LMFDB - Embedded newform 3276.2.hi.f.1369.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3276,2,Mod(1297,3276)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3276.1297"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3276, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3276.hi (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,3,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.1589917022$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1092)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1369.1
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	3276.1369
Dual form			3276.2.hi.f.1297.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13746 + 0.656712i) q^{5} +(-1.13746 + 2.38876i) q^{7} +(-3.00000 + 1.73205i) q^{11} +(-1.00000 + 3.46410i) q^{13} -0.274917 q^{17} +(-0.362541 - 0.209313i) q^{19} -8.27492 q^{23} +(-1.63746 + 2.83616i) q^{25} +(4.13746 - 7.16629i) q^{29} +(4.50000 + 2.59808i) q^{31} +(-0.274917 - 3.46410i) q^{35} -10.4498i q^{37} +(-3.41238 - 1.97014i) q^{41} +(5.13746 + 8.89834i) q^{43} +(1.86254 - 1.07534i) q^{47} +(-4.41238 - 5.43424i) q^{49} +(-4.41238 + 7.64246i) q^{53} +(2.27492 - 3.94027i) q^{55} -10.8685i q^{59} +(4.91238 - 8.50848i) q^{61} +(-1.13746 - 4.59698i) q^{65} +(10.1873 - 5.88164i) q^{67} +(-3.41238 + 1.97014i) q^{71} +(7.13746 + 4.12081i) q^{73} +(-0.725083 - 9.13642i) q^{77} +(0.774917 + 1.34220i) q^{79} +8.71780i q^{83} +(0.312707 - 0.180541i) q^{85} -16.9594i q^{89} +(-7.13746 - 6.32904i) q^{91} +0.549834 q^{95} +(-9.04983 + 5.22492i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{5} + 3 q^{7} - 12 q^{11} - 4 q^{13} + 14 q^{17} - 9 q^{19} - 18 q^{23} + q^{25} + 9 q^{29} + 18 q^{31} + 14 q^{35} + 9 q^{41} + 13 q^{43} + 15 q^{47} + 5 q^{49} + 5 q^{53} - 6 q^{55} - 3 q^{61}+ \cdots - 6 q^{97}+O(q^{100}) $ 4 * q + 3 * q^5 + 3 * q^7 - 12 * q^11 - 4 * q^13 + 14 * q^17 - 9 * q^19 - 18 * q^23 + q^25 + 9 * q^29 + 18 * q^31 + 14 * q^35 + 9 * q^41 + 13 * q^43 + 15 * q^47 + 5 * q^49 + 5 * q^53 - 6 * q^55 - 3 * q^61 + 3 * q^65 + 3 * q^67 + 9 * q^71 + 21 * q^73 - 18 * q^77 - 12 * q^79 + 39 * q^85 - 21 * q^91 - 28 * q^95 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3276\mathbb{Z}\right)^\times$.

$n$	$1639$	$2017$	$2341$	$2549$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−1.13746	+	0.656712i	−0.508687	+	0.293691i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	−1.13746	+	0.656712i	−0.508687	+	0.293691i	0.223607	+	0.974679i	$0.428217\pi$
$6$		0			0
$7$	−1.13746	+	2.38876i	−0.429919	+	0.902867i
$7$	−1.13746	+	2.38876i	−0.429919	+	0.902867i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.878668	−	0.477432i	$-0.841568\pi$
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.0258656	+	0.999665i	$0.508234\pi$
$12$		0			0
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.274917			−0.0666772			−0.0333386	−	0.999444i	$-0.510614\pi$
$17$	−0.274917			−0.0666772			−0.0333386	+	0.999444i	$0.510614\pi$
$18$		0			0
$19$	−0.362541	−	0.209313i	−0.0831727	−	0.0480198i	0.457837	−	0.889036i	$-0.348624\pi$
$19$	−0.362541	−	0.209313i	−0.0831727	−	0.0480198i	−0.541010	+	0.841016i	$0.681958\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−8.27492			−1.72544			−0.862720	−	0.505682i	$-0.831241\pi$
$23$	−8.27492			−1.72544			−0.862720	+	0.505682i	$0.831241\pi$
$24$		0			0
$25$	−1.63746	+	2.83616i	−0.327492	+	0.567232i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.13746	−	7.16629i	0.768307	−	1.33075i	−0.170174	−	0.985414i	$-0.554433\pi$
$29$	4.13746	−	7.16629i	0.768307	−	1.33075i	0.938480	−	0.345332i	$-0.112234\pi$
$30$		0			0
$31$	4.50000	+	2.59808i	0.808224	+	0.466628i	0.846339	−	0.532645i	$-0.178802\pi$
$31$	4.50000	+	2.59808i	0.808224	+	0.466628i	−0.0381148	+	0.999273i	$0.512135\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.274917	−	3.46410i	−0.0464695	−	0.585540i
$36$		0			0
$37$		−	10.4498i		−	1.71794i	−0.512022	−	0.858972i	$-0.671103\pi$
$37$		−	10.4498i		−	1.71794i	0.512022	−	0.858972i	$-0.328897\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.41238	−	1.97014i	−0.532924	−	0.307684i	0.209283	−	0.977855i	$-0.432887\pi$
$41$	−3.41238	−	1.97014i	−0.532924	−	0.307684i	−0.742206	+	0.670172i	$0.766220\pi$
$42$		0			0
$43$	5.13746	+	8.89834i	0.783455	+	1.35698i	0.929918	+	0.367768i	$0.119878\pi$
$43$	5.13746	+	8.89834i	0.783455	+	1.35698i	−0.146463	+	0.989216i	$0.546789\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.86254	−	1.07534i	0.271680	−	0.156854i	−0.357971	−	0.933733i	$-0.616531\pi$
$47$	1.86254	−	1.07534i	0.271680	−	0.156854i	0.629651	+	0.776878i	$0.283198\pi$
$48$		0			0
$49$	−4.41238	−	5.43424i	−0.630339	−	0.776320i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.41238	+	7.64246i	−0.606086	+	1.04977i	0.385792	+	0.922586i	$0.373928\pi$
$53$	−4.41238	+	7.64246i	−0.606086	+	1.04977i	−0.991879	+	0.127187i	$0.959405\pi$
$54$		0			0
$55$	2.27492	−	3.94027i	0.306750	−	0.531306i
$56$		0			0
$57$		0			0
$58$		0			0
$59$		−	10.8685i		−	1.41495i	−0.706736	−	0.707477i	$-0.749833\pi$
$59$		−	10.8685i		−	1.41495i	0.706736	−	0.707477i	$-0.250167\pi$
$60$		0			0
$61$	4.91238	−	8.50848i	0.628965	−	1.08940i	−0.358794	−	0.933417i	$-0.616812\pi$
$61$	4.91238	−	8.50848i	0.628965	−	1.08940i	0.987760	−	0.155983i	$-0.0498546\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.13746	−	4.59698i	−0.141084	−	0.570186i
$66$		0			0
$67$	10.1873	−	5.88164i	1.24458	−	0.718556i	0.274554	−	0.961572i	$-0.411470\pi$
$67$	10.1873	−	5.88164i	1.24458	−	0.718556i	0.970022	+	0.243016i	$0.0781366\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.41238	+	1.97014i	−0.404975	+	0.233812i	−0.688628	−	0.725115i	$-0.741787\pi$
$71$	−3.41238	+	1.97014i	−0.404975	+	0.233812i	0.283654	+	0.958927i	$0.408453\pi$
$72$		0			0
$73$	7.13746	+	4.12081i	0.835376	+	0.482305i	0.855690	−	0.517489i	$-0.173133\pi$
