LMFDB - Embedded newform 588.2.n.d.263.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			263.7
Character	$\chi$	$=$	588.263
Dual form			588.2.n.d.275.7

$q$-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 $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	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	$-0.576224\pi$
$5$	1.08570	−	0.626827i	0.485538	−	0.280326i	0.722722	+	0.691139i	$0.242891\pi$
$6$	−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	0.178962	+	0.983856i	$0.442726\pi$
$11$	−2.52914	+	4.38059i	−0.762563	+	1.32080i	−0.941525	+	0.336942i	$0.890607\pi$
$12$	1.35061	+	3.18996i	0.389887	+	0.920863i
$13$	−4.41798			−1.22533			−0.612664	−	0.790344i	$-0.709902\pi$
$13$	−4.41798			−1.22533			−0.612664	+	0.790344i	$0.709902\pi$
$14$		0			0
$15$	−2.11066	−	0.509947i	−0.544971	−	0.131668i
$16$	2.73107	+	2.92254i	0.682768	+	0.730636i
$17$	−5.06920	−	2.92671i	−1.22946	−	0.709831i	−0.262545	−	0.964920i	$-0.584562\pi$
$17$	−5.06920	−	2.92671i	−1.22946	−	0.709831i	−0.966918	+	0.255089i	$0.917895\pi$
$18$	4.19156	+	0.656397i	0.987959	+	0.154714i
$19$	−1.32654	+	0.765881i	−0.304330	+	0.175705i	−0.644386	−	0.764700i	$-0.722887\pi$
$19$	−1.32654	+	0.765881i	−0.304330	+	0.175705i	0.340056	+	0.940405i	$0.389554\pi$
$20$	−2.49104	+	0.285146i	−0.557014	+	0.0637607i
$21$		0			0
$22$	5.33816	+	4.76197i	1.13810	+	1.01525i
$23$	−0.156785	−	0.271560i	−0.0326920	−	0.0566242i	0.849217	−	0.528045i	$-0.177075\pi$
$23$	−0.156785	−	0.271560i	−0.0326920	−	0.0566242i	−0.881908	+	0.471421i	$0.843741\pi$
$24$	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	$-0.828071\pi$
$29$		−	5.53862i		−	1.02850i	0.857642	−	0.514248i	$-0.171929\pi$
$30$	−1.31319	+	2.77587i	−0.239754	+	0.506802i
$31$	4.24264	+	2.44949i	0.762001	+	0.439941i	0.830014	−	0.557743i	$-0.188333\pi$
$31$	4.24264	+	2.44949i	0.762001	+	0.439941i	−0.0680129	+	0.997684i	$0.521666\pi$
$32$	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	0.997597	−	0.0692872i	$-0.0220725\pi$
$37$	2.66908	+	4.62298i	0.438794	+	0.760013i	−0.558803	+	0.829301i	$0.688739\pi$
$38$	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	$0.0781119\pi$
$43$			3.18613i			0.485881i	−0.970041	+	0.242940i	$0.921888\pi$
$44$	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	−0.891189	−	0.453632i	$-0.850128\pi$
$47$	−5.74813	−	9.95606i	−0.838451	−	1.45224i	0.0527378	−	0.998608i	$-0.483205\pi$
$48$	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	−0.999678	−	0.0253856i	$-0.991919\pi$
$53$	−11.0767	−	6.39513i	−1.52150	−	0.878439i	−0.521823	−	0.853054i	$-0.674748\pi$
$54$	−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	0.481158	+	0.876634i	$0.340216\pi$
$59$	−3.98351	+	6.89964i	−0.518608	+	0.898256i	−0.999766	+	0.0216222i	$0.993117\pi$
$60$	3.46591	+	2.61673i	0.447447	+	0.337819i
$61$	−0.151445	−	0.262310i	−0.0193905	−	0.0335853i	0.856167	−	0.516699i	$-0.172839\pi$
$61$	−0.151445	−	0.262310i	−0.0193905	−	0.0335853i	−0.875558	+	0.483113i	$0.839506\pi$
$62$	4.61200	−	5.17005i	0.585725	−	0.656597i
$63$		0			0
$64$	−2.68236	−	7.53691i	−0.335295	−	0.942113i
$65$	−4.79659	+	2.76931i	−0.594943	+	0.343491i
$66$	−1.01145	−	12.3488i	−0.124500	−	1.52004i
$67$	−9.13122	−	5.27191i	−1.11556	−	0.644067i	−0.175293	−	0.984516i	$-0.556087\pi$
$67$	−9.13122	−	5.27191i	−1.11556	−	0.644067i	−0.940263	+	0.340450i	$0.889421\pi$
$68$	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	$-0.806960\pi$
