LMFDB - Embedded newform 280.2.s.c.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(13,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3, 2]))

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

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

chi := DirichletCharacter("280.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.s (of order $4$, degree $2$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	280.13
Dual form			280.2.s.c.237.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39041 + 0.258373i) q^{2} +(-1.88603 - 1.88603i) q^{3} +(1.86649 - 0.718491i) q^{4} +(-1.79374 - 1.33510i) q^{5} +(3.10966 + 2.13506i) q^{6} +(-2.30054 - 1.30671i) q^{7} +(-2.40954 + 1.48125i) q^{8} +4.11423i q^{9} +O(q^{10})$	\(q+(-1.39041 + 0.258373i) q^{2} +(-1.88603 - 1.88603i) q^{3} +(1.86649 - 0.718491i) q^{4} +(-1.79374 - 1.33510i) q^{5} +(3.10966 + 2.13506i) q^{6} +(-2.30054 - 1.30671i) q^{7} +(-2.40954 + 1.48125i) q^{8} +4.11423i q^{9} +(2.83899 + 1.39289i) q^{10} -4.00091i q^{11} +(-4.87535 - 2.16516i) q^{12} +(1.07557 + 1.07557i) q^{13} +(3.53632 + 1.22247i) q^{14} +(0.865000 + 5.90110i) q^{15} +(2.96754 - 2.68211i) q^{16} +(1.98582 + 1.98582i) q^{17} +(-1.06301 - 5.72048i) q^{18} +6.78591i q^{19} +(-4.30725 - 1.20317i) q^{20} +(1.87440 + 6.80340i) q^{21} +(1.03373 + 5.56290i) q^{22} +(-1.60154 - 1.60154i) q^{23} +(7.33816 + 1.75080i) q^{24} +(1.43500 + 4.78965i) q^{25} +(-1.77338 - 1.21758i) q^{26} +(2.10148 - 2.10148i) q^{27} +(-5.23279 - 0.786042i) q^{28} -9.33660 q^{29} +(-2.72739 - 7.98146i) q^{30} -3.62075i q^{31} +(-3.43312 + 4.49596i) q^{32} +(-7.54584 + 7.54584i) q^{33} +(-3.27418 - 2.24802i) q^{34} +(2.38198 + 5.41537i) q^{35} +(2.95604 + 7.67916i) q^{36} +(4.62071 + 4.62071i) q^{37} +(-1.75330 - 9.43521i) q^{38} -4.05711i q^{39} +(6.29971 + 0.560020i) q^{40} -1.56281i q^{41} +(-4.36400 - 8.97523i) q^{42} +(3.14208 - 3.14208i) q^{43} +(-2.87461 - 7.46764i) q^{44} +(5.49293 - 7.37986i) q^{45} +(2.64060 + 1.81301i) q^{46} +(-0.543878 - 0.543878i) q^{47} +(-10.6554 - 0.538343i) q^{48} +(3.58501 + 6.01230i) q^{49} +(-3.23275 - 6.28882i) q^{50} -7.49062i q^{51} +(2.78031 + 1.23475i) q^{52} +(-0.0419662 + 0.0419662i) q^{53} +(-2.37896 + 3.46489i) q^{54} +(-5.34162 + 7.17658i) q^{55} +(7.47883 - 0.259094i) q^{56} +(12.7985 - 12.7985i) q^{57} +(12.9817 - 2.41233i) q^{58} +2.25968i q^{59} +(5.85439 + 10.3928i) q^{60} -9.27084 q^{61} +(0.935506 + 5.03433i) q^{62} +(5.37612 - 9.46498i) q^{63} +(3.61181 - 7.13827i) q^{64} +(-0.493292 - 3.36528i) q^{65} +(8.54217 - 12.4415i) q^{66} +(-9.41132 - 9.41132i) q^{67} +(5.13329 + 2.27971i) q^{68} +6.04112i q^{69} +(-4.71112 - 6.91414i) q^{70} -10.5175 q^{71} +(-6.09420 - 9.91343i) q^{72} +(6.18305 - 6.18305i) q^{73} +(-7.61856 - 5.23082i) q^{74} +(6.32699 - 11.7399i) q^{75} +(4.87562 + 12.6658i) q^{76} +(-5.22803 + 9.20426i) q^{77} +(1.04825 + 5.64105i) q^{78} -0.539800i q^{79} +(-8.90388 + 0.849020i) q^{80} +4.41578 q^{81} +(0.403788 + 2.17295i) q^{82} +(0.836186 + 0.836186i) q^{83} +(8.38672 + 11.3517i) q^{84} +(-0.910764 - 6.21330i) q^{85} +(-3.55696 + 5.18062i) q^{86} +(17.6091 + 17.6091i) q^{87} +(5.92633 + 9.64036i) q^{88} -2.95941 q^{89} +(-5.73067 + 11.6803i) q^{90} +(-1.06893 - 3.87984i) q^{91} +(-4.13995 - 1.83856i) q^{92} +(-6.82885 + 6.82885i) q^{93} +(0.896737 + 0.615690i) q^{94} +(9.05990 - 12.1722i) q^{95} +(14.9545 - 2.00456i) q^{96} +(-10.2602 - 10.2602i) q^{97} +(-6.53805 - 7.43330i) q^{98} +16.4607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.39041	+	0.258373i	−0.983169	+	0.182698i
$2$	−1.39041	+	0.258373i	−0.983169	+	0.182698i
$3$	−1.88603	−	1.88603i	−1.08890	−	1.08890i	−0.995642	−	0.0932593i	$-0.970271\pi$
$3$	−1.88603	−	1.88603i	−1.08890	−	1.08890i	−0.0932593	−	0.995642i	$-0.529729\pi$
$4$	1.86649	−	0.718491i	0.933243	−	0.359245i
$5$	−1.79374	−	1.33510i	−0.802184	−	0.597077i
$5$	−1.79374	−	1.33510i	−0.802184	−	0.597077i
$6$	3.10966	+	2.13506i	1.26951	+	0.871634i
$7$	−2.30054	−	1.30671i	−0.869524	−	0.493891i
$7$	−2.30054	−	1.30671i	−0.869524	−	0.493891i
$8$	−2.40954	+	1.48125i	−0.851903	+	0.523700i
$9$			4.11423i			1.37141i
$10$	2.83899	+	1.39289i	0.897767	+	0.440470i
$11$		−	4.00091i		−	1.20632i	−0.797621	−	0.603159i	$-0.793908\pi$
$11$		−	4.00091i		−	1.20632i	0.797621	−	0.603159i	$-0.206092\pi$
$12$	−4.87535	−	2.16516i	−1.40739	−	0.625027i
$13$	1.07557	+	1.07557i	0.298308	+	0.298308i	0.840351	−	0.542043i	$-0.182349\pi$
$13$	1.07557	+	1.07557i	0.298308	+	0.298308i	−0.542043	+	0.840351i	$0.682349\pi$
$14$	3.53632	+	1.22247i	0.945122	+	0.326718i
$15$	0.865000	+	5.90110i	0.223342	+	1.52366i
$16$	2.96754	−	2.68211i	0.741886	−	0.670526i
$17$	1.98582	+	1.98582i	0.481631	+	0.481631i	0.905652	−	0.424021i	$-0.139382\pi$
$17$	1.98582	+	1.98582i	0.481631	+	0.481631i	−0.424021	+	0.905652i	$0.639382\pi$
$18$	−1.06301	−	5.72048i	−0.250554	−	1.34833i
$19$			6.78591i			1.55680i	0.627771	+	0.778398i	$0.283967\pi$
$19$			6.78591i			1.55680i	−0.627771	+	0.778398i	$0.716033\pi$
$20$	−4.30725	−	1.20317i	−0.963130	−	0.269037i
$21$	1.87440	+	6.80340i	0.409027	+	1.48462i
$22$	1.03373	+	5.56290i	0.220392	+	1.18602i
$23$	−1.60154	−	1.60154i	−0.333945	−	0.333945i	0.520138	−	0.854082i	$-0.325881\pi$
$23$	−1.60154	−	1.60154i	−0.333945	−	0.333945i	−0.854082	+	0.520138i	$0.825881\pi$
$24$	7.33816	+	1.75080i	1.49790	+	0.357380i
$25$	1.43500	+	4.78965i	0.286999	+	0.957931i
$26$	−1.77338	−	1.21758i	−0.347788	−	0.238787i
$27$	2.10148	−	2.10148i	0.404430	−	0.404430i
$28$	−5.23279	−	0.786042i	−0.988905	−	0.148548i
$29$	−9.33660			−1.73376			−0.866881	−	0.498515i	$-0.833879\pi$
$29$	−9.33660			−1.73376			−0.866881	+	0.498515i	$0.833879\pi$
$30$	−2.72739	−	7.98146i	−0.497951	−	1.45721i
$31$		−	3.62075i		−	0.650306i	−0.945661	−	0.325153i	$-0.894584\pi$
$31$		−	3.62075i		−	0.650306i	0.945661	−	0.325153i	$-0.105416\pi$
$32$	−3.43312	+	4.49596i	−0.606895	+	0.794782i
$33$	−7.54584	+	7.54584i	−1.31356	+	1.31356i
$34$	−3.27418	−	2.24802i	−0.561518	−	0.385532i
$35$	2.38198	+	5.41537i	0.402628	+	0.915364i
$36$	2.95604	+	7.67916i	0.492673	+	1.27986i
$37$	4.62071	+	4.62071i	0.759640	+	0.759640i	0.976257	−	0.216617i	$-0.0695022\pi$
$37$	4.62071	+	4.62071i	0.759640	+	0.759640i	−0.216617	+	0.976257i	$0.569502\pi$
$38$	−1.75330	−	9.43521i	−0.284423	−	1.53059i
$39$		−	4.05711i		−	0.649657i
$40$	6.29971	+	0.560020i	0.996072	+	0.0885470i
$41$		−	1.56281i		−	0.244070i	−0.992526	−	0.122035i	$-0.961058\pi$
$41$		−	1.56281i		−	0.244070i	0.992526	−	0.122035i	$-0.0389419\pi$
$42$	−4.36400	−	8.97523i	−0.673380	−	1.38491i
$43$	3.14208	−	3.14208i	0.479163	−	0.479163i	−0.425701	−	0.904864i	$-0.639972\pi$
$43$	3.14208	−	3.14208i	0.479163	−	0.479163i	0.904864	+	0.425701i	$0.139972\pi$
$44$	−2.87461	−	7.46764i	−0.433364	−	1.12579i
$45$	5.49293	−	7.37986i	0.818838	−	1.10012i
$46$	2.64060	+	1.81301i	0.389335	+	0.267313i
$47$	−0.543878	−	0.543878i	−0.0793327	−	0.0793327i	0.666327	−	0.745660i	$-0.267866\pi$
$47$	−0.543878	−	0.543878i	−0.0793327	−	0.0793327i	−0.745660	+	0.666327i	$0.767866\pi$
$48$	−10.6554	−	0.538343i	−1.53798	−	0.0777031i
$49$	3.58501	+	6.01230i	0.512144	+	0.858900i
$50$	−3.23275	−	6.28882i	−0.457180	−	0.889374i
$51$		−	7.49062i		−	1.04890i
$52$	2.78031	+	1.23475i	0.385560	+	0.171228i
$53$	−0.0419662	+	0.0419662i	−0.00576450	+	0.00576450i	−0.709983	−	0.704219i	$-0.751297\pi$
$53$	−0.0419662	+	0.0419662i	−0.00576450	+	0.00576450i	0.704219	+	0.709983i	$0.251297\pi$
$54$	−2.37896	+	3.46489i	−0.323735	+	0.471512i
$55$	−5.34162	+	7.17658i	−0.720265	+	0.967690i
$56$	7.47883	−	0.259094i	0.999400	−	0.0346229i
$57$	12.7985	−	12.7985i	1.69520	−	1.69520i
$58$	12.9817	−	2.41233i	1.70458	−	0.316754i
$59$			2.25968i			0.294186i	0.989123	+	0.147093i	$0.0469916\pi$
$59$			2.25968i			0.294186i	−0.989123	+	0.147093i	$0.953008\pi$
$60$	5.85439	+	10.3928i	0.755799	+	1.34171i
$61$	−9.27084			−1.18701			−0.593505	−	0.804830i	$-0.702256\pi$
$61$	−9.27084			−1.18701			−0.593505	+	0.804830i	$0.702256\pi$
$62$	0.935506	+	5.03433i	0.118809	+	0.639361i
$63$	5.37612	−	9.46498i	0.677328	−	1.19247i
$64$	3.61181	−	7.13827i	0.451476	−	0.892283i
$65$	−0.493292	−	3.36528i	−0.0611854	−	0.417411i
$66$	8.54217	−	12.4415i	1.05147	−	1.53144i
$67$	−9.41132	−	9.41132i	−1.14978	−	1.14978i	−0.986596	−	0.163179i	$-0.947825\pi$
$67$	−9.41132	−	9.41132i	−1.14978	−	1.14978i	−0.163179	−	0.986596i	$-0.552175\pi$
$68$	5.13329	+	2.27971i	0.622503	+	0.276455i
$69$			6.04112i			0.727266i
$70$	−4.71112	−	6.91414i	−0.563086	−	0.826398i
$71$	−10.5175			−1.24820			−0.624098	−	0.781346i	$-0.714533\pi$
$71$	−10.5175			−1.24820			−0.624098	+	0.781346i	$0.714533\pi$
$72$	−6.09420	−	9.91343i	−0.718208	−	1.16831i
$73$	6.18305	−	6.18305i	0.723671	−	0.723671i	−0.245680	−	0.969351i	$-0.579011\pi$
$73$	6.18305	−	6.18305i	0.723671	−	0.723671i	0.969351	+	0.245680i	$0.0790112\pi$
