LMFDB - Embedded newform 567.2.be.a.62.4

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			62.4
Character	$\chi$	$=$	567.62
Dual form			567.2.be.a.503.4

$q$-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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.735125	−	2.01974i	−0.519812	−	1.42817i	−0.870728	−	0.491765i	$-0.836352\pi$
$2$	−0.735125	−	2.01974i	−0.519812	−	1.42817i	0.350916	−	0.936407i	$-0.385870\pi$
$3$		0			0
$3$		0			0
$4$	−2.00685	+	1.68395i	−1.00343	+	0.841975i
$5$	0.0677816	+	0.384409i	0.0303129	+	0.171913i	0.996206	−	0.0870291i	$-0.0277373\pi$
$5$	0.0677816	+	0.384409i	0.0303129	+	0.171913i	−0.965893	+	0.258942i	$0.916626\pi$
$6$		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	0.838734	−	0.544541i	$-0.183296\pi$
$11$	4.77807	+	0.842503i	1.44064	+	0.254024i	0.601909	+	0.798565i	$0.294407\pi$
$12$		0			0
$13$	−1.96127	+	5.38855i	−0.543959	+	1.49451i	0.297783	+	0.954634i	$0.403753\pi$
$13$	−1.96127	+	5.38855i	−0.543959	+	1.49451i	−0.841742	+	0.539881i	$0.818469\pi$
$14$	−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	0.865841	+	0.500319i	$0.166784\pi$
$17$	3.57147	+	6.18597i	0.866209	+	1.50032i	0.000368279		1.00000i	$0.499883\pi$
$18$		0			0
$19$	−0.398672	−	0.230173i	−0.0914616	−	0.0528054i	0.453572	−	0.891220i	$-0.350150\pi$
$19$	−0.398672	−	0.230173i	−0.0914616	−	0.0528054i	−0.545033	+	0.838414i	$0.683483\pi$
$20$	−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	0.727323	−	0.686296i	$-0.240764\pi$
$23$	−0.358944	−	0.427773i	−0.0748450	−	0.0891968i	−0.802168	+	0.597099i	$0.796320\pi$
$24$		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	−0.990016	−	0.140952i	$-0.954984\pi$
$29$	−1.73522	−	4.76747i	−0.322222	−	0.885298i	0.667794	−	0.744346i	$-0.267239\pi$
$30$		0			0
$31$	−2.14159	−	2.55225i	−0.384641	−	0.458398i	0.538632	−	0.842541i	$-0.318941\pi$
$31$	−2.14159	−	2.55225i	−0.384641	−	0.458398i	−0.923273	+	0.384143i	$0.874497\pi$
$32$	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	0.764193	−	0.644988i	$-0.223138\pi$
$37$	−1.07348	−	1.85933i	−0.176479	−	0.305671i	−0.940672	+	0.339317i	$0.889804\pi$
$38$	−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	0.412690	−	0.910872i	$-0.364589\pi$
$41$	0.917771	+	0.334041i	0.143332	+	0.0521685i	−0.269358	+	0.963040i	$0.586812\pi$
$42$		0			0
$43$	1.16047	−	6.58138i	0.176971	−	1.00365i	−0.758874	−	0.651238i	$-0.774250\pi$
$43$	1.16047	−	6.58138i	0.176971	−	1.00365i	0.935845	−	0.352413i	$-0.114639\pi$
$44$	−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	0.411867	−	0.911244i	$-0.364877\pi$
$47$	−2.83834	−	2.38165i	−0.414014	−	0.347399i	−0.825880	+	0.563845i	$0.809321\pi$
$48$		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	$0.0690345\pi$
$53$			3.13310i			0.430364i	−0.976574	+	0.215182i	$0.930966\pi$
$54$		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	−0.995308	−	0.0967600i	$-0.969152\pi$
$59$	−0.715255	−	4.05641i	−0.0931183	−	0.528100i	0.902189	−	0.431340i	$-0.141959\pi$
$60$		0			0
$61$	−7.89549	+	9.40948i	−1.01091	+	1.20476i	−0.0322101	+	0.999481i	$0.510255\pi$
$61$	−7.89549	+	9.40948i	−1.01091	+	1.20476i	−0.978704	+	0.205279i	$0.934190\pi$
$62$	−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	0.697062	−	0.717011i	$-0.254490\pi$
$67$	6.30401	+	2.29447i	0.770158	+	0.280314i	0.0730953	+	0.997325i	$0.476712\pi$
$68$	−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	−0.815587	−	0.578635i	$-0.803586\pi$
$71$	−6.08593	+	3.51371i	−0.722267	+	0.417001i	0.0933194	+	0.995636i	$0.470252\pi$
$72$		0			0
$73$	6.55906	+	3.78687i	0.767680	+	0.443220i	0.832046	−	0.554706i	$-0.187169\pi$
