LMFDB - Embedded newform 432.2.v.a.179.3

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)

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")

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);

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			179.3
Character	$\chi$	$=$	432.179
Dual form			432.2.v.a.251.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29365 + 0.571371i) q^{2} +(1.34707 - 1.47831i) q^{4} +(3.81396 - 1.02195i) q^{5} +(1.46715 + 2.54117i) q^{7} +(-0.897978 + 2.68210i) q^{8} +(-4.35003 + 3.50123i) q^{10} +(2.65006 + 0.710081i) q^{11} +(-2.34729 + 0.628955i) q^{13} +(-3.34993 - 2.44911i) q^{14} +(-0.370800 - 3.98278i) q^{16} -2.89808i q^{17} +(-1.99906 + 1.99906i) q^{19} +(3.62692 - 7.01485i) q^{20} +(-3.83397 + 0.595568i) q^{22} +(2.07141 + 1.19593i) q^{23} +(9.17180 - 5.29534i) q^{25} +(2.67721 - 2.15482i) q^{26} +(5.73299 + 1.25424i) q^{28} +(-8.46218 - 2.26743i) q^{29} +(-0.439075 - 0.253500i) q^{31} +(2.75533 + 4.94046i) q^{32} +(1.65588 + 3.74911i) q^{34} +(8.19258 + 8.19258i) q^{35} +(1.36407 - 1.36407i) q^{37} +(1.44388 - 3.72828i) q^{38} +(-0.683892 + 11.1471i) q^{40} +(-0.745739 + 1.29166i) q^{41} +(-1.27136 + 4.74478i) q^{43} +(4.61954 - 2.96108i) q^{44} +(-3.36300 - 0.363572i) q^{46} +(3.25802 + 5.64306i) q^{47} +(-0.805035 + 1.39436i) q^{49} +(-8.83951 + 12.0908i) q^{50} +(-2.23218 + 4.31727i) q^{52} +(5.17979 + 5.17979i) q^{53} +10.8329 q^{55} +(-8.13313 + 1.65311i) q^{56} +(12.2427 - 1.90177i) q^{58} +(-0.664781 - 2.48100i) q^{59} +(2.99657 - 11.1833i) q^{61} +(0.712853 + 0.0770663i) q^{62} +(-6.38727 - 4.81693i) q^{64} +(-8.30972 + 4.79762i) q^{65} +(-2.53505 - 9.46095i) q^{67} +(-4.28427 - 3.90393i) q^{68} +(-15.2794 - 5.91735i) q^{70} -4.65399i q^{71} +4.91897i q^{73} +(-0.985240 + 2.54402i) q^{74} +(0.262354 + 5.64809i) q^{76} +(2.08358 + 7.77604i) q^{77} +(-3.61263 + 2.08575i) q^{79} +(-5.48441 - 14.8112i) q^{80} +(0.226711 - 2.09705i) q^{82} +(3.37411 - 12.5924i) q^{83} +(-2.96169 - 11.0532i) q^{85} +(-1.06633 - 6.86451i) q^{86} +(-4.28420 + 6.47007i) q^{88} -7.33327 q^{89} +(-5.04210 - 5.04210i) q^{91} +(4.55828 - 1.45118i) q^{92} +(-7.43902 - 5.43861i) q^{94} +(-5.58139 + 9.66725i) q^{95} +(2.50134 + 4.33245i) q^{97} +(0.244738 - 2.26379i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.29365	+	0.571371i	−0.914750	+	0.404020i
$2$	−1.29365	+	0.571371i	−0.914750	+	0.404020i
$3$		0			0
$3$		0			0
$4$	1.34707	−	1.47831i	0.673535	−	0.739155i
$5$	3.81396	−	1.02195i	1.70566	−	0.457029i	0.731302	−	0.682053i	$-0.238913\pi$
$5$	3.81396	−	1.02195i	1.70566	−	0.457029i	0.974353	+	0.225024i	$0.0722462\pi$
$6$		0			0
$7$	1.46715	+	2.54117i	0.554529	+	0.960473i	0.997940	+	0.0641541i	$0.0204349\pi$
$7$	1.46715	+	2.54117i	0.554529	+	0.960473i	−0.443411	+	0.896318i	$0.646232\pi$
$8$	−0.897978	+	2.68210i	−0.317483	+	0.948264i
$9$		0			0
$10$	−4.35003	+	3.50123i	−1.37560	+	1.10719i
$11$	2.65006	+	0.710081i	0.799022	+	0.214097i	0.635155	−	0.772385i	$-0.280936\pi$
$11$	2.65006	+	0.710081i	0.799022	+	0.214097i	0.163868	+	0.986482i	$0.447603\pi$
$12$		0			0
$13$	−2.34729	+	0.628955i	−0.651021	+	0.174441i	−0.569191	−	0.822206i	$-0.692743\pi$
$13$	−2.34729	+	0.628955i	−0.651021	+	0.174441i	−0.0818307	+	0.996646i	$0.526077\pi$
$14$	−3.34993	−	2.44911i	−0.895306	−	0.654551i
$15$		0			0
$16$	−0.370800	−	3.98278i	−0.0926999	−	0.995694i
$17$		−	2.89808i		−	0.702889i	−0.936209	−	0.351444i	$-0.885691\pi$
$17$		−	2.89808i		−	0.702889i	0.936209	−	0.351444i	$-0.114309\pi$
$18$		0			0
$19$	−1.99906	+	1.99906i	−0.458615	+	0.458615i	−0.898201	−	0.439586i	$-0.855125\pi$
$19$	−1.99906	+	1.99906i	−0.458615	+	0.458615i	0.439586	+	0.898201i	$0.355125\pi$
$20$	3.62692	−	7.01485i	0.811004	−	1.56857i
$21$		0			0
$22$	−3.83397	+	0.595568i	−0.817406	+	0.126976i
$23$	2.07141	+	1.19593i	0.431918	+	0.249368i	0.700163	−	0.713983i	$-0.253110\pi$
$23$	2.07141	+	1.19593i	0.431918	+	0.249368i	−0.268245	+	0.963351i	$0.586444\pi$
$24$		0			0
$25$	9.17180	−	5.29534i	1.83436	−	1.05907i
$26$	2.67721	−	2.15482i	0.525044	−	0.422595i
$27$		0			0
$28$	5.73299	+	1.25424i	1.08343	+	0.237029i
$29$	−8.46218	−	2.26743i	−1.57139	−	0.421052i	−0.635141	−	0.772396i	$-0.719058\pi$
$29$	−8.46218	−	2.26743i	−1.57139	−	0.421052i	−0.936246	+	0.351344i	$0.885725\pi$
$30$		0			0
$31$	−0.439075	−	0.253500i	−0.0788602	−	0.0455300i	0.460051	−	0.887892i	$-0.347831\pi$
$31$	−0.439075	−	0.253500i	−0.0788602	−	0.0455300i	−0.538912	+	0.842362i	$0.681164\pi$
$32$	2.75533	+	4.94046i	0.487078	+	0.873359i
$33$		0			0
$34$	1.65588	+	3.74911i	0.283981	+	0.642968i
$35$	8.19258	+	8.19258i	1.38480	+	1.38480i
$36$		0			0
$37$	1.36407	−	1.36407i	0.224251	−	0.224251i	−0.586035	−	0.810286i	$-0.699312\pi$
$37$	1.36407	−	1.36407i	0.224251	−	0.224251i	0.810286	+	0.586035i	$0.199312\pi$
$38$	1.44388	−	3.72828i	0.234228	−	0.604808i
$39$		0			0
$40$	−0.683892	+	11.1471i	−0.108133	+	1.76251i
$41$	−0.745739	+	1.29166i	−0.116465	+	0.201723i	−0.918364	−	0.395736i	$-0.870490\pi$
$41$	−0.745739	+	1.29166i	−0.116465	+	0.201723i	0.801899	+	0.597459i	$0.203823\pi$
$42$		0			0
$43$	−1.27136	+	4.74478i	−0.193881	+	0.723572i	0.798673	+	0.601765i	$0.205536\pi$
$43$	−1.27136	+	4.74478i	−0.193881	+	0.723572i	−0.992554	+	0.121807i	$0.961131\pi$
$44$	4.61954	−	2.96108i	0.696421	−	0.446399i
$45$		0			0
$46$	−3.36300	−	0.363572i	−0.495847	−	0.0536058i
$47$	3.25802	+	5.64306i	0.475231	+	0.823124i	0.999598	−	0.0283684i	$-0.00903115\pi$
$47$	3.25802	+	5.64306i	0.475231	+	0.823124i	−0.524367	+	0.851493i	$0.675698\pi$
$48$		0			0
$49$	−0.805035	+	1.39436i	−0.115005	+	0.199195i
$50$	−8.83951	+	12.0908i	−1.25010	+	1.70990i
$51$		0			0
$52$	−2.23218	+	4.31727i	−0.309547	+	0.598698i
$53$	5.17979	+	5.17979i	0.711499	+	0.711499i	0.966849	−	0.255349i	$-0.0821905\pi$
$53$	5.17979	+	5.17979i	0.711499	+	0.711499i	−0.255349	+	0.966849i	$0.582191\pi$
$54$		0			0
$55$	10.8329			1.46071
$56$	−8.13313	+	1.65311i	−1.08684	+	0.220906i
$57$		0			0
$58$	12.2427	−	1.90177i	1.60754	−	0.249715i
$59$	−0.664781	−	2.48100i	−0.0865472	−	0.322998i	0.909056	−	0.416675i	$-0.136805\pi$
$59$	−0.664781	−	2.48100i	−0.0865472	−	0.322998i	−0.995603	+	0.0936766i	$0.970138\pi$
$60$		0			0
$61$	2.99657	−	11.1833i	0.383671	−	1.43188i	−0.456580	−	0.889682i	$-0.650926\pi$
$61$	2.99657	−	11.1833i	0.383671	−	1.43188i	0.840251	−	0.542198i	$-0.182408\pi$
$62$	0.712853	+	0.0770663i	0.0905324	+	0.00978743i
$63$		0			0
$64$	−6.38727	−	4.81693i	−0.798409	−	0.602116i
$65$	−8.30972	+	4.79762i	−1.03069	+	0.595071i
$66$		0			0
$67$	−2.53505	−	9.46095i	−0.309706	−	1.15584i	−0.928818	−	0.370536i	$-0.879174\pi$
$67$	−2.53505	−	9.46095i	−0.309706	−	1.15584i	0.619112	−	0.785303i	$-0.287493\pi$
$68$	−4.28427	−	3.90393i	−0.519544	−	0.473421i
$69$		0			0
$70$	−15.2794	−	5.91735i	−1.82623	−	0.707259i
$71$		−	4.65399i		−	0.552327i	−0.961111	−	0.276164i	$-0.910937\pi$
$71$		−	4.65399i		−	0.552327i	0.961111	−	0.276164i	$-0.0890632\pi$
$72$		0			0
$73$			4.91897i			0.575722i	0.957672	+	0.287861i	$0.0929441\pi$
$73$			4.91897i			0.575722i	−0.957672	+	0.287861i	$0.907056\pi$
$74$	−0.985240	+	2.54402i	−0.114532	+	0.295736i
$75$		0			0
$76$	0.262354	+	5.64809i	0.0300940	+	0.647881i
$77$	2.08358	+	7.77604i	0.237446	+	0.886162i
$78$		0			0
$79$	−3.61263	+	2.08575i	−0.406453	+	0.234666i	−0.689264	−	0.724510i	$-0.742066\pi$
$79$	−3.61263	+	2.08575i	−0.406453	+	0.234666i	0.282812	+	0.959175i	$0.408733\pi$
$80$	−5.48441	−	14.8112i	−0.613175	−	1.65594i
$81$		0			0
$82$	0.226711	−	2.09705i	0.0250361	−	0.231580i
