LMFDB - Embedded newform 567.2.ba.a.341.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(143,567)] 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("567.143"); 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, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (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			341.6
Character	$\chi$	$=$	567.341
Dual form			567.2.ba.a.143.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02575 - 1.22245i) q^{2} +(-0.0949069 + 0.538244i) q^{4} +(-1.45366 - 1.21977i) q^{5} +(-2.50057 + 0.864386i) q^{7} +(-2.00866 + 1.15970i) q^{8} +3.02821i q^{10} +(-0.811915 - 0.967602i) q^{11} +(-0.326917 - 0.898197i) q^{13} +(3.62163 + 2.17016i) q^{14} +(4.50524 + 1.63977i) q^{16} +4.01374 q^{17} +7.67461i q^{19} +(0.794495 - 0.666660i) q^{20} +(-0.350017 + 1.98504i) q^{22} +(1.95808 + 5.37979i) q^{23} +(-0.242940 - 1.37778i) q^{25} +(-0.762661 + 1.32097i) q^{26} +(-0.227929 - 1.42795i) q^{28} +(1.22870 - 3.37583i) q^{29} +(-8.76565 - 1.54562i) q^{31} +(-1.03017 - 2.83037i) q^{32} +(-4.11711 - 4.90658i) q^{34} +(4.68933 + 1.79359i) q^{35} +(3.99935 + 6.92708i) q^{37} +(9.38179 - 7.87226i) q^{38} +(4.33449 + 0.764287i) q^{40} +(-3.01647 + 1.09790i) q^{41} +(0.111496 + 0.632326i) q^{43} +(0.597862 - 0.345176i) q^{44} +(4.56799 - 7.91199i) q^{46} +(1.48485 + 8.42098i) q^{47} +(5.50567 - 4.32291i) q^{49} +(-1.43506 + 1.71024i) q^{50} +(0.514475 - 0.0907159i) q^{52} +(-11.3329 + 6.54305i) q^{53} +2.39691i q^{55} +(4.02037 - 4.63618i) q^{56} +(-5.38712 + 1.96075i) q^{58} +(2.02915 - 0.738551i) q^{59} +(-3.03575 + 0.535284i) q^{61} +(7.10196 + 12.3010i) q^{62} +(2.39111 - 4.14152i) q^{64} +(-0.620364 + 1.70444i) q^{65} +(1.63854 + 1.37490i) q^{67} +(-0.380931 + 2.16037i) q^{68} +(-2.61754 - 7.57223i) q^{70} +(0.154696 + 0.0893139i) q^{71} +(9.96274 + 5.75199i) q^{73} +(4.36563 - 11.9945i) q^{74} +(-4.13081 - 0.728373i) q^{76} +(2.86663 + 1.71775i) q^{77} +(-0.935206 + 0.784731i) q^{79} +(-4.54896 - 7.87903i) q^{80} +(4.43628 + 2.56129i) q^{82} +(-5.11532 - 1.86183i) q^{83} +(-5.83462 - 4.89582i) q^{85} +(0.658617 - 0.784910i) q^{86} +(2.75300 + 1.00201i) q^{88} -5.63916 q^{89} +(1.59387 + 1.96342i) q^{91} +(-3.08147 + 0.543347i) q^{92} +(8.77111 - 10.4530i) q^{94} +(9.36123 - 11.1563i) q^{95} +(-5.97585 + 1.05370i) q^{97} +(-10.9320 - 2.29615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.02575	−	1.22245i	−0.725318	−	0.864400i	0.269818	−	0.962911i	$-0.413036\pi$
$2$	−1.02575	−	1.22245i	−0.725318	−	0.864400i	−0.995136	+	0.0985112i	$0.968592\pi$
$3$		0			0
$3$		0			0
$4$	−0.0949069	+	0.538244i	−0.0474534	+	0.269122i
$5$	−1.45366	−	1.21977i	−0.650097	−	0.545497i	0.257003	−	0.966411i	$-0.417265\pi$
$5$	−1.45366	−	1.21977i	−0.650097	−	0.545497i	−0.907101	+	0.420914i	$0.861709\pi$
$6$		0			0
$7$	−2.50057	+	0.864386i	−0.945126	+	0.326707i
$7$	−2.50057	+	0.864386i	−0.945126	+	0.326707i
$8$	−2.00866	+	1.15970i	−0.710170	+	0.410017i
$9$		0			0
$10$			3.02821i			0.957603i
$11$	−0.811915	−	0.967602i	−0.244802	−	0.291743i	0.629627	−	0.776898i	$-0.283208\pi$
$11$	−0.811915	−	0.967602i	−0.244802	−	0.291743i	−0.874428	+	0.485155i	$0.838763\pi$
$12$		0			0
$13$	−0.326917	−	0.898197i	−0.0906704	−	0.249115i	0.886066	−	0.463560i	$-0.153428\pi$
$13$	−0.326917	−	0.898197i	−0.0906704	−	0.249115i	−0.976736	+	0.214445i	$0.931206\pi$
$14$	3.62163	+	2.17016i	0.967922	+	0.580000i
$15$		0			0
$16$	4.50524	+	1.63977i	1.12631	+	0.409944i
$17$	4.01374			0.973474			0.486737	−	0.873549i	$-0.338187\pi$
$17$	4.01374			0.973474			0.486737	+	0.873549i	$0.338187\pi$
$18$		0			0
$19$			7.67461i			1.76068i	0.474348	+	0.880338i	$0.342684\pi$
$19$			7.67461i			1.76068i	−0.474348	+	0.880338i	$0.657316\pi$
$20$	0.794495	−	0.666660i	0.177654	−	0.149070i
$21$		0			0
$22$	−0.350017	+	1.98504i	−0.0746239	+	0.423213i
$23$	1.95808	+	5.37979i	0.408288	+	1.12176i	0.958090	+	0.286468i	$0.0924812\pi$
$23$	1.95808	+	5.37979i	0.408288	+	1.12176i	−0.549801	+	0.835295i	$0.685297\pi$
$24$		0			0
$25$	−0.242940	−	1.37778i	−0.0485879	−	0.275556i
$26$	−0.762661	+	1.32097i	−0.149570	+	0.259063i
$27$		0			0
$28$	−0.227929	−	1.42795i	−0.0430745	−	0.269857i
$29$	1.22870	−	3.37583i	0.228164	−	0.626876i	−0.771795	−	0.635871i	$-0.780641\pi$
$29$	1.22870	−	3.37583i	0.228164	−	0.626876i	0.999960	+	0.00899503i	$0.00286324\pi$
$30$		0			0
$31$	−8.76565	−	1.54562i	−1.57436	−	0.277602i	−0.682833	−	0.730575i	$-0.739252\pi$
$31$	−8.76565	−	1.54562i	−1.57436	−	0.277602i	−0.891524	+	0.452973i	$0.850363\pi$
$32$	−1.03017	−	2.83037i	−0.182110	−	0.500343i
$33$		0			0
$34$	−4.11711	−	4.90658i	−0.706078	−	0.841471i
$35$	4.68933	+	1.79359i	0.792641	+	0.303171i
$36$		0			0
$37$	3.99935	+	6.92708i	0.657489	+	1.13880i	0.981264	+	0.192670i	$0.0617148\pi$
$37$	3.99935	+	6.92708i	0.657489	+	1.13880i	−0.323774	+	0.946134i	$0.604952\pi$
$38$	9.38179	−	7.87226i	1.52193	−	1.27705i
$39$		0			0
$40$	4.33449	+	0.764287i	0.685343	+	0.120844i
$41$	−3.01647	+	1.09790i	−0.471093	+	0.171464i	−0.566647	−	0.823960i	$-0.691760\pi$
$41$	−3.01647	+	1.09790i	−0.471093	+	0.171464i	0.0955544	+	0.995424i	$0.469538\pi$
$42$		0			0
$43$	0.111496	+	0.632326i	0.0170030	+	0.0964289i	0.992128	−	0.125226i	$-0.0399654\pi$
$43$	0.111496	+	0.632326i	0.0170030	+	0.0964289i	−0.975125	+	0.221654i	$0.928854\pi$
$44$	0.597862	−	0.345176i	0.0901311	−	0.0520372i
$45$		0			0
$46$	4.56799	−	7.91199i	0.673513	−	1.16656i
$47$	1.48485	+	8.42098i	0.216587	+	1.22833i	0.878131	+	0.478420i	$0.158790\pi$
$47$	1.48485	+	8.42098i	0.216587	+	1.22833i	−0.661544	+	0.749906i	$0.730099\pi$
$48$		0			0
$49$	5.50567	−	4.32291i	0.786525	−	0.617558i
$50$	−1.43506	+	1.71024i	−0.202949	+	0.241865i
$51$		0			0
$52$	0.514475	−	0.0907159i	0.0713449	−	0.0125800i
$53$	−11.3329	+	6.54305i	−1.55669	+	0.898757i	−0.559123	+	0.829085i	$0.688862\pi$
$53$	−11.3329	+	6.54305i	−1.55669	+	0.898757i	−0.997570	+	0.0696726i	$0.977805\pi$
$54$		0			0
$55$			2.39691i			0.323200i
$56$	4.02037	−	4.63618i	0.537245	−	0.619535i
$57$		0			0
$58$	−5.38712	+	1.96075i	−0.707363	+	0.257459i
$59$	2.02915	−	0.738551i	0.264173	−	0.0961512i	−0.206538	−	0.978439i	$-0.566220\pi$
$59$	2.02915	−	0.738551i	0.264173	−	0.0961512i	0.470711	+	0.882287i	$0.343997\pi$
$60$		0			0
$61$	−3.03575	+	0.535284i	−0.388688	+	0.0685361i	−0.364577	−	0.931173i	$-0.618786\pi$
$61$	−3.03575	+	0.535284i	−0.388688	+	0.0685361i	−0.0241106	+	0.999709i	$0.507675\pi$
$62$	7.10196	+	12.3010i	0.901950	+	1.56222i
$63$		0			0
$64$	2.39111	−	4.14152i	0.298889	−	0.517690i
$65$	−0.620364	+	1.70444i	−0.0769467	+	0.211409i
$66$		0			0
$67$	1.63854	+	1.37490i	0.200180	+	0.167971i	0.737367	−	0.675492i	$-0.236069\pi$
$67$	1.63854	+	1.37490i	0.200180	+	0.167971i	−0.537187	+	0.843463i	$0.680513\pi$
$68$	−0.380931	+	2.16037i	−0.0461947	+	0.261983i
$69$		0			0
$70$	−2.61754	−	7.57223i	−0.312856	−	0.905055i
$71$	0.154696	+	0.0893139i	0.0183591	+	0.0105996i	0.509151	−	0.860677i	$-0.329959\pi$
$71$	0.154696	+	0.0893139i	0.0183591	+	0.0105996i	−0.490792	+	0.871277i	$0.663293\pi$
$72$		0			0
$73$	9.96274	+	5.75199i	1.16605	+	0.673220i	0.952747	−	0.303766i	$-0.0982442\pi$
$73$	9.96274	+	5.75199i	1.16605	+	0.673220i	0.213304	+	0.976986i	$0.431578\pi$
$74$	4.36563	−	11.9945i	0.507494	−	1.39433i
$75$		0			0
$76$	−4.13081	−	0.728373i	−0.473836	−	0.0835501i
$77$	2.86663	+	1.71775i	0.326683	+	0.195756i
$78$		0			0
$79$	−0.935206	+	0.784731i	−0.105219	+	0.0882891i	−0.693879	−	0.720091i	$-0.744100\pi$
$79$	−0.935206	+	0.784731i	−0.105219	+	0.0882891i	0.588661	+	0.808380i	$0.299655\pi$