$73$	7.13746	+	4.12081i	0.835376	+	0.482305i	−0.0203136	+	0.999794i	$0.506466\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.725083	−	9.13642i	−0.0826309	−	1.04119i
$78$		0			0
$79$	0.774917	+	1.34220i	0.0871850	+	0.151009i	0.906320	−	0.422592i	$-0.138880\pi$
$79$	0.774917	+	1.34220i	0.0871850	+	0.151009i	−0.819135	+	0.573600i	$0.805546\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			8.71780i			0.956903i	0.878114	+	0.478451i	$0.158802\pi$
$83$			8.71780i			0.956903i	−0.878114	+	0.478451i	$0.841198\pi$
$84$		0			0
$85$	0.312707	−	0.180541i	0.0339178	−	0.0195825i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	16.9594i		−	1.79770i	−0.438261	−	0.898848i	$-0.644405\pi$
$89$		−	16.9594i		−	1.79770i	0.438261	−	0.898848i	$-0.355595\pi$
$90$		0			0
$91$	−7.13746	−	6.32904i	−0.748209	−	0.663463i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.549834			0.0564118
$96$		0			0
$97$	−9.04983	+	5.22492i	−0.918871	+	0.530511i	−0.883275	−	0.468856i	$-0.844666\pi$
$97$	−9.04983	+	5.22492i	−0.918871	+	0.530511i	−0.0355966	+	0.999366i	$0.511333\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.27492	+	10.8685i	0.624378	+	1.08145i	0.988661	+	0.150166i	$0.0479807\pi$
$101$	6.27492	+	10.8685i	0.624378	+	1.08145i	−0.364283	+	0.931288i	$0.618686\pi$
$102$		0			0
$103$	0.862541	+	1.49397i	0.0849887	+	0.147205i	0.905386	−	0.424589i	$-0.139581\pi$
$103$	0.862541	+	1.49397i	0.0849887	+	0.147205i	−0.820398	+	0.571793i	$0.806248\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.27492			−0.799966			−0.399983	−	0.916522i	$-0.630984\pi$
$107$	−8.27492			−0.799966			−0.399983	+	0.916522i	$0.630984\pi$
$108$		0			0
$109$	−9.41238	−	5.43424i	−0.901542	−	0.520506i	−0.0238419	−	0.999716i	$-0.507590\pi$
$109$	−9.41238	−	5.43424i	−0.901542	−	0.520506i	−0.877700	+	0.479210i	$0.840923\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.13746	+	3.70219i	0.201075	+	0.348272i	0.948875	−	0.315652i	$-0.102223\pi$
$113$	2.13746	+	3.70219i	0.201075	+	0.348272i	−0.747800	+	0.663924i	$0.768890\pi$
$114$		0			0
$115$	9.41238	−	5.43424i	0.877709	−	0.506745i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.312707	−	0.656712i	0.0286658	−	0.0602007i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	10.8685i		−	0.972106i
$126$		0			0
$127$	4.86254	−	8.42217i	0.431481	−	0.747347i	−0.565520	−	0.824734i	$-0.691325\pi$
$127$	4.86254	−	8.42217i	0.431481	−	0.747347i	0.997001	+	0.0773878i	$0.0246579\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−10.1375	−	17.5586i	−0.885714	−	1.53410i	−0.844893	−	0.534935i	$-0.820336\pi$
$131$	−10.1375	−	17.5586i	−0.885714	−	1.53410i	−0.0408206	−	0.999166i	$-0.512997\pi$
$132$		0			0
$133$	0.912376	−	0.627940i	0.0791130	−	0.0544493i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	13.4953i		−	1.15298i	−0.817103	−	0.576492i	$-0.804421\pi$
$137$		−	13.4953i		−	1.15298i	0.817103	−	0.576492i	$-0.195579\pi$
$138$		0			0
$139$	−5.50000	−	9.52628i	−0.466504	−	0.808008i	0.532764	−	0.846264i	$-0.321153\pi$
$139$	−5.50000	−	9.52628i	−0.466504	−	0.808008i	−0.999268	+	0.0382553i	$0.987820\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.00000	−	12.1244i	−0.250873	−	1.01389i
$144$		0			0
$145$			10.8685i			0.902578i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.82475	+	5.67232i	0.804875	+	0.464695i	0.845173	−	0.534493i	$-0.179497\pi$
$149$	9.82475	+	5.67232i	0.804875	+	0.464695i	−0.0402979	+	0.999188i	$0.512831\pi$
$150$		0			0
$151$	12.4124	+	7.16629i	1.01010	+	0.583184i	0.911222	−	0.411915i	$-0.135140\pi$
$151$	12.4124	+	7.16629i	1.01010	+	0.583184i	0.0988825	+	0.995099i	$0.468473\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.82475			−0.548177
$156$		0			0
$157$	−4.04983	+	7.01452i	−0.323212	+	0.559820i	−0.981149	−	0.193254i	$-0.938096\pi$
$157$	−4.04983	+	7.01452i	−0.323212	+	0.559820i	0.657937	+	0.753073i	$0.271429\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9.41238	−	19.7668i	0.741799	−	1.55784i
$162$		0			0
$163$	−6.36254	−	3.67341i	−0.498353	−	0.287724i	0.229680	−	0.973266i	$-0.426232\pi$
$163$	−6.36254	−	3.67341i	−0.498353	−	0.287724i	−0.728033	+	0.685542i	$0.759565\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.412376	−	0.238085i	−0.0319106	−	0.0184236i	0.483960	−	0.875090i	$-0.339198\pi$
$167$	−0.412376	−	0.238085i	−0.0319106	−	0.0184236i	−0.515870	+	0.856667i	$0.672531\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.27492	−	3.94027i	0.172959	−	0.299573i	−0.766494	−	0.642251i	$-0.778001\pi$
$173$	2.27492	−	3.94027i	0.172959	−	0.299573i	0.939453	+	0.342678i	$0.111334\pi$
$174$		0			0
$175$	−4.91238	−	7.13752i	−0.371341	−	0.539546i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.27492	+	12.6005i	0.543753	+	0.941808i	0.998684	+	0.0512811i	$0.0163304\pi$
$179$	7.27492	+	12.6005i	0.543753	+	0.941808i	−0.454931	+	0.890526i	$0.650336\pi$
$180$		0			0
$181$	−12.7251			−0.945848			−0.472924	−	0.881103i	$-0.656801\pi$
$181$	−12.7251			−0.945848			−0.472924	+	0.881103i	$0.656801\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.86254	+	11.8863i	0.504544	+	0.873896i
$186$		0			0
$187$	0.824752	−	0.476171i	0.0603118	−	0.0348210i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.72508	+	4.71998i	−0.197180	+	0.341526i	−0.947613	−	0.319421i	$-0.896512\pi$
$191$	−2.72508	+	4.71998i	−0.197180	+	0.341526i	0.750433	+	0.660947i	$0.229845\pi$
$192$		0			0
$193$	16.5498	−	9.55505i	1.19128	−	0.687788i	0.232686	−	0.972552i	$-0.425249\pi$
$193$	16.5498	−	9.55505i	1.19128	−	0.687788i	0.958598	+	0.284764i	$0.0919154\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.58762	+	1.49397i	0.184361	+	0.106441i	0.589340	−	0.807885i	$-0.299388\pi$
$197$	2.58762	+	1.49397i	0.184361	+	0.106441i	−0.404979	+	0.914326i	$0.632721\pi$
$198$		0			0
$199$	−26.6495			−1.88913			−0.944567	−	0.328320i	$-0.893518\pi$
$199$	−26.6495			−1.88913			−0.944567	+	0.328320i	$0.893518\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	12.4124	+	18.0348i	0.871178	+	1.26579i
