LMFDB - Embedded newform 588.2.n.d.275.8

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			275.8
Character	$\chi$	$=$	588.275
Dual form			588.2.n.d.263.8

$q$ -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} +(1.25466 - 1.19408i) q^{3} +(-1.83454 + 0.796533i) q^{4} +(-1.08570 - 0.626827i) q^{5} +(2.01426 + 1.39383i) q^{6} +(-1.63059 - 2.31110i) q^{8} +(0.148364 - 2.99633i) q^{9} +(0.555662 - 1.68361i) q^{10} +(-2.52914 - 4.38059i) q^{11} +(-1.35061 + 3.18996i) q^{12} +4.41798 q^{13} +(-2.11066 + 0.509947i) q^{15} +(2.73107 - 2.92254i) q^{16} +(5.06920 - 2.92671i) q^{17} +(4.19156 - 0.656397i) 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} +(-4.80547 - 0.952605i) q^{24} +(-1.71417 - 2.96904i) q^{25} +(1.27074 + 6.11738i) q^{26} +(-3.39170 - 3.93654i) q^{27} +5.53862i q^{29} +(-1.31319 - 2.77587i) q^{30} +(-4.24264 + 2.44949i) q^{31} +(4.83225 + 2.94098i) q^{32} +(-8.40398 - 2.47619i) q^{33} +(5.51053 + 6.17729i) q^{34} +(2.11450 + 5.61506i) q^{36} +(2.66908 - 4.62298i) q^{37} +(-0.678928 + 2.05710i) q^{38} +(5.54308 - 5.27540i) q^{39} +(0.321666 + 3.53125i) q^{40} +1.97938i q^{41} -3.18613i q^{43} +(8.12909 + 6.02183i) q^{44} +(-2.03926 + 3.16011i) q^{45} +(-0.421113 - 0.138985i) q^{46} +(5.74813 - 9.95606i) q^{47} +(-0.0631619 - 6.92792i) q^{48} +(3.61805 - 3.22752i) q^{50} +(2.86544 - 9.72505i) q^{51} +(-8.10496 + 3.51907i) q^{52} +(-11.0767 + 6.39513i) q^{53} +(4.47521 - 5.82860i) q^{54} +6.34133i q^{55} +(2.57889 - 0.623072i) q^{57} +(-7.66908 + 1.59307i) q^{58} +(3.98351 + 6.89964i) q^{59} +(3.46591 - 2.61673i) 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} +(1.01145 - 12.3488i) q^{66} +(-9.13122 + 5.27191i) q^{67} +(-6.96844 + 9.40695i) q^{68} +(0.127550 + 0.527930i) q^{69} +4.53490 q^{71} +(-7.16673 + 4.54290i) q^{72} +(-0.707107 - 1.22474i) q^{73} +(7.16894 + 2.36605i) q^{74} +(-5.69597 - 1.67829i) q^{75} +(-3.04365 - 0.348402i) q^{76} +(8.89896 + 6.15790i) q^{78} +(6.00000 + 3.46410i) q^{79} +(-4.79704 + 1.46108i) q^{80} +(-8.95598 - 0.889094i) q^{81} +(-2.74076 + 0.569326i) q^{82} +6.78340 q^{83} -7.33816 q^{85} +(4.41169 - 0.916423i) q^{86} +(6.61354 + 6.94911i) q^{87} +(-6.00000 + 12.9880i) q^{88} +(4.15480 + 2.39878i) q^{89} +(-4.96221 - 1.91473i) q^{90} +(0.0713222 - 0.623072i) q^{92} +(-2.39821 + 8.13932i) q^{93} +(15.4390 + 5.09553i) q^{94} +(-0.960150 - 1.66303i) q^{95} +(9.57461 - 2.08012i) 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
$3$	1.25466	−	1.19408i	0.724381	−	0.689400i
$3$	1.25466	−	1.19408i	0.724381	−	0.689400i
$4$	−1.83454	+	0.796533i	−0.917270	+	0.398266i
$5$	−1.08570	−	0.626827i	−0.485538	−	0.280326i	0.237183	−	0.971465i	$-0.423776\pi$
$5$	−1.08570	−	0.626827i	−0.485538	−	0.280326i	−0.722722	+	0.691139i	$0.757109\pi$
$6$	2.01426	+	1.39383i	0.822319	+	0.569027i
$7$		0			0
$7$		0			0
$8$	−1.63059	−	2.31110i	−0.576500	−	0.817097i
$9$	0.148364	−	2.99633i	0.0494546	−	0.998776i
$10$	0.555662	−	1.68361i	0.175716	−	0.532404i
$11$	−2.52914	−	4.38059i	−0.762563	−	1.32080i	−0.941525	−	0.336942i	$-0.890607\pi$
$11$	−2.52914	−	4.38059i	−0.762563	−	1.32080i	0.178962	−	0.983856i	$-0.442726\pi$
$12$	−1.35061	+	3.18996i	−0.389887	+	0.920863i
$13$	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	0.262545	−	0.964920i	$-0.415438\pi$
$17$	5.06920	−	2.92671i	1.22946	−	0.709831i	0.966918	+	0.255089i	$0.0821048\pi$
$18$	4.19156	−	0.656397i	0.987959	−	0.154714i
$19$	1.32654	+	0.765881i	0.304330	+	0.175705i	0.644386	−	0.764700i	$-0.277113\pi$
$19$	1.32654	+	0.765881i	0.304330	+	0.175705i	−0.340056	+	0.940405i	$0.610446\pi$
$20$	2.49104	+	0.285146i	0.557014	+	0.0637607i
$21$		0			0
$22$	5.33816	−	4.76197i	1.13810	−	1.01525i
$23$	−0.156785	+	0.271560i	−0.0326920	+	0.0566242i	−0.881908	−	0.471421i	$-0.843741\pi$
$23$	−0.156785	+	0.271560i	−0.0326920	+	0.0566242i	0.849217	+	0.528045i	$0.177075\pi$
$24$	−4.80547	−	0.952605i	−0.980913	−	0.194450i
$25$	−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	$0.171929\pi$
$29$			5.53862i			1.02850i	−0.857642	+	0.514248i	$0.828071\pi$
$30$	−1.31319	−	2.77587i	−0.239754	−	0.506802i
$31$	−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
$33$	−8.40398	−	2.47619i	−1.46294	−	0.431049i
$34$	5.51053	+	6.17729i	0.945048	+	1.05940i
$35$		0			0
$36$	2.11450	+	5.61506i	0.352416	+	0.935843i
$37$	2.66908	−	4.62298i	0.438794	−	0.760013i	−0.558803	−	0.829301i	$-0.688739\pi$
$37$	2.66908	−	4.62298i	0.438794	−	0.760013i	0.997597	+	0.0692872i	$0.0220725\pi$
$38$	−0.678928	+	2.05710i	−0.110137	+	0.333705i
$39$	5.54308	−	5.27540i	0.887603	−	0.844741i
$40$	0.321666	+	3.53125i	0.0508598	+	0.558340i
$41$			1.97938i			0.309127i	0.987983	+	0.154564i	$0.0493971\pi$
$41$			1.97938i			0.309127i	−0.987983	+	0.154564i	$0.950603\pi$
$42$		0			0
$43$		−	3.18613i		−	0.485881i	−0.970041	−	0.242940i	$-0.921888\pi$
$43$		−	3.18613i		−	0.485881i	0.970041	−	0.242940i	$-0.0781119\pi$
$44$	8.12909	+	6.02183i	1.22551	+	0.907825i
$45$	−2.03926	+	3.16011i	−0.303995	+	0.471081i
$46$	−0.421113	−	0.138985i	−0.0620897	−	0.0204922i
$47$	5.74813	−	9.95606i	0.838451	−	1.45224i	−0.0527378	−	0.998608i	$-0.516795\pi$
$47$	5.74813	−	9.95606i	0.838451	−	1.45224i	0.891189	−	0.453632i	$-0.149872\pi$
$48$	−0.0631619	−	6.92792i	−0.00911663	−	0.999958i
$49$		0			0
$50$	3.61805	−	3.22752i	0.511669	−	0.456440i
$51$	2.86544	−	9.72505i	0.401242	−	1.36178i
$52$	−8.10496	+	3.51907i	−1.12396	+	0.488007i
$53$	−11.0767	+	6.39513i	−1.52150	+	0.878439i	−0.521823	+	0.853054i	$0.674748\pi$
$53$	−11.0767	+	6.39513i	−1.52150	+	0.878439i	−0.999678	+	0.0253856i	$0.991919\pi$
$54$	4.47521	−	5.82860i	0.608998	−	0.793171i
$55$			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	$0.00688310\pi$
$59$	3.98351	+	6.89964i	0.518608	+	0.898256i	−0.481158	+	0.876634i	$0.659784\pi$
