LMFDB - Embedded newform 880.2.bk.b.243.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(243,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.243"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bk (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [236] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$236$
Relative dimension:	$118$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.9
Character	$\chi$	$=$	880.243
Dual form			880.2.bk.b.507.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38403 - 0.290618i) q^{2} -1.48289 q^{3} +(1.83108 + 0.804450i) q^{4} +(2.23341 - 0.109047i) q^{5} +(2.05237 + 0.430957i) q^{6} +(-2.19311 + 2.19311i) q^{7} +(-2.30049 - 1.64553i) q^{8} -0.801024 q^{9} +(-3.12280 - 0.498145i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-2.71530 - 1.19291i) q^{12} -5.51002i q^{13} +(3.67269 - 2.39798i) q^{14} +(-3.31191 + 0.161705i) q^{15} +(2.70572 + 2.94603i) q^{16} +(2.04621 - 2.04621i) q^{17} +(1.10864 + 0.232792i) q^{18} +(4.09158 + 4.09158i) q^{19} +(4.17727 + 1.59699i) q^{20} +(3.25215 - 3.25215i) q^{21} +(-0.773159 - 1.18416i) q^{22} +(-4.54961 - 4.54961i) q^{23} +(3.41138 + 2.44015i) q^{24} +(4.97622 - 0.487092i) q^{25} +(-1.60131 + 7.62604i) q^{26} +5.63652 q^{27} +(-5.78002 + 2.25152i) q^{28} +(-1.59715 + 1.59715i) q^{29} +(4.63078 + 0.738697i) q^{30} -1.24961i q^{31} +(-2.88863 - 4.86372i) q^{32} +(-1.04856 - 1.04856i) q^{33} +(-3.42668 + 2.23735i) q^{34} +(-4.65896 + 5.13726i) q^{35} +(-1.46674 - 0.644384i) q^{36} +4.62475i q^{37} +(-4.47378 - 6.85196i) q^{38} +8.17078i q^{39} +(-5.31736 - 3.42428i) q^{40} -1.17037i q^{41} +(-5.44622 + 3.55594i) q^{42} +3.13884i q^{43} +(0.725938 + 1.86360i) q^{44} +(-1.78901 + 0.0873491i) q^{45} +(4.97460 + 7.61900i) q^{46} +(7.89511 + 7.89511i) q^{47} +(-4.01230 - 4.36865i) q^{48} -2.61948i q^{49} +(-7.02880 - 0.772031i) q^{50} +(-3.03431 + 3.03431i) q^{51} +(4.43254 - 10.0893i) q^{52} +12.9036 q^{53} +(-7.80111 - 1.63808i) q^{54} +(1.65637 + 1.50215i) q^{55} +(8.65405 - 1.43639i) q^{56} +(-6.06738 - 6.06738i) q^{57} +(2.67466 - 1.74634i) q^{58} +(7.33270 - 7.33270i) q^{59} +(-6.19446 - 2.36817i) q^{60} +(-4.32329 - 4.32329i) q^{61} +(-0.363160 + 1.72950i) q^{62} +(1.75674 - 1.75674i) q^{63} +(2.58447 + 7.57103i) q^{64} +(-0.600850 - 12.3061i) q^{65} +(1.14651 + 1.75598i) q^{66} +3.58742i q^{67} +(5.39284 - 2.10070i) q^{68} +(6.74659 + 6.74659i) q^{69} +(7.94113 - 5.75615i) q^{70} +6.64101 q^{71} +(1.84274 + 1.31811i) q^{72} +(0.355443 - 0.355443i) q^{73} +(1.34404 - 6.40080i) q^{74} +(-7.37920 + 0.722305i) q^{75} +(4.20054 + 10.7835i) q^{76} -3.10153 q^{77} +(2.37458 - 11.3086i) q^{78} +15.6652 q^{79} +(6.36423 + 6.28463i) q^{80} -5.95529 q^{81} +(-0.340132 + 1.61983i) q^{82} -5.14227 q^{83} +(8.57115 - 3.33876i) q^{84} +(4.34688 - 4.79315i) q^{85} +(0.912206 - 4.34426i) q^{86} +(2.36840 - 2.36840i) q^{87} +(-0.463124 - 2.79025i) q^{88} +10.2853 q^{89} +(2.50144 + 0.399027i) q^{90} +(12.0841 + 12.0841i) q^{91} +(-4.67077 - 11.9906i) q^{92} +1.85304i q^{93} +(-8.63261 - 13.2215i) q^{94} +(9.58433 + 8.69199i) q^{95} +(4.28353 + 7.21239i) q^{96} +(7.25059 - 7.25059i) q^{97} +(-0.761269 + 3.62544i) q^{98} +(-0.566410 - 0.566410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) $ 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.38403	−	0.290618i	−0.978657	−	0.205498i
$2$	−1.38403	−	0.290618i	−0.978657	−	0.205498i
$3$	−1.48289			−0.856149			−0.428075	−	0.903743i	$-0.640808\pi$
$3$	−1.48289			−0.856149			−0.428075	+	0.903743i	$0.640808\pi$
$4$	1.83108	+	0.804450i	0.915541	+	0.402225i
$5$	2.23341	−	0.109047i	0.998810	−	0.0487672i
$5$	2.23341	−	0.109047i	0.998810	−	0.0487672i
$6$	2.05237	+	0.430957i	0.837877	+	0.175937i
$7$	−2.19311	+	2.19311i	−0.828918	+	0.828918i	−0.987367	−	0.158449i	$-0.949351\pi$
$7$	−2.19311	+	2.19311i	−0.828918	+	0.828918i	0.158449	+	0.987367i	$0.449351\pi$
$8$	−2.30049	−	1.64553i	−0.813344	−	0.581783i
$9$	−0.801024			−0.267008
$10$	−3.12280	−	0.498145i	−0.987515	−	0.157527i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	−2.71530	−	1.19291i	−0.783840	−	0.344365i
$13$		−	5.51002i		−	1.52821i	−0.645095	−	0.764103i	$-0.723182\pi$
$13$		−	5.51002i		−	1.52821i	0.645095	−	0.764103i	$-0.276818\pi$
$14$	3.67269	−	2.39798i	0.981568	−	0.640886i
$15$	−3.31191	+	0.161705i	−0.855131	+	0.0417520i
$16$	2.70572	+	2.94603i	0.676430	+	0.736507i
$17$	2.04621	−	2.04621i	0.496278	−	0.496278i	−0.413999	−	0.910277i	$-0.635868\pi$
$17$	2.04621	−	2.04621i	0.496278	−	0.496278i	0.910277	+	0.413999i	$0.135868\pi$
$18$	1.10864	+	0.232792i	0.261309	+	0.0548697i
$19$	4.09158	+	4.09158i	0.938672	+	0.938672i	0.998225	−	0.0595530i	$-0.0189675\pi$
$19$	4.09158	+	4.09158i	0.938672	+	0.938672i	−0.0595530	+	0.998225i	$0.518968\pi$
$20$	4.17727	+	1.59699i	0.934067	+	0.357098i
$21$	3.25215	−	3.25215i	0.709678	−	0.709678i
$22$	−0.773159	−	1.18416i	−0.164838	−	0.252463i
$23$	−4.54961	−	4.54961i	−0.948659	−	0.948659i	0.0500863	−	0.998745i	$-0.484050\pi$
$23$	−4.54961	−	4.54961i	−0.948659	−	0.948659i	−0.998745	+	0.0500863i	$0.984050\pi$
$24$	3.41138	+	2.44015i	0.696344	+	0.498093i
$25$	4.97622	−	0.487092i	0.995244	−	0.0974183i
$26$	−1.60131	+	7.62604i	−0.314044	+	1.49559i
$27$	5.63652			1.08475
$28$	−5.78002	+	2.25152i	−1.09232	+	0.425497i
$29$	−1.59715	+	1.59715i	−0.296583	+	0.296583i	−0.839674	−	0.543091i	$-0.817254\pi$
$29$	−1.59715	+	1.59715i	−0.296583	+	0.296583i	0.543091	+	0.839674i	$0.317254\pi$
$30$	4.63078	+	0.738697i	0.845460	+	0.134867i
$31$		−	1.24961i		−	0.224437i	−0.993684	−	0.112218i	$-0.964204\pi$
$31$		−	1.24961i		−	0.224437i	0.993684	−	0.112218i	$-0.0357957\pi$
$32$	−2.88863	−	4.86372i	−0.510643	−	0.859793i
$33$	−1.04856	−	1.04856i	−0.182532	−	0.182532i
$34$	−3.42668	+	2.23735i	−0.587671	+	0.383702i
$35$	−4.65896	+	5.13726i	−0.787508	+	0.868356i
$36$	−1.46674	−	0.644384i	−0.244457	−	0.107397i
$37$			4.62475i			0.760305i	0.924924	+	0.380152i	$0.124128\pi$
$37$			4.62475i			0.760305i	−0.924924	+	0.380152i	$0.875872\pi$
$38$	−4.47378	−	6.85196i	−0.725743	−	1.11153i
$39$			8.17078i			1.30837i
$40$	−5.31736	−	3.42428i	−0.840749	−	0.541426i
$41$		−	1.17037i		−	0.182782i	−0.995815	−	0.0913908i	$-0.970869\pi$
$41$		−	1.17037i		−	0.182782i	0.995815	−	0.0913908i	$-0.0291312\pi$
$42$	−5.44622	+	3.55594i	−0.840369	+	0.548694i
$43$			3.13884i			0.478669i	0.970937	+	0.239335i	$0.0769293\pi$
$43$			3.13884i			0.478669i	−0.970937	+	0.239335i	$0.923071\pi$
$44$	0.725938	+	1.86360i	0.109439	+	0.280949i
$45$	−1.78901	+	0.0873491i	−0.266690	+	0.0130212i
$46$	4.97460	+	7.61900i	0.733464	+	1.12336i
$47$	7.89511	+	7.89511i	1.15162	+	1.15162i	0.986228	+	0.165392i	$0.0528888\pi$
$47$	7.89511	+	7.89511i	1.15162	+	1.15162i	0.165392	+	0.986228i	$0.447111\pi$
$48$	−4.01230	−	4.36865i	−0.579125	−	0.630560i
$49$		−	2.61948i		−	0.374211i
$50$	−7.02880	−	0.772031i	−0.994022	−	0.109182i
$51$	−3.03431	+	3.03431i	−0.424888	+	0.424888i
$52$	4.43254	−	10.0893i	0.614682	−	1.39913i
$53$	12.9036			1.77245			0.886224	−	0.463256i	$-0.153319\pi$
$53$	12.9036			1.77245			0.886224	+	0.463256i	$0.153319\pi$
$54$	−7.80111	−	1.63808i	−1.06160	−	0.222914i
$55$	1.65637	+	1.50215i	0.223344	+	0.202550i
$56$	8.65405	−	1.43639i	1.15645	−	0.191946i
$57$	−6.06738	−	6.06738i	−0.803644	−	0.803644i
$58$	2.67466	−	1.74634i	0.351200	−	0.229305i
$59$	7.33270	−	7.33270i	0.954636	−	0.954636i	−0.0443787	−	0.999015i	$-0.514131\pi$
$59$	7.33270	−	7.33270i	0.954636	−	0.954636i	0.999015	+	0.0443787i	$0.0141308\pi$
$60$	−6.19446	−	2.36817i	−0.799701	−	0.305729i
$61$	−4.32329	−	4.32329i	−0.553541	−	0.553541i	0.373920	−	0.927461i	$-0.378013\pi$
$61$	−4.32329	−	4.32329i	−0.553541	−	0.553541i	−0.927461	+	0.373920i	$0.878013\pi$
$62$	−0.363160	+	1.72950i	−0.0461214	+	0.219647i
$63$	1.75674	−	1.75674i	0.221328	−	0.221328i
$64$	2.58447	+	7.57103i	0.323058	+	0.946379i
$65$	−0.600850	−	12.3061i	−0.0745263	−	1.52639i
$66$	1.14651	+	1.75598i	0.141126	+	0.216146i
$67$			3.58742i			0.438273i	0.975694	+	0.219136i	$0.0703239\pi$
$67$			3.58742i			0.438273i	−0.975694	+	0.219136i	$0.929676\pi$
$68$	5.39284	−	2.10070i	0.653978	−	0.254748i
$69$	6.74659	+	6.74659i	0.812194	+	0.812194i
$70$	7.94113	−	5.75615i	0.949146	−	0.687992i
$71$	6.64101			0.788143			0.394072	−	0.919080i	$-0.371066\pi$
$71$	6.64101			0.788143			0.394072	+	0.919080i	$0.371066\pi$
$72$	1.84274	+	1.31811i	0.217170	+	0.155341i
$73$	0.355443	−	0.355443i	0.0416015	−	0.0416015i	−0.686000	−	0.727602i	$-0.740635\pi$
$73$	0.355443	−	0.355443i	0.0416015	−	0.0416015i	0.727602	+	0.686000i	$0.240635\pi$
$74$	1.34404	−	6.40080i	0.156241	−	0.744078i
$75$	−7.37920	+	0.722305i	−0.852077	+	0.0834046i
