LMFDB - Embedded newform 891.2.k.a.161.18

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			161.18
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71719 + 1.24761i) q^{2} +(0.774180 + 2.38268i) q^{4} +(-1.75074 - 2.40969i) q^{5} +(3.03899 - 0.987427i) q^{7} +(-0.331430 + 1.02004i) q^{8} -6.32217i q^{10} +(-2.38818 - 2.30144i) q^{11} +(1.50453 - 2.07081i) q^{13} +(6.45046 + 2.09588i) q^{14} +(2.21191 - 1.60705i) q^{16} +(-0.807393 + 0.586606i) q^{17} +(-3.66639 - 1.19128i) q^{19} +(4.38614 - 6.03700i) q^{20} +(-1.22966 - 6.93154i) q^{22} -5.27382i q^{23} +(-1.19643 + 3.68223i) q^{25} +(5.16715 - 1.67891i) q^{26} +(4.70544 + 6.47649i) q^{28} +(1.85154 + 5.69844i) q^{29} +(6.43584 + 4.67591i) q^{31} +7.94833 q^{32} -2.11831 q^{34} +(-7.69988 - 5.59429i) q^{35} +(1.32852 + 4.08876i) q^{37} +(-4.80964 - 6.61990i) q^{38} +(3.03823 - 0.987180i) q^{40} +(0.411450 - 1.26631i) q^{41} +3.29613i q^{43} +(3.63471 - 7.47199i) q^{44} +(6.57970 - 9.05618i) q^{46} +(5.03182 + 1.63494i) q^{47} +(2.59731 - 1.88706i) q^{49} +(-6.64851 + 4.83042i) q^{50} +(6.09886 + 1.98164i) q^{52} +(2.43390 - 3.34997i) q^{53} +(-1.36467 + 9.78400i) q^{55} +3.42715i q^{56} +(-3.93001 + 12.0953i) q^{58} +(-11.0565 + 3.59249i) q^{59} +(4.71908 + 6.49525i) q^{61} +(5.21785 + 16.0589i) q^{62} +(9.22499 + 6.70235i) q^{64} -7.62407 q^{65} -6.61239 q^{67} +(-2.02276 - 1.46962i) q^{68} +(-6.24267 - 19.2130i) q^{70} +(5.64201 + 7.76556i) q^{71} +(-0.706745 + 0.229635i) q^{73} +(-2.81987 + 8.67867i) q^{74} -9.65810i q^{76} +(-9.53014 - 4.63589i) q^{77} +(6.88586 - 9.47757i) q^{79} +(-7.74499 - 2.51650i) q^{80} +(2.28641 - 1.66117i) q^{82} +(-2.18571 + 1.58801i) q^{83} +(2.82708 + 0.918574i) q^{85} +(-4.11230 + 5.66010i) q^{86} +(3.13907 - 1.67327i) q^{88} -9.15275i q^{89} +(2.52748 - 7.77878i) q^{91} +(12.5658 - 4.08289i) q^{92} +(6.60084 + 9.08528i) q^{94} +(3.54829 + 10.9205i) q^{95} +(-7.54954 - 5.48506i) q^{97} +6.81440 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.71719	+	1.24761i	1.21424	+	0.882197i	0.995609	−	0.0936108i	$-0.0298409\pi$
$2$	1.71719	+	1.24761i	1.21424	+	0.882197i	0.218631	+	0.975808i	$0.429841\pi$
$3$		0			0
$3$		0			0
$4$	0.774180	+	2.38268i	0.387090	+	1.19134i
$5$	−1.75074	−	2.40969i	−0.782957	−	1.07765i	−0.994950	−	0.100376i	$-0.967995\pi$
$5$	−1.75074	−	2.40969i	−0.782957	−	1.07765i	0.211993	−	0.977271i	$-0.432005\pi$
$6$		0			0
$7$	3.03899	−	0.987427i	1.14863	−	0.373212i	0.328002	−	0.944677i	$-0.393625\pi$
$7$	3.03899	−	0.987427i	1.14863	−	0.373212i	0.820627	+	0.571465i	$0.193625\pi$
$8$	−0.331430	+	1.02004i	−0.117178	+	0.360638i
$9$		0			0
$10$		−	6.32217i		−	1.99924i
$11$	−2.38818	−	2.30144i	−0.720062	−	0.693909i
$11$	−2.38818	−	2.30144i	−0.720062	−	0.693909i
$12$		0			0
$13$	1.50453	−	2.07081i	0.417282	−	0.574340i	−0.547693	−	0.836679i	$-0.684494\pi$
$13$	1.50453	−	2.07081i	0.417282	−	0.574340i	0.964976	+	0.262339i	$0.0844940\pi$
$14$	6.45046	+	2.09588i	1.72396	+	0.560148i
$15$		0			0
$16$	2.21191	−	1.60705i	0.552978	−	0.401762i
$17$	−0.807393	+	0.586606i	−0.195822	+	0.142273i	−0.681376	−	0.731934i	$-0.738618\pi$
$17$	−0.807393	+	0.586606i	−0.195822	+	0.142273i	0.485554	+	0.874207i	$0.338618\pi$
$18$		0			0
$19$	−3.66639	−	1.19128i	−0.841127	−	0.273299i	−0.143402	−	0.989664i	$-0.545804\pi$
$19$	−3.66639	−	1.19128i	−0.841127	−	0.273299i	−0.697725	+	0.716366i	$0.745804\pi$
$20$	4.38614	−	6.03700i	0.980770	−	1.34991i
$21$		0			0
$22$	−1.22966	−	6.93154i	−0.262164	−	1.47781i
$23$		−	5.27382i		−	1.09967i	−0.835274	−	0.549834i	$-0.814691\pi$
$23$		−	5.27382i		−	1.09967i	0.835274	−	0.549834i	$-0.185309\pi$
$24$		0			0
$25$	−1.19643	+	3.68223i	−0.239286	+	0.736446i
$26$	5.16715	−	1.67891i	1.01336	−	0.329261i
$27$		0			0
$28$	4.70544	+	6.47649i	0.889245	+	1.22394i
$29$	1.85154	+	5.69844i	0.343822	+	1.05817i	0.962212	+	0.272303i	$0.0877852\pi$
$29$	1.85154	+	5.69844i	0.343822	+	1.05817i	−0.618390	+	0.785871i	$0.712215\pi$
$30$		0			0
$31$	6.43584	+	4.67591i	1.15591	+	0.839819i	0.989256	−	0.146196i	$-0.0467031\pi$
$31$	6.43584	+	4.67591i	1.15591	+	0.839819i	0.166656	+	0.986015i	$0.446703\pi$
$32$	7.94833			1.40508
$33$		0			0
$34$	−2.11831			−0.363287
$35$	−7.69988	−	5.59429i	−1.30152	−	0.945608i
$36$		0			0
$37$	1.32852	+	4.08876i	0.218407	+	0.672188i	0.998894	+	0.0470160i	$0.0149712\pi$
$37$	1.32852	+	4.08876i	0.218407	+	0.672188i	−0.780487	+	0.625172i	$0.785029\pi$
$38$	−4.80964	−	6.61990i	−0.780227	−	1.07389i
$39$		0			0
$40$	3.03823	−	0.987180i	0.480386	−	0.156087i
$41$	0.411450	−	1.26631i	0.0642576	−	0.197765i	−0.913773	−	0.406225i	$-0.866845\pi$
$41$	0.411450	−	1.26631i	0.0642576	−	0.197765i	0.978031	+	0.208460i	$0.0668451\pi$
$42$		0			0
$43$			3.29613i			0.502655i	0.967902	+	0.251328i	$0.0808671\pi$
$43$			3.29613i			0.502655i	−0.967902	+	0.251328i	$0.919133\pi$
$44$	3.63471	−	7.47199i	0.547953	−	1.12644i
$45$		0			0
$46$	6.57970	−	9.05618i	0.970124	−	1.33526i
$47$	5.03182	+	1.63494i	0.733967	+	0.238480i	0.652068	−	0.758160i	$-0.273902\pi$
$47$	5.03182	+	1.63494i	0.733967	+	0.238480i	0.0818987	+	0.996641i	$0.473902\pi$
$48$		0			0
$49$	2.59731	−	1.88706i	0.371044	−	0.269579i
$50$	−6.64851	+	4.83042i	−0.940241	+	0.683125i
$51$		0			0
$52$	6.09886	+	1.98164i	0.845760	+	0.274804i
$53$	2.43390	−	3.34997i	0.334322	−	0.460154i	−0.608450	−	0.793592i	$-0.708209\pi$
$53$	2.43390	−	3.34997i	0.334322	−	0.460154i	0.942772	+	0.333437i	$0.108209\pi$
$54$		0			0
$55$	−1.36467	+	9.78400i	−0.184012	+	1.31927i
$56$			3.42715i			0.457972i
$57$		0			0
$58$	−3.93001	+	12.0953i	−0.516036	+	1.58820i
$59$	−11.0565	+	3.59249i	−1.43944	+	0.467702i	−0.921722	−	0.387851i	$-0.873218\pi$
$59$	−11.0565	+	3.59249i	−1.43944	+	0.467702i	−0.517716	+	0.855552i	$0.673218\pi$
$60$		0			0
$61$	4.71908	+	6.49525i	0.604216	+	0.831632i	0.996086	−	0.0883887i	$-0.0281717\pi$
$61$	4.71908	+	6.49525i	0.604216	+	0.831632i	−0.391870	+	0.920021i	$0.628172\pi$
$62$	5.21785	+	16.0589i	0.662668	+	2.03948i
$63$		0			0
$64$	9.22499	+	6.70235i	1.15312	+	0.837794i
$65$	−7.62407			−0.945650
$66$		0			0
$67$	−6.61239			−0.807832			−0.403916	−	0.914796i	$-0.632351\pi$
$67$	−6.61239			−0.807832			−0.403916	+	0.914796i	$0.632351\pi$
$68$	−2.02276	−	1.46962i	−0.245296	−	0.178218i
$69$		0			0
$70$	−6.24267	−	19.2130i	−0.746142	−	2.29639i
$71$	5.64201	+	7.76556i	0.669583	+	0.921603i	0.999751	−	0.0223198i	$-0.00710521\pi$
$71$	5.64201	+	7.76556i	0.669583	+	0.921603i	−0.330167	+	0.943922i	$0.607105\pi$
$72$		0			0
$73$	−0.706745	+	0.229635i	−0.0827183	+	0.0268768i	−0.350084	−	0.936718i	$-0.613847\pi$
$73$	−0.706745	+	0.229635i	−0.0827183	+	0.0268768i	0.267366	+	0.963595i	$0.413847\pi$
$74$	−2.81987	+	8.67867i	−0.327803	+	1.00888i
$75$		0			0
$76$		−	9.65810i		−	1.10786i
$77$	−9.53014	−	4.63589i	−1.08606	−	0.528308i
$78$		0			0
$79$	6.88586	−	9.47757i	0.774719	−	1.06631i	−0.221126	−	0.975245i	$-0.570973\pi$
$79$	6.88586	−	9.47757i	0.774719	−	1.06631i	0.995845	−	0.0910643i	$-0.0290269\pi$
$80$	−7.74499	−	2.51650i	−0.865916	−	0.281353i
$81$		0			0
$82$	2.28641	−	1.66117i	0.252492	−	0.183446i
$83$	−2.18571	+	1.58801i	−0.239912	+	0.174307i	−0.701244	−	0.712921i	$-0.747372\pi$
$83$	−2.18571	+	1.58801i	−0.239912	+	0.174307i	0.461332	+	0.887228i	$0.347372\pi$
$84$		0			0
