.853987i	$-0.325822\pi$
$593$	25.3400			1.04059			0.520295	+	0.853987i	$0.325822\pi$
$594$		0			0
$595$	1.56962			0.0643481
$596$	−5.15877	−	3.74807i	−0.211312	−	0.153527i
$597$		0			0
$598$	6.32793	+	19.4754i	0.258768	+	0.796407i
$599$	12.7726	+	17.5799i	0.521873	+	0.718297i	0.985865	−	0.167543i	$-0.0535832\pi$
$599$	12.7726	+	17.5799i	0.521873	+	0.718297i	−0.463992	+	0.885840i	$0.653583\pi$
$600$		0			0
$601$	−17.8627	+	5.80394i	−0.728634	+	0.236748i	−0.649762	−	0.760137i	$-0.725132\pi$
$601$	−17.8627	+	5.80394i	−0.728634	+	0.236748i	−0.0788714	+	0.996885i	$0.525132\pi$
$602$	1.77206	−	5.45383i	0.0722236	−	0.222281i
$603$		0			0
$604$			15.9511i			0.649040i
$605$	−2.83630	−	21.5631i	−0.115312	−	0.876663i
$606$		0			0
$607$	28.2291	−	38.8540i	1.14578	−	1.57704i	0.391930	−	0.919995i	$-0.371807\pi$
$607$	28.2291	−	38.8540i	1.14578	−	1.57704i	0.753854	−	0.657042i	$-0.228193\pi$
$608$	34.9183	+	11.3456i	1.41612	+	0.460127i
$609$		0			0
$610$	−7.78745	+	5.65792i	−0.315305	+	0.229082i
$611$	−13.2734	+	9.64370i	−0.536985	+	0.390142i
$612$		0			0
$613$	1.96455	+	0.638321i	0.0793474	+	0.0257815i	0.348422	−	0.937338i	$-0.386718\pi$
$613$	1.96455	+	0.638321i	0.0793474	+	0.0257815i	−0.269074	+	0.963119i	$0.586718\pi$
$614$	13.3745	−	18.4085i	0.539753	−	0.742906i
$615$		0			0
$616$	−0.0623105	+	0.245289i	−0.00251056	+	0.00988296i
$617$		−	34.5882i		−	1.39247i	−0.717814	−	0.696235i	$-0.754857\pi$
$617$		−	34.5882i		−	1.39247i	0.717814	−	0.696235i	$-0.245143\pi$
$618$		0			0
$619$	8.47676	−	26.0888i	0.340710	−	1.04860i	−0.623131	−	0.782117i	$-0.714140\pi$
$619$	8.47676	−	26.0888i	0.340710	−	1.04860i	0.963841	−	0.266479i	$-0.0858603\pi$
$620$	1.17761	−	0.382630i	0.0472941	−	0.0153668i
$621$		0			0
$622$	−8.08033	−	11.1216i	−0.323992	−	0.445936i
$623$	−0.799083	−	2.45932i	−0.0320146	−	0.0985307i
$624$		0			0
$625$	14.8503	+	10.7894i	0.594012	+	0.431575i
$626$	56.4746			2.25718
$627$		0			0
$628$	−34.7345			−1.38606
$629$	15.5490	+	11.2970i	0.619979	+	0.450441i
$630$		0			0
$631$	−8.09100	−	24.9015i	−0.322098	−	0.991315i	−0.972734	−	0.231925i	$-0.925498\pi$
$631$	−8.09100	−	24.9015i	−0.322098	−	0.991315i	0.650636	−	0.759390i	$-0.274502\pi$
$632$	1.76591	+	2.43056i	0.0702439	+	0.0966825i
$633$		0			0
$634$	−56.1966	+	18.2594i	−2.23185	+	0.725173i
$635$	−2.30773	+	7.10247i	−0.0915796	+	0.281853i
$636$		0			0
$637$			13.2723i			0.525866i
$638$	31.0784	−	49.2501i	1.23041	−	1.94983i
$639$		0			0
$640$	−2.23267	+	3.07300i	−0.0882539	+	0.121471i
$641$	5.81496	+	1.88940i	0.229677	+	0.0746266i	0.421595	−	0.906784i	$-0.361471\pi$
$641$	5.81496	+	1.88940i	0.229677	+	0.0746266i	−0.191917	+	0.981411i	$0.561471\pi$
$642$		0			0
$643$	0.662093	−	0.481039i	0.0261104	−	0.0189703i	−0.574654	−	0.818397i	$-0.694863\pi$
$643$	0.662093	−	0.481039i	0.0261104	−	0.0189703i	0.600764	+	0.799426i	$0.294863\pi$
$644$	2.60461	−	1.89236i	0.102636	−	0.0745693i
$645$		0			0