$73$	6.55906	+	3.78687i	0.767680	+	0.443220i	−0.0643665	+	0.997926i	$0.520503\pi$
$74$	−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	−0.387665	−	0.921800i	$-0.626718\pi$
$79$	−0.818714	+	0.297987i	−0.0921125	+	0.0335262i	0.295553	+	0.955326i	$0.404496\pi$
$80$	−0.927591			−0.103708
$81$		0			0
$82$		−	2.09922i		−	0.231820i
$83$	6.78293	−	2.46878i	0.744523	−	0.270984i	0.0582238	−	0.998304i	$-0.481456\pi$
$83$	6.78293	−	2.46878i	0.744523	−	0.270984i	0.686299	+	0.727319i	$0.259234\pi$
$84$		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	−0.690068	−	0.723745i	$-0.742419\pi$
$89$	2.65800	−	4.60379i	0.281748	−	0.488001i	0.971815	+	0.235744i	$0.0757526\pi$
$90$		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	−0.403318	−	0.915060i	$-0.632143\pi$
$97$	−10.7873	−	1.90209i	−1.09528	−	0.193128i	−0.691964	+	0.721932i	$0.743254\pi$
$98$	−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	−0.0608307	−	0.998148i	$-0.519375\pi$
$101$	−10.5964	−	8.89141i	−1.05438	−	0.884728i	−0.993547	+	0.113420i	$0.963819\pi$
$102$		0			0
$103$	12.0281	−	2.12089i	1.18517	−	0.208977i	0.453890	−	0.891058i	$-0.350036\pi$
$103$	12.0281	−	2.12089i	1.18517	−	0.208977i	0.731277	+	0.682080i	$0.238925\pi$
$104$	−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	$-0.913226\pi$
$107$		−	5.57017i		−	0.538489i	0.963072	−	0.269244i	$-0.0867739\pi$
$108$		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	0.295397	−	0.955375i	$-0.404548\pi$
$113$	9.56433	−	1.68645i	0.899737	−	0.158648i	0.604340	+	0.796727i	$0.293437\pi$
$114$		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	−0.502631	−	0.864501i	$-0.667634\pi$
$127$	5.60501	−	9.70817i	0.497365	−	0.861461i	0.999995	+	0.00304049i	$0.000967819\pi$
$128$	−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	−0.471295	+	0.881976i	$0.656213\pi$
$131$	−16.2722	+	13.6540i	−1.42171	+	1.19296i	−0.950416	+	0.310982i	$0.899342\pi$
$132$		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	0.954329	−	0.298757i	$-0.0965721\pi$
$137$	0.365575	+	1.00441i	0.0312332	+	0.0858125i	−0.923096	+	0.384570i	$0.874350\pi$
$138$		0			0
$139$	3.73504	+	4.45125i	0.316802	+	0.377550i	0.900821	−	0.434190i	$-0.142965\pi$
$139$	3.73504	+	4.45125i	0.316802	+	0.377550i	−0.584020	+	0.811740i	$0.698521\pi$
$140$	−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	−0.957255	−	0.289246i	$-0.906595\pi$
$149$	−0.464232	+	1.27547i	−0.0380314	+	0.104490i	0.919223	+	0.393736i	$0.128818\pi$
$150$		0			0
$151$	−2.48969	+	14.1197i	−0.202608	+	1.14905i	0.698552	+	0.715559i	$0.253828\pi$
$151$	−2.48969	+	14.1197i	−0.202608	+	1.14905i	−0.901160	+	0.433487i	$0.857283\pi$
$152$	−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	−0.0960737	−	0.995374i	$-0.530628\pi$
$157$	1.93067	−	0.340430i	0.154085	−	0.0271693i	0.250158	+	0.968205i	$0.419517\pi$
$158$	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	0.948791	−	0.315905i	$-0.102308\pi$
$167$	−0.656828	−	3.72506i	−0.0508269	−	0.288254i	−0.999618	+	0.0276516i	$0.991197\pi$
$168$		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	−0.697277	−	0.716802i	$-0.745605\pi$
$173$	2.67149	−	15.1508i	0.203110	−	1.15189i	0.900387	−	0.435090i	$-0.143284\pi$
$174$		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	−0.921879	−	0.387477i	$-0.873347\pi$
$179$	−14.0113	+	8.08943i	−1.04725	+	0.604632i	−0.125374	+	0.992109i	$0.540013\pi$
$180$		0			0
$181$	−15.8886	−	9.17326i	−1.18099	−	0.681843i	−0.224744	−	0.974418i	$-0.572155\pi$
$181$	−15.8886	−	9.17326i	−1.18099	−	0.681843i	−0.956243	+	0.292575i	$0.905488\pi$
$182$	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	0.893903	+	0.448261i	$0.147956\pi$
