LMFDB - Embedded newform 280.2.s.c.237.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("280.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			237.34
Character	$\chi$	$=$	280.237
Dual form			280.2.s.c.13.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32946 - 0.482209i) q^{2} +(0.851048 - 0.851048i) q^{3} +(1.53495 - 1.28216i) q^{4} +(-2.18999 + 0.451591i) q^{5} +(0.721055 - 1.54182i) q^{6} +(2.50752 - 0.844017i) q^{7} +(1.42239 - 2.44475i) q^{8} +1.55144i q^{9} +O(q^{10})$	\(q+(1.32946 - 0.482209i) q^{2} +(0.851048 - 0.851048i) q^{3} +(1.53495 - 1.28216i) q^{4} +(-2.18999 + 0.451591i) q^{5} +(0.721055 - 1.54182i) q^{6} +(2.50752 - 0.844017i) q^{7} +(1.42239 - 2.44475i) q^{8} +1.55144i q^{9} +(-2.69375 + 1.65641i) q^{10} -2.51177i q^{11} +(0.215137 - 2.39749i) q^{12} +(-2.05614 + 2.05614i) q^{13} +(2.92666 - 2.33124i) q^{14} +(-1.47946 + 2.24811i) q^{15} +(0.712139 - 3.93610i) q^{16} +(0.323302 - 0.323302i) q^{17} +(0.748116 + 2.06258i) q^{18} -0.414250i q^{19} +(-2.78252 + 3.50109i) q^{20} +(1.41572 - 2.85231i) q^{21} +(-1.21120 - 3.33930i) q^{22} +(-5.60285 + 5.60285i) q^{23} +(-0.870076 - 3.29112i) q^{24} +(4.59213 - 1.97796i) q^{25} +(-1.74207 + 3.72505i) q^{26} +(3.87349 + 3.87349i) q^{27} +(2.76675 - 4.51056i) q^{28} -2.48079 q^{29} +(-0.882832 + 3.70220i) q^{30} +7.18461i q^{31} +(-0.951258 - 5.57630i) q^{32} +(-2.13763 - 2.13763i) q^{33} +(0.273919 - 0.585718i) q^{34} +(-5.11029 + 2.98076i) q^{35} +(1.98919 + 2.38137i) q^{36} +(-4.54475 + 4.54475i) q^{37} +(-0.199755 - 0.550730i) q^{38} +3.49974i q^{39} +(-2.01100 + 5.99632i) q^{40} +1.40978i q^{41} +(0.506734 - 4.47472i) q^{42} +(4.10811 + 4.10811i) q^{43} +(-3.22048 - 3.85543i) q^{44} +(-0.700614 - 3.39763i) q^{45} +(-4.74704 + 10.1505i) q^{46} +(5.84872 - 5.84872i) q^{47} +(-2.74374 - 3.95587i) q^{48} +(5.57527 - 4.23277i) q^{49} +(5.15128 - 4.84399i) q^{50} -0.550291i q^{51} +(-0.519772 + 5.79236i) q^{52} +(-7.59714 - 7.59714i) q^{53} +(7.01749 + 3.28183i) q^{54} +(1.13429 + 5.50075i) q^{55} +(1.50326 - 7.33077i) q^{56} +(-0.352547 - 0.352547i) q^{57} +(-3.29812 + 1.19626i) q^{58} -1.24364i q^{59} +(0.611538 + 5.34765i) q^{60} +11.7206 q^{61} +(3.46448 + 9.55169i) q^{62} +(1.30944 + 3.89025i) q^{63} +(-3.95360 - 6.95478i) q^{64} +(3.57439 - 5.43146i) q^{65} +(-3.87269 - 1.81112i) q^{66} +(-2.90850 + 2.90850i) q^{67} +(0.0817277 - 0.910777i) q^{68} +9.53658i q^{69} +(-5.35660 + 6.42704i) q^{70} -0.972317 q^{71} +(3.79287 + 2.20675i) q^{72} +(-10.4999 - 10.4999i) q^{73} +(-3.85056 + 8.23359i) q^{74} +(2.22478 - 5.59146i) q^{75} +(-0.531134 - 0.635853i) q^{76} +(-2.11997 - 6.29829i) q^{77} +(1.68761 + 4.65278i) q^{78} -5.80828i q^{79} +(0.217928 + 8.94162i) q^{80} +1.93874 q^{81} +(0.679808 + 1.87425i) q^{82} +(-9.17675 + 9.17675i) q^{83} +(-1.48406 - 6.19333i) q^{84} +(-0.562029 + 0.854029i) q^{85} +(7.44255 + 3.48062i) q^{86} +(-2.11127 + 2.11127i) q^{87} +(-6.14064 - 3.57272i) q^{88} -10.0566 q^{89} +(-2.56981 - 4.17919i) q^{90} +(-3.42038 + 6.89121i) q^{91} +(-1.41635 + 15.7838i) q^{92} +(6.11445 + 6.11445i) q^{93} +(4.95536 - 10.5960i) q^{94} +(0.187072 + 0.907204i) q^{95} +(-5.55526 - 3.93613i) q^{96} +(1.18210 - 1.18210i) q^{97} +(5.37104 - 8.31576i) q^{98} +3.89684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.32946	−	0.482209i	0.940073	−	0.340973i
$2$	1.32946	−	0.482209i	0.940073	−	0.340973i
$3$	0.851048	−	0.851048i	0.491353	−	0.491353i	−0.417380	−	0.908732i	$-0.637051\pi$
$3$	0.851048	−	0.851048i	0.491353	−	0.491353i	0.908732	+	0.417380i	$0.137051\pi$
$4$	1.53495	−	1.28216i	0.767475	−	0.641079i
$5$	−2.18999	+	0.451591i	−0.979394	+	0.201958i
$5$	−2.18999	+	0.451591i	−0.979394	+	0.201958i
$6$	0.721055	−	1.54182i	0.294369	−	0.629445i
$7$	2.50752	−	0.844017i	0.947752	−	0.319008i
$7$	2.50752	−	0.844017i	0.947752	−	0.319008i
$8$	1.42239	−	2.44475i	0.502891	−	0.864350i
$9$			1.55144i			0.517145i
$10$	−2.69375	+	1.65641i	−0.851840	+	0.523802i
$11$		−	2.51177i		−	0.757326i	−0.925535	−	0.378663i	$-0.876384\pi$
$11$		−	2.51177i		−	0.757326i	0.925535	−	0.378663i	$-0.123616\pi$
$12$	0.215137	−	2.39749i	0.0621047	−	0.692097i
$13$	−2.05614	+	2.05614i	−0.570270	+	0.570270i	−0.932204	−	0.361934i	$-0.882117\pi$
$13$	−2.05614	+	2.05614i	−0.570270	+	0.570270i	0.361934	+	0.932204i	$0.382117\pi$
$14$	2.92666	−	2.33124i	0.782183	−	0.623049i
$15$	−1.47946	+	2.24811i	−0.381996	+	0.580460i
$16$	0.712139	−	3.93610i	0.178035	−	0.984024i
$17$	0.323302	−	0.323302i	0.0784123	−	0.0784123i	−0.666813	−	0.745225i	$-0.732342\pi$
$17$	0.323302	−	0.323302i	0.0784123	−	0.0784123i	0.745225	+	0.666813i	$0.232342\pi$
$18$	0.748116	+	2.06258i	0.176333	+	0.486154i
$19$		−	0.414250i		−	0.0950355i	−0.998870	−	0.0475177i	$-0.984869\pi$
$19$		−	0.414250i		−	0.0950355i	0.998870	−	0.0475177i	$-0.0151311\pi$
$20$	−2.78252	+	3.50109i	−0.622189	+	0.782867i
$21$	1.41572	−	2.85231i	0.308935	−	0.622426i
$22$	−1.21120	−	3.33930i	−0.258228	−	0.711942i
$23$	−5.60285	+	5.60285i	−1.16827	+	1.16827i	−0.185660	+	0.982614i	$0.559442\pi$
$23$	−5.60285	+	5.60285i	−1.16827	+	1.16827i	−0.982614	+	0.185660i	$0.940558\pi$
$24$	−0.870076	−	3.29112i	−0.177603	−	0.671797i
$25$	4.59213	−	1.97796i	0.918426	−	0.395592i
$26$	−1.74207	+	3.72505i	−0.341649	+	0.730542i
$27$	3.87349	+	3.87349i	0.745453	+	0.745453i
$28$	2.76675	−	4.51056i	0.522866	−	0.852415i
$29$	−2.48079			−0.460670			−0.230335	−	0.973111i	$-0.573982\pi$
$29$	−2.48079			−0.460670			−0.230335	+	0.973111i	$0.573982\pi$
$30$	−0.882832	+	3.70220i	−0.161182	+	0.675925i
$31$			7.18461i			1.29039i	0.764016	+	0.645197i	$0.223225\pi$
$31$			7.18461i			1.29039i	−0.764016	+	0.645197i	$0.776775\pi$
$32$	−0.951258	−	5.57630i	−0.168160	−	0.985760i
$33$	−2.13763	−	2.13763i	−0.372114	−	0.372114i
$34$	0.273919	−	0.585718i	0.0469768	−	0.100450i
$35$	−5.11029	+	2.98076i	−0.863797	+	0.503841i
$36$	1.98919	+	2.38137i	0.331531	+	0.396896i
$37$	−4.54475	+	4.54475i	−0.747152	+	0.747152i	−0.973943	−	0.226792i	$-0.927176\pi$
$37$	−4.54475	+	4.54475i	−0.747152	+	0.747152i	0.226792	+	0.973943i	$0.427176\pi$
$38$	−0.199755	−	0.550730i	−0.0324045	−	0.0893403i
$39$			3.49974i			0.560407i
$40$	−2.01100	+	5.99632i	−0.317967	+	0.948102i
$41$			1.40978i			0.220171i	0.993922	+	0.110085i	$0.0351124\pi$
$41$			1.40978i			0.220171i	−0.993922	+	0.110085i	$0.964888\pi$
$42$	0.506734	−	4.47472i	0.0781908	−	0.690464i
$43$	4.10811	+	4.10811i	0.626481	+	0.626481i	0.947181	−	0.320700i	$-0.103918\pi$
$43$	4.10811	+	4.10811i	0.626481	+	0.626481i	−0.320700	+	0.947181i	$0.603918\pi$
$44$	−3.22048	−	3.85543i	−0.485506	−	0.581229i
$45$	−0.700614	−	3.39763i	−0.104441	−	0.506489i
$46$	−4.74704	+	10.1505i	−0.699913	+	1.49661i
$47$	5.84872	−	5.84872i	0.853124	−	0.853124i	−0.137393	−	0.990517i	$-0.543872\pi$
$47$	5.84872	−	5.84872i	0.853124	−	0.853124i	0.990517	+	0.137393i	$0.0438723\pi$
$48$	−2.74374	−	3.95587i	−0.396025	−	0.570981i
$49$	5.57527	−	4.23277i	0.796467	−	0.604681i
$50$	5.15128	−	4.84399i	0.728501	−	0.685044i
$51$		−	0.550291i		−	0.0770562i
$52$	−0.519772	+	5.79236i	−0.0720795	+	0.803256i
$53$	−7.59714	−	7.59714i	−1.04355	−	1.04355i	−0.999008	−	0.0445393i	$-0.985818\pi$
$53$	−7.59714	−	7.59714i	−1.04355	−	1.04355i	−0.0445393	−	0.999008i	$-0.514182\pi$
$54$	7.01749	+	3.28183i	0.954960	+	0.446601i
$55$	1.13429	+	5.50075i	0.152948	+	0.741721i
$56$	1.50326	−	7.33077i	0.200882	−	0.979616i
$57$	−0.352547	−	0.352547i	−0.0466959	−	0.0466959i
$58$	−3.29812	+	1.19626i	−0.433064	+	0.157076i
$59$		−	1.24364i		−	0.161909i	−0.996718	−	0.0809543i	$-0.974203\pi$
$59$		−	1.24364i		−	0.161909i	0.996718	−	0.0809543i	$-0.0257968\pi$
$60$	0.611538	+	5.34765i	0.0789492	+	0.690378i
$61$	11.7206			1.50067			0.750335	−	0.661058i	$-0.229892\pi$
$61$	11.7206			1.50067			0.750335	+	0.661058i	$0.229892\pi$
$62$	3.46448	+	9.55169i	0.439990	+	1.21307i
$63$	1.30944	+	3.89025i	0.164974	+	0.490125i
$64$	−3.95360	−	6.95478i	−0.494201	−	0.869348i
$65$	3.57439	−	5.43146i	0.443349	−	0.673690i
$66$	−3.87269	−	1.81112i	−0.476695	−	0.222934i
$67$	−2.90850	+	2.90850i	−0.355329	+	0.355329i	−0.862088	−	0.506759i	$-0.830844\pi$
$67$	−2.90850	+	2.90850i	−0.355329	+	0.355329i	0.506759	+	0.862088i	$0.330844\pi$
$68$	0.0817277	−	0.910777i	0.00991094	−	0.110448i
$69$			9.53658i			1.14807i
$70$	−5.35660	+	6.42704i	−0.640236	+	0.768178i
$71$	−0.972317			−0.115393			−0.0576964	−	0.998334i	$-0.518376\pi$
$71$	−0.972317			−0.115393			−0.0576964	+	0.998334i	$0.518376\pi$
$72$	3.79287	+	2.20675i	0.446994	+	0.260068i
$73$	−10.4999	−	10.4999i	−1.22892	−	1.22892i	−0.964372	−	0.264550i	$-0.914777\pi$
$73$	−10.4999	−	10.4999i	−1.22892	−	1.22892i	−0.264550	−	0.964372i	$-0.585223\pi$
$74$	−3.85056	+	8.23359i	−0.447618	+	0.957136i
$75$	2.22478	−	5.59146i	0.256896	−	0.645646i
$76$	−0.531134	−	0.635853i	−0.0609253	−	0.0729373i
$77$	−2.11997	−	6.29829i	−0.241593	−	0.717757i
$78$	1.68761	+	4.65278i	0.191084	+	0.526824i