$85$	2.82708	+	0.918574i	0.306640	+	0.0996333i
$86$	−4.11230	+	5.66010i	−0.443441	+	0.610344i
$87$		0			0
$88$	3.13907	−	1.67327i	0.334626	−	0.178371i
$89$		−	9.15275i		−	0.970189i	−0.874462	−	0.485095i	$-0.838785\pi$
$89$		−	9.15275i		−	0.970189i	0.874462	−	0.485095i	$-0.161215\pi$
$90$		0			0
$91$	2.52748	−	7.77878i	0.264952	−	0.815438i
$92$	12.5658	−	4.08289i	1.31008	−	0.425671i
$93$		0			0
$94$	6.60084	+	9.08528i	0.680825	+	0.937075i
$95$	3.54829	+	10.9205i	0.364046	+	1.12042i
$96$		0			0
$97$	−7.54954	−	5.48506i	−0.766540	−	0.556924i	0.134370	−	0.990931i	$-0.457099\pi$
$97$	−7.54954	−	5.48506i	−0.766540	−	0.556924i	−0.900909	+	0.434008i	$0.857099\pi$
$98$	6.81440			0.688359
$99$		0			0
$100$	−9.69983			−0.969983
$101$	−6.03378	−	4.38379i	−0.600383	−	0.436204i	0.245632	−	0.969363i	$-0.421005\pi$
$101$	−6.03378	−	4.38379i	−0.600383	−	0.436204i	−0.846015	+	0.533159i	$0.821005\pi$
$102$		0			0
$103$	−4.63094	−	14.2526i	−0.456300	−	1.40435i	−0.869602	−	0.493753i	$-0.835625\pi$
$103$	−4.63094	−	14.2526i	−0.456300	−	1.40435i	0.413302	−	0.910594i	$-0.364375\pi$
$104$	1.61366	+	2.22101i	0.158232	+	0.217788i
$105$		0			0
$106$	8.35896	−	2.71599i	0.811894	−	0.263800i
$107$	−5.29261	+	16.2890i	−0.511656	+	1.57472i	0.277628	+	0.960689i	$0.410452\pi$
$107$	−5.29261	+	16.2890i	−0.511656	+	1.57472i	−0.789285	+	0.614028i	$0.789548\pi$
$108$		0			0
$109$		−	0.449919i		−	0.0430944i	−0.999768	−	0.0215472i	$-0.993141\pi$
$109$		−	0.449919i		−	0.0430944i	0.999768	−	0.0215472i	$-0.00685922\pi$
$110$	−14.5501	+	15.0985i	−1.38729	+	1.43958i
$111$		0			0
$112$	5.13513	−	7.06790i	0.485224	−	0.667854i
$113$	−3.96010	−	1.28672i	−0.372535	−	0.121044i	0.116765	−	0.993160i	$-0.462748\pi$
$113$	−3.96010	−	1.28672i	−0.372535	−	0.121044i	−0.489300	+	0.872116i	$0.662748\pi$
$114$		0			0
$115$	−12.7083	+	9.23312i	−1.18505	+	0.860993i
$116$	−12.1441	+	8.82324i	−1.12756	+	0.819217i
$117$		0			0
$118$	−23.4683	−	7.62530i	−2.16043	−	0.701966i
$119$	−1.87443	+	2.57993i	−0.171829	+	0.236502i
$120$		0			0
$121$	0.406780	+	10.9925i	0.0369800	+	0.999316i
$122$			17.0412i			1.54284i
$123$		0			0
$124$	−6.15871	+	18.9546i	−0.553068	+	1.70217i
$125$	−3.19613	+	1.03849i	−0.285871	+	0.0928850i
$126$		0			0
$127$	9.90407	+	13.6318i	0.878844	+	1.20962i	0.976740	+	0.214428i	$0.0687888\pi$
$127$	9.90407	+	13.6318i	0.878844	+	1.20962i	−0.0978959	+	0.995197i	$0.531211\pi$
$128$	2.56682	+	7.89986i	0.226877	+	0.698256i
$129$		0			0
$130$	−13.0920	−	9.51190i	−1.14825	−	0.834249i
$131$	14.3217			1.25129			0.625647	−	0.780106i	$-0.284835\pi$
$131$	14.3217			1.25129			0.625647	+	0.780106i	$0.284835\pi$
$132$		0			0
$133$	−12.3184			−1.06814
$134$	−11.3548	−	8.24971i	−0.980901	−	0.712667i
$135$		0			0
$136$	−0.330765	−	1.01799i	−0.0283629	−	0.0872920i
$137$	1.41576	+	1.94863i	0.120956	+	0.166482i	0.865201	−	0.501424i	$-0.167190\pi$
$137$	1.41576	+	1.94863i	0.120956	+	0.166482i	−0.744245	+	0.667907i	$0.767190\pi$
$138$		0			0
$139$	4.05604	−	1.31789i	0.344029	−	0.111782i	−0.131906	−	0.991262i	$-0.542110\pi$
$139$	4.05604	−	1.31789i	0.344029	−	0.111782i	0.475935	+	0.879480i	$0.342110\pi$
$140$	7.36832	−	22.6774i	0.622737	−	1.91659i
$141$		0			0
$142$			20.3740i			1.70975i
$143$	−8.35893	+	1.48288i	−0.699009	+	0.124004i
$144$		0			0
$145$	10.4899	−	14.4381i	0.871141	−	1.19902i
$146$	−1.50012	−	0.487417i	−0.124150	−	0.0403389i
$147$		0			0
$148$	−8.71370	+	6.33087i	−0.716261	+	0.520394i
$149$	−3.21329	+	2.33459i	−0.263243	+	0.191257i	−0.711575	−	0.702610i	$-0.752018\pi$
$149$	−3.21329	+	2.33459i	−0.263243	+	0.191257i	0.448333	+	0.893867i	$0.352018\pi$
$150$		0			0
$151$	16.4430	+	5.34267i	1.33812	+	0.434780i	0.888678	−	0.458531i	$-0.151624\pi$
$151$	16.4430	+	5.34267i	1.33812	+	0.434780i	0.449438	+	0.893312i	$0.351624\pi$
$152$	2.43031	−	3.34503i	0.197124	−	0.271318i
$153$		0			0
$154$	−10.5813	−	19.8507i	−0.852665	−	1.59961i
$155$		−	23.6947i		−	1.90321i
$156$		0			0
$157$	0.112621	−	0.346613i	0.00898815	−	0.0276627i	−0.946462	−	0.322816i	$-0.895371\pi$
$157$	0.112621	−	0.346613i	0.00898815	−	0.0276627i	0.955450	+	0.295153i	$0.0953706\pi$
$158$	23.6487	−	7.68393i	1.88139	−	0.611301i
$159$		0			0
$160$	−13.9155	−	19.1530i	−1.10012	−	1.51418i
$161$	−5.20751	−	16.0271i	−0.410410	−	1.26311i
$162$		0			0
$163$	−2.44510	−	1.77647i	−0.191515	−	0.139144i	0.487896	−	0.872902i	$-0.337765\pi$
$163$	−2.44510	−	1.77647i	−0.191515	−	0.139144i	−0.679411	+	0.733758i	$0.737765\pi$
$164$	3.33575			0.260479
$165$		0			0
$166$	−5.73450			−0.445084
$167$	−6.22872	−	4.52543i	−0.481992	−	0.350188i	0.320104	−	0.947382i	$-0.396282\pi$
$167$	−6.22872	−	4.52543i	−0.481992	−	0.350188i	−0.802097	+	0.597194i	$0.796282\pi$
$168$		0			0
$169$	1.99258	+	6.13253i	0.153275	+	0.471733i
$170$	3.70862	+	5.10447i	0.284438	+	0.391495i
$171$		0			0
$172$	−7.85363	+	2.55180i	−0.598833	+	0.194573i
$173$	3.43195	−	10.5625i	0.260926	−	0.803049i	−0.731678	−	0.681651i	$-0.761262\pi$
$173$	3.43195	−	10.5625i	0.260926	−	0.803049i	0.992604	−	0.121398i	$-0.0387377\pi$
$174$		0			0
$175$			12.3716i			0.935208i
$176$	−8.98096	−	1.25266i	−0.676966	−	0.0944228i
$177$		0			0
$178$	11.4191	−	15.7170i	0.855898	−	1.17804i
$179$	7.87767	+	2.55961i	0.588805	+	0.191314i	0.588241	−	0.808686i	$-0.299821\pi$
$179$	7.87767	+	2.55961i	0.588805	+	0.191314i	0.000563753		1.00000i	$0.499821\pi$
$180$		0			0
$181$	−13.8429	+	10.0575i	−1.02894	+	0.747565i	−0.968095	−	0.250582i	$-0.919378\pi$
$181$	−13.8429	+	10.0575i	−1.02894	+	0.747565i	−0.0608402	+	0.998148i	$0.519378\pi$
$182$	14.0451	−	10.2044i	1.04109	−	0.756398i
$183$		0			0
$184$	5.37950	+	1.74791i	0.396582	+	0.128857i
$185$	7.52676	−	10.3597i	0.553378	−	0.761660i
$186$		0			0
$187$	3.27823	+	0.457246i	0.239728	+	0.0334372i
$188$			13.2550i			0.966718i
$189$		0			0
$190$	−7.53148	+	23.1795i	−0.546391	+	1.68162i
$191$	10.3620	−	3.36683i	0.749771	−	0.243615i	0.0908882	−	0.995861i	$-0.471029\pi$
$191$	10.3620	−	3.36683i	0.749771	−	0.243615i	0.658883	+	0.752246i	$0.271029\pi$
$192$		0			0
$193$	6.36278	+	8.75762i	0.458003	+	0.630387i	0.974093	−	0.226147i	$-0.0726130\pi$
$193$	6.36278	+	8.75762i	0.458003	+	0.630387i	−0.516090	+	0.856534i	$0.672613\pi$
$194$	−6.12078	−	18.8378i	−0.439447	−	1.35248i
$195$		0			0
$196$	6.50704	+	4.72764i	0.464788	+	0.337688i
$197$	1.78800			0.127390			0.0636948	−	0.997969i	$-0.479712\pi$
$197$	1.78800			0.127390			0.0636948	+	0.997969i	$0.479712\pi$
$198$		0			0
$199$	0.534305			0.0378759			0.0189379	−	0.999821i	$-0.493972\pi$
$199$	0.534305			0.0378759			0.0189379	+	0.999821i	$0.493972\pi$
$200$	−3.35948	−	2.44081i	−0.237551	−	0.172591i
$201$		0			0
$202$	−4.89188	−	15.0557i	−0.344191	−	1.05931i
$203$	11.2536	+	15.4892i	0.789847	+	1.08713i
$204$		0			0
$205$	−3.77177	+	1.22552i	−0.263432	+	0.0855941i
$206$	9.82949	−	30.2521i	0.684853	−	2.10776i
$207$		0			0
$208$		−	6.99831i		−	0.485246i
$209$	6.01433	+	11.2830i	0.416020	+	0.780458i
$210$		0			0
$211$	−3.02539	+	4.16409i	−0.208276	+	0.286668i	−0.900357	−	0.435153i	$-0.856694\pi$
$211$	−3.02539	+	4.16409i	−0.208276	+	0.286668i	0.692080	+	0.721820i	$0.256694\pi$
$212$	9.86620	+	3.20572i	0.677613	+	0.220170i
$213$		0			0
$214$	−29.4108	+	21.3682i	−2.01048	+	1.46070i
$215$	7.94266	−	5.77068i	0.541685	−	0.393557i
$216$		0			0