$73$	0.707107	−	1.22474i	0.0827606	−	0.143346i	0.904435	+	0.426612i	$0.140293\pi$
$74$	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	−0.122936	−	0.992415i	$-0.539231\pi$
$79$	6.00000	−	3.46410i	0.675053	−	0.389742i	0.797988	+	0.602673i	$0.205898\pi$
$80$	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	$-0.621426\pi$
$83$	−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
$87$	−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	$-0.748502\pi$
$89$	−4.15480	+	2.39878i	−0.440408	+	0.254270i	0.263363	+	0.964697i	$0.415168\pi$
$90$	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	$-0.255529\pi$
$97$	13.6844			1.38944			0.694719	+	0.719281i	$0.255529\pi$
$98$		0			0
$99$	−13.5009	−	6.92820i	−1.35689	−	0.696311i
$100$	5.50966	−	4.08142i	0.550966	−	0.408142i
$101$	−3.52631	−	2.03591i	−0.350881	−	0.202581i	0.314192	−	0.949359i	$-0.398266\pi$
$101$	−3.52631	−	2.03591i	−0.350881	−	0.202581i	−0.665073	+	0.746778i	$0.731600\pi$
$102$	14.2900	−	1.17044i	1.41492	−	0.115891i
$103$	−11.3239	+	6.53788i	−1.11578	+	0.644197i	−0.940321	−	0.340290i	$-0.889475\pi$
$103$	−11.3239	+	6.53788i	−1.11578	+	0.644197i	−0.175461	+	0.984486i	$0.556141\pi$
$104$	7.20391	−	10.2104i	0.706402	−	1.00121i
$105$		0			0
$106$	−12.0410	+	13.4980i	−1.16953	+	1.31104i
$107$	−1.95388	−	3.38422i	−0.188889	−	0.327165i	0.755991	−	0.654582i	$-0.227155\pi$
$107$	−1.95388	−	3.38422i	−0.188889	−	0.327165i	−0.944880	+	0.327417i	$0.893822\pi$
$108$	−9.35779	+	4.52015i	−0.900454	+	0.434951i
$109$	4.12398	−	7.14295i	0.395006	−	0.684170i	−0.598096	−	0.801424i	$-0.704076\pi$
$109$	4.12398	−	7.14295i	0.395006	−	0.684170i	0.993102	+	0.117254i	$0.0374092\pi$
$110$	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	$-0.102444\pi$
$114$	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	$0.123149\pi$
$127$			8.50404i			0.754611i	−0.926089	+	0.377306i	$0.876851\pi$
$128$	−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	$-0.286423\pi$
$131$	−4.20524	−	7.28368i	−0.367413	−	0.636378i	−0.989160	+	0.146840i	$0.953090\pi$
$132$	−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	0.913481	−	0.406882i	$-0.133384\pi$
$137$	11.9136	+	6.87834i	1.01785	+	0.587657i	0.104370	+	0.994539i	$0.466717\pi$
$138$	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	−0.843995	−	0.536351i	$-0.819802\pi$
$149$	−9.78354	+	5.64853i	−0.801499	+	0.462745i	0.0424963	+	0.999097i	$0.486469\pi$
$150$	−0.685528	−	8.36968i	−0.0559731	−	0.683382i
$151$	9.61268	+	5.54988i	0.782269	+	0.451643i	0.837234	−	0.546845i	$-0.184171\pi$
$151$	9.61268	+	5.54988i	0.782269	+	0.451643i	−0.0549650	+	0.998488i	$0.517505\pi$
$152$	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	0.403764	+	0.914863i	$0.367702\pi$
$157$	−7.39785	+	12.8135i	−0.590413	+	1.02262i	−0.994177	+	0.107762i	$0.965632\pi$
$158$	−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	−0.877156	−	0.480205i	$-0.840562\pi$
$163$	−11.4887	+	6.63300i	−0.899864	+	0.519537i	−0.0227080	+	0.999742i	$0.507229\pi$
$164$	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	$-0.559289\pi$
$167$	−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
$171$	−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	$-0.851224\pi$
$173$	−12.4811	+	7.20596i	−0.948920	+	0.547859i	−0.0561749	+	0.998421i	$0.517890\pi$
$174$	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	−0.878707	−	0.477361i	$-0.841594\pi$
$179$	−0.347150	+	0.601281i	−0.0259472	+	0.0449419i	0.852760	+	0.522303i	$0.174927\pi$
