LMFDB - Embedded newform 1152.2.w.a.431.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(143,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("1152.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.w (of order $8$, degree $4$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			431.8
Character	$\chi$	$=$	1152.431
Dual form			1152.2.w.a.719.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.97412 - 1.23192i) q^{5} +(-0.237717 - 0.237717i) q^{7} +O(q^{10})$	$q+(2.97412 - 1.23192i) q^{5} +(-0.237717 - 0.237717i) q^{7} +(-2.12394 + 0.879764i) q^{11} +(0.0390635 - 0.0943077i) q^{13} +4.16112 q^{17} +(4.25390 + 1.76202i) q^{19} +(4.84847 + 4.84847i) q^{23} +(3.79221 - 3.79221i) q^{25} +(2.90419 - 7.01132i) q^{29} -9.88480i q^{31} +(-0.999845 - 0.414149i) q^{35} +(0.175641 + 0.424034i) q^{37} +(-7.67919 + 7.67919i) q^{41} +(-2.99581 - 7.23252i) q^{43} +6.10937i q^{47} -6.88698i q^{49} +(4.28258 + 10.3391i) q^{53} +(-5.23304 + 5.23304i) q^{55} +(-1.19303 - 2.88024i) q^{59} +(6.29246 + 2.60642i) q^{61} -0.328605i q^{65} +(5.66771 - 13.6831i) q^{67} +(-3.49288 + 3.49288i) q^{71} +(-1.42542 - 1.42542i) q^{73} +(0.714030 + 0.295761i) q^{77} -1.53778 q^{79} +(2.95890 - 7.14340i) q^{83} +(12.3756 - 5.12616i) q^{85} +(-1.92767 - 1.92767i) q^{89} +(-0.0317046 + 0.0131325i) q^{91} +14.8223 q^{95} -12.9791 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) $ 32 * q - 8 * q^11 + 16 * q^29 + 24 * q^35 + 16 * q^53 + 32 * q^55 + 32 * q^59 + 32 * q^61 + 16 * q^67 + 16 * q^71 + 16 * q^77 + 32 * q^79 - 40 * q^83 + 48 * q^91 - 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.97412	−	1.23192i	1.33007	−	0.550931i	0.399391	−	0.916781i	$-0.369222\pi$
$5$	2.97412	−	1.23192i	1.33007	−	0.550931i	0.930674	+	0.365850i	$0.119222\pi$
$6$		0			0
$7$	−0.237717	−	0.237717i	−0.0898485	−	0.0898485i	0.660754	−	0.750603i	$-0.270237\pi$
$7$	−0.237717	−	0.237717i	−0.0898485	−	0.0898485i	−0.750603	+	0.660754i	$0.770237\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.12394	+	0.879764i	−0.640391	+	0.265259i	−0.679161	−	0.733989i	$-0.737656\pi$
$11$	−2.12394	+	0.879764i	−0.640391	+	0.265259i	0.0387695	+	0.999248i	$0.487656\pi$
$12$		0			0
$13$	0.0390635	−	0.0943077i	0.0108343	−	0.0261562i	−0.918370	−	0.395723i	$-0.870494\pi$
$13$	0.0390635	−	0.0943077i	0.0108343	−	0.0261562i	0.929204	+	0.369567i	$0.120494\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.16112			1.00922			0.504609	−	0.863348i	$-0.331636\pi$
$17$	4.16112			1.00922			0.504609	+	0.863348i	$0.331636\pi$
$18$		0			0
$19$	4.25390	+	1.76202i	0.975912	+	0.404236i	0.812910	−	0.582390i	$-0.197882\pi$
$19$	4.25390	+	1.76202i	0.975912	+	0.404236i	0.163002	+	0.986626i	$0.447882\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.84847	+	4.84847i	1.01098	+	1.01098i	0.999939	+	0.0110368i	$0.00351321\pi$
$23$	4.84847	+	4.84847i	1.01098	+	1.01098i	0.0110368	+	0.999939i	$0.496487\pi$
$24$		0			0
$25$	3.79221	−	3.79221i	0.758441	−	0.758441i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.90419	−	7.01132i	0.539294	−	1.30197i	−0.385923	−	0.922531i	$-0.626117\pi$
$29$	2.90419	−	7.01132i	0.539294	−	1.30197i	0.925217	−	0.379439i	$-0.123883\pi$
$30$		0			0
$31$		−	9.88480i		−	1.77536i	−0.460459	−	0.887681i	$-0.652315\pi$
$31$		−	9.88480i		−	1.77536i	0.460459	−	0.887681i	$-0.347685\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.999845	−	0.414149i	−0.169005	−	0.0700040i
$36$		0			0
$37$	0.175641	+	0.424034i	0.0288752	+	0.0697108i	0.937659	−	0.347556i	$-0.112988\pi$
$37$	0.175641	+	0.424034i	0.0288752	+	0.0697108i	−0.908784	+	0.417266i	$0.862988\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.67919	+	7.67919i	−1.19929	+	1.19929i	−0.224907	+	0.974380i	$0.572208\pi$
$41$	−7.67919	+	7.67919i	−1.19929	+	1.19929i	−0.974380	+	0.224907i	$0.927792\pi$
$42$		0			0
$43$	−2.99581	−	7.23252i	−0.456857	−	1.10295i	−0.969663	−	0.244445i	$-0.921394\pi$
$43$	−2.99581	−	7.23252i	−0.456857	−	1.10295i	0.512807	−	0.858504i	$-0.328606\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			6.10937i			0.891143i	0.895246	+	0.445571i	$0.146999\pi$
$47$			6.10937i			0.891143i	−0.895246	+	0.445571i	$0.853001\pi$
$48$		0			0
$49$		−	6.88698i		−	0.983855i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.28258	+	10.3391i	0.588258	+	1.42018i	0.885167	+	0.465274i	$0.154044\pi$
$53$	4.28258	+	10.3391i	0.588258	+	1.42018i	−0.296909	+	0.954906i	$0.595956\pi$
$54$		0			0
$55$	−5.23304	+	5.23304i	−0.705623	+	0.705623i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.19303	−	2.88024i	−0.155320	−	0.374975i	0.826996	−	0.562208i	$-0.190048\pi$
$59$	−1.19303	−	2.88024i	−0.155320	−	0.374975i	−0.982316	+	0.187233i	$0.940048\pi$
$60$		0			0
$61$	6.29246	+	2.60642i	0.805667	+	0.333718i	0.747224	−	0.664573i	$-0.231386\pi$
$61$	6.29246	+	2.60642i	0.805667	+	0.333718i	0.0584431	+	0.998291i	$0.481386\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	0.328605i		−	0.0407584i
$66$		0			0
$67$	5.66771	−	13.6831i	0.692420	−	1.67165i	−0.0474259	−	0.998875i	$-0.515102\pi$
$67$	5.66771	−	13.6831i	0.692420	−	1.67165i	0.739846	−	0.672776i	$-0.234898\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.49288	+	3.49288i	−0.414528	+	0.414528i	−0.883313	−	0.468784i	$-0.844692\pi$
$71$	−3.49288	+	3.49288i	−0.414528	+	0.414528i	0.468784	+	0.883313i	$0.344692\pi$
$72$		0			0
$73$	−1.42542	−	1.42542i	−0.166833	−	0.166833i	0.618753	−	0.785586i	$-0.287638\pi$
$73$	−1.42542	−	1.42542i	−0.166833	−	0.166833i	−0.785586	+	0.618753i	$0.787638\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.714030	+	0.295761i	0.0813713	+	0.0337051i
$78$		0			0
$79$	−1.53778			−0.173014			−0.0865070	−	0.996251i	$-0.527570\pi$
$79$	−1.53778			−0.173014			−0.0865070	+	0.996251i	$0.527570\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.95890	−	7.14340i	0.324781	−	0.784091i	−0.674182	−	0.738565i	$-0.735504\pi$
