LMFDB - Embedded newform 588.2.n.d.263.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(263,588)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			263.5
Character	$\chi$	$=$	588.263
Dual form			588.2.n.d.275.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.287629 + 1.38466i) q^{2} +(-1.66143 - 0.489533i) q^{3} +(-1.83454 - 0.796533i) q^{4} +(-1.08570 + 0.626827i) q^{5} +(1.15571 - 2.15971i) q^{6} +(1.63059 - 2.31110i) q^{8} +(2.52072 + 1.62665i) q^{9} +(-0.555662 - 1.68361i) q^{10} +(2.52914 - 4.38059i) q^{11} +(2.65803 + 2.22145i) q^{12} -4.41798 q^{13} +(2.11066 - 0.509947i) q^{15} +(2.73107 + 2.92254i) q^{16} +(5.06920 + 2.92671i) q^{17} +(-2.97738 + 3.02245i) q^{18} +(-1.32654 + 0.765881i) q^{19} +(2.49104 - 0.285146i) q^{20} +(5.33816 + 4.76197i) q^{22} +(0.156785 + 0.271560i) q^{23} +(-3.84047 + 3.04151i) q^{24} +(-1.71417 + 2.96904i) q^{25} +(1.27074 - 6.11738i) q^{26} +(-3.39170 - 3.93654i) q^{27} +5.53862i q^{29} +(0.0990132 + 3.06922i) q^{30} +(4.24264 + 2.44949i) q^{31} +(-4.83225 + 2.94098i) q^{32} +(-6.34643 + 6.03996i) q^{33} +(-5.51053 + 6.17729i) q^{34} +(-3.32867 - 4.99199i) q^{36} +(2.66908 + 4.62298i) q^{37} +(-0.678928 - 2.05710i) q^{38} +(7.34017 + 2.16275i) q^{39} +(-0.321666 + 3.53125i) q^{40} -1.97938i q^{41} +3.18613i q^{43} +(-8.12909 + 6.02183i) q^{44} +(-3.75636 - 0.185997i) q^{45} +(-0.421113 + 0.138985i) q^{46} +(5.74813 + 9.95606i) q^{47} +(-3.10681 - 6.19256i) q^{48} +(-3.61805 - 3.22752i) q^{50} +(-6.98942 - 7.34407i) q^{51} +(8.10496 + 3.51907i) q^{52} +(11.0767 + 6.39513i) q^{53} +(6.42631 - 3.56407i) q^{54} +6.34133i q^{55} +(2.57889 - 0.623072i) q^{57} +(-7.66908 - 1.59307i) q^{58} +(3.98351 - 6.89964i) q^{59} +(-4.27829 - 0.745696i) q^{60} +(-0.151445 - 0.262310i) q^{61} +(-4.61200 + 5.17005i) q^{62} +(-2.68236 - 7.53691i) q^{64} +(4.79659 - 2.76931i) q^{65} +(-6.53785 - 10.5249i) q^{66} +(-9.13122 - 5.27191i) q^{67} +(-6.96844 - 9.40695i) q^{68} +(-0.127550 - 0.527930i) q^{69} -4.53490 q^{71} +(7.86960 - 3.17322i) q^{72} +(0.707107 - 1.22474i) q^{73} +(-7.16894 + 2.36605i) q^{74} +(4.30143 - 4.09371i) q^{75} +(3.04365 - 0.348402i) q^{76} +(-5.10590 + 9.54154i) q^{78} +(6.00000 - 3.46410i) q^{79} +(-4.79704 - 1.46108i) q^{80} +(3.70801 + 8.20065i) q^{81} +(2.74076 + 0.569326i) q^{82} +6.78340 q^{83} -7.33816 q^{85} +(-4.41169 - 0.916423i) q^{86} +(2.71134 - 9.20204i) q^{87} +(-6.00000 - 12.9880i) q^{88} +(4.15480 - 2.39878i) q^{89} +(1.33798 - 5.14777i) q^{90} +(-0.0713222 - 0.623072i) q^{92} +(-5.84975 - 6.14657i) q^{93} +(-15.4390 + 5.09553i) q^{94} +(0.960150 - 1.66303i) q^{95} +(9.46816 - 2.52070i) q^{96} +13.6844 q^{97} +(13.5009 - 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) $ 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * q^88 - 24 * q^93

Character values

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

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

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
$3$	−1.66143	−	0.489533i	−0.959228	−	0.282632i
$3$	−1.66143	−	0.489533i	−0.959228	−	0.282632i
$4$	−1.83454	−	0.796533i	−0.917270	−	0.398266i
$5$	−1.08570	+	0.626827i	−0.485538	+	0.280326i	−0.722722	−	0.691139i	$-0.757109\pi$
$5$	−1.08570	+	0.626827i	−0.485538	+	0.280326i	0.237183	+	0.971465i	$0.423776\pi$
$6$	1.15571	−	2.15971i	0.471817	−	0.881697i
$7$		0			0
$7$		0			0
$8$	1.63059	−	2.31110i	0.576500	−	0.817097i
$9$	2.52072	+	1.62665i	0.840238	+	0.542217i
$10$	−0.555662	−	1.68361i	−0.175716	−	0.532404i
$11$	2.52914	−	4.38059i	0.762563	−	1.32080i	−0.178962	−	0.983856i	$-0.557274\pi$
$11$	2.52914	−	4.38059i	0.762563	−	1.32080i	0.941525	−	0.336942i	$-0.109393\pi$
$12$	2.65803	+	2.22145i	0.767308	+	0.641278i
$13$	−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	0.966918	−	0.255089i	$-0.0821048\pi$
$17$	5.06920	+	2.92671i	1.22946	+	0.709831i	0.262545	+	0.964920i	$0.415438\pi$
$18$	−2.97738	+	3.02245i	−0.701775	+	0.712398i
$19$	−1.32654	+	0.765881i	−0.304330	+	0.175705i	−0.644386	−	0.764700i	$-0.722887\pi$
$19$	−1.32654	+	0.765881i	−0.304330	+	0.175705i	0.340056	+	0.940405i	$0.389554\pi$
$20$	2.49104	−	0.285146i	0.557014	−	0.0637607i
$21$		0			0
$22$	5.33816	+	4.76197i	1.13810	+	1.01525i
$23$	0.156785	+	0.271560i	0.0326920	+	0.0566242i	0.881908	−	0.471421i	$-0.156259\pi$
$23$	0.156785	+	0.271560i	0.0326920	+	0.0566242i	−0.849217	+	0.528045i	$0.822925\pi$
$24$	−3.84047	+	3.04151i	−0.783933	+	0.620845i
$25$	−1.71417	+	2.96904i	−0.342835	+	0.593808i
$26$	1.27074	−	6.11738i	0.249212	−	1.19972i
$27$	−3.39170	−	3.93654i	−0.652733	−	0.757588i
$28$		0			0
$29$			5.53862i			1.02850i	0.857642	+	0.514248i	$0.171929\pi$
$29$			5.53862i			1.02850i	−0.857642	+	0.514248i	$0.828071\pi$
$30$	0.0990132	+	3.06922i	0.0180773	+	0.560360i
$31$	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
$33$	−6.34643	+	6.03996i	−1.10477	+	1.05142i
$34$	−5.51053	+	6.17729i	−0.945048	+	1.05940i
$35$		0			0
$36$	−3.32867	−	4.99199i	−0.554778	−	0.831998i
$37$	2.66908	+	4.62298i	0.438794	+	0.760013i	0.997597	−	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
$39$	7.34017	+	2.16275i	1.17537	+	0.346317i
$40$	−0.321666	+	3.53125i	−0.0508598	+	0.558340i
$41$		−	1.97938i		−	0.309127i	−0.987983	−	0.154564i	$-0.950603\pi$
$41$		−	1.97938i		−	0.309127i	0.987983	−	0.154564i	$-0.0493971\pi$
$42$		0			0
$43$			3.18613i			0.485881i	0.970041	+	0.242940i	$0.0781119\pi$
$43$			3.18613i			0.485881i	−0.970041	+	0.242940i	$0.921888\pi$
$44$	−8.12909	+	6.02183i	−1.22551	+	0.907825i
$45$	−3.75636	−	0.185997i	−0.559965	−	0.0277268i
$46$	−0.421113	+	0.138985i	−0.0620897	+	0.0204922i
$47$	5.74813	+	9.95606i	0.838451	+	1.45224i	0.891189	+	0.453632i	$0.149872\pi$
$47$	5.74813	+	9.95606i	0.838451	+	1.45224i	−0.0527378	+	0.998608i	$0.516795\pi$
$48$	−3.10681	−	6.19256i	−0.448429	−	0.893818i
$49$		0			0
$50$	−3.61805	−	3.22752i	−0.511669	−	0.456440i
$51$	−6.98942	−	7.34407i	−0.978715	−	1.02838i
$52$	8.10496	+	3.51907i	1.12396	+	0.488007i
$53$	11.0767	+	6.39513i	1.52150	+	0.878439i	0.999678	+	0.0253856i	$0.00808135\pi$
$53$	11.0767	+	6.39513i	1.52150	+	0.878439i	0.521823	+	0.853054i	$0.325252\pi$
$54$	6.42631	−	3.56407i	0.874509	−	0.485008i
$55$			6.34133i			0.855064i
$56$		0			0
$57$	2.57889	−	0.623072i	0.341582	−	0.0825279i
$58$	−7.66908	−	1.59307i	−1.00700	−	0.209180i
$59$	3.98351	−	6.89964i	0.518608	−	0.898256i	−0.481158	−	0.876634i	$-0.659784\pi$
$59$	3.98351	−	6.89964i	0.518608	−	0.898256i	0.999766	−	0.0216222i	$-0.00688310\pi$
$60$	−4.27829	−	0.745696i	−0.552324	−	0.0962689i
$61$	−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
$66$	−6.53785	−	10.5249i	−0.804754	−	1.29552i
$67$	−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	$-0.586725\pi$
$71$	−4.53490			−0.538194			−0.269097	+	0.963113i	$0.586725\pi$
$72$	7.86960	−	3.17322i	0.927442	−	0.373968i
$73$	0.707107	−	1.22474i	0.0827606	−	0.143346i	−0.821674	−	0.569958i	$-0.806960\pi$