$80$	−4.54896	−	7.87903i	−0.508589	−	0.880902i
$81$		0			0
$82$	4.43628	+	2.56129i	0.489906	+	0.282847i
$83$	−5.11532	−	1.86183i	−0.561480	−	0.204362i	0.0456599	−	0.998957i	$-0.485461\pi$
$83$	−5.11532	−	1.86183i	−0.561480	−	0.204362i	−0.607140	+	0.794595i	$0.707683\pi$
$84$		0			0
$85$	−5.83462	−	4.89582i	−0.632853	−	0.531027i
$86$	0.658617	−	0.784910i	0.0710205	−	0.0846390i
$87$		0			0
$88$	2.75300	+	1.00201i	0.293470	+	0.106814i
$89$	−5.63916			−0.597750			−0.298875	−	0.954292i	$-0.596611\pi$
$89$	−5.63916			−0.597750			−0.298875	+	0.954292i	$0.596611\pi$
$90$		0			0
$91$	1.59387	+	1.96342i	0.167083	+	0.205822i
$92$	−3.08147	+	0.543347i	−0.321266	+	0.0566478i
$93$		0			0
$94$	8.77111	−	10.4530i	0.904671	−	1.07814i
$95$	9.36123	−	11.1563i	0.960442	−	1.14461i
$96$		0			0
$97$	−5.97585	+	1.05370i	−0.606755	+	0.106987i	−0.468581	−	0.883421i	$-0.655235\pi$
$97$	−5.97585	+	1.05370i	−0.606755	+	0.106987i	−0.138174	+	0.990408i	$0.544123\pi$
$98$	−10.9320	−	2.29615i	−1.10430	−	0.231946i
$99$		0			0
$100$	0.764638			0.0764638
$101$	−6.52215	−	2.37387i	−0.648978	−	0.236209i	−0.00350738	−	0.999994i	$-0.501116\pi$
$101$	−6.52215	−	2.37387i	−0.648978	−	0.236209i	−0.645470	+	0.763785i	$0.723339\pi$
$102$		0			0
$103$	−8.28238	+	9.87055i	−0.816087	+	0.972574i	−0.999946	−	0.0103782i	$-0.996696\pi$
$103$	−8.28238	+	9.87055i	−0.816087	+	0.972574i	0.183859	+	0.982953i	$0.441141\pi$
$104$	1.69831	+	1.42505i	0.166533	+	0.139738i
$105$		0			0
$106$	19.6233	+	7.14230i	1.90598	+	0.693721i
$107$	−1.24002	−	0.715923i	−0.119877	−	0.0692109i	0.438863	−	0.898554i	$-0.355381\pi$
$107$	−1.24002	−	0.715923i	−0.119877	−	0.0692109i	−0.558739	+	0.829343i	$0.688715\pi$
$108$		0			0
$109$	−0.946256	−	1.63896i	−0.0906349	−	0.156984i	0.817144	−	0.576434i	$-0.195556\pi$
$109$	−0.946256	−	1.63896i	−0.0906349	−	0.156984i	−0.907778	+	0.419450i	$0.862223\pi$
$110$	2.93010	−	2.45865i	0.279374	−	0.234423i
$111$		0			0
$112$	−12.6831	−	0.206099i	−1.19844	−	0.0194745i
$113$	−0.855475	−	0.150843i	−0.0804763	−	0.0141901i	0.133265	−	0.991080i	$-0.457454\pi$
$113$	−0.855475	−	0.150843i	−0.0804763	−	0.0141901i	−0.213741	+	0.976890i	$0.568565\pi$
$114$		0			0
$115$	3.71570	−	10.2088i	0.346491	−	0.951976i
$116$	1.70041	+	0.981731i	0.157879	+	0.0911514i
$117$		0			0
$118$	−2.98425	−	1.72296i	−0.274723	−	0.158611i
$119$	−10.0366	+	3.46942i	−0.920055	+	0.318041i
$120$		0			0
$121$	1.63308	−	9.26166i	0.148462	−	0.841969i
$122$	3.76829	+	3.16197i	0.341165	+	0.286271i
$123$		0			0
$124$	1.66384	−	4.57136i	0.149417	−	0.410521i
$125$	−6.07147	+	10.5161i	−0.543049	+	0.940588i
$126$		0			0
$127$	−6.79273	−	11.7654i	−0.602757	−	1.04401i	−0.992402	−	0.123041i	$-0.960735\pi$
$127$	−6.79273	−	11.7654i	−0.602757	−	1.04401i	0.389644	−	0.920965i	$-0.372598\pi$
$128$	−13.4480	+	2.37124i	−1.18865	+	0.209590i
$129$		0			0
$130$	2.71992	−	0.989972i	0.238553	−	0.0868263i
$131$	−8.52376	+	3.10240i	−0.744725	+	0.271058i	−0.686384	−	0.727239i	$-0.740803\pi$
$131$	−8.52376	+	3.10240i	−0.744725	+	0.271058i	−0.0583404	+	0.998297i	$0.518581\pi$
$132$		0			0
$133$	−6.63382	−	19.1909i	−0.575225	−	1.66406i
$134$		−	3.41334i		−	0.294867i
$135$		0			0
$136$	−8.06225	+	4.65474i	−0.691332	+	0.399141i
$137$	−19.7829	+	3.48826i	−1.69017	+	0.298022i	−0.934243	−	0.356638i	$-0.883923\pi$
$137$	−19.7829	+	3.48826i	−1.69017	+	0.298022i	−0.755923	+	0.654660i	$0.772812\pi$
$138$		0			0
$139$	−4.91571	+	5.85831i	−0.416945	+	0.496895i	−0.933109	−	0.359594i	$-0.882915\pi$
$139$	−4.91571	+	5.85831i	−0.416945	+	0.496895i	0.516164	+	0.856490i	$0.327360\pi$
$140$	−1.41044	+	2.35378i	−0.119204	+	0.198931i
$141$		0			0
$142$	−0.0494988	−	0.280722i	−0.00415385	−	0.0235577i
$143$	−0.603669	+	1.04558i	−0.0504813	+	0.0874362i
$144$		0			0
$145$	−5.90385	+	3.40859i	−0.490288	+	0.283068i
$146$	−3.18782	−	18.0790i	−0.263826	−	1.49623i
$147$		0			0
$148$	−4.10802	+	1.49520i	−0.337677	+	0.122904i
$149$	7.28668	+	1.28484i	0.596948	+	0.105258i	0.463955	−	0.885859i	$-0.346430\pi$
$149$	7.28668	+	1.28484i	0.596948	+	0.105258i	0.132993	+	0.991117i	$0.457541\pi$
$150$		0			0
$151$	−4.72726	+	3.96664i	−0.384699	+	0.322801i	−0.814544	−	0.580102i	$-0.803013\pi$
$151$	−4.72726	+	3.96664i	−0.384699	+	0.322801i	0.429845	+	0.902903i	$0.358568\pi$
$152$	−8.90026	−	15.4157i	−0.721907	−	1.25038i
$153$		0			0
$154$	−0.840603	−	5.26629i	−0.0677377	−	0.424370i
$155$	10.8570	+	12.9389i	0.872055	+	1.03927i
$156$		0			0
$157$	6.49586	+	17.8472i	0.518426	+	1.42436i	0.872254	+	0.489053i	$0.162658\pi$
$157$	6.49586	+	17.8472i	0.518426	+	1.42436i	−0.353828	+	0.935311i	$0.615120\pi$
$158$	1.91858	+	0.338298i	0.152634	+	0.0269135i
$159$		0			0
$160$	−1.95487	+	5.37096i	−0.154546	+	0.424612i
$161$	−9.54653	−	11.7600i	−0.752372	−	0.926817i
$162$		0			0
$163$	−0.709039	+	1.22809i	−0.0555362	+	0.0961915i	−0.892457	−	0.451133i	$-0.851020\pi$
$163$	−0.709039	+	1.22809i	−0.0555362	+	0.0961915i	0.836921	+	0.547324i	$0.184353\pi$
$164$	−0.304657	−	1.72779i	−0.0237897	−	0.134918i
$165$		0			0
$166$	2.97108	+	8.16299i	0.230601	+	0.633571i
$167$	−2.73878	+	15.5324i	−0.211933	+	1.20193i	0.674217	+	0.738533i	$0.264481\pi$
$167$	−2.73878	+	15.5324i	−0.211933	+	1.20193i	−0.886150	+	0.463398i	$0.846630\pi$
$168$		0			0
$169$	9.25869	−	7.76897i	0.712207	−	0.597613i
$170$			12.1544i			0.932201i
$171$		0			0
$172$	−0.350927			−0.0267580
$173$	10.2513	+	3.73118i	0.779394	+	0.283676i	0.700920	−	0.713240i	$-0.252773\pi$
$173$	10.2513	+	3.73118i	0.779394	+	0.283676i	0.0784741	+	0.996916i	$0.474995\pi$
$174$		0			0
$175$	1.79842	+	3.23524i	0.135948	+	0.244561i
$176$	−2.07122	−	5.69064i	−0.156124	−	0.428948i
$177$		0			0
$178$	5.78440	+	6.89357i	0.433559	+	0.516695i
$179$		−	23.6413i		−	1.76703i	−0.468403	−	0.883515i	$-0.655170\pi$
$179$		−	23.6413i		−	1.76703i	0.468403	−	0.883515i	$-0.344830\pi$
$180$		0			0
$181$	−18.7421	+	10.8208i	−1.39309	+	0.804301i	−0.993656	−	0.112461i	$-0.964127\pi$
$181$	−18.7421	+	10.8208i	−1.39309	+	0.804301i	−0.399434	+	0.916762i	$0.630793\pi$
$182$	0.765260	−	3.96240i	0.0567248	−	0.293713i
$183$		0			0
$184$	−10.1721	−	8.53540i	−0.749896	−	0.629238i
$185$	2.63572	−	14.9479i	0.193782	−	1.09899i
$186$		0			0
$187$	−3.25881	−	3.88370i	−0.238308	−	0.284004i
$188$	−4.67346			−0.340847
$189$		0			0
$190$	−23.2403			−1.68603
$191$	14.0821	+	16.7824i	1.01894	+	1.21433i	0.976564	+	0.215228i	$0.0690495\pi$
$191$	14.0821	+	16.7824i	1.01894	+	1.21433i	0.0423797	+	0.999102i	$0.486506\pi$
$192$		0			0
$193$	2.52946	−	14.3453i	0.182074	−	1.03259i	−0.747583	−	0.664169i	$-0.768786\pi$
$193$	2.52946	−	14.3453i	0.182074	−	1.03259i	0.929657	−	0.368426i	$-0.120103\pi$
$194$	7.41785	+	6.22431i	0.532570	+	0.446880i
$195$		0			0
$196$	1.80425	+	3.37367i	0.128875	+	0.240976i
$197$	2.06396	−	1.19163i	0.147051	−	0.0849001i	−0.424669	−	0.905349i	$-0.639610\pi$
$197$	2.06396	−	1.19163i	0.147051	−	0.0849001i	0.571720	+	0.820449i	$0.306276\pi$
$198$		0			0
$199$		−	10.2598i		−	0.727298i	−0.931536	−	0.363649i	$-0.881531\pi$
$199$		−	10.2598i		−	0.727298i	0.931536	−	0.363649i	$-0.118469\pi$
$200$	2.08580	+	2.48576i	0.147488	+	0.175770i
$201$		0			0
$202$	3.78819	+	10.4080i	0.266536	+	0.732303i
$203$	−0.154432	+	9.50356i	−0.0108390	+	0.667019i
$204$		0			0
$205$	5.72411	+	2.08341i	0.399789	+	0.145511i
$206$	20.5619			1.43262
$207$		0			0
$208$		−	4.58267i		−	0.317751i
$209$	7.42597	−	6.23113i	0.513665	−	0.431016i
$210$		0			0
$211$	−1.98228	+	11.2421i	−0.136466	+	0.773938i	0.837361	+	0.546650i	$0.184097\pi$