$83$	2.95890	−	7.14340i	0.324781	−	0.784091i	0.998963	−	0.0455255i	$-0.0144962\pi$
$84$		0			0
$85$	12.3756	−	5.12616i	1.34233	−	0.556010i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.92767	−	1.92767i	−0.204333	−	0.204333i	0.597521	−	0.801853i	$-0.296153\pi$
$89$	−1.92767	−	1.92767i	−0.204333	−	0.204333i	−0.801853	+	0.597521i	$0.796153\pi$
$90$		0			0
$91$	−0.0317046	+	0.0131325i	−0.00332354	+	0.00137666i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	14.8223			1.52073
$96$		0			0
$97$	−12.9791			−1.31783			−0.658915	−	0.752218i	$-0.728984\pi$
$97$	−12.9791			−1.31783			−0.658915	+	0.752218i	$0.728984\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	10.2765	−	4.25666i	1.02255	−	0.423554i	0.192532	−	0.981291i	$-0.438330\pi$
$101$	10.2765	−	4.25666i	1.02255	−	0.423554i	0.830018	+	0.557737i	$0.188330\pi$
$102$		0			0
$103$	6.66422	+	6.66422i	0.656645	+	0.656645i	0.954585	−	0.297940i	$-0.0962994\pi$
$103$	6.66422	+	6.66422i	0.656645	+	0.656645i	−0.297940	+	0.954585i	$0.596299\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.1377	−	4.61340i	1.07673	−	0.445994i	0.227366	−	0.973809i	$-0.426989\pi$
$107$	11.1377	−	4.61340i	1.07673	−	0.445994i	0.849359	+	0.527815i	$0.176989\pi$
$108$		0			0
$109$	−3.68462	+	8.89546i	−0.352922	+	0.852030i	0.643334	+	0.765585i	$0.277551\pi$
$109$	−3.68462	+	8.89546i	−0.352922	+	0.852030i	−0.996257	+	0.0864447i	$0.972449\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.16123			−0.673672			−0.336836	−	0.941563i	$-0.609357\pi$
$113$	−7.16123			−0.673672			−0.336836	+	0.941563i	$0.609357\pi$
$114$		0			0
$115$	20.3928	+	8.44699i	1.90164	+	0.787686i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.989167	−	0.989167i	−0.0906768	−	0.0906768i
$120$		0			0
$121$	−4.04105	+	4.04105i	−0.367368	+	0.367368i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.447173	−	1.07957i	0.0399964	−	0.0965599i
$126$		0			0
$127$			9.41925i			0.835823i	0.908488	+	0.417911i	$0.137238\pi$
$127$			9.41925i			0.835823i	−0.908488	+	0.417911i	$0.862762\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.15026	+	1.30488i	0.275240	+	0.114008i	0.516034	−	0.856568i	$-0.327408\pi$
$131$	3.15026	+	1.30488i	0.275240	+	0.114008i	−0.240794	+	0.970576i	$0.577408\pi$
$132$		0			0
$133$	−0.592361	−	1.43009i	−0.0513642	−	0.124004i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.26376	+	8.26376i	−0.706021	+	0.706021i	−0.965696	−	0.259675i	$-0.916384\pi$
$137$	−8.26376	+	8.26376i	−0.706021	+	0.706021i	0.259675	+	0.965696i	$0.416384\pi$
$138$		0			0
$139$	−0.429473	−	1.03684i	−0.0364274	−	0.0879436i	0.904619	−	0.426222i	$-0.140156\pi$
$139$	−0.429473	−	1.03684i	−0.0364274	−	0.0879436i	−0.941046	+	0.338278i	$0.890156\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			0.234670i			0.0196241i
$144$		0			0
$145$		−	24.4302i		−	2.02882i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.253180	+	0.611230i	0.0207413	+	0.0500739i	0.933911	−	0.357506i	$-0.116373\pi$
$149$	0.253180	+	0.611230i	0.0207413	+	0.0500739i	−0.913170	+	0.407580i	$0.866373\pi$
$150$		0			0
$151$	−11.4878	+	11.4878i	−0.934862	+	0.934862i	−0.998005	−	0.0631423i	$-0.979888\pi$
$151$	−11.4878	+	11.4878i	−0.934862	+	0.934862i	0.0631423	+	0.998005i	$0.479888\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.1773	−	29.3985i	−0.978102	−	2.36135i
$156$		0			0
$157$	−13.7120	−	5.67968i	−1.09433	−	0.453288i	−0.238818	−	0.971064i	$-0.576760\pi$
$157$	−13.7120	−	5.67968i	−1.09433	−	0.453288i	−0.855516	+	0.517777i	$0.826760\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	2.30512i		−	0.181669i
$162$		0			0
$163$	−2.66632	+	6.43706i	−0.208842	+	0.504189i	−0.993241	−	0.116067i	$-0.962971\pi$
$163$	−2.66632	+	6.43706i	−0.208842	+	0.504189i	0.784399	+	0.620256i	$0.212971\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.53445	+	6.53445i	−0.505651	+	0.505651i	−0.913188	−	0.407538i	$-0.866387\pi$
$167$	−6.53445	+	6.53445i	−0.505651	+	0.505651i	0.407538	+	0.913188i	$0.366387\pi$
$168$		0			0
$169$	9.18502	+	9.18502i	0.706540	+	0.706540i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.24361	−	1.34355i	−0.246607	−	0.102148i	0.255956	−	0.966688i	$-0.417610\pi$
$173$	−3.24361	−	1.34355i	−0.246607	−	0.102148i	−0.502563	+	0.864540i	$0.667610\pi$
$174$		0			0
$175$	−1.80294			−0.136290
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.86789	+	23.8232i	−0.737560	+	1.78063i	−0.122013	+	0.992528i	$0.538935\pi$
$179$	−9.86789	+	23.8232i	−0.737560	+	1.78063i	−0.615547	+	0.788100i	$0.711065\pi$
$180$		0			0
$181$	12.1863	−	5.04772i	0.905799	−	0.375194i	0.119352	−	0.992852i	$-0.461918\pi$
$181$	12.1863	−	5.04772i	0.905799	−	0.375194i	0.786447	+	0.617658i	$0.211918\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.04475	+	1.04475i	0.0768117	+	0.0768117i
$186$		0			0
$187$	−8.83795	+	3.66080i	−0.646295	+	0.267704i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.7590			0.923208			0.461604	−	0.887086i	$-0.347274\pi$
$191$	12.7590			0.923208			0.461604	+	0.887086i	$0.347274\pi$
$192$		0			0
$193$	−12.6078			−0.907531			−0.453766	−	0.891121i	$-0.649920\pi$
$193$	−12.6078			−0.907531			−0.453766	+	0.891121i	$0.649920\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.666855	+	0.276221i	−0.0475115	+	0.0196799i	−0.406313	−	0.913734i	$-0.633186\pi$
$197$	−0.666855	+	0.276221i	−0.0475115	+	0.0196799i	0.358801	+	0.933414i	$0.383186\pi$
$198$		0			0
$199$	4.26928	+	4.26928i	0.302641	+	0.302641i	0.842046	−	0.539405i	$-0.181351\pi$
$199$	4.26928	+	4.26928i	0.302641	+	0.302641i	−0.539405	+	0.842046i	$0.681351\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.35708	+	0.976336i	−0.165435	+	0.0685253i
$204$		0			0
$205$	−13.3787	+	32.2989i	−0.934406	+	2.25586i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−10.5852			−0.732193
$210$		0			0