$76$	4.20054	+	10.7835i	0.481835	+	1.23695i
$77$	−3.10153			−0.353452
$78$	2.37458	−	11.3086i	0.268868	−	1.28045i
$79$	15.6652			1.76247			0.881234	−	0.472681i	$-0.156714\pi$
$79$	15.6652			1.76247			0.881234	+	0.472681i	$0.156714\pi$
$80$	6.36423	+	6.28463i	0.711543	+	0.702643i
$81$	−5.95529			−0.661699
$82$	−0.340132	+	1.61983i	−0.0375613	+	0.178881i
$83$	−5.14227			−0.564438			−0.282219	−	0.959350i	$-0.591070\pi$
$83$	−5.14227			−0.564438			−0.282219	+	0.959350i	$0.591070\pi$
$84$	8.57115	−	3.33876i	0.935189	−	0.364289i
$85$	4.34688	−	4.79315i	0.471486	−	0.519890i
$86$	0.912206	−	4.34426i	0.0983657	−	0.468453i
$87$	2.36840	−	2.36840i	0.253919	−	0.253919i
$88$	−0.463124	−	2.79025i	−0.0493692	−	0.297442i
$89$	10.2853			1.09024			0.545120	−	0.838358i	$-0.316484\pi$
$89$	10.2853			1.09024			0.545120	+	0.838358i	$0.316484\pi$
$90$	2.50144	+	0.399027i	0.263674	+	0.0420611i
$91$	12.0841	+	12.0841i	1.26676	+	1.26676i
$92$	−4.67077	−	11.9906i	−0.486962	−	1.25011i
$93$			1.85304i			0.192152i
$94$	−8.63261	−	13.2215i	−0.890385	−	1.36370i
$95$	9.58433	+	8.69199i	0.983332	+	0.891779i
$96$	4.28353	+	7.21239i	0.437186	+	0.736111i
$97$	7.25059	−	7.25059i	0.736186	−	0.736186i	−0.235652	−	0.971838i	$-0.575722\pi$
$97$	7.25059	−	7.25059i	0.736186	−	0.736186i	0.971838	+	0.235652i	$0.0757224\pi$
$98$	−0.761269	+	3.62544i	−0.0768998	+	0.366225i
$99$	−0.566410	−	0.566410i	−0.0569263	−	0.0569263i
$100$	9.50370	+	3.11121i	0.950370	+	0.311121i
$101$	10.7445	−	10.7445i	1.06911	−	1.06911i	0.0716874	−	0.997427i	$-0.477162\pi$
$101$	10.7445	−	10.7445i	1.06911	−	1.06911i	0.997427	−	0.0716874i	$-0.0228384\pi$
$102$	5.08140	−	3.31775i	0.503134	−	0.328506i
$103$	−0.329505	−	0.329505i	−0.0324671	−	0.0324671i	0.690687	−	0.723154i	$-0.257308\pi$
$103$	−0.329505	−	0.329505i	−0.0324671	−	0.0324671i	−0.723154	+	0.690687i	$0.757308\pi$
$104$	−9.06691	+	12.6757i	−0.889083	+	1.24296i
$105$	6.90875	−	7.61802i	0.674225	−	0.743443i
$106$	−17.8590	−	3.75003i	−1.73462	−	0.364235i
$107$	−14.1502			−1.36796			−0.683978	−	0.729503i	$-0.739751\pi$
$107$	−14.1502			−1.36796			−0.683978	+	0.729503i	$0.739751\pi$
$108$	10.3209	+	4.53430i	0.993131	+	0.436313i
$109$	−5.86928	+	5.86928i	−0.562175	+	0.562175i	−0.929925	−	0.367750i	$-0.880128\pi$
$109$	−5.86928	+	5.86928i	−0.562175	+	0.562175i	0.367750	+	0.929925i	$0.380128\pi$
$110$	−1.85591	−	2.56039i	−0.176954	−	0.244124i
$111$		−	6.85802i		−	0.650935i
$112$	−12.3949	−	0.527018i	−1.17121	−	0.0497985i
$113$	14.6843	+	14.6843i	1.38138	+	1.38138i	0.842167	+	0.539217i	$0.181280\pi$
$113$	14.6843	+	14.6843i	1.38138	+	1.38138i	0.539217	+	0.842167i	$0.318720\pi$
$114$	6.63414	+	10.1607i	0.621344	+	0.951639i
$115$	−10.6572	−	9.66501i	−0.993793	−	0.901266i
$116$	−4.20933	+	1.63968i	−0.390826	+	0.152241i
$117$			4.41366i			0.408043i
$118$	−12.2797	+	8.01766i	−1.13044	+	0.738086i
$119$			8.97512i			0.822748i
$120$	7.88508	+	5.07784i	0.719806	+	0.463541i
$121$			1.00000i			0.0909091i
$122$	4.72714	+	7.23999i	0.427975	+	0.655478i
$123$			1.73554i			0.156488i
$124$	1.00525	−	2.28814i	0.0902741	−	0.205481i
$125$	11.0608	−	1.63051i	0.989309	−	0.145838i
$126$	−2.94192	+	1.92084i	−0.262087	+	0.171122i
$127$	−9.50335	−	9.50335i	−0.843286	−	0.843286i	0.145999	−	0.989285i	$-0.453360\pi$
$127$	−9.50335	−	9.50335i	−0.843286	−	0.843286i	−0.989285	+	0.145999i	$0.953360\pi$
$128$	−1.37670	−	11.2296i	−0.121684	−	0.992569i
$129$		−	4.65458i		−	0.409812i
$130$	−2.74479	+	17.2067i	−0.240734	+	1.50913i
$131$	15.8232	−	15.8232i	1.38248	−	1.38248i	0.542276	−	0.840200i	$-0.317563\pi$
$131$	15.8232	−	15.8232i	1.38248	−	1.38248i	0.840200	−	0.542276i	$-0.182437\pi$
$132$	−1.07649	−	2.76353i	−0.0936964	−	0.240534i
$133$	−17.9466			−1.55617
$134$	1.04257	−	4.96509i	0.0900643	−	0.428919i
$135$	12.5886	−	0.614644i	1.08346	−	0.0529001i
$136$	−8.07436	+	1.34018i	−0.692371	+	0.114919i
$137$	5.84274	+	5.84274i	0.499179	+	0.499179i	0.911182	−	0.412004i	$-0.135171\pi$
$137$	5.84274	+	5.84274i	0.499179	+	0.499179i	−0.412004	+	0.911182i	$0.635171\pi$
$138$	−7.37680	−	11.2982i	−0.627955	−	0.961764i
$139$	−10.3005	+	10.3005i	−0.873678	+	0.873678i	−0.992871	−	0.119193i	$-0.961969\pi$
$139$	−10.3005	+	10.3005i	−0.873678	+	0.873678i	0.119193	+	0.992871i	$0.461969\pi$
$140$	−12.6636	+	5.65885i	−1.07027	+	0.478260i
$141$	−11.7076	−	11.7076i	−0.985959	−	0.985959i
$142$	−9.19136	−	1.93000i	−0.771322	−	0.161962i
$143$	3.89617	−	3.89617i	0.325815	−	0.325815i
$144$	−2.16735	−	2.35984i	−0.180612	−	0.196653i
$145$	−3.39291	+	3.74124i	−0.281766	+	0.310693i
$146$	−0.595243	+	0.388646i	−0.0492626	+	0.0321646i
$147$			3.88441i			0.320381i
$148$	−3.72038	+	8.46830i	−0.305814	+	0.696090i
$149$	−6.46667	−	6.46667i	−0.529770	−	0.529770i	0.390733	−	0.920504i	$-0.372221\pi$
$149$	−6.46667	−	6.46667i	−0.529770	−	0.529770i	−0.920504	+	0.390733i	$0.872221\pi$
$150$	10.4230	+	1.14484i	0.851031	+	0.0934758i
$151$	−3.27306			−0.266358			−0.133179	−	0.991092i	$-0.542519\pi$
$151$	−3.27306			−0.266358			−0.133179	+	0.991092i	$0.542519\pi$
$152$	−2.67980	−	16.1454i	−0.217361	−	1.30957i
$153$	−1.63906	+	1.63906i	−0.132510	+	0.132510i
$154$	4.29261	+	0.901362i	0.345908	+	0.0726338i
$155$	−0.136266	−	2.79089i	−0.0109452	−	0.224170i
$156$	−6.57298	+	14.9614i	−0.526260	+	1.19787i
$157$	−6.79801			−0.542540			−0.271270	−	0.962503i	$-0.587444\pi$
$157$	−6.79801			−0.542540			−0.271270	+	0.962503i	$0.587444\pi$
$158$	−21.6811	−	4.55258i	−1.72485	−	0.362184i
$159$	−19.1347			−1.51748
$160$	−6.98186	−	10.5477i	−0.551965	−	0.833867i
$161$	19.9556			1.57272
$162$	8.24230	+	1.73072i	0.647576	+	0.135978i
$163$	−6.28967			−0.492645			−0.246323	−	0.969188i	$-0.579222\pi$
$163$	−6.28967			−0.492645			−0.246323	+	0.969188i	$0.579222\pi$
$164$	0.941506	−	2.14305i	0.0735193	−	0.167344i
$165$	−2.45621	−	2.22753i	−0.191216	−	0.173413i
$166$	7.11706	+	1.49444i	0.552391	+	0.115991i
$167$	6.75821	−	6.75821i	0.522966	−	0.522966i	−0.395500	−	0.918466i	$-0.629429\pi$
$167$	6.75821	−	6.75821i	0.522966	−	0.522966i	0.918466	+	0.395500i	$0.129429\pi$
$168$	−12.8330	+	2.13002i	−0.990091	+	0.164334i
$169$	−17.3604			−1.33541
$170$	−7.40920	+	5.37058i	−0.568259	+	0.411904i
$171$	−3.27745	−	3.27745i	−0.250633	−	0.250633i
$172$	−2.52504	+	5.74748i	−0.192533	+	0.438241i
$173$		−	6.24583i		−	0.474862i	−0.971404	−	0.237431i	$-0.923695\pi$
$173$		−	6.24583i		−	0.474862i	0.971404	−	0.237431i	$-0.0763053\pi$
$174$	−3.96624	+	2.58964i	−0.300680	+	0.196320i
$175$	−9.84516	+	11.9816i	−0.744224	+	0.905727i
$176$	−0.169922	+	3.99639i	−0.0128083	+	0.301239i
$177$	−10.8736	+	10.8736i	−0.817311	+	0.817311i
$178$	−14.2352	−	2.98910i	−1.06697	−	0.224042i
$179$	3.13958	+	3.13958i	0.234663	+	0.234663i	0.814636	−	0.579973i	$-0.196937\pi$
$179$	3.13958	+	3.13958i	0.234663	+	0.234663i	−0.579973	+	0.814636i	$0.696937\pi$
$180$	−3.34610	−	1.27923i	−0.249403	−	0.0953481i
$181$	1.63944	−	1.63944i	0.121858	−	0.121858i	−0.643548	−	0.765406i	$-0.722538\pi$
$181$	1.63944	−	1.63944i	0.121858	−	0.121858i	0.765406	+	0.643548i	$0.222538\pi$
$182$	−13.2129	−	20.2366i	−0.979405	−	1.50004i
$183$	6.41098	+	6.41098i	0.473913	+	0.473913i
$184$	2.97979	+	17.9528i	0.219673	+	1.32350i
$185$	0.504314	+	10.3290i	0.0370779	+	0.759400i
$186$	0.538528	−	2.56467i	0.0394868	−	0.188051i
$187$	2.89377			0.211614
$188$	8.10537	+	20.8078i	0.591145	+	1.51756i
$189$	−12.3615	+	12.3615i	−0.899168	+	0.899168i
$190$	−10.7390	−	14.8154i	−0.779086	−	1.07482i
$191$		−	5.16890i		−	0.374008i	−0.982359	−	0.187004i	$-0.940122\pi$
$191$		−	5.16890i		−	0.374008i	0.982359	−	0.187004i	$-0.0598778\pi$
$192$	−3.83249	−	11.2270i	−0.276586	−	0.810242i
$193$	6.13913	+	6.13913i	0.441904	+	0.441904i	0.892652	−	0.450747i	$-0.148842\pi$
$193$	6.13913	+	6.13913i	0.441904	+	0.441904i	−0.450747	+	0.892652i	$0.648842\pi$
$194$	−12.1422	+	7.92788i	−0.871759	+	0.569189i
$195$	0.890997	+	18.2487i	0.0638056	+	1.30682i
$196$	2.10724	−	4.79648i	0.150517	−	0.342606i
$197$			20.1946i			1.43881i	0.694591	+	0.719405i	$0.255585\pi$
$197$			20.1946i			1.43881i	−0.694591	+	0.719405i	$0.744415\pi$
$198$	0.619319	+	0.948538i	0.0440131	+	0.0674096i
$199$		−	16.1362i		−	1.14387i	−0.820300	−	0.571933i	$-0.806194\pi$
$199$		−	16.1362i		−	1.14387i	0.820300	−	0.571933i	$-0.193806\pi$
$200$	−12.2492	−	7.06797i	−0.866152	−	0.499781i
$201$		−	5.31976i		−	0.375227i
$202$	−17.9932	+	11.7481i	−1.26600	+	0.826596i
$203$		−	7.00544i		−	0.491685i
$204$	−7.99702	+	3.11512i	−0.559903	+	0.218102i
$205$	−0.127625	−	2.61392i	−0.00891374	−	0.182564i
$206$	0.360284	+	0.551805i	0.0251022	+	0.0384460i
$207$	3.64435	+	3.64435i	0.253300	+	0.253300i
$208$	16.2327	−	14.9086i	1.12553	−	1.03372i