$180$	−1.22397	−	7.42168i	−0.0912296	−	0.553179i
$181$	−6.31042			−0.469050			−0.234525	−	0.972110i	$-0.575353\pi$
$181$	−6.31042			−0.469050			−0.234525	+	0.972110i	$0.575353\pi$
$182$		0			0
$183$	−0.123206	+	0.509947i	−0.00910763	+	0.0376964i
$184$	0.883254	+	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	0.786638	−	0.617415i	$-0.211820\pi$
$191$	−1.95388	−	3.38422i	−0.141378	−	0.244873i	−0.928016	+	0.372541i	$0.878487\pi$
$192$	−5.63419	+	12.6592i	−0.406612	+	0.913601i
$193$	−0.785825	+	1.36109i	−0.0565649	+	0.0979733i	−0.892921	−	0.450213i	$-0.851348\pi$
$193$	−0.785825	+	1.36109i	−0.0565649	+	0.0979733i	0.836356	+	0.548186i	$0.184681\pi$
$194$	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	$-0.0207980\pi$
$198$	−13.4764	+	16.7014i	−0.957728	+	1.18692i
$199$	3.17910	+	1.83546i	0.225361	+	0.130112i	0.608430	−	0.793608i	$-0.291800\pi$
$199$	3.17910	+	1.83546i	0.225361	+	0.130112i	−0.383069	+	0.923720i	$0.625133\pi$
$200$	−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	$-0.828881\pi$
$211$		−	14.8763i		−	1.02413i	0.858948	−	0.512063i	$-0.171119\pi$
$212$	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	$-0.717978\pi$
$227$	5.34136	−	9.25151i	0.354519	−	0.614045i	0.987035	+	0.160502i	$0.0513114\pi$
$228$	−4.23477	−	3.19722i	−0.280455	−	0.211741i
$229$	3.75075	+	6.49650i	0.247857	+	0.429301i	0.962931	−	0.269748i	$-0.0869404\pi$
$229$	3.75075	+	6.49650i	0.247857	+	0.429301i	−0.715074	+	0.699049i	$0.753607\pi$
$230$	−0.370081	+	0.414861i	−0.0244024	+	0.0273551i
$231$		0			0
$232$	12.8003	+	9.03122i	0.840381	+	0.592928i
$233$	2.42423	−	1.39963i	0.158817	−	0.0916930i	−0.418485	−	0.908224i	$-0.637439\pi$
$233$	2.42423	−	1.39963i	0.158817	−	0.0916930i	0.577302	+	0.816531i	$0.304105\pi$
$234$	−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	−0.413804	−	0.910366i	$-0.635800\pi$
$241$	9.02728	−	15.6357i	0.581499	−	1.00718i	0.995302	−	0.0968188i	$-0.0308667\pi$
$242$	−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	$-0.392689\pi$
$251$	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
$255$	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	$-0.750641\pi$
$257$	−7.24060	+	4.18036i	−0.451656	+	0.260764i	0.256873	+	0.966445i	$0.417308\pi$
$258$	−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	0.0852962	−	0.996356i	$-0.472816\pi$
$263$	14.6850	−	25.4352i	0.905517	−	1.56840i	0.820221	−	0.572046i	$-0.193850\pi$
$264$	−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	$-0.119721\pi$
$269$	17.6649	+	10.1988i	1.07705	+	0.621834i	0.146950	+	0.989144i	$0.453054\pi$
$270$	−8.51224	−	3.52291i	−0.518038	−	0.214397i
$271$	−17.8370	+	10.2982i	−1.08352	+	0.625572i	−0.931844	−	0.362858i	$-0.881801\pi$
$271$	−17.8370	+	10.2982i	−1.08352	+	0.625572i	−0.151678	+	0.988430i	$0.548468\pi$
$272$	−5.29093	−	22.8080i	−0.320810	−	1.38294i
$273$		0			0
$274$	12.9508	−	14.5179i	0.782389	−	0.877057i
$275$	−8.67076	−	15.0182i	−0.522867	−	0.905632i
$276$	0.654510	−	0.866910i	0.0393969	−	0.0521819i
$277$	1.97345	−	3.41811i	0.118573	−	0.205374i	−0.800629	−	0.599160i	$-0.795501\pi$
$277$	1.97345	−	3.41811i	0.118573	−	0.205374i	0.919202	+	0.393786i	$0.128835\pi$
$278$	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	$-0.0112649\pi$
$282$	25.4553	+	12.0422i	1.51584	+	0.717103i
$283$	−23.9744	−	13.8416i	−1.42513	−	0.822800i	−0.428401	−	0.903589i	$-0.640923\pi$
