LMFDB - Embedded newform 567.2.w.a.424.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(37,567)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("567.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.w (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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 $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			424.19
Character	$\chi$	$=$	567.424
Dual form			567.2.w.a.226.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42989 + 1.19982i) q^{2} +(0.257724 + 1.46163i) q^{4} +(1.12074 - 0.940415i) q^{5} +(-1.46549 - 2.20281i) q^{7} +(0.481419 - 0.833843i) q^{8} +2.73088 q^{10} +(3.49769 + 2.93491i) q^{11} +(0.925783 + 0.336957i) q^{13} +(0.547488 - 4.90810i) q^{14} +(4.47818 - 1.62992i) q^{16} +1.24047 q^{17} +1.43605 q^{19} +(1.66338 + 1.39574i) q^{20} +(1.47995 + 8.39323i) q^{22} +(0.896333 + 0.326239i) q^{23} +(-0.496556 + 2.81611i) q^{25} +(0.919482 + 1.59259i) q^{26} +(2.84199 - 2.70971i) q^{28} +(-5.18835 + 1.88840i) q^{29} +(-1.16126 - 6.58584i) q^{31} +(6.54939 + 2.38378i) q^{32} +(1.77374 + 1.48834i) q^{34} +(-3.71398 - 1.09061i) q^{35} +(1.44382 - 2.50077i) q^{37} +(2.05340 + 1.72301i) q^{38} +(-0.244611 - 1.38726i) q^{40} +(-11.1576 - 4.06104i) q^{41} +(0.559660 - 3.17399i) q^{43} +(-3.38830 + 5.86872i) q^{44} +(0.890232 + 1.54193i) q^{46} +(-1.96585 + 11.1489i) q^{47} +(-2.70470 + 6.45636i) q^{49} +(-4.08886 + 3.43096i) q^{50} +(-0.253909 + 1.43999i) q^{52} +(-2.32509 + 4.02717i) q^{53} +6.68005 q^{55} +(-2.54231 + 0.161512i) q^{56} +(-9.68454 - 3.52488i) q^{58} +(-5.93016 - 2.15840i) q^{59} +(0.911917 - 5.17174i) q^{61} +(6.24136 - 10.8104i) q^{62} +(1.73924 + 3.01245i) q^{64} +(1.35444 - 0.492978i) q^{65} +(-10.0646 + 8.44521i) q^{67} +(0.319698 + 1.81310i) q^{68} +(-4.00206 - 6.01559i) q^{70} +(5.80593 + 10.0562i) q^{71} +(-4.96509 - 8.59979i) q^{73} +(5.06499 - 1.84351i) q^{74} +(0.370105 + 2.09897i) q^{76} +(1.33922 - 12.0058i) q^{77} +(10.8394 + 9.09537i) q^{79} +(3.48608 - 6.03807i) q^{80} +(-11.0817 - 19.1940i) q^{82} +(7.82112 - 2.84665i) q^{83} +(1.39025 - 1.16656i) q^{85} +(4.60848 - 3.86697i) q^{86} +(4.13111 - 1.50360i) q^{88} +0.614975 q^{89} +(-0.614470 - 2.53313i) q^{91} +(-0.245832 + 1.39418i) q^{92} +(-16.1877 + 13.5831i) q^{94} +(1.60945 - 1.35049i) q^{95} +(-0.991251 + 5.62167i) q^{97} +(-11.6139 + 5.98675i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29}+ \cdots - 99 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	1.42989	+	1.19982i	1.01109	+	0.848403i	0.988482	−	0.151341i	$-0.0483592\pi$
$2$	1.42989	+	1.19982i	1.01109	+	0.848403i	0.0226062	+	0.999744i	$0.492804\pi$
$3$		0			0
$3$		0			0
$4$	0.257724	+	1.46163i	0.128862	+	0.730813i
$5$	1.12074	−	0.940415i	0.501212	−	0.420566i	−0.356812	−	0.934176i	$-0.616136\pi$
$5$	1.12074	−	0.940415i	0.501212	−	0.420566i	0.858024	+	0.513610i	$0.171692\pi$
$6$		0			0
$7$	−1.46549	−	2.20281i	−0.553902	−	0.832582i
$7$	−1.46549	−	2.20281i	−0.553902	−	0.832582i
$8$	0.481419	−	0.833843i	0.170207	−	0.294808i
$9$		0			0
$10$	2.73088			0.863579
$11$	3.49769	+	2.93491i	1.05459	+	0.884910i	0.993569	−	0.113227i	$-0.0361186\pi$
$11$	3.49769	+	2.93491i	1.05459	+	0.884910i	0.0610251	+	0.998136i	$0.480563\pi$
$12$		0			0
$13$	0.925783	+	0.336957i	0.256766	+	0.0934552i	0.467196	−	0.884154i	$-0.345264\pi$
$13$	0.925783	+	0.336957i	0.256766	+	0.0934552i	−0.210430	+	0.977609i	$0.567486\pi$
$14$	0.547488	−	4.90810i	0.146322	−	1.31175i
$15$		0			0
$16$	4.47818	−	1.62992i	1.11954	−	0.407481i
$17$	1.24047			0.300858			0.150429	−	0.988621i	$-0.451935\pi$
$17$	1.24047			0.300858			0.150429	+	0.988621i	$0.451935\pi$
$18$		0			0
$19$	1.43605			0.329453			0.164727	−	0.986339i	$-0.447326\pi$
$19$	1.43605			0.329453			0.164727	+	0.986339i	$0.447326\pi$
$20$	1.66338	+	1.39574i	0.371942	+	0.312097i
$21$		0			0
$22$	1.47995	+	8.39323i	0.315527	+	1.78944i
$23$	0.896333	+	0.326239i	0.186898	+	0.0680254i	0.433774	−	0.901022i	$-0.357182\pi$
$23$	0.896333	+	0.326239i	0.186898	+	0.0680254i	−0.246876	+	0.969047i	$0.579404\pi$
$24$		0			0
$25$	−0.496556	+	2.81611i	−0.0993113	+	0.563222i
$26$	0.919482	+	1.59259i	0.180325	+	0.312333i
$27$		0			0
$28$	2.84199	−	2.70971i	0.537085	−	0.512087i
$29$	−5.18835	+	1.88840i	−0.963452	+	0.350668i	−0.775385	−	0.631488i	$-0.782444\pi$
$29$	−5.18835	+	1.88840i	−0.963452	+	0.350668i	−0.188067	+	0.982156i	$0.560222\pi$
$30$		0			0
$31$	−1.16126	−	6.58584i	−0.208569	−	1.18285i	−0.891724	−	0.452579i	$-0.850504\pi$
$31$	−1.16126	−	6.58584i	−0.208569	−	1.18285i	0.683156	−	0.730273i	$-0.260607\pi$
$32$	6.54939	+	2.38378i	1.15778	+	0.421397i
$33$		0			0
$34$	1.77374	+	1.48834i	0.304194	+	0.255249i
$35$	−3.71398	−	1.09061i	−0.627778	−	0.184347i
$36$		0			0
$37$	1.44382	−	2.50077i	0.237363	−	0.411124i	−0.722594	−	0.691273i	$-0.757050\pi$
$37$	1.44382	−	2.50077i	0.237363	−	0.411124i	0.959957	+	0.280149i	$0.0903837\pi$
$38$	2.05340	+	1.72301i	0.333106	+	0.279509i
$39$		0			0
$40$	−0.244611	−	1.38726i	−0.0386764	−	0.219345i
$41$	−11.1576	−	4.06104i	−1.74253	−	0.634227i	−0.743135	−	0.669141i	$-0.766662\pi$
$41$	−11.1576	−	4.06104i	−1.74253	−	0.634227i	−0.999390	+	0.0349137i	$0.988884\pi$
$42$		0			0
$43$	0.559660	−	3.17399i	0.0853473	−	0.484029i	−0.911934	−	0.410337i	$-0.865411\pi$
$43$	0.559660	−	3.17399i	0.0853473	−	0.484029i	0.997281	−	0.0736913i	$-0.0234780\pi$
$44$	−3.38830	+	5.86872i	−0.510806	+	0.884742i
$45$		0			0
$46$	0.890232	+	1.54193i	0.131258	+	0.227345i
$47$	−1.96585	+	11.1489i	−0.286749	+	1.62623i	0.412223	+	0.911083i	$0.364752\pi$
$47$	−1.96585	+	11.1489i	−0.286749	+	1.62623i	−0.698972	+	0.715149i	$0.746359\pi$
$48$		0			0
$49$	−2.70470	+	6.45636i	−0.386386	+	0.922337i
$50$	−4.08886	+	3.43096i	−0.578252	+	0.485211i
$51$		0			0
$52$	−0.253909	+	1.43999i	−0.0352109	+	0.199691i
$53$	−2.32509	+	4.02717i	−0.319376	+	0.553175i	−0.980358	−	0.197227i	$-0.936806\pi$
$53$	−2.32509	+	4.02717i	−0.319376	+	0.553175i	0.660982	+	0.750402i	$0.270140\pi$
$54$		0			0
$55$	6.68005			0.900738
$56$	−2.54231	+	0.161512i	−0.339730	+	0.0215829i
$57$		0			0
$58$	−9.68454	−	3.52488i	−1.27164	−	0.462840i
$59$	−5.93016	−	2.15840i	−0.772042	−	0.281000i	−0.0741915	−	0.997244i	$-0.523638\pi$
$59$	−5.93016	−	2.15840i	−0.772042	−	0.281000i	−0.697850	+	0.716244i	$0.745860\pi$
$60$		0			0
$61$	0.911917	−	5.17174i	0.116759	−	0.662173i	−0.869105	−	0.494627i	$-0.835305\pi$
$61$	0.911917	−	5.17174i	0.116759	−	0.662173i	0.985864	−	0.167546i	$-0.0535843\pi$
$62$	6.24136	−	10.8104i	0.792654	−	1.37292i
$63$		0			0
$64$	1.73924	+	3.01245i	0.217405	+	0.376557i
$65$	1.35444	−	0.492978i	0.167998	−	0.0611463i
$66$		0			0
$67$	−10.0646	+	8.44521i	−1.22959	+	1.03175i	−0.231323	+	0.972877i	$0.574305\pi$
$67$	−10.0646	+	8.44521i	−1.22959	+	1.03175i	−0.998266	+	0.0588702i	$0.981250\pi$
$68$	0.319698	+	1.81310i	0.0387691	+	0.219871i
$69$		0			0
$70$	−4.00206	−	6.01559i	−0.478338	−	0.719000i
$71$	5.80593	+	10.0562i	0.689037	+	1.19345i	0.972150	+	0.234360i	$0.0752995\pi$
$71$	5.80593	+	10.0562i	0.689037	+	1.19345i	−0.283113	+	0.959087i	$0.591367\pi$
$72$		0			0
$73$	−4.96509	−	8.59979i	−0.581120	−	1.00653i	−0.995347	−	0.0963557i	$-0.969281\pi$
$73$	−4.96509	−	8.59979i	−0.581120	−	1.00653i	0.414227	−	0.910174i	$-0.364052\pi$
$74$	5.06499	−	1.84351i	0.588793	−	0.214303i
$75$		0			0
$76$	0.370105	+	2.09897i	0.0424540	+	0.240769i
$77$	1.33922	−	12.0058i	0.152618	−	1.36819i
$78$		0			0
$79$	10.8394	+	9.09537i	1.21953	+	1.02331i	0.998849	+	0.0479629i	$0.0152729\pi$
