LMFDB - Embedded newform 768.2.z.a.685.55

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			685.55
Character	$\chi$	$=$	768.685
Dual form			768.2.z.a.37.55

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22241 - 0.711131i) q^{2} +(-0.514103 - 0.857729i) q^{3} +(0.988587 - 1.73859i) q^{4} +(-0.780458 + 2.18123i) q^{5} +(-1.23840 - 0.682904i) q^{6} +(-3.19717 - 0.969849i) q^{7} +(-0.0279035 - 2.82829i) q^{8} +(-0.471397 + 0.881921i) q^{9} +O(q^{10})$	\(q+(1.22241 - 0.711131i) q^{2} +(-0.514103 - 0.857729i) q^{3} +(0.988587 - 1.73859i) q^{4} +(-0.780458 + 2.18123i) q^{5} +(-1.23840 - 0.682904i) q^{6} +(-3.19717 - 0.969849i) q^{7} +(-0.0279035 - 2.82829i) q^{8} +(-0.471397 + 0.881921i) q^{9} +(0.597100 + 3.22138i) q^{10} +(-4.82218 + 3.57637i) q^{11} +(-1.99947 + 0.0458749i) q^{12} +(-2.52892 + 5.34696i) q^{13} +(-4.59795 + 1.08805i) q^{14} +(2.27214 - 0.451957i) q^{15} +(-2.04539 - 3.43749i) q^{16} +(-4.74728 - 0.944293i) q^{17} +(0.0509197 + 1.41330i) q^{18} +(4.60322 + 0.226142i) q^{19} +(3.02072 + 3.51324i) q^{20} +(0.811804 + 3.24090i) q^{21} +(-3.35143 + 7.80100i) q^{22} +(0.811178 - 8.23603i) q^{23} +(-2.41156 + 1.47797i) q^{24} +(-0.283618 - 0.232759i) q^{25} +(0.710998 + 8.33459i) q^{26} +(0.998795 - 0.0490677i) q^{27} +(-4.84685 + 4.59978i) q^{28} +(-0.807720 + 0.119814i) q^{29} +(2.45610 - 2.16827i) q^{30} +(1.45817 - 0.603995i) q^{31} +(-4.94482 - 2.74750i) q^{32} +(5.54665 + 2.29750i) q^{33} +(-6.47465 + 2.22162i) q^{34} +(4.61072 - 6.21684i) q^{35} +(1.06728 + 1.69142i) q^{36} +(-5.85849 - 5.30983i) q^{37} +(5.78786 - 2.99705i) q^{38} +(5.88637 - 0.579757i) q^{39} +(6.19094 + 2.14650i) q^{40} +(0.378072 - 0.310276i) q^{41} +(3.29706 + 3.38442i) q^{42} +(2.56324 + 1.53635i) q^{43} +(1.45070 + 11.9193i) q^{44} +(-1.55577 - 1.71653i) q^{45} +(-4.86530 - 10.6447i) q^{46} +(-5.87190 + 3.92348i) q^{47} +(-1.89690 + 3.52162i) q^{48} +(3.46097 + 2.31255i) q^{49} +(-0.512220 - 0.0828384i) q^{50} +(1.63064 + 4.55734i) q^{51} +(6.79611 + 9.68270i) q^{52} +(2.86652 + 0.425209i) q^{53} +(1.18605 - 0.770255i) q^{54} +(-4.03740 - 13.3095i) q^{55} +(-2.65380 + 9.06957i) q^{56} +(-2.17256 - 4.06458i) q^{57} +(-0.902164 + 0.720856i) q^{58} +(-5.29025 - 11.1853i) q^{59} +(1.46044 - 4.39713i) q^{60} +(-3.59603 + 14.3562i) q^{61} +(1.35297 - 1.77528i) q^{62} +(2.36246 - 2.36246i) q^{63} +(-7.99844 + 0.157838i) q^{64} +(-9.68926 - 9.68926i) q^{65} +(8.41412 - 1.13590i) q^{66} +(7.09260 + 1.77660i) q^{67} +(-6.33484 + 7.32006i) q^{68} +(-7.48131 + 3.53840i) q^{69} +(1.21522 - 10.8784i) q^{70} +(-12.9788 + 6.93731i) q^{71} +(2.50748 + 1.30864i) q^{72} +(6.48097 - 1.96598i) q^{73} +(-10.9375 - 2.32465i) q^{74} +(-0.0538354 + 0.362929i) q^{75} +(4.94385 - 7.77956i) q^{76} +(18.8858 - 6.75746i) q^{77} +(6.78329 - 4.89468i) q^{78} +(-2.73458 + 4.09259i) q^{79} +(9.09433 - 1.77866i) q^{80} +(-0.555570 - 0.831470i) q^{81} +(0.241514 - 0.648144i) q^{82} +(7.42778 - 6.73215i) q^{83} +(6.43714 + 1.79252i) q^{84} +(5.76478 - 9.61795i) q^{85} +(4.22588 + 0.0552520i) q^{86} +(0.518019 + 0.631208i) q^{87} +(10.2496 + 13.5387i) q^{88} +(1.20458 + 12.2303i) q^{89} +(-3.12247 - 0.991951i) q^{90} +(13.2711 - 14.6424i) q^{91} +(-13.5172 - 9.55234i) q^{92} +(-1.26771 - 0.940202i) q^{93} +(-4.38778 + 8.97181i) q^{94} +(-4.08589 + 9.86422i) q^{95} +(0.185540 + 5.65381i) q^{96} +(-1.90671 - 4.60322i) q^{97} +(5.87526 + 0.365685i) q^{98} +(-0.880919 - 5.93867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{39}{64}\right)$

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 $

$2$	1.22241	−	0.711131i	0.864376	−	0.502845i
$2$	1.22241	−	0.711131i	0.864376	−	0.502845i
$3$	−0.514103	−	0.857729i	−0.296817	−	0.495210i
$3$	−0.514103	−	0.857729i	−0.296817	−	0.495210i
$4$	0.988587	−	1.73859i	0.494293	−	0.869295i
$5$	−0.780458	+	2.18123i	−0.349032	+	0.975478i	0.630851	+	0.775904i	$0.282706\pi$
$5$	−0.780458	+	2.18123i	−0.349032	+	0.975478i	−0.979883	+	0.199574i	$0.936044\pi$
$6$	−1.23840	−	0.682904i	−0.505576	−	0.278795i
$7$	−3.19717	−	0.969849i	−1.20841	−	0.366569i	−0.379103	−	0.925355i	$-0.623767\pi$
$7$	−3.19717	−	0.969849i	−1.20841	−	0.366569i	−0.829312	+	0.558786i	$0.811267\pi$
$8$	−0.0279035	−	2.82829i	−0.00986538	−	0.999951i
$9$	−0.471397	+	0.881921i	−0.157132	+	0.293974i
$10$	0.597100	+	3.22138i	0.188820	+	1.01869i
$11$	−4.82218	+	3.57637i	−1.45394	+	1.07832i	−0.473660	+	0.880708i	$0.657068\pi$
$11$	−4.82218	+	3.57637i	−1.45394	+	1.07832i	−0.980281	+	0.197609i	$0.936682\pi$
$12$	−1.99947	+	0.0458749i	−0.577198	+	0.0132430i
$13$	−2.52892	+	5.34696i	−0.701397	+	1.48298i	0.166398	+	0.986059i	$0.446786\pi$
$13$	−2.52892	+	5.34696i	−0.701397	+	1.48298i	−0.867796	+	0.496921i	$0.834464\pi$
$14$	−4.59795	+	1.08805i	−1.22885	+	0.290792i
$15$	2.27214	−	0.451957i	0.586665	−	0.116695i
$16$	−2.04539	−	3.43749i	−0.511348	−	0.859374i
$17$	−4.74728	−	0.944293i	−1.15138	−	0.229025i	−0.417746	−	0.908564i	$-0.637180\pi$
$17$	−4.74728	−	0.944293i	−1.15138	−	0.229025i	−0.733639	+	0.679539i	$0.762180\pi$
$18$	0.0509197	+	1.41330i	0.0120019	+	0.333117i
$19$	4.60322	+	0.226142i	1.05605	+	0.0518805i	0.569676	−	0.821869i	$-0.307069\pi$
$19$	4.60322	+	0.226142i	1.05605	+	0.0518805i	0.486376	+	0.873750i	$0.338319\pi$
$20$	3.02072	+	3.51324i	0.675454	+	0.785584i
$21$	0.811804	+	3.24090i	0.177150	+	0.707223i
$22$	−3.35143	+	7.80100i	−0.714526	+	1.66318i
$23$	0.811178	−	8.23603i	0.169142	−	1.71733i	−0.418505	−	0.908214i	$-0.637446\pi$
$23$	0.811178	−	8.23603i	0.169142	−	1.71733i	0.587648	−	0.809117i	$-0.300054\pi$
$24$	−2.41156	+	1.47797i	−0.492258	+	0.301688i
$25$	−0.283618	−	0.232759i	−0.0567235	−	0.0465518i
$26$	0.710998	+	8.33459i	0.139438	+	1.63455i
$27$	0.998795	−	0.0490677i	0.192218	−	0.00944308i
$28$	−4.84685	+	4.59978i	−0.915968	+	0.869277i
$29$	−0.807720	+	0.119814i	−0.149990	+	0.0222489i	−0.221303	−	0.975205i	$-0.571031\pi$
$29$	−0.807720	+	0.119814i	−0.149990	+	0.0222489i	0.0713133	+	0.997454i	$0.477281\pi$
$30$	2.45610	−	2.16827i	0.448420	−	0.395870i
$31$	1.45817	−	0.603995i	0.261896	−	0.108481i	−0.247872	−	0.968793i	$-0.579731\pi$
$31$	1.45817	−	0.603995i	0.261896	−	0.108481i	0.509768	+	0.860312i	$0.329731\pi$
$32$	−4.94482	−	2.74750i	−0.874129	−	0.485693i
$33$	5.54665	+	2.29750i	0.965548	+	0.399943i
$34$	−6.47465	+	2.22162i	−1.11039	+	0.381005i
$35$	4.61072	−	6.21684i	0.779355	−	1.05084i
$36$	1.06728	+	1.69142i	0.177881	+	0.281904i
$37$	−5.85849	−	5.30983i	−0.963130	−	0.872930i	0.0288168	−	0.999585i	$-0.490826\pi$
$37$	−5.85849	−	5.30983i	−0.963130	−	0.872930i	−0.991947	+	0.126654i	$0.959576\pi$
$38$	5.78786	−	2.99705i	0.938914	−	0.486186i
$39$	5.88637	−	0.579757i	0.942573	−	0.0928354i
$40$	6.19094	+	2.14650i	0.978874	+	0.339391i
$41$	0.378072	−	0.310276i	0.0590450	−	0.0484570i	−0.604408	−	0.796675i	$-0.706590\pi$
$41$	0.378072	−	0.310276i	0.0590450	−	0.0484570i	0.663453	+	0.748218i	$0.269090\pi$
$42$	3.29706	+	3.38442i	0.508748	+	0.522228i
$43$	2.56324	+	1.53635i	0.390890	+	0.234290i	0.696023	−	0.718019i	$-0.254951\pi$
$43$	2.56324	+	1.53635i	0.390890	+	0.234290i	−0.305133	+	0.952310i	$0.598701\pi$
$44$	1.45070	+	11.9193i	0.218702	+	1.79691i
$45$	−1.55577	−	1.71653i	−0.231921	−	0.255885i
$46$	−4.86530	−	10.6447i	−0.717349	−	1.56947i
$47$	−5.87190	+	3.92348i	−0.856505	+	0.572299i	−0.904464	−	0.426551i	$-0.859729\pi$
$47$	−5.87190	+	3.92348i	−0.856505	+	0.572299i	0.0479583	+	0.998849i	$0.484729\pi$
$48$	−1.89690	+	3.52162i	−0.273793	+	0.508302i
$49$	3.46097	+	2.31255i	0.494424	+	0.330364i
$50$	−0.512220	−	0.0828384i	−0.0724389	−	0.0117151i
$51$	1.63064	+	4.55734i	0.228336	+	0.638155i
$52$	6.79611	+	9.68270i	0.942451	+	1.34275i
$53$	2.86652	+	0.425209i	0.393747	+	0.0584069i	0.340669	−	0.940183i	$-0.389347\pi$
$53$	2.86652	+	0.425209i	0.393747	+	0.0584069i	0.0530788	+	0.998590i	$0.483097\pi$
$54$	1.18605	−	0.770255i	0.161401	−	0.104818i
$55$	−4.03740	−	13.3095i	−0.544402	−	1.79465i
$56$	−2.65380	+	9.06957i	−0.354629	+	1.21197i
$57$	−2.17256	−	4.06458i	−0.287763	−	0.538366i
$58$	−0.902164	+	0.720856i	−0.118460	+	0.0946531i
$59$	−5.29025	−	11.1853i	−0.688732	−	1.45620i	−0.880151	−	0.474694i	$-0.842559\pi$
$59$	−5.29025	−	11.1853i	−0.688732	−	1.45620i	0.191419	−	0.981508i	$-0.438691\pi$
$60$	1.46044	−	4.39713i	0.188542	−	0.567666i
$61$	−3.59603	+	14.3562i	−0.460424	+	1.83812i	0.0800977	+	0.996787i	$0.474477\pi$
$61$	−3.59603	+	14.3562i	−0.460424	+	1.83812i	−0.540522	+	0.841330i	$0.681773\pi$
$62$	1.35297	−	1.77528i	0.171827	−	0.225461i
$63$	2.36246	−	2.36246i	0.297643	−	0.297643i
$64$	−7.99844	+	0.157838i	−0.999805	+	0.0197298i
$65$	−9.68926	−	9.68926i	−1.20180	−	1.20180i
$66$	8.41412	−	1.13590i	1.03571	−	0.139820i
$67$	7.09260	+	1.77660i	0.866499	+	0.217047i	0.650648	−	0.759380i	$-0.274497\pi$
$67$	7.09260	+	1.77660i	0.866499	+	0.217047i	0.215851	+	0.976426i	$0.430747\pi$
$68$	−6.33484	+	7.32006i	−0.768212	+	0.887688i
$69$	−7.48131	+	3.53840i	−0.900644	+	0.425973i
$70$	1.21522	−	10.8784i	0.145247	−	1.30021i
$71$	−12.9788	+	6.93731i	−1.54030	+	0.823307i	−0.999837	−	0.0180603i	$-0.994251\pi$
$71$	−12.9788	+	6.93731i	−1.54030	+	0.823307i	−0.540463	+	0.841368i	$0.681751\pi$
$72$	2.50748	+	1.30864i	0.295510	+	0.154224i
$73$	6.48097	−	1.96598i	0.758540	−	0.230101i	0.112758	−	0.993622i	$-0.464031\pi$
$73$	6.48097	−	1.96598i	0.758540	−	0.230101i	0.645782	+	0.763522i	$0.276531\pi$
$74$	−10.9375	−	2.32465i	−1.27146	−	0.270235i