$74$	−7.61856	−	5.23082i	−0.885639	−	0.608070i
$75$	6.32699	−	11.7399i	0.730578	−	1.35561i
$76$	4.87562	+	12.6658i	0.559271	+	1.45287i
$77$	−5.22803	+	9.20426i	−0.595790	+	1.04892i
$78$	1.04825	+	5.64105i	0.118691	+	0.638723i
$79$		−	0.539800i		−	0.0607323i	−0.999539	−	0.0303661i	$-0.990333\pi$
$79$		−	0.539800i		−	0.0607323i	0.999539	−	0.0303661i	$-0.00966733\pi$
$80$	−8.90388	+	0.849020i	−0.995485	+	0.0949233i
$81$	4.41578			0.490642
$82$	0.403788	+	2.17295i	0.0445909	+	0.239962i
$83$	0.836186	+	0.836186i	0.0917834	+	0.0917834i	0.751508	−	0.659724i	$-0.229327\pi$
$83$	0.836186	+	0.836186i	0.0917834	+	0.0917834i	−0.659724	+	0.751508i	$0.729327\pi$
$84$	8.38672	+	11.3517i	0.915066	+	1.23857i
$85$	−0.910764	−	6.21330i	−0.0987863	−	0.673927i
$86$	−3.55696	+	5.18062i	−0.383556	+	0.558640i
$87$	17.6091	+	17.6091i	1.88790	+	1.88790i
$88$	5.92633	+	9.64036i	0.631749	+	1.02767i
$89$	−2.95941			−0.313697			−0.156849	−	0.987623i	$-0.550133\pi$
$89$	−2.95941			−0.313697			−0.156849	+	0.987623i	$0.550133\pi$
$90$	−5.73067	+	11.6803i	−0.604066	+	1.23121i
$91$	−1.06893	−	3.87984i	−0.112055	−	0.406718i
$92$	−4.13995	−	1.83856i	−0.431620	−	0.191684i
$93$	−6.82885	+	6.82885i	−0.708119	+	0.708119i
$94$	0.896737	+	0.615690i	0.0924914	+	0.0635036i
$95$	9.05990	−	12.1722i	0.929526	−	1.24884i
$96$	14.9545	−	2.00456i	1.52629	−	0.204589i
$97$	−10.2602	−	10.2602i	−1.04177	−	1.04177i	−0.999089	−	0.0426809i	$-0.986410\pi$
$97$	−10.2602	−	10.2602i	−1.04177	−	1.04177i	−0.0426809	−	0.999089i	$-0.513590\pi$
$98$	−6.53805	−	7.43330i	−0.660443	−	0.750876i
$99$	16.4607			1.65436
$100$	6.11972	+	7.90879i	0.611972	+	0.790879i
$101$	−3.97960			−0.395985			−0.197993	−	0.980204i	$-0.563442\pi$
$101$	−3.97960			−0.395985			−0.197993	+	0.980204i	$0.563442\pi$
$102$	1.93538	+	10.4150i	0.191631	+	1.03124i
$103$	−12.4327	+	12.4327i	−1.22503	+	1.22503i	−0.259212	+	0.965821i	$0.583463\pi$
$103$	−12.4327	+	12.4327i	−1.22503	+	1.22503i	−0.965821	+	0.259212i	$0.916537\pi$
$104$	−4.18481	−	0.998445i	−0.410354	−	0.0979056i
$105$	5.72107	−	14.7060i	0.558319	−	1.43516i
$106$	0.0475073	−	0.0691932i	0.00461432	−	0.00672064i
$107$	11.6614	+	11.6614i	1.12735	+	1.12735i	0.990606	+	0.136747i	$0.0436647\pi$
$107$	11.6614	+	11.6614i	1.12735	+	1.12735i	0.136747	+	0.990606i	$0.456335\pi$
$108$	2.41249	−	5.43228i	0.232142	−	0.522721i
$109$	−3.60435			−0.345235			−0.172617	−	0.984989i	$-0.555222\pi$
$109$	−3.60435			−0.345235			−0.172617	+	0.984989i	$0.555222\pi$
$110$	5.57282	−	11.3585i	0.531347	−	1.08299i
$111$		−	17.4296i		−	1.65435i
$112$	−10.3317	+	2.29258i	−0.976254	+	0.216628i
$113$	−5.01097	−	5.01097i	−0.471392	−	0.471392i	0.430973	−	0.902365i	$-0.358171\pi$
$113$	−5.01097	−	5.01097i	−0.471392	−	0.471392i	−0.902365	+	0.430973i	$0.858171\pi$
$114$	−14.4883	+	21.1019i	−1.35696	+	1.97637i
$115$	0.734523	+	5.01097i	0.0684947	+	0.467276i
$116$	−17.4266	+	6.70826i	−1.61802	+	0.622846i
$117$	−4.42513	+	4.42513i	−0.409104	+	0.409104i
$118$	−0.583842	−	3.14189i	−0.0537470	−	0.289234i
$119$	−1.97357	−	7.16335i	−0.180917	−	0.656663i
$120$	−10.8252	−	12.9377i	−0.988205	−	1.18104i
$121$	−5.00725			−0.455205
$122$	12.8903	−	2.39534i	1.16703	−	0.216864i
$123$	−2.94751	+	2.94751i	−0.265768	+	0.265768i
$124$	−2.60148	−	6.75808i	−0.233619	−	0.606894i
$125$	3.82068	−	10.5073i	0.341732	−	0.939798i
$126$	−5.02952	+	14.5493i	−0.448065	+	1.29615i
$127$	−11.0495	+	11.0495i	−0.980484	+	0.980484i	−0.999813	−	0.0193291i	$-0.993847\pi$
$127$	−11.0495	+	11.0495i	−0.980484	+	0.980484i	0.0193291	+	0.999813i	$0.493847\pi$
$128$	−3.17756	+	10.8583i	−0.280860	+	0.959749i
$129$	−11.8521			−1.04352
$130$	1.55538	+	4.55167i	0.136416	+	0.399208i
$131$	−4.16348			−0.363765			−0.181882	−	0.983320i	$-0.558219\pi$
$131$	−4.16348			−0.363765			−0.181882	+	0.983320i	$0.558219\pi$
$132$	−8.66259	+	19.5058i	−0.753982	+	1.69776i
$133$	8.86724	−	15.6113i	0.768887	−	1.35367i
$134$	15.5172	+	10.6540i	1.34049	+	0.920363i
$135$	−6.57520	+	0.963813i	−0.565903	+	0.0829518i
$136$	−7.72640	−	1.84343i	−0.662533	−	0.158073i
$137$	−12.8719	+	12.8719i	−1.09972	+	1.09972i	−0.105279	+	0.994443i	$0.533574\pi$
$137$	−12.8719	+	12.8719i	−1.09972	+	1.09972i	−0.994443	+	0.105279i	$0.966426\pi$
$138$	−1.56087	−	8.39964i	−0.132870	−	0.715025i
$139$			13.1998i			1.11959i	0.828632	+	0.559794i	$0.189120\pi$
$139$			13.1998i			1.11959i	−0.828632	+	0.559794i	$0.810880\pi$
$140$	8.33682	+	8.39628i	0.704590	+	0.709615i
$141$			2.05154i			0.172771i
$142$	14.6236	−	2.71744i	1.22719	−	0.228042i
$143$	4.30324	−	4.30324i	0.359855	−	0.359855i
$144$	11.0348	+	12.2092i	0.919568	+	1.01743i
$145$	16.7474	+	12.4653i	1.39080	+	1.03519i
$146$	−6.99944	+	10.1945i	−0.579278	+	0.843704i
$147$	4.57795	−	18.1008i	0.377583	−	1.49293i
$148$	11.9444	+	5.30456i	0.981826	+	0.436032i
$149$	3.69953			0.303077			0.151539	−	0.988451i	$-0.451577\pi$
$149$	3.69953			0.303077			0.151539	+	0.988451i	$0.451577\pi$
$150$	−5.76384	+	17.9580i	−0.470616	+	1.46626i
$151$	−5.27521			−0.429291			−0.214645	−	0.976692i	$-0.568860\pi$
$151$	−5.27521			−0.429291			−0.214645	+	0.976692i	$0.568860\pi$
$152$	−10.0516	−	16.3510i	−0.815294	−	1.32624i
$153$	−8.17011	+	8.17011i	−0.660514	+	0.660514i
$154$	4.89098	−	14.1485i	0.394126	−	1.14012i
$155$	−4.83408	+	6.49468i	−0.388283	+	0.521665i
$156$	−2.91499	−	7.57253i	−0.233386	−	0.606288i
$157$	7.53900	−	7.53900i	0.601678	−	0.601678i	−0.339080	−	0.940758i	$-0.610116\pi$
$157$	7.53900	−	7.53900i	0.601678	−	0.601678i	0.940758	+	0.339080i	$0.110116\pi$
$158$	0.139470	+	0.750544i	0.0110956	+	0.0597101i
$159$	0.158299			0.0125539
$160$	12.1607	−	3.48101i	0.961387	−	0.275198i
$161$	1.59166	+	5.77718i	0.125441	+	0.455305i
$162$	−6.13975	+	1.14092i	−0.482384	+	0.0896392i
$163$	−9.43600	+	9.43600i	−0.739084	+	0.739084i	−0.972401	−	0.233316i	$-0.925042\pi$
$163$	−9.43600	+	9.43600i	−0.739084	+	0.739084i	0.233316	+	0.972401i	$0.425042\pi$
$164$	−1.12286	−	2.91696i	−0.0876808	−	0.227776i
$165$	23.6097	−	3.46078i	1.83802	−	0.269422i
$166$	−1.37869	−	0.946594i	−0.107007	−	0.0734700i
$167$	−1.64196	−	1.64196i	−0.127058	−	0.127058i	0.640718	−	0.767776i	$-0.278637\pi$
$167$	−1.64196	−	1.64196i	−0.127058	−	0.127058i	−0.767776	+	0.640718i	$0.778637\pi$
$168$	−14.5940	−	13.6167i	−1.12595	−	1.05055i
$169$		−	10.6863i		−	0.822024i
$170$	2.87169	+	8.40373i	0.220249	+	0.644537i
$171$	−27.9188			−2.13501
$172$	3.60710	−	8.12221i	0.275039	−	0.619313i
$173$	9.51690	+	9.51690i	0.723556	+	0.723556i	0.969328	−	0.245771i	$-0.0790413\pi$
$173$	9.51690	+	9.51690i	0.723556	+	0.723556i	−0.245771	+	0.969328i	$0.579041\pi$
$174$	−29.0336	−	19.9342i	−2.20103	−	1.51121i
$175$	2.95743	−	12.8939i	0.223561	−	0.974690i
$176$	−10.7309	−	11.8729i	−0.808869	−	0.894950i
$177$	4.26184	−	4.26184i	0.320339	−	0.320339i
$178$	4.11480	−	0.764634i	0.308418	−	0.0573118i
$179$	2.36197			0.176542			0.0882711	−	0.996096i	$-0.471866\pi$
$179$	2.36197			0.176542			0.0882711	+	0.996096i	$0.471866\pi$
$180$	4.95012	−	17.7210i	0.368960	−	1.32085i
$181$	14.2162			1.05668			0.528342	−	0.849031i	$-0.322814\pi$
$181$	14.2162			1.05668			0.528342	+	0.849031i	$0.322814\pi$
$182$	2.48870	+	5.11839i	0.184475	+	0.379401i
$183$	17.4851	+	17.4851i	1.29254	+	1.29254i
$184$	6.23127	+	1.48671i	0.459375	+	0.109601i
$185$	−2.11922	−	14.4575i	−0.155808	−	1.06293i
$186$	7.73052	−	11.2593i	0.566829	−	0.825573i
$187$	7.94506	−	7.94506i	0.581001	−	0.581001i
$188$	−1.40591	−	0.624369i	−0.102537	−	0.0455368i
$189$	−7.58058	+	2.08852i	−0.551406	+	0.151917i
$190$	−9.45202	+	19.2651i	−0.685722	+	1.39764i
$191$	16.8933			1.22236			0.611178	−	0.791493i	$-0.290696\pi$
$191$	16.8933			1.22236			0.611178	+	0.791493i	$0.290696\pi$
$192$	−20.2750	+	6.65101i	−1.46322	+	0.479995i
$193$	−6.55600	−	6.55600i	−0.471911	−	0.471911i	0.430621	−	0.902533i	$-0.358294\pi$
$193$	−6.55600	−	6.55600i	−0.471911	−	0.471911i	−0.902533	+	0.430621i	$0.858294\pi$
$194$	16.9169	+	11.6150i	1.21456	+	0.833907i
$195$	−5.41666	+	7.27739i	−0.387895	+	0.521145i
$196$	11.0111	+	8.64608i	0.786510	+	0.617577i
$197$	−7.79462	−	7.79462i	−0.555343	−	0.555343i	0.372635	−	0.927978i	$-0.378454\pi$
$197$	−7.79462	−	7.79462i	−0.555343	−	0.555343i	−0.927978	+	0.372635i	$0.878454\pi$
$198$	−22.8871	+	4.25300i	−1.62651	+	0.302247i
$199$	−23.1271			−1.63944			−0.819720	−	0.572765i	$-0.805871\pi$
$199$	−23.1271			−1.63944			−0.819720	+	0.572765i	$0.805871\pi$
$200$	−10.5524	−	9.41530i	−0.746164	−	0.665762i
$201$			35.5001i			2.50398i
$202$	5.53328	−	1.02822i	0.389321	−	0.0723456i
$203$	21.4792	+	12.2002i	1.50755	+	0.856289i
$204$	−5.38194	−	13.9811i	−0.376811	−	0.978876i
$205$	−2.08651	+	2.80327i	−0.145728	+	0.195789i
$206$	14.0743	−	20.4989i	0.980603	−	1.42822i
$207$	6.58912	−	6.58912i	0.457976	−	0.457976i
$208$	6.07657	+	0.307006i	0.421334	+	0.0212871i
$209$	27.1498			1.87799
$210$	−4.15498	+	21.9256i	−0.286721	+	1.51301i
