LMFDB - Embedded newform 966.2.j.a.137.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(137,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("966.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.17
Character	$\chi$	$=$	966.137
Dual form			966.2.j.a.275.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.144090 + 1.72605i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.22533 - 3.85438i) q^{5} +(-0.987809 - 1.42276i) q^{6} +(1.67417 + 2.04869i) q^{7} +1.00000i q^{8} +(-2.95848 + 0.497412i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.144090 + 1.72605i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.22533 - 3.85438i) q^{5} +(-0.987809 - 1.42276i) q^{6} +(1.67417 + 2.04869i) q^{7} +1.00000i q^{8} +(-2.95848 + 0.497412i) q^{9} +(3.85438 + 2.22533i) q^{10} +(-1.94384 + 3.36683i) q^{11} +(1.56685 + 0.738238i) q^{12} +1.10062 q^{13} +(-2.47422 - 0.937135i) q^{14} +(6.33220 - 4.39640i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.70171 - 4.67951i) q^{17} +(2.31341 - 1.91001i) q^{18} +(5.17767 - 2.98933i) q^{19} -4.45066 q^{20} +(-3.29491 + 3.18490i) q^{21} -3.88768i q^{22} +(-0.497032 + 4.77001i) q^{23} +(-1.72605 + 0.144090i) q^{24} +(-7.40418 + 12.8244i) q^{25} +(-0.953164 + 0.550309i) q^{26} +(-1.28484 - 5.03480i) q^{27} +(2.61131 - 0.425529i) q^{28} +0.0647484i q^{29} +(-3.28564 + 6.97349i) q^{30} +(-3.67485 + 6.36502i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-6.09139 - 2.87003i) q^{33} +5.40343i q^{34} +(4.17087 - 11.0119i) q^{35} +(-1.04847 + 2.81082i) q^{36} +(0.378703 - 0.218644i) q^{37} +(-2.98933 + 5.17767i) q^{38} +(0.158588 + 1.89972i) q^{39} +(3.85438 - 2.22533i) q^{40} +7.37397i q^{41} +(1.26103 - 4.40566i) q^{42} +4.87375i q^{43} +(1.94384 + 3.36683i) q^{44} +(8.50080 + 10.2962i) q^{45} +(-1.95456 - 4.37946i) q^{46} +(-3.44355 + 1.98813i) q^{47} +(1.42276 - 0.987809i) q^{48} +(-1.39429 + 6.85973i) q^{49} -14.8084i q^{50} +(8.46634 + 3.98902i) q^{51} +(0.550309 - 0.953164i) q^{52} +(-3.54367 + 6.13782i) q^{53} +(3.63010 + 3.71784i) q^{54} +17.3027 q^{55} +(-2.04869 + 1.67417i) q^{56} +(5.90577 + 8.50617i) q^{57} +(-0.0323742 - 0.0560737i) q^{58} +(10.3128 + 5.95409i) q^{59} +(-0.641295 - 7.68204i) q^{60} +(-8.96275 + 5.17465i) q^{61} -7.34969i q^{62} +(-5.97204 - 5.22826i) q^{63} -1.00000 q^{64} +(-2.44924 - 4.24221i) q^{65} +(6.71032 - 0.560175i) q^{66} +(3.41741 + 1.97304i) q^{67} +(-2.70171 - 4.67951i) q^{68} +(-8.30487 - 0.170591i) q^{69} +(1.89388 + 11.6220i) q^{70} -1.36854i q^{71} +(-0.497412 - 2.95848i) q^{72} +(-2.17222 + 3.76239i) q^{73} +(-0.218644 + 0.378703i) q^{74} +(-23.2024 - 10.9321i) q^{75} -5.97866i q^{76} +(-10.1519 + 1.65432i) q^{77} +(-1.08720 - 1.56591i) q^{78} +(3.57139 - 2.06194i) q^{79} +(-2.22533 + 3.85438i) q^{80} +(8.50516 - 2.94316i) q^{81} +(-3.68699 - 6.38605i) q^{82} -11.8436 q^{83} +(1.11075 + 4.44592i) q^{84} -24.0488 q^{85} +(-2.43688 - 4.22079i) q^{86} +(-0.111759 + 0.00932958i) q^{87} +(-3.36683 - 1.94384i) q^{88} +(2.49126 + 4.31499i) q^{89} +(-12.5100 - 4.66637i) q^{90} +(1.84263 + 2.25483i) q^{91} +(3.88243 + 2.81545i) q^{92} +(-11.5158 - 5.42582i) q^{93} +(1.98813 - 3.44355i) q^{94} +(-23.0440 - 13.3045i) q^{95} +(-0.738238 + 1.56685i) q^{96} -0.0549934i q^{97} +(-2.22237 - 6.63785i) q^{98} +(4.07610 - 10.9276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.144090	+	1.72605i	0.0831903	+	0.996534i
$3$	0.144090	+	1.72605i	0.0831903	+	0.996534i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.22533	−	3.85438i	−0.995197	−	1.72373i	−0.582373	−	0.812922i	$-0.697876\pi$
$5$	−2.22533	−	3.85438i	−0.995197	−	1.72373i	−0.412824	−	0.910811i	$-0.635458\pi$
$6$	−0.987809	−	1.42276i	−0.403271	−	0.580838i
$7$	1.67417	+	2.04869i	0.632778	+	0.774334i
$7$	1.67417	+	2.04869i	0.632778	+	0.774334i
$8$			1.00000i			0.353553i
$9$	−2.95848	+	0.497412i	−0.986159	+	0.165804i
$10$	3.85438	+	2.22533i	1.21886	+	0.703711i
$11$	−1.94384	+	3.36683i	−0.586090	+	1.01514i	0.408649	+	0.912692i	$0.366000\pi$
$11$	−1.94384	+	3.36683i	−0.586090	+	1.01514i	−0.994739	+	0.102445i	$0.967333\pi$
$12$	1.56685	+	0.738238i	0.452309	+	0.213111i
$13$	1.10062			0.305257			0.152628	−	0.988284i	$-0.451226\pi$
$13$	1.10062			0.305257			0.152628	+	0.988284i	$0.451226\pi$
$14$	−2.47422	−	0.937135i	−0.661264	−	0.250460i
$15$	6.33220	−	4.39640i	1.63497	−	1.13515i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.70171	−	4.67951i	0.655262	−	1.13495i	−0.326566	−	0.945174i	$-0.605892\pi$
$17$	2.70171	−	4.67951i	0.655262	−	1.13495i	0.981828	−	0.189773i	$-0.0607751\pi$
$18$	2.31341	−	1.91001i	0.545276	−	0.450193i
$19$	5.17767	−	2.98933i	1.18784	−	0.685799i	0.230024	−	0.973185i	$-0.426120\pi$
$19$	5.17767	−	2.98933i	1.18784	−	0.685799i	0.957815	+	0.287386i	$0.0927862\pi$
$20$	−4.45066			−0.995197
$21$	−3.29491	+	3.18490i	−0.719008	+	0.695001i
$22$		−	3.88768i		−	0.828856i
$23$	−0.497032	+	4.77001i	−0.103638	+	0.994615i
$23$	−0.497032	+	4.77001i	−0.103638	+	0.994615i
$24$	−1.72605	+	0.144090i	−0.352328	+	0.0294122i
$25$	−7.40418	+	12.8244i	−1.48084	+	2.56488i
$26$	−0.953164	+	0.550309i	−0.186931	+	0.107925i
$27$	−1.28484	−	5.03480i	−0.247268	−	0.968947i
$28$	2.61131	−	0.425529i	0.493491	−	0.0804174i
$29$			0.0647484i			0.0120235i	0.999982	+	0.00601174i	$0.00191361\pi$
$29$			0.0647484i			0.0120235i	−0.999982	+	0.00601174i	$0.998086\pi$
$30$	−3.28564	+	6.97349i	−0.599874	+	1.27318i
$31$	−3.67485	+	6.36502i	−0.660022	+	1.14319i	0.320588	+	0.947219i	$0.396120\pi$
$31$	−3.67485	+	6.36502i	−0.660022	+	1.14319i	−0.980609	+	0.195972i	$0.937214\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−6.09139	−	2.87003i	−1.06038	−	0.499608i
$34$			5.40343i			0.926680i
$35$	4.17087	−	11.0119i	0.705005	−	1.86135i
$36$	−1.04847	+	2.81082i	−0.174745	+	0.468470i
$37$	0.378703	−	0.218644i	0.0622584	−	0.0359449i	−0.468548	−	0.883438i	$-0.655223\pi$
$37$	0.378703	−	0.218644i	0.0622584	−	0.0359449i	0.530806	+	0.847493i	$0.321889\pi$
$38$	−2.98933	+	5.17767i	−0.484933	+	0.839929i
$39$	0.158588	+	1.89972i	0.0253944	+	0.304199i
$40$	3.85438	−	2.22533i	0.609431	−	0.351855i
$41$			7.37397i			1.15162i	0.817583	+	0.575811i	$0.195313\pi$
$41$			7.37397i			1.15162i	−0.817583	+	0.575811i	$0.804687\pi$
$42$	1.26103	−	4.40566i	0.194581	−	0.679808i
$43$			4.87375i			0.743240i	0.928385	+	0.371620i	$0.121198\pi$
$43$			4.87375i			0.743240i	−0.928385	+	0.371620i	$0.878802\pi$
$44$	1.94384	+	3.36683i	0.293045	+	0.507568i
$45$	8.50080	+	10.2962i	1.26722	+	1.53487i
$46$	−1.95456	−	4.37946i	−0.288184	−	0.645717i
$47$	−3.44355	+	1.98813i	−0.502293	+	0.289999i	−0.729660	−	0.683810i	$-0.760322\pi$
$47$	−3.44355	+	1.98813i	−0.502293	+	0.289999i	0.227367	+	0.973809i	$0.426988\pi$
$48$	1.42276	−	0.987809i	0.205357	−	0.142578i
$49$	−1.39429	+	6.85973i	−0.199185	+	0.979962i
$50$		−	14.8084i		−	2.09422i
$51$	8.46634	+	3.98902i	1.18552	+	0.558574i
$52$	0.550309	−	0.953164i	0.0763142	−	0.132180i
$53$	−3.54367	+	6.13782i	−0.486761	+	0.843095i	−0.999884	−	0.0152203i	$-0.995155\pi$
$53$	−3.54367	+	6.13782i	−0.486761	+	0.843095i	0.513123	+	0.858315i	$0.328488\pi$
$54$	3.63010	+	3.71784i	0.493995	+	0.505934i
$55$	17.3027			2.33310
$56$	−2.04869	+	1.67417i	−0.273768	+	0.223721i
$57$	5.90577	+	8.50617i	0.782239	+	1.12667i
$58$	−0.0323742	−	0.0560737i	−0.00425094	−	0.00736284i
$59$	10.3128	+	5.95409i	1.34261	+	0.775157i	0.987190	−	0.159550i	$-0.0510043\pi$
$59$	10.3128	+	5.95409i	1.34261	+	0.775157i	0.355421	+	0.934706i	$0.384338\pi$
$60$	−0.641295	−	7.68204i	−0.0827908	−	0.991748i
$61$	−8.96275	+	5.17465i	−1.14756	+	0.662546i	−0.948292	−	0.317399i	$-0.897191\pi$
$61$	−8.96275	+	5.17465i	−1.14756	+	0.662546i	−0.199271	+	0.979944i	$0.563857\pi$
$62$		−	7.34969i		−	0.933412i
$63$	−5.97204	−	5.22826i	−0.752407	−	0.658699i
$64$	−1.00000			−0.125000
$65$	−2.44924	−	4.24221i	−0.303791	−	0.526181i
$66$	6.71032	−	0.560175i	0.825983	−	0.0689528i
$67$	3.41741	+	1.97304i	0.417503	+	0.241046i	0.694009	−	0.719967i	$-0.255843\pi$
$67$	3.41741	+	1.97304i	0.417503	+	0.241046i	−0.276505	+	0.961012i	$0.589176\pi$
$68$	−2.70171	−	4.67951i	−0.327631	−	0.567474i
$69$	−8.30487	−	0.170591i	−0.999789	−	0.0205367i
$70$	1.89388	+	11.6220i	0.226362	+	1.38910i
$71$		−	1.36854i		−	0.162416i	−0.996697	−	0.0812082i	$-0.974122\pi$
$71$		−	1.36854i		−	0.162416i	0.996697	−	0.0812082i	$-0.0258779\pi$
$72$	−0.497412	−	2.95848i	−0.0586205	−	0.348660i
$73$	−2.17222	+	3.76239i	−0.254239	+	0.440354i	−0.964688	−	0.263394i	$-0.915158\pi$
$73$	−2.17222	+	3.76239i	−0.254239	+	0.440354i	0.710450	+	0.703748i	$0.248492\pi$
$74$	−0.218644	+	0.378703i	−0.0254169	+	0.0440233i
$75$	−23.2024	−	10.9321i	−2.67918	−	1.26233i
$76$		−	5.97866i		−	0.685799i
$77$	−10.1519	+	1.65432i	−1.15692	+	0.188527i
$78$	−1.08720	−	1.56591i	−0.123101	−	0.177305i
$79$	3.57139	−	2.06194i	0.401813	−	0.231987i	−0.285453	−	0.958393i	$-0.592144\pi$
