LMFDB - Embedded newform 588.2.n.d.275.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			275.6
Character	$\chi$	$=$	588.275
Dual form			588.2.n.d.263.6

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.287629 - 1.38466i) q^{2} +(1.66143 - 0.489533i) q^{3} +(-1.83454 + 0.796533i) q^{4} +(1.08570 + 0.626827i) q^{5} +(-1.15571 - 2.15971i) q^{6} +(1.63059 + 2.31110i) q^{8} +(2.52072 - 1.62665i) q^{9} +(0.555662 - 1.68361i) q^{10} +(2.52914 + 4.38059i) q^{11} +(-2.65803 + 2.22145i) q^{12} +4.41798 q^{13} +(2.11066 + 0.509947i) q^{15} +(2.73107 - 2.92254i) q^{16} +(-5.06920 + 2.92671i) q^{17} +(-2.97738 - 3.02245i) 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} +(3.84047 + 3.04151i) q^{24} +(-1.71417 - 2.96904i) q^{25} +(-1.27074 - 6.11738i) q^{26} +(3.39170 - 3.93654i) q^{27} -5.53862i q^{29} +(0.0990132 - 3.06922i) q^{30} +(-4.24264 + 2.44949i) q^{31} +(-4.83225 - 2.94098i) q^{32} +(6.34643 + 6.03996i) q^{33} +(5.51053 + 6.17729i) q^{34} +(-3.32867 + 4.99199i) q^{36} +(2.66908 - 4.62298i) q^{37} +(0.678928 - 2.05710i) q^{38} +(7.34017 - 2.16275i) q^{39} +(0.321666 + 3.53125i) q^{40} -1.97938i q^{41} -3.18613i q^{43} +(-8.12909 - 6.02183i) q^{44} +(3.75636 - 0.185997i) q^{45} +(-0.421113 - 0.138985i) q^{46} +(-5.74813 + 9.95606i) q^{47} +(3.10681 - 6.19256i) q^{48} +(-3.61805 + 3.22752i) q^{50} +(-6.98942 + 7.34407i) q^{51} +(-8.10496 + 3.51907i) q^{52} +(11.0767 - 6.39513i) q^{53} +(-6.42631 - 3.56407i) q^{54} +6.34133i q^{55} +(2.57889 + 0.623072i) q^{57} +(-7.66908 + 1.59307i) q^{58} +(-3.98351 - 6.89964i) q^{59} +(-4.27829 + 0.745696i) 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} +(6.53785 - 10.5249i) q^{66} +(-9.13122 + 5.27191i) q^{67} +(6.96844 - 9.40695i) q^{68} +(0.127550 - 0.527930i) q^{69} -4.53490 q^{71} +(7.86960 + 3.17322i) q^{72} +(-0.707107 - 1.22474i) q^{73} +(-7.16894 - 2.36605i) q^{74} +(-4.30143 - 4.09371i) q^{75} +(-3.04365 - 0.348402i) q^{76} +(-5.10590 - 9.54154i) q^{78} +(6.00000 + 3.46410i) q^{79} +(4.79704 - 1.46108i) q^{80} +(3.70801 - 8.20065i) q^{81} +(-2.74076 + 0.569326i) q^{82} -6.78340 q^{83} -7.33816 q^{85} +(-4.41169 + 0.916423i) q^{86} +(-2.71134 - 9.20204i) q^{87} +(-6.00000 + 12.9880i) q^{88} +(-4.15480 - 2.39878i) q^{89} +(-1.33798 - 5.14777i) q^{90} +(-0.0713222 + 0.623072i) q^{92} +(-5.84975 + 6.14657i) q^{93} +(15.4390 + 5.09553i) q^{94} +(0.960150 + 1.66303i) q^{95} +(-9.46816 - 2.52070i) q^{96} -13.6844 q^{97} +(13.5009 + 6.92820i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100})$ 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * q^88 - 24 * q^93

