LMFDB - Embedded newform 1152.2.w.b.719.4

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			719.4
Character	$\chi$	$=$	1152.719
Dual form			1152.2.w.b.431.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0913223 - 0.0378270i) q^{5} +(3.05457 - 3.05457i) q^{7} +O(q^{10})$	$q+(-0.0913223 - 0.0378270i) q^{5} +(3.05457 - 3.05457i) q^{7} +(5.25649 + 2.17731i) q^{11} +(-1.57202 - 3.79519i) q^{13} -2.56471 q^{17} +(-2.64058 + 1.09376i) q^{19} +(4.03079 - 4.03079i) q^{23} +(-3.52863 - 3.52863i) q^{25} +(2.06984 + 4.99704i) q^{29} +1.44203i q^{31} +(-0.394496 + 0.163406i) q^{35} +(-2.07758 + 5.01573i) q^{37} +(0.296726 + 0.296726i) q^{41} +(2.72382 - 6.57588i) q^{43} -7.42367i q^{47} -11.6608i q^{49} +(1.53235 - 3.69941i) q^{53} +(-0.397674 - 0.397674i) q^{55} +(-0.988255 + 2.38586i) q^{59} +(10.4346 - 4.32215i) q^{61} +0.406051i q^{65} +(0.690522 + 1.66707i) q^{67} +(2.97957 + 2.97957i) q^{71} +(9.22401 - 9.22401i) q^{73} +(22.7071 - 9.40558i) q^{77} +1.12181 q^{79} +(4.13529 + 9.98348i) q^{83} +(0.234216 + 0.0970152i) q^{85} +(-12.0590 + 12.0590i) q^{89} +(-16.3945 - 6.79084i) q^{91} +0.282518 q^{95} -18.5545 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{8}\right)$

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
$5$	−0.0913223	−	0.0378270i	−0.0408406	−	0.0169167i	0.362170	−	0.932112i	$-0.382036\pi$
$5$	−0.0913223	−	0.0378270i	−0.0408406	−	0.0169167i	−0.403010	+	0.915195i	$0.632036\pi$
$6$		0			0
$7$	3.05457	−	3.05457i	1.15452	−	1.15452i	0.168884	−	0.985636i	$-0.445984\pi$
$7$	3.05457	−	3.05457i	1.15452	−	1.15452i	0.985636	−	0.168884i	$-0.0540163\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	5.25649	+	2.17731i	1.58489	+	0.656483i	0.989179	−	0.146715i	$-0.0468699\pi$
$11$	5.25649	+	2.17731i	1.58489	+	0.656483i	0.595712	+	0.803198i	$0.296870\pi$
$12$		0			0
$13$	−1.57202	−	3.79519i	−0.436000	−	1.05260i	−0.977318	−	0.211779i	$-0.932074\pi$
$13$	−1.57202	−	3.79519i	−0.436000	−	1.05260i	0.541317	−	0.840818i	$-0.317926\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.56471			−0.622034			−0.311017	−	0.950404i	$-0.600670\pi$
$17$	−2.56471			−0.622034			−0.311017	+	0.950404i	$0.600670\pi$
$18$		0			0
$19$	−2.64058	+	1.09376i	−0.605791	+	0.250927i	−0.664428	−	0.747353i	$-0.731325\pi$
$19$	−2.64058	+	1.09376i	−0.605791	+	0.250927i	0.0586367	+	0.998279i	$0.481325\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.03079	−	4.03079i	0.840477	−	0.840477i	−0.148443	−	0.988921i	$-0.547426\pi$
$23$	4.03079	−	4.03079i	0.840477	−	0.840477i	0.988921	+	0.148443i	$0.0474263\pi$
$24$		0			0
$25$	−3.52863	−	3.52863i	−0.705725	−	0.705725i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.06984	+	4.99704i	0.384360	+	0.927927i	0.991111	+	0.133035i	$0.0424723\pi$
$29$	2.06984	+	4.99704i	0.384360	+	0.927927i	−0.606752	+	0.794892i	$0.707528\pi$
$30$		0			0
$31$			1.44203i			0.258996i	0.991580	+	0.129498i	$0.0413366\pi$
$31$			1.44203i			0.258996i	−0.991580	+	0.129498i	$0.958663\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.394496	+	0.163406i	−0.0666820	+	0.0276206i
$36$		0			0
$37$	−2.07758	+	5.01573i	−0.341552	+	0.824581i	0.656007	+	0.754755i	$0.272244\pi$
$37$	−2.07758	+	5.01573i	−0.341552	+	0.824581i	−0.997559	+	0.0698256i	$0.977756\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.296726	+	0.296726i	0.0463409	+	0.0463409i	0.729897	−	0.683557i	$-0.239568\pi$
$41$	0.296726	+	0.296726i	0.0463409	+	0.0463409i	−0.683557	+	0.729897i	$0.739568\pi$
$42$		0			0
$43$	2.72382	−	6.57588i	0.415378	−	1.00281i	−0.568291	−	0.822828i	$-0.692395\pi$
$43$	2.72382	−	6.57588i	0.415378	−	1.00281i	0.983669	−	0.179984i	$-0.0576047\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	7.42367i		−	1.08285i	−0.840748	−	0.541427i	$-0.817884\pi$
$47$		−	7.42367i		−	1.08285i	0.840748	−	0.541427i	$-0.182116\pi$
$48$		0			0
$49$		−	11.6608i		−	1.66583i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.53235	−	3.69941i	0.210484	−	0.508153i	−0.783014	−	0.622004i	$-0.786319\pi$
$53$	1.53235	−	3.69941i	0.210484	−	0.508153i	0.993498	+	0.113851i	$0.0363187\pi$
$54$		0			0
$55$	−0.397674	−	0.397674i	−0.0536223	−	0.0536223i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.988255	+	2.38586i	−0.128660	+	0.310612i	−0.975062	−	0.221931i	$-0.928764\pi$
$59$	−0.988255	+	2.38586i	−0.128660	+	0.310612i	0.846402	+	0.532544i	$0.178764\pi$
$60$		0			0
$61$	10.4346	−	4.32215i	1.33601	−	0.553395i	0.403649	−	0.914914i	$-0.367742\pi$
$61$	10.4346	−	4.32215i	1.33601	−	0.553395i	0.932365	+	0.361519i	$0.117742\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			0.406051i			0.0503644i
$66$		0			0
$67$	0.690522	+	1.66707i	0.0843606	+	0.203665i	0.960431	−	0.278519i	$-0.0898437\pi$
$67$	0.690522	+	1.66707i	0.0843606	+	0.203665i	−0.876070	+	0.482184i	$0.839844\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.97957	+	2.97957i	0.353610	+	0.353610i	0.861451	−	0.507841i	$-0.169556\pi$
$71$	2.97957	+	2.97957i	0.353610	+	0.353610i	−0.507841	+	0.861451i	$0.669556\pi$
$72$		0			0
$73$	9.22401	−	9.22401i	1.07959	−	1.07959i	0.0830429	−	0.996546i	$-0.473536\pi$
$73$	9.22401	−	9.22401i	1.07959	−	1.07959i	0.996546	−	0.0830429i	$-0.0264638\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	22.7071	−	9.40558i	2.58771	−	1.07187i
$78$		0			0
$79$	1.12181			0.126213			0.0631065	−	0.998007i	$-0.479899\pi$
$79$	1.12181			0.126213			0.0631065	+	0.998007i	$0.479899\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.13529	+	9.98348i	0.453907	+	1.09583i	0.970824	+	0.239794i	$0.0770798\pi$
$83$	4.13529	+	9.98348i	0.453907	+	1.09583i	−0.516916	+	0.856036i	$0.672920\pi$
$84$		0			0
$85$	0.234216	+	0.0970152i	0.0254042	+	0.0105228i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−12.0590	+	12.0590i	−1.27825	+	1.27825i	−0.336609	+	0.941644i	$0.609280\pi$
