LMFDB - Embedded newform 714.2.w.f.83.9

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			83.9
Character	$\chi$	$=$	714.83
Dual form			714.2.w.f.671.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.256259 + 1.71299i) q^{3} -1.00000i q^{4} +(-2.17160 + 0.899506i) q^{5} +(-1.03006 - 1.39247i) q^{6} +(0.880980 - 2.49477i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86866 - 0.877938i) q^{9} +O(q^{10})$	\(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} +(0.880980 - 2.49477i) 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} +(1.14112 + 2.38702i) 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} +(4.04775 + 2.14842i) 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} +(-2.49477 - 0.880980i) 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} +(-4.38135 + 1.34303i) 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} +(-5.44775 - 4.39569i) 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} +(2.38702 - 1.14112i) 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} +(-4.71749 + 6.38320i) 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} +(-4.62519 - 4.15719i) 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} +(-10.4792 + 11.6589i) 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} +(2.14842 - 4.04775i) 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} +(4.73039 - 13.3956i) 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	−0.811147	−	0.584842i	$-0.801156\pi$
$5$	−2.17160	+	0.899506i	−0.971169	+	0.402271i	−0.160022	+	0.987114i	$0.551156\pi$
$6$	−1.03006	−	1.39247i	−0.420522	−	0.568473i
$7$	0.880980	−	2.49477i	0.332979	−	0.942934i
$7$	0.880980	−	2.49477i	0.332979	−	0.942934i
$8$	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	$-0.232636\pi$
$13$	5.36946			1.48922			0.744610	+	0.667500i	$0.232636\pi$
$14$	1.14112	+	2.38702i	0.304977	+	0.637957i
$15$	−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	−0.294716	−	0.955585i	$-0.595225\pi$
$19$	2.88066	−	2.88066i	0.660869	−	0.660869i	0.955585	+	0.294716i	$0.0952250\pi$
$20$	0.899506	+	2.17160i	0.201136	+	0.485584i
$21$	4.04775	+	2.14842i	0.883292	+	0.468823i
$22$	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
$28$	−2.49477	−	0.880980i	−0.471467	−	0.166490i
$29$	−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	−0.935273	−	0.353926i	$-0.884846\pi$
$31$	−7.49615	+	3.10501i	−1.34635	+	0.557676i	−0.411075	+	0.911602i	$0.634846\pi$
$32$	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	0.863346	−	0.504612i	$-0.168364\pi$
$41$	7.15235	+	2.96260i	1.11701	+	0.462681i	0.253664	+	0.967292i	$0.418364\pi$
$42$	−4.38135	+	1.34303i	−0.676058	+	0.207235i
$43$	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	$-0.956765\pi$
$47$		−	1.85665i		−	0.270821i	0.990790	−	0.135410i	$-0.0432353\pi$
$48$	0.256259	−	1.71299i	0.0369878	−	0.247249i
$49$	−5.44775	−	4.39569i	−0.778250	−	0.627955i
$50$			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
$56$	2.38702	−	1.14112i	0.318978	−	0.152489i
$57$	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	−0.317583	−	0.948231i	$-0.602871\pi$
$59$	4.84410	−	4.84410i	0.630648	−	0.630648i	0.948231	+	0.317583i	$0.102871\pi$
$60$	−3.95043	+	0.984351i	−0.509999	+	0.127079i
$61$	−0.313858	+	0.757721i	−0.0401854	+	0.0970162i	−0.942698	−	0.333647i	$-0.891720\pi$
$61$	−0.313858	+	0.757721i	−0.0401854	+	0.0970162i	0.902512	+	0.430664i	$0.141720\pi$
$62$	3.10501	−	7.49615i	0.394336	−	0.952012i
$63$	−4.71749	+	6.38320i	−0.594348	+	0.804208i
$64$			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
$70$	−4.62519	−	4.15719i	−0.552816	−	0.496880i
$71$	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	$0.0542050\pi$