$283$	−23.9744	−	13.8416i	−1.42513	−	0.822800i	−0.996731	+	0.0807885i	$0.974256\pi$
$284$	−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	$-0.931977\pi$
$311$	−5.37805	+	9.31506i	−0.304961	+	0.528209i	0.672291	+	0.740287i	$0.265310\pi$
$312$	−21.2305	+	4.20859i	−1.20194	+	0.238264i
$313$	2.47200	+	4.28163i	0.139726	+	0.242012i	0.927393	−	0.374089i	$-0.122045\pi$
$313$	2.47200	+	4.28163i	0.139726	+	0.242012i	−0.787667	+	0.616101i	$0.788711\pi$
$314$	15.6144	+	13.9290i	0.881170	+	0.786058i
$315$		0			0
$316$	−13.7665	+	1.57583i	−0.774427	+	0.0886476i
$317$	18.9960	−	10.9673i	1.06692	−	0.615987i	0.139582	−	0.990211i	$-0.455424\pi$
$317$	18.9960	−	10.9673i	1.06692	−	0.615987i	0.927338	+	0.374224i	$0.122091\pi$
$318$	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	−0.408286	−	0.912854i	$-0.633873\pi$
$331$	3.24073	−	1.87104i	0.178127	−	0.102841i	0.586412	+	0.810013i	$0.300540\pi$
$332$	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	−0.836021	−	0.548697i	$-0.815124\pi$
$347$	1.06505	−	1.84472i	0.0571750	−	0.0990299i	0.893196	+	0.449667i	$0.148457\pi$
$348$	17.6680	−	7.48052i	0.947103	−	0.400998i
$349$	3.55710			0.190407			0.0952036	−	0.995458i	$-0.469650\pi$
$349$	3.55710			0.190407			0.0952036	+	0.995458i	$0.469650\pi$
$350$		0			0
$351$	−14.9845	+	17.3916i	−0.799811	+	0.928293i
$352$	0.661842	+	28.6063i	0.0352763	+	1.52472i
$353$	−16.3912	−	9.46348i	−0.872417	−	0.503690i	−0.00426642	−	0.999991i	$-0.501358\pi$
$353$	−16.3912	−	9.46348i	−0.872417	−	0.503690i	−0.868151	+	0.496301i	$0.834691\pi$
$354$	−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	0.881748	−	0.471720i	$-0.156367\pi$
$359$	0.613000	+	1.06175i	0.0323529	+	0.0560369i	−0.849396	+	0.527757i	$0.823033\pi$
$360$	−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	$-0.156537\pi$
$367$	17.4966	+	10.1017i	0.913314	+	0.527302i	0.0318180	+	0.999494i	$0.489870\pi$
$368$	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	0.952272	−	0.305250i	$-0.0987400\pi$
$373$	4.09019	+	7.08442i	0.211782	+	0.366817i	−0.740490	+	0.672067i	$0.765407\pi$
$374$	−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	$-0.704105\pi$
$379$		−	31.2020i		−	1.60274i	0.598170	−	0.801369i	$-0.295895\pi$
$380$	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	0.988763	+	0.149495i	$0.0477647\pi$
$383$	12.2089	+	21.1465i	0.623848	+	1.08054i	−0.364915	+	0.931041i	$0.618902\pi$
$384$	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	0.287113	−	0.957897i	$-0.407304\pi$
$389$	−7.86740	−	4.54225i	−0.398893	−	0.230301i	−0.686006	+	0.727596i	$0.740638\pi$
$390$	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	0.994972	+	0.100151i	$0.0319326\pi$
$397$	11.6405	+	20.1619i	0.584220	+	1.01190i	−0.410753	+	0.911747i	$0.634734\pi$
$398$	3.45588	−	3.87403i	0.173227	−	0.194188i
$399$		0			0
$400$	−13.3587	+	3.09890i	−0.667934	+	0.154945i
$401$	−6.57424	+	3.79564i	−0.328302	+	0.189545i	−0.655087	−	0.755553i	$-0.727368\pi$
$401$	−6.57424	+	3.79564i	−0.328302	+	0.189545i	0.326785	+	0.945099i	$0.394035\pi$
$402$	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	$-0.883834\pi$
$409$	−3.19509	+	5.53406i	−0.157987	+	0.273642i	0.776156	+	0.630541i	$0.217167\pi$
$410$	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	$-0.752013\pi$
$419$	−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
$423$	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	−0.997646	−	0.0685802i	$-0.978153\pi$
