LMFDB - Embedded newform 567.2.be.a.62.1

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			62.1
Character	$\chi$	$=$	567.62
Dual form			567.2.be.a.503.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.924066 - 2.53885i) q^{2} +(-4.05977 + 3.40655i) q^{4} +(-0.268129 - 1.52064i) q^{5} +(-1.64503 + 2.07217i) q^{7} +(7.72059 + 4.45748i) q^{8} +(-3.61290 + 2.08591i) q^{10} +(-3.67329 - 0.647701i) q^{11} +(-0.202039 + 0.555096i) q^{13} +(6.78104 + 2.26166i) q^{14} +(2.34200 - 13.2821i) q^{16} +(2.21584 + 3.83794i) q^{17} +(5.88065 + 3.39519i) q^{19} +(6.26867 + 5.26004i) q^{20} +(1.74995 + 9.92446i) q^{22} +(-1.22335 - 1.45794i) q^{23} +(2.45802 - 0.894647i) q^{25} +1.59600 q^{26} +(-0.380517 - 14.0164i) q^{28} +(0.530750 + 1.45822i) q^{29} +(3.97747 + 4.74017i) q^{31} +(-18.3265 + 3.23145i) q^{32} +(7.69638 - 9.17219i) q^{34} +(3.59210 + 1.94588i) q^{35} +(-1.87480 - 3.24725i) q^{37} +(3.18578 - 18.0675i) q^{38} +(4.70810 - 12.9354i) q^{40} +(-1.26264 - 0.459562i) q^{41} +(-1.06487 + 6.03919i) q^{43} +(17.1192 - 9.88375i) q^{44} +(-2.57102 + 4.45314i) q^{46} +(4.70770 + 3.95023i) q^{47} +(-1.58777 - 6.81755i) q^{49} +(-4.54275 - 5.41384i) q^{50} +(-1.07073 - 2.94182i) q^{52} +2.96963i q^{53} +5.75941i q^{55} +(-21.9372 + 8.66568i) q^{56} +(3.21176 - 2.69499i) q^{58} +(0.751711 + 4.26316i) q^{59} +(-6.03545 + 7.19277i) q^{61} +(8.35913 - 14.4784i) q^{62} +(11.6520 + 20.1818i) q^{64} +(0.898272 + 0.158390i) q^{65} +(4.30322 + 1.56624i) q^{67} +(-22.0699 - 8.03280i) q^{68} +(1.62096 - 10.9179i) q^{70} +(-4.85796 + 2.80474i) q^{71} +(-4.50326 - 2.59996i) q^{73} +(-6.51183 + 7.76050i) q^{74} +(-35.4400 + 6.24903i) q^{76} +(7.38481 - 6.54620i) q^{77} +(-7.68222 + 2.79610i) q^{79} -20.8253 q^{80} +3.63031i q^{82} +(-4.97168 + 1.80954i) q^{83} +(5.24198 - 4.39855i) q^{85} +(16.3166 - 2.87706i) q^{86} +(-25.4729 - 21.3743i) q^{88} +(-2.95330 + 5.11527i) q^{89} +(-0.817895 - 1.33181i) q^{91} +(9.93307 + 1.75147i) q^{92} +(5.67881 - 15.6024i) q^{94} +(3.58608 - 9.85268i) q^{95} +(18.3882 + 3.24234i) q^{97} +(-15.8415 + 10.3310i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.943343\pi$
$5$	−0.268129	−	1.52064i	−0.119911	−	0.680049i	0.864290	−	0.502994i	$-0.167768\pi$
$6$		0			0
$7$	−1.64503	+	2.07217i	−0.621762	+	0.783206i
$7$	−1.64503	+	2.07217i	−0.621762	+	0.783206i
$8$	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	−0.964552	−	0.263893i	$-0.914994\pi$
$13$	−0.202039	+	0.555096i	−0.0560354	+	0.153956i	0.908517	+	0.417849i	$0.137216\pi$
$14$	6.78104	+	2.26166i	1.81231	+	0.604453i
$15$		0			0
$16$	2.34200	−	13.2821i	0.585500	−	3.32054i
$17$	2.21584	+	3.83794i	0.537419	+	0.930838i	0.999042	+	0.0437613i	$0.0139341\pi$
$17$	2.21584	+	3.83794i	0.537419	+	0.930838i	−0.461623	+	0.887076i	$0.652733\pi$
$18$		0			0
$19$	5.88065	+	3.39519i	1.34911	+	0.778911i	0.988124	−	0.153659i	$-0.0491058\pi$
$19$	5.88065	+	3.39519i	1.34911	+	0.778911i	0.360989	+	0.932570i	$0.382439\pi$
$20$	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	0.994071	−	0.108729i	$-0.0346782\pi$
$31$	3.97747	+	4.74017i	0.714375	+	0.851359i	−0.279696	+	0.960089i	$0.590234\pi$
$32$	−18.3265	+	3.23145i	−3.23969	+	0.571245i
$33$		0			0
$34$	7.69638	−	9.17219i	1.31992	−	1.57302i
$35$	3.59210	+	1.94588i	0.607175	+	0.328914i
$36$		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	0.241537	−	0.970392i	$-0.422349\pi$
$41$	−1.26264	−	0.459562i	−0.197191	−	0.0717716i	−0.438728	+	0.898620i	$0.644571\pi$
$42$		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	0.917952	−	0.396691i	$-0.129842\pi$
