LMFDB - Embedded newform 588.2.n.h.263.10

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			263.10
Character	$\chi$	$=$	588.263
Dual form			588.2.n.h.275.10

$q$ -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} +(1.25466 + 1.19408i) q^{3} +(1.60709 + 1.19049i) q^{4} +(1.08570 - 0.626827i) q^{5} +(1.15571 + 2.15971i) q^{6} +(1.63059 + 2.31110i) q^{8} +(0.148364 + 2.99633i) q^{9} +(1.73588 - 0.360587i) q^{10} +(2.52914 - 4.38059i) q^{11} +(0.594817 + 3.41265i) q^{12} -4.41798 q^{13} +(2.11066 + 0.509947i) q^{15} +(1.16546 + 3.82645i) q^{16} +(-5.06920 - 2.92671i) q^{17} +(-1.12883 + 4.08971i) 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} +(-0.713786 + 4.84670i) q^{24} +(-1.71417 + 2.96904i) q^{25} +(-5.93317 - 1.95820i) q^{26} +(-3.39170 + 3.93654i) q^{27} -5.53862i q^{29} +(2.60851 + 1.62036i) q^{30} +(-4.24264 - 2.44949i) q^{31} +(-0.130843 + 5.65534i) q^{32} +(8.40398 - 2.47619i) q^{33} +(-5.51053 - 6.17729i) q^{34} +(-3.32867 + 4.99199i) q^{36} +(2.66908 + 4.62298i) q^{37} +(2.12096 - 0.440578i) q^{38} +(-5.54308 - 5.27540i) q^{39} +(3.21899 + 1.48705i) q^{40} +1.97938i q^{41} -3.18613i q^{43} +(9.27960 - 4.02908i) q^{44} +(2.03926 + 3.16011i) q^{45} +(0.0901918 + 0.434187i) q^{46} +(5.74813 + 9.95606i) q^{47} +(-3.10681 + 6.19256i) q^{48} +(-3.61805 + 3.22752i) q^{50} +(-2.86544 - 9.72505i) q^{51} +(-7.10008 - 5.25957i) q^{52} +(-11.0767 - 6.39513i) q^{53} +(-6.29973 + 3.78331i) q^{54} -6.34133i q^{55} +(2.57889 + 0.623072i) q^{57} +(2.45490 - 7.43815i) q^{58} +(3.98351 - 6.89964i) q^{59} +(2.78493 + 3.33226i) 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} +(12.3837 + 0.399501i) q^{66} +(9.13122 + 5.27191i) q^{67} +(-4.66244 - 10.7383i) q^{68} +(-0.127550 + 0.527930i) q^{69} -4.53490 q^{71} +(-6.68289 + 5.22867i) q^{72} +(0.707107 - 1.22474i) q^{73} +(1.53541 + 7.39151i) q^{74} +(-5.69597 + 1.67829i) q^{75} +(3.04365 + 0.348402i) q^{76} +(-5.10590 - 9.54154i) q^{78} +(-6.00000 + 3.46410i) q^{79} +(3.66386 + 3.42382i) q^{80} +(-8.95598 + 0.889094i) q^{81} +(-0.877328 + 2.65823i) q^{82} +6.78340 q^{83} -7.33816 q^{85} +(1.41220 - 4.27885i) q^{86} +(6.61354 - 6.94911i) q^{87} +(14.2480 - 1.29786i) q^{88} +(-4.15480 + 2.39878i) q^{89} +(1.33798 + 5.14777i) q^{90} +(-0.0713222 + 0.623072i) q^{92} +(-2.39821 - 8.13932i) q^{93} +(3.30666 + 15.9184i) q^{94} +(0.960150 - 1.66303i) q^{95} +(-6.91707 + 6.93932i) 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 $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$ .

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.25466	+	1.19408i	0.724381	+	0.689400i
$3$	1.25466	+	1.19408i	0.724381	+	0.689400i
$4$	1.60709	+	1.19049i	0.803544	+	0.595246i
$5$	1.08570	−	0.626827i	0.485538	−	0.280326i	−0.237183	−	0.971465i	$-0.576224\pi$
$5$	1.08570	−	0.626827i	0.485538	−	0.280326i	0.722722	+	0.691139i	$0.242891\pi$
$6$	1.15571	+	2.15971i	0.471817	+	0.881697i
$7$		0			0
$7$		0			0
$8$	1.63059	+	2.31110i	0.576500	+	0.817097i
$9$	0.148364	+	2.99633i	0.0494546	+	0.998776i
$10$	1.73588	−	0.360587i	0.548933	−	0.114028i
$11$	2.52914	−	4.38059i	0.762563	−	1.32080i	−0.178962	−	0.983856i	$-0.557274\pi$
$11$	2.52914	−	4.38059i	0.762563	−	1.32080i	0.941525	−	0.336942i	$-0.109393\pi$
$12$	0.594817	+	3.41265i	0.171709	+	0.985148i
$13$	−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	$-0.584562\pi$
$17$	−5.06920	−	2.92671i	−1.22946	−	0.709831i	−0.966918	+	0.255089i	$0.917895\pi$
$18$	−1.12883	+	4.08971i	−0.266067	+	0.963954i
$19$	1.32654	−	0.765881i	0.304330	−	0.175705i	−0.340056	−	0.940405i	$-0.610446\pi$
$19$	1.32654	−	0.765881i	0.304330	−	0.175705i	0.644386	+	0.764700i	$0.277113\pi$
$20$	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	$-0.156259\pi$
$23$	0.156785	+	0.271560i	0.0326920	+	0.0566242i	−0.849217	+	0.528045i	$0.822925\pi$
$24$	−0.713786	+	4.84670i	−0.145701	+	0.989329i
$25$	−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	$-0.171929\pi$
$30$	2.60851	+	1.62036i	0.476247	+	0.295835i
$31$	−4.24264	−	2.44949i	−0.762001	−	0.439941i	0.0680129	−	0.997684i	$-0.478334\pi$
$31$	−4.24264	−	2.44949i	−0.762001	−	0.439941i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	−0.130843	+	5.65534i	−0.0231301	+	0.999732i
$33$	8.40398	−	2.47619i	1.46294	−	0.431049i
$34$	−5.51053	−	6.17729i	−0.945048	−	1.05940i
$35$		0			0
$36$	−3.32867	+	4.99199i	−0.554778	+	0.831998i
$37$	2.66908	+	4.62298i	0.438794	+	0.760013i	0.997597	−	0.0692872i	$-0.0220725\pi$
$37$	2.66908	+	4.62298i	0.438794	+	0.760013i	−0.558803	+	0.829301i	$0.688739\pi$
$38$	2.12096	−	0.440578i	0.344065	−	0.0714713i
$39$	−5.54308	−	5.27540i	−0.887603	−	0.844741i
$40$	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	$-0.921888\pi$
$43$		−	3.18613i		−	0.485881i	0.970041	−	0.242940i	$-0.0781119\pi$
$44$	9.27960	−	4.02908i	1.39895	−	0.607407i
$45$	2.03926	+	3.16011i	0.303995	+	0.471081i
$46$	0.0901918	+	0.434187i	0.0132981	+	0.0640174i
$47$	5.74813	+	9.95606i	0.838451	+	1.45224i	0.891189	+	0.453632i	$0.149872\pi$
$47$	5.74813	+	9.95606i	0.838451	+	1.45224i	−0.0527378	+	0.998608i	$0.516795\pi$
$48$	−3.10681	+	6.19256i	−0.448429	+	0.893818i
$49$		0			0
$50$	−3.61805	+	3.22752i	−0.511669	+	0.456440i
$51$	−2.86544	−	9.72505i	−0.401242	−	1.36178i
$52$	−7.10008	−	5.25957i	−0.984604	−	0.729371i
$53$	−11.0767	−	6.39513i	−1.52150	−	0.878439i	−0.999678	−	0.0253856i	$-0.991919\pi$
$53$	−11.0767	−	6.39513i	−1.52150	−	0.878439i	−0.521823	−	0.853054i	$-0.674748\pi$
$54$	−6.29973	+	3.78331i	−0.857284	+	0.514843i
$55$		−	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	−0.481158	−	0.876634i	$-0.659784\pi$
$59$	3.98351	−	6.89964i	0.518608	−	0.898256i	0.999766	−	0.0216222i	$-0.00688310\pi$
$60$	2.78493	+	3.33226i	0.359534	+	0.430193i
$61$	−0.151445	−	0.262310i	−0.0193905	−	0.0335853i	0.856167	−	0.516699i	$-0.172839\pi$
$61$	−0.151445	−	0.262310i	−0.0193905	−	0.0335853i	−0.875558	+	0.483113i	$0.839506\pi$
$62$	−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
$66$	12.3837	+	0.399501i	1.52433	+	0.0491751i
$67$	9.13122	+	5.27191i	1.11556	+	0.644067i	0.940263	−	0.340450i	$-0.110579\pi$
$67$	9.13122	+	5.27191i	1.11556	+	0.644067i	0.175293	+	0.984516i	$0.443913\pi$
$68$	−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	$-0.586725\pi$
