LMFDB - Embedded newform 3024.2.cz.g.2719.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1279,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2, 5]))

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

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

chi := DirichletCharacter("3024.1279");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cz (of order $6$, degree $2$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2719.2
Character	$\chi$	$=$	3024.2719
Dual form			3024.2.cz.g.1279.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.47441 - 1.42860i) q^{5} +(2.59845 + 0.498066i) q^{7} +(1.95865 - 1.13083i) q^{11} +(-5.59072 + 3.22780i) q^{13} +(4.74820 + 2.74137i) q^{17} +(1.59123 + 2.75609i) q^{19} +(-5.17495 - 2.98776i) q^{23} +(1.58180 + 2.73976i) q^{25} +(-1.06838 + 1.85049i) q^{29} +4.03351 q^{31} +(-5.71808 - 4.94456i) q^{35} +(-5.06680 - 8.77595i) q^{37} +(-9.02256 + 5.20918i) q^{41} +(-0.0397018 - 0.0229218i) q^{43} -5.74706 q^{47} +(6.50386 + 2.58840i) q^{49} +(2.43844 - 4.22350i) q^{53} -6.46199 q^{55} -6.20774 q^{59} +6.98818i q^{61} +18.4450 q^{65} +7.88250i q^{67} +15.5442i q^{71} +(11.0585 + 6.38460i) q^{73} +(5.65267 - 1.96285i) q^{77} +12.0116i q^{79} +(-1.88456 + 3.26415i) q^{83} +(-7.83265 - 13.5666i) q^{85} +(3.95155 - 2.28143i) q^{89} +(-16.1349 + 5.60273i) q^{91} -9.09294i q^{95} +(4.62721 + 2.67152i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} - 4 q^{7} - 9 q^{11} - 3 q^{13} + 3 q^{17} + 4 q^{19} - 6 q^{23} + 15 q^{25} - 18 q^{29} - 34 q^{31} - 42 q^{35} - 3 q^{37} - 36 q^{41} - 24 q^{43} - 42 q^{47} + 30 q^{49} + 12 q^{53} + 30 q^{55}+ \cdots + 3 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 - 4 * q^7 - 9 * q^11 - 3 * q^13 + 3 * q^17 + 4 * q^19 - 6 * q^23 + 15 * q^25 - 18 * q^29 - 34 * q^31 - 42 * q^35 - 3 * q^37 - 36 * q^41 - 24 * q^43 - 42 * q^47 + 30 * q^49 + 12 * q^53 + 30 * q^55 - 12 * q^59 + 48 * q^73 + 48 * q^77 - 48 * q^83 - 21 * q^85 - 39 * q^89 - 9 * q^91 + 3 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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
$5$	−2.47441	−	1.42860i	−1.10659	−	0.638890i	−0.168646	−	0.985677i	$-0.553939\pi$
$5$	−2.47441	−	1.42860i	−1.10659	−	0.638890i	−0.937944	+	0.346787i	$0.887273\pi$
$6$		0			0
$7$	2.59845	+	0.498066i	0.982121	+	0.188251i
$7$	2.59845	+	0.498066i	0.982121	+	0.188251i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.95865	−	1.13083i	0.590554	−	0.340957i	−0.174762	−	0.984611i	$-0.555916\pi$
$11$	1.95865	−	1.13083i	0.590554	−	0.340957i	0.765317	+	0.643654i	$0.222582\pi$
$12$		0			0
$13$	−5.59072	+	3.22780i	−1.55059	+	0.895232i	−0.552493	+	0.833517i	$0.686323\pi$
$13$	−5.59072	+	3.22780i	−1.55059	+	0.895232i	−0.998094	+	0.0617145i	$0.980343\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.74820	+	2.74137i	1.15161	+	0.664880i	0.949278	−	0.314437i	$-0.101816\pi$
$17$	4.74820	+	2.74137i	1.15161	+	0.664880i	0.202328	+	0.979318i	$0.435149\pi$
$18$		0			0
$19$	1.59123	+	2.75609i	0.365054	+	0.632292i	0.988785	−	0.149347i	$-0.0477173\pi$
$19$	1.59123	+	2.75609i	0.365054	+	0.632292i	−0.623731	+	0.781639i	$0.714384\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.17495	−	2.98776i	−1.07905	−	0.622990i	−0.148411	−	0.988926i	$-0.547416\pi$
$23$	−5.17495	−	2.98776i	−1.07905	−	0.622990i	−0.930640	+	0.365936i	$0.880749\pi$
$24$		0			0
$25$	1.58180	+	2.73976i	0.316360	+	0.547952i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.06838	+	1.85049i	−0.198394	+	0.343628i	−0.948008	−	0.318247i	$-0.896906\pi$
$29$	−1.06838	+	1.85049i	−0.198394	+	0.343628i	0.749614	+	0.661875i	$0.230239\pi$
$30$		0			0
$31$	4.03351			0.724440			0.362220	−	0.932093i	$-0.382019\pi$
$31$	4.03351			0.724440			0.362220	+	0.932093i	$0.382019\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.71808	−	4.94456i	−0.966533	−	0.835784i
$36$		0			0
$37$	−5.06680	−	8.77595i	−0.832977	−	1.44276i	−0.895667	−	0.444725i	$-0.853301\pi$
$37$	−5.06680	−	8.77595i	−0.832977	−	1.44276i	0.0626906	−	0.998033i	$-0.480032\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.02256	+	5.20918i	−1.40909	+	0.813537i	−0.995300	−	0.0968362i	$-0.969128\pi$
$41$	−9.02256	+	5.20918i	−1.40909	+	0.813537i	−0.413788	+	0.910373i	$0.635794\pi$
$42$		0			0
$43$	−0.0397018	−	0.0229218i	−0.00605446	−	0.00349555i	0.496970	−	0.867768i	$-0.334446\pi$
$43$	−0.0397018	−	0.0229218i	−0.00605446	−	0.00349555i	−0.503024	+	0.864272i	$0.667779\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.74706			−0.838295			−0.419147	−	0.907918i	$-0.637671\pi$
$47$	−5.74706			−0.838295			−0.419147	+	0.907918i	$0.637671\pi$
$48$		0			0
$49$	6.50386	+	2.58840i	0.929123	+	0.369771i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.43844	−	4.22350i	0.334945	−	0.580142i	−0.648529	−	0.761190i	$-0.724616\pi$
$53$	2.43844	−	4.22350i	0.334945	−	0.580142i	0.983474	+	0.181048i	$0.0579488\pi$
$54$		0			0
$55$	−6.46199			−0.871335
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.20774			−0.808179			−0.404090	−	0.914719i	$-0.632412\pi$
$59$	−6.20774			−0.808179			−0.404090	+	0.914719i	$0.632412\pi$
$60$		0			0
$61$			6.98818i			0.894744i	0.894348	+	0.447372i	$0.147640\pi$
$61$			6.98818i			0.894744i	−0.894348	+	0.447372i	$0.852360\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	18.4450			2.28782
$66$		0			0
$67$			7.88250i			0.963001i	0.876446	+	0.481500i	$0.159908\pi$
$67$			7.88250i			0.963001i	−0.876446	+	0.481500i	$0.840092\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			15.5442i			1.84475i	0.386291	+	0.922377i	$0.373756\pi$
$71$			15.5442i			1.84475i	−0.386291	+	0.922377i	$0.626244\pi$
$72$		0			0
$73$	11.0585	+	6.38460i	1.29429	+	0.747261i	0.979412	−	0.201870i	$-0.0647018\pi$
$73$	11.0585	+	6.38460i	1.29429	+	0.747261i	0.314882	+	0.949131i	$0.398035\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.65267	−	1.96285i	0.644181	−	0.223688i
$78$		0			0
$79$			12.0116i			1.35141i	0.737172	+	0.675706i	$0.236161\pi$
