LMFDB - Embedded newform 324.2.m.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(13,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("324.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.m (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$9$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	324.49
Dual form			324.2.m.a.205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71035 + 0.273337i) q^{3} +(0.101566 - 0.235457i) q^{5} +(0.0645556 + 1.10838i) q^{7} +(2.85057 - 0.935001i) q^{9} +O(q^{10})$	\(q+(-1.71035 + 0.273337i) q^{3} +(0.101566 - 0.235457i) q^{5} +(0.0645556 + 1.10838i) q^{7} +(2.85057 - 0.935001i) q^{9} +(-2.61611 + 3.51405i) q^{11} +(-0.112256 + 0.118984i) q^{13} +(-0.109355 + 0.430475i) q^{15} +(-0.676180 + 3.83481i) q^{17} +(0.862985 + 4.89423i) q^{19} +(-0.413373 - 1.87806i) q^{21} +(-0.206233 + 3.54089i) q^{23} +(3.38608 + 3.58904i) q^{25} +(-4.61990 + 2.37834i) q^{27} +(-4.32976 + 1.02617i) q^{29} +(2.25761 - 1.13382i) q^{31} +(3.51394 - 6.72533i) q^{33} +(0.267532 + 0.0973736i) q^{35} +(-0.682668 + 0.248471i) q^{37} +(0.159474 - 0.234188i) q^{39} +(-2.28815 - 7.64295i) q^{41} +(2.86218 + 0.334541i) q^{43} +(0.0693695 - 0.766152i) q^{45} +(-3.94249 - 1.97999i) q^{47} +(5.72834 - 0.669546i) q^{49} +(0.108309 - 6.74368i) q^{51} +(-1.43458 + 2.48476i) q^{53} +(0.561699 + 0.972892i) q^{55} +(-2.81378 - 8.13495i) q^{57} +(-2.10464 - 2.82703i) q^{59} +(12.2580 - 8.06224i) q^{61} +(1.22035 + 3.09915i) q^{63} +(0.0166143 + 0.0385162i) q^{65} +(-10.5184 - 2.49291i) q^{67} +(-0.615124 - 6.11252i) q^{69} +(7.47705 + 6.27399i) q^{71} +(-1.39879 + 1.17372i) q^{73} +(-6.77239 - 5.21296i) q^{75} +(-4.06378 - 2.67279i) q^{77} +(2.34765 - 7.84168i) q^{79} +(7.25155 - 5.33058i) q^{81} +(-0.543921 + 1.81682i) q^{83} +(0.834256 + 0.548699i) q^{85} +(7.12490 - 2.93859i) q^{87} +(5.12706 - 4.30211i) q^{89} +(-0.139126 - 0.116741i) q^{91} +(-3.55139 + 2.55631i) q^{93} +(1.24003 + 0.293893i) q^{95} +(5.07129 + 11.7566i) q^{97} +(-4.17178 + 12.4631i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q+O(q^{10}) $ 162 * q	$ 162 q + 27 q^{21} + 27 q^{23} + 27 q^{27} + 27 q^{29} + 27 q^{33} + 27 q^{35} - 18 q^{41} - 54 q^{45} - 54 q^{47} - 63 q^{51} - 54 q^{53} - 54 q^{57} - 63 q^{59} - 54 q^{63} - 90 q^{65} + 27 q^{67} - 90 q^{69} - 72 q^{71} - 90 q^{75} - 144 q^{77} + 54 q^{79} - 72 q^{81} - 72 q^{83} + 54 q^{85} - 144 q^{87} - 99 q^{89} - 90 q^{93} - 126 q^{95} + 27 q^{97} - 90 q^{99}+O(q^{100}) $ 162 * q + 27 * q^21 + 27 * q^23 + 27 * q^27 + 27 * q^29 + 27 * q^33 + 27 * q^35 - 18 * q^41 - 54 * q^45 - 54 * q^47 - 63 * q^51 - 54 * q^53 - 54 * q^57 - 63 * q^59 - 54 * q^63 - 90 * q^65 + 27 * q^67 - 90 * q^69 - 72 * q^71 - 90 * q^75 - 144 * q^77 + 54 * q^79 - 72 * q^81 - 72 * q^83 + 54 * q^85 - 144 * q^87 - 99 * q^89 - 90 * q^93 - 126 * q^95 + 27 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{16}{27}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.71035	+	0.273337i	−0.987469	+	0.157811i