$79$	10.8394	+	9.09537i	1.21953	+	1.02331i	0.220683	+	0.975346i	$0.429172\pi$
$80$	3.48608	−	6.03807i	0.389756	−	0.675077i
$81$		0			0
$82$	−11.0817	−	19.1940i	−1.22377	−	2.11962i
$83$	7.82112	−	2.84665i	0.858479	−	0.312461i	0.124987	−	0.992158i	$-0.460111\pi$
$83$	7.82112	−	2.84665i	0.858479	−	0.312461i	0.733493	+	0.679697i	$0.237889\pi$
$84$		0			0
$85$	1.39025	−	1.16656i	0.150793	−	0.126531i
$86$	4.60848	−	3.86697i	0.496945	−	0.416987i
$87$		0			0
$88$	4.13111	−	1.50360i	0.440378	−	0.160285i
$89$	0.614975			0.0651872			0.0325936	−	0.999469i	$-0.489623\pi$
$89$	0.614975			0.0651872			0.0325936	+	0.999469i	$0.489623\pi$
$90$		0			0
$91$	−0.614470	−	2.53313i	−0.0644140	−	0.265544i
$92$	−0.245832	+	1.39418i	−0.0256298	+	0.145354i
$93$		0			0
$94$	−16.1877	+	13.5831i	−1.66963	+	1.40099i
$95$	1.60945	−	1.35049i	0.165126	−	0.138557i
$96$		0			0
$97$	−0.991251	+	5.62167i	−0.100646	+	0.570794i	0.892224	+	0.451593i	$0.149144\pi$
$97$	−0.991251	+	5.62167i	−0.100646	+	0.570794i	−0.992870	+	0.119200i	$0.961967\pi$
$98$	−11.6139	+	5.98675i	−1.17318	+	0.604753i
$99$		0			0
$100$	−4.24407			−0.424407
$101$	−11.1289	+	4.05057i	−1.10736	+	0.403047i	−0.830025	−	0.557726i	$-0.811674\pi$
$101$	−11.1289	+	4.05057i	−1.10736	+	0.403047i	−0.277337	+	0.960773i	$0.589452\pi$
$102$		0			0
$103$	9.83084	−	8.24905i	0.968661	−	0.812803i	−0.0136790	−	0.999906i	$-0.504354\pi$
$103$	9.83084	−	8.24905i	0.968661	−	0.812803i	0.982340	+	0.187103i	$0.0599099\pi$
$104$	0.726659	−	0.609740i	0.0712548	−	0.0597899i
$105$		0			0
$106$	−8.15653	+	2.96873i	−0.792232	+	0.288349i
$107$	−5.52411	−	9.56804i	−0.534036	−	0.924977i	−0.999209	−	0.0397577i	$-0.987341\pi$
$107$	−5.52411	−	9.56804i	−0.534036	−	0.924977i	0.465173	−	0.885220i	$-0.345992\pi$
$108$		0			0
$109$	−9.52408	+	16.4962i	−0.912242	+	1.58005i	−0.101352	+	0.994851i	$0.532317\pi$
$109$	−9.52408	+	16.4962i	−0.912242	+	1.58005i	−0.810890	+	0.585198i	$0.801017\pi$
$110$	9.55177	+	8.01488i	0.910725	+	0.764189i
$111$		0			0
$112$	−10.1531	−	7.47592i	−0.959379	−	0.706408i
$113$	−1.36095	−	7.71833i	−0.128027	−	0.726080i	−0.979464	−	0.201621i	$-0.935379\pi$
$113$	−1.36095	−	7.71833i	−0.128027	−	0.726080i	0.851436	−	0.524458i	$-0.175732\pi$
$114$		0			0
$115$	1.31136	−	0.477295i	0.122285	−	0.0445080i
$116$	−4.09730	−	7.09674i	−0.380425	−	0.658915i
$117$		0			0
$118$	−5.88980	−	10.2014i	−0.542200	−	0.939119i
$119$	−1.81789	−	2.73251i	−0.166646	−	0.250489i
$120$		0			0
$121$	1.71001	+	9.69797i	0.155456	+	0.881633i
$122$	7.50912	−	6.30090i	0.679844	−	0.570457i
$123$		0			0
$124$	9.32674	−	3.39466i	0.837566	−	0.304849i
$125$	5.74937	+	9.95820i	0.514239	+	0.890688i
$126$		0			0
$127$	−6.35187	+	11.0018i	−0.563637	+	0.976249i	0.433538	+	0.901136i	$0.357265\pi$
$127$	−6.35187	+	11.0018i	−0.563637	+	0.976249i	−0.997175	+	0.0751132i	$0.976068\pi$
$128$	1.29307	−	7.33339i	0.114293	−	0.648186i
$129$		0			0
$130$	2.52820	+	0.920189i	0.221738	+	0.0807059i
$131$	−7.88900	−	2.87136i	−0.689265	−	0.250872i	−0.0264445	−	0.999650i	$-0.508419\pi$
$131$	−7.88900	−	2.87136i	−0.689265	−	0.250872i	−0.662820	+	0.748778i	$0.730641\pi$
$132$		0			0
$133$	−2.10452	−	3.16335i	−0.182485	−	0.274297i
$134$	−24.5241			−2.11856
$135$		0			0
$136$	0.597185	−	1.03436i	0.0512082	−	0.0886953i
$137$	0.403413	−	2.28787i	0.0344659	−	0.195466i	−0.962713	−	0.270524i	$-0.912803\pi$
$137$	0.403413	−	2.28787i	0.0344659	−	0.195466i	0.997179	+	0.0750580i	$0.0239142\pi$
$138$		0			0
$139$	16.4618	−	13.8131i	1.39627	−	1.17161i	0.433546	−	0.901131i	$-0.357262\pi$
$139$	16.4618	−	13.8131i	1.39627	−	1.17161i	0.962726	−	0.270480i	$-0.0871824\pi$
$140$	0.636886	−	5.70953i	0.0538267	−	0.482544i
$141$		0			0
$142$	−3.76376	+	21.3453i	−0.315848	+	1.79126i
$143$	2.24916	+	3.89567i	0.188085	+	0.325772i
$144$		0			0
$145$	−4.03892	+	6.99562i	−0.335414	+	0.580954i
$146$	3.21868	−	18.2540i	0.266380	−	1.51071i
$147$		0			0
$148$	4.02730	+	1.46582i	0.331042	+	0.120489i
$149$	−0.762741	−	4.32572i	−0.0624862	−	0.354377i	−0.999980	−	0.00637396i	$-0.997971\pi$
$149$	−0.762741	−	4.32572i	−0.0624862	−	0.354377i	0.937494	−	0.348003i	$-0.113140\pi$
$150$		0			0
$151$	11.3548	+	9.52783i	0.924042	+	0.775363i	0.974738	−	0.223351i	$-0.0716995\pi$
$151$	11.3548	+	9.52783i	0.924042	+	0.775363i	−0.0506960	+	0.998714i	$0.516144\pi$
$152$	0.691344	−	1.19744i	0.0560754	−	0.0971254i
$153$		0			0
$154$	16.3198	−	15.5602i	1.31509	−	1.25388i
$155$	−7.49490	−	6.28896i	−0.602005	−	0.505142i
$156$		0			0
$157$	−0.355417	−	0.129361i	−0.0283653	−	0.0103241i	0.327799	−	0.944748i	$-0.393693\pi$
$157$	−0.355417	−	0.129361i	−0.0283653	−	0.0103241i	−0.356164	+	0.934424i	$0.615916\pi$
$158$	4.58641	+	26.0108i	0.364875	+	2.06931i
$159$		0			0
$160$	9.58193	−	3.48754i	0.757518	−	0.275714i
$161$	−0.594923	−	2.45254i	−0.0468865	−	0.193288i
$162$		0			0
$163$	−2.58086	−	4.47018i	−0.202148	−	0.350131i	0.747072	−	0.664743i	$-0.231459\pi$
$163$	−2.58086	−	4.47018i	−0.202148	−	0.350131i	−0.949220	+	0.314612i	$0.898126\pi$
$164$	3.06013	−	17.3549i	0.238956	−	1.35519i
$165$		0			0
$166$	14.5989	+	5.31355i	1.13309	+	0.412411i
$167$	1.88838	+	10.7095i	0.146127	+	0.828727i	0.966455	+	0.256834i	$0.0826795\pi$
$167$	1.88838	+	10.7095i	0.146127	+	0.828727i	−0.820329	+	0.571893i	$0.806209\pi$
$168$		0			0
$169$	−9.21504	−	7.73234i	−0.708850	−	0.594795i
$170$	3.38757			0.259814
$171$		0			0
$172$	4.78342			0.364732
$173$	11.3791	−	4.14166i	0.865138	−	0.314884i	0.128941	−	0.991652i	$-0.458842\pi$
$173$	11.3791	−	4.14166i	0.865138	−	0.314884i	0.736196	+	0.676768i	$0.236620\pi$
$174$		0			0
$175$	6.93104	−	3.03315i	0.523937	−	0.229285i
$176$	20.4470	+	7.44209i	1.54125	+	0.560969i
$177$		0			0
$178$	0.879349	+	0.737861i	0.0659100	+	0.0553050i
$179$	−12.3778			−0.925158			−0.462579	−	0.886578i	$-0.653076\pi$
$179$	−12.3778			−0.925158			−0.462579	+	0.886578i	$0.653076\pi$
$180$		0			0
$181$	−7.93495	+	13.7437i	−0.589800	+	1.02156i	0.404458	+	0.914557i	$0.367460\pi$
$181$	−7.93495	+	13.7437i	−0.589800	+	1.02156i	−0.994258	+	0.107007i	$0.965873\pi$
$182$	2.16068	−	4.35936i	0.160160	−	0.323137i
$183$		0			0
$184$	0.703544	−	0.590343i	0.0518659	−	0.0435207i
$185$	−0.733610	−	4.16051i	−0.0539361	−	0.305887i
$186$		0			0
$187$	4.33878	+	3.64067i	0.317283	+	0.266232i
$188$	−16.8021			−1.22542
$189$		0			0
$190$	3.92168			0.284509
$191$	11.6459	+	9.77207i	0.842667	+	0.707082i	0.958162	−	0.286226i	$-0.0924009\pi$
$191$	11.6459	+	9.77207i	0.842667	+	0.707082i	−0.115495	+	0.993308i	$0.536845\pi$
$192$		0			0
$193$	−3.26476	−	18.5154i	−0.235003	−	1.33277i	−0.842608	−	0.538527i	$-0.818981\pi$
$193$	−3.26476	−	18.5154i	−0.235003	−	1.33277i	0.607605	−	0.794239i	$-0.292130\pi$
$194$	−8.16239	+	6.84906i	−0.586026	+	0.491734i
$195$		0			0
$196$	−10.1338	−	2.28930i	−0.723846	−	0.163522i
$197$	−0.130567	+	0.226149i	−0.00930255	+	0.0161125i	−0.870639	−	0.491922i	$-0.836294\pi$
$197$	−0.130567	+	0.226149i	−0.00930255	+	0.0161125i	0.861337	+	0.508035i	$0.169628\pi$
$198$		0			0
$199$	−1.63757			−0.116084			−0.0580421	−	0.998314i	$-0.518486\pi$
$199$	−1.63757			−0.116084			−0.0580421	+	0.998314i	$0.518486\pi$
$200$	2.10914	+	1.76978i	0.149139	+	0.125142i
$201$		0			0
$202$	−20.7731	−	7.56077i	−1.46159	−	0.531974i
$203$	11.7632	+	8.66149i	0.825617	+	0.607917i
$204$		0			0
$205$	−16.3239	+	5.94140i	−1.14011	+	0.414966i
$206$	23.9545			1.66899
$207$		0			0
$208$	4.69503			0.325542
$209$	5.02288	+	4.21469i	0.347440	+	0.291536i
$210$		0			0