$431$	−9.12282	+	15.8012i	−0.439431	+	0.761116i	0.558215	+	0.829696i	$0.311486\pi$
$432$	20.7677	−	0.838599i	0.999186	−	0.0403471i
$433$	−4.84842			−0.233000			−0.116500	−	0.993191i	$-0.537168\pi$
$433$	−4.84842			−0.233000			−0.116500	+	0.993191i	$0.537168\pi$
$434$		0			0
$435$	−2.82440	+	11.6902i	−0.135420	+	0.560501i
$436$	−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	$-0.506109\pi$
$439$	17.5388	−	10.1260i	0.837081	−	0.483289i	0.856271	+	0.516527i	$0.172775\pi$
$440$	−14.6554	−	10.3401i	−0.698670	−	0.492945i
$441$		0			0
$442$	24.3454	−	27.2912i	1.15799	−	1.29811i
$443$	11.2335	+	19.4570i	0.533719	+	0.924428i	0.999224	+	0.0393830i	$0.0125392\pi$
$443$	11.2335	+	19.4570i	0.533719	+	0.924428i	−0.465505	+	0.885045i	$0.654127\pi$
$444$	−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	$0.245773\pi$
$449$			29.5660i			1.39531i	−0.716435	+	0.697654i	$0.754227\pi$
$450$	−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	0.570913	−	0.821011i	$-0.306589\pi$
$457$	−9.09743	−	15.7572i	−0.425560	−	0.737091i	−0.996473	+	0.0839196i	$0.973256\pi$
$458$	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	$-0.952693\pi$
$463$		−	6.37226i		−	0.296144i	0.988977	−	0.148072i	$-0.0473068\pi$
$464$	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	−0.986943	−	0.161072i	$-0.948505\pi$
$467$	−13.6785	−	23.6918i	−0.632964	−	1.09633i	0.353979	−	0.935253i	$-0.384828\pi$
$468$	−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	$-0.983017\pi$
$479$	−9.91668	+	17.1762i	−0.453105	+	0.784800i	0.545472	+	0.838129i	$0.316350\pi$
$480$	−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	0.990845	+	0.135003i	$0.0431045\pi$
$487$	35.3792	+	20.4262i	1.60318	+	0.925599i	0.612339	+	0.790595i	$0.290229\pi$
$488$	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	−0.984825	−	0.173548i	$-0.944477\pi$
$499$	−29.6416	+	17.1136i	−1.32694	+	0.766110i	−0.342116	+	0.939658i	$0.611144\pi$
$500$	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	$-0.255863\pi$
$503$	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
$507$	−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	0.516549	−	0.856257i	$-0.327216\pi$
$509$	34.2107	−	19.7516i	1.51636	−	0.875474i	0.999815	−	0.0192162i	$-0.00611708\pi$
$510$	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	$-0.510452\pi$
$521$	−20.8808	−	12.0555i	−0.914803	−	0.528162i	−0.881973	+	0.471299i	$0.843785\pi$
$522$	3.63553	−	23.2154i	0.159123	−	1.01611i
$523$	8.02520	−	4.63335i	0.350917	−	0.202602i	−0.314172	−	0.949366i	$-0.601727\pi$
$523$	8.02520	−	4.63335i	0.350917	−	0.202602i	0.665089	+	0.746764i	$0.268394\pi$
$524$	1.91298	+	16.7118i	0.0835689	+	0.730059i
$525$		0			0
$526$	−30.9952	−	27.6496i	−1.35145	−	1.20558i
$527$	−14.3379	−	24.8339i	−0.624568	−	1.08178i
$528$	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	−0.997761	−	0.0668796i	$-0.978696\pi$
$541$	−12.9508	−	22.4315i	−0.556800	−	0.964406i	0.440961	−	0.897526i	$-0.354638\pi$
$542$	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	$0.248685\pi$
$547$			32.9387i			1.40836i	−0.710022	+	0.704179i	$0.751315\pi$
$548$	−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	−0.161847	−	0.986816i	$-0.551745\pi$
$557$	−25.8991	−	14.9528i	−1.09738	−	0.633572i	−0.935531	+	0.353244i	$0.885079\pi$
$558$	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	0.326284	+	0.945272i	$0.394203\pi$
$563$	−15.5531	+	26.9388i	−0.655487	+	1.13534i	−0.981771	+	0.190065i	$0.939130\pi$
