LMFDB - Embedded newform 891.2.n.g.460.2

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:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			460.2
Character	$\chi$	$=$	891.460
Dual form			891.2.n.g.676.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.448085 - 0.497649i) q^{2} +(0.162183 - 1.54307i) q^{4} +(1.84993 - 2.05455i) q^{5} +(1.37990 - 0.614370i) q^{7} +(-1.92410 + 1.39794i) q^{8} -1.85137 q^{10} +(-2.65125 - 1.99271i) q^{11} +(-1.45264 + 0.308769i) q^{13} +(-0.924052 - 0.411414i) q^{14} +(-1.47748 - 0.314048i) q^{16} +(-1.46138 - 4.49766i) q^{17} +(2.87328 - 2.08756i) q^{19} +(-2.87028 - 3.18777i) q^{20} +(0.196315 + 2.21229i) q^{22} +(1.04751 + 1.81434i) q^{23} +(-0.276313 - 2.62894i) q^{25} +(0.804567 + 0.584552i) q^{26} +(-0.724217 - 2.22891i) q^{28} +(-7.17542 + 3.19470i) q^{29} +(8.57593 - 1.82287i) q^{31} +(2.88407 + 4.99535i) q^{32} +(-1.58343 + 2.74259i) q^{34} +(1.29045 - 3.97161i) q^{35} +(4.16960 + 3.02939i) q^{37} +(-2.32634 - 0.494480i) q^{38} +(-0.687303 + 6.53925i) q^{40} +(-6.41924 - 2.85803i) q^{41} +(-1.45808 + 2.52546i) q^{43} +(-3.50487 + 3.76786i) q^{44} +(0.433531 - 1.33427i) q^{46} +(0.227425 + 2.16380i) q^{47} +(-3.15725 + 3.50648i) q^{49} +(-1.18448 + 1.31550i) q^{50} +(0.240857 + 2.29160i) q^{52} +(4.13417 - 12.7237i) q^{53} +(-8.99874 + 1.76076i) q^{55} +(-1.79621 + 3.11112i) q^{56} +(4.80504 + 2.13934i) q^{58} +(-0.702544 + 6.68426i) q^{59} +(10.1381 + 2.15492i) q^{61} +(-4.74990 - 3.45100i) q^{62} +(0.260092 - 0.800479i) q^{64} +(-2.05290 + 3.55573i) q^{65} +(-6.01970 - 10.4264i) q^{67} +(-7.17720 + 1.52556i) q^{68} +(-2.55470 + 1.13743i) q^{70} +(-3.34410 - 10.2921i) q^{71} +(3.63900 + 2.64389i) q^{73} +(-0.360762 - 3.43242i) q^{74} +(-2.75524 - 4.77222i) q^{76} +(-4.88271 - 1.12089i) q^{77} +(-10.3224 - 11.4642i) q^{79} +(-3.37845 + 2.45459i) q^{80} +(1.45407 + 4.47517i) q^{82} +(3.27510 + 0.696143i) q^{83} +(-11.9441 - 5.31787i) q^{85} +(1.91014 - 0.406012i) q^{86} +(7.88694 + 0.127887i) q^{88} +10.6583 q^{89} +(-1.81480 + 1.31853i) q^{91} +(2.96954 - 1.32212i) q^{92} +(0.974908 - 1.08275i) q^{94} +(1.02636 - 9.76513i) q^{95} +(1.48572 + 1.65006i) q^{97} +3.15971 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{4} - 8 q^{7} - 24 q^{10} - 8 q^{13} + 2 q^{16} + 20 q^{19} + 24 q^{22} + 16 q^{25} - 60 q^{28} + 6 q^{31} - 32 q^{34} + 24 q^{37} + 40 q^{40} + 80 q^{43} - 24 q^{46} - 40 q^{49} - 12 q^{52}+ \cdots + 46 q^{94}+O(q^{100}) $ 32 * q - 2 * q^4 - 8 * q^7 - 24 * q^10 - 8 * q^13 + 2 * q^16 + 20 * q^19 + 24 * q^22 + 16 * q^25 - 60 * q^28 + 6 * q^31 - 32 * q^34 + 24 * q^37 + 40 * q^40 + 80 * q^43 - 24 * q^46 - 40 * q^49 - 12 * q^52 + 112 * q^55 + 50 * q^58 + 6 * q^61 + 12 * q^64 - 64 * q^67 - 74 * q^70 - 64 * q^73 - 52 * q^76 + 4 * q^79 + 8 * q^82 - 70 * q^85 - 56 * q^88 - 188 * q^91 + 46 * q^94

Character values

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

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.448085	−	0.497649i	−0.316844	−	0.351891i	0.563594	−	0.826052i	$-0.309418\pi$
$2$	−0.448085	−	0.497649i	−0.316844	−	0.351891i	−0.880438	+	0.474161i	$0.842752\pi$
$3$		0			0
$3$		0			0
$4$	0.162183	−	1.54307i	0.0810914	−	0.771533i
$5$	1.84993	−	2.05455i	0.827313	−	0.918824i	−0.170471	−	0.985363i	$-0.554529\pi$
$5$	1.84993	−	2.05455i	0.827313	−	0.918824i	0.997784	+	0.0665386i	$0.0211955\pi$
$6$		0			0
$7$	1.37990	−	0.614370i	0.521552	−	0.232210i	−0.129037	−	0.991640i	$-0.541189\pi$
$7$	1.37990	−	0.614370i	0.521552	−	0.232210i	0.650589	+	0.759430i	$0.274522\pi$
$8$	−1.92410	+	1.39794i	−0.680271	+	0.494246i
$9$		0			0
$10$	−1.85137			−0.585455
$11$	−2.65125	−	1.99271i	−0.799381	−	0.600824i
$11$	−2.65125	−	1.99271i	−0.799381	−	0.600824i
$12$		0			0
$13$	−1.45264	+	0.308769i	−0.402891	+	0.0856371i	−0.404900	−	0.914361i	$-0.632694\pi$
$13$	−1.45264	+	0.308769i	−0.402891	+	0.0856371i	0.00200934	+	0.999998i	$0.499360\pi$
$14$	−0.924052	−	0.411414i	−0.246963	−	0.109955i
$15$		0			0
$16$	−1.47748	−	0.314048i	−0.369369	−	0.0785119i
$17$	−1.46138	−	4.49766i	−0.354436	−	1.09084i	−0.956336	−	0.292271i	$-0.905589\pi$
$17$	−1.46138	−	4.49766i	−0.354436	−	1.09084i	0.601899	−	0.798572i	$-0.294411\pi$
$18$		0			0
$19$	2.87328	−	2.08756i	0.659175	−	0.478919i	−0.207209	−	0.978297i	$-0.566438\pi$
$19$	2.87328	−	2.08756i	0.659175	−	0.478919i	0.866384	+	0.499378i	$0.166438\pi$
$20$	−2.87028	−	3.18777i	−0.641815	−	0.712808i
$21$		0			0
$22$	0.196315	+	2.21229i	0.0418544	+	0.471663i
$23$	1.04751	+	1.81434i	0.218421	+	0.378316i	0.954325	−	0.298769i	$-0.0965760\pi$
$23$	1.04751	+	1.81434i	0.218421	+	0.378316i	−0.735904	+	0.677086i	$0.763243\pi$
$24$		0			0
$25$	−0.276313	−	2.62894i	−0.0552626	−	0.525788i
$26$	0.804567	+	0.584552i	0.157788	+	0.114640i
$27$		0			0
$28$	−0.724217	−	2.22891i	−0.136864	−	0.421225i
$29$	−7.17542	+	3.19470i	−1.33244	+	0.593241i	−0.944521	−	0.328451i	$-0.893473\pi$
$29$	−7.17542	+	3.19470i	−1.33244	+	0.593241i	−0.387921	+	0.921693i	$0.626807\pi$
$30$		0			0
$31$	8.57593	−	1.82287i	1.54028	−	0.327397i	0.641962	−	0.766737i	$-0.278121\pi$
$31$	8.57593	−	1.82287i	1.54028	−	0.327397i	0.898321	+	0.439339i	$0.144787\pi$
$32$	2.88407	+	4.99535i	0.509836	+	0.883061i
$33$		0			0
$34$	−1.58343	+	2.74259i	−0.271557	+	0.470350i
$35$	1.29045	−	3.97161i	0.218127	−	0.671325i
$36$		0			0
$37$	4.16960	+	3.02939i	0.685478	+	0.498029i	0.875170	−	0.483815i	$-0.160749\pi$
$37$	4.16960	+	3.02939i	0.685478	+	0.498029i	−0.189693	+	0.981844i	$0.560749\pi$
$38$	−2.32634	−	0.494480i	−0.377383	−	0.0802152i
$39$		0			0
$40$	−0.687303	+	6.53925i	−0.108672	+	1.03395i
$41$	−6.41924	−	2.85803i	−1.00252	−	0.446350i	−0.161218	−	0.986919i	$-0.551542\pi$
$41$	−6.41924	−	2.85803i	−1.00252	−	0.446350i	−0.841299	+	0.540569i	$0.818209\pi$
$42$		0			0
$43$	−1.45808	+	2.52546i	−0.222355	+	0.385129i	−0.955522	−	0.294918i	$-0.904708\pi$
$43$	−1.45808	+	2.52546i	−0.222355	+	0.385129i	0.733168	+	0.680048i	$0.238041\pi$
$44$	−3.50487	+	3.76786i	−0.528379	+	0.568027i
$45$		0			0
$46$	0.433531	−	1.33427i	0.0639207	−	0.196728i
$47$	0.227425	+	2.16380i	0.0331733	+	0.315623i	0.998508	+	0.0546074i	$0.0173907\pi$
$47$	0.227425	+	2.16380i	0.0331733	+	0.315623i	−0.965335	+	0.261016i	$0.915943\pi$
$48$		0			0
$49$	−3.15725	+	3.50648i	−0.451036	+	0.500926i
$50$	−1.18448	+	1.31550i	−0.167511	+	0.186039i
$51$		0			0
$52$	0.240857	+	2.29160i	0.0334009	+	0.317788i
$53$	4.13417	−	12.7237i	0.567872	−	1.74773i	−0.0913880	−	0.995815i	$-0.529130\pi$
$53$	4.13417	−	12.7237i	0.567872	−	1.74773i	0.659260	−	0.751915i	$-0.270870\pi$
$54$		0			0
$55$	−8.99874	+	1.76076i	−1.21339	+	0.237421i
$56$	−1.79621	+	3.11112i	−0.240028	+	0.415741i
$57$		0			0
$58$	4.80504	+	2.13934i	0.630932	+	0.280909i
$59$	−0.702544	+	6.68426i	−0.0914634	+	0.870216i	0.848558	+	0.529102i	$0.177471\pi$
$59$	−0.702544	+	6.68426i	−0.0914634	+	0.870216i	−0.940022	+	0.341115i	$0.889196\pi$
$60$		0			0
$61$	10.1381	+	2.15492i	1.29805	+	0.275909i	0.804575	−	0.593851i	$-0.202393\pi$
$61$	10.1381	+	2.15492i	1.29805	+	0.275909i	0.493475	+	0.869760i	$0.335726\pi$
$62$	−4.74990	−	3.45100i	−0.603238	−	0.438278i
$63$		0			0
$64$	0.260092	−	0.800479i	0.0325114	−	0.100060i
$65$	−2.05290	+	3.55573i	−0.254631	+	0.441035i
$66$		0			0
$67$	−6.01970	−	10.4264i	−0.735423	−	1.27379i	−0.954538	−	0.298091i	$-0.903650\pi$
$67$	−6.01970	−	10.4264i	−0.735423	−	1.27379i	0.219115	−	0.975699i	$-0.429683\pi$
$68$	−7.17720	+	1.52556i	−0.870363	+	0.185001i
$69$		0			0
$70$	−2.55470	+	1.13743i	−0.305345	+	0.135948i
$71$	−3.34410	−	10.2921i	−0.396872	−	1.22145i	−0.927494	−	0.373838i	$-0.878042\pi$
$71$	−3.34410	−	10.2921i	−0.396872	−	1.22145i	0.530622	−	0.847608i	$-0.321958\pi$
$72$		0			0
$73$	3.63900	+	2.64389i	0.425913	+	0.309444i	0.780013	−	0.625764i	$-0.215213\pi$
