LMFDB - Embedded newform 483.2.m.a.137.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(137,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("483.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.m (of order $6$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.20
Character	$\chi$	$=$	483.137
Dual form			483.2.m.a.275.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.935072 + 0.539864i) q^{2} +(-0.991443 - 1.42023i) q^{3} +(-0.417093 + 0.722427i) q^{4} +(0.281343 + 0.487300i) q^{5} +(1.69380 + 0.792769i) q^{6} +(1.64560 - 2.07172i) q^{7} -3.06015i q^{8} +(-1.03408 + 2.81615i) q^{9} +O(q^{10})$	\(q+(-0.935072 + 0.539864i) q^{2} +(-0.991443 - 1.42023i) q^{3} +(-0.417093 + 0.722427i) q^{4} +(0.281343 + 0.487300i) q^{5} +(1.69380 + 0.792769i) q^{6} +(1.64560 - 2.07172i) q^{7} -3.06015i q^{8} +(-1.03408 + 2.81615i) q^{9} +(-0.526152 - 0.303774i) q^{10} +(-1.71744 + 2.97470i) q^{11} +(1.43953 - 0.123878i) q^{12} +0.0798910 q^{13} +(-0.420304 + 2.82560i) q^{14} +(0.413141 - 0.882701i) q^{15} +(0.817880 + 1.41661i) q^{16} +(2.35212 - 4.07399i) q^{17} +(-0.553395 - 3.19156i) q^{18} +(-2.32346 + 1.34145i) q^{19} -0.469385 q^{20} +(-4.57382 - 0.283126i) q^{21} -3.70875i q^{22} +(-0.200901 - 4.79162i) q^{23} +(-4.34611 + 3.03397i) q^{24} +(2.34169 - 4.05593i) q^{25} +(-0.0747039 + 0.0431303i) q^{26} +(5.02479 - 1.32342i) q^{27} +(0.810298 + 2.05292i) q^{28} +0.533757i q^{29} +(0.0902221 + 1.04843i) q^{30} +(4.67459 - 8.09663i) q^{31} +(3.77079 + 2.17706i) q^{32} +(5.92749 - 0.510088i) q^{33} +5.07930i q^{34} +(1.47253 + 0.219036i) q^{35} +(-1.60315 - 1.92164i) q^{36} +(-7.68608 + 4.43756i) q^{37} +(1.44840 - 2.50871i) q^{38} +(-0.0792074 - 0.113463i) q^{39} +(1.49121 - 0.860952i) q^{40} -4.72414i q^{41} +(4.42970 - 2.20450i) q^{42} -10.4180i q^{43} +(-1.43267 - 2.48146i) q^{44} +(-1.66324 + 0.288394i) q^{45} +(2.77468 + 4.37205i) q^{46} +(11.2492 - 6.49472i) q^{47} +(1.20102 - 2.56606i) q^{48} +(-1.58403 - 6.81842i) q^{49} +5.05678i q^{50} +(-8.11798 + 0.698589i) q^{51} +(-0.0333220 + 0.0577154i) q^{52} +(3.69989 - 6.40840i) q^{53} +(-3.98408 + 3.95020i) q^{54} -1.93276 q^{55} +(-6.33977 - 5.03577i) q^{56} +(4.20874 + 1.96987i) q^{57} +(-0.288157 - 0.499102i) q^{58} +(0.984330 + 0.568303i) q^{59} +(0.465369 + 0.666633i) q^{60} +(-7.19129 + 4.15189i) q^{61} +10.0946i q^{62} +(4.13258 + 6.77656i) q^{63} -7.97279 q^{64} +(0.0224768 + 0.0389309i) q^{65} +(-5.26726 + 3.67701i) q^{66} +(-4.27724 - 2.46947i) q^{67} +(1.96211 + 3.39847i) q^{68} +(-6.60600 + 5.03594i) q^{69} +(-1.49517 + 0.590150i) q^{70} +6.54622i q^{71} +(8.61783 + 3.16445i) q^{72} +(-4.22043 + 7.31000i) q^{73} +(4.79136 - 8.29887i) q^{74} +(-8.08199 + 0.695492i) q^{75} -2.23804i q^{76} +(3.33652 + 8.45321i) q^{77} +(0.135319 + 0.0633351i) q^{78} +(7.31051 - 4.22073i) q^{79} +(-0.460209 + 0.797106i) q^{80} +(-6.86135 - 5.82425i) q^{81} +(2.55039 + 4.41741i) q^{82} +3.31513 q^{83} +(2.11225 - 3.18616i) q^{84} +2.64701 q^{85} +(5.62428 + 9.74154i) q^{86} +(0.758056 - 0.529190i) q^{87} +(9.10304 + 5.25564i) q^{88} +(8.58122 + 14.8631i) q^{89} +(1.39956 - 1.16759i) q^{90} +(0.131468 - 0.165512i) q^{91} +(3.54539 + 1.85342i) q^{92} +(-16.1336 + 1.38837i) q^{93} +(-7.01254 + 12.1461i) q^{94} +(-1.30738 - 0.754815i) q^{95} +(-0.646597 - 7.51380i) q^{96} -0.273248i q^{97} +(5.16221 + 5.52055i) q^{98} +(-6.60121 - 7.91266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9}+O(q^{10}) $ 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9	$ 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9} + 14 q^{12} - 16 q^{13} - 60 q^{16} - 10 q^{18} - 24 q^{24} - 40 q^{25} - 20 q^{27} - 4 q^{31} + 64 q^{36} - 12 q^{39} - 20 q^{46} + 140 q^{48} - 48 q^{49} - 76 q^{52} - 2 q^{54} + 72 q^{55} - 28 q^{58} - 128 q^{64} - 20 q^{69} - 68 q^{70} + 6 q^{72} + 20 q^{73} + 20 q^{75} - 156 q^{78} - 62 q^{81} + 80 q^{82} + 112 q^{85} + 46 q^{87} - 38 q^{93} + 36 q^{94} + 72 q^{96}+O(q^{100}) $ 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9 + 14 * q^12 - 16 * q^13 - 60 * q^16 - 10 * q^18 - 24 * q^24 - 40 * q^25 - 20 * q^27 - 4 * q^31 + 64 * q^36 - 12 * q^39 - 20 * q^46 + 140 * q^48 - 48 * q^49 - 76 * q^52 - 2 * q^54 + 72 * q^55 - 28 * q^58 - 128 * q^64 - 20 * q^69 - 68 * q^70 + 6 * q^72 + 20 * q^73 + 20 * q^75 - 156 * q^78 - 62 * q^81 + 80 * q^82 + 112 * q^85 + 46 * q^87 - 38 * q^93 + 36 * q^94 + 72 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.935072	+	0.539864i	−0.661196	+	0.381742i	−0.792732	−	0.609570i	$-0.791342\pi$
$2$	−0.935072	+	0.539864i	−0.661196	+	0.381742i	0.131537	+	0.991311i	$0.458009\pi$
$3$	−0.991443	−	1.42023i	−0.572410	−	0.819968i
$3$	−0.991443	−	1.42023i	−0.572410	−	0.819968i
$4$	−0.417093	+	0.722427i	−0.208547	+	0.361213i
$5$	0.281343	+	0.487300i	0.125820	+	0.217927i	0.922053	−	0.387063i	$-0.126510\pi$
$5$	0.281343	+	0.487300i	0.125820	+	0.217927i	−0.796233	+	0.604990i	$0.793177\pi$
$6$	1.69380	+	0.792769i	0.691491	+	0.323647i
$7$	1.64560	−	2.07172i	0.621976	−	0.783036i
$7$	1.64560	−	2.07172i	0.621976	−	0.783036i
$8$		−	3.06015i		−	1.08193i
$9$	−1.03408	+	2.81615i	−0.344694	+	0.938715i
$10$	−0.526152	−	0.303774i	−0.166384	−	0.0960618i
$11$	−1.71744	+	2.97470i	−0.517829	+	0.896906i	0.481957	+	0.876195i	$0.339926\pi$
$11$	−1.71744	+	2.97470i	−0.517829	+	0.896906i	−0.999786	+	0.0207109i	$0.993407\pi$
$12$	1.43953	−	0.123878i	0.415557	−	0.0357606i
$13$	0.0798910			0.0221578			0.0110789	−	0.999939i	$-0.496473\pi$
$13$	0.0798910			0.0221578			0.0110789	+	0.999939i	$0.496473\pi$
$14$	−0.420304	+	2.82560i	−0.112331	+	0.755174i
$15$	0.413141	−	0.882701i	0.106673	−	0.227912i
$16$	0.817880	+	1.41661i	0.204470	+	0.354152i
$17$	2.35212	−	4.07399i	0.570473	−	0.988088i	−0.426045	−	0.904702i	$-0.640093\pi$
$17$	2.35212	−	4.07399i	0.570473	−	0.988088i	0.996517	−	0.0833856i	$-0.0265733\pi$
$18$	−0.553395	−	3.19156i	−0.130436	−	0.752259i
$19$	−2.32346	+	1.34145i	−0.533038	+	0.307750i	−0.742253	−	0.670120i	$-0.766243\pi$
$19$	−2.32346	+	1.34145i	−0.533038	+	0.307750i	0.209214	+	0.977870i	$0.432909\pi$
$20$	−0.469385			−0.104958
$21$	−4.57382	−	0.283126i	−0.998090	−	0.0617831i
$22$		−	3.70875i		−	0.790707i
$23$	−0.200901	−	4.79162i	−0.0418907	−	0.999122i
$23$	−0.200901	−	4.79162i	−0.0418907	−	0.999122i
$24$	−4.34611	+	3.03397i	−0.887145	+	0.619306i
$25$	2.34169	−	4.05593i	0.468338	−	0.811186i
$26$	−0.0747039	+	0.0431303i	−0.0146506	+	0.00845855i
$27$	5.02479	−	1.32342i	0.967022	−	0.254692i
$28$	0.810298	+	2.05292i	0.153132	+	0.387966i
$29$			0.533757i			0.0991163i	0.998771	+	0.0495581i	$0.0157813\pi$
$29$			0.533757i			0.0991163i	−0.998771	+	0.0495581i	$0.984219\pi$
$30$	0.0902221	+	1.04843i	0.0164722	+	0.191416i
$31$	4.67459	−	8.09663i	0.839581	−	1.45420i	−0.0506642	−	0.998716i	$-0.516134\pi$
$31$	4.67459	−	8.09663i	0.839581	−	1.45420i	0.890245	−	0.455481i	$-0.150533\pi$
$32$	3.77079	+	2.17706i	0.666587	+	0.384854i
$33$	5.92749	−	0.510088i	1.03184	−	0.0887949i
$34$			5.07930i			0.871093i
$35$	1.47253	+	0.219036i	0.248902	+	0.0370238i
$36$	−1.60315	−	1.92164i	−0.267192	−	0.320274i
$37$	−7.68608	+	4.43756i	−1.26358	+	0.729530i	−0.973766	−	0.227552i	$-0.926928\pi$
$37$	−7.68608	+	4.43756i	−1.26358	+	0.729530i	−0.289817	+	0.957082i	$0.593594\pi$
$38$	1.44840	−	2.50871i	0.234962	−	0.406966i
$39$	−0.0792074	−	0.113463i	−0.0126833	−	0.0181687i
$40$	1.49121	−	0.860952i	0.235782	−	0.136129i
$41$		−	4.72414i		−	0.737786i	−0.929472	−	0.368893i	$-0.879737\pi$
$41$		−	4.72414i		−	0.737786i	0.929472	−	0.368893i	$-0.120263\pi$
$42$	4.42970	−	2.20450i	0.683518	−	0.340162i
$43$		−	10.4180i		−	1.58872i	−0.607445	−	0.794362i	$-0.707806\pi$
$43$		−	10.4180i		−	1.58872i	0.607445	−	0.794362i	$-0.292194\pi$
$44$	−1.43267	−	2.48146i	−0.215983	−	0.374094i
$45$	−1.66324	+	0.288394i	−0.247941	+	0.0429913i
$46$	2.77468	+	4.37205i	0.409104	+	0.644624i
$47$	11.2492	−	6.49472i	1.64086	−	0.947353i	0.660336	−	0.750970i	$-0.270414\pi$
$47$	11.2492	−	6.49472i	1.64086	−	0.947353i	0.980527	−	0.196383i	$-0.0629195\pi$
$48$	1.20102	−	2.56606i	0.173353	−	0.370379i
$49$	−1.58403	−	6.81842i	−0.226291	−	0.974060i
$50$			5.05678i			0.715137i
$51$	−8.11798	+	0.698589i	−1.13674	+	0.0978220i
$52$	−0.0333220	+	0.0577154i	−0.00462093	+	0.00800369i
$53$	3.69989	−	6.40840i	0.508219	−	0.880262i	−0.491735	−	0.870745i	$-0.663637\pi$
$53$	3.69989	−	6.40840i	0.508219	−	0.880262i	0.999955	−	0.00951697i	$-0.00302939\pi$
$54$	−3.98408	+	3.95020i	−0.542165	+	0.537554i
$55$	−1.93276			−0.260614
$56$	−6.33977	−	5.03577i	−0.847188	−	0.672933i
$57$	4.20874	+	1.96987i	0.557461	+	0.260915i
$58$	−0.288157	−	0.499102i	−0.0378368	−	0.0655353i
$59$	0.984330	+	0.568303i	0.128149	+	0.0739867i	0.562704	−	0.826658i	$-0.309761\pi$
$59$	0.984330	+	0.568303i	0.128149	+	0.0739867i	−0.434555	+	0.900645i	$0.643094\pi$
$60$	0.465369	+	0.666633i	0.0600788	+	0.0860619i
$61$	−7.19129	+	4.15189i	−0.920750	+	0.531596i	−0.883874	−	0.467724i	$-0.845074\pi$
$61$	−7.19129	+	4.15189i	−0.920750	+	0.531596i	−0.0368761	+	0.999320i	$0.511741\pi$
$62$			10.0946i			1.28201i
$63$	4.13258	+	6.77656i	0.520656	+	0.853766i
$64$	−7.97279			−0.996599
$65$	0.0224768	+	0.0389309i	0.00278790	+	0.00482879i
