LMFDB - Embedded newform 280.2.s.c.13.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("280.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			13.13
Character	$\chi$	$=$	280.13
Dual form			280.2.s.c.237.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.482209 - 1.32946i) q^{2} +(-0.851048 - 0.851048i) q^{3} +(-1.53495 + 1.28216i) q^{4} +(2.18999 + 0.451591i) q^{5} +(-0.721055 + 1.54182i) q^{6} +(2.50752 + 0.844017i) q^{7} +(2.44475 + 1.42239i) q^{8} -1.55144i q^{9} +O(q^{10})$	\(q+(-0.482209 - 1.32946i) 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} +(2.44475 + 1.42239i) q^{8} -1.55144i q^{9} +(-0.455660 - 3.12928i) q^{10} -2.51177i q^{11} +(2.39749 + 0.215137i) q^{12} +(2.05614 + 2.05614i) q^{13} +(-0.0870566 - 3.74064i) q^{14} +(-1.47946 - 2.24811i) q^{15} +(0.712139 - 3.93610i) q^{16} +(0.323302 + 0.323302i) q^{17} +(-2.06258 + 0.748116i) q^{18} -0.414250i q^{19} +(-3.94054 + 2.11475i) q^{20} +(-1.41572 - 2.85231i) q^{21} +(-3.33930 + 1.21120i) 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} +(-4.93107 + 1.91951i) q^{28} +2.48079 q^{29} +(-2.27538 + 3.05095i) q^{30} -7.18461i q^{31} +(-5.57630 + 0.951258i) 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} +(-0.550730 + 0.199755i) q^{38} -3.49974i q^{39} +(4.71164 + 4.21905i) q^{40} -1.40978i q^{41} +(-3.10938 + 3.25756i) 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} +(-3.95587 + 2.74374i) q^{48} +(5.57527 + 4.23277i) q^{49} +(0.415262 - 7.05886i) q^{50} -0.550291i q^{51} +(-5.79236 - 0.519772i) q^{52} +(7.59714 - 7.59714i) q^{53} +(7.01749 + 3.28183i) q^{54} +(1.13429 - 5.50075i) q^{55} +(4.92973 + 5.63008i) q^{56} +(-0.352547 + 0.352547i) q^{57} +(-1.19626 - 3.29812i) q^{58} -1.24364i q^{59} +(5.15334 + 1.55383i) q^{60} -11.7206 q^{61} +(-9.55169 + 3.46448i) 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} +(-0.910777 - 0.0817277i) q^{68} +9.53658i q^{69} +(1.49859 - 8.23130i) q^{70} -0.972317 q^{71} +(2.20675 - 3.79287i) 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} +(-4.65278 + 1.68761i) q^{78} +5.80828i q^{79} +(3.33708 - 8.29843i) q^{80} +1.93874 q^{81} +(-1.87425 + 0.679808i) q^{82} +(9.17675 + 9.17675i) q^{83} +(5.83017 + 2.56298i) q^{84} +(0.562029 + 0.854029i) q^{85} +(7.44255 + 3.48062i) q^{86} +(-2.11127 - 2.11127i) q^{87} +(3.57272 - 6.14064i) q^{88} -10.0566 q^{89} +(-4.85487 + 0.706927i) q^{90} +(3.42038 + 6.89121i) q^{91} +(15.7838 + 1.41635i) 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} +(2.93887 - 9.45320i) 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 $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.482209	−	1.32946i	−0.340973	−	0.940073i
$2$	−0.482209	−	1.32946i	−0.340973	−	0.940073i
$3$	−0.851048	−	0.851048i	−0.491353	−	0.491353i	0.417380	−	0.908732i	$-0.362949\pi$
$3$	−0.851048	−	0.851048i	−0.491353	−	0.491353i	−0.908732	+	0.417380i	$0.862949\pi$
$4$	−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
$8$	2.44475	+	1.42239i	0.864350	+	0.502891i
$9$		−	1.55144i		−	0.517145i
$10$	−0.455660	−	3.12928i	−0.144092	−	0.989564i
$11$		−	2.51177i		−	0.757326i	−0.925535	−	0.378663i	$-0.876384\pi$
$11$		−	2.51177i		−	0.757326i	0.925535	−	0.378663i	$-0.123616\pi$
$12$	2.39749	+	0.215137i	0.692097	+	0.0621047i
$13$	2.05614	+	2.05614i	0.570270	+	0.570270i	0.932204	−	0.361934i	$-0.117883\pi$
$13$	2.05614	+	2.05614i	0.570270	+	0.570270i	−0.361934	+	0.932204i	$0.617883\pi$
$14$	−0.0870566	−	3.74064i	−0.0232668	−	0.999729i
$15$	−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	0.745225	−	0.666813i	$-0.232342\pi$
$17$	0.323302	+	0.323302i	0.0784123	+	0.0784123i	−0.666813	+	0.745225i	$0.732342\pi$
$18$	−2.06258	+	0.748116i	−0.486154	+	0.176333i
$19$		−	0.414250i		−	0.0950355i	−0.998870	−	0.0475177i	$-0.984869\pi$
$19$		−	0.414250i		−	0.0950355i	0.998870	−	0.0475177i	$-0.0151311\pi$
$20$	−3.94054	+	2.11475i	−0.881131	+	0.472872i
$21$	−1.41572	−	2.85231i	−0.308935	−	0.622426i
$22$	−3.33930	+	1.21120i	−0.711942	+	0.258228i
$23$	−5.60285	−	5.60285i	−1.16827	−	1.16827i	−0.982614	−	0.185660i	$-0.940558\pi$
$23$	−5.60285	−	5.60285i	−1.16827	−	1.16827i	−0.185660	−	0.982614i	$-0.559442\pi$
$24$	−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
$28$	−4.93107	+	1.91951i	−0.931885	+	0.362753i
$29$	2.48079			0.460670			0.230335	−	0.973111i	$-0.426018\pi$
$29$	2.48079			0.460670			0.230335	+	0.973111i	$0.426018\pi$
$30$	−2.27538	+	3.05095i	−0.415425	+	0.557025i
$31$		−	7.18461i		−	1.29039i	−0.764016	−	0.645197i	$-0.776775\pi$
$31$		−	7.18461i		−	1.29039i	0.764016	−	0.645197i	$-0.223225\pi$
$32$	−5.57630	+	0.951258i	−0.985760	+	0.168160i
$33$	−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	$-0.0728237\pi$
$37$	4.54475	+	4.54475i	0.747152	+	0.747152i	−0.226792	+	0.973943i	$0.572824\pi$
$38$	−0.550730	+	0.199755i	−0.0893403	+	0.0324045i
$39$		−	3.49974i		−	0.560407i
$40$	4.71164	+	4.21905i	0.744976	+	0.667091i
$41$		−	1.40978i		−	0.220171i	−0.993922	−	0.110085i	$-0.964888\pi$
$41$		−	1.40978i		−	0.220171i	0.993922	−	0.110085i	$-0.0351124\pi$
$42$	−3.10938	+	3.25756i	−0.479787	+	0.502652i
$43$	−4.10811	+	4.10811i	−0.626481	+	0.626481i	−0.947181	−	0.320700i	$-0.896082\pi$
$43$	−4.10811	+	4.10811i	−0.626481	+	0.626481i	0.320700	+	0.947181i	$0.396082\pi$
$44$	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	0.990517	−	0.137393i	$-0.0438723\pi$
$47$	5.84872	+	5.84872i	0.853124	+	0.853124i	−0.137393	+	0.990517i	$0.543872\pi$
$48$	−3.95587	+	2.74374i	−0.570981	+	0.396025i
$49$	5.57527	+	4.23277i	0.796467	+	0.604681i
$50$	0.415262	−	7.05886i	0.0587269	−	0.998274i
$51$		−	0.550291i		−	0.0770562i
$52$	−5.79236	−	0.519772i	−0.803256	−	0.0720795i
$53$	7.59714	−	7.59714i	1.04355	−	1.04355i	0.0445393	−	0.999008i	$-0.485818\pi$
$53$	7.59714	−	7.59714i	1.04355	−	1.04355i	0.999008	−	0.0445393i	$-0.0141820\pi$
$54$	7.01749	+	3.28183i	0.954960	+	0.446601i
$55$	1.13429	−	5.50075i	0.152948	−	0.741721i
$56$	4.92973	+	5.63008i	0.658762	+	0.752351i
$57$	−0.352547	+	0.352547i	−0.0466959	+	0.0466959i
$58$	−1.19626	−	3.29812i	−0.157076	−	0.433064i
$59$		−	1.24364i		−	0.161909i	−0.996718	−	0.0809543i	$-0.974203\pi$
$59$		−	1.24364i		−	0.161909i	0.996718	−	0.0809543i	$-0.0257968\pi$
$60$	5.15334	+	1.55383i	0.665293	+	0.200599i
$61$	−11.7206			−1.50067			−0.750335	−	0.661058i	$-0.770108\pi$
$61$	−11.7206			−1.50067			−0.750335	+	0.661058i	$0.770108\pi$
$62$	−9.55169	+	3.46448i	−1.21307	+	0.439990i
$63$	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	$-0.169156\pi$
$67$	2.90850	+	2.90850i	0.355329	+	0.355329i	−0.506759	+	0.862088i	$0.669156\pi$
$68$	−0.910777	−	0.0817277i	−0.110448	−	0.00991094i
$69$			9.53658i			1.14807i
$70$	1.49859	−	8.23130i	0.179116	−	0.983828i
$71$	−0.972317			−0.115393			−0.0576964	−	0.998334i	$-0.518376\pi$
$71$	−0.972317			−0.115393			−0.0576964	+	0.998334i	$0.518376\pi$
$72$	2.20675	−	3.79287i	0.260068	−	0.446994i
$73$	−10.4999	+	10.4999i	−1.22892	+	1.22892i	−0.264550	+	0.964372i	$0.585223\pi$