$211$	−15.6370	−	6.47704i	−1.07649	−	0.445898i	−0.227215	−	0.973845i	$-0.572962\pi$
$211$	−15.6370	−	6.47704i	−1.07649	−	0.445898i	−0.849278	+	0.527947i	$0.822962\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−17.8198	−	17.8198i	−1.21530	−	1.21530i
$216$		0			0
$217$	−2.34978	+	2.34978i	−0.159514	+	0.159514i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.162548	−	0.392425i	0.0109342	−	0.0263974i
$222$		0			0
$223$		−	29.4910i		−	1.97487i	−0.158038	−	0.987433i	$-0.550517\pi$
$223$		−	29.4910i		−	1.97487i	0.158038	−	0.987433i	$-0.449483\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−18.5140	−	7.66873i	−1.22881	−	0.508992i	−0.328613	−	0.944465i	$-0.606581\pi$
$227$	−18.5140	−	7.66873i	−1.22881	−	0.508992i	−0.900202	+	0.435473i	$0.856581\pi$
$228$		0			0
$229$	2.09503	+	5.05785i	0.138444	+	0.334232i	0.977861	−	0.209255i	$-0.0671037\pi$
$229$	2.09503	+	5.05785i	0.138444	+	0.334232i	−0.839418	+	0.543487i	$0.817104\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.699144	+	0.699144i	−0.0458024	+	0.0458024i	−0.729637	−	0.683835i	$-0.760311\pi$
$233$	−0.699144	+	0.699144i	−0.0458024	+	0.0458024i	0.683835	+	0.729637i	$0.260311\pi$
$234$		0			0
$235$	7.52625	+	18.1700i	0.490958	+	1.18528i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			22.1034i			1.42975i	0.699253	+	0.714875i	$0.253516\pi$
$239$			22.1034i			1.42975i	−0.699253	+	0.714875i	$0.746484\pi$
$240$		0			0
$241$			9.09381i			0.585784i	0.956146	+	0.292892i	$0.0946176\pi$
$241$			9.09381i			0.585784i	−0.956146	+	0.292892i	$0.905382\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8.48420	−	20.4827i	−0.542036	−	1.30859i
$246$		0			0
$247$	0.332345	−	0.332345i	0.0211466	−	0.0211466i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.43019	−	3.45279i	−0.0902728	−	0.217938i	0.872294	−	0.488981i	$-0.162631\pi$
$251$	−1.43019	−	3.45279i	−0.0902728	−	0.217938i	−0.962567	+	0.271043i	$0.912631\pi$
$252$		0			0
$253$	−14.5634	−	6.03234i	−0.915591	−	0.379250i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			3.05245i			0.190406i	0.995458	+	0.0952032i	$0.0303501\pi$
$257$			3.05245i			0.190406i	−0.995458	+	0.0952032i	$0.969650\pi$
$258$		0			0
$259$	0.0590473	−	0.142553i	0.00366902	−	0.00885780i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.44480	+	2.44480i	−0.150753	+	0.150753i	−0.778454	−	0.627701i	$-0.783996\pi$
$263$	−2.44480	+	2.44480i	−0.150753	+	0.150753i	0.627701	+	0.778454i	$0.283996\pi$
$264$		0			0
$265$	25.4738	+	25.4738i	1.56484	+	1.56484i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−13.7507	−	5.69573i	−0.838395	−	0.347275i	−0.0781745	−	0.996940i	$-0.524909\pi$
$269$	−13.7507	−	5.69573i	−0.838395	−	0.347275i	−0.760221	+	0.649665i	$0.774909\pi$
$270$		0			0
$271$	−24.0583			−1.46144			−0.730720	−	0.682677i	$-0.760816\pi$
$271$	−24.0583			−1.46144			−0.730720	+	0.682677i	$0.760816\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.71816	+	11.3907i	−0.284516	+	0.686882i
$276$		0			0
$277$	−6.48199	+	2.68493i	−0.389465	+	0.161322i	−0.568819	−	0.822463i	$-0.692599\pi$
$277$	−6.48199	+	2.68493i	−0.389465	+	0.161322i	0.179354	+	0.983785i	$0.442599\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.59744	−	4.59744i	−0.274260	−	0.274260i	0.556552	−	0.830813i	$-0.312124\pi$
$281$	−4.59744	−	4.59744i	−0.274260	−	0.274260i	−0.830813	+	0.556552i	$0.812124\pi$
$282$		0			0
$283$	−17.9590	+	7.43884i	−1.06755	+	0.442193i	−0.846125	−	0.532984i	$-0.821070\pi$
$283$	−17.9590	+	7.43884i	−1.06755	+	0.442193i	−0.221424	+	0.975178i	$0.571070\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.65094			0.215508
$288$		0			0
$289$	0.314890			0.0185229
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.0302145	+	0.0125153i	−0.00176515	+	0.000731150i	−0.383566	−	0.923514i	$-0.625304\pi$
$293$	−0.0302145	+	0.0125153i	−0.00176515	+	0.000731150i	0.381801	+	0.924245i	$0.375304\pi$
$294$		0			0
$295$	−7.09645	−	7.09645i	−0.413171	−	0.413171i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.646646	−	0.267850i	0.0373965	−	0.0154901i
$300$		0			0
$301$	−1.00714	+	2.43145i	−0.0580504	+	0.140146i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	21.9254			1.25544
$306$		0			0
$307$	21.7209	+	8.99707i	1.23967	+	0.513490i	0.903613	−	0.428350i	$-0.140905\pi$
$307$	21.7209	+	8.99707i	1.23967	+	0.513490i	0.336062	+	0.941840i	$0.390905\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.59830	−	3.59830i	−0.204041	−	0.204041i	0.597688	−	0.801729i	$-0.296086\pi$
$311$	−3.59830	−	3.59830i	−0.204041	−	0.204041i	−0.801729	+	0.597688i	$0.796086\pi$
$312$		0			0
$313$	1.24094	−	1.24094i	0.0701421	−	0.0701421i	−0.671165	−	0.741308i	$-0.734206\pi$
$313$	1.24094	−	1.24094i	0.0701421	−	0.0701421i	0.741308	+	0.671165i	$0.234206\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.92298	−	7.05670i	0.164171	−	0.396344i	−0.820290	−	0.571948i	$-0.806188\pi$
$317$	2.92298	−	7.05670i	0.164171	−	0.396344i	0.984461	+	0.175604i	$0.0561879\pi$
$318$		0			0
$319$			17.4466i			0.976823i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	17.7010	+	7.33199i	0.984909	+	0.407963i
$324$		0			0
$325$	−0.209497	−	0.505771i	−0.0116208	−	0.0280551i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.45230	−	1.45230i	0.0800678	−	0.0800678i
$330$		0			0
$331$	−11.2439	−	27.1453i	−0.618023	−	1.49204i	−0.853996	−	0.520280i	$-0.825828\pi$
$331$	−11.2439	−	27.1453i	−0.618023	−	1.49204i	0.235973	−	0.971760i	$-0.424172\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	47.6771i		−	2.60488i
$336$		0			0
$337$			13.3438i			0.726882i	0.931617	+	0.363441i	$0.118398\pi$
$337$			13.3438i			0.726882i	−0.931617	+	0.363441i	$0.881602\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	8.69629	+	20.9947i	0.470930	+	1.13693i
$342$		0			0
$343$	−3.30117	+	3.30117i	−0.178246	+	0.178246i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.38445	+	8.17078i	0.181687	+	0.438631i	0.988314	−	0.152429i	$-0.0487097\pi$