$66$	−5.26726	+	3.67701i	−0.648355	+	0.452609i
$67$	−4.27724	−	2.46947i	−0.522548	−	0.301693i	0.215428	−	0.976520i	$-0.430885\pi$
$67$	−4.27724	−	2.46947i	−0.522548	−	0.301693i	−0.737977	+	0.674826i	$0.764219\pi$
$68$	1.96211	+	3.39847i	0.237940	+	0.412125i
$69$	−6.60600	+	5.03594i	−0.795269	+	0.606256i
$70$	−1.49517	+	0.590150i	−0.178707	+	0.0705364i
$71$			6.54622i			0.776894i	0.921471	+	0.388447i	$0.126988\pi$
$71$			6.54622i			0.776894i	−0.921471	+	0.388447i	$0.873012\pi$
$72$	8.61783	+	3.16445i	1.01562	+	0.372934i
$73$	−4.22043	+	7.31000i	−0.493964	+	0.855571i	−0.999976	−	0.00695575i	$-0.997786\pi$
$73$	−4.22043	+	7.31000i	−0.493964	+	0.855571i	0.506012	+	0.862527i	$0.331119\pi$
$74$	4.79136	−	8.29887i	0.556984	−	0.964724i
$75$	−8.08199	+	0.695492i	−0.933228	+	0.0803085i
$76$		−	2.23804i		−	0.256721i
$77$	3.33652	+	8.45321i	0.380232	+	0.963333i
$78$	0.135319	+	0.0633351i	0.0153219	+	0.00717129i
$79$	7.31051	−	4.22073i	0.822497	−	0.474869i	−0.0287799	−	0.999586i	$-0.509162\pi$
$79$	7.31051	−	4.22073i	0.822497	−	0.474869i	0.851277	+	0.524717i	$0.175829\pi$
$80$	−0.460209	+	0.797106i	−0.0514530	+	0.0891192i
$81$	−6.86135	−	5.82425i	−0.762372	−	0.647139i
$82$	2.55039	+	4.41741i	0.281644	+	0.487821i
$83$	3.31513			0.363883			0.181941	−	0.983309i	$-0.441762\pi$
$83$	3.31513			0.363883			0.181941	+	0.983309i	$0.441762\pi$
$84$	2.11225	−	3.18616i	0.230465	−	0.347639i
$85$	2.64701			0.287108
$86$	5.62428	+	9.74154i	0.606482	+	1.05046i
$87$	0.758056	−	0.529190i	0.0812721	−	0.0567351i
$88$	9.10304	+	5.25564i	0.970387	+	0.560253i
$89$	8.58122	+	14.8631i	0.909608	+	1.57549i	0.814610	+	0.580010i	$0.196951\pi$
$89$	8.58122	+	14.8631i	0.909608	+	1.57549i	0.0949981	+	0.995477i	$0.469715\pi$
$90$	1.39956	−	1.16759i	0.147526	−	0.123075i
$91$	0.131468	−	0.165512i	0.0137816	−	0.0173503i
$92$	3.54539	+	1.85342i	0.369633	+	0.193232i
$93$	−16.1336	+	1.38837i	−1.67298	+	0.143967i
$94$	−7.01254	+	12.1461i	−0.723288	+	1.25277i
$95$	−1.30738	−	0.754815i	−0.134134	−	0.0774424i
$96$	−0.646597	−	7.51380i	−0.0659930	−	0.766874i
$97$		−	0.273248i		−	0.0277442i	−0.999904	−	0.0138721i	$-0.995584\pi$
$97$		−	0.273248i		−	0.0277442i	0.999904	−	0.0138721i	$-0.00441576\pi$
$98$	5.16221	+	5.52055i	0.521462	+	0.557660i
$99$	−6.60121	−	7.91266i	−0.663447	−	0.795252i
$100$	1.95341	+	3.38340i	0.195341	+	0.338340i
$101$	1.36547	+	0.788356i	0.135870	+	0.0784443i	0.566394	−	0.824135i	$-0.308338\pi$
$101$	1.36547	+	0.788356i	0.135870	+	0.0784443i	−0.430524	+	0.902579i	$0.641671\pi$
$102$	7.21375	−	5.03584i	0.714268	−	0.498622i
$103$	−7.26684	+	4.19551i	−0.716023	+	0.413396i	−0.813287	−	0.581862i	$-0.802324\pi$
$103$	−7.26684	+	4.19551i	−0.716023	+	0.413396i	0.0972641	+	0.995259i	$0.468991\pi$
$104$		−	0.244479i		−	0.0239731i
$105$	−1.14885	−	2.30848i	−0.112116	−	0.225285i
$106$			7.98976i			0.776034i
$107$	−6.53426	−	11.3177i	−0.631690	−	1.09412i	−0.987206	−	0.159450i	$-0.949028\pi$
$107$	−6.53426	−	11.3177i	−0.631690	−	1.09412i	0.355516	−	0.934670i	$-0.384305\pi$
$108$	−1.13974	+	4.18204i	−0.109671	+	0.402417i
$109$	14.9922	+	8.65573i	1.43599	+	0.829068i	0.997568	−	0.0697017i	$-0.0222047\pi$
$109$	14.9922	+	8.65573i	1.43599	+	0.829068i	0.438421	+	0.898770i	$0.355538\pi$
$110$	1.80727	−	1.04343i	0.172317	−	0.0994871i
$111$	13.9226	+	6.51638i	1.32148	+	0.618507i
$112$	4.28071	+	0.636749i	0.404489	+	0.0601671i
$113$	−19.2929			−1.81492			−0.907461	−	0.420137i	$-0.861982\pi$
$113$	−19.2929			−1.81492			−0.907461	+	0.420137i	$0.861982\pi$
$114$	−4.99894	+	0.430181i	−0.468193	+	0.0402902i
$115$	2.27844	−	1.44599i	0.212465	−	0.134839i
$116$	−0.385601	−	0.222627i	−0.0358021	−	0.0206704i
$117$	−0.0826139	+	0.224985i	−0.00763765	+	0.0207998i
$118$	−1.22723			−0.112975
$119$	−4.56952	−	11.5771i	−0.418888	−	1.06127i
$120$	−2.70120	−	1.26427i	−0.246585	−	0.115412i
$121$	−0.399230	−	0.691487i	−0.0362937	−	0.0628625i
$122$	4.48292	−	7.76464i	0.405864	−	0.702978i
$123$	−6.70934	+	4.68371i	−0.604961	+	0.422316i
$124$	3.89948	+	6.75410i	0.350184	+	0.606536i
$125$	5.44871			0.487347
$126$	−7.52268	−	4.10554i	−0.670174	−	0.365751i
$127$	−6.99087			−0.620340			−0.310170	−	0.950681i	$-0.600386\pi$
$127$	−6.99087			−0.620340			−0.310170	+	0.950681i	$0.600386\pi$
$128$	−0.0864326	+	0.0499019i	−0.00763963	+	0.00441074i
$129$	−14.7958	+	10.3288i	−1.30270	+	0.909401i
$130$	−0.0420348	−	0.0242688i	−0.00368670	−	0.00212852i
$131$	1.27595	−	0.736670i	0.111480	−	0.0643632i	−0.443223	−	0.896411i	$-0.646165\pi$
$131$	1.27595	−	0.736670i	0.111480	−	0.0643632i	0.554703	+	0.832048i	$0.312832\pi$
$132$	−2.10382	+	4.49494i	−0.183114	+	0.391234i
$133$	−1.04437	+	7.02104i	−0.0905581	+	0.608801i
$134$	5.33270			0.460676
$135$	2.05859	+	2.07625i	0.177175	+	0.178695i
$136$	−12.4670	−	7.19784i	−1.06904	−	0.617210i
$137$	−4.02419	+	6.97010i	−0.343810	+	0.595496i	−0.985137	−	0.171772i	$-0.945051\pi$
$137$	−4.02419	+	6.97010i	−0.343810	+	0.595496i	0.641327	+	0.767268i	$0.278384\pi$
$138$	3.45836	−	8.27532i	0.294395	−	0.704442i
$139$	−0.310056			−0.0262986			−0.0131493	−	0.999914i	$-0.504186\pi$
$139$	−0.310056			−0.0262986			−0.0131493	+	0.999914i	$0.504186\pi$
$140$	−0.772418	+	0.972434i	−0.0652812	+	0.0821857i
$141$	−20.3769	−	9.53724i	−1.71605	−	0.803181i
$142$	−3.53407	−	6.12119i	−0.296573	−	0.513679i
$143$	−0.137208	+	0.237652i	−0.0114739	+	0.0198735i
$144$	−4.83513	+	0.838378i	−0.402928	+	0.0698649i
$145$	−0.260100	+	0.150169i	−0.0216001	+	0.0124709i
$146$		−	9.11384i		−	0.754267i
$147$	−8.11321	+	9.00976i	−0.669167	+	0.743112i
$148$		−	7.40350i		−	0.608564i
$149$	−2.59626	−	4.49686i	−0.212694	−	0.368397i	0.739863	−	0.672758i	$-0.234890\pi$
$149$	−2.59626	−	4.49686i	−0.212694	−	0.368397i	−0.952557	+	0.304361i	$0.901557\pi$
$150$	7.18177	−	5.01351i	0.586389	−	0.409352i
$151$	6.41222	−	11.1063i	0.521819	−	0.903816i	−0.477859	−	0.878436i	$-0.658587\pi$
$151$	6.41222	−	11.1063i	0.521819	−	0.903816i	0.999678	−	0.0253800i	$-0.00807959\pi$
$152$	4.10504	+	7.11014i	0.332963	+	0.576709i
$153$	9.04067	+	10.8367i	0.730894	+	0.876099i
$154$	−7.68348	−	6.10310i	−0.619152	−	0.491801i
$155$	5.26065			0.422546
$156$	0.115006	−	0.00989677i	0.00920783	−	0.000792376i
$157$	10.7907	+	6.23002i	0.861192	+	0.497209i	0.864411	−	0.502785i	$-0.167691\pi$
$157$	10.7907	+	6.23002i	0.861192	+	0.497209i	−0.00321933	+	0.999995i	$0.501025\pi$
$158$	−4.55724	+	7.89337i	−0.362554	+	0.627963i
$159$	−12.7696	+	1.09888i	−1.01270	+	0.0871471i
$160$			2.45001i			0.193690i
$161$	−10.2575	−	7.46886i	−0.808404	−	0.588629i
$162$	9.56016	+	1.74190i	0.751117	+	0.136856i
$163$	3.81333	+	6.60488i	0.298683	+	0.517334i	0.975835	−	0.218509i	$-0.0701193\pi$
$163$	3.81333	+	6.60488i	0.298683	+	0.517334i	−0.677152	+	0.735843i	$0.736786\pi$
$164$	3.41284	+	1.97041i	0.266498	+	0.153863i
$165$	1.91623	+	2.74496i	0.149178	+	0.213695i
$166$	−3.09988	+	1.78972i	−0.240598	+	0.138909i
$167$		−	4.92640i		−	0.381216i	−0.981666	−	0.190608i	$-0.938954\pi$
$167$		−	4.92640i		−	0.381216i	0.981666	−	0.190608i	$-0.0610460\pi$
$168$	−0.866408	+	13.9966i	−0.0668448	+	1.07986i
$169$	−12.9936			−0.999509
$170$	−2.47514	+	1.42903i	−0.189835	+	0.109601i
$171$	−1.37507	−	7.93037i	−0.105154	−	0.606451i
$172$	7.52621	+	4.34526i	0.573868	+	0.331323i
$173$	−3.14498	+	1.81575i	−0.239108	+	0.138049i	−0.614767	−	0.788709i	$-0.710750\pi$
$173$	−3.14498	+	1.81575i	−0.239108	+	0.138049i	0.375659	+	0.926758i	$0.377417\pi$
$174$	−0.423146	+	0.904078i	−0.0320786	+	0.0685380i
$175$	−4.54927	−	11.5257i	−0.343892	−	0.871264i
$176$	−5.61865			−0.423522
$177$	−0.168788	−	1.96141i	−0.0126869	−	0.147429i
$178$	−16.0481	−	9.26539i	−1.20286	−	0.694470i
$179$	15.4763	+	8.93522i	1.15675	+	0.667850i	0.950523	−	0.310654i	$-0.100548\pi$
$179$	15.4763	+	8.93522i	1.15675	+	0.667850i	0.206227	+	0.978504i	$0.433881\pi$
$180$	0.485383	−	1.32186i	0.0361783	−	0.0985254i
$181$		−	16.6456i		−	1.23726i	−0.785682	−	0.618630i	$-0.787688\pi$
$181$		−	16.6456i		−	1.23726i	0.785682	−	0.618630i	$-0.212312\pi$
$182$	−0.0335785	+	0.225740i	−0.00248900	+	0.0167330i
$183$	13.0264	+	6.09689i	0.962938	+	0.450695i
$184$	−14.6631	+	0.614786i	−1.08098	+	0.0453226i
$185$	−4.32485	−	2.49695i	−0.317969	−	0.183580i
$186$	14.3366	−	10.0082i	1.05121	−	0.733836i
$187$	8.07927	+	13.9937i	0.590815	+	1.02332i
$188$			10.8356i			0.790269i
$189$	5.52703	−	12.5878i	0.402032	−	0.915626i
$190$	1.62999			0.118252
$191$	−6.44696	−	11.1665i	−0.466486	−	0.807977i	0.532781	−	0.846253i	$-0.321147\pi$
$191$	−6.44696	−	11.1665i	−0.466486	−	0.807977i	−0.999267	+	0.0382757i	$0.987813\pi$
$192$	7.90457	+	11.3232i	0.570463	+	0.817179i
$193$	10.3284	−	17.8893i	0.743452	−	1.28770i	−0.207462	−	0.978243i	$-0.566520\pi$
$193$	10.3284	−	17.8893i	0.743452	−	1.28770i	0.950914	−	0.309454i	$-0.100146\pi$
$194$	0.147517	+	0.255507i	0.0105911	+	0.0183443i
$195$	0.0330063	−	0.0705199i	0.00236363	−	0.00505003i
$196$	5.58650	+	1.69957i	0.399036	+	0.121398i
$197$		−	0.0890213i		−	0.00634251i	−0.999995	−	0.00317125i	$-0.998991\pi$
$197$		−	0.0890213i		−	0.00634251i	0.999995	−	0.00317125i	$-0.00100944\pi$
$198$	10.4444	+	3.83515i	0.742249	+	0.272552i
$199$	15.9997	+	9.23742i	1.13419	+	0.654823i	0.944985	−	0.327115i	$-0.106076\pi$
