LMFDB - Embedded newform 567.2.be.a.62.2

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			62.2
Character	$\chi$	$=$	567.62
Dual form			567.2.be.a.503.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.924066 - 2.53885i) q^{2} +(-4.05977 + 3.40655i) q^{4} +(0.268129 + 1.52064i) q^{5} +(1.75503 - 1.97986i) q^{7} +(7.72059 + 4.45748i) q^{8} +(3.61290 - 2.08591i) q^{10} +(-3.67329 - 0.647701i) q^{11} +(0.202039 - 0.555096i) q^{13} +(-6.64834 - 2.62624i) q^{14} +(2.34200 - 13.2821i) q^{16} +(-2.21584 - 3.83794i) q^{17} +(-5.88065 - 3.39519i) q^{19} +(-6.26867 - 5.26004i) q^{20} +(1.74995 + 9.92446i) q^{22} +(-1.22335 - 1.45794i) q^{23} +(2.45802 - 0.894647i) q^{25} -1.59600 q^{26} +(-0.380517 + 14.0164i) q^{28} +(0.530750 + 1.45822i) q^{29} +(-3.97747 - 4.74017i) q^{31} +(-18.3265 + 3.23145i) q^{32} +(-7.69638 + 9.17219i) q^{34} +(3.48123 + 2.13791i) q^{35} +(-1.87480 - 3.24725i) q^{37} +(-3.18578 + 18.0675i) q^{38} +(-4.70810 + 12.9354i) q^{40} +(1.26264 + 0.459562i) q^{41} +(-1.06487 + 6.03919i) q^{43} +(17.1192 - 9.88375i) q^{44} +(-2.57102 + 4.45314i) q^{46} +(-4.70770 - 3.95023i) q^{47} +(-0.839725 - 6.94945i) q^{49} +(-4.54275 - 5.41384i) q^{50} +(1.07073 + 2.94182i) q^{52} +2.96963i q^{53} -5.75941i q^{55} +(22.3751 - 7.46269i) q^{56} +(3.21176 - 2.69499i) q^{58} +(-0.751711 - 4.26316i) q^{59} +(6.03545 - 7.19277i) q^{61} +(-8.35913 + 14.4784i) q^{62} +(11.6520 + 20.1818i) q^{64} +(0.898272 + 0.158390i) q^{65} +(4.30322 + 1.56624i) q^{67} +(22.0699 + 8.03280i) q^{68} +(2.21094 - 10.8139i) q^{70} +(-4.85796 + 2.80474i) q^{71} +(4.50326 + 2.59996i) q^{73} +(-6.51183 + 7.76050i) q^{74} +(35.4400 - 6.24903i) q^{76} +(-7.72910 + 6.13589i) q^{77} +(-7.68222 + 2.79610i) q^{79} +20.8253 q^{80} -3.63031i q^{82} +(4.97168 - 1.80954i) q^{83} +(5.24198 - 4.39855i) q^{85} +(16.3166 - 2.87706i) q^{86} +(-25.4729 - 21.3743i) q^{88} +(2.95330 - 5.11527i) q^{89} +(-0.744431 - 1.37422i) q^{91} +(9.93307 + 1.75147i) q^{92} +(-5.67881 + 15.6024i) q^{94} +(3.58608 - 9.85268i) q^{95} +(-18.3882 - 3.24234i) q^{97} +(-16.8676 + 8.55369i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.924066	−	2.53885i	−0.653413	−	1.79524i	−0.604740	−	0.796423i	$-0.706723\pi$
$2$	−0.924066	−	2.53885i	−0.653413	−	1.79524i	−0.0486735	−	0.998815i	$-0.515499\pi$
$3$		0			0
$3$		0			0
$4$	−4.05977	+	3.40655i	−2.02989	+	1.70328i
$5$	0.268129	+	1.52064i	0.119911	+	0.680049i	0.984201	+	0.177055i	$0.0566571\pi$
$5$	0.268129	+	1.52064i	0.119911	+	0.680049i	−0.864290	+	0.502994i	$0.832232\pi$
$6$		0			0
$7$	1.75503	−	1.97986i	0.663340	−	0.748318i
$7$	1.75503	−	1.97986i	0.663340	−	0.748318i
$8$	7.72059	+	4.45748i	2.72964	+	1.57596i
$9$		0			0
$10$	3.61290	−	2.08591i	1.14250	−	0.659622i
$11$	−3.67329	−	0.647701i	−1.10754	−	0.195289i	−0.410176	−	0.912007i	$-0.634533\pi$
$11$	−3.67329	−	0.647701i	−1.10754	−	0.195289i	−0.697364	+	0.716717i	$0.745644\pi$
$12$		0			0
$13$	0.202039	−	0.555096i	0.0560354	−	0.153956i	−0.908517	−	0.417849i	$-0.862784\pi$
$13$	0.202039	−	0.555096i	0.0560354	−	0.153956i	0.964552	+	0.263893i	$0.0850065\pi$
$14$	−6.64834	−	2.62624i	−1.77684	−	0.701892i
$15$		0			0
$16$	2.34200	−	13.2821i	0.585500	−	3.32054i
$17$	−2.21584	−	3.83794i	−0.537419	−	0.930838i	−0.999042	−	0.0437613i	$-0.986066\pi$
$17$	−2.21584	−	3.83794i	−0.537419	−	0.930838i	0.461623	−	0.887076i	$-0.347267\pi$
$18$		0			0
$19$	−5.88065	−	3.39519i	−1.34911	−	0.778911i	−0.360989	−	0.932570i	$-0.617561\pi$
$19$	−5.88065	−	3.39519i	−1.34911	−	0.778911i	−0.988124	+	0.153659i	$0.950894\pi$
$20$	−6.26867	−	5.26004i	−1.40172	−	1.17618i
$21$		0			0
$22$	1.74995	+	9.92446i	0.373090	+	2.11590i
$23$	−1.22335	−	1.45794i	−0.255087	−	0.304001i	0.623269	−	0.782007i	$-0.285804\pi$
$23$	−1.22335	−	1.45794i	−0.255087	−	0.304001i	−0.878356	+	0.478006i	$0.841360\pi$
$24$		0			0
$25$	2.45802	−	0.894647i	0.491604	−	0.178929i
$26$	−1.59600			−0.313002
$27$		0			0
$28$	−0.380517	+	14.0164i	−0.0719109	+	2.64885i
$29$	0.530750	+	1.45822i	0.0985578	+	0.270785i	0.979167	−	0.203059i	$-0.0650882\pi$
$29$	0.530750	+	1.45822i	0.0985578	+	0.270785i	−0.880609	+	0.473844i	$0.842866\pi$
$30$		0			0
$31$	−3.97747	−	4.74017i	−0.714375	−	0.851359i	0.279696	−	0.960089i	$-0.409766\pi$
$31$	−3.97747	−	4.74017i	−0.714375	−	0.851359i	−0.994071	+	0.108729i	$0.965322\pi$
$32$	−18.3265	+	3.23145i	−3.23969	+	0.571245i
$33$		0			0
$34$	−7.69638	+	9.17219i	−1.31992	+	1.57302i
$35$	3.48123	+	2.13791i	0.588435	+	0.361372i
$36$		0			0
$37$	−1.87480	−	3.24725i	−0.308215	−	0.533844i	0.669757	−	0.742580i	$-0.266398\pi$
$37$	−1.87480	−	3.24725i	−0.308215	−	0.533844i	−0.977972	+	0.208736i	$0.933065\pi$
$38$	−3.18578	+	18.0675i	−0.516802	+	2.93093i
$39$		0			0
$40$	−4.70810	+	12.9354i	−0.744416	+	2.04527i
$41$	1.26264	+	0.459562i	0.197191	+	0.0717716i	0.438728	−	0.898620i	$-0.355429\pi$
$41$	1.26264	+	0.459562i	0.197191	+	0.0717716i	−0.241537	+	0.970392i	$0.577651\pi$
$42$		0			0
$43$	−1.06487	+	6.03919i	−0.162391	+	0.920968i	0.789322	+	0.613980i	$0.210432\pi$
$43$	−1.06487	+	6.03919i	−0.162391	+	0.920968i	−0.951713	+	0.306988i	$0.900679\pi$
$44$	17.1192	−	9.88375i	2.58081	−	1.49003i
$45$		0			0
$46$	−2.57102	+	4.45314i	−0.379076	+	0.656580i
$47$	−4.70770	−	3.95023i	−0.686688	−	0.576200i	0.231264	−	0.972891i	$-0.425714\pi$
$47$	−4.70770	−	3.95023i	−0.686688	−	0.576200i	−0.917952	+	0.396691i	$0.870158\pi$
$48$		0			0
$49$	−0.839725	−	6.94945i	−0.119961	−	0.992779i
$50$	−4.54275	−	5.41384i	−0.642441	−	0.765632i
$51$		0			0
$52$	1.07073	+	2.94182i	0.148484	+	0.407957i
$53$			2.96963i			0.407910i	0.978980	+	0.203955i	$0.0653796\pi$
$53$			2.96963i			0.407910i	−0.978980	+	0.203955i	$0.934620\pi$
$54$		0			0
$55$		−	5.75941i		−	0.776599i
$56$	22.3751	−	7.46269i	2.99000	−	0.997244i
$57$		0			0
$58$	3.21176	−	2.69499i	0.421725	−	0.353870i
$59$	−0.751711	−	4.26316i	−0.0978644	−	0.555017i	−0.993832	−	0.110897i	$-0.964628\pi$
$59$	−0.751711	−	4.26316i	−0.0978644	−	0.555017i	0.895967	−	0.444120i	$-0.146484\pi$
$60$		0			0
$61$	6.03545	−	7.19277i	0.772760	−	0.920939i	−0.225823	−	0.974168i	$-0.572507\pi$
$61$	6.03545	−	7.19277i	0.772760	−	0.920939i	0.998582	+	0.0532293i	$0.0169514\pi$
$62$	−8.35913	+	14.4784i	−1.06161	+	1.83876i
$63$		0			0
$64$	11.6520	+	20.1818i	1.45650	+	2.52273i
$65$	0.898272	+	0.158390i	0.111417	+	0.0196458i
$66$		0			0
$67$	4.30322	+	1.56624i	0.525722	+	0.191347i	0.591227	−	0.806505i	$-0.298644\pi$
$67$	4.30322	+	1.56624i	0.525722	+	0.191347i	−0.0655054	+	0.997852i	$0.520866\pi$
$68$	22.0699	+	8.03280i	2.67637	+	0.974121i
$69$		0			0
$70$	2.21094	−	10.8139i	0.264258	−	1.29251i
$71$	−4.85796	+	2.80474i	−0.576533	+	0.332862i	−0.759754	−	0.650210i	$-0.774681\pi$
$71$	−4.85796	+	2.80474i	−0.576533	+	0.332862i	0.183221	+	0.983072i	$0.441348\pi$
$72$		0			0
$73$	4.50326	+	2.59996i	0.527067	+	0.304302i	0.739821	−	0.672804i	$-0.234910\pi$
$73$	4.50326	+	2.59996i	0.527067	+	0.304302i	−0.212755	+	0.977106i	$0.568243\pi$
$74$	−6.51183	+	7.76050i	−0.756985	+	0.902140i
$75$		0			0
$76$	35.4400	−	6.24903i	4.06525	−	0.716813i
$77$	−7.72910	+	6.13589i	−0.880813	+	0.699249i
$78$		0			0
$79$	−7.68222	+	2.79610i	−0.864317	+	0.314586i	−0.735863	−	0.677130i	$-0.763223\pi$
$79$	−7.68222	+	2.79610i	−0.864317	+	0.314586i	−0.128453	+	0.991716i	$0.541001\pi$
$80$	20.8253			2.32834
$81$		0			0
$82$		−	3.63031i		−	0.400901i
$83$	4.97168	−	1.80954i	0.545712	−	0.198623i	−0.0544280	−	0.998518i	$-0.517334\pi$
