LMFDB - Embedded newform 432.2.i.d.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(145,432)] 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("432.145"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	432.289
Dual form			432.2.i.d.145.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68614 - 2.92048i) q^{5} +(-0.686141 + 1.18843i) q^{7} +(-0.500000 + 0.866025i) q^{11} +(-2.68614 - 4.65253i) q^{13} -0.372281 q^{17} -6.37228 q^{19} +(-2.68614 - 4.65253i) q^{23} +(-3.18614 + 5.51856i) q^{25} +(0.686141 - 1.18843i) q^{29} +(0.313859 + 0.543620i) q^{31} +4.62772 q^{35} -2.74456 q^{37} +(-0.127719 - 0.221215i) q^{41} +(4.87228 - 8.43904i) q^{43} +(0.686141 - 1.18843i) q^{47} +(2.55842 + 4.43132i) q^{49} +10.7446 q^{53} +3.37228 q^{55} +(-3.50000 - 6.06218i) q^{59} +(1.68614 - 2.92048i) q^{61} +(-9.05842 + 15.6896i) q^{65} +(3.87228 + 6.70699i) q^{67} -4.00000 q^{71} +5.11684 q^{73} +(-0.686141 - 1.18843i) q^{77} +(-0.313859 + 0.543620i) q^{79} +(-7.68614 + 13.3128i) q^{83} +(0.627719 + 1.08724i) q^{85} -6.00000 q^{89} +7.37228 q^{91} +(10.7446 + 18.6101i) q^{95} +(4.87228 - 8.43904i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{5} + 3 q^{7} - 2 q^{11} - 5 q^{13} + 10 q^{17} - 14 q^{19} - 5 q^{23} - 7 q^{25} - 3 q^{29} + 7 q^{31} + 30 q^{35} + 12 q^{37} - 12 q^{41} + 8 q^{43} - 3 q^{47} - 7 q^{49} + 20 q^{53} + 2 q^{55}+ \cdots + 8 q^{97}+O(q^{100}) $ 4 * q - q^5 + 3 * q^7 - 2 * q^11 - 5 * q^13 + 10 * q^17 - 14 * q^19 - 5 * q^23 - 7 * q^25 - 3 * q^29 + 7 * q^31 + 30 * q^35 + 12 * q^37 - 12 * q^41 + 8 * q^43 - 3 * q^47 - 7 * q^49 + 20 * q^53 + 2 * q^55 - 14 * q^59 + q^61 - 19 * q^65 + 4 * q^67 - 16 * q^71 - 14 * q^73 + 3 * q^77 - 7 * q^79 - 25 * q^83 + 14 * q^85 - 24 * q^89 + 18 * q^91 + 20 * q^95 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.68614	−	2.92048i	−0.754065	−	1.30608i	−0.945838	−	0.324640i	$-0.894757\pi$
$5$	−1.68614	−	2.92048i	−0.754065	−	1.30608i	0.191773	−	0.981439i	$-0.438576\pi$
$6$		0			0
$7$	−0.686141	+	1.18843i	−0.259337	+	0.449185i	−0.966064	−	0.258301i	$-0.916837\pi$
$7$	−0.686141	+	1.18843i	−0.259337	+	0.449185i	0.706728	+	0.707486i	$0.250171\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		0			0
$13$	−2.68614	−	4.65253i	−0.745001	−	1.29038i	−0.950194	−	0.311659i	$-0.899115\pi$
$13$	−2.68614	−	4.65253i	−0.745001	−	1.29038i	0.205193	−	0.978722i	$-0.434218\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.372281			−0.0902915			−0.0451457	−	0.998980i	$-0.514375\pi$
$17$	−0.372281			−0.0902915			−0.0451457	+	0.998980i	$0.514375\pi$
$18$		0			0
$19$	−6.37228			−1.46190			−0.730951	−	0.682430i	$-0.760923\pi$
$19$	−6.37228			−1.46190			−0.730951	+	0.682430i	$0.760923\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.68614	−	4.65253i	−0.560099	−	0.970120i	−0.997487	−	0.0708472i	$-0.977430\pi$
$23$	−2.68614	−	4.65253i	−0.560099	−	0.970120i	0.437388	−	0.899273i	$-0.355904\pi$
$24$		0			0
$25$	−3.18614	+	5.51856i	−0.637228	+	1.10371i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.686141	−	1.18843i	0.127413	−	0.220686i	−0.795261	−	0.606268i	$-0.792666\pi$
$29$	0.686141	−	1.18843i	0.127413	−	0.220686i	0.922674	+	0.385582i	$0.125999\pi$
$30$		0			0
$31$	0.313859	+	0.543620i	0.0563708	+	0.0976371i	0.892834	−	0.450386i	$-0.148714\pi$
$31$	0.313859	+	0.543620i	0.0563708	+	0.0976371i	−0.836463	+	0.548023i	$0.815380\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.62772			0.782227
$36$		0			0
$37$	−2.74456			−0.451203			−0.225602	−	0.974220i	$-0.572435\pi$
$37$	−2.74456			−0.451203			−0.225602	+	0.974220i	$0.572435\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.127719	−	0.221215i	−0.0199463	−	0.0345480i	0.855880	−	0.517175i	$-0.173016\pi$
$41$	−0.127719	−	0.221215i	−0.0199463	−	0.0345480i	−0.875826	+	0.482627i	$0.839683\pi$
$42$		0			0
$43$	4.87228	−	8.43904i	0.743016	−	1.28694i	−0.208100	−	0.978108i	$-0.566728\pi$
$43$	4.87228	−	8.43904i	0.743016	−	1.28694i	0.951116	−	0.308834i	$-0.0999387\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.686141	−	1.18843i	0.100084	−	0.173350i	−0.811635	−	0.584165i	$-0.801422\pi$
$47$	0.686141	−	1.18843i	0.100084	−	0.173350i	0.911719	+	0.410814i	$0.134756\pi$
$48$		0			0
$49$	2.55842	+	4.43132i	0.365489	+	0.633045i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.7446			1.47588			0.737940	−	0.674867i	$-0.235799\pi$
$53$	10.7446			1.47588			0.737940	+	0.674867i	$0.235799\pi$
$54$		0			0
$55$	3.37228			0.454718
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	0.543065	−	0.839691i	$-0.317264\pi$
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	−0.998726	+	0.0504625i	$0.983930\pi$
$60$		0			0
$61$	1.68614	−	2.92048i	0.215888	−	0.373929i	−0.737659	−	0.675174i	$-0.764069\pi$
$61$	1.68614	−	2.92048i	0.215888	−	0.373929i	0.953547	+	0.301244i	$0.0974020\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.05842	+	15.6896i	−1.12356	+	1.94606i
$66$		0			0
$67$	3.87228	+	6.70699i	0.473074	+	0.819389i	0.999525	−	0.0308167i	$-0.00981082\pi$
$67$	3.87228	+	6.70699i	0.473074	+	0.819389i	−0.526451	+	0.850206i	$0.676477\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$		0			0
$73$	5.11684			0.598881			0.299441	−	0.954115i	$-0.403200\pi$
$73$	5.11684			0.598881			0.299441	+	0.954115i	$0.403200\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.686141	−	1.18843i	−0.0781930	−	0.135434i
$78$		0			0
$79$	−0.313859	+	0.543620i	−0.0353119	+	0.0611621i	−0.883141	−	0.469107i	$-0.844576\pi$
$79$	−0.313859	+	0.543620i	−0.0353119	+	0.0611621i	0.847829	+	0.530269i	$0.177909\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.68614	+	13.3128i	−0.843664	+	1.46127i	0.0431132	+	0.999070i	$0.486272\pi$
$83$	−7.68614	+	13.3128i	−0.843664	+	1.46127i	−0.886777	+	0.462198i	$0.847061\pi$
$84$		0			0