$47$	4.70770	+	3.95023i	0.686688	+	0.576200i	−0.231264	+	0.972891i	$0.574286\pi$
$48$		0			0
$49$	−1.58777	−	6.81755i	−0.226824	−	0.973936i
$50$	−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
$56$	−21.9372	+	8.66568i	−2.93149	+	1.15800i
$57$		0			0
$58$	3.21176	−	2.69499i	0.421725	−	0.353870i
$59$	0.751711	+	4.26316i	0.0978644	+	0.555017i	0.993832	+	0.110897i	$0.0353724\pi$
$59$	0.751711	+	4.26316i	0.0978644	+	0.555017i	−0.895967	+	0.444120i	$0.853516\pi$
$60$		0			0
$61$	−6.03545	+	7.19277i	−0.772760	+	0.920939i	−0.998582	−	0.0532293i	$-0.983049\pi$
$61$	−6.03545	+	7.19277i	−0.772760	+	0.920939i	0.225823	+	0.974168i	$0.427493\pi$
$62$	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
$70$	1.62096	−	10.9179i	0.193742	−	1.30494i
$71$	−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	0.212755	−	0.977106i	$-0.431757\pi$
$73$	−4.50326	−	2.59996i	−0.527067	−	0.304302i	−0.739821	+	0.672804i	$0.765090\pi$
$74$	−6.51183	+	7.76050i	−0.756985	+	0.902140i
$75$		0			0
$76$	−35.4400	+	6.24903i	−4.06525	+	0.716813i
$77$	7.38481	−	6.54620i	0.841577	−	0.746008i
$78$		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	−0.600141	−	0.799895i	$-0.704889\pi$
$83$	−4.97168	+	1.80954i	−0.545712	+	0.198623i	0.0544280	+	0.998518i	$0.482666\pi$
$84$		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	−0.979021	−	0.203760i	$-0.934684\pi$
$89$	−2.95330	+	5.11527i	−0.313050	+	0.542218i	0.665971	+	0.745977i	$0.268017\pi$
$90$		0			0
$91$	−0.817895	−	1.33181i	−0.0857386	−	0.139611i
$92$	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	0.988828	−	0.149064i	$-0.0476261\pi$
$97$	18.3882	+	3.24234i	1.86704	+	0.329209i	0.878211	+	0.478273i	$0.158737\pi$
$98$	−15.8415	+	10.3310i	−1.60024	+	1.04359i
$99$		0			0
$100$	−6.93135	+	12.0054i	−0.693135	+	1.20054i
$101$	2.60176	+	2.18314i	0.258885	+	0.217230i	0.762987	−	0.646414i	$-0.223732\pi$
$101$	2.60176	+	2.18314i	0.258885	+	0.217230i	−0.504102	+	0.863644i	$0.668176\pi$
$102$		0			0
$103$	10.5626	−	1.86248i	1.04077	−	0.183516i	0.372959	−	0.927848i	$-0.378343\pi$
$103$	10.5626	−	1.86248i	1.04077	−	0.183516i	0.667810	+	0.744332i	$0.267232\pi$
$104$	−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
$112$	23.6702	+	26.7025i	2.23662	+	2.52315i
$113$	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
$119$	−11.5980	−	1.72193i	−1.06318	−	0.157849i
$120$		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	−0.954888	−	0.296967i	$-0.904025\pi$
$131$	−9.47971	+	7.95442i	−0.828246	+	0.694981i	0.126641	+	0.991949i	$0.459580\pi$
$132$		0			0
$133$	−16.7092	+	6.60051i	−1.44888	+	0.572337i
$134$		−	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	0.843882	−	0.536530i	$-0.180265\pi$
$139$	1.99206	+	2.37405i	0.168965	+	0.201364i	−0.674917	+	0.737894i	$0.735821\pi$
$140$	−21.2118	+	4.33684i	−1.79273	+	0.366530i
$141$		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
$154$	−23.4439	−	12.6998i	−1.88916	−	1.02338i
$155$	6.14159	−	7.31927i	0.493305	−	0.587898i
$156$		0			0
$157$	−19.6633	+	3.46718i	−1.56930	+	0.276711i	−0.889588	−	0.456764i	$-0.849008\pi$
$157$	−19.6633	+	3.46718i	−1.56930	+	0.276711i	−0.679717	+	0.733475i	$0.737897\pi$
$158$	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	$0.0780926\pi$
$167$	1.82951	+	10.3757i	0.141572	+	0.802894i	−0.828484	+	0.560013i	$0.810796\pi$
$168$		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	−0.997616	−	0.0690110i	$-0.978016\pi$
$173$	−0.480878	+	2.72719i	−0.0365604	+	0.207345i	0.961055	+	0.276356i	$0.0891268\pi$
$174$		0			0
