LMFDB - Embedded newform 714.2.w.f.83.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(83,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("714.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.w (of order $8$, degree $4$, 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:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.12
Character	$\chi$	$=$	714.83
Dual form			714.2.w.f.671.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.256259 - 1.71299i) q^{3} -1.00000i q^{4} +(2.17160 - 0.899506i) q^{5} +(1.03006 + 1.39247i) q^{6} +(-1.14112 + 2.38702i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86866 - 0.877938i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.256259 - 1.71299i) q^{3} -1.00000i q^{4} +(2.17160 - 0.899506i) q^{5} +(1.03006 + 1.39247i) q^{6} +(-1.14112 + 2.38702i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86866 - 0.877938i) q^{9} +(-0.899506 + 2.17160i) q^{10} +(-5.47402 - 2.26741i) q^{11} +(-1.71299 - 0.256259i) q^{12} -5.36946 q^{13} +(-0.880980 - 2.49477i) q^{14} +(-0.984351 - 3.95043i) q^{15} -1.00000 q^{16} +(-4.12265 - 0.0610632i) q^{17} +(2.64925 - 1.40765i) q^{18} +(-2.88066 + 2.88066i) q^{19} +(-0.899506 - 2.17160i) q^{20} +(3.79651 + 2.56642i) q^{21} +(5.47402 - 2.26741i) q^{22} +(5.51535 + 2.28453i) q^{23} +(1.39247 - 1.03006i) q^{24} +(0.371197 - 0.371197i) q^{25} +(3.79678 - 3.79678i) q^{26} +(-2.23902 + 4.68901i) q^{27} +(2.38702 + 1.14112i) q^{28} +(-2.90750 - 7.01932i) q^{29} +(3.48942 + 2.09734i) q^{30} +(7.49615 - 3.10501i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.28682 + 8.79589i) q^{33} +(2.95833 - 2.87198i) q^{34} +(-0.330923 + 6.21008i) q^{35} +(-0.877938 + 2.86866i) q^{36} +(0.629663 + 1.52014i) q^{37} -4.07387i q^{38} +(-1.37597 + 9.19782i) q^{39} +(2.17160 + 0.899506i) q^{40} +(-7.15235 - 2.96260i) q^{41} +(-4.49927 + 0.869802i) q^{42} +(5.86162 - 5.86162i) q^{43} +(-2.26741 + 5.47402i) q^{44} +(-7.01929 + 0.673848i) q^{45} +(-5.51535 + 2.28453i) q^{46} +1.85665i q^{47} +(-0.256259 + 1.71299i) q^{48} +(-4.39569 - 5.44775i) q^{49} +0.524952i q^{50} +(-1.16107 + 7.04641i) q^{51} +5.36946i q^{52} +(1.10030 - 1.10030i) q^{53} +(-1.73240 - 4.89886i) q^{54} -13.9269 q^{55} +(-2.49477 + 0.880980i) q^{56} +(4.19635 + 5.67274i) q^{57} +(7.01932 + 2.90750i) q^{58} +(-4.84410 + 4.84410i) q^{59} +(-3.95043 + 0.984351i) q^{60} +(0.313858 - 0.757721i) q^{61} +(-3.10501 + 7.49615i) q^{62} +(5.36914 - 5.84571i) q^{63} +1.00000i q^{64} +(-11.6603 + 4.82986i) q^{65} +(-2.48129 - 9.95798i) q^{66} -1.51487 q^{67} +(-0.0610632 + 4.12265i) q^{68} +(5.32673 - 8.86229i) q^{69} +(-4.15719 - 4.62519i) q^{70} +(4.66942 - 1.93414i) q^{71} +(-1.40765 - 2.64925i) q^{72} +(-3.49013 - 8.42592i) q^{73} +(-1.52014 - 0.629663i) q^{74} +(-0.540734 - 0.730979i) q^{75} +(2.88066 + 2.88066i) q^{76} +(11.6589 - 10.4792i) q^{77} +(-5.53088 - 7.47680i) q^{78} +(3.91211 - 9.44467i) q^{79} +(-2.17160 + 0.899506i) q^{80} +(7.45845 + 5.03702i) q^{81} +(7.15235 - 2.96260i) q^{82} +(0.354747 + 0.354747i) q^{83} +(2.56642 - 3.79651i) q^{84} +(-9.00768 + 3.57575i) q^{85} +8.28958i q^{86} +(-12.7691 + 3.18175i) q^{87} +(-2.26741 - 5.47402i) q^{88} +12.9846i q^{89} +(4.48691 - 5.43987i) q^{90} +(6.12720 - 12.8170i) q^{91} +(2.28453 - 5.51535i) q^{92} +(-3.39789 - 13.6365i) q^{93} +(-1.31285 - 1.31285i) q^{94} +(-3.66447 + 8.84681i) q^{95} +(-1.03006 - 1.39247i) q^{96} +(-0.646996 - 1.56199i) q^{97} +(6.96036 + 0.743920i) q^{98} +(13.7125 + 11.3103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 16 q^{7}+O(q^{10}) $ 80 * q - 16 * q^7	$ 80 q - 16 q^{7} + 16 q^{14} - 48 q^{15} - 80 q^{16} + 16 q^{18} + 32 q^{21} + 16 q^{23} - 32 q^{25} - 64 q^{29} + 16 q^{30} - 48 q^{37} + 64 q^{39} + 16 q^{43} + 16 q^{44} - 16 q^{46} + 16 q^{49} + 24 q^{51} + 80 q^{53} + 48 q^{57} - 16 q^{58} - 16 q^{60} - 32 q^{63} - 80 q^{65} - 144 q^{67} + 8 q^{70} - 16 q^{71} + 32 q^{74} + 24 q^{77} + 32 q^{79} - 16 q^{84} + 208 q^{85} + 16 q^{88} - 8 q^{91} - 16 q^{92} - 16 q^{93} + 16 q^{95} + 16 q^{98} + 48 q^{99}+O(q^{100}) $ 80 * q - 16 * q^7 + 16 * q^14 - 48 * q^15 - 80 * q^16 + 16 * q^18 + 32 * q^21 + 16 * q^23 - 32 * q^25 - 64 * q^29 + 16 * q^30 - 48 * q^37 + 64 * q^39 + 16 * q^43 + 16 * q^44 - 16 * q^46 + 16 * q^49 + 24 * q^51 + 80 * q^53 + 48 * q^57 - 16 * q^58 - 16 * q^60 - 32 * q^63 - 80 * q^65 - 144 * q^67 + 8 * q^70 - 16 * q^71 + 32 * q^74 + 24 * q^77 + 32 * q^79 - 16 * q^84 + 208 * q^85 + 16 * q^88 - 8 * q^91 - 16 * q^92 - 16 * q^93 + 16 * q^95 + 16 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.256259	−	1.71299i	0.147951	−	0.988995i
$3$	0.256259	−	1.71299i	0.147951	−	0.988995i
$4$		−	1.00000i		−	0.500000i
$5$	2.17160	−	0.899506i	0.971169	−	0.402271i	0.160022	−	0.987114i	$-0.448844\pi$
$5$	2.17160	−	0.899506i	0.971169	−	0.402271i	0.811147	+	0.584842i	$0.198844\pi$
$6$	1.03006	+	1.39247i	0.420522	+	0.568473i
$7$	−1.14112	+	2.38702i	−0.431303	+	0.902207i
$7$	−1.14112	+	2.38702i	−0.431303	+	0.902207i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.86866	−	0.877938i	−0.956221	−	0.292646i
$10$	−0.899506	+	2.17160i	−0.284449	+	0.686720i
$11$	−5.47402	−	2.26741i	−1.65048	−	0.683651i	−0.653188	−	0.757196i	$-0.726569\pi$
$11$	−5.47402	−	2.26741i	−1.65048	−	0.683651i	−0.997292	+	0.0735450i	$0.976569\pi$
$12$	−1.71299	−	0.256259i	−0.494497	−	0.0739757i
$13$	−5.36946			−1.48922			−0.744610	−	0.667500i	$-0.767364\pi$
$13$	−5.36946			−1.48922			−0.744610	+	0.667500i	$0.767364\pi$
$14$	−0.880980	−	2.49477i	−0.235452	−	0.666755i
$15$	−0.984351	−	3.95043i	−0.254158	−	1.02000i
$16$	−1.00000			−0.250000
$17$	−4.12265	−	0.0610632i	−0.999890	−	0.0148100i
$17$	−4.12265	−	0.0610632i	−0.999890	−	0.0148100i
$18$	2.64925	−	1.40765i	0.624433	−	0.331787i
$19$	−2.88066	+	2.88066i	−0.660869	+	0.660869i	−0.955585	−	0.294716i	$-0.904775\pi$
$19$	−2.88066	+	2.88066i	−0.660869	+	0.660869i	0.294716	+	0.955585i	$0.404775\pi$
$20$	−0.899506	−	2.17160i	−0.201136	−	0.485584i
$21$	3.79651	+	2.56642i	0.828466	+	0.560039i
$22$	5.47402	−	2.26741i	1.16707	−	0.483414i
$23$	5.51535	+	2.28453i	1.15003	+	0.476358i	0.874543	−	0.484948i	$-0.161161\pi$
$23$	5.51535	+	2.28453i	1.15003	+	0.476358i	0.275486	+	0.961305i	$0.411161\pi$
$24$	1.39247	−	1.03006i	0.284236	−	0.210261i
$25$	0.371197	−	0.371197i	0.0742394	−	0.0742394i
$26$	3.79678	−	3.79678i	0.744610	−	0.744610i
$27$	−2.23902	+	4.68901i	−0.430900	+	0.902400i
$28$	2.38702	+	1.14112i	0.451104	+	0.215652i
$29$	−2.90750	−	7.01932i	−0.539909	−	1.30346i	−0.924786	−	0.380487i	$-0.875756\pi$
$29$	−2.90750	−	7.01932i	−0.539909	−	1.30346i	0.384877	−	0.922968i	$-0.374244\pi$
$30$	3.48942	+	2.09734i	0.637078	+	0.382919i
$31$	7.49615	−	3.10501i	1.34635	−	0.557676i	0.411075	−	0.911602i	$-0.365154\pi$
$31$	7.49615	−	3.10501i	1.34635	−	0.557676i	0.935273	+	0.353926i	$0.115154\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−5.28682	+	8.79589i	−0.920318	+	1.53117i
$34$	2.95833	−	2.87198i	0.507350	−	0.492540i
$35$	−0.330923	+	6.21008i	−0.0559362	+	1.04970i
$36$	−0.877938	+	2.86866i	−0.146323	+	0.478110i
$37$	0.629663	+	1.52014i	0.103516	+	0.249909i	0.967148	−	0.254212i	$-0.0818162\pi$
$37$	0.629663	+	1.52014i	0.103516	+	0.249909i	−0.863633	+	0.504122i	$0.831816\pi$
$38$		−	4.07387i		−	0.660869i
$39$	−1.37597	+	9.19782i	−0.220332	+	1.47283i
$40$	2.17160	+	0.899506i	0.343360	+	0.142224i
$41$	−7.15235	−	2.96260i	−1.11701	−	0.462681i	−0.253664	−	0.967292i	$-0.581636\pi$
$41$	−7.15235	−	2.96260i	−1.11701	−	0.462681i	−0.863346	+	0.504612i	$0.831636\pi$
$42$	−4.49927	+	0.869802i	−0.694253	+	0.134213i
$43$	5.86162	−	5.86162i	0.893889	−	0.893889i	−0.100998	−	0.994887i	$-0.532204\pi$
$43$	5.86162	−	5.86162i	0.893889	−	0.893889i	0.994887	+	0.100998i	$0.0322035\pi$
$44$	−2.26741	+	5.47402i	−0.341826	+	0.825240i
$45$	−7.01929	+	0.673848i	−1.04637	+	0.100451i
$46$	−5.51535	+	2.28453i	−0.813193	+	0.336836i
$47$			1.85665i			0.270821i	0.990790	+	0.135410i	$0.0432353\pi$
$47$			1.85665i			0.270821i	−0.990790	+	0.135410i	$0.956765\pi$
$48$	−0.256259	+	1.71299i	−0.0369878	+	0.247249i
$49$	−4.39569	−	5.44775i	−0.627955	−	0.778250i
$50$			0.524952i			0.0742394i
$51$	−1.16107	+	7.04641i	−0.162582	+	0.986695i
$52$			5.36946i			0.744610i
$53$	1.10030	−	1.10030i	0.151138	−	0.151138i	−0.627488	−	0.778626i	$-0.715917\pi$
$53$	1.10030	−	1.10030i	0.151138	−	0.151138i	0.778626	+	0.627488i	$0.215917\pi$
$54$	−1.73240	−	4.89886i	−0.235750	−	0.666650i
$55$	−13.9269			−1.87791
$56$	−2.49477	+	0.880980i	−0.333378	+	0.117726i
$57$	4.19635	+	5.67274i	0.555820	+	0.751372i
$58$	7.01932	+	2.90750i	0.921682	+	0.381773i
$59$	−4.84410	+	4.84410i	−0.630648	+	0.630648i	−0.948231	−	0.317583i	$-0.897129\pi$
$59$	−4.84410	+	4.84410i	−0.630648	+	0.630648i	0.317583	+	0.948231i	$0.397129\pi$
$60$	−3.95043	+	0.984351i	−0.509999	+	0.127079i
$61$	0.313858	−	0.757721i	0.0401854	−	0.0970162i	−0.902512	−	0.430664i	$-0.858280\pi$
$61$	0.313858	−	0.757721i	0.0401854	−	0.0970162i	0.942698	+	0.333647i	$0.108280\pi$
$62$	−3.10501	+	7.49615i	−0.394336	+	0.952012i
$63$	5.36914	−	5.84571i	0.676449	−	0.736490i
$64$			1.00000i			0.125000i
$65$	−11.6603	+	4.82986i	−1.44628	+	0.599070i
$66$	−2.48129	−	9.95798i	−0.305425	−	1.22574i
$67$	−1.51487			−0.185071			−0.0925355	−	0.995709i	$-0.529497\pi$
