LMFDB - Embedded newform 1152.2.w.b.1007.1

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			1007.1
Character	$\chi$	$=$	1152.1007
Dual form			1152.2.w.b.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39555 - 3.36915i) q^{5} +(1.05755 + 1.05755i) q^{7} +O(q^{10})$	$q+(-1.39555 - 3.36915i) q^{5} +(1.05755 + 1.05755i) q^{7} +(-1.50977 - 3.64490i) q^{11} +(-2.23818 - 0.927086i) q^{13} -7.49610 q^{17} +(-0.818262 + 1.97546i) q^{19} +(5.80392 + 5.80392i) q^{23} +(-5.86809 + 5.86809i) q^{25} +(0.326633 + 0.135296i) q^{29} +1.71021i q^{31} +(2.08718 - 5.03889i) q^{35} +(0.387384 - 0.160460i) q^{37} +(-1.50401 + 1.50401i) q^{41} +(-7.40227 + 3.06612i) q^{43} -7.27404i q^{47} -4.76319i q^{49} +(3.94866 - 1.63559i) q^{53} +(-10.1733 + 10.1733i) q^{55} +(-12.7979 + 5.30105i) q^{59} +(-0.579943 + 1.40011i) q^{61} +8.83457i q^{65} +(7.96385 + 3.29874i) q^{67} +(-4.75505 + 4.75505i) q^{71} +(-7.99854 - 7.99854i) q^{73} +(2.25800 - 5.45130i) q^{77} -14.3967 q^{79} +(-1.35250 - 0.560224i) q^{83} +(10.4612 + 25.2555i) q^{85} +(-4.75638 - 4.75638i) q^{89} +(-1.38655 - 3.34742i) q^{91} +7.79754 q^{95} -1.28856 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

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
$5$	−1.39555	−	3.36915i	−0.624108	−	1.50673i	−0.846839	−	0.531850i	$-0.821497\pi$
$5$	−1.39555	−	3.36915i	−0.624108	−	1.50673i	0.222731	−	0.974880i	$-0.428503\pi$
$6$		0			0
$7$	1.05755	+	1.05755i	0.399715	+	0.399715i	0.878133	−	0.478417i	$-0.158789\pi$
$7$	1.05755	+	1.05755i	0.399715	+	0.399715i	−0.478417	+	0.878133i	$0.658789\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.50977	−	3.64490i	−0.455211	−	1.09898i	−0.970314	−	0.241849i	$-0.922246\pi$
$11$	−1.50977	−	3.64490i	−0.455211	−	1.09898i	0.515102	−	0.857129i	$-0.327754\pi$
$12$		0			0
$13$	−2.23818	−	0.927086i	−0.620761	−	0.257127i	0.0500610	−	0.998746i	$-0.484058\pi$
$13$	−2.23818	−	0.927086i	−0.620761	−	0.257127i	−0.670822	+	0.741619i	$0.734058\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−7.49610			−1.81807			−0.909036	−	0.416717i	$-0.863180\pi$
$17$	−7.49610			−1.81807			−0.909036	+	0.416717i	$0.863180\pi$
$18$		0			0
$19$	−0.818262	+	1.97546i	−0.187722	+	0.453201i	−0.989520	−	0.144393i	$-0.953877\pi$
$19$	−0.818262	+	1.97546i	−0.187722	+	0.453201i	0.801798	+	0.597595i	$0.203877\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.80392	+	5.80392i	1.21020	+	1.21020i	0.970960	+	0.239241i	$0.0768985\pi$
$23$	5.80392	+	5.80392i	1.21020	+	1.21020i	0.239241	+	0.970960i	$0.423102\pi$
$24$		0			0
$25$	−5.86809	+	5.86809i	−1.17362	+	1.17362i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.326633	+	0.135296i	0.0606542	+	0.0251238i	0.412804	−	0.910820i	$-0.364549\pi$
$29$	0.326633	+	0.135296i	0.0606542	+	0.0251238i	−0.352150	+	0.935944i	$0.614549\pi$
$30$		0			0
$31$			1.71021i			0.307163i	0.988136	+	0.153582i	$0.0490808\pi$
$31$			1.71021i			0.307163i	−0.988136	+	0.153582i	$0.950919\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.08718	−	5.03889i	0.352797	−	0.851728i
$36$		0			0
$37$	0.387384	−	0.160460i	0.0636856	−	0.0263794i	−0.350613	−	0.936520i	$-0.614027\pi$
$37$	0.387384	−	0.160460i	0.0636856	−	0.0263794i	0.414299	+	0.910141i	$0.364027\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.50401	+	1.50401i	−0.234887	+	0.234887i	−0.814729	−	0.579842i	$-0.803114\pi$
$41$	−1.50401	+	1.50401i	−0.234887	+	0.234887i	0.579842	+	0.814729i	$0.303114\pi$
$42$		0			0
$43$	−7.40227	+	3.06612i	−1.12884	+	0.467579i	−0.867385	−	0.497638i	$-0.834201\pi$
$43$	−7.40227	+	3.06612i	−1.12884	+	0.467579i	−0.261450	+	0.965217i	$0.584201\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	7.27404i		−	1.06103i	−0.847676	−	0.530514i	$-0.821999\pi$
$47$		−	7.27404i		−	1.06103i	0.847676	−	0.530514i	$-0.178001\pi$
$48$		0			0
$49$		−	4.76319i		−	0.680455i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.94866	−	1.63559i	0.542390	−	0.224665i	−0.0946303	−	0.995512i	$-0.530167\pi$
$53$	3.94866	−	1.63559i	0.542390	−	0.224665i	0.637020	+	0.770847i	$0.280167\pi$
$54$		0			0
$55$	−10.1733	+	10.1733i	−1.37176	+	1.37176i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−12.7979	+	5.30105i	−1.66614	+	0.690138i	−0.998521	−	0.0543646i	$-0.982687\pi$
$59$	−12.7979	+	5.30105i	−1.66614	+	0.690138i	−0.667619	+	0.744503i	$0.732687\pi$
$60$		0			0
$61$	−0.579943	+	1.40011i	−0.0742542	+	0.179265i	−0.956648	−	0.291245i	$-0.905930\pi$
$61$	−0.579943	+	1.40011i	−0.0742542	+	0.179265i	0.882394	+	0.470511i	$0.155930\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			8.83457i			1.09579i
$66$		0			0
$67$	7.96385	+	3.29874i	0.972940	+	0.403005i	0.811806	−	0.583928i	$-0.198485\pi$
$67$	7.96385	+	3.29874i	0.972940	+	0.403005i	0.161134	+	0.986933i	$0.448485\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.75505	+	4.75505i	−0.564320	+	0.564320i	−0.930532	−	0.366211i	$-0.880655\pi$
$71$	−4.75505	+	4.75505i	−0.564320	+	0.564320i	0.366211	+	0.930532i	$0.380655\pi$
$72$		0			0
$73$	−7.99854	−	7.99854i	−0.936158	−	0.936158i	0.0619229	−	0.998081i	$-0.480277\pi$
$73$	−7.99854	−	7.99854i	−0.936158	−	0.936158i	−0.998081	+	0.0619229i	$0.980277\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.25800	−	5.45130i	0.257323	−	0.621233i
$78$		0			0
$79$	−14.3967			−1.61975			−0.809877	−	0.586600i	$-0.800466\pi$
$79$	−14.3967			−1.61975			−0.809877	+	0.586600i	$0.800466\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.35250	−	0.560224i	−0.148456	−	0.0614926i	0.307218	−	0.951639i	$-0.400602\pi$
$83$	−1.35250	−	0.560224i	−0.148456	−	0.0614926i	−0.455674	+	0.890147i	$0.650602\pi$
$84$		0			0
$85$	10.4612	+	25.2555i	1.13467	+	2.73934i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.75638	−	4.75638i	−0.504176	−	0.504176i	0.408557	−	0.912733i	$-0.366032\pi$