$175$	−2.18965	+	6.56515i	−0.165522	+	0.496279i
$176$	−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	0.307378	−	0.951587i	$-0.400548\pi$
$181$	−4.88410	−	2.81983i	−0.363032	−	0.209597i	−0.670410	+	0.741991i	$0.733882\pi$
$182$	−2.62547	+	3.30719i	−0.194613	+	0.245145i
$183$		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
$196$	29.6703	+	22.2689i	2.11931	+	1.59063i
$197$	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	−0.435216	−	0.900326i	$-0.643328\pi$
$199$	1.78988	−	1.03339i	0.126881	−	0.0732548i	0.562097	+	0.827071i	$0.309995\pi$
$200$	22.9653	+	4.04939i	1.62389	+	0.286335i
$201$		0			0
$202$	3.13846	−	8.62285i	0.220821	−	0.606702i
$203$	−3.89479	−	1.29902i	−0.273360	−	0.0911730i
$204$		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	−0.887910	−	0.460017i	$-0.847843\pi$
$223$	−4.19171	+	4.99548i	−0.280697	+	0.334522i	0.607213	+	0.794539i	$0.292288\pi$
$224$	23.4514	−	43.2914i	1.56691	−	2.89253i
$225$		0			0
$226$	−21.3240	−	36.9343i	−1.41845	−	2.45683i
$227$	−0.904207	+	5.12801i	−0.0600143	+	0.340358i	−1.00000		0.000856752i	$-0.999727\pi$
$227$	−0.904207	+	5.12801i	−0.0600143	+	0.340358i	0.939985	+	0.341215i	$0.110838\pi$
$228$		0			0
$229$	1.95355	−	5.36734i	0.129094	−	0.354683i	−0.858260	−	0.513216i	$-0.828454\pi$
$229$	1.95355	−	5.36734i	0.129094	−	0.354683i	0.987354	+	0.158532i	$0.0506762\pi$
$230$	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
$238$	6.34557	+	31.0367i	0.411322	+	2.01181i
$239$	−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	$-0.908298\pi$
$241$	−6.31746	−	17.3571i	−0.406944	−	1.11807i	0.551845	−	0.833947i	$-0.313924\pi$
$242$		−	7.86920i		−	0.505852i
$243$		0			0
$244$		−	49.7611i		−	3.18563i
$245$	−9.94129	+	4.24240i	−0.635126	+	0.271037i
$246$		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	$0.410001\pi$
$251$	−10.9656	+	18.9930i	−0.692145	+	1.19883i	−0.971134	+	0.238536i	$0.923333\pi$
$252$		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	0.100271	−	0.994960i	$-0.468029\pi$
$257$	−7.41388	−	2.69843i	−0.462465	−	0.168324i	−0.562736	+	0.826637i	$0.690251\pi$
$258$		0			0
$259$	9.81294	+	1.45691i	0.609746	+	0.0905280i
$260$	−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
$266$	32.1981	+	36.3230i	1.97419	+	2.22710i
$267$		0			0
$268$	−22.8056	+	8.30055i	−1.39307	+	0.507037i
$269$	−15.1159			−0.921632			−0.460816	−	0.887496i	$-0.652443\pi$
$269$	−15.1159			−0.921632			−0.460816	+	0.887496i	$0.652443\pi$
$270$		0			0
$271$		−	20.2306i		−	1.22892i	−0.788948	−	0.614460i	$-0.789374\pi$
$271$		−	20.2306i		−	1.22892i	0.788948	−	0.614460i	$-0.210626\pi$
$272$	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
$280$	19.0594	+	31.0351i	1.13901	+	1.85470i
$281$	−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	−0.886699	−	0.462347i	$-0.847008\pi$
$283$	1.50970	−	4.14787i	0.0897424	−	0.246565i	0.976442	+	0.215781i	$0.0692298\pi$
$284$	10.1677	−	27.9355i	0.603341	−	1.65767i
$285$		0			0
$286$	−5.86259	−	1.03373i	−0.346662	−	0.0611259i
$287$	3.02936	−	1.86040i	0.178818	−	0.109816i
$288$		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	$-0.441379\pi$
$293$	20.2510	−	16.9926i	1.18308	−	0.992719i	0.999954	−	0.00962952i	$-0.00306522\pi$
$294$		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
$301$	−10.7625	−	12.1412i	−0.620339	−	0.699809i
$302$	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	−0.869181	−	0.494493i	$-0.835354\pi$
$307$	−15.3405	+	8.85684i	−0.875529	+	0.505487i	−0.00634703	+	0.999980i	$0.502020\pi$
$308$	−7.68069	+	51.7328i	−0.437648	+	2.94775i