$79$		−	5.80828i		−	0.653483i	−0.945114	−	0.326741i	$-0.894049\pi$
$79$		−	5.80828i		−	0.653483i	0.945114	−	0.326741i	$-0.105951\pi$
$80$	0.217928	+	8.94162i	0.0243651	+	0.999703i
$81$	1.93874			0.215416
$82$	0.679808	+	1.87425i	0.0750722	+	0.206976i
$83$	−9.17675	+	9.17675i	−1.00728	+	1.00728i	−0.00730635	+	0.999973i	$0.502326\pi$
$83$	−9.17675	+	9.17675i	−1.00728	+	1.00728i	−0.999973	+	0.00730635i	$0.997674\pi$
$84$	−1.48406	−	6.19333i	−0.161925	−	0.675748i
$85$	−0.562029	+	0.854029i	−0.0609606	+	0.0926325i
$86$	7.44255	+	3.48062i	0.802551	+	0.375325i
$87$	−2.11127	+	2.11127i	−0.226352	+	0.226352i
$88$	−6.14064	−	3.57272i	−0.654595	−	0.380853i
$89$	−10.0566			−1.06600			−0.533000	−	0.846115i	$-0.678935\pi$
$89$	−10.0566			−1.06600			−0.533000	+	0.846115i	$0.678935\pi$
$90$	−2.56981	−	4.17919i	−0.270882	−	0.440525i
$91$	−3.42038	+	6.89121i	−0.358554	+	0.722395i
$92$	−1.41635	+	15.7838i	−0.147664	+	1.64558i
$93$	6.11445	+	6.11445i	0.634039	+	0.634039i
$94$	4.95536	−	10.5960i	0.511106	−	1.09289i
$95$	0.187072	+	0.907204i	0.0191931	+	0.0930772i
$96$	−5.55526	−	3.93613i	−0.566982	−	0.401730i
$97$	1.18210	−	1.18210i	0.120025	−	0.120025i	−0.644543	−	0.764568i	$-0.722952\pi$
$97$	1.18210	−	1.18210i	0.120025	−	0.120025i	0.764568	+	0.644543i	$0.222952\pi$
$98$	5.37104	−	8.31576i	0.542557	−	0.840019i
$99$	3.89684			0.391648
$100$	4.51263	−	8.92391i	0.451263	−	0.892391i
$101$	0.133613			0.0132949			0.00664747	−	0.999978i	$-0.497884\pi$
$101$	0.133613			0.0132949			0.00664747	+	0.999978i	$0.497884\pi$
$102$	−0.265355	−	0.731592i	−0.0262741	−	0.0724384i
$103$	−13.2794	−	13.2794i	−1.30846	−	1.30846i	−0.922527	−	0.385932i	$-0.873880\pi$
$103$	−13.2794	−	13.2794i	−1.30846	−	1.30846i	−0.385932	−	0.922527i	$-0.626120\pi$
$104$	2.10211	+	7.95138i	0.206129	+	0.779697i
$105$	−1.81233	+	6.88587i	−0.176865	+	0.671992i
$106$	−13.7635	−	6.43671i	−1.33683	−	0.625189i
$107$	8.93593	−	8.93593i	0.863869	−	0.863869i	−0.127916	−	0.991785i	$-0.540829\pi$
$107$	8.93593	−	8.93593i	0.863869	−	0.863869i	0.991785	+	0.127916i	$0.0408288\pi$
$108$	10.9120	+	0.979182i	1.05001	+	0.0942218i
$109$	17.1604			1.64367			0.821836	−	0.569724i	$-0.192950\pi$
$109$	17.1604			1.64367			0.821836	+	0.569724i	$0.192950\pi$
$110$	4.16051	+	6.76608i	0.396689	+	0.645121i
$111$			7.73559i			0.734230i
$112$	−1.53643	−	10.4709i	−0.145179	−	0.989405i
$113$	3.28379	−	3.28379i	0.308913	−	0.308913i	−0.535575	−	0.844488i	$-0.679905\pi$
$113$	3.28379	−	3.28379i	0.308913	−	0.308913i	0.844488	+	0.535575i	$0.179905\pi$
$114$	−0.638699	−	0.298697i	−0.0598196	−	0.0279755i
$115$	9.73999	−	14.8004i	0.908259	−	1.38014i
$116$	−3.80788	+	3.18076i	−0.353553	+	0.295326i
$117$	−3.18997	−	3.18997i	−0.294912	−	0.294912i
$118$	−0.599696	−	1.65338i	−0.0552065	−	0.152206i
$119$	0.537813	−	1.08356i	0.0493012	−	0.0993295i
$120$	3.39170	+	6.81461i	0.309618	+	0.622086i
$121$	4.69103			0.426457
$122$	15.5821	−	5.65178i	1.41074	−	0.511688i
$123$	1.19979	+	1.19979i	0.108181	+	0.108181i
$124$	9.21181	+	11.0280i	0.827245	+	0.990345i
$125$	−9.16350	+	6.40548i	−0.819609	+	0.572924i
$126$	3.61676	+	4.54052i	0.322207	+	0.404502i
$127$	−2.75474	−	2.75474i	−0.244444	−	0.244444i	0.574242	−	0.818686i	$-0.305297\pi$
$127$	−2.75474	−	2.75474i	−0.244444	−	0.244444i	−0.818686	+	0.574242i	$0.805297\pi$
$128$	−8.60983	−	7.33967i	−0.761009	−	0.648741i
$129$	6.99239			0.615646
$130$	2.13293	−	8.94453i	0.187070	−	0.784487i
$131$	4.14619			0.362254			0.181127	−	0.983460i	$-0.442025\pi$
$131$	4.14619			0.362254			0.181127	+	0.983460i	$0.442025\pi$
$132$	−6.02194	−	0.540374i	−0.524143	−	0.0470335i
$133$	−0.349634	−	1.03874i	−0.0303171	−	0.0900700i
$134$	−2.46424	+	5.26924i	−0.212878	+	0.455193i
$135$	−10.2321	−	6.73368i	−0.880643	−	0.579543i
$136$	−0.330531	−	1.25025i	−0.0283428	−	0.107208i
$137$	−8.52736	−	8.52736i	−0.728542	−	0.728542i	0.241787	−	0.970329i	$-0.422266\pi$
$137$	−8.52736	−	8.52736i	−0.728542	−	0.728542i	−0.970329	+	0.241787i	$0.922266\pi$
$138$	4.59862	+	12.6785i	0.391461	+	1.07927i
$139$			5.99846i			0.508783i	0.967101	+	0.254391i	$0.0818751\pi$
$139$			5.99846i			0.508783i	−0.967101	+	0.254391i	$0.918125\pi$
$140$	−4.02223	+	11.1275i	−0.339940	+	0.940447i
$141$		−	9.95508i		−	0.838369i
$142$	−1.29266	+	0.468860i	−0.108478	+	0.0393458i
$143$	5.16454	+	5.16454i	0.431880	+	0.431880i
$144$	6.10660	+	1.10484i	0.508883	+	0.0920698i
$145$	5.43290	−	1.12030i	0.451178	−	0.0930359i
$146$	−19.0224	−	8.89611i	−1.57431	−	0.736247i
$147$	1.14253	−	8.34711i	0.0942345	−	0.688458i
$148$	−1.14887	+	12.8030i	−0.0944365	+	1.05240i
$149$	−5.59017			−0.457965			−0.228982	−	0.973431i	$-0.573540\pi$
$149$	−5.59017			−0.457965			−0.228982	+	0.973431i	$0.573540\pi$
$150$	0.261517	−	8.50646i	0.0213528	−	0.694549i
$151$	7.05684			0.574278			0.287139	−	0.957889i	$-0.407296\pi$
$151$	7.05684			0.574278			0.287139	+	0.957889i	$0.407296\pi$
$152$	−1.01274	−	0.589226i	−0.0821439	−	0.0477925i
$153$	0.501582	+	0.501582i	0.0405505	+	0.0405505i
$154$	−5.85552	−	7.35109i	−0.471851	−	0.592367i
$155$	−3.24451	−	15.7342i	−0.260605	−	1.26381i
$156$	4.48723	+	5.37193i	0.359266	+	0.430098i
$157$	−12.7347	−	12.7347i	−1.01634	−	1.01634i	−0.999864	−	0.0164774i	$-0.994755\pi$
$157$	−12.7347	−	12.7347i	−1.01634	−	1.01634i	−0.0164774	−	0.999864i	$-0.505245\pi$
$158$	−2.80081	−	7.72190i	−0.222820	−	0.614322i
$159$	−12.9311			−1.02550
$160$	4.60145	+	11.7825i	0.363777	+	0.931486i
$161$	−9.32033	+	18.7781i	−0.734545	+	1.47992i
$162$	2.57749	−	0.934878i	0.202506	−	0.0734510i
$163$	3.78159	+	3.78159i	0.296197	+	0.296197i	0.839522	−	0.543325i	$-0.182835\pi$
$163$	3.78159	+	3.78159i	0.296197	+	0.296197i	−0.543325	+	0.839522i	$0.682835\pi$
$164$	1.80756	+	2.16394i	0.141147	+	0.168975i
$165$	5.64674	+	3.71606i	0.439598	+	0.289295i
$166$	−7.77505	+	16.6253i	−0.603461	+	1.29037i
$167$	5.05575	−	5.05575i	0.391225	−	0.391225i	−0.483899	−	0.875124i	$-0.660780\pi$
$167$	5.05575	−	5.05575i	0.391225	−	0.391225i	0.875124	+	0.483899i	$0.160780\pi$
$168$	−4.95949	−	7.51818i	−0.382633	−	0.580040i
$169$			4.54459i			0.349584i
$170$	−0.335377	+	1.40642i	−0.0257222	+	0.107867i
$171$	0.642682			0.0491471
$172$	11.5730	+	1.03849i	0.882432	+	0.0791842i
$173$	15.9087	−	15.9087i	1.20951	−	1.20951i	0.238329	−	0.971184i	$-0.423400\pi$
$173$	15.9087	−	15.9087i	1.20951	−	1.20951i	0.971184	−	0.238329i	$-0.0765998\pi$
$174$	−1.78878	+	3.82493i	−0.135607	+	0.289967i
$175$	9.84541	−	8.83560i	0.744243	−	0.667909i
$176$	−9.88656	−	1.78873i	−0.745227	−	0.134830i
$177$	−1.05840	−	1.05840i	−0.0795542	−	0.0795542i
$178$	−13.3699	+	4.84939i	−1.00212	+	0.363477i
$179$	1.92015			0.143519			0.0717593	−	0.997422i	$-0.477139\pi$
$179$	1.92015			0.143519			0.0717593	+	0.997422i	$0.477139\pi$
$180$	−5.43171	−	4.31689i	−0.404856	−	0.321762i
$181$	8.92242			0.663199			0.331599	−	0.943420i	$-0.392412\pi$
$181$	8.92242			0.663199			0.331599	+	0.943420i	$0.392412\pi$
$182$	−1.22427	+	10.8110i	−0.0907492	+	0.801362i
$183$	9.97479	−	9.97479i	0.737358	−	0.737358i
$184$	5.72812	+	21.6670i	0.422282	+	1.59731i
$185$	7.90059	−	12.0053i	0.580863	−	0.882649i
$186$	11.0774	+	5.18050i	0.812233	+	0.379853i
$187$	−0.812059	−	0.812059i	−0.0593837	−	0.0593837i
$188$	1.47850	−	16.4765i	0.107831	−	1.20167i
$189$	12.9821	+	6.44355i	0.944311	+	0.468699i
$190$	0.686167	+	1.11589i	0.0497798	+	0.0809550i
$191$	25.8617			1.87129			0.935643	−	0.352947i	$-0.114820\pi$
$191$	25.8617			1.87129			0.935643	+	0.352947i	$0.114820\pi$
$192$	−9.28356	−	2.55415i	−0.669983	−	0.184330i
$193$	−3.91271	+	3.91271i	−0.281643	+	0.281643i	−0.833764	−	0.552121i	$-0.813819\pi$
$193$	−3.91271	+	3.91271i	−0.281643	+	0.281643i	0.552121	+	0.833764i	$0.313819\pi$
$194$	1.00154	−	2.14159i	0.0719067	−	0.153757i
$195$	−1.58045	−	7.66441i	−0.113179	−	0.548860i
$196$	3.13068	−	13.6455i	0.223620	−	0.974676i
$197$	−11.3964	+	11.3964i	−0.811963	+	0.811963i	−0.984928	−	0.172965i	$-0.944665\pi$
$197$	−11.3964	+	11.3964i	−0.811963	+	0.811963i	0.172965	+	0.984928i	$0.444665\pi$
$198$	5.18071	−	1.87909i	0.368177	−	0.133541i
$199$	−2.32255			−0.164641			−0.0823205	−	0.996606i	$-0.526233\pi$
$199$	−2.32255			−0.164641			−0.0823205	+	0.996606i	$0.526233\pi$
$200$	1.69619	−	14.0400i	0.119939	−	0.992781i
$201$			4.95054i			0.349184i
$202$	0.177633	−	0.0644292i	0.0124982	−	0.00453322i
$203$	−6.22061	+	2.09382i	−0.436601	+	0.146958i
$204$	−0.705560	−	0.844669i	−0.0493991	−	0.0591386i
$205$	−0.636644	−	3.08741i	−0.0444651	−	0.215634i
$206$	−24.0579	−	11.2510i	−1.67620	−	0.783898i
$207$	−8.69245	−	8.69245i	−0.604167	−	0.604167i
$208$	6.62890	+	9.55741i	0.459632	+	0.662687i
$209$	−1.04050			−0.0719728
$210$	0.910999	+	10.0284i	0.0628649	+	0.692028i
$211$		−	6.55987i		−	0.451600i	−0.974174	−	0.225800i	$-0.927500\pi$
$211$		−	6.55987i		−	0.451600i	0.974174	−	0.225800i	$-0.0724996\pi$
$212$	−21.4020	−	1.92049i	−1.46989	−	0.131899i