$71$	−4.53490			−0.538194			−0.269097	+	0.963113i	$0.586725\pi$
$72$	−6.68289	+	5.22867i	−0.787586	+	0.616204i
$73$	0.707107	−	1.22474i	0.0827606	−	0.143346i	−0.821674	−	0.569958i	$-0.806960\pi$
$73$	0.707107	−	1.22474i	0.0827606	−	0.143346i	0.904435	+	0.426612i	$0.140293\pi$
$74$	1.53541	+	7.39151i	0.178487	+	0.859245i
$75$	−5.69597	+	1.67829i	−0.657714	+	0.193792i
$76$	3.04365	+	0.348402i	0.349130	+	0.0399645i
$77$		0			0
$78$	−5.10590	−	9.54154i	−0.578130	−	1.08037i
$79$	−6.00000	+	3.46410i	−0.675053	+	0.389742i	−0.797988	−	0.602673i	$-0.794102\pi$
$79$	−6.00000	+	3.46410i	−0.675053	+	0.389742i	0.122936	+	0.992415i	$0.460769\pi$
$80$	3.66386	+	3.42382i	0.409632	+	0.382795i
$81$	−8.95598	+	0.889094i	−0.995108	+	0.0987883i
$82$	−0.877328	+	2.65823i	−0.0968847	+	0.293552i
$83$	6.78340			0.744575			0.372287	−	0.928118i	$-0.378574\pi$
$83$	6.78340			0.744575			0.372287	+	0.928118i	$0.378574\pi$
$84$		0			0
$85$	−7.33816			−0.795935
$86$	1.41220	−	4.27885i	0.152282	−	0.461400i
$87$	6.61354	−	6.94911i	0.709045	−	0.745023i
$88$	14.2480	−	1.29786i	1.51884	−	0.138353i
$89$	−4.15480	+	2.39878i	−0.440408	+	0.254270i	−0.703771	−	0.710427i	$-0.748502\pi$
$89$	−4.15480	+	2.39878i	−0.440408	+	0.254270i	0.263363	+	0.964697i	$0.415168\pi$
$90$	1.33798	+	5.14777i	0.141035	+	0.542622i
$91$		0			0
$92$	−0.0713222	+	0.623072i	−0.00743586	+	0.0649597i
$93$	−2.39821	−	8.13932i	−0.248683	−	0.844008i
$94$	3.30666	+	15.9184i	0.341055	+	1.64185i
$95$	0.960150	−	1.66303i	0.0985093	−	0.170623i
$96$	−6.91707	+	6.93932i	−0.705971	+	0.708241i
$97$	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	$-0.398266\pi$
$101$	−3.52631	−	2.03591i	−0.350881	−	0.202581i	−0.665073	+	0.746778i	$0.731600\pi$
$102$	0.462300	−	14.3304i	0.0457746	−	1.41892i
$103$	11.3239	−	6.53788i	1.11578	−	0.644197i	0.175461	−	0.984486i	$-0.443859\pi$
$103$	11.3239	−	6.53788i	1.11578	−	0.644197i	0.940321	+	0.340290i	$0.110525\pi$
$104$	−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	$-0.106178\pi$
$107$	1.95388	+	3.38422i	0.188889	+	0.327165i	−0.755991	+	0.654582i	$0.772845\pi$
$108$	−10.1372	+	2.28858i	−0.975450	+	0.220219i
$109$	4.12398	−	7.14295i	0.395006	−	0.684170i	−0.598096	−	0.801424i	$-0.704076\pi$
$109$	4.12398	−	7.14295i	0.395006	−	0.684170i	0.993102	+	0.117254i	$0.0374092\pi$
$110$	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	$-0.102444\pi$
$114$	3.18718	+	1.97981i	0.298507	+	0.185426i
$115$	0.340442	+	0.196554i	0.0317464	+	0.0183288i
$116$	6.59368	−	8.90105i	0.612208	−	0.826442i
$117$	−0.655469	−	13.2377i	−0.0605981	−	1.22383i
$118$	8.40785	−	7.50032i	0.774005	−	0.690460i
$119$		0			0
$120$	2.26309	+	5.70947i	0.206591	+	0.521201i
$121$	−7.29306	−	12.6320i	−0.663006	−	1.14836i
$122$	−0.0871196	−	0.419397i	−0.00788744	−	0.0379704i
$123$	−2.36353	+	2.48346i	−0.213112	+	0.223926i
$124$	−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	$-0.876851\pi$
$127$		−	8.50404i		−	0.754611i	0.926089	−	0.377306i	$-0.123149\pi$
$128$	−6.94291	+	8.93286i	−0.613672	+	0.789561i
$129$	3.80448	−	3.99752i	0.334966	−	0.351962i
$130$	−7.66908	+	1.59307i	−0.672623	+	0.139721i
$131$	4.20524	+	7.28368i	0.367413	+	0.636378i	0.989160	−	0.146840i	$-0.0469102\pi$
$131$	4.20524	+	7.28368i	0.367413	+	0.636378i	−0.621747	+	0.783218i	$0.713577\pi$
$132$	16.4538	+	6.02541i	1.43212	+	0.524445i
$133$		0			0
$134$	9.92618	+	11.1272i	0.857491	+	0.961247i
$135$	−1.21482	+	6.39990i	−0.104555	+	0.550816i
$136$	−1.50188	−	16.4877i	−0.128785	−	1.41381i
$137$	11.9136	+	6.87834i	1.01785	+	0.587657i	0.913481	−	0.406882i	$-0.133384\pi$
$137$	11.9136	+	6.87834i	1.01785	+	0.587657i	0.104370	+	0.994539i	$0.466717\pi$
$138$	−0.405292	+	0.652455i	−0.0345007	+	0.0555406i
$139$		−	13.1652i		−	1.11666i	−0.829620	−	0.558328i	$-0.811443\pi$
$139$		−	13.1652i		−	1.11666i	0.829620	−	0.558328i	$-0.188557\pi$
$140$		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
$144$	−11.2924	+	4.05981i	−0.941032	+	0.338317i
$145$	−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	$-0.819802\pi$
$149$	−9.78354	+	5.64853i	−0.801499	+	0.462745i	0.0424963	+	0.999097i	$0.486469\pi$
$150$	−8.39334	−	0.270770i	−0.685313	−	0.0221083i
$151$	−9.61268	−	5.54988i	−0.782269	−	0.451643i	0.0549650	−	0.998488i	$-0.482495\pi$
$151$	−9.61268	−	5.54988i	−0.782269	−	0.451643i	−0.837234	+	0.546845i	$0.815829\pi$
$152$	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
$156$	−2.62789	−	15.0770i	−0.210400	−	1.20713i
$157$	−7.39785	+	12.8135i	−0.590413	+	1.02262i	0.403764	+	0.914863i	$0.367702\pi$
$157$	−7.39785	+	12.8135i	−0.590413	+	1.02262i	−0.994177	+	0.107762i	$0.965632\pi$
$158$	−9.59317	+	1.99275i	−0.763192	+	0.158535i
$159$	−6.26126	−	21.2502i	−0.496550	−	1.68525i
$160$	3.40287	+	6.22200i	0.269020	+	0.491892i
$161$		0			0
$162$	−12.4216	−	2.77557i	−0.975933	−	0.218070i
$163$	11.4887	−	6.63300i	0.899864	−	0.519537i	0.0227080	−	0.999742i	$-0.492771\pi$
$163$	11.4887	−	6.63300i	0.899864	−	0.519537i	0.877156	+	0.480205i	$0.159438\pi$
$164$	−2.35643	+	3.18104i	−0.184007	+	0.248397i
$165$	7.57203	−	7.95624i	0.589482	−	0.619392i
$166$	9.10984	+	3.00663i	0.707060	+	0.233360i
$167$	4.78624			0.370371			0.185185	−	0.982704i	$-0.440711\pi$
$167$	4.78624			0.370371			0.185185	+	0.982704i	$0.440711\pi$
$168$		0			0
$169$	6.51854			0.501426
$170$	−9.85486	−	3.25252i	−0.755833	−	0.249457i
$171$	2.49164	+	3.86113i	0.190541	+	0.295268i
$172$	3.79306	−	5.12039i	0.289218	−	0.390426i
$173$	−12.4811	+	7.20596i	−0.948920	+	0.547859i	−0.892745	−	0.450562i	$-0.851224\pi$
$173$	−12.4811	+	7.20596i	−0.948920	+	0.547859i	−0.0561749	+	0.998421i	$0.517890\pi$
$174$	11.9618	−	6.40104i	0.906822	−	0.485261i
$175$		0			0
$176$	19.7097	+	4.57220i	1.48568	+	0.344643i
$177$	13.2367	−	3.90012i	0.994928	−	0.293151i
$178$	−6.64296	+	1.37991i	−0.497911	+	0.103429i
$179$	0.347150	−	0.601281i	0.0259472	−	0.0449419i	−0.852760	−	0.522303i	$-0.825073\pi$
$179$	0.347150	−	0.601281i	0.0259472	−	0.0449419i	0.878707	+	0.477361i	$0.158406\pi$
$180$	−0.484811	+	7.50629i	−0.0361357	+	0.559486i
$181$	−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
$186$	0.386920	−	11.9938i	0.0283703	−	0.879425i
$187$	−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	$-0.121513\pi$
$191$	1.95388	+	3.38422i	0.141378	+	0.244873i	−0.786638	+	0.617415i	$0.788180\pi$
