LMFDB - Embedded newform 280.2.bj.b.171.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [280,2,Mod(131,280)] 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("280.131"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(280, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-6,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			171.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	280.171
Dual form			280.2.bj.b.131.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} +(-0.275255 - 0.158919i) q^{3} -2.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.224745 - 0.389270i) q^{6} +(-2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +(-1.44949 - 2.51059i) q^{9} +(1.22474 - 0.707107i) q^{10} +(-2.44949 + 4.24264i) q^{11} +(0.550510 + 0.317837i) q^{12} -4.44949 q^{13} +(-1.22474 - 3.53553i) q^{14} +0.317837i q^{15} +4.00000 q^{16} +(-4.22474 - 2.43916i) q^{17} +(3.55051 - 2.04989i) q^{18} +(3.67423 - 2.12132i) q^{19} +(1.00000 + 1.73205i) q^{20} +(0.825765 + 0.158919i) q^{21} +(-6.00000 - 3.46410i) q^{22} +(3.94949 - 2.28024i) q^{23} +(-0.449490 + 0.778539i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.29253i q^{26} +1.87492i q^{27} +(5.00000 - 1.73205i) q^{28} +7.24604i q^{29} -0.449490 q^{30} +(-0.775255 + 1.34278i) q^{31} +5.65685i q^{32} +(1.34847 - 0.778539i) q^{33} +(3.44949 - 5.97469i) q^{34} +(2.00000 + 1.73205i) q^{35} +(2.89898 + 5.02118i) q^{36} +(-3.00000 + 1.73205i) q^{37} +(3.00000 + 5.19615i) q^{38} +(1.22474 + 0.707107i) q^{39} +(-2.44949 + 1.41421i) q^{40} -8.02458i q^{41} +(-0.224745 + 1.16781i) q^{42} -9.44949 q^{43} +(4.89898 - 8.48528i) q^{44} +(-1.44949 + 2.51059i) q^{45} +(3.22474 + 5.58542i) q^{46} +(3.00000 + 5.19615i) q^{47} +(-1.10102 - 0.635674i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-1.22474 - 0.707107i) q^{50} +(0.775255 + 1.34278i) q^{51} +8.89898 q^{52} +(-1.77526 - 1.02494i) q^{53} -2.65153 q^{54} +4.89898 q^{55} +(2.44949 + 7.07107i) q^{56} -1.34847 q^{57} -10.2474 q^{58} +(3.12372 + 1.80348i) q^{59} -0.635674i q^{60} +(0.174235 + 0.301783i) q^{61} +(-1.89898 - 1.09638i) q^{62} +(5.79796 + 5.02118i) q^{63} -8.00000 q^{64} +(2.22474 + 3.85337i) q^{65} +(1.10102 + 1.90702i) q^{66} +(-6.17423 + 10.6941i) q^{67} +(8.44949 + 4.87832i) q^{68} -1.44949 q^{69} +(-2.44949 + 2.82843i) q^{70} -1.41421i q^{71} +(-7.10102 + 4.09978i) q^{72} +(-9.67423 - 5.58542i) q^{73} +(-2.44949 - 4.24264i) q^{74} +(0.275255 - 0.158919i) q^{75} +(-7.34847 + 4.24264i) q^{76} +(2.44949 - 12.7279i) q^{77} +(-1.00000 + 1.73205i) q^{78} +(-6.67423 + 3.85337i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-4.05051 + 7.01569i) q^{81} +11.3485 q^{82} -1.87492i q^{83} +(-1.65153 - 0.317837i) q^{84} +4.87832i q^{85} -13.3636i q^{86} +(1.15153 - 1.99451i) q^{87} +(12.0000 + 6.92820i) q^{88} +(9.39898 - 5.42650i) q^{89} +(-3.55051 - 2.04989i) q^{90} +(11.1237 - 3.85337i) q^{91} +(-7.89898 + 4.56048i) q^{92} +(0.426786 - 0.246405i) q^{93} +(-7.34847 + 4.24264i) q^{94} +(-3.67423 - 2.12132i) q^{95} +(0.898979 - 1.55708i) q^{96} +11.9494i q^{97} +(6.12372 + 7.77817i) q^{98} +14.2020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 4 q^{6} - 10 q^{7} + 4 q^{9} + 12 q^{12} - 8 q^{13} + 16 q^{16} - 12 q^{17} + 24 q^{18} + 4 q^{20} + 18 q^{21} - 24 q^{22} + 6 q^{23} + 8 q^{24} - 2 q^{25} + 20 q^{28}+ \cdots + 96 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 4 * q^6 - 10 * q^7 + 4 * q^9 + 12 * q^12 - 8 * q^13 + 16 * q^16 - 12 * q^17 + 24 * q^18 + 4 * q^20 + 18 * q^21 - 24 * q^22 + 6 * q^23 + 8 * q^24 - 2 * q^25 + 20 * q^28 + 8 * q^30 - 8 * q^31 - 24 * q^33 + 4 * q^34 + 8 * q^35 - 8 * q^36 - 12 * q^37 + 12 * q^38 + 4 * q^42 - 28 * q^43 + 4 * q^45 + 8 * q^46 + 12 * q^47 - 24 * q^48 + 22 * q^49 + 8 * q^51 + 16 * q^52 - 12 * q^53 - 40 * q^54 + 24 * q^57 + 8 * q^58 - 12 * q^59 - 14 * q^61 + 12 * q^62 - 16 * q^63 - 32 * q^64 + 4 * q^65 + 24 * q^66 - 10 * q^67 + 24 * q^68 + 4 * q^69 - 48 * q^72 - 24 * q^73 + 6 * q^75 - 4 * q^78 - 12 * q^79 - 8 * q^80 - 26 * q^81 + 16 * q^82 - 36 * q^84 + 34 * q^87 + 48 * q^88 + 18 * q^89 - 24 * q^90 + 20 * q^91 - 12 * q^92 + 36 * q^93 - 16 * q^96 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			1.41421i			1.00000i
$2$			1.41421i			1.00000i
$3$	−0.275255	−	0.158919i	−0.158919	−	0.0917517i	0.418432	−	0.908248i	$-0.362580\pi$
$3$	−0.275255	−	0.158919i	−0.158919	−	0.0917517i	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−2.00000			−1.00000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.224745	−	0.389270i	0.0917517	−	0.158919i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		−	2.82843i		−	1.00000i
$9$	−1.44949	−	2.51059i	−0.483163	−	0.836863i
$10$	1.22474	−	0.707107i	0.387298	−	0.223607i
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	0.214600	+	0.976702i	$0.431155\pi$
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	−0.953149	+	0.302502i	$0.902178\pi$
$12$	0.550510	+	0.317837i	0.158919	+	0.0917517i
$13$	−4.44949			−1.23407			−0.617033	−	0.786937i	$-0.711666\pi$
$13$	−4.44949			−1.23407			−0.617033	+	0.786937i	$0.711666\pi$
$14$	−1.22474	−	3.53553i	−0.327327	−	0.944911i
$15$			0.317837i			0.0820652i
$16$	4.00000			1.00000
$17$	−4.22474	−	2.43916i	−1.02465	−	0.591583i	−0.109203	−	0.994019i	$-0.534830\pi$
$17$	−4.22474	−	2.43916i	−1.02465	−	0.591583i	−0.915448	+	0.402437i	$0.868163\pi$
$18$	3.55051	−	2.04989i	0.836863	−	0.483163i
$19$	3.67423	−	2.12132i	0.842927	−	0.486664i	−0.0153309	−	0.999882i	$-0.504880\pi$
$19$	3.67423	−	2.12132i	0.842927	−	0.486664i	0.858258	+	0.513218i	$0.171547\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$	0.825765	+	0.158919i	0.180197	+	0.0346789i
$22$	−6.00000	−	3.46410i	−1.27920	−	0.738549i
$23$	3.94949	−	2.28024i	0.823526	−	0.475463i	−0.0281052	−	0.999605i	$-0.508947\pi$
$23$	3.94949	−	2.28024i	0.823526	−	0.475463i	0.851631	+	0.524142i	$0.175614\pi$
$24$	−0.449490	+	0.778539i	−0.0917517	+	0.158919i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		−	6.29253i		−	1.23407i
$27$			1.87492i			0.360828i
$28$	5.00000	−	1.73205i	0.944911	−	0.327327i
$29$			7.24604i			1.34556i	0.739844	+	0.672778i	$0.234899\pi$
$29$			7.24604i			1.34556i	−0.739844	+	0.672778i	$0.765101\pi$
$30$	−0.449490			−0.0820652
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	−0.927209	−	0.374544i	$-0.877799\pi$
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	0.787969	+	0.615715i	$0.211133\pi$
$32$			5.65685i			1.00000i
$33$	1.34847	−	0.778539i	0.234738	−	0.135526i
$34$	3.44949	−	5.97469i	0.591583	−	1.02465i
$35$	2.00000	+	1.73205i	0.338062	+	0.292770i
$36$	2.89898	+	5.02118i	0.483163	+	0.836863i
$37$	−3.00000	+	1.73205i	−0.493197	+	0.284747i	−0.725900	−	0.687800i	$-0.758576\pi$
$37$	−3.00000	+	1.73205i	−0.493197	+	0.284747i	0.232703	+	0.972548i	$0.425243\pi$
$38$	3.00000	+	5.19615i	0.486664	+	0.842927i
$39$	1.22474	+	0.707107i	0.196116	+	0.113228i
$40$	−2.44949	+	1.41421i	−0.387298	+	0.223607i
$41$		−	8.02458i		−	1.25323i	−0.779329	−	0.626614i	$-0.784440\pi$
$41$		−	8.02458i		−	1.25323i	0.779329	−	0.626614i	$-0.215560\pi$
$42$	−0.224745	+	1.16781i	−0.0346789	+	0.180197i
$43$	−9.44949			−1.44103			−0.720517	−	0.693437i	$-0.756095\pi$
$43$	−9.44949			−1.44103			−0.720517	+	0.693437i	$0.756095\pi$
$44$	4.89898	−	8.48528i	0.738549	−	1.27920i
$45$	−1.44949	+	2.51059i	−0.216077	+	0.374257i
$46$	3.22474	+	5.58542i	0.475463	+	0.823526i
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$	−1.10102	−	0.635674i	−0.158919	−	0.0917517i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−1.22474	−	0.707107i	−0.173205	−	0.100000i
$51$	0.775255	+	1.34278i	0.108557	+	0.188027i
$52$	8.89898			1.23407
$53$	−1.77526	−	1.02494i	−0.243850	−	0.140787i	0.373095	−	0.927793i	$-0.378297\pi$
$53$	−1.77526	−	1.02494i	−0.243850	−	0.140787i	−0.616945	+	0.787006i	$0.711630\pi$
$54$	−2.65153			−0.360828
$55$	4.89898			0.660578
$56$	2.44949	+	7.07107i	0.327327	+	0.944911i
$57$	−1.34847			−0.178609
$58$	−10.2474			−1.34556
$59$	3.12372	+	1.80348i	0.406674	+	0.234794i	0.689360	−	0.724419i	$-0.257892\pi$
$59$	3.12372	+	1.80348i	0.406674	+	0.234794i	−0.282686	+	0.959213i	$0.591225\pi$
$60$		−	0.635674i		−	0.0820652i
$61$	0.174235	+	0.301783i	0.0223085	+	0.0386394i	0.876964	−	0.480556i	$-0.159565\pi$
$61$	0.174235	+	0.301783i	0.0223085	+	0.0386394i	−0.854656	+	0.519195i	$0.826232\pi$
$62$	−1.89898	−	1.09638i	−0.241171	−	0.139240i
$63$	5.79796	+	5.02118i	0.730474	+	0.632609i
$64$	−8.00000			−1.00000
$65$	2.22474	+	3.85337i	0.275946	+	0.477952i
$66$	1.10102	+	1.90702i	0.135526	+	0.234738i
$67$	−6.17423	+	10.6941i	−0.754303	+	1.30649i	0.191417	+	0.981509i	$0.438692\pi$
$67$	−6.17423	+	10.6941i	−0.754303	+	1.30649i	−0.945720	+	0.324982i	$0.894642\pi$