$79$	3.57139	−	2.06194i	0.401813	−	0.231987i	0.687266	+	0.726406i	$0.258811\pi$
$80$	−2.22533	+	3.85438i	−0.248799	+	0.430933i
$81$	8.50516	−	2.94316i	0.945018	−	0.327018i
$82$	−3.68699	−	6.38605i	−0.407160	−	0.705221i
$83$	−11.8436			−1.30000			−0.650002	−	0.759933i	$-0.725232\pi$
$83$	−11.8436			−1.30000			−0.650002	+	0.759933i	$0.725232\pi$
$84$	1.11075	+	4.44592i	0.121192	+	0.485090i
$85$	−24.0488			−2.60846
$86$	−2.43688	−	4.22079i	−0.262775	−	0.455140i
$87$	−0.111759	+	0.00932958i	−0.0119818	+	0.00100024i
$88$	−3.36683	−	1.94384i	−0.358905	−	0.207214i
$89$	2.49126	+	4.31499i	0.264073	+	0.457388i	0.967320	−	0.253557i	$-0.0816006\pi$
$89$	2.49126	+	4.31499i	0.264073	+	0.457388i	−0.703247	+	0.710945i	$0.748267\pi$
$90$	−12.5100	−	4.66637i	−1.31867	−	0.491878i
$91$	1.84263	+	2.25483i	0.193160	+	0.236371i
$92$	3.88243	+	2.81545i	0.404771	+	0.293530i
$93$	−11.5158	−	5.42582i	−1.19414	−	0.562632i
$94$	1.98813	−	3.44355i	0.205060	−	0.355175i
$95$	−23.0440	−	13.3045i	−2.36427	−	1.36501i
$96$	−0.738238	+	1.56685i	−0.0753461	+	0.159915i
$97$		−	0.0549934i		−	0.00558373i	−0.999996	−	0.00279187i	$-0.999111\pi$
$97$		−	0.0549934i		−	0.00558373i	0.999996	−	0.00279187i	$-0.000888680\pi$
$98$	−2.22237	−	6.63785i	−0.224494	−	0.670524i
$99$	4.07610	−	10.9276i	0.409664	−	1.09826i
$100$	7.40418	+	12.8244i	0.740418	+	1.28244i
$101$	9.02397	+	5.20999i	0.897918	+	0.518413i	0.876524	−	0.481358i	$-0.159856\pi$
$101$	9.02397	+	5.20999i	0.897918	+	0.518413i	0.0213942	+	0.999771i	$0.493189\pi$
$102$	−9.32657	+	0.778579i	−0.923468	+	0.0770908i
$103$	5.47408	−	3.16046i	0.539377	−	0.311410i	−0.205449	−	0.978668i	$-0.565866\pi$
$103$	5.47408	−	3.16046i	0.539377	−	0.311410i	0.744827	+	0.667258i	$0.232532\pi$
$104$			1.10062i			0.107925i
$105$	19.6081	+	5.61241i	1.91355	+	0.547715i
$106$		−	7.08735i		−	0.688384i
$107$	−0.208064	−	0.360377i	−0.0201143	−	0.0348390i	0.855793	−	0.517318i	$-0.173070\pi$
$107$	−0.208064	−	0.360377i	−0.0201143	−	0.0348390i	−0.875907	+	0.482479i	$0.839736\pi$
$108$	−5.00268	−	1.40469i	−0.481383	−	0.135167i
$109$	−5.88724	−	3.39900i	−0.563895	−	0.325565i	0.190812	−	0.981627i	$-0.438888\pi$
$109$	−5.88724	−	3.39900i	−0.563895	−	0.325565i	−0.754708	+	0.656061i	$0.772221\pi$
$110$	−14.9846	+	8.65136i	−1.42873	+	0.824875i
$111$	0.431957	+	0.622155i	0.0409996	+	0.0590523i
$112$	0.937135	−	2.47422i	0.0885509	−	0.233792i
$113$	1.62732			0.153085			0.0765426	−	0.997066i	$-0.475612\pi$
$113$	1.62732			0.153085			0.0765426	+	0.997066i	$0.475612\pi$
$114$	−9.36763	−	4.41367i	−0.877359	−	0.413378i
$115$	19.4915	−	8.69908i	1.81759	−	0.811194i
$116$	0.0560737	+	0.0323742i	0.00520632	+	0.00300587i
$117$	−3.25616	+	0.547461i	−0.301032	+	0.0506128i
$118$	−11.9082			−1.09624
$119$	14.1100	−	2.29931i	1.29346	−	0.210778i
$120$	4.39640	+	6.33220i	0.401335	+	0.578048i
$121$	−2.05702	−	3.56287i	−0.187002	−	0.323897i
$122$	5.17465	−	8.96275i	0.468491	−	0.811450i
$123$	−12.7278	+	1.06251i	−1.14763	+	0.0958037i
$124$	3.67485	+	6.36502i	0.330011	+	0.571596i
$125$	43.6536			3.90450
$126$	7.78607	+	1.54178i	0.693638	+	0.137353i
$127$	−2.91869			−0.258992			−0.129496	−	0.991580i	$-0.541336\pi$
$127$	−2.91869			−0.258992			−0.129496	+	0.991580i	$0.541336\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−8.41232	+	0.702258i	−0.740664	+	0.0618304i
$130$	4.24221	+	2.44924i	0.372066	+	0.214812i
$131$	0.0356159	−	0.0205628i	0.00311177	−	0.00179658i	−0.498443	−	0.866922i	$-0.666095\pi$
$131$	0.0356159	−	0.0205628i	0.00311177	−	0.00179658i	0.501555	+	0.865126i	$0.332761\pi$
$132$	−5.53122	+	3.84028i	−0.481431	+	0.334254i
$133$	14.7925	+	5.60281i	1.28268	+	0.485825i
$134$	−3.94609			−0.340890
$135$	−16.5468	+	16.1564i	−1.42413	+	1.39052i
$136$	4.67951	+	2.70171i	0.401264	+	0.231670i
$137$	−2.75518	+	4.77212i	−0.235391	+	0.407710i	−0.959386	−	0.282095i	$-0.908971\pi$
$137$	−2.75518	+	4.77212i	−0.235391	+	0.407710i	0.723995	+	0.689805i	$0.242304\pi$
$138$	7.27753	−	4.00470i	0.619504	−	0.340903i
$139$	4.27751			0.362813			0.181407	−	0.983408i	$-0.441935\pi$
$139$	4.27751			0.362813			0.181407	+	0.983408i	$0.441935\pi$
$140$	−7.45117	−	9.11804i	−0.629739	−	0.770615i
$141$	−3.92779	−	5.65725i	−0.330780	−	0.476427i
$142$	0.684272	+	1.18519i	0.0574228	+	0.0994593i
$143$	−2.13943	+	3.70559i	−0.178908	+	0.309877i
$144$	1.91001	+	2.31341i	0.159167	+	0.192784i
$145$	0.249565	−	0.144086i	0.0207252	−	0.0119657i
$146$		−	4.34443i		−	0.359548i
$147$	−12.0411	−	1.41820i	−0.993135	−	0.116971i
$148$		−	0.437289i		−	0.0359449i
$149$	−10.7042	−	18.5402i	−0.876922	−	1.51887i	−0.854701	−	0.519120i	$-0.826260\pi$
$149$	−10.7042	−	18.5402i	−0.876922	−	1.51887i	−0.0222202	−	0.999753i	$-0.507074\pi$
$150$	25.5599	−	2.13373i	2.08696	−	0.174219i
$151$	7.41248	−	12.8388i	0.603219	−	1.04481i	−0.389112	−	0.921191i	$-0.627218\pi$
$151$	7.41248	−	12.8388i	0.603219	−	1.04481i	0.992330	−	0.123615i	$-0.0394487\pi$
$152$	2.98933	+	5.17767i	0.242467	+	0.419964i
$153$	−5.66532	+	15.1881i	−0.458014	+	1.22788i
$154$	7.96466	−	6.50864i	0.641811	−	0.524481i
$155$	32.7110			2.62741
$156$	1.72450	+	0.812519i	0.138070	+	0.0650536i
$157$	−0.769849	−	0.444472i	−0.0614406	−	0.0354728i	0.468965	−	0.883217i	$-0.344627\pi$
$157$	−0.769849	−	0.444472i	−0.0614406	−	0.0354728i	−0.530406	+	0.847744i	$0.677960\pi$
$158$	−2.06194	+	3.57139i	−0.164039	+	0.284124i
$159$	−11.1048	−	5.23215i	−0.880666	−	0.414936i
$160$		−	4.45066i		−	0.351855i
$161$	−10.6044	+	6.96755i	−0.835744	+	0.549120i
$162$	−5.89411	+	6.80143i	−0.463085	+	0.534371i
$163$	1.92377	+	3.33207i	0.150682	+	0.260988i	0.931478	−	0.363797i	$-0.118520\pi$
$163$	1.92377	+	3.33207i	0.150682	+	0.260988i	−0.780797	+	0.624785i	$0.785187\pi$
$164$	6.38605	+	3.68699i	0.498667	+	0.287905i
$165$	2.49315	+	29.8653i	0.194091	+	2.32501i
$166$	10.2569	−	5.92180i	0.796086	−	0.459621i
$167$			18.3823i			1.42247i	0.702957	+	0.711233i	$0.251863\pi$
$167$			18.3823i			1.42247i	−0.702957	+	0.711233i	$0.748137\pi$
$168$	−3.18490	−	3.29491i	−0.245720	−	0.254208i
$169$	−11.7886			−0.906818
$170$	20.8269	−	12.0244i	1.59735	−	0.922230i
$171$	−13.8311	+	11.4193i	−1.05769	+	0.873255i
$172$	4.22079	+	2.43688i	0.321832	+	0.185810i
$173$	16.7398	−	9.66471i	1.27270	−	0.734794i	0.297205	−	0.954814i	$-0.403945\pi$
$173$	16.7398	−	9.66471i	1.27270	−	0.734794i	0.975495	+	0.220020i	$0.0706121\pi$
$174$	0.0921211	−	0.0639590i	0.00698368	−	0.00484872i
$175$	−38.6692	+	6.30138i	−2.92311	+	0.476340i
$176$	3.88768			0.293045
$177$	−8.79107	+	18.6583i	−0.660777	+	1.40244i
$178$	−4.31499	−	2.49126i	−0.323422	−	0.186728i
$179$	16.7438	+	9.66704i	1.25149	+	0.722548i	0.971405	−	0.237427i	$-0.0763041\pi$
$179$	16.7438	+	9.66704i	1.25149	+	0.722548i	0.280085	+	0.959975i	$0.409637\pi$
$180$	13.1672	−	2.21381i	0.981423	−	0.165008i
$181$		−	8.38429i		−	0.623199i	−0.950214	−	0.311599i	$-0.899135\pi$
$181$		−	8.38429i		−	0.623199i	0.950214	−	0.311599i	$-0.100865\pi$
$182$	−2.72318	−	1.03143i	−0.201855	−	0.0764546i
$183$	−10.2231	−	14.7245i	−0.755715	−	1.08847i
$184$	−4.77001	−	0.497032i	−0.351650	−	0.0366417i
$185$	−1.68548	−	0.973111i	−0.123919	−	0.0715445i
$186$	12.6859	−	1.05902i	0.930176	−	0.0776508i
$187$	10.5034	+	18.1924i	0.768084	+	1.33036i
$188$			3.97627i			0.289999i
$189$	8.16371	−	11.0614i	0.593823	−	0.804596i
$190$	26.6090			1.93042
$191$	1.32248	+	2.29059i	0.0956909	+	0.165742i	0.909897	−	0.414835i	$-0.136161\pi$
$191$	1.32248	+	2.29059i	0.0956909	+	0.165742i	−0.814206	+	0.580576i	$0.802827\pi$
$192$	−0.144090	−	1.72605i	−0.0103988	−	0.124567i
$193$	8.09115	−	14.0143i	0.582413	−	1.00877i	−0.412779	−	0.910831i	$-0.635442\pi$
$193$	8.09115	−	14.0143i	0.582413	−	1.00877i	0.995192	−	0.0979385i	$-0.0312248\pi$
$194$	0.0274967	+	0.0476257i	0.00197415	+	0.00341932i
$195$	6.96934	−	4.83876i	0.499085	−	0.346511i
$196$	5.24356	+	4.63736i	0.374540	+	0.331240i
$197$		−	8.02327i		−	0.571634i	−0.958284	−	0.285817i	$-0.907735\pi$
$197$		−	8.02327i		−	0.571634i	0.958284	−	0.285817i	$-0.0922650\pi$
$198$	1.93378	+	11.5016i	0.137428	+	0.817383i
$199$	−12.6765	−	7.31876i	−0.898610	−	0.518813i	−0.0218613	−	0.999761i	$-0.506959\pi$
$199$	−12.6765	−	7.31876i	−0.898610	−	0.518813i	−0.876749	+	0.480948i	$0.840293\pi$
$200$	−12.8244	−	7.40418i	−0.906823	−	0.523554i
$201$	−2.91315	+	6.18291i	−0.205478	+	0.436109i
$202$	−10.4200			−0.733147
$203$	−0.132650	+	0.108400i	−0.00931018	+	0.00760818i
$204$	7.68776	−	5.33756i	0.538251	−	0.373704i
$205$	28.4221	−	16.4095i	1.98509	−	1.14609i
$206$	−3.16046	+	5.47408i	−0.220200	+	0.381397i
$207$	−0.902200	−	14.3592i	−0.0627072	−	0.998032i
$208$	−0.550309	−	0.953164i	−0.0381571	−	0.0660900i
$209$			23.2431i			1.60776i
$210$	−19.7873	+	4.94355i	−1.36545	+	0.341137i
$211$	20.1164			1.38487			0.692435	−	0.721480i	$-0.256538\pi$
$211$	20.1164			1.38487			0.692435	+	0.721480i	$0.256538\pi$
$212$	3.54367	+	6.13782i	0.243380	+	0.421547i