$646$	21.9327	+	7.12636i	0.862930	+	0.280383i
$647$	−3.42533	+	4.71456i	−0.134664	+	0.185349i	−0.871023	−	0.491242i	$-0.836543\pi$
$647$	−3.42533	+	4.71456i	−0.134664	+	0.185349i	0.736360	+	0.676590i	$0.236543\pi$
$648$		0			0
$649$	−25.7068	+	1.68342i	−1.00908	+	0.0660800i
$650$		−	4.13220i		−	0.162078i
$651$		0			0
$652$	10.7711	−	33.1501i	0.421830	−	1.29826i
$653$	2.47667	−	0.804718i	0.0969195	−	0.0314911i	−0.260156	−	0.965567i	$-0.583774\pi$
$653$	2.47667	−	0.804718i	0.0969195	−	0.0314911i	0.357075	+	0.934076i	$0.383774\pi$
$654$		0			0
$655$	10.3662	+	14.2679i	0.405041	+	0.557491i
$656$	−13.0802	−	40.2567i	−0.510696	−	1.57176i
$657$		0			0
$658$	4.30944	+	3.13099i	0.168000	+	0.122059i
$659$	−22.5035			−0.876613			−0.438306	−	0.898826i	$-0.644422\pi$
$659$	−22.5035			−0.876613			−0.438306	+	0.898826i	$0.644422\pi$
$660$		0			0
$661$	−6.46574			−0.251488			−0.125744	−	0.992063i	$-0.540132\pi$
$661$	−6.46574			−0.251488			−0.125744	+	0.992063i	$0.540132\pi$
$662$	13.5945	+	9.87701i	0.528367	+	0.383881i
$663$		0			0
$664$	0.0320830	+	0.0987412i	0.00124506	+	0.00383190i
$665$	1.72447	+	2.37353i	0.0668720	+	0.0920414i
$666$		0			0
$667$	45.8417	−	14.8949i	1.77500	−	0.576732i
$668$	−7.94608	+	24.4555i	−0.307443	+	0.946213i
$669$		0			0
$670$		−	42.0807i		−	1.62572i
$671$	−3.03802	−	7.61613i	−0.117281	−	0.294017i
$672$		0			0
$673$	0.208907	−	0.287536i	0.00805278	−	0.0110837i	−0.804972	−	0.593313i	$-0.797820\pi$
$673$	0.208907	−	0.287536i	0.00805278	−	0.0110837i	0.813024	+	0.582230i	$0.197820\pi$
$674$	22.3665	+	7.26731i	0.861524	+	0.279926i
$675$		0			0
$676$	−14.1276	+	10.2643i	−0.543371	+	0.394782i
$677$	23.6606	−	17.1904i	0.909350	−	0.660681i	−0.0315007	−	0.999504i	$-0.510029\pi$
$677$	23.6606	−	17.1904i	0.909350	−	0.660681i	0.940850	+	0.338823i	$0.110029\pi$
$678$		0			0
$679$	2.60737	+	0.847185i	0.100062	+	0.0325120i
$680$	−0.699874	+	0.963294i	−0.0268389	+	0.0369406i
$681$		0			0
$682$	0.142333	+	2.17350i	0.00545021	+	0.0832278i
$683$		−	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
$686$	8.25607	−	2.68256i	0.315218	−	0.102421i
$687$		0			0
$688$	22.8257	+	31.4169i	0.870222	+	1.19776i
$689$	−1.06578	−	3.28012i	−0.0406029	−	0.124963i
$690$		0			0
$691$	−36.1043	−	26.2313i	−1.37347	−	0.997885i	−0.997457	−	0.0712711i	$-0.977294\pi$
$691$	−36.1043	−	26.2313i	−1.37347	−	0.997885i	−0.376014	−	0.926614i	$-0.622706\pi$
$692$	24.8415			0.944334
$693$		0			0
$694$	−28.4370			−1.07945
$695$	−11.5142	−	8.36552i	−0.436757	−	0.317322i
$696$		0			0
$697$	−7.74119	−	23.8249i	−0.293218	−	0.902433i
$698$	−37.3566	−	51.4170i	−1.41397	−	1.94616i
$699$		0			0
$700$	−0.617863	+	0.200756i	−0.0233530	+	0.00758786i
$701$	3.87098	−	11.9137i	0.146205	−	0.449972i	−0.850959	−	0.525232i	$-0.823979\pi$
$701$	3.87098	−	11.9137i	0.146205	−	0.449972i	0.997164	+	0.0752595i	$0.0239785\pi$
$702$		0			0
$703$			35.9241i			1.35490i
$704$	14.8329	+	17.8367i	0.559035	+	0.672245i
