LMFDB - Embedded newform 567.2.be.a.503.4

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			503.4
Character	$\chi$	$=$	567.503
Dual form			567.2.be.a.62.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.735125 + 2.01974i) q^{2} +(-2.00685 - 1.68395i) q^{4} +(0.0677816 - 0.384409i) q^{5} +(2.64076 - 0.162359i) q^{7} +(1.15362 - 0.666045i) q^{8} +(0.726578 + 0.419490i) q^{10} +(4.77807 - 0.842503i) q^{11} +(-1.96127 - 5.38855i) q^{13} +(-1.61337 + 5.45301i) q^{14} +(-0.412653 - 2.34027i) q^{16} +(3.57147 - 6.18597i) q^{17} +(-0.398672 + 0.230173i) q^{19} +(-0.783352 + 0.657311i) q^{20} +(-1.81084 + 10.2698i) q^{22} +(-0.358944 + 0.427773i) q^{23} +(4.55529 + 1.65799i) q^{25} +12.3252 q^{26} +(-5.57303 - 4.12109i) q^{28} +(-1.73522 + 4.76747i) q^{29} +(-2.14159 + 2.55225i) q^{31} +(7.65380 + 1.34957i) q^{32} +(9.86858 + 11.7609i) q^{34} +(0.116583 - 1.02614i) q^{35} +(-1.07348 + 1.85933i) q^{37} +(-0.171817 - 0.974420i) q^{38} +(-0.177839 - 0.488609i) q^{40} +(0.917771 - 0.334041i) q^{41} +(1.16047 + 6.58138i) q^{43} +(-11.0076 - 6.35525i) q^{44} +(-0.600121 - 1.03944i) q^{46} +(-2.83834 + 2.38165i) q^{47} +(6.94728 - 0.857502i) q^{49} +(-6.69741 + 7.98167i) q^{50} +(-5.13806 + 14.1167i) q^{52} -3.13310i q^{53} -1.89384i q^{55} +(2.93831 - 1.94617i) q^{56} +(-8.35346 - 7.00938i) q^{58} +(-0.715255 + 4.05641i) q^{59} +(-7.89549 - 9.40948i) q^{61} +(-3.58054 - 6.20168i) q^{62} +(-5.97591 + 10.3506i) q^{64} +(-2.20434 + 0.388685i) q^{65} +(6.30401 - 2.29447i) q^{67} +(-17.5843 + 6.40016i) q^{68} +(1.98683 + 0.989808i) q^{70} +(-6.08593 - 3.51371i) q^{71} +(6.55906 - 3.78687i) q^{73} +(-2.96621 - 3.53499i) q^{74} +(1.18768 + 0.209419i) q^{76} +(12.4810 - 3.00061i) q^{77} +(-0.818714 - 0.297987i) q^{79} -0.927591 q^{80} +2.09922i q^{82} +(6.78293 + 2.46878i) q^{83} +(-2.13586 - 1.79220i) q^{85} +(-14.1458 - 2.49428i) q^{86} +(4.95095 - 4.15434i) q^{88} +(2.65800 + 4.60379i) q^{89} +(-6.05413 - 13.9115i) q^{91} +(1.44070 - 0.254033i) q^{92} +(-2.72378 - 7.48351i) q^{94} +(0.0614580 + 0.168854i) q^{95} +(-10.7873 + 1.90209i) q^{97} +(-3.37519 + 14.6621i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.735125	+	2.01974i	−0.519812	+	1.42817i	0.350916	+	0.936407i	$0.385870\pi$
$2$	−0.735125	+	2.01974i	−0.519812	+	1.42817i	−0.870728	+	0.491765i	$0.836352\pi$
$3$		0			0
$3$		0			0
$4$	−2.00685	−	1.68395i	−1.00343	−	0.841975i
$5$	0.0677816	−	0.384409i	0.0303129	−	0.171913i	−0.965893	−	0.258942i	$-0.916626\pi$
$5$	0.0677816	−	0.384409i	0.0303129	−	0.171913i	0.996206	+	0.0870291i	$0.0277373\pi$
$6$		0			0
$7$	2.64076	−	0.162359i	0.998115	−	0.0613658i
$7$	2.64076	−	0.162359i	0.998115	−	0.0613658i
$8$	1.15362	−	0.666045i	0.407868	−	0.235483i
$9$		0			0
$10$	0.726578	+	0.419490i	0.229764	+	0.132654i
$11$	4.77807	−	0.842503i	1.44064	−	0.254024i	0.601909	−	0.798565i	$-0.294407\pi$
$11$	4.77807	−	0.842503i	1.44064	−	0.254024i	0.838734	+	0.544541i	$0.183296\pi$
$12$		0			0
$13$	−1.96127	−	5.38855i	−0.543959	−	1.49451i	−0.841742	−	0.539881i	$-0.818469\pi$
$13$	−1.96127	−	5.38855i	−0.543959	−	1.49451i	0.297783	−	0.954634i	$-0.403753\pi$
$14$	−1.61337	+	5.45301i	−0.431192	+	1.45738i
$15$		0			0
$16$	−0.412653	−	2.34027i	−0.103163	−	0.585068i
$17$	3.57147	−	6.18597i	0.866209	−	1.50032i	0.000368279	−	1.00000i	$-0.499883\pi$
$17$	3.57147	−	6.18597i	0.866209	−	1.50032i	0.865841	−	0.500319i	$-0.166784\pi$
$18$		0			0
$19$	−0.398672	+	0.230173i	−0.0914616	+	0.0528054i	−0.545033	−	0.838414i	$-0.683483\pi$
$19$	−0.398672	+	0.230173i	−0.0914616	+	0.0528054i	0.453572	+	0.891220i	$0.350150\pi$
$20$	−0.783352	+	0.657311i	−0.175163	+	0.146979i
$21$		0			0
$22$	−1.81084	+	10.2698i	−0.386073	+	2.18953i
$23$	−0.358944	+	0.427773i	−0.0748450	+	0.0891968i	−0.802168	−	0.597099i	$-0.796320\pi$
$23$	−0.358944	+	0.427773i	−0.0748450	+	0.0891968i	0.727323	+	0.686296i	$0.240764\pi$
$24$		0			0
$25$	4.55529	+	1.65799i	0.911057	+	0.331598i
$26$	12.3252			2.41718
$27$		0			0
$28$	−5.57303	−	4.12109i	−1.05320	−	0.778812i
$29$	−1.73522	+	4.76747i	−0.322222	+	0.885298i	0.667794	+	0.744346i	$0.267239\pi$
$29$	−1.73522	+	4.76747i	−0.322222	+	0.885298i	−0.990016	+	0.140952i	$0.954984\pi$
$30$		0			0
$31$	−2.14159	+	2.55225i	−0.384641	+	0.458398i	−0.923273	−	0.384143i	$-0.874497\pi$
$31$	−2.14159	+	2.55225i	−0.384641	+	0.458398i	0.538632	+	0.842541i	$0.318941\pi$
$32$	7.65380	+	1.34957i	1.35301	+	0.238573i
$33$		0			0
$34$	9.86858	+	11.7609i	1.69245	+	2.01698i
$35$	0.116583	−	1.02614i	0.0197062	−	0.173449i
$36$		0			0
$37$	−1.07348	+	1.85933i	−0.176479	+	0.305671i	−0.940672	−	0.339317i	$-0.889804\pi$
$37$	−1.07348	+	1.85933i	−0.176479	+	0.305671i	0.764193	+	0.644988i	$0.223138\pi$
$38$	−0.171817	−	0.974420i	−0.0278723	−	0.158072i
$39$		0			0
$40$	−0.177839	−	0.488609i	−0.0281188	−	0.0772558i
$41$	0.917771	−	0.334041i	0.143332	−	0.0521685i	−0.269358	−	0.963040i	$-0.586812\pi$
$41$	0.917771	−	0.334041i	0.143332	−	0.0521685i	0.412690	+	0.910872i	$0.364589\pi$
$42$		0			0
$43$	1.16047	+	6.58138i	0.176971	+	1.00365i	0.935845	+	0.352413i	$0.114639\pi$
$43$	1.16047	+	6.58138i	0.176971	+	1.00365i	−0.758874	+	0.651238i	$0.774250\pi$
$44$	−11.0076	−	6.35525i	−1.65946	−	0.958090i
$45$		0			0
$46$	−0.600121	−	1.03944i	−0.0884830	−	0.153257i
$47$	−2.83834	+	2.38165i	−0.414014	+	0.347399i	−0.825880	−	0.563845i	$-0.809321\pi$
$47$	−2.83834	+	2.38165i	−0.414014	+	0.347399i	0.411867	+	0.911244i	$0.364877\pi$
$48$		0			0
$49$	6.94728	−	0.857502i	0.992468	−	0.122500i
$50$	−6.69741	+	7.98167i	−0.947157	+	1.12878i
$51$		0			0
$52$	−5.13806	+	14.1167i	−0.712521	+	1.95763i
$53$		−	3.13310i		−	0.430364i	−0.976574	−	0.215182i	$-0.930966\pi$
$53$		−	3.13310i		−	0.430364i	0.976574	−	0.215182i	$-0.0690345\pi$
$54$		0			0
$55$		−	1.89384i		−	0.255365i
$56$	2.93831	−	1.94617i	0.392648	−	0.260068i
$57$		0			0
$58$	−8.35346	−	7.00938i	−1.09686	−	0.920377i
$59$	−0.715255	+	4.05641i	−0.0931183	+	0.528100i	0.902189	+	0.431340i	$0.141959\pi$
$59$	−0.715255	+	4.05641i	−0.0931183	+	0.528100i	−0.995308	+	0.0967600i	$0.969152\pi$
$60$		0			0
$61$	−7.89549	−	9.40948i	−1.01091	−	1.20476i	−0.978704	−	0.205279i	$-0.934190\pi$
$61$	−7.89549	−	9.40948i	−1.01091	−	1.20476i	−0.0322101	−	0.999481i	$-0.510255\pi$
$62$	−3.58054	−	6.20168i	−0.454730	−	0.787615i
$63$		0			0
$64$	−5.97591	+	10.3506i	−0.746989	+	1.29382i
$65$	−2.20434	+	0.388685i	−0.273415	+	0.0482104i
$66$		0			0
$67$	6.30401	−	2.29447i	0.770158	−	0.280314i	0.0730953	−	0.997325i	$-0.476712\pi$
$67$	6.30401	−	2.29447i	0.770158	−	0.280314i	0.697062	+	0.717011i	$0.254490\pi$
$68$	−17.5843	+	6.40016i	−2.13241	+	0.776133i
$69$		0			0
$70$	1.98683	+	0.989808i	0.237471	+	0.118305i
$71$	−6.08593	−	3.51371i	−0.722267	−	0.417001i	0.0933194	−	0.995636i	$-0.470252\pi$
$71$	−6.08593	−	3.51371i	−0.722267	−	0.417001i	−0.815587	+	0.578635i	$0.803586\pi$
$72$		0			0
$73$	6.55906	−	3.78687i	0.767680	−	0.443220i	−0.0643665	−	0.997926i	$-0.520503\pi$
$73$	6.55906	−	3.78687i	0.767680	−	0.443220i	0.832046	+	0.554706i	$0.187169\pi$
$74$	−2.96621	−	3.53499i	−0.344815	−	0.410935i
$75$		0			0
$76$	1.18768	+	0.209419i	0.136236	+	0.0240221i
$77$	12.4810	−	3.00061i	1.42234	−	0.341952i
$78$		0			0
$79$	−0.818714	−	0.297987i	−0.0921125	−	0.0335262i	0.295553	−	0.955326i	$-0.404496\pi$
$79$	−0.818714	−	0.297987i	−0.0921125	−	0.0335262i	−0.387665	+	0.921800i	$0.626718\pi$
$80$	−0.927591			−0.103708
$81$		0			0
$82$			2.09922i			0.231820i
$83$	6.78293	+	2.46878i	0.744523	+	0.270984i	0.686299	−	0.727319i	$-0.259234\pi$
