LMFDB - Embedded newform 891.2.k.a.161.19

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			161.19
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.89658 + 1.37794i) q^{2} +(1.08024 + 3.32465i) q^{4} +(1.71732 + 2.36369i) q^{5} +(-1.25106 + 0.406493i) q^{7} +(-1.08356 + 3.33484i) q^{8} +6.84930i q^{10} +(0.273229 + 3.30535i) q^{11} +(3.47331 - 4.78060i) q^{13} +(-2.93285 - 0.952942i) q^{14} +(-0.994050 + 0.722219i) q^{16} +(-3.07734 + 2.23582i) q^{17} +(-2.83716 - 0.921851i) q^{19} +(-6.00331 + 8.26284i) q^{20} +(-4.03639 + 6.64535i) q^{22} -0.0847109i q^{23} +(-1.09275 + 3.36315i) q^{25} +(13.1748 - 4.28075i) q^{26} +(-2.70289 - 3.72021i) q^{28} +(-1.36073 - 4.18789i) q^{29} +(2.08597 + 1.51555i) q^{31} +4.13245 q^{32} -8.91726 q^{34} +(-3.10929 - 2.25903i) q^{35} +(-2.11787 - 6.51815i) q^{37} +(-4.11064 - 5.65782i) q^{38} +(-9.74334 + 3.16580i) q^{40} +(-1.39682 + 4.29896i) q^{41} +3.38516i q^{43} +(-10.6940 + 4.47897i) q^{44} +(0.116727 - 0.160661i) q^{46} +(4.51901 + 1.46832i) q^{47} +(-4.26321 + 3.09740i) q^{49} +(-6.70672 + 4.87272i) q^{50} +(19.6458 + 6.38331i) q^{52} +(2.46224 - 3.38898i) q^{53} +(-7.34360 + 6.32218i) q^{55} -4.61254i q^{56} +(3.18995 - 9.81766i) q^{58} +(13.3498 - 4.33762i) q^{59} +(-5.77176 - 7.94414i) q^{61} +(1.86787 + 5.74871i) q^{62} +(9.82561 + 7.13872i) q^{64} +17.2646 q^{65} -3.78414 q^{67} +(-10.7576 - 7.81585i) q^{68} +(-2.78419 - 8.56886i) q^{70} +(2.61027 + 3.59273i) q^{71} +(8.30569 - 2.69868i) q^{73} +(4.96493 - 15.2805i) q^{74} -10.4284i q^{76} +(-1.68543 - 4.02412i) q^{77} +(-3.26965 + 4.50028i) q^{79} +(-3.41421 - 1.10934i) q^{80} +(-8.57291 + 6.22858i) q^{82} +(-1.02090 + 0.741727i) q^{83} +(-10.5696 - 3.43426i) q^{85} +(-4.66456 + 6.42021i) q^{86} +(-11.3189 - 2.67036i) q^{88} -13.6071i q^{89} +(-2.40203 + 7.39268i) q^{91} +(0.281634 - 0.0915083i) q^{92} +(6.54740 + 9.01173i) q^{94} +(-2.69335 - 8.28929i) q^{95} +(11.1424 + 8.09543i) q^{97} -12.3536 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.89658	+	1.37794i	1.34108	+	0.974354i	0.999403	+	0.0345375i	$0.0109958\pi$
$2$	1.89658	+	1.37794i	1.34108	+	0.974354i	0.341680	+	0.939816i	$0.389004\pi$
$3$		0			0
$3$		0			0
$4$	1.08024	+	3.32465i	0.540121	+	1.66232i
$5$	1.71732	+	2.36369i	0.768009	+	1.05707i	0.996505	+	0.0835293i	$0.0266192\pi$
$5$	1.71732	+	2.36369i	0.768009	+	1.05707i	−0.228496	+	0.973545i	$0.573381\pi$
$6$		0			0
$7$	−1.25106	+	0.406493i	−0.472855	+	0.153640i	−0.535744	−	0.844381i	$-0.679969\pi$
$7$	−1.25106	+	0.406493i	−0.472855	+	0.153640i	0.0628885	+	0.998021i	$0.479969\pi$
$8$	−1.08356	+	3.33484i	−0.383095	+	1.17904i
$9$		0			0
$10$			6.84930i			2.16594i
$11$	0.273229	+	3.30535i	0.0823816	+	0.996601i
$11$	0.273229	+	3.30535i	0.0823816	+	0.996601i
$12$		0			0
$13$	3.47331	−	4.78060i	0.963323	−	1.32590i	0.0179743	−	0.999838i	$-0.494278\pi$
$13$	3.47331	−	4.78060i	0.963323	−	1.32590i	0.945348	−	0.326062i	$-0.105722\pi$
$14$	−2.93285	−	0.952942i	−0.783838	−	0.254684i
$15$		0			0
$16$	−0.994050	+	0.722219i	−0.248512	+	0.180555i
$17$	−3.07734	+	2.23582i	−0.746365	+	0.542266i	−0.894698	−	0.446671i	$-0.852609\pi$
$17$	−3.07734	+	2.23582i	−0.746365	+	0.542266i	0.148333	+	0.988938i	$0.452609\pi$
$18$		0			0
$19$	−2.83716	−	0.921851i	−0.650890	−	0.211487i	−0.0350836	−	0.999384i	$-0.511170\pi$
$19$	−2.83716	−	0.921851i	−0.650890	−	0.211487i	−0.615807	+	0.787897i	$0.711170\pi$
$20$	−6.00331	+	8.26284i	−1.34238	+	1.84763i
$21$		0			0
$22$	−4.03639	+	6.64535i	−0.860561	+	1.41679i
$23$		−	0.0847109i		−	0.0176634i	−0.999961	−	0.00883172i	$-0.997189\pi$
$23$		−	0.0847109i		−	0.0176634i	0.999961	−	0.00883172i	$-0.00281126\pi$
$24$		0			0
$25$	−1.09275	+	3.36315i	−0.218550	+	0.672629i
$26$	13.1748	−	4.28075i	2.58379	−	0.839525i
$27$		0			0
$28$	−2.70289	−	3.72021i	−0.510799	−	0.703054i
$29$	−1.36073	−	4.18789i	−0.252681	−	0.777671i	−0.994278	−	0.106826i	$-0.965931\pi$
$29$	−1.36073	−	4.18789i	−0.252681	−	0.777671i	0.741597	−	0.670846i	$-0.234069\pi$
$30$		0			0
$31$	2.08597	+	1.51555i	0.374652	+	0.272200i	0.759137	−	0.650931i	$-0.225621\pi$
$31$	2.08597	+	1.51555i	0.374652	+	0.272200i	−0.384486	+	0.923131i	$0.625621\pi$
$32$	4.13245			0.730521
$33$		0			0
$34$	−8.91726			−1.52930
$35$	−3.10929	−	2.25903i	−0.525566	−	0.381846i
$36$		0			0
$37$	−2.11787	−	6.51815i	−0.348176	−	1.07158i	−0.959861	−	0.280475i	$-0.909508\pi$
$37$	−2.11787	−	6.51815i	−0.348176	−	1.07158i	0.611685	−	0.791102i	$-0.290492\pi$
$38$	−4.11064	−	5.65782i	−0.666835	−	0.917819i
$39$		0			0
$40$	−9.74334	+	3.16580i	−1.54056	+	0.500558i
$41$	−1.39682	+	4.29896i	−0.218146	+	0.671385i	0.780769	+	0.624820i	$0.214828\pi$
$41$	−1.39682	+	4.29896i	−0.218146	+	0.671385i	−0.998915	+	0.0465655i	$0.985172\pi$
$42$		0			0
$43$			3.38516i			0.516231i	0.966114	+	0.258116i	$0.0831016\pi$
$43$			3.38516i			0.516231i	−0.966114	+	0.258116i	$0.916898\pi$
$44$	−10.6940	+	4.47897i	−1.61218	+	0.675230i
$45$		0			0
$46$	0.116727	−	0.160661i	0.0172104	−	0.0236881i
$47$	4.51901	+	1.46832i	0.659166	+	0.214176i	0.619451	−	0.785035i	$-0.287355\pi$
$47$	4.51901	+	1.46832i	0.659166	+	0.214176i	0.0397146	+	0.999211i	$0.487355\pi$
$48$		0			0
$49$	−4.26321	+	3.09740i	−0.609030	+	0.442486i
$50$	−6.70672	+	4.87272i	−0.948473	+	0.689106i
$51$		0			0
$52$	19.6458	+	6.38331i	2.72439	+	0.885206i
$53$	2.46224	−	3.38898i	0.338215	−	0.465512i	−0.605704	−	0.795690i	$-0.707109\pi$
$53$	2.46224	−	3.38898i	0.338215	−	0.465512i	0.943919	+	0.330177i	$0.107109\pi$
$54$		0			0
$55$	−7.34360	+	6.32218i	−0.990211	+	0.852482i
$56$		−	4.61254i		−	0.616376i
$57$		0			0
$58$	3.18995	−	9.81766i	0.418861	−	1.28912i
$59$	13.3498	−	4.33762i	1.73800	−	0.564711i	0.743434	−	0.668810i	$-0.233196\pi$
$59$	13.3498	−	4.33762i	1.73800	−	0.564711i	0.994567	+	0.104099i	$0.0331959\pi$
$60$		0			0
$61$	−5.77176	−	7.94414i	−0.738998	−	1.01714i	−0.998676	−	0.0514476i	$-0.983616\pi$
$61$	−5.77176	−	7.94414i	−0.738998	−	1.01714i	0.259678	−	0.965695i	$-0.416384\pi$
$62$	1.86787	+	5.74871i	0.237219	+	0.730086i
$63$		0			0
$64$	9.82561	+	7.13872i	1.22820	+	0.892340i
$65$	17.2646			2.14142
$66$		0			0
$67$	−3.78414			−0.462306			−0.231153	−	0.972917i	$-0.574250\pi$
$67$	−3.78414			−0.462306			−0.231153	+	0.972917i	$0.574250\pi$
$68$	−10.7576	−	7.81585i	−1.30455	−	0.947810i
$69$		0			0
$70$	−2.78419	−	8.56886i	−0.332775	−	1.02417i
$71$	2.61027	+	3.59273i	0.309782	+	0.426379i	0.935313	−	0.353821i	$-0.115118\pi$
$71$	2.61027	+	3.59273i	0.309782	+	0.426379i	−0.625531	+	0.780199i	$0.715118\pi$
$72$		0			0
$73$	8.30569	−	2.69868i	0.972108	−	0.315857i	0.220441	−	0.975400i	$-0.429250\pi$
$73$	8.30569	−	2.69868i	0.972108	−	0.315857i	0.751667	+	0.659543i	$0.229250\pi$
$74$	4.96493	−	15.2805i	0.577162	−	1.77632i
$75$		0			0
$76$		−	10.4284i		−	1.19622i
$77$	−1.68543	−	4.02412i	−0.192072	−	0.458591i
$78$		0			0
$79$	−3.26965	+	4.50028i	−0.367864	+	0.506321i	−0.952319	−	0.305105i	$-0.901308\pi$
$79$	−3.26965	+	4.50028i	−0.367864	+	0.506321i	0.584455	+	0.811426i	$0.301308\pi$
$80$	−3.41421	−	1.10934i	−0.381720	−	0.124028i
$81$		0			0
$82$	−8.57291	+	6.22858i	−0.946719	+	0.687832i
$83$	−1.02090	+	0.741727i	−0.112058	+	0.0814152i	−0.642403	−	0.766367i	$-0.722062\pi$
$83$	−1.02090	+	0.741727i	−0.112058	+	0.0814152i	0.530345	+	0.847782i	$0.322062\pi$