$705$		0			0
$706$	7.50215	−	10.3258i	0.282347	−	0.388617i
$707$	0.498767	+	0.162059i	0.0187581	+	0.00609486i
$708$		0			0
$709$	9.09600	−	6.60863i	0.341607	−	0.248192i	−0.403732	−	0.914877i	$-0.632287\pi$
$709$	9.09600	−	6.60863i	0.341607	−	0.248192i	0.745340	+	0.666685i	$0.232287\pi$
$710$	−37.4934	+	27.2406i	−1.40710	+	1.02232i
$711$		0			0
$712$	1.86562	+	0.606176i	0.0699169	+	0.0227174i
$713$	−1.05967	+	1.45851i	−0.0396850	+	0.0546217i
$714$		0			0
$715$	−12.2262	−	3.10582i	−0.457235	−	0.116151i
$716$			10.6356i			0.397469i
$717$		0			0
$718$	−5.81508	+	17.8970i	−0.217017	+	0.667909i
$719$	−8.20360	+	2.66551i	−0.305942	+	0.0994067i	−0.457965	−	0.888970i	$-0.651421\pi$
$719$	−8.20360	+	2.66551i	−0.305942	+	0.0994067i	0.152022	+	0.988377i	$0.451421\pi$
$720$		0			0
$721$	−1.15086	−	1.58402i	−0.0428602	−	0.0589920i
$722$	1.75825	+	5.41133i	0.0654352	+	0.201389i
$723$		0			0
$724$	15.5900	+	11.3268i	0.579398	+	0.420957i
$725$	−9.72649			−0.361233
$726$		0			0
$727$	−47.4032			−1.75809			−0.879044	−	0.476740i	$-0.841818\pi$
$727$	−47.4032			−1.75809			−0.879044	+	0.476740i	$0.841818\pi$
$728$	0.118755	+	0.0862803i	0.00440134	+	0.00319776i
$729$		0			0
$730$	−0.147350	−	0.453496i	−0.00545366	−	0.0167847i
$731$	13.5088	+	18.5933i	0.499642	+	0.687698i
$732$		0			0
$733$	−14.7226	+	4.78367i	−0.543792	+	0.176689i	−0.568016	−	0.823018i	$-0.692289\pi$
$733$	−14.7226	+	4.78367i	−0.543792	+	0.176689i	0.0242235	+	0.999707i	$0.492289\pi$
$734$	4.91052	−	15.1130i	0.181251	−	0.557832i
$735$		0			0
$736$			42.4212i			1.56367i
$737$	34.7427	+	8.82565i	1.27976	+	0.325097i
$738$		0			0
$739$	25.0234	−	34.4418i	0.920502	−	1.26696i	−0.0429492	−	0.999077i	$-0.513675\pi$
$739$	25.0234	−	34.4418i	0.920502	−	1.26696i	0.963451	−	0.267885i	$-0.0863246\pi$
$740$	27.1127	+	8.80946i	0.996683	+	0.323842i
$741$		0			0
$742$	−0.905899	+	0.658174i	−0.0332566	+	0.0241623i
$743$	39.0636	−	28.3814i	1.43310	−	1.04121i	0.443676	−	0.896187i	$-0.353674\pi$
$743$	39.0636	−	28.3814i	1.43310	−	1.04121i	0.989428	−	0.145024i	$-0.0463259\pi$
$744$		0			0
$745$	6.38532	+	2.07472i	0.233940	+	0.0760118i
$746$	0.805983	−	1.10934i	0.0295091	−	0.0406159i
$747$		0			0
$748$	9.96770	+	11.9863i	0.364455	+	0.438261i
$749$		−	3.75967i		−	0.137375i
$750$		0			0
$751$	7.95196	−	24.4736i	0.290171	−	0.893055i	−0.694630	−	0.719368i	$-0.744432\pi$
$751$	7.95196	−	24.4736i	0.290171	−	0.893055i	0.984801	−	0.173688i	$-0.0555683\pi$
$752$	−34.3068	+	11.1470i	−1.25104	+	0.406488i
$753$		0			0
$754$	−19.8540	−	27.3266i	−0.723038	−	0.995177i
$755$	−5.18991	−	15.9729i	−0.188880	−	0.581314i
$756$		0			0
$757$	−41.1683	−	29.9105i	−1.49629	−	1.08712i	−0.971832	−	0.235676i	$-0.924269\pi$
$757$	−41.1683	−	29.9105i	−1.49629	−	1.08712i	−0.524454	−	0.851439i	$-0.675731\pi$
$758$	5.06324			0.183905
$759$		0			0
$760$	−2.22558			−0.0807302
$761$	17.2680	+	12.5459i	0.625964	+	0.454789i	0.854999	−	0.518629i	$-0.173557\pi$