$73$	3.49013	+	8.42592i	0.408489	+	0.986179i	−0.577047	+	0.816711i	$0.695795\pi$
$74$	−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
$77$	−10.4792	+	11.6589i	−1.19421	+	1.32865i
$78$	−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	0.687369	−	0.726308i	$-0.258765\pi$
$83$	−0.354747	−	0.354747i	−0.0389385	−	0.0389385i	−0.726308	+	0.687369i	$0.758765\pi$
$84$	2.14842	−	4.04775i	0.234412	−	0.441646i
$85$	−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	$-0.758408\pi$
$89$		−	12.9846i		−	1.37637i	0.725537	−	0.688183i	$-0.241592\pi$
$90$	−4.48691	+	5.43987i	−0.472962	+	0.573413i
$91$	4.73039	−	13.3956i	0.495879	−	1.40424i
$92$	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	0.953316	−	0.301973i	$-0.0976453\pi$
$97$	0.646996	+	1.56199i	0.0656925	+	0.158596i	−0.887624	+	0.460569i	$0.847645\pi$
$98$	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	$-0.367375\pi$
$101$	8.13441			0.809404			0.404702	+	0.914449i	$0.367375\pi$
$102$	−4.16157	−	5.80356i	−0.412056	−	0.574639i
$103$		−	7.03501i		−	0.693180i	−0.938017	−	0.346590i	$-0.887340\pi$
$103$		−	7.03501i		−	0.693180i	0.938017	−	0.346590i	$-0.112660\pi$
$104$	3.79678	+	3.79678i	0.372305	+	0.372305i
$105$	−10.7226	−	1.02452i	−1.04642	−	0.0999833i
$106$			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
$112$	−0.880980	+	2.49477i	−0.0832448	+	0.235734i
$113$	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
$119$	3.78432	−	10.2313i	0.346908	−	0.937899i
$120$	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
$126$	−1.17784	−	7.84938i	−0.104930	−	0.699278i
$127$	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	−0.574758	−	0.818324i	$-0.694904\pi$
$131$	−4.60717	+	1.90835i	−0.402531	+	0.166734i	0.172227	+	0.985057i	$0.444904\pi$
$132$	−8.79589	−	5.28682i	−0.765584	−	0.460159i
$133$	−4.64878	−	9.72439i	−0.403100	−	0.843212i
$134$	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	−0.0846879	−	0.996408i	$-0.526989\pi$
$139$	6.60225	−	2.73474i	0.559995	−	0.231958i	0.644683	+	0.764450i	$0.276989\pi$
$140$	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
$147$	8.92580	−	8.20550i	0.736187	−	0.676778i
$148$	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	$-0.403144\pi$
$157$	7.50820			0.599219			0.299610	+	0.954062i	$0.403144\pi$
$158$	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
$161$	10.5583	−	11.7469i	0.832110	−	0.925784i
$162$	−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	0.905383	−	0.424595i	$-0.139583\pi$
$167$	−0.452987	−	1.09361i	−0.0350532	−	0.0846259i	−0.940437	+	0.339969i	$0.889583\pi$
$168$	1.34303	+	4.38135i	0.103617	+	0.338029i
$169$	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	0.999965	−	0.00842187i	$-0.00268079\pi$
$173$	3.77394	+	9.11111i	0.286928	+	0.692705i	−0.713037	+	0.701127i	$0.752681\pi$
$174$	−6.77928	+	11.2789i	−0.513936	+	0.855055i
$175$	−0.599034	−	1.25307i	−0.0452827	−	0.0947230i
$176$	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	−0.488479	−	0.872576i	$-0.662448\pi$
$181$	−19.5197	−	8.08533i	−1.45089	−	0.600978i	−0.962411	+	0.271598i	$0.912448\pi$
$182$	6.12720	+	12.8170i	0.454178	+	0.950058i
$183$	−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
$189$	−9.72546	−	9.71676i	−0.707423	−	0.706790i
$190$	−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
$196$	−4.39569	+	5.44775i	−0.313978	+	0.389125i
$197$	−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	$-0.984619\pi$
$199$	−4.60877	−	11.1265i	−0.326707	−	0.788740i	0.672126	−	0.740437i	$-0.265381\pi$
$200$	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
$210$	8.30648	−	6.85758i	0.573201	−	0.473218i
$211$	−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	−0.822730	−	0.568432i	$-0.807550\pi$