$204$		0			0
$205$	5.17525			0.361455
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.45017			0.100310
$210$		0			0
$211$	−8.50000	+	14.7224i	−0.585164	+	1.01353i	0.409691	+	0.912224i	$0.365637\pi$
$211$	−8.50000	+	14.7224i	−0.585164	+	1.01353i	−0.994855	+	0.101310i	$0.967697\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−11.6873	−	6.74766i	−0.797067	−	0.460187i
$216$		0			0
$217$	−11.3248	+	7.79423i	−0.768774	+	0.529107i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.274917	−	0.952341i	0.0184929	−	0.0640614i
$222$		0			0
$223$	−20.6873	−	11.9438i	−1.38532	−	0.799817i	−0.392540	−	0.919735i	$-0.628403\pi$
$223$	−20.6873	−	11.9438i	−1.38532	−	0.799817i	−0.992784	+	0.119918i	$0.961737\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	7.28929i		−	0.483807i	−0.970300	−	0.241903i	$-0.922228\pi$
$227$		−	7.28929i		−	0.483807i	0.970300	−	0.241903i	$-0.0777717\pi$
$228$		0			0
$229$	−18.7749	+	10.8397i	−1.24068	+	0.716308i	−0.969233	−	0.246145i	$-0.920836\pi$
$229$	−18.7749	+	10.8397i	−1.24068	+	0.716308i	−0.271448	+	0.962453i	$0.587503\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.13746	−	12.3624i	−0.467590	−	0.809890i	0.531724	−	0.846918i	$-0.321544\pi$
$233$	−7.13746	−	12.3624i	−0.467590	−	0.809890i	−0.999314	+	0.0370274i	$0.988211\pi$
$234$		0			0
$235$	−1.41238	+	2.44631i	−0.0921332	+	0.159579i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			2.62685i			0.169917i	0.996385	+	0.0849583i	$0.0270757\pi$
$239$			2.62685i			0.169917i	−0.996385	+	0.0849583i	$0.972924\pi$
$240$		0			0
$241$		−	23.0504i		−	1.48481i	−0.669954	−	0.742403i	$-0.733686\pi$
$241$		−	23.0504i		−	1.48481i	0.669954	−	0.742403i	$-0.266314\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.58762	+	3.28356i	0.548643	+	0.209779i
$246$		0			0
$247$	1.08762	−	1.04657i	0.0692039	−	0.0665915i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	14.1375	+	24.4868i	0.892348	+	1.54559i	0.837052	+	0.547123i	$0.184277\pi$
$251$	14.1375	+	24.4868i	0.892348	+	1.54559i	0.0552962	+	0.998470i	$0.482390\pi$
$252$		0			0
$253$	24.8248	−	14.3326i	1.56072	−	0.901081i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	21.9244			1.36761			0.683804	−	0.729666i	$-0.260324\pi$
$257$	21.9244			1.36761			0.683804	+	0.729666i	$0.260324\pi$
$258$		0			0
$259$	24.9622	+	11.8863i	1.55108	+	0.738577i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.5498	+	18.2728i	0.650531	+	1.12675i	0.982994	+	0.183636i	$0.0587868\pi$
$263$	10.5498	+	18.2728i	0.650531	+	1.12675i	−0.332464	+	0.943116i	$0.607880\pi$
$264$		0			0
$265$		−	11.5906i		−	0.712007i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−21.3746			−1.30323			−0.651616	−	0.758549i	$-0.725909\pi$
$269$	−21.3746			−1.30323			−0.651616	+	0.758549i	$0.725909\pi$
$270$		0			0
$271$		−	9.61260i		−	0.583924i	−0.956430	−	0.291962i	$-0.905692\pi$
$271$		−	9.61260i		−	0.583924i	0.956430	−	0.291962i	$-0.0943080\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	11.3446i		−	0.684108i
$276$		0			0
$277$	12.4502			0.748058			0.374029	−	0.927417i	$-0.377976\pi$
$277$	12.4502			0.748058			0.374029	+	0.927417i	$0.377976\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	32.1293i		−	1.91667i	−0.285645	−	0.958335i	$-0.592208\pi$
$281$		−	32.1293i		−	1.91667i	0.285645	−	0.958335i	$-0.407792\pi$
$282$		0			0
$283$	−2.54983	−	4.41644i	−0.151572	−	0.262530i	0.780234	−	0.625488i	$-0.215100\pi$
$283$	−2.54983	−	4.41644i	−0.151572	−	0.262530i	−0.931806	+	0.362958i	$0.881767\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.58762	−	5.91041i	0.506911	−	0.348880i
$288$		0			0
$289$	−16.9244			−0.995554
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.41238	+	5.43424i	−0.549877	+	0.317472i	−0.749072	−	0.662488i	$-0.769500\pi$
$293$	−9.41238	+	5.43424i	−0.549877	+	0.317472i	0.199195	+	0.979960i	$0.436167\pi$
$294$		0			0
$295$	7.13746	+	12.3624i	0.415559	+	0.719769i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	8.27492	−	28.6652i	0.478551	−	1.65775i
$300$		0			0
$301$	−27.0997	+	2.15068i	−1.56200	+	0.123963i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			12.9041i			0.738885i
$306$		0			0
$307$		−	2.09313i		−	0.119461i	−0.998215	−	0.0597307i	$-0.980976\pi$
$307$		−	2.09313i		−	0.119461i	0.998215	−	0.0597307i	$-0.0190242\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.68729	−	15.0468i	0.492611	−	0.853228i	−0.507353	−	0.861739i	$-0.669376\pi$
$311$	8.68729	−	15.0468i	0.492611	−	0.853228i	0.999964	+	0.00851095i	$0.00270915\pi$
$312$		0			0
$313$	−8.68729	−	15.0468i	−0.491035	−	0.850497i	0.508912	−	0.860819i	$-0.330048\pi$
$313$	−8.68729	−	15.0468i	−0.491035	−	0.850497i	−0.999947	+	0.0103213i	$0.996715\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.5120	+	12.4200i	−1.20824	+	0.697576i	−0.962374	−	0.271729i	$-0.912405\pi$
$317$	−21.5120	+	12.4200i	−1.20824	+	0.697576i	−0.245863	+	0.969305i	$0.579071\pi$
$318$		0			0
$319$			28.6652i			1.60494i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.0996689	+	0.0575438i	0.00554572	+	0.00320183i
$324$		0			0
$325$	−8.18729	−	8.50848i	−0.454149	−	0.471966i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.450166	+	5.67232i	0.0248184	+	0.312725i
$330$		0			0
$331$	12.0997	+	6.98575i	0.665058	+	0.383971i	0.794201	−	0.607655i	$-0.207889\pi$
$331$	12.0997	+	6.98575i	0.665058	+	0.383971i	−0.129144	+	0.991626i	$0.541223\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.72508	+	13.3802i	−0.422066	+	0.731040i
$336$		0			0
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−18.0000			−0.974755
$342$		0			0
$343$	18.0000	−	4.35890i	0.971909	−	0.235358i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−28.8248			−1.54739			−0.773697	−	0.633556i	$-0.781595\pi$
$347$	−28.8248			−1.54739			−0.773697	+	0.633556i	$0.781595\pi$
$348$		0			0
