LMFDB - Embedded newform 936.2.t.f.217.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(217,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.217"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.t (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,6,0,1] 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			217.1
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	936.217
Dual form			936.2.t.f.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-0.561553 q^{5} +(-0.780776 - 1.35234i) q^{7} +(-0.780776 + 1.35234i) q^{11} +(-2.84233 + 2.21837i) q^{13} +(-2.50000 - 4.33013i) q^{17} +(-0.780776 - 1.35234i) q^{19} +(4.34233 - 7.52113i) q^{23} -4.68466 q^{25} +(-2.50000 + 4.33013i) q^{29} -8.00000 q^{31} +(0.438447 + 0.759413i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-3.62311 + 6.27540i) q^{41} +(1.21922 + 2.11176i) q^{43} -4.00000 q^{47} +(2.28078 - 3.95042i) q^{49} -8.56155 q^{53} +(0.438447 - 0.759413i) q^{55} +(0.780776 + 1.35234i) q^{59} +(-4.62311 - 8.00745i) q^{61} +(1.59612 - 1.24573i) q^{65} +(6.78078 - 11.7446i) q^{67} +(-2.34233 - 4.05703i) q^{71} -13.6847 q^{73} +2.43845 q^{77} -4.00000 q^{79} +14.2462 q^{83} +(1.40388 + 2.43160i) q^{85} +(1.34233 - 2.32498i) q^{89} +(5.21922 + 2.11176i) q^{91} +(0.438447 + 0.759413i) q^{95} +(8.90388 + 15.4220i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{5} + q^{7} + q^{11} + q^{13} - 10 q^{17} + q^{19} + 5 q^{23} + 6 q^{25} - 10 q^{29} - 32 q^{31} + 10 q^{35} + 2 q^{37} + 2 q^{41} + 9 q^{43} - 16 q^{47} + 5 q^{49} - 26 q^{53} + 10 q^{55}+ \cdots + 15 q^{97}+O(q^{100}) $ 4 * q + 6 * q^5 + q^7 + q^11 + q^13 - 10 * q^17 + q^19 + 5 * q^23 + 6 * q^25 - 10 * q^29 - 32 * q^31 + 10 * q^35 + 2 * q^37 + 2 * q^41 + 9 * q^43 - 16 * q^47 + 5 * q^49 - 26 * q^53 + 10 * q^55 - q^59 - 2 * q^61 + 27 * q^65 + 23 * q^67 + 3 * q^71 - 30 * q^73 + 18 * q^77 - 16 * q^79 + 24 * q^83 - 15 * q^85 - 7 * q^89 + 25 * q^91 + 10 * q^95 + 15 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$5$	−0.561553			−0.251134			−0.125567	−	0.992085i	$-0.540075\pi$
$5$	−0.561553			−0.251134			−0.125567	+	0.992085i	$0.540075\pi$
$6$		0			0
$7$	−0.780776	−	1.35234i	−0.295106	−	0.511138i	0.679904	−	0.733301i	$-0.262022\pi$
$7$	−0.780776	−	1.35234i	−0.295106	−	0.511138i	−0.975009	+	0.222163i	$0.928688\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.780776	+	1.35234i	−0.235413	+	0.407747i	−0.959393	−	0.282074i	$-0.908978\pi$
$11$	−0.780776	+	1.35234i	−0.235413	+	0.407747i	0.723980	+	0.689821i	$0.242311\pi$
$12$		0			0
$13$	−2.84233	+	2.21837i	−0.788320	+	0.615265i
$13$	−2.84233	+	2.21837i	−0.788320	+	0.615265i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	−0.991838	−	0.127502i	$-0.959304\pi$
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	0.385499	−	0.922708i	$-0.374029\pi$
$18$		0			0
$19$	−0.780776	−	1.35234i	−0.179122	−	0.310249i	0.762458	−	0.647038i	$-0.223992\pi$
$19$	−0.780776	−	1.35234i	−0.179122	−	0.310249i	−0.941580	+	0.336789i	$0.890659\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.34233	−	7.52113i	0.905438	−	1.56827i	0.0851104	−	0.996372i	$-0.472876\pi$
$23$	4.34233	−	7.52113i	0.905438	−	1.56827i	0.820328	−	0.571893i	$-0.193791\pi$
$24$		0			0
$25$	−4.68466			−0.936932
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	−0.999167	−	0.0408130i	$-0.987005\pi$
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	0.534928	+	0.844897i	$0.320339\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.438447	+	0.759413i	0.0741111	+	0.128364i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.62311	+	6.27540i	−0.565834	+	0.980053i	0.431138	+	0.902286i	$0.358112\pi$
$41$	−3.62311	+	6.27540i	−0.565834	+	0.980053i	−0.996972	+	0.0777671i	$0.975221\pi$
$42$		0			0
$43$	1.21922	+	2.11176i	0.185930	+	0.322040i	0.943889	−	0.330262i	$-0.107137\pi$
$43$	1.21922	+	2.11176i	0.185930	+	0.322040i	−0.757960	+	0.652301i	$0.773804\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.00000			−0.583460			−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000			−0.583460			−0.291730	+	0.956501i	$0.594231\pi$
$48$		0			0
$49$	2.28078	−	3.95042i	0.325825	−	0.564346i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.56155			−1.17602			−0.588010	−	0.808854i	$-0.700088\pi$
$53$	−8.56155			−1.17602			−0.588010	+	0.808854i	$0.700088\pi$
$54$		0			0
$55$	0.438447	−	0.759413i	0.0591202	−	0.102399i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.780776	+	1.35234i	0.101648	+	0.176060i	0.912364	−	0.409380i	$-0.134255\pi$
$59$	0.780776	+	1.35234i	0.101648	+	0.176060i	−0.810716	+	0.585440i	$0.800922\pi$
$60$		0			0
$61$	−4.62311	−	8.00745i	−0.591928	−	1.02525i	−0.993973	−	0.109629i	$-0.965034\pi$
$61$	−4.62311	−	8.00745i	−0.591928	−	1.02525i	0.402045	−	0.915620i	$-0.368300\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.59612	−	1.24573i	0.197974	−	0.154514i
$66$		0			0
$67$	6.78078	−	11.7446i	0.828404	−	1.43484i	−0.0708863	−	0.997484i	$-0.522583\pi$
$67$	6.78078	−	11.7446i	0.828404	−	1.43484i	0.899290	−	0.437353i	$-0.144084\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.34233	−	4.05703i	−0.277983	−	0.481481i	0.692900	−	0.721034i	$-0.256333\pi$
$71$	−2.34233	−	4.05703i	−0.277983	−	0.481481i	−0.970883	+	0.239552i	$0.922999\pi$
$72$		0			0
$73$	−13.6847			−1.60167			−0.800834	−	0.598886i	$-0.795610\pi$
$73$	−13.6847			−1.60167			−0.800834	+	0.598886i	$0.795610\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.43845			0.277887
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	14.2462			1.56372			0.781862	−	0.623451i	$-0.214270\pi$
$83$	14.2462			1.56372			0.781862	+	0.623451i	$0.214270\pi$
$84$		0			0
$85$	1.40388	+	2.43160i	0.152272	+	0.263744i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.34233	−	2.32498i	0.142287	−	0.246448i	−0.786071	−	0.618137i	$-0.787888\pi$