$211$	1.10692	+	6.27765i	0.0762034	+	0.432171i	0.998910	+	0.0466690i	$0.0148606\pi$
$211$	1.10692	+	6.27765i	0.0762034	+	0.432171i	−0.922707	+	0.385502i	$0.874028\pi$
$212$	−6.48545	−	2.36051i	−0.445423	−	0.162121i
$213$		0			0
$214$	3.58107	−	20.3092i	0.244797	−	1.38831i
$215$	−2.35763	−	4.08354i	−0.160789	−	0.278495i
$216$		0			0
$217$	−12.8055	+	12.2095i	−0.869294	+	0.828834i
$218$	−33.4110	+	12.1606i	−2.26288	+	0.823619i
$219$		0			0
$220$	1.72161	+	9.76374i	0.116071	+	0.658271i
$221$	1.14840	+	0.417985i	0.0772500	+	0.0281167i
$222$		0			0
$223$	4.42813	+	3.71564i	0.296529	+	0.248818i	0.778898	−	0.627151i	$-0.215779\pi$
$223$	4.42813	+	3.71564i	0.296529	+	0.248818i	−0.482369	+	0.875968i	$0.660223\pi$
$224$	−4.34703	−	17.9204i	−0.290448	−	1.19736i
$225$		0			0
$226$	7.31462	−	12.6693i	0.486562	−	0.842749i
$227$	−9.82241	−	8.24198i	−0.651936	−	0.547039i	0.255722	−	0.966750i	$-0.417687\pi$
$227$	−9.82241	−	8.24198i	−0.651936	−	0.547039i	−0.907658	+	0.419711i	$0.862131\pi$
$228$		0			0
$229$	−1.01772	−	5.77179i	−0.0672530	−	0.381411i	−0.999793	−	0.0203441i	$-0.993524\pi$
$229$	−1.01772	−	5.77179i	−0.0672530	−	0.381411i	0.932540	−	0.361067i	$-0.117587\pi$
$230$	2.44777	+	0.890917i	0.161401	+	0.0587453i
$231$		0			0
$232$	−0.923139	+	5.23538i	−0.0606070	+	0.343720i
$233$	0.485756	−	0.841355i	0.0318230	−	0.0551190i	−0.849675	−	0.527306i	$-0.823202\pi$
$233$	0.485756	−	0.841355i	0.0318230	−	0.0551190i	0.881498	+	0.472187i	$0.156535\pi$
$234$		0			0
$235$	8.28137	+	14.3438i	0.540217	+	0.935683i
$236$	1.62643	−	9.22395i	0.105872	−	0.600428i
$237$		0			0
$238$	0.679142	−	6.08835i	0.0440222	−	0.394649i
$239$	18.1999	−	15.2715i	1.17726	−	0.987834i	0.177262	−	0.984164i	$-0.443276\pi$
$239$	18.1999	−	15.2715i	1.17726	−	0.987834i	0.999993	−	0.00367051i	$-0.00116836\pi$
$240$		0			0
$241$	−0.0497028	+	0.281878i	−0.00320164	+	0.0181574i	−0.986367	−	0.164562i	$-0.947379\pi$
$241$	−0.0497028	+	0.281878i	−0.00320164	+	0.0181574i	0.983165	+	0.182719i	$0.0584900\pi$
$242$	−9.19071	+	15.9188i	−0.590801	+	1.02330i
$243$		0			0
$244$	7.79417			0.498971
$245$	3.04038	+	9.77946i	0.194243	+	0.624787i
$246$		0			0
$247$	1.32947	+	0.483889i	0.0845924	+	0.0307891i
$248$	−6.05061	−	2.20224i	−0.384214	−	0.139842i
$249$		0			0
$250$	−3.72709	+	21.1374i	−0.235722	+	1.33685i
$251$	−3.91719	+	6.78477i	−0.247251	+	0.428251i	−0.962762	−	0.270350i	$-0.912861\pi$
$251$	−3.91719	+	6.78477i	−0.247251	+	0.428251i	0.715511	+	0.698601i	$0.246194\pi$
$252$		0			0
$253$	2.17762	+	3.77174i	0.136906	+	0.237127i
$254$	−22.2827	+	8.11023i	−1.39814	+	0.508881i
$255$		0			0
$256$	15.9771	−	13.4064i	0.998568	−	0.837898i
$257$	1.67773	+	9.51485i	0.104654	+	0.593520i	0.991358	+	0.131184i	$0.0418777\pi$
$257$	1.67773	+	9.51485i	0.104654	+	0.593520i	−0.886704	+	0.462337i	$0.847011\pi$
$258$		0			0
$259$	−7.62461	+	0.484388i	−0.473770	+	0.0300984i
$260$	1.06962	+	1.85264i	0.0663351	+	0.114896i
$261$		0			0
$262$	−7.83530	−	13.5711i	−0.484067	−	0.838428i
$263$	17.2235	−	6.26884i	1.06205	−	0.386553i	0.248849	−	0.968542i	$-0.419948\pi$
$263$	17.2235	−	6.26884i	1.06205	−	0.386553i	0.813196	+	0.581989i	$0.197725\pi$
$264$		0			0
$265$	1.18139	+	6.69998i	0.0725720	+	0.411576i
$266$	0.786222	−	7.04830i	0.0482064	−	0.432159i
$267$		0			0
$268$	−14.9376	−	12.5342i	−0.912461	−	0.765646i
$269$	−2.28434	+	3.95659i	−0.139279	+	0.241238i	−0.927224	−	0.374508i	$-0.877812\pi$
$269$	−2.28434	+	3.95659i	−0.139279	+	0.241238i	0.787945	+	0.615745i	$0.211145\pi$
$270$		0			0
$271$	−6.60709	−	11.4438i	−0.401352	−	0.695162i	0.592537	−	0.805543i	$-0.298126\pi$
$271$	−6.60709	−	11.4438i	−0.401352	−	0.695162i	−0.993889	+	0.110381i	$0.964793\pi$
$272$	5.55504	−	2.02187i	0.336824	−	0.122594i
$273$		0			0
$274$	3.32188	−	2.78739i	0.200682	−	0.168392i
$275$	−10.0018	+	8.39254i	−0.603134	+	0.506089i
$276$		0			0
$277$	28.5431	−	10.3888i	1.71499	−	0.624205i	0.717602	−	0.696453i	$-0.245240\pi$
$277$	28.5431	−	10.3888i	1.71499	−	0.624205i	0.997387	+	0.0722480i	$0.0230173\pi$
$278$	40.1119			2.40575
$279$		0			0
$280$	−2.69738	+	2.57184i	−0.161200	+	0.153697i
$281$	−3.38213	+	19.1810i	−0.201761	+	1.14424i	0.700695	+	0.713461i	$0.252873\pi$
$281$	−3.38213	+	19.1810i	−0.201761	+	1.14424i	−0.902456	+	0.430782i	$0.858238\pi$
$282$		0			0
$283$	5.90670	−	4.95631i	0.351117	−	0.294622i	−0.450122	−	0.892967i	$-0.648619\pi$
$283$	5.90670	−	4.95631i	0.351117	−	0.294622i	0.801238	+	0.598345i	$0.204175\pi$
$284$	−13.2020	+	11.0778i	−0.783395	+	0.657347i
$285$		0			0
$286$	−1.45805	+	8.26899i	−0.0862161	+	0.488956i
$287$	7.40564	+	30.5294i	0.437141	+	1.80210i
$288$		0			0
$289$	−15.4612			−0.909485
$290$	−14.1687	+	5.15700i	−0.832017	+	0.302829i
$291$		0			0
$292$	11.2901	−	9.47348i	0.660700	−	0.554393i
$293$	−10.4784	+	8.79240i	−0.612153	+	0.513657i	−0.895326	−	0.445411i	$-0.853057\pi$
$293$	−10.4784	+	8.79240i	−0.612153	+	0.513657i	0.283173	+	0.959069i	$0.408613\pi$
$294$		0			0
$295$	−8.67599	+	3.15780i	−0.505135	+	0.183854i
$296$	−1.39017	−	2.40784i	−0.0808017	−	0.139953i
$297$		0			0
$298$	4.09946	−	7.10047i	0.237475	−	0.411319i
$299$	0.719881	+	0.604052i	0.0416318	+	0.0349332i
$300$		0			0
$301$	−7.81185	+	3.41861i	−0.450268	+	0.197046i
$302$	4.80448	+	27.2476i	0.276467	+	1.56792i
$303$		0			0
$304$	6.43090	−	2.34066i	0.368838	−	0.134246i
$305$	−3.84156	−	6.65377i	−0.219967	−	0.380994i
$306$		0			0
$307$	8.70668	+	15.0804i	0.496916	+	0.860684i	0.999994	−	0.00355714i	$-0.00113228\pi$
$307$	8.70668	+	15.0804i	0.496916	+	0.860684i	−0.503077	+	0.864241i	$0.667799\pi$
$308$	17.8932	−	1.13675i	1.01956	−	0.0647721i
$309$		0			0
$310$	−3.17126	−	17.9851i	−0.180115	−	1.02149i
$311$	−22.8968	+	19.2127i	−1.29836	+	1.08945i	−0.307935	+	0.951407i	$0.599638\pi$
$311$	−22.8968	+	19.2127i	−1.29836	+	1.08945i	−0.990426	+	0.138047i	$0.955918\pi$
$312$		0			0
$313$	−2.98036	+	1.08476i	−0.168460	+	0.0613144i	−0.424873	−	0.905253i	$-0.639681\pi$
$313$	−2.98036	+	1.08476i	−0.168460	+	0.0613144i	0.256413	+	0.966567i	$0.417459\pi$
$314$	−0.352998	−	0.611410i	−0.0199208	−	0.0345039i
$315$		0			0
$316$	−10.5004	+	18.1873i	−0.590696	+	1.02311i
$317$	1.15974	−	6.57721i	0.0651374	−	0.369413i	−0.934763	−	0.355273i	$-0.884388\pi$
$317$	1.15974	−	6.57721i	0.0651374	−	0.369413i	0.999900	−	0.0141397i	$-0.00450097\pi$
$318$		0			0
$319$	−23.6896	−	8.62229i	−1.32636	−	0.482756i
$320$	4.78220	+	1.74058i	0.267333	+	0.0973013i
$321$		0			0
$322$	2.09194	−	4.22068i	0.116579	−	0.235209i
$323$	1.78138			0.0991186
$324$		0			0
$325$	−1.40861	+	2.43979i	−0.0781358	+	0.135335i
$326$	1.67307	−	9.48845i	0.0926628	−	0.525517i
$327$		0			0
$328$	−8.75776	+	7.34863i	−0.483566	+	0.405760i
$329$	27.4398	−	12.0082i	1.51280	−	0.662031i
$330$		0			0
$331$	0.866389	−	4.91354i	0.0476210	−	0.270072i	−0.951695	−	0.307044i	$-0.900660\pi$
$331$	0.866389	−	4.91354i	0.0476210	−	0.270072i	0.999316	+	0.0369718i	$0.0117712\pi$
$332$	6.17643	+	10.6979i	0.338976	+	0.587123i
$333$		0			0
$334$	−10.1493	+	17.5792i	−0.555348	+	0.961890i
$335$	−3.33784	+	18.9298i	−0.182366	+	1.03425i
$336$		0			0
$337$	13.6802	+	4.97920i	0.745209	+	0.271234i	0.686588	−	0.727046i	$-0.259107\pi$
$337$	13.6802	+	4.97920i	0.745209	+	0.271234i	0.0586210	+	0.998280i	$0.481330\pi$
$338$	−3.89909	−	22.1129i	−0.212083	−	1.20278i
$339$		0			0
$340$	2.06337	+	1.73137i	0.111902	+	0.0938967i
$341$	15.2671	−	26.4434i	0.826761	−	1.43199i
$342$		0			0
$343$	18.1858	−	3.50377i	0.981941	−	0.189186i
$344$	−2.37718	−	1.99469i	−0.128169	−	0.107546i
$345$		0			0
$346$	21.2402	+	7.73079i	1.14188	+	0.415610i
