LMFDB - Embedded newform 560.2.ch.a.437.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(117,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 3, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("560.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ch (of order $12$, degree $4$, 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:	$4.47162251319$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			437.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	560.437
Dual form			560.2.ch.a.173.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 - 1.36603i) q^{2} +(0.366025 - 0.633975i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(-0.732051 - 0.732051i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.23205 + 2.13397i) q^{9} +(-2.36603 + 2.09808i) q^{10} +(0.500000 - 0.133975i) q^{11} +(-1.26795 + 0.732051i) q^{12} -5.73205 q^{13} +(2.09808 + 3.09808i) q^{14} +(-1.46410 + 0.732051i) q^{15} +(2.00000 + 3.46410i) q^{16} +(0.0980762 + 0.366025i) q^{17} +(3.36603 - 0.901924i) q^{18} +(-6.59808 - 1.76795i) q^{19} +(2.00000 + 4.00000i) q^{20} +(0.633975 + 1.83013i) q^{21} -0.732051i q^{22} +(0.598076 - 2.23205i) q^{23} +(0.535898 + 2.00000i) q^{24} +(1.96410 + 4.59808i) q^{25} +(-2.09808 + 7.83013i) q^{26} +4.00000 q^{27} +(5.00000 - 1.73205i) q^{28} +(-2.46410 - 2.46410i) q^{29} +(0.464102 + 2.26795i) q^{30} +(1.73205 + 1.00000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(0.0980762 - 0.366025i) q^{33} +0.535898 q^{34} +(5.69615 - 1.59808i) q^{35} -4.92820i q^{36} +(-2.76795 + 1.59808i) q^{37} +(-4.83013 + 8.36603i) q^{38} +(-2.09808 + 3.63397i) q^{39} +(6.19615 - 1.26795i) q^{40} +9.39230 q^{41} +(2.73205 - 0.196152i) q^{42} -4.19615 q^{43} +(-1.00000 - 0.267949i) q^{44} +(0.330127 - 5.50000i) q^{45} +(-2.83013 - 1.63397i) q^{46} +(-10.0622 - 2.69615i) q^{47} +2.92820 q^{48} +(-1.00000 - 6.92820i) q^{49} +(7.00000 - 1.00000i) q^{50} +(0.267949 + 0.0717968i) q^{51} +(9.92820 + 5.73205i) q^{52} +(-6.23205 + 10.7942i) q^{53} +(1.46410 - 5.46410i) q^{54} +(-1.09808 - 0.366025i) q^{55} +(-0.535898 - 7.46410i) q^{56} +(-3.53590 + 3.53590i) q^{57} +(-4.26795 + 2.46410i) q^{58} +(-9.83013 + 2.63397i) q^{59} +(3.26795 + 0.196152i) q^{60} +(3.00000 - 11.1962i) q^{61} +(2.00000 - 2.00000i) q^{62} +(-6.40192 - 1.23205i) q^{63} -8.00000i q^{64} +(10.6962 + 7.06218i) q^{65} +(-0.464102 - 0.267949i) q^{66} +(0.464102 - 0.803848i) q^{67} +(0.196152 - 0.732051i) q^{68} +(-1.19615 - 1.19615i) q^{69} +(-0.0980762 - 8.36603i) q^{70} -9.46410i q^{71} +(-6.73205 - 1.80385i) q^{72} +(-0.732051 - 2.73205i) q^{73} +(1.16987 + 4.36603i) q^{74} +(3.63397 + 0.437822i) q^{75} +(9.66025 + 9.66025i) q^{76} +(-0.598076 + 1.23205i) q^{77} +(4.19615 + 4.19615i) q^{78} +(-5.83013 + 3.36603i) q^{79} +(0.535898 - 8.92820i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(3.43782 - 12.8301i) q^{82} -15.4641 q^{83} +(0.732051 - 3.80385i) q^{84} +(0.267949 - 0.803848i) q^{85} +(-1.53590 + 5.73205i) q^{86} +(-2.46410 + 0.660254i) q^{87} +(-0.732051 + 1.26795i) q^{88} +(-0.803848 + 0.464102i) q^{89} +(-7.39230 - 2.46410i) q^{90} +(9.92820 - 11.4641i) q^{91} +(-3.26795 + 3.26795i) q^{92} +(1.26795 - 0.732051i) q^{93} +(-7.36603 + 12.7583i) q^{94} +(10.1340 + 11.4282i) q^{95} +(1.07180 - 4.00000i) q^{96} +(3.00000 - 3.00000i) q^{97} +(-9.83013 - 1.16987i) q^{98} +(0.901924 + 0.901924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 4 q^{5} + 4 q^{6} - 8 q^{8} - 2 q^{9} - 6 q^{10} + 2 q^{11} - 12 q^{12} - 16 q^{13} - 2 q^{14} + 8 q^{15} + 8 q^{16} - 10 q^{17} + 10 q^{18} - 16 q^{19} + 8 q^{20} + 6 q^{21} - 8 q^{23}+ \cdots + 14 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 + 4 * q^6 - 8 * q^8 - 2 * q^9 - 6 * q^10 + 2 * q^11 - 12 * q^12 - 16 * q^13 - 2 * q^14 + 8 * q^15 + 8 * q^16 - 10 * q^17 + 10 * q^18 - 16 * q^19 + 8 * q^20 + 6 * q^21 - 8 * q^23 + 16 * q^24 - 6 * q^25 + 2 * q^26 + 16 * q^27 + 20 * q^28 + 4 * q^29 - 12 * q^30 + 8 * q^32 - 10 * q^33 + 16 * q^34 + 2 * q^35 - 18 * q^37 - 2 * q^38 + 2 * q^39 + 4 * q^40 - 4 * q^41 + 4 * q^42 + 4 * q^43 - 4 * q^44 - 16 * q^45 + 6 * q^46 - 16 * q^47 - 16 * q^48 - 4 * q^49 + 28 * q^50 + 8 * q^51 + 12 * q^52 - 18 * q^53 - 8 * q^54 + 6 * q^55 - 16 * q^56 - 28 * q^57 - 24 * q^58 - 22 * q^59 + 20 * q^60 + 12 * q^61 + 8 * q^62 - 36 * q^63 + 22 * q^65 + 12 * q^66 - 12 * q^67 - 20 * q^68 + 16 * q^69 + 10 * q^70 - 20 * q^72 + 4 * q^73 + 22 * q^74 + 18 * q^75 + 4 * q^76 + 8 * q^77 - 4 * q^78 - 6 * q^79 + 16 * q^80 - 2 * q^81 + 38 * q^82 - 48 * q^83 - 4 * q^84 + 8 * q^85 - 20 * q^86 + 4 * q^87 + 4 * q^88 - 24 * q^89 + 12 * q^90 + 12 * q^91 - 20 * q^92 + 12 * q^93 - 26 * q^94 + 44 * q^95 + 32 * q^96 + 12 * q^97 - 22 * q^98 + 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$	0.366025	−	0.633975i	0.211325	−	0.366025i	−0.740805	−	0.671721i	$-0.765556\pi$
$3$	0.366025	−	0.633975i	0.211325	−	0.366025i	0.952129	+	0.305695i	$0.0988889\pi$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$6$	−0.732051	−	0.732051i	−0.298858	−	0.298858i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	1.23205	+	2.13397i	0.410684	+	0.711325i
$10$	−2.36603	+	2.09808i	−0.748203	+	0.663470i
$11$	0.500000	−	0.133975i	0.150756	−	0.0403949i	−0.182652	−	0.983178i	$-0.558468\pi$
$11$	0.500000	−	0.133975i	0.150756	−	0.0403949i	0.333408	+	0.942783i	$0.391801\pi$
$12$	−1.26795	+	0.732051i	−0.366025	+	0.211325i
$13$	−5.73205			−1.58978			−0.794892	−	0.606750i	$-0.792473\pi$
$13$	−5.73205			−1.58978			−0.794892	+	0.606750i	$0.792473\pi$
$14$	2.09808	+	3.09808i	0.560734	+	0.827996i
$15$	−1.46410	+	0.732051i	−0.378029	+	0.189015i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	0.0980762	+	0.366025i	0.0237870	+	0.0887742i	0.976799	−	0.214159i	$-0.0687009\pi$
$17$	0.0980762	+	0.366025i	0.0237870	+	0.0887742i	−0.953012	+	0.302933i	$0.902034\pi$
$18$	3.36603	−	0.901924i	0.793380	−	0.212585i
$19$	−6.59808	−	1.76795i	−1.51370	−	0.405595i	−0.596040	−	0.802955i	$-0.703260\pi$
$19$	−6.59808	−	1.76795i	−1.51370	−	0.405595i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	2.00000	+	4.00000i	0.447214	+	0.894427i
$21$	0.633975	+	1.83013i	0.138345	+	0.399366i
$22$		−	0.732051i		−	0.156074i
$23$	0.598076	−	2.23205i	0.124708	−	0.465415i	−0.875122	−	0.483903i	$-0.839219\pi$
$23$	0.598076	−	2.23205i	0.124708	−	0.465415i	0.999829	+	0.0184884i	$0.00588537\pi$
$24$	0.535898	+	2.00000i	0.109390	+	0.408248i
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	−2.09808	+	7.83013i	−0.411467	+	1.53561i
$27$	4.00000			0.769800
$28$	5.00000	−	1.73205i	0.944911	−	0.327327i
$29$	−2.46410	−	2.46410i	−0.457572	−	0.457572i	0.440286	−	0.897858i	$-0.354877\pi$
$29$	−2.46410	−	2.46410i	−0.457572	−	0.457572i	−0.897858	+	0.440286i	$0.854877\pi$
$30$	0.464102	+	2.26795i	0.0847330	+	0.414069i
$31$	1.73205	+	1.00000i	0.311086	+	0.179605i	0.647412	−	0.762140i	$-0.275851\pi$
$31$	1.73205	+	1.00000i	0.311086	+	0.179605i	−0.336327	+	0.941745i	$0.609185\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$	0.0980762	−	0.366025i	0.0170729	−	0.0637168i
$34$	0.535898			0.0919058
$35$	5.69615	−	1.59808i	0.962825	−	0.270124i
$36$		−	4.92820i		−	0.821367i
$37$	−2.76795	+	1.59808i	−0.455048	+	0.262722i	−0.709960	−	0.704242i	$-0.751287\pi$
$37$	−2.76795	+	1.59808i	−0.455048	+	0.262722i	0.254912	+	0.966964i	$0.417954\pi$
$38$	−4.83013	+	8.36603i	−0.783550	+	1.35715i
$39$	−2.09808	+	3.63397i	−0.335961	+	0.581902i
$40$	6.19615	−	1.26795i	0.979698	−	0.200480i
$41$	9.39230			1.46683			0.733416	−	0.679780i	$-0.237925\pi$
$41$	9.39230			1.46683			0.733416	+	0.679780i	$0.237925\pi$
$42$	2.73205	−	0.196152i	0.421565	−	0.0302670i
$43$	−4.19615			−0.639907			−0.319954	−	0.947433i	$-0.603667\pi$
$43$	−4.19615			−0.639907			−0.319954	+	0.947433i	$0.603667\pi$
$44$	−1.00000	−	0.267949i	−0.150756	−	0.0403949i
$45$	0.330127	−	5.50000i	0.0492124	−	0.819892i
$46$	−2.83013	−	1.63397i	−0.417279	−	0.240916i
$47$	−10.0622	−	2.69615i	−1.46772	−	0.393274i	−0.565571	−	0.824700i	$-0.691344\pi$
$47$	−10.0622	−	2.69615i	−1.46772	−	0.393274i	−0.902149	+	0.431425i	$0.858011\pi$
$48$	2.92820			0.422650
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	7.00000	−	1.00000i	0.989949	−	0.141421i
$51$	0.267949	+	0.0717968i	0.0375204	+	0.0100536i
$52$	9.92820	+	5.73205i	1.37679	+	0.794892i
$53$	−6.23205	+	10.7942i	−0.856038	+	1.48270i	0.0196407	+	0.999807i	$0.493748\pi$
$53$	−6.23205	+	10.7942i	−0.856038	+	1.48270i	−0.875679	+	0.482894i	$0.839586\pi$
$54$	1.46410	−	5.46410i	0.199239	−	0.743570i
$55$	−1.09808	−	0.366025i	−0.148065	−	0.0493549i
$56$	−0.535898	−	7.46410i	−0.0716124	−	0.997433i
$57$	−3.53590	+	3.53590i	−0.468341	+	0.468341i
$58$	−4.26795	+	2.46410i	−0.560409	+	0.323552i
$59$	−9.83013	+	2.63397i	−1.27977	+	0.342914i	−0.833768	−	0.552116i	$-0.813821\pi$
$59$	−9.83013	+	2.63397i	−1.27977	+	0.342914i	−0.446006	+	0.895030i	$0.647154\pi$
$60$	3.26795	+	0.196152i	0.421890	+	0.0253232i
$61$	3.00000	−	11.1962i	0.384111	−	1.43352i	−0.455453	−	0.890260i	$-0.650523\pi$
$61$	3.00000	−	11.1962i	0.384111	−	1.43352i	0.839564	−	0.543261i	$-0.182811\pi$
$62$	2.00000	−	2.00000i	0.254000	−	0.254000i
$63$	−6.40192	−	1.23205i	−0.806567	−	0.155224i
$64$		−	8.00000i		−	1.00000i
$65$	10.6962	+	7.06218i	1.32669	+	0.875955i
$66$	−0.464102	−	0.267949i	−0.0571270	−	0.0329823i
$67$	0.464102	−	0.803848i	0.0566990	−	0.0982056i	−0.836283	−	0.548298i	$-0.815276\pi$