$213$	2.36217	−	0.197193i	0.161853	−	0.0135115i
$214$	0.360377	+	0.208064i	0.0246349	+	0.0142229i
$215$	18.7853	−	10.8457i	1.28115	−	0.739671i
$216$	5.03480	−	1.28484i	0.342575	−	0.0874224i
$217$	−19.1923	+	3.12751i	−1.30286	+	0.212309i
$218$	6.79800			0.460419
$219$	−6.80706	−	3.20723i	−0.459978	−	0.216724i
$220$	8.65136	−	14.9846i	0.583275	−	1.01026i
$221$	2.97356	−	5.15035i	0.200023	−	0.346450i
$222$	−0.685164	−	0.322823i	−0.0459852	−	0.0216665i
$223$	−13.9283			−0.932706			−0.466353	−	0.884599i	$-0.654432\pi$
$223$	−13.9283			−0.932706			−0.466353	+	0.884599i	$0.654432\pi$
$224$	0.425529	+	2.61131i	0.0284318	+	0.174475i
$225$	15.5261	−	41.6236i	1.03507	−	2.77491i
$226$	−1.40930	+	0.813659i	−0.0937451	+	0.0541238i
$227$	0.0826673	−	0.143184i	0.00548682	−	0.00950346i	−0.863269	−	0.504744i	$-0.831587\pi$
$227$	0.0826673	−	0.143184i	0.00548682	−	0.00950346i	0.868756	+	0.495241i	$0.164920\pi$
$228$	10.3194	−	0.861464i	0.683422	−	0.0570518i
$229$	20.2812	−	11.7093i	1.34022	−	0.773776i	0.353379	−	0.935480i	$-0.385032\pi$
$229$	20.2812	−	11.7093i	1.34022	−	0.773776i	0.986839	+	0.161704i	$0.0516991\pi$
$230$	−12.5306	+	17.2794i	−0.826242	+	1.13937i
$231$	−4.31822	−	17.2843i	−0.284118	−	1.13723i
$232$	−0.0647484			−0.00425094
$233$	0.188185	−	0.108648i	0.0123284	−	0.00711780i	−0.493823	−	0.869562i	$-0.664401\pi$
$233$	0.188185	−	0.108648i	0.0123284	−	0.00711780i	0.506152	+	0.862445i	$0.331068\pi$
$234$	2.54618	−	2.10219i	0.166449	−	0.137425i
$235$	15.3260	+	8.84850i	0.999761	+	0.577212i
$236$	10.3128	−	5.95409i	0.671305	−	0.387578i
$237$	4.07361	+	5.86728i	0.264609	+	0.381121i
$238$	−11.0700	+	9.04627i	−0.717560	+	0.586383i
$239$			22.0686i			1.42750i	0.700402	+	0.713748i	$0.253004\pi$
$239$			22.0686i			1.42750i	−0.700402	+	0.713748i	$0.746996\pi$
$240$	−6.97349	−	3.28564i	−0.450137	−	0.212087i
$241$	23.3446	+	13.4780i	1.50376	+	0.868193i	0.999991	+	0.00435252i	$0.00138545\pi$
$241$	23.3446	+	13.4780i	1.50376	+	0.868193i	0.503765	+	0.863841i	$0.331948\pi$
$242$	3.56287	+	2.05702i	0.229030	+	0.132230i
$243$	6.30554	+	14.2562i	0.404501	+	0.914538i
$244$			10.3493i			0.662546i
$245$	29.5428	−	9.89102i	1.88742	−	0.631914i
$246$	10.4914	−	7.28408i	0.668905	−	0.464416i
$247$	5.69864	−	3.29011i	0.362596	−	0.209345i
$248$	−6.36502	−	3.67485i	−0.404179	−	0.233353i
$249$	−1.70654	−	20.4426i	−0.108148	−	1.29550i
$250$	−37.8052	+	21.8268i	−2.39101	+	1.38045i
$251$	−19.0773			−1.20415			−0.602074	−	0.798440i	$-0.705659\pi$
$251$	−19.0773			−1.20415			−0.602074	+	0.798440i	$0.705659\pi$
$252$	−7.51383	+	2.55781i	−0.473327	+	0.161127i
$253$	−15.0936	−	10.9455i	−0.948929	−	0.688141i
$254$	2.52766	−	1.45934i	0.158599	−	0.0915674i
$255$	−3.46519	−	41.5094i	−0.216999	−	2.59942i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−26.1266	+	15.0842i	−1.62974	+	0.940928i	−0.645564	+	0.763706i	$0.723378\pi$
$257$	−26.1266	+	15.0842i	−1.62974	+	0.940928i	−0.984171	+	0.177222i	$0.943289\pi$
$258$	6.93416	−	4.81434i	0.431702	−	0.299727i
$259$	1.08195	+	0.409798i	0.0672291	+	0.0254636i
$260$	−4.89848			−0.303791
$261$	−0.0322066	−	0.191557i	−0.00199354	−	0.0118571i
$262$	−0.0205628	+	0.0356159i	−0.00127038	+	0.00220036i
$263$	−6.63106	+	11.4853i	−0.408889	+	0.708216i	−0.994765	−	0.102184i	$-0.967417\pi$
$263$	−6.63106	+	11.4853i	−0.408889	+	0.708216i	0.585877	+	0.810400i	$0.300750\pi$
$264$	2.87003	−	6.09139i	0.176638	−	0.374899i
$265$	31.5434			1.93769
$266$	−15.6121	+	2.54409i	−0.957240	+	0.155988i
$267$	−7.08891	+	4.92178i	−0.433834	+	0.301208i
$268$	3.41741	−	1.97304i	0.208752	−	0.120523i
$269$	6.58183	+	3.80002i	0.401301	+	0.231691i	0.687045	−	0.726615i	$-0.258907\pi$
$269$	6.58183	+	3.80002i	0.401301	+	0.231691i	−0.285744	+	0.958306i	$0.592241\pi$
$270$	6.25181	−	22.2652i	0.380473	−	1.35502i
$271$	−9.15576	−	15.8582i	−0.556173	−	0.963320i	−0.997811	−	0.0661266i	$-0.978936\pi$
$271$	−9.15576	−	15.8582i	−0.556173	−	0.963320i	0.441638	−	0.897193i	$-0.354397\pi$
$272$	−5.40343			−0.327631
$273$	−3.62644	+	3.50536i	−0.219482	+	0.212154i
$274$		−	5.51037i		−	0.332894i
$275$	−28.7851	−	49.8572i	−1.73580	−	3.00650i
$276$	−4.30017	+	7.10693i	−0.258840	+	0.427787i
$277$	−2.50467	+	4.33822i	−0.150491	+	0.260658i	−0.931408	−	0.363977i	$-0.881419\pi$
$277$	−2.50467	+	4.33822i	−0.150491	+	0.260658i	0.780917	+	0.624635i	$0.214752\pi$
$278$	−3.70443	+	2.13875i	−0.222177	+	0.128274i
$279$	7.70591	−	20.6587i	0.461341	−	1.23680i
$280$	11.0119	+	4.17087i	0.658088	+	0.249257i
$281$	−15.0744			−0.899262			−0.449631	−	0.893214i	$-0.648444\pi$
$281$	−15.0744			−0.899262			−0.449631	+	0.893214i	$0.648444\pi$
$282$	6.23019	+	2.93543i	0.371003	+	0.174802i
$283$	−8.16963	−	4.71674i	−0.485634	−	0.280381i	0.237127	−	0.971479i	$-0.423794\pi$
$283$	−8.16963	−	4.71674i	−0.485634	−	0.280381i	−0.722761	+	0.691098i	$0.757127\pi$
$284$	−1.18519	−	0.684272i	−0.0703283	−	0.0406041i
$285$	19.6437	−	41.6921i	1.16360	−	2.46963i
$286$		−	4.27885i		−	0.253014i
$287$	−15.1070	+	12.3453i	−0.891739	+	0.728720i
$288$	−2.81082	−	1.04847i	−0.165629	−	0.0617815i
$289$	−6.09852	−	10.5629i	−0.358737	−	0.621350i
$290$	−0.144086	+	0.249565i	−0.00846105	+	0.0146550i
$291$	0.0949211	−	0.00792399i	0.00556438	−	0.000464512i
$292$	2.17222	+	3.76239i	0.127119	+	0.220177i
$293$	−10.3290			−0.603426			−0.301713	−	0.953399i	$-0.597558\pi$
$293$	−10.3290			−0.603426			−0.301713	+	0.953399i	$0.597558\pi$
$294$	11.1370	−	4.79237i	0.649524	−	0.279496i
$295$		−	52.9992i		−	3.08573i
$296$	0.218644	+	0.378703i	0.0127084	+	0.0220117i
$297$	19.4488	+	5.46099i	1.12854	+	0.316879i
$298$	18.5402	+	10.7042i	1.07401	+	0.620077i
$299$	−0.547042	+	5.24996i	−0.0316363	+	0.303613i
$300$	−21.0687	+	14.6278i	−1.21640	+	0.844538i
$301$	−9.98483	+	8.15950i	−0.575516	+	0.470306i
$302$			14.8250i			0.853080i
$303$	−7.69243	+	16.3265i	−0.441918	+	0.937933i
$304$	−5.17767	−	2.98933i	−0.296960	−	0.171450i
$305$	39.8902	+	23.0306i	2.28410	+	1.31873i
$306$	−2.68773	−	15.9859i	−0.153647	−	0.913854i
$307$	−1.66754			−0.0951716			−0.0475858	−	0.998867i	$-0.515153\pi$
$307$	−1.66754			−0.0951716			−0.0475858	+	0.998867i	$0.515153\pi$
$308$	−3.64328	+	9.61898i	−0.207595	+	0.548092i
$309$	6.24387	+	8.99313i	0.355201	+	0.511601i
$310$	−28.3285	+	16.3555i	−1.60895	+	0.928929i
$311$	−9.07103	−	5.23716i	−0.514371	−	0.296972i	0.220257	−	0.975442i	$-0.429310\pi$
$311$	−9.07103	−	5.23716i	−0.514371	−	0.296972i	−0.734629	+	0.678469i	$0.762644\pi$
$312$	−1.89972	+	0.158588i	−0.107550	+	0.00897828i
$313$	19.8659	−	11.4696i	1.12289	−	0.648299i	0.180751	−	0.983529i	$-0.442147\pi$
$313$	19.8659	−	11.4696i	1.12289	−	0.648299i	0.942136	+	0.335230i	$0.108814\pi$
$314$	0.888945			0.0501661
$315$	−6.86195	+	34.6531i	−0.386627	+	1.95248i
$316$		−	4.12388i		−	0.231987i
$317$	16.2683	−	9.39251i	0.913719	−	0.527536i	0.0320934	−	0.999485i	$-0.489783\pi$
$317$	16.2683	−	9.39251i	0.913719	−	0.527536i	0.881626	+	0.471949i	$0.156449\pi$
$318$	12.2331	−	1.02121i	0.685998	−	0.0572669i
$319$	−0.217997	−	0.125860i	−0.0122055	−	0.00704683i
$320$	2.22533	+	3.85438i	0.124400	+	0.215467i
$321$	0.592048	−	0.411055i	0.0330449	−	0.0229428i
$322$	5.69991	−	11.3363i	0.317643	−	0.631746i
$323$		−	32.3053i		−	1.79751i
$324$	1.70373	−	8.83727i	0.0946516	−	0.490959i
$325$	−8.14918	+	14.1148i	−0.452035	+	0.782948i
$326$	−3.33207	−	1.92377i	−0.184546	−	0.106548i
$327$	5.01854	−	10.6514i	0.277526	−	0.589025i
$328$	−7.37397			−0.407160
$329$	−9.83817	−	3.72630i	−0.542396	−	0.205437i
$330$	−17.0918	−	24.6175i	−0.940872	−	1.35515i
$331$	−1.18126	−	2.04601i	−0.0649281	−	0.112459i	0.831734	−	0.555174i	$-0.187348\pi$
$331$	−1.18126	−	2.04601i	−0.0649281	−	0.112459i	−0.896662	+	0.442716i	$0.854015\pi$
$332$	−5.92180	+	10.2569i	−0.325001	+	0.562918i
$333$	−1.01163	+	0.835225i	−0.0554368	+	0.0457701i
$334$	−9.19115	−	15.9195i	−0.502917	−	0.871079i
$335$		−	17.5627i		−	0.959552i
$336$	4.40566	+	1.26103i	0.240348	+	0.0687947i
$337$			2.79140i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$337$			2.79140i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$338$	10.2093	−	5.89432i	0.555311	−	0.320609i
$339$	0.234480	+	2.80883i	0.0127352	+	0.152555i
$340$	−12.0244	+	20.8269i	−0.652115	+	1.12950i
$341$	−14.2866	−	24.7451i	−0.773664	−	1.34002i
$342$	6.26843	−	16.8049i	0.338958	−	0.908707i
$343$	−16.3878	+	8.62789i	−0.884857	+	0.465863i
$344$	−4.87375			−0.262775
$345$	17.8235	+	32.3898i	0.959588	+	1.74381i
$346$	−9.66471	+	16.7398i	−0.519578	+	0.899935i
$347$	17.2546	+	9.96196i	0.926277	+	0.534786i	0.885632	−	0.464388i	$-0.153726\pi$
$347$	17.2546	+	9.96196i	0.926277	+	0.534786i	0.0406447	+	0.999174i	$0.487059\pi$
$348$	−0.0477997	+	0.101451i	−0.00256233	+	0.00543833i
$349$	−22.8243			−1.22176			−0.610880	−	0.791723i	$-0.709184\pi$
$349$	−22.8243			−1.22176			−0.610880	+	0.791723i	$0.709184\pi$