$89$	1.34233	−	2.32498i	0.142287	−	0.246448i	0.928357	+	0.371689i	$0.121221\pi$
$90$		0			0
$91$	5.21922	+	2.11176i	0.547123	+	0.221372i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.438447	+	0.759413i	0.0449837	+	0.0779141i
$96$		0			0
$97$	8.90388	+	15.4220i	0.904052	+	1.56586i	0.822184	+	0.569221i	$0.192755\pi$
$97$	8.90388	+	15.4220i	0.904052	+	1.56586i	0.0818678	+	0.996643i	$0.473911\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.62311	+	9.73950i	−0.559520	+	0.969117i	0.438017	+	0.898967i	$0.355681\pi$
$101$	−5.62311	+	9.73950i	−0.559520	+	0.969117i	−0.997536	+	0.0701500i	$0.977652\pi$
$102$		0			0
$103$	−2.24621			−0.221326			−0.110663	−	0.993858i	$-0.535297\pi$
$103$	−2.24621			−0.221326			−0.110663	+	0.993858i	$0.535297\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.34233	−	7.52113i	0.419789	−	0.727096i	−0.576129	−	0.817359i	$-0.695437\pi$
$107$	4.34233	−	7.52113i	0.419789	−	0.727096i	0.995918	+	0.0902631i	$0.0287708\pi$
$108$		0			0
$109$	−8.24621			−0.789844			−0.394922	−	0.918715i	$-0.629228\pi$
$109$	−8.24621			−0.789844			−0.394922	+	0.918715i	$0.629228\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.62311	−	6.27540i	−0.340833	−	0.590340i	0.643755	−	0.765232i	$-0.277376\pi$
$113$	−3.62311	−	6.27540i	−0.340833	−	0.590340i	−0.984588	+	0.174892i	$0.944042\pi$
$114$		0			0
$115$	−2.43845	+	4.22351i	−0.227386	+	0.393845i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.90388	+	6.76172i	−0.357868	+	0.619846i
$120$		0			0
$121$	4.28078	+	7.41452i	0.389161	+	0.674047i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.43845			0.486430
$126$		0			0
$127$	3.90388	−	6.76172i	0.346414	−	0.600006i	−0.639196	−	0.769044i	$-0.720733\pi$
$127$	3.90388	−	6.76172i	0.346414	−	0.600006i	0.985610	+	0.169038i	$0.0540661\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.75379			−0.153229			−0.0766146	−	0.997061i	$-0.524411\pi$
$131$	−1.75379			−0.153229			−0.0766146	+	0.997061i	$0.524411\pi$
$132$		0			0
$133$	−1.21922	+	2.11176i	−0.105720	+	0.183113i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.74621	+	9.95273i	0.490932	+	0.850319i	0.999946	−	0.0104394i	$-0.00332303\pi$
$137$	5.74621	+	9.95273i	0.490932	+	0.850319i	−0.509014	+	0.860759i	$0.669990\pi$
$138$		0			0
$139$	−3.65767	−	6.33527i	−0.310240	−	0.537351i	0.668175	−	0.744005i	$-0.267076\pi$
$139$	−3.65767	−	6.33527i	−0.310240	−	0.537351i	−0.978414	+	0.206654i	$0.933743\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.780776	−	5.57586i	−0.0652918	−	0.466277i
$144$		0			0
$145$	1.40388	−	2.43160i	0.116586	−	0.201933i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.62311	−	2.81130i	−0.132970	−	0.230311i	0.791850	−	0.610715i	$-0.209118\pi$
$149$	−1.62311	−	2.81130i	−0.132970	−	0.230311i	−0.924820	+	0.380405i	$0.875785\pi$
$150$		0			0
$151$	20.4924			1.66765			0.833825	−	0.552029i	$-0.186146\pi$
$151$	20.4924			1.66765			0.833825	+	0.552029i	$0.186146\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.49242			0.360840
$156$		0			0
$157$	2.80776			0.224084			0.112042	−	0.993703i	$-0.464261\pi$
$157$	2.80776			0.224084			0.112042	+	0.993703i	$0.464261\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−13.5616			−1.06880
$162$		0			0
$163$	11.4654	+	19.8587i	0.898042	+	1.55545i	0.829994	+	0.557773i	$0.188344\pi$
$163$	11.4654	+	19.8587i	0.898042	+	1.55545i	0.0680484	+	0.997682i	$0.478323\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.78078	+	8.28055i	−0.369948	+	0.640768i	−0.989557	−	0.144142i	$-0.953958\pi$
$167$	−4.78078	+	8.28055i	−0.369948	+	0.640768i	0.619609	+	0.784910i	$0.287291\pi$
$168$		0			0
$169$	3.15767	−	12.6107i	0.242898	−	0.970052i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.46543	+	11.1985i	0.491558	+	0.851403i	0.999953	−	0.00972081i	$-0.00309428\pi$
$173$	6.46543	+	11.1985i	0.491558	+	0.851403i	−0.508395	+	0.861124i	$0.669761\pi$
$174$		0			0
$175$	3.65767	+	6.33527i	0.276494	+	0.478902i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.34233	−	14.4493i	0.623535	−	1.07999i	−0.365287	−	0.930895i	$-0.619029\pi$
$179$	8.34233	−	14.4493i	0.623535	−	1.07999i	0.988822	−	0.149099i	$-0.0476374\pi$
$180$		0			0
$181$	10.8078			0.803335			0.401667	−	0.915786i	$-0.368431\pi$
$181$	10.8078			0.803335			0.401667	+	0.915786i	$0.368431\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.280776	+	0.486319i	−0.0206431	+	0.0357549i
$186$		0			0
$187$	7.80776			0.570960
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.34233	−	14.4493i	−0.603630	−	1.04552i	−0.992266	−	0.124126i	$-0.960387\pi$
$191$	−8.34233	−	14.4493i	−0.603630	−	1.04552i	0.388637	−	0.921391i	$-0.372946\pi$
$192$		0			0
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	−0.914949	−	0.403570i	$-0.867769\pi$
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	0.806976	+	0.590584i	$0.201102\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.34233	−	12.7173i	0.523119	−	0.906069i	−0.476519	−	0.879164i	$-0.658102\pi$
$197$	7.34233	−	12.7173i	0.523119	−	0.906069i	0.999638	−	0.0269049i	$-0.00856512\pi$
$198$		0			0
$199$	−6.78078	−	11.7446i	−0.480676	−	0.832556i	0.519078	−	0.854727i	$-0.326276\pi$
$199$	−6.78078	−	11.7446i	−0.480676	−	0.832556i	−0.999754	+	0.0221709i	$0.992942\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.80776			0.547998
$204$		0			0
$205$	2.03457	−	3.52397i	0.142100	−	0.246125i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.43845			0.168671
$210$		0			0
$211$	−12.3423	+	21.3775i	−0.849681	+	1.47169i	0.0318122	+	0.999494i	$0.489872\pi$
$211$	−12.3423	+	21.3775i	−0.849681	+	1.47169i	−0.881493	+	0.472197i	$0.843461\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.684658	−	1.18586i	−0.0466933	−	0.0808752i
$216$		0			0
$217$	6.24621	+	10.8188i	0.424020	+	0.734425i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	16.7116	+	6.76172i	1.12415	+	0.454843i
