LMFDB - Embedded newform 432.2.v.a.179.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(35,432)] 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("432.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			179.16
Character	$\chi$	$=$	432.179
Dual form			432.2.v.a.251.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.990880 + 1.00904i) q^{2} +(-0.0363133 + 1.99967i) q^{4} +(-3.73424 + 1.00059i) q^{5} +(-1.68236 - 2.91393i) q^{7} +(-2.05372 + 1.94479i) q^{8} +(-4.70981 - 2.77653i) q^{10} +(-0.211428 - 0.0566521i) q^{11} +(-2.71526 + 0.727551i) q^{13} +(1.27325 - 4.58492i) q^{14} +(-3.99736 - 0.145229i) q^{16} +4.23937i q^{17} +(-1.12365 + 1.12365i) q^{19} +(-1.86524 - 7.50358i) q^{20} +(-0.152336 - 0.269474i) q^{22} +(-3.33369 - 1.92471i) q^{23} +(8.61325 - 4.97286i) q^{25} +(-3.42462 - 2.01888i) q^{26} +(5.88800 - 3.25835i) q^{28} +(-2.03634 - 0.545635i) q^{29} +(7.21206 + 4.16388i) q^{31} +(-3.81437 - 4.17739i) q^{32} +(-4.27769 + 4.20071i) q^{34} +(9.19798 + 9.19798i) q^{35} +(-2.66564 + 2.66564i) q^{37} +(-2.24720 - 0.0204025i) q^{38} +(5.72317 - 9.31725i) q^{40} +(-1.70386 + 2.95117i) q^{41} +(-1.25664 + 4.68985i) q^{43} +(0.120963 - 0.420730i) q^{44} +(-1.36119 - 5.27098i) q^{46} +(2.34998 + 4.07028i) q^{47} +(-2.16067 + 3.74239i) q^{49} +(13.5525 + 3.76358i) q^{50} +(-1.35626 - 5.45604i) q^{52} +(-7.58271 - 7.58271i) q^{53} +0.846209 q^{55} +(9.12210 + 2.71258i) q^{56} +(-1.46720 - 2.59540i) q^{58} +(1.43167 + 5.34305i) q^{59} +(-2.33105 + 8.69958i) q^{61} +(2.94477 + 11.4031i) q^{62} +(0.435568 - 7.98813i) q^{64} +(9.41144 - 5.43370i) q^{65} +(1.38665 + 5.17504i) q^{67} +(-8.47735 - 0.153945i) q^{68} +(-0.167011 + 18.3952i) q^{70} -7.53614i q^{71} -3.22646i q^{73} +(-5.33107 - 0.0484011i) q^{74} +(-2.20612 - 2.28773i) q^{76} +(0.190618 + 0.711397i) q^{77} +(4.98587 - 2.87859i) q^{79} +(15.0724 - 3.45739i) q^{80} +(-4.66616 + 1.20500i) q^{82} +(-1.20739 + 4.50604i) q^{83} +(-4.24186 - 15.8308i) q^{85} +(-5.97741 + 3.37908i) q^{86} +(0.544392 - 0.294836i) q^{88} -2.96157 q^{89} +(6.68807 + 6.68807i) q^{91} +(3.96984 - 6.59639i) q^{92} +(-1.77852 + 6.40437i) q^{94} +(3.07166 - 5.32027i) q^{95} +(-7.63883 - 13.2308i) q^{97} +(-5.91718 + 1.52806i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.990880	+	1.00904i	0.700658	+	0.713497i
$2$	0.990880	+	1.00904i	0.700658	+	0.713497i
$3$		0			0
$3$		0			0
$4$	−0.0363133	+	1.99967i	−0.0181566	+	0.999835i
$5$	−3.73424	+	1.00059i	−1.67000	+	0.447476i	−0.965111	−	0.261839i	$-0.915671\pi$
$5$	−3.73424	+	1.00059i	−1.67000	+	0.447476i	−0.704891	+	0.709315i	$0.749004\pi$
$6$		0			0
$7$	−1.68236	−	2.91393i	−0.635872	−	1.10136i	−0.986330	−	0.164785i	$-0.947307\pi$
$7$	−1.68236	−	2.91393i	−0.635872	−	1.10136i	0.350457	−	0.936579i	$-0.386026\pi$
$8$	−2.05372	+	1.94479i	−0.726101	+	0.687588i
$9$		0			0
$10$	−4.70981	−	2.77653i	−1.48937	−	0.878015i
$11$	−0.211428	−	0.0566521i	−0.0637480	−	0.0170812i	0.226804	−	0.973940i	$-0.427172\pi$
$11$	−0.211428	−	0.0566521i	−0.0637480	−	0.0170812i	−0.290552	+	0.956859i	$0.593839\pi$
$12$		0			0
$13$	−2.71526	+	0.727551i	−0.753076	+	0.201786i	−0.614882	−	0.788619i	$-0.710796\pi$
$13$	−2.71526	+	0.727551i	−0.753076	+	0.201786i	−0.138194	+	0.990405i	$0.544130\pi$
$14$	1.27325	−	4.58492i	0.340291	−	1.22537i
$15$		0			0
$16$	−3.99736	−	0.145229i	−0.999341	−	0.0363073i
$17$			4.23937i			1.02820i	0.857731	+	0.514100i	$0.171874\pi$
$17$			4.23937i			1.02820i	−0.857731	+	0.514100i	$0.828126\pi$
$18$		0			0
$19$	−1.12365	+	1.12365i	−0.257782	+	0.257782i	−0.824152	−	0.566369i	$-0.808348\pi$
$19$	−1.12365	+	1.12365i	−0.257782	+	0.257782i	0.566369	+	0.824152i	$0.308348\pi$
$20$	−1.86524	−	7.50358i	−0.417081	−	1.67785i
$21$		0			0
$22$	−0.152336	−	0.269474i	−0.0324782	−	0.0574522i
$23$	−3.33369	−	1.92471i	−0.695123	−	0.401329i	0.110405	−	0.993887i	$-0.464785\pi$
$23$	−3.33369	−	1.92471i	−0.695123	−	0.401329i	−0.805528	+	0.592557i	$0.798118\pi$
$24$		0			0
$25$	8.61325	−	4.97286i	1.72265	−	0.994572i
$26$	−3.42462	−	2.01888i	−0.671623	−	0.395935i
$27$		0			0
$28$	5.88800	−	3.25835i	1.11273	−	0.615771i
$29$	−2.03634	−	0.545635i	−0.378138	−	0.101322i	0.0647434	−	0.997902i	$-0.479377\pi$
$29$	−2.03634	−	0.545635i	−0.378138	−	0.101322i	−0.442882	+	0.896580i	$0.646044\pi$
$30$		0			0
$31$	7.21206	+	4.16388i	1.29532	+	0.747856i	0.979593	−	0.200993i	$-0.0644169\pi$
$31$	7.21206	+	4.16388i	1.29532	+	0.747856i	0.315731	+	0.948849i	$0.397750\pi$
$32$	−3.81437	−	4.17739i	−0.674291	−	0.738466i
$33$		0			0
$34$	−4.27769	+	4.20071i	−0.733617	+	0.720416i
$35$	9.19798	+	9.19798i	1.55474	+	1.55474i
$36$		0			0
$37$	−2.66564	+	2.66564i	−0.438229	+	0.438229i	−0.891416	−	0.453187i	$-0.850287\pi$
$37$	−2.66564	+	2.66564i	−0.438229	+	0.438229i	0.453187	+	0.891416i	$0.350287\pi$
$38$	−2.24720	−	0.0204025i	−0.364544	−	0.00330972i
$39$		0			0
$40$	5.72317	−	9.31725i	0.904912	−	1.47319i
$41$	−1.70386	+	2.95117i	−0.266098	+	0.460895i	−0.967851	−	0.251526i	$-0.919068\pi$
$41$	−1.70386	+	2.95117i	−0.266098	+	0.460895i	0.701753	+	0.712420i	$0.252401\pi$
$42$		0			0
$43$	−1.25664	+	4.68985i	−0.191636	+	0.715195i	0.801476	+	0.598027i	$0.204048\pi$
$43$	−1.25664	+	4.68985i	−0.191636	+	0.715195i	−0.993112	+	0.117168i	$0.962618\pi$
$44$	0.120963	−	0.420730i	0.0182359	−	0.0634274i
$45$		0			0
$46$	−1.36119	−	5.27098i	−0.200696	−	0.777163i
$47$	2.34998	+	4.07028i	0.342779	+	0.593711i	0.984948	−	0.172852i	$-0.0552984\pi$
$47$	2.34998	+	4.07028i	0.342779	+	0.593711i	−0.642168	+	0.766564i	$0.721965\pi$
$48$		0			0
$49$	−2.16067	+	3.74239i	−0.308667	+	0.534628i
$50$	13.5525	+	3.76358i	1.91661	+	0.532251i
$51$		0			0
$52$	−1.35626	−	5.45604i	−0.188080	−	0.756616i
$53$	−7.58271	−	7.58271i	−1.04157	−	1.04157i	−0.999098	−	0.0424680i	$-0.986478\pi$
$53$	−7.58271	−	7.58271i	−1.04157	−	1.04157i	−0.0424680	−	0.999098i	$-0.513522\pi$
$54$		0			0
$55$	0.846209			0.114103
$56$	9.12210	+	2.71258i	1.21899	+	0.362483i
$57$		0			0
$58$	−1.46720	−	2.59540i	−0.192653	−	0.340793i
$59$	1.43167	+	5.34305i	0.186387	+	0.695605i	0.994329	+	0.106344i	$0.0339145\pi$
$59$	1.43167	+	5.34305i	0.186387	+	0.695605i	−0.807942	+	0.589261i	$0.799419\pi$
$60$		0			0
$61$	−2.33105	+	8.69958i	−0.298460	+	1.11387i	0.639971	+	0.768399i	$0.278946\pi$
$61$	−2.33105	+	8.69958i	−0.298460	+	1.11387i	−0.938431	+	0.345468i	$0.887720\pi$
$62$	2.94477	+	11.4031i	0.373986	+	1.44820i
$63$		0			0
$64$	0.435568	−	7.98813i	0.0544460	−	0.998517i
$65$	9.41144	−	5.43370i	1.16735	−	0.673967i
$66$		0			0
$67$	1.38665	+	5.17504i	0.169406	+	0.632231i	0.997437	+	0.0715493i	$0.0227943\pi$
$67$	1.38665	+	5.17504i	0.169406	+	0.632231i	−0.828031	+	0.560682i	$0.810539\pi$
$68$	−8.47735	−	0.153945i	−1.02803	−	0.0186686i
$69$		0			0
$70$	−0.167011	+	18.3952i	−0.0199617	+	2.19865i
$71$		−	7.53614i		−	0.894375i	−0.894440	−	0.447187i	$-0.852426\pi$
$71$		−	7.53614i		−	0.894375i	0.894440	−	0.447187i	$-0.147574\pi$
$72$		0			0
$73$		−	3.22646i		−	0.377629i	−0.982013	−	0.188814i	$-0.939536\pi$
$73$		−	3.22646i		−	0.377629i	0.982013	−	0.188814i	$-0.0604644\pi$
$74$	−5.33107	−	0.0484011i	−0.619724	−	0.00562651i
$75$		0			0
$76$	−2.20612	−	2.28773i	−0.253059	−	0.262420i
$77$	0.190618	+	0.711397i	0.0217230	+	0.0810712i
$78$		0			0
$79$	4.98587	−	2.87859i	0.560954	−	0.323867i	−0.192574	−	0.981282i	$-0.561684\pi$
$79$	4.98587	−	2.87859i	0.560954	−	0.323867i	0.753528	+	0.657415i	$0.228350\pi$
$80$	15.0724	−	3.45739i	1.68515	−	0.386548i
$81$		0			0
$82$	−4.66616	+	1.20500i	−0.515291	+	0.133070i
$83$	−1.20739	+	4.50604i	−0.132528	+	0.494602i	−0.999996	−	0.00289160i	$-0.999080\pi$