$83$	3.37411	−	12.5924i	0.370357	−	1.38219i	−0.489654	−	0.871917i	$-0.662877\pi$
$83$	3.37411	−	12.5924i	0.370357	−	1.38219i	0.860011	−	0.510275i	$-0.170456\pi$
$84$		0			0
$85$	−2.96169	−	11.0532i	−0.321241	−	1.19889i
$86$	−1.06633	−	6.86451i	−0.114985	−	0.740220i
$87$		0			0
$88$	−4.28420	+	6.47007i	−0.456697	+	0.689712i
$89$	−7.33327			−0.777325			−0.388662	−	0.921380i	$-0.627063\pi$
$89$	−7.33327			−0.777325			−0.388662	+	0.921380i	$0.627063\pi$
$90$		0			0
$91$	−5.04210	−	5.04210i	−0.528556	−	0.528556i
$92$	4.55828	−	1.45118i	0.475234	−	0.151296i
$93$		0			0
$94$	−7.43902	−	5.43861i	−0.767276	−	0.560950i
$95$	−5.58139	+	9.66725i	−0.572639	+	0.991839i
$96$		0			0
$97$	2.50134	+	4.33245i	0.253973	+	0.439893i	0.964616	−	0.263659i	$-0.0849294\pi$
$97$	2.50134	+	4.33245i	0.253973	+	0.439893i	−0.710643	+	0.703552i	$0.751596\pi$
$98$	0.244738	−	2.26379i	0.0247222	−	0.228678i
$99$		0			0
$100$	4.52691	−	20.6920i	0.452691	−	2.06920i
$101$	2.82933	−	10.5592i	0.281529	−	1.05068i	−0.669810	−	0.742533i	$-0.733624\pi$
$101$	2.82933	−	10.5592i	0.281529	−	1.05068i	0.951339	−	0.308147i	$-0.0997090\pi$
$102$		0			0
$103$	−0.321949	+	0.557632i	−0.0317226	+	0.0549451i	−0.881451	−	0.472276i	$-0.843433\pi$
$103$	−0.321949	+	0.557632i	−0.0317226	+	0.0549451i	0.849728	+	0.527221i	$0.176766\pi$
$104$	0.420899	−	6.86044i	0.0412726	−	0.672722i
$105$		0			0
$106$	−9.66043	−	3.74127i	−0.938304	−	0.363384i
$107$	−3.74155	+	3.74155i	−0.361709	+	0.361709i	−0.864442	−	0.502733i	$-0.832328\pi$
$107$	−3.74155	+	3.74155i	−0.361709	+	0.361709i	0.502733	+	0.864442i	$0.332328\pi$
$108$		0			0
$109$	6.00859	+	6.00859i	0.575518	+	0.575518i	0.933665	−	0.358147i	$-0.116591\pi$
$109$	6.00859	+	6.00859i	0.575518	+	0.575518i	−0.358147	+	0.933665i	$0.616591\pi$
$110$	−14.0140	+	6.18959i	−1.33618	+	0.590155i
$111$		0			0
$112$	9.57690	−	6.78558i	0.904932	−	0.641177i
$113$	−14.4387	−	8.33620i	−1.35828	−	0.784204i	−0.368889	−	0.929474i	$-0.620262\pi$
$113$	−14.4387	−	8.33620i	−1.35828	−	0.784204i	−0.989392	+	0.145270i	$0.953595\pi$
$114$		0			0
$115$	9.12244	+	2.44435i	0.850672	+	0.227937i
$116$	−14.7511	+	9.45533i	−1.36961	+	0.877905i
$117$		0			0
$118$	2.27757	+	2.82971i	0.209667	+	0.260496i
$119$	7.36453	−	4.25191i	0.675105	−	0.389772i
$120$		0			0
$121$	−3.00769	−	1.73649i	−0.273426	−	0.157863i
$122$	2.51332	+	16.1795i	0.227545	+	1.46482i
$123$		0			0
$124$	−0.966217	+	0.307606i	−0.0867689	+	0.0276239i
$125$	15.6093	−	15.6093i	1.39613	−	1.39613i
$126$		0			0
$127$			17.9975i			1.59702i	0.601983	+	0.798509i	$0.294377\pi$
$127$			17.9975i			1.59702i	−0.601983	+	0.798509i	$0.705623\pi$
$128$	11.0152	+	2.58193i	0.973611	+	0.228212i
$129$		0			0
$130$	8.00866	−	10.9544i	0.702406	−	0.960762i
$131$	−17.4121	+	4.66555i	−1.52130	+	0.407631i	−0.920170	−	0.391520i	$-0.871949\pi$
$131$	−17.4121	+	4.66555i	−1.52130	+	0.407631i	−0.601131	+	0.799151i	$0.705283\pi$
$132$		0			0
$133$	−8.01285	−	2.14704i	−0.694802	−	0.186172i
$134$	8.68519	+	10.7907i	0.750286	+	0.932176i
$135$		0			0
$136$	7.77294	+	2.60242i	0.666524	+	0.223155i
$137$	0.396155	+	0.686161i	0.0338458	+	0.0586227i	0.882452	−	0.470402i	$-0.155891\pi$
$137$	0.396155	+	0.686161i	0.0338458	+	0.0586227i	−0.848606	+	0.529025i	$0.822558\pi$
$138$		0			0
$139$	−20.5134	+	5.49654i	−1.73992	+	0.466211i	−0.982430	−	0.186633i	$-0.940242\pi$
$139$	−20.5134	+	5.49654i	−1.73992	+	0.466211i	−0.757492	+	0.652844i	$0.773576\pi$
$140$	23.1472	−	1.07519i	1.95629	−	0.0908697i
$141$		0			0
$142$	2.65916	+	6.02065i	0.223151	+	0.505242i
$143$	−6.66706			−0.557528
$144$		0			0
$145$	−34.5916			−2.87268
$146$	−2.81055	−	6.36343i	−0.232603	−	0.526641i
$147$		0			0
$148$	−0.179019	−	3.85401i	−0.0147152	−	0.316798i
$149$	11.3030	−	3.02863i	0.925977	−	0.248115i	0.235839	−	0.971792i	$-0.424216\pi$
$149$	11.3030	−	3.02863i	0.925977	−	0.248115i	0.690139	+	0.723677i	$0.257550\pi$
$150$		0			0
$151$	−4.24025	−	7.34432i	−0.345066	−	0.597673i	0.640299	−	0.768125i	$-0.278810\pi$
$151$	−4.24025	−	7.34432i	−0.345066	−	0.597673i	−0.985366	+	0.170453i	$0.945477\pi$
$152$	−3.56655	−	7.15677i	−0.289285	−	0.580490i
$153$		0			0
$154$	−7.13844	−	8.86899i	−0.575232	−	0.714684i
$155$	−1.93368	−	0.518128i	−0.155317	−	0.0416170i
$156$		0			0
$157$	3.53516	−	0.947242i	0.282136	−	0.0755981i	−0.114976	−	0.993368i	$-0.536679\pi$
$157$	3.53516	−	0.947242i	0.282136	−	0.0755981i	0.397112	+	0.917770i	$0.370012\pi$
$158$	3.48175	−	4.76239i	0.276993	−	0.378875i
$159$		0			0
$160$	15.5576	+	16.0269i	1.22994	+	1.26704i
$161$			7.01840i			0.553127i
$162$		0			0
$163$	−3.86060	+	3.86060i	−0.302385	+	0.302385i	−0.841946	−	0.539561i	$-0.818590\pi$
$163$	−3.86060	+	3.86060i	−0.302385	+	0.302385i	0.539561	+	0.841946i	$0.318590\pi$
$164$	0.904908	+	2.84239i	0.0706614	+	0.221953i
$165$		0			0
$166$	2.82998	+	18.2180i	0.219649	+	1.41399i
$167$	5.98224	+	3.45385i	0.462920	+	0.267267i	0.713271	−	0.700888i	$-0.247213\pi$
$167$	5.98224	+	3.45385i	0.462920	+	0.267267i	−0.250351	+	0.968155i	$0.580546\pi$
$168$		0			0
$169$	−6.14414	+	3.54732i	−0.472626	+	0.272871i
$170$	10.1469	+	12.6067i	0.778229	+	0.966894i
$171$		0			0
$172$	5.30164	+	8.27102i	0.404247	+	0.630659i
$173$	−3.86859	−	1.03659i	−0.294123	−	0.0788101i	0.108740	−	0.994070i	$-0.465318\pi$
$173$	−3.86859	−	1.03659i	−0.294123	−	0.0788101i	−0.402863	+	0.915260i	$0.631985\pi$
$174$		0			0
$175$	26.9127	+	15.5381i	2.03441	+	1.17457i
$176$	1.84545	−	10.8179i	0.139106	−	0.815429i
$177$		0			0
$178$	9.48669	−	4.19001i	0.711058	−	0.314055i
$179$	−10.0625	−	10.0625i	−0.752109	−	0.752109i	0.222764	−	0.974872i	$-0.428492\pi$
$179$	−10.0625	−	10.0625i	−0.752109	−	0.752109i	−0.974872	+	0.222764i	$0.928492\pi$
$180$		0			0
$181$	15.0346	−	15.0346i	1.11751	−	1.11751i	0.125405	−	0.992106i	$-0.459977\pi$
$181$	15.0346	−	15.0346i	1.11751	−	1.11751i	0.992106	−	0.125405i	$-0.0400229\pi$
$182$	9.40363	+	3.64181i	0.697044	+	0.269949i
$183$		0			0
$184$	−5.06767	+	4.48179i	−0.373593	+	0.330402i
$185$	3.80849	−	6.59651i	0.280006	−	0.484985i
$186$		0			0
$187$	2.05787	−	7.68009i	0.150487	−	0.561624i
$188$	12.7310	+	2.78523i	0.928501	+	0.203134i
$189$		0			0
$190$	1.69679	−	15.6951i	0.123098	−	1.13864i
$191$	10.9007	+	18.8806i	0.788749	+	1.36615i	0.926734	+	0.375719i	$0.122604\pi$
$191$	10.9007	+	18.8806i	0.788749	+	1.36615i	−0.137984	+	0.990434i	$0.544062\pi$
$192$		0			0
$193$	−2.34723	+	4.06553i	−0.168958	+	0.292643i	−0.938054	−	0.346490i	$-0.887373\pi$
$193$	−2.34723	+	4.06553i	−0.168958	+	0.292643i	0.769096	+	0.639133i	$0.220707\pi$
$194$	−5.71130	−	4.17549i	−0.410047	−	0.299782i
$195$		0			0
$196$	0.976859	+	3.06840i	0.0697757	+	0.219171i
$197$	−14.3226	−	14.3226i	−1.02044	−	1.02044i	−0.999787	−	0.0206566i	$-0.993424\pi$
$197$	−14.3226	−	14.3226i	−1.02044	−	1.02044i	−0.0206566	−	0.999787i	$-0.506576\pi$
$198$		0			0
$199$	−14.4965			−1.02763			−0.513816	−	0.857901i	$-0.671768\pi$
$199$	−14.4965			−1.02763			−0.513816	+	0.857901i	$0.671768\pi$
$200$	5.96653	+	29.3547i	0.421898	+	2.07569i
$201$		0			0
$202$	2.37305	+	15.2765i	0.166967	+	1.07485i
$203$	−6.65332	−	24.8305i	−0.466971	−	1.74276i
$204$		0			0
$205$	−1.52421	+	5.68844i	−0.106456	+	0.397298i
$206$	0.0978753	−	0.905334i	0.00681930	−	0.0630776i
$207$		0			0
$208$	3.37536	+	9.11552i	0.234039	+	0.632047i
$209$	−6.71710	+	3.87812i	−0.464632	+	0.268255i
$210$		0			0
$211$	−1.71268	−	6.39179i	−0.117905	−	0.440029i	0.881582	−	0.472030i	$-0.156479\pi$
$211$	−1.71268	−	6.39179i	−0.117905	−	0.440029i	−0.999488	+	0.0320010i	$0.989812\pi$
$212$	14.6349	−	0.679790i	1.00513	−	0.0466882i
$213$		0			0