$73$	3.63900	+	2.64389i	0.425913	+	0.309444i	−0.354099	+	0.935208i	$0.615213\pi$
$74$	−0.360762	−	3.43242i	−0.0419377	−	0.399011i
$75$		0			0
$76$	−2.75524	−	4.77222i	−0.316048	−	0.547411i
$77$	−4.88271	−	1.12089i	−0.556436	−	0.127737i
$78$		0			0
$79$	−10.3224	−	11.4642i	−1.16136	−	1.28983i	−0.949940	−	0.312432i	$-0.898856\pi$
$79$	−10.3224	−	11.4642i	−1.16136	−	1.28983i	−0.211425	−	0.977394i	$-0.567810\pi$
$80$	−3.37845	+	2.45459i	−0.377723	+	0.274432i
$81$		0			0
$82$	1.45407	+	4.47517i	0.160575	+	0.494200i
$83$	3.27510	+	0.696143i	0.359488	+	0.0764116i	0.384115	−	0.923285i	$-0.374506\pi$
$83$	3.27510	+	0.696143i	0.359488	+	0.0764116i	−0.0246270	+	0.999697i	$0.507840\pi$
$84$		0			0
$85$	−11.9441	−	5.31787i	−1.29552	−	0.576804i
$86$	1.91014	−	0.406012i	0.205975	−	0.0437814i
$87$		0			0
$88$	7.88694	+	0.127887i	0.840751	+	0.0136328i
$89$	10.6583			1.12978			0.564888	−	0.825167i	$-0.308919\pi$
$89$	10.6583			1.12978			0.564888	+	0.825167i	$0.308919\pi$
$90$		0			0
$91$	−1.81480	+	1.31853i	−0.190243	+	0.138219i
$92$	2.96954	−	1.32212i	0.309596	−	0.137841i
$93$		0			0
$94$	0.974908	−	1.08275i	0.100554	−	0.111677i
$95$	1.02636	−	9.76513i	0.105302	−	1.00188i
$96$		0			0
$97$	1.48572	+	1.65006i	0.150852	+	0.167538i	0.813835	−	0.581097i	$-0.197376\pi$
$97$	1.48572	+	1.65006i	0.150852	+	0.167538i	−0.662982	+	0.748635i	$0.730710\pi$
$98$	3.15971			0.319179
$99$		0			0
$100$	−4.10144			−0.410144
$101$	0.325123	+	0.361085i	0.0323509	+	0.0359293i	0.759103	−	0.650970i	$-0.225638\pi$
$101$	0.325123	+	0.361085i	0.0323509	+	0.0359293i	−0.726752	+	0.686900i	$0.758971\pi$
$102$		0			0
$103$	0.668220	−	6.35769i	0.0658417	−	0.626441i	−0.910989	−	0.412430i	$-0.864680\pi$
$103$	0.668220	−	6.35769i	0.0658417	−	0.626441i	0.976831	−	0.214012i	$-0.0686531\pi$
$104$	2.36339	−	2.62481i	0.231749	−	0.257384i
$105$		0			0
$106$	−8.18438	+	3.64392i	−0.794937	+	0.353929i
$107$	−9.78725	+	7.11085i	−0.946169	+	0.687432i	−0.949898	−	0.312561i	$-0.898813\pi$
$107$	−9.78725	+	7.11085i	−0.946169	+	0.687432i	0.00372856	+	0.999993i	$0.498813\pi$
$108$		0			0
$109$	−4.73854			−0.453870			−0.226935	−	0.973910i	$-0.572871\pi$
$109$	−4.73854			−0.453870			−0.226935	+	0.973910i	$0.572871\pi$
$110$	4.90844	+	3.68925i	0.468002	+	0.351756i
$111$		0			0
$112$	−2.23171	+	0.474364i	−0.210877	+	0.0448232i
$113$	16.7903	+	7.47551i	1.57950	+	0.703237i	0.994196	−	0.107581i	$-0.0343104\pi$
$113$	16.7903	+	7.47551i	1.57950	+	0.703237i	0.585299	+	0.810817i	$0.300977\pi$
$114$		0			0
$115$	5.66548	+	1.20424i	0.528309	+	0.112296i
$116$	3.76591	+	11.5903i	0.349656	+	1.07613i
$117$		0			0
$118$	3.64121	−	2.64550i	0.335201	−	0.243538i
$119$	−4.77978	−	5.30848i	−0.438162	−	0.486628i
$120$		0			0
$121$	3.05822	+	10.5663i	0.278020	+	0.960575i
$122$	−3.47034	−	6.01080i	−0.314190	−	0.544192i
$123$		0			0
$124$	−1.42194	−	13.5289i	−0.127694	−	1.21493i
$125$	5.27088	+	3.82952i	0.471442	+	0.342523i
$126$		0			0
$127$	−6.90430	−	21.2493i	−0.612658	−	1.88557i	−0.431501	−	0.902112i	$-0.642016\pi$
$127$	−6.90430	−	21.2493i	−0.612658	−	1.88557i	−0.181156	−	0.983454i	$-0.557984\pi$
$128$	10.0240	−	4.46297i	0.886005	−	0.394475i
$129$		0			0
$130$	2.68938	−	0.571646i	0.235874	−	0.0501367i
$131$	−1.98522	−	3.43851i	−0.173450	−	0.300424i	0.766174	−	0.642633i	$-0.222158\pi$
$131$	−1.98522	−	3.43851i	−0.173450	−	0.300424i	−0.939624	+	0.342209i	$0.888825\pi$
$132$		0			0
$133$	2.68229	−	4.64587i	0.232584	−	0.402848i
$134$	−2.49136	+	7.66762i	−0.215221	+	0.662381i
$135$		0			0
$136$	9.09929	+	6.61102i	0.780258	+	0.566890i
$137$	5.86012	+	1.24561i	0.500664	+	0.106419i	0.451320	−	0.892362i	$-0.350953\pi$
$137$	5.86012	+	1.24561i	0.500664	+	0.106419i	0.0493445	+	0.998782i	$0.484287\pi$
$138$		0			0
$139$	−1.79667	+	17.0942i	−0.152392	+	1.44991i	0.604623	+	0.796512i	$0.293324\pi$
$139$	−1.79667	+	17.0942i	−0.152392	+	1.44991i	−0.757014	+	0.653398i	$0.773343\pi$
$140$	−5.91917	−	2.63538i	−0.500261	−	0.222731i
$141$		0			0
$142$	−3.62340	+	6.27592i	−0.304069	+	0.526664i
$143$	4.46660	+	2.07607i	0.373516	+	0.173610i
$144$		0			0
$145$	−6.71032	+	20.6522i	−0.557262	+	1.71508i
$146$	−0.314854	−	2.99564i	−0.0260575	−	0.247921i
$147$		0			0
$148$	5.35079	−	5.94265i	0.439832	−	0.488483i
$149$	8.61520	−	9.56815i	0.705784	−	0.783853i	−0.278501	−	0.960436i	$-0.589838\pi$
$149$	8.61520	−	9.56815i	0.705784	−	0.783853i	0.984286	+	0.176583i	$0.0565043\pi$
$150$		0			0
$151$	0.878973	+	8.36287i	0.0715298	+	0.680560i	0.970261	+	0.242061i	$0.0778233\pi$
$151$	0.878973	+	8.36287i	0.0715298	+	0.680560i	−0.898731	+	0.438500i	$0.855510\pi$
$152$	−2.61019	+	8.03333i	−0.211714	+	0.651589i
$153$		0			0
$154$	1.63006	+	2.93213i	0.131354	+	0.236278i
$155$	12.1197	−	20.9919i	0.973476	−	1.68611i
$156$		0			0
$157$	10.7910	+	4.80445i	0.861214	+	0.383437i	0.789325	−	0.613976i	$-0.210431\pi$
$157$	10.7910	+	4.80445i	0.861214	+	0.383437i	0.0718888	+	0.997413i	$0.477097\pi$
$158$	−1.07983	+	10.2739i	−0.0859067	+	0.817347i
$159$		0			0
$160$	15.5985	+	3.31557i	1.23317	+	0.262119i
$161$	2.56013	+	1.86005i	0.201767	+	0.146592i
$162$		0			0
$163$	1.42569	−	4.38781i	0.111668	−	0.343680i	−0.879569	−	0.475771i	$-0.842169\pi$
$163$	1.42569	−	4.38781i	0.111668	−	0.343680i	0.991238	+	0.132091i	$0.0421691\pi$
$164$	−5.45122	+	9.44179i	−0.425669	+	0.737280i
$165$		0			0
$166$	−1.12109	−	1.94178i	−0.0870132	−	0.150711i
$167$	9.63126	−	2.04719i	0.745289	−	0.158416i	0.180412	−	0.983591i	$-0.442257\pi$
$167$	9.63126	−	2.04719i	0.745289	−	0.158416i	0.564877	+	0.825175i	$0.308924\pi$
$168$		0			0
$169$	−9.86126	+	4.39051i	−0.758558	+	0.337732i
$170$	2.70556	+	8.32684i	0.207507	+	0.638640i
$171$		0			0
$172$	3.66048	+	2.65949i	0.279109	+	0.202785i
$173$	1.53520	+	14.6065i	0.116719	+	1.11051i	0.883445	+	0.468535i	$0.155218\pi$
$173$	1.53520	+	14.6065i	0.116719	+	1.11051i	−0.766726	+	0.641975i	$0.778115\pi$
$174$		0			0
$175$	−1.99643	−	3.45791i	−0.150916	−	0.261393i
$176$	3.29135	+	3.77680i	0.248095	+	0.284687i
$177$		0			0
$178$	−4.77582	−	5.30409i	−0.357963	−	0.397558i
$179$	−9.16182	+	6.65645i	−0.684787	+	0.497527i	−0.874942	−	0.484227i	$-0.839101\pi$
$179$	−9.16182	+	6.65645i	−0.684787	+	0.497527i	0.190156	+	0.981754i	$0.439101\pi$
$180$		0			0
$181$	−1.94459	−	5.98485i	−0.144541	−	0.444850i	0.852411	−	0.522872i	$-0.175140\pi$
$181$	−1.94459	−	5.98485i	−0.144541	−	0.444850i	−0.996952	+	0.0780221i	$0.975140\pi$
$182$	1.46935	+	0.312320i	0.108915	+	0.0231507i
$183$		0			0
$184$	−4.55185	−	2.02661i	−0.335567	−	0.149404i
$185$	13.9375	−	2.96251i	1.02471	−	0.217808i
$186$		0			0
$187$	−5.08806	+	14.8365i	−0.372076	+	1.08495i
$188$	3.37577			0.246204
$189$		0			0
$190$	−5.31950	+	3.86484i	−0.385917	+	0.280385i
$191$	3.35252	−	1.49264i	0.242580	−	0.108004i	−0.281846	−	0.959460i	$-0.590947\pi$
$191$	3.35252	−	1.49264i	0.242580	−	0.108004i	0.524426	+	0.851456i	$0.324280\pi$
$192$		0			0
$193$	0.940575	−	1.04461i	0.0677041	−	0.0751930i	−0.708341	−	0.705870i	$-0.750556\pi$
$193$	0.940575	−	1.04461i	0.0677041	−	0.0751930i	0.776045	+	0.630677i	$0.217223\pi$
$194$	0.155421	−	1.47874i	0.0111586	−	0.106167i
$195$		0			0
$196$	4.89868	+	5.44053i	0.349906	+	0.388609i
$197$	3.38982			0.241514			0.120757	−	0.992682i	$-0.461468\pi$
$197$	3.38982			0.241514			0.120757	+	0.992682i	$0.461468\pi$
$198$		0			0
$199$	7.38470			0.523487			0.261744	−	0.965137i	$-0.415703\pi$
$199$	7.38470			0.523487			0.261744	+	0.965137i	$0.415703\pi$
$200$	4.20675	+	4.67207i	0.297462	+	0.330365i
$201$		0			0
$202$	0.0340111	−	0.323594i	0.00239301	−	0.0227680i
$203$	−7.93861	+	8.81672i	−0.557181	+	0.618812i
$204$		0			0
$205$	−17.7471	+	7.90153i	−1.23951	+	0.551866i
$206$	−3.46332	+	2.51625i	−0.241301	+	0.175315i
$207$		0			0
$208$	2.24322			0.155539
$209$	−11.7777	−	0.190975i	−0.814678	−	0.0132100i
$210$		0			0