$83$	4.97168	−	1.80954i	0.545712	−	0.198623i	0.600141	+	0.799895i	$0.295111\pi$
$84$		0			0
$85$	5.24198	−	4.39855i	0.568573	−	0.477089i
$86$	16.3166	−	2.87706i	1.75946	−	0.310241i
$87$		0			0
$88$	−25.4729	−	21.3743i	−2.71542	−	2.27851i
$89$	2.95330	−	5.11527i	0.313050	−	0.542218i	−0.665971	−	0.745977i	$-0.731983\pi$
$89$	2.95330	−	5.11527i	0.313050	−	0.542218i	0.979021	+	0.203760i	$0.0653161\pi$
$90$		0			0
$91$	−0.744431	−	1.37422i	−0.0780376	−	0.144058i
$92$	9.93307	+	1.75147i	1.03559	+	0.182603i
$93$		0			0
$94$	−5.67881	+	15.6024i	−0.585725	+	1.60927i
$95$	3.58608	−	9.85268i	0.367924	−	1.01086i
$96$		0			0
$97$	−18.3882	−	3.24234i	−1.86704	−	0.329209i	−0.878211	−	0.478273i	$-0.841263\pi$
$97$	−18.3882	−	3.24234i	−1.86704	−	0.329209i	−0.988828	+	0.149064i	$0.952374\pi$
$98$	−16.8676	+	8.55369i	−1.70389	+	0.864053i
$99$		0			0
$100$	−6.93135	+	12.0054i	−0.693135	+	1.20054i
$101$	−2.60176	−	2.18314i	−0.258885	−	0.217230i	0.504102	−	0.863644i	$-0.331824\pi$
$101$	−2.60176	−	2.18314i	−0.258885	−	0.217230i	−0.762987	+	0.646414i	$0.776268\pi$
$102$		0			0
$103$	−10.5626	+	1.86248i	−1.04077	+	0.183516i	−0.667810	−	0.744332i	$-0.732768\pi$
$103$	−10.5626	+	1.86248i	−1.04077	+	0.183516i	−0.372959	+	0.927848i	$0.621657\pi$
$104$	4.03419	−	3.38509i	0.395585	−	0.331935i
$105$		0			0
$106$	7.53944	−	2.74413i	0.732295	−	0.266534i
$107$			16.2364i			1.56963i	0.619731	+	0.784814i	$0.287242\pi$
$107$			16.2364i			1.56963i	−0.619731	+	0.784814i	$0.712758\pi$
$108$		0			0
$109$	1.02345			0.0980292			0.0490146	−	0.998798i	$-0.484392\pi$
$109$	1.02345			0.0980292			0.0490146	+	0.998798i	$0.484392\pi$
$110$	−14.6223	+	5.32207i	−1.39418	+	0.507440i
$111$		0			0
$112$	−22.1866	−	27.9474i	−2.09643	−	2.64078i
$113$	15.5453	−	2.74106i	1.46238	−	0.257857i	0.614866	−	0.788631i	$-0.289210\pi$
$113$	15.5453	−	2.74106i	1.46238	−	0.257857i	0.847513	+	0.530774i	$0.178099\pi$
$114$		0			0
$115$	1.88897	−	2.25119i	0.176148	−	0.209925i
$116$	−7.12224	−	4.11203i	−0.661284	−	0.381792i
$117$		0			0
$118$	−10.1289	+	5.84793i	−0.932441	+	0.538345i
$119$	−11.4875	−	2.34865i	−1.05305	−	0.215301i
$120$		0			0
$121$	2.73694	+	0.996165i	0.248813	+	0.0905605i
$122$	−23.8385	−	8.67650i	−2.15824	−	0.785534i
$123$		0			0
$124$	32.2953	+	5.69453i	2.90020	+	0.511384i
$125$	5.87974	+	10.1840i	0.525900	+	0.910885i
$126$		0			0
$127$	2.60535	−	4.51259i	0.231187	−	0.400428i	−0.726971	−	0.686668i	$-0.759072\pi$
$127$	2.60535	−	4.51259i	0.231187	−	0.400428i	0.958158	+	0.286241i	$0.0924057\pi$
$128$	16.5479	−	19.7211i	1.46265	−	1.74311i
$129$		0			0
$130$	−0.427935	−	2.42694i	−0.0375324	−	0.212857i
$131$	9.47971	−	7.95442i	0.828246	−	0.694981i	−0.126641	−	0.991949i	$-0.540420\pi$
$131$	9.47971	−	7.95442i	0.828246	−	0.694981i	0.954888	+	0.296967i	$0.0959753\pi$
$132$		0			0
$133$	−17.0427	+	5.68421i	−1.47779	+	0.492884i
$134$		−	12.3725i		−	1.06882i
$135$		0			0
$136$		−	39.5082i		−	3.38780i
$137$	−4.03432	−	11.0842i	−0.344675	−	0.946988i	−0.984018	−	0.178066i	$-0.943016\pi$
$137$	−4.03432	−	11.0842i	−0.344675	−	0.946988i	0.639343	−	0.768922i	$-0.279206\pi$
$138$		0			0
$139$	−1.99206	−	2.37405i	−0.168965	−	0.201364i	0.674917	−	0.737894i	$-0.264179\pi$
$139$	−1.99206	−	2.37405i	−0.168965	−	0.201364i	−0.843882	+	0.536530i	$0.819735\pi$
$140$	−21.4159	+	3.17958i	−1.80997	+	0.268724i
$141$		0			0
$142$	11.6099	+	9.74185i	0.974280	+	0.817518i
$143$	−1.10168	+	1.90817i	−0.0921274	+	0.159569i
$144$		0			0
$145$	−2.07512	+	1.19807i	−0.172329	+	0.0994943i
$146$	2.43959	−	13.8356i	0.201902	−	1.14504i
$147$		0			0
$148$	18.6732	+	6.79648i	1.53493	+	0.558667i
$149$	−2.66884	+	7.33258i	−0.218640	+	0.600709i	−0.999719	−	0.0237243i	$-0.992448\pi$
$149$	−2.66884	+	7.33258i	−0.218640	+	0.600709i	0.781078	+	0.624433i	$0.214670\pi$
$150$		0			0
$151$	−3.48892	+	19.7866i	−0.283924	+	1.61021i	0.425180	+	0.905109i	$0.360211\pi$
$151$	−3.48892	+	19.7866i	−0.283924	+	1.61021i	−0.709104	+	0.705104i	$0.750900\pi$
$152$	−30.2680	−	52.4258i	−2.45506	−	4.25229i
$153$		0			0
$154$	22.7203	+	13.9531i	1.83085	+	1.12437i
$155$	6.14159	−	7.31927i	0.493305	−	0.587898i
$156$		0			0
$157$	19.6633	−	3.46718i	1.56930	−	0.276711i	0.679717	−	0.733475i	$-0.262103\pi$
$157$	19.6633	−	3.46718i	1.56930	−	0.276711i	0.889588	+	0.456764i	$0.150992\pi$
$158$	14.1977	+	16.9202i	1.12951	+	1.34610i
$159$		0			0
$160$	−9.82772	−	27.0014i	−0.776950	−	2.13465i
$161$	−5.03354	−	0.136650i	−0.396699	−	0.0107696i
$162$		0			0
$163$	−2.13227			−0.167012			−0.0835061	−	0.996507i	$-0.526612\pi$
$163$	−2.13227			−0.167012			−0.0835061	+	0.996507i	$0.526612\pi$
$164$	−6.69154	+	2.43552i	−0.522522	+	0.190182i
$165$		0			0
$166$	−9.18831	−	10.9502i	−0.713151	−	0.849901i
$167$	−1.82951	−	10.3757i	−0.141572	−	0.802894i	−0.970056	−	0.242881i	$-0.921907\pi$
$167$	−1.82951	−	10.3757i	−0.141572	−	0.802894i	0.828484	−	0.560013i	$-0.189204\pi$
$168$		0			0
$169$	9.69127	+	8.13194i	0.745482	+	0.625534i
$170$	−16.0112	−	9.24406i	−1.22800	−	0.708987i
$171$		0			0
$172$	−16.2497	−	28.1453i	−1.23903	−	2.14606i
$173$	0.480878	−	2.72719i	0.0365604	−	0.207345i	−0.961055	−	0.276356i	$-0.910873\pi$
$173$	0.480878	−	2.72719i	0.0365604	−	0.207345i	0.997616	+	0.0690110i	$0.0219844\pi$
$174$		0			0
$175$	2.54263	−	6.43668i	0.192205	−	0.486567i
$176$	−17.2057	+	47.2723i	−1.29693	+	3.56328i
$177$		0			0
$178$	−15.7160	−	2.77115i	−1.17796	−	0.207706i
$179$	12.2011	−	7.04430i	0.911951	−	0.526515i	0.0308929	−	0.999523i	$-0.490165\pi$
$179$	12.2011	−	7.04430i	0.911951	−	0.526515i	0.881059	+	0.473007i	$0.156832\pi$
$180$		0			0
$181$	4.88410	+	2.81983i	0.363032	+	0.209597i	0.670410	−	0.741991i	$-0.266118\pi$
$181$	4.88410	+	2.81983i	0.363032	+	0.209597i	−0.307378	+	0.951587i	$0.599452\pi$
$182$	−2.80104	+	3.15987i	−0.207627	+	0.234225i
$183$		0			0
$184$	−2.94628	−	16.7092i	−0.217203	−	1.23182i
$185$	4.43519	−	3.72157i	0.326082	−	0.273615i
$186$		0			0
$187$	5.65358	+	15.5331i	0.413431	+	1.13589i
$188$	32.5688			2.37533
$189$		0			0
$190$	−28.3282			−2.05515
$191$	−3.67881	−	10.1075i	−0.266190	−	0.731350i	−0.998718	−	0.0506138i	$-0.983882\pi$
$191$	−3.67881	−	10.1075i	−0.266190	−	0.731350i	0.732529	−	0.680736i	$-0.238340\pi$
$192$		0			0
$193$	19.4039	−	16.2818i	1.39672	−	1.17199i	0.434194	−	0.900819i	$-0.357033\pi$
$193$	19.4039	−	16.2818i	1.39672	−	1.17199i	0.962531	−	0.271172i	$-0.0874112\pi$
$194$	8.76010	+	49.6810i	0.628939	+	3.56689i
$195$		0			0
$196$	27.0828	+	25.3526i	1.93448	+	1.81090i
$197$	11.7268	+	6.77045i	0.835497	+	0.482375i	0.855731	−	0.517421i	$-0.173108\pi$
$197$	11.7268	+	6.77045i	0.835497	+	0.482375i	−0.0202340	+	0.999795i	$0.506441\pi$
$198$		0			0
$199$	−1.78988	+	1.03339i	−0.126881	+	0.0732548i	−0.562097	−	0.827071i	$-0.690005\pi$
$199$	−1.78988	+	1.03339i	−0.126881	+	0.0732548i	0.435216	+	0.900326i	$0.356672\pi$
$200$	22.9653	+	4.04939i	1.62389	+	0.286335i
$201$		0			0
$202$	−3.13846	+	8.62285i	−0.220821	+	0.606702i
$203$	3.81857	+	1.50842i	0.268011	+	0.105870i
$204$		0			0
$205$	−0.360277	+	2.04323i	−0.0251629	+	0.142706i
$206$	14.4891	+	25.0959i	1.00951	+	1.74852i
$207$		0			0
$208$	−6.89970	−	3.98354i	−0.478408	−	0.276209i
$209$	19.4023	+	16.2804i	1.34208	+	1.12614i
$210$		0			0
$211$	−0.325203	−	1.84432i	−0.0223879	−	0.126968i	0.971565	−	0.236771i	$-0.0760891\pi$
$211$	−0.325203	−	1.84432i	−0.0223879	−	0.126968i	−0.993953	+	0.109803i	$0.964978\pi$
$212$	−10.1162	−	12.0560i	−0.694783	−	0.828010i