$79$			12.0116i			1.35141i	−0.737172	+	0.675706i	$0.763839\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.88456	+	3.26415i	−0.206857	+	0.358287i	−0.950723	−	0.310042i	$-0.899657\pi$
$83$	−1.88456	+	3.26415i	−0.206857	+	0.358287i	0.743866	+	0.668329i	$0.232990\pi$
$84$		0			0
$85$	−7.83265	−	13.5666i	−0.849571	−	1.47150i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.95155	−	2.28143i	0.418864	−	0.241831i	−0.275727	−	0.961236i	$-0.588919\pi$
$89$	3.95155	−	2.28143i	0.418864	−	0.241831i	0.694591	+	0.719405i	$0.255585\pi$
$90$		0			0
$91$	−16.1349	+	5.60273i	−1.69139	+	0.587326i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	9.09294i		−	0.932916i
$96$		0			0
$97$	4.62721	+	2.67152i	0.469822	+	0.271252i	0.716165	−	0.697931i	$-0.245896\pi$
$97$	4.62721	+	2.67152i	0.469822	+	0.271252i	−0.246343	+	0.969183i	$0.579229\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.16618	−	2.98270i	0.514055	−	0.296790i	−0.220444	−	0.975400i	$-0.570751\pi$
$101$	5.16618	−	2.98270i	0.514055	−	0.296790i	0.734499	+	0.678610i	$0.237417\pi$
$102$		0			0
$103$	4.43678	−	7.68473i	0.437169	−	0.757199i	−0.560301	−	0.828289i	$-0.689315\pi$
$103$	4.43678	−	7.68473i	0.437169	−	0.757199i	0.997470	+	0.0710903i	$0.0226479\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.10984	+	2.95016i	−0.493986	+	0.285203i	−0.726227	−	0.687455i	$-0.758728\pi$
$107$	−5.10984	+	2.95016i	−0.493986	+	0.285203i	0.232240	+	0.972658i	$0.425394\pi$
$108$		0			0
$109$	−0.416247	+	0.720960i	−0.0398692	+	0.0690555i	−0.885271	−	0.465075i	$-0.846027\pi$
$109$	−0.416247	+	0.720960i	−0.0398692	+	0.0690555i	0.845402	+	0.534130i	$0.179361\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.0601629	+	0.104205i	0.00565965	+	0.00980279i	0.868841	−	0.495091i	$-0.164865\pi$
$113$	0.0601629	+	0.104205i	0.00565965	+	0.00980279i	−0.863182	+	0.504893i	$0.831532\pi$
$114$		0			0
$115$	8.53662	+	14.7859i	0.796044	+	1.37879i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.9726	+	9.48823i	1.00585	+	0.869784i
$120$		0			0
$121$	−2.94247	+	5.09650i	−0.267497	+	0.463319i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			5.24696i			0.469302i
$126$		0			0
$127$		−	5.57295i		−	0.494520i	−0.968949	−	0.247260i	$-0.920470\pi$
$127$		−	5.57295i		−	0.494520i	0.968949	−	0.247260i	$-0.0795301\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.0314616	+	0.0544931i	−0.00274882	+	0.00476109i	−0.867397	−	0.497618i	$-0.834208\pi$
$131$	−0.0314616	+	0.0544931i	−0.00274882	+	0.00476109i	0.864648	+	0.502379i	$0.167542\pi$
$132$		0			0
$133$	2.76202	+	7.95411i	0.239497	+	0.689709i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.0178475	+	0.0309127i	0.00152481	+	0.00264105i	0.866787	−	0.498679i	$-0.166181\pi$
$137$	0.0178475	+	0.0309127i	0.00152481	+	0.00264105i	−0.865262	+	0.501320i	$0.832848\pi$
$138$		0			0
$139$	4.34888	+	7.53249i	0.368868	+	0.638897i	0.989389	−	0.145292i	$-0.0464123\pi$
$139$	4.34888	+	7.53249i	0.368868	+	0.638897i	−0.620521	+	0.784190i	$0.713079\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.30017	+	12.6443i	−0.610471	+	1.05737i
$144$		0			0
$145$	5.28723	−	3.05258i	0.439080	−	0.253503i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.44314	+	7.69574i	−0.363996	+	0.630459i	−0.988614	−	0.150471i	$-0.951921\pi$
$149$	−4.44314	+	7.69574i	−0.363996	+	0.630459i	0.624619	+	0.780930i	$0.285254\pi$
$150$		0			0
$151$	−13.9709	+	8.06613i	−1.13694	+	0.656412i	−0.945671	−	0.325126i	$-0.894593\pi$
$151$	−13.9709	+	8.06613i	−1.13694	+	0.656412i	−0.191268	+	0.981538i	$0.561260\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−9.98055	−	5.76227i	−0.801657	−	0.462837i
$156$		0			0
$157$		−	11.0788i		−	0.884187i	−0.896969	−	0.442093i	$-0.854236\pi$
$157$		−	11.0788i		−	0.884187i	0.896969	−	0.442093i	$-0.145764\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−11.9587	−	10.3410i	−0.942479	−	0.814984i
$162$		0			0
$163$	−6.35131	+	3.66693i	−0.497473	+	0.287216i	−0.727670	−	0.685928i	$-0.759397\pi$
$163$	−6.35131	+	3.66693i	−0.497473	+	0.287216i	0.230196	+	0.973144i	$0.426063\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.6879	+	21.9760i	0.981816	+	1.70056i	0.655308	+	0.755362i	$0.272539\pi$
$167$	12.6879	+	21.9760i	0.981816	+	1.70056i	0.326508	+	0.945194i	$0.394128\pi$
$168$		0			0
$169$	14.3374	−	24.8332i	1.10288	−	1.91024i
$170$		0			0
$171$		0			0
$172$		0			0
$173$			16.2227i			1.23339i	0.787202	+	0.616695i	$0.211529\pi$
$173$			16.2227i			1.23339i	−0.787202	+	0.616695i	$0.788471\pi$
$174$		0			0
$175$	2.74565	+	7.90696i	0.207551	+	0.597710i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−17.9324	−	10.3533i	−1.34033	−	0.773839i	−0.353474	−	0.935445i	$-0.615000\pi$
$179$	−17.9324	−	10.3533i	−1.34033	−	0.773839i	−0.986855	+	0.161605i	$0.948333\pi$
$180$		0			0
$181$			16.3983i			1.21888i	0.792833	+	0.609439i	$0.208605\pi$
$181$			16.3983i			1.21888i	−0.792833	+	0.609439i	$0.791395\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$			28.9537i			2.12872i
$186$		0			0
$187$	12.4001			0.906782
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	5.42747i		−	0.392718i	−0.980532	−	0.196359i	$-0.937088\pi$
$191$		−	5.42747i		−	0.392718i	0.980532	−	0.196359i	$-0.0629117\pi$
$192$		0			0
$193$	5.60988			0.403808			0.201904	−	0.979405i	$-0.435287\pi$
$193$	5.60988			0.403808			0.201904	+	0.979405i	$0.435287\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.09436			−0.647946			−0.323973	−	0.946066i	$-0.605019\pi$
$197$	−9.09436			−0.647946			−0.323973	+	0.946066i	$0.605019\pi$
$198$		0			0
$199$	−0.330072	+	0.571701i	−0.0233982	+	0.0405268i	−0.877487	−	0.479600i	$-0.840782\pi$
$199$	−0.330072	+	0.571701i	−0.0233982	+	0.0405268i	0.854089	+	0.520127i	$0.174115\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.69780	+	4.27628i	−0.259535	+	0.300136i
$204$		0			0
$205$	29.7674			2.07904
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.23332	+	3.59881i	0.431168	+	0.248935i