Character values

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

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

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.287629	−	1.38466i	−0.203384	−	0.979099i
$2$	−0.287629	−	1.38466i	−0.203384	−	0.979099i
$3$	1.66143	−	0.489533i	0.959228	−	0.282632i
$3$	1.66143	−	0.489533i	0.959228	−	0.282632i
$4$	−1.83454	+	0.796533i	−0.917270	+	0.398266i
$5$	1.08570	+	0.626827i	0.485538	+	0.280326i	0.722722	−	0.691139i	$-0.242891\pi$
$5$	1.08570	+	0.626827i	0.485538	+	0.280326i	−0.237183	+	0.971465i	$0.576224\pi$
$6$	−1.15571	−	2.15971i	−0.471817	−	0.881697i
$7$		0			0
$7$		0			0
$8$	1.63059	+	2.31110i	0.576500	+	0.817097i
$9$	2.52072	−	1.62665i	0.840238	−	0.542217i
$10$	0.555662	−	1.68361i	0.175716	−	0.532404i
$11$	2.52914	+	4.38059i	0.762563	+	1.32080i	0.941525	+	0.336942i	$0.109393\pi$
$11$	2.52914	+	4.38059i	0.762563	+	1.32080i	−0.178962	+	0.983856i	$0.557274\pi$
$12$	−2.65803	+	2.22145i	−0.767308	+	0.641278i
$13$	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
$16$	2.73107	−	2.92254i	0.682768	−	0.730636i
$17$	−5.06920	+	2.92671i	−1.22946	+	0.709831i	−0.966918	−	0.255089i	$-0.917895\pi$
$17$	−5.06920	+	2.92671i	−1.22946	+	0.709831i	−0.262545	+	0.964920i	$0.584562\pi$
$18$	−2.97738	−	3.02245i	−0.701775	−	0.712398i
$19$	1.32654	+	0.765881i	0.304330	+	0.175705i	0.644386	−	0.764700i	$-0.277113\pi$
$19$	1.32654	+	0.765881i	0.304330	+	0.175705i	−0.340056	+	0.940405i	$0.610446\pi$
$20$	−2.49104	−	0.285146i	−0.557014	−	0.0637607i
$21$		0			0
$22$	5.33816	−	4.76197i	1.13810	−	1.01525i
$23$	0.156785	−	0.271560i	0.0326920	−	0.0566242i	−0.849217	−	0.528045i	$-0.822925\pi$
$23$	0.156785	−	0.271560i	0.0326920	−	0.0566242i	0.881908	+	0.471421i	$0.156259\pi$
$24$	3.84047	+	3.04151i	0.783933	+	0.620845i
$25$	−1.71417	−	2.96904i	−0.342835	−	0.593808i
$26$	−1.27074	−	6.11738i	−0.249212	−	1.19972i
$27$	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	$-0.171929\pi$
$30$	0.0990132	−	3.06922i	0.0180773	−	0.560360i
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	0.0680129	+	0.997684i	$0.478334\pi$
$32$	−4.83225	−	2.94098i	−0.854229	−	0.519897i
$33$	6.34643	+	6.03996i	1.10477	+	1.05142i
$34$	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	−0.558803	−	0.829301i	$-0.688739\pi$
$37$	2.66908	−	4.62298i	0.438794	−	0.760013i	0.997597	+	0.0692872i	$0.0220725\pi$
$38$	0.678928	−	2.05710i	0.110137	−	0.333705i
$39$	7.34017	−	2.16275i	1.17537	−	0.346317i
$40$	0.321666	+	3.53125i	0.0508598	+	0.558340i
$41$		−	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	$-0.0781119\pi$
$44$	−8.12909	−	6.02183i	−1.22551	−	0.907825i
$45$	3.75636	−	0.185997i	0.559965	−	0.0277268i
$46$	−0.421113	−	0.138985i	−0.0620897	−	0.0204922i
$47$	−5.74813	+	9.95606i	−0.838451	+	1.45224i	0.0527378	+	0.998608i	$0.483205\pi$
$47$	−5.74813	+	9.95606i	−0.838451	+	1.45224i	−0.891189	+	0.453632i	$0.850128\pi$
$48$	3.10681	−	6.19256i	0.448429	−	0.893818i
$49$		0			0
$50$	−3.61805	+	3.22752i	−0.511669	+	0.456440i
$51$	−6.98942	+	7.34407i	−0.978715	+	1.02838i
$52$	−8.10496	+	3.51907i	−1.12396	+	0.488007i
$53$	11.0767	−	6.39513i	1.52150	−	0.878439i	0.521823	−	0.853054i	$-0.325252\pi$
$53$	11.0767	−	6.39513i	1.52150	−	0.878439i	0.999678	−	0.0253856i	$-0.00808135\pi$
$54$	−6.42631	−	3.56407i	−0.874509	−	0.485008i
$55$			6.34133i			0.855064i
$56$		0			0
$57$	2.57889	+	0.623072i	0.341582	+	0.0825279i
$58$	−7.66908	+	1.59307i	−1.00700	+	0.209180i
$59$	−3.98351	−	6.89964i	−0.518608	−	0.898256i	−0.999766	−	0.0216222i	$-0.993117\pi$
$59$	−3.98351	−	6.89964i	−0.518608	−	0.898256i	0.481158	−	0.876634i	$-0.340216\pi$
$60$	−4.27829	+	0.745696i	−0.552324	+	0.0962689i
$61$	0.151445	−	0.262310i	0.0193905	−	0.0335853i	−0.856167	−	0.516699i	$-0.827161\pi$
$61$	0.151445	−	0.262310i	0.0193905	−	0.0335853i	0.875558	+	0.483113i	$0.160494\pi$
$62$	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
$66$	6.53785	−	10.5249i	0.804754	−	1.29552i
$67$	−9.13122	+	5.27191i	−1.11556	+	0.644067i	−0.940263	−	0.340450i	$-0.889421\pi$
$67$	−9.13122	+	5.27191i	−1.11556	+	0.644067i	−0.175293	+	0.984516i	$0.556087\pi$
$68$	6.96844	−	9.40695i	0.845047	−	1.14076i
$69$	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	$0.586725\pi$
$72$	7.86960	+	3.17322i	0.927442	+	0.373968i
$73$	−0.707107	−	1.22474i	−0.0827606	−	0.143346i	0.821674	−	0.569958i	$-0.193040\pi$
$73$	−0.707107	−	1.22474i	−0.0827606	−	0.143346i	−0.904435	+	0.426612i	$0.859707\pi$
$74$	−7.16894	−	2.36605i	−0.833372	−	0.275048i
$75$	−4.30143	−	4.09371i	−0.496686	−	0.472701i
$76$	−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	$-0.205898\pi$
$79$	6.00000	+	3.46410i	0.675053	+	0.389742i	−0.122936	+	0.992415i	$0.539231\pi$
$80$	4.79704	−	1.46108i	0.536326	−	0.163354i
$81$	3.70801	−	8.20065i	0.412001	−	0.911183i
$82$	−2.74076	+	0.569326i	−0.302666	+	0.0628716i
$83$	−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
$86$	−4.41169	+	0.916423i	−0.475725	+	0.0988204i
$87$	−2.71134	−	9.20204i	−0.290686	−	0.986563i
$88$	−6.00000	+	12.9880i	−0.639602	+	1.38453i
$89$	−4.15480	−	2.39878i	−0.440408	−	0.254270i	0.263363	−	0.964697i	$-0.415168\pi$
$89$	−4.15480	−	2.39878i	−0.440408	−	0.254270i	−0.703771	+	0.710427i	$0.748502\pi$
$90$	−1.33798	−	5.14777i	−0.141035	−	0.542622i
$91$		0			0
$92$	−0.0713222	+	0.623072i	−0.00743586	+	0.0649597i
$93$	−5.84975	+	6.14657i	−0.606591	+	0.637370i
$94$	15.4390	+	5.09553i	1.59241	+	0.525564i
$95$	0.960150	+	1.66303i	0.0985093	+	0.170623i
$96$	−9.46816	−	2.52070i	−0.966340	−	0.257268i
$97$	−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
$100$	5.50966	+	4.08142i	0.550966	+	0.408142i
$101$	−3.52631	+	2.03591i	−0.350881	+	0.202581i	−0.665073	−	0.746778i	$-0.731600\pi$
$101$	−3.52631	+	2.03591i	−0.350881	+	0.202581i	0.314192	+	0.949359i	$0.398266\pi$
$102$	12.1794	+	7.56557i	1.20594	+	0.749103i
$103$	11.3239	+	6.53788i	1.11578	+	0.644197i	0.940321	−	0.340290i	$-0.110525\pi$
$103$	11.3239	+	6.53788i	1.11578	+	0.644197i	0.175461	+	0.984486i	$0.443859\pi$
$104$	7.20391	+	10.2104i	0.706402	+	1.00121i
$105$		0			0
$106$	−12.0410	−	13.4980i	−1.16953	−	1.31104i
$107$	1.95388	−	3.38422i	0.188889	−	0.327165i	−0.755991	−	0.654582i	$-0.772845\pi$
$107$	1.95388	−	3.38422i	0.188889	−	0.327165i	0.944880	+	0.327417i	$0.106178\pi$
$108$	−3.08662	+	9.92335i	−0.297010	+	0.954874i
$109$	4.12398	+	7.14295i	0.395006	+	0.684170i	0.993102	−	0.117254i	$-0.0374092\pi$
$109$	4.12398	+	7.14295i	0.395006	+	0.684170i	−0.598096	+	0.801424i	$0.704076\pi$
$110$	8.78055	−	1.82395i	0.837193	−	0.173907i
$111$	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	$-0.102444\pi$
$114$	0.120978	−	3.75008i	0.0113306	−	0.351227i
$115$	0.340442	−	0.196554i	0.0317464	−	0.0183288i
$116$	4.41169	+	10.1608i	0.409615	+	0.943408i
$117$	11.1365	−	7.18651i	1.02957	−	0.664393i
$118$	−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
$122$	−0.406768	−	0.134251i	−0.0368271	−	0.0121545i
$123$	−0.968971	−	3.28861i	−0.0873692	−	0.296524i
$124$	5.83219	−	7.87309i	0.523746	−	0.707024i
$125$		−	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	$-0.123149\pi$
$128$	11.2075	+	1.54631i	0.990616	+	0.136676i
$129$	−1.55972	−	5.29354i	−0.137325	−	0.466070i