$83$	−1.20739	+	4.50604i	−0.132528	+	0.494602i	0.867468	+	0.497494i	$0.165746\pi$
$84$		0			0
$85$	−4.24186	−	15.8308i	−0.460094	−	1.71710i
$86$	−5.97741	+	3.37908i	−0.644561	+	0.364376i
$87$		0			0
$88$	0.544392	−	0.294836i	0.0580324	−	0.0314297i
$89$	−2.96157			−0.313926			−0.156963	−	0.987605i	$-0.550170\pi$
$89$	−2.96157			−0.313926			−0.156963	+	0.987605i	$0.550170\pi$
$90$		0			0
$91$	6.68807	+	6.68807i	0.701100	+	0.701100i
$92$	3.96984	−	6.59639i	0.413884	−	0.687722i
$93$		0			0
$94$	−1.77852	+	6.40437i	−0.183440	+	0.660561i
$95$	3.07166	−	5.32027i	0.315146	−	0.545849i
$96$		0			0
$97$	−7.63883	−	13.2308i	−0.775606	−	1.34339i	−0.934453	−	0.356085i	$-0.884111\pi$
$97$	−7.63883	−	13.2308i	−0.775606	−	1.34339i	0.158848	−	0.987303i	$-0.449222\pi$
$98$	−5.91718	+	1.52806i	−0.597726	+	0.154358i
$99$		0			0
$100$	9.63131	+	17.4042i	0.963131	+	1.74042i
$101$	−0.0347486	+	0.129684i	−0.00345762	+	0.0129040i	−0.967633	−	0.252361i	$-0.918793\pi$
$101$	−0.0347486	+	0.129684i	−0.00345762	+	0.0129040i	0.964175	+	0.265265i	$0.0854595\pi$
$102$		0			0
$103$	−4.09117	+	7.08611i	−0.403115	+	0.698215i	−0.994100	−	0.108467i	$-0.965406\pi$
$103$	−4.09117	+	7.08611i	−0.403115	+	0.698215i	0.590985	+	0.806682i	$0.298739\pi$
$104$	4.16145	−	6.77480i	0.408064	−	0.664323i
$105$		0			0
$106$	0.137682	−	15.1648i	0.0133729	−	1.47294i
$107$	8.28837	−	8.28837i	0.801267	−	0.801267i	−0.182027	−	0.983294i	$-0.558266\pi$
$107$	8.28837	−	8.28837i	0.801267	−	0.801267i	0.983294	+	0.182027i	$0.0582658\pi$
$108$		0			0
$109$	6.31291	+	6.31291i	0.604667	+	0.604667i	0.941547	−	0.336881i	$-0.109372\pi$
$109$	6.31291	+	6.31291i	0.604667	+	0.604667i	−0.336881	+	0.941547i	$0.609372\pi$
$110$	0.838492	+	0.853857i	0.0799471	+	0.0814121i
$111$		0			0
$112$	6.30182	+	11.8924i	0.595466	+	1.12372i
$113$	−14.6562	−	8.46178i	−1.37874	−	0.796017i	−0.386735	−	0.922191i	$-0.626397\pi$
$113$	−14.6562	−	8.46178i	−1.37874	−	0.796017i	−0.992008	+	0.126174i	$0.959730\pi$
$114$		0			0
$115$	14.3746	+	3.85167i	1.34044	+	0.359171i
$116$	1.16504	−	4.05219i	0.108171	−	0.376236i
$117$		0			0
$118$	−3.97273	+	6.73892i	−0.365719	+	0.620368i
$119$	12.3533	−	7.13215i	1.13242	−	0.653803i
$120$		0			0
$121$	−9.48479	−	5.47604i	−0.862253	−	0.497822i
$122$	−11.0880	+	6.26813i	−1.00386	+	0.567490i
$123$		0			0
$124$	−8.58829	+	14.2705i	−0.771251	+	1.28153i
$125$	−13.5199	+	13.5199i	−1.20926	+	1.20926i
$126$		0			0
$127$			13.4028i			1.18931i	0.803981	+	0.594654i	$0.202711\pi$
$127$			13.4028i			1.18931i	−0.803981	+	0.594654i	$0.797289\pi$
$128$	8.49192	−	7.47578i	0.750587	−	0.660772i
$129$		0			0
$130$	14.8084	+	4.11235i	1.29878	+	0.360677i
$131$	−0.632708	+	0.169534i	−0.0552800	+	0.0148122i	−0.286353	−	0.958124i	$-0.592443\pi$
$131$	−0.632708	+	0.169534i	−0.0552800	+	0.0148122i	0.231073	+	0.972936i	$0.425776\pi$
$132$		0			0
$133$	5.16461	+	1.38385i	0.447829	+	0.119995i
$134$	−3.84781	+	6.52702i	−0.332400	+	0.563849i
$135$		0			0
$136$	−8.24470	−	8.70650i	−0.706977	−	0.746577i
$137$	10.5230	+	18.2263i	0.899037	+	1.55718i	0.828727	+	0.559652i	$0.189065\pi$
$137$	10.5230	+	18.2263i	0.899037	+	1.55718i	0.0703095	+	0.997525i	$0.477601\pi$
$138$		0			0
$139$	6.44400	−	1.72666i	0.546573	−	0.146454i	0.0250423	−	0.999686i	$-0.492028\pi$
$139$	6.44400	−	1.72666i	0.546573	−	0.146454i	0.521530	+	0.853233i	$0.325361\pi$
$140$	−18.7269	+	18.0589i	−1.58271	+	1.52626i
$141$		0			0
$142$	7.60424	−	7.46741i	0.638134	−	0.626651i
$143$	0.615299			0.0514539
$144$		0			0
$145$	8.15012			0.676831
$146$	3.25562	−	3.19703i	0.269437	−	0.264588i
$147$		0			0
$148$	−5.23361	−	5.42721i	−0.430200	−	0.446114i
$149$	21.5773	−	5.78161i	1.76768	−	0.473648i	0.779428	−	0.626492i	$-0.215510\pi$
$149$	21.5773	−	5.78161i	1.76768	−	0.473648i	0.988250	+	0.152844i	$0.0488431\pi$
$150$		0			0
$151$	−9.97506	−	17.2773i	−0.811759	−	1.40601i	−0.911632	−	0.411007i	$-0.865177\pi$
$151$	−9.97506	−	17.2773i	−0.811759	−	1.40601i	0.0998734	−	0.995000i	$-0.468156\pi$
$152$	0.122401	−	4.49292i	0.00992807	−	0.364424i
$153$		0			0
$154$	−0.528947	+	0.897250i	−0.0426237	+	0.0723025i
$155$	−31.0979	−	8.33265i	−2.49784	−	0.669295i
$156$		0			0
$157$	−14.3943	+	3.85693i	−1.14879	+	0.307817i	−0.782479	−	0.622677i	$-0.786045\pi$
$157$	−14.3943	+	3.85693i	−1.14879	+	0.307817i	−0.366308	+	0.930494i	$0.619378\pi$
$158$	7.84501	+	2.17859i	0.624115	+	0.173319i
$159$		0			0
$160$	18.4236	+	11.7828i	1.45651	+	0.931511i
$161$			12.9522i			1.02078i
$162$		0			0
$163$	−4.35766	+	4.35766i	−0.341318	+	0.341318i	−0.856863	−	0.515545i	$-0.827590\pi$
$163$	−4.35766	+	4.35766i	−0.341318	+	0.341318i	0.515545	+	0.856863i	$0.327590\pi$
$164$	−5.83949	−	3.51432i	−0.455987	−	0.274422i
$165$		0			0
$166$	−5.74314	+	3.24664i	−0.445754	+	0.251988i
$167$	11.8952	+	6.86770i	0.920479	+	0.531439i	0.883788	−	0.467888i	$-0.154985\pi$
$167$	11.8952	+	6.86770i	0.920479	+	0.531439i	0.0366910	+	0.999327i	$0.488318\pi$
$168$		0			0
$169$	−4.41505	+	2.54903i	−0.339619	+	0.196079i
$170$	11.7707	−	19.9667i	0.902774	−	1.53137i
$171$		0			0
$172$	−9.33252	−	2.68317i	−0.711598	−	0.204590i
$173$	−5.24342	−	1.40497i	−0.398650	−	0.106818i	0.0539235	−	0.998545i	$-0.482827\pi$
$173$	−5.24342	−	1.40497i	−0.398650	−	0.106818i	−0.452573	+	0.891727i	$0.649494\pi$
$174$		0			0
$175$	−28.9812	−	16.7323i	−2.19077	−	1.26484i
$176$	0.836928	+	0.257164i	0.0630858	+	0.0193845i
$177$		0			0
$178$	−2.93456	−	2.98833i	−0.219954	−	0.223985i
$179$	0.380130	+	0.380130i	0.0284123	+	0.0284123i	0.721170	−	0.692758i	$-0.243605\pi$
$179$	0.380130	+	0.380130i	0.0284123	+	0.0284123i	−0.692758	+	0.721170i	$0.743605\pi$
$180$		0			0
$181$	−4.98992	+	4.98992i	−0.370898	+	0.370898i	−0.867804	−	0.496906i	$-0.834469\pi$
$181$	−4.98992	+	4.98992i	−0.370898	+	0.370898i	0.496906	+	0.867804i	$0.334469\pi$
$182$	−0.121438	+	13.3756i	−0.00900157	+	0.991465i
$183$		0			0
$184$	10.5896	−	2.53052i	0.780679	−	0.186552i
$185$	7.28695	−	12.6214i	0.535747	−	0.927941i
$186$		0			0
$187$	0.240169	−	0.896324i	0.0175629	−	0.0655457i
$188$	−8.22455	+	4.55137i	−0.599837	+	0.331943i
$189$		0			0
$190$	8.41200	−	2.17233i	0.610271	−	0.157598i
$191$	−5.40555	−	9.36269i	−0.391132	−	0.677461i	0.601467	−	0.798898i	$-0.294583\pi$
$191$	−5.40555	−	9.36269i	−0.391132	−	0.677461i	−0.992599	+	0.121437i	$0.961250\pi$
$192$		0			0
$193$	2.60044	−	4.50410i	0.187184	−	0.324212i	−0.757126	−	0.653268i	$-0.773397\pi$
$193$	2.60044	−	4.50410i	0.187184	−	0.324212i	0.944310	+	0.329056i	$0.106731\pi$
$194$	5.78125	−	20.8180i	0.415070	−	1.49465i
$195$		0			0
$196$	−7.40509	−	4.45653i	−0.528935	−	0.318323i
$197$	−2.94550	−	2.94550i	−0.209858	−	0.209858i	0.594349	−	0.804207i	$-0.297410\pi$
$197$	−2.94550	−	2.94550i	−0.209858	−	0.209858i	−0.804207	+	0.594349i	$0.797410\pi$
$198$		0			0
$199$	2.57285			0.182384			0.0911921	−	0.995833i	$-0.470932\pi$
$199$	2.57285			0.182384			0.0911921	+	0.995833i	$0.470932\pi$
$200$	−8.01806	+	26.9639i	−0.566962	+	1.90663i
$201$		0			0
$202$	−0.165287	+	0.0934382i	−0.0116296	+	0.00657429i
$203$	1.83591	+	6.85170i	0.128856	+	0.480895i
$204$		0			0
$205$	3.40971	−	12.7252i	0.238145	−	0.888768i
$206$	−11.2040	+	2.89334i	−0.780620	+	0.201589i
$207$		0			0
$208$	10.9595	−	2.51395i	0.759906	−	0.174311i
$209$	0.301228	−	0.173914i	0.0208364	−	0.0120299i
$210$		0			0
$211$	−4.70786	−	17.5700i	−0.324103	−	1.20957i	−0.915211	−	0.402975i	$-0.867976\pi$
$211$	−4.70786	−	17.5700i	−0.324103	−	1.20957i	0.591108	−	0.806592i	$-0.298691\pi$
$212$	15.4383	−	14.8876i	1.06031	−	1.02248i
$213$		0			0