$84$		0			0
$85$	−10.5696	−	3.43426i	−1.14643	−	0.372498i
$86$	−4.66456	+	6.42021i	−0.502992	+	0.692309i
$87$		0			0
$88$	−11.3189	−	2.67036i	−1.20660	−	0.284661i
$89$		−	13.6071i		−	1.44234i	−0.692756	−	0.721172i	$-0.743604\pi$
$89$		−	13.6071i		−	1.44234i	0.692756	−	0.721172i	$-0.256396\pi$
$90$		0			0
$91$	−2.40203	+	7.39268i	−0.251801	+	0.774964i
$92$	0.281634	−	0.0915083i	0.0293623	−	0.00954040i
$93$		0			0
$94$	6.54740	+	9.01173i	0.675313	+	0.929489i
$95$	−2.69335	−	8.28929i	−0.276332	−	0.850463i
$96$		0			0
$97$	11.1424	+	8.09543i	1.13134	+	0.821967i	0.985889	−	0.167399i	$-0.0535367\pi$
$97$	11.1424	+	8.09543i	1.13134	+	0.821967i	0.145451	+	0.989365i	$0.453537\pi$
$98$	−12.3536			−1.24790
$99$		0			0
$100$	−12.3617			−1.23617
$101$	−10.1146	−	7.34872i	−1.00644	−	0.731225i	−0.0429843	−	0.999076i	$-0.513687\pi$
$101$	−10.1146	−	7.34872i	−1.00644	−	0.731225i	−0.963460	+	0.267851i	$0.913687\pi$
$102$		0			0
$103$	1.84979	+	5.69306i	0.182265	+	0.560954i	0.999891	−	0.0147963i	$-0.00470998\pi$
$103$	1.84979	+	5.69306i	0.182265	+	0.560954i	−0.817625	+	0.575750i	$0.804710\pi$
$104$	12.1790	+	16.7630i	1.19425	+	1.64375i
$105$		0			0
$106$	9.33966	−	3.03464i	0.907148	−	0.294750i
$107$	−0.951472	+	2.92833i	−0.0919823	+	0.283092i	−0.986455	−	0.164029i	$-0.947551\pi$
$107$	−0.951472	+	2.92833i	−0.0919823	+	0.283092i	0.894473	+	0.447122i	$0.147551\pi$
$108$		0			0
$109$		−	9.98777i		−	0.956655i	−0.878181	−	0.478328i	$-0.841243\pi$
$109$		−	9.98777i		−	0.956655i	0.878181	−	0.478328i	$-0.158757\pi$
$110$	−22.6393	+	1.87143i	−2.15857	+	0.178433i
$111$		0			0
$112$	0.950036	−	1.30761i	0.0897700	−	0.123558i
$113$	4.48352	+	1.45678i	0.421774	+	0.137043i	0.512211	−	0.858860i	$-0.328827\pi$
$113$	4.48352	+	1.45678i	0.421774	+	0.137043i	−0.0904375	+	0.995902i	$0.528827\pi$
$114$		0			0
$115$	0.200230	−	0.145476i	0.0186716	−	0.0135657i
$116$	12.4533	−	9.04787i	1.15626	−	0.840074i
$117$		0			0
$118$	31.2960	+	10.1687i	2.88103	+	0.936104i
$119$	2.94109	−	4.04806i	0.269609	−	0.371085i
$120$		0			0
$121$	−10.8507	+	1.80623i	−0.986427	+	0.164203i
$122$		−	23.0198i		−	2.08412i
$123$		0			0
$124$	−2.78530	+	8.57227i	−0.250127	+	0.769813i
$125$	4.06738	−	1.32157i	0.363797	−	0.118205i
$126$		0			0
$127$	−1.75209	−	2.41154i	−0.155473	−	0.213990i	0.724174	−	0.689617i	$-0.242221\pi$
$127$	−1.75209	−	2.41154i	−0.155473	−	0.213990i	−0.879647	+	0.475627i	$0.842221\pi$
$128$	6.24428	+	19.2179i	0.551921	+	1.69864i
$129$		0			0
$130$	32.7437	+	23.7897i	2.87182	+	2.08650i
$131$	7.78501			0.680180			0.340090	−	0.940393i	$-0.389542\pi$
$131$	7.78501			0.680180			0.340090	+	0.940393i	$0.389542\pi$
$132$		0			0
$133$	3.92418			0.340270
$134$	−7.17692	−	5.21434i	−0.619991	−	0.450450i
$135$		0			0
$136$	−4.12163	−	12.6851i	−0.353427	−	1.08774i
$137$	−3.69241	−	5.08217i	−0.315464	−	0.434199i	0.621612	−	0.783326i	$-0.286478\pi$
$137$	−3.69241	−	5.08217i	−0.315464	−	0.434199i	−0.937076	+	0.349127i	$0.886478\pi$
$138$		0			0
$139$	0.498861	−	0.162090i	0.0423128	−	0.0137483i	−0.287784	−	0.957695i	$-0.592919\pi$
$139$	0.498861	−	0.162090i	0.0423128	−	0.0137483i	0.330097	+	0.943947i	$0.392919\pi$
$140$	4.15169	−	12.7776i	0.350882	−	1.07990i
$141$		0			0
$142$			10.4107i			0.873646i
$143$	16.7506	+	10.1743i	1.40075	+	0.850819i
$144$		0			0
$145$	7.56206	−	10.4083i	0.627995	−	0.864361i
$146$	19.4710	+	6.32652i	1.61143	+	0.523587i
$147$		0			0
$148$	19.3827	−	14.0824i	1.59325	−	1.15756i
$149$	−7.77987	+	5.65240i	−0.637352	+	0.463063i	−0.858939	−	0.512077i	$-0.828876\pi$
$149$	−7.77987	+	5.65240i	−0.637352	+	0.463063i	0.221588	+	0.975140i	$0.428876\pi$
$150$		0			0
$151$	−9.51615	−	3.09198i	−0.774413	−	0.251622i	−0.104960	−	0.994476i	$-0.533471\pi$
$151$	−9.51615	−	3.09198i	−0.774413	−	0.251622i	−0.669453	+	0.742854i	$0.733471\pi$
$152$	6.14845	−	8.46262i	0.498705	−	0.686409i
$153$		0			0
$154$	2.34847	−	9.95448i	0.189245	−	0.802155i
$155$			7.53327i			0.605087i
$156$		0			0
$157$	1.01408	−	3.12100i	0.0809320	−	0.249083i	−0.902401	−	0.430898i	$-0.858197\pi$
$157$	1.01408	−	3.12100i	0.0809320	−	0.249083i	0.983333	+	0.181814i	$0.0581970\pi$
$158$	−12.4023	+	4.02975i	−0.986673	+	0.320589i
$159$		0			0
$160$	7.09674	+	9.76783i	0.561047	+	0.772214i
$161$	0.0344344	+	0.105978i	0.00271381	+	0.00835225i
$162$		0			0
$163$	−7.00394	−	5.08866i	−0.548591	−	0.398575i	0.278675	−	0.960386i	$-0.410105\pi$
$163$	−7.00394	−	5.08866i	−0.548591	−	0.398575i	−0.827266	+	0.561811i	$0.810105\pi$
$164$	−15.8014			−1.23388
$165$		0			0
$166$	−2.95828			−0.229607
$167$	−16.0518	−	11.6623i	−1.24212	−	0.902457i	−0.244387	−	0.969678i	$-0.578587\pi$
$167$	−16.0518	−	11.6623i	−1.24212	−	0.902457i	−0.997738	+	0.0672213i	$0.978587\pi$
$168$		0			0
$169$	−6.77304	−	20.8453i	−0.521003	−	1.60348i
$170$	−15.3138	−	21.0776i	−1.17451	−	1.61658i
$171$		0			0
$172$	−11.2544	+	3.65679i	−0.858143	+	0.278828i
$173$	−2.15797	+	6.64155i	−0.164068	+	0.504948i	−0.998966	−	0.0454555i	$-0.985526\pi$
$173$	−2.15797	+	6.64155i	−0.164068	+	0.504948i	0.834899	+	0.550403i	$0.185526\pi$
$174$		0			0
$175$		−	4.65169i		−	0.351634i
$176$	−2.65879	−	3.08835i	−0.200414	−	0.232793i
$177$		0			0
$178$	18.7498	−	25.8068i	1.40535	−	1.93430i
$179$	14.8154	+	4.81380i	1.10735	+	0.359800i	0.804928	−	0.593373i	$-0.202204\pi$
$179$	14.8154	+	4.81380i	1.10735	+	0.359800i	0.302424	+	0.953173i	$0.402204\pi$
$180$		0			0
$181$	−13.0927	+	9.51241i	−0.973173	+	0.707052i	−0.956173	−	0.292804i	$-0.905412\pi$
$181$	−13.0927	+	9.51241i	−0.973173	+	0.707052i	−0.0170005	+	0.999855i	$0.505412\pi$
$182$	−14.7423	+	10.7109i	−1.09278	+	0.793948i
$183$		0			0
$184$	0.282497	+	0.0917890i	0.0208260	+	0.00676677i
$185$	11.7698	−	16.1998i	0.865334	−	1.19103i
$186$		0			0
$187$	−8.23099	−	9.56081i	−0.601910	−	0.699156i
$188$			16.6103i			1.21143i
$189$		0			0
$190$	6.31403	−	19.4326i	0.458068	−	1.40979i
$191$	13.9998	−	4.54881i	1.01299	−	0.329140i	0.244945	−	0.969537i	$-0.421230\pi$
$191$	13.9998	−	4.54881i	1.01299	−	0.329140i	0.768044	+	0.640397i	$0.221230\pi$
$192$		0			0
$193$	4.02742	+	5.54327i	0.289900	+	0.399013i	0.928982	−	0.370126i	$-0.120685\pi$
$193$	4.02742	+	5.54327i	0.289900	+	0.399013i	−0.639082	+	0.769139i	$0.720685\pi$
$194$	9.97739	+	30.7072i	0.716335	+	2.20465i
$195$		0			0
$196$	−14.9031	−	10.8277i	−1.06451	−	0.773408i
$197$	−8.81639			−0.628141			−0.314071	−	0.949400i	$-0.601693\pi$
$197$	−8.81639			−0.628141			−0.314071	+	0.949400i	$0.601693\pi$
$198$		0			0
$199$	8.40540			0.595843			0.297921	−	0.954590i	$-0.403707\pi$
$199$	8.40540			0.595843			0.297921	+	0.954590i	$0.403707\pi$
$200$	−10.0315	−	7.28831i	−0.709334	−	0.515361i
$201$		0			0
$202$	−9.05708	−	27.8748i	−0.637254	−	1.96127i
$203$	3.40470	+	4.68616i	0.238963	+	0.328904i
$204$		0			0
$205$	−12.5602	+	4.08106i	−0.877243	+	0.285033i
$206$	−4.33646	+	13.3462i	−0.302135	+	0.929877i
$207$		0			0
$208$			7.26065i			0.503435i
$209$	2.27184	−	9.62970i	0.157147	−	0.666100i
$210$		0			0
$211$	10.2391	−	14.0929i	0.704886	−	0.970192i	−0.295006	−	0.955495i	$-0.595322\pi$
$211$	10.2391	−	14.0929i	0.704886	−	0.970192i	0.999892	−	0.0146969i	$-0.00467832\pi$
$212$	13.9270	+	4.52515i	0.956509	+	0.310788i
$213$		0			0
$214$	−5.83962	+	4.24273i	−0.399188	+	0.290027i