$73$	0.707107	−	1.22474i	0.0827606	−	0.143346i	0.904435	+	0.426612i	$0.140293\pi$
$74$	−7.16894	+	2.36605i	−0.833372	+	0.275048i
$75$	4.30143	−	4.09371i	0.496686	−	0.472701i
$76$	3.04365	−	0.348402i	0.349130	−	0.0399645i
$77$		0			0
$78$	−5.10590	+	9.54154i	−0.578130	+	1.08037i
$79$	6.00000	−	3.46410i	0.675053	−	0.389742i	−0.122936	−	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
$81$	3.70801	+	8.20065i	0.412001	+	0.911183i
$82$	2.74076	+	0.569326i	0.302666	+	0.0628716i
$83$	6.78340			0.744575			0.372287	−	0.928118i	$-0.378574\pi$
$83$	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
$87$	2.71134	−	9.20204i	0.290686	−	0.986563i
$88$	−6.00000	−	12.9880i	−0.639602	−	1.38453i
$89$	4.15480	−	2.39878i	0.440408	−	0.254270i	−0.263363	−	0.964697i	$-0.584832\pi$
$89$	4.15480	−	2.39878i	0.440408	−	0.254270i	0.703771	+	0.710427i	$0.251498\pi$
$90$	1.33798	−	5.14777i	0.141035	−	0.542622i
$91$		0			0
$92$	−0.0713222	−	0.623072i	−0.00743586	−	0.0649597i
$93$	−5.84975	−	6.14657i	−0.606591	−	0.637370i
$94$	−15.4390	+	5.09553i	−1.59241	+	0.525564i
$95$	0.960150	−	1.66303i	0.0985093	−	0.170623i
$96$	9.46816	−	2.52070i	0.966340	−	0.257268i
$97$	13.6844			1.38944			0.694719	−	0.719281i	$-0.255529\pi$
$97$	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	0.665073	−	0.746778i	$-0.268400\pi$
$101$	3.52631	+	2.03591i	0.350881	+	0.202581i	−0.314192	+	0.949359i	$0.601734\pi$
$102$	12.1794	−	7.56557i	1.20594	−	0.749103i
$103$	−11.3239	+	6.53788i	−1.11578	+	0.644197i	−0.940321	−	0.340290i	$-0.889475\pi$
$103$	−11.3239	+	6.53788i	−1.11578	+	0.644197i	−0.175461	+	0.984486i	$0.556141\pi$
$104$	−7.20391	+	10.2104i	−0.706402	+	1.00121i
$105$		0			0
$106$	−12.0410	+	13.4980i	−1.16953	+	1.31104i
$107$	1.95388	+	3.38422i	0.188889	+	0.327165i	0.944880	−	0.327417i	$-0.106178\pi$
$107$	1.95388	+	3.38422i	0.188889	+	0.327165i	−0.755991	+	0.654582i	$0.772845\pi$
$108$	3.08662	+	9.92335i	0.297010	+	0.954874i
$109$	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	$0.102444\pi$
$113$			6.72485i			0.632621i	−0.948656	+	0.316311i	$0.897556\pi$
$114$	0.120978	+	3.75008i	0.0113306	+	0.351227i
$115$	−0.340442	−	0.196554i	−0.0317464	−	0.0183288i
$116$	4.41169	−	10.1608i	0.409615	−	0.943408i
$117$	−11.1365	−	7.18651i	−1.02957	−	0.664393i
$118$	8.40785	+	7.50032i	0.774005	+	0.690460i
$119$		0			0
$120$	2.26309	−	5.70947i	0.206591	−	0.521201i
$121$	−7.29306	−	12.6320i	−0.663006	−	1.14836i
$122$	0.406768	−	0.134251i	0.0368271	−	0.0121545i
$123$	−0.968971	+	3.28861i	−0.0873692	+	0.296524i
$124$	−5.83219	−	7.87309i	−0.523746	−	0.707024i
$125$		−	10.5662i		−	0.945073i
$126$		0			0
$127$			8.50404i			0.754611i	0.926089	+	0.377306i	$0.123149\pi$
$127$			8.50404i			0.754611i	−0.926089	+	0.377306i	$0.876851\pi$
$128$	11.2075	−	1.54631i	0.990616	−	0.136676i
$129$	1.55972	−	5.29354i	0.137325	−	0.466070i
$130$	2.45490	+	7.43815i	0.215309	+	0.652369i
$131$	4.20524	+	7.28368i	0.367413	+	0.636378i	0.989160	−	0.146840i	$-0.0469102\pi$
$131$	4.20524	+	7.28368i	0.367413	+	0.636378i	−0.621747	+	0.783218i	$0.713577\pi$
$132$	16.4538	−	6.02541i	1.43212	−	0.524445i
$133$		0			0
$134$	9.92618	−	11.1272i	0.857491	−	0.961247i
$135$	6.14989	+	2.14788i	0.529298	+	0.184860i
$136$	15.0297	−	6.94318i	1.28879	−	0.595372i
$137$	−11.9136	−	6.87834i	−1.01785	−	0.587657i	−0.104370	−	0.994539i	$-0.533283\pi$
$137$	−11.9136	−	6.87834i	−1.01785	−	0.587657i	−0.913481	+	0.406882i	$0.866616\pi$
$138$	0.767688	−	0.0247657i	0.0653499	−	0.00210819i
$139$			13.1652i			1.11666i	0.829620	+	0.558328i	$0.188557\pi$
$139$			13.1652i			1.11666i	−0.829620	+	0.558328i	$0.811443\pi$
$140$		0			0
$141$	−4.67632	−	19.3552i	−0.393817	−	1.63000i
$142$	1.30437	−	6.27927i	0.109460	−	0.526945i
$143$	−11.1737	+	19.3534i	−0.934389	+	1.61841i
$144$	2.13029	+	11.8094i	0.177524	+	0.984116i
$145$	−3.47176	−	6.01326i	−0.288314	−	0.499374i
$146$	1.49247	+	1.33137i	0.123517	+	0.110185i
$147$		0			0
$148$	−1.21417	−	10.6071i	−0.0998046	−	0.871894i
$149$	9.78354	−	5.64853i	0.801499	−	0.462745i	−0.0424963	−	0.999097i	$-0.513531\pi$
$149$	9.78354	−	5.64853i	0.801499	−	0.462745i	0.843995	+	0.536351i	$0.180198\pi$
$150$	4.43116	+	7.13346i	0.361803	+	0.582445i
$151$	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
$156$	−11.7431	−	9.81433i	−0.940204	−	0.785776i
$157$	−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
$159$	−15.2726	−	16.0475i	−1.21119	−	1.27265i
$160$	3.40287	−	6.22200i	0.269020	−	0.491892i
$161$		0			0
$162$	−12.4216	+	2.77557i	−0.975933	+	0.218070i
$163$	−11.4887	+	6.63300i	−0.899864	+	0.519537i	−0.877156	−	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
$165$	3.10429	−	10.5357i	0.241668	−	0.820202i
$166$	−1.95110	+	9.39267i	−0.151435	+	0.729012i
$167$	4.78624			0.370371			0.185185	−	0.982704i	$-0.440711\pi$
$167$	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
$171$	−4.58966	−	0.227258i	−0.350980	−	0.0173789i
$172$	2.53786	−	5.84508i	0.193510	−	0.445684i
$173$	12.4811	−	7.20596i	0.948920	−	0.547859i	0.0561749	−	0.998421i	$-0.482110\pi$
$173$	12.4811	−	7.20596i	0.948920	−	0.547859i	0.892745	+	0.450562i	$0.148776\pi$
$174$	11.9618	+	6.40104i	0.906822	+	0.485261i
$175$		0			0
$176$	19.7097	−	4.57220i	1.48568	−	0.344643i
$177$	−9.99593	+	9.51322i	−0.751340	+	0.715058i
$178$	2.12644	+	6.44293i	0.159383	+	0.482918i
$179$	0.347150	−	0.601281i	0.0259472	−	0.0449419i	−0.852760	−	0.522303i	$-0.825073\pi$
$179$	0.347150	−	0.601281i	0.0259472	−	0.0449419i	0.878707	+	0.477361i	$0.158406\pi$
$180$	6.74304	+	3.33328i	0.502597	+	0.248448i
$181$	−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
$186$	10.1934	−	6.33196i	0.747419	−	0.464282i
$187$	25.6414	−	14.8041i	1.87509	−	1.08258i
$188$	−2.61485	−	22.8434i	−0.190707	−	1.66602i
$189$		0			0
$190$	2.02655	+	1.80781i	0.147022	+	0.131152i
$191$	1.95388	+	3.38422i	0.141378	+	0.244873i	0.928016	−	0.372541i	$-0.121513\pi$
$191$	1.95388	+	3.38422i	0.141378	+	0.244873i	−0.786638	+	0.617415i	$0.788180\pi$
$192$	0.766990	+	13.8352i	0.0553527	+	0.998467i
$193$	−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	$0.0207980\pi$
$197$			1.83285i			0.130585i	−0.997866	+	0.0652924i	$0.979202\pi$
$198$	5.70992	+	20.6869i	0.405786	+	1.47015i
$199$	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
$201$	12.5901	+	13.2290i	0.888039	+	0.933099i
$202$	−3.83331	+	4.29713i	−0.269710	+	0.302345i
$203$		0			0
$204$	6.97258	+	19.0403i	0.488178	+	1.33309i
$205$	1.24073	+	2.14901i	0.0866563	+	0.150093i
$206$	−5.79562	−	17.5602i	−0.403800	−	1.22348i
$207$	−0.0465225	+	0.939560i	−0.00323354	+	0.0653039i
$208$	−12.0658	−	12.9117i	−0.836614	−	0.895267i
$209$			7.74807i			0.535945i
$210$		0			0
$211$		−	14.8763i		−	1.02413i	−0.858948	−	0.512063i	$-0.828881\pi$
$211$		−	14.8763i		−	1.02413i	0.858948	−	0.512063i	$-0.171119\pi$
$212$	−15.2267	−	20.5551i	−1.04577	−	1.41173i
$213$	7.53443	+	2.21998i	0.516251	+	0.152111i
$214$	−5.24797	+	1.73205i	−0.358744	+	0.118401i
$215$	−1.99715	−	3.45917i	−0.136205	−	0.235914i