$83$	6.78293	+	2.46878i	0.744523	+	0.270984i	0.0582238	+	0.998304i	$0.481456\pi$
$84$		0			0
$85$	−2.13586	−	1.79220i	−0.231667	−	0.194391i
$86$	−14.1458	−	2.49428i	−1.52538	−	0.268965i
$87$		0			0
$88$	4.95095	−	4.15434i	0.527773	−	0.442854i
$89$	2.65800	+	4.60379i	0.281748	+	0.488001i	0.971815	−	0.235744i	$-0.0757526\pi$
$89$	2.65800	+	4.60379i	0.281748	+	0.488001i	−0.690068	+	0.723745i	$0.742419\pi$
$90$		0			0
$91$	−6.05413	−	13.9115i	−0.634646	−	1.45832i
$92$	1.44070	−	0.254033i	0.150203	−	0.0264848i
$93$		0			0
$94$	−2.72378	−	7.48351i	−0.280936	−	0.771865i
$95$	0.0614580	+	0.168854i	0.00630546	+	0.0173241i
$96$		0			0
$97$	−10.7873	+	1.90209i	−1.09528	+	0.193128i	−0.691964	−	0.721932i	$-0.743254\pi$
$97$	−10.7873	+	1.90209i	−1.09528	+	0.193128i	−0.403318	+	0.915060i	$0.632143\pi$
$98$	−3.37519	+	14.6621i	−0.340946	+	1.48109i
$99$		0			0
$100$	−6.34982	−	10.9982i	−0.634982	−	1.09982i
$101$	−10.5964	+	8.89141i	−1.05438	+	0.884728i	−0.993547	−	0.113420i	$-0.963819\pi$
$101$	−10.5964	+	8.89141i	−1.05438	+	0.884728i	−0.0608307	+	0.998148i	$0.519375\pi$
$102$		0			0
$103$	12.0281	+	2.12089i	1.18517	+	0.208977i	0.731277	−	0.682080i	$-0.238925\pi$
$103$	12.0281	+	2.12089i	1.18517	+	0.208977i	0.453890	+	0.891058i	$0.350036\pi$
$104$	−5.85159	−	4.91006i	−0.573795	−	0.481471i
$105$		0			0
$106$	6.32804	+	2.30322i	0.614634	+	0.223708i
$107$			5.57017i			0.538489i	0.963072	+	0.269244i	$0.0867739\pi$
$107$			5.57017i			0.538489i	−0.963072	+	0.269244i	$0.913226\pi$
$108$		0			0
$109$	−3.73204			−0.357464			−0.178732	−	0.983898i	$-0.557200\pi$
$109$	−3.73204			−0.357464			−0.178732	+	0.983898i	$0.557200\pi$
$110$	3.82506	+	1.39221i	0.364705	+	0.132742i
$111$		0			0
$112$	−1.46968	−	6.11311i	−0.138872	−	0.577635i
$113$	9.56433	+	1.68645i	0.899737	+	0.158648i	0.604340	−	0.796727i	$-0.293437\pi$
$113$	9.56433	+	1.68645i	0.899737	+	0.158648i	0.295397	+	0.955375i	$0.404548\pi$
$114$		0			0
$115$	0.140110	+	0.166976i	0.0130653	+	0.0155706i
$116$	11.5105	−	6.64560i	1.06872	−	0.617028i
$117$		0			0
$118$	−7.66710	−	4.42660i	−0.705814	−	0.407502i
$119$	8.42708	−	16.9156i	0.772509	−	1.55065i
$120$		0			0
$121$	11.7835	−	4.28886i	1.07123	−	0.389896i
$122$	24.8089	−	9.02969i	2.24609	−	0.817510i
$123$		0			0
$124$	8.59572	−	1.51566i	0.771919	−	0.136110i
$125$	1.92196	−	3.32893i	0.171905	−	0.297748i
$126$		0			0
$127$	5.60501	+	9.70817i	0.497365	+	0.861461i	0.999995	−	0.00304049i	$-0.000967819\pi$
$127$	5.60501	+	9.70817i	0.497365	+	0.861461i	−0.502631	+	0.864501i	$0.667634\pi$
$128$	−6.52112	−	7.77157i	−0.576391	−	0.686916i
$129$		0			0
$130$	0.835425	−	4.73793i	0.0732716	−	0.415544i
$131$	−16.2722	−	13.6540i	−1.42171	−	1.19296i	−0.950416	−	0.310982i	$-0.899342\pi$
$131$	−16.2722	−	13.6540i	−1.42171	−	1.19296i	−0.471295	−	0.881976i	$-0.656213\pi$
$132$		0			0
$133$	−1.01543	+	0.672562i	−0.0880488	+	0.0583185i
$134$			14.4192i			1.24563i
$135$		0			0
$136$		−	9.51505i		−	0.815909i
$137$	0.365575	−	1.00441i	0.0312332	−	0.0858125i	−0.923096	−	0.384570i	$-0.874350\pi$
$137$	0.365575	−	1.00441i	0.0312332	−	0.0858125i	0.954329	+	0.298757i	$0.0965721\pi$
$138$		0			0
$139$	3.73504	−	4.45125i	0.316802	−	0.377550i	−0.584020	−	0.811740i	$-0.698521\pi$
$139$	3.73504	−	4.45125i	0.316802	−	0.377550i	0.900821	+	0.434190i	$0.142965\pi$
$140$	−1.96193	+	1.86299i	−0.165813	+	0.157451i
$141$		0			0
$142$	11.5707	−	9.70898i	0.970993	−	0.814760i
$143$	−13.9110	−	24.0945i	−1.16329	−	2.01488i
$144$		0			0
$145$	1.71504	+	0.990180i	0.142427	+	0.0822300i
$146$	2.82677	+	16.0314i	0.233945	+	1.32677i
$147$		0			0
$148$	5.28533	−	1.92370i	0.434452	−	0.158127i
$149$	−0.464232	−	1.27547i	−0.0380314	−	0.104490i	0.919223	−	0.393736i	$-0.128818\pi$
$149$	−0.464232	−	1.27547i	−0.0380314	−	0.104490i	−0.957255	+	0.289246i	$0.906595\pi$
$150$		0			0
$151$	−2.48969	−	14.1197i	−0.202608	−	1.14905i	−0.901160	−	0.433487i	$-0.857283\pi$
$151$	−2.48969	−	14.1197i	−0.202608	−	1.14905i	0.698552	−	0.715559i	$-0.253828\pi$
$152$	−0.306612	+	0.531067i	−0.0248695	+	0.0430752i
$153$		0			0
$154$	−3.11462	+	27.4142i	−0.250983	+	2.20910i
$155$	0.835946	+	0.996242i	0.0671448	+	0.0800201i
$156$		0			0
$157$	1.93067	+	0.340430i	0.154085	+	0.0271693i	0.250158	−	0.968205i	$-0.419517\pi$
$157$	1.93067	+	0.340430i	0.154085	+	0.0271693i	−0.0960737	+	0.995374i	$0.530628\pi$
$158$	1.20371	−	1.43453i	0.0957624	−	0.114125i
$159$		0			0
$160$	1.03757	−	2.85071i	0.0820274	−	0.225369i
$161$	−0.878434	+	1.18792i	−0.0692303	+	0.0936216i
$162$		0			0
$163$	14.8246			1.16115			0.580575	−	0.814207i	$-0.302828\pi$
$163$	14.8246			1.16115			0.580575	+	0.814207i	$0.302828\pi$
$164$	−2.40434	−	0.875109i	−0.187748	−	0.0683345i
$165$		0			0
$166$	−9.97260	+	11.8849i	−0.774024	+	0.922446i
$167$	−0.656828	+	3.72506i	−0.0508269	+	0.288254i	−0.999618	−	0.0276516i	$-0.991197\pi$
$167$	−0.656828	+	3.72506i	−0.0508269	+	0.288254i	0.948791	+	0.315905i	$0.102308\pi$
$168$		0			0
$169$	−15.2313	+	12.7806i	−1.17164	+	0.983121i
$170$	5.18990	−	2.99639i	0.398048	−	0.229813i
$171$		0			0
$172$	8.75381	−	15.1620i	0.667472	−	1.15609i
$173$	2.67149	+	15.1508i	0.203110	+	1.15189i	0.900387	+	0.435090i	$0.143284\pi$
$173$	2.67149	+	15.1508i	0.203110	+	1.15189i	−0.697277	+	0.716802i	$0.745605\pi$
$174$		0			0
$175$	12.2986	+	3.63877i	0.929689	+	0.275065i
$176$	−3.94337	−	10.8343i	−0.297243	−	0.816669i
$177$		0			0
$178$	−11.2524	+	1.98411i	−0.843405	+	0.148715i
$179$	−14.0113	−	8.08943i	−1.04725	−	0.604632i	−0.125374	−	0.992109i	$-0.540013\pi$
$179$	−14.0113	−	8.08943i	−1.04725	−	0.604632i	−0.921879	+	0.387477i	$0.873347\pi$
$180$		0			0
$181$	−15.8886	+	9.17326i	−1.18099	+	0.681843i	−0.956243	−	0.292575i	$-0.905488\pi$
$181$	−15.8886	+	9.17326i	−1.18099	+	0.681843i	−0.224744	+	0.974418i	$0.572155\pi$
$182$	32.5481	−	2.00111i	2.41262	−	0.148332i
$183$		0			0
$184$	−0.129170	+	0.732562i	−0.00952257	+	0.0540052i
$185$	0.641978	+	0.538684i	0.0471992	+	0.0396048i
$186$		0			0
$187$	11.8531	−	32.5660i	0.866781	−	2.38146i
$188$	9.70670			0.707934
$189$		0			0
$190$	−0.386222			−0.0280195
$191$	6.87241	−	18.8818i	0.497270	−	1.36624i	−0.396633	−	0.917977i	$-0.629821\pi$
$191$	6.87241	−	18.8818i	0.497270	−	1.36624i	0.893903	−	0.448261i	$-0.147956\pi$
$192$		0			0
$193$	−16.4758	−	13.8249i	−1.18596	−	0.995136i	−0.999921	−	0.0125936i	$-0.995991\pi$
$193$	−16.4758	−	13.8249i	−1.18596	−	0.995136i	−0.186037	−	0.982543i	$-0.559564\pi$
$194$	4.08827	−	23.1858i	0.293521	−	1.66464i
$195$		0			0
$196$	−15.3862	−	9.97799i	−1.09901	−	0.712713i
$197$	−2.96839	+	1.71380i	−0.211489	+	0.122103i	−0.602003	−	0.798494i	$-0.705631\pi$
$197$	−2.96839	+	1.71380i	−0.211489	+	0.122103i	0.390514	+	0.920597i	$0.372297\pi$
$198$		0			0
$199$	9.32690	+	5.38489i	0.661166	+	0.381725i	0.792721	−	0.609584i	$-0.208664\pi$
$199$	9.32690	+	5.38489i	0.661166	+	0.381725i	−0.131555	+	0.991309i	$0.541997\pi$
$200$	6.35938	−	1.12133i	0.449676	−	0.0792901i
$201$		0			0
$202$	−10.1687	−	27.9382i	−0.715466	−	1.96573i
$203$	−3.80826	+	12.8715i	−0.267288	+	0.903403i
$204$		0			0
$205$	−0.0662004	−	0.375441i	−0.00462364	−	0.0262219i
$206$	−13.1258	+	22.7346i	−0.914520	+	1.58399i
$207$		0			0
$208$	−11.8014	+	6.81351i	−0.818276	+	0.472432i
$209$	−1.71096	+	1.43567i	−0.118350	+	0.0993072i
$210$		0			0
$211$	0.0518221	−	0.293898i	0.00356758	−	0.0202327i	−0.982972	−	0.183755i	$-0.941175\pi$
$211$	0.0518221	−	0.293898i	0.00356758	−	0.0202327i	0.986540	+	0.163523i	$0.0522857\pi$