$191$	6.87241	+	18.8818i	0.497270	+	1.36624i	−0.396633	+	0.917977i	$0.629821\pi$
$192$		0			0
$193$	−16.4758	+	13.8249i	−1.18596	+	0.995136i	−0.186037	+	0.982543i	$0.559564\pi$
$193$	−16.4758	+	13.8249i	−1.18596	+	0.995136i	−0.999921	+	0.0125936i	$0.995991\pi$
$194$	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	0.390514	−	0.920597i	$-0.372297\pi$
$197$	−2.96839	−	1.71380i	−0.211489	−	0.122103i	−0.602003	+	0.798494i	$0.705631\pi$
$198$		0			0
$199$	9.32690	−	5.38489i	0.661166	−	0.381725i	−0.131555	−	0.991309i	$-0.541997\pi$
$199$	9.32690	−	5.38489i	0.661166	−	0.381725i	0.792721	+	0.609584i	$0.208664\pi$
$200$	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	0.986540	−	0.163523i	$-0.0522857\pi$
$211$	0.0518221	+	0.293898i	0.00356758	+	0.0202327i	−0.982972	+	0.183755i	$0.941175\pi$
$212$	−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	−0.700835	−	0.713324i	$-0.747189\pi$
$223$	1.84202	−	2.19524i	0.123351	−	0.147004i	0.824185	+	0.566320i	$0.191633\pi$
$224$	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	−0.227897	−	0.973685i	$-0.573185\pi$
$227$	4.81038	−	27.2810i	0.319276	−	1.81070i	0.547173	−	0.837019i	$-0.315704\pi$
$228$		0			0
$229$	8.06759	−	22.1655i	0.533121	−	1.46474i	−0.322216	−	0.946666i	$-0.604428\pi$
$229$	8.06759	−	22.1655i	0.533121	−	1.46474i	0.855337	−	0.518072i	$-0.173350\pi$
$230$	−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	−0.723774	−	0.690038i	$-0.757594\pi$
$233$	−7.45007	+	4.30130i	−0.488070	+	0.281787i	0.235703	+	0.971825i	$0.424261\pi$
$234$		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	0.416344	−	0.909207i	$-0.363311\pi$
$239$	−8.52364	−	10.1581i	−0.551348	−	0.657071i	−0.967692	+	0.252136i	$0.918867\pi$
$240$		0			0
$241$	−3.73945	−	10.2740i	−0.240879	−	0.661809i	−0.999942	−	0.0107919i	$-0.996565\pi$
$241$	−3.73945	−	10.2740i	−0.240879	−	0.661809i	0.759063	−	0.651017i	$-0.225657\pi$
$242$		−	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	−0.981264	−	0.192670i	$-0.938285\pi$
$251$	−5.12956	+	8.88466i	−0.323775	+	0.560795i	0.657489	+	0.753464i	$0.271619\pi$
$252$		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	0.381375	−	0.924420i	$-0.375451\pi$
$257$	1.27159	+	0.462822i	0.0793198	+	0.0288700i	−0.302055	+	0.953290i	$0.597673\pi$
$258$		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	−0.888541	−	0.458798i	$-0.848280\pi$
$263$	−4.58008	+	5.45832i	−0.282420	+	0.336575i	0.606121	+	0.795372i	$0.292725\pi$
$264$		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	$-0.849380\pi$
$271$		−	15.0044i		−	0.911450i	0.890121	−	0.455725i	$-0.150620\pi$
$272$	−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	−0.999929	−	0.0118925i	$-0.996214\pi$
$277$	−19.7269	−	16.5529i	−1.18528	−	0.994566i	−0.185348	−	0.982673i	$-0.559341\pi$
$278$	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	0.405759	−	0.913980i	$-0.367007\pi$
$281$	7.95320	+	1.40236i	0.474448	+	0.0836580i	0.0686892	+	0.997638i	$0.478118\pi$
$282$		0			0
$283$	−2.15839	+	5.93013i	−0.128303	+	0.352510i	−0.987166	−	0.159695i	$-0.948949\pi$
$283$	−2.15839	+	5.93013i	−0.128303	+	0.352510i	0.858863	+	0.512205i	$0.171171\pi$
$284$	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	−0.441504	−	0.897259i	$-0.645555\pi$
$293$	6.25563	−	5.24910i	0.365458	−	0.306656i	0.806962	+	0.590604i	$0.201110\pi$
$294$		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	0.196151	−	0.980574i	$-0.437156\pi$
$307$	20.0345	−	11.5669i	1.14343	−	0.660159i	0.947277	+	0.320415i	$0.103822\pi$
$308$	−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	0.882479	−	0.470352i	$-0.155873\pi$