$73$	−10.4999	+	10.4999i	−1.22892	+	1.22892i	−0.964372	+	0.264550i	$0.914777\pi$
$74$	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
$78$	−4.65278	+	1.68761i	−0.526824	+	0.191084i
$79$			5.80828i			0.653483i	0.945114	+	0.326741i	$0.105951\pi$
$79$			5.80828i			0.653483i	−0.945114	+	0.326741i	$0.894049\pi$
$80$	3.33708	−	8.29843i	0.373097	−	0.927792i
$81$	1.93874			0.215416
$82$	−1.87425	+	0.679808i	−0.206976	+	0.0750722i
$83$	9.17675	+	9.17675i	1.00728	+	1.00728i	0.999973	+	0.00730635i	$0.00232570\pi$
$83$	9.17675	+	9.17675i	1.00728	+	1.00728i	0.00730635	+	0.999973i	$0.497674\pi$
$84$	5.83017	+	2.56298i	0.636124	+	0.279644i
$85$	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
$88$	3.57272	−	6.14064i	0.380853	−	0.654595i
$89$	−10.0566			−1.06600			−0.533000	−	0.846115i	$-0.678935\pi$
$89$	−10.0566			−1.06600			−0.533000	+	0.846115i	$0.678935\pi$
$90$	−4.85487	+	0.706927i	−0.511748	+	0.0745166i
$91$	3.42038	+	6.89121i	0.358554	+	0.722395i
$92$	15.7838	+	1.41635i	1.64558	+	0.147664i
$93$	−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	0.764568	−	0.644543i	$-0.222952\pi$
$97$	1.18210	+	1.18210i	0.120025	+	0.120025i	−0.644543	+	0.764568i	$0.722952\pi$
$98$	2.93887	−	9.45320i	0.296871	−	0.954918i
$99$	−3.89684			−0.391648
$100$	−9.58475	+	2.85177i	−0.958475	+	0.285177i
$101$	−0.133613			−0.0132949			−0.00664747	−	0.999978i	$-0.502116\pi$
$101$	−0.133613			−0.0132949			−0.00664747	+	0.999978i	$0.502116\pi$
$102$	−0.731592	+	0.265355i	−0.0724384	+	0.0262741i
$103$	−13.2794	+	13.2794i	−1.30846	+	1.30846i	−0.385932	+	0.922527i	$0.626120\pi$
$103$	−13.2794	+	13.2794i	−1.30846	+	1.30846i	−0.922527	+	0.385932i	$0.873880\pi$
$104$	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	$-0.459171\pi$
$107$	−8.93593	−	8.93593i	−0.863869	−	0.863869i	−0.991785	+	0.127916i	$0.959171\pi$
$108$	0.979182	−	10.9120i	0.0942218	−	1.05001i
$109$	−17.1604			−1.64367			−0.821836	−	0.569724i	$-0.807050\pi$
$109$	−17.1604			−1.64367			−0.821836	+	0.569724i	$0.807050\pi$
$110$	−7.86001	+	1.14451i	−0.749423	+	0.109125i
$111$		−	7.73559i		−	0.734230i
$112$	5.10783	−	9.26877i	0.482645	−	0.875816i
$113$	3.28379	+	3.28379i	0.308913	+	0.308913i	0.844488	−	0.535575i	$-0.179905\pi$
$113$	3.28379	+	3.28379i	0.308913	+	0.308913i	−0.535575	+	0.844488i	$0.679905\pi$
$114$	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
$118$	−1.65338	+	0.599696i	−0.152206	+	0.0552065i
$119$	0.537813	+	1.08356i	0.0493012	+	0.0993295i
$120$	−0.419218	−	7.60045i	−0.0382692	−	0.693823i
$121$	4.69103			0.426457
$122$	5.65178	+	15.5821i	0.511688	+	1.41074i
$123$	−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
$126$	−5.80337	+	0.135063i	−0.517005	+	0.0120323i
$127$	−2.75474	+	2.75474i	−0.244444	+	0.244444i	−0.818686	−	0.574242i	$-0.805297\pi$
$127$	−2.75474	+	2.75474i	−0.244444	+	0.244444i	0.574242	+	0.818686i	$0.305297\pi$
$128$	7.33967	−	8.60983i	0.648741	−	0.761009i
$129$	6.99239			0.615646
$130$	5.49733	−	7.37112i	0.482147	−	0.646490i
$131$	−4.14619			−0.362254			−0.181127	−	0.983460i	$-0.557975\pi$
$131$	−4.14619			−0.362254			−0.181127	+	0.983460i	$0.557975\pi$
$132$	0.540374	−	6.02194i	0.0470335	−	0.524143i
$133$	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	−0.970329	−	0.241787i	$-0.922266\pi$
$137$	−8.52736	+	8.52736i	−0.728542	+	0.728542i	0.241787	+	0.970329i	$0.422266\pi$
$138$	12.6785	−	4.59862i	1.07927	−	0.391461i
$139$			5.99846i			0.508783i	0.967101	+	0.254391i	$0.0818751\pi$
$139$			5.99846i			0.508783i	−0.967101	+	0.254391i	$0.918125\pi$
$140$	−11.6658	+	1.97689i	−0.985944	+	0.167077i
$141$		−	9.95508i		−	0.838369i
$142$	0.468860	+	1.29266i	0.0393458	+	0.108478i
$143$	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
$148$	−12.8030	−	1.14887i	−1.05240	−	0.0944365i
$149$	5.59017			0.457965			0.228982	−	0.973431i	$-0.426460\pi$
$149$	5.59017			0.457965			0.228982	+	0.973431i	$0.426460\pi$
$150$	−6.36084	+	5.65402i	−0.519360	+	0.461649i
$151$	7.05684			0.574278			0.287139	−	0.957889i	$-0.407296\pi$
$151$	7.05684			0.574278			0.287139	+	0.957889i	$0.407296\pi$
$152$	0.589226	−	1.01274i	0.0477925	−	0.0821439i
$153$	0.501582	−	0.501582i	0.0405505	−	0.0405505i
$154$	−9.39563	+	0.218666i	−0.757121	+	0.0176206i
$155$	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	0.0164774	−	0.999864i	$-0.494755\pi$
$157$	12.7347	−	12.7347i	1.01634	−	1.01634i	0.999864	−	0.0164774i	$-0.00524516\pi$
$158$	7.72190	−	2.80081i	0.614322	−	0.222820i
$159$	−12.9311			−1.02550
$160$	−12.6416	−	0.434958i	−0.999409	−	0.0343864i
$161$	−9.32033	−	18.7781i	−0.734545	−	1.47992i
$162$	−0.934878	−	2.57749i	−0.0734510	−	0.202506i
$163$	−3.78159	+	3.78159i	−0.296197	+	0.296197i	−0.839522	−	0.543325i	$-0.817165\pi$
$163$	−3.78159	+	3.78159i	−0.296197	+	0.296197i	0.543325	+	0.839522i	$0.317165\pi$
$164$	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	0.875124	−	0.483899i	$-0.160780\pi$
$167$	5.05575	+	5.05575i	0.391225	+	0.391225i	−0.483899	+	0.875124i	$0.660780\pi$
$168$	0.596033	−	8.98690i	0.0459850	−	0.693354i
$169$		−	4.54459i		−	0.349584i
$170$	0.864386	−	1.15902i	0.0662954	−	0.0888926i
$171$	−0.642682			−0.0491471
$172$	1.03849	−	11.5730i	0.0791842	−	0.882432i
$173$	−15.9087	−	15.9087i	−1.20951	−	1.20951i	−0.971184	−	0.238329i	$-0.923400\pi$
$173$	−15.9087	−	15.9087i	−1.20951	−	1.20951i	−0.238329	−	0.971184i	$-0.576600\pi$
$174$	−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
$178$	4.84939	+	13.3699i	0.363477	+	1.00212i
$179$	−1.92015			−0.143519			−0.0717593	−	0.997422i	$-0.522861\pi$
$179$	−1.92015			−0.143519			−0.0717593	+	0.997422i	$0.522861\pi$
$180$	3.28090	+	6.11349i	0.244544	+	0.455673i
$181$	−8.92242			−0.663199			−0.331599	−	0.943420i	$-0.607588\pi$
$181$	−8.92242			−0.663199			−0.331599	+	0.943420i	$0.607588\pi$
$182$	7.51228	−	7.87028i	0.556847	−	0.583384i
$183$	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
$188$	−16.4765	−	1.47850i	−1.20167	−	0.107831i
$189$	−12.9821	+	6.44355i	−0.944311	+	0.468699i
$190$	−1.29630	+	0.188757i	−0.0940437	+	0.0136939i
$191$	25.8617			1.87129			0.935643	−	0.352947i	$-0.114820\pi$
$191$	25.8617			1.87129			0.935643	+	0.352947i	$0.114820\pi$
$192$	2.55415	−	9.28356i	0.184330	−	0.669983i
$193$	−3.91271	−	3.91271i	−0.281643	−	0.281643i	0.552121	−	0.833764i	$-0.313819\pi$
$193$	−3.91271	−	3.91271i	−0.281643	−	0.281643i	−0.833764	+	0.552121i	$0.813819\pi$
$194$	1.00154	−	2.14159i	0.0719067	−	0.153757i
$195$	1.58045	−	7.66441i	0.113179	−	0.548860i
$196$	−13.9848	+	0.651295i	−0.998917	+	0.0465211i
$197$	11.3964	+	11.3964i	0.811963	+	0.811963i	0.984928	−	0.172965i	$-0.0553348\pi$
$197$	11.3964	+	11.3964i	0.811963	+	0.811963i	−0.172965	+	0.984928i	$0.555335\pi$
$198$	1.87909	+	5.18071i	0.133541	+	0.368177i
$199$	−2.32255			−0.164641			−0.0823205	−	0.996606i	$-0.526233\pi$
$199$	−2.32255			−0.164641			−0.0823205	+	0.996606i	$0.526233\pi$
$200$	8.41318	+	11.3674i	0.594901	+	0.803799i
$201$		−	4.95054i		−	0.349184i
$202$	0.0644292	+	0.177633i	0.00453322	+	0.0124982i