$60$	3.46591	−	2.61673i	0.447447	−	0.337819i
$61$	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
$66$	1.01145	−	12.3488i	0.124500	−	1.52004i
$67$	−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	$-0.413275\pi$
$71$	4.53490			0.538194			0.269097	+	0.963113i	$0.413275\pi$
$72$	−7.16673	+	4.54290i	−0.844608	+	0.535386i
$73$	−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
$75$	−5.69597	−	1.67829i	−0.657714	−	0.193792i
$76$	−3.04365	−	0.348402i	−0.349130	−	0.0399645i
$77$		0			0
$78$	8.89896	+	6.15790i	1.00761	+	0.697245i
$79$	6.00000	+	3.46410i	0.675053	+	0.389742i	0.797988	−	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
$81$	−8.95598	−	0.889094i	−0.995108	−	0.0987883i
$82$	−2.74076	+	0.569326i	−0.302666	+	0.0628716i
$83$	6.78340			0.744575			0.372287	−	0.928118i	$-0.378574\pi$
$83$	6.78340			0.744575			0.372287	+	0.928118i	$0.378574\pi$
$84$		0			0
$85$	−7.33816			−0.795935
$86$	4.41169	−	0.916423i	0.475725	−	0.0988204i
$87$	6.61354	+	6.94911i	0.709045	+	0.745023i
$88$	−6.00000	+	12.9880i	−0.639602	+	1.38453i
$89$	4.15480	+	2.39878i	0.440408	+	0.254270i	0.703771	−	0.710427i	$-0.251498\pi$
$89$	4.15480	+	2.39878i	0.440408	+	0.254270i	−0.263363	+	0.964697i	$0.584832\pi$
$90$	−4.96221	−	1.91473i	−0.523063	−	0.201831i
$91$		0			0
$92$	0.0713222	−	0.623072i	0.00743586	−	0.0649597i
$93$	−2.39821	+	8.13932i	−0.248683	+	0.844008i
$94$	15.4390	+	5.09553i	1.59241	+	0.525564i
$95$	−0.960150	−	1.66303i	−0.0985093	−	0.170623i
$96$	9.57461	−	2.08012i	0.977204	−	0.212302i
$97$	−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	−0.314192	−	0.949359i	$-0.601734\pi$
$101$	3.52631	−	2.03591i	0.350881	−	0.202581i	0.665073	+	0.746778i	$0.268400\pi$
$102$	14.2900	+	1.17044i	1.41492	+	0.115891i
$103$	11.3239	+	6.53788i	1.11578	+	0.644197i	0.940321	−	0.340290i	$-0.110525\pi$
$103$	11.3239	+	6.53788i	1.11578	+	0.644197i	0.175461	+	0.984486i	$0.443859\pi$
$104$	−7.20391	−	10.2104i	−0.706402	−	1.00121i
$105$		0			0
$106$	−12.0410	−	13.4980i	−1.16953	−	1.31104i
$107$	−1.95388	+	3.38422i	−0.188889	+	0.327165i	−0.944880	−	0.327417i	$-0.893822\pi$
$107$	−1.95388	+	3.38422i	−0.188889	+	0.327165i	0.755991	+	0.654582i	$0.227155\pi$
$108$	9.35779	+	4.52015i	0.900454	+	0.434951i
$109$	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	$0.102444\pi$
$113$			6.72485i			0.632621i	−0.948656	+	0.316311i	$0.897556\pi$
$114$	1.60450	+	3.39166i	0.150275	+	0.317658i
$115$	0.340442	−	0.196554i	0.0317464	−	0.0183288i
$116$	−4.41169	−	10.1608i	−0.409615	−	0.943408i
$117$	0.655469	−	13.2377i	0.0605981	−	1.22383i
$118$	−8.40785	+	7.50032i	−0.774005	+	0.690460i
$119$		0			0
$120$	4.62016	+	4.04644i	0.421761	+	0.369388i
$121$	−7.29306	+	12.6320i	−0.663006	+	1.14836i
$122$	0.406768	+	0.134251i	0.0368271	+	0.0121545i
$123$	2.36353	+	2.48346i	0.213112	+	0.223926i
$124$	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
$129$	−3.80448	−	3.99752i	−0.334966	−	0.351962i
$130$	2.45490	−	7.43815i	0.215309	−	0.652369i
$131$	4.20524	−	7.28368i	0.367413	−	0.636378i	−0.621747	−	0.783218i	$-0.713577\pi$
$131$	4.20524	−	7.28368i	0.367413	−	0.636378i	0.989160	+	0.146840i	$0.0469102\pi$
$132$	17.3898	−	2.15138i	1.51359	−	0.187253i
$133$		0			0
$134$	−9.92618	−	11.1272i	−0.857491	−	0.961247i
$135$	1.21482	+	6.39990i	0.104555	+	0.550816i
$136$	−15.0297	−	6.94318i	−1.28879	−	0.595372i
$137$	11.9136	−	6.87834i	1.01785	−	0.587657i	0.104370	−	0.994539i	$-0.466717\pi$
$137$	11.9136	−	6.87834i	1.01785	−	0.587657i	0.913481	+	0.406882i	$0.133384\pi$
$138$	−0.694314	+	0.328461i	−0.0591039	+	0.0279605i
$139$			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
$144$	−8.35171	−	8.61679i	−0.695975	−	0.718066i
$145$	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	0.0424963	−	0.999097i	$-0.486469\pi$
$149$	−9.78354	−	5.64853i	−0.801499	−	0.462745i	−0.843995	+	0.536351i	$0.819802\pi$
$150$	0.685528	−	8.36968i	0.0559731	−	0.683382i
$151$	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
$156$	−5.96697	+	14.0932i	−0.477740	+	1.12836i
$157$	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
$159$	−6.26126	+	21.2502i	−0.496550	+	1.68525i
$160$	−3.40287	−	6.22200i	−0.269020	−	0.491892i
$161$		0			0
$162$	−1.34491	−	12.6567i	−0.105666	−	0.994402i
$163$	−11.4887	−	6.63300i	−0.899864	−	0.519537i	−0.0227080	−	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
$165$	7.57203	+	7.95624i	0.589482	+	0.619392i
$166$	1.95110	+	9.39267i	0.151435	+	0.729012i
$167$	4.78624			0.370371			0.185185	−	0.982704i	$-0.440711\pi$
$167$	4.78624			0.370371			0.185185	+	0.982704i	$0.440711\pi$
$168$		0			0
$169$	6.51854			0.501426
$170$	−2.11066	−	10.1608i	−0.161881	−	0.779299i
$171$	2.49164	−	3.86113i	0.190541	−	0.295268i
$172$	2.53786	+	5.84508i	0.193510	+	0.445684i
$173$	12.4811	+	7.20596i	0.948920	+	0.547859i	0.892745	−	0.450562i	$-0.148776\pi$
$173$	12.4811	+	7.20596i	0.948920	+	0.547859i	0.0561749	+	0.998421i	$0.482110\pi$
$174$	−7.71988	+	11.1562i	−0.585242	+	0.845751i
$175$		0			0
$176$	−19.7097	−	4.57220i	−1.48568	−	0.344643i
$177$	13.2367	+	3.90012i	0.994928	+	0.293151i
$178$	−2.12644	+	6.44293i	−0.159383	+	0.482918i
$179$	−0.347150	−	0.601281i	−0.0259472	−	0.0449419i	0.852760	−	0.522303i	$-0.174927\pi$
$179$	−0.347150	−	0.601281i	−0.0259472	−	0.0449419i	−0.878707	+	0.477361i	$0.841594\pi$
$180$	1.22397	−	7.42168i	0.0912296	−	0.553179i
$181$	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
$186$	−11.9599	−	0.979593i	−0.876946	−	0.0718273i
$187$	−25.6414	−	14.8041i	−1.87509	−	1.08258i
$188$	−2.61485	+	22.8434i	−0.190707	+	1.66602i
$189$		0			0
$190$	2.02655	−	1.80781i	0.147022	−	0.131152i
$191$	−1.95388	+	3.38422i	−0.141378	+	0.244873i	−0.928016	−	0.372541i	$-0.878487\pi$
