LMFDB - Embedded newform 567.2.be.a.62.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(62,567)] 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("567.62"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.be (of order $18$, degree $6$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			62.13
Character	$\chi$	$=$	567.62
Dual form			567.2.be.a.503.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.234777 + 0.645045i) q^{2} +(1.17113 - 0.982692i) q^{4} +(-0.231854 - 1.31491i) q^{5} +(1.38106 + 2.25670i) q^{7} +(2.09779 + 1.21116i) q^{8} +(0.793741 - 0.458267i) q^{10} +(-0.216508 - 0.0381762i) q^{11} +(0.673991 - 1.85178i) q^{13} +(-1.13143 + 1.42066i) q^{14} +(0.242207 - 1.37362i) q^{16} +(0.469803 + 0.813723i) q^{17} +(3.04150 + 1.75601i) q^{19} +(-1.56368 - 1.31208i) q^{20} +(-0.0262057 - 0.148620i) q^{22} +(-1.17579 - 1.40126i) q^{23} +(3.02323 - 1.10037i) q^{25} +1.35272 q^{26} +(3.83503 + 1.28572i) q^{28} +(1.33239 + 3.66070i) q^{29} +(-5.95195 - 7.09326i) q^{31} +(5.71394 - 1.00752i) q^{32} +(-0.414589 + 0.494088i) q^{34} +(2.64715 - 2.33919i) q^{35} +(-1.56504 - 2.71072i) q^{37} +(-0.418631 + 2.37418i) q^{38} +(1.10618 - 3.03921i) q^{40} +(10.8664 + 3.95506i) q^{41} +(-0.261843 + 1.48498i) q^{43} +(-0.291074 + 0.168051i) q^{44} +(0.627824 - 1.08742i) q^{46} +(-5.18484 - 4.35059i) q^{47} +(-3.18536 + 6.23325i) q^{49} +(1.41957 + 1.69178i) q^{50} +(-1.03040 - 2.83099i) q^{52} -3.77077i q^{53} +0.293540i q^{55} +(0.163947 + 6.40675i) q^{56} +(-2.04850 + 1.71890i) q^{58} +(1.72130 + 9.76195i) q^{59} +(-6.04827 + 7.20805i) q^{61} +(3.17809 - 5.50461i) q^{62} +(0.596586 + 1.03332i) q^{64} +(-2.59119 - 0.456896i) q^{65} +(-6.36714 - 2.31745i) q^{67} +(1.34984 + 0.491301i) q^{68} +(2.13037 + 1.15834i) q^{70} +(-11.8706 + 6.85351i) q^{71} +(7.68223 + 4.43534i) q^{73} +(1.38110 - 1.64593i) q^{74} +(5.28760 - 0.932347i) q^{76} +(-0.212858 - 0.541316i) q^{77} +(-7.91776 + 2.88183i) q^{79} -1.86235 q^{80} +7.93789i q^{82} +(-16.1714 + 5.88589i) q^{83} +(0.961047 - 0.806414i) q^{85} +(-1.01936 + 0.179740i) q^{86} +(-0.407950 - 0.342311i) q^{88} +(3.46240 - 5.99705i) q^{89} +(5.10972 - 1.03641i) q^{91} +(-2.75401 - 0.485606i) q^{92} +(1.58905 - 4.36587i) q^{94} +(1.60381 - 4.40644i) q^{95} +(-4.42872 - 0.780904i) q^{97} +(-4.76858 - 0.591277i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) $ 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.234777	+	0.645045i	0.166012	+	0.456116i	0.994605	−	0.103737i	$-0.0330800\pi$
$2$	0.234777	+	0.645045i	0.166012	+	0.456116i	−0.828592	+	0.559852i	$0.810858\pi$
$3$		0			0
$3$		0			0
$4$	1.17113	−	0.982692i	0.585563	−	0.491346i
$5$	−0.231854	−	1.31491i	−0.103688	−	0.588045i	−0.991736	−	0.128294i	$-0.959050\pi$
$5$	−0.231854	−	1.31491i	−0.103688	−	0.588045i	0.888048	−	0.459751i	$-0.152061\pi$
$6$		0			0
$7$	1.38106	+	2.25670i	0.521990	+	0.852951i
$7$	1.38106	+	2.25670i	0.521990	+	0.852951i
$8$	2.09779	+	1.21116i	0.741680	+	0.428209i
$9$		0			0
$10$	0.793741	−	0.458267i	0.251003	−	0.144917i
$11$	−0.216508	−	0.0381762i	−0.0652796	−	0.0115106i	0.140913	−	0.990022i	$-0.454996\pi$
$11$	−0.216508	−	0.0381762i	−0.0652796	−	0.0115106i	−0.206193	+	0.978511i	$0.566107\pi$
$12$		0			0
$13$	0.673991	−	1.85178i	0.186932	−	0.513590i	−0.810458	−	0.585797i	$-0.800782\pi$
$13$	0.673991	−	1.85178i	0.186932	−	0.513590i	0.997390	+	0.0722062i	$0.0230040\pi$
$14$	−1.13143	+	1.42066i	−0.302387	+	0.379689i
$15$		0			0
$16$	0.242207	−	1.37362i	0.0605517	−	0.343406i
$17$	0.469803	+	0.813723i	0.113944	+	0.197357i	0.917357	−	0.398065i	$-0.130318\pi$
$17$	0.469803	+	0.813723i	0.113944	+	0.197357i	−0.803413	+	0.595422i	$0.796985\pi$
$18$		0			0
$19$	3.04150	+	1.75601i	0.697768	+	0.402857i	0.806516	−	0.591213i	$-0.201351\pi$
$19$	3.04150	+	1.75601i	0.697768	+	0.402857i	−0.108747	+	0.994069i	$0.534684\pi$
$20$	−1.56368	−	1.31208i	−0.349650	−	0.293391i
$21$		0			0
$22$	−0.0262057	−	0.148620i	−0.00558708	−	0.0316859i
$23$	−1.17579	−	1.40126i	−0.245170	−	0.292182i	0.629400	−	0.777082i	$-0.283301\pi$
$23$	−1.17579	−	1.40126i	−0.245170	−	0.292182i	−0.874570	+	0.484899i	$0.838856\pi$
$24$		0			0
$25$	3.02323	−	1.10037i	0.604647	−	0.220073i
$26$	1.35272			0.265289
$27$		0			0
$28$	3.83503	+	1.28572i	0.724753	+	0.242979i
$29$	1.33239	+	3.66070i	0.247418	+	0.679776i	0.999779	+	0.0210245i	$0.00669280\pi$
$29$	1.33239	+	3.66070i	0.247418	+	0.679776i	−0.752361	+	0.658751i	$0.771085\pi$
$30$		0			0
$31$	−5.95195	−	7.09326i	−1.06900	−	1.27399i	−0.960017	−	0.279943i	$-0.909684\pi$
$31$	−5.95195	−	7.09326i	−1.06900	−	1.27399i	−0.108985	−	0.994043i	$-0.534760\pi$
$32$	5.71394	−	1.00752i	1.01009	−	0.178106i
$33$		0			0
$34$	−0.414589	+	0.494088i	−0.0711014	+	0.0847353i
$35$	2.64715	−	2.33919i	0.447450	−	0.395395i
$36$		0			0
$37$	−1.56504	−	2.71072i	−0.257290	−	0.445640i	0.708225	−	0.705987i	$-0.249496\pi$
$37$	−1.56504	−	2.71072i	−0.257290	−	0.445640i	−0.965515	+	0.260347i	$0.916163\pi$
$38$	−0.418631	+	2.37418i	−0.0679110	+	0.385142i
$39$		0			0
$40$	1.10618	−	3.03921i	0.174903	−	0.480542i
$41$	10.8664	+	3.95506i	1.69705	+	0.617676i	0.995484	−	0.0949267i	$-0.0302617\pi$
$41$	10.8664	+	3.95506i	1.69705	+	0.617676i	0.701567	+	0.712603i	$0.252484\pi$
$42$		0			0
$43$	−0.261843	+	1.48498i	−0.0399307	+	0.226458i	−0.998242	−	0.0592676i	$-0.981123\pi$
$43$	−0.261843	+	1.48498i	−0.0399307	+	0.226458i	0.958311	+	0.285726i	$0.0922346\pi$
$44$	−0.291074	+	0.168051i	−0.0438810	+	0.0253347i
$45$		0			0
$46$	0.627824	−	1.08742i	0.0925676	−	0.160332i
$47$	−5.18484	−	4.35059i	−0.756286	−	0.634599i	0.180871	−	0.983507i	$-0.442108\pi$
$47$	−5.18484	−	4.35059i	−0.756286	−	0.634599i	−0.937157	+	0.348907i	$0.886553\pi$
$48$		0			0
$49$	−3.18536	+	6.23325i	−0.455052	+	0.890465i
$50$	1.41957	+	1.69178i	0.200758	+	0.239254i
$51$		0			0
$52$	−1.03040	−	2.83099i	−0.142890	−	0.392588i
$53$		−	3.77077i		−	0.517954i	−0.965883	−	0.258977i	$-0.916615\pi$
$53$		−	3.77077i		−	0.517954i	0.965883	−	0.258977i	$-0.0833855\pi$
$54$		0			0
$55$			0.293540i			0.0395809i
$56$	0.163947	+	6.40675i	0.0219083	+	0.856138i
$57$		0			0
$58$	−2.04850	+	1.71890i	−0.268982	+	0.225703i
$59$	1.72130	+	9.76195i	0.224094	+	1.27090i	0.864410	+	0.502787i	$0.167692\pi$
$59$	1.72130	+	9.76195i	0.224094	+	1.27090i	−0.640317	+	0.768111i	$0.721197\pi$
$60$		0			0
$61$	−6.04827	+	7.20805i	−0.774402	+	0.922896i	−0.998666	−	0.0516319i	$-0.983558\pi$
$61$	−6.04827	+	7.20805i	−0.774402	+	0.922896i	0.224264	+	0.974528i	$0.428002\pi$
$62$	3.17809	−	5.50461i	0.403617	−	0.699086i
$63$		0			0
$64$	0.596586	+	1.03332i	0.0745733	+	0.129165i
$65$	−2.59119	−	0.456896i	−0.321397	−	0.0566710i
$66$		0			0
$67$	−6.36714	−	2.31745i	−0.777871	−	0.283122i	−0.0775861	−	0.996986i	$-0.524721\pi$
$67$	−6.36714	−	2.31745i	−0.777871	−	0.283122i	−0.700284	+	0.713864i	$0.746943\pi$
$68$	1.34984	+	0.491301i	0.163692	+	0.0595790i
$69$		0			0
$70$	2.13037	+	1.15834i	0.254628	+	0.138448i
$71$	−11.8706	+	6.85351i	−1.40879	+	0.813362i	−0.995271	−	0.0971354i	$-0.969032\pi$
$71$	−11.8706	+	6.85351i	−1.40879	+	0.813362i	−0.413514	+	0.910498i	$0.635699\pi$
$72$		0			0
$73$	7.68223	+	4.43534i	0.899137	+	0.519117i	0.876920	−	0.480636i	$-0.159594\pi$
$73$	7.68223	+	4.43534i	0.899137	+	0.519117i	0.0222170	+	0.999753i	$0.492928\pi$
$74$	1.38110	−	1.64593i	0.160550	−	0.191336i
$75$		0			0
$76$	5.28760	−	0.932347i	0.606529	−	0.106948i
$77$	−0.212858	−	0.541316i	−0.0242574	−	0.0616887i
$78$		0			0
$79$	−7.91776	+	2.88183i	−0.890818	+	0.324231i	−0.746567	−	0.665310i	$-0.768299\pi$
