LMFDB - Embedded newform 3276.2.gv.g.2053.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3276,2,Mod(1117,3276)] 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("3276.1117"); 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, 4, 3])) 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.gv (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,0,0,0,0,0,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$26.1589917022$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 4 x^{18} - 108 x^{16} - 975 x^{14} + 2955 x^{12} + 75510 x^{10} + 144795 x^{8} + \cdots + 282475249 $ x^20 + 4x^18 - 108x^16 - 975x^14 + 2955x^12 + 75510x^10 + 144795x^8 - 2340975x^6 - 12706092x^4 + 23059204*x^2 + 282475249
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1092)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2053.1
Root			$-2.61286 + 0.415868i$ of defining polynomial
Character	$\chi$	$=$	3276.2053
Dual form			3276.2.gv.g.1117.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.57406 - 2.06348i) q^{5} +(-0.946280 + 2.47074i) q^{7} +(-4.18345 + 2.41532i) q^{11} +(-1.36787 + 3.33601i) q^{13} +(0.0965957 + 0.167309i) q^{17} +(-0.705391 - 0.407257i) q^{19} +(0.771274 - 1.33589i) q^{23} +(6.01592 + 10.4199i) q^{25} -0.154256 q^{29} +(-4.19837 + 2.42393i) q^{31} +(8.48038 - 6.87793i) q^{35} +(0.0959943 + 0.0554223i) q^{37} -1.85860i q^{41} -1.19319 q^{43} +(8.47781 + 4.89467i) q^{47} +(-5.20911 - 4.67602i) q^{49} +(-6.13559 - 10.6272i) q^{53} +19.9359 q^{55} +(-12.0519 + 6.95815i) q^{59} +(-2.63914 + 4.57113i) q^{61} +(11.7726 - 9.10050i) q^{65} +(10.1536 - 5.86217i) q^{67} -4.22059i q^{71} +(2.78758 - 1.60941i) q^{73} +(-2.00891 - 12.6218i) q^{77} +(5.86432 - 10.1573i) q^{79} -2.65589i q^{83} -0.797294i q^{85} +(-4.29436 - 2.47935i) q^{89} +(-6.94801 - 6.53644i) q^{91} +(1.68074 + 2.91112i) q^{95} -3.13454i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{13} - 4 q^{17} - 8 q^{23} + 24 q^{25} + 4 q^{29} + 38 q^{35} - 12 q^{43} + 4 q^{49} + 24 q^{53} - 24 q^{55} + 12 q^{65} - 26 q^{77} - 6 q^{79} - 7 q^{91} - 58 q^{95}+O(q^{100}) $ 20 * q + 2 * q^13 - 4 * q^17 - 8 * q^23 + 24 * q^25 + 4 * q^29 + 38 * q^35 - 12 * q^43 + 4 * q^49 + 24 * q^53 - 24 * q^55 + 12 * q^65 - 26 * q^77 - 6 * q^79 - 7 * q^91 - 58 * q^95

Character values

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

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

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
$5$	−3.57406	−	2.06348i	−1.59837	−	0.922817i	−0.991802	−	0.127783i	$-0.959214\pi$
$5$	−3.57406	−	2.06348i	−1.59837	−	0.922817i	−0.606564	−	0.795034i	$-0.707453\pi$
$6$		0			0
$7$	−0.946280	+	2.47074i	−0.357660	+	0.933852i
$7$	−0.946280	+	2.47074i	−0.357660	+	0.933852i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.18345	+	2.41532i	−1.26136	+	0.728246i	−0.973337	−	0.229378i	$-0.926331\pi$
$11$	−4.18345	+	2.41532i	−1.26136	+	0.728246i	−0.288021	+	0.957624i	$0.592997\pi$
$12$		0			0
$13$	−1.36787	+	3.33601i	−0.379379	+	0.925241i
$13$	−1.36787	+	3.33601i	−0.379379	+	0.925241i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.0965957	+	0.167309i	0.0234279	+	0.0405783i	0.877502	−	0.479574i	$-0.159209\pi$
$17$	0.0965957	+	0.167309i	0.0234279	+	0.0405783i	−0.854074	+	0.520152i	$0.825875\pi$
$18$		0			0
$19$	−0.705391	−	0.407257i	−0.161828	−	0.0934313i	0.416899	−	0.908953i	$-0.363117\pi$
$19$	−0.705391	−	0.407257i	−0.161828	−	0.0934313i	−0.578727	+	0.815522i	$0.696450\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.771274	−	1.33589i	0.160822	−	0.278551i	−0.774342	−	0.632767i	$-0.781919\pi$
$23$	0.771274	−	1.33589i	0.160822	−	0.278551i	0.935164	+	0.354216i	$0.115252\pi$
$24$		0			0
$25$	6.01592	+	10.4199i	1.20318	+	2.08398i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.154256			−0.0286447			−0.0143223	−	0.999897i	$-0.504559\pi$
$29$	−0.154256			−0.0286447			−0.0143223	+	0.999897i	$0.504559\pi$
$30$		0			0
$31$	−4.19837	+	2.42393i	−0.754049	+	0.435350i	−0.827155	−	0.561974i	$-0.810042\pi$
$31$	−4.19837	+	2.42393i	−0.754049	+	0.435350i	0.0731062	+	0.997324i	$0.476709\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	8.48038	−	6.87793i	1.43345	−	1.16258i
$36$		0			0
$37$	0.0959943	+	0.0554223i	0.0157814	+	0.00911138i	0.507870	−	0.861434i	$-0.330433\pi$
$37$	0.0959943	+	0.0554223i	0.0157814	+	0.00911138i	−0.492089	+	0.870545i	$0.663766\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	1.85860i		−	0.290264i	−0.989412	−	0.145132i	$-0.953639\pi$
$41$		−	1.85860i		−	0.290264i	0.989412	−	0.145132i	$-0.0463607\pi$
$42$		0			0
$43$	−1.19319			−0.181960			−0.0909800	−	0.995853i	$-0.529000\pi$
$43$	−1.19319			−0.181960			−0.0909800	+	0.995853i	$0.529000\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.47781	+	4.89467i	1.23662	+	0.713961i	0.968401	−	0.249398i	$-0.0802329\pi$
$47$	8.47781	+	4.89467i	1.23662	+	0.713961i	0.268215	+	0.963359i	$0.413566\pi$
$48$		0			0
$49$	−5.20911	−	4.67602i	−0.744159	−	0.668003i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.13559	−	10.6272i	−0.842789	−	1.45975i	−0.887528	−	0.460754i	$-0.847579\pi$
$53$	−6.13559	−	10.6272i	−0.842789	−	1.45975i	0.0447390	−	0.998999i	$-0.485754\pi$
$54$		0			0
$55$	19.9359			2.68815
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−12.0519	+	6.95815i	−1.56902	+	0.905874i	−0.572736	+	0.819740i	$0.694118\pi$
$59$	−12.0519	+	6.95815i	−1.56902	+	0.905874i	−0.996284	+	0.0861342i	$0.972549\pi$
$60$		0			0
$61$	−2.63914	+	4.57113i	−0.337908	+	0.585273i	−0.984039	−	0.177953i	$-0.943053\pi$
$61$	−2.63914	+	4.57113i	−0.337908	+	0.585273i	0.646131	+	0.763226i	$0.276386\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	11.7726	−	9.10050i	1.46022	−	1.12878i
$66$		0			0
$67$	10.1536	−	5.86217i	1.24046	−	0.716178i	0.271269	−	0.962504i	$-0.412557\pi$
$67$	10.1536	−	5.86217i	1.24046	−	0.716178i	0.969187	+	0.246326i	$0.0792233\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	4.22059i		−	0.500892i	−0.968131	−	0.250446i	$-0.919423\pi$