$222$		0			0
$223$	−4.34233	+	7.52113i	−0.290784	+	0.503652i	−0.973995	−	0.226568i	$-0.927249\pi$
$223$	−4.34233	+	7.52113i	−0.290784	+	0.503652i	0.683211	+	0.730221i	$0.260583\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	15.0270	+	26.0275i	0.997376	+	1.72751i	0.561382	+	0.827557i	$0.310270\pi$
$227$	15.0270	+	26.0275i	0.997376	+	1.72751i	0.435994	+	0.899950i	$0.356397\pi$
$228$		0			0
$229$	12.2462			0.809252			0.404626	−	0.914482i	$-0.367402\pi$
$229$	12.2462			0.809252			0.404626	+	0.914482i	$0.367402\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.2462			0.802276			0.401138	−	0.916018i	$-0.368615\pi$
$233$	12.2462			0.802276			0.401138	+	0.916018i	$0.368615\pi$
$234$		0			0
$235$	2.24621			0.146527
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−18.2462			−1.18025			−0.590125	−	0.807312i	$-0.700921\pi$
$239$	−18.2462			−1.18025			−0.590125	+	0.807312i	$0.700921\pi$
$240$		0			0
$241$	−3.74621	−	6.48863i	−0.241315	−	0.417969i	0.719774	−	0.694208i	$-0.244245\pi$
$241$	−3.74621	−	6.48863i	−0.241315	−	0.417969i	−0.961089	+	0.276239i	$0.910912\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.28078	+	2.21837i	−0.0818258	+	0.141726i
$246$		0			0
$247$	5.21922	+	2.11176i	0.332091	+	0.134368i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.534565	+	0.925894i	0.0337415	+	0.0584419i	0.882403	−	0.470494i	$-0.155924\pi$
$251$	0.534565	+	0.925894i	0.0337415	+	0.0584419i	−0.848662	+	0.528936i	$0.822591\pi$
$252$		0			0
$253$	6.78078	+	11.7446i	0.426304	+	0.738380i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.62311	−	4.54335i	0.163625	−	0.283407i	−0.772541	−	0.634965i	$-0.781015\pi$
$257$	2.62311	−	4.54335i	0.163625	−	0.283407i	0.936166	+	0.351558i	$0.114348\pi$
$258$		0			0
$259$	−1.56155			−0.0970302
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.90388	+	10.2258i	−0.364049	+	0.630551i	−0.988623	−	0.150414i	$-0.951939\pi$
$263$	−5.90388	+	10.2258i	−0.364049	+	0.630551i	0.624574	+	0.780966i	$0.285273\pi$
$264$		0			0
$265$	4.80776			0.295339
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.90388	−	5.02967i	−0.177053	−	0.306664i	0.763817	−	0.645433i	$-0.223323\pi$
$269$	−2.90388	−	5.02967i	−0.177053	−	0.306664i	−0.940870	+	0.338768i	$0.889990\pi$
$270$		0			0
$271$	4.78078	−	8.28055i	0.290411	−	0.503007i	−0.683496	−	0.729955i	$-0.739541\pi$
$271$	4.78078	−	8.28055i	0.290411	−	0.503007i	0.973907	+	0.226947i	$0.0728745\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.65767	−	6.33527i	0.220566	−	0.382031i
$276$		0			0
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	0.652140	−	0.758099i	$-0.273872\pi$
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	−0.982603	+	0.185720i	$0.940538\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−2.31534			−0.138122			−0.0690608	−	0.997612i	$-0.522000\pi$
$281$	−2.31534			−0.138122			−0.0690608	+	0.997612i	$0.522000\pi$
$282$		0			0
$283$	12.7808	−	22.1370i	0.759738	−	1.31591i	−0.183246	−	0.983067i	$-0.558660\pi$
$283$	12.7808	−	22.1370i	0.759738	−	1.31591i	0.942984	−	0.332838i	$-0.108006\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.3153			0.667923
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−10.7462	−	18.6130i	−0.627800	−	1.08738i	−0.987992	−	0.154504i	$-0.950622\pi$
$293$	−10.7462	−	18.6130i	−0.627800	−	1.08738i	0.360192	−	0.932878i	$-0.382711\pi$
$294$		0			0
$295$	−0.438447	−	0.759413i	−0.0255274	−	0.0442147i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.34233	+	31.0104i	0.251123	+	1.79338i
$300$		0			0
$301$	1.90388	−	3.29762i	0.109738	−	0.190072i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.59612	+	4.49661i	0.148653	+	0.257475i
$306$		0			0
$307$	−9.75379			−0.556678			−0.278339	−	0.960483i	$-0.589784\pi$
$307$	−9.75379			−0.556678			−0.278339	+	0.960483i	$0.589784\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.24621			−0.127371			−0.0636855	−	0.997970i	$-0.520285\pi$
$311$	−2.24621			−0.127371			−0.0636855	+	0.997970i	$0.520285\pi$
$312$		0			0
$313$	−15.7538			−0.890457			−0.445228	−	0.895417i	$-0.646878\pi$
$313$	−15.7538			−0.890457			−0.445228	+	0.895417i	$0.646878\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.5616			−1.15485			−0.577426	−	0.816443i	$-0.695943\pi$
$317$	−20.5616			−1.15485			−0.577426	+	0.816443i	$0.695943\pi$
$318$		0			0
$319$	−3.90388	−	6.76172i	−0.218575	−	0.378584i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.90388	+	6.76172i	−0.217218	+	0.376232i
$324$		0			0
$325$	13.3153	−	10.3923i	0.738602	−	0.576461i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.12311	+	5.40938i	0.172182	+	0.298229i
$330$		0			0
$331$	3.46543	+	6.00231i	0.190478	+	0.329917i	0.945409	−	0.325887i	$-0.105663\pi$
$331$	3.46543	+	6.00231i	0.190478	+	0.329917i	−0.754931	+	0.655804i	$0.772330\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.80776	+	6.59524i	−0.208040	+	0.360336i
$336$		0			0
$337$	20.5616			1.12006			0.560030	−	0.828473i	$-0.310790\pi$
$337$	20.5616			1.12006			0.560030	+	0.828473i	$0.310790\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.24621	−	10.8188i	0.338251	−	0.585868i
$342$		0			0
$343$	−18.0540			−0.974823
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.02699	+	1.77879i	0.0551316	+	0.0954907i	0.892274	−	0.451494i	$-0.149109\pi$
$347$	1.02699	+	1.77879i	0.0551316	+	0.0954907i	−0.837142	+	0.546985i	$0.815776\pi$
$348$		0			0
$349$	−8.21922	+	14.2361i	−0.439965	+	0.762042i	−0.997686	−	0.0679866i	$-0.978342\pi$
$349$	−8.21922	+	14.2361i	−0.439965	+	0.762042i	0.557721	+	0.830028i	$0.311676\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	−0.960574	−	0.278024i	$-0.910320\pi$
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	0.721063	+	0.692869i	$0.243654\pi$
$354$		0			0