$211$	1.90178	−	0.404237i	0.130924	−	0.0278288i	−0.141983	−	0.989869i	$-0.545348\pi$
$211$	1.90178	−	0.404237i	0.130924	−	0.0278288i	0.272908	+	0.962040i	$0.412015\pi$
$212$	−18.9630	−	8.44286i	−1.30238	−	0.579858i
$213$		0			0
$214$	7.92423	+	1.68435i	0.541689	+	0.115140i
$215$	2.49136	+	7.66762i	0.169909	+	0.522927i
$216$		0			0
$217$	10.7140	−	7.78417i	0.727313	−	0.528424i
$218$	2.12327	+	2.35813i	0.143806	+	0.159713i
$219$		0			0
$220$	1.25753	+	14.1712i	0.0847824	+	0.955423i
$221$	3.51160	+	6.08227i	0.236216	+	0.409138i
$222$		0			0
$223$	−1.77476	−	16.8857i	−0.118847	−	1.13075i	−0.877607	−	0.479381i	$-0.840861\pi$
$223$	−1.77476	−	16.8857i	−0.118847	−	1.13075i	0.758760	−	0.651370i	$-0.225806\pi$
$224$	7.04870	+	5.12118i	0.470961	+	0.342173i
$225$		0			0
$226$	−3.80329	−	11.7053i	−0.252991	−	0.778626i
$227$	14.8946	−	6.63150i	0.988590	−	0.440148i	0.152239	−	0.988344i	$-0.451352\pi$
$227$	14.8946	−	6.63150i	0.988590	−	0.440148i	0.836350	+	0.548195i	$0.184685\pi$
$228$		0			0
$229$	19.8772	−	4.22503i	1.31352	−	0.279198i	0.502686	−	0.864469i	$-0.332345\pi$
$229$	19.8772	−	4.22503i	1.31352	−	0.279198i	0.810838	+	0.585271i	$0.199012\pi$
$230$	−1.93933	−	3.35902i	−0.127876	−	0.221487i
$231$		0			0
$232$	9.34021	−	16.1777i	0.613215	−	1.06212i
$233$	0.139989	−	0.430843i	0.00917101	−	0.0282255i	−0.946366	−	0.323096i	$-0.895276\pi$
$233$	0.139989	−	0.430843i	0.00917101	−	0.0282255i	0.955537	+	0.294870i	$0.0952764\pi$
$234$		0			0
$235$	4.86637	+	3.53562i	0.317447	+	0.230639i
$236$	10.2003	+	2.16814i	0.663984	+	0.141134i
$237$		0			0
$238$	−0.500013	+	4.75730i	−0.0324110	+	0.308370i
$239$	17.3973	+	7.74579i	1.12534	+	0.501033i	0.883101	−	0.469183i	$-0.155452\pi$
$239$	17.3973	+	7.74579i	1.12534	+	0.501033i	0.242239	+	0.970217i	$0.422118\pi$
$240$		0			0
$241$	8.93559	−	15.4769i	0.575592	−	0.996955i	−0.420385	−	0.907346i	$-0.638105\pi$
$241$	8.93559	−	15.4769i	0.575592	−	0.996955i	0.995977	−	0.0896090i	$-0.0285617\pi$
$242$	3.88798	−	6.25653i	0.249929	−	0.402185i
$243$		0			0
$244$	4.96941	−	15.2943i	0.318134	−	0.979114i
$245$	1.36357	+	12.9735i	0.0871151	+	0.828845i
$246$		0			0
$247$	−3.52927	+	3.91966i	−0.224562	+	0.249402i
$248$	−13.9527	+	15.4960i	−0.885995	+	0.983998i
$249$		0			0
$250$	−0.456047	−	4.33900i	−0.0288430	−	0.274422i
$251$	3.85401	−	11.8614i	0.243263	−	0.748687i	−0.752654	−	0.658416i	$-0.771227\pi$
$251$	3.85401	−	11.8614i	0.243263	−	0.748687i	0.995917	−	0.0902709i	$-0.0287733\pi$
$252$		0			0
$253$	0.838246	−	6.89765i	0.0527001	−	0.433652i
$254$	−7.48095	+	12.9574i	−0.469397	+	0.813019i
$255$		0			0
$256$	−8.25041	−	3.67332i	−0.515651	−	0.229583i
$257$	2.51918	−	23.9684i	0.157142	−	1.49511i	−0.577353	−	0.816495i	$-0.695914\pi$
$257$	2.51918	−	23.9684i	0.157142	−	1.49511i	0.734495	−	0.678614i	$-0.237419\pi$
$258$		0			0
$259$	7.61478	+	1.61857i	0.473160	+	0.100573i
$260$	5.15379	+	3.74444i	0.319624	+	0.232221i
$261$		0			0
$262$	−0.821621	+	2.52869i	−0.0507599	+	0.156223i
$263$	9.07714	−	15.7221i	0.559720	−	0.969464i	−0.437799	−	0.899073i	$-0.644242\pi$
$263$	9.07714	−	15.7221i	0.559720	−	0.969464i	0.997519	−	0.0703912i	$-0.0224247\pi$
$264$		0			0
$265$	−18.4935	−	32.0317i	−1.13605	−	1.96769i
$266$	−3.51391	+	0.746904i	−0.215451	+	0.0457956i
$267$		0			0
$268$	−17.0649	+	7.59780i	−1.04241	+	0.464110i
$269$	4.12310	+	12.6896i	0.251390	+	0.773698i	0.994520	+	0.104551i	$0.0333405\pi$
$269$	4.12310	+	12.6896i	0.251390	+	0.773698i	−0.743130	+	0.669147i	$0.766660\pi$
$270$		0			0
$271$	5.26488	+	3.82516i	0.319819	+	0.232362i	0.736098	−	0.676875i	$-0.236666\pi$
$271$	5.26488	+	3.82516i	0.319819	+	0.232362i	−0.416279	+	0.909237i	$0.636666\pi$
$272$	0.746675	+	7.10414i	0.0452738	+	0.430752i
$273$		0			0
$274$	−2.00596	−	3.47442i	−0.121184	−	0.209898i
$275$	−4.50614	+	7.52058i	−0.271731	+	0.453508i
$276$		0			0
$277$	−9.07255	−	10.0761i	−0.545117	−	0.605413i	0.406141	−	0.913810i	$-0.366874\pi$
$277$	−9.07255	−	10.0761i	−0.545117	−	0.605413i	−0.951258	+	0.308397i	$0.900208\pi$
$278$	9.31197	−	6.76554i	0.558495	−	0.405770i
$279$		0			0
$280$	3.06911	+	9.44574i	0.183414	+	0.564491i
$281$	29.9118	+	6.35794i	1.78439	+	0.379283i	0.977418	−	0.211313i	$-0.0677739\pi$
$281$	29.9118	+	6.35794i	1.78439	+	0.379283i	0.806968	+	0.590596i	$0.201107\pi$
$282$		0			0
$283$	−0.686047	−	0.305448i	−0.0407812	−	0.0181570i	0.386245	−	0.922396i	$-0.373772\pi$
$283$	−0.686047	−	0.305448i	−0.0407812	−	0.0181570i	−0.427026	+	0.904239i	$0.640439\pi$
$284$	−16.4237	+	3.49097i	−0.974569	+	0.207151i
$285$		0			0
$286$	−0.968263	−	3.15306i	−0.0572546	−	0.186444i
$287$	−10.6138			−0.626512
$288$		0			0
$289$	−4.34004	+	3.15323i	−0.255297	+	0.185484i
$290$	13.2844	−	5.91458i	0.780085	−	0.347316i
$291$		0			0
$292$	4.66988	−	5.18643i	0.273284	−	0.303513i
$293$	−1.59034	+	15.1310i	−0.0929084	+	0.883964i	0.844459	+	0.535621i	$0.179922\pi$
$293$	−1.59034	+	15.1310i	−0.0929084	+	0.883964i	−0.937367	+	0.348343i	$0.886744\pi$
$294$		0			0
$295$	12.4335	+	13.8088i	0.723907	+	0.803980i
$296$	−12.2576			−0.712460
$297$		0			0
$298$	−8.62192			−0.499454
$299$	−2.08187	−	2.31215i	−0.120398	−	0.133715i
$300$		0			0
$301$	−0.460428	+	4.38068i	−0.0265386	+	0.252498i
$302$	3.76792	−	4.18470i	0.216819	−	0.240802i
$303$		0			0
$304$	−4.90079	+	2.18197i	−0.281080	+	0.125145i
$305$	23.1821	−	16.8428i	1.32741	−	0.964417i
$306$		0			0
$307$	2.79291			0.159400			0.0797000	−	0.996819i	$-0.474604\pi$
$307$	2.79291			0.159400			0.0797000	+	0.996819i	$0.474604\pi$
$308$	−2.52149	+	7.35255i	−0.143675	+	0.418950i
$309$		0			0
$310$	−15.8772	+	3.37481i	−0.901766	+	0.191676i
$311$	−21.2421	−	9.45760i	−1.20453	−	0.536291i	−0.296434	−	0.955053i	$-0.595798\pi$
$311$	−21.2421	−	9.45760i	−1.20453	−	0.536291i	−0.908096	+	0.418762i	$0.862464\pi$
$312$		0			0
$313$	13.6182	+	2.89465i	0.769748	+	0.163615i	0.576015	−	0.817439i	$-0.304607\pi$
$313$	13.6182	+	2.89465i	0.769748	+	0.163615i	0.193733	+	0.981054i	$0.437940\pi$
$314$	−2.44435	−	7.52292i	−0.137942	−	0.424543i
$315$		0			0
$316$	−19.3642	+	14.0689i	−1.08932	+	0.791437i
$317$	4.35049	+	4.83171i	0.244348	+	0.271376i	0.852826	−	0.522195i	$-0.174887\pi$
$317$	4.35049	+	4.83171i	0.244348	+	0.271376i	−0.608479	+	0.793570i	$0.708220\pi$
$318$		0			0
$319$	25.3899	+	5.82858i	1.42156	+	0.326338i
$320$	−1.16348	−	2.01520i	−0.0650403	−	0.112653i
$321$		0			0
$322$	−0.221508	−	2.10751i	−0.0123442	−	0.117447i
$323$	−13.5881	−	9.87231i	−0.756061	−	0.549310i
$324$		0			0
$325$	1.21312	+	3.73360i	0.0672918	+	0.207103i
$326$	−2.82242	+	1.25662i	−0.156319	+	0.0695978i
$327$		0			0
$328$	16.3466	−	3.47458i	0.902590	−	0.191851i
$329$	1.64320	+	2.84610i	0.0905924	+	0.156911i
$330$		0			0
$331$	6.50427	−	11.2657i	0.357507	−	0.619220i	−0.630037	−	0.776565i	$-0.716960\pi$
$331$	6.50427	−	11.2657i	0.357507	−	0.619220i	0.987544	+	0.157345i	$0.0502935\pi$
$332$	1.60536	−	4.94079i	0.0881055	−	0.271161i
$333$		0			0
$334$	−5.33441	−	3.87567i	−0.291886	−	0.212067i
$335$	−32.5576	−	6.92034i	−1.77881	−	0.378099i
$336$		0			0
$337$	−3.04908	+	29.0100i	−0.166094	+	1.58028i	0.520903	+	0.853616i	$0.325595\pi$
$337$	−3.04908	+	29.0100i	−0.166094	+	1.58028i	−0.686997	+	0.726661i	$0.741071\pi$
$338$	6.60362	+	2.94012i	0.359189	+	0.159921i
$339$		0			0
$340$	−10.1430	+	17.5681i	−0.550079	+	0.952765i
$341$	−26.3694	−	12.2565i	−1.42798	−	0.663725i
$342$		0			0
$343$	−5.46976	+	16.8342i	−0.295339	+	0.908961i
$344$	−0.724960	−	6.89754i	−0.0390872	−	0.371890i
$345$		0			0
$346$	6.58100	−	7.30894i	0.353797	−	0.392931i
$347$	15.4911	−	17.2046i	0.831604	−	0.923590i	−0.166443	−	0.986051i	$-0.553228\pi$
$347$	15.4911	−	17.2046i	0.831604	−	0.923590i	0.998047	+	0.0624611i	$0.0198949\pi$
$348$		0			0
$349$	0.887486	+	8.44386i	0.0475060	+	0.451990i	0.992257	+	0.124201i	$0.0396368\pi$