$347$	3.38445	+	8.17078i	0.181687	+	0.438631i	−0.806628	+	0.591060i	$0.798710\pi$
$348$		0			0
$349$	17.9607	+	7.43958i	0.961416	+	0.398232i	0.807510	−	0.589854i	$-0.200815\pi$
$349$	17.9607	+	7.43958i	0.961416	+	0.398232i	0.153906	+	0.988085i	$0.450815\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	30.1730i		−	1.60594i	−0.596016	−	0.802972i	$-0.703251\pi$
$353$		−	30.1730i		−	1.60594i	0.596016	−	0.802972i	$-0.296749\pi$
$354$		0			0
$355$	−6.08528	+	14.6912i	−0.322973	+	0.779726i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.24818	+	5.24818i	−0.276988	+	0.276988i	−0.831905	−	0.554917i	$-0.812750\pi$
$359$	−5.24818	+	5.24818i	−0.276988	+	0.276988i	0.554917	+	0.831905i	$0.312750\pi$
$360$		0			0
$361$	1.55592	+	1.55592i	0.0818907	+	0.0818907i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.99538	−	2.48337i	−0.313812	−	0.129985i
$366$		0			0
$367$	31.3373			1.63580			0.817898	−	0.575363i	$-0.195139\pi$
$367$	31.3373			1.63580			0.817898	+	0.575363i	$0.195139\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.43973	−	3.47581i	0.0747469	−	0.180455i
$372$		0			0
$373$	12.2609	−	5.07863i	0.634845	−	0.262962i	−0.0419649	−	0.999119i	$-0.513362\pi$
$373$	12.2609	−	5.07863i	0.634845	−	0.262962i	0.676810	+	0.736158i	$0.263362\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.547774	−	0.547774i	−0.0282118	−	0.0282118i
$378$		0			0
$379$	−23.5487	+	9.75417i	−1.20961	+	0.501038i	−0.894093	−	0.447881i	$-0.852179\pi$
$379$	−23.5487	+	9.75417i	−1.20961	+	0.501038i	−0.315520	+	0.948919i	$0.602179\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−16.6719			−0.851896			−0.425948	−	0.904748i	$-0.640059\pi$
$383$	−16.6719			−0.851896			−0.425948	+	0.904748i	$0.640059\pi$
$384$		0			0
$385$	2.48796			0.126798
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.38281	+	0.572777i	−0.0701110	+	0.0290409i	−0.417463	−	0.908694i	$-0.637081\pi$
$389$	−1.38281	+	0.572777i	−0.0701110	+	0.0290409i	0.347352	+	0.937735i	$0.387081\pi$
$390$		0			0
$391$	20.1750	+	20.1750i	1.02030	+	1.02030i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.57354	+	1.89442i	−0.230120	+	0.0953187i
$396$		0			0
$397$	4.37989	−	10.5740i	0.219821	−	0.530694i	−0.775044	−	0.631907i	$-0.782272\pi$
$397$	4.37989	−	10.5740i	0.219821	−	0.530694i	0.994865	+	0.101213i	$0.0322724\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	23.7727			1.18715			0.593576	−	0.804778i	$-0.297716\pi$
$401$	23.7727			1.18715			0.593576	+	0.804778i	$0.297716\pi$
$402$		0			0
$403$	−0.932212	−	0.386135i	−0.0464368	−	0.0192348i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.746100	−	0.746100i	−0.0369828	−	0.0369828i
$408$		0			0
$409$	−24.1735	+	24.1735i	−1.19530	+	1.19530i	−0.219743	+	0.975558i	$0.570522\pi$
$409$	−24.1735	+	24.1735i	−1.19530	+	1.19530i	−0.975558	+	0.219743i	$0.929478\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.401077	+	0.968286i	−0.0197357	+	0.0476462i
$414$		0			0
$415$		−	24.8904i		−	1.22182i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.78167	+	2.80906i	0.331306	+	0.137232i	0.542135	−	0.840291i	$-0.317616\pi$
$419$	6.78167	+	2.80906i	0.331306	+	0.137232i	−0.210828	+	0.977523i	$0.567616\pi$
$420$		0			0
$421$	−9.06067	−	21.8744i	−0.441590	−	1.06609i	−0.975391	−	0.220482i	$-0.929237\pi$
$421$	−9.06067	−	21.8744i	−0.441590	−	1.06609i	0.533801	−	0.845610i	$-0.320763\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	15.7798	−	15.7798i	0.765433	−	0.765433i
$426$		0			0
$427$	−0.876233	−	2.11541i	−0.0424039	−	0.102372i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			22.9164i			1.10384i	0.833896	+	0.551922i	$0.186105\pi$
$431$			22.9164i			1.10384i	−0.833896	+	0.551922i	$0.813895\pi$
$432$		0			0
$433$		−	17.6486i		−	0.848139i	−0.905630	−	0.424070i	$-0.860601\pi$
$433$		−	17.6486i		−	0.848139i	0.905630	−	0.424070i	$-0.139399\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.0818	+	29.1680i	0.577951	+	1.39530i
$438$		0			0
$439$	−11.5122	+	11.5122i	−0.549449	+	0.549449i	−0.926281	−	0.376832i	$-0.877013\pi$
$439$	−11.5122	+	11.5122i	−0.549449	+	0.549449i	0.376832	+	0.926281i	$0.377013\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.4242	+	32.4089i	0.637804	+	1.53980i	0.829598	+	0.558360i	$0.188569\pi$
$443$	13.4242	+	32.4089i	0.637804	+	1.53980i	−0.191794	+	0.981435i	$0.561431\pi$
$444$		0			0
$445$	−8.10785	−	3.35838i	−0.384349	−	0.159202i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	16.3232i		−	0.770339i	−0.922846	−	0.385170i	$-0.874143\pi$
$449$		−	16.3232i		−	0.770339i	0.922846	−	0.385170i	$-0.125857\pi$
$450$		0			0
$451$	9.55425	−	23.0660i	0.449892	−	1.08614i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0781149	+	0.0781149i	−0.00366208	+	0.00366208i
$456$		0			0
$457$	−22.1907	−	22.1907i	−1.03804	−	1.03804i	−0.999247	−	0.0387901i	$-0.987650\pi$
$457$	−22.1907	−	22.1907i	−1.03804	−	1.03804i	−0.0387901	−	0.999247i	$-0.512350\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−15.6722	−	6.49164i	−0.729927	−	0.302346i	−0.0134051	−	0.999910i	$-0.504267\pi$
$461$	−15.6722	−	6.49164i	−0.729927	−	0.302346i	−0.716522	+	0.697564i	$0.754267\pi$
$462$		0			0
$463$	21.1826			0.984441			0.492220	−	0.870471i	$-0.336185\pi$
$463$	21.1826			0.984441			0.492220	+	0.870471i	$0.336185\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.30158	−	10.3849i	0.199053	−	0.480557i	−0.792561	−	0.609793i	$-0.791253\pi$
$467$	4.30158	−	10.3849i	0.199053	−	0.480557i	0.991614	+	0.129236i	$0.0412525\pi$
$468$		0			0
$469$	−4.60000	+	1.90538i	−0.212408	+	0.0879824i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.7258	+	12.7258i	0.585134	+	0.585134i
$474$		0			0
$475$	22.8136	−	9.44971i	1.04676	−	0.433583i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−36.0607			−1.64766			−0.823828	−	0.566840i	$-0.808166\pi$