$213$	−0.827488	+	0.827488i	−0.0566985	+	0.0566985i
$214$	7.57101	−	16.1890i	0.517544	−	1.10666i
$215$	−10.8519	−	7.14154i	−0.740094	−	0.487049i
$216$	14.9793	−	3.96009i	1.01921	−	0.269450i
$217$	6.06393	+	18.0155i	0.411647	+	1.22297i
$218$	22.8142	−	8.27492i	1.54517	−	0.560448i
$219$	−17.8719			−1.20767
$220$	8.79391	+	6.98903i	0.592885	+	0.471200i
$221$			1.32951i			0.0894323i
$222$	3.73017	+	10.2842i	0.250353	+	0.690230i
$223$	12.6328	+	12.6328i	0.845955	+	0.845955i	0.989626	−	0.143670i	$-0.0458905\pi$
$223$	12.6328	+	12.6328i	0.845955	+	0.845955i	−0.143670	+	0.989626i	$0.545890\pi$
$224$	−7.09178	−	13.1798i	−0.473840	−	0.880611i
$225$	3.06868	+	7.12440i	0.204579	+	0.474960i
$226$	2.78221	−	5.94915i	0.185070	−	0.395732i
$227$	14.9681	+	14.9681i	0.993467	+	0.993467i	0.999979	−	0.00651216i	$-0.00207290\pi$
$227$	14.9681	+	14.9681i	0.993467	+	0.993467i	−0.00651216	+	0.999979i	$0.502073\pi$
$228$	−0.993162	−	0.0891205i	−0.0657737	−	0.00590215i
$229$			6.01142i			0.397246i	0.980076	+	0.198623i	$0.0636469\pi$
$229$			6.01142i			0.397246i	−0.980076	+	0.198623i	$0.936353\pi$
$230$	5.81210	−	24.3733i	0.383238	−	1.60713i
$231$	−7.16435	−	3.55595i	−0.471379	−	0.233964i
$232$	−3.52865	+	6.06490i	−0.231667	+	0.398180i
$233$	−12.6385	+	12.6385i	−0.827974	+	0.827974i	−0.987236	−	0.159262i	$-0.949089\pi$
$233$	−12.6385	+	12.6385i	−0.827974	+	0.827974i	0.159262	+	0.987236i	$0.449089\pi$
$234$	−5.77917	−	2.70271i	−0.377796	−	0.176682i
$235$	−10.1674	+	15.4499i	−0.663250	+	1.00784i
$236$	−1.59455	−	1.90893i	−0.103796	−	0.124261i
$237$	−4.94313	−	4.94313i	−0.321091	−	0.321091i
$238$	0.192502	−	1.69989i	0.0124780	−	0.110187i
$239$		−	1.33783i		−	0.0865372i	−0.999063	−	0.0432686i	$-0.986223\pi$
$239$		−	1.33783i		−	0.0865372i	0.999063	−	0.0432686i	$-0.0137771\pi$
$240$	7.79521	+	7.42428i	0.503179	+	0.479235i
$241$		−	27.6357i		−	1.78017i	−0.455795	−	0.890085i	$-0.650645\pi$
$241$		−	27.6357i		−	1.78017i	0.455795	−	0.890085i	$-0.349355\pi$
$242$	6.23655	−	2.26206i	0.400901	−	0.145410i
$243$	−9.97051	+	9.97051i	−0.639608	+	0.639608i
$244$	17.9905	−	15.0277i	1.15173	−	0.962048i
$245$	−10.2983	+	11.7875i	−0.657936	+	0.753074i
$246$	2.17363	+	1.01653i	0.138585	+	0.0648115i
$247$	0.851755	+	0.851755i	0.0541959	+	0.0541959i
$248$	17.5646	+	10.2193i	1.11535	+	0.648928i
$249$			15.6197i			0.989859i
$250$	−9.09377	+	12.9346i	−0.575140	+	0.818055i
$251$	−5.69321			−0.359352			−0.179676	−	0.983726i	$-0.557505\pi$
$251$	−5.69321			−0.359352			−0.179676	+	0.983726i	$0.557505\pi$
$252$	6.99784	+	4.29243i	0.440822	+	0.270398i
$253$	14.0730	+	14.0730i	0.884764	+	0.884764i
$254$	−4.99069	−	2.33397i	−0.313144	−	0.146446i
$255$	0.248506	+	1.20513i	0.0155621	+	0.0754684i
$256$	−14.9857	−	5.60609i	−0.936607	−	0.350381i
$257$	−21.1061	+	21.1061i	−1.31656	+	1.31656i	−0.400085	+	0.916478i	$0.631020\pi$
$257$	−21.1061	+	21.1061i	−1.31656	+	1.31656i	−0.916478	+	0.400085i	$0.868980\pi$
$258$	9.29614	−	3.37179i	0.578752	−	0.209919i
$259$	−7.56018	+	15.2319i	−0.469767	+	0.946462i
$260$	−1.47748	−	12.9200i	−0.0916294	−	0.801261i
$261$		−	3.84878i		−	0.238233i
$262$	5.51221	−	1.99933i	0.340545	−	0.123519i
$263$	5.43843	−	5.43843i	0.335348	−	0.335348i	−0.519265	−	0.854613i	$-0.673794\pi$
$263$	5.43843	−	5.43843i	0.335348	−	0.335348i	0.854613	+	0.519265i	$0.173794\pi$
$264$	−8.26653	+	2.18543i	−0.508770	+	0.134504i
$265$	20.0685	+	13.2069i	1.23280	+	0.811292i
$266$	−0.965715	−	1.21237i	−0.0592118	−	0.0743351i
$267$	−8.55867	+	8.55867i	−0.523782	+	0.523782i
$268$	−0.735241	+	8.19355i	−0.0449120	+	0.500501i
$269$			7.06975i			0.431050i	0.976498	+	0.215525i	$0.0691463\pi$
$269$			7.06975i			0.431050i	−0.976498	+	0.215525i	$0.930854\pi$
$270$	−16.8503	−	4.01815i	−1.02548	−	0.244537i
$271$		−	19.4793i		−	1.18328i	−0.806201	−	0.591642i	$-0.798480\pi$
$271$		−	19.4793i		−	1.18328i	0.806201	−	0.591642i	$-0.201520\pi$
$272$	−1.04231	−	1.50278i	−0.0631995	−	0.0911197i
$273$	2.95384	+	8.77566i	0.178775	+	0.531127i
$274$	−15.4488	−	7.22485i	−0.933296	−	0.436469i
$275$	−4.96818	−	11.5344i	−0.299592	−	0.695548i
$276$	12.2274	+	14.6382i	0.736003	+	0.881114i
$277$	−15.4758	+	15.4758i	−0.929850	+	0.929850i	−0.997696	−	0.0678454i	$-0.978388\pi$
$277$	−15.4758	+	15.4758i	−0.929850	+	0.929850i	0.0678454	+	0.997696i	$0.478388\pi$
$278$	2.89251	+	7.97474i	0.173481	+	0.478293i
$279$	−11.1465			−0.667321
$280$	0.0183819	+	16.7332i	0.00109853	+	0.999999i
$281$	−20.4129			−1.21773			−0.608865	−	0.793274i	$-0.708375\pi$
$281$	−20.4129			−1.21773			−0.608865	+	0.793274i	$0.708375\pi$
$282$	−4.80043	−	13.2349i	−0.285861	−	0.788128i
$283$	−4.96318	+	4.96318i	−0.295031	+	0.295031i	−0.839064	−	0.544033i	$-0.816897\pi$
$283$	−4.96318	+	4.96318i	−0.295031	+	0.295031i	0.544033	+	0.839064i	$0.316897\pi$
$284$	−1.49246	+	1.24666i	−0.0885610	+	0.0739759i
$285$	0.931281	+	0.612867i	0.0551643	+	0.0363031i
$286$	9.35645	+	4.37568i	0.553259	+	0.258739i
$287$	1.18988	+	3.53504i	0.0702362	+	0.208667i
$288$	8.65127	−	1.47582i	0.509781	−	0.0869633i
$289$			16.7910i			0.987703i
$290$	6.68263	−	4.10919i	0.392417	−	0.241300i
$291$		−	2.01205i		−	0.117949i
$292$	−29.5794	−	2.65428i	−1.73100	−	0.155330i
$293$	−8.15190	+	8.15190i	−0.476239	+	0.476239i	−0.903927	−	0.427688i	$-0.859328\pi$
$293$	−8.15190	+	8.15190i	−0.476239	+	0.476239i	0.427688	+	0.903927i	$0.359328\pi$
$294$	−2.50609	−	11.6481i	−0.146158	−	0.679332i
$295$	0.561618	+	2.72357i	0.0326987	+	0.158572i
$296$	4.64636	+	17.5752i	0.270064	+	1.02154i
$297$	9.72930	−	9.72930i	0.564551	−	0.564551i
$298$	−7.43193	+	2.69563i	−0.430520	+	0.156154i
$299$		−	23.0404i		−	1.33246i
$300$	−3.75421	−	11.4351i	−0.216749	−	0.660208i
$301$	13.7685	+	6.83384i	0.793601	+	0.393896i
$302$	9.38182	−	3.40287i	0.539863	−	0.195813i
$303$	0.113711	−	0.113711i	0.00653251	−	0.00653251i
$304$	−1.63053	−	0.295003i	−0.0935172	−	0.0169196i
$305$	−25.6680	+	5.29292i	−1.46975	+	0.303072i
$306$	0.908703	+	0.424968i	0.0519471	+	0.0242938i
$307$	10.8162	+	10.8162i	0.617313	+	0.617313i	0.944841	−	0.327529i	$-0.106216\pi$
$307$	10.8162	+	10.8162i	0.617313	+	0.617313i	−0.327529	+	0.944841i	$0.606216\pi$
$308$	−11.3295	−	6.94942i	−0.645556	−	0.395980i
$309$	−22.6028			−1.28583
$310$	−11.9006	−	19.3536i	−0.675911	−	1.09921i
$311$			24.5558i			1.39243i	0.717833	+	0.696215i	$0.245134\pi$
$311$			24.5558i			1.39243i	−0.717833	+	0.696215i	$0.754866\pi$
$312$	8.55600	+	4.97800i	0.484388	+	0.281824i
$313$	15.0111	+	15.0111i	0.848478	+	0.848478i	0.989943	−	0.141465i	$-0.0451813\pi$
$313$	15.0111	+	15.0111i	0.848478	+	0.848478i	−0.141465	+	0.989943i	$0.545181\pi$
$314$	−23.0712	−	10.7896i	−1.30198	−	0.608890i
$315$	−4.62446	−	7.92829i	−0.260559	−	0.446708i
$316$	−7.44714	−	8.91542i	−0.418934	−	0.501531i
$317$	18.2459	−	18.2459i	1.02479	−	1.02479i	0.0251044	−	0.999685i	$-0.492008\pi$
$317$	18.2459	−	18.2459i	1.02479	−	1.02479i	0.999685	−	0.0251044i	$-0.00799181\pi$
$318$	−17.1914	+	6.23547i	−0.964044	+	0.349668i
$319$			6.23115i			0.348878i
$320$	11.7991	+	13.4455i	0.659589	+	0.751627i
$321$		−	15.2098i		−	0.848929i
$322$	−3.33607	+	29.4592i	−0.185912	+	1.64170i
$323$	−0.133928	−	0.133928i	−0.00745195	−	0.00745195i
$324$	2.97587	−	2.48577i	0.165326	−	0.138099i
$325$	−5.37509	+	13.5090i	−0.298157	+	0.749345i
$326$	6.85101	+	3.20397i	0.379442	+	0.177452i
$327$	14.6044	−	14.6044i	0.807623	−	0.807623i
$328$	3.44656	+	2.00526i	0.190304	+	0.110722i
$329$	9.72934	−	19.6022i	0.536396	−	1.08070i
$330$	9.29905	+	2.21747i	0.511896	+	0.122068i
$331$			25.0233i			1.37541i	0.725991	+	0.687704i	$0.241381\pi$
$331$			25.0233i			1.37541i	−0.725991	+	0.687704i	$0.758619\pi$
$332$	−2.31980	+	25.8519i	−0.127315	+	1.41881i
$333$	−7.05088	−	7.05088i	−0.386386	−	0.386386i
$334$	4.28351	−	9.15936i	0.234383	−	0.501178i
$335$	5.05613	−	7.68303i	0.276246	−	0.419769i
$336$	−10.2188	−	7.60364i	−0.557481	−	0.414813i
$337$	12.7250	+	12.7250i	0.693173	+	0.693173i	0.962929	−	0.269756i	$-0.0869430\pi$
$337$	12.7250	+	12.7250i	0.693173	+	0.693173i	−0.269756	+	0.962929i	$0.586943\pi$
$338$	2.19144	+	6.04188i	0.119199	+	0.328635i
$339$		−	5.58932i		−	0.303570i
$340$	0.232315	+	2.03150i	0.0125991	+	0.110174i
$341$	18.0461			0.977250
$342$	0.854423	−	0.309907i	0.0462019	−	0.0167579i
$343$	10.4076	−	15.3194i	0.561955	−	0.827168i
$344$	15.8866	−	4.19996i	0.856550	−	0.226447i
$345$	−4.30663	−	20.8850i	−0.231861	−	1.12441i
$346$	13.4787	−	28.8213i	0.724620	−	1.54944i
$347$	8.40787	−	8.40787i	0.451358	−	0.451358i	−0.444447	−	0.895805i	$-0.646600\pi$
$347$	8.40787	−	8.40787i	0.451358	−	0.451358i	0.895805	+	0.444447i	$0.146600\pi$
$348$	−0.533709	+	5.94767i	−0.0286098	+	0.318828i
$349$		−	26.6448i		−	1.42626i	−0.701030	−	0.713132i	$-0.747276\pi$
$349$		−	26.6448i		−	1.42626i	0.701030	−	0.713132i	$-0.252724\pi$
$350$	8.82851	−	16.4942i	0.471904	−	0.881650i
$351$	−15.9289			−0.850219
$352$	−14.0064	+	2.38934i	−0.746542	+	0.127352i
