LMFDB - Embedded newform 588.2.n.h.263.9

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			263.9
Character	$\chi$	$=$	588.263
Dual form			588.2.n.h.275.9

$q$ -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	−0.722722	−	0.691139i	$-0.757109\pi$
$5$	−1.08570	+	0.626827i	−0.485538	+	0.280326i	0.237183	+	0.971465i	$0.423776\pi$
$6$	−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	$-0.290098\pi$
$13$	4.41798			1.22533			0.612664	+	0.790344i	$0.290098\pi$
$14$		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	0.966918	−	0.255089i	$-0.0821048\pi$
$17$	5.06920	+	2.92671i	1.22946	+	0.709831i	0.262545	+	0.964920i	$0.415438\pi$
$18$	−1.12883	+	4.08971i	−0.266067	+	0.963954i
$19$	−1.32654	+	0.765881i	−0.304330	+	0.175705i	−0.644386	−	0.764700i	$-0.722887\pi$
$19$	−1.32654	+	0.765881i	−0.304330	+	0.175705i	0.340056	+	0.940405i	$0.389554\pi$
$20$	−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	0.830014	−	0.557743i	$-0.188333\pi$
$31$	4.24264	+	2.44949i	0.762001	+	0.439941i	−0.0680129	+	0.997684i	$0.521666\pi$
$32$	−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	$-0.950603\pi$
$41$		−	1.97938i		−	0.309127i	0.987983	−	0.154564i	$-0.0493971\pi$
$42$		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	$-0.850128\pi$
$47$	−5.74813	−	9.95606i	−0.838451	−	1.45224i	0.0527378	−	0.998608i	$-0.483205\pi$
$48$	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	$0.340216\pi$
$59$	−3.98351	+	6.89964i	−0.518608	+	0.898256i	−0.999766	+	0.0216222i	$0.993117\pi$
$60$	2.78493	+	3.33226i	0.359534	+	0.430193i
$61$	0.151445	+	0.262310i	0.0193905	+	0.0335853i	0.875558	−	0.483113i	$-0.160494\pi$
$61$	0.151445	+	0.262310i	0.0193905	+	0.0335853i	−0.856167	+	0.516699i	$0.827161\pi$
$62$	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	−0.904435	−	0.426612i	$-0.859707\pi$
$73$	−0.707107	+	1.22474i	−0.0827606	+	0.143346i	0.821674	+	0.569958i	$0.193040\pi$
$74$	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	$-0.621426\pi$
$83$	−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
$87$	−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	−0.263363	−	0.964697i	$-0.584832\pi$
$89$	4.15480	−	2.39878i	0.440408	−	0.254270i	0.703771	+	0.710427i	$0.251498\pi$
$90$	−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	$-0.744471\pi$
$97$	−13.6844			−1.38944			−0.694719	+	0.719281i	$0.744471\pi$
$98$		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	0.665073	−	0.746778i	$-0.268400\pi$
$101$	3.52631	+	2.03591i	0.350881	+	0.202581i	−0.314192	+	0.949359i	$0.601734\pi$
$102$	0.462300	−	14.3304i	0.0457746	−	1.41892i
$103$	−11.3239	+	6.53788i	−1.11578	+	0.644197i	−0.940321	−	0.340290i	$-0.889475\pi$
$103$	−11.3239	+	6.53788i	−1.11578	+	0.644197i	−0.175461	+	0.984486i	$0.556141\pi$
$104$	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	0.621747	−	0.783218i	$-0.286423\pi$
$131$	−4.20524	−	7.28368i	−0.367413	−	0.636378i	−0.989160	+	0.146840i	$0.953090\pi$
$132$	−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	$0.188557\pi$
$139$			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
$144$	−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	$-0.632298\pi$
$157$	7.39785	−	12.8135i	0.590413	−	1.02262i	0.994177	−	0.107762i	$-0.0343684\pi$
$158$	−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	$-0.559289\pi$
$167$	−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
$171$	−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	0.0561749	−	0.998421i	$-0.482110\pi$
$173$	12.4811	−	7.20596i	0.948920	−	0.547859i	0.892745	+	0.450562i	$0.148776\pi$
$174$	−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	$-0.424647\pi$
$181$	6.31042			0.469050			0.234525	+	0.972110i	$0.424647\pi$
$182$		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	0.608430	−	0.793608i	$-0.291800\pi$
$199$	3.17910	+	1.83546i	0.225361	+	0.130112i	−0.383069	+	0.923720i	$0.625133\pi$