$349$	8.95017	+	5.16738i	0.479091	+	0.276604i	0.720038	−	0.693935i	$-0.244124\pi$
$349$	8.95017	+	5.16738i	0.479091	+	0.276604i	−0.240946	+	0.970538i	$0.577458\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.00000	−	3.46410i	0.319348	−	0.184376i	−0.331754	−	0.943366i	$-0.607640\pi$
$353$	6.00000	−	3.46410i	0.319348	−	0.184376i	0.651102	+	0.758990i	$0.274307\pi$
$354$		0			0
$355$	2.58762	−	4.48190i	0.137337	−	0.237874i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.4124	−	7.16629i	0.655100	−	0.378222i	−0.135307	−	0.990804i	$-0.543202\pi$
$359$	12.4124	−	7.16629i	0.655100	−	0.378222i	0.790407	+	0.612581i	$0.209869\pi$
$360$		0			0
$361$	−9.41238	−	16.3027i	−0.495388	−	0.858038i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.8248			−0.566593
$366$		0			0
$367$	6.54983	+	11.3446i	0.341899	+	0.592186i	0.984785	−	0.173776i	$-0.0555967\pi$
$367$	6.54983	+	11.3446i	0.341899	+	0.592186i	−0.642887	+	0.765961i	$0.722263\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−13.2371	−	19.2331i	−0.687237	−	0.998533i
$372$		0			0
$373$	−1.63746	+	2.83616i	−0.0847844	+	0.146851i	−0.905299	−	0.424774i	$-0.860353\pi$
$373$	−1.63746	+	2.83616i	−0.0847844	+	0.146851i	0.820515	+	0.571625i	$0.193687\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	20.6873	+	21.4989i	1.06545	+	1.10725i
$378$		0			0
$379$	15.0498	+	8.68903i	0.773058	+	0.446325i	0.833964	−	0.551818i	$-0.186066\pi$
$379$	15.0498	+	8.68903i	0.773058	+	0.446325i	−0.0609064	+	0.998143i	$0.519399\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.824752	+	0.476171i	0.0421428	+	0.0243312i	0.520923	−	0.853603i	$-0.325588\pi$
$383$	0.824752	+	0.476171i	0.0421428	+	0.0243312i	−0.478781	+	0.877935i	$0.658921\pi$
$384$		0			0
$385$	6.82475	+	9.91613i	0.347822	+	0.505373i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.4124	+	24.9630i	−0.730736	+	1.26567i	0.225832	+	0.974166i	$0.427490\pi$
$389$	−14.4124	+	24.9630i	−0.730736	+	1.26567i	−0.956569	+	0.291507i	$0.905844\pi$
$390$		0			0
$391$	2.27492			0.115048
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.76287	−	1.01779i	−0.0886997	−	0.0512108i
$396$		0			0
$397$	−12.0000	−	6.92820i	−0.602263	−	0.347717i	0.167668	−	0.985843i	$-0.446376\pi$
$397$	−12.0000	−	6.92820i	−0.602263	−	0.347717i	−0.769931	+	0.638127i	$0.779710\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	6.45203i		−	0.322199i	−0.986938	−	0.161100i	$-0.948496\pi$
$401$		−	6.45203i		−	0.322199i	0.986938	−	0.161100i	$-0.0515040\pi$
$402$		0			0
$403$	−13.5000	+	12.9904i	−0.672483	+	0.647097i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	18.0997	+	31.3495i	0.897167	+	1.55394i
$408$		0			0
$409$		−	12.5430i		−	0.620211i	−0.950702	−	0.310105i	$-0.899636\pi$
$409$		−	12.5430i		−	0.620211i	0.950702	−	0.310105i	$-0.100364\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	25.9622	+	12.3624i	1.27752	+	0.608316i
$414$		0			0
$415$	−5.72508	−	9.91613i	−0.281033	−	0.486764i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.68729	−	6.38658i	0.180136	−	0.312005i	−0.761791	−	0.647823i	$-0.775680\pi$
$419$	3.68729	−	6.38658i	0.180136	−	0.312005i	0.941927	+	0.335818i	$0.109013\pi$
$420$		0			0
$421$			29.9210i			1.45826i	0.684374	+	0.729131i	$0.260076\pi$
$421$			29.9210i			1.45826i	−0.684374	+	0.729131i	$0.739924\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.450166	−	0.779710i	0.0218362	−	0.0378215i
$426$		0			0
$427$	14.7371	+	21.4125i	0.713180	+	1.03623i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.1752	+	6.45203i	−0.538293	+	0.310783i	−0.744387	−	0.667749i	$-0.767258\pi$
$431$	−11.1752	+	6.45203i	−0.538293	+	0.310783i	0.206094	+	0.978532i	$0.433925\pi$
$432$		0			0
$433$	−4.22508	−	7.31806i	−0.203045	−	0.351683i	0.746463	−	0.665426i	$-0.231750\pi$
$433$	−4.22508	−	7.31806i	−0.203045	−	0.351683i	−0.949508	+	0.313743i	$0.898417\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.00000	+	1.73205i	0.143509	+	0.0828552i
$438$		0			0
$439$	−9.00000			−0.429547			−0.214773	−	0.976664i	$-0.568901\pi$
$439$	−9.00000			−0.429547			−0.214773	+	0.976664i	$0.568901\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	19.6873	+	34.0994i	0.935372	+	1.62011i	0.773970	+	0.633222i	$0.218268\pi$
$443$	19.6873	+	34.0994i	0.935372	+	1.62011i	0.161401	+	0.986889i	$0.448399\pi$
$444$		0			0
$445$	11.1375	+	19.2906i	0.527966	+	0.914464i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.96221	+	1.13288i	−0.0926024	+	0.0534640i	−0.545586	−	0.838055i	$-0.683693\pi$
$449$	−1.96221	+	1.13288i	−0.0926024	+	0.0534640i	0.452984	+	0.891519i	$0.350360\pi$
$450$		0			0
$451$	13.6495			0.642730
$452$		0			0
$453$		0			0
$454$		0			0
$455$	12.2749	+	2.51176i	0.575457	+	0.117753i
$456$		0			0
$457$		−	18.2153i		−	0.852076i	−0.904705	−	0.426038i	$-0.859909\pi$
$457$		−	18.2153i		−	0.852076i	0.904705	−	0.426038i	$-0.140091\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.13746	−	0.656712i	0.0529767	−	0.0305861i	−0.473278	−	0.880913i	$-0.656929\pi$
$461$	1.13746	−	0.656712i	0.0529767	−	0.0305861i	0.526254	+	0.850327i	$0.323596\pi$
$462$		0			0
$463$		−	1.78959i		−	0.0831695i	−0.999135	−	0.0415848i	$-0.986759\pi$
$463$		−	1.78959i		−	0.0831695i	0.999135	−	0.0415848i	$-0.0132407\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.13746	+	1.97014i	0.0526353	+	0.0911670i	0.891143	−	0.453723i	$-0.149905\pi$
$467$	1.13746	+	1.97014i	0.0526353	+	0.0911670i	−0.838507	+	0.544890i	$0.816571\pi$
$468$		0			0
$469$	2.46221	+	31.0251i	0.113694	+	1.43261i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−30.8248	−	17.7967i	−1.41732	−	0.818292i
$474$		0			0
$475$	1.18729	−	0.685484i	0.0544767	−	0.0314522i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−19.5498	+	11.2871i	−0.893255	+	0.515721i	−0.875006	−	0.484113i	$-0.839143\pi$
$479$	−19.5498	+	11.2871i	−0.893255	+	0.515721i	−0.0182490	+	0.999833i	$0.505809\pi$
$480$		0			0