$349$	0.887486	+	8.44386i	0.0475060	+	0.451990i	−0.944751	+	0.327789i	$0.893697\pi$
$350$	−0.826257	+	2.54296i	−0.0441653	+	0.135927i
$351$		0			0
$352$	2.30791	−	18.9910i	0.123012	−	1.01222i
$353$	0.687569	−	1.19090i	0.0365956	−	0.0633854i	−0.847148	−	0.531358i	$-0.821682\pi$
$353$	0.687569	−	1.19090i	0.0365956	−	0.0633854i	0.883743	+	0.467972i	$0.155015\pi$
$354$		0			0
$355$	−27.3320	−	12.1690i	−1.45063	−	0.645863i
$356$	1.72859	−	16.4464i	0.0916152	−	0.871660i
$357$		0			0
$358$	7.41785	+	1.57671i	0.392046	+	0.0833319i
$359$	16.8945	+	12.2746i	0.891658	+	0.647827i	0.936310	−	0.351175i	$-0.114218\pi$
$359$	16.8945	+	12.2746i	0.891658	+	0.647827i	−0.0446518	+	0.999003i	$0.514218\pi$
$360$		0			0
$361$	−1.97350	+	6.07381i	−0.103868	+	0.319674i
$362$	−2.10701	+	3.64945i	−0.110742	+	0.191811i
$363$		0			0
$364$	1.74025	+	3.01420i	0.0912138	+	0.157987i
$365$	12.1639	−	2.58552i	0.636688	−	0.135332i
$366$		0			0
$367$	11.3730	−	5.06358i	0.593666	−	0.264317i	−0.0878343	−	0.996135i	$-0.527995\pi$
$367$	11.3730	−	5.06358i	0.593666	−	0.264317i	0.681500	+	0.731818i	$0.261328\pi$
$368$	−0.977884	−	3.00962i	−0.0509757	−	0.156887i
$369$		0			0
$370$	−7.71948	−	5.60853i	−0.401316	−	0.291574i
$371$	−2.11231	−	20.0973i	−0.109666	−	1.04340i
$372$		0			0
$373$	14.2488	+	24.6796i	0.737774	+	1.27786i	0.953496	+	0.301407i	$0.0974563\pi$
$373$	14.2488	+	24.6796i	0.737774	+	1.27786i	−0.215722	+	0.976455i	$0.569210\pi$
$374$	9.66326	−	4.11596i	0.499675	−	0.212831i
$375$		0			0
$376$	−3.46245	−	3.84544i	−0.178562	−	0.198313i
$377$	9.43690	−	6.85631i	0.486025	−	0.353118i
$378$		0			0
$379$	−1.33092	−	4.09616i	−0.0683649	−	0.210405i	0.911038	−	0.412323i	$-0.135283\pi$
$379$	−1.33092	−	4.09616i	−0.0683649	−	0.210405i	−0.979402	+	0.201918i	$0.935283\pi$
$380$	−14.9018	−	3.16747i	−0.764445	−	0.162488i
$381$		0			0
$382$	−2.24503	−	0.999550i	−0.114866	−	0.0511414i
$383$	−17.5964	+	3.74024i	−0.899136	+	0.191117i	−0.634219	−	0.773154i	$-0.718678\pi$
$383$	−17.5964	+	3.74024i	−0.899136	+	0.191117i	−0.264918	+	0.964271i	$0.585345\pi$
$384$		0			0
$385$	−11.3356	+	7.95822i	−0.577715	+	0.405589i
$386$	−0.941309			−0.0479114
$387$		0			0
$388$	2.78711	−	2.02496i	0.141494	−	0.102802i
$389$	−32.7940	+	14.6008i	−1.66272	+	0.740291i	−0.999964	−	0.00854185i	$-0.997281\pi$
$389$	−32.7940	+	14.6008i	−1.66272	+	0.740291i	−0.662758	+	0.748833i	$0.730614\pi$
$390$		0			0
$391$	6.62949	−	7.36279i	0.335267	−	0.372352i
$392$	1.17301	−	11.1604i	0.0592460	−	0.563688i
$393$		0			0
$394$	−1.51893	−	1.68694i	−0.0765224	−	0.0849867i
$395$	−42.6496			−2.14594
$396$		0			0
$397$	19.8332			0.995398			0.497699	−	0.867350i	$-0.334178\pi$
$397$	19.8332			0.995398			0.497699	+	0.867350i	$0.334178\pi$
$398$	−3.30897	−	3.67499i	−0.165864	−	0.184210i
$399$		0			0
$400$	−0.417367	+	3.97098i	−0.0208683	+	0.198549i
$401$	−9.22764	+	10.2483i	−0.460807	+	0.511778i	−0.928103	−	0.372323i	$-0.878561\pi$
$401$	−9.22764	+	10.2483i	−0.460807	+	0.511778i	0.467297	+	0.884101i	$0.345228\pi$
$402$		0			0
$403$	−11.8949	+	5.29596i	−0.592529	+	0.263811i
$404$	0.609908	−	0.443124i	0.0303440	−	0.0220462i
$405$		0			0
$406$	7.94480			0.394294
$407$	−5.01794	−	16.3405i	−0.248730	−	0.809967i
$408$		0			0
$409$	−36.1043	+	7.67421i	−1.78524	+	0.379465i	−0.977644	−	0.210266i	$-0.932567\pi$
$409$	−36.1043	+	7.67421i	−1.78524	+	0.379465i	−0.807599	+	0.589731i	$0.799234\pi$
$410$	11.8844	+	5.29128i	0.586929	+	0.261318i
$411$		0			0
$412$	−9.70195	−	2.06221i	−0.477981	−	0.101598i
$413$	3.13717	+	9.65521i	0.154370	+	0.475102i
$414$		0			0
$415$	7.48895	−	5.44104i	0.367618	−	0.267090i
$416$	−5.73193	−	6.36595i	−0.281031	−	0.312116i
$417$		0			0
$418$	5.18236	+	5.94671i	0.253477	+	0.290863i
$419$	−1.16856	−	2.02400i	−0.0570879	−	0.0988791i	0.836069	−	0.548624i	$-0.184848\pi$
$419$	−1.16856	−	2.02400i	−0.0570879	−	0.0988791i	−0.893157	+	0.449745i	$0.851515\pi$
$420$		0			0
$421$	1.60297	+	15.2513i	0.0781242	+	0.743302i	0.961531	+	0.274696i	$0.0885771\pi$
$421$	1.60297	+	15.2513i	0.0781242	+	0.743302i	−0.883407	+	0.468606i	$0.844756\pi$
$422$	−1.05333	−	0.765289i	−0.0512753	−	0.0372537i
$423$		0			0
$424$	9.83236	+	30.2609i	0.477502	+	1.46960i
$425$	−11.4203	+	5.08464i	−0.553966	+	0.246641i
$426$		0			0
$427$	15.3134	−	3.25497i	0.741070	−	0.157519i
$428$	9.38519	+	16.2556i	0.453650	+	0.785745i
$429$		0			0
$430$	2.69944	−	4.67557i	0.130179	−	0.225476i
$431$	2.41444	−	7.43087i	0.116299	−	0.357932i	−0.875917	−	0.482463i	$-0.839742\pi$
$431$	2.41444	−	7.43087i	0.116299	−	0.357932i	0.992216	+	0.124530i	$0.0397424\pi$
$432$		0			0
$433$	−20.3571	−	14.7903i	−0.978301	−	0.710777i	−0.0209724	−	0.999780i	$-0.506676\pi$
$433$	−20.3571	−	14.7903i	−0.978301	−	0.710777i	−0.957328	+	0.289003i	$0.906676\pi$
$434$	−8.67456	−	1.84383i	−0.416392	−	0.0885069i
$435$		0			0
$436$	−0.768510	+	7.31188i	−0.0368049	+	0.350176i
$437$	6.79733	+	3.02637i	0.325160	+	0.144771i
$438$		0			0
$439$	−0.492942	+	0.853801i	−0.0235268	+	0.0407497i	−0.877549	−	0.479487i	$-0.840823\pi$
$439$	−0.492942	+	0.853801i	−0.0235268	+	0.0407497i	0.854022	+	0.520236i	$0.174156\pi$
$440$	14.8530	−	15.9676i	0.708090	−	0.761224i
$441$		0			0
$442$	1.45334	−	4.47292i	0.0691283	−	0.212755i
$443$	1.12634	+	10.7164i	0.0535139	+	0.509150i	0.988144	+	0.153529i	$0.0490639\pi$
$443$	1.12634	+	10.7164i	0.0535139	+	0.509150i	−0.934630	+	0.355621i	$0.884269\pi$
$444$		0			0
$445$	19.7171	−	21.8980i	0.934679	−	1.03807i
$446$	−7.60792	+	8.44945i	−0.360245	+	0.400093i
$447$		0			0
$448$	−0.132891	−	1.26437i	−0.00627850	−	0.0597359i
$449$	−7.13830	+	21.9694i	−0.336877	+	1.03680i	0.628913	+	0.777476i	$0.283500\pi$
$449$	−7.13830	+	21.9694i	−0.336877	+	1.03680i	−0.965790	+	0.259326i	$0.916500\pi$
$450$		0			0
$451$	11.3238	+	20.3690i	0.533216	+	0.959140i
$452$	14.2583	−	24.6961i	0.670654	−	1.16161i
$453$		0			0
$454$	−9.97421	−	4.44081i	−0.468113	−	0.208417i
$455$	−0.648261	+	6.16779i	−0.0303909	+	0.289150i
$456$		0			0
$457$	−26.7704	−	5.69023i	−1.25227	−	0.266178i	−0.466401	−	0.884573i	$-0.654450\pi$
$457$	−26.7704	−	5.69023i	−1.25227	−	0.266178i	−0.785867	+	0.618395i	$0.787783\pi$
$458$	−11.0093	−	7.99870i	−0.514429	−	0.373755i
$459$		0			0
$460$	2.77706	−	8.54690i	0.129481	−	0.398501i
$461$	−9.76471	+	16.9130i	−0.454788	+	0.787715i	−0.998676	−	0.0514422i	$-0.983618\pi$
$461$	−9.76471	+	16.9130i	−0.454788	+	0.787715i	0.543888	+	0.839158i	$0.316952\pi$
$462$		0			0
$463$	−7.29658	−	12.6380i	−0.339101	−	0.587340i	0.645163	−	0.764045i	$-0.276789\pi$
$463$	−7.29658	−	12.6380i	−0.339101	−	0.587340i	−0.984264	+	0.176705i	$0.943456\pi$
$464$	11.6048	−	2.46668i	0.538740	−	0.114513i
$465$		0			0
$466$	−0.277136	+	0.123389i	−0.0128381	+	0.00571587i
$467$	−1.87684	−	5.77631i	−0.0868496	−	0.267296i	0.898194	−	0.439598i	$-0.144879\pi$
$467$	−1.87684	−	5.77631i	−0.0868496	−	0.267296i	−0.985044	+	0.172303i	$0.944879\pi$
$468$		0			0
$469$	−14.7122	−	10.6891i	−0.679348	−	0.493575i
$470$	−0.421048	−	4.00600i	−0.0194215	−	0.184783i
$471$		0			0
$472$	−7.99242	−	13.8433i	−0.367881	−	0.637189i
$473$	8.89823	−	3.79010i	0.409141	−	0.174269i
$474$		0			0
$475$	−6.28199	−	6.97686i	−0.288238	−	0.320120i
$476$	−8.96654	+	6.51457i	−0.410980	+	0.298595i
$477$		0			0
$478$	−3.94080	−	12.1285i	−0.180248	−	0.554746i
$479$	−39.7307	−	8.44502i	−1.81534	−	0.385863i	−0.830181	−	0.557495i	$-0.811763\pi$
$479$	−39.7307	−	8.44502i	−1.81534	−	0.385863i	−0.985161	+	0.171632i	$0.945096\pi$
$480$		0			0
$481$	−6.99232	−	3.11318i	−0.318823	−	0.141949i
$482$	−11.7060	+	2.48818i	−0.533192	+	0.113334i
$483$		0			0
$484$	16.8005	−	3.00536i	0.763660	−	0.136607i
$485$	6.13862			0.278740
$486$		0			0
$487$	−11.9767	+	8.70158i	−0.542716	+	0.394306i	−0.825093	−	0.564998i	$-0.808877\pi$
$487$	−11.9767	+	8.70158i	−0.542716	+	0.394306i	0.282377	+	0.959304i	$0.408877\pi$