$191$	−1.95388	+	3.38422i	−0.141378	+	0.244873i	0.786638	+	0.617415i	$0.211820\pi$
$192$	5.63419	+	12.6592i	0.406612	+	0.913601i
$193$	−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	$0.0207980\pi$
$197$			1.83285i			0.130585i	−0.997866	+	0.0652924i	$0.979202\pi$
$198$	−13.4764	−	16.7014i	−0.957728	−	1.18692i
$199$	−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
$201$	−5.16155	+	17.5179i	−0.364068	+	1.23561i
$202$	3.83331	+	4.29713i	0.269710	+	0.302345i
$203$		0			0
$204$	2.48956	+	20.1234i	0.174304	+	1.40892i
$205$	1.24073	−	2.14901i	0.0866563	−	0.150093i
$206$	−5.79562	+	17.5602i	−0.403800	+	1.22348i
$207$	0.790422	+	0.510070i	0.0549381	+	0.0354523i
$208$	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
$213$	5.68978	−	5.41502i	0.389857	−	0.371031i
$214$	−5.24797	−	1.73205i	−0.358744	−	0.118401i
$215$	−1.99715	+	3.45917i	−0.136205	+	0.235914i
$216$	−3.56728	+	14.2574i	−0.242722	+	0.970096i
$217$		0			0
$218$	−8.70434	+	7.76481i	−0.589533	+	0.525899i
$219$	−2.34962	−	0.692304i	−0.158773	−	0.0467816i
$220$	−5.05108	−	11.6334i	−0.340543	−	0.784325i
$221$	22.3956	−	12.9301i	1.50649	−	0.869775i
$222$	11.8199	−	5.59166i	0.793297	−	0.375287i
$223$		−	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	0.632517	−	0.774547i	$-0.282022\pi$
$227$	−5.34136	−	9.25151i	−0.354519	−	0.614045i	−0.987035	+	0.160502i	$0.948689\pi$
$228$	−4.23477	+	3.19722i	−0.280455	+	0.211741i
$229$	−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	0.577302	−	0.816531i	$-0.304105\pi$
$233$	2.42423	+	1.39963i	0.158817	+	0.0916930i	−0.418485	+	0.908224i	$0.637439\pi$
$234$	18.5182	−	2.89995i	1.21057	−	0.189576i
$235$	−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	$-0.268633\pi$
$239$	20.5467			1.32905			0.664527	+	0.747265i	$0.268633\pi$
$240$	−4.27403	+	7.56121i	−0.275888	+	0.488074i
$241$	−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
$243$	−12.2984	+	9.57860i	−0.788942	+	0.614468i
$244$	−0.0688928	+	0.601848i	−0.00441041	+	0.0385294i
$245$		0			0
$246$	−2.75891	+	3.98699i	−0.175902	+	0.254201i
$247$	5.86064	+	3.38364i	0.372904	+	0.215296i
$248$	12.5790	+	5.81105i	0.798768	+	0.369002i
$249$	8.51088	−	8.09989i	0.539355	−	0.513310i
$250$	−14.6306	+	3.03915i	−0.925320	+	0.192213i
$251$	−10.4810			−0.661555			−0.330777	−	0.943709i	$-0.607311\pi$
$251$	−10.4810			−0.661555			−0.330777	+	0.943709i	$0.607311\pi$
$252$		0			0
$253$	1.58612			0.0997188
$254$	11.7752	−	2.44600i	0.738839	−	0.153476i
$255$	−9.20692	+	8.76232i	−0.576560	+	0.548718i
$256$	−1.08251	−	15.9633i	−0.0676566	−	0.997709i
$257$	7.24060	+	4.18036i	0.451656	+	0.260764i	0.708529	−	0.705681i	$-0.249359\pi$
$257$	7.24060	+	4.18036i	0.451656	+	0.260764i	−0.256873	+	0.966445i	$0.582692\pi$
$258$	4.44091	−	6.41770i	0.276479	−	0.399549i
$259$		0			0
$260$	11.0054	+	1.25977i	0.682524	+	0.0781277i
$261$	16.5955	+	0.821731i	1.02724	+	0.0508639i
$262$	11.2949	+	3.72781i	0.697803	+	0.230305i
$263$	14.6850	+	25.4352i	0.905517	+	1.56840i	0.820221	+	0.572046i	$0.193850\pi$
$263$	14.6850	+	25.4352i	0.905517	+	1.56840i	0.0852962	+	0.996356i	$0.472816\pi$
$264$	7.98072	+	23.4601i	0.491179	+	1.44387i
$265$	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	−0.930099	−	0.367310i	$-0.880279\pi$
$269$	−17.6649	+	10.1988i	−1.07705	+	0.621834i	−0.146950	+	0.989144i	$0.546946\pi$
$270$	−8.51224	+	3.52291i	−0.518038	+	0.214397i
$271$	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
$276$	−0.654510	−	0.866910i	−0.0393969	−	0.0521819i
$277$	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	$0.0112649\pi$
$281$			1.18623i			0.0707648i	−0.999374	+	0.0353824i	$0.988735\pi$
$282$	25.4553	−	12.0422i	1.51584	−	0.717103i
$283$	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
$285$	−3.19045	−	0.940050i	−0.188986	−	0.0556837i
$286$	23.5839	−	21.0383i	1.39454	−	1.24402i
$287$		0			0
$288$	9.52909	−	14.0427i	0.561507	−	0.827472i
$289$	8.63122	−	14.9497i	0.507719	−	0.879395i
$290$	9.32487	+	3.07760i	0.547575	+	0.180723i
$291$	−17.1693	+	16.3402i	−1.00648	+	0.957879i
$292$	2.27276	+	1.68361i	0.133004	+	0.0985258i
$293$			0.197795i			0.0115553i	0.999983	+	0.00577765i	$0.00183909\pi$
$293$			0.197795i			0.0115553i	−0.999983	+	0.00577765i	$0.998161\pi$
$294$		0			0
$295$		−	9.98789i		−	0.581517i
$296$	−15.0363	+	1.36968i	−0.873969	+	0.0796109i
$297$	−8.66633	+	24.8137i	−0.502871	+	1.43984i
$298$	5.00724	−	15.1715i	0.290061	−	0.878862i
$299$	−0.692674	+	1.19975i	−0.0400584	+	0.0693831i
$300$	11.7863	−	1.45814i	0.680482	−	0.0841857i
$301$		0			0
$302$	10.4496	+	11.7139i	0.601304	+	0.674061i
$303$	1.99329	−	6.76507i	0.114512	−	0.388643i
$304$	5.86120	−	1.78521i	0.336163	−	0.102389i
$305$	−0.328846	+	0.189859i	−0.0188297	+	0.0108713i
$306$	19.3268	−	15.5949i	1.10484	−	0.891499i
$307$		−	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	0.977253	−	0.212078i	$-0.0680231\pi$
$311$	5.37805	+	9.31506i	0.304961	+	0.528209i	−0.672291	+	0.740287i	$0.734690\pi$
$312$	−21.2305	−	4.20859i	−1.20194	−	0.238264i
$313$	−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	0.927338	−	0.374224i	$-0.122091\pi$
$317$	18.9960	+	10.9673i	1.06692	+	0.615987i	0.139582	+	0.990211i	$0.455424\pi$
$318$	−31.2251	−	2.55752i	−1.75101	−	0.143419i
$319$	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
$324$	17.1383	−	5.50265i	0.952127	−	0.305703i
$325$	−7.57319	−	13.1171i	−0.420085	−	0.727609i
$326$	5.87994	−	17.8157i	0.325660	−	0.986722i
$327$	13.7034	+	4.03765i	0.757802	+	0.223283i
$328$	4.57454	−	3.22756i	0.252587	−	0.178212i
$329$		0			0
$330$	−8.83871	+	12.7731i	−0.486555	+	0.703135i
$331$	3.24073	+	1.87104i	0.178127	+	0.102841i	0.586412	−	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
$333$	−13.4560	−	8.68332i	−0.737383	−	0.475843i