$89$	−4.75638	−	4.75638i	−0.504176	−	0.504176i	−0.912733	+	0.408557i	$0.866032\pi$
$90$		0			0
$91$	−1.38655	−	3.34742i	−0.145350	−	0.350905i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.79754			0.800011
$96$		0			0
$97$	−1.28856			−0.130834			−0.0654168	−	0.997858i	$-0.520838\pi$
$97$	−1.28856			−0.130834			−0.0654168	+	0.997858i	$0.520838\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.56084	−	11.0109i	−0.453821	−	1.09562i	−0.970858	−	0.239657i	$-0.922965\pi$
$101$	−4.56084	−	11.0109i	−0.453821	−	1.09562i	0.517037	−	0.855963i	$-0.327035\pi$
$102$		0			0
$103$	8.69287	+	8.69287i	0.856533	+	0.856533i	0.990928	−	0.134394i	$-0.0429089\pi$
$103$	8.69287	+	8.69287i	0.856533	+	0.856533i	−0.134394	+	0.990928i	$0.542909\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.21290	−	14.9993i	−0.600624	−	1.45003i	−0.872940	−	0.487827i	$-0.837790\pi$
$107$	−6.21290	−	14.9993i	−0.600624	−	1.45003i	0.272316	−	0.962208i	$-0.412210\pi$
$108$		0			0
$109$	1.20531	+	0.499254i	0.115447	+	0.0478198i	0.439659	−	0.898165i	$-0.355099\pi$
$109$	1.20531	+	0.499254i	0.115447	+	0.0478198i	−0.324212	+	0.945984i	$0.605099\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.83947			0.455259			0.227630	−	0.973748i	$-0.426902\pi$
$113$	4.83947			0.455259			0.227630	+	0.973748i	$0.426902\pi$
$114$		0			0
$115$	11.4546	−	27.6539i	1.06815	−	2.57874i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.92748	−	7.92748i	−0.726711	−	0.726711i
$120$		0			0
$121$	−3.22771	+	3.22771i	−0.293428	+	0.293428i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.1139	+	4.60353i	0.994059	+	0.411753i
$126$		0			0
$127$		−	1.85060i		−	0.164214i	−0.996624	−	0.0821069i	$-0.973835\pi$
$127$		−	1.85060i		−	0.164214i	0.996624	−	0.0821069i	$-0.0261649\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.44102	+	5.89314i	−0.213273	+	0.514886i	−0.993922	−	0.110083i	$-0.964888\pi$
$131$	−2.44102	+	5.89314i	−0.213273	+	0.514886i	0.780650	+	0.624969i	$0.214888\pi$
$132$		0			0
$133$	−2.95449	+	1.22379i	−0.256187	+	0.106116i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.65921	−	2.65921i	0.227192	−	0.227192i	−0.584327	−	0.811519i	$-0.698641\pi$
$137$	2.65921	−	2.65921i	0.227192	−	0.227192i	0.811519	+	0.584327i	$0.198641\pi$
$138$		0			0
$139$	11.7567	−	4.86980i	0.997193	−	0.413051i	0.176426	−	0.984314i	$-0.443546\pi$
$139$	11.7567	−	4.86980i	0.997193	−	0.413051i	0.820767	+	0.571263i	$0.193546\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			9.55763i			0.799250i
$144$		0			0
$145$		−	1.28929i		−	0.107070i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.23656	+	3.41170i	−0.674765	+	0.279497i	−0.693637	−	0.720325i	$-0.743993\pi$
$149$	−8.23656	+	3.41170i	−0.674765	+	0.279497i	0.0188714	+	0.999822i	$0.493993\pi$
$150$		0			0
$151$	11.9992	−	11.9992i	0.976478	−	0.976478i	−0.0232512	−	0.999730i	$-0.507402\pi$
$151$	11.9992	−	11.9992i	0.976478	−	0.976478i	0.999730	+	0.0232512i	$0.00740175\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.76197	−	2.38669i	0.462812	−	0.191703i
$156$		0			0
$157$	5.47915	−	13.2278i	0.437284	−	1.05570i	−0.539599	−	0.841922i	$-0.681424\pi$
$157$	5.47915	−	13.2278i	0.437284	−	1.05570i	0.976883	−	0.213775i	$-0.0685759\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			12.2758i			0.967471i
$162$		0			0
$163$	−10.3137	−	4.27206i	−0.807828	−	0.334614i	−0.0597412	−	0.998214i	$-0.519028\pi$
$163$	−10.3137	−	4.27206i	−0.807828	−	0.334614i	−0.748087	+	0.663600i	$0.769028\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.27058	+	6.27058i	−0.485232	+	0.485232i	−0.906798	−	0.421566i	$-0.861481\pi$
$167$	−6.27058	+	6.27058i	−0.485232	+	0.485232i	0.421566	+	0.906798i	$0.361481\pi$
$168$		0			0
$169$	−5.04241	−	5.04241i	−0.387878	−	0.387878i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.58864	−	23.1490i	0.729011	−	1.75999i	0.0831448	−	0.996537i	$-0.473504\pi$
$173$	9.58864	−	23.1490i	0.729011	−	1.75999i	0.645866	−	0.763451i	$-0.276496\pi$
$174$		0			0
$175$	−12.4116			−0.938226
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.32195	−	2.61864i	−0.472524	−	0.195726i	0.133697	−	0.991022i	$-0.457315\pi$
$179$	−6.32195	−	2.61864i	−0.472524	−	0.195726i	−0.606221	+	0.795296i	$0.707315\pi$
$180$		0			0
$181$	−1.02155	−	2.46625i	−0.0759314	−	0.183315i	0.881356	−	0.472453i	$-0.156631\pi$
$181$	−1.02155	−	2.46625i	−0.0759314	−	0.183315i	−0.957287	+	0.289138i	$0.906631\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.08123	−	1.08123i	−0.0794934	−	0.0794934i
$186$		0			0
$187$	11.3174	+	27.3225i	0.827607	+	1.99802i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	20.7890			1.50424			0.752121	−	0.659025i	$-0.229031\pi$
$191$	20.7890			1.50424			0.752121	+	0.659025i	$0.229031\pi$
$192$		0			0
$193$	14.9444			1.07572			0.537861	−	0.843034i	$-0.319233\pi$
$193$	14.9444			1.07572			0.537861	+	0.843034i	$0.319233\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.50419	+	22.9451i	0.677145	+	1.63477i	0.769191	+	0.639019i	$0.220659\pi$
$197$	9.50419	+	22.9451i	0.677145	+	1.63477i	−0.0920460	+	0.995755i	$0.529341\pi$
$198$		0			0
$199$	1.24926	+	1.24926i	0.0885579	+	0.0885579i	0.749998	−	0.661440i	$-0.230054\pi$
$199$	1.24926	+	1.24926i	0.0885579	+	0.0885579i	−0.661440	+	0.749998i	$0.730054\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.202348	+	0.488512i	0.0142021	+	0.0342868i
$204$		0			0
$205$	7.16615	+	2.96832i	0.500506	+	0.207316i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.43573			0.583512
$210$		0			0
$211$	4.04903	−	9.77521i	0.278746	−	0.672953i	−0.721055	−	0.692878i	$-0.756343\pi$
$211$	4.04903	−	9.77521i	0.278746	−	0.672953i	0.999801	+	0.0199244i	$0.00634254\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	20.6604	+	20.6604i	1.40903	+	1.40903i