$71$		−	4.22059i		−	0.500892i	0.968131	−	0.250446i	$-0.0805772\pi$
$72$		0			0
$73$	2.78758	−	1.60941i	0.326262	−	0.188368i	−0.327918	−	0.944706i	$-0.606347\pi$
$73$	2.78758	−	1.60941i	0.326262	−	0.188368i	0.654180	+	0.756339i	$0.273014\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.00891	−	12.6218i	−0.228936	−	1.43839i
$78$		0			0
$79$	5.86432	−	10.1573i	0.659788	−	1.14279i	−0.320883	−	0.947119i	$-0.603980\pi$
$79$	5.86432	−	10.1573i	0.659788	−	1.14279i	0.980670	−	0.195667i	$-0.0626871\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	2.65589i		−	0.291522i	−0.989320	−	0.145761i	$-0.953437\pi$
$83$		−	2.65589i		−	0.291522i	0.989320	−	0.145761i	$-0.0465630\pi$
$84$		0			0
$85$		−	0.797294i		−	0.0864787i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.29436	−	2.47935i	−0.455201	−	0.262811i	0.254823	−	0.966988i	$-0.417983\pi$
$89$	−4.29436	−	2.47935i	−0.455201	−	0.262811i	−0.710024	+	0.704177i	$0.751316\pi$
$90$		0			0
$91$	−6.94801	−	6.53644i	−0.728350	−	0.685205i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.68074	+	2.91112i	0.172440	+	0.298675i
$96$		0			0
$97$		−	3.13454i		−	0.318265i	−0.987257	−	0.159132i	$-0.949130\pi$
$97$		−	3.13454i		−	0.318265i	0.987257	−	0.159132i	$-0.0508697\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.75181	−	3.03422i	−0.174311	−	0.301916i	0.765611	−	0.643303i	$-0.222437\pi$
$101$	−1.75181	−	3.03422i	−0.174311	−	0.301916i	−0.939923	+	0.341387i	$0.889103\pi$
$102$		0			0
$103$	−6.30571	+	10.9218i	−0.621320	+	1.07616i	0.367921	+	0.929857i	$0.380070\pi$
$103$	−6.30571	+	10.9218i	−0.621320	+	1.07616i	−0.989240	+	0.146300i	$0.953264\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.96447	+	5.13460i	−0.286586	+	0.496381i	−0.972992	−	0.230837i	$-0.925854\pi$
$107$	−2.96447	+	5.13460i	−0.286586	+	0.496381i	0.686407	+	0.727218i	$0.259187\pi$
$108$		0			0
$109$	16.9988	−	9.81425i	1.62819	−	0.940035i	0.643555	−	0.765399i	$-0.277459\pi$
$109$	16.9988	−	9.81425i	1.62819	−	0.940035i	0.984633	−	0.174636i	$-0.0558748\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	16.2391			1.52764			0.763821	−	0.645428i	$-0.223321\pi$
$113$	16.2391			1.52764			0.763821	+	0.645428i	$0.223321\pi$
$114$		0			0
$115$	−5.51315	+	3.18302i	−0.514104	+	0.296818i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.504783	+	0.0803421i	−0.0462734	+	0.00736495i
$120$		0			0
$121$	6.16752	−	10.6825i	0.560683	−	0.971132i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	29.0201i		−	2.59564i
$126$		0			0
$127$	−1.61171			−0.143016			−0.0715080	−	0.997440i	$-0.522781\pi$
$127$	−1.61171			−0.143016			−0.0715080	+	0.997440i	$0.522781\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.44485	+	16.3590i	−0.825200	+	1.42929i	0.0765658	+	0.997065i	$0.475604\pi$
$131$	−9.44485	+	16.3590i	−0.825200	+	1.42929i	−0.901766	+	0.432224i	$0.857729\pi$
$132$		0			0
$133$	1.67372	−	1.35746i	0.145130	−	0.117706i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.690477	+	0.398647i	−0.0589914	+	0.0340587i	−0.529206	−	0.848494i	$-0.677510\pi$
$137$	−0.690477	+	0.398647i	−0.0589914	+	0.0340587i	0.470214	+	0.882552i	$0.344177\pi$
$138$		0			0
$139$	17.8065			1.51033			0.755164	−	0.655536i	$-0.227557\pi$
$139$	17.8065			1.51033			0.755164	+	0.655536i	$0.227557\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.33509	−	17.2599i	−0.195270	−	1.44334i
$144$		0			0
$145$	0.551320	+	0.318305i	0.0457847	+	0.0264338i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−14.0744	−	8.12586i	−1.15302	−	0.665697i	−0.203399	−	0.979096i	$-0.565199\pi$
$149$	−14.0744	−	8.12586i	−1.15302	−	0.665697i	−0.949621	+	0.313399i	$0.898532\pi$
$150$		0			0
$151$	−11.1879	+	6.45937i	−0.910462	+	0.525656i	−0.880580	−	0.473898i	$-0.842847\pi$
$151$	−11.1879	+	6.45937i	−0.910462	+	0.525656i	−0.0298825	+	0.999553i	$0.509513\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	20.0069			1.60700
$156$		0			0
$157$	−8.21006	−	14.2202i	−0.655234	−	1.13490i	−0.981835	−	0.189737i	$-0.939236\pi$
$157$	−8.21006	−	14.2202i	−0.655234	−	1.13490i	0.326600	−	0.945162i	$-0.394097\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.57079	+	3.16974i	0.202606	+	0.249810i
$162$		0			0
$163$	−17.9514	−	10.3642i	−1.40606	−	0.811789i	−0.411054	−	0.911611i	$-0.634839\pi$
$163$	−17.9514	−	10.3642i	−1.40606	−	0.811789i	−0.995005	+	0.0998224i	$0.968173\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	7.26484i		−	0.562170i	−0.959683	−	0.281085i	$-0.909306\pi$
$167$		−	7.26484i		−	0.562170i	0.959683	−	0.281085i	$-0.0906943\pi$
$168$		0			0
$169$	−9.25787	−	9.12644i	−0.712143	−	0.702034i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.21723	−	7.30445i	0.320630	−	0.555347i	−0.659988	−	0.751276i	$-0.729439\pi$
$173$	4.21723	−	7.30445i	0.320630	−	0.555347i	0.980618	+	0.195929i	$0.0627721\pi$
$174$		0			0
$175$	−31.4375	+	5.00365i	−2.37646	+	0.378241i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.11347	+	14.0529i	0.606429	+	1.05037i	0.991824	+	0.127614i	$0.0407320\pi$
$179$	8.11347	+	14.0529i	0.606429	+	1.05037i	−0.385395	+	0.922752i	$0.625935\pi$
$180$		0			0
$181$	−21.0247			−1.56276			−0.781378	−	0.624058i	$-0.785483\pi$
$181$	−21.0247			−1.56276			−0.781378	+	0.624058i	$0.785483\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.228726	−	0.396165i	−0.0168163	−	0.0291266i
$186$		0			0
$187$	−0.808207	−	0.466619i	−0.0591020	−	0.0341225i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.4343	−	19.8048i	0.827356	−	1.43302i	−0.0727493	−	0.997350i	$-0.523177\pi$
$191$	11.4343	−	19.8048i	0.827356	−	1.43302i	0.900105	−	0.435672i	$-0.143489\pi$
$192$		0			0
$193$	18.4096	−	10.6288i	1.32515	−	0.765076i	0.340605	−	0.940207i	$-0.389368\pi$
$193$	18.4096	−	10.6288i	1.32515	−	0.765076i	0.984545	+	0.175131i	$0.0560349\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			18.0759i			1.28785i	0.765087	+	0.643927i	$0.222696\pi$
$197$			18.0759i			1.28785i	−0.765087	+	0.643927i	$0.777304\pi$