$488$	−22.5191	+	10.0262i	−1.01939	+	0.453863i
$489$		0			0
$490$	5.84524	−	6.49180i	0.264061	−	0.293269i
$491$	−4.12695	+	39.2653i	−0.186247	+	1.77202i	0.358608	+	0.933488i	$0.383251\pi$
$491$	−4.12695	+	39.2653i	−0.186247	+	1.77202i	−0.544855	+	0.838530i	$0.683415\pi$
$492$		0			0
$493$	24.8547	+	27.6039i	1.11940	+	1.24322i
$494$	3.53203			0.158913
$495$		0			0
$496$	−13.2432			−0.594638
$497$	−10.9377	−	12.1475i	−0.490621	−	0.544890i
$498$		0			0
$499$	0.332064	−	3.15938i	0.0148652	−	0.141433i	−0.984572	−	0.174981i	$-0.944014\pi$
$499$	0.332064	−	3.15938i	0.0148652	−	0.141433i	0.999437	+	0.0335472i	$0.0106804\pi$
$500$	6.76405	−	7.51223i	0.302497	−	0.335957i
$501$		0			0
$502$	−7.62976	+	3.39699i	−0.340533	+	0.151615i
$503$	14.8735	−	10.8062i	0.663174	−	0.481824i	−0.204559	−	0.978854i	$-0.565576\pi$
$503$	14.8735	−	10.8062i	0.663174	−	0.481824i	0.867733	+	0.497030i	$0.165576\pi$
$504$		0			0
$505$	1.34332			0.0597771
$506$	−3.80821	+	2.67358i	−0.169296	+	0.118855i
$507$		0			0
$508$	−33.9088	+	7.20753i	−1.50446	+	0.319782i
$509$	14.3026	+	6.36791i	0.633950	+	0.282253i	0.698443	−	0.715665i	$-0.253876\pi$
$509$	14.3026	+	6.36791i	0.633950	+	0.282253i	−0.0644931	+	0.997918i	$0.520543\pi$
$510$		0			0
$511$	6.64578	+	1.41260i	0.293992	+	0.0624899i
$512$	−4.91260	−	15.1194i	−0.217108	−	0.668190i
$513$		0			0
$514$	−13.0567	+	9.48623i	−0.575905	+	0.418419i
$515$	−11.8260	−	13.1342i	−0.521118	−	0.578760i
$516$		0			0
$517$	3.70887	−	6.18996i	0.163116	−	0.272234i
$518$	−2.60659	−	4.51475i	−0.114527	−	0.198367i
$519$		0			0
$520$	−1.02071	−	9.71141i	−0.0447611	−	0.425874i
$521$	−14.6674	−	10.6565i	−0.642592	−	0.466870i	0.218148	−	0.975916i	$-0.429999\pi$
$521$	−14.6674	−	10.6565i	−0.642592	−	0.466870i	−0.860740	+	0.509045i	$0.829999\pi$
$522$		0			0
$523$	5.24113	+	16.1305i	0.229178	+	0.705339i	0.997840	+	0.0656837i	$0.0209228\pi$
$523$	5.24113	+	16.1305i	0.229178	+	0.705339i	−0.768662	+	0.639655i	$0.779077\pi$
$524$	−5.62781	+	2.50566i	−0.245852	+	0.109460i
$525$		0			0
$526$	−11.8914	+	2.52759i	−0.518490	+	0.110208i
$527$	−20.7313	−	35.9077i	−0.903071	−	1.56417i
$528$		0			0
$529$	9.30544	−	16.1175i	0.404584	−	0.700761i
$530$	−7.65389	+	23.5562i	−0.332464	+	1.02322i
$531$		0			0
$532$	−6.73386	−	4.89243i	−0.291950	−	0.212114i
$533$	10.2073	+	2.16964i	0.442129	+	0.0939775i
$534$		0			0
$535$	−3.49608	+	33.2630i	−0.151149	+	1.43808i
$536$	26.1580	+	11.6463i	1.12985	+	0.503043i
$537$		0			0
$538$	4.46746	−	7.73787i	0.192606	−	0.333603i
$539$	15.3580	−	3.00506i	0.661518	−	0.129437i
$540$		0			0
$541$	−2.07721	+	6.39299i	−0.0893062	+	0.274856i	−0.985728	−	0.168346i	$-0.946158\pi$
$541$	−2.07721	+	6.39299i	−0.0893062	+	0.274856i	0.896422	+	0.443202i	$0.146158\pi$
$542$	−0.455528	−	4.33406i	−0.0195666	−	0.186164i
$543$		0			0
$544$	18.2527	−	20.2716i	0.782577	−	0.869140i
$545$	−8.76596	+	9.73559i	−0.375493	+	0.417027i
$546$		0			0
$547$	−4.78907	−	45.5650i	−0.204766	−	1.94822i	−0.302846	−	0.953040i	$-0.597937\pi$
$547$	−4.78907	−	45.5650i	−0.204766	−	1.94822i	0.0980800	−	0.995179i	$-0.468730\pi$
$548$	2.87247	−	8.84054i	0.122706	−	0.377649i
$549$		0			0
$550$	5.76175	−	1.12738i	0.245682	−	0.0480719i
$551$	−13.9478	+	24.1584i	−0.594198	+	1.02918i
$552$		0			0
$553$	−21.2872	−	9.47766i	−0.905223	−	0.403031i
$554$	−0.949080	+	9.02989i	−0.0403225	+	0.383643i
$555$		0			0
$556$	26.0861	+	5.54477i	1.10630	+	0.235150i
$557$	−9.67054	−	7.02606i	−0.409754	−	0.297704i	0.363748	−	0.931497i	$-0.381497\pi$
$557$	−9.67054	−	7.02606i	−0.409754	−	0.297704i	−0.773502	+	0.633794i	$0.781497\pi$
$558$		0			0
$559$	1.33828	−	4.11881i	0.0566033	−	0.174207i
$560$	−3.15389	+	5.46270i	−0.133276	+	0.230841i
$561$		0			0
$562$	−10.2390	−	17.7345i	−0.431906	−	0.748083i
$563$	−33.6515	+	7.15285i	−1.41824	+	0.301457i	−0.852328	−	0.523008i	$-0.824810\pi$
$563$	−33.6515	+	7.15285i	−1.41824	+	0.301457i	−0.565914	+	0.824464i	$0.691476\pi$
$564$		0			0
$565$	46.4196	−	20.6673i	1.95289	−	0.869482i
$566$	0.155402	+	0.478277i	0.00653202	+	0.0201035i
$567$		0			0
$568$	20.8221	+	15.1281i	0.873675	+	0.634762i
$569$	1.20274	+	11.4433i	0.0504215	+	0.479729i	0.990373	+	0.138422i	$0.0442029\pi$
$569$	1.20274	+	11.4433i	0.0504215	+	0.479729i	−0.939952	+	0.341307i	$0.889130\pi$
$570$		0			0
$571$	18.2755	+	31.6542i	0.764807	+	1.32469i	0.940348	+	0.340213i	$0.110499\pi$
$571$	18.2755	+	31.6542i	0.764807	+	1.32469i	−0.175541	+	0.984472i	$0.556167\pi$
$572$	3.92792	−	6.55556i	0.164235	−	0.274102i
$573$		0			0
$574$	4.75588	+	5.28194i	0.198507	+	0.220464i
$575$	4.48036	−	3.25517i	0.186844	−	0.135750i
$576$		0			0
$577$	−6.88976	−	21.2045i	−0.286824	−	0.882754i	−0.985846	−	0.167654i	$-0.946381\pi$
$577$	−6.88976	−	21.2045i	−0.286824	−	0.882754i	0.699022	−	0.715101i	$-0.253619\pi$
$578$	3.51391	+	0.746904i	0.146159	+	0.0310671i
$579$		0			0
$580$	30.7795	+	13.7039i	1.27805	+	0.569024i
$581$	4.94698	−	1.05151i	0.205235	−	0.0436242i
$582$		0			0
$583$	−36.3153	+	25.4954i	−1.50403	+	1.05591i
$584$	−10.6978			−0.442678
$585$		0			0
$586$	8.24255	−	5.98856i	0.340497	−	0.247385i
$587$	21.4946	−	9.56999i	0.887175	−	0.394996i	0.0880187	−	0.996119i	$-0.471946\pi$
$587$	21.4946	−	9.56999i	0.887175	−	0.394996i	0.799157	+	0.601123i	$0.205280\pi$
$588$		0			0
$589$	20.8357	−	23.1404i	0.858519	−	0.953482i
$590$	1.30067	−	12.3750i	0.0535477	−	0.509473i
$591$		0			0
$592$	−5.20912	−	5.78531i	−0.214093	−	0.237775i
$593$	26.7811			1.09977			0.549884	−	0.835241i	$-0.314672\pi$
$593$	26.7811			1.09977			0.549884	+	0.835241i	$0.314672\pi$
$594$		0			0
$595$	−19.7488			−0.809622
$596$	−13.3670	−	14.8456i	−0.547535	−	0.608100i
$597$		0			0
$598$	−0.217785	+	2.07208i	−0.00890588	+	0.0847338i
$599$	−7.09422	+	7.87893i	−0.289862	+	0.321924i	−0.870435	−	0.492284i	$-0.836162\pi$
$599$	−7.09422	+	7.87893i	−0.289862	+	0.321924i	0.580573	+	0.814209i	$0.302829\pi$
$600$		0			0
$601$	−35.7548	+	15.9190i	−1.45847	+	0.649352i	−0.974224	−	0.225582i	$-0.927572\pi$
$601$	−35.7548	+	15.9190i	−1.45847	+	0.649352i	−0.484243	+	0.874933i	$0.660905\pi$
$602$	2.38635	−	1.73378i	0.0972603	−	0.0706638i
$603$		0			0
$604$	13.0470			0.530875
$605$	27.3666	+	13.2637i	1.11261	+	0.539245i
$606$		0			0
$607$	−8.40273	+	1.78605i	−0.341056	+	0.0724937i	−0.375256	−	0.926921i	$-0.622445\pi$
$607$	−8.40273	+	1.78605i	−0.341056	+	0.0724937i	0.0341997	+	0.999415i	$0.489112\pi$
$608$	18.7148	+	8.33236i	0.758985	+	0.337922i
$609$		0			0
$610$	−18.7694	−	3.98956i	−0.759950	−	0.161532i
$611$	−0.998482	−	3.07301i	−0.0403943	−	0.124321i
$612$		0			0
$613$	8.05694	−	5.85371i	0.325417	−	0.236429i	−0.413067	−	0.910701i	$-0.635542\pi$
$613$	8.05694	−	5.85371i	0.325417	−	0.236429i	0.738483	+	0.674272i	$0.235542\pi$
$614$	−1.25146	−	1.38989i	−0.0505049	−	0.0560914i
$615$		0			0
$616$	10.9617	−	4.66903i	0.441661	−	0.188121i
$617$	−3.64515	−	6.31358i	−0.146748	−	0.254175i	0.783276	−	0.621674i	$-0.213547\pi$
$617$	−3.64515	−	6.31358i	−0.146748	−	0.254175i	−0.930024	+	0.367499i	$0.880214\pi$
$618$		0			0
$619$	3.44301	+	32.7581i	0.138386	+	1.31666i	0.814631	+	0.579980i	$0.196940\pi$
$619$	3.44301	+	32.7581i	0.138386	+	1.31666i	−0.676244	+	0.736677i	$0.736394\pi$
$620$	−30.4263	−	22.1060i	−1.22195	−	0.887797i
$621$		0			0
$622$	4.81171	+	14.8089i	0.192932	+	0.593784i
$623$	14.7073	−	6.54813i	0.589237	−	0.262345i
$624$		0			0
$625$	30.5470	−	6.49296i	1.22188	−	0.259719i
$626$	−4.66161	−	8.07415i	−0.186315	−	0.322708i
$627$		0			0
$628$	9.16370	−	15.8720i	0.365671	−	0.633361i
$629$	7.53181	−	23.1805i	0.300313	−	0.924268i
$630$		0			0
$631$	6.31372	+	4.58719i	0.251345	+	0.182613i	0.706323	−	0.707890i	$-0.250353\pi$
$631$	6.31372	+	4.58719i	0.251345	+	0.182613i	−0.454978	+	0.890503i	$0.650353\pi$
$632$	35.8877	+	7.62816i	1.42753	+	0.303432i