$214$	2.70245	−	6.97808i	0.184736	−	0.477012i
$215$			19.3957i			1.32277i
$216$		0			0
$217$		−	1.48769i		−	0.100991i
$218$	−11.2062	−	4.33989i	−0.758976	−	0.293934i
$219$		0			0
$220$	14.5927	−	16.0144i	0.983837	−	1.07969i
$221$	1.82276	+	6.80265i	0.122612	+	0.457596i
$222$		0			0
$223$	1.59599	−	0.921443i	0.106875	−	0.0617044i	−0.445610	−	0.895227i	$-0.647013\pi$
$223$	1.59599	−	0.921443i	0.106875	−	0.0617044i	0.552485	+	0.833523i	$0.313680\pi$
$224$	−8.51209	+	14.2501i	−0.568738	+	0.952128i
$225$		0			0
$226$	23.4417	+	2.53428i	1.55932	+	0.168578i
$227$	0.184084	−	0.687012i	0.0122181	−	0.0455986i	−0.959548	−	0.281546i	$-0.909153\pi$
$227$	0.184084	−	0.687012i	0.0122181	−	0.0455986i	0.971766	+	0.235948i	$0.0758194\pi$
$228$		0			0
$229$	1.98433	+	7.40562i	0.131128	+	0.489377i	0.999984	−	0.00568843i	$-0.00181069\pi$
$229$	1.98433	+	7.40562i	0.131128	+	0.489377i	−0.868856	+	0.495066i	$0.835144\pi$
$230$	−13.1979	+	2.05016i	−0.870243	+	0.135183i
$231$		0			0
$232$	13.6803	−	20.6603i	0.898158	−	1.35641i
$233$	−1.36925			−0.0897024			−0.0448512	−	0.998994i	$-0.514281\pi$
$233$	−1.36925			−0.0897024			−0.0448512	+	0.998994i	$0.514281\pi$
$234$		0			0
$235$	18.1929	+	18.1929i	1.18677	+	1.18677i
$236$	−4.56319	−	2.35933i	−0.297038	−	0.153579i
$237$		0			0
$238$	−7.09772	+	9.70837i	−0.460077	+	0.629300i
$239$	0.773627	−	1.33996i	0.0500418	−	0.0866749i	−0.839919	−	0.542711i	$-0.817398\pi$
$239$	0.773627	−	1.33996i	0.0500418	−	0.0866749i	0.889961	+	0.456036i	$0.150731\pi$
$240$		0			0
$241$	3.83660	+	6.64519i	0.247137	+	0.428054i	0.962730	−	0.270463i	$-0.0871769\pi$
$241$	3.83660	+	6.64519i	0.247137	+	0.428054i	−0.715593	+	0.698517i	$0.753844\pi$
$242$	4.88308	+	0.527908i	0.313896	+	0.0339352i
$243$		0			0
$244$	−12.4959	−	19.4946i	−0.799965	−	1.24801i
$245$	−1.64541	+	6.14075i	−0.105121	+	0.392318i
$246$		0			0
$247$	3.43505	−	5.94968i	0.218567	−	0.378569i
$248$	1.07419	−	0.950004i	0.0682112	−	0.0603253i
$249$		0			0
$250$	−11.2743	+	29.1116i	−0.713048	+	1.84118i
$251$	5.46632	−	5.46632i	0.345031	−	0.345031i	−0.513224	−	0.858255i	$-0.671549\pi$
$251$	5.46632	−	5.46632i	0.345031	−	0.345031i	0.858255	+	0.513224i	$0.171549\pi$
$252$		0			0
$253$	4.64014	+	4.64014i	0.291723	+	0.291723i
$254$	−10.2832	−	23.2825i	−0.645227	−	1.46087i
$255$		0			0
$256$	−15.7250	+	2.95362i	−0.982813	+	0.184602i
$257$	20.5918	+	11.8887i	1.28448	+	0.741596i	0.977664	−	0.210172i	$-0.0674025\pi$
$257$	20.5918	+	11.8887i	1.28448	+	0.741596i	0.306818	+	0.951768i	$0.400736\pi$
$258$		0			0
$259$	5.46761	+	1.46504i	0.339741	+	0.0910333i
$260$	−4.10141	+	18.7471i	−0.254359	+	1.16264i
$261$		0			0
$262$	19.8594	−	15.9844i	1.22692	−	0.987517i
$263$	6.13704	−	3.54322i	0.378426	−	0.218484i	−0.298707	−	0.954345i	$-0.596555\pi$
$263$	6.13704	−	3.54322i	0.378426	−	0.218484i	0.677133	+	0.735860i	$0.263222\pi$
$264$		0			0
$265$	25.0490	+	14.4621i	1.53875	+	0.888397i
$266$	11.5926	−	1.80079i	0.710788	−	0.110414i
$267$		0			0
$268$	−17.4011	−	8.99698i	−1.06294	−	0.549578i
$269$	−20.6616	+	20.6616i	−1.25976	+	1.25976i	−0.308553	+	0.951207i	$0.599845\pi$
$269$	−20.6616	+	20.6616i	−1.25976	+	1.25976i	−0.951207	+	0.308553i	$0.900155\pi$
$270$		0			0
$271$		−	16.6901i		−	1.01385i	−0.861989	−	0.506927i	$-0.830782\pi$
$271$		−	16.6901i		−	1.01385i	0.861989	−	0.506927i	$-0.169218\pi$
$272$	−11.5424	+	1.07461i	−0.699862	+	0.0651577i
$273$		0			0
$274$	−0.904539	−	0.661302i	−0.0546452	−	0.0399507i
$275$	28.0659	−	7.52024i	1.69244	−	0.453487i
$276$		0			0
$277$	4.49217	+	1.20367i	0.269908	+	0.0723217i	0.391235	−	0.920291i	$-0.372048\pi$
$277$	4.49217	+	1.20367i	0.269908	+	0.0723217i	−0.121326	+	0.992613i	$0.538715\pi$
$278$	23.3966	−	18.8314i	1.40324	−	1.12943i
$279$		0			0
$280$	−29.3301	+	14.6165i	−1.75281	+	0.873505i
$281$	11.4153	+	19.7719i	0.680979	+	1.17949i	0.974682	+	0.223594i	$0.0717790\pi$
$281$	11.4153	+	19.7719i	0.680979	+	1.17949i	−0.293703	+	0.955897i	$0.594888\pi$
$282$		0			0
$283$	−24.9438	+	6.68368i	−1.48276	+	0.397303i	−0.907284	−	0.420518i	$-0.861848\pi$
$283$	−24.9438	+	6.68368i	−1.48276	+	0.397303i	−0.575472	+	0.817822i	$0.695182\pi$
$284$	−6.88004	−	6.26926i	−0.408256	−	0.372012i
$285$		0			0
$286$	8.62486	−	3.80937i	0.509999	−	0.225253i
$287$	−4.37643			−0.258333
$288$		0			0
$289$	8.60110			0.505947
$290$	44.7495	−	19.7646i	2.62778	−	1.16062i
$291$		0			0
$292$	7.27176	+	6.62620i	0.425547	+	0.387769i
$293$	2.76706	−	0.741431i	0.161653	−	0.0433149i	−0.177085	−	0.984196i	$-0.556667\pi$
$293$	2.76706	−	0.741431i	0.161653	−	0.0433149i	0.338738	+	0.940881i	$0.390000\pi$
$294$		0			0
$295$	−5.07090	−	8.78306i	−0.295239	−	0.511370i
$296$	2.43366	+	4.88346i	0.141453	+	0.283845i
$297$		0			0
$298$	−12.8917	+	10.3762i	−0.746794	+	0.601077i
$299$	−5.61438	−	1.50437i	−0.324688	−	0.0869998i
$300$		0			0
$301$	−13.9226	+	3.73054i	−0.802484	+	0.215025i
$302$	9.68174	+	7.07825i	0.557121	+	0.407307i
$303$		0			0
$304$	8.70304	+	7.22054i	0.499154	+	0.414127i
$305$		−	45.7152i		−	2.61764i
$306$		0			0
$307$	−7.67329	+	7.67329i	−0.437938	+	0.437938i	−0.891317	−	0.453380i	$-0.850218\pi$
$307$	−7.67329	+	7.67329i	−0.437938	+	0.437938i	0.453380	+	0.891317i	$0.350218\pi$
$308$	14.3021	+	7.39470i	0.814940	+	0.421352i
$309$		0			0
$310$	2.79755	−	0.434571i	0.158890	−	0.0246820i
$311$	−15.0777	−	8.70513i	−0.854980	−	0.493623i	0.00734815	−	0.999973i	$-0.497661\pi$
$311$	−15.0777	−	8.70513i	−0.854980	−	0.493623i	−0.862328	+	0.506350i	$0.830994\pi$
$312$		0			0
$313$	−21.3027	+	12.2991i	−1.20410	+	0.695189i	−0.961465	−	0.274928i	$-0.911346\pi$
$313$	−21.3027	+	12.2991i	−1.20410	+	0.695189i	−0.242638	+	0.970117i	$0.578013\pi$
$314$	−4.03203	+	3.24529i	−0.227541	+	0.183142i
$315$		0			0
$316$	−1.78308	+	8.15024i	−0.100306	+	0.458487i
$317$	7.99342	+	2.14183i	0.448955	+	0.120297i	0.476211	−	0.879331i	$-0.342010\pi$
$317$	7.99342	+	2.14183i	0.448955	+	0.120297i	−0.0272552	+	0.999629i	$0.508677\pi$
$318$		0			0
$319$	−20.8152	−	12.0177i	−1.16543	−	0.672860i
$320$	−29.2835	−	11.8441i	−1.63699	−	0.662106i
$321$		0			0
$322$	−4.01011	−	9.07937i	−0.223475	−	0.505973i
$323$	5.79343	+	5.79343i	0.322355	+	0.322355i
$324$		0			0
$325$	−18.1983	+	18.1983i	−1.00946	+	1.00946i
$326$	2.78844	−	7.20010i	0.154437	−	0.398777i
$327$		0			0
$328$	−2.79469	−	3.16003i	−0.154311	−	0.174483i
$329$	−9.55998	+	16.5584i	−0.527059	+	0.912893i
$330$		0			0
$331$	6.84245	−	25.5364i	0.376095	−	1.40361i	−0.475643	−	0.879639i	$-0.657784\pi$
$331$	6.84245	−	25.5364i	0.376095	−	1.40361i	0.851738	−	0.523968i	$-0.175549\pi$
$332$	−14.0702	−	21.9508i	−0.772205	−	1.20471i
$333$		0			0
$334$	−9.71236	−	1.05000i	−0.531437	−	0.0574535i
$335$	−19.3372	−	33.4930i	−1.05650	−	1.82992i
$336$		0			0
$337$	12.3368	−	21.3679i	0.672026	−	1.16398i	−0.305302	−	0.952256i	$-0.598757\pi$
$337$	12.3368	−	21.3679i	0.672026	−	1.16398i	0.977329	−	0.211728i	$-0.0679092\pi$
$338$	5.92154	−	8.09958i	0.322090	−	0.440559i
$339$		0			0
$340$	−20.3296	−	10.5111i	−1.10253	−	0.570046i
$341$	−0.983569	−	0.983569i	−0.0532632	−	0.0532632i
$342$		0			0
$343$	15.8156			0.853964
$344$	−11.5843	−	7.67062i	−0.624584	−	0.413572i
$345$		0			0
$346$	5.59688	−	0.869418i	0.300890	−	0.0467402i
$347$	−6.16895	−	23.0228i	−0.331166	−	1.23593i	−0.907966	−	0.419044i	$-0.862365\pi$
$347$	−6.16895	−	23.0228i	−0.331166	−	1.23593i	0.576799	−	0.816886i	$-0.304301\pi$
$348$		0			0
$349$	6.94337	−	25.9130i	0.371670	−	1.38709i	−0.486479	−	0.873692i	$-0.661719\pi$
$349$	6.94337	−	25.9130i	0.371670	−	1.38709i	0.858149	−	0.513400i	$-0.171614\pi$
