LMFDB - Embedded newform 891.2.n.l.190.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not 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:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			190.6
Character	$\chi$	$=$	891.190
Dual form			891.2.n.l.136.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.575085 - 0.256045i) q^{2} +(-1.07310 - 1.19179i) q^{4} +(-1.24862 + 0.555922i) q^{5} +(0.575145 - 0.122251i) q^{7} +(0.701028 + 2.15754i) q^{8} +0.860404 q^{10} +(3.22133 + 0.789325i) q^{11} +(-0.397199 - 3.77909i) q^{13} +(-0.362059 - 0.0769581i) q^{14} +(-0.185992 + 1.76960i) q^{16} +(0.156539 + 0.113732i) q^{17} +(-0.601281 - 1.85055i) q^{19} +(2.00243 + 0.891541i) q^{20} +(-1.65044 - 1.27873i) q^{22} +(-0.160616 + 0.278195i) q^{23} +(-2.09565 + 2.32745i) q^{25} +(-0.739193 + 2.27500i) q^{26} +(-0.762884 - 0.554268i) q^{28} +(4.08026 - 0.867285i) q^{29} +(-0.589080 - 5.60472i) q^{31} +(2.82863 - 4.89933i) q^{32} +(-0.0609029 - 0.105487i) q^{34} +(-0.650176 + 0.472381i) q^{35} +(3.17822 - 9.78156i) q^{37} +(-0.128036 + 1.21818i) q^{38} +(-2.07474 - 2.30423i) q^{40} +(-6.71088 - 1.42644i) q^{41} +(-3.40544 - 5.89840i) q^{43} +(-2.51609 - 4.68619i) q^{44} +(0.163598 - 0.118861i) q^{46} +(3.40443 - 3.78100i) q^{47} +(-6.07897 + 2.70653i) q^{49} +(1.80111 - 0.801905i) q^{50} +(-4.07767 + 4.52871i) q^{52} +(-6.36368 + 4.62348i) q^{53} +(-4.46102 + 0.805240i) q^{55} +(0.666954 + 1.15520i) q^{56} +(-2.56856 - 0.545964i) q^{58} +(-4.82083 - 5.35408i) q^{59} +(0.902848 - 8.59003i) q^{61} +(-1.09629 + 3.37402i) q^{62} +(-0.00210888 + 0.00153219i) q^{64} +(2.59683 + 4.49784i) q^{65} +(4.54870 - 7.87858i) q^{67} +(-0.0324361 - 0.308608i) q^{68} +(0.494857 - 0.105185i) q^{70} +(2.31775 + 1.68394i) q^{71} +(0.131206 - 0.403812i) q^{73} +(-4.33226 + 4.81146i) q^{74} +(-1.56025 + 2.70242i) q^{76} +(1.94923 + 0.0601658i) q^{77} +(-3.75053 - 1.66984i) q^{79} +(-0.751525 - 2.31296i) q^{80} +(3.49410 + 2.53861i) q^{82} +(0.777701 - 7.39933i) q^{83} +(-0.258684 - 0.0549851i) q^{85} +(0.448167 + 4.26403i) q^{86} +(0.555241 + 7.50349i) q^{88} +3.38915 q^{89} +(-0.690444 - 2.12497i) q^{91} +(0.503908 - 0.107109i) q^{92} +(-2.92594 + 1.30271i) q^{94} +(1.77953 + 1.97637i) q^{95} +(5.90535 + 2.62923i) q^{97} +4.18892 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52}+ \cdots + 66 q^{97}+O(q^{100}) $ 96 * q + 8 * q^4 + 14 * q^7 + 64 * q^10 + 14 * q^13 + 4 * q^16 - 16 * q^19 - 16 * q^22 + 20 * q^25 - 36 * q^28 + 4 * q^31 - 84 * q^34 - 24 * q^37 + 106 * q^40 - 84 * q^43 - 76 * q^46 + 54 * q^49 - 52 * q^52 - 72 * q^55 + 10 * q^58 + 6 * q^61 - 104 * q^64 - 76 * q^67 + 8 * q^70 - 92 * q^73 - 204 * q^76 + 102 * q^79 + 24 * q^82 - 54 * q^85 + 44 * q^91 + 118 * q^94 + 66 * q^97

Character values

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

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.575085	−	0.256045i	−0.406647	−	0.181051i	0.193211	−	0.981157i	$-0.438110\pi$
$2$	−0.575085	−	0.256045i	−0.406647	−	0.181051i	−0.599858	+	0.800106i	$0.704776\pi$
$3$		0			0
$3$		0			0
$4$	−1.07310	−	1.19179i	−0.536548	−	0.595897i
$5$	−1.24862	+	0.555922i	−0.558400	+	0.248616i	−0.666475	−	0.745527i	$-0.732198\pi$
$5$	−1.24862	+	0.555922i	−0.558400	+	0.248616i	0.108075	+	0.994143i	$0.465531\pi$
$6$		0			0
$7$	0.575145	−	0.122251i	0.217384	−	0.0462065i	−0.0979319	−	0.995193i	$-0.531223\pi$
$7$	0.575145	−	0.122251i	0.217384	−	0.0462065i	0.315316	+	0.948987i	$0.397889\pi$
$8$	0.701028	+	2.15754i	0.247851	+	0.762806i
$9$		0			0
$10$	0.860404			0.272084
$11$	3.22133	+	0.789325i	0.971268	+	0.237990i
$11$	3.22133	+	0.789325i	0.971268	+	0.237990i
$12$		0			0
$13$	−0.397199	−	3.77909i	−0.110163	−	1.04813i	−0.900320	−	0.435228i	$-0.856668\pi$
$13$	−0.397199	−	3.77909i	−0.110163	−	1.04813i	0.790157	−	0.612904i	$-0.209999\pi$
$14$	−0.362059	−	0.0769581i	−0.0967644	−	0.0205679i
$15$		0			0
$16$	−0.185992	+	1.76960i	−0.0464981	+	0.442400i
$17$	0.156539	+	0.113732i	0.0379663	+	0.0275842i	0.606607	−	0.795002i	$-0.292530\pi$
$17$	0.156539	+	0.113732i	0.0379663	+	0.0275842i	−0.568640	+	0.822586i	$0.692530\pi$
$18$		0			0
$19$	−0.601281	−	1.85055i	−0.137943	−	0.424546i	0.858093	−	0.513494i	$-0.171649\pi$
$19$	−0.601281	−	1.85055i	−0.137943	−	0.424546i	−0.996036	+	0.0889487i	$0.971649\pi$
$20$	2.00243	+	0.891541i	0.447758	+	0.199355i
$21$		0			0
$22$	−1.65044	−	1.27873i	−0.351874	−	0.272627i
$23$	−0.160616	+	0.278195i	−0.0334907	+	0.0580076i	−0.882285	−	0.470716i	$-0.843996\pi$
$23$	−0.160616	+	0.278195i	−0.0334907	+	0.0580076i	0.848794	+	0.528723i	$0.177329\pi$
$24$		0			0
$25$	−2.09565	+	2.32745i	−0.419130	+	0.465491i
$26$	−0.739193	+	2.27500i	−0.144968	+	0.446165i
$27$		0			0
$28$	−0.762884	−	0.554268i	−0.144172	−	0.104747i
$29$	4.08026	−	0.867285i	0.757684	−	0.161051i	0.187158	−	0.982330i	$-0.440072\pi$
$29$	4.08026	−	0.867285i	0.757684	−	0.161051i	0.570527	+	0.821279i	$0.306739\pi$
$30$		0			0
$31$	−0.589080	−	5.60472i	−0.105802	−	1.00664i	−0.910656	−	0.413165i	$-0.864423\pi$
$31$	−0.589080	−	5.60472i	−0.105802	−	1.00664i	0.804854	−	0.593472i	$-0.202243\pi$
$32$	2.82863	−	4.89933i	0.500036	−	0.866088i
$33$		0			0
$34$	−0.0609029	−	0.105487i	−0.0104448	−	0.0180908i
$35$	−0.650176	+	0.472381i	−0.109900	+	0.0798469i
$36$		0			0
$37$	3.17822	−	9.78156i	0.522496	−	1.60808i	−0.246718	−	0.969087i	$-0.579352\pi$
$37$	3.17822	−	9.78156i	0.522496	−	1.60808i	0.769214	−	0.638991i	$-0.220648\pi$
$38$	−0.128036	+	1.21818i	−0.0207702	+	0.197615i
$39$		0			0
$40$	−2.07474	−	2.30423i	−0.328046	−	0.364331i
$41$	−6.71088	−	1.42644i	−1.04806	−	0.222773i	−0.348475	−	0.937318i	$-0.613300\pi$
$41$	−6.71088	−	1.42644i	−1.04806	−	0.222773i	−0.699589	+	0.714545i	$0.746634\pi$
$42$		0			0
$43$	−3.40544	−	5.89840i	−0.519325	−	0.899497i	−0.999748	−	0.0224601i	$-0.992850\pi$
$43$	−3.40544	−	5.89840i	−0.519325	−	0.899497i	0.480423	−	0.877037i	$-0.340483\pi$
$44$	−2.51609	−	4.68619i	−0.379314	−	0.706469i
$45$		0			0
$46$	0.163598	−	0.118861i	0.0241212	−	0.0175251i
$47$	3.40443	−	3.78100i	0.496587	−	0.551516i	−0.441795	−	0.897116i	$-0.645658\pi$
$47$	3.40443	−	3.78100i	0.496587	−	0.551516i	0.938382	+	0.345600i	$0.112325\pi$
$48$		0			0
$49$	−6.07897	+	2.70653i	−0.868425	+	0.386648i
$50$	1.80111	−	0.801905i	0.254715	−	0.113407i
$51$		0			0
$52$	−4.07767	+	4.52871i	−0.565471	+	0.628019i
$53$	−6.36368	+	4.62348i	−0.874119	+	0.635084i	−0.931689	−	0.363257i	$-0.881665\pi$
$53$	−6.36368	+	4.62348i	−0.874119	+	0.635084i	0.0575702	+	0.998341i	$0.481665\pi$
$54$		0			0
$55$	−4.46102	+	0.805240i	−0.601524	+	0.108579i
$56$	0.666954	+	1.15520i	0.0891255	+	0.154370i
$57$		0			0
$58$	−2.56856	−	0.545964i	−0.337268	−	0.0716886i
$59$	−4.82083	−	5.35408i	−0.627619	−	0.697042i	0.342542	−	0.939502i	$-0.388712\pi$
$59$	−4.82083	−	5.35408i	−0.627619	−	0.697042i	−0.970161	+	0.242461i	$0.922045\pi$
$60$		0			0
$61$	0.902848	−	8.59003i	0.115598	−	1.09984i	−0.770852	−	0.637015i	$-0.780169\pi$
$61$	0.902848	−	8.59003i	0.115598	−	1.09984i	0.886449	−	0.462825i	$-0.153164\pi$
$62$	−1.09629	+	3.37402i	−0.139229	+	0.428501i
$63$		0			0
$64$	−0.00210888	+	0.00153219i	−0.000263611	+	0.000191524i
$65$	2.59683	+	4.49784i	0.322097	+	0.557889i
$66$		0			0
$67$	4.54870	−	7.87858i	0.555712	−	0.962522i	−0.442135	−	0.896948i	$-0.645779\pi$
$67$	4.54870	−	7.87858i	0.555712	−	0.962522i	0.997848	−	0.0655738i	$-0.0208878\pi$
$68$	−0.0324361	−	0.308608i	−0.00393345	−	0.0374243i
$69$		0			0
$70$	0.494857	−	0.105185i	0.0591467	−	0.0125720i
$71$	2.31775	+	1.68394i	0.275066	+	0.199847i	0.716763	−	0.697317i	$-0.245623\pi$
$71$	2.31775	+	1.68394i	0.275066	+	0.199847i	−0.441696	+	0.897165i	$0.645623\pi$
$72$		0			0
$73$	0.131206	−	0.403812i	0.0153565	−	0.0472626i	−0.943085	−	0.332553i	$-0.892090\pi$
$73$	0.131206	−	0.403812i	0.0153565	−	0.0472626i	0.958441	+	0.285290i	$0.0920900\pi$