$347$	1.50977	+	8.56234i	0.0810488	+	0.459650i	0.998139	+	0.0609718i	$0.0194200\pi$
$347$	1.50977	+	8.56234i	0.0810488	+	0.459650i	−0.917091	+	0.398679i	$0.869469\pi$
$348$		0			0
$349$	−10.4169	+	3.79143i	−0.557602	+	0.202950i	−0.605421	−	0.795906i	$-0.706995\pi$
$349$	−10.4169	+	3.79143i	−0.557602	+	0.202950i	0.0478190	+	0.998856i	$0.484773\pi$
$350$	13.5499	+	3.97894i	0.724273	+	0.212683i
$351$		0			0
$352$	15.9116	+	27.5596i	0.848090	+	1.46893i
$353$	4.02106	−	22.8045i	0.214019	−	1.21376i	−0.668581	−	0.743639i	$-0.733098\pi$
$353$	4.02106	−	22.8045i	0.214019	−	1.21376i	0.882600	−	0.470124i	$-0.155791\pi$
$354$		0			0
$355$	15.9639	+	5.81039i	0.847277	+	0.308384i
$356$	0.158494	+	0.898863i	0.00840015	+	0.0476396i
$357$		0			0
$358$	−17.6989	−	14.8511i	−0.935416	−	0.784907i
$359$	2.07932			0.109742			0.0548710	−	0.998493i	$-0.482525\pi$
$359$	2.07932			0.109742			0.0548710	+	0.998493i	$0.482525\pi$
$360$		0			0
$361$	−16.9378			−0.891461
$362$	−27.8362	+	10.1315i	−1.46304	+	0.532502i
$363$		0			0
$364$	3.54412	−	1.55097i	0.185762	−	0.0812931i
$365$	−13.6520	−	4.96891i	−0.714576	−	0.260085i
$366$		0			0
$367$	−11.7277	−	9.84075i	−0.612184	−	0.513683i	0.283152	−	0.959075i	$-0.408620\pi$
$367$	−11.7277	−	9.84075i	−0.612184	−	0.513683i	−0.895336	+	0.445392i	$0.853064\pi$
$368$	4.54568			0.236960
$369$		0			0
$370$	3.94289	−	6.82929i	0.204981	−	0.355038i
$371$	12.2785	−	0.780046i	0.637466	−	0.0404980i
$372$		0			0
$373$	23.4937	−	19.7136i	1.21646	−	1.02073i	0.217456	−	0.976070i	$-0.430224\pi$
$373$	23.4937	−	19.7136i	1.21646	−	1.02073i	0.999002	−	0.0446594i	$-0.0142202\pi$
$374$	1.83583	+	10.4115i	0.0949288	+	0.538368i
$375$		0			0
$376$	8.35002	+	7.00650i	0.430619	+	0.361333i
$377$	−5.43960			−0.280153
$378$		0			0
$379$	33.1265			1.70159			0.850797	−	0.525495i	$-0.176120\pi$
$379$	33.1265			1.70159			0.850797	+	0.525495i	$0.176120\pi$
$380$	2.38870	+	2.00436i	0.122538	+	0.102821i
$381$		0			0
$382$	4.92764	+	27.9460i	0.252120	+	1.42984i
$383$	9.10096	−	7.63661i	0.465037	−	0.390213i	−0.379943	−	0.925010i	$-0.624056\pi$
$383$	9.10096	−	7.63661i	0.465037	−	0.390213i	0.844980	+	0.534797i	$0.179612\pi$
$384$		0			0
$385$	−9.78952	−	14.7149i	−0.498920	−	0.749938i
$386$	17.5469	−	30.3922i	0.893115	−	1.54692i
$387$		0			0
$388$	−8.47224			−0.430113
$389$	−17.5208	−	14.7017i	−0.888338	−	0.745404i	0.0795384	−	0.996832i	$-0.474655\pi$
$389$	−17.5208	−	14.7017i	−0.888338	−	0.745404i	−0.967876	+	0.251428i	$0.919100\pi$
$390$		0			0
$391$	1.11187	+	0.404689i	0.0562298	+	0.0204660i
$392$	4.08149	+	5.36351i	0.206147	+	0.270898i
$393$		0			0
$394$	−0.458037	+	0.166712i	−0.0230756	+	0.00839882i
$395$	20.7016			1.04161
$396$		0			0
$397$	22.2946			1.11893			0.559466	−	0.828853i	$-0.311006\pi$
$397$	22.2946			1.11893			0.559466	+	0.828853i	$0.311006\pi$
$398$	−2.34155	−	1.96479i	−0.117371	−	0.0984862i
$399$		0			0
$400$	2.36638	+	13.4204i	0.118319	+	0.671020i
$401$	4.75414	+	1.73036i	0.237410	+	0.0864102i	0.457985	−	0.888960i	$-0.348571\pi$
$401$	4.75414	+	1.73036i	0.237410	+	0.0864102i	−0.220575	+	0.975370i	$0.570793\pi$
$402$		0			0
$403$	1.14407	−	6.48835i	0.0569903	−	0.323208i
$404$	−8.78859	−	15.2223i	−0.437249	−	0.757337i
$405$		0			0
$406$	6.42792	+	26.4988i	0.319013	+	1.31511i
$407$	12.3896	−	4.50944i	0.614129	−	0.223525i
$408$		0			0
$409$	3.94949	+	22.3987i	0.195290	+	1.10754i	0.912006	+	0.410178i	$0.134533\pi$
$409$	3.94949	+	22.3987i	0.195290	+	1.10754i	−0.716716	+	0.697365i	$0.754356\pi$
$410$	−30.4700	−	11.0902i	−1.50481	−	0.547705i
$411$		0			0
$412$	14.5907	+	12.2430i	0.718831	+	0.603171i
$413$	3.93603	+	16.2261i	0.193679	+	0.798435i
$414$		0			0
$415$	6.08843	−	10.5455i	0.298869	−	0.517657i
$416$	5.26008	+	4.41373i	0.257897	+	0.216401i
$417$		0			0
$418$	2.12529	+	12.0531i	0.103951	+	0.589538i
$419$	−28.5404	−	10.3878i	−1.39429	−	0.507480i	−0.467811	−	0.883829i	$-0.654957\pi$
$419$	−28.5404	−	10.3878i	−1.39429	−	0.507480i	−0.926478	+	0.376349i	$0.877179\pi$
$420$		0			0
$421$	5.43779	−	30.8393i	0.265022	−	1.50301i	−0.503951	−	0.863732i	$-0.668121\pi$
$421$	5.43779	−	30.8393i	0.265022	−	1.50301i	0.768973	−	0.639281i	$-0.220768\pi$
$422$	−5.94929	+	10.3045i	−0.289607	+	0.501614i
$423$		0			0
$424$	2.23869	+	3.87752i	0.108720	+	0.188309i
$425$	−0.615963	+	3.49330i	−0.0298786	+	0.169450i
$426$		0			0
$427$	−12.7287	+	5.57034i	−0.615987	+	0.269567i
$428$	12.5612	−	10.5401i	0.607168	−	0.509475i
$429$		0			0
$430$	1.52836	−	8.66777i	0.0737041	−	0.417997i
$431$	5.25777	−	9.10673i	0.253258	−	0.438656i	−0.711163	−	0.703027i	$-0.751831\pi$
$431$	5.25777	−	9.10673i	0.253258	−	0.438656i	0.964421	+	0.264372i	$0.0851645\pi$
$432$		0			0
$433$	−6.33812			−0.304591			−0.152295	−	0.988335i	$-0.548667\pi$
$433$	−6.33812			−0.304591			−0.152295	+	0.988335i	$0.548667\pi$
$434$	−32.9597	+	2.09392i	−1.58212	+	0.100511i
$435$		0			0
$436$	−26.5658	−	9.66918i	−1.27227	−	0.463070i
$437$	1.28718	+	0.468496i	0.0615743	+	0.0224112i
$438$		0			0
$439$	3.51431	−	19.9306i	0.167729	−	0.951236i	−0.778478	−	0.627672i	$-0.784008\pi$
$439$	3.51431	−	19.9306i	0.167729	−	0.951236i	0.946206	−	0.323564i	$-0.104881\pi$
$440$	3.21591	−	5.57011i	0.153312	−	0.265545i
$441$		0			0
$442$	1.14059	+	1.97556i	0.0542523	+	0.0939677i
$443$	8.34240	−	3.03638i	0.396359	−	0.144263i	−0.136148	−	0.990689i	$-0.543472\pi$
$443$	8.34240	−	3.03638i	0.396359	−	0.144263i	0.532507	+	0.846426i	$0.321250\pi$
$444$		0			0
$445$	0.689229	−	0.578331i	0.0326726	−	0.0274155i
$446$	1.87364	+	10.6259i	0.0887195	+	0.503153i
$447$		0			0
$448$	4.08702	−	8.24592i	0.193093	−	0.389583i
$449$	−6.01834	−	10.4241i	−0.284023	−	0.491943i	0.688349	−	0.725380i	$-0.258336\pi$
$449$	−6.01834	−	10.4241i	−0.284023	−	0.491943i	−0.972372	+	0.233437i	$0.925003\pi$
$450$		0			0
$451$	−27.1071	−	46.9509i	−1.27642	−	2.21083i
$452$	10.9306	−	3.97840i	0.514130	−	0.187128i
$453$		0			0
$454$	−4.15608	−	23.5703i	−0.195055	−	1.10621i
$455$	−3.07085	−	2.26113i	−0.143964	−	0.106003i
$456$		0			0
$457$	−2.46549	−	2.06879i	−0.115331	−	0.0967738i	0.583299	−	0.812258i	$-0.301762\pi$
$457$	−2.46549	−	2.06879i	−0.115331	−	0.0967738i	−0.698629	+	0.715484i	$0.746206\pi$
$458$	5.46990	−	9.47414i	0.255591	−	0.442697i
$459$		0			0
$460$	1.03560	+	1.79370i	0.0482849	+	0.0836319i
$461$	−32.0957	+	11.6819i	−1.49485	+	0.544080i	−0.954720	−	0.297505i	$-0.903846\pi$
$461$	−32.0957	+	11.6819i	−1.49485	+	0.544080i	−0.540126	+	0.841584i	$0.681623\pi$
$462$		0			0
$463$	8.38189	−	7.03324i	0.389539	−	0.326862i	−0.426894	−	0.904302i	$-0.640392\pi$
$463$	8.38189	−	7.03324i	0.389539	−	0.326862i	0.816434	+	0.577439i	$0.195948\pi$
$464$	−20.1564	+	16.9132i	−0.935737	+	0.785176i
$465$		0			0
$466$	1.70406	−	0.620226i	0.0789389	−	0.0287314i
$467$	41.4064			1.91606			0.958031	−	0.286666i	$-0.0925469\pi$
$467$	41.4064			1.91606			0.958031	+	0.286666i	$0.0925469\pi$
$468$		0			0
$469$	33.3527	+	9.79404i	1.54009	+	0.452247i
$470$	−5.36849	+	30.4462i	−0.247630	+	1.40438i
$471$		0			0
$472$	−4.65467	+	3.90573i	−0.214248	+	0.179776i
$473$	11.2729	−	9.45909i	0.518329	−	0.434929i
$474$		0			0
$475$	−0.713082	+	4.04409i	−0.0327184	+	0.185555i
$476$	3.52539	−	3.36131i	0.161586	−	0.154065i
$477$		0			0
$478$	44.3471			2.02839
$479$	7.80215	−	2.83975i	0.356489	−	0.129751i	−0.157566	−	0.987508i	$-0.550365\pi$
$479$	7.80215	−	2.83975i	0.356489	−	0.129751i	0.514055	+	0.857757i	$0.328143\pi$
$480$		0			0
$481$	2.17932	−	1.82866i	0.0993683	−	0.0833799i