$85$	0.627719	+	1.08724i	0.0680856	+	0.117928i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	7.37228			0.772825
$92$		0			0
$93$		0			0
$94$		0			0
$95$	10.7446	+	18.6101i	1.10237	+	1.90936i
$96$		0			0
$97$	4.87228	−	8.43904i	0.494705	−	0.856855i	−0.505276	−	0.862958i	$-0.668609\pi$
$97$	4.87228	−	8.43904i	0.494705	−	0.856855i	0.999981	+	0.00610314i	$0.00194270\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.05842	−	8.76144i	0.503332	−	0.871796i	−0.496661	−	0.867945i	$-0.665441\pi$
$101$	5.05842	−	8.76144i	0.503332	−	0.871796i	0.999993	−	0.00385151i	$-0.00122598\pi$
$102$		0			0
$103$	−3.31386	−	5.73977i	−0.326524	−	0.565557i	0.655295	−	0.755373i	$-0.272544\pi$
$103$	−3.31386	−	5.73977i	−0.326524	−	0.565557i	−0.981820	+	0.189816i	$0.939211\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.8614			1.53338			0.766690	−	0.642017i	$-0.221902\pi$
$107$	15.8614			1.53338			0.766690	+	0.642017i	$0.221902\pi$
$108$		0			0
$109$	6.74456			0.646012			0.323006	−	0.946397i	$-0.395307\pi$
$109$	6.74456			0.646012			0.323006	+	0.946397i	$0.395307\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.686141	+	1.18843i	0.0645467	+	0.111798i	0.896493	−	0.443058i	$-0.146107\pi$
$113$	0.686141	+	1.18843i	0.0645467	+	0.111798i	−0.831946	+	0.554856i	$0.812773\pi$
$114$		0			0
$115$	−9.05842	+	15.6896i	−0.844702	+	1.46307i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.255437	−	0.442430i	0.0234159	−	0.0405575i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	4.62772			0.413916
$126$		0			0
$127$	4.74456			0.421012			0.210506	−	0.977593i	$-0.432489\pi$
$127$	4.74456			0.421012			0.210506	+	0.977593i	$0.432489\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.31386	−	10.9359i	−0.551644	−	0.955476i	−0.998156	−	0.0606984i	$-0.980667\pi$
$131$	−6.31386	−	10.9359i	−0.551644	−	0.955476i	0.446512	−	0.894778i	$-0.352666\pi$
$132$		0			0
$133$	4.37228	−	7.57301i	0.379125	−	0.656664i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.12772	−	5.41737i	0.267219	−	0.462837i	−0.700924	−	0.713236i	$-0.747229\pi$
$137$	3.12772	−	5.41737i	0.267219	−	0.462837i	0.968143	+	0.250399i	$0.0805619\pi$
$138$		0			0
$139$	−2.87228	−	4.97494i	−0.243624	−	0.421969i	0.718120	−	0.695919i	$-0.245003\pi$
$139$	−2.87228	−	4.97494i	−0.243624	−	0.421969i	−0.961744	+	0.273951i	$0.911670\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.37228			0.449253
$144$		0			0
$145$	−4.62772			−0.384311
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.31386	−	2.27567i	−0.107636	−	0.186430i	0.807176	−	0.590310i	$-0.200995\pi$
$149$	−1.31386	−	2.27567i	−0.107636	−	0.186430i	−0.914812	+	0.403880i	$0.867661\pi$
$150$		0			0
$151$	−2.68614	+	4.65253i	−0.218595	+	0.378618i	−0.954379	−	0.298599i	$-0.903481\pi$
$151$	−2.68614	+	4.65253i	−0.218595	+	0.378618i	0.735784	+	0.677217i	$0.236814\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.05842	−	1.83324i	0.0850145	−	0.147249i
$156$		0			0
$157$	−7.05842	−	12.2255i	−0.563323	−	0.975705i	−0.997203	−	0.0747341i	$-0.976189\pi$
$157$	−7.05842	−	12.2255i	−0.563323	−	0.975705i	0.433880	−	0.900971i	$-0.357144\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.37228			0.581017
$162$		0			0
$163$	12.0000			0.939913			0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000			0.939913			0.469956	+	0.882690i	$0.344270\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.941578	+	1.63086i	0.0728615	+	0.126200i	0.900154	−	0.435571i	$-0.143454\pi$
$167$	0.941578	+	1.63086i	0.0728615	+	0.126200i	−0.827293	+	0.561771i	$0.810120\pi$
$168$		0			0
$169$	−7.93070	+	13.7364i	−0.610054	+	1.05664i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−5.31386	+	9.20387i	−0.404005	+	0.699758i	−0.994205	−	0.107500i	$-0.965716\pi$
$173$	−5.31386	+	9.20387i	−0.404005	+	0.699758i	0.590200	+	0.807257i	$0.299049\pi$
$174$		0			0
$175$	−4.37228	−	7.57301i	−0.330513	−	0.572466i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−22.9783			−1.71748			−0.858738	−	0.512416i	$-0.828751\pi$
$179$	−22.9783			−1.71748			−0.858738	+	0.512416i	$0.828751\pi$
$180$		0			0
$181$	−23.4891			−1.74593			−0.872966	−	0.487780i	$-0.837807\pi$
$181$	−23.4891			−1.74593			−0.872966	+	0.487780i	$0.837807\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.62772	+	8.01544i	0.340237	+	0.589307i
$186$		0			0
$187$	0.186141	−	0.322405i	0.0136120	−	0.0235766i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.43070	−	16.3345i	0.682382	−	1.18192i	−0.291870	−	0.956458i	$-0.594278\pi$
$191$	9.43070	−	16.3345i	0.682382	−	1.18192i	0.974252	−	0.225462i	$-0.0723891\pi$
$192$		0			0
$193$	4.87228	+	8.43904i	0.350714	+	0.607455i	0.986375	−	0.164514i	$-0.0526054\pi$
$193$	4.87228	+	8.43904i	0.350714	+	0.607455i	−0.635660	+	0.771969i	$0.719272\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−26.7446			−1.90547			−0.952736	−	0.303801i	$-0.901744\pi$
$197$	−26.7446			−1.90547			−0.952736	+	0.303801i	$0.901744\pi$
$198$		0			0
$199$	−18.2337			−1.29255			−0.646276	−	0.763104i	$-0.723674\pi$
$199$	−18.2337			−1.29255			−0.646276	+	0.763104i	$0.723674\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.941578	+	1.63086i	0.0660858	+	0.114464i
$204$		0			0
$205$	−0.430703	+	0.746000i	−0.0300816	+	0.0521029i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.18614	−	5.51856i	0.220390	−	0.381727i
$210$		0			0
$211$	−7.68614	−	13.3128i	−0.529136	−	0.916490i	−0.999423	−	0.0339764i	$-0.989183\pi$
$211$	−7.68614	−	13.3128i	−0.529136	−	0.916490i	0.470287	−	0.882514i	$-0.344150\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−32.8614			−2.24113
$216$		0			0
$217$	−0.861407			−0.0584761
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.00000	+	1.73205i	0.0672673	+	0.116510i
$222$		0			0
$223$	12.8030	−	22.1754i	0.857351	−	1.48498i	−0.0170952	−	0.999854i	$-0.505442\pi$