$211$			10.4345i			0.718342i	0.933272	+	0.359171i	$0.116940\pi$
$211$			10.4345i			0.718342i	−0.933272	+	0.359171i	$0.883060\pi$
$212$	−0.0481770	+	0.108482i	−0.00330881	+	0.00745055i
$213$	19.8363	+	19.8363i	1.35916	+	1.35916i
$214$	−19.2272	−	13.2012i	−1.31434	−	0.902414i
$215$	−9.83108	+	1.44107i	−0.670474	+	0.0982801i
$216$	−1.95080	+	8.17643i	−0.132735	+	0.556335i
$217$	−4.73128	+	8.32970i	−0.321180	+	0.565457i
$218$	5.01153	−	0.931269i	0.339424	−	0.0630735i
$219$	−23.3229			−1.57601
$220$	−4.81376	+	17.2329i	−0.324544	+	1.16184i
$221$			4.27175i			0.287349i
$222$	4.50335	+	24.2343i	0.302245	+	1.62650i
$223$	8.46109	−	8.46109i	0.566596	−	0.566596i	−0.364577	−	0.931173i	$-0.618786\pi$
$223$	8.46109	−	8.46109i	0.566596	−	0.566596i	0.931173	+	0.364577i	$0.118786\pi$
$224$	13.7730	−	5.85706i	0.920246	−	0.391341i
$225$	−19.7058	+	5.90391i	−1.31372	+	0.393594i
$226$	8.26201	+	5.67261i	0.549581	+	0.377336i
$227$	−9.13225	+	9.13225i	−0.606129	+	0.606129i	−0.941932	−	0.335803i	$-0.890992\pi$
$227$	−9.13225	+	9.13225i	−0.606129	+	0.606129i	0.335803	+	0.941932i	$0.390992\pi$
$228$	14.6926	−	33.0837i	0.973039	−	2.19102i
$229$		−	10.0420i		−	0.663596i	−0.943350	−	0.331798i	$-0.892345\pi$
$229$		−	10.0420i		−	0.663596i	0.943350	−	0.331798i	$-0.107655\pi$
$230$	−2.31599	−	6.77753i	−0.152712	−	0.446897i
$231$	27.2198	−	7.49929i	1.79093	−	0.493417i
$232$	22.4969	−	13.8298i	1.47700	−	0.907972i
$233$	4.60399	+	4.60399i	0.301617	+	0.301617i	0.841646	−	0.540029i	$-0.181587\pi$
$233$	4.60399	+	4.60399i	0.301617	+	0.301617i	−0.540029	+	0.841646i	$0.681587\pi$
$234$	5.00942	−	7.29609i	0.327476	−	0.476960i
$235$	0.249441	+	1.70171i	0.0162718	+	0.111007i
$236$	1.62356	+	4.21767i	0.105685	+	0.274547i
$237$	−1.01808	+	1.01808i	−0.0661315	+	0.0661315i
$238$	4.59489	+	9.45008i	0.297842	+	0.612558i
$239$		−	12.9081i		−	0.834958i	−0.908687	−	0.417479i	$-0.862914\pi$
$239$		−	12.9081i		−	0.834958i	0.908687	−	0.417479i	$-0.137086\pi$
$240$	18.3943	+	15.1917i	1.18735	+	0.980622i
$241$		−	3.90638i		−	0.251632i	−0.992054	−	0.125816i	$-0.959845\pi$
$241$		−	3.90638i		−	0.251632i	0.992054	−	0.125816i	$-0.0401549\pi$
$242$	6.96214	−	1.29374i	0.447543	−	0.0831648i
$243$	−14.6327	−	14.6327i	−0.938691	−	0.938691i
$244$	−17.3039	+	6.66101i	−1.10777	+	0.426428i
$245$	1.59648	−	15.5708i	0.101995	−	0.994785i
$246$	3.33669	−	4.85980i	0.212739	−	0.309850i
$247$	−7.29870	+	7.29870i	−0.464405	+	0.464405i
$248$	5.36323	+	8.72436i	0.340565	+	0.553998i
$249$		−	3.15415i		−	0.199886i
$250$	−2.59752	+	15.5966i	−0.164281	+	0.986414i
$251$	−14.9137			−0.941342			−0.470671	−	0.882309i	$-0.655988\pi$
$251$	−14.9137			−0.941342			−0.470671	+	0.882309i	$0.655988\pi$
$252$	3.23396	−	21.5289i	0.203720	−	1.35620i
$253$	−6.40762	+	6.40762i	−0.402844	+	0.402844i
$254$	12.5084	−	18.2182i	0.784850	−	1.14311i
$255$	−10.0008	+	13.4362i	−0.626272	+	0.841409i
$256$	1.61262	−	15.9185i	0.100789	−	0.994908i
$257$	−12.9153	−	12.9153i	−0.805636	−	0.805636i	0.178334	−	0.983970i	$-0.442929\pi$
$257$	−12.9153	−	12.9153i	−0.805636	−	0.805636i	−0.983970	+	0.178334i	$0.942929\pi$
$258$	16.4793	−	3.06228i	1.02596	−	0.190649i
$259$	−4.59221	−	16.6681i	−0.285346	−	1.03570i
$260$	−3.33864	−	5.92682i	−0.207054	−	0.367566i
$261$		−	38.4129i		−	2.37770i
$262$	5.78895	−	1.07573i	0.357642	−	0.0664589i
$263$	0.715659	+	0.715659i	0.0441294	+	0.0441294i	0.728827	−	0.684698i	$-0.240066\pi$
$263$	0.715659	+	0.715659i	0.0441294	+	0.0441294i	−0.684698	+	0.728827i	$0.740066\pi$
$264$	7.00478	−	29.3593i	0.431114	−	1.80694i
$265$	0.131306	−	0.0192472i	0.00806604	−	0.00118234i
$266$	−8.29556	+	23.9972i	−0.508634	+	1.47136i
$267$	5.58155	+	5.58155i	0.341585	+	0.341585i
$268$	−24.3280	−	10.8042i	−1.48607	−	0.659969i
$269$		−	17.4653i		−	1.06488i	−0.846468	−	0.532439i	$-0.821276\pi$
$269$		−	17.4653i		−	1.06488i	0.846468	−	0.532439i	$-0.178724\pi$
$270$	8.89321	−	3.03895i	0.541224	−	0.184945i
$271$		−	2.78914i		−	0.169428i	−0.996405	−	0.0847142i	$-0.973002\pi$
$271$		−	2.78914i		−	0.169428i	0.996405	−	0.0847142i	$-0.0269977\pi$
$272$	11.2192	+	0.566825i	0.680262	+	0.0343688i
$273$	−5.30147	+	9.33355i	−0.320860	+	0.564892i
$274$	14.5715	−	21.2230i	0.880296	−	1.28213i
$275$	19.1630	−	5.74129i	1.15557	−	0.346213i
$276$	4.34049	+	11.2757i	0.261267	+	0.678716i
$277$	−3.27529	−	3.27529i	−0.196793	−	0.196793i	0.601831	−	0.798624i	$-0.294438\pi$
$277$	−3.27529	−	3.27529i	−0.196793	−	0.196793i	−0.798624	+	0.601831i	$0.794438\pi$
$278$	−3.41047	−	18.3531i	−0.204546	−	1.10075i
$279$	14.8966			0.891837
$280$	−13.7610	−	9.52026i	−0.822376	−	0.568945i
$281$	17.0717			1.01841			0.509207	−	0.860644i	$-0.329939\pi$
$281$	17.0717			1.01841			0.509207	+	0.860644i	$0.329939\pi$
$282$	−0.530064	−	2.85249i	−0.0315648	−	0.169863i
$283$	−10.5734	−	10.5734i	−0.628521	−	0.628521i	0.319175	−	0.947696i	$-0.396594\pi$
$283$	−10.5734	−	10.5734i	−0.628521	−	0.628521i	−0.947696	+	0.319175i	$0.896594\pi$
$284$	−19.6307	+	7.55671i	−1.16487	+	0.448408i
$285$	−40.0443	+	5.86982i	−2.37202	+	0.347698i
$286$	−4.87143	+	7.09512i	−0.288054	+	0.419543i
$287$	−2.04214	+	3.59531i	−0.120544	+	0.212224i
$288$	−18.4974	−	14.1247i	−1.08997	−	0.832303i
$289$		−	9.11307i		−	0.536063i
$290$	−26.5065	−	13.0048i	−1.55652	−	0.763670i
$291$			38.7023i			2.26877i
$292$	7.09811	−	15.9830i	0.415386	−	0.935337i
$293$	−0.279226	−	0.279226i	−0.0163126	−	0.0163126i	0.698903	−	0.715216i	$-0.253672\pi$
$293$	−0.279226	−	0.279226i	−0.0163126	−	0.0163126i	−0.715216	+	0.698903i	$0.753672\pi$
$294$	−1.68847	+	26.3504i	−0.0984733	+	1.53679i
$295$	3.01691	−	4.05328i	0.175651	−	0.235991i
$296$	−17.9782	−	4.28939i	−1.04496	−	0.249316i
$297$	−8.40783	−	8.40783i	−0.487872	−	0.487872i
$298$	−5.14387	+	0.955860i	−0.297976	+	0.0553715i
$299$		−	3.44513i		−	0.199237i
$300$	3.37424	−	26.4582i	0.194812	−	1.52757i
$301$	−11.3343	+	3.12270i	−0.653298	+	0.179989i
$302$	7.33471	−	1.36297i	0.422065	−	0.0784304i
$303$	7.50566	+	7.50566i	0.431189	+	0.431189i
$304$	18.2005	+	20.1375i	1.04387	+	1.15496i
$305$	16.6295	+	12.3775i	0.952201	+	0.708736i
$306$	9.24887	−	13.4708i	0.528723	−	0.770072i
$307$	20.7058	−	20.7058i	1.18174	−	1.18174i	0.202448	−	0.979293i	$-0.435110\pi$
$307$	20.7058	−	20.7058i	1.18174	−	1.18174i	0.979293	−	0.202448i	$-0.0648896\pi$
$308$	−3.14488	+	20.9359i	−0.179196	+	1.19293i
$309$	46.8970			2.66788
$310$	5.04330	−	10.2793i	0.286440	−	0.583824i
$311$			19.8654i			1.12646i	0.826299	+	0.563231i	$0.190442\pi$
$311$			19.8654i			1.12646i	−0.826299	+	0.563231i	$0.809558\pi$
$312$	6.00958	+	9.77578i	0.340225	+	0.553444i
$313$	5.64662	−	5.64662i	0.319166	−	0.319166i	−0.529281	−	0.848447i	$-0.677538\pi$
$313$	5.64662	−	5.64662i	0.319166	−	0.319166i	0.848447	+	0.529281i	$0.177538\pi$
$314$	−8.53443	+	12.4302i	−0.481626	+	0.701476i
$315$	−22.2801	+	9.80001i	−1.25534	+	0.552168i
$316$	−0.387841	−	1.00753i	−0.0218178	−	0.0566780i
$317$	−13.5188	−	13.5188i	−0.759291	−	0.759291i	0.216903	−	0.976193i	$-0.430405\pi$
$317$	−13.5188	−	13.5188i	−0.759291	−	0.759291i	−0.976193	+	0.216903i	$0.930405\pi$
$318$	−0.220101	+	0.0409003i	−0.0123426	+	0.00229357i
$319$			37.3548i			2.09147i
$320$	−16.0090	+	7.98204i	−0.894928	+	0.446210i
$321$		−	43.9877i		−	2.45515i
$322$	−3.70574	−	7.62141i	−0.206513	−	0.424724i
$323$	−13.4756	+	13.4756i	−0.749801	+	0.749801i
$324$	8.24199	−	3.17270i	0.457889	−	0.176261i
$325$	−3.60816	+	6.69503i	−0.200145	+	0.371373i
$326$	10.6819	−	15.5579i	0.591616	−	0.861674i
$327$	6.79793	+	6.79793i	0.375926	+	0.375926i
$328$	2.31491	+	3.76565i	0.127819	+	0.207924i
$329$	0.540523	+	1.96191i	0.0298000	+	0.108163i
$330$	−31.9331	+	10.9120i	−1.75786	+	0.600688i
$331$		−	27.3945i		−	1.50574i	−0.658171	−	0.752869i	$-0.728669\pi$
$331$		−	27.3945i		−	1.50574i	0.658171	−	0.752869i	$-0.271331\pi$
$332$	2.16152	+	0.959938i	0.118629	+	0.0526834i
$333$	−19.0107	+	19.0107i	−1.04178	+	1.04178i
$334$	2.70723	+	1.85876i	0.148133	+	0.101707i
$335$	4.31636	+	29.4465i	0.235828	+	1.60884i
$336$	23.8098	+	15.1620i	1.29893	+	0.827158i
$337$	−15.8988	+	15.8988i	−0.866065	+	0.866065i	−0.992034	−	0.125969i	$-0.959796\pi$
$337$	−15.8988	+	15.8988i	−0.866065	+	0.866065i	0.125969	+	0.992034i	$0.459796\pi$
$338$	2.76106	+	14.8584i	0.150182	+	0.808189i
$339$			18.9017i			1.02660i
$340$	−6.16413	−	10.9427i	−0.334297	−	0.593450i
$341$	−14.4863			−0.784477
$342$	38.8187	−	7.21349i	2.09907	−	0.390061i
$343$	−0.391117	−	18.5161i	−0.0211183	−	0.999777i
$344$	−2.91679	+	12.2252i	−0.157263	+	0.659138i
$345$	8.06552	−	10.8362i	0.434233	−	0.583401i
$346$	−15.6913	−	10.7735i	−0.843570	−	0.579186i
$347$	8.75570	+	8.75570i	0.470030	+	0.470030i	0.901924	−	0.431894i	$-0.142155\pi$
$347$	8.75570	+	8.75570i	0.470030	+	0.470030i	−0.431894	+	0.901924i	$0.642155\pi$
$348$	45.5192	+	20.2152i	2.44008	+	1.08365i
$349$			8.60695i			0.460719i	0.973106	+	0.230360i	$0.0739903\pi$