$210$		0			0
$211$	−18.2479	+	10.5354i	−1.25624	+	0.725290i	−0.972341	−	0.233564i	$-0.924961\pi$
$211$	−18.2479	+	10.5354i	−1.25624	+	0.725290i	−0.283898	+	0.958854i	$0.591628\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.0654923	+	0.113436i	0.00446654	+	0.00773627i
$216$		0			0
$217$	10.4809	+	2.00896i	0.711487	+	0.136377i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−35.3945			−2.38089
$222$		0			0
$223$	−3.66945	+	6.35568i	−0.245725	+	0.425608i	−0.962335	−	0.271866i	$-0.912359\pi$
$223$	−3.66945	+	6.35568i	−0.245725	+	0.425608i	0.716610	+	0.697474i	$0.245693\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.70310	+	2.94986i	0.113039	+	0.195789i	0.916994	−	0.398901i	$-0.130608\pi$
$227$	1.70310	+	2.94986i	0.113039	+	0.195789i	−0.803955	+	0.594690i	$0.797275\pi$
$228$		0			0
$229$	16.5722	+	9.56799i	1.09512	+	0.632271i	0.934936	−	0.354816i	$-0.115456\pi$
$229$	16.5722	+	9.56799i	1.09512	+	0.632271i	0.160189	+	0.987086i	$0.448790\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.734443	+	1.27209i	0.0481150	+	0.0833376i	0.889080	−	0.457752i	$-0.151345\pi$
$233$	0.734443	+	1.27209i	0.0481150	+	0.0833376i	−0.840965	+	0.541090i	$0.818012\pi$
$234$		0			0
$235$	14.2206	+	8.21025i	0.927648	+	0.535578i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.40142	−	5.42791i	0.608127	−	0.351103i	−0.164105	−	0.986443i	$-0.552474\pi$
$239$	9.40142	−	5.42791i	0.608127	−	0.351103i	0.772232	+	0.635340i	$0.219140\pi$
$240$		0			0
$241$	−5.39678	+	3.11583i	−0.347637	+	0.200708i	−0.663644	−	0.748048i	$-0.730991\pi$
$241$	−5.39678	+	3.11583i	−0.347637	+	0.200708i	0.316007	+	0.948757i	$0.397658\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.3954	−	15.6962i	−0.791915	−	1.00279i
$246$		0			0
$247$	−17.7923	−	10.2724i	−1.13210	−	0.653615i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−20.2337			−1.27714			−0.638569	−	0.769565i	$-0.720473\pi$
$251$	−20.2337			−1.27714			−0.638569	+	0.769565i	$0.720473\pi$
$252$		0			0
$253$	−13.5145			−0.849651
$254$		0			0
$255$		0			0
$256$		0			0
$257$	24.1732	+	13.9564i	1.50788	+	0.870577i	0.999958	+	0.00917598i	$0.00292085\pi$
$257$	24.1732	+	13.9564i	1.50788	+	0.870577i	0.507926	+	0.861401i	$0.330412\pi$
$258$		0			0
$259$	−8.79481	−	25.3275i	−0.546483	−	1.57377i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.17765	−	2.41197i	0.257605	−	0.148728i	−0.365637	−	0.930758i	$-0.619149\pi$
$263$	4.17765	−	2.41197i	0.257605	−	0.148728i	0.623242	+	0.782029i	$0.285815\pi$
$264$		0			0
$265$	−12.0674	+	6.96711i	−0.741294	+	0.427986i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.82686	+	2.78679i	0.294299	+	0.169913i	0.639879	−	0.768476i	$-0.278985\pi$
$269$	4.82686	+	2.78679i	0.294299	+	0.169913i	−0.345580	+	0.938389i	$0.612318\pi$
$270$		0			0
$271$	−10.8266	−	18.7521i	−0.657666	−	1.13911i	−0.981218	−	0.192901i	$-0.938210\pi$
$271$	−10.8266	−	18.7521i	−0.657666	−	1.13911i	0.323552	−	0.946210i	$-0.395123\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.19638	+	3.57748i	0.373656	+	0.215730i
$276$		0			0
$277$	−7.22330	−	12.5111i	−0.434006	−	0.751720i	0.563208	−	0.826315i	$-0.309567\pi$
$277$	−7.22330	−	12.5111i	−0.434006	−	0.751720i	−0.997214	+	0.0745949i	$0.976234\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.82235	+	17.0128i	−0.585952	+	1.01490i	0.408804	+	0.912622i	$0.365946\pi$
$281$	−9.82235	+	17.0128i	−0.585952	+	1.01490i	−0.994756	+	0.102277i	$0.967387\pi$
$282$		0			0
$283$	30.9384			1.83910			0.919549	−	0.392976i	$-0.128554\pi$
$283$	30.9384			1.83910			0.919549	+	0.392976i	$0.128554\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−26.0392	+	9.04195i	−1.53704	+	0.533729i
$288$		0			0
$289$	6.53024	+	11.3107i	0.384132	+	0.665336i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.154987	−	0.0894817i	0.00905443	−	0.00522758i	−0.495466	−	0.868627i	$-0.665003\pi$
$293$	0.154987	−	0.0894817i	0.00905443	−	0.00522758i	0.504520	+	0.863400i	$0.331669\pi$
$294$		0			0
$295$	15.3605	+	8.86839i	0.894323	+	0.516337i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	38.5756			2.23088
$300$		0			0
$301$	−0.0917464	−	0.0793353i	−0.00528817	−	0.00457281i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.98331	−	17.2916i	0.571643	−	0.990115i
$306$		0			0
$307$	9.20787			0.525521			0.262760	−	0.964861i	$-0.415367\pi$
$307$	9.20787			0.525521			0.262760	+	0.964861i	$0.415367\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−31.4074			−1.78095			−0.890476	−	0.455030i	$-0.849629\pi$
$311$	−31.4074			−1.78095			−0.890476	+	0.455030i	$0.849629\pi$
$312$		0			0
$313$			5.18230i			0.292921i	0.989217	+	0.146460i	$0.0467881\pi$
$313$			5.18230i			0.292921i	−0.989217	+	0.146460i	$0.953212\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	19.3977			1.08949			0.544743	−	0.838603i	$-0.316627\pi$
$317$	19.3977			1.08949			0.544743	+	0.838603i	$0.316627\pi$
$318$		0			0
$319$			4.83261i			0.270574i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			17.4486i			0.970868i
$324$		0			0
$325$	−17.6868	−	10.2115i	−0.981088	−	0.566431i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−14.9334	−	2.86242i	−0.823307	−	0.157810i
$330$		0			0
$331$		−	15.7609i		−	0.866300i	−0.901322	−	0.433150i	$-0.857402\pi$
$331$		−	15.7609i		−	0.866300i	0.901322	−	0.433150i	$-0.142598\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	11.2610	−	19.5045i	0.615251	−	1.06565i
$336$		0			0
$337$	−0.00326615	−	0.00565714i	−0.000177918	−	0.000308164i	0.865936	−	0.500154i	$-0.166723\pi$
$337$	−0.00326615	−	0.00565714i	−0.000177918	−	0.000308164i	−0.866114	+	0.499846i	$0.833390\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	7.90022	−	4.56119i	0.427821	−	0.247003i
$342$		0			0
$343$	15.6107	+	9.96517i	0.842901	+	0.538069i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	3.21508i		−	0.172594i	−0.996269	−	0.0862972i	$-0.972497\pi$
$347$		−	3.21508i		−	0.172594i	0.996269	−	0.0862972i	$-0.0275035\pi$