$130$	2.45490	−	7.43815i	0.215309	−	0.652369i
$131$	−4.20524	+	7.28368i	−0.367413	+	0.636378i	−0.989160	−	0.146840i	$-0.953090\pi$
$131$	−4.20524	+	7.28368i	−0.367413	+	0.636378i	0.621747	+	0.783218i	$0.286423\pi$
$132$	−16.4538	−	6.02541i	−1.43212	−	0.524445i
$133$		0			0
$134$	9.92618	+	11.1272i	0.857491	+	0.961247i
$135$	6.14989	−	2.14788i	0.529298	−	0.184860i
$136$	−15.0297	−	6.94318i	−1.28879	−	0.595372i
$137$	−11.9136	+	6.87834i	−1.01785	+	0.587657i	−0.913481	−	0.406882i	$-0.866616\pi$
$137$	−11.9136	+	6.87834i	−1.01785	+	0.587657i	−0.104370	+	0.994539i	$0.533283\pi$
$138$	−0.767688	−	0.0247657i	−0.0653499	−	0.00210819i
$139$			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
$142$	1.30437	+	6.27927i	0.109460	+	0.526945i
$143$	11.1737	+	19.3534i	0.934389	+	1.61841i
$144$	2.13029	−	11.8094i	0.177524	−	0.984116i
$145$	3.47176	−	6.01326i	0.288314	−	0.499374i
$146$	−1.49247	+	1.33137i	−0.123517	+	0.110185i
$147$		0			0
$148$	−1.21417	+	10.6071i	−0.0998046	+	0.871894i
$149$	9.78354	+	5.64853i	0.801499	+	0.462745i	0.843995	−	0.536351i	$-0.180198\pi$
$149$	9.78354	+	5.64853i	0.801499	+	0.462745i	−0.0424963	+	0.999097i	$0.513531\pi$
$150$	−4.43116	+	7.13346i	−0.361803	+	0.582445i
$151$	9.61268	−	5.54988i	0.782269	−	0.451643i	−0.0549650	−	0.998488i	$-0.517505\pi$
$151$	9.61268	−	5.54988i	0.782269	−	0.451643i	0.837234	+	0.546845i	$0.184171\pi$
$152$	0.393023	+	4.31461i	0.0318784	+	0.349961i
$153$	−8.01729	+	15.6232i	−0.648159	+	1.26306i
$154$		0			0
$155$	−6.14163			−0.493307
$156$	−11.7431	+	9.81433i	−0.940204	+	0.785776i
$157$	7.39785	+	12.8135i	0.590413	+	1.02262i	0.994177	+	0.107762i	$0.0343684\pi$
$157$	7.39785	+	12.8135i	0.590413	+	1.02262i	−0.403764	+	0.914863i	$0.632298\pi$
$158$	3.07081	−	9.30431i	0.244301	−	0.740211i
$159$	15.2726	−	16.0475i	1.21119	−	1.27265i
$160$	−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	$-0.507229\pi$
$163$	−11.4887	−	6.63300i	−0.899864	−	0.519537i	−0.877156	+	0.480205i	$0.840562\pi$
$164$	1.57664	+	3.63125i	0.123115	+	0.283553i
$165$	3.10429	+	10.5357i	0.241668	+	0.820202i
$166$	1.95110	+	9.39267i	0.151435	+	0.729012i
$167$	−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
$170$	2.11066	+	10.1608i	0.161881	+	0.779299i
$171$	4.58966	−	0.227258i	0.350980	−	0.0173789i
$172$	2.53786	+	5.84508i	0.193510	+	0.445684i
$173$	−12.4811	−	7.20596i	−0.948920	−	0.547859i	−0.0561749	−	0.998421i	$-0.517890\pi$
$173$	−12.4811	−	7.20596i	−0.948920	−	0.547859i	−0.892745	+	0.450562i	$0.851224\pi$
$174$	−11.9618	+	6.40104i	−0.906822	+	0.485261i
$175$		0			0
$176$	19.7097	+	4.57220i	1.48568	+	0.344643i
$177$	−9.99593	−	9.51322i	−0.751340	−	0.715058i
$178$	−2.12644	+	6.44293i	−0.159383	+	0.482918i
$179$	0.347150	+	0.601281i	0.0259472	+	0.0449419i	0.878707	−	0.477361i	$-0.158406\pi$
$179$	0.347150	+	0.601281i	0.0259472	+	0.0449419i	−0.852760	+	0.522303i	$0.825073\pi$
$180$	−6.74304	+	3.33328i	−0.502597	+	0.248448i
$181$	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
$184$	0.883254	−	0.0804567i	0.0651144	−	0.00593134i
$185$	5.79562	−	3.34610i	0.426103	−	0.246010i
$186$	10.1934	+	6.33196i	0.747419	+	0.464282i
$187$	−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	−0.786638	−	0.617415i	$-0.788180\pi$
$191$	1.95388	−	3.38422i	0.141378	−	0.244873i	0.928016	+	0.372541i	$0.121513\pi$
$192$	−0.766990	+	13.8352i	−0.0553527	+	0.998467i
$193$	−0.785825	−	1.36109i	−0.0565649	−	0.0979733i	0.836356	−	0.548186i	$-0.184681\pi$
$193$	−0.785825	−	1.36109i	−0.0565649	−	0.0979733i	−0.892921	+	0.450213i	$0.851348\pi$
$194$	3.93602	+	18.9481i	0.282590	+	1.36040i
$195$	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	$-0.0207980\pi$
$198$	5.70992	−	20.6869i	0.405786	−	1.47015i
$199$	−3.17910	+	1.83546i	−0.225361	+	0.130112i	−0.608430	−	0.793608i	$-0.708200\pi$
$199$	−3.17910	+	1.83546i	−0.225361	+	0.130112i	0.383069	+	0.923720i	$0.374867\pi$
$200$	4.06663	−	8.80291i	0.287554	−	0.622460i
$201$	−12.5901	+	13.2290i	−0.888039	+	0.933099i
$202$	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
$206$	5.79562	−	17.5602i	0.403800	−	1.22348i
$207$	−0.0465225	−	0.939560i	−0.00323354	−	0.0653039i
$208$	12.0658	−	12.9117i	0.836614	−	0.895267i
$209$			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	$0.828881\pi$
$212$	−15.2267	+	20.5551i	−1.04577	+	1.41173i
$213$	−7.53443	+	2.21998i	−0.516251	+	0.152111i
$214$	−5.24797	−	1.73205i	−0.358744	−	0.118401i
$215$	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
$219$	−1.77436	−	1.68868i	−0.119900	−	0.114110i
$220$	−5.05108	−	11.6334i	−0.340543	−	0.784325i
$221$	−22.3956	+	12.9301i	−1.50649	+	0.869775i
$222$	−13.0690	−	0.421606i	−0.877131	−	0.0282963i
$223$		−	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
$226$	−9.31160	+	1.93426i	−0.619399	+	0.128665i
$227$	5.34136	+	9.25151i	0.354519	+	0.614045i	0.987035	−	0.160502i	$-0.0513114\pi$
$227$	5.34136	+	9.25151i	0.354519	+	0.614045i	−0.632517	+	0.774547i	$0.717978\pi$
$228$	−5.22737	+	0.911118i	−0.346191	+	0.0603403i
$229$	−3.75075	+	6.49650i	−0.247857	+	0.429301i	−0.962931	−	0.269748i	$-0.913060\pi$
$229$	−3.75075	+	6.49650i	−0.247857	+	0.429301i	0.715074	+	0.699049i	$0.246393\pi$
$230$	−0.370081	−	0.414861i	−0.0244024	−	0.0273551i
$231$		0			0
$232$	12.8003	−	9.03122i	0.840381	−	0.592928i
$233$	−2.42423	−	1.39963i	−0.158817	−	0.0916930i	0.418485	−	0.908224i	$-0.362561\pi$
$233$	−2.42423	−	1.39963i	−0.158817	−	0.0916930i	−0.577302	+	0.816531i	$0.695895\pi$
$234$	−13.1540	−	13.3531i	−0.859904	−	0.872921i
$235$	−12.4815	+	7.20617i	−0.814201	+	0.470079i
$236$	12.8037	+	9.48466i	0.833449	+	0.617399i
$237$	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	$0.731367\pi$
$240$	7.25472	−	4.77580i	0.468290	−	0.308277i
$241$	−9.02728	−	15.6357i	−0.581499	−	1.00718i	−0.995302	−	0.0968188i	$-0.969133\pi$
$241$	−9.02728	−	15.6357i	−0.581499	−	1.00718i	0.413804	−	0.910366i	$-0.364200\pi$
$242$	19.5886	+	6.46506i	1.25920	+	0.415590i
$243$	2.14612	−	15.4400i	0.137674	−	0.990478i
$244$	−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
$248$	−12.5790	−	5.81105i	−0.798768	−	0.369002i
$249$	−11.2702	+	3.32070i	−0.714217	+	0.210441i
$250$	−14.6306	+	3.03915i	−0.925320	+	0.192213i
$251$	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
$254$	−11.7752	+	2.44600i	−0.738839	+	0.153476i
$255$	−12.1919	+	3.59227i	−0.763483	+	0.224957i
$256$	−1.08251	−	15.9633i	−0.0676566	−	0.997709i
$257$	−7.24060	−	4.18036i	−0.451656	−	0.260764i	0.256873	−	0.966445i	$-0.417308\pi$
$257$	−7.24060	−	4.18036i	−0.451656	−	0.260764i	−0.708529	+	0.705681i	$0.750641\pi$
$258$	−6.88111	+	3.68224i	−0.428399	+	0.229246i
$259$		0			0
$260$	−11.0054	−	1.25977i	−0.682524	−	0.0781277i
$261$	−9.00941	−	13.9613i	−0.557668	−	0.864182i
$262$	11.2949	+	3.72781i	0.697803	+	0.230305i
$263$	−14.6850	−	25.4352i	−0.905517	−	1.56840i	−0.820221	−	0.572046i	$-0.806150\pi$
$263$	−14.6850	−	25.4352i	−0.905517	−	1.56840i	−0.0852962	−	0.996356i	$-0.527184\pi$
$264$	−3.61053	+	24.5159i	−0.222212	+	1.50885i
$265$	16.0346			0.984996
$266$		0			0
$267$	−8.07720	−	1.95149i	−0.494317	−	0.119429i
$268$	12.5523	−	16.9448i	0.766756	−	1.03507i
$269$	17.6649	−	10.1988i	1.07705	−	0.621834i	0.146950	−	0.989144i	$-0.453054\pi$