$75$	−0.0538354	+	0.362929i	−0.00621638	+	0.0419074i
$76$	4.94385	−	7.77956i	0.567099	−	0.892377i
$77$	18.8858	−	6.75746i	2.15224	−	0.770084i
$78$	6.78329	−	4.89468i	0.768056	−	0.554213i
$79$	−2.73458	+	4.09259i	−0.307665	+	0.460453i	−0.952793	−	0.303622i	$-0.901804\pi$
$79$	−2.73458	+	4.09259i	−0.307665	+	0.460453i	0.645128	+	0.764074i	$0.276804\pi$
$80$	9.09433	−	1.77866i	1.01678	−	0.198860i
$81$	−0.555570	−	0.831470i	−0.0617300	−	0.0923855i
$82$	0.241514	−	0.648144i	0.0266707	−	0.0715756i
$83$	7.42778	−	6.73215i	0.815305	−	0.738949i	−0.153133	−	0.988206i	$-0.548936\pi$
$83$	7.42778	−	6.73215i	0.815305	−	0.738949i	0.968437	+	0.249257i	$0.0801863\pi$
$84$	6.43714	+	1.79252i	0.702350	+	0.195580i
$85$	5.76478	−	9.61795i	0.625278	−	1.04321i
$86$	4.22588	+	0.0552520i	0.455688	+	0.00595798i
$87$	0.518019	+	0.631208i	0.0555375	+	0.0676726i
$88$	10.2496	+	13.5387i	1.09261	+	1.44323i
$89$	1.20458	+	12.2303i	0.127685	+	1.29641i	0.818974	+	0.573831i	$0.194543\pi$
$89$	1.20458	+	12.2303i	0.127685	+	1.29641i	−0.691289	+	0.722579i	$0.742957\pi$
$90$	−3.12247	−	0.991951i	−0.329137	−	0.104561i
$91$	13.2711	−	14.6424i	1.39119	−	1.53494i
$92$	−13.5172	−	9.55234i	−1.40926	−	0.995900i
$93$	−1.26771	−	0.940202i	−0.131456	−	0.0974944i
$94$	−4.38778	+	8.97181i	−0.452565	+	0.925371i
$95$	−4.08589	+	9.86422i	−0.419204	+	1.01205i
$96$	0.185540	+	5.65381i	0.0189366	+	0.577040i
$97$	−1.90671	−	4.60322i	−0.193597	−	0.467386i	0.797036	−	0.603931i	$-0.206400\pi$
$97$	−1.90671	−	4.60322i	−0.193597	−	0.467386i	−0.990634	+	0.136546i	$0.956400\pi$
$98$	5.87526	+	0.365685i	0.593491	+	0.0369398i
$99$	−0.880919	−	5.93867i	−0.0885357	−	0.596859i
$100$	−0.685053	+	0.262993i	−0.0685053	+	0.0262993i
$101$	0.441059	+	8.97796i	0.0438870	+	0.893341i	0.915296	+	0.402783i	$0.131957\pi$
$101$	0.441059	+	8.97796i	0.0438870	+	0.893341i	−0.871409	+	0.490558i	$0.836793\pi$
$102$	5.23418	+	4.41135i	0.518261	+	0.436789i
$103$	−0.900425	+	1.09717i	−0.0887215	+	0.108107i	−0.815479	−	0.578787i	$-0.803526\pi$
$103$	−0.900425	+	1.09717i	−0.0887215	+	0.108107i	0.726758	+	0.686894i	$0.241026\pi$
$104$	15.1933	+	7.00333i	1.48983	+	0.686733i
$105$	−7.70275	−	0.758654i	−0.751711	−	0.0740371i
$106$	3.80646	−	1.51869i	0.369716	−	0.147508i
$107$	−4.17865	+	1.04670i	−0.403966	+	0.101188i	−0.439637	−	0.898175i	$-0.644893\pi$
$107$	−4.17865	+	1.04670i	−0.403966	+	0.101188i	0.0356716	+	0.999364i	$0.488643\pi$
$108$	0.902087	−	1.78500i	0.0868034	−	0.171762i
$109$	0.757363	−	15.4165i	0.0725422	−	1.47663i	−0.636398	−	0.771361i	$-0.719576\pi$
$109$	0.757363	−	15.4165i	0.0725422	−	1.47663i	0.708940	−	0.705269i	$-0.249174\pi$
$110$	−14.4002	−	13.3986i	−1.37300	−	1.27751i
$111$	−1.54252	+	7.75479i	−0.146410	+	0.736052i
$112$	3.20561	+	12.9740i	0.302901	+	1.22592i
$113$	1.81938	+	9.14662i	0.171152	+	0.860442i	0.966967	+	0.254901i	$0.0820430\pi$
$113$	1.81938	+	9.14662i	0.171152	+	0.860442i	−0.795815	+	0.605540i	$0.792957\pi$
$114$	−5.54621	−	3.42362i	−0.519450	−	0.320651i
$115$	17.3316	+	8.19725i	1.61618	+	0.764397i
$116$	−0.590194	+	1.52274i	−0.0547981	+	0.141383i
$117$	−3.52347	−	4.75085i	−0.325745	−	0.439216i
$118$	−14.4211	−	9.91100i	−1.32757	−	0.912381i
$119$	14.2620	+	7.62321i	1.30740	+	0.698818i
$120$	−1.34167	−	6.41367i	−0.122477	−	0.585485i
$121$	7.26984	−	23.9655i	0.660895	−	2.17868i
$122$	5.81327	+	20.1064i	0.526308	+	1.82035i
$123$	−0.460501	−	0.164770i	−0.0415219	−	0.0148568i
$124$	0.391431	−	3.13227i	0.0351515	−	0.281286i
$125$	−9.20626	+	5.51802i	−0.823433	+	0.493547i
$126$	1.20789	−	4.56793i	0.107607	−	0.406943i
$127$		−	4.44291i		−	0.394245i	−0.980379	−	0.197122i	$-0.936840\pi$
$127$		−	4.44291i		−	0.394245i	0.980379	−	0.197122i	$-0.0631596\pi$
$128$	−9.66516	+	5.88088i	−0.854287	+	0.519801i
$129$		−	2.98840i		−	0.263114i
$130$	−18.7346	−	4.95395i	−1.64313	−	0.434490i
$131$	−4.40035	+	2.63747i	−0.384460	+	0.230436i	−0.693255	−	0.720692i	$-0.743824\pi$
$131$	−4.40035	+	2.63747i	−0.384460	+	0.230436i	0.308795	+	0.951129i	$0.400074\pi$
$132$	9.47775	−	7.37208i	0.824932	−	0.641657i
$133$	−14.4979	−	5.18745i	−1.25713	−	0.449809i
$134$	9.93348	−	2.87202i	0.858122	−	0.248105i
$135$	−0.672490	+	2.21690i	−0.0578787	+	0.190801i
$136$	−2.53827	+	13.4530i	−0.217655	+	1.15359i
$137$	−10.3088	−	5.51019i	−0.880744	−	0.470768i	−0.0319492	−	0.999489i	$-0.510171\pi$
$137$	−10.3088	−	5.51019i	−0.880744	−	0.470768i	−0.848795	+	0.528722i	$0.822671\pi$
$138$	−6.62899	+	9.64557i	−0.564297	+	0.821085i
$139$	0.339670	+	0.457992i	0.0288104	+	0.0388464i	0.817378	−	0.576102i	$-0.195427\pi$
$139$	0.339670	+	0.457992i	0.0288104	+	0.0388464i	−0.788567	+	0.614948i	$0.789177\pi$
$140$	−6.25044	−	14.1620i	−0.528259	−	1.19691i
$141$	6.38404	+	3.01943i	0.537634	+	0.254282i
$142$	−10.9321	+	17.7099i	−0.917403	+	1.48618i
$143$	−6.92779	−	34.8284i	−0.579331	−	2.91249i
$144$	3.99579	−	0.183452i	0.332983	−	0.0152876i
$145$	0.369049	−	1.85534i	0.0306479	−	0.154077i
$146$	6.52435	−	7.01206i	0.539959	−	0.580322i
$147$	0.204243	−	4.15746i	0.0168457	−	0.342901i
$148$	−15.0232	+	4.93629i	−1.23490	+	0.405761i
$149$	−12.6586	+	3.17080i	−1.03703	+	0.259762i	−0.723869	−	0.689938i	$-0.757638\pi$
$149$	−12.6586	+	3.17080i	−1.03703	+	0.259762i	−0.313161	+	0.949700i	$0.601388\pi$
$150$	0.192281	+	0.481933i	0.0156997	+	0.0393497i
$151$	0.607378	+	0.0598215i	0.0494277	+	0.00486821i	0.122701	−	0.992444i	$-0.460844\pi$
$151$	0.607378	+	0.0598215i	0.0494277	+	0.00486821i	−0.0732730	+	0.997312i	$0.523344\pi$
$152$	0.511149	−	13.0256i	0.0414596	−	1.05651i
$153$	3.07064	−	3.74159i	0.248247	−	0.302490i
$154$	18.2809	−	21.6907i	1.47311	−	1.74789i
$155$	0.179412	+	3.65201i	0.0144107	+	0.293337i
$156$	4.81123	−	10.8071i	0.385206	−	0.865262i
$157$	−0.0788092	−	0.531288i	−0.00628966	−	0.0424014i	0.985804	−	0.167897i	$-0.0536978\pi$
$157$	−0.0788092	−	0.531288i	−0.00628966	−	0.0424014i	−0.992094	+	0.125496i	$0.959948\pi$
$158$	−0.432422	+	6.94748i	−0.0344016	+	0.552712i
$159$	−1.10897	−	2.67730i	−0.0879474	−	0.212324i
$160$	9.85216	−	8.64151i	0.778882	−	0.683171i
$161$	−10.5812	+	25.5452i	−0.833914	+	2.01325i
$162$	−1.27042	−	0.621316i	−0.0998136	−	0.0488152i
$163$	−4.15362	−	3.08053i	−0.325337	−	0.241286i	0.420687	−	0.907206i	$-0.361789\pi$
$163$	−4.15362	−	3.08053i	−0.325337	−	0.241286i	−0.746023	+	0.665920i	$0.768039\pi$
$164$	−0.165685	−	0.964048i	−0.0129379	−	0.0752795i
$165$	−9.34031	+	10.3054i	−0.727142	+	0.802278i
$166$	4.29238	−	13.5116i	0.333153	−	1.04870i
$167$	−1.46453	−	14.8696i	−0.113329	−	1.15065i	−0.868697	−	0.495345i	$-0.835042\pi$
$167$	−1.46453	−	14.8696i	−0.113329	−	1.15065i	0.755368	−	0.655301i	$-0.227458\pi$
$168$	9.14356	−	2.38645i	0.705441	−	0.184119i
$169$	−13.9474	−	16.9950i	−1.07288	−	1.30731i
$170$	0.207320	−	15.8566i	0.0159007	−	1.21615i
$171$	−2.36938	+	3.95308i	−0.181191	+	0.302299i
$172$	5.20506	−	2.93761i	0.396882	−	0.223991i
$173$	−6.86372	+	6.22091i	−0.521839	+	0.472967i	−0.889463	−	0.457007i	$-0.848921\pi$
$173$	−6.86372	+	6.22091i	−0.521839	+	0.472967i	0.367624	+	0.929974i	$0.380171\pi$
$174$	1.08210	+	0.403218i	0.0820341	+	0.0305678i
$175$	0.681031	+	1.01924i	0.0514811	+	0.0770470i
$176$	22.1570	+	9.26113i	1.67015	+	0.698084i
$177$	−6.87422	+	10.2880i	−0.516698	+	0.773293i
$178$	10.1698	+	14.0939i	0.762261	+	1.05638i
$179$	12.6114	−	4.51243i	0.942619	−	0.337275i	0.179666	−	0.983728i	$-0.442498\pi$
$179$	12.6114	−	4.51243i	0.942619	−	0.337275i	0.762954	+	0.646453i	$0.223748\pi$
$180$	−4.52236	+	1.00791i	−0.337077	+	0.0751253i
$181$	0.665283	−	4.48498i	0.0494501	−	0.333366i	−0.950307	−	0.311315i	$-0.899231\pi$
$181$	0.665283	−	4.48498i	0.0494501	−	0.333366i	0.999757	−	0.0220505i	$-0.00701946\pi$
$182$	5.81012	−	27.3366i	0.430675	−	2.02632i
$183$	14.1624	−	4.29612i	1.04692	−	0.317578i
$184$	−23.3165	−	2.06443i	−1.71892	−	0.152192i
$185$	16.1543	−	8.63465i	1.18769	−	0.634832i
$186$	−2.21828	−	0.247804i	−0.162652	−	0.0181698i
$187$	26.2694	−	12.4245i	1.92101	−	0.908568i
$188$	1.01644	+	14.0875i	0.0741315	+	1.02744i
$189$	−3.24090	−	0.811804i	−0.235741	−	0.0590500i
$190$	2.02010	+	14.9637i	0.146553	+	1.08558i
$191$	5.98551	+	5.98551i	0.433096	+	0.433096i	0.889680	−	0.456584i	$-0.150927\pi$
$191$	5.98551	+	5.98551i	0.433096	+	0.433096i	−0.456584	+	0.889680i	$0.650927\pi$
$192$	4.24740	+	6.77935i	0.306530	+	0.489257i
$193$	−8.84828	+	8.84828i	−0.636913	+	0.636913i	−0.949793	−	0.312880i	$-0.898706\pi$
$193$	−8.84828	+	8.84828i	−0.636913	+	0.636913i	0.312880	+	0.949793i	$0.398706\pi$
$194$	−5.60428	−	4.27111i	−0.402364	−	0.306648i
$195$	−3.32948	+	13.2920i	−0.238429	+	0.951862i
$196$	7.44204	−	3.73106i	0.531574	−	0.266504i
$197$	1.45432	+	3.07490i	0.103616	+	0.219077i	0.949136	−	0.314866i	$-0.101960\pi$
$197$	1.45432	+	3.07490i	0.103616	+	0.219077i	−0.845520	+	0.533943i	$0.820710\pi$
$198$	−5.30002	−	6.63306i	−0.376656	−	0.471391i
$199$	10.9930	+	20.5665i	0.779276	+	1.45792i	0.886025	+	0.463637i	$0.153456\pi$
$199$	10.9930	+	20.5665i	0.779276	+	1.45792i	−0.106749	+	0.994286i	$0.534044\pi$
$200$	−0.650396	+	0.808648i	−0.0459899	+	0.0571800i
$201$	−2.12248	−	6.99688i	−0.149708	−	0.493522i
$202$	6.92366	+	10.6611i	0.487147	+	0.750114i
$203$	2.69862	+	0.400302i	0.189406	+	0.0280957i
$204$	9.53538	+	1.67031i	0.667610	+	0.116945i
$205$	0.381715	+	1.06682i	0.0266601	+	0.0745101i
$206$	−0.320459	+	1.98152i	−0.0223275	+	0.138059i
$207$	6.88114	+	4.59783i	0.478273	+	0.319572i