$348$		0			0
$349$	−29.6288	−	17.1062i	−1.58599	−	0.915674i	−0.993958	−	0.109762i	$-0.964991\pi$
$349$	−29.6288	−	17.1062i	−1.58599	−	0.915674i	−0.592035	−	0.805912i	$-0.701675\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.89661	−	3.40441i	0.313845	−	0.181198i	−0.334801	−	0.942289i	$-0.608669\pi$
$353$	5.89661	−	3.40441i	0.313845	−	0.181198i	0.648646	+	0.761091i	$0.275336\pi$
$354$		0			0
$355$	22.2064	−	38.4627i	1.17859	−	2.04139i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	19.5302	−	11.2758i	1.03077	−	0.595114i	0.113563	−	0.993531i	$-0.463774\pi$
$359$	19.5302	−	11.2758i	1.03077	−	0.595114i	0.917204	+	0.398417i	$0.130440\pi$
$360$		0			0
$361$	4.43596	−	7.68331i	0.233472	−	0.404385i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−18.2421	−	31.5962i	−0.954835	−	1.65382i
$366$		0			0
$367$	−11.5456	−	19.9975i	−0.602674	−	1.04386i	−0.992414	−	0.122937i	$-0.960769\pi$
$367$	−11.5456	−	19.9975i	−0.602674	−	1.04386i	0.389741	−	0.920925i	$-0.372565\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	8.43974	−	9.76004i	0.438169	−	0.506716i
$372$		0			0
$373$	6.23406	−	10.7977i	0.322787	−	0.559084i	−0.658275	−	0.752778i	$-0.728713\pi$
$373$	6.23406	−	10.7977i	0.322787	−	0.559084i	0.981062	+	0.193694i	$0.0620468\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	13.7941i		−	0.710433i
$378$		0			0
$379$			0.865461i			0.0444557i	0.999753	+	0.0222279i	$0.00707593\pi$
$379$			0.865461i			0.0444557i	−0.999753	+	0.0222279i	$0.992924\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.77345	+	9.99991i	−0.295010	+	0.510971i	−0.974987	−	0.222261i	$-0.928656\pi$
$383$	−5.77345	+	9.99991i	−0.295010	+	0.510971i	0.679978	+	0.733233i	$0.261989\pi$
$384$		0			0
$385$	−16.7911	−	3.21850i	−0.855756	−	0.164030i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.26417	−	3.92165i	−0.114798	−	0.198836i	0.802901	−	0.596112i	$-0.203289\pi$
$389$	−2.26417	−	3.92165i	−0.114798	−	0.198836i	−0.917699	+	0.397277i	$0.869955\pi$
$390$		0			0
$391$	−16.3811	−	28.3729i	−0.828428	−	1.43488i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	17.1598	−	29.7216i	0.863403	−	1.49546i
$396$		0			0
$397$	−1.62853	+	0.940235i	−0.0817338	+	0.0471890i	−0.540310	−	0.841466i	$-0.681693\pi$
$397$	−1.62853	+	0.940235i	−0.0817338	+	0.0471890i	0.458576	+	0.888655i	$0.348360\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.44812	+	16.3646i	−0.471817	+	0.817210i	−0.999480	−	0.0322433i	$-0.989735\pi$
$401$	−9.44812	+	16.3646i	−0.471817	+	0.817210i	0.527664	+	0.849453i	$0.323068\pi$
$402$		0			0
$403$	−22.5502	+	13.0194i	−1.12331	+	0.648541i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−19.8481	−	11.4593i	−0.983836	−	0.568018i
$408$		0			0
$409$		−	30.2959i		−	1.49803i	−0.662551	−	0.749017i	$-0.730526\pi$
$409$		−	30.2959i		−	1.49803i	0.662551	−	0.749017i	$-0.269474\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−16.1305	−	3.09187i	−0.793730	−	0.152141i
$414$		0			0
$415$	9.32634	−	5.38456i	0.457812	−	0.264318i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.90705	+	5.03516i	0.142019	+	0.245984i	0.928257	−	0.371940i	$-0.121307\pi$
$419$	2.90705	+	5.03516i	0.142019	+	0.245984i	−0.786238	+	0.617924i	$0.787974\pi$
$420$		0			0
$421$	−7.49878	+	12.9883i	−0.365468	+	0.633009i	−0.988851	−	0.148907i	$-0.952424\pi$
$421$	−7.49878	+	12.9883i	−0.365468	+	0.633009i	0.623383	+	0.781917i	$0.285758\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$			17.3452i			0.841367i
$426$		0			0
$427$	−3.48058	+	18.1584i	−0.168437	+	0.878747i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−20.0076	−	11.5514i	−0.963732	−	0.556411i	−0.0664126	−	0.997792i	$-0.521155\pi$
$431$	−20.0076	−	11.5514i	−0.963732	−	0.556411i	−0.897320	+	0.441381i	$0.854489\pi$
$432$		0			0
$433$		−	11.1544i		−	0.536045i	−0.963413	−	0.268022i	$-0.913630\pi$
$433$		−	11.1544i		−	0.536045i	0.963413	−	0.268022i	$-0.0863701\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	19.0169i		−	0.909699i
$438$		0			0
$439$	−7.38929			−0.352672			−0.176336	−	0.984330i	$-0.556424\pi$
$439$	−7.38929			−0.352672			−0.176336	+	0.984330i	$0.556424\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			1.72740i			0.0820712i	0.999158	+	0.0410356i	$0.0130657\pi$
$443$			1.72740i			0.0820712i	−0.999158	+	0.0410356i	$0.986934\pi$
$444$		0			0
$445$	−13.0370			−0.618014
$446$		0			0
$447$		0			0
$448$		0			0
$449$	37.3078			1.76067			0.880333	−	0.474357i	$-0.157319\pi$
$449$	37.3078			1.76067			0.880333	+	0.474357i	$0.157319\pi$
$450$		0			0
$451$	−11.7813	+	20.4059i	−0.554762	+	0.960876i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	47.9283	+	9.18682i	2.24691	+	0.430685i
$456$		0			0
$457$	−11.2540			−0.526441			−0.263220	−	0.964736i	$-0.584785\pi$
$457$	−11.2540			−0.526441			−0.263220	+	0.964736i	$0.584785\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	31.6005	+	18.2446i	1.47178	+	0.849734i	0.999497	−	0.0317125i	$-0.0100961\pi$
$461$	31.6005	+	18.2446i	1.47178	+	0.849734i	0.472285	+	0.881446i	$0.343429\pi$
$462$		0			0
$463$	−20.7706	+	11.9919i	−0.965294	+	0.557313i	−0.897798	−	0.440407i	$-0.854834\pi$
$463$	−20.7706	+	11.9919i	−0.965294	+	0.557313i	−0.0674955	+	0.997720i	$0.521501\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.322176	+	0.558026i	0.0149085	+	0.0258224i	0.873383	−	0.487033i	$-0.161921\pi$
$467$	0.322176	+	0.558026i	0.0149085	+	0.0258224i	−0.858475	+	0.512856i	$0.828588\pi$
$468$		0			0
$469$	−3.92601	+	20.4823i	−0.181286	+	0.945783i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.103682			−0.00476732
$474$		0			0
$475$	−5.03403	+	8.71919i	−0.230977	+	0.400064i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.9804	−	31.1430i	−0.821547	−	1.42296i	−0.904530	−	0.426411i	$-0.859778\pi$
$479$	−17.9804	−	31.1430i	−0.821547	−	1.42296i	0.0829823	−	0.996551i	$-0.473556\pi$
$480$		0			0
$481$	56.6541	+	32.7093i	2.58321	+	1.49141i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.63308	−	13.2209i	−0.346600	−	0.600329i