$199$	15.9997	+	9.23742i	1.13419	+	0.654823i	0.189203	+	0.981938i	$0.439410\pi$
$200$	−12.4118	−	7.16593i	−0.877644	−	0.506708i
$201$	0.733441	+	8.52298i	0.0517329	+	0.601165i
$202$	−1.70242			−0.119782
$203$	1.10580	+	0.878349i	0.0776116	+	0.0616480i
$204$	2.88128	−	6.15602i	0.201730	−	0.431008i
$205$	2.30207	−	1.32910i	0.160784	−	0.0928286i
$206$	4.53001	−	7.84621i	0.315621	−	0.546672i
$207$	13.7017	+	4.38916i	0.952331	+	0.305068i
$208$	0.0653412	+	0.113174i	0.00453060	+	0.00784723i
$209$		−	9.21547i		−	0.637447i
$210$	2.32052	+	1.53838i	0.160131	+	0.106158i
$211$	23.2474			1.60042			0.800208	−	0.599723i	$-0.204722\pi$
$211$	23.2474			1.60042			0.800208	+	0.599723i	$0.204722\pi$
$212$	3.08640	+	5.34580i	0.211975	+	0.367151i
$213$	9.29711	−	6.49021i	0.637028	−	0.444702i
$214$	12.2200	+	7.05522i	0.835342	+	0.482285i
$215$	5.07667	−	2.93102i	0.346226	−	0.199894i
$216$	−4.04986	−	15.3766i	−0.275558	−	1.04625i
$217$	−9.08145	−	23.0082i	−0.616489	−	1.56190i
$218$	−18.6917			−1.26596
$219$	14.5662	−	1.25348i	0.984290	−	0.0847026i
$220$	0.806143	−	1.39628i	0.0543501	−	0.0941372i
$221$	0.187913	−	0.325475i	0.0126404	−	0.0218938i
$222$	−16.5366	+	1.42305i	−1.10987	+	0.0955090i
$223$	8.87898			0.594581			0.297290	−	0.954787i	$-0.403917\pi$
$223$	8.87898			0.594581			0.297290	+	0.954787i	$0.403917\pi$
$224$	10.7154	−	4.22944i	0.715956	−	0.282591i
$225$	9.00059	+	10.7887i	0.600039	+	0.719247i
$226$	18.0402	−	10.4155i	1.20002	−	0.692831i
$227$	−5.88139	+	10.1869i	−0.390362	+	0.676126i	−0.992497	−	0.122268i	$-0.960983\pi$
$227$	−5.88139	+	10.1869i	−0.390362	+	0.676126i	0.602135	+	0.798394i	$0.294317\pi$
$228$	−3.17852	+	2.21889i	−0.210503	+	0.146950i
$229$	−19.9401	+	11.5124i	−1.31768	+	0.760761i	−0.983354	−	0.181698i	$-0.941841\pi$
$229$	−19.9401	+	11.5124i	−1.31768	+	0.760761i	−0.334322	+	0.942459i	$0.608507\pi$
$230$	−1.34987	+	2.58215i	−0.0890075	+	0.170262i
$231$	8.69750	−	13.1195i	0.572253	−	0.863200i
$232$	1.63338			0.107237
$233$	−11.4576	+	6.61507i	−0.750615	+	0.433368i	−0.825916	−	0.563793i	$-0.809342\pi$
$233$	−11.4576	+	6.61507i	−0.750615	+	0.433368i	0.0753012	+	0.997161i	$0.476008\pi$
$234$	−0.0442113	−	0.254977i	−0.00289018	−	0.0166684i
$235$	6.32976	+	3.65449i	0.412908	+	0.238393i
$236$	−0.821115	+	0.474071i	−0.0534500	+	0.0308594i
$237$	−13.2423	−	6.19797i	−0.860182	−	0.402601i
$238$	10.5229	+	8.35847i	0.682097	+	0.541799i
$239$		−	15.5114i		−	1.00335i	−0.865056	−	0.501676i	$-0.832717\pi$
$239$		−	15.5114i		−	1.00335i	0.865056	−	0.501676i	$-0.167283\pi$
$240$	1.58834	−	0.136684i	0.102527	−	0.00882292i
$241$	−7.09815	−	4.09812i	−0.457232	−	0.263983i	0.253648	−	0.967297i	$-0.418370\pi$
$241$	−7.09815	−	4.09812i	−0.457232	−	0.263983i	−0.710880	+	0.703314i	$0.751703\pi$
$242$	0.746618	+	0.431060i	0.0479944	+	0.0277096i
$243$	−1.46911	+	15.5191i	−0.0942435	+	0.995549i
$244$		−	6.92691i		−	0.443450i
$245$	2.87696	−	2.69021i	0.183802	−	0.171872i
$246$	3.74515	−	8.00174i	0.238782	−	0.510172i
$247$	−0.185624	+	0.107170i	−0.0118109	+	0.00681905i
$248$	−24.7769	−	14.3050i	−1.57334	−	0.908365i
$249$	−3.28676	−	4.70823i	−0.208290	−	0.298372i
$250$	−5.09493	+	2.94156i	−0.322232	+	0.186041i
$251$	−14.7606			−0.931682			−0.465841	−	0.884869i	$-0.654248\pi$
$251$	−14.7606			−0.931682			−0.465841	+	0.884869i	$0.654248\pi$
$252$	−6.61924	+	0.159028i	−0.416973	+	0.0100179i
$253$	14.5987	+	7.63172i	0.917811	+	0.479802i
$254$	6.53697	−	3.77412i	0.410166	−	0.236809i
$255$	−2.62436	−	3.75935i	−0.164344	−	0.235420i
$256$	8.02667	−	13.9026i	0.501667	−	0.868913i
$257$	−2.01630	+	1.16411i	−0.125773	+	0.0726152i	−0.561567	−	0.827432i	$-0.689801\pi$
$257$	−2.01630	+	1.16411i	−0.125773	+	0.0726152i	0.435793	+	0.900047i	$0.356468\pi$
$258$	8.25903	−	17.6459i	0.514185	−	1.09859i
$259$	−3.45480	+	23.2258i	−0.214671	+	1.44318i
$260$	−0.0374997			−0.00232563
$261$	−1.50314	−	0.551949i	−0.0930419	−	0.0341648i
$262$	−0.795404	+	1.37768i	−0.0491402	+	0.0851133i
$263$	−9.25345	+	16.0274i	−0.570592	+	0.988294i	0.425913	+	0.904764i	$0.359953\pi$
$263$	−9.25345	+	16.0274i	−0.570592	+	0.988294i	−0.996505	+	0.0835304i	$0.973380\pi$
$264$	−1.56095	−	18.1390i	−0.0960696	−	1.11638i
$265$	4.16376			0.255777
$266$	−2.81385	−	7.12900i	−0.172528	−	0.437107i
$267$	12.6012	−	26.9232i	0.771180	−	1.64767i
$268$	3.56802	−	2.06000i	0.217951	−	0.125834i
$269$	6.81123	+	3.93247i	0.415288	+	0.239767i	0.693059	−	0.720881i	$-0.256262\pi$
$269$	6.81123	+	3.93247i	0.415288	+	0.239767i	−0.277771	+	0.960647i	$0.589596\pi$
$270$	−3.04583	−	0.830083i	−0.185363	−	0.0505172i
$271$	4.14412	+	7.17783i	0.251738	+	0.436022i	0.964004	−	0.265887i	$-0.0856647\pi$
$271$	4.14412	+	7.17783i	0.251738	+	0.436022i	−0.712267	+	0.701909i	$0.752331\pi$
$272$	7.69500			0.466578
$273$	−0.365407	−	0.0226192i	−0.0221155	−	0.00136898i
$274$		−	8.69006i		−	0.524986i
$275$	8.04345	+	13.9317i	0.485038	+	0.840111i
$276$	−0.882781	−	6.87281i	−0.0531372	−	0.413695i
$277$	−5.61901	+	9.73241i	−0.337613	+	0.584764i	−0.983983	−	0.178261i	$-0.942953\pi$
$277$	−5.61901	+	9.73241i	−0.337613	+	0.584764i	0.646370	+	0.763024i	$0.276286\pi$
$278$	0.289925	−	0.167388i	0.0173885	−	0.0100393i
$279$	17.9674	+	21.5369i	1.07568	+	1.28938i
$280$	0.670282	−	4.50615i	0.0400570	−	0.269294i
$281$	−4.29580			−0.256266			−0.128133	−	0.991757i	$-0.540898\pi$
$281$	−4.29580			−0.256266			−0.128133	+	0.991757i	$0.540898\pi$
$282$	24.2027	−	2.08275i	1.44125	−	0.124026i
$283$	−1.33740	−	0.772147i	−0.0795001	−	0.0458994i	0.459723	−	0.888062i	$-0.347949\pi$
$283$	−1.33740	−	0.772147i	−0.0795001	−	0.0458994i	−0.539223	+	0.842163i	$0.681282\pi$
$284$	−4.72917	−	2.73039i	−0.280624	−	0.162019i
$285$	0.224183	+	2.60513i	0.0132795	+	0.154315i
$286$		−	0.296296i		−	0.0175203i
$287$	−9.78708	−	7.77402i	−0.577713	−	0.458886i
$288$	−10.0302	+	8.36782i	−0.591037	+	0.493078i
$289$	−2.56493	−	4.44259i	−0.150878	−	0.261329i
$290$	0.162142	−	0.280838i	0.00952129	−	0.0164914i
$291$	−0.388074	+	0.270910i	−0.0227493	+	0.0158810i
$292$	−3.52063	−	6.09790i	−0.206029	−	0.356853i
$293$	22.8664			1.33587			0.667934	−	0.744221i	$-0.267179\pi$
$293$	22.8664			1.33587			0.667934	+	0.744221i	$0.267179\pi$
$294$	2.72239	−	12.8048i	0.158773	−	0.746792i
$295$			0.639552i			0.0372362i
$296$	13.5796	+	23.5206i	0.789298	+	1.36710i
$297$	−4.69303	+	17.2202i	−0.272317	+	0.999215i
$298$	4.85539	+	2.80326i	0.281265	+	0.162388i
$299$	−0.0160502	−	0.382808i	−0.000928204	−	0.0221383i
$300$	2.86850	−	6.12873i	0.165613	−	0.353842i
$301$	−21.5831	−	17.1437i	−1.24403	−	0.988148i
$302$			13.8469i			0.796800i
$303$	−0.234145	−	2.72089i	−0.0134513	−	0.156311i
$304$	−3.80062	−	2.19429i	−0.217981	−	0.125851i
$305$	−4.04644	−	2.33621i	−0.231698	−	0.133771i
$306$	−14.3040	−	5.25241i	−0.817708	−	0.300260i
$307$	20.0245			1.14286			0.571430	−	0.820651i	$-0.306389\pi$
$307$	20.0245			1.14286			0.571430	+	0.820651i	$0.306389\pi$
$308$	−7.49847	−	1.11538i	−0.427265	−	0.0635549i
$309$	13.1632	+	6.16094i	0.748830	+	0.350484i
$310$	−4.91909	+	2.84004i	−0.279386	+	0.161303i
$311$	1.52369	+	0.879701i	0.0864003	+	0.0498833i	0.542578	−	0.840006i	$-0.317448\pi$
$311$	1.52369	+	0.879701i	0.0864003	+	0.0498833i	−0.456177	+	0.889889i	$0.650782\pi$
$312$	−0.347215	+	0.242387i	−0.0196572	+	0.0137224i
$313$	6.52484	−	3.76712i	0.368806	−	0.212930i	−0.304131	−	0.952630i	$-0.598366\pi$
$313$	6.52484	−	3.76712i	0.368806	−	0.212930i	0.672937	+	0.739700i	$0.265033\pi$
$314$	−13.4534			−0.759222
$315$	−2.13955	+	3.92035i	−0.120550	+	0.220886i
$316$			7.04175i			0.396129i
$317$	−0.290636	+	0.167799i	−0.0163237	+	0.00942451i	−0.508140	−	0.861275i	$-0.669667\pi$
$317$	−0.290636	+	0.167799i	−0.0163237	+	0.00942451i	0.491816	+	0.870699i	$0.336333\pi$
$318$	11.3473	−	7.92139i	0.636323	−	0.444209i
$319$	−1.58777	−	0.916699i	−0.0888980	−	0.0513253i
$320$	−2.24309	−	3.88515i	−0.125393	−	0.217186i
$321$	−9.59529	+	20.5009i	−0.535557	+	1.14425i
$322$	13.6237	+	1.44627i	0.759217	+	0.0805975i
$323$			12.6210i			0.702252i
$324$	7.06942	−	2.52757i	0.392745	−	0.140420i
$325$	0.187080	−	0.324032i	0.0103773	−	0.0179741i
$326$	−7.13148	−	4.11736i	−0.394976	−	0.228040i
$327$	−2.57078	−	29.8739i	−0.142165	−	1.65203i
$328$	−14.4566			−0.798231
$329$	5.05638	−	33.9928i	0.278767	−	1.87409i
$330$	−3.27371	−	1.53224i	−0.180212	−	0.0843468i
$331$	−3.89546	−	6.74714i	−0.214114	−	0.370856i	0.738884	−	0.673833i	$-0.235353\pi$
$331$	−3.89546	−	6.74714i	−0.214114	−	0.370856i	−0.952998	+	0.302976i	$0.902020\pi$
$332$	−1.38272	+	2.39494i	−0.0758865	+	0.131439i
$333$	−4.54878	−	26.2339i	−0.249271	−	1.43761i
$334$	2.65959	+	4.60654i	0.145526	+	0.252059i
$335$		−	2.77907i		−	0.151837i
$336$	−3.33976	−	6.71088i	−0.182199	−	0.366108i
$337$			9.31422i			0.507378i	0.967286	+	0.253689i	$0.0816440\pi$
$337$			9.31422i			0.507378i	−0.967286	+	0.253689i	$0.918356\pi$
$338$	12.1500	−	7.01479i	0.660871	−	0.381554i
$339$	19.1278	+	27.4002i	1.03888	+	1.48818i
$340$	−1.10405	+	1.91227i	−0.0598755	+	0.103707i
$341$	16.0567	+	27.8110i	0.869519	+	1.50605i
$342$	5.56711	+	6.67312i	0.301035	+	0.360841i
$343$	−16.7325	−	7.93868i	−0.903471	−	0.428649i
$344$	−31.8805			−1.71888
$345$	−4.31257	−	1.80228i	−0.232181	−	0.0970315i