$68$	8.44949	+	4.87832i	1.02465	+	0.591583i
$69$	−1.44949			−0.174498
$70$	−2.44949	+	2.82843i	−0.292770	+	0.338062i
$71$		−	1.41421i		−	0.167836i	−0.996473	−	0.0839181i	$-0.973257\pi$
$71$		−	1.41421i		−	0.167836i	0.996473	−	0.0839181i	$-0.0267434\pi$
$72$	−7.10102	+	4.09978i	−0.836863	+	0.483163i
$73$	−9.67423	−	5.58542i	−1.13228	−	0.653724i	−0.187775	−	0.982212i	$-0.560128\pi$
$73$	−9.67423	−	5.58542i	−1.13228	−	0.653724i	−0.944508	+	0.328488i	$0.893461\pi$
$74$	−2.44949	−	4.24264i	−0.284747	−	0.493197i
$75$	0.275255	−	0.158919i	0.0317837	−	0.0183503i
$76$	−7.34847	+	4.24264i	−0.842927	+	0.486664i
$77$	2.44949	−	12.7279i	0.279145	−	1.45048i
$78$	−1.00000	+	1.73205i	−0.113228	+	0.196116i
$79$	−6.67423	+	3.85337i	−0.750910	+	0.433538i	−0.826023	−	0.563637i	$-0.809402\pi$
$79$	−6.67423	+	3.85337i	−0.750910	+	0.433538i	0.0751126	+	0.997175i	$0.476068\pi$
$80$	−2.00000	−	3.46410i	−0.223607	−	0.387298i
$81$	−4.05051	+	7.01569i	−0.450057	+	0.779521i
$82$	11.3485			1.25323
$83$		−	1.87492i		−	0.205799i	−0.994692	−	0.102899i	$-0.967188\pi$
$83$		−	1.87492i		−	0.205799i	0.994692	−	0.102899i	$-0.0328120\pi$
$84$	−1.65153	−	0.317837i	−0.180197	−	0.0346789i
$85$			4.87832i			0.529128i
$86$		−	13.3636i		−	1.44103i
$87$	1.15153	−	1.99451i	0.123457	−	0.213834i
$88$	12.0000	+	6.92820i	1.27920	+	0.738549i
$89$	9.39898	−	5.42650i	0.996290	−	0.575208i	0.0891414	−	0.996019i	$-0.471588\pi$
$89$	9.39898	−	5.42650i	0.996290	−	0.575208i	0.907148	+	0.420811i	$0.138254\pi$
$90$	−3.55051	−	2.04989i	−0.374257	−	0.216077i
$91$	11.1237	−	3.85337i	1.16608	−	0.403943i
$92$	−7.89898	+	4.56048i	−0.823526	+	0.475463i
$93$	0.426786	−	0.246405i	0.0442556	−	0.0255510i
$94$	−7.34847	+	4.24264i	−0.757937	+	0.437595i
$95$	−3.67423	−	2.12132i	−0.376969	−	0.217643i
$96$	0.898979	−	1.55708i	0.0917517	−	0.158919i
$97$			11.9494i			1.21328i	0.794978	+	0.606638i	$0.207482\pi$
$97$			11.9494i			1.21328i	−0.794978	+	0.606638i	$0.792518\pi$
$98$	6.12372	+	7.77817i	0.618590	+	0.785714i
$99$	14.2020			1.42736
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	7.62372	−	13.2047i	0.758589	−	1.31391i	−0.184981	−	0.982742i	$-0.559222\pi$
$101$	7.62372	−	13.2047i	0.758589	−	1.31391i	0.943570	−	0.331173i	$-0.107444\pi$
$102$	−1.89898	+	1.09638i	−0.188027	+	0.108557i
$103$	−8.39898	−	14.5475i	−0.827576	−	1.43340i	−0.899935	−	0.436025i	$-0.856386\pi$
$103$	−8.39898	−	14.5475i	−0.827576	−	1.43340i	0.0723585	−	0.997379i	$-0.476947\pi$
$104$			12.5851i			1.23407i
$105$	−0.275255	−	0.794593i	−0.0268622	−	0.0775443i
$106$	1.44949	−	2.51059i	0.140787	−	0.243850i
$107$	2.72474	+	4.71940i	0.263411	+	0.456241i	0.967146	−	0.254221i	$-0.0818191\pi$
$107$	2.72474	+	4.71940i	0.263411	+	0.456241i	−0.703735	+	0.710462i	$0.748486\pi$
$108$		−	3.74983i		−	0.360828i
$109$	−6.82577	−	3.94086i	−0.653790	−	0.377466i	0.136117	−	0.990693i	$-0.456538\pi$
$109$	−6.82577	−	3.94086i	−0.653790	−	0.377466i	−0.789907	+	0.613227i	$0.789871\pi$
$110$			6.92820i			0.660578i
$111$	1.10102			0.104504
$112$	−10.0000	+	3.46410i	−0.944911	+	0.327327i
$113$	8.44949			0.794861			0.397431	−	0.917632i	$-0.369902\pi$
$113$	8.44949			0.794861			0.397431	+	0.917632i	$0.369902\pi$
$114$		−	1.90702i		−	0.178609i
$115$	−3.94949	−	2.28024i	−0.368292	−	0.212633i
$116$		−	14.4921i		−	1.34556i
$117$	6.44949	+	11.1708i	0.596256	+	1.03274i
$118$	−2.55051	+	4.41761i	−0.234794	+	0.406674i
$119$	12.6742	+	2.43916i	1.16185	+	0.223597i
$120$	0.898979			0.0820652
$121$	−6.50000	−	11.2583i	−0.590909	−	1.02348i
$122$	−0.426786	+	0.246405i	−0.0386394	+	0.0223085i
$123$	−1.27526	+	2.20881i	−0.114986	+	0.199161i
$124$	1.55051	−	2.68556i	0.139240	−	0.241171i
$125$	1.00000			0.0894427
$126$	−7.10102	+	8.19955i	−0.632609	+	0.730474i
$127$		−	6.92820i		−	0.614779i	−0.951584	−	0.307389i	$-0.900545\pi$
$127$		−	6.92820i		−	0.614779i	0.951584	−	0.307389i	$-0.0994554\pi$
$128$		−	11.3137i		−	1.00000i
$129$	2.60102	+	1.50170i	0.229007	+	0.132217i
$130$	−5.44949	+	3.14626i	−0.477952	+	0.275946i
$131$	−9.79796	+	5.65685i	−0.856052	+	0.494242i	−0.862688	−	0.505736i	$-0.831221\pi$
$131$	−9.79796	+	5.65685i	−0.856052	+	0.494242i	0.00663646	+	0.999978i	$0.497888\pi$
$132$	−2.69694	+	1.55708i	−0.234738	+	0.135526i
$133$	−7.34847	+	8.48528i	−0.637193	+	0.735767i
$134$	−15.1237	−	8.73169i	−1.30649	−	0.754303i
$135$	1.62372	−	0.937458i	0.139748	−	0.0806835i
$136$	−6.89898	+	11.9494i	−0.591583	+	1.02465i
$137$	4.89898	−	8.48528i	0.418548	−	0.724947i	−0.577246	−	0.816571i	$-0.695872\pi$
$137$	4.89898	−	8.48528i	0.418548	−	0.724947i	0.995794	+	0.0916241i	$0.0292058\pi$
$138$		−	2.04989i		−	0.174498i
$139$		−	6.92820i		−	0.587643i	−0.955860	−	0.293821i	$-0.905073\pi$
$139$		−	6.92820i		−	0.587643i	0.955860	−	0.293821i	$-0.0949270\pi$
$140$	−4.00000	−	3.46410i	−0.338062	−	0.292770i
$141$		−	1.90702i		−	0.160600i
$142$	2.00000			0.167836
$143$	10.8990	−	18.8776i	0.911418	−	1.57862i
$144$	−5.79796	−	10.0424i	−0.483163	−	0.836863i
$145$	6.27526	−	3.62302i	0.521132	−	0.300875i
$146$	7.89898	−	13.6814i	0.653724	−	1.13228i
$147$	−2.20204	+	0.317837i	−0.181621	+	0.0262148i
$148$	6.00000	−	3.46410i	0.493197	−	0.284747i
$149$	16.6237	−	9.59771i	1.36187	−	0.786275i	0.371996	−	0.928234i	$-0.378673\pi$
$149$	16.6237	−	9.59771i	1.36187	−	0.786275i	0.989873	+	0.141959i	$0.0453402\pi$
$150$	0.224745	+	0.389270i	0.0183503	+	0.0317837i
$151$	−6.67423	−	3.85337i	−0.543142	−	0.313583i	0.203210	−	0.979135i	$-0.434863\pi$
$151$	−6.67423	−	3.85337i	−0.543142	−	0.313583i	−0.746351	+	0.665552i	$0.768196\pi$
$152$	−6.00000	−	10.3923i	−0.486664	−	0.842927i
$153$			14.1421i			1.14332i
$154$	18.0000	+	3.46410i	1.45048	+	0.279145i
$155$	1.55051			0.124540
$156$	−2.44949	−	1.41421i	−0.196116	−	0.113228i
$157$	5.34847	−	9.26382i	0.426854	−	0.739333i	−0.569737	−	0.821827i	$-0.692955\pi$
$157$	5.34847	−	9.26382i	0.426854	−	0.739333i	0.996592	+	0.0824935i	$0.0262884\pi$
$158$	−5.44949	−	9.43879i	−0.433538	−	0.750910i
$159$	0.325765	+	0.564242i	0.0258349	+	0.0447473i
$160$	4.89898	−	2.82843i	0.387298	−	0.223607i
$161$	−7.89898	+	9.12096i	−0.622527	+	0.718832i
$162$	−9.92168	−	5.72829i	−0.779521	−	0.450057i
$163$	−2.89898	−	5.02118i	−0.227066	−	0.393289i	0.729872	−	0.683584i	$-0.239580\pi$
$163$	−2.89898	−	5.02118i	−0.227066	−	0.393289i	−0.956937	+	0.290295i	$0.906247\pi$
$164$			16.0492i			1.25323i
$165$	−1.34847	−	0.778539i	−0.104978	−	0.0606092i
$166$	2.65153			0.205799
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$	0.449490	−	2.33562i	0.0346789	−	0.180197i
$169$	6.79796			0.522920
$170$	−6.89898			−0.529128
$171$	−10.6515	−	6.14966i	−0.814543	−	0.470277i
$172$	18.8990			1.44103
$173$	−5.44949	−	9.43879i	−0.414317	−	0.717618i	0.581039	−	0.813875i	$-0.302646\pi$
$173$	−5.44949	−	9.43879i	−0.414317	−	0.717618i	−0.995356	+	0.0962572i	$0.969313\pi$
$174$	2.82066	+	1.62851i	0.213834	+	0.123457i
$175$	0.500000	−	2.59808i	0.0377964	−	0.196396i
$176$	−9.79796	+	16.9706i	−0.738549	+	1.27920i
$177$	−0.573214	−	0.992836i	−0.0430854	−	0.0746261i
$178$	7.67423	+	13.2922i	0.575208	+	0.996290i
$179$	−4.77526	+	8.27098i	−0.356919	+	0.618202i	−0.987444	−	0.157966i	$-0.949506\pi$
$179$	−4.77526	+	8.27098i	−0.356919	+	0.618202i	0.630525	+	0.776169i	$0.282840\pi$
$180$	2.89898	−	5.02118i	0.216077	−	0.374257i
$181$	−12.3485			−0.917854			−0.458927	−	0.888474i	$-0.651766\pi$
$181$	−12.3485			−0.917854			−0.458927	+	0.888474i	$0.651766\pi$
$182$	5.44949	+	15.7313i	0.403943	+	1.16608i
$183$		−	0.110756i		−	0.00818736i
$184$	−6.44949	−	11.1708i	−0.475463	−	0.823526i
$185$	3.00000	+	1.73205i	0.220564	+	0.127343i
$186$	0.348469	+	0.603566i	0.0255510	+	0.0442556i
$187$	20.6969	−	11.9494i	1.51351	−	0.873825i
$188$	−6.00000	−	10.3923i	−0.437595	−	0.757937i
$189$	−1.62372	−	4.68729i	−0.118109	−	0.340950i
$190$	3.00000	−	5.19615i	0.217643	−	0.376969i
$191$	−22.8990	+	13.2207i	−1.65691	+	0.956619i	−0.682784	+	0.730620i	$0.739231\pi$
$191$	−22.8990	+	13.2207i	−1.65691	+	0.956619i	−0.974128	+	0.225999i	$0.927435\pi$
$192$	2.20204	+	1.27135i	0.158919	+	0.0917517i
$193$	−11.3485	+	19.6561i	−0.816881	+	1.41488i	0.0910889	+	0.995843i	$0.470965\pi$
$193$	−11.3485	+	19.6561i	−0.816881	+	1.41488i	−0.907970	+	0.419036i	$0.862368\pi$
$194$	−16.8990			−1.21328
$195$		−	1.41421i		−	0.101274i
$196$	−11.0000	+	8.66025i	−0.785714	+	0.618590i
$197$			0.921404i			0.0656473i	0.999461	+	0.0328236i	$0.0104500\pi$
$197$			0.921404i			0.0656473i	−0.999461	+	0.0328236i	$0.989550\pi$
$198$			20.0847i			1.42736i
$199$	−12.3485	+	21.3882i	−0.875360	+	1.51617i	−0.0189808	+	0.999820i	$0.506042\pi$
$199$	−12.3485	+	21.3882i	−0.875360	+	1.51617i	−0.856379	+	0.516348i	$0.827291\pi$
$200$	2.44949	+	1.41421i	0.173205	+	0.100000i
$201$	3.39898	−	1.96240i	0.239746	−	0.138417i