$309$		0			0
$310$	−24.2578	−	8.82910i	−1.37775	−	0.501459i
$311$	−22.1660	−	8.06778i	−1.25692	−	0.457482i	−0.374186	−	0.927354i	$-0.622078\pi$
$311$	−22.1660	−	8.06778i	−1.25692	−	0.457482i	−0.882735	+	0.469872i	$0.844300\pi$
$312$		0			0
$313$	−13.1258	−	2.31444i	−0.741916	−	0.130820i	−0.210100	−	0.977680i	$-0.567379\pi$
$313$	−13.1258	−	2.31444i	−0.741916	−	0.130820i	−0.531816	+	0.846860i	$0.678490\pi$
$314$	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
$322$	−4.99826	−	12.6531i	−0.278542	−	0.705131i
$323$			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
$329$	−15.9298	+	3.25691i	−0.878240	+	0.179559i
$330$		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
$343$	16.7390	+	7.92493i	0.903823	+	0.427906i
$344$	−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	$-0.991603\pi$
$349$	−4.68587	−	12.8743i	−0.250829	−	0.689147i	0.748823	−	0.662770i	$-0.230619\pi$
$350$	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	0.665742	−	0.746182i	$-0.268115\pi$
$353$	31.1015	−	11.3200i	1.65537	−	0.602504i	0.989625	+	0.143677i	$0.0458927\pi$
$354$		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
$364$	7.85734	+	2.62063i	0.411836	+	0.137358i
$365$	−2.74613	+	7.54494i	−0.143739	+	0.394920i
$366$		0			0
$367$	19.2168	+	3.38845i	1.00311	+	0.176875i	0.650996	−	0.759081i	$-0.274352\pi$
$367$	19.2168	+	3.38845i	1.00311	+	0.176875i	0.352115	+	0.935957i	$0.385463\pi$
$368$	−22.2296	+	12.8343i	−1.15880	+	0.669033i
$369$		0			0
$370$	13.5469	+	7.82131i	0.704271	+	0.406611i
$371$	−6.15357	−	4.88512i	−0.319477	−	0.253623i
$372$		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	$0.149914\pi$
$383$	4.08890	+	23.1893i	0.208933	+	1.18492i	−0.682197	+	0.731169i	$0.738975\pi$
$384$		0			0
$385$	−11.9345	−	9.47439i	−0.608237	−	0.482859i
$386$	−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
$392$	18.1306	−	59.7130i	0.915735	−	3.01596i
$393$		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	0.00852412	−	0.999964i	$-0.497287\pi$
$397$	−17.0000	−	9.81498i	−0.853208	−	0.492600i	−0.861732	+	0.507364i	$0.830620\pi$
$398$	−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	0.587700	−	0.809079i	$-0.300034\pi$
$409$	−6.29242	−	7.49902i	−0.311140	−	0.370803i	−0.898840	+	0.438276i	$0.855589\pi$
$410$	5.52038	−	0.973393i	0.272632	−	0.0480724i
$411$		0			0
$412$	−36.5373	+	43.5435i	−1.80006	+	2.14523i
$413$	−10.0706	−	5.45535i	−0.495541	−	0.268440i
$414$		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	0.666866	−	0.745178i	$-0.267635\pi$
$419$	14.3025	+	5.20569i	0.698724	+	0.254315i	0.0318580	+	0.999492i	$0.489858\pi$
$420$		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
$427$	−4.97615	−	24.3388i	−0.240813	−	1.17784i
$428$	−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	$0.128801\pi$
$433$			16.3842i			0.787374i	−0.919244	+	0.393687i	$0.871199\pi$
$434$	16.2508	+	41.1389i	0.780062	+	1.97473i
$435$		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	−0.999069	−	0.0431343i	$-0.986266\pi$
$439$	−16.4078	+	19.5541i	−0.783104	+	0.933267i	0.215966	+	0.976401i	$0.430710\pi$
$440$	−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
$448$	−60.9880	−	9.05479i	−2.88141	−	0.427799i
$449$	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
$455$	−1.80589	+	1.60082i	−0.0846616	+	0.0750474i
$456$		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	−0.229167	−	0.973387i	$-0.573600\pi$
$461$	4.74427	−	1.72677i	0.220963	−	0.0804238i	0.450129	+	0.892963i	$0.351378\pi$