$74$	−4.33226	+	4.81146i	−0.503615	+	0.559321i
$75$		0			0
$76$	−1.56025	+	2.70242i	−0.178972	+	0.309989i
$77$	1.94923	+	0.0601658i	0.222135	+	0.00685653i
$78$		0			0
$79$	−3.75053	−	1.66984i	−0.421968	−	0.187872i	0.184757	−	0.982784i	$-0.440850\pi$
$79$	−3.75053	−	1.66984i	−0.421968	−	0.187872i	−0.606725	+	0.794912i	$0.707517\pi$
$80$	−0.751525	−	2.31296i	−0.0840230	−	0.258596i
$81$		0			0
$82$	3.49410	+	2.53861i	0.385859	+	0.280343i
$83$	0.777701	−	7.39933i	0.0853638	−	0.812182i	−0.865153	−	0.501508i	$-0.832779\pi$
$83$	0.777701	−	7.39933i	0.0853638	−	0.812182i	0.950517	−	0.310674i	$-0.100555\pi$
$84$		0			0
$85$	−0.258684	−	0.0549851i	−0.0280583	−	0.00596397i
$86$	0.448167	+	4.26403i	0.0483271	+	0.459802i
$87$		0			0
$88$	0.555241	+	7.50349i	0.0591889	+	0.799875i
$89$	3.38915			0.359249			0.179625	−	0.983735i	$-0.442512\pi$
$89$	3.38915			0.359249			0.179625	+	0.983735i	$0.442512\pi$
$90$		0			0
$91$	−0.690444	−	2.12497i	−0.0723782	−	0.222757i
$92$	0.503908	−	0.107109i	0.0525360	−	0.0111669i
$93$		0			0
$94$	−2.92594	+	1.30271i	−0.301788	+	0.134365i
$95$	1.77953	+	1.97637i	0.182576	+	0.202771i
$96$		0			0
$97$	5.90535	+	2.62923i	0.599598	+	0.266958i	0.684010	−	0.729473i	$-0.260235\pi$
$97$	5.90535	+	2.62923i	0.599598	+	0.266958i	−0.0844122	+	0.996431i	$0.526901\pi$
$98$	4.18892			0.423145
$99$		0			0
$100$	5.02268			0.502268
$101$	−16.8982	−	7.52357i	−1.68144	−	0.748623i	−0.999858	−	0.0168783i	$-0.994627\pi$
$101$	−16.8982	−	7.52357i	−1.68144	−	0.748623i	−0.681578	−	0.731745i	$-0.738706\pi$
$102$		0			0
$103$	2.16577	+	2.40533i	0.213399	+	0.237004i	0.840335	−	0.542067i	$-0.182358\pi$
$103$	2.16577	+	2.40533i	0.213399	+	0.237004i	−0.626936	+	0.779071i	$0.715691\pi$
$104$	7.87511	−	3.50622i	0.772218	−	0.343814i
$105$		0			0
$106$	4.84348	−	1.02951i	0.470440	−	0.0999951i
$107$	5.21311	+	16.0443i	0.503970	+	1.55106i	0.802495	+	0.596659i	$0.203506\pi$
$107$	5.21311	+	16.0443i	0.503970	+	1.55106i	−0.298524	+	0.954402i	$0.596494\pi$
$108$		0			0
$109$	8.90745			0.853179			0.426589	−	0.904445i	$-0.359715\pi$
$109$	8.90745			0.853179			0.426589	+	0.904445i	$0.359715\pi$
$110$	2.77165	+	0.679138i	0.264266	+	0.0647533i
$111$		0			0
$112$	0.109362	+	1.04051i	0.0103338	+	0.0983194i
$113$	−2.82239	−	0.599918i	−0.265508	−	0.0564355i	0.0732338	−	0.997315i	$-0.476668\pi$
$113$	−2.82239	−	0.599918i	−0.265508	−	0.0564355i	−0.338742	+	0.940879i	$0.610001\pi$
$114$		0			0
$115$	0.0458937	−	0.436650i	0.00427961	−	0.0407178i
$116$	−5.41213	−	3.93215i	−0.502504	−	0.365091i
$117$		0			0
$118$	1.40151	+	4.31340i	0.129019	+	0.397081i
$119$	0.103937	+	0.0462756i	0.00952786	+	0.00424208i
$120$		0			0
$121$	9.75393	+	5.08535i	0.886721	+	0.462305i
$122$	−2.71864	+	4.70883i	−0.246134	+	0.426317i
$123$		0			0
$124$	−6.04753	+	6.71647i	−0.543085	+	0.603157i
$125$	3.43459	−	10.5706i	0.307199	−	0.945461i
$126$		0			0
$127$	1.03914	+	0.754980i	0.0922088	+	0.0669936i	0.632934	−	0.774205i	$-0.281850\pi$
$127$	1.03914	+	0.754980i	0.0922088	+	0.0669936i	−0.540726	+	0.841199i	$0.681850\pi$
$128$	−11.0657	+	2.35208i	−0.978077	+	0.207897i
$129$		0			0
$130$	−0.341751	−	3.25155i	−0.0299736	−	0.285180i
$131$	3.16899	−	5.48885i	0.276876	−	0.479563i	−0.693731	−	0.720234i	$-0.744034\pi$
$131$	3.16899	−	5.48885i	0.276876	−	0.479563i	0.970607	+	0.240671i	$0.0773675\pi$
$132$		0			0
$133$	−0.572055	−	0.990829i	−0.0496035	−	0.0859157i
$134$	−4.63316	+	3.36619i	−0.400244	+	0.290794i
$135$		0			0
$136$	−0.135644	+	0.417470i	−0.0116314	+	0.0357977i
$137$	1.73141	−	16.4733i	0.147924	−	1.40741i	−0.628801	−	0.777566i	$-0.716454\pi$
$137$	1.73141	−	16.4733i	0.147924	−	1.40741i	0.776725	−	0.629840i	$-0.216879\pi$
$138$		0			0
$139$	11.6758	+	12.9673i	0.990327	+	1.09987i	0.994999	+	0.0998800i	$0.0318459\pi$
$139$	11.6758	+	12.9673i	0.990327	+	1.09987i	−0.00467295	+	0.999989i	$0.501487\pi$
$140$	1.26068	+	0.267966i	0.106547	+	0.0226473i
$141$		0			0
$142$	−0.901739	−	1.56186i	−0.0756723	−	0.131068i
$143$	1.70342	−	12.4872i	0.142447	−	1.04423i
$144$		0			0
$145$	−4.61255	+	3.35121i	−0.383051	+	0.278303i
$146$	−0.178849	+	0.198631i	−0.0148016	+	0.0164389i
$147$		0			0
$148$	−15.0681	+	6.70877i	−1.23859	+	0.551458i
$149$	−5.76068	+	2.56482i	−0.471933	+	0.210118i	−0.628901	−	0.777486i	$-0.716495\pi$
$149$	−5.76068	+	2.56482i	−0.471933	+	0.210118i	0.156968	+	0.987604i	$0.449828\pi$
$150$		0			0
$151$	10.8610	−	12.0624i	0.883859	−	0.981625i	−0.116074	−	0.993241i	$-0.537031\pi$
$151$	10.8610	−	12.0624i	0.883859	−	0.981625i	0.999933	+	0.0116160i	$0.00369757\pi$
$152$	3.57113	−	2.59458i	0.289657	−	0.210448i
$153$		0			0
$154$	−1.10557	−	0.533690i	−0.0890892	−	0.0430059i
$155$	3.85132	+	6.67068i	0.309346	+	0.535802i
$156$		0			0
$157$	16.6718	+	3.54369i	1.33055	+	0.282817i	0.817692	−	0.575656i	$-0.195253\pi$
$157$	16.6718	+	3.54369i	1.33055	+	0.282817i	0.512859	+	0.858473i	$0.328587\pi$
$158$	1.72932	+	1.92061i	0.137577	+	0.152795i
$159$		0			0
$160$	−0.808242	+	7.68991i	−0.0638971	+	0.607940i
$161$	−0.0583679	+	0.179638i	−0.00460003	+	0.0141574i
$162$		0			0
$163$	−15.0263	+	10.9173i	−1.17695	+	0.855105i	−0.991824	−	0.127609i	$-0.959270\pi$
$163$	−15.0263	+	10.9173i	−1.17695	+	0.855105i	−0.185127	+	0.982715i	$0.559270\pi$
$164$	5.50140	+	9.52870i	0.429587	+	0.744067i
$165$		0			0
$166$	−2.34180	+	4.05612i	−0.181759	+	0.314816i
$167$	0.989552	+	9.41496i	0.0765738	+	0.728551i	0.963693	+	0.267012i	$0.0860362\pi$
$167$	0.989552	+	9.41496i	0.0765738	+	0.728551i	−0.887119	+	0.461540i	$0.847297\pi$
$168$		0			0
$169$	−1.40787	+	0.299251i	−0.108297	+	0.0230193i
$170$	0.134687	+	0.0978558i	0.0103300	+	0.00750520i
$171$		0			0
$172$	−3.37531	+	10.3881i	−0.257365	+	0.792088i
$173$	−12.0230	+	13.3528i	−0.914088	+	1.01520i	0.0857336	+	0.996318i	$0.472677\pi$
$173$	−12.0230	+	13.3528i	−0.914088	+	1.01520i	−0.999822	+	0.0188797i	$0.993990\pi$
$174$		0			0
$175$	−0.920769	+	1.59482i	−0.0696036	+	0.120557i
$176$	−1.99593	+	5.55366i	−0.150449	+	0.418623i
$177$		0			0
$178$	−1.94905	−	0.867774i	−0.146088	−	0.0650424i
$179$	−8.17595	−	25.1630i	−0.611099	−	1.88077i	−0.447625	−	0.894221i	$-0.647730\pi$
$179$	−8.17595	−	25.1630i	−0.611099	−	1.88077i	−0.163474	−	0.986548i	$-0.552270\pi$
$180$		0			0
$181$	0.711098	+	0.516643i	0.0528555	+	0.0384018i	0.613899	−	0.789384i	$-0.289600\pi$
$181$	0.711098	+	0.516643i	0.0528555	+	0.0384018i	−0.561044	+	0.827786i	$0.689600\pi$
$182$	−0.147022	+	1.39882i	−0.0108980	+	0.103688i
$183$		0			0
$184$	−0.712813	−	0.151513i	−0.0525493	−	0.0111697i
$185$	1.46939	+	13.9803i	0.108032	+	1.02785i
$186$		0			0
$187$	0.414493	+	0.489930i	0.0303107	+	0.0358272i
$188$	−8.15946			−0.595090
$189$		0			0
$190$	−0.517344	−	1.59222i	−0.0375321	−	0.115512i
$191$	15.1823	−	3.22709i	1.09855	−	0.233504i	0.377240	−	0.926115i	$-0.376873\pi$
$191$	15.1823	−	3.22709i	1.09855	−	0.233504i	0.721311	+	0.692611i	$0.243540\pi$
$192$		0			0
$193$	8.83817	−	3.93501i	0.636185	−	0.283248i	−0.0631912	−	0.998001i	$-0.520128\pi$
$193$	8.83817	−	3.93501i	0.636185	−	0.283248i	0.699376	+	0.714754i	$0.253461\pi$
$194$	−2.72288	−	3.02407i	−0.195491	−	0.217115i
$195$		0			0
$196$	9.74896	+	4.34051i	0.696354	+	0.310037i
$197$	26.0364			1.85502			0.927508	−	0.373803i	$-0.121947\pi$
$197$	26.0364			1.85502			0.927508	+	0.373803i	$0.121947\pi$
$198$		0			0
$199$	−20.4538			−1.44993			−0.724967	−	0.688784i	$-0.758145\pi$
$199$	−20.4538			−1.44993			−0.724967	+	0.688784i	$0.758145\pi$
$200$	−6.49069	−	2.88984i	−0.458961	−	0.204343i
$201$		0			0
$202$	7.79155	+	8.65339i	0.548212	+	0.608851i
$203$	2.24071	−	0.997629i	0.157267	−	0.0700199i
$204$		0			0
$205$	9.17233	−	1.94964i	0.640624	−	0.136169i
$206$	−0.629630	−	1.93780i	−0.0438684	−	0.135013i
$207$		0			0
$208$	6.76136			0.468816
$209$	−0.476237	−	6.43584i	−0.0329420	−	0.445177i
$210$		0			0