$209$			5.78636i			0.400251i
$210$	−11.7759	+	8.53576i	−0.812611	+	0.589024i
$211$	−7.11951	+	7.11951i	−0.490127	+	0.490127i	−0.908346	−	0.418219i	$-0.862655\pi$
$211$	−7.11951	+	7.11951i	−0.490127	+	0.490127i	0.418219	+	0.908346i	$0.362655\pi$
$212$	23.6276	+	10.3803i	1.62275	+	0.712923i
$213$	−9.84792			−0.674768
$214$	19.5844	+	4.11232i	1.33876	+	0.281112i
$215$	0.342281	+	7.01032i	0.0233434	+	0.478100i
$216$	−12.9667	−	9.27506i	−0.882274	−	0.631088i
$217$	2.74054	+	2.74054i	0.186040	+	0.186040i
$218$	9.82898	−	6.41754i	0.665703	−	0.434651i
$219$	−0.527085	+	0.527085i	−0.0356171	+	0.0356171i
$220$	1.82454	+	4.08302i	0.123010	+	0.275277i
$221$	−11.2746	−	11.2746i	−0.758415	−	0.758415i
$222$	−1.99307	+	9.49171i	−0.133766	+	0.637042i
$223$	−8.30127	+	8.30127i	−0.555894	+	0.555894i	−0.928136	−	0.372241i	$-0.878589\pi$
$223$	−8.30127	+	8.30127i	−0.555894	+	0.555894i	0.372241	+	0.928136i	$0.378589\pi$
$224$	17.0018	+	4.33160i	1.13598	+	0.289417i
$225$	−3.98607	+	0.390172i	−0.265738	+	0.0260115i
$226$	−16.0560	−	24.5911i	−1.06803	−	1.63577i
$227$			18.6870i			1.24030i	0.784482	+	0.620151i	$0.212929\pi$
$227$			18.6870i			1.24030i	−0.784482	+	0.620151i	$0.787071\pi$
$228$	−6.22896	−	15.9908i	−0.412523	−	1.05901i
$229$	3.51295	+	3.51295i	0.232142	+	0.232142i	0.813586	−	0.581444i	$-0.197512\pi$
$229$	3.51295	+	3.51295i	0.232142	+	0.232142i	−0.581444	+	0.813586i	$0.697512\pi$
$230$	11.9411	+	16.4739i	0.787374	+	1.08625i
$231$	4.59924			0.302608
$232$	6.30236	−	1.04606i	0.413770	−	0.0686772i
$233$	18.2695	−	18.2695i	1.19687	−	1.19687i	0.221775	−	0.975098i	$-0.428815\pi$
$233$	18.2695	−	18.2695i	1.19687	−	1.19687i	0.975098	−	0.221775i	$-0.0711850\pi$
$234$	1.28269	−	6.10864i	0.0838522	−	0.399335i
$235$	18.4939	+	16.7721i	1.20641	+	1.09409i
$236$	19.3256	−	7.52798i	1.25799	−	0.490030i
$237$	−23.2298			−1.50894
$238$	2.60834	−	12.4218i	0.169073	−	0.805189i
$239$	−15.3798			−0.994834			−0.497417	−	0.867511i	$-0.665718\pi$
$239$	−15.3798			−0.994834			−0.497417	+	0.867511i	$0.665718\pi$
$240$	−9.43748	−	9.31944i	−0.609187	−	0.601567i
$241$	−3.05412			−0.196733			−0.0983666	−	0.995150i	$-0.531362\pi$
$241$	−3.05412			−0.196733			−0.0983666	+	0.995150i	$0.531362\pi$
$242$	0.290618	−	1.38403i	0.0186817	−	0.0889689i
$243$	−8.07849			−0.518235
$244$	−4.43843	−	11.3942i	−0.284141	−	0.729437i
$245$	−0.285646	−	5.85036i	−0.0182492	−	0.373766i
$246$	0.504380	−	2.40204i	0.0321581	−	0.153148i
$247$	22.5447	−	22.5447i	1.43448	−	1.43448i
$248$	−2.05627	+	2.87471i	−0.130574	+	0.182545i
$249$	7.62545			0.483243
$250$	−15.7824	−	0.957793i	−0.998164	−	0.0605761i
$251$	−14.4340	−	14.4340i	−0.911064	−	0.911064i	0.0852921	−	0.996356i	$-0.472818\pi$
$251$	−14.4340	−	14.4340i	−0.911064	−	0.911064i	−0.996356	+	0.0852921i	$0.972818\pi$
$252$	4.62993	−	1.80352i	0.291658	−	0.113611i
$253$		−	6.43412i		−	0.404509i
$254$	10.3911	+	15.9148i	0.651994	+	0.998582i
$255$	−6.44597	+	7.10773i	−0.403662	+	0.445103i
$256$	−1.35815	+	15.9423i	−0.0848842	+	0.996391i
$257$	12.3782	−	12.3782i	0.772131	−	0.772131i	−0.206348	−	0.978479i	$-0.566158\pi$
$257$	12.3782	−	12.3782i	0.772131	−	0.772131i	0.978479	+	0.206348i	$0.0661579\pi$
$258$	−1.35271	+	6.44207i	−0.0842158	+	0.401066i
$259$	−10.1426	−	10.1426i	−0.630231	−	0.630231i
$260$	8.79946	−	23.0169i	0.545719	−	1.42745i
$261$	1.27935	−	1.27935i	0.0791899	−	0.0791899i
$262$	−26.4983	+	17.3012i	−1.63707	+	1.06887i
$263$	−2.41966	−	2.41966i	−0.149202	−	0.149202i	0.628559	−	0.777762i	$-0.283645\pi$
$263$	−2.41966	−	2.41966i	−0.149202	−	0.149202i	−0.777762	+	0.628559i	$0.783645\pi$
$264$	0.686764	+	4.13765i	0.0422674	+	0.254655i
$265$	28.8190	−	1.40710i	1.77034	−	0.0864373i
$266$	24.8386	+	5.21561i	1.52295	+	0.319789i
$267$	−15.2520			−0.933408
$268$	−2.88590	+	6.56885i	−0.176284	+	0.401256i
$269$	−1.29652	+	1.29652i	−0.0790503	+	0.0790503i	−0.745526	−	0.666476i	$-0.767802\pi$
$269$	−1.29652	+	1.29652i	−0.0790503	+	0.0790503i	0.666476	+	0.745526i	$0.267802\pi$
$270$	−17.6017	−	2.80781i	−1.07120	−	0.170878i
$271$		−	8.61542i		−	0.523350i	−0.965156	−	0.261675i	$-0.915725\pi$
$271$		−	8.61542i		−	0.523350i	0.965156	−	0.261675i	$-0.0842748\pi$
$272$	11.5646	+	0.491716i	0.701210	+	0.0298146i
$273$	−17.9194	−	17.9194i	−1.08453	−	1.08453i
$274$	−6.38852	−	9.78454i	−0.385945	−	0.591105i
$275$	3.86314	+	3.17429i	0.232956	+	0.191417i
$276$	6.92626	+	17.7808i	0.416912	+	1.07028i
$277$			25.2568i			1.51754i	0.651361	+	0.758768i	$0.274199\pi$
$277$			25.2568i			1.51754i	−0.651361	+	0.758768i	$0.725801\pi$
$278$	17.2497	−	11.2627i	1.03457	−	0.675492i
$279$			1.00097i			0.0599265i
$280$	19.1714	−	4.15174i	1.14571	−	0.248114i
$281$			18.6659i			1.11352i	0.830674	+	0.556758i	$0.187955\pi$
$281$			18.6659i			1.11352i	−0.830674	+	0.556758i	$0.812045\pi$
$282$	12.8012	+	19.6061i	0.762303	+	1.16753i
$283$		−	13.9327i		−	0.828210i	−0.910229	−	0.414105i	$-0.864095\pi$
$283$		−	13.9327i		−	0.828210i	0.910229	−	0.414105i	$-0.135905\pi$
$284$	12.1602	+	5.34236i	0.721577	+	0.317011i
$285$	−14.2126	−	12.8893i	−0.841879	−	0.763496i
$286$	−6.52473	+	4.26012i	−0.385815	+	0.251906i
$287$	2.56676	+	2.56676i	0.151511	+	0.151511i
$288$	2.31386	+	3.89596i	0.136346	+	0.229572i
$289$			8.62607i			0.507416i
$290$	5.78317	−	4.19195i	0.339599	−	0.246160i
$291$	−10.7519	+	10.7519i	−0.630285	+	0.630285i
$292$	0.936782	−	0.364909i	0.0548210	−	0.0213547i
$293$	22.4514			1.31162			0.655812	−	0.754925i	$-0.272327\pi$
$293$	22.4514			1.31162			0.655812	+	0.754925i	$0.272327\pi$
$294$	1.12888	−	5.37614i	0.0658377	−	0.313543i
$295$	15.5773	−	17.1765i	0.906945	−	1.00006i
$296$	7.61017	−	10.6392i	0.442332	−	0.618390i
$297$	3.98562	+	3.98562i	0.231269	+	0.231269i
$298$	7.07074	+	10.8294i	0.409597	+	0.627331i
$299$	−25.0684	+	25.0684i	−1.44975	+	1.44975i
$300$	−14.0930	−	4.61360i	−0.813659	−	0.266366i
$301$	−6.88384	−	6.88384i	−0.396778	−	0.396778i
$302$	4.53002	+	0.951213i	0.260673	+	0.0547361i
$303$	−15.9329	+	15.9329i	−0.915322	+	0.915322i
$304$	−0.983230	+	23.1246i	−0.0563921	+	1.32628i
$305$	−10.1271	−	9.18423i	−0.579877	−	0.525887i
$306$	2.74485	−	1.79217i	0.156913	−	0.102452i
$307$			30.1191i			1.71899i	0.511145	+	0.859495i	$0.329222\pi$
$307$			30.1191i			1.71899i	−0.511145	+	0.859495i	$0.670778\pi$
$308$	−5.67915	−	2.49502i	−0.323600	−	0.142167i
$309$	0.488621	+	0.488621i	0.0277967	+	0.0277967i
$310$	−0.622489	+	3.90228i	−0.0353550	+	0.221635i
$311$	−6.13674			−0.347983			−0.173991	−	0.984747i	$-0.555666\pi$
$311$	−6.13674			−0.347983			−0.173991	+	0.984747i	$0.555666\pi$
$312$	13.4453	−	18.7968i	0.761188	−	1.06416i
$313$	−0.898128	+	0.898128i	−0.0507652	+	0.0507652i	−0.732034	−	0.681268i	$-0.761429\pi$
$313$	−0.898128	+	0.898128i	−0.0507652	+	0.0507652i	0.681268	+	0.732034i	$0.261429\pi$
$314$	9.40866	+	1.97563i	0.530961	+	0.111491i
$315$	3.73194	−	4.11507i	0.210271	−	0.231858i
$316$	28.6842	+	12.6018i	1.61361	+	0.708908i
$317$	−32.2648			−1.81217			−0.906085	−	0.423097i	$-0.860943\pi$
$317$	−32.2648			−1.81217			−0.906085	+	0.423097i	$0.860943\pi$
$318$	26.4830	+	5.56090i	1.48509	+	0.311840i
$319$	−2.25871			−0.126463
$320$	6.59776	+	16.6274i	0.368826	+	0.929498i
$321$	20.9833			1.17117
$322$	−27.6192	−	5.79946i	−1.53916	−	0.323192i
$323$	16.7444			0.931685
$324$	−10.9046	−	4.79073i	−0.605812	−	0.266152i
$325$	−2.68389	−	27.4191i	−0.148875	−	1.52094i
$326$	8.70510	+	1.82789i	0.482131	+	0.101238i
$327$	8.70352	−	8.70352i	0.481306	−	0.481306i
$328$	−1.92588	+	2.69243i	−0.106339	+	0.148664i
$329$	−34.6297			−1.90920
$330$	2.75212	+	3.79679i	0.151499	+	0.209006i
$331$	−1.63075	−	1.63075i	−0.0896344	−	0.0896344i	0.660868	−	0.750502i	$-0.270188\pi$
$331$	−1.63075	−	1.63075i	−0.0896344	−	0.0896344i	−0.750502	+	0.660868i	$0.770188\pi$
$332$	−9.41592	−	4.13670i	−0.516766	−	0.227031i
$333$		−	3.70454i		−	0.203008i
$334$	−11.3176	+	7.38950i	−0.619273	+	0.404336i
$335$	0.391196	+	8.01216i	0.0213733	+	0.437751i
$336$	18.3803	+	0.781511i	1.00273	+	0.0426349i
$337$	12.4558	−	12.4558i	0.678511	−	0.678511i	−0.281152	−	0.959663i	$-0.590717\pi$
$337$	12.4558	−	12.4558i	0.678511	−	0.678511i	0.959663	+	0.281152i	$0.0907165\pi$
$338$	24.0273	+	5.04524i	1.30691	+	0.274425i
$339$	−21.7753	−	21.7753i	−1.18267	−	1.18267i
$340$	11.8153	−	5.27979i	0.640777	−	0.286337i
$341$	0.883609	−	0.883609i	0.0478501	−	0.0478501i
$342$	3.58361	+	5.48858i	0.193779	+	0.296789i
$343$	−9.60697	−	9.60697i	−0.518728	−	0.518728i
$344$	5.16506	−	7.22087i	0.278481	−	0.389323i
$345$	15.8036	+	14.3322i	0.850836	+	0.771619i
$346$	−1.81515	+	8.64442i	−0.0975833	+	0.464727i
$347$	4.50534			0.241859			0.120930	−	0.992661i	$-0.461412\pi$