$481$	36.1993	+	10.4498i	1.65055	+	0.476472i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.86254	−	11.8863i	0.311612	−	0.539728i
$486$		0			0
$487$		−	17.3781i		−	0.787475i	−0.919223	−	0.393737i	$-0.871182\pi$
$487$		−	17.3781i		−	0.787475i	0.919223	−	0.393737i	$-0.128818\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.13746	+	3.70219i	−0.0964622	+	0.167077i	−0.910218	−	0.414130i	$-0.864086\pi$
$491$	−2.13746	+	3.70219i	−0.0964622	+	0.167077i	0.813756	+	0.581207i	$0.197419\pi$
$492$		0			0
$493$	−1.13746	+	1.97014i	−0.0512286	+	0.0887305i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.824752	−	10.3923i	−0.0369952	−	0.466159i
$498$		0			0
$499$	3.87459	−	2.23699i	0.173450	−	0.100142i	−0.410761	−	0.911743i	$-0.634737\pi$
$499$	3.87459	−	2.23699i	0.173450	−	0.100142i	0.584212	+	0.811601i	$0.301404\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2.68729	+	4.65453i	0.119820	+	0.207535i	0.919696	−	0.392630i	$-0.128435\pi$
$503$	2.68729	+	4.65453i	0.119820	+	0.207535i	−0.799876	+	0.600165i	$0.795101\pi$
$504$		0			0
$505$	−14.2749	−	8.24163i	−0.635225	−	0.366748i
$506$		0			0
$507$		0			0
$508$		0			0
$509$		−	33.3276i		−	1.47722i	−0.674133	−	0.738610i	$-0.735483\pi$
$509$		−	33.3276i		−	1.47722i	0.674133	−	0.738610i	$-0.264517\pi$
$510$		0			0
$511$	−17.9622	+	12.3624i	−0.794601	+	0.546882i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.96221	−	1.13288i	−0.0864653	−	0.0499208i
$516$		0			0
$517$	−3.72508	+	6.45203i	−0.163829	+	0.283760i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.1375	−	17.5586i	0.444130	−	0.769256i	−0.553861	−	0.832609i	$-0.686846\pi$
$521$	10.1375	−	17.5586i	0.444130	−	0.769256i	0.997991	+	0.0633532i	$0.0201795\pi$
$522$		0			0
$523$	−14.0997			−0.616535			−0.308268	−	0.951300i	$-0.599749\pi$
$523$	−14.0997			−0.616535			−0.308268	+	0.951300i	$0.599749\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.23713	−	0.714256i	−0.0538901	−	0.0311135i
$528$		0			0
$529$	45.4743			1.97714
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.2371	−	9.85068i	0.443419	−	0.426680i
$534$		0			0
$535$	9.41238	−	5.43424i	0.406932	−	0.234943i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	22.6495	+	8.66025i	0.975583	+	0.373024i
$540$		0			0
$541$	40.2371	−	23.2309i	1.72993	−	0.998775i	0.840225	−	0.542239i	$-0.182423\pi$
$541$	40.2371	−	23.2309i	1.72993	−	0.998775i	0.889705	−	0.456536i	$-0.150910\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	14.2749			0.611470
$546$		0			0
$547$	30.7251			1.31371			0.656855	−	0.754017i	$-0.271886\pi$
$547$	30.7251			1.31371			0.656855	+	0.754017i	$0.271886\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.00000	+	1.73205i	−0.127804	+	0.0737878i
$552$		0			0
$553$	−4.08762	+	0.324401i	−0.173823	+	0.0137949i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−24.0000	+	13.8564i	−1.01691	+	0.587115i	−0.913208	−	0.407493i	$-0.866403\pi$
$557$	−24.0000	+	13.8564i	−1.01691	+	0.587115i	−0.103704	+	0.994608i	$0.533070\pi$
$558$		0			0
$559$	−35.9622	+	8.89834i	−1.52104	+	0.376360i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−40.8248			−1.72056			−0.860279	−	0.509823i	$-0.829711\pi$
$563$	−40.8248			−1.72056			−0.860279	+	0.509823i	$0.829711\pi$
$564$		0			0
$565$	−4.86254	−	2.80739i	−0.204569	−	0.118108i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	23.3746			0.979914			0.489957	−	0.871747i	$-0.337013\pi$
$569$	23.3746			0.979914			0.489957	+	0.871747i	$0.337013\pi$
$570$		0			0
$571$	−1.50000	+	2.59808i	−0.0627730	+	0.108726i	−0.895704	−	0.444651i	$-0.853328\pi$
$571$	−1.50000	+	2.59808i	−0.0627730	+	0.108726i	0.832931	+	0.553377i	$0.186661\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	13.5498	−	23.4690i	0.565067	−	0.978725i
$576$		0			0
$577$	−10.4003	−	6.00463i	−0.432971	−	0.249976i	0.267640	−	0.963519i	$-0.413756\pi$
$577$	−10.4003	−	6.00463i	−0.432971	−	0.249976i	−0.700612	+	0.713543i	$0.747089\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−20.8248	−	9.91613i	−0.863956	−	0.411391i
$582$		0			0
$583$		−	30.5698i		−	1.26607i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.58762	−	1.49397i	−0.106803	−	0.0616626i	0.445647	−	0.895209i	$-0.352974\pi$
$587$	−2.58762	−	1.49397i	−0.106803	−	0.0616626i	−0.552450	+	0.833546i	$0.686307\pi$
$588$		0			0
$589$	−1.08762	−	1.88382i	−0.0448148	−	0.0776215i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−38.0619	+	21.9750i	−1.56301	+	0.902407i	−0.566064	+	0.824361i	$0.691535\pi$
$593$	−38.0619	+	21.9750i	−1.56301	+	0.902407i	−0.996950	+	0.0780454i	$0.975132\pi$
$594$		0			0
$595$	0.0755795	+	0.952341i	0.00309846	+	0.0390422i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.13746	+	1.97014i	−0.0464753	+	0.0804976i	−0.888327	−	0.459211i	$-0.848132\pi$
$599$	−1.13746	+	1.97014i	−0.0464753	+	0.0804976i	0.841852	+	0.539709i	$0.181466\pi$
$600$		0			0
$601$	9.77492	−	16.9307i	0.398727	−	0.690616i	−0.594842	−	0.803843i	$-0.702785\pi$
$601$	9.77492	−	16.9307i	0.398727	−	0.690616i	0.993569	+	0.113227i	$0.0361187\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$			1.31342i			0.0533983i
$606$		0			0
$607$	−8.63746	+	14.9605i	−0.350584	+	0.607229i	−0.986352	−	0.164651i	$-0.947350\pi$
$607$	−8.63746	+	14.9605i	−0.350584	+	0.607229i	0.635768	+	0.771880i	$0.280683\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.86254	+	7.52737i	0.0753504	+	0.304525i
$612$		0			0
$613$	−38.8368	+	22.4224i	−1.56860	+	0.905634i	−0.572271	+	0.820064i	$0.693938\pi$
$613$	−38.8368	+	22.4224i	−1.56860	+	0.905634i	−0.996332	+	0.0855692i	$0.972729\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.2371	−	5.91041i	0.412131	−	0.237944i	−0.279574	−	0.960124i	$-0.590193\pi$
$617$	10.2371	−	5.91041i	0.412131	−	0.237944i	0.691705	+	0.722180i	$0.256860\pi$
$618$		0			0
$619$	33.5120	+	19.3482i	1.34696	+	0.777669i	0.987818	−	0.155613i	$-0.0497351\pi$