$212$	−5.27598	+	6.28767i	−0.362356	+	0.431839i
$213$		0			0
$214$	−11.2503	−	4.09477i	−0.769054	−	0.279913i
$215$	2.60860			0.177905
$216$		0			0
$217$	−5.24106	+	7.08760i	−0.355786	+	0.481138i
$218$	2.74352	−	7.53775i	0.185814	−	0.510521i
$219$		0			0
$220$	−3.18913	+	3.80065i	−0.215011	+	0.256240i
$221$	−40.3380	−	7.11269i	−2.71343	−	0.478451i
$222$		0			0
$223$	1.84202	+	2.19524i	0.123351	+	0.147004i	0.824185	−	0.566320i	$-0.191633\pi$
$223$	1.84202	+	2.19524i	0.123351	+	0.147004i	−0.700835	+	0.713324i	$0.747189\pi$
$224$	20.4310	+	2.32124i	1.36510	+	0.155094i
$225$		0			0
$226$	−10.4372	+	18.0777i	−0.694270	+	1.20251i
$227$	4.81038	+	27.2810i	0.319276	+	1.81070i	0.547173	+	0.837019i	$0.315704\pi$
$227$	4.81038	+	27.2810i	0.319276	+	1.81070i	−0.227897	+	0.973685i	$0.573185\pi$
$228$		0			0
$229$	8.06759	+	22.1655i	0.533121	+	1.46474i	0.855337	+	0.518072i	$0.173350\pi$
$229$	8.06759	+	22.1655i	0.533121	+	1.46474i	−0.322216	+	0.946666i	$0.604428\pi$
$230$	−0.440247	+	0.160237i	−0.0290290	+	0.0105657i
$231$		0			0
$232$	1.17356	+	6.65561i	0.0770482	+	0.436962i
$233$	−7.45007	−	4.30130i	−0.488070	−	0.281787i	0.235703	−	0.971825i	$-0.424261\pi$
$233$	−7.45007	−	4.30130i	−0.488070	−	0.281787i	−0.723774	+	0.690038i	$0.757594\pi$
$234$		0			0
$235$	0.723139	+	1.25251i	0.0471724	+	0.0817049i
$236$	8.26621	−	6.93617i	0.538084	−	0.451506i
$237$		0			0
$238$	27.9701	+	29.4556i	1.81303	+	1.90932i
$239$	−8.52364	+	10.1581i	−0.551348	+	0.657071i	−0.967692	−	0.252136i	$-0.918867\pi$
$239$	−8.52364	+	10.1581i	−0.551348	+	0.657071i	0.416344	+	0.909207i	$0.363311\pi$
$240$		0			0
$241$	−3.73945	+	10.2740i	−0.240879	+	0.661809i	0.759063	+	0.651017i	$0.225657\pi$
$241$	−3.73945	+	10.2740i	−0.240879	+	0.661809i	−0.999942	+	0.0107919i	$0.996565\pi$
$242$			26.9525i			1.73258i
$243$		0			0
$244$			32.1790i			2.06005i
$245$	0.141267	−	2.72872i	0.00902520	−	0.174331i
$246$		0			0
$247$	2.02220	+	1.69683i	0.128670	+	0.107967i
$248$	−0.770678	+	4.37073i	−0.0489381	+	0.277542i
$249$		0			0
$250$	5.31069	+	6.32903i	0.335877	+	0.400283i
$251$	−5.12956	−	8.88466i	−0.323775	−	0.560795i	0.657489	−	0.753464i	$-0.271619\pi$
$251$	−5.12956	−	8.88466i	−0.323775	−	0.560795i	−0.981264	+	0.192670i	$0.938285\pi$
$252$		0			0
$253$	−1.35466	+	2.34634i	−0.0851667	+	0.147513i
$254$	−23.7284	+	4.18395i	−1.48885	+	0.262524i
$255$		0			0
$256$	−1.97169	+	0.717638i	−0.123231	+	0.0448524i
$257$	1.27159	−	0.462822i	0.0793198	−	0.0288700i	−0.302055	−	0.953290i	$-0.597673\pi$
$257$	1.27159	−	0.462822i	0.0793198	−	0.0288700i	0.381375	+	0.924420i	$0.375451\pi$
$258$		0			0
$259$	−2.53294	+	5.08433i	−0.157389	+	0.315925i
$260$	5.07832	+	2.93197i	0.314944	+	0.181833i
$261$		0			0
$262$	39.5397	−	22.8283i	2.44277	−	1.41033i
$263$	−4.58008	−	5.45832i	−0.282420	−	0.336575i	0.606121	−	0.795372i	$-0.292725\pi$
$263$	−4.58008	−	5.45832i	−0.282420	−	0.336575i	−0.888541	+	0.458798i	$0.848280\pi$
$264$		0			0
$265$	−1.20439	−	0.212366i	−0.0739851	−	0.0130456i
$266$	−0.611933	−	2.54532i	−0.0375200	−	0.156064i
$267$		0			0
$268$	−16.5150	−	6.01097i	−1.00881	−	0.367178i
$269$	−6.69363			−0.408118			−0.204059	−	0.978959i	$-0.565413\pi$
$269$	−6.69363			−0.408118			−0.204059	+	0.978959i	$0.565413\pi$
$270$		0			0
$271$			15.0044i			0.911450i	0.890121	+	0.455725i	$0.150620\pi$
$271$			15.0044i			0.911450i	−0.890121	+	0.455725i	$0.849380\pi$
$272$	−15.9506	−	5.80556i	−0.967150	−	0.352014i
$273$		0			0
$274$	1.75990	+	1.47673i	0.106320	+	0.0892128i
$275$	23.1624	+	4.08415i	1.39674	+	0.246283i
$276$		0			0
$277$	−19.7269	+	16.5529i	−1.18528	+	0.994566i	−0.185348	+	0.982673i	$0.559341\pi$
$277$	−19.7269	+	16.5529i	−1.18528	+	0.994566i	−0.999929	+	0.0118925i	$0.996214\pi$
$278$	6.24464	+	10.8160i	0.374529	+	0.648703i
$279$		0			0
$280$	−0.548961	−	1.26143i	−0.0328067	−	0.0753847i
$281$	7.95320	−	1.40236i	0.474448	−	0.0836580i	0.0686892	−	0.997638i	$-0.478118\pi$
$281$	7.95320	−	1.40236i	0.474448	−	0.0836580i	0.405759	+	0.913980i	$0.367007\pi$
$282$		0			0
$283$	−2.15839	−	5.93013i	−0.128303	−	0.352510i	0.858863	−	0.512205i	$-0.171171\pi$
$283$	−2.15839	−	5.93013i	−0.128303	−	0.352510i	−0.987166	+	0.159695i	$0.948949\pi$
$284$	6.29665	+	17.2999i	0.373638	+	1.02656i
$285$		0			0
$286$	58.8909	−	10.3841i	3.48229	−	0.614022i
$287$	2.36938	−	1.03113i	0.139860	−	0.0608659i
$288$		0			0
$289$	−17.0108	−	29.4636i	−1.00064	−	1.73316i
$290$	−3.26068	+	2.73603i	−0.191474	+	0.160665i
$291$		0			0
$292$	−19.5400	−	3.44542i	−1.14349	−	0.201628i
$293$	6.25563	+	5.24910i	0.365458	+	0.306656i	0.806962	−	0.590604i	$-0.201110\pi$
$293$	6.25563	+	5.24910i	0.365458	+	0.306656i	−0.441504	+	0.897259i	$0.645555\pi$
$294$		0			0
$295$	1.51084	+	0.549900i	0.0879644	+	0.0320164i
$296$			2.85995i			0.166231i
$297$		0			0
$298$	2.91738			0.168999
$299$	3.00906	+	1.09521i	0.174018	+	0.0633375i
$300$		0			0
$301$	4.13308	+	17.1915i	0.238227	+	0.990899i
$302$	30.3484	+	5.35124i	1.74635	+	0.307929i
$303$		0			0
$304$	0.703182	+	0.838020i	0.0403303	+	0.0480637i
$305$	−4.15225	+	2.39730i	−0.237757	+	0.137269i
$306$		0			0
$307$	20.0345	+	11.5669i	1.14343	+	0.660159i	0.947277	−	0.320415i	$-0.103822\pi$
$307$	20.0345	+	11.5669i	1.14343	+	0.660159i	0.196151	+	0.980574i	$0.437156\pi$
$308$	−30.1004	−	14.9955i	−1.71513	−	0.854451i
$309$		0			0
$310$	−2.62668	+	0.956032i	−0.149185	+	0.0542990i
$311$	22.1526	−	8.06290i	1.25616	−	0.457205i	0.373682	−	0.927557i	$-0.378095\pi$
$311$	22.1526	−	8.06290i	1.25616	−	0.457205i	0.882479	+	0.470352i	$0.155873\pi$
$312$		0			0
$313$	−11.7748	+	2.07621i	−0.665550	+	0.117354i	−0.496209	−	0.868203i	$-0.665275\pi$
$313$	−11.7748	+	2.07621i	−0.665550	+	0.117354i	−0.169341	+	0.985557i	$0.554164\pi$
$314$	−2.10687	+	3.64920i	−0.118897	+	0.205936i
$315$		0			0
$316$	1.14124	+	1.97669i	0.0641999	+	0.111197i
$317$	18.1039	+	21.5754i	1.01682	+	1.21179i	0.977143	+	0.212582i	$0.0681873\pi$
$317$	18.1039	+	21.5754i	1.01682	+	1.21179i	0.0396733	+	0.999213i	$0.487368\pi$
$318$		0			0
$319$	−4.27439	+	24.2413i	−0.239320	+	1.35725i
$320$	3.57380	+	2.99877i	0.199781	+	0.167636i
$321$		0			0
$322$	−1.75354	−	2.64748i	−0.0977210	−	0.147538i
$323$			3.28823i			0.182962i
$324$		0			0
$325$		−	27.7982i		−	1.54196i
$326$	−10.8979	+	29.9418i	−0.603580	+	1.65832i
$327$		0			0
$328$	0.836276	−	0.996635i	0.0461756	−	0.0550300i
$329$	−7.10870	+	6.75020i	−0.391915	+	0.372150i
$330$		0			0
$331$	−11.5569	+	9.69739i	−0.635224	+	0.533017i	−0.902547	−	0.430590i	$-0.858305\pi$
$331$	−11.5569	+	9.69739i	−0.635224	+	0.533017i	0.267323	+	0.963607i	$0.413861\pi$
$332$	−9.45503	−	16.3766i	−0.518912	−	0.898782i
$333$		0			0
$334$	−7.04080	−	4.06501i	−0.385255	−	0.222427i
$335$	−0.454719	−	2.57884i	−0.0248440	−	0.140897i
$336$		0			0
$337$	−15.3260	+	5.57821i	−0.834860	+	0.303864i	−0.723852	−	0.689955i	$-0.757630\pi$
$337$	−15.3260	+	5.57821i	−0.834860	+	0.303864i	−0.111008	+	0.993819i	$0.535408\pi$
$338$	−14.6165	−	40.1586i	−0.795034	−	2.18434i
$339$		0			0
$340$	1.26838	+	7.19337i	0.0687878	+	0.390115i
$341$	−8.08240	+	13.9991i	−0.437687	+	0.758096i
$342$		0			0
$343$	18.2069	−	3.39241i	0.983081	−	0.183173i
$344$	5.72225	+	6.81951i	0.308523	+	0.367683i
$345$		0			0
$346$	−32.5645	−	5.74200i	−1.75068	−	0.308692i
$347$	23.3846	−	27.8687i	1.25535	−	1.49607i	0.462552	−	0.886592i	$-0.346934\pi$
$347$	23.3846	−	27.8687i	1.25535	−	1.49607i	0.792802	−	0.609480i	$-0.208622\pi$
$348$		0			0
$349$	−2.98415	+	8.19888i	−0.159738	+	0.438876i	−0.993581	−	0.113126i	$-0.963914\pi$