$761$	17.2680	+	12.5459i	0.625964	+	0.454789i	−0.229036	+	0.973418i	$0.573557\pi$
$762$		0			0
$763$	−0.323452	−	0.995483i	−0.0117098	−	0.0360389i
$764$	6.23800	+	8.58587i	0.225683	+	0.310626i
$765$		0			0
$766$	11.6782	−	3.79447i	0.421950	−	0.137100i
$767$	−4.61738	+	14.2108i	−0.166724	+	0.513123i
$768$		0			0
$769$			21.6072i			0.779176i	0.920989	+	0.389588i	$0.127383\pi$
$769$			21.6072i			0.779176i	−0.920989	+	0.389588i	$0.872617\pi$
$770$	0.267624	+	4.08677i	0.00964451	+	0.147277i
$771$		0			0
$772$	19.8330	−	27.2978i	0.713806	−	0.982469i
$773$	−9.33763	−	3.03398i	−0.335851	−	0.109125i	0.136236	−	0.990676i	$-0.456499\pi$
$773$	−9.33763	−	3.03398i	−0.335851	−	0.109125i	−0.472088	+	0.881552i	$0.656499\pi$
$774$		0			0
$775$	0.294314	−	0.213832i	0.0105721	−	0.00768106i
$776$	−1.68252	+	1.22242i	−0.0603989	+	0.0438824i
$777$		0			0
$778$	−51.4606	−	16.7206i	−1.84495	−	0.599461i
$779$	27.5224	−	37.8813i	0.986091	−	1.35724i
$780$		0			0
$781$	−14.6268	−	36.6685i	−0.523388	−	1.31210i
$782$			26.6454i			0.952837i
$783$		0			0
$784$	−9.01729	+	27.7524i	−0.322046	+	0.991155i
$785$	34.7820	−	11.3014i	1.24142	−	0.403363i
$786$		0			0
$787$	−20.6415	−	28.4106i	−0.735791	−	1.01273i	−0.998850	−	0.0479495i	$-0.984731\pi$
$787$	−20.6415	−	28.4106i	−0.735791	−	1.01273i	0.263059	−	0.964780i	$-0.415269\pi$
$788$	−1.45688	−	4.48381i	−0.0518992	−	0.159729i
$789$		0			0
$790$	39.3332	+	28.5773i	1.39941	+	1.01673i
$791$	−1.64189			−0.0583787
$792$		0			0
$793$	−4.75591			−0.168887
$794$	11.8839	+	8.63415i	0.421744	+	0.306415i
$795$		0			0
$796$	7.09679	+	21.8417i	0.251539	+	0.774158i
$797$	−28.6152	−	39.3855i	−1.01360	−	1.39511i	−0.916592	−	0.399823i	$-0.869072\pi$
$797$	−28.6152	−	39.3855i	−1.01360	−	1.39511i	−0.0970114	−	0.995283i	$-0.530928\pi$
$798$		0			0
$799$	−20.3036	+	6.59705i	−0.718291	+	0.233387i
$800$	2.64525	−	8.14125i	0.0935238	−	0.287837i
$801$		0			0
$802$		−	4.90063i		−	0.173047i
$803$	0.405320	−	0.0265426i	0.0143034	−	0.000936667i
$804$		0			0
$805$	−1.99247	+	2.74240i	−0.0702252	+	0.0966567i
$806$	1.20152	+	0.390399i	0.0423219	+	0.0137512i
$807$		0			0
$808$	−0.321851	+	0.233839i	−0.0113227	+	0.00822642i
$809$	1.95603	−	1.42114i	0.0687705	−	0.0499647i	−0.552869	−	0.833268i	$-0.686467\pi$
$809$	1.95603	−	1.42114i	0.0687705	−	0.0499647i	0.621639	+	0.783304i	$0.286467\pi$
$810$		0			0
$811$	22.4513	+	7.29488i	0.788373	+	0.256158i	0.675411	−	0.737441i	$-0.263966\pi$
$811$	22.4513	+	7.29488i	0.788373	+	0.256158i	0.112962	+	0.993599i	$0.463966\pi$
$812$	−3.12142	+	4.29626i	−0.109540	+	0.150769i
$813$		0			0
$814$	−26.7625	+	42.4106i	−0.938026	+	1.48649i
$815$			36.7000i			1.28555i
$816$		0			0
$817$	−13.2746	+	40.8552i	−0.464421	+	1.42934i
$818$	−55.4693	+	18.0231i	−1.93944	+	0.630162i
$819$		0			0
$820$	−21.8407	−	30.0611i	−0.762710	−	1.04978i
$821$	11.0595	+	34.0375i	0.385978	+	1.18792i	0.935768	+	0.352615i	$0.114708\pi$