$215$	−8.00146	+	5.81340i	−0.545695	+	0.396471i
$216$		0			0
$217$	−3.22573	−	1.04810i	−0.218977	−	0.0711499i
$218$	13.7626	−	18.9426i	0.932121	−	1.28295i
$219$		0			0
$220$	−28.9519	−	17.5854i	−1.95193	−	1.18561i
$221$			22.4772i			1.51198i
$222$		0			0
$223$	5.29613	−	16.2998i	0.354655	−	1.09152i	−0.601554	−	0.798832i	$-0.705452\pi$
$223$	5.29613	−	16.2998i	0.354655	−	1.09152i	0.956209	−	0.292684i	$-0.0945485\pi$
$224$	−5.16993	+	1.67981i	−0.345431	+	0.112237i
$225$		0			0
$226$	6.49597	+	8.94094i	0.432106	+	0.594742i
$227$	5.34358	+	16.4458i	0.354666	+	1.09155i	0.956203	+	0.292704i	$0.0945551\pi$
$227$	5.34358	+	16.4458i	0.354666	+	1.09155i	−0.601537	+	0.798845i	$0.705445\pi$
$228$		0			0
$229$	−12.7856	−	9.28930i	−0.844898	−	0.613854i	0.0788364	−	0.996888i	$-0.474880\pi$
$229$	−12.7856	−	9.28930i	−0.844898	−	0.613854i	−0.923735	+	0.383033i	$0.874880\pi$
$230$	0.580210			0.0382579
$231$		0			0
$232$	15.4404			1.01371
$233$	2.75423	+	2.00107i	0.180436	+	0.131094i	0.674337	−	0.738424i	$-0.264430\pi$
$233$	2.75423	+	2.00107i	0.180436	+	0.131094i	−0.493901	+	0.869518i	$0.664430\pi$
$234$		0			0
$235$	4.28995	+	13.2031i	0.279846	+	0.861276i
$236$	28.8421	+	39.6978i	1.87746	+	2.58411i
$237$		0			0
$238$	11.1560	−	3.62481i	0.723136	−	0.234961i
$239$	−1.79419	+	5.52193i	−0.116056	+	0.357184i	−0.992166	−	0.124928i	$-0.960130\pi$
$239$	−1.79419	+	5.52193i	−0.116056	+	0.357184i	0.876110	+	0.482112i	$0.160130\pi$
$240$		0			0
$241$			3.01020i			0.193904i	0.995289	+	0.0969521i	$0.0309094\pi$
$241$			3.01020i			0.193904i	−0.995289	+	0.0969521i	$0.969091\pi$
$242$	−23.0681	−	11.5260i	−1.48287	−	0.740918i
$243$		0			0
$244$	20.1765	−	27.7706i	1.29167	−	1.77783i
$245$	−14.6426	−	4.75767i	−0.935482	−	0.303956i
$246$		0			0
$247$	−14.2614	+	10.3615i	−0.907428	+	0.659285i
$248$	−7.31437	+	5.31420i	−0.464463	+	0.337452i
$249$		0			0
$250$	9.53515	+	3.09816i	0.603056	+	0.195945i
$251$	−9.41803	+	12.9628i	−0.594461	+	0.818205i	−0.995187	−	0.0979925i	$-0.968758\pi$
$251$	−9.41803	+	12.9628i	−0.594461	+	0.818205i	0.400726	+	0.916198i	$0.368758\pi$
$252$		0			0
$253$	0.279999	−	0.0231455i	0.0176034	−	0.00145514i
$254$		−	6.98796i		−	0.438464i
$255$		0			0
$256$	−7.13235	+	21.9511i	−0.445772	+	1.37195i
$257$	−11.8335	+	3.84495i	−0.738156	+	0.239842i	−0.653877	−	0.756601i	$-0.726859\pi$
$257$	−11.8335	+	3.84495i	−0.738156	+	0.239842i	−0.0842791	+	0.996442i	$0.526859\pi$
$258$		0			0
$259$	5.29917	+	7.29368i	0.329274	+	0.453207i
$260$	18.6500	+	57.3988i	1.15662	+	3.55972i
$261$		0			0
$262$	14.7649	+	10.7273i	0.912178	+	0.662736i
$263$	−15.2873			−0.942655			−0.471328	−	0.881958i	$-0.656225\pi$
$263$	−15.2873			−0.942655			−0.471328	+	0.881958i	$0.656225\pi$
$264$		0			0
$265$	12.2390			0.751833
$266$	7.44252	+	5.40731i	0.456330	+	0.331543i
$267$		0			0
$268$	−4.08779	−	12.5809i	−0.249702	−	0.768502i
$269$	−1.18129	−	1.62591i	−0.0720247	−	0.0991335i	0.771485	−	0.636248i	$-0.219514\pi$
$269$	−1.18129	−	1.62591i	−0.0720247	−	0.0991335i	−0.843509	+	0.537114i	$0.819514\pi$
$270$		0			0
$271$	−20.2438	+	6.57759i	−1.22972	+	0.399560i	−0.850613	−	0.525792i	$-0.823769\pi$
$271$	−20.2438	+	6.57759i	−1.22972	+	0.399560i	−0.379107	+	0.925353i	$0.623769\pi$
$272$	1.44428	−	4.44503i	0.0875723	−	0.269520i
$273$		0			0
$274$		−	14.7267i		−	0.889670i
$275$	−11.4150	−	2.69302i	−0.688347	−	0.162395i
$276$		0			0
$277$	14.5106	−	19.9722i	0.871860	−	1.20001i	−0.106749	−	0.994286i	$-0.534044\pi$
$277$	14.5106	−	19.9722i	0.871860	−	1.20001i	0.978609	−	0.205727i	$-0.0659559\pi$
$278$	1.16948	+	0.379987i	0.0701407	+	0.0227901i
$279$		0			0
$280$	10.9026	−	7.92121i	0.651555	−	0.473383i
$281$	−10.5368	+	7.65541i	−0.628571	+	0.456683i	−0.855905	−	0.517133i	$-0.826999\pi$
$281$	−10.5368	+	7.65541i	−0.628571	+	0.456683i	0.227334	+	0.973817i	$0.426999\pi$
$282$		0			0
$283$	18.8011	+	6.10884i	1.11761	+	0.363133i	0.808854	−	0.588009i	$-0.200088\pi$
$283$	18.8011	+	6.10884i	1.11761	+	0.363133i	0.308754	+	0.951142i	$0.400088\pi$
$284$	−9.12482	+	12.5592i	−0.541459	+	0.745254i
$285$		0			0
$286$	17.7491	+	42.3777i	1.04953	+	2.50585i
$287$		−	5.94605i		−	0.350984i
$288$		0			0
$289$	−0.782142	+	2.40719i	−0.0460084	+	0.141599i
$290$	28.6841	−	9.32002i	1.68439	−	0.547291i
$291$		0			0
$292$	17.9443	+	24.6983i	1.05011	+	1.44536i
$293$	1.36972	+	4.21558i	0.0800202	+	0.246277i	0.983061	−	0.183278i	$-0.0586707\pi$
$293$	1.36972	+	4.21558i	0.0800202	+	0.246277i	−0.903041	+	0.429554i	$0.858671\pi$
$294$		0			0
$295$	33.1788	+	24.1058i	1.93174	+	1.40349i
$296$	24.0318			1.39682
$297$		0			0
$298$	−22.5438			−1.30593
$299$	−0.404969	−	0.294227i	−0.0234200	−	0.0170156i
$300$		0			0
$301$	−1.37604	−	4.23502i	−0.0793138	−	0.244103i
$302$	−13.7875	−	18.9769i	−0.793383	−	1.09200i
$303$		0			0
$304$	3.48606	−	1.13269i	0.199939	−	0.0649642i
$305$	8.86552	−	27.2853i	0.507638	−	1.56235i
$306$		0			0
$307$			11.0942i			0.633182i	0.948562	+	0.316591i	$0.102538\pi$
$307$			11.0942i			0.633182i	−0.948562	+	0.316591i	$0.897462\pi$
$308$	11.5581	−	9.95048i	0.658584	−	0.566981i
$309$		0			0
$310$	−10.3804	+	14.2874i	−0.589569	+	0.811472i
$311$	7.46221	+	2.42462i	0.423143	+	0.137487i	0.512845	−	0.858481i	$-0.328592\pi$
$311$	7.46221	+	2.42462i	0.423143	+	0.137487i	−0.0897022	+	0.995969i	$0.528592\pi$
$312$		0			0
$313$	−26.1681	+	19.0122i	−1.47911	+	1.07463i	−0.501265	+	0.865294i	$0.667132\pi$
$313$	−26.1681	+	19.0122i	−1.47911	+	1.07463i	−0.977843	+	0.209340i	$0.932868\pi$
$314$	6.22384	−	4.52188i	0.351232	−	0.255185i
$315$		0			0
$316$	−18.4939	−	6.00902i	−1.04036	−	0.338034i
$317$	−7.07124	+	9.73273i	−0.397161	+	0.546645i	−0.960029	−	0.279902i	$-0.909698\pi$
$317$	−7.07124	+	9.73273i	−0.397161	+	0.546645i	0.562868	+	0.826547i	$0.309698\pi$
$318$		0			0
$319$	13.4707	−	5.64193i	0.754212	−	0.315888i
$320$			35.4842i			1.98363i
$321$		0			0
$322$	−0.0807245	+	0.248445i	−0.00449860	+	0.0138453i
$323$	10.7920	−	3.50654i	0.600484	−	0.195109i
$324$		0			0
$325$	12.2824	+	16.9053i	0.681305	+	0.937735i
$326$	−6.27163	−	19.3021i	−0.347354	−	1.06904i
$327$		0			0
$328$	−12.8228	−	9.31633i	−0.708023	−	0.514409i
$329$	−6.25041			−0.344596
$330$		0			0
$331$	−30.0746			−1.65305			−0.826524	−	0.562901i	$-0.809685\pi$
$331$	−30.0746			−1.65305			−0.826524	+	0.562901i	$0.809685\pi$
$332$	−3.56880	−	2.59289i	−0.195863	−	0.142303i
$333$		0			0
$334$	−14.3735	−	44.2370i	−0.786481	−	2.42054i
$335$	−6.49858	−	8.94453i	−0.355056	−	0.488692i
$336$		0			0
$337$	−20.9200	+	6.79732i	−1.13958	+	0.370273i	−0.817211	−	0.576339i	$-0.804481\pi$
$337$	−20.9200	+	6.79732i	−1.13958	+	0.370273i	−0.322374	+	0.946612i	$0.604481\pi$
$338$	15.8780	−	48.8676i	0.863651	−	2.65805i
$339$		0			0
$340$		−	38.8499i		−	2.10693i
$341$	−4.43947	+	7.30896i	−0.240411	+	0.395802i
$342$		0			0
$343$	9.48682	−	13.0575i	0.512240	−	0.705038i
$344$	−11.2890	−	3.66800i	−0.608660	−	0.197766i
$345$		0			0
$346$	−13.2445	+	9.62266i	−0.712026	+	0.517317i
$347$	−12.2670	+	8.91252i	−0.658529	+	0.478449i	−0.866166	−	0.499757i	$-0.833423\pi$
$347$	−12.2670	+	8.91252i	−0.658529	+	0.478449i	0.207637	+	0.978206i	$0.433423\pi$
$348$		0			0
$349$	−17.8759	−	5.80824i	−0.956876	−	0.310908i	−0.211370	−	0.977406i	$-0.567792\pi$
$349$	−17.8759	−	5.80824i	−0.956876	−	0.310908i	−0.745507	+	0.666498i	$0.767792\pi$