$350$	−43.6937	−	4.72371i	−2.33553	−	0.252493i
$351$		0			0
$352$	3.79365	+	15.0490i	0.202202	+	0.802115i
$353$	−5.54075	+	3.19895i	−0.294904	+	0.170263i	−0.640151	−	0.768249i	$-0.721128\pi$
$353$	−5.54075	+	3.19895i	−0.294904	+	0.170263i	0.345247	+	0.938512i	$0.387795\pi$
$354$		0			0
$355$	−4.75614	−	17.7502i	−0.252430	−	0.942080i
$356$	−9.87843	+	10.8408i	−0.523556	+	0.574563i
$357$		0			0
$358$	18.7668	+	7.26798i	0.991859	+	0.384125i
$359$			17.2363i			0.909697i	0.890569	+	0.454849i	$0.150307\pi$
$359$			17.2363i			0.909697i	−0.890569	+	0.454849i	$0.849693\pi$
$360$		0			0
$361$			11.0076i			0.579345i
$362$	−10.8592	+	28.0398i	−0.570746	+	1.47374i
$363$		0			0
$364$	−14.2459	+	0.661719i	−0.746686	+	0.0346835i
$365$	5.02693	+	18.7608i	0.263121	+	0.981983i
$366$		0			0
$367$	−1.26366	+	0.729575i	−0.0659625	+	0.0380835i	−0.532619	−	0.846355i	$-0.678792\pi$
$367$	−1.26366	+	0.729575i	−0.0659625	+	0.0380835i	0.466656	+	0.884439i	$0.345459\pi$
$368$	3.99503	−	8.69340i	0.208255	−	0.453175i
$369$		0			0
$370$	−1.15782	+	10.7096i	−0.0601920	+	0.556768i
$371$	−5.56323	+	20.7623i	−0.288829	+	1.07792i
$372$		0			0
$373$	−2.08247	−	7.77189i	−0.107826	−	0.402413i	0.890824	−	0.454348i	$-0.150128\pi$
$373$	−2.08247	−	7.77189i	−0.107826	−	0.402413i	−0.998650	+	0.0519349i	$0.983461\pi$
$374$	1.72601	+	11.1112i	0.0892497	+	0.574545i
$375$		0			0
$376$	−18.0608	+	3.67098i	−0.931417	+	0.189316i
$377$	21.2893			1.09646
$378$		0			0
$379$	−16.4748	−	16.4748i	−0.846255	−	0.846255i	0.143409	−	0.989664i	$-0.454194\pi$
$379$	−16.4748	−	16.4748i	−0.846255	−	0.846255i	−0.989664	+	0.143409i	$0.954194\pi$
$380$	6.77266	+	21.2735i	0.347430	+	1.09131i
$381$		0			0
$382$	−24.8896	−	18.1966i	−1.27346	−	0.931019i
$383$	5.19654	−	9.00067i	0.265531	−	0.459913i	−0.702172	−	0.712008i	$-0.747786\pi$
$383$	5.19654	−	9.00067i	0.265531	−	0.459913i	0.967703	+	0.252095i	$0.0811195\pi$
$384$		0			0
$385$	15.8934	+	27.5282i	0.810004	+	1.40297i
$386$	0.713580	−	6.60052i	0.0363203	−	0.335958i
$387$		0			0
$388$	9.77418	+	2.13836i	0.496209	+	0.108559i
$389$	−6.24292	+	23.2989i	−0.316529	+	1.18130i	0.606029	+	0.795442i	$0.292761\pi$
$389$	−6.24292	+	23.2989i	−0.316529	+	1.18130i	−0.922558	+	0.385859i	$0.873905\pi$
$390$		0			0
$391$	3.46590	−	6.00311i	0.175278	−	0.303590i
$392$	−3.01691	−	3.41129i	−0.152377	−	0.172296i
$393$		0			0
$394$	26.7120	+	10.3449i	1.34573	+	0.521171i
$395$	−11.6469	+	11.6469i	−0.586019	+	0.586019i
$396$		0			0
$397$	8.37131	+	8.37131i	0.420144	+	0.420144i	0.885253	−	0.465109i	$-0.153985\pi$
$397$	8.37131	+	8.37131i	0.420144	+	0.420144i	−0.465109	+	0.885253i	$0.653985\pi$
$398$	18.7535	−	8.28289i	0.940026	−	0.415184i
$399$		0			0
$400$	−24.4911	−	34.5657i	−1.22455	−	1.72829i
$401$	3.16266	+	1.82596i	0.157936	+	0.0911842i	0.576885	−	0.816825i	$-0.304268\pi$
$401$	3.16266	+	1.82596i	0.157936	+	0.0911842i	−0.418949	+	0.908010i	$0.637601\pi$
$402$		0			0
$403$	1.19008	+	0.318880i	0.0592820	+	0.0158846i
$404$	−11.7985	−	18.4066i	−0.586996	−	0.915764i
$405$		0			0
$406$	22.7945	+	28.3205i	1.13127	+	1.40552i
$407$	4.58345	−	2.64626i	0.227193	−	0.131170i
$408$		0			0
$409$	−12.1263	−	7.00113i	−0.599607	−	0.346184i	0.169280	−	0.985568i	$-0.445856\pi$
$409$	−12.1263	−	7.00113i	−0.599607	−	0.346184i	−0.768887	+	0.639385i	$0.779189\pi$
$410$	−1.27841	−	8.22976i	−0.0631361	−	0.406439i
$411$		0			0
$412$	0.390665	+	1.22711i	0.0192467	+	0.0604554i
$413$	5.32931	−	5.32931i	0.262238	−	0.262238i
$414$		0			0
$415$		−	51.4750i		−	2.52681i
$416$	−9.57488	−	9.86373i	−0.469447	−	0.483609i
$417$		0			0
$418$	6.47375	−	8.85490i	0.316641	−	0.433107i
$419$	−0.601258	+	0.161107i	−0.0293734	+	0.00787057i	−0.273476	−	0.961879i	$-0.588173\pi$
$419$	−0.601258	+	0.161107i	−0.0293734	+	0.00787057i	0.244102	+	0.969749i	$0.421507\pi$
$420$		0			0
$421$	17.3705	+	4.65440i	0.846585	+	0.226842i	0.655936	−	0.754816i	$-0.272274\pi$
$421$	17.3705	+	4.65440i	0.846585	+	0.226842i	0.190649	+	0.981658i	$0.438941\pi$
$422$	5.86769	+	7.29018i	0.285635	+	0.354881i
$423$		0			0
$424$	−18.5440	+	9.24136i	−0.900578	+	0.448800i
$425$	−15.3463	−	26.5806i	−0.744407	−	1.28935i
$426$		0			0
$427$	32.8152	−	8.79280i	1.58804	−	0.425514i
$428$	0.491037	+	10.5713i	0.0237352	+	0.510983i
$429$		0			0
$430$	−11.0821	−	25.0913i	−0.534427	−	1.21001i
$431$	−6.34380			−0.305570			−0.152785	−	0.988259i	$-0.548824\pi$
$431$	−6.34380			−0.305570			−0.152785	+	0.988259i	$0.548824\pi$
$432$		0			0
$433$	26.7319			1.28465			0.642327	−	0.766430i	$-0.277969\pi$
$433$	26.7319			1.28465			0.642327	+	0.766430i	$0.277969\pi$
$434$	0.850021	+	1.92455i	0.0408023	+	0.0923813i
$435$		0			0
$436$	16.9765	−	0.788560i	0.813029	−	0.0377652i
$437$	−6.53158	+	1.75013i	−0.312448	+	0.0837202i
$438$		0			0
$439$	0.347800	+	0.602407i	0.0165996	+	0.0287513i	0.874206	−	0.485555i	$-0.161383\pi$
$439$	0.347800	+	0.602407i	0.0165996	+	0.0287513i	−0.857606	+	0.514307i	$0.828049\pi$
$440$	−9.72769	+	29.0548i	−0.463750	+	1.38513i
$441$		0			0
$442$	−6.24486	−	7.75878i	−0.297037	−	0.369048i
$443$	15.8656	+	4.25119i	0.753800	+	0.201980i	0.615203	−	0.788369i	$-0.289074\pi$
$443$	15.8656	+	4.25119i	0.753800	+	0.201980i	0.138597	+	0.990349i	$0.455741\pi$
$444$		0			0
$445$	−27.9688	+	7.49422i	−1.32585	+	0.355260i
$446$	−1.53816	+	2.10393i	−0.0728342	+	0.0996238i
$447$		0			0
$448$	2.86957	−	23.2983i	0.135575	−	1.10074i
$449$			12.0759i			0.569896i	0.958543	+	0.284948i	$0.0919763\pi$
$449$			12.0759i			0.569896i	−0.958543	+	0.284948i	$0.908024\pi$
$450$		0			0
$451$	−2.89343	+	2.89343i	−0.136247	+	0.136247i
$452$	−31.7735	+	10.1155i	−1.49450	+	0.475791i
$453$		0			0
$454$	0.154398	+	0.993935i	0.00724624	+	0.0466477i
$455$	−24.3831	−	14.0776i	−1.14310	−	0.659969i
$456$		0			0
$457$	−10.6069	+	6.12391i	−0.496171	+	0.286464i	−0.727131	−	0.686499i	$-0.759147\pi$
$457$	−10.6069	+	6.12391i	−0.496171	+	0.286464i	0.230960	+	0.972963i	$0.425813\pi$
$458$	−6.79839	−	8.44651i	−0.317668	−	0.394679i
$459$		0			0
$460$	15.9021	−	10.1931i	0.741438	−	0.475255i
$461$	30.3154	+	8.12298i	1.41193	+	0.378325i	0.882613	−	0.470101i	$-0.155783\pi$
$461$	30.3154	+	8.12298i	1.41193	+	0.378325i	0.529314	+	0.848426i	$0.322449\pi$
$462$		0			0
$463$	30.9163	+	17.8495i	1.43680	+	0.829538i	0.997626	−	0.0688633i	$-0.0219372\pi$
$463$	30.9163	+	17.8495i	1.43680	+	0.829538i	0.439176	+	0.898401i	$0.355271\pi$
$464$	−5.89291	+	34.5437i	−0.273572	+	1.60365i
$465$		0			0
$466$	1.77133	−	0.782348i	0.0820553	−	0.0362416i
$467$	7.64586	+	7.64586i	0.353808	+	0.353808i	0.861524	−	0.507716i	$-0.169510\pi$
$467$	7.64586	+	7.64586i	0.353808	+	0.353808i	−0.507716	+	0.861524i	$0.669510\pi$
$468$		0			0
$469$	20.3226	−	20.3226i	0.938411	−	0.938411i
$470$	−33.9301	−	13.1404i	−1.56508	−	0.606120i
$471$		0			0
$472$	7.25123	+	0.444875i	0.333765	+	0.0204770i
$473$	−6.73836	+	11.6712i	−0.309830	+	0.536641i
$474$		0			0
$475$	−7.74926	+	28.9206i	−0.355560	+	1.32697i
$476$	3.63490	−	16.6147i	0.166605	−	0.761533i
$477$		0			0
$478$	−0.235189	+	2.17547i	−0.0107573	+	0.0995038i
$479$	3.03628	+	5.25898i	0.138731	+	0.240289i	0.927017	−	0.375020i	$-0.122364\pi$
$479$	3.03628	+	5.25898i	0.138731	+	0.240289i	−0.788286	+	0.615310i	$0.789031\pi$
$480$		0			0
$481$	−2.34393	+	4.05980i	−0.106874	+	0.185111i
$482$	−8.76009	−	6.40444i	−0.399011	−	0.291714i
$483$		0			0
$484$	−6.61864	+	2.10712i	−0.300847	+	0.0957782i
$485$	13.9675	+	13.9675i	0.634234	+	0.634234i
$486$		0			0
$487$	−7.15811			−0.324365			−0.162183	−	0.986761i	$-0.551853\pi$
$487$	−7.15811			−0.324365			−0.162183	+	0.986761i	$0.551853\pi$