$216$		0			0
$217$	−1.80863	+	1.80863i	−0.122778	+	0.122778i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	16.7777	+	6.94954i	1.12859	+	0.467476i
$222$		0			0
$223$		−	19.2531i		−	1.28928i	−0.764485	−	0.644641i	$-0.777007\pi$
$223$		−	19.2531i		−	1.28928i	0.764485	−	0.644641i	$-0.222993\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.98915	+	14.4591i	−0.397514	+	0.959684i	0.590740	+	0.806862i	$0.298836\pi$
$227$	−5.98915	+	14.4591i	−0.397514	+	0.959684i	−0.988254	+	0.152822i	$0.951164\pi$
$228$		0			0
$229$	−7.93338	+	3.28612i	−0.524253	+	0.217153i	−0.629084	−	0.777337i	$-0.716570\pi$
$229$	−7.93338	+	3.28612i	−0.524253	+	0.217153i	0.104831	+	0.994490i	$0.466570\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.2337	+	12.2337i	−0.801455	+	0.801455i	−0.983323	−	0.181868i	$-0.941786\pi$
$233$	−12.2337	+	12.2337i	−0.801455	+	0.801455i	0.181868	+	0.983323i	$0.441786\pi$
$234$		0			0
$235$	−24.5073	+	10.1513i	−1.59868	+	0.662196i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			10.3650i			0.670459i	0.942137	+	0.335229i	$0.108814\pi$
$239$			10.3650i			0.670459i	−0.942137	+	0.335229i	$0.891186\pi$
$240$		0			0
$241$			14.1048i			0.908572i	0.890856	+	0.454286i	$0.150106\pi$
$241$			14.1048i			0.908572i	−0.890856	+	0.454286i	$0.849894\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−16.0479	+	6.64726i	−1.02526	+	0.424678i
$246$		0			0
$247$	3.66284	−	3.66284i	0.233061	−	0.233061i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.92406	−	2.03961i	0.310804	−	0.128739i	−0.221829	−	0.975086i	$-0.571203\pi$
$251$	4.92406	−	2.03961i	0.310804	−	0.128739i	0.532633	+	0.846346i	$0.321203\pi$
$252$		0			0
$253$	12.3921	−	29.9172i	0.779087	−	1.88088i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			20.2370i			1.26235i	0.775640	+	0.631175i	$0.217427\pi$
$257$			20.2370i			1.26235i	−0.775640	+	0.631175i	$0.782573\pi$
$258$		0			0
$259$	0.579371	+	0.239983i	0.0360004	+	0.0149118i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.63751	−	3.63751i	0.224299	−	0.224299i	−0.586007	−	0.810306i	$-0.699301\pi$
$263$	3.63751	−	3.63751i	0.224299	−	0.224299i	0.810306	+	0.586007i	$0.199301\pi$
$264$		0			0
$265$	−11.0211	−	11.0211i	−0.677019	−	0.677019i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.92241	−	7.05531i	0.178182	−	0.430170i	−0.809403	−	0.587254i	$-0.800209\pi$
$269$	2.92241	−	7.05531i	0.178182	−	0.430170i	0.987585	+	0.157083i	$0.0502092\pi$
$270$		0			0
$271$	7.63925			0.464052			0.232026	−	0.972710i	$-0.425465\pi$
$271$	7.63925			0.464052			0.232026	+	0.972710i	$0.425465\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	30.2480	+	12.5291i	1.82402	+	0.755535i
$276$		0			0
$277$	−6.85371	−	16.5463i	−0.411799	−	0.994172i	−0.984655	−	0.174515i	$-0.944164\pi$
$277$	−6.85371	−	16.5463i	−0.411799	−	0.994172i	0.572855	−	0.819657i	$-0.305836\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.5776	−	13.5776i	−0.809969	−	0.809969i	0.174660	−	0.984629i	$-0.444117\pi$
$281$	−13.5776	−	13.5776i	−0.809969	−	0.809969i	−0.984629	+	0.174660i	$0.944117\pi$
$282$		0			0
$283$	−7.17080	−	17.3118i	−0.426260	−	1.02908i	−0.980463	−	0.196701i	$-0.936977\pi$
$283$	−7.17080	−	17.3118i	−0.426260	−	1.02908i	0.554204	−	0.832381i	$-0.313023\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.18112			−0.187776
$288$		0			0
$289$	39.1916			2.30539
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.11909	−	2.70172i	−0.0653780	−	0.157836i	0.887814	−	0.460203i	$-0.152223\pi$
$293$	−1.11909	−	2.70172i	−0.0653780	−	0.157836i	−0.953192	+	0.302367i	$0.902223\pi$
$294$		0			0
$295$	35.7201	+	35.7201i	2.07970	+	2.07970i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.60951	−	18.3710i	−0.440069	−	1.06242i
$300$		0			0
$301$	−11.0708	−	4.58568i	−0.638111	−	0.264314i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5.52651			0.316447
$306$		0			0
$307$	−0.597072	+	1.44146i	−0.0340767	+	0.0822684i	−0.940002	−	0.341170i	$-0.889177\pi$
$307$	−0.597072	+	1.44146i	−0.0340767	+	0.0822684i	0.905925	+	0.423438i	$0.139177\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−16.3415	−	16.3415i	−0.926640	−	0.926640i	0.0708472	−	0.997487i	$-0.477430\pi$
$311$	−16.3415	−	16.3415i	−0.926640	−	0.926640i	−0.997487	+	0.0708472i	$0.977430\pi$
$312$		0			0
$313$	11.0100	−	11.0100i	0.622320	−	0.622320i	−0.323804	−	0.946124i	$-0.604962\pi$
$313$	11.0100	−	11.0100i	0.622320	−	0.622320i	0.946124	+	0.323804i	$0.104962\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.87945	−	2.84956i	−0.386388	−	0.160047i	0.181029	−	0.983478i	$-0.442057\pi$
$317$	−6.87945	−	2.84956i	−0.386388	−	0.160047i	−0.567417	+	0.823430i	$0.692057\pi$
$318$		0			0
$319$		−	1.39481i		−	0.0780943i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.13378	−	14.8082i	0.341292	−	0.823953i
$324$		0			0
$325$	18.5741	−	7.69364i	1.03030	−	0.426766i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.69264	−	7.69264i	0.424109	−	0.424109i
$330$		0			0
$331$	−3.18235	+	1.31817i	−0.174918	+	0.0724533i	−0.468424	−	0.883504i	$-0.655178\pi$
$331$	−3.18235	+	1.31817i	−0.174918	+	0.0724533i	0.293506	+	0.955957i	$0.405178\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	31.4350i		−	1.71748i
$336$		0			0
$337$		−	33.5837i		−	1.82942i	−0.404110	−	0.914710i	$-0.632419\pi$
$337$		−	33.5837i		−	1.82942i	0.404110	−	0.914710i	$-0.367581\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.23355	−	2.58202i	0.337566	−	0.139824i
$342$		0			0
$343$	12.4401	−	12.4401i	0.671704	−	0.671704i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.5727	−	4.37938i	0.567575	−	0.235097i	−0.0803952	−	0.996763i	$-0.525618\pi$
$347$	10.5727	−	4.37938i	0.567575	−	0.235097i	0.647970	+	0.761666i	$0.275618\pi$
$348$		0			0
$349$	−1.93540	+	4.67246i	−0.103599	+	0.250111i	−0.967176	−	0.254106i	$-0.918219\pi$