$350$	6.40977	−	8.82229i	0.342616	−	0.471571i
$351$		0			0
$352$	1.12910	+	13.6592i	0.0601815	+	0.728037i
$353$			8.84248i			0.470638i	0.971918	+	0.235319i	$0.0756134\pi$
$353$			8.84248i			0.470638i	−0.971918	+	0.235319i	$0.924387\pi$
$354$		0			0
$355$	−4.00942	+	12.3397i	−0.212798	+	0.654925i
$356$	45.2386	−	14.6989i	2.39764	−	0.779041i
$357$		0			0
$358$	21.4653	+	29.5445i	1.13448	+	1.56147i
$359$	−5.57195	−	17.1487i	−0.294076	−	0.905074i	−0.983530	−	0.180744i	$-0.942149\pi$
$359$	−5.57195	−	17.1487i	−0.294076	−	0.905074i	0.689454	−	0.724330i	$-0.257851\pi$
$360$		0			0
$361$	−8.17163	−	5.93703i	−0.430086	−	0.312476i
$362$	−37.9389			−1.99402
$363$		0			0
$364$	−27.1728			−1.42424
$365$	20.6424	+	14.9976i	1.08047	+	0.785009i
$366$		0			0
$367$	9.67789	+	29.7855i	0.505182	+	1.55479i	0.800465	+	0.599379i	$0.204586\pi$
$367$	9.67789	+	29.7855i	0.505182	+	1.55479i	−0.295284	+	0.955410i	$0.595414\pi$
$368$	0.0611798	+	0.0842068i	0.00318922	+	0.00438958i
$369$		0			0
$370$	44.6447	−	14.5059i	2.32097	−	0.754128i
$371$	−1.70280	+	5.24069i	−0.0884052	+	0.272083i
$372$		0			0
$373$		−	3.36802i		−	0.174390i	−0.996191	−	0.0871948i	$-0.972210\pi$
$373$		−	3.36802i		−	0.174390i	0.996191	−	0.0871948i	$-0.0277903\pi$
$374$	−2.43645	−	29.4747i	−0.125986	−	1.52410i
$375$		0			0
$376$	−9.79321	+	13.4792i	−0.505046	+	0.695136i
$377$	−24.7469	−	8.04074i	−1.27453	−	0.414119i
$378$		0			0
$379$	−19.5313	+	14.1903i	−1.00326	+	0.728908i	−0.962784	−	0.270273i	$-0.912886\pi$
$379$	−19.5313	+	14.1903i	−1.00326	+	0.728908i	−0.0404716	+	0.999181i	$0.512886\pi$
$380$	24.6495	−	17.9089i	1.26449	−	0.918707i
$381$		0			0
$382$	32.8197	+	10.6638i	1.67920	+	0.545605i
$383$	−5.31898	+	7.32094i	−0.271787	+	0.374083i	−0.922992	−	0.384819i	$-0.874264\pi$
$383$	−5.31898	+	7.32094i	−0.271787	+	0.374083i	0.651205	+	0.758902i	$0.274264\pi$
$384$		0			0
$385$	6.61735	−	10.8945i	0.337251	−	0.555237i
$386$			16.0628i			0.817575i
$387$		0			0
$388$	−14.8779	+	45.7896i	−0.755313	+	2.32461i
$389$	−24.8106	+	8.06147i	−1.25795	+	0.408733i	−0.860763	−	0.509005i	$-0.830013\pi$
$389$	−24.8106	+	8.06147i	−1.25795	+	0.408733i	−0.397186	+	0.917738i	$0.630013\pi$
$390$		0			0
$391$	0.189398	+	0.260684i	0.00957829	+	0.0131834i
$392$	−5.70992	−	17.5733i	−0.288395	−	0.887588i
$393$		0			0
$394$	−16.7210	−	12.1485i	−0.842390	−	0.612032i
$395$	−16.2523			−0.817742
$396$		0			0
$397$	19.8829			0.997896			0.498948	−	0.866632i	$-0.333720\pi$
$397$	19.8829			0.997896			0.498948	+	0.866632i	$0.333720\pi$
$398$	15.9415	+	11.5822i	0.799075	+	0.580562i
$399$		0			0
$400$	−1.34268	−	4.13234i	−0.0671340	−	0.206617i
$401$	−5.84032	−	8.03852i	−0.291652	−	0.401424i	0.637898	−	0.770121i	$-0.279804\pi$
$401$	−5.84032	−	8.03852i	−0.291652	−	0.401424i	−0.929550	+	0.368697i	$0.879804\pi$
$402$		0			0
$403$	14.4904	−	4.70823i	0.721821	−	0.234534i
$404$	13.5056	−	41.5660i	0.671929	−	2.06799i
$405$		0			0
$406$			13.5792i			0.673922i
$407$	20.9661	−	8.78127i	1.03925	−	0.435271i
$408$		0			0
$409$	0.000906684	−	0.00124794i	4.48326e−5	−	6.17068e-5i	−0.808995	−	0.587816i	$-0.799988\pi$
$409$	0.000906684	−	0.00124794i	4.48326e−5	−	6.17068e-5i	0.809039	+	0.587754i	$0.199988\pi$
$410$	−29.4449	−	9.56722i	−1.45418	−	0.472491i
$411$		0			0
$412$	−16.9292	+	12.2998i	−0.834042	+	0.605967i
$413$	−14.9382	+	10.8532i	−0.735061	+	0.534053i
$414$		0			0
$415$	−3.50643	−	1.13931i	−0.172124	−	0.0559264i
$416$	14.3533	−	19.7556i	0.703727	−	0.968597i
$417$		0			0
$418$	17.5779	−	15.1330i	0.859764	−	0.740179i
$419$		−	15.4410i		−	0.754342i	−0.926144	−	0.377171i	$-0.876897\pi$
$419$		−	15.4410i		−	0.754342i	0.926144	−	0.377171i	$-0.123103\pi$
$420$		0			0
$421$	7.57531	−	23.3144i	0.369198	−	1.13627i	−0.578112	−	0.815957i	$-0.696210\pi$
$421$	7.57531	−	23.3144i	0.369198	−	1.13627i	0.947310	−	0.320318i	$-0.103790\pi$
$422$	38.8383	−	12.6193i	1.89062	−	0.614300i
$423$		0			0
$424$	8.63374	+	11.8833i	0.419292	+	0.577105i
$425$	−4.15662	−	12.7928i	−0.201626	−	0.620540i
$426$		0			0
$427$	10.4500	+	7.59240i	0.505713	+	0.367422i
$428$	−10.7635			−0.520273
$429$		0			0
$430$	−23.1859			−1.11812
$431$	−9.71012	−	7.05482i	−0.467720	−	0.339818i	0.328832	−	0.944388i	$-0.393345\pi$
$431$	−9.71012	−	7.05482i	−0.467720	−	0.339818i	−0.796552	+	0.604570i	$0.793345\pi$
$432$		0			0
$433$	0.277208	+	0.853159i	0.0133218	+	0.0410002i	0.957496	−	0.288445i	$-0.0931383\pi$
$433$	0.277208	+	0.853159i	0.0133218	+	0.0410002i	−0.944175	+	0.329445i	$0.893138\pi$
$434$	−4.67362	−	6.43269i	−0.224341	−	0.308779i
$435$		0			0
$436$	33.2058	−	10.7892i	1.59027	−	0.516710i
$437$	−0.0780908	+	0.240339i	−0.00373559	+	0.0114970i
$438$		0			0
$439$			4.35120i			0.207672i	0.994594	+	0.103836i	$0.0331116\pi$
$439$			4.35120i			0.207672i	−0.994594	+	0.103836i	$0.966888\pi$
$440$	−13.1263	−	31.3402i	−0.625770	−	1.49408i
$441$		0			0
$442$	−30.9724	+	42.6299i	−1.47321	+	2.02770i
$443$	−36.5642	−	11.8804i	−1.73722	−	0.564456i	−0.742756	−	0.669563i	$-0.766482\pi$
$443$	−36.5642	−	11.8804i	−1.73722	−	0.564456i	−0.994461	+	0.105107i	$0.966482\pi$
$444$		0			0
$445$	32.1629	−	23.3677i	1.52467	−	1.10773i
$446$	32.5048	−	23.6161i	1.53915	−	1.11825i
$447$		0			0
$448$	−15.1942	−	4.93691i	−0.717861	−	0.233247i
$449$	−10.6492	+	14.6573i	−0.502566	+	0.691723i	−0.982644	−	0.185503i	$-0.940608\pi$
$449$	−10.6492	+	14.6573i	−0.502566	+	0.691723i	0.480078	+	0.877226i	$0.340608\pi$
$450$		0			0
$451$	−14.5912	−	3.44237i	−0.687075	−	0.162095i
$452$			16.4798i			0.775144i
$453$		0			0
$454$	−12.5269	+	38.5540i	−0.587919	+	1.80943i
$455$	−21.5991	+	7.01796i	−1.01258	+	0.329007i
$456$		0			0
$457$	−18.9286	−	26.0530i	−0.885444	−	1.21871i	−0.974883	−	0.222717i	$-0.928507\pi$
$457$	−18.9286	−	26.0530i	−0.885444	−	1.21871i	0.0894390	−	0.995992i	$-0.471493\pi$
$458$	−11.4488	−	35.2358i	−0.534967	−	1.64646i
$459$		0			0
$460$	0.699953	+	0.508545i	0.0326355	+	0.0237111i
$461$	39.0951			1.82084			0.910420	−	0.413684i	$-0.135758\pi$
$461$	39.0951			1.82084			0.910420	+	0.413684i	$0.135758\pi$
$462$		0			0
$463$	−17.0365			−0.791753			−0.395877	−	0.918304i	$-0.629559\pi$
$463$	−17.0365			−0.791753			−0.395877	+	0.918304i	$0.629559\pi$
$464$	4.37721	+	3.18023i	0.203207	+	0.147638i
$465$		0			0
$466$	2.46626	+	7.59036i	0.114247	+	0.351617i
$467$	13.3070	+	18.3156i	0.615776	+	0.847543i	0.997037	−	0.0769242i	$-0.0245100\pi$
$467$	13.3070	+	18.3156i	0.615776	+	0.847543i	−0.381261	+	0.924468i	$0.624510\pi$
$468$		0			0
$469$	4.73418	−	1.53823i	0.218604	−	0.0710287i
$470$	−10.0569	+	30.9521i	−0.463892	+	1.42771i
$471$		0			0
$472$			49.2196i			2.26552i
$473$	−11.1891	+	0.924922i	−0.514477	+	0.0425280i
$474$		0			0
$475$	6.20064	−	8.53445i	0.284505	−	0.391587i
$476$	16.6355	+	5.40519i	0.762485	+	0.247746i
$477$		0			0
$478$	−11.0117	+	8.00049i	−0.503665	+	0.365934i
$479$	11.0022	−	7.99356i	0.502703	−	0.365235i	−0.307346	−	0.951598i	$-0.599441\pi$
$479$	11.0022	−	7.99356i	0.502703	−	0.365235i	0.810048	+	0.586363i	$0.199441\pi$
$480$		0			0
$481$	−38.5167	−	12.5148i	−1.75621	−	0.570627i
$482$	−4.14789	+	5.70909i	−0.188931	+	0.260042i
$483$		0			0
$484$	−17.7265	−	34.1235i	−0.805749	−	1.55107i
$485$			40.2397i			1.82719i
$486$		0			0
$487$	2.70549	−	8.32664i	0.122597	−	0.377316i	−0.870858	−	0.491534i	$-0.836436\pi$