$269$	17.6649	−	10.1988i	1.07705	−	0.621834i	0.930099	+	0.367310i	$0.119721\pi$
$270$	−4.74296	−	7.89768i	−0.288648	−	0.480638i
$271$	17.8370	+	10.2982i	1.08352	+	0.625572i	0.931844	−	0.362858i	$-0.118199\pi$
$271$	17.8370	+	10.2982i	1.08352	+	0.625572i	0.151678	+	0.988430i	$0.451532\pi$
$272$	−5.29093	+	22.8080i	−0.320810	+	1.38294i
$273$		0			0
$274$	12.9508	+	14.5179i	0.782389	+	0.877057i
$275$	8.67076	−	15.0182i	0.522867	−	0.905632i
$276$	0.186517	+	1.07011i	0.0112270	+	0.0644128i
$277$	1.97345	+	3.41811i	0.118573	+	0.205374i	0.919202	−	0.393786i	$-0.128835\pi$
$277$	1.97345	+	3.41811i	0.118573	+	0.205374i	−0.800629	+	0.599160i	$0.795501\pi$
$278$	18.2292	−	3.78668i	1.09332	−	0.227110i
$279$	−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	$-0.0112649\pi$
$282$	28.1453	+	0.907971i	1.67603	+	0.0540689i
$283$	23.9744	−	13.8416i	1.42513	−	0.822800i	0.428401	−	0.903589i	$-0.359077\pi$
$283$	23.9744	−	13.8416i	1.42513	−	0.822800i	0.996731	+	0.0807885i	$0.0257438\pi$
$284$	8.31945	−	3.61220i	0.493669	−	0.214344i
$285$	2.40933	+	2.29298i	0.142716	+	0.135825i
$286$	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
$290$	−9.32487	−	3.07760i	−0.547575	−	0.180723i
$291$	−22.7357	+	6.69895i	−1.33279	+	0.392700i
$292$	2.27276	+	1.68361i	0.133004	+	0.0985258i
$293$		−	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
$296$	15.0363	−	1.36968i	0.873969	−	0.0796109i
$297$	25.8225	+	4.90159i	1.49837	+	0.284419i
$298$	5.00724	−	15.1715i	0.290061	−	0.878862i
$299$	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
$303$	−4.86207	+	5.10878i	−0.279319	+	0.293492i
$304$	5.86120	−	1.78521i	0.336163	−	0.102389i
$305$	0.328846	−	0.189859i	0.0188297	−	0.0108713i
$306$	23.9388	+	6.60749i	1.36849	+	0.377725i
$307$		−	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
$310$	1.76651	+	8.50404i	0.100331	+	0.482997i
$311$	−5.37805	−	9.31506i	−0.304961	−	0.528209i	0.672291	−	0.740287i	$-0.265310\pi$
$311$	−5.37805	−	9.31506i	−0.304961	−	0.528209i	−0.977253	+	0.212078i	$0.931977\pi$
$312$	16.9671	+	13.4373i	0.960575	+	0.760738i
$313$	−2.47200	+	4.28163i	−0.139726	+	0.242012i	−0.927393	−	0.374089i	$-0.877955\pi$
$313$	−2.47200	+	4.28163i	−0.139726	+	0.242012i	0.787667	+	0.616101i	$0.211289\pi$
$314$	15.6144	−	13.9290i	0.881170	−	0.786058i
$315$		0			0
$316$	−13.7665	−	1.57583i	−0.774427	−	0.0886476i
$317$	−18.9960	−	10.9673i	−1.06692	−	0.615987i	−0.139582	−	0.990211i	$-0.544576\pi$
$317$	−18.9960	−	10.9673i	−1.06692	−	0.615987i	−0.927338	+	0.374224i	$0.877909\pi$
$318$	−26.6131	−	16.5315i	−1.49239	−	0.927041i
$319$	24.2624	−	14.0079i	1.35844	−	0.784293i
$320$	−7.63656	+	6.50142i	−0.426897	+	0.363441i
$321$	1.58955	−	6.57914i	0.0887202	−	0.367212i
$322$		0			0
$323$	−8.96603			−0.498883
$324$	−0.270403	+	17.9980i	−0.0150224	+	0.999887i
$325$	−7.57319	−	13.1171i	−0.420085	−	0.727609i
$326$	−5.87994	+	17.8157i	−0.325660	+	0.986722i
$327$	10.3484	+	9.84870i	0.572269	+	0.544634i
$328$	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	$-0.300540\pi$
$331$	3.24073	+	1.87104i	0.178127	+	0.102841i	−0.408286	+	0.912854i	$0.633873\pi$
$332$	12.4444	−	5.40320i	0.682976	−	0.296539i
$333$	−0.791990	−	15.9949i	−0.0434008	−	0.876514i
$334$	1.37666	+	6.62730i	0.0753275	+	0.362629i
$335$	−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	$0.284761\pi$
$338$	−1.87492	−	9.02593i	−0.101982	−	0.490946i
$339$	−3.29204	−	11.1729i	−0.178799	−	0.606828i
$340$	13.4621	−	5.84508i	0.730087	−	0.316994i
$341$	−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
$345$	0.469402	−	0.493220i	0.0252718	−	0.0265541i
$346$	−6.38786	+	19.3547i	−0.343413	+	1.04051i
$347$	−1.06505	−	1.84472i	−0.0571750	−	0.0990299i	0.836021	−	0.548697i	$-0.184876\pi$
$347$	−1.06505	−	1.84472i	−0.0571750	−	0.0990299i	−0.893196	+	0.449667i	$0.851543\pi$
$348$	12.3038	+	14.7218i	0.659552	+	0.789174i
$349$	−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
$352$	0.661842	−	28.6063i	0.0352763	−	1.52472i
$353$	−16.3912	+	9.46348i	−0.872417	+	0.503690i	−0.868151	−	0.496301i	$-0.834691\pi$
$353$	−16.3912	+	9.46348i	−0.872417	+	0.503690i	−0.00426642	+	0.999991i	$0.501358\pi$
$354$	−10.2974	+	16.5772i	−0.547302	+	0.881068i
$355$	−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	−0.881748	−	0.471720i	$-0.843633\pi$
$359$	−0.613000	+	1.06175i	−0.0323529	+	0.0560369i	0.849396	+	0.527757i	$0.176967\pi$
$360$	6.55494	+	8.37804i	0.345476	+	0.441561i
$361$	−8.32685	−	14.4225i	−0.438255	−	0.759081i
$362$	−1.81506	−	8.73776i	−0.0953973	−	0.459246i
$363$	−5.93317	+	24.5573i	−0.311411	+	1.28893i
$364$		0			0
$365$		−	1.77294i		−	0.0927997i
$366$	−0.741538	−	0.0239221i	−0.0387608	−	0.00125043i
$367$	−17.4966	+	10.1017i	−0.913314	+	0.527302i	−0.881496	−	0.472192i	$-0.843463\pi$
$367$	−17.4966	+	10.1017i	−0.913314	+	0.527302i	−0.0318180	+	0.999494i	$0.510130\pi$
$368$	−0.365454	−	1.19986i	−0.0190506	−	0.0625471i
$369$	−3.21976	−	4.98945i	−0.167614	−	0.259740i
$370$	−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	−0.740490	−	0.672067i	$-0.765407\pi$
$373$	4.09019	−	7.08442i	0.211782	−	0.366817i	0.952272	+	0.305250i	$0.0987400\pi$
$374$	−13.1233	+	39.7626i	−0.678592	+	2.05607i
$375$	−5.17252	−	17.5551i	−0.267108	−	0.906541i
$376$	−32.3823	+	2.94974i	−1.66999	+	0.152121i
$377$		−	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	$0.704105\pi$
$380$	−3.08609	−	2.28610i	−0.158313	−	0.117274i
$381$	−4.16301	−	14.1289i	−0.213277	−	0.723845i
$382$	−5.24797	−	1.73205i	−0.268509	−	0.0886194i
$383$	12.2089	−	21.1465i	0.623848	−	1.08054i	−0.364915	−	0.931041i	$-0.618902\pi$
$383$	12.2089	−	21.1465i	0.623848	−	1.08054i	0.988763	−	0.149495i	$-0.0477647\pi$
$384$	19.3775	−	2.91737i	0.988856	−	0.148877i
$385$		0			0
$386$	−1.65861	+	1.47958i	−0.0844212	+	0.0753089i
$387$	−5.18273	−	8.03133i	−0.263453	−	0.408255i
$388$	25.1045	−	10.9001i	1.27449	−	0.553367i
$389$	7.86740	−	4.54225i	0.398893	−	0.230301i	−0.287113	−	0.957897i	$-0.592696\pi$
$389$	7.86740	−	4.54225i	0.398893	−	0.230301i	0.686006	+	0.727596i	$0.259362\pi$
$390$	0.437438	−	13.5597i	0.0221505	−	0.686624i
$391$			1.83546i			0.0928230i
$392$		0			0
$393$	−3.42111	+	14.1599i	−0.172572	+	0.714275i
$394$	−2.53786	+	0.527179i	−0.127855	+	0.0265589i
$395$	4.34279	+	7.52193i	0.218509	+	0.378469i
$396$	−30.2865	−	1.95613i	−1.52196	−	0.0982991i
$397$	−11.6405	+	20.1619i	−0.584220	+	1.01190i	0.410753	+	0.911747i	$0.365266\pi$
$397$	−11.6405	+	20.1619i	−0.584220	+	1.01190i	−0.994972	+	0.100151i	$0.968067\pi$
$398$	3.45588	+	3.87403i	0.173227	+	0.194188i
$399$		0			0
$400$	−13.3587	−	3.09890i	−0.667934	−	0.154945i
$401$	6.57424	+	3.79564i	0.328302	+	0.189545i	0.655087	−	0.755553i	$-0.272632\pi$
$401$	6.57424	+	3.79564i	0.328302	+	0.189545i	−0.326785	+	0.945099i	$0.605965\pi$
$402$	21.9388	+	13.6280i	1.09421	+	0.679701i
$403$	−18.7439	+	10.8218i	−0.933700	+	0.539072i
$404$	4.84748	−	6.54378i	0.241171	−	0.325565i
$405$	9.16617	−	6.57914i	0.455470	−	0.326920i
$406$		0			0
$407$	27.0019			1.33843
$408$	−28.3697	−	4.17809i	−1.40451	−	0.206846i
$409$	3.19509	+	5.53406i	0.157987	+	0.273642i	0.934143	−	0.356900i	$-0.116166\pi$
$409$	3.19509	+	5.53406i	0.157987	+	0.273642i	−0.776156	+	0.630541i	$0.782833\pi$