$346$	1.96052	−	3.39572i	0.105398	−	0.182555i
$347$	−14.0638	−	8.11971i	−0.754982	−	0.435889i	0.0725091	−	0.997368i	$-0.476899\pi$
$347$	−14.0638	−	8.11971i	−0.754982	−	0.435889i	−0.827491	+	0.561479i	$0.810233\pi$
$348$	0.0661210	+	0.768362i	0.00354446	+	0.0411885i
$349$	−30.1595			−1.61440			−0.807200	−	0.590278i	$-0.799018\pi$
$349$	−30.1595			−1.61440			−0.807200	+	0.590278i	$0.799018\pi$
$350$	10.4762	+	8.32142i	0.559978	+	0.444798i
$351$	0.401436	−	0.105729i	0.0214271	−	0.00564341i
$352$	−12.9522	+	7.47797i	−0.690356	+	0.398577i
$353$	−6.96574	−	4.02167i	−0.370749	−	0.214052i	0.303037	−	0.952979i	$-0.402000\pi$
$353$	−6.96574	−	4.02167i	−0.370749	−	0.214052i	−0.673786	+	0.738927i	$0.735333\pi$
$354$	1.21672	+	1.74294i	0.0646682	+	0.0926361i
$355$	−3.18998	+	1.84173i	−0.169306	+	0.0977491i
$356$	−14.3167			−0.758783
$357$	−11.9116	+	17.9678i	−0.630430	+	0.950955i
$358$	−19.2952			−1.01978
$359$	4.91789	+	8.51803i	0.259556	+	0.449565i	0.966123	−	0.258082i	$-0.0830904\pi$
$359$	4.91789	+	8.51803i	0.259556	+	0.449565i	−0.706567	+	0.707646i	$0.749757\pi$
$360$	0.882531	+	5.08977i	0.0465134	+	0.268254i
$361$	−5.90102	+	10.2209i	−0.310580	+	0.537940i
$362$	8.98638	+	15.5649i	0.472314	+	0.818072i
$363$	−0.586254	+	1.25257i	−0.0307703	+	0.0657427i
$364$	0.0647356	+	0.164010i	0.00339307	+	0.00859646i
$365$	−4.74955			−0.248603
$366$	−15.4721	+	1.33144i	−0.808740	+	0.0695957i
$367$	6.59851	+	3.80965i	0.344439	+	0.198862i	0.662233	−	0.749298i	$-0.269609\pi$
$367$	6.59851	+	3.80965i	0.344439	+	0.198862i	−0.317794	+	0.948160i	$0.602942\pi$
$368$	6.62354	−	4.20357i	0.345276	−	0.219126i
$369$	13.3039	+	4.88514i	0.692571	+	0.254310i
$370$	5.39206			0.280320
$371$	−7.18788	−	18.2108i	−0.373176	−	0.945456i
$372$	5.72623	−	12.2344i	0.296891	−	0.634326i
$373$	8.54002	−	4.93058i	0.442185	−	0.255296i	−0.262339	−	0.964976i	$-0.584494\pi$
$373$	8.54002	−	4.93058i	0.442185	−	0.255296i	0.704524	+	0.709680i	$0.251160\pi$
$374$	−15.1094	−	8.72342i	−0.781288	−	0.451077i
$375$	−5.40208	−	7.73839i	−0.278962	−	0.399609i
$376$	−19.8748	−	34.4242i	−1.02497	−	1.77529i
$377$			0.0426424i			0.00219620i
$378$	1.62752	+	14.7543i	0.0837104	+	0.758880i
$379$			15.1776i			0.779619i	0.920896	+	0.389809i	$0.127459\pi$
$379$			15.1776i			0.779619i	−0.920896	+	0.389809i	$0.872541\pi$
$380$	1.09060	−	0.629657i	0.0559465	−	0.0323007i
$381$	6.93105	+	9.92862i	0.355088	+	0.508658i
$382$	12.0568	+	6.96097i	0.616877	+	0.356154i
$383$	5.28180	+	9.14835i	0.269887	+	0.467459i	0.968833	−	0.247717i	$-0.0796802\pi$
$383$	5.28180	+	9.14835i	0.269887	+	0.467459i	−0.698945	+	0.715175i	$0.746347\pi$
$384$	0.156565	+	0.0732789i	0.00798967	+	0.00373950i
$385$	−3.18055	+	4.00414i	−0.162096	+	0.204070i
$386$			22.3037i			1.13523i
$387$	29.3385	+	10.7730i	1.49136	+	0.547623i
$388$	0.197402	+	0.113970i	0.0100216	+	0.00578596i
$389$	2.82345	−	4.89037i	0.143155	−	0.247951i	−0.785528	−	0.618826i	$-0.787609\pi$
$389$	2.82345	−	4.89037i	0.143155	−	0.247951i	0.928683	+	0.370874i	$0.120942\pi$
$390$	0.00720793	+	0.0837601i	0.000364988	+	0.00424136i
$391$	−19.9936	−	10.4520i	−1.01112	−	0.528580i
$392$	−20.8654	+	4.84738i	−1.05386	+	0.244830i
$393$	−2.31127	−	1.08177i	−0.116588	−	0.0545681i
$394$	0.0480594	+	0.0832414i	0.00242120	+	0.00419364i
$395$	4.11352	+	2.37494i	0.206974	+	0.119496i
$396$	8.46964	−	1.46858i	0.425615	−	0.0737987i
$397$	−12.1071	−	20.9701i	−0.607637	−	1.05246i	−0.991629	−	0.129122i	$-0.958784\pi$
$397$	−12.1071	−	20.9701i	−0.607637	−	1.05246i	0.383992	−	0.923337i	$-0.374549\pi$
$398$	−19.9478			−0.999893
$399$	11.0069	−	5.47772i	0.551034	−	0.274229i
$400$	7.66089			0.383044
$401$	−1.49821	−	2.59497i	−0.0748170	−	0.129587i	0.826190	−	0.563392i	$-0.190504\pi$
$401$	−1.49821	−	2.59497i	−0.0748170	−	0.129587i	−0.901007	+	0.433805i	$0.857171\pi$
$402$	−5.28707	−	7.57364i	−0.263695	−	0.377739i
$403$	0.373458	−	0.646848i	0.0186033	−	0.0322218i
$404$	−1.13906	+	0.657636i	−0.0566703	+	0.0327186i
$405$	0.907766	−	4.98215i	0.0451073	−	0.247565i
$406$	−1.50819	−	0.224340i	−0.0748501	−	0.0111338i
$407$		−	30.4850i		−	1.51109i
$408$	2.13779	+	24.8422i	0.105836	+	1.22987i
$409$	11.9584	−	20.7125i	0.591303	−	1.02417i	−0.402754	−	0.915308i	$-0.631947\pi$
$409$	11.9584	−	20.7125i	0.591303	−	1.02417i	0.994057	−	0.108858i	$-0.0347195\pi$
$410$	−1.43507	+	2.48561i	−0.0708731	+	0.122756i
$411$	13.8889	−	1.19520i	0.685087	−	0.0589548i
$412$		−	6.99968i		−	0.344850i
$413$	2.79717	−	1.10406i	0.137640	−	0.0543271i
$414$	−15.1816	+	3.29285i	−0.746134	+	0.161835i
$415$	0.932688	+	1.61546i	0.0457839	+	0.0793000i
$416$	0.301252	+	0.173928i	0.0147701	+	0.00852752i
$417$	0.307403	+	0.440350i	0.0150536	+	0.0215640i
$418$	4.97510	+	8.61713i	0.243340	+	0.421477i
$419$	−15.8895			−0.776254			−0.388127	−	0.921606i	$-0.626878\pi$
$419$	−15.8895			−0.776254			−0.388127	+	0.921606i	$0.626878\pi$
$420$	2.14688	+	0.132895i	0.104757	+	0.00648461i
$421$		−	4.57312i		−	0.222880i	−0.993771	−	0.111440i	$-0.964454\pi$
$421$		−	4.57312i		−	0.222880i	0.993771	−	0.111440i	$-0.0355463\pi$
$422$	−21.7380	+	12.5504i	−1.05819	+	0.610945i
$423$	6.65750	+	38.3954i	0.323699	+	1.86685i
$424$	−19.6107	−	11.3222i	−0.952379	−	0.549856i
$425$	−11.0159	−	19.0801i	−0.534349	−	0.925519i
$426$	−5.18964	+	11.0880i	−0.251439	+	0.537215i
$427$	−3.23240	+	21.7307i	−0.156427	+	1.05162i
$428$	10.9016			0.526948
$429$	0.473554	−	0.0407514i	0.0228634	−	0.00196750i
$430$	−3.16470	+	5.48143i	−0.152616	+	0.264338i
$431$	5.69814	−	9.86947i	0.274470	−	0.475396i	−0.695531	−	0.718496i	$-0.744831\pi$
$431$	5.69814	−	9.86947i	0.274470	−	0.475396i	0.970001	+	0.243100i	$0.0781643\pi$
$432$	5.98444	+	6.03577i	0.287927	+	0.290396i
$433$			18.9430i			0.910341i	0.890404	+	0.455170i	$0.150422\pi$
$433$			18.9430i			0.910341i	−0.890404	+	0.455170i	$0.849578\pi$
$434$	20.9131	+	16.6116i	1.00386	+	0.797381i
$435$	0.471148	+	0.220517i	0.0225898	+	0.0105730i
$436$	−12.5063	+	7.22049i	−0.598941	+	0.345799i
$437$	6.89451	+	10.8636i	0.329809	+	0.519679i
$438$	−12.9437	+	9.03585i	−0.618474	+	0.431750i
$439$	8.46659	+	14.6646i	0.404088	+	0.699901i	0.994215	−	0.107409i	$-0.0342555\pi$
$439$	8.46659	+	14.6646i	0.404088	+	0.699901i	−0.590127	+	0.807311i	$0.700922\pi$
$440$			5.91455i			0.281965i
$441$	20.8397	+	2.58993i	0.992366	+	0.123330i
$442$			0.405790i			0.0193015i
$443$	10.0063	−	5.77717i	0.475416	−	0.274481i	−0.243088	−	0.970004i	$-0.578160\pi$
$443$	10.0063	−	5.77717i	0.475416	−	0.274481i	0.718504	+	0.695523i	$0.244827\pi$
$444$	−10.5146	+	7.34015i	−0.499003	+	0.348348i
$445$	−4.82853	+	8.36327i	−0.228894	+	0.396457i
$446$	−8.30249	+	4.79344i	−0.393134	+	0.226976i
$447$	−3.81251	+	8.14566i	−0.180326	+	0.385277i
$448$	−13.1200	+	16.5174i	−0.619861	+	0.780373i
$449$			36.3011i			1.71316i	0.516018	+	0.856578i	$0.327414\pi$
$449$			36.3011i			1.71316i	−0.516018	+	0.856578i	$0.672586\pi$
$450$	−14.2406	−	5.22913i	−0.671310	−	0.246503i
$451$	14.0529	+	8.11344i	0.661725	+	0.382047i
$452$	8.04693	−	13.9377i	0.378496	−	0.655574i
$453$	−22.1308	+	1.90445i	−1.03979	+	0.0894790i
$454$		−	12.7006i		−	0.596069i
$455$	0.117642	+	0.0174990i	0.00551512	+	0.000820365i
$456$	6.02809	−	12.8794i	0.282291	−	0.603132i
$457$	28.0618	−	16.2015i	1.31268	−	0.757875i	0.330139	−	0.943932i	$-0.392904\pi$
$457$	28.0618	−	16.2015i	1.31268	−	0.757875i	0.982539	+	0.186058i	$0.0595711\pi$
$458$	12.4303	−	21.5299i	0.580828	−	1.00602i
$459$	6.42733	−	23.5838i	0.300002	−	1.10080i
$460$	0.0942997	+	2.24912i	0.00439675	+	0.104866i
$461$			21.9237i			1.02109i	0.859852	+	0.510544i	$0.170556\pi$
$461$			21.9237i			1.02109i	−0.859852	+	0.510544i	$0.829444\pi$
$462$	−1.05004	+	16.9631i	−0.0488524	+	0.789197i
$463$	−25.7017			−1.19446			−0.597230	−	0.802070i	$-0.703732\pi$
$463$	−25.7017			−1.19446			−0.597230	+	0.802070i	$0.703732\pi$
$464$	−0.756126	+	0.436549i	−0.0351023	+	0.0202663i
$465$	−5.21564	−	7.47131i	−0.241869	−	0.346474i
$466$	7.14248	−	12.3711i	0.330869	−	0.573082i
$467$	−12.1657	−	21.0716i	−0.562962	−	0.975079i	−0.997236	−	0.0742983i	$-0.976328\pi$
$467$	−12.1657	−	21.0716i	−0.562962	−	0.975079i	0.434274	−	0.900781i	$-0.357005\pi$
$468$	−0.128077	−	0.153522i	−0.00592038	−	0.00709656i
$469$	−12.1546	+	4.79750i	−0.561249	+	0.221528i
$470$	−7.89171			−0.364018
$471$	−1.85034	−	21.5019i	−0.0852591	−	0.990757i
$472$	1.73909	−	3.01220i	0.0800483	−	0.138648i
$473$	30.9903	+	17.8923i	1.42494	+	0.822687i
$474$	15.7286	−	1.35352i	0.722439	−	0.0621691i
$475$			12.5651i			0.576524i
$476$	10.2695	+	1.52757i	0.470702	+	0.0700161i
$477$	14.2210	+	17.0462i	0.651135	+	0.780494i
$478$	8.37407	+	14.5043i	0.383021	+	0.663412i
$479$	−8.43332	+	14.6069i	−0.385328	+	0.667408i	−0.991815	−	0.127686i	$-0.959245\pi$
$479$	−8.43332	+	14.6069i	−0.385328	+	0.667408i	0.606486	+	0.795094i	$0.292578\pi$
$480$	3.47956	−	2.42904i	0.158820	−	0.110870i
$481$	−0.614048	+	0.354521i	−0.0279982	+	0.0161648i
$482$	8.84971			0.403093
$483$	−0.437748	+	21.9729i	−0.0199182	+	0.999802i
$484$	0.666065			0.0302757
$485$	0.133154	−	0.0768765i	0.00604622	−	0.00349078i
$486$	−7.00447	−	15.3046i	−0.317729	−	0.694230i
$487$	−16.7143	+	28.9500i	−0.757396	+	1.31185i	0.186778	+	0.982402i	$0.440196\pi$