$203$	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
$208$	9.55741	−	6.62890i	0.662687	−	0.459632i
$209$	−1.04050			−0.0719728
$210$	−8.28060	+	5.72986i	−0.571415	+	0.395398i
$211$		−	6.55987i		−	0.451600i	−0.974174	−	0.225800i	$-0.927500\pi$
$211$		−	6.55987i		−	0.451600i	0.974174	−	0.225800i	$-0.0724996\pi$
$212$	−1.92049	+	21.4020i	−0.131899	+	1.46989i
$213$	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
$218$	8.27492	+	22.8142i	0.560448	+	1.54517i
$219$	17.8719			1.20767
$220$	5.31175	+	9.89771i	0.358118	+	0.667304i
$221$			1.32951i			0.0894323i
$222$	−10.2842	+	3.73017i	−0.690230	+	0.250353i
$223$	12.6328	−	12.6328i	0.845955	−	0.845955i	−0.143670	−	0.989626i	$-0.545890\pi$
$223$	12.6328	−	12.6328i	0.845955	−	0.845955i	0.989626	+	0.143670i	$0.0458905\pi$
$224$	−14.7855	−	2.32119i	−0.987900	−	0.155091i
$225$	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	$-0.997927\pi$
$227$	−14.9681	+	14.9681i	−0.993467	+	0.993467i	0.00651216	+	0.999979i	$0.497927\pi$
$228$	0.0891205	−	0.993162i	0.00590215	−	0.0657737i
$229$			6.01142i			0.397246i	0.980076	+	0.198623i	$0.0636469\pi$
$229$			6.01142i			0.397246i	−0.980076	+	0.198623i	$0.936353\pi$
$230$	−14.9799	+	20.0858i	−0.987743	+	1.32442i
$231$	−7.16435	+	3.55595i	−0.471379	+	0.233964i
$232$	6.06490	+	3.52865i	0.398180	+	0.231667i
$233$	−12.6385	−	12.6385i	−0.827974	−	0.827974i	0.159262	−	0.987236i	$-0.449089\pi$
$233$	−12.6385	−	12.6385i	−0.827974	−	0.827974i	−0.987236	+	0.159262i	$0.949089\pi$
$234$	−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
$238$	1.18121	−	1.23750i	0.0765666	−	0.0802154i
$239$			1.33783i			0.0865372i	0.999063	+	0.0432686i	$0.0137771\pi$
$239$			1.33783i			0.0865372i	−0.999063	+	0.0432686i	$0.986223\pi$
$240$	−9.90237	+	4.22234i	−0.639195	+	0.272551i
$241$			27.6357i			1.78017i	0.455795	+	0.890085i	$0.349355\pi$
$241$			27.6357i			1.78017i	−0.455795	+	0.890085i	$0.650645\pi$
$242$	−2.26206	−	6.23655i	−0.145410	−	0.400901i
$243$	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
$248$	10.2193	−	17.5646i	0.648928	−	1.11535i
$249$		−	15.6197i		−	0.989859i
$250$	4.09714	−	15.2713i	0.259126	−	0.965844i
$251$	5.69321			0.359352			0.179676	−	0.983726i	$-0.442495\pi$
$251$	5.69321			0.359352			0.179676	+	0.983726i	$0.442495\pi$
$252$	2.97800	+	7.65024i	0.187596	+	0.481920i
$253$	−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	−0.916478	−	0.400085i	$-0.868980\pi$
$257$	−21.1061	−	21.1061i	−1.31656	−	1.31656i	−0.400085	−	0.916478i	$-0.631020\pi$
$258$	−3.37179	−	9.29614i	−0.209919	−	0.578752i
$259$	7.56018	+	15.2319i	0.469767	+	0.946462i
$260$	−12.4505	−	3.75408i	−0.772147	−	0.232818i
$261$		−	3.84878i		−	0.238233i
$262$	1.99933	+	5.51221i	0.123519	+	0.340545i
$263$	5.43843	+	5.43843i	0.335348	+	0.335348i	0.854613	−	0.519265i	$-0.173794\pi$
$263$	5.43843	+	5.43843i	0.335348	+	0.335348i	−0.519265	+	0.854613i	$0.673794\pi$
$264$	−8.26653	+	2.18543i	−0.508770	+	0.134504i
$265$	20.0685	−	13.2069i	1.23280	−	0.811292i
$266$	−1.54956	+	0.0360632i	−0.0950097	+	0.00221118i
$267$	8.55867	+	8.55867i	0.523782	+	0.523782i
$268$	−8.19355	−	0.735241i	−0.500501	−	0.0449120i
$269$			7.06975i			0.431050i	0.976498	+	0.215525i	$0.0691463\pi$
$269$			7.06975i			0.431050i	−0.976498	+	0.215525i	$0.930854\pi$
$270$	13.8862	+	10.3562i	0.845088	+	0.630260i
$271$			19.4793i			1.18328i	0.806201	+	0.591642i	$0.201520\pi$
$271$			19.4793i			1.18328i	−0.806201	+	0.591642i	$0.798480\pi$
$272$	1.50278	−	1.04231i	0.0911197	−	0.0631995i
$273$	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	$-0.0216125\pi$
$277$	15.4758	+	15.4758i	0.929850	+	0.929850i	−0.0678454	+	0.997696i	$0.521612\pi$
$278$	7.97474	−	2.89251i	0.478293	−	0.173481i
$279$	−11.1465			−0.667321
$280$	8.25357	+	14.5560i	0.493245	+	0.869890i
$281$	−20.4129			−1.21773			−0.608865	−	0.793274i	$-0.708375\pi$
$281$	−20.4129			−1.21773			−0.608865	+	0.793274i	$0.708375\pi$
$282$	−13.2349	+	4.80043i	−0.788128	+	0.285861i
$283$	4.96318	+	4.96318i	0.295031	+	0.295031i	0.839064	−	0.544033i	$-0.183103\pi$
$283$	4.96318	+	4.96318i	0.295031	+	0.295031i	−0.544033	+	0.839064i	$0.683103\pi$
$284$	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
$288$	1.47582	+	8.65127i	0.0869633	+	0.509781i
$289$		−	16.7910i		−	0.987703i
$290$	−1.13039	−	7.76307i	−0.0663790	−	0.455863i
$291$		−	2.01205i		−	0.117949i
$292$	2.65428	−	29.5794i	0.155330	−	1.73100i
$293$	8.15190	+	8.15190i	0.476239	+	0.476239i	0.903927	−	0.427688i	$-0.140672\pi$
$293$	8.15190	+	8.15190i	0.476239	+	0.476239i	−0.427688	+	0.903927i	$0.640672\pi$
$294$	−10.5462	+	5.54401i	−0.615070	+	0.323333i
$295$	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
$298$	−2.69563	−	7.43193i	−0.156154	−	0.430520i
$299$		−	23.0404i		−	1.33246i
$300$	10.5841	+	5.73009i	0.611072	+	0.330827i
$301$	−13.7685	+	6.83384i	−0.793601	+	0.393896i
$302$	−3.40287	−	9.38182i	−0.195813	−	0.539863i
$303$	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	$-0.893784\pi$
$307$	−10.8162	+	10.8162i	−0.617313	+	0.617313i	0.327529	+	0.944841i	$0.393784\pi$
$308$	4.82136	+	12.3857i	0.274723	+	0.705741i
$309$	22.6028			1.28583
$310$	−22.4826	+	3.27374i	−1.27693	+	0.185936i
$311$		−	24.5558i		−	1.39243i	−0.717833	−	0.696215i	$-0.754866\pi$
$311$		−	24.5558i		−	1.39243i	0.717833	−	0.696215i	$-0.245134\pi$
$312$	4.97800	−	8.55600i	0.281824	−	0.484388i
$313$	15.0111	−	15.0111i	0.848478	−	0.848478i	−0.141465	−	0.989943i	$-0.545181\pi$
$313$	15.0111	−	15.0111i	0.848478	−	0.848478i	0.989943	+	0.141465i	$0.0451813\pi$
$314$	−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	−0.999685	−	0.0251044i	$-0.992008\pi$
$317$	−18.2459	−	18.2459i	−1.02479	−	1.02479i	−0.0251044	−	0.999685i	$-0.507992\pi$
$318$	6.23547	+	17.1914i	0.349668	+	0.964044i
$319$		−	6.23115i		−	0.348878i
$320$	5.51764	+	17.0163i	0.308446	+	0.951242i
$321$			15.2098i			0.848929i
$322$	−20.4705	+	21.4460i	−1.14078	+	1.19514i
$323$	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
$328$	2.00526	−	3.44656i	0.110722	−	0.190304i
$329$	9.72934	+	19.6022i	0.536396	+	1.08070i
$330$	7.66328	+	5.71521i	0.421850	+	0.314612i
$331$			25.0233i			1.37541i	0.725991	+	0.687704i	$0.241381\pi$
$331$			25.0233i			1.37541i	−0.725991	+	0.687704i	$0.758619\pi$
$332$	−25.8519	−	2.31980i	−1.41881	−	0.127315i
$333$	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
$336$	−12.2352	+	3.54116i	−0.667483	+	0.193186i
$337$	12.7250	−	12.7250i	0.693173	−	0.693173i	−0.269756	−	0.962929i	$-0.586943\pi$
$337$	12.7250	−	12.7250i	0.693173	−	0.693173i	0.962929	+	0.269756i	$0.0869430\pi$
$338$	−6.04188	+	2.19144i	−0.328635	+	0.119199i
$339$		−	5.58932i		−	0.303570i
$340$	−1.95769	−	0.590282i	−0.106170	−	0.0320125i
$341$	−18.0461			−0.977250
$342$	0.309907	+	0.854423i	0.0167579	+	0.0462019i
$343$	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	$-0.353400\pi$
$347$	−8.40787	−	8.40787i	−0.451358	−	0.451358i	−0.895805	+	0.444447i	$0.853400\pi$
$348$	5.94767	+	0.533709i	0.318828	+	0.0286098i