$821$	11.0595	+	34.0375i	0.385978	+	1.18792i	−0.549791	+	0.835303i	$0.685292\pi$
$822$		0			0
$823$	29.0377	+	21.0971i	1.01219	+	0.735400i	0.964667	−	0.263470i	$-0.0848672\pi$
$823$	29.0377	+	21.0971i	1.01219	+	0.735400i	0.0475233	+	0.998870i	$0.484867\pi$
$824$	1.48529			0.0517424
$825$		0			0
$826$	4.85122			0.168796
$827$	−11.6799	−	8.48596i	−0.406151	−	0.295086i	0.365891	−	0.930658i	$-0.380764\pi$
$827$	−11.6799	−	8.48596i	−0.406151	−	0.295086i	−0.772042	+	0.635572i	$0.780764\pi$
$828$		0			0
$829$	−16.7616	−	51.5868i	−0.582153	−	1.79168i	−0.610415	−	0.792082i	$-0.708997\pi$
$829$	−16.7616	−	51.5868i	−0.582153	−	1.79168i	0.0282623	−	0.999601i	$-0.491003\pi$
$830$	0.987561	+	1.35926i	0.0342787	+	0.0471806i
$831$		0			0
$832$	12.7967	−	4.15791i	0.443647	−	0.144150i
$833$	−5.33666	+	16.4245i	−0.184904	+	0.569077i
$834$		0			0
$835$		−	27.0744i		−	0.936948i
$836$	−7.17418	+	28.2416i	−0.248124	+	0.976754i
$837$		0			0
$838$	10.4702	−	14.4110i	0.361686	−	0.497819i
$839$	−52.8843	−	17.1832i	−1.82577	−	0.593228i	−0.999554	−	0.0298743i	$-0.990489\pi$
$839$	−52.8843	−	17.1832i	−1.82577	−	0.593228i	−0.826216	−	0.563354i	$-0.809511\pi$
$840$		0			0
$841$	−40.8607	+	29.6870i	−1.40899	+	1.02369i
$842$	−34.6248	+	25.1564i	−1.19325	+	0.866946i
$843$		0			0
$844$	−45.1299	−	14.6636i	−1.55343	−	0.504742i
$845$	10.8073	−	14.8750i	0.371784	−	0.511717i
$846$		0			0
$847$	−3.43025	−	0.636170i	−0.117865	−	0.0218591i
$848$		−	7.58286i		−	0.260396i
$849$		0			0
$850$	1.66152	−	5.11363i	0.0569897	−	0.175396i
$851$	−39.4756	+	12.8264i	−1.35321	+	0.439683i
$852$		0			0
$853$	9.48804	+	13.0592i	0.324864	+	0.447137i	0.939945	−	0.341327i	$-0.110876\pi$
$853$	9.48804	+	13.0592i	0.324864	+	0.447137i	−0.615080	+	0.788465i	$0.710876\pi$
$854$	0.477149	+	1.46851i	0.0163277	+	0.0502515i
$855$		0			0
$856$	2.30735	+	1.67639i	0.0788637	+	0.0572979i
$857$	−47.3541			−1.61758			−0.808792	−	0.588095i	$-0.799878\pi$
$857$	−47.3541			−1.61758			−0.808792	+	0.588095i	$0.799878\pi$
$858$		0			0
$859$	−8.33033			−0.284227			−0.142114	−	0.989850i	$-0.545390\pi$
$859$	−8.33033			−0.284227			−0.142114	+	0.989850i	$0.545390\pi$
$860$	27.5790	+	20.0373i	0.940437	+	0.683268i
$861$		0			0
$862$	−10.6899	−	32.9000i	−0.364098	−	1.12058i
$863$	3.57452	+	4.91990i	0.121678	+	0.167475i	0.865511	−	0.500890i	$-0.166994\pi$
$863$	3.57452	+	4.91990i	0.121678	+	0.167475i	−0.743833	+	0.668366i	$0.766994\pi$
$864$		0			0
$865$	−24.8756	+	8.08256i	−0.845795	+	0.274815i
$866$	9.55034	−	29.3929i	0.324534	−	0.998812i
$867$		0			0
$868$		−	0.198624i		−	0.00674172i
$869$	−31.8434	+	26.4808i	−1.08021	+	0.898299i
$870$		0			0
$871$	12.2207	−	16.8204i	0.414084	−	0.569938i
$872$	0.755163	+	0.245367i	0.0255730	+	0.00830918i
$873$		0			0
$874$	−40.2922	+	29.2740i	−1.36290	+	0.990208i
$875$	3.08996	−	2.24499i	0.104460	−	0.0758945i
$876$		0			0
$877$	−11.8358	−	3.84570i	−0.399668	−	0.129860i	0.102285	−	0.994755i	$-0.467385\pi$