$89$	−12.0590	+	12.0590i	−1.27825	+	1.27825i	−0.941644	+	0.336609i	$0.890720\pi$
$90$		0			0
$91$	−16.3945	−	6.79084i	−1.71862	−	0.711874i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.282518			0.0289857
$96$		0			0
$97$	−18.5545			−1.88393			−0.941963	−	0.335717i	$-0.891022\pi$
$97$	−18.5545			−1.88393			−0.941963	+	0.335717i	$0.891022\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.24603	+	2.17298i	0.521999	+	0.216219i	0.628095	−	0.778137i	$-0.283835\pi$
$101$	5.24603	+	2.17298i	0.521999	+	0.216219i	−0.106096	+	0.994356i	$0.533835\pi$
$102$		0			0
$103$	11.0095	−	11.0095i	1.08479	−	1.08479i	0.0887398	−	0.996055i	$-0.471716\pi$
$103$	11.0095	−	11.0095i	1.08479	−	1.08479i	0.996055	−	0.0887398i	$-0.0282839\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.182628	−	0.0756468i	−0.0176553	−	0.00731305i	0.373838	−	0.927494i	$-0.378041\pi$
$107$	−0.182628	−	0.0756468i	−0.0176553	−	0.00731305i	−0.391494	+	0.920181i	$0.628041\pi$
$108$		0			0
$109$	2.10265	+	5.07626i	0.201398	+	0.486217i	0.992019	−	0.126088i	$-0.0402423\pi$
$109$	2.10265	+	5.07626i	0.201398	+	0.486217i	−0.790621	+	0.612305i	$0.790242\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.91777			0.556697			0.278348	−	0.960480i	$-0.410213\pi$
$113$	5.91777			0.556697			0.278348	+	0.960480i	$0.410213\pi$
$114$		0			0
$115$	−0.520573	+	0.215629i	−0.0485437	+	0.0201075i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.83410	+	7.83410i	−0.718151	+	0.718151i
$120$		0			0
$121$	15.1118	+	15.1118i	1.37380	+	1.37380i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.377900	+	0.912331i	0.0338004	+	0.0816014i
$126$		0			0
$127$		−	9.70061i		−	0.860790i	−0.902641	−	0.430395i	$-0.858374\pi$
$127$		−	9.70061i		−	0.860790i	0.902641	−	0.430395i	$-0.141626\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−12.7327	+	5.27407i	−1.11246	+	0.460798i	−0.861786	−	0.507273i	$-0.830654\pi$
$131$	−12.7327	+	5.27407i	−1.11246	+	0.460798i	−0.250678	+	0.968070i	$0.580654\pi$
$132$		0			0
$133$	−4.72486	+	11.4068i	−0.409698	+	0.989098i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.62861	−	5.62861i	−0.480884	−	0.480884i	0.424530	−	0.905414i	$-0.360439\pi$
$137$	−5.62861	−	5.62861i	−0.480884	−	0.480884i	−0.905414	+	0.424530i	$0.860439\pi$
$138$		0			0
$139$	−0.202389	+	0.488610i	−0.0171664	+	0.0414434i	−0.932230	−	0.361865i	$-0.882140\pi$
$139$	−0.202389	+	0.488610i	−0.0171664	+	0.0414434i	0.915064	+	0.403309i	$0.132140\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	23.3722i		−	1.95448i
$144$		0			0
$145$		−	0.534637i		−	0.0443992i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.35052	−	3.26046i	0.110639	−	0.267107i	−0.858856	−	0.512217i	$-0.828824\pi$
$149$	1.35052	−	3.26046i	0.110639	−	0.267107i	0.969495	+	0.245110i	$0.0788242\pi$
$150$		0			0
$151$	13.6492	+	13.6492i	1.11076	+	1.11076i	0.993048	+	0.117709i	$0.0375552\pi$
$151$	13.6492	+	13.6492i	1.11076	+	1.11076i	0.117709	+	0.993048i	$0.462445\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.0545476	−	0.131690i	0.00438137	−	0.0105776i
$156$		0			0
$157$	−15.4587	+	6.40321i	−1.23374	+	0.511032i	−0.901753	−	0.432252i	$-0.857719\pi$
$157$	−15.4587	+	6.40321i	−1.23374	+	0.511032i	−0.331987	+	0.943284i	$0.607719\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	24.6247i		−	1.94070i
$162$		0			0
$163$	6.04288	+	14.5888i	0.473315	+	1.14268i	0.962689	+	0.270609i	$0.0872252\pi$
$163$	6.04288	+	14.5888i	0.473315	+	1.14268i	−0.489374	+	0.872074i	$0.662775\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.58872	−	6.58872i	−0.509850	−	0.509850i	0.404630	−	0.914480i	$-0.367400\pi$
$167$	−6.58872	−	6.58872i	−0.509850	−	0.509850i	−0.914480	+	0.404630i	$0.867400\pi$
$168$		0			0
$169$	−2.73986	+	2.73986i	−0.210759	+	0.210759i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−17.8204	+	7.38143i	−1.35486	+	0.561200i	−0.937640	−	0.347608i	$-0.886994\pi$
$173$	−17.8204	+	7.38143i	−1.35486	+	0.561200i	−0.417216	+	0.908807i	$0.636994\pi$
$174$		0			0
$175$	−21.5569			−1.62955
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.07369	+	9.83475i	0.304482	+	0.735084i	0.999865	+	0.0164446i	$0.00523471\pi$
$179$	4.07369	+	9.83475i	0.304482	+	0.735084i	−0.695383	+	0.718639i	$0.744765\pi$
$180$		0			0
$181$	8.06280	+	3.33972i	0.599303	+	0.248239i	0.661647	−	0.749815i	$-0.269858\pi$
$181$	8.06280	+	3.33972i	0.599303	+	0.248239i	−0.0623442	+	0.998055i	$0.519858\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.379459	−	0.379459i	0.0278984	−	0.0278984i
$186$		0			0
$187$	−13.4814	−	5.58417i	−0.985856	−	0.408355i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−13.0520			−0.944411			−0.472205	−	0.881489i	$-0.656542\pi$
$191$	−13.0520			−0.944411			−0.472205	+	0.881489i	$0.656542\pi$
$192$		0			0
$193$	−3.05926			−0.220210			−0.110105	−	0.993920i	$-0.535119\pi$
$193$	−3.05926			−0.220210			−0.110105	+	0.993920i	$0.535119\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.46774	−	2.26481i	−0.389560	−	0.161361i	0.179302	−	0.983794i	$-0.442616\pi$
$197$	−5.46774	−	2.26481i	−0.389560	−	0.161361i	−0.568862	+	0.822433i	$0.692616\pi$
$198$		0			0
$199$	4.48835	−	4.48835i	0.318170	−	0.318170i	−0.529894	−	0.848064i	$-0.677768\pi$
$199$	4.48835	−	4.48835i	0.318170	−	0.318170i	0.848064	+	0.529894i	$0.177768\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	21.5863	+	8.94133i	1.51506	+	0.627559i
$204$		0			0
$205$	−0.0158735	−	0.0383220i	−0.00110865	−	0.00267652i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−16.2617			−1.12484
$210$		0			0
$211$	−0.322439	+	0.133558i	−0.0221976	+	0.00919454i	−0.393755	−	0.919216i	$-0.628824\pi$
$211$	−0.322439	+	0.133558i	−0.0221976	+	0.00919454i	0.371557	+	0.928410i	$0.378824\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.497491	+	0.497491i	−0.0339286	+	0.0339286i