$198$		0			0
$199$	−3.53199	−	6.11758i	−0.250376	−	0.433664i	0.713253	−	0.700906i	$-0.247221\pi$
$199$	−3.53199	−	6.11758i	−0.250376	−	0.433664i	−0.963629	+	0.267243i	$0.913888\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.145970	−	0.381127i	0.0102451	−	0.0267499i
$204$		0			0
$205$	−3.83518	+	6.64273i	−0.267861	+	0.463948i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.93462			0.272164
$210$		0			0
$211$	19.3472			1.33191			0.665956	−	0.745991i	$-0.268024\pi$
$211$	19.3472			1.33191			0.665956	+	0.745991i	$0.268024\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.26453	+	2.46213i	0.290839	+	0.167916i
$216$		0			0
$217$	−2.01607	−	12.6668i	−0.136860	−	0.859877i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.690273	+	0.0933874i	−0.0464328	+	0.00628191i
$222$		0			0
$223$		−	14.4868i		−	0.970105i	−0.874485	−	0.485052i	$-0.838801\pi$
$223$		−	14.4868i		−	0.970105i	0.874485	−	0.485052i	$-0.161199\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	15.9288	−	9.19651i	1.05723	−	0.610394i	0.132567	−	0.991174i	$-0.457678\pi$
$227$	15.9288	−	9.19651i	1.05723	−	0.610394i	0.924666	+	0.380780i	$0.124345\pi$
$228$		0			0
$229$	−19.5505	−	11.2875i	−1.29193	−	0.745898i	−0.312937	−	0.949774i	$-0.601313\pi$
$229$	−19.5505	−	11.2875i	−1.29193	−	0.745898i	−0.978997	+	0.203876i	$0.934646\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.3216	+	17.8776i	−0.676192	+	1.17120i	0.299927	+	0.953962i	$0.403038\pi$
$233$	−10.3216	+	17.8776i	−0.676192	+	1.17120i	−0.976119	+	0.217237i	$0.930296\pi$
$234$		0			0
$235$	−20.2001	−	34.9876i	−1.31771	−	2.28234i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	2.81923i		−	0.182361i	−0.995834	−	0.0911805i	$-0.970936\pi$
$239$		−	2.81923i		−	0.182361i	0.995834	−	0.0911805i	$-0.0290640\pi$
$240$		0			0
$241$	19.2811	−	11.1319i	1.24200	−	0.717070i	0.272501	−	0.962156i	$-0.412149\pi$
$241$	19.2811	−	11.1319i	1.24200	−	0.717070i	0.969502	+	0.245085i	$0.0788159\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.96877	+	27.4613i	0.572993	+	1.75444i
$246$		0			0
$247$	2.32350	−	1.79611i	0.147840	−	0.114284i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	23.5673			1.48755			0.743777	−	0.668428i	$-0.233032\pi$
$251$	23.5673			1.48755			0.743777	+	0.668428i	$0.233032\pi$
$252$		0			0
$253$			7.45149i			0.468471i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.65411	−	8.06115i	0.290315	−	0.502841i	−0.683569	−	0.729886i	$-0.739573\pi$
$257$	4.65411	−	8.06115i	0.290315	−	0.502841i	0.973884	+	0.227045i	$0.0729065\pi$
$258$		0			0
$259$	−0.227772	+	0.184732i	−0.0141530	+	0.0114787i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.70911	+	15.0846i	0.537027	+	0.930158i	0.999062	+	0.0432962i	$0.0137859\pi$
$263$	8.70911	+	15.0846i	0.537027	+	0.930158i	−0.462036	+	0.886861i	$0.652881\pi$
$264$		0			0
$265$			50.6428i			3.11096i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.29695	+	3.97843i	0.140047	+	0.242569i	0.927514	−	0.373788i	$-0.121941\pi$
$269$	2.29695	+	3.97843i	0.140047	+	0.242569i	−0.787467	+	0.616357i	$0.788608\pi$
$270$		0			0
$271$	7.58853	+	4.38124i	0.460970	+	0.266141i	0.712452	−	0.701721i	$-0.247585\pi$
$271$	7.58853	+	4.38124i	0.460970	+	0.266141i	−0.251482	+	0.967862i	$0.580918\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−50.3346	−	29.0607i	−3.03529	−	1.75243i
$276$		0			0
$277$	6.36337	+	11.0217i	0.382338	+	0.662228i	0.991396	−	0.130897i	$-0.0417858\pi$
$277$	6.36337	+	11.0217i	0.382338	+	0.662228i	−0.609058	+	0.793125i	$0.708452\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			22.4986i			1.34215i	0.741388	+	0.671076i	$0.234168\pi$
$281$			22.4986i			1.34215i	−0.741388	+	0.671076i	$0.765832\pi$
$282$		0			0
$283$	−1.08414	−	1.87779i	−0.0644455	−	0.111623i	0.832002	−	0.554772i	$-0.187195\pi$
$283$	−1.08414	−	1.87779i	−0.0644455	−	0.111623i	−0.896448	+	0.443149i	$0.853861\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.59211	+	1.75875i	0.271064	+	0.103816i
$288$		0			0
$289$	8.48134	−	14.6901i	0.498902	−	0.864124i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	26.7146i		−	1.56068i	−0.625353	−	0.780342i	$-0.715045\pi$
$293$		−	26.7146i		−	1.56068i	0.625353	−	0.780342i	$-0.284955\pi$
$294$		0			0
$295$	57.4321			3.34382
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.40152	+	4.40029i	0.196715	+	0.254475i
$300$		0			0
$301$	1.12909	−	2.94807i	0.0650798	−	0.169924i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	18.8649	−	10.8917i	1.08020	−	0.623654i
$306$		0			0
$307$			14.5710i			0.831613i	0.909453	+	0.415806i	$0.136501\pi$
$307$			14.5710i			0.831613i	−0.909453	+	0.415806i	$0.863499\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.1967	+	21.1252i	0.691609	+	1.19790i	0.971311	+	0.237815i	$0.0764311\pi$
$311$	12.1967	+	21.1252i	0.691609	+	1.19790i	−0.279702	+	0.960087i	$0.590236\pi$
$312$		0			0
$313$	−14.9067	+	25.8192i	−0.842578	+	1.45939i	0.0451307	+	0.998981i	$0.485630\pi$
$313$	−14.9067	+	25.8192i	−0.842578	+	1.45939i	−0.887708	+	0.460406i	$0.847704\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.49278	+	1.43921i	0.140008	+	0.0808339i	0.568368	−	0.822774i	$-0.307575\pi$
$317$	2.49278	+	1.43921i	0.140008	+	0.0808339i	−0.428360	+	0.903608i	$0.640908\pi$
$318$		0			0
$319$	0.645324	−	0.372578i	0.0361312	−	0.0208603i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	0.157357i		−	0.00875559i
$324$		0			0
$325$	−42.9898	+	5.81610i	−2.38464	+	0.322619i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−20.1158	+	16.3147i	−1.10902	+	0.899461i
$330$		0			0
$331$	23.9549	+	13.8304i	1.31668	+	0.760186i	0.983193	−	0.182568i	$-0.0584410\pi$
$331$	23.9549	+	13.8304i	1.31668	+	0.760186i	0.333488	+	0.942754i	$0.391774\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−48.3859			−2.64361
$336$		0			0
$337$	12.7657			0.695390			0.347695	−	0.937608i	$-0.386964\pi$
$337$	12.7657			0.695390			0.347695	+	0.937608i	$0.386964\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.7091	−	20.2808i	0.634084	−	1.09827i
