LMFDB - Embedded newform 588.2.n.h.275.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] 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("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.4
Character	$\chi$	$=$	588.275
Dual form			588.2.n.h.263.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34296 + 0.443234i) q^{2} +(1.66143 - 0.489533i) q^{3} +(1.60709 - 1.19049i) q^{4} +(-1.08570 - 0.626827i) q^{5} +(-2.01426 + 1.39383i) q^{6} +(-1.63059 + 2.31110i) q^{8} +(2.52072 - 1.62665i) q^{9} +(1.73588 + 0.360587i) q^{10} +(-2.52914 - 4.38059i) q^{11} +(2.08728 - 2.76464i) q^{12} -4.41798 q^{13} +(-2.11066 - 0.509947i) q^{15} +(1.16546 - 3.82645i) q^{16} +(5.06920 - 2.92671i) q^{17} +(-2.66423 + 3.30180i) q^{18} +(1.32654 + 0.765881i) q^{19} +(-2.49104 + 0.285146i) q^{20} +(5.33816 + 4.76197i) q^{22} +(-0.156785 + 0.271560i) q^{23} +(-1.57776 + 4.63796i) q^{24} +(-1.71417 - 2.96904i) q^{25} +(5.93317 - 1.95820i) q^{26} +(3.39170 - 3.93654i) q^{27} -5.53862i q^{29} +(3.06057 - 0.250679i) q^{30} +(-4.24264 + 2.44949i) q^{31} +(0.130843 + 5.65534i) q^{32} +(-6.34643 - 6.03996i) q^{33} +(-5.51053 + 6.17729i) q^{34} +(2.11450 - 5.61506i) q^{36} +(2.66908 - 4.62298i) q^{37} +(-2.12096 - 0.440578i) q^{38} +(-7.34017 + 2.16275i) q^{39} +(3.21899 - 1.48705i) q^{40} +1.97938i q^{41} +3.18613i q^{43} +(-9.27960 - 4.02908i) q^{44} +(-3.75636 + 0.185997i) q^{45} +(0.0901918 - 0.434187i) q^{46} +(-5.74813 + 9.95606i) q^{47} +(0.0631619 - 6.92792i) q^{48} +(3.61805 + 3.22752i) q^{50} +(6.98942 - 7.34407i) q^{51} +(-7.10008 + 5.25957i) q^{52} +(11.0767 - 6.39513i) q^{53} +(-2.81011 + 6.78994i) q^{54} +6.34133i q^{55} +(2.57889 + 0.623072i) q^{57} +(2.45490 + 7.43815i) q^{58} +(-3.98351 - 6.89964i) q^{59} +(-3.99911 + 1.69320i) q^{60} +(-0.151445 + 0.262310i) q^{61} +(4.61200 - 5.17005i) q^{62} +(-2.68236 - 7.53691i) q^{64} +(4.79659 + 2.76931i) q^{65} +(11.2001 + 5.29848i) q^{66} +(9.13122 - 5.27191i) q^{67} +(4.66244 - 10.7383i) q^{68} +(-0.127550 + 0.527930i) q^{69} +4.53490 q^{71} +(-0.350899 + 8.47802i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-1.53541 + 7.39151i) q^{74} +(-4.30143 - 4.09371i) q^{75} +(3.04365 - 0.348402i) q^{76} +(8.89896 - 6.15790i) q^{78} +(-6.00000 - 3.46410i) q^{79} +(-3.66386 + 3.42382i) q^{80} +(3.70801 - 8.20065i) q^{81} +(-0.877328 - 2.65823i) q^{82} -6.78340 q^{83} -7.33816 q^{85} +(-1.41220 - 4.27885i) q^{86} +(-2.71134 - 9.20204i) q^{87} +(14.2480 + 1.29786i) q^{88} +(4.15480 + 2.39878i) q^{89} +(4.96221 - 1.91473i) q^{90} +(0.0713222 + 0.623072i) q^{92} +(-5.84975 + 6.14657i) q^{93} +(3.30666 - 15.9184i) q^{94} +(-0.960150 - 1.66303i) q^{95} +(2.98586 + 9.33191i) q^{96} +13.6844 q^{97} +(-13.5009 - 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 60 q^{16} + 24 q^{18} + 12 q^{25} + 36 q^{30} + 12 q^{36} - 96 q^{39} + 24 q^{46} + 12 q^{51} - 24 q^{57} + 48 q^{58} + 12 q^{60} - 48 q^{64} - 48 q^{67} - 36 q^{72} - 24 q^{78} - 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) $ 24 * q + 12 * q^4 + 60 * q^16 + 24 * q^18 + 12 * q^25 + 36 * q^30 + 12 * q^36 - 96 * q^39 + 24 * q^46 + 12 * q^51 - 24 * q^57 + 48 * q^58 + 12 * q^60 - 48 * q^64 - 48 * q^67 - 36 * q^72 - 24 * q^78 - 144 * q^79 + 12 * q^81 - 48 * q^85 + 192 * q^88 - 24 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.34296	+	0.443234i	−0.949617	+	0.313414i
$2$	−1.34296	+	0.443234i	−0.949617	+	0.313414i
$3$	1.66143	−	0.489533i	0.959228	−	0.282632i
$3$	1.66143	−	0.489533i	0.959228	−	0.282632i
$4$	1.60709	−	1.19049i	0.803544	−	0.595246i
$5$	−1.08570	−	0.626827i	−0.485538	−	0.280326i	0.237183	−	0.971465i	$-0.423776\pi$
$5$	−1.08570	−	0.626827i	−0.485538	−	0.280326i	−0.722722	+	0.691139i	$0.757109\pi$
$6$	−2.01426	+	1.39383i	−0.822319	+	0.569027i
$7$		0			0
$7$		0			0
$8$	−1.63059	+	2.31110i	−0.576500	+	0.817097i
$9$	2.52072	−	1.62665i	0.840238	−	0.542217i
$10$	1.73588	+	0.360587i	0.548933	+	0.114028i
$11$	−2.52914	−	4.38059i	−0.762563	−	1.32080i	−0.941525	−	0.336942i	$-0.890607\pi$
$11$	−2.52914	−	4.38059i	−0.762563	−	1.32080i	0.178962	−	0.983856i	$-0.442726\pi$
$12$	2.08728	−	2.76464i	0.602547	−	0.798084i
$13$	−4.41798			−1.22533			−0.612664	−	0.790344i	$-0.709902\pi$
$13$	−4.41798			−1.22533			−0.612664	+	0.790344i	$0.709902\pi$
$14$		0			0
$15$	−2.11066	−	0.509947i	−0.544971	−	0.131668i
$16$	1.16546	−	3.82645i	0.291365	−	0.956612i
$17$	5.06920	−	2.92671i	1.22946	−	0.709831i	0.262545	−	0.964920i	$-0.415438\pi$
$17$	5.06920	−	2.92671i	1.22946	−	0.709831i	0.966918	+	0.255089i	$0.0821048\pi$
$18$	−2.66423	+	3.30180i	−0.627966	+	0.778241i
$19$	1.32654	+	0.765881i	0.304330	+	0.175705i	0.644386	−	0.764700i	$-0.277113\pi$
$19$	1.32654	+	0.765881i	0.304330	+	0.175705i	−0.340056	+	0.940405i	$0.610446\pi$
$20$	−2.49104	+	0.285146i	−0.557014	+	0.0637607i
$21$		0			0
$22$	5.33816	+	4.76197i	1.13810	+	1.01525i
$23$	−0.156785	+	0.271560i	−0.0326920	+	0.0566242i	−0.881908	−	0.471421i	$-0.843741\pi$
$23$	−0.156785	+	0.271560i	−0.0326920	+	0.0566242i	0.849217	+	0.528045i	$0.177075\pi$
$24$	−1.57776	+	4.63796i	−0.322058	+	0.946720i
$25$	−1.71417	−	2.96904i	−0.342835	−	0.593808i
$26$	5.93317	−	1.95820i	1.16359	−	0.384034i
$27$	3.39170	−	3.93654i	0.652733	−	0.757588i
$28$		0			0
$29$		−	5.53862i		−	1.02850i	−0.857642	−	0.514248i	$-0.828071\pi$
$29$		−	5.53862i		−	1.02850i	0.857642	−	0.514248i	$-0.171929\pi$
$30$	3.06057	−	0.250679i	0.558780	−	0.0457675i
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	0.0680129	+	0.997684i	$0.478334\pi$
$32$	0.130843	+	5.65534i	0.0231301	+	0.999732i
$33$	−6.34643	−	6.03996i	−1.10477	−	1.05142i
$34$	−5.51053	+	6.17729i	−0.945048	+	1.05940i
$35$		0			0
$36$	2.11450	−	5.61506i	0.352416	−	0.935843i
$37$	2.66908	−	4.62298i	0.438794	−	0.760013i	−0.558803	−	0.829301i	$-0.688739\pi$
$37$	2.66908	−	4.62298i	0.438794	−	0.760013i	0.997597	+	0.0692872i	$0.0220725\pi$
$38$	−2.12096	−	0.440578i	−0.344065	−	0.0714713i
$39$	−7.34017	+	2.16275i	−1.17537	+	0.346317i
$40$	3.21899	−	1.48705i	0.508966	−	0.235124i
$41$			1.97938i			0.309127i	0.987983	+	0.154564i	$0.0493971\pi$
$41$			1.97938i			0.309127i	−0.987983	+	0.154564i	$0.950603\pi$
$42$		0			0
$43$			3.18613i			0.485881i	0.970041	+	0.242940i	$0.0781119\pi$
$43$			3.18613i			0.485881i	−0.970041	+	0.242940i	$0.921888\pi$
$44$	−9.27960	−	4.02908i	−1.39895	−	0.607407i
$45$	−3.75636	+	0.185997i	−0.559965	+	0.0277268i
$46$	0.0901918	−	0.434187i	0.0132981	−	0.0640174i
$47$	−5.74813	+	9.95606i	−0.838451	+	1.45224i	0.0527378	+	0.998608i	$0.483205\pi$
$47$	−5.74813	+	9.95606i	−0.838451	+	1.45224i	−0.891189	+	0.453632i	$0.850128\pi$
$48$	0.0631619	−	6.92792i	0.00911663	−	0.999958i
$49$		0			0
$50$	3.61805	+	3.22752i	0.511669	+	0.456440i
$51$	6.98942	−	7.34407i	0.978715	−	1.02838i
$52$	−7.10008	+	5.25957i	−0.984604	+	0.729371i
$53$	11.0767	−	6.39513i	1.52150	−	0.878439i	0.521823	−	0.853054i	$-0.325252\pi$
$53$	11.0767	−	6.39513i	1.52150	−	0.878439i	0.999678	−	0.0253856i	$-0.00808135\pi$
$54$	−2.81011	+	6.78994i	−0.382407	+	0.923994i
$55$			6.34133i			0.855064i
$56$		0			0
$57$	2.57889	+	0.623072i	0.341582	+	0.0825279i
$58$	2.45490	+	7.43815i	0.322345	+	0.976677i
$59$	−3.98351	−	6.89964i	−0.518608	−	0.898256i	−0.999766	−	0.0216222i	$-0.993117\pi$
$59$	−3.98351	−	6.89964i	−0.518608	−	0.898256i	0.481158	−	0.876634i	$-0.340216\pi$
$60$	−3.99911	+	1.69320i	−0.516283	+	0.218591i
$61$	−0.151445	+	0.262310i	−0.0193905	+	0.0335853i	−0.875558	−	0.483113i	$-0.839506\pi$
$61$	−0.151445	+	0.262310i	−0.0193905	+	0.0335853i	0.856167	+	0.516699i	$0.172839\pi$
$62$	4.61200	−	5.17005i	0.585725	−	0.656597i
$63$		0			0
$64$	−2.68236	−	7.53691i	−0.335295	−	0.942113i
$65$	4.79659	+	2.76931i	0.594943	+	0.343491i
$66$	11.2001	+	5.29848i	1.37864	+	0.652198i
$67$	9.13122	−	5.27191i	1.11556	−	0.644067i	0.175293	−	0.984516i	$-0.443913\pi$
$67$	9.13122	−	5.27191i	1.11556	−	0.644067i	0.940263	+	0.340450i	$0.110579\pi$
$68$	4.66244	−	10.7383i	0.565403	−	1.30221i
$69$	−0.127550	+	0.527930i	−0.0153553	+	0.0635553i
$70$		0			0
$71$	4.53490			0.538194			0.269097	−	0.963113i	$-0.413275\pi$
$71$	4.53490			0.538194			0.269097	+	0.963113i	$0.413275\pi$
$72$	−0.350899	+	8.47802i	−0.0413539	+	0.999145i
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	0.904435	−	0.426612i	$-0.140293\pi$
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	−0.821674	+	0.569958i	$0.806960\pi$
$74$	−1.53541	+	7.39151i	−0.178487	+	0.859245i
$75$	−4.30143	−	4.09371i	−0.496686	−	0.472701i
$76$	3.04365	−	0.348402i	0.349130	−	0.0399645i
$77$		0			0