$479$	−36.0607			−1.64766			−0.823828	+	0.566840i	$0.808166\pi$
$480$		0			0
$481$	0.0468509			0.00213622
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−38.6014	+	15.9892i	−1.75280	+	0.726033i
$486$		0			0
$487$	6.99084	+	6.99084i	0.316785	+	0.316785i	0.847531	−	0.530746i	$-0.178088\pi$
$487$	6.99084	+	6.99084i	0.316785	+	0.316785i	−0.530746	+	0.847531i	$0.678088\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.37664	−	2.64129i	0.287774	−	0.119200i	−0.234127	−	0.972206i	$-0.575223\pi$
$491$	6.37664	−	2.64129i	0.287774	−	0.119200i	0.521901	+	0.853006i	$0.325223\pi$
$492$		0			0
$493$	12.0847	−	29.1749i	0.544266	−	1.31397i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.66063			0.0744895
$498$		0			0
$499$	−7.43198	−	3.07843i	−0.332701	−	0.137809i	0.210078	−	0.977685i	$-0.432628\pi$
$499$	−7.43198	−	3.07843i	−0.332701	−	0.137809i	−0.542779	+	0.839875i	$0.682628\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−2.67081	−	2.67081i	−0.119086	−	0.119086i	0.645053	−	0.764138i	$-0.276835\pi$
$503$	−2.67081	−	2.67081i	−0.119086	−	0.119086i	−0.764138	+	0.645053i	$0.776835\pi$
$504$		0			0
$505$	25.3196	−	25.3196i	1.12671	−	1.12671i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9.36796	+	22.6162i	−0.415227	+	1.00245i	0.568484	+	0.822694i	$0.307530\pi$
$509$	−9.36796	+	22.6162i	−0.415227	+	1.00245i	−0.983712	+	0.179753i	$0.942470\pi$
$510$		0			0
$511$			0.677694i			0.0299794i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	28.0299	+	11.6104i	1.23515	+	0.511615i
$516$		0			0
$517$	−5.37480	−	12.9759i	−0.236384	−	0.570680i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−22.3821	+	22.3821i	−0.980579	+	0.980579i	−0.999815	−	0.0192357i	$-0.993877\pi$
$521$	−22.3821	+	22.3821i	−0.980579	+	0.980579i	0.0192357	+	0.999815i	$0.493877\pi$
$522$		0			0
$523$	−2.70300	−	6.52561i	−0.118194	−	0.285345i	0.853700	−	0.520765i	$-0.174353\pi$
$523$	−2.70300	−	6.52561i	−0.118194	−	0.285345i	−0.971894	+	0.235420i	$0.924353\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	41.1318i		−	1.79173i
$528$		0			0
$529$			24.0153i			1.04414i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.424230	+	1.02418i	0.0183755	+	0.0443623i
$534$		0			0
$535$	27.4416	−	27.4416i	1.18640	−	1.18640i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.05892	+	14.6275i	0.260976	+	0.630052i
$540$		0			0
$541$	−3.90965	−	1.61943i	−0.168089	−	0.0696246i	0.297052	−	0.954861i	$-0.403996\pi$
$541$	−3.90965	−	1.61943i	−0.168089	−	0.0696246i	−0.465141	+	0.885237i	$0.653996\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			30.9953i			1.32769i
$546$		0			0
$547$	−6.81941	+	16.4635i	−0.291577	+	0.703929i	−0.999998	−	0.00186067i	$-0.999408\pi$
$547$	−6.81941	+	16.4635i	−0.291577	+	0.703929i	0.708421	+	0.705790i	$0.249408\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	24.7082	−	24.7082i	1.05261	−	1.05261i
$552$		0			0
$553$	0.365556	+	0.365556i	0.0155450	+	0.0155450i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3.65431	−	1.51367i	−0.154838	−	0.0641361i	0.303918	−	0.952698i	$-0.401705\pi$
$557$	−3.65431	−	1.51367i	−0.154838	−	0.0641361i	−0.458757	+	0.888562i	$0.651705\pi$
$558$		0			0
$559$	−0.799109			−0.0337987
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.27091	−	3.06826i	0.0535626	−	0.129312i	−0.894833	−	0.446401i	$-0.852706\pi$
$563$	1.27091	−	3.06826i	0.0535626	−	0.129312i	0.948396	+	0.317089i	$0.102706\pi$
$564$		0			0
$565$	−21.2983	+	8.82206i	−0.896028	+	0.371147i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.04933	−	8.04933i	−0.337446	−	0.337446i	0.517960	−	0.855405i	$-0.326692\pi$
$569$	−8.04933	−	8.04933i	−0.337446	−	0.337446i	−0.855405	+	0.517960i	$0.826692\pi$
$570$		0			0
$571$	−24.5752	+	10.1794i	−1.02844	+	0.425994i	−0.832150	−	0.554551i	$-0.812890\pi$
$571$	−24.5752	+	10.1794i	−1.02844	+	0.425994i	−0.196292	+	0.980546i	$0.562890\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	36.7728			1.53353
$576$		0			0
$577$	6.56790			0.273425			0.136713	−	0.990611i	$-0.456346\pi$
$577$	6.56790			0.273425			0.136713	+	0.990611i	$0.456346\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.40149	+	0.994728i	−0.0996304	+	0.0412683i
$582$		0			0
$583$	−18.1919	−	18.1919i	−0.753430	−	0.753430i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−16.5921	+	6.87268i	−0.684830	+	0.283666i	−0.697844	−	0.716249i	$-0.745857\pi$
$587$	−16.5921	+	6.87268i	−0.684830	+	0.283666i	0.0130142	+	0.999915i	$0.495857\pi$
$588$		0			0
$589$	17.4172	−	42.0490i	0.717665	−	1.73260i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	28.8208			1.18353			0.591765	−	0.806111i	$-0.298431\pi$
$593$	28.8208			1.18353			0.591765	+	0.806111i	$0.298431\pi$
$594$		0			0
$595$	−4.16047	−	1.72332i	−0.170563	−	0.0706494i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.4840	+	17.4840i	0.714377	+	0.714377i	0.967448	−	0.253071i	$-0.0814405\pi$
$599$	17.4840	+	17.4840i	0.714377	+	0.714377i	−0.253071	+	0.967448i	$0.581440\pi$
$600$		0			0
$601$	33.1960	−	33.1960i	1.35409	−	1.35409i	0.473065	−	0.881028i	$-0.343148\pi$
$601$	33.1960	−	33.1960i	1.35409	−	1.35409i	0.881028	−	0.473065i	$-0.156852\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.04030	+	16.9968i	−0.286229	+	0.691017i
$606$		0			0
$607$		−	15.7874i		−	0.640790i	−0.947284	−	0.320395i	$-0.896184\pi$
$607$		−	15.7874i		−	0.640790i	0.947284	−	0.320395i	$-0.103816\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.576160	+	0.238653i	0.0233090	+	0.00965488i
$612$		0			0
$613$	−1.45651	−	3.51632i	−0.0588278	−	0.142023i	0.891733	−	0.452563i	$-0.149490\pi$
$613$	−1.45651	−	3.51632i	−0.0588278	−	0.142023i	−0.950560	+	0.310540i	$0.899490\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.98815	−	5.98815i	0.241074	−	0.241074i	−0.576220	−	0.817294i	$-0.695473\pi$
$617$	5.98815	−	5.98815i	0.241074	−	0.241074i	0.817294	+	0.576220i	$0.195473\pi$