$216$	−14.6282	+	1.41966i	−0.995324	+	0.0965958i
$217$		0			0
$218$	8.70434	+	7.76481i	0.589533	+	0.525899i
$219$	−1.77436	+	1.68868i	−0.119900	+	0.114110i
$220$	5.05108	−	11.6334i	0.340543	−	0.784325i
$221$	−22.3956	−	12.9301i	−1.50649	−	0.869775i
$222$	13.0690	−	0.421606i	0.877131	−	0.0282963i
$223$		−	19.4171i		−	1.30026i	−0.759821	−	0.650132i	$-0.774713\pi$
$223$		−	19.4171i		−	1.30026i	0.759821	−	0.650132i	$-0.225287\pi$
$224$		0			0
$225$	−9.15054	+	4.69573i	−0.610036	+	0.313049i
$226$	−9.31160	−	1.93426i	−0.619399	−	0.128665i
$227$	−5.34136	+	9.25151i	−0.354519	+	0.614045i	−0.987035	−	0.160502i	$-0.948689\pi$
$227$	−5.34136	+	9.25151i	−0.354519	+	0.614045i	0.632517	+	0.774547i	$0.282022\pi$
$228$	−5.22737	−	0.911118i	−0.346191	−	0.0603403i
$229$	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	−0.577302	−	0.816531i	$-0.695895\pi$
$233$	−2.42423	+	1.39963i	−0.158817	+	0.0916930i	0.418485	+	0.908224i	$0.362561\pi$
$234$	13.1540	−	13.3531i	0.859904	−	0.872921i
$235$	−12.4815	−	7.20617i	−0.814201	−	0.470079i
$236$	−12.8037	+	9.48466i	−0.833449	+	0.617399i
$237$	−11.6644	+	2.81817i	−0.757683	+	0.183060i
$238$		0			0
$239$	−20.5467			−1.32905			−0.664527	−	0.747265i	$-0.731367\pi$
$239$	−20.5467			−1.32905			−0.664527	+	0.747265i	$0.731367\pi$
$240$	7.25472	+	4.77580i	0.468290	+	0.308277i
$241$	9.02728	−	15.6357i	0.581499	−	1.00718i	−0.413804	−	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
$243$	−2.14612	−	15.4400i	−0.137674	−	0.990478i
$244$	0.0688928	+	0.601848i	0.00441041	+	0.0385294i
$245$		0			0
$246$	−4.27488	−	2.28759i	−0.272556	−	0.145851i
$247$	5.86064	−	3.38364i	0.372904	−	0.215296i
$248$	12.5790	−	5.81105i	0.798768	−	0.369002i
$249$	−11.2702	−	3.32070i	−0.714217	−	0.210441i
$250$	14.6306	+	3.03915i	0.925320	+	0.192213i
$251$	−10.4810			−0.661555			−0.330777	−	0.943709i	$-0.607311\pi$
$251$	−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
$255$	12.1919	+	3.59227i	0.763483	+	0.224957i
$256$	−1.08251	+	15.9633i	−0.0676566	+	0.997709i
$257$	7.24060	−	4.18036i	0.451656	−	0.260764i	−0.256873	−	0.966445i	$-0.582692\pi$
$257$	7.24060	−	4.18036i	0.451656	−	0.260764i	0.708529	+	0.705681i	$0.249359\pi$
$258$	6.88111	+	3.68224i	0.428399	+	0.229246i
$259$		0			0
$260$	−11.0054	+	1.25977i	−0.682524	+	0.0781277i
$261$	−9.00941	+	13.9613i	−0.557668	+	0.864182i
$262$	−11.2949	+	3.72781i	−0.697803	+	0.230305i
$263$	−14.6850	+	25.4352i	−0.905517	+	1.56840i	−0.0852962	+	0.996356i	$0.527184\pi$
$263$	−14.6850	+	25.4352i	−0.905517	+	1.56840i	−0.820221	+	0.572046i	$0.806150\pi$
$264$	3.61053	+	24.5159i	0.222212	+	1.50885i
$265$	−16.0346			−0.984996
$266$		0			0
$267$	−8.07720	+	1.95149i	−0.494317	+	0.119429i
$268$	12.5523	+	16.9448i	0.766756	+	1.03507i
$269$	−17.6649	−	10.1988i	−1.07705	−	0.621834i	−0.146950	−	0.989144i	$-0.546946\pi$
$269$	−17.6649	−	10.1988i	−1.07705	−	0.621834i	−0.930099	+	0.367310i	$0.880279\pi$
$270$	−4.74296	+	7.89768i	−0.288648	+	0.480638i
$271$	−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
$276$	−0.186517	+	1.07011i	−0.0112270	+	0.0644128i
$277$	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	$0.0112649\pi$
$281$			1.18623i			0.0707648i	−0.999374	+	0.0353824i	$0.988735\pi$
$282$	28.1453	−	0.907971i	1.67603	−	0.0540689i
$283$	−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
$285$	−2.40933	+	2.29298i	−0.142716	+	0.135825i
$286$	−23.5839	−	21.0383i	−1.39454	−	1.24402i
$287$		0			0
$288$	−16.9647	−	0.446999i	−0.999653	−	0.0263396i
$289$	8.63122	+	14.9497i	0.507719	+	0.879395i
$290$	9.32487	−	3.07760i	0.547575	−	0.180723i
$291$	−22.7357	−	6.69895i	−1.33279	−	0.392700i
$292$	−2.27276	+	1.68361i	−0.133004	+	0.0985258i
$293$		−	0.197795i		−	0.0115553i	−0.999983	−	0.00577765i	$-0.998161\pi$
$293$		−	0.197795i		−	0.0115553i	0.999983	−	0.00577765i	$-0.00183909\pi$
$294$		0			0
$295$			9.98789i			0.581517i
$296$	15.0363	+	1.36968i	0.873969	+	0.0796109i
$297$	−25.8225	+	4.90159i	−1.49837	+	0.284419i
$298$	5.00724	+	15.1715i	0.290061	+	0.878862i
$299$	−0.692674	−	1.19975i	−0.0400584	−	0.0693831i
$300$	−11.1519	+	4.08385i	−0.643856	+	0.235781i
$301$		0			0
$302$	−10.4496	+	11.7139i	−0.601304	+	0.674061i
$303$	−4.86207	−	5.10878i	−0.279319	−	0.293492i
$304$	−5.86120	−	1.78521i	−0.336163	−	0.102389i
$305$	0.328846	+	0.189859i	0.0188297	+	0.0108713i
$306$	−23.9388	+	6.60749i	−1.36849	+	0.377725i
$307$		−	16.6218i		−	0.948657i	−0.880348	−	0.474328i	$-0.842691\pi$
$307$		−	16.6218i		−	0.948657i	0.880348	−	0.474328i	$-0.157309\pi$
$308$		0			0
$309$	22.0145	−	5.31881i	1.25236	−	0.302576i
$310$	1.76651	−	8.50404i	0.100331	−	0.482997i
$311$	5.37805	−	9.31506i	0.304961	−	0.528209i	−0.672291	−	0.740287i	$-0.734690\pi$
$311$	5.37805	−	9.31506i	0.304961	−	0.528209i	0.977253	+	0.212078i	$0.0680231\pi$
$312$	16.9671	−	13.4373i	0.960575	−	0.760738i
$313$	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	−0.927338	−	0.374224i	$-0.877909\pi$
$317$	−18.9960	+	10.9673i	−1.06692	+	0.615987i	−0.139582	+	0.990211i	$0.544576\pi$
$318$	26.6131	−	16.5315i	1.49239	−	0.927041i
$319$	24.2624	+	14.0079i	1.35844	+	0.784293i
$320$	7.63656	+	6.50142i	0.426897	+	0.363441i
$321$	−1.58955	−	6.57914i	−0.0887202	−	0.367212i
$322$		0			0
$323$	−8.96603			−0.498883
$324$	−0.270403	−	17.9980i	−0.0150224	−	0.999887i
$325$	7.57319	−	13.1171i	0.420085	−	0.727609i
$326$	−5.87994	−	17.8157i	−0.325660	−	0.986722i
$327$	−10.3484	+	9.84870i	−0.572269	+	0.544634i
$328$	−4.57454	−	3.22756i	−0.252587	−	0.178212i
$329$		0			0
$330$	13.6954	+	7.32873i	0.753908	+	0.403433i
$331$	3.24073	−	1.87104i	0.178127	−	0.102841i	−0.408286	−	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
$333$	−0.791990	+	15.9949i	−0.0434008	+	0.876514i
$334$	−1.37666	+	6.62730i	−0.0753275	+	0.362629i
$335$	13.2183			0.722194
$336$		0			0
$337$	22.9774			1.25166			0.625829	−	0.779960i	$-0.284761\pi$
$337$	22.9774			1.25166			0.625829	+	0.779960i	$0.284761\pi$
$338$	−1.87492	+	9.02593i	−0.101982	+	0.490946i
$339$	3.29204	−	11.1729i	0.178799	−	0.606828i
$340$	13.4621	+	5.84508i	0.730087	+	0.316994i
$341$	21.4604	−	12.3902i	1.16215	−	0.670966i
$342$	1.63479	−	6.28973i	0.0883994	−	0.340110i
$343$		0			0
$344$	7.36347	+	5.19527i	0.397011	+	0.280110i
$345$	0.469402	+	0.493220i	0.0252718	+	0.0265541i
$346$	6.38786	+	19.3547i	0.343413	+	1.04051i
$347$	−1.06505	+	1.84472i	−0.0571750	+	0.0990299i	−0.893196	−	0.449667i	$-0.851543\pi$
$347$	−1.06505	+	1.84472i	−0.0571750	+	0.0990299i	0.836021	+	0.548697i	$0.184876\pi$
$348$	−12.3038	+	14.7218i	−0.659552	+	0.789174i
$349$	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	0.868151	−	0.496301i	$-0.165309\pi$
$353$	16.3912	+	9.46348i	0.872417	+	0.503690i	0.00426642	+	0.999991i	$0.498642\pi$
$354$	−10.2974	−	16.5772i	−0.547302	−	0.881068i
$355$	4.92353	−	2.84260i	0.261314	−	0.150869i
$356$	−9.53285	+	1.09121i	−0.505240	+	0.0578342i
$357$		0			0
$358$	0.732717	+	0.653628i	0.0387253	+	0.0345453i