$78$	8.89896	−	6.15790i	1.00761	−	0.697245i
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	0.122936	−	0.992415i	$-0.460769\pi$
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	−0.797988	+	0.602673i	$0.794102\pi$
$80$	−3.66386	+	3.42382i	−0.409632	+	0.382795i
$81$	3.70801	−	8.20065i	0.412001	−	0.911183i
$82$	−0.877328	−	2.65823i	−0.0968847	−	0.293552i
$83$	−6.78340			−0.744575			−0.372287	−	0.928118i	$-0.621426\pi$
$83$	−6.78340			−0.744575			−0.372287	+	0.928118i	$0.621426\pi$
$84$		0			0
$85$	−7.33816			−0.795935
$86$	−1.41220	−	4.27885i	−0.152282	−	0.461400i
$87$	−2.71134	−	9.20204i	−0.290686	−	0.986563i
$88$	14.2480	+	1.29786i	1.51884	+	0.138353i
$89$	4.15480	+	2.39878i	0.440408	+	0.254270i	0.703771	−	0.710427i	$-0.251498\pi$
$89$	4.15480	+	2.39878i	0.440408	+	0.254270i	−0.263363	+	0.964697i	$0.584832\pi$
$90$	4.96221	−	1.91473i	0.523063	−	0.201831i
$91$		0			0
$92$	0.0713222	+	0.623072i	0.00743586	+	0.0649597i
$93$	−5.84975	+	6.14657i	−0.606591	+	0.637370i
$94$	3.30666	−	15.9184i	0.341055	−	1.64185i
$95$	−0.960150	−	1.66303i	−0.0985093	−	0.170623i
$96$	2.98586	+	9.33191i	0.304743	+	0.952435i
$97$	13.6844			1.38944			0.694719	−	0.719281i	$-0.255529\pi$
$97$	13.6844			1.38944			0.694719	+	0.719281i	$0.255529\pi$
$98$		0			0
$99$	−13.5009	−	6.92820i	−1.35689	−	0.696311i
$100$	−6.28944	−	2.73079i	−0.628944	−	0.273079i
$101$	3.52631	−	2.03591i	0.350881	−	0.202581i	−0.314192	−	0.949359i	$-0.601734\pi$
$101$	3.52631	−	2.03591i	0.350881	−	0.202581i	0.665073	+	0.746778i	$0.268400\pi$
$102$	−6.13138	+	12.9607i	−0.607097	+	1.28330i
$103$	11.3239	+	6.53788i	1.11578	+	0.644197i	0.940321	−	0.340290i	$-0.110525\pi$
$103$	11.3239	+	6.53788i	1.11578	+	0.644197i	0.175461	+	0.984486i	$0.443859\pi$
$104$	7.20391	−	10.2104i	0.706402	−	1.00121i
$105$		0			0
$106$	−12.0410	+	13.4980i	−1.16953	+	1.31104i
$107$	−1.95388	+	3.38422i	−0.188889	+	0.327165i	−0.944880	−	0.327417i	$-0.893822\pi$
$107$	−1.95388	+	3.38422i	−0.188889	+	0.327165i	0.755991	+	0.654582i	$0.227155\pi$
$108$	0.764334	−	10.3642i	0.0735481	−	0.997292i
$109$	4.12398	+	7.14295i	0.395006	+	0.684170i	0.993102	−	0.117254i	$-0.0374092\pi$
$109$	4.12398	+	7.14295i	0.395006	+	0.684170i	−0.598096	+	0.801424i	$0.704076\pi$
$110$	−2.81069	−	8.51615i	−0.267989	−	0.811983i
$111$	2.17139	−	8.98737i	0.206100	−	0.853044i
$112$		0			0
$113$		−	6.72485i		−	0.632621i	−0.948656	−	0.316311i	$-0.897556\pi$
$113$		−	6.72485i		−	0.632621i	0.948656	−	0.316311i	$-0.102444\pi$
$114$	−3.73951	+	0.306289i	−0.350237	+	0.0286866i
$115$	0.340442	−	0.196554i	0.0317464	−	0.0183288i
$116$	−6.59368	−	8.90105i	−0.612208	−	0.826442i
$117$	−11.1365	+	7.18651i	−1.02957	+	0.664393i
$118$	8.40785	+	7.50032i	0.774005	+	0.690460i
$119$		0			0
$120$	4.62016	−	4.04644i	0.421761	−	0.369388i
$121$	−7.29306	+	12.6320i	−0.663006	+	1.14836i
$122$	0.0871196	−	0.419397i	0.00788744	−	0.0379704i
$123$	0.968971	+	3.28861i	0.0873692	+	0.296524i
$124$	−3.90220	+	8.98737i	−0.350428	+	0.807090i
$125$			10.5662i			0.945073i
$126$		0			0
$127$			8.50404i			0.754611i	0.926089	+	0.377306i	$0.123149\pi$
$127$			8.50404i			0.754611i	−0.926089	+	0.377306i	$0.876851\pi$
$128$	6.94291	+	8.93286i	0.613672	+	0.789561i
$129$	1.55972	+	5.29354i	0.137325	+	0.466070i
$130$	−7.66908	−	1.59307i	−0.672623	−	0.139721i
$131$	−4.20524	+	7.28368i	−0.367413	+	0.636378i	−0.989160	−	0.146840i	$-0.953090\pi$
$131$	−4.20524	+	7.28368i	−0.367413	+	0.636378i	0.621747	+	0.783218i	$0.286423\pi$
$132$	−17.3898	−	2.15138i	−1.51359	−	0.187253i
$133$		0			0
$134$	−9.92618	+	11.1272i	−0.857491	+	0.961247i
$135$	−6.14989	+	2.14788i	−0.529298	+	0.184860i
$136$	−1.50188	+	16.4877i	−0.128785	+	1.41381i
$137$	−11.9136	+	6.87834i	−1.01785	+	0.587657i	−0.913481	−	0.406882i	$-0.866616\pi$
$137$	−11.9136	+	6.87834i	−1.01785	+	0.587657i	−0.104370	+	0.994539i	$0.533283\pi$
$138$	−0.0627011	−	0.765524i	−0.00533747	−	0.0651657i
$139$			13.1652i			1.11666i	0.829620	+	0.558328i	$0.188557\pi$
$139$			13.1652i			1.11666i	−0.829620	+	0.558328i	$0.811443\pi$
$140$		0			0
$141$	−4.67632	+	19.3552i	−0.393817	+	1.63000i
$142$	−6.09019	+	2.01002i	−0.511078	+	0.168677i
$143$	11.1737	+	19.3534i	0.934389	+	1.61841i
$144$	−3.28650	−	11.5412i	−0.273875	−	0.961765i
$145$	−3.47176	+	6.01326i	−0.288314	+	0.499374i
$146$	−1.49247	−	1.33137i	−0.123517	−	0.110185i
$147$		0			0
$148$	−1.21417	−	10.6071i	−0.0998046	−	0.871894i
$149$	9.78354	+	5.64853i	0.801499	+	0.462745i	0.843995	−	0.536351i	$-0.180198\pi$
$149$	9.78354	+	5.64853i	0.801499	+	0.462745i	−0.0424963	+	0.999097i	$0.513531\pi$
$150$	7.59112	+	3.59116i	0.619812	+	0.293217i
$151$	−9.61268	+	5.54988i	−0.782269	+	0.451643i	−0.837234	−	0.546845i	$-0.815829\pi$
$151$	−9.61268	+	5.54988i	−0.782269	+	0.451643i	0.0549650	+	0.998488i	$0.482495\pi$
$152$	−3.93307	+	1.81694i	−0.319015	+	0.147373i
$153$	8.01729	−	15.6232i	0.648159	−	1.26306i
$154$		0			0
$155$	6.14163			0.493307
$156$	−9.22157	+	12.2141i	−0.738317	+	0.977914i
$157$	−7.39785	−	12.8135i	−0.590413	−	1.02262i	−0.994177	−	0.107762i	$-0.965632\pi$
$157$	−7.39785	−	12.8135i	−0.590413	−	1.02262i	0.403764	−	0.914863i	$-0.367702\pi$
$158$	9.59317	+	1.99275i	0.763192	+	0.158535i
$159$	15.2726	−	16.0475i	1.21119	−	1.27265i
$160$	3.40287	−	6.22200i	0.269020	−	0.491892i
$161$		0			0
$162$	−1.34491	+	12.6567i	−0.105666	+	0.994402i
$163$	11.4887	+	6.63300i	0.899864	+	0.519537i	0.877156	−	0.480205i	$-0.159438\pi$
$163$	11.4887	+	6.63300i	0.899864	+	0.519537i	0.0227080	+	0.999742i	$0.492771\pi$
$164$	2.35643	+	3.18104i	0.184007	+	0.248397i
$165$	3.10429	+	10.5357i	0.241668	+	0.820202i
$166$	9.10984	−	3.00663i	0.707060	−	0.233360i
$167$	−4.78624			−0.370371			−0.185185	−	0.982704i	$-0.559289\pi$
$167$	−4.78624			−0.370371			−0.185185	+	0.982704i	$0.559289\pi$
$168$		0			0
$169$	6.51854			0.501426
$170$	9.85486	−	3.25252i	0.755833	−	0.249457i
$171$	4.58966	−	0.227258i	0.350980	−	0.0173789i
$172$	3.79306	+	5.12039i	0.289218	+	0.390426i
$173$	12.4811	+	7.20596i	0.948920	+	0.547859i	0.892745	−	0.450562i	$-0.148776\pi$
$173$	12.4811	+	7.20596i	0.948920	+	0.547859i	0.0561749	+	0.998421i	$0.482110\pi$
$174$	7.71988	+	11.1562i	0.585242	+	0.845751i
$175$		0			0
$176$	−19.7097	+	4.57220i	−1.48568	+	0.344643i
$177$	−9.99593	−	9.51322i	−0.751340	−	0.715058i
$178$	−6.64296	−	1.37991i	−0.497911	−	0.103429i
$179$	−0.347150	−	0.601281i	−0.0259472	−	0.0449419i	0.852760	−	0.522303i	$-0.174927\pi$
$179$	−0.347150	−	0.601281i	−0.0259472	−	0.0449419i	−0.878707	+	0.477361i	$0.841594\pi$
$180$	−5.81537	+	4.77083i	−0.433452	+	0.355597i
$181$	−6.31042			−0.469050			−0.234525	−	0.972110i	$-0.575353\pi$
$181$	−6.31042			−0.469050			−0.234525	+	0.972110i	$0.575353\pi$
$182$		0			0
$183$	−0.123206	+	0.509947i	−0.00910763	+	0.0376964i
$184$	−0.371950	−	0.805149i	−0.0274205	−	0.0593564i
$185$	−5.79562	+	3.34610i	−0.426103	+	0.246010i
$186$	5.13162	−	10.8474i	0.376269	−	0.795371i
$187$	−25.6414	−	14.8041i	−1.87509	−	1.08258i
$188$	2.61485	+	22.8434i	0.190707	+	1.66602i
$189$		0			0
$190$	2.02655	+	1.80781i	0.147022	+	0.131152i
$191$	−1.95388	+	3.38422i	−0.141378	+	0.244873i	−0.928016	−	0.372541i	$-0.878487\pi$
$191$	−1.95388	+	3.38422i	−0.141378	+	0.244873i	0.786638	+	0.617415i	$0.211820\pi$
$192$	−8.14612	−	11.2090i	−0.587895	−	0.808937i
$193$	−0.785825	−	1.36109i	−0.0565649	−	0.0979733i	0.836356	−	0.548186i	$-0.184681\pi$
$193$	−0.785825	−	1.36109i	−0.0565649	−	0.0979733i	−0.892921	+	0.450213i	$0.851348\pi$
$194$	−18.3776	+	6.06538i	−1.31943	+	0.435469i
$195$	9.32487	+	2.25294i	0.667768	+	0.161336i
$196$		0			0
$197$		−	1.83285i		−	0.130585i	−0.997866	−	0.0652924i	$-0.979202\pi$
$197$		−	1.83285i		−	0.130585i	0.997866	−	0.0652924i	$-0.0207980\pi$
$198$	21.2020	+	3.32024i	1.50676	+	0.235959i
$199$	−3.17910	+	1.83546i	−0.225361	+	0.130112i	−0.608430	−	0.793608i	$-0.708200\pi$
$199$	−3.17910	+	1.83546i	−0.225361	+	0.130112i	0.383069	+	0.923720i	$0.374867\pi$
$200$	9.65686	+	0.879654i	0.682843	+	0.0622010i
$201$	12.5901	−	13.2290i	0.888039	−	0.933099i
$202$	−3.83331	+	4.29713i	−0.269710	+	0.302345i
$203$		0			0
$204$	2.48956	−	20.1234i	0.174304	−	1.40892i
$205$	1.24073	−	2.14901i	0.0866563	−	0.150093i
$206$	−18.1054	−	3.76096i	−1.26146	−	0.262039i
$207$	0.0465225	+	0.939560i	0.00323354	+	0.0653039i
$208$	−5.14898	+	16.9052i	−0.357018	+	1.17216i
$209$		−	7.74807i		−	0.535945i
$210$		0			0
$211$		−	14.8763i		−	1.02413i	−0.858948	−	0.512063i	$-0.828881\pi$
$211$		−	14.8763i		−	1.02413i	0.858948	−	0.512063i	$-0.171119\pi$
$212$	10.1879	−	23.4642i	0.699706	−	1.61153i