$200$	−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	$-0.774713\pi$
$223$		−	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	−0.632517	−	0.774547i	$-0.717978\pi$
$227$	5.34136	−	9.25151i	0.354519	−	0.614045i	0.987035	+	0.160502i	$0.0513114\pi$
$228$	3.40274	+	4.07147i	0.225352	+	0.269640i
$229$	−3.75075	−	6.49650i	−0.247857	−	0.429301i	0.715074	−	0.699049i	$-0.246393\pi$
$229$	−3.75075	−	6.49650i	−0.247857	−	0.429301i	−0.962931	+	0.269748i	$0.913060\pi$
$230$	−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	$0.364200\pi$
$241$	−9.02728	+	15.6357i	−0.581499	+	1.00718i	−0.995302	+	0.0968188i	$0.969133\pi$
$242$	−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	$-0.392689\pi$
$251$	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
$255$	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	−0.256873	−	0.966445i	$-0.582692\pi$
$257$	7.24060	−	4.18036i	0.451656	−	0.260764i	0.708529	+	0.705681i	$0.249359\pi$
$258$	−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	−0.146950	−	0.989144i	$-0.546946\pi$
$269$	−17.6649	−	10.1988i	−1.07705	−	0.621834i	−0.930099	+	0.367310i	$0.880279\pi$
$270$	−4.46811	+	8.05637i	−0.271921	+	0.490295i
$271$	−17.8370	+	10.2982i	−1.08352	+	0.625572i	−0.931844	−	0.362858i	$-0.881801\pi$
$271$	−17.8370	+	10.2982i	−1.08352	+	0.625572i	−0.151678	+	0.988430i	$0.548468\pi$
$272$	−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	−0.428401	−	0.903589i	$-0.640923\pi$
$283$	−23.9744	−	13.8416i	−1.42513	−	0.822800i	−0.996731	+	0.0807885i	$0.974256\pi$
$284$	−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	$-0.998161\pi$
$293$		−	0.197795i		−	0.0115553i	0.999983	−	0.00577765i	$-0.00183909\pi$
$294$		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	$-0.842691\pi$
$307$		−	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	−0.977253	−	0.212078i	$-0.931977\pi$
$311$	−5.37805	+	9.31506i	−0.304961	+	0.528209i	0.672291	+	0.740287i	$0.265310\pi$
$312$	3.15349	−	21.4126i	0.178531	−	1.21225i
$313$	−2.47200	−	4.28163i	−0.139726	−	0.242012i	0.787667	−	0.616101i	$-0.211289\pi$
$313$	−2.47200	−	4.28163i	−0.139726	−	0.242012i	−0.927393	+	0.374089i	$0.877955\pi$
$314$	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	$-0.530350\pi$
$349$	−3.55710			−0.190407			−0.0952036	+	0.995458i	$0.530350\pi$
$350$		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	0.868151	−	0.496301i	$-0.165309\pi$
$353$	16.3912	+	9.46348i	0.872417	+	0.503690i	0.00426642	+	0.999991i	$0.498642\pi$
$354$	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	0.881496	−	0.472192i	$-0.156537\pi$
$367$	17.4966	+	10.1017i	0.913314	+	0.527302i	0.0318180	+	0.999494i	$0.489870\pi$
$368$	−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	$0.0477647\pi$
$383$	12.2089	+	21.1465i	0.623848	+	1.08054i	−0.364915	+	0.931041i	$0.618902\pi$
$384$	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	$-0.968067\pi$
$397$	−11.6405	−	20.1619i	−0.584220	−	1.01190i	0.410753	−	0.911747i	$-0.365266\pi$
$398$	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	−0.776156	−	0.630541i	$-0.782833\pi$
$409$	3.19509	−	5.53406i	0.157987	−	0.273642i	0.934143	+	0.356900i	$0.116166\pi$
$410$	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	$-0.752013\pi$
$419$	−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
$423$	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	$-0.462832\pi$
$433$	4.84842			0.233000			0.116500	+	0.993191i	$0.462832\pi$
$434$		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	−0.0191902	−	0.999816i	$-0.506109\pi$
$439$	17.5388	−	10.1260i	0.837081	−	0.483289i	0.856271	+	0.516527i	$0.172775\pi$
$440$	−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	$0.197602\pi$
$461$			24.9782i			1.16335i	−0.813422	+	0.581675i	$0.802398\pi$
$462$		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	$-0.948505\pi$