$482$	−0.409274	+	0.343422i	−0.0186419	+	0.0156424i
$483$		0			0
$484$	−13.7341	+	4.99880i	−0.624277	+	0.227218i
$485$	4.17576	+	7.23263i	0.189612	+	0.328417i
$486$		0			0
$487$	11.9736	−	20.7388i	0.542574	−	0.939766i	−0.456181	−	0.889887i	$-0.650783\pi$
$487$	11.9736	−	20.7388i	0.542574	−	0.939766i	0.998755	−	0.0498789i	$-0.0158835\pi$
$488$	−3.87340	−	3.25017i	−0.175341	−	0.147128i
$489$		0			0
$490$	−7.38621	+	17.6315i	−0.333675	+	0.796511i
$491$	−6.82562	−	38.7100i	−0.308036	−	1.74696i	−0.608859	−	0.793278i	$-0.708373\pi$
$491$	−6.82562	−	38.7100i	−0.308036	−	1.74696i	0.300823	−	0.953680i	$-0.402739\pi$
$492$		0			0
$493$	−6.43598	+	2.34251i	−0.289862	+	0.105501i
$494$	1.32043	+	2.28704i	0.0594087	+	0.102899i
$495$		0			0
$496$	−15.9347	−	27.5998i	−0.715491	−	1.23927i
$497$	13.6433	−	27.5265i	0.611984	−	1.23473i
$498$		0			0
$499$	−1.08756	−	6.16784i	−0.0486857	−	0.276111i	0.950740	−	0.309989i	$-0.100325\pi$
$499$	−1.08756	−	6.16784i	−0.0486857	−	0.276111i	−0.999426	+	0.0338782i	$0.989214\pi$
$500$	−13.0734	+	10.9699i	−0.584660	+	0.490588i
$501$		0			0
$502$	−13.7417	+	5.00157i	−0.613322	+	0.223231i
$503$	1.54894	+	2.68284i	0.0690637	+	0.119622i	0.898489	−	0.438995i	$-0.144665\pi$
$503$	1.54894	+	2.68284i	0.0690637	+	0.119622i	−0.829426	+	0.558617i	$0.811332\pi$
$504$		0			0
$505$	−8.66337	+	15.0054i	−0.385515	+	0.667731i
$506$	−1.41166	+	8.00595i	−0.0627561	+	0.355908i
$507$		0			0
$508$	−17.7175	−	6.44864i	−0.786087	−	0.286112i
$509$	−4.54630	−	1.65472i	−0.201511	−	0.0733440i	0.239293	−	0.970947i	$-0.423084\pi$
$509$	−4.54630	−	1.65472i	−0.201511	−	0.0733440i	−0.440804	+	0.897603i	$0.645307\pi$
$510$		0			0
$511$	−11.6674	+	23.5400i	−0.516135	+	1.04135i
$512$	24.0378			1.06233
$513$		0			0
$514$	−9.01718	+	15.6182i	−0.397731	+	0.688890i
$515$	3.26031	−	18.4901i	0.143666	−	0.814773i
$516$		0			0
$517$	−39.5970	+	33.2258i	−1.74147	+	1.46127i
$518$	−11.4836	−	8.45556i	−0.504559	−	0.371516i
$519$		0			0
$520$	0.240990	−	1.36672i	0.0105681	−	0.0599348i
$521$	−15.2199	−	26.3617i	−0.666796	−	1.15493i	−0.978795	−	0.204842i	$-0.934332\pi$
$521$	−15.2199	−	26.3617i	−0.666796	−	1.15493i	0.311999	−	0.950083i	$-0.399002\pi$
$522$		0			0
$523$	−16.8711	+	29.2216i	−0.737723	+	1.27777i	0.215796	+	0.976439i	$0.430765\pi$
$523$	−16.8711	+	29.2216i	−0.737723	+	1.27777i	−0.953518	+	0.301335i	$0.902568\pi$
$524$	2.16367	−	12.2708i	0.0945203	−	0.536051i
$525$		0			0
$526$	32.1493	+	11.7014i	1.40177	+	0.510204i
$527$	−1.44051	−	8.16952i	−0.0627495	−	0.355870i
$528$		0			0
$529$	−16.9220	−	14.1993i	−0.735741	−	0.617360i
$530$	−6.34953	+	10.9977i	−0.275806	+	0.477710i
$531$		0			0
$532$	4.08124	−	3.89129i	0.176944	−	0.168709i
$533$	−8.96113	−	7.51928i	−0.388149	−	0.325696i
$534$		0			0
$535$	−15.1890	−	5.52836i	−0.656679	−	0.239012i
$536$	2.19668	+	12.4580i	0.0948822	+	0.538104i
$537$		0			0
$538$	−8.01357	+	2.91670i	−0.345490	+	0.125748i
$539$	−28.4091	+	14.6443i	−1.22367	+	0.630775i
$540$		0			0
$541$	7.87553	+	13.6408i	0.338596	+	0.586465i	0.984169	−	0.177234i	$-0.0567148\pi$
$541$	7.87553	+	13.6408i	0.338596	+	0.586465i	−0.645573	+	0.763698i	$0.723382\pi$
$542$	4.28312	−	24.2908i	0.183976	−	1.04338i
$543$		0			0
$544$	8.12431	+	2.95701i	0.348327	+	0.126781i
$545$	4.83922	+	27.4446i	0.207289	+	1.17560i
$546$		0			0
$547$	−16.6514	−	13.9722i	−0.711963	−	0.597408i	0.213186	−	0.977012i	$-0.431616\pi$
$547$	−16.6514	−	13.9722i	−0.711963	−	0.597408i	−0.925149	+	0.379603i	$0.876060\pi$
$548$	3.44798			0.147290
$549$		0			0
$550$	−24.3712			−1.03919
$551$	−7.45075	+	2.71185i	−0.317412	+	0.115529i
$552$		0			0
$553$	4.15028	−	37.2063i	0.176488	−	1.58217i
$554$	53.2784	+	19.3918i	2.26358	+	0.823877i
$555$		0			0
$556$	24.4322	+	20.5010i	1.03615	+	0.869437i
$557$	−24.7941			−1.05056			−0.525280	−	0.850930i	$-0.676039\pi$
$557$	−24.7941			−1.05056			−0.525280	+	0.850930i	$0.676039\pi$
$558$		0			0
$559$	1.58762	−	2.74984i	0.0671493	−	0.116306i
$560$	−18.4095	+	1.16955i	−0.777943	+	0.0494224i
$561$		0			0
$562$	−27.8499	+	23.3688i	−1.17478	+	0.985755i
$563$	−3.32030	−	18.8303i	−0.139934	−	0.793604i	−0.971296	−	0.237873i	$-0.923550\pi$
$563$	−3.32030	−	18.8303i	−0.139934	−	0.793604i	0.831362	−	0.555731i	$-0.187561\pi$
$564$		0			0
$565$	−8.78371	−	7.37041i	−0.369534	−	0.310075i
$566$	14.3927			0.604968
$567$		0			0
$568$	11.1803			0.469117
$569$	15.4566	+	12.9697i	0.647976	+	0.543717i	0.906456	−	0.422300i	$-0.138777\pi$
$569$	15.4566	+	12.9697i	0.647976	+	0.543717i	−0.258480	+	0.966017i	$0.583222\pi$
$570$		0			0
$571$	0.234729	+	1.33121i	0.00982309	+	0.0557095i	0.989325	−	0.145724i	$-0.0465511\pi$
$571$	0.234729	+	1.33121i	0.00982309	+	0.0557095i	−0.979502	+	0.201433i	$0.935440\pi$
$572$	−5.11434	+	4.29144i	−0.213841	+	0.179434i
$573$		0			0
$574$	−26.0406	+	52.5393i	−1.08692	+	2.19295i
$575$	−1.36380	+	2.36218i	−0.0568746	+	0.0985096i
$576$		0			0
$577$	12.1509			0.505848			0.252924	−	0.967486i	$-0.418608\pi$
$577$	12.1509			0.505848			0.252924	+	0.967486i	$0.418608\pi$
$578$	−22.1079	−	18.5508i	−0.919569	−	0.771610i
$579$		0			0
$580$	−11.2659	−	4.10045i	−0.467791	−	0.170262i
$581$	−17.7324	−	13.0567i	−0.735663	−	0.541682i
$582$		0			0
$583$	−19.9519	+	7.26188i	−0.826321	+	0.300756i
$584$	−9.56116			−0.395644
$585$		0			0
$586$	−25.5323			−1.05473
$587$	36.1996	+	30.3750i	1.49412	+	1.25371i	0.889282	+	0.457360i	$0.151205\pi$
$587$	36.1996	+	30.3750i	1.49412	+	1.25371i	0.604834	+	0.796352i	$0.293239\pi$
$588$		0			0
$589$	−1.66763	−	9.45762i	−0.0687136	−	0.389694i
$590$	−16.1945	−	5.89433i	−0.666719	−	0.242666i
$591$		0			0
$592$	2.38962	−	13.5522i	0.0982127	−	0.556992i
$593$	−5.30960	−	9.19649i	−0.218039	−	0.377655i	0.736169	−	0.676797i	$-0.236633\pi$
$593$	−5.30960	−	9.19649i	−0.218039	−	0.377655i	−0.954208	+	0.299143i	$0.903299\pi$
$594$		0			0
$595$	−4.60708	−	1.35287i	−0.188872	−	0.0554623i
$596$	6.12600	−	2.22968i	0.250931	−	0.0913314i
$597$		0			0
$598$	0.304598	+	1.72746i	0.0124559	+	0.0706411i
$599$	9.63714	+	3.50763i	0.393763	+	0.143318i	0.531311	−	0.847177i	$-0.321700\pi$
$599$	9.63714	+	3.50763i	0.393763	+	0.143318i	−0.137548	+	0.990495i	$0.543922\pi$
$600$		0			0
$601$	−19.1642	−	16.0807i	−0.781724	−	0.655945i	0.161958	−	0.986798i	$-0.448219\pi$
$601$	−19.1642	−	16.0807i	−0.781724	−	0.655945i	−0.943682	+	0.330853i	$0.892664\pi$
$602$	−15.2719	−	4.48459i	−0.622434	−	0.182778i
$603$		0			0
$604$	−10.9997	+	19.0520i	−0.447572	+	0.775217i
$605$	11.0366	+	9.26081i	0.448702	+	0.376505i
$606$		0			0
$607$	0.114124	+	0.647228i	0.00463214	+	0.0262702i	0.987036	−	0.160498i	$-0.0513099\pi$
$607$	0.114124	+	0.647228i	0.00463214	+	0.0262702i	−0.982404	+	0.186768i	$0.940199\pi$
$608$	9.40528	+	3.42324i	0.381434	+	0.138831i
$609$		0			0
$610$	2.49033	−	14.1234i	0.100831	−	0.571839i
$611$	−5.57665	+	9.65904i	−0.225607	+	0.390763i
$612$		0			0
$613$	13.8724	+	24.0277i	0.560301	+	0.970470i	0.997470	+	0.0710902i	$0.0226478\pi$
$613$	13.8724	+	24.0277i	0.560301	+	0.970470i	−0.437169	+	0.899379i	$0.644019\pi$
$614$	−5.64420	+	32.0099i	−0.227781	+	1.29181i
$615$		0			0
$616$	−9.36623	−	6.89653i	−0.377376	−	0.277869i
$617$	−12.7820	+	10.7253i	−0.514582	+	0.431786i	−0.862738	−	0.505651i	$-0.831252\pi$
$617$	−12.7820	+	10.7253i	−0.514582	+	0.431786i	0.348156	+	0.937437i	$0.386808\pi$
$618$		0			0
$619$	−1.65125	+	9.36470i	−0.0663693	+	0.376399i	0.933473	+	0.358647i	$0.116762\pi$
$619$	−1.65125	+	9.36470i	−0.0663693	+	0.376399i	−0.999842	+	0.0177517i	$0.994349\pi$
$620$	7.26050	−	12.5755i	0.291589	−	0.505046i