$79$	−7.91776	+	2.88183i	−0.890818	+	0.324231i	−0.144251	+	0.989541i	$0.546077\pi$
$80$	−1.86235			−0.208217
$81$		0			0
$82$			7.93789i			0.876594i
$83$	−16.1714	+	5.88589i	−1.77504	+	0.646061i	−0.775139	+	0.631791i	$0.782320\pi$
$83$	−16.1714	+	5.88589i	−1.77504	+	0.646061i	−0.999898	+	0.0142697i	$0.995458\pi$
$84$		0			0
$85$	0.961047	−	0.806414i	0.104240	−	0.0874679i
$86$	−1.01936	+	0.179740i	−0.109920	+	0.0193819i
$87$		0			0
$88$	−0.407950	−	0.342311i	−0.0434876	−	0.0364904i
$89$	3.46240	−	5.99705i	0.367014	−	0.635686i	−0.622084	−	0.782951i	$-0.713714\pi$
$89$	3.46240	−	5.99705i	0.367014	−	0.635686i	0.989097	+	0.147265i	$0.0470469\pi$
$90$		0			0
$91$	5.10972	−	1.03641i	0.535644	−	0.108646i
$92$	−2.75401	−	0.485606i	−0.287125	−	0.0506279i
$93$		0			0
$94$	1.58905	−	4.36587i	0.163898	−	0.450305i
$95$	1.60381	−	4.40644i	0.164548	−	0.452091i
$96$		0			0
$97$	−4.42872	−	0.780904i	−0.449669	−	0.0792887i	−0.0557722	−	0.998444i	$-0.517762\pi$
$97$	−4.42872	−	0.780904i	−0.449669	−	0.0792887i	−0.393897	+	0.919155i	$0.628873\pi$
$98$	−4.76858	−	0.591277i	−0.481699	−	0.0597280i
$99$		0			0
$100$	2.45927	−	4.25957i	0.245927	−	0.425957i
$101$	−0.750944	−	0.630116i	−0.0747217	−	0.0626989i	0.604662	−	0.796482i	$-0.293308\pi$
$101$	−0.750944	−	0.630116i	−0.0747217	−	0.0626989i	−0.679384	+	0.733783i	$0.737753\pi$
$102$		0			0
$103$	13.1659	−	2.32150i	1.29727	−	0.228744i	0.517974	−	0.855396i	$-0.326686\pi$
$103$	13.1659	−	2.32150i	1.29727	−	0.228744i	0.779299	+	0.626652i	$0.215575\pi$
$104$	3.65668	−	3.06832i	0.358567	−	0.300874i
$105$		0			0
$106$	2.43231	−	0.885289i	0.236247	−	0.0859869i
$107$		−	18.7220i		−	1.80992i	−0.425496	−	0.904960i	$-0.639900\pi$
$107$		−	18.7220i		−	1.80992i	0.425496	−	0.904960i	$-0.360100\pi$
$108$		0			0
$109$	−5.24050			−0.501949			−0.250975	−	0.967994i	$-0.580751\pi$
$109$	−5.24050			−0.501949			−0.250975	+	0.967994i	$0.580751\pi$
$110$	−0.189346	+	0.0689164i	−0.0180534	+	0.00657092i
$111$		0			0
$112$	3.43435	−	1.35046i	0.324516	−	0.127607i
$113$	−8.07557	+	1.42394i	−0.759686	+	0.133953i	−0.540055	−	0.841630i	$-0.681596\pi$
$113$	−8.07557	+	1.42394i	−0.759686	+	0.133953i	−0.219631	+	0.975583i	$0.570485\pi$
$114$		0			0
$115$	−1.56991	+	1.87095i	−0.146395	+	0.174467i
$116$	5.15774	+	2.97782i	0.478884	+	0.276484i
$117$		0			0
$118$	−5.89278	+	3.40220i	−0.542474	+	0.313198i
$119$	−1.18750	+	2.18400i	−0.108858	+	0.200207i
$120$		0			0
$121$	−10.2912	−	3.74569i	−0.935564	−	0.340517i
$122$	−6.06951	−	2.20912i	−0.549508	−	0.200004i
$123$		0			0
$124$	−13.9410	−	2.45817i	−1.25194	−	0.220750i
$125$	−5.48582	−	9.50171i	−0.490666	−	0.849859i
$126$		0			0
$127$	−0.479905	+	0.831220i	−0.0425847	+	0.0737588i	−0.886532	−	0.462667i	$-0.846893\pi$
$127$	−0.479905	+	0.831220i	−0.0425847	+	0.0737588i	0.843947	+	0.536426i	$0.180226\pi$
$128$	6.93255	−	8.26189i	0.612757	−	0.730255i
$129$		0			0
$130$	−0.313633	−	1.77870i	−0.0275074	−	0.156002i
$131$	−3.74843	+	3.14531i	−0.327502	+	0.274807i	−0.791681	−	0.610935i	$-0.790794\pi$
$131$	−3.74843	+	3.14531i	−0.327502	+	0.274807i	0.464179	+	0.885741i	$0.346349\pi$
$132$		0			0
$133$	0.237700	+	9.28890i	0.0206112	+	0.805450i
$134$		−	4.65118i		−	0.401801i
$135$		0			0
$136$			2.27602i			0.195167i
$137$	−3.97977	−	10.9343i	−0.340015	−	0.934183i	−0.985389	−	0.170317i	$-0.945521\pi$
$137$	−3.97977	−	10.9343i	−0.340015	−	0.934183i	0.645375	−	0.763866i	$-0.276701\pi$
$138$		0			0
$139$	5.90509	+	7.03742i	0.500864	+	0.596906i	0.955946	−	0.293544i	$-0.0948346\pi$
$139$	5.90509	+	7.03742i	0.500864	+	0.596906i	−0.455082	+	0.890449i	$0.650390\pi$
$140$	0.801444	−	5.34082i	0.0677344	−	0.451381i
$141$		0			0
$142$	−7.20778	−	6.04804i	−0.604863	−	0.507540i
$143$	−0.216618	+	0.375194i	−0.0181145	+	0.0313753i
$144$		0			0
$145$	4.50458	−	2.60072i	0.374085	−	0.215978i
$146$	−1.05738	+	5.99670i	−0.0875094	+	0.496290i
$147$		0			0
$148$	−4.49666	−	1.63665i	−0.369623	−	0.134532i
$149$	5.20678	−	14.3055i	0.426556	−	1.17195i	−0.521333	−	0.853353i	$-0.674565\pi$
$149$	5.20678	−	14.3055i	0.426556	−	1.17195i	0.947889	−	0.318600i	$-0.103213\pi$
$150$		0			0
$151$	−1.95736	+	11.1008i	−0.159288	+	0.903366i	0.795472	+	0.605990i	$0.207223\pi$
$151$	−1.95736	+	11.1008i	−0.159288	+	0.903366i	−0.954760	+	0.297376i	$0.903888\pi$
$152$	4.25361	+	7.36748i	0.345014	+	0.597581i
$153$		0			0
$154$	0.299199	−	0.264391i	0.0241101	−	0.0213053i
$155$	−7.94701	+	9.47087i	−0.638319	+	0.760719i
$156$		0			0
$157$	−12.3894	+	2.18459i	−0.988784	+	0.174349i	−0.644573	−	0.764543i	$-0.722965\pi$
$157$	−12.3894	+	2.18459i	−0.988784	+	0.174349i	−0.344211	+	0.938892i	$0.611854\pi$
$158$	−3.71782	−	4.43072i	−0.295774	−	0.352489i
$159$		0			0
$160$	−2.64960	−	7.27972i	−0.209469	−	0.575512i
$161$	1.53837	−	4.58863i	0.121241	−	0.361635i
$162$		0			0
$163$	−15.4955			−1.21370			−0.606850	−	0.794816i	$-0.707567\pi$
$163$	−15.4955			−1.21370			−0.606850	+	0.794816i	$0.707567\pi$
$164$	16.6126	−	6.04648i	1.29722	−	0.472151i
$165$		0			0
$166$	−7.59333	−	9.04938i	−0.589357	−	0.702368i
$167$	3.86013	+	21.8919i	0.298706	+	1.69405i	0.651746	+	0.758437i	$0.274037\pi$
$167$	3.86013	+	21.8919i	0.298706	+	1.69405i	−0.353040	+	0.935608i	$0.614852\pi$
$168$		0			0
$169$	6.98377	+	5.86008i	0.537213	+	0.450775i
$170$	0.745805	+	0.430591i	0.0572006	+	0.0330248i
$171$		0			0
$172$	1.15263	+	1.99642i	0.0878873	+	0.152225i
$173$	−0.814058	+	4.61675i	−0.0618917	+	0.351005i	0.938098	+	0.346371i	$0.112586\pi$
$173$	−0.814058	+	4.61675i	−0.0618917	+	0.351005i	−0.999989	+	0.00463414i	$0.998525\pi$
$174$		0			0
$175$	6.65845	+	5.30285i	0.503332	+	0.400858i
$176$	−0.104879	+	0.288154i	−0.00790558	+	0.0217204i
$177$		0			0
$178$	4.68126	+	0.825432i	0.350875	+	0.0618688i
$179$	−13.7669	+	7.94833i	−1.02899	+	0.594086i	−0.916694	−	0.399589i	$-0.869153\pi$
$179$	−13.7669	+	7.94833i	−1.02899	+	0.594086i	−0.112293	+	0.993675i	$0.535820\pi$
$180$		0			0
$181$	−4.81888	−	2.78218i	−0.358185	−	0.206798i	0.310100	−	0.950704i	$-0.399638\pi$
$181$	−4.81888	−	2.78218i	−0.358185	−	0.206798i	−0.668284	+	0.743906i	$0.732971\pi$
$182$	1.86818	+	3.05267i	0.138479	+	0.226279i
$183$		0			0
$184$	−0.769423	−	4.36361i	−0.0567226	−	0.321690i
$185$	−3.20150	+	2.68637i	−0.235379	+	0.197506i
$186$		0			0
$187$	−0.0706513	−	0.194113i	−0.00516653	−	0.0141949i
$188$	−10.3474			−0.754661
$189$		0			0
$190$	3.21889			0.233523
$191$	−0.626662	−	1.72174i	−0.0453437	−	0.124581i	0.914954	−	0.403558i	$-0.132227\pi$
$191$	−0.626662	−	1.72174i	−0.0453437	−	0.124581i	−0.960298	+	0.278978i	$0.910004\pi$
$192$		0			0
$193$	0.0889424	−	0.0746315i	0.00640221	−	0.00537209i	−0.639581	−	0.768724i	$-0.720892\pi$
$193$	0.0889424	−	0.0746315i	0.00640221	−	0.00537209i	0.645983	+	0.763352i	$0.276448\pi$
$194$	−0.536045	−	3.04006i	−0.0384858	−	0.218264i
$195$		0			0
$196$	2.39490	+	10.4302i	0.171065	+	0.745011i
$197$	13.5481	+	7.82201i	0.965264	+	0.557295i	0.897789	−	0.440425i	$-0.145172\pi$
$197$	13.5481	+	7.82201i	0.965264	+	0.557295i	0.0674749	+	0.997721i	$0.478506\pi$
$198$		0			0
$199$	8.33355	−	4.81138i	0.590750	−	0.341069i	−0.174644	−	0.984632i	$-0.555878\pi$
$199$	8.33355	−	4.81138i	0.590750	−	0.341069i	0.765394	+	0.643562i	$0.222544\pi$
$200$	7.67481	+	1.35328i	0.542691	+	0.0956911i
$201$		0			0
$202$	0.230149	−	0.632329i	0.0161932	−	0.0444905i
$203$	−6.42100	+	8.06244i	−0.450666	+	0.565872i
$204$		0			0
$205$	2.68112	−	15.2054i	0.187257	−	1.06199i
$206$	4.58852	+	7.94755i	0.319697	+	0.553732i
$207$		0			0
$208$	−2.38040	−	1.37432i	−0.165051	−	0.0952922i
$209$	−0.591471	−	0.496303i	−0.0409129	−	0.0343300i