$347$	4.50534			0.241859			0.120930	+	0.992661i	$0.461412\pi$
$348$	6.24199	−	2.43147i	0.334606	−	0.130341i
$349$	6.06237	−	6.06237i	0.324511	−	0.324511i	−0.525984	−	0.850495i	$-0.676303\pi$
$349$	6.06237	−	6.06237i	0.324511	−	0.324511i	0.850495	+	0.525984i	$0.176303\pi$
$350$	17.1081	−	13.7218i	0.914466	−	0.733460i
$351$		−	31.0573i		−	1.65772i
$352$	1.39660	−	5.48174i	0.0744391	−	0.292178i
$353$	−12.4880	−	12.4880i	−0.664668	−	0.664668i	0.291809	−	0.956477i	$-0.405743\pi$
$353$	−12.4880	−	12.4880i	−0.664668	−	0.664668i	−0.956477	+	0.291809i	$0.905743\pi$
$354$	18.2095	−	11.8893i	0.967824	−	0.631912i
$355$	14.8321	−	0.724181i	0.787205	−	0.0384355i
$356$	18.8332	+	8.27401i	0.998159	+	0.438522i
$357$		−	13.3092i		−	0.704395i
$358$	−3.43285	−	5.25769i	−0.181432	−	0.277877i
$359$		−	0.870077i		−	0.0459209i	−0.999736	−	0.0229605i	$-0.992691\pi$
$359$		−	0.870077i		−	0.0459209i	0.999736	−	0.0229605i	$-0.00730918\pi$
$360$	4.25934	+	2.74293i	0.224487	+	0.144565i
$361$			14.4820i			0.762211i
$362$	−2.74548	+	1.79258i	−0.144299	+	0.0942159i
$363$		−	1.48289i		−	0.0778318i
$364$	12.4059	+	31.8480i	0.650247	+	1.66929i
$365$	0.755090	−	0.832610i	0.0395232	−	0.0435808i
$366$	−7.00985	−	10.7361i	−0.366411	−	0.561187i
$367$	−11.5502	−	11.5502i	−0.602915	−	0.602915i	0.338170	−	0.941085i	$-0.390192\pi$
$367$	−11.5502	−	11.5502i	−0.602915	−	0.602915i	−0.941085	+	0.338170i	$0.890192\pi$
$368$	1.09330	−	25.7132i	0.0569920	−	1.34039i
$369$			0.937497i			0.0488042i
$370$	2.30380	−	14.4422i	0.119769	−	0.750812i
$371$	−28.2991	+	28.2991i	−1.46922	+	1.46922i
$372$	−1.49068	+	3.39307i	−0.0772882	+	0.175923i
$373$	−29.9521			−1.55086			−0.775430	−	0.631434i	$-0.782467\pi$
$373$	−29.9521			−1.55086			−0.775430	+	0.631434i	$0.782467\pi$
$374$	−4.00507	−	0.840984i	−0.207097	−	0.0434863i
$375$	−16.4020	+	2.41788i	−0.846996	+	0.124859i
$376$	−5.17095	−	31.1542i	−0.266671	−	1.60666i
$377$	8.80031	+	8.80031i	0.453239	+	0.453239i
$378$	20.7012	−	13.5162i	1.06475	−	0.695200i
$379$	−16.6821	+	16.6821i	−0.856903	+	0.856903i	−0.990972	−	0.134069i	$-0.957196\pi$
$379$	−16.6821	+	16.6821i	−0.856903	+	0.856903i	0.134069	+	0.990972i	$0.457196\pi$
$380$	10.5574	+	23.6259i	0.541585	+	1.21198i
$381$	14.0925	+	14.0925i	0.721979	+	0.721979i
$382$	−1.50218	+	7.15391i	−0.0768581	+	0.366026i
$383$	−13.6937	+	13.6937i	−0.699716	+	0.699716i	−0.964349	−	0.264633i	$-0.914749\pi$
$383$	−13.6937	+	13.6937i	−0.699716	+	0.699716i	0.264633	+	0.964349i	$0.414749\pi$
$384$	2.04150	+	16.6524i	0.104180	+	0.849787i
$385$	−6.92698	+	0.338212i	−0.353031	+	0.0172369i
$386$	−6.71260	−	10.2809i	−0.341662	−	0.523283i
$387$		−	2.51429i		−	0.127809i
$388$	19.1092	−	7.44369i	0.970121	−	0.377896i
$389$	−26.7915	−	26.7915i	−1.35838	−	1.35838i	−0.875910	−	0.482474i	$-0.839738\pi$
$389$	−26.7915	−	26.7915i	−1.35838	−	1.35838i	−0.482474	−	0.875910i	$-0.660262\pi$
$390$	4.07024	−	25.5157i	0.206105	−	1.29204i
$391$	−18.6189			−0.941597
$392$	−4.31043	+	6.02607i	−0.217710	+	0.304363i
$393$	−23.4641	+	23.4641i	−1.18361	+	1.18361i
$394$	5.86894	−	27.9500i	0.295673	−	1.40810i
$395$	34.9867	−	1.70823i	1.76037	−	0.0859506i
$396$	−0.581494	−	1.49279i	−0.0292212	−	0.0750156i
$397$	26.9669			1.35343			0.676715	−	0.736245i	$-0.263403\pi$
$397$	26.9669			1.35343			0.676715	+	0.736245i	$0.263403\pi$
$398$	−4.68948	+	22.3330i	−0.235063	+	1.11945i
$399$	26.6129			1.33231
$400$	14.8992	+	13.3421i	0.744962	+	0.667107i
$401$	−15.9541			−0.796711			−0.398356	−	0.917231i	$-0.630419\pi$
$401$	−15.9541			−0.796711			−0.398356	+	0.917231i	$0.630419\pi$
$402$	−1.54602	+	7.36271i	−0.0771085	+	0.367219i
$403$	−6.88539			−0.342986
$404$	28.3174	−	11.0306i	1.40884	−	0.548794i
$405$	−13.3006	+	0.649405i	−0.660911	+	0.0322692i
$406$	−2.03591	+	9.69574i	−0.101041	+	0.481192i
$407$	−3.27019	+	3.27019i	−0.162098	+	0.162098i
$408$	11.9734	−	1.98734i	0.592773	−	0.0983879i
$409$	−1.40302			−0.0693749			−0.0346875	−	0.999398i	$-0.511044\pi$
$409$	−1.40302			−0.0693749			−0.0346875	+	0.999398i	$0.511044\pi$
$410$	−0.583016	+	3.65484i	−0.0287931	+	0.180499i
$411$	−8.66416	−	8.66416i	−0.427372	−	0.427372i
$412$	−0.338280	−	0.868420i	−0.0166659	−	0.0427840i
$413$			32.1629i			1.58263i
$414$	−3.98477	−	6.10300i	−0.195841	−	0.299946i
$415$	−11.4848	+	0.560748i	−0.563766	+	0.0275260i
$416$	−26.7992	+	15.9164i	−1.31394	+	0.780367i
$417$	15.2746	−	15.2746i	0.747999	−	0.747999i
$418$	1.68162	−	8.00851i	0.0822509	−	0.391709i
$419$	13.0496	+	13.0496i	0.637514	+	0.637514i	0.949942	−	0.312428i	$-0.101142\pi$
$419$	13.0496	+	13.0496i	0.637514	+	0.637514i	−0.312428	+	0.949942i	$0.601142\pi$
$420$	18.7788	−	8.39148i	0.916311	−	0.409462i
$421$	4.03937	−	4.03937i	0.196867	−	0.196867i	−0.601789	−	0.798655i	$-0.705545\pi$
$421$	4.03937	−	4.03937i	0.196867	−	0.196867i	0.798655	+	0.601789i	$0.205545\pi$
$422$	11.9227	−	7.78456i	0.580387	−	0.378947i
$423$	−6.32417	−	6.32417i	−0.307492	−	0.307492i
$424$	−29.6846	−	21.2333i	−1.44161	−	1.03118i
$425$	9.18568	−	11.1791i	0.445571	−	0.542264i
$426$	13.6298	+	2.86199i	0.660367	+	0.138664i
$427$	18.9629			0.917680
$428$	−25.9102	−	11.3832i	−1.25242	−	0.550226i
$429$	−5.77762	+	5.77762i	−0.278946	+	0.278946i
$430$	1.56360	−	9.80197i	0.0754036	−	0.472693i
$431$		−	30.9927i		−	1.49287i	−0.665460	−	0.746434i	$-0.731764\pi$
$431$		−	30.9927i		−	1.49287i	0.665460	−	0.746434i	$-0.268236\pi$
$432$	15.2508	+	16.6053i	0.733757	+	0.798924i
$433$	0.375412	+	0.375412i	0.0180411	+	0.0180411i	0.716070	−	0.698029i	$-0.245939\pi$
$433$	0.375412	+	0.375412i	0.0180411	+	0.0180411i	−0.698029	+	0.716070i	$0.745939\pi$
$434$	−2.99654	−	4.58944i	−0.143838	−	0.220300i
$435$	5.03133	−	5.54786i	0.241234	−	0.266000i
$436$	−15.4687	+	6.02559i	−0.740815	+	0.288573i
$437$		−	37.2301i		−	1.78096i
$438$	0.882682	−	0.576321i	0.0421762	−	0.0275377i
$439$		−	19.1050i		−	0.911830i	−0.890023	−	0.455915i	$-0.849312\pi$
$439$		−	19.1050i		−	0.911830i	0.890023	−	0.455915i	$-0.150688\pi$
$440$	−1.33861	−	6.18127i	−0.0638158	−	0.294681i
$441$			2.09827i			0.0999174i
$442$	12.3278	+	18.8811i	0.586375	+	0.898081i
$443$			0.0931303i			0.00442475i	0.999998	+	0.00221238i	$0.000704222\pi$
$443$			0.0931303i			0.00442475i	−0.999998	+	0.00221238i	$0.999296\pi$
$444$	5.51693	−	12.5576i	0.261822	−	0.595957i
$445$	22.9713	−	1.12158i	1.08894	−	0.0531679i
$446$	13.9017	−	9.07671i	0.658266	−	0.429795i
$447$	9.58939	+	9.58939i	0.453563	+	0.453563i
$448$	−22.2721	−	10.9361i	−1.05226	−	0.516682i
$449$		−	0.170264i		−	0.00803526i	−0.999992	−	0.00401763i	$-0.998721\pi$
$449$		−	0.170264i		−	0.00803526i	0.999992	−	0.00401763i	$-0.00127885\pi$
$450$	5.63024	+	0.618416i	0.265412	+	0.0291524i
$451$	0.827579	−	0.827579i	0.0389692	−	0.0389692i
$452$	15.0754	+	38.7010i	0.709086	+	1.82034i
$453$	4.85361			0.228042
$454$	5.43080	−	25.8634i	0.254880	−	1.21383i
$455$	28.3064	+	25.6710i	1.32703	+	1.20347i
$456$	3.97386	+	23.9420i	0.186093	+	1.12118i
$457$	−1.82047	−	1.82047i	−0.0851582	−	0.0851582i	0.663245	−	0.748403i	$-0.269179\pi$
$457$	−1.82047	−	1.82047i	−0.0851582	−	0.0851582i	−0.748403	+	0.663245i	$0.769179\pi$
$458$	−3.84110	−	5.88296i	−0.179483	−	0.274893i
$459$	11.5335	−	11.5335i	0.538337	−	0.538337i
$460$	−11.7393	−	26.2706i	−0.547347	−	1.22487i
$461$	16.2757	+	16.2757i	0.758035	+	0.758035i	0.975965	−	0.217929i	$-0.0699302\pi$
$461$	16.2757	+	16.2757i	0.758035	+	0.758035i	−0.217929	+	0.975965i	$0.569930\pi$
$462$	−6.36549	−	1.33662i	−0.296149	−	0.0621854i
$463$	10.5729	−	10.5729i	0.491364	−	0.491364i	−0.417372	−	0.908736i	$-0.637049\pi$
$463$	10.5729	−	10.5729i	0.491364	−	0.491364i	0.908736	+	0.417372i	$0.137049\pi$
$464$	−9.02666	−	0.383803i	−0.419052	−	0.0178176i
$465$	0.202068	+	4.13860i	0.00937069	+	0.191923i
$466$	−30.5950	+	19.9761i	−1.41728	+	0.925373i
$467$			10.5930i			0.490184i	0.969500	+	0.245092i	$0.0788183\pi$
$467$			10.5930i			0.490184i	−0.969500	+	0.245092i	$0.921182\pi$
$468$	−3.55057	+	8.08178i	−0.164125	+	0.373580i
$469$	−7.86760	−	7.86760i	−0.363292	−	0.363292i
$470$	−20.7219	−	28.5877i	−0.955830	−	1.31865i
$471$	10.0807			0.464496
$472$	−28.9349	+	4.80259i	−1.33184	+	0.221057i
$473$	−2.21950	+	2.21950i	−0.102053	+	0.102053i
$474$	32.1507	+	6.75100i	1.47673	+	0.310084i
$475$	22.3536	+	18.3676i	1.02565	+	0.842764i
$476$	−7.22004	+	16.4342i	−0.330930	+	0.753260i
$477$	−10.3361			−0.473258
$478$	21.2861	+	4.46964i	0.973602	+	0.204437i
$479$	12.9220			0.590421			0.295211	−	0.955432i	$-0.404610\pi$
$479$	12.9220			0.590421			0.295211	+	0.955432i	$0.404610\pi$
$480$	10.3534	+	15.6411i	0.472564	+	0.713915i
$481$	25.4825			1.16190
$482$	4.22700	+	0.887584i	0.192534	+	0.0404283i
$483$	−29.5920			−1.34648