$192$	−12.3651	+	6.25335i	−0.892374	+	0.451297i
$193$	−0.785825	+	1.36109i	−0.0565649	+	0.0979733i	−0.892921	−	0.450213i	$-0.851348\pi$
$193$	−0.785825	+	1.36109i	−0.0565649	+	0.0979733i	0.836356	+	0.548186i	$0.184681\pi$
$194$	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	$-0.0207980\pi$
$198$	15.0604	+	15.2884i	1.07030	+	1.08650i
$199$	−3.17910	−	1.83546i	−0.225361	−	0.130112i	0.383069	−	0.923720i	$-0.374867\pi$
$199$	−3.17910	−	1.83546i	−0.225361	−	0.130112i	−0.608430	+	0.793608i	$0.708200\pi$
$200$	−9.65686	+	0.879654i	−0.682843	+	0.0622010i
$201$	5.16155	+	17.5179i	0.364068	+	1.23561i
$202$	−3.83331	−	4.29713i	−0.269710	−	0.302345i
$203$		0			0
$204$	6.97258	−	19.0403i	0.488178	−	1.33309i
$205$	1.24073	+	2.14901i	0.0866563	+	0.150093i
$206$	18.1054	−	3.76096i	1.26146	−	0.262039i
$207$	−0.790422	+	0.510070i	−0.0549381	+	0.0354523i
$208$	−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	$0.171119\pi$
$211$			14.8763i			1.02413i	−0.858948	+	0.512063i	$0.828881\pi$
$212$	−10.1879	−	23.4642i	−0.699706	−	1.61153i
$213$	−5.68978	−	5.41502i	−0.389857	−	0.371031i
$214$	1.12398	+	5.41090i	0.0768339	+	0.369881i
$215$	−1.99715	−	3.45917i	−0.136205	−	0.235914i
$216$	−14.6282	−	1.41966i	−0.995324	−	0.0965958i
$217$		0			0
$218$	8.70434	−	7.76481i	0.589533	−	0.525899i
$219$	2.34962	−	0.692304i	0.158773	−	0.0467816i
$220$	7.54930	−	10.1911i	0.508973	−	0.687082i
$221$	22.3956	+	12.9301i	1.50649	+	0.869775i
$222$	−6.89960	+	11.1073i	−0.463071	+	0.745470i
$223$			19.4171i			1.30026i	0.759821	+	0.650132i	$0.225287\pi$
$223$			19.4171i			1.30026i	−0.759821	+	0.650132i	$0.774713\pi$
$224$		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	$-0.948689\pi$
$227$	−5.34136	+	9.25151i	−0.354519	+	0.614045i	0.632517	+	0.774547i	$0.282022\pi$
$228$	3.40274	+	4.07147i	0.225352	+	0.269640i
$229$	3.75075	+	6.49650i	0.247857	+	0.429301i	0.962931	−	0.269748i	$-0.0869404\pi$
$229$	3.75075	+	6.49650i	0.247857	+	0.429301i	−0.715074	+	0.699049i	$0.753607\pi$
$230$	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	$-0.637439\pi$
$233$	2.42423	−	1.39963i	0.158817	−	0.0916930i	0.577302	+	0.816531i	$0.304105\pi$
$234$	4.98714	−	18.0683i	0.326019	−	1.18116i
$235$	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	$-0.731367\pi$
$239$	−20.5467			−1.32905			−0.664527	+	0.747265i	$0.731367\pi$
$240$	0.508610	+	8.67067i	0.0328307	+	0.559689i
$241$	9.02728	−	15.6357i	0.581499	−	1.00718i	−0.413804	−	0.910366i	$-0.635800\pi$
$241$	9.02728	−	15.6357i	0.581499	−	1.00718i	0.995302	−	0.0968188i	$-0.0308667\pi$
$242$	−4.19539	−	20.1968i	−0.269690	−	1.29830i
$243$	−12.2984	−	9.57860i	−0.788942	−	0.614468i
$244$	0.0688928	−	0.601848i	0.00441041	−	0.0385294i
$245$		0			0
$246$	−4.27488	+	2.28759i	−0.272556	+	0.145851i
$247$	−5.86064	+	3.38364i	−0.372904	+	0.215296i
$248$	−1.25699	−	13.7993i	−0.0798191	−	0.876255i
$249$	8.51088	+	8.09989i	0.539355	+	0.513310i
$250$	−4.68332	+	14.1900i	−0.296199	+	0.897457i
$251$	−10.4810			−0.661555			−0.330777	−	0.943709i	$-0.607311\pi$
$251$	−10.4810			−0.661555			−0.330777	+	0.943709i	$0.607311\pi$
$252$		0			0
$253$	1.58612			0.0997188
$254$	3.76928	−	11.4206i	0.236505	−	0.716591i
$255$	−9.20692	−	8.76232i	−0.576560	−	0.548718i
$256$	−13.2834	+	8.91915i	−0.830213	+	0.557447i
$257$	−7.24060	+	4.18036i	−0.451656	+	0.260764i	−0.708529	−	0.705681i	$-0.750641\pi$
$257$	−7.24060	+	4.18036i	−0.451656	+	0.260764i	0.256873	+	0.966445i	$0.417308\pi$
$258$	6.88111	−	3.68224i	0.428399	−	0.229246i
$259$		0			0
$260$	−11.0054	−	1.25977i	−0.682524	−	0.0781277i
$261$	16.5955	−	0.821731i	1.02724	−	0.0508639i
$262$	2.41909	+	11.6456i	0.149452	+	0.719468i
$263$	−14.6850	+	25.4352i	−0.905517	+	1.56840i	−0.0852962	+	0.996356i	$0.527184\pi$
$263$	−14.6850	+	25.4352i	−0.905517	+	1.56840i	−0.820221	+	0.572046i	$0.806150\pi$
$264$	19.4262	+	15.3848i	1.19560	+	0.946867i
$265$	−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	$-0.119721\pi$
$269$	17.6649	+	10.1988i	1.07705	+	0.621834i	0.146950	+	0.989144i	$0.453054\pi$
$270$	−4.46811	+	8.05637i	−0.271921	+	0.490295i
$271$	17.8370	−	10.2982i	1.08352	−	0.625572i	0.151678	−	0.988430i	$-0.451532\pi$
$271$	17.8370	−	10.2982i	1.08352	−	0.625572i	0.931844	+	0.362858i	$0.118199\pi$
$272$	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
$276$	−0.833481	+	0.696582i	−0.0501697	+	0.0419293i
$277$	1.97345	−	3.41811i	0.118573	−	0.205374i	−0.800629	−	0.599160i	$-0.795501\pi$
$277$	1.97345	−	3.41811i	0.118573	−	0.205374i	0.919202	+	0.393786i	$0.128835\pi$
$278$	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	$-0.0112649\pi$
$282$	−14.8590	+	23.9206i	−0.884840	+	1.42445i
$283$	23.9744	+	13.8416i	1.42513	+	0.822800i	0.996731	−	0.0807885i	$-0.0257438\pi$
$283$	23.9744	+	13.8416i	1.42513	+	0.822800i	0.428401	+	0.903589i	$0.359077\pi$
$284$	−7.28798	−	5.39876i	−0.432462	−	0.320357i
$285$	3.19045	−	0.940050i	0.188986	−	0.0556837i
$286$	−23.5839	+	21.0383i	−1.39454	+	1.24402i
$287$		0			0
$288$	−16.9647	+	0.446999i	−0.999653	+	0.0263396i
$289$	8.63122	+	14.9497i	0.507719	+	0.879395i
$290$	−1.99715	−	9.61438i	−0.117277	−	0.564576i
$291$	17.1693	+	16.3402i	1.00648	+	0.957879i
$292$	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
$297$	8.66633	+	24.8137i	0.502871	+	1.43984i
$298$	−15.6425	+	3.24936i	−0.906147	+	0.188230i
$299$	−0.692674	−	1.19975i	−0.0400584	−	0.0693831i
$300$	−11.1519	−	4.08385i	−0.643856	−	0.235781i
$301$		0			0
$302$	−10.4496	−	11.7139i	−0.601304	−	0.674061i
$303$	−1.99329	−	6.76507i	−0.114512	−	0.388643i
$304$	4.47664	+	4.18335i	0.256753	+	0.239931i
$305$	−0.328846	−	0.189859i	−0.0188297	−	0.0108713i
$306$	17.6916	−	17.4278i	1.01136	−	0.996283i
$307$			16.6218i			0.948657i	0.880348	+	0.474328i	$0.157309\pi$
$307$			16.6218i			0.948657i	−0.880348	+	0.474328i	$0.842691\pi$
$308$		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	$-0.734690\pi$
$311$	5.37805	−	9.31506i	0.304961	−	0.528209i	0.977253	+	0.212078i	$0.0680231\pi$
$312$	3.15349	−	21.4126i	0.178531	−	1.21225i
$313$	2.47200	+	4.28163i	0.139726	+	0.242012i	0.927393	−	0.374089i	$-0.122045\pi$
$313$	2.47200	+	4.28163i	0.139726	+	0.242012i	−0.787667	+	0.616101i	$0.788711\pi$
$314$	−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	$-0.455424\pi$