$350$	30.3378	−	24.7917i	1.62162	−	1.32517i
$351$	−1.41412	−	5.54139i	−0.0754802	−	0.295778i
$352$	−3.36683	+	1.94384i	−0.179453	+	0.103607i
$353$	−21.3549	−	12.3293i	−1.13661	−	0.656220i	−0.191019	−	0.981586i	$-0.561179\pi$
$353$	−21.3549	−	12.3293i	−1.13661	−	0.656220i	−0.945588	+	0.325366i	$0.894513\pi$
$354$	−1.71585	−	20.5541i	−0.0911963	−	1.09244i
$355$	−5.27489	+	3.04546i	−0.279962	+	0.161636i
$356$	4.98252			0.264073
$357$	6.00183	+	24.0232i	0.317651	+	1.27144i
$358$	−19.3341			−1.02184
$359$	−5.09007	−	8.81626i	−0.268644	−	0.465304i	0.699868	−	0.714272i	$-0.253242\pi$
$359$	−5.09007	−	8.81626i	−0.268644	−	0.465304i	−0.968512	+	0.248968i	$0.919909\pi$
$360$	−10.2962	+	8.50080i	−0.542657	+	0.448031i
$361$	8.37217	−	14.5010i	0.440641	−	0.763212i
$362$	4.19214	+	7.26100i	0.220334	+	0.381630i
$363$	5.85328	−	4.06389i	0.307217	−	0.213299i
$364$	2.87405	−	0.468345i	0.150641	−	0.0245480i
$365$	19.3356			1.01207
$366$	16.2157	+	7.64024i	0.847611	+	0.399362i
$367$	−6.49643	−	3.75071i	−0.339111	−	0.195786i	0.320768	−	0.947158i	$-0.396059\pi$
$367$	−6.49643	−	3.75071i	−0.339111	−	0.195786i	−0.659879	+	0.751372i	$0.729392\pi$
$368$	4.37946	−	1.95456i	0.228295	−	0.101889i
$369$	−3.66790	−	21.8157i	−0.190943	−	1.13568i
$370$	1.94622			0.101179
$371$	−18.5072	+	3.01587i	−0.960848	+	0.156576i
$372$	−10.4568	+	7.26009i	−0.542161	+	0.376418i
$373$	−2.02319	+	1.16809i	−0.104757	+	0.0604813i	−0.551463	−	0.834199i	$-0.685930\pi$
$373$	−2.02319	+	1.16809i	−0.104757	+	0.0604813i	0.446706	+	0.894681i	$0.352597\pi$
$374$	−18.1924	−	10.5034i	−0.940707	−	0.543118i
$375$	6.29004	+	75.3482i	0.324816	+	3.89096i
$376$	−1.98813	−	3.44355i	−0.102530	−	0.177587i
$377$			0.0712633i			0.00367025i
$378$	−1.53930	+	13.6613i	−0.0791729	+	0.702660i
$379$			25.0384i			1.28614i	0.765809	+	0.643068i	$0.222339\pi$
$379$			25.0384i			1.28614i	−0.765809	+	0.643068i	$0.777661\pi$
$380$	−23.0440	+	13.3045i	−1.18213	+	0.682505i
$381$	−0.420553	−	5.03779i	−0.0215456	−	0.258094i
$382$	−2.29059	−	1.32248i	−0.117197	−	0.0676637i
$383$	6.72775	+	11.6528i	0.343772	+	0.595430i	0.985130	−	0.171811i	$-0.0549620\pi$
$383$	6.72775	+	11.6528i	0.343772	+	0.595430i	−0.641358	+	0.767242i	$0.721629\pi$
$384$	0.987809	+	1.42276i	0.0504089	+	0.0726047i
$385$	28.9677	+	35.4480i	1.47633	+	1.80660i
$386$			16.1823i			0.823657i
$387$	−2.42426	−	14.4189i	−0.123232	−	0.732953i
$388$	−0.0476257	−	0.0274967i	−0.00241783	−	0.00139593i
$389$	−4.31583	+	7.47524i	−0.218821	+	0.379010i	−0.954448	−	0.298378i	$-0.903555\pi$
$389$	−4.31583	+	7.47524i	−0.218821	+	0.379010i	0.735626	+	0.677387i	$0.236888\pi$
$390$	−3.61624	+	7.67516i	−0.183116	+	0.388647i
$391$	20.9784	+	15.2131i	1.06093	+	0.769357i
$392$	−6.85973	−	1.39429i	−0.346469	−	0.0704225i
$393$	0.0406243	+	0.0585118i	0.00204922	+	0.00295153i
$394$	4.01163	+	6.94836i	0.202103	+	0.350053i
$395$	−15.8950	−	9.17700i	−0.799765	−	0.461745i
$396$	−7.42550	−	8.99379i	−0.373145	−	0.451955i
$397$	10.8220	+	18.7443i	0.543143	+	0.940750i	0.998721	+	0.0505550i	$0.0160990\pi$
$397$	10.8220	+	18.7443i	0.543143	+	0.940750i	−0.455579	+	0.890195i	$0.650568\pi$
$398$	14.6375			0.733712
$399$	−7.53926	+	26.3399i	−0.377435	+	1.31864i
$400$	14.8084			0.740418
$401$	−12.2621	−	21.2387i	−0.612342	−	1.06061i	−0.990845	−	0.135007i	$-0.956894\pi$
$401$	−12.2621	−	21.2387i	−0.612342	−	1.06061i	0.378502	−	0.925600i	$-0.376439\pi$
$402$	−0.568591	−	6.81113i	−0.0283587	−	0.339708i
$403$	−4.04461	+	7.00546i	−0.201476	+	0.348967i
$404$	9.02397	−	5.20999i	0.448959	−	0.259207i
$405$	−30.2709	−	26.2327i	−1.50417	−	1.30351i
$406$	0.0606780	−	0.160202i	0.00301140	−	0.00795069i
$407$			1.70004i			0.0842677i
$408$	−3.98902	+	8.46634i	−0.197486	+	0.419146i
$409$	9.15437	−	15.8558i	0.452654	−	0.784020i	−0.545896	−	0.837853i	$-0.683810\pi$
$409$	9.15437	−	15.8558i	0.452654	−	0.784020i	0.998550	+	0.0538328i	$0.0171438\pi$
$410$	−16.4095	+	28.4221i	−0.810408	+	1.40367i
$411$	−8.63390	−	4.06796i	−0.425879	−	0.200658i
$412$		−	6.32093i		−	0.311410i
$413$	5.06727	+	31.0959i	0.249344	+	1.53013i
$414$	7.96092	+	11.9843i	0.391258	+	0.588997i
$415$	26.3559	+	45.6498i	1.29376	+	2.24086i
$416$	0.953164	+	0.550309i	0.0467327	+	0.0269811i
$417$	0.616345	+	7.38318i	0.0301826	+	0.361556i
$418$	−11.6215	−	20.1291i	−0.568429	−	0.984547i
$419$	24.4003			1.19203			0.596016	−	0.802972i	$-0.296749\pi$
$419$	24.4003			1.19203			0.596016	+	0.802972i	$0.296749\pi$
$420$	14.6645	−	14.1749i	0.715555	−	0.691663i
$421$		−	9.78374i		−	0.476831i	−0.971163	−	0.238415i	$-0.923372\pi$
$421$		−	9.78374i		−	0.476831i	0.971163	−	0.238415i	$-0.0766279\pi$
$422$	−17.4213	+	10.0582i	−0.848056	+	0.489625i
$423$	9.19873	−	7.59470i	0.447258	−	0.369267i
$424$	−6.13782	−	3.54367i	−0.298079	−	0.172096i
$425$	40.0079	+	69.2958i	1.94067	+	3.36134i
$426$	−1.94710	+	1.35186i	−0.0943375	+	0.0654978i
$427$	−25.6065	−	9.69869i	−1.23918	−	0.469352i
$428$	−0.416128			−0.0201143
$429$	−6.70430	−	3.15881i	−0.323687	−	0.152509i
$430$	−10.8457	+	18.7853i	−0.523026	+	0.905908i
$431$	5.71126	−	9.89219i	0.275102	−	0.476490i	−0.695059	−	0.718953i	$-0.744622\pi$
$431$	5.71126	−	9.89219i	0.275102	−	0.476490i	0.970161	+	0.242462i	$0.0779551\pi$
$432$	−3.71784	+	3.63010i	−0.178875	+	0.174653i
$433$			13.4585i			0.646775i	0.946267	+	0.323388i	$0.104822\pi$
$433$			13.4585i			0.646775i	−0.946267	+	0.323388i	$0.895178\pi$
$434$	15.0573	−	12.3047i	0.722772	−	0.590642i
$435$	0.284660	+	0.410000i	0.0136484	+	0.0196580i
$436$	−5.88724	+	3.39900i	−0.281948	+	0.162783i
$437$	11.6857	+	26.1833i	0.559001	+	1.25252i
$438$	7.49870	−	0.625989i	0.358302	−	0.0299109i
$439$	−5.39491	−	9.34426i	−0.257485	−	0.445977i	0.708082	−	0.706130i	$-0.249561\pi$
$439$	−5.39491	−	9.34426i	−0.257485	−	0.445977i	−0.965568	+	0.260152i	$0.916227\pi$
$440$			17.3027i			0.824875i
$441$	0.712874	−	20.9879i	0.0339464	−	0.999424i
$442$			5.94712i			0.282875i
$443$	−25.3353	+	14.6273i	−1.20372	+	0.694966i	−0.961380	−	0.275226i	$-0.911247\pi$
$443$	−25.3353	+	14.6273i	−1.20372	+	0.694966i	−0.242337	+	0.970192i	$0.577914\pi$
$444$	0.754781	−	0.0630088i	0.0358203	−	0.00299027i
$445$	11.0878	−	19.2046i	0.525610	−	0.910383i
$446$	12.0622	−	6.96413i	0.571163	−	0.329761i
$447$	30.4589	−	21.1474i	1.44066	−	1.00024i
$448$	−1.67417	−	2.04869i	−0.0790972	−	0.0967917i
$449$			10.1804i			0.480442i	0.970718	+	0.240221i	$0.0772199\pi$
$449$			10.1804i			0.480442i	−0.970718	+	0.240221i	$0.922780\pi$
$450$	7.36585	+	43.8102i	0.347229	+	2.06523i
$451$	−24.8269	−	14.3338i	−1.16905	−	0.674953i
$452$	0.813659	−	1.40930i	0.0382713	−	0.0662878i
$453$	23.2284	+	10.9443i	1.09137	+	0.514210i
$454$			0.165335i			0.00775954i
$455$	4.59053	−	12.1199i	0.215208	−	0.568191i
$456$	−8.50617	+	5.90577i	−0.398338	+	0.276563i
$457$	−13.3422	+	7.70312i	−0.624121	+	0.360337i	−0.778472	−	0.627680i	$-0.784005\pi$
$457$	−13.3422	+	7.70312i	−0.624121	+	0.360337i	0.154351	+	0.988016i	$0.450671\pi$
$458$	−11.7093	+	20.2812i	−0.547142	+	0.947678i
$459$	−27.0316	−	7.59016i	−1.26173	−	0.354278i
$460$	2.21212	−	21.2297i	0.103141	−	0.989838i
$461$		−	24.1592i		−	1.12520i	−0.826728	−	0.562602i	$-0.809800\pi$
$461$		−	24.1592i		−	1.12520i	0.826728	−	0.562602i	$-0.190200\pi$
$462$	12.3819	+	12.8096i	0.576056	+	0.595954i
$463$	−10.2291			−0.475388			−0.237694	−	0.971340i	$-0.576391\pi$
$463$	−10.2291			−0.475388			−0.237694	+	0.971340i	$0.576391\pi$
$464$	0.0560737	−	0.0323742i	0.00260316	−	0.00150293i
$465$	4.71332	+	56.4607i	0.218575	+	2.61830i
$466$	−0.108648	+	0.188185i	−0.00503304	+	0.00871749i
$467$	17.4804	+	30.2769i	0.808896	+	1.40105i	0.913629	+	0.406549i	$0.133268\pi$
$467$	17.4804	+	30.2769i	0.808896	+	1.40105i	−0.104733	+	0.994500i	$0.533399\pi$
$468$	−1.15396	+	3.09364i	−0.0533419	+	0.143004i
$469$	1.67917	+	10.3044i	0.0775370	+	0.475815i
$470$	−17.6970			−0.816302
$471$	0.656253	−	1.39284i	0.0302385	−	0.0641786i
$472$	−5.95409	+	10.3128i	−0.274059	+	0.474685i
$473$	−16.4091	−	9.47379i	−0.754491	−	0.435605i
$474$	−6.46149	−	3.04441i	−0.296786	−	0.139834i
$475$			88.5341i			4.06222i
$476$	5.06374	−	13.3693i	0.232096	−	0.612780i
$477$	7.43085	−	19.9213i	0.340235	−	0.912132i
$478$	−11.0343	−	19.1119i	−0.504696	−	0.874160i
$479$	14.2513	−	24.6839i	0.651158	−	1.12784i	−0.331685	−	0.943390i	$-0.607617\pi$
$479$	14.2513	−	24.6839i	0.651158	−	1.12784i	0.982842	−	0.184448i	$-0.0590497\pi$
$480$	7.68204	−	0.641295i	0.350636	−	0.0292710i
$481$	0.416808	−	0.240644i	0.0190048	−	0.0109724i
$482$	−26.9560			−1.22781
$483$	−13.5543	−	17.2997i	−0.616742	−	0.787165i
$484$	−4.11404			−0.187002
$485$	−0.211966	+	0.122378i	−0.00962486	+	0.00555691i
$486$	−12.5889	−	9.19349i	−0.571043	−	0.417025i
$487$	3.60740	−	6.24821i	0.163467	−	0.283133i	−0.772643	−	0.634841i	$-0.781066\pi$
$487$	3.60740	−	6.24821i	0.163467	−	0.283133i	0.936110	+	0.351708i	$0.114399\pi$
$488$	−5.17465	−	8.96275i	−0.234245	−	0.405725i