$223$	−3.79748	+	3.79748i	−0.254298	+	0.254298i	0.568432	+	0.822730i	$0.307550\pi$
$224$	−1.14112	−	2.38702i	−0.0762444	−	0.159489i
$225$	−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	−0.823304	−	0.567600i	$-0.807872\pi$
$227$	2.41386	−	5.82758i	0.160214	−	0.386790i	0.983518	+	0.180810i	$0.0578719\pi$
$228$	5.67274	−	4.19635i	0.375686	−	0.277910i
$229$	15.2356	+	15.2356i	1.00680	+	1.00680i	0.999977	+	0.00682023i	$0.00217096\pi$
$229$	15.2356	+	15.2356i	1.00680	+	1.00680i	0.00682023	+	0.999977i	$0.497829\pi$
$230$	9.92217	−	9.92217i	0.654248	−	0.654248i
$231$	−17.2861	−	20.9384i	−1.13734	−	1.37765i
$232$	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
$238$	4.55869	+	9.91052i	0.295496	+	0.642403i
$239$		−	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	−0.538096	−	0.842883i	$-0.680856\pi$
$241$	−5.00778	+	2.07429i	−0.322580	+	0.133617i	0.215517	+	0.976500i	$0.430856\pi$
$242$	−24.1061			−1.54960
$243$	−10.5397	+	11.4855i	−0.676119	+	0.736792i
$244$	0.757721	+	0.313858i	0.0485081	+	0.0200927i
$245$	15.7843	+	4.64539i	1.00842	+	0.296783i
$246$	−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	$0.122372\pi$
$251$			11.8836i			0.750086i	−0.927007	+	0.375043i	$0.877628\pi$
$252$	6.38320	+	4.71749i	0.402104	+	0.297174i
$253$	−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	0.919944	−	0.392051i	$-0.128234\pi$
$257$	8.46277	+	8.46277i	0.527893	+	0.527893i	−0.392051	+	0.919944i	$0.628234\pi$
$258$	−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
$266$	10.1634	+	3.58900i	0.623156	+	0.220056i
$267$	22.2425	+	3.32743i	1.36122	+	0.203635i
$268$			1.51487i			0.0925355i
$269$	−4.73887	−	11.4406i	−0.288934	−	0.697548i	0.711050	−	0.703141i	$-0.248220\pi$
$269$	−4.73887	−	11.4406i	−0.288934	−	0.697548i	−0.999984	+	0.00559287i	$0.998220\pi$
$270$	−8.16863	−	9.08004i	−0.497127	−	0.552594i
$271$		−	10.2680i		−	0.623737i	−0.950125	−	0.311868i	$-0.899045\pi$
$271$		−	10.2680i		−	0.623737i	0.950125	−	0.311868i	$-0.100955\pi$
$272$	−4.12265	−	0.0610632i	−0.249973	−	0.00370250i
$273$	21.7342	+	11.5358i	1.31542	+	0.698180i
$274$	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
$280$	−4.15719	+	4.62519i	−0.248440	+	0.276408i
$281$	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	0.0415843	−	0.999135i	$-0.486760\pi$
$283$	−10.6909	−	4.42830i	−0.635506	−	0.263235i	−0.677091	+	0.735900i	$0.736760\pi$
$284$	−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
$287$	13.6921	−	15.2335i	0.808219	−	0.899204i
$288$	−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	$0.165667\pi$
$293$			17.0240i			0.994555i	−0.867592	+	0.497277i	$0.834333\pi$
$294$	−0.509329	+	12.1137i	−0.0297047	+	0.706483i
$295$	−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
$301$	−9.45942	−	19.7874i	−0.545232	−	1.14052i
$302$	−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	$0.0161420\pi$
$307$			1.77632i			0.101380i	−0.998714	+	0.0506899i	$0.983858\pi$
$308$	11.6589	+	10.4792i	0.664326	+	0.597107i
$309$	12.0509	+	1.80278i	0.685551	+	0.102557i
$310$			19.0716i			1.08319i
$311$	20.5593	−	8.51594i	1.16581	−	0.482895i	0.286005	−	0.958228i	$-0.407672\pi$
$311$	20.5593	−	8.51594i	1.16581	−	0.482895i	0.879806	+	0.475333i	$0.157672\pi$
$312$	−7.47680	+	5.53088i	−0.423291	+	0.313125i
$313$	−6.81435	+	16.4513i	−0.385170	+	0.929883i	0.605778	+	0.795634i	$0.292862\pi$
$313$	−6.81435	+	16.4513i	−0.385170	+	0.929883i	−0.990948	+	0.134249i	$0.957138\pi$
$314$	−5.30910	+	5.30910i	−0.299610	+	0.299610i
$315$	4.50276	−	18.1052i	0.253702	−	1.02011i
$316$	−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
$329$	−4.63192	−	1.63568i	−0.255366	−	0.0901777i
$330$	−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