$317$	18.9960	−	10.9673i	1.06692	−	0.615987i	0.927338	+	0.374224i	$0.122091\pi$
$318$	1.01017	−	31.3133i	0.0566476	−	1.75596i
$319$	−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
$324$	−15.4515	−	9.23316i	−0.858416	−	0.512953i
$325$	7.57319	−	13.1171i	0.420085	−	0.727609i
$326$	18.3688	−	3.81568i	1.01736	−	0.211331i
$327$	13.7034	−	4.03765i	0.757802	−	0.223283i
$328$	−4.57454	+	3.22756i	−0.252587	+	0.178212i
$329$		0			0
$330$	13.6954	−	7.32873i	0.753908	−	0.403433i
$331$	−3.24073	+	1.87104i	−0.178127	+	0.102841i	−0.586412	−	0.810013i	$-0.699460\pi$
$331$	−3.24073	+	1.87104i	−0.178127	+	0.102841i	0.408286	+	0.912854i	$0.366127\pi$
$332$	10.9015	+	8.07558i	0.598298	+	0.443205i
$333$	−13.4560	+	8.68332i	−0.737383	+	0.475843i
$334$	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
$339$	8.02999	−	8.43743i	0.436129	−	0.458258i
$340$	−11.7931	−	8.73601i	−0.639569	−	0.473777i
$341$	−21.4604	+	12.3902i	−1.16215	+	0.670966i
$342$	1.63479	+	6.28973i	0.0883994	+	0.340110i
$343$		0			0
$344$	7.36347	−	5.19527i	0.397011	−	0.280110i
$345$	0.192440	+	0.653124i	0.0103606	+	0.0351630i
$346$	−19.9556	+	4.14528i	−1.07282	+	0.222852i
$347$	−1.06505	+	1.84472i	−0.0571750	+	0.0990299i	−0.893196	−	0.449667i	$-0.851543\pi$
$347$	−1.06505	+	1.84472i	−0.0571750	+	0.0990299i	0.836021	+	0.548697i	$0.184876\pi$
$348$	18.9014	−	3.29447i	1.01322	−	0.176602i
$349$	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	$-0.501358\pi$
$353$	−16.3912	−	9.46348i	−0.872417	−	0.503690i	−0.868151	+	0.496301i	$0.834691\pi$
$354$	19.5050	+	0.629232i	1.03668	+	0.0334433i
$355$	−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	$-0.176967\pi$
$359$	−0.613000	−	1.06175i	−0.0323529	−	0.0560369i	−0.881748	+	0.471720i	$0.843633\pi$
$360$	−3.97812	+	9.86577i	−0.209666	+	0.519972i
$361$	−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
$366$	0.391486	−	0.630230i	0.0204633	−	0.0329426i
$367$	−17.4966	−	10.1017i	−0.913314	−	0.527302i	−0.0318180	−	0.999494i	$-0.510130\pi$
$367$	−17.4966	−	10.1017i	−0.913314	−	0.527302i	−0.881496	+	0.472192i	$0.843463\pi$
$368$	−0.856383	+	0.916423i	−0.0446420	+	0.0477718i
$369$	−5.93087	+	0.293668i	−0.308749	+	0.0152878i
$370$	6.30019	+	7.06250i	0.327531	+	0.367162i
$371$		0			0
$372$	5.83566	−	15.9357i	0.302565	−	0.826225i
$373$	4.09019	+	7.08442i	0.211782	+	0.366817i	0.952272	−	0.305250i	$-0.0987400\pi$
$373$	4.09019	+	7.08442i	0.211782	+	0.366817i	−0.740490	+	0.672067i	$0.765407\pi$
$374$	−40.9971	+	8.51615i	−2.11991	+	0.440360i
$375$	−12.6169	+	13.2571i	−0.651534	+	0.684593i
$376$	−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	$0.295895\pi$
$379$			31.2020i			1.60274i	−0.598170	+	0.801369i	$0.704105\pi$
$380$	3.52287	−	1.52958i	0.180719	−	0.0784659i
$381$	10.1545	−	10.6697i	0.520229	−	0.546626i
$382$	1.12398	+	5.41090i	0.0575080	+	0.276846i
$383$	−12.2089	−	21.1465i	−0.623848	−	1.08054i	−0.988763	−	0.149495i	$-0.952235\pi$
$383$	−12.2089	−	21.1465i	−0.623848	−	1.08054i	0.364915	−	0.931041i	$-0.381098\pi$
$384$	−19.3775	+	2.91737i	−0.988856	+	0.148877i
$385$		0			0
$386$	−1.65861	+	1.47958i	−0.0844212	+	0.0753089i
$387$	9.54670	−	0.472707i	0.485286	−	0.0240290i
$388$	21.9920	+	16.2911i	1.11647	+	0.827057i
$389$	−7.86740	−	4.54225i	−0.398893	−	0.230301i	0.287113	−	0.957897i	$-0.407304\pi$
$389$	−7.86740	−	4.54225i	−0.398893	−	0.230301i	−0.686006	+	0.727596i	$0.740638\pi$
$390$	−11.5244	−	7.15870i	−0.583559	−	0.362495i
$391$		−	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
$396$	13.4492	+	27.2070i	0.675848	+	1.36720i
$397$	11.6405	+	20.1619i	0.584220	+	1.01190i	0.994972	+	0.100151i	$0.0319326\pi$
$397$	11.6405	+	20.1619i	0.584220	+	1.01190i	−0.410753	+	0.911747i	$0.634734\pi$
$398$	−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	$-0.727368\pi$
$401$	−6.57424	+	3.79564i	−0.328302	+	0.189545i	0.326785	+	0.945099i	$0.394035\pi$
$402$	−0.832748	+	25.8136i	−0.0415337	+	1.28746i
$403$	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
$408$	17.8032	−	22.4799i	0.881390	−	1.11292i
$409$	−3.19509	+	5.53406i	−0.157987	+	0.273642i	−0.934143	−	0.356900i	$-0.883834\pi$
$409$	−3.19509	+	5.53406i	−0.157987	+	0.273642i	0.776156	+	0.630541i	$0.217167\pi$
$410$	0.713738	+	3.43596i	0.0352490	+	0.169690i
$411$	6.73435	+	22.8558i	0.332181	+	1.12739i
$412$	25.9819	+	2.97411i	1.28003	+	0.146524i
$413$		0			0
$414$	−1.28759	+	0.334662i	−0.0632814	+	0.0164477i
$415$	7.36471	−	4.25202i	0.361520	−	0.208723i
$416$	0.578064	−	24.9852i	0.0283419	−	1.22500i
$417$	15.7202	−	16.5179i	0.769823	−	0.808884i
$418$	3.43421	−	10.4054i	0.167972	−	0.508942i
$419$	29.1307			1.42313			0.711565	−	0.702620i	$-0.247987\pi$
$419$	29.1307			1.42313			0.711565	+	0.702620i	$0.247987\pi$
$420$		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
$423$	−28.9788	+	18.7004i	−1.40900	+	0.909245i
$424$	−3.28176	−	36.0272i	−0.159376	−	1.74963i
$425$	17.3790	−	10.0338i	0.843006	−	0.486710i
$426$	−5.24103	−	9.79405i	−0.253929	−	0.474523i
$427$		0			0
$428$	−0.888828	+	7.76481i	−0.0429631	+	0.375326i
$429$	−37.1286	+	10.9398i	−1.79259	+	0.528177i
$430$	−1.14888	−	5.53074i	−0.0554038	−	0.266716i
$431$	9.12282	−	15.8012i	0.439431	−	0.761116i	−0.558215	−	0.829696i	$-0.688514\pi$
$431$	9.12282	−	15.8012i	0.439431	−	0.761116i	0.997646	+	0.0685802i	$0.0218469\pi$
$432$	−19.0159	−	8.39027i	−0.914902	−	0.403677i
$433$	−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
$438$	3.46230	+	0.111694i	0.165435	+	0.00533695i
$439$	−17.5388	+	10.1260i	−0.837081	+	0.483289i	−0.856271	−	0.516527i	$-0.827225\pi$
$439$	−17.5388	+	10.1260i	−0.837081	+	0.483289i	0.0191902	+	0.999816i	$0.493891\pi$
$440$	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	−0.999224	−	0.0393830i	$-0.987461\pi$
$443$	−11.2335	−	19.4570i	−0.533719	−	0.924428i	0.465505	−	0.885045i	$-0.345873\pi$
$444$	−14.1890	+	11.8585i	−0.673381	+	0.562778i
$445$	−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	$0.754227\pi$
$450$	−10.2075	−	10.3620i	−0.481186	−	0.488470i
$451$	8.67086	+	5.00612i	0.408295	+	0.235729i
$452$	8.00588	−	10.8074i	0.376565	−	0.508339i
$453$	−5.43370	−	18.4415i	−0.255297	−	0.866458i
$454$	−11.2738	+	10.0569i	−0.529107	+	0.471996i
$455$		0			0
$456$	2.76513	+	6.97604i	0.129489	+	0.326683i
$457$	−9.09743	−	15.7572i	−0.425560	−	0.737091i	0.570913	−	0.821011i	$-0.306589\pi$