$487$	2.70549	−	8.32664i	0.122597	−	0.377316i	0.993456	+	0.114218i	$0.0364362\pi$
$488$	32.7465	−	10.6400i	1.48236	−	0.481649i
$489$		0			0
$490$	−21.2150	−	29.2000i	−0.958398	−	1.31912i
$491$	−10.3756	−	31.9327i	−0.468242	−	1.44110i	−0.854859	−	0.518861i	$-0.826356\pi$
$491$	−10.3756	−	31.9327i	−0.468242	−	1.44110i	0.386616	−	0.922241i	$-0.373644\pi$
$492$		0			0
$493$	13.5508	+	9.84523i	0.610297	+	0.443407i
$494$	−41.3253			−1.85931
$495$		0			0
$496$	−3.16812			−0.142253
$497$	−4.72602	−	3.43365i	−0.211991	−	0.154020i
$498$		0			0
$499$	0.694327	+	2.13692i	0.0310824	+	0.0956617i	0.965394	−	0.260795i	$-0.0839847\pi$
$499$	0.694327	+	2.13692i	0.0310824	+	0.0956617i	−0.934312	+	0.356457i	$0.883985\pi$
$500$	8.78751	+	12.0950i	0.392990	+	0.540904i
$501$		0			0
$502$	−35.7241	+	11.6075i	−1.59444	+	0.518066i
$503$	5.15181	−	15.8556i	0.229708	−	0.706968i	−0.768072	−	0.640364i	$-0.778784\pi$
$503$	5.15181	−	15.8556i	0.229708	−	0.706968i	0.997779	−	0.0666040i	$-0.0212164\pi$
$504$		0			0
$505$		−	36.5280i		−	1.62547i
$506$	0.562934	+	0.341926i	0.0250254	+	0.0152005i
$507$		0			0
$508$	6.12484	−	8.43012i	0.271746	−	0.374026i
$509$	−9.95760	−	3.23542i	−0.441363	−	0.143407i	0.0799015	−	0.996803i	$-0.474539\pi$
$509$	−9.95760	−	3.23542i	−0.441363	−	0.143407i	−0.521264	+	0.853395i	$0.674539\pi$
$510$		0			0
$511$	−9.29390	+	6.75242i	−0.411138	+	0.298709i
$512$	−11.0790	+	8.04940i	−0.489629	+	0.355737i
$513$		0			0
$514$	−27.7414	−	9.01372i	−1.22362	−	0.397578i
$515$	−10.2800	+	14.1491i	−0.452989	+	0.623486i
$516$		0			0
$517$	−3.61858	+	15.3381i	−0.159145	+	0.674570i
$518$			21.1350i			0.928618i
$519$		0			0
$520$	−18.7072	+	57.5749i	−0.820365	+	2.52482i
$521$	5.99155	−	1.94677i	0.262494	−	0.0852896i	−0.174813	−	0.984602i	$-0.555932\pi$
$521$	5.99155	−	1.94677i	0.262494	−	0.0852896i	0.437308	+	0.899312i	$0.355932\pi$
$522$		0			0
$523$	−12.7364	−	17.5301i	−0.556923	−	0.766538i	0.434008	−	0.900909i	$-0.357099\pi$
$523$	−12.7364	−	17.5301i	−0.556923	−	0.766538i	−0.990931	+	0.134370i	$0.957099\pi$
$524$	8.40970	+	25.8824i	0.367380	+	1.13068i
$525$		0			0
$526$	−28.9936	−	21.0651i	−1.26418	−	0.918480i
$527$	−9.80774			−0.427232
$528$		0			0
$529$	22.9928			0.999688
$530$	23.2121	+	16.8646i	1.00827	+	0.732551i
$531$		0			0
$532$	4.23907	+	13.0465i	0.183787	+	0.565638i
$533$	15.7001	+	21.6093i	0.680045	+	0.936001i
$534$		0			0
$535$	−8.55565	+	2.77990i	−0.369893	+	0.120186i
$536$	4.10033	−	12.6195i	0.177107	−	0.545080i
$537$		0			0
$538$		−	4.71142i		−	0.203124i
$539$	−11.4028	−	13.2451i	−0.491155	−	0.570507i
$540$		0			0
$541$	13.1964	−	18.1633i	0.567357	−	0.780899i	−0.424882	−	0.905249i	$-0.639684\pi$
$541$	13.1964	−	18.1633i	0.567357	−	0.780899i	0.992238	+	0.124349i	$0.0396844\pi$
$542$	−47.4574	−	15.4198i	−2.03847	−	0.662339i
$543$		0			0
$544$	−12.7170	+	9.23941i	−0.545235	+	0.396137i
$545$	23.6080	−	17.1522i	1.01126	−	0.734720i
$546$		0			0
$547$	−22.2818	−	7.23979i	−0.952701	−	0.309551i	−0.208888	−	0.977940i	$-0.566984\pi$
$547$	−22.2818	−	7.23979i	−0.952701	−	0.309551i	−0.743813	+	0.668388i	$0.766984\pi$
$548$	12.9077	−	17.7659i	0.551390	−	0.758923i
$549$		0			0
$550$	−17.9385	−	20.8367i	−0.764901	−	0.888480i
$551$			13.1361i			0.559617i
$552$		0			0
$553$	2.26118	−	6.95920i	0.0961552	−	0.295935i
$554$	55.0412	−	17.8840i	2.33847	−	0.759816i
$555$		0			0
$556$	1.07778	+	1.48344i	0.0457081	+	0.0629119i
$557$	−1.09525	−	3.37084i	−0.0464074	−	0.142827i	0.925168	−	0.379558i	$-0.123924\pi$
$557$	−1.09525	−	3.37084i	−0.0464074	−	0.142827i	−0.971575	+	0.236731i	$0.923924\pi$
$558$		0			0
$559$	16.1831	+	11.7577i	0.684471	+	0.497297i
$560$	4.72231			0.199554
$561$		0			0
$562$	−30.5325			−1.28794
$563$	14.9273	+	10.8453i	0.629110	+	0.457075i	0.856092	−	0.516824i	$-0.172886\pi$
$563$	14.9273	+	10.8453i	0.629110	+	0.457075i	−0.226982	+	0.973899i	$0.572886\pi$
$564$		0			0
$565$	4.25625	+	13.0994i	0.179062	+	0.551096i
$566$	27.2401	+	37.4927i	1.14499	+	1.57594i
$567$		0			0
$568$	−14.8096	+	4.81192i	−0.621395	+	0.201904i
$569$	4.42849	−	13.6295i	0.185652	−	0.571378i	−0.814307	−	0.580435i	$-0.802883\pi$
$569$	4.42849	−	13.6295i	0.185652	−	0.571378i	0.999959	+	0.00905622i	$0.00288272\pi$
$570$		0			0
$571$			40.1760i			1.68132i	0.541567	+	0.840658i	$0.317831\pi$
$571$			40.1760i			1.68132i	−0.541567	+	0.840658i	$0.682169\pi$
$572$	−15.7313	+	66.6804i	−0.657758	+	2.78805i
$573$		0			0
$574$	8.19333	−	11.2771i	0.341983	−	0.470699i
$575$	0.284895	+	0.0925680i	0.0118809	+	0.00386035i
$576$		0			0
$577$	24.3026	−	17.6568i	1.01173	−	0.735064i	0.0471580	−	0.998887i	$-0.484984\pi$
$577$	24.3026	−	17.6568i	1.01173	−	0.735064i	0.964571	+	0.263823i	$0.0849836\pi$
$578$	−4.80036	+	3.48767i	−0.199669	+	0.145068i
$579$		0			0
$580$	42.7727	+	13.8977i	1.77604	+	0.577071i
$581$	0.975698	−	1.34293i	0.0404788	−	0.0557142i
$582$		0			0
$583$	11.8745	+	7.21260i	0.491793	+	0.298715i
$584$			30.6223i			1.26716i
$585$		0			0
$586$	−3.21104	+	9.88258i	−0.132647	+	0.408246i
$587$	−11.6264	+	3.77764i	−0.479872	+	0.155920i	−0.538957	−	0.842333i	$-0.681182\pi$
$587$	−11.6264	+	3.77764i	−0.479872	+	0.155920i	0.0590851	+	0.998253i	$0.481182\pi$
$588$		0			0
$589$	−4.52114	−	6.22281i	−0.186290	−	0.256406i
$590$	29.7097	+	91.4370i	1.22313	+	3.76440i
$591$		0			0
$592$	6.81281	+	4.94979i	0.280005	+	0.203435i
$593$	26.0062			1.06795			0.533973	−	0.845502i	$-0.320699\pi$
$593$	26.0062			1.06795			0.533973	+	0.845502i	$0.320699\pi$
$594$		0			0
$595$	14.6191			0.599327
$596$	−27.1964	−	19.7593i	−1.11401	−	0.809374i
$597$		0			0
$598$	−0.362626	−	1.11605i	−0.0148289	−	0.0456387i
$599$	9.73610	+	13.4006i	0.397806	+	0.547534i	0.960192	−	0.279342i	$-0.0901162\pi$
$599$	9.73610	+	13.4006i	0.397806	+	0.547534i	−0.562385	+	0.826875i	$0.690116\pi$
$600$		0			0
$601$	31.6708	−	10.2905i	1.29188	−	0.419756i	0.419129	−	0.907927i	$-0.362336\pi$
$601$	31.6708	−	10.2905i	1.29188	−	0.419756i	0.872748	+	0.488170i	$0.162336\pi$
$602$	3.22586	−	9.92816i	0.131476	−	0.404642i
$603$		0			0
$604$		−	34.9779i		−	1.42323i
$605$	−22.9035	−	22.5458i	−0.931160	−	0.916616i
$606$		0			0
$607$	26.2150	−	36.0819i	1.06404	−	1.46452i	0.188064	−	0.982157i	$-0.439779\pi$
$607$	26.2150	−	36.0819i	1.06404	−	1.46452i	0.875972	−	0.482362i	$-0.160221\pi$
$608$	−11.7244	−	3.80950i	−0.475489	−	0.154496i
$609$		0			0
$610$	54.4118	−	39.5325i	2.20307	−	1.60062i
$611$	22.7154	−	16.5037i	0.918966	−	0.667668i
$612$		0			0
$613$	−11.7116	−	3.80532i	−0.473026	−	0.153695i	0.0627963	−	0.998026i	$-0.479998\pi$
$613$	−11.7116	−	3.80532i	−0.473026	−	0.153695i	−0.535822	+	0.844331i	$0.679998\pi$
$614$	−15.2873	+	21.0411i	−0.616943	+	0.849149i
$615$		0			0
$616$	15.2461	−	1.26028i	0.614281	−	0.0507781i
$617$			15.5987i			0.627979i	0.949426	+	0.313989i	$0.101666\pi$
$617$			15.5987i			0.627979i	−0.949426	+	0.313989i	$0.898334\pi$
$618$		0			0
$619$	−11.4359	+	35.1960i	−0.459647	+	1.41465i	0.405945	+	0.913897i	$0.366942\pi$
$619$	−11.4359	+	35.1960i	−0.459647	+	1.41465i	−0.865592	+	0.500750i	$0.833058\pi$
$620$	−25.0455	+	8.13776i	−1.00585	+	0.326820i
$621$		0			0
$622$	10.8117	+	14.8810i	0.433508	+	0.596673i
$623$	5.53118	+	17.0232i	0.221602	+	0.682020i
$624$		0			0
$625$	24.4131	+	17.7372i	0.976524	+	0.709486i