$484$	−0.804450	+	1.83108i	−0.0365659	+	0.0832310i
$485$	15.4029	−	16.9842i	0.699408	−	0.771212i
$486$	11.1809	+	2.34776i	0.507175	+	0.106497i
$487$	20.0321	−	20.0321i	0.907742	−	0.907742i	−0.0883480	−	0.996090i	$-0.528159\pi$
$487$	20.0321	−	20.0321i	0.907742	−	0.907742i	0.996090	+	0.0883480i	$0.0281588\pi$
$488$	2.83156	+	17.0598i	0.128179	+	0.772259i
$489$	9.32692			0.421778
$490$	−1.30488	+	8.18010i	−0.0589485	+	0.369539i
$491$	−17.3264	−	17.3264i	−0.781929	−	0.781929i	0.198227	−	0.980156i	$-0.436482\pi$
$491$	−17.3264	−	17.3264i	−0.781929	−	0.781929i	−0.980156	+	0.198227i	$0.936482\pi$
$492$	−1.39615	+	3.17792i	−0.0629435	+	0.143271i
$493$			6.53618i			0.294375i
$494$	−37.7544	+	24.6506i	−1.69865	+	1.10908i
$495$	−1.32679	−	1.20326i	−0.0596347	−	0.0540825i
$496$	3.68139	−	3.38110i	0.165299	−	0.151816i
$497$	−14.5645	+	14.5645i	−0.653306	+	0.653306i
$498$	−10.5539	−	2.21610i	−0.472930	−	0.0993057i
$499$	20.6914	+	20.6914i	0.926275	+	0.926275i	0.997463	−	0.0711883i	$-0.0226791\pi$
$499$	20.6914	+	20.6914i	0.926275	+	0.926275i	−0.0711883	+	0.997463i	$0.522679\pi$
$500$	21.5649	+	5.91226i	0.964412	+	0.264404i
$501$	−10.0217	+	10.0217i	−0.447737	+	0.447737i
$502$	15.7823	+	24.1718i	0.704397	+	1.07884i
$503$	7.41919	+	7.41919i	0.330805	+	0.330805i	0.852892	−	0.522087i	$-0.174846\pi$
$503$	7.41919	+	7.41919i	0.330805	+	0.330805i	−0.522087	+	0.852892i	$0.674846\pi$
$504$	−6.93211	+	1.15058i	−0.308781	+	0.0512511i
$505$	22.8251	−	25.1684i	1.01570	−	1.11998i
$506$	−1.86987	+	8.90501i	−0.0831260	+	0.395876i
$507$	25.7436			1.14331
$508$	−9.75644	−	25.0464i	−0.432872	−	1.11125i
$509$	23.8637	−	23.8637i	1.05774	−	1.05774i	0.0595131	−	0.998228i	$-0.481045\pi$
$509$	23.8637	−	23.8637i	1.05774	−	1.05774i	0.998228	−	0.0595131i	$-0.0189548\pi$
$510$	10.9871	−	7.96400i	0.486515	−	0.352652i
$511$			1.55905i			0.0689685i
$512$	6.51283	−	21.6699i	0.287829	−	0.957682i
$513$	23.0622	+	23.0622i	1.01822	+	1.01822i
$514$	−20.7291	+	13.5345i	−0.914323	+	0.596980i
$515$	−0.771849	−	0.699987i	−0.0340118	−	0.0308451i
$516$	3.74437	−	8.52291i	0.164837	−	0.375200i
$517$			11.1654i			0.491052i
$518$	11.0900	+	16.9853i	0.487269	+	0.746291i
$519$			9.26191i			0.406553i
$520$	−18.8678	+	29.2988i	−0.827410	+	1.28484i
$521$			27.8773i			1.22133i	0.791890	+	0.610663i	$0.209097\pi$
$521$			27.8773i			1.22133i	−0.791890	+	0.610663i	$0.790903\pi$
$522$	−2.14247	+	1.39886i	−0.0937732	+	0.0612264i
$523$		−	3.58356i		−	0.156698i	−0.996926	−	0.0783491i	$-0.975035\pi$
$523$		−	3.58356i		−	0.156698i	0.996926	−	0.0783491i	$-0.0249649\pi$
$524$	41.7025	−	16.2446i	1.82178	−	0.709647i
$525$	14.5993	−	17.7675i	0.637167	−	0.775438i
$526$	2.64568	+	4.05208i	0.115357	+	0.176679i
$527$	−2.55697	−	2.55697i	−0.111383	−	0.111383i
$528$	0.251976	−	5.92622i	0.0109659	−	0.257906i
$529$			18.3978i			0.799906i
$530$	−40.2954	−	6.42788i	−1.75032	−	0.279209i
$531$	−5.87367	+	5.87367i	−0.254896	+	0.254896i
$532$	−32.8616	−	14.4371i	−1.42473	−	0.625928i
$533$	−6.44878			−0.279328
$534$	21.1093	+	4.43252i	0.913487	+	0.191814i
$535$	−31.6032	+	1.54304i	−1.36633	+	0.0667113i
$536$	5.90320	−	8.25280i	0.254979	−	0.356467i
$537$	−4.65566	−	4.65566i	−0.200907	−	0.200907i
$538$	2.17122	−	1.41763i	0.0936078	−	0.0611184i
$539$	1.85225	−	1.85225i	0.0797821	−	0.0797821i
$540$	23.5453	+	9.00147i	1.01323	+	0.387361i
$541$	−8.00154	−	8.00154i	−0.344013	−	0.344013i	0.513861	−	0.857874i	$-0.328215\pi$
$541$	−8.00154	−	8.00154i	−0.344013	−	0.344013i	−0.857874	+	0.513861i	$0.828215\pi$
$542$	−2.50380	+	11.9240i	−0.107547	+	0.512180i
$543$	−2.43111	+	2.43111i	−0.104329	+	0.104329i
$544$	−15.8629	−	4.04145i	−0.680117	−	0.173276i
$545$	−12.4685	+	13.7485i	−0.534090	+	0.588922i
$546$	19.5933	+	30.0088i	0.838517	+	1.28426i
$547$		−	3.26578i		−	0.139635i	−0.997560	−	0.0698174i	$-0.977758\pi$
$547$		−	3.26578i		−	0.139635i	0.997560	−	0.0698174i	$-0.0222416\pi$
$548$	5.99834	+	15.3987i	0.256236	+	0.657801i
$549$	3.46306	+	3.46306i	0.147800	+	0.147800i
$550$	−4.42420	−	5.51602i	−0.188649	−	0.235204i
$551$	−13.0697			−0.556788
$552$	−4.41872	−	26.6221i	−0.188073	−	1.13311i
$553$	−34.3554	+	34.3554i	−1.46094	+	1.46094i
$554$	7.34011	−	34.9562i	0.311851	−	1.48515i
$555$	−0.747845	−	15.3168i	−0.0317442	−	0.650160i
$556$	−27.1473	+	10.5748i	−1.15130	+	0.448473i
$557$	−22.2526			−0.942871			−0.471436	−	0.881900i	$-0.656264\pi$
$557$	−22.2526			−0.942871			−0.471436	+	0.881900i	$0.656264\pi$
$558$	0.290900	−	1.38537i	0.0123148	−	0.0586475i
$559$	17.2951			0.731505
$560$	−27.7404	+	0.174580i	−1.17224	+	0.00737736i
$561$	−4.29116			−0.181173
$562$	5.42467	−	25.8342i	0.228826	−	1.08975i
$563$	33.3310			1.40473			0.702366	−	0.711816i	$-0.252127\pi$
$563$	33.3310			1.40473			0.702366	+	0.711816i	$0.252127\pi$
$564$	−12.0194	−	30.8558i	−0.506108	−	1.29926i
$565$	34.3973	+	31.1948i	1.44711	+	1.31237i
$566$	−4.04909	+	19.2832i	−0.170196	+	0.810534i
$567$	13.0606	−	13.0606i	0.548494	−	0.548494i
$568$	−15.2775	−	10.9280i	−0.641032	−	0.458528i
$569$	−21.0541			−0.882632			−0.441316	−	0.897352i	$-0.645488\pi$
$569$	−21.0541			−0.882632			−0.441316	+	0.897352i	$0.645488\pi$
$570$	15.9247	+	21.9696i	0.667014	+	0.920206i
$571$	3.48143	+	3.48143i	0.145693	+	0.145693i	0.776191	−	0.630498i	$-0.217149\pi$
$571$	3.48143	+	3.48143i	0.145693	+	0.145693i	−0.630498	+	0.776191i	$0.717149\pi$
$572$	10.2685	−	3.99994i	0.429347	−	0.167246i
$573$			7.66493i			0.320207i
$574$	−2.80653	−	4.29842i	−0.117142	−	0.179413i
$575$	−24.8559	−	20.4238i	−1.03656	−	0.851730i
$576$	−2.07022	−	6.06458i	−0.0862592	−	0.252691i
$577$	−28.0824	+	28.0824i	−1.16908	+	1.16908i	−0.186660	+	0.982425i	$0.559766\pi$
$577$	−28.0824	+	28.0824i	−1.16908	+	1.16908i	−0.982425	+	0.186660i	$0.940234\pi$
$578$	2.50690	−	11.9387i	0.104273	−	0.496586i
$579$	−9.10368	−	9.10368i	−0.378336	−	0.378336i
$580$	−9.22234	+	4.12109i	−0.382937	+	0.171119i
$581$	11.2776	−	11.2776i	0.467873	−	0.467873i
$582$	18.0056	−	11.7562i	0.746356	−	0.487311i
$583$	9.12424	+	9.12424i	0.377887	+	0.377887i
$584$	−1.40258	+	0.232800i	−0.0580394	+	0.00963332i
$585$	0.481296	+	9.85751i	0.0198991	+	0.407558i
$586$	−31.0734	−	6.52478i	−1.28363	−	0.269536i
$587$	−7.38946			−0.304996			−0.152498	−	0.988304i	$-0.548732\pi$
$587$	−7.38946			−0.304996			−0.152498	+	0.988304i	$0.548732\pi$
$588$	−3.12481	+	7.11267i	−0.128865	+	0.293322i
$589$	5.11288	−	5.11288i	0.210673	−	0.210673i
$590$	−26.5513	+	19.2458i	−1.09310	+	0.792336i
$591$		−	29.9465i		−	1.23184i
$592$	−13.6246	+	12.5133i	−0.559970	+	0.514293i
$593$	−22.3718	−	22.3718i	−0.918699	−	0.918699i	0.0782357	−	0.996935i	$-0.475071\pi$
$593$	−22.3718	−	22.3718i	−0.918699	−	0.918699i	−0.996935	+	0.0782357i	$0.975071\pi$
$594$	−4.35793	−	6.67451i	−0.178808	−	0.273859i
$595$	0.978708	+	20.0451i	0.0401231	+	0.821769i
$596$	−6.63889	−	17.0431i	−0.271940	−	0.698113i
$597$			23.9283i			0.979320i
$598$	41.9808	−	27.4101i	1.71672	−	1.12088i
$599$		−	25.5938i		−	1.04573i	−0.852414	−	0.522867i	$-0.824863\pi$
$599$		−	25.5938i		−	1.04573i	0.852414	−	0.522867i	$-0.175137\pi$
$600$	18.1643	+	10.4810i	0.741556	+	0.427887i
$601$			25.9120i			1.05697i	0.848941	+	0.528487i	$0.177241\pi$
$601$			25.9120i			1.05697i	−0.848941	+	0.528487i	$0.822759\pi$
$602$	7.52687	+	11.5280i	0.306772	+	0.469847i
$603$		−	2.87361i		−	0.117022i
$604$	−5.99325	−	2.63302i	−0.243862	−	0.107136i
$605$	0.109047	+	2.23341i	0.00443338	+	0.0908009i
$606$	26.6820	−	17.4212i	1.08388	−	0.707689i
$607$	4.71583	+	4.71583i	0.191410	+	0.191410i	0.796305	−	0.604895i	$-0.206785\pi$
$607$	4.71583	+	4.71583i	0.191410	+	0.191410i	−0.604895	+	0.796305i	$0.706785\pi$
$608$	8.08125	−	31.7194i	0.327738	−	1.28639i
$609$			10.3883i			0.420956i
$610$	11.3471	+	15.6544i	0.459432	+	0.633827i
$611$	43.5022	−	43.5022i	1.75991	−	1.75991i
$612$	−4.31980	+	1.68271i	−0.174618	+	0.0680197i
$613$	19.6034			0.791772			0.395886	−	0.918300i	$-0.370438\pi$
$613$	19.6034			0.791772			0.395886	+	0.918300i	$0.370438\pi$
$614$	8.75317	−	41.6858i	0.353249	−	1.68230i
$615$	0.189255	+	3.87617i	0.00763150	+	0.156302i
$616$	7.13502	+	5.10366i	0.287478	+	0.205632i
$617$	−15.6315	−	15.6315i	−0.629302	−	0.629302i	0.318591	−	0.947892i	$-0.396790\pi$
$617$	−15.6315	−	15.6315i	−0.629302	−	0.629302i	−0.947892	+	0.318591i	$0.896790\pi$
$618$	−0.534264	−	0.818268i	−0.0214912	−	0.0329156i
$619$	−11.4371	+	11.4371i	−0.459697	+	0.459697i	−0.898556	−	0.438859i	$-0.855383\pi$
$619$	−11.4371	+	11.4371i	−0.459697	+	0.459697i	0.438859	+	0.898556i	$0.355383\pi$
$620$	1.99562	−	5.21997i	0.0801460	−	0.209639i
$621$	−25.6439	−	25.6439i	−1.02906	−	1.02906i
$622$	8.49344	+	1.78345i	0.340556	+	0.0715098i