$349$	−1.93540	+	4.67246i	−0.103599	+	0.250111i	0.863577	+	0.504217i	$0.168219\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	11.8710i		−	0.631829i	−0.948788	−	0.315915i	$-0.897689\pi$
$353$		−	11.8710i		−	0.631829i	0.948788	−	0.315915i	$-0.102311\pi$
$354$		0			0
$355$	22.6564	+	9.38458i	1.20248	+	0.498082i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.19895	+	7.19895i	−0.379946	+	0.379946i	−0.871083	−	0.491137i	$-0.836582\pi$
$359$	−7.19895	+	7.19895i	−0.379946	+	0.379946i	0.491137	+	0.871083i	$0.336582\pi$
$360$		0			0
$361$	10.2021	+	10.2021i	0.536955	+	0.536955i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−15.7859	+	38.1106i	−0.826274	+	1.99480i
$366$		0			0
$367$	−5.49636			−0.286908			−0.143454	−	0.989657i	$-0.545821\pi$
$367$	−5.49636			−0.286908			−0.143454	+	0.989657i	$0.545821\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.90560	+	2.44618i	0.306603	+	0.126999i
$372$		0			0
$373$	9.45992	+	22.8383i	0.489816	+	1.18252i	0.954813	+	0.297208i	$0.0960556\pi$
$373$	9.45992	+	22.8383i	0.489816	+	1.18252i	−0.464996	+	0.885313i	$0.653944\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.605634	−	0.605634i	−0.0311917	−	0.0311917i
$378$		0			0
$379$	5.26808	+	12.7183i	0.270603	+	0.653293i	0.999509	−	0.0313200i	$-0.00997110\pi$
$379$	5.26808	+	12.7183i	0.270603	+	0.653293i	−0.728906	+	0.684613i	$0.759971\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.651517			−0.0332910			−0.0166455	−	0.999861i	$-0.505299\pi$
$383$	−0.651517			−0.0332910			−0.0166455	+	0.999861i	$0.505299\pi$
$384$		0			0
$385$	−21.5174			−1.09663
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.58251	−	15.8916i	−0.333747	−	0.805736i	−0.998288	−	0.0584844i	$-0.981373\pi$
$389$	−6.58251	−	15.8916i	−0.333747	−	0.805736i	0.664542	−	0.747251i	$-0.268627\pi$
$390$		0			0
$391$	−43.5068	−	43.5068i	−2.20023	−	2.20023i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	20.0913	+	48.5046i	1.01090	+	2.44053i
$396$		0			0
$397$	−23.5792	−	9.76681i	−1.18340	−	0.490182i	−0.297802	−	0.954628i	$-0.596254\pi$
$397$	−23.5792	−	9.76681i	−1.18340	−	0.490182i	−0.885602	+	0.464446i	$0.846254\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.64431			−0.281864			−0.140932	−	0.990019i	$-0.545010\pi$
$401$	−5.64431			−0.281864			−0.140932	+	0.990019i	$0.545010\pi$
$402$		0			0
$403$	1.58552	−	3.82777i	0.0789802	−	0.190675i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.16972	−	1.16972i	−0.0579808	−	0.0579808i
$408$		0			0
$409$	−15.4062	+	15.4062i	−0.761790	+	0.761790i	−0.976646	−	0.214856i	$-0.931072\pi$
$409$	−15.4062	+	15.4062i	−0.761790	+	0.761790i	0.214856	+	0.976646i	$0.431072\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−19.1405	−	7.92824i	−0.941840	−	0.390123i
$414$		0			0
$415$			5.33860i			0.262061i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.62264	+	23.2311i	−0.470097	+	1.13491i	0.494024	+	0.869449i	$0.335526\pi$
$419$	−9.62264	+	23.2311i	−0.470097	+	1.13491i	−0.964120	+	0.265466i	$0.914474\pi$
$420$		0			0
$421$	−2.00854	+	0.831963i	−0.0978901	+	0.0405474i	−0.431091	−	0.902308i	$-0.641871\pi$
$421$	−2.00854	+	0.831963i	−0.0978901	+	0.0405474i	0.333201	+	0.942856i	$0.391871\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	43.9878	−	43.9878i	2.13372	−	2.13372i
$426$		0			0
$427$	−2.09400	+	0.867362i	−0.101336	+	0.0419746i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	16.8804i		−	0.813100i	−0.913628	−	0.406550i	$-0.866732\pi$
$431$		−	16.8804i		−	0.813100i	0.913628	−	0.406550i	$-0.133268\pi$
$432$		0			0
$433$		−	0.162457i		−	0.00780716i	−0.999992	−	0.00390358i	$-0.998757\pi$
$433$		−	0.162457i		−	0.00780716i	0.999992	−	0.00390358i	$-0.00124255\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−16.2145	+	6.71628i	−0.775646	+	0.321283i
$438$		0			0
$439$	0.853136	−	0.853136i	0.0407180	−	0.0407180i	−0.686455	−	0.727173i	$-0.740834\pi$
$439$	0.853136	−	0.853136i	0.0407180	−	0.0407180i	0.727173	+	0.686455i	$0.240834\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−22.2491	+	9.21590i	−1.05709	+	0.437860i	−0.842417	−	0.538826i	$-0.818868\pi$
$443$	−22.2491	+	9.21590i	−1.05709	+	0.437860i	−0.214672	+	0.976686i	$0.568868\pi$
$444$		0			0
$445$	−9.38721	+	22.6627i	−0.444996	+	1.07432i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	23.1544i		−	1.09272i	−0.837549	−	0.546362i	$-0.816012\pi$
$449$		−	23.1544i		−	1.09272i	0.837549	−	0.546362i	$-0.183988\pi$
$450$		0			0
$451$	7.75266	+	3.21126i	0.365059	+	0.151212i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−9.34298	+	9.34298i	−0.438006	+	0.438006i
$456$		0			0
$457$	15.2233	+	15.2233i	0.712114	+	0.712114i	0.966977	−	0.254863i	$-0.0820304\pi$
$457$	15.2233	+	15.2233i	0.712114	+	0.712114i	−0.254863	+	0.966977i	$0.582030\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.2190	+	29.4992i	−0.569093	+	1.37391i	0.333227	+	0.942847i	$0.391862\pi$
$461$	−12.2190	+	29.4992i	−0.569093	+	1.37391i	−0.902320	+	0.431066i	$0.858138\pi$
$462$		0			0
$463$	−0.577924			−0.0268584			−0.0134292	−	0.999910i	$-0.504275\pi$
$463$	−0.577924			−0.0268584			−0.0134292	+	0.999910i	$0.504275\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.0132	+	10.3608i	1.15747	+	0.479441i	0.877033	−	0.480431i	$-0.159520\pi$
$467$	25.0132	+	10.3608i	1.15747	+	0.479441i	0.280440	+	0.959872i	$0.409520\pi$
$468$		0			0
$469$	4.93358	+	11.9107i	0.227812	+	0.549986i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	22.3514	+	22.3514i	1.02772	+	1.02772i
$474$		0			0
$475$	−6.79053	−	16.3938i	−0.311571	−	0.752199i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−20.6865			−0.945188			−0.472594	−	0.881280i	$-0.656682\pi$
$479$	−20.6865			−0.945188			−0.472594	+	0.881280i	$0.656682\pi$