$626$	−75.8276			−3.03068
$627$		0			0
$628$	11.4717			0.457770
$629$	21.0908	+	15.3234i	0.840947	+	0.610984i
$630$		0			0
$631$	13.3328	+	41.0343i	0.530772	+	1.63355i	0.752611	+	0.658465i	$0.228794\pi$
$631$	13.3328	+	41.0343i	0.530772	+	1.63355i	−0.221840	+	0.975083i	$0.571206\pi$
$632$	−11.4649	−	15.7801i	−0.456049	−	0.627697i
$633$		0			0
$634$	−26.8223	+	8.71510i	−1.06525	+	0.346121i
$635$	2.69124	−	8.28279i	0.106799	−	0.328692i
$636$		0			0
$637$			31.1390i			1.23377i
$638$	33.3224	+	7.86144i	1.31925	+	0.311238i
$639$		0			0
$640$	−34.7017	+	47.7629i	−1.37171	+	1.88799i
$641$	47.2318	+	15.3465i	1.86554	+	0.606152i	0.993075	+	0.117481i	$0.0374818\pi$
$641$	47.2318	+	15.3465i	1.86554	+	0.606152i	0.872468	+	0.488671i	$0.162518\pi$
$642$		0			0
$643$	−26.8339	+	19.4960i	−1.05823	+	0.768846i	−0.973759	−	0.227581i	$-0.926918\pi$
$643$	−26.8339	+	19.4960i	−1.05823	+	0.768846i	−0.0844660	+	0.996426i	$0.526918\pi$
$644$	−0.315142	+	0.228964i	−0.0124184	+	0.00902246i
$645$		0			0
$646$	25.2997	+	8.22038i	0.995405	+	0.323427i
$647$	−25.8770	+	35.6166i	−1.01733	+	1.40023i	−0.103268	+	0.994654i	$0.532930\pi$
$647$	−25.8770	+	35.6166i	−1.01733	+	1.40023i	−0.914060	+	0.405578i	$0.867070\pi$
$648$		0			0
$649$	17.9849	+	42.9407i	0.705970	+	1.68557i
$650$			48.9866i			1.92141i
$651$		0			0
$652$	9.35204	−	28.7826i	0.366254	−	1.12721i
$653$	−6.51319	+	2.11626i	−0.254881	+	0.0828158i	−0.433671	−	0.901072i	$-0.642782\pi$
$653$	−6.51319	+	2.11626i	−0.254881	+	0.0828158i	0.178790	+	0.983887i	$0.442782\pi$
$654$		0			0
$655$	13.3694	+	18.4014i	0.522384	+	0.719001i
$656$	−1.71629	−	5.28219i	−0.0670098	−	0.206235i
$657$		0			0
$658$	−11.8544	−	8.61271i	−0.462132	−	0.335759i
$659$	−11.7979			−0.459580			−0.229790	−	0.973240i	$-0.573804\pi$
$659$	−11.7979			−0.459580			−0.229790	+	0.973240i	$0.573804\pi$
$660$		0			0
$661$	44.8307			1.74371			0.871855	−	0.489764i	$-0.162917\pi$
$661$	44.8307			1.74371			0.871855	+	0.489764i	$0.162917\pi$
$662$	−57.0388	−	41.4411i	−2.21687	−	1.61065i
$663$		0			0
$664$	−1.36734	−	4.20824i	−0.0530631	−	0.163312i
$665$	6.73908	+	9.27555i	0.261330	+	0.359690i
$666$		0			0
$667$	−0.354760	+	0.115268i	−0.0137364	+	0.00446321i
$668$	21.4332	−	65.9646i	0.829276	−	2.55225i
$669$		0			0
$670$		−	25.9187i		−	1.00133i
$671$	24.6812	−	21.2482i	0.952806	−	0.820279i
$672$		0			0
$673$	−22.3404	+	30.7489i	−0.861159	+	1.18528i	0.120133	+	0.992758i	$0.461668\pi$
$673$	−22.3404	+	30.7489i	−0.861159	+	1.18528i	−0.981292	+	0.192525i	$0.938332\pi$
$674$	−49.0427	−	15.9349i	−1.88906	−	0.613791i
$675$		0			0
$676$	61.9866	−	45.0359i	2.38410	−	1.73215i
$677$	21.7019	−	15.7673i	0.834071	−	0.605988i	−0.0866368	−	0.996240i	$-0.527612\pi$
$677$	21.7019	−	15.7673i	0.834071	−	0.605988i	0.920708	+	0.390252i	$0.127612\pi$
$678$		0			0
$679$	−17.2305	−	5.59854i	−0.661247	−	0.214852i
$680$	22.9054	−	31.5266i	0.878384	−	1.20899i
$681$		0			0
$682$	−18.4911	+	7.74467i	−0.708062	+	0.296559i
$683$		−	4.41371i		−	0.168886i	−0.996428	−	0.0844429i	$-0.973089\pi$
$683$		−	4.41371i		−	0.168886i	0.996428	−	0.0844429i	$-0.0269111\pi$
$684$		0			0
$685$	5.67161	−	17.4554i	0.216701	−	0.666938i
$686$	35.9850	−	11.6922i	1.37391	−	0.446412i
$687$		0			0
$688$	−2.44482	−	3.36501i	−0.0932081	−	0.128290i
$689$	−7.64925	−	23.5420i	−0.291413	−	0.896877i
$690$		0			0
$691$	−13.3953	−	9.73223i	−0.509580	−	0.370231i	0.303084	−	0.952964i	$-0.401984\pi$
$691$	−13.3953	−	9.73223i	−0.509580	−	0.370231i	−0.812664	+	0.582732i	$0.801984\pi$
$692$	−24.4119			−0.928003
$693$		0			0
$694$	−35.5463			−1.34932
$695$	1.23983	+	0.900793i	0.0470296	+	0.0341690i
$696$		0			0
$697$	−5.31322	−	16.3524i	−0.201253	−	0.619392i
$698$	−25.8996	−	35.6478i	−0.980316	−	1.34929i
$699$		0			0
$700$	15.4652	−	5.02495i	0.584530	−	0.189925i
$701$	−3.17601	+	9.77475i	−0.119956	+	0.369187i	−0.992948	−	0.118547i	$-0.962176\pi$
$701$	−3.17601	+	9.77475i	−0.119956	+	0.369187i	0.872992	+	0.487734i	$0.162176\pi$
$702$		0			0
$703$			20.4454i			0.771114i
$704$	−20.9113	+	34.4276i	−0.788126	+	1.29754i
$705$		0			0
$706$	−12.1844	+	16.7704i	−0.458568	+	0.631164i
$707$	15.6412	+	5.08214i	0.588248	+	0.191133i
$708$		0			0
$709$	38.9344	−	28.2875i	1.46221	−	1.06236i	0.479434	−	0.877578i	$-0.340842\pi$
$709$	38.9344	−	28.2875i	1.46221	−	1.06236i	0.982779	−	0.184783i	$-0.0591581\pi$
$710$	−24.6077	+	17.8785i	−0.923509	+	0.670969i
$711$		0			0
$712$	45.3774	+	14.7440i	1.70059	+	0.552555i
$713$	0.128383	−	0.176704i	0.00480799	−	0.00661763i
$714$		0			0
$715$	4.71720	+	57.0657i	0.176413	+	2.13414i
$716$			54.4559i			2.03511i
$717$		0			0
$718$	13.0623	−	40.2017i	0.487482	−	1.50031i
$719$	−46.0534	+	14.9636i	−1.71750	+	0.558050i	−0.991553	−	0.129700i	$-0.958598\pi$
$719$	−46.0534	+	14.9636i	−1.71750	+	0.558050i	−0.725947	+	0.687750i	$0.758598\pi$
$720$		0			0
$721$	−4.62838	−	6.37042i	−0.172370	−	0.237247i
$722$	−7.31722	−	22.5201i	−0.272319	−	0.838111i
$723$		0			0
$724$	−45.7687	−	33.2529i	−1.70098	−	1.23583i
$725$	15.5714			0.578308
$726$		0			0
$727$	28.9349			1.07314			0.536568	−	0.843857i	$-0.319721\pi$
$727$	28.9349			1.07314			0.536568	+	0.843857i	$0.319721\pi$
$728$	−22.0507	−	16.0208i	−0.817253	−	0.593769i
$729$		0			0
$730$	18.4841	+	56.8881i	0.684126	+	2.10552i
$731$	−7.56860	−	10.4173i	−0.279935	−	0.385297i
$732$		0			0
$733$	15.9390	−	5.17891i	0.588722	−	0.191287i	0.000517936	−	1.00000i	$-0.499835\pi$
$733$	15.9390	−	5.17891i	0.588722	−	0.191287i	0.588204	+	0.808712i	$0.299835\pi$
$734$	−22.6879	+	69.8261i	−0.837424	+	2.57733i
$735$		0			0
$736$		−	0.350063i		−	0.0129035i
$737$	−1.03394	−	12.5079i	−0.0380855	−	0.460735i
$738$		0			0
$739$	16.0114	−	22.0378i	0.588990	−	0.810675i	−0.405655	−	0.914026i	$-0.632957\pi$
$739$	16.0114	−	22.0378i	0.588990	−	0.810675i	0.994645	+	0.103351i	$0.0329566\pi$
$740$	66.5727	+	21.6308i	2.44726	+	0.795163i
$741$		0			0
$742$	−10.4509	+	7.59301i	−0.383664	+	0.278748i
$743$	−35.8419	+	26.0407i	−1.31491	+	0.955340i	−0.314932	+	0.949114i	$0.601982\pi$
$743$	−35.8419	+	26.0407i	−1.31491	+	0.955340i	−0.999981	+	0.00622608i	$0.998018\pi$
$744$		0			0
$745$	−26.7211	−	8.68220i	−0.978984	−	0.318091i
$746$	4.64095	−	6.38772i	0.169917	−	0.233871i
$747$		0			0
$748$	22.8948	−	37.6931i	0.837118	−	1.37820i
$749$		−	4.05028i		−	0.147994i
$750$		0			0
$751$	8.73534	−	26.8846i	0.318757	−	0.981033i	−0.655423	−	0.755262i	$-0.727510\pi$
$751$	8.73534	−	26.8846i	0.318757	−	0.981033i	0.974180	−	0.225771i	$-0.0724902\pi$
$752$	−5.55257	+	1.80414i	−0.202481	+	0.0657902i
$753$		0			0
$754$	−35.8546	−	49.3497i	−1.30575	−	1.79721i
$755$	−9.03379	−	27.8031i	−0.328773	−	1.01186i
$756$		0			0
$757$	−13.9254	−	10.1174i	−0.506129	−	0.367724i	0.305224	−	0.952280i	$-0.401269\pi$
$757$	−13.9254	−	10.1174i	−0.506129	−	0.367724i	−0.811353	+	0.584556i	$0.801269\pi$
$758$	−56.5961			−2.05566
$759$		0			0
$760$	30.5619			1.10860
$761$	39.1803	+	28.4662i	1.42028	+	1.03190i	0.991725	+	0.128384i	$0.0409791\pi$
$761$	39.1803	+	28.4662i	1.42028	+	1.03190i	0.428560	+	0.903513i	$0.359021\pi$
$762$		0			0
$763$	4.05996	+	12.4953i	0.146981	+	0.452360i
$764$	30.2463	+	41.6305i	1.09427	+	1.50614i
$765$		0			0
$766$	−20.1757	+	6.55549i	−0.728978	+	0.236859i
$767$	25.6317	−	78.8862i	0.925506	−	2.84841i