$3$	−1.71035	+	0.273337i	−0.987469	+	0.157811i
$4$		0			0
$5$	0.101566	−	0.235457i	0.0454218	−	0.105300i	−0.893995	−	0.448078i	$-0.852109\pi$
$5$	0.101566	−	0.235457i	0.0454218	−	0.105300i	0.939416	+	0.342778i	$0.111368\pi$
$6$		0			0
$7$	0.0645556	+	1.10838i	0.0243997	+	0.418927i	0.988286	+	0.152613i	$0.0487688\pi$
$7$	0.0645556	+	1.10838i	0.0243997	+	0.418927i	−0.963886	+	0.266314i	$0.914194\pi$
$8$		0			0
$9$	2.85057	−	0.935001i	0.950191	−	0.311667i
$10$		0			0
$11$	−2.61611	+	3.51405i	−0.788788	+	1.05953i	0.207896	+	0.978151i	$0.433339\pi$
$11$	−2.61611	+	3.51405i	−0.788788	+	1.05953i	−0.996684	+	0.0813752i	$0.974069\pi$
$12$		0			0
$13$	−0.112256	+	0.118984i	−0.0311342	+	0.0330003i	−0.742754	−	0.669565i	$-0.766481\pi$
$13$	−0.112256	+	0.118984i	−0.0311342	+	0.0330003i	0.711619	+	0.702565i	$0.247962\pi$
$14$		0			0
$15$	−0.109355	+	0.430475i	−0.0282352	+	0.111148i
$16$		0			0
$17$	−0.676180	+	3.83481i	−0.163998	+	0.930078i	0.786094	+	0.618107i	$0.212100\pi$
$17$	−0.676180	+	3.83481i	−0.163998	+	0.930078i	−0.950092	+	0.311971i	$0.899011\pi$
$18$		0			0
$19$	0.862985	+	4.89423i	0.197982	+	1.12281i	0.908107	+	0.418738i	$0.137527\pi$
$19$	0.862985	+	4.89423i	0.197982	+	1.12281i	−0.710125	+	0.704076i	$0.751362\pi$
$20$		0			0
$21$	−0.413373	−	1.87806i	−0.0902053	−	0.409827i
$22$		0			0
$23$	−0.206233	+	3.54089i	−0.0430026	+	0.738326i	0.906043	+	0.423187i	$0.139088\pi$
$23$	−0.206233	+	3.54089i	−0.0430026	+	0.738326i	−0.949045	+	0.315140i	$0.897949\pi$
$24$		0			0
$25$	3.38608	+	3.58904i	0.677217	+	0.717808i
$26$		0			0
$27$	−4.61990	+	2.37834i	−0.889100	+	0.457712i
$28$		0			0
$29$	−4.32976	+	1.02617i	−0.804016	+	0.190555i	−0.612022	−	0.790841i	$-0.709644\pi$
$29$	−4.32976	+	1.02617i	−0.804016	+	0.190555i	−0.191994	+	0.981396i	$0.561495\pi$
$30$		0			0
$31$	2.25761	−	1.13382i	0.405479	−	0.203639i	−0.234357	−	0.972151i	$-0.575298\pi$
$31$	2.25761	−	1.13382i	0.405479	−	0.203639i	0.639836	+	0.768511i	$0.279002\pi$
$32$		0			0
$33$	3.51394	−	6.72533i	0.611699	−	1.17073i
$34$		0			0
$35$	0.267532	+	0.0973736i	0.0452211	+	0.0164591i
$36$		0			0
$37$	−0.682668	+	0.248471i	−0.112230	+	0.0408483i	−0.397525	−	0.917591i	$-0.630131\pi$
$37$	−0.682668	+	0.248471i	−0.112230	+	0.0408483i	0.285295	+	0.958440i	$0.407908\pi$