$216$		0			0
$217$	4.40478	+	4.40478i	0.299016	+	0.299016i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.03178	+	9.73358i	0.271207	+	0.654752i
$222$		0			0
$223$			19.1612i			1.28313i	0.767068	+	0.641566i	$0.221715\pi$
$223$			19.1612i			1.28313i	−0.767068	+	0.641566i	$0.778285\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.4451	+	8.05441i	−1.29061	+	0.534590i	−0.919169	−	0.393864i	$-0.871138\pi$
$227$	−19.4451	+	8.05441i	−1.29061	+	0.534590i	−0.371446	+	0.928455i	$0.621138\pi$
$228$		0			0
$229$	−6.97193	+	16.8317i	−0.460718	+	1.11227i	0.507385	+	0.861719i	$0.330612\pi$
$229$	−6.97193	+	16.8317i	−0.460718	+	1.11227i	−0.968103	+	0.250552i	$0.919388\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	16.7768	+	16.7768i	1.09909	+	1.09909i	0.994518	+	0.104569i	$0.0333462\pi$
$233$	16.7768	+	16.7768i	1.09909	+	1.09909i	0.104569	+	0.994518i	$0.466654\pi$
$234$		0			0
$235$	−0.280815	+	0.677947i	−0.0183183	+	0.0442244i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			9.10976i			0.589261i	0.955611	+	0.294631i	$0.0951966\pi$
$239$			9.10976i			0.589261i	−0.955611	+	0.294631i	$0.904803\pi$
$240$		0			0
$241$		−	7.39995i		−	0.476673i	−0.971183	−	0.238336i	$-0.923398\pi$
$241$		−	7.39995i		−	0.476673i	0.971183	−	0.238336i	$-0.0766020\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.441093	+	1.06489i	−0.0281804	+	0.0680336i
$246$		0			0
$247$	8.30210	+	8.30210i	0.528250	+	0.528250i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.84250	−	11.6908i	0.305656	−	0.737919i	−0.694180	−	0.719802i	$-0.744233\pi$
$251$	4.84250	−	11.6908i	0.305656	−	0.737919i	0.999836	−	0.0181174i	$-0.00576726\pi$
$252$		0			0
$253$	29.9641	−	12.4115i	1.88382	−	0.780306i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			6.02571i			0.375873i	0.982181	+	0.187937i	$0.0601800\pi$
$257$			6.02571i			0.375873i	−0.982181	+	0.187937i	$0.939820\pi$
$258$		0			0
$259$	8.97478	+	21.6670i	0.557666	+	1.34632i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.79218	+	6.79218i	0.418824	+	0.418824i	0.884798	−	0.465974i	$-0.154296\pi$
$263$	6.79218	+	6.79218i	0.418824	+	0.418824i	−0.465974	+	0.884798i	$0.654296\pi$
$264$		0			0
$265$	−0.279875	+	0.279875i	−0.0171926	+	0.0171926i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.8548	−	5.73883i	0.844740	−	0.349903i	0.0820193	−	0.996631i	$-0.473863\pi$
$269$	13.8548	−	5.73883i	0.844740	−	0.349903i	0.762721	+	0.646728i	$0.223863\pi$
$270$		0			0
$271$	−5.62497			−0.341692			−0.170846	−	0.985298i	$-0.554650\pi$
$271$	−5.62497			−0.341692			−0.170846	+	0.985298i	$0.554650\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.8653	−	26.2311i	−0.655201	−	1.58179i
$276$		0			0
$277$	−1.00843	−	0.417706i	−0.0605908	−	0.0250975i	0.352182	−	0.935931i	$-0.385440\pi$
$277$	−1.00843	−	0.417706i	−0.0605908	−	0.0250975i	−0.412773	+	0.910834i	$0.635440\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−21.7589	+	21.7589i	−1.29803	+	1.29803i	−0.368335	+	0.929693i	$0.620072\pi$
$281$	−21.7589	+	21.7589i	−1.29803	+	1.29803i	−0.929693	+	0.368335i	$0.879928\pi$
$282$		0			0
$283$	22.3614	+	9.26239i	1.32925	+	0.550592i	0.930441	−	0.366443i	$-0.119424\pi$
$283$	22.3614	+	9.26239i	1.32925	+	0.550592i	0.398807	+	0.917035i	$0.369424\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.81274			0.107003
$288$		0			0
$289$	−10.4223			−0.613074
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−29.2423	−	12.1126i	−1.70835	−	0.707623i	−0.999998	−	0.00176683i	$-0.999438\pi$
$293$	−29.2423	−	12.1126i	−1.70835	−	0.707623i	−0.708355	−	0.705856i	$-0.750562\pi$
$294$		0			0
$295$	0.180500	−	0.180500i	0.0105091	−	0.0105091i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−21.6341	−	8.96114i	−1.25113	−	0.518236i
$300$		0			0
$301$	−11.7664	−	28.4066i	−0.678204	−	1.63733i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.11641			−0.0639252
$306$		0			0
$307$	−13.7854	+	5.71009i	−0.786773	+	0.325892i	−0.739645	−	0.672997i	$-0.765007\pi$
$307$	−13.7854	+	5.71009i	−0.786773	+	0.325892i	−0.0471275	+	0.998889i	$0.515007\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	11.4220	−	11.4220i	0.647684	−	0.647684i	−0.304749	−	0.952433i	$-0.598573\pi$
$311$	11.4220	−	11.4220i	0.647684	−	0.647684i	0.952433	+	0.304749i	$0.0985725\pi$
$312$		0			0
$313$	2.24707	+	2.24707i	0.127012	+	0.127012i	0.767755	−	0.640743i	$-0.221374\pi$
$313$	2.24707	+	2.24707i	0.127012	+	0.127012i	−0.640743	+	0.767755i	$0.721374\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.05906	−	2.55679i	−0.0594826	−	0.143604i	0.891344	−	0.453328i	$-0.149763\pi$
$317$	−1.05906	−	2.55679i	−0.0594826	−	0.143604i	−0.950826	+	0.309724i	$0.899763\pi$
$318$		0			0
$319$			30.7736i			1.72299i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.77233	−	2.80519i	0.376823	−	0.156085i
$324$		0			0
$325$	−7.84475	+	18.9389i	−0.435148	+	1.05054i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−22.6761	−	22.6761i	−1.25018	−	1.25018i
$330$		0			0
$331$	0.123439	−	0.298008i	0.00678481	−	0.0163800i	−0.920451	−	0.390858i	$-0.872178\pi$
$331$	0.123439	−	0.298008i	0.00678481	−	0.0163800i	0.927236	+	0.374478i	$0.122178\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	0.178361i		−	0.00974489i
$336$		0			0
$337$			16.5067i			0.899179i	0.893235	+	0.449590i	$0.148430\pi$
$337$			16.5067i			0.899179i	−0.893235	+	0.449590i	$0.851570\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.13974	+	7.58001i	−0.170027	+	0.410481i
$342$		0			0
$343$	−14.2368	−	14.2368i	−0.768716	−	0.768716i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.96248	−	14.3947i	0.320083	−	0.772748i	−0.679166	−	0.733985i	$-0.737658\pi$
$347$	5.96248	−	14.3947i	0.320083	−	0.772748i	0.999248	−	0.0387633i	$-0.0123418\pi$
$348$		0			0