$334$	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
$339$	8.02999	+	8.43743i	0.436129	+	0.458258i
$340$	13.4621	−	5.84508i	0.730087	−	0.316994i
$341$	21.4604	+	12.3902i	1.16215	+	0.670966i
$342$	6.06301	+	2.33949i	0.327850	+	0.126505i
$343$		0			0
$344$	−7.36347	+	5.19527i	−0.397011	+	0.280110i
$345$	0.192440	−	0.653124i	0.0103606	−	0.0351630i
$346$	−6.38786	+	19.3547i	−0.343413	+	1.04051i
$347$	1.06505	+	1.84472i	0.0571750	+	0.0990299i	0.893196	−	0.449667i	$-0.148457\pi$
$347$	1.06505	+	1.84472i	0.0571750	+	0.0990299i	−0.836021	+	0.548697i	$0.815124\pi$
$348$	−17.6680	−	7.48052i	−0.947103	−	0.400998i
$349$	−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	0.00426642	−	0.999991i	$-0.498642\pi$
$353$	16.3912	−	9.46348i	0.872417	−	0.503690i	0.868151	+	0.496301i	$0.165309\pi$
$354$	−1.59307	+	19.4500i	−0.0846709	+	1.03376i
$355$	−4.92353	−	2.84260i	−0.261314	−	0.150869i
$356$	−9.53285	−	1.09121i	−0.505240	−	0.0578342i
$357$		0			0
$358$	0.732717	−	0.653628i	0.0387253	−	0.0345453i
$359$	0.613000	−	1.06175i	0.0323529	−	0.0560369i	−0.849396	−	0.527757i	$-0.823033\pi$
$359$	0.613000	−	1.06175i	0.0323529	−	0.0560369i	0.881748	+	0.471720i	$0.156367\pi$
$360$	10.6285	−	0.439906i	0.560172	−	0.0231851i
$361$	−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
$366$	0.670663	−	0.317273i	0.0350561	−	0.0165841i
$367$	−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
$369$	5.93087	+	0.293668i	0.308749	+	0.0152878i
$370$	−6.30019	−	7.06250i	−0.327531	−	0.367162i
$371$		0			0
$372$	−2.08363	−	16.8422i	−0.108031	−	0.873226i
$373$	4.09019	−	7.08442i	0.211782	−	0.366817i	−0.740490	−	0.672067i	$-0.765407\pi$
$373$	4.09019	−	7.08442i	0.211782	−	0.366817i	0.952272	+	0.305250i	$0.0987400\pi$
$374$	13.1233	−	39.7626i	0.678592	−	2.05607i
$375$	12.6169	+	13.2571i	0.651534	+	0.684593i
$376$	−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
$381$	−10.1545	−	10.6697i	−0.520229	−	0.546626i
$382$	−5.24797	−	1.73205i	−0.268509	−	0.0886194i
$383$	−12.2089	+	21.1465i	−0.623848	+	1.08054i	0.364915	+	0.931041i	$0.381098\pi$
$383$	−12.2089	+	21.1465i	−0.623848	+	1.08054i	−0.988763	+	0.149495i	$0.952235\pi$
$384$	−15.9081	+	11.4426i	−0.811807	+	0.583926i
$385$		0			0
$386$	1.65861	−	1.47958i	0.0844212	−	0.0753089i
$387$	−9.54670	−	0.472707i	−0.485286	−	0.0240290i
$388$	25.1045	−	10.9001i	1.27449	−	0.553367i
$389$	−7.86740	+	4.54225i	−0.398893	+	0.230301i	−0.686006	−	0.727596i	$-0.740638\pi$
$389$	−7.86740	+	4.54225i	−0.398893	+	0.230301i	0.287113	+	0.957897i	$0.407304\pi$
$390$	−5.80164	−	12.2637i	−0.293777	−	0.620998i
$391$			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
$396$	19.2494	−	23.4640i	0.967321	−	1.17911i
$397$	−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	0.326785	−	0.945099i	$-0.394035\pi$
$401$	−6.57424	−	3.79564i	−0.328302	−	0.189545i	−0.655087	+	0.755553i	$0.727368\pi$
$402$	−25.7408	−	2.10833i	−1.28383	−	0.105154i
$403$	−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
$408$	−27.1479	+	9.23525i	−1.34402	+	0.457213i
$409$	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
$411$	6.73435	−	22.8558i	0.332181	−	1.12739i
$412$	−25.9819	−	2.97411i	−1.28003	−	0.146524i
$413$		0			0
$414$	−0.478923	+	1.24117i	−0.0235378	+	0.0610003i
$415$	−7.36471	−	4.25202i	−0.361520	−	0.208723i
$416$	21.3488	+	12.9932i	1.04671	+	0.637044i
$417$	15.7202	+	16.5179i	0.769823	+	0.808884i
$418$	10.7284	−	2.22857i	0.524743	−	0.109003i
$419$	29.1307			1.42313			0.711565	−	0.702620i	$-0.247987\pi$
$419$	29.1307			1.42313			0.711565	+	0.702620i	$0.247987\pi$
$420$		0			0
$421$	−32.0821			−1.56358			−0.781792	−	0.623539i	$-0.785694\pi$
$421$	−32.0821			−1.56358			−0.781792	+	0.623539i	$0.785694\pi$
$422$	−20.5985	+	4.27885i	−1.00272	+	0.208291i
$423$	−28.9788	−	18.7004i	−1.40900	−	0.909245i
$424$	32.8413	+	15.1715i	1.59492	+	0.736793i
$425$	−17.3790	−	10.0338i	−0.843006	−	0.486710i
$426$	9.13447	+	6.32086i	0.442567	+	0.306247i
$427$		0			0
$428$	0.888828	−	7.76481i	0.0429631	−	0.375326i
$429$	−37.1286	−	10.9398i	−1.79259	−	0.528177i
$430$	−5.36420	−	1.77041i	−0.258685	−	0.0853769i
$431$	−9.12282	−	15.8012i	−0.439431	−	0.761116i	0.558215	−	0.829696i	$-0.311486\pi$
$431$	−9.12282	−	15.8012i	−0.439431	−	0.761116i	−0.997646	+	0.0685802i	$0.978153\pi$
$432$	−20.7677	−	0.838599i	−0.999186	−	0.0403471i
$433$	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
$438$	0.282784	−	3.45254i	0.0135120	−	0.164969i
$439$	−17.5388	−	10.1260i	−0.837081	−	0.483289i	0.0191902	−	0.999816i	$-0.493891\pi$
$439$	−17.5388	−	10.1260i	−0.837081	−	0.483289i	−0.856271	+	0.516527i	$0.827225\pi$
$440$	14.6554	−	10.3401i	0.698670	−	0.492945i
$441$		0			0
$442$	24.3454	+	27.2912i	1.15799	+	1.29811i
$443$	11.2335	−	19.4570i	0.533719	−	0.924428i	−0.465505	−	0.885045i	$-0.654127\pi$
$443$	11.2335	−	19.4570i	0.533719	−	0.924428i	0.999224	−	0.0393830i	$-0.0125392\pi$
$444$	11.1422	+	14.7581i	0.528788	+	0.700389i
$445$	−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	$-0.754227\pi$
$449$		−	29.5660i		−	1.39531i	0.716435	−	0.697654i	$-0.245773\pi$
$450$	−9.13393	−	11.3197i	−0.430578	−	0.533616i
$451$	8.67086	−	5.00612i	0.408295	−	0.235729i
$452$	−5.35657	−	12.3370i	−0.251952	−	0.580284i
$453$	5.43370	−	18.4415i	0.255297	−	0.866458i
$454$	11.2738	−	10.0569i	0.529107	−	0.471996i
$455$		0			0
$456$	−5.64509	−	4.94409i	−0.264355	−	0.231528i
$457$	−9.09743	+	15.7572i	−0.425560	+	0.737091i	−0.996473	−	0.0839196i	$-0.973256\pi$
$457$	−9.09743	+	15.7572i	−0.425560	+	0.737091i	0.570913	+	0.821011i	$0.306589\pi$
$458$	−10.0742	−	3.32492i	−0.470738	−	0.155363i
$459$	−28.7143	−	10.0286i	−1.34027	−	0.468097i
$460$	−0.467993	+	0.631761i	−0.0218203	+	0.0294560i
$461$		−	24.9782i		−	1.16335i	−0.813422	−	0.581675i	$-0.802398\pi$