$202$	18.6742	+	10.7816i	1.31391	+	0.758589i
$203$	−6.27526	−	18.1151i	−0.440437	−	1.27143i
$204$	−1.55051	−	2.68556i	−0.108557	−	0.188027i
$205$	−6.94949	+	4.01229i	−0.485373	+	0.280230i
$206$	20.5732	−	11.8780i	1.43340	−	0.827576i
$207$	−11.4495	−	6.61037i	−0.795795	−	0.459452i
$208$	−17.7980			−1.23407
$209$			20.7846i			1.43770i
$210$	1.12372	−	0.389270i	0.0775443	−	0.0268622i
$211$	8.24745			0.567778			0.283889	−	0.958857i	$-0.408375\pi$
$211$	8.24745			0.567778			0.283889	+	0.958857i	$0.408375\pi$
$212$	3.55051	+	2.04989i	0.243850	+	0.140787i
$213$	−0.224745	+	0.389270i	−0.0153993	+	0.0266723i
$214$	−6.67423	+	3.85337i	−0.456241	+	0.263411i
$215$	4.72474	+	8.18350i	0.322225	+	0.558110i
$216$	5.30306			0.360828
$217$	0.775255	−	4.02834i	0.0526277	−	0.273462i
$218$	5.57321	−	9.65309i	0.377466	−	0.653790i
$219$	1.77526	+	3.07483i	0.119961	+	0.207778i
$220$	−9.79796			−0.660578
$221$	18.7980	+	10.8530i	1.26449	+	0.730052i
$222$			1.55708i			0.104504i
$223$	24.6969			1.65383			0.826915	−	0.562327i	$-0.190094\pi$
$223$	24.6969			1.65383			0.826915	+	0.562327i	$0.190094\pi$
$224$	−4.89898	−	14.1421i	−0.327327	−	0.944911i
$225$	2.89898			0.193265
$226$			11.9494i			0.794861i
$227$	−9.24745	−	5.33902i	−0.613775	−	0.354363i	0.160667	−	0.987009i	$-0.448636\pi$
$227$	−9.24745	−	5.33902i	−0.613775	−	0.354363i	−0.774441	+	0.632646i	$0.781969\pi$
$228$	2.69694			0.178609
$229$	8.34847	+	14.4600i	0.551682	+	0.955542i	0.998153	+	0.0607438i	$0.0193473\pi$
$229$	8.34847	+	14.4600i	0.551682	+	0.955542i	−0.446471	+	0.894798i	$0.647319\pi$
$230$	3.22474	−	5.58542i	0.212633	−	0.368292i
$231$	−2.69694	+	3.11416i	−0.177446	+	0.204896i
$232$	20.4949			1.34556
$233$	0.123724	+	0.214297i	0.00810545	+	0.0140391i	0.870050	−	0.492964i	$-0.164087\pi$
$233$	0.123724	+	0.214297i	0.00810545	+	0.0140391i	−0.861944	+	0.507003i	$0.830753\pi$
$234$	−15.7980	+	9.12096i	−1.03274	+	0.596256i
$235$	3.00000	−	5.19615i	0.195698	−	0.338960i
$236$	−6.24745	−	3.60697i	−0.406674	−	0.234794i
$237$	2.44949			0.159111
$238$	−3.44949	+	17.9241i	−0.223597	+	1.16185i
$239$		−	3.32124i		−	0.214833i	−0.994214	−	0.107416i	$-0.965742\pi$
$239$		−	3.32124i		−	0.214833i	0.994214	−	0.107416i	$-0.0342578\pi$
$240$			1.27135i			0.0820652i
$241$	−17.6969	−	10.2173i	−1.13996	−	0.658156i	−0.193539	−	0.981093i	$-0.561997\pi$
$241$	−17.6969	−	10.2173i	−1.13996	−	0.658156i	−0.946421	+	0.322936i	$0.895330\pi$
$242$	15.9217	−	9.19239i	1.02348	−	0.590909i
$243$	7.10102	−	4.09978i	0.455531	−	0.263001i
$244$	−0.348469	−	0.603566i	−0.0223085	−	0.0386394i
$245$	−6.50000	−	2.59808i	−0.415270	−	0.165985i
$246$	−3.12372	−	1.80348i	−0.199161	−	0.114986i
$247$	−16.3485	+	9.43879i	−1.04023	+	0.600576i
$248$	3.79796	+	2.19275i	0.241171	+	0.139240i
$249$	−0.297959	+	0.516080i	−0.0188824	+	0.0327052i
$250$			1.41421i			0.0894427i
$251$			13.7135i			0.865591i	0.901492	+	0.432796i	$0.142473\pi$
$251$			13.7135i			0.865591i	−0.901492	+	0.432796i	$0.857527\pi$
$252$	−11.5959	−	10.0424i	−0.730474	−	0.632609i
$253$			22.3417i			1.40461i
$254$	9.79796			0.614779
$255$	0.775255	−	1.34278i	0.0485484	−	0.0840882i
$256$	16.0000			1.00000
$257$	−11.4495	+	6.61037i	−0.714200	+	0.412343i	−0.812614	−	0.582802i	$-0.801956\pi$
$257$	−11.4495	+	6.61037i	−0.714200	+	0.412343i	0.0984145	+	0.995146i	$0.468623\pi$
$258$	−2.12372	+	3.67840i	−0.132217	+	0.229007i
$259$	6.00000	−	6.92820i	0.372822	−	0.430498i
$260$	−4.44949	−	7.70674i	−0.275946	−	0.477952i
$261$	18.1918	−	10.5031i	1.12605	−	0.650123i
$262$	−8.00000	−	13.8564i	−0.494242	−	0.856052i
$263$	4.74745	+	2.74094i	0.292740	+	0.169014i	0.639177	−	0.769060i	$-0.279275\pi$
$263$	4.74745	+	2.74094i	0.292740	+	0.169014i	−0.346437	+	0.938073i	$0.612608\pi$
$264$	−2.20204	−	3.81405i	−0.135526	−	0.234738i
$265$			2.04989i			0.125924i
$266$	−12.0000	−	10.3923i	−0.735767	−	0.637193i
$267$	−3.44949			−0.211105
$268$	12.3485	−	21.3882i	0.754303	−	1.30649i
$269$	−8.17423	+	14.1582i	−0.498392	+	0.863240i	−0.999998	−	0.00185590i	$-0.999409\pi$
$269$	−8.17423	+	14.1582i	−0.498392	+	0.863240i	0.501606	+	0.865096i	$0.332743\pi$
$270$	1.32577	+	2.29629i	0.0806835	+	0.139748i
$271$	1.67423	+	2.89986i	0.101703	+	0.176154i	0.912386	−	0.409330i	$-0.134238\pi$
$271$	1.67423	+	2.89986i	0.101703	+	0.176154i	−0.810684	+	0.585484i	$0.800904\pi$
$272$	−16.8990	−	9.75663i	−1.02465	−	0.591583i
$273$	−3.67423	−	0.707107i	−0.222375	−	0.0427960i
$274$	12.0000	+	6.92820i	0.724947	+	0.418548i
$275$	−2.44949	−	4.24264i	−0.147710	−	0.255841i
$276$	2.89898			0.174498
$277$	5.02270	+	2.89986i	0.301785	+	0.174236i	0.643245	−	0.765661i	$-0.277588\pi$
$277$	5.02270	+	2.89986i	0.301785	+	0.174236i	−0.341459	+	0.939896i	$0.610921\pi$
$278$	9.79796			0.587643
$279$	4.49490			0.269102
$280$	4.89898	−	5.65685i	0.292770	−	0.338062i
$281$	16.8990			1.00811			0.504054	−	0.863672i	$-0.331841\pi$
$281$	16.8990			1.00811			0.504054	+	0.863672i	$0.331841\pi$
$282$	2.69694			0.160600
$283$	−7.34847	−	4.24264i	−0.436821	−	0.252199i	0.265427	−	0.964131i	$-0.414487\pi$
$283$	−7.34847	−	4.24264i	−0.436821	−	0.252199i	−0.702248	+	0.711932i	$0.747820\pi$
$284$			2.82843i			0.167836i
$285$	0.674235	+	1.16781i	0.0399382	+	0.0691750i
$286$	26.6969	+	15.4135i	1.57862	+	0.911418i
$287$	6.94949	+	20.0614i	0.410215	+	1.18419i
$288$	14.2020	−	8.19955i	0.836863	−	0.483163i
$289$	3.39898	+	5.88721i	0.199940	+	0.346306i
$290$	5.12372	+	8.87455i	0.300875	+	0.521132i
$291$	1.89898	−	3.28913i	0.111320	−	0.192812i
$292$	19.3485	+	11.1708i	1.13228	+	0.653724i
$293$	−24.4949			−1.43101			−0.715504	−	0.698609i	$-0.753803\pi$
$293$	−24.4949			−1.43101			−0.715504	+	0.698609i	$0.753803\pi$
$294$	−0.449490	−	3.11416i	−0.0262148	−	0.181621i
$295$		−	3.60697i		−	0.210006i
$296$	4.89898	+	8.48528i	0.284747	+	0.493197i
$297$	−7.95459	−	4.59259i	−0.461572	−	0.266489i
$298$	13.5732	+	23.5095i	0.786275	+	1.36187i
$299$	−17.5732	+	10.1459i	−1.01629	+	0.586753i
$300$	−0.550510	+	0.317837i	−0.0317837	+	0.0183503i
$301$	23.6237	−	8.18350i	1.36165	−	0.471689i
$302$	5.44949	−	9.43879i	0.313583	−	0.543142i
$303$	−4.19694	+	2.42310i	−0.241108	+	0.139204i
$304$	14.6969	−	8.48528i	0.842927	−	0.486664i
$305$	0.174235	−	0.301783i	0.00997664	−	0.0172801i
$306$	−20.0000			−1.14332
$307$		−	27.9664i		−	1.59613i	−0.602572	−	0.798064i	$-0.705857\pi$
$307$		−	27.9664i		−	1.59613i	0.602572	−	0.798064i	$-0.294143\pi$
$308$	−4.89898	+	25.4558i	−0.279145	+	1.45048i
$309$			5.33902i			0.303726i
$310$			2.19275i			0.124540i
$311$	−5.57321	+	9.65309i	−0.316028	+	0.547377i	−0.979655	−	0.200687i	$-0.935683\pi$
$311$	−5.57321	+	9.65309i	−0.316028	+	0.547377i	0.663628	+	0.748063i	$0.269016\pi$
$312$	2.00000	−	3.46410i	0.113228	−	0.196116i
$313$	−5.69694	+	3.28913i	−0.322010	+	0.185913i	−0.652288	−	0.757971i	$-0.726191\pi$
$313$	−5.69694	+	3.28913i	−0.322010	+	0.185913i	0.330278	+	0.943884i	$0.392857\pi$
$314$	13.1010	+	7.56388i	0.739333	+	0.426854i
$315$	1.44949	−	7.53177i	0.0816695	−	0.424367i
$316$	13.3485	−	7.70674i	0.750910	−	0.433538i
$317$	0.426786	−	0.246405i	0.0239707	−	0.0138395i	−0.487967	−	0.872862i	$-0.662261\pi$
$317$	0.426786	−	0.246405i	0.0239707	−	0.0138395i	0.511937	+	0.859023i	$0.328928\pi$
$318$	−0.797959	+	0.460702i	−0.0447473	+	0.0258349i
$319$	−30.7423	−	17.7491i	−1.72124	−	0.993759i
$320$	4.00000	+	6.92820i	0.223607	+	0.387298i
$321$		−	1.73205i		−	0.0966736i
$322$	−12.8990	−	11.1708i	−0.718832	−	0.622527i
$323$	−20.6969			−1.15161
$324$	8.10102	−	14.0314i	0.450057	−	0.779521i
$325$	2.22474	−	3.85337i	0.123407	−	0.213747i
$326$	7.10102	−	4.09978i	0.393289	−	0.227066i
$327$	1.25255	+	2.16948i	0.0692662	+	0.119973i
$328$	−22.6969			−1.25323
$329$	−12.0000	−	10.3923i	−0.661581	−	0.572946i
$330$	1.10102	−	1.90702i	0.0606092	−	0.104978i
$331$	1.57321	+	2.72489i	0.0864717	+	0.149773i	0.906017	−	0.423240i	$-0.139107\pi$
$331$	1.57321	+	2.72489i	0.0864717	+	0.149773i	−0.819546	+	0.573014i	$0.805774\pi$
$332$			3.74983i			0.205799i
$333$	8.69694	+	5.02118i	0.476589	+	0.275159i
$334$		−	4.24264i		−	0.232147i
$335$	12.3485			0.674669
$336$	3.30306	+	0.635674i	0.180197	+	0.0346789i
$337$	20.2474			1.10295			0.551474	−	0.834192i	$-0.314065\pi$
$337$	20.2474			1.10295			0.551474	+	0.834192i	$0.314065\pi$
$338$			9.61377i			0.522920i
$339$	−2.32577	−	1.34278i	−0.126318	−	0.0729299i
$340$		−	9.75663i		−	0.529128i
$341$	−3.79796	−	6.57826i	−0.205671	−	0.356233i
$342$	8.69694	−	15.0635i	0.470277	−	0.814543i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$			26.7272i			1.44103i
$345$	0.724745	+	1.25529i	0.0390190	+	0.0675828i
$346$	13.3485	−	7.70674i	0.717618	−	0.414317i
$347$	3.82577	−	6.62642i	0.205378	−	0.355725i	−0.744875	−	0.667204i	$-0.767491\pi$