$223$	12.8030	−	22.1754i	0.857351	−	1.48498i	0.874446	−	0.485122i	$-0.161225\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.50000	−	12.9904i	0.497792	−	0.862202i	−0.502204	−	0.864749i	$-0.667477\pi$
$227$	7.50000	−	12.9904i	0.497792	−	0.862202i	0.999997	+	0.00254715i	$0.000810783\pi$
$228$		0			0
$229$	8.80298	+	15.2472i	0.581718	+	1.00756i	0.995276	+	0.0970868i	$0.0309524\pi$
$229$	8.80298	+	15.2472i	0.581718	+	1.00756i	−0.413558	+	0.910478i	$0.635714\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.372281			0.0243890			0.0121945	−	0.999926i	$-0.496118\pi$
$233$	0.372281			0.0243890			0.0121945	+	0.999926i	$0.496118\pi$
$234$		0			0
$235$	−4.62772			−0.301879
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.43070	−	12.8704i	−0.480652	−	0.832514i	0.519101	−	0.854713i	$-0.326267\pi$
$239$	−7.43070	−	12.8704i	−0.480652	−	0.832514i	−0.999754	+	0.0221986i	$0.992933\pi$
$240$		0			0
$241$	2.87228	−	4.97494i	0.185020	−	0.320464i	−0.758563	−	0.651599i	$-0.774098\pi$
$241$	2.87228	−	4.97494i	0.185020	−	0.320464i	0.943583	+	0.331135i	$0.107432\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.62772	−	14.9436i	0.551205	−	0.954715i
$246$		0			0
$247$	17.1168	+	29.6472i	1.08912	+	1.88641i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	27.1168			1.71160			0.855800	−	0.517307i	$-0.173065\pi$
$251$	27.1168			1.71160			0.855800	+	0.517307i	$0.173065\pi$
$252$		0			0
$253$	5.37228			0.337752
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.24456	−	16.0121i	−0.576660	−	0.998804i	−0.995859	−	0.0909101i	$-0.971022\pi$
$257$	−9.24456	−	16.0121i	−0.576660	−	0.998804i	0.419199	−	0.907894i	$-0.362311\pi$
$258$		0			0
$259$	1.88316	−	3.26172i	0.117014	−	0.202674i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.94158	−	3.36291i	0.119723	−	0.207366i	−0.799935	−	0.600087i	$-0.795133\pi$
$263$	1.94158	−	3.36291i	0.119723	−	0.207366i	0.919658	+	0.392721i	$0.128466\pi$
$264$		0			0
$265$	−18.1168	−	31.3793i	−1.11291	−	1.92761i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.25544			0.0765454			0.0382727	−	0.999267i	$-0.487814\pi$
$269$	1.25544			0.0765454			0.0382727	+	0.999267i	$0.487814\pi$
$270$		0			0
$271$	−1.48913			−0.0904579			−0.0452290	−	0.998977i	$-0.514402\pi$
$271$	−1.48913			−0.0904579			−0.0452290	+	0.998977i	$0.514402\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.18614	−	5.51856i	−0.192132	−	0.332782i
$276$		0			0
$277$	−5.94158	+	10.2911i	−0.356995	+	0.618333i	−0.987457	−	0.157887i	$-0.949532\pi$
$277$	−5.94158	+	10.2911i	−0.356995	+	0.618333i	0.630462	+	0.776220i	$0.282865\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.43070	−	12.8704i	0.443279	−	0.767781i	−0.554652	−	0.832082i	$-0.687149\pi$
$281$	7.43070	−	12.8704i	0.443279	−	0.767781i	0.997931	+	0.0643014i	$0.0204819\pi$
$282$		0			0
$283$	−2.43070	−	4.21010i	−0.144490	−	0.250265i	0.784692	−	0.619885i	$-0.212821\pi$
$283$	−2.43070	−	4.21010i	−0.144490	−	0.250265i	−0.929183	+	0.369621i	$0.879488\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.350532			0.0206912
$288$		0			0
$289$	−16.8614			−0.991847
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.6861	+	21.9730i	0.741132	+	1.28368i	0.951980	+	0.306160i	$0.0990442\pi$
$293$	12.6861	+	21.9730i	0.741132	+	1.28368i	−0.210848	+	0.977519i	$0.567622\pi$
$294$		0			0
$295$	−11.8030	+	20.4434i	−0.687196	+	1.19026i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−14.4307	+	24.9947i	−0.834549	+	1.44548i
$300$		0			0
$301$	6.68614	+	11.5807i	0.385383	+	0.667502i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−11.3723			−0.651175
$306$		0			0
$307$	−25.6277			−1.46265			−0.731326	−	0.682029i	$-0.761098\pi$
$307$	−25.6277			−1.46265			−0.731326	+	0.682029i	$0.761098\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	14.0584	+	24.3499i	0.797180	+	1.38076i	0.921446	+	0.388507i	$0.127009\pi$
$311$	14.0584	+	24.3499i	0.797180	+	1.38076i	−0.124266	+	0.992249i	$0.539658\pi$
$312$		0			0
$313$	11.6168	−	20.1210i	0.656623	−	1.13730i	−0.324861	−	0.945762i	$-0.605318\pi$
$313$	11.6168	−	20.1210i	0.656623	−	1.13730i	0.981484	−	0.191543i	$-0.0613490\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.80298	+	8.31901i	−0.269762	+	0.467242i	−0.968800	−	0.247842i	$-0.920279\pi$
$317$	−4.80298	+	8.31901i	−0.269762	+	0.467242i	0.699038	+	0.715085i	$0.253612\pi$
$318$		0			0
$319$	0.686141	+	1.18843i	0.0384165	+	0.0665393i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.37228			0.131997
$324$		0			0
$325$	34.2337			1.89894
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.941578	+	1.63086i	0.0519109	+	0.0899123i
$330$		0			0
$331$	−1.56930	+	2.71810i	−0.0862563	+	0.149400i	−0.905926	−	0.423436i	$-0.860824\pi$
$331$	−1.56930	+	2.71810i	−0.0862563	+	0.149400i	0.819670	+	0.572837i	$0.194157\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	13.0584	−	22.6179i	0.713458	−	1.23575i
$336$		0			0
$337$	−12.9891	−	22.4978i	−0.707563	−	1.22553i	−0.965759	−	0.259442i	$-0.916461\pi$
$337$	−12.9891	−	22.4978i	−0.707563	−	1.22553i	0.258196	−	0.966093i	$-0.416872\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.627719			−0.0339929
$342$		0			0
$343$	−16.6277			−0.897812
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.3614	+	24.8747i	0.770961	+	1.33534i	0.937037	+	0.349230i	$0.113557\pi$
$347$	14.3614	+	24.8747i	0.770961	+	1.33534i	−0.166076	+	0.986113i	$0.553110\pi$
$348$		0			0
$349$	−17.0584	+	29.5461i	−0.913116	+	1.58156i	−0.103481	+	0.994631i	$0.532998\pi$
$349$	−17.0584	+	29.5461i	−0.913116	+	1.58156i	−0.809636	+	0.586933i	$0.800335\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	10.9891	−	19.0337i	0.584892	−	1.01306i	−0.409997	−	0.912087i	$-0.634470\pi$
$353$	10.9891	−	19.0337i	0.584892	−	1.01306i	0.994889	−	0.100976i	$-0.0321965\pi$
$354$		0			0