$214$	16.5761	+	0.150495i	1.13312	+	0.0102876i
$215$		−	18.7704i		−	1.28013i
$216$		0			0
$217$		−	28.0206i		−	1.90216i
$218$	−0.114626	+	12.6253i	−0.00776344	+	0.855093i
$219$		0			0
$220$	−0.0307286	+	1.69214i	−0.00207172	+	0.114084i
$221$	−3.08436	−	11.5110i	−0.207476	−	0.774312i
$222$		0			0
$223$	−2.82059	+	1.62847i	−0.188881	+	0.109050i	−0.591458	−	0.806336i	$-0.701448\pi$
$223$	−2.82059	+	1.62847i	−0.188881	+	0.109050i	0.402578	+	0.915386i	$0.368114\pi$
$224$	−5.75551	+	18.1427i	−0.384556	+	1.21221i
$225$		0			0
$226$	−5.98432	−	23.1733i	−0.398071	−	1.54147i
$227$	2.36663	−	8.83238i	0.157079	−	0.586226i	−0.841840	−	0.539728i	$-0.818527\pi$
$227$	2.36663	−	8.83238i	0.157079	−	0.586226i	0.998918	−	0.0464979i	$-0.0148061\pi$
$228$		0			0
$229$	1.36053	+	5.07755i	0.0899061	+	0.335534i	0.996198	−	0.0871183i	$-0.0277658\pi$
$229$	1.36053	+	5.07755i	0.0899061	+	0.335534i	−0.906292	+	0.422652i	$0.861099\pi$
$230$	10.3571	+	18.3211i	0.682925	+	1.20806i
$231$		0			0
$232$	5.24322	−	2.83967i	0.344234	−	0.186433i
$233$	14.1506			0.927034			0.463517	−	0.886088i	$-0.346587\pi$
$233$	14.1506			0.927034			0.463517	+	0.886088i	$0.346587\pi$
$234$		0			0
$235$	−12.8480	−	12.8480i	−0.838114	−	0.838114i
$236$	−10.7363	+	2.66883i	−0.698875	+	0.173726i
$237$		0			0
$238$	19.4372	+	5.39779i	1.25993	+	0.349886i
$239$	−7.51536	+	13.0170i	−0.486128	+	0.841999i	−0.999873	−	0.0159444i	$-0.994925\pi$
$239$	−7.51536	+	13.0170i	−0.486128	+	0.841999i	0.513745	+	0.857943i	$0.328258\pi$
$240$		0			0
$241$	7.18920	+	12.4521i	0.463097	+	0.802108i	0.999113	−	0.0420996i	$-0.0134047\pi$
$241$	7.18920	+	12.4521i	0.463097	+	0.802108i	−0.536016	+	0.844208i	$0.680071\pi$
$242$	−3.87275	−	14.9966i	−0.248950	−	0.964019i
$243$		0			0
$244$	−17.3116	−	4.97723i	−1.10826	−	0.318635i
$245$	4.32388	−	16.1369i	0.276242	−	1.03095i
$246$		0			0
$247$	2.23348	−	3.86850i	0.142113	−	0.246147i
$248$	−22.9095	+	5.47448i	−1.45475	+	0.347630i
$249$		0			0
$250$	−27.0387	−	0.245486i	−1.71007	−	0.0155259i
$251$	−3.59758	+	3.59758i	−0.227077	+	0.227077i	−0.811471	−	0.584393i	$-0.801333\pi$
$251$	−3.59758	+	3.59758i	−0.227077	+	0.227077i	0.584393	+	0.811471i	$0.301333\pi$
$252$		0			0
$253$	0.595798	+	0.595798i	0.0374575	+	0.0374575i
$254$	−13.5240	+	13.2806i	−0.848569	+	0.833299i
$255$		0			0
$256$	15.9578	+	1.16107i	0.997364	+	0.0725667i
$257$	4.92640	+	2.84426i	0.307300	+	0.177420i	0.645718	−	0.763576i	$-0.276558\pi$
$257$	4.92640	+	2.84426i	0.307300	+	0.177420i	−0.338418	+	0.940996i	$0.609892\pi$
$258$		0			0
$259$	12.2521	+	3.28294i	0.761307	+	0.203992i
$260$	10.5238	+	19.0171i	0.652661	+	1.17939i
$261$		0			0
$262$	−0.798004	−	0.470439i	−0.0493008	−	0.0290638i
$263$	−18.8392	+	10.8768i	−1.16167	+	0.670693i	−0.951705	−	0.307015i	$-0.900670\pi$
$263$	−18.8392	+	10.8768i	−1.16167	+	0.670693i	−0.209970	+	0.977708i	$0.567337\pi$
$264$		0			0
$265$	35.9028	+	20.7285i	2.20549	+	1.27334i
$266$	3.72115	+	6.58252i	0.228158	+	0.403600i
$267$		0			0
$268$	−10.3987	+	2.58491i	−0.635203	+	0.157899i
$269$	−7.43467	+	7.43467i	−0.453300	+	0.453300i	−0.896448	−	0.443148i	$-0.853861\pi$
$269$	−7.43467	+	7.43467i	−0.453300	+	0.453300i	0.443148	+	0.896448i	$0.353861\pi$
$270$		0			0
$271$			11.8875i			0.722111i	0.932544	+	0.361056i	$0.117584\pi$
$271$			11.8875i			0.722111i	−0.932544	+	0.361056i	$0.882416\pi$
$272$	0.615680	−	16.9463i	0.0373311	−	1.02752i
$273$		0			0
$274$	−7.96403	+	28.6781i	−0.481125	+	1.73251i
$275$	−2.10281	+	0.563445i	−0.126804	+	0.0339770i
$276$		0			0
$277$	−10.0081	−	2.68166i	−0.601329	−	0.161126i	−0.0547032	−	0.998503i	$-0.517421\pi$
$277$	−10.0081	−	2.68166i	−0.601329	−	0.161126i	−0.546626	+	0.837377i	$0.684088\pi$
$278$	8.12750	+	4.79132i	0.487455	+	0.287364i
$279$		0			0
$280$	−36.7783	−	1.00196i	−2.19792	−	0.0598784i
$281$	−7.05630	−	12.2219i	−0.420944	−	0.729096i	0.575088	−	0.818091i	$-0.304968\pi$
$281$	−7.05630	−	12.2219i	−0.420944	−	0.729096i	−0.996032	+	0.0889955i	$0.971634\pi$
$282$		0			0
$283$	−12.7951	+	3.42843i	−0.760588	+	0.203799i	−0.618209	−	0.786013i	$-0.712142\pi$
$283$	−12.7951	+	3.42843i	−0.760588	+	0.203799i	−0.142378	+	0.989812i	$0.545475\pi$
$284$	15.0698	+	0.273662i	0.894227	+	0.0162388i
$285$		0			0
$286$	0.609688	+	0.620860i	0.0360516	+	0.0367122i
$287$	11.4660			0.676817
$288$		0			0
$289$	−0.972286			−0.0571933
$290$	8.07580	+	8.22378i	0.474227	+	0.482917i
$291$		0			0
$292$	6.45186	+	0.117163i	0.377566	+	0.00685646i
$293$	−29.7073	+	7.96005i	−1.73552	+	0.465031i	−0.981443	−	0.191756i	$-0.938582\pi$
$293$	−29.7073	+	7.96005i	−1.73552	+	0.465031i	−0.754077	+	0.656787i	$0.771915\pi$
$294$		0			0
$295$	−10.6924	−	18.5197i	−0.622533	−	1.07826i
$296$	0.290375	−	10.6586i	0.0168777	−	0.619520i
$297$		0			0
$298$	27.2143	+	16.0434i	1.57648	+	0.929368i
$299$	10.4522	+	2.80065i	0.604463	+	0.161965i
$300$		0			0
$301$	15.7800	−	4.22825i	0.909546	−	0.243712i
$302$	7.54936	−	27.1849i	0.434417	−	1.56432i
$303$		0			0
$304$	4.65481	−	4.32844i	0.266972	−	0.248253i
$305$		−	34.8187i		−	1.99371i
$306$		0			0
$307$	23.8109	−	23.8109i	1.35896	−	1.35896i	0.483758	−	0.875202i	$-0.339272\pi$
$307$	23.8109	−	23.8109i	1.35896	−	1.35896i	0.875202	−	0.483758i	$-0.160728\pi$
$308$	−1.42948	+	0.355341i	−0.0814523	+	0.0202474i
$309$		0			0
$310$	−22.4063	−	39.6356i	−1.27259	−	2.25115i
$311$	9.20941	+	5.31706i	0.522218	+	0.301503i	0.737842	−	0.674974i	$-0.235845\pi$
$311$	9.20941	+	5.31706i	0.522218	+	0.301503i	−0.215624	+	0.976477i	$0.569178\pi$
$312$		0			0
$313$	−16.4634	+	9.50514i	−0.930565	+	0.537262i	−0.886990	−	0.461788i	$-0.847208\pi$
$313$	−16.4634	+	9.50514i	−0.930565	+	0.537262i	−0.0435750	+	0.999050i	$0.513875\pi$
$314$	−18.1548	−	10.7026i	−1.02453	−	0.603982i
$315$		0			0
$316$	5.57519	+	10.0746i	0.313629	+	0.566742i
$317$	11.8751	+	3.18193i	0.666972	+	0.178715i	0.576391	−	0.817174i	$-0.304461\pi$
$317$	11.8751	+	3.18193i	0.666972	+	0.178715i	0.0905818	+	0.995889i	$0.471127\pi$
$318$		0			0
$319$	0.399628	+	0.230725i	0.0223749	+	0.0129181i
$320$	6.36631	+	30.2654i	0.355887	+	1.69189i
$321$		0			0
$322$	−13.0693	+	12.8341i	−0.728322	+	0.715216i
$323$	−4.76356	−	4.76356i	−0.265052	−	0.265052i
$324$		0			0
$325$	−19.7692	+	19.7692i	−1.09660	+	1.09660i
$326$	−8.71496	−	0.0791237i	−0.482677	−	0.00438226i
$327$		0			0
$328$	−2.24015	−	9.37453i	−0.123692	−	0.517622i
$329$	7.90701	−	13.6953i	0.435928	−	0.755049i
$330$		0			0
$331$	−8.94844	+	33.3960i	−0.491851	+	1.83561i	0.0551468	+	0.998478i	$0.482437\pi$
$331$	−8.94844	+	33.3960i	−0.491851	+	1.83561i	−0.546998	+	0.837134i	$0.684229\pi$
$332$	−8.96675	−	2.57801i	−0.492114	−	0.141487i
$333$		0			0
$334$	4.85696	+	18.8078i	0.265761	+	1.02912i
$335$	−10.3561	−	17.9374i	−0.565817	−	0.980023i
$336$		0			0
$337$	−14.3693	+	24.8884i	−0.782746	+	1.35576i	0.147591	+	0.989049i	$0.452848\pi$
$337$	−14.3693	+	24.8884i	−0.782746	+	1.35576i	−0.930336	+	0.366707i	$0.880485\pi$
$338$	−6.94685	−	1.92917i	−0.377859	−	0.104933i
$339$		0			0
$340$	31.8105	−	7.90745i	1.72517	−	0.428842i
$341$	−1.28894	−	1.28894i	−0.0698001	−	0.0698001i
$342$		0			0
$343$	−9.01293			−0.486653
$344$	−6.53999	−	12.0756i	−0.352612	−	0.651071i
$345$		0			0
$346$	−3.77793	−	6.68297i	−0.203103	−	0.359278i
$347$	2.92992	+	10.9346i	0.157287	+	0.587002i	0.998899	+	0.0469191i	$0.0149403\pi$
$347$	2.92992	+	10.9346i	0.157287	+	0.587002i	−0.841612	+	0.540082i	$0.818393\pi$
$348$		0			0
$349$	−2.90715	+	10.8496i	−0.155616	+	0.580767i	0.843436	+	0.537230i	$0.180529\pi$
$349$	−2.90715	+	10.8496i	−0.155616	+	0.580767i	−0.999052	+	0.0435372i	$0.986137\pi$