$349$	1.57618	−	0.652873i	0.0843707	−	0.0349475i	−0.340099	−	0.940390i	$-0.610461\pi$
$349$	1.57618	−	0.652873i	0.0843707	−	0.0349475i	0.424470	+	0.905442i	$0.360461\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			18.7091i			0.995786i	0.867239	+	0.497893i	$0.165893\pi$
$353$			18.7091i			0.995786i	−0.867239	+	0.497893i	$0.834107\pi$
$354$		0			0
$355$	−0.159393	−	0.384810i	−0.00845972	−	0.0204236i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	23.5065	+	23.5065i	1.24062	+	1.24062i	0.959742	+	0.280882i	$0.0906270\pi$
$359$	23.5065	+	23.5065i	1.24062	+	1.24062i	0.280882	+	0.959742i	$0.409373\pi$
$360$		0			0
$361$	−7.65868	+	7.65868i	−0.403088	+	0.403088i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.19127	+	0.493442i	−0.0623542	+	0.0258279i
$366$		0			0
$367$	2.95190			0.154088			0.0770440	−	0.997028i	$-0.475452\pi$
$367$	2.95190			0.154088			0.0770440	+	0.997028i	$0.475452\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.61945	−	15.9808i	−0.343665	−	0.829680i
$372$		0			0
$373$	−19.7552	−	8.18287i	−1.02289	−	0.423693i	−0.192746	−	0.981249i	$-0.561739\pi$
$373$	−19.7552	−	8.18287i	−1.02289	−	0.423693i	−0.830140	+	0.557556i	$0.811739\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.7109	−	15.7109i	0.809152	−	0.809152i
$378$		0			0
$379$	−4.26476	−	1.76652i	−0.219066	−	0.0907402i	0.270451	−	0.962734i	$-0.412827\pi$
$379$	−4.26476	−	1.76652i	−0.219066	−	0.0907402i	−0.489518	+	0.871993i	$0.662827\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.45328			−0.483040			−0.241520	−	0.970396i	$-0.577646\pi$
$383$	−9.45328			−0.483040			−0.241520	+	0.970396i	$0.577646\pi$
$384$		0			0
$385$	−2.42945			−0.123816
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−20.8554	−	8.63860i	−1.05741	−	0.437994i	−0.214880	−	0.976640i	$-0.568936\pi$
$389$	−20.8554	−	8.63860i	−1.05741	−	0.437994i	−0.842532	+	0.538646i	$0.818936\pi$
$390$		0			0
$391$	−10.3378	+	10.3378i	−0.522806	+	0.522806i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.102446	−	0.0424345i	−0.00515461	−	0.00213511i
$396$		0			0
$397$	3.29268	+	7.94922i	0.165255	+	0.398960i	0.984714	−	0.174177i	$-0.0557264\pi$
$397$	3.29268	+	7.94922i	0.165255	+	0.398960i	−0.819460	+	0.573137i	$0.805726\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	32.5903			1.62748			0.813740	−	0.581229i	$-0.197428\pi$
$401$	32.5903			1.62748			0.813740	+	0.581229i	$0.197428\pi$
$402$		0			0
$403$	5.47278	−	2.26690i	0.272619	−	0.112922i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−21.8416	+	21.8416i	−1.08265	+	1.08265i
$408$		0			0
$409$	5.41708	+	5.41708i	0.267858	+	0.267858i	0.828236	−	0.560379i	$-0.189344\pi$
$409$	5.41708	+	5.41708i	0.267858	+	0.267858i	−0.560379	+	0.828236i	$0.689344\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.26908	+	10.3065i	0.210068	+	0.507149i
$414$		0			0
$415$		−	1.06814i		−	0.0524329i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	22.0298	−	9.12504i	1.07623	−	0.445787i	0.227042	−	0.973885i	$-0.427094\pi$
$419$	22.0298	−	9.12504i	1.07623	−	0.445787i	0.849184	+	0.528097i	$0.177094\pi$
$420$		0			0
$421$	2.82553	−	6.82144i	0.137708	−	0.332457i	−0.839948	−	0.542667i	$-0.817415\pi$
$421$	2.82553	−	6.82144i	0.137708	−	0.332457i	0.977656	+	0.210210i	$0.0674147\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.04991	+	9.04991i	0.438985	+	0.438985i
$426$		0			0
$427$	18.6709	−	45.0756i	0.903549	−	2.18136i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			6.73112i			0.324226i	0.986772	+	0.162113i	$0.0518310\pi$
$431$			6.73112i			0.324226i	−0.986772	+	0.162113i	$0.948169\pi$
$432$		0			0
$433$			12.1160i			0.582257i	0.956684	+	0.291129i	$0.0940308\pi$
$433$			12.1160i			0.582257i	−0.956684	+	0.291129i	$0.905969\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.23489	+	15.0524i	−0.298255	+	0.720052i
$438$		0			0
$439$	−14.0767	−	14.0767i	−0.671843	−	0.671843i	0.286298	−	0.958141i	$-0.407575\pi$
$439$	−14.0767	−	14.0767i	−0.671843	−	0.671843i	−0.958141	+	0.286298i	$0.907575\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.5313	+	35.0817i	−0.690404	+	1.66678i	0.0535615	+	0.998565i	$0.482943\pi$
$443$	−14.5313	+	35.0817i	−0.690404	+	1.66678i	−0.743965	+	0.668218i	$0.767057\pi$
$444$		0			0
$445$	1.55741	−	0.645102i	0.0738285	−	0.0305808i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	25.9809i		−	1.22611i	−0.790039	−	0.613056i	$-0.789940\pi$
$449$		−	25.9809i		−	1.22611i	0.790039	−	0.613056i	$-0.210060\pi$
$450$		0			0
$451$	0.913674	+	2.20580i	0.0430232	+	0.103867i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.24031	+	1.24031i	0.0581467	+	0.0581467i
$456$		0			0
$457$	6.23785	−	6.23785i	0.291794	−	0.291794i	−0.545994	−	0.837789i	$-0.683848\pi$
$457$	6.23785	−	6.23785i	0.291794	−	0.291794i	0.837789	+	0.545994i	$0.183848\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−23.3278	+	9.66269i	−1.08648	+	0.450036i	−0.852779	−	0.522271i	$-0.825085\pi$
$461$	−23.3278	+	9.66269i	−1.08648	+	0.450036i	−0.233704	+	0.972308i	$0.575085\pi$
$462$		0			0
$463$	−3.99595			−0.185707			−0.0928537	−	0.995680i	$-0.529599\pi$
$463$	−3.99595			−0.185707			−0.0928537	+	0.995680i	$0.529599\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.26272	+	17.5338i	0.336079	+	0.811366i	0.998084	+	0.0618671i	$0.0197055\pi$
$467$	7.26272	+	17.5338i	0.336079	+	0.811366i	−0.662006	+	0.749499i	$0.730294\pi$
$468$		0			0
$469$	7.20142	+	2.98293i	0.332531	+	0.137739i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	28.6354	−	28.6354i	1.31666	−	1.31666i
$474$		0			0
$475$	13.1771	+	5.45814i	0.604607	+	0.250437i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	21.7665			0.994537			0.497268	−	0.867597i	$-0.334336\pi$
$479$	21.7665			0.994537			0.497268	+	0.867597i	$0.334336\pi$
$480$		0			0
$481$	22.3017			1.01687