$623$	−22.5568	+	22.5568i	−0.903720	+	0.903720i
$624$	−24.0713	+	22.1079i	−0.963625	+	0.885023i
$625$	24.5255	−	4.84775i	0.981019	−	0.193910i
$626$	1.50405	−	0.982024i	0.0601139	−	0.0392496i
$627$		−	8.58057i		−	0.342675i
$628$	−12.4477	−	5.46866i	−0.496718	−	0.218223i
$629$	9.46320	+	9.46320i	0.377323	+	0.377323i
$630$	−6.36104	+	4.61082i	−0.253430	+	0.183699i
$631$	16.2960			0.648735			0.324367	−	0.945931i	$-0.394849\pi$
$631$	16.2960			0.648735			0.324367	+	0.945931i	$0.394849\pi$
$632$	−36.0375	−	25.7775i	−1.43349	−	1.02537i
$633$	10.5575	−	10.5575i	0.419622	−	0.419622i
$634$	44.6554	+	9.37673i	1.77349	+	0.372398i
$635$	−22.2612	−	20.1885i	−0.883407	−	0.801158i
$636$	−35.0372	−	15.3929i	−1.38932	−	0.610369i
$637$	−14.4334			−0.571872
$638$	3.12612	+	0.656421i	0.123764	+	0.0259880i
$639$	−5.31961			−0.210441
$640$	−4.29928	−	24.9302i	−0.169944	−	0.985454i
$641$	16.9318			0.668765			0.334382	−	0.942438i	$-0.391472\pi$
$641$	16.9318			0.668765			0.334382	+	0.942438i	$0.391472\pi$
$642$	−29.0415	−	6.09814i	−1.14618	−	0.240674i
$643$	19.5106			0.769423			0.384712	−	0.923037i	$-0.374301\pi$
$643$	19.5106			0.769423			0.384712	+	0.923037i	$0.374301\pi$
$644$	36.5403	+	16.0533i	1.43989	+	0.632588i
$645$	−0.507566	−	10.3956i	−0.0199854	−	0.409325i
$646$	−23.1748	−	4.86624i	−0.911800	−	0.191460i
$647$	−5.71847	+	5.71847i	−0.224816	+	0.224816i	−0.810523	−	0.585707i	$-0.800817\pi$
$647$	−5.71847	+	5.71847i	−0.224816	+	0.224816i	0.585707	+	0.810523i	$0.300817\pi$
$648$	13.7001	+	9.79960i	0.538189	+	0.384965i
$649$	10.3700			0.407058
$650$	−4.25391	+	38.7288i	−0.166852	+	1.51907i
$651$	−4.06393	−	4.06393i	−0.159278	−	0.159278i
$652$	−11.5169	−	5.05973i	−0.451037	−	0.198154i
$653$			22.6562i			0.886607i	0.896372	+	0.443303i	$0.146194\pi$
$653$			22.6562i			0.886607i	−0.896372	+	0.443303i	$0.853806\pi$
$654$	−14.5753	+	9.51653i	−0.569941	+	0.372126i
$655$	33.6141	−	37.0650i	1.31341	−	1.44825i
$656$	3.44795	−	3.16670i	0.134620	−	0.123639i
$657$	−0.284719	+	0.284719i	−0.0111079	+	0.0111079i
$658$	47.9286	+	10.0640i	1.86845	+	0.392337i
$659$	−22.2574	−	22.2574i	−0.867027	−	0.867027i	0.125115	−	0.992142i	$-0.460070\pi$
$659$	−22.2574	−	22.2574i	−0.867027	−	0.867027i	−0.992142	+	0.125115i	$0.960070\pi$
$660$	−2.70559	−	6.05469i	−0.105315	−	0.235678i
$661$	−21.9122	+	21.9122i	−0.852285	+	0.852285i	−0.990414	−	0.138129i	$-0.955891\pi$
$661$	−21.9122	+	21.9122i	−0.852285	+	0.852285i	0.138129	+	0.990414i	$0.455891\pi$
$662$	1.78309	+	2.73094i	0.0693016	+	0.106141i
$663$	16.7191	+	16.7191i	0.649317	+	0.649317i
$664$	11.8297	+	8.46176i	0.459082	+	0.328380i
$665$	−40.0820	+	1.95702i	−1.55431	+	0.0758898i
$666$	−1.07661	+	5.12720i	−0.0417177	+	0.198675i
$667$	14.5328			0.562711
$668$	17.8115	−	6.93819i	0.689146	−	0.268447i
$669$	12.3099	−	12.3099i	0.475929	−	0.475929i
$670$	1.78705	−	11.2028i	0.0690399	−	0.432801i
$671$		−	6.11406i		−	0.236030i
$672$	−25.2118	−	6.42330i	−0.972568	−	0.247784i
$673$	31.3884	+	31.3884i	1.20993	+	1.20993i	0.971048	+	0.238884i	$0.0767817\pi$
$673$	31.3884	+	31.3884i	1.20993	+	1.20993i	0.238884	+	0.971048i	$0.423218\pi$
$674$	−20.8591	+	13.6193i	−0.803463	+	0.524597i
$675$	28.0485	−	2.74550i	1.07959	−	0.105674i
$676$	−31.7882	−	13.9655i	−1.22262	−	0.537136i
$677$		−	0.108004i		−	0.00415095i	−0.999998	−	0.00207547i	$-0.999339\pi$
$677$		−	0.108004i		−	0.00415095i	0.999998	−	0.00207547i	$-0.000660644\pi$
$678$	23.8094	+	36.4660i	0.914393	+	1.40047i
$679$			31.8027i			1.22048i
$680$	−17.8872	+	3.87364i	−0.685943	+	0.148547i
$681$		−	27.7109i		−	1.06188i
$682$	−1.47974	+	0.966149i	−0.0566620	+	0.0369958i
$683$		−	9.55474i		−	0.365602i	−0.983150	−	0.182801i	$-0.941484\pi$
$683$		−	9.55474i		−	0.365602i	0.983150	−	0.182801i	$-0.0585164\pi$
$684$	−3.36474	−	8.63783i	−0.128654	−	0.330276i
$685$	13.6863	+	12.4121i	0.522928	+	0.474241i
$686$	10.5044	+	16.0883i	0.401059	+	0.614255i
$687$	−5.20933	−	5.20933i	−0.198748	−	0.198748i
$688$	−9.24712	+	8.49284i	−0.352543	+	0.323786i
$689$		−	71.0993i		−	2.70867i
$690$	−17.7074	−	24.4290i	−0.674110	−	0.929996i
$691$	−27.9207	+	27.9207i	−1.06215	+	1.06215i	−0.0642164	+	0.997936i	$0.520455\pi$
$691$	−27.9207	+	27.9207i	−1.06215	+	1.06215i	−0.997936	+	0.0642164i	$0.979545\pi$
$692$	5.02446	−	11.4366i	0.191001	−	0.434755i
$693$	2.48440			0.0943745
$694$	−6.23553	−	1.30934i	−0.236697	−	0.0497017i
$695$	−21.8820	+	24.1285i	−0.830032	+	0.915246i
$696$	−9.34573	+	1.55120i	−0.354249	+	0.0587979i
$697$	−2.39483	−	2.39483i	−0.0907105	−	0.0907105i
$698$	−10.1523	+	6.62867i	−0.384272	+	0.250899i
$699$	−27.0917	+	27.0917i	−1.02470	+	1.02470i
$700$	−27.6659	+	14.0194i	−1.04567	+	0.529885i
$701$	16.2443	+	16.2443i	0.613537	+	0.613537i	0.943866	−	0.330329i	$-0.107160\pi$
$701$	16.2443	+	16.2443i	0.613537	+	0.613537i	−0.330329	+	0.943866i	$0.607160\pi$
$702$	−9.02584	+	42.9843i	−0.340658	+	1.62234i
$703$	−18.9225	+	18.9225i	−0.713677	+	0.713677i
$704$	−3.52604	+	7.18102i	−0.132892	+	0.270645i
$705$	−27.4245	−	24.8712i	−1.03287	−	0.936703i
$706$	13.6545	+	20.9130i	0.513894	+	0.787070i
$707$			47.1276i			1.77242i
$708$	−28.6578	+	11.1632i	−1.07702	+	0.419539i
$709$	−28.9234	−	28.9234i	−1.08624	−	1.08624i	−0.995912	−	0.0903298i	$-0.971208\pi$
$709$	−28.9234	−	28.9234i	−1.08624	−	1.08624i	−0.0903298	−	0.995912i	$-0.528792\pi$
$710$	−20.7385	−	3.30819i	−0.778303	−	0.124154i
$711$	−12.5482			−0.470593
$712$	−23.6612	−	16.9248i	−0.886740	−	0.634282i
$713$	−5.68524	+	5.68524i	−0.212914	+	0.212914i
$714$	−3.86789	+	18.4203i	−0.144752	+	0.689362i
$715$	8.27688	−	9.12661i	0.309538	−	0.341316i
$716$	3.22319	+	8.27445i	0.120456	+	0.309231i
$717$	22.8066			0.851727
$718$	−0.252861	+	1.20421i	−0.00943667	+	0.0449408i
$719$	11.9484			0.445601			0.222800	−	0.974864i	$-0.428480\pi$
$719$	11.9484			0.445601			0.222800	+	0.974864i	$0.428480\pi$
$720$	−5.09790	−	5.03414i	−0.189988	−	0.187611i
$721$	1.44528			0.0538251
$722$	4.20874	−	20.0435i	0.156633	−	0.745943i
$723$	4.52894			0.168433
$724$	4.32079	−	1.68310i	0.160581	−	0.0625519i
$725$	−7.16979	+	8.72570i	−0.266279	+	0.324064i
$726$	−0.430957	+	2.05237i	−0.0159943	+	0.0761706i
$727$	24.3475	−	24.3475i	0.902998	−	0.902998i	−0.0926960	−	0.995694i	$-0.529548\pi$
$727$	24.3475	−	24.3475i	0.902998	−	0.902998i	0.995694	+	0.0926960i	$0.0295485\pi$
$728$	−7.91455	−	47.6840i	−0.293333	−	1.76729i
$729$	29.8454			1.10539
$730$	−1.28704	+	0.932914i	−0.0476355	+	0.0345287i
$731$	6.42273	+	6.42273i	0.237553	+	0.237553i
$732$	6.58172	+	16.8963i	0.243267	+	0.624507i
$733$		−	15.1091i		−	0.558067i	−0.960281	−	0.279034i	$-0.909986\pi$
$733$		−	15.1091i		−	0.558067i	0.960281	−	0.279034i	$-0.0900141\pi$
$734$	12.6291	+	19.3425i	0.466149	+	0.713945i
$735$	0.423582	+	8.67547i	0.0156241	+	0.320000i
$736$	−8.98590	+	35.2702i	−0.331225	+	1.30008i
$737$	−2.53669	+	2.53669i	−0.0934400	+	0.0934400i
$738$	0.272454	−	1.29753i	0.0100292	−	0.0477626i
$739$	−7.86814	−	7.86814i	−0.289434	−	0.289434i	0.547422	−	0.836857i	$-0.315609\pi$
$739$	−7.86814	−	7.86814i	−0.289434	−	0.289434i	−0.836857	+	0.547422i	$0.815609\pi$
$740$	−7.38569	+	19.3189i	−0.271503	+	0.710176i
$741$	−33.4314	+	33.4314i	−1.22813	+	1.22813i
$742$	47.3910	−	30.9426i	1.73978	−	1.13594i
$743$	14.6248	+	14.6248i	0.536531	+	0.536531i	0.922508	−	0.385978i	$-0.126136\pi$
$743$	14.6248	+	14.6248i	0.536531	+	0.536531i	−0.385978	+	0.922508i	$0.626136\pi$
$744$	3.04924	−	4.26290i	0.111790	−	0.156285i
$745$	−15.1479	−	13.7375i	−0.554976	−	0.503305i
$746$	41.4546	+	8.70463i	1.51776	+	0.318699i
$747$	4.11909			0.150710
$748$	5.29874	+	2.32790i	0.193741	+	0.0851163i
$749$	31.0331	−	31.0331i	1.13392	−	1.13392i
$750$	23.4036	+	1.42031i	0.854577	+	0.0518622i
$751$			3.57162i			0.130330i	0.997874	+	0.0651652i	$0.0207574\pi$
$751$			3.57162i			0.130330i	−0.997874	+	0.0651652i	$0.979243\pi$
$752$	−1.89724	+	44.6211i	−0.0691852	+	1.62717i
$753$	21.4040	+	21.4040i	0.780007	+	0.780007i
$754$	−9.62237	−	14.7374i	−0.350426	−	0.536706i
$755$	−7.31008	+	0.356917i	−0.266041	+	0.0129895i
$756$	−32.5792	+	12.6907i	−1.18489	+	0.461557i
$757$		−	14.1212i		−	0.513243i	−0.966512	−	0.256621i	$-0.917391\pi$
$757$		−	14.1212i		−	0.513243i	0.966512	−	0.256621i	$-0.0826093\pi$
$758$	27.9367	−	18.2404i	1.01471	−	0.662522i
$759$			9.54111i			0.346320i
$760$	−7.74570	−	35.7671i	−0.280966	−	1.29741i
$761$			10.1618i			0.368364i	0.982892	+	0.184182i	$0.0589635\pi$
$761$			10.1618i			0.368364i	−0.982892	+	0.184182i	$0.941036\pi$
$762$	−15.4089	−	23.5999i	−0.558204	−	0.854935i
$763$		−	25.7440i		−	0.931994i
$764$	4.15812	−	9.46467i	0.150435	−	0.342420i
$765$	−3.48196	+	3.83943i	−0.125890	+	0.138815i