$467$	−13.6785	−	23.6918i	−0.632964	−	1.09633i	0.353979	−	0.935253i	$-0.384828\pi$
$468$	−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	−0.998577	−	0.0533285i	$-0.983017\pi$
$479$	−9.91668	+	17.1762i	−0.453105	+	0.784800i	0.545472	+	0.838129i	$0.316350\pi$
$480$	−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	$-0.255863\pi$
$503$	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
$507$	−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	$0.672784\pi$
$509$	−34.2107	+	19.7516i	−1.51636	+	0.875474i	−0.999815	+	0.0192162i	$0.993883\pi$
$510$	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	0.881973	−	0.471299i	$-0.156215\pi$
$521$	20.8808	+	12.0555i	0.914803	+	0.528162i	0.0328296	+	0.999461i	$0.489548\pi$
$522$	22.6514	+	6.25215i	0.991423	+	0.273649i
$523$	8.02520	−	4.63335i	0.350917	−	0.202602i	−0.314172	−	0.949366i	$-0.601727\pi$
$523$	8.02520	−	4.63335i	0.350917	−	0.202602i	0.665089	+	0.746764i	$0.268394\pi$
$524$	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	$0.394203\pi$
$563$	−15.5531	+	26.9388i	−0.655487	+	1.13534i	−0.981771	+	0.190065i	$0.939130\pi$
$564$	−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	−0.818240	−	0.574877i	$-0.805050\pi$
$577$	2.13156	−	3.69196i	0.0887378	−	0.153698i	0.906978	+	0.421178i	$0.138383\pi$
$578$	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	$-0.148310\pi$
$587$	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
$591$	−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	−0.393903	−	0.919152i	$-0.628875\pi$
$593$	4.99583	−	2.88434i	0.205154	−	0.118446i	0.599057	+	0.800706i	$0.295542\pi$
$594$	−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	$-0.168507\pi$
$601$	42.3193			1.72624			0.863121	+	0.504998i	$0.168507\pi$
$602$		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	$0.744508\pi$
$607$	−41.0224	+	23.6843i	−1.66505	+	0.961316i	−0.970248	+	0.242115i	$0.922159\pi$
$608$	−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	0.595011	−	0.803717i	$-0.297148\pi$
$619$	4.88830	+	2.82226i	0.196477	+	0.113436i	−0.398534	+	0.917154i	$0.630481\pi$
$620$	−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	$0.0148600\pi$
$643$			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	−0.955747	−	0.294190i	$-0.904950\pi$
$647$	−5.67476	+	9.82897i	−0.223098	+	0.386417i	0.732649	+	0.680606i	$0.238284\pi$
$648$	−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	$0.483062\pi$
$661$	−21.5502	+	37.3261i	−0.838206	+	1.45182i	−0.891393	+	0.453232i	$0.850271\pi$
$662$	−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	−0.991868	−	0.127268i	$-0.959379\pi$
$677$	−35.8437	+	20.6944i	−1.37759	+	0.795349i	−0.385717	+	0.922617i	$0.626046\pi$
$678$	−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	0.0221779	−	0.999754i	$-0.492940\pi$
$691$	23.6340	−	13.6451i	0.899079	−	0.519084i	0.876901	+	0.480670i	$0.159607\pi$
$692$	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	0.839595	−	0.543214i	$-0.182793\pi$
$719$	−1.35786	−	2.35188i	−0.0506395	−	0.0877102i	−0.890234	+	0.455503i	$0.849459\pi$
$720$	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	$0.114456\pi$
$727$			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
$732$	0.805090	−	0.672854i	0.0297570	−	0.0248694i
$733$	−7.65295	−	13.2553i	−0.282668	−	0.489596i	0.689373	−	0.724407i	$-0.257886\pi$
$733$	−7.65295	−	13.2553i	−0.282668	−	0.489596i	−0.972041	+	0.234811i	$0.924553\pi$
$734$	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	−0.974149	−	0.225908i	$-0.927465\pi$
$761$	−34.9126	+	20.1568i	−1.26558	+	0.730684i	−0.291433	+	0.956591i	$0.594132\pi$
$762$	−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	$-0.378696\pi$
$769$	20.6279			0.743861			0.371930	+	0.928261i	$0.378696\pi$
$770$		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	0.816878	−	0.576811i	$-0.195703\pi$