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.69444	+	0.701861i	0.0769407	+	0.0318699i
$486$		0			0
$487$	9.10128	−	9.10128i	0.412419	−	0.412419i	−0.470162	−	0.882580i	$-0.655804\pi$
$487$	9.10128	−	9.10128i	0.412419	−	0.412419i	0.882580	+	0.470162i	$0.155804\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	15.2645	+	6.32276i	0.688876	+	0.285342i	0.699532	−	0.714601i	$-0.253392\pi$
$491$	15.2645	+	6.32276i	0.688876	+	0.285342i	−0.0106556	+	0.999943i	$0.503392\pi$
$492$		0			0
$493$	−5.30855	−	12.8160i	−0.239085	−	0.577202i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	18.2026			0.816500
$498$		0			0
$499$	32.2595	−	13.3623i	1.44413	−	0.598180i	0.483337	−	0.875434i	$-0.339425\pi$
$499$	32.2595	−	13.3623i	1.44413	−	0.598180i	0.960796	+	0.277255i	$0.0894246\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−7.34111	+	7.34111i	−0.327324	+	0.327324i	−0.851568	−	0.524244i	$-0.824348\pi$
$503$	−7.34111	+	7.34111i	−0.327324	+	0.327324i	0.524244	+	0.851568i	$0.324348\pi$
$504$		0			0
$505$	−0.396882	−	0.396882i	−0.0176610	−	0.0176610i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.55299	−	18.2345i	−0.334780	−	0.808231i	−0.998199	−	0.0599832i	$-0.980895\pi$
$509$	−7.55299	−	18.2345i	−0.334780	−	0.808231i	0.663419	−	0.748248i	$-0.269105\pi$
$510$		0			0
$511$		−	56.3508i		−	2.49281i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.42186	+	0.588955i	−0.0626548	+	0.0259525i
$516$		0			0
$517$	16.1636	−	39.0225i	0.710876	−	1.71621i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.3209	+	26.3209i	1.15314	+	1.15314i	0.985920	+	0.167218i	$0.0534785\pi$
$521$	26.3209	+	26.3209i	1.15314	+	1.15314i	0.167218	+	0.985920i	$0.446522\pi$
$522$		0			0
$523$	−5.50275	+	13.2848i	−0.240619	+	0.580905i	−0.997345	−	0.0728276i	$-0.976798\pi$
$523$	−5.50275	+	13.2848i	−0.240619	+	0.580905i	0.756726	+	0.653732i	$0.226798\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	3.69839i		−	0.161104i
$528$		0			0
$529$		−	9.49450i		−	0.412805i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.659674	−	1.59259i	0.0285737	−	0.0689829i
$534$		0			0
$535$	0.0138165	+	0.0138165i	0.000597339	+	0.000597339i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	25.3892	−	61.2950i	1.09359	−	2.64016i
$540$		0			0
$541$	1.34772	−	0.558245i	0.0579431	−	0.0240008i	−0.353524	−	0.935426i	$-0.615017\pi$
$541$	1.34772	−	0.558245i	0.0579431	−	0.0240008i	0.411467	+	0.911425i	$0.365017\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	0.543113i		−	0.0232644i
$546$		0			0
$547$	−3.11417	−	7.51828i	−0.133152	−	0.321458i	0.843215	−	0.537577i	$-0.180660\pi$
$547$	−3.11417	−	7.51828i	−0.133152	−	0.321458i	−0.976367	+	0.216119i	$0.930660\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−10.9312	−	10.9312i	−0.465683	−	0.465683i
$552$		0			0
$553$	3.42664	−	3.42664i	0.145715	−	0.145715i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	10.3810	−	4.29993i	0.439855	−	0.182194i	−0.151755	−	0.988418i	$-0.548492\pi$
$557$	10.3810	−	4.29993i	0.439855	−	0.182194i	0.591610	+	0.806224i	$0.298492\pi$
$558$		0			0
$559$	−29.2386			−1.23666
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.95005	−	4.70784i	−0.0821848	−	0.198412i	0.877445	−	0.479677i	$-0.159246\pi$
$563$	−1.95005	−	4.70784i	−0.0821848	−	0.198412i	−0.959630	+	0.281265i	$0.909246\pi$
$564$		0			0
$565$	−0.540424	−	0.223851i	−0.0227358	−	0.00941749i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.12423	−	3.12423i	0.130974	−	0.130974i	−0.638581	−	0.769555i	$-0.720478\pi$
$569$	3.12423	−	3.12423i	0.130974	−	0.130974i	0.769555	+	0.638581i	$0.220478\pi$
$570$		0			0
$571$	−33.4029	−	13.8360i	−1.39787	−	0.579017i	−0.448672	−	0.893697i	$-0.648103\pi$
$571$	−33.4029	−	13.8360i	−1.39787	−	0.579017i	−0.949198	+	0.314680i	$0.898103\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−28.4463			−1.18629
$576$		0			0
$577$	−14.0315			−0.584141			−0.292070	−	0.956397i	$-0.594344\pi$
$577$	−14.0315			−0.584141			−0.292070	+	0.956397i	$0.594344\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	43.1268	+	17.8637i	1.78920	+	0.741112i
$582$		0			0
$583$	16.1095	−	16.1095i	0.667188	−	0.667188i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.0165	−	4.97740i	−0.495975	−	0.205439i	0.120652	−	0.992695i	$-0.461501\pi$
$587$	−12.0165	−	4.97740i	−0.495975	−	0.205439i	−0.616627	+	0.787255i	$0.711501\pi$
$588$		0			0
$589$	−1.57724	−	3.80780i	−0.0649891	−	0.156898i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	17.6528			0.724914			0.362457	−	0.932000i	$-0.381938\pi$
$593$	17.6528			0.724914			0.362457	+	0.932000i	$0.381938\pi$
$594$		0			0
$595$	1.01177	−	0.419088i	0.0414785	−	0.0171809i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5.25995	−	5.25995i	0.214916	−	0.214916i	−0.591436	−	0.806352i	$-0.701439\pi$
$599$	5.25995	−	5.25995i	0.214916	−	0.214916i	0.806352	+	0.591436i	$0.201439\pi$
$600$		0			0
$601$	6.54574	+	6.54574i	0.267006	+	0.267006i	0.827893	−	0.560886i	$-0.189540\pi$
$601$	6.54574	+	6.54574i	0.267006	+	0.267006i	−0.560886	+	0.827893i	$0.689540\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.808413	−	1.95168i	−0.0328667	−	0.0793472i
$606$		0			0
$607$		−	1.72276i		−	0.0699248i	−0.999389	−	0.0349624i	$-0.988869\pi$
$607$		−	1.72276i		−	0.0699248i	0.999389	−	0.0349624i	$-0.0111311\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−28.1743	+	11.6702i	−1.13981	+	0.472125i
$612$		0			0
$613$	16.6267	−	40.1405i	0.671547	−	1.62126i	−0.107435	−	0.994212i	$-0.534264\pi$
$613$	16.6267	−	40.1405i	0.671547	−	1.62126i	0.778982	−	0.627046i	$-0.215736\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.78933	+	7.78933i	0.313587	+	0.313587i	0.846297	−	0.532711i	$-0.178827\pi$
$617$	7.78933	+	7.78933i	0.313587	+	0.313587i	−0.532711	+	0.846297i	$0.678827\pi$
$618$		0			0