$633$		0			0
$634$	0.455105	−	4.33003i	0.0180745	−	0.171968i
$635$	−56.4302	−	25.1243i	−2.23936	−	0.997029i
$636$		0			0
$637$	3.50367	−	6.06853i	0.138820	−	0.240444i
$638$	−8.47626	−	15.2470i	−0.335578	−	0.603633i
$639$		0			0
$640$	9.37426	−	28.8510i	0.370550	−	1.14044i
$641$	1.25810	+	11.9700i	0.0496920	+	0.472788i	0.990864	+	0.134861i	$0.0430589\pi$
$641$	1.25810	+	11.9700i	0.0496920	+	0.472788i	−0.941172	+	0.337927i	$0.890274\pi$
$642$		0			0
$643$	−22.6305	+	25.1337i	−0.892459	+	0.991177i	−0.999995	−	0.00302455i	$-0.999037\pi$
$643$	−22.6305	+	25.1337i	−0.892459	+	0.991177i	0.107536	+	0.994201i	$0.465704\pi$
$644$	3.28538	−	3.64879i	0.129462	−	0.143782i
$645$		0			0
$646$	1.17567	+	11.1857i	0.0462560	+	0.440097i
$647$	−5.98134	+	18.4087i	−0.235151	+	0.723719i	0.761951	+	0.647635i	$0.224242\pi$
$647$	−5.98134	+	18.4087i	−0.235151	+	0.723719i	−0.997101	+	0.0760844i	$0.975758\pi$
$648$		0			0
$649$	15.1824	−	16.3217i	0.595961	−	0.640681i
$650$	1.31444	−	2.27668i	0.0515566	−	0.0892986i
$651$		0			0
$652$	−6.53946	−	2.91155i	−0.256105	−	0.114025i
$653$	0.277176	−	2.63715i	0.0108467	−	0.103200i	−0.987759	−	0.155988i	$-0.950144\pi$
$653$	0.277176	−	2.63715i	0.0108467	−	0.103200i	0.998606	+	0.0527878i	$0.0168107\pi$
$654$		0			0
$655$	−10.7371	−	2.28224i	−0.419534	−	0.0891747i
$656$	8.58673	+	6.23863i	0.335256	+	0.243577i
$657$		0			0
$658$	0.680067	−	2.09303i	0.0265118	−	0.0815948i
$659$	1.34963	−	2.33764i	0.0525743	−	0.0910614i	−0.838541	−	0.544839i	$-0.816591\pi$
$659$	1.34963	−	2.33764i	0.0525743	−	0.0910614i	0.891115	+	0.453778i	$0.149924\pi$
$660$		0			0
$661$	6.28133	+	10.8796i	0.244315	+	0.423167i	0.961939	−	0.273265i	$-0.0881035\pi$
$661$	6.28133	+	10.8796i	0.244315	+	0.423167i	−0.717624	+	0.696431i	$0.754770\pi$
$662$	−8.52084	+	1.81116i	−0.331172	+	0.0703928i
$663$		0			0
$664$	−7.27477	+	3.23894i	−0.282316	+	0.125695i
$665$	−4.58313	−	14.1054i	−0.177726	−	0.546985i
$666$		0			0
$667$	−13.3126	−	9.67218i	−0.515466	−	0.374508i
$668$	−1.59692	−	15.1937i	−0.0617867	−	0.587861i
$669$		0			0
$670$	11.1447	+	19.3032i	0.430557	+	0.745747i
$671$	−22.5845	−	25.9155i	−0.871864	−	1.00046i
$672$		0			0
$673$	−15.1664	−	16.8440i	−0.584621	−	0.649287i	0.376174	−	0.926549i	$-0.377240\pi$
$673$	−15.1664	−	16.8440i	−0.584621	−	0.649287i	−0.960794	+	0.277262i	$0.910573\pi$
$674$	15.8031	−	11.4816i	0.608711	−	0.442254i
$675$		0			0
$676$	5.17553	+	15.9286i	0.199059	+	0.612640i
$677$	28.8786	+	6.13834i	1.10990	+	0.235915i	0.726159	−	0.687527i	$-0.241304\pi$
$677$	28.8786	+	6.13834i	1.10990	+	0.235915i	0.383736	+	0.923443i	$0.374637\pi$
$678$		0			0
$679$	3.06389	+	1.36413i	0.117581	+	0.0523506i
$680$	30.4157	−	6.46506i	1.16639	−	0.247924i
$681$		0			0
$682$	5.71631	+	18.6146i	0.218889	+	0.712791i
$683$	−16.5916			−0.634859			−0.317430	−	0.948282i	$-0.602820\pi$
$683$	−16.5916			−0.634859			−0.317430	+	0.948282i	$0.602820\pi$
$684$		0			0
$685$	13.4000	−	9.73565i	0.511987	−	0.371980i
$686$	10.8284	−	4.82113i	0.413432	−	0.184072i
$687$		0			0
$688$	2.94739	−	3.27341i	0.112368	−	0.124798i
$689$	−2.07680	+	19.7595i	−0.0791199	+	0.752775i
$690$		0			0
$691$	15.7421	+	17.4833i	0.598857	+	0.665098i	0.964015	−	0.265848i	$-0.0856519\pi$
$691$	15.7421	+	17.4833i	0.598857	+	0.665098i	−0.365158	+	0.930945i	$0.618985\pi$
$692$	22.7877			0.866260
$693$		0			0
$694$	−15.5032			−0.588492
$695$	31.7972	+	35.3144i	1.20614	+	1.33955i
$696$		0			0
$697$	−3.47351	+	33.0483i	−0.131569	+	1.25179i
$698$	3.80441	−	4.22523i	0.143999	−	0.159927i
$699$		0			0
$700$	−5.65957	+	2.51980i	−0.213912	+	0.0952396i
$701$	−18.3698	+	13.3465i	−0.693819	+	0.504089i	−0.877913	−	0.478820i	$-0.841065\pi$
$701$	−18.3698	+	13.3465i	−0.693819	+	0.504089i	0.184095	+	0.982909i	$0.441065\pi$
$702$		0			0
$703$	18.3044			0.690365
$704$	−2.28469	+	1.60398i	−0.0861075	+	0.0604523i
$705$		0			0
$706$	−0.900741	+	0.191458i	−0.0338998	+	0.00720563i
$707$	0.670476	+	0.298515i	0.0252158	+	0.0112268i
$708$		0			0
$709$	11.2512	+	2.39151i	0.422546	+	0.0898149i	0.414277	−	0.910151i	$-0.364035\pi$
$709$	11.2512	+	2.39151i	0.422546	+	0.0898149i	0.00826904	+	0.999966i	$0.497368\pi$
$710$	6.19118	+	19.0545i	0.232351	+	0.715102i
$711$		0			0
$712$	−20.5076	+	14.8996i	−0.768555	+	0.558388i
$713$	12.2907	+	13.6502i	0.460290	+	0.511204i
$714$		0			0
$715$	12.5283	−	5.33629i	0.468532	−	0.199566i
$716$	8.78545	+	15.2169i	0.328328	+	0.568680i
$717$		0			0
$718$	−1.46175	−	13.9076i	−0.0545519	−	0.519027i
$719$	37.1445	+	26.9870i	1.38526	+	1.00645i	0.996367	+	0.0851620i	$0.0271408\pi$
$719$	37.1445	+	26.9870i	1.38526	+	1.00645i	0.388888	+	0.921285i	$0.372859\pi$
$720$		0			0
$721$	−2.98390	−	9.18349i	−0.111126	−	0.342011i
$722$	3.90692	−	1.73947i	0.145401	−	0.0647365i
$723$		0			0
$724$	−9.55039	+	2.03000i	−0.354937	+	0.0754443i
$725$	10.3813	+	17.9810i	0.385554	+	0.667798i
$726$		0			0
$727$	0.417822	−	0.723690i	0.0154962	−	0.0268402i	−0.858173	−	0.513360i	$-0.828401\pi$
$727$	0.417822	−	0.723690i	0.0154962	−	0.0268402i	0.873670	+	0.486520i	$0.161734\pi$
$728$	1.64863	−	5.07396i	0.0611023	−	0.188053i
$729$		0			0
$730$	−6.73715	−	4.89483i	−0.249353	−	0.181166i
$731$	13.4895	+	2.86728i	0.498926	+	0.106050i
$732$		0			0
$733$	3.34101	−	31.7876i	0.123403	−	1.17410i	−0.741072	−	0.671426i	$-0.765682\pi$
$733$	3.34101	−	31.7876i	0.123403	−	1.17410i	0.864475	−	0.502676i	$-0.167651\pi$
$734$	−7.61596	−	3.39084i	−0.281110	−	0.125158i
$735$		0			0
$736$	−6.04218	+	10.4654i	−0.222718	+	0.385758i
$737$	−4.81712	+	39.6385i	−0.177441	+	1.46010i
$738$		0			0
$739$	2.00537	−	6.17190i	0.0737687	−	0.227037i	−0.907373	−	0.420326i	$-0.861916\pi$
$739$	2.00537	−	6.17190i	0.0737687	−	0.227037i	0.981142	+	0.193289i	$0.0619156\pi$
$740$	−2.31092	−	21.9870i	−0.0849512	−	0.808256i
$741$		0			0
$742$	−9.05489	+	10.0565i	−0.332415	+	0.369185i
$743$	7.45493	−	8.27954i	0.273495	−	0.303747i	−0.590713	−	0.806882i	$-0.701153\pi$
$743$	7.45493	−	8.27954i	0.273495	−	0.303747i	0.864208	+	0.503135i	$0.167820\pi$
$744$		0			0
$745$	−3.72077	−	35.4008i	−0.136318	−	1.29698i
$746$	5.89712	−	18.1495i	0.215909	−	0.664499i
$747$		0			0
$748$	22.0685	+	10.2574i	0.806905	+	0.375049i
$749$	−9.13670	+	15.8252i	−0.333848	+	0.578242i
$750$		0			0
$751$	−32.6141	−	14.5207i	−1.19010	−	0.529869i	−0.286435	−	0.958100i	$-0.592470\pi$
$751$	−32.6141	−	14.5207i	−1.19010	−	0.529869i	−0.903669	+	0.428231i	$0.859137\pi$
$752$	0.343522	−	3.26839i	0.0125269	−	0.119186i
$753$		0			0
$754$	−7.64057	−	1.62405i	−0.278253	−	0.0591445i
$755$	18.8080	+	13.6648i	0.684493	+	0.497313i
$756$		0			0
$757$	−1.57431	+	4.84524i	−0.0572194	+	0.176103i	−0.975581	−	0.219638i	$-0.929512\pi$
$757$	−1.57431	+	4.84524i	−0.0572194	+	0.176103i	0.918362	+	0.395741i	$0.129512\pi$
$758$	−1.44208	+	2.49776i	−0.0523788	+	0.0907227i
$759$		0			0
$760$	11.6762	+	20.2238i	0.423542	+	0.733596i
$761$	12.2197	−	2.59739i	0.442966	−	0.0941552i	0.0189711	−	0.999820i	$-0.493961\pi$
$761$	12.2197	−	2.59739i	0.442966	−	0.0941552i	0.423994	+	0.905665i	$0.360628\pi$
$762$		0			0
$763$	−6.53870	+	2.91122i	−0.236717	+	0.105393i
$764$	−1.75952	−	5.41525i	−0.0636572	−	0.195917i
$765$		0			0
$766$	9.74603	+	7.08091i	0.352138	+	0.255844i
$767$	−1.04335	−	9.92677i	−0.0376730	−	0.358435i
$768$		0			0
$769$	−2.74929	−	4.76192i	−0.0991421	−	0.171719i	0.812188	−	0.583396i	$-0.198277\pi$
$769$	−2.74929	−	4.76192i	−0.0991421	−	0.171719i	−0.911330	+	0.411677i	$0.864943\pi$
$770$	9.03971	+	2.07518i	0.325768	+	0.0747843i
$771$		0			0
$772$	−1.45936	−	1.62079i	−0.0525236	−	0.0583334i
$773$	−39.4097	+	28.6328i	−1.41747	+	1.02985i	−0.425284	+	0.905060i	$0.639826\pi$
$773$	−39.4097	+	28.6328i	−1.41747	+	1.02985i	−0.992183	+	0.124790i	$0.960174\pi$
$774$		0			0
$775$	−7.16186	−	22.0419i	−0.257262	−	0.791770i