$311$	22.1526	+	8.06290i	1.25616	+	0.457205i	0.373682	+	0.927557i	$0.378095\pi$
$312$		0			0
$313$	−11.7748	−	2.07621i	−0.665550	−	0.117354i	−0.169341	−	0.985557i	$-0.554164\pi$
$313$	−11.7748	−	2.07621i	−0.665550	−	0.117354i	−0.496209	+	0.868203i	$0.665275\pi$
$314$	−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	0.0396733	−	0.999213i	$-0.487368\pi$
$317$	18.1039	−	21.5754i	1.01682	−	1.21179i	0.977143	−	0.212582i	$-0.0681873\pi$
$318$		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	0.267323	−	0.963607i	$-0.413861\pi$
$331$	−11.5569	−	9.69739i	−0.635224	−	0.533017i	−0.902547	+	0.430590i	$0.858305\pi$
$332$	−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	−0.111008	−	0.993819i	$-0.535408\pi$
$337$	−15.3260	−	5.57821i	−0.834860	−	0.303864i	−0.723852	+	0.689955i	$0.757630\pi$
$338$	−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	0.792802	+	0.609480i	$0.208622\pi$
$347$	23.3846	+	27.8687i	1.25535	+	1.49607i	0.462552	+	0.886592i	$0.346934\pi$
$348$		0			0
$349$	−2.98415	−	8.19888i	−0.159738	−	0.438876i	0.833843	−	0.552002i	$-0.186136\pi$
$349$	−2.98415	−	8.19888i	−0.159738	−	0.438876i	−0.993581	+	0.113126i	$0.963914\pi$
$350$	−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	−0.559370	−	0.828918i	$-0.688957\pi$
$353$	−8.54968	+	3.11183i	−0.455053	+	0.165626i	0.104316	+	0.994544i	$0.466735\pi$
$354$		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	0.511685	−	0.859173i	$-0.329022\pi$
$359$	0.444525	+	0.256647i	0.0234611	+	0.0135453i	−0.488224	+	0.872719i	$0.662355\pi$
$360$		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	−0.697977	−	0.716120i	$-0.745916\pi$
$367$	−30.6284	−	5.40061i	−1.59879	−	0.281910i	−0.900812	+	0.434210i	$0.857028\pi$
$368$	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	0.842945	+	0.537999i	$0.180820\pi$
$373$	4.53556	+	25.7224i	0.234842	+	1.33186i	−0.608103	+	0.793858i	$0.708069\pi$
$374$	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	−0.983428	−	0.181299i	$-0.941970\pi$
$383$	−2.37420	−	13.4648i	−0.121316	−	0.688017i	0.862112	−	0.506718i	$-0.169141\pi$
$384$		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	−0.493318	−	0.869849i	$-0.664216\pi$
$389$	−24.7405	−	4.36241i	−1.25439	−	0.221183i	−0.761073	+	0.648666i	$0.775327\pi$
$390$		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	0.320779	−	0.947154i	$-0.396055\pi$
$397$	−6.75634	−	3.90078i	−0.339091	−	0.195774i	−0.659870	+	0.751380i	$0.729389\pi$
$398$	−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	0.742173	−	0.670208i	$-0.233795\pi$
$401$	−0.935778	−	1.11522i	−0.0467305	−	0.0556913i	−0.788903	+	0.614517i	$0.789351\pi$
$402$		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	0.896621	−	0.442799i	$-0.146014\pi$
$409$	6.16526	+	7.34748i	0.304853	+	0.363309i	−0.591768	+	0.806108i	$0.701570\pi$
$410$	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	−0.217956	−	0.975959i	$-0.569939\pi$
$419$	−20.7203	−	7.54159i	−1.01225	−	0.368431i	−0.794298	+	0.607528i	$0.792161\pi$
$420$		0			0
$421$	−4.79615	+	27.2003i	−0.233750	+	1.32566i	0.611481	+	0.791259i	$0.290574\pi$
$421$	−4.79615	+	27.2003i	−0.233750	+	1.32566i	−0.845230	+	0.534402i	$0.820537\pi$
$422$	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	$0.108966\pi$
$431$			13.9378i			0.671358i	−0.941976	+	0.335679i	$0.891034\pi$
$432$		0			0
$433$			20.8489i			1.00193i	0.865467	+	0.500966i	$0.167022\pi$
$433$			20.8489i			1.00193i	−0.865467	+	0.500966i	$0.832978\pi$
$434$	−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	−0.820183	−	0.572101i	$-0.806129\pi$
$439$	−2.39592	+	2.85534i	−0.114351	+	0.136278i	0.705833	+	0.708379i	$0.250573\pi$