$353$	−2.82560	−	2.82560i	−0.150391	−	0.150391i	0.627902	−	0.778293i	$-0.283914\pi$
$353$	−2.82560	−	2.82560i	−0.150391	−	0.150391i	−0.778293	+	0.627902i	$0.783914\pi$
$354$	−1.91747	−	0.896735i	−0.101913	−	0.0476609i
$355$	2.12937	−	0.439089i	0.113015	−	0.0233044i
$356$	−15.4364	+	12.8942i	−0.818128	+	0.683391i
$357$	−0.464455	−	1.37986i	−0.0245816	−	0.0730301i
$358$	2.55277	−	0.925913i	0.134918	−	0.0489360i
$359$			24.9399i			1.31628i	0.752896	+	0.658140i	$0.228656\pi$
$359$			24.9399i			1.31628i	−0.752896	+	0.658140i	$0.771344\pi$
$360$	−9.30291	−	3.11994i	−0.490306	−	0.164435i
$361$	18.8284			0.990968
$362$	11.8620	−	4.30247i	0.623455	−	0.226133i
$363$	3.99229	−	3.99229i	0.209541	−	0.209541i
$364$	3.58551	+	14.9631i	0.187932	+	0.784281i
$365$	27.7364	+	18.2531i	1.45179	+	0.955409i
$366$	8.45119	−	18.0711i	0.441751	−	0.944589i
$367$	−17.0197	+	17.0197i	−0.888422	+	0.888422i	−0.994371	−	0.105950i	$-0.966212\pi$
$367$	−17.0197	+	17.0197i	−0.888422	+	0.888422i	0.105950	+	0.994371i	$0.466212\pi$
$368$	18.0633	+	26.0433i	0.941617	+	1.35760i
$369$	−2.18718			−0.113860
$370$	4.71448	−	19.7704i	0.245094	−	1.02781i
$371$	−25.4621	−	12.6378i	−1.32192	−	0.656123i
$372$	17.2251	+	1.54568i	0.893078	+	0.0801395i
$373$	−14.7233	−	14.7233i	−0.762342	−	0.762342i	0.214403	−	0.976745i	$-0.431219\pi$
$373$	−14.7233	−	14.7233i	−0.762342	−	0.762342i	−0.976745	+	0.214403i	$0.931219\pi$
$374$	−1.47119	−	0.688021i	−0.0760732	−	0.0355767i
$375$	−2.34721	+	13.2500i	−0.121209	+	0.684225i
$376$	−5.97949	−	22.6178i	−0.308369	−	1.16643i
$377$	5.10084	−	5.10084i	0.262706	−	0.262706i
$378$	20.3664	+	2.30637i	1.04753	+	0.118627i
$379$	11.4933			0.590371			0.295185	−	0.955440i	$-0.404619\pi$
$379$	11.4933			0.590371			0.295185	+	0.955440i	$0.404619\pi$
$380$	1.45033	+	1.15266i	0.0744001	+	0.0591301i
$381$	−4.68883			−0.240216
$382$	34.3822	−	12.4707i	1.75915	−	0.638058i
$383$	−6.48827	−	6.48827i	−0.331535	−	0.331535i	0.521634	−	0.853169i	$-0.325323\pi$
$383$	−6.48827	−	6.48827i	−0.331535	−	0.331535i	−0.853169	+	0.521634i	$0.825323\pi$
$384$	−13.5738	+	1.08097i	−0.692685	+	0.0551629i
$385$	7.48698	+	12.8359i	0.381572	+	0.654176i
$386$	−3.31507	+	7.08855i	−0.168732	+	0.360798i
$387$	−6.37347	+	6.37347i	−0.323981	+	0.323981i
$388$	0.298825	−	3.33012i	0.0151705	−	0.169061i
$389$	−6.70580			−0.339998			−0.169999	−	0.985444i	$-0.554376\pi$
$389$	−6.70580			−0.339998			−0.169999	+	0.985444i	$0.554376\pi$
$390$	−5.79700	−	9.42745i	−0.293543	−	0.477377i
$391$			3.62282i			0.183214i
$392$	−2.41784	−	19.6508i	−0.122120	−	0.992515i
$393$	3.52860	−	3.52860i	0.177994	−	0.177994i
$394$	−9.65569	+	20.6466i	−0.486447	+	1.04016i
$395$	2.62297	+	12.7201i	0.131976	+	0.640017i
$396$	5.98146	−	4.99637i	0.300580	−	0.251077i
$397$	−5.39493	−	5.39493i	−0.270764	−	0.270764i	0.558644	−	0.829408i	$-0.311322\pi$
$397$	−5.39493	−	5.39493i	−0.270764	−	0.270764i	−0.829408	+	0.558644i	$0.811322\pi$
$398$	−3.08774	+	1.11995i	−0.154774	+	0.0561381i
$399$	−1.18157	−	0.586461i	−0.0591525	−	0.0293598i
$400$	−4.51521	−	19.4837i	−0.225761	−	0.974183i
$401$	−5.72101			−0.285693			−0.142847	−	0.989745i	$-0.545626\pi$
$401$	−5.72101			−0.285693			−0.142847	+	0.989745i	$0.545626\pi$
$402$	2.38719	+	6.58156i	0.119062	+	0.328259i
$403$	−14.7726	−	14.7726i	−0.735873	−	0.735873i
$404$	0.205089	−	0.171312i	0.0102035	−	0.00852312i
$405$	−4.24583	+	0.875518i	−0.210977	+	0.0435048i
$406$	−7.26042	+	5.78330i	−0.360328	+	0.287020i
$407$	11.4153	+	11.4153i	0.565837	+	0.565837i
$408$	−1.34532	−	0.782729i	−0.0666035	−	0.0387509i
$409$	−21.0532			−1.04102			−0.520508	−	0.853857i	$-0.674257\pi$
$409$	−21.0532			−1.04102			−0.520508	+	0.853857i	$0.674257\pi$
$410$	−2.33517	−	3.79760i	−0.115326	−	0.187550i
$411$	−14.5144			−0.715942
$412$	−37.4095	−	3.35691i	−1.84304	−	0.165383i
$413$	−1.04966	−	3.11846i	−0.0516502	−	0.153449i
$414$	−15.7479	−	7.36473i	−0.773966	−	0.361957i
$415$	15.9529	−	24.2412i	0.783096	−	1.18995i
$416$	13.4216	+	9.50972i	0.658046	+	0.466252i
$417$	5.10498	+	5.10498i	0.249992	+	0.249992i
$418$	−1.38331	+	0.501738i	−0.0676597	+	0.0245408i
$419$		−	35.9170i		−	1.75466i	−0.479887	−	0.877330i	$-0.659322\pi$
$419$		−	35.9170i		−	1.75466i	0.479887	−	0.877330i	$-0.340678\pi$
$420$	6.04694	+	12.8932i	0.295061	+	0.629122i
$421$		−	18.7985i		−	0.916182i	−0.888905	−	0.458091i	$-0.848533\pi$
$421$		−	18.7985i		−	0.916182i	0.888905	−	0.458091i	$-0.151467\pi$
$422$	−3.16323	−	8.72111i	−0.153984	−	0.424537i
$423$	9.07391	+	9.07391i	0.441189	+	0.441189i
$424$	−29.3792	+	7.76700i	−1.42678	+	0.377199i
$425$	0.845167	−	2.12412i	0.0409966	−	0.103035i
$426$	−0.701093	+	1.49914i	−0.0339681	+	0.0726334i
$427$	29.3896	−	9.89238i	1.42226	−	0.478726i
$428$	2.25892	−	25.1735i	0.109189	−	1.21681i
$429$	8.79054			0.424411
$430$	−17.8709	−	4.26154i	−0.861813	−	0.205509i
$431$	6.87702			0.331255			0.165627	−	0.986188i	$-0.447035\pi$
$431$	6.87702			0.331255			0.165627	+	0.986188i	$0.447035\pi$
$432$	18.0049	−	12.4880i	0.866261	−	0.600828i
$433$	−2.77952	−	2.77952i	−0.133575	−	0.133575i	0.637158	−	0.770733i	$-0.280110\pi$
$433$	−2.77952	−	2.77952i	−0.133575	−	0.133575i	−0.770733	+	0.637158i	$0.780110\pi$
$434$	16.7490	+	21.0269i	0.803979	+	1.00932i
$435$	3.67023	−	5.57709i	0.175974	−	0.267401i
$436$	26.3404	−	22.0024i	1.26148	−	1.05372i
$437$	2.32098	+	2.32098i	0.111027	+	0.111027i
$438$	−23.7600	+	8.61797i	−1.13530	+	0.411782i
$439$	24.3654			1.16290			0.581448	−	0.813583i	$-0.302486\pi$
$439$	24.3654			1.16290			0.581448	+	0.813583i	$0.302486\pi$
$440$	15.0614	+	5.05116i	0.718022	+	0.240805i
$441$	6.56687	+	8.64967i	0.312708	+	0.411889i
$442$	0.641100	+	1.76753i	0.0304940	+	0.0840729i
$443$	8.80104	+	8.80104i	0.418150	+	0.418150i	0.884566	−	0.466416i	$-0.154455\pi$
$443$	8.80104	+	8.80104i	0.418150	+	0.418150i	−0.466416	+	0.884566i	$0.654455\pi$
$444$	9.91825	+	11.8737i	0.470699	+	0.563503i
$445$	22.0239	−	4.54148i	1.04403	−	0.215287i
$446$	22.8865	+	10.7032i	1.08371	+	0.506812i
$447$	−4.75750	+	4.75750i	−0.225022	+	0.225022i
$448$	−15.7837	−	14.1023i	−0.745709	−	0.666272i
$449$		−	20.2530i		−	0.955799i	−0.878415	−	0.477900i	$-0.841398\pi$
$449$		−	20.2530i		−	0.955799i	0.878415	−	0.477900i	$-0.158602\pi$
$450$	7.51514	+	7.99188i	0.354267	+	0.376741i
$451$	3.54104			0.166741
$452$	0.830111	−	9.25079i	0.0390451	−	0.435120i
$453$	6.00571	−	6.00571i	0.282173	−	0.282173i
$454$	27.1173	+	12.6818i	1.27268	+	0.595186i
$455$	4.37860	−	16.6363i	0.205272	−	0.779923i
$456$	−1.36335	+	0.360429i	−0.0638446	+	0.0168786i
$457$	2.82521	+	2.82521i	0.132158	+	0.132158i	0.770091	−	0.637934i	$-0.220211\pi$
$457$	2.82521	+	2.82521i	0.132158	+	0.132158i	−0.637934	+	0.770091i	$0.720211\pi$
$458$	2.89876	+	7.99196i	0.135450	+	0.373440i
$459$	2.50461			0.116905
$460$	−4.02604	−	35.2061i	−0.187715	−	1.64149i
$461$	−4.24667			−0.197787			−0.0988936	−	0.995098i	$-0.531530\pi$
$461$	−4.24667			−0.197787			−0.0988936	+	0.995098i	$0.531530\pi$
$462$	−11.2395	−	1.27280i	−0.522907	−	0.0592159i
$463$	−7.90420	+	7.90420i	−0.367339	+	0.367339i	−0.866506	−	0.499167i	$-0.833639\pi$
$463$	−7.90420	+	7.90420i	−0.367339	+	0.367339i	0.499167	+	0.866506i	$0.333639\pi$
$464$	−1.76666	+	9.76461i	−0.0820153	+	0.453311i
$465$	−16.1518	−	10.6294i	−0.749023	−	0.492925i
$466$	−10.7080	+	22.8968i	−0.496039	+	1.06067i
$467$	5.43216	+	5.43216i	0.251370	+	0.251370i	0.821532	−	0.570162i	$-0.193120\pi$
$467$	5.43216	+	5.43216i	0.251370	+	0.251370i	−0.570162	+	0.821532i	$0.693120\pi$
$468$	−8.98648	−	0.806393i	−0.415400	−	0.0372755i
$469$	−4.83828	+	9.74792i	−0.223411	+	0.450117i
$470$	−6.06715	+	25.4429i	−0.279857	+	1.17359i
$471$	−21.6757			−0.998764
$472$	−3.04040	−	1.76895i	−0.139946	−	0.0814224i
$473$	10.3186	−	10.3186i	0.474450	−	0.474450i
$474$	−8.95533	−	4.18809i	−0.411332	−	0.192365i
$475$	−0.819370	−	1.90229i	−0.0375953	−	0.0872831i
$476$	−0.563777	−	2.35277i	−0.0258407	−	0.107839i
$477$	11.7865	−	11.7865i	0.539665	−	0.539665i
$478$	−0.645115	−	1.77860i	−0.0295069	−	0.0813513i
$479$	9.52909			0.435395			0.217698	−	0.976016i	$-0.430145\pi$
$479$	9.52909			0.435395			0.217698	+	0.976016i	$0.430145\pi$
$480$	13.9435	+	6.11139i	0.636431	+	0.278945i
$481$		−	18.6892i		−	0.852156i
$482$	−13.3262	−	36.7406i	−0.606990	−	1.67349i
$483$	8.04903	+	23.9131i	0.366244	+	1.08808i
$484$	7.20049	−	6.01464i	0.327295	−	0.273393i
$485$	−2.05497	+	3.12263i	−0.0933115	+	0.141791i
$486$	−8.44756	+	18.0633i	−0.383189	+	0.819368i
$487$	−20.9631	−	20.9631i	−0.949928	−	0.949928i	0.0488768	−	0.998805i	$-0.484436\pi$
$487$	−20.9631	−	20.9631i	−0.949928	−	0.949928i	−0.998805	+	0.0488768i	$0.984436\pi$
$488$	16.6713	−	28.6539i	0.754674	−	1.29710i
$489$	6.43663			0.291074
$490$	−8.00722	+	20.6370i	−0.361729	+	0.932283i
$491$			14.3399i			0.647149i	0.946203	+	0.323575i	$0.104885\pi$
$491$			14.3399i			0.647149i	−0.946203	+	0.323575i	$0.895115\pi$