$210$		0			0
$211$	2.41262	+	13.6827i	0.166092	+	0.941954i	0.947932	+	0.318474i	$0.103170\pi$
$211$	2.41262	+	13.6827i	0.166092	+	0.941954i	−0.781840	+	0.623479i	$0.785719\pi$
$212$	−3.70550	−	4.41604i	−0.254495	−	0.303295i
$213$		0			0
$214$	12.0765	−	4.39549i	0.825533	−	0.300469i
$215$	2.01333			0.137308
$216$		0			0
$217$	7.78735	−	23.2279i	0.528640	−	1.57682i
$218$	−1.23035	−	3.38036i	−0.0833298	−	0.228947i
$219$		0			0
$220$	0.288459	+	0.343772i	0.0194479	+	0.0231771i
$221$	1.82348	−	0.321528i	0.122660	−	0.0216283i
$222$		0			0
$223$	11.6645	−	13.9012i	0.781115	−	0.930896i	−0.217869	−	0.975978i	$-0.569910\pi$
$223$	11.6645	−	13.9012i	0.781115	−	0.930896i	0.998983	+	0.0450820i	$0.0143549\pi$
$224$	10.1650	+	11.5032i	0.679175	+	0.768590i
$225$		0			0
$226$	−2.81446	−	4.87479i	−0.187215	−	0.324267i
$227$	4.49086	−	25.4689i	0.298069	−	1.69043i	−0.356393	−	0.934336i	$-0.615994\pi$
$227$	4.49086	−	25.4689i	0.298069	−	1.69043i	0.654462	−	0.756095i	$-0.272895\pi$
$228$		0			0
$229$	−3.70816	+	10.1881i	−0.245042	+	0.673247i	0.754809	+	0.655945i	$0.227730\pi$
$229$	−3.70816	+	10.1881i	−0.245042	+	0.673247i	−0.999850	+	0.0173016i	$0.994492\pi$
$230$	−1.57543	−	0.573409i	−0.103881	−	0.0378094i
$231$		0			0
$232$	−1.63863	+	9.29311i	−0.107581	+	0.610122i
$233$	−2.36196	+	1.36368i	−0.154737	+	0.0893375i	−0.575369	−	0.817894i	$-0.695142\pi$
$233$	−2.36196	+	1.36368i	−0.154737	+	0.0893375i	0.420632	+	0.907231i	$0.361808\pi$
$234$		0			0
$235$	−4.51851	+	7.82629i	−0.294755	+	0.510531i
$236$	11.6088	+	9.74098i	0.755672	+	0.634084i
$237$		0			0
$238$	−1.68758	−	0.253238i	−0.109389	−	0.0164150i
$239$	19.4562	+	23.1870i	1.25852	+	1.49984i	0.785599	+	0.618736i	$0.212355\pi$
$239$	19.4562	+	23.1870i	1.25852	+	1.49984i	0.472919	+	0.881106i	$0.343200\pi$
$240$		0			0
$241$	8.39131	+	23.0549i	0.540531	+	1.48510i	0.846150	+	0.532944i	$0.178914\pi$
$241$	8.39131	+	23.0549i	0.540531	+	1.48510i	−0.305619	+	0.952154i	$0.598863\pi$
$242$		−	7.51769i		−	0.483255i
$243$		0			0
$244$			14.3851i			0.920914i
$245$	8.93470	+	2.74326i	0.570817	+	0.175260i
$246$		0			0
$247$	5.30169	−	4.44864i	0.337338	−	0.283060i
$248$	−3.89487	−	22.0889i	−0.247324	−	1.40265i
$249$		0			0
$250$	4.84109	−	5.76938i	0.306177	−	0.364888i
$251$	12.0630	−	20.8937i	0.761409	−	1.31880i	−0.180715	−	0.983536i	$-0.557841\pi$
$251$	12.0630	−	20.8937i	0.761409	−	1.31880i	0.942124	−	0.335264i	$-0.108826\pi$
$252$		0			0
$253$	0.201074	+	0.348271i	0.0126414	+	0.0218956i
$254$	−0.648845	−	0.114409i	−0.0407121	−	0.00717865i
$255$		0			0
$256$	9.19933	+	3.34828i	0.574958	+	0.209268i
$257$	−11.0337	−	4.01595i	−0.688265	−	0.250508i	−0.0258727	−	0.999665i	$-0.508236\pi$
$257$	−11.0337	−	4.01595i	−0.688265	−	0.250508i	−0.662392	+	0.749157i	$0.730459\pi$
$258$		0			0
$259$	3.95588	−	7.27548i	0.245806	−	0.452076i
$260$	−3.48359	+	2.01125i	−0.216043	+	0.124733i
$261$		0			0
$262$	−2.90891	−	1.67946i	−0.179713	−	0.103757i
$263$	−12.7126	+	15.1503i	−0.783891	+	0.934205i	−0.999102	−	0.0423623i	$-0.986512\pi$
$263$	−12.7126	+	15.1503i	−0.783891	+	0.934205i	0.215211	+	0.976568i	$0.430956\pi$
$264$		0			0
$265$	−4.95821	+	0.874267i	−0.304581	+	0.0537058i
$266$	−5.93595	+	2.33415i	−0.363956	+	0.143116i
$267$		0			0
$268$	−9.73407	+	3.54291i	−0.594603	+	0.216418i
$269$	−17.1269			−1.04424			−0.522122	−	0.852871i	$-0.674859\pi$
$269$	−17.1269			−1.04424			−0.522122	+	0.852871i	$0.674859\pi$
$270$		0			0
$271$		−	16.5484i		−	1.00525i	−0.864506	−	0.502623i	$-0.832368\pi$
$271$		−	16.5484i		−	1.00525i	0.864506	−	0.502623i	$-0.167632\pi$
$272$	1.23154	−	0.448244i	0.0746730	−	0.0271788i
$273$		0			0
$274$	6.11877	−	5.13426i	0.369649	−	0.310172i
$275$	−0.696561	+	0.122823i	−0.0420042	+	0.00740648i
$276$		0			0
$277$	−13.1995	−	11.0757i	−0.793078	−	0.665472i	0.153427	−	0.988160i	$-0.450969\pi$
$277$	−13.1995	−	11.0757i	−0.793078	−	0.665472i	−0.946505	+	0.322688i	$0.895413\pi$
$278$	−3.15307	+	5.46127i	−0.189108	+	0.327545i
$279$		0			0
$280$	8.38628	−	1.70100i	0.501176	−	0.101654i
$281$	14.1177	+	2.48933i	0.842190	+	0.148501i	0.578068	−	0.815988i	$-0.303807\pi$
$281$	14.1177	+	2.48933i	0.842190	+	0.148501i	0.264122	+	0.964489i	$0.414918\pi$
$282$		0			0
$283$	−4.76130	+	13.0816i	−0.283030	+	0.777618i	0.713967	+	0.700179i	$0.246897\pi$
$283$	−4.76130	+	13.0816i	−0.283030	+	0.777618i	−0.996997	+	0.0774390i	$0.975326\pi$
$284$	−7.16712	+	19.6915i	−0.425290	+	1.16848i
$285$		0			0
$286$	−0.292874	−	0.0516415i	−0.0173180	−	0.00305363i
$287$	6.08179	+	29.9844i	0.358997	+	1.76992i
$288$		0			0
$289$	8.05857	−	13.9579i	0.474034	−	0.821050i
$290$	2.73515	+	2.29506i	0.160614	+	0.134771i
$291$		0			0
$292$	13.3554	−	2.35492i	0.781568	−	0.137811i
$293$	9.24858	−	7.76048i	0.540308	−	0.453372i	−0.331335	−	0.943513i	$-0.607499\pi$
$293$	9.24858	−	7.76048i	0.540308	−	0.453372i	0.871643	+	0.490141i	$0.163055\pi$
$294$		0			0
$295$	12.4370	−	4.52670i	0.724110	−	0.263554i
$296$		−	7.58203i		−	0.440696i
$297$		0			0
$298$	10.4501			0.605359
$299$	−3.38729	+	1.23287i	−0.195892	+	0.0712989i
$300$		0			0
$301$	−3.71278	+	1.45995i	−0.214001	+	0.0841500i
$302$	−7.62002	+	1.34362i	−0.438483	+	0.0773164i
$303$		0			0
$304$	3.14877	−	3.75256i	0.180594	−	0.215224i
$305$	10.8803	+	6.28172i	0.623001	+	0.359690i
$306$		0			0
$307$	−19.5181	+	11.2688i	−1.11396	+	0.643144i	−0.939852	−	0.341583i	$-0.889037\pi$
$307$	−19.5181	+	11.2688i	−1.11396	+	0.643144i	−0.174107	+	0.984727i	$0.555704\pi$
$308$	−0.781230	−	0.424776i	−0.0445147	−	0.0242039i
$309$		0			0
$310$	−7.97491	−	2.90263i	−0.452945	−	0.164858i
$311$	−2.46202	−	0.896103i	−0.139608	−	0.0508133i	0.271271	−	0.962503i	$-0.412556\pi$
$311$	−2.46202	−	0.896103i	−0.139608	−	0.0508133i	−0.410879	+	0.911690i	$0.634778\pi$
$312$		0			0
$313$	5.70705	+	1.00631i	0.322582	+	0.0568798i	0.332594	−	0.943070i	$-0.392076\pi$
$313$	5.70705	+	1.00631i	0.322582	+	0.0568798i	−0.0100126	+	0.999950i	$0.503187\pi$
$314$	−4.31791	−	7.47885i	−0.243674	−	0.422056i
$315$		0			0
$316$	−6.44075	+	11.1557i	−0.362320	+	0.627557i
$317$	9.51195	−	11.3359i	0.534244	−	0.636687i	−0.429643	−	0.902999i	$-0.641361\pi$
$317$	9.51195	−	11.3359i	0.534244	−	0.636687i	0.963887	+	0.266312i	$0.0858050\pi$
$318$		0			0
$319$	−0.148721	−	0.843437i	−0.00832676	−	0.0472234i
$320$	1.22040	−	1.02404i	0.0682223	−	0.0572453i
$321$		0			0
$322$	3.32105	−	0.0849845i	0.185075	−	0.00473600i
$323$			3.29992i			0.183612i
$324$		0			0
$325$		−	6.33999i		−	0.351679i
$326$	−3.63798	−	9.99528i	−0.201489	−	0.553587i
$327$		0			0
$328$	18.0053	+	21.4578i	0.994174	+	1.18481i
$329$	2.65742	−	17.7090i	0.146508	−	0.976330i
$330$		0			0
$331$	7.87879	+	6.61109i	0.433057	+	0.363378i	0.833104	−	0.553117i	$-0.186562\pi$
$331$	7.87879	+	6.61109i	0.433057	+	0.363378i	−0.400047	+	0.916495i	$0.631006\pi$
$332$	−13.1547	+	22.7846i	−0.721957	+	1.25047i
$333$		0			0
$334$	−13.2150	+	7.62967i	−0.723092	+	0.417477i
$335$	−1.57099	+	8.90953i	−0.0858324	+	0.486780i
$336$		0			0
$337$	25.9383	+	9.44078i	1.41295	+	0.514272i	0.931995	−	0.362472i	$-0.118067\pi$
$337$	25.9383	+	9.44078i	1.41295	+	0.514272i	0.480957	+	0.876744i	$0.340289\pi$
$338$	−2.14038	+	5.88065i	−0.116421	+	0.319865i
$339$		0			0
$340$	0.333051	−	1.88883i	0.0180622	−	0.102436i
$341$	1.01785	+	1.76297i	0.0551197	+	0.0954701i
$342$		0			0
$343$	−18.4657	+	1.42008i	−0.997056	+	0.0766769i
$344$	−2.34784	+	2.79805i	−0.126587	+	0.150861i
$345$		0			0
$346$	−3.16913	+	0.558804i	−0.170374	+	0.0300415i
$347$	−4.96950	−	5.92242i	−0.266777	−	0.317932i	0.615981	−	0.787761i	$-0.288760\pi$