$457$	−9.09743	−	15.7572i	−0.425560	−	0.737091i	−0.996473	+	0.0839196i	$0.973256\pi$
$458$	2.15765	+	10.3870i	0.100820	+	0.485353i
$459$	28.7143	−	10.0286i	1.34027	−	0.468097i
$460$	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	$0.0473068\pi$
$463$			6.37226i			0.296144i	−0.988977	+	0.148072i	$0.952693\pi$
$464$	21.1932	−	6.45504i	0.983872	−	0.299668i
$465$	−7.70568	−	7.33357i	−0.357342	−	0.340086i
$466$	3.87602	−	0.805149i	0.179553	−	0.0372978i
$467$	13.6785	+	23.6918i	0.632964	+	1.09633i	0.986943	+	0.161072i	$0.0514951\pi$
$467$	13.6785	+	23.6918i	0.632964	+	1.09633i	−0.353979	+	0.935253i	$0.615172\pi$
$468$	14.7060	−	22.0545i	0.679785	−	1.01947i
$469$		0			0
$470$	13.5681	+	15.2098i	0.625849	+	0.701576i
$471$	−24.5821	+	7.24298i	−1.13268	+	0.333739i
$472$	22.4412	−	2.04420i	1.03294	−	0.0940918i
$473$	−13.9571	−	8.05816i	−0.641750	−	0.370515i
$474$	−14.4157	−	8.95475i	−0.662135	−	0.411305i
$475$			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	$-0.683650\pi$
$479$	9.91668	−	17.1762i	0.453105	−	0.784800i	0.998577	+	0.0533285i	$0.0169830\pi$
$480$	−3.16009	+	11.8698i	−0.144238	+	0.541780i
$481$	−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
$486$	−12.2707	−	18.3148i	−0.556610	−	0.830774i
$487$	−35.3792	−	20.4262i	−1.60318	−	0.925599i	−0.990845	−	0.135003i	$-0.956896\pi$
$487$	−35.3792	−	20.4262i	−1.60318	−	0.925599i	−0.612339	−	0.790595i	$-0.709771\pi$
$488$	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	$-0.348541\pi$
$491$	20.3003			0.916137			0.458069	+	0.888917i	$0.348541\pi$
$492$	−6.75493	+	1.17737i	−0.304536	+	0.0530799i
$493$	−16.2099	+	28.0764i	−0.730058	+	1.26450i
$494$	−9.37036	+	1.94647i	−0.421593	+	0.0875757i
$495$	19.0007	−	0.940824i	0.854018	−	0.0422869i
$496$	4.42821	−	19.0890i	0.198833	−	0.857123i
$497$		0			0
$498$	7.83964	+	14.6502i	0.351303	+	0.656489i
$499$	29.6416	−	17.1136i	1.32694	−	0.766110i	0.342116	−	0.939658i	$-0.388856\pi$
$499$	29.6416	−	17.1136i	1.32694	−	0.766110i	0.984825	+	0.173548i	$0.0555231\pi$
$500$	−12.5790	+	16.9809i	−0.562551	+	0.759408i
$501$	6.00513	+	5.71514i	0.268289	+	0.255334i
$502$	−14.0756	−	4.64553i	−0.628223	−	0.207340i
$503$	−31.1279			−1.38792			−0.693962	−	0.720011i	$-0.744137\pi$
$503$	−31.1279			−1.38792			−0.693962	+	0.720011i	$0.744137\pi$
$504$		0			0
$505$	−5.10467			−0.227155
$506$	2.13010	+	0.703024i	0.0946946	+	0.0312532i
$507$	8.17858	+	7.78364i	0.363224	+	0.345683i
$508$	10.1240	−	13.6667i	0.449179	−	0.606363i
$509$	34.2107	−	19.7516i	1.51636	−	0.875474i	0.516549	−	0.856257i	$-0.327216\pi$
$509$	34.2107	−	19.7516i	1.51636	−	0.875474i	0.999815	−	0.0192162i	$-0.00611708\pi$
$510$	−8.48078	−	15.8483i	−0.375535	−	0.701773i
$511$		0			0
$512$	−21.7924	+	6.09041i	−0.963095	+	0.269161i
$513$	−1.48431	+	7.81964i	−0.0655341	+	0.345245i
$514$	−11.5767	+	2.40478i	−0.510627	+	0.106070i
$515$	8.19625	−	14.1963i	0.361170	−	0.625564i
$516$	10.8732	−	1.89517i	0.478664	−	0.0834301i
$517$	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	$-0.510452\pi$
$521$	−20.8808	−	12.0555i	−0.914803	−	0.528162i	−0.881973	+	0.471299i	$0.843785\pi$
$522$	22.6514	+	6.25215i	0.991423	+	0.273649i
$523$	−8.02520	+	4.63335i	−0.350917	+	0.202602i	−0.665089	−	0.746764i	$-0.731606\pi$
$523$	−8.02520	+	4.63335i	−0.350917	+	0.202602i	0.314172	+	0.949366i	$0.398273\pi$
$524$	−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
$528$	19.2695	+	29.2715i	0.838598	+	1.27388i
$529$	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
$534$	−9.98240	−	6.20087i	−0.431981	−	0.268338i
$535$	4.24264	+	2.44949i	0.183425	+	0.105901i
$536$	2.70536	+	29.6995i	0.116854	+	1.28282i
$537$	1.15353	−	0.339883i	0.0497786	−	0.0146670i
$538$	19.2028	+	21.5263i	0.827892	+	0.928066i
$539$		0			0
$540$	−9.57136	+	8.83897i	−0.411886	+	0.380369i
$541$	−12.9508	−	22.4315i	−0.556800	−	0.964406i	−0.997761	−	0.0668796i	$-0.978696\pi$
$541$	−12.9508	−	22.4315i	−0.556800	−	0.964406i	0.440961	−	0.897526i	$-0.354638\pi$
$542$	28.5189	−	5.92412i	1.22499	−	0.254463i
$543$	−7.91746	−	7.53512i	−0.339771	−	0.323363i
$544$	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	$-0.751315\pi$
$547$		−	32.9387i		−	1.40836i	0.710022	−	0.704179i	$-0.248685\pi$
$548$	10.9577	+	25.2372i	0.468088	+	1.07808i
$549$	0.763497	−	0.492695i	0.0325853	−	0.0210277i
$550$	4.98792	+	24.0120i	0.212686	+	1.02388i
$551$	−4.24192	−	7.34722i	−0.180712	−	0.313002i
$552$	−1.42808	+	0.566055i	−0.0607832	+	0.0240929i
$553$		0			0
$554$	4.16528	−	3.71569i	0.176966	−	0.157864i
$555$	3.27606	+	11.1186i	0.139061	+	0.471960i
$556$	15.6730	−	21.1576i	0.664685	−	0.897282i
$557$	−25.8991	−	14.9528i	−1.09738	−	0.633572i	−0.161847	−	0.986816i	$-0.551745\pi$
$557$	−25.8991	−	14.9528i	−1.09738	−	0.633572i	−0.935531	+	0.353244i	$0.885079\pi$
$558$	14.8069	−	14.5861i	0.626827	−	0.617480i
$559$			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	−0.326284	−	0.945272i	$-0.605797\pi$
$563$	15.5531	−	26.9388i	0.655487	−	1.13534i	0.981771	−	0.190065i	$-0.0608699\pi$
$564$	−30.5575	+	25.5384i	−1.28670	+	1.07536i
$565$	−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	$-0.787436\pi$
$569$	−15.3022	+	8.83472i	−0.641501	+	0.370371i	0.143691	+	0.989623i	$0.454103\pi$
$570$	4.70131	+	0.151665i	0.196916	+	0.00635253i
$571$	−6.51130	−	3.75930i	−0.272490	−	0.157322i	0.357529	−	0.933902i	$-0.383619\pi$
$571$	−6.51130	−	3.75930i	−0.272490	−	0.157322i	−0.630018	+	0.776580i	$0.716953\pi$
$572$	−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
$576$	−22.9810	−	6.91902i	−0.957542	−	0.288292i
$577$	−2.13156	+	3.69196i	−0.0887378	+	0.153698i	−0.906978	−	0.421178i	$-0.861617\pi$
$577$	−2.13156	+	3.69196i	−0.0887378	+	0.153698i	0.818240	+	0.574877i	$0.194950\pi$
$578$	4.96517	+	23.9025i	0.206524	+	0.994214i
$579$	−2.61119	+	0.769374i	−0.108517	+	0.0319741i
$580$	1.57932	−	13.7969i	0.0655776	−	0.572887i
$581$		0			0
$582$	15.8152	+	29.5542i	0.655560	+	1.22506i
$583$	−56.0289	+	32.3483i	−2.32048	+	1.33973i
$584$	3.98351	−	0.362862i	0.164839	−	0.0150154i
$585$	−9.00941	−	13.9613i	−0.372493	−	0.577228i
$586$	−0.0876693	+	0.265631i	−0.00362159	+	0.0109731i
$587$	−43.2909			−1.78681			−0.893404	−	0.449253i	$-0.851690\pi$
$587$	−43.2909			−1.78681			−0.893404	+	0.449253i	$0.851690\pi$