$342$		0			0
$343$	16.4825	−	8.44553i	0.889972	−	0.456016i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.90946	−	10.2355i	−0.317237	−	0.549470i	0.662674	−	0.748908i	$-0.269422\pi$
$347$	−5.90946	−	10.2355i	−0.317237	−	0.549470i	−0.979910	+	0.199438i	$0.936088\pi$
$348$		0			0
$349$			3.23665i			0.173254i	0.996241	+	0.0866268i	$0.0276088\pi$
$349$			3.23665i			0.173254i	−0.996241	+	0.0866268i	$0.972391\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−25.5940	+	14.7767i	−1.36223	+	0.786485i	−0.989921	−	0.141623i	$-0.954768\pi$
$353$	−25.5940	+	14.7767i	−1.36223	+	0.786485i	−0.372312	+	0.928108i	$0.621435\pi$
$354$		0			0
$355$	−8.70911	+	15.0846i	−0.462232	+	0.800609i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	22.7413	+	13.1297i	1.20024	+	0.692960i	0.960609	−	0.277904i	$-0.0896397\pi$
$359$	22.7413	+	13.1297i	1.20024	+	0.692960i	0.239633	+	0.970864i	$0.422973\pi$
$360$		0			0
$361$	−9.16828	−	15.8799i	−0.482541	−	0.835786i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.2840			−0.695315
$366$		0			0
$367$	2.77223	+	4.80164i	0.144709	+	0.250644i	0.929264	−	0.369415i	$-0.120442\pi$
$367$	2.77223	+	4.80164i	0.144709	+	0.250644i	−0.784555	+	0.620059i	$0.787109\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	32.0629	−	5.10319i	1.66462	−	0.264945i
$372$		0			0
$373$	0.150644	−	0.260922i	0.00780003	−	0.0135100i	−0.862099	−	0.506740i	$-0.830850\pi$
$373$	0.150644	−	0.260922i	0.00780003	−	0.0135100i	0.869899	+	0.493230i	$0.164184\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.211002	−	0.514600i	0.0108672	−	0.0265032i
$378$		0			0
$379$		−	13.2573i		−	0.680983i	−0.940248	−	0.340491i	$-0.889407\pi$
$379$		−	13.2573i		−	0.680983i	0.940248	−	0.340491i	$-0.110593\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−20.8564	−	12.0414i	−1.06571	−	0.615288i	−0.138704	−	0.990334i	$-0.544294\pi$
$383$	−20.8564	−	12.0414i	−1.06571	−	0.615288i	−0.927006	+	0.375046i	$0.877627\pi$
$384$		0			0
$385$	−18.8649	+	49.2563i	−0.961444	+	2.51033i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.33769	+	12.7093i	0.372036	+	0.644385i	0.989879	−	0.141917i	$-0.0453265\pi$
$389$	7.33769	+	12.7093i	0.372036	+	0.644385i	−0.617843	+	0.786302i	$0.711993\pi$
$390$		0			0
$391$	0.298007			0.0150709
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−41.9188	+	24.2018i	−2.10916	+	1.21773i
$396$		0			0
$397$	−3.98265	−	2.29938i	−0.199883	−	0.115403i	0.396718	−	0.917941i	$-0.370149\pi$
$397$	−3.98265	−	2.29938i	−0.199883	−	0.115403i	−0.596601	+	0.802538i	$0.703483\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	17.4198	+	10.0573i	0.869905	+	0.502240i	0.867317	−	0.497757i	$-0.165843\pi$
$401$	17.4198	+	10.0573i	0.869905	+	0.502240i	0.00258811	+	0.999997i	$0.499176\pi$
$402$		0			0
$403$	−2.34342	−	17.3214i	−0.116734	−	0.862840i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.535450			−0.0265413
$408$		0			0
$409$	−13.6675	+	7.89091i	−0.675812	+	0.390180i	−0.798275	−	0.602293i	$-0.794254\pi$
$409$	−13.6675	+	7.89091i	−0.675812	+	0.390180i	0.122463	+	0.992473i	$0.460921\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−5.78734	−	36.3614i	−0.284776	−	1.78923i
$414$		0			0
$415$	−5.48038	+	9.49230i	−0.269021	+	0.465959i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	20.3544			0.994376			0.497188	−	0.867643i	$-0.334366\pi$
$419$	20.3544			0.994376			0.497188	+	0.867643i	$0.334366\pi$
$420$		0			0
$421$		−	24.9704i		−	1.21698i	−0.793560	−	0.608492i	$-0.791775\pi$
$421$		−	24.9704i		−	1.21698i	0.793560	−	0.608492i	$-0.208225\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.16222	+	2.01303i	−0.0563761	+	0.0976463i
$426$		0			0
$427$	−8.79671	−	10.8462i	−0.425703	−	0.524885i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−17.1157	+	9.88175i	−0.824434	+	0.475987i	−0.851943	−	0.523634i	$-0.824576\pi$
$431$	−17.1157	+	9.88175i	−0.824434	+	0.475987i	0.0275092	+	0.999622i	$0.491242\pi$
$432$		0			0
$433$	26.1982			1.25901			0.629503	−	0.776998i	$-0.283259\pi$
$433$	26.1982			1.25901			0.629503	+	0.776998i	$0.283259\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.08810	+	0.628214i	−0.0520508	+	0.0300516i
$438$		0			0
$439$	−8.97133	+	15.5388i	−0.428178	+	0.741626i	−0.996711	−	0.0810339i	$-0.974178\pi$
$439$	−8.97133	+	15.5388i	−0.428178	+	0.741626i	0.568533	+	0.822660i	$0.307511\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.53199	−	13.0458i	0.357855	−	0.619824i	−0.629747	−	0.776800i	$-0.716841\pi$
$443$	7.53199	−	13.0458i	0.357855	−	0.619824i	0.987602	+	0.156977i	$0.0501747\pi$
$444$		0			0
$445$	10.2322	+	17.7227i	0.485052	+	0.840135i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			14.1148i			0.666116i	0.942906	+	0.333058i	$0.108081\pi$
$449$			14.1148i			0.666116i	−0.942906	+	0.333058i	$0.891919\pi$
$450$		0			0
$451$	4.48910	+	7.77535i	0.211384	+	0.366127i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	11.3448	+	37.6987i	0.531850	+	1.76734i
$456$		0			0
$457$	25.0890	+	14.4852i	1.17361	+	0.677587i	0.954529	−	0.298119i	$-0.0963591\pi$
$457$	25.0890	+	14.4852i	1.17361	+	0.677587i	0.219086	+	0.975706i	$0.429692\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			9.98197i			0.464907i	0.972608	+	0.232453i	$0.0746753\pi$
$461$			9.98197i			0.464907i	−0.972608	+	0.232453i	$0.925325\pi$
$462$		0			0
$463$		−	24.2951i		−	1.12909i	−0.825402	−	0.564545i	$-0.809052\pi$
$463$		−	24.2951i		−	1.12909i	0.825402	−	0.564545i	$-0.190948\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.13819	+	7.16755i	−0.191493	+	0.331675i	−0.945745	−	0.324910i	$-0.894666\pi$
$467$	−4.13819	+	7.16755i	−0.191493	+	0.331675i	0.754253	+	0.656584i	$0.227999\pi$
$468$		0			0
$469$	4.87577	+	30.6341i	0.225142	+	1.41455i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.99166	−	2.88194i	0.229517	−	0.132512i
$474$		0			0