$211$	1.66376	+	15.8297i	0.114538	+	1.08976i	0.889243	+	0.457435i	$0.151232\pi$
$211$	1.66376	+	15.8297i	0.114538	+	1.08976i	−0.774705	+	0.632323i	$0.782102\pi$
$212$	12.3391	+	2.62275i	0.847452	+	0.180132i
$213$		0			0
$214$	1.11007	−	10.5616i	0.0758830	−	0.721979i
$215$	7.53115	+	5.47170i	0.513620	+	0.373167i
$216$		0			0
$217$	−1.02399	−	3.15151i	−0.0695128	−	0.213939i
$218$	−5.12254	−	2.28070i	−0.346942	−	0.154469i
$219$		0			0
$220$	5.74679	+	4.45252i	0.387448	+	0.300189i
$221$	0.367628	−	0.636751i	0.0247294	−	0.0428325i
$222$		0			0
$223$	1.67391	−	1.85906i	0.112093	−	0.124492i	−0.684487	−	0.729025i	$-0.739974\pi$
$223$	1.67391	−	1.85906i	0.112093	−	0.124492i	0.796580	+	0.604533i	$0.206640\pi$
$224$	1.02793	−	3.16363i	0.0686812	−	0.211379i
$225$		0			0
$226$	1.46951	+	1.06766i	0.0977504	+	0.0710198i
$227$	−15.7616	+	3.35024i	−1.04614	+	0.222363i	−0.698756	−	0.715360i	$-0.746263\pi$
$227$	−15.7616	+	3.35024i	−1.04614	+	0.222363i	−0.347382	+	0.937724i	$0.612929\pi$
$228$		0			0
$229$	−0.345439	−	3.28663i	−0.0228273	−	0.217187i	−0.999989	−	0.00469002i	$-0.998507\pi$
$229$	−0.345439	−	3.28663i	−0.0228273	−	0.217187i	0.977162	−	0.212497i	$-0.0681596\pi$
$230$	−0.138195	+	0.239360i	−0.00911228	+	0.0157829i
$231$		0			0
$232$	4.73158	+	8.19533i	0.310643	+	0.538050i
$233$	−3.48837	+	2.53445i	−0.228531	+	0.166037i	−0.696158	−	0.717888i	$-0.745109\pi$
$233$	−3.48837	+	2.53445i	−0.228531	+	0.166037i	0.467627	+	0.883926i	$0.345109\pi$
$234$		0			0
$235$	−2.14890	+	6.61363i	−0.140179	+	0.431426i
$236$	−1.20774	+	11.4909i	−0.0786173	+	0.747993i
$237$		0			0
$238$	−0.0479238	−	0.0532248i	−0.00310644	−	0.00345005i
$239$	14.7115	+	3.12702i	0.951606	+	0.202270i	0.657459	−	0.753490i	$-0.271631\pi$
$239$	14.7115	+	3.12702i	0.951606	+	0.202270i	0.294147	+	0.955760i	$0.404965\pi$
$240$		0			0
$241$	−6.88547	−	11.9260i	−0.443532	−	0.768220i	0.554417	−	0.832239i	$-0.312941\pi$
$241$	−6.88547	−	11.9260i	−0.443532	−	0.768220i	−0.997949	+	0.0640192i	$0.979608\pi$
$242$	−4.30727	−	5.42195i	−0.276882	−	0.348536i
$243$		0			0
$244$	−11.2064	+	8.14192i	−0.717416	+	0.521233i
$245$	6.08571	−	6.75886i	0.388802	−	0.431808i
$246$		0			0
$247$	−6.75458	+	3.00733i	−0.429784	+	0.191352i
$248$	11.6795	−	5.20003i	0.741646	−	0.330202i
$249$		0			0
$250$	−4.68172	+	5.19958i	−0.296098	+	0.328850i
$251$	−22.3625	+	16.2473i	−1.41151	+	1.02552i	−0.418409	+	0.908259i	$0.637412\pi$
$251$	−22.3625	+	16.2473i	−1.41151	+	1.02552i	−0.993101	+	0.117264i	$0.962588\pi$
$252$		0			0
$253$	−0.736983	+	0.769379i	−0.0463337	+	0.0483705i
$254$	−0.404286	−	0.700244i	−0.0253672	−	0.0439372i
$255$		0			0
$256$	6.97104	+	1.48174i	0.435690	+	0.0926088i
$257$	−7.34877	−	8.16164i	−0.458404	−	0.509109i	0.468986	−	0.883206i	$-0.344619\pi$
$257$	−7.34877	−	8.16164i	−0.458404	−	0.509109i	−0.927390	+	0.374097i	$0.877953\pi$
$258$		0			0
$259$	0.632134	−	6.01435i	0.0392789	−	0.373714i
$260$	2.57385	−	7.92151i	0.159624	−	0.491271i
$261$		0			0
$262$	−3.22783	+	2.34516i	−0.199416	+	0.144884i
$263$	8.97517	+	15.5455i	0.553433	+	0.958574i	0.998024	+	0.0628399i	$0.0200157\pi$
$263$	8.97517	+	15.5455i	0.553433	+	0.958574i	−0.444591	+	0.895734i	$0.646651\pi$
$264$		0			0
$265$	5.37553	−	9.31068i	0.330216	−	0.571951i
$266$	0.0752843	+	0.716283i	0.00461598	+	0.0439181i
$267$		0			0
$268$	−14.2709	+	3.03336i	−0.871731	+	0.185292i
$269$	19.5359	+	14.1937i	1.19113	+	0.865404i	0.993383	−	0.114850i	$-0.0366388\pi$
$269$	19.5359	+	14.1937i	1.19113	+	0.865404i	0.197743	+	0.980254i	$0.436639\pi$
$270$		0			0
$271$	−4.49596	+	13.8371i	−0.273110	+	0.840547i	0.716603	+	0.697481i	$0.245696\pi$
$271$	−4.49596	+	13.8371i	−0.273110	+	0.840547i	−0.989713	+	0.143065i	$0.954304\pi$
$272$	−0.230376	+	0.255858i	−0.0139686	+	0.0155137i
$273$		0			0
$274$	−5.21360	+	9.03022i	−0.314965	+	0.545535i
$275$	−8.58789	+	5.84335i	−0.517869	+	0.352367i
$276$		0			0
$277$	22.0271	+	9.80708i	1.32348	+	0.589250i	0.942151	−	0.335190i	$-0.108800\pi$
$277$	22.0271	+	9.80708i	1.32348	+	0.589250i	0.381327	+	0.924440i	$0.375467\pi$
$278$	−3.39437	−	10.4468i	−0.203581	−	0.626558i
$279$		0			0
$280$	−1.47497	−	1.07163i	−0.0881465	−	0.0640422i
$281$	0.124170	−	1.18140i	0.00740739	−	0.0704766i	−0.990194	−	0.139701i	$-0.955386\pi$
$281$	0.124170	−	1.18140i	0.00740739	−	0.0704766i	0.997601	+	0.0692245i	$0.0220525\pi$
$282$		0			0
$283$	−15.0167	−	3.19190i	−0.892652	−	0.189739i	−0.261320	−	0.965252i	$-0.584158\pi$
$283$	−15.0167	−	3.19190i	−0.892652	−	0.189739i	−0.631331	+	0.775513i	$0.717491\pi$
$284$	−0.480254	−	4.56932i	−0.0284979	−	0.271139i
$285$		0			0
$286$	−4.17690	+	6.74507i	−0.246985	+	0.398844i
$287$	−4.03412			−0.238126
$288$		0			0
$289$	−5.24172	−	16.1324i	−0.308336	−	0.948962i
$290$	3.51067	−	0.746216i	0.206154	−	0.0438193i
$291$		0			0
$292$	−0.622058	+	0.276958i	−0.0364032	+	0.0162077i
$293$	21.4775	+	23.8532i	1.25473	+	1.39352i	0.885802	+	0.464063i	$0.153609\pi$
$293$	21.4775	+	23.8532i	1.25473	+	1.39352i	0.368929	+	0.929458i	$0.379725\pi$
$294$		0			0
$295$	8.99584	+	4.00521i	0.523758	+	0.233192i
$296$	23.3321			1.35615
$297$		0			0
$298$	3.96959			0.229952
$299$	1.11512	+	0.496484i	0.0644891	+	0.0287124i
$300$		0			0
$301$	−2.67971	−	2.97612i	−0.154456	−	0.171540i
$302$	−9.33454	+	4.15600i	−0.537142	+	0.239151i
$303$		0			0
$304$	3.38657	−	0.719837i	0.194233	−	0.0412855i
$305$	3.64807	+	11.2276i	0.208888	+	0.642890i
$306$		0			0
$307$	33.1199			1.89025			0.945126	−	0.326707i	$-0.105939\pi$
$307$	33.1199			1.89025			0.945126	+	0.326707i	$0.105939\pi$
$308$	−2.02000	−	2.38764i	−0.115100	−	0.136049i
$309$		0			0
$310$	−0.506847	−	4.82232i	−0.0287870	−	0.273890i
$311$	−33.2398	−	7.06534i	−1.88486	−	0.400639i	−0.886756	−	0.462237i	$-0.847047\pi$
$311$	−33.2398	−	7.06534i	−1.88486	−	0.400639i	−0.998101	+	0.0615985i	$0.980380\pi$
$312$		0			0
$313$	−0.492672	+	4.68746i	−0.0278475	+	0.264951i	0.971735	+	0.236072i	$0.0758603\pi$
$313$	−0.492672	+	4.68746i	−0.0278475	+	0.264951i	−0.999583	+	0.0288785i	$0.990806\pi$
$314$	−8.68034	−	6.30664i	−0.489860	−	0.355904i
$315$		0			0
$316$	2.03457	+	6.26176i	0.114454	+	0.352252i
$317$	−15.9113	−	7.08418i	−0.893669	−	0.397887i	−0.0920723	−	0.995752i	$-0.529349\pi$
$317$	−15.9113	−	7.08418i	−0.893669	−	0.397887i	−0.801597	+	0.597865i	$0.796016\pi$
$318$		0			0
$319$	13.8284	+	0.426835i	0.774243	+	0.0238982i
$320$	0.00178142	−	0.00308550i	9.95842e−5	−	0.000172485i
$321$		0			0
$322$	0.0795618	−	0.0883623i	0.00443381	−	0.00492424i
$323$	0.116344	−	0.358069i	0.00647353	−	0.0199235i
$324$		0			0
$325$	9.62806	+	6.99519i	0.534068	+	0.388023i
$326$	11.4367	−	2.43095i	0.633421	−	0.134638i
$327$		0			0
$328$	−1.62691	−	15.4790i	−0.0898309	−	0.854684i
$329$	1.49581	−	2.59082i	0.0824667	−	0.142837i
$330$		0			0
$331$	−6.48845	−	11.2383i	−0.356637	−	0.617714i	0.630759	−	0.775978i	$-0.282743\pi$
$331$	−6.48845	−	11.2383i	−0.356637	−	0.617714i	−0.987397	+	0.158264i	$0.949410\pi$
$332$	−9.65303	+	7.01334i	−0.529779	+	0.384907i
$333$		0			0
$334$	1.84157	−	5.66778i	0.100766	−	0.310127i
$335$	−1.29973	+	12.3661i	−0.0710117	+	0.675631i
$336$		0			0
$337$	−6.92122	−	7.68679i	−0.377023	−	0.418726i	0.524532	−	0.851391i	$-0.324240\pi$
$337$	−6.92122	−	7.68679i	−0.377023	−	0.418726i	−0.901555	+	0.432664i	$0.857574\pi$
$338$	0.886264	+	0.188381i	0.0482064	+	0.0102466i
$339$		0			0
$340$	0.212062	+	0.367303i	0.0115007	+	0.0199198i
$341$	2.52632	−	18.5196i	0.136808	−	1.00289i
$342$		0			0
$343$	−6.49530	+	4.71911i	−0.350713	+	0.254808i
$344$	10.3387	−	11.4823i	0.557427	−	0.619085i
$345$		0			0
$346$	10.3331	−	4.60061i	0.555513	−	0.247331i
$347$	−5.61255	+	2.49887i	−0.301297	+	0.134146i	−0.551817	−	0.833965i	$-0.686065\pi$
$347$	−5.61255	+	2.49887i	−0.301297	+	0.134146i	0.250520	+	0.968112i	$0.419399\pi$
$348$		0			0
$349$	13.6357	−	15.1439i	0.729900	−	0.810636i	−0.257932	−	0.966163i	$-0.583041\pi$