$618$		0			0
$619$	7.03768	+	16.9905i	0.282868	+	0.682905i	0.999900	−	0.0141358i	$-0.00449972\pi$
$619$	7.03768	+	16.9905i	0.282868	+	0.682905i	−0.717032	+	0.697041i	$0.754500\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			0.916479i			0.0367179i
$624$		0			0
$625$			23.0533i			0.922132i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.730862	+	1.76446i	0.0291414	+	0.0703535i
$630$		0			0
$631$	19.0530	−	19.0530i	0.758486	−	0.758486i	−0.217561	−	0.976047i	$-0.569810\pi$
$631$	19.0530	−	19.0530i	0.758486	−	0.758486i	0.976047	+	0.217561i	$0.0698100\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	11.6037	+	28.0139i	0.460481	+	1.11170i
$636$		0			0
$637$	−0.649495	−	0.269030i	−0.0257339	−	0.0106593i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			4.84179i			0.191239i	0.995418	+	0.0956197i	$0.0304833\pi$
$641$			4.84179i			0.191239i	−0.995418	+	0.0956197i	$0.969517\pi$
$642$		0			0
$643$	1.99669	−	4.82043i	0.0787417	−	0.190099i	−0.879606	−	0.475702i	$-0.842194\pi$
$643$	1.99669	−	4.82043i	0.0787417	−	0.190099i	0.958348	+	0.285603i	$0.0921939\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.0278	−	23.0278i	0.905316	−	0.905316i	−0.0905742	−	0.995890i	$-0.528870\pi$
$647$	23.0278	−	23.0278i	0.905316	−	0.905316i	0.995890	+	0.0905742i	$0.0288702\pi$
$648$		0			0
$649$	5.06786	+	5.06786i	0.198931	+	0.198931i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	25.3058	+	10.4820i	0.990294	+	0.410193i	0.818229	−	0.574893i	$-0.194956\pi$
$653$	25.3058	+	10.4820i	0.990294	+	0.410193i	0.172065	+	0.985086i	$0.444956\pi$
$654$		0			0
$655$	10.9768			0.428897
$656$		0			0
$657$		0			0
$658$		0			0
$659$	8.74923	−	21.1225i	0.340821	−	0.822816i	−0.656812	−	0.754055i	$-0.728095\pi$
$659$	8.74923	−	21.1225i	0.340821	−	0.822816i	0.997633	−	0.0687611i	$-0.0219046\pi$
$660$		0			0
$661$	14.1409	−	5.85735i	0.550017	−	0.227824i	−0.0903280	−	0.995912i	$-0.528792\pi$
$661$	14.1409	−	5.85735i	0.550017	−	0.227824i	0.640345	+	0.768088i	$0.278792\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.52350	−	3.52350i	−0.136635	−	0.136635i
$666$		0			0
$667$	48.0751	−	19.9133i	1.86147	−	0.771048i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−15.6578			−0.604464
$672$		0			0
$673$	38.4339			1.48152			0.740758	−	0.671772i	$-0.234466\pi$
$673$	38.4339			1.48152			0.740758	+	0.671772i	$0.234466\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.0186	−	4.56407i	0.423481	−	0.175412i	−0.160757	−	0.986994i	$-0.551394\pi$
$677$	11.0186	−	4.56407i	0.423481	−	0.175412i	0.584238	+	0.811583i	$0.301394\pi$
$678$		0			0
$679$	3.08535	+	3.08535i	0.118405	+	0.118405i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	44.4586	−	18.4153i	1.70116	−	0.704643i	0.701195	−	0.712970i	$-0.252650\pi$
$683$	44.4586	−	18.4153i	1.70116	−	0.704643i	0.999965	+	0.00832649i	$0.00265043\pi$
$684$		0			0
$685$	−14.3971	+	34.7577i	−0.550085	+	1.32802i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.14235			0.0435199
$690$		0			0
$691$	2.14643	+	0.889080i	0.0816540	+	0.0338222i	0.423137	−	0.906066i	$-0.360929\pi$
$691$	2.14643	+	0.889080i	0.0816540	+	0.0338222i	−0.341483	+	0.939888i	$0.610929\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.55461	−	2.55461i	−0.0969017	−	0.0969017i
$696$		0			0
$697$	−31.9540	+	31.9540i	−1.21034	+	1.21034i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	11.0073	−	26.5740i	0.415740	−	1.00368i	−0.567828	−	0.823147i	$-0.692216\pi$
$701$	11.0073	−	26.5740i	0.415740	−	1.00368i	0.983568	−	0.180537i	$-0.0577837\pi$
$702$		0			0
$703$			2.11328i			0.0797040i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.45478	−	1.43101i	−0.129930	−	0.0538189i
$708$		0			0
$709$	2.62019	+	6.32569i	0.0984031	+	0.237566i	0.965413	−	0.260724i	$-0.0839613\pi$
$709$	2.62019	+	6.32569i	0.0984031	+	0.237566i	−0.867010	+	0.498290i	$0.833961\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	47.9261	−	47.9261i	1.79485	−	1.79485i
$714$		0			0
$715$	0.289095	+	0.697937i	0.0108115	+	0.0261014i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			17.1528i			0.639691i	0.947470	+	0.319845i	$0.103631\pi$
$719$			17.1528i			0.639691i	−0.947470	+	0.319845i	$0.896369\pi$
$720$		0			0
$721$		−	3.16839i		−	0.117997i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.5751	−	37.6017i	−0.578445	−	1.39649i
$726$		0			0
$727$	7.52775	−	7.52775i	0.279189	−	0.279189i	−0.553596	−	0.832785i	$-0.686745\pi$
$727$	7.52775	−	7.52775i	0.279189	−	0.279189i	0.832785	+	0.553596i	$0.186745\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.4659	−	30.0954i	−0.461068	−	1.11312i
$732$		0			0
$733$	−7.56986	−	3.13554i	−0.279599	−	0.115814i	0.238477	−	0.971148i	$-0.423352\pi$
$733$	−7.56986	−	3.13554i	−0.279599	−	0.115814i	−0.518076	+	0.855334i	$0.673352\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			34.0482i			1.25418i
$738$		0			0
$739$	−3.52118	+	8.50088i	−0.129529	+	0.312710i	−0.975317	−	0.220808i	$-0.929130\pi$
$739$	−3.52118	+	8.50088i	−0.129529	+	0.312710i	0.845789	+	0.533518i	$0.179130\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.66625	+	6.66625i	−0.244561	+	0.244561i	−0.818734	−	0.574173i	$-0.805324\pi$
$743$	−6.66625	+	6.66625i	−0.244561	+	0.244561i	0.574173	+	0.818734i	$0.305324\pi$
$744$		0			0
$745$	1.50597	+	1.50597i	0.0551745	+	0.0551745i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.74431	−	1.55094i	−0.136814	−	0.0566702i
$750$		0			0
$751$	−8.17302			−0.298238			−0.149119	−	0.988819i	$-0.547644\pi$
$751$	−8.17302			−0.298238			−0.149119	+	0.988819i	$0.547644\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−20.0140	+	48.3180i	−0.728383	+	1.75847i
$756$		0			0
$757$	−17.8950	+	7.41237i	−0.650406	+	0.269407i	−0.683395	−	0.730049i	$-0.739497\pi$
$757$	−17.8950	+	7.41237i	−0.650406	+	0.269407i	0.0329891	+	0.999456i	$0.489497\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	30.8536	+	30.8536i	1.11844	+	1.11844i	0.991970	+	0.126471i	$0.0403650\pi$