$462$		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	$-0.570601\pi$
$467$	15.8795	−	27.5042i	0.734818	−	1.27274i	0.954803	−	0.297238i	$-0.0960656\pi$
$468$		0			0
$469$	−10.3244	+	6.34048i	−0.476738	+	0.292776i
$470$	−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
$476$	52.9510	−	32.5185i	2.42701	−	1.49048i
$477$		0			0
$478$	−24.9259	+	43.1730i	−1.14009	+	1.97469i
$479$	13.9459	+	11.7020i	0.637206	+	0.534679i	0.903159	−	0.429307i	$-0.141242\pi$
$479$	13.9459	+	11.7020i	0.637206	+	0.534679i	−0.265953	+	0.963986i	$0.585687\pi$
$480$		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
$490$	19.9572	+	21.3192i	0.901576	+	0.963102i
$491$	−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
$497$	2.17957	−	14.6804i	0.0977672	−	0.658505i
$498$		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	0.996489	−	0.0837201i	$-0.0266802\pi$
$503$	9.54837	+	16.5383i	0.425741	+	0.737405i	−0.570748	+	0.821125i	$0.693347\pi$
$504$		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	−0.446894	−	0.894587i	$-0.647470\pi$
$509$	8.04301	−	6.74889i	0.356500	−	0.299139i	0.803394	+	0.595448i	$0.203025\pi$
$510$		0			0
$511$	12.7955	−	5.05451i	0.566041	−	0.223598i
$512$			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
$518$	−5.36892	−	26.2599i	−0.235897	−	1.15379i
$519$		0			0
$520$	6.22917	+	5.22690i	0.273167	+	0.229215i
$521$	4.56525	−	7.90725i	0.200007	−	0.346423i	−0.748523	−	0.663109i	$-0.769237\pi$
$521$	4.56525	−	7.90725i	0.200007	−	0.346423i	0.948530	+	0.316686i	$0.102570\pi$
$522$		0			0
$523$	23.7892	−	13.7347i	1.04023	−	0.600575i	0.120329	−	0.992734i	$-0.461605\pi$
$523$	23.7892	−	13.7347i	1.04023	−	0.600575i	0.919898	+	0.392159i	$0.128272\pi$
$524$	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
$532$	45.3507	−	83.7175i	1.96620	−	3.62961i
$533$	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
$553$	6.84347	−	20.5185i	0.291014	−	0.872536i
$554$	−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
$560$	34.2581	−	43.1535i	1.44767	−	1.82357i
$561$		0			0
$562$	6.66942	+	37.8242i	0.281333	+	1.59552i
$563$	25.1194	−	21.0777i	1.05866	−	0.888320i	0.0646809	−	0.997906i	$-0.479397\pi$
$563$	25.1194	−	21.0777i	1.05866	−	0.888320i	0.993977	+	0.109586i	$0.0349526\pi$
$564$		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
$574$	−7.52262	−	5.97196i	−0.313988	−	0.249265i
$575$	−4.31137	−	2.48917i	−0.179796	−	0.103806i
$576$		0			0
$577$	27.4313	−	15.8374i	1.14198	−	0.659321i	0.195059	−	0.980792i	$-0.437510\pi$
$577$	27.4313	−	15.8374i	1.14198	−	0.659321i	0.946920	+	0.321470i	$0.104177\pi$
$578$	7.02365	+	1.23846i	0.292145	+	0.0515131i
$579$		0			0
$580$	−4.34322	+	11.9329i	−0.180342	+	0.495487i
$581$	4.42887	−	13.2789i	0.183740	−	0.550902i
$582$		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	0.975173	−	0.221442i	$-0.0710765\pi$
$587$	22.4457	+	18.8342i	0.926432	+	0.777369i	−0.0487411	+	0.998811i	$0.515521\pi$
$588$		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	$-0.200424\pi$
$593$	39.3635			1.61647			0.808234	+	0.588862i	$0.200424\pi$
$594$		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	−0.841505	−	0.540249i	$-0.818330\pi$
$601$	−4.00429	+	4.77213i	−0.163338	+	0.194659i	0.678167	+	0.734908i	$0.262775\pi$
$602$	−20.8795	+	38.5436i	−0.850985	+	1.57092i
$603$		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	$0.288239\pi$
$607$	−8.90150	+	24.4567i	−0.361301	+	0.992665i	−0.978570	+	0.205914i	$0.933983\pi$
$608$	−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
$616$	86.1947	−	17.6228i	3.47288	−	0.710043i