$213$		0			0
$214$	41.2217	−	15.0035i	2.81786	−	1.02562i
$215$	−9.46893			−0.645776
$216$		0			0
$217$	−16.3655	−	0.444289i	−1.11096	−	0.0301603i
$218$	−0.945739	−	2.59840i	−0.0640536	−	0.175986i
$219$		0			0
$220$	19.6197	+	23.3819i	1.32276	+	1.57641i
$221$	−2.57811	+	0.454591i	−0.173423	+	0.0305791i
$222$		0			0
$223$	4.19171	−	4.99548i	0.280697	−	0.334522i	−0.607213	−	0.794539i	$-0.707712\pi$
$223$	4.19171	−	4.99548i	0.280697	−	0.334522i	0.887910	+	0.460017i	$0.152157\pi$
$224$	−25.7657	+	41.9552i	−1.72154	+	2.80325i
$225$		0			0
$226$	−21.3240	−	36.9343i	−1.41845	−	2.45683i
$227$	0.904207	−	5.12801i	0.0600143	−	0.340358i	−0.939985	−	0.341215i	$-0.889162\pi$
$227$	0.904207	−	5.12801i	0.0600143	−	0.340358i	1.00000		0.000856752i	$0.000272713\pi$
$228$		0			0
$229$	−1.95355	+	5.36734i	−0.129094	+	0.354683i	−0.987354	−	0.158532i	$-0.949324\pi$
$229$	−1.95355	+	5.36734i	−0.129094	+	0.354683i	0.858260	+	0.513216i	$0.171546\pi$
$230$	−7.46097	−	2.71557i	−0.491962	−	0.179060i
$231$		0			0
$232$	−2.40231	+	13.6242i	−0.157719	+	0.894470i
$233$	−18.1292	+	10.4669i	−1.18768	+	0.685709i	−0.957779	−	0.287504i	$-0.907175\pi$
$233$	−18.1292	+	10.4669i	−1.18768	+	0.685709i	−0.229904	+	0.973213i	$0.573841\pi$
$234$		0			0
$235$	4.74459	−	8.21787i	0.309503	−	0.536075i
$236$	17.5745	+	14.7467i	1.14400	+	0.959931i
$237$		0			0
$238$	4.65230	+	31.3353i	0.301564	+	2.03116i
$239$	−11.8604	−	14.1346i	−0.767182	−	0.914292i	0.231097	−	0.972931i	$-0.425769\pi$
$239$	−11.8604	−	14.1346i	−0.767182	−	0.914292i	−0.998279	+	0.0586383i	$0.981324\pi$
$240$		0			0
$241$	6.31746	+	17.3571i	0.406944	+	1.11807i	0.958788	+	0.284122i	$0.0917019\pi$
$241$	6.31746	+	17.3571i	0.406944	+	1.11807i	−0.551845	+	0.833947i	$0.686076\pi$
$242$		−	7.86920i		−	0.505852i
$243$		0			0
$244$			49.7611i			3.18563i
$245$	10.3424	−	3.14027i	0.660754	−	0.200624i
$246$		0			0
$247$	−3.07278	+	2.57837i	−0.195516	+	0.164058i
$248$	−9.57921	−	54.3264i	−0.608281	−	3.44973i
$249$		0			0
$250$	20.4224	−	24.3385i	1.29163	−	1.53930i
$251$	10.9656	−	18.9930i	0.692145	−	1.19883i	−0.278989	−	0.960294i	$-0.589999\pi$
$251$	10.9656	−	18.9930i	0.692145	−	1.19883i	0.971134	−	0.238536i	$-0.0766675\pi$
$252$		0			0
$253$	3.54943	+	6.14779i	0.223151	+	0.386508i
$254$	−13.8643	−	2.44465i	−0.869924	−	0.153391i
$255$		0			0
$256$	−21.5631	−	7.84831i	−1.34769	−	0.490520i
$257$	7.41388	+	2.69843i	0.462465	+	0.168324i	0.562736	−	0.826637i	$-0.309749\pi$
$257$	7.41388	+	2.69843i	0.462465	+	0.168324i	−0.100271	+	0.994960i	$0.531971\pi$
$258$		0			0
$259$	−9.71944	−	1.98717i	−0.603937	−	0.123477i
$260$	−4.18634	+	2.41699i	−0.259626	+	0.149895i
$261$		0			0
$262$	−28.9550	−	16.7172i	−1.78884	−	1.03279i
$263$	18.4770	−	22.0201i	1.13934	−	1.35781i	0.214835	−	0.976650i	$-0.431079\pi$
$263$	18.4770	−	22.0201i	1.13934	−	1.35781i	0.924507	−	0.381165i	$-0.124477\pi$
$264$		0			0
$265$	−4.51572	+	0.796244i	−0.277399	+	0.0489129i
$266$	30.1800	+	38.0164i	1.85045	+	2.33093i
$267$		0			0
$268$	−22.8056	+	8.30055i	−1.39307	+	0.507037i
$269$	15.1159			0.921632			0.460816	−	0.887496i	$-0.347557\pi$
$269$	15.1159			0.921632			0.460816	+	0.887496i	$0.347557\pi$
$270$		0			0
$271$			20.2306i			1.22892i	0.788948	+	0.614460i	$0.210626\pi$
$271$			20.2306i			1.22892i	−0.788948	+	0.614460i	$0.789374\pi$
$272$	−56.1656	+	20.4426i	−3.40554	+	1.23951i
$273$		0			0
$274$	−24.4132	+	20.4851i	−1.47485	+	1.23755i
$275$	−9.60849	+	1.69424i	−0.579414	+	0.102166i
$276$		0			0
$277$	−12.6623	−	10.6250i	−0.760806	−	0.638392i	0.177531	−	0.984115i	$-0.443189\pi$
$277$	−12.6623	−	10.6250i	−0.760806	−	0.638392i	−0.938336	+	0.345723i	$0.887634\pi$
$278$	−4.18656	+	7.25133i	−0.251093	+	0.434906i
$279$		0			0
$280$	17.3475	+	32.0234i	1.03671	+	1.91377i
$281$	−13.9997	−	2.46852i	−0.835151	−	0.147260i	−0.260310	−	0.965525i	$-0.583825\pi$
$281$	−13.9997	−	2.46852i	−0.835151	−	0.147260i	−0.574841	+	0.818265i	$0.694936\pi$
$282$		0			0
$283$	−1.50970	+	4.14787i	−0.0897424	+	0.246565i	−0.976442	−	0.215781i	$-0.930770\pi$
$283$	−1.50970	+	4.14787i	−0.0897424	+	0.246565i	0.886699	+	0.462347i	$0.152992\pi$
$284$	10.1677	−	27.9355i	0.603341	−	1.65767i
$285$		0			0
$286$	5.86259	+	1.03373i	0.346662	+	0.0611259i
$287$	3.12584	−	1.69330i	0.184512	−	0.0999526i
$288$		0			0
$289$	−1.31987	+	2.28608i	−0.0776392	+	0.134475i
$290$	4.95927	+	4.16132i	0.291218	+	0.244361i
$291$		0			0
$292$	−27.1391	+	4.78536i	−1.58820	+	0.280042i
$293$	−20.2510	+	16.9926i	−1.18308	+	0.992719i	−0.183123	+	0.983090i	$0.558621\pi$
$293$	−20.2510	+	16.9926i	−1.18308	+	0.992719i	−0.999954	+	0.00962952i	$0.996935\pi$
$294$		0			0
$295$	6.28117	−	2.28616i	0.365704	−	0.133105i
$296$		−	33.4275i		−	1.94294i
$297$		0			0
$298$	21.0825			1.22128
$299$	−1.05646	+	0.384520i	−0.0610967	+	0.0222374i
$300$		0			0
$301$	10.0879	+	12.7073i	0.581456	+	0.732435i
$302$	53.4592	−	9.42631i	3.07623	−	0.542423i
$303$		0			0
$304$	−58.8679	+	70.1561i	−3.37631	+	4.02373i
$305$	12.5559	+	7.24913i	0.718946	+	0.415084i
$306$		0			0
$307$	15.3405	−	8.85684i	0.875529	−	0.505487i	0.00634703	−	0.999980i	$-0.497980\pi$
$307$	15.3405	−	8.85684i	0.875529	−	0.505487i	0.869181	+	0.494493i	$0.164646\pi$
$308$	10.4762	−	51.2399i	0.596936	−	2.91966i
$309$		0			0
$310$	−24.2578	−	8.82910i	−1.37775	−	0.501459i
$311$	22.1660	+	8.06778i	1.25692	+	0.457482i	0.882735	−	0.469872i	$-0.155700\pi$
$311$	22.1660	+	8.06778i	1.25692	+	0.457482i	0.374186	+	0.927354i	$0.377922\pi$
$312$		0			0
$313$	13.1258	+	2.31444i	0.741916	+	0.130820i	0.531816	−	0.846860i	$-0.321510\pi$
$313$	13.1258	+	2.31444i	0.741916	+	0.130820i	0.210100	+	0.977680i	$0.432621\pi$
$314$	−26.9729	−	46.7183i	−1.52217	−	2.63647i
$315$		0			0
$316$	21.6630	−	37.5214i	1.21864	−	2.11074i
$317$	−13.2017	+	15.7332i	−0.741484	+	0.883666i	−0.996528	−	0.0832635i	$-0.973466\pi$
$317$	−13.2017	+	15.7332i	−0.741484	+	0.883666i	0.255044	+	0.966930i	$0.417910\pi$
$318$		0			0
$319$	−1.00511	−	5.70025i	−0.0562752	−	0.319153i
$320$	−27.5650	+	23.1298i	−1.54093	+	1.29299i
$321$		0			0
$322$	4.30439	+	12.9057i	0.239874	+	0.719205i
$323$			30.0928i			1.67441i
$324$		0			0
$325$		−	1.54519i		−	0.0857118i
$326$	1.97036	+	5.41351i	0.109128	+	0.299827i
$327$		0			0
$328$	7.69981	+	9.17628i	0.425151	+	0.506675i
$329$	−16.0831	+	2.38783i	−0.886689	+	0.131645i
$330$		0			0
$331$	0.871850	+	0.731569i	0.0479212	+	0.0402107i	0.666434	−	0.745564i	$-0.267820\pi$
$331$	0.871850	+	0.731569i	0.0479212	+	0.0402107i	−0.618512	+	0.785775i	$0.712264\pi$
$332$	−14.0196	+	24.2826i	−0.769424	+	1.33268i
$333$		0			0
$334$	−24.6517	+	14.2327i	−1.34888	+	0.778777i
$335$	−1.22787	+	6.96358i	−0.0670856	+	0.380461i
$336$		0			0
$337$	−3.57167	−	1.29998i	−0.194561	−	0.0708145i	0.242902	−	0.970051i	$-0.421901\pi$
$337$	−3.57167	−	1.29998i	−0.194561	−	0.0708145i	−0.437463	+	0.899236i	$0.644123\pi$
$338$	11.6904	−	32.1191i	0.635874	−	1.74705i
$339$		0			0
$340$	−6.29738	+	35.7142i	−0.341523	+	1.93687i
$341$	11.5402	+	19.9882i	0.624937	+	1.08242i
$342$		0			0
$343$	−15.2327	−	10.5340i	−0.822489	−	0.568781i
$344$	−35.1410	+	41.8794i	−1.89468	+	2.25799i
$345$		0			0
$346$	−7.36829	+	1.29923i	−0.396122	+	0.0698470i
$347$	3.58267	+	4.26966i	0.192328	+	0.229208i	0.853587	−	0.520950i	$-0.174422\pi$
$347$	3.58267	+	4.26966i	0.192328	+	0.229208i	−0.661259	+	0.750157i	$0.729978\pi$
$348$		0			0
$349$	4.68587	+	12.8743i	0.250829	+	0.689147i	0.999652	+	0.0263773i	$0.00839712\pi$