$67$	−1.51487			−0.185071			−0.0925355	+	0.995709i	$0.529497\pi$
$68$	−0.0610632	+	4.12265i	−0.00740500	+	0.499945i
$69$	5.32673	−	8.86229i	0.641263	−	1.06689i
$70$	−4.15719	−	4.62519i	−0.496880	−	0.552816i
$71$	4.66942	−	1.93414i	0.554158	−	0.229540i	−0.0879889	−	0.996121i	$-0.528044\pi$
$71$	4.66942	−	1.93414i	0.554158	−	0.229540i	0.642147	+	0.766582i	$0.278044\pi$
$72$	−1.40765	−	2.64925i	−0.165894	−	0.312217i
$73$	−3.49013	−	8.42592i	−0.408489	−	0.986179i	−0.985536	−	0.169468i	$-0.945795\pi$
$73$	−3.49013	−	8.42592i	−0.408489	−	0.986179i	0.577047	−	0.816711i	$-0.304205\pi$
$74$	−1.52014	−	0.629663i	−0.176713	−	0.0731968i
$75$	−0.540734	−	0.730979i	−0.0624385	−	0.0844062i
$76$	2.88066	+	2.88066i	0.330435	+	0.330435i
$77$	11.6589	−	10.4792i	1.32865	−	1.19421i
$78$	−5.53088	−	7.47680i	−0.626249	−	0.846581i
$79$	3.91211	−	9.44467i	0.440147	−	1.06261i	−0.535750	−	0.844377i	$-0.679971\pi$
$79$	3.91211	−	9.44467i	0.440147	−	1.06261i	0.975897	−	0.218232i	$-0.0700289\pi$
$80$	−2.17160	+	0.899506i	−0.242792	+	0.100568i
$81$	7.45845	+	5.03702i	0.828716	+	0.559669i
$82$	7.15235	−	2.96260i	0.789845	−	0.327165i
$83$	0.354747	+	0.354747i	0.0389385	+	0.0389385i	0.726308	−	0.687369i	$-0.241235\pi$
$83$	0.354747	+	0.354747i	0.0389385	+	0.0389385i	−0.687369	+	0.726308i	$0.741235\pi$
$84$	2.56642	−	3.79651i	0.280020	−	0.414233i
$85$	−9.00768	+	3.57575i	−0.977020	+	0.387844i
$86$			8.28958i			0.893889i
$87$	−12.7691	+	3.18175i	−1.36899	+	0.341119i
$88$	−2.26741	−	5.47402i	−0.241707	−	0.583533i
$89$			12.9846i			1.37637i	0.725537	+	0.688183i	$0.241592\pi$
$89$			12.9846i			1.37637i	−0.725537	+	0.688183i	$0.758408\pi$
$90$	4.48691	−	5.43987i	0.472962	−	0.573413i
$91$	6.12720	−	12.8170i	0.642305	−	1.34358i
$92$	2.28453	−	5.51535i	0.238179	−	0.575014i
$93$	−3.39789	−	13.6365i	−0.352344	−	1.41404i
$94$	−1.31285	−	1.31285i	−0.135410	−	0.135410i
$95$	−3.66447	+	8.84681i	−0.375967	+	0.907664i
$96$	−1.03006	−	1.39247i	−0.105130	−	0.142118i
$97$	−0.646996	−	1.56199i	−0.0656925	−	0.158596i	0.887624	−	0.460569i	$-0.152355\pi$
$97$	−0.646996	−	1.56199i	−0.0656925	−	0.158596i	−0.953316	+	0.301973i	$0.902355\pi$
$98$	6.96036	+	0.743920i	0.703102	+	0.0751473i
$99$	13.7125	+	11.3103i	1.37816	+	1.13673i
$100$	−0.371197	−	0.371197i	−0.0371197	−	0.0371197i
$101$	−8.13441			−0.809404			−0.404702	−	0.914449i	$-0.632625\pi$
$101$	−8.13441			−0.809404			−0.404702	+	0.914449i	$0.632625\pi$
$102$	−4.16157	−	5.80356i	−0.412056	−	0.574639i
$103$			7.03501i			0.693180i	0.938017	+	0.346590i	$0.112660\pi$
$103$			7.03501i			0.693180i	−0.938017	+	0.346590i	$0.887340\pi$
$104$	−3.79678	−	3.79678i	−0.372305	−	0.372305i
$105$	10.5530	+	2.15826i	1.02987	+	0.210625i
$106$			1.55606i			0.151138i
$107$	−2.00613	−	4.84323i	−0.193940	−	0.468213i	0.796757	−	0.604300i	$-0.206547\pi$
$107$	−2.00613	−	4.84323i	−0.193940	−	0.468213i	−0.990697	+	0.136087i	$0.956547\pi$
$108$	4.68901	+	2.23902i	0.451200	+	0.215450i
$109$	−7.29879	−	3.02326i	−0.699097	−	0.289575i	0.00468746	−	0.999989i	$-0.498508\pi$
$109$	−7.29879	−	3.02326i	−0.699097	−	0.289575i	−0.703784	+	0.710414i	$0.748508\pi$
$110$	9.84783	−	9.84783i	0.938953	−	0.938953i
$111$	2.76534	−	0.689055i	0.262474	−	0.0654022i
$112$	1.14112	−	2.38702i	0.107826	−	0.225552i
$113$	2.97676	+	1.23302i	0.280030	+	0.115992i	0.518278	−	0.855212i	$-0.326573\pi$
$113$	2.97676	+	1.23302i	0.280030	+	0.115992i	−0.238248	+	0.971204i	$0.576573\pi$
$114$	−6.97850	−	1.04397i	−0.653596	−	0.0977765i
$115$	14.0321			1.30850
$116$	−7.01932	+	2.90750i	−0.651728	+	0.269954i
$117$	15.4032	+	4.71405i	1.42402	+	0.435814i
$118$		−	6.85059i		−	0.630648i
$119$	4.85021	−	9.77116i	0.444618	−	0.895720i
$120$	2.09734	−	3.48942i	0.191460	−	0.318539i
$121$	17.0456	+	17.0456i	1.54960	+	1.54960i
$122$	0.313858	+	0.757721i	0.0284154	+	0.0686008i
$123$	−6.90776	+	11.4927i	−0.622852	+	1.03626i
$124$	−3.10501	−	7.49615i	−0.278838	−	0.673174i
$125$	−4.02533	+	9.71801i	−0.360037	+	0.869205i
$126$	0.336982	+	7.93010i	0.0300207	+	0.706469i
$127$	6.26091	−	6.26091i	0.555566	−	0.555566i	−0.372476	−	0.928042i	$-0.621491\pi$
$127$	6.26091	−	6.26091i	0.555566	−	0.555566i	0.928042	+	0.372476i	$0.121491\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−8.53880	−	11.5430i	−0.751799	−	1.01630i
$130$	4.82986	−	11.6603i	0.423607	−	1.02268i
$131$	4.60717	−	1.90835i	0.402531	−	0.166734i	−0.172227	−	0.985057i	$-0.555096\pi$
$131$	4.60717	−	1.90835i	0.402531	−	0.166734i	0.574758	+	0.818324i	$0.305096\pi$
$132$	8.79589	+	5.28682i	0.765584	+	0.460159i
$133$	−3.58900	−	10.1634i	−0.311206	−	0.881276i
$134$	1.07118	−	1.07118i	0.0925355	−	0.0925355i
$135$	−0.644464	+	12.1967i	−0.0554667	+	1.04972i
$136$	−2.87198	−	2.95833i	−0.246270	−	0.253675i
$137$		−	14.8692i		−	1.27036i	−0.772362	−	0.635182i	$-0.780925\pi$
$137$		−	14.8692i		−	1.27036i	0.772362	−	0.635182i	$-0.219075\pi$
$138$	2.50002	+	10.0332i	0.212816	+	0.854079i
$139$	−6.60225	+	2.73474i	−0.559995	+	0.231958i	−0.644683	−	0.764450i	$-0.723011\pi$
$139$	−6.60225	+	2.73474i	−0.559995	+	0.231958i	0.0846879	+	0.996408i	$0.473011\pi$
$140$	6.21008	+	0.330923i	0.524848	+	0.0279681i
$141$	3.18043	+	0.475785i	0.267840	+	0.0400683i
$142$	−1.93414	+	4.66942i	−0.162309	+	0.391849i
$143$	29.3925	+	12.1748i	2.45793	+	1.01811i
$144$	2.86866	+	0.877938i	0.239055	+	0.0731615i
$145$	−12.6278	−	12.6278i	−1.04868	−	1.04868i
$146$	8.42592	+	3.49013i	0.697334	+	0.288845i
$147$	−10.4584	+	6.13373i	−0.862591	+	0.505901i
$148$	1.52014	−	0.629663i	0.124955	−	0.0517579i
$149$	−21.9200			−1.79576			−0.897878	−	0.440245i	$-0.854892\pi$
$149$	−21.9200			−1.79576			−0.897878	+	0.440245i	$0.854892\pi$
$150$	0.899237	+	0.134524i	0.0734224	+	0.0109838i
$151$	6.02678	+	6.02678i	0.490453	+	0.490453i	0.908449	−	0.417996i	$-0.137267\pi$
$151$	6.02678	+	6.02678i	0.490453	+	0.490453i	−0.417996	+	0.908449i	$0.637267\pi$
$152$	−4.07387			−0.330435
$153$	11.7729	+	3.79461i	0.951782	+	0.306776i
$154$	−0.834169	+	15.6540i	−0.0672193	+	1.26143i
$155$	13.4857	−	13.4857i	1.08319	−	1.08319i
$156$	9.19782	+	1.37597i	0.736415	+	0.110166i
$157$	−7.50820			−0.599219			−0.299610	−	0.954062i	$-0.596856\pi$
$157$	−7.50820			−0.599219			−0.299610	+	0.954062i	$0.596856\pi$
$158$	3.91211	+	9.44467i	0.311231	+	0.751378i
$159$	−1.60284	−	2.16676i	−0.127113	−	0.171836i
$160$	0.899506	−	2.17160i	0.0711122	−	0.171680i
$161$	−11.7469	+	10.5583i	−0.925784	+	0.832110i
$162$	−8.83563	+	1.71221i	−0.694193	+	0.134524i
$163$	−11.1182	−	4.60531i	−0.870844	−	0.360715i	−0.0979051	−	0.995196i	$-0.531214\pi$
$163$	−11.1182	−	4.60531i	−0.870844	−	0.360715i	−0.772939	+	0.634480i	$0.781214\pi$
$164$	−2.96260	+	7.15235i	−0.231340	+	0.558505i
$165$	−3.56890	+	23.8567i	−0.277839	+	1.85724i
$166$	−0.501688			−0.0389385
$167$	0.452987	+	1.09361i	0.0350532	+	0.0846259i	0.940437	−	0.339969i	$-0.110417\pi$
$167$	0.452987	+	1.09361i	0.0350532	+	0.0846259i	−0.905383	+	0.424595i	$0.860417\pi$
$168$	0.869802	+	4.49927i	0.0671067	+	0.347126i
$169$	15.8311			1.21777
$170$	3.84095	−	8.89782i	0.294588	−	0.682432i
$171$	10.7927	−	5.73460i	0.825338	−	0.438536i
$172$	−5.86162	−	5.86162i	−0.446944	−	0.446944i
$173$	−3.77394	−	9.11111i	−0.286928	−	0.692705i	0.713037	−	0.701127i	$-0.247319\pi$
$173$	−3.77394	−	9.11111i	−0.286928	−	0.692705i	−0.999965	+	0.00842187i	$0.997319\pi$
$174$	6.77928	−	11.2789i	0.513936	−	0.855055i
$175$	0.462472	+	1.30963i	0.0349596	+	0.0989990i
$176$	5.47402	+	2.26741i	0.412620	+	0.170913i
$177$	7.05654	+	9.53923i	0.530402	+	0.717012i
$178$	−9.18151	−	9.18151i	−0.688183	−	0.688183i
$179$	−12.1206	−	12.1206i	−0.905933	−	0.905933i	0.0900079	−	0.995941i	$-0.471311\pi$
$179$	−12.1206	−	12.1206i	−0.905933	−	0.905933i	−0.995941	+	0.0900079i	$0.971311\pi$
$180$	0.673848	+	7.01929i	0.0502257	+	0.523187i
$181$	19.5197	+	8.08533i	1.45089	+	0.600978i	0.962411	−	0.271598i	$-0.0875520\pi$
$181$	19.5197	+	8.08533i	1.45089	+	0.600978i	0.488479	+	0.872576i	$0.337552\pi$
$182$	4.73039	+	13.3956i	0.350640	+	0.992945i
$183$	−1.21754	−	0.731809i	−0.0900030	−	0.0540968i
$184$	2.28453	+	5.51535i	0.168418	+	0.406597i
$185$	2.73475	+	2.73475i	0.201063	+	0.201063i
$186$	12.0451	+	7.23980i	0.883192	+	0.530848i
$187$	22.4290	+	9.68202i	1.64017	+	0.708020i
$188$	1.85665			0.135410
$189$	−8.63774	−	10.6953i	−0.628303	−	0.777969i
$190$	−3.66447	−	8.84681i	−0.265849	−	0.641815i
$191$	2.28750			0.165518			0.0827590	−	0.996570i	$-0.473627\pi$
$191$	2.28750			0.165518			0.0827590	+	0.996570i	$0.473627\pi$
$192$	1.71299	+	0.256259i	0.123624	+	0.0184939i
$193$	−1.03302	+	2.49394i	−0.0743585	+	0.179517i	−0.956688	−	0.291114i	$-0.905974\pi$
$193$	−1.03302	+	2.49394i	−0.0743585	+	0.179517i	0.882330	+	0.470632i	$0.155974\pi$
$194$	1.56199	+	0.646996i	0.112144	+	0.0464516i
$195$	5.28543	+	21.2117i	0.378498	+	1.51900i
$196$	−5.44775	+	4.39569i	−0.389125	+	0.313978i
$197$	−3.71607	+	8.97138i	−0.264759	+	0.639184i	−0.999221	−	0.0394654i	$-0.987435\pi$
$197$	−3.71607	+	8.97138i	−0.264759	+	0.639184i	0.734462	+	0.678650i	$0.237435\pi$
$198$	−17.6938	+	1.69859i	−1.25744	+	0.120714i
$199$	4.60877	+	11.1265i	0.326707	+	0.788740i	0.998833	+	0.0483031i	$0.0153813\pi$
$199$	4.60877	+	11.1265i	0.326707	+	0.788740i	−0.672126	+	0.740437i	$0.734619\pi$