$877$	−11.8358	−	3.84570i	−0.399668	−	0.129860i	−0.501953	+	0.864895i	$0.667385\pi$
$878$	−13.8040	+	18.9996i	−0.465862	+	0.641204i
$879$		0			0
$880$	−23.4550	−	14.8009i	−0.790668	−	0.498938i
$881$		−	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	0.444325	+	0.895866i	$0.353444\pi$
$883$	−13.1258	+	40.3970i	−0.441718	+	1.35947i	−0.886043	+	0.463603i	$0.846556\pi$
$884$	8.59941	−	2.79412i	0.289229	−	0.0939764i
$885$		0			0
$886$	17.8736	+	24.6009i	0.600475	+	0.826483i
$887$	7.11097	+	21.8853i	0.238763	+	0.734837i	0.996600	+	0.0823929i	$0.0262562\pi$
$887$	7.11097	+	21.8853i	0.238763	+	0.734837i	−0.757837	+	0.652444i	$0.773744\pi$
$888$		0			0
$889$	0.969159	+	0.704135i	0.0325045	+	0.0236159i
$890$	31.7446			1.06408
$891$		0			0
$892$	26.4561			0.885815
$893$	−32.2825	−	23.4546i	−1.08029	−	0.784878i
$894$		0			0
$895$	−3.46043	−	10.6501i	−0.115670	−	0.355994i
$896$	0.358144	+	0.492943i	0.0119648	+	0.0164681i
$897$		0			0
$898$	−43.6418	+	14.1801i	−1.45635	+	0.473196i
$899$	0.918932	−	2.82818i	0.0306481	−	0.0943251i
$900$		0			0
$901$		−	4.48773i		−	0.149508i
$902$	60.7124	−	24.2177i	2.02150	−	0.806362i
$903$		0			0
$904$	0.732096	−	1.00764i	0.0243492	−	0.0335137i
$905$	−19.2967	−	6.26988i	−0.641444	−	0.208418i
$906$		0			0
$907$	9.13320	−	6.63566i	0.303263	−	0.220333i	−0.425737	−	0.904847i	$-0.639985\pi$
$907$	9.13320	−	6.63566i	0.303263	−	0.220333i	0.729000	+	0.684513i	$0.239985\pi$
$908$	−23.6736	+	17.1999i	−0.785637	+	0.570799i
$909$		0			0
$910$	2.25919	+	0.734055i	0.0748914	+	0.0243337i
$911$	14.3967	−	19.8153i	0.476983	−	0.656511i	−0.500939	−	0.865483i	$-0.667012\pi$
$911$	14.3967	−	19.8153i	0.476983	−	0.656511i	0.977922	+	0.208972i	$0.0670118\pi$
$912$		0			0
$913$	−1.32936	+	0.530271i	−0.0439953	+	0.0175494i
$914$			1.21763i			0.0402756i
$915$		0			0
$916$	11.9436	−	36.7585i	0.394626	−	1.21454i
$917$	2.69055	−	0.874214i	0.0888499	−	0.0288691i
$918$		0			0
$919$	20.6927	+	28.4811i	0.682590	+	0.939504i	0.999961	−	0.00879691i	$-0.00280018\pi$
$919$	20.6927	+	28.4811i	0.682590	+	0.939504i	−0.317371	+	0.948301i	$0.602800\pi$
$920$	−0.794623	−	2.44560i	−0.0261980	−	0.0806290i
$921$		0			0
$922$	36.2555	+	26.3412i	1.19401	+	0.867501i
$923$	−22.8978			−0.753689
$924$		0			0
$925$	8.37575			0.275393
$926$	11.2929	+	8.20480i	0.371109	+	0.269626i
$927$		0			0
$928$	−21.6229	−	66.5485i	−0.709807	−	2.18456i
$929$	−10.6528	−	14.6623i	−0.349506	−	0.481054i	0.597681	−	0.801734i	$-0.296089\pi$
$929$	−10.6528	−	14.6623i	−0.349506	−	0.481054i	−0.947188	+	0.320679i	$0.896089\pi$
$930$		0			0
$931$	−30.6998	+	9.97496i	−1.00614	+	0.326916i
$932$	−1.51953	+	4.67663i	−0.0497738	+	0.153188i
$933$		0			0
$934$			11.7324i			0.383894i
$935$	−13.8813	−	8.75954i	−0.453966	−	0.286468i
$936$		0			0
$937$	−17.7777	+	24.4689i	−0.580772	+	0.799365i	−0.993780	−	0.111363i	$-0.964478\pi$
$937$	−17.7777	+	24.4689i	−0.580772	+	0.799365i	0.413007	+	0.910728i	$0.364478\pi$