$349$			8.60695i			0.460719i	−0.973106	+	0.230360i	$0.926010\pi$
$350$	−0.780591	+	18.6920i	−0.0417243	+	0.999129i
$351$	4.52057			0.241290
$352$	17.9879	+	13.7356i	0.958760	+	0.732109i
$353$	−10.0893	+	10.0893i	−0.537000	+	0.537000i	−0.922647	−	0.385647i	$-0.873978\pi$
$353$	−10.0893	+	10.0893i	−0.537000	+	0.537000i	0.385647	+	0.922647i	$0.373978\pi$
$354$	−4.82456	+	7.02685i	−0.256422	+	0.373473i
$355$	18.8656	+	14.0419i	1.00128	+	0.745268i
$356$	−5.52371	+	2.12631i	−0.292756	+	0.112694i
$357$	−9.78809	+	17.2325i	−0.518041	+	0.912041i
$358$	−3.28411	+	0.610271i	−0.173571	+	0.0322538i
$359$			5.77319i			0.304698i	0.988327	+	0.152349i	$0.0486837\pi$
$359$			5.77319i			0.304698i	−0.988327	+	0.152349i	$0.951316\pi$
$360$	−2.30406	+	25.9185i	−0.121434	+	1.36602i
$361$	−27.0486			−1.42361
$362$	−19.7664	+	3.67310i	−1.03890	+	0.193054i
$363$	9.44384	+	9.44384i	0.495673	+	0.495673i
$364$	−4.78278	−	6.47366i	−0.250686	−	0.339312i
$365$	−19.3458	+	2.83576i	−1.01260	+	0.148431i
$366$	−28.8292	−	19.7938i	−1.50693	−	1.03464i
$367$	14.6713	+	14.6713i	0.765834	+	0.765834i	0.977370	−	0.211536i	$-0.0678465\pi$
$367$	14.6713	+	14.6713i	0.765834	+	0.765834i	−0.211536	+	0.977370i	$0.567847\pi$
$368$	−9.04815	−	0.457139i	−0.471668	−	0.0238300i
$369$	6.42976			0.334720
$370$	6.68201	+	19.5543i	0.347381	+	1.01658i
$371$	0.151383	−	0.0417073i	0.00785940	−	0.00216534i
$372$	−7.83950	+	17.6524i	−0.406459	+	0.915236i
$373$	10.1812	−	10.1812i	0.527162	−	0.527162i	−0.392563	−	0.919725i	$-0.628411\pi$
$373$	10.1812	−	10.1812i	0.527162	−	0.527162i	0.919725	+	0.392563i	$0.128411\pi$
$374$	−8.99411	+	13.0997i	−0.465074	+	0.677369i
$375$	−27.0229	+	12.6111i	−1.39546	+	0.651235i
$376$	2.11612	+	0.504880i	0.109130	+	0.0260372i
$377$	−10.0421	−	10.0421i	−0.517196	−	0.517196i
$378$	10.0005	−	4.86252i	0.514371	−	0.250101i
$379$	−24.2398			−1.24511			−0.622557	−	0.782575i	$-0.713906\pi$
$379$	−24.2398			−1.24511			−0.622557	+	0.782575i	$0.713906\pi$
$380$	8.16460	−	29.2286i	0.418835	−	1.49940i
$381$	41.6794			2.13530
$382$	−23.4886	+	4.36478i	−1.20178	+	0.223321i
$383$	1.73225	−	1.73225i	0.0885140	−	0.0885140i	−0.661463	−	0.749977i	$-0.730064\pi$
$383$	1.73225	−	1.73225i	0.0885140	−	0.0885140i	0.749977	+	0.661463i	$0.230064\pi$
$384$	26.4721	−	14.4862i	1.35090	−	0.739243i
$385$	21.6664	−	9.53007i	1.10422	−	0.485697i
$386$	10.8094	+	7.42164i	0.550186	+	0.377752i
$387$	12.9273	+	12.9273i	0.657130	+	0.657130i
$388$	−26.5225	−	11.7787i	−1.34648	−	0.597974i
$389$	7.57448			0.384041			0.192021	−	0.981391i	$-0.438496\pi$
$389$	7.57448			0.384041			0.192021	+	0.981391i	$0.438496\pi$
$390$	5.65110	−	11.5181i	0.286154	−	0.583241i
$391$		−	6.36074i		−	0.321676i
$392$	−17.5439	−	9.17662i	−0.886103	−	0.463489i
$393$	7.85245	+	7.85245i	0.396104	+	0.396104i
$394$	12.8516	+	8.82380i	0.647456	+	0.444537i
$395$	−0.720689	+	0.968261i	−0.0362618	+	0.0487185i
$396$	30.7236	−	11.8268i	1.54392	−	0.594321i
$397$	3.65408	−	3.65408i	0.183393	−	0.183393i	−0.609440	−	0.792833i	$-0.708605\pi$
$397$	3.65408	−	3.65408i	0.183393	−	0.183393i	0.792833	+	0.609440i	$0.208605\pi$
$398$	32.1562	−	5.97544i	1.61185	−	0.299522i
$399$	−46.1673	+	12.7195i	−2.31126	+	0.636772i
$400$	17.1048	+	10.3647i	0.855239	+	0.518235i
$401$	−15.3955			−0.768815			−0.384407	−	0.923164i	$-0.625594\pi$
$401$	−15.3955			−0.768815			−0.384407	+	0.923164i	$0.625594\pi$
$402$	−9.17228	−	49.3597i	−0.457472	−	2.46184i
$403$	3.89436	−	3.89436i	0.193992	−	0.193992i
$404$	−7.42788	+	2.85931i	−0.369551	+	0.142256i
$405$	−7.92076	−	5.89552i	−0.393586	−	0.292951i
$406$	−33.0172	−	11.4137i	−1.63862	−	0.566452i
$407$	18.4870	−	18.4870i	0.916368	−	0.916368i
$408$	11.0955	+	18.0490i	0.549308	+	0.893558i
$409$	−18.9943			−0.939208			−0.469604	−	0.882877i	$-0.655603\pi$
$409$	−18.9943			−0.939208			−0.469604	+	0.882877i	$0.655603\pi$
$410$	2.17682	−	4.43679i	0.107505	−	0.219118i
$411$	48.5537			2.39498
$412$	−14.2727	+	32.1383i	−0.703166	+	1.58334i
$413$	2.95276	−	5.19850i	0.145296	−	0.255802i
$414$	−7.45913	+	10.8640i	−0.366596	+	0.533939i
$415$	−0.383504	−	2.61629i	−0.0188255	−	0.128429i
$416$	−8.52826	+	1.14316i	−0.418132	+	0.0560480i
$417$	24.8952	−	24.8952i	1.21912	−	1.21912i
$418$	−37.7494	+	7.01479i	−1.84638	+	0.343105i
$419$		−	24.5279i		−	1.19827i	−0.800650	−	0.599133i	$-0.795512\pi$
$419$		−	24.5279i		−	1.19827i	0.800650	−	0.599133i	$-0.204488\pi$
$420$	0.112140	−	31.5592i	0.00547187	−	1.53993i
$421$			12.5411i			0.611214i	0.952158	+	0.305607i	$0.0988594\pi$
$421$			12.5411i			0.611214i	−0.952158	+	0.305607i	$0.901141\pi$
$422$	−2.69600	−	14.5083i	−0.131239	−	0.706252i
$423$	2.23764	−	2.23764i	0.108798	−	0.108798i
$424$	0.0389571	−	0.163282i	0.00189192	−	0.00792966i
$425$	−6.66173	+	12.3610i	−0.323141	+	0.599597i
$426$	−32.7058	−	22.4555i	−1.58460	−	1.08797i
$427$	21.3280	+	12.1143i	1.03213	+	0.586253i
$428$	30.1445	+	13.3873i	1.45709	+	0.647098i
$429$	−16.2321			−0.783693
$430$	13.2969	−	4.54377i	0.641234	−	0.219120i
$431$	3.29958			0.158935			0.0794676	−	0.996837i	$-0.474678\pi$
$431$	3.29958			0.158935			0.0794676	+	0.996837i	$0.474678\pi$
$432$	0.599840	−	11.8726i	0.0288598	−	0.571222i
$433$	−5.95095	+	5.95095i	−0.285984	+	0.285984i	−0.835490	−	0.549506i	$-0.814816\pi$
$433$	−5.95095	+	5.95095i	−0.285984	+	0.285984i	0.549506	+	0.835490i	$0.314816\pi$
$434$	4.42625	−	12.8041i	0.212467	−	0.614619i
$435$	−8.07616	−	55.0962i	−0.387222	−	2.64166i
$436$	−6.72748	+	2.58969i	−0.322188	+	0.124024i
$437$	10.8679	−	10.8679i	0.519884	−	0.519884i
$438$	32.4284	−	6.02601i	1.54949	−	0.287934i
$439$	17.9112			0.854854			0.427427	−	0.904050i	$-0.359420\pi$
$439$	17.9112			0.854854			0.427427	+	0.904050i	$0.359420\pi$
$440$	2.24059	−	25.2046i	0.106816	−	1.20158i
$441$	−24.7360	+	14.7496i	−1.17790	+	0.702360i
$442$	−1.10371	−	5.93949i	−0.0524980	−	0.282513i
$443$	20.1432	−	20.1432i	0.957032	−	0.957032i	−0.0420822	−	0.999114i	$-0.513399\pi$
$443$	20.1432	−	20.1432i	0.957032	−	0.957032i	0.999114	+	0.0420822i	$0.0133991\pi$
$444$	−12.5230	−	32.5321i	−0.594316	−	1.54391i
$445$	5.30842	+	3.95113i	0.251643	+	0.187301i
$446$	−9.57827	+	13.9505i	−0.453544	+	0.660576i
$447$	−6.97743	−	6.97743i	−0.330021	−	0.330021i
$448$	−17.6368	+	11.7023i	−0.833260	+	0.552882i
$449$			40.1923i			1.89679i	0.317087	+	0.948396i	$0.397295\pi$
$449$			40.1923i			1.89679i	−0.317087	+	0.948396i	$0.602705\pi$
$450$	25.8737	−	13.3003i	1.21970	−	0.626982i
$451$	−6.25265			−0.294426
$452$	−12.9532	−	5.75257i	−0.609269	−	0.270578i
$453$	9.94922	+	9.94922i	0.467455	+	0.467455i
$454$	10.3381	−	15.0571i	0.485189	−	0.706665i
$455$	−3.26261	+	8.38656i	−0.152954	+	0.393168i
$456$	−11.8808	+	49.7961i	−0.556368	+	2.33192i
$457$	6.11023	−	6.11023i	0.285824	−	0.285824i	−0.549602	−	0.835427i	$-0.685221\pi$
$457$	6.11023	−	6.11023i	0.285824	−	0.285824i	0.835427	+	0.549602i	$0.185221\pi$
$458$	2.59459	+	13.9626i	0.121237	+	0.652427i
$459$	8.34631			0.389572
$460$	4.97132	+	8.82517i	0.231789	+	0.411476i
$461$	16.5532			0.770958			0.385479	−	0.922717i	$-0.374036\pi$
$461$	16.5532			0.770958			0.385479	+	0.922717i	$0.374036\pi$
$462$	−35.9091	+	17.4600i	−1.67064	+	0.812311i
$463$	−16.7074	−	16.7074i	−0.776458	−	0.776458i	0.202769	−	0.979227i	$-0.435006\pi$
$463$	−16.7074	−	16.7074i	−0.776458	−	0.776458i	−0.979227	+	0.202769i	$0.935006\pi$
$464$	−27.7067	+	25.0417i	−1.28625	+	1.16253i
$465$	21.3664	−	3.13195i	0.990843	−	0.145241i
$466$	−7.59098	−	5.21188i	−0.351645	−	0.241436i
$467$	−11.8575	+	11.8575i	−0.548702	+	0.548702i	−0.926065	−	0.377364i	$-0.876831\pi$
$467$	−11.8575	+	11.8575i	−0.548702	+	0.548702i	0.377364	+	0.926065i	$0.376831\pi$
$468$	−5.08003	+	11.4389i	−0.234825	+	0.528762i
$469$	9.35327	+	33.9490i	0.431894	+	1.56762i
$470$	−0.786502	−	2.30162i	−0.0362786	−	0.106166i
$471$	−28.4376			−1.31033
$472$	−3.34715	−	5.44481i	−0.154065	−	0.250618i
$473$	−12.5712	−	12.5712i	−0.578023	−	0.578023i
$474$	1.15251	−	1.67860i	0.0529363	−	0.0771005i
$475$	−32.5022	+	9.73776i	−1.49130	+	0.446799i
$476$	−8.83043	−	11.9523i	−0.404742	−	0.547833i
$477$	−0.172659	−	0.172659i	−0.00790550	−	0.00790550i
$478$	3.33512	+	17.9476i	0.152545	+	0.820905i
$479$	21.0171			0.960296			0.480148	−	0.877188i	$-0.340583\pi$
$479$	21.0171			0.960296			0.480148	+	0.877188i	$0.340583\pi$
$480$	−29.5008	−	16.3702i	−1.34652	−	0.747192i
$481$			9.93976i			0.453214i
$482$	1.00931	+	5.43148i	0.0459726	+	0.247397i
$483$	7.89401	−	13.8979i	0.359190	−	0.632375i
$484$	−9.34597	+	3.59766i	−0.424817	+	0.163530i
$485$	4.70570	+	32.1027i	0.213675	+	1.45771i
$486$	24.1262	+	16.5648i	1.09439	+	0.751396i
$487$	13.3091	−	13.3091i	0.603095	−	0.603095i	−0.338038	−	0.941133i	$-0.609763\pi$
$487$	13.3091	−	13.3091i	0.603095	−	0.603095i	0.941133	+	0.338038i	$0.109763\pi$
$488$	22.3385	−	13.7324i	1.01122	−	0.621637i
$489$	35.5932			1.60958
$490$	1.80333	+	22.0624i	0.0814661	+	0.996676i