$217$	24.1756	+	7.85512i	1.64114	+	0.533240i
$218$	0.561325	−	0.772598i	0.0380178	−	0.0523270i
$219$		0			0
$220$	−24.3686	+	4.32301i	−1.64293	+	0.291457i
$221$			2.55453i			0.171836i
$222$		0			0
$223$	1.29767	−	3.99381i	0.0868983	−	0.267445i	−0.898159	−	0.439670i	$-0.855095\pi$
$223$	1.29767	−	3.99381i	0.0868983	−	0.267445i	0.985058	+	0.172224i	$0.0550954\pi$
$224$	24.1549	−	7.84839i	1.61391	−	0.524393i
$225$		0			0
$226$	−5.19494	−	7.15023i	−0.345562	−	0.475626i
$227$	5.16611	+	15.8996i	0.342887	+	1.05530i	0.962705	+	0.270552i	$0.0872061\pi$
$227$	5.16611	+	15.8996i	0.342887	+	1.05530i	−0.619819	+	0.784745i	$0.712794\pi$
$228$		0			0
$229$	21.0325	+	15.2810i	1.38986	+	1.00980i	0.995880	+	0.0906785i	$0.0289036\pi$
$229$	21.0325	+	15.2810i	1.38986	+	1.00980i	0.393984	+	0.919117i	$0.371096\pi$
$230$	−33.3420			−2.19851
$231$		0			0
$232$	−6.42628			−0.421906
$233$	14.0790	+	10.2290i	0.922345	+	0.670123i	0.944107	−	0.329641i	$-0.106928\pi$
$233$	14.0790	+	10.2290i	0.922345	+	0.670123i	−0.0217619	+	0.999763i	$0.506928\pi$
$234$		0			0
$235$	−4.86974	−	14.9875i	−0.317667	−	0.977677i
$236$	−17.1195	−	23.5630i	−1.11438	−	1.53382i
$237$		0			0
$238$	−6.43751	+	2.09167i	−0.417282	+	0.135583i
$239$	0.770057	−	2.36999i	0.0498109	−	0.153302i	−0.923057	−	0.384663i	$-0.874318\pi$
$239$	0.770057	−	2.36999i	0.0498109	−	0.153302i	0.972868	+	0.231361i	$0.0743177\pi$
$240$		0			0
$241$		−	22.8683i		−	1.47308i	−0.676394	−	0.736540i	$-0.736458\pi$
$241$		−	22.8683i		−	1.47308i	0.676394	−	0.736540i	$-0.263542\pi$
$242$	−13.0159	+	19.3837i	−0.836691	+	1.24603i
$243$		0			0
$244$	−11.8227	+	16.2725i	−0.756871	+	1.04174i
$245$	−9.09445	−	2.95497i	−0.581023	−	0.188786i
$246$		0			0
$247$	−7.98312	+	5.80008i	−0.507954	+	0.369050i
$248$	−6.90264	+	5.01506i	−0.438318	+	0.318457i
$249$		0			0
$250$	−6.78401	−	2.20426i	−0.429059	−	0.139410i
$251$	−5.77288	+	7.94569i	−0.364381	+	0.501528i	−0.951363	−	0.308073i	$-0.900316\pi$
$251$	−5.77288	+	7.94569i	−0.364381	+	0.501528i	0.586982	+	0.809600i	$0.300316\pi$
$252$		0			0
$253$	−12.1374	+	12.5948i	−0.763070	+	0.791830i
$254$			35.7649i			2.24409i
$255$		0			0
$256$	1.59902	−	4.92126i	0.0999385	−	0.307579i
$257$	14.1588	−	4.60048i	0.883203	−	0.286970i	0.167917	−	0.985801i	$-0.446296\pi$
$257$	14.1588	−	4.60048i	0.883203	−	0.286970i	0.715287	+	0.698831i	$0.246296\pi$
$258$		0			0
$259$	8.07470	+	11.1139i	0.501737	+	0.690582i
$260$	−5.90240	−	18.1657i	−0.366051	−	1.12659i
$261$		0			0
$262$	24.5932	+	17.8680i	1.51937	+	1.10389i
$263$	−5.92380			−0.365277			−0.182639	−	0.983180i	$-0.558464\pi$
$263$	−5.92380			−0.365277			−0.182639	+	0.983180i	$0.558464\pi$
$264$		0			0
$265$	−12.3335			−0.757644
$266$	−21.1531	−	15.3686i	−1.29698	−	0.942311i
$267$		0			0
$268$	−5.11918	−	15.7552i	−0.312704	−	0.962403i
$269$	3.97084	+	5.46539i	0.242106	+	0.333230i	0.912727	−	0.408570i	$-0.133972\pi$
$269$	3.97084	+	5.46539i	0.242106	+	0.333230i	−0.670621	+	0.741800i	$0.733972\pi$
$270$		0			0
$271$	−6.02268	+	1.95689i	−0.365852	+	0.118872i	−0.486173	−	0.873863i	$-0.661608\pi$
$271$	−6.02268	+	1.95689i	−0.365852	+	0.118872i	0.120321	+	0.992735i	$0.461608\pi$
$272$	−0.843180	+	2.59504i	−0.0511253	+	0.157348i
$273$		0			0
$274$			5.11249i			0.308857i
$275$	11.3317	−	6.04031i	0.683328	−	0.364245i
$276$		0			0
$277$	−1.22289	+	1.68317i	−0.0734766	+	0.101132i	−0.844173	−	0.536070i	$-0.819908\pi$
$277$	−1.22289	+	1.68317i	−0.0734766	+	0.101132i	0.770697	+	0.637202i	$0.219908\pi$
$278$	8.60922	+	2.79731i	0.516347	+	0.167771i
$279$		0			0
$280$	8.25837	−	6.00006i	0.493532	−	0.358572i
$281$	5.82179	−	4.22978i	0.347299	−	0.252327i	−0.400436	−	0.916325i	$-0.631141\pi$
$281$	5.82179	−	4.22978i	0.347299	−	0.252327i	0.747735	+	0.663997i	$0.231141\pi$
$282$		0			0
$283$	−22.8994	−	7.44045i	−1.36123	−	0.442289i	−0.464773	−	0.885430i	$-0.653864\pi$
$283$	−22.8994	−	7.44045i	−1.36123	−	0.442289i	−0.896452	+	0.443141i	$0.853864\pi$
$284$	−14.1349	+	19.4551i	−0.838753	+	1.15444i
$285$		0			0
$286$	−16.2040	−	7.88233i	−0.958161	−	0.466092i
$287$		−	4.25458i		−	0.251140i
$288$		0			0
$289$	−4.94551	+	15.2207i	−0.290912	+	0.895336i
$290$	36.0265	−	11.7057i	2.11555	−	0.687383i
$291$		0			0
$292$	−1.09430	−	1.50617i	−0.0640388	−	0.0881419i
$293$	6.72926	+	20.7105i	0.393128	+	1.20992i	0.930410	+	0.366520i	$0.119451\pi$
$293$	6.72926	+	20.7105i	0.393128	+	1.20992i	−0.537282	+	0.843402i	$0.680549\pi$
$294$		0			0
$295$	28.0140	+	20.3533i	1.63104	+	1.18502i
$296$	−4.61100			−0.268009
$297$		0			0
$298$	−8.43051			−0.488366
$299$	−10.9211	−	7.93464i	−0.631583	−	0.458872i
$300$		0			0
$301$	3.25469	+	10.0169i	0.187597	+	0.577364i
$302$	21.5703	+	29.6890i	1.24123	+	1.70841i
$303$		0			0
$304$	−10.0242	+	3.25706i	−0.574926	+	0.186805i
$305$	7.38967	−	22.7431i	0.423131	−	1.30226i
$306$		0			0
$307$		−	27.7403i		−	1.58322i	−0.611023	−	0.791612i	$-0.709242\pi$
$307$		−	27.7403i		−	1.58322i	0.611023	−	0.791612i	$-0.290758\pi$
$308$	3.66779	−	26.2963i	0.208992	−	1.49837i
$309$		0			0
$310$	29.5619	−	40.6885i	1.67900	−	2.31095i
$311$	−20.6834	−	6.72045i	−1.17285	−	0.381082i	−0.343144	−	0.939283i	$-0.611492\pi$
$311$	−20.6834	−	6.72045i	−1.17285	−	0.381082i	−0.829706	+	0.558201i	$0.811492\pi$
$312$		0			0
$313$	−4.51010	+	3.27678i	−0.254926	+	0.185215i	−0.707907	−	0.706306i	$-0.750360\pi$
$313$	−4.51010	+	3.27678i	−0.254926	+	0.185215i	0.452981	+	0.891520i	$0.350360\pi$
$314$	0.625831	−	0.454693i	0.0353177	−	0.0256598i
$315$		0			0
$316$	27.9129	+	9.06945i	1.57022	+	0.510197i
$317$	−8.02289	+	11.0426i	−0.450610	+	0.620212i	−0.972529	−	0.232784i	$-0.925217\pi$
$317$	−8.02289	+	11.0426i	−0.450610	+	0.620212i	0.521918	+	0.852996i	$0.325217\pi$
$318$		0			0
$319$	8.69281	−	17.8701i	0.486704	−	1.00053i
$320$		−	33.9635i		−	1.89862i
$321$		0			0
$322$	11.0533	−	34.0186i	0.615977	−	1.89578i
$323$	3.65903	−	1.18889i	0.203594	−	0.0661517i
$324$		0			0
$325$	5.82514	+	8.01761i	0.323121	+	0.444737i
$326$	−1.98236	−	6.10108i	−0.109793	−	0.337908i
$327$		0			0
$328$	1.15532	+	0.839389i	0.0637918	+	0.0463475i
$329$	16.9060			0.932059
$330$		0			0
$331$	7.95544			0.437270			0.218635	−	0.975807i	$-0.429840\pi$
$331$	7.95544			0.437270			0.218635	+	0.975807i	$0.429840\pi$
$332$	−5.47585	−	3.97843i	−0.300526	−	0.218345i
$333$		0			0
$334$	−5.04993	−	15.5421i	−0.276320	−	0.850424i
$335$	11.5766	+	15.9338i	0.632497	+	0.870558i
$336$		0			0
$337$	−29.8353	+	9.69408i	−1.62523	+	0.528070i	−0.973169	−	0.230093i	$-0.926097\pi$
$337$	−29.8353	+	9.69408i	−1.62523	+	0.528070i	−0.652065	+	0.758163i	$0.726097\pi$
$338$	−4.22939	+	13.0167i	−0.230048	+	0.708016i
$339$		0			0
$340$			7.44717i			0.403879i
$341$	−4.60861	−	25.9786i	−0.249570	−	1.40682i
$342$		0			0
$343$	−7.11752	+	9.79643i	−0.384310	+	0.528957i
$344$	−3.36218	−	1.09244i	−0.181277	−	0.0589003i
$345$		0			0
$346$	19.0712	−	13.8560i	1.02527	−	0.744905i
$347$	−1.83775	+	1.33520i	−0.0986553	+	0.0716773i	−0.636019	−	0.771673i	$-0.719420\pi$
$347$	−1.83775	+	1.33520i	−0.0986553	+	0.0716773i	0.537364	+	0.843350i	$0.319420\pi$
$348$		0			0
$349$	−26.0063	−	8.44995i	−1.39208	−	0.452316i	−0.485461	−	0.874258i	$-0.661348\pi$
$349$	−26.0063	−	8.44995i	−1.39208	−	0.452316i	−0.906623	+	0.421943i	$0.861348\pi$
$350$	−15.4350	+	21.2445i	−0.825037	+	1.13557i