$200$	0.524952			0.0371197
$201$	−0.388200	+	2.59496i	−0.0273815	+	0.183034i
$202$	5.75190	−	5.75190i	0.404702	−	0.404702i
$203$	20.0730	+	1.06965i	1.40885	+	0.0750749i
$204$	7.04641	+	1.16107i	0.493348	+	0.0812911i
$205$	−18.1969			−1.27093
$206$	−4.97450	−	4.97450i	−0.346590	−	0.346590i
$207$	−13.8160	−	11.3957i	−0.960277	−	0.792055i
$208$	5.36946			0.372305
$209$	22.3005	−	9.23715i	1.54255	−	0.638947i
$210$	−8.98822	+	5.93598i	−0.620246	+	0.409622i
$211$	−10.9121	−	4.51995i	−0.751222	−	0.311166i	−0.0259818	−	0.999662i	$-0.508271\pi$
$211$	−10.9121	−	4.51995i	−0.751222	−	0.311166i	−0.725240	+	0.688496i	$0.758271\pi$
$212$	−1.10030	−	1.10030i	−0.0755689	−	0.0755689i
$213$	−2.11657	−	8.49430i	−0.145025	−	0.582020i
$214$	4.84323	+	2.00613i	0.331076	+	0.137136i
$215$	7.45653	−	18.0017i	0.508531	−	1.22770i
$216$	−4.89886	+	1.73240i	−0.333325	+	0.117875i
$217$	−1.14232	+	21.4366i	−0.0775454	+	1.45521i
$218$	7.29879	−	3.02326i	0.494336	−	0.204761i
$219$	−15.3279	+	3.81933i	−1.03576	+	0.258087i
$220$			13.9269i			0.938953i
$221$	22.1364	+	0.327876i	1.48906	+	0.0220553i
$222$	−1.46815	+	2.44263i	−0.0985361	+	0.163938i
$223$	3.79748	−	3.79748i	0.254298	−	0.254298i	−0.568432	−	0.822730i	$-0.692450\pi$
$223$	3.79748	−	3.79748i	0.254298	−	0.254298i	0.822730	+	0.568432i	$0.192450\pi$
$224$	0.880980	+	2.49477i	0.0588630	+	0.166689i
$225$	−1.39073	+	0.738951i	−0.0927151	+	0.0492634i
$226$	−2.97676	+	1.23302i	−0.198011	+	0.0820189i
$227$	−2.41386	+	5.82758i	−0.160214	+	0.386790i	−0.983518	−	0.180810i	$-0.942128\pi$
$227$	−2.41386	+	5.82758i	−0.160214	+	0.386790i	0.823304	+	0.567600i	$0.192128\pi$
$228$	5.67274	−	4.19635i	0.375686	−	0.277910i
$229$	−15.2356	−	15.2356i	−1.00680	−	1.00680i	−0.999977	−	0.00682023i	$-0.997829\pi$
$229$	−15.2356	−	15.2356i	−1.00680	−	1.00680i	−0.00682023	−	0.999977i	$-0.502171\pi$
$230$	−9.92217	+	9.92217i	−0.654248	+	0.654248i
$231$	−14.9630	−	22.6569i	−0.984495	−	1.49072i
$232$	2.90750	−	7.01932i	0.190887	−	0.460841i
$233$	8.25203	+	19.9222i	0.540608	+	1.30514i	0.924294	+	0.381680i	$0.124654\pi$
$233$	8.25203	+	19.9222i	0.540608	+	1.30514i	−0.383686	+	0.923464i	$0.625346\pi$
$234$	−14.2250	+	7.55834i	−0.929919	+	0.494104i
$235$	1.67007	+	4.03191i	0.108943	+	0.263013i
$236$	4.84410	+	4.84410i	0.315324	+	0.315324i
$237$	−15.1761	−	9.12169i	−0.985794	−	0.592517i
$238$	3.47964	+	10.3389i	0.225551	+	0.670169i
$239$		−	22.4045i		−	1.44923i	−0.689155	−	0.724614i	$-0.742018\pi$
$239$		−	22.4045i		−	1.44923i	0.689155	−	0.724614i	$-0.257982\pi$
$240$	0.984351	+	3.95043i	0.0635396	+	0.254999i
$241$	5.00778	−	2.07429i	0.322580	−	0.133617i	−0.215517	−	0.976500i	$-0.569144\pi$
$241$	5.00778	−	2.07429i	0.322580	−	0.133617i	0.538096	+	0.842883i	$0.319144\pi$
$242$	−24.1061			−1.54960
$243$	10.5397	−	11.4855i	0.676119	−	0.736792i
$244$	−0.757721	−	0.313858i	−0.0485081	−	0.0200927i
$245$	−14.4459	−	7.87638i	−0.922918	−	0.503203i
$246$	−3.24205	−	13.0111i	−0.206705	−	0.829557i
$247$	15.4676	−	15.4676i	0.984179	−	0.984179i
$248$	7.49615	+	3.10501i	0.476006	+	0.197168i
$249$	0.698585	−	0.516771i	0.0442710	−	0.0327490i
$250$	−4.02533	−	9.71801i	−0.254584	−	0.614621i
$251$		−	11.8836i		−	0.750086i	−0.927007	−	0.375043i	$-0.877628\pi$
$251$		−	11.8836i		−	0.750086i	0.927007	−	0.375043i	$-0.122372\pi$
$252$	−5.84571	−	5.36914i	−0.368245	−	0.338224i
$253$	−25.0111	−	25.0111i	−1.57244	−	1.57244i
$254$			8.85426i			0.555566i
$255$	3.81691	+	16.3464i	0.239024	+	1.02365i
$256$	1.00000			0.0625000
$257$	−8.46277	−	8.46277i	−0.527893	−	0.527893i	0.392051	−	0.919944i	$-0.371766\pi$
$257$	−8.46277	−	8.46277i	−0.527893	−	0.527893i	−0.919944	+	0.392051i	$0.871766\pi$
$258$	14.2000	+	2.12428i	0.884051	+	0.132252i
$259$	−4.34712	−	0.231649i	−0.270117	−	0.0143940i
$260$	4.82986	+	11.6603i	0.299535	+	0.723142i
$261$	2.17810	+	22.6887i	0.134821	+	1.40439i
$262$	−1.90835	+	4.60717i	−0.117899	+	0.284632i
$263$	7.70634	+	7.70634i	0.475193	+	0.475193i	0.903591	−	0.428397i	$-0.140922\pi$
$263$	7.70634	+	7.70634i	0.475193	+	0.475193i	−0.428397	+	0.903591i	$0.640922\pi$
$264$	−9.95798	+	2.48129i	−0.612872	+	0.152713i
$265$	1.39968	−	3.37914i	0.0859819	−	0.207579i
$266$	9.72439	+	4.64878i	0.596241	+	0.285035i
$267$	22.2425	+	3.32743i	1.36122	+	0.203635i
$268$			1.51487i			0.0925355i
$269$	4.73887	+	11.4406i	0.288934	+	0.697548i	0.999984	−	0.00559287i	$-0.00178027\pi$
$269$	4.73887	+	11.4406i	0.288934	+	0.697548i	−0.711050	+	0.703141i	$0.751780\pi$
$270$	−8.16863	−	9.08004i	−0.497127	−	0.552594i
$271$			10.2680i			0.623737i	0.950125	+	0.311868i	$0.100955\pi$
$271$			10.2680i			0.623737i	−0.950125	+	0.311868i	$0.899045\pi$
$272$	4.12265	+	0.0610632i	0.249973	+	0.00370250i
$273$	−20.3852	−	13.7803i	−1.23377	−	0.834021i
$274$	10.5141	+	10.5141i	0.635182	+	0.635182i
$275$	−2.87360	+	1.19028i	−0.173284	+	0.0717768i
$276$	−8.86229	−	5.32673i	−0.533447	−	0.320632i
$277$	21.6725	−	8.97704i	1.30217	−	0.539378i	0.379582	−	0.925158i	$-0.376068\pi$
$277$	21.6725	−	8.97704i	1.30217	−	0.539378i	0.922591	+	0.385780i	$0.126068\pi$
$278$	2.73474	−	6.60225i	0.164019	−	0.395976i
$279$	−24.2299	+	2.32606i	−1.45061	+	0.139258i
$280$	−4.62519	+	4.15719i	−0.276408	+	0.248440i
$281$	13.7591	+	13.7591i	0.820796	+	0.820796i	0.986222	−	0.165426i	$-0.0528999\pi$
$281$	13.7591	+	13.7591i	0.820796	+	0.820796i	−0.165426	+	0.986222i	$0.552900\pi$
$282$	−2.58533	+	1.91247i	−0.153954	+	0.113886i
$283$	10.6909	+	4.42830i	0.635506	+	0.263235i	0.677091	−	0.735900i	$-0.263240\pi$
$283$	10.6909	+	4.42830i	0.635506	+	0.263235i	−0.0415843	+	0.999135i	$0.513240\pi$
$284$	−1.93414	−	4.66942i	−0.114770	−	0.277079i
$285$	14.2154	+	8.54427i	0.842050	+	0.506119i
$286$	−29.3925	+	12.1748i	−1.73802	+	0.719910i
$287$	15.2335	−	13.6921i	0.899204	−	0.808219i
$288$	−2.64925	+	1.40765i	−0.156108	+	0.0829468i
$289$	16.9925	+	0.503485i	0.999561	+	0.0296167i
$290$	17.8585			1.04868
$291$	−2.84147	+	0.708024i	−0.166570	+	0.0415051i
$292$	−8.42592	+	3.49013i	−0.493090	+	0.204244i
$293$		−	17.0240i		−	0.994555i	−0.867592	−	0.497277i	$-0.834333\pi$
$293$		−	17.0240i		−	0.994555i	0.867592	−	0.497277i	$-0.165667\pi$
$294$	3.05798	−	11.7324i	0.178345	−	0.684246i
$295$	−6.16214	+	14.8767i	−0.358774	+	0.866157i
$296$	−0.629663	+	1.52014i	−0.0365984	+	0.0883563i
$297$	22.8884	−	20.5909i	1.32812	−	1.19481i
$298$	15.4998	−	15.4998i	0.897878	−	0.897878i
$299$	−29.6144	−	12.2667i	−1.71265	−	0.709401i
$300$	−0.730979	+	0.540734i	−0.0422031	+	0.0312193i
$301$	7.30296	+	20.6806i	0.420936	+	1.19201i
$302$	−8.52316			−0.490453
$303$	−2.08452	+	13.9342i	−0.119752	+	0.800496i
$304$	2.88066	−	2.88066i	0.165217	−	0.165217i
$305$		−	1.92778i		−	0.110385i
$306$	−11.0079	+	5.64150i	−0.629279	+	0.322503i
$307$		−	1.77632i		−	0.101380i	−0.998714	−	0.0506899i	$-0.983858\pi$
$307$		−	1.77632i		−	0.101380i	0.998714	−	0.0506899i	$-0.0161420\pi$
$308$	−10.4792	−	11.6589i	−0.597107	−	0.664326i
$309$	12.0509	+	1.80278i	0.685551	+	0.102557i
$310$			19.0716i			1.08319i
$311$	−20.5593	+	8.51594i	−1.16581	+	0.482895i	−0.879806	−	0.475333i	$-0.842328\pi$
$311$	−20.5593	+	8.51594i	−1.16581	+	0.482895i	−0.286005	+	0.958228i	$0.592328\pi$
$312$	−7.47680	+	5.53088i	−0.423291	+	0.313125i
$313$	6.81435	−	16.4513i	0.385170	−	0.929883i	−0.605778	−	0.795634i	$-0.707138\pi$
$313$	6.81435	−	16.4513i	0.385170	−	0.929883i	0.990948	−	0.134249i	$-0.0428621\pi$
$314$	5.30910	−	5.30910i	0.299610	−	0.299610i
$315$	6.40138	−	17.5241i	0.360677	−	0.987372i
$316$	−9.44467	−	3.91211i	−0.531304	−	0.220073i
$317$	−31.9626	−	13.2394i	−1.79520	−	0.743596i	−0.988224	−	0.153012i	$-0.951103\pi$
$317$	−31.9626	−	13.2394i	−1.79520	−	0.743596i	−0.806976	−	0.590584i	$-0.798897\pi$
$318$	2.66551	+	0.398755i	0.149475	+	0.0223610i
$319$			45.0164i			2.52044i
$320$	0.899506	+	2.17160i	0.0502839	+	0.121396i
$321$	−8.81049	+	2.19536i	−0.491754	+	0.122533i
$322$	0.840466	−	15.7721i	0.0468374	−	0.878947i
$323$	12.0519	−	11.7001i	0.670584	−	0.651009i
$324$	5.03702	−	7.45845i	0.279834	−	0.414358i
$325$	−1.99313	+	1.99313i	−0.110559	+	0.110559i
$326$	11.1182	−	4.60531i	0.615780	−	0.255064i
$327$	−7.04919	+	11.7280i	−0.389821	+	0.648560i
$328$	−2.96260	−	7.15235i	−0.163582	−	0.394923i
$329$	−4.43186	−	2.11867i	−0.244336	−	0.116806i
$330$	−14.3456	−	19.3928i	−0.789701	−	1.06754i
$331$	−18.8095	+	18.8095i	−1.03386	+	1.03386i	−0.0344549	+	0.999406i	$0.510969\pi$
$331$	−18.8095	+	18.8095i	−1.03386	+	1.03386i	−0.999406	+	0.0344549i	$0.989031\pi$
$332$	0.354747	−	0.354747i	0.0194693	−	0.0194693i
$333$	−0.471700	−	4.91357i	−0.0258490	−	0.269262i
$334$	−1.09361	−	0.452987i	−0.0598395	−	0.0247864i
$335$	−3.28969	+	1.36264i	−0.179735	+	0.0744487i
$336$	−3.79651	−	2.56642i	−0.207117	−	0.140010i
$337$	−2.38017	−	5.74623i	−0.129656	−	0.313017i	0.845698	−	0.533661i	$-0.179184\pi$
$337$	−2.38017	−	5.74623i	−0.129656	−	0.313017i	−0.975354	+	0.220644i	$0.929184\pi$
$338$	−11.1943	+	11.1943i	−0.608887	+	0.608887i
$339$	2.87496	−	4.78319i	0.156147	−	0.259787i
$340$	3.57575	+	9.00768i	0.193922	+	0.488510i
$341$	−48.0744			−2.60338
$342$	−3.57661	+	11.6866i	−0.193401	+	0.631937i
$343$	18.0199	−	4.27603i	0.972981	−	0.230884i
$344$	8.28958			0.446944
$345$	3.59585	−	24.0368i	0.193594	−	1.29410i
$346$	9.11111	+	3.77394i	0.489816	+	0.202889i