$489$	−5.47412	+	3.80064i	−0.247548	+	0.171871i
$490$	−20.6393	+	23.3373i	−0.932389	+	1.05427i
$491$			18.4548i			0.832852i	0.909170	+	0.416426i	$0.136717\pi$
$491$			18.4548i			0.832852i	−0.909170	+	0.416426i	$0.863283\pi$
$492$	−5.44375	+	11.5539i	−0.245423	+	0.520889i
$493$	0.302990	+	0.174932i	0.0136460	+	0.00787852i
$494$	−3.29011	+	5.69864i	−0.148029	+	0.256394i
$495$	−51.1897	+	8.60658i	−2.30081	+	0.386837i
$496$	7.34969			0.330011
$497$	2.80373	−	2.29118i	0.125764	−	0.102773i
$498$	11.6992	+	16.8505i	0.524254	+	0.755091i
$499$	−1.52695	−	2.64476i	−0.0683557	−	0.118396i	0.829822	−	0.558028i	$-0.188442\pi$
$499$	−1.52695	−	2.64476i	−0.0683557	−	0.118396i	−0.898178	+	0.439633i	$0.855109\pi$
$500$	21.8268	−	37.8052i	0.976125	−	1.69070i
$501$	−31.7287	+	2.64870i	−1.41753	+	0.118335i
$502$	16.5214	−	9.53865i	0.737387	−	0.425731i
$503$	−16.1615			−0.720607			−0.360304	−	0.932835i	$-0.617327\pi$
$503$	−16.1615			−0.720607			−0.360304	+	0.932835i	$0.617327\pi$
$504$	5.22826	−	5.97204i	0.232885	−	0.266016i
$505$		−	46.3758i		−	2.06369i
$506$	18.5442	+	1.93230i	0.824392	+	0.0859012i
$507$	−1.69862	−	20.3477i	−0.0754385	−	0.903675i
$508$	−1.45934	+	2.52766i	−0.0647479	+	0.112147i
$509$	35.8739	−	20.7118i	1.59008	−	0.918035i	0.596791	−	0.802397i	$-0.296442\pi$
$509$	35.8739	−	20.7118i	1.59008	−	0.918035i	0.993291	−	0.115638i	$-0.0368912\pi$
$510$	23.7556	+	34.2156i	1.05192	+	1.51509i
$511$	−11.3446	+	1.84868i	−0.501858	+	0.0817808i
$512$		−	1.00000i		−	0.0441942i
$513$	−21.7032	−	22.2277i	−0.958218	−	0.981377i
$514$	15.0842	−	26.1266i	0.665337	−	1.15240i
$515$	−24.3633	−	14.0661i	−1.07357	−	0.619828i
$516$	−3.59799	+	7.63642i	−0.158393	+	0.336174i
$517$		−	15.4584i		−	0.679861i
$518$	−1.14189	+	0.186079i	−0.0501720	+	0.00817584i
$519$	19.0938	+	27.5010i	0.838123	+	1.20716i
$520$	4.24221	−	2.44924i	0.186033	−	0.107406i
$521$	5.71029	−	9.89050i	0.250172	−	0.433311i	−0.713401	−	0.700756i	$-0.752846\pi$
$521$	5.71029	−	9.89050i	0.250172	−	0.433311i	0.963573	+	0.267445i	$0.0861794\pi$
$522$	0.123670	+	0.149790i	0.00541289	+	0.00655611i
$523$	33.9256	−	19.5869i	1.48346	−	0.856477i	0.483638	−	0.875268i	$-0.339315\pi$
$523$	33.9256	−	19.5869i	1.48346	−	0.856477i	0.999823	+	0.0187915i	$0.00598187\pi$
$524$		−	0.0411257i		−	0.00179658i
$525$	−16.4483	−	65.8368i	−0.717863	−	2.87335i
$526$		−	13.2621i		−	0.578256i
$527$	19.8568	+	34.3929i	0.864974	+	1.49818i
$528$	0.560175	+	6.71032i	0.0243785	+	0.292029i
$529$	−22.5059	−	4.74169i	−0.978518	−	0.206160i
$530$	−27.3173	+	15.7717i	−1.18659	+	0.685078i
$531$	−33.4718	−	12.4853i	−1.45255	−	0.541817i
$532$	12.2484	−	10.0093i	0.531037	−	0.433958i
$533$			8.11594i			0.351540i
$534$	3.67829	−	7.80684i	0.159175	−	0.337835i
$535$	−0.926021	+	1.60391i	−0.0400354	+	0.0693433i
$536$	−1.97304	+	3.41741i	−0.0852225	+	0.147610i
$537$	−14.2731	+	30.2935i	−0.615932	+	1.30726i
$538$	−7.60005			−0.327661
$539$	−20.3853	−	18.0286i	−0.878055	−	0.776545i
$540$	5.71839	+	22.4082i	0.246080	+	0.964294i
$541$	5.64665	+	9.78029i	0.242769	+	0.420488i	0.961502	−	0.274798i	$-0.0886111\pi$
$541$	5.64665	+	9.78029i	0.242769	+	0.420488i	−0.718733	+	0.695286i	$0.755278\pi$
$542$	15.8582	+	9.15576i	0.681170	+	0.393274i
$543$	14.4717	−	1.20809i	0.621039	−	0.0518441i
$544$	4.67951	−	2.70171i	0.200632	−	0.115835i
$545$			30.2556i			1.29601i
$546$	1.38791	−	4.84895i	0.0593971	−	0.207516i
$547$	−28.1826			−1.20500			−0.602500	−	0.798119i	$-0.705829\pi$
$547$	−28.1826			−1.20500			−0.602500	+	0.798119i	$0.705829\pi$
$548$	2.75518	+	4.77212i	0.117696	+	0.203855i
$549$	23.9422	−	19.7673i	1.02183	−	0.843646i
$550$	49.8572	+	28.7851i	2.12592	+	1.22740i
$551$	0.193554	+	0.335246i	0.00824569	+	0.0142819i
$552$	0.170591	−	8.30487i	0.00726082	−	0.353479i
$553$	10.2034	+	3.86463i	0.433893	+	0.164341i
$554$		−	5.00934i		−	0.212827i
$555$	1.43677	−	3.04943i	0.0609877	−	0.129441i
$556$	2.13875	−	3.70443i	0.0907034	−	0.157103i
$557$	16.7471	−	29.0068i	0.709598	−	1.22906i	−0.255409	−	0.966833i	$-0.582210\pi$
$557$	16.7471	−	29.0068i	0.709598	−	1.22906i	0.965006	−	0.262226i	$-0.0844566\pi$
$558$	3.65582	+	21.7439i	0.154763	+	0.920492i
$559$			5.36414i			0.226879i
$560$	−11.6220	+	1.89388i	−0.491121	+	0.0800312i
$561$	−29.8875	+	20.7507i	−1.26185	+	0.876095i
$562$	13.0548	−	7.53719i	0.550683	−	0.317937i
$563$	23.5543	−	40.7973i	0.992696	−	1.71940i	0.391871	−	0.920020i	$-0.371828\pi$
$563$	23.5543	−	40.7973i	0.992696	−	1.71940i	0.600825	−	0.799380i	$-0.294839\pi$
$564$	−6.86322	+	0.572939i	−0.288994	+	0.0241251i
$565$	−3.62132	−	6.27231i	−0.152350	−	0.263878i
$566$	9.43347			0.396518
$567$	20.2687	+	12.4971i	0.851207	+	0.524830i
$568$	1.36854			0.0574228
$569$	−3.25546	−	5.63863i	−0.136476	−	0.236383i	0.789684	−	0.613513i	$-0.210244\pi$
$569$	−3.25546	−	5.63863i	−0.136476	−	0.236383i	−0.926160	+	0.377130i	$0.876911\pi$
$570$	3.83408	+	45.9283i	0.160592	+	1.92373i
$571$	−7.96579	−	4.59905i	−0.333358	−	0.192464i	0.323973	−	0.946066i	$-0.394981\pi$
$571$	−7.96579	−	4.59905i	−0.333358	−	0.192464i	−0.657331	+	0.753602i	$0.728315\pi$
$572$	2.13943	+	3.70559i	0.0894539	+	0.154939i
$573$	−3.76312	+	2.61271i	−0.157206	+	0.109147i
$574$	6.91041	−	18.2449i	0.288435	−	0.761526i
$575$	−57.4924	−	41.6921i	−2.39760	−	1.73868i
$576$	2.95848	−	0.497412i	0.123270	−	0.0207255i
$577$	−13.9197	+	24.1097i	−0.579486	+	1.00370i	0.416052	+	0.909341i	$0.363413\pi$
$577$	−13.9197	+	24.1097i	−0.579486	+	1.00370i	−0.995538	+	0.0943587i	$0.969920\pi$
$578$	10.5629	+	6.09852i	0.439361	+	0.253665i
$579$	25.3552	+	11.9464i	1.05372	+	0.496475i
$580$		−	0.288173i		−	0.0119657i
$581$	−19.8282	−	24.2639i	−0.822613	−	1.00664i
$582$	−0.0782421	+	0.0543229i	−0.00324324	+	0.00225176i
$583$	−13.7767	−	23.8619i	−0.570571	−	0.988258i
$584$	−3.76239	−	2.17222i	−0.155689	−	0.0898870i
$585$	9.35614	+	11.3322i	0.386829	+	0.468528i
$586$	8.94517	−	5.16450i	0.369522	−	0.213343i
$587$		−	29.7668i		−	1.22861i	−0.789070	−	0.614304i	$-0.789437\pi$
$587$		−	29.7668i		−	1.22861i	0.789070	−	0.614304i	$-0.210563\pi$
$588$	−7.24876	+	9.71882i	−0.298934	+	0.400797i
$589$			43.9413i			1.81057i
$590$	26.4996	+	45.8987i	1.09097	+	1.88962i
$591$	13.8485	−	1.15607i	0.569653	−	0.0475544i
$592$	−0.378703	−	0.218644i	−0.0155646	−	0.00898622i
$593$	−5.06577	+	2.92473i	−0.208026	+	0.120104i	−0.600394	−	0.799704i	$-0.704990\pi$
$593$	−5.06577	+	2.92473i	−0.208026	+	0.120104i	0.392367	+	0.919809i	$0.371656\pi$
$594$	−19.5737	+	4.99505i	−0.803117	+	0.204950i
$595$	−40.2619	−	49.2687i	−1.65058	−	2.01982i
$596$	−21.4084			−0.876922
$597$	10.8060	−	22.9347i	0.442259	−	0.938656i
$598$	−2.15123	−	4.82012i	−0.0879702	−	0.197109i
$599$	−2.13068	−	1.23015i	−0.0870571	−	0.0502624i	0.455839	−	0.890062i	$-0.349339\pi$
$599$	−2.13068	−	1.23015i	−0.0870571	−	0.0502624i	−0.542897	+	0.839800i	$0.682672\pi$
$600$	10.9321	−	23.2024i	0.446301	−	0.947234i
$601$	−0.702628			−0.0286608			−0.0143304	−	0.999897i	$-0.504562\pi$
$601$	−0.702628			−0.0286608			−0.0143304	+	0.999897i	$0.504562\pi$
$602$	4.56736	−	12.0587i	0.186152	−	0.491478i
$603$	−11.0917	−	4.13734i	−0.451691	−	0.168486i
$604$	−7.41248	−	12.8388i	−0.301609	−	0.522403i
$605$	−9.15510	+	15.8571i	−0.372208	+	0.644683i
$606$	−1.50141	−	17.9854i	−0.0609908	−	0.730606i
$607$	11.9786	+	20.7475i	0.486194	+	0.842114i	0.999874	−	0.0158686i	$-0.00505133\pi$
$607$	11.9786	+	20.7475i	0.486194	+	0.842114i	−0.513680	+	0.857982i	$0.671718\pi$
$608$	5.97866			0.242467
$609$	−0.206217	−	0.213340i	−0.00835633	−	0.00864498i
$610$	−46.0612			−1.86496
$611$	−3.79003	+	2.18818i	−0.153328	+	0.0885241i
$612$	10.3206	+	12.5003i	0.417185	+	0.505297i
$613$	−22.0574	−	12.7348i	−0.890888	−	0.514355i	−0.0166555	−	0.999861i	$-0.505302\pi$
$613$	−22.0574	−	12.7348i	−0.890888	−	0.514355i	−0.874233	+	0.485507i	$0.838635\pi$
$614$	1.44413	−	0.833771i	0.0582805	−	0.0336483i
$615$	32.4189	+	46.6935i	1.30726	+	1.88286i
$616$	−1.65432	−	10.1519i	−0.0666544	−	0.409033i
$617$	7.66416			0.308547			0.154274	−	0.988028i	$-0.450696\pi$
$617$	7.66416			0.308547			0.154274	+	0.988028i	$0.450696\pi$
$618$	−9.90391	−	4.66635i	−0.398394	−	0.187708i
$619$	27.9036	+	16.1101i	1.12154	+	0.647521i	0.941794	−	0.336192i	$-0.109139\pi$
$619$	27.9036	+	16.1101i	1.12154	+	0.647521i	0.179746	+	0.983713i	$0.442472\pi$
$620$	16.3555	−	28.3285i	0.656852	−	1.13770i
$621$	24.6546	−	3.62625i	0.989356	−	0.145516i
$622$	10.4743			0.419982
$623$	−4.66930	+	12.3279i	−0.187071	+	0.493906i
$624$	1.56591	−	1.08720i	0.0626866	−	0.0435229i
$625$	−60.1228	−	104.136i	−2.40491	−	4.16543i
$626$	−11.4696	+	19.8659i	−0.458417	+	0.794001i
$627$	−40.1187	+	3.34909i	−1.60219	+	0.133750i
$628$	−0.769849	+	0.444472i	−0.0307203	+	0.0177364i
$629$		−	2.36286i		−	0.0942133i
$630$	−11.3839	−	33.4415i	−0.453547	−	1.33234i
$631$		−	20.4023i		−	0.812203i	−0.913828	−	0.406101i	$-0.866888\pi$