$350$	−11.8334	−	45.8228i	−0.632520	−	2.44933i
$351$		0			0
$352$	0.569807	+	1.09931i	0.0303708	+	0.0585935i
$353$	−1.85946	+	1.07356i	−0.0989689	+	0.0571397i	−0.548668	−	0.836041i	$-0.684865\pi$
$353$	−1.85946	+	1.07356i	−0.0989689	+	0.0571397i	0.449699	+	0.893180i	$0.351531\pi$
$354$		0			0
$355$	7.54056	+	28.1417i	0.400211	+	1.49361i
$356$	0.107544	−	5.92216i	0.00569983	−	0.313874i
$357$		0			0
$358$	−0.00690217	+	0.760229i	−0.000364791	+	0.0401793i
$359$			11.0166i			0.581435i	0.956809	+	0.290718i	$0.0938941\pi$
$359$			11.0166i			0.581435i	−0.956809	+	0.290718i	$0.906106\pi$
$360$		0			0
$361$			16.4748i			0.867097i
$362$	−9.97944	−	0.0906039i	−0.524508	−	0.00476204i
$363$		0			0
$364$	−13.6168	+	13.1311i	−0.713714	+	0.688255i
$365$	3.22835	+	12.0484i	0.168980	+	0.630641i
$366$		0			0
$367$	20.1365	−	11.6258i	1.05112	−	0.606863i	0.128156	−	0.991754i	$-0.459094\pi$
$367$	20.1365	−	11.6258i	1.05112	−	0.606863i	0.922962	+	0.384891i	$0.125761\pi$
$368$	13.0465	+	8.17791i	0.680094	+	0.426303i
$369$		0			0
$370$	19.9559	−	5.15345i	1.03746	−	0.267915i
$371$	−9.33867	+	34.8524i	−0.484839	+	1.80945i
$372$		0			0
$373$	−2.66079	−	9.93021i	−0.137771	−	0.514167i	−0.999971	−	0.00759967i	$-0.997581\pi$
$373$	−2.66079	−	9.93021i	−0.137771	−	0.514167i	0.862201	−	0.506567i	$-0.169086\pi$
$374$	1.14240	−	0.645810i	0.0590723	−	0.0333940i
$375$		0			0
$376$	−12.7420	−	3.78901i	−0.657121	−	0.195404i
$377$	5.92615			0.305212
$378$		0			0
$379$	−6.14819	−	6.14819i	−0.315811	−	0.315811i	0.531345	−	0.847156i	$-0.321687\pi$
$379$	−6.14819	−	6.14819i	−0.315811	−	0.315811i	−0.847156	+	0.531345i	$0.821687\pi$
$380$	10.5273	+	6.33551i	0.540037	+	0.325005i
$381$		0			0
$382$	4.09105	−	14.7317i	0.209316	−	0.753740i
$383$	−1.40170	+	2.42782i	−0.0716238	+	0.124056i	−0.899613	−	0.436688i	$-0.856151\pi$
$383$	−1.40170	+	2.42782i	−0.0716238	+	0.124056i	0.827989	+	0.560744i	$0.189485\pi$
$384$		0			0
$385$	−1.42363	−	2.46580i	−0.0725548	−	0.125669i
$386$	7.12153	−	1.83908i	0.362476	−	0.0936066i
$387$		0			0
$388$	26.7347	−	14.7947i	1.35725	−	0.751086i
$389$	−7.82350	+	29.1977i	−0.396667	+	1.48038i	0.422255	+	0.906477i	$0.361239\pi$
$389$	−7.82350	+	29.1977i	−0.396667	+	1.48038i	−0.818922	+	0.573905i	$0.805428\pi$
$390$		0			0
$391$	8.15956	−	14.1328i	0.412647	−	0.714725i
$392$	−2.84075	−	11.8879i	−0.143480	−	0.600430i
$393$		0			0
$394$	0.0534825	−	5.89075i	0.00269441	−	0.296772i
$395$	−15.7382	+	15.7382i	−0.791873	+	0.791873i
$396$		0			0
$397$	1.95789	+	1.95789i	0.0982636	+	0.0982636i	0.754530	−	0.656266i	$-0.227865\pi$
$397$	1.95789	+	1.95789i	0.0982636	+	0.0982636i	−0.656266	+	0.754530i	$0.727865\pi$
$398$	2.54938	+	2.59610i	0.127789	+	0.130131i
$399$		0			0
$400$	−35.1525	+	18.6274i	−1.75762	+	0.931372i
$401$	28.7356	+	16.5905i	1.43499	+	0.828489i	0.997495	−	0.0707337i	$-0.0225340\pi$
$401$	28.7356	+	16.5905i	1.43499	+	0.828489i	0.437490	+	0.899223i	$0.355867\pi$
$402$		0			0
$403$	−22.6120	−	6.05887i	−1.12638	−	0.301814i
$404$	−0.258063	−	0.0741950i	−0.0128391	−	0.00369134i
$405$		0			0
$406$	−5.09446	+	8.64172i	−0.252834	+	0.428881i
$407$	0.714607	−	0.412578i	0.0354217	−	0.0204508i
$408$		0			0
$409$	22.8959	+	13.2190i	1.13213	+	0.653636i	0.944470	−	0.328598i	$-0.106576\pi$
$409$	22.8959	+	13.2190i	1.13213	+	0.653636i	0.187660	+	0.982234i	$0.439910\pi$
$410$	16.2188	−	9.16864i	0.800991	−	0.452807i
$411$		0			0
$412$	−14.0213	−	8.43831i	−0.690781	−	0.415725i
$413$	13.1607	−	13.1607i	0.647596	−	0.647596i
$414$		0			0
$415$		−	18.0347i		−	0.885290i
$416$	13.3962	+	8.56755i	0.656805	+	0.420059i
$417$		0			0
$418$	0.473966	+	0.131622i	0.0231824	+	0.00643785i
$419$	0.499479	−	0.133835i	0.0244012	−	0.00653827i	−0.246598	−	0.969118i	$-0.579313\pi$
$419$	0.499479	−	0.133835i	0.0244012	−	0.00653827i	0.270999	+	0.962580i	$0.412646\pi$
$420$		0			0
$421$	12.8514	+	3.44352i	0.626339	+	0.167827i	0.558008	−	0.829836i	$-0.311566\pi$
$421$	12.8514	+	3.44352i	0.626339	+	0.167827i	0.0683313	+	0.997663i	$0.478233\pi$
$422$	13.0638	−	22.1601i	0.635938	−	1.07874i
$423$		0			0
$424$	30.3196	+	0.826002i	1.47245	+	0.0401142i
$425$	21.0818	+	36.5148i	1.02262	+	1.77123i
$426$		0			0
$427$	29.2717	−	7.84332i	1.41655	−	0.379565i
$428$	16.2730	+	16.8750i	0.786586	+	0.815683i
$429$		0			0
$430$	18.9400	−	18.5992i	0.913370	−	0.896934i
$431$	8.61129			0.414791			0.207396	−	0.978257i	$-0.433501\pi$
$431$	8.61129			0.414791			0.207396	+	0.978257i	$0.433501\pi$
$432$		0			0
$433$	6.43973			0.309474			0.154737	−	0.987956i	$-0.450547\pi$
$433$	6.43973			0.309474			0.154737	+	0.987956i	$0.450547\pi$
$434$	28.2738	−	27.7651i	1.35719	−	1.33277i
$435$		0			0
$436$	−12.8530	+	12.3945i	−0.615546	+	0.593588i
$437$	5.90859	−	1.58320i	0.282646	−	0.0757348i
$438$		0			0
$439$	14.4510	+	25.0298i	0.689707	+	1.19461i	0.971933	+	0.235260i	$0.0755941\pi$
$439$	14.4510	+	25.0298i	0.689707	+	1.19461i	−0.282225	+	0.959348i	$0.591073\pi$
$440$	−1.73788	+	1.64570i	−0.0828502	+	0.0784557i
$441$		0			0
$442$	8.55878	−	14.5182i	0.407100	−	0.690562i
$443$	31.1860	+	8.35627i	1.48169	+	0.397018i	0.906923	−	0.421297i	$-0.138425\pi$
$443$	31.1860	+	8.35627i	1.48169	+	0.397018i	0.574770	+	0.818315i	$0.305092\pi$
$444$		0			0
$445$	11.0592	−	2.96330i	0.524257	−	0.140474i
$446$	−4.43805	−	1.23246i	−0.210148	−	0.0583588i
$447$		0			0
$448$	−24.0097	+	12.1697i	−1.13435	+	0.574964i
$449$			10.7097i			0.505423i	0.967542	+	0.252711i	$0.0813223\pi$
$449$			10.7097i			0.505423i	−0.967542	+	0.252711i	$0.918678\pi$
$450$		0			0
$451$	0.527433	−	0.527433i	0.0248359	−	0.0248359i
$452$	17.4530	−	29.0004i	0.820920	−	1.36406i
$453$		0			0
$454$	11.2572	−	6.36381i	0.528329	−	0.298668i
$455$	−31.6669	−	18.2829i	−1.48457	−	0.857114i
$456$		0			0
$457$	13.1358	−	7.58393i	0.614465	−	0.354761i	−0.160246	−	0.987077i	$-0.551229\pi$
$457$	13.1358	−	7.58393i	0.614465	−	0.354761i	0.774711	+	0.632316i	$0.217895\pi$
$458$	−3.77532	+	6.40406i	−0.176409	+	0.299242i
$459$		0			0
$460$	−8.22407	+	28.6047i	−0.383449	+	1.33370i
$461$	11.5696	+	3.10006i	0.538849	+	0.144384i	0.517971	−	0.855398i	$-0.326687\pi$
$461$	11.5696	+	3.10006i	0.538849	+	0.144384i	0.0208774	+	0.999782i	$0.493354\pi$
$462$		0			0
$463$	−2.03363	−	1.17412i	−0.0945107	−	0.0545658i	0.452000	−	0.892018i	$-0.350711\pi$
$463$	−2.03363	−	1.17412i	−0.0945107	−	0.0545658i	−0.546510	+	0.837452i	$0.684044\pi$
$464$	8.06073	+	2.47684i	0.374210	+	0.114984i
$465$		0			0
$466$	14.0215	+	14.2784i	0.649534	+	0.661436i
$467$	−24.1509	−	24.1509i	−1.11757	−	1.11757i	−0.992097	−	0.125473i	$-0.959955\pi$
$467$	−24.1509	−	24.1509i	−1.11757	−	1.11757i	−0.125473	−	0.992097i	$-0.540045\pi$
$468$		0			0
$469$	12.7469	−	12.7469i	0.588596	−	0.588596i
$470$	0.233287	−	25.6950i	0.0107607	−	1.18522i
$471$		0			0
$472$	−13.3314	−	8.18886i	−0.613626	−	0.376923i
$473$	0.531379	−	0.920376i	0.0244328	−	0.0423189i
$474$		0			0
$475$	−4.09051	+	15.2660i	−0.187685	+	0.700452i
$476$	13.8134	+	24.9614i	0.633135	+	1.14410i
$477$		0			0
$478$	−20.5814	+	5.31499i	−0.941373	+	0.243102i
$479$	2.40917	+	4.17281i	0.110078	+	0.190660i	0.915801	−	0.401631i	$-0.131557\pi$
$479$	2.40917	+	4.17281i	0.110078	+	0.190660i	−0.805724	+	0.592292i	$0.798223\pi$
$480$		0			0
$481$	5.29851	−	9.17730i	0.241591	−	0.418449i
$482$	−5.44096	+	19.5927i	−0.247829	+	0.892422i
$483$		0			0
$484$	11.2947	−	18.7676i	0.513396	−	0.853072i
$485$	41.7638	+	41.7638i	1.89640	+	1.89640i
$486$		0			0
$487$	37.5042			1.69948			0.849739	−	0.527204i	$-0.176760\pi$
$487$	37.5042			1.69948			0.849739	+	0.527204i	$0.176760\pi$
$488$	−12.1315	−	22.3999i	−0.549169	−	1.01400i