$349$		−	26.6448i		−	1.42626i	−0.701030	−	0.713132i	$-0.747276\pi$
$349$		−	26.6448i		−	1.42626i	0.701030	−	0.713132i	$-0.252724\pi$
$350$	6.99907	−	17.3497i	0.374116	−	0.927382i
$351$	−15.9289			−0.850219
$352$	2.38934	+	14.0064i	0.127352	+	0.746542i
$353$	−2.82560	+	2.82560i	−0.150391	+	0.150391i	−0.778293	−	0.627902i	$-0.783914\pi$
$353$	−2.82560	+	2.82560i	−0.150391	+	0.150391i	0.627902	+	0.778293i	$0.283914\pi$
$354$	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
$358$	0.925913	+	2.55277i	0.0489360	+	0.134918i
$359$		−	24.9399i		−	1.31628i	−0.752896	−	0.658140i	$-0.771344\pi$
$359$		−	24.9399i		−	1.31628i	0.752896	−	0.658140i	$-0.228656\pi$
$360$	6.54559	−	7.30981i	0.344983	−	0.385261i
$361$	18.8284			0.990968
$362$	4.30247	+	11.8620i	0.226133	+	0.623455i
$363$	−3.99229	−	3.99229i	−0.209541	−	0.209541i
$364$	−14.0857	−	6.19219i	−0.738294	−	0.324559i
$365$	−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	0.105950	−	0.994371i	$-0.466212\pi$
$367$	−17.0197	−	17.0197i	−0.888422	−	0.888422i	−0.994371	+	0.105950i	$0.966212\pi$
$368$	−26.0433	+	18.0633i	−1.35760	+	0.941617i
$369$	−2.18718			−0.113860
$370$	12.1509	−	16.2926i	0.631696	−	0.847013i
$371$	25.4621	−	12.6378i	1.32192	−	0.656123i
$372$	1.54568	−	17.2251i	0.0801395	−	0.893078i
$373$	14.7233	−	14.7233i	0.762342	−	0.762342i	−0.214403	−	0.976745i	$-0.568781\pi$
$373$	14.7233	−	14.7233i	0.762342	−	0.762342i	0.976745	+	0.214403i	$0.0687805\pi$
$374$	−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
$378$	14.8266	+	14.1521i	0.762596	+	0.727907i
$379$	−11.4933			−0.590371			−0.295185	−	0.955440i	$-0.595381\pi$
$379$	−11.4933			−0.590371			−0.295185	+	0.955440i	$0.595381\pi$
$380$	0.876034	+	1.63237i	0.0449396	+	0.0837387i
$381$	4.68883			0.240216
$382$	−12.4707	−	34.3822i	−0.638058	−	1.75915i
$383$	−6.48827	+	6.48827i	−0.331535	+	0.331535i	−0.853169	−	0.521634i	$-0.825323\pi$
$383$	−6.48827	+	6.48827i	−0.331535	+	0.331535i	0.521634	+	0.853169i	$0.325323\pi$
$384$	−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
$388$	−3.33012	−	0.298825i	−0.169061	−	0.0151705i
$389$	6.70580			0.339998			0.169999	−	0.985444i	$-0.445624\pi$
$389$	6.70580			0.339998			0.169999	+	0.985444i	$0.445624\pi$
$390$	−10.9517	+	1.59469i	−0.554559	+	0.0807504i
$391$		−	3.62282i		−	0.183214i
$392$	7.60949	+	18.2783i	0.384337	+	0.923193i
$393$	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	$-0.688678\pi$
$397$	5.39493	−	5.39493i	0.270764	−	0.270764i	0.829408	+	0.558644i	$0.188678\pi$
$398$	1.11995	+	3.08774i	0.0561381	+	0.154774i
$399$	−1.18157	+	0.586461i	−0.0591525	+	0.0293598i
$400$	11.0557	−	16.6665i	0.552784	−	0.833325i
$401$	−5.72101			−0.285693			−0.142847	−	0.989745i	$-0.545626\pi$
$401$	−5.72101			−0.285693			−0.142847	+	0.989745i	$0.545626\pi$
$402$	−6.58156	+	2.38719i	−0.328259	+	0.119062i
$403$	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
$406$	−0.215969	−	9.27974i	−0.0107183	−	0.460546i
$407$	11.4153	−	11.4153i	0.565837	−	0.565837i
$408$	0.782729	−	1.34532i	0.0387509	−	0.0666035i
$409$	−21.0532			−1.04102			−0.520508	−	0.853857i	$-0.674257\pi$
$409$	−21.0532			−1.04102			−0.520508	+	0.853857i	$0.674257\pi$
$410$	−4.41159	+	0.642380i	−0.217873	+	0.0317249i
$411$	14.5144			0.715942
$412$	3.35691	−	37.4095i	0.165383	−	1.84304i
$413$	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
$418$	0.501738	+	1.38331i	0.0245408	+	0.0676597i
$419$		−	35.9170i		−	1.75466i	−0.479887	−	0.877330i	$-0.659322\pi$
$419$		−	35.9170i		−	1.75466i	0.479887	−	0.877330i	$-0.340678\pi$
$420$	11.6106	+	8.24577i	0.566540	+	0.402352i
$421$		−	18.7985i		−	0.916182i	−0.888905	−	0.458091i	$-0.848533\pi$
$421$		−	18.7985i		−	0.916182i	0.888905	−	0.458091i	$-0.151467\pi$
$422$	−8.72111	+	3.16323i	−0.424537	+	0.153984i
$423$	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
$428$	25.1735	+	2.25892i	1.21681	+	0.109189i
$429$	−8.79054			−0.424411
$430$	14.7273	+	10.9835i	0.710214	+	0.529672i
$431$	6.87702			0.331255			0.165627	−	0.986188i	$-0.447035\pi$
$431$	6.87702			0.331255			0.165627	+	0.986188i	$0.447035\pi$
$432$	12.4880	+	18.0049i	0.600828	+	0.866261i
$433$	−2.77952	+	2.77952i	−0.133575	+	0.133575i	−0.770733	−	0.637158i	$-0.780110\pi$
$433$	−2.77952	+	2.77952i	−0.133575	+	0.133575i	0.637158	+	0.770733i	$0.280110\pi$
$434$	−26.8751	+	0.625468i	−1.29005	+	0.0300234i
$435$	−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
$438$	−8.61797	−	23.7600i	−0.411782	−	1.13530i
$439$	24.3654			1.16290			0.581448	−	0.813583i	$-0.302486\pi$
$439$	24.3654			1.16290			0.581448	+	0.813583i	$0.302486\pi$
$440$	10.5973	−	11.8345i	0.505205	−	0.564190i
$441$	6.56687	−	8.64967i	0.312708	−	0.411889i
$442$	1.76753	−	0.641100i	0.0840729	−	0.0304940i
$443$	−8.80104	+	8.80104i	−0.418150	+	0.418150i	−0.884566	−	0.466416i	$-0.845545\pi$
$443$	−8.80104	+	8.80104i	−0.418150	+	0.418150i	0.466416	+	0.884566i	$0.345545\pi$
$444$	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
$448$	4.04377	+	20.7761i	0.191050	+	0.981580i
$449$			20.2530i			0.955799i	0.878415	+	0.477900i	$0.158602\pi$
$449$			20.2530i			0.955799i	−0.878415	+	0.477900i	$0.841398\pi$
$450$	−10.9514	−	0.644252i	−0.516253	−	0.0303703i
$451$	−3.54104			−0.166741
$452$	−9.25079	−	0.830111i	−0.435120	−	0.0390451i
$453$	−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	−0.637934	−	0.770091i	$-0.720211\pi$
$457$	2.82521	−	2.82521i	0.132158	−	0.132158i	0.770091	+	0.637934i	$0.220211\pi$
$458$	7.99196	−	2.89876i	0.373440	−	0.135450i
$459$	−2.50461			−0.116905
$460$	33.9268	+	10.2296i	1.58185	+	0.476958i
$461$	4.24667			0.197787			0.0988936	−	0.995098i	$-0.468470\pi$
$461$	4.24667			0.197787			0.0988936	+	0.995098i	$0.468470\pi$
$462$	8.18222	+	7.81003i	0.380671	+	0.363356i
$463$	−7.90420	−	7.90420i	−0.367339	−	0.367339i	0.499167	−	0.866506i	$-0.333639\pi$
$463$	−7.90420	−	7.90420i	−0.367339	−	0.367339i	−0.866506	+	0.499167i	$0.833639\pi$
$464$	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	$-0.806880\pi$
$467$	−5.43216	+	5.43216i	−0.251370	+	0.251370i	0.570162	+	0.821532i	$0.306880\pi$
$468$	−0.806393	+	8.98648i	−0.0372755	+	0.415400i
$469$	4.83828	+	9.74792i	0.223411	+	0.450117i
$470$	15.6372	−	20.9673i	0.721292	−	0.967149i
$471$	−21.6757			−0.998764
$472$	1.76895	−	3.04040i	0.0814224	−	0.139946i
$473$	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
$476$	−2.21481	−	0.973644i	−0.101516	−	0.0446269i
$477$	−11.7865	−	11.7865i	−0.539665	−	0.539665i
$478$	1.77860	−	0.645115i	0.0813513	−	0.0295069i
$479$	9.52909			0.435395			0.217698	−	0.976016i	$-0.430145\pi$
$479$	9.52909			0.435395			0.217698	+	0.976016i	$0.430145\pi$
$480$	10.3885	+	11.1288i	0.474166	+	0.507958i
$481$			18.6892i			0.852156i
$482$	36.7406	−	13.3262i	1.67349	−	0.606990i
$483$	−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	−0.998805	−	0.0488768i	$-0.984436\pi$
$487$	−20.9631	+	20.9631i	−0.949928	+	0.949928i	0.0488768	+	0.998805i	$0.484436\pi$
$488$	−28.6539	−	16.6713i	−1.29710	−	0.754674i