$588$		0			0
$589$	−7.50407			−0.309200
$590$	4.42697	−	13.4133i	0.182255	−	0.552218i
$591$	2.18856	−	2.29961i	0.0900252	−	0.0945931i
$592$	−14.5789	+	15.6010i	−0.599189	+	0.641197i
$593$	−4.99583	+	2.88434i	−0.205154	+	0.118446i	−0.599057	−	0.800706i	$-0.704458\pi$
$593$	−4.99583	+	2.88434i	−0.205154	+	0.118446i	0.393903	+	0.919152i	$0.371125\pi$
$594$	0.640266	+	37.1650i	0.0262704	+	1.52490i
$595$		0			0
$596$	−22.4475	−	2.56954i	−0.919486	−	0.105252i
$597$	−1.79703	−	6.09897i	−0.0735477	−	0.249614i
$598$	−0.398466	−	1.91823i	−0.0162945	−	0.0784422i
$599$	17.8985	−	31.0011i	0.731312	−	1.26667i	−0.225010	−	0.974356i	$-0.572242\pi$
$599$	17.8985	−	31.0011i	0.731312	−	1.26667i	0.956323	−	0.292313i	$-0.0944251\pi$
$600$	−13.1665	−	10.4274i	−0.537520	−	0.425695i
$601$	−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
$606$	0.321592	−	9.96872i	0.0130638	−	0.404951i
$607$	41.0224	−	23.6843i	1.66505	−	0.961316i	0.694801	−	0.719202i	$-0.255492\pi$
$607$	41.0224	−	23.6843i	1.66505	−	0.961316i	0.970248	−	0.242115i	$-0.0778411\pi$
$608$	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
$612$	31.4838	−	15.5634i	1.27266	−	0.629112i
$613$	−1.39456	+	2.41545i	−0.0563257	+	0.0975590i	−0.892813	−	0.450427i	$-0.851272\pi$
$613$	−1.39456	+	2.41545i	−0.0563257	+	0.0975590i	0.836488	+	0.547986i	$0.184605\pi$
$614$	−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	$-0.143569\pi$
$618$	27.2071	+	16.9005i	1.09443	+	0.679838i
$619$	−4.88830	−	2.82226i	−0.196477	−	0.113436i	0.398534	−	0.917154i	$-0.369519\pi$
$619$	−4.88830	−	2.82226i	−0.196477	−	0.113436i	−0.595011	+	0.803717i	$0.702852\pi$
$620$	−9.87013	−	7.31156i	−0.396394	−	0.293639i
$621$	−1.60078	−	0.303857i	−0.0642369	−	0.0121934i
$622$	11.3513	−	10.1260i	0.455144	−	0.406017i
$623$		0			0
$624$	13.7258	−	27.3586i	0.549472	−	1.09522i
$625$	−1.94767	−	3.37346i	−0.0779067	−	0.134938i
$626$	1.42203	+	6.84573i	0.0568359	+	0.273610i
$627$	9.25178	−	9.72122i	0.369481	−	0.388228i
$628$	−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	$0.0404828\pi$
$631$			6.37226i			0.253676i	−0.991923	+	0.126838i	$0.959517\pi$
$632$	−17.7894	−	8.21807i	−0.707625	−	0.326897i
$633$	−17.7634	+	18.6648i	−0.706033	+	0.741858i
$634$	30.3719	−	6.30904i	1.20622	−	0.250564i
$635$	−5.33056	−	9.23281i	−0.211537	−	0.366393i
$636$	15.2358	−	41.6048i	0.604137	−	1.64974i
$637$		0			0
$638$	−26.3747	−	29.5660i	−1.04419	−	1.17053i
$639$	−0.672815	−	13.5881i	−0.0266162	−	0.537535i
$640$	−1.93854	+	14.0504i	−0.0766274	+	0.555390i
$641$	−14.2860	−	8.24802i	−0.564263	−	0.325777i	0.190592	−	0.981669i	$-0.438959\pi$
$641$	−14.2860	−	8.24802i	−0.564263	−	0.325777i	−0.754855	+	0.655892i	$0.772293\pi$
$642$	−5.05080	+	8.13098i	−0.199339	+	0.320904i
$643$		−	2.36672i		−	0.0933343i	−0.998910	−	0.0466671i	$-0.985140\pi$
$643$		−	2.36672i		−	0.0933343i	0.998910	−	0.0466671i	$-0.0148600\pi$
$644$		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	$-0.761716\pi$
$647$	5.67476	−	9.82897i	0.223098	−	0.386417i	0.955747	+	0.294190i	$0.0950497\pi$
$648$	−16.6583	−	19.2484i	−0.654400	−	0.756149i
$649$	−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	−0.510522	+	0.859865i	$0.670548\pi$
$653$	−38.5978	+	22.2844i	−1.51045	+	0.872057i	−0.999926	+	0.0121923i	$0.996119\pi$
$654$	20.1928	+	0.651421i	0.789601	+	0.0254726i
$655$	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	$-0.503661\pi$
$659$	−0.590533			−0.0230039			−0.0115019	+	0.999934i	$0.503661\pi$
$660$	21.6407	−	3.77193i	0.842365	−	0.146822i
$661$	21.5502	−	37.3261i	0.838206	−	1.45182i	−0.0531863	−	0.998585i	$-0.516938\pi$
$661$	21.5502	−	37.3261i	0.838206	−	1.45182i	0.891393	−	0.453232i	$-0.149729\pi$
$662$	−5.18148	+	1.07633i	−0.201384	+	0.0418326i
$663$	12.6594	+	42.9651i	0.491652	+	1.66862i
$664$	11.0609	+	15.6771i	0.429248	+	0.608390i
$665$		0			0
$666$	−21.9196	+	5.69722i	−0.849367	+	0.220763i
$667$	1.50407	−	0.868374i	0.0582377	−	0.0336236i
$668$	7.69191	+	5.69798i	0.297609	+	0.220461i
$669$	−23.1855	+	24.3619i	−0.896403	+	0.941887i
$670$	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
$675$	−5.87379	−	16.8180i	−0.226082	−	0.647325i
$676$	10.4759	+	7.76027i	0.402918	+	0.298472i
$677$	35.8437	−	20.6944i	1.37759	−	0.795349i	0.385717	−	0.922617i	$-0.373954\pi$
$677$	35.8437	−	20.6944i	1.37759	−	0.795349i	0.991868	+	0.127268i	$0.0406207\pi$
$678$	14.5237	−	7.77198i	0.557780	−	0.298481i
$679$		0			0
$680$	−11.9655	−	16.9592i	−0.458857	−	0.650356i
$681$	−17.7486	+	5.22955i	−0.680129	+	0.200397i
$682$	−34.3123	+	7.12755i	−1.31388	+	0.272928i
$683$	−2.26745	+	3.92734i	−0.0867615	+	0.150275i	−0.906140	−	0.422977i	$-0.860985\pi$
$683$	−2.26745	+	3.92734i	−0.0867615	+	0.150275i	0.819379	+	0.573252i	$0.194318\pi$
$684$	−0.592360	+	9.17146i	−0.0226495	+	0.350679i
$685$	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
$690$	−0.0310476	+	0.962416i	−0.00118196	+	0.0366385i
$691$	−23.6340	+	13.6451i	−0.899079	+	0.519084i	−0.876901	−	0.480670i	$-0.840393\pi$
$691$	−23.6340	+	13.6451i	−0.899079	+	0.519084i	−0.0221779	+	0.999754i	$0.507060\pi$
$692$	−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
$696$	26.8440	+	3.95339i	1.01752	+	0.149853i
$697$	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	$0.944389\pi$
$702$	27.8321	−	16.7146i	1.05045	−	0.630851i
$703$	7.08130	+	4.08839i	0.267076	+	0.154197i
$704$	26.2321	+	30.8122i	0.988659	+	1.16128i
$705$	7.05532	+	23.9451i	0.265719	+	0.901826i
$706$	−17.8182	−	19.9742i	−0.670598	−	0.751740i
$707$		0			0
$708$	25.9155	+	9.49030i	0.973965	+	0.356667i
$709$	14.8003	+	25.6349i	0.555837	+	0.962738i	0.997838	+	0.0657232i	$0.0209354\pi$
$709$	14.8003	+	25.6349i	0.555837	+	0.962738i	−0.442001	+	0.897015i	$0.645731\pi$
$710$	−7.87204	+	1.63523i	−0.295432	+	0.0613689i
$711$	−11.2698	−	17.4640i	−0.422649	−	0.654952i
$712$	−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
$717$	−25.7792	−	24.5343i	−0.962740	−	0.916249i
$718$	−0.352633	−	1.69759i	−0.0131601	−	0.0633534i
$719$	1.35786	+	2.35188i	0.0506395	+	0.0877102i	0.890234	−	0.455503i	$-0.150541\pi$
$719$	1.35786	+	2.35188i	0.0506395	+	0.0877102i	−0.839595	+	0.543214i	$0.817207\pi$
$720$	−9.71531	+	11.4861i	−0.362068	+	0.428062i
$721$		0			0
$722$	−17.5752	+	15.6782i	−0.654081	+	0.583480i