$347$	−4.96950	−	5.92242i	−0.266777	−	0.317932i	−0.882757	+	0.469829i	$0.844316\pi$
$348$		0			0
$349$	−10.3198	−	28.3535i	−0.552407	−	1.51773i	−0.830414	−	0.557147i	$-0.811896\pi$
$349$	−10.3198	−	28.3535i	−0.552407	−	1.51773i	0.278007	−	0.960579i	$-0.410326\pi$
$350$	−1.85732	+	5.53999i	−0.0992782	+	0.296125i
$351$		0			0
$352$	−1.27558			−0.0679885
$353$	13.2988	−	4.84037i	0.707824	−	0.257627i	0.0370764	−	0.999312i	$-0.488196\pi$
$353$	13.2988	−	4.84037i	0.707824	−	0.257627i	0.670748	+	0.741685i	$0.265973\pi$
$354$		0			0
$355$	11.7640	+	14.0198i	0.624369	+	0.744093i
$356$	−1.83835	−	10.4258i	−0.0974321	−	0.552565i
$357$		0			0
$358$	−8.35919	−	7.01419i	−0.441797	−	0.370711i
$359$	22.1647	+	12.7968i	1.16981	+	0.675389i	0.953635	−	0.300966i	$-0.0973089\pi$
$359$	22.1647	+	12.7968i	1.16981	+	0.675389i	0.216174	+	0.976355i	$0.430642\pi$
$360$		0			0
$361$	−3.33285	−	5.77266i	−0.175413	−	0.303824i
$362$	0.663269	−	3.76159i	0.0348607	−	0.197705i
$363$		0			0
$364$	4.96565	−	6.23505i	0.260271	−	0.326805i
$365$	4.05091	−	11.1298i	0.212034	−	0.582560i
$366$		0			0
$367$	17.3863	+	3.06568i	0.907559	+	0.160027i	0.607895	−	0.794017i	$-0.292014\pi$
$367$	17.3863	+	3.06568i	0.907559	+	0.160027i	0.299664	+	0.954045i	$0.403125\pi$
$368$	−2.20959	+	1.27571i	−0.115183	+	0.0665007i
$369$		0			0
$370$	−2.48447	−	1.43441i	−0.129161	−	0.0745714i
$371$	8.50947	−	5.20764i	0.441790	−	0.270367i
$372$		0			0
$373$	−1.01057	−	5.73121i	−0.0523252	−	0.296751i	0.947404	−	0.320041i	$-0.103697\pi$
$373$	−1.01057	−	5.73121i	−0.0523252	−	0.296751i	−0.999729	+	0.0232906i	$0.992586\pi$
$374$	0.108624	−	0.0911465i	0.00561682	−	0.00471307i
$375$		0			0
$376$	−5.60743	−	15.4063i	−0.289181	−	0.794518i
$377$	7.67682			0.395377
$378$		0			0
$379$	28.0324			1.43993			0.719964	−	0.694011i	$-0.244158\pi$
$379$	28.0324			1.43993			0.719964	+	0.694011i	$0.244158\pi$
$380$	−2.45190	−	6.73655i	−0.125780	−	0.345578i
$381$		0			0
$382$	0.963473	−	0.808450i	0.0492956	−	0.0413639i
$383$	−0.202834	−	1.15033i	−0.0103643	−	0.0587790i	0.979187	−	0.202960i	$-0.0650563\pi$
$383$	−0.202834	−	1.15033i	−0.0103643	−	0.0587790i	−0.989551	+	0.144181i	$0.953945\pi$
$384$		0			0
$385$	−0.662430	+	0.405395i	−0.0337606	+	0.0206608i
$386$	0.0690223	+	0.0398500i	0.00351314	+	0.00202831i
$387$		0			0
$388$	−5.95398	+	3.43753i	−0.302268	+	0.174514i
$389$	22.4622	+	3.96069i	1.13888	+	0.200815i	0.711115	−	0.703076i	$-0.248191\pi$
$389$	22.4622	+	3.96069i	1.13888	+	0.200815i	0.427763	+	0.903891i	$0.359302\pi$
$390$		0			0
$391$	0.587844	−	1.61509i	0.0297285	−	0.0816785i
$392$	−14.2317	+	9.21806i	−0.718808	+	0.465582i
$393$		0			0
$394$	−1.86476	+	10.5756i	−0.0939452	+	0.532790i
$395$	5.62511	+	9.74298i	0.283030	+	0.490222i
$396$		0			0
$397$	−13.0866	−	7.55554i	−0.656797	−	0.379202i	0.134259	−	0.990946i	$-0.457135\pi$
$397$	−13.0866	−	7.55554i	−0.656797	−	0.379202i	−0.791055	+	0.611745i	$0.790468\pi$
$398$	5.06008	+	4.24591i	0.253639	+	0.212828i
$399$		0			0
$400$	−0.779242	−	4.41930i	−0.0389621	−	0.220965i
$401$	2.49029	+	2.96781i	0.124359	+	0.148205i	0.824631	−	0.565670i	$-0.191383\pi$
$401$	2.49029	+	2.96781i	0.124359	+	0.148205i	−0.700272	+	0.713876i	$0.746938\pi$
$402$		0			0
$403$	−17.1467	+	6.24088i	−0.854137	+	0.310881i
$404$	−1.49866			−0.0745611
$405$		0			0
$406$	−6.70814	−	2.24896i	−0.332919	−	0.111614i
$407$	0.235358	+	0.646640i	0.0116663	+	0.0320528i
$408$		0			0
$409$	−15.1865	−	18.0986i	−0.750926	−	0.894919i	0.246312	−	0.969191i	$-0.420781\pi$
$409$	−15.1865	−	18.0986i	−0.750926	−	0.894919i	−0.997238	+	0.0742715i	$0.976337\pi$
$410$	10.4376	−	1.84043i	0.515477	−	0.0908925i
$411$		0			0
$412$	13.1376	−	15.6568i	0.647243	−	0.771354i
$413$	−19.6526	+	17.3663i	−0.967040	+	0.854538i
$414$		0			0
$415$	11.4888	+	19.8992i	0.563963	+	0.976813i
$416$	1.98544	−	11.2600i	0.0973443	−	0.552067i
$417$		0			0
$418$	0.181274	−	0.498046i	0.00886640	−	0.0243602i
$419$	19.8064	+	7.20893i	0.967605	+	0.352179i	0.777009	−	0.629489i	$-0.216736\pi$
$419$	19.8064	+	7.20893i	0.967605	+	0.352179i	0.190596	+	0.981669i	$0.438958\pi$
$420$		0			0
$421$	2.68706	−	15.2391i	0.130959	−	0.742708i	−0.846629	−	0.532183i	$-0.821372\pi$
$421$	2.68706	−	15.2391i	0.130959	−	0.742708i	0.977589	−	0.210524i	$-0.0675172\pi$
$422$	−8.25950	+	4.76863i	−0.402066	+	0.232133i
$423$		0			0
$424$	4.56699	−	7.91026i	0.221793	−	0.384156i
$425$	2.31572	+	1.94312i	0.112329	+	0.0942551i
$426$		0			0
$427$	−24.6194	−	3.69439i	−1.19142	−	0.178784i
$428$	−18.3979	−	21.9258i	−0.889297	−	1.05982i
$429$		0			0
$430$	0.472684	+	1.29869i	0.0227948	+	0.0626283i
$431$		−	22.9807i		−	1.10694i	−0.832868	−	0.553472i	$-0.813303\pi$
$431$		−	22.9807i		−	1.10694i	0.832868	−	0.553472i	$-0.186697\pi$
$432$		0			0
$433$			24.6163i			1.18299i	0.806310	+	0.591493i	$0.201461\pi$
$433$			24.6163i			1.18299i	−0.806310	+	0.591493i	$0.798539\pi$
$434$	16.8114	−	0.430197i	0.806971	−	0.0206501i
$435$		0			0
$436$	−6.13729	+	5.14980i	−0.293923	+	0.246631i
$437$	−1.11556	−	6.32664i	−0.0533643	−	0.302644i
$438$		0			0
$439$	12.4166	−	14.7975i	0.592613	−	0.706248i	−0.383493	−	0.923544i	$-0.625279\pi$
$439$	12.4166	−	14.7975i	0.592613	−	0.706248i	0.976106	+	0.217296i	$0.0697235\pi$
$440$	−0.355523	+	0.615783i	−0.0169489	+	0.0293563i
$441$		0			0
$442$	0.635511	+	1.10074i	0.0302282	+	0.0523567i
$443$	−19.7211	−	3.47737i	−0.936980	−	0.165215i	−0.315749	−	0.948843i	$-0.602256\pi$
$443$	−19.7211	−	3.47737i	−0.936980	−	0.165215i	−0.621231	+	0.783628i	$0.713367\pi$
$444$		0			0
$445$	−8.68835	−	3.16230i	−0.411867	−	0.149907i
$446$	11.7055	+	4.26045i	0.554271	+	0.201738i
$447$		0			0
$448$	−1.50797	+	2.77338i	−0.0712447	+	0.131030i
$449$	10.4575	−	6.03767i	0.493522	−	0.284935i	−0.232512	−	0.972593i	$-0.574695\pi$
$449$	10.4575	−	6.03767i	0.493522	−	0.284935i	0.726034	+	0.687658i	$0.241361\pi$
$450$		0			0
$451$	−2.20168	−	1.27114i	−0.103673	−	0.0598557i
$452$	−8.05822	+	9.60341i	−0.379027	+	0.451706i
$453$		0			0
$454$	17.4829	−	3.08271i	0.820515	−	0.144679i
$455$	−2.54750	−	6.47852i	−0.119429	−	0.303718i
$456$		0			0
$457$	16.7442	−	6.09438i	0.783259	−	0.285083i	0.0807282	−	0.996736i	$-0.474275\pi$
$457$	16.7442	−	6.09438i	0.783259	−	0.285083i	0.702531	+	0.711653i	$0.252053\pi$
$458$	−7.44235			−0.347758
$459$		0			0
$460$			3.73386i			0.174092i
$461$	−11.0937	+	4.03778i	−0.516685	+	0.188058i	−0.587183	−	0.809454i	$-0.699763\pi$
$461$	−11.0937	+	4.03778i	−0.516685	+	0.188058i	0.0704983	+	0.997512i	$0.477541\pi$
$462$		0			0
$463$	−5.77577	+	4.84645i	−0.268423	+	0.225234i	−0.767057	−	0.641579i	$-0.778280\pi$
$463$	−5.77577	+	4.84645i	−0.268423	+	0.225234i	0.498634	+	0.866813i	$0.333835\pi$
$464$	5.35114	−	0.943551i	0.248421	−	0.0438033i
$465$		0			0
$466$	−1.43417	−	1.20341i	−0.0664365	−	0.0557468i
$467$	5.54773	−	9.60896i	0.256719	−	0.444650i	−0.708642	−	0.705568i	$-0.750692\pi$
$467$	5.54773	−	9.60896i	0.256719	−	0.444650i	0.965361	+	0.260918i	$0.0840253\pi$
$468$		0			0
$469$	−3.56360	−	17.5692i	−0.164552	−	0.811273i
$470$	−6.10915	−	1.07721i	−0.281794	−	0.0496879i
$471$		0			0
$472$	−8.21235	+	22.5633i	−0.378004	+	1.03856i
$473$	0.113382	−	0.311515i	0.00521331	−	0.0143235i
$474$		0			0
$475$	11.1274	+	1.96206i	0.510561	+	0.0900257i
$476$	0.755486	+	3.72469i	0.0346276	+	0.170721i
$477$		0			0
$478$	−10.3888	+	17.9939i	−0.475172	+	0.823022i
$479$	−0.344634	−	0.289182i	−0.0157467	−	0.0132131i	0.634880	−	0.772611i	$-0.281049\pi$
$479$	−0.344634	−	0.289182i	−0.0157467	−	0.0132131i	−0.650627	+	0.759397i	$0.725494\pi$
$480$		0			0