$773$	20.1789	+	11.6503i	0.725784	+	0.419032i	−0.0910936	+	0.995842i	$0.529036\pi$
$774$	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	0.548406	−	0.836212i	$-0.315235\pi$
$787$	2.76123	+	1.59420i	0.0984271	+	0.0568269i	−0.449978	+	0.893039i	$0.648568\pi$
$788$	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	$-0.540832\pi$
$797$		−	55.9985i		−	1.98357i	0.127925	−	0.991784i	$-0.459168\pi$
$798$		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	$0.377432\pi$
$811$			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
$816$	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	$-0.641090\pi$
$829$	16.3511	−	28.3210i	0.567898	−	0.983628i	0.996774	−	0.0802647i	$-0.0255766\pi$
$830$	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	$-0.724805\pi$
$839$	−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
$843$	−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	$-0.531024\pi$
$853$	−5.68417			−0.194622			−0.0973112	+	0.995254i	$0.531024\pi$
$854$		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	−0.0483040	−	0.998833i	$-0.515382\pi$
$857$	−27.4440	−	15.8448i	−0.937471	−	0.541249i	−0.889166	+	0.457584i	$0.848715\pi$
$858$	−54.7111	−	1.76499i	−1.86781	−	0.0602556i
$859$	−5.22874	+	3.01882i	−0.178402	+	0.103001i	−0.586542	−	0.809919i	$-0.699511\pi$
$859$	−5.22874	+	3.01882i	−0.178402	+	0.103001i	0.408139	+	0.912920i	$0.366178\pi$
$860$	−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	$-0.993174\pi$
$881$		−	1.27293i		−	0.0428860i	0.999770	−	0.0214430i	$-0.00682603\pi$
$882$		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	0.998478	−	0.0551585i	$-0.0175664\pi$
$887$	13.4459	+	23.2890i	0.451470	+	0.781969i	−0.547007	+	0.837128i	$0.684233\pi$
$888$	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	0.169473	−	0.985535i	$-0.445793\pi$
$929$	33.7624	−	19.4927i	1.10771	−	0.639535i	0.938235	+	0.345999i	$0.112460\pi$
$930$	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	$-0.372981\pi$
$937$	23.7865			0.777072			0.388536	+	0.921434i	$0.372981\pi$
$938$		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	0.00115159	−	0.999999i	$-0.499633\pi$
$941$	−26.5129	−	15.3073i	−0.864297	−	0.499002i	−0.865449	+	0.500997i	$0.832967\pi$
$942$	−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	0.999135	−	0.0415934i	$-0.0132434\pi$
$971$	14.4445	+	25.0186i	0.463546	+	0.802886i	−0.535588	+	0.844479i	$0.679910\pi$
$972$	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	−0.561440	−	0.827517i	$-0.689753\pi$
$983$	13.6677	−	23.6731i	0.435931	−	0.755054i	0.997371	+	0.0724632i	$0.0230860\pi$
$984$	−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	−0.754787	−	0.655970i	$-0.772260\pi$
$997$	6.02119	−	10.4290i	0.190693	−	0.330290i	0.945480	+	0.325680i	$0.105593\pi$
$998$	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.263.9		24
3.2	odd	2	inner	588.2.n.h.263.3		24
4.3	odd	2		588.2.n.d.263.8		24
7.2	even	3		588.2.n.d.275.6		24
7.3	odd	6		588.2.e.f.491.8	yes	24
7.4	even	3		588.2.e.f.491.7	yes	24
7.5	odd	6		588.2.n.d.275.5		24
7.6	odd	2	inner	588.2.n.h.263.10		24
12.11	even	2		588.2.n.d.263.6		24
21.2	odd	6		588.2.n.d.275.8		24
21.5	even	6		588.2.n.d.275.7		24
21.11	odd	6		588.2.e.f.491.18	yes	24
21.17	even	6		588.2.e.f.491.17	yes	24
21.20	even	2	inner	588.2.n.h.263.4		24
28.3	even	6		588.2.e.f.491.19	yes	24
28.11	odd	6		588.2.e.f.491.20	yes	24
28.19	even	6	inner	588.2.n.h.275.4		24
28.23	odd	6	inner	588.2.n.h.275.3		24
28.27	even	2		588.2.n.d.263.7		24
84.11	even	6		588.2.e.f.491.5	✓	24
84.23	even	6	inner	588.2.n.h.275.9		24
84.47	odd	6	inner	588.2.n.h.275.10		24
84.59	odd	6		588.2.e.f.491.6	yes	24
84.83	odd	2		588.2.n.d.263.5		24

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

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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.263.9

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