$410$	−3.33250	−	1.09987i	−0.164580	−	0.0543185i
$411$	−16.4265	+	17.2600i	−0.810261	+	0.851374i
$412$	−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
$416$	−21.3488	−	12.9932i	−1.04671	−	0.637044i
$417$	6.44479	+	21.8731i	0.315603	+	1.07113i
$418$	10.7284	−	2.22857i	0.524743	−	0.109003i
$419$	−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	$0.785694\pi$
$422$	20.5985	−	4.27885i	1.00272	−	0.208291i
$423$	1.70563	+	34.4466i	0.0829306	+	1.67485i
$424$	32.8413	+	15.1715i	1.59492	+	0.736793i
$425$	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
$429$	28.0384	+	26.6844i	1.35371	+	1.28834i
$430$	−5.36420	−	1.77041i	−0.258685	−	0.0853769i
$431$	9.12282	+	15.8012i	0.439431	+	0.761116i	0.997646	−	0.0685802i	$-0.0218469\pi$
$431$	9.12282	+	15.8012i	0.439431	+	0.761116i	−0.558215	+	0.829696i	$0.688514\pi$
$432$	−2.24175	−	20.6634i	−0.107856	−	0.994167i
$433$	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
$436$	−13.2552	−	9.81913i	−0.634809	−	0.470251i
$437$	0.415965	−	0.240157i	0.0198983	−	0.0114883i
$438$	−1.82788	+	2.94259i	−0.0873395	+	0.140603i
$439$	−17.5388	−	10.1260i	−0.837081	−	0.483289i	0.0191902	−	0.999816i	$-0.493891\pi$
$439$	−17.5388	−	10.1260i	−0.837081	−	0.483289i	−0.856271	+	0.516527i	$0.827225\pi$
$440$	−14.6554	+	10.3401i	−0.698670	+	0.492945i
$441$		0			0
$442$	24.3454	+	27.2912i	1.15799	+	1.29811i
$443$	−11.2335	+	19.4570i	−0.533719	+	0.924428i	0.465505	+	0.885045i	$0.345873\pi$
$443$	−11.2335	+	19.4570i	−0.533719	+	0.924428i	−0.999224	+	0.0393830i	$0.987461\pi$
$444$	3.17523	+	18.2173i	0.150690	+	0.864554i
$445$	−3.00724	−	5.20869i	−0.142557	−	0.246915i
$446$	−26.8860	+	5.58491i	−1.27309	+	0.264453i
$447$	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	$0.754227\pi$
$450$	−3.87002	+	14.0210i	−0.182434	+	0.660955i
$451$	8.67086	−	5.00612i	0.408295	−	0.235729i
$452$	5.35657	+	12.3370i	0.251952	+	0.580284i
$453$	13.2540	−	13.9265i	0.622726	−	0.654323i
$454$	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	−0.996473	−	0.0839196i	$-0.973256\pi$
$457$	−9.09743	+	15.7572i	−0.425560	+	0.737091i	0.570913	+	0.821011i	$0.306589\pi$
$458$	10.0742	+	3.32492i	0.470738	+	0.155363i
$459$	−5.67210	+	29.8817i	−0.264751	+	1.39476i
$460$	−0.467993	+	0.631761i	−0.0218203	+	0.0294560i
$461$			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	$0.952693\pi$
$464$	−16.1869	−	15.1264i	−0.751456	−	0.702224i
$465$	−10.2039	+	3.00653i	−0.473195	+	0.139424i
$466$	−1.24073	+	3.75930i	−0.0574757	+	0.174146i
$467$	−13.6785	+	23.6918i	−0.632964	+	1.09633i	0.353979	+	0.935253i	$0.384828\pi$
$467$	−13.6785	+	23.6918i	−0.632964	+	1.09633i	−0.986943	+	0.161072i	$0.948505\pi$
$468$	−14.7060	+	22.0545i	−0.679785	+	1.01947i
$469$		0			0
$470$	13.5681	+	15.2098i	0.625849	+	0.701576i
$471$	18.5636	+	17.6672i	0.855367	+	0.814061i
$472$	9.45028	−	20.4568i	0.434984	−	0.941598i
$473$	13.9571	−	8.05816i	0.641750	−	0.370515i
$474$	0.547187	−	16.9617i	0.0251331	−	0.779078i
$475$		−	5.25141i		−	0.240951i
$476$		0			0
$477$	17.5185	−	34.1382i	0.802119	−	1.56308i
$478$	5.90981	+	28.4500i	0.270308	+	1.30127i
$479$	−9.91668	−	17.1762i	−0.453105	−	0.784800i	0.545472	−	0.838129i	$-0.316350\pi$
$479$	−9.91668	−	17.1762i	−0.453105	−	0.784800i	−0.998577	+	0.0533285i	$0.983017\pi$
$480$	−8.69951	−	8.67162i	−0.397076	−	0.395804i
$481$	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
$486$	−21.9964	+	1.46936i	−0.997776	+	0.0666513i
$487$	35.3792	−	20.4262i	1.60318	−	0.925599i	0.612339	−	0.790595i	$-0.290229\pi$
$487$	35.3792	−	20.4262i	1.60318	−	0.925599i	0.990845	−	0.135003i	$-0.0431045\pi$
$488$	0.853168	−	0.0777160i	0.0386211	−	0.00351804i
$489$	−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	$0.348541\pi$
$492$	4.39710	+	5.26126i	0.198236	+	0.237196i
$493$	16.2099	+	28.0764i	0.730058	+	1.26450i
$494$	2.99949	−	9.08821i	0.134954	−	0.408898i
$495$	10.3151	+	15.9847i	0.463631	+	0.718458i
$496$	−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	$-0.611144\pi$
$499$	−29.6416	−	17.1136i	−1.32694	−	0.766110i	−0.984825	+	0.173548i	$0.944477\pi$
$500$	8.41636	+	19.3842i	0.376391	+	0.866887i
$501$	−7.95202	+	2.34302i	−0.355270	+	0.104679i
$502$	−3.01464	−	14.5126i	−0.134550	−	0.647728i
$503$	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
$506$	−0.456215	−	2.19624i	−0.0202812	−	0.0976346i
$507$	10.8301	−	3.19104i	0.480982	−	0.141719i
$508$	6.77375	+	15.6010i	0.300536	+	0.692182i
$509$	34.2107	+	19.7516i	1.51636	+	0.875474i	0.999815	+	0.0192162i	$0.00611708\pi$
$509$	34.2107	+	19.7516i	1.51636	+	0.875474i	0.516549	+	0.856257i	$0.327216\pi$
$510$	8.48078	+	15.8483i	0.375535	+	0.701773i
$511$		0			0
$512$	−21.7924	+	6.09041i	−0.963095	+	0.269161i
$513$	7.51416	−	2.62436i	0.331758	−	0.115868i
$514$	−3.70576	+	11.2281i	−0.163454	+	0.495251i
$515$	8.19625	+	14.1963i	0.361170	+	0.625564i
$516$	7.07784	+	8.46885i	0.311585	+	0.372820i
$517$	−58.1512			−2.55749
$518$		0			0
$519$	−24.2641	−	5.86232i	−1.06507	−	0.257327i
$520$	1.42111	+	15.6010i	0.0623199	+	0.684149i
$521$	−20.8808	+	12.0555i	−0.914803	+	0.528162i	−0.881973	−	0.471299i	$-0.843785\pi$
$521$	−20.8808	+	12.0555i	−0.914803	+	0.528162i	−0.0328296	+	0.999461i	$0.510452\pi$
$522$	−16.7402	+	16.4906i	−0.732699	+	0.721773i
$523$	−8.02520	−	4.63335i	−0.350917	−	0.202602i	0.314172	−	0.949366i	$-0.398273\pi$
$523$	−8.02520	−	4.63335i	−0.350917	−	0.202602i	−0.665089	+	0.746764i	$0.731606\pi$
$524$	1.91298	−	16.7118i	0.0835689	−	0.730059i
$525$		0			0
$526$	−30.9952	+	27.6496i	−1.35145	+	1.20558i
$527$	14.3379	−	24.8339i	0.624568	−	1.08178i
$528$	34.9846	−	2.05215i	1.52251	−	0.0893085i
$529$	11.4508	+	19.8334i	0.497862	+	0.862323i
$530$	−4.61200	−	22.2024i	−0.200333	−	0.964409i
$531$	−21.2646	−	10.9122i	−0.922805	−	0.473551i
$532$		0			0
$533$		−	8.74486i		−	0.378782i
$534$	−0.378909	+	11.7454i	−0.0163970	+	0.508275i
$535$	4.24264	−	2.44949i	0.183425	−	0.105901i
$536$	−27.0732	−	12.5068i	−1.16938	−	0.540213i
$537$	0.871113	+	0.829047i	0.0375913	+	0.0357760i
$538$	−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	0.440961	+	0.897526i	$0.354638\pi$
$541$	−12.9508	+	22.4315i	−0.556800	+	0.964406i	−0.997761	+	0.0668796i	$0.978696\pi$
$542$	9.12903	−	27.6602i	0.392125	−	1.18811i
$543$	10.4843	−	3.08916i	0.449926	−	0.132568i
$544$	33.1030	+	0.765881i	1.41928	+	0.0328369i
$545$			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	$-0.248685\pi$
$548$	16.3772	−	22.1082i	0.699600	−	0.944415i
$549$	−0.0449378	−	0.907556i	−0.00191790	−	0.0387335i
$550$	−23.2890	−	7.68635i	−0.993046	−	0.327747i
$551$	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
$555$	7.99101	−	8.39647i	0.339199	−	0.356410i
$556$	−10.4865	−	24.1520i	−0.444727	−	1.02427i
$557$	25.8991	−	14.9528i	1.09738	−	0.633572i	0.161847	−	0.986816i	$-0.448255\pi$
$557$	25.8991	−	14.9528i	1.09738	−	0.633572i	0.935531	+	0.353244i	$0.114921\pi$
$558$	20.0354	+	5.53010i	0.848167	+	0.234108i
$559$		−	14.0763i		−	0.595363i
$560$		0			0
$561$	−49.8486	−	12.0437i	−2.10461	−	0.508484i
$562$	−1.64252	+	0.341195i	−0.0692857	+	0.0143924i
$563$	−15.5531	−	26.9388i	−0.655487	−	1.13534i	−0.981771	−	0.190065i	$-0.939130\pi$