$440$	−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	0.0494956	−	0.998774i	$-0.484239\pi$
$443$	−5.16917	−	0.911464i	−0.245595	−	0.0433050i	−0.295090	+	0.955469i	$0.595350\pi$
$444$		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	0.134247	−	0.990948i	$-0.457138\pi$
$449$	22.4516	−	12.9624i	1.05956	−	0.611735i	0.925310	+	0.379212i	$0.123805\pi$
$450$		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	0.156913	−	0.987612i	$-0.449846\pi$
$457$	19.4951	−	7.09562i	0.911940	−	0.331919i	0.755027	+	0.655693i	$0.227624\pi$
$458$	−50.6993			−2.36902
$459$		0			0
$460$			0.571034i			0.0266246i
$461$	0.166492	−	0.0605983i	0.00775433	−	0.00282234i	−0.338140	−	0.941096i	$-0.609798\pi$
$461$	0.166492	−	0.0605983i	0.00775433	−	0.00282234i	0.345894	+	0.938273i	$0.387576\pi$
$462$		0			0
$463$	22.1677	−	18.6009i	1.03022	−	0.864457i	0.0393425	−	0.999226i	$-0.487474\pi$
$463$	22.1677	−	18.6009i	1.03022	−	0.864457i	0.990877	+	0.134769i	$0.0430292\pi$
$464$	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	−0.950223	−	0.311571i	$-0.899145\pi$
$467$	−4.43621	+	7.68373i	−0.205283	+	0.355561i	0.744940	+	0.667132i	$0.232478\pi$
$468$		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	0.747071	−	0.664744i	$-0.231460\pi$
$479$	4.86205	+	4.07975i	0.222153	+	0.186408i	−0.524918	+	0.851153i	$0.675904\pi$
$480$		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	0.139409	−	0.990235i	$-0.455480\pi$
$491$	13.4965	−	2.37981i	0.609091	−	0.107399i	0.469682	+	0.882836i	$0.344369\pi$
$492$		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	−0.507714	−	0.861526i	$-0.669509\pi$
$499$	−32.4000	−	11.7926i	−1.45042	−	0.527911i	−0.942709	+	0.333615i	$0.891732\pi$
$500$	−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	0.883087	+	0.469209i	$0.155461\pi$
$503$	19.0162	+	32.9370i	0.847891	+	1.46859i	−0.0351966	+	0.999380i	$0.511206\pi$
$504$		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	−0.695254	−	0.718765i	$-0.744708\pi$
$509$	−2.43971	+	2.04716i	−0.108138	+	0.0907387i	0.587115	+	0.809503i	$0.300263\pi$
$510$		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	−0.422841	−	0.906204i	$-0.638967\pi$
$521$	13.0875	−	22.6683i	0.573375	−	0.993115i	0.996216	−	0.0869113i	$-0.0276997\pi$
$522$		0			0
$523$	−14.0356	+	8.10349i	−0.613736	+	0.354341i	−0.774426	−	0.632664i	$-0.781961\pi$
$523$	−14.0356	+	8.10349i	−0.613736	+	0.354341i	0.160690	+	0.987005i	$0.448628\pi$
$524$	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	0.477880	−	0.878425i	$-0.341405\pi$
$547$	−7.11504	−	5.97023i	−0.304217	−	0.255269i	−0.782097	+	0.623157i	$0.785850\pi$
$548$	−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	−0.703548	−	0.710648i	$-0.748402\pi$
$557$	−10.3816	+	5.99382i	−0.439882	+	0.253966i	0.263665	+	0.964614i	$0.415069\pi$
$558$		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	−0.641217	−	0.767359i	$-0.721570\pi$
$563$	0.0744631	−	0.0624819i	0.00313824	−	0.00263330i	0.644355	+	0.764726i	$0.277126\pi$
$564$		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	−0.998983	−	0.0450941i	$-0.985641\pi$
$569$	−6.26646	−	17.2169i	−0.262704	−	0.721772i	0.736279	−	0.676678i	$-0.236581\pi$
$570$		0			0
$571$	11.0847	−	9.30116i	0.463880	−	0.389241i	−0.380676	−	0.924708i	$-0.624309\pi$
$571$	11.0847	−	9.30116i	0.463880	−	0.389241i	0.844556	+	0.535467i	$0.179864\pi$
$572$	−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	−0.878272	−	0.478161i	$-0.841304\pi$
$577$	−21.6982	+	12.5275i	−0.903309	+	0.521526i	−0.0250367	+	0.999687i	$0.507970\pi$
$578$	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	0.0866537	−	0.996238i	$-0.472383\pi$