$619$	33.5120	+	19.3482i	1.34696	+	0.777669i	0.359145	+	0.933282i	$0.383068\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	40.5120	+	19.2906i	1.62308	+	0.772863i
$624$		0			0
$625$	−1.04983	−	1.81837i	−0.0419934	−	0.0727347i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			2.87284i			0.114548i
$630$		0			0
$631$	−3.04983	+	1.76082i	−0.121412	+	0.0700972i	−0.559476	−	0.828846i	$-0.688998\pi$
$631$	−3.04983	+	1.76082i	−0.121412	+	0.0700972i	0.438064	+	0.898944i	$0.355664\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$			12.7732i			0.506887i
$636$		0			0
$637$	23.2371	−	9.85068i	0.920689	−	0.390298i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−42.8248			−1.69148			−0.845738	−	0.533598i	$-0.820839\pi$
$641$	−42.8248			−1.69148			−0.845738	+	0.533598i	$0.820839\pi$
$642$		0			0
$643$	32.6873	−	18.8720i	1.28906	−	0.744240i	0.310574	−	0.950549i	$-0.399479\pi$
$643$	32.6873	−	18.8720i	1.28906	−	0.744240i	0.978487	+	0.206309i	$0.0661453\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.0997	+	29.6175i	0.672257	+	1.16438i	0.977262	+	0.212033i	$0.0680085\pi$
$647$	17.0997	+	29.6175i	0.672257	+	1.16438i	−0.305005	+	0.952351i	$0.598658\pi$
$648$		0			0
$649$	18.8248	+	32.6054i	0.738936	+	1.27987i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.72508			−0.0675077			−0.0337539	−	0.999430i	$-0.510746\pi$
$653$	−1.72508			−0.0675077			−0.0337539	+	0.999430i	$0.510746\pi$
$654$		0			0
$655$	23.0619	+	13.3148i	0.901102	+	0.520252i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.41238	−	4.17836i	−0.0939728	−	0.162766i	0.815207	−	0.579170i	$-0.196623\pi$
$659$	−2.41238	−	4.17836i	−0.0939728	−	0.162766i	−0.909179	+	0.416405i	$0.863290\pi$
$660$		0			0
$661$	11.5378	−	6.66135i	0.448768	−	0.259096i	−0.258542	−	0.966000i	$-0.583242\pi$
$661$	11.5378	−	6.66135i	0.448768	−	0.259096i	0.707310	+	0.706904i	$0.249909\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.625414	+	1.31342i	−0.0242525	+	0.0509324i
$666$		0			0
$667$	−34.2371	+	59.3004i	−1.32567	+	2.29612i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			34.0339i			1.31387i
$672$		0			0
$673$	6.96221	−	12.0589i	0.268373	−	0.464837i	−0.700068	−	0.714076i	$-0.746847\pi$
$673$	6.96221	−	12.0589i	0.268373	−	0.464837i	0.968442	+	0.249239i	$0.0801805\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.13746	−	5.43424i	−0.120582	−	0.208855i	0.799415	−	0.600779i	$-0.205143\pi$
$677$	−3.13746	−	5.43424i	−0.120582	−	0.208855i	−0.919997	+	0.391924i	$0.871810\pi$
$678$		0			0
$679$	−2.18729	−	27.5610i	−0.0839406	−	1.05770i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			15.1698i			0.580457i	0.956957	+	0.290229i	$0.0937314\pi$
$683$			15.1698i			0.580457i	−0.956957	+	0.290229i	$0.906269\pi$
$684$		0			0
$685$	8.86254	+	15.3504i	0.338620	+	0.586508i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−22.0619	−	22.9274i	−0.840491	−	0.873464i
$690$		0			0
$691$			18.6339i			0.708868i	0.935081	+	0.354434i	$0.115326\pi$
$691$			18.6339i			0.708868i	−0.935081	+	0.354434i	$0.884674\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.5120	+	7.22383i	0.474609	+	0.274016i
$696$		0			0
$697$	0.938121	+	0.541624i	0.0355339	+	0.0205155i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	40.5498			1.53155			0.765773	−	0.643111i	$-0.222357\pi$
$701$	40.5498			1.53155			0.765773	+	0.643111i	$0.222357\pi$
$702$		0			0
$703$	−2.18729	+	3.78850i	−0.0824953	+	0.142886i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−33.0997	+	2.62685i	−1.24484	+	0.0987928i
$708$		0			0
$709$	−0.987955	−	0.570396i	−0.0371034	−	0.0214217i	0.481334	−	0.876538i	$-0.340153\pi$
$709$	−0.987955	−	0.570396i	−0.0371034	−	0.0214217i	−0.518437	+	0.855116i	$0.673486\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−37.2371	−	21.4989i	−1.39454	−	0.805139i
$714$		0			0
$715$	11.3746	+	11.8208i	0.425385	+	0.442073i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−23.0997	+	40.0098i	−0.861472	+	1.49211i	0.00903554	+	0.999959i	$0.497124\pi$
$719$	−23.0997	+	40.0098i	−0.861472	+	1.49211i	−0.870508	+	0.492155i	$0.836209\pi$
$720$		0			0
$721$	−4.54983	+	0.361083i	−0.169445	+	0.0134474i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.5498	+	23.4690i	0.503228	+	0.871617i
$726$		0			0
$727$	−13.6254			−0.505339			−0.252669	−	0.967553i	$-0.581308\pi$
$727$	−13.6254			−0.505339			−0.252669	+	0.967553i	$0.581308\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.41238	−	2.44631i	−0.0522386	−	0.0904799i
$732$		0			0
$733$	−14.2251	+	8.21286i	−0.525415	+	0.303349i	−0.739148	−	0.673544i	$-0.764771\pi$
$733$	−14.2251	+	8.21286i	−0.525415	+	0.303349i	0.213732	+	0.976892i	$0.431438\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−20.3746	+	35.2898i	−0.750508	+	1.29992i
$738$		0			0
$739$	−1.81271	+	1.04657i	−0.0666815	+	0.0384986i	−0.532970	−	0.846134i	$-0.678924\pi$
$739$	−1.81271	+	1.04657i	−0.0666815	+	0.0384986i	0.466289	+	0.884633i	$0.345591\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16.8625	+	9.73559i	0.618627	+	0.357164i	0.776334	−	0.630322i	$-0.217077\pi$
$743$	16.8625	+	9.73559i	0.618627	+	0.357164i	−0.157707	+	0.987486i	$0.550410\pi$
$744$		0			0
$745$	−14.9003			−0.545906
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.41238	−	19.7668i	0.343921	−	0.722264i
$750$		0			0
$751$	−22.4502			−0.819218			−0.409609	−	0.912261i	$-0.634335\pi$
$751$	−22.4502			−0.819218			−0.409609	+	0.912261i	$0.634335\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−18.8248			−0.685103
$756$		0			0
$757$	12.4124	−	21.4989i	0.451135	−	0.781390i	−0.547321	−	0.836923i	$-0.684352\pi$
$757$	12.4124	−	21.4989i	0.451135	−	0.781390i	0.998457	+	0.0555330i	$0.0176858\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−28.5498	−	16.4833i	−1.03493	−	0.597518i	−0.116537	−	0.993186i	$-0.537179\pi$
$761$	−28.5498	−	16.4833i	−1.03493	−	0.597518i	−0.918393	+	0.395669i	$0.870513\pi$
$762$		0			0