$486$		0			0
$487$	24.4569	+	14.1202i	1.10825	+	0.639848i	0.938376	−	0.345617i	$-0.112330\pi$
$487$	24.4569	+	14.1202i	1.10825	+	0.639848i	0.169874	+	0.985466i	$0.445664\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.6928	+	6.75082i	−0.527687	+	0.304660i	−0.740074	−	0.672526i	$-0.765210\pi$
$491$	−11.6928	+	6.75082i	−0.527687	+	0.304660i	0.212387	+	0.977186i	$0.431876\pi$
$492$		0			0
$493$	−10.1458	+	5.85767i	−0.456943	+	0.263816i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.74203	+	40.3907i	−0.347278	+	1.81177i
$498$		0			0
$499$	−11.9450	−	6.89643i	−0.534730	−	0.308727i	0.208210	−	0.978084i	$-0.433236\pi$
$499$	−11.9450	−	6.89643i	−0.534730	−	0.308727i	−0.742941	+	0.669357i	$0.766570\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	22.6371			1.00934			0.504669	−	0.863313i	$-0.331615\pi$
$503$	22.6371			1.00934			0.504669	+	0.863313i	$0.331615\pi$
$504$		0			0
$505$	−17.0443			−0.758463
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.36782	+	3.09911i	0.237925	+	0.137366i	0.614222	−	0.789133i	$-0.289470\pi$
$509$	5.36782	+	3.09911i	0.237925	+	0.137366i	−0.376298	+	0.926499i	$0.622803\pi$
$510$		0			0
$511$	25.5549	+	22.0979i	1.13048	+	0.977553i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−21.9568	+	12.6768i	−0.967533	+	0.558605i
$516$		0			0
$517$	−11.2565	+	6.49892i	−0.495059	+	0.285822i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−33.7303	−	19.4742i	−1.47775	−	0.853181i	−0.478068	−	0.878323i	$-0.658663\pi$
$521$	−33.7303	−	19.4742i	−1.47775	−	0.853181i	−0.999684	+	0.0251422i	$0.991996\pi$
$522$		0			0
$523$	4.02860	+	6.97774i	0.176158	+	0.305115i	0.940562	−	0.339623i	$-0.110300\pi$
$523$	4.02860	+	6.97774i	0.176158	+	0.305115i	−0.764403	+	0.644739i	$0.776966\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	19.1519	+	11.0573i	0.834269	+	0.481666i
$528$		0			0
$529$	6.35337	+	11.0044i	0.276234	+	0.478451i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	33.6284	−	58.2461i	1.45661	−	2.52292i
$534$		0			0
$535$	16.8584			0.728854
$536$		0			0
$537$		0			0
$538$		0			0
$539$	15.6658	−	2.28497i	0.674773	−	0.0984207i
$540$		0			0
$541$	−7.96878	−	13.8023i	−0.342605	−	0.593409i	0.642311	−	0.766444i	$-0.277976\pi$
$541$	−7.96878	−	13.8023i	−0.342605	−	0.593409i	−0.984916	+	0.173035i	$0.944643\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.05993	−	1.18930i	0.0882377	−	0.0509440i
$546$		0			0
$547$	4.79363	+	2.76760i	0.204961	+	0.118334i	0.598967	−	0.800773i	$-0.295578\pi$
$547$	4.79363	+	2.76760i	0.204961	+	0.118334i	−0.394006	+	0.919108i	$0.628911\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.80018			−0.289697
$552$		0			0
$553$	−5.98258	+	31.2115i	−0.254405	+	1.32725i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.2941	−	19.5619i	0.478546	−	0.828866i	−0.521151	−	0.853464i	$-0.674497\pi$
$557$	11.2941	−	19.5619i	0.478546	−	0.828866i	0.999697	+	0.0245983i	$0.00783067\pi$
$558$		0			0
$559$	0.295949			0.0125173
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.9543			0.840975			0.420488	−	0.907298i	$-0.361859\pi$
$563$	19.9543			0.840975			0.420488	+	0.907298i	$0.361859\pi$
$564$		0			0
$565$		−	0.343795i		−	0.0144636i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	31.5615			1.32313			0.661563	−	0.749889i	$-0.269893\pi$
$569$	31.5615			1.32313			0.661563	+	0.749889i	$0.269893\pi$
$570$		0			0
$571$			9.88433i			0.413646i	0.978378	+	0.206823i	$0.0663125\pi$
$571$			9.88433i			0.413646i	−0.978378	+	0.206823i	$0.933688\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	18.9041i		−	0.788357i
$576$		0			0
$577$	17.9384	+	10.3568i	0.746787	+	0.431157i	0.824532	−	0.565816i	$-0.191439\pi$
$577$	17.9384	+	10.3568i	0.746787	+	0.431157i	−0.0777451	+	0.996973i	$0.524772\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.52269	+	7.54309i	−0.270607	+	0.312940i
$582$		0			0
$583$		−	11.0298i		−	0.456807i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.4423	+	19.8186i	−0.472272	+	0.818000i	−0.999497	−	0.0317264i	$-0.989899\pi$
$587$	−11.4423	+	19.8186i	−0.472272	+	0.818000i	0.527224	+	0.849726i	$0.323233\pi$
$588$		0			0
$589$	6.41825	+	11.1167i	0.264459	+	0.458057i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−36.8909	+	21.2990i	−1.51493	+	0.874644i	−0.515081	+	0.857141i	$0.672238\pi$
$593$	−36.8909	+	21.2990i	−1.51493	+	0.874644i	−0.999847	+	0.0175029i	$0.994428\pi$
$594$		0			0
$595$	−13.5957	−	39.1532i	−0.557369	−	1.60512i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			2.44324i			0.0998283i	0.998754	+	0.0499141i	$0.0158948\pi$
$599$			2.44324i			0.0998283i	−0.998754	+	0.0499141i	$0.984105\pi$
$600$		0			0
$601$	−11.6323	−	6.71589i	−0.474490	−	0.273947i	0.243627	−	0.969869i	$-0.421663\pi$
$601$	−11.6323	−	6.71589i	−0.474490	−	0.273947i	−0.718117	+	0.695922i	$0.754996\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	14.5617	−	8.40722i	0.592019	−	0.341802i
$606$		0			0
$607$	−11.5370	+	19.9826i	−0.468271	+	0.811068i	−0.999342	−	0.0362583i	$-0.988456\pi$
$607$	−11.5370	+	19.9826i	−0.468271	+	0.811068i	0.531072	+	0.847327i	$0.321789\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	32.1302	−	18.5504i	1.29985	−	0.750468i
$612$		0			0
$613$	−6.57373	+	11.3860i	−0.265511	+	0.459878i	−0.967697	−	0.252115i	$-0.918874\pi$
$613$	−6.57373	+	11.3860i	−0.265511	+	0.459878i	0.702187	+	0.711993i	$0.252207\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.44699	+	5.97036i	0.138771	+	0.240358i	0.927032	−	0.374983i	$-0.122352\pi$
$617$	3.44699	+	5.97036i	0.138771	+	0.240358i	−0.788261	+	0.615341i	$0.789018\pi$
$618$		0			0
$619$	−17.7739	−	30.7853i	−0.714394	−	1.23737i	−0.963193	−	0.268811i	$-0.913369\pi$
$619$	−17.7739	−	30.7853i	−0.714394	−	1.23737i	0.248799	−	0.968555i	$-0.419964\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.4042	−	3.96004i	0.456900	−	0.158656i
$624$		0			0