$38$		0			0
$39$	0.159474	−	0.234188i	0.0255362	−	0.0375001i
$40$		0			0
$41$	−2.28815	−	7.64295i	−0.357349	−	1.19363i	−0.928045	−	0.372467i	$-0.878512\pi$
$41$	−2.28815	−	7.64295i	−0.357349	−	1.19363i	0.570696	−	0.821161i	$-0.306673\pi$
$42$		0			0
$43$	2.86218	+	0.334541i	0.436479	+	0.0510171i	0.331495	−	0.943457i	$-0.392447\pi$
$43$	2.86218	+	0.334541i	0.436479	+	0.0510171i	0.104984	+	0.994474i	$0.466521\pi$
$44$		0			0
$45$	0.0693695	−	0.766152i	0.0103410	−	0.114211i
$46$		0			0
$47$	−3.94249	−	1.97999i	−0.575072	−	0.288812i	0.137397	−	0.990516i	$-0.456126\pi$
$47$	−3.94249	−	1.97999i	−0.575072	−	0.288812i	−0.712468	+	0.701704i	$0.752423\pi$
$48$		0			0
$49$	5.72834	−	0.669546i	0.818334	−	0.0956495i
$50$		0			0
$51$	0.108309	−	6.74368i	0.0151663	−	0.944304i
$52$		0			0
$53$	−1.43458	+	2.48476i	−0.197054	+	0.341308i	−0.947572	−	0.319542i	$-0.896471\pi$
$53$	−1.43458	+	2.48476i	−0.197054	+	0.341308i	0.750518	+	0.660850i	$0.229804\pi$
$54$		0			0
$55$	0.561699	+	0.972892i	0.0757395	+	0.131185i
$56$		0			0
$57$	−2.81378	−	8.13495i	−0.372694	−	1.07750i
$58$		0			0
$59$	−2.10464	−	2.82703i	−0.274001	−	0.368048i	0.643728	−	0.765255i	$-0.277387\pi$
$59$	−2.10464	−	2.82703i	−0.274001	−	0.368048i	−0.917729	+	0.397207i	$0.869980\pi$
$60$		0			0
$61$	12.2580	−	8.06224i	1.56948	−	1.03226i	0.596146	−	0.802876i	$-0.296698\pi$
$61$	12.2580	−	8.06224i	1.56948	−	1.03226i	0.973335	−	0.229388i	$-0.0736725\pi$
$62$		0			0
$63$	1.22035	+	3.09915i	0.153750	+	0.390456i
$64$		0			0
$65$	0.0166143	+	0.0385162i	0.00206075	+	0.00477735i
$66$		0			0
$67$	−10.5184	−	2.49291i	−1.28503	−	0.304557i	−0.469323	−	0.883027i	$-0.655502\pi$
$67$	−10.5184	−	2.49291i	−1.28503	−	0.304557i	−0.815704	+	0.578470i	$0.803650\pi$
$68$		0			0
$69$	−0.615124	−	6.11252i	−0.0740523	−	0.735861i
$70$		0			0
$71$	7.47705	+	6.27399i	0.887363	+	0.744586i	0.967679	−	0.252184i	$-0.0811487\pi$
$71$	7.47705	+	6.27399i	0.887363	+	0.744586i	−0.0803167	+	0.996769i	$0.525593\pi$
$72$		0			0
$73$	−1.39879	+	1.17372i	−0.163716	+	0.137374i	−0.720965	−	0.692972i	$-0.756301\pi$
$73$	−1.39879	+	1.17372i	−0.163716	+	0.137374i	0.557249	+	0.830345i	$0.311857\pi$
$74$		0			0
$75$	−6.77239	−	5.21296i	−0.782009	−	0.601941i
$76$		0			0
$77$	−4.06378	−	2.67279i	−0.463110	−	0.304593i
$78$		0			0
$79$	2.34765	−	7.84168i	0.264131	−	0.882258i	−0.718316	−	0.695717i	$-0.755087\pi$
$79$	2.34765	−	7.84168i	0.264131	−	0.882258i	0.982447	−	0.186542i	$-0.0597279\pi$
$80$		0			0
$81$	7.25155	−	5.33058i	0.805727	−	0.592287i
$82$		0			0
$83$	−0.543921	+	1.81682i	−0.0597031	+	0.199422i	−0.982638	−	0.185534i	$-0.940598\pi$