$489$	6.43663			0.291074
$490$	10.7051	−	19.3753i	0.483606	−	0.875286i
$491$			14.3399i			0.647149i	0.946203	+	0.323575i	$0.104885\pi$
$491$			14.3399i			0.647149i	−0.946203	+	0.323575i	$0.895115\pi$
$492$	0.303296	−	3.37994i	0.0136736	−	0.152379i
$493$	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
$498$	−20.7658	+	7.53196i	−0.930540	+	0.337515i
$499$	−18.4667			−0.826681			−0.413340	−	0.910577i	$-0.635638\pi$
$499$	−18.4667			−0.826681			−0.413340	+	0.910577i	$0.635638\pi$
$500$	−22.2784	+	1.91697i	−0.996318	+	0.0857295i
$501$		−	8.60536i		−	0.384459i
$502$	−2.74532	−	7.56892i	−0.122529	−	0.337817i
$503$	18.4374	−	18.4374i	0.822085	−	0.822085i	−0.164322	−	0.986407i	$-0.552544\pi$
$503$	18.4374	−	18.4374i	0.822085	−	0.822085i	0.986407	+	0.164322i	$0.0525436\pi$
$504$	8.73470	−	7.64815i	0.389075	−	0.340676i
$505$	−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
$508$	0.696373	−	7.76040i	0.0308965	−	0.344312i
$509$		−	2.89831i		−	0.128465i	−0.997935	−	0.0642326i	$-0.979540\pi$
$509$		−	2.89831i		−	0.128465i	0.997935	−	0.0642326i	$-0.0204600\pi$
$510$	−1.72201	+	0.250745i	−0.0762520	+	0.0111032i
$511$	−35.1908	+	17.4666i	−1.55675	+	0.772677i
$512$	−0.226853	+	22.6263i	−0.0100256	+	0.999950i
$513$	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
$518$	16.6046	−	17.3959i	0.729565	−	0.764333i
$519$			27.0781i			1.18860i
$520$	1.01283	+	18.3627i	0.0444157	+	0.805260i
$521$			9.89476i			0.433497i	0.976227	+	0.216749i	$0.0695452\pi$
$521$			9.89476i			0.433497i	−0.976227	+	0.216749i	$0.930455\pi$
$522$	−5.11681	+	1.85592i	−0.223957	+	0.0812312i
$523$	−3.93390	−	3.93390i	−0.172018	−	0.172018i	0.615848	−	0.787865i	$-0.288814\pi$
$523$	−3.93390	−	3.93390i	−0.172018	−	0.172018i	−0.787865	+	0.615848i	$0.788814\pi$
$524$	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
$528$	6.89164	+	9.93622i	0.299920	+	0.432419i
$529$			39.7838i			1.72973i
$530$	−27.2353	−	20.3118i	−1.18302	−	0.882290i
$531$	−1.92943			−0.0837303
$532$	0.795157	+	2.04270i	0.0344744	+	0.0885621i
$533$	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
$538$	9.39898	−	3.40910i	0.405219	−	0.146977i
$539$	10.6317	−	14.0038i	0.457941	−	0.603186i
$540$	7.07218	−	23.4551i	0.304338	−	1.00935i
$541$			14.7951i			0.636092i	0.948075	+	0.318046i	$0.103027\pi$
$541$			14.7951i			0.636092i	−0.948075	+	0.318046i	$0.896973\pi$
$542$	25.8971	−	9.39310i	1.11237	−	0.403468i
$543$	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
$546$	−13.0913	+	0.304676i	−0.560256	+	0.0130389i
$547$	22.6498	+	22.6498i	0.968434	+	0.968434i	0.999517	−	0.0310824i	$-0.00989542\pi$
$547$	22.6498	+	22.6498i	0.968434	+	0.968434i	−0.0310824	+	0.999517i	$0.509895\pi$
$548$	2.15564	−	24.0225i	0.0920843	−	1.02619i
$549$			18.1838i			0.776064i
$550$	−17.7302	−	1.04304i	−0.756019	−	0.0444754i
$551$		−	1.02767i		−	0.0437800i
$552$	−13.5647	+	23.3145i	−0.577354	+	0.992333i
$553$	−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	$-0.123032\pi$
$557$	12.9631	+	12.9631i	0.549263	+	0.549263i	−0.376965	+	0.926228i	$0.623032\pi$
$558$	5.37492	+	14.8188i	0.227539	+	0.627331i
$559$	−16.8937			−0.714526
$560$	15.3718	−	17.9919i	0.649577	−	0.760296i
$561$	−1.38220			−0.0583566
$562$	9.84327	+	27.1382i	0.415213	+	1.14476i
$563$	−16.6820	−	16.6820i	−0.703064	−	0.703064i	0.262003	−	0.965067i	$-0.415617\pi$
$563$	−16.6820	−	16.6820i	−0.703064	−	0.703064i	−0.965067	+	0.262003i	$0.915617\pi$
$564$	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
$568$	−2.37707	−	1.38302i	−0.0997397	−	0.0580300i
$569$			21.6112i			0.905989i	0.891513	+	0.452994i	$0.149644\pi$
$569$			21.6112i			0.905989i	−0.891513	+	0.452994i	$0.850356\pi$
$570$	1.26386	+	0.942574i	0.0529371	+	0.0394801i
$571$		−	22.2231i		−	0.930008i	−0.885309	−	0.465004i	$-0.846053\pi$
$571$		−	22.2231i		−	0.930008i	0.885309	−	0.465004i	$-0.153947\pi$
$572$	−1.30555	+	14.5491i	−0.0545877	+	0.608327i
$573$	−22.0095	−	22.0095i	−0.919462	−	0.919462i
$574$	−5.27348	+	0.122731i	−0.220111	+	0.00512267i
$575$	−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	0.346900	−	0.937902i	$-0.387234\pi$
$577$	−14.1964	−	14.1964i	−0.591003	−	0.591003i	−0.937902	+	0.346900i	$0.887234\pi$
$578$	−22.3230	+	8.09675i	−0.928513	+	0.336780i
$579$			6.65981i			0.276772i
$580$	−9.77563	+	5.24624i	−0.405911	+	0.217838i
$581$	15.2655	+	30.7562i	0.633321	+	1.27598i
$582$	−2.67495	+	0.970231i	−0.110880	+	0.0402174i
$583$	−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	$-0.703567\pi$
$587$	4.98042	−	4.98042i	0.205564	−	0.205564i	0.802379	+	0.596815i	$0.203567\pi$
$588$	12.4561	+	11.3475i	0.513679	+	0.467962i
$589$	−2.97623			−0.122633
$590$	−3.89171	+	0.566678i	−0.160219	+	0.0233298i
$591$		−	19.3978i		−	0.797920i
$592$	21.1250	−	14.6521i	0.868234	−	0.602196i
$593$	21.3875	−	21.3875i	0.878280	−	0.878280i	−0.115077	−	0.993357i	$-0.536711\pi$
$593$	21.3875	−	21.3875i	0.878280	−	0.878280i	0.993357	+	0.115077i	$0.0367114\pi$
$594$	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
$598$	−30.6314	+	11.1103i	−1.25261	+	0.454334i
$599$		−	16.9265i		−	0.691599i	−0.938308	−	0.345799i	$-0.887608\pi$
$599$		−	16.9265i		−	0.691599i	0.938308	−	0.345799i	$-0.112392\pi$
$600$	2.51421	−	16.8342i	0.102642	−	0.687255i
$601$		−	2.76188i		−	0.112659i	−0.998412	−	0.0563297i	$-0.982060\pi$
$601$		−	2.76188i		−	0.112659i	0.998412	−	0.0563297i	$-0.0179398\pi$
$602$	15.7246	+	15.0093i	0.640887	+	0.611735i
$603$	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	0.810213	−	0.586136i	$-0.199352\pi$
$607$	5.52065	+	5.52065i	0.224076	+	0.224076i	−0.586136	+	0.810213i	$0.699352\pi$
$608$	0.394059	+	2.30998i	0.0159812	+	0.0936821i
$609$	−3.51209	−	7.07598i	−0.142317	−	0.286733i
$610$	5.34061	+	36.6770i	0.216235	+	1.48501i
$611$			24.0516i			0.973022i
$612$	−0.126795	+	1.41301i	−0.00512540	+	0.0571176i
$613$	16.4031	−	16.4031i	0.662513	−	0.662513i	−0.293459	−	0.955972i	$-0.594806\pi$
$613$	16.4031	−	16.4031i	0.662513	−	0.662513i	0.955972	+	0.293459i	$0.0948063\pi$
$614$	19.5954	+	9.16407i	0.790806	+	0.369832i
$615$	−3.16934	+	2.08572i	−0.127800	+	0.0841042i
$616$	14.1414	−	12.3823i	0.569775	−	0.498898i
$617$	−24.2013	+	24.2013i	−0.974306	+	0.974306i	−0.999678	−	0.0253716i	$-0.991923\pi$
$617$	−24.2013	+	24.2013i	−0.974306	+	0.974306i	0.0253716	+	0.999678i	$0.491923\pi$
$618$	−10.8993	−	30.0496i	−0.438433	−	1.20877i
$619$			18.2586i			0.733873i	0.930246	+	0.366937i	$0.119593\pi$
$619$			18.2586i			0.733873i	−0.930246	+	0.366937i	$0.880407\pi$
$620$	15.1936	+	28.3112i	0.610192	+	1.13701i
$621$	43.4051			1.74179
$622$	−32.6460	+	11.8410i	−1.30899	+	0.474781i
$623$	−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
$628$	−3.21922	+	35.8751i	−0.128461	+	1.43157i
$629$			2.93865i			0.117172i
$630$	−12.7703	−	2.32496i	−0.508782	−	0.0926287i
$631$	17.6351			0.702041			0.351021	−	0.936368i	$-0.385835\pi$
$631$	17.6351			0.702041			0.351021	+	0.936368i	$0.385835\pi$
$632$	−8.26165	+	14.1998i	−0.328631	+	0.564838i