$208$	23.5528	−	2.24347i	1.63309	−	0.155557i
$209$	−23.0063	+	15.3723i	−1.59138	+	1.06333i
$210$	−9.95544	+	4.55027i	−0.686991	+	0.313998i
$211$	8.33152	+	9.19242i	0.573565	+	0.632832i	0.956775	−	0.290830i	$-0.0939313\pi$
$211$	8.33152	+	9.19242i	0.573565	+	0.632832i	−0.383209	+	0.923661i	$0.625181\pi$
$212$	3.57307	−	4.56336i	0.245400	−	0.313413i
$213$	12.6228	+	7.56579i	0.864898	+	0.518400i
$214$	−4.36370	+	4.25106i	−0.298296	+	0.290597i
$215$	−5.35163	+	4.39197i	−0.364978	+	0.299530i
$216$	−0.166647	−	2.82351i	−0.0113389	−	0.192116i
$217$	−5.24781	+	0.516864i	−0.356244	+	0.0350870i
$218$	−10.0373	−	19.3839i	−0.679813	−	1.31284i
$219$	−5.01816	−	4.54820i	−0.339096	−	0.307339i
$220$	−27.1311	−	6.13823i	−1.82918	−	0.413839i
$221$	17.0546	−	22.9955i	1.14722	−	1.54684i
$222$	3.62907	+	10.5765i	0.243567	+	0.709848i
$223$	−1.23321	−	0.510811i	−0.0825817	−	0.0342065i	0.341010	−	0.940060i	$-0.389231\pi$
$223$	−1.23321	−	0.510811i	−0.0825817	−	0.0342065i	−0.423592	+	0.905853i	$0.639231\pi$
$224$	13.1448	+	13.5799i	0.878271	+	0.907347i
$225$	0.338972	−	0.140407i	0.0225981	−	0.00936044i
$226$	8.72847	+	9.88713i	0.580609	+	0.657682i
$227$	3.38746	−	0.502482i	0.224834	−	0.0333509i	−0.0333630	−	0.999443i	$-0.510622\pi$
$227$	3.38746	−	0.502482i	0.224834	−	0.0333509i	0.258197	+	0.966092i	$0.416872\pi$
$228$	−9.21440	−	0.240992i	−0.610238	−	0.0159601i
$229$	4.58706	−	0.225348i	0.303122	−	0.0148914i	0.103061	−	0.994675i	$-0.467136\pi$
$229$	4.58706	−	0.225348i	0.303122	−	0.0148914i	0.200060	+	0.979784i	$0.435886\pi$
$230$	27.0157	−	2.30463i	1.78136	−	0.151963i
$231$	−15.5053	−	12.7249i	−1.02018	−	0.837237i
$232$	0.361407	+	2.28112i	0.0237275	+	0.149763i
$233$	0.358064	−	3.63548i	0.0234575	−	0.238168i	−0.976305	−	0.216397i	$-0.930569\pi$
$233$	0.358064	−	3.63548i	0.0234575	−	0.238168i	0.999763	−	0.0217713i	$-0.00693055\pi$
$234$	−7.68561	−	3.30185i	−0.502424	−	0.215849i
$235$	−3.97526	−	15.8701i	−0.259317	−	1.03525i
$236$	−24.6765	−	1.86006i	−1.60631	−	0.121079i
$237$	4.91619	+	0.241517i	0.319341	+	0.0156882i
$238$	22.8552	−	0.823449i	1.48148	−	0.0533763i
$239$	−24.8818	−	4.94931i	−1.60947	−	0.320144i	−0.693214	−	0.720732i	$-0.743806\pi$
$239$	−24.8818	−	4.94931i	−1.60947	−	0.320144i	−0.916258	+	0.400588i	$0.868806\pi$
$240$	−6.20103	−	6.88605i	−0.400275	−	0.444493i
$241$	16.0107	−	3.18473i	1.03134	−	0.205147i	0.349723	−	0.936853i	$-0.386276\pi$
$241$	16.0107	−	3.18473i	1.03134	−	0.205147i	0.681620	+	0.731707i	$0.261276\pi$
$242$	−8.15582	−	34.4655i	−0.524276	−	2.21553i
$243$	−0.427555	+	0.903989i	−0.0274277	+	0.0579909i
$244$	21.4045	+	20.4443i	1.37028	+	1.30881i
$245$	−7.74535	+	5.74434i	−0.494832	+	0.366993i
$246$	−0.680095	+	0.126059i	−0.0433613	+	0.00803725i
$247$	−12.8504	+	24.0414i	−0.817650	+	1.52971i
$248$	−1.74896	−	4.10728i	−0.111059	−	0.260813i
$249$	−9.59299	−	2.91000i	−0.607931	−	0.184414i
$250$	−7.32982	+	13.2922i	−0.463579	+	0.840670i
$251$	−5.20793	+	14.5552i	−0.328722	+	0.918715i	0.657525	+	0.753433i	$0.271604\pi$
$251$	−5.20793	+	14.5552i	−0.328722	+	0.918715i	−0.986246	+	0.165282i	$0.947146\pi$
$252$	−1.77186	−	6.44286i	−0.111616	−	0.405862i
$253$	25.5435	+	42.6167i	1.60590	+	2.67929i
$254$	−3.15949	−	5.43107i	−0.198244	−	0.340776i
$255$	−11.2133			−0.702203
$256$	−7.63274	+	14.0621i	−0.477046	+	0.878878i
$257$	18.9340			1.18107			0.590537	−	0.807011i	$-0.298916\pi$
$257$	18.9340			1.18107			0.590537	+	0.807011i	$0.298916\pi$
$258$	−2.12514	−	3.65306i	−0.132306	−	0.227430i
$259$	13.5808	+	22.6583i	0.843872	+	1.40792i
$260$	−26.4243	+	7.26698i	−1.63877	+	0.450679i
$261$	0.275090	−	0.768825i	0.0170276	−	0.0475891i
$262$	−3.50346	+	6.35329i	−0.216444	+	0.392508i
$263$	−15.3974	−	4.67075i	−0.949443	−	0.288011i	−0.222675	−	0.974893i	$-0.571479\pi$
$263$	−15.3974	−	4.67075i	−0.949443	−	0.288011i	−0.726769	+	0.686882i	$0.758979\pi$
$264$	6.34322	−	15.7516i	0.390398	−	0.969447i
$265$	−3.16468	+	5.92071i	−0.194405	+	0.363706i
$266$	−21.4114	+	3.96873i	−1.31282	+	0.243338i
$267$	9.87100	−	7.32083i	0.604095	−	0.448028i
$268$	10.1004	−	10.5748i	0.616982	−	0.645958i
$269$	4.34527	−	9.18730i	0.264936	−	0.560160i	−0.727039	−	0.686596i	$-0.759104\pi$
$269$	4.34527	−	9.18730i	0.264936	−	0.560160i	0.991975	+	0.126437i	$0.0403540\pi$
$270$	0.754447	+	3.18820i	0.0459142	+	0.194028i
$271$	7.61870	−	1.51545i	0.462803	−	0.0920573i	0.0418190	−	0.999125i	$-0.486685\pi$
$271$	7.61870	−	1.51545i	0.462803	−	0.0920573i	0.420984	+	0.907068i	$0.361685\pi$
$272$	6.46405	+	18.2502i	0.391941	+	1.10658i
$273$	−19.3820	−	3.85531i	−1.17305	−	0.233334i
$274$	−16.5201	+	0.595204i	−0.998018	+	0.0359576i
$275$	2.20009	+	0.108083i	0.132670	+	0.00651767i
$276$	−1.24410	+	16.5049i	−0.0748862	+	0.993481i
$277$	2.12429	+	8.48066i	0.127636	+	0.509553i	0.999793	+	0.0203271i	$0.00647075\pi$
$277$	2.12429	+	8.48066i	0.127636	+	0.509553i	−0.872157	+	0.489226i	$0.837279\pi$
$278$	0.740909	+	0.318305i	0.0444367	+	0.0190907i
$279$	−0.154702	+	1.57072i	−0.00926177	+	0.0940363i
$280$	−17.7117	−	12.8670i	−1.05848	−	0.768950i
$281$	10.2831	+	8.43914i	0.613440	+	0.503437i	0.889037	−	0.457836i	$-0.151375\pi$
$281$	10.2831	+	8.43914i	0.613440	+	0.503437i	−0.275597	+	0.961273i	$0.588875\pi$
$282$	9.95115	−	0.848901i	0.592582	−	0.0505513i
$283$	−8.61034	+	0.422999i	−0.511832	+	0.0251447i	−0.303345	−	0.952881i	$-0.598104\pi$
$283$	−8.61034	+	0.422999i	−0.511832	+	0.0251447i	−0.208486	+	0.978025i	$0.566854\pi$
$284$	−0.769524	+	29.4229i	−0.0456628	+	1.74593i
$285$	10.5614	−	1.56663i	0.625603	−	0.0927994i
$286$	−33.2361	−	37.6481i	−1.96529	−	2.22618i
$287$	−1.50968	+	0.625330i	−0.0891136	+	0.0369121i
$288$	4.75405	−	3.06578i	0.280135	−	0.180653i
$289$	5.93902	+	2.46002i	0.349354	+	0.144707i
$290$	−0.868256	−	2.53043i	−0.0509857	−	0.148592i
$291$	−2.96806	+	4.00197i	−0.173991	+	0.234600i
$292$	2.98897	−	13.2113i	0.174916	−	0.773133i
$293$	15.6542	+	14.1882i	0.914529	+	0.828881i	0.985687	−	0.168584i	$-0.0539196\pi$
$293$	15.6542	+	14.1882i	0.914529	+	0.828881i	−0.0711584	+	0.997465i	$0.522670\pi$
$294$	−2.70683	−	5.22738i	−0.157865	−	0.304867i
$295$	28.5266	−	2.80962i	1.66088	−	0.163583i
$296$	−14.8543	+	16.7177i	−0.863386	+	0.971695i
$297$	−4.64089	+	3.80868i	−0.269291	+	0.221002i
$298$	−13.2191	+	12.8779i	−0.765763	+	0.745998i
$299$	41.9863	+	25.1656i	2.42813	+	1.45537i
$300$	0.577764	+	0.452385i	0.0333572	+	0.0261184i
$301$	−6.70507	−	7.39790i	−0.386474	−	0.426408i
$302$	0.785008	−	0.358799i	0.0451721	−	0.0206465i
$303$	7.47390	−	4.99390i	0.429365	−	0.286892i
$304$	−8.63804	−	16.2861i	−0.495425	−	0.934072i
$305$	−28.5076	−	19.0482i	−1.63234	−	1.09069i
$306$	1.09284	−	6.75740i	0.0624733	−	0.386295i
$307$	−8.82305	−	24.6588i	−0.503558	−	1.40735i	−0.877356	−	0.479841i	$-0.840694\pi$
$307$	−8.82305	−	24.6588i	−0.503558	−	1.40735i	0.373797	−	0.927510i	$-0.378056\pi$
$308$	6.92183	−	39.5151i	0.394408	−	2.25158i
$309$	1.40399	+	0.208262i	0.0798699	+	0.0118476i
$310$	2.81637	+	4.33668i	0.159959	+	0.246307i
$311$	−2.19479	−	7.23526i	−0.124455	−	0.410274i	0.872467	−	0.488674i	$-0.162519\pi$
$311$	−2.19479	−	7.23526i	−0.124455	−	0.410274i	−0.996922	+	0.0783993i	$0.975019\pi$
$312$	−1.80397	−	16.6322i	−0.102130	−	0.941611i
$313$	−0.574903	−	1.07557i	−0.0324954	−	0.0607947i	0.865150	−	0.501514i	$-0.167223\pi$
$313$	−0.574903	−	1.07557i	−0.0324954	−	0.0607947i	−0.897645	+	0.440719i	$0.854723\pi$
$314$	−0.474153	−	0.593410i	−0.0267580	−	0.0334881i
$315$	3.30928	+	6.99689i	0.186457	+	0.394230i
$316$	4.41197	+	8.80020i	0.248193	+	0.495050i
$317$	−3.95986	+	15.8086i	−0.222408	+	0.887901i	0.751274	+	0.659990i	$0.229440\pi$
$317$	−3.95986	+	15.8086i	−0.222408	+	0.887901i	−0.973682	+	0.227911i	$0.926810\pi$
$318$	−3.25954	−	2.48414i	−0.182786	−	0.139304i
$319$	3.46647	−	3.46647i	0.194085	−	0.194085i
$320$	5.89817	−	17.5697i	0.329718	−	0.982174i
$321$	3.04604	+	3.04604i	0.170013	+	0.170013i
$322$	5.23142	+	38.7514i	0.291536	+	2.15953i
$323$	−21.6392	−	5.42035i	−1.20404	−	0.301596i
$324$	−1.99481	+	0.143929i	−0.110823	+	0.00799607i
$325$	1.96180	−	0.927863i	0.108821	−	0.0514686i
$326$	−7.26810	−	0.811919i	−0.402543	−	0.0449680i
$327$	−13.6125	+	7.27604i	−0.752773	+	0.402366i
$328$	−0.888100	−	1.06064i	−0.0490371	−	0.0585641i
$329$	22.5786	−	6.84915i	1.24480	−	0.377606i
$330$	−4.08920	+	19.2397i	−0.225103	+	1.05911i
$331$	−3.19202	+	21.5189i	−0.175449	+	1.18278i	0.705198	+	0.709010i	$0.250858\pi$
$331$	−3.19202	+	21.5189i	−0.175449	+	1.18278i	−0.880647	+	0.473773i	$0.842892\pi$
$332$	−4.36144	−	19.5692i	−0.239365	−	1.07400i
$333$	7.44452	−	2.66369i	0.407957	−	0.145969i
$334$	−12.3645	−	17.1353i	−0.676555	−	0.937604i
$335$	−9.41066	+	14.0841i	−0.514160	+	0.769494i
$336$	9.48013	−	9.41949i	0.517183	−	0.513875i
$337$	2.67880	+	4.00911i	0.145924	+	0.218390i	0.897230	−	0.441563i	$-0.145576\pi$
$337$	2.67880	+	4.00911i	0.145924	+	0.218390i	−0.751306	+	0.659953i	$0.770576\pi$
$338$	−29.1352	−	10.8564i	−1.58474	−	0.590513i
$339$	6.90997	−	6.26283i	0.375298	−	0.340150i
$340$	−11.0227	−	19.5308i	−0.597789	−	1.05920i
$341$	−4.87146	+	8.12754i	−0.263804	+	0.440131i
$342$	−0.0852108	+	6.51723i	−0.00460767	+	0.352412i
$343$	6.01421	+	7.32834i	0.324737	+	0.395693i
$344$	4.27371	−	7.29245i	0.230423	−	0.393182i
$345$	−1.87922	−	19.0801i	−0.101174	−	1.02724i
$346$	−3.96642	+	12.4855i	−0.213236	+	0.671226i
$347$	−3.09076	+	3.41013i	−0.165921	+	0.183065i	−0.818236	−	0.574882i	$-0.805048\pi$