$347$	3.82577	−	6.62642i	0.205378	−	0.355725i	0.950253	+	0.311479i	$0.100824\pi$
$348$	−2.30306	+	3.98902i	−0.123457	+	0.213834i
$349$	7.24745			0.387947			0.193974	−	0.981007i	$-0.437862\pi$
$349$	7.24745			0.387947			0.193974	+	0.981007i	$0.437862\pi$
$350$	3.67423	+	0.707107i	0.196396	+	0.0377964i
$351$		−	8.34242i		−	0.445285i
$352$	−24.0000	−	13.8564i	−1.27920	−	0.738549i
$353$	29.8207	+	17.2170i	1.58719	+	0.916367i	0.993767	+	0.111479i	$0.0355587\pi$
$353$	29.8207	+	17.2170i	1.58719	+	0.916367i	0.593427	+	0.804888i	$0.297775\pi$
$354$	1.40408	−	0.810647i	0.0746261	−	0.0430854i
$355$	−1.22474	+	0.707107i	−0.0650027	+	0.0375293i
$356$	−18.7980	+	10.8530i	−0.996290	+	0.575208i
$357$	−3.10102	−	2.68556i	−0.164123	−	0.142135i
$358$	−11.6969	−	6.75323i	−0.618202	−	0.356919i
$359$	19.7753	−	11.4172i	1.04370	−	0.602579i	0.122820	−	0.992429i	$-0.460806\pi$
$359$	19.7753	−	11.4172i	1.04370	−	0.602579i	0.920879	+	0.389850i	$0.127473\pi$
$360$	7.10102	+	4.09978i	0.374257	+	0.216077i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$		−	17.4634i		−	0.917854i
$363$			4.13188i			0.216868i
$364$	−22.2474	+	7.70674i	−1.16608	+	0.403943i
$365$			11.1708i			0.584709i
$366$	0.156633			0.00818736
$367$	−4.05051	+	7.01569i	−0.211435	+	0.366216i	−0.952164	−	0.305588i	$-0.901147\pi$
$367$	−4.05051	+	7.01569i	−0.211435	+	0.366216i	0.740729	+	0.671804i	$0.234480\pi$
$368$	15.7980	−	9.12096i	0.823526	−	0.475463i
$369$	−20.1464	+	11.6315i	−1.04878	+	0.605514i
$370$	−2.44949	+	4.24264i	−0.127343	+	0.220564i
$371$	5.32577	+	1.02494i	0.276500	+	0.0532124i
$372$	−0.853572	+	0.492810i	−0.0442556	+	0.0255510i
$373$	−15.0000	+	8.66025i	−0.776671	+	0.448411i	−0.835249	−	0.549872i	$-0.814677\pi$
$373$	−15.0000	+	8.66025i	−0.776671	+	0.448411i	0.0585785	+	0.998283i	$0.481343\pi$
$374$	16.8990	+	29.2699i	0.873825	+	1.51351i
$375$	−0.275255	−	0.158919i	−0.0142141	−	0.00820652i
$376$	14.6969	−	8.48528i	0.757937	−	0.437595i
$377$		−	32.2412i		−	1.66051i
$378$	6.62883	−	2.29629i	0.340950	−	0.118109i
$379$	−17.3485			−0.891131			−0.445566	−	0.895249i	$-0.646997\pi$
$379$	−17.3485			−0.891131			−0.445566	+	0.895249i	$0.646997\pi$
$380$	7.34847	+	4.24264i	0.376969	+	0.217643i
$381$	−1.10102	+	1.90702i	−0.0564070	+	0.0976998i
$382$	−18.6969	−	32.3840i	−0.956619	−	1.65691i
$383$	−2.60102	−	4.50510i	−0.132906	−	0.230200i	0.791890	−	0.610664i	$-0.209097\pi$
$383$	−2.60102	−	4.50510i	−0.132906	−	0.230200i	−0.924796	+	0.380464i	$0.875764\pi$
$384$	−1.79796	+	3.11416i	−0.0917517	+	0.158919i
$385$	−12.2474	+	4.24264i	−0.624188	+	0.216225i
$386$	−27.7980	−	16.0492i	−1.41488	−	0.816881i
$387$	13.6969	+	23.7238i	0.696255	+	1.20595i
$388$		−	23.8988i		−	1.21328i
$389$	−9.79796	−	5.65685i	−0.496776	−	0.286814i	0.230605	−	0.973047i	$-0.425929\pi$
$389$	−9.79796	−	5.65685i	−0.496776	−	0.286814i	−0.727381	+	0.686234i	$0.759263\pi$
$390$	2.00000			0.101274
$391$	−22.2474			−1.12510
$392$	−12.2474	−	15.5563i	−0.618590	−	0.785714i
$393$	3.59592			0.181390
$394$	−1.30306			−0.0656473
$395$	6.67423	+	3.85337i	0.335817	+	0.193884i
$396$	−28.4041			−1.42736
$397$	−0.348469	−	0.603566i	−0.0174892	−	0.0302921i	0.857148	−	0.515070i	$-0.172234\pi$
$397$	−0.348469	−	0.603566i	−0.0174892	−	0.0302921i	−0.874638	+	0.484777i	$0.838901\pi$
$398$	−30.2474	−	17.4634i	−1.51617	−	0.875360i
$399$	3.37117	−	1.16781i	0.168770	−	0.0584636i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	15.3990	+	26.6718i	0.768988	+	1.33193i	0.938112	+	0.346332i	$0.112573\pi$
$401$	15.3990	+	26.6718i	0.768988	+	1.33193i	−0.169124	+	0.985595i	$0.554094\pi$
$402$	2.77526	+	4.80688i	0.138417	+	0.239746i
$403$	3.44949	−	5.97469i	0.171831	−	0.297621i
$404$	−15.2474	+	26.4094i	−0.758589	+	1.31391i
$405$	8.10102			0.402543
$406$	25.6186	−	8.87455i	1.27143	−	0.440437i
$407$		−	16.9706i		−	0.841200i
$408$	3.79796	−	2.19275i	0.188027	−	0.108557i
$409$	−10.1969	−	5.88721i	−0.504206	−	0.291104i	0.226243	−	0.974071i	$-0.427356\pi$
$409$	−10.1969	−	5.88721i	−0.504206	−	0.291104i	−0.730449	+	0.682967i	$0.760689\pi$
$410$	−5.67423	−	9.82806i	−0.280230	−	0.485373i
$411$	−2.69694	+	1.55708i	−0.133030	+	0.0768050i
$412$	16.7980	+	29.0949i	0.827576	+	1.43340i
$413$	−9.37117	−	1.80348i	−0.461125	−	0.0887436i
$414$	9.34847	−	16.1920i	0.459452	−	0.795795i
$415$	−1.62372	+	0.937458i	−0.0797055	+	0.0460180i
$416$		−	25.1701i		−	1.23407i
$417$	−1.10102	+	1.90702i	−0.0539172	+	0.0933873i
$418$	−29.3939			−1.43770
$419$		−	16.6848i		−	0.815107i	−0.913181	−	0.407554i	$-0.866382\pi$
$419$		−	16.6848i		−	0.815107i	0.913181	−	0.407554i	$-0.133618\pi$
$420$	0.550510	+	1.58919i	0.0268622	+	0.0775443i
$421$		−	4.06767i		−	0.198246i	−0.995075	−	0.0991230i	$-0.968396\pi$
$421$		−	4.06767i		−	0.198246i	0.995075	−	0.0991230i	$-0.0316037\pi$
$422$			11.6637i			0.567778i
$423$	8.69694	−	15.0635i	0.422860	−	0.732414i
$424$	−2.89898	+	5.02118i	−0.140787	+	0.243850i
$425$	4.22474	−	2.43916i	0.204930	−	0.118317i
$426$	−0.550510	−	0.317837i	−0.0266723	−	0.0153993i
$427$	−0.696938	−	0.603566i	−0.0337272	−	0.0292086i
$428$	−5.44949	−	9.43879i	−0.263411	−	0.456241i
$429$	−6.00000	+	3.46410i	−0.289683	+	0.167248i
$430$	−11.5732	+	6.68180i	−0.558110	+	0.322225i
$431$	8.20204	+	4.73545i	0.395078	+	0.228099i	0.684358	−	0.729146i	$-0.260082\pi$
$431$	8.20204	+	4.73545i	0.395078	+	0.228099i	−0.289280	+	0.957245i	$0.593416\pi$
$432$			7.49966i			0.360828i
$433$			7.70674i			0.370362i	0.982704	+	0.185181i	$0.0592872\pi$
$433$			7.70674i			0.370362i	−0.982704	+	0.185181i	$0.940713\pi$
$434$	5.69694	+	1.09638i	0.273462	+	0.0526277i
$435$	−2.30306			−0.110423
$436$	13.6515	+	7.88171i	0.653790	+	0.377466i
$437$	9.67423	−	16.7563i	0.462781	−	0.801561i
$438$	−4.34847	+	2.51059i	−0.207778	+	0.119961i
$439$	−5.55051	−	9.61377i	−0.264911	−	0.458840i	0.702629	−	0.711556i	$-0.252009\pi$
$439$	−5.55051	−	9.61377i	−0.264911	−	0.458840i	−0.967540	+	0.252716i	$0.918676\pi$
$440$		−	13.8564i		−	0.660578i
$441$	−18.8434	−	7.53177i	−0.897303	−	0.358656i
$442$	−15.3485	+	26.5843i	−0.730052	+	1.26449i
$443$	8.17423	+	14.1582i	0.388370	+	0.672676i	0.992230	−	0.124414i	$-0.0397051\pi$
$443$	8.17423	+	14.1582i	0.388370	+	0.672676i	−0.603861	+	0.797090i	$0.706372\pi$
$444$	−2.20204			−0.104504
$445$	−9.39898	−	5.42650i	−0.445554	−	0.257241i
$446$			34.9267i			1.65383i
$447$	−6.10102			−0.288568
$448$	20.0000	−	6.92820i	0.944911	−	0.327327i
$449$	−1.40408			−0.0662627			−0.0331314	−	0.999451i	$-0.510548\pi$
$449$	−1.40408			−0.0662627			−0.0331314	+	0.999451i	$0.510548\pi$
$450$			4.09978i			0.193265i
$451$	34.0454	+	19.6561i	1.60314	+	0.925571i
$452$	−16.8990			−0.794861
$453$	1.22474	+	2.12132i	0.0575435	+	0.0996683i
$454$	7.55051	−	13.0779i	0.354363	−	0.613775i
$455$	−8.89898	−	7.70674i	−0.417191	−	0.361298i
$456$			3.81405i			0.178609i
$457$	−4.79796	−	8.31031i	−0.224439	−	0.388740i	0.731712	−	0.681614i	$-0.238722\pi$
$457$	−4.79796	−	8.31031i	−0.224439	−	0.388740i	−0.956151	+	0.292874i	$0.905388\pi$
$458$	−20.4495	+	11.8065i	−0.955542	+	0.551682i
$459$	4.57321	−	7.92104i	0.213459	−	0.369722i
$460$	7.89898	+	4.56048i	0.368292	+	0.212633i
$461$	−38.6969			−1.80230			−0.901148	−	0.433511i	$-0.857274\pi$
$461$	−38.6969			−1.80230			−0.901148	+	0.433511i	$0.857274\pi$
$462$	−4.40408	−	3.81405i	−0.204896	−	0.177446i
$463$		−	12.1244i		−	0.563467i	−0.959493	−	0.281733i	$-0.909091\pi$
$463$		−	12.1244i		−	0.563467i	0.959493	−	0.281733i	$-0.0909093\pi$
$464$			28.9842i			1.34556i
$465$	−0.426786	−	0.246405i	−0.0197917	−	0.0114268i
$466$	−0.303062	+	0.174973i	−0.0140391	+	0.00810545i
$467$	−19.6237	+	11.3298i	−0.908078	+	0.524279i	−0.879812	−	0.475322i	$-0.842332\pi$
$467$	−19.6237	+	11.3298i	−0.908078	+	0.524279i	−0.0282655	+	0.999600i	$0.508998\pi$
$468$	−12.8990	−	22.3417i	−0.596256	−	1.03274i
$469$	6.17423	−	32.0823i	0.285100	−	1.48142i
$470$	7.34847	+	4.24264i	0.338960	+	0.195698i
$471$	−2.94439	+	1.69994i	−0.135670	+	0.0783292i
$472$	5.10102	−	8.83523i	0.234794	−	0.406674i
$473$	23.1464	−	40.0908i	1.06427	−	1.84338i
$474$			3.46410i			0.159111i
$475$			4.24264i			0.194666i
$476$	−25.3485	−	4.87832i	−1.16185	−	0.223597i
$477$			5.94258i			0.272092i
$478$	4.69694			0.214833
$479$	−4.22474	+	7.31747i	−0.193034	+	0.334344i	−0.946254	−	0.323424i	$-0.895166\pi$
$479$	−4.22474	+	7.31747i	−0.193034	+	0.334344i	0.753221	+	0.657768i	$0.228499\pi$
$480$	−1.79796			−0.0820652
$481$	13.3485	−	7.70674i	0.608638	−	0.351397i
$482$	14.4495	−	25.0273i	0.658156	−	1.13996i
$483$	3.62372	−	1.25529i	0.164885	−	0.0571179i
$484$	13.0000	+	22.5167i	0.590909	+	1.02348i
$485$	10.3485	−	5.97469i	0.469900	−	0.271297i
$486$	5.79796	+	10.0424i	0.263001	+	0.455531i
$487$	26.3939	+	15.2385i	1.19602	+	0.690523i	0.959666	−	0.281144i	$-0.0907138\pi$