$487$	−16.7143	+	28.9500i	−0.757396	+	1.31185i	−0.944174	+	0.329447i	$0.893138\pi$
$488$	12.7054	+	22.0064i	0.575148	+	0.996185i
$489$	5.59972	−	11.9642i	0.253228	−	0.541038i
$490$	−1.23782	+	4.06871i	−0.0559188	+	0.183806i
$491$		−	8.42845i		−	0.380371i	−0.981748	−	0.190185i	$-0.939091\pi$
$491$		−	8.42845i		−	0.380371i	0.981748	−	0.190185i	$-0.0609089\pi$
$492$	−0.585218	−	6.80055i	−0.0263837	−	0.306593i
$493$	2.17452	+	1.25546i	0.0979356	+	0.0565431i
$494$	0.115714	−	0.200423i	0.00520623	−	0.00901746i
$495$	1.99864	−	5.44294i	0.0898320	−	0.244642i
$496$	15.2930			0.686676
$497$	13.5619	+	10.7724i	0.608336	+	0.483210i
$498$	5.61516	+	2.62813i	0.251621	+	0.117769i
$499$	2.23483	+	3.87084i	0.100045	+	0.173283i	0.911703	−	0.410850i	$-0.134768\pi$
$499$	2.23483	+	3.87084i	0.100045	+	0.173283i	−0.811658	+	0.584133i	$0.801435\pi$
$500$	−2.27262	+	3.93629i	−0.101635	+	0.176036i
$501$	−6.99660	+	4.88424i	−0.312585	+	0.218212i
$502$	13.8022	−	7.96873i	0.616024	−	0.355662i
$503$	16.5989			0.740106			0.370053	−	0.929011i	$-0.379339\pi$
$503$	16.5989			0.740106			0.370053	+	0.929011i	$0.379339\pi$
$504$	20.7373	−	12.6463i	0.923713	−	0.563312i
$505$			0.887194i			0.0394796i
$506$	−17.7709	+	0.745089i	−0.790013	+	0.0331233i
$507$	12.8824	+	18.4539i	0.572129	+	0.819565i
$508$	2.91585	−	5.05039i	0.129370	−	0.224075i
$509$	36.4224	−	21.0285i	1.61440	−	0.932072i	0.626062	−	0.779774i	$-0.284666\pi$
$509$	36.4224	−	21.0285i	1.61440	−	0.932072i	0.988335	−	0.152299i	$-0.0486675\pi$
$510$	4.48350	+	2.09847i	0.198533	+	0.0929217i
$511$	8.19914	+	20.7728i	0.362709	+	0.918937i
$512$			17.1336i			0.757207i
$513$	−9.89961	+	9.81542i	−0.437079	+	0.433362i
$514$	1.25692	−	2.17705i	0.0554405	−	0.0960258i
$515$	−4.08895	−	2.36076i	−0.180181	−	0.104027i
$516$	−1.29056	−	14.9970i	−0.0568137	−	0.660206i
$517$			44.6173i			1.96227i
$518$	−9.30830	−	23.5829i	−0.408983	−	1.03617i
$519$	5.69685	+	2.66636i	0.250064	+	0.117040i
$520$	0.119135	−	0.0687824i	0.00522440	−	0.00301631i
$521$	8.09081	−	14.0137i	0.354465	−	0.613951i	−0.632561	−	0.774510i	$-0.717996\pi$
$521$	8.09081	−	14.0137i	0.354465	−	0.613951i	0.987026	+	0.160559i	$0.0513297\pi$
$522$	1.70352	−	0.295379i	0.0745611	−	0.0129284i
$523$	28.3772	−	16.3836i	1.24085	−	0.716404i	0.271582	−	0.962415i	$-0.412453\pi$
$523$	28.3772	−	16.3836i	1.24085	−	0.716404i	0.969267	+	0.246011i	$0.0791200\pi$
$524$			1.22904i			0.0536909i
$525$	−11.8588	+	17.8881i	−0.517561	+	0.780701i
$526$		−	19.9824i		−	0.871275i
$527$	−21.9904	−	38.0885i	−0.957916	−	1.65916i
$528$	5.57057	+	7.97975i	0.242428	+	0.347274i
$529$	−22.9193	+	1.92528i	−0.996490	+	0.0837078i
$530$	−3.89341	+	2.24786i	−0.169119	+	0.0976409i
$531$	−2.61830	+	2.18434i	−0.113625	+	0.0947924i
$532$	−4.63659	−	3.68291i	−0.201022	−	0.159674i
$533$		−	0.377416i		−	0.0163477i
$534$	2.75186	+	31.9781i	0.119085	+	1.38383i
$535$	3.67673	−	6.36829i	0.158959	−	0.275325i
$536$	−7.55694	+	13.0890i	−0.326410	+	0.565359i
$537$	−2.65380	−	30.8385i	−0.114520	−	1.33078i
$538$	−8.49199			−0.366116
$539$	23.0032	+	6.99823i	0.990820	+	0.301435i
$540$	−2.35856	+	0.621193i	−0.101496	+	0.0267319i
$541$	−10.2846	−	17.8134i	−0.442167	−	0.765856i	0.555683	−	0.831394i	$-0.312457\pi$
$541$	−10.2846	−	17.8134i	−0.442167	−	0.765856i	−0.997850	+	0.0655380i	$0.979124\pi$
$542$	−7.75011	−	4.47453i	−0.332896	−	0.192197i
$543$	−23.6406	+	16.5032i	−1.01451	+	0.708220i
$544$	17.7387	−	10.2414i	0.760539	−	0.439098i
$545$			9.74091i			0.417255i
$546$	0.353893	−	0.176120i	0.0151452	−	0.00753723i
$547$	−24.7627			−1.05878			−0.529389	−	0.848379i	$-0.677579\pi$
$547$	−24.7627			−1.05878			−0.529389	+	0.848379i	$0.677579\pi$
$548$	−3.35692	−	5.81436i	−0.143401	−	0.248377i
$549$	−4.25595	−	24.5451i	−0.181640	−	1.04756i
$550$	−15.0424	−	8.68474i	−0.641411	−	0.370319i
$551$	−0.716009	−	1.24016i	−0.0305030	−	0.0528328i
$552$	15.4108	+	20.2154i	0.655925	+	0.860423i
$553$	3.28599	−	22.0909i	0.139734	−	0.939402i
$554$		−	12.1340i		−	0.515524i
$555$	0.741604	+	8.61784i	0.0314794	+	0.365807i
$556$	0.129322	−	0.223993i	0.00548449	−	0.00949942i
$557$	−19.6026	+	33.9527i	−0.830590	+	1.43862i	0.0669817	+	0.997754i	$0.478663\pi$
$557$	−19.6026	+	33.9527i	−0.830590	+	1.43862i	−0.897571	+	0.440869i	$0.854670\pi$
$558$	−28.4278	−	10.4386i	−1.20344	−	0.441902i
$559$		−	0.832301i		−	0.0352026i
$560$	0.894061	+	2.26514i	0.0377810	+	0.0957196i
$561$	11.8641	−	25.3483i	0.500902	−	1.07021i
$562$	4.01689	−	2.31915i	0.169442	−	0.0978275i
$563$	10.9983	−	19.0496i	0.463524	−	0.802847i	−0.535610	−	0.844466i	$-0.679918\pi$
$563$	10.9983	−	19.0496i	0.463524	−	0.802847i	0.999134	+	0.0416189i	$0.0132515\pi$
$564$	15.3890	−	10.7429i	0.647995	−	0.452358i
$565$	−5.42792	−	9.40143i	−0.228354	−	0.395521i
$566$	1.66742			0.0700869
$567$	−23.3572	+	4.63043i	−0.980911	+	0.194460i
$568$	20.0324			0.840542
$569$	−3.38477	−	5.86259i	−0.141897	−	0.245773i	0.786314	−	0.617827i	$-0.211987\pi$
$569$	−3.38477	−	5.86259i	−0.141897	−	0.245773i	−0.928211	+	0.372054i	$0.878654\pi$
$570$	−1.61604	−	2.31496i	−0.0676886	−	0.0969628i
$571$	−24.5523	−	14.1753i	−1.02748	−	0.593218i	−0.111221	−	0.993796i	$-0.535476\pi$
$571$	−24.5523	−	14.1753i	−1.02748	−	0.593218i	−0.916263	+	0.400578i	$0.868809\pi$
$572$	−0.114457	−	0.198246i	−0.00478570	−	0.00828908i
$573$	−9.46711	+	20.2271i	−0.395494	+	0.844997i
$574$	13.3485	+	1.98557i	0.557157	+	0.0828762i
$575$	−19.9049	−	10.4057i	−0.830093	−	0.433946i
$576$	8.24452	−	22.4525i	0.343522	−	0.935523i
$577$	−10.7191	+	18.5660i	−0.446241	+	0.772913i	−0.998138	−	0.0610001i	$-0.980571\pi$
$577$	−10.7191	+	18.5660i	−0.446241	+	0.772913i	0.551896	+	0.833913i	$0.313904\pi$
$578$	4.79679	+	2.76943i	0.199520	+	0.115193i
$579$	−35.6468	+	3.06757i	−1.48143	+	0.127484i
$580$		−	0.250538i		−	0.0104030i
$581$	5.45536	−	6.86801i	0.226326	−	0.284933i
$582$	0.216623	−	0.462828i	0.00897931	−	0.0191848i
$583$	12.7087	+	22.0121i	0.526341	+	0.911650i
$584$	22.3697	+	12.9152i	0.925665	+	0.534433i
$585$	−0.132878	+	0.0230401i	−0.00549383	+	0.000952592i
$586$	−21.3817	+	12.3447i	−0.883270	+	0.509956i
$587$		−	26.7107i		−	1.10247i	−0.834350	−	0.551235i	$-0.814157\pi$
$587$		−	26.7107i		−	1.10247i	0.834350	−	0.551235i	$-0.185843\pi$
$588$	−3.12492	−	9.61911i	−0.128870	−	0.396686i
$589$			25.0829i			1.03352i
$590$	−0.345271	−	0.598028i	−0.0142146	−	0.0246204i
$591$	−0.126430	+	0.0882596i	−0.00520065	+	0.00363051i
$592$	−12.5726	−	7.25878i	−0.516729	−	0.298334i
$593$	14.1900	−	8.19263i	0.582715	−	0.336431i	−0.179496	−	0.983759i	$-0.557447\pi$
$593$	14.1900	−	8.19263i	0.582715	−	0.336431i	0.762212	+	0.647328i	$0.224113\pi$
$594$	−4.90822	−	18.6357i	−0.201387	−	0.764632i
$595$	4.35591	−	5.48386i	0.178575	−	0.224816i
$596$	4.33154			0.177427
$597$	−2.74355	−	31.8815i	−0.112286	−	1.30482i
$598$	0.221672	+	0.349288i	0.00906485	+	0.0142834i
$599$	−17.8698	−	10.3171i	−0.730140	−	0.421547i	0.0883331	−	0.996091i	$-0.471846\pi$
$599$	−17.8698	−	10.3171i	−0.730140	−	0.421547i	−0.818474	+	0.574544i	$0.805179\pi$
$600$	2.12831	+	24.7321i	0.0868879	+	1.00968i
$601$	34.7478			1.41739			0.708696	−	0.705514i	$-0.249284\pi$
$601$	34.7478			1.41739			0.708696	+	0.705514i	$0.249284\pi$
$602$	29.4370	+	4.37870i	1.19976	+	0.178463i
$603$	11.3774	−	9.49170i	0.463323	−	0.386532i
$604$	5.34898	+	9.26471i	0.217647	+	0.376976i
$605$	0.224641	−	0.389090i	0.00913297	−	0.0158188i
$606$	1.68785	+	2.41782i	0.0685643	+	0.0982173i
$607$	5.08674	+	8.81050i	0.206465	+	0.357607i	0.950598	−	0.310424i	$-0.100471\pi$
$607$	5.08674	+	8.81050i	0.206465	+	0.357607i	−0.744134	+	0.668031i	$0.767138\pi$
$608$	−11.6817			−0.473755
$609$	0.151120	−	2.44131i	0.00612371	−	0.0989269i
$610$	5.04495			0.204264
$611$	0.898710	−	0.518870i	0.0363579	−	0.0209912i
$612$	−11.5996	+	2.01128i	−0.468884	+	0.0813013i
$613$	−9.90261	−	5.71728i	−0.399963	−	0.230919i	0.286505	−	0.958079i	$-0.407506\pi$
$613$	−9.90261	−	5.71728i	−0.399963	−	0.230919i	−0.686468	+	0.727160i	$0.740840\pi$
$614$	−18.7244	+	10.8105i	−0.755655	+	0.436277i
$615$	−4.17000	−	1.95173i	−0.168151	−	0.0787015i
$616$	25.8681	−	10.2103i	1.04226	−	0.411384i
$617$	36.4166			1.46608			0.733039	−	0.680187i	$-0.238101\pi$
$617$	36.4166			1.46608			0.733039	+	0.680187i	$0.238101\pi$
$618$	−15.6346	+	1.34543i	−0.628918	+	0.0541212i
$619$	9.80109	+	5.65866i	0.393939	+	0.227441i	0.683866	−	0.729608i	$-0.260297\pi$
$619$	9.80109	+	5.65866i	0.393939	+	0.227441i	−0.289926	+	0.957049i	$0.593631\pi$
$620$	−2.19418	+	3.80044i	−0.0881205	+	0.152629i
$621$	−7.35080	−	23.8110i	−0.294978	−	0.955504i
$622$	−1.89968			−0.0761701
$623$	44.9134	+	6.68079i	1.79942	+	0.267660i
$624$	0.0959510	−	0.205005i	0.00384111	−	0.00820678i
$625$	−10.1755	−	17.6245i	−0.407020	−	0.704980i
$626$	−4.06747	+	7.04506i	−0.162569	+	0.281577i
$627$	−13.0880	+	9.13661i	−0.522686	+	0.364881i
$628$	−9.00146	+	5.19700i	−0.359197	+	0.207383i
$629$			41.7507i			1.66471i
$630$	−0.115822	−	4.82087i	−0.00461447	−	0.192068i
$631$		−	3.14042i		−	0.125018i	−0.998044	−	0.0625091i	$-0.980090\pi$
$631$		−	3.14042i		−	0.125018i	0.998044	−	0.0625091i	$-0.0199102\pi$
$632$	−12.9161	−	22.3713i	−0.513773	−	0.889882i