$67$	0.464102	−	0.803848i	0.0566990	−	0.0982056i	0.892982	+	0.450093i	$0.148609\pi$
$68$	0.196152	−	0.732051i	0.0237870	−	0.0887742i
$69$	−1.19615	−	1.19615i	−0.144000	−	0.144000i
$70$	−0.0980762	−	8.36603i	−0.0117223	−	0.999931i
$71$		−	9.46410i		−	1.12318i	−0.827415	−	0.561591i	$-0.810189\pi$
$71$		−	9.46410i		−	1.12318i	0.827415	−	0.561591i	$-0.189811\pi$
$72$	−6.73205	−	1.80385i	−0.793380	−	0.212585i
$73$	−0.732051	−	2.73205i	−0.0856801	−	0.319762i	0.909762	−	0.415130i	$-0.136264\pi$
$73$	−0.732051	−	2.73205i	−0.0856801	−	0.319762i	−0.995442	+	0.0953678i	$0.969597\pi$
$74$	1.16987	+	4.36603i	0.135995	+	0.507540i
$75$	3.63397	+	0.437822i	0.419615	+	0.0505553i
$76$	9.66025	+	9.66025i	1.10811	+	1.10811i
$77$	−0.598076	+	1.23205i	−0.0681571	+	0.140405i
$78$	4.19615	+	4.19615i	0.475121	+	0.475121i
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	−0.790728	−	0.612167i	$-0.790298\pi$
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	0.134788	+	0.990874i	$0.456965\pi$
$80$	0.535898	−	8.92820i	0.0599153	−	0.998203i
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$	3.43782	−	12.8301i	0.379644	−	1.41685i
$83$	−15.4641			−1.69741			−0.848703	−	0.528870i	$-0.822616\pi$
$83$	−15.4641			−1.69741			−0.848703	+	0.528870i	$0.822616\pi$
$84$	0.732051	−	3.80385i	0.0798733	−	0.415034i
$85$	0.267949	−	0.803848i	0.0290632	−	0.0871895i
$86$	−1.53590	+	5.73205i	−0.165620	+	0.618103i
$87$	−2.46410	+	0.660254i	−0.264179	+	0.0707867i
$88$	−0.732051	+	1.26795i	−0.0780369	+	0.135164i
$89$	−0.803848	+	0.464102i	−0.0852077	+	0.0491947i	−0.541998	−	0.840379i	$-0.682332\pi$
$89$	−0.803848	+	0.464102i	−0.0852077	+	0.0491947i	0.456791	+	0.889574i	$0.348999\pi$
$90$	−7.39230	−	2.46410i	−0.779217	−	0.259739i
$91$	9.92820	−	11.4641i	1.04076	−	1.20176i
$92$	−3.26795	+	3.26795i	−0.340707	+	0.340707i
$93$	1.26795	−	0.732051i	0.131480	−	0.0759101i
$94$	−7.36603	+	12.7583i	−0.759748	+	1.31592i
$95$	10.1340	+	11.4282i	1.03972	+	1.17251i
$96$	1.07180	−	4.00000i	0.109390	−	0.408248i
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	−0.538208	−	0.842812i	$-0.680899\pi$
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	0.842812	+	0.538208i	$0.180899\pi$
$98$	−9.83013	−	1.16987i	−0.992993	−	0.118175i
$99$	0.901924	+	0.901924i	0.0906468	+	0.0906468i
$100$	1.19615	−	9.92820i	0.119615	−	0.992820i
$101$	4.66025	+	17.3923i	0.463713	+	1.73060i	0.661122	+	0.750278i	$0.270080\pi$
$101$	4.66025	+	17.3923i	0.463713	+	1.73060i	−0.197410	+	0.980321i	$0.563253\pi$
$102$	0.196152	−	0.339746i	0.0194220	−	0.0336399i
$103$	7.09808	+	1.90192i	0.699394	+	0.187402i	0.590959	−	0.806701i	$-0.298749\pi$
$103$	7.09808	+	1.90192i	0.699394	+	0.187402i	0.108435	+	0.994104i	$0.465416\pi$
$104$	11.4641	−	11.4641i	1.12415	−	1.12415i
$105$	1.07180	−	4.19615i	0.104597	−	0.409503i
$106$	12.4641	+	12.4641i	1.21062	+	1.21062i
$107$	7.73205	−	4.46410i	0.747486	−	0.431561i	−0.0772991	−	0.997008i	$-0.524630\pi$
$107$	7.73205	−	4.46410i	0.747486	−	0.431561i	0.824785	+	0.565447i	$0.191296\pi$
$108$	−6.92820	−	4.00000i	−0.666667	−	0.384900i
$109$	16.3923	−	4.39230i	1.57010	−	0.420707i	0.634255	−	0.773124i	$-0.281307\pi$
$109$	16.3923	−	4.39230i	1.57010	−	0.420707i	0.935843	+	0.352417i	$0.114640\pi$
$110$	−0.901924	+	1.36603i	−0.0859951	+	0.130245i
$111$			2.33975i			0.222079i
$112$	−10.3923	−	2.00000i	−0.981981	−	0.188982i
$113$	2.92820	−	2.92820i	0.275462	−	0.275462i	−0.555832	−	0.831294i	$-0.687600\pi$
$113$	2.92820	−	2.92820i	0.275462	−	0.275462i	0.831294	+	0.555832i	$0.187600\pi$
$114$	3.53590	+	6.12436i	0.331167	+	0.573598i
$115$	−3.86603	+	3.42820i	−0.360509	+	0.319682i
$116$	1.80385	+	6.73205i	0.167483	+	0.625055i
$117$	−7.06218	−	12.2321i	−0.652899	−	1.13085i
$118$			14.3923i			1.32492i
$119$	−0.901924	−	0.437822i	−0.0826792	−	0.0401351i
$120$	1.46410	−	4.39230i	0.133654	−	0.400961i
$121$	−9.29423	+	5.36603i	−0.844930	+	0.487820i
$122$	−14.1962	−	8.19615i	−1.28526	−	0.742045i
$123$	3.43782	−	5.95448i	0.309978	−	0.536898i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	−4.02628	+	8.29423i	−0.358689	+	0.738909i
$127$	−9.36603	−	9.36603i	−0.831100	−	0.831100i	0.156567	−	0.987667i	$-0.449957\pi$
$127$	−9.36603	−	9.36603i	−0.831100	−	0.831100i	−0.987667	+	0.156567i	$0.949957\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$	−1.53590	+	2.66025i	−0.135228	+	0.234222i
$130$	13.5622	−	12.0263i	1.18948	−	1.05477i
$131$	−0.330127	+	1.23205i	−0.0288433	+	0.107645i	−0.978847	−	0.204595i	$-0.934412\pi$
$131$	−0.330127	+	1.23205i	−0.0288433	+	0.107645i	0.950003	+	0.312239i	$0.101079\pi$
$132$	−0.535898	+	0.535898i	−0.0466440	+	0.0466440i
$133$	14.9641	−	10.1340i	1.29755	−	0.878727i
$134$	−0.928203	−	0.928203i	−0.0801845	−	0.0801845i
$135$	−7.46410	−	4.92820i	−0.642408	−	0.424152i
$136$	−0.928203	−	0.535898i	−0.0795928	−	0.0459529i
$137$	3.33975	+	12.4641i	0.285334	+	1.06488i	0.948595	+	0.316492i	$0.102505\pi$
$137$	3.33975	+	12.4641i	0.285334	+	1.06488i	−0.663261	+	0.748388i	$0.730828\pi$
$138$	−2.07180	+	1.19615i	−0.176363	+	0.101823i
$139$	−5.53590	−	5.53590i	−0.469549	−	0.469549i	0.432220	−	0.901768i	$-0.357731\pi$
$139$	−5.53590	−	5.53590i	−0.469549	−	0.469549i	−0.901768	+	0.432220i	$0.857731\pi$
$140$	−11.4641	−	2.92820i	−0.968893	−	0.247478i
$141$	−5.39230	+	5.39230i	−0.454114	+	0.454114i
$142$	−12.9282	−	3.46410i	−1.08491	−	0.290701i
$143$	−2.86603	+	0.767949i	−0.239669	+	0.0642191i
$144$	−4.92820	+	8.53590i	−0.410684	+	0.711325i
$145$	1.56218	+	7.63397i	0.129732	+	0.633967i
$146$	−4.00000			−0.331042
$147$	−4.75833	−	1.90192i	−0.392460	−	0.156868i
$148$	6.39230			0.525444
$149$	10.8301	+	2.90192i	0.887239	+	0.237735i	0.673528	−	0.739162i	$-0.264778\pi$
$149$	10.8301	+	2.90192i	0.887239	+	0.237735i	0.213711	+	0.976897i	$0.431445\pi$
$150$	1.92820	−	4.80385i	0.157437	−	0.392233i
$151$	−14.8301	−	8.56218i	−1.20686	−	0.696780i	−0.244787	−	0.969577i	$-0.578718\pi$
$151$	−14.8301	−	8.56218i	−1.20686	−	0.696780i	−0.962072	+	0.272797i	$0.912051\pi$
$152$	16.7321	−	9.66025i	1.35715	−	0.783550i
$153$	−0.660254	+	0.660254i	−0.0533784	+	0.0533784i
$154$	1.46410	+	1.26795i	0.117981	+	0.102174i
$155$	−2.00000	−	4.00000i	−0.160644	−	0.321288i
$156$	7.26795	−	4.19615i	0.581902	−	0.335961i
$157$	−0.866025	−	0.500000i	−0.0691164	−	0.0399043i	0.465044	−	0.885288i	$-0.346039\pi$
$157$	−0.866025	−	0.500000i	−0.0691164	−	0.0399043i	−0.534160	+	0.845383i	$0.679372\pi$
$158$	2.46410	+	9.19615i	0.196033	+	0.731607i
$159$	4.56218	+	7.90192i	0.361804	+	0.626663i
$160$	−12.0000	−	4.00000i	−0.948683	−	0.316228i
$161$	3.42820	+	5.06218i	0.270180	+	0.398956i
$162$	4.46410	+	4.46410i	0.350733	+	0.350733i
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	−0.629492	−	0.777007i	$-0.716737\pi$
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	0.358162	+	0.933659i	$0.383403\pi$
$164$	−16.2679	−	9.39230i	−1.27031	−	0.733416i
$165$	−0.633975	+	0.562178i	−0.0493549	+	0.0437655i
$166$	−5.66025	+	21.1244i	−0.439321	+	1.63957i
$167$	−10.0981	−	10.0981i	−0.781413	−	0.781413i	0.198657	−	0.980069i	$-0.436342\pi$
$167$	−10.0981	−	10.0981i	−0.781413	−	0.781413i	−0.980069	+	0.198657i	$0.936342\pi$
$168$	−4.92820	−	2.39230i	−0.380219	−	0.184570i
$169$	19.8564			1.52742
$170$	−1.00000	−	0.660254i	−0.0766965	−	0.0506392i
$171$	−4.35641	−	16.2583i	−0.333143	−	1.24331i
$172$	7.26795	+	4.19615i	0.554176	+	0.319954i
$173$	−3.23205	−	5.59808i	−0.245728	−	0.425614i	0.716608	−	0.697476i	$-0.245694\pi$
$173$	−3.23205	−	5.59808i	−0.245728	−	0.425614i	−0.962336	+	0.271862i	$0.912360\pi$
$174$			3.60770i			0.273499i
$175$	−12.5981	−	4.03590i	−0.952325	−	0.305085i
$176$	1.46410	+	1.46410i	0.110361	+	0.110361i
$177$	−1.92820	+	7.19615i	−0.144933	+	0.540896i
$178$	0.339746	+	1.26795i	0.0254650	+	0.0950368i
$179$	15.0622	−	4.03590i	1.12580	−	0.301657i	0.352572	−	0.935785i	$-0.385307\pi$
$179$	15.0622	−	4.03590i	1.12580	−	0.301657i	0.773228	+	0.634128i	$0.218641\pi$
$180$	−6.07180	+	9.19615i	−0.452565	+	0.685441i
$181$	−0.464102	+	0.464102i	−0.0344964	+	0.0344964i	−0.724145	−	0.689648i	$-0.757765\pi$
$181$	−0.464102	+	0.464102i	−0.0344964	+	0.0344964i	0.689648	+	0.724145i	$0.257765\pi$
$182$	−12.0263	−	17.7583i	−0.891447	−	1.31634i
$183$	−6.00000	−	6.00000i	−0.443533	−	0.443533i
$184$	3.26795	+	5.66025i	0.240916	+	0.417279i
$185$	7.13397	+	0.428203i	0.524500	+	0.0314821i
$186$	−0.535898	−	2.00000i	−0.0392940	−	0.146647i
$187$	0.0980762	+	0.169873i	0.00717204	+	0.0124223i
$188$	14.7321	+	14.7321i	1.07445	+	1.07445i
$189$	−6.92820	+	8.00000i	−0.503953	+	0.581914i
$190$	19.3205	−	9.66025i	1.40166	−	0.700828i
$191$	11.9282	+	20.6603i	0.863094	+	1.49492i	0.868927	+	0.494941i	$0.164810\pi$
$191$	11.9282	+	20.6603i	0.863094	+	1.49492i	−0.00583236	+	0.999983i	$0.501857\pi$
$192$	−5.07180	−	2.92820i	−0.366025	−	0.211325i
$193$	−0.660254	−	2.46410i	−0.0475261	−	0.177370i	0.938083	−	0.346411i	$-0.112600\pi$
$193$	−0.660254	−	2.46410i	−0.0475261	−	0.177370i	−0.985609	+	0.169041i	$0.945933\pi$
$194$	−3.00000	−	5.19615i	−0.215387	−	0.373062i
$195$	8.39230	−	4.19615i	0.600985	−	0.300493i
$196$	−5.19615	+	13.0000i	−0.371154	+	0.928571i
$197$			19.9282i			1.41983i	0.704290	+	0.709913i	$0.251266\pi$
$197$			19.9282i			1.41983i	−0.704290	+	0.709913i	$0.748734\pi$
$198$	1.56218	−	0.901924i	0.111019	−	0.0640969i