$617$	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	$0.0746709\pi$
$619$	9.37859	+	25.7675i	0.376957	+	1.03568i	−0.595654	+	0.803241i	$0.703107\pi$
$620$			50.6362i			2.03360i
$621$		0			0
$622$			63.7314i			2.55540i
$623$	−5.74144	−	14.5345i	−0.230026	−	0.582313i
$624$		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
$637$	4.10519	+	0.496044i	0.162653	+	0.0196540i
$638$	−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	−0.434703	−	0.900574i	$-0.643147\pi$
$643$	−13.5707	+	2.39288i	−0.535176	+	0.0943660i	−0.100473	+	0.994940i	$0.532036\pi$
$644$	−19.9695	+	17.7018i	−0.786909	+	0.697548i
$645$		0			0
$646$	76.4011	−	27.8077i	3.00596	−	1.09408i
$647$	−33.5335			−1.31834			−0.659170	−	0.751994i	$-0.729092\pi$
$647$	−33.5335			−1.31834			−0.659170	+	0.751994i	$0.729092\pi$
$648$		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
$658$	22.9890	+	37.4339i	0.896206	+	1.45932i
$659$	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	$0.329218\pi$
$661$	−11.1294	+	30.5776i	−0.432882	+	1.18933i	−0.944036	+	0.329843i	$0.893004\pi$
$662$	1.05170	−	2.88951i	0.0408754	−	0.112304i
$663$		0			0
$664$	−46.4503	−	8.19044i	−1.80262	−	0.317851i
$665$	14.5172	+	23.6389i	0.562953	+	0.916677i
$666$		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	−0.413223	−	0.910630i	$-0.635597\pi$
$677$	−3.75793	+	1.36778i	−0.144429	+	0.0525679i	0.268794	+	0.963198i	$0.413375\pi$
$678$		0			0
$679$	−36.9678	+	32.7697i	−1.41869	+	1.25759i
$680$	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
$686$	4.65225	−	49.8211i	0.177624	−	1.90218i
$687$		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	0.271906	−	0.962324i	$-0.412346\pi$
$691$	5.21218	+	0.919049i	0.198281	+	0.0349623i	−0.0736256	+	0.997286i	$0.523457\pi$
$692$	−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
$700$	−13.4751	−	34.1122i	−0.509309	−	1.28932i
$701$		−	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
$707$	−8.80381	+	1.79997i	−0.331101	+	0.0676949i
$708$		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	$-0.872833\pi$
$719$	−21.3837	−	37.0377i	−0.797479	−	1.38127i	0.123775	−	0.992310i	$-0.460500\pi$
$720$		0			0
$721$	−13.5165	+	24.9514i	−0.503380	+	0.929239i
$722$	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	$-0.755122\pi$
$727$	−16.5881	−	45.5755i	−0.615219	−	1.69030i	0.103173	−	0.994663i	$-0.467100\pi$
$728$	−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	$0.201036\pi$
$733$	33.7990	+	40.2800i	1.24839	+	1.48778i	0.441293	+	0.897363i	$0.354520\pi$
$734$	−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
$742$	−6.71628	+	20.1372i	−0.246562	+	0.739258i
$743$	−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
$749$	−33.6445	−	26.7093i	−1.22934	−	0.975935i
$750$		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	$0.220891\pi$
$761$	7.31335	+	41.4761i	0.265109	+	1.50351i	−0.503616	+	0.863928i	$0.667997\pi$
$762$		0			0
$763$	−1.68361	+	2.12077i	−0.0609508	+	0.0767771i
$764$	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	−0.968306	−	0.249766i	$-0.919646\pi$
$769$	−1.83007	+	5.02807i	−0.0659939	+	0.181317i	0.902312	+	0.431083i	$0.141868\pi$
$770$	−13.0258	+	39.0548i	−0.469418	+	1.40744i
$771$		0			0
$772$	−23.3106	+	132.201i	−0.838967	+	4.75802i
$773$	1.71685	+	2.97367i	0.0617508	+	0.106956i	0.895248	−	0.445568i	$-0.146998\pi$
$773$	1.71685	+	2.97367i	0.0617508	+	0.106956i	−0.833497	+	0.552524i	$0.813665\pi$
$774$		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	0.871706	−	0.490028i	$-0.163014\pi$