$487$	26.3939	+	15.2385i	1.19602	+	0.690523i	0.236355	+	0.971667i	$0.424047\pi$
$488$	0.853572	−	0.492810i	0.0386394	−	0.0223085i
$489$			1.84281i			0.0833346i
$490$	3.67423	−	9.19239i	0.165985	−	0.415270i
$491$	0.853572			0.0385212			0.0192606	−	0.999814i	$-0.493869\pi$
$491$	0.853572			0.0385212			0.0192606	+	0.999814i	$0.493869\pi$
$492$	2.55051	−	4.41761i	0.114986	−	0.199161i
$493$	17.6742	−	30.6127i	0.796007	−	1.37873i
$494$	−13.3485	−	23.1202i	−0.600576	−	1.04023i
$495$	−7.10102	−	12.2993i	−0.319167	−	0.552814i
$496$	−3.10102	+	5.37113i	−0.139240	+	0.241171i
$497$	1.22474	+	3.53553i	0.0549373	+	0.158590i
$498$	−0.729847	−	0.421378i	−0.0327052	−	0.0188824i
$499$	13.6969	+	23.7238i	0.613159	+	1.06202i	0.990704	+	0.136032i	$0.0434349\pi$
$499$	13.6969	+	23.7238i	0.613159	+	1.06202i	−0.377545	+	0.925991i	$0.623232\pi$
$500$	−2.00000			−0.0894427
$501$	0.825765	+	0.476756i	0.0368925	+	0.0212999i
$502$	−19.3939			−0.865591
$503$	23.6969			1.05659			0.528297	−	0.849060i	$-0.322831\pi$
$503$	23.6969			1.05659			0.528297	+	0.849060i	$0.322831\pi$
$504$	14.2020	−	16.3991i	0.632609	−	0.730474i
$505$	−15.2474			−0.678503
$506$	−31.5959			−1.40461
$507$	−1.87117	−	1.08032i	−0.0831017	−	0.0479788i
$508$			13.8564i			0.614779i
$509$	−8.72474	−	15.1117i	−0.386718	−	0.669814i	0.605288	−	0.796006i	$-0.293058\pi$
$509$	−8.72474	−	15.1117i	−0.386718	−	0.669814i	−0.992006	+	0.126192i	$0.959724\pi$
$510$	1.89898	+	1.09638i	0.0840882	+	0.0485484i
$511$	29.0227	+	5.58542i	1.28389	+	0.247085i
$512$			22.6274i			1.00000i
$513$	3.97730	+	6.88888i	0.175602	+	0.304151i
$514$	−9.34847	−	16.1920i	−0.412343	−	0.714200i
$515$	−8.39898	+	14.5475i	−0.370103	+	0.641038i
$516$	−5.20204	−	3.00340i	−0.229007	−	0.132217i
$517$	−29.3939			−1.29274
$518$	9.79796	+	8.48528i	0.430498	+	0.372822i
$519$			3.46410i			0.152057i
$520$	10.8990	−	6.29253i	0.477952	−	0.275946i
$521$	−9.24745	−	5.33902i	−0.405138	−	0.233907i	0.283560	−	0.958954i	$-0.408484\pi$
$521$	−9.24745	−	5.33902i	−0.405138	−	0.233907i	−0.688699	+	0.725048i	$0.741818\pi$
$522$	14.8536	+	25.7271i	0.650123	+	1.12605i
$523$	−10.3485	+	5.97469i	−0.452507	+	0.261255i	−0.708888	−	0.705321i	$-0.750803\pi$
$523$	−10.3485	+	5.97469i	−0.452507	+	0.261255i	0.256381	+	0.966576i	$0.417470\pi$
$524$	19.5959	−	11.3137i	0.856052	−	0.494242i
$525$	−0.550510	+	0.635674i	−0.0240262	+	0.0277431i
$526$	−3.87628	+	6.71391i	−0.169014	+	0.292740i
$527$	6.55051	−	3.78194i	0.285345	−	0.164744i
$528$	5.39388	−	3.11416i	0.234738	−	0.135526i
$529$	−1.10102	+	1.90702i	−0.0478705	+	0.0829141i
$530$	−2.89898			−0.125924
$531$		−	10.4565i		−	0.453774i
$532$	14.6969	−	16.9706i	0.637193	−	0.735767i
$533$			35.7053i			1.54657i
$534$		−	4.87832i		−	0.211105i
$535$	2.72474	−	4.71940i	0.117801	−	0.204037i
$536$	30.2474	+	17.4634i	1.30649	+	0.754303i
$537$	2.62883	−	1.51775i	0.113442	−	0.0654959i
$538$	−20.0227	−	11.5601i	−0.863240	−	0.498392i
$539$	4.89898	+	33.9411i	0.211014	+	1.46195i
$540$	−3.24745	+	1.87492i	−0.139748	+	0.0806835i
$541$	24.5227	−	14.1582i	1.05431	−	0.608708i	0.130460	−	0.991454i	$-0.458355\pi$
$541$	24.5227	−	14.1582i	1.05431	−	0.608708i	0.923854	+	0.382746i	$0.125021\pi$
$542$	−4.10102	+	2.36773i	−0.176154	+	0.101703i
$543$	3.39898	+	1.96240i	0.145864	+	0.0842147i
$544$	13.7980	−	23.8988i	0.591583	−	1.02465i
$545$			7.88171i			0.337616i
$546$	1.00000	−	5.19615i	0.0427960	−	0.222375i
$547$	9.04541			0.386754			0.193377	−	0.981125i	$-0.438056\pi$
$547$	9.04541			0.386754			0.193377	+	0.981125i	$0.438056\pi$
$548$	−9.79796	+	16.9706i	−0.418548	+	0.724947i
$549$	0.505103	−	0.874863i	0.0215573	−	0.0373383i
$550$	6.00000	−	3.46410i	0.255841	−	0.147710i
$551$	15.3712	+	26.6237i	0.654834	+	1.13421i
$552$			4.09978i			0.174498i
$553$	13.3485	−	15.4135i	0.567635	−	0.655448i
$554$	−4.10102	+	7.10318i	−0.174236	+	0.301785i
$555$	−0.550510	−	0.953512i	−0.0233679	−	0.0404743i
$556$			13.8564i			0.587643i
$557$	13.8990	+	8.02458i	0.588919	+	0.340012i	0.764670	−	0.644422i	$-0.222902\pi$
$557$	13.8990	+	8.02458i	0.588919	+	0.340012i	−0.175751	+	0.984435i	$0.556235\pi$
$558$			6.35674i			0.269102i
$559$	42.0454			1.77833
$560$	8.00000	+	6.92820i	0.338062	+	0.292770i
$561$	−7.59592			−0.320700
$562$			23.8988i			1.00811i
$563$	16.6237	+	9.59771i	0.700606	+	0.404495i	0.807573	−	0.589767i	$-0.200781\pi$
$563$	16.6237	+	9.59771i	0.700606	+	0.404495i	−0.106967	+	0.994263i	$0.534114\pi$
$564$			3.81405i			0.160600i
$565$	−4.22474	−	7.31747i	−0.177736	−	0.307848i
$566$	6.00000	−	10.3923i	0.252199	−	0.436821i
$567$	4.05051	−	21.0471i	0.170105	−	0.883894i
$568$	−4.00000			−0.167836
$569$	−20.6969	−	35.8481i	−0.867661	−	1.50283i	−0.864381	−	0.502838i	$-0.832289\pi$
$569$	−20.6969	−	35.8481i	−0.867661	−	1.50283i	−0.00328010	−	0.999995i	$-0.501044\pi$
$570$	−1.65153	+	0.953512i	−0.0691750	+	0.0399382i
$571$	−5.22474	+	9.04952i	−0.218649	+	0.378711i	−0.954395	−	0.298546i	$-0.903498\pi$
$571$	−5.22474	+	9.04952i	−0.218649	+	0.378711i	0.735746	+	0.677257i	$0.236832\pi$
$572$	−21.7980	+	37.7552i	−0.911418	+	1.57862i
$573$	8.40408			0.351086
$574$	−28.3712	+	9.82806i	−1.18419	+	0.410215i
$575$			4.56048i			0.190185i
$576$	11.5959	+	20.0847i	0.483163	+	0.836863i
$577$	25.3485	+	14.6349i	1.05527	+	0.609261i	0.924120	−	0.382102i	$-0.124800\pi$
$577$	25.3485	+	14.6349i	1.05527	+	0.609261i	0.131150	+	0.991362i	$0.458133\pi$
$578$	−8.32577	+	4.80688i	−0.346306	+	0.199940i
$579$	6.24745	−	3.60697i	0.259635	−	0.149900i
$580$	−12.5505	+	7.24604i	−0.521132	+	0.300875i
$581$	1.62372	+	4.68729i	0.0673634	+	0.194461i
$582$	4.65153	+	2.68556i	0.192812	+	0.111320i
$583$	8.69694	−	5.02118i	0.360190	−	0.207956i
$584$	−15.7980	+	27.3629i	−0.653724	+	1.13228i
$585$	6.44949	−	11.1708i	0.266654	−	0.461858i
$586$		−	34.6410i		−	1.43101i
$587$			5.30691i			0.219040i	0.993985	+	0.109520i	$0.0349313\pi$
$587$			5.30691i			0.219040i	−0.993985	+	0.109520i	$0.965069\pi$
$588$	4.40408	−	0.635674i	0.181621	−	0.0262148i
$589$			6.57826i			0.271052i
$590$	5.10102			0.210006
$591$	0.146428	−	0.253621i	0.00602325	−	0.0104326i
$592$	−12.0000	+	6.92820i	−0.493197	+	0.284747i
$593$	8.57321	−	4.94975i	0.352060	−	0.203262i	−0.313532	−	0.949578i	$-0.601512\pi$
$593$	8.57321	−	4.94975i	0.352060	−	0.203262i	0.665592	+	0.746316i	$0.268179\pi$
$594$	6.49490	−	11.2495i	0.266489	−	0.461572i
$595$	−4.22474	−	12.1958i	−0.173198	−	0.499979i
$596$	−33.2474	+	19.1954i	−1.36187	+	0.786275i
$597$	6.79796	−	3.92480i	0.278222	−	0.160632i
$598$	−14.3485	−	24.8523i	−0.586753	−	1.01629i
$599$	−11.1464	−	6.43539i	−0.455431	−	0.262943i	0.254690	−	0.967023i	$-0.418026\pi$
$599$	−11.1464	−	6.43539i	−0.455431	−	0.262943i	−0.710121	+	0.704080i	$0.751360\pi$
$600$	−0.449490	−	0.778539i	−0.0183503	−	0.0317837i
$601$		−	25.8058i		−	1.05264i	−0.850287	−	0.526320i	$-0.823571\pi$
$601$		−	25.8058i		−	1.05264i	0.850287	−	0.526320i	$-0.176429\pi$
$602$	11.5732	+	33.4090i	0.471689	+	1.36165i
$603$	35.7980			1.45781
$604$	13.3485	+	7.70674i	0.543142	+	0.313583i
$605$	−6.50000	+	11.2583i	−0.264263	+	0.457716i
$606$	−3.42679	−	5.93537i	−0.139204	−	0.241108i
$607$	−10.8485	−	18.7901i	−0.440326	−	0.762667i	0.557388	−	0.830252i	$-0.311804\pi$
$607$	−10.8485	−	18.7901i	−0.440326	−	0.762667i	−0.997713	+	0.0675857i	$0.978470\pi$
$608$	12.0000	+	20.7846i	0.486664	+	0.842927i
$609$	−1.15153	+	5.98353i	−0.0466624	+	0.242465i
$610$	0.426786	+	0.246405i	0.0172801	+	0.00997664i
$611$	−13.3485	−	23.1202i	−0.540021	−	0.935344i
$612$		−	28.2843i		−	1.14332i
$613$	0.674235	+	0.389270i	0.0272321	+	0.0157224i	0.513554	−	0.858057i	$-0.328329\pi$
$613$	0.674235	+	0.389270i	0.0272321	+	0.0157224i	−0.486322	+	0.873780i	$0.661662\pi$
$614$	39.5505			1.59613
$615$	2.55051			0.102846
$616$	−36.0000	−	6.92820i	−1.45048	−	0.279145i
$617$	3.30306			0.132976			0.0664881	−	0.997787i	$-0.478821\pi$
$617$	3.30306			0.132976			0.0664881	+	0.997787i	$0.478821\pi$
$618$	−7.55051			−0.303726
$619$	−13.3485	−	7.70674i	−0.536520	−	0.309760i	0.207147	−	0.978310i	$-0.433582\pi$
$619$	−13.3485	−	7.70674i	−0.536520	−	0.309760i	−0.743668	+	0.668550i	$0.766915\pi$
$620$	−3.10102			−0.124540
$621$	4.27526	+	7.40496i	0.171560	+	0.297151i
$622$	−13.6515	−	7.88171i	−0.547377	−	0.316028i
$623$	−18.7980	+	21.7060i	−0.753124	+	0.869633i
$624$	4.89898	+	2.82843i	0.196116	+	0.113228i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.65153	−	8.05669i	−0.185913	−	0.322010i
$627$	3.30306	−	5.72107i	0.131912	−	0.228478i
$628$	−10.6969	+	18.5276i	−0.426854	+	0.739333i
$629$	16.8990			0.673806
$630$	10.6515	+	2.04989i	0.424367	+	0.0816695i
$631$		−	39.3123i		−	1.56500i	−0.622653	−	0.782498i	$-0.713945\pi$
$631$		−	39.3123i		−	1.56500i	0.622653	−	0.782498i	$-0.286055\pi$
$632$	10.8990	+	18.8776i	0.433538	+	0.750910i