$355$	6.74456	+	11.6819i	0.357964	+	0.620012i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−14.2337			−0.751225			−0.375613	−	0.926777i	$-0.622568\pi$
$359$	−14.2337			−0.751225			−0.375613	+	0.926777i	$0.622568\pi$
$360$		0			0
$361$	21.6060			1.13716
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−8.62772	−	14.9436i	−0.451595	−	0.782186i
$366$		0			0
$367$	11.6861	−	20.2410i	0.610012	−	1.05657i	−0.381226	−	0.924482i	$-0.624498\pi$
$367$	11.6861	−	20.2410i	0.610012	−	1.05657i	0.991238	−	0.132089i	$-0.0421686\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.37228	+	12.7692i	−0.382750	+	0.662942i
$372$		0			0
$373$	−1.94158	−	3.36291i	−0.100531	−	0.174125i	0.811372	−	0.584529i	$-0.198721\pi$
$373$	−1.94158	−	3.36291i	−0.100531	−	0.174125i	−0.911904	+	0.410404i	$0.865388\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.37228			−0.379692
$378$		0			0
$379$	23.1168			1.18743			0.593716	−	0.804674i	$-0.297660\pi$
$379$	23.1168			1.18743			0.593716	+	0.804674i	$0.297660\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	15.1753	+	26.2843i	0.775420	+	1.34307i	0.934558	+	0.355810i	$0.115795\pi$
$383$	15.1753	+	26.2843i	0.775420	+	1.34307i	−0.159138	+	0.987256i	$0.550872\pi$
$384$		0			0
$385$	−2.31386	+	4.00772i	−0.117925	+	0.204252i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.8030	+	25.6395i	−0.750541	+	1.29998i	0.197020	+	0.980400i	$0.436874\pi$
$389$	−14.8030	+	25.6395i	−0.750541	+	1.29998i	−0.947561	+	0.319576i	$0.896460\pi$
$390$		0			0
$391$	1.00000	+	1.73205i	0.0505722	+	0.0875936i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.11684			0.106510
$396$		0			0
$397$	16.2337			0.814745			0.407373	−	0.913262i	$-0.366445\pi$
$397$	16.2337			0.814745			0.407373	+	0.913262i	$0.366445\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.61684	+	14.9248i	0.430305	+	0.745310i	0.996899	−	0.0786871i	$-0.0250728\pi$
$401$	8.61684	+	14.9248i	0.430305	+	0.745310i	−0.566595	+	0.823997i	$0.691739\pi$
$402$		0			0
$403$	1.68614	−	2.92048i	0.0839926	−	0.145480i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.37228	−	2.37686i	0.0680215	−	0.117817i
$408$		0			0
$409$	2.87228	+	4.97494i	0.142025	+	0.245995i	0.928259	−	0.371934i	$-0.121305\pi$
$409$	2.87228	+	4.97494i	0.142025	+	0.245995i	−0.786234	+	0.617929i	$0.787972\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9.60597			0.472679
$414$		0			0
$415$	51.8397			2.54471
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−13.8030	−	23.9075i	−0.674320	−	1.16796i	−0.976667	−	0.214759i	$-0.931104\pi$
$419$	−13.8030	−	23.9075i	−0.674320	−	1.16796i	0.302347	−	0.953198i	$-0.402230\pi$
$420$		0			0
$421$	8.94158	−	15.4873i	0.435786	−	0.754803i	−0.561574	−	0.827427i	$-0.689804\pi$
$421$	8.94158	−	15.4873i	0.435786	−	0.754803i	0.997359	+	0.0726236i	$0.0231372\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.18614	−	2.05446i	0.0575363	−	0.0996557i
$426$		0			0
$427$	2.31386	+	4.00772i	0.111976	+	0.193947i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.7446			−0.613884			−0.306942	−	0.951728i	$-0.599306\pi$
$431$	−12.7446			−0.613884			−0.306942	+	0.951728i	$0.599306\pi$
$432$		0			0
$433$	14.8832			0.715239			0.357619	−	0.933867i	$-0.383589\pi$
$433$	14.8832			0.715239			0.357619	+	0.933867i	$0.383589\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.1168	+	29.6472i	0.818810	+	1.41822i
$438$		0			0
$439$	−5.05842	+	8.76144i	−0.241425	+	0.418161i	−0.961121	−	0.276129i	$-0.910948\pi$
$439$	−5.05842	+	8.76144i	−0.241425	+	0.418161i	0.719695	+	0.694290i	$0.244282\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.3614	−	23.1426i	0.634820	−	1.09954i	−0.351734	−	0.936100i	$-0.614408\pi$
$443$	13.3614	−	23.1426i	0.634820	−	1.09954i	0.986553	−	0.163440i	$-0.0522589\pi$
$444$		0			0
$445$	10.1168	+	17.5229i	0.479584	+	0.830665i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	33.1168			1.56288			0.781440	−	0.623980i	$-0.214485\pi$
$449$	33.1168			1.56288			0.781440	+	0.623980i	$0.214485\pi$
$450$		0			0
$451$	0.255437			0.0120281
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−12.4307	−	21.5306i	−0.582760	−	1.00937i
$456$		0			0
$457$	−3.87228	+	6.70699i	−0.181138	+	0.313740i	−0.942268	−	0.334859i	$-0.891311\pi$
$457$	−3.87228	+	6.70699i	−0.181138	+	0.313740i	0.761131	+	0.648599i	$0.224645\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.0584	+	20.8858i	−0.561617	+	0.972749i	0.435739	+	0.900073i	$0.356487\pi$
$461$	−12.0584	+	20.8858i	−0.561617	+	0.972749i	−0.997356	+	0.0726756i	$0.976846\pi$
$462$		0			0
$463$	−5.17527	−	8.96382i	−0.240515	−	0.416584i	0.720346	−	0.693615i	$-0.243983\pi$
$463$	−5.17527	−	8.96382i	−0.240515	−	0.416584i	−0.960861	+	0.277031i	$0.910650\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.62772			0.0753218			0.0376609	−	0.999291i	$-0.488009\pi$
$467$	1.62772			0.0753218			0.0376609	+	0.999291i	$0.488009\pi$
$468$		0			0
$469$	−10.6277			−0.490742
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.87228	+	8.43904i	0.224028	+	0.388027i
$474$		0			0
$475$	20.3030	−	35.1658i	0.931565	−	1.61352i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.8030	+	25.6395i	−0.676366	+	1.17150i	0.299702	+	0.954033i	$0.403113\pi$
$479$	−14.8030	+	25.6395i	−0.676366	+	1.17150i	−0.976068	+	0.217467i	$0.930221\pi$
$480$		0			0
$481$	7.37228	+	12.7692i	0.336147	+	0.582224i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−32.8614			−1.49216
$486$		0			0
$487$	4.74456			0.214997			0.107498	−	0.994205i	$-0.465716\pi$
$487$	4.74456			0.214997			0.107498	+	0.994205i	$0.465716\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.87228	−	10.1711i	−0.265012	−	0.459015i	0.702555	−	0.711630i	$-0.252043\pi$
$491$	−5.87228	−	10.1711i	−0.265012	−	0.459015i	−0.967567	+	0.252615i	$0.918709\pi$
$492$		0			0