$481$	−6.07448	+	1.07109i	−0.276972	+	0.0488377i
$482$	−12.9014	+	10.8255i	−0.587641	+	0.493090i
$483$		0			0
$484$	−15.7332	+	5.72640i	−0.715143	+	0.260291i
$485$			6.00443i			0.272647i
$486$		0			0
$487$	−24.3678			−1.10421			−0.552105	−	0.833774i	$-0.686175\pi$
$487$	−24.3678			−1.10421			−0.552105	+	0.833774i	$0.686175\pi$
$488$	−21.4181	+	7.79554i	−0.969551	+	0.352888i
$489$		0			0
$490$	0.328138	+	6.40734i	0.0148238	+	0.289454i
$491$	−12.6614	+	2.23255i	−0.571402	+	0.100754i	−0.451881	−	0.892078i	$-0.649247\pi$
$491$	−12.6614	+	2.23255i	−0.571402	+	0.100754i	−0.119521	+	0.992832i	$0.538136\pi$
$492$		0			0
$493$	−2.35284	+	2.80401i	−0.105967	+	0.126286i
$494$	4.11429	+	2.37539i	0.185111	+	0.106874i
$495$		0			0
$496$	−11.1851	+	6.45770i	−0.502224	+	0.289959i
$497$	−31.8603	−	17.3233i	−1.42913	−	0.777058i
$498$		0			0
$499$	27.7006	+	10.0822i	1.24005	+	0.451341i	0.877028	−	0.480439i	$-0.159523\pi$
$499$	27.7006	+	10.0822i	1.24005	+	0.451341i	0.363022	+	0.931781i	$0.381745\pi$
$500$	−15.7618	−	5.73684i	−0.704891	−	0.256559i
$501$		0			0
$502$	16.3095	+	2.87580i	0.727929	+	0.128353i
$503$	−6.61558	−	11.4585i	−0.294974	−	0.510910i	0.680005	−	0.733208i	$-0.261978\pi$
$503$	−6.61558	−	11.4585i	−0.294974	−	0.510910i	−0.974979	+	0.222298i	$0.928644\pi$
$504$		0			0
$505$	−0.654437	+	1.13352i	−0.0291221	+	0.0504409i
$506$	−0.177443	+	0.211468i	−0.00788829	+	0.00940089i
$507$		0			0
$508$	0.254803	+	1.44506i	0.0113051	+	0.0641143i
$509$	10.7916	−	9.05526i	0.478331	−	0.401367i	−0.371491	−	0.928436i	$-0.621153\pi$
$509$	10.7916	−	9.05526i	0.478331	−	0.401367i	0.849823	+	0.527069i	$0.176709\pi$
$510$		0			0
$511$	0.600383	+	23.4619i	0.0265594	+	1.03789i
$512$		−	14.8502i		−	0.656292i
$513$		0			0
$514$		−	8.06010i		−	0.355516i
$515$	−6.10512	−	16.7737i	−0.269024	−	0.739137i
$516$		0			0
$517$	0.956469	+	1.13988i	0.0420655	+	0.0501317i
$518$	5.62176	+	0.843602i	0.247006	+	0.0370658i
$519$		0			0
$520$	−4.88238	−	4.09680i	−0.214107	−	0.179657i
$521$	−4.03394	+	6.98699i	−0.176730	+	0.306105i	−0.940759	−	0.339077i	$-0.889885\pi$
$521$	−4.03394	+	6.98699i	−0.176730	+	0.306105i	0.764029	+	0.645182i	$0.223219\pi$
$522$		0			0
$523$	−10.5643	+	6.09931i	−0.461945	+	0.266704i	−0.712862	−	0.701305i	$-0.752601\pi$
$523$	−10.5643	+	6.09931i	−0.461945	+	0.266704i	0.250917	+	0.968009i	$0.419268\pi$
$524$	−1.29902	+	7.36711i	−0.0567479	+	0.321833i
$525$		0			0
$526$	−12.7572	−	4.64325i	−0.556241	−	0.202455i
$527$	2.97570	−	8.17568i	0.129624	−	0.356138i
$528$		0			0
$529$	3.41288	−	19.3554i	0.148386	−	0.841539i
$530$	−1.72802	−	2.99301i	−0.0750602	−	0.130008i
$531$		0			0
$532$	9.40650	+	10.6449i	0.407824	+	0.461515i
$533$	14.6478	−	17.4565i	0.634465	−	0.756126i
$534$		0			0
$535$	−24.6177	+	4.34076i	−1.06432	+	0.187668i
$536$	−10.5501	−	12.5731i	−0.455695	−	0.543077i
$537$		0			0
$538$	−4.02100	−	11.0476i	−0.173357	−	0.476296i
$539$	0.927618	−	1.22794i	0.0399553	−	0.0528913i
$540$		0			0
$541$	−17.3576			−0.746264			−0.373132	−	0.927778i	$-0.621716\pi$
$541$	−17.3576			−0.746264			−0.373132	+	0.927778i	$0.621716\pi$
$542$	10.6745	−	3.88519i	0.458508	−	0.166883i
$543$		0			0
$544$	3.50427	+	4.17623i	0.150245	+	0.179054i
$545$	1.21503	+	6.89079i	0.0520462	+	0.295169i
$546$		0			0
$547$	5.51648	+	4.62888i	0.235868	+	0.197916i	0.753058	−	0.657954i	$-0.228578\pi$
$547$	5.51648	+	4.62888i	0.235868	+	0.197916i	−0.517191	+	0.855870i	$0.673022\pi$
$548$	−15.4059	−	8.89460i	−0.658107	−	0.379958i
$549$		0			0
$550$	−0.242763	−	0.420477i	−0.0103514	−	0.0179292i
$551$	−2.37578	+	13.4737i	−0.101212	+	0.574000i
$552$		0			0
$553$	−17.4383	−	13.8880i	−0.741552	−	0.590579i
$554$	4.04537	−	11.1145i	0.171871	−	0.472212i
$555$		0			0
$556$	13.8312	+	2.43882i	0.586575	+	0.103429i
$557$	15.7336	−	9.08382i	0.666655	−	0.384894i	−0.128153	−	0.991754i	$-0.540905\pi$
$557$	15.7336	−	9.08382i	0.666655	−	0.384894i	0.794808	+	0.606861i	$0.207571\pi$
$558$		0			0
$559$	2.57338	+	1.48574i	0.108842	+	0.0628402i
$560$	−2.57201	−	4.20275i	−0.108687	−	0.177599i
$561$		0			0
$562$	1.70878	+	9.69097i	0.0720805	+	0.408789i
$563$	−6.45074	+	5.41282i	−0.271866	+	0.228123i	−0.768520	−	0.639826i	$-0.779006\pi$
$563$	−6.45074	+	5.41282i	−0.271866	+	0.228123i	0.496653	+	0.867949i	$0.334562\pi$
$564$		0			0
$565$	3.74471	+	10.2885i	0.157541	+	0.432840i
$566$	−9.55604			−0.401670
$567$		0			0
$568$	−33.2027			−1.39316
$569$	13.8694	+	38.1057i	0.581434	+	1.59748i	0.785732	+	0.618567i	$0.212286\pi$
$569$	13.8694	+	38.1057i	0.581434	+	1.59748i	−0.204298	+	0.978909i	$0.565491\pi$
$570$		0			0
$571$	−15.0780	+	12.6519i	−0.630994	+	0.529467i	−0.901238	−	0.433325i	$-0.857340\pi$
$571$	−15.0780	+	12.6519i	−0.630994	+	0.529467i	0.270244	+	0.962792i	$0.412896\pi$
$572$	0.115012	+	0.652268i	0.00480891	+	0.0272727i
$573$		0			0
$574$	−17.9134	+	10.9627i	−0.747692	+	0.457573i
$575$	−5.09660	−	2.94252i	−0.212543	−	0.122712i
$576$		0			0
$577$	33.4084	−	19.2884i	1.39081	−	0.802985i	0.397405	−	0.917643i	$-0.369911\pi$
$577$	33.4084	−	19.2884i	1.39081	−	0.802985i	0.993405	+	0.114658i	$0.0365774\pi$
$578$	10.8954	+	1.92115i	0.453189	+	0.0799095i
$579$		0			0
$580$	2.71972	−	7.47238i	0.112930	−	0.310274i
$581$	−35.6162	−	28.3651i	−1.47761	−	1.17678i
$582$		0			0
$583$	−0.143953	+	0.816400i	−0.00596194	+	0.0338118i
$584$	10.7438	+	18.6088i	0.444581	+	0.770037i
$585$		0			0
$586$	7.17721	+	4.14376i	0.296488	+	0.171177i
$587$	−26.1514	−	21.9436i	−1.07938	−	0.905710i	−0.0835134	−	0.996507i	$-0.526614\pi$
$587$	−26.1514	−	21.9436i	−1.07938	−	0.905710i	−0.995869	+	0.0907969i	$0.971059\pi$
$588$		0			0
$589$	−5.64702	−	32.0258i	−0.232681	−	1.31960i
$590$	5.83984	+	6.95965i	0.240423	+	0.286524i
$591$		0			0
$592$	−4.10258	+	1.49322i	−0.168615	+	0.0613708i
$593$	−6.67349			−0.274048			−0.137024	−	0.990568i	$-0.543754\pi$
$593$	−6.67349			−0.274048			−0.137024	+	0.990568i	$0.543754\pi$
$594$		0			0
$595$	3.14709	+	1.05509i	0.129018	+	0.0432544i
$596$	−7.96011	−	21.8702i	−0.326059	−	0.895839i
$597$		0			0
$598$	−1.59052	−	1.89550i	−0.0650411	−	0.0775129i
$599$	−25.4041	+	4.47942i	−1.03798	+	0.183024i	−0.666569	−	0.745443i	$-0.732238\pi$
$599$	−25.4041	+	4.47942i	−1.03798	+	0.183024i	−0.371413	+	0.928468i	$0.621127\pi$
$600$		0			0
$601$	−12.8387	+	15.3005i	−0.523699	+	0.624121i	−0.961451	−	0.274975i	$-0.911330\pi$
$601$	−12.8387	+	15.3005i	−0.523699	+	0.624121i	0.437752	+	0.899096i	$0.355775\pi$
$602$	−1.81341	−	2.05215i	−0.0739090	−	0.0836393i
$603$		0			0
$604$	8.61630	+	14.9239i	0.350592	+	0.607243i
$605$	−2.53919	+	14.4005i	−0.103233	+	0.585462i
$606$		0			0
$607$	−11.2649	+	30.9501i	−0.457228	+	1.25622i	0.470312	+	0.882500i	$0.344141\pi$
$607$	−11.2649	+	30.9501i	−0.457228	+	1.25622i	−0.927540	+	0.373724i	$0.878081\pi$
$608$	19.1482	+	6.96937i	0.776562	+	0.282645i
$609$		0			0
$610$	−1.49755	+	8.49305i	−0.0606342	+	0.343874i
$611$	−11.5509	+	6.66889i	−0.467298	+	0.269795i
$612$		0			0
$613$	15.5747	−	26.9761i	0.629055	−	1.08956i	−0.358687	−	0.933458i	$-0.616775\pi$
$613$	15.5747	−	26.9761i	0.629055	−	1.08956i	0.987742	−	0.156097i	$-0.0498913\pi$
$614$	−11.8513	−	9.94441i	−0.478279	−	0.401324i
$615$		0			0
$616$	0.209089	−	1.39337i	0.00842445	−	0.0561405i
$617$	21.5216	+	25.6485i	0.866428	+	1.03257i	0.999142	+	0.0414139i	$0.0131862\pi$
$617$	21.5216	+	25.6485i	0.866428	+	1.03257i	−0.132714	+	0.991154i	$0.542369\pi$
$618$		0			0
$619$	1.15081	+	3.16183i	0.0462550	+	0.127085i	0.960669	−	0.277695i	$-0.0895705\pi$
$619$	1.15081	+	3.16183i	0.0462550	+	0.127085i	−0.914414	+	0.404780i	$0.867348\pi$