$213$	7.53443	−	2.21998i	0.516251	−	0.152111i
$214$	1.12398	−	5.41090i	0.0768339	−	0.369881i
$215$	1.99715	−	3.45917i	0.136205	−	0.235914i
$216$	3.56728	+	14.2574i	0.242722	+	0.970096i
$217$		0			0
$218$	−8.70434	−	7.76481i	−0.589533	−	0.525899i
$219$	1.77436	+	1.68868i	0.119900	+	0.114110i
$220$	7.54930	+	10.1911i	0.508973	+	0.687082i
$221$	−22.3956	+	12.9301i	−1.50649	+	0.869775i
$222$	1.06741	+	13.0321i	0.0716399	+	0.874659i
$223$		−	19.4171i		−	1.30026i	−0.759821	−	0.650132i	$-0.774713\pi$
$223$		−	19.4171i		−	1.30026i	0.759821	−	0.650132i	$-0.225287\pi$
$224$		0			0
$225$	−9.15054	−	4.69573i	−0.610036	−	0.313049i
$226$	2.98068	+	9.03122i	0.198272	+	0.600748i
$227$	5.34136	+	9.25151i	0.354519	+	0.614045i	0.987035	−	0.160502i	$-0.0513114\pi$
$227$	5.34136	+	9.25151i	0.354519	+	0.614045i	−0.632517	+	0.774547i	$0.717978\pi$
$228$	4.88626	−	2.06881i	0.323600	−	0.137010i
$229$	3.75075	−	6.49650i	0.247857	−	0.429301i	−0.715074	−	0.699049i	$-0.753607\pi$
$229$	3.75075	−	6.49650i	0.247857	−	0.429301i	0.962931	+	0.269748i	$0.0869404\pi$
$230$	−0.370081	+	0.414861i	−0.0244024	+	0.0273551i
$231$		0			0
$232$	12.8003	+	9.03122i	0.840381	+	0.592928i
$233$	−2.42423	−	1.39963i	−0.158817	−	0.0916930i	0.418485	−	0.908224i	$-0.362561\pi$
$233$	−2.42423	−	1.39963i	−0.158817	−	0.0916930i	−0.577302	+	0.816531i	$0.695895\pi$
$234$	11.7705	−	14.5873i	0.769464	−	0.953599i
$235$	12.4815	−	7.20617i	0.814201	−	0.470079i
$236$	−14.6158	−	6.34599i	−0.951408	−	0.413089i
$237$	−11.6644	−	2.81817i	−0.757683	−	0.183060i
$238$		0			0
$239$	20.5467			1.32905			0.664527	−	0.747265i	$-0.268633\pi$
$239$	20.5467			1.32905			0.664527	+	0.747265i	$0.268633\pi$
$240$	−4.41118	+	7.48202i	−0.284741	+	0.482963i
$241$	9.02728	+	15.6357i	0.581499	+	1.00718i	0.995302	+	0.0968188i	$0.0308667\pi$
$241$	9.02728	+	15.6357i	0.581499	+	1.00718i	−0.413804	+	0.910366i	$0.635800\pi$
$242$	4.19539	−	20.1968i	0.269690	−	1.29830i
$243$	2.14612	−	15.4400i	0.137674	−	0.990478i
$244$	0.0688928	+	0.601848i	0.00441041	+	0.0385294i
$245$		0			0
$246$	−2.75891	−	3.98699i	−0.175902	−	0.254201i
$247$	−5.86064	−	3.38364i	−0.372904	−	0.215296i
$248$	1.25699	−	13.7993i	0.0798191	−	0.876255i
$249$	−11.2702	+	3.32070i	−0.714217	+	0.210441i
$250$	−4.68332	−	14.1900i	−0.296199	−	0.897457i
$251$	10.4810			0.661555			0.330777	−	0.943709i	$-0.392689\pi$
$251$	10.4810			0.661555			0.330777	+	0.943709i	$0.392689\pi$
$252$		0			0
$253$	1.58612			0.0997188
$254$	−3.76928	−	11.4206i	−0.236505	−	0.716591i
$255$	−12.1919	+	3.59227i	−0.763483	+	0.224957i
$256$	−13.2834	−	8.91915i	−0.830213	−	0.557447i
$257$	7.24060	+	4.18036i	0.451656	+	0.260764i	0.708529	−	0.705681i	$-0.249359\pi$
$257$	7.24060	+	4.18036i	0.451656	+	0.260764i	−0.256873	+	0.966445i	$0.582692\pi$
$258$	−4.44091	−	6.41770i	−0.276479	−	0.399549i
$259$		0			0
$260$	11.0054	−	1.25977i	0.682524	−	0.0781277i
$261$	−9.00941	−	13.9613i	−0.557668	−	0.864182i
$262$	2.41909	−	11.6456i	0.149452	−	0.719468i
$263$	14.6850	+	25.4352i	0.905517	+	1.56840i	0.820221	+	0.572046i	$0.193850\pi$
$263$	14.6850	+	25.4352i	0.905517	+	1.56840i	0.0852962	+	0.996356i	$0.472816\pi$
$264$	24.3074	−	4.81853i	1.49602	−	0.296560i
$265$	−16.0346			−0.984996
$266$		0			0
$267$	8.07720	+	1.95149i	0.494317	+	0.119429i
$268$	8.39850	−	19.3431i	0.513020	−	1.18157i
$269$	−17.6649	+	10.1988i	−1.07705	+	0.621834i	−0.930099	−	0.367310i	$-0.880279\pi$
$269$	−17.6649	+	10.1988i	−1.07705	+	0.621834i	−0.146950	+	0.989144i	$0.546946\pi$
$270$	7.30705	−	5.61036i	0.444693	−	0.341436i
$271$	17.8370	+	10.2982i	1.08352	+	0.625572i	0.931844	−	0.362858i	$-0.118199\pi$
$271$	17.8370	+	10.2982i	1.08352	+	0.625572i	0.151678	+	0.988430i	$0.451532\pi$
$272$	−5.29093	−	22.8080i	−0.320810	−	1.38294i
$273$		0			0
$274$	12.9508	−	14.5179i	0.782389	−	0.877057i
$275$	−8.67076	+	15.0182i	−0.522867	+	0.905632i
$276$	0.423511	+	1.00028i	0.0254924	+	0.0602096i
$277$	1.97345	+	3.41811i	0.118573	+	0.205374i	0.919202	−	0.393786i	$-0.128835\pi$
$277$	1.97345	+	3.41811i	0.118573	+	0.205374i	−0.800629	+	0.599160i	$0.795501\pi$
$278$	−5.83525	−	17.6803i	−0.349975	−	1.06039i
$279$	−6.71002	+	13.0758i	−0.401719	+	0.782825i
$280$		0			0
$281$		−	1.18623i		−	0.0707648i	−0.999374	−	0.0353824i	$-0.988735\pi$
$281$		−	1.18623i		−	0.0707648i	0.999374	−	0.0353824i	$-0.0112649\pi$
$282$	−2.29878	−	28.0660i	−0.136890	−	1.67131i
$283$	23.9744	−	13.8416i	1.42513	−	0.822800i	0.428401	−	0.903589i	$-0.359077\pi$
$283$	23.9744	−	13.8416i	1.42513	−	0.822800i	0.996731	+	0.0807885i	$0.0257438\pi$
$284$	7.28798	−	5.39876i	0.432462	−	0.320357i
$285$	−2.40933	−	2.29298i	−0.142716	−	0.135825i
$286$	−23.5839	−	21.0383i	−1.39454	−	1.24402i
$287$		0			0
$288$	9.52909	+	14.0427i	0.561507	+	0.827472i
$289$	8.63122	−	14.9497i	0.507719	−	0.879395i
$290$	1.99715	−	9.61438i	0.117277	−	0.564576i
$291$	22.7357	−	6.69895i	1.33279	−	0.392700i
$292$	2.59443	+	1.12647i	0.151828	+	0.0659215i
$293$			0.197795i			0.0115553i	0.999983	+	0.00577765i	$0.00183909\pi$
$293$			0.197795i			0.0115553i	−0.999983	+	0.00577765i	$0.998161\pi$
$294$		0			0
$295$			9.98789i			0.581517i
$296$	6.33199	+	13.7067i	0.368040	+	0.796685i
$297$	−25.8225	−	4.90159i	−1.49837	−	0.284419i
$298$	−15.6425	−	3.24936i	−0.906147	−	0.188230i
$299$	0.692674	−	1.19975i	0.0400584	−	0.0693831i
$300$	−11.7863	−	1.45814i	−0.680482	−	0.0841857i
$301$		0			0
$302$	10.4496	−	11.7139i	0.601304	−	0.674061i
$303$	4.86207	−	5.10878i	0.279319	−	0.293492i
$304$	4.47664	−	4.18335i	0.256753	−	0.239931i
$305$	0.328846	−	0.189859i	0.0188297	−	0.0108713i
$306$	−3.84216	+	24.5349i	−0.219642	+	1.40257i
$307$		−	16.6218i		−	0.948657i	−0.880348	−	0.474328i	$-0.842691\pi$
$307$		−	16.6218i		−	0.948657i	0.880348	−	0.474328i	$-0.157309\pi$
$308$		0			0
$309$	22.0145	+	5.31881i	1.25236	+	0.302576i
$310$	−8.24797	+	2.72218i	−0.468453	+	0.154609i
$311$	−5.37805	−	9.31506i	−0.304961	−	0.528209i	0.672291	−	0.740287i	$-0.265310\pi$
$311$	−5.37805	−	9.31506i	−0.304961	−	0.528209i	−0.977253	+	0.212078i	$0.931977\pi$
$312$	6.97049	−	20.4904i	0.394626	−	1.16004i
$313$	2.47200	−	4.28163i	0.139726	−	0.242012i	−0.787667	−	0.616101i	$-0.788711\pi$
$313$	2.47200	−	4.28163i	0.139726	−	0.242012i	0.927393	+	0.374089i	$0.122045\pi$
$314$	15.6144	+	13.9290i	0.881170	+	0.786058i
$315$		0			0
$316$	−13.7665	+	1.57583i	−0.774427	+	0.0886476i
$317$	−18.9960	−	10.9673i	−1.06692	−	0.615987i	−0.139582	−	0.990211i	$-0.544576\pi$
$317$	−18.9960	−	10.9673i	−1.06692	−	0.615987i	−0.927338	+	0.374224i	$0.877909\pi$
$318$	−13.3977	+	28.3205i	−0.751303	+	1.58813i
$319$	−24.2624	+	14.0079i	−1.35844	+	0.784293i
$320$	−1.81211	+	9.86417i	−0.101300	+	0.551424i
$321$	−1.58955	+	6.57914i	−0.0887202	+	0.367212i
$322$		0			0
$323$	8.96603			0.498883
$324$	−3.80371	−	17.5935i	−0.211317	−	0.977418i
$325$	7.57319	+	13.1171i	0.420085	+	0.727609i
$326$	−18.3688	−	3.81568i	−1.01736	−	0.211331i
$327$	10.3484	+	9.84870i	0.572269	+	0.544634i
$328$	−4.57454	−	3.22756i	−0.252587	−	0.178212i
$329$		0			0
$330$	−8.83871	−	12.7731i	−0.486555	−	0.703135i
$331$	−3.24073	−	1.87104i	−0.178127	−	0.102841i	0.408286	−	0.912854i	$-0.366127\pi$
$331$	−3.24073	−	1.87104i	−0.178127	−	0.102841i	−0.586412	+	0.810013i	$0.699460\pi$
$332$	−10.9015	+	8.07558i	−0.598298	+	0.443205i
$333$	−0.791990	−	15.9949i	−0.0434008	−	0.876514i
$334$	6.42774	−	2.12142i	0.351710	−	0.116079i
$335$	−13.2183			−0.722194
$336$		0			0
$337$	22.9774			1.25166			0.625829	−	0.779960i	$-0.284761\pi$
$337$	22.9774			1.25166			0.625829	+	0.779960i	$0.284761\pi$
$338$	−8.75415	+	2.88924i	−0.476163	+	0.157154i
$339$	−3.29204	−	11.1729i	−0.178799	−	0.606828i
$340$	−11.7931	+	8.73601i	−0.639569	+	0.473777i
$341$	21.4604	+	12.3902i	1.16215	+	0.670966i
$342$	−6.06301	+	2.33949i	−0.327850	+	0.126505i
$343$		0			0
$344$	−7.36347	−	5.19527i	−0.397011	−	0.280110i
$345$	0.469402	−	0.493220i	0.0252718	−	0.0265541i
$346$	−19.9556	−	4.14528i	−1.07282	−	0.222852i
$347$	1.06505	+	1.84472i	0.0571750	+	0.0990299i	0.893196	−	0.449667i	$-0.148457\pi$
$347$	1.06505	+	1.84472i	0.0571750	+	0.0990299i	−0.836021	+	0.548697i	$0.815124\pi$
$348$	−15.3123	−	11.5607i	−0.820826	−	0.619717i
$349$	3.55710			0.190407			0.0952036	−	0.995458i	$-0.469650\pi$
$349$	3.55710			0.190407			0.0952036	+	0.995458i	$0.469650\pi$
$350$		0			0
$351$	−14.9845	+	17.3916i	−0.799811	+	0.928293i
$352$	24.4428	−	14.8763i	1.30281	−	0.792909i
$353$	16.3912	−	9.46348i	0.872417	−	0.503690i	0.00426642	−	0.999991i	$-0.498642\pi$
$353$	16.3912	−	9.46348i	0.872417	−	0.503690i	0.868151	+	0.496301i	$0.165309\pi$