$336$	−4.04775	−	2.14842i	−0.220823	−	0.117206i
$337$	−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
$343$	−15.7656	+	9.71836i	−0.851261	+	0.524742i
$344$	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	$0.0300842\pi$
$349$	20.3612	+	20.3612i	1.08991	+	1.08991i	0.0943718	+	0.995537i	$0.469916\pi$
$350$	1.30963	+	0.462472i	0.0700029	+	0.0247202i
$351$	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	$0.173546\pi$
$353$			19.4872i			1.03720i	−0.855018	+	0.518599i	$0.826454\pi$
$354$	−11.7350	−	1.75553i	−0.623707	−	0.0933052i
$355$	−8.40033	+	8.40033i	−0.445843	+	0.445843i
$356$	−12.9846			−0.688183
$357$	16.5563	+	9.10435i	0.876252	+	0.481853i
$358$	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
$364$	−13.3956	−	4.73039i	−0.702118	−	0.247940i
$365$	−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	−0.721967	−	0.691927i	$-0.756762\pi$
$367$	5.32202	−	12.8485i	0.277807	−	0.670686i	0.999774	+	0.0212415i	$0.00676190\pi$
$368$	−5.51535	−	2.28453i	−0.287507	−	0.119089i
$369$	−17.9167	−	14.7780i	−0.932706	−	0.769314i
$370$	3.86752			0.201063
$371$	−1.77565	−	3.71434i	−0.0921873	−	0.192839i
$372$	−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
$378$	13.7477	−	0.00614997i	0.707107	−	0.000316320i
$379$	−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	−0.535955	−	0.844247i	$-0.680048\pi$
$383$	6.03339	−	6.03339i	0.308292	−	0.308292i	0.844247	+	0.535955i	$0.180048\pi$
$384$	1.39247	−	1.03006i	0.0710591	−	0.0525652i
$385$	12.2694	−	34.7445i	0.625304	−	1.77074i
$386$	−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	−0.103989	−	0.994578i	$-0.533161\pi$
$397$	−17.5497	−	7.26932i	−0.880794	−	0.364837i	−0.776805	+	0.629742i	$0.783161\pi$
$398$	11.1265	+	4.60877i	0.557723	+	0.231017i
$399$	17.8491	−	5.47134i	0.893571	−	0.273910i
$400$	−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
$406$	13.4374	−	14.9501i	0.666888	−	0.741963i
$407$		−	9.74898i		−	0.483239i
$408$	−5.80356	+	4.16157i	−0.287319	+	0.206028i
$409$			6.91010i			0.341682i	0.985299	+	0.170841i	$0.0546485\pi$
$409$			6.91010i			0.341682i	−0.985299	+	0.170841i	$0.945351\pi$
$410$	12.8672	−	12.8672i	0.635464	−	0.635464i
$411$	25.4708	+	3.81038i	1.25638	+	0.187952i
$412$	−7.03501			−0.346590
$413$	−7.81735	−	16.3525i	−0.384667	−	0.804652i
$414$	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	−0.900787	−	0.434261i	$-0.857010\pi$
$419$	0.884988	−	2.13655i	0.0432345	−	0.104377i	0.944022	+	0.329884i	$0.107010\pi$
$420$	−1.02452	+	10.7226i	−0.0499916	+	0.523210i
$421$		−	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
$427$	1.61384	+	1.45054i	0.0780990	+	0.0701966i
$428$	−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	0.957835	−	0.287319i	$-0.0927640\pi$
$433$	13.9525	+	13.9525i	0.670516	+	0.670516i	−0.287319	+	0.957835i	$0.592764\pi$
$434$	−15.9657	−	14.3502i	−0.766379	−	0.688833i
$435$	−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	0.404255	−	0.914646i	$-0.367531\pi$
$439$	28.0103	−	11.6022i	1.33686	−	0.553745i	0.932604	+	0.360901i	$0.117531\pi$
$440$	9.84783	+	9.84783i	0.469477	+	0.469477i
$441$	11.7686	+	17.3925i	0.560410	+	0.828215i
$442$	−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
$448$	2.49477	+	0.880980i	0.117867	+	0.0416224i
$449$	−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	0.658790	−	0.752327i	$-0.271068\pi$
$461$	−2.00831	−	2.00831i	−0.0935363	−	0.0935363i	−0.752327	+	0.658790i	$0.771068\pi$
$462$	27.0288	+	2.58255i	1.25750	+	0.120151i
$463$			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	−0.932052	−	0.362325i	$-0.881983\pi$
$467$	−12.3119	+	12.3119i	−0.569727	+	0.569727i	0.362325	+	0.932052i	$0.381983\pi$