$83$	−0.543921	+	1.81682i	−0.0597031	+	0.199422i	0.922935	+	0.384957i	$0.125784\pi$
$84$		0			0
$85$	0.834256	+	0.548699i	0.0904877	+	0.0595147i
$86$		0			0
$87$	7.12490	−	2.93859i	0.763869	−	0.315050i
$88$		0			0
$89$	5.12706	−	4.30211i	0.543467	−	0.456023i	−0.329255	−	0.944241i	$-0.606797\pi$
$89$	5.12706	−	4.30211i	0.543467	−	0.456023i	0.872722	+	0.488218i	$0.162353\pi$
$90$		0			0
$91$	−0.139126	−	0.116741i	−0.0145844	−	0.0122377i
$92$		0			0
$93$	−3.55139	+	2.55631i	−0.368262	+	0.265077i
$94$		0			0
$95$	1.24003	+	0.293893i	0.127225	+	0.0301528i
$96$		0			0
$97$	5.07129	+	11.7566i	0.514912	+	1.19370i	0.955232	+	0.295859i	$0.0956058\pi$
$97$	5.07129	+	11.7566i	0.514912	+	1.19370i	−0.440320	+	0.897841i	$0.645135\pi$
$98$		0			0
$99$	−4.17178	+	12.4631i	−0.419280	+	1.25259i
$100$		0			0
$101$	−7.89152	+	5.19034i	−0.785236	+	0.516458i	−0.877673	−	0.479261i	$-0.840905\pi$
$101$	−7.89152	+	5.19034i	−0.785236	+	0.516458i	0.0924366	+	0.995719i	$0.470534\pi$
$102$		0			0
$103$	−8.61511	−	11.5721i	−0.848872	−	1.14023i	−0.988678	−	0.150054i	$-0.952055\pi$
$103$	−8.61511	−	11.5721i	−0.848872	−	1.14023i	0.139806	−	0.990179i	$-0.455352\pi$
$104$		0			0
$105$	−0.484188	−	0.0934164i	−0.0472519	−	0.00911651i
$106$		0			0
$107$	1.39527	+	2.41667i	0.134886	+	0.233629i	0.925554	−	0.378616i	$-0.123600\pi$
$107$	1.39527	+	2.41667i	0.134886	+	0.233629i	−0.790668	+	0.612245i	$0.790267\pi$
$108$		0			0
$109$	−9.26041	+	16.0395i	−0.886987	+	1.53631i	−0.0435668	+	0.999051i	$0.513872\pi$
$109$	−9.26041	+	16.0395i	−0.886987	+	1.53631i	−0.843420	+	0.537255i	$0.819461\pi$
$110$		0			0
$111$	1.09968	−	0.611569i	0.104377	−	0.0580476i
$112$		0			0
$113$	−8.93727	+	1.04462i	−0.840747	+	0.0982693i	−0.525556	−	0.850759i	$-0.676143\pi$
$113$	−8.93727	+	1.04462i	−0.840747	+	0.0982693i	−0.315191	+	0.949028i	$0.602069\pi$
$114$		0			0
$115$	0.812781	+	0.408194i	0.0757922	+	0.0380643i
$116$		0			0
$117$	−0.208743	+	0.444133i	−0.0192983	+	0.0410601i
$118$		0			0
$119$	−4.29406	−	0.501904i	−0.393636	−	0.0460095i
$120$		0			0
$121$	−2.34967	−	7.84843i	−0.213606	−	0.713494i
$122$		0			0
$123$	6.00263	+	12.4467i	0.541239	+	1.12228i
$124$		0			0
$125$	2.39380	−	0.871271i	0.214108	−	0.0779289i
$126$		0			0
$127$	10.4592	+	3.80685i	0.928107	+	0.337803i	0.761459	−	0.648213i	$-0.224483\pi$
$127$	10.4592	+	3.80685i	0.928107	+	0.337803i	0.166648	+	0.986016i	$0.446706\pi$
$128$		0			0
$129$	−4.98677	+	0.210158i	−0.439061	+	0.0185034i
$130$		0			0
$131$	19.1007	−	9.59275i	1.66884	−	0.838123i	0.673770	−	0.738941i	$-0.264674\pi$
$131$	19.1007	−	9.59275i	1.66884	−	0.838123i	0.995069	−	0.0991819i	$-0.0316226\pi$