$347$	−3.09076	+	3.41013i	−0.165921	+	0.183065i	0.652315	+	0.757948i	$0.273798\pi$
$348$	1.60952	−	0.276619i	0.0862792	−	0.0148283i
$349$	9.59137	+	7.11344i	0.513414	+	0.380774i	0.821163	−	0.570694i	$-0.193326\pi$
$349$	9.59137	+	7.11344i	0.513414	+	0.380774i	−0.307749	+	0.951468i	$0.599576\pi$
$350$	1.55731	+	0.761625i	0.0832418	+	0.0407105i
$351$	−2.26351	+	5.46461i	−0.120817	+	0.291679i
$352$	33.6709	−	4.43560i	1.79466	−	0.236418i
$353$	−10.8664	−	26.2338i	−0.578360	−	1.39629i	−0.894284	−	0.447501i	$-0.852314\pi$
$353$	−10.8664	−	26.2338i	−0.578360	−	1.39629i	0.315923	−	0.948785i	$-0.397686\pi$
$354$	−1.08703	+	17.4646i	−0.0577748	+	0.928235i
$355$	−5.00250	−	33.7241i	−0.265505	−	1.78989i
$356$	22.4543	+	9.99644i	1.19008	+	0.529810i
$357$	−0.793499	−	16.1521i	−0.0419964	−	0.854857i
$358$	12.2074	−	14.4844i	0.645181	−	0.765524i
$359$	−10.4012	+	12.6739i	−0.548954	+	0.668902i	−0.971390	−	0.237490i	$-0.923675\pi$
$359$	−10.4012	+	12.6739i	−0.548954	+	0.668902i	0.422436	+	0.906393i	$0.361175\pi$
$360$	−4.81143	+	4.44807i	−0.253585	+	0.234434i
$361$	2.23001	+	0.219637i	0.117369	+	0.0115598i
$362$	−2.37615	−	5.95559i	−0.124888	−	0.313019i
$363$	−24.2933	+	6.08515i	−1.27507	+	0.319388i
$364$	−12.3375	−	37.5484i	−0.646663	−	1.96807i
$365$	−0.769861	+	15.6709i	−0.0402964	+	0.820252i
$366$	14.2572	−	15.3230i	0.745236	−	0.800944i
$367$	4.90387	−	24.6534i	0.255980	−	1.28690i	−0.612222	−	0.790686i	$-0.709724\pi$
$367$	4.90387	−	24.6534i	0.255980	−	1.28690i	0.868202	−	0.496212i	$-0.165276\pi$
$368$	−29.9705	+	14.0575i	−1.56232	+	0.732798i
$369$	0.0954169	+	0.479693i	0.00496721	+	0.0249718i
$370$	13.6069	−	22.0429i	0.707386	−	1.14596i
$371$	−8.75237	−	4.13956i	−0.454400	−	0.214915i
$372$	−2.88787	+	1.27457i	−0.149729	+	0.0660832i
$373$	15.7074	+	21.1790i	0.813298	+	1.09660i	0.993596	+	0.112993i	$0.0360437\pi$
$373$	15.7074	+	21.1790i	0.813298	+	1.09660i	−0.180298	+	0.983612i	$0.557706\pi$
$374$	23.2766	−	33.8688i	1.20360	−	1.75131i
$375$	9.46593	+	5.05964i	0.488818	+	0.261279i
$376$	11.2606	+	16.4980i	0.580720	+	0.850818i
$377$	1.40202	−	4.62185i	0.0722078	−	0.238037i
$378$	−4.53902	+	1.31235i	−0.233462	+	0.0674998i
$379$	−28.5614	−	10.2194i	−1.46710	−	0.524936i	−0.522350	−	0.852731i	$-0.674945\pi$
$379$	−28.5614	−	10.2194i	−1.46710	−	0.524936i	−0.944749	+	0.327795i	$0.893695\pi$
$380$	13.1106	+	16.8553i	0.672558	+	0.864660i
$381$	−3.81081	+	2.28411i	−0.195234	+	0.117019i
$382$	11.5732	+	3.06029i	0.592139	+	0.156578i
$383$			0.983848i			0.0502723i	0.999684	+	0.0251361i	$0.00800193\pi$
$383$			0.983848i			0.0502723i	−0.999684	+	0.0251361i	$0.991998\pi$
$384$	10.0131	+	5.26670i	0.510978	+	0.268765i
$385$			46.4684i			2.36825i
$386$	−4.52397	+	17.1085i	−0.230264	+	0.870801i
$387$	−2.56324	+	1.53635i	−0.130297	+	0.0780968i
$388$	−9.88806	−	1.23568i	−0.501990	−	0.0627323i
$389$	21.2311	+	7.59662i	1.07646	+	0.385164i	0.814649	−	0.579955i	$-0.196930\pi$
$389$	21.2311	+	7.59662i	1.07646	+	0.385164i	0.261812	+	0.965119i	$0.415680\pi$
$390$	5.38237	+	18.6160i	0.272547	+	0.942660i
$391$	−11.6281	+	38.3328i	−0.588059	+	1.93857i
$392$	6.44398	−	9.85315i	0.325470	−	0.497659i
$393$	4.52446	+	2.41837i	0.228229	+	0.121991i
$394$	3.96443	+	2.72458i	0.199725	+	0.137263i
$395$	−6.79268	−	9.15886i	−0.341777	−	0.460832i
$396$	−11.1958	−	4.33933i	−0.562609	−	0.218060i
$397$	−13.4661	−	6.36897i	−0.675842	−	0.319649i	0.0586387	−	0.998279i	$-0.481324\pi$
$397$	−13.4661	−	6.36897i	−0.675842	−	0.319649i	−0.734480	+	0.678630i	$0.762574\pi$
$398$	28.0635	+	17.3233i	1.40670	+	0.868339i
$399$	3.00401	+	15.1022i	0.150389	+	0.756055i
$400$	−0.219998	+	1.45102i	−0.0109999	+	0.0725509i
$401$	−0.237548	+	1.19423i	−0.0118626	+	0.0596371i	−0.986263	−	0.165182i	$-0.947179\pi$
$401$	−0.237548	+	1.19423i	−0.0118626	+	0.0596371i	0.974401	+	0.224819i	$0.0721790\pi$
$402$	−7.57024	−	7.04372i	−0.377569	−	0.351309i
$403$	−0.458071	+	9.32425i	−0.0228182	+	0.464474i
$404$	16.0450	+	8.10867i	0.798270	+	0.403422i
$405$	2.24723	−	0.562902i	0.111666	−	0.0279708i
$406$	3.58349	−	1.42973i	0.177846	−	0.0709565i
$407$	47.2406	+	4.65279i	2.34163	+	0.230630i
$408$	12.8440	−	4.73910i	0.635872	−	0.234620i
$409$	−3.49065	+	4.25337i	−0.172601	+	0.210316i	−0.852125	−	0.523338i	$-0.824686\pi$
$409$	−3.49065	+	4.25337i	−0.172601	+	0.210316i	0.679524	+	0.733654i	$0.262186\pi$
$410$	1.22526	+	1.03265i	0.0605114	+	0.0509988i
$411$	0.573556	+	11.6750i	0.0282914	+	0.575885i
$412$	1.01738	+	2.65012i	0.0501228	+	0.130562i
$413$	6.06576	+	40.8920i	0.298476	+	2.01216i
$414$	11.6813	+	0.727059i	0.574103	+	0.0357330i
$415$	8.88732	+	21.4559i	0.436261	+	1.05323i
$416$	27.1958	−	19.4916i	1.33339	−	0.955652i
$417$	0.218207	−	0.526799i	0.0106857	−	0.0257975i
$418$	−17.1915	+	35.1518i	−0.840863	+	1.71933i
$419$	−3.33616	−	2.47426i	−0.162982	−	0.120876i	0.511134	−	0.859501i	$-0.329225\pi$
$419$	−3.33616	−	2.47426i	−0.162982	−	0.120876i	−0.674116	+	0.738625i	$0.735475\pi$
$420$	−8.93382	+	12.6419i	−0.435926	+	0.616863i
$421$	−20.0822	+	22.1573i	−0.978748	+	1.07988i	0.0180432	+	0.999837i	$0.494256\pi$
$421$	−20.0822	+	22.1573i	−0.978748	+	1.07988i	−0.996791	+	0.0800449i	$0.974494\pi$
$422$	16.7216	+	5.31213i	0.813993	+	0.258590i
$423$	−0.692205	−	7.02807i	−0.0336562	−	0.341717i
$424$	1.12263	−	8.11923i	0.0545196	−	0.394305i
$425$	1.12662	+	1.37279i	0.0546491	+	0.0665901i
$426$	20.8105	+	0.272091i	1.00827	+	0.0131828i
$427$	25.4204	−	42.4114i	1.23018	−	2.05243i
$428$	−2.31118	+	8.29972i	−0.111715	+	0.401182i
$429$	−26.3117	+	23.8475i	−1.27034	+	1.15137i
$430$	−3.41864	+	9.17451i	−0.164861	+	0.442434i
$431$	−17.4902	−	26.1760i	−0.842474	−	1.26085i	−0.963367	−	0.268186i	$-0.913576\pi$
$431$	−17.4902	−	26.1760i	−0.842474	−	1.26085i	0.120893	−	0.992666i	$-0.461424\pi$
$432$	−2.21160	−	3.33299i	−0.106406	−	0.160359i
$433$	−2.20654	+	3.30232i	−0.106040	+	0.158700i	−0.880694	−	0.473685i	$-0.842924\pi$
$433$	−2.20654	+	3.30232i	−0.106040	+	0.158700i	0.774655	+	0.632384i	$0.217924\pi$
$434$	−6.04743	+	4.36370i	−0.290286	+	0.209464i
$435$	−1.78110	+	0.637289i	−0.0853974	+	0.0305557i
$436$	−26.0542	−	16.5573i	−1.24777	−	0.792949i
$437$	5.59655	−	37.7289i	0.267719	−	1.80482i
$438$	−9.36863	−	1.99121i	−0.447650	−	0.0951435i
$439$	−18.6583	+	5.65994i	−0.890514	+	0.270134i	−0.702204	−	0.711975i	$-0.747801\pi$
$439$	−18.6583	+	5.65994i	−0.890514	+	0.270134i	−0.188309	+	0.982110i	$0.560301\pi$
$440$	−37.5305	+	11.7903i	−1.78920	+	0.562081i
$441$	−3.67097	+	1.96218i	−0.174808	+	0.0934370i
$442$	4.49499	−	40.2380i	0.213805	−	1.91393i
$443$	−31.7937	+	15.0373i	−1.51056	+	0.714444i	−0.990220	−	0.139513i	$-0.955446\pi$
$443$	−31.7937	+	15.0373i	−1.51056	+	0.714444i	−0.520344	+	0.853957i	$0.674196\pi$
$444$	11.9575	+	10.3481i	0.567477	+	0.491099i
$445$	−27.6173	−	6.91777i	−1.30918	−	0.327934i
$446$	−1.87074	+	0.252549i	−0.0885822	+	0.0119586i
$447$	9.22749	+	9.22749i	0.436445	+	0.436445i
$448$	25.7254	+	7.25265i	1.21541	+	0.342656i
$449$	24.3624	−	24.3624i	1.14973	−	1.14973i	0.163128	−	0.986605i	$-0.447842\pi$
$449$	24.3624	−	24.3624i	1.14973	−	1.14973i	0.986605	−	0.163128i	$-0.0521583\pi$
$450$	0.314516	−	0.412688i	0.0148264	−	0.0194543i
$451$	−0.713470	+	2.84833i	−0.0335960	+	0.134123i
$452$	17.7008	+	5.87908i	0.832577	+	0.276529i
$453$	−0.260944	−	0.551720i	−0.0122602	−	0.0259221i
$454$	3.78354	−	3.02317i	0.177571	−	0.141884i
$455$	21.5810	+	40.3753i	1.01173	+	1.89282i
$456$	−11.4352	+	6.25805i	−0.535501	+	0.293060i
$457$	−3.78958	−	12.4926i	−0.177269	−	0.584378i	−0.999876	−	0.0157668i	$-0.994981\pi$
$457$	−3.78958	−	12.4926i	−0.177269	−	0.584378i	0.822607	−	0.568611i	$-0.192519\pi$
$458$	5.44703	−	3.53747i	0.254523	−	0.165295i
$459$	−4.78790	−	0.710217i	−0.223480	−	0.0331501i
$460$	31.3855	−	22.0289i	1.46336	−	1.02710i
$461$	−0.842913	−	2.35578i	−0.0392584	−	0.109720i	0.920315	−	0.391177i	$-0.127932\pi$
$461$	−0.842913	−	2.35578i	−0.0392584	−	0.109720i	−0.959574	+	0.281458i	$0.909182\pi$
$462$	−28.0030	−	4.52876i	−1.30282	−	0.210697i
$463$	−28.1497	−	18.8090i	−1.30823	−	0.874128i	−0.311136	−	0.950365i	$-0.600709\pi$
$463$	−28.1497	−	18.8090i	−1.30823	−	0.874128i	−0.997090	+	0.0762371i	$0.975709\pi$
$464$	2.06396	+	2.53147i	0.0958171	+	0.117520i
$465$	3.04020	−	2.03140i	0.140986	−	0.0942037i
$466$	−2.14760	−	4.69869i	−0.0994856	−	0.217663i
$467$	18.6363	+	20.5620i	0.862385	+	0.951496i	0.999235	−	0.0390962i	$-0.0124479\pi$
$467$	18.6363	+	20.5620i	0.862385	+	0.951496i	−0.136850	+	0.990592i	$0.543698\pi$
$468$	−11.7430	+	1.42924i	−0.542822	+	0.0660669i
$469$	−20.9532	−	12.5588i	−0.967527	−	0.579914i
$470$	−16.1451	−	16.5729i	−0.744719	−	0.764451i
$471$	−0.415185	+	0.340734i	−0.0191307	+	0.0157002i
$472$	−31.4877	+	15.2745i	−1.44934	+	0.703065i
$473$	−17.8549	+	1.75856i	−0.820970	+	0.0808585i
$474$	6.18136	−	3.20082i	0.283919	−	0.147018i
$475$	−1.25292	−	1.13558i	−0.0574879	−	0.0521040i
$476$	27.3529	−	17.2596i	1.25372	−	0.791093i
$477$	−1.72627	+	2.32761i	−0.0790405	+	0.106574i
$478$	−33.9355	+	11.6441i	−1.55217	+	0.532591i
$479$	−10.7875	−	4.46834i	−0.492895	−	0.204164i	0.122369	−	0.992485i	$-0.460951\pi$
$479$	−10.7875	−	4.46834i	−0.492895	−	0.204164i	−0.615264	+	0.788321i	$0.710951\pi$
$480$	−12.4771	−	4.00786i	−0.569499	−	0.182933i
$481$	43.2071	−	17.8970i	1.97008	−	0.816032i
$482$	17.3070	−	15.2788i	0.788311	−	0.695930i