$763$	23.6873	−	16.3027i	0.857538	−	0.590198i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	37.6495	+	10.8685i	1.35944	+	0.392438i
$768$		0			0
$769$	−2.12541	−	1.22711i	−0.0766444	−	0.0442507i	0.461188	−	0.887302i	$-0.347423\pi$
$769$	−2.12541	−	1.22711i	−0.0766444	−	0.0442507i	−0.537832	+	0.843052i	$0.680757\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			3.10302i			0.111608i	0.998442	+	0.0558039i	$0.0177722\pi$
$773$			3.10302i			0.111608i	−0.998442	+	0.0558039i	$0.982228\pi$
$774$		0			0
$775$	−14.7371	+	8.50848i	−0.529373	+	0.305634i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.824752	+	1.42851i	0.0295498	+	0.0511817i
$780$		0			0
$781$	6.82475	−	11.8208i	0.244209	−	0.422982i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	10.6383i		−	0.379697i
$786$		0			0
$787$			11.1720i			0.398239i	0.979975	+	0.199120i	$0.0638082\pi$
$787$			11.1720i			0.398239i	−0.979975	+	0.199120i	$0.936192\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−11.2749	+	0.894797i	−0.400890	+	0.0318153i
$792$		0			0
$793$	24.5619	+	25.5255i	0.872218	+	0.906435i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.96221	+	13.7910i	0.282036	+	0.488501i	0.971886	−	0.235452i	$-0.0756569\pi$
$797$	7.96221	+	13.7910i	0.282036	+	0.488501i	−0.689850	+	0.723952i	$0.742324\pi$
$798$		0			0
$799$	−0.512045	+	0.295629i	−0.0181148	+	0.0104586i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−28.5498			−1.00750
$804$		0			0
$805$	2.27492	+	28.6652i	0.0801803	+	1.01031i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.2749	+	21.2608i	0.431563	+	0.747489i	0.997008	−	0.0772968i	$-0.0246289\pi$
$809$	12.2749	+	21.2608i	0.431563	+	0.747489i	−0.565445	+	0.824786i	$0.691296\pi$
$810$		0			0
$811$		−	4.83507i		−	0.169782i	−0.996390	−	0.0848911i	$-0.972946\pi$
$811$		−	4.83507i		−	0.169782i	0.996390	−	0.0848911i	$-0.0270542\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	9.64950			0.338007
$816$		0			0
$817$		−	4.30136i		−	0.150485i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			23.7725i			0.829667i	0.909897	+	0.414834i	$0.136160\pi$
$821$			23.7725i			0.829667i	−0.909897	+	0.414834i	$0.863840\pi$
$822$		0			0
$823$	−26.8248			−0.935052			−0.467526	−	0.883979i	$-0.654855\pi$
$823$	−26.8248			−0.935052			−0.467526	+	0.883979i	$0.654855\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	2.62685i		−	0.0913445i	−0.998956	−	0.0456722i	$-0.985457\pi$
$827$		−	2.62685i		−	0.0913445i	0.998956	−	0.0456722i	$-0.0145430\pi$
$828$		0			0
$829$	−22.0997	−	38.2777i	−0.767553	−	1.32944i	−0.938886	−	0.344228i	$-0.888141\pi$
$829$	−22.0997	−	38.2777i	−0.767553	−	1.32944i	0.171333	−	0.985213i	$-0.445193\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.21304	+	1.49397i	0.0420293	+	0.0517628i
$834$		0			0
$835$	0.625414			0.0216433
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.03779	+	0.599168i	−0.0358285	+	0.0206856i	−0.517807	−	0.855497i	$-0.673252\pi$
$839$	−1.03779	+	0.599168i	−0.0358285	+	0.0206856i	0.481979	+	0.876183i	$0.339918\pi$
$840$		0			0
$841$	−19.7371	−	34.1857i	−0.680591	−	1.17882i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	17.0619	+	0.656712i	0.586946	+	0.0225916i
$846$		0			0
$847$	1.50000	+	2.17945i	0.0515406	+	0.0748868i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			86.4716i			2.96421i
$852$		0			0
$853$		−	30.9885i		−	1.06102i	−0.847677	−	0.530512i	$-0.822000\pi$
$853$		−	30.9885i		−	1.06102i	0.847677	−	0.530512i	$-0.178000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.31271	+	5.73778i	−0.113160	+	0.195999i	−0.917043	−	0.398789i	$-0.869431\pi$
$857$	−3.31271	+	5.73778i	−0.113160	+	0.195999i	0.803883	+	0.594788i	$0.202764\pi$
$858$		0			0
$859$	−26.5000	−	45.8993i	−0.904168	−	1.56607i	−0.822030	−	0.569445i	$-0.807158\pi$
$859$	−26.5000	−	45.8993i	−0.904168	−	1.56607i	−0.0821386	−	0.996621i	$-0.526175\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−30.5120	+	17.6161i	−1.03864	+	0.599660i	−0.919448	−	0.393211i	$-0.871364\pi$
$863$	−30.5120	+	17.6161i	−1.03864	+	0.599660i	−0.119194	+	0.992871i	$0.538031\pi$
$864$		0			0
$865$			5.97586i			0.203185i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.64950	−	2.68439i	−0.157724	−	0.0910618i
$870$		0			0
$871$	10.1873	+	41.1715i	0.345183	+	1.39504i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	25.9622	+	12.3624i	0.877683	+	0.417927i
$876$		0			0
$877$	22.5498	+	13.0192i	0.761454	+	0.439626i	0.829817	−	0.558035i	$-0.188444\pi$
$877$	22.5498	+	13.0192i	0.761454	+	0.439626i	−0.0683637	+	0.997660i	$0.521778\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	17.9622	−	31.1115i	0.605162	−	1.04817i	−0.386864	−	0.922137i	$-0.626442\pi$
$881$	17.9622	−	31.1115i	0.605162	−	1.04817i	0.992026	−	0.126035i	$-0.0402251\pi$
$882$		0			0
$883$	−38.1993			−1.28551			−0.642755	−	0.766072i	$-0.722209\pi$
$883$	−38.1993			−1.28551			−0.642755	+	0.766072i	$0.722209\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.2749			0.613612			0.306806	−	0.951772i	$-0.400740\pi$
$887$	18.2749			0.613612			0.306806	+	0.951772i	$0.400740\pi$
$888$		0			0
$889$	14.5876	+	21.1953i	0.489253	+	0.710868i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.900331			−0.0301284
$894$		0			0
$895$	−16.5498	−	9.55505i	−0.553200	−	0.319390i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	37.2371	−	21.4989i	1.24193	−	0.717027i
$900$		0			0
$901$	1.21304	−	2.10104i	0.0404122	−	0.0699959i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.4743	−	8.35671i	0.481141	−	0.277787i
$906$		0			0
$907$	4.08762	+	7.07997i	0.135727	+	0.235087i	0.925875	−	0.377830i	$-0.123330\pi$
$907$	4.08762	+	7.07997i	0.135727	+	0.235087i	−0.790148	+	0.612916i	$0.789996\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	24.7492			0.819977			0.409988	−	0.912091i	$-0.365533\pi$
$911$	24.7492			0.819977			0.409988	+	0.912091i	$0.365533\pi$
$912$		0			0