$787$	6.66979	+	7.94875i	0.237752	+	0.283342i	−0.633954	+	0.773371i	$0.718569\pi$
$788$	−70.6719	+	12.4614i	−2.51758	+	0.443918i
$789$		0			0
$790$	21.9227	−	26.1264i	0.779973	−	0.929536i
$791$	−19.8925	+	36.7216i	−0.707297	+	1.30567i
$792$		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	−0.164952	−	0.986302i	$-0.552747\pi$
$797$	−26.1222	−	9.50770i	−0.925296	−	0.336780i	−0.760343	+	0.649522i	$0.774969\pi$
$798$		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
$805$	−1.55743	−	7.61755i	−0.0548924	−	0.268483i
$806$	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	$0.0886498\pi$
$811$			15.6581i			0.549830i	−0.961468	+	0.274915i	$0.911350\pi$
$812$	20.2371	−	7.99409i	0.710183	−	0.280538i
$813$		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
$826$	−4.54444	+	30.6088i	−0.158121	+	1.06502i
$827$	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	−0.286863	−	0.957972i	$-0.592612\pi$
$829$	−36.2761	−	20.9440i	−1.25992	−	0.727416i	−0.973059	+	0.230556i	$0.925946\pi$
$830$	14.1876	−	16.9082i	0.492460	−	0.586891i
$831$		0			0
$832$	−13.5570	+	2.39047i	−0.470005	+	0.0828746i
$833$	22.6471	−	21.2003i	0.784676	−	0.734548i
$834$		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	−0.601762	−	0.798676i	$-0.705534\pi$
$839$	−15.9125	+	5.79166i	−0.549359	+	0.199950i	0.0524025	+	0.998626i	$0.483312\pi$
$840$		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
$847$	−6.56657	+	4.03268i	−0.225630	+	0.138565i
$848$	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	0.593080	−	0.805144i	$-0.297912\pi$
$853$	25.5559	+	4.50619i	0.875017	+	0.154289i	0.281937	+	0.959433i	$0.409023\pi$
$854$	−57.1942	+	35.1243i	−1.95714	+	1.20193i
$855$		0			0
$856$	−72.3733	+	125.354i	−2.47367	+	4.28452i
$857$	10.0030	+	8.39351i	0.341696	+	0.286717i	0.797445	−	0.603391i	$-0.206184\pi$
$857$	10.0030	+	8.39351i	0.341696	+	0.286717i	−0.455750	+	0.890108i	$0.650629\pi$
$858$		0			0
$859$	−10.8516	+	1.91344i	−0.370253	+	0.0652856i	−0.355679	−	0.934608i	$-0.615750\pi$
$859$	−10.8516	+	1.91344i	−0.370253	+	0.0652856i	−0.0145741	+	0.999894i	$0.504639\pi$
$860$	−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
$868$	64.9266	−	57.5536i	2.20375	−	1.95350i
$869$	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
$875$	30.7753	+	4.56916i	1.04040	+	0.154466i
$876$		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	0.994897	−	0.100895i	$-0.0321706\pi$
$881$	12.1716	+	21.0818i	0.410071	+	0.710264i	−0.584826	+	0.811159i	$0.698837\pi$
$882$		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	−0.955138	−	0.296160i	$-0.904294\pi$
$887$	−24.6997	+	20.7255i	−0.829336	+	0.695896i	0.125802	+	0.992055i	$0.459850\pi$
$888$		0			0
$889$	5.06498	+	12.8221i	0.169874	+	0.430038i
$890$		−	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
$896$	13.6436	+	66.7318i	0.455799	+	2.22935i
$897$		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
$910$	5.73300	+	3.10563i	0.190047	+	0.102951i
$911$	−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	$0.281928\pi$
$929$	−6.90932	+	39.1847i	−0.226688	+	1.28561i	−0.859433	+	0.511249i	$0.829183\pi$
$930$		0			0
$931$	13.8098	−	45.4824i	0.452598	−	1.49063i
$932$	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	0.797655	−	0.603114i	$-0.206074\pi$
$937$	20.6367	+	11.9146i	0.674170	+	0.389232i	−0.123485	+	0.992346i	$0.539407\pi$
$938$	25.6380	+	20.3532i	0.837110	+	0.664554i
$939$		0			0
$940$	8.73266	+	49.5254i	0.284828	+	1.61534i
$941$	−16.7484	+	14.0535i	−0.545981	+	0.458132i	−0.873577	−	0.486685i	$-0.838206\pi$