$349$	13.6357	−	15.1439i	0.729900	−	0.810636i	0.987832	+	0.155527i	$0.0497076\pi$
$350$	0.937866	−	0.681399i	0.0501310	−	0.0364223i
$351$		0			0
$352$	12.9791	−	13.5497i	0.691790	−	0.722200i
$353$	−5.99407	−	10.3820i	−0.319032	−	0.552580i	0.661254	−	0.750162i	$-0.270024\pi$
$353$	−5.99407	−	10.3820i	−0.319032	−	0.552580i	−0.980286	+	0.197582i	$0.936691\pi$
$354$		0			0
$355$	−3.83013	−	0.814119i	−0.203282	−	0.0432090i
$356$	−3.63689	−	4.03917i	−0.192755	−	0.214076i
$357$		0			0
$358$	−1.74097	+	16.5643i	−0.0920134	+	0.875449i
$359$	−5.52583	+	17.0067i	−0.291642	+	0.897582i	0.692687	+	0.721239i	$0.256427\pi$
$359$	−5.52583	+	17.0067i	−0.291642	+	0.897582i	−0.984329	+	0.176343i	$0.943573\pi$
$360$		0			0
$361$	12.3083	−	8.94252i	0.647806	−	0.470659i
$362$	−0.276659	−	0.479187i	−0.0145409	−	0.0251855i
$363$		0			0
$364$	−1.79161	+	3.10317i	−0.0939061	+	0.162650i
$365$	0.0606607	+	0.577148i	0.00317512	+	0.0302093i
$366$		0			0
$367$	−27.0158	+	5.74239i	−1.41021	+	0.299750i	−0.849207	−	0.528060i	$-0.822919\pi$
$367$	−27.0158	+	5.74239i	−1.41021	+	0.299750i	−0.561008	+	0.827811i	$0.689586\pi$
$368$	−0.462420	−	0.335968i	−0.0241053	−	0.0175135i
$369$		0			0
$370$	2.73455	−	8.41609i	0.142163	−	0.437532i
$371$	−3.09481	+	3.43714i	−0.160675	+	0.178447i
$372$		0			0
$373$	−6.19435	+	10.7289i	−0.320731	+	0.555523i	−0.980639	−	0.195824i	$-0.937262\pi$
$373$	−6.19435	+	10.7289i	−0.320731	+	0.555523i	0.659908	+	0.751347i	$0.270595\pi$
$374$	−0.112925	−	0.387880i	−0.00583920	−	0.0200568i
$375$		0			0
$376$	10.5443	+	4.69461i	0.543779	+	0.242106i
$377$	−4.89822	−	15.0752i	−0.252271	−	0.776411i
$378$		0			0
$379$	−13.6170	−	9.89335i	−0.699459	−	0.508187i	0.180297	−	0.983612i	$-0.442294\pi$
$379$	−13.6170	−	9.89335i	−0.699459	−	0.508187i	−0.879756	+	0.475425i	$0.842294\pi$
$380$	0.445818	−	4.24168i	0.0228700	−	0.217593i
$381$		0			0
$382$	−9.55739	−	2.03149i	−0.488999	−	0.103940i
$383$	−1.30127	−	12.3808i	−0.0664920	−	0.632629i	−0.976124	−	0.217214i	$-0.930303\pi$
$383$	−1.30127	−	12.3808i	−0.0664920	−	0.632629i	0.909632	−	0.415415i	$-0.136364\pi$
$384$		0			0
$385$	−2.46729	+	1.00849i	−0.125745	+	0.0513976i
$386$	−6.09024			−0.309985
$387$		0			0
$388$	−3.20351	−	9.85939i	−0.162634	−	0.500534i
$389$	1.20194	−	0.255479i	0.0609406	−	0.0129533i	−0.177341	−	0.984150i	$-0.556749\pi$
$389$	1.20194	−	0.255479i	0.0609406	−	0.0129533i	0.238281	+	0.971196i	$0.423416\pi$
$390$		0			0
$391$	−0.0567825	+	0.0252812i	−0.00287161	+	0.00127852i
$392$	−10.1010	−	11.2183i	−0.510177	−	0.566609i
$393$		0			0
$394$	−14.9731	−	6.66648i	−0.754336	−	0.335852i
$395$	5.61129			0.282335
$396$		0			0
$397$	20.5917			1.03347			0.516734	−	0.856146i	$-0.327148\pi$
$397$	20.5917			1.03347			0.516734	+	0.856146i	$0.327148\pi$
$398$	11.7627	+	5.23709i	0.589611	+	0.262512i
$399$		0			0
$400$	−3.72889	−	4.14135i	−0.186444	−	0.207067i
$401$	−6.15612	+	2.74088i	−0.307422	+	0.136873i	−0.554649	−	0.832085i	$-0.687147\pi$
$401$	−6.15612	+	2.74088i	−0.307422	+	0.136873i	0.247227	+	0.968958i	$0.420481\pi$
$402$		0			0
$403$	−20.9468	+	4.45237i	−1.04343	+	0.221789i
$404$	9.16687	+	28.2127i	0.456069	+	1.40364i
$405$		0			0
$406$	−1.54404			−0.0766294
$407$	17.9589	−	29.0010i	0.890191	−	1.43752i
$408$		0			0
$409$	−3.04915	−	29.0107i	−0.150771	−	1.43449i	−0.764323	−	0.644833i	$-0.776927\pi$
$409$	−3.04915	−	29.0107i	−0.150771	−	1.43449i	0.613552	−	0.789654i	$-0.289740\pi$
$410$	−5.77407	−	1.22732i	−0.285161	−	0.0606128i
$411$		0			0
$412$	0.542579	−	5.16230i	0.0267310	−	0.254328i
$413$	−3.42722	−	2.49002i	−0.168642	−	0.122526i
$414$		0			0
$415$	3.14239	+	9.67129i	0.154254	+	0.474745i
$416$	−19.6386	−	8.74366i	−0.962860	−	0.428693i
$417$		0			0
$418$	−1.37399	+	3.82310i	−0.0672038	+	0.186994i
$419$	18.9851	−	32.8832i	0.927483	−	1.60645i	0.139965	−	0.990156i	$-0.455301\pi$
$419$	18.9851	−	32.8832i	0.927483	−	1.60645i	0.787518	−	0.616292i	$-0.211366\pi$
$420$		0			0
$421$	−5.42549	+	6.02561i	−0.264422	+	0.293671i	−0.860705	−	0.509104i	$-0.829977\pi$
$421$	−5.42549	+	6.02561i	−0.264422	+	0.293671i	0.596283	+	0.802774i	$0.296644\pi$
$422$	3.09629	−	9.52940i	0.150725	−	0.463884i
$423$		0			0
$424$	−14.4365	−	10.4887i	−0.701098	−	0.509377i
$425$	−0.592758	+	0.125995i	−0.0287530	+	0.00611164i
$426$		0			0
$427$	−0.530870	−	5.05089i	−0.0256906	−	0.244430i
$428$	13.5273	−	23.4301i	0.653869	−	1.13253i
$429$		0			0
$430$	−2.93006	−	5.07500i	−0.141300	−	0.244738i
$431$	−24.6339	+	17.8976i	−1.18657	+	0.862095i	−0.992898	−	0.118971i	$-0.962041\pi$
$431$	−24.6339	+	17.8976i	−1.18657	+	0.862095i	−0.193674	+	0.981066i	$0.562041\pi$
$432$		0			0
$433$	7.44285	−	22.9067i	0.357681	−	1.10083i	−0.596758	−	0.802421i	$-0.703545\pi$
$433$	7.44285	−	22.9067i	0.357681	−	1.10083i	0.954439	−	0.298407i	$-0.0964551\pi$
$434$	−0.218047	+	2.07457i	−0.0104666	+	0.0995828i
$435$		0			0
$436$	−9.55855	−	10.6158i	−0.457772	−	0.508407i
$437$	0.611389	+	0.129955i	0.0292467	+	0.00621658i
$438$		0			0
$439$	−17.1588	−	29.7199i	−0.818943	−	1.41845i	−0.906461	−	0.422289i	$-0.861227\pi$
$439$	−17.1588	−	29.7199i	−0.818943	−	1.41845i	0.0875179	−	0.996163i	$-0.472106\pi$
$440$	−4.86464	−	9.06035i	−0.231913	−	0.431935i
$441$		0			0
$442$	−0.374454	+	0.272057i	−0.0178110	+	0.0129404i
$443$	5.71451	−	6.34661i	0.271505	−	0.301536i	−0.591938	−	0.805983i	$-0.701637\pi$
$443$	5.71451	−	6.34661i	0.271505	−	0.301536i	0.863443	+	0.504447i	$0.168304\pi$
$444$		0			0
$445$	−4.23176	+	1.88410i	−0.200605	+	0.0893150i
$446$	−1.43864	+	0.640524i	−0.0681216	+	0.0303297i
$447$		0			0
$448$	−0.00102560	+	0.00113905i	−4.84552e−5	+	5.38149e-5i
$449$	−29.8272	+	21.6707i	−1.40763	+	1.02271i	−0.413972	+	0.910290i	$0.635859\pi$
$449$	−29.8272	+	21.6707i	−1.40763	+	1.02271i	−0.993661	+	0.112416i	$0.964141\pi$
$450$		0			0
$451$	−20.4920	−	9.89211i	−0.964933	−	0.465801i
$452$	2.31372	+	4.00748i	0.108828	+	0.188496i
$453$		0			0
$454$	9.92211	+	2.10901i	0.465667	+	0.0989807i
$455$	2.04342	+	2.26945i	0.0957970	+	0.106393i
$456$		0			0
$457$	−2.47566	+	23.5543i	−0.115806	+	1.10182i	0.770088	+	0.637938i	$0.220212\pi$
$457$	−2.47566	+	23.5543i	−0.115806	+	1.10182i	−0.885894	+	0.463887i	$0.846454\pi$
$458$	−0.642868	+	1.97854i	−0.0300392	+	0.0924513i
$459$		0			0
$460$	−0.569645	+	0.413871i	−0.0265598	+	0.0192969i
$461$	14.3431	+	24.8430i	0.668024	+	1.15705i	0.978456	+	0.206456i	$0.0661931\pi$
$461$	14.3431	+	24.8430i	0.668024	+	1.15705i	−0.310432	+	0.950596i	$0.600474\pi$
$462$		0			0
$463$	−5.43156	+	9.40774i	−0.252426	+	0.437215i	−0.964193	−	0.265201i	$-0.914562\pi$
$463$	−5.43156	+	9.40774i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$464$	0.775851	+	7.38173i	0.0360180	+	0.342688i
$465$		0			0
$466$	2.65505	−	0.564347i	0.122993	−	0.0261429i
$467$	23.8560	+	17.3324i	1.10392	+	0.802046i	0.981696	−	0.190456i	$-0.0609966\pi$
$467$	23.8560	+	17.3324i	1.10392	+	0.802046i	0.122226	+	0.992502i	$0.460997\pi$
$468$		0			0
$469$	1.65300	−	5.08741i	0.0763285	−	0.234915i
$470$	2.92919	−	3.25319i	0.135113	−	0.150058i
$471$		0			0
$472$	8.17211	−	14.1545i	0.376152	−	0.651514i
$473$	−6.31430	−	21.6887i	−0.290332	−	0.997247i
$474$		0			0
$475$	5.56715	+	2.47865i	0.255438	+	0.113728i
$476$	−0.0563831	−	0.173529i	−0.00258431	−	0.00795370i
$477$		0			0
$478$	−7.65970	−	5.56510i	−0.350346	−	0.254542i
$479$	−2.23242	+	21.2400i	−0.102002	+	0.970482i	0.817109	+	0.576483i	$0.195575\pi$
$479$	−2.23242	+	21.2400i	−0.102002	+	0.970482i	−0.919111	+	0.393999i	$0.871091\pi$
$480$		0			0
$481$	−38.2278	−	8.12557i	−1.74304	−	0.370494i
$482$	0.906150	+	8.62145i	0.0412740	+	0.392696i
$483$		0			0
$484$	−4.40622	−	17.0818i	−0.200283	−	0.776444i
$485$	−8.83519			−0.401185
$486$		0			0
$487$	−0.703448	−	2.16499i	−0.0318763	−	0.0981051i	0.933853	−	0.357658i	$-0.116425\pi$