$199$	−0.464102	−	0.267949i	−0.0328993	−	0.0189944i	0.483460	−	0.875366i	$-0.339380\pi$
$199$	−0.464102	−	0.267949i	−0.0328993	−	0.0189944i	−0.516359	+	0.856372i	$0.672713\pi$
$200$	−13.1244	−	5.26795i	−0.928032	−	0.372500i
$201$	−0.339746	−	0.588457i	−0.0239638	−	0.0415066i
$202$	25.4641			1.79165
$203$	9.19615	−	0.660254i	0.645443	−	0.0463407i
$204$	−0.392305	−	0.392305i	−0.0274668	−	0.0274668i
$205$	−17.5263	−	11.5718i	−1.22409	−	0.808209i
$206$	5.19615	−	9.00000i	0.362033	−	0.627060i
$207$	5.50000	−	1.47372i	0.382276	−	0.102431i
$208$	−11.4641	−	19.8564i	−0.794892	−	1.37679i
$209$	−3.53590			−0.244583
$210$	−5.33975	−	3.00000i	−0.368477	−	0.207020i
$211$	4.63397	−	4.63397i	0.319016	−	0.319016i	−0.529373	−	0.848389i	$-0.677573\pi$
$211$	4.63397	−	4.63397i	0.319016	−	0.319016i	0.848389	+	0.529373i	$0.177573\pi$
$212$	21.5885	−	12.4641i	1.48270	−	0.856038i
$213$	−6.00000	−	3.46410i	−0.411113	−	0.237356i
$214$	−3.26795	−	12.1962i	−0.223392	−	0.833712i
$215$	7.83013	+	5.16987i	0.534010	+	0.352582i
$216$	−8.00000	+	8.00000i	−0.544331	+	0.544331i
$217$	−5.00000	+	1.73205i	−0.339422	+	0.117579i
$218$		−	24.0000i		−	1.62549i
$219$	−2.00000	−	0.535898i	−0.135147	−	0.0362127i
$220$	1.53590	+	1.73205i	0.103550	+	0.116775i
$221$	−0.562178	−	2.09808i	−0.0378162	−	0.141132i
$222$	3.19615	+	0.856406i	0.214512	+	0.0574782i
$223$	−5.53590	−	5.53590i	−0.370711	−	0.370711i	0.497025	−	0.867736i	$-0.334426\pi$
$223$	−5.53590	−	5.53590i	−0.370711	−	0.370711i	−0.867736	+	0.497025i	$0.834426\pi$
$224$	−6.53590	+	13.4641i	−0.436698	+	0.899608i
$225$	−7.39230	+	9.85641i	−0.492820	+	0.657094i
$226$	−2.92820	−	5.07180i	−0.194781	−	0.337371i
$227$	3.80385	+	2.19615i	0.252470	+	0.145764i	0.620895	−	0.783894i	$-0.286769\pi$
$227$	3.80385	+	2.19615i	0.252470	+	0.145764i	−0.368425	+	0.929658i	$0.620103\pi$
$228$	9.66025	−	2.58846i	0.639766	−	0.171425i
$229$	2.39230	−	8.92820i	0.158088	−	0.589992i	−0.840733	−	0.541450i	$-0.817876\pi$
$229$	2.39230	−	8.92820i	0.158088	−	0.589992i	0.998821	−	0.0485426i	$-0.0154577\pi$
$230$	3.26795	+	6.53590i	0.215482	+	0.430964i
$231$	0.562178	+	0.830127i	0.0369886	+	0.0546183i
$232$	9.85641			0.647105
$233$	1.97372	−	7.36603i	0.129303	−	0.482564i	−0.870654	−	0.491896i	$-0.836304\pi$
$233$	1.97372	−	7.36603i	0.129303	−	0.482564i	0.999956	+	0.00933206i	$0.00297053\pi$
$234$	−19.2942	+	5.16987i	−1.26130	+	0.337965i
$235$	15.4545	+	17.4282i	1.00814	+	1.13689i
$236$	19.6603	+	5.26795i	1.27977	+	0.342914i
$237$			4.92820i			0.320121i
$238$	−0.928203	+	1.07180i	−0.0601665	+	0.0694743i
$239$			7.66025i			0.495501i	0.968824	+	0.247750i	$0.0796913\pi$
$239$			7.66025i			0.495501i	−0.968824	+	0.247750i	$0.920309\pi$
$240$	−5.46410	−	3.60770i	−0.352706	−	0.232876i
$241$	10.1603	+	5.86603i	0.654479	+	0.377864i	0.790170	−	0.612887i	$-0.209992\pi$
$241$	10.1603	+	5.86603i	0.654479	+	0.377864i	−0.135691	+	0.990751i	$0.543325\pi$
$242$	3.92820	+	14.6603i	0.252514	+	0.942397i
$243$	7.63397	+	13.2224i	0.489720	+	0.848219i
$244$	−16.3923	+	16.3923i	−1.04941	+	1.04941i
$245$	−6.66987	+	14.1603i	−0.426123	+	0.904665i
$246$	−6.87564	−	6.87564i	−0.438375	−	0.438375i
$247$	37.8205	+	10.1340i	2.40646	+	0.644809i
$248$	−5.46410	+	1.46410i	−0.346971	+	0.0929705i
$249$	−5.66025	+	9.80385i	−0.358704	+	0.621294i
$250$	−14.2942	−	6.75833i	−0.904046	−	0.427434i
$251$	10.3660	−	10.3660i	0.654298	−	0.654298i	−0.299727	−	0.954025i	$-0.596896\pi$
$251$	10.3660	−	10.3660i	0.654298	−	0.654298i	0.954025	+	0.299727i	$0.0968957\pi$
$252$	9.85641	+	8.53590i	0.620895	+	0.537711i
$253$		−	1.19615i		−	0.0752015i
$254$	−16.2224	+	9.36603i	−1.01789	+	0.587677i
$255$	−0.411543	−	0.464102i	−0.0257718	−	0.0290632i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−8.73205	−	2.33975i	−0.544690	−	0.145949i	−0.0240268	−	0.999711i	$-0.507649\pi$
$257$	−8.73205	−	2.33975i	−0.544690	−	0.145949i	−0.520664	+	0.853762i	$0.674315\pi$
$258$	3.07180	+	3.07180i	0.191242	+	0.191242i
$259$	1.59808	−	8.30385i	0.0992996	−	0.515976i
$260$	−11.4641	−	22.9282i	−0.710973	−	1.42195i
$261$	2.22243	−	8.29423i	0.137565	−	0.513400i
$262$	1.56218	+	0.901924i	0.0965117	+	0.0557210i
$263$	−2.83013	+	0.758330i	−0.174513	+	0.0467606i	−0.345017	−	0.938596i	$-0.612127\pi$
$263$	−2.83013	+	0.758330i	−0.174513	+	0.0467606i	0.170504	+	0.985357i	$0.445460\pi$
$264$	0.535898	+	0.928203i	0.0329823	+	0.0571270i
$265$	24.9282	−	12.4641i	1.53133	−	0.765664i
$266$	−8.36603	−	24.1506i	−0.512954	−	1.48077i
$267$			0.679492i			0.0415842i
$268$	−1.60770	+	0.928203i	−0.0982056	+	0.0566990i
$269$	8.12436	+	30.3205i	0.495351	+	1.84867i	0.528057	+	0.849209i	$0.322921\pi$
$269$	8.12436	+	30.3205i	0.495351	+	1.84867i	−0.0327062	+	0.999465i	$0.510413\pi$
$270$	−9.46410	+	8.39230i	−0.575967	+	0.510739i
$271$	0.803848	−	0.464102i	0.0488303	−	0.0281922i	−0.475386	−	0.879777i	$-0.657692\pi$
$271$	0.803848	−	0.464102i	0.0488303	−	0.0281922i	0.524216	+	0.851585i	$0.324358\pi$
$272$	−1.07180	+	1.07180i	−0.0649872	+	0.0649872i
$273$	−3.63397	−	10.4904i	−0.219938	−	0.634907i
$274$	18.2487			1.10244
$275$	1.59808	+	2.03590i	0.0963676	+	0.122769i
$276$	0.875644	+	3.26795i	0.0527076	+	0.196707i
$277$	−6.80385	−	3.92820i	−0.408804	−	0.236023i	0.281472	−	0.959569i	$-0.409177\pi$
$277$	−6.80385	−	3.92820i	−0.408804	−	0.236023i	−0.690276	+	0.723547i	$0.742511\pi$
$278$	−9.58846	+	5.53590i	−0.575077	+	0.332021i
$279$			4.92820i			0.295044i
$280$	−8.19615	+	14.5885i	−0.489814	+	0.871827i
$281$			9.00000i			0.536895i	0.963294	+	0.268447i	$0.0865106\pi$
$281$			9.00000i			0.536895i	−0.963294	+	0.268447i	$0.913489\pi$
$282$	5.39230	+	9.33975i	0.321107	+	0.556174i
$283$	18.2942	+	10.5622i	1.08748	+	0.627856i	0.932904	−	0.360125i	$-0.117266\pi$
$283$	18.2942	+	10.5622i	1.08748	+	0.627856i	0.154575	+	0.987981i	$0.450599\pi$
$284$	−9.46410	+	16.3923i	−0.561591	+	0.972704i
$285$	10.9545	−	2.24167i	0.648888	−	0.132785i
$286$			4.19615i			0.248124i
$287$	−16.2679	+	18.7846i	−0.960267	+	1.10882i
$288$	9.85641	+	9.85641i	0.580794	+	0.580794i
$289$	14.5981	−	8.42820i	0.858710	−	0.495777i
$290$	11.0000	+	0.660254i	0.645942	+	0.0387715i
$291$	−0.803848	−	3.00000i	−0.0471224	−	0.175863i
$292$	−1.46410	+	5.46410i	−0.0856801	+	0.319762i
$293$		−	5.00000i		−	0.292103i	−0.989277	−	0.146052i	$-0.953343\pi$
$293$		−	5.00000i		−	0.292103i	0.989277	−	0.146052i	$-0.0466565\pi$
$294$	−4.33975	+	5.80385i	−0.253099	+	0.338487i
$295$	21.5885	+	7.19615i	1.25693	+	0.418976i
$296$	2.33975	−	8.73205i	0.135995	−	0.507540i
$297$	2.00000	−	0.535898i	0.116052	−	0.0310960i
$298$	7.92820	−	13.7321i	0.459268	−	0.795476i
$299$	−3.42820	+	12.7942i	−0.198258	+	0.739909i
$300$	−5.85641	−	4.39230i	−0.338120	−	0.253590i
$301$	7.26795	−	8.39230i	0.418918	−	0.483724i
$302$	−17.1244	+	17.1244i	−0.985396	+	0.985396i
$303$	12.7321	+	3.41154i	0.731437	+	0.195988i
$304$	−7.07180	−	26.3923i	−0.405595	−	1.51370i
$305$	−19.3923	+	17.1962i	−1.11040	+	0.984649i
$306$	0.660254	+	1.14359i	0.0377442	+	0.0653749i
$307$			14.7321i			0.840803i	0.907338	+	0.420401i	$0.138111\pi$
$307$			14.7321i			0.840803i	−0.907338	+	0.420401i	$0.861889\pi$
$308$	2.26795	−	1.53590i	0.129228	−	0.0875159i
$309$	3.80385	−	3.80385i	0.216393	−	0.216393i
$310$	−6.19615	+	1.26795i	−0.351918	+	0.0720147i
$311$	−10.8564	+	18.8038i	−0.615610	+	1.06627i	0.374667	+	0.927160i	$0.377757\pi$
$311$	−10.8564	+	18.8038i	−0.615610	+	1.06627i	−0.990277	+	0.139109i	$0.955576\pi$
$312$	−3.07180	−	11.4641i	−0.173906	−	0.649027i
$313$	−15.3923	−	4.12436i	−0.870025	−	0.233122i	−0.203926	−	0.978986i	$-0.565370\pi$
$313$	−15.3923	−	4.12436i	−0.870025	−	0.233122i	−0.666098	+	0.745864i	$0.732037\pi$
$314$	−1.00000	+	1.00000i	−0.0564333	+	0.0564333i
$315$	10.4282	+	10.1865i	0.587563	+	0.573946i
$316$	13.4641			0.757415
$317$	−4.19615	−	7.26795i	−0.235679	−	0.408209i	0.723791	−	0.690020i	$-0.242398\pi$
$317$	−4.19615	−	7.26795i	−0.235679	−	0.408209i	−0.959470	+	0.281811i	$0.909065\pi$
$318$	12.4641	−	3.33975i	0.698952	−	0.187284i
$319$	−1.56218	−	0.901924i	−0.0874652	−	0.0504980i
$320$	−9.85641	+	14.9282i	−0.550990	+	0.834512i
$321$		−	6.53590i		−	0.364798i
$322$	8.16987	−	2.83013i	0.455289	−	0.157717i
$323$		−	2.58846i		−	0.144026i
$324$	7.73205	−	4.46410i	0.429558	−	0.248006i
$325$	−11.2583	−	26.3564i	−0.624500	−	1.46199i
$326$	1.46410	+	5.46410i	0.0810891	+	0.302629i
$327$	3.21539	−	12.0000i	0.177811	−	0.663602i
$328$	−18.7846	+	18.7846i	−1.03721	+	1.03721i
$329$	22.8205	−	15.4545i	1.25814	−	0.852033i
$330$	0.535898	+	1.07180i	0.0295002	+	0.0590005i
$331$	2.30385	−	8.59808i	0.126631	−	0.472593i	−0.873262	−	0.487252i	$-0.837999\pi$
$331$	2.30385	−	8.59808i	0.126631	−	0.472593i	0.999893	+	0.0146586i	$0.00466614\pi$
$332$	26.7846	+	15.4641i	1.47000	+	0.848703i
$333$	−6.82051	−	3.93782i	−0.373762	−	0.215791i
$334$	−17.4904	+	10.0981i	−0.957031	+	0.552542i
$335$	−1.85641	+	0.928203i	−0.101426	+	0.0507132i
$336$	−5.07180	+	5.85641i	−0.276689	+	0.319493i
$337$	−11.9282	−	11.9282i	−0.649771	−	0.649771i	0.303167	−	0.952937i	$-0.401956\pi$
$337$	−11.9282	−	11.9282i	−0.649771	−	0.649771i	−0.952937	+	0.303167i	$0.901956\pi$
$338$	7.26795	−	27.1244i	0.395324	−	1.47537i
$339$	−0.784610	−	2.92820i	−0.0426141	−	0.159038i
$340$	−1.26795	+	1.12436i	−0.0687642	+	0.0609767i
$341$	1.00000	+	0.267949i	0.0541530	+	0.0145103i
$342$	−23.8038			−1.28716
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	8.39230	−	8.39230i	0.452483	−	0.452483i