$488$	27.3039	+	18.0795i	1.23599	+	0.818419i
$489$		0			0
$490$	−1.38006	−	8.88413i	−0.0623446	−	0.401344i
$491$	7.24226	+	27.0285i	0.326838	+	1.21978i	0.912451	+	0.409187i	$0.134187\pi$
$491$	7.24226	+	27.0285i	0.326838	+	1.21978i	−0.585612	+	0.810591i	$0.699146\pi$
$492$		0			0
$493$	−6.57122	+	24.5241i	−0.295953	+	1.10451i
$494$	−1.04429	+	9.65950i	−0.0469846	+	0.434602i
$495$		0			0
$496$	−0.846826	+	1.84274i	−0.0380236	+	0.0827413i
$497$	11.8266	−	6.82809i	0.530495	−	0.306282i
$498$		0			0
$499$	11.4708	+	42.8097i	0.513505	+	1.91643i	0.378568	+	0.925573i	$0.376416\pi$
$499$	11.4708	+	42.8097i	0.513505	+	1.91643i	0.134937	+	0.990854i	$0.456917\pi$
$500$	−2.04854	−	44.1021i	−0.0916135	−	1.97231i
$501$		0			0
$502$	−3.94822	+	10.1948i	−0.176218	+	0.455017i
$503$		−	3.93000i		−	0.175230i	−0.996154	−	0.0876151i	$-0.972075\pi$
$503$		−	3.93000i		−	0.175230i	0.996154	−	0.0876151i	$-0.0279245\pi$
$504$		0			0
$505$		−	43.1638i		−	1.92077i
$506$	−8.65397	−	3.35149i	−0.384716	−	0.148992i
$507$		0			0
$508$	26.6058	+	24.2439i	1.18044	+	1.07565i
$509$	−10.8415	−	40.4609i	−0.480539	−	1.79340i	−0.599358	−	0.800481i	$-0.704577\pi$
$509$	−10.8415	−	40.4609i	−0.480539	−	1.79340i	0.118819	−	0.992916i	$-0.462089\pi$
$510$		0			0
$511$	−12.4999	+	7.21684i	−0.552965	+	0.319254i
$512$	18.6551	−	12.8058i	0.824446	−	0.565941i
$513$		0			0
$514$	−33.4315	−	3.61427i	−1.47460	−	0.159418i
$515$	−0.658030	+	2.45580i	−0.0289963	+	0.108216i
$516$		0			0
$517$	4.62691	+	17.2679i	0.203491	+	0.759441i
$518$	−7.91027	+	1.22878i	−0.347557	+	0.0539895i
$519$		0			0
$520$	−5.40572	−	26.5956i	−0.237057	−	1.16629i
$521$	26.1826			1.14708			0.573540	−	0.819178i	$-0.305570\pi$
$521$	26.1826			1.14708			0.573540	+	0.819178i	$0.305570\pi$
$522$		0			0
$523$	7.29036	+	7.29036i	0.318785	+	0.318785i	0.848300	−	0.529515i	$-0.177626\pi$
$523$	7.29036	+	7.29036i	0.318785	+	0.318785i	−0.529515	+	0.848300i	$0.677626\pi$
$524$	−16.5582	+	32.0253i	−0.723347	+	1.39903i
$525$		0			0
$526$	−5.91470	+	8.09022i	−0.257893	+	0.352750i
$527$	−0.734665	+	1.27248i	−0.0320025	+	0.0554300i
$528$		0			0
$529$	−8.63952	−	14.9641i	−0.375631	−	0.650612i
$530$	−40.6679	−	4.39659i	−1.76650	−	0.190976i
$531$		0			0
$532$	−13.9679	+	8.95326i	−0.605584	+	0.388173i
$533$	0.938073	−	3.50093i	0.0406324	−	0.151642i
$534$		0			0
$535$	−10.4465	+	18.0938i	−0.451640	+	0.782263i
$536$	27.6516	+	1.69647i	1.19437	+	0.0732763i
$537$		0			0
$538$	14.9235	−	38.5344i	0.643397	−	1.66133i
$539$	−3.12350	+	3.12350i	−0.134539	+	0.134539i
$540$		0			0
$541$	13.6906	+	13.6906i	0.588607	+	0.588607i	0.937254	−	0.348647i	$-0.113359\pi$
$541$	13.6906	+	13.6906i	0.588607	+	0.588607i	−0.348647	+	0.937254i	$0.613359\pi$
$542$	9.53625	+	21.5912i	0.409617	+	0.927422i
$543$		0			0
$544$	14.3179	−	7.98517i	0.613874	−	0.342361i
$545$	29.0570	+	16.7761i	1.24466	+	0.718607i
$546$		0			0
$547$	29.0133	+	7.77408i	1.24052	+	0.332396i	0.818666	−	0.574269i	$-0.194714\pi$
$547$	29.0133	+	7.77408i	1.24052	+	0.332396i	0.421851	+	0.906665i	$0.361380\pi$
$548$	1.54801	+	0.338667i	0.0661276	+	0.0144672i
$549$		0			0
$550$	−32.0107	+	25.7646i	−1.36494	+	1.09861i
$551$	21.4491	−	12.3836i	0.913762	−	0.527561i
$552$		0			0
$553$	−10.6005	−	6.12021i	−0.450780	−	0.260258i
$554$	−6.49904	+	1.00956i	−0.276118	+	0.0428921i
$555$		0			0
$556$	−19.5074	+	37.7294i	−0.827297	+	1.60008i
$557$	1.85284	−	1.85284i	0.0785074	−	0.0785074i	−0.666763	−	0.745270i	$-0.732321\pi$
$557$	1.85284	−	1.85284i	0.0785074	−	0.0785074i	0.745270	+	0.666763i	$0.232321\pi$
$558$		0			0
$559$		−	11.9370i		−	0.504882i
$560$	29.5914	−	35.6670i	1.25047	−	1.50721i
$561$		0			0
$562$	−26.0645	−	19.0556i	−1.09946	−	0.803810i
$563$	−26.1400	+	7.00420i	−1.10167	+	0.295192i	−0.763445	−	0.645873i	$-0.776494\pi$
$563$	−26.1400	+	7.00420i	−1.10167	+	0.295192i	−0.338226	+	0.941065i	$0.609827\pi$
$564$		0			0
$565$	−63.5879	−	17.0383i	−2.67516	−	0.716808i
$566$	28.4498	−	22.8985i	1.19583	−	0.962496i
$567$		0			0
$568$	12.4825	+	4.17918i	0.523752	+	0.175355i
$569$	−5.84691	−	10.1271i	−0.245115	−	0.424552i	0.717049	−	0.697023i	$-0.245492\pi$
$569$	−5.84691	−	10.1271i	−0.245115	−	0.424552i	−0.962164	+	0.272471i	$0.912159\pi$
$570$		0			0
$571$	44.1127	−	11.8200i	1.84606	−	0.494650i	0.846756	−	0.531982i	$-0.178553\pi$
$571$	44.1127	−	11.8200i	1.84606	−	0.494650i	0.999303	+	0.0373319i	$0.0118859\pi$
$572$	−8.98101	+	9.85599i	−0.375515	+	0.412100i
$573$		0			0
$574$	5.66158	−	2.50057i	0.236310	−	0.104372i
$575$	25.3314			1.05639
$576$		0			0
$577$	−32.6884			−1.36083			−0.680417	−	0.732825i	$-0.738202\pi$
$577$	−32.6884			−1.36083			−0.680417	+	0.732825i	$0.738202\pi$
$578$	−11.1268	+	4.91442i	−0.462815	+	0.204413i
$579$		0			0
$580$	−46.5974	+	51.1372i	−1.93485	+	2.12335i
$581$	36.9497	−	9.90064i	1.53293	−	0.410748i
$582$		0			0
$583$	10.0487	+	17.4048i	0.416174	+	0.720834i
$584$	−13.1931	−	4.41713i	−0.545936	−	0.182782i
$585$		0			0
$586$	−3.15598	+	2.54017i	−0.130372	+	0.104933i
$587$	−28.3101	−	7.58567i	−1.16848	−	0.313094i	−0.378134	−	0.925751i	$-0.623434\pi$
$587$	−28.3101	−	7.58567i	−1.16848	−	0.313094i	−0.790349	+	0.612657i	$0.790101\pi$
$588$		0			0
$589$	1.38450	−	0.370975i	0.0570472	−	0.0152858i
$590$	11.5784	+	8.46486i	0.476674	+	0.348493i
$591$		0			0
$592$	−5.93857	−	4.92698i	−0.244074	−	0.202498i
$593$			43.9681i			1.80555i	0.430111	+	0.902776i	$0.358474\pi$
$593$			43.9681i			1.80555i	−0.430111	+	0.902776i	$0.641526\pi$
$594$		0			0
$595$	23.7428	−	23.7428i	0.973360	−	0.973360i
$596$	10.7487	−	20.7891i	0.440283	−	0.851555i
$597$		0			0
$598$	8.12260	−	1.26176i	0.332158	−	0.0515973i
$599$	−2.81411	−	1.62473i	−0.114982	−	0.0663846i	0.441406	−	0.897307i	$-0.354480\pi$
$599$	−2.81411	−	1.62473i	−0.114982	−	0.0663846i	−0.556388	+	0.830923i	$0.687813\pi$
$600$		0			0
$601$	12.6206	−	7.28651i	0.514806	−	0.297223i	−0.220001	−	0.975500i	$-0.570606\pi$
$601$	12.6206	−	7.28651i	0.514806	−	0.297223i	0.734807	+	0.678276i	$0.237273\pi$
$602$	15.8794	−	12.7810i	0.647198	−	0.520914i
$603$		0			0
$604$	−16.5691	−	3.62493i	−0.674187	−	0.147496i
$605$	−13.2458	−	3.54920i	−0.538519	−	0.144296i
$606$		0			0
$607$	32.0317	+	18.4935i	1.30013	+	0.750629i	0.980426	−	0.196889i	$-0.0630838\pi$
$607$	32.0317	+	18.4935i	1.30013	+	0.750629i	0.319702	+	0.947518i	$0.396417\pi$
$608$	−15.3843	−	4.36821i	−0.623916	−	0.177154i
$609$		0			0
$610$	26.1203	+	59.1395i	1.05758	+	2.39449i
$611$	−11.1967	−	11.1967i	−0.452972	−	0.452972i
$612$		0			0
$613$	3.34985	−	3.34985i	0.135299	−	0.135299i	−0.636214	−	0.771513i	$-0.719500\pi$
$613$	3.34985	−	3.34985i	0.135299	−	0.135299i	0.771513	+	0.636214i	$0.219500\pi$
$614$	5.54227	−	14.3109i	0.223668	−	0.577539i
$615$		0			0
$616$	−22.7271	−	1.39434i	−0.915701	−	0.0561797i
$617$	4.04358	−	7.00369i	0.162789	−	0.281958i	−0.773079	−	0.634309i	$-0.781285\pi$
$617$	4.04358	−	7.00369i	0.162789	−	0.281958i	0.935868	+	0.352352i	$0.114618\pi$
$618$		0			0
$619$	11.6692	−	43.5499i	0.469023	−	1.75042i	−0.174171	−	0.984715i	$-0.555725\pi$
$619$	11.6692	−	43.5499i	0.469023	−	1.75042i	0.643194	−	0.765703i	$-0.277609\pi$
$620$	−3.37076	+	2.16062i	−0.135373	+	0.0867727i
$621$		0			0
$622$	24.4792	+	2.64644i	0.981526	+	0.106112i
$623$	−10.7590	−	18.6351i	−0.431049	−	0.746599i
$624$		0			0
$625$	17.1046	−	29.6260i	0.684182	−	1.18504i
$626$	20.5310	−	28.0826i	0.820583	−	1.12241i
$627$		0			0
$628$	3.36179	−	6.50206i	0.134150	−	0.259460i
$629$	−3.95318	−	3.95318i	−0.157624	−	0.157624i
$630$		0			0
$631$	−3.49919			−0.139300			−0.0696502	−	0.997571i	$-0.522188\pi$