$491$			12.0782i			0.545079i	0.962145	+	0.272540i	$0.0878636\pi$
$491$			12.0782i			0.545079i	−0.962145	+	0.272540i	$0.912136\pi$
$492$	−3.38372	+	7.61923i	−0.152550	+	0.343502i
$493$	−18.5408	−	18.5408i	−0.835034	−	0.835034i
$494$	8.26241	−	12.0340i	0.371743	−	0.541435i
$495$	−29.5261	−	21.9767i	−1.32710	−	0.987779i
$496$	−9.71124	−	10.7447i	−0.436048	−	0.482453i
$497$	24.1959	+	13.7433i	1.08534	+	0.616472i
$498$	0.814948	+	4.38556i	0.0365187	+	0.196522i
$499$	−21.3572			−0.956078			−0.478039	−	0.878339i	$-0.658652\pi$
$499$	−21.3572			−0.956078			−0.478039	+	0.878339i	$0.658652\pi$
$500$	−0.418124	−	22.3568i	−0.0186991	−	0.999825i
$501$			6.19357i			0.276708i
$502$	20.7361	−	3.85330i	0.925499	−	0.171981i
$503$	14.0259	−	14.0259i	0.625386	−	0.625386i	−0.321518	−	0.946903i	$-0.604193\pi$
$503$	14.0259	−	14.0259i	0.625386	−	0.625386i	0.946903	+	0.321518i	$0.104193\pi$
$504$	1.06597	+	30.7696i	0.0474822	+	1.37059i
$505$	7.13837	+	5.31318i	0.317653	+	0.236434i
$506$	7.25367	−	10.5648i	0.322465	−	0.469662i
$507$	−20.1547	+	20.1547i	−0.895103	+	0.895103i
$508$	−12.6848	+	28.5627i	−0.562796	+	1.26726i
$509$		−	17.8179i		−	0.789763i	−0.918732	−	0.394881i	$-0.870786\pi$
$509$		−	17.8179i		−	0.789763i	0.918732	−	0.394881i	$-0.129214\pi$
$510$	10.4336	−	21.2658i	0.462008	−	0.941666i
$511$	−22.3038	+	6.14491i	−0.986664	+	0.271835i
$512$	1.87072	+	22.5500i	0.0826751	+	0.996577i
$513$	14.2605	+	14.2605i	0.629615	+	0.629615i
$514$	21.2946	+	14.6206i	0.939264	+	0.644888i
$515$	38.9000	−	5.70208i	1.71414	−	0.251264i
$516$	−22.1219	+	8.51565i	−0.973860	+	0.374881i
$517$	−2.17600	+	2.17600i	−0.0957005	+	0.0957005i
$518$	10.6916	+	21.9890i	0.469764	+	0.966141i
$519$		−	35.8984i		−	1.57576i
$520$	6.17342	+	7.37810i	0.270722	+	0.323551i
$521$			19.2833i			0.844817i	0.906406	+	0.422408i	$0.138815\pi$
$521$			19.2833i			0.844817i	−0.906406	+	0.422408i	$0.861185\pi$
$522$	9.92488	+	53.4098i	0.434400	+	2.33768i
$523$	−20.0550	−	20.0550i	−0.876943	−	0.876943i	0.116274	−	0.993217i	$-0.462905\pi$
$523$	−20.0550	−	20.0550i	−0.876943	−	0.876943i	−0.993217	+	0.116274i	$0.962905\pi$
$524$	−7.77107	+	2.99142i	−0.339481	+	0.130681i
$525$	−29.8962	+	18.7406i	−1.30478	+	0.817906i
$526$	−1.17997	−	0.810153i	−0.0514490	−	0.0353243i
$527$	7.19015	−	7.19015i	0.313208	−	0.313208i
$528$	−2.15386	+	42.6313i	−0.0937347	+	1.85529i
$529$		−	17.8701i		−	0.776962i
$530$	−0.177596	+	0.0606873i	−0.00771427	+	0.00263609i
$531$	−9.29687			−0.403450
$532$	5.33401	−	35.5093i	0.231259	−	1.53952i
$533$	1.68090	−	1.68090i	0.0728080	−	0.0728080i
$534$	−9.20278	−	6.31853i	−0.398243	−	0.273429i
$535$	−5.34834	−	36.4868i	−0.231229	−	1.57746i
$536$	36.6175	+	8.73650i	1.58163	+	0.377359i
$537$	−4.45476	−	4.45476i	−0.192237	−	0.192237i
$538$	4.51257	+	24.2839i	0.194551	+	1.04696i
$539$	24.0546	−	14.3433i	1.03611	−	0.617808i
$540$	−11.5800	+	6.52316i	−0.498325	+	0.280712i
$541$			14.1933i			0.610219i	0.952317	+	0.305110i	$0.0986931\pi$
$541$			14.1933i			0.610219i	−0.952317	+	0.305110i	$0.901307\pi$
$542$	0.720641	+	3.87806i	0.0309542	+	0.166577i
$543$	−26.8123	−	26.8123i	−1.15063	−	1.15063i
$544$	−15.7457	+	2.11061i	−0.675091	+	0.0904918i
$545$	6.46527	+	4.81219i	0.276942	+	0.206131i
$546$	4.95968	−	14.3472i	0.212255	−	0.614005i
$547$	−11.8429	−	11.8429i	−0.506367	−	0.506367i	0.407042	−	0.913409i	$-0.366560\pi$
$547$	−11.8429	−	11.8429i	−0.506367	−	0.506367i	−0.913409	+	0.407042i	$0.866560\pi$
$548$	−14.7769	+	33.2736i	−0.631238	+	1.42138i
$549$		−	38.1424i		−	1.62788i
$550$	−25.1610	+	12.9339i	−1.07287	+	0.551505i
$551$		−	63.3573i		−	2.69911i
$552$	−8.94840	−	14.5564i	−0.380869	−	0.619560i
$553$	−0.705364	+	1.24183i	−0.0299951	+	0.0528082i
$554$	5.40024	+	3.70775i	0.229434	+	0.157527i
$555$	−23.2703	+	31.2642i	−0.987771	+	1.32709i
$556$	9.48390	+	24.6372i	0.402207	+	1.04485i
$557$	−29.2335	−	29.2335i	−1.23866	−	1.23866i	−0.960547	−	0.278118i	$-0.910290\pi$
$557$	−29.2335	−	29.2335i	−1.23866	−	1.23866i	−0.278118	−	0.960547i	$-0.589710\pi$
$558$	−20.7124	+	3.84889i	−0.876827	+	0.162937i
$559$	6.75904			0.285877
$560$	21.5932	+	9.68161i	0.912479	+	0.409123i
$561$	−29.9693			−1.26530
$562$	−23.7367	+	4.41088i	−1.00127	+	0.186062i
$563$	5.62265	+	5.62265i	0.236967	+	0.236967i	0.815593	−	0.578626i	$-0.196411\pi$
$563$	5.62265	+	5.62265i	0.236967	+	0.236967i	−0.578626	+	0.815593i	$0.696411\pi$
$564$	1.47401	+	3.82917i	0.0620672	+	0.161237i
$565$	2.29821	+	15.6785i	0.0966862	+	0.659601i
$566$	17.4332	+	11.9695i	0.732772	+	0.503114i
$567$	−10.1587	−	5.77016i	−0.426625	−	0.242324i
$568$	25.3423	−	15.5790i	1.06334	−	0.653680i
$569$			3.01126i			0.126239i	0.998006	+	0.0631194i	$0.0201049\pi$
$569$			3.01126i			0.126239i	−0.998006	+	0.0631194i	$0.979895\pi$
$570$	54.1615	−	18.5079i	2.26858	−	0.775209i
$571$		−	35.7412i		−	1.49572i	−0.663854	−	0.747862i	$-0.731080\pi$
$571$		−	35.7412i		−	1.49572i	0.663854	−	0.747862i	$-0.268920\pi$
$572$	4.94010	−	11.1238i	0.206556	−	0.465109i
$573$	−31.8613	−	31.8613i	−1.33102	−	1.33102i
$574$	1.91048	−	5.52659i	0.0797420	−	0.230675i
$575$	5.37263	−	9.96904i	0.224054	−	0.415738i
$576$	29.3685	+	14.8598i	1.22369	+	0.619160i
$577$	−24.4488	−	24.4488i	−1.01782	−	1.01782i	−0.999838	−	0.0179771i	$-0.994277\pi$
$577$	−24.4488	−	24.4488i	−1.01782	−	1.01782i	−0.0179771	−	0.999838i	$-0.505723\pi$
$578$	2.35458	+	12.6709i	0.0979374	+	0.527041i
$579$			24.7297i			1.02773i
$580$	40.2150	+	11.2335i	1.66984	+	0.466446i
$581$	−0.831028	−	3.01634i	−0.0344769	−	0.125139i
$582$	−9.99964	−	53.8121i	−0.414499	−	2.23058i
$583$	0.167903	+	0.167903i	0.00695382	+	0.00695382i
$584$	−5.73970	+	24.0570i	−0.237511	+	0.995484i
$585$	13.8455	−	2.02952i	0.572443	−	0.0839103i
$586$	0.460384	+	0.316094i	0.0190183	+	0.0130577i
$587$	−10.4697	+	10.4697i	−0.432130	+	0.432130i	−0.889352	−	0.457223i	$-0.848844\pi$
$587$	−10.4697	+	10.4697i	−0.432130	+	0.432130i	0.457223	+	0.889352i	$0.348844\pi$
$588$	−4.46058	−	37.0742i	−0.183951	−	1.52891i
$589$	24.5701			1.01239
$590$	−3.14749	+	6.41522i	−0.129580	+	0.264110i
$591$			29.4018i			1.20943i
$592$	26.1054	+	1.31892i	1.07292	+	0.0542073i
$593$	13.8793	−	13.8793i	0.569955	−	0.569955i	−0.362161	−	0.932116i	$-0.617961\pi$
$593$	13.8793	−	13.8793i	0.569955	−	0.569955i	0.932116	+	0.362161i	$0.117961\pi$
$594$	13.8627	+	9.51798i	0.568793	+	0.390527i
$595$	−6.02375	+	15.4841i	−0.246950	+	0.634786i
$596$	6.90512	−	2.65808i	0.282845	−	0.108879i
$597$	43.6185	+	43.6185i	1.78519	+	1.78519i
$598$	0.890130	+	4.79015i	0.0364001	+	0.195884i
$599$			19.3676i			0.791339i	0.918393	+	0.395670i	$0.129487\pi$
$599$			19.3676i			0.791339i	−0.918393	+	0.395670i	$0.870513\pi$
$600$	2.14452	+	37.6596i	0.0875495	+	1.53745i
$601$			39.3372i			1.60460i	0.596922	+	0.802300i	$0.296390\pi$
$601$			39.3372i			1.60460i	−0.596922	+	0.802300i	$0.703610\pi$
$602$	14.9525	−	7.27032i	0.609419	−	0.296316i
$603$	38.7204	−	38.7204i	1.57682	−	1.57682i
$604$	−9.84611	+	3.79019i	−0.400632	+	0.154221i
$605$	8.98170	+	6.68520i	0.365158	+	0.271792i
$606$	−12.3752	−	8.49669i	−0.502709	−	0.345154i
$607$	17.2334	+	17.2334i	0.699483	+	0.699483i	0.964299	−	0.264816i	$-0.0853112\pi$
$607$	17.2334	+	17.2334i	0.699483	+	0.699483i	−0.264816	+	0.964299i	$0.585311\pi$
$608$	−30.5092	−	23.2969i	−1.23731	−	0.944812i
$609$	−17.5005	−	63.5206i	−0.709156	−	2.57398i
$610$	−26.3198	−	12.9133i	−1.06566	−	0.522842i
$611$		−	1.16995i		−	0.0473312i
$612$	−9.37925	+	21.1195i	−0.379134	+	0.853707i
$613$	8.80551	−	8.80551i	0.355651	−	0.355651i	−0.506556	−	0.862207i	$-0.669082\pi$
$613$	8.80551	−	8.80551i	0.355651	−	0.355651i	0.862207	+	0.506556i	$0.169082\pi$
$614$	−23.4397	+	34.1394i	−0.945950	+	1.37775i
$615$	9.22228	−	1.35183i	0.371878	−	0.0545110i
$616$	−1.03661	−	29.9221i	−0.0417662	−	1.20560i
$617$	22.2596	−	22.2596i	0.896137	−	0.896137i	−0.0989545	−	0.995092i	$-0.531550\pi$
$617$	22.2596	−	22.2596i	0.896137	−	0.896137i	0.995092	+	0.0989545i	$0.0315498\pi$
$618$	−65.2061	+	12.1169i	−2.62298	+	0.487415i
$619$		−	22.5937i		−	0.908116i	−0.890972	−	0.454058i	$-0.849976\pi$
$619$		−	22.5937i		−	0.908116i	0.890972	−	0.454058i	$-0.150024\pi$
$620$	−4.35637	+	15.5955i	−0.174956	+	0.626329i
$621$	−6.73122			−0.270115
$622$	−5.13269	−	27.6211i	−0.205802	−	1.10750i
$623$	6.80826	+	3.86710i	0.272767	+	0.154932i
$624$	−10.8816	−	12.0396i	−0.435612	−	0.481971i
$625$	−20.8816	+	13.7463i	−0.835263	+	0.549851i
$626$	−6.39218	+	9.31005i	−0.255483	+	0.372105i
$627$	−51.2054	−	51.2054i	−2.04495	−	2.04495i
$628$	8.65474	−	19.4881i	0.345362	−	0.777661i
$629$			18.3518i			0.731733i
$630$	28.4464	−	19.3826i	1.13333	−	0.772222i
$631$	11.8476			0.471645			0.235822	−	0.971796i	$-0.424222\pi$
$631$	11.8476			0.471645			0.235822	+	0.971796i	$0.424222\pi$
$632$	0.799578	+	1.30067i	0.0318055	+	0.0517380i
$633$	19.6798	−	19.6798i	0.782203	−	0.782203i
$634$	22.2896	+	15.3038i	0.885232	+	0.607790i