$587$	−21.3062	−	17.8781i	−0.879402	−	0.737906i	−0.966056	+	0.258332i	$0.916827\pi$
$588$		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	−0.355768	−	0.934574i	$-0.615781\pi$
$599$	−9.06627	+	1.59863i	−0.370438	+	0.0653181i	−0.0146695	+	0.999892i	$0.504670\pi$
$600$		0			0
$601$	25.8812	−	30.8440i	1.05571	−	1.25815i	0.0907219	−	0.995876i	$-0.471083\pi$
$601$	25.8812	−	30.8440i	1.05571	−	1.25815i	0.964993	−	0.262276i	$-0.0844730\pi$
$602$	−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	−0.951320	−	0.308205i	$-0.900272\pi$
$607$	−0.602537	+	1.65546i	−0.0244562	+	0.0671930i	0.926864	+	0.375398i	$0.122494\pi$
$608$	−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	−0.998682	−	0.0513222i	$-0.983656\pi$
$613$	−11.2627	+	19.5075i	−0.454895	+	0.787901i	0.543787	+	0.839223i	$0.316990\pi$
$614$	−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	0.444761	−	0.895649i	$-0.353289\pi$
$617$	−12.7802	−	15.2309i	−0.514513	−	0.613173i	−0.959274	+	0.282476i	$0.908844\pi$
$618$		0			0
$619$	−1.43450	−	3.94126i	−0.0576575	−	0.158413i	0.907520	−	0.420009i	$-0.137973\pi$
$619$	−1.43450	−	3.94126i	−0.0576575	−	0.158413i	−0.965177	+	0.261597i	$0.915751\pi$
$620$			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	0.972014	−	0.234921i	$-0.0754833\pi$
$631$	7.09781	+	12.2938i	0.282559	+	0.489407i	−0.689455	+	0.724328i	$0.742150\pi$
$632$	−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	−0.987664	−	0.156588i	$-0.949951\pi$
$641$	−16.7592	+	19.9729i	−0.661949	+	0.788881i	0.325715	+	0.945468i	$0.394395\pi$
$642$		0			0
$643$	−35.5086	+	6.26113i	−1.40032	+	0.246915i	−0.822277	−	0.569088i	$-0.807296\pi$
$643$	−35.5086	+	6.26113i	−1.40032	+	0.246915i	−0.578048	+	0.816003i	$0.696185\pi$
$644$	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	−0.791424	−	0.611268i	$-0.790660\pi$
$653$	−33.8858	+	5.97498i	−1.32605	+	0.233819i	−0.534629	+	0.845087i	$0.679549\pi$
$654$		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	0.856255	−	0.516554i	$-0.172785\pi$
$659$	38.1009	+	6.71821i	1.48420	+	0.261704i	0.627944	+	0.778258i	$0.283896\pi$
$660$		0			0
$661$	10.2109	−	28.0542i	0.397158	−	1.09118i	−0.566504	−	0.824059i	$-0.691704\pi$
$661$	10.2109	−	28.0542i	0.397158	−	1.09118i	0.963662	−	0.267124i	$-0.0860733\pi$
$662$	−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	0.0809075	−	0.996722i	$-0.474218\pi$
$673$	20.3275	−	7.39859i	0.783566	−	0.285195i	0.702659	+	0.711527i	$0.251996\pi$
$674$			35.0552i			1.35028i
$675$		0			0
$676$	52.0888			2.00342
$677$	7.25316	−	2.63993i	0.278761	−	0.101461i	−0.198856	−	0.980029i	$-0.563723\pi$
$677$	7.25316	−	2.63993i	0.278761	−	0.101461i	0.477618	+	0.878568i	$0.341500\pi$
$678$		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	0.343659	−	0.939094i	$-0.388333\pi$
$683$	−7.78254	−	4.49325i	−0.297791	−	0.171930i	−0.641450	+	0.767165i	$0.721667\pi$
$684$		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	0.778253	−	0.627951i	$-0.216106\pi$
$691$	34.0362	+	6.00150i	1.29480	+	0.228308i	0.516546	+	0.856259i	$0.327217\pi$
$692$	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	$-0.855514\pi$
$701$		−	23.2192i		−	0.876977i	0.898737	−	0.438488i	$-0.144486\pi$
$702$		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	0.989337	−	0.145643i	$-0.0465250\pi$
$709$	27.0985	+	22.7383i	1.01770	+	0.853955i	0.0283665	+	0.999598i	$0.490969\pi$
$710$	−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	−0.989871	−	0.141969i	$-0.954657\pi$
$719$	−16.5681	−	28.6967i	−0.617884	−	1.07021i	0.371987	−	0.928238i	$-0.378677\pi$
$720$		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	0.975841	−	0.218480i	$-0.0701100\pi$