$563$	−15.5531	−	26.9388i	−0.655487	−	1.13534i	0.326284	−	0.945272i	$-0.394203\pi$
$564$	−6.83818	−	39.2328i	−0.287939	−	1.65200i
$565$	4.21532	−	7.30115i	0.177340	−	0.307162i
$566$	−26.0616	−	29.2151i	−1.09545	−	1.22800i
$567$		0			0
$568$	−7.39456	−	10.4806i	−0.310269	−	0.439756i
$569$	15.3022	+	8.83472i	0.641501	+	0.370371i	0.785193	−	0.619252i	$-0.212564\pi$
$569$	15.3022	+	8.83472i	0.641501	+	0.370371i	−0.143691	+	0.989623i	$0.545897\pi$
$570$	2.48200	−	3.99562i	0.103960	−	0.167358i
$571$	6.51130	−	3.75930i	0.272490	−	0.157322i	−0.357529	−	0.933902i	$-0.616381\pi$
$571$	6.51130	−	3.75930i	0.272490	−	0.157322i	0.630018	+	0.776580i	$0.283047\pi$
$572$	−35.9141	−	26.6043i	−1.50165	−	1.11238i
$573$	1.58955	−	6.57914i	0.0664045	−	0.274847i
$574$		0			0
$575$	−1.07503			−0.0448318
$576$	5.49846	+	23.3617i	0.229103	+	0.973402i
$577$	2.13156	+	3.69196i	0.0887378	+	0.153698i	0.906978	−	0.421178i	$-0.138383\pi$
$577$	2.13156	+	3.69196i	0.0887378	+	0.153698i	−0.818240	+	0.574877i	$0.805050\pi$
$578$	−23.1828	−	7.65130i	−0.964277	−	0.318252i
$579$	−1.97189	−	1.87667i	−0.0819491	−	0.0779917i
$580$	−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
$584$	1.67751	−	3.63125i	0.0694157	−	0.150262i
$585$	16.5955	−	0.821731i	0.686141	−	0.0339744i
$586$	−0.273878	+	0.0568914i	−0.0113138	+	0.00235016i
$587$	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
$590$	−13.8298	+	2.87280i	−0.569363	+	0.118271i
$591$	−0.897238	−	3.04515i	−0.0369074	−	0.125261i
$592$	−6.22141	−	20.4262i	−0.255698	−	0.839511i
$593$	−4.99583	−	2.88434i	−0.205154	−	0.118446i	0.393903	−	0.919152i	$-0.371125\pi$
$593$	−4.99583	−	2.88434i	−0.205154	−	0.118446i	−0.599057	+	0.800706i	$0.704458\pi$
$594$	−0.640266	−	37.1650i	−0.0262704	−	1.52490i
$595$		0			0
$596$	−22.4475	−	2.56954i	−0.919486	−	0.105252i
$597$	−4.38335	+	4.60576i	−0.179399	+	0.188501i
$598$	−1.86047	−	0.614033i	−0.0760802	−	0.0251097i
$599$	17.8985	+	31.0011i	0.731312	+	1.26667i	0.956323	+	0.292313i	$0.0944251\pi$
$599$	17.8985	+	31.0011i	0.731312	+	1.26667i	−0.225010	+	0.974356i	$0.572242\pi$
$600$	2.44711	−	16.6162i	0.0999028	−	0.678353i
$601$	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
$604$	−13.2142	+	17.8383i	−0.537677	+	0.725830i
$605$	−15.8361	+	9.14298i	−0.643829	+	0.371715i
$606$	8.47236	+	5.26286i	0.344166	+	0.213789i
$607$	41.0224	+	23.6843i	1.66505	+	0.961316i	0.970248	+	0.242115i	$0.0778411\pi$
$607$	41.0224	+	23.6843i	1.66505	+	0.961316i	0.694801	+	0.719202i	$0.255492\pi$
$608$	−4.15775	−	7.60227i	−0.168619	−	0.308313i
$609$		0			0
$610$	−0.357475	−	0.400729i	−0.0144737	−	0.0162250i
$611$	−25.3951	+	43.9857i	−1.02738	+	1.77947i
$612$	2.26362	−	35.0475i	0.0915015	−	1.41671i
$613$	−1.39456	−	2.41545i	−0.0563257	−	0.0975590i	0.836488	−	0.547986i	$-0.184605\pi$
$613$	−1.39456	−	2.41545i	−0.0563257	−	0.0975590i	−0.892813	+	0.450427i	$0.851272\pi$
$614$	−23.0155	+	4.78091i	−0.928829	+	0.192942i
$615$	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	$-0.143569\pi$
$618$	1.03272	−	32.0123i	0.0415421	−	1.28772i
$619$	−4.88830	+	2.82226i	−0.196477	+	0.113436i	−0.595011	−	0.803717i	$-0.702852\pi$
$619$	−4.88830	+	2.82226i	−0.196477	+	0.113436i	0.398534	+	0.917154i	$0.369519\pi$
$620$	11.2671	−	4.89201i	0.452496	−	0.196468i
$621$	−0.537240	−	1.53824i	−0.0215587	−	0.0617275i
$622$	−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
$626$	6.63959	+	2.19135i	0.265371	+	0.0875838i
$627$	3.79293	+	12.8729i	0.151475	+	0.514094i
$628$	−23.7780	−	17.6142i	−0.948845	−	0.702881i
$629$			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	$0.959517\pi$
$632$	1.77766	+	19.5151i	0.0707113	+	0.776270i
$633$	7.28244	+	24.7160i	0.289451	+	0.982372i
$634$	−9.72219	+	29.4574i	−0.386117	+	1.16990i
$635$	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
$639$	−11.4312	+	7.37670i	−0.452211	+	0.291818i
$640$	11.1987	+	8.70401i	0.442668	+	0.344056i
$641$	14.2860	−	8.24802i	0.564263	−	0.325777i	−0.190592	−	0.981669i	$-0.561041\pi$
$641$	14.2860	−	8.24802i	0.564263	−	0.325777i	0.754855	+	0.655892i	$0.227707\pi$
$642$	−9.56704	−	0.308633i	−0.377581	−	0.0121808i
$643$			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
$646$	2.57889	+	12.4149i	0.101465	+	0.488456i
$647$	−5.67476	−	9.82897i	−0.223098	−	0.386417i	0.732649	−	0.680606i	$-0.238284\pi$
$647$	−5.67476	−	9.82897i	−0.223098	−	0.386417i	−0.955747	+	0.294190i	$0.904950\pi$
$648$	24.9988	−	4.80232i	0.982044	−	0.188653i
$649$	20.1497	−	34.9002i	0.790944	−	1.36995i
$650$	−15.9845	+	14.2591i	−0.626962	+	0.559289i
$651$		0			0
$652$	26.3599	+	3.01738i	1.03233	+	0.118170i
$653$	38.5978	+	22.2844i	1.51045	+	0.872057i	0.999926	+	0.0121923i	$0.00388102\pi$
$653$	38.5978	+	22.2844i	1.51045	+	0.872057i	0.510522	+	0.859865i	$0.329452\pi$
$654$	10.6605	−	17.1618i	0.416860	−	0.671078i
$655$	−9.13122	+	5.27191i	−0.356786	+	0.205991i
$656$	−5.78482	−	5.40582i	−0.225859	−	0.211062i
$657$	−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	$0.503661\pi$
$660$	−14.0870	−	16.8555i	−0.548334	−	0.656098i
$661$	−21.5502	−	37.3261i	−0.838206	−	1.45182i	−0.891393	−	0.453232i	$-0.850271\pi$
$661$	−21.5502	−	37.3261i	−0.838206	−	1.45182i	0.0531863	−	0.998585i	$-0.483062\pi$
$662$	1.65861	−	5.02546i	0.0644638	−	0.195320i
$663$	−30.8791	+	32.4459i	−1.19925	+	1.26010i
$664$	−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
$668$	8.78055	−	3.81240i	0.339730	−	0.147506i
$669$	−9.50530	−	32.2602i	−0.367496	−	1.24725i
$670$	3.80197	+	18.3028i	0.146883	+	0.707099i
$671$	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	$0.404907\pi$
$674$	−6.60896	−	31.8158i	−0.254567	−	1.22550i
$675$	−17.5017	−	3.32216i	−0.673641	−	0.127870i
$676$	−11.9585	+	5.19223i	−0.459943	+	0.199701i
$677$	35.8437	+	20.6944i	1.37759	+	0.795349i	0.991868	−	0.127268i	$-0.0406207\pi$
$677$	35.8437	+	20.6944i	1.37759	+	0.795349i	0.385717	+	0.922617i	$0.373954\pi$
$678$	−14.5237	+	7.77198i	−0.557780	+	0.298481i
$679$		0			0
$680$	−11.9655	−	16.9592i	−0.458857	−	0.650356i
$681$	13.4032	+	12.7560i	0.513613	+	0.488811i
$682$	−10.9835	+	33.2791i	−0.420580	+	1.27432i
$683$	−2.26745	−	3.92734i	−0.0867615	−	0.150275i	0.819379	−	0.573252i	$-0.194318\pi$
$683$	−2.26745	−	3.92734i	−0.0867615	−	0.150275i	−0.906140	+	0.422977i	$0.860985\pi$
$684$	−8.23890	+	4.07273i	−0.315022	+	0.155725i
$685$	−17.2461			−0.658941
$686$		0			0
$687$	−3.05138	+	12.6296i	−0.116417	+	0.481850i
$688$	−9.31160	−	8.70155i	−0.355002	−	0.331744i
$689$	48.9366	−	28.2536i	1.86434	−	1.07638i
$690$	−0.817953	−	0.508096i	−0.0311389	−	0.0193429i
$691$	−23.6340	−	13.6451i	−0.899079	−	0.519084i	−0.0221779	−	0.999754i	$-0.507060\pi$
$691$	−23.6340	−	13.6451i	−0.899079	−	0.519084i	−0.876901	+	0.480670i	$0.840393\pi$
$692$	28.6369	+	3.27802i	1.08861	+	0.124612i
$693$		0			0
$694$	−2.24797	+	2.00532i	−0.0853316	+	0.0761211i
$695$	−8.25229	+	14.2934i	−0.313027	+	0.542179i
$696$	16.8458	−	21.2709i	0.638537	−	0.806272i
$697$	5.79306	+	10.0339i	0.219428	+	0.380060i
$698$	1.02312	+	4.92536i	0.0387258	+	0.186428i
$699$	−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	$0.944389\pi$
$702$	−28.3913	−	15.7460i	−1.07156	−	0.594294i
$703$	7.08130	−	4.08839i	0.267076	−	0.154197i