$475$		−	9.80011i		−	0.449660i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	25.2370	−	14.5706i	1.15311	−	0.665747i	0.203465	−	0.979082i	$-0.434780\pi$
$479$	25.2370	−	14.5706i	1.15311	−	0.665747i	0.949643	+	0.313335i	$0.101446\pi$
$480$		0			0
$481$	−0.316197	+	0.244427i	−0.0144173	+	0.0111449i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.46808	+	11.2030i	−0.293700	+	0.508704i
$486$		0			0
$487$	10.6887	−	6.17113i	0.484352	−	0.279641i	−0.237877	−	0.971295i	$-0.576451\pi$
$487$	10.6887	−	6.17113i	0.484352	−	0.279641i	0.722228	+	0.691655i	$0.243118\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	21.8406			0.985650			0.492825	−	0.870128i	$-0.335964\pi$
$491$	21.8406			0.985650			0.492825	+	0.870128i	$0.335964\pi$
$492$		0			0
$493$	−0.0149005	−	0.0258084i	−0.000671084	−	0.00116235i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.4280	+	3.99386i	0.467759	+	0.179149i
$498$		0			0
$499$	−15.4742	−	8.93404i	−0.692721	−	0.399943i	0.111909	−	0.993718i	$-0.464303\pi$
$499$	−15.4742	−	8.93404i	−0.692721	−	0.399943i	−0.804631	+	0.593776i	$0.797637\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.63823			0.162221			0.0811103	−	0.996705i	$-0.474153\pi$
$503$	3.63823			0.162221			0.0811103	+	0.996705i	$0.474153\pi$
$504$		0			0
$505$			14.4593i			0.643430i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.3453	−	8.85962i	−0.680169	−	0.392696i	0.119750	−	0.992804i	$-0.461791\pi$
$509$	−15.3453	−	8.85962i	−0.680169	−	0.392696i	−0.799919	+	0.600108i	$0.795124\pi$
$510$		0			0
$511$	1.33861	+	8.41035i	0.0592164	+	0.372052i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	45.0739	−	26.0234i	1.98619	−	1.14673i
$516$		0			0
$517$	−47.2887			−2.07975
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.81911	−	8.34695i	−0.211129	−	0.365687i	0.740939	−	0.671572i	$-0.234381\pi$
$521$	−4.81911	−	8.34695i	−0.211129	−	0.365687i	−0.952068	+	0.305886i	$0.901047\pi$
$522$		0			0
$523$	−14.6072	+	25.3005i	−0.638729	+	1.10631i	0.346983	+	0.937872i	$0.387206\pi$
$523$	−14.6072	+	25.3005i	−0.638729	+	1.10631i	−0.985712	+	0.168440i	$0.946127\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.811088	−	0.468282i	−0.0353316	−	0.0203987i
$528$		0			0
$529$	10.3103	+	17.8579i	0.448273	+	0.776431i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.20029	+	2.54232i	0.268564	+	0.110120i
$534$		0			0
$535$	21.1903	−	12.2342i	0.916138	−	0.528932i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	33.0861	+	6.98026i	1.42512	+	0.300661i
$540$		0			0
$541$	−10.8456	−	6.26173i	−0.466290	−	0.269213i	0.248395	−	0.968659i	$-0.420097\pi$
$541$	−10.8456	−	6.26173i	−0.466290	−	0.269213i	−0.714685	+	0.699446i	$0.753430\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−81.0062			−3.46992
$546$		0			0
$547$	−25.0456			−1.07087			−0.535436	−	0.844576i	$-0.679853\pi$
$547$	−25.0456			−1.07087			−0.535436	+	0.844576i	$0.679853\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.108811	+	0.0628220i	0.00463550	+	0.00267631i
$552$		0			0
$553$	19.5468	+	24.1009i	0.831213	+	1.02487i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−20.7745	+	11.9942i	−0.880244	+	0.508209i	−0.870739	−	0.491746i	$-0.836359\pi$
$557$	−20.7745	+	11.9942i	−0.880244	+	0.508209i	−0.00950510	+	0.999955i	$0.503026\pi$
$558$		0			0
$559$	1.63213	−	3.98049i	0.0690318	−	0.168357i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.98944	−	8.64196i	−0.210280	−	0.364215i	0.741522	−	0.670928i	$-0.234104\pi$
$563$	−4.98944	−	8.64196i	−0.210280	−	0.364215i	−0.951802	+	0.306713i	$0.900771\pi$
$564$		0			0
$565$	−58.0393	−	33.5090i	−2.44173	−	1.40973i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.82368	+	10.0869i	−0.244141	+	0.422865i	−0.961890	−	0.273437i	$-0.911839\pi$
$569$	−5.82368	+	10.0869i	−0.244141	+	0.422865i	0.717748	+	0.696303i	$0.245173\pi$
$570$		0			0
$571$	−5.89435	−	10.2093i	−0.246671	−	0.427247i	0.715929	−	0.698173i	$-0.246003\pi$
$571$	−5.89435	−	10.2093i	−0.246671	−	0.427247i	−0.962600	+	0.270926i	$0.912670\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	18.5597			0.773992
$576$		0			0
$577$	26.4357	−	15.2627i	1.10053	−	0.635392i	0.164171	−	0.986432i	$-0.447505\pi$
$577$	26.4357	−	15.2627i	1.10053	−	0.635392i	0.936361	+	0.351039i	$0.114172\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.56202	+	2.51322i	0.272238	+	0.104266i
$582$		0			0
$583$	51.3359	+	29.6388i	2.12612	+	1.22751i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	9.85549i		−	0.406780i	−0.979098	−	0.203390i	$-0.934804\pi$
$587$		−	9.85549i		−	0.406780i	0.979098	−	0.203390i	$-0.0651959\pi$
$588$		0			0
$589$	3.94865			0.162701
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.96865	−	2.86865i	−0.204038	−	0.117802i	0.394499	−	0.918896i	$-0.370918\pi$
$593$	−4.96865	−	2.86865i	−0.204038	−	0.117802i	−0.598538	+	0.801095i	$0.704251\pi$
$594$		0			0
$595$	1.96991	+	0.754463i	0.0807583	+	0.0309300i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−17.4962	−	30.3042i	−0.714873	−	1.23820i	−0.963008	−	0.269472i	$-0.913151\pi$
$599$	−17.4962	−	30.3042i	−0.714873	−	1.23820i	0.248135	−	0.968726i	$-0.420182\pi$
$600$		0			0
$601$	−12.9037			−0.526354			−0.263177	−	0.964748i	$-0.584770\pi$
$601$	−12.9037			−0.526354			−0.263177	+	0.964748i	$0.584770\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−44.0861	+	25.4531i	−1.79235	+	1.03482i
$606$		0			0
$607$	9.54334	−	16.5295i	0.387352	−	0.670914i	−0.604740	−	0.796423i	$-0.706723\pi$
$607$	9.54334	−	16.5295i	0.387352	−	0.670914i	0.992092	+	0.125509i	$0.0400564\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−27.9252	+	21.5868i	−1.12973	+	0.873307i
$612$		0			0
$613$	−4.85487	+	2.80296i	−0.196086	+	0.113210i	−0.594829	−	0.803853i	$-0.702780\pi$
$613$	−4.85487	+	2.80296i	−0.196086	+	0.113210i	0.398742	+	0.917063i	$0.369447\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	28.9162i		−	1.16412i	−0.813146	−	0.582060i	$-0.802247\pi$
$617$		−	28.9162i		−	1.16412i	0.813146	−	0.582060i	$-0.197753\pi$
$618$		0			0