$492$	3.37994	+	0.303296i	0.152379	+	0.0136736i
$493$	−0.802043	+	0.802043i	−0.0361222	+	0.0361222i
$494$	1.54310	+	0.721654i	0.0694274	+	0.0324687i
$495$	−8.53406	+	1.75978i	−0.383577	+	0.0790962i
$496$	28.2793	+	5.11644i	1.26978	+	0.229735i
$497$	−2.43810	+	0.820651i	−0.109364	+	0.0368112i
$498$	7.53196	+	20.7658i	0.337515	+	0.930540i
$499$	18.4667			0.826681			0.413340	−	0.910577i	$-0.364362\pi$
$499$	18.4667			0.826681			0.413340	+	0.910577i	$0.364362\pi$
$500$	−5.85266	+	21.5812i	−0.261739	+	0.965139i
$501$		−	8.60536i		−	0.384459i
$502$	−7.56892	+	2.74532i	−0.337817	+	0.122529i
$503$	18.4374	+	18.4374i	0.822085	+	0.822085i	0.986407	−	0.164322i	$-0.0525436\pi$
$503$	18.4374	+	18.4374i	0.822085	+	0.822085i	−0.164322	+	0.986407i	$0.552544\pi$
$504$	11.3732	+	2.33221i	0.506603	+	0.103885i
$505$	−0.292610	+	0.0603382i	−0.0130210	+	0.00268502i
$506$	25.4957	+	11.9235i	1.13342	+	0.530062i
$507$	3.86767	+	3.86767i	0.171769	+	0.171769i
$508$	−7.76040	−	0.696373i	−0.344312	−	0.0308965i
$509$		−	2.89831i		−	0.128465i	−0.997935	−	0.0642326i	$-0.979540\pi$
$509$		−	2.89831i		−	0.128465i	0.997935	−	0.0642326i	$-0.0204600\pi$
$510$	0.911506	+	1.48235i	0.0403622	+	0.0656395i
$511$	−35.1908	−	17.4666i	−1.55675	−	0.772677i
$512$	−22.6263	−	0.226853i	−0.999950	−	0.0100256i
$513$	1.60459	−	1.60459i	0.0708445	−	0.0708445i
$514$	−17.8823	+	38.2374i	−0.788753	+	1.68658i
$515$	35.0787	+	23.0849i	1.54575	+	1.01724i
$516$	10.7330	−	8.96536i	0.472493	−	0.394678i
$517$	−14.6906	−	14.6906i	−0.646093	−	0.646093i
$518$	−2.70605	+	23.8958i	−0.118897	+	1.04992i
$519$		−	27.0781i		−	1.18860i
$520$	−8.19437	−	16.4642i	−0.359347	−	0.722001i
$521$		−	9.89476i		−	0.433497i	−0.976227	−	0.216749i	$-0.930455\pi$
$521$		−	9.89476i		−	0.433497i	0.976227	−	0.216749i	$-0.0695452\pi$
$522$	−1.85592	−	5.11681i	−0.0812312	−	0.223957i
$523$	3.93390	−	3.93390i	0.172018	−	0.172018i	−0.615848	−	0.787865i	$-0.711186\pi$
$523$	3.93390	−	3.93390i	0.172018	−	0.172018i	0.787865	+	0.615848i	$0.211186\pi$
$524$	6.36419	−	5.31607i	0.278021	−	0.232234i
$525$	0.859393	−	15.8984i	0.0375070	−	0.693865i
$526$	4.60774	−	9.85266i	0.200907	−	0.429596i
$527$	2.32280	+	2.32280i	0.101183	+	0.101183i
$528$	−9.93622	+	6.89164i	−0.432419	+	0.299920i
$529$		−	39.7838i		−	1.72973i
$530$	33.0488	+	7.88087i	1.43555	+	0.342323i
$531$	1.92943			0.0837303
$532$	−1.86850	−	1.14612i	−0.0810097	−	0.0496908i
$533$	−2.89870	−	2.89870i	−0.125557	−	0.125557i
$534$	−7.25138	+	15.5055i	−0.313798	+	0.670989i
$535$	−15.5342	+	23.6050i	−0.671603	+	1.02053i
$536$	2.97353	+	11.2476i	0.128437	+	0.485821i
$537$	1.63414	−	1.63414i	0.0705183	−	0.0705183i
$538$	3.40910	+	9.39898i	0.146977	+	0.405219i
$539$	−10.6317	−	14.0038i	−0.457941	−	0.603186i
$540$	−24.3395	+	2.78338i	−1.04740	+	0.119777i
$541$			14.7951i			0.636092i	0.948075	+	0.318046i	$0.103027\pi$
$541$			14.7951i			0.636092i	−0.948075	+	0.318046i	$0.896973\pi$
$542$	−9.39310	−	25.8971i	−0.403468	−	1.11237i
$543$	7.59341	−	7.59341i	0.325864	−	0.325864i
$544$	−2.11037	−	1.49529i	−0.0904815	−	0.0641098i
$545$	−37.5812	+	7.74950i	−1.60980	+	0.331952i
$546$	8.15873	+	10.2426i	0.349161	+	0.438341i
$547$	−22.6498	+	22.6498i	−0.968434	+	0.968434i	−0.999517	−	0.0310824i	$-0.990105\pi$
$547$	−22.6498	+	22.6498i	−0.968434	+	0.968434i	0.0310824	+	0.999517i	$0.490105\pi$
$548$	−24.0225	−	2.15564i	−1.02619	−	0.0920843i
$549$			18.1838i			0.776064i
$550$	−12.1670	−	12.9388i	−0.518802	−	0.551713i
$551$			1.02767i			0.0437800i
$552$	23.3145	+	13.5647i	0.992333	+	0.577354i
$553$	−4.90229	−	14.5644i	−0.208466	−	0.619340i
$554$	−13.1119	+	28.0371i	−0.557073	+	1.19118i
$555$	−3.49332	−	16.9409i	−0.148283	−	0.719100i
$556$	7.69098	+	9.20733i	0.326170	+	0.390478i
$557$	−12.9631	+	12.9631i	−0.549263	+	0.549263i	−0.926228	−	0.376965i	$-0.876968\pi$
$557$	−12.9631	+	12.9631i	−0.549263	+	0.549263i	0.376965	+	0.926228i	$0.376968\pi$
$558$	−14.8188	+	5.37492i	−0.627331	+	0.227539i
$559$	−16.8937			−0.714526
$560$	8.09333	+	22.2373i	0.342006	+	0.939698i
$561$	−1.38220			−0.0583566
$562$	−27.1382	+	9.84327i	−1.14476	+	0.415213i
$563$	16.6820	−	16.6820i	0.703064	−	0.703064i	−0.262003	−	0.965067i	$-0.584383\pi$
$563$	16.6820	−	16.6820i	0.703064	−	0.703064i	0.965067	+	0.262003i	$0.0843830\pi$
$564$	−12.7640	−	15.2805i	−0.537461	−	0.643427i
$565$	−5.70854	+	8.67440i	−0.240160	+	0.364935i
$566$	−4.20508	+	8.99166i	−0.176753	+	0.377948i
$567$	4.86142	−	1.63633i	0.204161	−	0.0687194i
$568$	−1.38302	+	2.37707i	−0.0580300	+	0.0997397i
$569$		−	21.6112i		−	0.905989i	−0.891513	−	0.452994i	$-0.850356\pi$
$569$		−	21.6112i		−	0.905989i	0.891513	−	0.452994i	$-0.149644\pi$
$570$	1.53363	+	0.365713i	0.0642369	+	0.0153180i
$571$		−	22.2231i		−	0.930008i	−0.885309	−	0.465004i	$-0.846053\pi$
$571$		−	22.2231i		−	0.930008i	0.885309	−	0.465004i	$-0.153947\pi$
$572$	14.5491	+	1.30555i	0.608327	+	0.0545877i
$573$	22.0095	−	22.0095i	0.919462	−	0.919462i
$574$	3.28653	+	4.12594i	0.137177	+	0.172214i
$575$	−14.6468	+	36.8112i	−0.610813	+	1.53513i
$576$	10.7899	−	6.13376i	0.449579	−	0.255573i
$577$	−14.1964	+	14.1964i	−0.591003	+	0.591003i	−0.937902	−	0.346900i	$-0.887234\pi$
$577$	−14.1964	+	14.1964i	−0.591003	+	0.591003i	0.346900	+	0.937902i	$0.387234\pi$
$578$	8.09675	+	22.3230i	0.336780	+	0.928513i
$579$			6.65981i			0.276772i
$580$	6.90283	−	8.68545i	0.286624	−	0.360643i
$581$	−15.2655	+	30.7562i	−0.633321	+	1.27598i
$582$	−0.970231	−	2.67495i	−0.0402174	−	0.110880i
$583$	−19.0822	+	19.0822i	−0.790305	+	0.790305i
$584$	−40.6047	+	10.7347i	−1.68023	+	0.444204i
$585$	8.42656	+	5.54544i	0.348395	+	0.229276i
$586$	−6.90674	+	14.7686i	−0.285315	+	0.610084i
$587$	−4.98042	−	4.98042i	−0.205564	−	0.205564i	0.596815	−	0.802379i	$-0.296433\pi$
$587$	−4.98042	−	4.98042i	−0.205564	−	0.205564i	−0.802379	+	0.596815i	$0.796433\pi$
$588$	−8.94859	−	14.2773i	−0.369034	−	0.588786i
$589$	2.97623			0.122633
$590$	2.05998	+	3.35007i	0.0848081	+	0.137920i
$591$			19.3978i			0.797920i
$592$	14.6521	+	21.1250i	0.602196	+	0.868234i
$593$	21.3875	+	21.3875i	0.878280	+	0.878280i	0.993357	−	0.115077i	$-0.0367114\pi$
$593$	21.3875	+	21.3875i	0.878280	+	0.878280i	−0.115077	+	0.993357i	$0.536711\pi$
$594$	8.24320	−	17.6263i	0.338223	−	0.723216i
$595$	−0.688481	+	2.61585i	−0.0282250	+	0.107240i
$596$	−8.58063	+	7.16748i	−0.351476	+	0.293592i
$597$	−1.97660	+	1.97660i	−0.0808967	+	0.0808967i
$598$	−11.1103	−	30.6314i	−0.454334	−	1.25261i
$599$			16.9265i			0.691599i	0.938308	+	0.345799i	$0.112392\pi$
$599$			16.9265i			0.691599i	−0.938308	+	0.345799i	$0.887608\pi$
$600$	−10.5052	−	13.3923i	−0.428874	−	0.546738i
$601$			2.76188i			0.112659i	0.998412	+	0.0563297i	$0.0179398\pi$
$601$			2.76188i			0.112659i	−0.998412	+	0.0563297i	$0.982060\pi$
$602$	21.6000	+	2.44607i	0.880351	+	0.0996942i
$603$	−4.51234	−	4.51234i	−0.183757	−	0.183757i
$604$	10.8319	−	9.04799i	0.440743	−	0.368157i
$605$	−10.2733	+	2.11843i	−0.417670	+	0.0861263i
$606$	0.0963420	−	0.206007i	0.00391362	−	0.00836844i
$607$	5.52065	−	5.52065i	0.224076	−	0.224076i	−0.586136	−	0.810213i	$-0.699352\pi$
$607$	5.52065	−	5.52065i	0.224076	−	0.224076i	0.810213	+	0.586136i	$0.199352\pi$
$608$	−2.30998	+	0.394059i	−0.0936821	+	0.0159812i
$609$	−3.51209	+	7.07598i	−0.142317	+	0.286733i
$610$	−31.5724	+	19.4141i	−1.27833	+	0.786054i
$611$			24.0516i			0.973022i
$612$	1.41301	+	0.126795i	0.0571176	+	0.00512540i
$613$	−16.4031	−	16.4031i	−0.662513	−	0.662513i	0.293459	−	0.955972i	$-0.405194\pi$
$613$	−16.4031	−	16.4031i	−0.662513	−	0.662513i	−0.955972	+	0.293459i	$0.905194\pi$
$614$	19.5954	+	9.16407i	0.790806	+	0.369832i
$615$	−3.16934	−	2.08572i	−0.127800	−	0.0841042i
$616$	−18.4132	−	3.77584i	−0.741888	−	0.152133i
$617$	−24.2013	−	24.2013i	−0.974306	−	0.974306i	0.0253716	−	0.999678i	$-0.491923\pi$
$617$	−24.2013	−	24.2013i	−0.974306	−	0.974306i	−0.999678	+	0.0253716i	$0.991923\pi$
$618$	−30.0496	+	10.8993i	−1.20877	+	0.438433i
$619$			18.2586i			0.733873i	0.930246	+	0.366937i	$0.119593\pi$
$619$			18.2586i			0.733873i	−0.930246	+	0.366937i	$0.880407\pi$
$620$	−25.1540	−	19.9913i	−1.01021	−	0.802870i
$621$	−43.4051			−1.74179
$622$	11.8410	+	32.6460i	0.474781	+	1.30899i
$623$	−25.2171	+	8.48796i	−1.01030	+	0.340063i
$624$	13.7753	+	2.49230i	0.551454	+	0.0997719i
$625$	17.1753	−	18.1661i	0.687014	−	0.726645i
$626$	27.1952	+	12.7182i	1.08694	+	0.508323i
$627$	−0.885515	+	0.885515i	−0.0353640	+	0.0353640i
$628$	−35.8751	−	3.21922i	−1.43157	−	0.128461i
$629$			2.93865i			0.117172i
$630$	−9.97114	−	8.31042i	−0.397260	−	0.331095i
$631$	17.6351			0.702041			0.351021	−	0.936368i	$-0.385835\pi$
$631$	17.6351			0.702041			0.351021	+	0.936368i	$0.385835\pi$
$632$	−14.1998	−	8.26165i	−0.564838	−	0.328631i
$633$	−5.58276	−	5.58276i	−0.221895	−	0.221895i
$634$	15.4589	−	33.0555i	0.613951	−	1.31280i
$635$	7.27688	+	4.78884i	0.288774	+	0.190039i