$351$		0			0
$352$	−18.9820	−	18.2926i	−1.01174	−	0.974997i
$353$			19.9733i			1.06307i	0.847036	+	0.531535i	$0.178385\pi$
$353$			19.9733i			1.06307i	−0.847036	+	0.531535i	$0.821615\pi$
$354$		0			0
$355$	8.83490	−	27.1910i	0.468908	−	1.44315i
$356$	21.8081	−	7.08587i	1.15583	−	0.375551i
$357$		0			0
$358$	10.3341	+	14.2237i	0.546174	+	0.751743i
$359$	6.60849	+	20.3388i	0.348783	+	1.07344i	0.959527	+	0.281615i	$0.0908701\pi$
$359$	6.60849	+	20.3388i	0.348783	+	1.07344i	−0.610745	+	0.791827i	$0.709130\pi$
$360$		0			0
$361$	−3.34807	−	2.43251i	−0.176214	−	0.128027i
$362$	−36.3188			−1.90887
$363$		0			0
$364$	20.4911			1.07402
$365$	1.79068	+	1.30101i	0.0937285	+	0.0680978i
$366$		0			0
$367$	−5.94919	−	18.3097i	−0.310545	−	0.955759i	−0.977550	−	0.210706i	$-0.932424\pi$
$367$	−5.94919	−	18.3097i	−0.310545	−	0.955759i	0.667005	−	0.745054i	$-0.267576\pi$
$368$	−8.47529	−	11.6652i	−0.441805	−	0.608093i
$369$		0			0
$370$	25.8498	−	8.39911i	1.34387	−	0.436649i
$371$	4.08873	−	12.5838i	0.212276	−	0.653320i
$372$		0			0
$373$		−	6.89609i		−	0.357066i	−0.983934	−	0.178533i	$-0.942865\pi$
$373$		−	6.89609i		−	0.357066i	0.983934	−	0.178533i	$-0.0571351\pi$
$374$	5.05890	+	4.87515i	0.261589	+	0.252088i
$375$		0			0
$376$	−3.33540	+	4.59078i	−0.172010	+	0.236752i
$377$	14.5861	+	4.73931i	0.751222	+	0.244087i
$378$		0			0
$379$	27.7790	−	20.1826i	1.42691	−	1.03671i	0.436329	−	0.899787i	$-0.356278\pi$
$379$	27.7790	−	20.1826i	1.42691	−	1.03671i	0.990582	−	0.136924i	$-0.0437215\pi$
$380$	−23.2731	+	16.9089i	−1.19388	+	0.867407i
$381$		0			0
$382$	21.9941	+	7.14633i	1.12532	+	0.365638i
$383$	0.940164	−	1.29403i	0.0480402	−	0.0661216i	−0.784321	−	0.620355i	$-0.786989\pi$
$383$	0.940164	−	1.29403i	0.0480402	−	0.0661216i	0.832361	+	0.554233i	$0.186989\pi$
$384$		0			0
$385$	5.51378	+	31.0810i	0.281008	+	1.58403i
$386$			22.9768i			1.16949i
$387$		0			0
$388$	7.22445	−	22.2346i	0.366766	−	1.12879i
$389$	−22.5779	+	7.33601i	−1.14475	+	0.371951i	−0.819162	−	0.573562i	$-0.805561\pi$
$389$	−22.5779	+	7.33601i	−1.14475	+	0.371951i	−0.325584	+	0.945513i	$0.605561\pi$
$390$		0			0
$391$	3.09365	+	4.25805i	0.156453	+	0.215339i
$392$	1.06404	+	3.27478i	0.0537422	+	0.165401i
$393$		0			0
$394$	3.07034	+	2.23073i	0.154682	+	0.112383i
$395$	−34.8934			−1.75568
$396$		0			0
$397$	−15.1190			−0.758803			−0.379401	−	0.925232i	$-0.623870\pi$
$397$	−15.1190			−0.758803			−0.379401	+	0.925232i	$0.623870\pi$
$398$	0.917506	+	0.666607i	0.0459904	+	0.0334140i
$399$		0			0
$400$	3.27113	+	10.0675i	0.163556	+	0.503375i
$401$	−15.3082	−	21.0699i	−0.764454	−	1.05218i	−0.996831	−	0.0795544i	$-0.974650\pi$
$401$	−15.3082	−	21.0699i	−0.764454	−	1.05218i	0.232377	−	0.972626i	$-0.425350\pi$
$402$		0			0
$403$	19.3659	−	6.29235i	0.964683	−	0.313444i
$404$	5.77396	−	17.7704i	0.287265	−	0.884111i
$405$		0			0
$406$			40.6382i			2.01684i
$407$	6.23728	−	12.8222i	0.309171	−	0.635572i
$408$		0			0
$409$	−5.04394	+	6.94239i	−0.249407	+	0.343279i	−0.915303	−	0.402765i	$-0.868049\pi$
$409$	−5.04394	+	6.94239i	−0.249407	+	0.343279i	0.665897	+	0.746044i	$0.268049\pi$
$410$	−8.00583	−	2.60125i	−0.395380	−	0.128467i
$411$		0			0
$412$	30.3741	−	22.0681i	1.49643	−	1.08722i
$413$	−30.0533	+	21.8350i	−1.47883	+	1.07443i
$414$		0			0
$415$	7.65322	+	2.48668i	0.375682	+	0.122066i
$416$	11.9585	−	16.4595i	0.586314	−	0.806993i
$417$		0			0
$418$	−3.74901	+	26.8786i	−0.183370	+	1.31467i
$419$			17.8881i			0.873892i	0.899488	+	0.436946i	$0.143940\pi$
$419$			17.8881i			0.873892i	−0.899488	+	0.436946i	$0.856060\pi$
$420$		0			0
$421$	−1.07540	+	3.30975i	−0.0524120	+	0.161307i	−0.973836	−	0.227250i	$-0.927027\pi$
$421$	−1.07540	+	3.30975i	−0.0524120	+	0.161307i	0.921424	+	0.388558i	$0.127027\pi$
$422$	−10.3904	+	3.37603i	−0.505795	+	0.164343i
$423$		0			0
$424$	2.61043	+	3.59295i	0.126774	+	0.174489i
$425$	−1.19403	−	3.67484i	−0.0579189	−	0.178256i
$426$		0			0
$427$	20.7548	+	15.0792i	1.00440	+	0.729736i
$428$	−42.9089			−2.07408
$429$		0			0
$430$	20.8387			1.00493
$431$	22.8883	+	16.6293i	1.10249	+	0.801005i	0.981464	−	0.191644i	$-0.0613820\pi$
$431$	22.8883	+	16.6293i	1.10249	+	0.801005i	0.121025	+	0.992650i	$0.461382\pi$
$432$		0			0
$433$	1.03161	+	3.17496i	0.0495758	+	0.152579i	0.972780	−	0.231732i	$-0.0744392\pi$
$433$	1.03161	+	3.17496i	0.0495758	+	0.152579i	−0.923204	+	0.384311i	$0.874439\pi$
$434$	31.7140	+	43.6506i	1.52232	+	2.09529i
$435$		0			0
$436$	1.07201	−	0.348318i	0.0513401	−	0.0166814i
$437$	−6.28261	+	19.3359i	−0.300538	+	0.924961i
$438$		0			0
$439$		−	15.1602i		−	0.723556i	−0.932264	−	0.361778i	$-0.882170\pi$
$439$		−	15.1602i		−	0.723556i	0.932264	−	0.361778i	$-0.117830\pi$
$440$	−9.52776	−	4.63473i	−0.454218	−	0.220952i
$441$		0			0
$442$	−3.18706	+	4.38662i	−0.151593	+	0.208650i
$443$	10.0392	+	3.26193i	0.476976	+	0.154979i	0.537632	−	0.843180i	$-0.319319\pi$
$443$	10.0392	+	3.26193i	0.476976	+	0.154979i	−0.0606557	+	0.998159i	$0.519319\pi$
$444$		0			0
$445$	−22.0553	+	16.0241i	−1.04552	+	0.759616i
$446$	7.21109	−	5.23916i	0.341455	−	0.248081i
$447$		0			0
$448$	34.6527	+	11.2593i	1.63719	+	0.531954i
$449$	9.24496	−	12.7246i	0.436297	−	0.600511i	−0.533087	−	0.846060i	$-0.678968\pi$
$449$	9.24496	−	12.7246i	0.436297	−	0.600511i	0.969384	+	0.245549i	$0.0789683\pi$
$450$		0			0
$451$	−3.89695	+	2.07725i	−0.183500	+	0.0978140i
$452$		−	10.4318i		−	0.490671i
$453$		0			0
$454$	−10.9654	+	33.7481i	−0.514633	+	1.58388i
$455$	−23.1694	+	7.52821i	−1.08620	+	0.352928i
$456$		0			0
$457$	−1.79378	−	2.46893i	−0.0839097	−	0.115492i	0.764999	−	0.644032i	$-0.222740\pi$
$457$	−1.79378	−	2.46893i	−0.0839097	−	0.115492i	−0.848908	+	0.528540i	$0.822740\pi$
$458$	17.0521	+	52.4808i	0.796790	+	2.45227i
$459$		0			0
$460$	−31.8381	−	23.1317i	−1.48446	−	1.07852i
$461$	0.491689			0.0229002			0.0114501	−	0.999934i	$-0.496355\pi$
$461$	0.491689			0.0229002			0.0114501	+	0.999934i	$0.496355\pi$
$462$		0			0
$463$	8.98358			0.417502			0.208751	−	0.977969i	$-0.433060\pi$
$463$	8.98358			0.417502			0.208751	+	0.977969i	$0.433060\pi$
$464$	13.2531	+	9.62895i	0.615260	+	0.447013i
$465$		0			0
$466$	11.4145	+	35.1303i	0.528767	+	1.62738i
$467$	1.33494	+	1.83738i	0.0617735	+	0.0850239i	0.838786	−	0.544461i	$-0.183266\pi$
$467$	1.33494	+	1.83738i	0.0617735	+	0.0850239i	−0.777013	+	0.629485i	$0.783266\pi$
$468$		0			0
$469$	−20.0950	+	6.52925i	−0.927899	+	0.301493i
$470$	10.3364	−	31.8120i	0.476780	−	1.46738i
$471$		0			0
$472$		−	12.4687i		−	0.573921i
$473$	7.58583	−	7.87174i	0.348797	−	0.361943i
$474$		0			0
$475$	8.77315	−	12.0752i	0.402540	−	0.554048i
$476$	−7.59829	−	2.46883i	−0.348267	−	0.113159i
$477$		0			0
$478$	4.27918	−	3.10900i	0.195725	−	0.142202i
$479$	9.37003	−	6.80772i	0.428127	−	0.311053i	−0.352772	−	0.935709i	$-0.614761\pi$
$479$	9.37003	−	6.80772i	0.428127	−	0.311053i	0.780900	+	0.624656i	$0.214761\pi$
$480$		0			0
$481$	10.4658	+	3.40056i	0.477202	+	0.155052i
$482$	28.5309	−	39.2694i	1.29955	−	1.78867i
$483$		0			0
$484$	−25.8766	+	9.47938i	−1.17621	+	0.430881i
$485$			27.7950i			1.26211i
$486$		0			0
$487$	11.3865	−	35.0439i	0.515970	−	1.58799i	−0.265541	−	0.964100i	$-0.585551\pi$
$487$	11.3865	−	35.0439i	0.515970	−	1.58799i	0.781511	−	0.623892i	$-0.214449\pi$