$938$	−6.41983	−	2.08593i	−0.209615	−	0.0681080i
$939$		0			0
$940$	−25.6181	+	18.6127i	−0.835571	+	0.607078i
$941$	−21.1984	+	15.4015i	−0.691047	+	0.502075i	−0.877004	−	0.480483i	$-0.840461\pi$
$941$	−21.1984	+	15.4015i	−0.691047	+	0.502075i	0.185957	+	0.982558i	$0.440461\pi$
$942$		0			0
$943$	51.4529	+	16.7180i	1.67554	+	0.544414i
$944$	−19.3099	+	26.5778i	−0.628484	+	0.865035i
$945$		0			0
$946$	−46.1076	+	38.3428i	−1.49909	+	1.24663i
$947$			32.3323i			1.05066i	0.850899	+	0.525330i	$0.176058\pi$
$947$			32.3323i			1.05066i	−0.850899	+	0.525330i	$0.823942\pi$
$948$		0			0
$949$	0.0728024	−	0.224063i	0.00236327	−	0.00727339i
$950$	9.55809	−	3.10561i	0.310106	−	0.100759i
$951$		0			0
$952$	0.112267	+	0.154523i	0.00363861	+	0.00500812i
$953$	10.9868	+	33.8138i	0.355897	+	1.09534i	0.955488	+	0.295031i	$0.0953299\pi$
$953$	10.9868	+	33.8138i	0.355897	+	1.09534i	−0.599591	+	0.800306i	$0.704670\pi$
$954$		0			0
$955$	−9.04008	−	6.56800i	−0.292530	−	0.212536i
$956$	−41.8179			−1.35249
$957$		0			0
$958$	3.47017			0.112116
$959$	−1.23759	−	0.899164i	−0.0399640	−	0.0290355i
$960$		0			0
$961$	−9.54516	−	29.3770i	−0.307908	−	0.947644i
$962$	17.0968	+	23.5317i	0.551223	+	0.758693i
$963$		0			0
$964$	−43.9090	+	14.2669i	−1.41421	+	0.459506i
$965$	−10.9784	+	33.7881i	−0.353408	+	1.08768i
$966$		0			0
$967$		−	43.8479i		−	1.41005i	−0.709181	−	0.705027i	$-0.750935\pi$
$967$		−	43.8479i		−	1.41005i	0.709181	−	0.705027i	$-0.249065\pi$
$968$	1.91993	−	1.82153i	0.0617090	−	0.0585461i
$969$		0			0
$970$	−19.7822	+	27.2278i	−0.635168	+	0.874233i
$971$	−24.4501	−	7.94432i	−0.784641	−	0.254945i	−0.110820	−	0.993840i	$-0.535348\pi$
$971$	−24.4501	−	7.94432i	−0.784641	−	0.254945i	−0.673820	+	0.738895i	$0.735348\pi$
$972$		0			0
$973$	−1.84700	+	1.34192i	−0.0592120	+	0.0430200i
$974$	−27.7356	+	20.1511i	−0.888706	+	0.645683i
$975$		0			0
$976$	−9.94464	−	3.23121i	−0.318320	−	0.103428i
$977$	−9.75359	+	13.4247i	−0.312045	+	0.429493i	−0.936018	−	0.351953i	$-0.885518\pi$
$977$	−9.75359	+	13.4247i	−0.312045	+	0.429493i	0.623973	+	0.781446i	$0.285518\pi$
$978$		0			0
$979$	−6.65784	+	26.2090i	−0.212785	+	0.837642i
$980$			25.6159i			0.818269i
$981$		0			0
$982$	20.4485	−	62.9340i	0.652538	−	2.00830i
$983$	−39.8580	+	12.9506i	−1.27127	+	0.413061i	−0.865498	−	0.500912i	$-0.832998\pi$
$983$	−39.8580	+	12.9506i	−1.27127	+	0.413061i	−0.405774	+	0.913974i	$0.632998\pi$
$984$		0			0
$985$	2.91775	+	4.01594i	0.0929672	+	0.127958i
$986$	−13.5817	−	41.8001i	−0.432528	−	1.33119i
$987$		0			0
$988$	13.6729	+	9.93397i	0.434994	+	0.316042i
$989$	−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	$0.613561\pi$
$992$	2.11732	+	1.53833i	0.0672251	+	0.0488419i
$993$		0			0
$994$	2.29728	+	7.07030i	0.0728653	+	0.224256i
$995$	−14.2130	−	19.5625i	−0.450583	−	0.620174i
$996$		0			0
$997$	45.0088	−	14.6242i	1.42544	−	0.463154i	0.508115	−	0.861289i	$-0.330342\pi$