$359$	−0.613000	−	1.06175i	−0.0323529	−	0.0560369i	0.849396	−	0.527757i	$-0.176967\pi$
$359$	−0.613000	−	1.06175i	−0.0323529	−	0.0560369i	−0.881748	+	0.471720i	$0.843633\pi$
$360$	−6.55494	+	8.37804i	−0.345476	+	0.441561i
$361$	−8.32685	+	14.4225i	−0.438255	+	0.759081i
$362$	1.81506	−	8.73776i	0.0953973	−	0.459246i
$363$	5.93317	+	24.5573i	0.311411	+	1.28893i
$364$		0			0
$365$			1.77294i			0.0927997i
$366$	−0.741538	+	0.0239221i	−0.0387608	+	0.00125043i
$367$	17.4966	+	10.1017i	0.913314	+	0.527302i	0.881496	−	0.472192i	$-0.156537\pi$
$367$	17.4966	+	10.1017i	0.913314	+	0.527302i	0.0318180	+	0.999494i	$0.489870\pi$
$368$	−0.365454	+	1.19986i	−0.0190506	+	0.0625471i
$369$	3.21976	−	4.98945i	0.167614	−	0.259740i
$370$	6.30019	−	7.06250i	0.327531	−	0.367162i
$371$		0			0
$372$	5.83566	+	15.9357i	0.302565	+	0.826225i
$373$	4.09019	+	7.08442i	0.211782	+	0.366817i	0.952272	−	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
$375$	−5.17252	+	17.5551i	−0.267108	+	0.906541i
$376$	32.3823	+	2.94974i	1.66999	+	0.152121i
$377$		−	24.4695i		−	1.26024i
$378$		0			0
$379$		−	31.2020i		−	1.60274i	−0.598170	−	0.801369i	$-0.704105\pi$
$379$		−	31.2020i		−	1.60274i	0.598170	−	0.801369i	$-0.295895\pi$
$380$	−3.08609	+	2.28610i	−0.158313	+	0.117274i
$381$	4.16301	−	14.1289i	0.213277	−	0.723845i
$382$	−5.24797	+	1.73205i	−0.268509	+	0.0886194i
$383$	−12.2089	−	21.1465i	−0.623848	−	1.08054i	−0.988763	−	0.149495i	$-0.952235\pi$
$383$	−12.2089	−	21.1465i	−0.623848	−	1.08054i	0.364915	−	0.931041i	$-0.381098\pi$
$384$	−19.3775	−	2.91737i	−0.988856	−	0.148877i
$385$		0			0
$386$	−1.65861	−	1.47958i	−0.0844212	−	0.0753089i
$387$	−5.18273	+	8.03133i	−0.263453	+	0.408255i
$388$	−25.1045	−	10.9001i	−1.27449	−	0.553367i
$389$	7.86740	+	4.54225i	0.398893	+	0.230301i	0.686006	−	0.727596i	$-0.259362\pi$
$389$	7.86740	+	4.54225i	0.398893	+	0.230301i	−0.287113	+	0.957897i	$0.592696\pi$
$390$	−0.437438	−	13.5597i	−0.0221505	−	0.686624i
$391$			1.83546i			0.0928230i
$392$		0			0
$393$	−3.42111	−	14.1599i	−0.172572	−	0.714275i
$394$	−2.53786	−	0.527179i	−0.127855	−	0.0265589i
$395$	−4.34279	+	7.52193i	−0.218509	+	0.378469i
$396$	−30.2865	+	1.95613i	−1.52196	+	0.0982991i
$397$	11.6405	+	20.1619i	0.584220	+	1.01190i	0.994972	+	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	−0.326785	−	0.945099i	$-0.605965\pi$
$401$	6.57424	−	3.79564i	0.328302	−	0.189545i	0.655087	+	0.755553i	$0.272632\pi$
$402$	−21.9388	+	13.6280i	−1.09421	+	0.679701i
$403$	−18.7439	−	10.8218i	−0.933700	−	0.539072i
$404$	−4.84748	−	6.54378i	−0.241171	−	0.325565i
$405$	−9.16617	−	6.57914i	−0.455470	−	0.326920i
$406$		0			0
$407$	27.0019			1.33843
$408$	−28.3697	+	4.17809i	−1.40451	+	0.206846i
$409$	−3.19509	+	5.53406i	−0.157987	+	0.273642i	−0.934143	−	0.356900i	$-0.883834\pi$
$409$	−3.19509	+	5.53406i	−0.157987	+	0.273642i	0.776156	+	0.630541i	$0.217167\pi$
$410$	−3.33250	+	1.09987i	−0.164580	+	0.0543185i
$411$	16.4265	+	17.2600i	0.810261	+	0.851374i
$412$	25.9819	−	2.97411i	1.28003	−	0.146524i
$413$		0			0
$414$	−1.28759	−	0.334662i	−0.0632814	−	0.0164477i
$415$	−7.36471	+	4.25202i	−0.361520	+	0.208723i
$416$	21.3488	−	12.9932i	1.04671	−	0.637044i
$417$	6.44479	−	21.8731i	0.315603	−	1.07113i
$418$	−10.7284	−	2.22857i	−0.524743	−	0.109003i
$419$	29.1307			1.42313			0.711565	−	0.702620i	$-0.247987\pi$
$419$	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
$423$	−1.70563	+	34.4466i	−0.0829306	+	1.67485i
$424$	32.8413	−	15.1715i	1.59492	−	0.736793i
$425$	−17.3790	+	10.0338i	−0.843006	+	0.486710i
$426$	−5.24103	+	9.79405i	−0.253929	+	0.474523i
$427$		0			0
$428$	−0.888828	−	7.76481i	−0.0429631	−	0.375326i
$429$	28.0384	−	26.6844i	1.35371	−	1.28834i
$430$	5.36420	−	1.77041i	0.258685	−	0.0853769i
$431$	9.12282	−	15.8012i	0.439431	−	0.761116i	−0.558215	−	0.829696i	$-0.688514\pi$
$431$	9.12282	−	15.8012i	0.439431	−	0.761116i	0.997646	+	0.0685802i	$0.0218469\pi$
$432$	2.24175	−	20.6634i	0.107856	−	0.994167i
$433$	−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
$438$	−1.82788	−	2.94259i	−0.0873395	−	0.140603i
$439$	17.5388	−	10.1260i	0.837081	−	0.483289i	−0.0191902	−	0.999816i	$-0.506109\pi$
$439$	17.5388	−	10.1260i	0.837081	−	0.483289i	0.856271	+	0.516527i	$0.172775\pi$
$440$	14.6554	+	10.3401i	0.698670	+	0.492945i
$441$		0			0
$442$	24.3454	−	27.2912i	1.15799	−	1.29811i
$443$	−11.2335	−	19.4570i	−0.533719	−	0.924428i	−0.999224	−	0.0393830i	$-0.987461\pi$
$443$	−11.2335	−	19.4570i	−0.533719	−	0.924428i	0.465505	−	0.885045i	$-0.345873\pi$
$444$	−3.17523	+	18.2173i	−0.150690	+	0.864554i
$445$	−3.00724	+	5.20869i	−0.142557	+	0.246915i
$446$	26.8860	+	5.58491i	1.27309	+	0.264453i
$447$	−19.0198	+	4.59528i	−0.899607	+	0.217349i
$448$		0			0
$449$		−	29.5660i		−	1.39531i	−0.716435	−	0.697654i	$-0.754227\pi$
$449$		−	29.5660i		−	1.39531i	0.716435	−	0.697654i	$-0.245773\pi$
$450$	−3.87002	−	14.0210i	−0.182434	−	0.660955i
$451$	−8.67086	−	5.00612i	−0.408295	−	0.235729i
$452$	5.35657	−	12.3370i	0.251952	−	0.580284i
$453$	−13.2540	−	13.9265i	−0.622726	−	0.654323i
$454$	−11.2738	−	10.0569i	−0.529107	−	0.471996i
$455$		0			0
$456$	2.76513	−	6.97604i	0.129489	−	0.326683i
$457$	−9.09743	−	15.7572i	−0.425560	−	0.737091i	0.570913	−	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
$459$	−5.67210	−	29.8817i	−0.264751	−	1.39476i
$460$	0.467993	+	0.631761i	0.0218203	+	0.0294560i
$461$			24.9782i			1.16335i	0.813422	+	0.581675i	$0.197602\pi$
$461$			24.9782i			1.16335i	−0.813422	+	0.581675i	$0.802398\pi$
$462$		0			0
$463$		−	6.37226i		−	0.296144i	−0.988977	−	0.148072i	$-0.952693\pi$
$463$		−	6.37226i		−	0.296144i	0.988977	−	0.148072i	$-0.0473068\pi$
$464$	−16.1869	+	15.1264i	−0.751456	+	0.702224i
$465$	10.2039	+	3.00653i	0.473195	+	0.139424i
$466$	−1.24073	−	3.75930i	−0.0574757	−	0.174146i
$467$	13.6785	+	23.6918i	0.632964	+	1.09633i	0.986943	+	0.161072i	$0.0514951\pi$
$467$	13.6785	+	23.6918i	0.632964	+	1.09633i	−0.353979	+	0.935253i	$0.615172\pi$
$468$	14.7060	+	22.0545i	0.679785	+	1.01947i
$469$		0			0
$470$	13.5681	−	15.2098i	0.625849	−	0.701576i
$471$	18.5636	−	17.6672i	0.855367	−	0.814061i
$472$	−9.45028	−	20.4568i	−0.434984	−	0.941598i
$473$	13.9571	+	8.05816i	0.641750	+	0.370515i
$474$	−0.547187	−	16.9617i	−0.0251331	−	0.779078i
$475$		−	5.25141i		−	0.240951i
$476$		0			0
$477$	17.5185	+	34.1382i	0.802119	+	1.56308i
$478$	5.90981	−	28.4500i	0.270308	−	1.30127i
$479$	9.91668	−	17.1762i	0.453105	−	0.784800i	−0.545472	−	0.838129i	$-0.683650\pi$
$479$	9.91668	−	17.1762i	0.453105	−	0.784800i	0.998577	+	0.0533285i	$0.0169830\pi$
$480$	−8.69951	+	8.67162i	−0.397076	+	0.395804i
$481$	−11.7919	−	20.4242i	−0.537666	−	0.931265i
$482$	19.0536	+	16.9970i	0.867866	+	0.774190i
$483$		0			0
$484$	3.31764	+	28.9830i	0.150802	+	1.31741i
$485$	−14.8571	+	8.57774i	−0.674625	+	0.389495i
$486$	21.9964	+	1.46936i	0.997776	+	0.0666513i
$487$	35.3792	+	20.4262i	1.60318	+	0.925599i	0.990845	+	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	$-0.348541\pi$