$354$	17.6407	+	8.34535i	0.937594	+	0.443550i
$355$	−4.92353	−	2.84260i	−0.261314	−	0.150869i
$356$	9.53285	−	1.09121i	0.505240	−	0.0578342i
$357$		0			0
$358$	0.732717	+	0.653628i	0.0387253	+	0.0345453i
$359$	0.613000	−	1.06175i	0.0323529	−	0.0560369i	−0.849396	−	0.527757i	$-0.823033\pi$
$359$	0.613000	−	1.06175i	0.0323529	−	0.0560369i	0.881748	+	0.471720i	$0.156367\pi$
$360$	5.69523	−	8.98461i	0.300165	−	0.473530i
$361$	−8.32685	−	14.4225i	−0.438255	−	0.759081i
$362$	8.47465	−	2.79699i	0.445418	−	0.147007i
$363$	−5.93317	+	24.5573i	−0.311411	+	1.28893i
$364$		0			0
$365$		−	1.77294i		−	0.0927997i
$366$	−0.0605653	−	0.739448i	−0.00316580	−	0.0386516i
$367$	−17.4966	+	10.1017i	−0.913314	+	0.527302i	−0.881496	−	0.472192i	$-0.843463\pi$
$367$	−17.4966	+	10.1017i	−0.913314	+	0.527302i	−0.0318180	+	0.999494i	$0.510130\pi$
$368$	0.856383	+	0.916423i	0.0446420	+	0.0477718i
$369$	3.21976	+	4.98945i	0.167614	+	0.259740i
$370$	6.30019	−	7.06250i	0.327531	−	0.367162i
$371$		0			0
$372$	−2.08363	+	16.8422i	−0.108031	+	0.873226i
$373$	4.09019	−	7.08442i	0.211782	−	0.366817i	−0.740490	−	0.672067i	$-0.765407\pi$
$373$	4.09019	−	7.08442i	0.211782	−	0.366817i	0.952272	+	0.305250i	$0.0987400\pi$
$374$	40.9971	+	8.51615i	2.11991	+	0.440360i
$375$	5.17252	+	17.5551i	0.267108	+	0.906541i
$376$	−13.6366	−	29.5187i	−0.703253	−	1.52231i
$377$			24.4695i			1.26024i
$378$		0			0
$379$		−	31.2020i		−	1.60274i	−0.598170	−	0.801369i	$-0.704105\pi$
$379$		−	31.2020i		−	1.60274i	0.598170	−	0.801369i	$-0.295895\pi$
$380$	−3.52287	−	1.52958i	−0.180719	−	0.0784659i
$381$	4.16301	+	14.1289i	0.213277	+	0.723845i
$382$	1.12398	−	5.41090i	0.0575080	−	0.276846i
$383$	12.2089	−	21.1465i	0.623848	−	1.08054i	−0.364915	−	0.931041i	$-0.618902\pi$
$383$	12.2089	−	21.1465i	0.623848	−	1.08054i	0.988763	−	0.149495i	$-0.0477647\pi$
$384$	15.9081	+	11.4426i	0.811807	+	0.583926i
$385$		0			0
$386$	1.65861	+	1.47958i	0.0844212	+	0.0753089i
$387$	5.18273	+	8.03133i	0.263453	+	0.408255i
$388$	21.9920	−	16.2911i	1.11647	−	0.827057i
$389$	7.86740	−	4.54225i	0.398893	−	0.230301i	−0.287113	−	0.957897i	$-0.592696\pi$
$389$	7.86740	−	4.54225i	0.398893	−	0.230301i	0.686006	+	0.727596i	$0.259362\pi$
$390$	−13.5215	+	1.10750i	−0.684688	+	0.0560802i
$391$			1.83546i			0.0928230i
$392$		0			0
$393$	−3.42111	+	14.1599i	−0.172572	+	0.714275i
$394$	0.812379	+	2.46144i	0.0409271	+	0.124006i
$395$	4.34279	+	7.52193i	0.218509	+	0.378469i
$396$	−29.9451	+	4.93851i	−1.50480	+	0.248170i
$397$	11.6405	−	20.1619i	0.584220	−	1.01190i	−0.410753	−	0.911747i	$-0.634734\pi$
$397$	11.6405	−	20.1619i	0.584220	−	1.01190i	0.994972	−	0.100151i	$-0.0319326\pi$
$398$	3.45588	−	3.87403i	0.173227	−	0.194188i
$399$		0			0
$400$	−13.3587	+	3.09890i	−0.667934	+	0.154945i
$401$	6.57424	+	3.79564i	0.328302	+	0.189545i	0.655087	−	0.755553i	$-0.272632\pi$
$401$	6.57424	+	3.79564i	0.328302	+	0.189545i	−0.326785	+	0.945099i	$0.605965\pi$
$402$	−11.0445	+	23.3463i	−0.550851	+	1.16441i
$403$	18.7439	−	10.8218i	0.933700	−	0.539072i
$404$	3.24335	−	7.46993i	0.161362	−	0.371643i
$405$	−9.16617	+	6.57914i	−0.455470	+	0.326920i
$406$		0			0
$407$	−27.0019			−1.33843
$408$	5.57599	+	28.1284i	0.276053	+	1.39256i
$409$	−3.19509	−	5.53406i	−0.157987	−	0.273642i	0.776156	−	0.630541i	$-0.217167\pi$
$409$	−3.19509	−	5.53406i	−0.157987	−	0.273642i	−0.934143	+	0.356900i	$0.883834\pi$
$410$	−0.713738	+	3.43596i	−0.0352490	+	0.169690i
$411$	−16.4265	+	17.2600i	−0.810261	+	0.851374i
$412$	25.9819	−	2.97411i	1.28003	−	0.146524i
$413$		0			0
$414$	−0.478923	−	1.24117i	−0.0235378	−	0.0610003i
$415$	7.36471	+	4.25202i	0.361520	+	0.208723i
$416$	−0.578064	−	24.9852i	−0.0283419	−	1.22500i
$417$	6.44479	+	21.8731i	0.315603	+	1.07113i
$418$	3.43421	+	10.4054i	0.167972	+	0.508942i
$419$	−29.1307			−1.42313			−0.711565	−	0.702620i	$-0.752013\pi$
$419$	−29.1307			−1.42313			−0.711565	+	0.702620i	$0.752013\pi$
$420$		0			0
$421$	−32.0821			−1.56358			−0.781792	−	0.623539i	$-0.785694\pi$
$421$	−32.0821			−1.56358			−0.781792	+	0.623539i	$0.785694\pi$
$422$	6.59368	+	19.9783i	0.320975	+	0.972528i
$423$	1.70563	+	34.4466i	0.0829306	+	1.67485i
$424$	−3.28176	+	36.0272i	−0.159376	+	1.74963i
$425$	−17.3790	−	10.0338i	−0.843006	−	0.486710i
$426$	−9.13447	+	6.32086i	−0.442567	+	0.306247i
$427$		0			0
$428$	0.888828	+	7.76481i	0.0429631	+	0.375326i
$429$	28.0384	+	26.6844i	1.35371	+	1.28834i
$430$	−1.14888	+	5.53074i	−0.0554038	+	0.266716i
$431$	−9.12282	−	15.8012i	−0.439431	−	0.761116i	0.558215	−	0.829696i	$-0.311486\pi$
$431$	−9.12282	−	15.8012i	−0.439431	−	0.761116i	−0.997646	+	0.0685802i	$0.978153\pi$
$432$	−11.1101	−	17.5660i	−0.534534	−	0.845147i
$433$	−4.84842			−0.233000			−0.116500	−	0.993191i	$-0.537168\pi$
$433$	−4.84842			−0.233000			−0.116500	+	0.993191i	$0.537168\pi$
$434$		0			0
$435$	−2.82440	+	11.6902i	−0.135420	+	0.560501i
$436$	15.1312	+	6.56978i	0.724654	+	0.314635i
$437$	−0.415965	+	0.240157i	−0.0198983	+	0.0114883i
$438$	−3.13138	−	1.48137i	−0.149623	−	0.0707827i
$439$	−17.5388	−	10.1260i	−0.837081	−	0.483289i	0.0191902	−	0.999816i	$-0.493891\pi$
$439$	−17.5388	−	10.1260i	−0.837081	−	0.483289i	−0.856271	+	0.516527i	$0.827225\pi$
$440$	−14.6554	−	10.3401i	−0.698670	−	0.492945i
$441$		0			0
$442$	24.3454	−	27.2912i	1.15799	−	1.29811i
$443$	11.2335	−	19.4570i	0.533719	−	0.924428i	−0.465505	−	0.885045i	$-0.654127\pi$
$443$	11.2335	−	19.4570i	0.533719	−	0.924428i	0.999224	−	0.0393830i	$-0.0125392\pi$
$444$	−7.20977	−	17.0285i	−0.342161	−	0.808138i
$445$	−3.00724	−	5.20869i	−0.142557	−	0.246915i
$446$	8.60631	+	26.0764i	0.407521	+	1.23475i
$447$	19.0198	+	4.59528i	0.899607	+	0.217349i
$448$		0			0
$449$			29.5660i			1.39531i	0.716435	+	0.697654i	$0.245773\pi$
$449$			29.5660i			1.39531i	−0.716435	+	0.697654i	$0.754227\pi$
$450$	14.3701	+	2.25036i	0.677414	+	0.106083i
$451$	8.67086	−	5.00612i	0.408295	−	0.235729i
$452$	−8.00588	−	10.8074i	−0.376565	−	0.508339i
$453$	−13.2540	+	13.9265i	−0.622726	+	0.654323i
$454$	−11.2738	−	10.0569i	−0.529107	−	0.471996i
$455$		0			0
$456$	−5.64509	+	4.94409i	−0.264355	+	0.231528i
$457$	−9.09743	+	15.7572i	−0.425560	+	0.737091i	−0.996473	−	0.0839196i	$-0.973256\pi$
$457$	−9.09743	+	15.7572i	−0.425560	+	0.737091i	0.570913	+	0.821011i	$0.306589\pi$
$458$	−2.15765	+	10.3870i	−0.100820	+	0.485353i
$459$	5.67210	−	29.8817i	0.264751	−	1.39476i
$460$	0.313124	−	0.721174i	0.0145995	−	0.0336249i
$461$		−	24.9782i		−	1.16335i	−0.813422	−	0.581675i	$-0.802398\pi$
$461$		−	24.9782i		−	1.16335i	0.813422	−	0.581675i	$-0.197602\pi$
$462$		0			0
$463$		−	6.37226i		−	0.296144i	−0.988977	−	0.148072i	$-0.952693\pi$
$463$		−	6.37226i		−	0.296144i	0.988977	−	0.148072i	$-0.0473068\pi$
$464$	−21.1932	−	6.45504i	−0.983872	−	0.299668i
$465$	10.2039	−	3.00653i	0.473195	−	0.139424i
$466$	3.87602	+	0.805149i	0.179553	+	0.0372978i
$467$	−13.6785	+	23.6918i	−0.632964	+	1.09633i	0.353979	+	0.935253i	$0.384828\pi$
$467$	−13.6785	+	23.6918i	−0.632964	+	1.09633i	−0.986943	+	0.161072i	$0.948505\pi$
$468$	−9.34180	+	24.8072i	−0.431825	+	1.14671i
$469$		0			0
$470$	−13.5681	+	15.2098i	−0.625849	+	0.701576i
$471$	−18.5636	−	17.6672i	−0.855367	−	0.814061i
$472$	22.4412	+	2.04420i	1.03294	+	0.0940918i
$473$	13.9571	−	8.05816i	0.641750	−	0.370515i
$474$	16.9139	−	1.38535i	0.776882	−	0.0636314i
$475$		−	5.25141i		−	0.240951i
$476$		0			0
$477$	17.5185	−	34.1382i	0.802119	−	1.56308i
$478$	−27.5934	+	9.10698i	−1.26209	+	0.416543i
$479$	−9.91668	−	17.1762i	−0.453105	−	0.784800i	0.545472	−	0.838129i	$-0.316350\pi$
$479$	−9.91668	−	17.1762i	−0.453105	−	0.784800i	−0.998577	+	0.0533285i	$0.983017\pi$
$480$	2.60776	−	12.0032i	0.119027	−	0.547871i
$481$	−11.7919	+	20.4242i	−0.537666	+	0.931265i
$482$	−19.0536	−	16.9970i	−0.867866	−	0.774190i
$483$		0			0
$484$	3.31764	+	28.9830i	0.150802	+	1.31741i
$485$	−14.8571	−	8.57774i	−0.674625	−	0.389495i
$486$	3.96138	+	21.6866i	0.179692	+	0.983723i
$487$	−35.3792	+	20.4262i	−1.60318	+	0.925599i	−0.612339	+	0.790595i	$0.709771\pi$
$487$	−35.3792	+	20.4262i	−1.60318	+	0.925599i	−0.990845	+	0.135003i	$0.956896\pi$
$488$	−0.359280	−	0.777723i	−0.0162638	−	0.0352059i
$489$	22.3348	+	5.39619i	1.01001	+	0.244024i
$490$		0			0
$491$	−20.3003			−0.916137			−0.458069	−	0.888917i	$-0.651459\pi$
$491$	−20.3003			−0.916137			−0.458069	+	0.888917i	$0.651459\pi$
$492$	5.47228	+	4.13152i	0.246709	+	0.186263i
$493$	−16.2099	−	28.0764i	−0.730058	−	1.26450i
$494$	9.37036	+	1.94647i	0.421593	+	0.0875757i