$625$	15.4048	−	26.6819i	0.616193	−	1.06728i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	55.5599i		−	2.21532i
$630$		0			0
$631$		−	24.2459i		−	0.965213i	−0.875837	−	0.482607i	$-0.839690\pi$
$631$		−	24.2459i		−	0.965213i	0.875837	−	0.482607i	$-0.160310\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−7.96153	+	13.7898i	−0.315944	+	0.547230i
$636$		0			0
$637$	−44.7161	+	6.52217i	−1.77172	+	0.258418i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.1194	−	27.9196i	−0.636677	−	1.10276i	−0.986157	−	0.165814i	$-0.946975\pi$
$641$	−16.1194	−	27.9196i	−0.636677	−	1.10276i	0.349480	−	0.936944i	$-0.386358\pi$
$642$		0			0
$643$	−7.26173	−	12.5777i	−0.286375	−	0.496016i	0.686567	−	0.727067i	$-0.259117\pi$
$643$	−7.26173	−	12.5777i	−0.286375	−	0.496016i	−0.972942	+	0.231051i	$0.925784\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.5332	+	19.9760i	−0.453416	+	0.785339i	−0.998596	−	0.0529801i	$-0.983128\pi$
$647$	−11.5332	+	19.9760i	−0.453416	+	0.785339i	0.545180	+	0.838319i	$0.316461\pi$
$648$		0			0
$649$	−12.1588	+	7.01987i	−0.477274	+	0.275554i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	14.0767	−	24.3816i	0.550865	−	0.954126i	−0.447348	−	0.894360i	$-0.647631\pi$
$653$	14.0767	−	24.3816i	0.550865	−	0.954126i	0.998212	−	0.0597655i	$-0.0190353\pi$
$654$		0			0
$655$	0.155698	−	0.0898922i	0.00608362	−	0.00351238i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−5.32112	−	3.07215i	−0.207281	−	0.119674i	0.392766	−	0.919638i	$-0.371518\pi$
$659$	−5.32112	−	3.07215i	−0.207281	−	0.119674i	−0.600047	+	0.799965i	$0.704852\pi$
$660$		0			0
$661$			1.66168i			0.0646317i	0.999478	+	0.0323159i	$0.0102882\pi$
$661$			1.66168i			0.0646317i	−0.999478	+	0.0323159i	$0.989712\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.52889	−	23.6275i	0.175623	−	0.916237i
$666$		0			0
$667$	11.0576	−	6.38413i	0.428153	−	0.247194i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.90241	+	13.6874i	0.305069	+	0.528395i
$672$		0			0
$673$	−5.12788	+	8.88175i	−0.197665	+	0.342366i	−0.947771	−	0.318952i	$-0.896669\pi$
$673$	−5.12788	+	8.88175i	−0.197665	+	0.342366i	0.750106	+	0.661318i	$0.230003\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			22.3830i			0.860247i	0.902770	+	0.430123i	$0.141530\pi$
$677$			22.3830i			0.860247i	−0.902770	+	0.430123i	$0.858470\pi$
$678$		0			0
$679$	10.6930	+	9.24647i	0.410359	+	0.354847i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	27.3196	+	15.7730i	1.04535	+	0.603536i	0.921345	−	0.388745i	$-0.127091\pi$
$683$	27.3196	+	15.7730i	1.04535	+	0.603536i	0.124009	+	0.992281i	$0.460425\pi$
$684$		0			0
$685$		−	0.101988i		−	0.00389675i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			31.4832i			1.19941i
$690$		0			0
$691$	26.3023			1.00059			0.500294	−	0.865856i	$-0.333225\pi$
$691$	26.3023			1.00059			0.500294	+	0.865856i	$0.333225\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	24.8513i		−	0.942663i
$696$		0			0
$697$	−57.1212			−2.16362
$698$		0			0
$699$		0			0
$700$		0			0
$701$	5.62320			0.212385			0.106193	−	0.994346i	$-0.466134\pi$
$701$	5.62320			0.212385			0.106193	+	0.994346i	$0.466134\pi$
$702$		0			0
$703$	16.1249	−	27.9292i	0.608162	−	1.05337i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	14.9096	−	5.17728i	0.560735	−	0.194712i
$708$		0			0
$709$	25.1226			0.943500			0.471750	−	0.881732i	$-0.343622\pi$
$709$	25.1226			0.943500			0.471750	+	0.881732i	$0.343622\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−20.8732	−	12.0511i	−0.781707	−	0.451319i
$714$		0			0
$715$	36.1272	−	20.8580i	1.35108	−	0.780047i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.846263	−	1.46577i	−0.0315603	−	0.0546640i	0.849814	−	0.527083i	$-0.176714\pi$
$719$	−0.846263	−	1.46577i	−0.0315603	−	0.0546640i	−0.881374	+	0.472419i	$0.843381\pi$
$720$		0			0
$721$	15.3562	−	17.7586i	0.571896	−	0.661363i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.75987			−0.251055
$726$		0			0
$727$	16.1636	−	27.9962i	0.599476	−	1.03832i	−0.393423	−	0.919358i	$-0.628709\pi$
$727$	16.1636	−	27.9962i	0.599476	−	1.03832i	0.992898	−	0.118965i	$-0.0379576\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.125674	−	0.217675i	−0.00464824	−	0.00805099i
$732$		0			0
$733$	−39.4670	−	22.7863i	−1.45775	−	0.841631i	−0.458847	−	0.888516i	$-0.651737\pi$
$733$	−39.4670	−	22.7863i	−1.45775	−	0.841631i	−0.998900	+	0.0468850i	$0.985071\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.91373	+	15.4390i	0.328342	+	0.568704i
$738$		0			0
$739$	−1.86030	−	1.07404i	−0.0684321	−	0.0395093i	0.465394	−	0.885104i	$-0.345913\pi$
$739$	−1.86030	−	1.07404i	−0.0684321	−	0.0395093i	−0.533826	+	0.845595i	$0.679246\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	38.9145	−	22.4673i	1.42763	−	0.824244i	0.430700	−	0.902495i	$-0.358267\pi$
$743$	38.9145	−	22.4673i	1.42763	−	0.824244i	0.996934	+	0.0782508i	$0.0249335\pi$
$744$		0			0
$745$	21.9883	−	12.6949i	0.805588	−	0.465107i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−14.7470	+	5.12081i	−0.538844	+	0.187110i
$750$		0			0
$751$	−23.9954	−	13.8537i	−0.875604	−	0.505530i	−0.00639780	−	0.999980i	$-0.502036\pi$
$751$	−23.9954	−	13.8537i	−0.875604	−	0.505530i	−0.869207	+	0.494449i	$0.835370\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	46.0931			1.67750
$756$		0			0
$757$	−8.18716			−0.297568			−0.148784	−	0.988870i	$-0.547536\pi$
$757$	−8.18716			−0.297568			−0.148784	+	0.988870i	$0.547536\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−26.8605	−	15.5079i	−0.973693	−	0.562162i	−0.0733328	−	0.997308i	$-0.523364\pi$
$761$	−26.8605	−	15.5079i	−0.973693	−	0.562162i	−0.900360	+	0.435146i	$0.856697\pi$
$762$		0			0
$763$	−1.44068	+	1.66606i	−0.0521562	+	0.0603154i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	34.7058	−	20.0374i	1.25315	−	0.723508i
$768$		0			0
$769$	−4.32392	+	2.49641i	−0.155924	+	0.0900230i	−0.575932	−	0.817498i	$-0.695361\pi$