$489$		0			0
$490$	20.5672	−	11.6268i	0.929132	−	0.525246i
$491$	0.504576	+	1.88310i	0.0227712	+	0.0849832i	0.976376	−	0.216077i	$-0.0693262\pi$
$491$	0.504576	+	1.88310i	0.0227712	+	0.0849832i	−0.953605	+	0.301060i	$0.902660\pi$
$492$		0			0
$493$	2.31315	−	8.63279i	0.104179	−	0.388801i
$494$	6.11657	−	1.57955i	0.275198	−	0.0710675i
$495$		0			0
$496$	−28.2245	−	17.6920i	−1.26732	−	0.794392i
$497$	−21.9598	+	12.6785i	−0.985032	+	0.568708i
$498$		0			0
$499$	−2.91509	−	10.8793i	−0.130497	−	0.487023i	0.869478	−	0.493971i	$-0.164455\pi$
$499$	−2.91509	−	10.8793i	−0.130497	−	0.487023i	−0.999976	+	0.00694794i	$0.997788\pi$
$500$	−26.5444	−	27.5263i	−1.18710	−	1.23101i
$501$		0			0
$502$	−7.19487	−	0.0653226i	−0.321123	−	0.00291549i
$503$		−	15.3339i		−	0.683706i	−0.939753	−	0.341853i	$-0.888945\pi$
$503$		−	15.3339i		−	0.683706i	0.939753	−	0.341853i	$-0.111055\pi$
$504$		0			0
$505$		−	0.519039i		−	0.0230969i
$506$	−0.0108181	+	1.19155i	−0.000480925	+	0.0529708i
$507$		0			0
$508$	−26.8012	−	0.486700i	−1.18911	−	0.0215938i
$509$	−8.59758	−	32.0866i	−0.381081	−	1.42221i	−0.844253	−	0.535945i	$-0.819955\pi$
$509$	−8.59758	−	32.0866i	−0.381081	−	1.42221i	0.463172	−	0.886269i	$-0.346711\pi$
$510$		0			0
$511$	−9.40169	+	5.42807i	−0.415906	+	0.240124i
$512$	14.6407	+	17.2525i	0.647035	+	0.762461i
$513$		0			0
$514$	2.01151	+	7.78924i	0.0887238	+	0.343568i
$515$	8.18713	−	30.5548i	0.360768	−	1.34641i
$516$		0			0
$517$	−0.266262	−	0.993703i	−0.0117102	−	0.0437030i
$518$	8.82774	+	15.6158i	0.387869	+	0.686119i
$519$		0			0
$520$	−8.76109	+	29.4626i	−0.384199	+	1.29202i
$521$	−20.5032			−0.898262			−0.449131	−	0.893466i	$-0.648266\pi$
$521$	−20.5032			−0.898262			−0.449131	+	0.893466i	$0.648266\pi$
$522$		0			0
$523$	−29.2406	−	29.2406i	−1.27860	−	1.27860i	−0.941451	−	0.337151i	$-0.890537\pi$
$523$	−29.2406	−	29.2406i	−1.27860	−	1.27860i	−0.337151	−	0.941451i	$-0.609463\pi$
$524$	−0.316036	−	1.27136i	−0.0138061	−	0.0555398i
$525$		0			0
$526$	−29.6425	−	8.23184i	−1.29247	−	0.358925i
$527$	−17.6523	+	30.5746i	−0.768944	+	1.33185i
$528$		0			0
$529$	−4.09099	−	7.08581i	−0.177869	−	0.308079i
$530$	14.6596	+	56.7668i	0.636771	+	2.46579i
$531$		0			0
$532$	−2.95479	+	10.2773i	−0.128107	+	0.445576i
$533$	2.47928	−	9.25281i	0.107390	−	0.400784i
$534$		0			0
$535$	−22.6575	+	39.2440i	−0.979570	+	1.69667i
$536$	−12.9122	−	7.93136i	−0.557720	−	0.342583i
$537$		0			0
$538$	−14.8687	−	0.134994i	−0.641036	−	0.00582001i
$539$	0.668841	−	0.668841i	0.0288090	−	0.0288090i
$540$		0			0
$541$	20.5836	+	20.5836i	0.884956	+	0.884956i	0.994033	−	0.109077i	$-0.0347895\pi$
$541$	20.5836	+	20.5836i	0.884956	+	0.884956i	−0.109077	+	0.994033i	$0.534790\pi$
$542$	−11.9949	+	11.7790i	−0.515224	+	0.505953i
$543$		0			0
$544$	17.7095	−	16.1705i	0.759290	−	0.693305i
$545$	−29.8905	−	17.2573i	−1.28037	−	0.739221i
$546$		0			0
$547$	−38.0779	−	10.2029i	−1.62809	−	0.436246i	−0.674728	−	0.738067i	$-0.735739\pi$
$547$	−38.0779	−	10.2029i	−1.62809	−	0.436246i	−0.953365	+	0.301821i	$0.902406\pi$
$548$	−36.8287	+	20.3806i	−1.57324	+	0.870616i
$549$		0			0
$550$	−2.65217	−	1.56350i	−0.113089	−	0.0666680i
$551$	2.90122	−	1.67502i	0.123596	−	0.0713584i
$552$		0			0
$553$	−16.7761	−	9.68566i	−0.713391	−	0.411876i
$554$	−7.21093	−	12.7558i	−0.306363	−	0.541940i
$555$		0			0
$556$	3.21876	+	12.9486i	0.136506	+	0.549142i
$557$	−1.52288	+	1.52288i	−0.0645265	+	0.0645265i	−0.738634	−	0.674107i	$-0.764529\pi$
$557$	−1.52288	+	1.52288i	−0.0645265	+	0.0645265i	0.674107	+	0.738634i	$0.264529\pi$
$558$		0			0
$559$		−	13.6484i		−	0.577266i
$560$	−35.4318	−	38.1035i	−1.49727	−	1.61017i
$561$		0			0
$562$	5.34038	−	19.2305i	0.225270	−	0.811189i
$563$	4.85715	−	1.30147i	0.204705	−	0.0548504i	−0.155010	−	0.987913i	$-0.549541\pi$
$563$	4.85715	−	1.30147i	0.204705	−	0.0548504i	0.359714	+	0.933063i	$0.382874\pi$
$564$		0			0
$565$	63.1966	+	16.9335i	2.65870	+	0.712397i
$566$	−16.1378	−	9.51354i	−0.678322	−	0.399884i
$567$		0			0
$568$	14.6562	+	15.4771i	0.614961	+	0.649407i
$569$	−17.4710	−	30.2606i	−0.732421	−	1.26859i	−0.955846	−	0.293869i	$-0.905057\pi$
$569$	−17.4710	−	30.2606i	−0.732421	−	1.26859i	0.223425	−	0.974721i	$-0.428276\pi$
$570$		0			0
$571$	34.1869	−	9.16034i	1.43068	−	0.383348i	0.541417	−	0.840754i	$-0.317888\pi$
$571$	34.1869	−	9.16034i	1.43068	−	0.383348i	0.889258	+	0.457406i	$0.151221\pi$
$572$	−0.0223435	+	1.23040i	−0.000934229	+	0.0514454i
$573$		0			0
$574$	11.3614	+	11.5696i	0.474217	+	0.482907i
$575$	−38.2852			−1.59660
$576$		0			0
$577$	−17.4865			−0.727972			−0.363986	−	0.931404i	$-0.618584\pi$
$577$	−17.4865			−0.727972			−0.363986	+	0.931404i	$0.618584\pi$
$578$	−0.963419	−	0.981073i	−0.0400730	−	0.0408073i
$579$		0			0
$580$	−0.295958	+	16.2976i	−0.0122890	+	0.676719i
$581$	15.1616	−	4.06253i	0.629008	−	0.168542i
$582$		0			0
$583$	1.17362	+	2.03278i	0.0486065	+	0.0841890i
$584$	6.27479	+	6.62626i	0.259653	+	0.274197i
$585$		0			0
$586$	−37.4684	−	22.0883i	−1.54780	−	0.912461i
$587$	−12.3561	−	3.31081i	−0.509991	−	0.136652i	−0.00535825	−	0.999986i	$-0.501706\pi$
$587$	−12.3561	−	3.31081i	−0.509991	−	0.136652i	−0.504633	+	0.863334i	$0.668372\pi$
$588$		0			0
$589$	−12.7825	+	3.42507i	−0.526696	+	0.141128i
$590$	8.09224	−	29.1398i	0.333152	−	1.19967i
$591$		0			0
$592$	11.0427	−	10.2684i	0.453851	−	0.422029i
$593$			25.7816i			1.05872i	0.848397	+	0.529361i	$0.177568\pi$
$593$			25.7816i			1.05872i	−0.848397	+	0.529361i	$0.822432\pi$
$594$		0			0
$595$	−38.9937	+	38.9937i	−1.59858	+	1.59858i
$596$	10.7778	+	43.3574i	0.441475	+	1.77599i
$597$		0			0
$598$	7.53087	+	13.3217i	0.307960	+	0.544765i
$599$	27.3647	+	15.7990i	1.11809	+	0.645531i	0.940913	−	0.338647i	$-0.109969\pi$
$599$	27.3647	+	15.7990i	1.11809	+	0.645531i	0.177180	+	0.984179i	$0.443303\pi$
$600$		0			0
$601$	−23.3729	+	13.4944i	−0.953401	+	0.550447i	−0.894136	−	0.447796i	$-0.852209\pi$
$601$	−23.3729	+	13.4944i	−0.953401	+	0.550447i	−0.0592656	+	0.998242i	$0.518876\pi$
$602$	19.9026	+	11.7330i	0.811169	+	0.478200i
$603$		0			0
$604$	34.9111	−	19.3194i	1.42051	−	0.786097i
$605$	40.8977	+	10.9585i	1.66273	+	0.445527i
$606$		0			0
$607$	21.2314	+	12.2579i	0.861755	+	0.497534i	0.864600	−	0.502462i	$-0.167572\pi$
$607$	21.2314	+	12.2579i	0.861755	+	0.497534i	−0.00284471	+	0.999996i	$0.500905\pi$
$608$	8.97992	+	0.407915i	0.364184	+	0.0165431i
$609$		0			0
$610$	35.1334	−	34.5012i	1.42251	−	1.39691i
$611$	−9.34212	−	9.34212i	−0.377942	−	0.377942i
$612$		0			0
$613$	−30.3894	+	30.3894i	−1.22742	+	1.22742i	−0.262481	+	0.964937i	$0.584541\pi$
$613$	−30.3894	+	30.3894i	−1.22742	+	1.22742i	−0.964937	+	0.262481i	$0.915459\pi$
$614$	47.6198	+	0.432343i	1.92178	+	0.0174480i
$615$		0			0
$616$	−1.77500	−	1.09030i	−0.0715167	−	0.0439295i
$617$	−15.8393	+	27.4345i	−0.637668	+	1.10447i	0.348275	+	0.937392i	$0.386767\pi$
$617$	−15.8393	+	27.4345i	−0.637668	+	1.10447i	−0.985943	+	0.167081i	$0.946566\pi$
$618$		0			0
$619$	5.39413	−	20.1312i	0.216809	−	0.809141i	−0.768713	−	0.639593i	$-0.779103\pi$
$619$	5.39413	−	20.1312i	0.216809	−	0.809141i	0.985522	−	0.169547i	$-0.0542305\pi$
$620$	17.7918	−	61.8829i	0.714537	−	2.48528i
$621$		0			0
$622$	3.76031	+	14.5612i	0.150775	+	0.583851i
$623$	4.98242	+	8.62981i	0.199617	+	0.345746i
$624$		0			0
$625$	12.0944	−	20.9481i	0.483775	−	0.837923i
$626$	−25.9043	−	7.19372i	−1.03534	−	0.287519i
$627$		0			0
$628$	−7.18989	−	28.9238i	−0.286908	−	1.15419i
$629$	−11.3007	−	11.3007i	−0.450587	−	0.450587i
$630$		0			0
$631$	−19.9953			−0.796002			−0.398001	−	0.917385i	$-0.630296\pi$