$349$	4.68587	+	12.8743i	0.250829	+	0.689147i	−0.748823	+	0.662770i	$0.769381\pi$
$350$	−18.6913	−	0.507431i	−0.999093	−	0.0271233i
$351$		0			0
$352$	69.4115			3.69964
$353$	−31.1015	+	11.3200i	−1.65537	+	0.602504i	−0.989625	−	0.143677i	$-0.954107\pi$
$353$	−31.1015	+	11.3200i	−1.65537	+	0.602504i	−0.665742	+	0.746182i	$0.731885\pi$
$354$		0			0
$355$	−5.56755	−	6.63515i	−0.295495	−	0.352157i
$356$	5.43571	+	30.8274i	0.288092	+	1.63385i
$357$		0			0
$358$	−29.1590	−	24.4673i	−1.54110	−	1.29314i
$359$	11.9268	+	6.88593i	0.629472	+	0.363426i	0.780547	−	0.625097i	$-0.214940\pi$
$359$	11.9268	+	6.88593i	0.629472	+	0.363426i	−0.151076	+	0.988522i	$0.548274\pi$
$360$		0			0
$361$	13.5547	+	23.4774i	0.713404	+	1.23565i
$362$	2.64591	−	15.0057i	0.139066	−	0.788682i
$363$		0			0
$364$	7.70358	+	3.04308i	0.403777	+	0.159501i
$365$	−2.74613	+	7.54494i	−0.143739	+	0.394920i
$366$		0			0
$367$	−19.2168	−	3.38845i	−1.00311	−	0.176875i	−0.352115	−	0.935957i	$-0.614537\pi$
$367$	−19.2168	−	3.38845i	−1.00311	−	0.176875i	−0.650996	+	0.759081i	$0.725648\pi$
$368$	−22.2296	+	12.8343i	−1.15880	+	0.669033i
$369$		0			0
$370$	−13.5469	−	7.82131i	−0.704271	−	0.406611i
$371$	5.87946	+	5.21179i	0.305246	+	0.270583i
$372$		0			0
$373$	−0.191635	−	1.08681i	−0.00992246	−	0.0562731i	0.979445	−	0.201714i	$-0.0646511\pi$
$373$	−0.191635	−	1.08681i	−0.00992246	−	0.0562731i	−0.989367	+	0.145441i	$0.953540\pi$
$374$	34.2119	−	28.7072i	1.76905	−	1.48441i
$375$		0			0
$376$	−18.7381	−	51.4826i	−0.966345	−	2.65501i
$377$	0.916687			0.0472118
$378$		0			0
$379$	1.32497			0.0680590			0.0340295	−	0.999421i	$-0.489166\pi$
$379$	1.32497			0.0680590			0.0340295	+	0.999421i	$0.489166\pi$
$380$	19.0050	+	52.2158i	0.974936	+	2.67861i
$381$		0			0
$382$	−22.2619	+	18.6799i	−1.13902	+	0.955747i
$383$	−4.08890	−	23.1893i	−0.208933	−	1.18492i	−0.891130	−	0.453749i	$-0.850086\pi$
$383$	−4.08890	−	23.1893i	−0.208933	−	1.18492i	0.682197	−	0.731169i	$-0.261025\pi$
$384$		0			0
$385$	−11.4028	−	10.1079i	−0.581143	−	0.515149i
$386$	−59.2676	−	34.2182i	−3.01664	−	1.74166i
$387$		0			0
$388$	85.6971	−	49.4772i	4.35061	−	2.51183i
$389$	11.4440	+	2.01789i	0.580234	+	0.102311i	0.456059	−	0.889949i	$-0.349261\pi$
$389$	11.4440	+	2.01789i	0.580234	+	0.102311i	0.124175	+	0.992260i	$0.460372\pi$
$390$		0			0
$391$	−2.88472	+	7.92571i	−0.145887	+	0.400820i
$392$	24.4939	−	57.3969i	1.23713	−	2.89898i
$393$		0			0
$394$	6.35285	−	36.0288i	0.320052	−	1.81511i
$395$	−6.31167	−	10.9321i	−0.317575	−	0.550056i
$396$		0			0
$397$	17.0000	+	9.81498i	0.853208	+	0.492600i	0.861732	−	0.507364i	$-0.169380\pi$
$397$	17.0000	+	9.81498i	0.853208	+	0.492600i	−0.00852412	+	0.999964i	$0.502713\pi$
$398$	4.27758	+	3.58931i	0.214416	+	0.179916i
$399$		0			0
$400$	−6.12614	−	34.7431i	−0.306307	−	1.73715i
$401$	6.30065	+	7.50882i	0.314640	+	0.374973i	0.900067	−	0.435752i	$-0.143518\pi$
$401$	6.30065	+	7.50882i	0.314640	+	0.374973i	−0.585427	+	0.810725i	$0.699073\pi$
$402$		0			0
$403$	−3.43485	+	1.25018i	−0.171102	+	0.0622761i
$404$	17.9996			0.895511
$405$		0			0
$406$	0.301034	−	11.0887i	0.0149401	−	0.550321i
$407$	4.78344	+	13.1424i	0.237106	+	0.651444i
$408$		0			0
$409$	6.29242	+	7.49902i	0.311140	+	0.370803i	0.898840	−	0.438276i	$-0.144411\pi$
$409$	6.29242	+	7.49902i	0.311140	+	0.370803i	−0.587700	+	0.809079i	$0.699966\pi$
$410$	5.52038	−	0.973393i	0.272632	−	0.0480724i
$411$		0			0
$412$	36.5373	−	43.5435i	1.80006	−	2.14523i
$413$	−9.75976	−	5.99370i	−0.480247	−	0.294931i
$414$		0			0
$415$	4.08471	+	7.07492i	0.200510	+	0.347294i
$416$	−1.90889	+	10.8258i	−0.0935909	+	0.530780i
$417$		0			0
$418$	23.4046	−	64.3036i	1.14476	−	3.14519i
$419$	−14.3025	−	5.20569i	−0.698724	−	0.254315i	−0.0318580	−	0.999492i	$-0.510142\pi$
$419$	−14.3025	−	5.20569i	−0.698724	−	0.254315i	−0.666866	+	0.745178i	$0.732365\pi$
$420$		0			0
$421$	0.990993	−	5.62020i	0.0482981	−	0.273912i	−0.951089	−	0.308917i	$-0.900034\pi$
$421$	0.990993	−	5.62020i	0.0482981	−	0.273912i	0.999387	+	0.0350049i	$0.0111447\pi$
$422$	−4.38193	+	2.52991i	−0.213309	+	0.123154i
$423$		0			0
$424$	−13.2371	+	22.9273i	−0.642849	+	1.11345i
$425$	−8.88018	−	7.45135i	−0.430752	−	0.361444i
$426$		0			0
$427$	−3.64830	−	24.5729i	−0.176553	−	1.18917i
$428$	−55.3100	−	65.9159i	−2.67351	−	3.18617i
$429$		0			0
$430$	8.74992	+	24.0402i	0.421958	+	1.15932i
$431$		−	19.8527i		−	0.956271i	−0.878286	−	0.478135i	$-0.841313\pi$
$431$		−	19.8527i		−	0.956271i	0.878286	−	0.478135i	$-0.158687\pi$
$432$		0			0
$433$		−	16.3842i		−	0.787374i	−0.919244	−	0.393687i	$-0.871199\pi$
$433$		−	16.3842i		−	0.787374i	0.919244	−	0.393687i	$-0.128801\pi$
$434$	13.9948	+	41.9601i	0.671772	+	2.01415i
$435$		0			0
$436$	−4.15499	+	3.48645i	−0.198988	+	0.166971i
$437$	2.24414	+	12.7271i	0.107352	+	0.608821i
$438$		0			0
$439$	16.4078	−	19.5541i	0.783104	−	0.933267i	−0.215966	−	0.976401i	$-0.569290\pi$
$439$	16.4078	−	19.5541i	0.783104	−	0.933267i	0.999069	+	0.0431343i	$0.0137343\pi$
$440$	25.6725	−	44.4660i	1.22389	−	2.11984i
$441$		0			0
$442$	3.53648	+	6.12537i	0.168213	+	0.291354i
$443$	22.6046	+	3.98580i	1.07398	+	0.189371i	0.682550	−	0.730838i	$-0.260871\pi$
$443$	22.6046	+	3.98580i	1.07398	+	0.189371i	0.391426	+	0.920210i	$0.371982\pi$
$444$		0			0
$445$	8.57033	+	3.11935i	0.406273	+	0.147871i
$446$	−16.5562	−	6.02596i	−0.783958	−	0.285338i
$447$		0			0
$448$	60.4069	+	12.3504i	2.85396	+	0.583502i
$449$	12.1267	−	7.00134i	0.572293	−	0.330414i	−0.185771	−	0.982593i	$-0.559478\pi$
$449$	12.1267	−	7.00134i	0.572293	−	0.330414i	0.758065	+	0.652179i	$0.226145\pi$
$450$		0			0
$451$	−4.34038	−	2.50592i	−0.204380	−	0.117999i
$452$	−53.7728	+	64.0840i	−2.52926	+	3.01426i
$453$		0			0
$454$	−13.8548	+	2.44298i	−0.650238	+	0.114655i
$455$	1.89009	−	1.50048i	0.0886086	−	0.0703435i
$456$		0			0
$457$	−19.2648	+	7.01181i	−0.901169	+	0.327999i	−0.750721	−	0.660619i	$-0.770294\pi$
$457$	−19.2648	+	7.01181i	−0.901169	+	0.327999i	−0.150448	+	0.988618i	$0.548072\pi$
$458$	15.4321			0.721093
$459$		0			0
$460$			15.5742i			0.726151i
$461$	−4.74427	+	1.72677i	−0.220963	+	0.0804238i	−0.450129	−	0.892963i	$-0.648622\pi$
$461$	−4.74427	+	1.72677i	−0.220963	+	0.0804238i	0.229167	+	0.973387i	$0.426400\pi$
$462$		0			0
$463$	20.9354	−	17.5669i	0.972950	−	0.816402i	−0.0100609	−	0.999949i	$-0.503203\pi$
$463$	20.9354	−	17.5669i	0.972950	−	0.816402i	0.983011	+	0.183547i	$0.0587581\pi$
$464$	20.6114	−	3.63434i	0.956858	−	0.168720i
$465$		0			0
$466$	43.3265	+	36.3552i	2.00706	+	1.68412i
$467$	−15.8795	+	27.5042i	−0.734818	+	1.27274i	0.219986	+	0.975503i	$0.429399\pi$
$467$	−15.8795	+	27.5042i	−0.734818	+	1.27274i	−0.954803	+	0.297238i	$0.903934\pi$
$468$		0			0
$469$	10.6532	−	5.77098i	0.491921	−	0.266479i
$470$	−25.2482	−	4.45195i	−1.16461	−	0.205353i
$471$		0			0
$472$	13.1993	−	36.2649i	0.607549	−	1.66923i
$473$	7.82317	−	21.4940i	0.359710	−	0.988294i
$474$		0			0
$475$	−17.4923	−	3.08436i	−0.802600	−	0.141520i
$476$	54.6373	−	29.5977i	2.50430	−	1.35661i
$477$		0			0
$478$	−24.9259	+	43.1730i	−1.14009	+	1.97469i
$479$	−13.9459	−	11.7020i	−0.637206	−	0.534679i	0.265953	−	0.963986i	$-0.414313\pi$
$479$	−13.9459	−	11.7020i	−0.637206	−	0.534679i	−0.903159	+	0.429307i	$0.858758\pi$
$480$		0			0
$481$	−2.18132	+	0.384625i	−0.0994595	+	0.0175374i
$482$	38.2293	−	32.0782i	1.74130	−	1.46112i
$483$		0			0
$484$	−14.5048	+	5.27933i	−0.659311	+	0.239970i