$345$	0.758330	+	3.70577i	0.0408271	+	0.199512i
$346$	−8.83013	+	2.36603i	−0.474711	+	0.127198i
$347$	−30.5885	−	17.6603i	−1.64207	−	0.948052i	−0.980095	−	0.198530i	$-0.936383\pi$
$347$	−30.5885	−	17.6603i	−1.64207	−	0.948052i	−0.661980	−	0.749522i	$-0.730283\pi$
$348$	4.92820	+	1.32051i	0.264179	+	0.0707867i
$349$	−2.07180	+	2.07180i	−0.110901	+	0.110901i	−0.760380	−	0.649479i	$-0.774987\pi$
$349$	−2.07180	+	2.07180i	−0.110901	+	0.110901i	0.649479	+	0.760380i	$0.274987\pi$
$350$	−10.1244	+	15.7321i	−0.541170	+	0.840913i
$351$	−22.9282			−1.22382
$352$	2.53590	−	1.46410i	0.135164	−	0.0780369i
$353$	−18.6603	+	5.00000i	−0.993185	+	0.266123i	−0.718588	−	0.695436i	$-0.755211\pi$
$353$	−18.6603	+	5.00000i	−0.993185	+	0.266123i	−0.274597	+	0.961559i	$0.588545\pi$
$354$	9.12436	+	5.26795i	0.484954	+	0.279988i
$355$	−11.6603	+	17.6603i	−0.618862	+	0.937309i
$356$	1.85641			0.0983893
$357$	−0.607695	+	0.411543i	−0.0321626	+	0.0217812i
$358$		−	22.0526i		−	1.16551i
$359$	−1.56218	−	2.70577i	−0.0824486	−	0.142805i	0.821853	−	0.569700i	$-0.192941\pi$
$359$	−1.56218	−	2.70577i	−0.0824486	−	0.142805i	−0.904301	+	0.426895i	$0.859607\pi$
$360$	10.3397	+	11.6603i	0.544952	+	0.614549i
$361$	23.9545	+	13.8301i	1.26076	+	0.727901i
$362$	0.464102	+	0.803848i	0.0243926	+	0.0422493i
$363$			7.85641i			0.412354i
$364$	−28.6603	+	9.92820i	−1.50221	+	0.520379i
$365$	−2.00000	+	6.00000i	−0.104685	+	0.314054i
$366$	−10.3923	+	6.00000i	−0.543214	+	0.313625i
$367$	2.30385	+	8.59808i	0.120260	+	0.448816i	0.999626	−	0.0273294i	$-0.00870029\pi$
$367$	2.30385	+	8.59808i	0.120260	+	0.448816i	−0.879367	+	0.476145i	$0.842034\pi$
$368$	8.92820	−	2.39230i	0.465415	−	0.124708i
$369$	11.5718	+	20.0429i	0.602404	+	1.04339i
$370$	3.19615	−	9.58846i	0.166160	−	0.498480i
$371$	−10.7942	−	31.1603i	−0.560408	−	1.61776i
$372$	−2.92820			−0.151820
$373$	14.8564	+	25.7321i	0.769236	+	1.33236i	0.937978	+	0.346695i	$0.112696\pi$
$373$	14.8564	+	25.7321i	0.769236	+	1.33236i	−0.168742	+	0.985660i	$0.553971\pi$
$374$	0.267949	−	0.0717968i	0.0138553	−	0.00371252i
$375$	−6.24167	−	5.29423i	−0.322318	−	0.273393i
$376$	25.5167	−	14.7321i	1.31592	−	0.759748i
$377$	14.1244	+	14.1244i	0.727441	+	0.727441i
$378$	8.39230	+	12.3923i	0.431654	+	0.637391i
$379$	−12.8301	+	12.8301i	−0.659039	+	0.659039i	−0.955153	−	0.296113i	$-0.904309\pi$
$379$	−12.8301	+	12.8301i	−0.659039	+	0.659039i	0.296113	+	0.955153i	$0.404309\pi$
$380$	−6.12436	−	29.9282i	−0.314173	−	1.53528i
$381$	−9.36603	+	2.50962i	−0.479836	+	0.128572i
$382$	32.5885	−	8.73205i	1.66737	−	0.446771i
$383$	1.99038	−	7.42820i	0.101704	−	0.379563i	−0.896247	−	0.443556i	$-0.853717\pi$
$383$	1.99038	−	7.42820i	0.101704	−	0.379563i	0.997950	+	0.0639926i	$0.0203834\pi$
$384$	−5.85641	+	5.85641i	−0.298858	+	0.298858i
$385$	2.63397	−	1.56218i	0.134240	−	0.0796160i
$386$	−3.60770			−0.183627
$387$	−5.16987	−	8.95448i	−0.262799	−	0.455182i
$388$	−8.19615	+	2.19615i	−0.416097	+	0.111493i
$389$	−2.85641	−	10.6603i	−0.144826	−	0.540496i	−0.999763	−	0.0217654i	$-0.993071\pi$
$389$	−2.85641	−	10.6603i	−0.144826	−	0.540496i	0.854938	−	0.518731i	$-0.173595\pi$
$390$	−2.66025	−	13.0000i	−0.134707	−	0.658281i
$391$	0.875644			0.0442832
$392$	15.8564	+	11.8564i	0.800869	+	0.598839i
$393$	0.660254	+	0.660254i	0.0333054	+	0.0333054i
$394$	27.2224	+	7.29423i	1.37145	+	0.367478i
$395$	15.0263	+	0.901924i	0.756054	+	0.0453807i
$396$	−0.660254	−	2.46410i	−0.0331790	−	0.123826i
$397$	14.0718	−	8.12436i	0.706243	−	0.407750i	−0.103425	−	0.994637i	$-0.532980\pi$
$397$	14.0718	−	8.12436i	0.706243	−	0.407750i	0.809668	+	0.586888i	$0.199647\pi$
$398$	−0.535898	+	0.535898i	−0.0268622	+	0.0268622i
$399$	−0.947441	−	13.1962i	−0.0474314	−	0.660634i
$400$	−12.0000	+	16.0000i	−0.600000	+	0.800000i
$401$	−2.93782	−	5.08846i	−0.146708	−	0.254105i	0.783301	−	0.621643i	$-0.213534\pi$
$401$	−2.93782	−	5.08846i	−0.146708	−	0.254105i	−0.930009	+	0.367537i	$0.880201\pi$
$402$	−0.928203	+	0.248711i	−0.0462946	+	0.0124046i
$403$	−9.92820	−	5.73205i	−0.494559	−	0.285534i
$404$	9.32051	−	34.7846i	0.463713	−	1.73060i
$405$	8.92820	−	4.46410i	0.443646	−	0.221823i
$406$	2.46410	−	12.8038i	0.122291	−	0.635444i
$407$	−1.16987	+	1.16987i	−0.0579885	+	0.0579885i
$408$	−0.679492	+	0.392305i	−0.0336399	+	0.0194220i
$409$	−25.5167	−	14.7321i	−1.26172	−	0.728453i	−0.288311	−	0.957537i	$-0.593094\pi$
$409$	−25.5167	−	14.7321i	−1.26172	−	0.728453i	−0.973407	+	0.229084i	$0.926427\pi$
$410$	−22.2224	+	19.7058i	−1.09749	+	0.973199i
$411$	9.12436	+	2.44486i	0.450071	+	0.120596i
$412$	−10.3923	−	10.3923i	−0.511992	−	0.511992i
$413$	11.7583	−	24.2224i	0.578590	−	1.19191i
$414$		−	8.05256i		−	0.395762i
$415$	28.8564	+	19.0526i	1.41651	+	0.935253i
$416$	−31.3205	+	8.39230i	−1.53561	+	0.411467i
$417$	−5.53590	+	1.48334i	−0.271094	+	0.0726394i
$418$	−1.29423	+	4.83013i	−0.0633028	+	0.236249i
$419$	1.75833	−	1.75833i	0.0859001	−	0.0859001i	−0.662851	−	0.748751i	$-0.730654\pi$
$419$	1.75833	−	1.75833i	0.0859001	−	0.0859001i	0.748751	+	0.662851i	$0.230654\pi$
$420$	−6.05256	+	6.19615i	−0.295335	+	0.302341i
$421$	−16.3205	−	16.3205i	−0.795413	−	0.795413i	0.186955	−	0.982368i	$-0.440138\pi$
$421$	−16.3205	−	16.3205i	−0.795413	−	0.795413i	−0.982368	+	0.186955i	$0.940138\pi$
$422$	−4.63397	−	8.02628i	−0.225578	−	0.390713i
$423$	−6.64359	−	24.7942i	−0.323023	−	1.20554i
$424$	−9.12436	−	34.0526i	−0.443118	−	1.65374i
$425$	−1.49038	+	1.16987i	−0.0722941	+	0.0567472i
$426$	−6.92820	+	6.92820i	−0.335673	+	0.335673i
$427$	17.1962	+	25.3923i	0.832180	+	1.22882i
$428$	−17.8564			−0.863122
$429$	−0.562178	+	2.09808i	−0.0271422	+	0.101296i
$430$	9.92820	−	8.80385i	0.478780	−	0.424559i
$431$	2.19615	−	3.80385i	0.105785	−	0.183225i	−0.808274	−	0.588807i	$-0.799598\pi$
$431$	2.19615	−	3.80385i	0.105785	−	0.183225i	0.914059	+	0.405582i	$0.132931\pi$
$432$	8.00000	+	13.8564i	0.384900	+	0.666667i
$433$	−2.73205	−	2.73205i	−0.131294	−	0.131294i	0.638406	−	0.769700i	$-0.279594\pi$
$433$	−2.73205	−	2.73205i	−0.131294	−	0.131294i	−0.769700	+	0.638406i	$0.779594\pi$
$434$	0.535898	+	7.46410i	0.0257239	+	0.358288i
$435$	5.41154	+	1.80385i	0.259464	+	0.0864879i
$436$	−32.7846	−	8.78461i	−1.57010	−	0.420707i
$437$	−7.89230	+	13.6699i	−0.377540	+	0.653919i
$438$	−1.46410	+	2.53590i	−0.0699575	+	0.121170i
$439$	−33.2942	+	19.2224i	−1.58905	+	0.917437i	−0.595582	+	0.803294i	$0.703079\pi$
$439$	−33.2942	+	19.2224i	−1.58905	+	0.917437i	−0.993464	+	0.114142i	$0.963588\pi$
$440$	2.92820	−	1.46410i	0.139597	−	0.0697983i
$441$	13.5526	−	10.6699i	0.645360	−	0.508089i
$442$	−3.07180			−0.146110
$443$	16.6603	+	28.8564i	0.791553	+	1.37101i	0.925005	+	0.379954i	$0.124060\pi$
$443$	16.6603	+	28.8564i	0.791553	+	1.37101i	−0.133453	+	0.991055i	$0.542606\pi$
$444$	2.33975	−	4.05256i	0.111039	−	0.192326i
$445$	2.07180	+	0.124356i	0.0982126	+	0.00589502i
$446$	−9.58846	+	5.53590i	−0.454027	+	0.262132i
$447$	5.80385	−	5.80385i	0.274513	−	0.274513i
$448$	16.0000	+	13.8564i	0.755929	+	0.654654i
$449$		−	0.0717968i		−	0.00338830i	−0.999999	−	0.00169415i	$-0.999461\pi$
$449$		−	0.0717968i		−	0.00338830i	0.999999	−	0.00169415i	$-0.000539265\pi$
$450$	10.7583	+	13.7058i	0.507153	+	0.646096i
$451$	4.69615	−	1.25833i	0.221133	−	0.0592525i
$452$	−8.00000	+	2.14359i	−0.376288	+	0.100826i
$453$	−10.8564	+	6.26795i	−0.510078	+	0.294494i
$454$	4.39230	−	4.39230i	0.206141	−	0.206141i
$455$	−32.6506	+	9.16025i	−1.53069	+	0.429439i
$456$		−	14.1436i		−	0.662334i
$457$	−30.7583	−	8.24167i	−1.43881	−	0.385529i	−0.546696	−	0.837331i	$-0.684115\pi$
$457$	−30.7583	−	8.24167i	−1.43881	−	0.385529i	−0.892118	+	0.451802i	$0.850781\pi$
$458$	−11.3205	−	6.53590i	−0.528973	−	0.305402i
$459$	0.392305	+	1.46410i	0.0183112	+	0.0683384i
$460$	10.1244	−	2.07180i	0.472051	−	0.0965980i
$461$	−13.7321	−	13.7321i	−0.639565	−	0.639565i	0.310883	−	0.950448i	$-0.399375\pi$
$461$	−13.7321	−	13.7321i	−0.639565	−	0.639565i	−0.950448	+	0.310883i	$0.899375\pi$
$462$	1.33975	−	0.464102i	0.0623306	−	0.0215920i
$463$	−2.56218	+	2.56218i	−0.119075	+	0.119075i	−0.764133	−	0.645059i	$-0.776833\pi$
$463$	−2.56218	+	2.56218i	−0.119075	+	0.119075i	0.645059	+	0.764133i	$0.276833\pi$
$464$	3.60770	−	13.4641i	0.167483	−	0.625055i
$465$	−3.26795	−	0.196152i	−0.151548	−	0.00909635i
$466$	−9.33975	−	5.39230i	−0.432655	−	0.249794i
$467$	−3.75833	+	2.16987i	−0.173915	+	0.100410i	−0.584430	−	0.811444i	$-0.698682\pi$
$467$	−3.75833	+	2.16987i	−0.173915	+	0.100410i	0.410516	+	0.911854i	$0.365349\pi$
$468$			28.2487i			1.30580i
$469$	0.803848	+	2.32051i	0.0371182	+	0.107151i
$470$	29.4641	−	14.7321i	1.35908	−	0.679539i
$471$	−0.633975	+	0.366025i	−0.0292120	+	0.0168656i
$472$	14.3923	−	24.9282i	0.662460	−	1.14741i
$473$	−2.09808	+	0.562178i	−0.0964696	+	0.0258490i
$474$	6.73205	+	1.80385i	0.309213	+	0.0828535i
$475$	−4.83013	−	33.8109i	−0.221621	−	1.55135i
$476$	1.12436	+	1.66025i	0.0515348	+	0.0760976i
$477$	−30.7128			−1.40624
$478$	10.4641	+	2.80385i	0.478617	+	0.128245i
$479$	−3.53590	+	6.12436i	−0.161559	+	0.279829i	−0.935428	−	0.353517i	$-0.884986\pi$
$479$	−3.53590	+	6.12436i	−0.161559	+	0.279829i	0.773869	+	0.633346i	$0.218319\pi$
$480$	−6.92820	+	6.14359i	−0.316228	+	0.280415i
$481$	15.8660	−	9.16025i	0.723428	−	0.417672i
$482$	11.7321	−	11.7321i	0.534380	−	0.534380i
$483$	4.46410	−	0.320508i	0.203124	−	0.0145836i