$776$	−5.16536	−	1.09793i	−0.185426	−	0.0394134i
$777$		0			0
$778$	21.9606	+	9.77749i	0.787325	+	0.350540i
$779$	−24.4106	+	5.18863i	−0.874599	+	0.185902i
$780$		0			0
$781$	−11.6431	+	33.9507i	−0.416623	+	1.21485i
$782$	−6.63466			−0.237255
$783$		0			0
$784$	5.76597	−	4.18922i	0.205927	−	0.149615i
$785$	29.8335	−	13.2827i	1.06480	−	0.474082i
$786$		0			0
$787$	13.6091	−	15.1145i	0.485114	−	0.538773i	−0.450043	−	0.893007i	$-0.648591\pi$
$787$	13.6091	−	15.1145i	0.485114	−	0.538773i	0.935157	+	0.354233i	$0.115258\pi$
$788$	0.549770	−	5.23071i	0.0195847	−	0.186336i
$789$		0			0
$790$	19.1107	+	21.2245i	0.679927	+	0.755135i
$791$	27.7616			0.987088
$792$		0			0
$793$	−15.3924			−0.546601
$794$	−8.88695	−	9.86995i	−0.315386	−	0.350272i
$795$		0			0
$796$	1.19767	−	11.3951i	0.0424503	−	0.403888i
$797$	11.5649	−	12.8441i	0.409650	−	0.454963i	−0.502647	−	0.864492i	$-0.667640\pi$
$797$	11.5649	−	12.8441i	0.409650	−	0.454963i	0.912297	+	0.409529i	$0.134307\pi$
$798$		0			0
$799$	9.39969	−	4.18501i	0.332537	−	0.148055i
$800$	12.3356	−	8.96232i	0.436128	−	0.316866i
$801$		0			0
$802$	9.23484			0.326094
$803$	−4.37939	−	14.2611i	−0.154545	−	0.503263i
$804$		0			0
$805$	8.55763	−	1.81898i	0.301617	−	0.0641106i
$806$	7.96547	+	3.54646i	0.280572	+	0.124919i
$807$		0			0
$808$	−1.13034	−	0.240262i	−0.0397653	−	0.00845238i
$809$	3.94755	+	12.1493i	0.138789	+	0.427147i	0.996160	−	0.0875508i	$-0.0279040\pi$
$809$	3.94755	+	12.1493i	0.138789	+	0.427147i	−0.857371	+	0.514698i	$0.827904\pi$
$810$		0			0
$811$	−14.3899	+	10.4549i	−0.505298	+	0.367121i	−0.811037	−	0.584995i	$-0.801097\pi$
$811$	−14.3899	+	10.4549i	−0.505298	+	0.367121i	0.305739	+	0.952115i	$0.401097\pi$
$812$	12.3173	+	13.6797i	0.432252	+	0.480064i
$813$		0			0
$814$	−5.88335	+	9.81909i	−0.206211	+	0.344159i
$815$	−6.37757	−	11.0463i	−0.223397	−	0.386934i
$816$		0			0
$817$	1.08259	+	10.3002i	0.0378751	+	0.360357i
$818$	19.9969	+	14.5286i	0.699174	+	0.507980i
$819$		0			0
$820$	9.31430	+	28.6665i	0.325269	+	1.00108i
$821$	−27.7585	+	12.3589i	−0.968780	+	0.431329i	−0.829243	−	0.558888i	$-0.811228\pi$
$821$	−27.7585	+	12.3589i	−0.968780	+	0.431329i	−0.139537	+	0.990217i	$0.544561\pi$
$822$		0			0
$823$	−25.0774	+	5.33037i	−0.874143	+	0.185805i	−0.623073	−	0.782164i	$-0.714116\pi$
$823$	−25.0774	+	5.33037i	−0.874143	+	0.185805i	−0.251071	+	0.967969i	$0.580783\pi$
$824$	7.60194	+	13.1669i	0.264826	+	0.458692i
$825$		0			0
$826$	3.39919	−	5.88756i	0.118273	−	0.204855i
$827$	−3.14133	+	9.66803i	−0.109235	+	0.336190i	−0.990701	−	0.136057i	$-0.956557\pi$
$827$	−3.14133	+	9.66803i	−0.109235	+	0.336190i	0.881466	+	0.472247i	$0.156557\pi$
$828$		0			0
$829$	−2.17360	−	1.57922i	−0.0754924	−	0.0548484i	0.549399	−	0.835560i	$-0.314857\pi$
$829$	−2.17360	−	1.57922i	−0.0754924	−	0.0548484i	−0.624891	+	0.780712i	$0.714857\pi$
$830$	−6.06342	−	1.28882i	−0.210464	−	0.0447356i
$831$		0			0
$832$	−0.130657	+	1.24312i	−0.00452972	+	0.0430974i
$833$	20.3849	+	9.07594i	0.706295	+	0.314463i
$834$		0			0
$835$	13.6111	−	23.5751i	0.471031	−	0.815850i
$836$	−2.20482	+	18.1427i	−0.0762553	+	0.627479i
$837$		0			0
$838$	−0.483630	+	1.48846i	−0.0167067	+	0.0514180i
$839$	−1.36910	−	13.0262i	−0.0472667	−	0.449713i	−0.992402	−	0.123035i	$-0.960737\pi$
$839$	−1.36910	−	13.0262i	−0.0472667	−	0.449713i	0.945136	−	0.326678i	$-0.105929\pi$
$840$		0			0
$841$	21.8757	−	24.2954i	0.754335	−	0.837774i
$842$	6.87152	−	7.63159i	0.236808	−	0.263002i
$843$		0			0
$844$	−0.315327	−	3.00014i	−0.0108540	−	0.103269i
$845$	−9.22207	+	28.3826i	−0.317249	+	0.976391i
$846$		0			0
$847$	10.7117	+	12.7016i	0.368057	+	0.436431i
$848$	−10.1040	+	17.5006i	−0.346972	+	0.600973i
$849$		0			0
$850$	7.64763	+	3.40494i	0.262312	+	0.116789i
$851$	−1.12865	+	10.7384i	−0.0386897	+	0.368108i
$852$		0			0
$853$	−1.57801	−	0.335417i	−0.0540301	−	0.0114844i	0.180817	−	0.983517i	$-0.442126\pi$
$853$	−1.57801	−	0.335417i	−0.0540301	−	0.0114844i	−0.234847	+	0.972032i	$0.575459\pi$
$854$	−8.48156	−	6.16221i	−0.290233	−	0.210867i
$855$		0			0
$856$	8.89109	−	27.3639i	0.303891	−	0.935281i
$857$	20.7735	−	35.9807i	0.709608	−	1.22908i	−0.255395	−	0.966837i	$-0.582205\pi$
$857$	20.7735	−	35.9807i	0.709608	−	1.22908i	0.965003	−	0.262240i	$-0.0844612\pi$
$858$		0			0
$859$	−19.0349	−	32.9695i	−0.649463	−	1.12490i	−0.983251	−	0.182255i	$-0.941660\pi$
$859$	−19.0349	−	32.9695i	−0.649463	−	1.12490i	0.333788	−	0.942648i	$-0.391673\pi$
$860$	12.2357	−	2.60078i	0.417234	−	0.0886858i
$861$		0			0
$862$	−4.77984	+	2.12812i	−0.162802	+	0.0724841i
$863$	13.1442	+	40.4536i	0.447433	+	1.37706i	0.879793	+	0.475357i	$0.157681\pi$
$863$	13.1442	+	40.4536i	0.447433	+	1.37706i	−0.432360	+	0.901701i	$0.642319\pi$
$864$		0			0
$865$	32.8498	+	23.8668i	1.11693	+	0.811495i
$866$	1.76134	+	16.7580i	0.0598527	+	0.569461i
$867$		0			0
$868$	−10.2739	−	17.7948i	−0.348717	−	0.603996i
$869$	4.52245	+	50.9641i	0.153414	+	1.72884i
$870$		0			0
$871$	11.9638	+	13.2872i	0.405379	+	0.450219i
$872$	9.11742	−	6.62419i	0.308755	−	0.224323i
$873$		0			0
$874$	−1.53971	−	4.73875i	−0.0520816	−	0.160291i
$875$	9.62601	+	2.04607i	0.325419	+	0.0691699i
$876$		0			0
$877$	−7.22380	−	3.21624i	−0.243930	−	0.108605i	0.281130	−	0.959670i	$-0.409291\pi$
$877$	−7.22380	−	3.21624i	−0.243930	−	0.108605i	−0.525061	+	0.851065i	$0.675957\pi$
$878$	0.645773	−	0.137263i	0.0217938	−	0.00463241i
$879$		0			0
$880$	13.8484	+	0.224552i	0.466830	+	0.00756963i
$881$	41.5877			1.40113			0.700563	−	0.713591i	$-0.252932\pi$
$881$	41.5877			1.40113			0.700563	+	0.713591i	$0.252932\pi$
$882$		0			0
$883$	−9.71314	+	7.05701i	−0.326873	+	0.237487i	−0.739103	−	0.673593i	$-0.764750\pi$
$883$	−9.71314	+	7.05701i	−0.326873	+	0.237487i	0.412229	+	0.911080i	$0.364750\pi$
$884$	9.95486	−	4.43219i	0.334818	−	0.149071i
$885$		0			0
$886$	4.82830	−	5.36237i	0.162210	−	0.180152i
$887$	4.98779	−	47.4557i	0.167474	−	1.59341i	−0.511527	−	0.859267i	$-0.670920\pi$
$887$	4.98779	−	47.4557i	0.167474	−	1.59341i	0.679000	−	0.734138i	$-0.262413\pi$
$888$		0			0
$889$	−22.5821	−	25.0800i	−0.757380	−	0.841156i
$890$	−19.7325			−0.661434
$891$		0			0
$892$	−26.3436			−0.882050
$893$	5.17052	+	5.74244i	0.173025	+	0.192163i
$894$		0			0
$895$	−3.27267	+	31.1374i	−0.109393	+	1.04081i
$896$	11.0902	−	12.3169i	0.370497	−	0.411478i
$897$		0			0
$898$	14.1316	−	6.29181i	0.471579	−	0.209960i
$899$	−55.7124	+	40.4774i	−1.85811	+	1.35000i
$900$		0			0
$901$	−63.2683			−2.10777
$902$	5.06261	−	14.7623i	0.168567	−	0.491532i
$903$		0			0
$904$	−42.7564	+	9.08816i	−1.42206	+	0.302268i
$905$	−15.8935	−	7.07626i	−0.528319	−	0.235223i
$906$		0			0
$907$	2.19782	+	0.467161i	0.0729774	+	0.0155118i	0.244256	−	0.969711i	$-0.421456\pi$
$907$	2.19782	+	0.467161i	0.0729774	+	0.0155118i	−0.171278	+	0.985223i	$0.554790\pi$
$908$	−7.81720	−	24.0589i	−0.259423	−	0.798422i
$909$		0			0
$910$	3.35987	−	2.44109i	0.111379	−	0.0809213i
$911$	8.56488	+	9.51226i	0.283767	+	0.315155i	0.868130	−	0.496337i	$-0.165322\pi$
$911$	8.56488	+	9.51226i	0.283767	+	0.315155i	−0.584363	+	0.811493i	$0.698655\pi$
$912$		0			0
$913$	−7.29588	−	8.37196i	−0.241458	−	0.277071i
$914$	9.16370	+	15.8720i	0.303108	+	0.524999i
$915$		0			0
$916$	−3.29576	−	31.3571i	−0.108895	−	1.03607i
$917$	−4.85192	−	3.52513i	−0.160224	−	0.116410i
$918$		0			0
$919$	3.53256	+	10.8721i	0.116528	+	0.358637i	0.992263	−	0.124156i	$-0.0396223\pi$
$919$	3.53256	+	10.8721i	0.116528	+	0.358637i	−0.875734	+	0.482793i	$0.839622\pi$
$920$	−12.5844	+	5.60293i	−0.414895	+	0.184723i
$921$		0			0
$922$	12.7921	−	2.71905i	0.421287	−	0.0895472i
$923$	8.03567	+	13.9182i	0.264497	+	0.458123i
$924$		0			0
$925$	6.81198	−	11.7987i	0.223976	−	0.387939i
$926$	−3.01982	+	9.29405i	−0.0992375	+	0.305422i
$927$		0			0
$928$	−36.6530	−	26.6300i	−1.20319	−	0.874172i