$493$	−0.255437	+	0.442430i	−0.0115043	+	0.0199261i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.74456	−	4.75372i	0.123110	−	0.213234i
$498$		0			0
$499$	12.9891	+	22.4978i	0.581473	+	1.00714i	0.995305	+	0.0967877i	$0.0308568\pi$
$499$	12.9891	+	22.4978i	0.581473	+	1.00714i	−0.413832	+	0.910353i	$0.635810\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	29.4891			1.31486			0.657428	−	0.753518i	$-0.271645\pi$
$503$	29.4891			1.31486			0.657428	+	0.753518i	$0.271645\pi$
$504$		0			0
$505$	−34.1168			−1.51818
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.94158	−	12.0232i	−0.307680	−	0.532917i	0.670174	−	0.742204i	$-0.266219\pi$
$509$	−6.94158	−	12.0232i	−0.307680	−	0.532917i	−0.977854	+	0.209286i	$0.932886\pi$
$510$		0			0
$511$	−3.51087	+	6.08101i	−0.155312	+	0.269008i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−11.1753	+	19.3561i	−0.492441	+	0.852933i
$516$		0			0
$517$	0.686141	+	1.18843i	0.0301764	+	0.0522671i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.11684			0.224173			0.112087	−	0.993698i	$-0.464247\pi$
$521$	5.11684			0.224173			0.112087	+	0.993698i	$0.464247\pi$
$522$		0			0
$523$	−9.48913			−0.414930			−0.207465	−	0.978242i	$-0.566521\pi$
$523$	−9.48913			−0.414930			−0.207465	+	0.978242i	$0.566521\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.116844	−	0.202380i	−0.00508980	−	0.00881580i
$528$		0			0
$529$	−2.93070	+	5.07613i	−0.127422	+	0.220701i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.686141	+	1.18843i	−0.0297201	+	0.0514766i
$534$		0			0
$535$	−26.7446	−	46.3229i	−1.15627	−	2.00272i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.11684			−0.220398
$540$		0			0
$541$	−32.2337			−1.38583			−0.692917	−	0.721017i	$-0.743675\pi$
$541$	−32.2337			−1.38583			−0.692917	+	0.721017i	$0.743675\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11.3723	−	19.6974i	−0.487135	−	0.843743i
$546$		0			0
$547$	−13.8723	+	24.0275i	−0.593136	+	1.02734i	0.400671	+	0.916222i	$0.368777\pi$
$547$	−13.8723	+	24.0275i	−0.593136	+	1.02734i	−0.993807	+	0.111120i	$0.964556\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4.37228	+	7.57301i	−0.186265	+	0.322621i
$552$		0			0
$553$	−0.430703	−	0.746000i	−0.0183154	−	0.0317231i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.0000			0.593199			0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000			0.593199			0.296600	+	0.955002i	$0.404147\pi$
$558$		0			0
$559$	−52.3505			−2.21419
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.872281	+	1.51084i	0.0367623	+	0.0636741i	0.883821	−	0.467825i	$-0.154962\pi$
$563$	0.872281	+	1.51084i	0.0367623	+	0.0636741i	−0.847059	+	0.531499i	$0.821629\pi$
$564$		0			0
$565$	2.31386	−	4.00772i	0.0973448	−	0.168606i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.61684	+	6.26456i	−0.151626	+	0.262624i	−0.931825	−	0.362907i	$-0.881784\pi$
$569$	−3.61684	+	6.26456i	−0.151626	+	0.262624i	0.780199	+	0.625531i	$0.215118\pi$
$570$		0			0
$571$	−1.75544	−	3.04051i	−0.0734628	−	0.127241i	0.826954	−	0.562270i	$-0.190072\pi$
$571$	−1.75544	−	3.04051i	−0.0734628	−	0.127241i	−0.900417	+	0.435028i	$0.856738\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	34.2337			1.42764
$576$		0			0
$577$	−13.8614			−0.577058			−0.288529	−	0.957471i	$-0.593166\pi$
$577$	−13.8614			−0.577058			−0.288529	+	0.957471i	$0.593166\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−10.5475	−	18.2689i	−0.437586	−	0.757921i
$582$		0			0
$583$	−5.37228	+	9.30506i	−0.222497	+	0.385376i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.6168	−	21.8530i	0.520753	−	0.901970i	−0.478956	−	0.877839i	$-0.658985\pi$
$587$	12.6168	−	21.8530i	0.520753	−	0.901970i	0.999709	−	0.0241315i	$-0.00768204\pi$
$588$		0			0
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	26.0000			1.06769			0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000			1.06769			0.533846	+	0.845582i	$0.320746\pi$
$594$		0			0
$595$	−1.72281			−0.0706285
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−5.56930	−	9.64630i	−0.227555	−	0.394137i	0.729528	−	0.683951i	$-0.239740\pi$
$599$	−5.56930	−	9.64630i	−0.227555	−	0.394137i	−0.957083	+	0.289814i	$0.906407\pi$
$600$		0			0
$601$	19.9891	−	34.6222i	0.815373	−	1.41227i	−0.0936860	−	0.995602i	$-0.529865\pi$
$601$	19.9891	−	34.6222i	0.815373	−	1.41227i	0.909059	−	0.416666i	$-0.136802\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	16.8614	−	29.2048i	0.685514	−	1.18734i
$606$		0			0
$607$	3.05842	+	5.29734i	0.124138	+	0.215012i	0.921395	−	0.388626i	$-0.127050\pi$
$607$	3.05842	+	5.29734i	0.124138	+	0.215012i	−0.797258	+	0.603639i	$0.793717\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.37228			−0.298251
$612$		0			0
$613$	−1.25544			−0.0507066			−0.0253533	−	0.999679i	$-0.508071\pi$
$613$	−1.25544			−0.0507066			−0.0253533	+	0.999679i	$0.508071\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.98913	−	6.90937i	−0.160596	−	0.278161i	0.774487	−	0.632590i	$-0.218008\pi$
$617$	−3.98913	−	6.90937i	−0.160596	−	0.278161i	−0.935083	+	0.354430i	$0.884675\pi$
$618$		0			0
$619$	−6.61684	+	11.4607i	−0.265953	+	0.460645i	−0.967813	−	0.251671i	$-0.919020\pi$
$619$	−6.61684	+	11.4607i	−0.265953	+	0.460645i	0.701860	+	0.712315i	$0.252353\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.11684	−	7.13058i	0.164938	−	0.285681i
$624$		0			0
$625$	8.12772	+	14.0776i	0.325109	+	0.563105i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.02175			0.0407398
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.00000	−	13.8564i	−0.317470	−	0.549875i
$636$		0			0
$637$	13.7446	−	23.8063i	0.544579	−	0.943239i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15.6168	+	27.0492i	−0.616828	+	1.06838i	0.373233	+	0.927738i	$0.378249\pi$
$641$	−15.6168	+	27.0492i	−0.616828	+	1.06838i	−0.990061	+	0.140640i	$0.955084\pi$