$484$	21.4641			0.975641
$485$	−9.29423	+	1.90192i	−0.422029	+	0.0863619i
$486$	20.8564	−	5.58846i	0.946066	−	0.253498i
$487$	3.09808	+	11.5622i	0.140387	+	0.523932i	0.999917	+	0.0128474i	$0.00408956\pi$
$487$	3.09808	+	11.5622i	0.140387	+	0.523932i	−0.859530	+	0.511085i	$0.829244\pi$
$488$	16.3923	+	28.3923i	0.742045	+	1.28526i
$489$			2.92820i			0.132418i
$490$	16.9019	+	14.2942i	0.763551	+	0.645747i
$491$	1.39230	+	1.39230i	0.0628338	+	0.0628338i	0.737825	−	0.674992i	$-0.235853\pi$
$491$	1.39230	+	1.39230i	0.0628338	+	0.0628338i	−0.674992	+	0.737825i	$0.735853\pi$
$492$	−11.9090	+	6.87564i	−0.536898	+	0.309978i
$493$	0.660254	−	1.14359i	0.0297363	−	0.0515049i
$494$	27.6865	−	47.9545i	1.24568	−	2.15757i
$495$	−0.571797	−	2.79423i	−0.0257004	−	0.125591i
$496$			8.00000i			0.359211i
$497$	18.9282	+	16.3923i	0.849046	+	0.735295i
$498$	11.3205	+	11.3205i	0.507284	+	0.507284i
$499$	2.95448	−	11.0263i	0.132261	−	0.493604i	−0.867733	−	0.497030i	$-0.834424\pi$
$499$	2.95448	−	11.0263i	0.132261	−	0.493604i	0.999994	+	0.00342600i	$0.00109053\pi$
$500$	−14.4641	+	17.0526i	−0.646854	+	0.762614i
$501$	−10.0981	+	2.70577i	−0.451149	+	0.120885i
$502$	−10.3660	−	17.9545i	−0.462658	−	0.801348i
$503$	10.0718	−	10.0718i	0.449079	−	0.449079i	−0.445969	−	0.895048i	$-0.647141\pi$
$503$	10.0718	−	10.0718i	0.449079	−	0.449079i	0.895048	+	0.445969i	$0.147141\pi$
$504$	15.2679	−	10.3397i	0.680089	−	0.460569i
$505$	12.7321	−	38.1962i	0.566569	−	1.69971i
$506$	−1.63397	−	0.437822i	−0.0726390	−	0.0194636i
$507$	7.26795	−	12.5885i	0.322781	−	0.559073i
$508$	6.85641	+	25.5885i	0.304204	+	1.13530i
$509$	0.366025	+	0.0980762i	0.0162238	+	0.00434715i	0.266922	−	0.963718i	$-0.413993\pi$
$509$	0.366025	+	0.0980762i	0.0162238	+	0.00434715i	−0.250698	+	0.968065i	$0.580660\pi$
$510$	−0.784610	+	0.392305i	−0.0347431	+	0.0173716i
$511$	6.73205	+	3.26795i	0.297808	+	0.144566i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−26.3923	−	7.07180i	−1.16525	−	0.312227i
$514$	−6.39230	+	11.0718i	−0.281952	+	0.488356i
$515$	−10.9019	−	12.2942i	−0.480396	−	0.541748i
$516$	5.32051	−	3.07180i	0.234222	−	0.135228i
$517$	−5.39230			−0.237153
$518$	−10.7583	−	5.22243i	−0.472694	−	0.229460i
$519$	−4.73205			−0.207714
$520$	−35.5167	+	7.26795i	−1.55751	+	0.318721i
$521$	−15.9904	+	27.6962i	−0.700551	+	1.21339i	0.267722	+	0.963496i	$0.413729\pi$
$521$	−15.9904	+	27.6962i	−0.700551	+	1.21339i	−0.968273	+	0.249894i	$0.919604\pi$
$522$	−10.5167	−	6.07180i	−0.460302	−	0.265755i
$523$	14.5359	−	8.39230i	0.635610	−	0.366970i	−0.147311	−	0.989090i	$-0.547062\pi$
$523$	14.5359	−	8.39230i	0.635610	−	0.366970i	0.782922	+	0.622120i	$0.213729\pi$
$524$	1.80385	−	1.80385i	0.0788014	−	0.0788014i
$525$	−7.16987	+	6.50962i	−0.312919	+	0.284103i
$526$			4.14359i			0.180669i
$527$	−0.196152	+	0.732051i	−0.00854453	+	0.0318886i
$528$	1.46410	−	0.392305i	0.0637168	−	0.0170729i
$529$	15.2942	+	8.83013i	0.664966	+	0.383919i
$530$	−7.90192	−	38.6147i	−0.343238	−	1.67732i
$531$	−17.7321	−	17.7321i	−0.769505	−	0.769505i
$532$	−36.0526	+	2.58846i	−1.56308	+	0.112224i
$533$	−53.8372			−2.33195
$534$	0.928203	+	0.248711i	0.0401673	+	0.0107628i
$535$	−19.9282	−	1.19615i	−0.861571	−	0.0517142i
$536$	0.679492	+	2.53590i	0.0293496	+	0.109534i
$537$	2.95448	−	11.0263i	0.127495	−	0.475819i
$538$	44.3923			1.91389
$539$	−1.42820	−	3.33013i	−0.0615171	−	0.143439i
$540$	8.00000	+	16.0000i	0.344265	+	0.688530i
$541$	−22.9282	−	6.14359i	−0.985760	−	0.264134i	−0.270292	−	0.962778i	$-0.587120\pi$
$541$	−22.9282	−	6.14359i	−0.985760	−	0.264134i	−0.715469	+	0.698645i	$0.753787\pi$
$542$	−0.339746	−	1.26795i	−0.0145933	−	0.0544631i
$543$	0.124356	+	0.464102i	0.00533661	+	0.0199165i
$544$	1.07180	+	1.85641i	0.0459529	+	0.0795928i
$545$	−36.0000	−	12.0000i	−1.54207	−	0.514024i
$546$	−15.6603	+	1.12436i	−0.670197	+	0.0481180i
$547$	24.7846			1.05971			0.529857	−	0.848087i	$-0.322246\pi$
$547$	24.7846			1.05971			0.529857	+	0.848087i	$0.322246\pi$
$548$	6.67949	−	24.9282i	0.285334	−	1.06488i
$549$	27.5885	−	7.39230i	1.17745	−	0.315496i
$550$	3.36603	−	1.43782i	0.143528	−	0.0613089i
$551$	11.9019	+	20.6147i	0.507039	+	0.878217i
$552$	4.78461			0.203647
$553$	3.36603	−	17.4904i	0.143138	−	0.743767i
$554$	−7.85641	+	7.85641i	−0.333787	+	0.333787i
$555$	2.88269	−	4.36603i	0.122363	−	0.185327i
$556$	4.05256	+	15.1244i	0.171867	+	0.641416i
$557$	−10.4019	+	18.0167i	−0.440744	+	0.763390i	−0.997745	−	0.0671213i	$-0.978619\pi$
$557$	−10.4019	+	18.0167i	−0.440744	+	0.763390i	0.557001	+	0.830512i	$0.311952\pi$
$558$	6.73205	+	1.80385i	0.284990	+	0.0763630i
$559$	24.0526			1.01731
$560$	16.9282	+	16.5359i	0.715347	+	0.698769i
$561$	0.143594			0.00606252
$562$	12.2942	+	3.29423i	0.518601	+	0.138959i
$563$	11.2224	−	19.4378i	0.472969	−	0.819207i	−0.526552	−	0.850143i	$-0.676516\pi$
$563$	11.2224	−	19.4378i	0.472969	−	0.819207i	0.999521	+	0.0309362i	$0.00984888\pi$
$564$	14.7321	−	3.94744i	0.620331	−	0.166217i
$565$	−9.07180	+	1.85641i	−0.381653	+	0.0780996i
$566$	21.1244	−	21.1244i	0.887923	−	0.887923i
$567$	−3.86603	−	11.1603i	−0.162358	−	0.468687i
$568$	18.9282	+	18.9282i	0.794210	+	0.794210i
$569$	2.79423	+	4.83975i	0.117140	+	0.202893i	0.918633	−	0.395111i	$-0.129294\pi$
$569$	2.79423	+	4.83975i	0.117140	+	0.202893i	−0.801493	+	0.598004i	$0.795961\pi$
$570$	0.947441	−	15.7846i	0.0396839	−	0.661145i
$571$	−42.8827	+	11.4904i	−1.79458	+	0.480857i	−0.993111	−	0.117173i	$-0.962617\pi$
$571$	−42.8827	+	11.4904i	−1.79458	+	0.480857i	−0.801473	+	0.598031i	$0.795950\pi$
$572$	5.73205	+	1.53590i	0.239669	+	0.0642191i
$573$	17.4641			0.729573
$574$	19.7058	+	29.0981i	0.822503	+	1.21453i
$575$	11.4378	−	1.63397i	0.476990	−	0.0681415i
$576$	17.0718	−	9.85641i	0.711325	−	0.410684i
$577$	−7.39230	−	27.5885i	−0.307746	−	1.14852i	−0.930556	−	0.366150i	$-0.880676\pi$
$577$	−7.39230	−	27.5885i	−0.307746	−	1.14852i	0.622810	−	0.782373i	$-0.285991\pi$
$578$	−6.16987	−	23.0263i	−0.256633	−	0.957767i
$579$	−1.80385	−	0.483340i	−0.0749653	−	0.0200869i
$580$	4.92820	−	14.7846i	0.204633	−	0.613898i
$581$	26.7846	−	30.9282i	1.11121	−	1.28312i
$582$	−4.39230			−0.182067
$583$	−1.66987	+	6.23205i	−0.0691591	+	0.258105i
$584$	6.92820	+	4.00000i	0.286691	+	0.165521i
$585$	−1.89230	+	31.5263i	−0.0782372	+	1.30345i
$586$	−6.83013	−	1.83013i	−0.282150	−	0.0756019i
$587$	−24.9282			−1.02890			−0.514449	−	0.857521i	$-0.672003\pi$
$587$	−24.9282			−1.02890			−0.514449	+	0.857521i	$0.672003\pi$
$588$	6.33975	+	8.05256i	0.261447	+	0.332082i
$589$	−9.66025	−	9.66025i	−0.398044	−	0.398044i
$590$	17.7321	−	26.8564i	0.730017	−	1.10566i
$591$	12.6340	+	7.29423i	0.519692	+	0.300044i
$592$	−11.0718	−	6.39230i	−0.455048	−	0.262722i
$593$	4.92820	−	18.3923i	0.202377	−	0.755281i	−0.787856	−	0.615859i	$-0.788809\pi$
$593$	4.92820	−	18.3923i	0.202377	−	0.755281i	0.990233	−	0.139422i	$-0.0445244\pi$
$594$		−	2.92820i		−	0.120146i
$595$	1.14359	+	1.92820i	0.0468828	+	0.0790486i
$596$	−15.8564	−	15.8564i	−0.649504	−	0.649504i
$597$	−0.339746	+	0.196152i	−0.0139049	+	0.00802798i
$598$	16.2224	+	9.36603i	0.663385	+	0.383005i
$599$	7.43782	−	12.8827i	0.303901	−	0.526372i	−0.673115	−	0.739538i	$-0.735044\pi$
$599$	7.43782	−	12.8827i	0.303901	−	0.526372i	0.977016	+	0.213166i	$0.0683774\pi$
$600$	−8.14359	+	6.39230i	−0.332461	+	0.260965i
$601$	−36.6410			−1.49462			−0.747309	−	0.664477i	$-0.768655\pi$
$601$	−36.6410			−1.49462			−0.747309	+	0.664477i	$0.768655\pi$
$602$	−8.80385	−	13.0000i	−0.358818	−	0.529840i
$603$	2.28719			0.0931415
$604$	17.1244	+	29.6603i	0.696780	+	1.20686i
$605$	23.9545	+	1.43782i	0.973888	+	0.0584558i
$606$	9.32051	−	16.1436i	0.378620	−	0.655789i
$607$	−24.6244	−	6.59808i	−0.999472	−	0.267808i	−0.278248	−	0.960509i	$-0.589754\pi$
$607$	−24.6244	−	6.59808i	−0.999472	−	0.267808i	−0.721224	+	0.692702i	$0.756420\pi$
$608$	−38.6410			−1.56710
$609$	2.94744	−	6.07180i	0.119436	−	0.246042i
$610$	16.3923	+	32.7846i	0.663705	+	1.32741i
$611$	57.6769	+	15.4545i	2.33336	+	0.625221i
$612$	1.80385	−	0.483340i	0.0729162	−	0.0195378i
$613$	18.4282	−	31.9186i	0.744308	−	1.28918i	−0.206209	−	0.978508i	$-0.566113\pi$
$613$	18.4282	−	31.9186i	0.744308	−	1.28918i	0.950517	−	0.310672i	$-0.100554\pi$
$614$	20.1244	+	5.39230i	0.812153	+	0.217616i
$615$	−13.7513	+	6.87564i	−0.554505	+	0.277253i
$616$	−1.26795	−	3.66025i	−0.0510871	−	0.147476i
$617$	−1.33975	+	1.33975i	−0.0539361	+	0.0539361i	−0.733560	−	0.679624i	$-0.762143\pi$
$617$	−1.33975	+	1.33975i	−0.0539361	+	0.0539361i	0.679624	+	0.733560i	$0.262143\pi$
$618$	−3.80385	−	6.58846i	−0.153013	−	0.265027i
$619$	28.5526	−	7.65064i	1.14762	−	0.307505i	0.365612	−	0.930768i	$-0.380860\pi$
$619$	28.5526	−	7.65064i	1.14762	−	0.307505i	0.782013	+	0.623263i	$0.214193\pi$
$620$	−0.535898	+	8.92820i	−0.0215222	+	0.358565i
$621$	2.39230	−	8.92820i	0.0959999	−	0.358276i
$622$	21.7128	+	21.7128i	0.870604	+	0.870604i
$623$	0.464102	−	2.41154i	0.0185938	−	0.0966164i
$624$	−16.7846			−0.671922
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	−11.2679	+	19.5167i	−0.450358	+	0.780043i
$627$	−1.29423	+	2.24167i	−0.0516865	+	0.0895237i
$628$	1.00000	+	1.73205i	0.0399043	+	0.0691164i
$629$	−0.856406	−	0.856406i	−0.0341472	−	0.0341472i
$630$	17.7321	−	10.5167i	0.706462	−	0.418994i
$631$		−	45.5692i		−	1.81408i	−0.421042	−	0.907041i	$-0.638336\pi$