$631$	−19.9953			−0.796002			−0.398001	+	0.917385i	$0.630296\pi$
$632$	−4.64134	+	15.6083i	−0.184623	+	0.620866i
$633$		0			0
$634$	8.55612	+	15.1353i	0.339807	+	0.601101i
$635$	−13.4107	−	50.0494i	−0.532187	−	1.98615i
$636$		0			0
$637$	3.14400	−	11.7335i	0.124570	−	0.464900i
$638$	0.163173	+	0.631861i	0.00646008	+	0.0250156i
$639$		0			0
$640$	−24.2307	+	36.4133i	−0.957803	+	1.43936i
$641$	−12.6976	+	7.33098i	−0.501526	+	0.289556i	−0.729344	−	0.684148i	$-0.760174\pi$
$641$	−12.6976	+	7.33098i	−0.501526	+	0.289556i	0.227818	+	0.973704i	$0.426841\pi$
$642$		0			0
$643$	−3.45056	−	12.8777i	−0.136077	−	0.507846i	−0.999991	−	0.00420705i	$-0.998661\pi$
$643$	−3.45056	−	12.8777i	−0.136077	−	0.507846i	0.863914	−	0.503639i	$-0.168006\pi$
$644$	−25.9002	−	0.470337i	−1.02061	−	0.0185339i
$645$		0			0
$646$	0.0864938	−	9.52673i	0.00340305	−	0.374824i
$647$			30.5078i			1.19939i	0.800231	+	0.599693i	$0.204710\pi$
$647$			30.5078i			1.19939i	−0.800231	+	0.599693i	$0.795290\pi$
$648$		0			0
$649$		−	1.21078i		−	0.0475272i
$650$	−39.5367	−	0.358956i	−1.55076	−	0.0140794i
$651$		0			0
$652$	−8.55564	−	8.87212i	−0.335065	−	0.347459i
$653$	−5.39824	−	20.1465i	−0.211249	−	0.788394i	−0.987453	−	0.157912i	$-0.949524\pi$
$653$	−5.39824	−	20.1465i	−0.211249	−	0.788394i	0.776204	−	0.630482i	$-0.217143\pi$
$654$		0			0
$655$	2.19305	−	1.26616i	0.0856896	−	0.0494729i
$656$	7.23953	−	11.5494i	0.282656	−	0.450930i
$657$		0			0
$658$	21.6540	−	5.59198i	0.844162	−	0.217998i
$659$	3.90477	−	14.5728i	0.152108	−	0.567676i	−0.847227	−	0.531230i	$-0.821730\pi$
$659$	3.90477	−	14.5728i	0.152108	−	0.567676i	0.999336	−	0.0364452i	$-0.0116034\pi$
$660$		0			0
$661$	2.44325	+	9.11835i	0.0950316	+	0.354663i	0.997024	−	0.0770887i	$-0.0245625\pi$
$661$	2.44325	+	9.11835i	0.0950316	+	0.354663i	−0.901993	+	0.431751i	$0.857896\pi$
$662$	−42.5647	+	24.0622i	−1.65432	+	0.935202i
$663$		0			0
$664$	−6.28366	−	11.6023i	−0.243853	−	0.450256i
$665$	−20.6706			−0.801570
$666$		0			0
$667$	5.73833	+	5.73833i	0.222189	+	0.222189i
$668$	−14.1651	+	23.5371i	−0.548064	+	0.910678i
$669$		0			0
$670$	7.83778	−	28.2235i	0.302800	−	1.09037i
$671$	0.985698	−	1.70728i	0.0380525	−	0.0659088i
$672$		0			0
$673$	−16.1140	−	27.9103i	−0.621149	−	1.07586i	−0.989272	−	0.146085i	$-0.953333\pi$
$673$	−16.1140	−	27.9103i	−0.621149	−	1.07586i	0.368123	−	0.929777i	$-0.380001\pi$
$674$	−39.3516	+	10.1622i	−1.51577	+	0.391434i
$675$		0			0
$676$	−4.93689	−	8.92120i	−0.189880	−	0.343123i
$677$	4.16296	−	15.5364i	0.159996	−	0.597111i	−0.838630	−	0.544701i	$-0.816643\pi$
$677$	4.16296	−	15.5364i	0.159996	−	0.597111i	0.998626	−	0.0524101i	$-0.0166903\pi$
$678$		0			0
$679$	−25.7025	+	44.5181i	−0.986372	+	1.70845i
$680$	39.4993	+	24.2626i	1.51473	+	0.930430i
$681$		0			0
$682$	0.0234038	−	2.57778i	0.000896177	−	0.0987081i
$683$	28.6734	−	28.6734i	1.09716	−	1.09716i	0.102416	−	0.994742i	$-0.467343\pi$
$683$	28.6734	−	28.6734i	1.09716	−	1.09716i	0.994742	−	0.102416i	$-0.0326571\pi$
$684$		0			0
$685$	−57.5322	−	57.5322i	−2.19819	−	2.19819i
$686$	−8.93074	−	9.09439i	−0.340977	−	0.347225i
$687$		0			0
$688$	5.70435	−	18.5645i	0.217476	−	0.707766i
$689$	26.1058	+	15.0722i	0.994552	+	0.574205i
$690$		0			0
$691$	44.0504	+	11.8033i	1.67575	+	0.449017i	0.966653	−	0.256089i	$-0.0824340\pi$
$691$	44.0504	+	11.8033i	1.67575	+	0.449017i	0.709102	+	0.705106i	$0.249101\pi$
$692$	2.99988	−	10.4341i	0.114038	−	0.396645i
$693$		0			0
$694$	−8.13025	+	13.7913i	−0.308620	+	0.523511i
$695$	−22.3358	+	12.8956i	−0.847243	+	0.489156i
$696$		0			0
$697$	−12.5111	−	7.22328i	−0.473892	−	0.273601i
$698$	−13.8283	+	7.81726i	−0.523410	+	0.295888i
$699$		0			0
$700$	34.5115	−	57.3452i	1.30441	−	2.16744i
$701$	13.0178	−	13.0178i	0.491676	−	0.491676i	−0.417158	−	0.908834i	$-0.636974\pi$
$701$	13.0178	−	13.0178i	0.491676	−	0.491676i	0.908834	+	0.417158i	$0.136974\pi$
$702$		0			0
$703$		−	5.99049i		−	0.225935i
$704$	−0.544635	+	1.66424i	−0.0205267	+	0.0627235i
$705$		0			0
$706$	−2.92576	−	0.812494i	−0.110112	−	0.0305786i
$707$	0.436349	−	0.116919i	0.0164106	−	0.00439721i
$708$		0			0
$709$	−16.3841	−	4.39011i	−0.615319	−	0.164874i	−0.0623199	−	0.998056i	$-0.519850\pi$
$709$	−16.3841	−	4.39011i	−0.615319	−	0.164874i	−0.552999	+	0.833182i	$0.686517\pi$
$710$	−20.9243	+	35.4938i	−0.785274	+	1.33206i
$711$		0			0
$712$	6.08224	−	5.75963i	0.227942	−	0.215851i
$713$	−16.0285	−	27.7622i	−0.600273	−	1.03970i
$714$		0			0
$715$	−2.29767	+	0.615660i	−0.0859282	+	0.0230244i
$716$	−0.773939	+	0.746331i	−0.0289234	+	0.0278917i
$717$		0			0
$718$	−11.1162	+	10.9162i	−0.414853	+	0.407387i
$719$	43.0731			1.60635			0.803177	−	0.595740i	$-0.203141\pi$
$719$	43.0731			1.60635			0.803177	+	0.595740i	$0.203141\pi$
$720$		0			0
$721$	27.5313			1.02532
$722$	−16.6237	+	16.3246i	−0.618671	+	0.607538i
$723$		0			0
$724$	−9.79700	−	10.1594i	−0.364103	−	0.377571i
$725$	−20.2528	+	5.42673i	−0.752171	+	0.201544i
$726$		0			0
$727$	15.3101	+	26.5179i	0.567821	+	0.983495i	0.996781	+	0.0801716i	$0.0255468\pi$
$727$	15.3101	+	26.5179i	0.567821	+	0.983495i	−0.428960	+	0.903324i	$0.641120\pi$
$728$	−26.7424	−	0.728547i	−0.991138	−	0.0270017i
$729$		0			0
$730$	−8.95835	+	15.1960i	−0.331563	+	0.562430i
$731$	−19.8820	−	5.32737i	−0.735363	−	0.197040i
$732$		0			0
$733$	−2.53658	+	0.679676i	−0.0936909	+	0.0251044i	−0.305360	−	0.952237i	$-0.598777\pi$
$733$	−2.53658	+	0.679676i	−0.0936909	+	0.0251044i	0.211669	+	0.977341i	$0.432110\pi$
$734$	31.6838	+	8.79870i	1.16947	+	0.324766i
$735$		0			0
$736$	4.67566	+	21.2677i	0.172347	+	0.783937i
$737$		−	1.17271i		−	0.0431972i
$738$		0			0
$739$	13.1402	−	13.1402i	0.483370	−	0.483370i	−0.422836	−	0.906206i	$-0.638965\pi$
$739$	13.1402	−	13.1402i	0.483370	−	0.483370i	0.906206	+	0.422836i	$0.138965\pi$
$740$	24.9739	+	15.0298i	0.918061	+	0.552507i
$741$		0			0
$742$	−44.4209	+	25.1115i	−1.63074	+	0.921871i
$743$	1.79055	+	1.03378i	0.0656890	+	0.0379255i	0.532485	−	0.846440i	$-0.321258\pi$
$743$	1.79055	+	1.03378i	0.0656890	+	0.0379255i	−0.466796	+	0.884365i	$0.654592\pi$
$744$		0			0
$745$	−74.7897	+	43.1798i	−2.74008	+	1.58199i
$746$	7.38343	−	12.5245i	0.270327	−	0.458554i
$747$		0			0
$748$	1.78363	+	0.512808i	0.0652160	+	0.0187501i
$749$	−38.0958	−	10.2077i	−1.39199	−	0.372982i
$750$		0			0
$751$	7.86676	+	4.54188i	0.287062	+	0.165735i	0.636616	−	0.771181i	$-0.280334\pi$
$751$	7.86676	+	4.54188i	0.287062	+	0.165735i	−0.349554	+	0.936916i	$0.613667\pi$
$752$	−8.80258	−	16.6117i	−0.320997	−	0.605765i
$753$		0			0
$754$	5.87211	+	5.97971i	0.213849	+	0.217768i
$755$	54.5367	+	54.5367i	1.98479	+	1.98479i
$756$		0			0
$757$	18.3910	−	18.3910i	0.668433	−	0.668433i	−0.288920	−	0.957353i	$-0.593296\pi$
$757$	18.3910	−	18.3910i	0.668433	−	0.668433i	0.957353	+	0.288920i	$0.0932961\pi$
$758$	0.111635	−	12.2959i	0.00405476	−	0.446606i
$759$		0			0
$760$	4.03848	+	16.9001i	0.146491	+	0.613032i
$761$	−14.1080	+	24.4358i	−0.511415	+	0.885797i	0.488497	+	0.872565i	$0.337545\pi$
$761$	−14.1080	+	24.4358i	−0.511415	+	0.885797i	−0.999912	+	0.0132318i	$0.995788\pi$
$762$		0			0
$763$	7.77481	−	29.0160i	0.281467	−	1.05045i
$764$	18.9186	−	10.4693i	0.684451	−	0.378767i
$765$		0			0
$766$	−3.83869	+	0.991310i	−0.138697	+	0.0358175i
$767$	−7.77467	−	13.4661i	−0.280727	−	0.486234i
$768$		0			0
$769$	−14.6064	+	25.2991i	−0.526722	+	0.912309i	0.472794	+	0.881173i	$0.343246\pi$
$769$	−14.6064	+	25.2991i	−0.526722	+	0.912309i	−0.999515	+	0.0311354i	$0.990088\pi$
$770$	1.07744	−	3.87980i	0.0388281	−	0.139818i
$771$		0			0