$642$		0			0
$643$	1.50000	+	2.59808i	0.0591542	+	0.102458i	0.894086	−	0.447895i	$-0.147826\pi$
$643$	1.50000	+	2.59808i	0.0591542	+	0.102458i	−0.834932	+	0.550353i	$0.814493\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.7228			−0.932640			−0.466320	−	0.884616i	$-0.654420\pi$
$647$	−23.7228			−0.932640			−0.466320	+	0.884616i	$0.654420\pi$
$648$		0			0
$649$	7.00000			0.274774
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−20.0584	−	34.7422i	−0.784947	−	1.35957i	−0.929031	−	0.370002i	$-0.879357\pi$
$653$	−20.0584	−	34.7422i	−0.784947	−	1.35957i	0.144084	−	0.989565i	$-0.453976\pi$
$654$		0			0
$655$	−21.2921	+	36.8790i	−0.831952	+	1.44098i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.941578	+	1.63086i	−0.0366787	+	0.0635293i	−0.883782	−	0.467899i	$-0.845011\pi$
$659$	−0.941578	+	1.63086i	−0.0366787	+	0.0635293i	0.847103	+	0.531428i	$0.178344\pi$
$660$		0			0
$661$	−8.54755	−	14.8048i	−0.332461	−	0.575839i	0.650533	−	0.759478i	$-0.274546\pi$
$661$	−8.54755	−	14.8048i	−0.332461	−	0.575839i	−0.982994	+	0.183639i	$0.941212\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−29.4891			−1.14354
$666$		0			0
$667$	−7.37228			−0.285456
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.68614	+	2.92048i	0.0650927	+	0.112744i
$672$		0			0
$673$	−2.68614	+	4.65253i	−0.103543	+	0.179342i	−0.913142	−	0.407642i	$-0.866351\pi$
$673$	−2.68614	+	4.65253i	−0.103543	+	0.179342i	0.809599	+	0.586983i	$0.199685\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.80298	−	16.9793i	0.376759	−	0.652566i	−0.613829	−	0.789439i	$-0.710372\pi$
$677$	9.80298	−	16.9793i	0.376759	−	0.652566i	0.990589	+	0.136872i	$0.0437051\pi$
$678$		0			0
$679$	6.68614	+	11.5807i	0.256591	+	0.444428i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−9.62772			−0.368394			−0.184197	−	0.982889i	$-0.558969\pi$
$683$	−9.62772			−0.368394			−0.184197	+	0.982889i	$0.558969\pi$
$684$		0			0
$685$	−21.0951			−0.806002
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−28.8614	−	49.9894i	−1.09953	−	1.90445i
$690$		0			0
$691$	−1.05842	+	1.83324i	−0.0402643	+	0.0697398i	−0.885455	−	0.464725i	$-0.846153\pi$
$691$	−1.05842	+	1.83324i	−0.0402643	+	0.0697398i	0.845191	+	0.534464i	$0.179487\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.68614	+	16.7769i	−0.367416	+	0.636384i
$696$		0			0
$697$	0.0475473	+	0.0823543i	0.00180098	+	0.00311939i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	12.5109			0.472529			0.236265	−	0.971689i	$-0.424077\pi$
$701$	12.5109			0.472529			0.236265	+	0.971689i	$0.424077\pi$
$702$		0			0
$703$	17.4891			0.659615
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.94158	+	12.0232i	0.261065	+	0.452178i
$708$		0			0
$709$	−5.80298	+	10.0511i	−0.217936	+	0.377476i	−0.954177	−	0.299244i	$-0.903266\pi$
$709$	−5.80298	+	10.0511i	−0.217936	+	0.377476i	0.736241	+	0.676719i	$0.236599\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.68614	−	2.92048i	0.0631465	−	0.109373i
$714$		0			0
$715$	−9.05842	−	15.6896i	−0.338766	−	0.586760i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	22.5109			0.839514			0.419757	−	0.907637i	$-0.362115\pi$
$719$	22.5109			0.839514			0.419757	+	0.907637i	$0.362115\pi$
$720$		0			0
$721$	9.09509			0.338719
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.37228	+	7.57301i	0.162382	+	0.281255i
$726$		0			0
$727$	14.0584	−	24.3499i	0.521398	−	0.903088i	−0.478292	−	0.878201i	$-0.658744\pi$
$727$	14.0584	−	24.3499i	0.521398	−	0.903088i	0.999690	−	0.0248871i	$-0.00792263\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.81386	+	3.14170i	−0.0670880	+	0.116200i
$732$		0			0
$733$	4.56930	+	7.91425i	0.168771	+	0.292320i	0.937988	−	0.346668i	$-0.112687\pi$
$733$	4.56930	+	7.91425i	0.168771	+	0.292320i	−0.769217	+	0.638987i	$0.779354\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.74456			−0.285275
$738$		0			0
$739$	−24.8832			−0.915342			−0.457671	−	0.889122i	$-0.651316\pi$
$739$	−24.8832			−0.915342			−0.457671	+	0.889122i	$0.651316\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−20.6861	−	35.8294i	−0.758901	−	1.31445i	−0.943412	−	0.331624i	$-0.892403\pi$
$743$	−20.6861	−	35.8294i	−0.758901	−	1.31445i	0.184511	−	0.982831i	$-0.440930\pi$
$744$		0			0
$745$	−4.43070	+	7.67420i	−0.162328	+	0.281161i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.8832	+	18.8502i	−0.397662	+	0.688771i
$750$		0			0
$751$	−21.6861	−	37.5615i	−0.791339	−	1.37064i	−0.925138	−	0.379630i	$-0.876051\pi$
$751$	−21.6861	−	37.5615i	−0.791339	−	1.37064i	0.133800	−	0.991008i	$-0.457282\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	18.1168			0.659339
$756$		0			0
$757$	31.4891			1.14449			0.572246	−	0.820082i	$-0.306072\pi$
$757$	31.4891			1.14449			0.572246	+	0.820082i	$0.306072\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.1753	+	28.0164i	0.586353	+	1.01559i	0.994705	+	0.102769i	$0.0327701\pi$
$761$	16.1753	+	28.0164i	0.586353	+	1.01559i	−0.408352	+	0.912824i	$0.633897\pi$
$762$		0			0
$763$	−4.62772	+	8.01544i	−0.167535	+	0.290179i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−18.8030	+	32.5677i	−0.678936	+	1.17595i
$768$		0			0
$769$	−7.94158	−	13.7552i	−0.286381	−	0.496026i	0.686562	−	0.727071i	$-0.259119\pi$
$769$	−7.94158	−	13.7552i	−0.286381	−	0.496026i	−0.972943	+	0.231045i	$0.925786\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	16.9783			0.610665			0.305333	−	0.952246i	$-0.401232\pi$
$773$	16.9783			0.610665			0.305333	+	0.952246i	$0.401232\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.813859	+	1.40965i	0.0291595	+	0.0505058i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−23.8030	+	41.2280i	−0.849565	+	1.47149i
$786$		0			0
$787$	−15.9198	−	27.5740i	−0.567481	−	0.982905i	−0.996814	−	0.0797592i	$-0.974585\pi$