$619$	−11.0171	+	26.5976i	−0.442814	+	1.06905i	0.532143	+	0.846655i	$0.321387\pi$
$619$	−11.0171	+	26.5976i	−0.442814	+	1.06905i	−0.974957	+	0.222394i	$0.928613\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			73.6703i			2.95154i
$624$		0			0
$625$			24.8535i			0.994141i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.32840	−	12.8639i	0.212457	−	0.512917i
$630$		0			0
$631$	21.0548	+	21.0548i	0.838177	+	0.838177i	0.988619	−	0.150442i	$-0.0480696\pi$
$631$	21.0548	+	21.0548i	0.838177	+	0.838177i	−0.150442	+	0.988619i	$0.548070\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.366944	+	0.885882i	−0.0145617	+	0.0351552i
$636$		0			0
$637$	−44.2551	+	18.3311i	−1.75345	+	0.726303i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	5.65123i		−	0.223210i	−0.993753	−	0.111605i	$-0.964401\pi$
$641$		−	5.65123i		−	0.223210i	0.993753	−	0.111605i	$-0.0355992\pi$
$642$		0			0
$643$	−17.0022	−	41.0470i	−0.670502	−	1.61874i	−0.780759	−	0.624833i	$-0.785167\pi$
$643$	−17.0022	−	41.0470i	−0.670502	−	1.61874i	0.110256	−	0.993903i	$-0.464833\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.0151270	−	0.0151270i	−0.000594703	−	0.000594703i	0.706809	−	0.707404i	$-0.250134\pi$
$647$	−0.0151270	−	0.0151270i	−0.000594703	−	0.000594703i	−0.707404	+	0.706809i	$0.750134\pi$
$648$		0			0
$649$	−10.3895	+	10.3895i	−0.407824	+	0.407824i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−28.8575	+	11.9531i	−1.12928	+	0.467763i	−0.867536	−	0.497375i	$-0.834297\pi$
$653$	−28.8575	+	11.9531i	−1.12928	+	0.467763i	−0.261744	+	0.965137i	$0.584297\pi$
$654$		0			0
$655$	1.36228			0.0532289
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.25678	−	17.5194i	−0.282684	−	0.682459i	0.717212	−	0.696855i	$-0.245418\pi$
$659$	−7.25678	−	17.5194i	−0.282684	−	0.682459i	−0.999896	+	0.0143952i	$0.995418\pi$
$660$		0			0
$661$	−15.6310	−	6.47456i	−0.607974	−	0.251831i	0.0573877	−	0.998352i	$-0.481723\pi$
$661$	−15.6310	−	6.47456i	−0.607974	−	0.251831i	−0.665362	+	0.746521i	$0.731723\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.862971	−	0.862971i	0.0334646	−	0.0334646i
$666$		0			0
$667$	28.4851	+	11.7989i	1.10295	+	0.456856i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	64.2600			2.48073
$672$		0			0
$673$	26.5987			1.02530			0.512652	−	0.858596i	$-0.328663\pi$
$673$	26.5987			1.02530			0.512652	+	0.858596i	$0.328663\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	26.3000	+	10.8938i	1.01079	+	0.418683i	0.825743	−	0.564047i	$-0.190756\pi$
$677$	26.3000	+	10.8938i	1.01079	+	0.418683i	0.185047	+	0.982730i	$0.440756\pi$
$678$		0			0
$679$	−56.6761	+	56.6761i	−2.17503	+	2.17503i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−29.9528	−	12.4069i	−1.14611	−	0.474735i	−0.272884	−	0.962047i	$-0.587978\pi$
$683$	−29.9528	−	12.4069i	−1.14611	−	0.474735i	−0.873228	+	0.487312i	$0.837978\pi$
$684$		0			0
$685$	0.301105	+	0.726931i	0.0115046	+	0.0277746i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−16.4489			−0.626652
$690$		0			0
$691$	9.94272	−	4.11841i	0.378239	−	0.156672i	−0.185460	−	0.982652i	$-0.559378\pi$
$691$	9.94272	−	4.11841i	0.378239	−	0.156672i	0.563699	+	0.825980i	$0.309378\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.0369653	−	0.0369653i	0.00140217	−	0.00140217i
$696$		0			0
$697$	−0.761018	−	0.761018i	−0.0288256	−	0.0288256i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−5.59430	−	13.5058i	−0.211294	−	0.510108i	0.782329	−	0.622866i	$-0.214032\pi$
$701$	−5.59430	−	13.5058i	−0.211294	−	0.510108i	−0.993623	+	0.112757i	$0.964032\pi$
$702$		0			0
$703$		−	15.5168i		−	0.585228i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	22.6619	−	9.38686i	0.852288	−	0.353029i
$708$		0			0
$709$	4.92207	−	11.8829i	0.184852	−	0.446273i	−0.804102	−	0.594491i	$-0.797354\pi$
$709$	4.92207	−	11.8829i	0.184852	−	0.446273i	0.988955	+	0.148218i	$0.0473537\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.81252	+	5.81252i	0.217680	+	0.217680i
$714$		0			0
$715$	−0.884098	+	2.13440i	−0.0330634	+	0.0798221i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	16.1029i		−	0.600537i	−0.953855	−	0.300268i	$-0.902924\pi$
$719$		−	16.1029i		−	0.600537i	0.953855	−	0.300268i	$-0.0970762\pi$
$720$		0			0
$721$		−	67.2584i		−	2.50483i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.3290	−	24.9364i	0.383609	−	0.926113i
$726$		0			0
$727$	−21.0560	−	21.0560i	−0.780923	−	0.780923i	0.199064	−	0.979987i	$-0.436210\pi$
$727$	−21.0560	−	21.0560i	−0.780923	−	0.780923i	−0.979987	+	0.199064i	$0.936210\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.98581	+	16.8652i	−0.258379	+	0.623783i
$732$		0			0
$733$	41.2426	−	17.0832i	1.52333	−	0.630984i	0.545074	−	0.838388i	$-0.316501\pi$
$733$	41.2426	−	17.0832i	1.52333	−	0.630984i	0.978255	+	0.207404i	$0.0665015\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			10.2664i			0.378168i
$738$		0			0
$739$	−11.2262	−	27.1024i	−0.412962	−	0.996977i	−0.984338	−	0.176290i	$-0.943591\pi$
$739$	−11.2262	−	27.1024i	−0.412962	−	0.996977i	0.571377	−	0.820688i	$-0.306409\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	15.8059	+	15.8059i	0.579863	+	0.579863i	0.934865	−	0.355003i	$-0.115520\pi$
$743$	15.8059	+	15.8059i	0.579863	+	0.579863i	−0.355003	+	0.934865i	$0.615520\pi$
$744$		0			0
$745$	−0.246666	+	0.246666i	−0.00903715	+	0.00903715i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.788918	+	0.326780i	−0.0288264	+	0.0119403i
$750$		0			0
$751$	12.4955			0.455969			0.227984	−	0.973665i	$-0.426787\pi$
$751$	12.4955			0.455969			0.227984	+	0.973665i	$0.426787\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.730170	−	1.76279i	−0.0265736	−	0.0641544i
$756$		0			0
$757$	30.0398	+	12.4429i	1.09182	+	0.452245i	0.854639	−	0.519222i	$-0.173778\pi$