$488$	−8.18945	+	2.66091i	−0.370719	+	0.120454i
$489$		0			0
$490$	−11.9303	−	16.4206i	−0.538955	−	0.741808i
$491$	−4.30496	−	13.2493i	−0.194280	−	0.597933i	−0.999984	−	0.00561479i	$-0.998213\pi$
$491$	−4.30496	−	13.2493i	−0.194280	−	0.597933i	0.805704	−	0.592318i	$-0.201787\pi$
$492$		0			0
$493$	−4.83766	−	3.51476i	−0.217877	−	0.158297i
$494$	−20.9448			−0.942353
$495$		0			0
$496$	21.7500			0.976602
$497$	24.8139	+	18.0284i	1.11306	+	0.808683i
$498$		0			0
$499$	3.90314	+	12.0126i	0.174729	+	0.537760i	0.999621	−	0.0275302i	$-0.00876425\pi$
$499$	3.90314	+	12.0126i	0.174729	+	0.537760i	−0.824892	+	0.565290i	$0.808764\pi$
$500$	−4.94876	−	6.81139i	−0.221315	−	0.304615i
$501$		0			0
$502$	−19.8263	+	6.44196i	−0.884892	+	0.287519i
$503$	10.4111	−	32.0422i	0.464210	−	1.42869i	−0.395764	−	0.918352i	$-0.629520\pi$
$503$	10.4111	−	32.0422i	0.464210	−	1.42869i	0.859974	−	0.510339i	$-0.170480\pi$
$504$		0			0
$505$			22.2145i			0.988530i
$506$	−36.5557	+	6.48500i	−1.62510	+	0.288293i
$507$		0			0
$508$	−24.8126	+	34.1517i	−1.10088	+	1.51524i
$509$	20.9648	+	6.81188i	0.929248	+	0.301931i	0.734255	−	0.678874i	$-0.237532\pi$
$509$	20.9648	+	6.81188i	0.929248	+	0.301931i	0.194993	+	0.980805i	$0.437532\pi$
$510$		0			0
$511$	−1.92104	+	1.39572i	−0.0849819	+	0.0617429i
$512$	22.3257	−	16.2206i	0.986666	−	0.716855i
$513$		0			0
$514$	30.0531	+	9.76484i	1.32558	+	0.430709i
$515$	−26.2367	+	36.1117i	−1.15613	+	1.59127i
$516$		0			0
$517$	−8.25418	−	15.4849i	−0.363018	−	0.681027i
$518$			29.1588i			1.28116i
$519$		0			0
$520$	2.52685	−	7.77684i	0.110810	−	0.341037i
$521$	−23.0301	+	7.48292i	−1.00896	+	0.327833i	−0.766442	−	0.642313i	$-0.777975\pi$
$521$	−23.0301	+	7.48292i	−1.00896	+	0.327833i	−0.242523	+	0.970146i	$0.577975\pi$
$522$		0			0
$523$	−0.785047	−	1.08052i	−0.0343277	−	0.0472480i	0.791508	−	0.611159i	$-0.209296\pi$
$523$	−0.785047	−	1.08052i	−0.0343277	−	0.0472480i	−0.825836	+	0.563911i	$0.809296\pi$
$524$	11.0876	+	34.1241i	0.484363	+	1.49072i
$525$		0			0
$526$	−10.1723	−	7.39062i	−0.443534	−	0.322247i
$527$	−7.93917			−0.345836
$528$		0			0
$529$	−4.81321			−0.209270
$530$	−21.1791	−	15.3875i	−0.919961	−	0.668391i
$531$		0			0
$532$	−9.53667	−	29.3508i	−0.413467	−	1.27252i
$533$	−2.00325	−	2.75724i	−0.0867705	−	0.119429i
$534$		0			0
$535$	48.5175	−	15.7643i	2.09759	−	0.681549i
$536$	2.19155	−	6.74489i	0.0946604	−	0.291335i
$537$		0			0
$538$			14.3392i			0.618207i
$539$	−10.5458	−	1.47092i	−0.454239	−	0.0633570i
$540$		0			0
$541$	22.6301	−	31.1477i	0.972944	−	1.33914i	0.0323981	−	0.999475i	$-0.489686\pi$
$541$	22.6301	−	31.1477i	0.972944	−	1.33914i	0.940546	−	0.339667i	$-0.110314\pi$
$542$	−12.7836	−	4.15363i	−0.549101	−	0.178414i
$543$		0			0
$544$	−6.41743	+	4.66253i	−0.275145	+	0.199904i
$545$	−1.08417	+	0.787693i	−0.0464406	+	0.0337411i
$546$		0			0
$547$	−29.9931	−	9.74534i	−1.28241	−	0.416681i	−0.412983	−	0.910739i	$-0.635513\pi$
$547$	−29.9931	−	9.74534i	−1.28241	−	0.416681i	−0.869429	+	0.494058i	$0.835513\pi$
$548$	−3.54690	+	4.88189i	−0.151516	+	0.208544i
$549$		0			0
$550$	26.9947	+	3.76521i	1.15106	+	0.160549i
$551$		−	23.0984i		−	0.984025i
$552$		0			0
$553$	11.5676	−	35.6015i	0.491905	−	1.51393i
$554$	−4.19989	+	1.36463i	−0.178436	+	0.0579775i
$555$		0			0
$556$	6.28021	+	8.64396i	0.266340	+	0.366586i
$557$	4.42923	+	13.6318i	0.187673	+	0.577597i	0.999984	−	0.00562684i	$-0.00179109\pi$
$557$	4.42923	+	13.6318i	0.187673	+	0.577597i	−0.812312	+	0.583224i	$0.801791\pi$
$558$		0			0
$559$	6.82566	+	4.95913i	0.288695	+	0.209749i
$560$	−26.0218			−1.09962
$561$		0			0
$562$	15.2743			0.644307
$563$	11.7638	+	8.54689i	0.495785	+	0.360209i	0.807405	−	0.589998i	$-0.200872\pi$
$563$	11.7638	+	8.54689i	0.495785	+	0.360209i	−0.311620	+	0.950207i	$0.600872\pi$
$564$		0			0
$565$	3.83254	+	11.7953i	0.161236	+	0.496234i
$566$	−30.0398	−	41.3463i	−1.26267	−	1.73791i
$567$		0			0
$568$	−9.79110	+	3.18132i	−0.410826	+	0.133485i
$569$	4.80561	−	14.7902i	0.201462	−	0.620035i	−0.798378	−	0.602156i	$-0.794309\pi$
$569$	4.80561	−	14.7902i	0.201462	−	0.620035i	0.999840	−	0.0178794i	$-0.00569149\pi$
$570$		0			0
$571$		−	30.8824i		−	1.29239i	−0.763172	−	0.646195i	$-0.776359\pi$
$571$		−	30.8824i		−	1.29239i	0.763172	−	0.646195i	$-0.223641\pi$
$572$	−10.0045	−	18.7686i	−0.418311	−	0.784757i
$573$		0			0
$574$	5.30808	−	7.30594i	0.221555	−	0.304944i
$575$	19.4194	+	6.30976i	0.809846	+	0.263135i
$576$		0			0
$577$	−32.9843	+	23.9645i	−1.37316	+	0.997656i	−0.375672	+	0.926753i	$0.622588\pi$
$577$	−32.9843	+	23.9645i	−1.37316	+	0.997656i	−0.997483	+	0.0709027i	$0.977412\pi$
$578$	−27.4820	+	19.9668i	−1.14310	+	0.830511i
$579$		0			0
$580$	42.5226	+	13.8164i	1.76565	+	0.573696i
$581$	−5.07429	+	6.98416i	−0.210517	+	0.289752i
$582$		0			0
$583$	−13.5223	+	2.39887i	−0.560038	+	0.0993510i
$584$		−	0.797015i		−	0.0329807i
$585$		0			0
$586$	−14.2833	+	43.9595i	−0.590039	+	1.81595i
$587$	17.1307	−	5.56610i	0.707059	−	0.229737i	0.0666554	−	0.997776i	$-0.478767\pi$
$587$	17.1307	−	5.56610i	0.707059	−	0.229737i	0.640403	+	0.768039i	$0.278767\pi$
$588$		0			0
$589$	−18.0260	−	24.8106i	−0.742747	−	1.02230i
$590$	22.7123	+	69.9013i	0.935050	+	2.87779i
$591$		0			0
$592$	9.50941	+	6.90899i	0.390834	+	0.283958i
$593$	12.6974			0.521422			0.260711	−	0.965417i	$-0.416043\pi$
$593$	12.6974			0.521422			0.260711	+	0.965417i	$0.416043\pi$
$594$		0			0
$595$	9.49848			0.389400
$596$	−8.05025	−	5.84885i	−0.329751	−	0.239578i
$597$		0			0
$598$	−8.85427	−	27.2506i	−0.362078	−	1.11436i
$599$	5.69678	+	7.84094i	0.232764	+	0.320372i	0.909382	−	0.415962i	$-0.136555\pi$
$599$	5.69678	+	7.84094i	0.232764	+	0.320372i	−0.676618	+	0.736334i	$0.736555\pi$
$600$		0			0
$601$	−4.82038	+	1.56624i	−0.196627	+	0.0638881i	−0.405675	−	0.914017i	$-0.632964\pi$
$601$	−4.82038	+	1.56624i	−0.196627	+	0.0638881i	0.209048	+	0.977905i	$0.432964\pi$
$602$	−6.90830	+	21.2616i	−0.281561	+	0.866556i
$603$		0			0
$604$			43.3147i			1.76245i
$605$	25.7763	−	20.2252i	1.04796	−	0.822273i
$606$		0			0
$607$	16.9860	−	23.3793i	0.689442	−	0.948935i	−0.310557	−	0.950555i	$-0.600516\pi$
$607$	16.9860	−	23.3793i	0.689442	−	0.948935i	0.999999	+	0.00161969i	$0.000515563\pi$
$608$	−29.1417	−	9.46870i	−1.18185	−	0.384006i
$609$		0			0
$610$	41.0641	−	29.8348i	1.66264	−	1.20798i
$611$	10.9562	−	7.96014i	0.443240	−	0.322033i
$612$		0			0
$613$	−29.6117	−	9.62142i	−1.19600	−	0.388606i	−0.357715	−	0.933831i	$-0.616444\pi$
$613$	−29.6117	−	9.62142i	−1.19600	−	0.388606i	−0.838290	+	0.545225i	$0.816444\pi$
$614$	34.6093	−	47.6356i	1.39672	−	1.92241i
$615$		0			0
$616$	7.88736	−	8.18463i	0.317791	−	0.329768i
$617$			28.7025i			1.15552i	0.816207	+	0.577760i	$0.196073\pi$
$617$			28.7025i			1.15552i	−0.816207	+	0.577760i	$0.803927\pi$
$618$		0			0
$619$	4.88396	−	15.0313i	0.196303	−	0.604158i	−0.803656	−	0.595094i	$-0.797115\pi$
$619$	4.88396	−	15.0313i	0.196303	−	0.604158i	0.999959	−	0.00906388i	$-0.00288516\pi$
$620$	56.4570	−	18.3440i	2.26737	−	0.736712i
$621$		0			0
$622$	−27.1329	−	37.3453i	−1.08793	−	1.49741i
$623$	−9.03767	−	27.8151i	−0.362086	−	1.11439i
$624$		0			0
$625$	23.7595	+	17.2623i	0.950380	+	0.690492i
$626$	−11.8329			−0.472937
$627$		0			0
$628$	0.913056			0.0364349
$629$	−3.47113	−	2.52192i	−0.138403	−	0.100556i