$461$		−	24.9782i		−	1.16335i	0.813422	−	0.581675i	$-0.197602\pi$
$462$		0			0
$463$			6.37226i			0.296144i	0.988977	+	0.148072i	$0.0473068\pi$
$463$			6.37226i			0.296144i	−0.988977	+	0.148072i	$0.952693\pi$
$464$	16.1869	+	15.1264i	0.751456	+	0.702224i
$465$	7.70568	−	7.33357i	0.357342	−	0.340086i
$466$	−1.24073	+	3.75930i	−0.0574757	+	0.174146i
$467$	13.6785	−	23.6918i	0.632964	−	1.09633i	−0.353979	−	0.935253i	$-0.615172\pi$
$467$	13.6785	−	23.6918i	0.632964	−	1.09633i	0.986943	−	0.161072i	$-0.0514951\pi$
$468$	9.34180	+	24.8072i	0.431825	+	1.14671i
$469$		0			0
$470$	−13.5681	−	15.2098i	−0.625849	−	0.701576i
$471$	24.5821	+	7.24298i	1.13268	+	0.333739i
$472$	9.45028	−	20.4568i	0.434984	−	0.941598i
$473$	−13.9571	+	8.05816i	−0.641750	+	0.370515i
$474$	7.25721	+	15.3406i	0.333335	+	0.704615i
$475$		−	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	0.998577	−	0.0533285i	$-0.0169830\pi$
$479$	9.91668	+	17.1762i	0.453105	+	0.784800i	−0.545472	+	0.838129i	$0.683650\pi$
$480$	−11.6990	−	3.74324i	−0.533984	−	0.170855i
$481$	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
$486$	−16.8004	−	14.2739i	−0.762083	−	0.647479i
$487$	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	$-0.651459\pi$
$491$	−20.3003			−0.916137			−0.458069	+	0.888917i	$0.651459\pi$
$492$	−6.31414	−	2.67337i	−0.284664	−	0.120525i
$493$	16.2099	+	28.0764i	0.730058	+	1.26450i
$494$	−2.99949	+	9.08821i	−0.134954	+	0.408898i
$495$	19.0007	+	0.940824i	0.854018	+	0.0422869i
$496$	−4.42821	+	19.0890i	−0.198833	+	0.857123i
$497$		0			0
$498$	13.6635	+	9.45488i	0.612278	+	0.423683i
$499$	−29.6416	−	17.1136i	−1.32694	−	0.766110i	−0.342116	−	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
$501$	6.00513	−	5.71514i	0.268289	−	0.255334i
$502$	−3.01464	−	14.5126i	−0.134550	−	0.647728i
$503$	−31.1279			−1.38792			−0.693962	−	0.720011i	$-0.744137\pi$
$503$	−31.1279			−1.38792			−0.693962	+	0.720011i	$0.744137\pi$
$504$		0			0
$505$	−5.10467			−0.227155
$506$	0.456215	+	2.19624i	0.0202812	+	0.0976346i
$507$	8.17858	−	7.78364i	0.363224	−	0.345683i
$508$	6.77375	+	15.6010i	0.300536	+	0.692182i
$509$	−34.2107	−	19.7516i	−1.51636	−	0.875474i	−0.999815	−	0.0192162i	$-0.993883\pi$
$509$	−34.2107	−	19.7516i	−1.51636	−	0.875474i	−0.516549	−	0.856257i	$-0.672784\pi$
$510$	−14.7810	−	10.2281i	−0.654512	−	0.452909i
$511$		0			0
$512$	21.7924	−	6.09041i	0.963095	−	0.269161i
$513$	−1.48431	−	7.81964i	−0.0655341	−	0.345245i
$514$	−3.70576	+	11.2281i	−0.163454	+	0.495251i
$515$	−8.19625	−	14.1963i	−0.361170	−	0.625564i
$516$	10.1636	+	4.30322i	0.447429	+	0.189439i
$517$	−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	0.0328296	−	0.999461i	$-0.489548\pi$
$521$	20.8808	−	12.0555i	0.914803	−	0.528162i	0.881973	+	0.471299i	$0.156215\pi$
$522$	3.63553	+	23.2154i	0.159123	+	1.01611i
$523$	−8.02520	−	4.63335i	−0.350917	−	0.202602i	0.314172	−	0.949366i	$-0.398273\pi$
$523$	−8.02520	−	4.63335i	−0.350917	−	0.202602i	−0.665089	+	0.746764i	$0.731606\pi$
$524$	−1.91298	+	16.7118i	−0.0835689	+	0.730059i
$525$		0			0
$526$	−30.9952	+	27.6496i	−1.35145	+	1.20558i
$527$	−14.3379	+	24.8339i	−0.624568	+	1.08178i
$528$	−30.1886	+	17.7983i	−1.31379	+	0.774573i
$529$	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
$534$	5.02538	+	10.6228i	0.217469	+	0.459695i
$535$	4.24264	−	2.44949i	0.183425	−	0.105901i
$536$	27.0732	+	12.5068i	1.16938	+	0.540213i
$537$	−1.15353	−	0.339883i	−0.0497786	−	0.0146670i
$538$	−19.2028	−	21.5263i	−0.827892	−	0.928066i
$539$		0			0
$540$	−7.32637	−	10.7732i	−0.315277	−	0.463606i
$541$	−12.9508	+	22.4315i	−0.556800	+	0.964406i	0.440961	+	0.897526i	$0.354638\pi$
$541$	−12.9508	+	22.4315i	−0.556800	+	0.964406i	−0.997761	+	0.0668796i	$0.978696\pi$
$542$	−9.12903	+	27.6602i	−0.392125	+	1.18811i
$543$	7.91746	−	7.53512i	0.339771	−	0.323363i
$544$	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
$549$	−0.763497	−	0.492695i	−0.0325853	−	0.0210277i
$550$	−23.2890	−	7.68635i	−0.993046	−	0.327747i
$551$	−4.24192	+	7.34722i	−0.180712	+	0.313002i
$552$	1.01212	−	1.15562i	0.0430785	−	0.0491864i
$553$		0			0
$554$	−4.16528	+	3.71569i	−0.176966	+	0.157864i
$555$	−3.27606	+	11.1186i	−0.139061	+	0.471960i
$556$	−10.4865	−	24.1520i	−0.444727	−	1.02427i
$557$	−25.8991	+	14.9528i	−1.09738	+	0.633572i	−0.935531	−	0.353244i	$-0.885079\pi$
$557$	−25.8991	+	14.9528i	−1.09738	+	0.633572i	−0.161847	+	0.986816i	$0.551745\pi$
$558$	−16.1754	+	13.0520i	−0.684760	+	0.552537i
$559$		−	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	$0.0608699\pi$
$563$	15.5531	+	26.9388i	0.655487	+	1.13534i	−0.326284	+	0.945272i	$0.605797\pi$
$564$	23.9960	+	31.7831i	1.01041	+	1.33831i
$565$	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	0.143691	−	0.989623i	$-0.454103\pi$
$569$	−15.3022	−	8.83472i	−0.641501	−	0.370371i	−0.785193	+	0.619252i	$0.787436\pi$
$570$	0.383981	−	4.68806i	0.0160832	−	0.196361i
$571$	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
$576$	22.1851	+	9.15543i	0.924379	+	0.381476i
$577$	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
$579$	−2.61119	−	0.769374i	−0.108517	−	0.0319741i
$580$	−1.57932	+	13.7969i	−0.0655776	+	0.572887i
$581$		0			0
$582$	−27.5639	−	19.0736i	−1.14256	−	0.790628i
$583$	56.0289	+	32.3483i	2.32048	+	1.33973i
$584$	−1.67751	+	3.63125i	−0.0694157	+	0.150262i
$585$	−9.00941	+	13.9613i	−0.372493	+	0.577228i
$586$	−0.273878	+	0.0568914i	−0.0113138	+	0.00235016i
$587$	−43.2909			−1.78681			−0.893404	−	0.449253i	$-0.851690\pi$
$587$	−43.2909			−1.78681			−0.893404	+	0.449253i	$0.851690\pi$
$588$		0			0
$589$	−7.50407			−0.309200
$590$	13.8298	−	2.87280i	0.569363	−	0.118271i
$591$	2.18856	+	2.29961i	0.0900252	+	0.0945931i
$592$	−6.22141	−	20.4262i	−0.255698	−	0.839511i