$564$	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	−0.785193	−	0.619252i	$-0.787436\pi$
$569$	−15.3022	+	8.83472i	−0.641501	+	0.370371i	0.143691	+	0.989623i	$0.454103\pi$
$570$	−0.383981	−	4.68806i	−0.0160832	−	0.196361i
$571$	6.51130	+	3.75930i	0.272490	+	0.157322i	0.630018	−	0.776580i	$-0.283047\pi$
$571$	6.51130	+	3.75930i	0.272490	+	0.157322i	−0.357529	+	0.933902i	$0.616381\pi$
$572$	−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	$-0.861617\pi$
$577$	−2.13156	+	3.69196i	−0.0887378	+	0.153698i	0.818240	+	0.574877i	$0.194950\pi$
$578$	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	$-0.148310\pi$
$587$	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
$591$	−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	$-0.704458\pi$
$593$	−4.99583	+	2.88434i	−0.205154	+	0.118446i	0.393903	+	0.919152i	$0.371125\pi$
$594$	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	0.225010	+	0.974356i	$0.427758\pi$
$599$	−17.8985	+	31.0011i	−0.731312	+	1.26667i	−0.956323	+	0.292313i	$0.905575\pi$
$600$	−5.40910	+	15.9006i	−0.220825	+	0.649137i
$601$	−42.3193			−1.72624			−0.863121	−	0.504998i	$-0.831493\pi$
$601$	−42.3193			−1.72624			−0.863121	+	0.504998i	$0.831493\pi$
$602$		0			0
$603$	14.4416	−	28.1423i	0.588109	−	1.14604i
$604$	−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	−0.694801	+	0.719202i	$0.744508\pi$
$607$	−41.0224	+	23.6843i	−1.66505	+	0.961316i	−0.970248	+	0.242115i	$0.922159\pi$
$608$	−4.15775	+	7.60227i	−0.168619	+	0.308313i
$609$		0			0
$610$	−0.357475	+	0.400729i	−0.0144737	+	0.0162250i
$611$	25.3951	+	43.9857i	1.02738	+	1.77947i
$612$	−27.1524	+	22.2754i	−1.09757	+	0.900429i
$613$	−1.39456	+	2.41545i	−0.0563257	+	0.0975590i	−0.892813	−	0.450427i	$-0.851272\pi$
$613$	−1.39456	+	2.41545i	−0.0563257	+	0.0975590i	0.836488	+	0.547986i	$0.184605\pi$
$614$	−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	$-0.143569\pi$
$618$	13.6967	−	28.9526i	0.550962	−	1.16464i
$619$	4.88830	+	2.82226i	0.196477	+	0.113436i	0.595011	−	0.803717i	$-0.297148\pi$
$619$	4.88830	+	2.82226i	0.196477	+	0.113436i	−0.398534	+	0.917154i	$0.630481\pi$
$620$	−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	$-0.959517\pi$
$631$		−	6.37226i		−	0.253676i	0.991923	−	0.126838i	$-0.0404828\pi$
$632$	−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	0.190592	−	0.981669i	$-0.438959\pi$
$641$	−14.2860	−	8.24802i	−0.564263	−	0.325777i	−0.754855	+	0.655892i	$0.772293\pi$
$642$	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	$-0.904950\pi$
$647$	−5.67476	+	9.82897i	−0.223098	+	0.386417i	0.732649	+	0.680606i	$0.238284\pi$
$648$	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	−0.510522	+	0.859865i	$0.670548\pi$
$653$	−38.5978	+	22.2844i	−1.51045	+	0.872057i	−0.999926	+	0.0121923i	$0.996119\pi$
$654$	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	−0.0531863	−	0.998585i	$-0.516938\pi$
$661$	21.5502	−	37.3261i	0.838206	−	1.45182i	0.891393	−	0.453232i	$-0.149729\pi$
$662$	−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	$-0.373954\pi$
$677$	35.8437	−	20.6944i	1.37759	−	0.795349i	0.991868	+	0.127268i	$0.0406207\pi$
$678$	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	−0.819379	−	0.573252i	$-0.805682\pi$
$683$	2.26745	−	3.92734i	0.0867615	−	0.150275i	0.906140	+	0.422977i	$0.139015\pi$
$684$	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	$-0.492940\pi$
$691$	23.6340	−	13.6451i	0.899079	−	0.519084i	0.876901	+	0.480670i	$0.159607\pi$