$633$	−23.0485	−	33.0165i	−0.916094	−	1.31229i
$634$	0.181177	−	0.313808i	0.00719546	−	0.0124629i
$635$	−1.96683	−	3.40665i	−0.0780514	−	0.135189i
$636$	4.53226	−	9.68344i	0.179716	−	0.383974i
$637$	−0.126550	−	0.544730i	−0.00501410	−	0.0215830i
$638$	1.97957			0.0783720
$639$	−18.4351	−	6.76933i	−0.729282	−	0.267791i
$640$	−0.0486344	−	0.0280791i	−0.00192244	−	0.00110992i
$641$	−6.91952	+	11.9850i	−0.273305	+	0.473378i	−0.969706	−	0.244275i	$-0.921450\pi$
$641$	−6.91952	+	11.9850i	−0.273305	+	0.473378i	0.696401	+	0.717653i	$0.254783\pi$
$642$	−2.09543	−	24.3500i	−0.0827000	−	0.961018i
$643$		−	42.0799i		−	1.65947i	−0.558157	−	0.829736i	$-0.688491\pi$
$643$		−	42.0799i		−	1.65947i	0.558157	−	0.829736i	$-0.311509\pi$
$644$	9.67404	−	4.29508i	0.381210	−	0.169250i
$645$	−9.19594	−	4.30408i	−0.362090	−	0.169473i
$646$	−6.81363	−	11.8016i	−0.268079	−	0.464326i
$647$	−7.60409	−	4.39022i	−0.298948	−	0.172597i	0.343022	−	0.939327i	$-0.388549\pi$
$647$	−7.60409	−	4.39022i	−0.298948	−	0.172597i	−0.641970	+	0.766730i	$0.721883\pi$
$648$	−17.8231	+	20.9968i	−0.700157	+	0.824831i
$649$	−3.38106	+	1.95206i	−0.132718	+	0.0766250i
$650$			0.403992i			0.0158459i
$651$	−23.6731	+	35.7090i	−0.927822	+	1.39955i
$652$	−6.36206			−0.249158
$653$	−2.52887	+	1.46004i	−0.0989622	+	0.0571359i	−0.548664	−	0.836043i	$-0.684863\pi$
$653$	−2.52887	+	1.46004i	−0.0989622	+	0.0571359i	0.449702	+	0.893179i	$0.351530\pi$
$654$	18.5317	+	26.5464i	0.724648	+	1.03805i
$655$	0.717959	+	0.414514i	0.0280530	+	0.0161964i
$656$	6.69226	−	3.86378i	0.261289	−	0.150855i
$657$	−16.2218	−	19.4445i	−0.632871	−	0.758602i
$658$	13.6234	+	34.5155i	0.531097	+	1.34556i
$659$	−5.08039			−0.197904			−0.0989519	−	0.995092i	$-0.531549\pi$
$659$	−5.08039			−0.197904			−0.0989519	+	0.995092i	$0.531549\pi$
$660$	−2.78228	+	0.239428i	−0.108300	+	0.00931971i
$661$	−3.78644	−	2.18610i	−0.147275	−	0.0850295i	0.424552	−	0.905404i	$-0.360432\pi$
$661$	−3.78644	−	2.18610i	−0.147275	−	0.0850295i	−0.571827	+	0.820374i	$0.693765\pi$
$662$	7.28508	+	4.20604i	0.283143	+	0.163472i
$663$	−0.648554	+	0.0558110i	−0.0251877	+	0.00216752i
$664$		−	10.1448i		−	0.393694i
$665$	−3.71518	+	1.46640i	−0.144069	+	0.0568645i
$666$	18.4162	+	22.0749i	0.713612	+	0.855384i
$667$	2.55756	−	0.107232i	0.0990293	−	0.00415205i
$668$	3.55896	+	2.05477i	0.137700	+	0.0795014i
$669$	−8.80301	−	12.6102i	−0.340344	−	0.487537i
$670$	1.50032	+	2.59863i	0.0579624	+	0.100394i
$671$		−	28.5226i		−	1.10110i
$672$	−16.6305	−	11.0251i	−0.641536	−	0.425303i
$673$	30.5982			1.17948			0.589738	−	0.807595i	$-0.299231\pi$
$673$	30.5982			1.17948			0.589738	+	0.807595i	$0.299231\pi$
$674$	−5.02841	−	8.70947i	−0.193687	−	0.335476i
$675$	6.39883	−	23.4793i	0.246291	−	0.903717i
$676$	5.41955	−	9.38694i	0.208444	−	0.361036i
$677$	19.3683	+	33.5469i	0.744386	+	1.28931i	0.950481	+	0.310782i	$0.100591\pi$
$677$	19.3683	+	33.5469i	0.744386	+	1.28931i	−0.206096	+	0.978532i	$0.566076\pi$
$678$	−32.6783	−	15.2948i	−1.25500	−	0.587393i
$679$	−0.566094	−	0.449656i	−0.0217247	−	0.0172562i
$680$		−	8.10025i		−	0.310630i
$681$	20.2987	−	1.74680i	0.777849	−	0.0669374i
$682$	−30.0283	−	17.3369i	−1.14984	−	0.663863i
$683$	15.3655	+	8.87129i	0.587946	+	0.339451i	0.764285	−	0.644879i	$-0.223092\pi$
$683$	15.3655	+	8.87129i	0.587946	+	0.339451i	−0.176339	+	0.984329i	$0.556426\pi$
$684$	6.30265	+	2.31432i	0.240988	+	0.0884901i
$685$	−4.52871			−0.173033
$686$	19.9319	−	1.61005i	0.761005	−	0.0614718i
$687$	36.1196	+	16.9055i	1.37805	+	0.644985i
$688$	14.7582	−	8.52063i	0.562650	−	0.324846i
$689$	0.295588	−	0.511974i	0.0112610	−	0.0195046i
$690$	5.00555	−	0.642940i	0.190558	−	0.0244763i
$691$	16.4795	+	28.5434i	0.626911	+	1.08584i	0.988168	+	0.153376i	$0.0490145\pi$
$691$	16.4795	+	28.5434i	0.626911	+	1.08584i	−0.361257	+	0.932466i	$0.617652\pi$
$692$		−	3.02936i		−	0.115159i
$693$	−27.2557	+	0.654824i	−1.03536	+	0.0248747i
$694$	17.5342			0.665588
$695$	−0.0872322	−	0.151091i	−0.00330890	−	0.00573119i
$696$	−1.61940	−	2.31977i	−0.0613833	−	0.0879305i
$697$	−19.2461	−	11.1117i	−0.728998	−	0.420887i
$698$	28.2013	−	16.2820i	1.06743	−	0.616284i
$699$	20.7545	+	9.71397i	0.785007	+	0.367416i
$700$	10.2240	+	1.52080i	0.386430	+	0.0574808i
$701$	−3.10021			−0.117093			−0.0585467	−	0.998285i	$-0.518647\pi$
$701$	−3.10021			−0.117093			−0.0585467	+	0.998285i	$0.518647\pi$
$702$	−0.318292	+	0.315585i	−0.0120132	+	0.0119110i
$703$	11.9055	−	20.6210i	0.449025	−	0.777735i
$704$	13.6928	−	23.7167i	0.516068	−	0.893856i
$705$	−1.08540	−	12.6129i	−0.0408785	−	0.475030i
$706$	8.68463			0.326850
$707$	3.88027	−	1.53156i	0.145932	−	0.0576002i
$708$	1.48738	+	0.696154i	0.0558990	+	0.0261631i
$709$	−21.3510	+	12.3270i	−0.801854	+	0.462950i	−0.844119	−	0.536156i	$-0.819876\pi$
$709$	−21.3510	+	12.3270i	−0.801854	+	0.462950i	0.0422653	+	0.999106i	$0.486543\pi$
$710$	1.98857	−	3.44431i	0.0746298	−	0.129263i
$711$	4.32651	+	24.9520i	0.162257	+	0.935775i
$712$	45.4834	−	26.2598i	1.70456	−	0.984129i
$713$	−39.7351	−	20.7722i	−1.48809	−	0.777927i
$714$	1.43808	−	23.2318i	0.0538188	−	0.869429i
$715$	−0.154410			−0.00577462
$716$	−12.9101	+	7.45364i	−0.482473	+	0.278556i
$717$	−22.0297	+	15.3787i	−0.822716	+	0.574328i
$718$	−9.19716	−	5.30998i	−0.343235	−	0.198167i
$719$	−22.2599	+	12.8518i	−0.830155	+	0.479290i	−0.853906	−	0.520428i	$-0.825772\pi$
$719$	−22.2599	+	12.8518i	−0.830155	+	0.479290i	0.0237509	+	0.999718i	$0.492439\pi$
$720$	−1.76887	−	2.12029i	−0.0659220	−	0.0790185i
$721$	−3.26636	+	21.9590i	−0.121645	+	0.817794i
$722$		−	12.7430i		−	0.474245i
$723$	1.21716	+	14.1440i	0.0452666	+	0.526022i
$724$	12.0253	+	6.94278i	0.446915	+	0.258027i
$725$	2.16488	+	1.24990i	0.0804017	+	0.0464200i
$726$	−0.128027	−	1.48774i	−0.00475151	−	0.0552151i
$727$			33.5015i			1.24250i	0.783611	+	0.621251i	$0.213375\pi$
$727$			33.5015i			1.24250i	−0.783611	+	0.621251i	$0.786625\pi$
$728$	−0.506491	−	0.402313i	−0.0187718	−	0.0149107i
$729$	23.4971	−	13.2998i	0.870264	−	0.492586i
$730$	4.44118	−	2.56411i	0.164375	−	0.0949021i
$731$	−42.4426	−	24.5043i	−1.56980	−	0.906323i
$732$	−9.83777	+	6.86763i	−0.363615	+	0.253835i
$733$	31.4287	−	18.1454i	1.16085	−	0.670214i	0.209339	−	0.977843i	$-0.432869\pi$
$733$	31.4287	−	18.1454i	1.16085	−	0.670214i	0.951506	+	0.307629i	$0.0995355\pi$
$734$	−8.22677			−0.303656
$735$	−6.67306	−	1.41874i	−0.246139	−	0.0523310i
$736$	9.67411	−	18.5055i	0.356593	−	0.682124i
$737$	14.6918	−	8.48234i	0.541181	−	0.312451i
$738$	−15.0774	+	2.61431i	−0.555006	+	0.0962342i
$739$	−8.76530	+	15.1819i	−0.322437	+	0.558477i	−0.980990	−	0.194057i	$-0.937835\pi$
$739$	−8.76530	+	15.1819i	−0.322437	+	0.558477i	0.658553	+	0.752534i	$0.271169\pi$
$740$	3.60773	−	2.08292i	0.132623	−	0.0765698i
$741$	0.336241	+	0.157375i	0.0123521	+	0.00578130i
$742$	16.5525	+	13.1479i	0.607662	+	0.482675i
$743$	−27.4447			−1.00685			−0.503424	−	0.864039i	$-0.667927\pi$
$743$	−27.4447			−1.00685			−0.503424	+	0.864039i	$0.667927\pi$
$744$	4.24863	+	49.3713i	0.155762	+	1.81004i
$745$	1.46088	−	2.53032i	0.0535225	−	0.0927038i
$746$	−5.32369	+	9.22090i	−0.194914	+	0.337601i
$747$	−3.42811	+	9.33588i	−0.125428	+	0.341582i
$748$	−13.4792			−0.492850
$749$	−34.1998	−	5.08715i	−1.24963	−	0.185881i
$750$	9.22902	+	4.31956i	0.336996	+	0.157728i
$751$	−0.822968	+	0.475141i	−0.0300305	+	0.0173381i	−0.514940	−	0.857226i	$-0.672186\pi$
$751$	−0.822968	+	0.475141i	−0.0300305	+	0.0173381i	0.484910	+	0.874564i	$0.338853\pi$
$752$	18.4010	+	10.6238i	0.671014	+	0.387410i
$753$	14.6343	+	20.9634i	0.533304	+	0.763949i
$754$	−0.0230211	−	0.0398738i	−0.000838380	−	0.00145212i
$755$	7.21613			0.262622
$756$	6.78846	+	9.24315i	0.246894	+	0.336170i
$757$			17.0054i			0.618070i	0.951051	+	0.309035i	$0.100006\pi$
$757$			17.0054i			0.618070i	−0.951051	+	0.309035i	$0.899994\pi$
$758$	−8.19382	−	14.1921i	−0.297613	−	0.515481i
$759$	−3.63498	−	28.2998i	−0.131942	−	1.02722i
$760$	−2.30985	+	4.00078i	−0.0837871	+	0.145123i
$761$	−37.4411	+	21.6167i	−1.35724	+	0.783603i	−0.989251	−	0.146227i	$-0.953287\pi$
$761$	−37.4411	+	21.6167i	−1.35724	+	0.783603i	−0.367989	+	0.929830i	$0.619954\pi$
$762$	−11.8411	−	5.54215i	−0.428959	−	0.200771i
$763$	42.6033	−	16.8157i	1.54234	−	0.608770i
$764$	10.7559			0.389136
$765$	−2.73722	+	7.45436i	−0.0989645	+	0.269513i
$766$	−9.87773	−	5.70291i	−0.356897	−	0.206054i
$767$	0.0786391	+	0.0454023i	0.00283949	+	0.00163938i
$768$	−27.7028	+	2.38395i	−0.999640	+	0.0860235i
$769$		−	35.0234i		−	1.26298i	−0.775385	−	0.631489i	$-0.782444\pi$
$769$		−	35.0234i		−	1.26298i	0.775385	−	0.631489i	$-0.217556\pi$
$770$	0.812348	−	5.46123i	0.0292750	−	0.196809i
$771$	3.65234	+	1.70945i	0.131536	+	0.0615643i
$772$	8.61579	+	14.9230i	0.310089	+	0.537090i
$773$	24.6257	−	42.6529i	0.885723	−	1.53412i	0.0408411	−	0.999166i	$-0.486996\pi$
$773$	24.6257	−	42.6529i	0.885723	−	1.53412i	0.844882	−	0.534952i	$-0.179670\pi$
$774$	−33.2496	+	5.76524i	−1.19513	+	0.207227i
$775$	−21.8929	−	37.9196i	−0.786416	−	1.36211i
$776$	−0.836182			−0.0300172
$777$	36.4111	−	18.1205i	1.30624	−	0.650068i
$778$			6.09713i			0.218593i
$779$	6.33720	+	10.9763i	0.227054	+	0.393268i