$468$	−4.71405	+	15.4032i	−0.217907	+	0.712011i
$469$	−1.33457	+	3.77925i	−0.0616248	+	0.174510i
$470$	−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
$476$	−10.2313	−	3.78432i	−0.468950	−	0.173454i
$477$	−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	0.875586	−	0.483063i	$-0.160476\pi$
$479$	−1.86302	−	4.49774i	−0.0851237	−	0.205507i	−0.960710	+	0.277556i	$0.910476\pi$
$480$	−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
$483$	17.4166	+	21.0965i	0.792484	+	0.959923i
$484$	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
$490$	−14.4459	+	7.87638i	−0.652601	+	0.355818i
$491$	−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	0.0442980	−	0.999018i	$-0.485895\pi$
$503$	−14.1472	−	5.85995i	−0.630791	−	0.261282i	−0.675089	+	0.737736i	$0.735895\pi$
$504$	−7.84938	+	1.17784i	−0.349639	+	0.0524651i
$505$	−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	$-0.655543\pi$
$509$	−21.1819			−0.938871			−0.469436	+	0.882967i	$0.655543\pi$
$510$	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
$518$	−2.91008	+	3.23768i	−0.127861	+	0.142255i
$519$	−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	$0.308156\pi$
$521$	−9.50660	+	22.9510i	−0.416492	+	1.00550i	−0.983356	+	0.181689i	$0.941844\pi$
$522$	−17.5835	−	14.5032i	−0.769607	−	0.634786i
$523$	18.9549			0.828842			0.414421	−	0.910085i	$-0.363984\pi$
$523$	18.9549			0.828842			0.414421	+	0.910085i	$0.363984\pi$
$524$	1.90835	+	4.60717i	0.0833668	+	0.201265i
$525$	2.30000	−	0.705028i	0.100380	−	0.0307699i
$526$	−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
$532$	−9.72439	+	4.64878i	−0.421606	+	0.201550i
$533$	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
$539$	19.8542	+	36.4144i	0.855183	+	1.56848i
$540$	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
$546$	−23.5255	+	7.21136i	−1.00680	+	0.308618i
$547$	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
$553$	−20.1158	−	18.0804i	−0.855410	−	0.768856i
$554$	−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	0.247655	−	0.968848i	$-0.420340\pi$
$563$	−17.1122	−	17.1122i	−0.721194	−	0.721194i	−0.968848	+	0.247655i	$0.920340\pi$
$564$	0.475785	−	3.18043i	0.0200341	−	0.133920i
$565$	−7.57344			−0.318617
$566$	10.6909	−	4.42830i	0.449371	−	0.186136i
$567$	19.1369	−	14.1696i	0.803676	−	0.595067i
$568$	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	$0.339508\pi$
$577$			42.0634i			1.75112i	−0.483107	+	0.875561i	$0.660492\pi$
$578$	−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
$581$	−1.19754	+	0.572487i	−0.0496822	+	0.0237508i
$582$	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	−0.424219	−	0.905560i	$-0.639451\pi$
$587$	11.6620	−	11.6620i	0.481341	−	0.481341i	0.905560	+	0.424219i	$0.139451\pi$
$588$	−8.20550	−	8.92580i	−0.338389	−	0.368094i
$589$	−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	0.277844	−	0.960626i	$-0.410380\pi$
$593$	−16.6268	−	16.6268i	−0.682782	−	0.682782i	−0.960626	+	0.277844i	$0.910380\pi$
$594$	1.62452	−	30.7445i	0.0666550	−	1.26146i
$595$	0.985074	+	25.6222i	0.0403841	+	1.05041i
$596$			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	0.613767	−	0.789487i	$-0.289654\pi$
$601$	12.0006	+	4.97080i	0.489514	+	0.202763i	−0.124253	+	0.992251i	$0.539654\pi$
$602$	20.6806	+	7.30296i	0.842878	+	0.297646i
$603$	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	$0.155938\pi$
$607$	14.5647	+	35.1622i	0.591161	+	1.42719i	−0.291221	+	0.956656i	$0.594062\pi$
$608$		−	4.07387i		−	0.165217i
$609$	3.31160	−	34.6590i	0.134193	−	1.40445i
$610$	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	$-0.720737\pi$
$619$	8.87140	−	21.4175i	0.356572	−	0.860840i	0.995777	−	0.0918040i	$-0.0292633\pi$