$692$	28.6369	−	3.27802i	1.08861	−	0.124612i
$693$		0			0
$694$	−2.24797	−	2.00532i	−0.0853316	−	0.0761211i
$695$	8.25229	+	14.2934i	0.313027	+	0.542179i
$696$	−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	$0.0556114\pi$
$701$			9.20431i			0.347642i	−0.984777	+	0.173821i	$0.944389\pi$
$702$	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	0.997838	+	0.0657232i	$0.0209354\pi$
$709$	14.8003	+	25.6349i	0.555837	+	0.962738i	−0.442001	+	0.897015i	$0.645731\pi$
$710$	−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	$-0.182793\pi$
$719$	−1.35786	−	2.35188i	−0.0506395	−	0.0877102i	−0.890234	+	0.455503i	$0.849459\pi$
$720$	−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	$-0.0754471\pi$
$733$	7.65295	+	13.2553i	0.282668	+	0.489596i	−0.689373	+	0.724407i	$0.742114\pi$
$734$	19.0198	−	21.3212i	0.702035	−	0.786980i
$735$		0			0
$736$	−1.55628	−	0.851142i	−0.0573652	−	0.0313735i
$737$	46.1882	−	26.6668i	1.70136	−	0.982283i
$738$	−1.29926	+	8.29668i	−0.0478264	+	0.305405i
$739$	−23.2697	−	13.4348i	−0.855989	−	0.494205i	0.00667810	−	0.999978i	$-0.497874\pi$
$739$	−23.2697	−	13.4348i	−0.855989	−	0.494205i	−0.862667	+	0.505772i	$0.831208\pi$
$740$	−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	−0.945567	−	0.325427i	$-0.894492\pi$
$751$	−31.1457	+	17.9820i	−1.13652	+	0.656172i	−0.190955	+	0.981599i	$0.561159\pi$
$752$	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	$-0.405868\pi$
$761$	34.9126	−	20.1568i	1.26558	−	0.730684i	0.974149	+	0.225908i	$0.0725347\pi$
$762$	−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	$-0.621304\pi$
$769$	−20.6279			−0.743861			−0.371930	+	0.928261i	$0.621304\pi$
$770$		0			0
$771$	14.0762	+	3.40088i	0.506942	+	0.122480i
$772$	2.52578	−	1.87104i	0.0909048	−	0.0673401i
$773$	−20.1789	−	11.6503i	−0.725784	−	0.419032i	0.0910936	−	0.995842i	$-0.470964\pi$
$773$	−20.1789	−	11.6503i	−0.725784	−	0.419032i	−0.816878	+	0.576811i	$0.804297\pi$
$774$	−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	$-0.315235\pi$
$787$	2.76123	+	1.59420i	0.0984271	+	0.0568269i	−0.449978	+	0.893039i	$0.648568\pi$
$788$	−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	0.138457	−	0.990368i	$-0.455786\pi$
$809$	−18.4879	−	10.6740i	−0.649999	−	0.375277i	−0.788456	+	0.615091i	$0.789119\pi$
$810$	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	−0.409488	−	0.912316i	$-0.634293\pi$
$821$	5.03883	−	2.90917i	0.175857	−	0.101531i	0.585344	+	0.810785i	$0.300959\pi$
$822$	−33.5844	+	2.75077i	−1.17139	+	0.0959441i
$823$	−8.78912	−	5.07440i	−0.306369	−	0.176882i	0.338931	−	0.940811i	$-0.389935\pi$
$823$	−8.78912	−	5.07440i	−0.306369	−	0.176882i	−0.645301	+	0.763929i	$0.723268\pi$
$824$	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	0.428876	+	0.903364i	$0.358910\pi$
$829$	−16.3511	+	28.3210i	−0.567898	+	0.983628i	−0.996774	+	0.0802647i	$0.974423\pi$
$830$	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	$-0.724805\pi$
$839$	−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
$843$	−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	$-0.468976\pi$
$853$	5.68417			0.194622			0.0973112	+	0.995254i	$0.468976\pi$
$854$		0			0
$855$	−5.12543	−	2.63019i	−0.175286	−	0.0899507i
$856$	11.0072	+	1.00266i	0.376220	+	0.0342703i
$857$	27.4440	+	15.8448i	0.937471	+	0.541249i	0.889166	−	0.457584i	$-0.151285\pi$
$857$	27.4440	+	15.8448i	0.937471	+	0.541249i	0.0483040	+	0.998833i	$0.484618\pi$