$780$	0.0371788	+	0.0532580i	0.00133121	+	0.00190694i
$781$	−19.4731	−	11.2428i	−0.696801	−	0.402298i
$782$	24.3381	−	1.02043i	0.870328	−	0.0364907i
$783$	0.706384	+	2.68202i	0.0252441	+	0.0958476i
$784$	8.36349	−	7.82060i	0.298696	−	0.279307i
$785$			7.01109i			0.250236i
$786$	2.74521	−	0.236238i	0.0979185	−	0.00842633i
$787$	27.7286	+	16.0091i	0.988419	+	0.570664i	0.904801	−	0.425834i	$-0.140019\pi$
$787$	27.7286	+	16.0091i	0.988419	+	0.570664i	0.0836179	+	0.996498i	$0.473352\pi$
$788$	0.0643114	+	0.0371302i	0.00229100	+	0.00132271i
$789$	31.9369	−	2.74831i	1.13698	−	0.0978424i
$790$	−5.12859			−0.182467
$791$	−31.7483	+	39.9694i	−1.12884	+	1.42115i
$792$	−24.2139	+	20.2007i	−0.860405	+	0.717801i
$793$	−0.574520	+	0.331699i	−0.0204018	+	0.0117790i
$794$	22.6420	+	13.0724i	0.803534	+	0.463921i
$795$	−4.12813	−	5.91347i	−0.146410	−	0.209729i
$796$	−13.3467	+	7.70573i	−0.473062	+	0.273122i
$797$	−17.3803			−0.615641			−0.307820	−	0.951445i	$-0.599600\pi$
$797$	−17.3803			−0.615641			−0.307820	+	0.951445i	$0.599600\pi$
$798$	−7.33501	+	11.0643i	−0.259657	+	0.391672i
$799$		−	61.1055i		−	2.16176i
$800$	17.6600	−	10.1960i	0.624377	−	0.360484i
$801$	−50.7304	+	8.79630i	−1.79247	+	0.310802i
$802$	2.80187	+	1.61766i	0.0989374	+	0.0571215i
$803$	−14.4967	−	25.1090i	−0.511578	−	0.886079i
$804$	−6.46314	−	3.02502i	−0.227937	−	0.106684i
$805$	0.753705	−	7.09979i	0.0265646	−	0.250235i
$806$			0.806466i			0.0284065i
$807$	−1.16796	−	13.5723i	−0.0411141	−	0.477768i
$808$	2.41249	−	4.17855i	0.0848710	−	0.147001i
$809$	25.5069	+	14.7264i	0.896775	+	0.517753i	0.876152	−	0.482034i	$-0.160102\pi$
$809$	25.5069	+	14.7264i	0.896775	+	0.517753i	0.0206223	+	0.999787i	$0.493435\pi$
$810$	1.84086	+	5.14874i	0.0646811	+	0.180908i
$811$	8.73312			0.306661			0.153331	−	0.988175i	$-0.451000\pi$
$811$	8.73312			0.306661			0.153331	+	0.988175i	$0.451000\pi$
$812$	−1.09576	+	0.432503i	−0.0384537	+	0.0151779i
$813$	6.08548	−	13.0020i	0.213427	−	0.456000i
$814$	16.4578	+	28.5057i	0.576845	+	0.999125i
$815$	−2.14571	+	3.71648i	−0.0751609	+	0.130182i
$816$	−7.62916	−	10.9286i	−0.267074	−	0.382579i
$817$	13.9752	+	24.2057i	0.488929	+	0.846850i
$818$			25.8236i			0.902900i
$819$	0.330156	+	0.541386i	0.0115366	+	0.0189176i
$820$			2.21744i			0.0774364i
$821$	−16.6620	+	9.61982i	−0.581508	+	0.335734i	−0.761733	−	0.647892i	$-0.775651\pi$
$821$	−16.6620	+	9.61982i	−0.581508	+	0.335734i	0.180224	+	0.983626i	$0.442318\pi$
$822$	−12.3418	+	8.61570i	−0.430471	+	0.300507i
$823$	−8.96612	+	15.5298i	−0.312539	+	0.541334i	−0.978911	−	0.204285i	$-0.934513\pi$
$823$	−8.96612	+	15.5298i	−0.312539	+	0.541334i	0.666372	+	0.745619i	$0.267846\pi$
$824$	12.8389	+	22.2376i	0.447264	+	0.774685i
$825$	11.8115	−	25.2360i	0.411223	−	0.878604i
$826$	−2.01952	+	2.54247i	−0.0702680	+	0.0884637i
$827$	11.4036			0.396541			0.198271	−	0.980147i	$-0.436467\pi$
$827$	11.4036			0.396541			0.198271	+	0.980147i	$0.436467\pi$
$828$	−8.88572	+	8.06775i	−0.308800	+	0.280374i
$829$	−3.52366	+	6.10315i	−0.122382	+	0.211971i	−0.920706	−	0.390256i	$-0.872387\pi$
$829$	−3.52366	+	6.10315i	−0.122382	+	0.211971i	0.798325	+	0.602227i	$0.205720\pi$
$830$	−1.74426	−	1.00705i	−0.0605442	−	0.0349552i
$831$	19.3931	−	1.66887i	0.672741	−	0.0578924i
$832$	−0.636955			−0.0220824
$833$	−31.5040	−	9.58440i	−1.09155	−	0.332080i
$834$	−0.525173	−	0.245803i	−0.0181853	−	0.00851146i
$835$	2.40064	−	1.38601i	0.0830774	−	0.0479648i
$836$	6.65750	+	3.84371i	0.230254	+	0.132937i
$837$	12.7736	−	46.8703i	0.441521	−	1.62008i
$838$	14.8579	−	8.57819i	0.513256	−	0.296328i
$839$	43.9707			1.51804			0.759018	−	0.651069i	$-0.225679\pi$
$839$	43.9707			1.51804			0.759018	+	0.651069i	$0.225679\pi$
$840$	−7.06430	+	3.51564i	−0.243742	+	0.121301i
$841$	28.7151			0.990176
$842$	2.46886	+	4.27620i	0.0850827	+	0.147368i
$843$	4.25904	+	6.10101i	0.146689	+	0.210130i
$844$	−9.69633	+	16.7945i	−0.333761	+	0.578092i
$845$	−3.65566	−	6.33179i	−0.125759	−	0.217820i
$846$	−26.9536	−	32.3084i	−0.926683	−	1.11078i
$847$	−2.08954	−	0.310815i	−0.0717974	−	0.0106797i
$848$	12.1043			0.415662
$849$	0.229331	+	2.66495i	0.00787061	+	0.0914608i
$850$	20.6013	+	11.8942i	0.706618	+	0.407966i
$851$	22.8072	+	35.9373i	0.781822	+	1.23191i
$852$	0.810935	+	9.42351i	0.0277822	+	0.322844i
$853$	35.8916			1.22890			0.614452	−	0.788954i	$-0.289377\pi$
$853$	35.8916			1.22890			0.614452	+	0.788954i	$0.289377\pi$
$854$	−8.70908	−	22.0648i	−0.298019	−	0.755042i
$855$	3.47761	−	2.90123i	0.118932	−	0.0992199i
$856$	−34.6338	+	19.9958i	−1.18376	+	0.683443i
$857$	26.2622	+	15.1625i	0.897101	+	0.517941i	0.876258	−	0.481841i	$-0.160032\pi$
$857$	26.2622	+	15.1625i	0.897101	+	0.517941i	0.0208424	+	0.999783i	$0.493365\pi$
$858$	−0.420807	+	0.293760i	−0.0143661	+	0.0100288i
$859$	−10.5029	−	18.1915i	−0.358354	−	0.620687i	0.629332	−	0.777137i	$-0.283329\pi$
$859$	−10.5029	−	18.1915i	−0.358354	−	0.620687i	−0.987686	+	0.156449i	$0.949995\pi$
$860$			4.89003i			0.166749i
$861$	−1.33752	+	21.6074i	−0.0455827	+	0.736377i
$862$			12.3049i			0.419106i
$863$	18.0816	−	10.4394i	0.615505	−	0.355362i	−0.159612	−	0.987180i	$-0.551024\pi$
$863$	18.0816	−	10.4394i	0.615505	−	0.355362i	0.775117	+	0.631818i	$0.217691\pi$
$864$	21.8286	+	5.94897i	0.742624	+	0.202388i
$865$	−1.76964	−	1.02170i	−0.0601694	−	0.0347388i
$866$	−10.2266	−	17.7130i	−0.347515	−	0.601914i
$867$	−3.76650	+	8.04736i	−0.127917	+	0.273303i
$868$	20.4096	+	3.03589i	0.692745	+	0.103045i
$869$			28.9954i			0.983603i
$870$	−0.559607	+	0.0481567i	−0.0189725	+	0.00163267i
$871$	−0.341713	−	0.197288i	−0.0115785	−	0.00668485i
$872$	26.4878	−	45.8783i	0.896991	−	1.55363i
$873$	0.769507	+	0.282561i	0.0260439	+	0.00956325i
$874$	−12.3118	−	6.43619i	−0.416451	−	0.217708i
$875$	8.96636	−	11.2882i	0.303118	−	0.381610i
$876$	−5.16990	+	11.0458i	−0.174675	+	0.373203i
$877$	4.94770	+	8.56968i	0.167072	+	0.289377i	0.937389	−	0.348284i	$-0.113235\pi$
$877$	4.94770	+	8.56968i	0.167072	+	0.289377i	−0.770317	+	0.637661i	$0.779902\pi$
$878$	−15.8337	−	9.14162i	−0.534363	−	0.308515i
$879$	−22.6707	−	32.4754i	−0.764663	−	1.09537i
$880$	−1.58077	−	2.73797i	−0.0532877	−	0.0922970i
$881$	45.1629			1.52158			0.760788	−	0.649001i	$-0.224813\pi$
$881$	45.1629			1.52158			0.760788	+	0.649001i	$0.224813\pi$
$882$	−20.8848	+	8.82882i	−0.703228	+	0.297282i
$883$	−3.99294			−0.134373			−0.0671866	−	0.997740i	$-0.521402\pi$
$883$	−3.99294			−0.134373			−0.0671866	+	0.997740i	$0.521402\pi$
$884$	0.156755	+	0.271507i	0.00527223	+	0.00913177i
$885$	0.908309	−	0.634080i	0.0305325	−	0.0213144i
$886$	−6.23777	+	10.8041i	−0.209562	+	0.362972i
$887$	0.215810	−	0.124598i	0.00724619	−	0.00418359i	−0.496373	−	0.868110i	$-0.665335\pi$
$887$	0.215810	−	0.124598i	0.00724619	−	0.00418359i	0.503619	+	0.863926i	$0.332002\pi$
$888$	19.9411	−	42.6054i	0.669179	−	1.42974i
$889$	−11.5041	+	14.4831i	−0.385837	+	0.485748i
$890$		−	10.4270i		−	0.349514i
$891$	29.1094	−	10.4076i	0.975201	−	0.348669i
$892$	−3.70336	+	6.41442i	−0.123998	+	0.214771i
$893$	−17.4247	+	30.1805i	−0.583095	+	1.00995i
$894$	−0.832579	−	9.67502i	−0.0278456	−	0.323581i
$895$			10.0554i			0.336117i
$896$	−0.0388504	+	0.261182i	−0.00129790	+	0.00872548i
$897$	−0.527760	+	0.402327i	−0.0176214	+	0.0134333i
$898$	−19.5977	−	33.9442i	−0.653983	−	1.13273i
$899$	4.32163	+	2.49510i	0.144135	+	0.0832161i
$900$	−11.5481	+	2.00237i	−0.384938	+	0.0667456i
$901$	−17.4052	−	30.1467i	−0.579851	−	1.00433i
$902$	−17.5206			−0.583373
$903$	−2.94959	+	47.6499i	−0.0981563	+	1.58569i
$904$			59.0391i			1.96361i
$905$	8.11143	−	4.68313i	0.269633	−	0.155673i
$906$	19.6657	−	13.7284i	0.653350	−	0.456096i
$907$	−11.8701	−	6.85323i	−0.394142	−	0.227558i	0.289811	−	0.957084i	$-0.406407\pi$
$907$	−11.8701	−	6.85323i	−0.394142	−	0.227558i	−0.683953	+	0.729526i	$0.739741\pi$
$908$	−4.90618	−	8.49775i	−0.162817	−	0.282008i
$909$	−3.63213	+	3.03014i	−0.120470	+	0.100504i
$910$	−0.119450	+	0.0471477i	−0.00395974	+	0.00156293i
$911$	−35.9999			−1.19273			−0.596365	−	0.802713i	$-0.703389\pi$
$911$	−35.9999			−1.19273			−0.596365	+	0.802713i	$0.703389\pi$
$912$	0.651713	+	7.57325i	0.0215804	+	0.250776i
$913$	−5.69355	+	9.86151i	−0.188429	+	0.326368i
$914$	−17.4932	+	30.2992i	−0.578625	+	1.00221i
$915$	0.693864	+	8.06308i	0.0229384	+	0.266557i
$916$		−	19.2070i		−	0.634617i
$917$	0.573524	−	3.85567i	0.0189394	−	0.127325i
$918$	6.72204	+	25.5224i	0.221860	+	0.842366i
$919$	−0.00648483	+	0.00374402i	−0.000213915	+	0.000123504i	−0.500107	−	0.865964i	$-0.666706\pi$
$919$	−0.00648483	+	0.00374402i	−0.000213915	+	0.000123504i	0.499893	+	0.866087i	$0.333373\pi$
$920$	−4.42494	−	6.97236i	−0.145886	−	0.229872i
$921$	−19.8532	−	28.4394i	−0.654185	−	0.937109i
$922$	−11.8358	−	20.5002i	−0.389791	−	0.675139i
$923$			0.522985i			0.0172142i
$924$	5.85021	+	11.7554i	0.192458	+	0.386723i
$925$			41.5656i			1.36667i
$926$	24.0330	−	13.8754i	0.789772	−	0.455975i
$927$	−4.30067	−	24.8030i	−0.141252	−	0.814637i
$928$	−1.16202	+	2.01268i	−0.0381453	+	0.0660696i
$929$	35.6082	−	20.5584i	1.16827	−	0.674499i	0.214996	−	0.976615i	$-0.431026\pi$
$929$	35.6082	−	20.5584i	1.16827	−	0.674499i	0.953271	+	0.302116i	$0.0976929\pi$