$621$		0			0
$622$	−55.7920			−2.23705
$623$	−0.901237	−	1.35467i	−0.0361073	−	0.0542737i
$624$		0			0
$625$	2.37289	+	0.863661i	0.0949156	+	0.0345464i
$626$	−5.56312	−	2.02481i	−0.222347	−	0.0809277i
$627$		0			0
$628$	0.0974780	−	0.552825i	0.00388980	−	0.0220601i
$629$	1.79101	−	3.10213i	0.0714124	−	0.123690i
$630$		0			0
$631$	−22.9465	−	39.7445i	−0.913486	−	1.58220i	−0.809103	−	0.587667i	$-0.800047\pi$
$631$	−22.9465	−	39.7445i	−0.913486	−	1.58220i	−0.104383	−	0.994537i	$-0.533287\pi$
$632$	12.8024	−	4.65970i	0.509253	−	0.185353i
$633$		0			0
$634$	9.54979	−	8.01323i	0.379271	−	0.318246i
$635$	3.22741	+	18.3035i	0.128076	+	0.726354i
$636$		0			0
$637$	−4.67949	+	5.06582i	−0.185408	+	0.200715i
$638$	−23.5283	−	40.7523i	−0.931495	−	1.61340i
$639$		0			0
$640$	−5.44723	−	9.43487i	−0.215321	−	0.372946i
$641$	−26.9575	+	9.81173i	−1.06476	+	0.387540i	−0.814214	−	0.580565i	$-0.802832\pi$
$641$	−26.9575	+	9.81173i	−1.06476	+	0.387540i	−0.250544	+	0.968105i	$0.580609\pi$
$642$		0			0
$643$	0.172431	+	0.977906i	0.00680002	+	0.0385648i	0.988019	−	0.154332i	$-0.0493227\pi$
$643$	0.172431	+	0.977906i	0.00680002	+	0.0385648i	−0.981219	+	0.192897i	$0.938212\pi$
$644$	3.43138	−	1.50163i	0.135215	−	0.0591727i
$645$		0			0
$646$	2.54718	+	2.13734i	0.100218	+	0.0840925i
$647$	−8.87356	+	15.3695i	−0.348856	+	0.604236i	−0.986046	−	0.166470i	$-0.946763\pi$
$647$	−8.87356	+	15.3695i	−0.348856	+	0.604236i	0.637191	+	0.770706i	$0.280096\pi$
$648$		0			0
$649$	−14.4072	−	24.9540i	−0.565531	−	0.979528i
$650$	−4.94148	+	1.79855i	−0.193821	+	0.0705451i
$651$		0			0
$652$	5.86857	−	4.92432i	0.229831	−	0.192851i
$653$	13.9574	−	11.7117i	0.546196	−	0.458313i	−0.327455	−	0.944867i	$-0.606191\pi$
$653$	13.9574	−	11.7117i	0.546196	−	0.458313i	0.873650	+	0.486554i	$0.161746\pi$
$654$		0			0
$655$	−11.5418	+	4.20088i	−0.450976	+	0.164142i
$656$	−56.5849			−2.20927
$657$		0			0
$658$	53.6436	+	15.7525i	2.09125	+	0.614095i
$659$	0.516836	−	2.93112i	0.0201331	−	0.114180i	−0.973085	−	0.230446i	$-0.925981\pi$
$659$	0.516836	−	2.93112i	0.0201331	−	0.114180i	0.993218	+	0.116266i	$0.0370925\pi$
$660$		0			0
$661$	18.7503	−	15.7334i	0.729303	−	0.611958i	−0.200639	−	0.979665i	$-0.564302\pi$
$661$	18.7503	−	15.7334i	0.729303	−	0.611958i	0.929941	+	0.367708i	$0.119857\pi$
$662$	7.13422	−	5.98632i	0.277279	−	0.232665i
$663$		0			0
$664$	1.39158	−	7.89202i	0.0540036	−	0.306270i
$665$	−5.33348	−	1.56618i	−0.206824	−	0.0607338i
$666$		0			0
$667$	−5.26656			−0.203922
$668$	−15.1666	+	5.52020i	−0.586814	+	0.213583i
$669$		0			0
$670$	−27.4852	+	23.0628i	−1.06185	+	0.890995i
$671$	18.3682	−	15.4128i	0.709097	−	0.595003i
$672$		0			0
$673$	23.3965	−	8.51562i	0.901868	−	0.328253i	0.150867	−	0.988554i	$-0.451794\pi$
$673$	23.3965	−	8.51562i	0.901868	−	0.328253i	0.751001	+	0.660301i	$0.229571\pi$
$674$	13.5871	+	23.5336i	0.523356	+	0.906480i
$675$		0			0
$676$	8.92685	−	15.4618i	0.343340	−	0.594683i
$677$	−6.77852	−	5.68785i	−0.260520	−	0.218602i	0.503167	−	0.864189i	$-0.332168\pi$
$677$	−6.77852	−	5.68785i	−0.260520	−	0.218602i	−0.763686	+	0.645587i	$0.776613\pi$
$678$		0			0
$679$	13.8361	−	6.05494i	0.530981	−	0.232367i
$680$	−0.303432	−	1.72085i	−0.0116361	−	0.0659916i
$681$		0			0
$682$	53.5578	−	19.4935i	2.05084	−	0.746443i
$683$	3.14016	+	5.43892i	0.120155	+	0.208114i	0.919829	−	0.392320i	$-0.128328\pi$
$683$	3.14016	+	5.43892i	0.120155	+	0.208114i	−0.799674	+	0.600435i	$0.794994\pi$
$684$		0			0
$685$	−1.69943	−	2.94349i	−0.0649317	−	0.112465i
$686$	30.2077	+	16.8097i	1.15333	+	0.641799i
$687$		0			0
$688$	−2.66710	−	15.1259i	−0.101682	−	0.576669i
$689$	−3.50951	+	2.94483i	−0.133702	+	0.112189i
$690$		0			0
$691$	10.5686	−	3.84667i	0.402050	−	0.146334i	−0.133077	−	0.991106i	$-0.542486\pi$
$691$	10.5686	−	3.84667i	0.402050	−	0.146334i	0.535127	+	0.844771i	$0.320264\pi$
$692$	8.98622	+	15.5646i	0.341605	+	0.591677i
$693$		0			0
$694$	−8.11448	+	14.0547i	−0.308022	+	0.533509i
$695$	5.45941	−	30.9619i	0.207087	−	1.17445i
$696$		0			0
$697$	−13.8407	−	5.03759i	−0.524252	−	0.190812i
$698$	−19.4441	−	7.07706i	−0.735968	−	0.267871i
$699$		0			0
$700$	6.21963	+	9.34887i	0.235080	+	0.353354i
$701$	−11.0400			−0.416976			−0.208488	−	0.978025i	$-0.566854\pi$
$701$	−11.0400			−0.416976			−0.208488	+	0.978025i	$0.566854\pi$
$702$		0			0
$703$	2.07340	−	3.59124i	0.0781999	−	0.135446i
$704$	−2.75796	+	15.6412i	−0.103945	+	0.589499i
$705$		0			0
$706$	33.1111	−	27.7835i	1.24615	−	1.04565i
$707$	25.2318	+	18.5786i	0.948940	+	0.698722i
$708$		0			0
$709$	−3.29290	+	18.6750i	−0.123668	+	0.701353i	0.858423	+	0.512943i	$0.171445\pi$
$709$	−3.29290	+	18.6750i	−0.123668	+	0.701353i	−0.982090	+	0.188411i	$0.939666\pi$
$710$	15.8553	+	27.4621i	0.595038	+	1.03064i
$711$		0			0
$712$	0.296061	−	0.512792i	0.0110953	−	0.0192177i
$713$	1.10768	−	6.28195i	0.0414828	−	0.235261i
$714$		0			0
$715$	6.18428	+	2.25089i	0.231279	+	0.0841786i
$716$	−3.19005	−	18.0917i	−0.119218	−	0.676117i
$717$		0			0
$718$	2.97320	+	2.49481i	0.110959	+	0.0931055i
$719$	1.77058	−	3.06674i	0.0660316	−	0.114370i	−0.831120	−	0.556094i	$-0.812300\pi$
$719$	1.77058	−	3.06674i	0.0660316	−	0.114370i	0.897151	+	0.441724i	$0.145633\pi$
$720$		0			0
$721$	−32.5780	−	9.56655i	−1.21327	−	0.356277i
$722$	−24.2192	−	20.3223i	−0.901345	−	0.756318i
$723$		0			0
$724$	−22.1332	−	8.05584i	−0.822575	−	0.299393i
$725$	−2.74165	−	15.5487i	−0.101822	−	0.577463i
$726$		0			0
$727$	34.1662	−	12.4355i	1.26715	−	0.461206i	0.380990	−	0.924579i	$-0.375583\pi$
$727$	34.1662	−	12.4355i	1.26715	−	0.461206i	0.886163	+	0.463373i	$0.153361\pi$
$728$	−2.40805	−	0.707124i	−0.0892481	−	0.0262078i
$729$		0			0
$730$	−13.5590	−	23.4850i	−0.501843	−	0.869217i
$731$	0.694240	−	3.93723i	0.0256774	−	0.145624i
$732$		0			0
$733$	20.2090	+	7.35546i	0.746435	+	0.271680i	0.687105	−	0.726558i	$-0.258881\pi$
$733$	20.2090	+	7.35546i	0.746435	+	0.271680i	0.0593303	+	0.998238i	$0.481103\pi$
$734$	−4.96227	−	28.1425i	−0.183161	−	1.03876i
$735$		0			0
$736$	5.09275	+	4.27333i	0.187721	+	0.157517i
$737$	−59.9889			−2.20972
$738$		0			0
$739$	7.19530			0.264683			0.132342	−	0.991204i	$-0.457750\pi$
$739$	7.19530			0.264683			0.132342	+	0.991204i	$0.457750\pi$
$740$	5.89204	−	2.14453i	0.216596	−	0.0788344i
$741$		0			0
$742$	18.4928	+	13.6166i	0.678893	+	0.499881i
$743$	5.28136	+	1.92226i	0.193754	+	0.0705207i	0.437075	−	0.899425i	$-0.356015\pi$
$743$	5.28136	+	1.92226i	0.193754	+	0.0705207i	−0.243321	+	0.969946i	$0.578237\pi$
$744$		0			0
$745$	−4.92281	−	4.13073i	−0.180358	−	0.151338i
$746$	57.2463			2.09594
$747$		0			0
$748$	−4.20308	+	7.27996i	−0.153680	+	0.266182i
$749$	−12.9810	+	26.1904i	−0.474316	+	0.956975i
$750$		0			0
$751$	32.8983	−	27.6050i	1.20048	−	1.00732i	0.200861	−	0.979620i	$-0.435626\pi$
$751$	32.8983	−	27.6050i	1.20048	−	1.00732i	0.999616	−	0.0276999i	$-0.00881827\pi$
$752$	9.36841	+	53.1309i	0.341631	+	1.93748i
$753$		0			0
$754$	−7.77805	−	6.52656i	−0.283260	−	0.237683i
$755$	21.6859			0.789232
$756$		0			0
$757$	−18.7190			−0.680354			−0.340177	−	0.940361i	$-0.610487\pi$
$757$	−18.7190			−0.680354			−0.340177	+	0.940361i	$0.610487\pi$
$758$	47.3674	+	39.7460i	1.72046	+	1.44364i
$759$		0			0
$760$	−0.351274	−	1.99218i	−0.0127421	−	0.0722638i
$761$	9.59380	−	8.05016i	0.347775	−	0.291818i	−0.452121	−	0.891957i	$-0.649332\pi$
$761$	9.59380	−	8.05016i	0.347775	−	0.291818i	0.799896	+	0.600139i	$0.204888\pi$
$762$		0			0
$763$	50.2953	−	3.19524i	1.82081	−	0.115676i