$132$		0			0
$133$	−5.36894	+	1.27246i	−0.465546	+	0.110337i
$134$		0			0
$135$	0.0907717	+	1.32935i	0.00781238	+	0.114412i
$136$		0			0
$137$	1.92085	+	2.03598i	0.164110	+	0.173946i	0.804210	−	0.594345i	$-0.202589\pi$
$137$	1.92085	+	2.03598i	0.164110	+	0.173946i	−0.640100	+	0.768291i	$0.721107\pi$
$138$		0			0
$139$	−0.260028	+	4.46450i	−0.0220552	+	0.378674i	0.969161	+	0.246427i	$0.0792564\pi$
$139$	−0.260028	+	4.46450i	−0.0220552	+	0.378674i	−0.991217	+	0.132247i	$0.957781\pi$
$140$		0			0
$141$	7.28424	+	2.30885i	0.613443	+	0.194440i
$142$		0			0
$143$	−0.124443	−	0.705749i	−0.0104064	−	0.0590177i
$144$		0			0
$145$	−0.198138	+	1.12370i	−0.0164545	+	0.0933179i
$146$		0			0
$147$	−9.61443	+	2.71092i	−0.792985	+	0.223593i
$148$		0			0
$149$	10.6262	−	11.2631i	0.870530	−	0.922707i	−0.127074	−	0.991893i	$-0.540559\pi$
$149$	10.6262	−	11.2631i	0.870530	−	0.922707i	0.997604	+	0.0691858i	$0.0220401\pi$
$150$		0			0
$151$	3.39467	−	4.55984i	0.276254	−	0.371074i	−0.642243	−	0.766501i	$-0.721996\pi$
$151$	3.39467	−	4.55984i	0.276254	−	0.371074i	0.918497	+	0.395427i	$0.129403\pi$
$152$		0			0
$153$	1.65805	+	11.5636i	0.134045	+	0.934864i
$154$		0			0
$155$	−0.0376676	−	0.646729i	−0.00302554	−	0.0519465i
$156$		0			0
$157$	5.78989	−	13.4225i	0.462083	−	1.07123i	−0.514772	−	0.857327i	$-0.672123\pi$
$157$	5.78989	−	13.4225i	0.462083	−	1.07123i	0.976855	−	0.213902i	$-0.0686175\pi$
$158$		0			0
$159$	1.77445	−	4.64193i	0.140723	−	0.368129i
$160$		0			0
$161$	−3.93795			−0.310354
$162$		0			0
$163$	−20.2917			−1.58937			−0.794683	−	0.607024i	$-0.792363\pi$
$163$	−20.2917			−1.58937			−0.794683	+	0.607024i	$0.792363\pi$
$164$		0			0
$165$	−1.22663	−	1.51045i	−0.0954928	−	0.117588i
$166$		0			0
$167$	2.13058	−	4.93924i	0.164869	−	0.382210i	−0.815674	−	0.578511i	$-0.803634\pi$
$167$	2.13058	−	4.93924i	0.164869	−	0.382210i	0.980544	+	0.196301i	$0.0628931\pi$
$168$		0			0
$169$	0.754327	+	12.9513i	0.0580251	+	0.996253i
$170$		0			0
$171$	7.03612	+	13.1445i	0.538065	+	1.00518i
$172$		0			0
$173$	−12.7048	+	17.0655i	−0.965928	+	1.29747i	−0.0112147	+	0.999937i	$0.503570\pi$
$173$	−12.7048	+	17.0655i	−0.965928	+	1.29747i	−0.954713	+	0.297529i	$0.903838\pi$
$174$		0			0
$175$	−3.75942	+	3.98475i	−0.284185	+	0.301219i
$176$		0			0
$177$	4.37240	+	4.25992i	0.328650	+	0.320195i
$178$		0			0
$179$	−1.32585	+	7.51929i	−0.0990989	+	0.562018i	0.894315	+	0.447438i	$0.147663\pi$
$179$	−1.32585	+	7.51929i	−0.0990989	+	0.562018i	−0.993414	+	0.114580i	$0.963448\pi$
$180$		0			0
$181$	0.00732463	+	0.0415400i	0.000544435	+	0.00308765i	0.985079	−	0.172104i	$-0.0550566\pi$