$347$	−5.42421	+	13.0952i	−0.291187	+	0.702987i	−0.999997	−	0.00241195i	$-0.999232\pi$
$347$	−5.42421	+	13.0952i	−0.291187	+	0.702987i	0.708810	+	0.705399i	$0.249232\pi$
$348$	3.18175	+	12.7691i	0.170559	+	0.684495i
$349$	−20.3612	−	20.3612i	−1.08991	−	1.08991i	−0.995537	−	0.0943718i	$-0.969916\pi$
$349$	−20.3612	−	20.3612i	−1.08991	−	1.08991i	−0.0943718	−	0.995537i	$-0.530084\pi$
$350$	−1.25307	−	0.599034i	−0.0669793	−	0.0320197i
$351$	12.0223	−	25.1774i	0.641704	−	1.34387i
$352$	−5.47402	+	2.26741i	−0.291766	+	0.120854i
$353$		−	19.4872i		−	1.03720i	−0.855018	−	0.518599i	$-0.826454\pi$
$353$		−	19.4872i		−	1.03720i	0.855018	−	0.518599i	$-0.173546\pi$
$354$	−11.7350	−	1.75553i	−0.623707	−	0.0933052i
$355$	8.40033	−	8.40033i	0.445843	−	0.445843i
$356$	12.9846			0.688183
$357$	−15.4950	−	10.8123i	−0.820081	−	0.572247i
$358$	17.1411			0.905933
$359$	−11.0834	+	11.0834i	−0.584961	+	0.584961i	−0.936263	−	0.351301i	$-0.885739\pi$
$359$	−11.0834	+	11.0834i	−0.584961	+	0.584961i	0.351301	+	0.936263i	$0.385739\pi$
$360$	−5.43987	−	4.48691i	−0.286706	−	0.236481i
$361$			2.40358i			0.126504i
$362$	−19.5197	+	8.08533i	−1.02593	+	0.424956i
$363$	33.5670	−	24.8308i	1.76181	−	1.30328i
$364$	−12.8170	−	6.12720i	−0.671792	−	0.321153i
$365$	−15.1583	−	15.1583i	−0.793423	−	0.793423i
$366$	1.37840	−	0.343463i	0.0720499	−	0.0179531i
$367$	−5.32202	+	12.8485i	−0.277807	+	0.670686i	−0.999774	−	0.0212415i	$-0.993238\pi$
$367$	−5.32202	+	12.8485i	−0.277807	+	0.670686i	0.721967	+	0.691927i	$0.243238\pi$
$368$	−5.51535	−	2.28453i	−0.287507	−	0.119089i
$369$	17.9167	+	14.7780i	0.932706	+	0.769314i
$370$	−3.86752			−0.201063
$371$	1.37086	+	3.88201i	0.0711714	+	0.201544i
$372$	−13.6365	+	3.39789i	−0.707020	+	0.176172i
$373$	30.0648			1.55670			0.778348	−	0.627833i	$-0.216058\pi$
$373$	30.0648			1.55670			0.778348	+	0.627833i	$0.216058\pi$
$374$	−22.7059	+	9.01350i	−1.17410	+	0.466077i
$375$	15.6153	+	9.38568i	0.806371	+	0.484674i
$376$	−1.31285	+	1.31285i	−0.0677052	+	0.0677052i
$377$	15.6117	+	37.6899i	0.804043	+	1.94113i
$378$	13.6705	+	1.45491i	0.703136	+	0.0748327i
$379$	−21.3314	+	8.83574i	−1.09572	+	0.453861i	−0.855997	−	0.516980i	$-0.827056\pi$
$379$	−21.3314	+	8.83574i	−1.09572	+	0.453861i	−0.239721	+	0.970842i	$0.577056\pi$
$380$	8.84681	+	3.66447i	0.453832	+	0.187983i
$381$	−9.12045	−	12.3293i	−0.467255	−	0.631648i
$382$	−1.61751	+	1.61751i	−0.0827590	+	0.0827590i
$383$	−6.03339	+	6.03339i	−0.308292	+	0.308292i	−0.844247	−	0.535955i	$-0.819952\pi$
$383$	−6.03339	+	6.03339i	−0.308292	+	0.308292i	0.535955	+	0.844247i	$0.319952\pi$
$384$	−1.39247	+	1.03006i	−0.0710591	+	0.0525652i
$385$	15.8923	−	33.2438i	0.809947	−	1.69426i
$386$	−1.03302	−	2.49394i	−0.0525794	−	0.126938i
$387$	−21.9612	+	11.6689i	−1.11635	+	0.593162i
$388$	−1.56199	+	0.646996i	−0.0792979	+	0.0328463i
$389$	−0.632878	+	0.632878i	−0.0320882	+	0.0320882i	−0.722969	−	0.690881i	$-0.757223\pi$
$389$	−0.632878	+	0.632878i	−0.0320882	+	0.0320882i	0.690881	+	0.722969i	$0.257223\pi$
$390$	−18.7363	−	11.2616i	−0.948749	−	0.570251i
$391$	−22.5984	−	9.75511i	−1.14285	−	0.493337i
$392$	0.743920	−	6.96036i	0.0375736	−	0.351551i
$393$	−2.08836	−	8.38107i	−0.105344	−	0.422769i
$394$	−3.71607	−	8.97138i	−0.187213	−	0.451972i
$395$		−	24.0290i		−	1.20903i
$396$	11.3103	−	13.7125i	0.568364	−	0.689078i
$397$	17.5497	+	7.26932i	0.880794	+	0.364837i	0.776805	−	0.629742i	$-0.216839\pi$
$397$	17.5497	+	7.26932i	0.880794	+	0.364837i	0.103989	+	0.994578i	$0.466839\pi$
$398$	−11.1265	−	4.60877i	−0.557723	−	0.231017i
$399$	−18.3295	+	3.54346i	−0.917620	+	0.177395i
$400$	−0.371197	+	0.371197i	−0.0185598	+	0.0185598i
$401$	−0.0106900	+	0.0258079i	−0.000533832	+	0.00128878i	−0.924146	−	0.382039i	$-0.875222\pi$
$401$	−0.0106900	+	0.0258079i	−0.000533832	+	0.00128878i	0.923612	+	0.383328i	$0.125222\pi$
$402$	−1.56041	−	2.10941i	−0.0778264	−	0.105208i
$403$	−40.2503	+	16.6722i	−2.00501	+	0.830502i
$404$			8.13441i			0.404702i
$405$	20.7276	+	4.22947i	1.02996	+	0.210164i
$406$	−14.9501	+	13.4374i	−0.741963	+	0.666888i
$407$		−	9.74898i		−	0.483239i
$408$	−5.80356	+	4.16157i	−0.287319	+	0.206028i
$409$		−	6.91010i		−	0.341682i	−0.985299	−	0.170841i	$-0.945351\pi$
$409$		−	6.91010i		−	0.341682i	0.985299	−	0.170841i	$-0.0546485\pi$
$410$	12.8672	−	12.8672i	0.635464	−	0.635464i
$411$	−25.4708	−	3.81038i	−1.25638	−	0.187952i
$412$	7.03501			0.346590
$413$	−6.03523	−	17.0906i	−0.296974	−	0.840975i
$414$	17.8273	−	1.71141i	0.876166	−	0.0841114i
$415$	1.08947	+	0.451271i	0.0534797	+	0.0221520i
$416$	−3.79678	+	3.79678i	−0.186152	+	0.186152i
$417$	2.99269	+	12.0104i	0.146553	+	0.588151i
$418$	−9.23715	+	22.3005i	−0.451804	+	1.09075i
$419$	−0.884988	+	2.13655i	−0.0432345	+	0.104377i	−0.944022	−	0.329884i	$-0.892990\pi$
$419$	−0.884988	+	2.13655i	−0.0432345	+	0.104377i	0.900787	+	0.434261i	$0.142990\pi$
$420$	2.15826	−	10.5530i	0.105312	−	0.514934i
$421$		−	12.4741i		−	0.607953i	−0.952680	−	0.303976i	$-0.901686\pi$
$421$		−	12.4741i		−	0.607953i	0.952680	−	0.303976i	$-0.0983144\pi$
$422$	10.9121	−	4.51995i	0.531194	−	0.220028i
$423$	1.63003	−	5.32611i	0.0792546	−	0.258964i
$424$	1.55606			0.0755689
$425$	−1.55298	+	1.50765i	−0.0753307	+	0.0731318i
$426$	7.50302	+	4.50973i	0.363522	+	0.218497i
$427$	1.45054	+	1.61384i	0.0701966	+	0.0780990i
$428$	−4.84323	+	2.00613i	−0.234106	+	0.0969701i
$429$	28.3874	−	47.2292i	1.37056	−	2.28025i
$430$	7.45653	+	18.0017i	0.359586	+	0.868117i
$431$	22.0300	+	9.12512i	1.06115	+	0.439541i	0.843858	−	0.536566i	$-0.180279\pi$
$431$	22.0300	+	9.12512i	1.06115	+	0.439541i	0.217289	+	0.976107i	$0.430279\pi$
$432$	2.23902	−	4.68901i	0.107725	−	0.225600i
$433$	−13.9525	−	13.9525i	−0.670516	−	0.670516i	0.287319	−	0.957835i	$-0.407236\pi$
$433$	−13.9525	−	13.9525i	−0.670516	−	0.670516i	−0.957835	+	0.287319i	$0.907236\pi$
$434$	−14.3502	−	15.9657i	−0.688833	−	0.766379i
$435$	−24.8673	+	18.3953i	−1.19230	+	0.881989i
$436$	−3.02326	+	7.29879i	−0.144788	+	0.349549i
$437$	−22.4688	+	9.30688i	−1.07483	+	0.445209i
$438$	8.13777	−	13.5391i	0.388838	−	0.646925i
$439$	−28.0103	+	11.6022i	−1.33686	+	0.553745i	−0.932604	−	0.360901i	$-0.882469\pi$
$439$	−28.0103	+	11.6022i	−1.33686	+	0.553745i	−0.404255	+	0.914646i	$0.632469\pi$
$440$	−9.84783	−	9.84783i	−0.469477	−	0.469477i
$441$	7.82695	+	19.4869i	0.372712	+	0.927947i
$442$	−15.8847	+	15.4210i	−0.755556	+	0.733500i
$443$		−	30.3350i		−	1.44126i	−0.693319	−	0.720630i	$-0.743852\pi$
$443$		−	30.3350i		−	1.44126i	0.693319	−	0.720630i	$-0.256148\pi$
$444$	−0.689055	−	2.76534i	−0.0327011	−	0.131237i
$445$	11.6797	+	28.1974i	0.553673	+	1.33668i
$446$			5.37045i			0.254298i
$447$	−5.61720	+	37.5487i	−0.265684	+	1.77599i
$448$	−2.38702	−	1.14112i	−0.112776	−	0.0539129i
$449$	−9.76445	+	23.5735i	−0.460813	+	1.11250i	0.507251	+	0.861798i	$0.330662\pi$
$449$	−9.76445	+	23.5735i	−0.460813	+	1.11250i	−0.968064	+	0.250702i	$0.919338\pi$
$450$	0.460875	−	1.50591i	0.0217259	−	0.0709893i
$451$	32.4347	+	32.4347i	1.52729	+	1.52729i
$452$	1.23302	−	2.97676i	0.0579962	−	0.140015i
$453$	11.8682	−	8.77939i	0.557618	−	0.412492i
$454$	−2.41386	−	5.82758i	−0.113288	−	0.273502i
$455$	1.77688	−	33.3448i	0.0833013	−	1.56323i
$456$	−1.04397	+	6.97850i	−0.0488882	+	0.326798i
$457$	−26.6848	−	26.6848i	−1.24826	−	1.24826i	−0.956488	−	0.291773i	$-0.905755\pi$
$457$	−26.6848	−	26.6848i	−1.24826	−	1.24826i	−0.291773	−	0.956488i	$-0.594245\pi$
$458$	21.5464			1.00680
$459$	9.51703	−	19.1944i	0.444217	−	0.895919i
$460$		−	14.0321i		−	0.654248i
$461$	2.00831	+	2.00831i	0.0935363	+	0.0935363i	0.752327	−	0.658790i	$-0.228932\pi$
$461$	2.00831	+	2.00831i	0.0935363	+	0.0935363i	−0.658790	+	0.752327i	$0.728932\pi$
$462$	26.6013	+	5.44040i	1.23760	+	0.253110i
$463$			37.3051i			1.73371i	0.498558	+	0.866857i	$0.333863\pi$
$463$			37.3051i			1.73371i	−0.498558	+	0.866857i	$0.666137\pi$
$464$	2.90750	+	7.01932i	0.134977	+	0.325864i
$465$	−19.6450	−	26.5566i	−0.911013	−	1.23153i
$466$	−19.9222	−	8.25203i	−0.922876	−	0.382268i
$467$	12.3119	−	12.3119i	0.569727	−	0.569727i	−0.362325	−	0.932052i	$-0.618017\pi$
$467$	12.3119	−	12.3119i	0.569727	−	0.569727i	0.932052	+	0.362325i	$0.118017\pi$
$468$	4.71405	−	15.4032i	0.217907	−	0.712011i
$469$	1.72865	−	3.61602i	0.0798217	−	0.166972i
$470$	−4.03191	−	1.67007i	−0.185978	−	0.0770346i
$471$	−1.92404	+	12.8615i	−0.0886553	+	0.592625i
$472$	−6.85059			−0.315324
$473$	−45.3774	+	18.7959i	−2.08645	+	0.864237i
$474$	17.1811	−	4.28112i	0.789156	−	0.196638i
$475$			2.13859i			0.0981250i
$476$	−9.77116	−	4.85021i	−0.447860	−	0.222309i
$477$	−4.12239	+	2.19039i	−0.188751	+	0.100291i
$478$	15.8424	+	15.8424i	0.724614	+	0.724614i
$479$	1.86302	+	4.49774i	0.0851237	+	0.205507i	0.960710	−	0.277556i	$-0.0895244\pi$
$479$	1.86302	+	4.49774i	0.0851237	+	0.205507i	−0.875586	+	0.483063i	$0.839524\pi$
$480$	−3.48942	−	2.09734i	−0.159269	−	0.0957298i
$481$	−3.38095	−	8.16233i	−0.154158	−	0.372170i
$482$	−2.07429	+	5.00778i	−0.0944814	+	0.228098i
$483$	15.0760	+	22.8279i	0.685981	+	1.03871i
$484$	17.0456	−	17.0456i	0.774799	−	0.774799i
$485$	−2.81003	−	2.81003i	−0.127597	−	0.127597i
$486$	0.668786	+	15.5741i	0.0303367	+	0.706456i
$487$	7.10307	−	17.1483i	0.321871	−	0.777065i	−0.677275	−	0.735730i	$-0.736839\pi$