$620$			18.9011i			0.759084i
$621$		0			0
$622$		−	1.79850i		−	0.0721132i
$623$	18.3153	−	0.468682i	0.733787	−	0.0187774i
$624$		0			0
$625$	1.10083	−	0.923703i	0.0440330	−	0.0369481i
$626$	0.690772	+	3.91756i	0.0276088	+	0.156577i
$627$		0			0
$628$	−12.3628	+	14.7334i	−0.493330	+	0.587928i
$629$	1.47052	−	2.54701i	0.0586334	−	0.101556i
$630$		0			0
$631$	−9.48269	−	16.4245i	−0.377500	−	0.653849i	0.613198	−	0.789929i	$-0.289883\pi$
$631$	−9.48269	−	16.4245i	−0.377500	−	0.653849i	−0.990698	+	0.136080i	$0.956549\pi$
$632$	−20.1001	−	3.54419i	−0.799540	−	0.140980i
$633$		0			0
$634$	9.54535	+	3.47422i	0.379094	+	0.137979i
$635$	1.20425	+	0.438310i	0.0477891	+	0.0173938i
$636$		0			0
$637$	9.39568	+	10.0997i	0.372271	+	0.400166i
$638$	0.509138	−	0.293951i	0.0201570	−	0.0116376i
$639$		0			0
$640$	−12.4710	−	7.20013i	−0.492959	−	0.284610i
$641$	−12.8204	+	15.2788i	−0.506376	+	0.603475i	−0.957303	−	0.289085i	$-0.906649\pi$
$641$	−12.8204	+	15.2788i	−0.506376	+	0.603475i	0.450927	+	0.892561i	$0.351093\pi$
$642$		0			0
$643$	32.5518	−	5.73976i	1.28372	−	0.226354i	0.510160	−	0.860080i	$-0.329586\pi$
$643$	32.5518	−	5.73976i	1.28372	−	0.226354i	0.773558	+	0.633726i	$0.218475\pi$
$644$	−2.70758	−	6.88561i	−0.106693	−	0.271331i
$645$		0			0
$646$	−2.12860	+	0.774746i	−0.0837485	+	0.0304820i
$647$	22.6934			0.892168			0.446084	−	0.894991i	$-0.352818\pi$
$647$	22.6934			0.892168			0.446084	+	0.894991i	$0.352818\pi$
$648$		0			0
$649$		−	2.17925i		−	0.0855431i
$650$	4.08958	−	1.48848i	0.160406	−	0.0583831i
$651$		0			0
$652$	−18.1472	+	15.2273i	−0.710698	+	0.596346i
$653$	−17.5842	+	3.10057i	−0.688122	+	0.121335i	−0.506767	−	0.862083i	$-0.669160\pi$
$653$	−17.5842	+	3.10057i	−0.688122	+	0.121335i	−0.181355	+	0.983418i	$0.558048\pi$
$654$		0			0
$655$	5.00488	+	4.19960i	0.195557	+	0.164092i
$656$	8.06469	−	13.9684i	0.314873	−	0.545376i
$657$		0			0
$658$	12.0470	−	2.44352i	0.469642	−	0.0952583i
$659$	15.8260	+	2.79056i	0.616495	+	0.108705i	0.473170	−	0.880971i	$-0.343109\pi$
$659$	15.8260	+	2.79056i	0.616495	+	0.108705i	0.143325	+	0.989676i	$0.454221\pi$
$660$		0			0
$661$	14.4940	−	39.8218i	0.563750	−	1.54889i	−0.250344	−	0.968157i	$-0.580544\pi$
$661$	14.4940	−	39.8218i	0.563750	−	1.54889i	0.814094	−	0.580733i	$-0.197234\pi$
$662$	−2.41469	+	6.63430i	−0.0938495	+	0.257849i
$663$		0			0
$664$	−41.0528	−	7.23872i	−1.59316	−	0.280917i
$665$	12.1590	−	2.46622i	0.471504	−	0.0956360i
$666$		0			0
$667$	3.56298	−	6.17126i	0.137959	−	0.238952i
$668$	26.0337	+	21.8449i	1.00727	+	0.845203i
$669$		0			0
$670$	−6.11588	+	1.07839i	−0.236277	+	0.0416620i
$671$	1.58467	−	1.32970i	0.0611757	−	0.0513325i
$672$		0			0
$673$	−10.5299	+	3.83256i	−0.405897	+	0.147734i	−0.536897	−	0.843648i	$-0.680403\pi$
$673$	−10.5299	+	3.83256i	−0.405897	+	0.147734i	0.131000	+	0.991382i	$0.458181\pi$
$674$			18.9479i			0.729845i
$675$		0			0
$676$	13.9375			0.536059
$677$	4.46954	−	1.62678i	0.171778	−	0.0625222i	−0.254699	−	0.967020i	$-0.581976\pi$
$677$	4.46954	−	1.62678i	0.171778	−	0.0625222i	0.426478	+	0.904498i	$0.359754\pi$
$678$		0			0
$679$	−4.35406	−	11.0728i	−0.167093	−	0.424934i
$680$	2.99277	−	0.527705i	0.114767	−	0.0202366i
$681$		0			0
$682$	−0.898226	+	1.07046i	−0.0343948	+	0.0409902i
$683$	−22.2708	−	12.8581i	−0.852170	−	0.492001i	0.00921244	−	0.999958i	$-0.497068\pi$
$683$	−22.2708	−	12.8581i	−0.852170	−	0.492001i	−0.861382	+	0.507957i	$0.830401\pi$
$684$		0			0
$685$	−13.4549	+	7.76821i	−0.514086	+	0.296808i
$686$	−5.25134	−	11.5778i	−0.200497	−	0.442043i
$687$		0			0
$688$	1.97639	+	0.719347i	0.0753492	+	0.0274248i
$689$	−6.98261	−	2.54146i	−0.266016	−	0.0968220i
$690$		0			0
$691$	−6.87549	−	1.21234i	−0.261556	−	0.0461194i	0.0413322	−	0.999145i	$-0.486840\pi$
$691$	−6.87549	−	1.21234i	−0.261556	−	0.0461194i	−0.302888	+	0.953026i	$0.597951\pi$
$692$	3.58348	+	6.20677i	0.136223	+	0.235946i
$693$		0			0
$694$	2.65350	−	4.59600i	0.100726	−	0.174462i
$695$	7.88445	−	9.39632i	0.299074	−	0.356423i
$696$		0			0
$697$	1.88676	+	10.7004i	0.0714663	+	0.405305i
$698$	15.8664	−	13.3135i	0.600552	−	0.503923i
$699$		0			0
$700$	13.0090	−	0.332895i	0.491692	−	0.0125822i
$701$			4.24261i			0.160241i	0.996785	+	0.0801206i	$0.0255305\pi$
$701$			4.24261i			0.160241i	−0.996785	+	0.0801206i	$0.974469\pi$
$702$		0			0
$703$		−	10.9929i		−	0.414605i
$704$	−0.0897175	−	0.246497i	−0.00338135	−	0.00929020i
$705$		0			0
$706$	6.24451	+	7.44192i	0.235015	+	0.280080i
$707$	0.384886	−	2.56488i	0.0144751	−	0.0964622i
$708$		0			0
$709$	20.5679	+	17.2586i	0.772445	+	0.648159i	0.941334	−	0.337477i	$-0.109573\pi$
$709$	20.5679	+	17.2586i	0.772445	+	0.648159i	−0.168889	+	0.985635i	$0.554018\pi$
$710$	−6.28148	+	10.8798i	−0.235740	+	0.408313i
$711$		0			0
$712$	14.5268	−	8.38702i	0.544413	−	0.314317i
$713$	−2.94121	+	16.6804i	−0.110149	+	0.624687i
$714$		0			0
$715$	0.543570	+	0.197843i	0.0203283	+	0.00739891i
$716$	−8.31204	+	22.8371i	−0.310635	+	0.853464i
$717$		0			0
$718$	−3.05074	+	17.3016i	−0.113853	+	0.645691i
$719$	−18.0874	−	31.3282i	−0.674545	−	1.16835i	−0.976602	−	0.215057i	$-0.931006\pi$
$719$	−18.0874	−	31.3282i	−0.674545	−	1.16835i	0.302056	−	0.953290i	$-0.402327\pi$
$720$		0			0
$721$	23.4218	+	26.5053i	0.872272	+	0.987108i
$722$	2.94115	−	3.50512i	0.109458	−	0.130447i
$723$		0			0
$724$	−8.37755	+	1.47719i	−0.311349	+	0.0548992i
$725$	8.05623	+	9.60105i	0.299201	+	0.356574i
$726$		0			0
$727$	−6.90637	−	18.9751i	−0.256143	−	0.703748i	−0.999396	−	0.0347375i	$-0.988940\pi$
$727$	−6.90637	−	18.9751i	−0.256143	−	0.703748i	0.743253	−	0.669010i	$-0.233282\pi$
$728$	11.9744	+	4.01450i	0.443799	+	0.148787i
$729$		0			0
$730$	8.13027			0.300915
$731$	−1.33138	+	0.484583i	−0.0492429	+	0.0179230i
$732$		0			0
$733$	−0.867738	−	1.03413i	−0.0320506	−	0.0381965i	0.749781	−	0.661686i	$-0.230159\pi$
$733$	−0.867738	−	1.03413i	−0.0320506	−	0.0381965i	−0.781832	+	0.623490i	$0.785714\pi$
$734$	2.10441	+	11.9347i	0.0776753	+	0.440518i
$735$		0			0
$736$	−8.13022	−	6.82207i	−0.299684	−	0.251465i
$737$	1.29007	+	0.744820i	0.0475202	+	0.0274358i
$738$		0			0
$739$	8.05469	+	13.9511i	0.296297	+	0.513201i	0.975286	−	0.220948i	$-0.0709150\pi$
$739$	8.05469	+	13.9511i	0.296297	+	0.513201i	−0.678989	+	0.734148i	$0.737582\pi$
$740$	−1.10948	+	6.29217i	−0.0407853	+	0.231305i
$741$		0			0
$742$	5.35699	+	4.26636i	0.196661	+	0.156623i
$743$	10.0891	−	27.7195i	0.370132	−	1.01693i	−0.605178	−	0.796090i	$-0.706898\pi$
$743$	10.0891	−	27.7195i	0.370132	−	1.01693i	0.975310	−	0.220840i	$-0.0708798\pi$
$744$		0			0
$745$	−20.0177	−	3.52965i	−0.733390	−	0.129316i
$746$	3.45963	−	1.99742i	0.126666	−	0.0731307i
$747$		0			0
$748$	−0.273495	−	0.157902i	−0.00999995	−	0.00577348i
$749$	42.2498	−	25.8561i	1.54377	−	0.944761i
$750$		0			0
$751$	−1.81313	−	10.2828i	−0.0661622	−	0.375224i	−0.999853	−	0.0171442i	$-0.994543\pi$
$751$	−1.81313	−	10.2828i	−0.0661622	−	0.375224i	0.933691	−	0.358080i	$-0.116569\pi$
$752$	−7.23188	+	6.06827i	−0.263720	+	0.221287i
$753$		0			0
$754$	1.80234	+	4.95189i	0.0656374	+	0.180337i
$755$	15.0503			0.547737
$756$		0			0
$757$	28.0501			1.01950			0.509749	−	0.860323i	$-0.329738\pi$
$757$	28.0501			1.01950			0.509749	+	0.860323i	$0.329738\pi$
$758$	6.58137	+	18.0822i	0.239046	+	0.656774i
$759$		0			0
$760$	8.70135	−	7.30130i	0.315631	−	0.264846i
$761$	4.79778	+	27.2096i	0.173919	+	0.986346i	0.939384	+	0.342867i	$0.111398\pi$
$761$	4.79778	+	27.2096i	0.173919	+	0.986346i	−0.765464	+	0.643478i	$0.777491\pi$
$762$		0			0
$763$	−7.23743	−	11.8262i	−0.262013	−	0.428138i