$349$	−2.98415	+	8.19888i	−0.159738	+	0.438876i	0.833843	+	0.552002i	$0.186136\pi$
$350$	−16.3904	+	22.1651i	−0.876104	+	1.18477i
$351$		0			0
$352$	37.7074			2.00981
$353$	−8.54968	−	3.11183i	−0.455053	−	0.165626i	0.104316	−	0.994544i	$-0.466735\pi$
$353$	−8.54968	−	3.11183i	−0.455053	−	0.165626i	−0.559370	+	0.828918i	$0.688957\pi$
$354$		0			0
$355$	−1.76322	+	2.10132i	−0.0935818	+	0.111526i
$356$	2.41834	−	13.7151i	0.128172	−	0.726897i
$357$		0			0
$358$	26.6386	−	22.3524i	1.40789	−	1.18136i
$359$	0.444525	−	0.256647i	0.0234611	−	0.0135453i	−0.488224	−	0.872719i	$-0.662355\pi$
$359$	0.444525	−	0.256647i	0.0234611	−	0.0135453i	0.511685	+	0.859173i	$0.329022\pi$
$360$		0			0
$361$	−9.39404	+	16.2710i	−0.494423	+	0.856366i
$362$	−6.84752	−	38.8342i	−0.359898	−	2.04108i
$363$		0			0
$364$	−11.2764	+	38.1131i	−0.591046	+	1.99767i
$365$	−1.01112	−	2.77804i	−0.0529246	−	0.145409i
$366$		0			0
$367$	−30.6284	+	5.40061i	−1.59879	+	0.281910i	−0.900812	−	0.434210i	$-0.857028\pi$
$367$	−30.6284	+	5.40061i	−1.59879	+	0.281910i	−0.697977	+	0.716120i	$0.745916\pi$
$368$	1.14922	+	0.663505i	0.0599075	+	0.0345876i
$369$		0			0
$370$	−1.55994	+	0.900630i	−0.0810972	+	0.0468215i
$371$	−0.508685	−	8.27377i	−0.0264096	−	0.429553i
$372$		0			0
$373$	4.53556	−	25.7224i	0.234842	−	1.33186i	−0.608103	−	0.793858i	$-0.708069\pi$
$373$	4.53556	−	25.7224i	0.234842	−	1.33186i	0.842945	−	0.537999i	$-0.180820\pi$
$374$	57.0614	+	47.8802i	2.95057	+	2.47583i
$375$		0			0
$376$	−1.68809	+	4.63799i	−0.0870565	+	0.239186i
$377$	29.0930			1.49837
$378$		0			0
$379$	−28.5024			−1.46407			−0.732035	−	0.681267i	$-0.761429\pi$
$379$	−28.5024			−1.46407			−0.732035	+	0.681267i	$0.761429\pi$
$380$	0.161005	−	0.442358i	0.00825940	−	0.0226925i
$381$		0			0
$382$	33.0842	+	27.7610i	1.69274	+	1.42037i
$383$	−2.37420	+	13.4648i	−0.121316	+	0.688017i	0.862112	+	0.506718i	$0.169141\pi$
$383$	−2.37420	+	13.4648i	−0.121316	+	0.688017i	−0.983428	+	0.181299i	$0.941970\pi$
$384$		0			0
$385$	−0.307481	−	5.00118i	−0.0156707	−	0.254884i
$386$	40.0345	−	23.1139i	2.03770	−	1.17647i
$387$		0			0
$388$	24.8515	+	14.3480i	1.26164	+	0.728410i
$389$	−24.7405	+	4.36241i	−1.25439	+	0.221183i	−0.761073	−	0.648666i	$-0.775327\pi$
$389$	−24.7405	+	4.36241i	−1.25439	+	0.221183i	−0.493318	+	0.869849i	$0.664216\pi$
$390$		0			0
$391$	1.36423	+	3.74820i	0.0689922	+	0.189554i
$392$	7.44341	−	5.61644i	0.375949	−	0.283673i
$393$		0			0
$394$	−1.27929	−	7.25523i	−0.0644498	−	0.365513i
$395$	−0.170043	+	0.294523i	−0.00855578	+	0.0148190i
$396$		0			0
$397$	−6.75634	+	3.90078i	−0.339091	+	0.195774i	−0.659870	−	0.751380i	$-0.729389\pi$
$397$	−6.75634	+	3.90078i	−0.339091	+	0.195774i	0.320779	+	0.947154i	$0.396055\pi$
$398$	−17.7325	+	14.8794i	−0.888851	+	0.745834i
$399$		0			0
$400$	2.00039	−	11.3448i	0.100020	−	0.567240i
$401$	−0.935778	+	1.11522i	−0.0467305	+	0.0556913i	−0.788903	−	0.614517i	$-0.789351\pi$
$401$	−0.935778	+	1.11522i	−0.0467305	+	0.0556913i	0.742173	+	0.670208i	$0.233795\pi$
$402$		0			0
$403$	17.9532	+	6.53442i	0.894311	+	0.325503i
$404$	36.2380			1.80291
$405$		0			0
$406$	−23.1975	−	17.1539i	−1.15128	−	0.851333i
$407$	−3.56269	+	9.78840i	−0.176596	+	0.485193i
$408$		0			0
$409$	6.16526	−	7.34748i	0.304853	−	0.363309i	−0.591768	−	0.806108i	$-0.701570\pi$
$409$	6.16526	−	7.34748i	0.304853	−	0.363309i	0.896621	+	0.442799i	$0.146014\pi$
$410$	0.806959	+	0.142289i	0.0398529	+	0.00702714i
$411$		0			0
$412$	−20.5672	−	24.5111i	−1.01328	−	1.20757i
$413$	−1.23023	+	10.8282i	−0.0605355	+	0.532819i
$414$		0			0
$415$	1.40878	−	2.44008i	0.0691543	−	0.119779i
$416$	−7.73895	−	43.8898i	−0.379433	−	2.15187i
$417$		0			0
$418$	−1.64190	−	4.51109i	−0.0803081	−	0.220645i
$419$	−20.7203	+	7.54159i	−1.01225	+	0.368431i	−0.794298	−	0.607528i	$-0.792161\pi$
$419$	−20.7203	+	7.54159i	−1.01225	+	0.368431i	−0.217956	+	0.975959i	$0.569939\pi$
$420$		0			0
$421$	−4.79615	−	27.2003i	−0.233750	−	1.32566i	−0.845230	−	0.534402i	$-0.820537\pi$
$421$	−4.79615	−	27.2003i	−0.233750	−	1.32566i	0.611481	−	0.791259i	$-0.290574\pi$
$422$	0.555501	+	0.320719i	0.0270414	+	0.0156123i
$423$		0			0
$424$	−2.08678	−	3.61442i	−0.101343	−	0.175532i
$425$	26.5254	−	22.2574i	1.28667	−	1.07964i
$426$		0			0
$427$	−22.3778	−	23.5663i	−1.08294	−	1.14045i
$428$	9.37988	−	11.1785i	0.453394	−	0.540334i
$429$		0			0
$430$	−1.91765	+	5.26869i	−0.0924771	+	0.254079i
$431$		−	13.9378i		−	0.671358i	−0.941976	−	0.335679i	$-0.891034\pi$
$431$		−	13.9378i		−	0.671358i	0.941976	−	0.335679i	$-0.108966\pi$
$432$		0			0
$433$		−	20.8489i		−	1.00193i	−0.865467	−	0.500966i	$-0.832978\pi$
$433$		−	20.8489i		−	1.00193i	0.865467	−	0.500966i	$-0.167022\pi$
$434$	−10.4623	−	15.7959i	−0.502205	−	0.758225i
$435$		0			0
$436$	7.48965	+	6.28456i	0.358689	+	0.300976i
$437$	0.0446390	−	0.253160i	0.00213537	−	0.0121103i
$438$		0			0
$439$	−2.39592	−	2.85534i	−0.114351	−	0.136278i	0.705833	−	0.708379i	$-0.250573\pi$
$439$	−2.39592	−	2.85534i	−0.114351	−	0.136278i	−0.820183	+	0.572101i	$0.806129\pi$
$440$	−1.26138	−	2.18478i	−0.0601340	−	0.104155i
$441$		0			0
$442$	44.0193	−	76.2437i	2.09378	−	3.62654i
$443$	−5.16917	+	0.911464i	−0.245595	+	0.0433050i	−0.295090	−	0.955469i	$-0.595350\pi$
$443$	−5.16917	+	0.911464i	−0.245595	+	0.0433050i	0.0494956	+	0.998774i	$0.484239\pi$
$444$		0			0
$445$	1.94990	−	0.709706i	0.0924342	−	0.0336433i
$446$	−5.78792	+	2.10663i	−0.274066	+	0.0997519i
$447$		0			0
$448$	−14.1005	+	28.3037i	−0.666185	+	1.33722i
$449$	22.4516	+	12.9624i	1.05956	+	0.611735i	0.925310	−	0.379212i	$-0.123805\pi$
$449$	22.4516	+	12.9624i	1.05956	+	0.611735i	0.134247	+	0.990948i	$0.457138\pi$
$450$		0			0
$451$	4.10375	−	2.36930i	0.193238	−	0.111566i
$452$	−16.3543	−	19.4903i	−0.769242	−	0.916747i
$453$		0			0
$454$	−58.6368	−	10.3392i	−2.75196	−	0.485245i
$455$	−5.75804	+	1.38432i	−0.269941	+	0.0648979i
$456$		0			0
$457$	19.4951	+	7.09562i	0.911940	+	0.331919i	0.755027	−	0.655693i	$-0.227624\pi$
$457$	19.4951	+	7.09562i	0.911940	+	0.331919i	0.156913	+	0.987612i	$0.449846\pi$
$458$	−50.6993			−2.36902
$459$		0			0
$460$		−	0.571034i		−	0.0266246i
$461$	0.166492	+	0.0605983i	0.00775433	+	0.00282234i	0.345894	−	0.938273i	$-0.387576\pi$
$461$	0.166492	+	0.0605983i	0.00775433	+	0.00282234i	−0.338140	+	0.941096i	$0.609798\pi$
$462$		0			0
$463$	22.1677	+	18.6009i	1.03022	+	0.864457i	0.990877	−	0.134769i	$-0.0430292\pi$
$463$	22.1677	+	18.6009i	1.03022	+	0.864457i	0.0393425	+	0.999226i	$0.487474\pi$
$464$	11.8732	+	2.09357i	0.551201	+	0.0971916i
$465$		0			0
$466$	14.1642	−	11.8852i	0.656146	−	0.550572i
$467$	−4.43621	−	7.68373i	−0.205283	−	0.355561i	0.744940	−	0.667132i	$-0.232478\pi$
$467$	−4.43621	−	7.68373i	−0.205283	−	0.355561i	−0.950223	+	0.311571i	$0.899145\pi$
$468$		0			0
$469$	16.2749	−	7.08267i	0.751504	−	0.327047i
$470$	−3.06135	+	0.539798i	−0.141209	+	0.0248990i
$471$		0			0
$472$	1.87662	+	5.15597i	0.0863784	+	0.237323i
$473$	11.0897	+	30.4686i	0.509903	+	1.40095i
$474$		0			0
$475$	−2.19769	+	0.387512i	−0.100837	+	0.0177803i
$476$	−45.3969	+	19.7563i	−2.08076	+	0.905527i
$477$		0			0
$478$	−14.2507	−	24.6830i	−0.651813	−	1.12897i
$479$	4.86205	−	4.07975i	0.222153	−	0.186408i	−0.524918	−	0.851153i	$-0.675904\pi$
$479$	4.86205	−	4.07975i	0.222153	−	0.186408i	0.747071	+	0.664744i	$0.231460\pi$
$480$		0			0
$481$	12.1245	+	2.13787i	0.552828	+	0.0974784i
$482$	−18.0019	−	15.1054i	−0.819966	−	0.688033i
$483$		0			0
$484$	−30.8701	−	11.2358i	−1.40318	−	0.510717i