$485$		−	28.8311i		−	1.30915i
$486$		0			0
$487$	25.8036			1.16927			0.584637	−	0.811295i	$-0.301237\pi$
$487$	25.8036			1.16927			0.584637	+	0.811295i	$0.301237\pi$
$488$	78.6588	−	28.6295i	3.56072	−	1.29600i
$489$		0			0
$490$	−17.5298	−	23.3561i	−0.791914	−	1.05512i
$491$	−28.9536	+	5.10530i	−1.30666	+	0.230399i	−0.783262	−	0.621692i	$-0.786446\pi$
$491$	−28.9536	+	5.10530i	−1.30666	+	0.230399i	−0.523394	+	0.852090i	$0.675335\pi$
$492$		0			0
$493$	4.42052	−	5.26818i	0.199090	−	0.237267i
$494$	9.38553	+	5.41874i	0.422275	+	0.243801i
$495$		0			0
$496$	−72.2748	+	41.7279i	−3.24524	+	1.87364i
$497$	−2.97286	+	14.5405i	−0.133351	+	0.652231i
$498$		0			0
$499$	−16.0431	−	5.83922i	−0.718189	−	0.261399i	−0.0430323	−	0.999074i	$-0.513702\pi$
$499$	−16.0431	−	5.83922i	−0.718189	−	0.261399i	−0.675157	+	0.737674i	$0.735924\pi$
$500$	−58.5627	−	21.3151i	−2.61900	−	0.953240i
$501$		0			0
$502$	−58.3535	−	10.2893i	−2.60444	−	0.459233i
$503$	−9.54837	−	16.5383i	−0.425741	−	0.737405i	0.570748	−	0.821125i	$-0.306653\pi$
$503$	−9.54837	−	16.5383i	−0.425741	−	0.737405i	−0.996489	+	0.0837201i	$0.973320\pi$
$504$		0			0
$505$	2.62215	−	4.54170i	0.116684	−	0.202103i
$506$	12.3284	−	14.6924i	0.548065	−	0.653158i
$507$		0			0
$508$	4.79527	+	27.1953i	0.212756	+	1.20660i
$509$	−8.04301	+	6.74889i	−0.356500	+	0.299139i	−0.803394	−	0.595448i	$-0.796975\pi$
$509$	−8.04301	+	6.74889i	−0.356500	+	0.299139i	0.446894	+	0.894587i	$0.352530\pi$
$510$		0			0
$511$	13.0509	−	4.35283i	0.577339	−	0.192558i
$512$			10.5097i			0.464467i
$513$		0			0
$514$		−	21.3163i		−	0.940220i
$515$	−5.66431	−	15.5626i	−0.249599	−	0.685768i
$516$		0			0
$517$	14.7342	+	17.5595i	0.648009	+	0.772267i
$518$	3.93626	+	26.5125i	0.172949	+	1.16489i
$519$		0			0
$520$	6.22917	+	5.22690i	0.273167	+	0.229215i
$521$	−4.56525	+	7.90725i	−0.200007	+	0.346423i	−0.948530	−	0.316686i	$-0.897430\pi$
$521$	−4.56525	+	7.90725i	−0.200007	+	0.346423i	0.748523	+	0.663109i	$0.230763\pi$
$522$		0			0
$523$	−23.7892	+	13.7347i	−1.04023	+	0.600575i	−0.919898	−	0.392159i	$-0.871728\pi$
$523$	−23.7892	+	13.7347i	−1.04023	+	0.600575i	−0.120329	+	0.992734i	$0.538395\pi$
$524$	−11.3883	+	64.5863i	−0.497500	+	2.82146i
$525$		0			0
$526$	−72.9796	−	26.5624i	−3.18206	−	1.15818i
$527$	−9.37906	+	25.7687i	−0.408558	+	1.12250i
$528$		0			0
$529$	3.36492	−	19.0834i	0.146301	−	0.829715i
$530$	6.19437	+	10.7290i	0.269066	+	0.466036i
$531$		0			0
$532$	49.8261	−	81.1336i	2.16024	−	3.51759i
$533$	0.510203	−	0.608036i	0.0220993	−	0.0263370i
$534$		0			0
$535$	−24.6896	+	4.35344i	−1.06742	+	0.188216i
$536$	26.2419	+	31.2738i	1.13348	+	1.35082i
$537$		0			0
$538$	−13.9681	−	38.3770i	−0.602206	−	1.65455i
$539$	−1.41661	+	26.0713i	−0.0610175	+	1.12297i
$540$		0			0
$541$	19.0517			0.819099			0.409549	−	0.912288i	$-0.365686\pi$
$541$	19.0517			0.819099			0.409549	+	0.912288i	$0.365686\pi$
$542$	51.3624	−	18.6944i	2.20620	−	0.802992i
$543$		0			0
$544$	53.0106	+	63.1756i	2.27281	+	2.70863i
$545$	0.274418	+	1.55630i	0.0117548	+	0.0666647i
$546$		0			0
$547$	5.27460	+	4.42591i	0.225526	+	0.189238i	0.748548	−	0.663080i	$-0.230751\pi$
$547$	5.27460	+	4.42591i	0.225526	+	0.189238i	−0.523023	+	0.852319i	$0.675196\pi$
$548$	54.1374	+	31.2562i	2.31263	+	1.33520i
$549$		0			0
$550$	13.1803	+	22.8289i	0.562010	+	0.973429i
$551$	1.82980	−	10.3773i	0.0779520	−	0.442088i
$552$		0			0
$553$	−7.94664	+	20.1170i	−0.337925	+	0.855461i
$554$	−15.2743	+	41.9659i	−0.648945	+	1.78296i
$555$		0			0
$556$	16.1746	+	2.85203i	0.685958	+	0.120953i
$557$	5.66374	−	3.26996i	0.239980	−	0.138553i	−0.375187	−	0.926949i	$-0.622422\pi$
$557$	5.66374	−	3.26996i	0.239980	−	0.138553i	0.615168	+	0.788396i	$0.289088\pi$
$558$		0			0
$559$	3.13719	+	1.81126i	0.132689	+	0.0766079i
$560$	36.5490	−	41.2312i	1.54448	−	1.74234i
$561$		0			0
$562$	6.66942	+	37.8242i	0.281333	+	1.59552i
$563$	−25.1194	+	21.0777i	−1.05866	+	0.888320i	−0.993977	−	0.109586i	$-0.965047\pi$
$563$	−25.1194	+	21.0777i	−1.05866	+	0.888320i	−0.0646809	+	0.997906i	$0.520603\pi$
$564$		0			0
$565$	8.33630	+	22.9038i	0.350711	+	0.963570i
$566$	11.9259			0.501282
$567$		0			0
$568$	−50.0084			−2.09831
$569$	−3.57085	−	9.81082i	−0.149698	−	0.411291i	0.842066	−	0.539375i	$-0.181339\pi$
$569$	−3.57085	−	9.81082i	−0.149698	−	0.411291i	−0.991763	+	0.128084i	$0.959117\pi$
$570$		0			0
$571$	−32.6363	+	27.3851i	−1.36579	+	1.14603i	−0.391640	+	0.920118i	$0.628092\pi$
$571$	−32.6363	+	27.3851i	−1.36579	+	1.14603i	−0.974147	+	0.225914i	$0.927463\pi$
$572$	−2.02770	−	11.4997i	−0.0847826	−	0.480826i
$573$		0			0
$574$	−7.18753	−	6.37131i	−0.300002	−	0.265934i
$575$	−4.31137	−	2.48917i	−0.179796	−	0.103806i
$576$		0			0
$577$	−27.4313	+	15.8374i	−1.14198	+	0.659321i	−0.946920	−	0.321470i	$-0.895823\pi$
$577$	−27.4313	+	15.8374i	−1.14198	+	0.659321i	−0.195059	+	0.980792i	$0.562490\pi$
$578$	7.02365	+	1.23846i	0.292145	+	0.0515131i
$579$		0			0
$580$	4.34322	−	11.9329i	0.180342	−	0.495487i
$581$	5.14280	−	13.0191i	0.213359	−	0.540121i
$582$		0			0
$583$	1.92343	−	10.9083i	0.0796603	−	0.451776i
$584$	23.1785	+	40.1464i	0.959135	+	1.66127i
$585$		0			0
$586$	61.8550	+	35.7120i	2.55521	+	1.47525i
$587$	−22.4457	−	18.8342i	−0.926432	−	0.777369i	0.0487411	−	0.998811i	$-0.484479\pi$
$587$	−22.4457	−	18.8342i	−0.926432	−	0.777369i	−0.975173	+	0.221442i	$0.928924\pi$
$588$		0			0
$589$	7.29633	+	41.3795i	0.300640	+	1.70501i
$590$	−11.6084	−	13.8344i	−0.477911	−	0.569552i
$591$		0			0
$592$	−47.5212	+	17.2963i	−1.95311	+	0.710873i
$593$	−39.3635			−1.61647			−0.808234	−	0.588862i	$-0.799576\pi$
$593$	−39.3635			−1.61647			−0.808234	+	0.588862i	$0.799576\pi$
$594$		0			0
$595$	0.491324	−	18.0980i	0.0201423	−	0.741946i
$596$	−14.1439	−	38.8602i	−0.579359	−	1.59177i
$597$		0			0
$598$	1.95248	+	2.32687i	0.0798427	+	0.0951528i
$599$	−19.7367	+	3.48012i	−0.806422	+	0.142194i	−0.561637	−	0.827384i	$-0.689828\pi$
$599$	−19.7367	+	3.48012i	−0.806422	+	0.142194i	−0.244785	+	0.969578i	$0.578717\pi$
$600$		0			0
$601$	4.00429	−	4.77213i	0.163338	−	0.194659i	−0.678167	−	0.734908i	$-0.737225\pi$
$601$	4.00429	−	4.77213i	0.163338	−	0.194659i	0.841505	+	0.540249i	$0.181670\pi$
$602$	22.9400	−	37.3540i	0.934964	−	1.52243i
$603$		0			0
$604$	−53.2400	−	92.2143i	−2.16630	−	3.75215i
$605$	−0.780951	+	4.42899i	−0.0317502	+	0.180064i
$606$		0			0
$607$	8.90150	−	24.4567i	0.361301	−	0.992665i	−0.617269	−	0.786752i	$-0.711761\pi$
$607$	8.90150	−	24.4567i	0.361301	−	0.992665i	0.978570	−	0.205914i	$-0.0660166\pi$
$608$	118.743	+	43.2189i	4.81566	+	1.75276i
$609$		0			0
$610$	6.80201	−	38.5761i	0.275405	−	1.56190i
$611$	−3.14389	+	1.81513i	−0.127188	+	0.0734322i
$612$		0			0
$613$	−13.5782	+	23.5181i	−0.548417	+	0.949886i	0.449966	+	0.893046i	$0.351436\pi$
$613$	−13.5782	+	23.5181i	−0.548417	+	0.949886i	−0.998383	+	0.0568405i	$0.981897\pi$
$614$	−36.6618	−	30.7629i	−1.47955	−	1.24149i
$615$		0			0
$616$	−87.0239	+	12.9203i	−3.50629	+	0.520573i
$617$	8.14874	+	9.71129i	0.328056	+	0.390962i	0.904711	−	0.426026i	$-0.140087\pi$
$617$	8.14874	+	9.71129i	0.328056	+	0.390962i	−0.576655	+	0.816988i	$0.695642\pi$
$618$		0			0
$619$	−9.37859	−	25.7675i	−0.376957	−	1.03568i	−0.972611	−	0.232440i	$-0.925329\pi$
$619$	−9.37859	−	25.7675i	−0.376957	−	1.03568i	0.595654	−	0.803241i	$-0.296893\pi$
$620$			50.6362i			2.03360i
$621$		0			0
$622$		−	63.7314i		−	2.55540i
$623$	−4.94440	−	14.8246i	−0.198093	−	0.593935i