$355$	1.31534	+	2.27824i	0.0698111	+	0.120916i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−28.4924			−1.50377			−0.751886	−	0.659293i	$-0.770856\pi$
$359$	−28.4924			−1.50377			−0.751886	+	0.659293i	$0.770856\pi$
$360$		0			0
$361$	8.28078	−	14.3427i	0.435830	−	0.754880i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	7.68466			0.402233
$366$		0			0
$367$	−6.58854	+	11.4117i	−0.343919	+	0.595685i	−0.985157	−	0.171657i	$-0.945088\pi$
$367$	−6.58854	+	11.4117i	−0.343919	+	0.595685i	0.641238	+	0.767342i	$0.278421\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.68466	+	11.5782i	0.347050	+	0.601109i
$372$		0			0
$373$	−2.62311	−	4.54335i	−0.135819	−	0.235246i	0.790091	−	0.612990i	$-0.210033\pi$
$373$	−2.62311	−	4.54335i	−0.135819	−	0.235246i	−0.925910	+	0.377744i	$0.876700\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.50000	−	17.8536i	−0.128757	−	0.919506i
$378$		0			0
$379$	−1.46543	+	2.53821i	−0.0752743	+	0.130379i	−0.901206	−	0.433392i	$-0.857317\pi$
$379$	−1.46543	+	2.53821i	−0.0752743	+	0.130379i	0.825931	+	0.563771i	$0.190650\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.5885	−	25.2681i	−0.745440	−	1.29114i	−0.949989	−	0.312283i	$-0.898906\pi$
$383$	−14.5885	−	25.2681i	−0.745440	−	1.29114i	0.204550	−	0.978856i	$-0.434427\pi$
$384$		0			0
$385$	−1.36932			−0.0697869
$386$		0			0
$387$		0			0
$388$		0			0
$389$	29.6847			1.50507			0.752536	−	0.658551i	$-0.228830\pi$
$389$	29.6847			1.50507			0.752536	+	0.658551i	$0.228830\pi$
$390$		0			0
$391$	−43.4233			−2.19601
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.24621			0.113019
$396$		0			0
$397$	4.65767	+	8.06732i	0.233762	+	0.404887i	0.958912	−	0.283703i	$-0.0915631\pi$
$397$	4.65767	+	8.06732i	0.233762	+	0.404887i	−0.725150	+	0.688591i	$0.758230\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.7462	−	20.3450i	0.586578	−	1.01598i	−0.408099	−	0.912938i	$-0.633808\pi$
$401$	11.7462	−	20.3450i	0.586578	−	1.01598i	0.994677	−	0.103045i	$-0.0328585\pi$
$402$		0			0
$403$	22.7386	−	17.7470i	1.13269	−	0.884039i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.780776	+	1.35234i	0.0387016	+	0.0670332i
$408$		0			0
$409$	7.62311	+	13.2036i	0.376938	+	0.652876i	0.990615	−	0.136681i	$-0.0436435\pi$
$409$	7.62311	+	13.2036i	0.376938	+	0.652876i	−0.613677	+	0.789557i	$0.710310\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.21922	−	2.11176i	0.0599941	−	0.103913i
$414$		0			0
$415$	−8.00000			−0.392705
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.46543	−	12.9305i	0.364710	−	0.631697i	−0.624019	−	0.781409i	$-0.714501\pi$
$419$	7.46543	−	12.9305i	0.364710	−	0.631697i	0.988730	+	0.149712i	$0.0478347\pi$
$420$		0			0
$421$	−33.6847			−1.64169			−0.820845	−	0.571151i	$-0.806497\pi$
$421$	−33.6847			−1.64169			−0.820845	+	0.571151i	$0.806497\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	11.7116	+	20.2852i	0.568098	+	0.983975i
$426$		0			0
$427$	−7.21922	+	12.5041i	−0.349363	+	0.605114i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.4654	−	26.7869i	0.744944	−	1.29028i	−0.205277	−	0.978704i	$-0.565810\pi$
$431$	15.4654	−	26.7869i	0.744944	−	1.29028i	0.950221	−	0.311577i	$-0.100857\pi$
$432$		0			0
$433$	−15.7462	−	27.2732i	−0.756715	−	1.31067i	−0.944517	−	0.328461i	$-0.893470\pi$
$433$	−15.7462	−	27.2732i	−0.756715	−	1.31067i	0.187803	−	0.982207i	$-0.439863\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.5616			−0.648737
$438$		0			0
$439$	4.53457	−	7.85410i	0.216423	−	0.374856i	−0.737289	−	0.675578i	$-0.763894\pi$
$439$	4.53457	−	7.85410i	0.216423	−	0.374856i	0.953712	+	0.300722i	$0.0972276\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−38.2462			−1.81713			−0.908566	−	0.417741i	$-0.862822\pi$
$443$	−38.2462			−1.81713			−0.908566	+	0.417741i	$0.862822\pi$
$444$		0			0
$445$	−0.753789	+	1.30560i	−0.0357330	+	0.0618914i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−12.0270	−	20.8314i	−0.567589	−	0.983092i	−0.996804	−	0.0798900i	$-0.974543\pi$
$449$	−12.0270	−	20.8314i	−0.567589	−	0.983092i	0.429215	−	0.903202i	$-0.358790\pi$
$450$		0			0
$451$	−5.65767	−	9.79937i	−0.266409	−	0.461434i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.93087	−	1.18586i	−0.137401	−	0.0555941i
$456$		0			0
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	−0.741370	−	0.671096i	$-0.765824\pi$
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	0.951871	+	0.306497i	$0.0991571\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.7462	+	20.3450i	0.547076	+	0.947563i	0.998473	+	0.0552398i	$0.0175923\pi$
$461$	11.7462	+	20.3450i	0.547076	+	0.947563i	−0.451398	+	0.892323i	$0.649074\pi$
$462$		0			0
$463$	−32.9848			−1.53294			−0.766468	−	0.642283i	$-0.777988\pi$
$463$	−32.9848			−1.53294			−0.766468	+	0.642283i	$0.777988\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−26.2462			−1.21453			−0.607265	−	0.794499i	$-0.707733\pi$
$467$	−26.2462			−1.21453			−0.607265	+	0.794499i	$0.707733\pi$
$468$		0			0
$469$	−21.1771			−0.977867
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.80776			−0.175081
$474$		0			0
$475$	3.65767	+	6.33527i	0.167825	+	0.290682i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−10.1501	+	17.5805i	−0.463770	+	0.803273i	−0.999145	−	0.0413417i	$-0.986837\pi$
$479$	−10.1501	+	17.5805i	−0.463770	+	0.803273i	0.535375	+	0.844614i	$0.320170\pi$
$480$		0			0
$481$	0.500000	+	3.57071i	0.0227980	+	0.162811i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	17.2192	+	29.8246i	0.780278	+	1.35148i	0.931780	+	0.363023i	$0.118256\pi$
$487$	17.2192	+	29.8246i	0.780278	+	1.35148i	−0.151503	+	0.988457i	$0.548411\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.02699	+	1.77879i	−0.0463473	+	0.0802759i	−0.888268	−	0.459325i	$-0.848091\pi$
$491$	−1.02699	+	1.77879i	−0.0463473	+	0.0802759i	0.841921	+	0.539601i	$0.181425\pi$
$492$		0			0
$493$	25.0000			1.12594