$757$	30.0398	+	12.4429i	1.09182	+	0.452245i	0.237176	+	0.971467i	$0.423778\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.5032	+	15.5032i	−0.561992	+	0.561992i	−0.929873	−	0.367881i	$-0.880083\pi$
$761$	−15.5032	+	15.5032i	−0.561992	+	0.561992i	0.367881	+	0.929873i	$0.380083\pi$
$762$		0			0
$763$	21.9285	+	9.08308i	0.793865	+	0.328830i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.6084			0.383046
$768$		0			0
$769$	−7.08253			−0.255403			−0.127701	−	0.991813i	$-0.540760\pi$
$769$	−7.08253			−0.255403			−0.127701	+	0.991813i	$0.540760\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−30.3534	−	12.5728i	−1.09173	−	0.452211i	−0.237123	−	0.971480i	$-0.576204\pi$
$773$	−30.3534	−	12.5728i	−1.09173	−	0.452211i	−0.854611	+	0.519268i	$0.826204\pi$
$774$		0			0
$775$	5.08838	−	5.08838i	0.182780	−	0.182780i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.10808	−	0.458981i	−0.0397011	−	0.0164447i
$780$		0			0
$781$	9.17464	+	22.1495i	0.328294	+	0.792573i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.65394			0.0590316
$786$		0			0
$787$	37.1276	−	15.3788i	1.32346	−	0.548194i	0.394675	−	0.918821i	$-0.370857\pi$
$787$	37.1276	−	15.3788i	1.32346	−	0.548194i	0.928782	+	0.370627i	$0.120857\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	18.0763	−	18.0763i	0.642718	−	0.642718i
$792$		0			0
$793$	−32.8068	−	32.8068i	−1.16500	−	1.16500i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.87919	−	4.53677i	−0.0665644	−	0.160701i	0.887097	−	0.461584i	$-0.152719\pi$
$797$	−1.87919	−	4.53677i	−0.0665644	−	0.160701i	−0.953661	+	0.300883i	$0.902719\pi$
$798$		0			0
$799$			19.0396i			0.673572i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	68.5694	−	28.4024i	2.41976	−	1.00230i
$804$		0			0
$805$	−0.931476	+	2.24878i	−0.0328302	+	0.0792592i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−30.6738	−	30.6738i	−1.07843	−	1.07843i	−0.996650	−	0.0817820i	$-0.973939\pi$
$809$	−30.6738	−	30.6738i	−1.07843	−	1.07843i	−0.0817820	−	0.996650i	$-0.526061\pi$
$810$		0			0
$811$	2.57082	−	6.20650i	0.0902736	−	0.217940i	−0.872294	−	0.488982i	$-0.837368\pi$
$811$	2.57082	−	6.20650i	0.0902736	−	0.217940i	0.962567	+	0.271042i	$0.0873683\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		−	1.56087i		−	0.0546748i
$816$		0			0
$817$			20.3434i			0.711724i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.97965	+	21.6788i	−0.313392	+	0.756595i	0.686183	+	0.727429i	$0.259285\pi$
$821$	−8.97965	+	21.6788i	−0.313392	+	0.756595i	−0.999575	+	0.0291659i	$0.990715\pi$
$822$		0			0
$823$	−17.8793	−	17.8793i	−0.623234	−	0.623234i	0.323123	−	0.946357i	$-0.395267\pi$
$823$	−17.8793	−	17.8793i	−0.623234	−	0.623234i	−0.946357	+	0.323123i	$0.895267\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.5945	+	37.6486i	−0.542275	+	1.30917i	0.380838	+	0.924642i	$0.375635\pi$
$827$	−15.5945	+	37.6486i	−0.542275	+	1.30917i	−0.923114	+	0.384527i	$0.874365\pi$
$828$		0			0
$829$	−46.3584	+	19.2023i	−1.61009	+	0.666922i	−0.992797	−	0.119808i	$-0.961772\pi$
$829$	−46.3584	+	19.2023i	−1.61009	+	0.666922i	−0.617296	+	0.786731i	$0.711772\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			29.9067i			1.03620i
$834$		0			0
$835$	0.352466	+	0.850928i	0.0121976	+	0.0294476i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−33.5966	−	33.5966i	−1.15988	−	1.15988i	−0.984500	−	0.175383i	$-0.943884\pi$
$839$	−33.5966	−	33.5966i	−1.15988	−	1.15988i	−0.175383	−	0.984500i	$-0.556116\pi$
$840$		0			0
$841$	−0.180047	+	0.180047i	−0.00620852	+	0.00620852i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.353851	−	0.146570i	0.0121729	−	0.00504216i
$846$		0			0
$847$	92.3203			3.17216
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.8430	+	28.5916i	0.405974	+	0.980108i
$852$		0			0
$853$	−0.0647873	−	0.0268358i	−0.00221827	−	0.000918839i	0.381574	−	0.924338i	$-0.375382\pi$
$853$	−0.0647873	−	0.0268358i	−0.00221827	−	0.000918839i	−0.383792	+	0.923419i	$0.625382\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22.9971	−	22.9971i	0.785567	−	0.785567i	−0.195197	−	0.980764i	$-0.562535\pi$
$857$	22.9971	−	22.9971i	0.785567	−	0.785567i	0.980764	+	0.195197i	$0.0625347\pi$
$858$		0			0
$859$	14.9596	+	6.19647i	0.510415	+	0.211421i	0.623001	−	0.782221i	$-0.285913\pi$
$859$	14.9596	+	6.19647i	0.510415	+	0.211421i	−0.112586	+	0.993642i	$0.535913\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−20.2047			−0.687775			−0.343888	−	0.939011i	$-0.611744\pi$
$863$	−20.2047			−0.687775			−0.343888	+	0.939011i	$0.611744\pi$
$864$		0			0
$865$	1.90661			0.0648268
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.89676	+	2.44252i	0.200034	+	0.0828567i
$870$		0			0
$871$	5.24133	−	5.24133i	0.177596	−	0.177596i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.94110	+	1.63246i	0.133234	+	0.0551872i
$876$		0			0
$877$	8.55444	+	20.6523i	0.288863	+	0.697377i	0.999984	−	0.00569289i	$-0.00181211\pi$
$877$	8.55444	+	20.6523i	0.288863	+	0.697377i	−0.711121	+	0.703070i	$0.751812\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−29.9972			−1.01063			−0.505315	−	0.862935i	$-0.668624\pi$
$881$	−29.9972			−1.01063			−0.505315	+	0.862935i	$0.668624\pi$
$882$		0			0
$883$	−28.2360	+	11.6957i	−0.950217	+	0.393593i	−0.803312	−	0.595558i	$-0.796931\pi$
$883$	−28.2360	+	11.6957i	−0.950217	+	0.393593i	−0.146905	+	0.989151i	$0.546931\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.07846	−	4.07846i	0.136941	−	0.136941i	−0.635313	−	0.772254i	$-0.719129\pi$
$887$	4.07846	−	4.07846i	0.136941	−	0.136941i	0.772254	+	0.635313i	$0.219129\pi$
$888$		0			0
$889$	−29.6312	−	29.6312i	−0.993799	−	0.993799i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.11975	+	19.6028i	0.271717	+	0.655983i
$894$		0			0
$895$		−	1.05223i		−	0.0351721i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.20588	+	2.98477i	−0.240329	+	0.0995477i