$491$	20.3003			0.916137			0.458069	+	0.888917i	$0.348541\pi$
$492$	4.39710	−	5.26126i	0.198236	−	0.237196i
$493$	−16.2099	+	28.0764i	−0.730058	+	1.26450i
$494$	2.99949	+	9.08821i	0.134954	+	0.408898i
$495$	−10.3151	+	15.9847i	−0.463631	+	0.718458i
$496$	4.42821	+	19.0890i	0.198833	+	0.857123i
$497$		0			0
$498$	7.83964	−	14.6502i	0.351303	−	0.656489i
$499$	−29.6416	+	17.1136i	−1.32694	+	0.766110i	−0.984825	−	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
$501$	−7.95202	−	2.34302i	−0.355270	−	0.104679i
$502$	3.01464	−	14.5126i	0.134550	−	0.647728i
$503$	−31.1279			−1.38792			−0.693962	−	0.720011i	$-0.744137\pi$
$503$	−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
$507$	−10.8301	−	3.19104i	−0.480982	−	0.141719i
$508$	6.77375	−	15.6010i	0.300536	−	0.692182i
$509$	−34.2107	+	19.7516i	−1.51636	+	0.875474i	−0.516549	+	0.856257i	$0.672784\pi$
$509$	−34.2107	+	19.7516i	−1.51636	+	0.875474i	−0.999815	+	0.0192162i	$0.993883\pi$
$510$	−8.48078	+	15.8483i	−0.375535	+	0.701773i
$511$		0			0
$512$	−21.7924	−	6.09041i	−0.963095	−	0.269161i
$513$	7.51416	+	2.62436i	0.331758	+	0.115868i
$514$	3.70576	+	11.2281i	0.163454	+	0.495251i
$515$	8.19625	−	14.1963i	0.361170	−	0.625564i
$516$	−7.07784	+	8.46885i	−0.311585	+	0.372820i
$517$	58.1512			2.55749
$518$		0			0
$519$	−24.2641	+	5.86232i	−1.06507	+	0.257327i
$520$	1.42111	−	15.6010i	0.0623199	−	0.684149i
$521$	20.8808	+	12.0555i	0.914803	+	0.528162i	0.881973	−	0.471299i	$-0.156215\pi$
$521$	20.8808	+	12.0555i	0.914803	+	0.528162i	0.0328296	+	0.999461i	$0.489548\pi$
$522$	−16.7402	−	16.4906i	−0.732699	−	0.721773i
$523$	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
$528$	−34.9846	−	2.05215i	−1.52251	−	0.0893085i
$529$	11.4508	−	19.8334i	0.497862	−	0.862323i
$530$	4.61200	−	22.2024i	0.200333	−	0.964409i
$531$	21.2646	−	10.9122i	0.922805	−	0.473551i
$532$		0			0
$533$			8.74486i			0.378782i
$534$	−0.378909	−	11.7454i	−0.0163970	−	0.508275i
$535$	−4.24264	−	2.44949i	−0.183425	−	0.105901i
$536$	−27.0732	+	12.5068i	−1.16938	+	0.540213i
$537$	−0.871113	+	0.829047i	−0.0375913	+	0.0357760i
$538$	19.2028	−	21.5263i	0.827892	−	0.928066i
$539$		0			0
$540$	−9.57136	−	8.83897i	−0.411886	−	0.380369i
$541$	−12.9508	−	22.4315i	−0.556800	−	0.964406i	−0.997761	−	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
$543$	10.4843	+	3.08916i	0.449926	+	0.132568i
$544$	−33.1030	+	0.765881i	−1.41928	+	0.0328369i
$545$			10.3401i			0.442921i
$546$		0			0
$547$			32.9387i			1.40836i	0.710022	+	0.704179i	$0.248685\pi$
$547$			32.9387i			1.40836i	−0.710022	+	0.704179i	$0.751315\pi$
$548$	16.3772	+	22.1082i	0.699600	+	0.944415i
$549$	0.0449378	−	0.907556i	0.00191790	−	0.0387335i
$550$	−23.2890	+	7.68635i	−0.993046	+	0.327747i
$551$	−4.24192	−	7.34722i	−0.180712	−	0.313002i
$552$	−1.42808	−	0.566055i	−0.0607832	−	0.0240929i
$553$		0			0
$554$	4.16528	+	3.71569i	0.176966	+	0.157864i
$555$	7.99101	+	8.39647i	0.339199	+	0.356410i
$556$	10.4865	−	24.1520i	0.444727	−	1.02427i
$557$	25.8991	+	14.9528i	1.09738	+	0.633572i	0.935531	−	0.353244i	$-0.114921\pi$
$557$	25.8991	+	14.9528i	1.09738	+	0.633572i	0.161847	+	0.986816i	$0.448255\pi$
$558$	−20.0354	+	5.53010i	−0.848167	+	0.234108i
$559$		−	14.0763i		−	0.595363i
$560$		0			0
$561$	−49.8486	+	12.0437i	−2.10461	+	0.508484i
$562$	−1.64252	−	0.341195i	−0.0692857	−	0.0143924i
$563$	15.5531	−	26.9388i	0.655487	−	1.13534i	−0.326284	−	0.945272i	$-0.605797\pi$
$563$	15.5531	−	26.9388i	0.655487	−	1.13534i	0.981771	−	0.190065i	$-0.0608699\pi$
$564$	−6.83818	+	39.2328i	−0.287939	+	1.65200i
$565$	−4.21532	−	7.30115i	−0.177340	−	0.307162i
$566$	26.0616	−	29.2151i	1.09545	−	1.22800i
$567$		0			0
$568$	−7.39456	+	10.4806i	−0.310269	+	0.439756i
$569$	15.3022	−	8.83472i	0.641501	−	0.370371i	−0.143691	−	0.989623i	$-0.545897\pi$
$569$	15.3022	−	8.83472i	0.641501	−	0.370371i	0.785193	+	0.619252i	$0.212564\pi$
$570$	−2.48200	−	3.99562i	−0.103960	−	0.167358i
$571$	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
$576$	5.49846	−	23.3617i	0.229103	−	0.973402i
$577$	−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
$579$	1.97189	−	1.87667i	0.0819491	−	0.0779917i
$580$	1.57932	+	13.7969i	0.0655776	+	0.572887i
$581$		0			0
$582$	15.8152	−	29.5542i	0.655560	−	1.22506i
$583$	56.0289	−	32.3483i	2.32048	−	1.33973i
$584$	−1.67751	−	3.63125i	−0.0694157	−	0.150262i
$585$	16.5955	+	0.821731i	0.686141	+	0.0339744i
$586$	0.273878	+	0.0568914i	0.0113138	+	0.00235016i
$587$	−43.2909			−1.78681			−0.893404	−	0.449253i	$-0.851690\pi$
$587$	−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
$591$	0.897238	−	3.04515i	0.0369074	−	0.125261i
$592$	−6.22141	+	20.4262i	−0.255698	+	0.839511i
$593$	4.99583	−	2.88434i	0.205154	−	0.118446i	−0.393903	−	0.919152i	$-0.628875\pi$
$593$	4.99583	−	2.88434i	0.205154	−	0.118446i	0.599057	+	0.800706i	$0.295542\pi$
$594$	0.640266	−	37.1650i	0.0262704	−	1.52490i
$595$		0			0
$596$	−22.4475	+	2.56954i	−0.919486	+	0.105252i
$597$	−4.38335	−	4.60576i	−0.179399	−	0.188501i
$598$	1.86047	−	0.614033i	0.0760802	−	0.0251097i
$599$	17.8985	−	31.0011i	0.731312	−	1.26667i	−0.225010	−	0.974356i	$-0.572242\pi$
$599$	17.8985	−	31.0011i	0.731312	−	1.26667i	0.956323	−	0.292313i	$-0.0944251\pi$
$600$	−2.44711	−	16.6162i	−0.0999028	−	0.678353i
$601$	−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
$606$	8.47236	−	5.26286i	0.344166	−	0.213789i
$607$	−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
$612$	−2.26362	−	35.0475i	−0.0915015	−	1.41671i
$613$	−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	$0.143569\pi$
$617$			21.6549i			0.871795i	−0.899996	+	0.435898i	$0.856431\pi$
$618$	1.03272	+	32.0123i	0.0415421	+	1.28772i
$619$	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
$621$	0.537240	−	1.53824i	0.0215587	−	0.0617275i
$622$	11.3513	+	10.1260i	0.455144	+	0.406017i
$623$		0			0
$624$	13.7258	+	27.3586i	0.549472	+	1.09522i
$625$	−1.94767	−	3.37346i	−0.0779067	−	0.134938i
$626$	−6.63959	+	2.19135i	−0.265371	+	0.0875838i
$627$	3.79293	−	12.8729i	0.151475	−	0.514094i
$628$	23.7780	−	17.6142i	0.948845	−	0.702881i
$629$			31.2464i			1.24588i
$630$		0			0
$631$		−	6.37226i		−	0.253676i	−0.991923	−	0.126838i	$-0.959517\pi$
$631$		−	6.37226i		−	0.253676i	0.991923	−	0.126838i	$-0.0404828\pi$
$632$	1.77766	−	19.5151i	0.0707113	−	0.776270i
$633$	−7.28244	+	24.7160i	−0.289451	+	0.982372i
$634$	−9.72219	−	29.4574i	−0.386117	−	1.16990i
$635$	−5.33056	−	9.23281i	−0.211537	−	0.366393i
$636$	15.2358	+	41.6048i	0.604137	+	1.64974i
$637$		0			0
$638$	−26.3747	+	29.5660i	−1.04419	+	1.17053i
$639$	−11.4312	−	7.37670i	−0.452211	−	0.291818i
$640$	−11.1987	+	8.70401i	−0.442668	+	0.344056i
$641$	14.2860	+	8.24802i	0.564263	+	0.325777i	0.754855	−	0.655892i	$-0.227707\pi$
$641$	14.2860	+	8.24802i	0.564263	+	0.325777i	−0.190592	+	0.981669i	$0.561041\pi$
$642$	9.56704	−	0.308633i	0.377581	−	0.0121808i