$593$	4.99583	+	2.88434i	0.205154	+	0.118446i	0.599057	−	0.800706i	$-0.295542\pi$
$593$	4.99583	+	2.88434i	0.205154	+	0.118446i	−0.393903	+	0.919152i	$0.628875\pi$
$594$	−36.8511	−	4.86274i	−1.51202	−	0.199521i
$595$		0			0
$596$	22.4475	+	2.56954i	0.919486	+	0.105252i
$597$	−1.79703	+	6.09897i	−0.0735477	+	0.249614i
$598$	−1.86047	−	0.614033i	−0.0760802	−	0.0251097i
$599$	−17.8985	−	31.0011i	−0.731312	−	1.26667i	−0.956323	−	0.292313i	$-0.905575\pi$
$599$	−17.8985	−	31.0011i	−0.731312	−	1.26667i	0.225010	−	0.974356i	$-0.427758\pi$
$600$	5.40910	+	15.9006i	0.220825	+	0.649137i
$601$	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
$606$	9.94061	+	0.814197i	0.403810	+	0.0330745i
$607$	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
$612$	27.1524	+	22.2754i	1.09757	+	0.900429i
$613$	−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	$0.143569\pi$
$617$			21.6549i			0.871795i	−0.899996	+	0.435898i	$0.856431\pi$
$618$	13.6967	+	28.9526i	0.550962	+	1.16464i
$619$	−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
$621$	1.60078	−	0.303857i	0.0642369	−	0.0121934i
$622$	−11.3513	+	10.1260i	−0.455144	+	0.406017i
$623$		0			0
$624$	−0.279048	−	30.6074i	−0.0111709	−	1.22528i
$625$	−1.94767	+	3.37346i	−0.0779067	+	0.134938i
$626$	−6.63959	−	2.19135i	−0.265371	−	0.0875838i
$627$	−9.25178	−	9.72122i	−0.369481	−	0.388228i
$628$	−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
$633$	17.7634	+	18.6648i	0.706033	+	0.741858i
$634$	−9.72219	+	29.4574i	−0.386117	+	1.16990i
$635$	−5.33056	+	9.23281i	−0.211537	+	0.366393i
$636$	−5.43993	−	43.9716i	−0.215707	−	1.74359i
$637$		0			0
$638$	26.3747	+	29.5660i	1.04419	+	1.17053i
$639$	0.672815	−	13.5881i	0.0266162	−	0.537535i
$640$	11.1987	+	8.70401i	0.442668	+	0.344056i
$641$	−14.2860	+	8.24802i	−0.564263	+	0.325777i	−0.754855	−	0.655892i	$-0.772293\pi$
$641$	−14.2860	+	8.24802i	−0.564263	+	0.325777i	0.190592	+	0.981669i	$0.438959\pi$
$642$	−8.65264	+	4.09333i	−0.341492	+	0.161551i
$643$			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	0.955747	−	0.294190i	$-0.0950497\pi$
$647$	5.67476	+	9.82897i	0.223098	+	0.386417i	−0.732649	+	0.680606i	$0.761716\pi$
$648$	12.5487	+	22.1479i	0.492961	+	0.870051i
$649$	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	$-0.996119\pi$
$653$	−38.5978	−	22.2844i	−1.51045	−	0.872057i	−0.510522	−	0.859865i	$-0.670548\pi$
$654$	−1.64925	+	20.1359i	−0.0644909	+	0.787375i
$655$	−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	$-0.496339\pi$
$659$	0.590533			0.0230039			0.0115019	+	0.999934i	$0.496339\pi$
$660$	−20.2286	−	8.56466i	−0.787397	−	0.333379i
$661$	−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
$663$	12.6594	−	42.9651i	0.491652	−	1.66862i
$664$	−11.0609	−	15.6771i	−0.429248	−	0.608390i
$665$		0			0
$666$	8.15308	−	21.1295i	0.315926	−	0.818750i
$667$	−1.50407	−	0.868374i	−0.0582377	−	0.0336236i
$668$	−8.78055	+	3.81240i	−0.339730	+	0.147506i
$669$	−23.1855	−	24.3619i	−0.896403	−	0.941887i
$670$	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
$675$	−5.87379	+	16.8180i	−0.226082	+	0.647325i
$676$	−11.9585	+	5.19223i	−0.459943	+	0.199701i
$677$	−35.8437	−	20.6944i	−1.37759	−	0.795349i	−0.385717	−	0.922617i	$-0.626046\pi$
$677$	−35.8437	−	20.6944i	−1.37759	−	0.795349i	−0.991868	+	0.127268i	$0.959379\pi$
$678$	−9.37328	+	13.5456i	−0.359979	+	0.520216i
$679$		0			0
$680$	11.9655	+	16.9592i	0.458857	+	0.650356i
$681$	−17.7486	−	5.22955i	−0.680129	−	0.200397i
$682$	−10.9835	+	33.2791i	−0.420580	+	1.27432i
$683$	2.26745	+	3.92734i	0.0867615	+	0.150275i	0.906140	−	0.422977i	$-0.139015\pi$
$683$	2.26745	+	3.92734i	0.0867615	+	0.150275i	−0.819379	+	0.573252i	$0.805682\pi$
$684$	−1.49550	+	9.06808i	−0.0571817	+	0.346727i
$685$	−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
$690$	0.959703	+	0.0786055i	0.0365353	+	0.00299246i
$691$	−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
$696$	5.27612	−	26.6157i	0.199991	−	1.00886i
$697$	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	$-0.944389\pi$
$701$		−	9.20431i		−	0.347642i	0.984777	−	0.173821i	$-0.0556114\pi$
$702$	19.7714	−	25.7506i	0.746222	−	0.971894i
$703$	7.08130	−	4.08839i	0.267076	−	0.154197i
$704$	39.8002	−	7.31156i	1.50003	−	0.275565i
$705$	−7.05532	+	23.9451i	−0.265719	+	0.901826i
$706$	17.8182	+	19.9742i	0.670598	+	0.751740i
$707$		0			0
$708$	−27.3897	+	3.38852i	−1.02937	+	0.127348i
$709$	14.8003	−	25.6349i	0.555837	−	0.962738i	−0.442001	−	0.897015i	$-0.645731\pi$
$709$	14.8003	−	25.6349i	0.555837	−	0.962738i	0.997838	−	0.0657232i	$-0.0209354\pi$
$710$	2.51987	−	7.63500i	0.0945691	−	0.286536i
$711$	11.2698	−	17.4640i	0.422649	−	0.654952i
$712$	−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
$717$	25.7792	−	24.5343i	0.962740	−	0.916249i
$718$	1.64647	+	0.543405i	0.0614457	+	0.0202797i
$719$	1.35786	−	2.35188i	0.0506395	−	0.0877102i	−0.839595	−	0.543214i	$-0.817207\pi$
$719$	1.35786	−	2.35188i	0.0506395	−	0.0877102i	0.890234	+	0.455503i	$0.150541\pi$
$720$	3.66618	+	14.5903i	0.136631	+	0.543748i
$721$		0			0
$722$	17.5752	−	15.6782i	0.654081	−	0.583480i
$723$	−29.9964	−	8.83830i	−1.11558	−	0.328700i
$724$	−11.5767	+	5.02646i	−0.430245	+	0.186807i
$725$	16.4444	−	9.49416i	0.610729	−	0.352604i
$726$	−32.2969	+	15.2788i	−1.19865	+	0.567049i
$727$			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
$732$	0.632215	+	0.837380i	0.0233674	+	0.0309505i
$733$	−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
$738$	1.29926	+	8.29668i	0.0478264	+	0.305405i
$739$	−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	$-0.641699\pi$
$743$	−23.4748			−0.861208			−0.430604	+	0.902541i	$0.641699\pi$
$744$	22.7213	−	7.72939i	0.833003	−	0.283373i
$745$	7.08130	+	12.2652i	0.259439	+	0.449361i