$485$			4.27565i			0.194147i
$486$		0			0
$487$	5.19850			0.235566			0.117783	−	0.993039i	$-0.462421\pi$
$487$	5.19850			0.235566			0.117783	+	0.993039i	$0.462421\pi$
$488$	−15.3756	−	5.59625i	−0.696019	−	0.253330i
$489$		0			0
$490$	5.40745	+	2.29127i	0.244284	+	0.103509i
$491$	13.4965	+	2.37981i	0.609091	+	0.107399i	0.469682	−	0.882836i	$-0.344369\pi$
$491$	13.4965	+	2.37981i	0.609091	+	0.107399i	0.139409	+	0.990235i	$0.455480\pi$
$492$		0			0
$493$	23.2942	+	27.7609i	1.04912	+	1.25029i
$494$	−4.91373	+	2.83694i	−0.221079	+	0.127640i
$495$		0			0
$496$	6.85670	+	3.95872i	0.307875	+	0.177752i
$497$	−16.6420	−	8.29079i	−0.746496	−	0.371893i
$498$		0			0
$499$	−32.4000	+	11.7926i	−1.45042	+	0.527911i	−0.942709	−	0.333615i	$-0.891732\pi$
$499$	−32.4000	+	11.7926i	−1.45042	+	0.527911i	−0.507714	+	0.861526i	$0.669509\pi$
$500$	−9.46283	+	3.44419i	−0.423191	+	0.154029i
$501$		0			0
$502$	21.7156	−	3.82904i	0.969213	−	0.170898i
$503$	19.0162	−	32.9370i	0.847891	−	1.46859i	−0.0351966	−	0.999380i	$-0.511206\pi$
$503$	19.0162	−	32.9370i	0.847891	−	1.46859i	0.883087	−	0.469209i	$-0.155461\pi$
$504$		0			0
$505$	2.69969	+	4.67601i	0.120135	+	0.208080i
$506$	−3.74315	−	4.46092i	−0.166403	−	0.198312i
$507$		0			0
$508$	5.09963	−	28.9214i	0.226259	−	1.28318i
$509$	−2.43971	−	2.04716i	−0.108138	−	0.0907387i	0.587115	−	0.809503i	$-0.300263\pi$
$509$	−2.43971	−	2.04716i	−0.108138	−	0.0907387i	−0.695254	+	0.718765i	$0.744708\pi$
$510$		0			0
$511$	16.7061	−	11.0652i	0.739034	−	0.489494i
$512$		−	24.8000i		−	1.09601i
$513$		0			0
$514$			2.90852i			0.128289i
$515$	1.63057	−	4.47996i	0.0718516	−	0.197411i
$516$		0			0
$517$	−11.5552	+	13.7710i	−0.508198	+	0.605647i
$518$	−8.40700	−	8.85350i	−0.369383	−	0.389000i
$519$		0			0
$520$	−2.28410	+	1.91659i	−0.100164	+	0.0840479i
$521$	13.0875	+	22.6683i	0.573375	+	0.993115i	0.996216	+	0.0869113i	$0.0276997\pi$
$521$	13.0875	+	22.6683i	0.573375	+	0.993115i	−0.422841	+	0.906204i	$0.638967\pi$
$522$		0			0
$523$	−14.0356	−	8.10349i	−0.613736	−	0.354341i	0.160690	−	0.987005i	$-0.448628\pi$
$523$	−14.0356	−	8.10349i	−0.613736	−	0.354341i	−0.774426	+	0.632664i	$0.781961\pi$
$524$	9.66329	+	54.8032i	0.422143	+	2.39409i
$525$		0			0
$526$	14.3913	−	5.23801i	0.627492	−	0.228388i
$527$	8.13951	+	22.3631i	0.354563	+	0.974153i
$528$		0			0
$529$	3.93976	+	22.3435i	0.171294	+	0.971456i
$530$	1.31430	−	2.27644i	0.0570897	−	0.0988822i
$531$		0			0
$532$	3.17038	+	0.360198i	0.137453	+	0.0156166i
$533$	−3.60000	−	4.29031i	−0.155933	−	0.185834i
$534$		0			0
$535$	2.14122	+	0.377555i	0.0925731	+	0.0163231i
$536$	5.74424	−	6.84572i	0.248113	−	0.295690i
$537$		0			0
$538$	4.92065	−	13.5194i	0.212144	−	0.582862i
$539$	32.4722	−	9.95031i	1.39867	−	0.428590i
$540$		0			0
$541$	9.50292			0.408562			0.204281	−	0.978912i	$-0.434514\pi$
$541$	9.50292			0.408562			0.204281	+	0.978912i	$0.434514\pi$
$542$	−30.3049	−	11.0301i	−1.30171	−	0.473783i
$543$		0			0
$544$	35.6838	−	42.5263i	1.52993	−	1.82330i
$545$	−0.252964	+	1.43463i	−0.0108358	+	0.0614527i
$546$		0			0
$547$	−7.11504	+	5.97023i	−0.304217	+	0.255269i	−0.782097	−	0.623157i	$-0.785850\pi$
$547$	−7.11504	+	5.97023i	−0.304217	+	0.255269i	0.477880	+	0.878425i	$0.341405\pi$
$548$	−2.42503	+	1.40009i	−0.103592	+	0.0598090i
$549$		0			0
$550$	−25.2762	+	43.7796i	−1.07778	+	1.86677i
$551$	−0.405563	−	2.30006i	−0.0172775	−	0.0979858i
$552$		0			0
$553$	−2.21041	−	0.653990i	−0.0939963	−	0.0278105i
$554$	−18.9307	−	52.0117i	−0.804289	−	2.20977i
$555$		0			0
$556$	−14.9913	+	2.64338i	−0.635775	+	0.112104i
$557$	−10.3816	−	5.99382i	−0.439882	−	0.253966i	0.263665	−	0.964614i	$-0.415069\pi$
$557$	−10.3816	−	5.99382i	−0.439882	−	0.253966i	−0.703548	+	0.710648i	$0.748402\pi$
$558$		0			0
$559$	33.1881	−	19.1611i	1.40371	−	0.810430i
$560$	−2.44955	+	0.150602i	−0.103512	+	0.00636412i
$561$		0			0
$562$	−3.01419	+	17.0943i	−0.127146	+	0.721080i
$563$	0.0744631	+	0.0624819i	0.00313824	+	0.00263330i	0.644355	−	0.764726i	$-0.277126\pi$
$563$	0.0744631	+	0.0624819i	0.00313824	+	0.00263330i	−0.641217	+	0.767359i	$0.721570\pi$
$564$		0			0
$565$	1.29657	−	3.56230i	0.0545472	−	0.149867i
$566$	13.5640			0.570138
$567$		0			0
$568$	−9.36117			−0.392786
$569$	−6.26646	+	17.2169i	−0.262704	+	0.721772i	0.736279	+	0.676678i	$0.236581\pi$
$569$	−6.26646	+	17.2169i	−0.262704	+	0.721772i	−0.998983	+	0.0450941i	$0.985641\pi$
$570$		0			0
$571$	11.0847	+	9.30116i	0.463880	+	0.389241i	0.844556	−	0.535467i	$-0.179864\pi$
$571$	11.0847	+	9.30116i	0.463880	+	0.389241i	−0.380676	+	0.924708i	$0.624309\pi$
$572$	−12.6567	+	71.7795i	−0.529201	+	3.00125i
$573$		0			0
$574$	0.340827	+	5.54355i	0.0142258	+	0.231383i
$575$	−2.34434	+	1.35350i	−0.0977655	+	0.0564450i
$576$		0			0
$577$	−21.6982	−	12.5275i	−0.903309	−	0.521526i	−0.0250367	−	0.999687i	$-0.507970\pi$
$577$	−21.6982	−	12.5275i	−0.903309	−	0.521526i	−0.878272	+	0.478161i	$0.841304\pi$
$578$	72.0140	−	12.6980i	2.99539	−	0.528168i
$579$		0			0
$580$	−1.77442	−	4.87519i	−0.0736790	−	0.202431i
$581$	18.3129	+	5.41821i	0.759749	+	0.224785i
$582$		0			0
$583$	−2.63964	−	14.9702i	−0.109323	−	0.620001i
$584$	5.04446	−	8.73726i	0.208741	−	0.361550i
$585$		0			0
$586$	−15.2005	+	8.77601i	−0.627927	+	0.362534i
$587$	−21.3062	+	17.8781i	−0.879402	+	0.737906i	−0.966056	−	0.258332i	$-0.916827\pi$
$587$	−21.3062	+	17.8781i	−0.879402	+	0.737906i	0.0866537	+	0.996238i	$0.472383\pi$
$588$		0			0
$589$	0.266333	−	1.51045i	0.0109741	−	0.0622369i
$590$	−2.22131	+	2.64726i	−0.0914500	+	0.108986i
$591$		0			0
$592$	4.79431	+	1.74498i	0.197045	+	0.0717184i
$593$	−43.7366			−1.79605			−0.898023	−	0.439949i	$-0.854996\pi$
$593$	−43.7366			−1.79605			−0.898023	+	0.439949i	$0.854996\pi$
$594$		0			0
$595$	−5.93129	−	4.38600i	−0.243159	−	0.179809i
$596$	−1.21618	+	3.34142i	−0.0498165	+	0.136870i
$597$		0			0
$598$	−4.42407	+	5.27240i	−0.180914	+	0.215605i
$599$	−9.06627	−	1.59863i	−0.370438	−	0.0653181i	−0.0146695	−	0.999892i	$-0.504670\pi$
$599$	−9.06627	−	1.59863i	−0.370438	−	0.0653181i	−0.355768	+	0.934574i	$0.615781\pi$
$600$		0			0
$601$	25.8812	+	30.8440i	1.05571	+	1.25815i	0.964993	+	0.262276i	$0.0844730\pi$
$601$	25.8812	+	30.8440i	1.05571	+	1.25815i	0.0907219	+	0.995876i	$0.471083\pi$
$602$	−37.7606	−	4.29012i	−1.53901	−	0.174852i
$603$		0			0
$604$	−18.7804	+	32.5287i	−0.764166	+	1.32357i
$605$	−0.849967	−	4.82040i	−0.0345561	−	0.195977i
$606$		0			0
$607$	−0.602537	−	1.65546i	−0.0244562	−	0.0671930i	0.926864	−	0.375398i	$-0.122494\pi$
$607$	−0.602537	−	1.65546i	−0.0244562	−	0.0671930i	−0.951320	+	0.308205i	$0.900272\pi$
$608$	−3.36199	+	1.22367i	−0.136347	+	0.0496262i
$609$		0			0
$610$	−1.78951	−	10.1488i	−0.0724550	−	0.410913i
$611$	18.4004	+	10.6235i	0.744399	+	0.429779i
$612$		0			0
$613$	−11.2627	−	19.5075i	−0.454895	−	0.787901i	0.543787	−	0.839223i	$-0.316990\pi$
$613$	−11.2627	−	19.5075i	−0.454895	−	0.787901i	−0.998682	+	0.0513222i	$0.983656\pi$
$614$	−38.0900	+	31.9613i	−1.53719	+	1.28985i
$615$		0			0
$616$	12.3998	−	11.7745i	0.499603	−	0.474407i
$617$	−12.7802	+	15.2309i	−0.514513	+	0.613173i	−0.959274	−	0.282476i	$-0.908844\pi$
$617$	−12.7802	+	15.2309i	−0.514513	+	0.613173i	0.444761	+	0.895649i	$0.353289\pi$
$618$		0			0
$619$	−1.43450	+	3.94126i	−0.0576575	+	0.158413i	−0.965177	−	0.261597i	$-0.915751\pi$
$619$	−1.43450	+	3.94126i	−0.0576575	+	0.158413i	0.907520	+	0.420009i	$0.137973\pi$
$620$		−	3.40700i		−	0.136829i
$621$		0			0
$622$			50.6698i			2.03167i