$181$	0.00732463	+	0.0415400i	0.000544435	+	0.00308765i	−0.984534	+	0.175192i	$0.943945\pi$
$182$		0			0
$183$	−18.7618	+	17.1398i	−1.38691	+	1.26701i
$184$		0			0
$185$	−0.0108318	+	0.185975i	−0.000796371	+	0.0136732i
$186$		0			0
$187$	−11.7067	−	12.4084i	−0.856082	−	0.907394i
$188$		0			0
$189$	−2.93434	−	4.96706i	−0.213442	−	0.361300i
$190$		0			0
$191$	25.5630	−	6.05855i	1.84968	−	0.438381i	0.853150	−	0.521666i	$-0.174689\pi$
$191$	25.5630	−	6.05855i	1.84968	−	0.438381i	0.996526	+	0.0832852i	$0.0265413\pi$
$192$		0			0
$193$	−7.36687	+	3.69978i	−0.530279	+	0.266316i	−0.693730	−	0.720235i	$-0.744034\pi$
$193$	−7.36687	+	3.69978i	−0.530279	+	0.266316i	0.163451	+	0.986551i	$0.447738\pi$
$194$		0			0
$195$	−0.0389441	−	0.0613348i	−0.00278884	−	0.00439228i
$196$		0			0
$197$	25.4783	+	9.27334i	1.81525	+	0.660698i	0.996212	+	0.0869634i	$0.0277163\pi$
$197$	25.4783	+	9.27334i	1.81525	+	0.660698i	0.819041	+	0.573735i	$0.194506\pi$
$198$		0			0
$199$	−5.87208	+	2.13726i	−0.416261	+	0.151506i	−0.541656	−	0.840600i	$-0.682202\pi$
$199$	−5.87208	+	2.13726i	−0.416261	+	0.151506i	0.125395	+	0.992107i	$0.459980\pi$
$200$		0			0
$201$	18.6715	+	1.38867i	1.31699	+	0.0979493i
$202$		0			0
$203$	−1.41690	−	4.73276i	−0.0994466	−	0.332175i
$204$		0			0
$205$	−2.03199	−	0.237505i	−0.141920	−	0.0165881i
$206$		0			0
$207$	2.72285	+	10.2864i	0.189251	+	0.714954i
$208$		0			0
$209$	−19.4562	−	9.77129i	−1.34582	−	0.675894i
$210$		0			0
$211$	−10.1737	+	1.18914i	−0.700387	+	0.0818634i	−0.458831	−	0.888524i	$-0.651732\pi$
$211$	−10.1737	+	1.18914i	−0.700387	+	0.0818634i	−0.241556	+	0.970387i	$0.577658\pi$
$212$		0			0
$213$	−14.5033	−	8.68695i	−0.993747	−	0.595220i
$214$		0			0
$215$	0.369472	−	0.639943i	0.0251977	−	0.0436438i
$216$		0			0
$217$	1.40244	+	2.42909i	0.0952037	+	0.164898i
$218$		0			0
$219$	2.07159	−	2.38981i	0.139985	−	0.161488i
$220$		0			0
$221$	−0.380377	−	0.510934i	−0.0255869	−	0.0343692i
$222$		0			0
$223$	13.3231	−	8.76274i	0.892181	−	0.586797i	−0.0185357	−	0.999828i	$-0.505900\pi$
$223$	13.3231	−	8.76274i	0.892181	−	0.586797i	0.910717	+	0.413032i	$0.135530\pi$
$224$		0			0
$225$	13.0080	+	7.06483i	0.867203	+	0.470989i
$226$		0			0
$227$	−0.170392	−	0.395014i	−0.0113093	−	0.0262180i	0.912468	−	0.409148i	$-0.134174\pi$
$227$	−0.170392	−	0.395014i	−0.0113093	−	0.0262180i	−0.923777	+	0.382930i	$0.874915\pi$
$228$		0			0
$229$	−6.65426	−	1.57709i	−0.439726	−	0.104217i	0.00478884	−	0.999989i	$-0.498476\pi$
$229$	−6.65426	−	1.57709i	−0.439726	−	0.104217i	−0.444515	+	0.895772i	$0.646624\pi$
$230$		0			0
$231$	7.68104	+	3.46062i	0.505375	+	0.227692i
$232$		0			0