$211$	−1.98228	+	11.2421i	−0.136466	+	0.773938i	−0.973828	+	0.227288i	$0.927014\pi$
$212$	−2.44619	−	6.72084i	−0.168005	−	0.461589i
$213$		0			0
$214$	0.396774	+	2.25021i	0.0271229	+	0.153821i
$215$	0.609213	−	1.05519i	0.0415480	−	0.0719632i
$216$		0			0
$217$	23.2551	−	3.71197i	1.57866	−	0.251985i
$218$	−1.03292	+	2.83792i	−0.0699581	+	0.192208i
$219$		0			0
$220$	−1.29012	−	0.227484i	−0.0869801	−	0.0153369i
$221$	−1.31216	−	3.60512i	−0.0882653	−	0.242507i
$222$		0			0
$223$	−7.05545	−	8.40836i	−0.472468	−	0.563065i	0.476201	−	0.879336i	$-0.342013\pi$
$223$	−7.05545	−	8.40836i	−0.472468	−	0.563065i	−0.948669	+	0.316271i	$0.897569\pi$
$224$	5.02254	+	6.18706i	0.335582	+	0.413390i
$225$		0			0
$226$	0.693109	+	1.20050i	0.0461049	+	0.0798561i
$227$	−11.5294	+	9.67429i	−0.765231	+	0.642105i	−0.939483	−	0.342596i	$-0.888694\pi$
$227$	−11.5294	+	9.67429i	−0.765231	+	0.642105i	0.174252	+	0.984701i	$0.444249\pi$
$228$		0			0
$229$	−22.1302	−	3.90215i	−1.46240	−	0.257861i	−0.614881	−	0.788620i	$-0.710796\pi$
$229$	−22.1302	−	3.90215i	−1.46240	−	0.257861i	−0.847523	+	0.530758i	$0.821907\pi$
$230$	−16.2911	+	5.92948i	−1.07420	+	0.390978i
$231$		0			0
$232$	1.44691	+	8.20584i	0.0949944	+	0.538740i
$233$	25.4109	−	14.6710i	1.66472	−	0.961128i	0.694310	−	0.719676i	$-0.255710\pi$
$233$	25.4109	−	14.6710i	1.66472	−	0.961128i	0.970413	−	0.241452i	$-0.0776236\pi$
$234$		0			0
$235$	8.11317	−	14.0524i	0.529245	−	0.916679i
$236$	0.204940	+	1.16227i	0.0133405	+	0.0756575i
$237$		0			0
$238$	14.5363	+	8.71046i	0.942247	+	0.564615i
$239$	17.8608	−	21.2856i	1.15532	−	1.37685i	0.241661	−	0.970361i	$-0.422308\pi$
$239$	17.8608	−	21.2856i	1.15532	−	1.37685i	0.913655	−	0.406491i	$-0.133248\pi$
$240$		0			0
$241$	0.0739095	−	0.0130322i	0.00476093	−	0.000839480i	−0.171267	−	0.985225i	$-0.554786\pi$
$241$	0.0739095	−	0.0130322i	0.00476093	−	0.000839480i	0.176028	+	0.984385i	$0.443675\pi$
$242$	−12.9970	+	7.50384i	−0.835481	+	0.482365i
$243$		0			0
$244$		−	1.68477i		−	0.107857i
$245$	−13.2763	−	0.431593i	−0.848194	−	0.0275735i
$246$		0			0
$247$	6.89331	−	2.50896i	0.438611	−	0.159641i
$248$	19.3997	−	7.06092i	1.23188	−	0.448369i
$249$		0			0
$250$	19.0832	−	3.36488i	1.20693	−	0.212814i
$251$	9.64254	+	16.7014i	0.608632	+	1.05418i	0.991466	+	0.130364i	$0.0416147\pi$
$251$	9.64254	+	16.7014i	0.608632	+	1.05418i	−0.382834	+	0.923817i	$0.625052\pi$
$252$		0			0
$253$	3.61570	−	6.26258i	0.227317	−	0.393725i
$254$	−7.41484	+	20.3721i	−0.465248	+	1.27826i
$255$		0			0
$256$	9.36627	+	7.85923i	0.585392	+	0.491202i
$257$	0.541867	−	3.07308i	0.0338008	−	0.191694i	−0.963232	−	0.268671i	$-0.913416\pi$
$257$	0.541867	−	3.07308i	0.0338008	−	0.191694i	0.997033	+	0.0769770i	$0.0245268\pi$
$258$		0			0
$259$	−15.9883	−	13.8646i	−0.993465	−	0.861507i
$260$	−0.858526	−	0.495670i	−0.0532435	−	0.0307402i
$261$		0			0
$262$	12.5358	+	7.23755i	0.774464	+	0.447137i
$263$	−1.49413	+	4.10510i	−0.0921322	+	0.253131i	−0.977196	−	0.212338i	$-0.931892\pi$
$263$	−1.49413	+	4.10510i	−0.0921322	+	0.253131i	0.885064	+	0.465469i	$0.154114\pi$
$264$		0			0
$265$	24.4552	+	4.31211i	1.50227	+	0.264891i
$266$	−16.6551	+	27.7946i	−1.02119	+	1.70420i
$267$		0			0
$268$	−0.895540	+	0.751447i	−0.0547038	+	0.0459019i
$269$	−0.429514	−	0.743940i	−0.0261879	−	0.0453588i	0.852634	−	0.522508i	$-0.175003\pi$
$269$	−0.429514	−	0.743940i	−0.0261879	−	0.0453588i	−0.878822	+	0.477149i	$0.841670\pi$
$270$		0			0
$271$	4.73193	+	2.73198i	0.287444	+	0.165956i	0.636789	−	0.771038i	$-0.280262\pi$
$271$	4.73193	+	2.73198i	0.287444	+	0.165956i	−0.349344	+	0.936994i	$0.613596\pi$
$272$	18.0829	+	6.58162i	1.09643	+	0.399069i
$273$		0			0
$274$	24.5566	+	20.6054i	1.48352	+	1.24482i
$275$	−1.13590	+	1.35371i	−0.0684971	+	0.0816317i
$276$		0			0
$277$	18.3788	+	6.68933i	1.10427	+	0.401923i	0.828890	−	0.559412i	$-0.188973\pi$
$277$	18.3788	+	6.68933i	1.10427	+	0.401923i	0.275383	+	0.961334i	$0.411195\pi$
$278$	12.2038			0.731934
$279$		0			0
$280$	−11.4993	+	1.83552i	−0.687216	+	0.109693i
$281$	13.1907	−	2.32587i	0.786890	−	0.138750i	0.234257	−	0.972175i	$-0.424734\pi$
$281$	13.1907	−	2.32587i	0.786890	−	0.138750i	0.552633	+	0.833425i	$0.313623\pi$
$282$		0			0
$283$	6.91516	−	8.24117i	0.411064	−	0.489886i	−0.520297	−	0.853986i	$-0.674179\pi$
$283$	6.91516	−	8.24117i	0.411064	−	0.489886i	0.931360	+	0.364099i	$0.118623\pi$
$284$	−0.0627544	+	0.0747877i	−0.00372379	+	0.00443784i
$285$		0			0
$286$	1.89739	−	0.334561i	0.112195	−	0.0197830i
$287$	6.59387	−	5.35278i	0.389224	−	0.315964i
$288$		0			0
$289$	−0.889923			−0.0523484
$290$	10.2227	+	3.72076i	0.600298	+	0.218491i
$291$		0			0
$292$	−4.04151	+	4.81648i	−0.236511	+	0.281863i
$293$	−6.87623	−	5.76984i	−0.401714	−	0.337078i	0.419442	−	0.907782i	$-0.362226\pi$
$293$	−6.87623	−	5.76984i	−0.401714	−	0.337078i	−0.821156	+	0.570704i	$0.806670\pi$
$294$		0			0
$295$	−3.85056	−	1.40149i	−0.224188	−	0.0815979i
$296$	−16.0667	−	9.27612i	−0.933858	−	0.539163i
$297$		0			0
$298$	−5.90370	−	10.2255i	−0.341992	−	0.592348i
$299$	4.19198	−	3.51749i	0.242428	−	0.203422i
$300$		0			0
$301$	−0.825378	−	1.48480i	−0.0475740	−	0.0855824i
$302$	9.69802	+	1.71002i	0.558058	+	0.0984007i
$303$		0			0
$304$	−12.5846	+	34.5760i	−0.721778	+	1.98307i
$305$	5.06588	+	2.92478i	0.290071	+	0.167473i
$306$		0			0
$307$	17.4494	+	10.0744i	0.995890	+	0.574977i	0.907030	−	0.421067i	$-0.138344\pi$
$307$	17.4494	+	10.0744i	0.995890	+	0.574977i	0.0888603	+	0.996044i	$0.471678\pi$
$308$	−1.19663	+	1.37992i	−0.0681843	+	0.0786282i
$309$		0			0
$310$	4.68046	−	26.5442i	0.265832	−	1.50761i
$311$	2.17551	+	1.82547i	0.123362	+	0.103513i	0.702382	−	0.711801i	$-0.252120\pi$
$311$	2.17551	+	1.82547i	0.123362	+	0.103513i	−0.579020	+	0.815314i	$0.696565\pi$
$312$		0			0
$313$	−3.18984	+	8.76400i	−0.180300	+	0.495371i	−0.996613	−	0.0822401i	$-0.973793\pi$
$313$	−3.18984	+	8.76400i	−0.180300	+	0.495371i	0.816312	+	0.577611i	$0.196015\pi$
$314$	15.1541	−	26.2477i	0.855197	−	1.48124i
$315$		0			0
$316$	−0.333619	−	0.577845i	−0.0187675	−	0.0325063i
$317$	−17.3656	+	3.06203i	−0.975352	+	0.171981i	−0.638538	−	0.769590i	$-0.720460\pi$
$317$	−17.3656	+	3.06203i	−0.975352	+	0.171981i	−0.336814	+	0.941571i	$0.609349\pi$
$318$		0			0
$319$	−4.26406	+	1.55199i	−0.238742	+	0.0868949i
$320$	−8.52756	+	3.10378i	−0.476705	+	0.173506i
$321$		0			0
$322$	−4.58356	+	23.7330i	−0.255432	+	1.32259i
$323$			30.8038i			1.71397i
$324$		0			0
$325$	−1.15810	+	0.668627i	−0.0642396	+	0.0370887i
$326$	2.22858	−	0.392958i	0.123429	−	0.0217639i
$327$		0			0
$328$	4.78583	−	5.70353i	0.264253	−	0.314925i
$329$	−10.9919	−	19.7738i	−0.606005	−	1.09016i
$330$		0			0
$331$	4.75223	+	26.9513i	0.261206	+	1.48138i	0.779624	+	0.626248i	$0.215410\pi$
$331$	4.75223	+	26.9513i	0.261206	+	1.48138i	−0.518418	+	0.855128i	$0.673479\pi$
$332$	1.48760	−	2.57659i	0.0816424	−	0.141409i
$333$		0			0
$334$	21.7968	−	12.5844i	1.19267	−	0.688588i
$335$	−0.704828	−	3.99728i	−0.0385089	−	0.218395i
$336$		0			0
$337$	−14.1672	+	5.15645i	−0.771738	+	0.280889i	−0.697723	−	0.716368i	$-0.745803\pi$
$337$	−14.1672	+	5.15645i	−0.771738	+	0.280889i	−0.0740145	+	0.997257i	$0.523581\pi$
$338$	−18.9943	−	3.34921i	−1.03315	−	0.182173i
$339$		0			0
$340$	3.18889	−	2.67580i	0.172942	−	0.145116i
$341$	5.62141	+	9.73657i	0.304417	+	0.527265i
$342$		0			0
$343$	−10.0307	+	15.5688i	−0.541604	+	0.840634i
$344$	−0.957269	−	1.14083i	−0.0516125	−	0.0615094i
$345$		0			0
$346$	−5.95418	−	16.3590i	−0.320099	−	0.879464i