$620$	−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
$623$	−32.3936	−	11.4392i	−1.29782	−	0.458302i
$624$	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
$630$	9.61835	+	15.9862i	0.383204	+	0.636906i
$631$	−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
$637$	−29.2514	−	23.6024i	−1.15898	−	0.935163i
$638$	−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	−0.845812	−	0.533481i	$-0.820884\pi$
$643$	−27.0479	+	11.2036i	−1.06666	+	0.441826i	−0.220851	+	0.975307i	$0.570884\pi$
$644$	−11.7469	−	10.5583i	−0.462892	−	0.416055i
$645$	−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	$-0.524825\pi$
$647$	−3.96349			−0.155821			−0.0779104	+	0.996960i	$0.524825\pi$
$648$	1.71221	+	8.83563i	0.0672620	+	0.347096i
$649$	−37.5003	+	15.5331i	−1.47201	+	0.609728i
$650$			2.81871i			0.110559i
$651$	−37.0134	−	3.53656i	−1.45067	−	0.138609i
$652$	−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
$658$	4.43186	−	2.11867i	0.172772	−	0.0825942i
$659$	−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	−0.443772	−	0.896140i	$-0.646360\pi$
$661$	11.6303	−	11.6303i	0.452368	−	0.452368i	0.896140	+	0.443772i	$0.146360\pi$
$662$		−	26.6006i		−	1.03386i
$663$	−6.23431	+	37.8354i	−0.242120	+	1.46941i
$664$		−	0.501688i		−	0.0194693i
$665$	18.8424	+	16.9359i	0.730678	+	0.656745i
$666$	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
$672$	4.38135	−	1.34303i	0.169014	−	0.0518086i
$673$	−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	0.941345	−	0.337445i	$-0.109563\pi$
$677$	0.965419	+	2.33073i	0.0371041	+	0.0895771i	−0.904241	+	0.427022i	$0.859563\pi$
$678$	−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
$686$	4.27603	−	18.0199i	0.163260	−	0.688002i
$687$	−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	0.578178	−	0.815911i	$-0.303764\pi$
$691$	10.7796	+	4.46505i	0.410075	+	0.169859i	−0.168103	+	0.985769i	$0.553764\pi$
$692$	9.11111	−	3.77394i	0.346352	−	0.143464i
$693$	40.2970	−	24.2453i	1.53076	−	0.921003i
$694$	−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
$700$	−1.25307	+	0.599034i	−0.0473615	+	0.0226413i
$701$	−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
$707$	7.16626	−	20.2935i	0.269515	−	0.763215i
$708$	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
$714$	−18.1448	+	5.26932i	−0.679053	+	0.197199i
$715$	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	0.584377	−	0.811483i	$-0.301339\pi$
$719$	42.1357	−	17.4532i	1.57140	−	0.650894i	0.987022	+	0.160588i	$0.0513391\pi$
$720$	−7.01929	+	0.673848i	−0.261594	+	0.0251128i
$721$	−17.5507	−	6.19770i	−0.653623	−	0.230814i
$722$	−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	$-0.657488\pi$
$727$	−25.6052			−0.949645			−0.474823	+	0.880081i	$0.657488\pi$
$728$	12.8170	−	6.12720i	0.475029	−	0.227089i
$729$	−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	−0.332402	−	0.943138i	$-0.607859\pi$
$733$	16.5350	−	16.5350i	0.610736	−	0.610736i	0.943138	+	0.332402i	$0.107859\pi$
$734$	5.32202	+	12.8485i	0.196439	+	0.474246i
$735$	−12.0024	+	25.8478i	−0.442714	+	0.953412i
$736$	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
$742$	3.88201	+	1.37086i	0.142513	+	0.0503258i
$743$	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
$756$	−9.71676	+	9.72546i	−0.353395	+	0.353712i
$757$	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	$0.156351\pi$
$761$			26.0236i			0.943353i	−0.881772	+	0.471677i	$0.843649\pi$
$762$	−15.1672	−	2.26899i	−0.549451	−	0.0821967i
$763$	−13.9724	+	15.5454i	−0.505835	+	0.562780i
$764$		−	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	$-0.653940\pi$
$769$	−25.7888			−0.929967			−0.464983	+	0.885319i	$0.653940\pi$
$770$	15.8923	+	33.2438i	0.572719	+	1.19802i