$643$			2.36672i			0.0933343i	0.998910	+	0.0466671i	$0.0148600\pi$
$643$			2.36672i			0.0933343i	−0.998910	+	0.0466671i	$0.985140\pi$
$644$		0			0
$645$	1.62476	+	6.72485i	0.0639748	+	0.264791i
$646$	2.57889	−	12.4149i	0.101465	−	0.488456i
$647$	5.67476	−	9.82897i	0.223098	−	0.386417i	−0.732649	−	0.680606i	$-0.761716\pi$
$647$	5.67476	−	9.82897i	0.223098	−	0.386417i	0.955747	+	0.294190i	$0.0950497\pi$
$648$	24.9988	+	4.80232i	0.982044	+	0.188653i
$649$	−20.1497	−	34.9002i	−0.790944	−	1.36995i
$650$	15.9845	+	14.2591i	0.626962	+	0.559289i
$651$		0			0
$652$	26.3599	−	3.01738i	1.03233	−	0.118170i
$653$	38.5978	−	22.2844i	1.51045	−	0.872057i	0.510522	−	0.859865i	$-0.329452\pi$
$653$	38.5978	−	22.2844i	1.51045	−	0.872057i	0.999926	−	0.0121923i	$-0.00388102\pi$
$654$	−10.6605	−	17.1618i	−0.416860	−	0.671078i
$655$	−9.13122	−	5.27191i	−0.356786	−	0.205991i
$656$	5.78482	−	5.40582i	0.225859	−	0.211062i
$657$	3.77465	−	1.93702i	0.147263	−	0.0755702i
$658$		0			0
$659$	−0.590533			−0.0230039			−0.0115019	−	0.999934i	$-0.503661\pi$
$659$	−0.590533			−0.0230039			−0.0115019	+	0.999934i	$0.503661\pi$
$660$	−14.0870	+	16.8555i	−0.548334	+	0.656098i
$661$	21.5502	−	37.3261i	0.838206	−	1.45182i	−0.0531863	−	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
$663$	30.8791	+	32.4459i	1.19925	+	1.26010i
$664$	11.0609	−	15.6771i	0.429248	−	0.608390i
$665$		0			0
$666$	−21.9196	−	5.69722i	−0.849367	−	0.220763i
$667$	−1.50407	+	0.868374i	−0.0582377	+	0.0336236i
$668$	−8.78055	−	3.81240i	−0.339730	−	0.147506i
$669$	−9.50530	+	32.2602i	−0.367496	+	1.24725i
$670$	−3.80197	+	18.3028i	−0.146883	+	0.707099i
$671$	−1.53210			−0.0591459
$672$		0			0
$673$	15.2706			0.588637			0.294319	−	0.955707i	$-0.404907\pi$
$673$	15.2706			0.588637			0.294319	+	0.955707i	$0.404907\pi$
$674$	−6.60896	+	31.8158i	−0.254567	+	1.22550i
$675$	17.5017	−	3.32216i	0.673641	−	0.127870i
$676$	−11.9585	−	5.19223i	−0.459943	−	0.199701i
$677$	−35.8437	+	20.6944i	−1.37759	+	0.795349i	−0.991868	−	0.127268i	$-0.959379\pi$
$677$	−35.8437	+	20.6944i	−1.37759	+	0.795349i	−0.385717	+	0.922617i	$0.626046\pi$
$678$	14.5237	+	7.77198i	0.557780	+	0.298481i
$679$		0			0
$680$	−11.9655	+	16.9592i	−0.458857	+	0.650356i
$681$	13.4032	−	12.7560i	0.513613	−	0.488811i
$682$	10.9835	+	33.2791i	0.420580	+	1.27432i
$683$	−2.26745	+	3.92734i	−0.0867615	+	0.150275i	−0.906140	−	0.422977i	$-0.860985\pi$
$683$	−2.26745	+	3.92734i	−0.0867615	+	0.150275i	0.819379	+	0.573252i	$0.194318\pi$
$684$	8.23890	+	4.07273i	0.315022	+	0.155725i
$685$	17.2461			0.658941
$686$		0			0
$687$	−3.05138	−	12.6296i	−0.116417	−	0.481850i
$688$	−9.31160	+	8.70155i	−0.355002	+	0.331744i
$689$	−48.9366	−	28.2536i	−1.86434	−	1.07638i
$690$	−0.817953	+	0.508096i	−0.0311389	+	0.0193429i
$691$	23.6340	−	13.6451i	0.899079	−	0.519084i	0.0221779	−	0.999754i	$-0.492940\pi$
$691$	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
$696$	−16.8458	−	21.2709i	−0.638537	−	0.806272i
$697$	5.79306	−	10.0339i	0.219428	−	0.380060i
$698$	−1.02312	+	4.92536i	−0.0387258	+	0.186428i
$699$	4.71287	−	1.13865i	0.178257	−	0.0430678i
$700$		0			0
$701$		−	9.20431i		−	0.347642i	−0.984777	−	0.173821i	$-0.944389\pi$
$701$		−	9.20431i		−	0.347642i	0.984777	−	0.173821i	$-0.0556114\pi$
$702$	−28.3913	+	15.7460i	−1.07156	+	0.594294i
$703$	−7.08130	−	4.08839i	−0.267076	−	0.154197i
$704$	−39.8002	−	7.31156i	−1.50003	−	0.275565i
$705$	17.2094	+	18.0827i	0.648145	+	0.681032i
$706$	−17.8182	+	19.9742i	−0.670598	+	0.751740i
$707$		0			0
$708$	25.9155	−	9.49030i	0.973965	−	0.356667i
$709$	14.8003	+	25.6349i	0.555837	+	0.962738i	0.997838	+	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
$711$	20.7592	+	1.02790i	0.778530	+	0.0385491i
$712$	1.23097	−	13.5136i	0.0461325	−	0.506443i
$713$			1.53617i			0.0575302i
$714$		0			0
$715$		−	28.0159i		−	1.04773i
$716$	−1.11580	+	0.826558i	−0.0416994	+	0.0308899i
$717$	34.1369	+	10.0583i	1.27487	+	0.375633i
$718$	1.64647	−	0.543405i	0.0614457	−	0.0202797i
$719$	1.35786	+	2.35188i	0.0506395	+	0.0877102i	0.890234	−	0.455503i	$-0.150541\pi$
$719$	1.35786	+	2.35188i	0.0506395	+	0.0877102i	−0.839595	+	0.543214i	$0.817207\pi$
$720$	−9.71531	−	11.4861i	−0.362068	−	0.428062i
$721$		0			0
$722$	−17.5752	−	15.6782i	−0.654081	−	0.583480i
$723$	−22.6524	+	21.5585i	−0.842453	+	0.801770i
$724$	11.5767	+	5.02646i	0.430245	+	0.186807i
$725$	−16.4444	−	9.49416i	−0.610729	−	0.352604i
$726$	−35.7100	+	1.15201i	−1.32532	+	0.0427550i
$727$			18.9752i			0.703753i	0.936046	+	0.351876i	$0.114456\pi$
$727$			18.9752i			0.703753i	−0.936046	+	0.351876i	$0.885544\pi$
$728$		0			0
$729$	−3.99276	+	26.7031i	−0.147880	+	0.989005i
$730$	−2.45490	−	0.509947i	−0.0908601	−	0.0188740i
$731$	−9.32487	+	16.1512i	−0.344893	+	0.597372i
$732$	0.180164	−	1.03366i	0.00665905	−	0.0382050i
$733$	7.65295	+	13.2553i	0.282668	+	0.489596i	0.972041	−	0.234811i	$-0.0754471\pi$
$733$	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
$738$	5.98257	+	5.89337i	0.220222	+	0.216938i
$739$	−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	$-0.358301\pi$
$743$	23.4748			0.861208			0.430604	+	0.902541i	$0.358301\pi$
$744$	−23.7439	+	3.49682i	−0.870493	+	0.128200i
$745$	−7.08130	+	12.2652i	−0.259439	+	0.449361i
$746$	−10.9859	+	3.62582i	−0.402224	+	0.132751i
$747$	17.0990	+	11.0342i	0.625620	+	0.403721i
$748$	−58.8321	+	6.73444i	−2.15112	+	0.246235i
$749$		0			0
$750$	−22.8200	−	12.2115i	−0.833268	−	0.445901i
$751$	−31.1457	+	17.9820i	−1.13652	+	0.656172i	−0.945567	−	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
$753$	17.4135	+	5.13079i	0.634582	+	0.186977i
$754$	33.8818	+	7.03813i	1.23390	+	0.256314i
$755$	−13.9153			−0.506429
$756$		0			0
$757$	23.4202			0.851222			0.425611	−	0.904906i	$-0.360059\pi$
$757$	23.4202			0.851222			0.425611	+	0.904906i	$0.360059\pi$
$758$	43.2040	+	8.97458i	1.56924	+	0.325972i
$759$	−2.63524	−	0.776460i	−0.0956531	−	0.0281837i
$760$	−2.27781	−	4.93072i	−0.0826250	−	0.178856i
$761$	−34.9126	+	20.1568i	−1.26558	+	0.730684i	−0.974149	−	0.225908i	$-0.927465\pi$
$761$	−34.9126	+	20.1568i	−1.26558	+	0.730684i	−0.291433	+	0.956591i	$0.594132\pi$
$762$	18.3662	+	9.82820i	0.665338	+	0.356038i
$763$		0			0
$764$	−0.888828	−	7.76481i	−0.0321567	−	0.280921i
$765$	−18.4974	−	11.9366i	−0.668775	−	0.431570i
$766$	32.7922	−	10.8228i	1.18483	−	0.391045i
$767$	−17.5991	+	30.4825i	−0.635465	+	1.10066i
$768$	9.61309	−	25.9921i	0.346882	−	0.937909i
$769$	−20.6279			−0.743861			−0.371930	−	0.928261i	$-0.621304\pi$
$769$	−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	0.816878	−	0.576811i	$-0.195703\pi$
$773$	20.1789	+	11.6503i	0.725784	+	0.419032i	−0.0910936	+	0.995842i	$0.529036\pi$
$774$	−9.62992	−	9.48633i	−0.346140	−	0.340979i
$775$	−14.5453	+	8.39771i	−0.522481	+	0.301655i
$776$	22.3136	−	31.6260i	0.801012	−	1.13531i
$777$		0			0
$778$	−8.55233	+	9.58716i	−0.306616	+	0.343716i
$779$	1.51597	+	2.62573i	0.0543152	+	0.0940767i