$768$		0			0
$769$		−	10.3749i		−	0.374129i	−0.982348	−	0.187065i	$-0.940103\pi$
$769$		−	10.3749i		−	0.374129i	0.982348	−	0.187065i	$-0.0598974\pi$
$770$	27.5624	−	11.5440i	0.993279	−	0.416017i
$771$		0			0
$772$	−14.0788	+	19.3778i	−0.506707	+	0.697423i
$773$	7.58873	+	2.46573i	0.272947	+	0.0886860i	0.442293	−	0.896871i	$-0.354165\pi$
$773$	7.58873	+	2.46573i	0.272947	+	0.0886860i	−0.169345	+	0.985557i	$0.554165\pi$
$774$		0			0
$775$	−7.37646	+	5.35931i	−0.264970	+	0.192512i
$776$	−39.0704	+	28.3863i	−1.40255	+	1.01901i
$777$		0			0
$778$	−58.1636	−	18.8985i	−2.08527	−	0.677544i
$779$	7.92601	−	10.9092i	0.283979	−	0.390863i
$780$		0			0
$781$	−11.1620	+	9.60950i	−0.399409	+	0.343855i
$782$			0.755389i			0.0270126i
$783$		0			0
$784$	2.00084	−	6.15795i	0.0714585	−	0.219927i
$785$	9.11857	−	2.96280i	0.325456	−	0.105747i
$786$		0			0
$787$	10.4053	+	14.3217i	0.370909	+	0.510513i	0.953148	−	0.302505i	$-0.0978230\pi$
$787$	10.4053	+	14.3217i	0.370909	+	0.510513i	−0.582239	+	0.813018i	$0.697823\pi$
$788$	−9.52384	−	29.3114i	−0.339273	−	1.04417i
$789$		0			0
$790$	−30.8238	−	22.3948i	−1.09666	−	0.796770i
$791$	−6.20131			−0.220493
$792$		0			0
$793$	−58.0249			−2.06052
$794$	37.7095	+	27.3976i	1.33826	+	0.972304i
$795$		0			0
$796$	9.07987	+	27.9450i	0.321827	+	0.990483i
$797$	18.4947	+	25.4558i	0.655116	+	0.901690i	0.999307	−	0.0372092i	$-0.0118468\pi$
$797$	18.4947	+	25.4558i	0.655116	+	0.901690i	−0.344191	+	0.938900i	$0.611847\pi$
$798$		0			0
$799$	−17.1894	+	5.58519i	−0.608119	+	0.197590i
$800$	−4.51574	+	13.8980i	−0.159656	+	0.491370i
$801$		0			0
$802$		−	23.2933i		−	0.822516i
$803$	11.1895	+	26.7159i	0.394867	+	0.942783i
$804$		0			0
$805$	−0.191365	+	0.263391i	−0.00674472	+	0.00928331i
$806$	33.9699	+	11.0375i	1.19654	+	0.388780i
$807$		0			0
$808$	35.4666	−	25.7680i	1.24771	−	0.906515i
$809$	17.3896	−	12.6343i	0.611384	−	0.444197i	−0.238517	−	0.971138i	$-0.576661\pi$
$809$	17.3896	−	12.6343i	0.611384	−	0.444197i	0.849902	+	0.526942i	$0.176661\pi$
$810$		0			0
$811$	31.2311	+	10.1476i	1.09667	+	0.356331i	0.800822	−	0.598903i	$-0.204396\pi$
$811$	31.2311	+	10.1476i	1.09667	+	0.356331i	0.295852	+	0.955234i	$0.404396\pi$
$812$	−11.9019	+	16.3816i	−0.417676	+	0.574882i
$813$		0			0
$814$	51.8639	+	12.2358i	1.81783	+	0.428864i
$815$		−	25.2940i		−	0.886011i
$816$		0			0
$817$	3.12061	−	9.60424i	0.109176	−	0.336010i
$818$	0.00343919	−	0.00111746i	0.000120249	−	3.90711e-5i
$819$		0			0
$820$	−27.1361	−	37.3497i	−0.947635	−	1.30431i
$821$	17.3211	+	53.3089i	0.604511	+	1.86049i	0.500116	+	0.865959i	$0.333291\pi$
$821$	17.3211	+	53.3089i	0.604511	+	1.86049i	0.104396	+	0.994536i	$0.466709\pi$
$822$		0			0
$823$	−43.2106	−	31.3943i	−1.50623	−	1.09434i	−0.967817	−	0.251653i	$-0.919026\pi$
$823$	−43.2106	−	31.3943i	−1.50623	−	1.09434i	−0.538409	−	0.842684i	$-0.680974\pi$
$824$	−20.9898			−0.731215
$825$		0			0
$826$	−43.2866			−1.50613
$827$	−15.2821	−	11.1031i	−0.531410	−	0.386092i	0.289475	−	0.957186i	$-0.406519\pi$
$827$	−15.2821	−	11.1031i	−0.531410	−	0.386092i	−0.820885	+	0.571094i	$0.806519\pi$
$828$		0			0
$829$	−8.51237	−	26.1984i	−0.295647	−	0.909907i	−0.983003	−	0.183587i	$-0.941229\pi$
$829$	−8.51237	−	26.1984i	−0.295647	−	0.909907i	0.687357	−	0.726320i	$-0.258771\pi$
$830$	−5.08031	−	6.99245i	−0.176340	−	0.242711i
$831$		0			0
$832$	68.2548	−	22.1773i	2.36631	−	0.768860i
$833$	6.19412	−	19.0635i	0.214614	−	0.660513i
$834$		0			0
$835$		−	57.9694i		−	2.00611i
$836$	34.4695	−	2.84934i	1.19215	−	0.0985464i
$837$		0			0
$838$	21.2768	−	29.2850i	0.734996	−	1.01164i
$839$	−3.41825	−	1.11066i	−0.118011	−	0.0383441i	0.249416	−	0.968396i	$-0.419761\pi$
$839$	−3.41825	−	1.11066i	−0.118011	−	0.0383441i	−0.367427	+	0.930052i	$0.619761\pi$
$840$		0			0
$841$	7.77466	−	5.64862i	0.268092	−	0.194780i
$842$	46.4931	−	33.7792i	1.60226	−	1.16411i
$843$		0			0
$844$	57.9144	+	18.8175i	1.99350	+	0.647726i
$845$	37.6403	−	51.8074i	1.29487	−	1.78223i
$846$		0			0
$847$	12.8406	−	6.67044i	0.441209	−	0.229199i
$848$			5.14709i			0.176752i
$849$		0			0
$850$	9.74436	−	29.9900i	0.334229	−	1.02865i
$851$	−0.552158	+	0.179407i	−0.0189277	+	0.00614999i
$852$		0			0
$853$	8.06180	+	11.0961i	0.276031	+	0.379924i	0.924414	−	0.381390i	$-0.124555\pi$
$853$	8.06180	+	11.0961i	0.276031	+	0.379924i	−0.648383	+	0.761314i	$0.724555\pi$
$854$	9.35741	+	28.7991i	0.320204	+	0.985486i
$855$		0			0
$856$	−8.73455	−	6.34602i	−0.298541	−	0.216902i
$857$	−3.65311			−0.124788			−0.0623939	−	0.998052i	$-0.519873\pi$
$857$	−3.65311			−0.124788			−0.0623939	+	0.998052i	$0.519873\pi$
$858$		0			0
$859$	24.8986			0.849529			0.424764	−	0.905304i	$-0.360357\pi$
$859$	24.8986			0.849529			0.424764	+	0.905304i	$0.360357\pi$
$860$	−27.9710	−	20.3221i	−0.953803	−	0.692979i
$861$		0			0
$862$	−8.69486	−	26.7600i	−0.296148	−	0.911450i
$863$	4.84824	+	6.67303i	0.165036	+	0.227152i	0.883523	−	0.468388i	$-0.155165\pi$
$863$	4.84824	+	6.67303i	0.165036	+	0.227152i	−0.718487	+	0.695540i	$0.755165\pi$
$864$		0			0
$865$	−19.4045	+	6.30490i	−0.659773	+	0.214373i
$866$	−0.649859	+	2.00006i	−0.0220831	+	0.0679648i
$867$		0			0
$868$		−	11.8566i		−	0.402440i
$869$	−15.7684	−	9.57772i	−0.534906	−	0.324902i
$870$		0			0
$871$	−13.1435	+	18.0905i	−0.445350	+	0.612972i
$872$	33.3076	+	10.8223i	1.12794	+	0.366490i
$873$		0			0
$874$	−0.479279	+	0.348216i	−0.0162118	+	0.0117786i
$875$	−4.55131	+	3.30672i	−0.153863	+	0.111788i
$876$		0			0
$877$	9.45445	+	3.07194i	0.319254	+	0.103732i	0.464260	−	0.885699i	$-0.346320\pi$
$877$	9.45445	+	3.07194i	0.319254	+	0.103732i	−0.145006	+	0.989431i	$0.546320\pi$
$878$	−5.99572	+	8.25240i	−0.202346	+	0.278505i
$879$		0			0
$880$	2.73391	−	11.5883i	0.0921600	−	0.390640i
$881$		−	46.2212i		−	1.55723i	−0.627501	−	0.778616i	$-0.715922\pi$
$881$		−	46.2212i		−	1.55723i	0.627501	−	0.778616i	$-0.284078\pi$
$882$		0			0
$883$	9.04674	−	27.8430i	0.304447	−	0.936991i	−0.675436	−	0.737419i	$-0.736045\pi$
$883$	9.04674	−	27.8430i	0.304447	−	0.936991i	0.979883	−	0.199573i	$-0.0639554\pi$
$884$	−74.7289	+	24.2809i	−2.51340	+	0.816654i
$885$		0			0
$886$	−52.9763	−	72.9156i	−1.77977	−	2.44965i
$887$	15.4801	+	47.6429i	0.519772	+	1.59969i	0.774428	+	0.632662i	$0.218038\pi$
$887$	15.4801	+	47.6429i	0.519772	+	1.59969i	−0.254656	+	0.967032i	$0.581962\pi$
$888$		0			0
$889$	3.17224	+	2.30477i	0.106393	+	0.0772994i
$890$	93.1987			3.12403
$891$		0			0
$892$	59.9122			2.00601
$893$	−11.4676	−	8.33171i	−0.383749	−	0.278810i
$894$		0			0
$895$	14.0644	+	43.2858i	0.470121	+	1.44688i
$896$	−15.6239	−	21.5045i	−0.521958	−	0.718413i
$897$		0			0
$898$	−40.3940	+	13.1248i	−1.34797	+	0.437980i
$899$	3.50850	−	10.7981i	0.117015	−	0.360136i
$900$		0			0
$901$			15.9342i			0.530845i
$902$	−22.9300	−	26.6346i	−0.763486	−	0.886837i
$903$		0			0
$904$	−9.71628	+	13.3733i	−0.323159	+	0.444790i
$905$	−44.9688	−	14.6112i	−1.49481	−	0.485694i
$906$		0			0
$907$	−11.2620	+	8.18232i	−0.373949	+	0.271690i	−0.758846	−	0.651270i	$-0.774237\pi$
$907$	−11.2620	+	8.18232i	−0.373949	+	0.271690i	0.384898	+	0.922959i	$0.374237\pi$
$908$	−48.9042	+	35.5310i	−1.62294	+	1.17914i
$909$		0			0
$910$	−50.6347	−	16.4522i	−1.67852	−	0.545385i
$911$	−8.15884	+	11.2297i	−0.270315	+	0.372056i	−0.922496	−	0.386007i	$-0.873854\pi$