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.65767	+	6.33527i	−0.164069	+	0.284176i
$498$		0			0
$499$	−16.4924			−0.738302			−0.369151	−	0.929369i	$-0.620352\pi$
$499$	−16.4924			−0.738302			−0.369151	+	0.929369i	$0.620352\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−16.3423	−	28.3057i	−0.728668	−	1.26209i	−0.957446	−	0.288612i	$-0.906806\pi$
$503$	−16.3423	−	28.3057i	−0.728668	−	1.26209i	0.228778	−	0.973479i	$-0.426527\pi$
$504$		0			0
$505$	3.15767	−	5.46925i	0.140515	−	0.243378i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.5000	+	28.5788i	−0.731350	+	1.26673i	0.224957	+	0.974369i	$0.427776\pi$
$509$	−16.5000	+	28.5788i	−0.731350	+	1.26673i	−0.956306	+	0.292366i	$0.905557\pi$
$510$		0			0
$511$	10.6847	+	18.5064i	0.472661	+	0.818674i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.26137			0.0555824
$516$		0			0
$517$	3.12311	−	5.40938i	0.137354	−	0.237904i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.05398			−0.396662			−0.198331	−	0.980135i	$-0.563552\pi$
$521$	−9.05398			−0.396662			−0.198331	+	0.980135i	$0.563552\pi$
$522$		0			0
$523$	6.15009	−	10.6523i	0.268925	−	0.465791i	−0.699660	−	0.714476i	$-0.746665\pi$
$523$	6.15009	−	10.6523i	0.268925	−	0.465791i	0.968584	+	0.248685i	$0.0799984\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.0000	+	34.6410i	0.871214	+	1.50899i
$528$		0			0
$529$	−26.2116	−	45.3999i	−1.13964	−	1.97391i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.62311	−	25.8741i	−0.156934	−	1.12073i
$534$		0			0
$535$	−2.43845	+	4.22351i	−0.105423	+	0.182598i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.56155	+	6.16879i	0.153407	+	0.265709i
$540$		0			0
$541$	−5.68466			−0.244403			−0.122201	−	0.992505i	$-0.538995\pi$
$541$	−5.68466			−0.244403			−0.122201	+	0.992505i	$0.538995\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.63068			0.198357
$546$		0			0
$547$	16.4924			0.705165			0.352583	−	0.935781i	$-0.385304\pi$
$547$	16.4924			0.705165			0.352583	+	0.935781i	$0.385304\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.80776			0.332622
$552$		0			0
$553$	3.12311	+	5.40938i	0.132808	+	0.230030i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15.7462	−	27.2732i	0.667188	−	1.15560i	−0.311499	−	0.950247i	$-0.600831\pi$
$557$	15.7462	−	27.2732i	0.667188	−	1.15560i	0.978687	−	0.205358i	$-0.0658357\pi$
$558$		0			0
$559$	−8.15009	−	3.29762i	−0.344712	−	0.139474i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.02699	+	5.24290i	0.127572	+	0.220962i	0.922736	−	0.385434i	$-0.125948\pi$
$563$	3.02699	+	5.24290i	0.127572	+	0.220962i	−0.795163	+	0.606396i	$0.792615\pi$
$564$		0			0
$565$	2.03457	+	3.52397i	0.0855948	+	0.148255i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.34233	−	16.1814i	0.391651	−	0.678359i	−0.601017	−	0.799237i	$-0.705237\pi$
$569$	9.34233	−	16.1814i	0.391651	−	0.678359i	0.992667	+	0.120877i	$0.0385708\pi$
$570$		0			0
$571$	−8.49242			−0.355397			−0.177698	−	0.984085i	$-0.556865\pi$
$571$	−8.49242			−0.355397			−0.177698	+	0.984085i	$0.556865\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−20.3423	+	35.2339i	−0.848334	+	1.46936i
$576$		0			0
$577$	−27.4384			−1.14228			−0.571139	−	0.820854i	$-0.693498\pi$
$577$	−27.4384			−1.14228			−0.571139	+	0.820854i	$0.693498\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−11.1231	−	19.2658i	−0.461464	−	0.799279i
$582$		0			0
$583$	6.68466	−	11.5782i	0.276850	−	0.479519i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.46543	−	12.9305i	0.308131	−	0.533699i	−0.669822	−	0.742522i	$-0.733630\pi$
$587$	7.46543	−	12.9305i	0.308131	−	0.533699i	0.977954	+	0.208822i	$0.0669630\pi$
$588$		0			0
$589$	6.24621	+	10.8188i	0.257371	+	0.445779i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	19.4384			0.798241			0.399121	−	0.916898i	$-0.369315\pi$
$593$	19.4384			0.798241			0.399121	+	0.916898i	$0.369315\pi$
$594$		0			0
$595$	2.19224	−	3.79706i	0.0898729	−	0.155664i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−26.7386			−1.09251			−0.546255	−	0.837619i	$-0.683947\pi$
$599$	−26.7386			−1.09251			−0.546255	+	0.837619i	$0.683947\pi$
$600$		0			0
$601$	−13.9924	+	24.2356i	−0.570763	+	0.988590i	0.425725	+	0.904853i	$0.360019\pi$
$601$	−13.9924	+	24.2356i	−0.570763	+	0.988590i	−0.996488	+	0.0837376i	$0.973314\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.40388	−	4.16365i	−0.0977317	−	0.169276i
$606$		0			0
$607$	−9.65767	−	16.7276i	−0.391993	−	0.678951i	0.600720	−	0.799460i	$-0.294881\pi$
$607$	−9.65767	−	16.7276i	−0.391993	−	0.678951i	−0.992712	+	0.120508i	$0.961548\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	11.3693	−	8.87348i	0.459953	−	0.358983i
$612$		0			0
$613$	4.50000	−	7.79423i	0.181753	−	0.314806i	−0.760724	−	0.649075i	$-0.775156\pi$
$613$	4.50000	−	7.79423i	0.181753	−	0.314806i	0.942478	+	0.334269i	$0.108489\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12.6231	+	21.8639i	0.508187	+	0.880206i	0.999955	+	0.00947959i	$0.00301749\pi$
$617$	12.6231	+	21.8639i	0.508187	+	0.880206i	−0.491768	+	0.870726i	$0.663649\pi$
$618$		0			0
$619$	−28.9848			−1.16500			−0.582500	−	0.812831i	$-0.697925\pi$
$619$	−28.9848			−1.16500			−0.582500	+	0.812831i	$0.697925\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.19224			−0.167958
$624$		0			0
$625$	20.3693			0.814773
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.00000			−0.199363
$630$		0			0
$631$	−5.02699	−	8.70700i	−0.200121	−	0.346620i	0.748446	−	0.663196i	$-0.230800\pi$
$631$	−5.02699	−	8.70700i	−0.200121	−	0.346620i	−0.948567	+	0.316576i	$0.897467\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.19224	+	3.79706i	−0.0869962	+	0.150682i
$636$		0			0
$637$	2.28078	+	16.2880i	0.0903677	+	0.645354i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.746211	−	1.29248i	−0.0294736	−	0.0510497i	0.850912	−	0.525308i	$-0.176050\pi$