$772$	8.91228	+	5.36358i	0.320760	+	0.193040i
$773$	−10.5491	−	10.5491i	−0.379425	−	0.379425i	0.491470	−	0.870895i	$-0.336460\pi$
$773$	−10.5491	−	10.5491i	−0.379425	−	0.379425i	−0.870895	+	0.491470i	$0.836460\pi$
$774$		0			0
$775$	82.8256			2.97518
$776$	41.4193	+	12.3166i	1.48687	+	0.442139i
$777$		0			0
$778$	−37.2137	+	21.0372i	−1.33418	+	0.754220i
$779$	−1.40154	−	5.23060i	−0.0502152	−	0.187406i
$780$		0			0
$781$	−0.426938	+	1.59335i	−0.0152770	+	0.0570146i
$782$	22.3456	−	5.77058i	0.799078	−	0.206356i
$783$		0			0
$784$	9.18049	−	14.6459i	0.327875	−	0.523068i
$785$	49.8924	−	28.8054i	1.78074	−	1.02811i
$786$		0			0
$787$	−9.05729	−	33.8023i	−0.322857	−	1.20492i	−0.916448	−	0.400153i	$-0.868957\pi$
$787$	−9.05729	−	33.8023i	−0.322857	−	1.20492i	0.593591	−	0.804767i	$-0.297710\pi$
$788$	5.99698	−	5.78306i	0.213634	−	0.206013i
$789$		0			0
$790$	−31.4750	−	0.285764i	−1.11983	−	0.0101670i
$791$			56.9431i			2.02466i
$792$		0			0
$793$		−	25.3175i		−	0.899052i
$794$	−0.0355501	+	3.91561i	−0.00126163	+	0.138960i
$795$		0			0
$796$	−0.0934284	+	5.14484i	−0.00331148	+	0.182354i
$797$	7.41329	+	27.6668i	0.262592	+	0.980007i	0.963708	+	0.266959i	$0.0860190\pi$
$797$	7.41329	+	27.6668i	0.262592	+	0.980007i	−0.701116	+	0.713048i	$0.747314\pi$
$798$		0			0
$799$	−17.2554	+	9.96243i	−0.610453	+	0.352445i
$800$	−53.6277	−	17.0126i	−1.89602	−	0.601487i
$801$		0			0
$802$	11.7331	+	45.4344i	0.414309	+	1.60435i
$803$	−0.182786	+	0.682165i	−0.00645036	+	0.0240731i
$804$		0			0
$805$	−12.9598	−	48.3667i	−0.456773	−	1.70470i
$806$	−16.2922	−	28.8200i	−0.573867	−	1.01514i
$807$		0			0
$808$	−0.180844	−	0.333913i	−0.00636205	−	0.0117470i
$809$	−39.9831			−1.40573			−0.702865	−	0.711323i	$-0.748096\pi$
$809$	−39.9831			−1.40573			−0.702865	+	0.711323i	$0.748096\pi$
$810$		0			0
$811$	−33.5121	−	33.5121i	−1.17677	−	1.17677i	−0.980563	−	0.196204i	$-0.937138\pi$
$811$	−33.5121	−	33.5121i	−1.17677	−	1.17677i	−0.196204	−	0.980563i	$-0.562862\pi$
$812$	−13.7678	+	3.42240i	−0.483156	+	0.120103i
$813$		0			0
$814$	1.12440	+	0.312249i	0.0394101	+	0.0109443i
$815$	11.9123	−	20.6328i	0.417271	−	0.722734i
$816$		0			0
$817$	−3.85771	−	6.68176i	−0.134964	−	0.233765i
$818$	9.34868	+	36.2012i	0.326869	+	1.26575i
$819$		0			0
$820$	25.3224	+	7.28039i	0.884297	+	0.254242i
$821$	2.91908	−	10.8942i	0.101877	−	0.380209i	−0.896096	−	0.443861i	$-0.853608\pi$
$821$	2.91908	−	10.8942i	0.101877	−	0.380209i	0.997972	+	0.0636527i	$0.0202750\pi$
$822$		0			0
$823$	27.4702	−	47.5798i	0.957551	−	1.65853i	0.229131	−	0.973396i	$-0.426412\pi$
$823$	27.4702	−	47.5798i	0.957551	−	1.65853i	0.728420	−	0.685131i	$-0.240255\pi$
$824$	−5.37888	−	22.5094i	−0.187382	−	0.784152i
$825$		0			0
$826$	26.3203	+	0.238964i	0.915801	+	0.00831462i
$827$	14.2104	−	14.2104i	0.494144	−	0.494144i	−0.415465	−	0.909609i	$-0.636381\pi$
$827$	14.2104	−	14.2104i	0.494144	−	0.494144i	0.909609	+	0.415465i	$0.136381\pi$
$828$		0			0
$829$	6.15512	+	6.15512i	0.213776	+	0.213776i	0.805869	−	0.592093i	$-0.201698\pi$
$829$	6.15512	+	6.15512i	0.213776	+	0.213776i	−0.592093	+	0.805869i	$0.701698\pi$
$830$	18.1977	−	17.8703i	0.631652	−	0.620286i
$831$		0			0
$832$	4.62909	+	22.0067i	0.160485	+	0.762946i
$833$	−15.8654	−	9.15989i	−0.549704	−	0.317371i
$834$		0			0
$835$	−51.2913	−	13.7435i	−1.77501	−	0.475612i
$836$	0.336832	+	0.608672i	0.0116496	+	0.0210513i
$837$		0			0
$838$	0.629969	+	0.371379i	0.0217619	+	0.0128291i
$839$	21.5384	−	12.4352i	0.743590	−	0.429312i	−0.0797833	−	0.996812i	$-0.525423\pi$
$839$	21.5384	−	12.4352i	0.743590	−	0.429312i	0.823373	+	0.567500i	$0.192089\pi$
$840$		0			0
$841$	−21.2658	−	12.2778i	−0.733303	−	0.423373i
$842$	9.25956	+	16.3797i	0.319105	+	0.564481i
$843$		0			0
$844$	35.3051	−	8.77615i	1.21525	−	0.302087i
$845$	13.9363	−	13.9363i	0.479424	−	0.479424i
$846$		0			0
$847$			36.8507i			1.26621i
$848$	29.2096	+	31.4121i	1.00306	+	1.07870i
$849$		0			0
$850$	−15.9552	+	57.4541i	−0.547260	+	1.97066i
$851$	14.0170	−	3.75585i	0.480497	−	0.128749i
$852$		0			0
$853$	18.8477	+	5.05023i	0.645334	+	0.172917i	0.566618	−	0.823980i	$-0.308251\pi$
$853$	18.8477	+	5.05023i	0.645334	+	0.172917i	0.0787157	+	0.996897i	$0.474918\pi$
$854$	36.9189	+	21.7644i	1.26334	+	0.744763i
$855$		0			0
$856$	−0.902871	+	33.1412i	−0.0308595	+	1.13274i
$857$	−18.6982	−	32.3862i	−0.638717	−	1.10629i	−0.985715	−	0.168424i	$-0.946132\pi$
$857$	−18.6982	−	32.3862i	−0.638717	−	1.10629i	0.346998	−	0.937866i	$-0.387201\pi$
$858$		0			0
$859$	26.5180	−	7.10549i	0.904784	−	0.242436i	0.223714	−	0.974655i	$-0.428182\pi$
$859$	26.5180	−	7.10549i	0.904784	−	0.242436i	0.681070	+	0.732219i	$0.261515\pi$
$860$	37.5346	+	0.681614i	1.27992	+	0.0232429i
$861$		0			0
$862$	8.53276	+	8.68912i	0.290627	+	0.295953i
$863$	−10.1797			−0.346520			−0.173260	−	0.984876i	$-0.555430\pi$
$863$	−10.1797			−0.346520			−0.173260	+	0.984876i	$0.555430\pi$
$864$		0			0
$865$	20.9860			0.713545
$866$	6.38100	+	6.49793i	0.216835	+	0.220808i
$867$		0			0
$868$	56.0320	+	1.01752i	1.90185	+	0.0345369i
$869$	−1.21723	+	0.326156i	−0.0412918	+	0.0110641i
$870$		0			0
$871$	−7.53020	−	13.0427i	−0.255151	−	0.441935i
$872$	−25.2423	−	0.687680i	−0.854811	−	0.0232878i
$873$		0			0
$874$	7.45221	+	4.39322i	0.252075	+	0.148603i
$875$	62.1414	+	16.6507i	2.10076	+	0.562897i
$876$		0			0
$877$	25.7779	−	6.90717i	0.870458	−	0.233239i	0.204172	−	0.978935i	$-0.434550\pi$
$877$	25.7779	−	6.90717i	0.870458	−	0.233239i	0.666286	+	0.745696i	$0.267883\pi$
$878$	−10.9368	+	39.3831i	−0.369101	+	1.32912i
$879$		0			0
$880$	−3.38261	−	0.122894i	−0.114028	−	0.00414276i
$881$		−	30.7798i		−	1.03700i	−0.855078	−	0.518499i	$-0.826491\pi$
$881$		−	30.7798i		−	1.03700i	0.855078	−	0.518499i	$-0.173509\pi$
$882$		0			0
$883$	−19.8089	+	19.8089i	−0.666622	+	0.666622i	−0.956933	−	0.290310i	$-0.906241\pi$
$883$	−19.8089	+	19.8089i	−0.666622	+	0.666622i	0.290310	+	0.956933i	$0.406241\pi$
$884$	23.1302	−	5.74970i	0.777952	−	0.193383i
$885$		0			0
$886$	22.4698	+	39.7479i	0.754888	+	1.33536i
$887$	−21.0940	−	12.1786i	−0.708266	−	0.408918i	0.102153	−	0.994769i	$-0.467427\pi$
$887$	−21.0940	−	12.1786i	−0.708266	−	0.408918i	−0.810419	+	0.585851i	$0.800760\pi$
$888$		0			0
$889$	39.0550	−	22.5484i	1.30986	−	0.756249i
$890$	13.9484	+	8.22287i	0.467552	+	0.275631i
$891$		0			0
$892$	−3.15397	−	5.69938i	−0.105603	−	0.190829i
$893$	−7.21410	−	1.93301i	−0.241411	−	0.0646858i
$894$		0			0
$895$	−1.79985	−	1.03914i	−0.0601624	−	0.0347348i
$896$	−36.0704	−	12.1679i	−1.20503	−	0.406502i
$897$		0			0
$898$	−10.8065	+	10.6120i	−0.360618	+	0.354128i
$899$	−12.4142	−	12.4142i	−0.414037	−	0.414037i
$900$		0			0
$901$	32.1460	−	32.1460i	1.07094	−	1.07094i
$902$	1.05482	+	0.00957680i	0.0351218	+	0.000318873i
$903$		0			0
$904$	46.5563	−	11.1252i	1.54844	−	0.370017i
$905$	13.6407	−	23.6264i	0.453433	−	0.785369i
$906$		0			0
$907$	−15.0239	+	56.0698i	−0.498859	+	1.86177i	0.00838605	+	0.999965i	$0.497331\pi$
$907$	−15.0239	+	56.0698i	−0.498859	+	1.86177i	−0.507245	+	0.861802i	$0.669336\pi$
$908$	17.5759	+	5.05321i	0.583277	+	0.167697i
$909$		0			0
$910$	−12.9300	−	50.0692i	−0.428624	−	1.65978i
$911$	11.9347	+	20.6715i	0.395414	+	0.684877i	0.993154	−	0.116813i	$-0.0372678\pi$
$911$	11.9347	+	20.6715i	0.395414	+	0.684877i	−0.597740	+	0.801690i	$0.703934\pi$
$912$		0			0
$913$	0.510553	−	0.884303i	0.0168968	−	0.0292662i
$914$	20.6684	+	5.73970i	0.683651	+	0.189852i
$915$		0			0
$916$	−10.2028	+	2.53622i	−0.337111	+	0.0837991i
$917$	1.55845	+	1.55845i	0.0514646	+	0.0514646i
$918$		0			0