$619$	12.8975	−	7.44636i	0.518393	−	0.299295i	−0.217884	−	0.975975i	$-0.569915\pi$
$619$	12.8975	−	7.44636i	0.518393	−	0.299295i	0.736277	+	0.676680i	$0.236582\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.1895	−	8.26409i	0.408233	−	0.331094i
$624$		0			0
$625$	−29.8030	+	51.6202i	−1.19212	+	2.06481i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			0.0214142i			0.000853842i
$630$		0			0
$631$			12.2217i			0.486539i	0.969959	+	0.243269i	$0.0782199\pi$
$631$			12.2217i			0.486539i	−0.969959	+	0.243269i	$0.921780\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.76034	+	3.32573i	0.228592	+	0.131978i
$636$		0			0
$637$	22.7246	−	10.9814i	0.900382	−	0.435100i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−11.7231	−	20.3051i	−0.463036	−	0.802002i	0.536074	−	0.844171i	$-0.319907\pi$
$641$	−11.7231	−	20.3051i	−0.463036	−	0.802002i	−0.999111	+	0.0421687i	$0.986573\pi$
$642$		0			0
$643$		−	19.7831i		−	0.780171i	−0.920779	−	0.390085i	$-0.872445\pi$
$643$		−	19.7831i		−	0.780171i	0.920779	−	0.390085i	$-0.127555\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.0779	−	22.6516i	−0.514147	−	0.890528i	−0.999865	−	0.0164129i	$-0.994775\pi$
$647$	−13.0779	−	22.6516i	−0.514147	−	0.890528i	0.485719	−	0.874115i	$-0.338558\pi$
$648$		0			0
$649$	33.6123	−	58.2182i	1.31940	−	2.28526i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.27113	−	2.20165i	0.0497430	−	0.0861574i	−0.840082	−	0.542460i	$-0.817493\pi$
$653$	1.27113	−	2.20165i	0.0497430	−	0.0861574i	0.889825	+	0.456302i	$0.150826\pi$
$654$		0			0
$655$	67.5128	−	38.9786i	2.63795	−	1.52302i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−16.6064			−0.646893			−0.323447	−	0.946246i	$-0.604842\pi$
$659$	−16.6064			−0.646893			−0.323447	+	0.946246i	$0.604842\pi$
$660$		0			0
$661$	15.3340	−	8.85309i	0.596424	−	0.344345i	−0.171210	−	0.985235i	$-0.554768\pi$
$661$	15.3340	−	8.85309i	0.596424	−	0.344345i	0.767633	+	0.640889i	$0.221434\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.78307	+	1.39793i	−0.340593	+	0.0542094i
$666$		0			0
$667$	−0.118974	+	0.206069i	−0.00460668	+	0.00797901i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	25.4975i		−	0.984319i
$672$		0			0
$673$	−36.7173			−1.41535			−0.707675	−	0.706538i	$-0.750256\pi$
$673$	−36.7173			−1.41535			−0.707675	+	0.706538i	$0.750256\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.2385	+	40.2503i	−0.893128	+	1.54694i	−0.0570239	+	0.998373i	$0.518161\pi$
$677$	−23.2385	+	40.2503i	−0.893128	+	1.54694i	−0.836104	+	0.548571i	$0.815172\pi$
$678$		0			0
$679$	7.74464	+	2.96616i	0.297212	+	0.113831i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	22.1111	−	12.7658i	0.846057	−	0.488471i	−0.0132613	−	0.999912i	$-0.504221\pi$
$683$	22.1111	−	12.7658i	0.846057	−	0.488471i	0.859319	+	0.511441i	$0.170888\pi$
$684$		0			0
$685$	3.29040			0.125720
$686$		0			0
$687$		0			0
$688$		0			0
$689$	43.8450	−	5.93181i	1.67036	−	0.225984i
$690$		0			0
$691$	10.2064	+	5.89267i	0.388270	+	0.224168i	0.681410	−	0.731902i	$-0.261367\pi$
$691$	10.2064	+	5.89267i	0.388270	+	0.224168i	−0.293140	+	0.956069i	$0.594700\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−63.6415	−	36.7434i	−2.41406	−	1.39376i
$696$		0			0
$697$	0.310959	−	0.179532i	0.0117784	−	0.00680028i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−35.6275			−1.34563			−0.672816	−	0.739810i	$-0.734915\pi$
$701$	−35.6275			−1.34563			−0.672816	+	0.739810i	$0.734915\pi$
$702$		0			0
$703$	−0.0451423	−	0.0781888i	−0.00170257	−	0.00294895i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.15446	−	1.45704i	0.344289	−	0.0547976i
$708$		0			0
$709$	−25.4099	−	14.6704i	−0.954289	−	0.550959i	−0.0598786	−	0.998206i	$-0.519071\pi$
$709$	−25.4099	−	14.6704i	−0.954289	−	0.550959i	−0.894411	+	0.447246i	$0.852405\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			7.47805i			0.280055i
$714$		0			0
$715$	−27.2697	+	66.5061i	−1.01983	+	2.48719i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.3686	+	33.5474i	−0.722327	+	1.25111i	0.237738	+	0.971329i	$0.423594\pi$
$719$	−19.3686	+	33.5474i	−0.722327	+	1.25111i	−0.960065	+	0.279777i	$0.909739\pi$
$720$		0			0
$721$	−21.0180	−	25.9148i	−0.782750	−	0.965119i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.927993	−	1.60733i	−0.0344648	−	0.0596948i
$726$		0			0
$727$	13.3601			0.495498			0.247749	−	0.968824i	$-0.420309\pi$
$727$	13.3601			0.495498			0.247749	+	0.968824i	$0.420309\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.115257	−	0.199631i	−0.00426294	−	0.00738363i
$732$		0			0
$733$	9.51541	+	5.49372i	0.351460	+	0.202915i	0.665328	−	0.746551i	$-0.268292\pi$
$733$	9.51541	+	5.49372i	0.351460	+	0.202915i	−0.313868	+	0.949467i	$0.601625\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−28.3180	+	49.0482i	−1.04311	+	1.80671i
$738$		0			0
$739$	−0.706969	+	0.408169i	−0.0260063	+	0.0150147i	−0.512947	−	0.858420i	$-0.671446\pi$
$739$	−0.706969	+	0.408169i	−0.0260063	+	0.0150147i	0.486940	+	0.873435i	$0.338113\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			11.1384i			0.408628i	0.978905	+	0.204314i	$0.0654964\pi$
$743$			11.1384i			0.408628i	−0.978905	+	0.204314i	$0.934504\pi$
$744$		0			0
$745$	33.5352	+	58.0846i	1.22863	+	2.12805i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−9.88106	−	12.1832i	−0.361046	−	0.445164i
$750$		0			0
$751$	−2.32003	+	4.01841i	−0.0846591	+	0.146634i	−0.905246	−	0.424888i	$-0.860313\pi$
$751$	−2.32003	+	4.01841i	−0.0846591	+	0.146634i	0.820587	+	0.571522i	$0.193647\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	53.3151			1.94034
$756$		0			0
$757$	−18.7608			−0.681872			−0.340936	−	0.940087i	$-0.610744\pi$
$757$	−18.7608			−0.681872			−0.340936	+	0.940087i	$0.610744\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.6334	−	6.71655i	−0.421710	−	0.243475i	0.274098	−	0.961702i	$-0.411621\pi$
$761$	−11.6334	−	6.71655i	−0.421710	−	0.243475i	−0.695809	+	0.718227i	$0.744954\pi$
$762$		0			0