$771$	−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	−0.547390	−	0.836878i	$-0.684378\pi$
$773$	8.04860	−	8.04860i	0.289488	−	0.289488i	0.836878	+	0.547390i	$0.184378\pi$
$774$	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
$777$	−0.717176	+	7.50593i	−0.0257286	+	0.269274i
$778$		−	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
$784$	5.44775	+	4.39569i	0.194562	+	0.156989i
$785$	−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	0.933195	−	0.359372i	$-0.117009\pi$
$787$	0.538972	+	1.30119i	0.0192123	+	0.0463825i	−0.913982	+	0.405754i	$0.867009\pi$
$788$	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
$791$	5.69856	−	6.34007i	0.202617	−	0.225427i
$792$	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	0.535407	−	0.844594i	$-0.320158\pi$
$797$	−8.72874	−	8.72874i	−0.309188	−	0.309188i	−0.844594	+	0.535407i	$0.820158\pi$
$798$	−8.75237	+	16.4900i	−0.309831	+	0.583740i
$799$	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
$805$	−12.3620	+	35.0068i	−0.435702	+	1.23383i
$806$	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	$0.0677121\pi$
$811$	12.4044	+	29.9469i	0.435578	+	1.05158i	−0.541882	+	0.840455i	$0.682288\pi$
$812$	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
$819$	−25.3304	+	34.2743i	−0.885114	+	1.19764i
$820$			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
$826$	17.0906	+	6.03523i	0.594659	+	0.209993i
$827$	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	$-0.676367\pi$
$829$	−30.2985			−1.05231			−0.526155	+	0.850388i	$0.676367\pi$
$830$	−1.08947	+	0.451271i	−0.0378159	+	0.0156639i
$831$	9.82379	+	39.4252i	0.340783	+	1.36764i
$832$			5.36946i			0.186152i
$833$	−22.1908	−	18.4545i	−0.768864	−	0.639412i
$834$	−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	−0.967239	−	0.253866i	$-0.918298\pi$
$839$	−3.00626	+	7.25776i	−0.103788	+	0.250566i	0.863452	+	0.504431i	$0.168298\pi$
$840$	−6.85758	−	8.30648i	−0.236609	−	0.286601i
$841$	−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
$847$	57.5416	−	27.5080i	1.97715	−	0.945184i
$848$	−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	0.138342	−	0.990384i	$-0.455823\pi$
$853$	27.3508	−	11.3291i	0.936473	−	0.387900i	0.798130	+	0.602485i	$0.205823\pi$
$854$	−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	0.599558	−	0.800332i	$-0.295343\pi$
$857$	13.3957	+	5.54869i	0.457589	+	0.189540i	−0.141969	+	0.989871i	$0.545343\pi$
$858$	13.3232	+	53.4690i	0.454845	+	1.82540i
$859$	−13.8122	−	13.8122i	−0.471265	−	0.471265i	0.431059	−	0.902324i	$-0.358140\pi$
$859$	−13.8122	−	13.8122i	−0.471265	−	0.471265i	−0.902324	+	0.431059i	$0.858140\pi$
$860$	18.0017	+	7.45653i	0.613851	+	0.254265i
$861$	22.5861	+	27.3581i	0.769731	+	0.932362i
$862$	−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
$875$	−20.6980	−	18.6036i	−0.699719	−	0.628918i
$876$	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	$0.136508\pi$
$881$	16.6337	+	40.1573i	0.560404	+	1.35294i	−0.349039	+	0.937108i	$0.613492\pi$
$882$	−20.6200	−	3.97671i	−0.694313	−	0.133903i
$883$	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	0.791385	−	0.611318i	$-0.209360\pi$
$887$	−5.97069	−	14.4145i	−0.200476	−	0.483992i	−0.991861	+	0.127326i	$0.959360\pi$
$888$	−2.44263	−	1.46815i	−0.0819692	−	0.0492681i
$889$	−10.1038	−	21.1353i	−0.338870	−	0.708854i
$890$	−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
$896$	−2.38702	+	1.14112i	−0.0797446	+	0.0381222i
$897$	−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
$903$	36.3196	−	11.1332i	1.20864	−	0.370489i
$904$	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
$910$	−24.8348	−	22.3219i	−0.823265	−	0.739963i