$723$	29.9964	−	8.83830i	1.11558	−	0.328700i
$724$	−10.1414	−	7.51250i	−0.376902	−	0.279200i
$725$	16.4444	+	9.49416i	0.610729	+	0.352604i
$726$	18.8527	−	30.3498i	0.699688	−	1.12638i
$727$		−	18.9752i		−	0.703753i	−0.936046	−	0.351876i	$-0.885544\pi$
$727$		−	18.9752i		−	0.703753i	0.936046	−	0.351876i	$-0.114456\pi$
$728$		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
$732$	0.805090	−	0.672854i	0.0297570	−	0.0248694i
$733$	7.65295	+	13.2553i	0.282668	+	0.489596i	0.972041	−	0.234811i	$-0.0754471\pi$
$733$	7.65295	+	13.2553i	0.282668	+	0.489596i	−0.689373	+	0.724407i	$0.742114\pi$
$734$	−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
$738$	−8.09509	−	2.23438i	−0.297984	−	0.0822486i
$739$	23.2697	+	13.4348i	0.855989	+	0.494205i	0.862667	−	0.505772i	$-0.168792\pi$
$739$	23.2697	+	13.4348i	0.855989	+	0.494205i	−0.00667810	+	0.999978i	$0.502126\pi$
$740$	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	$-0.358301\pi$
$743$	23.4748			0.861208			0.430604	+	0.902541i	$0.358301\pi$
$744$	14.9003	−	18.8144i	0.546271	−	0.689769i
$745$	−7.08130	+	12.2652i	−0.259439	+	0.449361i
$746$	2.35291	+	11.3270i	0.0861462	+	0.414711i
$747$	1.00641	+	20.3253i	0.0368227	+	0.743663i
$748$	−58.8321	−	6.73444i	−2.15112	−	0.246235i
$749$		0			0
$750$	−22.8200	+	12.2115i	−0.833268	+	0.445901i
$751$	31.1457	−	17.9820i	1.13652	−	0.656172i	0.190955	−	0.981599i	$-0.438841\pi$
$751$	31.1457	−	17.9820i	1.13652	−	0.656172i	0.945567	+	0.325427i	$0.105508\pi$
$752$	−31.3971	+	33.5983i	−1.14493	+	1.22520i
$753$	−13.1501	−	12.5151i	−0.479217	−	0.456076i
$754$	−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
$759$	1.99005	+	1.89395i	0.0722344	+	0.0687462i
$760$	5.40903	−	0.492715i	0.196206	−	0.0178727i
$761$	34.9126	−	20.1568i	1.26558	−	0.730684i	0.291433	−	0.956591i	$-0.405868\pi$
$761$	34.9126	−	20.1568i	1.26558	−	0.730684i	0.974149	+	0.225908i	$0.0725347\pi$
$762$	18.3662	−	9.82820i	0.665338	−	0.356038i
$763$		0			0
$764$	−0.888828	+	7.76481i	−0.0321567	+	0.280921i
$765$	−1.08872	−	21.9875i	−0.0393627	−	0.794961i
$766$	−7.02328	−	33.8103i	−0.253761	−	1.22162i
$767$	−17.5991	+	30.4825i	−0.635465	+	1.10066i
$768$	−27.3164	−	4.67086i	−0.985694	−	0.168545i
$769$	−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	$-0.470964\pi$
$773$	−20.1789	−	11.6503i	−0.725784	−	0.419032i	−0.816878	+	0.576811i	$0.804297\pi$
$774$	13.0304	+	3.59659i	0.468367	+	0.129277i
$775$	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
$780$	−12.3038	−	14.7218i	−0.440546	−	0.527127i
$781$	−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
$786$	−10.8706	+	17.4999i	−0.387741	+	0.624201i
$787$	−2.76123	−	1.59420i	−0.0984271	−	0.0568269i	0.449978	−	0.893039i	$-0.351432\pi$
$787$	−2.76123	−	1.59420i	−0.0984271	−	0.0568269i	−0.548406	+	0.836212i	$0.684765\pi$
$788$	2.18199	−	2.94554i	0.0777301	−	0.104931i
$789$	−48.7964	+	14.3776i	−1.73720	+	0.511856i
$790$	−9.16617	+	8.17678i	−0.326118	+	0.290917i
$791$		0			0
$792$	6.00271	+	42.4990i	0.213297	+	1.51014i
$793$	0.669079	+	1.15888i	0.0237597	+	0.0411530i
$794$	6.69628	+	32.2361i	0.237642	+	1.14402i
$795$	−20.1180	−	19.1465i	−0.713512	−	0.679057i
$796$	−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
$801$	−7.80395	−	12.0933i	−0.275739	−	0.427294i
$802$	−10.5113	+	2.18347i	−0.371167	+	0.0771010i
$803$	−3.57674	−	6.19509i	−0.126220	−	0.218620i
$804$	−12.5598	+	34.2975i	−0.442950	+	1.20958i
$805$		0			0
$806$	20.3757	+	22.8412i	0.717705	+	0.804546i
$807$	9.98534	+	33.8894i	0.351500	+	1.19296i
$808$	−1.04476	−	11.4694i	−0.0367545	−	0.403491i
$809$	−18.4879	−	10.6740i	−0.649999	−	0.375277i	0.138457	−	0.990368i	$-0.455786\pi$
$809$	−18.4879	−	10.6740i	−0.649999	−	0.375277i	−0.788456	+	0.615091i	$0.789119\pi$
$810$	−15.2259	+	4.77277i	−0.534984	+	0.167698i
$811$		−	52.7856i		−	1.85355i	−0.375614	−	0.926776i	$-0.622568\pi$
$811$		−	52.7856i		−	1.85355i	0.375614	−	0.926776i	$-0.377432\pi$
$812$		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
$816$	33.8728	−	22.2986i	1.18579	−	0.780607i
$817$	−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	$-0.634293\pi$
$821$	5.03883	−	2.90917i	0.175857	−	0.101531i	0.585344	+	0.810785i	$0.300959\pi$
$822$	−1.08650	+	33.6793i	−0.0378960	+	1.17470i
$823$	8.78912	+	5.07440i	0.306369	+	0.176882i	0.645301	−	0.763929i	$-0.276732\pi$
$823$	8.78912	+	5.07440i	0.306369	+	0.176882i	−0.338931	+	0.940811i	$0.610065\pi$
$824$	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	$-0.126624\pi$
$827$	53.0241			1.84383			0.921915	+	0.387393i	$0.126624\pi$
$828$	−1.87751	−	0.121263i	−0.0652480	−	0.00421420i
$829$	−16.3511	+	28.3210i	−0.567898	+	0.983628i	0.428876	+	0.903364i	$0.358910\pi$
$829$	−16.3511	+	28.3210i	−0.567898	+	0.983628i	−0.996774	+	0.0802647i	$0.974423\pi$
$830$	11.7752	−	2.44600i	0.408722	−	0.0849021i
$831$	6.55749	−	1.93213i	0.227477	−	0.0670250i
$832$	11.8506	−	33.2979i	0.410845	−	1.15440i
$833$		0			0
$834$	28.4329	−	15.2151i	0.984552	−	0.526857i
$835$	5.19641	−	3.00015i	0.179829	−	0.103824i
$836$	9.22401	−	12.4518i	0.319019	−	0.430655i
$837$	24.0323	−	8.39341i	0.830677	−	0.290119i
$838$	39.1214	+	12.9117i	1.35143	+	0.446028i
$839$	37.5962			1.29796			0.648982	−	0.760803i	$-0.275195\pi$
$839$	37.5962			1.29796			0.648982	+	0.760803i	$0.275195\pi$
$840$		0			0
$841$	−1.67632			−0.0578040
$842$	−43.0849	−	14.2199i	−1.48481	−	0.490049i
$843$	1.41645	−	1.48833i	0.0487853	−	0.0512606i
$844$	−17.7101	+	23.9075i	−0.609607	+	0.822931i
$845$	7.07716	−	4.08600i	0.243462	−	0.140563i
$846$	−47.2061	+	12.2695i	−1.62298	+	0.421835i
$847$		0			0
$848$	11.5612	−	49.8377i	0.397013	−	1.71143i
$849$	13.5519	+	45.9939i	0.465099	+	1.57851i
$850$	27.7866	−	5.77200i	0.953074	−	0.197978i
$851$	−0.836944	+	1.44963i	−0.0286901	+	0.0496927i
$852$	−2.69744	−	15.4760i	−0.0924127	−	0.530200i
$853$	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	$-0.151285\pi$
$857$	27.4440	+	15.8448i	0.937471	+	0.541249i	0.0483040	+	0.998833i	$0.484618\pi$
$858$	−54.7111	−	1.76499i	−1.86781	−	0.0602556i
$859$	5.22874	−	3.01882i	0.178402	−	0.103001i	−0.408139	−	0.912920i	$-0.633822\pi$
$859$	5.22874	−	3.01882i	0.178402	−	0.103001i	0.586542	+	0.809919i	$0.300489\pi$
$860$	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	−0.974140	−	0.225944i	$-0.927453\pi$