$727$	2.36915	+	6.50919i	0.0878670	+	0.241413i	−0.887974	+	0.459893i	$0.847888\pi$
$728$	−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	0.990982	−	0.133993i	$-0.0427800\pi$
$733$	18.5983	+	22.1646i	0.686943	+	0.818666i	−0.304040	+	0.952659i	$0.598336\pi$
$734$	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	0.978633	−	0.205613i	$-0.0659187\pi$
$739$	8.46122	+	14.6553i	0.311251	+	0.539103i	−0.667382	+	0.744715i	$0.732585\pi$
$740$	−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	−0.836446	−	0.548049i	$-0.815371\pi$
$743$	4.26829	−	11.7270i	0.156588	−	0.430223i	0.993034	+	0.117827i	$0.0375928\pi$
$744$		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	−0.994800	−	0.101849i	$-0.967524\pi$
$751$	−2.59871	−	14.7380i	−0.0948283	−	0.537798i	0.899972	−	0.435949i	$-0.143587\pi$
$752$	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	0.789620	+	0.613596i	$0.210278\pi$
$761$	7.10296	+	40.2829i	0.257482	+	1.46025i	−0.532138	+	0.846657i	$0.678611\pi$
$762$		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	0.738713	+	0.674020i	$0.235434\pi$
$769$	−7.22183	+	19.8418i	−0.260426	+	0.715514i	−0.999139	+	0.0414940i	$0.986788\pi$
$770$	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	0.875569	−	0.483093i	$-0.160487\pi$
$773$	0.539761	+	0.934893i	0.0194138	+	0.0336258i	−0.856155	+	0.516719i	$0.827153\pi$
$774$		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	0.999431	−	0.0337197i	$-0.0107354\pi$
$787$	22.2373	+	26.5014i	0.792674	+	0.944673i	−0.206757	+	0.978392i	$0.566291\pi$
$788$	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	0.573498	−	0.819207i	$-0.305586\pi$
$797$	13.7273	+	4.99634i	0.486247	+	0.176980i	−0.0872509	+	0.996186i	$0.527808\pi$
$798$		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	$-0.888657\pi$
$809$		−	19.4950i		−	0.685407i	0.939444	−	0.342704i	$-0.111343\pi$
$810$		0			0
$811$		−	8.74742i		−	0.307163i	−0.988136	−	0.153582i	$-0.950919\pi$
$811$		−	8.74742i		−	0.307163i	0.988136	−	0.153582i	$-0.0490808\pi$
$812$	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	0.426836	−	0.904329i	$-0.359628\pi$
$821$	14.8604	+	2.62030i	0.518633	+	0.0914490i	0.0917964	+	0.995778i	$0.470739\pi$
$822$		0			0
$823$	45.4998	+	16.5606i	1.58602	+	0.577265i	0.976503	−	0.215505i	$-0.0691396\pi$
$823$	45.4998	+	16.5606i	1.58602	+	0.577265i	0.609521	+	0.792770i	$0.291362\pi$
$824$	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	−0.532251	−	0.846586i	$-0.678654\pi$
$827$	−1.87534	+	1.08273i	−0.0652119	+	0.0376501i	0.467040	+	0.884236i	$0.345321\pi$
$828$		0			0
$829$	−34.8737	−	20.1344i	−1.21121	−	0.699295i	−0.248191	−	0.968711i	$-0.579836\pi$
$829$	−34.8737	−	20.1344i	−1.21121	−	0.699295i	−0.963024	+	0.269416i	$0.913169\pi$
$830$	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	−0.482155	−	0.876086i	$-0.660146\pi$
$839$	−8.35277	+	3.04016i	−0.288370	+	0.104958i	0.193785	+	0.981044i	$0.437924\pi$
$840$		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	0.293121	−	0.956075i	$-0.405306\pi$
$853$	7.05528	+	1.24404i	0.241568	+	0.0425950i	−0.0515532	+	0.998670i	$0.516417\pi$
$854$	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	0.977344	−	0.211655i	$-0.0678852\pi$
$857$	27.4777	+	23.0565i	0.938619	+	0.787595i	−0.0387252	+	0.999250i	$0.512330\pi$
$858$		0			0
$859$	−4.46217	+	0.786801i	−0.152247	+	0.0268453i	−0.249252	−	0.968439i	$-0.580185\pi$
$859$	−4.46217	+	0.786801i	−0.152247	+	0.0268453i	0.0970050	+	0.995284i	$0.469074\pi$
$860$	−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	$-0.809713\pi$
$863$		−	33.0683i		−	1.12566i	0.826573	−	0.562830i	$-0.190287\pi$