$347$	23.8521	+	4.20577i	1.28045	+	0.225777i	0.772170	−	0.635416i	$-0.219171\pi$
$347$	23.8521	+	4.20577i	1.28045	+	0.225777i	0.508278	+	0.861193i	$0.330282\pi$
$348$		0			0
$349$	1.92048	−	5.27647i	0.102801	−	0.282443i	−0.877620	−	0.479357i	$-0.840870\pi$
$349$	1.92048	−	5.27647i	0.102801	−	0.282443i	0.980421	+	0.196914i	$0.0630921\pi$
$350$	2.11017	−	5.51703i	0.112793	−	0.294898i
$351$		0			0
$352$	−1.90226	+	3.29481i	−0.101391	+	0.175614i
$353$	3.76585	+	21.3572i	0.200436	+	1.13673i	0.904462	+	0.426555i	$0.140273\pi$
$353$	3.76585	+	21.3572i	0.200436	+	1.13673i	−0.704026	+	0.710174i	$0.748616\pi$
$354$		0			0
$355$	−0.115934	−	0.318526i	−0.00615313	−	0.0169056i
$356$	0.535195	−	3.03524i	0.0283653	−	0.160868i
$357$		0			0
$358$	−28.9002	+	24.2501i	−1.52742	+	1.28166i
$359$		−	21.9401i		−	1.15795i	−0.815344	−	0.578976i	$-0.803452\pi$
$359$		−	21.9401i		−	1.15795i	0.815344	−	0.578976i	$-0.196548\pi$
$360$		0			0
$361$	−39.8996			−2.09998
$362$	32.4526	+	11.8118i	1.70567	+	0.620813i
$363$		0			0
$364$	−1.20807	+	0.671546i	−0.0633199	+	0.0351986i
$365$	−7.46637	−	20.5137i	−0.390808	−	1.07374i
$366$		0			0
$367$	7.32658	+	8.73148i	0.382444	+	0.455780i	0.922584	−	0.385796i	$-0.126073\pi$
$367$	7.32658	+	8.73148i	0.382444	+	0.455780i	−0.540140	+	0.841575i	$0.681629\pi$
$368$			27.4481i			1.43083i
$369$		0			0
$370$	−20.9766	+	12.1109i	−1.09052	+	0.629613i
$371$	22.6830	−	26.1573i	1.17764	−	1.35802i
$372$		0			0
$373$	−28.7091	−	24.0898i	−1.48650	−	1.24732i	−0.898885	−	0.438184i	$-0.855622\pi$
$373$	−28.7091	−	24.0898i	−1.48650	−	1.24732i	−0.587617	−	0.809139i	$-0.699934\pi$
$374$	−1.40488	+	7.96745i	−0.0726444	+	0.411987i
$375$		0			0
$376$	−12.7484	−	15.1929i	−0.657448	−	0.783516i
$377$	−3.43384			−0.176852
$378$		0			0
$379$	4.71335			0.242108			0.121054	−	0.992646i	$-0.461373\pi$
$379$	4.71335			0.242108			0.121054	+	0.992646i	$0.461373\pi$
$380$	5.11635	+	6.09743i	0.262463	+	0.312792i
$381$		0			0
$382$	6.07079	−	34.4292i	0.310609	−	1.76155i
$383$	−5.74641	−	4.82181i	−0.293628	−	0.246383i	0.484058	−	0.875036i	$-0.339162\pi$
$383$	−5.74641	−	4.82181i	−0.293628	−	0.246383i	−0.777686	+	0.628653i	$0.783607\pi$
$384$		0			0
$385$	−2.07186	−	5.99365i	−0.105592	−	0.305464i
$386$	−20.1309	+	11.6226i	−1.02464	+	0.591574i
$387$		0			0
$388$		−	3.31647i		−	0.168368i
$389$	−14.8316	−	17.6756i	−0.751993	−	0.896190i	0.245320	−	0.969442i	$-0.421107\pi$
$389$	−14.8316	−	17.6756i	−0.751993	−	0.896190i	−0.997313	+	0.0732516i	$0.976662\pi$
$390$		0			0
$391$	7.85923	+	21.5931i	0.397458	+	1.09201i
$392$	−6.04576	+	15.0682i	−0.305357	+	0.761060i
$393$		0			0
$394$	−3.57382	−	1.30076i	−0.180047	−	0.0655316i
$395$	2.31666			0.116564
$396$		0			0
$397$			17.4192i			0.874245i	0.899402	+	0.437122i	$0.144002\pi$
$397$			17.4192i			0.874245i	−0.899402	+	0.437122i	$0.855998\pi$
$398$	−12.5421	+	10.5240i	−0.628677	+	0.527522i
$399$		0			0
$400$	1.16475	−	6.60560i	0.0582373	−	0.330280i
$401$	−7.35970	−	20.2206i	−0.367526	−	1.00977i	−0.976299	−	0.216425i	$-0.930560\pi$
$401$	−7.35970	−	20.2206i	−0.367526	−	1.00977i	0.608773	−	0.793344i	$-0.291662\pi$
$402$		0			0
$403$	1.47737	+	8.37857i	0.0735929	+	0.417366i
$404$	1.89672	−	3.28521i	0.0943651	−	0.163445i
$405$		0			0
$406$	11.7760	−	9.55954i	0.584433	−	0.474432i
$407$	3.45553	−	9.49398i	0.171284	−	0.470599i
$408$		0			0
$409$	26.2126	+	4.62199i	1.29613	+	0.228543i	0.778815	−	0.627253i	$-0.215821\pi$
$409$	26.2126	+	4.62199i	1.29613	+	0.228543i	0.517314	+	0.855796i	$0.326932\pi$
$410$	−3.32468	−	9.13448i	−0.164194	−	0.451120i
$411$		0			0
$412$	−4.52671	−	5.39472i	−0.223015	−	0.265779i
$413$	−4.43564	+	3.60077i	−0.218264	+	0.177182i
$414$		0			0
$415$	5.16496	+	8.94597i	0.253538	+	0.439140i
$416$	−2.20545	+	1.85059i	−0.108131	+	0.0907326i
$417$		0			0
$418$	−15.2344	−	2.68624i	−0.745140	−	0.131388i
$419$	5.47160	−	1.99150i	0.267305	−	0.0972911i	−0.204890	−	0.978785i	$-0.565684\pi$
$419$	5.47160	−	1.99150i	0.267305	−	0.0972911i	0.472196	+	0.881494i	$0.343462\pi$
$420$		0			0
$421$	−0.858573	−	4.86921i	−0.0418443	−	0.237311i	0.956711	−	0.291039i	$-0.0940008\pi$
$421$	−0.858573	−	4.86921i	−0.0418443	−	0.237311i	−0.998556	+	0.0537277i	$0.982890\pi$
$422$	15.7762	−	9.10839i	0.767973	−	0.443389i
$423$		0			0
$424$	15.1760	−	26.2856i	0.737011	−	1.27654i
$425$	−0.975096	−	5.53004i	−0.0472991	−	0.268246i
$426$		0			0
$427$	7.12840	−	3.96257i	0.344968	−	0.191762i
$428$	0.503027	−	0.599485i	0.0243147	−	0.0289772i
$429$		0			0
$430$	−1.91481	+	0.337633i	−0.0923405	+	0.0162821i
$431$	10.1898	−	5.88309i	0.490826	−	0.283378i	−0.234091	−	0.972215i	$-0.575211\pi$
$431$	10.1898	−	5.88309i	0.490826	−	0.283378i	0.724917	+	0.688836i	$0.241878\pi$
$432$		0			0
$433$		−	28.6389i		−	1.37630i	−0.725569	−	0.688150i	$-0.758423\pi$
$433$		−	28.6389i		−	1.37630i	0.725569	−	0.688150i	$-0.241577\pi$
$434$	−28.3917	−	24.6205i	−1.36285	−	1.18182i
$435$		0			0
$436$	0.971968	−	0.353767i	0.0465488	−	0.0169424i
$437$	−41.2878	+	15.0275i	−1.97506	+	0.718863i
$438$		0			0
$439$	10.5707	−	1.86390i	0.504513	−	0.0889593i	0.0844017	−	0.996432i	$-0.473102\pi$
$439$	10.5707	−	1.86390i	0.504513	−	0.0889593i	0.420111	+	0.907473i	$0.361991\pi$
$440$	−2.77971	−	4.81460i	−0.132517	−	0.229527i
$441$		0			0
$442$	−3.06112	+	5.30202i	−0.145603	+	0.252191i
$443$	−5.48081	+	15.0584i	−0.260401	+	0.715447i	0.738739	+	0.673991i	$0.235422\pi$
$443$	−5.48081	+	15.0584i	−0.260401	+	0.715447i	−0.999140	+	0.0414550i	$0.986801\pi$
$444$		0			0
$445$	8.19744	+	6.87847i	0.388596	+	0.326071i
$446$	−3.04161	+	17.2498i	−0.144024	+	0.816802i
$447$		0			0
$448$	−2.39926	+	12.4230i	−0.113354	+	0.586931i
$449$	15.5368	+	8.97017i	0.733226	+	0.423328i	0.819601	−	0.572934i	$-0.194195\pi$
$449$	15.5368	+	8.97017i	0.733226	+	0.423328i	−0.0863750	+	0.996263i	$0.527528\pi$
$450$		0			0
$451$	3.51145	+	2.02734i	0.165348	+	0.0954635i
$452$	0.162381	−	0.446138i	0.00763775	−	0.0209846i
$453$		0			0
$454$	23.6526	+	4.17059i	1.11007	+	0.195736i
$455$	0.0779720	−	4.79829i	0.00365538	−	0.224948i
$456$		0			0
$457$	−17.5604	+	14.7349i	−0.821441	+	0.689271i	−0.953309	−	0.301997i	$-0.902347\pi$
$457$	−17.5604	+	14.7349i	−0.821441	+	0.689271i	0.131868	+	0.991267i	$0.457902\pi$
$458$	17.9300	+	31.0556i	0.837813	+	1.45113i
$459$		0			0
$460$	5.14218	+	2.96884i	0.239755	+	0.138423i
$461$	11.2905	+	4.10942i	0.525852	+	0.191395i	0.591285	−	0.806462i	$-0.298621\pi$
$461$	11.2905	+	4.10942i	0.525852	+	0.191395i	−0.0654330	+	0.997857i	$0.520843\pi$
$462$		0			0
$463$	−0.859491	−	0.721198i	−0.0399439	−	0.0335169i	0.622597	−	0.782543i	$-0.286078\pi$
$463$	−0.859491	−	0.721198i	−0.0399439	−	0.0335169i	−0.662541	+	0.749026i	$0.730522\pi$
$464$	11.0712	−	13.1941i	0.513968	−	0.612523i
$465$		0			0
$466$	−43.9998	−	16.0146i	−2.03825	−	0.741863i
$467$	13.1684			0.609360			0.304680	−	0.952455i	$-0.401450\pi$
$467$	13.1684			0.609360			0.304680	+	0.952455i	$0.401450\pi$
$468$		0			0
$469$	−5.28573	−	2.02170i	−0.244072	−	0.0933533i
$470$	−25.5005	+	4.49642i	−1.17625	+	0.207404i
$471$		0			0
$472$	−3.21939	+	3.83672i	−0.148184	+	0.176599i
$473$	0.521315	−	0.621279i	0.0239701	−	0.0285664i
$474$		0			0
$475$	10.5739	−	1.86447i	0.485164	−	0.0855476i
$476$	−0.914847	−	5.73142i	−0.0419319	−	0.262699i
$477$		0			0
$478$	−44.3413			−2.02812
$479$	−21.0370	−	7.65686i	−0.961207	−	0.349851i	−0.186701	−	0.982417i	$-0.559779\pi$
$479$	−21.0370	−	7.65686i	−0.961207	−	0.349851i	−0.774506	+	0.632566i	$0.782002\pi$
$480$		0			0
$481$	4.91442	−	5.85678i	0.224078	−	0.267046i
$482$	−0.0917442	−	0.0769825i	−0.00417883	−	0.00350646i