$623$	7.76662	+	11.7260i	0.311163	+	0.469792i
$624$		0			0
$625$	17.4181	+	14.6155i	0.696725	+	0.584622i
$626$	4.46253	−	25.3083i	0.178359	−	1.01152i
$627$		0			0
$628$	−3.30131	−	3.93435i	−0.131737	−	0.156998i
$629$	7.66783	+	13.2811i	0.305736	+	0.529551i
$630$		0			0
$631$	7.09781	−	12.2938i	0.282559	−	0.489407i	−0.689455	−	0.724328i	$-0.742150\pi$
$631$	7.09781	−	12.2938i	0.282559	−	0.489407i	0.972014	+	0.234921i	$0.0754833\pi$
$632$	−1.14296	+	0.201535i	−0.0454645	+	0.00801663i
$633$		0			0
$634$	−56.8853	+	20.7046i	−2.25920	+	0.822283i
$635$	4.11182	−	1.49658i	0.163173	−	0.0593900i
$636$		0			0
$637$	−18.2462	−	35.7540i	−0.722940	−	1.41662i
$638$	−45.8188	−	26.4535i	−1.81399	−	1.04730i
$639$		0			0
$640$	−3.42947	+	1.98001i	−0.135562	+	0.0782666i
$641$	−16.7592	−	19.9729i	−0.661949	−	0.788881i	0.325715	−	0.945468i	$-0.394395\pi$
$641$	−16.7592	−	19.9729i	−0.661949	−	0.788881i	−0.987664	+	0.156588i	$0.949951\pi$
$642$		0			0
$643$	−35.5086	−	6.26113i	−1.40032	−	0.246915i	−0.578048	−	0.816003i	$-0.696185\pi$
$643$	−35.5086	−	6.26113i	−1.40032	−	0.246915i	−0.822277	+	0.569088i	$0.807296\pi$
$644$	3.76329	−	0.904752i	0.148295	−	0.0356522i
$645$		0			0
$646$	−6.64138	−	2.41726i	−0.261301	−	0.0951059i
$647$	14.1360			0.555744			0.277872	−	0.960618i	$-0.410371\pi$
$647$	14.1360			0.555744			0.277872	+	0.960618i	$0.410371\pi$
$648$		0			0
$649$			19.9844i			0.784458i
$650$	56.1451	+	20.4351i	2.20219	+	0.801532i
$651$		0			0
$652$	−29.7507	−	24.9638i	−1.16513	−	0.977659i
$653$	−33.8858	−	5.97498i	−1.32605	−	0.233819i	−0.534629	−	0.845087i	$-0.679549\pi$
$653$	−33.8858	−	5.97498i	−1.32605	−	0.233819i	−0.791424	+	0.611268i	$0.790660\pi$
$654$		0			0
$655$	−6.35168	+	5.32969i	−0.248181	+	0.208248i
$656$	−1.16047	−	2.00999i	−0.0453087	−	0.0784770i
$657$		0			0
$658$	−8.40786	−	19.3200i	−0.327773	−	0.753171i
$659$	38.1009	−	6.71821i	1.48420	−	0.261704i	0.627944	−	0.778258i	$-0.283896\pi$
$659$	38.1009	−	6.71821i	1.48420	−	0.261704i	0.856255	+	0.516554i	$0.172785\pi$
$660$		0			0
$661$	10.2109	+	28.0542i	0.397158	+	1.09118i	0.963662	+	0.267124i	$0.0860733\pi$
$661$	10.2109	+	28.0542i	0.397158	+	1.09118i	−0.566504	+	0.824059i	$0.691704\pi$
$662$	−11.0904	−	30.4707i	−0.431042	−	1.18428i
$663$		0			0
$664$	9.46927	−	1.66969i	0.367479	−	0.0647964i
$665$	0.189711	+	0.435927i	0.00735668	+	0.0169045i
$666$		0			0
$667$	−1.41655	−	2.45353i	−0.0548490	−	0.0950013i
$668$	7.59097	−	6.36958i	0.293703	−	0.246446i
$669$		0			0
$670$	5.54286	+	0.977356i	0.214139	+	0.0377586i
$671$	−45.6527	−	38.3072i	−1.76240	−	1.47883i
$672$		0			0
$673$	20.3275	+	7.39859i	0.783566	+	0.285195i	0.702659	−	0.711527i	$-0.251996\pi$
$673$	20.3275	+	7.39859i	0.783566	+	0.285195i	0.0809075	+	0.996722i	$0.474218\pi$
$674$		−	35.0552i		−	1.35028i
$675$		0			0
$676$	52.0888			2.00342
$677$	7.25316	+	2.63993i	0.278761	+	0.101461i	0.477618	−	0.878568i	$-0.341500\pi$
$677$	7.25316	+	2.63993i	0.278761	+	0.101461i	−0.198856	+	0.980029i	$0.563723\pi$
$678$		0			0
$679$	−28.1778	+	6.77437i	−1.08137	+	0.259976i
$680$	−3.65767	−	0.644945i	−0.140265	−	0.0247325i
$681$		0			0
$682$	−22.3330	−	26.6155i	−0.855176	−	1.01916i
$683$	−7.78254	+	4.49325i	−0.297791	+	0.171930i	−0.641450	−	0.767165i	$-0.721667\pi$
$683$	−7.78254	+	4.49325i	−0.297791	+	0.171930i	0.343659	+	0.939094i	$0.388333\pi$
$684$		0			0
$685$	−0.361325	−	0.208611i	−0.0138055	−	0.00797061i
$686$	−6.53257	+	39.2671i	−0.249415	+	1.49922i
$687$		0			0
$688$	14.9234	−	5.43166i	0.568947	−	0.207080i
$689$	−16.8828	+	6.14485i	−0.643185	+	0.234100i
$690$		0			0
$691$	34.0362	−	6.00150i	1.29480	−	0.228308i	0.516546	−	0.856259i	$-0.327217\pi$
$691$	34.0362	−	6.00150i	1.29480	−	0.228308i	0.778253	+	0.627951i	$0.216106\pi$
$692$	20.1518	−	34.9040i	0.766058	−	1.32685i
$693$		0			0
$694$	39.0970	+	67.7179i	1.48410	+	2.57054i
$695$	−1.45793	−	1.73749i	−0.0553025	−	0.0659069i
$696$		0			0
$697$	1.21142	−	6.87033i	0.0458860	−	0.260232i
$698$	−14.3659	−	12.0544i	−0.543757	−	0.456266i
$699$		0			0
$700$	−18.5540	−	28.0128i	−0.701277	−	1.05878i
$701$			23.2192i			0.876977i	0.898737	+	0.438488i	$0.144486\pi$
$701$			23.2192i			0.876977i	−0.898737	+	0.438488i	$0.855514\pi$
$702$		0			0
$703$		−	0.988348i		−	0.0372763i
$704$	−19.8329	+	54.4906i	−0.747482	+	2.05369i
$705$		0			0
$706$	12.5702	−	14.9805i	0.473085	−	0.563800i
$707$	−26.5389	+	25.2005i	−0.998099	+	0.947763i
$708$		0			0
$709$	27.0985	−	22.7383i	1.01770	−	0.853955i	0.0283665	−	0.999598i	$-0.490969\pi$
$709$	27.0985	−	22.7383i	1.01770	−	0.853955i	0.989337	+	0.145643i	$0.0465250\pi$
$710$	−2.94793	−	5.10597i	−0.110634	−	0.191624i
$711$		0			0
$712$	6.13267	+	3.54070i	0.229831	+	0.132693i
$713$	−0.323071	−	1.83223i	−0.0120991	−	0.0686175i
$714$		0			0
$715$	−10.2050	+	3.71433i	−0.381647	+	0.138908i
$716$	14.4964	+	39.8286i	0.541757	+	1.48847i
$717$		0			0
$718$	0.191578	+	1.08649i	0.00714963	+	0.0405476i
$719$	−16.5681	+	28.6967i	−0.617884	+	1.07021i	0.371987	+	0.928238i	$0.378677\pi$
$719$	−16.5681	+	28.6967i	−0.617884	+	1.07021i	−0.989871	+	0.141969i	$0.954657\pi$
$720$		0			0
$721$	32.1078	+	3.64789i	1.19576	+	0.135854i
$722$	−25.9573	−	30.9347i	−0.966031	−	1.15127i
$723$		0			0
$724$	47.3333	+	8.34614i	1.75913	+	0.310182i
$725$	−15.8088	+	18.8402i	−0.587126	+	0.699709i
$726$		0			0
$727$	2.36915	−	6.50919i	0.0878670	−	0.241413i	−0.887974	−	0.459893i	$-0.847888\pi$
$727$	2.36915	−	6.50919i	0.0878670	−	0.241413i	0.975841	+	0.218480i	$0.0701100\pi$
$728$	−16.2499	−	12.0163i	−0.602260	−	0.445353i
$729$		0			0
$730$	6.35422			0.235180
$731$	44.8568	+	16.3266i	1.65909	+	0.603859i
$732$		0			0
$733$	18.5983	−	22.1646i	0.686943	−	0.818666i	−0.304040	−	0.952659i	$-0.598336\pi$
$733$	18.5983	−	22.1646i	0.686943	−	0.818666i	0.990982	+	0.133993i	$0.0427800\pi$
$734$	11.6079	−	65.8315i	0.428454	−	2.42989i
$735$		0			0
$736$	−3.32460	+	2.78967i	−0.122546	+	0.102828i
$737$	28.1879	−	16.2743i	1.03832	−	0.599472i
$738$		0			0
$739$	8.46122	−	14.6553i	0.311251	−	0.539103i	−0.667382	−	0.744715i	$-0.732585\pi$
$739$	8.46122	−	14.6553i	0.311251	−	0.539103i	0.978633	+	0.205613i	$0.0659187\pi$
$740$	−0.381240	−	2.16212i	−0.0140147	−	0.0794811i
$741$		0			0
$742$	17.0848	+	5.05485i	0.627204	+	0.185569i
$743$	4.26829	+	11.7270i	0.156588	+	0.430223i	0.993034	−	0.117827i	$-0.0375928\pi$
$743$	4.26829	+	11.7270i	0.156588	+	0.430223i	−0.836446	+	0.548049i	$0.815371\pi$
$744$		0			0
$745$	−0.521767	+	0.0920016i	−0.0191161	+	0.00337068i
$746$	48.6184	+	28.0699i	1.78005	+	1.02771i
$747$		0			0
$748$	−78.6268	+	45.3952i	−2.87488	+	1.65981i
$749$	0.904365	+	14.7095i	0.0330448	+	0.537474i
$750$		0			0
$751$	−2.59871	+	14.7380i	−0.0948283	+	0.537798i	0.899972	+	0.435949i	$0.143587\pi$
$751$	−2.59871	+	14.7380i	−0.0948283	+	0.537798i	−0.994800	+	0.101849i	$0.967524\pi$
$752$	6.74495	+	5.65969i	0.245963	+	0.206388i
$753$		0			0
$754$	−21.3870	+	58.7603i	−0.778869	+	2.13992i
$755$	−5.59649			−0.203677
$756$		0			0
$757$	−48.2688			−1.75436			−0.877180	−	0.480162i	$-0.840578\pi$
$757$	−48.2688			−1.75436			−0.877180	+	0.480162i	$0.840578\pi$
$758$	20.9528	−	57.5674i	0.761041	−	2.09094i
$759$		0			0
$760$	0.183364	+	0.153861i	0.00665132	+	0.00558112i
$761$	7.10296	−	40.2829i	0.257482	−	1.46025i	−0.532138	−	0.846657i	$-0.678611\pi$
$761$	7.10296	−	40.2829i	0.257482	−	1.46025i	0.789620	−	0.613596i	$-0.210278\pi$
$762$		0			0
$763$	−9.85543	+	0.605928i	−0.356791	+	0.0219361i
$764$	−45.5879	+	26.3202i	−1.64931	+	0.952231i
$765$		0			0