$864$		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	0.131366	−	0.991334i	$-0.458064\pi$
$877$	−12.0002	−	4.36773i	−0.405219	−	0.147488i	−0.536585	+	0.843846i	$0.680286\pi$
$878$	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	0.687436	−	0.726245i	$-0.258736\pi$
$881$	−8.46605	−	14.6636i	−0.285229	−	0.494030i	−0.972665	+	0.232215i	$0.925403\pi$
$882$		0			0
$883$	4.01408	−	6.95260i	0.135085	−	0.233973i	−0.790545	−	0.612404i	$-0.790203\pi$
$883$	4.01408	−	6.95260i	0.135085	−	0.233973i	0.925630	+	0.378430i	$0.123536\pi$
$884$	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	−0.166891	−	0.985975i	$-0.553373\pi$
$887$	23.0852	−	19.3708i	0.775125	−	0.650408i	0.942016	+	0.335568i	$0.108928\pi$
$888$		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	0.820058	+	0.572281i	$0.193941\pi$
$907$	−4.40531	+	24.9838i	−0.146276	+	0.829572i	−0.966334	+	0.257292i	$0.917170\pi$
$908$	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	−0.752366	−	0.658745i	$-0.771088\pi$
$911$	0.815474	−	0.971845i	0.0270179	−	0.0321986i	0.779384	+	0.626546i	$0.215532\pi$
$912$		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	−0.711285	−	0.702904i	$-0.751886\pi$
$929$	6.02005	−	34.1414i	0.197512	−	1.12014i	0.908796	−	0.417240i	$-0.137002\pi$
$930$		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	0.846367	−	0.532599i	$-0.178785\pi$
$937$	24.7426	+	14.2852i	0.808307	+	0.466676i	−0.0380609	+	0.999275i	$0.512118\pi$
$938$	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	−0.215623	+	0.976477i	$0.569178\pi$
$941$	−37.2620	+	31.2666i	−1.21471	+	1.01926i	−0.999084	+	0.0427842i	$0.986377\pi$
$942$		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	0.998827	−	0.0484279i	$-0.0154211\pi$
$947$	6.23321	+	17.1256i	0.202552	+	0.556508i	−0.796275	+	0.604935i	$0.793199\pi$
$948$		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	−0.0313712	−	0.999508i	$-0.509987\pi$
$953$	−28.1743	−	16.2665i	−0.912656	−	0.526922i	−0.881285	+	0.472586i	$0.843321\pi$
$954$		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	0.987814	−	0.155640i	$-0.0497441\pi$
$967$	0.197163	+	1.11816i	0.00634032	+	0.0359577i	−0.981473	+	0.191598i	$0.938633\pi$
$968$	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	0.315390	−	0.948962i	$-0.397865\pi$
$977$	29.2666	−	5.16050i	0.936323	−	0.165099i	0.620933	+	0.783863i	$0.286754\pi$
$978$		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	−0.976576	−	0.215172i	$-0.930969\pi$
$983$	0.460838	−	2.61354i	0.0146984	−	0.0833590i	0.991275	+	0.131813i	$0.0420799\pi$
$984$		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	0.485622	+	0.874169i	$0.338593\pi$
$991$	−16.1884	+	28.0391i	−0.514242	+	0.890693i	−0.999863	+	0.0165236i	$0.994740\pi$
$992$	−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	0.882053	−	0.471151i	$-0.156161\pi$
$997$	−3.04666	−	8.37063i	−0.0964887	−	0.265100i	−0.978541	+	0.206050i	$0.933939\pi$
$998$			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.62.4		132
3.2	odd	2		189.2.be.a.20.20	yes	132
7.6	odd	2	inner	567.2.be.a.62.3		132
21.20	even	2		189.2.be.a.20.19	✓	132
27.4	even	9		189.2.be.a.104.19	yes	132
27.23	odd	18	inner	567.2.be.a.503.3		132
189.104	even	18	inner	567.2.be.a.503.4		132
189.139	odd	18		189.2.be.a.104.20	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.19	✓	132	21.20	even	2
189.2.be.a.20.20	yes	132	3.2	odd	2
189.2.be.a.104.19	yes	132	27.4	even	9
189.2.be.a.104.20	yes	132	189.139	odd	18
567.2.be.a.62.3		132	7.6	odd	2	inner
567.2.be.a.62.4		132	1.1	even	1	trivial
567.2.be.a.503.3		132	27.23	odd	18	inner
567.2.be.a.503.4		132	189.104	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more