$929$	9.03552	+	1.92056i	0.296446	+	0.0630115i	0.353734	−	0.935346i	$-0.384912\pi$
$929$	9.03552	+	1.92056i	0.296446	+	0.0630115i	−0.0572878	+	0.998358i	$0.518245\pi$
$930$		0			0
$931$	−1.75167	+	16.6660i	−0.0574087	+	0.546207i
$932$	−0.642115	−	0.285888i	−0.0210332	−	0.00936457i
$933$		0			0
$934$	−2.03359	+	3.52228i	−0.0665411	+	0.115253i
$935$	21.0699	+	37.9002i	0.689058	+	1.23947i
$936$		0			0
$937$	−10.4711	+	32.2266i	−0.342075	+	1.05280i	0.621056	+	0.783766i	$0.286704\pi$
$937$	−10.4711	+	32.2266i	−0.342075	+	1.05280i	−0.963131	+	0.269032i	$0.913296\pi$
$938$	1.27293	+	12.1111i	0.0415627	+	0.395443i
$939$		0			0
$940$	6.24494	−	6.93570i	0.203687	−	0.226218i
$941$	−7.07680	+	7.85958i	−0.230697	+	0.256215i	−0.847368	−	0.531006i	$-0.821814\pi$
$941$	−7.07680	+	7.85958i	−0.230697	+	0.256215i	0.616671	+	0.787221i	$0.288481\pi$
$942$		0			0
$943$	−1.53878	−	14.6405i	−0.0501096	−	0.476761i
$944$	3.13717	−	9.65521i	0.102106	−	0.314250i
$945$		0			0
$946$	−5.87331	−	2.72991i	−0.190958	−	0.0887570i
$947$	−1.82612	+	3.16292i	−0.0593408	+	0.102781i	−0.894170	−	0.447728i	$-0.852233\pi$
$947$	−1.82612	+	3.16292i	−0.0593408	+	0.102781i	0.834829	+	0.550510i	$0.185567\pi$
$948$		0			0
$949$	−6.10253	−	2.71702i	−0.198096	−	0.0881982i
$950$	−0.657159	+	6.25245i	−0.0213211	+	0.202856i
$951$		0			0
$952$	16.6177	+	3.53220i	0.538583	+	0.114479i
$953$	−11.6292	−	8.44909i	−0.376706	−	0.273693i	0.383280	−	0.923632i	$-0.374794\pi$
$953$	−11.6292	−	8.44909i	−0.376706	−	0.273693i	−0.759986	+	0.649939i	$0.774794\pi$
$954$		0			0
$955$	3.13522	−	9.64922i	0.101453	−	0.312241i
$956$	14.7738	−	25.5890i	0.477819	−	0.827607i
$957$		0			0
$958$	13.6001	+	23.5560i	0.439399	+	0.761061i
$959$	8.85163	−	1.88147i	0.285834	−	0.0607559i
$960$		0			0
$961$	41.9039	−	18.6568i	1.35174	−	0.601832i
$962$	1.58388	+	4.87469i	0.0510665	+	0.157166i
$963$		0			0
$964$	−22.4327	−	16.2983i	−0.722508	−	0.524933i
$965$	−0.406220	−	3.86492i	−0.0130767	−	0.124416i
$966$		0			0
$967$	−17.6955	−	30.6496i	−0.569050	−	0.985623i	−0.996660	−	0.0816600i	$-0.973978\pi$
$967$	−17.6955	−	30.6496i	−0.569050	−	0.985623i	0.427610	−	0.903963i	$-0.359356\pi$
$968$	−20.6554	−	16.0554i	−0.663889	−	0.516041i
$969$		0			0
$970$	−2.75062	−	3.05488i	−0.0883172	−	0.0980862i
$971$	0.118477	−	0.0860787i	0.00380211	−	0.00276240i	−0.585883	−	0.810396i	$-0.699252\pi$
$971$	0.118477	−	0.0860787i	0.00380211	−	0.00276240i	0.589685	+	0.807634i	$0.299252\pi$
$972$		0			0
$973$	8.02293	+	24.6920i	0.257203	+	0.791591i
$974$	9.69691	+	2.06114i	0.310709	+	0.0660432i
$975$		0			0
$976$	−14.3021	−	6.36769i	−0.457798	−	0.203825i
$977$	39.1373	−	8.31889i	1.25211	−	0.266145i	0.466310	−	0.884622i	$-0.345583\pi$
$977$	39.1373	−	8.31889i	1.25211	−	0.266145i	0.785803	+	0.618477i	$0.212250\pi$
$978$		0			0
$979$	−28.2578	−	21.2389i	−0.903122	−	0.678798i
$980$	20.2401			0.646545
$981$		0			0
$982$	21.3896	−	15.5404i	0.682568	−	0.495915i
$983$	−13.9510	+	6.21137i	−0.444967	+	0.198112i	−0.616974	−	0.786984i	$-0.711641\pi$
$983$	−13.9510	+	6.21137i	−0.444967	+	0.198112i	0.172007	+	0.985096i	$0.444975\pi$
$984$		0			0
$985$	6.27092	−	6.96456i	0.199808	−	0.221909i
$986$	2.60005	−	24.7378i	0.0828025	−	0.787813i
$987$		0			0
$988$	5.47590	+	6.08160i	0.174212	+	0.193482i
$989$	−6.10940			−0.194268
$990$		0			0
$991$	21.5067			0.683184			0.341592	−	0.939848i	$-0.389034\pi$
$991$	21.5067			0.683184			0.341592	+	0.939848i	$0.389034\pi$
$992$	33.8394	+	37.5825i	1.07440	+	1.19325i
$993$		0			0
$994$	−1.14419	+	10.8862i	−0.0362915	+	0.345290i
$995$	13.6612	−	15.1723i	0.433088	−	0.480993i
$996$		0			0
$997$	−20.1502	+	8.97143i	−0.638162	+	0.284128i	−0.700201	−	0.713946i	$-0.746906\pi$
$997$	−20.1502	+	8.97143i	−0.638162	+	0.284128i	0.0620390	+	0.998074i	$0.480240\pi$
$998$	−1.72106	+	1.25042i	−0.0544791	+	0.0395814i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.g.460.2		32
3.2	odd	2	inner	891.2.n.g.460.3		32
9.2	odd	6		297.2.f.c.163.3	yes	16
9.4	even	3	inner	891.2.n.g.757.3		32
9.5	odd	6	inner	891.2.n.g.757.2		32
9.7	even	3		297.2.f.c.163.2	yes	16
11.5	even	5	inner	891.2.n.g.379.3		32
33.5	odd	10	inner	891.2.n.g.379.2		32
99.5	odd	30	inner	891.2.n.g.676.3		32
99.7	odd	30		3267.2.a.bh.1.5		8
99.16	even	15		297.2.f.c.82.2	✓	16
99.29	even	30		3267.2.a.bh.1.4		8
99.38	odd	30		297.2.f.c.82.3	yes	16
99.49	even	15	inner	891.2.n.g.676.2		32
99.70	even	15		3267.2.a.bg.1.4		8
99.92	odd	30		3267.2.a.bg.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.c.82.2	✓	16	99.16	even	15
297.2.f.c.82.3	yes	16	99.38	odd	30
297.2.f.c.163.2	yes	16	9.7	even	3
297.2.f.c.163.3	yes	16	9.2	odd	6
891.2.n.g.379.2		32	33.5	odd	10	inner
891.2.n.g.379.3		32	11.5	even	5	inner
891.2.n.g.460.2		32	1.1	even	1	trivial
891.2.n.g.460.3		32	3.2	odd	2	inner
891.2.n.g.676.2		32	99.49	even	15	inner
891.2.n.g.676.3		32	99.5	odd	30	inner
891.2.n.g.757.2		32	9.5	odd	6	inner
891.2.n.g.757.3		32	9.4	even	3	inner
3267.2.a.bg.1.4		8	99.70	even	15
3267.2.a.bg.1.5		8	99.92	odd	30
3267.2.a.bh.1.4		8	99.29	even	30
3267.2.a.bh.1.5		8	99.7	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)

\(f(q)\)	\(=\)	\(q+(-0.448085 - 0.497649i) q^{2} +(0.162183 - 1.54307i) q^{4} +(1.84993 - 2.05455i) q^{5} +(1.37990 - 0.614370i) q^{7} +(-1.92410 + 1.39794i) q^{8} -1.85137 q^{10} +(-2.65125 - 1.99271i) q^{11} +(-1.45264 + 0.308769i) q^{13} +(-0.924052 - 0.411414i) q^{14} +(-1.47748 - 0.314048i) q^{16} +(-1.46138 - 4.49766i) q^{17} +(2.87328 - 2.08756i) q^{19} +(-2.87028 - 3.18777i) q^{20} +(0.196315 + 2.21229i) q^{22} +(1.04751 + 1.81434i) q^{23} +(-0.276313 - 2.62894i) q^{25} +(0.804567 + 0.584552i) q^{26} +(-0.724217 - 2.22891i) q^{28} +(-7.17542 + 3.19470i) q^{29} +(8.57593 - 1.82287i) q^{31} +(2.88407 + 4.99535i) q^{32} +(-1.58343 + 2.74259i) q^{34} +(1.29045 - 3.97161i) q^{35} +(4.16960 + 3.02939i) q^{37} +(-2.32634 - 0.494480i) q^{38} +(-0.687303 + 6.53925i) q^{40} +(-6.41924 - 2.85803i) q^{41} +(-1.45808 + 2.52546i) q^{43} +(-3.50487 + 3.76786i) q^{44} +(0.433531 - 1.33427i) q^{46} +(0.227425 + 2.16380i) q^{47} +(-3.15725 + 3.50648i) q^{49} +(-1.18448 + 1.31550i) q^{50} +(0.240857 + 2.29160i) q^{52} +(4.13417 - 12.7237i) q^{53} +(-8.99874 + 1.76076i) q^{55} +(-1.79621 + 3.11112i) q^{56} +(4.80504 + 2.13934i) q^{58} +(-0.702544 + 6.68426i) q^{59} +(10.1381 + 2.15492i) q^{61} +(-4.74990 - 3.45100i) q^{62} +(0.260092 - 0.800479i) q^{64} +(-2.05290 + 3.55573i) q^{65} +(-6.01970 - 10.4264i) q^{67} +(-7.17720 + 1.52556i) q^{68} +(-2.55470 + 1.13743i) q^{70} +(-3.34410 - 10.2921i) q^{71} +(3.63900 + 2.64389i) q^{73} +(-0.360762 - 3.43242i) q^{74} +(-2.75524 - 4.77222i) q^{76} +(-4.88271 - 1.12089i) q^{77} +(-10.3224 - 11.4642i) q^{79} +(-3.37845 + 2.45459i) q^{80} +(1.45407 + 4.47517i) q^{82} +(3.27510 + 0.696143i) q^{83} +(-11.9441 - 5.31787i) q^{85} +(1.91014 - 0.406012i) q^{86} +(7.88694 + 0.127887i) q^{88} +10.6583 q^{89} +(-1.81480 + 1.31853i) q^{91} +(2.96954 - 1.32212i) q^{92} +(0.974908 - 1.08275i) q^{94} +(1.02636 - 9.76513i) q^{95} +(1.48572 + 1.65006i) q^{97} +3.15971 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{4} - 8 q^{7} - 24 q^{10} - 8 q^{13} + 2 q^{16} + 20 q^{19} + 24 q^{22} + 16 q^{25} - 60 q^{28} + 6 q^{31} - 32 q^{34} + 24 q^{37} + 40 q^{40} + 80 q^{43} - 24 q^{46} - 40 q^{49} - 12 q^{52}+ \cdots + 46 q^{94}+O(q^{100}) \) 32 * q - 2 * q^4 - 8 * q^7 - 24 * q^10 - 8 * q^13 + 2 * q^16 + 20 * q^19 + 24 * q^22 + 16 * q^25 - 60 * q^28 + 6 * q^31 - 32 * q^34 + 24 * q^37 + 40 * q^40 + 80 * q^43 - 24 * q^46 - 40 * q^49 - 12 * q^52 + 112 * q^55 + 50 * q^58 + 6 * q^61 + 12 * q^64 - 64 * q^67 - 74 * q^70 - 64 * q^73 - 52 * q^76 + 4 * q^79 + 8 * q^82 - 70 * q^85 - 56 * q^88 - 188 * q^91 + 46 * q^94

Introduction

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