$631$		−	20.4023i		−	0.812203i	0.913828	−	0.406101i	$-0.133112\pi$
$632$	2.06194	+	3.57139i	0.0820196	+	0.142062i
$633$	2.89857	+	34.7218i	0.115208	+	1.38007i
$634$	−9.39251	+	16.2683i	−0.373024	+	0.646097i
$635$	6.49504	+	11.2497i	0.257748	+	0.446432i
$636$	−10.0836	+	7.00094i	−0.399839	+	0.277605i
$637$	−1.53459	+	7.54995i	−0.0608025	+	0.299140i
$638$	0.251721			0.00996572
$639$	0.680730	+	4.04881i	0.0269293	+	0.160168i
$640$	−3.85438	−	2.22533i	−0.152358	−	0.0879638i
$641$	−15.6879	+	27.1723i	−0.619637	+	1.07324i	0.369915	+	0.929065i	$0.379387\pi$
$641$	−15.6879	+	27.1723i	−0.619637	+	1.07324i	−0.989552	+	0.144177i	$0.953947\pi$
$642$	−0.307201	+	0.652008i	−0.0121243	+	0.0257327i
$643$			17.2946i			0.682033i	0.940057	+	0.341017i	$0.110771\pi$
$643$			17.2946i			0.682033i	−0.940057	+	0.341017i	$0.889229\pi$
$644$	0.731873	+	12.6675i	0.0288398	+	0.499168i
$645$	21.4270	+	30.8616i	0.843686	+	1.21517i
$646$	16.1526	+	27.9772i	0.635517	+	1.10075i
$647$	3.05042	+	1.76116i	0.119924	+	0.0692384i	0.558762	−	0.829328i	$-0.311276\pi$
$647$	3.05042	+	1.76116i	0.119924	+	0.0692384i	−0.438838	+	0.898566i	$0.644610\pi$
$648$	2.94316	+	8.50516i	0.115618	+	0.334114i
$649$	−40.0928	+	23.1476i	−1.57378	+	0.908622i
$650$		−	16.2984i		−	0.639274i
$651$	−8.16364	−	32.6762i	−0.319958	−	1.28068i
$652$	3.84755			0.150682
$653$	−38.4883	+	22.2212i	−1.50616	+	0.869584i	−0.506189	+	0.862422i	$0.668946\pi$
$653$	−38.4883	+	22.2212i	−1.50616	+	0.869584i	−0.999974	+	0.00716158i	$0.997720\pi$
$654$	0.979523	+	11.7337i	0.0383024	+	0.458823i
$655$	−0.158514	−	0.0915181i	−0.00619366	−	0.00357591i
$656$	6.38605	−	3.68699i	0.249333	−	0.143953i
$657$	4.55499	−	12.2114i	0.177707	−	0.476413i
$658$	10.3832	−	1.69202i	0.404781	−	0.0659616i
$659$	10.3285			0.402341			0.201171	−	0.979556i	$-0.435525\pi$
$659$	10.3285			0.402341			0.201171	+	0.979556i	$0.435525\pi$
$660$	27.1107	+	12.7735i	1.05528	+	0.497209i
$661$	−14.7149	−	8.49568i	−0.572345	−	0.330444i	0.185740	−	0.982599i	$-0.440532\pi$
$661$	−14.7149	−	8.49568i	−0.572345	−	0.330444i	−0.758085	+	0.652155i	$0.773865\pi$
$662$	2.04601	+	1.18126i	0.0795203	+	0.0459111i
$663$	9.31821	+	4.39039i	0.361889	+	0.170509i
$664$		−	11.8436i		−	0.459621i
$665$	−11.3229	−	69.4842i	−0.439082	−	2.69448i
$666$	0.458483	−	1.22914i	0.0177658	−	0.0476282i
$667$	−0.308850	−	0.0321820i	−0.0119587	−	0.00124609i
$668$	15.9195	+	9.19115i	0.615946	+	0.355616i
$669$	−2.00692	−	24.0408i	−0.0775921	−	0.929473i
$670$	8.78134	+	15.2097i	0.339253	+	0.587603i
$671$		−	40.2347i		−	1.55324i
$672$	−4.44592	+	1.11075i	−0.171505	+	0.0428479i
$673$	17.5022			0.674661			0.337330	−	0.941386i	$-0.390476\pi$
$673$	17.5022			0.674661			0.337330	+	0.941386i	$0.390476\pi$
$674$	−1.39570	−	2.41742i	−0.0537603	−	0.0931156i
$675$	74.0815	+	20.8012i	2.85140	+	0.800638i
$676$	−5.89432	+	10.2093i	−0.226705	+	0.392664i
$677$	−5.74093	−	9.94358i	−0.220642	−	0.382163i	0.734361	−	0.678759i	$-0.237482\pi$
$677$	−5.74093	−	9.94358i	−0.220642	−	0.382163i	−0.955003	+	0.296596i	$0.904148\pi$
$678$	−1.60748	−	2.31528i	−0.0617349	−	0.0889176i
$679$	0.112665	−	0.0920684i	0.00432367	−	0.00353326i
$680$		−	24.0488i		−	0.922230i
$681$	0.259054	+	0.122056i	0.00992697	+	0.00467721i
$682$	24.7451	+	14.2866i	0.947541	+	0.547063i
$683$	7.76030	+	4.48041i	0.296939	+	0.171438i	0.641067	−	0.767485i	$-0.278492\pi$
$683$	7.76030	+	4.48041i	0.296939	+	0.171438i	−0.344128	+	0.938923i	$0.611825\pi$
$684$	2.97385	+	17.6877i	0.113708	+	0.676307i
$685$	24.5248			0.937043
$686$	9.87829	−	15.6659i	0.377155	−	0.598126i
$687$	23.1332	+	33.3191i	0.882587	+	1.27120i
$688$	4.22079	−	2.43688i	0.160916	−	0.0929050i
$689$	−3.90023	+	6.75540i	−0.148587	+	0.257360i
$690$	−31.6305	−	19.1386i	−1.20415	−	0.728594i
$691$	16.5489	+	28.6635i	0.629549	+	1.09041i	0.987642	+	0.156725i	$0.0500937\pi$
$691$	16.5489	+	28.6635i	0.629549	+	1.09041i	−0.358093	+	0.933686i	$0.616573\pi$
$692$		−	19.3294i		−	0.734794i
$693$	29.2113	−	9.94395i	1.10965	−	0.377739i
$694$	−19.9239			−0.756302
$695$	−9.51886	−	16.4872i	−0.361071	−	0.625393i
$696$	−0.00932958	−	0.111759i	−0.000353637	−	0.00423620i
$697$	34.5066	+	19.9224i	1.30703	+	0.754614i
$698$	19.7665	−	11.4122i	0.748172	−	0.431957i
$699$	0.214648	+	0.309160i	0.00811873	+	0.0116935i
$700$	−13.8774	+	36.6392i	−0.524517	+	1.38483i
$701$	8.23201			0.310919			0.155459	−	0.987842i	$-0.450314\pi$
$701$	8.23201			0.310919			0.155459	+	0.987842i	$0.450314\pi$
$702$	3.99536	+	4.09193i	0.150795	+	0.154440i
$703$	1.30720	−	2.26414i	0.0493020	−	0.0853935i
$704$	1.94384	−	3.36683i	0.0732612	−	0.126892i
$705$	−13.0646	+	27.7285i	−0.492041	+	1.04431i
$706$	24.6585			0.928036
$707$	4.43400	+	27.2098i	0.166758	+	1.02333i
$708$	11.7630	+	16.9424i	0.442081	+	0.636736i
$709$	−32.8810	+	18.9839i	−1.23487	+	0.712954i	−0.968042	−	0.250789i	$-0.919310\pi$
$709$	−32.8810	+	18.9839i	−1.23487	+	0.712954i	−0.266831	+	0.963743i	$0.585976\pi$
$710$	3.04546	−	5.27489i	0.114294	−	0.197963i
$711$	−9.54023	+	7.87666i	−0.357787	+	0.295398i
$712$	−4.31499	+	2.49126i	−0.161711	+	0.0933640i
$713$	−28.5347	−	20.6927i	−1.06863	−	0.774946i
$714$	−17.2094	−	17.8038i	−0.644044	−	0.666291i
$715$	19.0437			0.712194
$716$	16.7438	−	9.66704i	0.625745	−	0.361274i
$717$	−38.0914	+	3.17986i	−1.42255	+	0.118754i
$718$	8.81626	+	5.09007i	0.329020	+	0.189960i
$719$	40.8240	−	23.5697i	1.52248	−	0.879003i	0.522831	−	0.852436i	$-0.324876\pi$
$719$	40.8240	−	23.5697i	1.52248	−	0.879003i	0.999647	−	0.0265672i	$-0.00845759\pi$
$720$	4.66637	−	12.5100i	0.173905	−	0.466220i
$721$	15.6394	+	5.92356i	0.582441	+	0.220605i
$722$			16.7443i			0.623160i
$723$	−19.8999	+	42.2358i	−0.740086	+	1.57077i
$724$	−7.26100	−	4.19214i	−0.269853	−	0.155800i
$725$	−0.830360	−	0.479408i	−0.0308388	−	0.0178048i
$726$	−3.03714	+	6.44607i	−0.112719	+	0.239236i
$727$		−	4.20859i		−	0.156088i	−0.996950	−	0.0780439i	$-0.975133\pi$
$727$		−	4.20859i		−	0.156088i	0.996950	−	0.0780439i	$-0.0248674\pi$
$728$	−2.25483	+	1.84263i	−0.0835696	+	0.0682923i
$729$	−23.6984	+	12.9378i	−0.877717	+	0.479179i
$730$	−16.7451	+	9.66779i	−0.619764	+	0.357821i
$731$	22.8068	+	13.1675i	0.843538	+	0.487017i
$732$	−17.8634	+	1.49123i	−0.660249	+	0.0551174i
$733$	−20.7279	+	11.9673i	−0.765602	+	0.442021i	−0.831304	−	0.555819i	$-0.812405\pi$
$733$	−20.7279	+	11.9673i	−0.765602	+	0.442021i	0.0657013	+	0.997839i	$0.479072\pi$
$734$	7.50143			0.276883
$735$	21.3292	+	49.5671i	0.786739	+	1.82831i
$736$	−2.81545	+	3.88243i	−0.103779	+	0.143108i
$737$	−13.2858	+	7.67056i	−0.489389	+	0.282549i
$738$	14.0844	+	17.0590i	0.518452	+	0.627951i
$739$	20.7546	−	35.9480i	0.763470	−	1.32237i	−0.177582	−	0.984106i	$-0.556827\pi$
$739$	20.7546	−	35.9480i	0.763470	−	1.32237i	0.941052	−	0.338263i	$-0.109839\pi$
$740$	−1.68548	+	0.973111i	−0.0619594	+	0.0357723i
$741$	6.50000	+	9.36205i	0.238784	+	0.343924i
$742$	14.5198	−	11.8654i	0.533039	−	0.435594i
$743$	−31.5904			−1.15894			−0.579471	−	0.814993i	$-0.696741\pi$
$743$	−31.5904			−1.15894			−0.579471	+	0.814993i	$0.696741\pi$
$744$	5.42582	−	11.5158i	0.198920	−	0.422191i
$745$	−47.6407	+	82.5161i	−1.74542	+	3.02316i
$746$	1.16809	−	2.02319i	0.0427667	−	0.0740741i
$747$	35.0390	−	5.89114i	1.28201	−	0.215546i
$748$	21.0068			0.768084
$749$	0.389968	−	1.02959i	0.0142491	−	0.0376205i
$750$	−43.1214	−	62.1084i	−1.57457	−	2.26788i
$751$	−21.1274	+	12.1979i	−0.770951	+	0.445108i	−0.833214	−	0.552951i	$-0.813502\pi$
$751$	−21.1274	+	12.1979i	−0.770951	+	0.445108i	0.0622631	+	0.998060i	$0.480168\pi$
$752$	3.44355	+	1.98813i	0.125573	+	0.0724997i
$753$	−2.74885	−	32.9283i	−0.100173	−	1.19997i
$754$	−0.0356316	−	0.0617158i	−0.00129763	−	0.00224756i
$755$	−65.9808			−2.40129
$756$	−5.49757	−	12.6007i	−0.199945	−	0.458282i
$757$			17.6367i			0.641018i	0.947246	+	0.320509i	$0.103854\pi$
$757$			17.6367i			0.641018i	−0.947246	+	0.320509i	$0.896146\pi$
$758$	−12.5192	−	21.6839i	−0.454717	−	0.787594i
$759$	16.7177	−	27.6295i	0.606814	−	1.00289i
$760$	13.3045	−	23.0440i	0.482604	−	0.835895i
$761$	30.3993	−	17.5511i	1.10197	−	0.636225i	0.165236	−	0.986254i	$-0.447162\pi$
$761$	30.3993	−	17.5511i	1.10197	−	0.636225i	0.936739	+	0.350029i	$0.113828\pi$
$762$	2.88311	+	4.15258i	0.104444	+	0.150432i
$763$	−2.89275	−	17.7517i	−0.104724	−	0.642654i
$764$	2.64495			0.0956909
$765$	71.1478	−	11.9622i	2.57236	−	0.432493i
$766$	−11.6528	−	6.72775i	−0.421033	−	0.243083i
$767$	11.3504	+	6.55318i	0.409841	+	0.236622i
$768$	−1.56685	−	0.738238i	−0.0565387	−	0.0266389i
$769$		−	13.2168i		−	0.476610i	−0.971190	−	0.238305i	$-0.923408\pi$
$769$		−	13.2168i		−	0.476610i	0.971190	−	0.238305i	$-0.0765918\pi$
$770$	−42.8108	−	16.2150i	−1.54279	−	0.584348i
$771$	−29.8007	−	42.9223i	−1.07324	−	1.54581i
$772$	−8.09115	−	14.0143i	−0.291207	−	0.504385i
$773$	−1.52183	+	2.63588i	−0.0547364	+	0.0948062i	−0.892095	−	0.451847i	$-0.850765\pi$