$919$	−15.7779			−0.520466			−0.260233	−	0.965546i	$-0.583799\pi$
$919$	−15.7779			−0.520466			−0.260233	+	0.965546i	$0.583799\pi$
$920$	−37.0123	+	20.0454i	−1.22026	+	0.660878i
$921$		0			0
$922$	8.33599	+	14.7459i	0.274531	+	0.485631i
$923$	5.48292	+	20.4625i	0.180473	+	0.673533i
$924$		0			0
$925$	−9.70397	+	36.2157i	−0.319065	+	1.19077i
$926$	−0.830355	−	3.21541i	−0.0272872	−	0.105665i
$927$		0			0
$928$	5.48800	+	10.5878i	0.180152	+	0.347563i
$929$	−14.3132	+	8.26371i	−0.469600	+	0.271123i	−0.716072	−	0.698026i	$-0.754062\pi$
$929$	−14.3132	+	8.26371i	−0.469600	+	0.271123i	0.246472	+	0.969150i	$0.420729\pi$
$930$		0			0
$931$	−1.77730	−	6.63296i	−0.0582485	−	0.217387i
$932$	−0.513853	+	28.2965i	−0.0168318	+	0.926881i
$933$		0			0
$934$	0.438517	−	48.2998i	0.0143487	−	1.58042i
$935$			3.58740i			0.117320i
$936$		0			0
$937$			5.92940i			0.193705i	0.995299	+	0.0968526i	$0.0308775\pi$
$937$			5.92940i			0.193705i	−0.995299	+	0.0968526i	$0.969122\pi$
$938$	25.4927	+	0.231450i	0.832366	+	0.00755710i
$939$		0			0
$940$	26.1584	−	25.2253i	0.853193	−	0.822758i
$941$	5.52232	+	20.6096i	0.180022	+	0.671853i	0.995641	+	0.0932635i	$0.0297299\pi$
$941$	5.52232	+	20.6096i	0.180022	+	0.671853i	−0.815619	+	0.578589i	$0.803603\pi$
$942$		0			0
$943$	11.3603	−	6.55886i	0.369941	−	0.213586i
$944$	−4.94692	−	21.5660i	−0.161008	−	0.701914i
$945$		0			0
$946$	1.45523	−	0.375800i	0.0473135	−	0.0122183i
$947$	8.57071	−	31.9863i	0.278511	−	1.03942i	−0.674941	−	0.737871i	$-0.735831\pi$
$947$	8.57071	−	31.9863i	0.278511	−	1.03942i	0.953452	−	0.301545i	$-0.0975022\pi$
$948$		0			0
$949$	2.34741	+	8.76066i	0.0762002	+	0.284383i
$950$	−19.4572	+	10.9993i	−0.631274	+	0.356864i
$951$		0			0
$952$	−11.4996	+	38.6720i	−0.372705	+	1.25337i
$953$	−0.546564			−0.0177049			−0.00885247	−	0.999961i	$-0.502818\pi$
$953$	−0.546564			−0.0177049			−0.00885247	+	0.999961i	$0.502818\pi$
$954$		0			0
$955$	29.5538	+	29.5538i	0.956339	+	0.956339i
$956$	−25.7568	−	15.5009i	−0.833034	−	0.501336i
$957$		0			0
$958$	−1.82332	+	6.56570i	−0.0589088	+	0.212128i
$959$	35.4068	−	61.3264i	1.14335	−	1.98033i
$960$		0			0
$961$	19.1758	+	33.2135i	0.618576	+	1.07140i
$962$	14.5104	−	3.74720i	0.467835	−	0.120815i
$963$		0			0
$964$	−25.1611	+	13.9239i	−0.810384	+	0.448457i
$965$	−5.20393	+	19.4213i	−0.167521	+	0.625195i
$966$		0			0
$967$	−7.49046	+	12.9739i	−0.240877	+	0.417211i	−0.960964	−	0.276672i	$-0.910768\pi$
$967$	−7.49046	+	12.9739i	−0.240877	+	0.417211i	0.720087	+	0.693883i	$0.244102\pi$
$968$	30.1289	−	7.19965i	0.968380	−	0.231406i
$969$		0			0
$970$	−0.758322	+	83.5242i	−0.0243482	+	2.68180i
$971$	−29.4725	+	29.4725i	−0.945816	+	0.945816i	−0.998606	−	0.0527896i	$-0.983189\pi$
$971$	−29.4725	+	29.4725i	−0.945816	+	0.945816i	0.0527896	+	0.998606i	$0.483189\pi$
$972$		0			0
$973$	−15.8725	−	15.8725i	−0.508849	−	0.508849i
$974$	37.1622	+	37.8431i	1.19075	+	1.21257i
$975$		0			0
$976$	10.5815	−	34.4368i	0.338704	−	1.10230i
$977$	−2.02199	−	1.16740i	−0.0646892	−	0.0373483i	0.467307	−	0.884095i	$-0.345224\pi$
$977$	−2.02199	−	1.16740i	−0.0646892	−	0.0373483i	−0.531996	+	0.846747i	$0.678558\pi$
$978$		0			0
$979$	0.626159	+	0.167779i	0.0200121	+	0.00536224i
$980$	32.1115	+	9.23231i	1.02577	+	0.294915i
$981$		0			0
$982$	−1.40015	+	2.37506i	−0.0446805	+	0.0757913i
$983$	−21.5089	+	12.4182i	−0.686029	+	0.396079i	−0.802123	−	0.597159i	$-0.796296\pi$
$983$	−21.5089	+	12.4182i	−0.686029	+	0.396079i	0.116094	+	0.993238i	$0.462963\pi$
$984$		0			0
$985$	13.9464	+	8.05197i	0.444370	+	0.256557i
$986$	11.0029	−	6.22001i	0.350403	−	0.198085i
$987$		0			0
$988$	7.65462	+	4.60670i	0.243526	+	0.146559i
$989$	13.2158	−	13.2158i	0.420240	−	0.420240i
$990$		0			0
$991$			7.12527i			0.226342i	0.993576	+	0.113171i	$0.0361008\pi$
$991$			7.12527i			0.226342i	−0.993576	+	0.113171i	$0.963899\pi$
$992$	−10.1152	−	46.0102i	−0.321159	−	1.46082i
$993$		0			0
$994$	−34.5526	−	9.59539i	−1.09594	−	0.304347i
$995$	−9.60763	+	2.57436i	−0.304582	+	0.0816126i
$996$		0			0
$997$	−47.5897	−	12.7516i	−1.50718	−	0.403848i	−0.591684	−	0.806170i	$-0.701537\pi$
$997$	−47.5897	−	12.7516i	−1.50718	−	0.403848i	−0.915498	+	0.402322i	$0.868203\pi$
$998$	8.08908	−	13.7215i	0.256055	−	0.434346i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.179.16		88
3.2	odd	2		144.2.u.a.131.7	yes	88
4.3	odd	2		1728.2.z.a.1583.1		88
9.2	odd	6	inner	432.2.v.a.35.9		88
9.7	even	3		144.2.u.a.83.14	yes	88
12.11	even	2		576.2.y.a.239.15		88
16.5	even	4		1728.2.z.a.719.1		88
16.11	odd	4	inner	432.2.v.a.395.9		88
36.7	odd	6		576.2.y.a.47.3		88
36.11	even	6		1728.2.z.a.1007.1		88
48.5	odd	4		576.2.y.a.527.3		88
48.11	even	4		144.2.u.a.59.14	yes	88
144.11	even	12	inner	432.2.v.a.251.16		88
144.43	odd	12		144.2.u.a.11.7	✓	88
144.101	odd	12		1728.2.z.a.143.1		88
144.133	even	12		576.2.y.a.335.15		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.7	✓	88	144.43	odd	12
144.2.u.a.59.14	yes	88	48.11	even	4
144.2.u.a.83.14	yes	88	9.7	even	3
144.2.u.a.131.7	yes	88	3.2	odd	2
432.2.v.a.35.9		88	9.2	odd	6	inner
432.2.v.a.179.16		88	1.1	even	1	trivial
432.2.v.a.251.16		88	144.11	even	12	inner
432.2.v.a.395.9		88	16.11	odd	4	inner
576.2.y.a.47.3		88	36.7	odd	6
576.2.y.a.239.15		88	12.11	even	2
576.2.y.a.335.15		88	144.133	even	12
576.2.y.a.527.3		88	48.5	odd	4
1728.2.z.a.143.1		88	144.101	odd	12
1728.2.z.a.719.1		88	16.5	even	4
1728.2.z.a.1007.1		88	36.11	even	6
1728.2.z.a.1583.1		88	4.3	odd	2

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.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.990880 + 1.00904i) q^{2} +(-0.0363133 + 1.99967i) q^{4} +(-3.73424 + 1.00059i) q^{5} +(-1.68236 - 2.91393i) q^{7} +(-2.05372 + 1.94479i) q^{8} +(-4.70981 - 2.77653i) q^{10} +(-0.211428 - 0.0566521i) q^{11} +(-2.71526 + 0.727551i) q^{13} +(1.27325 - 4.58492i) q^{14} +(-3.99736 - 0.145229i) q^{16} +4.23937i q^{17} +(-1.12365 + 1.12365i) q^{19} +(-1.86524 - 7.50358i) q^{20} +(-0.152336 - 0.269474i) q^{22} +(-3.33369 - 1.92471i) q^{23} +(8.61325 - 4.97286i) q^{25} +(-3.42462 - 2.01888i) q^{26} +(5.88800 - 3.25835i) q^{28} +(-2.03634 - 0.545635i) q^{29} +(7.21206 + 4.16388i) q^{31} +(-3.81437 - 4.17739i) q^{32} +(-4.27769 + 4.20071i) q^{34} +(9.19798 + 9.19798i) q^{35} +(-2.66564 + 2.66564i) q^{37} +(-2.24720 - 0.0204025i) q^{38} +(5.72317 - 9.31725i) q^{40} +(-1.70386 + 2.95117i) q^{41} +(-1.25664 + 4.68985i) q^{43} +(0.120963 - 0.420730i) q^{44} +(-1.36119 - 5.27098i) q^{46} +(2.34998 + 4.07028i) q^{47} +(-2.16067 + 3.74239i) q^{49} +(13.5525 + 3.76358i) q^{50} +(-1.35626 - 5.45604i) q^{52} +(-7.58271 - 7.58271i) q^{53} +0.846209 q^{55} +(9.12210 + 2.71258i) q^{56} +(-1.46720 - 2.59540i) q^{58} +(1.43167 + 5.34305i) q^{59} +(-2.33105 + 8.69958i) q^{61} +(2.94477 + 11.4031i) q^{62} +(0.435568 - 7.98813i) q^{64} +(9.41144 - 5.43370i) q^{65} +(1.38665 + 5.17504i) q^{67} +(-8.47735 - 0.153945i) q^{68} +(-0.167011 + 18.3952i) q^{70} -7.53614i q^{71} -3.22646i q^{73} +(-5.33107 - 0.0484011i) q^{74} +(-2.20612 - 2.28773i) q^{76} +(0.190618 + 0.711397i) q^{77} +(4.98587 - 2.87859i) q^{79} +(15.0724 - 3.45739i) q^{80} +(-4.66616 + 1.20500i) q^{82} +(-1.20739 + 4.50604i) q^{83} +(-4.24186 - 15.8308i) q^{85} +(-5.97741 + 3.37908i) q^{86} +(0.544392 - 0.294836i) q^{88} -2.96157 q^{89} +(6.68807 + 6.68807i) q^{91} +(3.96984 - 6.59639i) q^{92} +(-1.77852 + 6.40437i) q^{94} +(3.07166 - 5.32027i) q^{95} +(-7.63883 - 13.2308i) q^{97} +(-5.91718 + 1.52806i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Introduction

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