$487$	7.10307	−	17.1483i	0.321871	−	0.777065i	0.999145	−	0.0413345i	$-0.0131609\pi$
$488$	0.757721	−	0.313858i	0.0343004	−	0.0142077i
$489$	−10.7380	+	17.8652i	−0.485588	+	0.807892i
$490$	15.7843	−	4.64539i	0.713060	−	0.209857i
$491$	−10.4959	+	10.4959i	−0.473675	+	0.473675i	−0.903102	−	0.429427i	$-0.858716\pi$
$491$	−10.4959	+	10.4959i	−0.473675	+	0.473675i	0.429427	+	0.903102i	$0.358716\pi$
$492$	11.4927	+	6.90776i	0.518131	+	0.311426i
$493$	11.5580	+	29.1158i	0.520545	+	1.31131i
$494$			21.8745i			0.984179i
$495$	39.9517	+	12.2270i	1.79569	+	0.549562i
$496$	−7.49615	+	3.10501i	−0.336587	+	0.139419i
$497$	−0.711558	+	13.3531i	−0.0319177	+	0.598966i
$498$	−0.128562	+	0.859386i	−0.00576101	+	0.0385100i
$499$	2.22049	−	5.36073i	0.0994026	−	0.239979i	−0.866353	−	0.499432i	$-0.833542\pi$
$499$	2.22049	−	5.36073i	0.0994026	−	0.239979i	0.965756	+	0.259453i	$0.0835422\pi$
$500$	9.71801	+	4.02533i	0.434603	+	0.180018i
$501$	1.98942	−	0.495715i	0.0888807	−	0.0221469i
$502$	8.40297	+	8.40297i	0.375043	+	0.375043i
$503$	14.1472	+	5.85995i	0.630791	+	0.261282i	0.675089	−	0.737736i	$-0.264105\pi$
$503$	14.1472	+	5.85995i	0.630791	+	0.261282i	−0.0442980	+	0.999018i	$0.514105\pi$
$504$	7.93010	−	0.336982i	0.353235	−	0.0150103i
$505$	−17.6647	+	7.31695i	−0.786068	+	0.325600i
$506$	35.3711			1.57244
$507$	4.05686	−	27.1185i	0.180171	−	1.20437i
$508$	−6.26091	−	6.26091i	−0.277783	−	0.277783i
$509$	21.1819			0.938871			0.469436	−	0.882967i	$-0.344457\pi$
$509$	21.1819			0.938871			0.469436	+	0.882967i	$0.344457\pi$
$510$	−14.2576	−	8.85966i	−0.631337	−	0.392312i
$511$	24.0955	+	1.28400i	1.06592	+	0.0568008i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−7.05758	−	19.9573i	−0.311600	−	0.881136i
$514$	11.9682			0.527893
$515$	6.32803	+	15.2772i	0.278846	+	0.673194i
$516$	−11.5430	+	8.53880i	−0.508152	+	0.375900i
$517$	4.20980	−	10.1634i	0.185147	−	0.446984i
$518$	3.23768	−	2.91008i	0.142255	−	0.127861i
$519$	−16.5743	+	4.12992i	−0.727533	+	0.181283i
$520$	−11.6603	−	4.82986i	−0.511338	−	0.211803i
$521$	9.50660	−	22.9510i	0.416492	−	1.00550i	−0.566864	−	0.823811i	$-0.691844\pi$
$521$	9.50660	−	22.9510i	0.416492	−	1.00550i	0.983356	−	0.181689i	$-0.0581564\pi$
$522$	−17.5835	−	14.5032i	−0.769607	−	0.634786i
$523$	−18.9549			−0.828842			−0.414421	−	0.910085i	$-0.636016\pi$
$523$	−18.9549			−0.828842			−0.414421	+	0.910085i	$0.636016\pi$
$524$	−1.90835	−	4.60717i	−0.0833668	−	0.201265i
$525$	2.36190	−	0.456604i	0.103082	−	0.0199278i
$526$	−10.8984			−0.475193
$527$	−31.0936	+	12.3431i	−1.35446	+	0.537675i
$528$	5.28682	−	8.79589i	0.230079	−	0.382792i
$529$	8.93649	+	8.93649i	0.388543	+	0.388543i
$530$	1.39968	+	3.37914i	0.0607984	+	0.146780i
$531$	18.1489	−	9.64326i	0.787595	−	0.418482i
$532$	−10.1634	+	3.58900i	−0.440638	+	0.155603i
$533$	38.4043	+	15.9076i	1.66347	+	0.689033i
$534$	−18.0807	+	13.3750i	−0.782427	+	0.578792i
$535$	−8.71303	−	8.71303i	−0.376697	−	0.376697i
$536$	−1.07118	−	1.07118i	−0.0462677	−	0.0462677i
$537$	−23.8684	+	17.6564i	−1.03000	+	0.761929i
$538$	−11.4406	−	4.73887i	−0.493241	−	0.204307i
$539$	11.7098	+	39.7879i	0.504376	+	1.71379i
$540$	12.1967	+	0.644464i	0.524860	+	0.0277333i
$541$	10.2826	+	24.8244i	0.442084	+	1.06729i	0.975216	+	0.221254i	$0.0710148\pi$
$541$	10.2826	+	24.8244i	0.442084	+	1.06729i	−0.533132	+	0.846032i	$0.678985\pi$
$542$	−7.26057	−	7.26057i	−0.311868	−	0.311868i
$543$	18.8522	−	31.3651i	0.809025	−	1.34601i
$544$	−2.95833	+	2.87198i	−0.126838	+	0.123135i
$545$	−18.5695			−0.795429
$546$	24.1586	−	4.67036i	1.03389	−	0.199873i
$547$	12.2863	+	29.6618i	0.525326	+	1.26825i	0.934556	+	0.355817i	$0.115797\pi$
$547$	12.2863	+	29.6618i	0.525326	+	1.26825i	−0.409230	+	0.912431i	$0.634203\pi$
$548$	−14.8692			−0.635182
$549$	−1.56559	+	1.89810i	−0.0668176	+	0.0810088i
$550$	1.19028	−	2.87360i	0.0507538	−	0.122531i
$551$	28.5958	+	11.8448i	1.21822	+	0.504604i
$552$	10.0332	−	2.50002i	0.427040	−	0.106408i
$553$	18.0804	+	20.1158i	0.768856	+	0.855410i
$554$	−8.97704	+	21.6725i	−0.381398	+	0.920775i
$555$	5.38540	−	3.98379i	0.228597	−	0.169102i
$556$	2.73474	+	6.60225i	0.115979	+	0.279998i
$557$	29.5709			1.25296			0.626479	−	0.779438i	$-0.284495\pi$
$557$	29.5709			1.25296			0.626479	+	0.779438i	$0.284495\pi$
$558$	15.4884	−	18.7779i	0.655675	−	0.794933i
$559$	−31.4737	+	31.4737i	−1.33120	+	1.33120i
$560$	0.330923	−	6.21008i	0.0139841	−	0.262424i
$561$	22.3328	−	35.9396i	0.942894	−	1.51737i
$562$	−19.4582			−0.820796
$563$	17.1122	+	17.1122i	0.721194	+	0.721194i	0.968848	−	0.247655i	$-0.0796599\pi$
$563$	17.1122	+	17.1122i	0.721194	+	0.721194i	−0.247655	+	0.968848i	$0.579660\pi$
$564$	0.475785	−	3.18043i	0.0200341	−	0.133920i
$565$	7.57344			0.318617
$566$	−10.6909	+	4.42830i	−0.449371	+	0.186136i
$567$	−20.5344	+	12.0556i	−0.862365	+	0.506287i
$568$	4.66942	+	1.93414i	0.195924	+	0.0811545i
$569$	13.2216	+	13.2216i	0.554279	+	0.554279i	0.927673	−	0.373394i	$-0.121806\pi$
$569$	13.2216	+	13.2216i	0.554279	+	0.554279i	−0.373394	+	0.927673i	$0.621806\pi$
$570$	−16.0935	+	4.01012i	−0.674084	+	0.167965i
$571$	7.77314	+	3.21974i	0.325296	+	0.134742i	0.539354	−	0.842079i	$-0.318668\pi$
$571$	7.77314	+	3.21974i	0.325296	+	0.134742i	−0.214059	+	0.976821i	$0.568668\pi$
$572$	12.1748	−	29.3925i	0.509053	−	1.22896i
$573$	0.586194	−	3.91847i	0.0244886	−	0.163696i
$574$	−1.08993	+	20.4535i	−0.0454926	+	0.853711i
$575$	2.89529	−	1.19927i	0.120742	−	0.0500130i
$576$	0.877938	−	2.86866i	0.0365808	−	0.119528i
$577$		−	42.0634i		−	1.75112i	−0.483107	−	0.875561i	$-0.660492\pi$
$577$		−	42.0634i		−	1.75112i	0.483107	−	0.875561i	$-0.339508\pi$
$578$	−12.3716	+	11.6595i	−0.514589	+	0.484972i
$579$	4.00736	+	2.40865i	0.166540	+	0.100100i
$580$	−12.6278	+	12.6278i	−0.524342	+	0.524342i
$581$	−1.25160	+	0.441977i	−0.0519249	+	0.0183363i
$582$	1.50857	−	2.50987i	0.0625323	−	0.104037i
$583$	−8.51790	+	3.52823i	−0.352776	+	0.146124i
$584$	3.49013	−	8.42592i	0.144423	−	0.348667i
$585$	37.6898	−	3.61820i	1.55828	−	0.149594i
$586$	12.0378	+	12.0378i	0.497277	+	0.497277i
$587$	−11.6620	+	11.6620i	−0.481341	+	0.481341i	−0.905560	−	0.424219i	$-0.860549\pi$
$587$	−11.6620	+	11.6620i	−0.481341	+	0.481341i	0.424219	+	0.905560i	$0.360549\pi$
$588$	6.13373	+	10.4584i	0.252951	+	0.431296i
$589$	−12.6494	+	30.5383i	−0.521209	+	1.25831i
$590$	−6.16214	−	14.8767i	−0.253691	−	0.612465i
$591$	14.4156	+	8.66458i	0.592978	+	0.356413i
$592$	−0.629663	−	1.52014i	−0.0258790	−	0.0624774i
$593$	16.6268	+	16.6268i	0.682782	+	0.682782i	0.960626	−	0.277844i	$-0.0896199\pi$
$593$	16.6268	+	16.6268i	0.682782	+	0.682782i	−0.277844	+	0.960626i	$0.589620\pi$
$594$	−1.62452	+	30.7445i	−0.0666550	+	1.26146i
$595$	1.74349	−	25.5818i	0.0714761	−	1.04875i
$596$			21.9200i			0.897878i
$597$	20.2407	−	5.04349i	0.828396	−	0.206416i
$598$	29.6144	−	12.2667i	1.21102	−	0.501622i
$599$	23.4765			0.959222			0.479611	−	0.877481i	$-0.340778\pi$
$599$	23.4765			0.959222			0.479611	+	0.877481i	$0.340778\pi$
$600$	0.134524	−	0.899237i	0.00549191	−	0.0367112i
$601$	−12.0006	−	4.97080i	−0.489514	−	0.202763i	0.124253	−	0.992251i	$-0.460346\pi$
$601$	−12.0006	−	4.97080i	−0.489514	−	0.202763i	−0.613767	+	0.789487i	$0.710346\pi$
$602$	−19.7874	−	9.45942i	−0.806473	−	0.385537i
$603$	4.34565	+	1.32996i	0.176969	+	0.0541603i
$604$	6.02678	−	6.02678i	0.245226	−	0.245226i
$605$	52.3487	+	21.6836i	2.12828	+	0.881562i
$606$	−8.37896	−	11.3269i	−0.340372	−	0.460124i
$607$	−14.5647	−	35.1622i	−0.591161	−	1.42719i	−0.882382	−	0.470533i	$-0.844062\pi$
$607$	−14.5647	−	35.1622i	−0.591161	−	1.42719i	0.291221	−	0.956656i	$-0.405938\pi$
$608$			4.07387i			0.165217i
$609$	6.97620	−	34.1108i	0.282690	−	1.38224i
$610$	1.36315	+	1.36315i	0.0551923	+	0.0551923i
$611$		−	9.96922i		−	0.403312i
$612$	3.79461	−	11.7729i	0.153388	−	0.475891i
$613$	−36.8561			−1.48860			−0.744302	−	0.667843i	$-0.767218\pi$
$613$	−36.8561			−1.48860			−0.744302	+	0.667843i	$0.767218\pi$
$614$	1.25605	+	1.25605i	0.0506899	+	0.0506899i
$615$	−4.66313	+	31.1711i	−0.188035	+	1.25694i
$616$	15.6540	+	0.834169i	0.630716	+	0.0336096i
$617$	5.58712	+	13.4885i	0.224929	+	0.543027i	0.995547	−	0.0942711i	$-0.0300521\pi$
$617$	5.58712	+	13.4885i	0.224929	+	0.543027i	−0.770617	+	0.637298i	$0.780052\pi$
$618$	−9.79603	+	7.24650i	−0.394054	+	0.291497i
$619$	−8.87140	+	21.4175i	−0.356572	+	0.860840i	0.639205	+	0.769036i	$0.279263\pi$
$619$	−8.87140	+	21.4175i	−0.356572	+	0.860840i	−0.995777	+	0.0918040i	$0.970737\pi$
$620$	−13.4857	−	13.4857i	−0.541597	−	0.541597i
$621$	−23.0611	+	20.7464i	−0.925412	+	0.832524i
$622$	8.51594	−	20.5593i	0.341458	−	0.824353i
$623$	−30.9945	−	14.8170i	−1.24177	−	0.593632i
$624$	1.37597	−	9.19782i	0.0550830	−	0.368208i
$625$			27.3492i			1.09397i
$626$	6.81435	+	16.4513i	0.272356	+	0.657526i
$627$	−10.1084	−	40.5675i	−0.403692	−	1.62011i
$628$			7.50820i			0.299610i
$629$	−2.50306	−	6.30546i	−0.0998034	−	0.251415i
$630$	7.86496	+	16.9179i	0.313347	+	0.674024i
$631$	−33.7116	−	33.7116i	−1.34204	−	1.34204i	−0.894028	−	0.448012i	$-0.852132\pi$
$631$	−33.7116	−	33.7116i	−1.34204	−	1.34204i	−0.448012	−	0.894028i	$-0.647868\pi$
$632$	9.44467	−	3.91211i	0.375689	−	0.155615i
$633$	−10.5390	+	17.5341i	−0.418886	+	0.696917i