$787$	−15.9198	−	27.5740i	−0.567481	−	0.982905i	0.429334	−	0.903146i	$-0.358748\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.88316			−0.0669573
$792$		0			0
$793$	−18.1168			−0.643348
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.8030	+	37.7639i	0.772301	+	1.33767i	0.936299	+	0.351204i	$0.114228\pi$
$797$	21.8030	+	37.7639i	0.772301	+	1.33767i	−0.163997	+	0.986461i	$0.552439\pi$
$798$		0			0
$799$	−0.255437	+	0.442430i	−0.00903672	+	0.0156521i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.55842	+	4.43132i	−0.0902848	+	0.156378i
$804$		0			0
$805$	−12.4307	−	21.5306i	−0.438125	−	0.758854i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−41.8614			−1.47177			−0.735884	−	0.677107i	$-0.763233\pi$
$809$	−41.8614			−1.47177			−0.735884	+	0.677107i	$0.763233\pi$
$810$		0			0
$811$	41.3505			1.45201			0.726007	−	0.687688i	$-0.241374\pi$
$811$	41.3505			1.45201			0.726007	+	0.687688i	$0.241374\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−20.2337	−	35.0458i	−0.708755	−	1.22760i
$816$		0			0
$817$	−31.0475	+	53.7759i	−1.08622	+	1.88138i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.6861	−	21.9730i	0.442749	−	0.766864i	−0.555143	−	0.831755i	$-0.687336\pi$
$821$	12.6861	−	21.9730i	0.442749	−	0.766864i	0.997892	+	0.0648905i	$0.0206698\pi$
$822$		0			0
$823$	21.0584	+	36.4743i	0.734050	+	1.27141i	0.955139	+	0.296159i	$0.0957058\pi$
$823$	21.0584	+	36.4743i	0.734050	+	1.27141i	−0.221088	+	0.975254i	$0.570961\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14.9783			−0.520845			−0.260422	−	0.965495i	$-0.583862\pi$
$827$	−14.9783			−0.520845			−0.260422	+	0.965495i	$0.583862\pi$
$828$		0			0
$829$	−7.48913			−0.260108			−0.130054	−	0.991507i	$-0.541515\pi$
$829$	−7.48913			−0.260108			−0.130054	+	0.991507i	$0.541515\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.952453	−	1.64970i	−0.0330005	−	0.0571586i
$834$		0			0
$835$	3.17527	−	5.49972i	0.109885	−	0.190326i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	16.5475	−	28.6612i	0.571285	−	0.989494i	−0.425150	−	0.905123i	$-0.639779\pi$
$839$	16.5475	−	28.6612i	0.571285	−	0.989494i	0.996434	−	0.0843712i	$-0.0268881\pi$
$840$		0			0
$841$	13.5584	+	23.4839i	0.467532	+	0.809789i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	53.4891			1.84008
$846$		0			0
$847$	−13.7228			−0.471521
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.37228	+	12.7692i	0.252719	+	0.437721i
$852$		0			0
$853$	−7.94158	+	13.7552i	−0.271914	+	0.470970i	−0.969352	−	0.245676i	$-0.920990\pi$
$853$	−7.94158	+	13.7552i	−0.271914	+	0.470970i	0.697438	+	0.716646i	$0.254323\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.94158	−	17.2193i	0.339598	−	0.588201i	−0.644759	−	0.764386i	$-0.723042\pi$
$857$	9.94158	−	17.2193i	0.339598	−	0.588201i	0.984357	+	0.176185i	$0.0563757\pi$
$858$		0			0
$859$	10.2446	+	17.7441i	0.349540	+	0.605421i	0.986168	−	0.165750i	$-0.0530046\pi$
$859$	10.2446	+	17.7441i	0.349540	+	0.605421i	−0.636628	+	0.771171i	$0.719671\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	26.9783			0.918350			0.459175	−	0.888346i	$-0.348145\pi$
$863$	26.9783			0.918350			0.459175	+	0.888346i	$0.348145\pi$
$864$		0			0
$865$	35.8397			1.21858
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.313859	−	0.543620i	−0.0106469	−	0.0184411i
$870$		0			0
$871$	20.8030	−	36.0318i	0.704882	−	1.22089i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.17527	+	5.49972i	−0.107344	+	0.185925i
$876$		0			0
$877$	0.430703	+	0.746000i	0.0145438	+	0.0251906i	0.873206	−	0.487352i	$-0.162037\pi$
$877$	0.430703	+	0.746000i	0.0145438	+	0.0251906i	−0.858662	+	0.512542i	$0.828704\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	20.9783			0.706775			0.353388	−	0.935477i	$-0.385030\pi$
$881$	20.9783			0.706775			0.353388	+	0.935477i	$0.385030\pi$
$882$		0			0
$883$	42.8397			1.44167			0.720835	−	0.693107i	$-0.243759\pi$
$883$	42.8397			1.44167			0.720835	+	0.693107i	$0.243759\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.43070	+	14.6024i	0.283075	+	0.490301i	0.972141	−	0.234398i	$-0.0753120\pi$
$887$	8.43070	+	14.6024i	0.283075	+	0.490301i	−0.689065	+	0.724699i	$0.741979\pi$
$888$		0			0
$889$	−3.25544	+	5.63858i	−0.109184	+	0.189112i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.37228	+	7.57301i	−0.146313	+	0.253421i
$894$		0			0
$895$	38.7446	+	67.1076i	1.29509	+	2.24316i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.861407			0.0287295
$900$		0			0
$901$	−4.00000			−0.133259
$902$		0			0
$903$		0			0
$904$		0			0
$905$	39.6060	+	68.5996i	1.31655	+	2.28033i
$906$		0			0
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	−0.376228	−	0.926527i	$-0.622779\pi$
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	0.990510	−	0.137441i	$-0.0438878\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	9.05842	−	15.6896i	0.300119	−	0.519821i	−0.676044	−	0.736861i	$-0.736307\pi$
$911$	9.05842	−	15.6896i	0.300119	−	0.519821i	0.976163	+	0.217040i	$0.0696403\pi$
$912$		0			0
$913$	−7.68614	−	13.3128i	−0.254374	−	0.440589i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	17.3288			0.572247
$918$		0			0
$919$	−1.76631			−0.0582653			−0.0291326	−	0.999576i	$-0.509275\pi$
$919$	−1.76631			−0.0582653			−0.0291326	+	0.999576i	$0.509275\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	10.7446	+	18.6101i	0.353662	+	0.612560i
$924$		0			0
$925$	8.74456	−	15.1460i	0.287519	−	0.497998i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−24.2921	+	42.0752i	−0.796998	+	1.38044i	0.124564	+	0.992212i	$0.460247\pi$
$929$	−24.2921	+	42.0752i	−0.796998	+	1.38044i	−0.921563	+	0.388230i	$0.873087\pi$
$930$		0			0
$931$	−16.3030	−	28.2376i	−0.534309	−	0.925450i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.25544			−0.0410572