$233$	9.08896	+	7.62654i	0.595437	+	0.499631i	0.889975	−	0.456009i	$-0.150721\pi$
$233$	9.08896	+	7.62654i	0.595437	+	0.499631i	−0.294538	+	0.955640i	$0.595166\pi$
$234$		0			0
$235$	−0.866628	+	0.727187i	−0.0565326	+	0.0474365i
$236$		0			0
$237$	−1.87187	+	14.0537i	−0.121591	+	0.912886i
$238$		0			0
$239$	8.89896	+	5.85294i	0.575626	+	0.378595i	0.803687	−	0.595052i	$-0.202868\pi$
$239$	8.89896	+	5.85294i	0.575626	+	0.378595i	−0.228062	+	0.973647i	$0.573239\pi$
$240$		0			0
$241$	1.08582	−	3.62689i	0.0699438	−	0.233628i	−0.915869	−	0.401477i	$-0.868497\pi$
$241$	1.08582	−	3.62689i	0.0699438	−	0.233628i	0.985813	+	0.167849i	$0.0536821\pi$
$242$		0			0
$243$	−10.9456	+	11.0993i	−0.702162	+	0.712018i
$244$		0			0
$245$	0.424156	−	1.41678i	0.0270984	−	0.0905148i
$246$		0			0
$247$	−0.679211	−	0.446724i	−0.0432172	−	0.0284244i
$248$		0			0
$249$	0.433689	−	3.25607i	0.0274840	−	0.206345i
$250$		0			0
$251$	14.4677	−	12.1398i	0.913193	−	0.766260i	−0.0595305	−	0.998226i	$-0.518960\pi$
$251$	14.4677	−	12.1398i	0.913193	−	0.766260i	0.972724	+	0.231966i	$0.0745159\pi$
$252$		0			0
$253$	−11.9033	−	9.98808i	−0.748356	−	0.627945i
$254$		0			0
$255$	−1.57685	−	0.710432i	−0.0987459	−	0.0444890i
$256$		0			0
$257$	−19.4349	−	4.60616i	−1.21232	−	0.287325i	−0.425757	−	0.904837i	$-0.639992\pi$
$257$	−19.4349	−	4.60616i	−1.21232	−	0.287325i	−0.786561	+	0.617513i	$0.788140\pi$
$258$		0			0
$259$	−0.319469	−	0.740613i	−0.0198509	−	0.0460195i
$260$		0			0
$261$	−11.3828	+	6.97351i	−0.704579	+	0.431649i
$262$		0			0
$263$	15.8612	−	10.4320i	0.978041	−	0.643267i	0.0434736	−	0.999055i	$-0.486158\pi$
$263$	15.8612	−	10.4320i	0.978041	−	0.643267i	0.934567	+	0.355787i	$0.115787\pi$
$264$		0			0
$265$	0.439350	+	0.590149i	0.0269890	+	0.0362526i
$266$		0			0
$267$	−7.59312	+	8.75952i	−0.464691	+	0.536074i
$268$		0			0
$269$	−6.22935	−	10.7896i	−0.379810	−	0.657851i	0.611224	−	0.791458i	$-0.290677\pi$
$269$	−6.22935	−	10.7896i	−0.379810	−	0.657851i	−0.991034	+	0.133607i	$0.957344\pi$
$270$		0			0
$271$	0.439706	−	0.761593i	0.0267102	−	0.0462635i	−0.852361	−	0.522953i	$-0.824830\pi$
$271$	0.439706	−	0.761593i	0.0267102	−	0.0462635i	0.879072	+	0.476690i	$0.158164\pi$
$272$		0			0
$273$	0.269863	+	0.161639i	0.0163329	+	0.00978283i
$274$		0			0
$275$	−21.4704	+	2.50954i	−1.29472	+	0.151331i
$276$		0			0
$277$	11.8732	+	5.96296i	0.713393	+	0.358279i	0.768193	−	0.640218i	$-0.221156\pi$
$277$	11.8732	+	5.96296i	0.713393	+	0.358279i	−0.0548004	+	0.998497i	$0.517452\pi$
$278$		0			0
$279$	5.37538	−	5.34290i	0.321815	−	0.319871i
$280$		0			0
$281$	−5.76049	−	0.673305i	−0.343642	−	0.0401660i	−0.0574784	−	0.998347i	$-0.518306\pi$