$630$		0			0
$631$	9.43085	+	29.0252i	0.375436	+	1.15547i	0.943184	+	0.332271i	$0.107815\pi$
$631$	9.43085	+	29.0252i	0.375436	+	1.15547i	−0.567748	+	0.823203i	$0.692185\pi$
$632$	7.38530	+	10.1650i	0.293771	+	0.404342i
$633$		0			0
$634$	−27.5537	+	8.95275i	−1.09430	+	0.355559i
$635$	15.5089	−	47.7315i	0.615452	−	1.89417i
$636$		0			0
$637$		−	8.21767i		−	0.325596i
$638$	37.2222	−	19.8411i	1.47364	−	0.785518i
$639$		0			0
$640$	14.5424	−	20.0159i	0.574839	−	0.791197i
$641$	17.2873	+	5.61698i	0.682807	+	0.221858i	0.629824	−	0.776738i	$-0.283127\pi$
$641$	17.2873	+	5.61698i	0.682807	+	0.221858i	0.0529832	+	0.998595i	$0.483127\pi$
$642$		0			0
$643$	−7.37203	+	5.35609i	−0.290725	+	0.211224i	−0.723582	−	0.690239i	$-0.757505\pi$
$643$	−7.37203	+	5.35609i	−0.290725	+	0.211224i	0.432857	+	0.901463i	$0.357505\pi$
$644$	34.1559	−	24.8157i	1.34593	−	0.977875i
$645$		0			0
$646$	7.76655	+	2.52350i	0.305571	+	0.0992859i
$647$	18.9534	−	26.0871i	0.745136	−	1.02559i	−0.253171	−	0.967422i	$-0.581473\pi$
$647$	18.9534	−	26.0871i	0.745136	−	1.02559i	0.998307	−	0.0581699i	$-0.0185265\pi$
$648$		0			0
$649$	34.6728	+	16.8664i	1.36103	+	0.662065i
$650$			21.0353i			0.825073i
$651$		0			0
$652$	2.33981	−	7.20120i	0.0916340	−	0.282021i
$653$	20.4313	−	6.63853i	0.799538	−	0.259786i	0.119378	−	0.992849i	$-0.461910\pi$
$653$	20.4313	−	6.63853i	0.799538	−	0.259786i	0.680160	+	0.733063i	$0.261910\pi$
$654$		0			0
$655$	−25.0737	−	34.5109i	−0.979709	−	1.34845i
$656$	−1.12493	−	3.46219i	−0.0439213	−	0.135176i
$657$		0			0
$658$	29.0309	+	21.0922i	1.13174	+	0.822260i
$659$	30.1358			1.17393			0.586963	−	0.809614i	$-0.300324\pi$
$659$	30.1358			1.17393			0.586963	+	0.809614i	$0.300324\pi$
$660$		0			0
$661$	−44.9664			−1.74899			−0.874496	−	0.485033i	$-0.838808\pi$
$661$	−44.9664			−1.74899			−0.874496	+	0.485033i	$0.838808\pi$
$662$	13.6610	+	9.92532i	0.530951	+	0.385758i
$663$		0			0
$664$	−0.895419	−	2.75582i	−0.0347490	−	0.106946i
$665$	21.5664	+	29.6836i	0.836309	+	1.15108i
$666$		0			0
$667$	30.0526	−	9.76467i	1.16364	−	0.378090i
$668$	5.96050	−	18.3445i	0.230619	−	0.709771i
$669$		0			0
$670$			41.8046i			1.61505i
$671$	3.67842	−	26.3725i	0.142004	−	1.01810i
$672$		0			0
$673$	−23.7932	+	32.7486i	−0.917162	+	1.26236i	0.0474995	+	0.998871i	$0.484875\pi$
$673$	−23.7932	+	32.7486i	−0.917162	+	1.26236i	−0.964661	+	0.263494i	$0.915125\pi$
$674$	−63.3275	−	20.5764i	−2.43929	−	0.792572i
$675$		0			0
$676$	−13.0692	+	9.49536i	−0.502663	+	0.365206i
$677$	−26.3382	+	19.1358i	−1.01226	+	0.735448i	−0.964681	−	0.263419i	$-0.915150\pi$
$677$	−26.3382	+	19.1358i	−1.01226	+	0.735448i	−0.0475763	+	0.998868i	$0.515150\pi$
$678$		0			0
$679$	−28.3590	−	9.21441i	−1.08832	−	0.353617i
$680$	−1.87396	+	2.57928i	−0.0718631	+	0.0989111i
$681$		0			0
$682$	24.4974	−	50.3601i	0.938054	−	1.92839i
$683$		−	9.42972i		−	0.360818i	−0.983592	−	0.180409i	$-0.942258\pi$
$683$		−	9.42972i		−	0.360818i	0.983592	−	0.180409i	$-0.0577422\pi$
$684$		0			0
$685$	2.21696	−	6.82309i	0.0847055	−	0.260697i
$686$	−24.4443	+	7.94244i	−0.933289	+	0.303244i
$687$		0			0
$688$	5.29704	+	7.29076i	0.201948	+	0.277957i
$689$	−3.27528	−	10.0803i	−0.124778	−	0.384028i
$690$		0			0
$691$	−6.24048	−	4.53397i	−0.237399	−	0.172480i	0.462725	−	0.886502i	$-0.346872\pi$
$691$	−6.24048	−	4.53397i	−0.237399	−	0.172480i	−0.700124	+	0.714022i	$0.746872\pi$
$692$	27.8239			1.05771
$693$		0			0
$694$	−4.82158			−0.183025
$695$	−10.2768	−	7.46652i	−0.389821	−	0.283221i
$696$		0			0
$697$	0.410624	+	1.26377i	0.0155535	+	0.0478687i
$698$	−34.1155	−	46.9560i	−1.29129	−	1.77731i
$699$		0			0
$700$	−29.4777	+	9.57787i	−1.11415	+	0.362010i
$701$	−4.21571	+	12.9746i	−0.159225	+	0.490044i	−0.998564	−	0.0535633i	$-0.982942\pi$
$701$	−4.21571	+	12.9746i	−0.159225	+	0.490044i	0.839339	+	0.543608i	$0.182942\pi$
$702$		0			0
$703$		−	16.5736i		−	0.625086i
$704$	−6.60589	−	37.2371i	−0.248969	−	1.40343i
$705$		0			0
$706$	−24.9189	+	34.2980i	−0.937837	+	1.29082i
$707$	−22.6652	−	7.36438i	−0.852414	−	0.276966i
$708$		0			0
$709$	−13.1477	+	9.55236i	−0.493772	+	0.358746i	−0.806633	−	0.591052i	$-0.798713\pi$
$709$	−13.1477	+	9.55236i	−0.493772	+	0.358746i	0.312861	+	0.949799i	$0.398713\pi$
$710$	49.0952	−	35.6697i	1.84251	−	1.33866i
$711$		0			0
$712$	9.33615	+	3.03350i	0.349887	+	0.113685i
$713$	24.6599	−	33.9415i	0.923522	−	1.27112i
$714$		0			0
$715$	18.2076	+	17.5463i	0.680927	+	0.656195i
$716$			20.7516i			0.775523i
$717$		0			0
$718$	−14.0270	+	43.1706i	−0.523482	+	1.61111i
$719$	12.0892	−	3.92803i	0.450852	−	0.146491i	−0.0747848	−	0.997200i	$-0.523827\pi$
$719$	12.0892	−	3.92803i	0.450852	−	0.146491i	0.525637	+	0.850709i	$0.323827\pi$
$720$		0			0
$721$	−28.1467	−	38.7407i	−1.04824	−	1.44278i
$722$	−2.71444	−	8.35420i	−0.101021	−	0.310911i
$723$		0			0
$724$	−34.6806	−	25.1970i	−1.28890	−	0.936437i
$725$	−23.1982			−0.861560
$726$		0			0
$727$	29.4959			1.09394			0.546972	−	0.837151i	$-0.315781\pi$
$727$	29.4959			1.09394			0.546972	+	0.837151i	$0.315781\pi$
$728$	7.09697	+	5.15625i	0.263031	+	0.191103i
$729$		0			0
$730$	1.45179	+	4.46816i	0.0537333	+	0.165374i
$731$	−1.93353	−	2.66127i	−0.0715141	−	0.0984308i
$732$		0			0
$733$	36.6838	−	11.9193i	1.35495	−	0.440249i	0.460594	−	0.887611i	$-0.347637\pi$
$733$	36.6838	−	11.9193i	1.35495	−	0.440249i	0.894353	+	0.447362i	$0.147637\pi$
$734$	12.6276	−	38.8636i	0.466092	−	1.43448i
$735$		0			0
$736$		−	41.9181i		−	1.54512i
$737$	15.7916	+	15.2180i	0.581689	+	0.560562i
$738$		0			0
$739$	−13.6543	+	18.7936i	−0.502282	+	0.691332i	−0.982594	−	0.185766i	$-0.940523\pi$
$739$	−13.6543	+	18.7936i	−0.502282	+	0.691332i	0.480312	+	0.877098i	$0.340523\pi$
$740$	30.5109	+	9.91360i	1.12160	+	0.364431i
$741$		0			0
$742$	22.7209	−	16.5077i	0.834111	−	0.606017i
$743$	2.99034	−	2.17261i	0.109705	−	0.0797052i	−0.531580	−	0.847008i	$-0.678402\pi$
$743$	2.99034	−	2.17261i	0.109705	−	0.0797052i	0.641285	+	0.767303i	$0.278402\pi$
$744$		0			0
$745$	11.2513	+	3.65577i	0.412215	+	0.133937i
$746$	8.60366	−	11.8419i	0.315002	−	0.433564i
$747$		0			0
$748$	1.44847	+	8.16498i	0.0529613	+	0.298541i
$749$			54.7281i			1.99972i
$750$		0			0
$751$	−15.2699	+	46.9958i	−0.557206	+	1.71490i	0.132841	+	0.991137i	$0.457590\pi$
$751$	−15.2699	+	46.9958i	−0.557206	+	1.71490i	−0.690046	+	0.723765i	$0.742410\pi$
$752$	13.7574	−	4.47005i	0.501680	−	0.163006i
$753$		0			0
$754$	19.1343	+	26.3361i	0.696831	+	0.959106i
$755$	−15.9134	−	48.9763i	−0.579147	−	1.78243i
$756$		0			0
$757$	−34.6804	−	25.1968i	−1.26048	−	0.915792i	−0.261698	−	0.965150i	$-0.584282\pi$
$757$	−34.6804	−	25.1968i	−1.26048	−	0.915792i	−0.998781	+	0.0493580i	$0.984282\pi$
$758$	72.8820			2.64719
$759$		0			0
$760$	−12.3153			−0.446724
$761$	−33.9827	−	24.6899i	−1.23187	−	0.895008i	−0.234844	−	0.972033i	$-0.575458\pi$
$761$	−33.9827	−	24.6899i	−1.23187	−	0.895008i	−0.997029	+	0.0770250i	$0.975458\pi$
$762$		0			0
$763$	−0.444262	−	1.36730i	−0.0160834	−	0.0494995i
$764$	16.0442	+	22.0829i	0.580457	+	0.798931i
$765$		0			0
$766$	3.22889	−	1.04913i	0.116665	−	0.0379066i
$767$	−9.19556	+	28.3010i	−0.332032	+	1.02189i
$768$		0			0
$769$			4.13165i			0.148991i	0.997221	+	0.0744955i	$0.0237346\pi$
$769$			4.13165i			0.148991i	−0.997221	+	0.0744955i	$0.976265\pi$