$780$	18.9014	+	3.29447i	0.676778	+	0.117961i
$781$	−11.4694	+	19.8655i	−0.410407	+	0.710845i
$782$	−2.54147	−	0.527930i	−0.0908829	−	0.0188787i
$783$	21.8030	−	18.7853i	0.779177	−	0.671333i
$784$		0			0
$785$		−	18.5487i		−	0.662032i
$786$	20.5906	−	0.664256i	0.734444	−	0.0236932i
$787$	2.76123	+	1.59420i	0.0984271	+	0.0568269i	0.548406	−	0.836212i	$-0.315235\pi$
$787$	2.76123	+	1.59420i	0.0984271	+	0.0568269i	−0.449978	+	0.893039i	$0.648568\pi$
$788$	1.45992	−	3.36243i	0.0520076	−	0.119782i
$789$	36.8495	−	35.0701i	1.31188	−	1.24853i
$790$	−9.16617	−	8.17678i	−0.326118	−	0.290917i
$791$		0			0
$792$	6.00271	−	42.4990i	0.213297	−	1.51014i
$793$	0.669079	+	1.15888i	0.0237597	+	0.0411530i
$794$	−31.2654	+	10.3189i	−1.10957	+	0.366205i
$795$	26.6404	+	7.84945i	0.944836	+	0.278391i
$796$	−4.37019	−	5.89948i	−0.154897	−	0.209102i
$797$		−	55.9985i		−	1.98357i	−0.127925	−	0.991784i	$-0.540832\pi$
$797$		−	55.9985i		−	1.98357i	0.127925	−	0.991784i	$-0.459168\pi$
$798$		0			0
$799$			67.2924i			2.38063i
$800$	−0.448577	−	19.3885i	−0.0158596	−	0.685487i
$801$	14.3750	+	0.711784i	0.507917	+	0.0251496i
$802$	3.36471	+	10.1948i	0.118812	+	0.359991i
$803$	−3.57674	−	6.19509i	−0.126220	−	0.218620i
$804$	−12.5598	−	34.2975i	−0.442950	−	1.20958i
$805$		0			0
$806$	20.3757	−	22.8412i	0.717705	−	0.804546i
$807$	24.3564	+	25.5922i	0.857385	+	0.900890i
$808$	10.4552	−	4.82990i	0.367811	−	0.169915i
$809$	18.4879	+	10.6740i	0.649999	+	0.375277i	0.788456	−	0.615091i	$-0.210881\pi$
$809$	18.4879	+	10.6740i	0.649999	+	0.375277i	−0.138457	+	0.990368i	$0.544214\pi$
$810$	11.7463	−	10.7996i	0.412722	−	0.379460i
$811$			52.7856i			1.85355i	0.375614	+	0.926776i	$0.377432\pi$
$811$			52.7856i			1.85355i	−0.375614	+	0.926776i	$0.622568\pi$
$812$		0			0
$813$	34.6763	−	8.37797i	1.21615	−	0.293828i
$814$	−7.76651	+	37.3883i	−0.272216	+	1.31046i
$815$	8.31549	−	14.4029i	0.291279	−	0.504510i
$816$	2.37474	−	40.4840i	0.0831326	−	1.41722i
$817$	−2.44020	−	4.22654i	−0.0853717	−	0.147868i
$818$	−6.74377	−	6.01585i	−0.235790	−	0.210339i
$819$		0			0
$820$	−0.564413	−	4.93072i	−0.0197101	−	0.172188i
$821$	−5.03883	+	2.90917i	−0.175857	+	0.101531i	−0.585344	−	0.810785i	$-0.699041\pi$
$821$	−5.03883	+	2.90917i	−0.175857	+	0.101531i	0.409488	+	0.912316i	$0.365707\pi$
$822$	−28.6239	+	17.7806i	−0.998374	+	0.620170i
$823$	−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	$-0.126624\pi$
$827$	53.0241			1.84383			0.921915	+	0.387393i	$0.126624\pi$
$828$	0.833738	−	1.68660i	0.0289744	−	0.0586135i
$829$	−16.3511	+	28.3210i	−0.567898	+	0.983628i	0.428876	+	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
$831$	−4.95202	+	4.71289i	−0.171784	+	0.163488i
$832$	11.8506	+	33.2979i	0.410845	+	1.15440i
$833$		0			0
$834$	28.4329	+	15.2151i	0.984552	+	0.526857i
$835$	−5.19641	+	3.00015i	−0.179829	+	0.103824i
$836$	6.17159	−	14.2141i	0.213449	−	0.491606i
$837$	−4.74723	−	25.0093i	−0.164088	−	0.864447i
$838$	−8.37884	+	40.3360i	−0.289442	+	1.39339i
$839$	37.5962			1.29796			0.648982	−	0.760803i	$-0.275195\pi$
$839$	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
$843$	0.580701	−	1.97085i	0.0200004	−	0.0678796i
$844$	−11.8495	+	27.2912i	−0.407875	+	0.939401i
$845$	−7.07716	+	4.08600i	−0.243462	+	0.140563i
$846$	−47.2061	−	12.2695i	−1.62298	−	0.421835i
$847$		0			0
$848$	11.5612	+	49.8377i	0.397013	+	1.71143i
$849$	33.0560	+	34.7332i	1.13448	+	1.19204i
$850$	−8.89462	−	26.9499i	−0.305083	−	0.924375i
$851$	−0.836944	+	1.44963i	−0.0286901	+	0.0496927i
$852$	−12.0539	−	10.0741i	−0.412960	−	0.345132i
$853$	5.68417			0.194622			0.0973112	−	0.995254i	$-0.468976\pi$
$853$	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	−0.0483040	−	0.998833i	$-0.515382\pi$
$857$	−27.4440	−	15.8448i	−0.937471	−	0.541249i	−0.889166	+	0.457584i	$0.848715\pi$
$858$	28.8841	+	46.4987i	0.986086	+	1.58744i
$859$	−5.22874	+	3.01882i	−0.178402	+	0.103001i	−0.586542	−	0.809919i	$-0.699511\pi$
$859$	−5.22874	+	3.01882i	−0.178402	+	0.103001i	0.408139	+	0.912920i	$0.366178\pi$
$860$	0.908514	+	7.93679i	0.0309801	+	0.270642i
$861$		0			0
$862$	19.2552	+	17.1768i	0.655835	+	0.585045i
$863$	−20.0569	−	34.7395i	−0.682744	−	1.18255i	−0.974140	−	0.225944i	$-0.927453\pi$
$863$	−20.0569	−	34.7395i	−0.682744	−	1.18255i	0.291396	−	0.956602i	$-0.405880\pi$
$864$	27.9668	+	9.04742i	0.951451	+	0.307800i
$865$	−9.03379	+	15.6470i	−0.307158	+	0.532013i
$866$	1.39454	−	6.71339i	0.0473885	−	0.228130i
$867$	−7.02181	−	29.0632i	−0.238473	−	0.987038i
$868$		0			0
$869$		−	35.0447i		−	1.18881i
$870$	−16.9992	+	0.548397i	−0.576328	+	0.0185924i
$871$	40.3415	+	23.2912i	1.36692	+	0.789192i
$872$	−9.78354	−	21.1781i	−0.331312	−	0.717183i
$873$	34.4944	+	22.2597i	1.16746	+	0.753377i
$874$	0.452179	−	0.506892i	0.0152952	−	0.0171459i
$875$		0			0
$876$	4.60023	−	1.68461i	0.155427	−	0.0569177i
$877$	21.9436	+	38.0074i	0.740983	+	1.28342i	0.952048	+	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
$879$	−0.0968270	+	0.328623i	−0.00326590	+	0.0110842i
$880$	−18.5328	+	17.3186i	−0.624740	+	0.583810i
$881$		−	1.27293i		−	0.0428860i	−0.999770	−	0.0214430i	$-0.993174\pi$
$881$		−	1.27293i		−	0.0428860i	0.999770	−	0.0214430i	$-0.00682603\pi$
$882$		0			0
$883$			19.5118i			0.656625i	0.944569	+	0.328312i	$0.106480\pi$
$883$			19.5118i			0.656625i	−0.944569	+	0.328312i	$0.893520\pi$
$884$	30.7864	+	41.5597i	1.03546	+	1.39780i
$885$	4.88940	−	16.5942i	0.164355	−	0.557808i
$886$	30.1722	−	9.95812i	1.01366	−	0.334550i
$887$	−13.4459	−	23.2890i	−0.451470	−	0.781969i	0.547007	−	0.837128i	$-0.315767\pi$
$887$	−13.4459	−	23.2890i	−0.451470	−	0.781969i	−0.998478	+	0.0551585i	$0.982434\pi$
$888$	−24.3114	−	9.63641i	−0.815836	−	0.323377i
$889$		0			0
$890$	−6.34727	−	5.66215i	−0.212761	−	0.189796i
$891$	45.3018	+	4.49728i	1.51767	+	0.150665i
$892$	−15.4664	+	35.6214i	−0.517852	+	1.19269i
$893$	−15.2503	−	8.80477i	−0.510332	−	0.294640i
$894$	−0.892237	−	27.6576i	−0.0298409	−	0.925010i
$895$			0.870412i			0.0290947i
$896$		0			0
$897$	0.563515	+	2.33238i	0.0188152	+	0.0778760i
$898$	40.9388	+	8.50404i	1.36614	+	0.283783i
$899$	−13.5668	+	23.4984i	−0.452478	+	0.783715i
$900$	20.5273	−	1.32581i	0.684244	−	0.0441935i
$901$	37.4334	+	64.8365i	1.24709	+	2.16002i
$902$	9.42574	−	10.5662i	0.313843	−	0.351817i
$903$		0			0
$904$	15.5418	+	10.9655i	0.516913	+	0.364706i
$905$	6.85120	−	3.95554i	0.227742	−	0.131487i
$906$	23.0956	−	14.3465i	0.767299	−	0.476631i
$907$	−16.1538	−	9.32642i	−0.536379	−	0.309679i	0.207231	−	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	$-0.542996\pi$
$911$	−8.12909			−0.269329			−0.134664	+	0.990891i	$0.542996\pi$
$912$	8.86408	+	5.83525i	0.293519	+	0.193225i
$913$	17.1561	−	29.7153i	0.567785	−	0.983433i
$914$	24.4350	−	8.06458i	0.808237	−	0.266753i
$915$	−0.453413	−	0.476419i	−0.0149894	−	0.0157499i
$916$	−1.70623	−	14.9057i	−0.0563755	−	0.492497i
$917$		0			0
$918$	43.0072	+	0.740913i	1.41945	+	0.0244538i