$766$	22.9322	−	14.9729i	0.828572	−	0.540992i
$767$	−40.4033	−	40.4033i	−1.45888	−	1.45888i
$768$	2.01399	−	23.6407i	0.0726736	−	0.853059i
$769$			0.681365i			0.0245707i	0.999925	+	0.0122853i	$0.00391064\pi$
$769$			0.681365i			0.0245707i	−0.999925	+	0.0122853i	$0.996089\pi$
$770$	9.68544	+	1.54501i	0.349039	+	0.0556784i
$771$	−18.3556	+	18.3556i	−0.661059	+	0.661059i
$772$	6.30263	+	16.1799i	0.226836	+	0.582326i
$773$	23.7986			0.855976			0.427988	−	0.903784i	$-0.359222\pi$
$773$	23.7986			0.855976			0.427988	+	0.903784i	$0.359222\pi$
$774$	−0.730700	+	3.47986i	−0.0262645	+	0.125081i
$775$	−0.608676	−	6.21834i	−0.0218643	−	0.223369i
$776$	−28.6109	+	4.74882i	−1.02707	+	0.170473i
$777$	15.0404	+	15.0404i	0.539572	+	0.539572i
$778$	29.2942	+	44.8664i	1.05025	+	1.60854i
$779$	4.78867	−	4.78867i	0.171572	−	0.171572i
$780$	−13.0487	+	34.1316i	−0.467217	+	1.22211i
$781$	4.69590	+	4.69590i	0.168033	+	0.168033i
$782$	25.7691	+	5.41099i	0.921501	+	0.193497i
$783$	−9.00234	+	9.00234i	−0.321717	+	0.321717i
$784$	7.71705	−	7.08758i	0.275609	−	0.253128i
$785$	−15.1827	+	0.741301i	−0.541895	+	0.0264582i
$786$	39.2941	−	25.6559i	1.40157	−	0.915116i
$787$		−	9.40986i		−	0.335425i	−0.985836	−	0.167713i	$-0.946362\pi$
$787$		−	9.40986i		−	0.335425i	0.985836	−	0.167713i	$-0.0536381\pi$
$788$	−16.2456	+	36.9781i	−0.578725	+	1.31729i
$789$	3.58809	+	3.58809i	0.127740	+	0.127740i
$790$	−48.9191	−	7.80353i	−1.74046	−	0.277637i
$791$	−64.4087			−2.29011
$792$	0.370973	+	2.23506i	0.0131820	+	0.0794194i
$793$	−23.8214	+	23.8214i	−0.845924	+	0.845924i
$794$	−37.3230	−	7.83708i	−1.32454	−	0.278127i
$795$	−42.7356	+	2.08658i	−1.51568	+	0.0740033i
$796$	12.9808	−	29.5467i	0.460091	−	1.04726i
$797$	−51.8776			−1.83760			−0.918800	−	0.394724i	$-0.870840\pi$
$797$	−51.8776			−1.83760			−0.918800	+	0.394724i	$0.870840\pi$
$798$	−36.8330	−	7.73419i	−1.30388	−	0.273787i
$799$	32.3100			1.14305
$800$	−16.7435	−	22.7959i	−0.591973	−	0.805958i
$801$	−8.23878			−0.291103
$802$	22.0810	+	4.63656i	0.779707	+	0.163723i
$803$	0.502673			0.0177389
$804$	4.27948	−	9.74091i	0.150926	−	0.343535i
$805$	44.5690	−	2.17609i	1.57085	−	0.0766972i
$806$	9.52959	+	2.00102i	0.335666	+	0.0704830i
$807$	1.92260	−	1.92260i	0.0676788	−	0.0676788i
$808$	−42.3978	+	7.03715i	−1.49155	+	0.247566i
$809$	28.3189			0.995641			0.497820	−	0.867280i	$-0.334134\pi$
$809$	28.3189			0.995641			0.497820	+	0.867280i	$0.334134\pi$
$810$	18.5971	+	2.96660i	0.653437	+	0.104236i
$811$	10.7735	+	10.7735i	0.378308	+	0.378308i	0.870492	−	0.492183i	$-0.163801\pi$
$811$	10.7735	+	10.7735i	0.378308	+	0.378308i	−0.492183	+	0.870492i	$0.663801\pi$
$812$	5.63552	−	12.8275i	0.197768	−	0.450158i
$813$			12.7758i			0.448066i
$814$	5.47643	−	3.57567i	0.191949	−	0.125327i
$815$	−14.0474	+	0.685868i	−0.492059	+	0.0240249i
$816$	−17.1491	−	0.729162i	−0.600340	−	0.0255258i
$817$	−12.8428	+	12.8428i	−0.449314	+	0.449314i
$818$	1.94182	+	0.407744i	0.0678943	+	0.0142564i
$819$	−9.67966	−	9.67966i	−0.338235	−	0.338235i
$820$	1.86907	−	4.88897i	0.0652709	−	0.170730i
$821$	−5.79112	+	5.79112i	−0.202112	+	0.202112i	−0.800904	−	0.598793i	$-0.795647\pi$
$821$	−5.79112	+	5.79112i	−0.202112	+	0.202112i	0.598793	+	0.800904i	$0.295647\pi$
$822$	9.47350	+	14.5094i	0.330426	+	0.506075i
$823$	−36.2734	−	36.2734i	−1.26441	−	1.26441i	−0.948932	−	0.315481i	$-0.897834\pi$
$823$	−36.2734	−	36.2734i	−1.26441	−	1.26441i	−0.315481	−	0.948932i	$-0.602166\pi$
$824$	0.215811	+	1.30023i	0.00751813	+	0.0452957i
$825$	−5.72863	−	4.70714i	−0.199445	−	0.163882i
$826$	9.34712	−	44.5144i	0.325228	−	1.54885i
$827$	35.0757			1.21970			0.609852	−	0.792516i	$-0.291229\pi$
$827$	35.0757			1.21970			0.609852	+	0.792516i	$0.291229\pi$
$828$	3.74140	+	9.60479i	0.130023	+	0.333789i
$829$	−4.44003	+	4.44003i	−0.154209	+	0.154209i	−0.779995	−	0.625786i	$-0.784778\pi$
$829$	−4.44003	+	4.44003i	−0.154209	+	0.154209i	0.625786	+	0.779995i	$0.284778\pi$
$830$	16.0583	+	2.56160i	0.557391	+	0.0889145i
$831$		−	37.4532i		−	1.29924i
$832$	41.7166	−	14.2405i	1.44626	−	0.493699i
$833$	−5.36000	−	5.36000i	−0.185713	−	0.185713i
$834$	−25.5796	+	16.7014i	−0.885748	+	0.578322i
$835$	14.3569	−	15.8308i	0.496840	−	0.547847i
$836$	−4.65484	+	10.5953i	−0.160991	+	0.366446i
$837$		−	7.04346i		−	0.243458i
$838$	−14.2686	−	21.8535i	−0.492900	−	0.754916i
$839$			1.93776i			0.0668990i	0.999440	+	0.0334495i	$0.0106493\pi$
$839$			1.93776i			0.0668990i	−0.999440	+	0.0334495i	$0.989351\pi$
$840$	−28.4291	+	6.15660i	−0.980899	+	0.212423i
$841$			23.8983i			0.824078i
$842$	−6.76453	+	4.41670i	−0.233121	+	0.152209i
$843$		−	27.6796i		−	0.953337i
$844$	−18.7637	+	7.30912i	−0.645873	+	0.251590i
$845$	−38.7727	+	1.89309i	−1.33382	+	0.0651243i
$846$	6.91493	+	10.5908i	0.237740	+	0.364118i
$847$	−2.19311	−	2.19311i	−0.0753562	−	0.0753562i
$848$	34.9136	+	38.0144i	1.19894	+	1.30542i
$849$			20.6607i			0.709072i
$850$	−15.9621	+	12.8026i	−0.547496	+	0.439127i
$851$	21.0408	−	21.0408i	0.721270	−	0.721270i
$852$	−18.0323	−	7.92216i	−0.617778	−	0.271409i
$853$	−56.6627			−1.94009			−0.970046	−	0.242921i	$-0.921894\pi$
$853$	−56.6627			−1.94009			−0.970046	+	0.242921i	$0.921894\pi$
$854$	−26.2453	−	5.51097i	−0.898094	−	0.188582i
$855$	−7.67728	−	6.96249i	−0.262558	−	0.238112i
$856$	32.5524	+	23.2846i	1.11262	+	0.795852i
$857$	−19.6058	−	19.6058i	−0.669722	−	0.669722i	0.287930	−	0.957652i	$-0.407033\pi$
$857$	−19.6058	−	19.6058i	−0.669722	−	0.669722i	−0.957652	+	0.287930i	$0.907033\pi$
$858$	9.67548	−	6.31732i	0.330315	−	0.215670i
$859$	−14.2892	+	14.2892i	−0.487541	+	0.487541i	−0.907529	−	0.419989i	$-0.862034\pi$
$859$	−14.2892	+	14.2892i	−0.487541	+	0.487541i	0.419989	+	0.907529i	$0.362034\pi$
$860$	−5.01271	+	13.1118i	−0.170932	+	0.447109i
$861$	−3.80623	−	3.80623i	−0.129716	−	0.129716i
$862$	−9.00706	+	42.8949i	−0.306782	+	1.46101i
$863$	39.3071	−	39.3071i	1.33803	−	1.33803i	0.440063	−	0.897967i	$-0.354956\pi$
$863$	39.3071	−	39.3071i	1.33803	−	1.33803i	0.897967	−	0.440063i	$-0.145044\pi$
$864$	−16.2818	−	27.4145i	−0.553919	−	0.932659i
$865$	−0.681088	−	13.9495i	−0.0231577	−	0.474297i
$866$	−0.410480	−	0.628683i	−0.0139487	−	0.0213635i
$867$		−	12.7916i		−	0.434424i
$868$	2.81353	+	7.22278i	0.0954973	+	0.245157i
$869$	11.0769	+	11.0769i	0.375759	+	0.375759i
$870$	−8.57583	+	6.21622i	−0.290748	+	0.210749i
$871$	19.7667			0.669771
$872$	23.1603	−	3.84412i	0.784305	−	0.130178i
$873$	−5.80790	+	5.80790i	−0.196568	+	0.196568i
$874$	−10.8198	+	51.5276i	−0.365984	+	1.74295i
$875$	−20.6817	+	27.8335i	−0.699168	+	0.940943i
$876$	−1.38915	+	0.541122i	−0.0469350	+	0.0182828i
$877$	31.9993			1.08054			0.540270	−	0.841492i	$-0.318322\pi$
$877$	31.9993			1.08054			0.540270	+	0.841492i	$0.318322\pi$
$878$	−5.55225	+	26.4418i	−0.187379	+	0.892369i
$879$	−33.2930			−1.12295
$880$	0.0562884	+	8.94409i	0.00189748	+	0.301505i
$881$	−19.4378			−0.654876			−0.327438	−	0.944873i	$-0.606185\pi$
$881$	−19.4378			−0.654876			−0.327438	+	0.944873i	$0.606185\pi$
$882$	0.609795	−	2.90406i	0.0205329	−	0.0977849i
$883$	21.0141			0.707181			0.353591	−	0.935400i	$-0.384961\pi$
$883$	21.0141			0.707181			0.353591	+	0.935400i	$0.384961\pi$
$884$	−11.5749	−	29.7147i	−0.389307	−	0.999413i
$885$	−23.0995	+	25.4710i	−0.776481	+	0.856197i
$886$	0.0270654	−	0.128895i	0.000909280	−	0.00433032i
$887$	−35.8516	+	35.8516i	−1.20378	+	1.20378i	−0.230773	+	0.973008i	$0.574125\pi$
$887$	−35.8516	+	35.8516i	−1.20378	+	1.20378i	−0.973008	+	0.230773i	$0.925875\pi$
$888$	−11.2851	+	15.7768i	−0.378702	+	0.529434i
$889$	41.6838			1.39803
$890$	−32.1189	−	5.12358i	−1.07663	−	0.171743i
$891$	−4.21102	−	4.21102i	−0.141075	−	0.141075i
$892$	−21.8783	+	8.52235i	−0.732539	+	0.285349i
$893$			64.6069i			2.16199i
$894$	−10.4852	−	16.0589i	−0.350676	−	0.537089i
$895$	7.35431	+	6.66959i	0.245828	+	0.222940i
$896$	27.6471	+	21.6086i	0.923625	+	0.721892i
$897$	37.1738	−	37.1738i	1.24120	−	1.24120i
$898$	−0.0494819	+	0.235651i	−0.00165123	+	0.00786376i
$899$	1.99581	+	1.99581i	0.0665641	+	0.0665641i
$900$	−7.61270	−	2.49216i	−0.253757	−	0.0830719i
$901$	26.4035	−	26.4035i	0.879628	−	0.879628i
$902$	−1.38590	+	0.904885i	−0.0461456	+	0.0301294i
$903$	10.2080	+	10.2080i	0.339701	+	0.339701i
$904$	−9.61758	−	57.9445i	−0.319876	−	1.92721i
$905$	3.48276	−	3.84031i	0.115771	−	0.127656i
$906$	−6.71754	−	1.41055i	−0.223175	−	0.0468623i
$907$	−19.9911			−0.663793			−0.331896	−	0.943316i	$-0.607688\pi$
$907$	−19.9911			−0.663793			−0.331896	+	0.943316i	$0.607688\pi$
$908$	−15.0328	+	34.2175i	−0.498880	+	1.13555i
$909$	−8.60658	+	8.60658i	−0.285462	+	0.285462i
$910$	−31.7165	−	43.7558i	−1.05139	−	1.45049i