$770$	−29.3088	+	60.2511i	−1.05622	+	2.17130i
$771$		0			0
$772$	−15.9407	+	21.9405i	−0.573717	+	0.789654i
$773$	−21.2989	−	6.92044i	−0.766069	−	0.248911i	−0.100188	−	0.994969i	$-0.531944\pi$
$773$	−21.2989	−	6.92044i	−0.766069	−	0.248911i	−0.665882	+	0.746057i	$0.731944\pi$
$774$		0			0
$775$	−24.9178	+	18.1039i	−0.895075	+	0.650310i
$776$	8.09712	−	5.88290i	0.290670	−	0.211184i
$777$		0			0
$778$	−47.9232	−	15.5712i	−1.71813	−	0.558254i
$779$	−3.01707	+	4.15264i	−0.108098	+	0.148784i
$780$		0			0
$781$	4.39783	−	31.5303i	0.157367	−	1.12824i
$782$			11.1716i			0.399495i
$783$		0			0
$784$	2.71243	−	8.34801i	0.0968726	−	0.298143i
$785$	−1.03240	+	0.335447i	−0.0368480	+	0.0119726i
$786$		0			0
$787$	−4.93902	−	6.79798i	−0.176057	−	0.242322i	0.711864	−	0.702317i	$-0.247851\pi$
$787$	−4.93902	−	6.79798i	−0.176057	−	0.242322i	−0.887921	+	0.459995i	$0.847851\pi$
$788$	1.38423	+	4.26023i	0.0493112	+	0.151764i
$789$		0			0
$790$	−59.9187	−	43.5335i	−2.13181	−	1.54885i
$791$	−13.3052			−0.473080
$792$		0			0
$793$	20.5504			0.729768
$794$	−25.9623	−	18.8627i	−0.921369	−	0.669413i
$795$		0			0
$796$	0.413648	+	1.27308i	0.0146614	+	0.0451231i
$797$	−4.60369	−	6.33643i	−0.163071	−	0.224448i	0.719660	−	0.694327i	$-0.244298\pi$
$797$	−4.60369	−	6.33643i	−0.163071	−	0.224448i	−0.882731	+	0.469879i	$0.844298\pi$
$798$		0			0
$799$	−5.02172	+	1.63166i	−0.177656	+	0.0577239i
$800$	−9.50961	+	29.2676i	−0.336216	+	1.03476i
$801$		0			0
$802$		−	55.2798i		−	1.95200i
$803$	2.21632	+	1.07812i	0.0782124	+	0.0380460i
$804$		0			0
$805$	−29.5033	+	40.6078i	−1.03986	+	1.43124i
$806$	41.1054	+	13.3560i	1.44788	+	0.470443i
$807$		0			0
$808$	6.47141	−	4.70176i	0.227664	−	0.165407i
$809$	−32.0318	+	23.2725i	−1.12618	+	0.818216i	−0.985134	−	0.171787i	$-0.945046\pi$
$809$	−32.0318	+	23.2725i	−1.12618	+	0.818216i	−0.141044	+	0.990003i	$0.545046\pi$
$810$		0			0
$811$	−43.7729	−	14.2227i	−1.53708	−	0.499426i	−0.586508	−	0.809944i	$-0.699498\pi$
$811$	−43.7729	−	14.2227i	−1.53708	−	0.499426i	−0.950568	+	0.310518i	$0.899498\pi$
$812$	−28.1936	+	38.8052i	−0.989401	+	1.36179i
$813$		0			0
$814$	26.7078	−	14.2365i	0.936107	−	0.498987i
$815$			9.00208i			0.315329i
$816$		0			0
$817$	3.92662	−	12.0849i	0.137375	−	0.422797i
$818$	−17.3228	+	5.62853i	−0.605679	+	0.196797i
$819$		0			0
$820$	−5.84005	−	8.03814i	−0.203943	−	0.280704i
$821$	−5.42862	−	16.7076i	−0.189460	−	0.583099i	0.810536	−	0.585688i	$-0.199176\pi$
$821$	−5.42862	−	16.7076i	−0.189460	−	0.583099i	−0.999997	+	0.00258952i	$0.999176\pi$
$822$		0			0
$823$	−35.6517	−	25.9025i	−1.24274	−	0.902904i	−0.244963	−	0.969532i	$-0.578776\pi$
$823$	−35.6517	−	25.9025i	−1.24274	−	0.902904i	−0.997778	+	0.0666279i	$0.978776\pi$
$824$	16.0730			0.559929
$825$		0			0
$826$	−78.8492			−2.74351
$827$	−41.6792	−	30.2817i	−1.44933	−	1.05300i	−0.985988	−	0.166818i	$-0.946651\pi$
$827$	−41.6792	−	30.2817i	−1.44933	−	1.05300i	−0.463341	−	0.886180i	$-0.653349\pi$
$828$		0			0
$829$	6.34753	+	19.5357i	0.220459	+	0.678503i	0.998721	+	0.0505630i	$0.0161016\pi$
$829$	6.34753	+	19.5357i	0.220459	+	0.678503i	−0.778262	+	0.627940i	$0.783898\pi$
$830$	10.0397	+	13.8184i	0.348481	+	0.479643i
$831$		0			0
$832$	27.7586	−	9.01932i	0.962356	−	0.312689i
$833$	−0.990093	+	3.04719i	−0.0343047	+	0.105579i
$834$		0			0
$835$			22.9322i			0.793600i
$836$	−22.2275	+	23.0653i	−0.768754	+	0.797729i
$837$		0			0
$838$	−22.3175	+	30.7174i	−0.770945	+	1.06111i
$839$	−40.8430	−	13.2707i	−1.41006	−	0.458155i	−0.497628	−	0.867391i	$-0.665796\pi$
$839$	−40.8430	−	13.2707i	−1.41006	−	0.458155i	−0.912429	+	0.409235i	$0.865796\pi$
$840$		0			0
$841$	−5.58256	+	4.05597i	−0.192502	+	0.139861i
$842$	−5.97597	+	4.34180i	−0.205946	+	0.149628i
$843$		0			0
$844$	−12.2639	−	3.98478i	−0.422140	−	0.137162i
$845$	11.2890	−	15.5380i	0.388354	−	0.534523i
$846$		0			0
$847$	12.0905	+	33.0043i	0.415433	+	1.13404i
$848$		−	11.3213i		−	0.388773i
$849$		0			0
$850$	2.53441	−	7.80010i	0.0869294	−	0.267541i
$851$	21.5634	−	7.00637i	0.739184	−	0.240175i
$852$		0			0
$853$	15.2572	+	20.9997i	0.522396	+	0.719016i	0.985948	−	0.167053i	$-0.0534252\pi$
$853$	15.2572	+	20.9997i	0.522396	+	0.719016i	−0.463552	+	0.886070i	$0.653425\pi$
$854$	16.8269	+	51.7880i	0.575806	+	1.77215i
$855$		0			0
$856$	−14.8613	−	10.7973i	−0.507947	−	0.369045i
$857$	10.4772			0.357895			0.178948	−	0.983859i	$-0.442731\pi$
$857$	10.4772			0.357895			0.178948	+	0.983859i	$0.442731\pi$
$858$		0			0
$859$	23.6244			0.806053			0.403026	−	0.915188i	$-0.367958\pi$
$859$	23.6244			0.806053			0.403026	+	0.915188i	$0.367958\pi$
$860$	19.8987	+	14.4573i	0.678541	+	0.492989i
$861$		0			0
$862$	18.5566	+	57.1115i	0.632042	+	1.94522i
$863$	2.46666	+	3.39507i	0.0839661	+	0.115569i	0.848934	−	0.528499i	$-0.177245\pi$
$863$	2.46666	+	3.39507i	0.0839661	+	0.115569i	−0.764968	+	0.644069i	$0.777245\pi$
$864$		0			0
$865$	−31.4607	+	10.2222i	−1.06970	+	0.347566i
$866$	−2.18965	+	6.73906i	−0.0744075	+	0.229003i
$867$		0			0
$868$			63.6839i			2.16157i
$869$	−38.2567	+	6.78675i	−1.29777	+	0.230225i
$870$		0			0
$871$	−9.94855	+	13.6930i	−0.337094	+	0.463970i
$872$	0.458934	+	0.149117i	0.0155415	+	0.00504973i
$873$		0			0
$874$	−34.9122	+	25.3652i	−1.18092	+	0.857991i
$875$	−8.68757	+	6.31189i	−0.293694	+	0.213381i
$876$		0			0
$877$	−30.5461	−	9.92504i	−1.03147	−	0.335145i	−0.256099	−	0.966651i	$-0.582437\pi$
$877$	−30.5461	−	9.92504i	−1.03147	−	0.335145i	−0.775371	+	0.631506i	$0.782437\pi$
$878$	18.9141	−	26.0330i	0.638319	−	0.878570i
$879$		0			0
$880$	12.7048	+	23.8345i	0.428280	+	0.803459i
$881$			16.9977i			0.572666i	0.958130	+	0.286333i	$0.0924364\pi$
$881$			16.9977i			0.572666i	−0.958130	+	0.286333i	$0.907564\pi$
$882$		0			0
$883$	6.18492	−	19.0352i	0.208139	−	0.640586i	−0.791431	−	0.611259i	$-0.790663\pi$
$883$	6.18492	−	19.0352i	0.208139	−	0.640586i	0.999570	−	0.0293274i	$-0.00933653\pi$
$884$	−6.08662	+	1.97766i	−0.204715	+	0.0665160i
$885$		0			0
$886$	13.1696	+	18.1264i	0.442441	+	0.608968i
$887$	−0.00102104	−	0.00314245i	−3.42833e−5	−	0.000105513i	0.951039	−	0.309070i	$-0.100018\pi$
$887$	−0.00102104	−	0.00314245i	−3.42833e−5	−	0.000105513i	−0.951074	+	0.308964i	$0.900018\pi$
$888$		0			0
$889$	43.5587	+	31.6473i	1.46091	+	1.06141i
$890$	−57.8652			−1.93965
$891$		0			0
$892$	10.5206			0.352256
$893$	−16.5009	−	11.9886i	−0.552183	−	0.401185i
$894$		0			0
$895$	−7.62392	−	23.4640i	−0.254839	−	0.784315i
$896$	15.6011	+	21.4730i	0.521195	+	0.717363i
$897$		0			0
$898$	31.7508	−	10.3165i	1.05954	−	0.344265i
$899$	−14.7292	+	45.3319i	−0.491247	+	1.51190i
$900$		0			0
$901$			4.13249i			0.137673i
$902$	−9.28343	−	1.29485i	−0.309104	−	0.0431137i
$903$		0			0
$904$	2.62500	−	3.61300i	0.0873061	−	0.120167i
$905$	48.4708	+	15.7491i	1.61122	+	0.523518i
$906$		0			0
$907$	24.6575	−	17.9148i	0.818740	−	0.594850i	−0.0976112	−	0.995225i	$-0.531120\pi$
$907$	24.6575	−	17.9148i	0.818740	−	0.594850i	0.916351	+	0.400375i	$0.131120\pi$
$908$	−33.8843	+	24.6184i	−1.12449	+	0.816990i
$909$		0			0
$910$	−49.1788	−	15.9791i	−1.63026	−	0.529703i
$911$	−22.3820	+	30.8062i	−0.741549	+	1.02065i	0.256979	+	0.966417i	$0.417273\pi$
$911$	−22.3820	+	30.8062i	−0.741549	+	1.02065i	−0.998528	+	0.0542375i	$0.982727\pi$