$769$	−4.32392	+	2.49641i	−0.155924	+	0.0900230i	0.420008	+	0.907521i	$0.362027\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.5944	+	6.69400i	0.417020	+	0.240767i	0.693802	−	0.720166i	$-0.255935\pi$
$773$	11.5944	+	6.69400i	0.417020	+	0.240767i	−0.276782	+	0.960933i	$0.589268\pi$
$774$		0			0
$775$	6.38021	+	11.0508i	0.229184	+	0.396958i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−28.7140	−	16.5780i	−1.02879	−	0.593970i
$780$		0			0
$781$	17.5777	+	30.4456i	0.628981	+	1.08943i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.8272	+	27.4136i	−0.564898	+	0.978432i
$786$		0			0
$787$	−24.2635			−0.864900			−0.432450	−	0.901658i	$-0.642351\pi$
$787$	−24.2635			−0.864900			−0.432450	+	0.901658i	$0.642351\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.104429	+	0.300737i	0.00371307	+	0.0106930i
$792$		0			0
$793$	−22.5565	−	39.0689i	−0.801004	−	1.38738i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−36.4623	+	21.0515i	−1.29156	+	0.745682i	−0.978931	−	0.204193i	$-0.934543\pi$
$797$	−36.4623	+	21.0515i	−1.29156	+	0.745682i	−0.312629	+	0.949875i	$0.601210\pi$
$798$		0			0
$799$	−27.2882	−	15.7548i	−0.965386	−	0.557366i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	28.8795			1.01913
$804$		0			0
$805$	14.8176	+	42.6721i	0.522253	+	1.50399i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.07111	+	1.85521i	−0.0376582	+	0.0652258i	−0.884240	−	0.467032i	$-0.845323\pi$
$809$	−1.07111	+	1.85521i	−0.0376582	+	0.0652258i	0.846582	+	0.532258i	$0.178656\pi$
$810$		0			0
$811$	11.5213			0.404566			0.202283	−	0.979327i	$-0.435164\pi$
$811$	11.5213			0.404566			0.202283	+	0.979327i	$0.435164\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	20.9543			0.733998
$816$		0			0
$817$		−	0.145896i		−	0.00510425i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	18.8542			0.658018			0.329009	−	0.944327i	$-0.393285\pi$
$821$	18.8542			0.658018			0.329009	+	0.944327i	$0.393285\pi$
$822$		0			0
$823$		−	29.3902i		−	1.02448i	−0.858843	−	0.512240i	$-0.828816\pi$
$823$		−	29.3902i		−	1.02448i	0.858843	−	0.512240i	$-0.171184\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	22.6869i		−	0.788900i	−0.918917	−	0.394450i	$-0.870935\pi$
$827$		−	22.6869i		−	0.788900i	0.918917	−	0.394450i	$-0.129065\pi$
$828$		0			0
$829$	−19.3396	−	11.1657i	−0.671691	−	0.387801i	0.125026	−	0.992153i	$-0.460098\pi$
$829$	−19.3396	−	11.1657i	−0.671691	−	0.387801i	−0.796717	+	0.604353i	$0.793432\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	23.7858	+	30.1197i	0.824130	+	1.04359i
$834$		0			0
$835$		−	72.5036i		−	2.50909i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−24.6526	+	42.6995i	−0.851101	+	1.47415i	0.0291142	+	0.999576i	$0.490731\pi$
$839$	−24.6526	+	42.6995i	−0.851101	+	1.47415i	−0.880215	+	0.474574i	$0.842602\pi$
$840$		0			0
$841$	12.2171	+	21.1607i	0.421280	+	0.729678i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−70.9534	+	40.9650i	−2.44087	+	1.40924i
$846$		0			0
$847$	−10.1842	+	11.7775i	−0.349935	+	0.404678i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			60.5534i			2.07575i
$852$		0			0
$853$	−2.37362	−	1.37041i	−0.0812712	−	0.0469220i	0.458814	−	0.888533i	$-0.348275\pi$
$853$	−2.37362	−	1.37041i	−0.0812712	−	0.0469220i	−0.540085	+	0.841611i	$0.681608\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.29909	+	1.32738i	−0.0785355	+	0.0453425i	−0.538753	−	0.842463i	$-0.681105\pi$
$857$	−2.29909	+	1.32738i	−0.0785355	+	0.0453425i	0.460218	+	0.887806i	$0.347771\pi$
$858$		0			0
$859$	−20.4410	+	35.4049i	−0.697440	+	1.20800i	0.271912	+	0.962322i	$0.412344\pi$
$859$	−20.4410	+	35.4049i	−0.697440	+	1.20800i	−0.969351	+	0.245679i	$0.920989\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−36.5486	+	21.1013i	−1.24413	+	0.718298i	−0.969932	−	0.243376i	$-0.921745\pi$
$863$	−36.5486	+	21.1013i	−1.24413	+	0.718298i	−0.274196	+	0.961674i	$0.588412\pi$
$864$		0			0
$865$	23.1758	−	40.1416i	0.788000	−	1.36486i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	13.5830	+	23.5265i	0.460773	+	0.798082i
$870$		0			0
$871$	−25.4432	−	44.0689i	−0.862109	−	1.49322i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.61333	+	13.6339i	−0.0883468	+	0.460912i
$876$		0			0
$877$	27.9149	−	48.3501i	0.942620	−	1.63267i	0.182171	−	0.983267i	$-0.441687\pi$
$877$	27.9149	−	48.3501i	0.942620	−	1.63267i	0.760448	−	0.649399i	$-0.224979\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	49.2533i		−	1.65939i	−0.558219	−	0.829693i	$-0.688515\pi$
$881$		−	49.2533i		−	1.65939i	0.558219	−	0.829693i	$-0.311485\pi$
$882$		0			0
$883$		−	3.87310i		−	0.130340i	−0.997874	−	0.0651701i	$-0.979241\pi$
$883$		−	3.87310i		−	0.130340i	0.997874	−	0.0651701i	$-0.0207590\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.897157	−	1.55392i	0.0301236	−	0.0521756i	−0.850571	−	0.525861i	$-0.823743\pi$
$887$	0.897157	−	1.55392i	0.0301236	−	0.0521756i	0.880694	+	0.473685i	$0.157077\pi$
$888$		0			0
$889$	2.77570	−	14.4810i	0.0930940	−	0.485678i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.14491	−	15.8394i	−0.306023	−	0.530047i
$894$		0			0
$895$	29.5814	+	51.2364i	0.988796	+	1.71265i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.30933	+	7.46398i	−0.143724	+	0.248938i
$900$		0			0
$901$	23.1564	−	13.3693i	0.771450	−	0.445397i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	23.4267	−	40.5761i	0.778728	−	1.34880i
$906$		0			0
$907$	−13.4331	+	7.75561i	−0.446039	+	0.257521i	−0.706156	−	0.708056i	$-0.749572\pi$
$907$	−13.4331	+	7.75561i	−0.446039	+	0.257521i	0.260117	+	0.965577i	$0.416239\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−38.1263	−	22.0122i	−1.26318	−	0.729297i	−0.289491	−	0.957181i	$-0.593486\pi$
$911$	−38.1263	−	22.0122i	−1.26318	−	0.729297i	−0.973688	+	0.227883i	$0.926819\pi$
$912$		0			0
$913$			8.52443i			0.282117i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.108893	+	0.125928i	−0.00359595	+	0.00415850i
$918$		0			0
$919$	−30.4488	+	17.5796i	−1.00441	+	0.579899i	−0.909551	−	0.415591i	$-0.863575\pi$