$495$	10.3151	+	15.9847i	0.463631	+	0.718458i
$496$	4.42821	+	19.0890i	0.198833	+	0.857123i
$497$		0			0
$498$	13.6635	−	9.45488i	0.612278	−	0.423683i
$499$	29.6416	+	17.1136i	1.32694	+	0.766110i	0.984825	−	0.173548i	$-0.0555231\pi$
$499$	29.6416	+	17.1136i	1.32694	+	0.766110i	0.342116	+	0.939658i	$0.388856\pi$
$500$	12.5790	+	16.9809i	0.562551	+	0.759408i
$501$	−7.95202	+	2.34302i	−0.355270	+	0.104679i
$502$	−14.0756	+	4.64553i	−0.628223	+	0.207340i
$503$	31.1279			1.38792			0.693962	−	0.720011i	$-0.255863\pi$
$503$	31.1279			1.38792			0.693962	+	0.720011i	$0.255863\pi$
$504$		0			0
$505$	−5.10467			−0.227155
$506$	−2.13010	+	0.703024i	−0.0946946	+	0.0312532i
$507$	10.8301	−	3.19104i	0.480982	−	0.141719i
$508$	10.1240	+	13.6667i	0.449179	+	0.606363i
$509$	−34.2107	−	19.7516i	−1.51636	−	0.875474i	−0.999815	−	0.0192162i	$-0.993883\pi$
$509$	−34.2107	−	19.7516i	−1.51636	−	0.875474i	−0.516549	−	0.856257i	$-0.672784\pi$
$510$	14.7810	−	10.2281i	0.654512	−	0.452909i
$511$		0			0
$512$	21.7924	+	6.09041i	0.963095	+	0.269161i
$513$	7.51416	−	2.62436i	0.331758	−	0.115868i
$514$	−11.5767	−	2.40478i	−0.510627	−	0.106070i
$515$	−8.19625	−	14.1963i	−0.361170	−	0.625564i
$516$	8.80852	+	6.65036i	0.387773	+	0.292766i
$517$	58.1512			2.55749
$518$		0			0
$519$	24.2641	+	5.86232i	1.06507	+	0.257327i
$520$	−14.2214	+	6.56978i	−0.623650	+	0.288104i
$521$	20.8808	−	12.0555i	0.914803	−	0.528162i	0.0328296	−	0.999461i	$-0.489548\pi$
$521$	20.8808	−	12.0555i	0.914803	−	0.528162i	0.881973	+	0.471299i	$0.156215\pi$
$522$	18.2874	+	14.7562i	0.800417	+	0.645861i
$523$	−8.02520	−	4.63335i	−0.350917	−	0.202602i	0.314172	−	0.949366i	$-0.398273\pi$
$523$	−8.02520	−	4.63335i	−0.350917	−	0.202602i	−0.665089	+	0.746764i	$0.731606\pi$
$524$	1.91298	+	16.7118i	0.0835689	+	0.730059i
$525$		0			0
$526$	−30.9952	−	27.6496i	−1.35145	−	1.20558i
$527$	−14.3379	+	24.8339i	−0.624568	+	1.08178i
$528$	−30.5081	+	17.2450i	−1.32770	+	0.750490i
$529$	11.4508	+	19.8334i	0.497862	+	0.862323i
$530$	21.5338	−	7.10707i	0.935369	−	0.308711i
$531$	−21.2646	−	10.9122i	−0.922805	−	0.473551i
$532$		0			0
$533$		−	8.74486i		−	0.378782i
$534$	−11.7123	+	0.959312i	−0.506842	+	0.0415135i
$535$	4.24264	−	2.44949i	0.183425	−	0.105901i
$536$	−2.70536	+	29.6995i	−0.116854	+	1.28282i
$537$	−0.871113	−	0.829047i	−0.0375913	−	0.0357760i
$538$	19.2028	−	21.5263i	0.827892	−	0.928066i
$539$		0			0
$540$	−7.32637	+	10.7732i	−0.315277	+	0.463606i
$541$	−12.9508	+	22.4315i	−0.556800	+	0.964406i	0.440961	+	0.897526i	$0.354638\pi$
$541$	−12.9508	+	22.4315i	−0.556800	+	0.964406i	−0.997761	+	0.0668796i	$0.978696\pi$
$542$	−28.5189	−	5.92412i	−1.22499	−	0.254463i
$543$	−10.4843	+	3.08916i	−0.449926	+	0.132568i
$544$	17.2148	+	28.2851i	0.738078	+	1.21272i
$545$		−	10.3401i		−	0.442921i
$546$		0			0
$547$			32.9387i			1.40836i	0.710022	+	0.704179i	$0.248685\pi$
$547$			32.9387i			1.40836i	−0.710022	+	0.704179i	$0.751315\pi$
$548$	−10.9577	+	25.2372i	−0.468088	+	1.07808i
$549$	0.0449378	+	0.907556i	0.00191790	+	0.0387335i
$550$	4.98792	−	24.0120i	0.212686	−	1.02388i
$551$	4.24192	−	7.34722i	0.180712	−	0.313002i
$552$	−1.01212	−	1.15562i	−0.0430785	−	0.0491864i
$553$		0			0
$554$	−4.16528	−	3.71569i	−0.176966	−	0.157864i
$555$	−7.99101	+	8.39647i	−0.339199	+	0.356410i
$556$	15.6730	+	21.1576i	0.664685	+	0.897282i
$557$	25.8991	−	14.9528i	1.09738	−	0.633572i	0.161847	−	0.986816i	$-0.448255\pi$
$557$	25.8991	−	14.9528i	1.09738	−	0.633572i	0.935531	+	0.353244i	$0.114921\pi$
$558$	3.21568	−	20.5343i	0.136130	−	0.869288i
$559$		−	14.0763i		−	0.595363i
$560$		0			0
$561$	−49.8486	−	12.0437i	−2.10461	−	0.508484i
$562$	0.525779	+	1.59307i	0.0221787	+	0.0671994i
$563$	−15.5531	−	26.9388i	−0.655487	−	1.13534i	−0.981771	−	0.190065i	$-0.939130\pi$
$563$	−15.5531	−	26.9388i	−0.655487	−	1.13534i	0.326284	−	0.945272i	$-0.394203\pi$
$564$	15.5270	+	36.6726i	0.653803	+	1.54420i
$565$	−4.21532	+	7.30115i	−0.177340	+	0.307162i
$566$	−26.0616	+	29.2151i	−1.09545	+	1.22800i
$567$		0			0
$568$	−7.39456	+	10.4806i	−0.310269	+	0.439756i
$569$	15.3022	+	8.83472i	0.641501	+	0.370371i	0.785193	−	0.619252i	$-0.212564\pi$
$569$	15.3022	+	8.83472i	0.641501	+	0.370371i	−0.143691	+	0.989623i	$0.545897\pi$
$570$	4.25197	+	2.01149i	0.178095	+	0.0842521i
$571$	−6.51130	+	3.75930i	−0.272490	+	0.157322i	−0.630018	−	0.776580i	$-0.716953\pi$
$571$	−6.51130	+	3.75930i	−0.272490	+	0.157322i	0.357529	+	0.933902i	$0.383619\pi$
$572$	40.9971	+	17.8004i	1.71417	+	0.744272i
$573$	−1.58955	+	6.57914i	−0.0664045	+	0.274847i
$574$		0			0
$575$	1.07503			0.0448318
$576$	−19.0214	−	14.6351i	−0.792557	−	0.609797i
$577$	−2.13156	−	3.69196i	−0.0887378	−	0.153698i	0.818240	−	0.574877i	$-0.194950\pi$
$577$	−2.13156	−	3.69196i	−0.0887378	−	0.153698i	−0.906978	+	0.421178i	$0.861617\pi$
$578$	−4.96517	+	23.9025i	−0.206524	+	0.994214i
$579$	−1.97189	−	1.87667i	−0.0819491	−	0.0779917i
$580$	1.57932	+	13.7969i	0.0655776	+	0.572887i
$581$		0			0
$582$	−27.5639	+	19.0736i	−1.14256	+	0.790628i
$583$	−56.0289	−	32.3483i	−2.32048	−	1.33973i
$584$	−3.98351	−	0.362862i	−0.164839	−	0.0150154i
$585$	16.5955	−	0.821731i	0.686141	−	0.0339744i
$586$	−0.0876693	−	0.265631i	−0.00362159	−	0.0109731i
$587$	43.2909			1.78681			0.893404	−	0.449253i	$-0.148310\pi$
$587$	43.2909			1.78681			0.893404	+	0.449253i	$0.148310\pi$
$588$		0			0
$589$	−7.50407			−0.309200
$590$	−4.42697	−	13.4133i	−0.182255	−	0.552218i
$591$	−0.897238	−	3.04515i	−0.0369074	−	0.125261i
$592$	−14.5789	−	15.6010i	−0.599189	−	0.641197i
$593$	4.99583	+	2.88434i	0.205154	+	0.118446i	0.599057	−	0.800706i	$-0.295542\pi$
$593$	4.99583	+	2.88434i	0.205154	+	0.118446i	−0.393903	+	0.919152i	$0.628875\pi$
$594$	36.8511	−	4.86274i	1.51202	−	0.199521i
$595$		0			0
$596$	22.4475	−	2.56954i	0.919486	−	0.105252i
$597$	−4.38335	+	4.60576i	−0.179399	+	0.188501i
$598$	−0.398466	+	1.91823i	−0.0162945	+	0.0784422i
$599$	−17.8985	−	31.0011i	−0.731312	−	1.26667i	−0.956323	−	0.292313i	$-0.905575\pi$
$599$	−17.8985	−	31.0011i	−0.731312	−	1.26667i	0.225010	−	0.974356i	$-0.427758\pi$
$600$	16.4748	−	3.26586i	0.672582	−	0.133328i
$601$	−42.3193			−1.72624			−0.863121	−	0.504998i	$-0.831493\pi$
$601$	−42.3193			−1.72624			−0.863121	+	0.504998i	$0.831493\pi$
$602$		0			0
$603$	14.4416	−	28.1423i	0.588109	−	1.14604i
$604$	−8.84133	+	20.3630i	−0.359749	+	0.828557i
$605$	15.8361	−	9.14298i	0.643829	−	0.371715i
$606$	−4.26519	+	9.01592i	−0.173262	+	0.366247i
$607$	41.0224	+	23.6843i	1.66505	+	0.961316i	0.970248	+	0.242115i	$0.0778411\pi$
$607$	41.0224	+	23.6843i	1.66505	+	0.961316i	0.694801	+	0.719202i	$0.255492\pi$
$608$	−4.15775	+	7.60227i	−0.168619	+	0.308313i
$609$		0			0
$610$	−0.357475	+	0.400729i	−0.0144737	+	0.0162250i
$611$	25.3951	−	43.9857i	1.02738	−	1.77947i
$612$	−5.71483	−	34.6524i	−0.231008	−	1.40074i
$613$	−1.39456	−	2.41545i	−0.0563257	−	0.0975590i	0.836488	−	0.547986i	$-0.184605\pi$
$613$	−1.39456	−	2.41545i	−0.0563257	−	0.0975590i	−0.892813	+	0.450427i	$0.851272\pi$
$614$	7.36735	+	22.3224i	0.297322	+	0.900860i
$615$	1.00938	−	4.17781i	0.0407021	−	0.168465i
$616$		0			0
$617$		−	21.6549i		−	0.871795i	−0.899996	−	0.435898i	$-0.856431\pi$
$617$		−	21.6549i		−	0.871795i	0.899996	−	0.435898i	$-0.143569\pi$
$618$	−31.9221	+	2.61461i	−1.28409	+	0.105175i
$619$	−4.88830	+	2.82226i	−0.196477	+	0.113436i	−0.595011	−	0.803717i	$-0.702852\pi$
$619$	−4.88830	+	2.82226i	−0.196477	+	0.113436i	0.398534	+	0.917154i	$0.369519\pi$
$620$	9.87013	−	7.31156i	0.396394	−	0.293639i
$621$	0.537240	+	1.53824i	0.0215587	+	0.0617275i
$622$	11.3513	+	10.1260i	0.455144	+	0.406017i
$623$		0			0
$624$	−0.279048	+	30.6074i	−0.0111709	+	1.22528i
$625$	−1.94767	+	3.37346i	−0.0779067	+	0.134938i
$626$	−1.42203	+	6.84573i	−0.0568359	+	0.273610i
$627$	−3.79293	−	12.8729i	−0.151475	−	0.514094i
$628$	−27.1433	−	11.7853i	−1.08314	−	0.470283i
$629$		−	31.2464i		−	1.24588i
$630$		0			0
$631$		−	6.37226i		−	0.253676i	−0.991923	−	0.126838i	$-0.959517\pi$
$631$		−	6.37226i		−	0.253676i	0.991923	−	0.126838i	$-0.0404828\pi$
$632$	17.7894	−	8.21807i	0.707625	−	0.326897i
$633$	−7.28244	−	24.7160i	−0.289451	−	0.982372i
$634$	30.3719	+	6.30904i	1.20622	+	0.250564i
$635$	5.33056	−	9.23281i	0.211537	−	0.366393i
$636$	5.43993	−	43.9716i	0.215707	−	1.74359i
$637$		0			0
$638$	26.3747	−	29.5660i	1.04419	−	1.17053i
$639$	11.4312	−	7.37670i	0.452211	−	0.291818i
$640$	−1.93854	−	14.0504i	−0.0766274	−	0.555390i
$641$	14.2860	−	8.24802i	0.564263	−	0.325777i	−0.190592	−	0.981669i	$-0.561041\pi$