$936$		0			0
$937$	30.0000			0.980057			0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000			0.980057			0.490029	+	0.871706i	$0.336986\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−23.9198	−	41.4304i	−0.779764	−	1.35059i	−0.932078	−	0.362259i	$-0.882006\pi$
$941$	−23.9198	−	41.4304i	−0.779764	−	1.35059i	0.152313	−	0.988332i	$-0.451328\pi$
$942$		0			0
$943$	−0.686141	+	1.18843i	−0.0223438	+	0.0387006i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	21.1277	−	36.5943i	0.686559	−	1.18915i	−0.286386	−	0.958114i	$-0.592454\pi$
$947$	21.1277	−	36.5943i	0.686559	−	1.18915i	0.972944	−	0.231040i	$-0.0742128\pi$
$948$		0			0
$949$	−13.7446	−	23.8063i	−0.446167	−	0.772785i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	25.1168			0.813614			0.406807	−	0.913514i	$-0.366642\pi$
$953$	25.1168			0.813614			0.406807	+	0.913514i	$0.366642\pi$
$954$		0			0
$955$	−63.6060			−2.05824
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.29211	+	7.43415i	0.138599	+	0.240061i
$960$		0			0
$961$	15.3030	−	26.5055i	0.493645	−	0.855018i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	16.4307	−	28.4588i	0.528923	−	0.916122i
$966$		0			0
$967$	−1.31386	−	2.27567i	−0.0422509	−	0.0731806i	0.844127	−	0.536144i	$-0.180120\pi$
$967$	−1.31386	−	2.27567i	−0.0422509	−	0.0731806i	−0.886378	+	0.462963i	$0.846786\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	17.4891			0.561253			0.280626	−	0.959817i	$-0.409458\pi$
$971$	17.4891			0.561253			0.280626	+	0.959817i	$0.409458\pi$
$972$		0			0
$973$	7.88316			0.252722
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.87228	+	10.1711i	0.187871	+	0.325402i	0.944540	−	0.328396i	$-0.106508\pi$
$977$	5.87228	+	10.1711i	0.187871	+	0.325402i	−0.756669	+	0.653798i	$0.773175\pi$
$978$		0			0
$979$	3.00000	−	5.19615i	0.0958804	−	0.166070i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.9416	+	32.8078i	−0.604143	+	1.04641i	0.388044	+	0.921641i	$0.373151\pi$
$983$	−18.9416	+	32.8078i	−0.604143	+	1.04641i	−0.992186	+	0.124765i	$0.960182\pi$
$984$		0			0
$985$	45.0951	+	78.1070i	1.43685	+	2.48870i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−52.3505			−1.66465
$990$		0			0
$991$	−5.02175			−0.159521			−0.0797606	−	0.996814i	$-0.525416\pi$
$991$	−5.02175			−0.159521			−0.0797606	+	0.996814i	$0.525416\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	30.7446	+	53.2511i	0.974668	+	1.68817i
$996$		0			0
$997$	1.17527	−	2.03562i	0.0372210	−	0.0644687i	−0.846815	−	0.531888i	$-0.821483\pi$
$997$	1.17527	−	2.03562i	0.0372210	−	0.0644687i	0.884036	+	0.467419i	$0.154816\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.i.d.289.1		4
3.2	odd	2		144.2.i.d.97.2		4
4.3	odd	2		216.2.i.b.73.1		4
8.3	odd	2		1728.2.i.i.1153.2		4
8.5	even	2		1728.2.i.j.1153.2		4
9.2	odd	6		1296.2.a.n.1.1		2
9.4	even	3	inner	432.2.i.d.145.1		4
9.5	odd	6		144.2.i.d.49.2		4
9.7	even	3		1296.2.a.p.1.2		2
12.11	even	2		72.2.i.b.25.1	✓	4
24.5	odd	2		576.2.i.l.385.1		4
24.11	even	2		576.2.i.j.385.2		4
36.7	odd	6		648.2.a.g.1.2		2
36.11	even	6		648.2.a.f.1.1		2
36.23	even	6		72.2.i.b.49.1	yes	4
36.31	odd	6		216.2.i.b.145.1		4
72.5	odd	6		576.2.i.l.193.1		4
72.11	even	6		5184.2.a.bt.1.2		2
72.13	even	6		1728.2.i.j.577.2		4
72.29	odd	6		5184.2.a.bs.1.2		2
72.43	odd	6		5184.2.a.bp.1.1		2
72.59	even	6		576.2.i.j.193.2		4
72.61	even	6		5184.2.a.bo.1.1		2
72.67	odd	6		1728.2.i.i.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.i.b.25.1	✓	4	12.11	even	2
72.2.i.b.49.1	yes	4	36.23	even	6
144.2.i.d.49.2		4	9.5	odd	6
144.2.i.d.97.2		4	3.2	odd	2
216.2.i.b.73.1		4	4.3	odd	2
216.2.i.b.145.1		4	36.31	odd	6
432.2.i.d.145.1		4	9.4	even	3	inner
432.2.i.d.289.1		4	1.1	even	1	trivial
576.2.i.j.193.2		4	72.59	even	6
576.2.i.j.385.2		4	24.11	even	2
576.2.i.l.193.1		4	72.5	odd	6
576.2.i.l.385.1		4	24.5	odd	2
648.2.a.f.1.1		2	36.11	even	6
648.2.a.g.1.2		2	36.7	odd	6
1296.2.a.n.1.1		2	9.2	odd	6
1296.2.a.p.1.2		2	9.7	even	3
1728.2.i.i.577.2		4	72.67	odd	6
1728.2.i.i.1153.2		4	8.3	odd	2
1728.2.i.j.577.2		4	72.13	even	6
1728.2.i.j.1153.2		4	8.5	even	2
5184.2.a.bo.1.1		2	72.61	even	6
5184.2.a.bp.1.1		2	72.43	odd	6
5184.2.a.bs.1.2		2	72.29	odd	6
5184.2.a.bt.1.2		2	72.11	even	6

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.68614 - 2.92048i) q^{5} +(-0.686141 + 1.18843i) q^{7} +(-0.500000 + 0.866025i) q^{11} +(-2.68614 - 4.65253i) q^{13} -0.372281 q^{17} -6.37228 q^{19} +(-2.68614 - 4.65253i) q^{23} +(-3.18614 + 5.51856i) q^{25} +(0.686141 - 1.18843i) q^{29} +(0.313859 + 0.543620i) q^{31} +4.62772 q^{35} -2.74456 q^{37} +(-0.127719 - 0.221215i) q^{41} +(4.87228 - 8.43904i) q^{43} +(0.686141 - 1.18843i) q^{47} +(2.55842 + 4.43132i) q^{49} +10.7446 q^{53} +3.37228 q^{55} +(-3.50000 - 6.06218i) q^{59} +(1.68614 - 2.92048i) q^{61} +(-9.05842 + 15.6896i) q^{65} +(3.87228 + 6.70699i) q^{67} -4.00000 q^{71} +5.11684 q^{73} +(-0.686141 - 1.18843i) q^{77} +(-0.313859 + 0.543620i) q^{79} +(-7.68614 + 13.3128i) q^{83} +(0.627719 + 1.08724i) q^{85} -6.00000 q^{89} +7.37228 q^{91} +(10.7446 + 18.6101i) q^{95} +(4.87228 - 8.43904i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{5} + 3 q^{7} - 2 q^{11} - 5 q^{13} + 10 q^{17} - 14 q^{19} - 5 q^{23} - 7 q^{25} - 3 q^{29} + 7 q^{31} + 30 q^{35} + 12 q^{37} - 12 q^{41} + 8 q^{43} - 3 q^{47} - 7 q^{49} + 20 q^{53} + 2 q^{55}+ \cdots + 8 q^{97}+O(q^{100}) \) 4 * q - q^5 + 3 * q^7 - 2 * q^11 - 5 * q^13 + 10 * q^17 - 14 * q^19 - 5 * q^23 - 7 * q^25 - 3 * q^29 + 7 * q^31 + 30 * q^35 + 12 * q^37 - 12 * q^41 + 8 * q^43 - 3 * q^47 - 7 * q^49 + 20 * q^53 + 2 * q^55 - 14 * q^59 + q^61 - 19 * q^65 + 4 * q^67 - 16 * q^71 - 14 * q^73 + 3 * q^77 - 7 * q^79 - 25 * q^83 + 14 * q^85 - 24 * q^89 + 18 * q^91 + 20 * q^95 + 8 * q^97

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