$863$	−20.0569	−	34.7395i	−0.682744	−	1.18255i	0.291396	−	0.956602i	$-0.405880\pi$
$864$	−21.8187	−	19.6963i	−0.742288	−	0.670081i
$865$	−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
$870$	8.97454	−	14.4476i	0.304265	−	0.489818i
$871$	−40.3415	−	23.2912i	−1.36692	−	0.789192i
$872$	23.2326	−	2.11628i	0.786755	−	0.0716664i
$873$	2.03027	+	41.0029i	0.0687142	+	1.38774i
$874$	0.452179	+	0.506892i	0.0152952	+	0.0171459i
$875$		0			0
$876$	4.60023	+	1.68461i	0.155427	+	0.0569177i
$877$	21.9436	+	38.0074i	0.740983	+	1.28342i	0.952048	+	0.305948i	$0.0989733\pi$
$877$	21.9436	+	38.0074i	0.740983	+	1.28342i	−0.211066	+	0.977472i	$0.567693\pi$
$878$	−28.0421	+	5.82507i	−0.946375	+	0.196587i
$879$	−0.236182	+	0.248166i	−0.00796622	+	0.00837043i
$880$	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	$-0.893520\pi$
$883$		−	19.5118i		−	0.656625i	0.944569	−	0.328312i	$-0.106480\pi$
$884$	20.5985	+	47.4417i	0.692804	+	1.59564i
$885$	11.9263	−	12.5314i	0.400898	−	0.421240i
$886$	−6.46214	−	31.1090i	−0.217100	−	1.04513i
$887$	−13.4459	−	23.2890i	−0.451470	−	0.781969i	0.547007	−	0.837128i	$-0.315767\pi$
$887$	−13.4459	−	23.2890i	−0.451470	−	0.781969i	−0.998478	+	0.0551585i	$0.982434\pi$
$888$	−24.3114	+	9.63641i	−0.815836	+	0.323377i
$889$		0			0
$890$	−6.34727	+	5.66215i	−0.212761	+	0.189796i
$891$	−18.7561	+	41.4811i	−0.628354	+	1.38967i
$892$	−23.1159	+	31.2050i	−0.773977	+	1.04482i
$893$	15.2503	+	8.80477i	0.510332	+	0.294640i
$894$	−23.5061	−	14.6015i	−0.786161	−	0.488348i
$895$		−	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
$900$	−9.11548	−	18.4401i	−0.303849	−	0.614670i
$901$	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
$906$	0.876655	−	27.1746i	0.0291249	−	0.902816i
$907$	16.1538	+	9.32642i	0.536379	+	0.309679i	0.743610	−	0.668613i	$-0.233112\pi$
$907$	16.1538	+	9.32642i	0.536379	+	0.309679i	−0.207231	+	0.978292i	$0.566445\pi$
$908$	−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	$-0.542996\pi$
$911$	−8.12909			−0.269329			−0.134664	+	0.990891i	$0.542996\pi$
$912$	0.621439	+	10.5941i	0.0205779	+	0.350807i
$913$	17.1561	−	29.7153i	0.567785	−	0.983433i
$914$	−5.23336	−	25.1936i	−0.173104	−	0.833330i
$915$	−0.185885	−	0.630877i	−0.00614516	−	0.0208561i
$916$	−1.70623	+	14.9057i	−0.0563755	+	0.492497i
$917$		0			0
$918$	43.0072	−	0.740913i	1.41945	−	0.0244538i
$919$	−15.2109	+	8.78201i	−0.501761	+	0.289692i	−0.729440	−	0.684044i	$-0.760219\pi$
$919$	−15.2109	+	8.78201i	−0.501761	+	0.289692i	0.227680	+	0.973736i	$0.426886\pi$
$920$	0.100865	+	1.10730i	0.00332542	+	0.0365065i
$921$	−19.8477	+	20.8548i	−0.654004	+	0.687189i
$922$	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
$927$	21.2697	+	32.9603i	0.698589	+	1.08256i
$928$	31.3228	+	0.724692i	1.02822	+	0.0237892i
$929$	−33.7624	+	19.4927i	−1.10771	+	0.639535i	−0.938235	−	0.345999i	$-0.887540\pi$
$929$	−33.7624	+	19.4927i	−1.10771	+	0.639535i	−0.169473	+	0.985535i	$0.554207\pi$
$930$	−7.09794	−	13.2641i	−0.232751	−	0.434948i
$931$		0			0
$932$	5.56221	+	0.636699i	0.182196	+	0.0208558i
$933$	17.8705	−	5.26547i	0.585055	−	0.172384i
$934$	7.86863	+	37.8799i	0.257470	+	1.23947i
$935$	−18.5592	+	32.1455i	−0.606951	+	1.05127i
$936$	29.5249	−	23.1001i	0.965051	−	0.755052i
$937$	−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	$-0.167033\pi$
$941$	26.5129	+	15.3073i	0.864297	+	0.499002i	−0.00115159	+	0.999999i	$0.500367\pi$
$942$	−36.2231	−	1.16856i	−1.18021	−	0.0380737i
$943$	−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	$-0.0858438\pi$
$947$	7.73005	+	13.3888i	0.251193	+	0.435079i	−0.712662	+	0.701508i	$0.752510\pi$
$948$	−15.3907	−	18.4154i	−0.499866	−	0.598104i
$949$	−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	$0.930099\pi$
$954$	38.6579	−	38.0815i	1.25160	−	1.23293i
$955$	4.24264	+	2.44949i	0.137289	+	0.0792636i
$956$	−33.0203	−	24.4606i	−1.06795	−	0.791113i
$957$	−13.7147	−	46.5464i	−0.443333	−	1.50463i
$958$	20.9308	−	18.6715i	0.676243	−	0.603250i
$959$		0			0
$960$	−9.50498	+	14.5400i	−0.306772	+	0.469277i
$961$	−3.50000	−	6.06218i	−0.112903	−	0.195554i
$962$	−6.78340	−	32.6555i	−0.218705	−	1.05286i
$963$	−9.85035	+	6.35656i	−0.317423	+	0.204837i
$964$	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	$0.230179\pi$
$967$			41.1554i			1.32347i	−0.749738	+	0.661734i	$0.769821\pi$
$968$	17.3017	−	37.4525i	0.556098	−	1.20377i
$969$	−11.2494	−	10.7061i	−0.361381	−	0.343930i
$970$	23.7544	−	4.93441i	0.762709	−	0.158434i
$971$	−14.4445	−	25.0186i	−0.463546	−	0.802886i	0.535588	−	0.844479i	$-0.320090\pi$
$971$	−14.4445	−	25.0186i	−0.463546	−	0.802886i	−0.999135	+	0.0415934i	$0.986757\pi$
$972$	−8.36134	−	30.0348i	−0.268190	−	0.963366i
$973$		0			0
$974$	−38.4593	−	43.1128i	−1.23232	−	1.38142i
$975$	25.1647	−	7.41465i	0.805915	−	0.237459i
$976$	0.827212	−	0.885206i	0.0264784	−	0.0283348i
$977$	40.6932	+	23.4942i	1.30189	+	0.751646i	0.980728	−	0.195378i	$-0.0625935\pi$
$977$	40.6932	+	23.4942i	1.30189	+	0.751646i	0.321161	+	0.947024i	$0.395927\pi$
$978$	27.6029	+	17.1464i	0.882645	+	0.548281i
$979$			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	$-0.976914\pi$
$983$	−13.6677	+	23.6731i	−0.435931	+	0.755054i	0.561440	+	0.827517i	$0.310247\pi$
$984$	−9.59346	−	1.41285i	−0.305828	−	0.0450401i
$985$	−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
$990$	25.9342	+	7.15827i	0.824243	+	0.227505i
$991$	18.0000	+	10.3923i	0.571789	+	0.330122i	0.757863	−	0.652413i	$-0.226243\pi$
$991$	18.0000	+	10.3923i	0.571789	+	0.330122i	−0.186075	+	0.982536i	$0.559577\pi$
$992$	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
$996$	4.03488	+	23.1494i	0.127850	+	0.733516i
$997$	−6.02119	+	10.4290i	−0.190693	+	0.330290i	−0.945480	−	0.325680i	$-0.894407\pi$
$997$	−6.02119	+	10.4290i	−0.190693	+	0.330290i	0.754787	+	0.655970i	$0.227740\pi$
$998$	47.3929	−	9.84472i	1.50020	−	0.311629i
$999$	−27.2513	−	5.17281i	−0.862192	−	0.163660i

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

)

Twists

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

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

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	588.2.n.h.263.10

Level	$588$
Weight	$2$
Character	588.263
Analytic conductor	$4.695$
Analytic rank	$0$
Dimension	$24$
Inner twists	$8$