$763$	8.16287	+	51.2866i	0.295516	+	1.85670i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.72704	−	49.7229i	−0.242899	−	1.79539i
$768$		0			0
$769$		−	41.4834i		−	1.49593i	−0.663738	−	0.747965i	$-0.731031\pi$
$769$		−	41.4834i		−	1.49593i	0.663738	−	0.747965i	$-0.268969\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.16020	−	0.669841i	0.0417294	−	0.0240925i	−0.478990	−	0.877820i	$-0.658997\pi$
$773$	1.16020	−	0.669841i	0.0417294	−	0.0240925i	0.520720	+	0.853728i	$0.325664\pi$
$774$		0			0
$775$	−50.5141	−	29.1643i	−1.81452	−	1.04761i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.756927	+	1.31104i	−0.0271197	+	0.0469728i
$780$		0			0
$781$	10.1941	+	17.6566i	0.364772	+	0.631804i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			67.7653i			2.41865i
$786$		0			0
$787$	−20.6947	+	11.9481i	−0.737687	+	0.425904i	−0.821228	−	0.570600i	$-0.806711\pi$
$787$	−20.6947	+	11.9481i	−0.737687	+	0.425904i	0.0835406	+	0.996504i	$0.473377\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−15.3667	+	40.1225i	−0.546376	+	1.42659i
$792$		0			0
$793$	−11.6393	−	15.0569i	−0.413324	−	0.534687i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−48.8615			−1.73076			−0.865382	−	0.501113i	$-0.832924\pi$
$797$	−48.8615			−1.73076			−0.865382	+	0.501113i	$0.832924\pi$
$798$		0			0
$799$			1.89122i			0.0669064i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.77449	+	13.4658i	−0.274356	+	0.475198i
$804$		0			0
$805$	−2.64743	−	16.6336i	−0.0933097	−	0.586257i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.80564	−	6.59157i	−0.133799	−	0.231747i	0.791339	−	0.611378i	$-0.209384\pi$
$809$	−3.80564	−	6.59157i	−0.133799	−	0.231747i	−0.925138	+	0.379631i	$0.876051\pi$
$810$		0			0
$811$			45.4292i			1.59523i	0.603165	+	0.797617i	$0.293906\pi$
$811$			45.4292i			1.59523i	−0.603165	+	0.797617i	$0.706094\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	42.7728	+	74.0846i	1.49827	+	2.59507i
$816$		0			0
$817$	0.841666	+	0.485936i	0.0294462	+	0.0170008i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.84693	−	1.64368i	−0.0993585	−	0.0573647i	0.449497	−	0.893282i	$-0.351603\pi$
$821$	−2.84693	−	1.64368i	−0.0993585	−	0.0573647i	−0.548856	+	0.835917i	$0.684936\pi$
$822$		0			0
$823$	−15.5599	−	26.9505i	−0.542383	−	0.939435i	−0.998767	−	0.0496519i	$-0.984189\pi$
$823$	−15.5599	−	26.9505i	−0.542383	−	0.939435i	0.456383	−	0.889783i	$-0.349145\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			25.6551i			0.892116i	0.895004	+	0.446058i	$0.147173\pi$
$827$			25.6551i			0.892116i	−0.895004	+	0.446058i	$0.852827\pi$
$828$		0			0
$829$	−20.5815	−	35.6481i	−0.714824	−	1.23811i	−0.963027	−	0.269403i	$-0.913174\pi$
$829$	−20.5815	−	35.6481i	−0.714824	−	1.23811i	0.248204	−	0.968708i	$-0.420160\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.279161	−	1.32321i	0.00967236	−	0.0458466i
$834$		0			0
$835$	−14.9909	+	25.9649i	−0.518780	+	0.898554i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	23.9529i		−	0.826946i	−0.910516	−	0.413473i	$-0.864316\pi$
$839$		−	23.9529i		−	0.826946i	0.910516	−	0.413473i	$-0.135684\pi$
$840$		0			0
$841$	−28.9762			−0.999179
$842$		0			0
$843$		0			0
$844$		0			0
$845$	14.2559	+	51.7219i	0.490417	+	1.77929i
$846$		0			0
$847$	20.5574	+	25.3469i	0.706359	+	0.870930i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.148076	−	0.0854916i	0.00507597	−	0.00293061i
$852$		0			0
$853$			22.4638i			0.769145i	0.923095	+	0.384572i	$0.125651\pi$
$853$			22.4638i			0.769145i	−0.923095	+	0.384572i	$0.874349\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.0366373	+	0.0634577i	0.00125151	+	0.00216767i	0.866650	−	0.498916i	$-0.166268\pi$
$857$	0.0366373	+	0.0634577i	0.00125151	+	0.00216767i	−0.865399	+	0.501083i	$0.832935\pi$
$858$		0			0
$859$	16.7303	−	28.9777i	0.570830	−	0.988707i	−0.425651	−	0.904888i	$-0.639955\pi$
$859$	16.7303	−	28.9777i	0.570830	−	0.988707i	0.996481	−	0.0838196i	$-0.0267120\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	21.7166	+	12.5381i	0.739240	+	0.426800i	0.821793	−	0.569786i	$-0.192974\pi$
$863$	21.7166	+	12.5381i	0.739240	+	0.426800i	−0.0825529	+	0.996587i	$0.526307\pi$
$864$		0			0
$865$	−30.1452	+	17.4043i	−1.02497	+	0.591765i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			56.6568i			1.92195i
$870$		0			0
$871$	5.66746	+	41.8911i	0.192035	+	1.41942i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	71.7012	+	27.4612i	2.42394	+	0.928357i
$876$		0			0
$877$	14.5232	+	8.38499i	0.490414	+	0.283141i	0.724746	−	0.689016i	$-0.241957\pi$
$877$	14.5232	+	8.38499i	0.490414	+	0.283141i	−0.234332	+	0.972157i	$0.575290\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	18.0174			0.607023			0.303511	−	0.952828i	$-0.401841\pi$
$881$	18.0174			0.607023			0.303511	+	0.952828i	$0.401841\pi$
$882$		0			0
$883$	−22.5443			−0.758676			−0.379338	−	0.925258i	$-0.623848\pi$
$883$	−22.5443			−0.758676			−0.379338	+	0.925258i	$0.623848\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.51245	−	11.2799i	0.218667	−	0.378742i	−0.735734	−	0.677271i	$-0.763163\pi$
$887$	6.51245	−	11.2799i	0.218667	−	0.378742i	0.954401	+	0.298529i	$0.0964959\pi$
$888$		0			0
$889$	1.52513	−	3.98211i	0.0511511	−	0.133556i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.98678	−	6.90530i	−0.133412	−	0.231077i
$894$		0			0
$895$		−	66.9680i		−	2.23849i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.647624	−	0.373906i	0.0215995	−	0.0124705i
$900$		0			0
$901$	1.18534	−	2.05308i	0.0394895	−	0.0683979i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	75.1436	+	43.3842i	2.49786	+	1.44214i
$906$		0			0
$907$	12.8678	+	22.2877i	0.427268	+	0.740050i	0.996629	−	0.0820378i	$-0.0261428\pi$
$907$	12.8678	+	22.2877i	0.427268	+	0.740050i	−0.569361	+	0.822087i	$0.692809\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−30.1342			−0.998392			−0.499196	−	0.866489i	$-0.666371\pi$
$911$	−30.1342			−0.998392			−0.499196	+	0.866489i	$0.666371\pi$
$912$		0			0