$766$	−25.4500	−	14.6936i	−0.919545	−	0.530900i
$767$	23.2610	−	4.10154i	0.839905	−	0.148098i
$768$		0			0
$769$	−7.22183	−	19.8418i	−0.260426	−	0.715514i	−0.999139	−	0.0414940i	$-0.986788\pi$
$769$	−7.22183	−	19.8418i	−0.260426	−	0.715514i	0.738713	−	0.674020i	$-0.235434\pi$
$770$	10.3271	+	3.05546i	0.372164	+	0.110111i
$771$		0			0
$772$	9.78421	+	55.4890i	0.352141	+	1.99709i
$773$	0.539761	−	0.934893i	0.0194138	−	0.0336258i	−0.856155	−	0.516719i	$-0.827153\pi$
$773$	0.539761	−	0.934893i	0.0194138	−	0.0336258i	0.875569	+	0.483093i	$0.160487\pi$
$774$		0			0
$775$	−13.9872	+	8.07550i	−0.502434	+	0.290080i
$776$	−11.1776	+	9.37910i	−0.401252	+	0.336690i
$777$		0			0
$778$	9.37640	−	53.1762i	0.336160	−	1.90646i
$779$	−0.289002	+	0.344420i	−0.0103546	+	0.0123401i
$780$		0			0
$781$	−32.0393	−	11.6614i	−1.14646	−	0.417276i
$782$	−8.57326			−0.306579
$783$		0			0
$784$	−4.87361	−	15.9047i	−0.174057	−	0.568024i
$785$	0.261728	−	0.719093i	0.00934149	−	0.0256655i
$786$		0			0
$787$	22.2373	−	26.5014i	0.792674	−	0.944673i	−0.206757	−	0.978392i	$-0.566291\pi$
$787$	22.2373	−	26.5014i	0.792674	−	0.944673i	0.999431	+	0.0337197i	$0.0107354\pi$
$788$	8.84307	+	1.55927i	0.315021	+	0.0555467i
$789$		0			0
$790$	−0.469856	−	0.559953i	−0.0167167	−	0.0199222i
$791$	25.5310	+	2.90067i	0.907776	+	0.103136i
$792$		0			0
$793$	−35.2182	+	60.9998i	−1.25064	+	2.16616i
$794$	−2.91180	−	16.5136i	−0.103336	−	0.586046i
$795$		0			0
$796$	−9.64984	−	26.5127i	−0.342029	−	0.939718i
$797$	13.7273	−	4.99634i	0.486247	−	0.176980i	−0.0872509	−	0.996186i	$-0.527808\pi$
$797$	13.7273	−	4.99634i	0.486247	−	0.176980i	0.573498	+	0.819207i	$0.305586\pi$
$798$		0			0
$799$	4.59576	+	26.0639i	0.162586	+	0.922073i
$800$	32.6277	+	18.8376i	1.15356	+	0.666010i
$801$		0			0
$802$	−1.56453	−	2.70985i	−0.0552456	−	0.0956882i
$803$	28.1492	−	23.6200i	0.993364	−	0.833531i
$804$		0			0
$805$	0.397107	+	0.418197i	0.0139962	+	0.0147395i
$806$	−26.3957	+	31.4571i	−0.929747	+	1.10803i
$807$		0			0
$808$	−6.30214	+	17.3150i	−0.221709	+	0.609140i
$809$			19.4950i			0.685407i	0.939444	+	0.342704i	$0.111343\pi$
$809$			19.4950i			0.685407i	−0.939444	+	0.342704i	$0.888657\pi$
$810$		0			0
$811$			8.74742i			0.307163i	0.988136	+	0.153582i	$0.0490808\pi$
$811$			8.74742i			0.307163i	−0.988136	+	0.153582i	$0.950919\pi$
$812$	29.3176	−	19.4183i	1.02885	−	0.681449i
$813$		0			0
$814$	−17.1510	−	14.3914i	−0.601143	−	0.504419i
$815$	1.00483	−	5.69869i	0.0351978	−	0.199617i
$816$		0			0
$817$	−1.97751	−	2.35670i	−0.0691842	−	0.0824505i
$818$	10.3078	+	17.8535i	0.360402	+	0.624235i
$819$		0			0
$820$	−0.499369	+	0.864933i	−0.0174387	+	0.0302048i
$821$	14.8604	−	2.62030i	0.518633	−	0.0914490i	0.0917964	−	0.995778i	$-0.470739\pi$
$821$	14.8604	−	2.62030i	0.518633	−	0.0914490i	0.426836	+	0.904329i	$0.359628\pi$
$822$		0			0
$823$	45.4998	−	16.5606i	1.58602	−	0.577265i	0.609521	−	0.792770i	$-0.291362\pi$
$823$	45.4998	−	16.5606i	1.58602	−	0.577265i	0.976503	+	0.215505i	$0.0691396\pi$
$824$	15.2886	−	5.56458i	0.532602	−	0.193851i
$825$		0			0
$826$	−20.9657	−	10.4448i	−0.729490	−	0.363421i
$827$	−1.87534	−	1.08273i	−0.0652119	−	0.0376501i	0.467040	−	0.884236i	$-0.345321\pi$
$827$	−1.87534	−	1.08273i	−0.0652119	−	0.0376501i	−0.532251	+	0.846586i	$0.678654\pi$
$828$		0			0
$829$	−34.8737	+	20.1344i	−1.21121	+	0.699295i	−0.963024	−	0.269416i	$-0.913169\pi$
$829$	−34.8737	+	20.1344i	−1.21121	+	0.699295i	−0.248191	+	0.968711i	$0.579836\pi$
$830$	3.89269	+	4.63913i	0.135117	+	0.161027i
$831$		0			0
$832$	67.4950	+	11.9012i	2.33997	+	0.412600i
$833$	19.5075	−	46.0382i	0.675896	−	1.59513i
$834$		0			0
$835$	1.38742	+	0.504981i	0.0480138	+	0.0174756i
$836$	5.85124			0.202369
$837$		0			0
$838$		−	47.3937i		−	1.63719i
$839$	−8.35277	−	3.04016i	−0.288370	−	0.104958i	0.193785	−	0.981044i	$-0.437924\pi$
$839$	−8.35277	−	3.04016i	−0.288370	−	0.104958i	−0.482155	+	0.876086i	$0.660146\pi$
$840$		0			0
$841$	2.49746	+	2.09562i	0.0861194	+	0.0722628i
$842$	58.4633	+	10.3087i	2.01478	+	0.355260i
$843$		0			0
$844$	−0.598908	+	0.502543i	−0.0206153	+	0.0172983i
$845$	3.88056	+	6.72133i	0.133495	+	0.231221i
$846$		0			0
$847$	30.4212	−	13.2390i	1.04529	−	0.454898i
$848$	−7.33230	+	1.29288i	−0.251792	+	0.0443978i
$849$		0			0
$850$	25.4547	+	69.9363i	0.873091	+	2.39880i
$851$	−0.410049	−	1.12660i	−0.0140563	−	0.0386194i
$852$		0			0
$853$	7.05528	−	1.24404i	0.241568	−	0.0425950i	−0.0515532	−	0.998670i	$-0.516417\pi$
$853$	7.05528	−	1.24404i	0.241568	−	0.0425950i	0.293121	+	0.956075i	$0.405306\pi$
$854$	64.0484	−	27.8732i	2.19169	−	0.953802i
$855$		0			0
$856$	3.70998	+	6.42588i	0.126805	+	0.219632i
$857$	27.4777	−	23.0565i	0.938619	−	0.787595i	−0.0387252	−	0.999250i	$-0.512330\pi$
$857$	27.4777	−	23.0565i	0.938619	−	0.787595i	0.977344	+	0.211655i	$0.0678852\pi$
$858$		0			0
$859$	−4.46217	−	0.786801i	−0.152247	−	0.0268453i	0.0970050	−	0.995284i	$-0.469074\pi$
$859$	−4.46217	−	0.786801i	−0.152247	−	0.0268453i	−0.249252	+	0.968439i	$0.580185\pi$
$860$	−5.23507	−	4.39275i	−0.178514	−	0.149791i
$861$		0			0
$862$	28.1506	+	10.2460i	0.958815	+	0.348980i
$863$			33.0683i			1.12566i	0.826573	+	0.562830i	$0.190287\pi$
$863$			33.0683i			1.12566i	−0.826573	+	0.562830i	$0.809713\pi$
$864$		0			0
$865$	6.00516			0.204182
$866$	42.1093	+	15.3265i	1.43093	+	0.520817i
$867$		0			0
$868$	22.4532	−	5.39808i	0.762111	−	0.183223i
$869$	−4.16293	−	0.734037i	−0.141218	−	0.0249005i
$870$		0			0
$871$	−24.7278	−	29.4694i	−0.837868	−	0.998532i
$872$	−4.30537	+	2.48571i	−0.145798	+	0.0841766i
$873$		0			0
$874$	0.478503	+	0.276264i	0.0161856	+	0.00934476i
$875$	4.53496	−	9.10296i	0.153310	−	0.307736i
$876$		0			0
$877$	−12.0002	+	4.36773i	−0.405219	+	0.147488i	−0.536585	−	0.843846i	$-0.680286\pi$
$877$	−12.0002	+	4.36773i	−0.405219	+	0.147488i	0.131366	+	0.991334i	$0.458064\pi$
$878$	7.52835	−	2.74009i	0.254069	−	0.0924737i
$879$		0			0
$880$	−4.43210	+	0.781499i	−0.149406	+	0.0263443i
$881$	−8.46605	+	14.6636i	−0.285229	+	0.494030i	−0.972665	−	0.232215i	$-0.925403\pi$
$881$	−8.46605	+	14.6636i	−0.285229	+	0.494030i	0.687436	+	0.726245i	$0.258736\pi$
$882$		0			0
$883$	4.01408	+	6.95260i	0.135085	+	0.233973i	0.925630	−	0.378430i	$-0.123536\pi$
$883$	4.01408	+	6.95260i	0.135085	+	0.233973i	−0.790545	+	0.612404i	$0.790203\pi$
$884$	68.9751	+	82.2013i	2.31988	+	2.76473i
$885$		0			0
$886$	1.95907	−	11.1104i	0.0658161	−	0.373262i
$887$	23.0852	+	19.3708i	0.775125	+	0.650408i	0.942016	−	0.335568i	$-0.108928\pi$
$887$	23.0852	+	19.3708i	0.775125	+	0.650408i	−0.166891	+	0.985975i	$0.553373\pi$
$888$		0			0
$889$	16.3777	+	24.7270i	0.549291	+	0.829316i
$890$			4.46002i			0.149500i
$891$		0			0
$892$		−	7.50739i		−	0.251366i
$893$	0.583374	−	1.60281i	0.0195218	−	0.0536358i
$894$		0			0
$895$	−4.05935	+	4.83775i	−0.135689	+	0.161708i
$896$	−18.4825	−	19.4641i	−0.617458	−	0.650251i
$897$		0			0
$898$	−42.6855	+	35.8174i	−1.42443	+	1.19524i
$899$	−8.45166	−	14.6387i	−0.281879	−	0.488228i
$900$		0			0
$901$	−19.3813	−	11.1898i	−0.645683	−	0.372785i
$902$	1.76860	+	10.0302i	0.0588880	+	0.333970i
$903$		0			0
$904$	12.1569	−	4.42475i	0.404332	−	0.147165i
$905$	2.44933	+	6.72947i	0.0814184	+	0.223695i
$906$		0			0
$907$	−4.40531	−	24.9838i	−0.146276	−	0.829572i	−0.966334	−	0.257292i	$-0.917170\pi$
$907$	−4.40531	−	24.9838i	−0.146276	−	0.829572i	0.820058	−	0.572281i	$-0.193941\pi$
$908$	36.2861	−	62.8494i	1.20420	−	2.08573i
$909$		0			0
$910$	1.43692	−	12.6474i	0.0476334	−	0.419257i