$483$	27.3507	−	4.05709i	1.24450	−	0.184604i
$484$	−34.4792	−	36.3312i	−1.56724	−	1.65142i
$485$	11.5288	−	0.566374i	0.523496	−	0.0257177i
$486$	0.120206	+	1.40910i	0.00545263	+	0.0639179i
$487$	−1.27375	−	1.04534i	−0.0577192	−	0.0473689i	0.605091	−	0.796156i	$-0.293137\pi$
$487$	−1.27375	−	1.04534i	−0.0577192	−	0.0473689i	−0.662811	+	0.748787i	$0.730637\pi$
$488$	40.7037	+	9.77002i	1.84257	+	0.442268i
$489$	−0.506875	+	5.14639i	−0.0229217	+	0.232728i
$490$	−5.38304	+	12.5299i	−0.243181	+	0.566044i
$491$	−2.87121	−	11.4625i	−0.129576	−	0.517296i	−0.999701	−	0.0244647i	$-0.992212\pi$
$491$	−2.87121	−	11.4625i	−0.129576	−	0.517296i	0.870125	−	0.492832i	$-0.164038\pi$
$492$	−0.741712	+	0.637733i	−0.0334390	+	0.0287512i
$493$	3.94761	+	0.193934i	0.177791	+	0.00873434i
$494$	1.38808	+	38.5268i	0.0624527	+	1.73340i
$495$	13.6412	+	2.71339i	0.613124	+	0.121958i
$496$	−5.05877	−	3.77706i	−0.227145	−	0.169595i
$497$	48.2235	−	9.59225i	2.16312	−	0.430271i
$498$	−13.7960	+	3.26465i	−0.618213	+	0.146292i
$499$	8.55107	−	18.0797i	0.382799	−	0.809359i	−0.616952	−	0.787001i	$-0.711633\pi$
$499$	8.55107	−	18.0797i	0.382799	−	0.809359i	0.999750	−	0.0223583i	$-0.00711745\pi$
$500$	0.492390	+	21.4610i	0.0220203	+	0.959763i
$501$	−12.0012	+	8.90068i	−0.536173	+	0.397653i
$502$	3.98440	+	21.4960i	0.177832	+	0.959412i
$503$	−12.2210	+	22.8639i	−0.544907	+	1.01945i	0.447244	+	0.894412i	$0.352405\pi$
$503$	−12.2210	+	22.8639i	−0.544907	+	1.01945i	−0.992152	+	0.125038i	$0.960095\pi$
$504$	−6.74765	−	6.61581i	−0.300564	−	0.294692i
$505$	−19.9273	−	6.04487i	−0.886752	−	0.268993i
$506$	61.5307	+	33.9305i	2.73537	+	1.50839i
$507$	−7.40667	+	20.7003i	−0.328942	+	0.919331i
$508$	−7.72440	−	4.39220i	−0.342715	−	0.194872i
$509$	−13.6565	−	22.7844i	−0.605312	−	1.00990i	−0.995998	−	0.0893775i	$-0.971512\pi$
$509$	−13.6565	−	22.7844i	−0.605312	−	1.00990i	0.390686	−	0.920524i	$-0.372238\pi$
$510$	−13.7073	+	7.97411i	−0.606968	+	0.353099i
$511$	−22.6274			−1.00098
$512$	0.669597	+	22.6175i	0.0295923	+	0.999562i
$513$	4.60877			0.203482
$514$	23.1452	−	13.4646i	1.02089	−	0.593897i
$515$	−1.69044	−	2.82033i	−0.0744898	−	0.124279i
$516$	−5.19560	−	2.95429i	−0.228724	−	0.130056i
$517$	14.2835	−	39.9198i	0.628190	−	1.75567i
$518$	32.7144	+	18.0400i	1.43739	+	0.792632i
$519$	8.86451	+	2.68902i	0.389109	+	0.118035i
$520$	−27.1337	+	27.6744i	−1.18989	+	1.21360i
$521$	−7.20370	+	13.4772i	−0.315600	+	0.590446i	−0.988841	−	0.148977i	$-0.952402\pi$
$521$	−7.20370	+	13.4772i	−0.315600	+	0.590446i	0.673241	+	0.739423i	$0.264902\pi$
$522$	−0.210461	−	1.13545i	−0.00921165	−	0.0496972i
$523$	−25.6253	+	19.0050i	−1.12052	+	0.831031i	−0.987112	−	0.160031i	$-0.948841\pi$
$523$	−25.6253	+	19.0050i	−1.12052	+	0.831031i	−0.133404	+	0.991062i	$0.542591\pi$
$524$	0.235349	+	10.2578i	0.0102813	+	0.448112i
$525$	0.524107	−	1.10813i	0.0228739	−	0.0483628i
$526$	−22.1435	+	5.23997i	−0.965501	+	0.228474i
$527$	−7.49271	+	1.49039i	−0.326387	+	0.0649225i
$528$	−3.44744	−	23.7659i	−0.150031	−	1.03428i
$529$	−44.6162	−	8.87470i	−1.93983	−	0.385857i
$530$	0.341845	+	9.48805i	0.0148488	+	0.412135i
$531$	12.3584	+	0.607127i	0.536307	+	0.0263471i
$532$	−23.3513	+	20.0777i	−1.01241	+	0.870480i
$533$	0.702917	+	2.80620i	0.0304467	+	0.121550i
$534$	6.86037	−	15.9686i	0.296877	−	0.691031i
$535$	0.978170	−	9.93153i	0.0422900	−	0.429377i
$536$	4.82684	−	20.1095i	0.208488	−	0.868598i
$537$	−10.3540	−	8.49730i	−0.446808	−	0.366685i
$538$	−1.22166	−	14.3207i	−0.0526694	−	0.617411i
$539$	−24.9599	+	1.22620i	−1.07510	+	0.0528163i
$540$	3.18947	+	3.36079i	0.137253	+	0.144625i
$541$	−23.7089	+	3.51688i	−1.01932	+	0.151202i	−0.635417	−	0.772169i	$-0.719172\pi$
$541$	−23.7089	+	3.51688i	−1.01932	+	0.151202i	−0.383907	+	0.923372i	$0.625422\pi$
$542$	8.23552	−	7.27040i	0.353746	−	0.312291i
$543$	−4.18892	+	1.73511i	−0.179764	+	0.0744605i
$544$	20.8800	+	17.7125i	0.895223	+	0.759417i
$545$	33.0359	+	13.6839i	1.41510	+	0.586154i
$546$	−26.4344	+	9.07032i	−1.13129	+	0.388174i
$547$	21.8524	−	29.4646i	0.934342	−	1.25981i	−0.0311858	−	0.999514i	$-0.509928\pi$
$547$	21.8524	−	29.4646i	0.934342	−	1.25981i	0.965528	−	0.260301i	$-0.0838217\pi$
$548$	−19.7712	+	12.4756i	−0.844582	+	0.532930i
$549$	−10.9658	−	9.93886i	−0.468011	−	0.424180i
$550$	2.76628	−	1.43243i	0.117954	−	0.0610789i
$551$	−3.74521	+	0.368871i	−0.159551	+	0.0157144i
$552$	10.2164	+	21.0606i	0.434837	+	0.896398i
$553$	12.7121	−	10.4326i	0.540574	−	0.443638i
$554$	8.62762	+	8.85621i	0.366552	+	0.376264i
$555$	−15.7111	−	9.41690i	−0.666901	−	0.399725i
$556$	1.13205	−	0.137782i	0.0480097	−	0.00584326i
$557$	16.9417	+	18.6923i	0.717844	+	0.792019i	0.985169	−	0.171588i	$-0.0548897\pi$
$557$	16.9417	+	18.6923i	0.717844	+	0.792019i	−0.267325	+	0.963606i	$0.586140\pi$
$558$	0.927874	+	2.03008i	0.0392800	+	0.0859400i
$559$	−14.6970	+	9.82023i	−0.621617	+	0.415351i
$560$	−30.8011	−	3.13346i	−1.30158	−	0.132413i
$561$	−24.1620	−	16.1445i	−1.02012	−	0.681622i
$562$	18.5716	+	3.00347i	0.783394	+	0.126694i
$563$	−2.70006	−	7.54617i	−0.113794	−	0.318033i	0.871122	−	0.491067i	$-0.163393\pi$
$563$	−2.70006	−	7.54617i	−0.113794	−	0.318033i	−0.984916	+	0.173034i	$0.944643\pi$
$564$	11.5607	−	8.11427i	0.486795	−	0.341672i
$565$	−21.3709	−	3.17007i	−0.899079	−	0.133366i
$566$	−10.2246	+	6.64015i	−0.429771	+	0.279106i
$567$	0.969849	+	3.19717i	0.0407298	+	0.134268i
$568$	19.9829	+	36.5142i	0.838463	+	1.53210i
$569$	−8.21398	−	15.3673i	−0.344348	−	0.644230i	0.648818	−	0.760944i	$-0.275264\pi$
$569$	−8.21398	−	15.3673i	−0.344348	−	0.644230i	−0.993166	+	0.116714i	$0.962764\pi$
$570$	11.7963	−	9.42560i	0.494092	−	0.394795i
$571$	5.65033	+	11.9466i	0.236459	+	0.499950i	0.986969	−	0.160908i	$-0.0514423\pi$
$571$	5.65033	+	11.9466i	0.236459	+	0.499950i	−0.750510	+	0.660859i	$0.770192\pi$
$572$	−67.4010	−	22.3863i	−2.81818	−	0.936017i
$573$	2.05678	−	8.21111i	0.0859230	−	0.343024i
$574$	−1.40076	+	1.83799i	−0.0584667	+	0.0767163i
$575$	−2.14708	+	2.14708i	−0.0895392	+	0.0895392i
$576$	3.63124	−	7.12840i	0.151302	−	0.297017i
$577$	24.1206	+	24.1206i	1.00415	+	1.00415i	0.999991	+	0.00416238i	$0.00132493\pi$
$577$	24.1206	+	24.1206i	1.00415	+	1.00415i	0.00416238	+	0.999991i	$0.498675\pi$
$578$	9.00934	−	1.21626i	0.374739	−	0.0505896i
$579$	12.1383	+	3.04050i	0.504452	+	0.126359i
$580$	−2.86083	−	2.47579i	−0.118790	−	0.102801i
$581$	−30.2770	+	14.3200i	−1.25610	+	0.594092i
$582$	−0.782276	+	7.00274i	−0.0324264	+	0.290273i
$583$	−15.3436	+	8.20132i	−0.635467	+	0.339664i
$584$	−5.74121	−	18.2752i	−0.237573	−	0.756233i
$585$	13.1126	−	3.97768i	0.542141	−	0.164457i
$586$	29.2255	+	6.21159i	1.20730	+	0.256598i
$587$	1.71630	−	11.5704i	0.0708394	−	0.477560i	−0.924504	−	0.381172i	$-0.875521\pi$
$587$	1.71630	−	11.5704i	0.0708394	−	0.477560i	0.995344	−	0.0963890i	$-0.0307293\pi$
$588$	−7.02621	−	4.46510i	−0.289756	−	0.184138i
$589$	6.84889	−	2.45057i	0.282203	−	0.100974i
$590$	32.8733	−	23.7206i	1.35337	−	0.976564i
$591$	1.88976	−	2.82822i	0.0777343	−	0.116338i
$592$	−6.26959	+	30.9992i	−0.257678	+	1.27406i
$593$	−5.85529	−	8.76307i	−0.240448	−	0.359856i	0.691544	−	0.722334i	$-0.256931\pi$
$593$	−5.85529	−	8.76307i	−0.240448	−	0.359856i	−0.931992	+	0.362478i	$0.881931\pi$
$594$	−2.96461	+	7.95605i	−0.121640	+	0.326441i
$595$	−27.7589	+	25.1592i	−1.13800	+	1.03143i
$596$	−7.00135	+	25.1427i	−0.286787	+	1.02988i
$597$	11.9890	−	20.0024i	0.490675	−	0.818642i
$598$	69.2207	+	0.905039i	2.83064	+	0.0370098i
$599$	6.42991	+	7.83487i	0.262719	+	0.320124i	0.887617	−	0.460582i	$-0.152359\pi$
$599$	6.42991	+	7.83487i	0.262719	+	0.320124i	−0.624898	+	0.780706i	$0.714859\pi$
$600$	1.02797	+	0.142135i	0.0419667	+	0.00580265i
$601$	2.79549	+	28.3831i	0.114030	+	1.15777i	0.866512	+	0.499156i	$0.166357\pi$
$601$	2.79549	+	28.3831i	0.114030	+	1.15777i	−0.752482	+	0.658613i	$0.771143\pi$
$602$	−13.4572	−	4.27511i	−0.548476	−	0.174241i
$603$	−4.91025	+	5.41763i	−0.199961	+	0.220623i
$604$	0.704451	−	0.996843i	0.0286637	−	0.0405610i
$605$	46.6005	+	34.5613i	1.89458	+	1.40512i
$606$	5.58488	−	11.4195i	0.226870	−	0.463887i
$607$	−12.2284	+	29.5220i	−0.496335	+	1.19826i	0.455108	+	0.890436i	$0.349601\pi$
$607$	−12.2284	+	29.5220i	−0.496335	+	1.19826i	−0.951443	+	0.307824i	$0.900399\pi$
$608$	−22.1408	−	13.7656i	−0.897928	−	0.558268i
$609$	−1.04402	−	2.52048i	−0.0423056	−	0.102135i
$610$	−48.3938	−	3.01210i	−1.95941	−	0.121956i
$611$	−6.12910	−	41.3190i	−0.247957	−	1.67159i
$612$	−3.46950	−	9.03748i	−0.140246	−	0.365318i
$613$	−2.14763	−	43.7159i	−0.0867418	−	1.76567i	−0.510485	−	0.859887i	$-0.670534\pi$
$613$	−2.14763	−	43.7159i	−0.0867418	−	1.76567i	0.423743	−	0.905782i	$-0.360716\pi$
$614$	−28.3210	−	23.8689i	−1.14294	−	0.963269i
$615$	0.718803	−	0.875864i	0.0289849	−	0.0353182i
$616$	−19.6390	−	53.2261i	−0.791279	−	2.14454i
$617$	16.8974	+	1.66424i	0.680262	+	0.0670000i	0.432246	−	0.901756i	$-0.357721\pi$
$617$	16.8974	+	1.66424i	0.680262	+	0.0670000i	0.248016	+	0.968756i	$0.420221\pi$
$618$	1.86435	−	0.743835i	0.0749952	−	0.0299214i
$619$	−40.7302	+	10.2024i	−1.63708	+	0.410068i	−0.948928	−	0.315494i	$-0.897830\pi$
$619$	−40.7302	+	10.2024i	−1.63708	+	0.410068i	−0.688156	+	0.725562i	$0.741580\pi$
$620$	6.52672	+	3.29841i	0.262119	+	0.132467i
$621$	0.406078	−	8.26591i	0.0162954	−	0.331700i
$622$	−7.82816	−	7.28370i	−0.313881	−	0.292050i
$623$	8.01031	−	40.2705i	0.320926	−	1.61341i