$704$	−39.8002	+	7.31156i	−1.50003	+	0.275565i
$705$	−17.2094	+	18.0827i	−0.648145	+	0.681032i
$706$	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	−0.442001	−	0.897015i	$-0.645731\pi$
$709$	14.8003	−	25.6349i	0.555837	−	0.962738i	0.997838	−	0.0657232i	$-0.0209354\pi$
$710$	−2.51987	+	7.63500i	−0.0945691	+	0.286536i
$711$	20.7592	−	1.02790i	0.778530	−	0.0385491i
$712$	−1.23097	−	13.5136i	−0.0461325	−	0.506443i
$713$			1.53617i			0.0575302i
$714$		0			0
$715$			28.0159i			1.04773i
$716$	−1.11580	−	0.826558i	−0.0416994	−	0.0308899i
$717$	−34.1369	+	10.0583i	−1.27487	+	0.375633i
$718$	1.64647	+	0.543405i	0.0614457	+	0.0202797i
$719$	−1.35786	+	2.35188i	−0.0506395	+	0.0877102i	−0.890234	−	0.455503i	$-0.849459\pi$
$719$	−1.35786	+	2.35188i	−0.0506395	+	0.0877102i	0.839595	+	0.543214i	$0.182793\pi$
$720$	9.71531	−	11.4861i	0.362068	−	0.428062i
$721$		0			0
$722$	−17.5752	+	15.6782i	−0.654081	+	0.583480i
$723$	−22.6524	−	21.5585i	−0.842453	−	0.801770i
$724$	−11.5767	+	5.02646i	−0.430245	+	0.186807i
$725$	−16.4444	+	9.49416i	−0.610729	+	0.352604i
$726$	35.7100	+	1.15201i	1.32532	+	0.0427550i
$727$			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
$730$	−2.45490	+	0.509947i	−0.0908601	+	0.0188740i
$731$	9.32487	+	16.1512i	0.344893	+	0.597372i
$732$	0.180164	+	1.03366i	0.00665905	+	0.0382050i
$733$	−7.65295	+	13.2553i	−0.282668	+	0.489596i	−0.972041	−	0.234811i	$-0.924553\pi$
$733$	−7.65295	+	13.2553i	−0.282668	+	0.489596i	0.689373	+	0.724407i	$0.257886\pi$
$734$	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
$738$	−5.98257	+	5.89337i	−0.220222	+	0.216938i
$739$	−23.2697	+	13.4348i	−0.855989	+	0.494205i	−0.862667	−	0.505772i	$-0.831208\pi$
$739$	−23.2697	+	13.4348i	−0.855989	+	0.494205i	0.00667810	+	0.999978i	$0.497874\pi$
$740$	−7.96701	+	10.7550i	−0.292873	+	0.395360i
$741$	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	$0.358301\pi$
$744$	−23.7439	−	3.49682i	−0.870493	−	0.128200i
$745$	7.08130	+	12.2652i	0.259439	+	0.449361i
$746$	−10.9859	−	3.62582i	−0.402224	−	0.132751i
$747$	−17.0990	+	11.0342i	−0.625620	+	0.403721i
$748$	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	$-0.561159\pi$
$751$	−31.1457	−	17.9820i	−1.13652	−	0.656172i	−0.945567	+	0.325427i	$0.894492\pi$
$752$	13.3984	+	43.9899i	0.488591	+	1.60415i
$753$	17.4135	−	5.13079i	0.634582	−	0.186977i
$754$	−33.8818	+	7.03813i	−1.23390	+	0.256314i
$755$	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	$0.360059\pi$
$758$	43.2040	−	8.97458i	1.56924	−	0.325972i
$759$	2.63524	−	0.776460i	0.0956531	−	0.0281837i
$760$	−2.27781	+	4.93072i	−0.0826250	+	0.178856i
$761$	34.9126	+	20.1568i	1.26558	+	0.730684i	0.974149	−	0.225908i	$-0.0725347\pi$
$761$	34.9126	+	20.1568i	1.26558	+	0.730684i	0.291433	+	0.956591i	$0.405868\pi$
$762$	−18.3662	+	9.82820i	−0.665338	+	0.356038i
$763$		0			0
$764$	−0.888828	+	7.76481i	−0.0321567	+	0.280921i
$765$	−18.4974	+	11.9366i	−0.668775	+	0.431570i
$766$	−32.7922	−	10.8228i	−1.18483	−	0.391045i
$767$	−17.5991	−	30.4825i	−0.635465	−	1.10066i
$768$	−9.61309	−	25.9921i	−0.346882	−	0.937909i
$769$	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
$772$	2.52578	+	1.87104i	0.0909048	+	0.0673401i
$773$	−20.1789	+	11.6503i	−0.725784	+	0.419032i	−0.816878	−	0.576811i	$-0.804297\pi$
$773$	−20.1789	+	11.6503i	−0.725784	+	0.419032i	0.0910936	+	0.995842i	$0.470964\pi$
$774$	−9.62992	+	9.48633i	−0.346140	+	0.340979i
$775$	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
$780$	−18.9014	+	3.29447i	−0.676778	+	0.117961i
$781$	−11.4694	−	19.8655i	−0.410407	−	0.710845i
$782$	2.54147	−	0.527930i	0.0908829	−	0.0188787i
$783$	−21.8030	−	18.7853i	−0.779177	−	0.671333i
$784$		0			0
$785$			18.5487i			0.662032i
$786$	20.5906	+	0.664256i	0.734444	+	0.0236932i
$787$	−2.76123	+	1.59420i	−0.0984271	+	0.0568269i	−0.548406	−	0.836212i	$-0.684765\pi$
$787$	−2.76123	+	1.59420i	−0.0984271	+	0.0568269i	0.449978	+	0.893039i	$0.351432\pi$
$788$	1.45992	+	3.36243i	0.0520076	+	0.119782i
$789$	−36.8495	−	35.0701i	−1.31188	−	1.24853i
$790$	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
$794$	31.2654	+	10.3189i	1.10957	+	0.366205i
$795$	26.6404	−	7.84945i	0.944836	−	0.278391i
$796$	4.37019	−	5.89948i	0.154897	−	0.209102i
$797$		−	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
$800$	−0.448577	+	19.3885i	−0.0158596	+	0.685487i
$801$	−14.3750	+	0.711784i	−0.507917	+	0.0251496i
$802$	3.36471	−	10.1948i	0.118812	−	0.359991i
$803$	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
$807$	24.3564	−	25.5922i	0.857385	−	0.900890i
$808$	−10.4552	−	4.82990i	−0.367811	−	0.169915i
$809$	18.4879	−	10.6740i	0.649999	−	0.375277i	−0.138457	−	0.990368i	$-0.544214\pi$
$809$	18.4879	−	10.6740i	0.649999	−	0.375277i	0.788456	+	0.615091i	$0.210881\pi$
$810$	−11.7463	−	10.7996i	−0.412722	−	0.379460i
$811$			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
$814$	−7.76651	−	37.3883i	−0.272216	−	1.31046i
$815$	−8.31549	−	14.4029i	−0.291279	−	0.504510i
$816$	2.37474	+	40.4840i	0.0831326	+	1.41722i
$817$	2.44020	−	4.22654i	0.0853717	−	0.147868i
$818$	6.74377	−	6.01585i	0.235790	−	0.210339i
$819$		0			0
$820$	−0.564413	+	4.93072i	−0.0197101	+	0.172188i
$821$	−5.03883	−	2.90917i	−0.175857	−	0.101531i	0.409488	−	0.912316i	$-0.365707\pi$
$821$	−5.03883	−	2.90917i	−0.175857	−	0.101531i	−0.585344	+	0.810785i	$0.699041\pi$
$822$	28.6239	+	17.7806i	0.998374	+	0.620170i
$823$	−8.78912	+	5.07440i	−0.306369	+	0.176882i	−0.645301	−	0.763929i	$-0.723268\pi$
$823$	−8.78912	+	5.07440i	−0.306369	+	0.176882i	0.338931	+	0.940811i	$0.389935\pi$
$824$	3.35501	+	36.8314i	0.116877	+	1.28308i
$825$	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	$0.126624\pi$
$828$	0.833738	+	1.68660i	0.0289744	+	0.0586135i
$829$	16.3511	+	28.3210i	0.567898	+	0.983628i	0.996774	+	0.0802647i	$0.0255766\pi$
$829$	16.3511	+	28.3210i	0.567898	+	0.983628i	−0.428876	+	0.903364i	$0.641090\pi$
$830$	−3.76928	+	11.4206i	−0.130834	+	0.396414i
$831$	4.95202	+	4.71289i	0.171784	+	0.163488i
$832$	−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
$836$	−6.17159	−	14.2141i	−0.213449	−	0.491606i
$837$	−4.74723	+	25.0093i	−0.164088	+	0.864447i
$838$	8.37884	+	40.3360i	0.289442	+	1.39339i
$839$	−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
$842$	9.22772	+	44.4226i	0.318008	+	1.53090i
$843$	−0.580701	−	1.97085i	−0.0200004	−	0.0678796i
$844$	−11.8495	−	27.2912i	−0.407875	−	0.939401i
$845$	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
$849$	33.0560	−	34.7332i	1.13448	−	1.19204i
$850$	8.89462	−	26.9499i	0.305083	−	0.924375i
$851$	−0.836944	−	1.44963i	−0.0286901	−	0.0496927i
$852$	12.0539	−	10.0741i	0.412960	−	0.345132i
$853$	−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
$856$	11.0072	−	1.00266i	0.376220	−	0.0342703i
$857$	27.4440	−	15.8448i	0.937471	−	0.541249i	0.0483040	−	0.998833i	$-0.484618\pi$
$857$	27.4440	−	15.8448i	0.937471	−	0.541249i	0.889166	+	0.457584i	$0.151285\pi$
$858$	28.8841	−	46.4987i	0.986086	−	1.58744i
$859$	5.22874	+	3.01882i	0.178402	+	0.103001i	0.586542	−	0.809919i	$-0.300489\pi$
$859$	5.22874	+	3.01882i	0.178402	+	0.103001i	−0.408139	+	0.912920i	$0.633822\pi$
$860$	−0.908514	+	7.93679i	−0.0309801	+	0.270642i