$641$	−0.746211	−	1.29248i	−0.0294736	−	0.0510497i	−0.880386	+	0.474258i	$0.842716\pi$
$642$		0			0
$643$	−10.1501	−	17.5805i	−0.400281	−	0.693306i	0.593479	−	0.804849i	$-0.297754\pi$
$643$	−10.1501	−	17.5805i	−0.400281	−	0.693306i	−0.993760	+	0.111543i	$0.964421\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.4654	−	19.8587i	0.450753	−	0.780727i	−0.547680	−	0.836688i	$-0.684489\pi$
$647$	11.4654	−	19.8587i	0.450753	−	0.780727i	0.998433	+	0.0559611i	$0.0178223\pi$
$648$		0			0
$649$	−2.43845			−0.0957174
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.2732	+	21.2578i	−0.480287	+	0.831882i	−0.999744	−	0.0226145i	$-0.992801\pi$
$653$	−12.2732	+	21.2578i	−0.480287	+	0.831882i	0.519457	+	0.854497i	$0.326134\pi$
$654$		0			0
$655$	0.984845			0.0384811
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.7808	+	18.6729i	0.419959	+	0.727391i	0.995935	−	0.0900759i	$-0.0287110\pi$
$659$	10.7808	+	18.6729i	0.419959	+	0.727391i	−0.575975	+	0.817467i	$0.695378\pi$
$660$		0			0
$661$	−2.86932	+	4.96980i	−0.111603	+	0.193303i	−0.916417	−	0.400225i	$-0.868932\pi$
$661$	−2.86932	+	4.96980i	−0.111603	+	0.193303i	0.804813	+	0.593528i	$0.202265\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.684658	−	1.18586i	0.0265499	−	0.0459858i
$666$		0			0
$667$	21.7116	+	37.6057i	0.840678	+	1.45610i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	14.4384			0.557390
$672$		0			0
$673$	−8.62311	+	14.9357i	−0.332396	+	0.575727i	−0.982981	−	0.183706i	$-0.941190\pi$
$673$	−8.62311	+	14.9357i	−0.332396	+	0.575727i	0.650585	+	0.759434i	$0.274524\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	28.7386			1.10452			0.552258	−	0.833673i	$-0.313766\pi$
$677$	28.7386			1.10452			0.552258	+	0.833673i	$0.313766\pi$
$678$		0			0
$679$	13.9039	−	24.0822i	0.533582	−	0.924191i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.65767	+	6.33527i	0.139957	+	0.242412i	0.927480	−	0.373873i	$-0.121970\pi$
$683$	3.65767	+	6.33527i	0.139957	+	0.242412i	−0.787523	+	0.616285i	$0.788637\pi$
$684$		0			0
$685$	−3.22680	−	5.58898i	−0.123290	−	0.213544i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	24.3348	−	18.9927i	0.927080	−	0.723564i
$690$		0			0
$691$	12.7808	−	22.1370i	0.486204	−	0.842129i	−0.513671	−	0.857987i	$-0.671715\pi$
$691$	12.7808	−	22.1370i	0.486204	−	0.842129i	0.999874	+	0.0158581i	$0.00504799\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.05398	+	3.55759i	0.0779117	+	0.134947i
$696$		0			0
$697$	36.2311			1.37235
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−32.7386			−1.23652			−0.618261	−	0.785973i	$-0.712162\pi$
$701$	−32.7386			−1.23652			−0.618261	+	0.785973i	$0.712162\pi$
$702$		0			0
$703$	−1.56155			−0.0588951
$704$		0			0
$705$		0			0
$706$		0			0
$707$	17.5616			0.660470
$708$		0			0
$709$	−16.8693	−	29.2185i	−0.633540	−	1.09732i	−0.986822	−	0.161807i	$-0.948268\pi$
$709$	−16.8693	−	29.2185i	−0.633540	−	1.09732i	0.353282	−	0.935517i	$-0.385066\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−34.7386	+	60.1691i	−1.30097	+	2.25335i
$714$		0			0
$715$	0.438447	+	3.13114i	0.0163970	+	0.117098i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−21.4654	−	37.1792i	−0.800526	−	1.38655i	−0.919271	−	0.393626i	$-0.871220\pi$
$719$	−21.4654	−	37.1792i	−0.800526	−	1.38655i	0.118745	−	0.992925i	$-0.462113\pi$
$720$		0			0
$721$	1.75379	+	3.03765i	0.0653145	+	0.113128i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	11.7116	−	20.2852i	0.434960	−	0.753372i
$726$		0			0
$727$	6.73863			0.249922			0.124961	−	0.992162i	$-0.460119\pi$
$727$	6.73863			0.249922			0.124961	+	0.992162i	$0.460119\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6.09612	−	10.5588i	0.225473	−	0.390531i
$732$		0			0
$733$	−1.19224			−0.0440362			−0.0220181	−	0.999758i	$-0.507009\pi$
$733$	−1.19224			−0.0440362			−0.0220181	+	0.999758i	$0.507009\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.5885	+	18.3399i	0.390034	+	0.675559i
$738$		0			0
$739$	−23.4654	+	40.6433i	−0.863190	+	1.49509i	0.00564328	+	0.999984i	$0.498204\pi$
$739$	−23.4654	+	40.6433i	−0.863190	+	1.49509i	−0.868833	+	0.495105i	$0.835130\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.53457	+	7.85410i	−0.166357	+	0.288139i	−0.937136	−	0.348963i	$-0.886534\pi$
$743$	−4.53457	+	7.85410i	−0.166357	+	0.288139i	0.770779	+	0.637102i	$0.219867\pi$
$744$		0			0
$745$	0.911460	+	1.57869i	0.0333933	+	0.0578389i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−13.5616			−0.495528
$750$		0			0
$751$	24.1501	−	41.8292i	0.881249	−	1.52637i	0.0312965	−	0.999510i	$-0.490036\pi$
$751$	24.1501	−	41.8292i	0.881249	−	1.52637i	0.849953	−	0.526859i	$-0.176630\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−11.5076			−0.418804
$756$		0			0
$757$	8.27320	−	14.3296i	0.300695	−	0.520818i	−0.675599	−	0.737269i	$-0.736115\pi$
$757$	8.27320	−	14.3296i	0.300695	−	0.520818i	0.976293	+	0.216451i	$0.0694482\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.5346	−	19.9785i	−0.418128	−	0.724218i	0.577623	−	0.816303i	$-0.303980\pi$
$761$	−11.5346	−	19.9785i	−0.418128	−	0.724218i	−0.995751	+	0.0920850i	$0.970647\pi$
$762$		0			0
$763$	6.43845	+	11.1517i	0.233087	+	0.403719i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.21922	−	2.11176i	−0.188455	−	0.0762511i
$768$		0			0
$769$	−0.465435	+	0.806157i	−0.0167840	+	0.0290708i	−0.874295	−	0.485394i	$-0.838676\pi$
$769$	−0.465435	+	0.806157i	−0.0167840	+	0.0290708i	0.857511	+	0.514465i	$0.172009\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	17.0961	+	29.6113i	0.614905	+	1.06505i	0.990401	+	0.138222i	$0.0441388\pi$
$773$	17.0961	+	29.6113i	0.614905	+	1.06505i	−0.375497	+	0.926824i	$0.622528\pi$
$774$		0			0
$775$	37.4773			1.34622
$776$		0			0
$777$		0			0
$778$		0			0
$779$	11.3153			0.405414
$780$		0			0