$480$		0			0
$481$	−1.01580			−0.0463164
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.79825	+	4.34136i	0.0816543	+	0.197131i
$486$		0			0
$487$	17.8979	+	17.8979i	0.811031	+	0.811031i	0.984788	−	0.173757i	$-0.0555909\pi$
$487$	17.8979	+	17.8979i	0.811031	+	0.811031i	−0.173757	+	0.984788i	$0.555591\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.919341	+	2.21949i	0.0414893	+	0.100164i	0.943266	−	0.332039i	$-0.107736\pi$
$491$	0.919341	+	2.21949i	0.0414893	+	0.100164i	−0.901776	+	0.432203i	$0.857736\pi$
$492$		0			0
$493$	−2.44848	−	1.01419i	−0.110274	−	0.0456769i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.0574			−0.451135
$498$		0			0
$499$	−8.65228	+	20.8884i	−0.387329	+	0.935095i	0.603175	+	0.797609i	$0.293902\pi$
$499$	−8.65228	+	20.8884i	−0.387329	+	0.935095i	−0.990504	+	0.137486i	$0.956098\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.91458	−	9.91458i	−0.442069	−	0.442069i	0.450638	−	0.892707i	$-0.351197\pi$
$503$	−9.91458	−	9.91458i	−0.442069	−	0.442069i	−0.892707	+	0.450638i	$0.851197\pi$
$504$		0			0
$505$	−30.7323	+	30.7323i	−1.36757	+	1.36757i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	8.70757	+	3.60679i	0.385956	+	0.159868i	0.567220	−	0.823566i	$-0.308019\pi$
$509$	8.70757	+	3.60679i	0.385956	+	0.159868i	−0.181264	+	0.983434i	$0.558019\pi$
$510$		0			0
$511$		−	16.9177i		−	0.748393i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	17.1563	−	41.4189i	0.755995	−	1.82513i
$516$		0			0
$517$	−26.5131	+	10.9821i	−1.16605	+	0.482992i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.843541	−	0.843541i	0.0369562	−	0.0369562i	−0.688387	−	0.725343i	$-0.741681\pi$
$521$	0.843541	−	0.843541i	0.0369562	−	0.0369562i	0.725343	+	0.688387i	$0.241681\pi$
$522$		0			0
$523$	−0.0207812	+	0.00860784i	−0.000908697	+	0.000376395i	−0.383138	−	0.923691i	$-0.625157\pi$
$523$	−0.0207812	+	0.00860784i	−0.000908697	+	0.000376395i	0.382229	+	0.924068i	$0.375157\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	12.8199i		−	0.558445i
$528$		0			0
$529$			44.3710i			1.92917i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.76060	−	1.97190i	0.206204	−	0.0854126i
$534$		0			0
$535$	−41.8644	+	41.8644i	−1.80996	+	1.80996i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−17.3613	+	7.19130i	−0.747805	+	0.309751i
$540$		0			0
$541$	1.78856	−	4.31796i	0.0768961	−	0.185644i	−0.880757	−	0.473569i	$-0.842965\pi$
$541$	1.78856	−	4.31796i	0.0768961	−	0.185644i	0.957653	+	0.287925i	$0.0929655\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	4.75759i		−	0.203793i
$546$		0			0
$547$	−26.9790	−	11.1751i	−1.15354	−	0.477811i	−0.277819	−	0.960633i	$-0.589612\pi$
$547$	−26.9790	−	11.1751i	−1.15354	−	0.477811i	−0.875718	+	0.482823i	$0.839612\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.534543	+	0.534543i	−0.0227723	+	0.0227723i
$552$		0			0
$553$	−15.2252	−	15.2252i	−0.647440	−	0.647440i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.15147	+	5.19412i	−0.0911609	+	0.220082i	−0.962883	−	0.269918i	$-0.913003\pi$
$557$	−2.15147	+	5.19412i	−0.0911609	+	0.220082i	0.871722	+	0.490000i	$0.163003\pi$
$558$		0			0
$559$	19.4102			0.820964
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−15.9450	−	6.60465i	−0.672003	−	0.278353i	0.0204766	−	0.999790i	$-0.493482\pi$
$563$	−15.9450	−	6.60465i	−0.672003	−	0.278353i	−0.692479	+	0.721438i	$0.743482\pi$
$564$		0			0
$565$	−6.75372	−	16.3049i	−0.284131	−	0.685953i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.67703	−	1.67703i	−0.0703046	−	0.0703046i	0.671080	−	0.741385i	$-0.265831\pi$
$569$	−1.67703	−	1.67703i	−0.0703046	−	0.0703046i	−0.741385	+	0.671080i	$0.765831\pi$
$570$		0			0
$571$	2.41843	+	5.83861i	0.101208	+	0.244338i	0.966371	−	0.257154i	$-0.0827847\pi$
$571$	2.41843	+	5.83861i	0.101208	+	0.244338i	−0.865162	+	0.501492i	$0.832785\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−68.1158			−2.84063
$576$		0			0
$577$	10.8983			0.453703			0.226851	−	0.973929i	$-0.427157\pi$
$577$	10.8983			0.453703			0.226851	+	0.973929i	$0.427157\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.837869	−	2.02280i	−0.0347607	−	0.0839197i
$582$		0			0
$583$	−11.9231	−	11.9231i	−0.493804	−	0.493804i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.0840	−	29.1734i	−0.498760	−	1.20411i	−0.950152	−	0.311788i	$-0.899072\pi$
$587$	−12.0840	−	29.1734i	−0.498760	−	1.20411i	0.451392	−	0.892326i	$-0.350928\pi$
$588$		0			0
$589$	−3.37846	−	1.39940i	−0.139207	−	0.0576614i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	25.8516			1.06160			0.530800	−	0.847497i	$-0.321892\pi$
$593$	25.8516			1.06160			0.530800	+	0.847497i	$0.321892\pi$
$594$		0			0
$595$	−15.6457	+	37.7721i	−0.641411	+	1.54850i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.76404	+	7.76404i	0.317230	+	0.317230i	0.847702	−	0.530472i	$-0.177985\pi$
$599$	7.76404	+	7.76404i	0.317230	+	0.317230i	−0.530472	+	0.847702i	$0.677985\pi$
$600$		0			0
$601$	27.7695	−	27.7695i	1.13274	−	1.13274i	0.143020	−	0.989720i	$-0.454319\pi$
$601$	27.7695	−	27.7695i	1.13274	−	1.13274i	0.989720	−	0.143020i	$-0.0456812\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	15.3790	+	6.37021i	0.625247	+	0.258986i
$606$		0			0
$607$		−	6.83755i		−	0.277527i	−0.990326	−	0.138764i	$-0.955687\pi$
$607$		−	6.83755i		−	0.277527i	0.990326	−	0.138764i	$-0.0443129\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.74366	+	16.2806i	−0.272819	+	0.658644i
$612$		0			0
$613$	1.88592	−	0.781173i	0.0761716	−	0.0315513i	−0.344272	−	0.938870i	$-0.611874\pi$
$613$	1.88592	−	0.781173i	0.0761716	−	0.0315513i	0.420444	+	0.907319i	$0.361874\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−16.5582	+	16.5582i	−0.666610	+	0.666610i	−0.956930	−	0.290320i	$-0.906238\pi$