$483$		0			0
$484$	4.83004	+	1.75799i	0.219547	+	0.0799087i
$485$	9.97214	+	5.75742i	0.452811	+	0.261431i
$486$		0			0
$487$	14.1370	+	24.4860i	0.640609	+	1.10957i	0.985297	+	0.170850i	$0.0546514\pi$
$487$	14.1370	+	24.4860i	0.640609	+	1.10957i	−0.344688	+	0.938717i	$0.612015\pi$
$488$	5.47703	−	4.59577i	0.247934	−	0.208041i
$489$		0			0
$490$	13.0907	+	16.6723i	0.591376	+	0.753178i
$491$	−36.4384	−	6.42508i	−1.64444	−	0.289960i	−0.726647	−	0.687012i	$-0.758922\pi$
$491$	−36.4384	−	6.42508i	−1.64444	−	0.289960i	−0.917796	+	0.397052i	$0.870033\pi$
$492$		0			0
$493$	4.93168	−	13.5497i	0.222112	−	0.610247i
$494$	−10.1379	−	5.85312i	−0.456126	−	0.263344i
$495$		0			0
$496$	−36.9569	−	21.3371i	−1.65941	−	0.958063i
$497$	−0.464030	−	0.0896182i	−0.0208146	−	0.00401993i
$498$		0			0
$499$	−2.84889	+	16.1568i	−0.127534	+	0.723279i	0.852237	+	0.523156i	$0.175245\pi$
$499$	−2.84889	+	16.1568i	−0.127534	+	0.723279i	−0.979771	+	0.200123i	$0.935866\pi$
$500$	−5.08400	−	4.26598i	−0.227363	−	0.190780i
$501$		0			0
$502$	10.5257	−	28.9190i	0.469783	−	1.29072i
$503$	−4.98173	+	8.62860i	−0.222124	+	0.384730i	−0.955453	−	0.295144i	$-0.904632\pi$
$503$	−4.98173	+	8.62860i	−0.222124	+	0.384730i	0.733329	+	0.679874i	$0.237966\pi$
$504$		0			0
$505$	6.58543	+	11.4063i	0.293048	+	0.507574i
$506$	−11.3645	+	2.00386i	−0.505213	+	0.0890827i
$507$		0			0
$508$	6.97730	−	2.53953i	0.309568	−	0.112673i
$509$	−6.46284	+	2.35228i	−0.286461	+	0.104263i	−0.481254	−	0.876581i	$-0.659819\pi$
$509$	−6.46284	+	2.35228i	−0.286461	+	0.104263i	0.194794	+	0.980844i	$0.437596\pi$
$510$		0			0
$511$	−29.8844	−	5.77159i	−1.32201	−	0.255320i
$512$			7.79950i			0.344692i
$513$		0			0
$514$	−4.31250	+	2.48982i	−0.190216	+	0.109821i
$515$	24.0796	−	4.24588i	1.06107	−	0.187096i
$516$		0			0
$517$	6.94259	−	8.27386i	0.305335	−	0.363884i
$518$	−0.548705	+	33.7666i	−0.0241087	+	1.48362i
$519$		0			0
$520$	−0.730537	−	4.14308i	−0.0320362	−	0.181686i
$521$	6.74329	−	11.6797i	0.295429	−	0.511698i	−0.679656	−	0.733531i	$-0.737871\pi$
$521$	6.74329	−	11.6797i	0.295429	−	0.511698i	0.975085	+	0.221833i	$0.0712041\pi$
$522$		0			0
$523$	30.3095	−	17.4992i	1.32534	−	0.765188i	0.340768	−	0.940147i	$-0.389313\pi$
$523$	30.3095	−	17.4992i	1.32534	−	0.765188i	0.984576	+	0.174960i	$0.0559796\pi$
$524$	−0.860881	−	4.88230i	−0.0376078	−	0.213284i
$525$		0			0
$526$	6.55088	−	2.38432i	0.285632	−	0.103961i
$527$	−35.1830	−	6.20371i	−1.53260	−	0.270238i
$528$		0			0
$529$	−7.48901	+	6.28403i	−0.325609	+	0.273219i
$530$	−19.8137	−	34.3183i	−0.860652	−	1.49069i
$531$		0			0
$532$	10.9590	−	1.74927i	0.475131	−	0.0758403i
$533$	1.97227	+	2.35046i	0.0854284	+	0.101810i
$534$		0			0
$535$	0.929304	+	2.55324i	0.0401773	+	0.110386i
$536$	−4.88576	−	0.861490i	−0.211032	−	0.0372107i
$537$		0			0
$538$	−0.468851	+	1.28816i	−0.0202136	+	0.0555364i
$539$	−8.65300	−	1.81747i	−0.372711	−	0.0782840i
$540$		0			0
$541$	0.619421	−	1.07287i	0.0266310	−	0.0461262i	−0.852403	−	0.522886i	$-0.824855\pi$
$541$	0.619421	−	1.07287i	0.0266310	−	0.0461262i	0.879034	+	0.476760i	$0.158189\pi$
$542$	−1.51410	−	8.58688i	−0.0650361	−	0.368838i
$543$		0			0
$544$	−4.13483	−	11.3603i	−0.177279	−	0.487071i
$545$	−0.623617	+	3.53671i	−0.0267128	+	0.151496i
$546$		0			0
$547$	21.3784	−	17.9386i	0.914076	−	0.767000i	−0.0588145	−	0.998269i	$-0.518732\pi$
$547$	21.3784	−	17.9386i	0.914076	−	0.767000i	0.972890	+	0.231269i	$0.0742876\pi$
$548$		−	10.9791i		−	0.469003i
$549$		0			0
$550$	2.81999			0.120245
$551$	25.9082	+	9.42980i	1.10372	+	0.401723i
$552$		0			0
$553$	1.66024	−	2.77065i	0.0706004	−	0.117820i
$554$	−10.6748	−	29.3287i	−0.453527	−	1.24606i
$555$		0			0
$556$	−2.68666	−	3.20184i	−0.113940	−	0.135788i
$557$		−	3.08064i		−	0.130531i	−0.997868	−	0.0652654i	$-0.979211\pi$
$557$		−	3.08064i		−	0.130531i	0.997868	−	0.0652654i	$-0.0207894\pi$
$558$		0			0
$559$	0.531504	−	0.306864i	0.0224802	−	0.0129790i
$560$	18.1855	+	15.7700i	0.768478	+	0.666404i
$561$		0			0
$562$	−16.3736	−	13.7391i	−0.690681	−	0.579550i
$563$	0.842562	−	4.77841i	0.0355098	−	0.201386i	−0.961892	−	0.273431i	$-0.911841\pi$
$563$	0.842562	−	4.77841i	0.0355098	−	0.201386i	0.997401	+	0.0720452i	$0.0229526\pi$
$564$		0			0
$565$	1.05958	+	1.26276i	0.0445768	+	0.0531245i
$566$	−17.1676			−0.721610
$567$		0			0
$568$	−0.414310			−0.0173841
$569$	−5.87514	−	7.00171i	−0.246298	−	0.293527i	0.628705	−	0.777644i	$-0.283585\pi$
$569$	−5.87514	−	7.00171i	−0.246298	−	0.293527i	−0.875003	+	0.484117i	$0.839141\pi$
$570$		0			0
$571$	−7.38382	+	41.8757i	−0.309003	+	1.75244i	0.295033	+	0.955487i	$0.404669\pi$
$571$	−7.38382	+	41.8757i	−0.309003	+	1.75244i	−0.604036	+	0.796957i	$0.706442\pi$
$572$	−0.505487	−	0.424154i	−0.0211355	−	0.0177348i
$573$		0			0
$574$	−13.3072	−	2.57002i	−0.555431	−	0.107270i
$575$	6.93646	−	4.00477i	0.289271	−	0.167010i
$576$		0			0
$577$		−	36.8985i		−	1.53611i	−0.640386	−	0.768053i	$-0.721226\pi$
$577$		−	36.8985i		−	1.53611i	0.640386	−	0.768053i	$-0.278774\pi$
$578$	0.912842	+	1.08788i	0.0379692	+	0.0452500i
$579$		0			0
$580$	−1.27433	−	3.50121i	−0.0529139	−	0.145380i
$581$	14.4005	+	0.234008i	0.597435	+	0.00970829i
$582$		0			0
$583$	15.5324	+	5.65334i	0.643287	+	0.234137i
$584$	−26.6824			−1.10413
$585$		0			0
$586$			14.3243i			0.591730i
$587$	−21.4793	+	18.0233i	−0.886545	+	0.743900i	−0.967514	−	0.252817i	$-0.918643\pi$
$587$	−21.4793	+	18.0233i	−0.886545	+	0.743900i	0.0809690	+	0.996717i	$0.474199\pi$
$588$		0			0
$589$	11.8620	−	67.2729i	0.488766	−	2.77193i
$590$	2.23648	+	6.14469i	0.0920746	+	0.252973i
$591$		0			0
$592$	6.65920	+	37.7662i	0.273691	+	1.55218i
$593$	12.0746	−	20.9138i	0.495845	−	0.858828i	−0.504144	−	0.863620i	$-0.668192\pi$
$593$	12.0746	−	20.9138i	0.495845	−	0.858828i	0.999989	+	0.00479135i	$0.00152514\pi$
$594$		0			0
$595$	18.8217	+	7.19898i	0.771616	+	0.295129i
$596$	−1.38311	+	3.80007i	−0.0566545	+	0.155657i
$597$		0			0
$598$	−8.59988	−	1.51639i	−0.351675	−	0.0620098i
$599$	12.4973	+	34.3360i	0.510625	+	1.40293i	0.880588	+	0.473883i	$0.157148\pi$
$599$	12.4973	+	34.3360i	0.510625	+	1.40293i	−0.369963	+	0.929046i	$0.620630\pi$
$600$		0			0
$601$	7.41347	+	8.83503i	0.302402	+	0.360388i	0.895750	−	0.444557i	$-0.146639\pi$
$601$	7.41347	+	8.83503i	0.302402	+	0.360388i	−0.593349	+	0.804945i	$0.702195\pi$
$602$	−0.968453	+	2.53202i	−0.0394712	+	0.103197i
$603$		0			0
$604$	−1.68637	−	2.92088i	−0.0686175	−	0.118849i
$605$	−13.6710	+	11.4714i	−0.555806	+	0.466377i
$606$		0			0
$607$	−23.6818	−	4.17574i	−0.961215	−	0.169488i	−0.329042	−	0.944315i	$-0.606726\pi$
$607$	−23.6818	−	4.17574i	−0.961215	−	0.169488i	−0.632173	+	0.774827i	$0.717837\pi$
$608$	21.7219	−	7.90614i	0.880941	−	0.320636i
$609$		0			0
$610$	−1.62095	−	9.19287i	−0.0656304	−	0.372208i
$611$	7.07828	−	4.08664i	0.286356	−	0.165328i
$612$		0			0
$613$	16.8432	−	29.1732i	0.680289	−	1.17830i	−0.294604	−	0.955620i	$-0.595188\pi$
$613$	16.8432	−	29.1732i	0.680289	−	1.17830i	0.974893	−	0.222676i	$-0.0714790\pi$
$614$	−5.58336	−	31.6648i	−0.225326	−	1.27789i
$615$		0			0
$616$	−7.75017	−	0.125940i	−0.312263	−	0.00507426i
$617$	−5.69508	+	6.78713i	−0.229275	+	0.273240i	−0.868401	−	0.495863i	$-0.834852\pi$
$617$	−5.69508	+	6.78713i	−0.229275	+	0.273240i	0.639126	+	0.769102i	$0.279296\pi$
$618$		0			0
$619$	−3.94848	+	0.696223i	−0.158703	+	0.0279836i	−0.252435	−	0.967614i	$-0.581231\pi$
$619$	−3.94848	+	0.696223i	−0.158703	+	0.0279836i	0.0937322	+	0.995597i	$0.470120\pi$
$620$	−7.99466	+	4.61572i	−0.321073	+	0.185372i