$631$		−	45.5692i		−	1.81408i	0.421042	−	0.907041i	$-0.361664\pi$
$632$	4.92820	−	18.3923i	0.196033	−	0.731607i
$633$	−1.24167	−	4.63397i	−0.0493519	−	0.184184i
$634$	−11.4641	+	3.07180i	−0.455298	+	0.121997i
$635$	5.93782	+	29.0167i	0.235635	+	1.15149i
$636$		−	18.2487i		−	0.723608i
$637$	5.73205	+	39.7128i	0.227112	+	1.57348i
$638$	−1.80385	+	1.80385i	−0.0714150	+	0.0714150i
$639$	20.1962	−	11.6603i	0.798947	−	0.461273i
$640$	16.7846	+	18.9282i	0.663470	+	0.748203i
$641$	1.96410	−	3.40192i	0.0775773	−	0.134368i	−0.824627	−	0.565677i	$-0.808615\pi$
$641$	1.96410	−	3.40192i	0.0775773	−	0.134368i	0.902204	+	0.431309i	$0.141948\pi$
$642$	−8.92820	−	2.39230i	−0.352368	−	0.0944167i
$643$	−18.1962			−0.717586			−0.358793	−	0.933417i	$-0.616812\pi$
$643$	−18.1962			−0.717586			−0.358793	+	0.933417i	$0.616812\pi$
$644$	−0.875644	−	12.1962i	−0.0345052	−	0.480596i
$645$	6.14359	−	3.07180i	0.241904	−	0.120952i
$646$	−3.53590	−	0.947441i	−0.139118	−	0.0372766i
$647$	26.8923	−	7.20577i	1.05725	−	0.283288i	0.312003	−	0.950081i	$-0.399000\pi$
$647$	26.8923	−	7.20577i	1.05725	−	0.283288i	0.745243	+	0.666793i	$0.232334\pi$
$648$	−3.26795	−	12.1962i	−0.128377	−	0.479110i
$649$	−4.56218	+	2.63397i	−0.179081	+	0.103393i
$650$	−40.1244	+	5.73205i	−1.57381	+	0.224830i
$651$	−0.732051	+	3.80385i	−0.0286913	+	0.149085i
$652$	8.00000			0.313304
$653$	18.1865	−	10.5000i	0.711694	−	0.410897i	−0.0999939	−	0.994988i	$-0.531882\pi$
$653$	18.1865	−	10.5000i	0.711694	−	0.410897i	0.811688	+	0.584091i	$0.198549\pi$
$654$	−15.2154	−	8.78461i	−0.594969	−	0.343505i
$655$	2.13397	−	1.89230i	0.0833813	−	0.0739385i
$656$	18.7846	+	32.5359i	0.733416	+	1.27031i
$657$	4.92820	−	4.92820i	0.192268	−	0.192268i
$658$	−12.7583	−	36.8301i	−0.497371	−	1.43579i
$659$	−18.8038	−	18.8038i	−0.732494	−	0.732494i	0.238619	−	0.971113i	$-0.423305\pi$
$659$	−18.8038	−	18.8038i	−0.732494	−	0.732494i	−0.971113	+	0.238619i	$0.923305\pi$
$660$	1.66025	−	0.339746i	0.0646253	−	0.0132246i
$661$	6.26795	+	23.3923i	0.243795	+	0.909855i	0.973985	+	0.226611i	$0.0727647\pi$
$661$	6.26795	+	23.3923i	0.243795	+	0.909855i	−0.730190	+	0.683244i	$0.760569\pi$
$662$	−10.9019	−	6.29423i	−0.423715	−	0.244632i
$663$	−1.53590	−	0.411543i	−0.0596494	−	0.0159830i
$664$	30.9282	−	30.9282i	1.20025	−	1.20025i
$665$	−40.4090	+	0.473721i	−1.56699	+	0.0183701i
$666$	−7.87564	+	7.87564i	−0.305175	+	0.305175i
$667$	−6.97372	+	4.02628i	−0.270024	+	0.155898i
$668$	7.39230	+	27.5885i	0.286017	+	1.06743i
$669$	−5.53590	+	1.48334i	−0.214030	+	0.0573492i
$670$	0.588457	+	2.87564i	0.0227341	+	0.111096i
$671$		−	6.00000i		−	0.231627i
$672$	6.14359	+	9.07180i	0.236994	+	0.349952i
$673$	−27.9282	+	27.9282i	−1.07655	+	1.07655i	−0.0797372	+	0.996816i	$0.525408\pi$
$673$	−27.9282	+	27.9282i	−1.07655	+	1.07655i	−0.996816	+	0.0797372i	$0.974592\pi$
$674$	−20.6603	+	11.9282i	−0.795803	+	0.459457i
$675$	7.85641	+	18.3923i	0.302393	+	0.707920i
$676$	−34.3923	−	19.8564i	−1.32278	−	0.763708i
$677$	7.66987	+	13.2846i	0.294777	+	0.510569i	0.974933	−	0.222498i	$-0.0714212\pi$
$677$	7.66987	+	13.2846i	0.294777	+	0.510569i	−0.680156	+	0.733068i	$0.738088\pi$
$678$	−4.28719			−0.164648
$679$	0.803848	+	11.1962i	0.0308488	+	0.429669i
$680$	1.07180	+	2.14359i	0.0411015	+	0.0822031i
$681$	2.78461	−	1.60770i	0.106706	−	0.0616070i
$682$	0.732051	−	1.26795i	0.0280317	−	0.0485523i
$683$	−4.73205	+	8.19615i	−0.181067	+	0.313617i	−0.942244	−	0.334927i	$-0.891288\pi$
$683$	−4.73205	+	8.19615i	−0.181067	+	0.313617i	0.761177	+	0.648544i	$0.224622\pi$
$684$	−8.71281	+	32.5167i	−0.333143	+	1.24331i
$685$	9.12436	−	27.3731i	0.348624	−	1.04587i
$686$	19.3660	−	17.6340i	0.739398	−	0.673268i
$687$	−4.78461	−	4.78461i	−0.182544	−	0.182544i
$688$	−8.39230	−	14.5359i	−0.319954	−	0.554176i
$689$	35.7224	−	61.8731i	1.36092	−	2.35718i
$690$	5.33975	+	0.320508i	0.203281	+	0.0122015i
$691$	−8.24167	+	30.7583i	−0.313528	+	1.17010i	0.611824	+	0.790994i	$0.290436\pi$
$691$	−8.24167	+	30.7583i	−0.313528	+	1.17010i	−0.925352	+	0.379108i	$0.876231\pi$
$692$			12.9282i			0.491457i
$693$	−3.36603	+	0.241670i	−0.127865	+	0.00918027i
$694$	−35.3205	+	35.3205i	−1.34075	+	1.34075i
$695$	3.50962	+	17.1506i	0.133127	+	0.650561i
$696$	3.60770	−	6.24871i	0.136749	−	0.236857i
$697$	0.921162	+	3.43782i	0.0348915	+	0.130217i
$698$	2.07180	+	3.58846i	0.0784187	+	0.135825i
$699$	−3.94744	−	3.94744i	−0.149306	−	0.149306i
$700$	17.7846	+	19.5885i	0.672195	+	0.740374i
$701$	−11.9282	+	11.9282i	−0.450522	+	0.450522i	−0.895528	−	0.445006i	$-0.853202\pi$
$701$	−11.9282	+	11.9282i	−0.450522	+	0.450522i	0.445006	+	0.895528i	$0.353202\pi$
$702$	−8.39230	+	31.3205i	−0.316747	+	1.18212i
$703$	21.0885	−	5.65064i	0.795366	−	0.213118i
$704$	−1.07180	−	4.00000i	−0.0403949	−	0.150756i
$705$	16.7058	−	3.41858i	0.629176	−	0.128751i
$706$			27.3205i			1.02822i
$707$	−42.8564	−	20.8038i	−1.61178	−	0.782409i
$708$	10.5359	−	10.5359i	0.395963	−	0.395963i
$709$	−39.6865	−	10.6340i	−1.49046	−	0.399367i	−0.580567	−	0.814212i	$-0.697169\pi$
$709$	−39.6865	−	10.6340i	−1.49046	−	0.399367i	−0.909892	+	0.414845i	$0.863836\pi$
$710$	19.8564	+	22.3923i	0.745198	+	0.840368i
$711$	−14.3660	−	8.29423i	−0.538768	−	0.311058i
$712$	0.679492	−	2.53590i	0.0254650	−	0.0950368i
$713$	3.26795	−	3.26795i	0.122386	−	0.122386i
$714$	0.339746	+	0.980762i	0.0127147	+	0.0367041i
$715$	6.29423	+	2.09808i	0.235391	+	0.0784636i
$716$	−30.1244	−	8.07180i	−1.12580	−	0.301657i
$717$	4.85641	+	2.80385i	0.181366	+	0.104712i
$718$	−4.26795	+	1.14359i	−0.159278	+	0.0426785i
$719$	6.12436	+	10.6077i	0.228400	+	0.395600i	0.957334	−	0.288984i	$-0.0933173\pi$
$719$	6.12436	+	10.6077i	0.228400	+	0.395600i	−0.728934	+	0.684584i	$0.759984\pi$
$720$	19.7128	−	9.85641i	0.734653	−	0.367327i
$721$	−16.0981	+	10.9019i	−0.599524	+	0.406009i
$722$	27.6603	−	27.6603i	1.02941	−	1.02941i
$723$	7.43782	−	4.29423i	0.276616	−	0.159704i
$724$	1.26795	−	0.339746i	0.0471230	−	0.0126266i
$725$	6.49038	−	16.1699i	0.241047	−	0.600534i
$726$	10.7321	+	2.87564i	0.398304	+	0.106725i
$727$	30.2942	+	30.2942i	1.12355	+	1.12355i	0.991203	+	0.132347i	$0.0422514\pi$
$727$	30.2942	+	30.2942i	1.12355	+	1.12355i	0.132347	+	0.991203i	$0.457749\pi$
$728$	3.07180	+	42.7846i	0.113848	+	1.58570i
$729$	−2.21539			−0.0820515
$730$	7.46410	+	4.92820i	0.276259	+	0.182401i
$731$	−0.411543	−	1.53590i	−0.0152215	−	0.0568073i
$732$	4.39230	+	16.3923i	0.162344	+	0.605877i
$733$	20.2846	+	35.1340i	0.749229	+	1.29770i	0.948193	+	0.317696i	$0.102909\pi$
$733$	20.2846	+	35.1340i	0.749229	+	1.29770i	−0.198963	+	0.980007i	$0.563758\pi$
$734$	12.5885			0.464648
$735$	6.53590	+	9.41154i	0.241080	+	0.347150i
$736$		−	13.0718i		−	0.481833i
$737$	0.124356	−	0.464102i	0.00458070	−	0.0170954i
$738$	31.6147	−	8.47114i	1.16375	−	0.311827i
$739$	−29.8205	+	7.99038i	−1.09697	+	0.293931i	−0.761528	−	0.648132i	$-0.775551\pi$
$739$	−29.8205	+	7.99038i	−1.09697	+	0.293931i	−0.335437	+	0.942063i	$0.608884\pi$
$740$	−11.9282	−	7.87564i	−0.438489	−	0.289514i
$741$	20.2679	−	20.2679i	0.744562	−	0.744562i
$742$	−46.5167	+	3.33975i	−1.70768	+	0.122606i
$743$	2.43782	+	2.43782i	0.0894350	+	0.0894350i	0.750409	−	0.660974i	$-0.229857\pi$
$743$	2.43782	+	2.43782i	0.0894350	+	0.0894350i	−0.660974	+	0.750409i	$0.729857\pi$
$744$	−1.07180	+	4.00000i	−0.0392940	+	0.146647i
$745$	−16.6340	−	18.7583i	−0.609422	−	0.687252i
$746$	40.5885	−	10.8756i	1.48605	−	0.398186i
$747$	−19.0526	−	33.0000i	−0.697097	−	1.20741i
$748$		−	0.392305i		−	0.0143441i
$749$	−4.46410	+	23.1962i	−0.163115	+	0.847569i
$750$	−9.51666	+	6.58846i	−0.347499	+	0.240576i
$751$	−24.5622	−	42.5429i	−0.896287	−	1.55241i	−0.832204	−	0.554469i	$-0.812921\pi$
$751$	−24.5622	−	42.5429i	−0.896287	−	1.55241i	−0.0640824	−	0.997945i	$-0.520412\pi$
$752$	−10.7846	−	40.2487i	−0.393274	−	1.46772i
$753$	−2.77757	−	10.3660i	−0.101220	−	0.377759i
$754$	24.4641	−	14.1244i	0.890930	−	0.514379i
$755$	17.1244	+	34.2487i	0.623219	+	1.24644i
$756$	20.0000	−	6.92820i	0.727393	−	0.251976i
$757$			36.6410i			1.33174i	0.746068	+	0.665870i	$0.231940\pi$
$757$			36.6410i			1.33174i	−0.746068	+	0.665870i	$0.768060\pi$
$758$	12.8301	+	22.2224i	0.466011	+	0.807155i
$759$	−0.758330	−	0.437822i	−0.0275256	−	0.0158919i
$760$	−43.1244	−	2.58846i	−1.56428	−	0.0938932i
$761$	−11.5263	−	19.9641i	−0.417827	−	0.723698i	0.577893	−	0.816112i	$-0.303875\pi$
$761$	−11.5263	−	19.9641i	−0.417827	−	0.723698i	−0.995721	+	0.0924142i	$0.970542\pi$
$762$			13.7128i			0.496763i
$763$	−19.6077	+	40.3923i	−0.709846	+	1.46230i
$764$		−	47.7128i		−	1.72619i
$765$	2.04552	−	0.418584i	0.0739558	−	0.0151339i
$766$	−9.41858	−	5.43782i	−0.340307	−	0.196477i
$767$	56.3468	−	15.0981i	2.03456	−	0.545160i
$768$	5.85641	+	10.1436i	0.211325	+	0.366025i
$769$	4.21539			0.152011			0.0760054	−	0.997107i	$-0.475783\pi$
$769$	4.21539			0.152011			0.0760054	+	0.997107i	$0.475783\pi$
$770$	−1.16987	−	4.16987i	−0.0421593	−	0.150272i
$771$	−4.67949	+	4.67949i	−0.168528	+	0.168528i
$772$	−1.32051	+	4.92820i	−0.0475261	+	0.177370i
$773$	8.89230	+	5.13397i	0.319834	+	0.184656i	0.651319	−	0.758804i	$-0.274216\pi$
$773$	8.89230	+	5.13397i	0.319834	+	0.184656i	−0.331485	+	0.943461i	$0.607549\pi$
$774$	−14.1244	+	3.78461i	−0.507689	+	0.136035i
$775$	−1.19615	+	9.92820i	−0.0429671	+	0.356632i
$776$			12.0000i			0.430775i
$777$	−4.67949	−	4.05256i	−0.167876	−	0.145385i
$778$	−15.6077			−0.559563