$781$	7.31534			0.261764
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.57671			−0.0562751
$786$		0			0
$787$	13.7116	+	23.7493i	0.488767	+	0.846570i	0.999917	−	0.0129221i	$-0.00411334\pi$
$787$	13.7116	+	23.7493i	0.488767	+	0.846570i	−0.511149	+	0.859492i	$0.670780\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−5.65767	+	9.79937i	−0.201164	+	0.348426i
$792$		0			0
$793$	30.9039	+	12.5041i	1.09743	+	0.444032i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.46543	+	11.1985i	0.229017	+	0.396670i	0.957517	−	0.288376i	$-0.0931154\pi$
$797$	6.46543	+	11.1985i	0.229017	+	0.396670i	−0.728500	+	0.685046i	$0.759782\pi$
$798$		0			0
$799$	10.0000	+	17.3205i	0.353775	+	0.612756i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.6847	−	18.5064i	0.377053	−	0.653076i
$804$		0			0
$805$	7.61553			0.268412
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11.6231	+	20.1318i	−0.408647	+	0.707797i	−0.994738	−	0.102448i	$-0.967332\pi$
$809$	−11.6231	+	20.1318i	−0.408647	+	0.707797i	0.586092	+	0.810245i	$0.300666\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.43845	−	11.1517i	−0.225529	−	0.390628i
$816$		0			0
$817$	1.90388	−	3.29762i	0.0666084	−	0.115369i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.90388	+	11.9579i	−0.240947	+	0.417333i	−0.960984	−	0.276603i	$-0.910791\pi$
$821$	−6.90388	+	11.9579i	−0.240947	+	0.417333i	0.720037	+	0.693935i	$0.244125\pi$
$822$		0			0
$823$	0.588540	+	1.01938i	0.0205152	+	0.0355334i	0.876101	−	0.482128i	$-0.160136\pi$
$823$	0.588540	+	1.01938i	0.0205152	+	0.0355334i	−0.855586	+	0.517661i	$0.826803\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.9848			1.28609			0.643045	−	0.765829i	$-0.277671\pi$
$827$	36.9848			1.28609			0.643045	+	0.765829i	$0.277671\pi$
$828$		0			0
$829$	−3.25379	+	5.63573i	−0.113009	+	0.195737i	−0.916982	−	0.398929i	$-0.869382\pi$
$829$	−3.25379	+	5.63573i	−0.113009	+	0.195737i	0.803973	+	0.594665i	$0.202715\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−22.8078			−0.790242
$834$		0			0
$835$	2.68466	−	4.64996i	0.0929064	−	0.160919i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	13.6577	+	23.6558i	0.471515	+	0.816688i	0.999469	−	0.0325849i	$-0.0103739\pi$
$839$	13.6577	+	23.6558i	0.471515	+	0.816688i	−0.527954	+	0.849273i	$0.677041\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.77320	+	7.08156i	−0.0609999	+	0.243613i
$846$		0			0
$847$	6.68466	−	11.5782i	0.229688	−	0.397831i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.34233	−	7.52113i	−0.148853	−	0.257821i
$852$		0			0
$853$	−48.4233			−1.65798			−0.828991	−	0.559262i	$-0.811085\pi$
$853$	−48.4233			−1.65798			−0.828991	+	0.559262i	$0.811085\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.9460			0.510546			0.255273	−	0.966869i	$-0.417835\pi$
$857$	14.9460			0.510546			0.255273	+	0.966869i	$0.417835\pi$
$858$		0			0
$859$	−22.2462			−0.759031			−0.379515	−	0.925185i	$-0.623909\pi$
$859$	−22.2462			−0.759031			−0.379515	+	0.925185i	$0.623909\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	21.7538			0.740508			0.370254	−	0.928931i	$-0.379271\pi$
$863$	21.7538			0.740508			0.370254	+	0.928931i	$0.379271\pi$
$864$		0			0
$865$	−3.63068	−	6.28853i	−0.123447	−	0.213816i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.12311	−	5.40938i	0.105944	−	0.183501i
$870$		0			0
$871$	6.78078	+	48.4244i	0.229758	+	1.64080i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.24621	−	7.35465i	−0.143548	−	0.248633i
$876$		0			0
$877$	19.8693	+	34.4147i	0.670939	+	1.16210i	0.977638	+	0.210294i	$0.0674422\pi$
$877$	19.8693	+	34.4147i	0.670939	+	1.16210i	−0.306699	+	0.951807i	$0.599224\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−7.62311	+	13.2036i	−0.256829	+	0.444841i	−0.965391	−	0.260808i	$-0.916011\pi$
$881$	−7.62311	+	13.2036i	−0.256829	+	0.444841i	0.708562	+	0.705649i	$0.249344\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.3423	−	17.9134i	0.347261	−	0.601474i	−0.638501	−	0.769621i	$-0.720445\pi$
$887$	10.3423	−	17.9134i	0.347261	−	0.601474i	0.985762	+	0.168147i	$0.0537783\pi$
$888$		0			0
$889$	−12.1922			−0.408914
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.12311	+	5.40938i	0.104511	+	0.181018i
$894$		0			0
$895$	−4.68466	+	8.11407i	−0.156591	+	0.271223i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	20.0000	−	34.6410i	0.667037	−	1.15534i
$900$		0			0
$901$	21.4039	+	37.0726i	0.713067	+	1.23507i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.06913			−0.201745
$906$		0			0
$907$	20.1501	−	34.9010i	0.669073	−	1.15887i	−0.309091	−	0.951033i	$-0.600025\pi$
$907$	20.1501	−	34.9010i	0.669073	−	1.15887i	0.978164	−	0.207836i	$-0.0666419\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	30.7386			1.01842			0.509208	−	0.860643i	$-0.329938\pi$
$911$	30.7386			1.01842			0.509208	+	0.860643i	$0.329938\pi$
$912$		0			0
$913$	−11.1231	+	19.2658i	−0.368121	+	0.637604i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.36932	+	2.37173i	0.0452188	+	0.0783213i
$918$		0			0
$919$	−29.2732	−	50.7027i	−0.965634	−	1.67253i	−0.707903	−	0.706310i	$-0.750358\pi$
$919$	−29.2732	−	50.7027i	−0.965634	−	1.67253i	−0.257731	−	0.966217i	$-0.582975\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	15.6577	+	6.33527i	0.515379	+	0.208528i
$924$		0			0
$925$	−2.34233	+	4.05703i	−0.0770153	+	0.133394i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−18.9924	−	32.8958i	−0.623121	−	1.07928i	−0.988901	−	0.148576i	$-0.952531\pi$
$929$	−18.9924	−	32.8958i	−0.623121	−	1.07928i	0.365780	−	0.930701i	$-0.380802\pi$
$930$		0			0
$931$	−7.12311			−0.233450
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.38447			−0.143388
$936$		0			0
$937$	−13.6847			−0.447058			−0.223529	−	0.974697i	$-0.571758\pi$