$633$	−2.27015	−	1.31067i	−0.0902305	−	0.0520946i
$634$	0.348469	+	0.603566i	0.0138395	+	0.0239707i
$635$	−6.00000	+	3.46410i	−0.238103	+	0.137469i
$636$	−0.651531	−	1.12848i	−0.0258349	−	0.0447473i
$637$	−24.4722	+	19.2669i	−0.969624	+	0.763381i
$638$	25.1010	−	43.4762i	0.993759	−	1.72124i
$639$	−3.55051	+	2.04989i	−0.140456	+	0.0810923i
$640$	−9.79796	+	5.65685i	−0.387298	+	0.223607i
$641$	21.6464	−	37.4927i	0.854983	−	1.48087i	−0.0216787	−	0.999765i	$-0.506901\pi$
$641$	21.6464	−	37.4927i	0.854983	−	1.48087i	0.876661	−	0.481108i	$-0.159766\pi$
$642$	2.44949			0.0966736
$643$			6.57826i			0.259421i	0.991552	+	0.129711i	$0.0414048\pi$
$643$			6.57826i			0.259421i	−0.991552	+	0.129711i	$0.958595\pi$
$644$	15.7980	−	18.2419i	0.622527	−	0.718832i
$645$		−	3.00340i		−	0.118259i
$646$		−	29.2699i		−	1.15161i
$647$	−5.29796	+	9.17633i	−0.208284	+	0.360759i	−0.951174	−	0.308655i	$-0.900121\pi$
$647$	−5.29796	+	9.17633i	−0.208284	+	0.360759i	0.742890	+	0.669414i	$0.233455\pi$
$648$	19.8434	+	11.4566i	0.779521	+	0.450057i
$649$	−15.3031	+	8.83523i	−0.600698	+	0.346813i
$650$	5.44949	+	3.14626i	0.213747	+	0.123407i
$651$	−0.853572	+	0.985620i	−0.0334541	+	0.0386295i
$652$	5.79796	+	10.0424i	0.227066	+	0.393289i
$653$	16.7753	−	9.68520i	0.656466	−	0.379011i	−0.134463	−	0.990919i	$-0.542931\pi$
$653$	16.7753	−	9.68520i	0.656466	−	0.379011i	0.790929	+	0.611908i	$0.209598\pi$
$654$	−3.06811	+	1.77138i	−0.119973	+	0.0692662i
$655$	9.79796	+	5.65685i	0.382838	+	0.221032i
$656$		−	32.0983i		−	1.25323i
$657$			32.3840i			1.26342i
$658$	14.6969	−	16.9706i	0.572946	−	0.661581i
$659$	−36.7423			−1.43128			−0.715639	−	0.698470i	$-0.753865\pi$
$659$	−36.7423			−1.43128			−0.715639	+	0.698470i	$0.753865\pi$
$660$	2.69694	+	1.55708i	0.104978	+	0.0606092i
$661$	−24.8712	+	43.0781i	−0.967377	+	1.67555i	−0.264287	+	0.964444i	$0.585137\pi$
$661$	−24.8712	+	43.0781i	−0.967377	+	1.67555i	−0.703090	+	0.711101i	$0.748197\pi$
$662$	−3.85357	+	2.22486i	−0.149773	+	0.0864717i
$663$	−3.44949	−	5.97469i	−0.133967	−	0.232038i
$664$	−5.30306			−0.205799
$665$	11.0227	+	2.12132i	0.427442	+	0.0822613i
$666$	−7.10102	+	12.2993i	−0.275159	+	0.476589i
$667$	16.5227	+	28.6182i	0.639762	+	1.10810i
$668$	6.00000			0.232147
$669$	−6.79796	−	3.92480i	−0.262824	−	0.151742i
$670$			17.4634i			0.674669i
$671$	−1.70714			−0.0659035
$672$	−0.898979	+	4.67123i	−0.0346789	+	0.180197i
$673$	−26.8990			−1.03688			−0.518440	−	0.855114i	$-0.673487\pi$
$673$	−26.8990			−1.03688			−0.518440	+	0.855114i	$0.673487\pi$
$674$			28.6342i			1.10295i
$675$	−1.62372	−	0.937458i	−0.0624972	−	0.0360828i
$676$	−13.5959			−0.522920
$677$	15.6742	+	27.1486i	0.602410	+	1.04340i	0.992455	+	0.122609i	$0.0391260\pi$
$677$	15.6742	+	27.1486i	0.602410	+	1.04340i	−0.390045	+	0.920796i	$0.627541\pi$
$678$	1.89898	−	3.28913i	0.0729299	−	0.126318i
$679$	−10.3485	−	29.8735i	−0.397138	−	1.14644i
$680$	13.7980			0.529128
$681$	1.69694	+	2.93918i	0.0650268	+	0.112630i
$682$	9.30306	−	5.37113i	0.356233	−	0.205671i
$683$	5.72474	−	9.91555i	0.219051	−	0.379408i	−0.735467	−	0.677561i	$-0.763037\pi$
$683$	5.72474	−	9.91555i	0.219051	−	0.379408i	0.954518	+	0.298153i	$0.0963705\pi$
$684$	21.3031	+	12.2993i	0.814543	+	0.470277i
$685$	−9.79796			−0.374361
$686$	−22.0454	−	14.1421i	−0.841698	−	0.539949i
$687$		−	5.30691i		−	0.202471i
$688$	−37.7980			−1.44103
$689$	7.89898	+	4.56048i	0.300927	+	0.173740i
$690$	−1.77526	+	1.02494i	−0.0675828	+	0.0390190i
$691$	−27.0000	+	15.5885i	−1.02713	+	0.593013i	−0.916161	−	0.400811i	$-0.868728\pi$
$691$	−27.0000	+	15.5885i	−1.02713	+	0.593013i	−0.110968	+	0.993824i	$0.535395\pi$
$692$	10.8990	+	18.8776i	0.414317	+	0.717618i
$693$	−35.5051	+	12.2993i	−1.34873	+	0.467213i
$694$	9.37117	+	5.41045i	0.355725	+	0.205378i
$695$	−6.00000	+	3.46410i	−0.227593	+	0.131401i
$696$	−5.64133	−	3.25702i	−0.213834	−	0.123457i
$697$	−19.5732	+	33.9018i	−0.741388	+	1.28412i
$698$			10.2494i			0.387947i
$699$		−	0.0786484i		−	0.00297476i
$700$	−1.00000	+	5.19615i	−0.0377964	+	0.196396i
$701$		−	23.5809i		−	0.890639i	−0.895372	−	0.445320i	$-0.853090\pi$
$701$		−	23.5809i		−	0.890639i	0.895372	−	0.445320i	$-0.146910\pi$
$702$	11.7980			0.445285
$703$	−7.34847	+	12.7279i	−0.277153	+	0.480043i
$704$	19.5959	−	33.9411i	0.738549	−	1.27920i
$705$	−1.65153	+	0.953512i	−0.0622002	+	0.0359113i
$706$	−24.3485	+	42.1728i	−0.916367	+	1.58719i
$707$	−7.62372	+	39.6140i	−0.286720	+	1.48984i
$708$	1.14643	+	1.98567i	0.0430854	+	0.0746261i
$709$	9.21964	−	5.32296i	0.346251	−	0.199908i	−0.316782	−	0.948498i	$-0.602602\pi$
$709$	9.21964	−	5.32296i	0.346251	−	0.199908i	0.663033	+	0.748590i	$0.269269\pi$
$710$	−1.00000	−	1.73205i	−0.0375293	−	0.0650027i
$711$	19.3485	+	11.1708i	0.725624	+	0.418939i
$712$	−15.3485	−	26.5843i	−0.575208	−	0.996290i
$713$			7.07107i			0.264814i
$714$	3.79796	−	4.38551i	0.142135	−	0.164123i
$715$	−21.7980			−0.815197
$716$	9.55051	−	16.5420i	0.356919	−	0.618202i
$717$	−0.527806	+	0.914188i	−0.0197113	+	0.0341410i
$718$	16.1464	+	27.9664i	0.602579	+	1.04370i
$719$	19.5959	+	33.9411i	0.730804	+	1.26579i	0.956540	+	0.291602i	$0.0941882\pi$
$719$	19.5959	+	33.9411i	0.730804	+	1.26579i	−0.225735	+	0.974189i	$0.572478\pi$
$720$	−5.79796	+	10.0424i	−0.216077	+	0.374257i
$721$	33.5959	+	29.0949i	1.25118	+	1.08355i
$722$	−1.22474	−	0.707107i	−0.0455803	−	0.0263158i
$723$	3.24745	+	5.62475i	0.120774	+	0.209187i
$724$	24.6969			0.917854
$725$	−6.27526	−	3.62302i	−0.233057	−	0.134556i
$726$	−5.84337			−0.216868
$727$	14.5959			0.541333			0.270666	−	0.962673i	$-0.412756\pi$
$727$	14.5959			0.541333			0.270666	+	0.962673i	$0.412756\pi$
$728$	−10.8990	−	31.4626i	−0.403943	−	1.16608i
$729$	21.6969			0.803590
$730$	−15.7980			−0.584709
$731$	39.9217	+	23.0488i	1.47656	+	0.852490i
$732$			0.221513i			0.00818736i
$733$	−8.55051	−	14.8099i	−0.315820	−	0.547017i	0.663791	−	0.747918i	$-0.268946\pi$
$733$	−8.55051	−	14.8099i	−0.315820	−	0.547017i	−0.979612	+	0.200901i	$0.935613\pi$
$734$	−9.92168	−	5.72829i	−0.366216	−	0.211435i
$735$	1.37628	+	1.74810i	0.0507647	+	0.0644798i
$736$	12.8990	+	22.3417i	0.475463	+	0.823526i
$737$	−30.2474	−	52.3901i	−1.11418	−	1.92981i
$738$	−16.4495	−	28.4914i	−0.605514	−	1.04878i
$739$	0.348469	−	0.603566i	0.0128186	−	0.0222025i	−0.859545	−	0.511060i	$-0.829253\pi$
$739$	0.348469	−	0.603566i	0.0128186	−	0.0222025i	0.872364	+	0.488858i	$0.162586\pi$
$740$	−6.00000	−	3.46410i	−0.220564	−	0.127343i
$741$	6.00000			0.220416
$742$	−1.44949	+	7.53177i	−0.0532124	+	0.276500i
$743$			51.1509i			1.87654i	0.345899	+	0.938272i	$0.387574\pi$
$743$			51.1509i			1.87654i	−0.345899	+	0.938272i	$0.612426\pi$
$744$	−0.696938	−	1.20713i	−0.0255510	−	0.0442556i
$745$	−16.6237	−	9.59771i	−0.609046	−	0.351633i
$746$	−12.2474	−	21.2132i	−0.448411	−	0.776671i
$747$	−4.70714	+	2.71767i	−0.172225	+	0.0994344i
$748$	−41.3939	+	23.8988i	−1.51351	+	0.873825i
$749$	−10.8990	−	9.43879i	−0.398240	−	0.344886i
$750$	0.224745	−	0.389270i	0.00820652	−	0.0142141i
$751$	−43.0454	+	24.8523i	−1.57075	+	0.906872i	−0.574672	+	0.818384i	$0.694870\pi$
$751$	−43.0454	+	24.8523i	−1.57075	+	0.906872i	−0.996077	+	0.0884887i	$0.971796\pi$
$752$	12.0000	+	20.7846i	0.437595	+	0.757937i
$753$	2.17934	−	3.77472i	0.0794195	−	0.137559i
$754$	45.5959			1.66051
$755$			7.70674i			0.280477i
$756$	3.24745	+	9.37458i	0.118109	+	0.340950i
$757$		−	33.5125i		−	1.21803i	−0.793157	−	0.609017i	$-0.791564\pi$
$757$		−	33.5125i		−	1.21803i	0.793157	−	0.609017i	$-0.208436\pi$
$758$		−	24.5344i		−	0.891131i
$759$	3.55051	−	6.14966i	0.128875	−	0.223219i
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	10.5959	−	6.11756i	0.384102	−	0.221761i	−0.295500	−	0.955343i	$-0.595486\pi$
$761$	10.5959	−	6.11756i	0.384102	−	0.221761i	0.679601	+	0.733582i	$0.262153\pi$
$762$	−2.69694	−	1.55708i	−0.0976998	−	0.0564070i
$763$	20.4773	+	3.94086i	0.741328	+	0.142669i
$764$	45.7980	−	26.4415i	1.65691	−	0.956619i
$765$	12.2474	−	7.07107i	0.442807	−	0.255655i
$766$	6.37117	−	3.67840i	0.230200	−	0.132906i
$767$	−13.8990	−	8.02458i	−0.501863	−	0.289751i
$768$	−4.40408	−	2.54270i	−0.158919	−	0.0917517i
$769$		−	46.5904i		−	1.68009i	−0.542515	−	0.840046i	$-0.682528\pi$
$769$		−	46.5904i		−	1.68009i	0.542515	−	0.840046i	$-0.317472\pi$
$770$	−6.00000	−	17.3205i	−0.216225	−	0.624188i
$771$	4.20204			0.151333
$772$	22.6969	−	39.3123i	0.816881	−	1.41488i
$773$	−5.87628	+	10.1780i	−0.211355	+	0.366078i	−0.952139	−	0.305666i	$-0.901121\pi$
$773$	−5.87628	+	10.1780i	−0.211355	+	0.366078i	0.740784	+	0.671743i	$0.234454\pi$
$774$	−33.5505	+	19.3704i	−1.20595	+	0.696255i
$775$	−0.775255	−	1.34278i	−0.0278480	−	0.0482341i
$776$	33.7980			1.21328
$777$	−2.75255	+	0.953512i	−0.0987472	+	0.0342070i