$635$	34.5721	−	5.06768i	1.37195	−	0.201105i
$636$	0.295463	−	0.113736i	0.0117159	−	0.00450994i
$637$	−2.61072	+	10.3225i	−0.103440	+	0.408994i
$638$	−9.65150	−	51.9386i	−0.382107	−	2.05627i
$639$		−	43.2714i		−	1.71179i
$640$	20.1967	−	15.2346i	0.798345	−	0.602201i
$641$	33.9795			1.34211			0.671055	−	0.741408i	$-0.265842\pi$
$641$	33.9795			1.34211			0.671055	+	0.741408i	$0.265842\pi$
$642$	11.3652	+	61.1609i	0.448550	+	2.41383i
$643$	9.65027	+	9.65027i	0.380569	+	0.380569i	0.871307	−	0.490738i	$-0.163273\pi$
$643$	9.65027	+	9.65027i	0.380569	+	0.380569i	−0.490738	+	0.871307i	$0.663273\pi$
$644$	7.12167	+	9.63942i	0.280633	+	0.379847i
$645$	21.2596	+	15.8238i	0.837097	+	0.623063i
$646$	15.2549	−	22.2183i	0.600194	−	0.874168i
$647$	−1.29786	−	1.29786i	−0.0510241	−	0.0510241i	0.681134	−	0.732158i	$-0.261487\pi$
$647$	−1.29786	−	1.29786i	−0.0510241	−	0.0510241i	−0.732158	+	0.681134i	$0.761487\pi$
$648$	−10.6400	+	6.54087i	−0.417979	+	0.256949i
$649$	9.04078			0.354882
$650$	3.28701	−	10.2411i	0.128927	−	0.401689i
$651$	24.6334	−	6.78673i	0.965460	−	0.265993i
$652$	−10.8325	+	24.3918i	−0.424233	+	0.955258i
$653$	−19.0589	+	19.0589i	−0.745833	+	0.745833i	−0.973694	−	0.227861i	$-0.926827\pi$
$653$	−19.0589	+	19.0589i	−0.745833	+	0.745833i	0.227861	+	0.973694i	$0.426827\pi$
$654$	−11.2083	−	7.69551i	−0.438280	−	0.300918i
$655$	7.46819	+	5.55867i	0.291806	+	0.217195i
$656$	−4.19162	−	4.63770i	−0.163655	−	0.181072i
$657$	25.4385	+	25.4385i	0.992451	+	0.992451i
$658$	−1.25845	−	2.58820i	−0.0490596	−	0.100899i
$659$	−9.48784			−0.369594			−0.184797	−	0.982777i	$-0.559163\pi$
$659$	−9.48784			−0.369594			−0.184797	+	0.982777i	$0.559163\pi$
$660$	41.5807	−	23.4229i	1.61853	−	0.911734i
$661$	16.7454			0.651321			0.325661	−	0.945487i	$-0.394413\pi$
$661$	16.7454			0.651321			0.325661	+	0.945487i	$0.394413\pi$
$662$	7.07801	+	38.0896i	0.275095	+	1.48039i
$663$	8.05666	−	8.05666i	0.312895	−	0.312895i
$664$	−3.25343	−	0.776229i	−0.126257	−	0.0301235i
$665$	−36.7482	+	16.1639i	−1.42503	+	0.626809i
$666$	21.5208	−	31.3445i	0.833915	−	1.21458i
$667$	14.9530	+	14.9530i	0.578981	+	0.578981i
$668$	−4.24442	−	1.88496i	−0.164222	−	0.0729313i
$669$	−31.9158			−1.23393
$670$	−13.6097	−	39.8276i	−0.525789	−	1.53867i
$671$			37.0918i			1.43191i
$672$	−37.0229	−	14.9297i	−1.42819	−	0.575924i
$673$	−19.7325	−	19.7325i	−0.760632	−	0.760632i	0.215805	−	0.976437i	$-0.430762\pi$
$673$	−19.7325	−	19.7325i	−0.760632	−	0.760632i	−0.976437	+	0.215805i	$0.930762\pi$
$674$	17.9981	−	26.2138i	0.693260	−	1.00972i
$675$	13.0810	+	7.04975i	0.503487	+	0.271345i
$676$	−7.67802	−	19.9459i	−0.295308	−	0.767148i
$677$	−13.4810	+	13.4810i	−0.518117	+	0.518117i	−0.917001	−	0.398884i	$-0.869398\pi$
$677$	−13.4810	+	13.4810i	−0.518117	+	0.518117i	0.398884	+	0.917001i	$0.369398\pi$
$678$	−4.88370	−	26.2811i	−0.187557	−	1.00932i
$679$	10.1970	+	37.0113i	0.391323	+	1.42036i
$680$	11.3980	+	13.6222i	0.437092	+	0.522386i
$681$	34.4474			1.32003
$682$	20.1419	−	3.74287i	0.771273	−	0.143322i
$683$	−20.7299	+	20.7299i	−0.793206	+	0.793206i	−0.982014	−	0.188808i	$-0.939538\pi$
$683$	−20.7299	+	20.7299i	−0.793206	+	0.793206i	0.188808	+	0.982014i	$0.439538\pi$
$684$	−52.1101	+	20.0594i	−1.99248	+	0.766991i
$685$	40.2742	−	5.90351i	1.53880	−	0.225561i
$686$	5.32789	+	25.6440i	0.203420	+	0.979092i
$687$	−18.9396	+	18.9396i	−0.722591	+	0.722591i
$688$	0.896866	−	17.7517i	0.0341927	−	0.676776i
$689$	−0.0902748			−0.00343920
$690$	−8.41461	+	17.1507i	−0.320339	+	0.652915i
$691$	6.46239			0.245841			0.122920	−	0.992417i	$-0.460774\pi$
$691$	6.46239			0.245841			0.122920	+	0.992417i	$0.460774\pi$
$692$	24.6010	+	10.9254i	0.935188	+	0.415320i
$693$	−37.8685	−	21.5094i	−1.43850	−	0.817073i
$694$	−14.4363	−	9.91178i	−0.547993	−	0.376246i
$695$	17.6230	−	23.6769i	0.668480	−	0.898117i
$696$	−68.5134	−	16.3465i	−2.59699	−	0.619612i
$697$	3.10345	−	3.10345i	0.117551	−	0.117551i
$698$	−2.22381	−	11.9672i	−0.0841723	−	0.452965i
$699$		−	17.3665i		−	0.656862i
$700$	−3.74417	−	26.1912i	−0.141516	−	0.989936i
$701$			2.14398i			0.0809771i	0.999180	+	0.0404886i	$0.0128914\pi$
$701$			2.14398i			0.0809771i	−0.999180	+	0.0404886i	$0.987109\pi$
$702$	−6.28544	+	1.16799i	−0.237229	+	0.0440831i
$703$	−31.3557	+	31.3557i	−1.18260	+	1.18260i
$704$	−28.5595	−	14.4505i	−1.07638	−	0.544624i
$705$	2.73902	−	3.67993i	0.103157	−	0.138594i
$706$	11.4215	−	16.6351i	0.429853	−	0.626070i
$707$	9.15525	+	5.20020i	0.344319	+	0.195574i
$708$	4.89257	−	11.0167i	0.183874	−	0.414035i
$709$	−26.9293			−1.01135			−0.505675	−	0.862724i	$-0.668757\pi$
$709$	−26.9293			−1.01135			−0.505675	+	0.862724i	$0.668757\pi$
$710$	−29.8590	−	14.6497i	−1.12059	−	0.549793i
$711$	2.22087			0.0832889
$712$	7.13084	−	4.38363i	0.267240	−	0.164283i
$713$	−5.79879	+	5.79879i	−0.217166	+	0.217166i
$714$	9.15705	−	26.4893i	0.342694	−	0.991336i
$715$	−13.4642	+	1.97362i	−0.503531	+	0.0738091i
$716$	4.40859	−	1.69706i	0.164757	−	0.0634220i
$717$	−24.3452	+	24.3452i	−0.909187	+	0.909187i
$718$	−1.49164	−	8.02711i	−0.0556675	−	0.299569i
$719$	−9.73319			−0.362987			−0.181493	−	0.983392i	$-0.558093\pi$
$719$	−9.73319			−0.362987			−0.181493	+	0.983392i	$0.558093\pi$
$720$	−3.49307	−	36.6327i	−0.130179	−	1.36522i
$721$	44.8480	−	12.3560i	1.67023	−	0.460163i
$722$	37.6087	−	6.98865i	1.39965	−	0.260091i
$723$	−7.36756	+	7.36756i	−0.274003	+	0.274003i
$724$	26.5344	−	10.2142i	0.986144	−	0.379609i
$725$	−13.3980	−	44.7191i	−0.497588	−	1.66082i
$726$	−15.5709	−	10.6908i	−0.577888	−	0.396772i
$727$	−12.9901	−	12.9901i	−0.481776	−	0.481776i	0.423923	−	0.905698i	$-0.360653\pi$
$727$	−12.9901	−	12.9901i	−0.481776	−	0.481776i	−0.905698	+	0.423923i	$0.860653\pi$
$728$	8.32265	+	7.76530i	0.308458	+	0.287801i
$729$			41.9483i			1.55364i
$730$	26.1659	−	8.94131i	0.968444	−	0.330933i
$731$	12.4792			0.461560
$732$	45.1986	+	20.0728i	1.67059	+	0.741913i
$733$	14.1314	+	14.1314i	0.521956	+	0.521956i	0.918162	−	0.396206i	$-0.129673\pi$
$733$	14.1314	+	14.1314i	0.521956	+	0.521956i	−0.396206	+	0.918162i	$0.629673\pi$
$734$	−24.1898	−	16.6084i	−0.892861	−	0.613029i
$735$	−32.3781	+	26.3561i	−1.19429	+	0.972160i
$736$	12.6988	−	1.70219i	0.468083	−	0.0627436i
$737$	−37.6538	+	37.6538i	−1.38700	+	1.38700i
$738$	−8.94001	+	1.66128i	−0.329086	+	0.0611525i
$739$	41.6005			1.53030			0.765149	−	0.643854i	$-0.222665\pi$
$739$	41.6005			1.53030			0.765149	+	0.643854i	$0.222665\pi$
$740$	−14.3431	−	25.4620i	−0.527261	−	0.936003i
$741$	27.5312			1.01138
$742$	−0.199708	+	0.0971036i	−0.00733152	+	0.00356479i
$743$	−13.0703	−	13.0703i	−0.479504	−	0.479504i	0.425469	−	0.904973i	$-0.360109\pi$
$743$	−13.0703	−	13.0703i	−0.479504	−	0.479504i	−0.904973	+	0.425469i	$0.860109\pi$
$744$	6.33920	−	26.5697i	0.232406	−	0.974091i
$745$	−6.63599	−	4.93925i	−0.243124	−	0.180960i
$746$	−11.5255	+	16.7866i	−0.421978	+	0.614601i
$747$	−3.44027	+	3.44027i	−0.125873	+	0.125873i
$748$	9.12090	−	20.5378i	0.333493	−	0.750936i
$749$	−11.5895	−	42.0658i	−0.423471	−	1.53705i
$750$	34.3146	−	24.5166i	1.25299	−	0.895221i
$751$	−6.31226			−0.230337			−0.115169	−	0.993346i	$-0.536741\pi$
$751$	−6.31226			−0.230337			−0.115169	+	0.993346i	$0.536741\pi$
$752$	−3.07272	−	0.155243i	−0.112050	−	0.00566112i
$753$	28.1277	+	28.1277i	1.02503	+	1.02503i
$754$	16.5573	+	11.3681i	0.602982	+	0.414001i
$755$	9.46235	+	7.04295i	0.344370	+	0.256319i
$756$	−12.6485	+	9.34477i	−0.460020	+	0.339866i
$757$	−22.0249	−	22.0249i	−0.800510	−	0.800510i	0.182665	−	0.983175i	$-0.441528\pi$
$757$	−22.0249	−	22.0249i	−0.800510	−	0.800510i	−0.983175	+	0.182665i	$0.941528\pi$
$758$	33.7033	−	6.26291i	1.22416	−	0.227479i
$759$	24.1700			0.877314
$760$	−3.80025	+	42.7493i	−0.137850	+	1.55068i
$761$		−	52.2491i		−	1.89403i	−0.321190	−	0.947015i	$-0.604083\pi$
$761$		−	52.2491i		−	1.89403i	0.321190	−	0.947015i	$-0.395917\pi$
$762$	−57.9515	+	10.7688i	−2.09936	+	0.390114i
$763$	8.29198	+	4.70985i	0.300190	+	0.170508i
$764$	31.5311	−	12.1377i	1.14076	−	0.439126i
$765$	25.5630	−	3.74710i	0.924232	−	0.135477i
$766$	−1.96098	+	2.85611i	−0.0708529	+	0.103196i
$767$	−2.43044	+	2.43044i	−0.0877581	+	0.0877581i
$768$	−33.0643	+	26.9814i	−1.19311	+	0.973607i
$769$	−48.8671			−1.76219			−0.881097	−	0.472935i	$-0.843194\pi$
$769$	−48.8671			−1.76219			−0.881097	+	0.472935i	$0.843194\pi$
$770$	−27.6628	+	18.8487i	−0.996900	+	0.679261i
$771$			48.7174i			1.75452i
$772$	−16.9471	−	7.52626i	−0.609940	−	0.270876i
$773$	21.3322	+	21.3322i	0.767265	+	0.767265i	0.977624	−	0.210359i	$-0.0674633\pi$
$773$	21.3322	+	21.3322i	0.767265	+	0.767265i	−0.210359	+	0.977624i	$0.567463\pi$
$774$	−21.3143	−	14.6342i	−0.766126	−	0.526014i
$775$	17.3421	−	5.19577i	0.622948	−	0.186637i
$776$	39.9205	+	9.52455i	1.43306	+	0.341911i
$777$	−22.7755	+	40.0976i	−0.817066	+	1.43849i
$778$	−10.5316	+	1.95704i	−0.377578	+	0.0701635i