$617$	−16.5582	+	16.5582i	−0.666610	+	0.666610i	0.290320	+	0.956930i	$0.406238\pi$
$618$		0			0
$619$	−34.0627	+	14.1093i	−1.36910	+	0.567099i	−0.941544	−	0.336891i	$-0.890625\pi$
$619$	−34.0627	+	14.1093i	−1.36910	+	0.567099i	−0.427554	+	0.903990i	$0.640625\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	10.0602i		−	0.403053i
$624$		0			0
$625$		−	2.37526i		−	0.0950104i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.90387	+	1.20282i	−0.115785	+	0.0479597i
$630$		0			0
$631$	18.8332	−	18.8332i	0.749737	−	0.749737i	−0.224693	−	0.974430i	$-0.572138\pi$
$631$	18.8332	−	18.8332i	0.749737	−	0.749737i	0.974430	+	0.224693i	$0.0721379\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.23494	+	2.58260i	−0.247426	+	0.102487i
$636$		0			0
$637$	−4.41589	+	10.6609i	−0.174964	+	0.422400i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	34.0636i		−	1.34543i	−0.739900	−	0.672716i	$-0.765127\pi$
$641$		−	34.0636i		−	1.34543i	0.739900	−	0.672716i	$-0.234873\pi$
$642$		0			0
$643$	−8.14924	−	3.37552i	−0.321374	−	0.133118i	0.216164	−	0.976357i	$-0.430646\pi$
$643$	−8.14924	−	3.37552i	−0.321374	−	0.133118i	−0.537538	+	0.843239i	$0.680646\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	15.9458	−	15.9458i	0.626894	−	0.626894i	−0.320391	−	0.947285i	$-0.603814\pi$
$647$	15.9458	−	15.9458i	0.626894	−	0.626894i	0.947285	+	0.320391i	$0.103814\pi$
$648$		0			0
$649$	38.6436	+	38.6436i	1.51689	+	1.51689i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	10.3560	−	25.0017i	0.405263	−	0.978391i	−0.581104	−	0.813829i	$-0.697379\pi$
$653$	10.3560	−	25.0017i	0.405263	−	0.978391i	0.986367	−	0.164562i	$-0.0526210\pi$
$654$		0			0
$655$	23.2614			0.908900
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.976716	−	0.404569i	−0.0380475	−	0.0157598i	0.363579	−	0.931564i	$-0.381555\pi$
$659$	−0.976716	−	0.404569i	−0.0380475	−	0.0157598i	−0.401626	+	0.915804i	$0.631555\pi$
$660$		0			0
$661$	−10.6003	−	25.5914i	−0.412304	−	0.995389i	−0.984518	−	0.175285i	$-0.943915\pi$
$661$	−10.6003	−	25.5914i	−0.412304	−	0.995389i	0.572214	−	0.820104i	$-0.306085\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	8.24627	+	8.24627i	0.319777	+	0.319777i
$666$		0			0
$667$	1.11051	+	2.68100i	0.0429990	+	0.103809i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.97883			0.230810
$672$		0			0
$673$	−17.3400			−0.668409			−0.334205	−	0.942501i	$-0.608468\pi$
$673$	−17.3400			−0.668409			−0.334205	+	0.942501i	$0.608468\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.10411	−	2.66556i	−0.0424344	−	0.102446i	0.901241	−	0.433318i	$-0.142657\pi$
$677$	−1.10411	−	2.66556i	−0.0424344	−	0.102446i	−0.943676	+	0.330872i	$0.892657\pi$
$678$		0			0
$679$	−1.36271	−	1.36271i	−0.0522962	−	0.0522962i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.51934	+	22.9817i	0.364247	+	0.879371i	0.994669	+	0.103118i	$0.0328820\pi$
$683$	9.51934	+	22.9817i	0.364247	+	0.879371i	−0.630422	+	0.776253i	$0.717118\pi$
$684$		0			0
$685$	−12.6703	−	5.24823i	−0.484109	−	0.200525i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−10.3542			−0.394462
$690$		0			0
$691$	−8.56212	+	20.6708i	−0.325719	+	0.786354i	0.673182	+	0.739477i	$0.264927\pi$
$691$	−8.56212	+	20.6708i	−0.325719	+	0.786354i	−0.998901	+	0.0468774i	$0.985073\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−32.8142	−	32.8142i	−1.24471	−	1.24471i
$696$		0			0
$697$	11.2742	−	11.2742i	0.427041	−	0.427041i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−40.4517	−	16.7556i	−1.52784	−	0.632852i	−0.548695	−	0.836022i	$-0.684875\pi$
$701$	−40.4517	−	16.7556i	−1.52784	−	0.632852i	−0.979143	+	0.203171i	$0.934875\pi$
$702$		0			0
$703$			0.896560i			0.0338144i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.82119	−	16.4678i	0.256537	−	0.619335i
$708$		0			0
$709$	−16.2624	+	6.73611i	−0.610748	+	0.252980i	−0.666548	−	0.745462i	$-0.732229\pi$
$709$	−16.2624	+	6.73611i	−0.610748	+	0.252980i	0.0558005	+	0.998442i	$0.482229\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.92594	+	9.92594i	−0.371730	+	0.371730i
$714$		0			0
$715$	32.2011	−	13.3381i	1.20425	−	0.498818i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			23.5642i			0.878796i	0.898292	+	0.439398i	$0.144808\pi$
$719$			23.5642i			0.878796i	−0.898292	+	0.439398i	$0.855192\pi$
$720$		0			0
$721$			18.3862i			0.684739i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.71064	+	1.12278i	−0.100671	+	0.0416991i
$726$		0			0
$727$	16.5208	−	16.5208i	0.612724	−	0.612724i	−0.330931	−	0.943655i	$-0.607363\pi$
$727$	16.5208	−	16.5208i	0.612724	−	0.612724i	0.943655	+	0.330931i	$0.107363\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	55.4882	−	22.9840i	2.05230	−	0.850092i
$732$		0			0
$733$	−8.74219	+	21.1055i	−0.322900	+	0.779550i	0.676183	+	0.736734i	$0.263633\pi$
$733$	−8.74219	+	21.1055i	−0.322900	+	0.779550i	−0.999083	+	0.0428159i	$0.986367\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	34.0077i		−	1.25269i
$738$		0			0
$739$	−41.5366	−	17.2050i	−1.52795	−	0.632897i	−0.548785	−	0.835964i	$-0.684909\pi$
$739$	−41.5366	−	17.2050i	−1.52795	−	0.632897i	−0.979165	+	0.203066i	$0.934909\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.3232	−	19.3232i	0.708900	−	0.708900i	−0.257404	−	0.966304i	$-0.582867\pi$
$743$	19.3232	−	19.3232i	0.708900	−	0.708900i	0.966304	+	0.257404i	$0.0828672\pi$
$744$		0			0
$745$	22.9890	+	22.9890i	0.842253	+	0.842253i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.29200	−	22.4329i	0.339522	−	0.819679i
$750$		0			0
$751$	9.32371			0.340227			0.170114	−	0.985424i	$-0.445587\pi$
$751$	9.32371			0.340227			0.170114	+	0.985424i	$0.445587\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−57.1724	−	23.6816i	−2.08072	−	0.861861i
$756$		0			0