$636$	−19.8485	+	16.5797i	−0.787045	+	0.657426i
$637$	−2.76037	+	20.1667i	−0.109370	+	0.799033i
$638$	3.00472	+	8.28410i	0.118958	+	0.327970i
$639$		−	1.50849i		−	0.0596748i
$640$	22.1700	+	12.1857i	0.876346	+	0.481682i
$641$	21.4669			0.847892			0.423946	−	0.905688i	$-0.360645\pi$
$641$	21.4669			0.847892			0.423946	+	0.905688i	$0.360645\pi$
$642$	−7.33430	−	20.2209i	−0.289462	−	0.798055i
$643$	25.8525	−	25.8525i	1.01952	−	1.01952i	0.0197188	−	0.999806i	$-0.493723\pi$
$643$	25.8525	−	25.8525i	1.01952	−	1.01952i	0.999806	−	0.0197188i	$-0.00627711\pi$
$644$	9.77029	+	40.7736i	0.385004	+	1.60670i
$645$	−15.3133	+	3.15770i	−0.602960	+	0.124334i
$646$	−0.242634	−	0.113471i	−0.00954629	−	0.00446446i
$647$	4.65011	−	4.65011i	0.182815	−	0.182815i	−0.609766	−	0.792581i	$-0.708737\pi$
$647$	4.65011	−	4.65011i	0.182815	−	0.182815i	0.792581	+	0.609766i	$0.208737\pi$
$648$	2.75765	−	4.73974i	0.108331	−	0.186194i
$649$	−3.12374			−0.122618
$650$	−0.631828	+	20.5517i	−0.0247823	+	0.806103i
$651$	20.4928	+	10.1714i	0.803175	+	0.398648i
$652$	10.6532	+	0.955951i	0.417210	+	0.0374379i
$653$	15.5113	+	15.5113i	0.607003	+	0.607003i	0.942162	−	0.335159i	$-0.108790\pi$
$653$	15.5113	+	15.5113i	0.607003	+	0.607003i	−0.335159	+	0.942162i	$0.608790\pi$
$654$	12.3736	−	26.4583i	0.483847	−	1.03460i
$655$	−9.08012	+	1.87238i	−0.354789	+	0.0731599i
$656$	5.54903	+	1.00396i	0.216653	+	0.0391980i
$657$	16.2899	−	16.2899i	0.635531	−	0.635531i
$658$	3.48247	−	30.7520i	0.135761	−	1.19884i
$659$	16.0797			0.626376			0.313188	−	0.949691i	$-0.398603\pi$
$659$	16.0797			0.626376			0.313188	+	0.949691i	$0.398603\pi$
$660$	13.4320	−	1.53604i	0.522841	−	0.0597903i
$661$	−31.7560			−1.23517			−0.617583	−	0.786505i	$-0.711888\pi$
$661$	−31.7560			−1.23517			−0.617583	+	0.786505i	$0.711888\pi$
$662$	12.0665	+	33.2676i	0.468977	+	1.29298i
$663$	1.13147	+	1.13147i	0.0439428	+	0.0439428i
$664$	9.38193	+	35.4878i	0.364090	+	1.37719i
$665$	1.23478	+	2.11694i	0.0478827	+	0.0820913i
$666$	−12.7739	−	5.97389i	−0.494978	−	0.231484i
$667$	13.8995	−	13.8995i	0.538189	−	0.538189i
$668$	1.27805	−	14.2426i	0.0494491	−	0.551062i
$669$	21.5022			0.831325
$670$	3.01712	−	12.6524i	0.116562	−	0.488806i
$671$		−	29.4394i		−	1.13650i
$672$	−17.2521	−	5.18118i	−0.665513	−	0.199868i
$673$	25.3785	−	25.3785i	0.978269	−	0.978269i	−0.0215000	−	0.999769i	$-0.506844\pi$
$673$	25.3785	−	25.3785i	0.978269	−	0.978269i	0.999769	+	0.0215000i	$0.00684418\pi$
$674$	23.0535	+	10.7813i	0.887986	+	0.415280i
$675$	25.4492	+	10.1260i	0.979539	+	0.389748i
$676$	5.82689	+	6.97572i	0.224111	+	0.268297i
$677$	33.3281	+	33.3281i	1.28090	+	1.28090i	0.940154	+	0.340751i	$0.110681\pi$
$677$	33.3281	+	33.3281i	1.28090	+	1.28090i	0.340751	+	0.940154i	$0.389319\pi$
$678$	−2.69522	−	7.43080i	−0.103509	−	0.285378i
$679$	1.96643	−	3.96186i	0.0754647	−	0.152042i
$680$	1.28846	+	2.58878i	0.0494103	+	0.0992753i
$681$	25.4771			0.976285
$682$	23.9916	−	8.70197i	0.918686	−	0.333216i
$683$	3.99641	+	3.99641i	0.152918	+	0.152918i	0.779420	−	0.626502i	$-0.215514\pi$
$683$	3.99641	+	3.99641i	0.152918	+	0.152918i	−0.626502	+	0.779420i	$0.715514\pi$
$684$	0.986485	−	0.824020i	0.0377192	−	0.0315072i
$685$	22.5257	+	14.8240i	0.860664	+	0.566395i
$686$	6.44934	−	25.3852i	0.246237	−	0.969210i
$687$	5.11600	+	5.11600i	0.195188	+	0.195188i
$688$	19.0955	−	13.2444i	0.728008	−	0.504937i
$689$	31.2415			1.19021
$690$	−15.7965	−	25.6892i	−0.601361	−	0.977971i
$691$	−37.9666			−1.44432			−0.722158	−	0.691728i	$-0.756850\pi$
$691$	−37.9666			−1.44432			−0.722158	+	0.691728i	$0.756850\pi$
$692$	4.02156	−	44.8164i	0.152877	−	1.70367i
$693$	9.77140	−	3.28900i	0.371185	−	0.124939i
$694$	7.12361	−	15.2323i	0.270408	−	0.578210i
$695$	−2.70885	−	13.1366i	−0.102753	−	0.498299i
$696$	2.15847	+	8.16457i	0.0818166	+	0.309477i
$697$	0.455785	+	0.455785i	0.0172641	+	0.0172641i
$698$	−12.8484	−	35.4233i	−0.486318	−	1.34079i
$699$			21.5119i			0.813655i
$700$	3.78356	−	26.1856i	0.143005	−	0.989722i
$701$		−	35.0204i		−	1.32270i	−0.750077	−	0.661350i	$-0.769984\pi$
$701$		−	35.0204i		−	1.32270i	0.750077	−	0.661350i	$-0.230016\pi$
$702$	−21.1768	+	7.68103i	−0.799268	+	0.289902i
$703$	1.88266	+	1.88266i	0.0710059	+	0.0710059i
$704$	−17.4688	+	9.93053i	−0.658380	+	0.374271i
$705$	4.49562	+	21.8015i	0.169315	+	0.821094i
$706$	−5.11906	−	2.39400i	−0.192658	−	0.0900994i
$707$	0.335036	−	0.112771i	0.0126003	−	0.00424120i
$708$	−2.98163	−	0.267554i	−0.112056	−	0.0100553i
$709$	−36.6280			−1.37559			−0.687797	−	0.725903i	$-0.741422\pi$
$709$	−36.6280			−1.37559			−0.687797	+	0.725903i	$0.741422\pi$
$710$	2.61918	−	1.61055i	0.0982962	−	0.0604430i
$711$	9.01118			0.337945
$712$	−14.3045	+	24.5859i	−0.536082	+	0.921397i
$713$	−40.2543	−	40.2543i	−1.50753	−	1.50753i
$714$	−1.28286	−	1.61051i	−0.0480098	−	0.0602720i
$715$	−13.6426	−	8.97804i	−0.510203	−	0.335760i
$716$	2.94733	−	2.46194i	0.110147	−	0.0920068i
$717$	−1.13856	−	1.13856i	−0.0425203	−	0.0425203i
$718$	12.0263	+	33.1568i	0.448816	+	1.23740i
$719$	35.7912			1.33478			0.667392	−	0.744706i	$-0.267410\pi$
$719$	35.7912			1.33478			0.667392	+	0.744706i	$0.267410\pi$
$720$	−13.8723	+	0.338101i	−0.516992	+	0.0126003i
$721$	−44.5064	−	22.0903i	−1.65750	−	0.822685i
$722$	25.0317	−	9.07922i	0.931583	−	0.337894i
$723$	−23.5193	−	23.5193i	−0.874691	−	0.874691i
$724$	13.6955	−	11.4400i	0.508988	−	0.425163i
$725$	−11.3921	+	4.90690i	−0.423092	+	0.182238i
$726$	3.38249	−	7.23272i	0.125536	−	0.268432i
$727$	−17.9668	+	17.9668i	−0.666353	+	0.666353i	−0.956870	−	0.290517i	$-0.906173\pi$
$727$	−17.9668	+	17.9668i	−0.666353	+	0.666353i	0.290517	+	0.956870i	$0.406173\pi$
$728$	11.9822	+	18.1640i	0.444089	+	0.673202i
$729$			22.7870i			0.843962i
$730$	45.6763	+	10.8921i	1.69056	+	0.403133i
$731$	2.65632			0.0982476
$732$	2.52153	−	28.1001i	0.0931986	−	1.03861i
$733$	−14.2478	+	14.2478i	−0.526254	+	0.526254i	−0.919453	−	0.393199i	$-0.871368\pi$
$733$	−14.2478	+	14.2478i	−0.526254	+	0.526254i	0.393199	+	0.919453i	$0.371368\pi$
$734$	−14.4200	+	30.8341i	−0.532253	+	1.13811i
$735$	1.26734	+	18.7961i	0.0467466	+	0.693303i
$736$	36.5729	+	25.9134i	1.34809	+	0.955180i
$737$	7.30546	+	7.30546i	0.269100	+	0.269100i
$738$	−2.90778	+	1.05468i	−0.107037	+	0.0388232i
$739$	−27.1860			−1.00005			−0.500027	−	0.866010i	$-0.666677\pi$
$739$	−27.1860			−1.00005			−0.500027	+	0.866010i	$0.666677\pi$
$740$	−3.26572	−	28.5574i	−0.120050	−	1.04979i
$741$	1.44977			0.0532586
$742$	−39.9450	−	4.52352i	−1.46643	−	0.166064i
$743$	4.15036	−	4.15036i	0.152262	−	0.152262i	−0.626866	−	0.779127i	$-0.715662\pi$
$743$	4.15036	−	4.15036i	0.152262	−	0.152262i	0.779127	+	0.626866i	$0.215662\pi$
$744$	23.6454	−	6.25116i	0.866884	−	0.229179i
$745$	12.2424	−	2.52447i	0.448528	−	0.0924894i
$746$	−26.6738	−	12.4744i	−0.976596	−	0.456719i
$747$	−14.2371	−	14.2371i	−0.520910	−	0.520910i
$748$	−2.28766	−	0.205281i	−0.0836451	−	0.00750582i
$749$	14.8649	−	29.9491i	0.543152	−	1.09431i
$750$	3.26872	+	18.7472i	0.119357	+	0.684550i
$751$	−5.39262			−0.196779			−0.0983897	−	0.995148i	$-0.531369\pi$
$751$	−5.39262			−0.196779			−0.0983897	+	0.995148i	$0.531369\pi$
$752$	−18.8560	−	27.1862i	−0.687609	−	0.991380i
$753$	−4.84519	+	4.84519i	−0.176569	+	0.176569i
$754$	4.32171	−	9.24105i	0.157387	−	0.336539i
$755$	−15.4544	+	3.18681i	−0.562444	+	0.115980i
$756$	28.1885	−	6.75463i	1.02521	−	0.245663i
$757$	34.4647	−	34.4647i	1.25264	−	1.25264i	0.298108	−	0.954532i	$-0.403644\pi$
$757$	34.4647	−	34.4647i	1.25264	−	1.25264i	0.954532	−	0.298108i	$-0.0963555\pi$
$758$	15.2799	−	5.54216i	0.554991	−	0.201300i
$759$	23.9537			0.869463
$760$	2.48398	+	0.833057i	0.0901033	+	0.0302181i
$761$			46.5220i			1.68642i	0.537583	+	0.843211i	$0.319337\pi$
$761$			46.5220i			1.68642i	−0.537583	+	0.843211i	$0.680663\pi$
$762$	−6.23363	+	2.26100i	−0.225821	+	0.0819072i
$763$	43.0301	−	14.4837i	1.55779	−	0.524345i
$764$	39.6964	−	33.1588i	1.43616	−	1.19964i
$765$	−1.32497	−	0.871951i	−0.0479044	−	0.0315255i
$766$	−11.7546	−	5.49722i	−0.424712	−	0.198623i
$767$	2.55710	+	2.55710i	0.0923316	+	0.0923316i
$768$	−17.5246	+	7.98251i	−0.632365	+	0.288044i
$769$	21.4981			0.775240			0.387620	−	0.921819i	$-0.373297\pi$
$769$	21.4981			0.775240			0.387620	+	0.921819i	$0.373297\pi$
$770$	16.1432	+	13.4545i	0.581762	+	0.484867i
$771$			35.9246i			1.29379i
$772$	−0.989097	+	11.0225i	−0.0355984	+	0.396710i
$773$	12.2376	−	12.2376i	0.440157	−	0.440157i	−0.451907	−	0.892065i	$-0.649256\pi$
$773$	12.2376	−	12.2376i	0.440157	−	0.440157i	0.892065	+	0.451907i	$0.149256\pi$
$774$	−5.39995	+	11.5466i	−0.194097	+	0.415035i
$775$	14.2109	+	32.9927i	0.510470	+	1.18513i
$776$	−1.20853	−	4.57137i	−0.0433839	−	0.164102i
$777$	6.52897	+	19.3971i	0.234225	+	0.695868i
$778$	−8.91512	+	3.23360i	−0.319622	+	0.115930i
$779$	0.584001			0.0209240
$780$	−12.2529	−	9.73809i	−0.438724	−	0.348680i