$773$	−1.52183	+	2.63588i	−0.0547364	+	0.0948062i	0.837359	+	0.546654i	$0.184099\pi$
$774$	9.30891	+	11.2750i	0.334602	+	0.405271i
$775$	−54.4184	−	94.2555i	−1.95477	−	3.38576i
$776$	0.0549934			0.00197415
$777$	−0.551433	+	1.92654i	−0.0197826	+	0.0691143i
$778$		−	8.63167i		−	0.309460i
$779$	22.0432	+	38.1800i	0.789781	+	1.36794i
$780$	−0.705821	−	8.45500i	−0.0252724	−	0.302738i
$781$	4.60765	+	2.66023i	0.164875	+	0.0951905i
$782$	−25.7744	−	2.68568i	−0.921690	−	0.0960396i
$783$	0.325995	−	0.0831914i	0.0116501	−	0.00297302i
$784$	6.63785	−	2.22237i	0.237066	−	0.0793705i
$785$			3.95639i			0.141210i
$786$	−0.0644375	−	0.0303605i	−0.00229841	−	0.00108292i
$787$	−21.3621	−	12.3334i	−0.761476	−	0.439638i	0.0683494	−	0.997661i	$-0.478227\pi$
$787$	−21.3621	−	12.3334i	−0.761476	−	0.439638i	−0.829825	+	0.558023i	$0.811560\pi$
$788$	−6.94836	−	4.01163i	−0.247525	−	0.142909i
$789$	−20.7797	−	9.79060i	−0.739777	−	0.348555i
$790$	18.3540			0.653006
$791$	2.72441	+	3.33388i	0.0968689	+	0.118539i
$792$	10.9276	+	4.07610i	0.388294	+	0.144838i
$793$	−9.86458	+	5.69532i	−0.350301	+	0.202247i
$794$	−18.7443	−	10.8220i	−0.665211	−	0.384060i
$795$	4.54508	+	54.4453i	0.161197	+	1.93098i
$796$	−12.6765	+	7.31876i	−0.449305	+	0.259406i
$797$	5.86325			0.207687			0.103843	−	0.994594i	$-0.466886\pi$
$797$	5.86325			0.207687			0.103843	+	0.994594i	$0.466886\pi$
$798$	−6.64077	−	26.5807i	−0.235081	−	0.940945i
$799$			21.4855i			0.760101i
$800$	−12.8244	+	7.40418i	−0.453411	+	0.261777i
$801$	−9.51666	−	11.5266i	−0.336255	−	0.407273i
$802$	21.2387	+	12.2621i	0.749963	+	0.432991i
$803$	−8.44488	−	14.6270i	−0.298013	−	0.516174i
$804$	3.89798	+	5.61432i	0.137471	+	0.198002i
$805$	50.4539	+	25.3683i	1.77827	+	0.894116i
$806$		−	8.08921i		−	0.284930i
$807$	−5.61064	+	11.9081i	−0.197504	+	0.419185i
$808$	−5.20999	+	9.02397i	−0.183287	+	0.317462i
$809$	25.8683	+	14.9351i	0.909481	+	0.525089i	0.880264	−	0.474484i	$-0.157365\pi$
$809$	25.8683	+	14.9351i	0.909481	+	0.525089i	0.0292168	+	0.999573i	$0.490699\pi$
$810$	39.3317	+	7.58272i	1.38197	+	0.266430i
$811$	−49.3046			−1.73132			−0.865660	−	0.500633i	$-0.833101\pi$
$811$	−49.3046			−1.73132			−0.865660	+	0.500633i	$0.833101\pi$
$812$	0.0275523	+	0.169078i	0.000966896	+	0.00593347i
$813$	26.0528	−	18.0883i	0.913712	−	0.634384i
$814$	−0.850019	−	1.47228i	−0.0297931	−	0.0516032i
$815$	8.56205	−	14.8299i	0.299916	−	0.519469i
$816$	−0.778579	−	9.32657i	−0.0272557	−	0.326495i
$817$	14.5692	+	25.2347i	0.509713	+	0.882850i
$818$			18.3087i			0.640150i
$819$	−6.57294	−	5.75432i	−0.229677	−	0.201072i
$820$		−	32.8190i		−	1.14609i
$821$	−8.75254	+	5.05328i	−0.305466	+	0.176361i	−0.644896	−	0.764271i	$-0.723099\pi$
$821$	−8.75254	+	5.05328i	−0.305466	+	0.176361i	0.339430	+	0.940631i	$0.389766\pi$
$822$	9.51116	−	0.793988i	0.331740	−	0.0276935i
$823$	22.1414	−	38.3500i	0.771799	−	1.33680i	−0.164777	−	0.986331i	$-0.552690\pi$
$823$	22.1414	−	38.3500i	0.771799	−	1.33680i	0.936576	−	0.350464i	$-0.113976\pi$
$824$	3.16046	+	5.47408i	0.110100	+	0.190699i
$825$	81.9082	−	56.8683i	2.85168	−	1.97990i
$826$	−19.9363	−	24.3962i	−0.693674	−	0.848853i
$827$	1.37000			0.0476397			0.0238198	−	0.999716i	$-0.492417\pi$
$827$	1.37000			0.0476397			0.0238198	+	0.999716i	$0.492417\pi$
$828$	−12.8865	−	6.39826i	−0.447837	−	0.222355i
$829$	15.3633	−	26.6101i	0.533590	−	0.924205i	−0.465640	−	0.884974i	$-0.654176\pi$
$829$	15.3633	−	26.6101i	0.533590	−	0.924205i	0.999230	−	0.0392311i	$-0.0124909\pi$
$830$	−45.6498	−	26.3559i	−1.58453	−	0.914827i
$831$	−7.84887	−	3.69809i	−0.272274	−	0.128285i
$832$	−1.10062			−0.0381571
$833$	28.3332	+	25.0576i	0.981687	+	0.868196i
$834$	−4.22536	−	6.08585i	−0.146312	−	0.210736i
$835$	70.8524	−	40.9067i	2.45195	−	1.41563i
$836$	20.1291	+	11.6215i	0.696180	+	0.401940i
$837$	36.7682	+	10.3241i	1.27089	+	0.356852i
$838$	−21.1313	+	12.2002i	−0.729968	+	0.421447i
$839$	23.3311			0.805480			0.402740	−	0.915314i	$-0.368058\pi$
$839$	23.3311			0.805480			0.402740	+	0.915314i	$0.368058\pi$
$840$	−5.61241	+	19.6081i	−0.193646	+	0.676543i
$841$	28.9958			0.999855
$842$	4.89187	+	8.47297i	0.168585	+	0.291998i
$843$	−2.17206	−	26.0191i	−0.0748098	−	0.896144i
$844$	10.0582	−	17.4213i	0.346217	−	0.599666i
$845$	26.2336	+	45.4379i	0.902463	+	1.56311i
$846$	−4.16898	+	11.1766i	−0.143333	+	0.384258i
$847$	3.85541	−	10.1791i	0.132474	−	0.349757i
$848$	7.08735			0.243380
$849$	6.96415	−	14.7808i	0.239009	−	0.507276i
$850$	−69.2958	−	40.0079i	−2.37683	−	1.37226i
$851$	0.854707	+	1.91509i	0.0292990	+	0.0656484i
$852$	1.01031	−	2.14430i	0.0346127	−	0.0734624i
$853$	49.4266			1.69234			0.846168	−	0.532917i	$-0.178904\pi$
$853$	49.4266			1.69234			0.846168	+	0.532917i	$0.178904\pi$
$854$	27.0252	−	4.40392i	0.924783	−	0.150699i
$855$	74.7930	+	27.8986i	2.55787	+	0.954113i
$856$	0.360377	−	0.208064i	0.0123174	−	0.00711147i
$857$	−20.1937	−	11.6588i	−0.689803	−	0.398258i	0.113735	−	0.993511i	$-0.463718\pi$
$857$	−20.1937	−	11.6588i	−0.689803	−	0.398258i	−0.803538	+	0.595253i	$0.797052\pi$
$858$	7.38550	−	0.616539i	0.252137	−	0.0210483i
$859$	−10.3943	−	18.0035i	−0.354650	−	0.614272i	0.632408	−	0.774636i	$-0.282067\pi$
$859$	−10.3943	−	18.0035i	−0.354650	−	0.614272i	−0.987058	+	0.160363i	$0.948733\pi$
$860$		−	21.6914i		−	0.739671i
$861$	−23.4853	−	24.2966i	−0.800378	−	0.828025i
$862$			11.4225i			0.389053i
$863$	−4.94066	+	2.85249i	−0.168182	+	0.0971000i	−0.581728	−	0.813383i	$-0.697623\pi$
$863$	−4.94066	+	2.85249i	−0.168182	+	0.0971000i	0.413546	+	0.910483i	$0.364290\pi$
$864$	1.40469	−	5.00268i	0.0477886	−	0.170195i
$865$	−74.5030	−	43.0143i	−2.53318	−	1.46253i
$866$	−6.72926	−	11.6554i	−0.228670	−	0.396067i
$867$	17.3534	−	12.0483i	0.589353	−	0.409183i
$868$	−6.88765	+	18.1848i	−0.233782	+	0.617231i
$869$			16.0323i			0.543860i
$870$	−0.451522	−	0.212740i	−0.0153080	−	0.00721257i
$871$	3.76127	+	2.17157i	0.127446	+	0.0735808i
$872$	3.39900	−	5.88724i	0.115105	−	0.199367i
$873$	0.0273543	+	0.162697i	0.000925804	+	0.00550645i
$874$	−23.2117	−	16.8326i	−0.785148	−	0.569371i
$875$	73.0837	+	89.4329i	2.47068	+	3.02338i
$876$	−6.18107	+	4.29147i	−0.208839	+	0.144995i
$877$	−0.928298	−	1.60786i	−0.0313464	−	0.0542936i	0.849927	−	0.526901i	$-0.176646\pi$
$877$	−0.928298	−	1.60786i	−0.0313464	−	0.0542936i	−0.881273	+	0.472608i	$0.843313\pi$
$878$	9.34426	+	5.39491i	0.315354	+	0.182070i
$879$	−1.48830	−	17.8283i	−0.0501992	−	0.601335i
$880$	−8.65136	−	14.9846i	−0.291637	−	0.505131i
$881$	−6.73561			−0.226929			−0.113464	−	0.993542i	$-0.536195\pi$
$881$	−6.73561			−0.226929			−0.113464	+	0.993542i	$0.536195\pi$
$882$	9.87658	+	18.5325i	0.332562	+	0.624021i
$883$	−45.5447			−1.53270			−0.766350	−	0.642423i	$-0.777929\pi$
$883$	−45.5447			−1.53270			−0.766350	+	0.642423i	$0.777929\pi$
$884$	−2.97356	−	5.15035i	−0.100012	−	0.173225i
$885$	91.4792	−	7.63665i	3.07504	−	0.256703i
$886$	14.6273	−	25.3353i	0.491415	−	0.851156i
$887$	10.1953	−	5.88626i	0.342325	−	0.197641i	−0.318975	−	0.947763i	$-0.603339\pi$
$887$	10.1953	−	5.88626i	0.342325	−	0.197641i	0.661300	+	0.750122i	$0.270005\pi$
$888$	−0.622155	+	0.431957i	−0.0208781	+	0.0144955i
$889$	−4.88638	−	5.97950i	−0.163884	−	0.200546i
$890$			22.1755i			0.743325i
$891$	−6.62355	+	34.3565i	−0.221897	+	1.15098i
$892$	−6.96413	+	12.0622i	−0.233176	+	0.403874i
$893$	−11.8864	+	20.5878i	−0.397762	+	0.688944i
$894$	−15.8045	+	33.5436i	−0.528581	+	1.12187i
$895$		−	86.0493i		−	2.87631i
$896$	2.47422	+	0.937135i	0.0826580	+	0.0313075i
$897$	−9.14050	−	0.187755i	−0.305192	−	0.00626897i
$898$	−5.09019	−	8.81647i	−0.169862	−	0.294210i
$899$	−0.412125	−	0.237940i	−0.0137451	−	0.00793575i
$900$	−28.2841	−	34.2578i	−0.942803	−	1.14193i
$901$	19.1480	+	33.1653i	0.637912	+	1.10490i
$902$	28.6676			0.954528
$903$	−15.5224	−	16.0586i	−0.516553	−	0.534396i
$904$			1.62732i			0.0541238i
$905$	−32.3162	+	18.6578i	−1.07423	+	0.620206i
$906$	−25.5886	+	2.13612i	−0.850123	+	0.0709680i
$907$	44.6166	+	25.7594i	1.48147	+	0.855326i	0.999779	−	0.0210158i	$-0.00669002\pi$
$907$	44.6166	+	25.7594i	1.48147	+	0.855326i	0.481689	+	0.876342i	$0.340023\pi$
$908$	−0.0826673	−	0.143184i	−0.00274341	−	0.00475173i
$909$	−29.2887	−	10.9250i	−0.971445	−	0.362360i
$910$	2.08444	+	12.7914i	0.0690986	+	0.424032i
$911$	−0.305064			−0.0101072			−0.00505361	−	0.999987i	$-0.501609\pi$
$911$	−0.305064			−0.0101072			−0.00505361	+	0.999987i	$0.501609\pi$
$912$	4.41367	−	9.36763i	0.146151	−	0.310193i
$913$	23.0220	−	39.8754i	0.761919	−	1.31968i
$914$	7.70312	−	13.3422i	0.254796	−	0.441320i
$915$	−34.0041	+	72.1707i	−1.12414	+	2.38589i
$916$		−	23.4187i		−	0.773776i
$917$	0.101754	+	0.0385403i	0.00336021	+	0.00127271i
$918$	27.2052	−	6.94255i	0.897904	−	0.229138i
$919$	−2.16944	+	1.25253i	−0.0715632	+	0.0413170i	−0.535355	−	0.844627i	$-0.679822\pi$