$641$	14.2860	−	8.24802i	0.564263	−	0.325777i	0.754855	+	0.655892i	$0.227707\pi$
$642$	−0.781390	−	9.54007i	−0.0308390	−	0.376516i
$643$			2.36672i			0.0933343i	0.998910	+	0.0466671i	$0.0148600\pi$
$643$			2.36672i			0.0933343i	−0.998910	+	0.0466671i	$0.985140\pi$
$644$		0			0
$645$	1.62476	−	6.72485i	0.0639748	−	0.264791i
$646$	−12.0410	+	3.97405i	−0.473748	+	0.156357i
$647$	−5.67476	−	9.82897i	−0.223098	−	0.386417i	0.732649	−	0.680606i	$-0.238284\pi$
$647$	−5.67476	−	9.82897i	−0.223098	−	0.386417i	−0.955747	+	0.294190i	$0.904950\pi$
$648$	12.9063	+	21.9415i	0.507006	+	0.861942i
$649$	−20.1497	+	34.9002i	−0.790944	+	1.36995i
$650$	−15.9845	−	14.2591i	−0.626962	−	0.559289i
$651$		0			0
$652$	26.3599	−	3.01738i	1.03233	−	0.118170i
$653$	38.5978	+	22.2844i	1.51045	+	0.872057i	0.999926	+	0.0121923i	$0.00388102\pi$
$653$	38.5978	+	22.2844i	1.51045	+	0.872057i	0.510522	+	0.859865i	$0.329452\pi$
$654$	−18.2628	−	8.63965i	−0.714132	−	0.337837i
$655$	9.13122	−	5.27191i	0.356786	−	0.205991i
$656$	7.57399	+	2.30689i	0.295715	+	0.0900689i
$657$	3.77465	+	1.93702i	0.147263	+	0.0755702i
$658$		0			0
$659$	0.590533			0.0230039			0.0115019	−	0.999934i	$-0.496339\pi$
$659$	0.590533			0.0230039			0.0115019	+	0.999934i	$0.496339\pi$
$660$	17.5315	+	13.2361i	0.682413	+	0.515216i
$661$	21.5502	+	37.3261i	0.838206	+	1.45182i	0.891393	+	0.453232i	$0.149729\pi$
$661$	21.5502	+	37.3261i	0.838206	+	1.45182i	−0.0531863	+	0.998585i	$0.516938\pi$
$662$	5.18148	+	1.07633i	0.201384	+	0.0418326i
$663$	−30.8791	+	32.4459i	−1.19925	+	1.26010i
$664$	11.0609	−	15.6771i	0.429248	−	0.608390i
$665$		0			0
$666$	8.15308	+	21.1295i	0.315926	+	0.818750i
$667$	1.50407	+	0.868374i	0.0582377	+	0.0336236i
$668$	−7.69191	+	5.69798i	−0.297609	+	0.220461i
$669$	−9.50530	−	32.2602i	−0.367496	−	1.24725i
$670$	17.7517	−	5.85880i	0.685807	−	0.226345i
$671$	1.53210			0.0591459
$672$		0			0
$673$	15.2706			0.588637			0.294319	−	0.955707i	$-0.404907\pi$
$673$	15.2706			0.588637			0.294319	+	0.955707i	$0.404907\pi$
$674$	−30.8577	+	10.1844i	−1.18860	+	0.392287i
$675$	−17.5017	−	3.32216i	−0.673641	−	0.127870i
$676$	10.4759	−	7.76027i	0.402918	−	0.298472i
$677$	−35.8437	−	20.6944i	−1.37759	−	0.795349i	−0.385717	−	0.922617i	$-0.626046\pi$
$677$	−35.8437	−	20.6944i	−1.37759	−	0.795349i	−0.991868	+	0.127268i	$0.959379\pi$
$678$	9.37328	+	13.5456i	0.359979	+	0.520216i
$679$		0			0
$680$	11.9655	−	16.9592i	0.458857	−	0.650356i
$681$	13.4032	+	12.7560i	0.513613	+	0.488811i
$682$	−34.3123	−	7.12755i	−1.31388	−	0.272928i
$683$	2.26745	+	3.92734i	0.0867615	+	0.150275i	0.906140	−	0.422977i	$-0.139015\pi$
$683$	2.26745	+	3.92734i	0.0867615	+	0.150275i	−0.819379	+	0.573252i	$0.805682\pi$
$684$	7.10544	−	5.82918i	0.271683	−	0.222884i
$685$	17.2461			0.658941
$686$		0			0
$687$	3.05138	−	12.6296i	0.116417	−	0.481850i
$688$	12.1916	+	3.71331i	0.464799	+	0.141569i
$689$	−48.9366	+	28.2536i	−1.86434	+	1.07638i
$690$	−0.411777	+	0.870430i	−0.0156761	+	0.0331367i
$691$	−23.6340	−	13.6451i	−0.899079	−	0.519084i	−0.0221779	−	0.999754i	$-0.507060\pi$
$691$	−23.6340	−	13.6451i	−0.899079	−	0.519084i	−0.876901	+	0.480670i	$0.840393\pi$
$692$	28.6369	−	3.27802i	1.08861	−	0.124612i
$693$		0			0
$694$	−2.24797	−	2.00532i	−0.0853316	−	0.0761211i
$695$	8.25229	−	14.2934i	0.313027	−	0.542179i
$696$	25.6879	+	8.73859i	0.973698	+	0.331235i
$697$	5.79306	+	10.0339i	0.219428	+	0.380060i
$698$	−4.77705	+	1.57663i	−0.180814	+	0.0596762i
$699$	−4.71287	−	1.13865i	−0.178257	−	0.0430678i
$700$		0			0
$701$			9.20431i			0.347642i	0.984777	+	0.173821i	$0.0556114\pi$
$701$			9.20431i			0.347642i	−0.984777	+	0.173821i	$0.944389\pi$
$702$	12.4150	−	29.9978i	0.468574	−	1.13219i
$703$	7.08130	−	4.08839i	0.267076	−	0.154197i
$704$	−26.2321	+	30.8122i	−0.988659	+	1.16128i
$705$	17.2094	−	18.0827i	0.648145	−	0.681032i
$706$	−17.8182	+	19.9742i	−0.670598	+	0.751740i
$707$		0			0
$708$	−27.3897	−	3.38852i	−1.02937	−	0.127348i
$709$	14.8003	−	25.6349i	0.555837	−	0.962738i	−0.442001	−	0.897015i	$-0.645731\pi$
$709$	14.8003	−	25.6349i	0.555837	−	0.962738i	0.997838	−	0.0657232i	$-0.0209354\pi$
$710$	7.87204	+	1.63523i	0.295432	+	0.0613689i
$711$	−20.7592	+	1.02790i	−0.778530	+	0.0385491i
$712$	−12.3186	+	5.69074i	−0.461659	+	0.213270i
$713$		−	1.53617i		−	0.0575302i
$714$		0			0
$715$		−	28.0159i		−	1.04773i
$716$	−1.27372	−	0.553033i	−0.0476012	−	0.0206678i
$717$	34.1369	−	10.0583i	1.27487	−	0.375633i
$718$	−0.352633	+	1.69759i	−0.0131601	+	0.0633534i
$719$	−1.35786	+	2.35188i	−0.0506395	+	0.0877102i	−0.890234	−	0.455503i	$-0.849459\pi$
$719$	−1.35786	+	2.35188i	−0.0506395	+	0.0877102i	0.839595	+	0.543214i	$0.182793\pi$
$720$	−3.66618	+	14.5903i	−0.136631	+	0.543748i
$721$		0			0
$722$	17.5752	+	15.6782i	0.654081	+	0.583480i
$723$	22.6524	+	21.5585i	0.842453	+	0.801770i
$724$	−10.1414	+	7.51250i	−0.376902	+	0.279200i
$725$	−16.4444	+	9.49416i	−0.610729	+	0.352604i
$726$	−2.91662	−	35.6093i	−0.108246	−	1.32159i
$727$			18.9752i			0.703753i	0.936046	+	0.351876i	$0.114456\pi$
$727$			18.9752i			0.703753i	−0.936046	+	0.351876i	$0.885544\pi$
$728$		0			0
$729$	−3.99276	−	26.7031i	−0.147880	−	0.989005i
$730$	0.785825	+	2.38098i	0.0290847	+	0.0881241i
$731$	9.32487	+	16.1512i	0.344893	+	0.597372i
$732$	0.409085	+	0.966205i	0.0151202	+	0.0357120i
$733$	7.65295	−	13.2553i	0.282668	−	0.489596i	−0.689373	−	0.724407i	$-0.742114\pi$
$733$	7.65295	−	13.2553i	0.282668	−	0.489596i	0.972041	+	0.234811i	$0.0754471\pi$
$734$	19.0198	−	21.3212i	0.702035	−	0.786980i
$735$		0			0
$736$	−1.55628	−	0.851142i	−0.0573652	−	0.0313735i
$737$	−46.1882	−	26.6668i	−1.70136	−	0.982283i
$738$	−6.53551	−	5.27353i	−0.240575	−	0.194121i
$739$	23.2697	−	13.4348i	0.855989	−	0.494205i	−0.00667810	−	0.999978i	$-0.502126\pi$
$739$	23.2697	−	13.4348i	0.855989	−	0.494205i	0.862667	+	0.505772i	$0.168792\pi$
$740$	−5.33056	+	12.2771i	−0.195955	+	0.451316i
$741$	−11.3935	−	2.75272i	−0.418550	−	0.101124i
$742$		0			0
$743$	−23.4748			−0.861208			−0.430604	−	0.902541i	$-0.641699\pi$
$743$	−23.4748			−0.861208			−0.430604	+	0.902541i	$0.641699\pi$
$744$	−4.66679	−	23.5419i	−0.171093	−	0.863088i
$745$	−7.08130	−	12.2652i	−0.259439	−	0.449361i
$746$	−2.35291	+	11.3270i	−0.0861462	+	0.414711i
$747$	−17.0990	+	11.0342i	−0.625620	+	0.403721i
$748$	−58.8321	+	6.73444i	−2.15112	+	0.246235i
$749$		0			0
$750$	−14.7275	−	21.2832i	−0.537772	−	0.777151i
$751$	31.1457	+	17.9820i	1.13652	+	0.656172i	0.945567	−	0.325427i	$-0.105508\pi$
$751$	31.1457	+	17.9820i	1.13652	+	0.656172i	0.190955	+	0.981599i	$0.438841\pi$
$752$	31.3971	+	33.5983i	1.14493	+	1.22520i
$753$	17.4135	−	5.13079i	0.634582	−	0.186977i
$754$	−10.8457	−	32.8616i	−0.394978	−	1.19675i
$755$	13.9153			0.506429
$756$		0			0
$757$	23.4202			0.851222			0.425611	−	0.904906i	$-0.360059\pi$
$757$	23.4202			0.851222			0.425611	+	0.904906i	$0.360059\pi$
$758$	13.8298	+	41.9030i	0.502320	+	1.52199i
$759$	2.63524	−	0.776460i	0.0956531	−	0.0281837i
$760$	5.40903	+	0.492715i	0.196206	+	0.0178727i
$761$	−34.9126	−	20.1568i	−1.26558	−	0.730684i	−0.291433	−	0.956591i	$-0.594132\pi$
$761$	−34.9126	−	20.1568i	−1.26558	−	0.730684i	−0.974149	+	0.225908i	$0.927465\pi$
$762$	−11.8532	−	17.1294i	−0.429394	−	0.620531i
$763$		0			0
$764$	0.888828	+	7.76481i	0.0321567	+	0.280921i
$765$	−18.4974	+	11.9366i	−0.668775	+	0.431570i
$766$	−7.02328	+	33.8103i	−0.253761	+	1.22162i
$767$	17.5991	+	30.4825i	0.635465	+	1.10066i
$768$	−26.4357	−	8.31590i	−0.953916	−	0.300074i
$769$	−20.6279			−0.743861			−0.371930	−	0.928261i	$-0.621304\pi$
$769$	−20.6279			−0.743861			−0.371930	+	0.928261i	$0.621304\pi$
$770$		0			0
$771$	14.0762	+	3.40088i	0.506942	+	0.122480i
$772$	−2.88325	−	1.25187i	−0.103771	−	0.0450558i
$773$	20.1789	−	11.6503i	0.725784	−	0.419032i	−0.0910936	−	0.995842i	$-0.529036\pi$
$773$	20.1789	−	11.6503i	0.725784	−	0.419032i	0.816878	+	0.576811i	$0.195703\pi$
$774$	−10.5200	−	8.48860i	−0.378132	−	0.305117i
$775$	14.5453	+	8.39771i	0.522481	+	0.301655i
$776$	−22.3136	+	31.6260i	−0.801012	+	1.13531i
$777$		0			0
$778$	−8.55233	+	9.58716i	−0.306616	+	0.343716i
$779$	−1.51597	+	2.62573i	−0.0543152	+	0.0940767i
$780$	17.6680	−	7.48052i	0.632615	−	0.267845i
$781$	−11.4694	−	19.8655i	−0.410407	−	0.710845i
$782$	−0.813537	−	2.46495i	−0.0290920	−	0.0881463i
$783$	−21.8030	−	18.7853i	−0.779177	−	0.671333i
$784$		0			0
$785$			18.5487i			0.662032i
$786$	−1.68175	−	20.5326i	−0.0599859	−	0.732374i
$787$	−2.76123	+	1.59420i	−0.0984271	+	0.0568269i	−0.548406	−	0.836212i	$-0.684765\pi$