$911$			35.4617i			1.17490i	0.809261	+	0.587449i	$0.199868\pi$
$911$			35.4617i			1.17490i	−0.809261	+	0.587449i	$0.800132\pi$
$912$	1.45803	−	34.2913i	0.0482801	−	1.13550i
$913$	−3.63614	−	3.63614i	−0.120339	−	0.120339i
$914$	1.99053	+	3.04866i	0.0658409	+	0.100841i
$915$	15.0174	+	13.6192i	0.496461	+	0.450238i
$916$	3.60651	+	9.25849i	0.119162	+	0.305909i
$917$			69.4039i			2.29192i
$918$	−19.3145	+	12.6109i	−0.637475	+	0.416220i
$919$			26.0319i			0.858715i	0.903135	+	0.429357i	$0.141260\pi$
$919$			26.0319i			0.858715i	−0.903135	+	0.429357i	$0.858740\pi$
$920$	8.61279	+	39.7710i	0.283955	+	1.31121i
$921$		−	44.6635i		−	1.47171i
$922$	−17.7961	−	27.2561i	−0.586082	−	0.897632i
$923$		−	36.5921i		−	1.20444i
$924$	8.42158	+	3.69986i	0.277050	+	0.121716i
$925$	2.25268	+	23.0138i	0.0740676	+	0.756688i
$926$	−17.7059	+	11.5605i	−0.581852	+	0.379903i
$927$	0.263941	+	0.263941i	0.00866897	+	0.00866897i
$928$	12.3816	+	3.15451i	0.406447	+	0.103552i
$929$			16.9766i			0.556984i	0.960439	+	0.278492i	$0.0898345\pi$
$929$			16.9766i			0.556984i	−0.960439	+	0.278492i	$0.910165\pi$
$930$	0.923085	−	5.78667i	0.0302691	−	0.189752i
$931$	10.7178	−	10.7178i	0.351262	−	0.351262i
$932$	48.1498	−	18.7560i	1.57720	−	0.614374i
$933$	9.10014			0.297925
$934$	3.07851	−	14.6610i	0.100732	−	0.479723i
$935$	6.46298	−	0.315557i	0.211362	−	0.0103198i
$936$	7.26281	−	10.1536i	0.237392	−	0.331880i
$937$	−10.0622	−	10.0622i	−0.328717	−	0.328717i	0.523381	−	0.852099i	$-0.324670\pi$
$937$	−10.0622	−	10.0622i	−0.328717	−	0.328717i	−0.852099	+	0.523381i	$0.824670\pi$
$938$	8.60253	+	13.1755i	0.280883	+	0.430195i
$939$	1.33183	−	1.33183i	0.0434626	−	0.0434626i
$940$	20.3716	+	45.5884i	0.664449	+	1.48693i
$941$	27.9672	+	27.9672i	0.911706	+	0.911706i	0.996406	−	0.0847003i	$-0.0269933\pi$
$941$	27.9672	+	27.9672i	0.911706	+	0.911706i	−0.0847003	+	0.996406i	$0.526993\pi$
$942$	−13.9520	−	2.92965i	−0.454582	−	0.0954531i
$943$	−5.32474	+	5.32474i	−0.173397	+	0.173397i
$944$	41.4426	+	1.76209i	1.34884	+	0.0573512i
$945$	−26.2603	+	28.9563i	−0.854248	+	0.941948i
$946$	3.71688	−	2.42683i	0.120846	−	0.0789029i
$947$		−	53.1835i		−	1.72823i	−0.503294	−	0.864115i	$-0.667879\pi$
$947$		−	53.1835i		−	1.72823i	0.503294	−	0.864115i	$-0.332121\pi$
$948$	−42.5356	−	18.6872i	−1.38149	−	0.606931i
$949$	−1.95850	−	1.95850i	−0.0635756	−	0.0635756i
$950$	−25.6000	−	31.9177i	−0.830575	−	1.03555i
$951$	47.8452			1.55149
$952$	14.7688	−	20.6471i	0.478660	−	0.669178i
$953$	27.8188	−	27.8188i	0.901141	−	0.901141i	−0.0943941	−	0.995535i	$-0.530091\pi$
$953$	27.8188	−	27.8188i	0.901141	−	0.901141i	0.995535	+	0.0943941i	$0.0300914\pi$
$954$	14.3055	+	3.00387i	0.463158	+	0.0972538i
$955$	−0.563651	−	11.5443i	−0.0182393	−	0.373563i
$956$	−28.1616	−	12.3723i	−0.910812	−	0.400147i
$957$	3.34942			0.108271
$958$	−17.8845	−	3.75537i	−0.577820	−	0.121331i
$959$	−25.6276			−0.827557
$960$	−9.78378	−	24.6566i	−0.315770	−	0.795790i
$961$	29.4385			0.949628
$962$	−35.2686	−	7.40569i	−1.13710	−	0.238769i
$963$	11.3347			0.365255
$964$	−5.59235	−	2.45689i	−0.180117	−	0.0791310i
$965$	14.3806	+	13.0417i	0.462929	+	0.419828i
$966$	40.9563	+	8.59999i	1.31775	+	0.276700i
$967$	3.26348	−	3.26348i	0.104947	−	0.104947i	−0.652684	−	0.757630i	$-0.726357\pi$
$967$	3.26348	−	3.26348i	0.104947	−	0.104947i	0.757630	+	0.652684i	$0.226357\pi$
$968$	1.64553	−	2.30049i	0.0528893	−	0.0739404i
$969$	−24.8302			−0.797662
$970$	−26.2540	+	19.0303i	−0.842964	+	0.611025i
$971$	−22.2197	−	22.2197i	−0.713064	−	0.713064i	0.254111	−	0.967175i	$-0.418217\pi$
$971$	−22.2197	−	22.2197i	−0.713064	−	0.713064i	−0.967175	+	0.254111i	$0.918217\pi$
$972$	−14.7924	−	6.49874i	−0.474466	−	0.208447i
$973$		−	45.1804i		−	1.44842i
$974$	−33.5468	+	21.9034i	−1.07491	+	0.701829i
$975$	3.97992	+	40.6596i	0.127459	+	1.30215i
$976$	1.03891	−	24.4341i	0.0332548	−	0.782118i
$977$	26.3478	−	26.3478i	0.842940	−	0.842940i	−0.146300	−	0.989240i	$-0.546736\pi$
$977$	26.3478	−	26.3478i	0.842940	−	0.842940i	0.989240	+	0.146300i	$0.0467364\pi$
$978$	−12.9087	−	2.71058i	−0.412776	−	0.0866746i
$979$	7.27281	+	7.27281i	0.232440	+	0.232440i
$980$	4.18328	−	10.9423i	0.133630	−	0.349538i
$981$	4.70144	−	4.70144i	0.150105	−	0.150105i
$982$	18.9449	+	29.0156i	0.604555	+	0.925926i
$983$	−3.02980	−	3.02980i	−0.0966357	−	0.0966357i	0.657136	−	0.753772i	$-0.271768\pi$
$983$	−3.02980	−	3.02980i	−0.0966357	−	0.0966357i	−0.753772	+	0.657136i	$0.771768\pi$
$984$	2.85588	−	3.99258i	0.0910422	−	0.127279i
$985$	2.20216	+	45.1029i	0.0701667	+	1.43710i
$986$	1.89954	−	9.04628i	0.0604935	−	0.288092i
$987$	51.3522			1.63456
$988$	59.4172	−	23.1451i	1.89031	−	0.736344i
$989$	14.2805	−	14.2805i	0.454094	−	0.454094i
$990$	1.48663	+	2.05094i	0.0472481	+	0.0651830i
$991$		−	49.6108i		−	1.57594i	−0.615715	−	0.787969i	$-0.711133\pi$
$991$		−	49.6108i		−	1.57594i	0.615715	−	0.787969i	$-0.288867\pi$
$992$	−6.07777	+	3.60967i	−0.192969	+	0.114607i
$993$	2.41824	+	2.41824i	0.0767404	+	0.0767404i
$994$	24.3904	−	15.9250i	0.773616	−	0.505110i
$995$	−1.75960	−	36.0387i	−0.0557831	−	1.14251i
$996$	13.9628	+	6.13429i	0.442429	+	0.194372i
$997$		−	4.40815i		−	0.139608i	−0.997561	−	0.0698038i	$-0.977763\pi$
$997$		−	4.40815i		−	0.139608i	0.997561	−	0.0698038i	$-0.0222373\pi$
$998$	−22.6242	−	34.6508i	−0.716158	−	1.09685i
$999$			26.0675i			0.824739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bk.b.243.9	yes	236
5.2	odd	4		880.2.s.b.67.67	✓	236
16.11	odd	4		880.2.s.b.683.67	yes	236
80.27	even	4	inner	880.2.bk.b.507.9	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.s.b.67.67	✓	236	5.2	odd	4
880.2.s.b.683.67	yes	236	16.11	odd	4
880.2.bk.b.243.9	yes	236	1.1	even	1	trivial
880.2.bk.b.507.9	yes	236	80.27	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38403 - 0.290618i) q^{2} -1.48289 q^{3} +(1.83108 + 0.804450i) q^{4} +(2.23341 - 0.109047i) q^{5} +(2.05237 + 0.430957i) q^{6} +(-2.19311 + 2.19311i) q^{7} +(-2.30049 - 1.64553i) q^{8} -0.801024 q^{9} +(-3.12280 - 0.498145i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-2.71530 - 1.19291i) q^{12} -5.51002i q^{13} +(3.67269 - 2.39798i) q^{14} +(-3.31191 + 0.161705i) q^{15} +(2.70572 + 2.94603i) q^{16} +(2.04621 - 2.04621i) q^{17} +(1.10864 + 0.232792i) q^{18} +(4.09158 + 4.09158i) q^{19} +(4.17727 + 1.59699i) q^{20} +(3.25215 - 3.25215i) q^{21} +(-0.773159 - 1.18416i) q^{22} +(-4.54961 - 4.54961i) q^{23} +(3.41138 + 2.44015i) q^{24} +(4.97622 - 0.487092i) q^{25} +(-1.60131 + 7.62604i) q^{26} +5.63652 q^{27} +(-5.78002 + 2.25152i) q^{28} +(-1.59715 + 1.59715i) q^{29} +(4.63078 + 0.738697i) q^{30} -1.24961i q^{31} +(-2.88863 - 4.86372i) q^{32} +(-1.04856 - 1.04856i) q^{33} +(-3.42668 + 2.23735i) q^{34} +(-4.65896 + 5.13726i) q^{35} +(-1.46674 - 0.644384i) q^{36} +4.62475i q^{37} +(-4.47378 - 6.85196i) q^{38} +8.17078i q^{39} +(-5.31736 - 3.42428i) q^{40} -1.17037i q^{41} +(-5.44622 + 3.55594i) q^{42} +3.13884i q^{43} +(0.725938 + 1.86360i) q^{44} +(-1.78901 + 0.0873491i) q^{45} +(4.97460 + 7.61900i) q^{46} +(7.89511 + 7.89511i) q^{47} +(-4.01230 - 4.36865i) q^{48} -2.61948i q^{49} +(-7.02880 - 0.772031i) q^{50} +(-3.03431 + 3.03431i) q^{51} +(4.43254 - 10.0893i) q^{52} +12.9036 q^{53} +(-7.80111 - 1.63808i) q^{54} +(1.65637 + 1.50215i) q^{55} +(8.65405 - 1.43639i) q^{56} +(-6.06738 - 6.06738i) q^{57} +(2.67466 - 1.74634i) q^{58} +(7.33270 - 7.33270i) q^{59} +(-6.19446 - 2.36817i) q^{60} +(-4.32329 - 4.32329i) q^{61} +(-0.363160 + 1.72950i) q^{62} +(1.75674 - 1.75674i) q^{63} +(2.58447 + 7.57103i) q^{64} +(-0.600850 - 12.3061i) q^{65} +(1.14651 + 1.75598i) q^{66} +3.58742i q^{67} +(5.39284 - 2.10070i) q^{68} +(6.74659 + 6.74659i) q^{69} +(7.94113 - 5.75615i) q^{70} +6.64101 q^{71} +(1.84274 + 1.31811i) q^{72} +(0.355443 - 0.355443i) q^{73} +(1.34404 - 6.40080i) q^{74} +(-7.37920 + 0.722305i) q^{75} +(4.20054 + 10.7835i) q^{76} -3.10153 q^{77} +(2.37458 - 11.3086i) q^{78} +15.6652 q^{79} +(6.36423 + 6.28463i) q^{80} -5.95529 q^{81} +(-0.340132 + 1.61983i) q^{82} -5.14227 q^{83} +(8.57115 - 3.33876i) q^{84} +(4.34688 - 4.79315i) q^{85} +(0.912206 - 4.34426i) q^{86} +(2.36840 - 2.36840i) q^{87} +(-0.463124 - 2.79025i) q^{88} +10.2853 q^{89} +(2.50144 + 0.399027i) q^{90} +(12.0841 + 12.0841i) q^{91} +(-4.67077 - 11.9906i) q^{92} +1.85304i q^{93} +(-8.63261 - 13.2215i) q^{94} +(9.58433 + 8.69199i) q^{95} +(4.28353 + 7.21239i) q^{96} +(7.25059 - 7.25059i) q^{97} +(-0.761269 + 3.62544i) q^{98} +(-0.566410 - 0.566410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) \) 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

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