$757$	−9.71720	−	23.4594i	−0.353178	−	0.852647i	−0.996224	−	0.0868193i	$-0.972330\pi$
$757$	−9.71720	−	23.4594i	−0.353178	−	0.852647i	0.643046	−	0.765827i	$-0.277670\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.9092	−	21.9092i	−0.794207	−	0.794207i	0.187968	−	0.982175i	$-0.439810\pi$
$761$	−21.9092	−	21.9092i	−0.794207	−	0.794207i	−0.982175	+	0.187968i	$0.939810\pi$
$762$		0			0
$763$	0.746683	+	1.80265i	0.0270317	+	0.0652604i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	33.5585			1.21173
$768$		0			0
$769$	−11.9106			−0.429508			−0.214754	−	0.976668i	$-0.568895\pi$
$769$	−11.9106			−0.429508			−0.214754	+	0.976668i	$0.568895\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.39696	+	8.20098i	0.122180	+	0.294969i	0.973122	−	0.230291i	$-0.0739680\pi$
$773$	3.39696	+	8.20098i	0.122180	+	0.294969i	−0.850942	+	0.525260i	$0.823968\pi$
$774$		0			0
$775$	−10.0357	−	10.0357i	−0.360492	−	0.360492i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.74044	−	4.20178i	−0.0623576	−	0.150545i
$780$		0			0
$781$	24.5107	+	10.1527i	0.877061	+	0.363290i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−52.2130			−1.86356
$786$		0			0
$787$	−6.32430	+	15.2682i	−0.225437	+	0.544253i	−0.995612	−	0.0935798i	$-0.970169\pi$
$787$	−6.32430	+	15.2682i	−0.225437	+	0.544253i	0.770175	+	0.637833i	$0.220169\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.11797	+	5.11797i	0.181974	+	0.181974i
$792$		0			0
$793$	2.59604	−	2.59604i	0.0921881	−	0.0921881i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.4382	−	5.56628i	−0.476005	−	0.197168i	0.131765	−	0.991281i	$-0.457936\pi$
$797$	−13.4382	−	5.56628i	−0.476005	−	0.197168i	−0.607770	+	0.794113i	$0.707936\pi$
$798$		0			0
$799$			54.5269i			1.92902i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17.0779	+	41.2298i	−0.602667	+	1.45497i
$804$		0			0
$805$	41.3591	−	17.1315i	1.45772	−	0.603807i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−17.2173	+	17.2173i	−0.605330	+	0.605330i	−0.941722	−	0.336392i	$-0.890793\pi$
$809$	−17.2173	+	17.2173i	−0.605330	+	0.605330i	0.336392	+	0.941722i	$0.390793\pi$
$810$		0			0
$811$	7.51193	−	3.11154i	0.263779	−	0.109261i	−0.246874	−	0.969048i	$-0.579403\pi$
$811$	7.51193	−	3.11154i	0.263779	−	0.109261i	0.510654	+	0.859787i	$0.329403\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			40.7101i			1.42601i
$816$		0			0
$817$		−	17.1318i		−	0.599365i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	26.2833	−	10.8869i	0.917293	−	0.379955i	0.126449	−	0.991973i	$-0.459642\pi$
$821$	26.2833	−	10.8869i	0.917293	−	0.379955i	0.790844	+	0.612018i	$0.209642\pi$
$822$		0			0
$823$	0.913996	−	0.913996i	0.0318599	−	0.0318599i	−0.690997	−	0.722857i	$-0.742828\pi$
$823$	0.913996	−	0.913996i	0.0318599	−	0.0318599i	0.722857	+	0.690997i	$0.242828\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	20.8973	−	8.65593i	0.726669	−	0.300996i	0.0114866	−	0.999934i	$-0.496344\pi$
$827$	20.8973	−	8.65593i	0.726669	−	0.300996i	0.715182	+	0.698938i	$0.246344\pi$
$828$		0			0
$829$	0.859841	−	2.07584i	0.0298635	−	0.0720969i	−0.908244	−	0.418440i	$-0.862577\pi$
$829$	0.859841	−	2.07584i	0.0298635	−	0.0720969i	0.938108	+	0.346344i	$0.112577\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			35.7054i			1.23712i
$834$		0			0
$835$	29.8774	+	12.3756i	1.03395	+	0.428277i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−29.5340	+	29.5340i	−1.01963	+	1.01963i	−0.0198249	+	0.999803i	$0.506311\pi$
$839$	−29.5340	+	29.5340i	−1.01963	+	1.01963i	−0.999803	+	0.0198249i	$0.993689\pi$
$840$		0			0
$841$	−20.4177	−	20.4177i	−0.704059	−	0.704059i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−9.95171	+	24.0256i	−0.342349	+	0.826504i
$846$		0			0
$847$	−6.82690			−0.234575
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.17964	+	1.31705i	0.108997	+	0.0451479i
$852$		0			0
$853$	−13.7113	−	33.1021i	−0.469467	−	1.13339i	−0.964397	−	0.264460i	$-0.914806\pi$
$853$	−13.7113	−	33.1021i	−0.469467	−	1.13339i	0.494930	−	0.868933i	$-0.335194\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.6839	−	10.6839i	−0.364955	−	0.364955i	0.500679	−	0.865633i	$-0.333084\pi$
$857$	−10.6839	−	10.6839i	−0.364955	−	0.364955i	−0.865633	+	0.500679i	$0.833084\pi$
$858$		0			0
$859$	15.9567	+	38.5229i	0.544435	+	1.31438i	0.921566	+	0.388223i	$0.126911\pi$
$859$	15.9567	+	38.5229i	0.544435	+	1.31438i	−0.377130	+	0.926160i	$0.623089\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	53.2679			1.81326			0.906630	−	0.421927i	$-0.138646\pi$
$863$	53.2679			1.81326			0.906630	+	0.421927i	$0.138646\pi$
$864$		0			0
$865$	−91.3740			−3.10681
$866$		0			0
$867$		0			0
$868$		0			0
$869$	21.7356	+	52.4744i	0.737330	+	1.78007i
$870$		0			0
$871$	−14.7664	−	14.7664i	−0.500339	−	0.500339i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.88503	+	16.6219i	0.232757	+	0.561924i
$876$		0			0
$877$	34.8915	+	14.4525i	1.17820	+	0.488027i	0.883896	−	0.467684i	$-0.154911\pi$
$877$	34.8915	+	14.4525i	1.17820	+	0.488027i	0.294306	+	0.955711i	$0.404911\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	49.2340			1.65874			0.829368	−	0.558703i	$-0.188701\pi$
$881$	49.2340			1.65874			0.829368	+	0.558703i	$0.188701\pi$
$882$		0			0
$883$	15.3303	−	37.0107i	0.515907	−	1.24551i	−0.424491	−	0.905432i	$-0.639547\pi$
$883$	15.3303	−	37.0107i	0.515907	−	1.24551i	0.940398	−	0.340077i	$-0.110453\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.81816	−	9.81816i	−0.329661	−	0.329661i	0.522796	−	0.852458i	$-0.324889\pi$
$887$	−9.81816	−	9.81816i	−0.329661	−	0.329661i	−0.852458	+	0.522796i	$0.824889\pi$
$888$		0			0
$889$	1.95709	−	1.95709i	0.0656388	−	0.0656388i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	14.3696	+	5.95207i	0.480859	+	0.199178i
$894$		0			0