$779$	10.6051			0.379966
$780$	−4.88138	+	17.4750i	−0.174782	+	0.625704i
$781$			42.0795i			1.50572i
$782$	1.64345	+	8.84404i	0.0587695	+	0.316262i
$783$	−19.6207	+	19.6207i	−0.701186	+	0.701186i
$784$	26.7643	+	8.22639i	0.955867	+	0.293800i
$785$	−23.5883	+	3.45765i	−0.841904	+	0.123409i
$786$	−12.9470	−	8.88927i	−0.461804	−	0.317070i
$787$	11.2139	−	11.2139i	0.399733	−	0.399733i	−0.478406	−	0.878139i	$-0.658785\pi$
$787$	11.2139	−	11.2139i	0.399733	−	0.399733i	0.878139	+	0.478406i	$0.158785\pi$
$788$	−20.1489	−	8.94819i	−0.717775	−	0.318766i
$789$		−	2.69951i		−	0.0961051i
$790$	0.751882	−	1.53249i	0.0267508	−	0.0545235i
$791$	4.98006	+	18.0759i	0.177071	+	0.642703i
$792$	−39.6627	+	24.3823i	−1.40935	+	0.866388i
$793$	−9.97141	−	9.97141i	−0.354095	−	0.354095i
$794$	−4.13656	+	6.02479i	−0.146801	+	0.213812i
$795$	−0.283947	−	0.211346i	−0.0100706	−	0.00749566i
$796$	−43.1665	+	16.6166i	−1.53000	+	0.588961i
$797$	−27.0730	+	27.0730i	−0.958976	+	0.958976i	−0.999191	−	0.0402154i	$-0.987196\pi$
$797$	−27.0730	+	27.0730i	−0.958976	+	0.958976i	0.0402154	+	0.999191i	$0.487196\pi$
$798$	60.9051	−	29.6137i	2.15602	−	1.04832i
$799$		−	2.16008i		−	0.0764182i
$800$	−26.4606	−	9.99176i	−0.935524	−	0.353262i
$801$		−	12.1757i		−	0.430208i
$802$	21.4061	−	3.97779i	0.755875	−	0.140461i
$803$	−24.7378	−	24.7378i	−0.872978	−	0.872978i
$804$	25.5065	+	66.2605i	0.899544	+	2.33683i
$805$	4.85810	−	12.4878i	0.171226	−	0.440136i
$806$	−4.40856	+	6.42096i	−0.155285	+	0.226169i
$807$	−32.9401	+	32.9401i	−1.15955	+	1.15955i
$808$	9.58903	−	5.89478i	0.337341	−	0.207378i
$809$			6.78361i			0.238499i	0.992864	+	0.119249i	$0.0380488\pi$
$809$			6.78361i			0.238499i	−0.992864	+	0.119249i	$0.961951\pi$
$810$	12.5364	+	6.15069i	0.440483	+	0.216113i
$811$	27.2106			0.955493			0.477746	−	0.878498i	$-0.341454\pi$
$811$	27.2106			0.955493			0.477746	+	0.878498i	$0.341454\pi$
$812$	48.8565	+	7.33895i	1.71453	+	0.257547i
$813$	−5.26042	+	5.26042i	−0.184491	+	0.184491i
$814$	−20.9280	+	30.4811i	−0.733527	+	1.06836i
$815$	29.5238	−	4.32768i	1.03417	−	0.151592i
$816$	−20.0906	−	22.2287i	−0.703313	−	0.778162i
$817$	21.3219	+	21.3219i	0.745959	+	0.745959i
$818$	26.4099	−	4.90762i	0.923400	−	0.171591i
$819$	15.9626	−	4.39784i	0.557778	−	0.153673i
$820$	−1.88032	+	6.73140i	−0.0656637	+	0.235071i
$821$		−	18.0379i		−	0.629527i	−0.949170	−	0.314764i	$-0.898075\pi$
$821$		−	18.0379i		−	0.629527i	0.949170	−	0.314764i	$-0.101925\pi$
$822$	−67.5096	+	12.5450i	−2.35467	+	0.437556i
$823$	32.6371	+	32.6371i	1.13766	+	1.13766i	0.988869	+	0.148790i	$0.0475380\pi$
$823$	32.6371	+	32.6371i	1.13766	+	1.13766i	0.148790	+	0.988869i	$0.452462\pi$
$824$	11.5413	−	48.3731i	0.402059	−	1.68516i
$825$	−46.9702	−	25.3137i	−1.63529	−	0.881310i
$826$	−2.76239	+	7.99097i	−0.0961159	+	0.278041i
$827$	1.44029	+	1.44029i	0.0500836	+	0.0500836i	0.731705	−	0.681621i	$-0.238725\pi$
$827$	1.44029	+	1.44029i	0.0500836	+	0.0500836i	−0.681621	+	0.731705i	$0.738725\pi$
$828$	7.56428	−	17.0327i	0.262877	−	0.591928i
$829$			46.8342i			1.62662i	0.581832	+	0.813309i	$0.302336\pi$
$829$			46.8342i			1.62662i	−0.581832	+	0.813309i	$0.697664\pi$
$830$	1.20921	+	3.53864i	0.0419723	+	0.122828i
$831$			12.3546i			0.428576i
$832$	11.5624	−	3.79294i	0.400855	−	0.131496i
$833$	−4.82016	+	19.0585i	−0.167009	+	0.660337i
$834$	−28.1823	+	41.0468i	−0.975872	+	1.42133i
$835$	0.753059	+	5.13743i	0.0260607	+	0.177788i
$836$	50.6747	−	19.5069i	1.75262	−	0.674660i
$837$	−7.60894	−	7.60894i	−0.263003	−	0.263003i
$838$	6.33736	+	34.1039i	0.218920	+	1.17810i
$839$	−34.1026			−1.17735			−0.588675	−	0.808369i	$-0.700350\pi$
$839$	−34.1026			−1.17735			−0.588675	+	0.808369i	$0.700350\pi$
$840$	7.99813	+	43.9092i	0.275962	+	1.51501i
$841$	58.1720			2.00593
$842$	−3.24028	−	17.4372i	−0.111667	−	0.600927i
$843$	−32.1978	−	32.1978i	−1.10895	−	1.10895i
$844$	7.49710	+	19.4759i	0.258061	+	0.670388i
$845$	−14.2673	+	19.1685i	−0.490811	+	0.659415i
$846$	−2.53309	+	3.68939i	−0.0870895	+	0.126844i
$847$	11.5194	+	6.54304i	0.395811	+	0.224821i
$848$	−0.0119787	+	0.237094i	−0.000411350	+	0.00814185i
$849$			39.8834i			1.36880i
$850$	6.06879	−	18.9081i	0.208158	−	0.648542i
$851$		−	14.8005i		−	0.507356i
$852$	51.2764	+	22.7720i	1.75670	+	0.780156i
$853$	−39.7698	−	39.7698i	−1.36169	−	1.36169i	−0.871763	−	0.489928i	$-0.837023\pi$
$853$	−39.7698	−	39.7698i	−1.36169	−	1.36169i	−0.489928	−	0.871763i	$-0.662977\pi$
$854$	−32.7847	−	11.3333i	−1.12187	−	0.387818i
$855$	50.0791	+	37.2745i	1.71267	+	1.27476i
$856$	−45.3722	−	10.8253i	−1.55079	−	0.370000i
$857$	−6.22122	−	6.22122i	−0.212513	−	0.212513i	0.592821	−	0.805334i	$-0.298014\pi$
$857$	−6.22122	−	6.22122i	−0.212513	−	0.212513i	−0.805334	+	0.592821i	$0.798014\pi$
$858$	22.5693	−	4.19394i	0.770503	−	0.143179i
$859$			29.4611i			1.00520i	0.864519	+	0.502600i	$0.167623\pi$
$859$			29.4611i			1.00520i	−0.864519	+	0.502600i	$0.832377\pi$
$860$	−17.3142	+	9.75327i	−0.590409	+	0.332584i
$861$	10.6324	−	2.92932i	0.362352	−	0.0998311i
$862$	−4.58777	+	0.852524i	−0.156260	+	0.0290371i
$863$	37.5520	+	37.5520i	1.27828	+	1.27828i	0.941627	+	0.336657i	$0.109296\pi$
$863$	37.5520	+	37.5520i	1.27828	+	1.27828i	0.336657	+	0.941627i	$0.390704\pi$
$864$	2.23355	+	16.6628i	0.0759868	+	0.566881i
$865$	−4.36478	−	29.7769i	−0.148407	−	1.01244i
$866$	6.73670	−	9.81183i	0.228922	−	0.333420i
$867$	−17.1875	+	17.1875i	−0.583720	+	0.583720i
$868$	−2.84606	+	18.9467i	−0.0966016	+	0.643091i
$869$	−2.15969			−0.0732625
$870$	25.4646	+	74.5196i	0.863329	+	2.52645i
$871$		−	20.2450i		−	0.685976i
$872$	8.68485	−	5.33894i	0.294106	−	0.180799i
$873$	42.2130	−	42.2130i	1.42869	−	1.42869i
$874$	−12.3029	+	17.9189i	−0.416152	+	0.606115i
$875$	−22.5196	+	19.1799i	−0.761301	+	0.648398i
$876$	−43.5318	+	16.7573i	−1.47080	+	0.566175i
$877$	27.6201	+	27.6201i	0.932665	+	0.932665i	0.997872	−	0.0652066i	$-0.0207706\pi$
$877$	27.6201	+	27.6201i	0.932665	+	0.932665i	−0.0652066	+	0.997872i	$0.520771\pi$
$878$	−24.9039	+	4.62778i	−0.840466	+	0.156180i
$879$			1.05326i			0.0355255i
$880$	3.39685	+	35.6236i	0.114508	+	1.20087i
$881$			21.1780i			0.713505i	0.934199	+	0.356753i	$0.116116\pi$
$881$			21.1780i			0.713505i	−0.934199	+	0.356753i	$0.883884\pi$
$882$	30.5823	−	26.8991i	1.02976	−	0.905739i
$883$	−14.0291	+	14.0291i	−0.472116	+	0.472116i	−0.902599	−	0.430483i	$-0.858343\pi$
$883$	−14.0291	+	14.0291i	−0.472116	+	0.472116i	0.430483	+	0.902599i	$0.358343\pi$
$884$	3.06921	+	7.97317i	0.103229	+	0.268167i
$885$	−13.3346	+	1.95463i	−0.448238	+	0.0657041i
$886$	−22.8029	+	33.2118i	−0.766077	+	1.11577i
$887$	−18.9432	−	18.9432i	−0.636052	−	0.636052i	0.313527	−	0.949579i	$-0.398489\pi$
$887$	−18.9432	−	18.9432i	−0.636052	−	0.636052i	−0.949579	+	0.313527i	$0.898489\pi$
$888$	25.8176	+	41.9974i	0.866381	+	1.40934i
$889$	39.8584	−	10.9813i	1.33681	−	0.368302i
$890$	−8.40175	−	4.12214i	−0.281627	−	0.138174i
$891$		−	17.6671i		−	0.591871i
$892$	9.71329	−	21.8717i	0.325225	−	0.732319i
$893$	3.69071	−	3.69071i	0.123505	−	0.123505i
$894$	11.5043	+	7.89871i	0.384761	+	0.264173i
$895$	−4.23676	−	3.15348i	−0.141619	−	0.105409i
$896$	21.4988	−	20.8279i	0.718225	−	0.695811i
$897$	−6.49763	+	6.49763i	−0.216950	+	0.216950i
$898$	−10.3846	−	55.8838i	−0.346539	−	1.86487i
$899$			33.8055i			1.12748i
$900$	−32.5386	+	25.1780i	−1.08462	+	0.839266i
$901$	−0.166674			−0.00555272
$902$	8.69375	−	1.61552i	0.289470	−	0.0537909i
$903$	27.2664	+	15.4873i	0.907368	+	0.515386i
$904$	19.4966	+	4.65167i	0.648449	+	0.154712i
$905$	−25.5002	−	18.9802i	−0.847656	−	0.630922i
$906$	−16.4041	−	11.2629i	−0.544990	−	0.374184i
$907$	−0.0552780	−	0.0552780i	−0.00183548	−	0.00183548i	0.706188	−	0.708024i	$-0.250413\pi$
$907$	−0.0552780	−	0.0552780i	−0.00183548	−	0.00183548i	−0.708024	+	0.706188i	$0.750413\pi$
$908$	−10.4838	+	23.6067i	−0.347917	+	0.783414i
$909$		−	16.3730i		−	0.543059i
$910$	2.36950	−	12.5037i	0.0785483	−	0.414495i
$911$	−44.7235			−1.48175			−0.740877	−	0.671641i	$-0.765590\pi$
$911$	−44.7235			−1.48175			−0.740877	+	0.671641i	$0.765590\pi$
$912$	3.65315	−	72.3068i	0.120968	−	2.39432i
$913$	3.34550	−	3.34550i	0.110720	−	0.110720i
$914$	−6.91701	+	10.0745i	−0.228794	+	0.333233i
$915$	−8.01928	−	54.7082i	−0.265109	−	1.80860i
$916$	−7.21511	−	18.7433i	−0.238394	−	0.619297i
$917$	9.57826	+	5.44047i	0.316302	+	0.179660i
$918$	−11.6048	+	2.15646i	−0.383016	+	0.0711739i
$919$		−	0.471136i		−	0.0155413i	−0.999970	−	0.00777067i	$-0.997526\pi$
$919$		−	0.471136i		−	0.0155413i	0.999970	−	0.00777067i	$-0.00247351\pi$
$920$	−9.19236	−	10.9862i	−0.303063	−	0.362203i
$921$	−78.1035			−2.57360
$922$	−23.0157	+	4.27690i	−0.757982	+	0.140852i
$923$	−11.3123	−	11.3123i	−0.372347	−	0.372347i
$924$	45.4172	−	33.5545i	1.49411	−	1.10386i
$925$	−15.5009	+	28.7623i	−0.509667	+	0.945699i
$926$	27.5469	+	18.9134i	0.905247	+	0.621533i