$621$		0			0
$622$		−	4.53193i		−	0.181714i
$623$	14.1011	−	4.87441i	0.564949	−	0.195289i
$624$		0			0
$625$	15.0798	−	5.48858i	0.603190	−	0.219543i
$626$	13.9855	−	5.09031i	0.558973	−	0.203450i
$627$		0			0
$628$	−10.2227	+	1.80253i	−0.407929	+	0.0719288i
$629$	16.0523	+	27.8035i	0.640049	+	1.10860i
$630$		0			0
$631$	−6.55511	+	11.3538i	−0.260955	+	0.451987i	−0.966496	−	0.256682i	$-0.917371\pi$
$631$	−6.55511	+	11.3538i	−0.260955	+	0.451987i	0.705541	+	0.708669i	$0.250704\pi$
$632$	0.968460	−	2.66082i	0.0385233	−	0.105842i
$633$		0			0
$634$	21.5561	+	18.0877i	0.856100	+	0.718354i
$635$	−4.47666	+	25.3884i	−0.177651	+	1.00751i
$636$		0			0
$637$	−5.68272	−	3.53195i	−0.225158	−	0.139941i
$638$	6.27111	+	3.62063i	0.248276	+	0.143342i
$639$		0			0
$640$	22.4412	+	12.9564i	0.887066	+	0.512148i
$641$	−2.73177	+	7.50547i	−0.107898	+	0.296448i	−0.981878	−	0.189514i	$-0.939309\pi$
$641$	−2.73177	+	7.50547i	−0.107898	+	0.296448i	0.873980	+	0.485963i	$0.161531\pi$
$642$		0			0
$643$	−38.0449	−	6.70834i	−1.50034	−	0.264551i	−0.637669	−	0.770310i	$-0.720101\pi$
$643$	−38.0449	−	6.70834i	−1.50034	−	0.264551i	−0.862675	+	0.505759i	$0.831213\pi$
$644$	7.23577	−	4.02226i	0.285129	−	0.158499i
$645$		0			0
$646$	37.6560	−	31.5972i	1.48156	−	1.24317i
$647$	−19.9091	−	34.4836i	−0.782707	−	1.35569i	−0.930359	−	0.366650i	$-0.880505\pi$
$647$	−19.9091	−	34.4836i	−0.782707	−	1.35569i	0.147652	−	0.989039i	$-0.452829\pi$
$648$		0			0
$649$	−2.36212	−	1.36377i	−0.0927214	−	0.0535327i
$650$	2.00528	+	0.729863i	0.0786536	+	0.0286276i
$651$		0			0
$652$	−0.593720	−	0.498190i	−0.0232519	−	0.0195106i
$653$	18.7469	−	22.3417i	0.733623	−	0.874298i	−0.262255	−	0.964999i	$-0.584466\pi$
$653$	18.7469	−	22.3417i	0.733623	−	0.874298i	0.995878	+	0.0907005i	$0.0289106\pi$
$654$		0			0
$655$	16.1749	+	5.88717i	0.632005	+	0.230031i
$656$	−15.3902			−0.600888
$657$		0			0
$658$	−12.8973	+	33.7201i	−0.502790	+	1.31454i
$659$	−20.9180	+	3.68841i	−0.814851	+	0.143680i	−0.565516	−	0.824737i	$-0.691323\pi$
$659$	−20.9180	+	3.68841i	−0.814851	+	0.143680i	−0.249335	+	0.968417i	$0.580212\pi$
$660$		0			0
$661$	−14.2388	+	16.9691i	−0.553824	+	0.660021i	−0.968227	−	0.250072i	$-0.919546\pi$
$661$	−14.2388	+	16.9691i	−0.553824	+	0.660021i	0.414404	+	0.910093i	$0.363990\pi$
$662$	28.0718	−	33.4547i	1.09104	−	1.30025i
$663$		0			0
$664$	12.4341	−	2.19247i	0.482538	−	0.0850845i
$665$	−13.7651	+	35.9888i	−0.533786	+	1.39558i
$666$		0			0
$667$	20.5672			0.796363
$668$	−8.10028	−	2.94826i	−0.313409	−	0.114072i
$669$		0			0
$670$	−4.16348	+	4.96184i	−0.160849	+	0.191693i
$671$	2.98271	+	2.50279i	0.115146	+	0.0966192i
$672$		0			0
$673$	15.9545	+	5.80696i	0.615000	+	0.223842i	0.630690	−	0.776035i	$-0.282772\pi$
$673$	15.9545	+	5.80696i	0.615000	+	0.223842i	−0.0156895	+	0.999877i	$0.504994\pi$
$674$	20.8356	+	12.0294i	0.802556	+	0.463356i
$675$		0			0
$676$	3.30288	+	5.72076i	0.127034	+	0.220029i
$677$	−32.1184	+	26.9506i	−1.23441	+	1.03579i	−0.236471	+	0.971638i	$0.575991\pi$
$677$	−32.1184	+	26.9506i	−1.23441	+	1.03579i	−0.997940	+	0.0641557i	$0.979565\pi$
$678$		0			0
$679$	14.0322	−	7.80029i	0.538507	−	0.299348i
$680$	17.3975	+	3.06765i	0.667163	+	0.117639i
$681$		0			0
$682$	6.13625	−	16.8592i	0.234969	−	0.645572i
$683$	−1.35935	−	0.784820i	−0.0520140	−	0.0300303i	0.473767	−	0.880650i	$-0.342894\pi$
$683$	−1.35935	−	0.784820i	−0.0520140	−	0.0300303i	−0.525782	+	0.850620i	$0.676227\pi$
$684$		0			0
$685$	33.0125	+	19.0598i	1.26134	+	0.728236i
$686$	29.3209	−	3.70778i	1.11948	−	0.141564i
$687$		0			0
$688$	−0.534555	+	3.03161i	−0.0203797	+	0.115579i
$689$	9.58186	+	8.04014i	0.365040	+	0.306305i
$690$		0			0
$691$	12.6872	−	34.8577i	0.482643	−	1.32605i	−0.424577	−	0.905392i	$-0.639577\pi$
$691$	12.6872	−	34.8577i	0.482643	−	1.32605i	0.907219	−	0.420658i	$-0.138201\pi$
$692$	−2.98121	+	5.16360i	−0.113328	+	0.196291i
$693$		0			0
$694$	−19.3251	−	33.4720i	−0.733569	−	1.27058i
$695$	14.2916	−	2.51999i	0.542109	−	0.0955885i
$696$		0			0
$697$	−12.1073	+	4.40670i	−0.458597	+	0.166916i
$698$	−8.42014	+	3.06468i	−0.318707	+	0.116000i
$699$		0			0
$700$	−1.91203	+	0.660942i	−0.0722679	+	0.0249813i
$701$		−	8.24161i		−	0.311281i	−0.987814	−	0.155641i	$-0.950256\pi$
$701$		−	8.24161i		−	0.311281i	0.987814	−	0.155641i	$-0.0497442\pi$
$702$		0			0
$703$	−53.1626	+	30.6934i	−2.00506	+	1.15762i
$704$	−5.94872	+	1.04892i	−0.224201	+	0.0395327i
$705$		0			0
$706$	22.2452	−	26.5108i	0.837209	−	0.997747i
$707$	18.3610	+	0.298365i	0.690537	+	0.0112212i
$708$		0			0
$709$	2.29888	+	13.0376i	0.0863361	+	0.489636i	0.997060	+	0.0766212i	$0.0244132\pi$
$709$	2.29888	+	13.0376i	0.0863361	+	0.489636i	−0.910724	+	0.413015i	$0.864476\pi$
$710$	−0.270461	+	0.468452i	−0.0101502	+	0.0175807i
$711$		0			0
$712$	11.3272	−	6.53976i	0.424504	−	0.245088i
$713$	−8.84875	−	50.1838i	−0.331388	−	1.87940i
$714$		0			0
$715$	2.15290	−	0.783592i	0.0805139	−	0.0293047i
$716$	12.7248	+	2.24372i	0.475546	+	0.0838517i
$717$		0			0
$718$	−26.8206	+	22.5051i	−1.00093	+	0.839884i
$719$	−5.67371	−	9.82715i	−0.211594	−	0.366491i	0.740620	−	0.671924i	$-0.234532\pi$
$719$	−5.67371	−	9.82715i	−0.211594	−	0.366491i	−0.952213	+	0.305433i	$0.901199\pi$
$720$		0			0
$721$	12.1787	−	31.8411i	0.453558	−	1.18583i
$722$	40.9271	+	48.7751i	1.52315	+	1.81522i
$723$		0			0
$724$	−4.04545	−	11.1148i	−0.150348	−	0.413078i
$725$	−4.94965	−	0.872757i	−0.183825	−	0.0324134i
$726$		0			0
$727$	7.94102	−	21.8178i	0.294516	−	0.809176i	−0.700876	−	0.713284i	$-0.747207\pi$
$727$	7.94102	−	21.8178i	0.294516	−	0.809176i	0.995392	−	0.0958928i	$-0.0305706\pi$
$728$	−5.47853	−	2.09544i	−0.203048	−	0.0776622i
$729$		0			0
$730$	−17.4182	+	30.1692i	−0.644677	+	1.11661i
$731$	0.447516	+	2.53799i	0.0165520	+	0.0938710i
$732$		0			0
$733$	5.56879	+	15.3001i	0.205688	+	0.565123i	0.999048	−	0.0436299i	$-0.0138922\pi$
$733$	5.56879	+	15.3001i	0.205688	+	0.565123i	−0.793360	+	0.608753i	$0.791670\pi$
$734$	3.15849	−	17.9127i	0.116582	−	0.661170i
$735$		0			0
$736$	13.2096	−	11.0842i	0.486913	−	0.408568i
$737$		−	2.70176i		−	0.0995205i
$738$		0			0
$739$	−10.8959			−0.400813			−0.200406	−	0.979713i	$-0.564226\pi$
$739$	−10.8959			−0.400813			−0.200406	+	0.979713i	$0.564226\pi$
$740$	7.79547	+	2.83732i	0.286567	+	0.104302i
$741$		0			0
$742$	−55.2431	−	0.897697i	−2.02804	−	0.0329555i
$743$	16.4197	+	45.1128i	0.602381	+	1.65503i	0.746435	+	0.665458i	$0.231764\pi$
$743$	16.4197	+	45.1128i	0.602381	+	1.65503i	−0.144054	+	0.989570i	$0.546014\pi$
$744$		0			0
$745$	−9.02517	−	10.7558i	−0.330657	−	0.394061i
$746$			59.8056i			2.18964i
$747$		0			0
$748$	2.39966	−	1.38544i	0.0877403	−	0.0506569i
$749$	3.71958	+	0.718363i	0.135910	+	0.0262484i
$750$		0			0
$751$	16.0679	+	13.4826i	0.586328	+	0.491987i	0.887018	−	0.461734i	$-0.152773\pi$
$751$	16.0679	+	13.4826i	0.586328	+	0.491987i	−0.300690	+	0.953722i	$0.597217\pi$
$752$	−7.11892	+	40.3734i	−0.259600	+	1.47227i
$753$		0			0
$754$	3.52228	+	4.19769i	0.128274	+	0.152871i
$755$	11.7102			0.426179
$756$		0			0
$757$	−24.6333			−0.895314			−0.447657	−	0.894205i	$-0.647741\pi$
$757$	−24.6333			−0.895314			−0.447657	+	0.894205i	$0.647741\pi$
$758$	−4.83473	−	5.76181i	−0.175605	−	0.209278i
$759$		0			0
$760$	−5.86560	+	33.2655i	−0.212768	+	1.20667i
$761$	7.15928	+	6.00735i	0.259524	+	0.217766i	0.763260	−	0.646091i	$-0.223597\pi$
$761$	7.15928	+	6.00735i	0.259524	+	0.217766i	−0.503737	+	0.863857i	$0.668042\pi$
$762$		0			0
$763$	3.78287	+	3.28041i	0.136949	+	0.118759i