$487$	−0.703448	−	2.16499i	−0.0318763	−	0.0981051i	−0.965729	+	0.259553i	$0.916425\pi$
$488$	19.1663	−	4.07392i	0.867616	−	0.184418i
$489$		0			0
$490$	−5.23037	+	2.32871i	−0.236284	+	0.105200i
$491$	−6.37392	−	7.07895i	−0.287651	−	0.319469i	0.581949	−	0.813225i	$-0.302290\pi$
$491$	−6.37392	−	7.07895i	−0.287651	−	0.319469i	−0.869600	+	0.493756i	$0.835623\pi$
$492$		0			0
$493$	0.737358	+	0.328293i	0.0332089	+	0.0147856i
$494$	4.65447			0.209415
$495$		0			0
$496$	10.0277			0.450256
$497$	1.53891	+	0.685165i	0.0690294	+	0.0307338i
$498$		0			0
$499$	−8.51351	−	9.45521i	−0.381117	−	0.423274i	0.521814	−	0.853060i	$-0.325256\pi$
$499$	−8.51351	−	9.45521i	−0.381117	−	0.423274i	−0.902931	+	0.429786i	$0.858589\pi$
$500$	−16.2836	+	7.24992i	−0.728225	+	0.324226i
$501$		0			0
$502$	17.0204	−	3.61780i	0.759658	−	0.161470i
$503$	−1.78686	−	5.49939i	−0.0796722	−	0.245206i	0.903285	−	0.429041i	$-0.141149\pi$
$503$	−1.78686	−	5.49939i	−0.0796722	−	0.245206i	−0.982957	+	0.183836i	$0.941149\pi$
$504$		0			0
$505$	25.2820			1.12503
$506$	0.620823	−	0.253758i	0.0275990	−	0.0112809i
$507$		0			0
$508$	−0.215317	−	2.04861i	−0.00955317	−	0.0908923i
$509$	9.04564	+	1.92271i	0.400941	+	0.0852226i	0.403969	−	0.914773i	$-0.367630\pi$
$509$	9.04564	+	1.92271i	0.400941	+	0.0852226i	−0.00302783	+	0.999995i	$0.500964\pi$
$510$		0			0
$511$	0.0260964	−	0.248290i	0.00115444	−	0.0109837i
$512$	14.6751	+	10.6621i	0.648553	+	0.471201i
$513$		0			0
$514$	2.13643	+	6.57525i	0.0942338	+	0.290022i
$515$	−4.04139	−	1.79934i	−0.178085	−	0.0792886i
$516$		0			0
$517$	13.9512	−	9.49266i	0.613575	−	0.417487i
$518$	−1.90347	+	3.29691i	−0.0836338	+	0.144858i
$519$		0			0
$520$	−7.88383	+	8.75588i	−0.345729	+	0.383971i
$521$	7.83400	−	24.1106i	0.343214	−	1.05630i	−0.619320	−	0.785139i	$-0.712591\pi$
$521$	7.83400	−	24.1106i	0.343214	−	1.05630i	0.962533	−	0.271164i	$-0.0874085\pi$
$522$		0			0
$523$	−16.9781	−	12.3353i	−0.742398	−	0.539384i	0.151063	−	0.988524i	$-0.451730\pi$
$523$	−16.9781	−	12.3353i	−0.742398	−	0.539384i	−0.893461	+	0.449140i	$0.851730\pi$
$524$	−9.94222	+	2.11328i	−0.434328	+	0.0923192i
$525$		0			0
$526$	−1.18116	−	11.2380i	−0.0515011	−	0.490000i
$527$	0.545224	−	0.944356i	0.0237503	−	0.0411368i
$528$		0			0
$529$	11.4484	+	19.8292i	0.497757	+	0.862140i
$530$	−5.47534	+	3.97806i	−0.237833	+	0.172796i
$531$		0			0
$532$	−0.566994	+	1.74503i	−0.0245823	+	0.0756565i
$533$	−2.72510	+	25.9276i	−0.118037	+	1.12305i
$534$		0			0
$535$	−15.4286	−	17.1352i	−0.667035	−	0.740818i
$536$	20.1871	+	4.29091i	0.871952	+	0.185339i
$537$		0			0
$538$	−7.60061	−	13.1646i	−0.327686	−	0.567568i
$539$	−21.7187	+	3.92035i	−0.935491	+	0.168862i
$540$		0			0
$541$	9.02363	−	6.55605i	0.387956	−	0.281867i	−0.376661	−	0.926351i	$-0.622928\pi$
$541$	9.02363	−	6.55605i	0.387956	−	0.281867i	0.764617	+	0.644484i	$0.222928\pi$
$542$	6.12849	−	6.80637i	0.263241	−	0.292359i
$543$		0			0
$544$	1.00000	−	0.445231i	0.0428749	−	0.0190891i
$545$	−11.1220	+	4.95184i	−0.476415	+	0.212114i
$546$		0			0
$547$	4.07927	−	4.53049i	0.174417	−	0.193710i	−0.649598	−	0.760278i	$-0.725063\pi$
$547$	4.07927	−	4.53049i	0.174417	−	0.193710i	0.824015	+	0.566568i	$0.191729\pi$
$548$	−21.4907	+	15.6139i	−0.918038	+	0.666994i
$549$		0			0
$550$	6.43493	−	1.16154i	0.274386	−	0.0495283i
$551$	−4.05833	−	7.02924i	−0.172891	−	0.299456i
$552$		0			0
$553$	−2.36124	−	0.501897i	−0.100410	−	0.0213428i
$554$	−10.1564	−	11.2798i	−0.431504	−	0.479234i
$555$		0			0
$556$	2.92508	−	27.8303i	0.124051	−	1.18027i
$557$	−3.05982	+	9.41715i	−0.129649	+	0.399018i	−0.994719	−	0.102632i	$-0.967273\pi$
$557$	−3.05982	+	9.41715i	−0.129649	+	0.399018i	0.865071	+	0.501650i	$0.167273\pi$
$558$		0			0
$559$	−20.9380	+	15.2123i	−0.885581	+	0.643412i
$560$	−0.714997	−	1.23841i	−0.0302141	−	0.0523324i
$561$		0			0
$562$	−0.373900	+	0.647614i	−0.0157720	+	0.0273180i
$563$	−0.0576534	−	0.548535i	−0.00242980	−	0.0231180i	0.993240	−	0.116080i	$-0.0370330\pi$
$563$	−0.0576534	−	0.548535i	−0.00242980	−	0.0231180i	−0.995670	+	0.0929624i	$0.970366\pi$
$564$		0			0
$565$	3.85760	−	0.819959i	0.162291	−	0.0344959i
$566$	7.81863	+	5.68057i	0.328642	+	0.238772i
$567$		0			0
$568$	−2.00837	+	6.18113i	−0.0842694	+	0.259355i
$569$	12.8799	−	14.3046i	0.539952	−	0.599678i	−0.409995	−	0.912088i	$-0.634470\pi$
$569$	12.8799	−	14.3046i	0.539952	−	0.599678i	0.949947	+	0.312410i	$0.101136\pi$
$570$		0			0
$571$	−13.7061	+	23.7396i	−0.573582	+	0.993473i	0.422612	+	0.906311i	$0.361113\pi$
$571$	−13.7061	+	23.7396i	−0.573582	+	0.993473i	−0.996194	+	0.0871624i	$0.972220\pi$
$572$	−16.7101	+	11.3699i	−0.698686	+	0.475398i
$573$		0			0
$574$	2.31996	+	1.03291i	0.0968333	+	0.0431130i
$575$	−0.310891	−	0.956825i	−0.0129651	−	0.0399024i
$576$		0			0
$577$	24.2732	+	17.6355i	1.01050	+	0.734175i	0.964315	−	0.264758i	$-0.0852921\pi$
$577$	24.2732	+	17.6355i	1.01050	+	0.734175i	0.0461898	+	0.998933i	$0.485292\pi$
$578$	−1.11616	+	10.6196i	−0.0464263	+	0.441717i
$579$		0			0
$580$	8.94367	+	1.90103i	0.371366	+	0.0789362i
$581$	−0.457284	−	4.35076i	−0.0189713	−	0.180500i
$582$		0			0
$583$	−24.1489	+	9.87076i	−1.00015	+	0.408805i
$584$	0.963220			0.0398583
$585$		0			0
$586$	−6.24393	−	19.2169i	−0.257935	−	0.793841i
$587$	5.71432	−	1.21462i	0.235855	−	0.0501325i	−0.0884676	−	0.996079i	$-0.528197\pi$
$587$	5.71432	−	1.21462i	0.235855	−	0.0501325i	0.324323	+	0.945947i	$0.394864\pi$
$588$		0			0
$589$	−10.0176	+	4.46013i	−0.412769	+	0.183777i
$590$	−4.14787	−	4.60667i	−0.170765	−	0.189654i
$591$		0			0
$592$	16.7183	+	7.44347i	0.687118	+	0.305925i
$593$	35.2941			1.44936			0.724678	−	0.689088i	$-0.241989\pi$
$593$	35.2941			1.44936			0.724678	+	0.689088i	$0.241989\pi$
$594$		0			0
$595$	−0.155503			−0.00637500
$596$	9.23850	+	4.11324i	0.378424	+	0.168485i
$597$		0			0
$598$	−0.514168	−	0.571041i	−0.0210259	−	0.0233516i
$599$	20.8608	−	9.28782i	0.852349	−	0.379490i	0.0664086	−	0.997793i	$-0.478846\pi$
$599$	20.8608	−	9.28782i	0.852349	−	0.379490i	0.785940	+	0.618302i	$0.212179\pi$
$600$		0			0
$601$	−11.2320	+	2.38744i	−0.458163	+	0.0973856i	−0.431211	−	0.902251i	$-0.641914\pi$
$601$	−11.2320	+	2.38744i	−0.458163	+	0.0973856i	−0.0269523	+	0.999637i	$0.508580\pi$
$602$	0.779042	+	2.39765i	0.0317514	+	0.0977207i
$603$		0			0
$604$	−26.0309			−1.05918
$605$	−15.0060	−	0.927250i	−0.610081	−	0.0376981i
$606$		0			0
$607$	−1.35058	−	12.8499i	−0.0548183	−	0.521561i	−0.987132	−	0.159910i	$-0.948880\pi$
$607$	−1.35058	−	12.8499i	−0.0548183	−	0.521561i	0.932313	−	0.361652i	$-0.117787\pi$
$608$	−10.7673	−	2.28865i	−0.436671	−	0.0928172i
$609$		0			0
$610$	0.776814	−	7.39089i	0.0314523	−	0.299249i
$611$	−15.6410	−	11.3639i	−0.632767	−	0.459732i
$612$		0			0
$613$	7.44676	+	22.9188i	0.300772	+	0.925680i	0.981221	+	0.192885i	$0.0617845\pi$
$613$	7.44676	+	22.9188i	0.300772	+	0.925680i	−0.680450	+	0.732795i	$0.738216\pi$
$614$	−19.0468	−	8.48016i	−0.768665	−	0.342232i
$615$		0			0
$616$	1.23665	+	4.24772i	0.0498262	+	0.171145i
$617$	−11.3955	+	19.7377i	−0.458767	+	0.794608i	−0.998896	−	0.0469742i	$-0.985042\pi$
$617$	−11.3955	+	19.7377i	−0.458767	+	0.794608i	0.540129	+	0.841582i	$0.318375\pi$
$618$		0			0
$619$	−13.5950	+	15.0988i	−0.546428	+	0.606870i	−0.951588	−	0.307376i	$-0.900549\pi$
$619$	−13.5950	+	15.0988i	−0.546428	+	0.606870i	0.405160	+	0.914246i	$0.367216\pi$
$620$	3.81725	−	11.7483i	0.153304	−	0.471822i
$621$		0			0
$622$	17.3067	+	12.5740i	0.693935	+	0.504173i
$623$	1.94925	−	0.414327i	0.0780952	−	0.0165997i
$624$		0			0
$625$	−0.0489485	−	0.465714i	−0.00195794	−	0.0186286i
$626$	1.48353	−	2.56954i	0.0592937	−	0.102700i
$627$		0			0
$628$	−13.6671	−	23.6720i	−0.545375	−	0.944617i
$629$	1.61000	−	1.16973i	0.0641947	−	0.0466402i
$630$		0			0
$631$	4.74547	−	14.6051i	0.188914	−	0.581418i	−0.811080	−	0.584936i	$-0.801120\pi$