$781$			2.44223i			0.0873899i
$782$	1.74696	+	4.81641i	0.0624711	+	0.172235i
$783$	−9.60930	−	9.60930i	−0.343408	−	0.343408i
$784$	−12.6902	−	24.9591i	−0.453222	−	0.891397i
$785$	33.6398	+	22.1381i	1.20066	+	0.790141i
$786$	2.98963	−	6.39267i	0.106636	−	0.228019i
$787$	−31.2056	−	31.2056i	−1.11236	−	1.11236i	−0.992831	−	0.119529i	$-0.961862\pi$
$787$	−31.2056	−	31.2056i	−1.11236	−	1.11236i	−0.119529	−	0.992831i	$-0.538138\pi$
$788$	−2.88091	+	32.1050i	−0.102628	+	1.14369i
$789$		−	9.25673i		−	0.329548i
$790$	9.62088	+	15.6461i	0.342296	+	0.556663i
$791$	5.46258	−	11.0057i	0.194227	−	0.391318i
$792$	5.54284	−	9.52681i	0.196956	−	0.338520i
$793$	−24.0992	+	24.0992i	−0.855787	+	0.855787i
$794$	−9.77385	−	4.57088i	−0.346861	−	0.162215i
$795$	28.3189	−	5.83955i	1.00437	−	0.207107i
$796$	−3.56499	+	2.97787i	−0.126358	+	0.105548i
$797$	14.3254	+	14.3254i	0.507431	+	0.507431i	0.913737	−	0.406306i	$-0.133183\pi$
$797$	14.3254	+	14.3254i	0.507431	+	0.507431i	−0.406306	+	0.913737i	$0.633183\pi$
$798$	−1.85365	−	0.209915i	−0.0656186	−	0.00743090i
$799$		−	3.78181i		−	0.133791i
$800$	−15.3980	−	23.7255i	−0.544402	−	0.838825i
$801$		−	15.6022i		−	0.551277i
$802$	−7.60587	+	2.75872i	−0.268573	+	0.0974138i
$803$	−26.3733	+	26.3733i	−0.930695	+	0.930695i
$804$	6.34738	+	7.59883i	0.223855	+	0.267990i
$805$	11.9314	−	45.3329i	0.420527	−	1.59778i
$806$	−26.7630	−	12.5161i	−0.942688	−	0.440862i
$807$	6.01670	+	6.01670i	0.211798	+	0.211798i
$808$	0.190049	−	0.326649i	0.00668591	−	0.0114915i
$809$			26.5709i			0.934183i	0.884209	+	0.467091i	$0.154698\pi$
$809$			26.5709i			0.934183i	−0.884209	+	0.467091i	$0.845302\pi$
$810$	−5.22249	+	3.21135i	−0.183500	+	0.112835i
$811$	−5.10317			−0.179197			−0.0895983	−	0.995978i	$-0.528558\pi$
$811$	−5.10317			−0.179197			−0.0895983	+	0.995978i	$0.528558\pi$
$812$	−6.86371	+	11.1897i	−0.240869	+	0.392682i
$813$	−16.5778	−	16.5778i	−0.581410	−	0.581410i
$814$	20.6809	+	9.67170i	0.724864	+	0.338993i
$815$	−9.98939	−	6.57392i	−0.349913	−	0.230275i
$816$	−2.16600	−	0.391883i	−0.0758251	−	0.0137187i
$817$	1.70178	−	1.70178i	0.0595379	−	0.0595379i
$818$	−27.9895	+	10.1521i	−0.978631	+	0.354959i
$819$	−10.6913	−	5.30650i	−0.373583	−	0.185424i
$820$	−4.93576	−	3.92273i	−0.172364	−	0.136988i
$821$			24.8927i			0.868760i	0.900730	+	0.434380i	$0.143033\pi$
$821$			24.8927i			0.868760i	−0.900730	+	0.434380i	$0.856967\pi$
$822$	−19.2964	+	6.99897i	−0.673038	+	0.244117i
$823$	−8.95105	+	8.95105i	−0.312014	+	0.312014i	−0.845689	−	0.533675i	$-0.820810\pi$
$823$	−8.95105	+	8.95105i	−0.312014	+	0.312014i	0.533675	+	0.845689i	$0.320810\pi$
$824$	−51.3534	+	13.5763i	−1.78898	+	0.472953i
$825$	−14.0444	−	5.58814i	−0.488965	−	0.194554i
$826$	−2.89923	−	3.63972i	−0.100877	−	0.126642i
$827$	−5.03438	+	5.03438i	−0.175063	+	0.175063i	−0.789200	−	0.614137i	$-0.789504\pi$
$827$	−5.03438	+	5.03438i	−0.175063	+	0.175063i	0.614137	+	0.789200i	$0.289504\pi$
$828$	−24.4876	−	2.19737i	−0.851002	−	0.0763639i
$829$		−	15.1494i		−	0.526161i	−0.964774	−	0.263081i	$-0.915261\pi$
$829$		−	15.1494i		−	0.526161i	0.964774	−	0.263081i	$-0.0847385\pi$
$830$	9.51948	−	39.9204i	0.330426	−	1.38566i
$831$			26.3413i			0.913769i
$832$	22.4291	+	6.17084i	0.777591	+	0.213935i
$833$	0.434034	−	3.17096i	0.0150384	−	0.109867i
$834$	9.24855	+	4.32522i	0.320251	+	0.149770i
$835$	−8.78892	+	13.3552i	−0.304153	+	0.462175i
$836$	−1.59711	+	1.33409i	−0.0552373	+	0.0461403i
$837$	−27.8295	+	27.8295i	−0.961929	+	0.961929i
$838$	−17.3195	−	47.7504i	−0.598292	−	1.64951i
$839$	20.9224			0.722320			0.361160	−	0.932504i	$-0.382381\pi$
$839$	20.9224			0.722320			0.361160	+	0.932504i	$0.382381\pi$
$840$	14.2564	+	14.2251i	0.491892	+	0.490813i
$841$	−22.8457			−0.787783
$842$	−9.06479	−	24.9919i	−0.312393	−	0.861278i
$843$	−17.3723	+	17.3723i	−0.598335	+	0.598335i
$844$	−8.41080	−	10.0691i	−0.289512	−	0.346592i
$845$	−2.05230	−	9.95263i	−0.0706012	−	0.342381i
$846$	16.4390	+	7.68792i	0.565183	+	0.264316i
$847$	11.7628	−	3.95931i	0.404176	−	0.136043i
$848$	−35.3133	+	24.4929i	−1.21266	+	0.841088i
$849$			8.44781i			0.289928i
$850$	0.0993471	−	3.23149i	0.00340758	−	0.110839i
$851$		−	50.9270i		−	1.74576i
$852$	−0.209181	+	2.33112i	−0.00716643	+	0.0798629i
$853$	−9.15082	+	9.15082i	−0.313318	+	0.313318i	−0.846194	−	0.532876i	$-0.821111\pi$
$853$	−9.15082	+	9.15082i	−0.313318	+	0.313318i	0.532876	+	0.846194i	$0.321111\pi$
$854$	34.3022	−	27.3235i	1.17380	−	0.934991i
$855$	−1.40747	+	0.290229i	−0.0481344	+	0.00992564i
$856$	−9.13572	−	34.5565i	−0.312253	−	1.18112i
$857$	14.9046	−	14.9046i	0.509131	−	0.509131i	−0.405128	−	0.914260i	$-0.632773\pi$
$857$	14.9046	−	14.9046i	0.509131	−	0.509131i	0.914260	+	0.405128i	$0.132773\pi$
$858$	11.6867	−	4.23887i	0.398977	−	0.144713i
$859$			27.4269i			0.935793i	0.883783	+	0.467897i	$0.154988\pi$
$859$			27.4269i			0.935793i	−0.883783	+	0.467897i	$0.845012\pi$
$860$	−25.8137	+	2.95197i	−0.880241	+	0.100661i
$861$	4.02113	+	1.99585i	0.137040	+	0.0680184i
$862$	9.14275	−	3.31616i	0.311403	−	0.112949i
$863$	−7.01745	+	7.01745i	−0.238877	+	0.238877i	−0.816385	−	0.577508i	$-0.804025\pi$
$863$	−7.01745	+	7.01745i	−0.238877	+	0.238877i	0.577508	+	0.816385i	$0.304025\pi$
$864$	17.9150	−	25.2844i	0.609482	−	0.860193i
$865$	−27.6557	+	42.0241i	−0.940320	+	1.42886i
$866$	−5.03558	−	2.35496i	−0.171116	−	0.0800248i
$867$	14.2899	+	14.2899i	0.485310	+	0.485310i
$868$	32.4066	+	19.8780i	1.09995	+	0.674703i
$869$	−14.5890			−0.494900
$870$	2.19012	−	9.18435i	0.0742519	−	0.311379i
$871$		−	11.9605i		−	0.405267i
$872$	24.4089	−	41.9530i	0.826589	−	1.42071i
$873$	1.83396	+	1.83396i	0.0620701	+	0.0620701i
$874$	4.20485	+	1.96646i	0.142231	+	0.0665165i
$875$	−17.5713	+	23.7960i	−0.594018	+	0.804452i
$876$	−27.4324	+	22.9146i	−0.926855	+	0.774211i
$877$	26.0087	−	26.0087i	0.878250	−	0.878250i	−0.115104	−	0.993353i	$-0.536720\pi$
$877$	26.0087	−	26.0087i	0.878250	−	0.878250i	0.993353	+	0.115104i	$0.0367200\pi$
$878$	32.3929	−	11.7492i	1.09321	−	0.396517i
$879$			13.8753i			0.468003i
$880$	22.4593	−	0.547384i	0.757101	−	0.0184523i
$881$			0.348598i			0.0117446i	0.999983	+	0.00587228i	$0.00186922\pi$
$881$			0.348598i			0.0117446i	−0.999983	+	0.00587228i	$0.998131\pi$
$882$	12.9014	+	8.33283i	0.434412	+	0.280581i
$883$	−38.4627	−	38.4627i	−1.29437	−	1.29437i	−0.932054	−	0.362319i	$-0.881985\pi$
$883$	−38.4627	−	38.4627i	−1.29437	−	1.29437i	−0.362319	−	0.932054i	$-0.618015\pi$
$884$	1.70464	+	2.04073i	0.0573332	+	0.0686370i
$885$	2.79585	+	1.83992i	0.0939815	+	0.0618484i
$886$	15.9446	+	7.45673i	0.535670	+	0.250514i
$887$	−12.0426	+	12.0426i	−0.404351	+	0.404351i	−0.879763	−	0.475412i	$-0.842299\pi$
$887$	−12.0426	+	12.0426i	−0.404351	+	0.404351i	0.475412	+	0.879763i	$0.342299\pi$
$888$	18.9116	+	11.0030i	0.634631	+	0.369238i
$889$	−9.23260	−	4.58251i	−0.309652	−	0.153692i
$890$	27.0901	−	16.6579i	0.908062	−	0.558373i
$891$		−	4.86967i		−	0.163140i
$892$	35.5880	+	3.19346i	1.19157	+	0.106925i
$893$	−2.42283	−	2.42283i	−0.0810770	−	0.0810770i
$894$	−4.03082	+	8.61904i	−0.134811	+	0.288264i
$895$	−4.20511	+	0.867122i	−0.140561	+	0.0289847i
$896$	−27.7841	−	11.1375i	−0.928202	−	0.372078i
$897$	−19.6085	−	19.6085i	−0.654709	−	0.654709i
$898$	−9.76618	−	26.9257i	−0.325902	−	0.898521i
$899$		−	17.8235i		−	0.594447i
$900$	13.8449	+	7.00105i	0.461496	+	0.233368i
$901$	−4.91234			−0.163654
$902$	4.70768	−	1.70752i	0.156749	−	0.0568542i
$903$	17.5335	−	5.90170i	0.583480	−	0.196396i
$904$	−3.35721	−	12.6989i	−0.111659	−	0.422358i
$905$	−19.5400	+	4.02929i	−0.649533	+	0.133938i
$906$	5.08837	−	10.8804i	0.169050	−	0.361476i
$907$	−15.6043	+	15.6043i	−0.518132	+	0.518132i	−0.917006	−	0.398874i	$-0.869401\pi$
$907$	−15.6043	+	15.6043i	−0.518132	+	0.518132i	0.398874	+	0.917006i	$0.369401\pi$
$908$	42.1667	+	3.78379i	1.39935	+	0.125570i
$909$			0.207291i			0.00687542i
$910$	−2.20098	−	24.2288i	−0.0729618	−	0.803176i
$911$	27.1278			0.898784			0.449392	−	0.893335i	$-0.351641\pi$
$911$	27.1278			0.898784			0.449392	+	0.893335i	$0.351641\pi$
$912$	−1.63872	+	1.13660i	−0.0542634	+	0.0376364i
$913$	23.0499	+	23.0499i	0.762839	+	0.762839i
$914$	5.11836	+	2.39367i	0.169300	+	0.0791757i
$915$	−17.3402	+	26.3492i	−0.573249	+	0.871079i
$916$	7.70759	+	9.22722i	0.254666	+	0.304876i
$917$	10.3966	−	3.49945i	0.343327	−	0.115562i
$918$	3.32979	−	1.20775i	0.109900	−	0.0398616i
$919$		−	16.0238i		−	0.528576i	−0.964444	−	0.264288i	$-0.914863\pi$
$919$		−	16.0238i		−	0.528576i	0.964444	−	0.264288i	$-0.0851370\pi$
$920$	−22.3291	−	44.8638i	−0.736170	−	1.47912i
$921$	18.4102			0.606636
$922$	−5.64580	+	2.04778i	−0.185934	+	0.0674401i
$923$	1.99922	−	1.99922i	0.0658050	−	0.0658050i
$924$	−15.5562	+	3.72762i	−0.511761	+	0.122630i
$925$	−11.8807	+	29.8594i	−0.390636	+	0.981771i
$926$	−6.69687	+	14.3198i	−0.220073	+	0.470578i
$927$	20.6021	−	20.6021i	0.676663	−	0.676663i