$631$	−3.49919			−0.139300			−0.0696502	+	0.997571i	$0.522188\pi$
$632$	−2.35013	−	11.5624i	−0.0934830	−	0.459927i
$633$		0			0
$634$	−11.5645	+	1.79642i	−0.459284	+	0.0713451i
$635$	18.3925	+	68.6417i	0.729883	+	2.72396i
$636$		0			0
$637$	1.01266	−	3.77930i	0.0401231	−	0.149741i
$638$	33.7942	+	3.65348i	1.33792	+	0.144643i
$639$		0			0
$640$	44.6500	−	1.40955i	1.76495	−	0.0557174i
$641$	−4.01739	+	2.31944i	−0.158677	+	0.0916125i	−0.577236	−	0.816577i	$-0.695869\pi$
$641$	−4.01739	+	2.31944i	−0.158677	+	0.0916125i	0.418559	+	0.908190i	$0.362535\pi$
$642$		0			0
$643$	−10.6535	−	39.7595i	−0.420134	−	1.56796i	−0.774324	−	0.632789i	$-0.781910\pi$
$643$	−10.6535	−	39.7595i	−0.420134	−	1.56796i	0.354190	−	0.935173i	$-0.384757\pi$
$644$	10.3754	+	9.45428i	0.408847	+	0.372551i
$645$		0			0
$646$	−10.8049	−	4.18449i	−0.425112	−	0.164636i
$647$		−	2.08960i		−	0.0821505i	−0.999156	−	0.0410752i	$-0.986922\pi$
$647$		−	2.08960i		−	0.0821505i	0.999156	−	0.0410752i	$-0.0130783\pi$
$648$		0			0
$649$		−	7.04684i		−	0.276613i
$650$	13.1443	−	33.9403i	0.515563	−	1.33125i
$651$		0			0
$652$	0.506660	+	10.9077i	0.0198423	+	0.427177i
$653$	−4.75454	−	17.7442i	−0.186059	−	0.694383i	−0.994401	−	0.105670i	$-0.966301\pi$
$653$	−4.75454	−	17.7442i	−0.186059	−	0.694383i	0.808342	−	0.588713i	$-0.200365\pi$
$654$		0			0
$655$	−61.6410	+	35.5885i	−2.40851	+	1.39056i
$656$	5.42091	+	2.49117i	0.211651	+	0.0972637i
$657$		0			0
$658$	2.90632	−	26.8831i	0.113300	−	1.04801i
$659$	7.84088	−	29.2626i	0.305437	−	1.13991i	−0.627131	−	0.778914i	$-0.715771\pi$
$659$	7.84088	−	29.2626i	0.305437	−	1.13991i	0.932568	−	0.360994i	$-0.117562\pi$
$660$		0			0
$661$	12.5011	+	46.6546i	0.486235	+	1.81465i	0.574434	+	0.818551i	$0.305222\pi$
$661$	12.5011	+	46.6546i	0.486235	+	1.81465i	−0.0881985	+	0.996103i	$0.528111\pi$
$662$	5.73899	+	36.9448i	0.223052	+	1.43590i
$663$		0			0
$664$	30.7440	+	20.3574i	1.19310	+	0.790019i
$665$	−32.7549			−1.27018
$666$		0			0
$667$	−14.8169	−	14.8169i	−0.573714	−	0.573714i
$668$	13.1644	−	4.19103i	0.509344	−	0.162156i
$669$		0			0
$670$	44.1525	+	32.2796i	1.70576	+	1.24707i
$671$	15.8822	−	27.5087i	0.613124	−	1.06196i
$672$		0			0
$673$	8.92590	+	15.4601i	0.344068	+	0.595944i	0.985184	−	0.171500i	$-0.0548615\pi$
$673$	8.92590	+	15.4601i	0.344068	+	0.595944i	−0.641116	+	0.767444i	$0.721528\pi$
$674$	−3.75049	+	34.6915i	−0.144463	+	1.33627i
$675$		0			0
$676$	−3.03255	+	13.8614i	−0.116637	+	0.533132i
$677$	−0.575049	+	2.14611i	−0.0221009	+	0.0824818i	−0.976095	−	0.217342i	$-0.930261\pi$
$677$	−0.575049	+	2.14611i	−0.0221009	+	0.0824818i	0.953995	+	0.299824i	$0.0969279\pi$
$678$		0			0
$679$	−7.33966	+	12.7127i	−0.281670	+	0.487867i
$680$	32.3052	+	1.98198i	1.23885	+	0.0760053i
$681$		0			0
$682$	1.83438	+	0.710413i	0.0702420	+	0.0272031i
$683$	−0.857818	+	0.857818i	−0.0328235	+	0.0328235i	−0.723328	−	0.690505i	$-0.757389\pi$
$683$	−0.857818	+	0.857818i	−0.0328235	+	0.0328235i	0.690505	+	0.723328i	$0.257389\pi$
$684$		0			0
$685$	2.21214	+	2.21214i	0.0845216	+	0.0845216i
$686$	−20.4599	+	9.03659i	−0.781163	+	0.345019i
$687$		0			0
$688$	19.3688	+	3.30418i	0.738429	+	0.125971i
$689$	−15.4163	−	8.90063i	−0.587316	−	0.339087i
$690$		0			0
$691$	−37.8791	−	10.1497i	−1.44099	−	0.386112i	−0.548109	−	0.836407i	$-0.684652\pi$
$691$	−37.8791	−	10.1497i	−1.44099	−	0.386112i	−0.892880	+	0.450295i	$0.851319\pi$
$692$	−6.74366	+	4.32262i	−0.256355	+	0.164321i
$693$		0			0
$694$	21.1350	+	26.2588i	0.802275	+	0.996769i
$695$	−72.6201	+	41.9272i	−2.75464	+	1.59039i
$696$		0			0
$697$	3.74334	+	2.16122i	0.141789	+	0.0818619i
$698$	5.82363	+	37.4897i	0.220428	+	1.41900i
$699$		0			0
$700$	59.2235	−	18.8545i	2.23844	−	0.712632i
$701$	14.3403	−	14.3403i	0.541627	−	0.541627i	−0.382379	−	0.924006i	$-0.624895\pi$
$701$	14.3403	−	14.3403i	0.541627	−	0.541627i	0.924006	+	0.382379i	$0.124895\pi$
$702$		0			0
$703$			5.45369i			0.205690i
$704$	−13.5062	−	17.3006i	−0.509035	−	0.652041i
$705$		0			0
$706$	5.34001	−	7.30415i	0.200974	−	0.274895i
$707$	30.9838	−	8.30208i	1.16527	−	0.312232i
$708$		0			0
$709$	−4.26177	−	1.14194i	−0.160054	−	0.0428864i	0.177902	−	0.984048i	$-0.443069\pi$
$709$	−4.26177	−	1.14194i	−0.160054	−	0.0428864i	−0.337956	+	0.941162i	$0.609736\pi$
$710$	16.2947	+	20.2450i	0.611529	+	0.759781i
$711$		0			0
$712$	6.58511	−	19.6685i	0.246787	−	0.737109i
$713$	−0.606335	−	1.05020i	−0.0227074	−	0.0393304i
$714$		0			0
$715$	−25.4279	+	6.81339i	−0.950951	+	0.254806i
$716$	−28.4305	+	1.32059i	−1.06250	+	0.0493530i
$717$		0			0
$718$	−9.84832	−	22.2978i	−0.367536	−	0.832146i
$719$	49.2509			1.83675			0.918374	−	0.395714i	$-0.129503\pi$
$719$	49.2509			1.83675			0.918374	+	0.395714i	$0.129503\pi$
$720$		0			0
$721$	−1.88938			−0.0703644
$722$	−6.28939	−	14.2399i	−0.234067	−	0.529956i
$723$		0			0
$724$	−1.97312	−	42.4784i	−0.0733304	−	1.57870i
$725$	−89.6203	+	24.0137i	−3.32841	+	0.891846i
$726$		0			0
$727$	−2.18154	−	3.77855i	−0.0809090	−	0.140139i	0.822732	−	0.568430i	$-0.192449\pi$
$727$	−2.18154	−	3.77855i	−0.0809090	−	0.140139i	−0.903641	+	0.428291i	$0.859116\pi$
$728$	18.0511	−	8.99570i	0.669018	−	0.333403i
$729$		0			0
$730$	−17.2224	−	21.3976i	−0.637431	−	0.791962i
$731$	13.7508	+	3.68451i	0.508591	+	0.136277i
$732$		0			0
$733$	30.7314	−	8.23445i	1.13509	−	0.304146i	0.358114	−	0.933678i	$-0.383420\pi$
$733$	30.7314	−	8.23445i	1.13509	−	0.304146i	0.776975	+	0.629532i	$0.216753\pi$
$734$	1.21788	−	1.66583i	0.0449527	−	0.0614871i
$735$		0			0
$736$	−0.201029	+	13.5289i	−0.00741003	+	0.498681i
$737$		−	26.8722i		−	0.989849i
$738$		0			0
$739$	−32.4463	+	32.4463i	−1.19356	+	1.19356i	−0.217495	+	0.976061i	$0.569789\pi$
$739$	−32.4463	+	32.4463i	−1.19356	+	1.19356i	−0.976061	+	0.217495i	$0.930211\pi$
$740$	−4.62137	−	14.5161i	−0.169885	−	0.533622i
$741$		0			0
$742$	−4.66606	−	30.0378i	−0.171297	−	1.10272i
$743$	10.8406	+	6.25880i	0.397702	+	0.229613i	0.685492	−	0.728080i	$-0.259587\pi$
$743$	10.8406	+	6.25880i	0.397702	+	0.229613i	−0.287790	+	0.957693i	$0.592921\pi$
$744$		0			0
$745$	40.0141	−	23.1021i	1.46600	−	0.846397i
$746$	7.13463	+	8.86426i	0.261217	+	0.324544i
$747$		0			0
$748$	−8.58145	−	13.3878i	−0.313769	−	0.489507i
$749$	−14.9973	−	4.01852i	−0.547990	−	0.146834i
$750$		0			0
$751$	−34.0479	−	19.6575i	−1.24242	−	0.717314i	−0.272837	−	0.962060i	$-0.587962\pi$
$751$	−34.0479	−	19.6575i	−1.24242	−	0.717314i	−0.969587	+	0.244747i	$0.921295\pi$
$752$	21.2670	−	15.0684i	0.775526	−	0.549488i
$753$		0			0
$754$	−27.5410	+	12.1641i	−1.00298	+	0.442990i
$755$	−23.6777	−	23.6777i	−0.861718	−	0.861718i
$756$		0			0
$757$	−25.3026	+	25.3026i	−0.919640	+	0.919640i	−0.997003	−	0.0773631i	$-0.975350\pi$
$757$	−25.3026	+	25.3026i	−0.919640	+	0.919640i	0.0773631	+	0.997003i	$0.475350\pi$
$758$	30.7259	+	11.8995i	1.11602	+	0.432208i
$759$		0			0
$760$	−20.9165	−	23.6508i	−0.758722	−	0.857905i
$761$	−11.0907	+	19.2097i	−0.402039	+	0.696352i	−0.993972	−	0.109635i	$-0.965032\pi$
$761$	−11.0907	+	19.2097i	−0.402039	+	0.696352i	0.591933	+	0.805987i	$0.298365\pi$
$762$		0			0
$763$	−6.45338	+	24.0843i	−0.233628	+	0.871911i
$764$	42.5955	+	9.31888i	1.54105	+	0.337145i
$765$		0			0
$766$	−1.57979	+	14.6129i	−0.0570803	+	0.527985i
$767$	3.12087	+	5.40551i	0.112688	+	0.195182i
$768$		0			0
$769$	0.792978	−	1.37348i	0.0285955	−	0.0495289i	−0.851374	−	0.524560i	$-0.824230\pi$
$769$	0.792978	−	1.37348i	0.0285955	−	0.0495289i	0.879969	+	0.475031i	$0.157563\pi$
$770$	−36.2894	−	26.5309i	−1.30778	−	0.956107i
$771$		0			0
$772$	2.84822	+	8.94650i	0.102510	+	0.321991i