$633$	−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
$638$	−8.28410	+	3.00472i	−0.327970	+	0.118958i
$639$			1.50849i			0.0596748i
$640$	19.9619	−	15.5409i	0.789065	−	0.614309i
$641$	21.4669			0.847892			0.423946	−	0.905688i	$-0.360645\pi$
$641$	21.4669			0.847892			0.423946	+	0.905688i	$0.360645\pi$
$642$	20.2209	−	7.33430i	0.798055	−	0.289462i
$643$	−25.8525	−	25.8525i	−1.01952	−	1.01952i	−0.999806	−	0.0197188i	$-0.993723\pi$
$643$	−25.8525	−	25.8525i	−1.01952	−	1.01952i	−0.0197188	−	0.999806i	$-0.506277\pi$
$644$	38.3828	+	16.8733i	1.51249	+	0.664902i
$645$	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	0.792581	−	0.609766i	$-0.208737\pi$
$647$	4.65011	+	4.65011i	0.182815	+	0.182815i	−0.609766	+	0.792581i	$0.708737\pi$
$648$	4.73974	+	2.75765i	0.186194	+	0.108331i
$649$	−3.12374			−0.122618
$650$	15.3678	−	13.6602i	0.602776	−	0.535796i
$651$	−20.4928	+	10.1714i	−0.803175	+	0.398648i
$652$	0.955951	−	10.6532i	0.0374379	−	0.417210i
$653$	−15.5113	+	15.5113i	−0.607003	+	0.607003i	−0.942162	−	0.335159i	$-0.891210\pi$
$653$	−15.5113	+	15.5113i	−0.607003	+	0.607003i	0.335159	+	0.942162i	$0.391210\pi$
$654$	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
$658$	21.3688	−	22.3872i	0.833043	−	0.872742i
$659$	−16.0797			−0.626376			−0.313188	−	0.949691i	$-0.601397\pi$
$659$	−16.0797			−0.626376			−0.313188	+	0.949691i	$0.601397\pi$
$660$	3.90287	−	12.9440i	0.151919	−	0.503844i
$661$	31.7560			1.23517			0.617583	−	0.786505i	$-0.288112\pi$
$661$	31.7560			1.23517			0.617583	+	0.786505i	$0.288112\pi$
$662$	33.2676	−	12.0665i	1.29298	−	0.468977i
$663$	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
$668$	−14.2426	−	1.27805i	−0.551062	−	0.0494491i
$669$	−21.5022			−0.831325
$670$	7.77621	−	10.4268i	0.300421	−	0.402821i
$671$			29.4394i			1.13650i
$672$	10.6077	+	14.5586i	0.409203	+	0.561612i
$673$	25.3785	+	25.3785i	0.978269	+	0.978269i	0.999769	−	0.0215000i	$-0.00684418\pi$
$673$	25.3785	+	25.3785i	0.978269	+	0.978269i	−0.0215000	+	0.999769i	$0.506844\pi$
$674$	−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	−0.340751	+	0.940154i	$0.610681\pi$
$677$	−33.3281	+	33.3281i	−1.28090	+	1.28090i	−0.940154	+	0.340751i	$0.889319\pi$
$678$	−7.43080	+	2.69522i	−0.285378	+	0.103509i
$679$	1.96643	+	3.96186i	0.0754647	+	0.152042i
$680$	0.159256	+	2.88731i	0.00610717	+	0.110723i
$681$	25.4771			0.976285
$682$	8.70197	+	23.9916i	0.333216	+	0.918686i
$683$	−3.99641	+	3.99641i	−0.152918	+	0.152918i	−0.779420	−	0.626502i	$-0.784486\pi$
$683$	−3.99641	+	3.99641i	−0.152918	+	0.152918i	0.626502	+	0.779420i	$0.284486\pi$
$684$	0.986485	−	0.824020i	0.0377192	−	0.0315072i
$685$	−22.5257	+	14.8240i	−0.860664	+	0.566395i
$686$	15.3479	−	21.2236i	0.585986	−	0.810321i
$687$	5.11600	−	5.11600i	0.195188	−	0.195188i
$688$	13.2444	+	19.0955i	0.504937	+	0.728008i
$689$	31.2415			1.19021
$690$	29.8426	−	4.34543i	1.13609	−	0.165428i
$691$	37.9666			1.44432			0.722158	−	0.691728i	$-0.243150\pi$
$691$	37.9666			1.44432			0.722158	+	0.691728i	$0.243150\pi$
$692$	44.8164	+	4.02156i	1.70367	+	0.152877i
$693$	−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
$698$	−35.4233	+	12.8484i	−1.34079	+	0.486318i
$699$			21.5119i			0.813655i
$700$	−26.4409	−	0.938826i	−0.999370	−	0.0354843i
$701$		−	35.0204i		−	1.32270i	−0.750077	−	0.661350i	$-0.769984\pi$
$701$		−	35.0204i		−	1.32270i	0.750077	−	0.661350i	$-0.230016\pi$
$702$	7.68103	+	21.1768i	0.289902	+	0.799268i
$703$	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
$708$	0.267554	−	2.98163i	0.0100553	−	0.112056i
$709$	36.6280			1.37559			0.687797	−	0.725903i	$-0.258578\pi$
$709$	36.6280			1.37559			0.687797	+	0.725903i	$0.258578\pi$
$710$	0.443046	+	3.04265i	0.0166272	+	0.114189i
$711$	9.01118			0.337945
$712$	−24.5859	−	14.3045i	−0.921397	−	0.536082i
$713$	−40.2543	+	40.2543i	−1.50753	+	1.50753i
$714$	−2.05844	+	0.0479064i	−0.0770353	+	0.00179285i
$715$	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
$718$	−33.1568	+	12.0263i	−1.23740	+	0.448816i
$719$	35.7912			1.33478			0.667392	−	0.744706i	$-0.267410\pi$
$719$	35.7912			1.33478			0.667392	+	0.744706i	$0.267410\pi$
$720$	−12.8745	−	5.17727i	−0.479803	−	0.192945i
$721$	−44.5064	+	22.0903i	−1.65750	+	0.822685i
$722$	−9.07922	−	25.0317i	−0.337894	−	0.931583i
$723$	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	0.290517	−	0.956870i	$-0.406173\pi$
$727$	−17.9668	−	17.9668i	−0.666353	−	0.666353i	−0.956870	+	0.290517i	$0.906173\pi$
$728$	−1.44002	+	21.7124i	−0.0533707	+	0.804716i
$729$		−	22.7870i		−	0.843962i
$730$	37.6415	+	28.0728i	1.39318	+	1.03902i
$731$	−2.65632			−0.0982476
$732$	−28.1001	−	2.52153i	−1.03861	−	0.0931986i
$733$	14.2478	+	14.2478i	0.526254	+	0.526254i	0.919453	−	0.393199i	$-0.128632\pi$
$733$	14.2478	+	14.2478i	0.526254	+	0.526254i	−0.393199	+	0.919453i	$0.628632\pi$
$734$	−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
$738$	1.05468	+	2.90778i	0.0388232	+	0.107037i
$739$	27.1860			1.00005			0.500027	−	0.866010i	$-0.333323\pi$
$739$	27.1860			1.00005			0.500027	+	0.866010i	$0.333323\pi$
$740$	−27.5197	−	8.29775i	−1.01165	−	0.305031i
$741$	−1.44977			−0.0532586
$742$	−29.0796	−	27.7568i	−1.06754	−	1.01898i
$743$	4.15036	+	4.15036i	0.152262	+	0.152262i	0.779127	−	0.626866i	$-0.215662\pi$
$743$	4.15036	+	4.15036i	0.152262	+	0.152262i	−0.626866	+	0.779127i	$0.715662\pi$
$744$	−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
$748$	−0.205281	+	2.28766i	−0.00750582	+	0.0836451i
$749$	−14.8649	−	29.9491i	−0.543152	−	1.09431i
$750$	−16.4835	+	9.50977i	−0.601892	+	0.347248i
$751$	−5.39262			−0.196779			−0.0983897	−	0.995148i	$-0.531369\pi$
$751$	−5.39262			−0.196779			−0.0983897	+	0.995148i	$0.531369\pi$
$752$	27.1862	−	18.8560i	0.991380	−	0.687609i
$753$	−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
$756$	11.6653	−	26.5357i	0.424261	−	0.965093i
$757$	−34.4647	−	34.4647i	−1.25264	−	1.25264i	−0.954532	−	0.298108i	$-0.903644\pi$
$757$	−34.4647	−	34.4647i	−1.25264	−	1.25264i	−0.298108	−	0.954532i	$-0.596356\pi$
$758$	5.54216	+	15.2799i	0.201300	+	0.554991i
$759$	23.9537			0.869463
$760$	1.74774	−	1.95180i	0.0633973	−	0.0707992i
$761$		−	46.5220i		−	1.68642i	−0.537583	−	0.843211i	$-0.680663\pi$
$761$		−	46.5220i		−	1.68642i	0.537583	−	0.843211i	$-0.319337\pi$
$762$	−2.26100	−	6.23363i	−0.0819072	−	0.225821i
$763$	−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
$768$	7.98251	+	17.5246i	0.288044	+	0.632365i
$769$	21.4981			0.775240			0.387620	−	0.921819i	$-0.373297\pi$
$769$	21.4981			0.775240			0.387620	+	0.921819i	$0.373297\pi$
$770$	−20.6751	−	3.76410i	−0.745079	−	0.135649i
$771$			35.9246i			1.29379i
$772$	11.0225	+	0.989097i	0.396710	+	0.0355984i
$773$	−12.2376	−	12.2376i	−0.440157	−	0.440157i	0.451907	−	0.892065i	$-0.350744\pi$
$773$	−12.2376	−	12.2376i	−0.440157	−	0.440157i	−0.892065	+	0.451907i	$0.850744\pi$
$774$	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
$778$	−3.23360	−	8.91512i	−0.115930	−	0.319622i
$779$	−0.584001			−0.0209240