$761$	30.8536	+	30.8536i	1.11844	+	1.11844i	0.126471	+	0.991970i	$0.459635\pi$
$762$		0			0
$763$	2.99049	−	1.23870i	0.108263	−	0.0448441i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.318233			−0.0114907
$768$		0			0
$769$	36.0834			1.30120			0.650599	−	0.759421i	$-0.274518\pi$
$769$	36.0834			1.30120			0.650599	+	0.759421i	$0.274518\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	14.9974	−	6.21213i	0.539419	−	0.223435i	−0.0963038	−	0.995352i	$-0.530702\pi$
$773$	14.9974	−	6.21213i	0.539419	−	0.223435i	0.635723	+	0.771917i	$0.280702\pi$
$774$		0			0
$775$	−37.4852	−	37.4852i	−1.34651	−	1.34651i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−46.1974	+	19.1356i	−1.65519	+	0.685604i
$780$		0			0
$781$	4.34575	−	10.4916i	0.155503	−	0.375418i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−47.7779			−1.70527
$786$		0			0
$787$	−43.7262	−	18.1120i	−1.55867	−	0.645623i	−0.573813	−	0.818986i	$-0.694536\pi$
$787$	−43.7262	−	18.1120i	−1.55867	−	0.645623i	−0.984858	+	0.173364i	$0.944536\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.70234	+	1.70234i	0.0605284	+	0.0605284i
$792$		0			0
$793$	0.491611	−	0.491611i	0.0174576	−	0.0174576i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−10.6617	+	25.7396i	−0.377656	+	0.911742i	0.614748	+	0.788723i	$0.289258\pi$
$797$	−10.6617	+	25.7396i	−0.377656	+	0.911742i	−0.992404	+	0.123019i	$0.960742\pi$
$798$		0			0
$799$			25.4218i			0.899358i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.28155	+	1.77347i	0.151092	+	0.0625845i
$804$		0			0
$805$	−2.83973	−	6.85571i	−0.100087	−	0.241632i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−7.10579	+	7.10579i	−0.249826	+	0.249826i	−0.820899	−	0.571073i	$-0.806527\pi$
$809$	−7.10579	+	7.10579i	−0.249826	+	0.249826i	0.571073	+	0.820899i	$0.306527\pi$
$810$		0			0
$811$	12.7431	+	30.7646i	0.447471	+	1.08029i	0.973266	+	0.229680i	$0.0737680\pi$
$811$	12.7431	+	30.7646i	0.447471	+	1.08029i	−0.525795	+	0.850611i	$0.676232\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			22.4292i			0.785662i
$816$		0			0
$817$		−	36.0451i		−	1.26106i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.6756	−	42.6728i	−0.616884	−	1.48929i	−0.855303	−	0.518128i	$-0.826629\pi$
$821$	−17.6756	−	42.6728i	−0.616884	−	1.48929i	0.238419	−	0.971162i	$-0.423371\pi$
$822$		0			0
$823$	26.0687	−	26.0687i	0.908697	−	0.908697i	−0.0874705	−	0.996167i	$-0.527878\pi$
$823$	26.0687	−	26.0687i	0.908697	−	0.908697i	0.996167	+	0.0874705i	$0.0278784\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.996651	+	2.40613i	0.0346569	+	0.0836693i	0.940260	−	0.340456i	$-0.110582\pi$
$827$	0.996651	+	2.40613i	0.0346569	+	0.0836693i	−0.905603	+	0.424126i	$0.860582\pi$
$828$		0			0
$829$	15.8506	+	6.56553i	0.550514	+	0.228030i	0.640561	−	0.767907i	$-0.278702\pi$
$829$	15.8506	+	6.56553i	0.550514	+	0.228030i	−0.0900472	+	0.995938i	$0.528702\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		−	28.6575i		−	0.992925i
$834$		0			0
$835$	−11.3843	+	27.4841i	−0.393970	+	0.951127i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−22.7964	+	22.7964i	−0.787019	+	0.787019i	−0.981004	−	0.193985i	$-0.937859\pi$
$839$	−22.7964	+	22.7964i	−0.787019	+	0.787019i	0.193985	+	0.981004i	$0.437859\pi$
$840$		0			0
$841$	−20.2183	−	20.2183i	−0.697182	−	0.697182i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	38.6325	+	16.0021i	1.32900	+	0.550489i
$846$		0			0
$847$	1.92125			0.0660149
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.20433	+	2.90751i	−0.0412839	+	0.0996681i
$852$		0			0
$853$	−12.7603	+	5.28551i	−0.436906	+	0.180972i	−0.590285	−	0.807195i	$-0.700985\pi$
$853$	−12.7603	+	5.28551i	−0.436906	+	0.180972i	0.153379	+	0.988167i	$0.450985\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	18.2677	+	18.2677i	0.624014	+	0.624014i	0.946555	−	0.322542i	$-0.104537\pi$
$857$	18.2677	+	18.2677i	0.624014	+	0.624014i	−0.322542	+	0.946555i	$0.604537\pi$
$858$		0			0
$859$	11.7109	−	4.85082i	0.399572	−	0.165508i	−0.173843	−	0.984773i	$-0.555618\pi$
$859$	11.7109	−	4.85082i	0.399572	−	0.165508i	0.573414	+	0.819265i	$0.305618\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.2378			−0.416579			−0.208290	−	0.978067i	$-0.566790\pi$
$863$	−12.2378			−0.416579			−0.208290	+	0.978067i	$0.566790\pi$
$864$		0			0
$865$	−11.3020			−0.384280
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.26615	−	1.35288i	0.110797	−	0.0458935i
$870$		0			0
$871$	−1.06902	−	1.06902i	−0.0362222	−	0.0362222i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.362933	+	0.150332i	−0.0122694	+	0.00508214i
$876$		0			0
$877$	11.9105	−	28.7545i	0.402189	−	0.970971i	−0.584944	−	0.811073i	$-0.698884\pi$
$877$	11.9105	−	28.7545i	0.402189	−	0.970971i	0.987134	−	0.159897i	$-0.0511164\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.8002			−0.936611			−0.468306	−	0.883567i	$-0.655135\pi$
$881$	−27.8002			−0.936611			−0.468306	+	0.883567i	$0.655135\pi$
$882$		0			0
$883$	−39.6413	−	16.4200i	−1.33404	−	0.552576i	−0.402232	−	0.915538i	$-0.631765\pi$
$883$	−39.6413	−	16.4200i	−1.33404	−	0.552576i	−0.931804	+	0.362962i	$0.881765\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.491398	+	0.491398i	0.0164995	+	0.0164995i	0.715308	−	0.698809i	$-0.246286\pi$
$887$	0.491398	+	0.491398i	0.0164995	+	0.0164995i	−0.698809	+	0.715308i	$0.746286\pi$
$888$		0			0
$889$	2.23911	−	2.23911i	0.0750974	−	0.0750974i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−10.7649	+	25.9887i	−0.360232	+	0.869677i
$894$		0			0
$895$			83.0093i			2.77470i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−69.3055	−	28.7073i	−2.31147	−	0.957442i
$900$		0			0
$901$	17.8203	+	43.0220i	0.593681	+	1.43327i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	30.0250	−	30.0250i	0.998065	−	0.998065i