$746$	10.9859	+	3.62582i	0.402224	+	0.132751i
$747$	1.00641	−	20.3253i	0.0368227	−	0.743663i
$748$	58.8321	+	6.73444i	2.15112	+	0.246235i
$749$		0			0
$750$	−14.7275	+	21.2832i	−0.537772	+	0.777151i
$751$	−31.1457	−	17.9820i	−1.13652	−	0.656172i	−0.190955	−	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
$753$	−13.1501	+	12.5151i	−0.479217	+	0.456076i
$754$	−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
$759$	1.99005	−	1.89395i	0.0722344	−	0.0687462i
$760$	−2.27781	+	4.93072i	−0.0826250	+	0.178856i
$761$	−34.9126	−	20.1568i	−1.26558	−	0.730684i	−0.291433	−	0.956591i	$-0.594132\pi$
$761$	−34.9126	−	20.1568i	−1.26558	−	0.730684i	−0.974149	+	0.225908i	$0.927465\pi$
$762$	11.8532	−	17.1294i	0.429394	−	0.620531i
$763$		0			0
$764$	0.888828	−	7.76481i	0.0321567	−	0.280921i
$765$	−1.08872	+	21.9875i	−0.0393627	+	0.794961i
$766$	−32.7922	−	10.8228i	−1.18483	−	0.391045i
$767$	17.5991	+	30.4825i	0.635465	+	1.10066i
$768$	−20.4196	−	18.7360i	−0.736830	−	0.676078i
$769$	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	−0.0910936	−	0.995842i	$-0.529036\pi$
$773$	20.1789	−	11.6503i	0.725784	−	0.419032i	0.816878	+	0.576811i	$0.195703\pi$
$774$	−2.09137	−	13.3548i	−0.0751727	−	0.480030i
$775$	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
$780$	15.3123	−	11.5607i	0.548269	−	0.413938i
$781$	−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
$786$	18.6226	−	8.80987i	0.664247	−	0.314238i
$787$	−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
$789$	48.7964	+	14.3776i	1.73720	+	0.511856i
$790$	9.16617	−	8.17678i	0.326118	−	0.290917i
$791$		0			0
$792$	38.0262	+	19.9049i	1.35120	+	0.707291i
$793$	0.669079	−	1.15888i	0.0237597	−	0.0411530i
$794$	−31.2654	−	10.3189i	−1.10957	−	0.366205i
$795$	20.1180	−	19.1465i	0.713512	−	0.679057i
$796$	4.37019	−	5.89948i	0.154897	−	0.209102i
$797$			55.9985i			1.98357i	0.127925	+	0.991784i	$0.459168\pi$
$797$			55.9985i			1.98357i	−0.127925	+	0.991784i	$0.540832\pi$
$798$		0			0
$799$		−	67.2924i		−	2.38063i
$800$	0.448577	−	19.3885i	0.0158596	−	0.685487i
$801$	7.80395	−	12.0933i	0.275739	−	0.427294i
$802$	3.36471	−	10.1948i	0.118812	−	0.359991i
$803$	−3.57674	+	6.19509i	−0.126220	+	0.218620i
$804$	−4.48448	−	36.2485i	−0.158155	−	1.27839i
$805$		0			0
$806$	−20.3757	−	22.8412i	−0.717705	−	0.804546i
$807$	−9.98534	+	33.8894i	−0.351500	+	1.19296i
$808$	−10.4552	−	4.82990i	−0.367811	−	0.169915i
$809$	−18.4879	+	10.6740i	−0.649999	+	0.375277i	−0.788456	−	0.615091i	$-0.789119\pi$
$809$	−18.4879	+	10.6740i	−0.649999	+	0.375277i	0.138457	+	0.990368i	$0.455786\pi$
$810$	−6.47338	+	14.5843i	−0.227452	+	0.512441i
$811$			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
$816$	−20.5962	−	34.9342i	−0.721010	−	1.22294i
$817$	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	0.585344	−	0.810785i	$-0.300959\pi$
$821$	5.03883	+	2.90917i	0.175857	+	0.101531i	−0.409488	+	0.912316i	$0.634293\pi$
$822$	33.5844	+	2.75077i	1.17139	+	0.0959441i
$823$	−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	$-0.873376\pi$
$827$	−53.0241			−1.84383			−0.921915	+	0.387393i	$0.873376\pi$
$828$	−1.85635	−	0.306146i	−0.0645125	−	0.0106393i
$829$	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
$831$	6.55749	+	1.93213i	0.227477	+	0.0670250i
$832$	−11.8506	+	33.2979i	−0.410845	+	1.15440i
$833$		0			0
$834$	−18.3500	+	26.5181i	−0.635408	+	0.918247i
$835$	−5.19641	−	3.00015i	−0.179829	−	0.103824i
$836$	6.17159	+	14.2141i	0.213449	+	0.491606i
$837$	24.0323	+	8.39341i	0.830677	+	0.290119i
$838$	8.37884	+	40.3360i	0.289442	+	1.39339i
$839$	37.5962			1.29796			0.648982	−	0.760803i	$-0.275195\pi$
$839$	37.5962			1.29796			0.648982	+	0.760803i	$0.275195\pi$
$840$		0			0
$841$	−1.67632			−0.0578040
$842$	−9.22772	−	44.4226i	−0.318008	−	1.53090i
$843$	1.41645	+	1.48833i	0.0487853	+	0.0512606i
$844$	−11.8495	−	27.2912i	−0.407875	−	0.939401i
$845$	−7.07716	−	4.08600i	−0.243462	−	0.140563i
$846$	17.5585	−	45.5044i	0.603673	−	1.56447i
$847$		0			0
$848$	−11.5612	+	49.8377i	−0.397013	+	1.71143i
$849$	13.5519	−	45.9939i	0.465099	−	1.57851i
$850$	8.89462	−	26.9499i	0.305083	−	0.924375i
$851$	0.836944	+	1.44963i	0.0286901	+	0.0496927i
$852$	−6.12488	+	14.4662i	−0.209835	+	0.495602i
$853$	−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	−0.889166	−	0.457584i	$-0.848715\pi$
$857$	−27.4440	+	15.8448i	−0.937471	+	0.541249i	−0.0483040	+	0.998833i	$0.515382\pi$
$858$	4.46854	−	54.5569i	0.152554	−	1.86254i
$859$	5.22874	+	3.01882i	0.178402	+	0.103001i	0.586542	−	0.809919i	$-0.300489\pi$
$859$	5.22874	+	3.01882i	0.178402	+	0.103001i	−0.408139	+	0.912920i	$0.633822\pi$
$860$	0.908514	−	7.93679i	0.0309801	−	0.270642i
$861$		0			0
$862$	19.2552	−	17.1768i	0.655835	−	0.585045i
$863$	20.0569	−	34.7395i	0.682744	−	1.18255i	−0.291396	−	0.956602i	$-0.594120\pi$
$863$	20.0569	−	34.7395i	0.682744	−	1.18255i	0.974140	−	0.225944i	$-0.0725468\pi$
$864$	−4.81221	−	28.9973i	−0.163715	−	0.986508i
$865$	−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
$870$	15.3745	−	7.27325i	0.521243	−	0.246586i
$871$	−40.3415	+	23.2912i	−1.36692	+	0.789192i
$872$	9.78354	−	21.1781i	0.331312	−	0.717183i
$873$	−2.03027	+	41.0029i	−0.0687142	+	1.38774i
$874$	−0.452179	−	0.506892i	−0.0152952	−	0.0171459i
$875$		0			0
$876$	4.86191	−	0.601491i	0.164269	−	0.0203225i
$877$	21.9436	−	38.0074i	0.740983	−	1.28342i	−0.211066	−	0.977472i	$-0.567693\pi$
$877$	21.9436	−	38.0074i	0.740983	−	1.28342i	0.952048	−	0.305948i	$-0.0989733\pi$
$878$	8.97639	−	27.1977i	0.302939	−	0.917878i
$879$	0.236182	+	0.248166i	0.00796622	+	0.00837043i
$880$	18.5328	+	17.3186i	0.624740	+	0.583810i
$881$			1.27293i			0.0428860i	0.999770	+	0.0214430i	$0.00682603\pi$
$881$			1.27293i			0.0428860i	−0.999770	+	0.0214430i	$0.993174\pi$