$631$	4.74547	−	14.6051i	0.188914	−	0.581418i	0.999994	+	0.00351764i	$0.00111970\pi$
$632$	0.973532	−	9.26253i	0.0387250	−	0.368444i
$633$		0			0
$634$	7.33651	+	8.14801i	0.291370	+	0.323599i
$635$	−1.71720	−	0.365002i	−0.0681451	−	0.0144847i
$636$		0			0
$637$	12.6428	+	21.8980i	0.500926	+	0.867629i
$638$	−7.84323	−	3.78616i	−0.310517	−	0.149895i
$639$		0			0
$640$	12.5093	−	9.08850i	0.494472	−	0.359255i
$641$	9.05528	−	10.0569i	0.357662	−	0.397224i	−0.537282	−	0.843403i	$-0.680549\pi$
$641$	9.05528	−	10.0569i	0.357662	−	0.397224i	0.894944	+	0.446179i	$0.147216\pi$
$642$		0			0
$643$	11.5552	−	5.14469i	0.455691	−	0.202887i	−0.166038	−	0.986119i	$-0.553097\pi$
$643$	11.5552	−	5.14469i	0.455691	−	0.202887i	0.621729	+	0.783233i	$0.286431\pi$
$644$	0.276726	−	0.123206i	0.0109045	−	0.00485501i
$645$		0			0
$646$	−0.158589	+	0.176131i	−0.00623961	+	0.00692979i
$647$	1.31179	−	0.953069i	0.0515717	−	0.0374690i	−0.561701	−	0.827340i	$-0.689853\pi$
$647$	1.31179	−	0.953069i	0.0515717	−	0.0374690i	0.613272	+	0.789871i	$0.289853\pi$
$648$		0			0
$649$	−11.3034	−	21.0525i	−0.443697	−	0.826381i
$650$	−3.74587	−	6.48804i	−0.146925	−	0.254482i
$651$		0			0
$652$	29.1358	+	6.19301i	1.14105	+	0.242537i
$653$	22.1173	+	24.5638i	0.865518	+	0.961255i	0.999558	−	0.0297211i	$-0.00946191\pi$
$653$	22.1173	+	24.5638i	0.865518	+	0.961255i	−0.134041	+	0.990976i	$0.542795\pi$
$654$		0			0
$655$	−0.905494	+	8.61520i	−0.0353806	+	0.336624i
$656$	3.77240	−	11.6103i	0.147288	−	0.453305i
$657$		0			0
$658$	−1.52358	+	1.10695i	−0.0593955	+	0.0431534i
$659$	23.9506	+	41.4836i	0.932983	+	1.61597i	0.778192	+	0.628026i	$0.216137\pi$
$659$	23.9506	+	41.4836i	0.932983	+	1.61597i	0.154790	+	0.987947i	$0.450530\pi$
$660$		0			0
$661$	9.25259	−	16.0260i	0.359884	−	0.623337i	−0.628057	−	0.778167i	$-0.716150\pi$
$661$	9.25259	−	16.0260i	0.359884	−	0.623337i	0.987941	+	0.154830i	$0.0494830\pi$
$662$	0.853901	+	8.12433i	0.0331878	+	0.315761i
$663$		0			0
$664$	16.5096	−	3.50921i	0.640695	−	0.136184i
$665$	1.26510	+	0.919151i	0.0490586	+	0.0356431i
$666$		0			0
$667$	−0.414080	+	1.27441i	−0.0160332	+	0.0493452i
$668$	10.1588	−	11.2825i	0.393056	−	0.436533i
$669$		0			0
$670$	3.91372	−	6.77876i	0.151200	−	0.261887i
$671$	9.68869	−	26.9587i	0.374028	−	1.04073i
$672$		0			0
$673$	35.7517	+	15.9177i	1.37813	+	0.613581i	0.956110	−	0.293007i	$-0.0946560\pi$
$673$	35.7517	+	15.9177i	1.37813	+	0.613581i	0.422016	+	0.906588i	$0.361323\pi$
$674$	2.01213	+	6.19270i	0.0775044	+	0.238534i
$675$		0			0
$676$	1.86742	+	1.35676i	0.0718239	+	0.0521831i
$677$	1.30488	−	12.4151i	0.0501507	−	0.477152i	−0.940407	−	0.340052i	$-0.889555\pi$
$677$	1.30488	−	12.4151i	0.0501507	−	0.477152i	0.990557	−	0.137100i	$-0.0437781\pi$
$678$		0			0
$679$	3.71786	+	0.790255i	0.142678	+	0.0303272i
$680$	−0.0627124	−	0.596668i	−0.00240491	−	0.0228812i
$681$		0			0
$682$	−6.19470	+	10.0035i	−0.237207	+	0.383054i
$683$	17.3888			0.665363			0.332681	−	0.943039i	$-0.392047\pi$
$683$	17.3888			0.665363			0.332681	+	0.943039i	$0.392047\pi$
$684$		0			0
$685$	6.99597	+	21.5314i	0.267302	+	0.822672i
$686$	4.94365	−	1.05081i	0.188750	−	0.0401199i
$687$		0			0
$688$	11.0712	−	4.92921i	0.422085	−	0.187924i
$689$	20.0002	+	22.2125i	0.761948	+	0.846229i
$690$		0			0
$691$	3.33887	+	1.48656i	0.127017	+	0.0565514i	0.469261	−	0.883060i	$-0.344520\pi$
$691$	3.33887	+	1.48656i	0.127017	+	0.0565514i	−0.342244	+	0.939611i	$0.611187\pi$
$692$	28.8156			1.09541
$693$		0			0
$694$	3.86751			0.146809
$695$	−21.7874	−	9.70037i	−0.826443	−	0.367956i
$696$		0			0
$697$	−0.888284	−	0.986539i	−0.0336461	−	0.0373678i
$698$	−11.7192	+	5.21772i	−0.443578	+	0.197494i
$699$		0			0
$700$	2.88877	−	0.614027i	0.109185	−	0.0232080i
$701$	1.72623	+	5.31280i	0.0651989	+	0.200662i	0.978349	−	0.206962i	$-0.0663576\pi$
$701$	1.72623	+	5.31280i	0.0651989	+	0.200662i	−0.913150	+	0.407624i	$0.866358\pi$
$702$		0			0
$703$	−20.0123			−0.754777
$704$	−0.00800281	+	0.00327111i	−0.000301617	+	0.000123285i
$705$		0			0
$706$	0.788839	+	7.50530i	0.0296884	+	0.282466i
$707$	−10.6387	−	2.26132i	−0.400109	−	0.0850458i
$708$		0			0
$709$	−1.44846	+	13.7812i	−0.0543980	+	0.517563i	0.933065	+	0.359709i	$0.117124\pi$
$709$	−1.44846	+	13.7812i	−0.0543980	+	0.517563i	−0.987463	+	0.157853i	$0.949543\pi$
$710$	1.99420	+	1.44887i	0.0748410	+	0.0543752i
$711$		0			0
$712$	2.37589	+	7.31224i	0.0890403	+	0.274038i
$713$	1.65382	+	0.736328i	0.0619360	+	0.0275757i
$714$		0			0
$715$	4.81499	+	16.5388i	0.180070	+	0.618515i
$716$	−21.2155	+	36.7464i	−0.792861	+	1.37328i
$717$		0			0
$718$	7.53231	−	8.36548i	0.281103	−	0.312197i
$719$	8.24222	−	25.3669i	0.307383	−	0.946027i	−0.671394	−	0.741100i	$-0.734304\pi$
$719$	8.24222	−	25.3669i	0.307383	−	0.946027i	0.978777	−	0.204927i	$-0.0656957\pi$
$720$		0			0
$721$	1.53968	+	1.11865i	0.0573408	+	0.0416605i
$722$	−9.36802	+	1.99123i	−0.348642	+	0.0741061i
$723$		0			0
$724$	−0.147345	−	1.40189i	−0.00547602	−	0.0521009i
$725$	−6.53222	+	11.3141i	−0.242600	+	0.420196i
$726$		0			0
$727$	11.3198	+	19.6065i	0.419830	+	0.727166i	0.995922	−	0.0902184i	$-0.0287565\pi$
$727$	11.3198	+	19.6065i	0.419830	+	0.727166i	−0.576092	+	0.817385i	$0.695423\pi$
$728$	4.10069	−	2.97933i	0.151982	−	0.110421i
$729$		0			0
$730$	0.112890	−	0.347441i	0.00417826	−	0.0128594i
$731$	0.137754	−	1.31064i	0.00509501	−	0.0484757i
$732$		0			0
$733$	14.7453	+	16.3763i	0.544628	+	0.604871i	0.951134	−	0.308777i	$-0.0999196\pi$
$733$	14.7453	+	16.3763i	0.544628	+	0.604871i	−0.406506	+	0.913648i	$0.633253\pi$
$734$	17.0067	+	3.61489i	0.627729	+	0.133428i
$735$		0			0
$736$	0.908646	+	1.57382i	0.0334932	+	0.0580118i
$737$	20.8716	−	21.7891i	0.768816	−	0.802612i
$738$		0			0
$739$	−39.3226	+	28.5696i	−1.44651	+	1.05095i	−0.459875	+	0.887984i	$0.652106\pi$
$739$	−39.3226	+	28.5696i	−1.44651	+	1.05095i	−0.986632	+	0.162965i	$0.947894\pi$
$740$	15.0848	−	16.7534i	0.554530	−	0.615868i
$741$		0			0
$742$	2.65984	−	1.18424i	0.0976459	−	0.0434748i
$743$	5.02834	−	2.23876i	0.184472	−	0.0821321i	−0.312422	−	0.949943i	$-0.601140\pi$
$743$	5.02834	−	2.23876i	0.184472	−	0.0821321i	0.496894	+	0.867811i	$0.334474\pi$
$744$		0			0
$745$	5.76706	−	6.40497i	0.211289	−	0.234660i
$746$	6.30937	−	4.58402i	0.231002	−	0.167833i
$747$		0			0
$748$	0.139105	−	1.01973i	0.00508618	−	0.0372851i
$749$	4.95973	+	8.59050i	0.181224	+	0.313890i
$750$		0			0
$751$	3.63935	+	0.773568i	0.132802	+	0.0282279i	0.273833	−	0.961777i	$-0.411708\pi$
$751$	3.63935	+	0.773568i	0.132802	+	0.0282279i	−0.141031	+	0.990005i	$0.545042\pi$
$752$	6.05766	+	6.72772i	0.220900	+	0.245335i
$753$		0			0
$754$	−1.04302	+	9.92368i	−0.0379846	+	0.361399i
$755$	−6.85556	+	21.0993i	−0.249499	+	0.767880i
$756$		0			0
$757$	24.6209	−	17.8881i	0.894862	−	0.650155i	−0.0422792	−	0.999106i	$-0.513462\pi$
$757$	24.6209	−	17.8881i	0.894862	−	0.650155i	0.937141	+	0.348951i	$0.113462\pi$
$758$	5.29781	+	9.17608i	0.192425	+	0.333290i
$759$		0			0
$760$	−3.01660	+	5.22491i	−0.109424	+	0.189527i
$761$	2.34771	+	22.3370i	0.0851044	+	0.809715i	0.950938	+	0.309382i	$0.100122\pi$
$761$	2.34771	+	22.3370i	0.0851044	+	0.809715i	−0.865833	+	0.500332i	$0.833211\pi$
$762$		0			0
$763$	5.12307	−	1.08894i	0.185468	−	0.0394224i
$764$	−20.1381	−	14.6312i	−0.728571	−	0.529338i
$765$		0			0
$766$	−2.42169	+	7.45320i	−0.0874992	+	0.269295i
$767$	−18.3187	+	20.3450i	−0.661451	+	0.734616i
$768$		0			0
$769$	−19.4798	+	33.7399i	−0.702458	+	1.21669i	0.265143	+	0.964209i	$0.414581\pi$
$769$	−19.4798	+	33.7399i	−0.702458	+	1.21669i	−0.967601	+	0.252484i	$0.918752\pi$
$770$	1.67712	+	0.0517669i	0.0604393	+	0.00186555i
$771$		0			0
$772$	−14.1739	−	6.31064i	−0.510131	−	0.227125i
$773$	−16.4951	−	50.7667i	−0.593287	−	1.82595i	−0.563074	−	0.826407i	$-0.690381\pi$
$773$	−16.4951	−	50.7667i	−0.593287	−	1.82595i	−0.0302135	−	0.999543i	$-0.509619\pi$