$919$	−2.16944	+	1.25253i	−0.0715632	+	0.0413170i	0.463791	+	0.885944i	$0.346489\pi$
$920$	8.69908	+	19.4915i	0.286800	+	0.642615i
$921$	−0.240276	−	2.87826i	−0.00791736	−	0.0948417i
$922$	12.0796	+	20.9224i	0.397820	+	0.689044i
$923$		−	1.50625i		−	0.0495787i
$924$	−17.1278	−	4.90247i	−0.563462	−	0.161280i
$925$			6.47552i			0.212914i
$926$	8.85868	−	5.11456i	0.291114	−	0.168075i
$927$	−14.6229	+	12.0730i	−0.480279	+	0.396530i
$928$	−0.0323742	+	0.0560737i	−0.00106273	+	0.00184071i
$929$	−46.6200	+	26.9161i	−1.52955	+	0.883088i	−0.530173	+	0.847889i	$0.677873\pi$
$929$	−46.6200	+	26.9161i	−1.52955	+	0.883088i	−0.999380	+	0.0351989i	$0.988794\pi$
$930$	−32.3122	−	46.5397i	−1.05956	−	1.52610i
$931$	13.2868	+	39.6854i	0.435457	+	1.30064i
$932$		−	0.217297i		−	0.00711780i
$933$	7.73255	−	16.4117i	0.253152	−	0.537293i
$934$	−30.2769	−	17.4804i	−0.990691	−	0.571976i
$935$	46.7470	−	80.9682i	1.52879	−	2.64794i
$936$	−0.547461	−	3.25616i	−0.0178943	−	0.106431i
$937$			50.2375i			1.64119i	0.571513	+	0.820593i	$0.306357\pi$
$937$			50.2375i			1.64119i	−0.571513	+	0.820593i	$0.693643\pi$
$938$	−6.60643	−	8.08433i	−0.215708	−	0.263963i
$939$	22.6595	+	32.6368i	0.739465	+	1.06506i
$940$	15.3260	−	8.84850i	0.499881	−	0.288606i
$941$	−9.58838	+	16.6076i	−0.312572	+	0.541391i	−0.978918	−	0.204252i	$-0.934524\pi$
$941$	−9.58838	+	16.6076i	−0.312572	+	0.541391i	0.666346	+	0.745642i	$0.267857\pi$
$942$	0.128088	+	1.53436i	0.00417333	+	0.0499922i
$943$	−35.1739	−	3.66510i	−1.14542	−	0.119352i
$944$		−	11.9082i		−	0.387578i
$945$	−60.8017	−	6.85089i	−1.97788	−	0.222859i
$946$	18.9476			0.616039
$947$	−7.88482	+	4.55230i	−0.256222	+	0.147930i	−0.622610	−	0.782532i	$-0.713928\pi$
$947$	−7.88482	+	4.55230i	−0.256222	+	0.147930i	0.366388	+	0.930462i	$0.380594\pi$
$948$	7.11802	−	0.594210i	0.231182	−	0.0192990i
$949$	−2.39078	+	4.14096i	−0.0776081	+	0.134421i
$950$	−44.2670	−	76.6728i	−1.43621	−	2.48759i
$951$	18.5560	+	26.7265i	0.601720	+	0.866666i
$952$	2.29931	+	14.1100i	0.0745212	+	0.457308i
$953$	1.57117			0.0508951			0.0254476	−	0.999676i	$-0.491899\pi$
$953$	1.57117			0.0508951			0.0254476	+	0.999676i	$0.491899\pi$
$954$	3.52533	+	20.9677i	0.114137	+	0.678856i
$955$	5.88588	−	10.1946i	0.190463	−	0.329891i
$956$	19.1119	+	11.0343i	0.618124	+	0.356874i
$957$	0.185830	−	0.394408i	0.00600703	−	0.0127494i
$958$			28.5026i			0.920876i
$959$	−14.3893	+	2.34482i	−0.464654	+	0.0757182i
$960$	−6.33220	+	4.39640i	−0.204371	+	0.141893i
$961$	−11.5090	−	19.9341i	−0.371258	−	0.643037i
$962$	−0.240644	+	0.416808i	−0.00775867	+	0.0134384i
$963$	0.794807	+	0.962674i	0.0256123	+	0.0310217i
$964$	23.3446	−	13.4780i	0.751878	−	0.434097i
$965$	−72.0218			−2.31847
$966$	20.3882	+	8.20486i	0.655981	+	0.263987i
$967$	−14.1297			−0.454379			−0.227190	−	0.973851i	$-0.572954\pi$
$967$	−14.1297			−0.454379			−0.227190	+	0.973851i	$0.572954\pi$
$968$	3.56287	−	2.05702i	0.114515	−	0.0661152i
$969$	55.7604	−	4.65486i	1.79128	−	0.149536i
$970$	0.122378	−	0.211966i	0.00392933	−	0.00680580i
$971$	−6.00101	−	10.3941i	−0.192582	−	0.333561i	0.753523	−	0.657421i	$-0.228353\pi$
$971$	−6.00101	−	10.3941i	−0.192582	−	0.333561i	−0.946105	+	0.323860i	$0.895019\pi$
$972$	15.4990	+	1.66736i	0.497132	+	0.0534805i
$973$	7.16129	+	8.76330i	0.229580	+	0.280939i
$974$			7.21481i			0.231177i
$975$	−25.5370	−	12.0321i	−0.817839	−	0.385334i
$976$	8.96275	+	5.17465i	0.286891	+	0.165636i
$977$	−1.80558	+	3.12735i	−0.0577655	+	0.100053i	−0.893462	−	0.449139i	$-0.851731\pi$
$977$	−1.80558	+	3.12735i	−0.0577655	+	0.100053i	0.835697	+	0.549192i	$0.185064\pi$
$978$	2.84040	−	6.02851i	0.0908261	−	0.192770i
$979$	−19.3704			−0.619082
$980$	6.20553	−	30.5303i	0.198228	−	0.975255i
$981$	19.1080	+	7.12748i	0.610070	+	0.227563i
$982$	−9.22738	−	15.9823i	−0.294458	−	0.510015i
$983$	−4.38987	+	7.60347i	−0.140015	+	0.242513i	−0.927502	−	0.373818i	$-0.878048\pi$
$983$	−4.38987	+	7.60347i	−0.140015	+	0.242513i	0.787487	+	0.616331i	$0.211382\pi$
$984$	−1.06251	−	12.7278i	−0.0338717	−	0.405748i
$985$	−30.9248	+	17.8544i	−0.985345	+	0.568889i
$986$	−0.349863			−0.0111419
$987$	5.01418	−	17.5181i	0.159603	−	0.557606i
$988$		−	6.58022i		−	0.209345i
$989$	−23.2478	−	2.42241i	−0.739238	−	0.0770281i
$990$	40.0283	−	33.0484i	1.27218	−	1.05035i
$991$	−3.32792	+	5.76412i	−0.105715	+	0.183103i	−0.914030	−	0.405647i	$-0.867046\pi$
$991$	−3.32792	+	5.76412i	−0.105715	+	0.183103i	0.808315	+	0.588750i	$0.200380\pi$
$992$	−6.36502	+	3.67485i	−0.202090	+	0.116676i
$993$	3.36130	−	2.33372i	0.106668	−	0.0740585i
$994$	−1.28251	+	3.38608i	−0.0406788	+	0.107400i
$995$			65.1466i			2.06529i
$996$	−18.5571	−	8.74339i	−0.588004	−	0.277045i
$997$	11.9460	−	20.6910i	0.378333	−	0.655291i	−0.612487	−	0.790481i	$-0.709831\pi$
$997$	11.9460	−	20.6910i	0.378333	−	0.655291i	0.990820	+	0.135189i	$0.0431642\pi$
$998$	2.64476	+	1.52695i	0.0837183	+	0.0483348i
$999$	−1.58740	−	1.62577i	−0.0502232	−	0.0514371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.j.a.137.17	✓	128
3.2	odd	2	inner	966.2.j.a.137.38	yes	128
7.2	even	3	inner	966.2.j.a.275.37	yes	128
21.2	odd	6	inner	966.2.j.a.275.18	yes	128
23.22	odd	2	inner	966.2.j.a.137.18	yes	128
69.68	even	2	inner	966.2.j.a.137.37	yes	128
161.114	odd	6	inner	966.2.j.a.275.38	yes	128
483.275	even	6	inner	966.2.j.a.275.17	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.j.a.137.17	✓	128	1.1	even	1	trivial
966.2.j.a.137.18	yes	128	23.22	odd	2	inner
966.2.j.a.137.37	yes	128	69.68	even	2	inner
966.2.j.a.137.38	yes	128	3.2	odd	2	inner
966.2.j.a.275.17	yes	128	483.275	even	6	inner
966.2.j.a.275.18	yes	128	21.2	odd	6	inner
966.2.j.a.275.37	yes	128	7.2	even	3	inner
966.2.j.a.275.38	yes	128	161.114	odd	6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.144090 + 1.72605i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.22533 - 3.85438i) q^{5} +(-0.987809 - 1.42276i) q^{6} +(1.67417 + 2.04869i) q^{7} +1.00000i q^{8} +(-2.95848 + 0.497412i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.144090 + 1.72605i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.22533 - 3.85438i) q^{5} +(-0.987809 - 1.42276i) q^{6} +(1.67417 + 2.04869i) q^{7} +1.00000i q^{8} +(-2.95848 + 0.497412i) q^{9} +(3.85438 + 2.22533i) q^{10} +(-1.94384 + 3.36683i) q^{11} +(1.56685 + 0.738238i) q^{12} +1.10062 q^{13} +(-2.47422 - 0.937135i) q^{14} +(6.33220 - 4.39640i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.70171 - 4.67951i) q^{17} +(2.31341 - 1.91001i) q^{18} +(5.17767 - 2.98933i) q^{19} -4.45066 q^{20} +(-3.29491 + 3.18490i) q^{21} -3.88768i q^{22} +(-0.497032 + 4.77001i) q^{23} +(-1.72605 + 0.144090i) q^{24} +(-7.40418 + 12.8244i) q^{25} +(-0.953164 + 0.550309i) q^{26} +(-1.28484 - 5.03480i) q^{27} +(2.61131 - 0.425529i) q^{28} +0.0647484i q^{29} +(-3.28564 + 6.97349i) q^{30} +(-3.67485 + 6.36502i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-6.09139 - 2.87003i) q^{33} +5.40343i q^{34} +(4.17087 - 11.0119i) q^{35} +(-1.04847 + 2.81082i) q^{36} +(0.378703 - 0.218644i) q^{37} +(-2.98933 + 5.17767i) q^{38} +(0.158588 + 1.89972i) q^{39} +(3.85438 - 2.22533i) q^{40} +7.37397i q^{41} +(1.26103 - 4.40566i) q^{42} +4.87375i q^{43} +(1.94384 + 3.36683i) q^{44} +(8.50080 + 10.2962i) q^{45} +(-1.95456 - 4.37946i) q^{46} +(-3.44355 + 1.98813i) q^{47} +(1.42276 - 0.987809i) q^{48} +(-1.39429 + 6.85973i) q^{49} -14.8084i q^{50} +(8.46634 + 3.98902i) q^{51} +(0.550309 - 0.953164i) q^{52} +(-3.54367 + 6.13782i) q^{53} +(3.63010 + 3.71784i) q^{54} +17.3027 q^{55} +(-2.04869 + 1.67417i) q^{56} +(5.90577 + 8.50617i) q^{57} +(-0.0323742 - 0.0560737i) q^{58} +(10.3128 + 5.95409i) q^{59} +(-0.641295 - 7.68204i) q^{60} +(-8.96275 + 5.17465i) q^{61} -7.34969i q^{62} +(-5.97204 - 5.22826i) q^{63} -1.00000 q^{64} +(-2.44924 - 4.24221i) q^{65} +(6.71032 - 0.560175i) q^{66} +(3.41741 + 1.97304i) q^{67} +(-2.70171 - 4.67951i) q^{68} +(-8.30487 - 0.170591i) q^{69} +(1.89388 + 11.6220i) q^{70} -1.36854i q^{71} +(-0.497412 - 2.95848i) q^{72} +(-2.17222 + 3.76239i) q^{73} +(-0.218644 + 0.378703i) q^{74} +(-23.2024 - 10.9321i) q^{75} -5.97866i q^{76} +(-10.1519 + 1.65432i) q^{77} +(-1.08720 - 1.56591i) q^{78} +(3.57139 - 2.06194i) q^{79} +(-2.22533 + 3.85438i) q^{80} +(8.50516 - 2.94316i) q^{81} +(-3.68699 - 6.38605i) q^{82} -11.8436 q^{83} +(1.11075 + 4.44592i) q^{84} -24.0488 q^{85} +(-2.43688 - 4.22079i) q^{86} +(-0.111759 + 0.00932958i) q^{87} +(-3.36683 - 1.94384i) q^{88} +(2.49126 + 4.31499i) q^{89} +(-12.5100 - 4.66637i) q^{90} +(1.84263 + 2.25483i) q^{91} +(3.88243 + 2.81545i) q^{92} +(-11.5158 - 5.42582i) q^{93} +(1.98813 - 3.44355i) q^{94} +(-23.0440 - 13.3045i) q^{95} +(-0.738238 + 1.56685i) q^{96} -0.0549934i q^{97} +(-2.22237 - 6.63785i) q^{98} +(4.07610 - 10.9276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

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