$911$	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
$924$	−20.9384	+	17.2861i	−0.688823	+	0.568672i
$925$	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	$-0.737410\pi$
$929$	9.77251	−	23.5929i	0.320626	−	0.774059i	0.999218	−	0.0395437i	$-0.0125904\pi$
$930$	−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	$-0.439149\pi$
$937$	35.8690	−	35.8690i	1.17179	−	1.17179i	0.981783	−	0.190006i	$-0.0608507\pi$
$938$	−1.72865	−	3.61602i	−0.0564425	−	0.118067i
$939$	−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	$-0.541965\pi$
$941$	20.3217	−	49.0609i	0.662468	−	1.59934i	0.793923	−	0.608018i	$-0.208035\pi$
$942$	−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
$945$	29.8601	+	12.3528i	0.971348	+	0.401837i
$946$	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
$952$	9.91052	−	4.55869i	0.321202	−	0.147748i
$953$			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
$959$	−37.0953	−	13.0995i	−1.19787	−	0.423005i
$960$	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
$966$	−27.2329	−	2.60205i	−0.876204	−	0.0837195i
$967$	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	$0.0274477\pi$
$971$	33.7288	+	33.7288i	1.08241	+	1.08241i	0.0861227	+	0.996285i	$0.472552\pi$
$972$	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
$980$	4.64539	−	15.7843i	0.148391	−	0.504210i
$981$	18.2835	+	15.0806i	0.583748	+	0.481486i
$982$		−	14.8435i		−	0.473675i
$983$	4.99286	+	12.0538i	0.159248	+	0.384458i	0.983284	−	0.182079i	$-0.0582828\pi$
$983$	4.99286	+	12.0538i	0.159248	+	0.384458i	−0.824036	+	0.566537i	$0.808283\pi$
$984$	−13.0111	+	3.24205i	−0.414779	+	0.103353i
$985$		−	22.8249i		−	0.727261i
$986$	28.7607	+	12.4152i	0.915927	+	0.395381i
$987$	3.98887	−	7.51527i	0.126967	−	0.239214i
$988$	−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
$994$	9.94518	+	8.93889i	0.315442	+	0.283524i
$995$	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	0.355702	−	0.934600i	$-0.384242\pi$
$997$	−1.69374	−	0.701569i	−0.0536412	−	0.0222189i	−0.409343	+	0.912381i	$0.634242\pi$
$998$	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.83.9	yes	80
3.2	odd	2		714.2.w.e.83.5	✓	80
7.6	odd	2	inner	714.2.w.f.83.12	yes	80
17.8	even	8		714.2.w.e.671.16	yes	80
21.20	even	2		714.2.w.e.83.16	yes	80
51.8	odd	8	inner	714.2.w.f.671.12	yes	80
119.76	odd	8		714.2.w.e.671.5	yes	80
357.314	even	8	inner	714.2.w.f.671.9	yes	80

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.256259 + 1.71299i) q^{3} -1.00000i q^{4} +(-2.17160 + 0.899506i) q^{5} +(-1.03006 - 1.39247i) q^{6} +(0.880980 - 2.49477i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86866 - 0.877938i) q^{9} +O(q^{10})\)	\(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} +(0.880980 - 2.49477i) 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} +(1.14112 + 2.38702i) 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} +(4.04775 + 2.14842i) 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} +(-2.49477 - 0.880980i) 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} +(-4.38135 + 1.34303i) 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} +(-5.44775 - 4.39569i) 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} +(2.38702 - 1.14112i) 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} +(-4.71749 + 6.38320i) 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} +(-4.62519 - 4.15719i) 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} +(-10.4792 + 11.6589i) 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} +(2.14842 - 4.04775i) 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} +(4.73039 - 13.3956i) 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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