$778$	8.00000	−	13.8564i	0.286814	−	0.496776i
$779$	−17.0227	−	29.4842i	−0.609902	−	1.05638i
$780$			2.82843i			0.101274i
$781$	6.00000	+	3.46410i	0.214697	+	0.123955i
$782$		−	31.4626i		−	1.12510i
$783$	−13.5857			−0.485514
$784$	22.0000	−	17.3205i	0.785714	−	0.618590i
$785$	−10.6969			−0.381790
$786$			5.08540i			0.181390i
$787$	−7.87117	−	4.54442i	−0.280577	−	0.161991i	0.353108	−	0.935583i	$-0.385125\pi$
$787$	−7.87117	−	4.54442i	−0.280577	−	0.161991i	−0.633685	+	0.773592i	$0.718458\pi$
$788$		−	1.84281i		−	0.0656473i
$789$	−0.871173	−	1.50892i	−0.0310146	−	0.0537188i
$790$	−5.44949	+	9.43879i	−0.193884	+	0.335817i
$791$	−21.1237	+	7.31747i	−0.751073	+	0.260179i
$792$		−	40.1694i		−	1.42736i
$793$	−0.775255	−	1.34278i	−0.0275301	−	0.0476836i
$794$	0.853572	−	0.492810i	0.0302921	−	0.0174892i
$795$	0.325765	−	0.564242i	0.0115537	−	0.0200116i
$796$	24.6969	−	42.7764i	0.875360	−	1.51617i
$797$	−3.30306			−0.117000			−0.0585002	−	0.998287i	$-0.518632\pi$
$797$	−3.30306			−0.117000			−0.0585002	+	0.998287i	$0.518632\pi$
$798$	1.65153	+	4.76756i	0.0584636	+	0.168770i
$799$		−	29.2699i		−	1.03549i
$800$	−4.89898	−	2.82843i	−0.173205	−	0.100000i
$801$	−27.2474	−	15.7313i	−0.962741	−	0.555839i
$802$	−37.7196	+	21.7774i	−1.33193	+	0.768988i
$803$	47.3939	−	27.3629i	1.67249	−	0.965615i
$804$	−6.79796	+	3.92480i	−0.239746	+	0.138417i
$805$	11.8485	+	2.28024i	0.417604	+	0.0803679i
$806$	8.44949	+	4.87832i	0.297621	+	0.171831i
$807$	4.50000	−	2.59808i	0.158408	−	0.0914566i
$808$	−37.3485	−	21.5631i	−1.31391	−	0.758589i
$809$	6.39898	−	11.0834i	0.224976	−	0.389670i	−0.731336	−	0.682017i	$-0.761103\pi$
$809$	6.39898	−	11.0834i	0.224976	−	0.389670i	0.956312	+	0.292347i	$0.0944363\pi$
$810$			11.4566i			0.402543i
$811$		−	47.3689i		−	1.66335i	−0.555264	−	0.831674i	$-0.687383\pi$
$811$		−	47.3689i		−	1.66335i	0.555264	−	0.831674i	$-0.312617\pi$
$812$	12.5505	+	36.2302i	0.440437	+	1.27143i
$813$		−	1.06427i		−	0.0373255i
$814$	24.0000			0.841200
$815$	−2.89898	+	5.02118i	−0.101547	+	0.175884i
$816$	3.10102	+	5.37113i	0.108557	+	0.188027i
$817$	−34.7196	+	20.0454i	−1.21469	+	0.701300i
$818$	8.32577	−	14.4206i	0.291104	−	0.504206i
$819$	−25.7980	−	22.3417i	−0.901454	−	0.780682i
$820$	13.8990	−	8.02458i	0.485373	−	0.280230i
$821$	−43.2929	+	24.9951i	−1.51093	+	0.872336i	−0.511013	+	0.859573i	$0.670729\pi$
$821$	−43.2929	+	24.9951i	−1.51093	+	0.872336i	−0.999919	+	0.0127632i	$0.995937\pi$
$822$	−2.20204	−	3.81405i	−0.0768050	−	0.133030i
$823$	9.15153	+	5.28364i	0.319002	+	0.184176i	0.650948	−	0.759123i	$-0.274372\pi$
$823$	9.15153	+	5.28364i	0.319002	+	0.184176i	−0.331945	+	0.943299i	$0.607705\pi$
$824$	−41.1464	+	23.7559i	−1.43340	+	0.827576i
$825$			1.55708i			0.0542105i
$826$	2.55051	−	13.2528i	0.0887436	−	0.461125i
$827$	−13.0454			−0.453633			−0.226817	−	0.973937i	$-0.572832\pi$
$827$	−13.0454			−0.453633			−0.226817	+	0.973937i	$0.572832\pi$
$828$	22.8990	+	13.2207i	0.795795	+	0.459452i
$829$	−12.6515	+	21.9131i	−0.439406	+	0.761073i	−0.997644	−	0.0686077i	$-0.978144\pi$
$829$	−12.6515	+	21.9131i	−0.439406	+	0.761073i	0.558238	+	0.829681i	$0.311478\pi$
$830$	−1.32577	−	2.29629i	−0.0460180	−	0.0797055i
$831$	−0.921683	−	1.59640i	−0.0319728	−	0.0553786i
$832$	35.5959			1.23407
$833$	−33.7980	+	4.87832i	−1.17103	+	0.169024i
$834$	−2.69694	−	1.55708i	−0.0933873	−	0.0539172i
$835$	1.50000	+	2.59808i	0.0519096	+	0.0899101i
$836$		−	41.5692i		−	1.43770i
$837$	−2.51760	−	1.45354i	−0.0870210	−	0.0502416i
$838$	23.5959			0.815107
$839$	−30.4949			−1.05280			−0.526400	−	0.850237i	$-0.676459\pi$
$839$	−30.4949			−1.05280			−0.526400	+	0.850237i	$0.676459\pi$
$840$	−2.24745	+	0.778539i	−0.0775443	+	0.0268622i
$841$	−23.5051			−0.810521
$842$	5.75255			0.198246
$843$	−4.65153	−	2.68556i	−0.160207	−	0.0924957i
$844$	−16.4949			−0.567778
$845$	−3.39898	−	5.88721i	−0.116928	−	0.202526i
$846$	21.3031	+	12.2993i	0.732414	+	0.422860i
$847$	26.0000	+	22.5167i	0.893371	+	0.773682i
$848$	−7.10102	−	4.09978i	−0.243850	−	0.140787i
$849$	1.34847	+	2.33562i	0.0462793	+	0.0801582i
$850$	3.44949	+	5.97469i	0.118317	+	0.204930i
$851$	−7.89898	+	13.6814i	−0.270774	+	0.468994i
$852$	0.449490	−	0.778539i	0.0153993	−	0.0266723i
$853$	48.4495			1.65888			0.829439	−	0.558597i	$-0.188660\pi$
$853$	48.4495			1.65888			0.829439	+	0.558597i	$0.188660\pi$
$854$	0.853572	−	0.985620i	0.0292086	−	0.0337272i
$855$			12.2993i			0.420628i
$856$	13.3485	−	7.70674i	0.456241	−	0.263411i
$857$	48.1918	+	27.8236i	1.64620	+	0.950435i	0.978562	+	0.205950i	$0.0660285\pi$
$857$	48.1918	+	27.8236i	1.64620	+	0.950435i	0.667639	+	0.744485i	$0.267305\pi$
$858$	−4.89898	−	8.48528i	−0.167248	−	0.289683i
$859$	21.0000	−	12.1244i	0.716511	−	0.413678i	−0.0969563	−	0.995289i	$-0.530911\pi$
$859$	21.0000	−	12.1244i	0.716511	−	0.413678i	0.813467	+	0.581611i	$0.197577\pi$
$860$	−9.44949	−	16.3670i	−0.322225	−	0.558110i
$861$	1.27526	−	6.62642i	0.0434606	−	0.225828i
$862$	−6.69694	+	11.5994i	−0.228099	+	0.395078i
$863$	−2.05051	+	1.18386i	−0.0698002	+	0.0402992i	−0.534494	−	0.845172i	$-0.679498\pi$
$863$	−2.05051	+	1.18386i	−0.0698002	+	0.0402992i	0.464694	+	0.885471i	$0.346164\pi$
$864$	−10.6061			−0.360828
$865$	−5.44949	+	9.43879i	−0.185288	+	0.320929i
$866$	−10.8990			−0.370362
$867$		−	2.16064i		−	0.0733793i
$868$	−1.55051	+	8.05669i	−0.0526277	+	0.273462i
$869$		−	37.7552i		−	1.28076i
$870$		−	3.25702i		−	0.110423i
$871$	27.4722	−	47.5832i	0.930860	−	1.61230i
$872$	−11.1464	+	19.3062i	−0.377466	+	0.653790i
$873$	30.0000	−	17.3205i	1.01535	−	0.586210i
$874$	23.6969	+	13.6814i	0.801561	+	0.462781i
$875$	−2.50000	+	0.866025i	−0.0845154	+	0.0292770i
$876$	−3.55051	−	6.14966i	−0.119961	−	0.207778i
$877$	−1.71964	+	0.992836i	−0.0580682	+	0.0335257i	−0.528753	−	0.848776i	$-0.677340\pi$
$877$	−1.71964	+	0.992836i	−0.0580682	+	0.0335257i	0.470685	+	0.882301i	$0.344007\pi$
$878$	13.5959	−	7.84961i	0.458840	−	0.264911i
$879$	6.74235	+	3.89270i	0.227414	+	0.131297i
$880$	19.5959			0.660578
$881$			36.6588i			1.23507i	0.786545	+	0.617533i	$0.211868\pi$
$881$			36.6588i			1.23507i	−0.786545	+	0.617533i	$0.788132\pi$
$882$	10.6515	−	26.6485i	0.358656	−	0.897303i
$883$	−40.4949			−1.36276			−0.681381	−	0.731929i	$-0.738620\pi$
$883$	−40.4949			−1.36276			−0.681381	+	0.731929i	$0.738620\pi$
$884$	−37.5959	−	21.7060i	−1.26449	−	0.730052i
$885$	−0.573214	+	0.992836i	−0.0192684	+	0.0333738i
$886$	−20.0227	+	11.5601i	−0.672676	+	0.388370i
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	0.545302	−	0.838240i	$-0.316415\pi$
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	−0.998588	+	0.0531258i	$0.983082\pi$
$888$		−	3.11416i		−	0.104504i
$889$	6.00000	+	17.3205i	0.201234	+	0.580911i
$890$	7.67423	−	13.2922i	0.257241	−	0.445554i
$891$	−19.8434	−	34.3697i	−0.664778	−	1.15143i
$892$	−49.3939			−1.65383
$893$	22.0454	+	12.7279i	0.737721	+	0.425924i
$894$		−	8.62815i		−	0.288568i
$895$	9.55051			0.319238
$896$	9.79796	+	28.2843i	0.327327	+	0.944911i
$897$	6.44949			0.215342
$898$		−	1.98567i		−	0.0662627i
$899$	−9.72985	−	5.61753i	−0.324509	−	0.187355i
$900$	−5.79796			−0.193265
$901$	5.00000	+	8.66025i	0.166574	+	0.288515i
$902$	−27.7980	+	48.1475i	−0.925571	+	1.60314i
$903$	−7.80306	−	1.50170i	−0.259670	−	0.0499734i
$904$		−	23.8988i		−	0.794861i
$905$	6.17423	+	10.6941i	0.205239	+	0.355484i
$906$	−3.00000	+	1.73205i	−0.0996683	+	0.0575435i
$907$	4.17423	−	7.22999i	0.138603	−	0.240068i	−0.788365	−	0.615208i	$-0.789072\pi$
$907$	4.17423	−	7.22999i	0.138603	−	0.240068i	0.926968	+	0.375140i	$0.122405\pi$
$908$	18.4949	+	10.6780i	0.613775	+	0.354363i
$909$	−44.2020			−1.46609
$910$	10.8990	−	12.5851i	0.361298	−	0.417191i
$911$		−	41.5050i		−	1.37512i	−0.726127	−	0.687561i	$-0.758681\pi$
$911$		−	41.5050i		−	1.37512i	0.726127	−	0.687561i	$-0.241319\pi$
$912$	−5.39388			−0.178609
$913$	7.95459	+	4.59259i	0.263259	+	0.151992i
$914$	11.7526	−	6.78534i	0.388740	−	0.224439i
$915$	−0.0959179	+	0.0553782i	−0.00317095	+	0.00183075i
$916$	−16.6969	−	28.9199i	−0.551682	−	0.955542i
$917$	19.5959	−	22.6274i	0.647114	−	0.747223i
$918$	11.2020	+	6.46750i	0.369722	+	0.213459i
$919$	−12.3712	+	7.14250i	−0.408087	+	0.235609i	−0.689968	−	0.723840i	$-0.742375\pi$
$919$	−12.3712	+	7.14250i	−0.408087	+	0.235609i	0.281880	+	0.959450i	$0.409042\pi$
$920$	−6.44949	+	11.1708i	−0.212633	+	0.368292i
$921$	−4.44439	+	7.69790i	−0.146448	+	0.253655i
$922$		−	54.7257i		−	1.80230i
$923$			6.29253i			0.207121i
$924$	5.39388	−	6.22831i	0.177446	−	0.204896i
$925$		−	3.46410i		−	0.113899i
$926$	17.1464			0.563467
$927$	−24.3485	+	42.1728i	−0.799709	+	1.38514i
$928$	−40.9898			−1.34556
$929$	−5.29796	+	3.05878i	−0.173820	+	0.100355i	−0.584386	−	0.811476i	$-0.698665\pi$