$912$		0			0
$913$	8.87455	+	1.23782i	0.293705	+	0.0409658i
$914$		−	6.47759i		−	0.214260i
$915$		0			0
$916$	−20.1268	+	61.9439i	−0.665008	+	2.04668i
$917$	43.5235	−	14.1416i	1.43727	−	0.466998i
$918$		0			0
$919$	14.7418	+	20.2904i	0.486288	+	0.669318i	0.979698	−	0.200479i	$-0.0642497\pi$
$919$	14.7418	+	20.2904i	0.486288	+	0.669318i	−0.493410	+	0.869797i	$0.664250\pi$
$920$	−5.20621	−	16.0231i	−0.171644	−	0.528265i
$921$		0			0
$922$	0.844325	+	0.613438i	0.0278064	+	0.0202025i
$923$	24.5696			0.808718
$924$		0			0
$925$	−16.6452			−0.547292
$926$	15.4265	+	11.2080i	0.506948	+	0.368319i
$927$		0			0
$928$	14.7166	+	45.2931i	0.483096	+	1.48682i
$929$	−3.82694	−	5.26733i	−0.125558	−	0.172815i	0.741610	−	0.670831i	$-0.234062\pi$
$929$	−3.82694	−	5.26733i	−0.125558	−	0.172815i	−0.867168	+	0.498015i	$0.834062\pi$
$930$		0			0
$931$	−11.7708	+	3.82455i	−0.385771	+	0.125345i
$932$	−13.4727	+	41.4648i	−0.441314	+	1.35822i
$933$		0			0
$934$			4.82063i			0.157736i
$935$	−4.63753	−	8.70006i	−0.151663	−	0.284522i
$936$		0			0
$937$	4.31370	−	5.93730i	0.140923	−	0.193963i	−0.732722	−	0.680528i	$-0.761750\pi$
$937$	4.31370	−	5.93730i	0.140923	−	0.193963i	0.873644	+	0.486565i	$0.161750\pi$
$938$	−42.6529	−	13.8588i	−1.39267	−	0.452505i
$939$		0			0
$940$	31.9404	−	23.2061i	1.04178	−	0.756898i
$941$	−19.7910	+	14.3790i	−0.645167	+	0.468741i	−0.861621	−	0.507551i	$-0.830551\pi$
$941$	−19.7910	+	14.3790i	−0.645167	+	0.468741i	0.216454	+	0.976293i	$0.430551\pi$
$942$		0			0
$943$	−6.67830	−	2.16991i	−0.217476	−	0.0706621i
$944$	−18.6828	+	25.7147i	−0.608073	+	0.836941i
$945$		0			0
$946$	22.8473	−	4.05311i	0.742828	−	0.131778i
$947$			36.2379i			1.17757i	0.808288	+	0.588787i	$0.200394\pi$
$947$			36.2379i			1.17757i	−0.808288	+	0.588787i	$0.799606\pi$
$948$		0			0
$949$	−0.587789	+	1.80903i	−0.0190805	+	0.0587236i
$950$	30.1304	−	9.78996i	0.977560	−	0.317628i
$951$		0			0
$952$	−2.01038	−	2.76705i	−0.0651569	−	0.0896807i
$953$	−16.2642	−	50.0560i	−0.526848	−	1.62147i	−0.760632	−	0.649183i	$-0.775111\pi$
$953$	−16.2642	−	50.0560i	−0.526848	−	1.62147i	0.233784	−	0.972289i	$-0.424889\pi$
$954$		0			0
$955$	−26.2543	−	19.0749i	−0.849570	−	0.617248i
$956$	6.24310			0.201916
$957$		0			0
$958$	24.5836			0.794259
$959$	6.22660	+	4.52389i	0.201067	+	0.146084i
$960$		0			0
$961$	9.97638	+	30.7041i	0.321819	+	0.990456i
$962$	13.7293	+	18.8968i	0.442651	+	0.609256i
$963$		0			0
$964$	54.4880	−	17.7042i	1.75494	−	0.570214i
$965$	9.96357	−	30.6647i	0.320739	−	0.987132i
$966$		0			0
$967$		−	21.1895i		−	0.681409i	−0.940171	−	0.340704i	$-0.889335\pi$
$967$		−	21.1895i		−	0.681409i	0.940171	−	0.340704i	$-0.110665\pi$
$968$	−11.3476	−	3.22831i	−0.364724	−	0.103762i
$969$		0			0
$970$	−34.6775	+	47.7294i	−1.11343	+	1.53250i
$971$	−38.9482	−	12.6550i	−1.24991	−	0.406119i	−0.392019	−	0.919957i	$-0.628223\pi$
$971$	−38.9482	−	12.6550i	−1.24991	−	0.406119i	−0.857887	+	0.513838i	$0.828223\pi$
$972$		0			0
$973$	11.0249	−	8.01008i	0.353443	−	0.256791i
$974$	63.2741	−	45.9713i	2.02743	−	1.47302i
$975$		0			0
$976$	20.8764	+	6.78315i	0.668237	+	0.217123i
$977$	−35.9665	+	49.5036i	−1.15067	+	1.58376i	−0.409701	+	0.912220i	$0.634367\pi$
$977$	−35.9665	+	49.5036i	−1.15067	+	1.58376i	−0.740968	+	0.671540i	$0.765633\pi$
$978$		0			0
$979$	−21.0645	+	21.8584i	−0.673223	+	0.698597i
$980$		−	23.9568i		−	0.765273i
$981$		0			0
$982$	9.13758	−	28.1226i	0.291592	−	0.897428i
$983$	−54.8070	+	17.8079i	−1.74807	+	0.567983i	−0.995857	−	0.0909365i	$-0.971014\pi$
$983$	−54.8070	+	17.8079i	−1.74807	+	0.567983i	−0.752214	+	0.658919i	$0.771014\pi$
$984$		0			0
$985$	−3.13033	−	4.30853i	−0.0997405	−	0.137281i
$986$	−3.92213	−	12.0711i	−0.124906	−	0.384421i
$987$		0			0
$988$	−20.0001	−	14.5309i	−0.636288	−	0.462290i
$989$	17.3832			0.552754
$990$		0			0
$991$	−15.6063			−0.495750			−0.247875	−	0.968792i	$-0.579732\pi$
$991$	−15.6063			−0.495750			−0.247875	+	0.968792i	$0.579732\pi$
$992$	51.1542	+	37.1657i	1.62415	+	1.18001i
$993$		0			0
$994$	20.1179	+	61.9164i	0.638100	+	1.96387i
$995$	−0.935432	−	1.28751i	−0.0296552	−	0.0408169i
$996$		0			0
$997$	−10.8263	+	3.51767i	−0.342872	+	0.111406i	−0.475391	−	0.879775i	$-0.657693\pi$
$997$	−10.8263	+	3.51767i	−0.342872	+	0.111406i	0.132519	+	0.991180i	$0.457693\pi$
$998$	−8.28469	+	25.4977i	−0.262247	+	0.807115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.161.18		80
3.2	odd	2	inner	891.2.k.a.161.3		80
9.2	odd	6		297.2.t.a.260.2		80
9.4	even	3		297.2.t.a.62.2		80
9.5	odd	6		99.2.p.a.29.9	✓	80
9.7	even	3		99.2.p.a.95.9	yes	80
11.8	odd	10	inner	891.2.k.a.404.3		80
33.8	even	10	inner	891.2.k.a.404.18		80
99.41	even	30		99.2.p.a.74.9	yes	80
99.52	odd	30		99.2.p.a.41.9	yes	80
99.74	even	30		297.2.t.a.206.2		80
99.85	odd	30		297.2.t.a.8.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.9	✓	80	9.5	odd	6
99.2.p.a.41.9	yes	80	99.52	odd	30
99.2.p.a.74.9	yes	80	99.41	even	30
99.2.p.a.95.9	yes	80	9.7	even	3
297.2.t.a.8.2		80	99.85	odd	30
297.2.t.a.62.2		80	9.4	even	3
297.2.t.a.206.2		80	99.74	even	30
297.2.t.a.260.2		80	9.2	odd	6
891.2.k.a.161.3		80	3.2	odd	2	inner
891.2.k.a.161.18		80	1.1	even	1	trivial
891.2.k.a.404.3		80	11.8	odd	10	inner
891.2.k.a.404.18		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)

\(f(q)\)	\(=\)	\(q+(1.71719 + 1.24761i) q^{2} +(0.774180 + 2.38268i) q^{4} +(-1.75074 - 2.40969i) q^{5} +(3.03899 - 0.987427i) q^{7} +(-0.331430 + 1.02004i) q^{8} -6.32217i q^{10} +(-2.38818 - 2.30144i) q^{11} +(1.50453 - 2.07081i) q^{13} +(6.45046 + 2.09588i) q^{14} +(2.21191 - 1.60705i) q^{16} +(-0.807393 + 0.586606i) q^{17} +(-3.66639 - 1.19128i) q^{19} +(4.38614 - 6.03700i) q^{20} +(-1.22966 - 6.93154i) q^{22} -5.27382i q^{23} +(-1.19643 + 3.68223i) q^{25} +(5.16715 - 1.67891i) q^{26} +(4.70544 + 6.47649i) q^{28} +(1.85154 + 5.69844i) q^{29} +(6.43584 + 4.67591i) q^{31} +7.94833 q^{32} -2.11831 q^{34} +(-7.69988 - 5.59429i) q^{35} +(1.32852 + 4.08876i) q^{37} +(-4.80964 - 6.61990i) q^{38} +(3.03823 - 0.987180i) q^{40} +(0.411450 - 1.26631i) q^{41} +3.29613i q^{43} +(3.63471 - 7.47199i) q^{44} +(6.57970 - 9.05618i) q^{46} +(5.03182 + 1.63494i) q^{47} +(2.59731 - 1.88706i) q^{49} +(-6.64851 + 4.83042i) q^{50} +(6.09886 + 1.98164i) q^{52} +(2.43390 - 3.34997i) q^{53} +(-1.36467 + 9.78400i) q^{55} +3.42715i q^{56} +(-3.93001 + 12.0953i) q^{58} +(-11.0565 + 3.59249i) q^{59} +(4.71908 + 6.49525i) q^{61} +(5.21785 + 16.0589i) q^{62} +(9.22499 + 6.70235i) q^{64} -7.62407 q^{65} -6.61239 q^{67} +(-2.02276 - 1.46962i) q^{68} +(-6.24267 - 19.2130i) q^{70} +(5.64201 + 7.76556i) q^{71} +(-0.706745 + 0.229635i) q^{73} +(-2.81987 + 8.67867i) q^{74} -9.65810i q^{76} +(-9.53014 - 4.63589i) q^{77} +(6.88586 - 9.47757i) q^{79} +(-7.74499 - 2.51650i) q^{80} +(2.28641 - 1.66117i) q^{82} +(-2.18571 + 1.58801i) q^{83} +(2.82708 + 0.918574i) q^{85} +(-4.11230 + 5.66010i) q^{86} +(3.13907 - 1.67327i) q^{88} -9.15275i q^{89} +(2.52748 - 7.77878i) q^{91} +(12.5658 - 4.08289i) q^{92} +(6.60084 + 9.08528i) q^{94} +(3.54829 + 10.9205i) q^{95} +(-7.54954 - 5.48506i) q^{97} +6.81440 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 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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