$773$	0.198602	+	0.198602i	0.00714323	+	0.00714323i	0.710669	−	0.703526i	$-0.248392\pi$
$773$	0.198602	+	0.198602i	0.00714323	+	0.00714323i	−0.703526	+	0.710669i	$0.748392\pi$
$774$		0			0
$775$	−5.36948			−0.192877
$776$	−13.8662	+	2.81839i	−0.497767	+	0.101174i
$777$		0			0
$778$	−5.23614	−	33.7077i	−0.187725	−	1.20848i
$779$	−1.09132	−	4.07287i	−0.0391007	−	0.145926i
$780$		0			0
$781$	3.30471	−	12.3334i	0.118252	−	0.441322i
$782$	−1.05366	+	9.74625i	−0.0376789	+	0.348525i
$783$		0			0
$784$	5.85194	+	2.68925i	0.208998	+	0.0960445i
$785$	12.5149	−	7.22549i	0.446676	−	0.257889i
$786$		0			0
$787$	−3.76684	−	14.0581i	−0.134274	−	0.501116i	−1.00000		0.000597888i	$-0.999810\pi$
$787$	−3.76684	−	14.0581i	−0.134274	−	0.501116i	0.865726	−	0.500518i	$-0.166857\pi$
$788$	−40.4668	+	1.87968i	−1.44157	+	0.0669609i
$789$		0			0
$790$	8.41234	−	21.7217i	0.299298	−	0.772825i
$791$		−	48.9217i		−	1.73946i
$792$		0			0
$793$			28.1353i			0.999112i
$794$	−15.6127	−	6.04644i	−0.554073	−	0.214580i
$795$		0			0
$796$	−19.5278	+	21.4304i	−0.692146	+	0.759579i
$797$	3.12214	+	11.6520i	0.110592	+	0.412734i	0.998919	−	0.0464762i	$-0.0147992\pi$
$797$	3.12214	+	11.6520i	0.110592	+	0.412734i	−0.888328	+	0.459210i	$0.848132\pi$
$798$		0			0
$799$	16.3541	−	9.44202i	0.578565	−	0.334035i
$800$	51.4327	+	30.7225i	1.81842	+	1.08621i
$801$		0			0
$802$	−5.13468	−	0.555109i	−0.181312	−	0.0196016i
$803$	−3.49286	+	13.0355i	−0.123261	+	0.460015i
$804$		0			0
$805$	7.17244	+	26.7679i	0.252795	+	0.943445i
$806$	−1.72174	+	0.267455i	−0.0606459	+	0.00942071i
$807$		0			0
$808$	25.7801	+	17.0705i	0.906941	+	0.600537i
$809$	5.40097			0.189888			0.0949441	−	0.995483i	$-0.469733\pi$
$809$	5.40097			0.189888			0.0949441	+	0.995483i	$0.469733\pi$
$810$		0			0
$811$	19.4041	+	19.4041i	0.681371	+	0.681371i	0.960309	−	0.278938i	$-0.0899823\pi$
$811$	19.4041	+	19.4041i	0.681371	+	0.681371i	−0.278938	+	0.960309i	$0.589982\pi$
$812$	−45.6697	−	23.6128i	−1.60269	−	0.828647i
$813$		0			0
$814$	−4.41740	+	6.04219i	−0.154830	+	0.211779i
$815$	−10.7788	+	18.6695i	−0.377566	+	0.653964i
$816$		0			0
$817$	−6.94356	−	12.0266i	−0.242924	−	0.420758i
$818$	19.6875	+	2.12840i	0.688356	+	0.0744179i
$819$		0			0
$820$	6.35606	+	9.91600i	0.221963	+	0.346282i
$821$	5.53178	−	20.6449i	0.193061	−	0.720512i	−0.799700	−	0.600400i	$-0.795008\pi$
$821$	5.53178	−	20.6449i	0.193061	−	0.720512i	0.992760	−	0.120112i	$-0.0383253\pi$
$822$		0			0
$823$	−15.8047	+	27.3746i	−0.550918	+	0.954217i	0.447291	+	0.894389i	$0.352389\pi$
$823$	−15.8047	+	27.3746i	−0.550918	+	0.954217i	−0.998209	+	0.0598289i	$0.980944\pi$
$824$	−1.20652	−	1.36424i	−0.0420311	−	0.0475255i
$825$		0			0
$826$	−3.84926	+	9.93929i	−0.133933	+	0.345832i
$827$	11.4058	−	11.4058i	0.396617	−	0.396617i	−0.480421	−	0.877038i	$-0.659516\pi$
$827$	11.4058	−	11.4058i	0.396617	−	0.396617i	0.877038	+	0.480421i	$0.159516\pi$
$828$		0			0
$829$	−15.8083	−	15.8083i	−0.549043	−	0.549043i	0.377121	−	0.926164i	$-0.376914\pi$
$829$	−15.8083	−	15.8083i	−0.549043	−	0.549043i	−0.926164	+	0.377121i	$0.876914\pi$
$830$	29.4113	+	66.5907i	1.02088	+	2.31140i
$831$		0			0
$832$	18.0224	+	7.28942i	0.624815	+	0.252715i
$833$	4.04098	+	2.33306i	0.140012	+	0.0808357i
$834$		0			0
$835$	26.3457	+	7.05931i	0.911730	+	0.244297i
$836$	−3.31535	+	15.1541i	−0.114664	+	0.524114i
$837$		0			0
$838$	0.685767	−	0.551957i	0.0236894	−	0.0190670i
$839$	28.2922	−	16.3345i	0.976755	−	0.563930i	0.0754662	−	0.997148i	$-0.475956\pi$
$839$	28.2922	−	16.3345i	0.976755	−	0.563930i	0.901289	+	0.433219i	$0.142622\pi$
$840$		0			0
$841$	41.3525	+	23.8749i	1.42595	+	0.823272i
$842$	−25.1307	+	3.90380i	−0.866062	+	0.134534i
$843$		0			0
$844$	−11.7561	−	6.07833i	−0.404663	−	0.209225i
$845$	−19.8083	+	19.8083i	−0.681428	+	0.681428i
$846$		0			0
$847$		−	10.1907i		−	0.350158i
$848$	18.7093	−	22.5506i	0.642480	−	0.774392i
$849$		0			0
$850$	35.0402	+	25.6177i	1.20187	+	0.878678i
$851$	4.45686	−	1.19421i	0.152779	−	0.0409371i
$852$		0			0
$853$	38.7224	+	10.3756i	1.32583	+	0.355255i	0.851159	−	0.524907i	$-0.175900\pi$
$853$	38.7224	+	10.3756i	1.32583	+	0.355255i	0.474672	+	0.880163i	$0.342567\pi$
$854$	−37.4275	+	30.1245i	−1.28074	+	1.03084i
$855$		0			0
$856$	−6.67537	−	13.3950i	−0.228159	−	0.457833i
$857$	0.0140657	+	0.0243624i	0.000480474	+	0.000832205i	0.866266	−	0.499584i	$-0.166514\pi$
$857$	0.0140657	+	0.0243624i	0.000480474	+	0.000832205i	−0.865785	+	0.500416i	$0.833180\pi$
$858$		0			0
$859$	11.7598	−	3.15104i	0.401240	−	0.107512i	−0.0525549	−	0.998618i	$-0.516736\pi$
$859$	11.7598	−	3.15104i	0.401240	−	0.107512i	0.453795	+	0.891106i	$0.350070\pi$
$860$	28.6728	+	26.1274i	0.977735	+	0.890935i
$861$		0			0
$862$	8.20667	−	3.62466i	0.279520	−	0.123457i
$863$	−40.1140			−1.36550			−0.682748	−	0.730654i	$-0.739215\pi$
$863$	−40.1140			−1.36550			−0.682748	+	0.730654i	$0.739215\pi$
$864$		0			0
$865$	−15.8140			−0.537692
$866$	−34.5818	+	15.2738i	−1.17514	+	0.519026i
$867$		0			0
$868$	−2.19926	−	2.00402i	−0.0746478	−	0.0680209i
$869$	−11.0547	+	2.96211i	−0.375006	+	0.100483i
$870$		0			0
$871$	11.9010	+	20.6132i	0.403251	+	0.698451i
$872$	−21.5112	+	10.7200i	−0.728461	+	0.363026i
$873$		0			0
$874$	7.44962	−	5.99602i	0.251987	−	0.202818i
$875$	62.5669	+	16.7647i	2.11515	+	0.566752i
$876$		0			0
$877$	−45.8849	+	12.2948i	−1.54942	+	0.415167i	−0.929297	−	0.369334i	$-0.879586\pi$
$877$	−45.8849	+	12.2948i	−1.54942	+	0.415167i	−0.620127	+	0.784501i	$0.712919\pi$
$878$	−0.794129	−	0.580582i	−0.0268006	−	0.0195937i
$879$		0			0
$880$	−4.01683	−	43.1450i	−0.135407	−	1.45442i
$881$			20.6694i			0.696371i	0.937426	+	0.348186i	$0.113202\pi$
$881$			20.6694i			0.696371i	−0.937426	+	0.348186i	$0.886798\pi$
$882$		0			0
$883$	−37.7611	+	37.7611i	−1.27076	+	1.27076i	−0.325075	+	0.945688i	$0.605390\pi$
$883$	−37.7611	+	37.7611i	−1.27076	+	1.27076i	−0.945688	+	0.325075i	$0.894610\pi$
$884$	12.5118	+	6.46904i	0.420818	+	0.217577i
$885$		0			0
$886$	−22.9536	+	3.56561i	−0.771142	+	0.119789i
$887$	24.4908	+	14.1398i	0.822322	+	0.474768i	0.851216	−	0.524815i	$-0.175865\pi$
$887$	24.4908	+	14.1398i	0.822322	+	0.474768i	−0.0288948	+	0.999582i	$0.509199\pi$
$888$		0			0
$889$	−45.7347	+	26.4049i	−1.53389	+	0.885593i
$890$	31.8999	−	25.6755i	1.06929	−	0.860643i
$891$		0			0
$892$	0.787728	−	3.60061i	0.0263751	−	0.120557i
$893$	−17.7937	−	4.76782i	−0.595445	−	0.159549i
$894$		0			0
$895$	−48.6615	−	28.0947i	−1.62657	−	0.939103i
$896$	9.59973	+	31.7795i	0.320704	+	1.06168i
$897$		0			0
$898$	−6.89980	−	15.6220i	−0.230249	−	0.521312i
$899$	3.14074	+	3.14074i	0.104750	+	0.104750i
$900$		0			0
$901$	15.0115	−	15.0115i	0.500105	−	0.500105i
$902$	2.08987	−	5.39632i	0.0695852	−	0.179678i
$903$		0			0
$904$	35.3241	−	31.2403i	1.17486	−	1.03904i
$905$	41.9767	−	72.7058i	1.39535	−	2.41682i
$906$		0			0
$907$	−9.12179	+	34.0430i	−0.302884	+	1.13038i	0.631867	+	0.775077i	$0.282289\pi$
$907$	−9.12179	+	34.0430i	−0.302884	+	1.13038i	−0.934751	+	0.355302i	$0.884378\pi$
$908$	−0.767642	−	1.19759i	−0.0254751	−	0.0397434i
$909$		0			0
$910$	39.5868	+	4.27972i	1.31229	+	0.141871i
$911$	8.81619	+	15.2701i	0.292093	+	0.505921i	0.974305	−	0.225235i	$-0.0723149\pi$
$911$	8.81619	+	15.2701i	0.292093	+	0.505921i	−0.682211	+	0.731155i	$0.738982\pi$
$912$		0			0
$913$	17.8832	−	30.9746i	0.591847	−	1.02511i
$914$	10.2226	−	13.9827i	0.338135	−	0.462506i
$915$		0			0
$916$	13.6208	+	7.04244i	0.450045	+	0.232689i
$917$	−37.4020	−	37.4020i	−1.23512	−	1.23512i
$918$		0			0