$895$			24.9540i			0.834121i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.231385	+	0.558612i	−0.00771712	+	0.0186308i
$900$		0			0
$901$	−29.5995	+	12.2605i	−0.986104	+	0.408457i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.88353	+	6.88353i	−0.228816	+	0.228816i
$906$		0			0
$907$	3.54772	−	1.46951i	0.117800	−	0.0487944i	−0.323005	−	0.946397i	$-0.604693\pi$
$907$	3.54772	−	1.46951i	0.117800	−	0.0487944i	0.440805	+	0.897603i	$0.354693\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			54.8756i			1.81811i	0.416678	+	0.909054i	$0.363194\pi$
$911$			54.8756i			1.81811i	−0.416678	+	0.909054i	$0.636806\pi$
$912$		0			0
$913$			5.77553i			0.191142i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.81377	+	3.65078i	−0.291056	+	0.120559i
$918$		0			0
$919$	−1.01238	+	1.01238i	−0.0333953	+	0.0333953i	−0.723607	−	0.690212i	$-0.757517\pi$
$919$	−1.01238	+	1.01238i	−0.0333953	+	0.0333953i	0.690212	+	0.723607i	$0.257517\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	15.0510	−	6.23433i	0.495410	−	0.205206i
$924$		0			0
$925$	−1.33161	+	3.21480i	−0.0437831	+	0.105702i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			43.1188i			1.41468i	0.706873	+	0.707341i	$0.250105\pi$
$929$			43.1188i			1.41468i	−0.706873	+	0.707341i	$0.749895\pi$
$930$		0			0
$931$	9.40948	+	3.89754i	0.308383	+	0.127737i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	76.2598	−	76.2598i	2.49396	−	2.49396i
$936$		0			0
$937$	−38.1126	−	38.1126i	−1.24508	−	1.24508i	−0.957865	−	0.287218i	$-0.907270\pi$
$937$	−38.1126	−	38.1126i	−1.24508	−	1.24508i	−0.287218	−	0.957865i	$-0.592730\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−6.30761	+	15.2279i	−0.205622	+	0.496416i	−0.992725	−	0.120406i	$-0.961580\pi$
$941$	−6.30761	+	15.2279i	−0.205622	+	0.496416i	0.787103	+	0.616822i	$0.211580\pi$
$942$		0			0
$943$	−17.4583			−0.568521
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.4534	+	5.15836i	0.404681	+	0.167624i	0.575733	−	0.817638i	$-0.304717\pi$
$947$	12.4534	+	5.15836i	0.404681	+	0.167624i	−0.171052	+	0.985262i	$0.554717\pi$
$948$		0			0
$949$	10.4869	+	25.3175i	0.340418	+	0.821842i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	23.0665	+	23.0665i	0.747197	+	0.747197i	0.973952	−	0.226755i	$-0.0728116\pi$
$953$	23.0665	+	23.0665i	0.747197	+	0.747197i	−0.226755	+	0.973952i	$0.572812\pi$
$954$		0			0
$955$	−29.0121	−	70.0414i	−0.938809	−	2.26649i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.62448			0.181624
$960$		0			0
$961$	28.0752			0.905651
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−20.8556	−	50.3499i	−0.671366	−	1.62082i
$966$		0			0
$967$	−5.28781	−	5.28781i	−0.170045	−	0.170045i	0.616954	−	0.786999i	$-0.288366\pi$
$967$	−5.28781	−	5.28781i	−0.170045	−	0.170045i	−0.786999	+	0.616954i	$0.788366\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.8434	+	35.8352i	0.476348	+	1.15001i	0.961310	+	0.275470i	$0.0888335\pi$
$971$	14.8434	+	35.8352i	0.476348	+	1.15001i	−0.484962	+	0.874535i	$0.661167\pi$
$972$		0			0
$973$	17.5833	+	7.28326i	0.563696	+	0.233491i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	47.4029			1.51655			0.758277	−	0.651932i	$-0.226041\pi$
$977$	47.4029			1.51655			0.758277	+	0.651932i	$0.226041\pi$
$978$		0			0
$979$	−10.1555	+	24.5176i	−0.324571	+	0.783584i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	25.5390	+	25.5390i	0.814567	+	0.814567i	0.985315	−	0.170748i	$-0.0546184\pi$
$983$	25.5390	+	25.5390i	0.814567	+	0.814567i	−0.170748	+	0.985315i	$0.554618\pi$
$984$		0			0
$985$	64.0421	−	64.0421i	2.04055	−	2.04055i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−60.7577	−	25.1667i	−1.93198	−	0.800253i
$990$		0			0
$991$			6.52875i			0.207392i	0.994609	+	0.103696i	$0.0330670\pi$
$991$			6.52875i			0.207392i	−0.994609	+	0.103696i	$0.966933\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.46555	−	5.95236i	0.0781631	−	0.188702i
$996$		0			0
$997$	11.0113	−	4.56102i	0.348731	−	0.144449i	−0.201441	−	0.979501i	$-0.564562\pi$
$997$	11.0113	−	4.56102i	0.348731	−	0.144449i	0.550172	+	0.835052i	$0.314562\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.b.1007.1		32
3.2	odd	2		1152.2.w.a.1007.8		32
4.3	odd	2		288.2.w.a.179.2	✓	32
12.11	even	2		288.2.w.b.179.7	yes	32
32.5	even	8		288.2.w.b.251.7	yes	32
32.27	odd	8		1152.2.w.a.143.8		32
96.5	odd	8		288.2.w.a.251.2	yes	32
96.59	even	8	inner	1152.2.w.b.143.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.2	✓	32	4.3	odd	2
288.2.w.a.251.2	yes	32	96.5	odd	8
288.2.w.b.179.7	yes	32	12.11	even	2
288.2.w.b.251.7	yes	32	32.5	even	8
1152.2.w.a.143.8		32	32.27	odd	8
1152.2.w.a.1007.8		32	3.2	odd	2
1152.2.w.b.143.1		32	96.59	even	8	inner
1152.2.w.b.1007.1		32	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.39555 - 3.36915i) q^{5} +(1.05755 + 1.05755i) q^{7} +O(q^{10})\)	\(q+(-1.39555 - 3.36915i) q^{5} +(1.05755 + 1.05755i) q^{7} +(-1.50977 - 3.64490i) q^{11} +(-2.23818 - 0.927086i) q^{13} -7.49610 q^{17} +(-0.818262 + 1.97546i) q^{19} +(5.80392 + 5.80392i) q^{23} +(-5.86809 + 5.86809i) q^{25} +(0.326633 + 0.135296i) q^{29} +1.71021i q^{31} +(2.08718 - 5.03889i) q^{35} +(0.387384 - 0.160460i) q^{37} +(-1.50401 + 1.50401i) q^{41} +(-7.40227 + 3.06612i) q^{43} -7.27404i q^{47} -4.76319i q^{49} +(3.94866 - 1.63559i) q^{53} +(-10.1733 + 10.1733i) q^{55} +(-12.7979 + 5.30105i) q^{59} +(-0.579943 + 1.40011i) q^{61} +8.83457i q^{65} +(7.96385 + 3.29874i) q^{67} +(-4.75505 + 4.75505i) q^{71} +(-7.99854 - 7.99854i) q^{73} +(2.25800 - 5.45130i) q^{77} -14.3967 q^{79} +(-1.35250 - 0.560224i) q^{83} +(10.4612 + 25.2555i) q^{85} +(-4.75638 - 4.75638i) q^{89} +(-1.38655 - 3.34742i) q^{91} +7.79754 q^{95} -1.28856 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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