$913$	−15.0997	−	26.1534i	−0.499726	−	0.865551i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	53.4743	−	4.24381i	1.76588	−	0.140143i
$918$		0			0
$919$	−20.4622	+	35.4416i	−0.674986	+	1.16911i	0.301487	+	0.953470i	$0.402517\pi$
$919$	−20.4622	+	35.4416i	−0.674986	+	1.16911i	−0.976473	+	0.215640i	$0.930816\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.41238	−	13.7910i	−0.112320	−	0.453935i
$924$		0			0
$925$	29.6375	+	17.1112i	0.974474	+	0.562613i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.82475	−	5.67232i	−0.322340	−	0.186103i	0.330095	−	0.943948i	$-0.392919\pi$
$929$	−9.82475	−	5.67232i	−0.322340	−	0.186103i	−0.652435	+	0.757845i	$0.726252\pi$
$930$		0			0
$931$	0.462210	+	2.89371i	0.0151483	+	0.0948374i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.625414	+	1.08325i	−0.0204532	+	0.0354260i
$936$		0			0
$937$	−16.7251			−0.546385			−0.273192	−	0.961959i	$-0.588080\pi$
$937$	−16.7251			−0.546385			−0.273192	+	0.961959i	$0.588080\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	37.9622	+	21.9175i	1.23753	+	0.714490i	0.968589	−	0.248666i	$-0.0799922\pi$
$941$	37.9622	+	21.9175i	1.23753	+	0.714490i	0.268943	+	0.963156i	$0.413326\pi$
$942$		0			0
$943$	28.2371	+	16.3027i	0.919527	+	0.530889i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			26.5145i			0.861605i	0.902446	+	0.430802i	$0.141769\pi$
$947$			26.5145i			0.861605i	−0.902446	+	0.430802i	$0.858231\pi$
$948$		0			0
$949$	−21.4124	+	20.6041i	−0.695075	+	0.668836i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	5.41238	+	9.37451i	0.175324	+	0.303670i	0.940273	−	0.340420i	$-0.110569\pi$
$953$	5.41238	+	9.37451i	0.175324	+	0.303670i	−0.764949	+	0.644090i	$0.777236\pi$
$954$		0			0
$955$		−	7.15838i		−	0.231640i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	32.2371	+	15.3504i	1.04099	+	0.495689i
$960$		0			0
$961$	−2.00000	−	3.46410i	−0.0645161	−	0.111745i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.5498	+	21.7370i	−0.403993	+	0.699737i
$966$		0			0
$967$		−	22.2707i		−	0.716176i	−0.933688	−	0.358088i	$-0.883429\pi$
$967$		−	22.2707i		−	0.716176i	0.933688	−	0.358088i	$-0.116571\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.5498	−	35.5934i	0.659476	−	1.14225i	−0.321276	−	0.946986i	$-0.604112\pi$
$971$	20.5498	−	35.5934i	0.659476	−	1.14225i	0.980752	−	0.195260i	$-0.0625549\pi$
$972$		0			0
$973$	29.0120	−	2.30245i	0.930083	−	0.0738131i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.17525	−	1.25588i	0.0695924	−	0.0401792i	−0.464800	−	0.885416i	$-0.653874\pi$
$977$	2.17525	−	1.25588i	0.0695924	−	0.0401792i	0.534392	+	0.845236i	$0.320540\pi$
$978$		0			0
$979$	29.3746	+	50.8783i	0.938816	+	1.62608i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−3.51204	−	2.02768i	−0.112017	−	0.0646729i	0.442945	−	0.896549i	$-0.353934\pi$
$983$	−3.51204	−	2.02768i	−0.112017	−	0.0646729i	−0.554962	+	0.831876i	$0.687267\pi$
$984$		0			0
$985$	−3.92442			−0.125042
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−42.5120	−	73.6330i	−1.35180	−	2.34139i
$990$		0			0
$991$	−5.36254	−	9.28819i	−0.170347	−	0.295049i	0.768194	−	0.640217i	$-0.221155\pi$
$991$	−5.36254	−	9.28819i	−0.170347	−	0.295049i	−0.938541	+	0.345167i	$0.887822\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	30.3127	−	17.5010i	0.960977	−	0.554821i
$996$		0			0
$997$	9.37459			0.296896			0.148448	−	0.988920i	$-0.452572\pi$
$997$	9.37459			0.296896			0.148448	+	0.988920i	$0.452572\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3276.2.hi.f.1369.1		4
3.2	odd	2		1092.2.cx.c.277.2	yes	4
7.2	even	3		3276.2.fe.f.2305.2		4
13.10	even	6		3276.2.fe.f.361.2		4
21.2	odd	6		1092.2.cf.c.121.1	✓	4
39.23	odd	6		1092.2.cf.c.361.1	yes	4
91.23	even	6	inner	3276.2.hi.f.1297.1		4
273.23	odd	6		1092.2.cx.c.205.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1092.2.cf.c.121.1	✓	4	21.2	odd	6
1092.2.cf.c.361.1	yes	4	39.23	odd	6
1092.2.cx.c.205.2	yes	4	273.23	odd	6
1092.2.cx.c.277.2	yes	4	3.2	odd	2
3276.2.fe.f.361.2		4	13.10	even	6
3276.2.fe.f.2305.2		4	7.2	even	3
3276.2.hi.f.1297.1		4	91.23	even	6	inner
3276.2.hi.f.1369.1		4	1.1	even	1	trivial

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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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3276.hi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13746 + 0.656712i) q^{5} +(-1.13746 + 2.38876i) q^{7} +(-3.00000 + 1.73205i) q^{11} +(-1.00000 + 3.46410i) q^{13} -0.274917 q^{17} +(-0.362541 - 0.209313i) q^{19} -8.27492 q^{23} +(-1.63746 + 2.83616i) q^{25} +(4.13746 - 7.16629i) q^{29} +(4.50000 + 2.59808i) q^{31} +(-0.274917 - 3.46410i) q^{35} -10.4498i q^{37} +(-3.41238 - 1.97014i) q^{41} +(5.13746 + 8.89834i) q^{43} +(1.86254 - 1.07534i) q^{47} +(-4.41238 - 5.43424i) q^{49} +(-4.41238 + 7.64246i) q^{53} +(2.27492 - 3.94027i) q^{55} -10.8685i q^{59} +(4.91238 - 8.50848i) q^{61} +(-1.13746 - 4.59698i) q^{65} +(10.1873 - 5.88164i) q^{67} +(-3.41238 + 1.97014i) q^{71} +(7.13746 + 4.12081i) q^{73} +(-0.725083 - 9.13642i) q^{77} +(0.774917 + 1.34220i) q^{79} +8.71780i q^{83} +(0.312707 - 0.180541i) q^{85} -16.9594i q^{89} +(-7.13746 - 6.32904i) q^{91} +0.549834 q^{95} +(-9.04983 + 5.22492i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{5} + 3 q^{7} - 12 q^{11} - 4 q^{13} + 14 q^{17} - 9 q^{19} - 18 q^{23} + q^{25} + 9 q^{29} + 18 q^{31} + 14 q^{35} + 9 q^{41} + 13 q^{43} + 15 q^{47} + 5 q^{49} + 5 q^{53} - 6 q^{55} - 3 q^{61}+ \cdots - 6 q^{97}+O(q^{100}) \) 4 * q + 3 * q^5 + 3 * q^7 - 12 * q^11 - 4 * q^13 + 14 * q^17 - 9 * q^19 - 18 * q^23 + q^25 + 9 * q^29 + 18 * q^31 + 14 * q^35 + 9 * q^41 + 13 * q^43 + 15 * q^47 + 5 * q^49 + 5 * q^53 - 6 * q^55 - 3 * q^61 + 3 * q^65 + 3 * q^67 + 9 * q^71 + 21 * q^73 - 18 * q^77 - 12 * q^79 + 39 * q^85 - 21 * q^91 - 28 * q^95 - 6 * q^97

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