$624$		0			0
$625$	−3.89065	+	3.26464i	−0.155626	+	0.130586i
$626$	−6.25313	−	35.4632i	−0.249925	−	1.41740i
$627$		0			0
$628$	−68.0175	+	81.0601i	−2.71419	+	3.23465i
$629$	−8.30850	+	14.3907i	−0.331281	+	0.573796i
$630$		0			0
$631$	6.73167	+	11.6596i	0.267983	+	0.464161i	0.968341	−	0.249631i	$-0.0803094\pi$
$631$	6.73167	+	11.6596i	0.267983	+	0.464161i	−0.700358	+	0.713792i	$0.746976\pi$
$632$	−71.7748	−	12.6558i	−2.85505	−	0.503422i
$633$		0			0
$634$	52.1436	+	18.9787i	2.07089	+	0.753741i
$635$	7.56058	+	2.75183i	0.300032	+	0.109203i
$636$		0			0
$637$	−4.02727	−	0.937929i	−0.159566	−	0.0371621i
$638$	−13.5433	+	7.81923i	−0.536184	+	0.309566i
$639$		0			0
$640$	34.4256	+	19.8756i	1.36079	+	0.785652i
$641$	2.24686	−	2.67770i	0.0887456	−	0.105763i	−0.719844	−	0.694136i	$-0.755787\pi$
$641$	2.24686	−	2.67770i	0.0887456	−	0.105763i	0.808590	+	0.588373i	$0.200231\pi$
$642$		0			0
$643$	13.5707	−	2.39288i	0.535176	−	0.0943660i	0.100473	−	0.994940i	$-0.467964\pi$
$643$	13.5707	−	2.39288i	0.535176	−	0.0943660i	0.434703	+	0.900574i	$0.356853\pi$
$644$	20.9005	−	16.5923i	0.823596	−	0.653826i
$645$		0			0
$646$	76.4011	−	27.8077i	3.00596	−	1.09408i
$647$	33.5335			1.31834			0.659170	−	0.751994i	$-0.270908\pi$
$647$	33.5335			1.31834			0.659170	+	0.751994i	$0.270908\pi$
$648$		0			0
$649$			16.1467i			0.633815i
$650$	−3.92301	+	1.42786i	−0.153873	+	0.0560052i
$651$		0			0
$652$	8.65653	−	7.26369i	0.339016	−	0.284468i
$653$	−8.49895	+	1.49859i	−0.332589	+	0.0586445i	−0.337449	−	0.941344i	$-0.609564\pi$
$653$	−8.49895	+	1.49859i	−0.332589	+	0.0586445i	0.00485985	+	0.999988i	$0.498453\pi$
$654$		0			0
$655$	14.6376	+	12.2824i	0.571937	+	0.479912i
$656$	9.06107	−	15.6942i	0.353775	−	0.612757i
$657$		0			0
$658$	20.9242	+	38.6260i	0.815709	+	1.50580i
$659$	45.2808	+	7.98422i	1.76389	+	0.311021i	0.959211	−	0.282691i	$-0.0912273\pi$
$659$	45.2808	+	7.98422i	1.76389	+	0.311021i	0.804677	+	0.593713i	$0.202338\pi$
$660$		0			0
$661$	11.1294	−	30.5776i	0.432882	−	1.18933i	−0.511154	−	0.859489i	$-0.670782\pi$
$661$	11.1294	−	30.5776i	0.432882	−	1.18933i	0.944036	−	0.329843i	$-0.106996\pi$
$662$	1.05170	−	2.88951i	0.0408754	−	0.112304i
$663$		0			0
$664$	46.4503	+	8.19044i	1.80262	+	0.317851i
$665$	−13.2133	−	24.3917i	−0.512389	−	0.945870i
$666$		0			0
$667$	1.47670	−	2.55772i	0.0571782	−	0.0990355i
$668$	42.7727	+	35.8906i	1.65493	+	1.38865i
$669$		0			0
$670$	18.8141	−	3.31744i	0.726853	−	0.128164i
$671$	−26.8287	+	22.5120i	−1.03571	+	0.869065i
$672$		0			0
$673$	5.75164	−	2.09342i	0.221709	−	0.0806956i	−0.228777	−	0.973479i	$-0.573473\pi$
$673$	5.75164	−	2.09342i	0.221709	−	0.0806956i	0.450487	+	0.892783i	$0.351251\pi$
$674$			10.2692i			0.395555i
$675$		0			0
$676$	−67.0462			−2.57870
$677$	3.75793	−	1.36778i	0.144429	−	0.0525679i	−0.268794	−	0.963198i	$-0.586625\pi$
$677$	3.75793	−	1.36778i	0.144429	−	0.0525679i	0.413223	+	0.910630i	$0.364403\pi$
$678$		0			0
$679$	−38.6913	+	30.7157i	−1.48483	+	1.17876i
$680$	60.0777	−	10.5933i	2.30387	−	0.406235i
$681$		0			0
$682$	40.0832	−	47.7693i	1.53487	−	1.82918i
$683$	−18.1293	−	10.4670i	−0.693699	−	0.400507i	0.111297	−	0.993787i	$-0.464499\pi$
$683$	−18.1293	−	10.4670i	−0.693699	−	0.400507i	−0.804996	+	0.593280i	$0.797833\pi$
$684$		0			0
$685$	15.7733	−	9.10674i	0.602668	−	0.347951i
$686$	−12.6681	+	48.4077i	−0.483671	+	1.84821i
$687$		0			0
$688$	77.7194	+	28.2876i	2.96303	+	1.07845i
$689$	1.64843	+	0.599979i	0.0628002	+	0.0228574i
$690$		0			0
$691$	−5.21218	−	0.919049i	−0.198281	−	0.0349623i	0.0736256	−	0.997286i	$-0.476543\pi$
$691$	−5.21218	−	0.919049i	−0.198281	−	0.0349623i	−0.271906	+	0.962324i	$0.587654\pi$
$692$	7.33807	+	12.7099i	0.278952	+	0.483158i
$693$		0			0
$694$	7.52941	−	13.0413i	0.285812	−	0.495042i
$695$	3.07593	−	3.66576i	0.116677	−	0.139050i
$696$		0			0
$697$	−1.03402	−	5.86424i	−0.0391665	−	0.222124i
$698$	28.3559	−	23.7935i	1.07329	−	0.900596i
$699$		0			0
$700$	11.6044	+	34.7931i	0.438606	+	1.31505i
$701$		−	11.0468i		−	0.417232i	−0.977998	−	0.208616i	$-0.933104\pi$
$701$		−	11.0468i		−	0.417232i	0.977998	−	0.208616i	$-0.0668959\pi$
$702$		0			0
$703$			25.4612i			0.960288i
$704$	−29.7294	−	81.6808i	−1.12047	−	3.07846i
$705$		0			0
$706$	57.4797	+	68.5016i	2.16328	+	2.57809i
$707$	−8.88850	+	1.31966i	−0.334286	+	0.0496309i
$708$		0			0
$709$	−32.6424	−	27.3902i	−1.22591	−	1.02866i	−0.998494	−	0.0548636i	$-0.982528\pi$
$709$	−32.6424	−	27.3902i	−1.22591	−	1.02866i	−0.227417	−	0.973798i	$-0.573028\pi$
$710$	−11.7009	+	20.2665i	−0.439126	+	0.760588i
$711$		0			0
$712$	45.6025	−	26.3286i	1.70903	−	0.986706i
$713$	−2.04501	+	11.5978i	−0.0765861	+	0.434341i
$714$		0			0
$715$	−3.19703	−	1.16362i	−0.119562	−	0.0435170i
$716$	−25.5368	+	70.1619i	−0.954356	+	2.62207i
$717$		0			0
$718$	6.46122	−	36.6434i	0.241130	−	1.36752i
$719$	21.3837	+	37.0377i	0.797479	+	1.38127i	0.921253	+	0.388963i	$0.127167\pi$
$719$	21.3837	+	37.0377i	0.797479	+	1.38127i	−0.123775	+	0.992310i	$0.539500\pi$
$720$		0			0
$721$	−14.8503	+	24.1813i	−0.553055	+	0.900559i
$722$	47.0802	−	56.1080i	1.75214	−	2.08812i
$723$		0			0
$724$	−29.4342	+	5.19005i	−1.09391	+	0.192887i
$725$	2.60919	+	3.10951i	0.0969029	+	0.115484i
$726$		0			0
$727$	16.5881	+	45.5755i	0.615219	+	1.69030i	0.718393	+	0.695638i	$0.244878\pi$
$727$	16.5881	+	45.5755i	0.615219	+	1.69030i	−0.103173	+	0.994663i	$0.532900\pi$
$728$	0.378119	−	13.9281i	0.0140140	−	0.516209i
$729$		0			0
$730$	21.6931			0.802897
$731$	25.5376	−	9.29494i	0.944544	−	0.343786i
$732$		0			0
$733$	−33.7990	−	40.2800i	−1.24839	−	1.48778i	−0.807100	−	0.590414i	$-0.798964\pi$
$733$	−33.7990	−	40.2800i	−1.24839	−	1.48778i	−0.441293	−	0.897363i	$-0.645480\pi$
$734$	9.15486	+	51.9198i	0.337912	+	1.91639i
$735$		0			0
$736$	27.1310	+	22.7656i	1.00006	+	0.839152i
$737$	−14.7925	−	8.54046i	−0.544889	−	0.314592i
$738$		0			0
$739$	−18.2526	−	31.6144i	−0.671431	−	1.16295i	−0.977498	−	0.210943i	$-0.932347\pi$
$739$	−18.2526	−	31.6144i	−0.671431	−	1.16295i	0.306067	−	0.952010i	$-0.400987\pi$
$740$	−5.32815	+	30.2174i	−0.195867	+	1.11082i
$741$		0			0
$742$	7.79895	−	19.7431i	0.286308	−	0.724792i
$743$	−9.45684	+	25.9825i	−0.346938	+	0.953204i	0.636391	+	0.771367i	$0.280427\pi$
$743$	−9.45684	+	25.9825i	−0.346938	+	0.953204i	−0.983329	+	0.181837i	$0.941796\pi$
$744$		0			0
$745$	−11.8658	−	2.09226i	−0.434729	−	0.0766544i
$746$	−2.58217	+	1.49082i	−0.0945401	+	0.0545827i
$747$		0			0
$748$	−75.8665	−	43.8016i	−2.77395	−	1.60154i
$749$	32.1458	+	28.4953i	1.17458	+	1.04120i
$750$		0			0
$751$	−4.50550	−	25.5520i	−0.164408	−	0.932404i	−0.949673	−	0.313244i	$-0.898584\pi$
$751$	−4.50550	−	25.5520i	−0.164408	−	0.932404i	0.785265	−	0.619160i	$-0.212527\pi$
$752$	−63.4929	+	53.2769i	−2.31535	+	1.94281i
$753$		0			0
$754$	−0.847079	−	2.32733i	−0.0308488	−	0.0847564i
$755$	−31.0237			−1.12907
$756$		0			0
$757$	20.1349			0.731816			0.365908	−	0.930651i	$-0.380758\pi$
$757$	20.1349			0.731816			0.365908	+	0.930651i	$0.380758\pi$
$758$	−1.22436	−	3.36389i	−0.0444707	−	0.122182i
$759$		0			0
$760$	71.6048	−	60.0836i	2.59738	−	2.17946i
$761$	−7.31335	−	41.4761i	−0.265109	−	1.50351i	−0.768725	−	0.639579i	$-0.779109\pi$
$761$	−7.31335	−	41.4761i	−0.265109	−	1.50351i	0.503616	−	0.863928i	$-0.332003\pi$
$762$		0			0
$763$	1.79620	−	2.02630i	0.0650267	−	0.0733570i
$764$	49.3667	+	28.5019i	1.78603	+	1.03116i
$765$		0			0