$882$		0			0
$883$		−	19.5118i		−	0.656625i	−0.944569	−	0.328312i	$-0.893520\pi$
$883$		−	19.5118i		−	0.656625i	0.944569	−	0.328312i	$-0.106480\pi$
$884$	−30.7864	+	41.5597i	−1.03546	+	1.39780i
$885$	−11.9263	−	12.5314i	−0.400898	−	0.421240i
$886$	30.1722	+	9.95812i	1.01366	+	0.334550i
$887$	−13.4459	+	23.2890i	−0.451470	+	0.781969i	−0.998478	−	0.0551585i	$-0.982434\pi$
$887$	−13.4459	+	23.2890i	−0.451470	+	0.781969i	0.547007	+	0.837128i	$0.315767\pi$
$888$	−17.2301	+	19.6730i	−0.578203	+	0.660183i
$889$		0			0
$890$	6.34727	−	5.66215i	0.212761	−	0.189796i
$891$	18.7561	+	41.4811i	0.628354	+	1.38967i
$892$	15.4664	+	35.6214i	0.517852	+	1.19269i
$893$	15.2503	−	8.80477i	0.510332	−	0.294640i
$894$	−11.8335	−	25.0142i	−0.395772	−	0.836599i
$895$			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
$900$	13.0467	−	15.9032i	0.434891	−	0.530107i
$901$	−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
$906$	27.0980	+	2.21949i	0.900271	+	0.0737378i
$907$	−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	$-0.457004\pi$
$911$	8.12909			0.269329			0.134664	+	0.990891i	$0.457004\pi$
$912$	5.22217	−	9.23856i	0.172923	−	0.305919i
$913$	−17.1561	−	29.7153i	−0.567785	−	0.983433i
$914$	−24.4350	−	8.06458i	−0.808237	−	0.266753i
$915$	−0.185885	+	0.630877i	−0.00614516	+	0.0208561i
$916$	1.70623	−	14.9057i	0.0563755	−	0.492497i
$917$		0			0
$918$	5.62715	−	42.6440i	0.185724	−	1.40746i
$919$	15.2109	+	8.78201i	0.501761	+	0.289692i	0.729440	−	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
$921$	−19.8477	−	20.8548i	−0.654004	−	0.687189i
$922$	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
$927$	21.2697	−	32.9603i	0.698589	−	1.08256i
$928$	−16.2890	+	26.7640i	−0.534712	+	0.878571i
$929$	33.7624	+	19.4927i	1.10771	+	0.639535i	0.938235	−	0.345999i	$-0.112460\pi$
$929$	33.7624	+	19.4927i	1.10771	+	0.639535i	0.169473	+	0.985535i	$0.445793\pi$
$930$	12.3708	+	8.56036i	0.405656	+	0.280705i
$931$		0			0
$932$	−5.56221	−	0.636699i	−0.182196	−	0.0208558i
$933$	17.8705	+	5.26547i	0.585055	+	0.172384i
$934$	36.7393	+	12.1255i	1.20215	+	0.396759i
$935$	18.5592	+	32.1455i	0.606951	+	1.05127i
$936$	−31.6625	+	20.0704i	−1.03492	+	0.656023i
$937$	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	−0.865449	−	0.500997i	$-0.832967\pi$
$941$	−26.5129	+	15.3073i	−0.864297	+	0.499002i	0.00115159	+	0.999999i	$0.499633\pi$
$942$	−2.95853	+	36.1210i	−0.0963941	+	1.17688i
$943$	−0.537520	−	0.310337i	−0.0175041	−	0.0101060i
$944$	31.0437	+	7.20143i	1.01039	+	0.234387i
$945$		0			0
$946$	−15.1722	−	17.0081i	−0.493292	−	0.552980i
$947$	−7.73005	+	13.3888i	−0.251193	+	0.435079i	−0.963855	−	0.266429i	$-0.914156\pi$
$947$	−7.73005	+	13.3888i	−0.251193	+	0.435079i	0.712662	+	0.701508i	$0.247490\pi$
$948$	−19.1540	+	14.4611i	−0.622093	+	0.469675i
$949$	−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	$-0.930099\pi$
$953$		−	13.4497i		−	0.435679i	0.975985	−	0.217839i	$-0.0699009\pi$
$954$	−42.2308	+	34.0763i	−1.36727	+	1.10326i
$955$	4.24264	−	2.44949i	0.137289	−	0.0792636i
$956$	−37.6937	+	16.3661i	−1.21910	+	0.529317i
$957$	13.7147	−	46.5464i	0.443333	−	1.50463i
$958$	−20.9308	+	18.6715i	−0.676243	+	0.603250i
$959$		0			0
$960$	1.81813	−	17.2757i	0.0586799	−	0.557572i
$961$	−3.50000	+	6.06218i	−0.112903	+	0.195554i
$962$	31.6722	+	10.4532i	1.02115	+	0.337024i
$963$	9.85035	+	6.35656i	0.317423	+	0.204837i
$964$	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
$969$	11.2494	−	10.7061i	0.361381	−	0.343930i
$970$	−7.60389	+	23.0391i	−0.244146	+	0.739742i
$971$	−14.4445	+	25.0186i	−0.463546	+	0.802886i	−0.999135	−	0.0415934i	$-0.986757\pi$
$971$	−14.4445	+	25.0186i	−0.463546	+	0.802886i	0.535588	+	0.844479i	$0.320090\pi$
$972$	14.9322	−	27.3684i	0.478951	−	0.877842i
$973$		0			0
$974$	38.4593	+	43.1128i	1.23232	+	1.38142i
$975$	−25.1647	−	7.41465i	−0.805915	−	0.237459i
$976$	−0.353005	−	1.15899i	−0.0112994	−	0.0370984i
$977$	40.6932	−	23.4942i	1.30189	−	0.751646i	0.321161	−	0.947024i	$-0.395927\pi$
$977$	40.6932	−	23.4942i	1.30189	−	0.751646i	0.980728	+	0.195378i	$0.0625935\pi$
$978$	−13.8960	−	29.3738i	−0.444344	−	0.939272i
$979$		−	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	0.561440	−	0.827517i	$-0.310247\pi$
$983$	−13.6677	−	23.6731i	−0.435931	−	0.755054i	−0.997371	+	0.0724632i	$0.976914\pi$
$984$	1.88557	−	9.51185i	0.0601097	−	0.303227i
$985$	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
$990$	4.16243	+	26.5800i	0.132291	+	0.844769i
$991$	−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
$996$	−9.16172	+	21.6388i	−0.290300	+	0.685651i
$997$	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
$999$	−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.d.275.8		24
3.2	odd	2	inner	588.2.n.d.275.6		24
4.3	odd	2		588.2.n.h.275.9		24
7.2	even	3		588.2.e.f.491.18	yes	24
7.3	odd	6		588.2.n.h.263.4		24
7.4	even	3		588.2.n.h.263.3		24
7.5	odd	6		588.2.e.f.491.17	yes	24
7.6	odd	2	inner	588.2.n.d.275.7		24
12.11	even	2		588.2.n.h.275.3		24
21.2	odd	6		588.2.e.f.491.7	yes	24
21.5	even	6		588.2.e.f.491.8	yes	24
21.11	odd	6		588.2.n.h.263.9		24
21.17	even	6		588.2.n.h.263.10		24
21.20	even	2	inner	588.2.n.d.275.5		24
28.3	even	6	inner	588.2.n.d.263.5		24
28.11	odd	6	inner	588.2.n.d.263.6		24
28.19	even	6		588.2.e.f.491.6	yes	24
28.23	odd	6		588.2.e.f.491.5	✓	24
28.27	even	2		588.2.n.h.275.10		24
84.11	even	6	inner	588.2.n.d.263.8		24
84.23	even	6		588.2.e.f.491.20	yes	24
84.47	odd	6		588.2.e.f.491.19	yes	24
84.59	odd	6	inner	588.2.n.d.263.7		24
84.83	odd	2		588.2.n.h.275.4		24

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

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	588.2.n.d.275.8

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