$764$	−11.2817	+	19.5404i	−0.408157	+	0.706948i
$765$		0			0
$766$	22.1760			0.801251
$767$	−4.76275	−	3.99643i	−0.171973	−	0.144303i
$768$		0			0
$769$	18.4388	+	6.71117i	0.664920	+	0.242011i	0.652359	−	0.757910i	$-0.273779\pi$
$769$	18.4388	+	6.71117i	0.664920	+	0.242011i	0.0125608	+	0.999921i	$0.496002\pi$
$770$	3.65725	−	32.7864i	0.131798	−	1.18154i
$771$		0			0
$772$	26.2211	−	9.54372i	0.943720	−	0.343486i
$773$	−10.7971			−0.388343			−0.194171	−	0.980968i	$-0.562202\pi$
$773$	−10.7971			−0.388343			−0.194171	+	0.980968i	$0.562202\pi$
$774$		0			0
$775$	19.1231			0.686921
$776$	4.21038	+	3.53293i	0.151144	+	0.126825i
$777$		0			0
$778$	−7.41343	−	42.0436i	−0.265784	−	1.50734i
$779$	−16.0229	−	5.83187i	−0.574081	−	0.208948i
$780$		0			0
$781$	−9.20661	+	52.2133i	−0.329438	+	1.86834i
$782$	1.10431	+	1.91271i	0.0394899	+	0.0683985i
$783$		0			0
$784$	−1.58876	+	33.3212i	−0.0567415	+	1.19004i
$785$	−0.519984	+	0.189259i	−0.0185590	+	0.00675493i
$786$		0			0
$787$	7.28184	+	41.2973i	0.259569	+	1.47209i	0.784065	+	0.620678i	$0.213143\pi$
$787$	7.28184	+	41.2973i	0.259569	+	1.47209i	−0.524496	+	0.851413i	$0.675746\pi$
$788$	−0.364196	−	0.132557i	−0.0129740	−	0.00472213i
$789$		0			0
$790$	29.6012	+	24.8383i	1.05316	+	0.883708i
$791$	−15.0075	+	14.3090i	−0.533606	+	0.508770i
$792$		0			0
$793$	2.58689	−	4.48063i	0.0918633	−	0.159112i
$794$	31.8789	+	26.7495i	1.13134	+	0.949306i
$795$		0			0
$796$	−0.422041	−	2.39351i	−0.0149588	−	0.0848358i
$797$	12.2053	+	4.44238i	0.432335	+	0.157357i	0.549015	−	0.835812i	$-0.315003\pi$
$797$	12.2053	+	4.44238i	0.432335	+	0.157357i	−0.116680	+	0.993170i	$0.537225\pi$
$798$		0			0
$799$	−2.43857	+	13.8298i	−0.0862705	+	0.489265i
$800$	−9.96514	+	17.2601i	−0.352321	+	0.610238i
$801$		0			0
$802$	4.72178	+	8.17836i	0.166732	+	0.288788i
$803$	7.87327	−	44.6515i	0.277842	−	1.57572i
$804$		0			0
$805$	−2.97317	−	2.18920i	−0.104790	−	0.0771591i
$806$	9.42078	−	7.90497i	0.331833	−	0.278441i
$807$		0			0
$808$	−1.98011	+	11.2297i	−0.0696599	+	0.395061i
$809$	14.8787	−	25.7707i	0.523109	−	0.906051i	−0.476529	−	0.879159i	$-0.658105\pi$
$809$	14.8787	−	25.7707i	0.523109	−	0.906051i	0.999638	−	0.0268927i	$-0.00856125\pi$
$810$		0			0
$811$	38.9051			1.36614			0.683072	−	0.730351i	$-0.260643\pi$
$811$	38.9051			1.36614			0.683072	+	0.730351i	$0.260643\pi$
$812$	−9.62819	+	19.4257i	−0.337883	+	0.681709i
$813$		0			0
$814$	23.1263	+	8.41729i	0.810577	+	0.295026i
$815$	−7.09630	−	2.58284i	−0.248572	−	0.0904730i
$816$		0			0
$817$	0.803702	−	4.55802i	0.0281180	−	0.159465i
$818$	−21.2271	+	36.7664i	−0.742188	+	1.28551i
$819$		0			0
$820$	−12.8912	−	22.3281i	−0.450179	−	0.779733i
$821$	37.3616	−	13.5985i	1.30393	−	0.474591i	0.405654	−	0.914027i	$-0.367044\pi$
$821$	37.3616	−	13.5985i	1.30393	−	0.474591i	0.898274	+	0.439436i	$0.144822\pi$
$822$		0			0
$823$	−29.8699	+	25.0638i	−1.04120	+	0.873669i	−0.992141	−	0.125127i	$-0.960066\pi$
$823$	−29.8699	+	25.0638i	−1.04120	+	0.873669i	−0.0490570	+	0.998796i	$0.515622\pi$
$824$	−2.14566	−	12.1686i	−0.0747475	−	0.423914i
$825$		0			0
$826$	−13.8404	+	27.9242i	−0.481568	+	0.971606i
$827$	−15.3937	−	26.6626i	−0.535290	−	0.927150i	−0.999149	−	0.0412408i	$-0.986869\pi$
$827$	−15.3937	−	26.6626i	−0.535290	−	0.927150i	0.463859	−	0.885909i	$-0.346464\pi$
$828$		0			0
$829$	12.7647	+	22.1090i	0.443335	+	0.767878i	0.997935	−	0.0642389i	$-0.0204620\pi$
$829$	12.7647	+	22.1090i	0.443335	+	0.767878i	−0.554600	+	0.832117i	$0.687129\pi$
$830$	21.3585	−	7.77386i	0.741365	−	0.269835i
$831$		0			0
$832$	0.595091	+	3.37493i	0.0206311	+	0.117005i
$833$	−3.35510	+	8.00891i	−0.116247	+	0.277492i
$834$		0			0
$835$	12.1878	+	10.2268i	0.421775	+	0.353911i
$836$	−4.86579	+	8.42779i	−0.168287	+	0.291481i
$837$		0			0
$838$	−28.3461	−	49.0969i	−0.979201	−	1.69603i
$839$	15.4625	−	5.62791i	0.533826	−	0.194297i	−0.0610197	−	0.998137i	$-0.519435\pi$
$839$	15.4625	−	5.62791i	0.533826	−	0.194297i	0.594846	+	0.803840i	$0.297213\pi$
$840$		0			0
$841$	1.13760	−	0.954559i	0.0392275	−	0.0329158i
$842$	44.7771	−	37.5725i	1.54312	−	1.29483i
$843$		0			0
$844$	−8.89029	+	3.23580i	−0.306016	+	0.111381i
$845$	−17.5993			−0.605435
$846$		0			0
$847$	18.8567	−	17.9791i	0.647925	−	0.617768i
$848$	−3.84818	+	21.8241i	−0.132147	+	0.749443i
$849$		0			0
$850$	−5.07210	+	4.25600i	−0.173972	+	0.145980i
$851$	2.10999	−	1.77049i	0.0723295	−	0.0606917i
$852$		0			0
$853$	−1.40699	+	7.97942i	−0.0481743	+	0.273210i	−0.999374	−	0.0353643i	$-0.988741\pi$
$853$	−1.40699	+	7.97942i	−0.0481743	+	0.273210i	0.951200	+	0.308575i	$0.0998519\pi$
$854$	−24.8842	−	7.30725i	−0.851519	−	0.250049i
$855$		0			0
$856$	−10.6377			−0.363588
$857$	−6.41442	+	2.33466i	−0.219112	+	0.0797504i	−0.449244	−	0.893409i	$-0.648307\pi$
$857$	−6.41442	+	2.33466i	−0.219112	+	0.0797504i	0.230132	+	0.973160i	$0.426084\pi$
$858$		0			0
$859$	−34.9781	+	29.3501i	−1.19344	+	1.00141i	−0.193643	+	0.981072i	$0.562030\pi$
$859$	−34.9781	+	29.3501i	−1.19344	+	1.00141i	−0.999793	+	0.0203395i	$0.993525\pi$
$860$	5.36099	−	4.49840i	0.182808	−	0.153394i
$861$		0			0
$862$	18.4445	−	6.71326i	0.628223	−	0.228655i
$863$	−0.791478	−	1.37088i	−0.0269422	−	0.0466653i	0.852240	−	0.523151i	$-0.175244\pi$
$863$	−0.791478	−	1.37088i	−0.0269422	−	0.0466653i	−0.879182	+	0.476486i	$0.841910\pi$
$864$		0			0
$865$	8.85818	−	15.3428i	0.301187	−	0.521672i
$866$	−9.06285	−	7.60463i	−0.307968	−	0.258416i
$867$		0			0
$868$	−21.1460	−	15.5702i	−0.717741	−	0.528486i
$869$	11.2189	+	63.6256i	0.380575	+	2.15835i
$870$		0			0
$871$	−12.1633	+	4.42709i	−0.412139	+	0.150006i
$872$	9.17016	+	15.8832i	0.310541	+	0.537872i
$873$		0			0
$874$	1.27842	+	2.21429i	0.0432433	+	0.0748995i
$875$	13.5103	−	27.2583i	0.456733	−	0.921500i
$876$		0			0
$877$	3.85909	+	21.8860i	0.130312	+	0.739037i	0.978010	+	0.208558i	$0.0668769\pi$
$877$	3.85909	+	21.8860i	0.130312	+	0.739037i	−0.847698	+	0.530479i	$0.822012\pi$
$878$	28.9383	−	24.2821i	0.976621	−	0.819482i
$879$		0			0
$880$	29.9145	−	10.8880i	1.00842	−	0.367033i
$881$	−12.8210	−	22.2065i	−0.431949	−	0.748158i	0.565092	−	0.825028i	$-0.308841\pi$
$881$	−12.8210	−	22.2065i	−0.431949	−	0.748158i	−0.997041	+	0.0768702i	$0.975507\pi$
$882$		0			0
$883$	−17.2315	+	29.8458i	−0.579886	+	1.00439i	0.415606	+	0.909545i	$0.363569\pi$
$883$	−17.2315	+	29.8458i	−0.579886	+	1.00439i	−0.995492	+	0.0948467i	$0.969764\pi$
$884$	−0.314966	+	1.78626i	−0.0105935	+	0.0600785i
$885$		0			0
$886$	15.5719	+	5.66770i	0.523147	+	0.190410i
$887$	11.7083	+	4.26148i	0.393127	+	0.143086i	0.531017	−	0.847361i	$-0.321810\pi$
$887$	11.7083	+	4.26148i	0.393127	+	0.143086i	−0.137890	+	0.990447i	$0.544032\pi$
$888$		0			0
$889$	33.5433	−	2.13099i	1.12501	−	0.0714713i
$890$	1.67942			0.0562943
$891$		0			0
$892$	−4.28964	+	7.42988i	−0.143628	+	0.248771i
$893$	−2.82307	+	16.0104i	−0.0944703	+	0.535768i
$894$		0			0
$895$	−13.8723	+	11.6402i	−0.463700	+	0.389090i
$896$	−18.0490	+	7.89859i	−0.602975	+	0.263873i
$897$		0			0
$898$	3.90146	−	22.1263i	0.130193	−	0.738364i
$899$	18.4618	+	31.9767i	0.615734	+	1.06648i
$900$		0			0
$901$	−2.88420	+	4.99558i	−0.0960866	+	0.166427i
$902$	17.5725	−	99.6585i	0.585100	−	3.31827i
$903$		0			0
$904$	−7.09106	−	2.58094i	−0.235845	−	0.0858407i
$905$	4.03178	+	22.8653i	0.134021	+	0.760070i
$906$		0			0
$907$	15.5305	+	13.0316i	0.515682	+	0.432708i	0.863123	−	0.504993i	$-0.168505\pi$
$907$	15.5305	+	13.0316i	0.515682	+	0.432708i	−0.347442	+	0.937702i	$0.612950\pi$
$908$	9.51522	−	16.4808i	0.315774	−	0.546936i