$766$	−55.0957	+	31.8095i	−1.99069	+	1.14933i
$767$	−2.51834	−	0.444052i	−0.0909321	−	0.0160338i
$768$		0			0
$769$	1.83007	−	5.02807i	0.0659939	−	0.181317i	−0.902312	−	0.431083i	$-0.858132\pi$
$769$	1.83007	−	5.02807i	0.0659939	−	0.181317i	0.968306	+	0.249766i	$0.0803538\pi$
$770$	−15.1256	+	38.2905i	−0.545088	+	1.37989i
$771$		0			0
$772$	−23.3106	+	132.201i	−0.838967	+	4.75802i
$773$	−1.71685	−	2.97367i	−0.0617508	−	0.106956i	0.833497	−	0.552524i	$-0.186335\pi$
$773$	−1.71685	−	2.97367i	−0.0617508	−	0.106956i	−0.895248	+	0.445568i	$0.853002\pi$
$774$		0			0
$775$	−14.0175	−	8.09300i	−0.503523	−	0.290709i
$776$	−127.515	−	106.998i	−4.57752	−	3.84100i
$777$		0			0
$778$	−5.45190	−	30.9193i	−0.195460	−	1.10851i
$779$	−5.86482	−	6.98942i	−0.210129	−	0.250422i
$780$		0			0
$781$	19.6613	−	7.15614i	0.703538	−	0.256067i
$782$	22.7879			0.814892
$783$		0			0
$784$	−94.2702	−	5.12226i	−3.36679	−	0.182938i
$785$	10.5446	+	28.9711i	0.376354	+	1.03402i
$786$		0			0
$787$	−6.66979	−	7.94875i	−0.237752	−	0.283342i	0.633954	−	0.773371i	$-0.281431\pi$
$787$	−6.66979	−	7.94875i	−0.237752	−	0.283342i	−0.871706	+	0.490028i	$0.836986\pi$
$788$	−70.6719	+	12.4614i	−2.51758	+	0.443918i
$789$		0			0
$790$	−21.9227	+	26.1264i	−0.779973	+	0.929536i
$791$	21.8556	−	35.5882i	0.777095	−	1.26537i
$792$		0			0
$793$	−2.77329	−	4.80347i	−0.0984822	−	0.170576i
$794$	9.20960	−	52.2302i	0.326837	−	1.85358i
$795$		0			0
$796$	3.74621	−	10.2926i	0.132781	−	0.364812i
$797$	26.1222	+	9.50770i	0.925296	+	0.336780i	0.760343	−	0.649522i	$-0.225031\pi$
$797$	26.1222	+	9.50770i	0.925296	+	0.336780i	0.164952	+	0.986302i	$0.447253\pi$
$798$		0			0
$799$	−4.72926	+	26.8209i	−0.167309	+	0.948857i
$800$	−42.1558	+	24.3387i	−1.49043	+	0.860503i
$801$		0			0
$802$	13.2416	−	22.9351i	0.467576	−	0.809865i
$803$	−14.8578	−	12.4672i	−0.524320	−	0.439957i
$804$		0			0
$805$	−1.14184	−	7.69083i	−0.0402447	−	0.271066i
$806$	6.34806	+	7.56532i	0.223601	+	0.266477i
$807$		0			0
$808$	−10.3558	−	28.4525i	−0.364317	−	1.00095i
$809$		−	46.1025i		−	1.62088i	−0.585823	−	0.810439i	$-0.699229\pi$
$809$		−	46.1025i		−	1.62088i	0.585823	−	0.810439i	$-0.300771\pi$
$810$		0			0
$811$		−	15.6581i		−	0.549830i	−0.961468	−	0.274915i	$-0.911350\pi$
$811$		−	15.6581i		−	0.549830i	0.961468	−	0.274915i	$-0.0886498\pi$
$812$	−20.6410	+	6.88433i	−0.724358	+	0.241593i
$813$		0			0
$814$	28.9464	−	24.2889i	1.01457	−	0.851325i
$815$	−0.571724	−	3.24241i	−0.0200266	−	0.113577i
$816$		0			0
$817$	26.7664	−	31.8989i	0.936436	−	1.11600i
$818$	13.2243	−	22.9051i	0.462376	−	0.800858i
$819$		0			0
$820$	−5.49774	−	9.52237i	−0.191989	−	0.332536i
$821$	1.44801	+	0.255324i	0.0505360	+	0.00891087i	0.198859	−	0.980028i	$-0.436276\pi$
$821$	1.44801	+	0.255324i	0.0505360	+	0.00891087i	−0.148323	+	0.988939i	$0.547388\pi$
$822$		0			0
$823$	−36.3320	−	13.2238i	−1.26645	−	0.460952i	−0.380524	−	0.924771i	$-0.624257\pi$
$823$	−36.3320	−	13.2238i	−1.26645	−	0.460952i	−0.885930	+	0.463819i	$0.846479\pi$
$824$	−89.8518	−	32.7034i	−3.13014	−	1.13928i
$825$		0			0
$826$	−6.19845	+	30.3172i	−0.215672	+	1.05487i
$827$	20.8625	−	12.0449i	0.725459	−	0.418844i	−0.0912997	−	0.995823i	$-0.529102\pi$
$827$	20.8625	−	12.0449i	0.725459	−	0.418844i	0.816759	+	0.576980i	$0.195769\pi$
$828$		0			0
$829$	36.2761	+	20.9440i	1.25992	+	0.727416i	0.973059	−	0.230556i	$-0.0740543\pi$
$829$	36.2761	+	20.9440i	1.25992	+	0.727416i	0.286863	+	0.957972i	$0.407388\pi$
$830$	14.1876	−	16.9082i	0.492460	−	0.586891i
$831$		0			0
$832$	13.5570	−	2.39047i	0.470005	−	0.0828746i
$833$	−24.8109	+	18.6217i	−0.859647	+	0.645203i
$834$		0			0
$835$	15.2871	−	5.56404i	0.529031	−	0.192552i
$836$	−134.229			−4.64241
$837$		0			0
$838$			41.1224i			1.42055i
$839$	15.9125	−	5.79166i	0.549359	−	0.199950i	−0.0524025	−	0.998626i	$-0.516688\pi$
$839$	15.9125	−	5.79166i	0.549359	−	0.199950i	0.601762	+	0.798676i	$0.294466\pi$
$840$		0			0
$841$	20.3706	−	17.0929i	0.702433	−	0.589412i
$842$	−15.1846	+	2.67745i	−0.523296	+	0.0922711i
$843$		0			0
$844$	7.60301	+	6.37968i	0.261706	+	0.219598i
$845$	−9.76721	+	16.9173i	−0.336002	+	0.581973i
$846$		0			0
$847$	6.77569	−	3.67047i	0.232815	−	0.126119i
$848$	39.4430	+	6.95487i	1.35448	+	0.238831i
$849$		0			0
$850$	−10.7120	+	29.4310i	−0.367419	+	1.00947i
$851$	−2.44074	+	6.70587i	−0.0836674	+	0.229874i
$852$		0			0
$853$	−25.5559	−	4.50619i	−0.875017	−	0.154289i	−0.281937	−	0.959433i	$-0.590977\pi$
$853$	−25.5559	−	4.50619i	−0.875017	−	0.154289i	−0.593080	+	0.805144i	$0.702088\pi$
$854$	−59.0156	+	31.9695i	−2.01947	+	1.09397i
$855$		0			0
$856$	−72.3733	+	125.354i	−2.47367	+	4.28452i
$857$	−10.0030	−	8.39351i	−0.341696	−	0.286717i	0.455750	−	0.890108i	$-0.349371\pi$
$857$	−10.0030	−	8.39351i	−0.341696	−	0.286717i	−0.797445	+	0.603391i	$0.793816\pi$
$858$		0			0
$859$	10.8516	−	1.91344i	0.370253	−	0.0652856i	0.0145741	−	0.999894i	$-0.495361\pi$
$859$	10.8516	−	1.91344i	0.370253	−	0.0652856i	0.355679	+	0.934608i	$0.384250\pi$
$860$	38.4417	−	32.2564i	1.31085	−	1.09993i
$861$		0			0
$862$	−50.4030	+	18.3452i	−1.71673	+	0.624840i
$863$			4.80238i			0.163475i	0.996654	+	0.0817375i	$0.0260469\pi$
$863$			4.80238i			0.163475i	−0.996654	+	0.0817375i	$0.973953\pi$
$864$		0			0
$865$	4.27601			0.145389
$866$	−41.5970	+	15.1401i	−1.41352	+	0.514481i
$867$		0			0
$868$	67.9536	−	53.9462i	2.30650	−	1.83105i
$869$	30.0301	−	5.29511i	1.01870	−	0.179624i
$870$		0			0
$871$	1.73883	−	2.07226i	0.0589181	−	0.0702158i
$872$	7.90167	+	4.56203i	0.267584	+	0.154490i
$873$		0			0
$874$	30.2385	−	17.4582i	1.02283	−	0.590534i
$875$	30.4821	+	6.23217i	1.03048	+	0.210686i
$876$		0			0
$877$	−2.77444	−	1.00981i	−0.0936861	−	0.0340989i	0.294752	−	0.955574i	$-0.404763\pi$
$877$	−2.77444	−	1.00981i	−0.0936861	−	0.0340989i	−0.388438	+	0.921475i	$0.626985\pi$
$878$	−64.8069	−	23.5878i	−2.18713	−	0.796049i
$879$		0			0
$880$	−76.4973	−	13.4885i	−2.57872	−	0.454698i
$881$	−12.1716	−	21.0818i	−0.410071	−	0.710264i	0.584826	−	0.811159i	$-0.301163\pi$
$881$	−12.1716	−	21.0818i	−0.410071	−	0.710264i	−0.994897	+	0.100895i	$0.967829\pi$
$882$		0			0
$883$	−5.42908	+	9.40345i	−0.182703	+	0.316451i	−0.942800	−	0.333358i	$-0.891818\pi$
$883$	−5.42908	+	9.40345i	−0.182703	+	0.316451i	0.760097	+	0.649810i	$0.225151\pi$
$884$	8.91796	−	10.6280i	0.299944	−	0.357459i
$885$		0			0
$886$	−10.7688	−	61.0728i	−0.361784	−	2.05178i
$887$	24.6997	−	20.7255i	0.829336	−	0.695896i	−0.125802	−	0.992055i	$-0.540150\pi$
$887$	24.6997	−	20.7255i	0.829336	−	0.695896i	0.955138	+	0.296160i	$0.0957060\pi$
$888$		0			0
$889$	−4.36185	−	13.0780i	−0.146292	−	0.438621i
$890$		−	24.6413i		−	0.825977i
$891$		0			0
$892$			34.5598i			1.15715i
$893$	14.2725	+	39.2135i	0.477612	+	1.31223i
$894$		0			0
$895$	13.9833	+	16.6646i	0.467409	+	0.557037i
$896$	−10.0029	−	67.3738i	−0.334173	−	2.25080i
$897$		0			0
$898$	−28.9812	−	24.3181i	−0.967115	−	0.811506i
$899$	4.80118	−	8.31589i	0.160128	−	0.277351i
$900$		0			0
$901$	11.3973	−	6.58021i	0.379698	−	0.219219i
$902$	−2.35136	+	13.3352i	−0.0782916	+	0.444014i
$903$		0			0
$904$	132.237	+	48.1304i	4.39814	+	1.60079i
$905$	−2.97837	+	8.18301i	−0.0990045	+	0.272013i
$906$		0			0
$907$	8.73599	−	49.5443i	0.290074	−	1.64509i	−0.396503	−	0.918033i	$-0.629776\pi$
$907$	8.73599	−	49.5443i	0.290074	−	1.64509i	0.686577	−	0.727057i	$-0.259113\pi$
$908$	13.7980	+	23.8988i	0.457902	+	0.793109i
$909$		0			0