$929$	−5.29796	+	3.05878i	−0.173820	+	0.100355i	0.410566	+	0.911831i	$0.365331\pi$
$930$	0.348469	−	0.603566i	0.0114268	−	0.0197917i
$931$	11.0227	−	27.5772i	0.361255	−	0.903805i
$932$	−0.247449	−	0.428594i	−0.00810545	−	0.0140391i
$933$	3.06811	−	1.77138i	0.100445	−	0.0579922i
$934$	−16.0227	−	27.7521i	−0.524279	−	0.908078i
$935$	−20.6969	−	11.9494i	−0.676862	−	0.390787i
$936$	31.5959	−	18.2419i	1.03274	−	0.596256i
$937$			10.0424i			0.328070i	0.986455	+	0.164035i	$0.0524509\pi$
$937$			10.0424i			0.328070i	−0.986455	+	0.164035i	$0.947549\pi$
$938$	45.3712	+	8.73169i	1.48142	+	0.285100i
$939$	2.09082			0.0682312
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$	−7.89898	+	13.6814i	−0.257499	+	0.446002i	−0.965571	−	0.260138i	$-0.916232\pi$
$941$	−7.89898	+	13.6814i	−0.257499	+	0.446002i	0.708072	+	0.706140i	$0.249565\pi$
$942$	−2.40408	−	4.16399i	−0.0783292	−	0.135670i
$943$	−18.2980	−	31.6930i	−0.595864	−	1.03207i
$944$	12.4949	+	7.21393i	0.406674	+	0.234794i
$945$	−3.24745	+	3.74983i	−0.105640	+	0.121982i
$946$	56.6969	+	32.7340i	1.84338	+	1.06427i
$947$	−23.7247	−	41.0925i	−0.770951	−	1.33533i	−0.937042	−	0.349215i	$-0.886448\pi$
$947$	−23.7247	−	41.0925i	−0.770951	−	1.33533i	0.166092	−	0.986110i	$-0.446885\pi$
$948$	−4.89898			−0.159111
$949$	43.0454	+	24.8523i	1.39731	+	0.806739i
$950$	−6.00000			−0.194666
$951$	−0.156633			−0.00507918
$952$	6.89898	−	35.8481i	0.223597	−	1.16185i
$953$	−10.8990			−0.353053			−0.176526	−	0.984296i	$-0.556486\pi$
$953$	−10.8990			−0.353053			−0.176526	+	0.984296i	$0.556486\pi$
$954$	−8.40408			−0.272092
$955$	22.8990	+	13.2207i	0.740994	+	0.427813i
$956$			6.64247i			0.214833i
$957$	5.64133	+	9.77106i	0.182358	+	0.315854i
$958$	−10.3485	−	5.97469i	−0.334344	−	0.193034i
$959$	−4.89898	+	25.4558i	−0.158196	+	0.822012i
$960$		−	2.54270i		−	0.0820652i
$961$	14.2980	+	24.7648i	0.461224	+	0.798864i
$962$	10.8990	+	18.8776i	0.351397	+	0.608638i
$963$	7.89898	−	13.6814i	0.254541	−	0.440878i
$964$	35.3939	+	20.4347i	1.13996	+	0.658156i
$965$	22.6969			0.730640
$966$	1.77526	+	5.12472i	0.0571179	+	0.164885i
$967$			52.6437i			1.69291i	0.532461	+	0.846454i	$0.321267\pi$
$967$			52.6437i			1.69291i	−0.532461	+	0.846454i	$0.678733\pi$
$968$	−31.8434	+	18.3848i	−1.02348	+	0.590909i
$969$	5.69694	+	3.28913i	0.183012	+	0.105662i
$970$	8.44949	+	14.6349i	0.271297	+	0.469900i
$971$	−26.1464	+	15.0956i	−0.839079	+	0.484442i	−0.856951	−	0.515398i	$-0.827644\pi$
$971$	−26.1464	+	15.0956i	−0.839079	+	0.484442i	0.0178722	+	0.999840i	$0.494311\pi$
$972$	−14.2020	+	8.19955i	−0.455531	+	0.263001i
$973$	6.00000	+	17.3205i	0.192351	+	0.555270i
$974$	−21.5505	+	37.3266i	−0.690523	+	1.19602i
$975$	−1.22474	+	0.707107i	−0.0392232	+	0.0226455i
$976$	0.696938	+	1.20713i	0.0223085	+	0.0386394i
$977$	14.6969	−	25.4558i	0.470197	−	0.814405i	−0.529222	−	0.848483i	$-0.677516\pi$
$977$	14.6969	−	25.4558i	0.470197	−	0.814405i	0.999419	+	0.0340785i	$0.0108496\pi$
$978$	−2.60612			−0.0833346
$979$			53.1687i			1.69928i
$980$	13.0000	+	5.19615i	0.415270	+	0.165985i
$981$			22.8489i			0.729510i
$982$			1.20713i			0.0385212i
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	−0.960489	−	0.278319i	$-0.910223\pi$
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	0.721276	+	0.692648i	$0.243556\pi$
$984$	6.24745	+	3.60697i	0.199161	+	0.114986i
$985$	0.797959	−	0.460702i	0.0254251	−	0.0146792i
$986$	43.2929	+	24.9951i	1.37873	+	0.796007i
$987$	1.65153	+	4.76756i	0.0525688	+	0.151753i
$988$	32.6969	−	18.8776i	1.04023	−	0.600576i
$989$	−37.3207	+	21.5471i	−1.18673	+	0.685158i
$990$	17.3939	−	10.0424i	0.552814	−	0.319167i
$991$	25.7196	+	14.8492i	0.817011	+	0.471702i	0.849385	−	0.527774i	$-0.176973\pi$
$991$	25.7196	+	14.8492i	0.817011	+	0.471702i	−0.0323734	+	0.999476i	$0.510307\pi$
$992$	−7.59592	−	4.38551i	−0.241171	−	0.139240i
$993$		−	1.00005i		−	0.0317357i
$994$	−5.00000	+	1.73205i	−0.158590	+	0.0549373i
$995$	24.6969			0.782946
$996$	0.595918	−	1.03216i	0.0188824	−	0.0327052i
$997$	−13.3258	+	23.0809i	−0.422031	+	0.730980i	−0.996138	−	0.0878009i	$-0.972016\pi$
$997$	−13.3258	+	23.0809i	−0.422031	+	0.730980i	0.574107	+	0.818780i	$0.305349\pi$
$998$	−33.5505	+	19.3704i	−1.06202	+	0.613159i
$999$	−3.24745	−	5.62475i	−0.102745	−	0.177959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.b.171.2	yes	4
4.3	odd	2		1120.2.bz.b.591.1		4
7.5	odd	6		280.2.bj.c.131.2	yes	4
8.3	odd	2		280.2.bj.c.171.2	yes	4
8.5	even	2		1120.2.bz.c.591.1		4
28.19	even	6		1120.2.bz.c.271.1		4
56.5	odd	6		1120.2.bz.b.271.1		4
56.19	even	6	inner	280.2.bj.b.131.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.b.131.1	✓	4	56.19	even	6	inner
280.2.bj.b.171.2	yes	4	1.1	even	1	trivial
280.2.bj.c.131.2	yes	4	7.5	odd	6
280.2.bj.c.171.2	yes	4	8.3	odd	2
1120.2.bz.b.271.1		4	56.5	odd	6
1120.2.bz.b.591.1		4	4.3	odd	2
1120.2.bz.c.271.1		4	28.19	even	6
1120.2.bz.c.591.1		4	8.5	even	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-0.275255 - 0.158919i) q^{3} -2.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.224745 - 0.389270i) q^{6} +(-2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +(-1.44949 - 2.51059i) q^{9} +(1.22474 - 0.707107i) q^{10} +(-2.44949 + 4.24264i) q^{11} +(0.550510 + 0.317837i) q^{12} -4.44949 q^{13} +(-1.22474 - 3.53553i) q^{14} +0.317837i q^{15} +4.00000 q^{16} +(-4.22474 - 2.43916i) q^{17} +(3.55051 - 2.04989i) q^{18} +(3.67423 - 2.12132i) q^{19} +(1.00000 + 1.73205i) q^{20} +(0.825765 + 0.158919i) q^{21} +(-6.00000 - 3.46410i) q^{22} +(3.94949 - 2.28024i) q^{23} +(-0.449490 + 0.778539i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.29253i q^{26} +1.87492i q^{27} +(5.00000 - 1.73205i) q^{28} +7.24604i q^{29} -0.449490 q^{30} +(-0.775255 + 1.34278i) q^{31} +5.65685i q^{32} +(1.34847 - 0.778539i) q^{33} +(3.44949 - 5.97469i) q^{34} +(2.00000 + 1.73205i) q^{35} +(2.89898 + 5.02118i) q^{36} +(-3.00000 + 1.73205i) q^{37} +(3.00000 + 5.19615i) q^{38} +(1.22474 + 0.707107i) q^{39} +(-2.44949 + 1.41421i) q^{40} -8.02458i q^{41} +(-0.224745 + 1.16781i) q^{42} -9.44949 q^{43} +(4.89898 - 8.48528i) q^{44} +(-1.44949 + 2.51059i) q^{45} +(3.22474 + 5.58542i) q^{46} +(3.00000 + 5.19615i) q^{47} +(-1.10102 - 0.635674i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-1.22474 - 0.707107i) q^{50} +(0.775255 + 1.34278i) q^{51} +8.89898 q^{52} +(-1.77526 - 1.02494i) q^{53} -2.65153 q^{54} +4.89898 q^{55} +(2.44949 + 7.07107i) q^{56} -1.34847 q^{57} -10.2474 q^{58} +(3.12372 + 1.80348i) q^{59} -0.635674i q^{60} +(0.174235 + 0.301783i) q^{61} +(-1.89898 - 1.09638i) q^{62} +(5.79796 + 5.02118i) q^{63} -8.00000 q^{64} +(2.22474 + 3.85337i) q^{65} +(1.10102 + 1.90702i) q^{66} +(-6.17423 + 10.6941i) q^{67} +(8.44949 + 4.87832i) q^{68} -1.44949 q^{69} +(-2.44949 + 2.82843i) q^{70} -1.41421i q^{71} +(-7.10102 + 4.09978i) q^{72} +(-9.67423 - 5.58542i) q^{73} +(-2.44949 - 4.24264i) q^{74} +(0.275255 - 0.158919i) q^{75} +(-7.34847 + 4.24264i) q^{76} +(2.44949 - 12.7279i) q^{77} +(-1.00000 + 1.73205i) q^{78} +(-6.67423 + 3.85337i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-4.05051 + 7.01569i) q^{81} +11.3485 q^{82} -1.87492i q^{83} +(-1.65153 - 0.317837i) q^{84} +4.87832i q^{85} -13.3636i q^{86} +(1.15153 - 1.99451i) q^{87} +(12.0000 + 6.92820i) q^{88} +(9.39898 - 5.42650i) q^{89} +(-3.55051 - 2.04989i) q^{90} +(11.1237 - 3.85337i) q^{91} +(-7.89898 + 4.56048i) q^{92} +(0.426786 - 0.246405i) q^{93} +(-7.34847 + 4.24264i) q^{94} +(-3.67423 - 2.12132i) q^{95} +(0.898979 - 1.55708i) q^{96} +11.9494i q^{97} +(6.12372 + 7.77817i) q^{98} +14.2020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 4 q^{6} - 10 q^{7} + 4 q^{9} + 12 q^{12} - 8 q^{13} + 16 q^{16} - 12 q^{17} + 24 q^{18} + 4 q^{20} + 18 q^{21} - 24 q^{22} + 6 q^{23} + 8 q^{24} - 2 q^{25} + 20 q^{28}+ \cdots + 96 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 4 * q^6 - 10 * q^7 + 4 * q^9 + 12 * q^12 - 8 * q^13 + 16 * q^16 - 12 * q^17 + 24 * q^18 + 4 * q^20 + 18 * q^21 - 24 * q^22 + 6 * q^23 + 8 * q^24 - 2 * q^25 + 20 * q^28 + 8 * q^30 - 8 * q^31 - 24 * q^33 + 4 * q^34 + 8 * q^35 - 8 * q^36 - 12 * q^37 + 12 * q^38 + 4 * q^42 - 28 * q^43 + 4 * q^45 + 8 * q^46 + 12 * q^47 - 24 * q^48 + 22 * q^49 + 8 * q^51 + 16 * q^52 - 12 * q^53 - 40 * q^54 + 24 * q^57 + 8 * q^58 - 12 * q^59 - 14 * q^61 + 12 * q^62 - 16 * q^63 - 32 * q^64 + 4 * q^65 + 24 * q^66 - 10 * q^67 + 24 * q^68 + 4 * q^69 - 48 * q^72 - 24 * q^73 + 6 * q^75 - 4 * q^78 - 12 * q^79 - 8 * q^80 - 26 * q^81 + 16 * q^82 - 36 * q^84 + 34 * q^87 + 48 * q^88 + 18 * q^89 - 24 * q^90 + 20 * q^91 - 12 * q^92 + 36 * q^93 - 16 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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