$774$		0			0
$775$	14.2792	+	10.3745i	0.512925	+	0.372662i
$776$	−1.53286	+	14.5842i	−0.0550265	+	0.523543i
$777$		0			0
$778$	−0.756630	−	0.160827i	−0.0271265	−	0.00576592i
$779$	1.39542	+	13.2765i	0.0499961	+	0.475681i
$780$		0			0
$781$	6.13706	+	7.25399i	0.219601	+	0.259568i
$782$	0.0391279			0.00139921
$783$		0			0
$784$	−3.65884	−	11.2607i	−0.130673	−	0.402169i
$785$	−22.7867	+	4.84346i	−0.813292	+	0.172871i
$786$		0			0
$787$	26.3397	−	11.7272i	0.938909	−	0.418029i	0.120531	−	0.992710i	$-0.461540\pi$
$787$	26.3397	−	11.7272i	0.938909	−	0.418029i	0.818378	+	0.574680i	$0.194874\pi$
$788$	−27.9396	−	31.0300i	−0.995306	−	1.10540i
$789$		0			0
$790$	−3.22697	−	1.43674i	−0.114810	−	0.0511169i
$791$	−1.69662			−0.0603250
$792$		0			0
$793$	−32.8211			−1.16551
$794$	−11.8420	−	5.27240i	−0.420257	−	0.187110i
$795$		0			0
$796$	21.9489	+	24.3768i	0.777959	+	0.864012i
$797$	30.3048	−	13.4926i	1.07345	−	0.477931i	0.207589	−	0.978216i	$-0.433438\pi$
$797$	30.3048	−	13.4926i	1.07345	−	0.477931i	0.865861	+	0.500285i	$0.166772\pi$
$798$		0			0
$799$	0.962949	−	0.204681i	0.0340667	−	0.00724110i
$800$	5.47516	+	16.8508i	0.193576	+	0.595766i
$801$		0			0
$802$	4.24208			0.149793
$803$	0.741397	−	1.19725i	0.0261633	−	0.0422499i
$804$		0			0
$805$	−0.0269852	−	0.256747i	−0.000951105	−	0.00904916i
$806$	13.1862	+	2.80281i	0.464464	+	0.0987248i
$807$		0			0
$808$	4.38630	−	41.7329i	0.154310	−	1.46816i
$809$	−19.8771	−	14.4416i	−0.698842	−	0.507739i	0.180713	−	0.983536i	$-0.442160\pi$
$809$	−19.8771	−	14.4416i	−0.698842	−	0.507739i	−0.879555	+	0.475797i	$0.842160\pi$
$810$		0			0
$811$	11.5446	+	35.5307i	0.405387	+	1.24765i	0.920572	+	0.390573i	$0.127723\pi$
$811$	11.5446	+	35.5307i	0.405387	+	1.24765i	−0.515185	+	0.857079i	$0.672277\pi$
$812$	−3.59347	−	1.59992i	−0.126106	−	0.0561461i
$813$		0			0
$814$	−17.7535	+	12.0798i	−0.622258	+	0.423395i
$815$	12.6930	−	21.9850i	0.444617	−	0.770099i
$816$		0			0
$817$	−8.86766	+	9.84854i	−0.310240	+	0.344557i
$818$	−5.67451	+	17.4644i	−0.198405	+	0.610627i
$819$		0			0
$820$	−12.1664	−	8.83939i	−0.424868	−	0.308685i
$821$	−11.9345	+	2.53676i	−0.416517	+	0.0885334i	−0.411403	−	0.911454i	$-0.634961\pi$
$821$	−11.9345	+	2.53676i	−0.416517	+	0.0885334i	−0.00511389	+	0.999987i	$0.501628\pi$
$822$		0			0
$823$	5.17192	+	49.2075i	0.180282	+	1.71527i	0.593667	+	0.804711i	$0.297680\pi$
$823$	5.17192	+	49.2075i	0.180282	+	1.71527i	−0.413385	+	0.910556i	$0.635654\pi$
$824$	−3.67133	+	6.35893i	−0.127897	+	0.221524i
$825$		0			0
$826$	1.33339	+	2.30950i	0.0463945	+	0.0803576i
$827$	−2.45628	+	1.78459i	−0.0854134	+	0.0620564i	−0.629672	−	0.776861i	$-0.716811\pi$
$827$	−2.45628	+	1.78459i	−0.0854134	+	0.0620564i	0.544259	+	0.838917i	$0.316811\pi$
$828$		0			0
$829$	−14.8814	+	45.8003i	−0.516853	+	1.59071i	0.263032	+	0.964787i	$0.415278\pi$
$829$	−14.8814	+	45.8003i	−0.516853	+	1.59071i	−0.779885	+	0.625923i	$0.784722\pi$
$830$	0.669137	−	6.36641i	0.0232261	−	0.220981i
$831$		0			0
$832$	0.00662795	+	0.00736109i	0.000229783	+	0.000255200i
$833$	−1.25942	−	0.267698i	−0.0436362	−	0.00927517i
$834$		0			0
$835$	−6.46955	−	11.2056i	−0.223888	−	0.387786i
$836$	−7.15915	+	7.47386i	−0.247605	+	0.258489i
$837$		0			0
$838$	−19.3376	+	14.0496i	−0.668007	+	0.485335i
$839$	−26.0547	+	28.9367i	−0.899509	+	0.999006i	0.100482	+	0.994939i	$0.467961\pi$
$839$	−26.0547	+	28.9367i	−0.899509	+	0.999006i	−0.999992	+	0.00406761i	$0.998705\pi$
$840$		0			0
$841$	−10.5965	+	4.71787i	−0.365397	+	0.162685i
$842$	4.66294	−	2.07608i	0.160696	−	0.0715463i
$843$		0			0
$844$	17.0803	−	18.9696i	0.587929	−	0.652961i
$845$	1.59153	−	1.15631i	0.0547503	−	0.0397784i
$846$		0			0
$847$	6.23162	+	1.73239i	0.214121	+	0.0595255i
$848$	−6.99812	−	12.1211i	−0.240316	−	0.416240i
$849$		0			0
$850$	0.373147	+	0.0793148i	0.0127988	+	0.00272048i
$851$	2.21071	+	2.45524i	0.0757820	+	0.0841645i
$852$		0			0
$853$	3.86864	−	36.8076i	0.132460	−	1.26027i	−0.703188	−	0.711004i	$-0.748241\pi$
$853$	3.86864	−	36.8076i	0.132460	−	1.26027i	0.835648	−	0.549265i	$-0.185092\pi$
$854$	−0.987956	+	3.04062i	−0.0338072	+	0.104048i
$855$		0			0
$856$	−30.9617	+	22.4950i	−1.05825	+	0.768864i
$857$	−14.2713	−	24.7186i	−0.487499	−	0.844372i	0.512398	−	0.858748i	$-0.328757\pi$
$857$	−14.2713	−	24.7186i	−0.487499	−	0.844372i	−0.999897	+	0.0143758i	$0.995424\pi$
$858$		0			0
$859$	−19.1707	+	33.2046i	−0.654094	+	1.13292i	0.328025	+	0.944669i	$0.393617\pi$
$859$	−19.1707	+	33.2046i	−0.654094	+	1.13292i	−0.982120	+	0.188256i	$0.939717\pi$
$860$	−1.56051	−	14.8472i	−0.0532129	−	0.506287i
$861$		0			0
$862$	18.7492	−	3.98526i	0.638599	−	0.135738i
$863$	−22.6247	−	16.4378i	−0.770153	−	0.559549i	0.131855	−	0.991269i	$-0.457907\pi$
$863$	−22.6247	−	16.4378i	−0.770153	−	0.559549i	−0.902008	+	0.431720i	$0.857907\pi$
$864$		0			0
$865$	7.58897	−	23.3565i	0.258033	−	0.794143i
$866$	−10.1454	+	11.2676i	−0.344755	+	0.382890i
$867$		0			0
$868$	−2.65712	+	4.60226i	−0.0901884	+	0.156211i
$869$	−10.7636	−	8.33950i	−0.365132	−	0.282898i
$870$		0			0
$871$	−31.5806	−	14.0606i	−1.07007	−	0.476426i
$872$	6.24437	+	19.2182i	0.211461	+	0.650810i
$873$		0			0
$874$	−0.318327	−	0.231278i	−0.0107676	−	0.00782309i
$875$	0.683124	−	6.49949i	0.0230938	−	0.219723i
$876$		0			0
$877$	20.5799	+	4.37439i	0.694934	+	0.147713i	0.541818	−	0.840496i	$-0.317736\pi$
$877$	20.5799	+	4.37439i	0.694934	+	0.147713i	0.153115	+	0.988208i	$0.451069\pi$
$878$	2.25815	+	21.4849i	0.0762089	+	0.725079i
$879$		0			0
$880$	−0.595237	−	8.04399i	−0.0200654	−	0.271163i
$881$	17.0076			0.573000			0.286500	−	0.958080i	$-0.407508\pi$
$881$	17.0076			0.573000			0.286500	+	0.958080i	$0.407508\pi$
$882$		0			0
$883$	2.08724	+	6.42388i	0.0702414	+	0.216181i	0.980015	−	0.198924i	$-0.0637448\pi$
$883$	2.08724	+	6.42388i	0.0702414	+	0.216181i	−0.909773	+	0.415105i	$0.863745\pi$
$884$	−1.15338	+	0.245158i	−0.0387923	+	0.00824555i
$885$		0			0
$886$	−4.91135	+	2.18667i	−0.165000	+	0.0734627i
$887$	22.6495	+	25.1548i	0.760496	+	0.844617i	0.991738	−	0.128280i	$-0.0409455\pi$
$887$	22.6495	+	25.1548i	0.760496	+	0.844617i	−0.231242	+	0.972896i	$0.574279\pi$
$888$		0			0
$889$	0.689954	+	0.307187i	0.0231403	+	0.0103027i
$890$	2.91604			0.0977459
$891$		0			0
$892$	−4.01188			−0.134328
$893$	−9.04396	−	4.02663i	−0.302645	−	0.134746i
$894$		0			0
$895$	24.1973	+	26.8738i	0.808826	+	0.898293i
$896$	−6.07682	+	2.70558i	−0.203012	+	0.0903870i
$897$		0			0
$898$	22.7019	−	4.82543i	0.757571	−	0.161027i
$899$	−7.26448	−	22.3578i	−0.242284	−	0.745674i
$900$		0			0
$901$	−1.52201			−0.0507054
$902$	9.25186	+	10.9357i	0.308053	+	0.364118i
$903$		0			0
$904$	−0.684227	−	6.50999i	−0.0227571	−	0.216519i
$905$	−1.17511	−	0.249776i	−0.0390618	−	0.00830285i
$906$		0			0
$907$	−2.94213	+	27.9925i	−0.0976918	+	0.929475i	0.830411	+	0.557151i	$0.188106\pi$
$907$	−2.94213	+	27.9925i	−0.0976918	+	0.929475i	−0.928103	+	0.372324i	$0.878561\pi$
$908$	20.9066	+	15.1895i	0.693809	+	0.504082i
$909$		0			0
$910$	−0.594061	−	1.82833i	−0.0196929	−	0.0606086i
$911$	7.47517	+	3.32816i	0.247663	+	0.110267i	0.526814	−	0.849980i	$-0.323386\pi$
$911$	7.47517	+	3.32816i	0.247663	+	0.110267i	−0.279151	+	0.960247i	$0.590053\pi$
$912$		0			0
$913$	8.34570	−	23.2218i	0.276202	−	0.768530i
$914$	7.45467	−	12.9119i	0.246579	−	0.427087i
$915$		0			0
$916$	−3.54630	+	3.93857i	−0.117173	+	0.130134i
$917$	1.15161	−	3.54430i	0.0380296	−	0.117043i
$918$		0			0
$919$	−9.43023	−	6.85146i	−0.311075	−	0.226009i	0.421283	−	0.906929i	$-0.361580\pi$
$919$	−9.43023	−	6.85146i	−0.311075	−	0.226009i	−0.732357	+	0.680920i	$0.761580\pi$
$920$	0.974263	−	0.207086i	0.0321205	−	0.00682742i
$921$		0			0
$922$	−1.88760	−	17.9593i	−0.0621647	−	0.591458i
$923$	5.44317	−	9.42785i	0.179164	−	0.310322i
$924$		0			0