$624$	−14.0328	−	19.0485i	−0.561763	−	0.762551i
$625$	−5.20889	−	26.1869i	−0.208356	−	1.04747i
$626$	−1.46764	−	0.905957i	−0.0586586	−	0.0362093i
$627$	25.0129	+	11.8302i	0.998919	+	0.472454i
$628$	−1.00160	−	0.388208i	−0.0399683	−	0.0154912i
$629$	22.7979	+	30.7394i	0.909011	+	1.22566i
$630$	9.02102	+	6.19976i	0.359406	+	0.247004i
$631$	16.1961	+	8.65702i	0.644758	+	0.344630i	0.761153	−	0.648573i	$-0.224634\pi$
$631$	16.1961	+	8.65702i	0.644758	+	0.344630i	−0.116395	+	0.993203i	$0.537134\pi$
$632$	11.6513	+	7.61999i	0.463465	+	0.303107i
$633$	3.60134	−	11.8720i	0.143140	−	0.471871i
$634$	6.40142	+	22.1407i	0.254233	+	0.879318i
$635$	9.69103	+	3.46751i	0.384577	+	0.137604i
$636$	−5.75105	−	0.718692i	−0.228044	−	0.0284980i
$637$	−21.1176	+	12.6574i	−0.836711	+	0.501505i
$638$	1.77235	−	6.70257i	0.0701678	−	0.265357i
$639$		−	14.7165i		−	0.582176i
$640$	−5.28433	−	25.6718i	−0.208881	−	1.01477i
$641$		−	24.1402i		−	0.953481i	−0.879044	−	0.476740i	$-0.841818\pi$
$641$		−	24.1402i		−	0.953481i	0.879044	−	0.476740i	$-0.158182\pi$
$642$	5.88965	+	1.55739i	0.232446	+	0.0614651i
$643$	35.3810	−	21.2066i	1.39529	−	0.836306i	0.398565	−	0.917140i	$-0.369508\pi$
$643$	35.3810	−	21.2066i	1.39529	−	0.836306i	0.996728	+	0.0808344i	$0.0257585\pi$
$644$	33.9523	+	43.6500i	1.33791	+	1.72005i
$645$	6.51840	+	2.33232i	0.256662	+	0.0918351i
$646$	−30.3067	+	8.76242i	−1.19240	+	0.344753i
$647$	3.72736	−	12.2874i	0.146537	−	0.483069i	−0.852688	−	0.522421i	$-0.825029\pi$
$647$	3.72736	−	12.2874i	0.146537	−	0.483069i	0.999225	+	0.0393512i	$0.0125291\pi$
$648$	−2.33613	+	1.59451i	−0.0917720	+	0.0626384i
$649$	65.5133	+	35.0176i	2.57162	+	1.37456i
$650$	1.73830	−	2.52933i	0.0681817	−	0.0992084i
$651$	3.14124	+	4.23547i	0.123115	+	0.166001i
$652$	−9.46200	+	4.17607i	−0.370560	+	0.163547i
$653$	−21.1879	−	10.0211i	−0.829146	−	0.392157i	−0.0346298	−	0.999400i	$-0.511025\pi$
$653$	−21.1879	−	10.0211i	−0.829146	−	0.392157i	−0.794516	+	0.607244i	$0.792275\pi$
$654$	−11.4659	+	18.5746i	−0.448352	+	0.726324i
$655$	−2.31865	−	11.6566i	−0.0905970	−	0.455462i
$656$	−1.83988	−	0.664986i	−0.0718352	−	0.0259633i
$657$	−1.32127	+	6.64246i	−0.0515476	+	0.259147i
$658$	22.7298	−	24.4289i	0.886099	−	0.952336i
$659$	−1.87388	+	38.1437i	−0.0729960	+	1.48587i	0.631066	+	0.775729i	$0.282618\pi$
$659$	−1.87388	+	38.1437i	−0.0729960	+	1.48587i	−0.704062	+	0.710139i	$0.748632\pi$
$660$	8.68324	+	26.4268i	0.337995	+	1.02866i
$661$	−4.73545	+	1.18617i	−0.184188	+	0.0461366i	−0.333976	−	0.942581i	$-0.608391\pi$
$661$	−4.73545	+	1.18617i	−0.184188	+	0.0461366i	0.149789	+	0.988718i	$0.452141\pi$
$662$	11.4007	+	28.5749i	0.443103	+	1.11059i
$663$	−28.4917	−	2.80619i	−1.10653	−	0.108983i
$664$	−19.2477	−	20.8201i	−0.746956	−	0.807975i
$665$	22.6301	−	27.5748i	0.877557	−	1.06931i
$666$	7.20605	−	8.55016i	0.279229	−	0.331312i
$667$	0.331586	+	6.74960i	0.0128391	+	0.261345i
$668$	−27.3000	−	12.1537i	−1.05627	−	0.470240i
$669$	0.195858	+	1.32037i	0.00757231	+	0.0510483i
$670$	−1.48812	+	23.9087i	−0.0574910	+	0.923675i
$671$	−34.0022	−	82.0887i	−1.31264	−	3.16900i
$672$	4.89014	−	18.2561i	0.188641	−	0.704245i
$673$	−7.21125	+	17.4095i	−0.277973	+	0.671087i	−0.999779	−	0.0210083i	$-0.993312\pi$
$673$	−7.21125	+	17.4095i	−0.277973	+	0.671087i	0.721806	+	0.692096i	$0.243312\pi$
$674$	6.12560	+	2.99581i	0.235949	+	0.115394i
$675$	−0.294697	−	0.218562i	−0.0113429	−	0.00841246i
$676$	−43.3355	+	7.44784i	−1.66675	+	0.286455i
$677$	−22.6368	+	24.9759i	−0.870004	+	0.959901i	−0.999498	−	0.0316791i	$-0.989915\pi$
$677$	−22.6368	+	24.9759i	−0.870004	+	0.959901i	0.129494	+	0.991580i	$0.458665\pi$
$678$	3.99315	−	12.5697i	0.153356	−	0.482735i
$679$	1.63165	+	16.5665i	0.0626171	+	0.635763i
$680$	−27.3632	−	16.0361i	−1.04933	−	0.614956i
$681$	−2.17250	−	2.64719i	−0.0832502	−	0.101441i
$682$	−0.175194	+	13.3995i	−0.00670852	+	0.513092i
$683$	−20.8954	+	34.8618i	−0.799540	+	1.33395i	0.139528	+	0.990218i	$0.455442\pi$
$683$	−20.8954	+	34.8618i	−0.799540	+	1.33395i	−0.939067	+	0.343733i	$0.888308\pi$
$684$	4.53044	+	8.02735i	0.173226	+	0.306933i
$685$	20.0647	−	18.1855i	0.766631	−	0.694834i
$686$	12.5633	+	4.68137i	0.479667	+	0.178735i
$687$	−2.55151	−	3.81860i	−0.0973462	−	0.145689i
$688$	0.0383520	−	11.9535i	0.00146216	−	0.455725i
$689$	−9.52280	+	14.2519i	−0.362790	+	0.542953i
$690$	−15.8656	−	21.9873i	−0.603993	−	0.837044i
$691$	27.8816	−	9.97619i	1.06067	−	0.379512i	0.251967	−	0.967736i	$-0.418922\pi$
$691$	27.8816	−	9.97619i	1.06067	−	0.379512i	0.808698	+	0.588223i	$0.200172\pi$
$692$	4.03024	+	18.0831i	0.153207	+	0.687417i
$693$	−2.94317	+	19.8413i	−0.111802	+	0.753708i
$694$	−1.35314	+	6.36651i	−0.0513644	+	0.241670i
$695$	−1.26409	+	0.383456i	−0.0479495	+	0.0145453i
$696$	1.77078	−	1.48272i	0.0671214	−	0.0562024i
$697$	−2.08781	+	1.11596i	−0.0790813	+	0.0422698i
$698$	16.7832	+	1.87485i	0.635254	+	0.0709641i
$699$	−3.30234	+	1.56189i	−0.124906	+	0.0590761i
$700$	2.44529	−	0.176432i	0.0924233	−	0.00666850i
$701$	18.8636	+	4.72509i	0.712469	+	0.178464i	0.582236	−	0.813019i	$-0.302178\pi$
$701$	18.8636	+	4.72509i	0.712469	+	0.178464i	0.130232	+	0.991484i	$0.458428\pi$
$702$	1.11910	+	8.28966i	0.0422377	+	0.312873i
$703$	−25.7672	−	25.7672i	−0.971827	−	0.971827i
$704$	38.0054	−	29.3665i	1.43238	−	1.10679i
$705$	−11.5686	+	11.5686i	−0.435697	+	0.435697i
$706$	−31.9389	−	24.3411i	−1.20204	−	0.916090i
$707$	7.29713	−	29.1318i	0.274437	−	1.09561i
$708$	11.0908	+	22.1220i	0.416820	+	0.831397i
$709$	0.628227	+	1.32827i	0.0235936	+	0.0498844i	0.915442	−	0.402450i	$-0.131841\pi$
$709$	0.628227	+	1.32827i	0.0235936	+	0.0498844i	−0.891848	+	0.452335i	$0.850591\pi$
$710$	−30.0973	−	37.6673i	−1.12953	−	1.41363i
$711$	−2.32027	−	4.34092i	−0.0870169	−	0.162797i
$712$	34.5572	−	3.74817i	1.29509	−	0.140469i
$713$	−3.79169	−	12.4995i	−0.142000	−	0.468110i
$714$	−12.4562	−	19.1802i	−0.466162	−	0.717801i
$715$	81.3757	+	12.0709i	3.04328	+	0.451428i
$716$	4.62219	−	26.3870i	0.172739	−	0.986127i
$717$	8.54666	+	23.8863i	0.319181	+	0.892051i
$718$	−3.70176	+	22.8893i	−0.138149	+	0.854222i
$719$	15.6422	+	10.4518i	0.583356	+	0.389786i	0.811942	−	0.583738i	$-0.198410\pi$
$719$	15.6422	+	10.4518i	0.583356	+	0.389786i	−0.228587	+	0.973524i	$0.573410\pi$
$720$	−2.71840	+	8.85893i	−0.101309	+	0.330153i
$721$	3.94290	−	2.63456i	0.146841	−	0.0981161i
$722$	2.88219	−	1.31734i	0.107264	−	0.0490264i
$723$	−10.9628	−	12.0956i	−0.407711	−	0.449840i
$724$	−7.13984	−	5.59044i	−0.265350	−	0.207767i
$725$	0.256971	+	0.154023i	0.00954368	+	0.00572026i
$726$	−25.3691	+	24.7143i	−0.941536	+	0.917233i
$727$	24.8067	−	20.3584i	0.920031	−	0.755050i	−0.0498175	−	0.998758i	$-0.515864\pi$
$727$	24.8067	−	20.3584i	0.920031	−	0.755050i	0.969849	+	0.243708i	$0.0783640\pi$
$728$	−41.7834	−	37.1260i	−1.54859	−	1.37598i
$729$	0.995185	−	0.0980171i	0.0368587	−	0.00363026i
$730$	10.2030	+	19.7038i	0.377628	+	0.729269i
$731$	−10.7176	−	9.71391i	−0.396406	−	0.359282i
$732$	6.53158	−	28.8697i	0.241414	−	1.06706i
$733$	−0.141219	+	0.190411i	−0.00521603	+	0.00703300i	−0.805808	−	0.592177i	$-0.798269\pi$
$733$	−0.141219	+	0.190411i	−0.00521603	+	0.00703300i	0.800592	+	0.599210i	$0.204519\pi$
$734$	−11.5372	−	33.6239i	−0.425847	−	1.24108i
$735$	8.90899	+	3.69023i	0.328613	+	0.136116i
$736$	−26.6396	+	38.4970i	−0.981949	+	1.41902i
$737$	−40.5556	+	16.7987i	−1.49388	+	0.618787i
$738$	0.457763	+	0.518529i	0.0168505	+	0.0190873i
$739$	28.2814	−	4.19514i	1.04035	−	0.154321i	0.395369	−	0.918522i	$-0.370617\pi$
$739$	28.2814	−	4.19514i	1.04035	−	0.154321i	0.644978	+	0.764201i	$0.276867\pi$
$740$	0.957801	−	36.6218i	0.0352095	−	1.34624i
$741$	27.2274	−	1.33759i	1.00022	−	0.0491378i
$742$	−13.6428	+	1.16382i	−0.500842	+	0.0427252i
$743$	−31.2172	−	25.6193i	−1.14525	−	0.939881i	−0.146466	−	0.989216i	$-0.546790\pi$
$743$	−31.2172	−	25.6193i	−1.14525	−	0.939881i	−0.998782	+	0.0493344i	$0.984290\pi$
$744$	−2.62379	+	3.61170i	−0.0961927	+	0.132411i
$745$	2.96321	−	30.0860i	0.108564	−	1.10226i
$746$	34.2619	+	14.7194i	1.25442	+	0.538917i
$747$	2.43579	+	9.72423i	0.0891210	+	0.355791i
$748$	4.36846	−	57.9544i	0.159727	−	2.11902i
$749$	14.3750	+	0.706198i	0.525250	+	0.0258039i
$750$	15.1693	−	0.546536i	0.553906	−	0.0199567i
$751$	−3.33784	−	0.663938i	−0.121800	−	0.0242274i	0.133814	−	0.991006i	$-0.457277\pi$
$751$	−3.33784	−	0.663938i	−0.121800	−	0.0242274i	−0.255614	+	0.966779i	$0.582277\pi$
$752$	25.4973	+	12.1596i	0.929791	+	0.443414i
$753$	15.1618	−	3.01587i	0.552527	−	0.109904i
$754$	−1.57289	−	6.64683i	−0.0572812	−	0.242063i
$755$	−0.604518	+	1.27815i	−0.0220007	+	0.0465165i
$756$	−4.61531	+	4.83206i	−0.167857	+	0.175740i
$757$	13.6391	−	10.1154i	0.495721	−	0.367652i	−0.318766	−	0.947833i	$-0.603268\pi$
$757$	13.6391	−	10.1154i	0.495721	−	0.367652i	0.814487	+	0.580182i	$0.197018\pi$
$758$	−42.1811	+	7.81851i	−1.53209	+	0.283981i
$759$	23.4216	−	43.8187i	0.850150	−	1.59052i
$760$	28.0129	+	11.2808i	1.01613	+	0.409199i
$761$	39.6879	+	12.0392i	1.43868	+	0.436420i	0.910783	−	0.412885i	$-0.135479\pi$
$761$	39.6879	+	12.0392i	1.43868	+	0.436420i	0.527902	+	0.849305i	$0.322979\pi$
$762$	−3.03408	+	5.50211i	−0.109913	+	0.199321i
$763$	−17.3731	+	48.5545i	−0.628947	+	1.75779i
$764$	16.3235	−	4.48915i	0.590565	−	0.162412i
$765$	5.76478	+	9.61795i	0.208426	+	0.347738i
$766$	0.699644	+	1.20267i	0.0252792	+	0.0434542i