$634$	31.9626	−	13.2394i	1.26940	−	0.525802i
$635$	7.96446	−	19.2279i	0.316060	−	0.763036i
$636$	−2.16676	+	1.60284i	−0.0859178	+	0.0635567i
$637$	23.6024	+	29.2514i	0.935163	+	1.15898i
$638$	−31.8314	−	31.8314i	−1.26022	−	1.26022i
$639$	−15.0930	+	1.44892i	−0.597071	+	0.0573185i
$640$	−2.17160	−	0.899506i	−0.0858400	−	0.0355561i
$641$	−14.0504	−	33.9205i	−0.554956	−	1.33978i	−0.913717	−	0.406352i	$-0.866801\pi$
$641$	−14.0504	−	33.9205i	−0.554956	−	1.33978i	0.358761	−	0.933429i	$-0.383199\pi$
$642$	4.67761	−	7.78231i	0.184610	−	0.307143i
$643$	27.0479	−	11.2036i	1.06666	−	0.441826i	0.220851	−	0.975307i	$-0.429116\pi$
$643$	27.0479	−	11.2036i	1.06666	−	0.441826i	0.845812	+	0.533481i	$0.179116\pi$
$644$	10.5583	+	11.7469i	0.416055	+	0.462892i
$645$	−28.9258	−	17.3860i	−1.13895	−	0.684575i
$646$	−0.248763	+	16.7952i	−0.00978747	+	0.660797i
$647$	3.96349			0.155821			0.0779104	−	0.996960i	$-0.475175\pi$
$647$	3.96349			0.155821			0.0779104	+	0.996960i	$0.475175\pi$
$648$	1.71221	+	8.83563i	0.0672620	+	0.347096i
$649$	37.5003	−	15.5331i	1.47201	−	0.609728i
$650$		−	2.81871i		−	0.110559i
$651$	36.4280	+	7.45010i	1.42772	+	0.291993i
$652$	−4.60531	+	11.1182i	−0.180358	+	0.435422i
$653$	1.15672	−	2.79258i	0.0452661	−	0.109282i	−0.899629	−	0.436655i	$-0.856163\pi$
$653$	1.15672	−	2.79258i	0.0452661	−	0.109282i	0.944895	+	0.327373i	$0.106163\pi$
$654$	−3.30842	−	13.2775i	−0.129370	−	0.519191i
$655$	8.28836	−	8.28836i	0.323853	−	0.323853i
$656$	7.15235	+	2.96260i	0.279252	+	0.115670i
$657$	2.61457	+	27.2352i	0.102004	+	1.06255i
$658$	4.63192	−	1.63568i	0.180571	−	0.0637653i
$659$	−0.0195045			−0.000759789			−0.000379894	−	1.00000i	$-0.500121\pi$
$659$	−0.0195045			−0.000759789			−0.000379894		1.00000i	$0.500121\pi$
$660$	23.8567	+	3.56890i	0.928620	+	0.138919i
$661$	−11.6303	+	11.6303i	−0.452368	+	0.452368i	−0.896140	−	0.443772i	$-0.853640\pi$
$661$	−11.6303	+	11.6303i	−0.452368	+	0.452368i	0.443772	+	0.896140i	$0.353640\pi$
$662$		−	26.6006i		−	1.03386i
$663$	6.23431	−	37.8354i	0.242120	−	1.46941i
$664$			0.501688i			0.0194693i
$665$	−16.9359	−	18.8424i	−0.656745	−	0.730678i
$666$	3.80796	+	3.14088i	0.147556	+	0.121707i
$667$		−	45.3562i		−	1.75620i
$668$	1.09361	−	0.452987i	0.0423129	−	0.0175266i
$669$	−5.53191	−	7.47819i	−0.213876	−	0.289123i
$670$	1.36264	−	3.28969i	0.0526432	−	0.127092i
$671$	−3.43613	+	3.43613i	−0.132650	+	0.132650i
$672$	4.49927	−	0.869802i	0.173563	−	0.0335533i
$673$	−25.5749	−	10.5935i	−0.985839	−	0.408348i	−0.169254	−	0.985572i	$-0.554136\pi$
$673$	−25.5749	−	10.5935i	−0.985839	−	0.408348i	−0.816586	+	0.577224i	$0.804136\pi$
$674$	5.74623	+	2.38017i	0.221337	+	0.0916806i
$675$	0.909428	+	2.57166i	0.0350039	+	0.0989833i
$676$		−	15.8311i		−	0.608887i
$677$	−0.965419	−	2.33073i	−0.0371041	−	0.0895771i	0.904241	−	0.427022i	$-0.140437\pi$
$677$	−0.965419	−	2.33073i	−0.0371041	−	0.0895771i	−0.941345	+	0.337445i	$0.890437\pi$
$678$	1.34932	+	5.41513i	0.0518203	+	0.207967i
$679$	4.46679	+	0.238026i	0.171420	+	0.00913462i
$680$	−8.89782	−	3.84095i	−0.341216	−	0.147294i
$681$	9.36401	+	5.62829i	0.358830	+	0.215677i
$682$	33.9937	−	33.9937i	1.30169	−	1.30169i
$683$	3.08077	−	1.27610i	0.117882	−	0.0488284i	−0.322963	−	0.946412i	$-0.604679\pi$
$683$	3.08077	−	1.27610i	0.117882	−	0.0488284i	0.440845	+	0.897583i	$0.354679\pi$
$684$	−5.73460	−	10.7927i	−0.219268	−	0.412669i
$685$	−13.3750	−	32.2900i	−0.511031	−	1.23374i
$686$	−9.71836	+	15.7656i	−0.371049	+	0.601933i
$687$	−30.0027	+	22.1942i	−1.14467	+	0.846760i
$688$	−5.86162	+	5.86162i	−0.223472	+	0.223472i
$689$	−5.90802	+	5.90802i	−0.225077	+	0.225077i
$690$	14.4539	+	19.5392i	0.550251	+	0.743845i
$691$	−10.7796	−	4.46505i	−0.410075	−	0.169859i	0.168103	−	0.985769i	$-0.446236\pi$
$691$	−10.7796	−	4.46505i	−0.410075	−	0.169859i	−0.578178	+	0.815911i	$0.696236\pi$
$692$	−9.11111	+	3.77394i	−0.346352	+	0.143464i
$693$	−42.6454	+	19.8255i	−1.61997	+	0.753107i
$694$	−5.42421	−	13.0952i	−0.205900	−	0.497087i
$695$	−11.8775	+	11.8775i	−0.450540	+	0.450540i
$696$	−11.2789	−	6.77928i	−0.427527	−	0.256968i
$697$	29.3058	+	12.6505i	1.11004	+	0.479173i
$698$	28.7951			1.08991
$699$	36.2411	−	9.03040i	1.37076	−	0.341561i
$700$	1.30963	−	0.462472i	0.0494995	−	0.0174798i
$701$	−36.9852			−1.39691			−0.698456	−	0.715653i	$-0.746129\pi$
$701$	−36.9852			−1.39691			−0.698456	+	0.715653i	$0.746129\pi$
$702$	9.30206	+	26.3042i	0.351084	+	0.992788i
$703$	−6.19285	−	2.56516i	−0.233568	−	0.0967470i
$704$	2.26741	−	5.47402i	0.0854564	−	0.206310i
$705$	7.33458	−	1.82760i	0.276236	−	0.0688314i
$706$	13.7795	+	13.7795i	0.518599	+	0.518599i
$707$	9.28235	−	19.4170i	0.349099	−	0.730250i
$708$	9.53923	−	7.05654i	0.358506	−	0.265201i
$709$	−5.24881	+	2.17413i	−0.197123	+	0.0816511i	−0.479061	−	0.877782i	$-0.659023\pi$
$709$	−5.24881	+	2.17413i	−0.197123	+	0.0816511i	0.281938	+	0.959433i	$0.409023\pi$
$710$			11.8799i			0.445843i
$711$	−19.5144	+	23.6590i	−0.731846	+	0.887281i
$712$	−9.18151	+	9.18151i	−0.344092	+	0.344092i
$713$	48.4373			1.81399
$714$	18.6021	−	3.31115i	0.696164	−	0.123917i
$715$	74.7801			2.79662
$716$	−12.1206	+	12.1206i	−0.452967	+	0.452967i
$717$	−38.3787	−	5.74136i	−1.43328	−	0.214415i
$718$		−	15.6743i		−	0.584961i
$719$	−42.1357	+	17.4532i	−1.57140	+	0.650894i	−0.987022	−	0.160588i	$-0.948661\pi$
$719$	−42.1357	+	17.4532i	−1.57140	+	0.650894i	−0.584377	+	0.811483i	$0.698661\pi$
$720$	7.01929	−	0.673848i	0.261594	−	0.0251128i
$721$	−16.7927	−	8.02779i	−0.625392	−	0.298971i
$722$	−1.69959	−	1.69959i	−0.0632520	−	0.0632520i
$723$	−2.26995	−	9.10983i	−0.0844203	−	0.338798i
$724$	8.08533	−	19.5197i	0.300489	−	0.725445i
$725$	−3.68481	−	1.52630i	−0.136850	−	0.0566852i
$726$	−6.17740	+	41.2934i	−0.229265	+	1.53254i
$727$	25.6052			0.949645			0.474823	−	0.880081i	$-0.342512\pi$
$727$	25.6052			0.949645			0.474823	+	0.880081i	$0.342512\pi$
$728$	13.3956	−	4.73039i	0.496472	−	0.175320i
$729$	−16.9736	−	20.9976i	−0.628651	−	0.777687i
$730$	21.4371			0.793423
$731$	−24.5234	+	23.8075i	−0.907029	+	0.880552i
$732$	−0.731809	+	1.21754i	−0.0270484	+	0.0450015i
$733$	−16.5350	+	16.5350i	−0.610736	+	0.610736i	−0.943138	−	0.332402i	$-0.892141\pi$
$733$	−16.5350	+	16.5350i	−0.610736	+	0.610736i	0.332402	+	0.943138i	$0.392141\pi$
$734$	−5.32202	−	12.8485i	−0.196439	−	0.474246i
$735$	−17.1941	+	22.7273i	−0.634212	+	0.838311i
$736$	5.51535	−	2.28453i	0.203298	−	0.0842089i
$737$	8.29244	+	3.43484i	0.305456	+	0.126524i
$738$	−23.1187	+	2.21938i	−0.851010	+	0.0816965i
$739$	13.6325	−	13.6325i	0.501481	−	0.501481i	−0.410417	−	0.911898i	$-0.634617\pi$
$739$	13.6325	−	13.6325i	0.501481	−	0.501481i	0.911898	+	0.410417i	$0.134617\pi$
$740$	2.73475	−	2.73475i	0.100531	−	0.100531i
$741$	−22.5321	−	30.4595i	−0.827737	−	1.11896i
$742$	−3.71434	−	1.77565i	−0.136358	−	0.0651862i
$743$	6.19140	+	14.9474i	0.227140	+	0.548365i	0.995827	−	0.0912601i	$-0.0290895\pi$
$743$	6.19140	+	14.9474i	0.227140	+	0.548365i	−0.768687	+	0.639625i	$0.779089\pi$
$744$	7.23980	−	12.0451i	0.265424	−	0.441596i
$745$	−47.6014	+	19.7172i	−1.74398	+	0.722381i
$746$	−21.2590	+	21.2590i	−0.778348	+	0.778348i
$747$	−0.706203	−	1.32910i	−0.0258386	−	0.0486291i
$748$	9.68202	−	22.4290i	0.354010	−	0.820087i
$749$	13.8501	+	0.738045i	0.506072	+	0.0269676i
$750$	−17.6784	+	4.40502i	−0.645523	+	0.160849i
$751$	−5.88306	−	14.2030i	−0.214676	−	0.518274i	0.779455	−	0.626458i	$-0.215496\pi$
$751$	−5.88306	−	14.2030i	−0.214676	−	0.518274i	−0.994131	+	0.108185i	$0.965496\pi$
$752$		−	1.85665i		−	0.0677052i
$753$	−20.3565	−	3.04528i	−0.741831	−	0.110976i
$754$	−37.6899	−	15.6117i	−1.37259	−	0.568544i
$755$	18.5089	+	7.66663i	0.673607	+	0.279017i
$756$	−10.6953	+	8.63774i	−0.388984	+	0.314152i
$757$	38.2088	−	38.2088i	1.38872	−	1.38872i	0.560714	−	0.828010i	$-0.310527\pi$
$757$	38.2088	−	38.2088i	1.38872	−	1.38872i	0.828010	−	0.560714i	$-0.189473\pi$
$758$	8.83574	−	21.3314i	0.320928	−	0.774790i
$759$	−49.2531	+	36.4345i	−1.78778	+	1.32249i
$760$	−8.84681	+	3.66447i	−0.320908	+	0.132924i
$761$		−	26.0236i		−	0.943353i	−0.881772	−	0.471677i	$-0.843649\pi$
$761$		−	26.0236i		−	0.943353i	0.881772	−	0.471677i	$-0.156351\pi$
$762$	15.1672	+	2.26899i	0.549451	+	0.0821967i
$763$	15.5454	−	13.9724i	0.562780	−	0.505835i
$764$		−	2.28750i		−	0.0827590i
$765$	28.9793	−	2.34942i	1.04775	−	0.0849435i
$766$		−	8.53251i		−	0.308292i
$767$	26.0102	−	26.0102i	0.939173	−	0.939173i
$768$	0.256259	−	1.71299i	0.00924696	−	0.0618122i
$769$	25.7888			0.929967			0.464983	−	0.885319i	$-0.346060\pi$
$769$	25.7888			0.929967			0.464983	+	0.885319i	$0.346060\pi$
$770$	12.2694	+	34.7445i	0.442157	+	1.25210i
$771$	−16.6653	+	12.3280i	−0.600186	+	0.443981i
$772$	2.49394	+	1.03302i	0.0897587	+	0.0371793i
$773$	−8.04860	+	8.04860i	−0.289488	+	0.289488i	−0.836878	−	0.547390i	$-0.815622\pi$
$773$	−8.04860	+	8.04860i	−0.289488	+	0.289488i	0.547390	+	0.836878i	$0.315622\pi$
$774$	7.27774	−	23.7800i	0.261593	−	0.854755i
$775$	1.62998	−	3.93512i	0.0585506	−	0.141354i
$776$	0.646996	−	1.56199i	0.0232258	−	0.0560721i
$777$	−1.51080	+	7.38720i	−0.0541997	+	0.265014i
$778$		−	0.895025i		−	0.0320882i
$779$	29.1378	−	12.0693i	1.04397	−	0.432426i
$780$	21.2117	−	5.28543i	0.759500	−	0.189249i
$781$	−29.9460			−1.07155