$911$	0.815474	+	0.971845i	0.0270179	+	0.0321986i	0.779384	−	0.626546i	$-0.215532\pi$
$911$	0.815474	+	0.971845i	0.0270179	+	0.0321986i	−0.752366	+	0.658745i	$0.771088\pi$
$912$		0			0
$913$	34.4893	+	6.08139i	1.14143	+	0.201265i
$914$	−28.6626	+	34.1588i	−0.948075	+	1.12987i
$915$		0			0
$916$	21.1352	−	58.0683i	0.698325	−	1.91863i
$917$	−45.1880	−	33.4151i	−1.49224	−	1.10346i
$918$		0			0
$919$	38.7081			1.27686			0.638430	−	0.769680i	$-0.279584\pi$
$919$	38.7081			1.27686			0.638430	+	0.769680i	$0.279584\pi$
$920$	0.272848	+	0.0993084i	0.00899552	+	0.00327410i
$921$		0			0
$922$	−0.244786	+	0.291724i	−0.00806159	+	0.00960743i
$923$	−6.99766	+	39.6857i	−0.230331	+	1.30627i
$924$		0			0
$925$	−7.97276	+	6.68994i	−0.262143	+	0.219964i
$926$	−53.8650	+	31.0990i	−1.77011	+	1.02198i
$927$		0			0
$928$	−19.7151	+	34.1475i	−0.647179	+	1.12095i
$929$	6.02005	+	34.1414i	0.197512	+	1.12014i	0.908796	+	0.417240i	$0.137002\pi$
$929$	6.02005	+	34.1414i	0.197512	+	1.12014i	−0.711285	+	0.702904i	$0.751886\pi$
$930$		0			0
$931$	−2.57231	+	1.94094i	−0.0843041	+	0.0636118i
$932$	7.70802	+	21.1776i	0.252485	+	0.693696i
$933$		0			0
$934$	18.7803	−	3.31148i	0.614511	−	0.108355i
$935$	−11.7152	−	6.76379i	−0.383129	−	0.221200i
$936$		0			0
$937$	24.7426	−	14.2852i	0.808307	−	0.466676i	−0.0380609	−	0.999275i	$-0.512118\pi$
$937$	24.7426	−	14.2852i	0.808307	−	0.466676i	0.846367	+	0.532599i	$0.178785\pi$
$938$	2.34108	+	38.0777i	0.0764390	+	1.24328i
$939$		0			0
$940$	0.657936	−	3.73134i	0.0214595	−	0.121703i
$941$	−37.2620	−	31.2666i	−1.21471	−	1.01926i	−0.999084	−	0.0427842i	$-0.986377\pi$
$941$	−37.2620	−	31.2666i	−1.21471	−	1.01926i	−0.215623	−	0.976477i	$-0.569178\pi$
$942$		0			0
$943$	−0.186535	+	0.512500i	−0.00607440	+	0.0166893i
$944$	9.78827			0.318581
$945$		0			0
$946$	−69.6909			−2.26585
$947$	6.23321	−	17.1256i	0.202552	−	0.556508i	−0.796275	−	0.604935i	$-0.793199\pi$
$947$	6.23321	−	17.1256i	0.202552	−	0.556508i	0.998827	+	0.0484279i	$0.0154211\pi$
$948$		0			0
$949$	−33.2698	−	27.9167i	−1.07999	−	0.906215i
$950$	0.832904	−	4.72363i	0.0270230	−	0.153255i
$951$		0			0
$952$	−1.54485	−	25.1270i	−0.0500689	−	0.814371i
$953$	−28.1743	+	16.2665i	−0.912656	+	0.526922i	−0.881285	−	0.472586i	$-0.843321\pi$
$953$	−28.1743	+	16.2665i	−0.912656	+	0.526922i	−0.0313712	+	0.999508i	$0.509987\pi$
$954$		0			0
$955$	−6.79250	−	3.92165i	−0.219800	−	0.126902i
$956$	34.2114	−	6.03239i	1.10647	−	0.195101i
$957$		0			0
$958$	4.66581	+	12.8192i	0.150746	+	0.414170i
$959$	0.802324	−	2.71176i	0.0259084	−	0.0875675i
$960$		0			0
$961$	3.45553	+	19.5973i	0.111469	+	0.632170i
$962$	−13.2309	+	22.9167i	−0.426582	+	0.738863i
$963$		0			0
$964$	24.8055	−	14.3215i	0.798931	−	0.461263i
$965$	−6.43116	+	5.39639i	−0.207026	+	0.173716i
$966$		0			0
$967$	0.197163	−	1.11816i	0.00634032	−	0.0359577i	−0.981473	−	0.191598i	$-0.938633\pi$
$967$	0.197163	−	1.11816i	0.00634032	−	0.0359577i	0.987814	+	0.155640i	$0.0497441\pi$
$968$	10.7372	−	12.7961i	0.345107	−	0.411282i
$969$		0			0
$970$	−8.63569	−	3.14314i	−0.277275	−	0.100920i
$971$	−37.6895			−1.20951			−0.604757	−	0.796410i	$-0.706730\pi$
$971$	−37.6895			−1.20951			−0.604757	+	0.796410i	$0.706730\pi$
$972$		0			0
$973$	9.14066	−	12.3611i	0.293036	−	0.396279i
$974$	−3.82155	+	10.4996i	−0.122450	+	0.336429i
$975$		0			0
$976$	−18.7626	+	22.3604i	−0.600578	+	0.715741i
$977$	29.2666	+	5.16050i	0.936323	+	0.165099i	0.620933	−	0.783863i	$-0.286754\pi$
$977$	29.2666	+	5.16050i	0.936323	+	0.165099i	0.315390	+	0.948962i	$0.397865\pi$
$978$		0			0
$979$	16.5788	+	19.7579i	0.529862	+	0.631465i
$980$	−4.87852	+	5.23825i	−0.155839	+	0.167330i
$981$		0			0
$982$	−14.7282	+	25.5101i	−0.469997	+	0.814059i
$983$	0.460838	+	2.61354i	0.0146984	+	0.0833590i	0.991275	−	0.131813i	$-0.0420799\pi$
$983$	0.460838	+	2.61354i	0.0146984	+	0.0833590i	−0.976576	+	0.215172i	$0.930969\pi$
$984$		0			0
$985$	0.457597	+	1.25724i	0.0145803	+	0.0400589i
$986$	−73.1940	+	26.6404i	−2.33097	+	0.848404i
$987$		0			0
$988$	−1.20089	−	6.81058i	−0.0382054	−	0.216673i
$989$	−3.23188	−	1.86593i	−0.102768	−	0.0593330i
$990$		0			0
$991$	−16.1884	−	28.0391i	−0.514242	−	0.890693i	−0.999863	−	0.0165236i	$-0.994740\pi$
$991$	−16.1884	−	28.0391i	−0.514242	−	0.890693i	0.485622	−	0.874169i	$-0.338593\pi$
$992$	−19.8358	+	16.6442i	−0.629786	+	0.528453i
$993$		0			0
$994$	28.9792	−	27.5177i	0.919164	−	0.872810i
$995$	2.70219	−	3.22034i	0.0856652	−	0.102092i
$996$		0			0
$997$	−3.04666	+	8.37063i	−0.0964887	+	0.265100i	−0.978541	−	0.206050i	$-0.933939\pi$
$997$	−3.04666	+	8.37063i	−0.0964887	+	0.265100i	0.882053	+	0.471151i	$0.156161\pi$
$998$		−	74.1087i		−	2.34587i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.503.4		132
3.2	odd	2		189.2.be.a.104.20	yes	132
7.6	odd	2	inner	567.2.be.a.503.3		132
21.20	even	2		189.2.be.a.104.19	yes	132
27.7	even	9		189.2.be.a.20.19	✓	132
27.20	odd	18	inner	567.2.be.a.62.3		132
189.20	even	18	inner	567.2.be.a.62.4		132
189.34	odd	18		189.2.be.a.20.20	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.19	✓	132	27.7	even	9
189.2.be.a.20.20	yes	132	189.34	odd	18
189.2.be.a.104.19	yes	132	21.20	even	2
189.2.be.a.104.20	yes	132	3.2	odd	2
567.2.be.a.62.3		132	27.20	odd	18	inner
567.2.be.a.62.4		132	189.20	even	18	inner
567.2.be.a.503.3		132	7.6	odd	2	inner
567.2.be.a.503.4		132	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.735125 + 2.01974i) q^{2} +(-2.00685 - 1.68395i) q^{4} +(0.0677816 - 0.384409i) q^{5} +(2.64076 - 0.162359i) q^{7} +(1.15362 - 0.666045i) q^{8} +(0.726578 + 0.419490i) q^{10} +(4.77807 - 0.842503i) q^{11} +(-1.96127 - 5.38855i) q^{13} +(-1.61337 + 5.45301i) q^{14} +(-0.412653 - 2.34027i) q^{16} +(3.57147 - 6.18597i) q^{17} +(-0.398672 + 0.230173i) q^{19} +(-0.783352 + 0.657311i) q^{20} +(-1.81084 + 10.2698i) q^{22} +(-0.358944 + 0.427773i) q^{23} +(4.55529 + 1.65799i) q^{25} +12.3252 q^{26} +(-5.57303 - 4.12109i) q^{28} +(-1.73522 + 4.76747i) q^{29} +(-2.14159 + 2.55225i) q^{31} +(7.65380 + 1.34957i) q^{32} +(9.86858 + 11.7609i) q^{34} +(0.116583 - 1.02614i) q^{35} +(-1.07348 + 1.85933i) q^{37} +(-0.171817 - 0.974420i) q^{38} +(-0.177839 - 0.488609i) q^{40} +(0.917771 - 0.334041i) q^{41} +(1.16047 + 6.58138i) q^{43} +(-11.0076 - 6.35525i) q^{44} +(-0.600121 - 1.03944i) q^{46} +(-2.83834 + 2.38165i) q^{47} +(6.94728 - 0.857502i) q^{49} +(-6.69741 + 7.98167i) q^{50} +(-5.13806 + 14.1167i) q^{52} -3.13310i q^{53} -1.89384i q^{55} +(2.93831 - 1.94617i) q^{56} +(-8.35346 - 7.00938i) q^{58} +(-0.715255 + 4.05641i) q^{59} +(-7.89549 - 9.40948i) q^{61} +(-3.58054 - 6.20168i) q^{62} +(-5.97591 + 10.3506i) q^{64} +(-2.20434 + 0.388685i) q^{65} +(6.30401 - 2.29447i) q^{67} +(-17.5843 + 6.40016i) q^{68} +(1.98683 + 0.989808i) q^{70} +(-6.08593 - 3.51371i) q^{71} +(6.55906 - 3.78687i) q^{73} +(-2.96621 - 3.53499i) q^{74} +(1.18768 + 0.209419i) q^{76} +(12.4810 - 3.00061i) q^{77} +(-0.818714 - 0.297987i) q^{79} -0.927591 q^{80} +2.09922i q^{82} +(6.78293 + 2.46878i) q^{83} +(-2.13586 - 1.79220i) q^{85} +(-14.1458 - 2.49428i) q^{86} +(4.95095 - 4.15434i) q^{88} +(2.65800 + 4.60379i) q^{89} +(-6.05413 - 13.9115i) q^{91} +(1.44070 - 0.254033i) q^{92} +(-2.72378 - 7.48351i) q^{94} +(0.0614580 + 0.168854i) q^{95} +(-10.7873 + 1.90209i) q^{97} +(-3.37519 + 14.6621i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 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

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