$764$	−2.42584	−	1.40056i	−0.0877638	−	0.0506704i
$765$		0			0
$766$	0.694392	−	0.400908i	0.0250894	−	0.0144854i
$767$	19.2371	+	3.39202i	0.694611	+	0.122479i
$768$		0			0
$769$	13.9253	−	38.2594i	0.502159	−	1.37967i	−0.387004	−	0.922078i	$-0.626490\pi$
$769$	13.9253	−	38.2594i	0.502159	−	1.37967i	0.889162	−	0.457592i	$-0.151288\pi$
$770$	−0.417021	−	0.332120i	−0.0150284	−	0.0119688i
$771$		0			0
$772$	0.0308230	−	0.174806i	0.00110934	−	0.00629140i
$773$	−10.5422	−	18.2596i	−0.379176	−	0.656752i	0.611767	−	0.791038i	$-0.290459\pi$
$773$	−10.5422	−	18.2596i	−0.379176	−	0.656752i	−0.990943	+	0.134286i	$0.957126\pi$
$774$		0			0
$775$	−25.7993	−	14.8952i	−0.926739	−	0.535053i
$776$	−8.34472	−	7.00205i	−0.299558	−	0.251359i
$777$		0			0
$778$	2.71878	+	15.4190i	0.0974732	+	0.552798i
$779$	26.1051	+	31.1109i	0.935314	+	1.11466i
$780$		0			0
$781$	2.83173	−	1.03066i	0.101327	−	0.0368801i
$782$	1.17982			0.0421901
$783$		0			0
$784$	7.79063	+	5.88523i	0.278237	+	0.210187i
$785$	5.74508	+	15.7845i	0.205051	+	0.563372i
$786$		0			0
$787$	−9.72249	−	11.5868i	−0.346569	−	0.413025i	0.564399	−	0.825502i	$-0.309108\pi$
$787$	−9.72249	−	11.5868i	−0.346569	−	0.413025i	−0.910968	+	0.412477i	$0.864664\pi$
$788$	23.5532	−	4.15306i	0.839048	−	0.147947i
$789$		0			0
$790$	−4.96401	+	5.91588i	−0.176612	+	0.210477i
$791$	−14.3662	−	16.2576i	−0.510804	−	0.578053i
$792$		0			0
$793$	9.27121	+	16.0582i	0.329230	+	0.570244i
$794$	1.80123	−	10.2153i	0.0639234	−	0.362527i
$795$		0			0
$796$	5.03154	−	13.8240i	0.178338	−	0.489980i
$797$	21.7035	+	7.89942i	0.768776	+	0.279812i	0.696484	−	0.717572i	$-0.254746\pi$
$797$	21.7035	+	7.89942i	0.768776	+	0.279812i	0.0722918	+	0.997384i	$0.476969\pi$
$798$		0			0
$799$	1.10433	−	6.26295i	0.0390683	−	0.221567i
$800$	16.1659	−	9.33341i	0.571552	−	0.329986i
$801$		0			0
$802$	−1.32971	+	2.30312i	−0.0469536	+	0.0813260i
$803$	−1.49394	−	1.25356i	−0.0527200	−	0.0442373i
$804$		0			0
$805$	−6.39031	−	0.958931i	−0.225229	−	0.0337979i
$806$	−8.05130	−	9.59516i	−0.283595	−	0.337975i
$807$		0			0
$808$	−0.812149	−	2.23136i	−0.0285713	−	0.0784990i
$809$			28.4204i			0.999209i	0.866254	+	0.499604i	$0.166521\pi$
$809$			28.4204i			0.999209i	−0.866254	+	0.499604i	$0.833479\pi$
$810$		0			0
$811$			19.4101i			0.681580i	0.940139	+	0.340790i	$0.110695\pi$
$811$			19.4101i			0.681580i	−0.940139	+	0.340790i	$0.889305\pi$
$812$	0.403088	+	15.7520i	0.0141456	+	0.552787i
$813$		0			0
$814$	−0.361855	+	0.303633i	−0.0126830	+	0.0106423i
$815$	3.59269	+	20.3752i	0.125846	+	0.713711i
$816$		0			0
$817$	−3.40405	+	4.05678i	−0.119092	+	0.141929i
$818$	8.10897	−	14.0451i	0.283523	−	0.491077i
$819$		0			0
$820$	−11.8023	−	20.4421i	−0.412153	−	0.713870i
$821$	−20.0727	−	3.53937i	−0.700544	−	0.123525i	−0.187979	−	0.982173i	$-0.560194\pi$
$821$	−20.0727	−	3.53937i	−0.700544	−	0.123525i	−0.512565	+	0.858648i	$0.671305\pi$
$822$		0			0
$823$	16.5465	+	6.02243i	0.576774	+	0.209929i	0.613903	−	0.789382i	$-0.289599\pi$
$823$	16.5465	+	6.02243i	0.576774	+	0.209929i	−0.0371281	+	0.999311i	$0.511821\pi$
$824$	30.4309	+	11.0759i	1.06011	+	0.385849i
$825$		0			0
$826$	−15.8160	−	8.59959i	−0.550309	−	0.299218i
$827$	15.2517	−	8.80555i	0.530352	−	0.306199i	−0.210808	−	0.977528i	$-0.567609\pi$
$827$	15.2517	−	8.80555i	0.530352	−	0.306199i	0.741160	+	0.671329i	$0.234276\pi$
$828$		0			0
$829$	35.2758	+	20.3665i	1.22518	+	0.707357i	0.966017	−	0.258477i	$-0.0832206\pi$
$829$	35.2758	+	20.3665i	1.22518	+	0.707357i	0.259161	+	0.965834i	$0.416554\pi$
$830$	−10.1386	+	12.0827i	−0.351915	+	0.419396i
$831$		0			0
$832$	2.31557	−	0.408297i	0.0802778	−	0.0141551i
$833$	−6.56864	+	0.336399i	−0.227590	+	0.0116555i
$834$		0			0
$835$	27.8909	−	10.1514i	0.965203	−	0.351305i
$836$	−1.18040			−0.0408250
$837$		0			0
$838$			14.4685i			0.499806i
$839$	−48.4147	+	17.6215i	−1.67146	+	0.608362i	−0.992101	−	0.125442i	$-0.959965\pi$
$839$	−48.4147	+	17.6215i	−1.67146	+	0.608362i	−0.679361	+	0.733804i	$0.737743\pi$
$840$		0			0
$841$	10.5898	−	8.88589i	0.365165	−	0.306410i
$842$	10.4608	−	1.84451i	0.360501	−	0.0635661i
$843$		0			0
$844$	16.2713	+	13.6533i	0.560082	+	0.469965i
$845$	6.08626	−	10.5417i	0.209374	−	0.362646i
$846$		0			0
$847$	−5.75984	−	28.3971i	−0.197911	−	0.975737i
$848$	−5.17961	−	0.913305i	−0.177869	−	0.0313630i
$849$		0			0
$850$	−0.709721	+	1.94994i	−0.0243432	+	0.0668825i
$851$	−1.95826	+	5.38028i	−0.0671283	+	0.184433i
$852$		0			0
$853$	−34.7100	−	6.12032i	−1.18845	−	0.209556i	−0.455750	−	0.890108i	$-0.650629\pi$
$853$	−34.7100	−	6.12032i	−1.18845	−	0.209556i	−0.732700	+	0.680552i	$0.761740\pi$
$854$	−3.39702	−	16.7480i	−0.116244	−	0.573104i
$855$		0			0
$856$	22.6753	−	39.2747i	0.775024	−	1.34238i
$857$	−11.0923	−	9.30753i	−0.378905	−	0.317939i	0.433367	−	0.901217i	$-0.357325\pi$
$857$	−11.0923	−	9.30753i	−0.378905	−	0.317939i	−0.812272	+	0.583278i	$0.801770\pi$
$858$		0			0
$859$	25.8833	−	4.56392i	0.883125	−	0.155719i	0.286348	−	0.958126i	$-0.407559\pi$
$859$	25.8833	−	4.56392i	0.883125	−	0.155719i	0.596777	+	0.802407i	$0.296448\pi$
$860$	2.35786	−	1.97848i	0.0804025	−	0.0674657i
$861$		0			0
$862$	14.8236	−	5.39535i	0.504894	−	0.183766i
$863$			30.3370i			1.03269i	0.856382	+	0.516343i	$0.172707\pi$
$863$			30.3370i			1.03269i	−0.856382	+	0.516343i	$0.827293\pi$
$864$		0			0
$865$	6.25936			0.212824
$866$	−15.8786	+	5.77935i	−0.539578	+	0.196390i
$867$		0			0
$868$	−13.7059	−	34.8554i	−0.465210	−	1.18307i
$869$	1.82428	−	0.321669i	0.0618843	−	0.0109119i
$870$		0			0
$871$	−8.58280	+	10.2286i	−0.290817	+	0.346582i
$872$	−10.9935	−	6.34707i	−0.372285	−	0.214939i
$873$		0			0
$874$	3.81906	−	2.20493i	0.129182	−	0.0745830i
$875$	13.8663	−	25.5022i	0.468765	−	0.862133i
$876$		0			0
$877$	9.84932	+	3.58486i	0.332588	+	0.121052i	0.502916	−	0.864335i	$-0.332261\pi$
$877$	9.84932	+	3.58486i	0.332588	+	0.121052i	−0.170328	+	0.985387i	$0.554483\pi$
$878$	12.4602	+	4.53515i	0.420512	+	0.153054i
$879$		0			0
$880$	0.403213	+	0.0710973i	0.0135923	+	0.00239669i
$881$	−11.9814	−	20.7524i	−0.403664	−	0.699166i	0.590501	−	0.807037i	$-0.298930\pi$
$881$	−11.9814	−	20.7524i	−0.403664	−	0.699166i	−0.994165	+	0.107871i	$0.965597\pi$
$882$		0			0
$883$	−4.74787	+	8.22356i	−0.159779	+	0.276745i	−0.934789	−	0.355204i	$-0.884411\pi$
$883$	−4.74787	+	8.22356i	−0.159779	+	0.276745i	0.775010	+	0.631949i	$0.217745\pi$
$884$	1.81956	−	2.16847i	0.0611984	−	0.0729334i
$885$		0			0
$886$	−2.38701	−	13.5374i	−0.0801933	−	0.454799i
$887$	−7.75777	+	6.50955i	−0.260481	+	0.218569i	−0.763670	−	0.645607i	$-0.776604\pi$
$887$	−7.75777	+	6.50955i	−0.260481	+	0.218569i	0.503189	+	0.864176i	$0.332160\pi$
$888$		0			0
$889$	−2.53859	+	0.0649616i	−0.0851415	+	0.00217874i
$890$		−	6.34681i		−	0.212746i
$891$		0			0
$892$		−	27.7427i		−	0.928896i
$893$	−8.12999	−	22.3370i	−0.272060	−	0.747478i
$894$		0			0
$895$	13.6433	+	16.2594i	0.456044	+	0.543492i
$896$	28.2188	+	4.23453i	0.942725	+	0.141466i
$897$		0			0
$898$	6.34976	+	5.32808i	0.211894	+	0.177800i
$899$	18.0360	−	31.2393i	0.601535	−	1.04189i
$900$		0			0
$901$	3.06836	−	1.77152i	0.102222	−	0.0590178i
$902$	0.303038	−	1.71862i	0.0100901	−	0.0572237i
$903$		0			0
$904$	−18.6654	−	6.79366i	−0.620803	−	0.225954i
$905$	−2.54104	+	6.98145i	−0.0844671	+	0.232071i
$906$		0			0
$907$	1.43669	−	8.14786i	0.0477044	−	0.270545i	−0.951621	−	0.307275i	$-0.900583\pi$
$907$	1.43669	−	8.14786i	0.0477044	−	0.270545i	0.999325	+	0.0367297i	$0.0116940\pi$
$908$	−19.7687	−	34.2405i	−0.656048	−	1.13631i
$909$		0			0