$900$		0			0
$901$	−3.93003	+	9.48792i	−0.130928	+	0.316088i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.609982	−	0.609982i	−0.0202765	−	0.0202765i
$906$		0			0
$907$	−13.3711	+	32.2808i	−0.443981	+	1.07187i	0.530558	+	0.847649i	$0.321982\pi$
$907$	−13.3711	+	32.2808i	−0.443981	+	1.07187i	−0.974539	+	0.224217i	$0.928018\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	30.1517i		−	0.998971i	−0.866322	−	0.499486i	$-0.833522\pi$
$911$		−	30.1517i		−	0.998971i	0.866322	−	0.499486i	$-0.166478\pi$
$912$		0			0
$913$			61.4819i			2.03475i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−22.7830	+	55.0031i	−0.752362	+	1.81636i
$918$		0			0
$919$	1.45081	+	1.45081i	0.0478579	+	0.0478579i	0.730631	−	0.682773i	$-0.239226\pi$
$919$	1.45081	+	1.45081i	0.0478579	+	0.0478579i	−0.682773	+	0.730631i	$0.739226\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.62411	−	15.9920i	0.218035	−	0.526383i
$924$		0			0
$925$	25.0296	−	10.3676i	0.822969	−	0.340885i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			52.1840i			1.71210i	0.516890	+	0.856052i	$0.327089\pi$
$929$			52.1840i			1.71210i	−0.516890	+	0.856052i	$0.672911\pi$
$930$		0			0
$931$	12.7542	+	30.7914i	0.418002	+	1.00915i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.01992	+	1.01992i	0.0333549	+	0.0333549i
$936$		0			0
$937$	1.45171	−	1.45171i	0.0474253	−	0.0474253i	−0.682996	−	0.730422i	$-0.739324\pi$
$937$	1.45171	−	1.45171i	0.0474253	−	0.0474253i	0.730422	+	0.682996i	$0.239324\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.19665	−	1.32409i	0.104208	−	0.0431642i	−0.329971	−	0.943991i	$-0.607039\pi$
$941$	3.19665	−	1.32409i	0.104208	−	0.0431642i	0.434178	+	0.900827i	$0.357039\pi$
$942$		0			0
$943$	2.39208			0.0778969
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.34992	+	10.5016i	0.141353	+	0.341257i	0.978663	−	0.205472i	$-0.0658728\pi$
$947$	4.34992	+	10.5016i	0.141353	+	0.341257i	−0.837310	+	0.546729i	$0.815873\pi$
$948$		0			0
$949$	−49.5073	−	20.5066i	−1.60707	−	0.665672i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.74508	+	8.74508i	−0.283281	+	0.283281i	−0.834416	−	0.551135i	$-0.814195\pi$
$953$	−8.74508	+	8.74508i	−0.283281	+	0.283281i	0.551135	+	0.834416i	$0.314195\pi$
$954$		0			0
$955$	1.19194	+	0.493718i	0.0385703	+	0.0159763i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−34.3860			−1.11038
$960$		0			0
$961$	28.9206			0.932921
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.279378	+	0.115722i	0.00899351	+	0.00372523i
$966$		0			0
$967$	−30.3193	+	30.3193i	−0.975003	+	0.975003i	−0.999695	−	0.0246926i	$-0.992139\pi$
$967$	−30.3193	+	30.3193i	−0.975003	+	0.975003i	0.0246926	+	0.999695i	$0.492139\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	50.2589	+	20.8179i	1.61288	+	0.668078i	0.993162	−	0.116743i	$-0.0372455\pi$
$971$	50.2589	+	20.8179i	1.61288	+	0.668078i	0.619722	+	0.784822i	$0.287246\pi$
$972$		0			0
$973$	0.874284	+	2.11071i	0.0280283	+	0.0676662i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−28.6269			−0.915857			−0.457928	−	0.888989i	$-0.651408\pi$
$977$	−28.6269			−0.915857			−0.457928	+	0.888989i	$0.651408\pi$
$978$		0			0
$979$	−89.6443	+	37.1319i	−2.86505	+	1.18674i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.81670	−	3.81670i	0.121734	−	0.121734i	−0.643615	−	0.765349i	$-0.722566\pi$
$983$	3.81670	−	3.81670i	0.121734	−	0.121734i	0.765349	+	0.643615i	$0.222566\pi$
$984$		0			0
$985$	0.413656	+	0.413656i	0.0131802	+	0.0131802i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−15.5268	−	37.4851i	−0.493725	−	1.19196i
$990$		0			0
$991$			27.6845i			0.879426i	0.898138	+	0.439713i	$0.144920\pi$
$991$			27.6845i			0.879426i	−0.898138	+	0.439713i	$0.855080\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.579667	+	0.240106i	−0.0183767	+	0.00761187i
$996$		0			0
$997$	−5.51070	+	13.3040i	−0.174526	+	0.421342i	−0.986802	−	0.161930i	$-0.948228\pi$
$997$	−5.51070	+	13.3040i	−0.174526	+	0.421342i	0.812277	+	0.583273i	$0.198228\pi$
$998$		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.719.4		32
3.2	odd	2		1152.2.w.a.719.5		32
4.3	odd	2		288.2.w.a.107.3	yes	32
12.11	even	2		288.2.w.b.107.6	yes	32
32.3	odd	8		1152.2.w.a.431.5		32
32.29	even	8		288.2.w.b.35.6	yes	32
96.29	odd	8		288.2.w.a.35.3	✓	32
96.35	even	8	inner	1152.2.w.b.431.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.3	✓	32	96.29	odd	8
288.2.w.a.107.3	yes	32	4.3	odd	2
288.2.w.b.35.6	yes	32	32.29	even	8
288.2.w.b.107.6	yes	32	12.11	even	2
1152.2.w.a.431.5		32	32.3	odd	8
1152.2.w.a.719.5		32	3.2	odd	2
1152.2.w.b.431.4		32	96.35	even	8	inner
1152.2.w.b.719.4		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)

\(f(q)\)	\(=\)	\(q+(-0.0913223 - 0.0378270i) q^{5} +(3.05457 - 3.05457i) q^{7} +O(q^{10})\)	\(q+(-0.0913223 - 0.0378270i) q^{5} +(3.05457 - 3.05457i) q^{7} +(5.25649 + 2.17731i) q^{11} +(-1.57202 - 3.79519i) q^{13} -2.56471 q^{17} +(-2.64058 + 1.09376i) q^{19} +(4.03079 - 4.03079i) q^{23} +(-3.52863 - 3.52863i) q^{25} +(2.06984 + 4.99704i) q^{29} +1.44203i q^{31} +(-0.394496 + 0.163406i) q^{35} +(-2.07758 + 5.01573i) q^{37} +(0.296726 + 0.296726i) q^{41} +(2.72382 - 6.57588i) q^{43} -7.42367i q^{47} -11.6608i q^{49} +(1.53235 - 3.69941i) q^{53} +(-0.397674 - 0.397674i) q^{55} +(-0.988255 + 2.38586i) q^{59} +(10.4346 - 4.32215i) q^{61} +0.406051i q^{65} +(0.690522 + 1.66707i) q^{67} +(2.97957 + 2.97957i) q^{71} +(9.22401 - 9.22401i) q^{73} +(22.7071 - 9.40558i) q^{77} +1.12181 q^{79} +(4.13529 + 9.98348i) q^{83} +(0.234216 + 0.0970152i) q^{85} +(-12.0590 + 12.0590i) q^{89} +(-16.3945 - 6.79084i) q^{91} +0.282518 q^{95} -18.5545 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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