$782$	22.8774	−	9.08154i	0.818093	−	0.324755i
$783$	39.4236	+	2.08312i	1.40888	+	0.0744447i
$784$	4.39569	+	5.44775i	0.156989	+	0.194562i
$785$	−16.3048	+	6.75367i	−0.581943	+	0.241049i
$786$	7.40301	+	4.44962i	0.264056	+	0.158713i
$787$	−0.538972	−	1.30119i	−0.0192123	−	0.0463825i	0.913982	−	0.405754i	$-0.132991\pi$
$787$	−0.538972	−	1.30119i	−0.0192123	−	0.0463825i	−0.933195	+	0.359372i	$0.882991\pi$
$788$	8.97138	+	3.71607i	0.319592	+	0.132379i
$789$	15.1757	−	11.2261i	0.540269	−	0.399658i
$790$	16.9911	+	16.9911i	0.604515	+	0.604515i
$791$	−6.34007	+	5.69856i	−0.225427	+	0.202617i
$792$	1.69859	+	17.6938i	0.0603568	+	0.628721i
$793$	−1.68525	+	4.06855i	−0.0598449	+	0.144478i
$794$	−17.5497	+	7.26932i	−0.622815	+	0.257979i
$795$	−5.42974	−	3.26358i	−0.192573	−	0.115747i
$796$	11.1265	−	4.60877i	0.394370	−	0.163353i
$797$	8.72874	+	8.72874i	0.309188	+	0.309188i	0.844594	−	0.535407i	$-0.179842\pi$
$797$	8.72874	+	8.72874i	0.309188	+	0.309188i	−0.535407	+	0.844594i	$0.679842\pi$
$798$	10.4553	−	15.4665i	0.370113	−	0.547508i
$799$	0.113373	−	7.65434i	0.00401085	−	0.270791i
$800$		−	0.524952i		−	0.0185598i
$801$	11.3997	−	37.2485i	0.402788	−	1.31611i
$802$	−0.0106900	−	0.0258079i	−0.000377476	−	0.000911308i
$803$			54.0372i			1.90693i
$804$	2.59496	+	0.388200i	0.0915171	+	0.0136907i
$805$	−16.0123	+	33.4948i	−0.564359	+	1.18054i
$806$	16.6722	−	40.2503i	0.587253	−	1.41775i
$807$	20.8121	−	5.18586i	0.732619	−	0.182551i
$808$	−5.75190	−	5.75190i	−0.202351	−	0.202351i
$809$	−10.8381	+	26.1655i	−0.381047	+	0.919929i	0.610717	+	0.791849i	$0.290881\pi$
$809$	−10.8381	+	26.1655i	−0.381047	+	0.919929i	−0.991764	+	0.128080i	$0.959119\pi$
$810$	−17.6473	+	11.6659i	−0.620063	+	0.409899i
$811$	−12.4044	−	29.9469i	−0.435578	−	1.05158i	−0.977459	−	0.211123i	$-0.932288\pi$
$811$	−12.4044	−	29.9469i	−0.435578	−	1.05158i	0.541882	−	0.840455i	$-0.317712\pi$
$812$	1.06965	−	20.0730i	0.0375375	−	0.704425i
$813$	17.5890	+	2.63127i	0.616872	+	0.0922827i
$814$	6.89357	+	6.89357i	0.241620	+	0.241620i
$815$	−28.2868			−0.990842
$816$	1.16107	−	7.04641i	0.0406455	−	0.246674i
$817$			33.7707i			1.18149i
$818$	4.88618	+	4.88618i	0.170841	+	0.170841i
$819$	−28.8294	+	31.3883i	−1.00738	+	1.09680i
$820$			18.1969i			0.635464i
$821$	−17.1888	−	41.4974i	−0.599892	−	1.44827i	−0.873691	−	0.486481i	$-0.838280\pi$
$821$	−17.1888	−	41.4974i	−0.599892	−	1.44827i	0.273799	−	0.961787i	$-0.411720\pi$
$822$	20.7049	−	15.3163i	0.722168	−	0.534216i
$823$	−14.7054	−	6.09116i	−0.512596	−	0.212324i	0.111365	−	0.993780i	$-0.464478\pi$
$823$	−14.7054	−	6.09116i	−0.512596	−	0.212324i	−0.623961	+	0.781455i	$0.714478\pi$
$824$	−4.97450	+	4.97450i	−0.173295	+	0.173295i
$825$	1.30256	+	5.22746i	0.0453492	+	0.181997i
$826$	16.3525	+	7.81735i	0.568975	+	0.272000i
$827$	29.4613	+	12.2033i	1.02447	+	0.424349i	0.830713	−	0.556701i	$-0.187933\pi$
$827$	29.4613	+	12.2033i	1.02447	+	0.424349i	0.193756	+	0.981050i	$0.437933\pi$
$828$	−11.3957	+	13.8160i	−0.396027	+	0.480139i
$829$	30.2985			1.05231			0.526155	−	0.850388i	$-0.323633\pi$
$829$	30.2985			1.05231			0.526155	+	0.850388i	$0.323633\pi$
$830$	−1.08947	+	0.451271i	−0.0378159	+	0.0156639i
$831$	−9.82379	−	39.4252i	−0.340783	−	1.36764i
$832$		−	5.36946i		−	0.186152i
$833$	17.7892	+	22.7276i	0.616360	+	0.787464i
$834$	−10.6088	−	6.37647i	−0.367352	−	0.220799i
$835$	1.96741	+	1.96741i	0.0680851	+	0.0680851i
$836$	−9.23715	−	22.3005i	−0.319474	−	0.771277i
$837$	−2.22463	+	42.1017i	−0.0768944	+	1.45525i
$838$	−0.884988	−	2.13655i	−0.0305714	−	0.0738059i
$839$	3.00626	−	7.25776i	0.103788	−	0.250566i	−0.863452	−	0.504431i	$-0.831702\pi$
$839$	3.00626	−	7.25776i	0.103788	−	0.250566i	0.967239	+	0.253866i	$0.0817021\pi$
$840$	5.93598	+	8.98822i	0.204811	+	0.310123i
$841$	−20.3112	+	20.3112i	−0.700387	+	0.700387i
$842$	8.82055	+	8.82055i	0.303976	+	0.303976i
$843$	27.0950	−	20.0432i	0.933201	−	0.690325i
$844$	−4.51995	+	10.9121i	−0.155583	+	0.375611i
$845$	34.3787	−	14.2401i	1.18266	−	0.489876i
$846$	2.61353	+	4.91873i	0.0898549	+	0.169110i
$847$	−60.1391	+	21.2370i	−2.06640	+	0.729711i
$848$	−1.10030	+	1.10030i	−0.0377845	+	0.0377845i
$849$	10.3253	−	17.1786i	0.354362	−	0.589566i
$850$	0.0320552	−	2.16419i	0.00109949	−	0.0742313i
$851$			9.82258i			0.336714i
$852$	−8.49430	+	2.11657i	−0.291010	+	0.0725126i
$853$	−27.3508	+	11.3291i	−0.936473	+	0.387900i	−0.798130	−	0.602485i	$-0.794177\pi$
$853$	−27.3508	+	11.3291i	−0.936473	+	0.387900i	−0.138342	+	0.990384i	$0.544177\pi$
$854$	−2.16684	−	0.115467i	−0.0741478	−	0.00395119i
$855$	18.2791	−	22.1613i	0.625131	−	0.757902i
$856$	2.00613	−	4.84323i	0.0685682	−	0.165538i
$857$	−13.3957	−	5.54869i	−0.457589	−	0.189540i	0.141969	−	0.989871i	$-0.454657\pi$
$857$	−13.3957	−	5.54869i	−0.457589	−	0.189540i	−0.599558	+	0.800332i	$0.704657\pi$
$858$	13.3232	+	53.4690i	0.454845	+	1.82540i
$859$	13.8122	+	13.8122i	0.471265	+	0.471265i	0.902324	−	0.431059i	$-0.141860\pi$
$859$	13.8122	+	13.8122i	0.471265	+	0.471265i	−0.431059	+	0.902324i	$0.641860\pi$
$860$	−18.0017	−	7.45653i	−0.613851	−	0.254265i
$861$	−19.5507	−	29.6035i	−0.666285	−	1.00888i
$862$	−22.0300	+	9.12512i	−0.750344	+	0.310803i
$863$	8.51418			0.289826			0.144913	−	0.989444i	$-0.453710\pi$
$863$	8.51418			0.289826			0.144913	+	0.989444i	$0.453710\pi$
$864$	1.73240	+	4.89886i	0.0589375	+	0.166662i
$865$	−16.3910	−	16.3910i	−0.557310	−	0.557310i
$866$	19.7319			0.670516
$867$	5.21696	−	28.9790i	0.177177	−	0.984179i
$868$	21.4366	+	1.14232i	0.727606	+	0.0387727i
$869$	−42.8300	+	42.8300i	−1.45291	+	1.45291i
$870$	4.57639	−	30.5913i	0.155154	−	1.03714i
$871$	8.13404			0.275611
$872$	−3.02326	−	7.29879i	−0.102380	−	0.247168i
$873$	0.484686	+	5.04884i	0.0164041	+	0.170877i
$874$	9.30688	−	22.4688i	0.314810	−	0.760019i
$875$	−18.6036	−	20.6980i	−0.628918	−	0.699719i
$876$	3.81933	+	15.3279i	0.129043	+	0.517881i
$877$	−15.3816	−	6.37128i	−0.519401	−	0.215143i	0.107553	−	0.994199i	$-0.465698\pi$
$877$	−15.3816	−	6.37128i	−0.519401	−	0.215143i	−0.626954	+	0.779057i	$0.715698\pi$
$878$	11.6022	−	28.0103i	0.391557	−	0.945302i
$879$	−29.1620	−	4.36257i	−0.983609	−	0.147146i
$880$	13.9269			0.469477
$881$	−16.6337	−	40.1573i	−0.560404	−	1.35294i	−0.909444	−	0.415827i	$-0.863492\pi$
$881$	−16.6337	−	40.1573i	−0.560404	−	1.35294i	0.349039	−	0.937108i	$-0.386508\pi$
$882$	−19.3138	−	8.24482i	−0.650330	−	0.277618i
$883$	49.7234			1.67333			0.836663	−	0.547718i	$-0.184503\pi$
$883$	49.7234			1.67333			0.836663	+	0.547718i	$0.184503\pi$
$884$	0.327876	−	22.1364i	0.0110277	−	0.744528i
$885$	23.9046	+	14.3680i	0.803543	+	0.482974i
$886$	21.4501	+	21.4501i	0.720630	+	0.720630i
$887$	5.97069	+	14.4145i	0.200476	+	0.483992i	0.991861	−	0.127326i	$-0.0406395\pi$
$887$	5.97069	+	14.4145i	0.200476	+	0.483992i	−0.791385	+	0.611318i	$0.790640\pi$
$888$	2.44263	+	1.46815i	0.0819692	+	0.0492681i
$889$	7.80043	+	22.0893i	0.261618	+	0.740852i
$890$	−28.1974	−	11.6797i	−0.945178	−	0.391506i
$891$	−29.4067	−	44.4841i	−0.985162	−	1.49027i
$892$	−3.79748	−	3.79748i	−0.127149	−	0.127149i
$893$	−5.34839	−	5.34839i	−0.178977	−	0.178977i
$894$	−22.5790	−	30.5229i	−0.755154	−	1.02084i
$895$	−37.2235	−	15.4185i	−1.24424	−	0.515383i
$896$	2.49477	−	0.880980i	0.0833444	−	0.0294315i
$897$	−28.6017	+	47.5857i	−0.954982	+	1.58884i
$898$	−9.76445	−	23.5735i	−0.325844	−	0.786657i
$899$	−43.5901	−	43.5901i	−1.45381	−	1.45381i
$900$	0.738951	+	1.39073i	0.0246317	+	0.0463576i
$901$	−4.60334	+	4.46897i	−0.153360	+	0.148883i
$902$	−45.8696			−1.52729
$903$	37.2971	−	7.21030i	1.24117	−	0.239944i
$904$	1.23302	+	2.97676i	0.0410095	+	0.0990056i
$905$	49.6618			1.65081
$906$	−2.18414	+	14.6001i	−0.0725631	+	0.485055i
$907$	−0.120435	+	0.290756i	−0.00399898	+	0.00965440i	−0.925866	−	0.377851i	$-0.876663\pi$
$907$	−0.120435	+	0.290756i	−0.00399898	+	0.00965440i	0.921867	+	0.387505i	$0.126663\pi$
$908$	5.82758	+	2.41386i	0.193395	+	0.0801069i
$909$	23.3349	+	7.14151i	0.773969	+	0.236869i
$910$	22.3219	+	24.8348i	0.739963	+	0.823265i
$911$	5.19629	−	12.5449i	0.172161	−	0.415633i	−0.814123	−	0.580693i	$-0.802782\pi$
$911$	5.19629	−	12.5449i	0.172161	−	0.415633i	0.986284	+	0.165060i	$0.0527818\pi$
$912$	−4.19635	−	5.67274i	−0.138955	−	0.187843i
$913$	−1.13753	−	2.74625i	−0.0376469	−	0.0908876i
$914$	37.7380			1.24826
$915$	−3.30227	−	0.494012i	−0.109170	−	0.0163315i
$916$	−15.2356	+	15.2356i	−0.503398	+	0.503398i
$917$	−0.702073	+	13.1751i	−0.0231845	+	0.435079i
$918$	6.84296	+	20.3021i	0.225851	+	0.670068i
$919$	−57.6519			−1.90176			−0.950880	−	0.309559i	$-0.899819\pi$
$919$	−57.6519			−1.90176			−0.950880	+	0.309559i	$0.899819\pi$
$920$	9.92217	+	9.92217i	0.327124	+	0.327124i
$921$	−3.04281	−	0.455198i	−0.100264	−	0.0149993i
$922$	−2.84018			−0.0935363
$923$	−25.0722	+	10.3853i	−0.825263	+	0.341835i
$924$	−22.6569	+	14.9630i	−0.745358	+	0.492247i
$925$	0.798000	+	0.330543i	0.0262381	+	0.0108682i
$926$	−26.3787	−	26.3787i	−0.866857	−	0.866857i
$927$	6.17630	−	20.1811i	0.202856	−	0.662833i
$928$	−7.01932	−	2.90750i	−0.230420	−	0.0954433i
$929$	−9.77251	+	23.5929i	−0.320626	+	0.774059i	0.678592	+	0.734515i	$0.262590\pi$
$929$	−9.77251	+	23.5929i	−0.320626	+	0.774059i	−0.999218	+	0.0395437i	$0.987410\pi$