$925$	16.1057	+	27.8959i	0.529552	+	0.917211i
$926$	5.53241	−	4.01953i	0.181806	−	0.132090i
$927$		0			0
$928$	7.29242	−	22.4438i	0.239385	−	0.736753i
$929$	−3.32120	+	31.5991i	−0.108965	+	1.03673i	0.794264	+	0.607573i	$0.207857\pi$
$929$	−3.32120	+	31.5991i	−0.108965	+	1.03673i	−0.903229	+	0.429159i	$0.858810\pi$
$930$		0			0
$931$	8.66375	+	9.62206i	0.283943	+	0.315350i
$932$	6.76391	+	1.43771i	0.221559	+	0.0470939i
$933$		0			0
$934$	−9.28136	−	16.0758i	−0.303695	−	0.526016i
$935$	−0.789907	−	0.381311i	−0.0258327	−	0.0124702i
$936$		0			0
$937$	34.9908	−	25.4223i	1.14310	−	0.830510i	0.155551	−	0.987828i	$-0.450285\pi$
$937$	34.9908	−	25.4223i	1.14310	−	0.830510i	0.987548	+	0.157318i	$0.0502847\pi$
$938$	−2.25322	+	2.50245i	−0.0735702	+	0.0817080i
$939$		0			0
$940$	10.1881	−	4.53602i	0.332298	−	0.147949i
$941$	−11.1472	+	4.96303i	−0.363387	+	0.161790i	−0.580304	−	0.814400i	$-0.697066\pi$
$941$	−11.1472	+	4.96303i	−0.363387	+	0.161790i	0.216918	+	0.976190i	$0.430400\pi$
$942$		0			0
$943$	1.47470	−	1.63782i	0.0480229	−	0.0533349i
$944$	10.3712	−	7.53513i	0.337554	−	0.245248i
$945$		0			0
$946$	−1.92201	+	14.0896i	−0.0624898	+	0.458092i
$947$	−15.5930	−	27.0079i	−0.506706	−	0.877640i	−0.999970	−	0.00776032i	$-0.997530\pi$
$947$	−15.5930	−	27.0079i	−0.506706	−	0.877640i	0.493264	−	0.869879i	$-0.335804\pi$
$948$		0			0
$949$	−1.57816	−	0.335448i	−0.0512291	−	0.0108891i
$950$	−2.56694	−	2.85088i	−0.0832825	−	0.0924946i
$951$		0			0
$952$	−0.0269790	+	0.256688i	−0.000874395	+	0.00831931i
$953$	−5.66371	+	17.4311i	−0.183466	+	0.564649i	−0.999919	−	0.0127629i	$-0.995937\pi$
$953$	−5.66371	+	17.4311i	−0.183466	+	0.564649i	0.816453	+	0.577412i	$0.195937\pi$
$954$		0			0
$955$	−17.1629	+	12.4696i	−0.555378	+	0.403506i
$956$	−12.0601	−	20.8887i	−0.390050	−	0.675587i
$957$		0			0
$958$	6.72223	−	11.6432i	0.217185	−	0.376176i
$959$	−1.01806	−	9.68618i	−0.0328748	−	0.312783i
$960$		0			0
$961$	−0.743284	+	0.157990i	−0.0239769	+	0.00509645i
$962$	19.9037	+	14.4609i	0.641723	+	0.466239i
$963$		0			0
$964$	−6.82455	+	21.0038i	−0.219804	+	0.676487i
$965$	−8.84796	+	9.82666i	−0.284826	+	0.316331i
$966$		0			0
$967$	−10.4254	+	18.0573i	−0.335258	+	0.580683i	−0.983534	−	0.180722i	$-0.942157\pi$
$967$	−10.4254	+	18.0573i	−0.335258	+	0.580683i	0.648277	+	0.761405i	$0.275490\pi$
$968$	−4.13408	+	24.6095i	−0.132874	+	0.790979i
$969$		0			0
$970$	5.08099	+	2.26220i	0.163141	+	0.0726349i
$971$	−8.79427	−	27.0660i	−0.282222	−	0.868589i	−0.987218	−	0.159378i	$-0.949051\pi$
$971$	−8.79427	−	27.0660i	−0.282222	−	0.868589i	0.704996	−	0.709211i	$-0.250949\pi$
$972$		0			0
$973$	8.30053	+	6.03069i	0.266103	+	0.193335i
$974$	−0.149791	+	1.42517i	−0.00479962	+	0.0456653i
$975$		0			0
$976$	15.0330	+	3.19536i	0.481194	+	0.102281i
$977$	2.32671	+	22.1371i	0.0744380	+	0.708230i	0.966561	+	0.256437i	$0.0825487\pi$
$977$	2.32671	+	22.1371i	0.0744380	+	0.708230i	−0.892123	+	0.451793i	$0.850785\pi$
$978$		0			0
$979$	10.9176	+	2.67514i	0.348927	+	0.0854979i
$980$	−14.5857			−0.465924
$981$		0			0
$982$	1.85302	+	5.70301i	0.0591322	+	0.181990i
$983$	22.5888	−	4.80140i	0.720471	−	0.153141i	0.166937	−	0.985968i	$-0.446612\pi$
$983$	22.5888	−	4.80140i	0.720471	−	0.153141i	0.553534	+	0.832827i	$0.313279\pi$
$984$		0			0
$985$	−32.5096	+	14.4742i	−1.03584	+	0.461186i
$986$	−0.339986	−	0.377593i	−0.0108274	−	0.0120250i
$987$		0			0
$988$	10.8324	+	4.82291i	0.344626	+	0.153437i
$989$	2.18787			0.0695703
$990$		0			0
$991$	−6.16408			−0.195809			−0.0979043	−	0.995196i	$-0.531214\pi$
$991$	−6.16408			−0.195809			−0.0979043	+	0.995196i	$0.531214\pi$
$992$	−29.1257	−	12.9676i	−0.924741	−	0.411721i
$993$		0			0
$994$	−0.709570	−	0.788057i	−0.0225062	−	0.0249956i
$995$	25.5391	−	11.3707i	0.809643	−	0.360476i
$996$		0			0
$997$	−24.8248	+	5.27667i	−0.786209	+	0.167114i	−0.583487	−	0.812122i	$-0.698312\pi$
$997$	−24.8248	+	5.27667i	−0.786209	+	0.167114i	−0.202722	+	0.979236i	$0.564979\pi$
$998$	2.47504	+	7.61739i	0.0783461	+	0.241124i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.l.190.6		96
3.2	odd	2	inner	891.2.n.l.190.7		96
9.2	odd	6	inner	891.2.n.l.784.6		96
9.4	even	3		891.2.f.g.487.7	yes	48
9.5	odd	6		891.2.f.g.487.6	✓	48
9.7	even	3	inner	891.2.n.l.784.7		96
11.4	even	5	inner	891.2.n.l.433.7		96
33.26	odd	10	inner	891.2.n.l.433.6		96
99.4	even	15		891.2.f.g.730.7	yes	48
99.13	odd	30		9801.2.a.cq.1.15		24
99.31	even	15		9801.2.a.cr.1.10		24
99.59	odd	30		891.2.f.g.730.6	yes	48
99.68	even	30		9801.2.a.cq.1.10		24
99.70	even	15	inner	891.2.n.l.136.6		96
99.86	odd	30		9801.2.a.cr.1.15		24
99.92	odd	30	inner	891.2.n.l.136.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.g.487.6	✓	48	9.5	odd	6
891.2.f.g.487.7	yes	48	9.4	even	3
891.2.f.g.730.6	yes	48	99.59	odd	30
891.2.f.g.730.7	yes	48	99.4	even	15
891.2.n.l.136.6		96	99.70	even	15	inner
891.2.n.l.136.7		96	99.92	odd	30	inner
891.2.n.l.190.6		96	1.1	even	1	trivial
891.2.n.l.190.7		96	3.2	odd	2	inner
891.2.n.l.433.6		96	33.26	odd	10	inner
891.2.n.l.433.7		96	11.4	even	5	inner
891.2.n.l.784.6		96	9.2	odd	6	inner
891.2.n.l.784.7		96	9.7	even	3	inner
9801.2.a.cq.1.10		24	99.68	even	30
9801.2.a.cq.1.15		24	99.13	odd	30
9801.2.a.cr.1.10		24	99.31	even	15
9801.2.a.cr.1.15		24	99.86	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.575085 - 0.256045i) q^{2} +(-1.07310 - 1.19179i) q^{4} +(-1.24862 + 0.555922i) q^{5} +(0.575145 - 0.122251i) q^{7} +(0.701028 + 2.15754i) q^{8} +0.860404 q^{10} +(3.22133 + 0.789325i) q^{11} +(-0.397199 - 3.77909i) q^{13} +(-0.362059 - 0.0769581i) q^{14} +(-0.185992 + 1.76960i) q^{16} +(0.156539 + 0.113732i) q^{17} +(-0.601281 - 1.85055i) q^{19} +(2.00243 + 0.891541i) q^{20} +(-1.65044 - 1.27873i) q^{22} +(-0.160616 + 0.278195i) q^{23} +(-2.09565 + 2.32745i) q^{25} +(-0.739193 + 2.27500i) q^{26} +(-0.762884 - 0.554268i) q^{28} +(4.08026 - 0.867285i) q^{29} +(-0.589080 - 5.60472i) q^{31} +(2.82863 - 4.89933i) q^{32} +(-0.0609029 - 0.105487i) q^{34} +(-0.650176 + 0.472381i) q^{35} +(3.17822 - 9.78156i) q^{37} +(-0.128036 + 1.21818i) q^{38} +(-2.07474 - 2.30423i) q^{40} +(-6.71088 - 1.42644i) q^{41} +(-3.40544 - 5.89840i) q^{43} +(-2.51609 - 4.68619i) q^{44} +(0.163598 - 0.118861i) q^{46} +(3.40443 - 3.78100i) q^{47} +(-6.07897 + 2.70653i) q^{49} +(1.80111 - 0.801905i) q^{50} +(-4.07767 + 4.52871i) q^{52} +(-6.36368 + 4.62348i) q^{53} +(-4.46102 + 0.805240i) q^{55} +(0.666954 + 1.15520i) q^{56} +(-2.56856 - 0.545964i) q^{58} +(-4.82083 - 5.35408i) q^{59} +(0.902848 - 8.59003i) q^{61} +(-1.09629 + 3.37402i) q^{62} +(-0.00210888 + 0.00153219i) q^{64} +(2.59683 + 4.49784i) q^{65} +(4.54870 - 7.87858i) q^{67} +(-0.0324361 - 0.308608i) q^{68} +(0.494857 - 0.105185i) q^{70} +(2.31775 + 1.68394i) q^{71} +(0.131206 - 0.403812i) q^{73} +(-4.33226 + 4.81146i) q^{74} +(-1.56025 + 2.70242i) q^{76} +(1.94923 + 0.0601658i) q^{77} +(-3.75053 - 1.66984i) q^{79} +(-0.751525 - 2.31296i) q^{80} +(3.49410 + 2.53861i) q^{82} +(0.777701 - 7.39933i) q^{83} +(-0.258684 - 0.0549851i) q^{85} +(0.448167 + 4.26403i) q^{86} +(0.555241 + 7.50349i) q^{88} +3.38915 q^{89} +(-0.690444 - 2.12497i) q^{91} +(0.503908 - 0.107109i) q^{92} +(-2.92594 + 1.30271i) q^{94} +(1.77953 + 1.97637i) q^{95} +(5.90535 + 2.62923i) q^{97} +4.18892 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52}+ \cdots + 66 q^{97}+O(q^{100}) \) 96 * q + 8 * q^4 + 14 * q^7 + 64 * q^10 + 14 * q^13 + 4 * q^16 - 16 * q^19 - 16 * q^22 + 20 * q^25 - 36 * q^28 + 4 * q^31 - 84 * q^34 - 24 * q^37 + 106 * q^40 - 84 * q^43 - 76 * q^46 + 54 * q^49 - 52 * q^52 - 72 * q^55 + 10 * q^58 + 6 * q^61 - 104 * q^64 - 76 * q^67 + 8 * q^70 - 92 * q^73 - 204 * q^76 + 102 * q^79 + 24 * q^82 - 54 * q^85 + 44 * q^91 + 118 * q^94 + 66 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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