$910$	3.58084	−	3.16426i	0.118704	−	0.104894i
$911$	−29.3546	+	34.9835i	−0.972562	+	1.15905i	0.0146900	+	0.999892i	$0.495324\pi$
$911$	−29.3546	+	34.9835i	−0.972562	+	1.15905i	−0.987252	+	0.159163i	$0.949121\pi$
$912$		0			0
$913$	3.72593	−	0.656981i	0.123310	−	0.0217429i
$914$	7.86230	+	9.36992i	0.260062	+	0.309929i
$915$		0			0
$916$	5.66902	+	15.5755i	0.187310	+	0.514629i
$917$	−12.2748	−	4.11523i	−0.405350	−	0.135897i
$918$		0			0
$919$	30.8173			1.01657			0.508285	−	0.861189i	$-0.330280\pi$
$919$	30.8173			1.01657			0.508285	+	0.861189i	$0.330280\pi$
$920$	−5.55936	+	2.02344i	−0.183287	+	0.0667109i
$921$		0			0
$922$	−5.20909	−	6.20796i	−0.171552	−	0.204448i
$923$	4.69047	+	26.6010i	0.154389	+	0.875582i
$924$		0			0
$925$	−7.71426	−	6.47303i	−0.253643	−	0.212832i
$926$	−4.48220	−	2.58780i	−0.147294	−	0.0850403i
$927$		0			0
$928$	11.3014	+	19.5746i	0.370988	+	0.642569i
$929$	−2.61616	+	14.8370i	−0.0858334	+	0.486786i	0.911340	+	0.411654i	$0.135049\pi$
$929$	−2.61616	+	14.8370i	−0.0858334	+	0.486786i	−0.997174	+	0.0751316i	$0.976062\pi$
$930$		0			0
$931$	−20.6340	+	13.3649i	−0.676251	+	0.438017i
$932$	−1.42608	+	3.91812i	−0.0467127	+	0.128342i
$933$		0			0
$934$	7.50069	+	1.32257i	0.245430	+	0.0432759i
$935$	−0.238860	+	0.137906i	−0.00781156	+	0.00451000i
$936$		0			0
$937$	3.52097	+	2.03283i	0.115025	+	0.0664097i	0.556409	−	0.830909i	$-0.312179\pi$
$937$	3.52097	+	2.03283i	0.115025	+	0.0664097i	−0.441384	+	0.897318i	$0.645512\pi$
$938$	10.4963	−	6.42354i	0.342716	−	0.209736i
$939$		0			0
$940$	2.39908	+	13.6059i	0.0782495	+	0.443775i
$941$	−7.66760	+	6.43388i	−0.249957	+	0.209738i	−0.759154	−	0.650912i	$-0.774387\pi$
$941$	−7.66760	+	6.43388i	−0.249957	+	0.209738i	0.509197	+	0.860650i	$0.329942\pi$
$942$		0			0
$943$	−7.23464	−	19.8770i	−0.235592	−	0.647285i
$944$	13.8262			0.450003
$945$		0			0
$946$	0.227560			0.00739863
$947$	17.9748	+	49.3853i	0.584102	+	1.60481i	0.781102	+	0.624403i	$0.214658\pi$
$947$	17.9748	+	49.3853i	0.584102	+	1.60481i	−0.197001	+	0.980403i	$0.563120\pi$
$948$		0			0
$949$	13.3910	−	11.2364i	0.434691	−	0.364749i
$950$	1.34684	+	7.63833i	0.0436974	+	0.247820i
$951$		0			0
$952$	−5.13630	+	3.14332i	−0.166468	+	0.101876i
$953$	−40.6849	−	23.4895i	−1.31791	−	0.760898i	−0.334521	−	0.942388i	$-0.608575\pi$
$953$	−40.6849	−	23.4895i	−1.31791	−	0.760898i	−0.983393	+	0.181490i	$0.941908\pi$
$954$		0			0
$955$	−2.11864	+	1.22320i	−0.0685575	+	0.0395817i
$956$	45.5714	+	8.03546i	1.47388	+	0.259885i
$957$		0			0
$958$	0.105623	−	0.290197i	0.00341253	−	0.00937585i
$959$	19.1792	−	24.0821i	0.619328	−	0.777651i
$960$		0			0
$961$	−9.50550	+	53.9084i	−0.306629	+	1.73898i
$962$	−2.11705	−	3.66684i	−0.0682565	−	0.118224i
$963$		0			0
$964$	32.4832	+	18.7542i	1.04621	+	0.604031i
$965$	−0.118755	−	0.0996476i	−0.00382287	−	0.00320777i
$966$		0			0
$967$	1.24818	+	7.07876i	0.0401386	+	0.227638i	0.998278	−	0.0586658i	$-0.0186846\pi$
$967$	1.24818	+	7.07876i	0.0401386	+	0.227638i	−0.958139	+	0.286303i	$0.907574\pi$
$968$	−17.0521	−	20.3219i	−0.548076	−	0.653172i
$969$		0			0
$970$	−3.87312	+	1.40970i	−0.124359	+	0.0452628i
$971$	13.7938			0.442663			0.221331	−	0.975199i	$-0.428960\pi$
$971$	13.7938			0.442663			0.221331	+	0.975199i	$0.428960\pi$
$972$		0			0
$973$	−7.72605	+	23.0451i	−0.247686	+	0.738791i
$974$	−5.72100	−	15.7183i	−0.183313	−	0.503648i
$975$		0			0
$976$	8.43622	+	10.0539i	0.270037	+	0.321817i
$977$	12.3023	−	2.16922i	0.393584	−	0.0693996i	0.0266464	−	0.999645i	$-0.491517\pi$
$977$	12.3023	−	2.16922i	0.393584	−	0.0693996i	0.366938	+	0.930245i	$0.380406\pi$
$978$		0			0
$979$	−0.978581	+	1.16623i	−0.0312756	+	0.0372728i
$980$	13.1594	−	5.56736i	0.420363	−	0.177843i
$981$		0			0
$982$	−4.41271	−	7.64304i	−0.140815	−	0.243899i
$983$	−5.29506	+	30.0298i	−0.168886	+	0.957801i	0.776081	+	0.630634i	$0.217205\pi$
$983$	−5.29506	+	30.0298i	−0.168886	+	0.957801i	−0.944967	+	0.327167i	$0.893906\pi$
$984$		0			0
$985$	7.14405	−	19.6281i	0.227628	−	0.625404i
$986$	−2.36110	−	0.859371i	−0.0751928	−	0.0273679i
$987$		0			0
$988$	1.83730	−	10.4198i	0.0584523	−	0.331500i
$989$	2.38872	−	1.37913i	0.0759569	−	0.0438537i
$990$		0			0
$991$	−26.4504	+	45.8134i	−0.840224	+	1.45531i	0.0494806	+	0.998775i	$0.484243\pi$
$991$	−26.4504	+	45.8134i	−0.840224	+	1.45531i	−0.889705	+	0.456536i	$0.849090\pi$
$992$	−41.1557	−	34.5337i	−1.30670	−	1.09645i
$993$		0			0
$994$	3.69425	−	24.6185i	0.117175	−	0.780850i
$995$	−8.25869	−	9.84233i	−0.261818	−	0.312023i
$996$		0			0
$997$	12.3634	+	33.9682i	0.391553	+	1.07578i	0.966293	+	0.257446i	$0.0828811\pi$
$997$	12.3634	+	33.9682i	0.391553	+	1.07578i	−0.574740	+	0.818336i	$0.694897\pi$
$998$			20.2352i			0.640534i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.62.13		132
3.2	odd	2		189.2.be.a.20.10	yes	132
7.6	odd	2	inner	567.2.be.a.62.14		132
21.20	even	2		189.2.be.a.20.9	✓	132
27.4	even	9		189.2.be.a.104.9	yes	132
27.23	odd	18	inner	567.2.be.a.503.14		132
189.104	even	18	inner	567.2.be.a.503.13		132
189.139	odd	18		189.2.be.a.104.10	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.9	✓	132	21.20	even	2
189.2.be.a.20.10	yes	132	3.2	odd	2
189.2.be.a.104.9	yes	132	27.4	even	9
189.2.be.a.104.10	yes	132	189.139	odd	18
567.2.be.a.62.13		132	1.1	even	1	trivial
567.2.be.a.62.14		132	7.6	odd	2	inner
567.2.be.a.503.13		132	189.104	even	18	inner
567.2.be.a.503.14		132	27.23	odd	18	inner

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.be (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.234777 + 0.645045i) q^{2} +(1.17113 - 0.982692i) q^{4} +(-0.231854 - 1.31491i) q^{5} +(1.38106 + 2.25670i) q^{7} +(2.09779 + 1.21116i) q^{8} +(0.793741 - 0.458267i) q^{10} +(-0.216508 - 0.0381762i) q^{11} +(0.673991 - 1.85178i) q^{13} +(-1.13143 + 1.42066i) q^{14} +(0.242207 - 1.37362i) q^{16} +(0.469803 + 0.813723i) q^{17} +(3.04150 + 1.75601i) q^{19} +(-1.56368 - 1.31208i) q^{20} +(-0.0262057 - 0.148620i) q^{22} +(-1.17579 - 1.40126i) q^{23} +(3.02323 - 1.10037i) q^{25} +1.35272 q^{26} +(3.83503 + 1.28572i) q^{28} +(1.33239 + 3.66070i) q^{29} +(-5.95195 - 7.09326i) q^{31} +(5.71394 - 1.00752i) q^{32} +(-0.414589 + 0.494088i) q^{34} +(2.64715 - 2.33919i) q^{35} +(-1.56504 - 2.71072i) q^{37} +(-0.418631 + 2.37418i) q^{38} +(1.10618 - 3.03921i) q^{40} +(10.8664 + 3.95506i) q^{41} +(-0.261843 + 1.48498i) q^{43} +(-0.291074 + 0.168051i) q^{44} +(0.627824 - 1.08742i) q^{46} +(-5.18484 - 4.35059i) q^{47} +(-3.18536 + 6.23325i) q^{49} +(1.41957 + 1.69178i) q^{50} +(-1.03040 - 2.83099i) q^{52} -3.77077i q^{53} +0.293540i q^{55} +(0.163947 + 6.40675i) q^{56} +(-2.04850 + 1.71890i) q^{58} +(1.72130 + 9.76195i) q^{59} +(-6.04827 + 7.20805i) q^{61} +(3.17809 - 5.50461i) q^{62} +(0.596586 + 1.03332i) q^{64} +(-2.59119 - 0.456896i) q^{65} +(-6.36714 - 2.31745i) q^{67} +(1.34984 + 0.491301i) q^{68} +(2.13037 + 1.15834i) q^{70} +(-11.8706 + 6.85351i) q^{71} +(7.68223 + 4.43534i) q^{73} +(1.38110 - 1.64593i) q^{74} +(5.28760 - 0.932347i) q^{76} +(-0.212858 - 0.541316i) q^{77} +(-7.91776 + 2.88183i) q^{79} -1.86235 q^{80} +7.93789i q^{82} +(-16.1714 + 5.88589i) q^{83} +(0.961047 - 0.806414i) q^{85} +(-1.01936 + 0.179740i) q^{86} +(-0.407950 - 0.342311i) q^{88} +(3.46240 - 5.99705i) q^{89} +(5.10972 - 1.03641i) q^{91} +(-2.75401 - 0.485606i) q^{92} +(1.58905 - 4.36587i) q^{94} +(1.60381 - 4.40644i) q^{95} +(-4.42872 - 0.780904i) q^{97} +(-4.76858 - 0.591277i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Introduction

L-functions

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