$764$	−10.3695	+	5.98683i	−0.375155	+	0.216596i
$765$		0			0
$766$			11.9707i			0.432518i
$767$	−1.32673	−	1.58113i	−0.0479054	−	0.0570914i
$768$		0			0
$769$	−3.02496	−	8.31100i	−0.109083	−	0.299702i	0.873126	−	0.487494i	$-0.162089\pi$
$769$	−3.02496	−	8.31100i	−0.109083	−	0.299702i	−0.982209	+	0.187792i	$0.939867\pi$
$770$	−5.20169	+	8.68074i	−0.187456	+	0.312832i
$771$		0			0
$772$	7.48119	+	2.72293i	0.269254	+	0.0980004i
$773$	−14.1312			−0.508263			−0.254131	−	0.967170i	$-0.581790\pi$
$773$	−14.1312			−0.508263			−0.254131	+	0.967170i	$0.581790\pi$
$774$		0			0
$775$			12.4526i			0.447311i
$776$	10.7815	−	9.04675i	0.387033	−	0.324759i
$777$		0			0
$778$	−6.39392	+	36.2617i	−0.229233	+	1.30005i
$779$	−8.42598	−	23.1502i	−0.301892	−	0.829442i
$780$		0			0
$781$	−0.0391798	−	0.222200i	−0.00140196	−	0.00795093i
$782$	18.3347	−	31.7566i	0.655648	−	1.13562i
$783$		0			0
$784$	31.8930	−	10.4477i	1.13904	−	0.373132i
$785$	12.3267	−	33.8673i	0.439958	−	1.20878i
$786$		0			0
$787$	−27.1926	−	4.79479i	−0.969312	−	0.170916i	−0.333492	−	0.942753i	$-0.608227\pi$
$787$	−27.1926	−	4.79479i	−0.969312	−	0.170916i	−0.635820	+	0.771837i	$0.719338\pi$
$788$	0.445503	+	1.22401i	0.0158704	+	0.0436035i
$789$		0			0
$790$	−2.37633	−	2.83200i	−0.0845459	−	0.100758i
$791$	2.26956	−	0.362266i	0.0806962	−	0.0128807i
$792$		0			0
$793$	1.47323	+	2.55171i	0.0523159	+	0.0906137i
$794$	21.2940	−	17.8678i	0.755697	−	0.634105i
$795$		0			0
$796$	5.52227	+	0.973726i	0.195732	+	0.0345128i
$797$	32.0647	−	11.6706i	1.13579	−	0.413394i	0.295399	−	0.955374i	$-0.404547\pi$
$797$	32.0647	−	11.6706i	1.13579	−	0.413394i	0.840391	+	0.541980i	$0.182325\pi$
$798$		0			0
$799$	5.95978	+	33.7996i	0.210842	+	1.19574i
$800$	−3.64935	+	2.10695i	−0.129024	+	0.0744921i
$801$		0			0
$802$	−17.1694	+	29.7382i	−0.606272	+	1.05009i
$803$	−2.52326	−	14.3101i	−0.0890438	−	0.504992i
$804$		0			0
$805$	−0.467017	+	28.7396i	−0.0164602	+	1.01294i
$806$	8.72693	−	10.4004i	0.307393	−	0.366337i
$807$		0			0
$808$	15.8538	−	2.79545i	0.557734	−	0.0983436i
$809$	−8.13629	+	4.69749i	−0.286057	+	0.165155i	−0.636162	−	0.771555i	$-0.719479\pi$
$809$	−8.13629	+	4.69749i	−0.286057	+	0.165155i	0.350105	+	0.936710i	$0.386146\pi$
$810$		0			0
$811$		−	31.3300i		−	1.10014i	−0.835117	−	0.550072i	$-0.814600\pi$
$811$		−	31.3300i		−	1.10014i	0.835117	−	0.550072i	$-0.185400\pi$
$812$	−5.10058	−	0.985076i	−0.178995	−	0.0345694i
$813$		0			0
$814$	−15.1504	+	5.51429i	−0.531021	+	0.193276i
$815$	2.52869	−	0.920367i	0.0885761	−	0.0322391i
$816$		0			0
$817$	−4.85286	+	0.855689i	−0.169780	+	0.0299368i
$818$	−21.2375	−	36.7845i	−0.742554	−	1.28614i
$819$		0			0
$820$	−1.66464	+	2.88324i	−0.0581317	+	0.100687i
$821$	−2.24413	+	6.16570i	−0.0783208	+	0.215185i	−0.972673	−	0.232179i	$-0.925415\pi$
$821$	−2.24413	+	6.16570i	−0.0783208	+	0.215185i	0.894352	+	0.447363i	$0.147637\pi$
$822$		0			0
$823$	−17.8354	−	14.9657i	−0.621704	−	0.521672i	0.276634	−	0.960975i	$-0.410781\pi$
$823$	−17.8354	−	14.9657i	−0.621704	−	0.521672i	−0.898339	+	0.439303i	$0.855225\pi$
$824$	5.18961	−	29.4317i	0.180789	−	1.02530i
$825$		0			0
$826$	8.95162	+	1.72883i	0.311467	+	0.0601537i
$827$	−33.9354	−	19.5926i	−1.18005	−	0.681302i	−0.224023	−	0.974584i	$-0.571919\pi$
$827$	−33.9354	−	19.5926i	−1.18005	−	0.681302i	−0.956026	+	0.293282i	$0.905252\pi$
$828$		0			0
$829$	−31.3173	−	18.0811i	−1.08770	−	0.627981i	−0.154733	−	0.987956i	$-0.549452\pi$
$829$	−31.3173	−	18.0811i	−1.08770	−	0.627981i	−0.932962	+	0.359975i	$0.882785\pi$
$830$	5.63799	−	15.4903i	0.195698	−	0.537675i
$831$		0			0
$832$	−4.50160	−	0.793753i	−0.156065	−	0.0275184i
$833$	22.0983	−	17.3510i	0.765662	−	0.601177i
$834$		0			0
$835$	22.9272	−	19.2382i	0.793427	−	0.665764i
$836$	2.64909	+	4.58836i	0.0916206	+	0.158692i
$837$		0			0
$838$	−8.04702	−	4.64595i	−0.277980	−	0.160492i
$839$	35.7513	+	13.0124i	1.23427	+	0.449238i	0.875058	−	0.484018i	$-0.160823\pi$
$839$	35.7513	+	13.0124i	1.23427	+	0.449238i	0.359212	+	0.933256i	$0.383045\pi$
$840$		0			0
$841$	12.3288	+	10.3451i	0.425130	+	0.356726i
$842$	−5.07166	+	6.04417i	−0.174781	+	0.208296i
$843$		0			0
$844$	−5.86285	−	2.13390i	−0.201808	−	0.0734520i
$845$	−22.9353			−0.789000
$846$		0			0
$847$	3.92202	+	24.5710i	0.134762	+	0.844270i
$848$	−61.7866	+	10.8946i	−2.12176	+	0.374124i
$849$		0			0
$850$	−5.75997	+	6.86447i	−0.197565	+	0.235449i
$851$	−29.4352	+	35.0794i	−1.00902	+	1.20251i
$852$		0			0
$853$	−30.3259	+	5.34727i	−1.03834	+	0.183087i	−0.666728	−	0.745301i	$-0.732306\pi$
$853$	−30.3259	+	5.34727i	−1.03834	+	0.183087i	−0.371611	+	0.928389i	$0.621194\pi$
$854$	−12.1560	−	4.64946i	−0.415970	−	0.159101i
$855$		0			0
$856$	3.32104			0.113511
$857$	19.0597	+	6.93716i	0.651067	+	0.236969i	0.646375	−	0.763020i	$-0.276284\pi$
$857$	19.0597	+	6.93716i	0.651067	+	0.236969i	0.00469191	+	0.999989i	$0.498507\pi$
$858$		0			0
$859$	−22.2737	+	26.5448i	−0.759969	+	0.905696i	−0.997846	−	0.0655991i	$-0.979104\pi$
$859$	−22.2737	+	26.5448i	−0.759969	+	0.905696i	0.237877	+	0.971295i	$0.423549\pi$
$860$	0.510130	+	0.428050i	0.0173953	+	0.0145964i
$861$		0			0
$862$	−17.6440	−	6.42189i	−0.600957	−	0.218731i
$863$	32.8141	+	18.9452i	1.11700	+	0.644902i	0.940634	−	0.339422i	$-0.110231\pi$
$863$	32.8141	+	18.9452i	1.11700	+	0.644902i	0.176369	+	0.984324i	$0.443565\pi$
$864$		0			0
$865$	−10.3508	−	17.9281i	−0.351938	−	0.609574i
$866$	−35.0096	+	29.3765i	−1.18967	+	0.998255i
$867$		0			0
$868$	−0.209124	+	12.8692i	−0.00709813	+	0.436809i
$869$	1.51862	+	0.267773i	0.0515155	+	0.00908357i
$870$		0			0
$871$	0.699263	−	1.92121i	0.0236936	−	0.0650977i
$872$	3.80142	+	2.19475i	0.128732	+	0.0743237i
$873$		0			0
$874$	60.7214	+	35.0575i	2.05393	+	1.18584i
$875$	6.09216	−	31.5443i	0.205953	−	1.06639i
$876$		0			0
$877$	−2.06483	+	11.7102i	−0.0697243	+	0.395426i	0.929895	+	0.367826i	$0.119898\pi$
$877$	−2.06483	+	11.7102i	−0.0697243	+	0.395426i	−0.999619	+	0.0276005i	$0.991213\pi$
$878$	−13.1215	−	11.0102i	−0.442829	−	0.371577i
$879$		0			0
$880$	−3.93040	+	10.7987i	−0.132494	+	0.364024i
$881$	−19.8758	+	34.4258i	−0.669631	+	1.15984i	0.308376	+	0.951265i	$0.400215\pi$
$881$	−19.8758	+	34.4258i	−0.669631	+	1.15984i	−0.978007	+	0.208571i	$0.933119\pi$
$882$		0			0
$883$	25.4955	+	44.1595i	0.857992	+	1.48609i	0.873842	+	0.486211i	$0.161621\pi$
$883$	25.4955	+	44.1595i	0.857992	+	1.48609i	−0.0158499	+	0.999874i	$0.505045\pi$
$884$	2.06497	−	0.364110i	0.0694524	−	0.0122463i
$885$		0			0
$886$	24.0301	−	8.74623i	0.807306	−	0.293835i
$887$	−25.2472	+	9.18922i	−0.847717	+	0.308544i	−0.729109	−	0.684398i	$-0.760065\pi$
$887$	−25.2472	+	9.18922i	−0.847717	+	0.308544i	−0.118608	+	0.992941i	$0.537843\pi$
$888$		0			0
$889$	27.1555	+	23.5485i	0.910765	+	0.789792i
$890$		−	17.0765i		−	0.572407i
$891$		0			0
$892$	5.19536	−	2.99954i	0.173953	−	0.100432i
$893$	−64.6277	+	11.3956i	−2.16268	+	0.381339i
$894$		0			0
$895$	−28.8368	+	34.3664i	−0.963909	+	1.14874i
$896$	31.5779	−	17.5537i	1.05494	−	0.586428i
$897$		0			0
$898$	−4.97138	−	28.1941i	−0.165897	−	0.940849i
$899$	−15.9881	+	27.6922i	−0.533234	+	0.923588i
$900$		0			0
$901$	−45.4873	+	26.2621i	−1.51540	+	0.874917i
$902$	−1.12357	−	6.37211i	−0.0374109	−	0.212168i
$903$		0			0
$904$	1.89330	−	0.689103i	0.0629701	−	0.0229192i
$905$	40.4435	+	7.13128i	1.34439	+	0.237052i
$906$		0			0
$907$	−30.9893	+	26.0031i	−1.02898	+	0.863418i	−0.990729	−	0.135850i	$-0.956623\pi$
$907$	−30.9893	+	26.0031i	−1.02898	+	0.863418i	−0.0382522	+	0.999268i	$0.512179\pi$