$767$	73.1860			2.64259
$768$	15.9854	−	0.682522i	0.576825	−	0.0246284i
$769$	11.0239			0.397532			0.198766	−	0.980047i	$-0.436307\pi$
$769$	11.0239			0.397532			0.198766	+	0.980047i	$0.436307\pi$
$770$	33.0451	+	56.8035i	1.19086	+	2.04706i
$771$	−9.73405	−	16.2403i	−0.350563	−	0.584879i
$772$	6.63624	+	24.1308i	0.238844	+	0.868487i
$773$	4.71155	−	13.1679i	0.169463	−	0.473616i	−0.826546	−	0.562869i	$-0.809698\pi$
$773$	4.71155	−	13.1679i	0.169463	−	0.473616i	0.996009	+	0.0892522i	$0.0284477\pi$
$774$	−2.04079	+	3.70084i	−0.0733548	+	0.133024i
$775$	−0.554149	−	0.168099i	−0.0199056	−	0.00603831i
$776$	−12.9660	+	5.52119i	−0.465453	+	0.198199i
$777$	12.4527	−	23.2973i	0.446738	−	0.835787i
$778$	31.3554	−	5.81190i	1.12415	−	0.208367i
$779$	1.81052	−	1.34277i	0.0648685	−	0.0481098i
$780$	19.8179	+	18.9289i	0.709595	+	0.677764i
$781$	37.7757	−	79.8699i	1.35172	−	2.85797i
$782$	13.0452	+	55.1276i	0.466497	+	1.97136i
$783$	−0.800868	+	0.159303i	−0.0286207	+	0.00569301i
$784$	0.870323	−	16.6271i	0.0310830	−	0.593826i
$785$	1.22037	+	0.242747i	0.0435569	+	0.00866401i
$786$	7.25054	−	0.261230i	0.258618	−	0.00931776i
$787$	−28.4174	−	1.39606i	−1.01297	−	0.0497641i	−0.464195	−	0.885733i	$-0.653656\pi$
$787$	−28.4174	−	1.39606i	−1.01297	−	0.0497641i	−0.548777	+	0.835969i	$0.684906\pi$
$788$	6.78371	+	0.511339i	0.241659	+	0.0182157i
$789$	3.90961	+	15.6080i	0.139186	+	0.555660i
$790$	−14.8166	−	6.36543i	−0.527151	−	0.226472i
$791$	3.05400	−	31.0078i	0.108588	−	1.10251i
$792$	−16.7717	+	2.65720i	−0.595956	+	0.0944196i
$793$	−67.6677	−	55.5334i	−2.40295	−	1.97205i
$794$	−20.9902	+	1.79061i	−0.744916	+	0.0635464i
$795$	6.70533	−	0.329412i	0.237814	−	0.0116830i
$796$	46.6244	+	1.21941i	1.65256	+	0.0432207i
$797$	42.9703	−	6.37404i	1.52209	−	0.225780i	0.667311	−	0.744780i	$-0.267445\pi$
$797$	42.9703	−	6.37404i	1.52209	−	0.225780i	0.854774	+	0.519000i	$0.173695\pi$
$798$	14.4118	+	16.3249i	0.510171	+	0.577894i
$799$	31.5805	−	13.0811i	1.11724	−	0.462775i
$800$	0.762934	+	1.93019i	0.0269738	+	0.0682425i
$801$	−11.3540	−	4.70298i	−0.401174	−	0.166172i
$802$	0.558874	+	1.62877i	0.0197345	+	0.0575140i
$803$	−24.2213	+	32.6587i	−0.854752	+	1.15250i
$804$	−14.2630	−	3.22690i	−0.503016	−	0.113804i
$805$	−47.4620	−	43.0170i	−1.67282	−	1.51615i
$806$	6.07081	+	11.7238i	0.213835	+	0.412955i
$807$	−10.1141	+	0.996155i	−0.356034	+	0.0350663i
$808$	25.3800	−	1.49796i	0.892864	−	0.0526980i
$809$	19.6735	−	16.1456i	0.691684	−	0.567650i	−0.221519	−	0.975156i	$-0.571101\pi$
$809$	19.6735	−	16.1456i	0.691684	−	0.567650i	0.913203	+	0.407506i	$0.133601\pi$
$810$	2.34675	−	2.28617i	0.0824563	−	0.0803279i
$811$	11.3136	+	6.78114i	0.397276	+	0.238118i	0.698765	−	0.715352i	$-0.253734\pi$
$811$	11.3136	+	6.78114i	0.397276	+	0.238118i	−0.301489	+	0.953470i	$0.597484\pi$
$812$	3.36378	−	4.29605i	0.118045	−	0.150762i
$813$	−5.21665	−	5.75568i	−0.182956	−	0.201861i
$814$	61.0563	−	27.9066i	2.14002	−	0.978126i
$815$	9.96109	−	6.65579i	0.348922	−	0.233142i
$816$	12.3305	−	14.9269i	0.431655	−	0.522545i
$817$	11.4517	+	7.65179i	0.400645	+	0.267702i
$818$	−1.24231	+	7.68168i	−0.0434365	+	0.268584i
$819$	6.65751	+	18.6065i	0.232632	+	0.650164i
$820$	2.23213	+	0.391000i	0.0779492	+	0.0136543i
$821$	−6.85807	−	1.01730i	−0.239348	−	0.0355040i	0.0259785	−	0.999663i	$-0.491730\pi$
$821$	−6.85807	−	1.01730i	−0.239348	−	0.0355040i	−0.265327	+	0.964159i	$0.585480\pi$
$822$	9.00357	+	13.8638i	0.314036	+	0.483556i
$823$	−11.4057	−	37.5994i	−0.397577	−	1.31063i	−0.896136	−	0.443779i	$-0.853638\pi$
$823$	−11.4057	−	37.5994i	−0.397577	−	1.31063i	0.498560	−	0.866855i	$-0.333862\pi$
$824$	3.12824	+	2.51605i	0.108977	+	0.0876506i
$825$	−1.03836	−	1.94264i	−0.0361512	−	0.0676342i
$826$	36.4944	+	45.6734i	1.26980	+	1.58918i
$827$	−11.5640	−	24.4500i	−0.402119	−	0.850210i	−0.998858	−	0.0477745i	$-0.984787\pi$
$827$	−11.5640	−	24.4500i	−0.402119	−	0.850210i	0.596739	−	0.802436i	$-0.296463\pi$
$828$	14.7964	−	7.41813i	0.514209	−	0.257798i
$829$	9.42219	−	37.6155i	0.327246	−	1.30644i	−0.553499	−	0.832850i	$-0.686708\pi$
$829$	9.42219	−	37.6155i	0.327246	−	1.30644i	0.880745	−	0.473590i	$-0.157042\pi$
$830$	26.1219	+	19.9079i	0.906705	+	0.691014i
$831$	6.18200	−	6.18200i	0.214451	−	0.214451i
$832$	19.3835	−	43.1665i	0.672002	−	1.49653i
$833$	−14.2465	−	14.2465i	−0.493611	−	0.493611i
$834$	−0.107884	−	0.799140i	−0.00373570	−	0.0276720i
$835$	33.5771	+	8.41063i	1.16198	+	0.291062i
$836$	3.98245	+	55.1955i	0.137736	+	1.90898i
$837$	1.42678	−	0.674817i	0.0493167	−	0.0233251i
$838$	−5.83769	−	0.652128i	−0.201660	−	0.0225274i
$839$	−20.8920	+	11.1670i	−0.721272	+	0.385528i	−0.790819	−	0.612051i	$-0.790345\pi$
$839$	−20.8920	+	11.1670i	−0.721272	+	0.385528i	0.0695463	+	0.997579i	$0.477845\pi$
$840$	−1.93076	+	21.8068i	−0.0666176	+	0.752405i
$841$	−27.1132	+	8.22470i	−0.934938	+	0.283610i
$842$	−8.79203	+	41.3665i	−0.302993	+	1.42558i
$843$	1.95191	−	13.1587i	0.0672274	−	0.453210i
$844$	24.2183	−	5.39760i	0.833627	−	0.185793i
$845$	47.9554	−	17.1587i	1.64972	−	0.590278i
$846$	−5.84404	−	8.09896i	−0.200922	−	0.278448i
$847$	−46.4858	+	69.5709i	−1.59727	+	2.39048i
$848$	−4.40152	−	10.7234i	−0.151149	−	0.368242i
$849$	4.78942	+	7.16787i	0.164372	+	0.246001i
$850$	2.35343	+	0.876943i	0.0807219	+	0.0300789i
$851$	−48.4842	+	43.9435i	−1.66202	+	1.50636i
$852$	25.6325	−	14.4664i	0.878156	−	0.495610i
$853$	−3.08596	+	5.14861i	−0.105661	+	0.176285i	−0.906018	−	0.423238i	$-0.860893\pi$
$853$	−3.08596	+	5.14861i	−0.105661	+	0.176285i	0.800357	+	0.599524i	$0.204643\pi$
$854$	0.914202	−	69.9214i	0.0312833	−	2.39266i
$855$	−6.77339	−	8.25339i	−0.231645	−	0.282260i
$856$	3.07696	+	11.7892i	0.105168	+	0.402948i
$857$	−4.51177	−	45.8088i	−0.154119	−	1.56480i	−0.692075	−	0.721825i	$-0.743303\pi$
$857$	−4.51177	−	45.8088i	−0.154119	−	1.56480i	0.537956	−	0.842973i	$-0.319197\pi$
$858$	−15.2050	+	47.8626i	−0.519092	+	1.63400i
$859$	−21.2006	+	23.3912i	−0.723354	+	0.798098i	−0.985991	−	0.166796i	$-0.946658\pi$
$859$	−21.2006	+	23.3912i	−0.723354	+	0.798098i	0.262637	+	0.964895i	$0.415408\pi$
$860$	2.34528	+	13.6461i	0.0799735	+	0.465329i
$861$	1.31249	+	0.973412i	0.0447297	+	0.0331738i
$862$	−39.9948	−	19.5600i	−1.36223	−	0.666216i
$863$	9.05100	−	21.8510i	0.308100	−	0.743818i	−0.691667	−	0.722216i	$-0.743123\pi$
$863$	9.05100	−	21.8510i	0.308100	−	0.743818i	0.999767	−	0.0216016i	$-0.00687654\pi$
$864$	−5.07368	−	2.50156i	−0.172610	−	0.0851047i
$865$	−8.21242	−	19.8265i	−0.279231	−	0.674123i
$866$	−0.348922	+	5.60594i	−0.0118569	+	0.190498i
$867$	−0.943235	−	6.35878i	−0.0320339	−	0.215955i
$868$	−4.28930	+	9.63475i	−0.145588	+	0.327025i
$869$	−1.44998	−	29.5151i	−0.0491873	−	1.00123i
$870$	−1.72405	+	2.04563i	−0.0584507	+	0.0693533i
$871$	−27.4361	+	33.4309i	−0.929636	+	1.13276i
$872$	−43.6234	−	1.71187i	−1.47727	−	0.0579711i
$873$	4.95849	+	0.488369i	0.167820	+	0.0165288i
$874$	−19.9888	−	50.1001i	−0.676133	−	1.69466i
$875$	34.7856	−	8.71334i	1.17597	−	0.294565i
$876$	−12.8683	+	4.22824i	−0.434781	+	0.142859i
$877$	−0.918815	+	18.7029i	−0.0310262	+	0.631552i	0.932051	+	0.362327i	$0.118018\pi$
$877$	−0.918815	+	18.7029i	−0.0310262	+	0.631552i	−0.963077	+	0.269225i	$0.913232\pi$
$878$	−18.7832	+	20.1873i	−0.633903	+	0.681288i
$879$	4.12171	−	20.7212i	0.139022	−	0.698910i
$880$	−37.4933	+	41.1017i	−1.26390	+	1.38554i
$881$	−1.22038	−	6.13526i	−0.0411156	−	0.206702i	0.954767	−	0.297355i	$-0.0961045\pi$
$881$	−1.22038	−	6.13526i	−0.0411156	−	0.206702i	−0.995883	+	0.0906531i	$0.971105\pi$
$882$	−3.09208	+	5.00913i	−0.104116	+	0.168666i
$883$	−11.8275	−	5.59401i	−0.398028	−	0.188253i	0.218051	−	0.975937i	$-0.430030\pi$
$883$	−11.8275	−	5.59401i	−0.398028	−	0.188253i	−0.616079	+	0.787684i	$0.711280\pi$
$884$	−23.1198	−	52.3840i	−0.777601	−	1.76186i
$885$	−17.0755	−	23.0236i	−0.573986	−	0.773931i
$886$	−28.1716	+	40.9913i	−0.946442	+	1.37713i
$887$	7.41456	+	3.96316i	0.248957	+	0.133070i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	7.41456	+	3.96316i	0.248957	+	0.133070i	−0.342199	+	0.939627i	$0.611172\pi$
$888$	21.9758	+	4.14632i	0.737461	+	0.139141i
$889$	−4.30895	+	14.2047i	−0.144518	+	0.476411i
$890$	−38.6792	+	11.1831i	−1.29653	+	0.374859i
$891$	5.65270	+	2.02257i	0.189373	+	0.0677586i
$892$	−2.10722	+	1.63906i	−0.0705551	+	0.0548798i
$893$	−27.9170	+	16.7328i	−0.934205	+	0.559941i
$894$	17.8417	+	4.71785i	0.596717	+	0.157789i
$895$			31.0302i			1.03722i
$896$	36.6047	−	9.42840i	1.22288	−	0.314981i
$897$		−	48.9506i		−	1.63441i
$898$	12.4561	−	47.1058i	0.415664	−	1.57194i
$899$	−1.10543	+	0.662568i	−0.0368681	+	0.0220979i
$900$	0.0909932	−	0.728137i	0.00303311	−	0.0242712i
$901$	−13.2067	−	4.72542i	−0.439978	−	0.157427i
$902$	1.15338	+	3.98921i	0.0384034	+	0.132826i
$903$	−2.89830	+	9.55441i	−0.0964493	+	0.317951i
$904$	25.8185	−	5.40094i	0.858711	−	0.179633i
$905$	9.26356	+	4.95147i	0.307931	+	0.164593i
$906$	−0.711326	−	0.488864i	−0.0236322	−	0.0162414i
$907$	−18.6906	−	25.2014i	−0.620612	−	0.836799i	0.375321	−	0.926895i	$-0.377533\pi$
$907$	−18.6906	−	25.2014i	−0.620612	−	0.836799i	−0.995933	+	0.0900962i	$0.971283\pi$
$908$	2.47519	−	6.38615i	0.0821420	−	0.211932i
$909$	−8.12577	−	3.84320i	−0.269515	−	0.127471i
$910$	55.0930	+	34.0083i	1.82632	+	1.12736i
$911$	−1.58405	−	7.96355i	−0.0524819	−	0.263844i	0.945632	−	0.325240i	$-0.105445\pi$