$858$	4.46854	+	54.5569i	0.152554	+	1.86254i
$859$	−5.22874	+	3.01882i	−0.178402	+	0.103001i	−0.586542	−	0.809919i	$-0.699511\pi$
$859$	−5.22874	+	3.01882i	−0.178402	+	0.103001i	0.408139	+	0.912920i	$0.366178\pi$
$860$	−0.908514	−	7.93679i	−0.0309801	−	0.270642i
$861$		0			0
$862$	19.2552	+	17.1768i	0.655835	+	0.585045i
$863$	20.0569	+	34.7395i	0.682744	+	1.18255i	0.974140	+	0.225944i	$0.0725468\pi$
$863$	20.0569	+	34.7395i	0.682744	+	1.18255i	−0.291396	+	0.956602i	$0.594120\pi$
$864$	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	0.952048	+	0.305948i	$0.0989733\pi$
$877$	21.9436	+	38.0074i	0.740983	+	1.28342i	−0.211066	+	0.977472i	$0.567693\pi$
$878$	−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	$0.106480\pi$
$883$			19.5118i			0.656625i	−0.944569	+	0.328312i	$0.893520\pi$
$884$	−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	$-0.0175664\pi$
$887$	13.4459	+	23.2890i	0.451470	+	0.781969i	−0.547007	+	0.837128i	$0.684233\pi$
$888$	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	0.207231	−	0.978292i	$-0.433555\pi$
$907$	−16.1538	−	9.32642i	−0.536379	−	0.309679i	−0.743610	+	0.668613i	$0.766888\pi$
$908$	−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	−0.227680	−	0.973736i	$-0.573114\pi$
$919$	15.2109	−	8.78201i	0.501761	−	0.289692i	0.729440	+	0.684044i	$0.239781\pi$
$920$	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	$-0.887540\pi$
$929$	−33.7624	+	19.4927i	−1.10771	+	0.639535i	−0.169473	+	0.985535i	$0.554207\pi$
$930$	−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	$-0.627019\pi$
$937$	−23.7865			−0.777072			−0.388536	+	0.921434i	$0.627019\pi$
$938$		0			0
$939$	2.01106	−	8.32376i	0.0656285	−	0.271636i
$940$	17.1578	+	23.1619i	0.559625	+	0.755458i
$941$	26.5129	+	15.3073i	0.864297	+	0.499002i	0.865449	−	0.500997i	$-0.167033\pi$
$941$	26.5129	+	15.3073i	0.864297	+	0.499002i	−0.00115159	+	0.999999i	$0.500367\pi$
$942$	−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	0.712662	−	0.701508i	$-0.247490\pi$
$947$	−7.73005	−	13.3888i	−0.251193	−	0.435079i	−0.963855	+	0.266429i	$0.914156\pi$
$948$	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	$0.0699009\pi$
$953$			13.4497i			0.435679i	−0.975985	+	0.217839i	$0.930099\pi$
$954$	−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	$-0.769821\pi$
$967$		−	41.1554i		−	1.32347i	0.749738	−	0.661734i	$-0.230179\pi$
$968$	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	$-0.0132434\pi$
$971$	14.4445	+	25.0186i	0.463546	+	0.802886i	−0.535588	+	0.844479i	$0.679910\pi$
$972$	−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	0.980728	−	0.195378i	$-0.0625935\pi$
$977$	40.6932	+	23.4942i	1.30189	+	0.751646i	0.321161	+	0.947024i	$0.395927\pi$
$978$	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	$-0.689753\pi$
$983$	13.6677	−	23.6731i	0.435931	−	0.755054i	0.997371	+	0.0724632i	$0.0230860\pi$
$984$	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	0.186075	−	0.982536i	$-0.440423\pi$
$991$	−18.0000	−	10.3923i	−0.571789	−	0.330122i	−0.757863	+	0.652413i	$0.773757\pi$
$992$	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	$-0.894407\pi$
$997$	−6.02119	+	10.4290i	−0.190693	+	0.330290i	0.754787	+	0.655970i	$0.227740\pi$
$998$	15.1707	+	45.9658i	0.480219	+	1.45502i
$999$	27.2513	+	5.17281i	0.862192	+	0.163660i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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