$928$	2.35987	+	13.8336i	0.0774664	+	0.454110i
$929$	25.8081			0.846735			0.423367	−	0.905958i	$-0.360848\pi$
$929$	25.8081			0.846735			0.423367	+	0.905958i	$0.360848\pi$
$930$	−26.5988	−	6.34281i	−0.872210	−	0.207989i
$931$	−1.75343	−	2.30956i	−0.0574662	−	0.0756927i
$932$	−3.19489	+	35.6040i	−0.104652	+	1.16625i
$933$	20.8981	+	20.8981i	0.684174	+	0.684174i
$934$	9.84130	+	4.60243i	0.322017	+	0.150596i
$935$	2.14512	+	1.41168i	0.0701530	+	0.0461670i
$936$	−12.3360	+	3.26129i	−0.403216	+	0.106599i
$937$	−0.712338	+	0.712338i	−0.0232711	+	0.0232711i	−0.718647	−	0.695376i	$-0.755238\pi$
$937$	−0.712338	+	0.712338i	−0.0232711	+	0.0232711i	0.695376	+	0.718647i	$0.255238\pi$
$938$	−1.73179	+	15.2926i	−0.0565449	+	0.499320i
$939$	25.5503			0.833804
$940$	4.20272	+	36.7510i	0.137078	+	1.19869i
$941$	19.4618			0.634436			0.317218	−	0.948353i	$-0.397251\pi$
$941$	19.4618			0.634436			0.317218	+	0.948353i	$0.397251\pi$
$942$	−28.8171	+	10.4522i	−0.938911	+	0.340552i
$943$	−7.89878	−	7.89878i	−0.257220	−	0.257220i
$944$	−4.89510	−	0.885647i	−0.159322	−	0.0288253i
$945$	−31.3406	−	8.24871i	−1.01951	−	0.268330i
$946$	8.74250	−	18.6939i	0.284243	−	0.607793i
$947$	16.5040	−	16.5040i	0.536309	−	0.536309i	−0.386134	−	0.922443i	$-0.626190\pi$
$947$	16.5040	−	16.5040i	0.536309	−	0.536309i	0.922443	+	0.386134i	$0.126190\pi$
$948$	−13.9253	−	1.24958i	−0.452273	−	0.0405843i
$949$	43.1785			1.40163
$950$	−2.00662	−	2.13392i	−0.0651035	−	0.0692335i
$951$		−	31.0562i		−	1.00707i
$952$	−1.88405	−	2.85606i	−0.0610623	−	0.0925655i
$953$	−15.0426	+	15.0426i	−0.487279	+	0.487279i	−0.907446	−	0.420168i	$-0.861971\pi$
$953$	−15.0426	+	15.0426i	−0.487279	+	0.487279i	0.420168	+	0.907446i	$0.361971\pi$
$954$	9.98615	−	21.3532i	0.323313	−	0.691336i
$955$	−56.6369	+	11.6789i	−1.83273	+	0.377921i
$956$	−1.71531	−	2.05351i	−0.0554772	−	0.0664151i
$957$	5.30301	+	5.30301i	0.171422	+	0.171422i
$958$	12.6686	−	4.59501i	0.409303	−	0.148458i
$959$	−28.5797	−	14.1853i	−0.922888	−	0.458066i
$960$	21.4844	+	1.40119i	0.693404	+	0.0452233i
$961$	−20.6187			−0.665118
$962$	−9.01212	−	24.8467i	−0.290562	−	0.801089i
$963$	13.8635	+	13.8635i	0.446746	+	0.446746i
$964$	−35.4333	−	42.4193i	−1.14123	−	1.36624i
$965$	6.80186	−	10.3358i	0.218960	−	0.332720i
$966$	22.2320	+	27.9103i	0.715303	+	0.898000i
$967$	13.5634	+	13.5634i	0.436171	+	0.436171i	0.890721	−	0.454550i	$-0.150200\pi$
$967$	13.5634	+	13.5634i	0.436171	+	0.436171i	−0.454550	+	0.890721i	$0.650200\pi$
$968$	6.67248	−	11.4684i	0.214462	−	0.368608i
$969$	−0.227958			−0.00732307
$970$	−1.22625	+	5.14235i	−0.0393726	+	0.165111i
$971$	56.7239			1.82036			0.910178	−	0.414217i	$-0.135945\pi$
$971$	56.7239			1.82036			0.910178	+	0.414217i	$0.135945\pi$
$972$	−2.52045	+	28.0880i	−0.0808435	+	0.900923i
$973$	5.06280	+	15.0412i	0.162306	+	0.482200i
$974$	−37.9782	−	17.7611i	−1.21690	−	0.569102i
$975$	6.92236	+	16.0713i	0.221693	+	0.514693i
$976$	8.34669	−	46.1334i	0.267171	−	1.47669i
$977$	−18.9559	−	18.9559i	−0.606455	−	0.606455i	0.335563	−	0.942018i	$-0.391073\pi$
$977$	−18.9559	−	18.9559i	−0.606455	−	0.606455i	−0.942018	+	0.335563i	$0.891073\pi$
$978$	8.55727	−	3.10380i	0.273631	−	0.0992486i
$979$			25.2599i			0.807310i
$980$	−0.693987	+	31.2973i	−0.0221686	+	0.999754i
$981$			26.6233i			0.850017i
$982$	6.91481	+	19.0643i	0.220661	+	0.608368i
$983$	−14.6499	−	14.6499i	−0.467260	−	0.467260i	0.433765	−	0.901026i	$-0.357185\pi$
$983$	−14.6499	−	14.6499i	−0.467260	−	0.467260i	−0.901026	+	0.433765i	$0.857185\pi$
$984$	4.63976	−	1.22661i	0.147910	−	0.0391030i
$985$	19.8116	−	30.1046i	0.631250	−	0.959214i
$986$	−0.679535	+	1.45304i	−0.0216408	+	0.0462742i
$987$	−8.40225	−	24.9625i	−0.267447	−	0.794566i
$988$	2.39949	+	0.215316i	0.0763378	+	0.00685011i
$989$	−46.0342			−1.46380
$990$	−10.4971	+	6.45476i	−0.333621	+	0.205146i
$991$	4.37107			0.138852			0.0694258	−	0.997587i	$-0.477883\pi$
$991$	4.37107			0.138852			0.0694258	+	0.997587i	$0.477883\pi$
$992$	40.0636	−	6.83442i	1.27202	−	0.216993i
$993$	21.2961	+	21.2961i	0.675810	+	0.675810i
$994$	−2.84564	+	2.26670i	−0.0902582	+	0.0718954i
$995$	5.08636	−	1.04884i	0.161248	−	0.0332505i
$996$	20.0269	+	23.9755i	0.634578	+	0.759692i
$997$	−3.54219	−	3.54219i	−0.112182	−	0.112182i	0.648787	−	0.760970i	$-0.275276\pi$
$997$	−3.54219	−	3.54219i	−0.112182	−	0.112182i	−0.760970	+	0.648787i	$0.775276\pi$
$998$	24.5508	−	8.90478i	0.777140	−	0.281876i
$999$	−35.2080			−1.11393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.c.237.34	yes	72
4.3	odd	2		1120.2.w.c.657.11		72
5.3	odd	4	inner	280.2.s.c.13.14	yes	72
7.6	odd	2	inner	280.2.s.c.237.33	yes	72
8.3	odd	2		1120.2.w.c.657.26		72
8.5	even	2	inner	280.2.s.c.237.13	yes	72
20.3	even	4		1120.2.w.c.433.12		72
28.27	even	2		1120.2.w.c.657.25		72
35.13	even	4	inner	280.2.s.c.13.13	✓	72
40.3	even	4		1120.2.w.c.433.25		72
40.13	odd	4	inner	280.2.s.c.13.33	yes	72
56.13	odd	2	inner	280.2.s.c.237.14	yes	72
56.27	even	2		1120.2.w.c.657.12		72
140.83	odd	4		1120.2.w.c.433.26		72
280.13	even	4	inner	280.2.s.c.13.34	yes	72
280.83	odd	4		1120.2.w.c.433.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.c.13.13	✓	72	35.13	even	4	inner
280.2.s.c.13.14	yes	72	5.3	odd	4	inner
280.2.s.c.13.33	yes	72	40.13	odd	4	inner
280.2.s.c.13.34	yes	72	280.13	even	4	inner
280.2.s.c.237.13	yes	72	8.5	even	2	inner
280.2.s.c.237.14	yes	72	56.13	odd	2	inner
280.2.s.c.237.33	yes	72	7.6	odd	2	inner
280.2.s.c.237.34	yes	72	1.1	even	1	trivial
1120.2.w.c.433.11		72	280.83	odd	4
1120.2.w.c.433.12		72	20.3	even	4
1120.2.w.c.433.25		72	40.3	even	4
1120.2.w.c.433.26		72	140.83	odd	4
1120.2.w.c.657.11		72	4.3	odd	2
1120.2.w.c.657.12		72	56.27	even	2
1120.2.w.c.657.25		72	28.27	even	2
1120.2.w.c.657.26		72	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.32946 - 0.482209i) q^{2} +(0.851048 - 0.851048i) q^{3} +(1.53495 - 1.28216i) q^{4} +(-2.18999 + 0.451591i) q^{5} +(0.721055 - 1.54182i) q^{6} +(2.50752 - 0.844017i) q^{7} +(1.42239 - 2.44475i) q^{8} +1.55144i q^{9} +O(q^{10})\)	\(q+(1.32946 - 0.482209i) q^{2} +(0.851048 - 0.851048i) q^{3} +(1.53495 - 1.28216i) q^{4} +(-2.18999 + 0.451591i) q^{5} +(0.721055 - 1.54182i) q^{6} +(2.50752 - 0.844017i) q^{7} +(1.42239 - 2.44475i) q^{8} +1.55144i q^{9} +(-2.69375 + 1.65641i) q^{10} -2.51177i q^{11} +(0.215137 - 2.39749i) q^{12} +(-2.05614 + 2.05614i) q^{13} +(2.92666 - 2.33124i) q^{14} +(-1.47946 + 2.24811i) q^{15} +(0.712139 - 3.93610i) q^{16} +(0.323302 - 0.323302i) q^{17} +(0.748116 + 2.06258i) q^{18} -0.414250i q^{19} +(-2.78252 + 3.50109i) q^{20} +(1.41572 - 2.85231i) q^{21} +(-1.21120 - 3.33930i) q^{22} +(-5.60285 + 5.60285i) q^{23} +(-0.870076 - 3.29112i) q^{24} +(4.59213 - 1.97796i) q^{25} +(-1.74207 + 3.72505i) q^{26} +(3.87349 + 3.87349i) q^{27} +(2.76675 - 4.51056i) q^{28} -2.48079 q^{29} +(-0.882832 + 3.70220i) q^{30} +7.18461i q^{31} +(-0.951258 - 5.57630i) q^{32} +(-2.13763 - 2.13763i) q^{33} +(0.273919 - 0.585718i) q^{34} +(-5.11029 + 2.98076i) q^{35} +(1.98919 + 2.38137i) q^{36} +(-4.54475 + 4.54475i) q^{37} +(-0.199755 - 0.550730i) q^{38} +3.49974i q^{39} +(-2.01100 + 5.99632i) q^{40} +1.40978i q^{41} +(0.506734 - 4.47472i) q^{42} +(4.10811 + 4.10811i) q^{43} +(-3.22048 - 3.85543i) q^{44} +(-0.700614 - 3.39763i) q^{45} +(-4.74704 + 10.1505i) q^{46} +(5.84872 - 5.84872i) q^{47} +(-2.74374 - 3.95587i) q^{48} +(5.57527 - 4.23277i) q^{49} +(5.15128 - 4.84399i) q^{50} -0.550291i q^{51} +(-0.519772 + 5.79236i) q^{52} +(-7.59714 - 7.59714i) q^{53} +(7.01749 + 3.28183i) q^{54} +(1.13429 + 5.50075i) q^{55} +(1.50326 - 7.33077i) q^{56} +(-0.352547 - 0.352547i) q^{57} +(-3.29812 + 1.19626i) q^{58} -1.24364i q^{59} +(0.611538 + 5.34765i) q^{60} +11.7206 q^{61} +(3.46448 + 9.55169i) q^{62} +(1.30944 + 3.89025i) q^{63} +(-3.95360 - 6.95478i) q^{64} +(3.57439 - 5.43146i) q^{65} +(-3.87269 - 1.81112i) q^{66} +(-2.90850 + 2.90850i) q^{67} +(0.0817277 - 0.910777i) q^{68} +9.53658i q^{69} +(-5.35660 + 6.42704i) q^{70} -0.972317 q^{71} +(3.79287 + 2.20675i) q^{72} +(-10.4999 - 10.4999i) q^{73} +(-3.85056 + 8.23359i) q^{74} +(2.22478 - 5.59146i) q^{75} +(-0.531134 - 0.635853i) q^{76} +(-2.11997 - 6.29829i) q^{77} +(1.68761 + 4.65278i) q^{78} -5.80828i q^{79} +(0.217928 + 8.94162i) q^{80} +1.93874 q^{81} +(0.679808 + 1.87425i) q^{82} +(-9.17675 + 9.17675i) q^{83} +(-1.48406 - 6.19333i) q^{84} +(-0.562029 + 0.854029i) q^{85} +(7.44255 + 3.48062i) q^{86} +(-2.11127 + 2.11127i) q^{87} +(-6.14064 - 3.57272i) q^{88} -10.0566 q^{89} +(-2.56981 - 4.17919i) q^{90} +(-3.42038 + 6.89121i) q^{91} +(-1.41635 + 15.7838i) q^{92} +(6.11445 + 6.11445i) q^{93} +(4.95536 - 10.5960i) q^{94} +(0.187072 + 0.907204i) q^{95} +(-5.55526 - 3.93613i) q^{96} +(1.18210 - 1.18210i) q^{97} +(5.37104 - 8.31576i) q^{98} +3.89684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

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