$911$	−1.58405	−	7.96355i	−0.0524819	−	0.263844i	−0.998114	+	0.0613953i	$0.980445\pi$
$912$	−9.52822	+	15.7818i	−0.315511	+	0.522588i
$913$	−11.7414	+	59.0281i	−0.388584	+	1.95354i
$914$	−13.5163	−	12.5762i	−0.447079	−	0.415983i
$915$	−1.68232	+	34.2445i	−0.0556159	+	1.13209i
$916$	4.14292	−	8.19780i	0.136886	−	0.270863i
$917$	16.6266	−	4.16474i	0.549058	−	0.137532i
$918$	−6.35784	+	2.53664i	−0.209840	+	0.0837216i
$919$	−2.47693	−	0.243956i	−0.0817064	−	0.00804738i	0.0570813	−	0.998370i	$-0.481821\pi$
$919$	−2.47693	−	0.243956i	−0.0817064	−	0.00804738i	−0.138788	+	0.990322i	$0.544321\pi$
$920$	22.7006	−	49.2476i	0.748416	−	1.62365i
$921$	−16.6146	+	20.2449i	−0.547469	+	0.667093i
$922$	−2.70566	−	2.28032i	−0.0891061	−	0.0750983i
$923$	−4.27114	−	86.9411i	−0.140586	−	2.86170i
$924$	−37.4517	+	14.3778i	−1.23207	+	0.472993i
$925$	0.425662	+	2.86958i	0.0139957	+	0.0943512i
$926$	−47.7862	−	2.97428i	−1.57035	−	0.0977410i
$927$	−0.543161	−	1.31131i	−0.0178397	−	0.0430690i
$928$	4.32322	+	1.62675i	0.141917	+	0.0534007i
$929$	−3.14650	+	7.59633i	−0.103233	+	0.249228i	−0.967054	−	0.254573i	$-0.918065\pi$
$929$	−3.14650	+	7.59633i	−0.103233	+	0.249228i	0.863820	+	0.503800i	$0.168065\pi$
$930$	2.27179	−	4.64518i	0.0744950	−	0.152322i
$931$	15.4087	+	11.4278i	0.504998	+	0.374532i
$932$	−5.96663	−	4.21651i	−0.195444	−	0.138117i
$933$	−5.07754	+	5.60221i	−0.166231	+	0.183408i
$934$	37.4035	+	11.8824i	1.22388	+	0.388804i
$935$	6.59857	+	66.9965i	0.215796	+	2.19102i
$936$	−13.3385	+	10.0980i	−0.435981	+	0.330062i
$937$	24.8490	+	30.2786i	0.811782	+	0.989160i	0.999975	+	0.00702754i	$0.00223695\pi$
$937$	24.8490	+	30.2786i	0.811782	+	0.989160i	−0.188193	+	0.982132i	$0.560263\pi$
$938$	−34.5444	−	0.451657i	−1.12791	−	0.0147471i
$939$	−0.626986	+	1.04606i	−0.0204609	+	0.0341370i
$940$	−31.5215	−	8.77764i	−1.02812	−	0.286295i
$941$	12.4706	−	11.3027i	0.406531	−	0.368458i	−0.442530	−	0.896754i	$-0.645919\pi$
$941$	12.4706	−	11.3027i	0.406531	−	0.368458i	0.849060	+	0.528296i	$0.177169\pi$
$942$	−0.265222	+	0.711768i	−0.00864139	+	0.0231907i
$943$	−2.24876	−	3.36551i	−0.0732297	−	0.109596i
$944$	−27.6288	+	41.0635i	−0.899240	+	1.33650i
$945$	4.30012	−	6.43559i	0.139883	−	0.209350i
$946$	−20.5755	+	14.8469i	−0.668968	+	0.482713i
$947$	13.9433	−	4.98898i	0.453095	−	0.162120i	−0.100445	−	0.994943i	$-0.532027\pi$
$947$	13.9433	−	4.98898i	0.453095	−	0.162120i	0.553540	+	0.832823i	$0.313277\pi$
$948$	5.27998	−	8.30848i	0.171486	−	0.269847i
$949$	−5.87786	+	39.6253i	−0.190803	+	1.28629i
$950$	−2.33913	−	0.497158i	−0.0758914	−	0.0161299i
$951$	15.5953	−	4.73078i	0.505712	−	0.153406i
$952$	21.1627	−	40.5498i	0.685886	−	1.31423i
$953$	43.9353	−	23.4839i	1.42320	−	0.760719i	0.433139	−	0.901327i	$-0.357406\pi$
$953$	43.9353	−	23.4839i	1.42320	−	0.760719i	0.990065	+	0.140608i	$0.0449058\pi$
$954$	−0.454984	+	4.07290i	−0.0147306	+	0.131865i
$955$	−17.7272	+	8.38436i	−0.573640	+	0.271312i
$956$	−33.2027	+	38.3665i	−1.07385	+	1.24086i
$957$	−4.75541	−	1.19117i	−0.153721	−	0.0385050i
$958$	−16.3644	+	2.20918i	−0.528709	+	0.0713755i
$959$	27.6150	+	27.6150i	0.891736	+	0.891736i
$960$	−18.1023	+	3.97359i	−0.584248	+	0.128247i
$961$	−20.1589	+	20.1589i	−0.650286	+	0.650286i
$962$	40.0899	−	52.6034i	1.29255	−	1.69600i
$963$	1.04670	−	4.17865i	0.0337294	−	0.134655i
$964$	10.2911	−	30.9845i	0.331453	−	0.997944i
$965$	−12.3945	−	26.2059i	−0.398992	−	0.843597i
$966$	30.5487	−	24.4094i	0.982889	−	0.785358i
$967$	−22.8642	−	42.7759i	−0.735263	−	1.37558i	−0.919655	−	0.392728i	$-0.871531\pi$
$967$	−22.8642	−	42.7759i	−0.735263	−	1.37558i	0.184391	−	0.982853i	$-0.440969\pi$
$968$	−67.9841	−	19.8925i	−2.18509	−	0.639369i
$969$	6.47561	+	21.3472i	0.208026	+	0.685771i
$970$	13.6902	−	8.89083i	0.439566	−	0.285467i
$971$	−14.9211	−	2.21334i	−0.478841	−	0.0710294i	−0.0970531	−	0.995279i	$-0.530942\pi$
$971$	−14.9211	−	2.21334i	−0.478841	−	0.0710294i	−0.381788	+	0.924250i	$0.624692\pi$
$972$	1.14899	+	1.63701i	0.0368539	+	0.0525073i
$973$	−0.641797	−	1.79370i	−0.0205751	−	0.0575035i
$974$	−2.30042	−	0.372034i	−0.0737103	−	0.0119208i
$975$	−1.80442	−	1.20568i	−0.0577877	−	0.0386125i
$976$	56.7045	−	17.0026i	1.81507	−	0.544241i
$977$	−24.4104	+	16.3105i	−0.780958	+	0.521819i	−0.880973	−	0.473167i	$-0.843111\pi$
$977$	−24.4104	+	16.3105i	−0.780958	+	0.521819i	0.100015	+	0.994986i	$0.468111\pi$
$978$	3.04014	+	6.65147i	0.0972131	+	0.212690i
$979$	−49.5488	−	54.6687i	−1.58359	−	1.74722i
$980$	2.33011	+	19.1448i	0.0744326	+	0.611557i
$981$	13.2391	+	7.93521i	0.422692	+	0.253352i
$982$	−11.6612	−	11.9701i	−0.372122	−	0.381982i
$983$	−34.1888	+	28.0580i	−1.09045	+	0.894912i	−0.994935	−	0.100516i	$-0.967951\pi$
$983$	−34.1888	+	28.0580i	−1.09045	+	0.894912i	−0.0955179	+	0.995428i	$0.530451\pi$
$984$	−0.453167	+	1.30703i	−0.0144464	+	0.0416665i
$985$	−7.84211	+	0.772380i	−0.249870	+	0.0246101i
$986$	4.96352	−	2.57020i	0.158071	−	0.0818518i
$987$	−17.4825	−	15.8452i	−0.556473	−	0.504357i
$988$	29.0944	+	46.1085i	0.925615	+	1.46691i
$989$	14.7326	−	19.8647i	0.468470	−	0.631659i
$990$	18.6047	−	6.38375i	0.591296	−	0.202889i
$991$	2.82550	+	1.17036i	0.0897551	+	0.0371778i	0.427109	−	0.904200i	$-0.359532\pi$
$991$	2.82550	+	1.17036i	0.0897551	+	0.0371778i	−0.337354	+	0.941378i	$0.609532\pi$
$992$	−8.86988	−	1.01968i	−0.281619	−	0.0323748i
$993$	20.0984	−	8.32501i	0.637802	−	0.264186i
$994$	52.1277	−	46.0189i	1.65339	−	1.45963i
$995$	−53.4401	+	7.92708i	−1.69416	+	0.251305i
$996$	−14.5428	+	13.8015i	−0.460807	+	0.437317i
$997$	−6.84324	+	0.336187i	−0.216728	+	0.0106471i	−0.157142	−	0.987576i	$-0.550228\pi$
$997$	−6.84324	+	0.336187i	−0.216728	+	0.0106471i	−0.0595858	+	0.998223i	$0.518978\pi$
$998$	−2.40410	−	28.1818i	−0.0761005	−	0.892080i
$999$	−6.11198	−	5.01597i	−0.193374	−	0.158698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.685.55	yes	2048
256.37	even	64	inner	768.2.z.a.37.55	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.37.55	✓	2048	256.37	even	64	inner
768.2.z.a.685.55	yes	2048	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22241 - 0.711131i) q^{2} +(-0.514103 - 0.857729i) q^{3} +(0.988587 - 1.73859i) q^{4} +(-0.780458 + 2.18123i) q^{5} +(-1.23840 - 0.682904i) q^{6} +(-3.19717 - 0.969849i) q^{7} +(-0.0279035 - 2.82829i) q^{8} +(-0.471397 + 0.881921i) q^{9} +O(q^{10})\)	\(q+(1.22241 - 0.711131i) q^{2} +(-0.514103 - 0.857729i) q^{3} +(0.988587 - 1.73859i) q^{4} +(-0.780458 + 2.18123i) q^{5} +(-1.23840 - 0.682904i) q^{6} +(-3.19717 - 0.969849i) q^{7} +(-0.0279035 - 2.82829i) q^{8} +(-0.471397 + 0.881921i) q^{9} +(0.597100 + 3.22138i) q^{10} +(-4.82218 + 3.57637i) q^{11} +(-1.99947 + 0.0458749i) q^{12} +(-2.52892 + 5.34696i) q^{13} +(-4.59795 + 1.08805i) q^{14} +(2.27214 - 0.451957i) q^{15} +(-2.04539 - 3.43749i) q^{16} +(-4.74728 - 0.944293i) q^{17} +(0.0509197 + 1.41330i) q^{18} +(4.60322 + 0.226142i) q^{19} +(3.02072 + 3.51324i) q^{20} +(0.811804 + 3.24090i) q^{21} +(-3.35143 + 7.80100i) q^{22} +(0.811178 - 8.23603i) q^{23} +(-2.41156 + 1.47797i) q^{24} +(-0.283618 - 0.232759i) q^{25} +(0.710998 + 8.33459i) q^{26} +(0.998795 - 0.0490677i) q^{27} +(-4.84685 + 4.59978i) q^{28} +(-0.807720 + 0.119814i) q^{29} +(2.45610 - 2.16827i) q^{30} +(1.45817 - 0.603995i) q^{31} +(-4.94482 - 2.74750i) q^{32} +(5.54665 + 2.29750i) q^{33} +(-6.47465 + 2.22162i) q^{34} +(4.61072 - 6.21684i) q^{35} +(1.06728 + 1.69142i) q^{36} +(-5.85849 - 5.30983i) q^{37} +(5.78786 - 2.99705i) q^{38} +(5.88637 - 0.579757i) q^{39} +(6.19094 + 2.14650i) q^{40} +(0.378072 - 0.310276i) q^{41} +(3.29706 + 3.38442i) q^{42} +(2.56324 + 1.53635i) q^{43} +(1.45070 + 11.9193i) q^{44} +(-1.55577 - 1.71653i) q^{45} +(-4.86530 - 10.6447i) q^{46} +(-5.87190 + 3.92348i) q^{47} +(-1.89690 + 3.52162i) q^{48} +(3.46097 + 2.31255i) q^{49} +(-0.512220 - 0.0828384i) q^{50} +(1.63064 + 4.55734i) q^{51} +(6.79611 + 9.68270i) q^{52} +(2.86652 + 0.425209i) q^{53} +(1.18605 - 0.770255i) q^{54} +(-4.03740 - 13.3095i) q^{55} +(-2.65380 + 9.06957i) q^{56} +(-2.17256 - 4.06458i) q^{57} +(-0.902164 + 0.720856i) q^{58} +(-5.29025 - 11.1853i) q^{59} +(1.46044 - 4.39713i) q^{60} +(-3.59603 + 14.3562i) q^{61} +(1.35297 - 1.77528i) q^{62} +(2.36246 - 2.36246i) q^{63} +(-7.99844 + 0.157838i) q^{64} +(-9.68926 - 9.68926i) q^{65} +(8.41412 - 1.13590i) q^{66} +(7.09260 + 1.77660i) q^{67} +(-6.33484 + 7.32006i) q^{68} +(-7.48131 + 3.53840i) q^{69} +(1.21522 - 10.8784i) q^{70} +(-12.9788 + 6.93731i) q^{71} +(2.50748 + 1.30864i) q^{72} +(6.48097 - 1.96598i) q^{73} +(-10.9375 - 2.32465i) q^{74} +(-0.0538354 + 0.362929i) q^{75} +(4.94385 - 7.77956i) q^{76} +(18.8858 - 6.75746i) q^{77} +(6.78329 - 4.89468i) q^{78} +(-2.73458 + 4.09259i) q^{79} +(9.09433 - 1.77866i) q^{80} +(-0.555570 - 0.831470i) q^{81} +(0.241514 - 0.648144i) q^{82} +(7.42778 - 6.73215i) q^{83} +(6.43714 + 1.79252i) q^{84} +(5.76478 - 9.61795i) q^{85} +(4.22588 + 0.0552520i) q^{86} +(0.518019 + 0.631208i) q^{87} +(10.2496 + 13.5387i) q^{88} +(1.20458 + 12.2303i) q^{89} +(-3.12247 - 0.991951i) q^{90} +(13.2711 - 14.6424i) q^{91} +(-13.5172 - 9.55234i) q^{92} +(-1.26771 - 0.940202i) q^{93} +(-4.38778 + 8.97181i) q^{94} +(-4.08589 + 9.86422i) q^{95} +(0.185540 + 5.65381i) q^{96} +(-1.90671 - 4.60322i) q^{97} +(5.87526 + 0.365685i) q^{98} +(-0.880919 - 5.93867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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