$937$	−13.6847			−0.447058			−0.223529	+	0.974697i	$0.571758\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−14.0000			−0.456387			−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000			−0.456387			−0.228193	+	0.973616i	$0.573282\pi$
$942$		0			0
$943$	31.4654	+	54.4997i	1.02466	+	1.77476i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.71165	−	13.3570i	0.250595	−	0.434043i	−0.713095	−	0.701068i	$-0.752707\pi$
$947$	7.71165	−	13.3570i	0.250595	−	0.434043i	0.963690	+	0.267025i	$0.0860405\pi$
$948$		0			0
$949$	38.8963	−	30.3576i	1.26263	−	0.985450i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−12.9039	−	22.3502i	−0.417998	−	0.723993i	0.577740	−	0.816221i	$-0.303935\pi$
$953$	−12.9039	−	22.3502i	−0.417998	−	0.723993i	−0.995738	+	0.0922274i	$0.970601\pi$
$954$		0			0
$955$	4.68466	+	8.11407i	0.151592	+	0.262565i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	8.97301	−	15.5417i	0.289754	−	0.501868i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.842329	−	1.45896i	0.0271155	−	0.0469655i
$966$		0			0
$967$	5.75379			0.185029			0.0925147	−	0.995711i	$-0.470509\pi$
$967$	5.75379			0.185029			0.0925147	+	0.995711i	$0.470509\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.65767	+	16.7276i	0.309929	+	0.536813i	0.978347	−	0.206973i	$-0.0663612\pi$
$971$	9.65767	+	16.7276i	0.309929	+	0.536813i	−0.668417	+	0.743787i	$0.733028\pi$
$972$		0			0
$973$	−5.71165	+	9.89286i	−0.183107	+	0.317151i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.623106	−	1.07925i	0.0199349	−	0.0345283i	−0.855886	−	0.517165i	$-0.826987\pi$
$977$	0.623106	−	1.07925i	0.0199349	−	0.0345283i	0.875821	+	0.482636i	$0.160321\pi$
$978$		0			0
$979$	2.09612	+	3.63058i	0.0669922	+	0.116034i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	24.9848			0.796893			0.398446	−	0.917192i	$-0.369549\pi$
$983$	24.9848			0.796893			0.398446	+	0.917192i	$0.369549\pi$
$984$		0			0
$985$	−4.12311	+	7.14143i	−0.131373	+	0.227545i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	21.1771			0.673392
$990$		0			0
$991$	−1.84991	+	3.20413i	−0.0587642	+	0.101783i	−0.893911	−	0.448245i	$-0.852049\pi$
$991$	−1.84991	+	3.20413i	−0.0587642	+	0.101783i	0.835147	+	0.550027i	$0.185383\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	3.80776	+	6.59524i	0.120714	+	0.209083i
$996$		0			0
$997$	21.6231	+	37.4523i	0.684811	+	1.18613i	0.973496	+	0.228703i	$0.0734484\pi$
$997$	21.6231	+	37.4523i	0.684811	+	1.18613i	−0.288686	+	0.957424i	$0.593218\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.t.f.217.1		4
3.2	odd	2		104.2.i.b.9.2	✓	4
4.3	odd	2		1872.2.t.s.1153.1		4
12.11	even	2		208.2.i.e.113.1		4
13.3	even	3	inner	936.2.t.f.289.1		4
24.5	odd	2		832.2.i.o.321.1		4
24.11	even	2		832.2.i.l.321.2		4
39.2	even	12		1352.2.o.c.361.3		8
39.5	even	4		1352.2.o.c.1161.3		8
39.8	even	4		1352.2.o.c.1161.4		8
39.11	even	12		1352.2.o.c.361.4		8
39.17	odd	6		1352.2.a.h.1.1		2
39.20	even	12		1352.2.f.d.337.2		4
39.23	odd	6		1352.2.i.e.1329.2		4
39.29	odd	6		104.2.i.b.81.2	yes	4
39.32	even	12		1352.2.f.d.337.1		4
39.35	odd	6		1352.2.a.f.1.1		2
39.38	odd	2		1352.2.i.e.529.2		4
52.3	odd	6		1872.2.t.s.289.1		4
156.35	even	6		2704.2.a.q.1.2		2
156.59	odd	12		2704.2.f.l.337.4		4
156.71	odd	12		2704.2.f.l.337.3		4
156.95	even	6		2704.2.a.r.1.2		2
156.107	even	6		208.2.i.e.81.1		4
312.29	odd	6		832.2.i.o.705.1		4
312.107	even	6		832.2.i.l.705.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.i.b.9.2	✓	4	3.2	odd	2
104.2.i.b.81.2	yes	4	39.29	odd	6
208.2.i.e.81.1		4	156.107	even	6
208.2.i.e.113.1		4	12.11	even	2
832.2.i.l.321.2		4	24.11	even	2
832.2.i.l.705.2		4	312.107	even	6
832.2.i.o.321.1		4	24.5	odd	2
832.2.i.o.705.1		4	312.29	odd	6
936.2.t.f.217.1		4	1.1	even	1	trivial
936.2.t.f.289.1		4	13.3	even	3	inner
1352.2.a.f.1.1		2	39.35	odd	6
1352.2.a.h.1.1		2	39.17	odd	6
1352.2.f.d.337.1		4	39.32	even	12
1352.2.f.d.337.2		4	39.20	even	12
1352.2.i.e.529.2		4	39.38	odd	2
1352.2.i.e.1329.2		4	39.23	odd	6
1352.2.o.c.361.3		8	39.2	even	12
1352.2.o.c.361.4		8	39.11	even	12
1352.2.o.c.1161.3		8	39.5	even	4
1352.2.o.c.1161.4		8	39.8	even	4
1872.2.t.s.289.1		4	52.3	odd	6
1872.2.t.s.1153.1		4	4.3	odd	2
2704.2.a.q.1.2		2	156.35	even	6
2704.2.a.r.1.2		2	156.95	even	6
2704.2.f.l.337.3		4	156.71	odd	12
2704.2.f.l.337.4		4	156.59	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.561553 q^{5} +(-0.780776 - 1.35234i) q^{7} +(-0.780776 + 1.35234i) q^{11} +(-2.84233 + 2.21837i) q^{13} +(-2.50000 - 4.33013i) q^{17} +(-0.780776 - 1.35234i) q^{19} +(4.34233 - 7.52113i) q^{23} -4.68466 q^{25} +(-2.50000 + 4.33013i) q^{29} -8.00000 q^{31} +(0.438447 + 0.759413i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-3.62311 + 6.27540i) q^{41} +(1.21922 + 2.11176i) q^{43} -4.00000 q^{47} +(2.28078 - 3.95042i) q^{49} -8.56155 q^{53} +(0.438447 - 0.759413i) q^{55} +(0.780776 + 1.35234i) q^{59} +(-4.62311 - 8.00745i) q^{61} +(1.59612 - 1.24573i) q^{65} +(6.78078 - 11.7446i) q^{67} +(-2.34233 - 4.05703i) q^{71} -13.6847 q^{73} +2.43845 q^{77} -4.00000 q^{79} +14.2462 q^{83} +(1.40388 + 2.43160i) q^{85} +(1.34233 - 2.32498i) q^{89} +(5.21922 + 2.11176i) q^{91} +(0.438447 + 0.759413i) q^{95} +(8.90388 + 15.4220i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{5} + q^{7} + q^{11} + q^{13} - 10 q^{17} + q^{19} + 5 q^{23} + 6 q^{25} - 10 q^{29} - 32 q^{31} + 10 q^{35} + 2 q^{37} + 2 q^{41} + 9 q^{43} - 16 q^{47} + 5 q^{49} - 26 q^{53} + 10 q^{55}+ \cdots + 15 q^{97}+O(q^{100}) \) 4 * q + 6 * q^5 + q^7 + q^11 + q^13 - 10 * q^17 + q^19 + 5 * q^23 + 6 * q^25 - 10 * q^29 - 32 * q^31 + 10 * q^35 + 2 * q^37 + 2 * q^41 + 9 * q^43 - 16 * q^47 + 5 * q^49 - 26 * q^53 + 10 * q^55 - q^59 - 2 * q^61 + 27 * q^65 + 23 * q^67 + 3 * q^71 - 30 * q^73 + 18 * q^77 - 16 * q^79 + 24 * q^83 - 15 * q^85 - 7 * q^89 + 25 * q^91 + 10 * q^95 + 15 * q^97

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