$787$	−2.76123	+	1.59420i	−0.0984271	+	0.0568269i	0.449978	+	0.893039i	$0.351432\pi$
$788$	−2.18199	−	2.94554i	−0.0777301	−	0.104931i
$789$	36.8495	+	35.0701i	1.31188	+	1.24853i
$790$	−9.16617	−	8.17678i	−0.326118	−	0.290917i
$791$		0			0
$792$	38.0262	−	19.9049i	1.35120	−	0.707291i
$793$	0.669079	−	1.15888i	0.0237597	−	0.0411530i
$794$	−6.69628	+	32.2361i	−0.237642	+	1.14402i
$795$	−26.6404	+	7.84945i	−0.944836	+	0.278391i
$796$	−2.92400	+	6.73444i	−0.103639	+	0.238696i
$797$			55.9985i			1.98357i	0.127925	+	0.991784i	$0.459168\pi$
$797$			55.9985i			1.98357i	−0.127925	+	0.991784i	$0.540832\pi$
$798$		0			0
$799$			67.2924i			2.38063i
$800$	16.5666	−	10.0827i	0.585719	−	0.356478i
$801$	14.3750	−	0.711784i	0.507917	−	0.0251496i
$802$	−10.5113	−	2.18347i	−0.371167	−	0.0771010i
$803$	3.57674	−	6.19509i	0.126220	−	0.218620i
$804$	4.48448	−	36.2485i	0.158155	−	1.27839i
$805$		0			0
$806$	−20.3757	+	22.8412i	−0.717705	+	0.804546i
$807$	−24.3564	+	25.5922i	−0.857385	+	0.900890i
$808$	−1.04476	+	11.4694i	−0.0367545	+	0.403491i
$809$	18.4879	−	10.6740i	0.649999	−	0.375277i	−0.138457	−	0.990368i	$-0.544214\pi$
$809$	18.4879	−	10.6740i	0.649999	−	0.375277i	0.788456	+	0.615091i	$0.210881\pi$
$810$	9.39371	−	12.8983i	0.330061	−	0.453199i
$811$			52.7856i			1.85355i	0.375614	+	0.926776i	$0.377432\pi$
$811$			52.7856i			1.85355i	−0.375614	+	0.926776i	$0.622568\pi$
$812$		0			0
$813$	34.6763	+	8.37797i	1.21615	+	0.293828i
$814$	36.2624	−	11.9681i	1.27100	−	0.419483i
$815$	−8.31549	−	14.4029i	−0.291279	−	0.504510i
$816$	−19.9558	−	35.3039i	−0.698593	−	1.23588i
$817$	−2.44020	+	4.22654i	−0.0853717	+	0.147868i
$818$	6.74377	+	6.01585i	0.235790	+	0.210339i
$819$		0			0
$820$	−0.564413	−	4.93072i	−0.0197101	−	0.172188i
$821$	−5.03883	−	2.90917i	−0.175857	−	0.101531i	0.409488	−	0.912316i	$-0.365707\pi$
$821$	−5.03883	−	2.90917i	−0.175857	−	0.101531i	−0.585344	+	0.810785i	$0.699041\pi$
$822$	14.4100	−	30.4603i	0.502605	−	1.06243i
$823$	8.78912	−	5.07440i	0.306369	−	0.176882i	−0.338931	−	0.940811i	$-0.610065\pi$
$823$	8.78912	−	5.07440i	0.306369	−	0.176882i	0.645301	+	0.763929i	$0.276732\pi$
$824$	−33.5744	+	15.5102i	−1.16962	+	0.540322i
$825$	−7.05398	+	29.1964i	−0.245588	+	1.01649i
$826$		0			0
$827$	−53.0241			−1.84383			−0.921915	−	0.387393i	$-0.873376\pi$
$827$	−53.0241			−1.84383			−0.921915	+	0.387393i	$0.873376\pi$
$828$	1.19330	+	1.45457i	0.0414702	+	0.0505498i
$829$	−16.3511	−	28.3210i	−0.567898	−	0.983628i	−0.996774	−	0.0802647i	$-0.974423\pi$
$829$	−16.3511	−	28.3210i	−0.567898	−	0.983628i	0.428876	−	0.903364i	$-0.358910\pi$
$830$	−11.7752	−	2.44600i	−0.408722	−	0.0849021i
$831$	4.95202	+	4.71289i	0.171784	+	0.163488i
$832$	11.8506	+	33.2979i	0.410845	+	1.15440i
$833$		0			0
$834$	−18.3500	−	26.5181i	−0.635408	−	0.918247i
$835$	5.19641	+	3.00015i	0.179829	+	0.103824i
$836$	−9.22401	−	12.4518i	−0.319019	−	0.430655i
$837$	−4.74723	+	25.0093i	−0.164088	+	0.864447i
$838$	39.1214	−	12.9117i	1.35143	−	0.446028i
$839$	−37.5962			−1.29796			−0.648982	−	0.760803i	$-0.724805\pi$
$839$	−37.5962			−1.29796			−0.648982	+	0.760803i	$0.724805\pi$
$840$		0			0
$841$	−1.67632			−0.0578040
$842$	43.0849	−	14.2199i	1.48481	−	0.490049i
$843$	−0.580701	−	1.97085i	−0.0200004	−	0.0678796i
$844$	−17.7101	−	23.9075i	−0.609607	−	0.822931i
$845$	−7.07716	−	4.08600i	−0.243462	−	0.140563i
$846$	−17.5585	−	45.5044i	−0.603673	−	1.56447i
$847$		0			0
$848$	−11.5612	−	49.8377i	−0.397013	−	1.71143i
$849$	33.0560	−	34.7332i	1.13448	−	1.19204i
$850$	27.7866	+	5.77200i	0.953074	+	0.197978i
$851$	0.836944	+	1.44963i	0.0286901	+	0.0496927i
$852$	9.46562	−	12.5374i	0.324287	−	0.429523i
$853$	5.68417			0.194622			0.0973112	−	0.995254i	$-0.468976\pi$
$853$	5.68417			0.194622			0.0973112	+	0.995254i	$0.468976\pi$
$854$		0			0
$855$	−5.12543	−	2.63019i	−0.175286	−	0.0899507i
$856$	−4.63529	−	10.0339i	−0.158431	−	0.342951i
$857$	−27.4440	+	15.8448i	−0.937471	+	0.541249i	−0.889166	−	0.457584i	$-0.848715\pi$
$857$	−27.4440	+	15.8448i	−0.937471	+	0.541249i	−0.0483040	+	0.998833i	$0.515382\pi$
$858$	−49.4819	−	23.4086i	−1.68929	−	0.799156i
$859$	5.22874	+	3.01882i	0.178402	+	0.103001i	0.586542	−	0.809919i	$-0.300489\pi$
$859$	5.22874	+	3.01882i	0.178402	+	0.103001i	−0.408139	+	0.912920i	$0.633822\pi$
$860$	−0.908514	−	7.93679i	−0.0309801	−	0.270642i
$861$		0			0
$862$	19.2552	+	17.1768i	0.655835	+	0.585045i
$863$	20.0569	−	34.7395i	0.682744	−	1.18255i	−0.291396	−	0.956602i	$-0.594120\pi$
$863$	20.0569	−	34.7395i	0.682744	−	1.18255i	0.974140	−	0.225944i	$-0.0725468\pi$
$864$	22.7063	+	18.6661i	0.772483	+	0.635035i
$865$	−9.03379	−	15.6470i	−0.307158	−	0.532013i
$866$	6.51124	−	2.14898i	0.221261	−	0.0730254i
$867$	7.02181	−	29.0632i	0.238473	−	0.987038i
$868$		0			0
$869$			35.0447i			1.18881i
$870$	−1.38842	−	16.9513i	−0.0470717	−	0.574703i
$871$	−40.3415	+	23.2912i	−1.36692	+	0.789192i
$872$	−23.2326	−	2.11628i	−0.786755	−	0.0716664i
$873$	34.4944	−	22.2597i	1.16746	−	0.753377i
$874$	0.452179	−	0.506892i	0.0152952	−	0.0171459i
$875$		0			0
$876$	4.86191	+	0.601491i	0.164269	+	0.0203225i
$877$	21.9436	−	38.0074i	0.740983	−	1.28342i	−0.211066	−	0.977472i	$-0.567693\pi$
$877$	21.9436	−	38.0074i	0.740983	−	1.28342i	0.952048	−	0.305948i	$-0.0989733\pi$
$878$	28.0421	+	5.82507i	0.946375	+	0.196587i
$879$	0.0968270	+	0.328623i	0.00326590	+	0.0110842i
$880$	24.2648	+	7.39057i	0.817965	+	0.249136i
$881$			1.27293i			0.0428860i	0.999770	+	0.0214430i	$0.00682603\pi$
$881$			1.27293i			0.0428860i	−0.999770	+	0.0214430i	$0.993174\pi$
$882$		0			0
$883$			19.5118i			0.656625i	0.944569	+	0.328312i	$0.106480\pi$
$883$			19.5118i			0.656625i	−0.944569	+	0.328312i	$0.893520\pi$
$884$	−20.5985	+	47.4417i	−0.692804	+	1.59564i
$885$	4.88940	+	16.5942i	0.164355	+	0.557808i
$886$	−6.46214	+	31.1090i	−0.217100	+	1.04513i
$887$	13.4459	−	23.2890i	0.451470	−	0.781969i	−0.547007	−	0.837128i	$-0.684233\pi$
$887$	13.4459	−	23.2890i	0.451470	−	0.781969i	0.998478	+	0.0551585i	$0.0175664\pi$
$888$	17.2301	+	19.6730i	0.578203	+	0.660183i
$889$		0			0
$890$	6.34727	+	5.66215i	0.212761	+	0.189796i
$891$	−45.3018	+	4.49728i	−1.51767	+	0.150665i
$892$	−23.1159	−	31.2050i	−0.773977	−	1.04482i
$893$	−15.2503	+	8.80477i	−0.510332	+	0.294640i
$894$	−27.5797	+	2.25894i	−0.922402	+	0.0755504i
$895$			0.870412i			0.0290947i
$896$		0			0
$897$	0.563515	−	2.33238i	0.0188152	−	0.0778760i
$898$	−13.1047	−	39.7060i	−0.437308	−	1.32501i
$899$	13.5668	+	23.4984i	0.452478	+	0.783715i
$900$	−20.2959	+	3.34718i	−0.676532	+	0.111573i
$901$	37.4334	−	64.8365i	1.24709	−	2.16002i
$902$	−9.42574	+	10.5662i	−0.313843	+	0.351817i
$903$		0			0
$904$	15.5418	+	10.9655i	0.516913	+	0.364706i
$905$	6.85120	+	3.95554i	0.227742	+	0.131487i
$906$	11.6269	−	24.5773i	0.386277	−	0.816527i
$907$	16.1538	−	9.32642i	0.536379	−	0.309679i	−0.207231	−	0.978292i	$-0.566445\pi$
$907$	16.1538	−	9.32642i	0.536379	−	0.309679i	0.743610	+	0.668613i	$0.233112\pi$
$908$	19.5979	+	8.50914i	0.650379	+	0.282386i
$909$	5.57709	−	10.8680i	0.184980	−	0.360470i
$910$		0			0
$911$	8.12909			0.269329			0.134664	−	0.990891i	$-0.457004\pi$
$911$	8.12909			0.269329			0.134664	+	0.990891i	$0.457004\pi$
$912$	5.38974	−	9.14181i	0.178472	−	0.302716i
$913$	17.1561	+	29.7153i	0.567785	+	0.983433i
$914$	5.23336	−	25.1936i	0.173104	−	0.833330i
$915$	0.453413	−	0.476419i	0.0149894	−	0.0157499i
$916$	−1.70623	−	14.9057i	−0.0563755	−	0.492497i
$917$		0			0
$918$	5.62715	+	42.6440i	0.185724	+	1.40746i
$919$	−15.2109	−	8.78201i	−0.501761	−	0.289692i	0.227680	−	0.973736i	$-0.426886\pi$
$919$	−15.2109	−	8.78201i	−0.501761	−	0.289692i	−0.729440	+	0.684044i	$0.760219\pi$
$920$	−0.100865	+	1.10730i	−0.00332542	+	0.0365065i
$921$	−8.13692	−	27.6160i	−0.268121	−	0.909979i
$922$	11.0712	+	33.5447i	0.364610	+	1.10474i
$923$	−20.0351			−0.659463
$924$		0			0
$925$	−18.3011			−0.601736
$926$	2.82440	+	8.55770i	0.0928156	+	0.281223i
$927$	39.1793	−	1.93997i	1.28682	−	0.0637170i
$928$	31.3228	−	0.724692i	1.02822	−	0.0237892i
$929$	33.7624	+	19.4927i	1.10771	+	0.639535i	0.938235	−	0.345999i	$-0.112460\pi$
$929$	33.7624	+	19.4927i	1.10771	+	0.639535i	0.169473	+	0.985535i	$0.445793\pi$
$930$	−12.3708	+	8.56036i	−0.405656	+	0.280705i
$931$		0			0
$932$	−5.56221	+	0.636699i	−0.182196	+	0.0208558i
$933$	−13.4953	−	12.8436i	−0.441816	−	0.420481i
$934$	7.86863	−	37.8799i	0.257470	−	1.23947i
$935$	18.5592	+	32.1455i	0.606951	+	1.05127i
$936$	1.55027	−	37.4557i	0.0506720	−	1.22428i
$937$	−23.7865			−0.777072			−0.388536	−	0.921434i	$-0.627019\pi$