$997$	45.0088	−	14.6242i	1.42544	−	0.463154i	0.917327	+	0.398135i	$0.130342\pi$
$998$	−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	891.2.k.a.161.17		80
3.2	odd	2	inner	891.2.k.a.161.4		80
9.2	odd	6		99.2.p.a.95.2	yes	80
9.4	even	3		99.2.p.a.29.2	✓	80
9.5	odd	6		297.2.t.a.62.9		80
9.7	even	3		297.2.t.a.260.9		80
11.8	odd	10	inner	891.2.k.a.404.4		80
33.8	even	10	inner	891.2.k.a.404.17		80
99.41	even	30		297.2.t.a.8.9		80
99.52	odd	30		297.2.t.a.206.9		80
99.74	even	30		99.2.p.a.41.2	yes	80
99.85	odd	30		99.2.p.a.74.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.2	✓	80	9.4	even	3
99.2.p.a.41.2	yes	80	99.74	even	30
99.2.p.a.74.2	yes	80	99.85	odd	30
99.2.p.a.95.2	yes	80	9.2	odd	6
297.2.t.a.8.9		80	99.41	even	30
297.2.t.a.62.9		80	9.5	odd	6
297.2.t.a.206.9		80	99.52	odd	30
297.2.t.a.260.9		80	9.7	even	3
891.2.k.a.161.4		80	3.2	odd	2	inner
891.2.k.a.161.17		80	1.1	even	1	trivial
891.2.k.a.404.4		80	11.8	odd	10	inner
891.2.k.a.404.17		80	33.8	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.59313 + 1.15748i) q^{2} +(0.580279 + 1.78592i) q^{4} +(-1.16215 - 1.59956i) q^{5} +(-0.301636 + 0.0980075i) q^{7} +(0.0743474 - 0.228818i) q^{8} -3.89347i q^{10} +(3.21453 + 0.816584i) q^{11} +(1.13071 - 1.55629i) q^{13} +(-0.593987 - 0.192998i) q^{14} +(3.42168 - 2.48599i) q^{16} +(2.02504 - 1.47127i) q^{17} +(4.44962 + 1.44577i) q^{19} +(2.18231 - 3.00369i) q^{20} +(4.17599 + 5.02167i) q^{22} +5.40571i q^{23} +(0.337083 - 1.03743i) q^{25} +(3.60274 - 1.17060i) q^{26} +(-0.350066 - 0.481825i) q^{28} +(-2.75540 - 8.48024i) q^{29} +(0.269809 + 0.196028i) q^{31} +7.84748 q^{32} +4.92912 q^{34} +(0.507314 + 0.368585i) q^{35} +(2.37275 + 7.30257i) q^{37} +(5.41539 + 7.45364i) q^{38} +(-0.452410 + 0.146997i) q^{40} +(3.09266 - 9.51824i) q^{41} +9.18172i q^{43} +(0.406974 + 6.21472i) q^{44} +(-6.25699 + 8.61201i) q^{46} +(-8.11146 - 2.63557i) q^{47} +(-5.58174 + 4.05537i) q^{49} +(1.73782 - 1.26260i) q^{50} +(3.43553 + 1.11627i) q^{52} +(1.05383 - 1.45047i) q^{53} +(-2.42958 - 6.09082i) q^{55} +0.0763063i q^{56} +(5.42598 - 16.6994i) q^{58} +(-7.38731 + 2.40028i) q^{59} +(-1.45318 - 2.00013i) q^{61} +(0.202944 + 0.624596i) q^{62} +(5.65871 + 4.11130i) q^{64} -3.80343 q^{65} +10.8080 q^{67} +(3.80266 + 2.76279i) q^{68} +(0.381589 + 1.17441i) q^{70} +(-6.99647 - 9.62982i) q^{71} +(0.116476 - 0.0378454i) q^{73} +(-4.67246 + 14.3804i) q^{74} +8.78560i q^{76} +(-1.04965 + 0.0687367i) q^{77} +(-7.33980 + 10.1024i) q^{79} +(-7.95299 - 2.58408i) q^{80} +(15.9442 - 11.5841i) q^{82} +(-0.349113 + 0.253646i) q^{83} +(-4.70678 - 1.52933i) q^{85} +(-10.6276 + 14.6277i) q^{86} +(0.425841 - 0.674830i) q^{88} +8.15328i q^{89} +(-0.188535 + 0.580251i) q^{91} +(-9.65415 + 3.13682i) q^{92} +(-9.87200 - 13.5876i) q^{94} +(-2.85852 - 8.79763i) q^{95} +(-6.99321 - 5.08086i) q^{97} -13.5864 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

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