$780$	7.40107	+	13.7909i	0.265001	+	0.493792i
$781$			2.44223i			0.0873899i
$782$	−4.81641	+	1.74696i	−0.172235	+	0.0624711i
$783$	−9.60930	+	9.60930i	−0.343408	+	0.343408i
$784$	20.6310	−	18.9305i	0.736820	−	0.676089i
$785$	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	0.119529	−	0.992831i	$-0.461862\pi$
$787$	31.2056	−	31.2056i	1.11236	−	1.11236i	0.992831	−	0.119529i	$-0.0381384\pi$
$788$	−32.1050	−	2.88091i	−1.14369	−	0.102628i
$789$		−	9.25673i		−	0.329548i
$790$	18.1757	−	2.64660i	0.646663	−	0.0941618i
$791$	5.46258	+	11.0057i	0.194227	+	0.391318i
$792$	−9.52681	−	5.54284i	−0.338520	−	0.196956i
$793$	−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	$-0.866817\pi$
$797$	−14.3254	+	14.3254i	−0.507431	+	0.507431i	0.406306	+	0.913737i	$0.366817\pi$
$798$	1.34944	+	1.28806i	0.0477698	+	0.0455968i
$799$			3.78181i			0.133791i
$800$	−27.4886	−	6.66140i	−0.971870	−	0.235516i
$801$			15.6022i			0.551277i
$802$	2.75872	+	7.60587i	0.0974138	+	0.268573i
$803$	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
$808$	−0.326649	−	0.190049i	−0.0114915	−	0.00668591i
$809$		−	26.5709i		−	0.934183i	−0.884209	−	0.467091i	$-0.845302\pi$
$809$		−	26.5709i		−	0.934183i	0.884209	−	0.467091i	$-0.154698\pi$
$810$	−0.883406	−	6.06686i	−0.0310397	−	0.213168i
$811$	5.10317			0.179197			0.0895983	−	0.995978i	$-0.471442\pi$
$811$	5.10317			0.179197			0.0895983	+	0.995978i	$0.471442\pi$
$812$	−12.2329	+	4.76189i	−0.429292	+	0.167110i
$813$	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
$818$	10.1521	+	27.9895i	0.354959	+	0.978631i
$819$	10.6913	−	5.30650i	0.373583	−	0.185424i
$820$	2.98133	+	5.55529i	0.104113	+	0.193999i
$821$			24.8927i			0.868760i	0.900730	+	0.434380i	$0.143033\pi$
$821$			24.8927i			0.868760i	−0.900730	+	0.434380i	$0.856967\pi$
$822$	−6.99897	−	19.2964i	−0.244117	−	0.673038i
$823$	−8.95105	−	8.95105i	−0.312014	−	0.312014i	0.533675	−	0.845689i	$-0.320810\pi$
$823$	−8.95105	−	8.95105i	−0.312014	−	0.312014i	−0.845689	+	0.533675i	$0.820810\pi$
$824$	−51.3534	+	13.5763i	−1.78898	+	0.472953i
$825$	−14.0444	+	5.58814i	−0.488965	+	0.194554i
$826$	−4.65203	+	0.108267i	−0.161865	+	0.00376710i
$827$	5.03438	+	5.03438i	0.175063	+	0.175063i	0.789200	−	0.614137i	$-0.210496\pi$
$827$	5.03438	+	5.03438i	0.175063	+	0.175063i	−0.614137	+	0.789200i	$0.710496\pi$
$828$	2.19737	−	24.4876i	0.0763639	−	0.851002i
$829$		−	15.1494i		−	0.526161i	−0.964774	−	0.263081i	$-0.915261\pi$
$829$		−	15.1494i		−	0.526161i	0.964774	−	0.263081i	$-0.0847385\pi$
$830$	24.5351	−	32.8981i	0.851627	−	1.14191i
$831$		−	26.3413i		−	0.913769i
$832$	−6.17084	+	22.4291i	−0.213935	+	0.777591i
$833$	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
$838$	−47.7504	+	17.3195i	−1.64951	+	0.598292i
$839$	20.9224			0.722320			0.361160	−	0.932504i	$-0.382381\pi$
$839$	20.9224			0.722320			0.361160	+	0.932504i	$0.382381\pi$
$840$	5.36371	−	19.4121i	0.185066	−	0.669780i
$841$	−22.8457			−0.787783
$842$	−24.9919	+	9.06479i	−0.861278	+	0.312393i
$843$	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
$848$	−24.4929	−	35.3133i	−0.841088	−	1.21266i
$849$		−	8.44781i		−	0.289928i
$850$	2.41640	−	2.14789i	0.0828818	−	0.0736720i
$851$		−	50.9270i		−	1.74576i
$852$	−2.33112	−	0.209181i	−0.0798629	−	0.00716643i
$853$	9.15082	+	9.15082i	0.313318	+	0.313318i	0.846194	−	0.532876i	$-0.178889\pi$
$853$	9.15082	+	9.15082i	0.313318	+	0.313318i	−0.532876	+	0.846194i	$0.678889\pi$
$854$	1.02036	+	43.8426i	0.0349158	+	1.50026i
$855$	−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	0.914260	−	0.405128i	$-0.132773\pi$
$857$	14.9046	+	14.9046i	0.509131	+	0.509131i	−0.405128	+	0.914260i	$0.632773\pi$
$858$	4.23887	+	11.6867i	0.144713	+	0.398977i
$859$			27.4269i			0.935793i	0.883783	+	0.467897i	$0.154988\pi$
$859$			27.4269i			0.935793i	−0.883783	+	0.467897i	$0.845012\pi$
$860$	7.50054	−	24.8758i	0.255766	−	0.848257i
$861$	−4.02113	+	1.99585i	−0.137040	+	0.0680184i
$862$	−3.31616	−	9.14275i	−0.112949	−	0.311403i
$863$	−7.01745	−	7.01745i	−0.238877	−	0.238877i	0.577508	−	0.816385i	$-0.304025\pi$
$863$	−7.01745	−	7.01745i	−0.238877	−	0.238877i	−0.816385	+	0.577508i	$0.804025\pi$
$864$	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
$868$	13.7909	+	35.4279i	0.468095	+	1.20250i
$869$	14.5890			0.494900
$870$	−5.64472	+	7.56876i	−0.191374	+	0.256605i
$871$			11.9605i			0.405267i
$872$	−41.9530	−	24.4089i	−1.42071	−	0.826589i
$873$	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	$-0.463280\pi$
$877$	−26.0087	−	26.0087i	−0.878250	−	0.878250i	−0.993353	+	0.115104i	$0.963280\pi$
$878$	−11.7492	−	32.3929i	−0.396517	−	1.09321i
$879$		−	13.8753i		−	0.468003i
$880$	−20.8437	−	8.38197i	−0.702641	−	0.282556i
$881$		−	0.348598i		−	0.0117446i	−0.999983	−	0.00587228i	$-0.998131\pi$
$881$		−	0.348598i		−	0.0117446i	0.999983	−	0.00587228i	$-0.00186922\pi$
$882$	−14.6660	−	4.55947i	−0.493831	−	0.153525i
$883$	38.4627	−	38.4627i	1.29437	−	1.29437i	0.362319	−	0.932054i	$-0.381985\pi$
$883$	38.4627	−	38.4627i	1.29437	−	1.29437i	0.932054	−	0.362319i	$-0.118015\pi$
$884$	−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	0.475412	−	0.879763i	$-0.342299\pi$
$887$	−12.0426	−	12.0426i	−0.404351	−	0.404351i	−0.879763	+	0.475412i	$0.842299\pi$
$888$	11.0030	−	18.9116i	0.369238	−	0.634631i
$889$	−9.23260	+	4.58251i	−0.309652	+	0.153692i
$890$	4.58240	+	31.4700i	0.153602	+	1.05488i
$891$		−	4.86967i		−	0.163140i
$892$	−3.19346	+	35.5880i	−0.106925	+	1.19157i
$893$	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
$896$	25.6712	−	15.3945i	0.857614	−	0.514294i
$897$	−19.6085	+	19.6085i	−0.654709	+	0.654709i
$898$	26.9257	−	9.76618i	0.898521	−	0.325902i
$899$		−	17.8235i		−	0.594447i
$900$	4.42434	+	14.8701i	0.147478	+	0.495671i
$901$	4.91234			0.163654
$902$	1.70752	+	4.70768i	0.0568542	+	0.156749i
$903$	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	$-0.130599\pi$
$907$	15.6043	+	15.6043i	0.518132	+	0.518132i	−0.398874	+	0.917006i	$0.630599\pi$
$908$	3.78379	−	42.1667i	0.125570	−	1.39935i
$909$			0.207291i			0.00687542i
$910$	20.0060	−	13.8434i	0.663192	−	0.458903i
$911$	27.1278			0.898784			0.449392	−	0.893335i	$-0.351641\pi$
$911$	27.1278			0.898784			0.449392	+	0.893335i	$0.351641\pi$
$912$	1.13660	+	1.63872i	0.0376364	+	0.0542634i
$913$	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
$918$	1.20775	+	3.32979i	0.0398616	+	0.109900i
$919$			16.0238i			0.528576i	0.964444	+	0.264288i	$0.0851370\pi$
$919$			16.0238i			0.528576i	−0.964444	+	0.264288i	$0.914863\pi$
$920$	−2.75991	−	50.0373i	−0.0909915	−	1.64968i
$921$	18.4102			0.606636
$922$	−2.04778	−	5.64580i	−0.0674401	−	0.185934i
$923$	−1.99922	−	1.99922i	−0.0658050	−	0.0658050i
$924$	6.43762	−	14.6440i	0.211782	−	0.481753i
$925$	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
$928$	−13.8336	+	2.35987i	−0.454110	+	0.0774664i
$929$	25.8081			0.846735			0.423367	−	0.905958i	$-0.360848\pi$
$929$	25.8081			0.846735			0.423367	+	0.905958i	$0.360848\pi$