$937$	−23.7865			−0.777072			−0.388536	+	0.921434i	$0.627019\pi$
$938$		0			0
$939$	2.01106	−	8.32376i	0.0656285	−	0.271636i
$940$	11.4799	−	26.4400i	0.374433	−	0.862378i
$941$	−26.5129	+	15.3073i	−0.864297	+	0.499002i	−0.865449	−	0.500997i	$-0.832967\pi$
$941$	−26.5129	+	15.3073i	−0.864297	+	0.499002i	0.00115159	+	0.999999i	$0.499633\pi$
$942$	32.7609	+	15.4983i	1.06741	+	0.504963i
$943$	−0.537520	−	0.310337i	−0.0175041	−	0.0101060i
$944$	−31.0437	+	7.20143i	−1.01039	+	0.234387i
$945$		0			0
$946$	−15.1722	+	17.0081i	−0.493292	+	0.552980i
$947$	−7.73005	+	13.3888i	−0.251193	+	0.435079i	−0.963855	−	0.266429i	$-0.914156\pi$
$947$	−7.73005	+	13.3888i	−0.251193	+	0.435079i	0.712662	+	0.701508i	$0.247490\pi$
$948$	−22.1007	+	9.35730i	−0.717797	+	0.303911i
$949$	−3.12398	−	5.41090i	−0.101409	−	0.175645i
$950$	2.32760	+	7.05244i	0.0755175	+	0.228811i
$951$	−36.9294	−	8.92233i	−1.19752	−	0.289326i
$952$		0			0
$953$			13.4497i			0.435679i	0.975985	+	0.217839i	$0.0699009\pi$
$953$			13.4497i			0.435679i	−0.975985	+	0.217839i	$0.930099\pi$
$954$	−8.39549	+	53.6111i	−0.271814	+	1.73572i
$955$	4.24264	−	2.44949i	0.137289	−	0.0792636i
$956$	33.0203	−	24.4606i	1.06795	−	0.791113i
$957$	−33.4531	+	35.1505i	−1.08138	+	1.13625i
$958$	20.9308	+	18.6715i	0.676243	+	0.603250i
$959$		0			0
$960$	1.81813	+	17.2757i	0.0586799	+	0.557572i
$961$	−3.50000	+	6.06218i	−0.112903	+	0.195554i
$962$	6.78340	−	32.6555i	0.218705	−	1.05286i
$963$	0.579770	+	11.7089i	0.0186828	+	0.377315i
$964$	33.1218	+	14.3811i	1.06678	+	0.463183i
$965$			1.97031i			0.0634264i
$966$		0			0
$967$		−	41.1554i		−	1.32347i	−0.749738	−	0.661734i	$-0.769821\pi$
$967$		−	41.1554i		−	1.32347i	0.749738	−	0.661734i	$-0.230179\pi$
$968$	−17.3017	−	37.4525i	−0.556098	−	1.20377i
$969$	14.8965	−	4.38917i	0.478543	−	0.141000i
$970$	23.7544	+	4.93441i	0.762709	+	0.158434i
$971$	14.4445	−	25.0186i	0.463546	−	0.802886i	−0.535588	−	0.844479i	$-0.679910\pi$
$971$	14.4445	−	25.0186i	0.463546	−	0.802886i	0.999135	+	0.0415934i	$0.0132434\pi$
$972$	−14.9322	−	27.3684i	−0.478951	−	0.877842i
$973$		0			0
$974$	38.4593	−	43.1128i	1.23232	−	1.38142i
$975$	19.0036	+	18.0859i	0.608603	+	0.579213i
$976$	0.827212	+	0.885206i	0.0264784	+	0.0283348i
$977$	−40.6932	+	23.4942i	−1.30189	+	0.751646i	−0.980728	−	0.195378i	$-0.937407\pi$
$977$	−40.6932	+	23.4942i	−1.30189	+	0.751646i	−0.321161	+	0.947024i	$0.604073\pi$
$978$	−32.3865	+	2.65265i	−1.03561	+	0.0848225i
$979$		−	24.2673i		−	0.775587i
$980$		0			0
$981$	22.0145	+	11.2971i	0.702868	+	0.360687i
$982$	27.2624	−	8.99776i	0.869979	−	0.287130i
$983$	13.6677	+	23.6731i	0.435931	+	0.755054i	0.997371	−	0.0724632i	$-0.0230860\pi$
$983$	13.6677	+	23.6731i	0.435931	+	0.755054i	−0.561440	+	0.827517i	$0.689753\pi$
$984$	−9.18029	−	3.12298i	−0.292657	−	0.0995568i
$985$	−1.14888	+	1.98991i	−0.0366063	+	0.0634039i
$986$	34.2137	+	30.5207i	1.08959	+	0.971978i
$987$		0			0
$988$	−13.4468	+	1.53923i	−0.427799	+	0.0489696i
$989$	−0.865226	−	0.499538i	−0.0275126	−	0.0158844i
$990$	−20.9378	−	16.8948i	−0.665446	−	0.536951i
$991$	18.0000	−	10.3923i	0.571789	−	0.330122i	−0.186075	−	0.982536i	$-0.559577\pi$
$991$	18.0000	−	10.3923i	0.571789	−	0.330122i	0.757863	+	0.652413i	$0.226243\pi$
$992$	−14.4078	−	23.6731i	−0.457449	−	0.751621i
$993$	−6.30019	−	1.52216i	−0.199930	−	0.0483042i
$994$		0			0
$995$	4.60206			0.145895
$996$	−14.1589	+	18.7537i	−0.448641	+	0.594233i
$997$	−6.02119	−	10.4290i	−0.190693	−	0.330290i	0.754787	−	0.655970i	$-0.227740\pi$
$997$	−6.02119	−	10.4290i	−0.190693	−	0.330290i	−0.945480	+	0.325680i	$0.894407\pi$
$998$	−47.3929	−	9.84472i	−1.50020	−	0.311629i
$999$	−9.14586	−	26.1867i	−0.289362	−	0.828511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.h.275.4		24
3.2	odd	2	inner	588.2.n.h.275.10		24
4.3	odd	2		588.2.n.d.275.5		24
7.2	even	3		588.2.e.f.491.19	yes	24
7.3	odd	6		588.2.n.d.263.8		24
7.4	even	3		588.2.n.d.263.7		24
7.5	odd	6		588.2.e.f.491.20	yes	24
7.6	odd	2	inner	588.2.n.h.275.3		24
12.11	even	2		588.2.n.d.275.7		24
21.2	odd	6		588.2.e.f.491.6	yes	24
21.5	even	6		588.2.e.f.491.5	✓	24
21.11	odd	6		588.2.n.d.263.5		24
21.17	even	6		588.2.n.d.263.6		24
21.20	even	2	inner	588.2.n.h.275.9		24
28.3	even	6	inner	588.2.n.h.263.9		24
28.11	odd	6	inner	588.2.n.h.263.10		24
28.19	even	6		588.2.e.f.491.7	yes	24
28.23	odd	6		588.2.e.f.491.8	yes	24
28.27	even	2		588.2.n.d.275.6		24
84.11	even	6	inner	588.2.n.h.263.4		24
84.23	even	6		588.2.e.f.491.17	yes	24
84.47	odd	6		588.2.e.f.491.18	yes	24
84.59	odd	6	inner	588.2.n.h.263.3		24
84.83	odd	2		588.2.n.d.275.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.5	✓	24	21.5	even	6
588.2.e.f.491.6	yes	24	21.2	odd	6
588.2.e.f.491.7	yes	24	28.19	even	6
588.2.e.f.491.8	yes	24	28.23	odd	6
588.2.e.f.491.17	yes	24	84.23	even	6
588.2.e.f.491.18	yes	24	84.47	odd	6
588.2.e.f.491.19	yes	24	7.2	even	3
588.2.e.f.491.20	yes	24	7.5	odd	6
588.2.n.d.263.5		24	21.11	odd	6
588.2.n.d.263.6		24	21.17	even	6
588.2.n.d.263.7		24	7.4	even	3
588.2.n.d.263.8		24	7.3	odd	6
588.2.n.d.275.5		24	4.3	odd	2
588.2.n.d.275.6		24	28.27	even	2
588.2.n.d.275.7		24	12.11	even	2
588.2.n.d.275.8		24	84.83	odd	2
588.2.n.h.263.3		24	84.59	odd	6	inner
588.2.n.h.263.4		24	84.11	even	6	inner
588.2.n.h.263.9		24	28.3	even	6	inner
588.2.n.h.263.10		24	28.11	odd	6	inner
588.2.n.h.275.3		24	7.6	odd	2	inner
588.2.n.h.275.4		24	1.1	even	1	trivial
588.2.n.h.275.9		24	21.20	even	2	inner
588.2.n.h.275.10		24	3.2	odd	2	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34296 + 0.443234i) q^{2} +(1.66143 - 0.489533i) q^{3} +(1.60709 - 1.19049i) q^{4} +(-1.08570 - 0.626827i) q^{5} +(-2.01426 + 1.39383i) q^{6} +(-1.63059 + 2.31110i) q^{8} +(2.52072 - 1.62665i) q^{9} +(1.73588 + 0.360587i) q^{10} +(-2.52914 - 4.38059i) q^{11} +(2.08728 - 2.76464i) q^{12} -4.41798 q^{13} +(-2.11066 - 0.509947i) q^{15} +(1.16546 - 3.82645i) q^{16} +(5.06920 - 2.92671i) q^{17} +(-2.66423 + 3.30180i) q^{18} +(1.32654 + 0.765881i) q^{19} +(-2.49104 + 0.285146i) q^{20} +(5.33816 + 4.76197i) q^{22} +(-0.156785 + 0.271560i) q^{23} +(-1.57776 + 4.63796i) q^{24} +(-1.71417 - 2.96904i) q^{25} +(5.93317 - 1.95820i) q^{26} +(3.39170 - 3.93654i) q^{27} -5.53862i q^{29} +(3.06057 - 0.250679i) q^{30} +(-4.24264 + 2.44949i) q^{31} +(0.130843 + 5.65534i) q^{32} +(-6.34643 - 6.03996i) q^{33} +(-5.51053 + 6.17729i) q^{34} +(2.11450 - 5.61506i) q^{36} +(2.66908 - 4.62298i) q^{37} +(-2.12096 - 0.440578i) q^{38} +(-7.34017 + 2.16275i) q^{39} +(3.21899 - 1.48705i) q^{40} +1.97938i q^{41} +3.18613i q^{43} +(-9.27960 - 4.02908i) q^{44} +(-3.75636 + 0.185997i) q^{45} +(0.0901918 - 0.434187i) q^{46} +(-5.74813 + 9.95606i) q^{47} +(0.0631619 - 6.92792i) q^{48} +(3.61805 + 3.22752i) q^{50} +(6.98942 - 7.34407i) q^{51} +(-7.10008 + 5.25957i) q^{52} +(11.0767 - 6.39513i) q^{53} +(-2.81011 + 6.78994i) q^{54} +6.34133i q^{55} +(2.57889 + 0.623072i) q^{57} +(2.45490 + 7.43815i) q^{58} +(-3.98351 - 6.89964i) q^{59} +(-3.99911 + 1.69320i) q^{60} +(-0.151445 + 0.262310i) q^{61} +(4.61200 - 5.17005i) q^{62} +(-2.68236 - 7.53691i) q^{64} +(4.79659 + 2.76931i) q^{65} +(11.2001 + 5.29848i) q^{66} +(9.13122 - 5.27191i) q^{67} +(4.66244 - 10.7383i) q^{68} +(-0.127550 + 0.527930i) q^{69} +4.53490 q^{71} +(-0.350899 + 8.47802i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-1.53541 + 7.39151i) q^{74} +(-4.30143 - 4.09371i) q^{75} +(3.04365 - 0.348402i) q^{76} +(8.89896 - 6.15790i) q^{78} +(-6.00000 - 3.46410i) q^{79} +(-3.66386 + 3.42382i) q^{80} +(3.70801 - 8.20065i) q^{81} +(-0.877328 - 2.65823i) q^{82} -6.78340 q^{83} -7.33816 q^{85} +(-1.41220 - 4.27885i) q^{86} +(-2.71134 - 9.20204i) q^{87} +(14.2480 + 1.29786i) q^{88} +(4.15480 + 2.39878i) q^{89} +(4.96221 - 1.91473i) q^{90} +(0.0713222 + 0.623072i) q^{92} +(-5.84975 + 6.14657i) q^{93} +(3.30666 - 15.9184i) q^{94} +(-0.960150 - 1.66303i) q^{95} +(2.98586 + 9.33191i) q^{96} +13.6844 q^{97} +(-13.5009 - 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 60 q^{16} + 24 q^{18} + 12 q^{25} + 36 q^{30} + 12 q^{36} - 96 q^{39} + 24 q^{46} + 12 q^{51} - 24 q^{57} + 48 q^{58} + 12 q^{60} - 48 q^{64} - 48 q^{67} - 36 q^{72} - 24 q^{78} - 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) \) 24 * q + 12 * q^4 + 60 * q^16 + 24 * q^18 + 12 * q^25 + 36 * q^30 + 12 * q^36 - 96 * q^39 + 24 * q^46 + 12 * q^51 - 24 * q^57 + 48 * q^58 + 12 * q^60 - 48 * q^64 - 48 * q^67 - 36 * q^72 - 24 * q^78 - 144 * q^79 + 12 * q^81 - 48 * q^85 + 192 * q^88 - 24 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more