$909$		0			0
$910$	−1.67804	−	6.91765i	−0.0556266	−	0.229318i
$911$	16.6560	+	13.9761i	0.551838	+	0.463047i	0.875563	−	0.483104i	$-0.160491\pi$
$911$	16.6560	+	13.9761i	0.551838	+	0.463047i	−0.323725	+	0.946151i	$0.604935\pi$
$912$		0			0
$913$	35.7106	+	12.9976i	1.18185	+	0.430157i
$914$	−1.04320	−	5.91630i	−0.0345061	−	0.195694i
$915$		0			0
$916$	8.17391	−	2.97506i	0.270073	−	0.0982987i
$917$	5.23617	+	21.5859i	0.172913	+	0.712828i
$918$		0			0
$919$	−8.04117	−	13.9277i	−0.265254	−	0.459433i	0.702376	−	0.711806i	$-0.252122\pi$
$919$	−8.04117	−	13.9277i	−0.265254	−	0.459433i	−0.967630	+	0.252373i	$0.918789\pi$
$920$	0.233324	−	1.32325i	0.00769246	−	0.0436261i
$921$		0			0
$922$	−59.9097	−	21.8053i	−1.97302	−	0.718120i
$923$	1.98653	+	11.2662i	0.0653874	+	0.370831i
$924$		0			0
$925$	6.32551	+	5.30773i	0.207981	+	0.174517i
$926$	20.4239			0.671170
$927$		0			0
$928$	−38.4821			−1.26324
$929$	−42.7404	+	15.5562i	−1.40227	+	0.510383i	−0.928850	−	0.370456i	$-0.879201\pi$
$929$	−42.7404	+	15.5562i	−1.40227	+	0.510383i	−0.473416	+	0.880839i	$0.656979\pi$
$930$		0			0
$931$	−3.88410	+	9.27168i	−0.127296	+	0.303867i
$932$	1.35494	+	0.493157i	0.0443824	+	0.0161539i
$933$		0			0
$934$	59.2068	+	49.6804i	1.93731	+	1.62559i
$935$	8.28639			0.270994
$936$		0			0
$937$	19.6409	−	34.0190i	0.641639	−	1.11135i	−0.343428	−	0.939179i	$-0.611588\pi$
$937$	19.6409	−	34.0190i	0.641639	−	1.11135i	0.985067	−	0.172172i	$-0.0550784\pi$
$938$	35.9397	+	54.0218i	1.17347	+	1.76387i
$939$		0			0
$940$	−18.8309	+	15.8010i	−0.614196	+	0.515371i
$941$	6.32310	+	35.8601i	0.206127	+	1.16900i	0.895656	+	0.444747i	$0.146706\pi$
$941$	6.32310	+	35.8601i	0.206127	+	1.16900i	−0.689529	+	0.724258i	$0.742182\pi$
$942$		0			0
$943$	−8.67606	−	7.28008i	−0.282532	−	0.237072i
$944$	−30.0744			−0.978837
$945$		0			0
$946$	27.4683			0.893071
$947$	−12.9431	−	10.8605i	−0.420594	−	0.352920i	0.407795	−	0.913074i	$-0.366298\pi$
$947$	−12.9431	−	10.8605i	−0.420594	−	0.352920i	−0.828389	+	0.560153i	$0.810742\pi$
$948$		0			0
$949$	−1.69883	−	9.63456i	−0.0551465	−	0.312751i
$950$	−5.87182	+	4.92704i	−0.190507	+	0.159854i
$951$		0			0
$952$	−3.15365	+	0.200350i	−0.102210	+	0.00649339i
$953$	10.9661	−	18.9938i	0.355226	−	0.615270i	−0.631930	−	0.775025i	$-0.717737\pi$
$953$	10.9661	−	18.9938i	0.355226	−	0.615270i	0.987157	+	0.159755i	$0.0510705\pi$
$954$		0			0
$955$	22.2419			0.719730
$956$	27.0118	+	22.6656i	0.873625	+	0.733059i
$957$		0			0
$958$	14.5634	+	5.30066i	0.470523	+	0.171257i
$959$	−5.63093	+	2.46420i	−0.181832	+	0.0795732i
$960$		0			0
$961$	−12.8943	+	4.69313i	−0.415944	+	0.151391i
$962$	5.31027			0.171210
$963$		0			0
$964$	−0.424810			−0.0136822
$965$	−21.0711	−	17.6808i	−0.678303	−	0.569164i
$966$		0			0
$967$	2.64027	+	14.9737i	0.0849053	+	0.481522i	0.997377	+	0.0723820i	$0.0230601\pi$
$967$	2.64027	+	14.9737i	0.0849053	+	0.481522i	−0.912472	+	0.409140i	$0.865829\pi$
$968$	8.90981	+	3.24291i	0.286372	+	0.104231i
$969$		0			0
$970$	−2.70698	+	15.3521i	−0.0869160	+	0.492925i
$971$	12.0551	+	20.8800i	0.386866	+	0.670072i	0.992026	−	0.126032i	$-0.0402241\pi$
$971$	12.0551	+	20.8800i	0.386866	+	0.670072i	−0.605160	+	0.796104i	$0.706891\pi$
$972$		0			0
$973$	−54.5521	−	16.0193i	−1.74886	−	0.513554i
$974$	42.0039	−	15.2882i	1.34589	−	0.489864i
$975$		0			0
$976$	−4.34581	−	24.6463i	−0.139106	−	0.788910i
$977$	27.0184	+	9.83390i	0.864396	+	0.314614i	0.735896	−	0.677095i	$-0.236761\pi$
$977$	27.0184	+	9.83390i	0.864396	+	0.314614i	0.128500	+	0.991709i	$0.458984\pi$
$978$		0			0
$979$	2.15099	+	1.80490i	0.0687460	+	0.0576848i
$980$	−13.5103	+	6.96430i	−0.431572	+	0.222467i
$981$		0			0
$982$	36.6853	−	63.5407i	1.17067	−	2.02767i
$983$	−3.68325	−	3.09061i	−0.117477	−	0.0985752i	0.582157	−	0.813077i	$-0.302209\pi$
$983$	−3.68325	−	3.09061i	−0.117477	−	0.0985752i	−0.699634	+	0.714502i	$0.746654\pi$
$984$		0			0
$985$	0.0663418	+	0.376243i	0.00211383	+	0.0119881i
$986$	−12.0134	−	4.37251i	−0.382583	−	0.139249i
$987$		0			0
$988$	−0.364627	+	2.06790i	−0.0116003	+	0.0657887i
$989$	1.53712	−	2.66237i	0.0488775	−	0.0846584i
$990$		0			0
$991$	−26.3768	−	45.6860i	−0.837888	−	1.45126i	−0.891657	−	0.452711i	$-0.850457\pi$
$991$	−26.3768	−	45.6860i	−0.837888	−	1.45126i	0.0537691	−	0.998553i	$-0.482877\pi$
$992$	8.09366	−	45.9014i	0.256974	−	1.45737i
$993$		0			0
$994$	52.5353	−	22.9905i	1.66632	−	0.729213i
$995$	−1.83529	+	1.53999i	−0.0581827	+	0.0488211i
$996$		0			0
$997$	8.91880	−	50.5810i	0.282461	−	1.60192i	−0.431754	−	0.901992i	$-0.642105\pi$
$997$	8.91880	−	50.5810i	0.282461	−	1.60192i	0.714215	−	0.699926i	$-0.246784\pi$
$998$	5.84523	−	10.1242i	0.185028	−	0.320477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.w.a.424.19		132
3.2	odd	2		189.2.w.a.88.4	yes	132
7.2	even	3		567.2.u.a.100.19		132
21.2	odd	6		189.2.u.a.142.4	yes	132
27.4	even	9		567.2.u.a.550.19		132
27.23	odd	18		189.2.u.a.4.4	✓	132
189.23	odd	18		189.2.w.a.58.4	yes	132
189.58	even	9	inner	567.2.w.a.226.19		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.4	✓	132	27.23	odd	18
189.2.u.a.142.4	yes	132	21.2	odd	6
189.2.w.a.58.4	yes	132	189.23	odd	18
189.2.w.a.88.4	yes	132	3.2	odd	2
567.2.u.a.100.19		132	7.2	even	3
567.2.u.a.550.19		132	27.4	even	9
567.2.w.a.226.19		132	189.58	even	9	inner
567.2.w.a.424.19		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.w (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.42989 + 1.19982i) q^{2} +(0.257724 + 1.46163i) q^{4} +(1.12074 - 0.940415i) q^{5} +(-1.46549 - 2.20281i) q^{7} +(0.481419 - 0.833843i) q^{8} +2.73088 q^{10} +(3.49769 + 2.93491i) q^{11} +(0.925783 + 0.336957i) q^{13} +(0.547488 - 4.90810i) q^{14} +(4.47818 - 1.62992i) q^{16} +1.24047 q^{17} +1.43605 q^{19} +(1.66338 + 1.39574i) q^{20} +(1.47995 + 8.39323i) q^{22} +(0.896333 + 0.326239i) q^{23} +(-0.496556 + 2.81611i) q^{25} +(0.919482 + 1.59259i) q^{26} +(2.84199 - 2.70971i) q^{28} +(-5.18835 + 1.88840i) q^{29} +(-1.16126 - 6.58584i) q^{31} +(6.54939 + 2.38378i) q^{32} +(1.77374 + 1.48834i) q^{34} +(-3.71398 - 1.09061i) q^{35} +(1.44382 - 2.50077i) q^{37} +(2.05340 + 1.72301i) q^{38} +(-0.244611 - 1.38726i) q^{40} +(-11.1576 - 4.06104i) q^{41} +(0.559660 - 3.17399i) q^{43} +(-3.38830 + 5.86872i) q^{44} +(0.890232 + 1.54193i) q^{46} +(-1.96585 + 11.1489i) q^{47} +(-2.70470 + 6.45636i) q^{49} +(-4.08886 + 3.43096i) q^{50} +(-0.253909 + 1.43999i) q^{52} +(-2.32509 + 4.02717i) q^{53} +6.68005 q^{55} +(-2.54231 + 0.161512i) q^{56} +(-9.68454 - 3.52488i) q^{58} +(-5.93016 - 2.15840i) q^{59} +(0.911917 - 5.17174i) q^{61} +(6.24136 - 10.8104i) q^{62} +(1.73924 + 3.01245i) q^{64} +(1.35444 - 0.492978i) q^{65} +(-10.0646 + 8.44521i) q^{67} +(0.319698 + 1.81310i) q^{68} +(-4.00206 - 6.01559i) q^{70} +(5.80593 + 10.0562i) q^{71} +(-4.96509 - 8.59979i) q^{73} +(5.06499 - 1.84351i) q^{74} +(0.370105 + 2.09897i) q^{76} +(1.33922 - 12.0058i) q^{77} +(10.8394 + 9.09537i) q^{79} +(3.48608 - 6.03807i) q^{80} +(-11.0817 - 19.1940i) q^{82} +(7.82112 - 2.84665i) q^{83} +(1.39025 - 1.16656i) q^{85} +(4.60848 - 3.86697i) q^{86} +(4.13111 - 1.50360i) q^{88} +0.614975 q^{89} +(-0.614470 - 2.53313i) q^{91} +(-0.245832 + 1.39418i) q^{92} +(-16.1877 + 13.5831i) q^{94} +(1.60945 - 1.35049i) q^{95} +(-0.991251 + 5.62167i) q^{97} +(-11.6139 + 5.98675i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29}+ \cdots - 99 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

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