$930$	21.9199	+	16.3477i	0.718782	+	0.536062i
$931$	1.75343	−	2.30956i	0.0574662	−	0.0756927i
$932$	35.6040	+	3.19489i	1.16625	+	0.104652i
$933$	−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	0.695376	−	0.718647i	$-0.255238\pi$
$937$	−0.712338	−	0.712338i	−0.0232711	−	0.0232711i	−0.718647	+	0.695376i	$0.755238\pi$
$938$	10.6264	−	11.1329i	0.346966	−	0.363501i
$939$	−25.5503			−0.833804
$940$	−35.4157	−	10.6785i	−1.15513	−	0.348295i
$941$	−19.4618			−0.634436			−0.317218	−	0.948353i	$-0.602749\pi$
$941$	−19.4618			−0.634436			−0.317218	+	0.948353i	$0.602749\pi$
$942$	10.4522	+	28.8171i	0.340552	+	0.938911i
$943$	−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	$-0.373810\pi$
$947$	−16.5040	−	16.5040i	−0.536309	−	0.536309i	−0.922443	+	0.386134i	$0.873810\pi$
$948$	−1.24958	+	13.9253i	−0.0405843	+	0.452273i
$949$	−43.1785			−1.40163
$950$	−2.92413	−	0.172022i	−0.0948714	−	0.00558114i
$951$			31.0562i			1.00707i
$952$	−0.226425	+	3.41401i	−0.00733849	+	0.110649i
$953$	−15.0426	−	15.0426i	−0.487279	−	0.487279i	0.420168	−	0.907446i	$-0.361971\pi$
$953$	−15.0426	−	15.0426i	−0.487279	−	0.487279i	−0.907446	+	0.420168i	$0.861971\pi$
$954$	−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
$958$	−4.59501	−	12.6686i	−0.148458	−	0.409303i
$959$	−28.5797	+	14.1853i	−0.922888	+	0.458066i
$960$	9.78593	−	19.1775i	0.315840	−	0.618951i
$961$	−20.6187			−0.665118
$962$	24.8467	−	9.01212i	0.801089	−	0.290562i
$963$	−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
$966$	35.6729	−	0.830222i	1.14776	−	0.0267119i
$967$	13.5634	−	13.5634i	0.436171	−	0.436171i	−0.454550	−	0.890721i	$-0.650200\pi$
$967$	13.5634	−	13.5634i	0.436171	−	0.436171i	0.890721	+	0.454550i	$0.150200\pi$
$968$	11.4684	+	6.67248i	0.368608	+	0.214462i
$969$	−0.227958			−0.00732307
$970$	3.16049	−	4.23777i	0.101477	−	0.136067i
$971$	−56.7239			−1.82036			−0.910178	−	0.414217i	$-0.864055\pi$
$971$	−56.7239			−1.82036			−0.910178	+	0.414217i	$0.864055\pi$
$972$	−28.0880	−	2.52045i	−0.900923	−	0.0808435i
$973$	−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	−0.942018	−	0.335563i	$-0.891073\pi$
$977$	−18.9559	+	18.9559i	−0.606455	+	0.606455i	0.335563	+	0.942018i	$0.391073\pi$
$978$	−3.10380	−	8.55727i	−0.0992486	−	0.273631i
$979$			25.2599i			0.807310i
$980$	−30.9208	−	4.88910i	−0.987729	−	0.156176i
$981$			26.6233i			0.850017i
$982$	19.0643	−	6.91481i	0.608368	−	0.220661i
$983$	−14.6499	+	14.6499i	−0.467260	+	0.467260i	−0.901026	−	0.433765i	$-0.857185\pi$
$983$	−14.6499	+	14.6499i	−0.467260	+	0.467260i	0.433765	+	0.901026i	$0.357185\pi$
$984$	−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
$988$	−0.215316	+	2.39949i	−0.00685011	+	0.0763378i
$989$	46.0342			1.46380
$990$	1.77563	+	12.1943i	0.0564334	+	0.387560i
$991$	4.37107			0.138852			0.0694258	−	0.997587i	$-0.477883\pi$
$991$	4.37107			0.138852			0.0694258	+	0.997587i	$0.477883\pi$
$992$	6.83442	+	40.0636i	0.216993	+	1.27202i
$993$	21.2961	−	21.2961i	0.675810	−	0.675810i
$994$	0.0846465	+	3.63709i	0.00268483	+	0.115362i
$995$	−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	$-0.724724\pi$
$997$	3.54219	−	3.54219i	0.112182	−	0.112182i	0.760970	+	0.648787i	$0.224724\pi$
$998$	8.90478	+	24.5508i	0.281876	+	0.777140i
$999$	−35.2080			−1.11393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.c.13.13	✓	72
4.3	odd	2		1120.2.w.c.433.26		72
5.2	odd	4	inner	280.2.s.c.237.33	yes	72
7.6	odd	2	inner	280.2.s.c.13.14	yes	72
8.3	odd	2		1120.2.w.c.433.11		72
8.5	even	2	inner	280.2.s.c.13.34	yes	72
20.7	even	4		1120.2.w.c.657.25		72
28.27	even	2		1120.2.w.c.433.12		72
35.27	even	4	inner	280.2.s.c.237.34	yes	72
40.27	even	4		1120.2.w.c.657.12		72
40.37	odd	4	inner	280.2.s.c.237.14	yes	72
56.13	odd	2	inner	280.2.s.c.13.33	yes	72
56.27	even	2		1120.2.w.c.433.25		72
140.27	odd	4		1120.2.w.c.657.11		72
280.27	odd	4		1120.2.w.c.657.26		72
280.237	even	4	inner	280.2.s.c.237.13	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.c.13.13	✓	72	1.1	even	1	trivial
280.2.s.c.13.14	yes	72	7.6	odd	2	inner
280.2.s.c.13.33	yes	72	56.13	odd	2	inner
280.2.s.c.13.34	yes	72	8.5	even	2	inner
280.2.s.c.237.13	yes	72	280.237	even	4	inner
280.2.s.c.237.14	yes	72	40.37	odd	4	inner
280.2.s.c.237.33	yes	72	5.2	odd	4	inner
280.2.s.c.237.34	yes	72	35.27	even	4	inner
1120.2.w.c.433.11		72	8.3	odd	2
1120.2.w.c.433.12		72	28.27	even	2
1120.2.w.c.433.25		72	56.27	even	2
1120.2.w.c.433.26		72	4.3	odd	2
1120.2.w.c.657.11		72	140.27	odd	4
1120.2.w.c.657.12		72	40.27	even	4
1120.2.w.c.657.25		72	20.7	even	4
1120.2.w.c.657.26		72	280.27	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.482209 - 1.32946i) q^{2} +(-0.851048 - 0.851048i) q^{3} +(-1.53495 + 1.28216i) q^{4} +(2.18999 + 0.451591i) q^{5} +(-0.721055 + 1.54182i) q^{6} +(2.50752 + 0.844017i) q^{7} +(2.44475 + 1.42239i) q^{8} -1.55144i q^{9} +O(q^{10})\)	\(q+(-0.482209 - 1.32946i) 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} +(2.44475 + 1.42239i) q^{8} -1.55144i q^{9} +(-0.455660 - 3.12928i) q^{10} -2.51177i q^{11} +(2.39749 + 0.215137i) q^{12} +(2.05614 + 2.05614i) q^{13} +(-0.0870566 - 3.74064i) q^{14} +(-1.47946 - 2.24811i) q^{15} +(0.712139 - 3.93610i) q^{16} +(0.323302 + 0.323302i) q^{17} +(-2.06258 + 0.748116i) q^{18} -0.414250i q^{19} +(-3.94054 + 2.11475i) q^{20} +(-1.41572 - 2.85231i) q^{21} +(-3.33930 + 1.21120i) 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} +(-4.93107 + 1.91951i) q^{28} +2.48079 q^{29} +(-2.27538 + 3.05095i) q^{30} -7.18461i q^{31} +(-5.57630 + 0.951258i) 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} +(-0.550730 + 0.199755i) q^{38} -3.49974i q^{39} +(4.71164 + 4.21905i) q^{40} -1.40978i q^{41} +(-3.10938 + 3.25756i) 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} +(-3.95587 + 2.74374i) q^{48} +(5.57527 + 4.23277i) q^{49} +(0.415262 - 7.05886i) q^{50} -0.550291i q^{51} +(-5.79236 - 0.519772i) q^{52} +(7.59714 - 7.59714i) q^{53} +(7.01749 + 3.28183i) q^{54} +(1.13429 - 5.50075i) q^{55} +(4.92973 + 5.63008i) q^{56} +(-0.352547 + 0.352547i) q^{57} +(-1.19626 - 3.29812i) q^{58} -1.24364i q^{59} +(5.15334 + 1.55383i) q^{60} -11.7206 q^{61} +(-9.55169 + 3.46448i) 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} +(-0.910777 - 0.0817277i) q^{68} +9.53658i q^{69} +(1.49859 - 8.23130i) q^{70} -0.972317 q^{71} +(2.20675 - 3.79287i) 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} +(-4.65278 + 1.68761i) q^{78} +5.80828i q^{79} +(3.33708 - 8.29843i) q^{80} +1.93874 q^{81} +(-1.87425 + 0.679808i) q^{82} +(9.17675 + 9.17675i) q^{83} +(5.83017 + 2.56298i) q^{84} +(0.562029 + 0.854029i) q^{85} +(7.44255 + 3.48062i) q^{86} +(-2.11127 - 2.11127i) q^{87} +(3.57272 - 6.14064i) q^{88} -10.0566 q^{89} +(-4.85487 + 0.706927i) q^{90} +(3.42038 + 6.89121i) q^{91} +(15.7838 + 1.41635i) 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} +(2.93887 - 9.45320i) 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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