$861$		0			0
$862$	19.2552	−	17.1768i	0.655835	−	0.585045i
$863$	−20.0569	+	34.7395i	−0.682744	+	1.18255i	0.291396	+	0.956602i	$0.405880\pi$
$863$	−20.0569	+	34.7395i	−0.682744	+	1.18255i	−0.974140	+	0.225944i	$0.927453\pi$
$864$	−27.9668	+	9.04742i	−0.951451	+	0.307800i
$865$	−9.03379	−	15.6470i	−0.307158	−	0.532013i
$866$	−1.39454	−	6.71339i	−0.0473885	−	0.228130i
$867$	7.02181	−	29.0632i	0.238473	−	0.987038i
$868$		0			0
$869$			35.0447i			1.18881i
$870$	−16.9992	−	0.548397i	−0.576328	−	0.0185924i
$871$	−40.3415	+	23.2912i	−1.36692	+	0.789192i
$872$	−9.78354	+	21.1781i	−0.331312	+	0.717183i
$873$	−34.4944	+	22.2597i	−1.16746	+	0.753377i
$874$	−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	−0.211066	−	0.977472i	$-0.567693\pi$
$877$	21.9436	−	38.0074i	0.740983	−	1.28342i	0.952048	−	0.305948i	$-0.0989733\pi$
$878$	−8.97639	+	27.1977i	−0.302939	+	0.917878i
$879$	−0.0968270	−	0.328623i	−0.00326590	−	0.0110842i
$880$	18.5328	+	17.3186i	0.624740	+	0.583810i
$881$		−	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	$-0.106480\pi$
$884$	30.7864	−	41.5597i	1.03546	−	1.39780i
$885$	−4.88940	−	16.5942i	−0.164355	−	0.557808i
$886$	30.1722	+	9.95812i	1.01366	+	0.334550i
$887$	13.4459	−	23.2890i	0.451470	−	0.781969i	−0.547007	−	0.837128i	$-0.684233\pi$
$887$	13.4459	−	23.2890i	0.451470	−	0.781969i	0.998478	+	0.0551585i	$0.0175664\pi$
$888$	24.3114	−	9.63641i	0.815836	−	0.323377i
$889$		0			0
$890$	−6.34727	+	5.66215i	−0.212761	+	0.189796i
$891$	45.3018	−	4.49728i	1.51767	−	0.150665i
$892$	15.4664	+	35.6214i	0.517852	+	1.19269i
$893$	−15.2503	+	8.80477i	−0.510332	+	0.294640i
$894$	0.892237	−	27.6576i	0.0298409	−	0.925010i
$895$			0.870412i			0.0290947i
$896$		0			0
$897$	0.563515	−	2.33238i	0.0188152	−	0.0778760i
$898$	40.9388	−	8.50404i	1.36614	−	0.283783i
$899$	13.5668	+	23.4984i	0.452478	+	0.783715i
$900$	20.5273	+	1.32581i	0.684244	+	0.0441935i
$901$	−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
$906$	−23.0956	−	14.3465i	−0.767299	−	0.476631i
$907$	−16.1538	+	9.32642i	−0.536379	+	0.309679i	−0.743610	−	0.668613i	$-0.766888\pi$
$907$	−16.1538	+	9.32642i	−0.536379	+	0.309679i	0.207231	+	0.978292i	$0.433555\pi$
$908$	−17.1681	−	12.7177i	−0.569743	−	0.422052i
$909$	−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	$0.542996\pi$
$912$	8.86408	−	5.83525i	0.293519	−	0.193225i
$913$	−17.1561	−	29.7153i	−0.567785	−	0.983433i
$914$	24.4350	+	8.06458i	0.808237	+	0.266753i
$915$	0.453413	−	0.476419i	0.0149894	−	0.0157499i
$916$	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	$-0.239781\pi$
$919$	15.2109	+	8.78201i	0.501761	+	0.289692i	−0.227680	+	0.973736i	$0.573114\pi$
$920$	1.00938	+	0.466296i	0.0332782	+	0.0153733i
$921$	−8.13692	−	27.6160i	−0.268121	−	0.909979i
$922$	34.5862	−	7.18444i	1.13903	−	0.236607i
$923$	−20.0351			−0.659463
$924$		0			0
$925$	−18.3011			−0.601736
$926$	8.82339	−	1.83285i	0.289954	−	0.0602310i
$927$	39.1793	−	1.93997i	1.28682	−	0.0637170i
$928$	−16.2890	+	26.7640i	−0.534712	+	0.878571i
$929$	−33.7624	−	19.4927i	−1.10771	−	0.639535i	−0.169473	−	0.985535i	$-0.554207\pi$
$929$	−33.7624	−	19.4927i	−1.10771	−	0.639535i	−0.938235	+	0.345999i	$0.887540\pi$
$930$	7.09794	+	13.2641i	0.232751	+	0.434948i
$931$		0			0
$932$	5.56221	+	0.636699i	0.182196	+	0.0208558i
$933$	−13.4953	−	12.8436i	−0.441816	−	0.420481i
$934$	36.7393	+	12.1255i	1.20215	+	0.396759i
$935$	−18.5592	−	32.1455i	−0.606951	−	1.05127i
$936$	34.7677	+	14.0192i	1.13642	+	0.458233i
$937$	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
$940$	17.1578	−	23.1619i	0.559625	−	0.755458i
$941$	26.5129	−	15.3073i	0.864297	−	0.499002i	−0.00115159	−	0.999999i	$-0.500367\pi$
$941$	26.5129	−	15.3073i	0.864297	−	0.499002i	0.865449	+	0.500997i	$0.167033\pi$
$942$	19.1235	−	30.7858i	0.623079	−	1.00306i
$943$	−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	−0.712662	−	0.701508i	$-0.752510\pi$
$947$	7.73005	−	13.3888i	0.251193	−	0.435079i	0.963855	+	0.266429i	$0.0858438\pi$
$948$	−23.6435	+	4.12102i	−0.767907	+	0.133844i
$949$	−3.12398	−	5.41090i	−0.101409	−	0.175645i
$950$	−7.27140	+	1.51046i	−0.235915	+	0.0490057i
$951$	−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	$0.930099\pi$
$954$	−52.3085	−	14.4380i	−1.69355	−	0.467448i
$955$	4.24264	−	2.44949i	0.137289	−	0.0792636i
$956$	37.6937	−	16.3661i	1.21910	−	0.529317i
$957$	33.4531	−	35.1505i	1.08138	−	1.13625i
$958$	−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
$962$	−31.6722	−	10.4532i	−1.02115	−	0.337024i
$963$	−0.579770	−	11.7089i	−0.0186828	−	0.377315i
$964$	29.0153	+	21.4938i	0.934519	+	0.692269i
$965$		−	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	$0.769821\pi$
$968$	−41.0857	+	3.74254i	−1.32054	+	0.120290i
$969$	−14.8965	+	4.38917i	−0.478543	+	0.141000i
$970$	−7.60389	+	23.0391i	−0.244146	+	0.739742i
$971$	14.4445	−	25.0186i	0.463546	−	0.802886i	−0.535588	−	0.844479i	$-0.679910\pi$
$971$	14.4445	−	25.0186i	0.463546	−	0.802886i	0.999135	+	0.0415934i	$0.0132434\pi$
$972$	8.36134	+	30.0348i	0.268190	+	0.963366i
$973$		0			0
$974$	−38.4593	−	43.1128i	−1.23232	−	1.38142i
$975$	−19.0036	−	18.0859i	−0.608603	−	0.579213i
$976$	−0.353005	−	1.15899i	−0.0112994	−	0.0370984i
$977$	−40.6932	+	23.4942i	−1.30189	+	0.751646i	−0.980728	−	0.195378i	$-0.937407\pi$
$977$	−40.6932	+	23.4942i	−1.30189	+	0.751646i	−0.321161	+	0.947024i	$0.604073\pi$
$978$	−1.04774	+	32.4780i	−0.0335032	+	1.03853i
$979$		−	24.2673i		−	0.775587i
$980$		0			0
$981$	22.0145	+	11.2971i	0.702868	+	0.360687i
$982$	−5.83893	−	28.1088i	−0.186328	−	0.896989i
$983$	13.6677	+	23.6731i	0.435931	+	0.755054i	0.997371	−	0.0724632i	$-0.0230860\pi$
$983$	13.6677	+	23.6731i	0.435931	+	0.755054i	−0.561440	+	0.827517i	$0.689753\pi$
$984$	6.02030	−	7.60175i	0.191920	−	0.242335i
$985$	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
$990$	19.1663	−	18.8805i	0.609146	−	0.600063i
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	−0.757863	−	0.652413i	$-0.773757\pi$
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	0.186075	+	0.982536i	$0.440423\pi$
$992$	27.7054	+	0.640999i	0.879647	+	0.0203517i
$993$	6.30019	+	1.52216i	0.199930	+	0.0483042i
$994$		0			0
$995$	−4.60206			−0.145895
$996$	18.0305	−	15.0690i	0.571318	−	0.477479i
$997$	6.02119	+	10.4290i	0.190693	+	0.330290i	0.945480	−	0.325680i	$-0.105593\pi$
$997$	6.02119	+	10.4290i	0.190693	+	0.330290i	−0.754787	+	0.655970i	$0.772260\pi$
$998$	−15.1707	+	45.9658i	−0.480219	+	1.45502i
$999$	−9.14586	−	26.1867i	−0.289362	−	0.828511i

Display

a_p

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p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

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a_n

with

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up to: 50 250 1000 (See only

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)

Twists

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

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

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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.d.275.6

Level	$588$
Weight	$2$
Character	588.275
Analytic conductor	$4.695$
Analytic rank	$0$
Dimension	$24$
Inner twists	$8$