$930$	8.91049	+	4.17048i	0.292187	+	0.136755i
$931$	12.8270	+	13.7174i	0.420388	+	0.449570i
$932$		−	11.0364i		−	0.361510i
$933$	−0.261275	−	3.03615i	−0.00855375	−	0.0993992i
$934$	22.7516	+	13.1357i	0.744457	+	0.429812i
$935$	−4.54609	+	7.87406i	−0.148673	+	0.257509i
$936$	0.688487	+	0.252811i	0.0225039	+	0.00826338i
$937$		−	37.7428i		−	1.23300i	−0.787353	−	0.616502i	$-0.788549\pi$
$937$		−	37.7428i		−	1.23300i	0.787353	−	0.616502i	$-0.211451\pi$
$938$	8.77547	−	11.0479i	0.286529	−	0.360725i
$939$	−11.8192	−	5.53186i	−0.385704	−	0.180526i
$940$	−5.28020	+	3.04853i	−0.172221	+	0.0994320i
$941$	18.1409	−	31.4210i	0.591377	−	1.02429i	−0.402671	−	0.915345i	$-0.631918\pi$
$941$	18.1409	−	31.4210i	0.591377	−	1.02429i	0.994047	−	0.108949i	$-0.0347486\pi$
$942$	13.3383	+	19.1069i	0.434586	+	0.622538i
$943$	−22.6363	+	0.949082i	−0.737139	+	0.0309064i
$944$			1.85921i			0.0605123i
$945$	7.68902	−	0.848158i	0.250124	−	0.0275906i
$946$	−38.6376			−1.25622
$947$	−28.8683	+	16.6671i	−0.938095	+	0.541609i	−0.889363	−	0.457203i	$-0.848851\pi$
$947$	−28.8683	+	16.6671i	−0.938095	+	0.541609i	−0.0487321	+	0.998812i	$0.515518\pi$
$948$	10.0009	−	6.98149i	0.324813	−	0.226748i
$949$	−0.337175	+	0.584003i	−0.0109451	+	0.0189576i
$950$	−6.78342	−	11.7492i	−0.220083	−	0.381196i
$951$	0.526461	+	0.246406i	0.0170717	+	0.00799025i
$952$	−35.4276	+	13.9834i	−1.14821	+	0.453206i
$953$	34.8537			1.12902			0.564511	−	0.825426i	$-0.309065\pi$
$953$	34.8537			1.12902			0.564511	+	0.825426i	$0.309065\pi$
$954$	−22.5003	−	8.26206i	−0.728475	−	0.267494i
$955$	3.62762	−	6.28322i	0.117387	−	0.203320i
$956$	11.2059	+	6.46972i	0.362424	+	0.209246i
$957$	0.272263	+	3.16384i	0.00880102	+	0.102273i
$958$		−	18.2114i		−	0.588383i
$959$	7.81790	+	19.8069i	0.252453	+	0.639599i
$960$	−3.29389	+	7.03759i	−0.106310	+	0.227137i
$961$	−28.2036	−	48.8500i	−0.909793	−	1.57581i
$962$	0.382786	−	0.663006i	0.0123415	−	0.0213762i
$963$	38.6291	−	6.69803i	1.24481	−	0.215841i
$964$	5.92119	−	3.41860i	0.190709	−	0.110106i
$965$	11.6233			0.374166
$966$	−11.4531	−	20.7826i	−0.368496	−	0.668668i
$967$	−7.29895			−0.234718			−0.117359	−	0.993090i	$-0.537443\pi$
$967$	−7.29895			−0.234718			−0.117359	+	0.993090i	$0.537443\pi$
$968$	−2.11606	+	1.22171i	−0.0680126	+	0.0392671i
$969$	17.9247	−	12.5130i	0.575824	−	0.401976i
$970$	−0.0830058	+	0.143770i	−0.00266516	+	0.00461618i
$971$	14.2503	+	24.6823i	0.457314	+	0.792092i	0.998818	−	0.0486068i	$-0.0154781\pi$
$971$	14.2503	+	24.6823i	0.457314	+	0.792092i	−0.541504	+	0.840698i	$0.682145\pi$
$972$	−10.5986	−	7.53423i	−0.339952	−	0.241660i
$973$	−0.510227	+	0.642349i	−0.0163571	+	0.0205928i
$974$		−	36.0938i		−	1.15652i
$975$	−0.645678	+	0.0555636i	−0.0206783	+	0.00177946i
$976$	−11.7632	−	6.79150i	−0.376532	−	0.217391i
$977$	−16.3816	+	28.3737i	−0.524093	+	0.907756i	0.475514	+	0.879708i	$0.342262\pi$
$977$	−16.3816	+	28.3737i	−0.524093	+	0.907756i	−0.999607	+	0.0280472i	$0.991071\pi$
$978$	1.22287	+	14.2104i	0.0391032	+	0.454400i
$979$	−58.9511			−1.88409
$980$	0.743522	+	3.20046i	0.0237509	+	0.102235i
$981$	−39.8789	+	33.2694i	−1.27324	+	1.06221i
$982$	4.55022	+	7.88121i	0.145203	+	0.251500i
$983$	18.4344	−	31.9293i	0.587966	−	1.01839i	−0.406533	−	0.913636i	$-0.633262\pi$
$983$	18.4344	−	31.9293i	0.587966	−	1.01839i	0.994499	−	0.104750i	$-0.0334043\pi$
$984$	14.3329	+	20.5316i	0.456915	+	0.654523i
$985$	0.0433801	−	0.0250455i	0.00138221	−	0.000798017i
$986$	−2.71111			−0.0863395
$987$	−53.2906	+	26.5208i	−1.69626	+	0.844165i
$988$		−	0.178799i		−	0.00568836i
$989$	−49.9189	+	2.09297i	−1.58733	+	0.0665527i
$990$	1.06958	+	6.16854i	0.0339935	+	0.196049i
$991$	19.7335	−	34.1794i	0.626855	−	1.08575i	−0.361324	−	0.932440i	$-0.617675\pi$
$991$	19.7335	−	34.1794i	0.626855	−	1.08575i	0.988179	−	0.153305i	$-0.0489916\pi$
$992$	35.2537	−	20.3538i	1.11931	−	0.646233i
$993$	−5.72033	+	12.2218i	−0.181529	+	0.387848i
$994$	−18.4970	−	2.75140i	−0.586690	−	0.0872692i
$995$			10.3955i			0.329561i
$996$	4.77224	−	0.410673i	0.151214	−	0.0130127i
$997$	−10.5685	+	18.3053i	−0.334709	+	0.579733i	−0.983429	−	0.181294i	$-0.941971\pi$
$997$	−10.5685	+	18.3053i	−0.334709	+	0.579733i	0.648720	+	0.761027i	$0.275305\pi$
$998$	−4.17945	−	2.41301i	−0.132298	−	0.0763825i
$999$	−32.7482	+	32.4697i	−1.03611	+	1.02730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.m.a.137.20	yes	120
3.2	odd	2	inner	483.2.m.a.137.41	yes	120
7.2	even	3	inner	483.2.m.a.275.42	yes	120
21.2	odd	6	inner	483.2.m.a.275.19	yes	120
23.22	odd	2	inner	483.2.m.a.137.19	✓	120
69.68	even	2	inner	483.2.m.a.137.42	yes	120
161.114	odd	6	inner	483.2.m.a.275.41	yes	120
483.275	even	6	inner	483.2.m.a.275.20	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.m.a.137.19	✓	120	23.22	odd	2	inner
483.2.m.a.137.20	yes	120	1.1	even	1	trivial
483.2.m.a.137.41	yes	120	3.2	odd	2	inner
483.2.m.a.137.42	yes	120	69.68	even	2	inner
483.2.m.a.275.19	yes	120	21.2	odd	6	inner
483.2.m.a.275.20	yes	120	483.275	even	6	inner
483.2.m.a.275.41	yes	120	161.114	odd	6	inner
483.2.m.a.275.42	yes	120	7.2	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.935072 + 0.539864i) q^{2} +(-0.991443 - 1.42023i) q^{3} +(-0.417093 + 0.722427i) q^{4} +(0.281343 + 0.487300i) q^{5} +(1.69380 + 0.792769i) q^{6} +(1.64560 - 2.07172i) q^{7} -3.06015i q^{8} +(-1.03408 + 2.81615i) q^{9} +O(q^{10})\)	\(q+(-0.935072 + 0.539864i) q^{2} +(-0.991443 - 1.42023i) q^{3} +(-0.417093 + 0.722427i) q^{4} +(0.281343 + 0.487300i) q^{5} +(1.69380 + 0.792769i) q^{6} +(1.64560 - 2.07172i) q^{7} -3.06015i q^{8} +(-1.03408 + 2.81615i) q^{9} +(-0.526152 - 0.303774i) q^{10} +(-1.71744 + 2.97470i) q^{11} +(1.43953 - 0.123878i) q^{12} +0.0798910 q^{13} +(-0.420304 + 2.82560i) q^{14} +(0.413141 - 0.882701i) q^{15} +(0.817880 + 1.41661i) q^{16} +(2.35212 - 4.07399i) q^{17} +(-0.553395 - 3.19156i) q^{18} +(-2.32346 + 1.34145i) q^{19} -0.469385 q^{20} +(-4.57382 - 0.283126i) q^{21} -3.70875i q^{22} +(-0.200901 - 4.79162i) q^{23} +(-4.34611 + 3.03397i) q^{24} +(2.34169 - 4.05593i) q^{25} +(-0.0747039 + 0.0431303i) q^{26} +(5.02479 - 1.32342i) q^{27} +(0.810298 + 2.05292i) q^{28} +0.533757i q^{29} +(0.0902221 + 1.04843i) q^{30} +(4.67459 - 8.09663i) q^{31} +(3.77079 + 2.17706i) q^{32} +(5.92749 - 0.510088i) q^{33} +5.07930i q^{34} +(1.47253 + 0.219036i) q^{35} +(-1.60315 - 1.92164i) q^{36} +(-7.68608 + 4.43756i) q^{37} +(1.44840 - 2.50871i) q^{38} +(-0.0792074 - 0.113463i) q^{39} +(1.49121 - 0.860952i) q^{40} -4.72414i q^{41} +(4.42970 - 2.20450i) q^{42} -10.4180i q^{43} +(-1.43267 - 2.48146i) q^{44} +(-1.66324 + 0.288394i) q^{45} +(2.77468 + 4.37205i) q^{46} +(11.2492 - 6.49472i) q^{47} +(1.20102 - 2.56606i) q^{48} +(-1.58403 - 6.81842i) q^{49} +5.05678i q^{50} +(-8.11798 + 0.698589i) q^{51} +(-0.0333220 + 0.0577154i) q^{52} +(3.69989 - 6.40840i) q^{53} +(-3.98408 + 3.95020i) q^{54} -1.93276 q^{55} +(-6.33977 - 5.03577i) q^{56} +(4.20874 + 1.96987i) q^{57} +(-0.288157 - 0.499102i) q^{58} +(0.984330 + 0.568303i) q^{59} +(0.465369 + 0.666633i) q^{60} +(-7.19129 + 4.15189i) q^{61} +10.0946i q^{62} +(4.13258 + 6.77656i) q^{63} -7.97279 q^{64} +(0.0224768 + 0.0389309i) q^{65} +(-5.26726 + 3.67701i) q^{66} +(-4.27724 - 2.46947i) q^{67} +(1.96211 + 3.39847i) q^{68} +(-6.60600 + 5.03594i) q^{69} +(-1.49517 + 0.590150i) q^{70} +6.54622i q^{71} +(8.61783 + 3.16445i) q^{72} +(-4.22043 + 7.31000i) q^{73} +(4.79136 - 8.29887i) q^{74} +(-8.08199 + 0.695492i) q^{75} -2.23804i q^{76} +(3.33652 + 8.45321i) q^{77} +(0.135319 + 0.0633351i) q^{78} +(7.31051 - 4.22073i) q^{79} +(-0.460209 + 0.797106i) q^{80} +(-6.86135 - 5.82425i) q^{81} +(2.55039 + 4.41741i) q^{82} +3.31513 q^{83} +(2.11225 - 3.18616i) q^{84} +2.64701 q^{85} +(5.62428 + 9.74154i) q^{86} +(0.758056 - 0.529190i) q^{87} +(9.10304 + 5.25564i) q^{88} +(8.58122 + 14.8631i) q^{89} +(1.39956 - 1.16759i) q^{90} +(0.131468 - 0.165512i) q^{91} +(3.54539 + 1.85342i) q^{92} +(-16.1336 + 1.38837i) q^{93} +(-7.01254 + 12.1461i) q^{94} +(-1.30738 - 0.754815i) q^{95} +(-0.646597 - 7.51380i) q^{96} -0.273248i q^{97} +(5.16221 + 5.52055i) q^{98} +(-6.60121 - 7.91266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9}+O(q^{10}) \) 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9	\( 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9} + 14 q^{12} - 16 q^{13} - 60 q^{16} - 10 q^{18} - 24 q^{24} - 40 q^{25} - 20 q^{27} - 4 q^{31} + 64 q^{36} - 12 q^{39} - 20 q^{46} + 140 q^{48} - 48 q^{49} - 76 q^{52} - 2 q^{54} + 72 q^{55} - 28 q^{58} - 128 q^{64} - 20 q^{69} - 68 q^{70} + 6 q^{72} + 20 q^{73} + 20 q^{75} - 156 q^{78} - 62 q^{81} + 80 q^{82} + 112 q^{85} + 46 q^{87} - 38 q^{93} + 36 q^{94} + 72 q^{96}+O(q^{100}) \) 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9 + 14 * q^12 - 16 * q^13 - 60 * q^16 - 10 * q^18 - 24 * q^24 - 40 * q^25 - 20 * q^27 - 4 * q^31 + 64 * q^36 - 12 * q^39 - 20 * q^46 + 140 * q^48 - 48 * q^49 - 76 * q^52 - 2 * q^54 + 72 * q^55 - 28 * q^58 - 128 * q^64 - 20 * q^69 - 68 * q^70 + 6 * q^72 + 20 * q^73 + 20 * q^75 - 156 * q^78 - 62 * q^81 + 80 * q^82 + 112 * q^85 + 46 * q^87 - 38 * q^93 + 36 * q^94 + 72 * q^96

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