$919$	−30.4488	+	17.5796i	−1.00441	+	0.579899i	−0.0948631	+	0.995490i	$0.530241\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−50.1736	−	86.9032i	−1.65148	−	2.86045i
$924$		0			0
$925$	16.0293	−	27.7636i	0.527041	−	0.912862i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			28.6223i			0.939069i	0.882914	+	0.469534i	$0.155578\pi$
$929$			28.6223i			0.939069i	−0.882914	+	0.469534i	$0.844422\pi$
$930$		0			0
$931$	3.21528	+	22.0440i	0.105377	+	0.722463i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−30.6828	−	17.7147i	−1.00344	−	0.579334i
$936$		0			0
$937$		−	2.42605i		−	0.0792555i	−0.999215	−	0.0396277i	$-0.987383\pi$
$937$		−	2.42605i		−	0.0792555i	0.999215	−	0.0396277i	$-0.0126172\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	33.6961i		−	1.09846i	−0.835671	−	0.549231i	$-0.814921\pi$
$941$		−	33.6961i		−	1.09846i	0.835671	−	0.549231i	$-0.185079\pi$
$942$		0			0
$943$	62.2550			2.02730
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	54.7789i		−	1.78007i	−0.455888	−	0.890037i	$-0.650678\pi$
$947$		−	54.7789i		−	1.78007i	0.455888	−	0.890037i	$-0.349322\pi$
$948$		0			0
$949$	−82.4330			−2.67589
$950$		0			0
$951$		0			0
$952$		0			0
$953$	34.7473			1.12558			0.562789	−	0.826601i	$-0.309729\pi$
$953$	34.7473			1.12558			0.562789	+	0.826601i	$0.309729\pi$
$954$		0			0
$955$	−7.75368	+	13.4298i	−0.250903	+	0.434577i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.0309791	+	0.0892143i	0.00100037	+	0.00288088i
$960$		0			0
$961$	−14.7308			−0.475187
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−13.8811	−	8.01428i	−0.446850	−	0.257989i
$966$		0			0
$967$	−9.75555	+	5.63237i	−0.313717	+	0.181125i	−0.648589	−	0.761139i	$-0.724640\pi$
$967$	−9.75555	+	5.63237i	−0.313717	+	0.181125i	0.334871	+	0.942264i	$0.391307\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.41975	−	16.3155i	−0.302294	−	0.523589i	0.674361	−	0.738402i	$-0.264419\pi$
$971$	−9.41975	−	16.3155i	−0.302294	−	0.523589i	−0.976655	+	0.214813i	$0.931086\pi$
$972$		0			0
$973$	7.54867	+	21.7388i	0.241999	+	0.696914i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.17446			0.197538			0.0987692	−	0.995110i	$-0.468509\pi$
$977$	6.17446			0.197538			0.0987692	+	0.995110i	$0.468509\pi$
$978$		0			0
$979$	5.15980	−	8.93704i	0.164908	−	0.285629i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	13.3296	+	23.0876i	0.425150	+	0.736381i	0.996434	−	0.0843710i	$-0.0268881\pi$
$983$	13.3296	+	23.0876i	0.425150	+	0.736381i	−0.571285	+	0.820752i	$0.693555\pi$
$984$		0			0
$985$	22.5032	+	12.9922i	0.717010	+	0.413966i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.136970	+	0.237238i	0.00435538	+	0.00754374i
$990$		0			0
$991$	42.6887	+	24.6463i	1.35605	+	0.782917i	0.989089	−	0.147319i	$-0.0470644\pi$
$991$	42.6887	+	24.6463i	1.35605	+	0.782917i	0.366962	+	0.930236i	$0.380398\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.63347	−	0.943082i	0.0517844	−	0.0298977i
$996$		0			0
$997$	−6.78110	+	3.91507i	−0.214760	+	0.123992i	−0.603521	−	0.797347i	$-0.706236\pi$
$997$	−6.78110	+	3.91507i	−0.214760	+	0.123992i	0.388762	+	0.921338i	$0.372903\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cz.g.2719.2		24
3.2	odd	2		1008.2.cz.h.367.6	yes	24
4.3	odd	2		3024.2.cz.h.2719.2		24
7.5	odd	6		3024.2.bf.g.2287.2		24
9.4	even	3		3024.2.bf.h.1711.11		24
9.5	odd	6		1008.2.bf.g.31.2	✓	24
12.11	even	2		1008.2.cz.g.367.7	yes	24
21.5	even	6		1008.2.bf.h.943.11	yes	24
28.19	even	6		3024.2.bf.h.2287.2		24
36.23	even	6		1008.2.bf.h.31.11	yes	24
36.31	odd	6		3024.2.bf.g.1711.11		24
63.5	even	6		1008.2.cz.g.607.7	yes	24
63.40	odd	6		3024.2.cz.h.1279.2		24
84.47	odd	6		1008.2.bf.g.943.2	yes	24
252.103	even	6	inner	3024.2.cz.g.1279.2		24
252.131	odd	6		1008.2.cz.h.607.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.2	✓	24	9.5	odd	6
1008.2.bf.g.943.2	yes	24	84.47	odd	6
1008.2.bf.h.31.11	yes	24	36.23	even	6
1008.2.bf.h.943.11	yes	24	21.5	even	6
1008.2.cz.g.367.7	yes	24	12.11	even	2
1008.2.cz.g.607.7	yes	24	63.5	even	6
1008.2.cz.h.367.6	yes	24	3.2	odd	2
1008.2.cz.h.607.6	yes	24	252.131	odd	6
3024.2.bf.g.1711.11		24	36.31	odd	6
3024.2.bf.g.2287.2		24	7.5	odd	6
3024.2.bf.h.1711.11		24	9.4	even	3
3024.2.bf.h.2287.2		24	28.19	even	6
3024.2.cz.g.1279.2		24	252.103	even	6	inner
3024.2.cz.g.2719.2		24	1.1	even	1	trivial
3024.2.cz.h.1279.2		24	63.40	odd	6
3024.2.cz.h.2719.2		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.47441 - 1.42860i) q^{5} +(2.59845 + 0.498066i) q^{7} +(1.95865 - 1.13083i) q^{11} +(-5.59072 + 3.22780i) q^{13} +(4.74820 + 2.74137i) q^{17} +(1.59123 + 2.75609i) q^{19} +(-5.17495 - 2.98776i) q^{23} +(1.58180 + 2.73976i) q^{25} +(-1.06838 + 1.85049i) q^{29} +4.03351 q^{31} +(-5.71808 - 4.94456i) q^{35} +(-5.06680 - 8.77595i) q^{37} +(-9.02256 + 5.20918i) q^{41} +(-0.0397018 - 0.0229218i) q^{43} -5.74706 q^{47} +(6.50386 + 2.58840i) q^{49} +(2.43844 - 4.22350i) q^{53} -6.46199 q^{55} -6.20774 q^{59} +6.98818i q^{61} +18.4450 q^{65} +7.88250i q^{67} +15.5442i q^{71} +(11.0585 + 6.38460i) q^{73} +(5.65267 - 1.96285i) q^{77} +12.0116i q^{79} +(-1.88456 + 3.26415i) q^{83} +(-7.83265 - 13.5666i) q^{85} +(3.95155 - 2.28143i) q^{89} +(-16.1349 + 5.60273i) q^{91} -9.09294i q^{95} +(4.62721 + 2.67152i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 4 q^{7} - 9 q^{11} - 3 q^{13} + 3 q^{17} + 4 q^{19} - 6 q^{23} + 15 q^{25} - 18 q^{29} - 34 q^{31} - 42 q^{35} - 3 q^{37} - 36 q^{41} - 24 q^{43} - 42 q^{47} + 30 q^{49} + 12 q^{53} + 30 q^{55}+ \cdots + 3 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 - 4 * q^7 - 9 * q^11 - 3 * q^13 + 3 * q^17 + 4 * q^19 - 6 * q^23 + 15 * q^25 - 18 * q^29 - 34 * q^31 - 42 * q^35 - 3 * q^37 - 36 * q^41 - 24 * q^43 - 42 * q^47 + 30 * q^49 + 12 * q^53 + 30 * q^55 - 12 * q^59 + 48 * q^73 + 48 * q^77 - 48 * q^83 - 21 * q^85 - 39 * q^89 - 9 * q^91 + 3 * q^97

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