$911$	−8.15884	+	11.2297i	−0.270315	+	0.372056i	0.652181	+	0.758063i	$0.273854\pi$
$912$		0			0
$913$	−2.73061	−	3.17177i	−0.0903700	−	0.104970i
$914$		−	75.4942i		−	2.49713i
$915$		0			0
$916$	17.0721	−	52.5424i	0.564077	−	1.73605i
$917$	−9.73950	+	3.16456i	−0.321627	+	0.104503i
$918$		0			0
$919$	11.1835	+	15.3927i	0.368908	+	0.507759i	0.952604	−	0.304214i	$-0.0983938\pi$
$919$	11.1835	+	15.3927i	0.368908	+	0.507759i	−0.583695	+	0.811973i	$0.698394\pi$
$920$	0.268178	+	0.825367i	0.00884157	+	0.0272116i
$921$		0			0
$922$	74.1469	+	53.8709i	2.44190	+	1.77414i
$923$	26.2417			0.863755
$924$		0			0
$925$	24.2358			0.796868
$926$	−32.3111	−	23.4754i	−1.06181	−	0.771448i
$927$		0			0
$928$	−5.62314	−	17.3062i	−0.184588	−	0.568105i
$929$	9.51861	+	13.1012i	0.312296	+	0.429838i	0.936095	−	0.351746i	$-0.114412\pi$
$929$	9.51861	+	13.1012i	0.312296	+	0.429838i	−0.623800	+	0.781584i	$0.714412\pi$
$930$		0			0
$931$	14.9508	−	4.85780i	0.489992	−	0.159208i
$932$	−3.67760	+	11.3185i	−0.120464	+	0.370749i
$933$		0			0
$934$			53.0733i			1.73661i
$935$	8.46353	−	35.8745i	0.276787	−	1.17322i
$936$		0			0
$937$	−24.7387	+	34.0498i	−0.808177	+	1.11236i	0.183425	+	0.983034i	$0.441281\pi$
$937$	−24.7387	+	34.0498i	−0.808177	+	1.11236i	−0.991602	+	0.129326i	$0.958719\pi$
$938$	11.0983	+	3.60607i	0.362373	+	0.117742i
$939$		0			0
$940$	−39.2615	+	28.5251i	−1.28057	+	0.930388i
$941$	0.342321	−	0.248710i	0.0111593	−	0.00810773i	−0.582192	−	0.813052i	$-0.697805\pi$
$941$	0.342321	−	0.248710i	0.0111593	−	0.00810773i	0.593351	+	0.804944i	$0.297805\pi$
$942$		0			0
$943$	0.364169	+	0.118326i	0.0118590	+	0.00385322i
$944$	−10.1377	+	13.9533i	−0.329954	+	0.454142i
$945$		0			0
$946$	−22.4955	−	13.6638i	−0.731393	−	0.444249i
$947$		−	12.5861i		−	0.408994i	−0.978867	−	0.204497i	$-0.934444\pi$
$947$		−	12.5861i		−	0.408994i	0.978867	−	0.204497i	$-0.0655558\pi$
$948$		0			0
$949$	15.9469	−	49.0796i	0.517659	−	1.59319i
$950$	23.5200	−	7.64211i	0.763089	−	0.247943i
$951$		0			0
$952$	10.3128	+	14.1944i	0.334240	+	0.460042i
$953$	16.7845	+	51.6574i	0.543703	+	1.67335i	0.724053	+	0.689745i	$0.242277\pi$
$953$	16.7845	+	51.6574i	0.543703	+	1.67335i	−0.180349	+	0.983603i	$0.557723\pi$
$954$		0			0
$955$	34.7941	+	25.2794i	1.12591	+	0.818022i
$956$	−20.2966			−0.656440
$957$		0			0
$958$	31.8812			1.03003
$959$	6.68529	+	4.85714i	0.215879	+	0.156845i
$960$		0			0
$961$	−7.52513	−	23.1600i	−0.242746	−	0.747096i
$962$	−55.8052	−	76.8092i	−1.79923	−	2.47643i
$963$		0			0
$964$	−10.0079	+	3.25175i	−0.322332	+	0.104732i
$965$	−6.18619	+	19.0391i	−0.199141	+	0.612892i
$966$		0			0
$967$		−	26.8497i		−	0.863429i	−0.902010	−	0.431714i	$-0.857909\pi$
$967$		−	26.8497i		−	0.863429i	0.902010	−	0.431714i	$-0.142091\pi$
$968$	5.73382	−	38.1425i	0.184292	−	1.22595i
$969$		0			0
$970$	−55.4480	+	76.3177i	−1.78033	+	2.45041i
$971$	25.9476	+	8.43088i	0.832697	+	0.270560i	0.694181	−	0.719801i	$-0.255767\pi$
$971$	25.9476	+	8.43088i	0.832697	+	0.270560i	0.138516	+	0.990360i	$0.455767\pi$
$972$		0			0
$973$	−0.558215	+	0.405567i	−0.0178956	+	0.0130019i
$974$	16.6048	−	12.0641i	0.532053	−	0.386559i
$975$		0			0
$976$	11.4748	+	3.72840i	0.367300	+	0.119343i
$977$	20.2465	−	27.8669i	0.647742	−	0.891540i	−0.351257	−	0.936279i	$-0.614246\pi$
$977$	20.2465	−	27.8669i	0.647742	−	0.891540i	0.998999	+	0.0447387i	$0.0142455\pi$
$978$		0			0
$979$	44.9761	−	3.71784i	1.43744	−	0.118823i
$980$		−	53.8209i		−	1.71925i
$981$		0			0
$982$	24.3234	−	74.8598i	0.776191	−	2.38887i
$983$	−15.6042	+	5.07013i	−0.497698	+	0.161712i	−0.547100	−	0.837067i	$-0.684268\pi$
$983$	−15.6042	+	5.07013i	−0.497698	+	0.161712i	0.0494022	+	0.998779i	$0.484268\pi$
$984$		0			0
$985$	−15.1406	−	20.8392i	−0.482419	−	0.663992i
$986$	12.1340	+	37.3445i	0.386424	+	1.18929i
$987$		0			0
$988$	−49.8540	−	36.2210i	−1.58607	−	1.15234i
$989$	0.286760			0.00911842
$990$		0			0
$991$	59.6539			1.89497			0.947484	−	0.319804i	$-0.103617\pi$
$991$	59.6539			1.89497			0.947484	+	0.319804i	$0.103617\pi$
$992$	8.62017	+	6.26292i	0.273691	+	0.198848i
$993$		0			0
$994$	−4.23188	−	13.0244i	−0.134227	−	0.413108i
$995$	14.4348	+	19.8677i	0.457613	+	0.629850i
$996$		0			0
$997$	38.7308	−	12.5844i	1.22662	−	0.398551i	0.377128	−	0.926161i	$-0.376912\pi$
$997$	38.7308	−	12.5844i	1.22662	−	0.398551i	0.849487	+	0.527610i	$0.176912\pi$
$998$	−1.62771	+	5.00958i	−0.0515243	+	0.158575i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.161.19		80
3.2	odd	2	inner	891.2.k.a.161.2		80
9.2	odd	6		297.2.t.a.260.1		80
9.4	even	3		297.2.t.a.62.1		80
9.5	odd	6		99.2.p.a.29.10	✓	80
9.7	even	3		99.2.p.a.95.10	yes	80
11.8	odd	10	inner	891.2.k.a.404.2		80
33.8	even	10	inner	891.2.k.a.404.19		80
99.41	even	30		99.2.p.a.74.10	yes	80
99.52	odd	30		99.2.p.a.41.10	yes	80
99.74	even	30		297.2.t.a.206.1		80
99.85	odd	30		297.2.t.a.8.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.10	✓	80	9.5	odd	6
99.2.p.a.41.10	yes	80	99.52	odd	30
99.2.p.a.74.10	yes	80	99.41	even	30
99.2.p.a.95.10	yes	80	9.7	even	3
297.2.t.a.8.1		80	99.85	odd	30
297.2.t.a.62.1		80	9.4	even	3
297.2.t.a.206.1		80	99.74	even	30
297.2.t.a.260.1		80	9.2	odd	6
891.2.k.a.161.2		80	3.2	odd	2	inner
891.2.k.a.161.19		80	1.1	even	1	trivial
891.2.k.a.404.2		80	11.8	odd	10	inner
891.2.k.a.404.19		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)

\(f(q)\)	\(=\)	\(q+(1.89658 + 1.37794i) q^{2} +(1.08024 + 3.32465i) q^{4} +(1.71732 + 2.36369i) q^{5} +(-1.25106 + 0.406493i) q^{7} +(-1.08356 + 3.33484i) q^{8} +6.84930i q^{10} +(0.273229 + 3.30535i) q^{11} +(3.47331 - 4.78060i) q^{13} +(-2.93285 - 0.952942i) q^{14} +(-0.994050 + 0.722219i) q^{16} +(-3.07734 + 2.23582i) q^{17} +(-2.83716 - 0.921851i) q^{19} +(-6.00331 + 8.26284i) q^{20} +(-4.03639 + 6.64535i) q^{22} -0.0847109i q^{23} +(-1.09275 + 3.36315i) q^{25} +(13.1748 - 4.28075i) q^{26} +(-2.70289 - 3.72021i) q^{28} +(-1.36073 - 4.18789i) q^{29} +(2.08597 + 1.51555i) q^{31} +4.13245 q^{32} -8.91726 q^{34} +(-3.10929 - 2.25903i) q^{35} +(-2.11787 - 6.51815i) q^{37} +(-4.11064 - 5.65782i) q^{38} +(-9.74334 + 3.16580i) q^{40} +(-1.39682 + 4.29896i) q^{41} +3.38516i q^{43} +(-10.6940 + 4.47897i) q^{44} +(0.116727 - 0.160661i) q^{46} +(4.51901 + 1.46832i) q^{47} +(-4.26321 + 3.09740i) q^{49} +(-6.70672 + 4.87272i) q^{50} +(19.6458 + 6.38331i) q^{52} +(2.46224 - 3.38898i) q^{53} +(-7.34360 + 6.32218i) q^{55} -4.61254i q^{56} +(3.18995 - 9.81766i) q^{58} +(13.3498 - 4.33762i) q^{59} +(-5.77176 - 7.94414i) q^{61} +(1.86787 + 5.74871i) q^{62} +(9.82561 + 7.13872i) q^{64} +17.2646 q^{65} -3.78414 q^{67} +(-10.7576 - 7.81585i) q^{68} +(-2.78419 - 8.56886i) q^{70} +(2.61027 + 3.59273i) q^{71} +(8.30569 - 2.69868i) q^{73} +(4.96493 - 15.2805i) q^{74} -10.4284i q^{76} +(-1.68543 - 4.02412i) q^{77} +(-3.26965 + 4.50028i) q^{79} +(-3.41421 - 1.10934i) q^{80} +(-8.57291 + 6.22858i) q^{82} +(-1.02090 + 0.741727i) q^{83} +(-10.5696 - 3.43426i) q^{85} +(-4.66456 + 6.42021i) q^{86} +(-11.3189 - 2.67036i) q^{88} -13.6071i q^{89} +(-2.40203 + 7.39268i) q^{91} +(0.281634 - 0.0915083i) q^{92} +(6.54740 + 9.01173i) q^{94} +(-2.69335 - 8.28929i) q^{95} +(11.1424 + 8.09543i) q^{97} -12.3536 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more