$919$	40.6483			1.34086			0.670431	−	0.741972i	$-0.266109\pi$
$919$	40.6483			1.34086			0.670431	+	0.741972i	$0.266109\pi$
$920$	−14.7477	+	22.2723i	−0.486218	+	0.734295i
$921$		0			0
$922$	−43.8588	+	6.81301i	−1.44441	+	0.224374i
$923$	2.92715	+	10.9243i	0.0963483	+	0.359577i
$924$		0			0
$925$	5.28775	−	19.7341i	0.173860	−	0.648855i
$926$	−50.1936	−	5.42641i	−1.64946	−	0.178323i
$927$		0			0
$928$	−12.1139	−	48.0546i	−0.397658	−	1.57747i
$929$	46.7331	−	26.9814i	1.53326	−	0.885230i	0.534055	−	0.845450i	$-0.320667\pi$
$929$	46.7331	−	26.9814i	1.53326	−	0.885230i	0.999208	−	0.0397807i	$-0.0126659\pi$
$930$		0			0
$931$	−1.17810	−	4.39672i	−0.0386106	−	0.144097i
$932$	−1.84447	+	2.02417i	−0.0604177	+	0.0663040i
$933$		0			0
$934$	−14.2597	−	5.52246i	−0.466592	−	0.180701i
$935$		−	31.3946i		−	1.02671i
$936$		0			0
$937$		−	47.0464i		−	1.53694i	−0.639886	−	0.768470i	$-0.721018\pi$
$937$		−	47.0464i		−	1.53694i	0.639886	−	0.768470i	$-0.278982\pi$
$938$	−14.6786	+	37.9021i	−0.479274	+	1.23755i
$939$		0			0
$940$	51.4018	−	2.38761i	1.67654	−	0.0778753i
$941$	−0.645083	−	2.40748i	−0.0210291	−	0.0784816i	0.954614	−	0.297846i	$-0.0962683\pi$
$941$	−0.645083	−	2.40748i	−0.0210291	−	0.0784816i	−0.975643	+	0.219365i	$0.929602\pi$
$942$		0			0
$943$	−3.08946	+	1.78370i	−0.100607	+	0.0580853i
$944$	−9.63476	+	3.56763i	−0.313585	+	0.116116i
$945$		0			0
$946$	2.04852	−	18.9485i	0.0666031	−	0.616070i
$947$	−13.4692	+	50.2676i	−0.437689	+	1.63348i	0.296859	+	0.954921i	$0.404061\pi$
$947$	−13.4692	+	50.2676i	−0.437689	+	1.63348i	−0.734548	+	0.678557i	$0.762606\pi$
$948$		0			0
$949$	−3.09381	−	11.5462i	−0.100429	−	0.374807i
$950$	−6.49955	−	41.8409i	−0.210873	−	1.35750i
$951$		0			0
$952$	4.79085	+	23.5705i	0.155272	+	0.763924i
$953$	−61.2734			−1.98484			−0.992420	−	0.122896i	$-0.960782\pi$
$953$	−61.2734			−1.98484			−0.992420	+	0.122896i	$0.960782\pi$
$954$		0			0
$955$	60.8700	+	60.8700i	1.96971	+	1.96971i
$956$	−0.938748	−	2.94868i	−0.0303613	−	0.0953673i
$957$		0			0
$958$	−6.93271	−	5.06846i	−0.223986	−	0.163754i
$959$	−1.16244	+	2.01340i	−0.0375370	+	0.0650160i
$960$		0			0
$961$	−15.3715	−	26.6242i	−0.495854	−	0.858844i
$962$	0.712574	−	6.59122i	0.0229743	−	0.212509i
$963$		0			0
$964$	14.9918	+	3.27985i	0.482854	+	0.105637i
$965$	−4.79750	+	17.9045i	−0.154437	+	0.576367i
$966$		0			0
$967$	−3.75805	+	6.50913i	−0.120851	+	0.209319i	−0.920103	−	0.391676i	$-0.871896\pi$
$967$	−3.75805	+	6.50913i	−0.120851	+	0.209319i	0.799253	+	0.600995i	$0.205229\pi$
$968$	7.35827	−	6.50758i	0.236504	−	0.209161i
$969$		0			0
$970$	−26.0498	−	10.0885i	−0.836409	−	0.323922i
$971$	20.5494	−	20.5494i	0.659461	−	0.659461i	−0.295791	−	0.955253i	$-0.595583\pi$
$971$	20.5494	−	20.5494i	0.659461	−	0.659461i	0.955253	+	0.295791i	$0.0955833\pi$
$972$		0			0
$973$	−44.0638	−	44.0638i	−1.41262	−	1.41262i
$974$	9.26011	−	4.08994i	0.296713	−	0.131050i
$975$		0			0
$976$	−45.6519	−	7.78788i	−1.46128	−	0.249284i
$977$	−48.8661	−	28.2129i	−1.56337	−	0.902610i	−0.996913	−	0.0785154i	$-0.974982\pi$
$977$	−48.8661	−	28.2129i	−1.56337	−	0.902610i	−0.566453	−	0.824094i	$-0.691685\pi$
$978$		0			0
$979$	−19.4336	−	5.20721i	−0.621100	−	0.166423i
$980$	6.86144	+	10.7044i	0.219181	+	0.341941i
$981$		0			0
$982$	−24.8122	−	30.8274i	−0.791790	−	0.983743i
$983$	−5.17882	+	2.98999i	−0.165179	+	0.0953660i	−0.580311	−	0.814395i	$-0.697069\pi$
$983$	−5.17882	+	2.98999i	−0.165179	+	0.0953660i	0.415132	+	0.909761i	$0.363735\pi$
$984$		0			0
$985$	−69.2628	−	39.9889i	−2.20690	−	1.27415i
$986$	−5.51150	−	35.4803i	−0.175522	−	1.12992i
$987$		0			0
$988$	−4.16822	−	13.0927i	−0.132609	−	0.416535i
$989$	−8.30792	+	8.30792i	−0.264176	+	0.264176i
$990$		0			0
$991$			20.2358i			0.642812i	0.946942	+	0.321406i	$0.104155\pi$
$991$			20.2358i			0.642812i	−0.946942	+	0.321406i	$0.895845\pi$
$992$	0.0426121	−	2.86771i	0.00135293	−	0.0910499i
$993$		0			0
$994$	−11.3981	+	15.5905i	−0.361527	+	0.494502i
$995$	−55.2892	+	14.8147i	−1.75278	+	0.469657i
$996$		0			0
$997$	0.647795	+	0.173576i	0.0205159	+	0.00549721i	0.269062	−	0.963123i	$-0.413286\pi$
$997$	0.647795	+	0.173576i	0.0205159	+	0.00549721i	−0.248547	+	0.968620i	$0.579953\pi$
$998$	−39.2995	−	48.8268i	−1.24400	−	1.54559i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.179.3		88
3.2	odd	2		144.2.u.a.131.20	yes	88
4.3	odd	2		1728.2.z.a.1583.22		88
9.2	odd	6	inner	432.2.v.a.35.5		88
9.7	even	3		144.2.u.a.83.18	yes	88
12.11	even	2		576.2.y.a.239.3		88
16.5	even	4		1728.2.z.a.719.22		88
16.11	odd	4	inner	432.2.v.a.395.5		88
36.7	odd	6		576.2.y.a.47.9		88
36.11	even	6		1728.2.z.a.1007.22		88
48.5	odd	4		576.2.y.a.527.9		88
48.11	even	4		144.2.u.a.59.18	yes	88
144.11	even	12	inner	432.2.v.a.251.3		88
144.43	odd	12		144.2.u.a.11.20	✓	88
144.101	odd	12		1728.2.z.a.143.22		88
144.133	even	12		576.2.y.a.335.3		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.20	✓	88	144.43	odd	12
144.2.u.a.59.18	yes	88	48.11	even	4
144.2.u.a.83.18	yes	88	9.7	even	3
144.2.u.a.131.20	yes	88	3.2	odd	2
432.2.v.a.35.5		88	9.2	odd	6	inner
432.2.v.a.179.3		88	1.1	even	1	trivial
432.2.v.a.251.3		88	144.11	even	12	inner
432.2.v.a.395.5		88	16.11	odd	4	inner
576.2.y.a.47.9		88	36.7	odd	6
576.2.y.a.239.3		88	12.11	even	2
576.2.y.a.335.3		88	144.133	even	12
576.2.y.a.527.9		88	48.5	odd	4
1728.2.z.a.143.22		88	144.101	odd	12
1728.2.z.a.719.22		88	16.5	even	4
1728.2.z.a.1007.22		88	36.11	even	6
1728.2.z.a.1583.22		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)

\(f(q)\)	\(=\)	\(q+(-1.29365 + 0.571371i) q^{2} +(1.34707 - 1.47831i) q^{4} +(3.81396 - 1.02195i) q^{5} +(1.46715 + 2.54117i) q^{7} +(-0.897978 + 2.68210i) q^{8} +(-4.35003 + 3.50123i) q^{10} +(2.65006 + 0.710081i) q^{11} +(-2.34729 + 0.628955i) q^{13} +(-3.34993 - 2.44911i) q^{14} +(-0.370800 - 3.98278i) q^{16} -2.89808i q^{17} +(-1.99906 + 1.99906i) q^{19} +(3.62692 - 7.01485i) q^{20} +(-3.83397 + 0.595568i) q^{22} +(2.07141 + 1.19593i) q^{23} +(9.17180 - 5.29534i) q^{25} +(2.67721 - 2.15482i) q^{26} +(5.73299 + 1.25424i) q^{28} +(-8.46218 - 2.26743i) q^{29} +(-0.439075 - 0.253500i) q^{31} +(2.75533 + 4.94046i) q^{32} +(1.65588 + 3.74911i) q^{34} +(8.19258 + 8.19258i) q^{35} +(1.36407 - 1.36407i) q^{37} +(1.44388 - 3.72828i) q^{38} +(-0.683892 + 11.1471i) q^{40} +(-0.745739 + 1.29166i) q^{41} +(-1.27136 + 4.74478i) q^{43} +(4.61954 - 2.96108i) q^{44} +(-3.36300 - 0.363572i) q^{46} +(3.25802 + 5.64306i) q^{47} +(-0.805035 + 1.39436i) q^{49} +(-8.83951 + 12.0908i) q^{50} +(-2.23218 + 4.31727i) q^{52} +(5.17979 + 5.17979i) q^{53} +10.8329 q^{55} +(-8.13313 + 1.65311i) q^{56} +(12.2427 - 1.90177i) q^{58} +(-0.664781 - 2.48100i) q^{59} +(2.99657 - 11.1833i) q^{61} +(0.712853 + 0.0770663i) q^{62} +(-6.38727 - 4.81693i) q^{64} +(-8.30972 + 4.79762i) q^{65} +(-2.53505 - 9.46095i) q^{67} +(-4.28427 - 3.90393i) q^{68} +(-15.2794 - 5.91735i) q^{70} -4.65399i q^{71} +4.91897i q^{73} +(-0.985240 + 2.54402i) q^{74} +(0.262354 + 5.64809i) q^{76} +(2.08358 + 7.77604i) q^{77} +(-3.61263 + 2.08575i) q^{79} +(-5.48441 - 14.8112i) q^{80} +(0.226711 - 2.09705i) q^{82} +(3.37411 - 12.5924i) q^{83} +(-2.96169 - 11.0532i) q^{85} +(-1.06633 - 6.86451i) q^{86} +(-4.28420 + 6.47007i) q^{88} -7.33327 q^{89} +(-5.04210 - 5.04210i) q^{91} +(4.55828 - 1.45118i) q^{92} +(-7.43902 - 5.43861i) q^{94} +(-5.58139 + 9.66725i) q^{95} +(2.50134 + 4.33245i) q^{97} +(0.244738 - 2.26379i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 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

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