$927$	−51.1511	−	51.1511i	−1.68002	−	1.68002i
$928$	32.0536	−	41.9770i	1.05221	−	1.37796i
$929$	−52.0237			−1.70684			−0.853421	−	0.521222i	$-0.825476\pi$
$929$	−52.0237			−1.70684			−0.853421	+	0.521222i	$0.825476\pi$
$930$	−28.8989	+	9.87521i	−0.947632	+	0.323821i
$931$	−40.7989	+	24.3275i	−1.33713	+	0.797303i
$932$	11.9012	+	5.28536i	0.389837	+	0.173128i
$933$	37.4668	−	37.4668i	1.22661	−	1.22661i
$934$	13.4232	−	19.5505i	0.439220	−	0.639713i
$935$	−24.8588	+	3.64388i	−0.812971	+	0.119168i
$936$	4.10784	−	17.2173i	0.134269	−	0.562764i
$937$	−9.57759	−	9.57759i	−0.312886	−	0.312886i	0.533141	−	0.846027i	$-0.321012\pi$
$937$	−9.57759	−	9.57759i	−0.312886	−	0.312886i	−0.846027	+	0.533141i	$0.821012\pi$
$938$	−21.7764	−	44.7865i	−0.711025	−	1.46233i
$939$	−21.2994			−0.695080
$940$	1.68824	+	2.99699i	0.0550643	+	0.0977511i
$941$	−46.0496			−1.50117			−0.750587	−	0.660772i	$-0.770229\pi$
$941$	−46.0496			−1.50117			−0.750587	+	0.660772i	$0.770229\pi$
$942$	39.5399	−	7.34752i	1.28828	−	0.239395i
$943$	−2.50290	+	2.50290i	−0.0815058	+	0.0815058i
$944$	6.06071	+	6.70571i	0.197259	+	0.218252i
$945$	16.3860	+	6.37461i	0.533036	+	0.207366i
$946$	20.7272	+	14.2310i	0.673898	+	0.462691i
$947$	−40.3064	−	40.3064i	−1.30978	−	1.30978i	−0.921570	−	0.388212i	$-0.873093\pi$
$947$	−40.3064	−	40.3064i	−1.30978	−	1.30978i	−0.388212	−	0.921570i	$-0.626907\pi$
$948$	−1.16875	+	2.63172i	−0.0379593	+	0.0854741i
$949$	13.3006			0.431754
$950$	42.6754	−	21.9372i	1.38457	−	0.711737i
$951$			50.9937i			1.65358i
$952$	15.3661	+	14.3371i	0.498018	+	0.464667i
$953$	6.52676	+	6.52676i	0.211422	+	0.211422i	0.804871	−	0.593449i	$-0.202234\pi$
$953$	6.52676	+	6.52676i	0.211422	+	0.211422i	−0.593449	+	0.804871i	$0.702234\pi$
$954$	0.284677	+	0.195456i	0.00921676	+	0.00632813i
$955$	−30.3021	−	22.5543i	−0.980555	−	0.729840i
$956$	−9.27438	−	24.0929i	−0.299955	−	0.779219i
$957$	70.4524	−	70.4524i	2.27740	−	2.27740i
$958$	−29.2224	+	5.43026i	−0.944133	+	0.175444i
$959$	46.4323	−	12.7925i	1.49938	−	0.413092i
$960$	45.2478	+	15.1390i	1.46037	+	0.488610i
$961$	17.8902			0.577102
$962$	−2.56817	−	13.8204i	−0.0828011	−	0.445586i
$963$	−47.9778	+	47.9778i	−1.54606	+	1.54606i
$964$	−2.80670	−	7.29121i	−0.0903977	−	0.234834i
$965$	3.00681	+	20.5127i	0.0967927	+	0.660327i
$966$	−7.38508	+	21.3634i	−0.237611	+	0.687355i
$967$	−10.9344	+	10.9344i	−0.351627	+	0.351627i	−0.860715	−	0.509088i	$-0.829983\pi$
$967$	−10.9344	+	10.9344i	−0.351627	+	0.351627i	0.509088	+	0.860715i	$0.329983\pi$
$968$	12.0652	−	7.41698i	0.387790	−	0.238391i
$969$	50.8307			1.63292
$970$	−14.8373	−	43.4201i	−0.476398	−	1.39414i
$971$	10.1154			0.324618			0.162309	−	0.986740i	$-0.448106\pi$
$971$	10.1154			0.324618			0.162309	+	0.986740i	$0.448106\pi$
$972$	−37.8253	−	16.7983i	−1.21325	−	0.538807i
$973$	17.2483	−	30.3666i	0.552955	−	0.973509i
$974$	−15.0665	+	21.9439i	−0.482760	+	0.703128i
$975$	19.4321	−	5.82193i	0.622326	−	0.186451i
$976$	−27.5116	+	24.8654i	−0.880626	+	0.795922i
$977$	0.176316	−	0.176316i	0.00564083	−	0.00564083i	−0.704281	−	0.709922i	$-0.748730\pi$
$977$	0.176316	−	0.176316i	0.00564083	−	0.00564083i	0.709922	+	0.704281i	$0.248730\pi$
$978$	−49.4892	+	9.19633i	−1.58249	+	0.294066i
$979$			11.8403i			0.378419i
$980$	−8.20770	−	30.2098i	−0.262185	−	0.965018i
$981$		−	14.8292i		−	0.473459i
$982$	−3.12067	−	16.7936i	−0.0995847	−	0.535905i
$983$	5.94414	−	5.94414i	0.189589	−	0.189589i	−0.605930	−	0.795518i	$-0.707199\pi$
$983$	5.94414	−	5.94414i	0.189589	−	0.189589i	0.795518	+	0.605930i	$0.207199\pi$
$984$	2.73616	−	11.4681i	0.0872256	−	0.365591i
$985$	3.57488	+	24.3881i	0.113905	+	0.777070i
$986$	30.5697	+	20.9888i	0.973538	+	0.668421i
$987$	2.68077	−	4.71966i	0.0853300	−	0.150228i
$988$	−8.37888	+	18.8670i	−0.266568	+	0.600239i
$989$	−10.0644			−0.320028
$990$	46.7317	+	22.9279i	1.48523	+	0.728696i
$991$	34.5577			1.09776			0.548880	−	0.835901i	$-0.315054\pi$
$991$	34.5577			1.09776			0.548880	+	0.835901i	$0.315054\pi$
$992$	16.2788	+	12.4305i	0.516851	+	0.394668i
$993$	−51.6669	+	51.6669i	−1.63960	+	1.63960i
$994$	−37.1932	−	12.8573i	−1.17970	−	0.407808i
$995$	41.4840	+	30.8771i	1.31513	+	0.978871i
$996$	−2.26623	−	5.88717i	−0.0718081	−	0.186542i
$997$	35.9018	−	35.9018i	1.13702	−	1.13702i	0.148042	−	0.988981i	$-0.452703\pi$
$997$	35.9018	−	35.9018i	1.13702	−	1.13702i	0.988981	−	0.148042i	$-0.0472969\pi$
$998$	29.6952	−	5.51812i	0.939986	−	0.174673i
$999$	19.4207			0.614443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.c.13.3	✓	72
4.3	odd	2		1120.2.w.c.433.31		72
5.2	odd	4	inner	280.2.s.c.237.17	yes	72
7.6	odd	2	inner	280.2.s.c.13.4	yes	72
8.3	odd	2		1120.2.w.c.433.6		72
8.5	even	2	inner	280.2.s.c.13.18	yes	72
20.7	even	4		1120.2.w.c.657.32		72
28.27	even	2		1120.2.w.c.433.5		72
35.27	even	4	inner	280.2.s.c.237.18	yes	72
40.27	even	4		1120.2.w.c.657.5		72
40.37	odd	4	inner	280.2.s.c.237.4	yes	72
56.13	odd	2	inner	280.2.s.c.13.17	yes	72
56.27	even	2		1120.2.w.c.433.32		72
140.27	odd	4		1120.2.w.c.657.6		72
280.27	odd	4		1120.2.w.c.657.31		72
280.237	even	4	inner	280.2.s.c.237.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.c.13.3	✓	72	1.1	even	1	trivial
280.2.s.c.13.4	yes	72	7.6	odd	2	inner
280.2.s.c.13.17	yes	72	56.13	odd	2	inner
280.2.s.c.13.18	yes	72	8.5	even	2	inner
280.2.s.c.237.3	yes	72	280.237	even	4	inner
280.2.s.c.237.4	yes	72	40.37	odd	4	inner
280.2.s.c.237.17	yes	72	5.2	odd	4	inner
280.2.s.c.237.18	yes	72	35.27	even	4	inner
1120.2.w.c.433.5		72	28.27	even	2
1120.2.w.c.433.6		72	8.3	odd	2
1120.2.w.c.433.31		72	4.3	odd	2
1120.2.w.c.433.32		72	56.27	even	2
1120.2.w.c.657.5		72	40.27	even	4
1120.2.w.c.657.6		72	140.27	odd	4
1120.2.w.c.657.31		72	280.27	odd	4
1120.2.w.c.657.32		72	20.7	even	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39041 + 0.258373i) q^{2} +(-1.88603 - 1.88603i) q^{3} +(1.86649 - 0.718491i) q^{4} +(-1.79374 - 1.33510i) q^{5} +(3.10966 + 2.13506i) q^{6} +(-2.30054 - 1.30671i) q^{7} +(-2.40954 + 1.48125i) q^{8} +4.11423i q^{9} +O(q^{10})\)	\(q+(-1.39041 + 0.258373i) q^{2} +(-1.88603 - 1.88603i) q^{3} +(1.86649 - 0.718491i) q^{4} +(-1.79374 - 1.33510i) q^{5} +(3.10966 + 2.13506i) q^{6} +(-2.30054 - 1.30671i) q^{7} +(-2.40954 + 1.48125i) q^{8} +4.11423i q^{9} +(2.83899 + 1.39289i) q^{10} -4.00091i q^{11} +(-4.87535 - 2.16516i) q^{12} +(1.07557 + 1.07557i) q^{13} +(3.53632 + 1.22247i) q^{14} +(0.865000 + 5.90110i) q^{15} +(2.96754 - 2.68211i) q^{16} +(1.98582 + 1.98582i) q^{17} +(-1.06301 - 5.72048i) q^{18} +6.78591i q^{19} +(-4.30725 - 1.20317i) q^{20} +(1.87440 + 6.80340i) q^{21} +(1.03373 + 5.56290i) q^{22} +(-1.60154 - 1.60154i) q^{23} +(7.33816 + 1.75080i) q^{24} +(1.43500 + 4.78965i) q^{25} +(-1.77338 - 1.21758i) q^{26} +(2.10148 - 2.10148i) q^{27} +(-5.23279 - 0.786042i) q^{28} -9.33660 q^{29} +(-2.72739 - 7.98146i) q^{30} -3.62075i q^{31} +(-3.43312 + 4.49596i) q^{32} +(-7.54584 + 7.54584i) q^{33} +(-3.27418 - 2.24802i) q^{34} +(2.38198 + 5.41537i) q^{35} +(2.95604 + 7.67916i) q^{36} +(4.62071 + 4.62071i) q^{37} +(-1.75330 - 9.43521i) q^{38} -4.05711i q^{39} +(6.29971 + 0.560020i) q^{40} -1.56281i q^{41} +(-4.36400 - 8.97523i) q^{42} +(3.14208 - 3.14208i) q^{43} +(-2.87461 - 7.46764i) q^{44} +(5.49293 - 7.37986i) q^{45} +(2.64060 + 1.81301i) q^{46} +(-0.543878 - 0.543878i) q^{47} +(-10.6554 - 0.538343i) q^{48} +(3.58501 + 6.01230i) q^{49} +(-3.23275 - 6.28882i) q^{50} -7.49062i q^{51} +(2.78031 + 1.23475i) q^{52} +(-0.0419662 + 0.0419662i) q^{53} +(-2.37896 + 3.46489i) q^{54} +(-5.34162 + 7.17658i) q^{55} +(7.47883 - 0.259094i) q^{56} +(12.7985 - 12.7985i) q^{57} +(12.9817 - 2.41233i) q^{58} +2.25968i q^{59} +(5.85439 + 10.3928i) q^{60} -9.27084 q^{61} +(0.935506 + 5.03433i) q^{62} +(5.37612 - 9.46498i) q^{63} +(3.61181 - 7.13827i) q^{64} +(-0.493292 - 3.36528i) q^{65} +(8.54217 - 12.4415i) q^{66} +(-9.41132 - 9.41132i) q^{67} +(5.13329 + 2.27971i) q^{68} +6.04112i q^{69} +(-4.71112 - 6.91414i) q^{70} -10.5175 q^{71} +(-6.09420 - 9.91343i) q^{72} +(6.18305 - 6.18305i) q^{73} +(-7.61856 - 5.23082i) q^{74} +(6.32699 - 11.7399i) q^{75} +(4.87562 + 12.6658i) q^{76} +(-5.22803 + 9.20426i) q^{77} +(1.04825 + 5.64105i) q^{78} -0.539800i q^{79} +(-8.90388 + 0.849020i) q^{80} +4.41578 q^{81} +(0.403788 + 2.17295i) q^{82} +(0.836186 + 0.836186i) q^{83} +(8.38672 + 11.3517i) q^{84} +(-0.910764 - 6.21330i) q^{85} +(-3.55696 + 5.18062i) q^{86} +(17.6091 + 17.6091i) q^{87} +(5.92633 + 9.64036i) q^{88} -2.95941 q^{89} +(-5.73067 + 11.6803i) q^{90} +(-1.06893 - 3.87984i) q^{91} +(-4.13995 - 1.83856i) q^{92} +(-6.82885 + 6.82885i) q^{93} +(0.896737 + 0.615690i) q^{94} +(9.05990 - 12.1722i) q^{95} +(14.9545 - 2.00456i) q^{96} +(-10.2602 - 10.2602i) q^{97} +(-6.53805 - 7.43330i) q^{98} +16.4607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

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