$779$	−61.9711	−	16.6051i	−2.22035	−	0.594940i
$780$	−18.7321	−	1.12436i	−0.670715	−	0.0402584i
$781$	−1.26795	−	4.73205i	−0.0453708	−	0.169326i
$782$	0.320508	−	1.19615i	0.0114613	−	0.0427743i
$783$	−9.85641	−	9.85641i	−0.352239	−	0.352239i
$784$	22.0000	−	17.3205i	0.785714	−	0.618590i
$785$	1.00000	+	2.00000i	0.0356915	+	0.0713831i
$786$	1.14359	−	0.660254i	0.0407906	−	0.0235505i
$787$	−3.97372	−	2.29423i	−0.141648	−	0.0817804i	0.427501	−	0.904015i	$-0.359394\pi$
$787$	−3.97372	−	2.29423i	−0.141648	−	0.0817804i	−0.569149	+	0.822234i	$0.692727\pi$
$788$	19.9282	−	34.5167i	0.709913	−	1.22961i
$789$	−0.555136	+	2.07180i	−0.0197634	+	0.0737579i
$790$	6.73205	−	20.1962i	0.239516	−	0.718547i
$791$	0.784610	+	10.9282i	0.0278975	+	0.388562i
$792$	−3.60770			−0.128194
$793$	−17.1962	+	64.1769i	−0.610653	+	2.27899i
$794$	−5.94744	−	22.1962i	−0.211067	−	0.787712i
$795$	1.22243	−	20.3660i	0.0433552	−	0.722308i
$796$	0.535898	+	0.928203i	0.0189944	+	0.0328993i
$797$			34.0000i			1.20434i	0.798367	+	0.602171i	$0.205697\pi$
$797$			34.0000i			1.20434i	−0.798367	+	0.602171i	$0.794303\pi$
$798$	−18.3731	−	3.53590i	−0.650400	−	0.125169i
$799$		−	3.94744i		−	0.139650i
$800$	17.4641	+	22.2487i	0.617449	+	0.786611i
$801$	−1.98076	−	1.14359i	−0.0699868	−	0.0404069i
$802$	−8.02628	+	2.15064i	−0.283418	+	0.0759416i
$803$	−0.732051	−	1.26795i	−0.0258335	−	0.0447450i
$804$			1.35898i			0.0479277i
$805$	−0.160254	−	13.6699i	−0.00564821	−	0.481800i
$806$	−11.4641	+	11.4641i	−0.403806	+	0.403806i
$807$	22.1962	+	5.94744i	0.781342	+	0.209360i
$808$	−44.1051	−	25.4641i	−1.55161	−	0.895824i
$809$	5.62436	−	9.74167i	0.197742	−	0.342499i	−0.750054	−	0.661377i	$-0.769973\pi$
$809$	5.62436	−	9.74167i	0.197742	−	0.342499i	0.947796	+	0.318878i	$0.103306\pi$
$810$	−2.83013	−	13.8301i	−0.0994405	−	0.485941i
$811$	5.56218	−	5.56218i	0.195314	−	0.195314i	−0.602673	−	0.797988i	$-0.705898\pi$
$811$	5.56218	−	5.56218i	0.195314	−	0.195314i	0.797988	+	0.602673i	$0.205898\pi$
$812$	−16.5885	−	8.05256i	−0.582141	−	0.282589i
$813$		−	0.679492i		−	0.0238308i
$814$	1.16987	+	2.02628i	0.0410040	+	0.0710211i
$815$	8.92820	+	0.535898i	0.312741	+	0.0187717i
$816$	0.287187	+	1.07180i	0.0100536	+	0.0375204i
$817$	27.6865	+	7.41858i	0.968629	+	0.259543i
$818$	−29.4641	+	29.4641i	−1.03019	+	1.03019i
$819$	36.6962	+	7.06218i	1.28227	+	0.246772i
$820$	18.7846	+	37.5692i	0.655987	+	1.31197i
$821$	−5.36603	+	20.0263i	−0.187276	+	0.698922i	0.806856	+	0.590748i	$0.201167\pi$
$821$	−5.36603	+	20.0263i	−0.187276	+	0.698922i	−0.994132	+	0.108174i	$0.965500\pi$
$822$	6.67949	−	11.5692i	0.232974	−	0.403523i
$823$	28.9545	−	7.75833i	1.00929	−	0.270438i	0.283957	−	0.958837i	$-0.408353\pi$
$823$	28.9545	−	7.75833i	1.00929	−	0.270438i	0.725333	+	0.688399i	$0.241686\pi$
$824$	−18.0000	+	10.3923i	−0.627060	+	0.362033i
$825$	1.87564	−	0.267949i	0.0653016	−	0.00932879i
$826$	−28.7846	−	24.9282i	−1.00154	−	0.867363i
$827$			39.3731i			1.36914i	0.728949	+	0.684568i	$0.240009\pi$
$827$			39.3731i			1.36914i	−0.728949	+	0.684568i	$0.759991\pi$
$828$	−11.0000	−	2.94744i	−0.382276	−	0.102431i
$829$	5.24167	+	19.5622i	0.182051	+	0.679423i	0.995243	+	0.0974270i	$0.0310612\pi$
$829$	5.24167	+	19.5622i	0.182051	+	0.679423i	−0.813192	+	0.581996i	$0.802272\pi$
$830$	36.5885	−	32.4449i	1.27000	−	1.12618i
$831$	−4.98076	+	2.87564i	−0.172781	+	0.0997550i
$832$			45.8564i			1.58978i
$833$	2.43782	−	1.04552i	0.0844655	−	0.0362250i
$834$			8.10512i			0.280657i
$835$	6.40192	+	31.2846i	0.221548	+	1.08265i
$836$	6.12436	+	3.53590i	0.211815	+	0.122292i
$837$	6.92820	+	4.00000i	0.239474	+	0.138260i
$838$	−1.75833	−	3.04552i	−0.0607405	−	0.105206i
$839$		−	11.2679i		−	0.389013i	−0.980901	−	0.194506i	$-0.937689\pi$
$839$		−	11.2679i		−	0.389013i	0.980901	−	0.194506i	$-0.0623105\pi$
$840$	6.24871	+	10.5359i	0.215601	+	0.363523i
$841$		−	16.8564i		−	0.581255i
$842$	−28.2679	+	16.3205i	−0.974178	+	0.562442i
$843$	5.70577	+	3.29423i	0.196517	+	0.113459i
$844$	−12.6603	+	3.39230i	−0.435784	+	0.116768i
$845$	−37.0526	−	24.4641i	−1.27465	−	0.841591i
$846$	−36.3013			−1.24806
$847$	5.36603	−	27.8827i	0.184379	−	0.958060i
$848$	−49.8564			−1.71208
$849$	13.3923	−	7.73205i	0.459623	−	0.265363i
$850$	1.05256	+	2.46410i	0.0361025	+	0.0845180i
$851$	1.91154	+	7.13397i	0.0655268	+	0.244549i
$852$	6.92820	+	12.0000i	0.237356	+	0.411113i
$853$			24.2679i			0.830919i	0.909612	+	0.415459i	$0.136379\pi$
$853$			24.2679i			0.830919i	−0.909612	+	0.415459i	$0.863621\pi$
$854$	40.9808	−	14.1962i	1.40233	−	0.485782i
$855$	−11.9019	+	35.7058i	−0.407037	+	1.22111i
$856$	−6.53590	+	24.3923i	−0.223392	+	0.833712i
$857$	−25.6865	+	6.88269i	−0.877435	+	0.235108i	−0.669300	−	0.742992i	$-0.733406\pi$
$857$	−25.6865	+	6.88269i	−0.877435	+	0.235108i	−0.208135	+	0.978100i	$0.566739\pi$
$858$	2.66025	+	1.53590i	0.0908196	+	0.0524347i
$859$	−8.43782	+	31.4904i	−0.287895	+	1.07444i	0.658803	+	0.752315i	$0.271063\pi$
$859$	−8.43782	+	31.4904i	−0.287895	+	1.07444i	−0.946698	+	0.322123i	$0.895604\pi$
$860$	−8.39230	−	16.7846i	−0.286175	−	0.572350i
$861$	5.95448	+	17.1891i	0.202928	+	0.585803i
$862$	−4.39230	−	4.39230i	−0.149602	−	0.149602i
$863$	−51.8468	−	13.8923i	−1.76489	−	0.472900i	−0.777187	−	0.629270i	$-0.783354\pi$
$863$	−51.8468	−	13.8923i	−1.76489	−	0.472900i	−0.987698	+	0.156371i	$0.950021\pi$
$864$	21.8564	−	5.85641i	0.743570	−	0.199239i
$865$	−0.866025	+	14.4282i	−0.0294457	+	0.490574i
$866$	−4.73205	+	2.73205i	−0.160802	+	0.0928389i
$867$		−	12.3397i		−	0.419080i
$868$	10.3923	+	2.00000i	0.352738	+	0.0678844i
$869$	−2.46410	+	2.46410i	−0.0835889	+	0.0835889i
$870$	4.44486	−	6.73205i	0.150695	−	0.228238i
$871$	−2.66025	+	4.60770i	−0.0901393	+	0.156126i
$872$	−24.0000	+	41.5692i	−0.812743	+	1.40771i
$873$	10.0981	+	2.70577i	0.341768	+	0.0915765i
$874$	15.7846	+	15.7846i	0.533922	+	0.533922i
$875$	18.5359	+	23.0526i	0.626628	+	0.779319i
$876$	2.92820	+	2.92820i	0.0989348	+	0.0989348i
$877$	−10.5263	−	18.2321i	−0.355447	−	0.615653i	0.631747	−	0.775174i	$-0.282338\pi$
$877$	−10.5263	−	18.2321i	−0.355447	−	0.615653i	−0.987194	+	0.159522i	$0.949005\pi$
$878$	14.0718	+	52.5167i	0.474900	+	1.77235i
$879$	−3.16987	−	1.83013i	−0.106917	−	0.0617287i
$880$	−0.928203	−	4.53590i	−0.0312897	−	0.152905i
$881$			40.8564i			1.37649i	0.725480	+	0.688244i	$0.241618\pi$
$881$			40.8564i			1.37649i	−0.725480	+	0.688244i	$0.758382\pi$
$882$	−9.61474	−	22.4186i	−0.323745	−	0.754873i
$883$			7.85641i			0.264389i	0.991224	+	0.132195i	$0.0422024\pi$
$883$			7.85641i			0.264389i	−0.991224	+	0.132195i	$0.957798\pi$
$884$	−1.12436	+	4.19615i	−0.0378162	+	0.141132i
$885$	12.4641	−	11.0526i	0.418976	−	0.371528i
$886$	45.5167	−	12.1962i	1.52916	−	0.409738i
$887$	5.77757	−	21.5622i	0.193992	−	0.723987i	−0.798534	−	0.601950i	$-0.794391\pi$
$887$	5.77757	−	21.5622i	0.193992	−	0.723987i	0.992526	−	0.122037i	$-0.0389427\pi$
$888$	−4.67949	−	4.67949i	−0.157033	−	0.157033i
$889$	34.9545	−	2.50962i	1.17234	−	0.0841699i
$890$	0.928203	−	2.78461i	0.0311134	−	0.0933403i
$891$	−0.598076	+	2.23205i	−0.0200363	+	0.0747765i
$892$	4.05256	+	15.1244i	0.135690	+	0.506401i
$893$	61.6244	+	35.5788i	2.06218	+	1.19060i
$894$	−5.80385	−	10.0526i	−0.194110	−	0.336208i
$895$	−33.0788	−	11.0263i	−1.10570	−	0.368568i
$896$	24.7846	−	16.7846i	0.827996	−	0.560734i
$897$	6.85641	+	6.85641i	0.228929	+	0.228929i
$898$	−0.0980762	−	0.0262794i	−0.00327285	−	0.000876956i
$899$	−1.80385	−	6.73205i	−0.0601617	−	0.224526i
$900$	22.6603	−	9.67949i	0.755342	−	0.322650i
$901$	−4.56218	−	1.22243i	−0.151988	−	0.0407251i
$902$		−	6.87564i		−	0.228934i
$903$	−2.66025	−	7.67949i	−0.0885277	−	0.255557i
$904$			11.7128i			0.389562i
$905$	1.43782	−	0.294229i	0.0477948	−	0.00978049i
$906$	4.58846	+	17.1244i	0.152441	+	0.568919i
$907$	−50.0263	−	28.8827i	−1.66110	−	0.959034i	−0.972193	−	0.234179i	$-0.924760\pi$
$907$	−50.0263	−	28.8827i	−1.66110	−	0.959034i	−0.688902	−	0.724855i	$-0.741907\pi$
$908$	−4.39230	−	7.60770i	−0.145764	−	0.252470i
$909$	−31.3731	+	31.3731i	−1.04058	+	1.04058i
$910$	0.562178	+	47.9545i	0.0186360	+	1.58968i
$911$	12.7321			0.421832			0.210916	−	0.977504i	$-0.432355\pi$
$911$	12.7321			0.421832			0.210916	+	0.977504i	$0.432355\pi$
$912$	−19.3205	−	5.17691i	−0.639766	−	0.171425i
$913$	−7.73205	+	2.07180i	−0.255894	+	0.0685665i
$914$	−22.5167	+	39.0000i	−0.744785	+	1.29001i
$915$	3.80385	+	18.5885i	0.125751	+	0.614515i
$916$	−13.0718	+	13.0718i	−0.431904	+	0.431904i
$917$	−1.89230	−	2.79423i	−0.0624894	−	0.0922736i
$918$	2.14359			0.0707491
$919$	−13.3660	−	23.1506i	−0.440904	−	0.763669i	0.556852	−	0.830612i	$-0.312009\pi$
$919$	−13.3660	−	23.1506i	−0.440904	−	0.763669i	−0.997757	+	0.0669425i	$0.978676\pi$
$920$	0.875644	−	14.5885i	0.0288691	−	0.480967i
$921$	9.33975	+	5.39230i	0.307755	+	0.177682i
$922$	−23.7846	+	13.7321i	−0.783304	+	0.452241i
$923$			54.2487i			1.78562i
$924$	−0.143594	−	2.00000i	−0.00472388	−	0.0657952i
$925$	−12.7846	−	9.58846i	−0.420355	−	0.315267i
$926$	2.56218	+	4.43782i	0.0841984	+	0.145836i
$927$	4.68653	+	17.4904i	0.153926	+	0.574459i
$928$	−17.0718	−	9.85641i	−0.560409	−	0.323552i
$929$	−18.8660	−	32.6769i	−0.618974	−	1.07209i	−0.989673	−	0.143342i	$-0.954215\pi$
$929$	−18.8660	−	32.6769i	−0.618974	−	1.07209i	0.370699	−	0.928753i	$-0.379118\pi$
$930$	−1.46410	+	4.39230i	−0.0480098	+	0.144029i