$941$	−16.7484	+	14.0535i	−0.545981	+	0.458132i	0.327596	+	0.944818i	$0.393761\pi$
$942$		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
$952$	−81.8677	−	64.9921i	−2.65335	−	2.10641i
$953$	−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
$959$	29.6049	+	9.87404i	0.955993	+	0.318849i
$960$		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	$-0.658136\pi$
$971$	−29.7033			−0.953225			−0.476613	+	0.879113i	$0.658136\pi$
$972$		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
$980$	25.9074	−	51.0887i	0.827581	−	1.63197i
$981$		0			0
$982$	39.7166	+	68.7911i	1.26741	+	2.19521i
$983$	7.18185	−	40.7303i	0.229065	−	1.29909i	−0.625694	−	0.780069i	$-0.715184\pi$
$983$	7.18185	−	40.7303i	0.229065	−	1.29909i	0.854759	−	0.519025i	$-0.173705\pi$
$984$		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
$994$	−39.2854	+	8.03203i	−1.24606	+	0.254761i
$995$	−2.05132	−	2.44467i	−0.0650313	−	0.0775013i
$996$		0			0
$997$	−9.65589	−	26.5294i	−0.305805	−	0.840193i	−0.993463	−	0.114158i	$-0.963583\pi$
$997$	−9.65589	−	26.5294i	−0.305805	−	0.840193i	0.687657	−	0.726035i	$-0.258639\pi$
$998$			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.62.1		132
3.2	odd	2		189.2.be.a.20.21	✓	132
7.6	odd	2	inner	567.2.be.a.62.2		132
21.20	even	2		189.2.be.a.20.22	yes	132
27.4	even	9		189.2.be.a.104.22	yes	132
27.23	odd	18	inner	567.2.be.a.503.2		132
189.104	even	18	inner	567.2.be.a.503.1		132
189.139	odd	18		189.2.be.a.104.21	yes	132

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

\(f(q)\)	\(=\)	\(q+(-0.924066 - 2.53885i) q^{2} +(-4.05977 + 3.40655i) q^{4} +(-0.268129 - 1.52064i) q^{5} +(-1.64503 + 2.07217i) q^{7} +(7.72059 + 4.45748i) q^{8} +(-3.61290 + 2.08591i) q^{10} +(-3.67329 - 0.647701i) q^{11} +(-0.202039 + 0.555096i) q^{13} +(6.78104 + 2.26166i) q^{14} +(2.34200 - 13.2821i) q^{16} +(2.21584 + 3.83794i) q^{17} +(5.88065 + 3.39519i) q^{19} +(6.26867 + 5.26004i) q^{20} +(1.74995 + 9.92446i) q^{22} +(-1.22335 - 1.45794i) q^{23} +(2.45802 - 0.894647i) q^{25} +1.59600 q^{26} +(-0.380517 - 14.0164i) q^{28} +(0.530750 + 1.45822i) q^{29} +(3.97747 + 4.74017i) q^{31} +(-18.3265 + 3.23145i) q^{32} +(7.69638 - 9.17219i) q^{34} +(3.59210 + 1.94588i) q^{35} +(-1.87480 - 3.24725i) q^{37} +(3.18578 - 18.0675i) q^{38} +(4.70810 - 12.9354i) q^{40} +(-1.26264 - 0.459562i) q^{41} +(-1.06487 + 6.03919i) q^{43} +(17.1192 - 9.88375i) q^{44} +(-2.57102 + 4.45314i) q^{46} +(4.70770 + 3.95023i) q^{47} +(-1.58777 - 6.81755i) q^{49} +(-4.54275 - 5.41384i) q^{50} +(-1.07073 - 2.94182i) q^{52} +2.96963i q^{53} +5.75941i q^{55} +(-21.9372 + 8.66568i) q^{56} +(3.21176 - 2.69499i) q^{58} +(0.751711 + 4.26316i) q^{59} +(-6.03545 + 7.19277i) q^{61} +(8.35913 - 14.4784i) q^{62} +(11.6520 + 20.1818i) q^{64} +(0.898272 + 0.158390i) q^{65} +(4.30322 + 1.56624i) q^{67} +(-22.0699 - 8.03280i) q^{68} +(1.62096 - 10.9179i) q^{70} +(-4.85796 + 2.80474i) q^{71} +(-4.50326 - 2.59996i) q^{73} +(-6.51183 + 7.76050i) q^{74} +(-35.4400 + 6.24903i) q^{76} +(7.38481 - 6.54620i) q^{77} +(-7.68222 + 2.79610i) q^{79} -20.8253 q^{80} +3.63031i q^{82} +(-4.97168 + 1.80954i) q^{83} +(5.24198 - 4.39855i) q^{85} +(16.3166 - 2.87706i) q^{86} +(-25.4729 - 21.3743i) q^{88} +(-2.95330 + 5.11527i) q^{89} +(-0.817895 - 1.33181i) q^{91} +(9.93307 + 1.75147i) q^{92} +(5.67881 - 15.6024i) q^{94} +(3.58608 - 9.85268i) q^{95} +(18.3882 + 3.24234i) q^{97} +(-15.8415 + 10.3310i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 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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