$930$	32.6694	+	4.88727i	1.07127	+	0.160260i
$931$	28.3556	+	3.03063i	0.929317	+	0.0993250i
$932$	19.9222	−	8.25203i	0.652572	−	0.270304i
$933$	9.31921	+	37.4002i	0.305097	+	1.22443i
$934$			17.4117i			0.569727i
$935$	57.4159	+	0.850423i	1.87770	+	0.0278118i
$936$	7.55834	+	14.2250i	0.247052	+	0.464959i
$937$	−35.8690	+	35.8690i	−1.17179	+	1.17179i	−0.190006	+	0.981783i	$0.560851\pi$
$937$	−35.8690	+	35.8690i	−1.17179	+	1.17179i	−0.981783	+	0.190006i	$0.939149\pi$
$938$	1.33457	+	3.77925i	0.0435753	+	0.123397i
$939$	−26.4347	−	15.8887i	−0.862663	−	0.518508i
$940$	4.03191	−	1.67007i	0.131506	−	0.0544717i
$941$	−20.3217	+	49.0609i	−0.662468	+	1.59934i	0.131455	+	0.991322i	$0.458035\pi$
$941$	−20.3217	+	49.0609i	−0.662468	+	1.59934i	−0.793923	+	0.608018i	$0.791965\pi$
$942$	−7.73392	−	10.4549i	−0.251985	−	0.340640i
$943$	−32.6795	−	32.6795i	−1.06419	−	1.06419i
$944$	4.84410	−	4.84410i	0.157662	−	0.157662i
$945$	−28.3782	−	15.4562i	−0.923143	−	0.502790i
$946$	18.7959	−	45.3774i	0.611108	−	1.47535i
$947$	13.7193	+	33.1213i	0.445817	+	1.07630i	0.973874	+	0.227088i	$0.0729206\pi$
$947$	13.7193	+	33.1213i	0.445817	+	1.07630i	−0.528057	+	0.849209i	$0.677079\pi$
$948$	−9.12169	+	15.1761i	−0.296259	+	0.492897i
$949$	18.7401	+	45.2426i	0.608330	+	1.46864i
$950$	−1.51221	−	1.51221i	−0.0490625	−	0.0490625i
$951$	−30.8696	+	51.3589i	−1.00101	+	1.66543i
$952$	10.3389	−	3.47964i	0.335085	−	0.112776i
$953$			15.1280i			0.490045i	0.969517	+	0.245023i	$0.0787954\pi$
$953$			15.1280i			0.490045i	−0.969517	+	0.245023i	$0.921205\pi$
$954$	1.36612	−	4.46381i	0.0442299	−	0.144521i
$955$	4.96754	−	2.05762i	0.160746	−	0.0665831i
$956$	−22.4045			−0.724614
$957$	77.1126	+	11.5359i	2.49270	+	0.372902i
$958$	−4.49774	−	1.86302i	−0.145315	−	0.0601915i
$959$	35.4931	+	16.9676i	1.14613	+	0.547912i
$960$	3.95043	−	0.984351i	0.127500	−	0.0317698i
$961$	24.6309	−	24.6309i	0.794544	−	0.794544i
$962$	8.16233	+	3.38095i	0.263164	+	0.109006i
$963$	1.50286	+	15.6549i	0.0484289	+	0.504471i
$964$	−2.07429	−	5.00778i	−0.0668084	−	0.161290i
$965$			6.34504i			0.204254i
$966$	−26.8021	−	5.48147i	−0.862344	−	0.176363i
$967$	3.28759	+	3.28759i	0.105722	+	0.105722i	0.757989	−	0.652267i	$-0.226182\pi$
$967$	3.28759	+	3.28759i	0.105722	+	0.105722i	−0.652267	+	0.757989i	$0.726182\pi$
$968$			24.1061i			0.774799i
$969$	−16.9537	−	23.6430i	−0.544631	−	0.759522i
$970$	3.97399			0.127597
$971$	−33.7288	−	33.7288i	−1.08241	−	1.08241i	−0.996285	−	0.0861227i	$-0.972552\pi$
$971$	−33.7288	−	33.7288i	−1.08241	−	1.08241i	−0.0861227	−	0.996285i	$-0.527448\pi$
$972$	−11.4855	−	10.5397i	−0.368396	−	0.338059i
$973$	1.00610	−	18.8803i	0.0322540	−	0.605276i
$974$	7.10307	+	17.1483i	0.227597	+	0.549468i
$975$	2.90345	+	3.92496i	0.0929847	+	0.125699i
$976$	−0.313858	+	0.757721i	−0.0100464	+	0.0242540i
$977$	27.3853	+	27.3853i	0.876133	+	0.876133i	0.993132	−	0.116999i	$-0.0373274\pi$
$977$	27.3853	+	27.3853i	0.876133	+	0.876133i	−0.116999	+	0.993132i	$0.537327\pi$
$978$	−5.03970	−	20.2255i	−0.161152	−	0.646740i
$979$	29.4415	−	71.0781i	0.940955	−	2.27167i
$980$	−7.87638	+	14.4459i	−0.251602	+	0.461459i
$981$	18.2835	+	15.0806i	0.583748	+	0.481486i
$982$		−	14.8435i		−	0.473675i
$983$	−4.99286	−	12.0538i	−0.159248	−	0.384458i	0.824036	−	0.566537i	$-0.191717\pi$
$983$	−4.99286	−	12.0538i	−0.159248	−	0.384458i	−0.983284	+	0.182079i	$0.941717\pi$
$984$	−13.0111	+	3.24205i	−0.414779	+	0.103353i
$985$			22.8249i			0.727261i
$986$	−28.7607	−	12.4152i	−0.915927	−	0.395381i
$987$	−4.76496	+	7.04880i	−0.151670	+	0.224366i
$988$	−15.4676	−	15.4676i	−0.492090	−	0.492090i
$989$	45.7199	−	18.9378i	1.45381	−	0.602187i
$990$	−36.8959	+	19.6043i	−1.17263	+	0.623066i
$991$	−27.7868	+	11.5097i	−0.882676	+	0.365616i	−0.777534	−	0.628841i	$-0.783530\pi$
$991$	−27.7868	+	11.5097i	−0.882676	+	0.365616i	−0.105142	+	0.994457i	$0.533530\pi$
$992$	3.10501	−	7.49615i	0.0985841	−	0.238003i
$993$	27.4003	+	37.0405i	0.869522	+	1.17544i
$994$	−8.93889	−	9.94518i	−0.283524	−	0.315442i
$995$	20.0168	+	20.0168i	0.634575	+	0.634575i
$996$	−0.516771	−	0.698585i	−0.0163745	−	0.0221355i
$997$	1.69374	+	0.701569i	0.0536412	+	0.0222189i	0.409343	−	0.912381i	$-0.365758\pi$
$997$	1.69374	+	0.701569i	0.0536412	+	0.0222189i	−0.355702	+	0.934600i	$0.615758\pi$
$998$	2.22049	+	5.36073i	0.0702882	+	0.169691i
$999$	−8.53777	−	0.451131i	−0.270123	−	0.0142732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.w.f.83.12	yes	80
3.2	odd	2		714.2.w.e.83.16	yes	80
7.6	odd	2	inner	714.2.w.f.83.9	yes	80
17.8	even	8		714.2.w.e.671.5	yes	80
21.20	even	2		714.2.w.e.83.5	✓	80
51.8	odd	8	inner	714.2.w.f.671.9	yes	80
119.76	odd	8		714.2.w.e.671.16	yes	80
357.314	even	8	inner	714.2.w.f.671.12	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.w.e.83.5	✓	80	21.20	even	2
714.2.w.e.83.16	yes	80	3.2	odd	2
714.2.w.e.671.5	yes	80	17.8	even	8
714.2.w.e.671.16	yes	80	119.76	odd	8
714.2.w.f.83.9	yes	80	7.6	odd	2	inner
714.2.w.f.83.12	yes	80	1.1	even	1	trivial
714.2.w.f.671.9	yes	80	51.8	odd	8	inner
714.2.w.f.671.12	yes	80	357.314	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.256259 - 1.71299i) q^{3} -1.00000i q^{4} +(2.17160 - 0.899506i) q^{5} +(1.03006 + 1.39247i) q^{6} +(-1.14112 + 2.38702i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86866 - 0.877938i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.256259 - 1.71299i) q^{3} -1.00000i q^{4} +(2.17160 - 0.899506i) q^{5} +(1.03006 + 1.39247i) q^{6} +(-1.14112 + 2.38702i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86866 - 0.877938i) q^{9} +(-0.899506 + 2.17160i) q^{10} +(-5.47402 - 2.26741i) q^{11} +(-1.71299 - 0.256259i) q^{12} -5.36946 q^{13} +(-0.880980 - 2.49477i) q^{14} +(-0.984351 - 3.95043i) q^{15} -1.00000 q^{16} +(-4.12265 - 0.0610632i) q^{17} +(2.64925 - 1.40765i) q^{18} +(-2.88066 + 2.88066i) q^{19} +(-0.899506 - 2.17160i) q^{20} +(3.79651 + 2.56642i) q^{21} +(5.47402 - 2.26741i) q^{22} +(5.51535 + 2.28453i) q^{23} +(1.39247 - 1.03006i) q^{24} +(0.371197 - 0.371197i) q^{25} +(3.79678 - 3.79678i) q^{26} +(-2.23902 + 4.68901i) q^{27} +(2.38702 + 1.14112i) q^{28} +(-2.90750 - 7.01932i) q^{29} +(3.48942 + 2.09734i) q^{30} +(7.49615 - 3.10501i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.28682 + 8.79589i) q^{33} +(2.95833 - 2.87198i) q^{34} +(-0.330923 + 6.21008i) q^{35} +(-0.877938 + 2.86866i) q^{36} +(0.629663 + 1.52014i) q^{37} -4.07387i q^{38} +(-1.37597 + 9.19782i) q^{39} +(2.17160 + 0.899506i) q^{40} +(-7.15235 - 2.96260i) q^{41} +(-4.49927 + 0.869802i) q^{42} +(5.86162 - 5.86162i) q^{43} +(-2.26741 + 5.47402i) q^{44} +(-7.01929 + 0.673848i) q^{45} +(-5.51535 + 2.28453i) q^{46} +1.85665i q^{47} +(-0.256259 + 1.71299i) q^{48} +(-4.39569 - 5.44775i) q^{49} +0.524952i q^{50} +(-1.16107 + 7.04641i) q^{51} +5.36946i q^{52} +(1.10030 - 1.10030i) q^{53} +(-1.73240 - 4.89886i) q^{54} -13.9269 q^{55} +(-2.49477 + 0.880980i) q^{56} +(4.19635 + 5.67274i) q^{57} +(7.01932 + 2.90750i) q^{58} +(-4.84410 + 4.84410i) q^{59} +(-3.95043 + 0.984351i) q^{60} +(0.313858 - 0.757721i) q^{61} +(-3.10501 + 7.49615i) q^{62} +(5.36914 - 5.84571i) q^{63} +1.00000i q^{64} +(-11.6603 + 4.82986i) q^{65} +(-2.48129 - 9.95798i) q^{66} -1.51487 q^{67} +(-0.0610632 + 4.12265i) q^{68} +(5.32673 - 8.86229i) q^{69} +(-4.15719 - 4.62519i) q^{70} +(4.66942 - 1.93414i) q^{71} +(-1.40765 - 2.64925i) q^{72} +(-3.49013 - 8.42592i) q^{73} +(-1.52014 - 0.629663i) q^{74} +(-0.540734 - 0.730979i) q^{75} +(2.88066 + 2.88066i) q^{76} +(11.6589 - 10.4792i) q^{77} +(-5.53088 - 7.47680i) q^{78} +(3.91211 - 9.44467i) q^{79} +(-2.17160 + 0.899506i) q^{80} +(7.45845 + 5.03702i) q^{81} +(7.15235 - 2.96260i) q^{82} +(0.354747 + 0.354747i) q^{83} +(2.56642 - 3.79651i) q^{84} +(-9.00768 + 3.57575i) q^{85} +8.28958i q^{86} +(-12.7691 + 3.18175i) q^{87} +(-2.26741 - 5.47402i) q^{88} +12.9846i q^{89} +(4.48691 - 5.43987i) q^{90} +(6.12720 - 12.8170i) q^{91} +(2.28453 - 5.51535i) q^{92} +(-3.39789 - 13.6365i) q^{93} +(-1.31285 - 1.31285i) q^{94} +(-3.66447 + 8.84681i) q^{95} +(-1.03006 - 1.39247i) q^{96} +(-0.646996 - 1.56199i) q^{97} +(6.96036 + 0.743920i) q^{98} +(13.7125 + 11.3103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 16 q^{7}+O(q^{10}) \) 80 * q - 16 * q^7	\( 80 q - 16 q^{7} + 16 q^{14} - 48 q^{15} - 80 q^{16} + 16 q^{18} + 32 q^{21} + 16 q^{23} - 32 q^{25} - 64 q^{29} + 16 q^{30} - 48 q^{37} + 64 q^{39} + 16 q^{43} + 16 q^{44} - 16 q^{46} + 16 q^{49} + 24 q^{51} + 80 q^{53} + 48 q^{57} - 16 q^{58} - 16 q^{60} - 32 q^{63} - 80 q^{65} - 144 q^{67} + 8 q^{70} - 16 q^{71} + 32 q^{74} + 24 q^{77} + 32 q^{79} - 16 q^{84} + 208 q^{85} + 16 q^{88} - 8 q^{91} - 16 q^{92} - 16 q^{93} + 16 q^{95} + 16 q^{98} + 48 q^{99}+O(q^{100}) \) 80 * q - 16 * q^7 + 16 * q^14 - 48 * q^15 - 80 * q^16 + 16 * q^18 + 32 * q^21 + 16 * q^23 - 32 * q^25 - 64 * q^29 + 16 * q^30 - 48 * q^37 + 64 * q^39 + 16 * q^43 + 16 * q^44 - 16 * q^46 + 16 * q^49 + 24 * q^51 + 80 * q^53 + 48 * q^57 - 16 * q^58 - 16 * q^60 - 32 * q^63 - 80 * q^65 - 144 * q^67 + 8 * q^70 - 16 * q^71 + 32 * q^74 + 24 * q^77 + 32 * q^79 - 16 * q^84 + 208 * q^85 + 16 * q^88 - 8 * q^91 - 16 * q^92 - 16 * q^93 + 16 * q^95 + 16 * q^98 + 48 * q^99

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