$910$	−5.55605	−	3.41211i	−0.184181	−	0.113110i
$911$	−19.0150	+	22.6612i	−0.629995	+	0.750799i	−0.982755	−	0.184915i	$-0.940799\pi$
$911$	−19.0150	+	22.6612i	−0.629995	+	0.750799i	0.352759	+	0.935714i	$0.385244\pi$
$912$		0			0
$913$	−19.4345	+	3.42682i	−0.643187	+	0.113411i
$914$	35.6039	+	42.4311i	1.17767	+	1.40349i
$915$		0			0
$916$	−10.3531	−	28.4450i	−0.342078	−	0.939850i
$917$	0.888520	−	32.7288i	0.0293415	−	1.08080i
$918$		0			0
$919$	38.0493			1.25513			0.627566	−	0.778564i	$-0.284051\pi$
$919$	38.0493			1.25513			0.627566	+	0.778564i	$0.284051\pi$
$920$	24.6186	−	8.96045i	0.811653	−	0.295417i
$921$		0			0
$922$	8.76803	+	10.4493i	0.288760	+	0.344131i
$923$	0.575408	+	3.26330i	0.0189398	+	0.107413i
$924$		0			0
$925$	−7.51343	−	6.30452i	−0.247040	−	0.207291i
$926$	−63.9453	−	36.9189i	−2.10137	−	1.21323i
$927$		0			0
$928$	−14.4390	−	25.0090i	−0.473982	−	0.820961i
$929$	6.90932	−	39.1847i	0.226688	−	1.28561i	−0.632745	−	0.774360i	$-0.718072\pi$
$929$	6.90932	−	39.1847i	0.226688	−	1.28561i	0.859433	−	0.511249i	$-0.170817\pi$
$930$		0			0
$931$	−18.6566	+	43.7183i	−0.611445	+	1.43281i
$932$	37.9444	−	104.251i	1.24291	−	3.41486i
$933$		0			0
$934$	84.5027	+	14.9001i	2.76501	+	0.487546i
$935$	−22.1043	+	12.7619i	−0.722887	+	0.417359i
$936$		0			0
$937$	−20.6367	−	11.9146i	−0.674170	−	0.389232i	0.123485	−	0.992346i	$-0.460593\pi$
$937$	−20.6367	−	11.9146i	−0.674170	−	0.389232i	−0.797655	+	0.603114i	$0.793926\pi$
$938$	−24.4959	−	21.7142i	−0.799821	−	0.708993i
$939$		0			0
$940$	8.73266	+	49.5254i	0.284828	+	1.61534i
$941$	16.7484	−	14.0535i	0.545981	−	0.458132i	−0.327596	−	0.944818i	$-0.606239\pi$
$941$	16.7484	−	14.0535i	0.545981	−	0.458132i	0.873577	+	0.486685i	$0.161794\pi$
$942$		0			0
$943$	−0.874639	−	2.40305i	−0.0284822	−	0.0782541i
$944$	−58.3845			−1.90025
$945$		0			0
$946$	−61.7991			−2.00926
$947$	10.2309	+	28.1093i	0.332461	+	0.913430i	0.987470	+	0.157808i	$0.0504428\pi$
$947$	10.2309	+	28.1093i	0.332461	+	0.913430i	−0.655009	+	0.755621i	$0.727335\pi$
$948$		0			0
$949$	2.35306	−	1.97445i	0.0763835	−	0.0640934i
$950$	8.33328	+	47.2604i	0.270367	+	1.53333i
$951$		0			0
$952$	−78.2210	−	69.3382i	−2.53516	−	2.24726i
$953$	−12.7773	−	7.37698i	−0.413898	−	0.238964i	0.278565	−	0.960417i	$-0.410141\pi$
$953$	−12.7773	−	7.37698i	−0.413898	−	0.238964i	−0.692463	+	0.721453i	$0.743474\pi$
$954$		0			0
$955$	14.3834	−	8.30424i	0.465435	−	0.268719i
$956$	96.3007	+	16.9804i	3.11459	+	0.549186i
$957$		0			0
$958$	−16.8227	+	46.2201i	−0.543518	+	1.49330i
$959$	−29.0256	−	11.4657i	−0.937286	−	0.370248i
$960$		0			0
$961$	−1.26581	+	7.17874i	−0.0408324	+	0.231572i
$962$	2.99219	+	5.18262i	0.0964719	+	0.167094i
$963$		0			0
$964$	−84.7753	−	48.9451i	−2.73043	−	1.57641i
$965$	29.9615	+	25.1407i	0.964495	+	0.809307i
$966$		0			0
$967$	2.25593	+	12.7940i	0.0725459	+	0.411428i	0.999356	+	0.0358968i	$0.0114288\pi$
$967$	2.25593	+	12.7940i	0.0725459	+	0.411428i	−0.926810	+	0.375532i	$0.877460\pi$
$968$	16.6904	+	19.8909i	0.536450	+	0.639316i
$969$		0			0
$970$	−73.1979	+	26.6419i	−2.35024	+	0.855418i
$971$	29.7033			0.953225			0.476613	−	0.879113i	$-0.341864\pi$
$971$	29.7033			0.953225			0.476613	+	0.879113i	$0.341864\pi$
$972$		0			0
$973$	−8.19643	−	0.222516i	−0.262765	−	0.00713354i
$974$	−23.8443	−	65.5115i	−0.764019	−	2.09913i
$975$		0			0
$976$	−81.4003	−	97.0091i	−2.60556	−	3.10519i
$977$	37.2441	−	6.56715i	1.19155	−	0.210102i	0.457505	−	0.889207i	$-0.348743\pi$
$977$	37.2441	−	6.56715i	1.19155	−	0.210102i	0.734041	+	0.679105i	$0.237632\pi$
$978$		0			0
$979$	−14.1615	+	16.8770i	−0.452604	+	0.539392i
$980$	−31.2904	+	47.9808i	−0.999536	+	1.53269i
$981$		0			0
$982$	39.7166	+	68.7911i	1.26741	+	2.19521i
$983$	−7.18185	+	40.7303i	−0.229065	+	1.29909i	0.625694	+	0.780069i	$0.284816\pi$
$983$	−7.18185	+	40.7303i	−0.229065	+	1.29909i	−0.854759	+	0.519025i	$0.826295\pi$
$984$		0			0
$985$	−7.15110	+	19.6475i	−0.227853	+	0.626021i
$986$	−17.4600	−	6.35491i	−0.556038	−	0.202381i
$987$		0			0
$988$	3.69143	−	20.9352i	0.117440	−	0.666036i
$989$	10.1075	−	5.83555i	0.321399	−	0.185560i
$990$		0			0
$991$	7.82595	−	13.5549i	0.248599	−	0.430587i	−0.714538	−	0.699597i	$-0.753363\pi$
$991$	7.82595	−	13.5549i	0.248599	−	0.430587i	0.963137	+	0.269010i	$0.0866964\pi$
$992$	88.2106	+	74.0175i	2.80069	+	2.35006i
$993$		0			0
$994$	39.6633	−	5.88874i	1.25804	−	0.186780i
$995$	−2.05132	−	2.44467i	−0.0650313	−	0.0775013i
$996$		0			0
$997$	9.65589	+	26.5294i	0.305805	+	0.840193i	0.993463	+	0.114158i	$0.0364169\pi$
$997$	9.65589	+	26.5294i	0.305805	+	0.840193i	−0.687657	+	0.726035i	$0.741361\pi$
$998$			46.1269i			1.46012i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.62.2		132
3.2	odd	2		189.2.be.a.20.22	yes	132
7.6	odd	2	inner	567.2.be.a.62.1		132
21.20	even	2		189.2.be.a.20.21	✓	132
27.4	even	9		189.2.be.a.104.21	yes	132
27.23	odd	18	inner	567.2.be.a.503.1		132
189.104	even	18	inner	567.2.be.a.503.2		132
189.139	odd	18		189.2.be.a.104.22	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.21	✓	132	21.20	even	2
189.2.be.a.20.22	yes	132	3.2	odd	2
189.2.be.a.104.21	yes	132	27.4	even	9
189.2.be.a.104.22	yes	132	189.139	odd	18
567.2.be.a.62.1		132	7.6	odd	2	inner
567.2.be.a.62.2		132	1.1	even	1	trivial
567.2.be.a.503.1		132	27.23	odd	18	inner
567.2.be.a.503.2		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)

\(f(q)\)	\(=\)	\(q+(-0.924066 - 2.53885i) q^{2} +(-4.05977 + 3.40655i) q^{4} +(0.268129 + 1.52064i) q^{5} +(1.75503 - 1.97986i) q^{7} +(7.72059 + 4.45748i) q^{8} +(3.61290 - 2.08591i) q^{10} +(-3.67329 - 0.647701i) q^{11} +(0.202039 - 0.555096i) q^{13} +(-6.64834 - 2.62624i) q^{14} +(2.34200 - 13.2821i) q^{16} +(-2.21584 - 3.83794i) q^{17} +(-5.88065 - 3.39519i) q^{19} +(-6.26867 - 5.26004i) q^{20} +(1.74995 + 9.92446i) q^{22} +(-1.22335 - 1.45794i) q^{23} +(2.45802 - 0.894647i) q^{25} -1.59600 q^{26} +(-0.380517 + 14.0164i) q^{28} +(0.530750 + 1.45822i) q^{29} +(-3.97747 - 4.74017i) q^{31} +(-18.3265 + 3.23145i) q^{32} +(-7.69638 + 9.17219i) q^{34} +(3.48123 + 2.13791i) q^{35} +(-1.87480 - 3.24725i) q^{37} +(-3.18578 + 18.0675i) q^{38} +(-4.70810 + 12.9354i) q^{40} +(1.26264 + 0.459562i) q^{41} +(-1.06487 + 6.03919i) q^{43} +(17.1192 - 9.88375i) q^{44} +(-2.57102 + 4.45314i) q^{46} +(-4.70770 - 3.95023i) q^{47} +(-0.839725 - 6.94945i) q^{49} +(-4.54275 - 5.41384i) q^{50} +(1.07073 + 2.94182i) q^{52} +2.96963i q^{53} -5.75941i q^{55} +(22.3751 - 7.46269i) q^{56} +(3.21176 - 2.69499i) q^{58} +(-0.751711 - 4.26316i) q^{59} +(6.03545 - 7.19277i) q^{61} +(-8.35913 + 14.4784i) q^{62} +(11.6520 + 20.1818i) q^{64} +(0.898272 + 0.158390i) q^{65} +(4.30322 + 1.56624i) q^{67} +(22.0699 + 8.03280i) q^{68} +(2.21094 - 10.8139i) q^{70} +(-4.85796 + 2.80474i) q^{71} +(4.50326 + 2.59996i) q^{73} +(-6.51183 + 7.76050i) q^{74} +(35.4400 - 6.24903i) q^{76} +(-7.72910 + 6.13589i) q^{77} +(-7.68222 + 2.79610i) q^{79} +20.8253 q^{80} -3.63031i q^{82} +(4.97168 - 1.80954i) q^{83} +(5.24198 - 4.39855i) q^{85} +(16.3166 - 2.87706i) q^{86} +(-25.4729 - 21.3743i) q^{88} +(2.95330 - 5.11527i) q^{89} +(-0.744431 - 1.37422i) q^{91} +(9.93307 + 1.75147i) q^{92} +(-5.67881 + 15.6024i) q^{94} +(3.58608 - 9.85268i) q^{95} +(-18.3882 - 3.24234i) q^{97} +(-16.8676 + 8.55369i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 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

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