$931$	−5.65064	+	47.4808i	−0.185192	+	1.55612i
$932$	−10.7846	+	10.7846i	−0.353262	+	0.353262i
$933$	7.94744	+	13.7654i	0.260188	+	0.450658i
$934$	1.58846	+	5.92820i	0.0519759	+	0.193977i
$935$	0.0262794	−	0.437822i	0.000859430	−	0.0143183i
$936$	38.5885	+	10.3397i	1.26130	+	0.337965i
$937$	−10.0718	−	10.0718i	−0.329031	−	0.329031i	0.523187	−	0.852218i	$-0.324743\pi$
$937$	−10.0718	−	10.0718i	−0.329031	−	0.329031i	−0.852218	+	0.523187i	$0.824743\pi$
$938$	3.46410	−	0.248711i	0.113107	−	0.00812071i
$939$	−8.24871	+	8.24871i	−0.269187	+	0.269187i
$940$	−9.33975	−	45.6410i	−0.304629	−	1.48865i
$941$	4.00000	−	1.07180i	0.130396	−	0.0349396i	−0.193031	−	0.981193i	$-0.561832\pi$
$941$	4.00000	−	1.07180i	0.130396	−	0.0349396i	0.323427	+	0.946253i	$0.395165\pi$
$942$	0.267949	+	1.00000i	0.00873026	+	0.0325818i
$943$	5.61731	−	20.9641i	0.182925	−	0.682685i
$944$	−28.7846	−	28.7846i	−0.936859	−	0.936859i
$945$	22.7846	−	6.39230i	0.741183	−	0.207942i
$946$			3.07180i			0.0998727i
$947$	16.6865	+	28.9019i	0.542239	+	0.939186i	0.998775	+	0.0494812i	$0.0157568\pi$
$947$	16.6865	+	28.9019i	0.542239	+	0.939186i	−0.456536	+	0.889705i	$0.650910\pi$
$948$	4.92820	−	8.53590i	0.160061	−	0.277233i
$949$	4.19615	+	15.6603i	0.136213	+	0.508353i
$950$	−47.9545	−	5.77757i	−1.55585	−	0.187449i
$951$	−6.14359			−0.199220
$952$	2.67949	−	0.928203i	0.0868428	−	0.0300832i
$953$	10.5885	+	10.5885i	0.342994	+	0.342994i	0.857492	−	0.514498i	$-0.172022\pi$
$953$	10.5885	+	10.5885i	0.342994	+	0.342994i	−0.514498	+	0.857492i	$0.672022\pi$
$954$	−11.2417	+	41.9545i	−0.363962	+	1.35833i
$955$	3.19615	−	53.2487i	0.103425	−	1.72309i
$956$	7.66025	−	13.2679i	0.247750	−	0.429116i
$957$	−1.14359	+	0.660254i	−0.0369671	+	0.0213430i
$958$	7.07180	+	7.07180i	0.228479	+	0.228479i
$959$	−30.7128	−	14.9090i	−0.991768	−	0.481436i
$960$	5.85641	+	11.7128i	0.189015	+	0.378029i
$961$	−13.5000	−	23.3827i	−0.435484	−	0.754280i
$962$	−6.70577	−	25.0263i	−0.216203	−	0.806880i
$963$	19.0526	+	11.0000i	0.613960	+	0.354470i
$964$	−11.7321	−	20.3205i	−0.377864	−	0.654479i
$965$	−1.80385	+	5.41154i	−0.0580679	+	0.174204i
$966$	1.19615	−	6.21539i	0.0384856	−	0.199977i
$967$	−17.5359	+	17.5359i	−0.563916	+	0.563916i	−0.930418	−	0.366501i	$-0.880556\pi$
$967$	−17.5359	+	17.5359i	−0.563916	+	0.563916i	0.366501	+	0.930418i	$0.380556\pi$
$968$	7.85641	−	29.3205i	0.252514	−	0.942397i
$969$	−1.64102	−	0.947441i	−0.0527170	−	0.0304362i
$970$	−0.803848	+	13.3923i	−0.0258100	+	0.430001i
$971$	−22.5263	−	6.03590i	−0.722903	−	0.193701i	−0.121436	−	0.992599i	$-0.538750\pi$
$971$	−22.5263	−	6.03590i	−0.722903	−	0.193701i	−0.601466	+	0.798898i	$0.705417\pi$
$972$		−	30.5359i		−	0.979439i
$973$	20.6603	−	1.48334i	0.662337	−	0.0475537i
$974$	16.9282			0.542415
$975$	−20.8301	−	2.50962i	−0.667098	−	0.0803721i
$976$	44.7846	−	12.0000i	1.43352	−	0.384111i
$977$	5.90192	−	1.58142i	0.188819	−	0.0505940i	−0.163170	−	0.986598i	$-0.552172\pi$
$977$	5.90192	−	1.58142i	0.188819	−	0.0505940i	0.351989	+	0.936004i	$0.385505\pi$
$978$	4.00000	+	1.07180i	0.127906	+	0.0342723i
$979$	−0.339746	+	0.339746i	−0.0108583	+	0.0108583i
$980$	25.7128	−	17.8564i	0.821366	−	0.570402i
$981$	29.5692	+	29.5692i	0.944073	+	0.944073i
$982$	2.41154	−	1.39230i	0.0769554	−	0.0444302i
$983$	−4.13397	−	15.4282i	−0.131853	−	0.492083i	0.868138	−	0.496323i	$-0.165317\pi$
$983$	−4.13397	−	15.4282i	−0.131853	−	0.492083i	−0.999991	+	0.00424016i	$0.998650\pi$
$984$	5.03332	+	18.7846i	0.160456	+	0.598831i
$985$	24.5526	−	37.1865i	0.782310	−	1.18486i
$986$	−1.32051	−	1.32051i	−0.0420535	−	0.0420535i
$987$	−1.44486	−	20.1244i	−0.0459905	−	0.640565i
$988$	−55.3731	−	55.3731i	−1.76165	−	1.76165i
$989$	−2.50962	+	9.36603i	−0.0798012	+	0.297822i
$990$	−4.02628	−	0.241670i	−0.127964	−	0.00768077i
$991$	26.7128	−	46.2679i	0.848560	−	1.46975i	−0.0339324	−	0.999424i	$-0.510803\pi$
$991$	26.7128	−	46.2679i	0.848560	−	1.46975i	0.882493	−	0.470326i	$-0.155864\pi$
$992$	10.9282	+	2.92820i	0.346971	+	0.0929705i
$993$	−4.60770	−	4.60770i	−0.146221	−	0.146221i
$994$	29.3205	−	19.8564i	0.929990	−	0.629807i
$995$	0.535898	+	1.07180i	0.0169891	+	0.0339782i
$996$	19.6077	−	11.3205i	0.621294	−	0.358704i
$997$	16.3205	−	28.2679i	0.516876	−	0.895255i	−0.482932	−	0.875658i	$-0.660428\pi$
$997$	16.3205	−	28.2679i	0.516876	−	0.895255i	0.999808	−	0.0195972i	$-0.00623839\pi$
$998$	−13.9808	−	8.07180i	−0.442553	−	0.255508i
$999$	−11.0718	+	6.39230i	−0.350296	+	0.202244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ch.a.437.1	yes	4
5.3	odd	4		560.2.cz.a.213.1	yes	4
7.5	odd	6		560.2.ch.b.117.1	yes	4
16.13	even	4		560.2.cz.b.157.1	yes	4
35.33	even	12		560.2.cz.b.453.1	yes	4
80.13	odd	4		560.2.ch.b.493.1	yes	4
112.61	odd	12		560.2.cz.a.397.1	yes	4
560.173	even	12	inner	560.2.ch.a.173.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.a.173.1	✓	4	560.173	even	12	inner
560.2.ch.a.437.1	yes	4	1.1	even	1	trivial
560.2.ch.b.117.1	yes	4	7.5	odd	6
560.2.ch.b.493.1	yes	4	80.13	odd	4
560.2.cz.a.213.1	yes	4	5.3	odd	4
560.2.cz.a.397.1	yes	4	112.61	odd	12
560.2.cz.b.157.1	yes	4	16.13	even	4
560.2.cz.b.453.1	yes	4	35.33	even	12

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(0.366025 - 0.633975i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(-0.732051 - 0.732051i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.23205 + 2.13397i) q^{9} +(-2.36603 + 2.09808i) q^{10} +(0.500000 - 0.133975i) q^{11} +(-1.26795 + 0.732051i) q^{12} -5.73205 q^{13} +(2.09808 + 3.09808i) q^{14} +(-1.46410 + 0.732051i) q^{15} +(2.00000 + 3.46410i) q^{16} +(0.0980762 + 0.366025i) q^{17} +(3.36603 - 0.901924i) q^{18} +(-6.59808 - 1.76795i) q^{19} +(2.00000 + 4.00000i) q^{20} +(0.633975 + 1.83013i) q^{21} -0.732051i q^{22} +(0.598076 - 2.23205i) q^{23} +(0.535898 + 2.00000i) q^{24} +(1.96410 + 4.59808i) q^{25} +(-2.09808 + 7.83013i) q^{26} +4.00000 q^{27} +(5.00000 - 1.73205i) q^{28} +(-2.46410 - 2.46410i) q^{29} +(0.464102 + 2.26795i) q^{30} +(1.73205 + 1.00000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(0.0980762 - 0.366025i) q^{33} +0.535898 q^{34} +(5.69615 - 1.59808i) q^{35} -4.92820i q^{36} +(-2.76795 + 1.59808i) q^{37} +(-4.83013 + 8.36603i) q^{38} +(-2.09808 + 3.63397i) q^{39} +(6.19615 - 1.26795i) q^{40} +9.39230 q^{41} +(2.73205 - 0.196152i) q^{42} -4.19615 q^{43} +(-1.00000 - 0.267949i) q^{44} +(0.330127 - 5.50000i) q^{45} +(-2.83013 - 1.63397i) q^{46} +(-10.0622 - 2.69615i) q^{47} +2.92820 q^{48} +(-1.00000 - 6.92820i) q^{49} +(7.00000 - 1.00000i) q^{50} +(0.267949 + 0.0717968i) q^{51} +(9.92820 + 5.73205i) q^{52} +(-6.23205 + 10.7942i) q^{53} +(1.46410 - 5.46410i) q^{54} +(-1.09808 - 0.366025i) q^{55} +(-0.535898 - 7.46410i) q^{56} +(-3.53590 + 3.53590i) q^{57} +(-4.26795 + 2.46410i) q^{58} +(-9.83013 + 2.63397i) q^{59} +(3.26795 + 0.196152i) q^{60} +(3.00000 - 11.1962i) q^{61} +(2.00000 - 2.00000i) q^{62} +(-6.40192 - 1.23205i) q^{63} -8.00000i q^{64} +(10.6962 + 7.06218i) q^{65} +(-0.464102 - 0.267949i) q^{66} +(0.464102 - 0.803848i) q^{67} +(0.196152 - 0.732051i) q^{68} +(-1.19615 - 1.19615i) q^{69} +(-0.0980762 - 8.36603i) q^{70} -9.46410i q^{71} +(-6.73205 - 1.80385i) q^{72} +(-0.732051 - 2.73205i) q^{73} +(1.16987 + 4.36603i) q^{74} +(3.63397 + 0.437822i) q^{75} +(9.66025 + 9.66025i) q^{76} +(-0.598076 + 1.23205i) q^{77} +(4.19615 + 4.19615i) q^{78} +(-5.83013 + 3.36603i) q^{79} +(0.535898 - 8.92820i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(3.43782 - 12.8301i) q^{82} -15.4641 q^{83} +(0.732051 - 3.80385i) q^{84} +(0.267949 - 0.803848i) q^{85} +(-1.53590 + 5.73205i) q^{86} +(-2.46410 + 0.660254i) q^{87} +(-0.732051 + 1.26795i) q^{88} +(-0.803848 + 0.464102i) q^{89} +(-7.39230 - 2.46410i) q^{90} +(9.92820 - 11.4641i) q^{91} +(-3.26795 + 3.26795i) q^{92} +(1.26795 - 0.732051i) q^{93} +(-7.36603 + 12.7583i) q^{94} +(10.1340 + 11.4282i) q^{95} +(1.07180 - 4.00000i) q^{96} +(3.00000 - 3.00000i) q^{97} +(-9.83013 - 1.16987i) q^{98} +(0.901924 + 0.901924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 4 q^{5} + 4 q^{6} - 8 q^{8} - 2 q^{9} - 6 q^{10} + 2 q^{11} - 12 q^{12} - 16 q^{13} - 2 q^{14} + 8 q^{15} + 8 q^{16} - 10 q^{17} + 10 q^{18} - 16 q^{19} + 8 q^{20} + 6 q^{21} - 8 q^{23}+ \cdots + 14 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 + 4 * q^6 - 8 * q^8 - 2 * q^9 - 6 * q^10 + 2 * q^11 - 12 * q^12 - 16 * q^13 - 2 * q^14 + 8 * q^15 + 8 * q^16 - 10 * q^17 + 10 * q^18 - 16 * q^19 + 8 * q^20 + 6 * q^21 - 8 * q^23 + 16 * q^24 - 6 * q^25 + 2 * q^26 + 16 * q^27 + 20 * q^28 + 4 * q^29 - 12 * q^30 + 8 * q^32 - 10 * q^33 + 16 * q^34 + 2 * q^35 - 18 * q^37 - 2 * q^38 + 2 * q^39 + 4 * q^40 - 4 * q^41 + 4 * q^42 + 4 * q^43 - 4 * q^44 - 16 * q^45 + 6 * q^46 - 16 * q^47 - 16 * q^48 - 4 * q^49 + 28 * q^50 + 8 * q^51 + 12 * q^52 - 18 * q^53 - 8 * q^54 + 6 * q^55 - 16 * q^56 - 28 * q^57 - 24 * q^58 - 22 * q^59 + 20 * q^60 + 12 * q^61 + 8 * q^62 - 36 * q^63 + 22 * q^65 + 12 * q^66 - 12 * q^67 - 20 * q^68 + 16 * q^69 + 10 * q^70 - 20 * q^72 + 4 * q^73 + 22 * q^74 + 18 * q^75 + 4 * q^76 + 8 * q^77 - 4 * q^78 - 6 * q^79 + 16 * q^80 - 2 * q^81 + 38 * q^82 - 48 * q^83 - 4 * q^84 + 8 * q^85 - 20 * q^86 + 4 * q^87 + 4 * q^88 - 24 * q^89 + 12 * q^90 + 12 * q^91 - 20 * q^92 + 12 * q^93 - 26 * q^94 + 44 * q^95 + 32 * q^96 + 12 * q^97 - 22 * q^98 + 14 * q^99

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