$913$	6.41482	+	11.1108i	0.212300	+	0.367714i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−31.4813	−	38.8159i	−1.03960	−	1.28181i
$918$		0			0
$919$	28.8942	−	50.0462i	0.953131	−	1.65087i	0.214543	−	0.976715i	$-0.431174\pi$
$919$	28.8942	−	50.0462i	0.953131	−	1.65087i	0.738588	−	0.674157i	$-0.235493\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	14.0799	+	5.77322i	0.463446	+	0.190028i
$924$		0			0
$925$			1.33367i			0.0438506i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.44066	−	1.98647i	−0.112884	−	0.0651739i	0.442495	−	0.896771i	$-0.354094\pi$
$929$	−3.44066	−	1.98647i	−0.112884	−	0.0651739i	−0.555379	+	0.831597i	$0.687427\pi$
$930$		0			0
$931$	1.77011	+	5.41987i	0.0580131	+	0.177629i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.92572	+	3.33544i	0.0629777	+	0.109081i
$936$		0			0
$937$	−14.0852			−0.460144			−0.230072	−	0.973174i	$-0.573896\pi$
$937$	−14.0852			−0.460144			−0.230072	+	0.973174i	$0.573896\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.38168	−	0.797711i	0.0450414	−	0.0260046i	−0.477310	−	0.878735i	$-0.658388\pi$
$941$	1.38168	−	0.797711i	0.0450414	−	0.0260046i	0.522352	+	0.852730i	$0.325055\pi$
$942$		0			0
$943$	−2.48287	−	1.43349i	−0.0808535	−	0.0466808i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.86720	−	1.07803i	−0.0606759	−	0.0350312i	0.469355	−	0.883009i	$-0.344486\pi$
$947$	−1.86720	−	1.07803i	−0.0606759	−	0.0350312i	−0.530031	+	0.847978i	$0.677820\pi$
$948$		0			0
$949$	1.55596	+	11.5009i	0.0505085	+	0.373334i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	34.4024			1.11440			0.557202	−	0.830377i	$-0.311875\pi$
$953$	34.4024			1.11440			0.557202	+	0.830377i	$0.311875\pi$
$954$		0			0
$955$	−81.7336	+	47.1889i	−2.64484	+	1.52700i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.331569	−	2.08322i	−0.0107069	−	0.0672707i
$960$		0			0
$961$	−3.74915	+	6.49371i	−0.120940	+	0.209475i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−87.7291			−2.82410
$966$		0			0
$967$			41.1646i			1.32376i	0.749609	+	0.661881i	$0.230242\pi$
$967$			41.1646i			1.32376i	−0.749609	+	0.661881i	$0.769758\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.66677	−	9.81514i	0.181855	−	0.314983i	−0.760657	−	0.649154i	$-0.775123\pi$
$971$	5.66677	−	9.81514i	0.181855	−	0.314983i	0.942512	+	0.334171i	$0.108456\pi$
$972$		0			0
$973$	−16.8499	+	43.9953i	−0.540184	+	1.41042i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.8932	−	6.28922i	0.348506	−	0.201210i	−0.315521	−	0.948919i	$-0.602179\pi$
$977$	10.8932	−	6.28922i	0.348506	−	0.201210i	0.664027	+	0.747709i	$0.268846\pi$
$978$		0			0
$979$	23.9537			0.765563
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.93090	+	3.42421i	−0.189166	+	0.109215i	−0.591592	−	0.806237i	$-0.701500\pi$
$983$	−5.93090	+	3.42421i	−0.189166	+	0.109215i	0.402426	+	0.915453i	$0.368167\pi$
$984$		0			0
$985$	37.2993	−	64.6042i	1.18845	−	2.05846i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.920277	+	1.59397i	−0.0292631	+	0.0506852i
$990$		0			0
$991$	−9.03445	−	15.6481i	−0.286989	−	0.497079i	0.686101	−	0.727506i	$-0.259321\pi$
$991$	−9.03445	−	15.6481i	−0.286989	−	0.497079i	−0.973090	+	0.230427i	$0.925988\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			29.1528i			0.924205i
$996$		0			0
$997$	−21.0105	−	36.3912i	−0.665409	−	1.15252i	−0.979174	−	0.203021i	$-0.934924\pi$
$997$	−21.0105	−	36.3912i	−0.665409	−	1.15252i	0.313766	−	0.949500i	$-0.398409\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3276.2.gv.g.2053.1		20
3.2	odd	2		1092.2.cu.c.961.10	yes	20
7.4	even	3	inner	3276.2.gv.g.1117.10		20
13.12	even	2	inner	3276.2.gv.g.2053.10		20
21.2	odd	6		7644.2.e.o.4705.1		10
21.5	even	6		7644.2.e.n.4705.10		10
21.11	odd	6		1092.2.cu.c.25.1	✓	20
39.38	odd	2		1092.2.cu.c.961.1	yes	20
91.25	even	6	inner	3276.2.gv.g.1117.1		20
273.116	odd	6		1092.2.cu.c.25.10	yes	20
273.194	even	6		7644.2.e.n.4705.1		10
273.233	odd	6		7644.2.e.o.4705.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1092.2.cu.c.25.1	✓	20	21.11	odd	6
1092.2.cu.c.25.10	yes	20	273.116	odd	6
1092.2.cu.c.961.1	yes	20	39.38	odd	2
1092.2.cu.c.961.10	yes	20	3.2	odd	2
3276.2.gv.g.1117.1		20	91.25	even	6	inner
3276.2.gv.g.1117.10		20	7.4	even	3	inner
3276.2.gv.g.2053.1		20	1.1	even	1	trivial
3276.2.gv.g.2053.10		20	13.12	even	2	inner
7644.2.e.n.4705.1		10	273.194	even	6
7644.2.e.n.4705.10		10	21.5	even	6
7644.2.e.o.4705.1		10	21.2	odd	6
7644.2.e.o.4705.10		10	273.233	odd	6

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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.gv (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.57406 - 2.06348i) q^{5} +(-0.946280 + 2.47074i) q^{7} +(-4.18345 + 2.41532i) q^{11} +(-1.36787 + 3.33601i) q^{13} +(0.0965957 + 0.167309i) q^{17} +(-0.705391 - 0.407257i) q^{19} +(0.771274 - 1.33589i) q^{23} +(6.01592 + 10.4199i) q^{25} -0.154256 q^{29} +(-4.19837 + 2.42393i) q^{31} +(8.48038 - 6.87793i) q^{35} +(0.0959943 + 0.0554223i) q^{37} -1.85860i q^{41} -1.19319 q^{43} +(8.47781 + 4.89467i) q^{47} +(-5.20911 - 4.67602i) q^{49} +(-6.13559 - 10.6272i) q^{53} +19.9359 q^{55} +(-12.0519 + 6.95815i) q^{59} +(-2.63914 + 4.57113i) q^{61} +(11.7726 - 9.10050i) q^{65} +(10.1536 - 5.86217i) q^{67} -4.22059i q^{71} +(2.78758 - 1.60941i) q^{73} +(-2.00891 - 12.6218i) q^{77} +(5.86432 - 10.1573i) q^{79} -2.65589i q^{83} -0.797294i q^{85} +(-4.29436 - 2.47935i) q^{89} +(-6.94801 - 6.53644i) q^{91} +(1.68074 + 2.91112i) q^{95} -3.13454i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{13} - 4 q^{17} - 8 q^{23} + 24 q^{25} + 4 q^{29} + 38 q^{35} - 12 q^{43} + 4 q^{49} + 24 q^{53} - 24 q^{55} + 12 q^{65} - 26 q^{77} - 6 q^{79} - 7 q^{91} - 58 q^{95}+O(q^{100}) \) 20 * q + 2 * q^13 - 4 * q^17 - 8 * q^23 + 24 * q^25 + 4 * q^29 + 38 * q^35 - 12 * q^43 + 4 * q^49 + 24 * q^53 - 24 * q^55 + 12 * q^65 - 26 * q^77 - 6 * q^79 - 7 * q^91 - 58 * q^95

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