$906$		0			0
$907$	−0.533580	−	1.28817i	−0.0177172	−	0.0427731i	0.914773	−	0.403967i	$-0.132369\pi$
$907$	−0.533580	−	1.28817i	−0.0177172	−	0.0427731i	−0.932491	+	0.361194i	$0.882369\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	19.5482i		−	0.647661i	−0.946115	−	0.323830i	$-0.895029\pi$
$911$		−	19.5482i		−	0.647661i	0.946115	−	0.323830i	$-0.104971\pi$
$912$		0			0
$913$			17.7753i			0.588276i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.438678	−	1.05906i	−0.0144864	−	0.0349733i
$918$		0			0
$919$	−13.3357	+	13.3357i	−0.439905	+	0.439905i	−0.891980	−	0.452075i	$-0.850684\pi$
$919$	−13.3357	+	13.3357i	−0.439905	+	0.439905i	0.452075	+	0.891980i	$0.350684\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.192961	+	0.465849i	0.00635139	+	0.0153336i
$924$		0			0
$925$	2.27409	+	0.941960i	0.0747717	+	0.0309714i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	10.1690i		−	0.333632i	−0.985988	−	0.166816i	$-0.946651\pi$
$929$		−	10.1690i		−	0.333632i	0.985988	−	0.166816i	$-0.0533487\pi$
$930$		0			0
$931$	12.1350	−	29.2965i	0.397709	−	0.960155i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−21.7753	+	21.7753i	−0.712128	+	0.712128i
$936$		0			0
$937$	−19.7470	−	19.7470i	−0.645107	−	0.645107i	0.306699	−	0.951806i	$-0.400775\pi$
$937$	−19.7470	−	19.7470i	−0.645107	−	0.645107i	−0.951806	+	0.306699i	$0.900775\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	30.2481	+	12.5292i	0.986059	+	0.408439i	0.816667	−	0.577109i	$-0.195819\pi$
$941$	30.2481	+	12.5292i	0.986059	+	0.408439i	0.169393	+	0.985549i	$0.445819\pi$
$942$		0			0
$943$	−74.4646			−2.42490
$944$		0			0
$945$		0			0
$946$		0			0
$947$	21.4716	−	51.8370i	0.697732	−	1.68448i	−0.0308563	−	0.999524i	$-0.509823\pi$
$947$	21.4716	−	51.8370i	0.697732	−	1.68448i	0.728589	−	0.684951i	$-0.240177\pi$
$948$		0			0
$949$	−0.190110	+	0.0787463i	−0.00617124	+	0.00255621i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−39.2913	−	39.2913i	−1.27277	−	1.27277i	−0.944628	−	0.328143i	$-0.893577\pi$
$953$	−39.2913	−	39.2913i	−1.27277	−	1.27277i	−0.328143	−	0.944628i	$-0.606423\pi$
$954$		0			0
$955$	37.9467	−	15.7180i	1.22793	−	0.508624i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.92887			0.126870
$960$		0			0
$961$	−66.7092			−2.15191
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−37.4971	+	15.5318i	−1.20708	+	0.499987i
$966$		0			0
$967$	6.93096	+	6.93096i	0.222885	+	0.222885i	0.809712	−	0.586827i	$-0.199623\pi$
$967$	6.93096	+	6.93096i	0.222885	+	0.222885i	−0.586827	+	0.809712i	$0.699623\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−10.2938	+	4.26384i	−0.330345	+	0.136833i	−0.541690	−	0.840578i	$-0.682215\pi$
$971$	−10.2938	+	4.26384i	−0.330345	+	0.136833i	0.211346	+	0.977411i	$0.432215\pi$
$972$		0			0
$973$	−0.144381	+	0.348567i	−0.00462865	+	0.0111745i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−59.9974			−1.91949			−0.959743	−	0.280879i	$-0.909374\pi$
$977$	−59.9974			−1.91949			−0.959743	+	0.280879i	$0.909374\pi$
$978$		0			0
$979$	5.79015	+	2.39836i	0.185054	+	0.0766518i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−8.59392	−	8.59392i	−0.274104	−	0.274104i	0.556646	−	0.830750i	$-0.312088\pi$
$983$	−8.59392	−	8.59392i	−0.274104	−	0.274104i	−0.830750	+	0.556646i	$0.812088\pi$
$984$		0			0
$985$	−1.64302	+	1.64302i	−0.0523511	+	0.0523511i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	20.5416	−	49.5918i	0.653184	−	1.57693i
$990$		0			0
$991$			17.4869i			0.555488i	0.960655	+	0.277744i	$0.0895867\pi$
$991$			17.4869i			0.555488i	−0.960655	+	0.277744i	$0.910413\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	17.9567	+	7.43792i	0.569267	+	0.235798i
$996$		0			0
$997$	19.1891	+	46.3265i	0.607724	+	1.46718i	0.865469	+	0.500963i	$0.167021\pi$
$997$	19.1891	+	46.3265i	0.607724	+	1.46718i	−0.257745	+	0.966213i	$0.582979\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.a.431.8		32
3.2	odd	2		1152.2.w.b.431.1		32
4.3	odd	2		288.2.w.b.35.4	yes	32
12.11	even	2		288.2.w.a.35.5	✓	32
32.11	odd	8		1152.2.w.b.719.1		32
32.21	even	8		288.2.w.a.107.5	yes	32
96.11	even	8	inner	1152.2.w.a.719.8		32
96.53	odd	8		288.2.w.b.107.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.5	✓	32	12.11	even	2
288.2.w.a.107.5	yes	32	32.21	even	8
288.2.w.b.35.4	yes	32	4.3	odd	2
288.2.w.b.107.4	yes	32	96.53	odd	8
1152.2.w.a.431.8		32	1.1	even	1	trivial
1152.2.w.a.719.8		32	96.11	even	8	inner
1152.2.w.b.431.1		32	3.2	odd	2
1152.2.w.b.719.1		32	32.11	odd	8

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.w (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.97412 - 1.23192i) q^{5} +(-0.237717 - 0.237717i) q^{7} +O(q^{10})\)	\(q+(2.97412 - 1.23192i) q^{5} +(-0.237717 - 0.237717i) q^{7} +(-2.12394 + 0.879764i) q^{11} +(0.0390635 - 0.0943077i) q^{13} +4.16112 q^{17} +(4.25390 + 1.76202i) q^{19} +(4.84847 + 4.84847i) q^{23} +(3.79221 - 3.79221i) q^{25} +(2.90419 - 7.01132i) q^{29} -9.88480i q^{31} +(-0.999845 - 0.414149i) q^{35} +(0.175641 + 0.424034i) q^{37} +(-7.67919 + 7.67919i) q^{41} +(-2.99581 - 7.23252i) q^{43} +6.10937i q^{47} -6.88698i q^{49} +(4.28258 + 10.3391i) q^{53} +(-5.23304 + 5.23304i) q^{55} +(-1.19303 - 2.88024i) q^{59} +(6.29246 + 2.60642i) q^{61} -0.328605i q^{65} +(5.66771 - 13.6831i) q^{67} +(-3.49288 + 3.49288i) q^{71} +(-1.42542 - 1.42542i) q^{73} +(0.714030 + 0.295761i) q^{77} -1.53778 q^{79} +(2.95890 - 7.14340i) q^{83} +(12.3756 - 5.12616i) q^{85} +(-1.92767 - 1.92767i) q^{89} +(-0.0317046 + 0.0131325i) q^{91} +14.8223 q^{95} -12.9791 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) \) 32 * q - 8 * q^11 + 16 * q^29 + 24 * q^35 + 16 * q^53 + 32 * q^55 + 32 * q^59 + 32 * q^61 + 16 * q^67 + 16 * q^71 + 16 * q^77 + 32 * q^79 - 40 * q^83 + 48 * q^91 - 80 * q^95

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