$908$	−4.11291	−	7.12377i	−0.136492	−	0.236411i
$909$		0			0
$910$	−5.94564	+	4.82655i	−0.197096	+	0.159999i
$911$	−12.3517	−	14.7202i	−0.409231	−	0.487702i	0.521581	−	0.853202i	$-0.325342\pi$
$911$	−12.3517	−	14.7202i	−0.409231	−	0.487702i	−0.930811	+	0.365500i	$0.880898\pi$
$912$		0			0
$913$	2.35170	+	6.46124i	0.0778299	+	0.213836i
$914$	36.0253	+	6.35223i	1.19161	+	0.210113i
$915$		0			0
$916$	4.20062	−	11.5411i	0.138792	−	0.381329i
$917$	18.6326	−	15.1256i	0.615302	−	0.499490i
$918$		0			0
$919$	1.00540	−	1.74140i	0.0331650	−	0.0574435i	−0.848966	−	0.528447i	$-0.822775\pi$
$919$	1.00540	−	1.74140i	0.0331650	−	0.0574435i	0.882132	+	0.471003i	$0.156108\pi$
$920$	4.37558	+	24.8152i	0.144259	+	0.818132i
$921$		0			0
$922$	−6.55777	−	18.0173i	−0.215969	−	0.593369i
$923$	0.0296486	−	0.168146i	0.000975897	−	0.00553459i
$924$		0			0
$925$	8.57238	−	7.19308i	0.281858	−	0.236507i
$926$			1.79045i			0.0588380i
$927$		0			0
$928$	−10.8206			−0.355204
$929$	3.28266	+	1.19479i	0.107700	+	0.0391998i	0.395308	−	0.918548i	$-0.370638\pi$
$929$	3.28266	+	1.19479i	0.107700	+	0.0391998i	−0.287608	+	0.957748i	$0.592860\pi$
$930$		0			0
$931$	33.1766	+	42.2539i	1.08732	+	1.38482i
$932$	5.48490	+	15.0696i	0.179664	+	0.493622i
$933$		0			0
$934$	−13.5075	−	16.0976i	−0.441980	−	0.526731i
$935$			9.62058i			0.314627i
$936$		0			0
$937$	29.0222	−	16.7560i	0.948114	−	0.547394i	0.0556194	−	0.998452i	$-0.482287\pi$
$937$	29.0222	−	16.7560i	0.948114	−	0.547394i	0.892495	+	0.451058i	$0.148953\pi$
$938$	2.95044	+	8.53528i	0.0963353	+	0.278687i
$939$		0			0
$940$	6.79363	+	5.70054i	0.221584	+	0.185931i
$941$	5.86663	−	33.2713i	0.191247	−	1.08461i	−0.726416	−	0.687255i	$-0.758816\pi$
$941$	5.86663	−	33.2713i	0.191247	−	1.08461i	0.917663	−	0.397359i	$-0.130073\pi$
$942$		0			0
$943$	−11.8130	−	14.0782i	−0.384684	−	0.458448i
$944$	10.3529			0.336958
$945$		0			0
$946$	−1.29422			−0.0420788
$947$	−1.00618	−	1.19912i	−0.0326965	−	0.0389662i	0.749448	−	0.662063i	$-0.230319\pi$
$947$	−1.00618	−	1.19912i	−0.0326965	−	0.0389662i	−0.782145	+	0.623097i	$0.785874\pi$
$948$		0			0
$949$	1.90943	−	10.8289i	0.0619828	−	0.351522i
$950$	−13.1254	−	11.0136i	−0.425846	−	0.357327i
$951$		0			0
$952$	16.1367	−	18.6084i	0.522994	−	0.603101i
$953$	13.8156	−	7.97645i	0.447532	−	0.258383i	−0.259255	−	0.965809i	$-0.583477\pi$
$953$	13.8156	−	7.97645i	0.447532	−	0.258383i	0.706787	+	0.707426i	$0.250144\pi$
$954$		0			0
$955$		−	41.5728i		−	1.34526i
$956$	9.76174	+	11.6336i	0.315717	+	0.376257i
$957$		0			0
$958$	12.2187	+	33.5707i	0.394770	+	1.08462i
$959$	46.4532	−	25.8227i	1.50005	−	0.833857i
$960$		0			0
$961$	45.3172	+	16.4941i	1.46184	+	0.532068i
$962$	−12.2006			−0.393363
$963$		0			0
$964$			0.0410182i			0.00132111i
$965$	−21.1749	+	17.7678i	−0.681643	+	0.571966i
$966$		0			0
$967$	0.704391	−	3.99480i	0.0226517	−	0.128464i	−0.971385	−	0.237510i	$-0.923669\pi$
$967$	0.704391	−	3.99480i	0.0226517	−	0.128464i	0.994037	+	0.109046i	$0.0347797\pi$
$968$	7.46047	+	20.4975i	0.239789	+	0.658814i
$969$		0			0
$970$	−3.19083	−	18.0961i	−0.102451	−	0.581031i
$971$	−20.1944	+	34.9777i	−0.648068	+	1.12249i	0.335515	+	0.942035i	$0.391090\pi$
$971$	−20.1944	+	34.9777i	−0.648068	+	1.12249i	−0.983584	+	0.180453i	$0.942244\pi$
$972$		0			0
$973$	7.22821	−	18.8982i	0.231726	−	0.605847i
$974$	15.4317	−	42.3984i	0.494465	−	1.35853i
$975$		0			0
$976$	−14.5545	−	2.56636i	−0.465879	−	0.0821471i
$977$	2.97539	+	8.17481i	0.0951910	+	0.261535i	0.978145	−	0.207925i	$-0.0666709\pi$
$977$	2.97539	+	8.17481i	0.0951910	+	0.261535i	−0.882954	+	0.469460i	$0.844449\pi$
$978$		0			0
$979$	4.57852	+	5.45647i	0.146330	+	0.174389i
$980$	1.49232	−	7.10494i	0.0476703	−	0.226959i
$981$		0			0
$982$	29.5226	+	51.1346i	0.942102	+	1.63177i
$983$	25.8458	−	21.6872i	0.824352	−	0.691714i	−0.129635	−	0.991562i	$-0.541380\pi$
$983$	25.8458	−	21.6872i	0.824352	−	0.691714i	0.953987	+	0.299848i	$0.0969360\pi$
$984$		0			0
$985$	−4.45381	−	0.785328i	−0.141910	−	0.0250226i
$986$	−21.6225	+	7.86994i	−0.688600	+	0.250630i
$987$		0			0
$988$	0.696209	+	3.94840i	0.0221493	+	0.125615i
$989$	−3.18346	+	1.83797i	−0.101228	+	0.0584442i
$990$		0			0
$991$	12.7307	−	22.0503i	0.404405	−	0.700450i	−0.589847	−	0.807515i	$-0.700812\pi$
$991$	12.7307	−	22.0503i	0.404405	−	0.700450i	0.994252	+	0.107065i	$0.0341453\pi$
$992$	4.65543	+	26.4022i	0.147810	+	0.838272i
$993$		0			0
$994$	0.366427	+	0.659178i	0.0116224	+	0.0209079i
$995$	−12.5146	+	14.9143i	−0.396739	+	0.472815i
$996$		0			0
$997$	8.61062	−	1.51829i	0.272701	−	0.0480846i	−0.0356252	−	0.999365i	$-0.511342\pi$
$997$	8.61062	−	1.51829i	0.272701	−	0.0480846i	0.308326	+	0.951281i	$0.400231\pi$
$998$	22.6731	−	13.0903i	0.717705	−	0.414367i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.341.6		132
3.2	odd	2		189.2.ba.a.131.17	yes	132
7.3	odd	6		567.2.bd.a.17.17		132
21.17	even	6		189.2.bd.a.185.6	yes	132
27.7	even	9		189.2.bd.a.47.6	yes	132
27.20	odd	18		567.2.bd.a.467.17		132
189.101	even	18	inner	567.2.ba.a.143.6		132
189.115	odd	18		189.2.ba.a.101.17	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.17	✓	132	189.115	odd	18
189.2.ba.a.131.17	yes	132	3.2	odd	2
189.2.bd.a.47.6	yes	132	27.7	even	9
189.2.bd.a.185.6	yes	132	21.17	even	6
567.2.ba.a.143.6		132	189.101	even	18	inner
567.2.ba.a.341.6		132	1.1	even	1	trivial
567.2.bd.a.17.17		132	7.3	odd	6
567.2.bd.a.467.17		132	27.20	odd	18

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.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02575 - 1.22245i) q^{2} +(-0.0949069 + 0.538244i) q^{4} +(-1.45366 - 1.21977i) q^{5} +(-2.50057 + 0.864386i) q^{7} +(-2.00866 + 1.15970i) q^{8} +3.02821i q^{10} +(-0.811915 - 0.967602i) q^{11} +(-0.326917 - 0.898197i) q^{13} +(3.62163 + 2.17016i) q^{14} +(4.50524 + 1.63977i) q^{16} +4.01374 q^{17} +7.67461i q^{19} +(0.794495 - 0.666660i) q^{20} +(-0.350017 + 1.98504i) q^{22} +(1.95808 + 5.37979i) q^{23} +(-0.242940 - 1.37778i) q^{25} +(-0.762661 + 1.32097i) q^{26} +(-0.227929 - 1.42795i) q^{28} +(1.22870 - 3.37583i) q^{29} +(-8.76565 - 1.54562i) q^{31} +(-1.03017 - 2.83037i) q^{32} +(-4.11711 - 4.90658i) q^{34} +(4.68933 + 1.79359i) q^{35} +(3.99935 + 6.92708i) q^{37} +(9.38179 - 7.87226i) q^{38} +(4.33449 + 0.764287i) q^{40} +(-3.01647 + 1.09790i) q^{41} +(0.111496 + 0.632326i) q^{43} +(0.597862 - 0.345176i) q^{44} +(4.56799 - 7.91199i) q^{46} +(1.48485 + 8.42098i) q^{47} +(5.50567 - 4.32291i) q^{49} +(-1.43506 + 1.71024i) q^{50} +(0.514475 - 0.0907159i) q^{52} +(-11.3329 + 6.54305i) q^{53} +2.39691i q^{55} +(4.02037 - 4.63618i) q^{56} +(-5.38712 + 1.96075i) q^{58} +(2.02915 - 0.738551i) q^{59} +(-3.03575 + 0.535284i) q^{61} +(7.10196 + 12.3010i) q^{62} +(2.39111 - 4.14152i) q^{64} +(-0.620364 + 1.70444i) q^{65} +(1.63854 + 1.37490i) q^{67} +(-0.380931 + 2.16037i) q^{68} +(-2.61754 - 7.57223i) q^{70} +(0.154696 + 0.0893139i) q^{71} +(9.96274 + 5.75199i) q^{73} +(4.36563 - 11.9945i) q^{74} +(-4.13081 - 0.728373i) q^{76} +(2.86663 + 1.71775i) q^{77} +(-0.935206 + 0.784731i) q^{79} +(-4.54896 - 7.87903i) q^{80} +(4.43628 + 2.56129i) q^{82} +(-5.11532 - 1.86183i) q^{83} +(-5.83462 - 4.89582i) q^{85} +(0.658617 - 0.784910i) q^{86} +(2.75300 + 1.00201i) q^{88} -5.63916 q^{89} +(1.59387 + 1.96342i) q^{91} +(-3.08147 + 0.543347i) q^{92} +(8.77111 - 10.4530i) q^{94} +(9.36123 - 11.1563i) q^{95} +(-5.97585 + 1.05370i) q^{97} +(-10.9320 - 2.29615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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