$919$	15.2109	−	8.78201i	0.501761	−	0.289692i	−0.227680	−	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
$921$	−8.13692	+	27.6160i	−0.268121	+	0.909979i
$922$	−34.5862	−	7.18444i	−1.13903	−	0.236607i
$923$	20.0351			0.659463
$924$		0			0
$925$	−18.3011			−0.601736
$926$	8.82339	+	1.83285i	0.289954	+	0.0602310i
$927$	−39.1793	−	1.93997i	−1.28682	−	0.0637170i
$928$	−16.2890	−	26.7640i	−0.534712	−	0.878571i
$929$	33.7624	−	19.4927i	1.10771	−	0.639535i	0.169473	−	0.985535i	$-0.445793\pi$
$929$	33.7624	−	19.4927i	1.10771	−	0.639535i	0.938235	+	0.345999i	$0.112460\pi$
$930$	−7.09794	+	13.2641i	−0.232751	+	0.434948i
$931$		0			0
$932$	5.56221	−	0.636699i	0.182196	−	0.0208558i
$933$	−13.4953	+	12.8436i	−0.441816	+	0.420481i
$934$	−36.7393	+	12.1255i	−1.20215	+	0.396759i
$935$	−18.5592	+	32.1455i	−0.606951	+	1.05127i
$936$	−34.7677	+	14.0192i	−1.13642	+	0.458233i
$937$	−23.7865			−0.777072			−0.388536	−	0.921434i	$-0.627019\pi$
$937$	−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	0.00115159	−	0.999999i	$-0.499633\pi$
$941$	−26.5129	−	15.3073i	−0.864297	−	0.499002i	−0.865449	+	0.500997i	$0.832967\pi$
$942$	19.1235	+	30.7858i	0.623079	+	1.00306i
$943$	0.537520	−	0.310337i	0.0175041	−	0.0101060i
$944$	31.0437	−	7.20143i	1.01039	−	0.234387i
$945$		0			0
$946$	−15.1722	+	17.0081i	−0.493292	+	0.552980i
$947$	7.73005	+	13.3888i	0.251193	+	0.435079i	0.963855	−	0.266429i	$-0.0858438\pi$
$947$	7.73005	+	13.3888i	0.251193	+	0.435079i	−0.712662	+	0.701508i	$0.752510\pi$
$948$	23.6435	+	4.12102i	0.767907	+	0.133844i
$949$	−3.12398	+	5.41090i	−0.101409	+	0.175645i
$950$	7.27140	+	1.51046i	0.235915	+	0.0490057i
$951$	36.9294	−	8.92233i	1.19752	−	0.289326i
$952$		0			0
$953$		−	13.4497i		−	0.435679i	−0.975985	−	0.217839i	$-0.930099\pi$
$953$		−	13.4497i		−	0.435679i	0.975985	−	0.217839i	$-0.0699009\pi$
$954$	−52.3085	+	14.4380i	−1.69355	+	0.467448i
$955$	−4.24264	−	2.44949i	−0.137289	−	0.0792636i
$956$	37.6937	+	16.3661i	1.21910	+	0.529317i
$957$	−33.4531	−	35.1505i	−1.08138	−	1.13625i
$958$	20.9308	+	18.6715i	0.676243	+	0.603250i
$959$		0			0
$960$	−9.50498	−	14.5400i	−0.306772	−	0.469277i
$961$	−3.50000	−	6.06218i	−0.112903	−	0.195554i
$962$	31.6722	−	10.4532i	1.02115	−	0.337024i
$963$	−0.579770	+	11.7089i	−0.0186828	+	0.377315i
$964$	−29.0153	+	21.4938i	−0.934519	+	0.692269i
$965$		−	1.97031i		−	0.0634264i
$966$		0			0
$967$		−	41.1554i		−	1.32347i	−0.749738	−	0.661734i	$-0.769821\pi$
$967$		−	41.1554i		−	1.32347i	0.749738	−	0.661734i	$-0.230179\pi$
$968$	−41.0857	−	3.74254i	−1.32054	−	0.120290i
$969$	14.8965	+	4.38917i	0.478543	+	0.141000i
$970$	−7.60389	−	23.0391i	−0.244146	−	0.739742i
$971$	−14.4445	−	25.0186i	−0.463546	−	0.802886i	0.535588	−	0.844479i	$-0.320090\pi$
$971$	−14.4445	−	25.0186i	−0.463546	−	0.802886i	−0.999135	+	0.0415934i	$0.986757\pi$
$972$	−8.36134	+	30.0348i	−0.268190	+	0.963366i
$973$		0			0
$974$	−38.4593	+	43.1128i	−1.23232	+	1.38142i
$975$	−19.0036	+	18.0859i	−0.608603	+	0.579213i
$976$	0.353005	−	1.15899i	0.0112994	−	0.0370984i
$977$	−40.6932	−	23.4942i	−1.30189	−	0.751646i	−0.321161	−	0.947024i	$-0.604073\pi$
$977$	−40.6932	−	23.4942i	−1.30189	−	0.751646i	−0.980728	+	0.195378i	$0.937407\pi$
$978$	1.04774	+	32.4780i	0.0335032	+	1.03853i
$979$		−	24.2673i		−	0.775587i
$980$		0			0
$981$	22.0145	−	11.2971i	0.702868	−	0.360687i
$982$	−5.83893	+	28.1088i	−0.186328	+	0.896989i
$983$	−13.6677	+	23.6731i	−0.435931	+	0.755054i	−0.997371	−	0.0724632i	$-0.976914\pi$
$983$	−13.6677	+	23.6731i	−0.435931	+	0.755054i	0.561440	+	0.827517i	$0.310247\pi$
$984$	6.02030	+	7.60175i	0.191920	+	0.242335i
$985$	−1.14888	−	1.98991i	−0.0366063	−	0.0634039i
$986$	−34.2137	−	30.5207i	−1.08959	−	0.971978i
$987$		0			0
$988$	−13.4468	+	1.53923i	−0.427799	+	0.0489696i
$989$	−0.865226	+	0.499538i	−0.0275126	+	0.0158844i
$990$	−19.1663	−	18.8805i	−0.609146	−	0.600063i
$991$	−18.0000	−	10.3923i	−0.571789	−	0.330122i	0.186075	−	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
$996$	18.0305	+	15.0690i	0.571318	+	0.477479i
$997$	−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
$999$	9.14586	−	26.1867i	0.289362	−	0.828511i

Twists

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

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

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 $\F_{q}$

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} +(-1.66143 - 0.489533i) q^{3} +(-1.83454 - 0.796533i) q^{4} +(-1.08570 + 0.626827i) q^{5} +(1.15571 - 2.15971i) q^{6} +(1.63059 - 2.31110i) q^{8} +(2.52072 + 1.62665i) q^{9} +(-0.555662 - 1.68361i) q^{10} +(2.52914 - 4.38059i) q^{11} +(2.65803 + 2.22145i) q^{12} -4.41798 q^{13} +(2.11066 - 0.509947i) q^{15} +(2.73107 + 2.92254i) q^{16} +(5.06920 + 2.92671i) q^{17} +(-2.97738 + 3.02245i) q^{18} +(-1.32654 + 0.765881i) q^{19} +(2.49104 - 0.285146i) q^{20} +(5.33816 + 4.76197i) q^{22} +(0.156785 + 0.271560i) q^{23} +(-3.84047 + 3.04151i) q^{24} +(-1.71417 + 2.96904i) q^{25} +(1.27074 - 6.11738i) q^{26} +(-3.39170 - 3.93654i) q^{27} +5.53862i q^{29} +(0.0990132 + 3.06922i) q^{30} +(4.24264 + 2.44949i) q^{31} +(-4.83225 + 2.94098i) q^{32} +(-6.34643 + 6.03996i) q^{33} +(-5.51053 + 6.17729i) q^{34} +(-3.32867 - 4.99199i) q^{36} +(2.66908 + 4.62298i) q^{37} +(-0.678928 - 2.05710i) q^{38} +(7.34017 + 2.16275i) q^{39} +(-0.321666 + 3.53125i) q^{40} -1.97938i q^{41} +3.18613i q^{43} +(-8.12909 + 6.02183i) q^{44} +(-3.75636 - 0.185997i) q^{45} +(-0.421113 + 0.138985i) q^{46} +(5.74813 + 9.95606i) q^{47} +(-3.10681 - 6.19256i) q^{48} +(-3.61805 - 3.22752i) q^{50} +(-6.98942 - 7.34407i) q^{51} +(8.10496 + 3.51907i) q^{52} +(11.0767 + 6.39513i) q^{53} +(6.42631 - 3.56407i) q^{54} +6.34133i q^{55} +(2.57889 - 0.623072i) q^{57} +(-7.66908 - 1.59307i) q^{58} +(3.98351 - 6.89964i) q^{59} +(-4.27829 - 0.745696i) q^{60} +(-0.151445 - 0.262310i) q^{61} +(-4.61200 + 5.17005i) q^{62} +(-2.68236 - 7.53691i) q^{64} +(4.79659 - 2.76931i) q^{65} +(-6.53785 - 10.5249i) q^{66} +(-9.13122 - 5.27191i) q^{67} +(-6.96844 - 9.40695i) q^{68} +(-0.127550 - 0.527930i) q^{69} -4.53490 q^{71} +(7.86960 - 3.17322i) q^{72} +(0.707107 - 1.22474i) q^{73} +(-7.16894 + 2.36605i) q^{74} +(4.30143 - 4.09371i) q^{75} +(3.04365 - 0.348402i) q^{76} +(-5.10590 + 9.54154i) q^{78} +(6.00000 - 3.46410i) q^{79} +(-4.79704 - 1.46108i) q^{80} +(3.70801 + 8.20065i) q^{81} +(2.74076 + 0.569326i) q^{82} +6.78340 q^{83} -7.33816 q^{85} +(-4.41169 - 0.916423i) q^{86} +(2.71134 - 9.20204i) q^{87} +(-6.00000 - 12.9880i) q^{88} +(4.15480 - 2.39878i) q^{89} +(1.33798 - 5.14777i) q^{90} +(-0.0713222 - 0.623072i) q^{92} +(-5.84975 - 6.14657i) q^{93} +(-15.4390 + 5.09553i) q^{94} +(0.960150 - 1.66303i) q^{95} +(9.46816 - 2.52070i) q^{96} +13.6844 q^{97} +(13.5009 - 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) \) 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * q^88 - 24 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more