$281$	−5.76049	−	0.673305i	−0.343642	−	0.0401660i	−0.286164	+	0.958181i	$0.592380\pi$
$282$		0			0
$283$	−2.01769	−	6.73957i	−0.119939	−	0.400626i	0.876843	−	0.480776i	$-0.159645\pi$
$283$	−2.01769	−	6.73957i	−0.119939	−	0.400626i	−0.996783	+	0.0801505i	$0.974460\pi$
$284$		0			0
$285$	−2.20122	−	0.163713i	−0.130389	−	0.00969750i
$286$		0			0
$287$	8.32356	−	3.02953i	0.491324	−	0.178827i
$288$		0			0
$289$	1.72624	+	0.628299i	0.101543	+	0.0369588i
$290$		0			0
$291$	−11.8872	−	18.7217i	−0.696839	−	1.09748i
$292$		0			0
$293$	16.9396	−	8.50740i	0.989623	−	0.497008i	0.121092	−	0.992641i	$-0.461360\pi$
$293$	16.9396	−	8.50740i	0.989623	−	0.497008i	0.868532	+	0.495634i	$0.165064\pi$
$294$		0			0
$295$	−0.879404	+	0.208423i	−0.0512009	+	0.0121348i
$296$		0			0
$297$	3.72857	−	22.4566i	0.216353	−	1.30306i
$298$		0			0
$299$	−0.398159	−	0.422024i	−0.0230261	−	0.0244063i
$300$		0			0
$301$	−0.186028	+	3.19398i	−0.0107225	+	0.184098i
$302$		0			0
$303$	12.0785	−	11.0343i	0.693894	−	0.633905i
$304$		0			0
$305$	−0.653308	−	3.70509i	−0.0374083	−	0.212153i
$306$		0			0
$307$	5.10196	−	28.9347i	0.291184	−	1.65139i	−0.391134	−	0.920334i	$-0.627917\pi$
$307$	5.10196	−	28.9347i	0.291184	−	1.65139i	0.682319	−	0.731055i	$-0.260972\pi$
$308$		0			0
$309$	17.8979	+	17.4375i	1.01818	+	0.991984i
$310$		0			0
$311$	22.2653	−	23.5998i	1.26255	−	1.33822i	0.346032	−	0.938223i	$-0.387529\pi$
$311$	22.2653	−	23.5998i	1.26255	−	1.33822i	0.916515	−	0.400000i	$-0.130990\pi$
$312$		0			0
$313$	−17.9867	+	24.1603i	−1.01667	+	1.36562i	−0.0874160	+	0.996172i	$0.527861\pi$
$313$	−17.9867	+	24.1603i	−1.01667	+	1.36562i	−0.929251	+	0.369449i	$0.879546\pi$
$314$		0			0
$315$	0.853664	+	0.0274281i	0.0480985	+	0.00154540i
$316$		0			0
$317$	−1.03348	−	17.7442i	−0.0580462	−	0.996616i	−0.894071	−	0.447924i	$-0.852163\pi$
$317$	−1.03348	−	17.7442i	−0.0580462	−	0.996616i	0.836025	−	0.548691i	$-0.184874\pi$
$318$		0			0
$319$	7.72112	−	17.8996i	0.432300	−	1.00218i
$320$		0			0
$321$	−3.04696	−	3.75197i	−0.170065	−	0.209415i
$322$		0			0
$323$	−19.3520			−1.07677
$324$		0			0
$325$	−0.807147			−0.0447724
$326$		0			0
$327$	11.4543	−	29.9643i	0.633426	−	1.65703i
$328$		0			0
$329$	1.94007	−	4.49759i	0.106960	−	0.247960i
$330$		0			0
$331$	−1.64835	−	28.3011i	−0.0906017	−	1.55557i	−0.671136	−	0.741334i	$-0.734193\pi$
$331$	−1.64835	−	28.3011i	−0.0906017	−	1.55557i	0.580534	−	0.814236i	$-0.302844\pi$
$332$		0			0
$333$	−1.71367	+	1.34658i	−0.0939088	+	0.0737921i
$334$		0			0
$335$	−1.65529	+	2.22344i	−0.0904380	+	0.121479i
$336$		0			0
$337$	−6.44855	+	6.83506i	−0.351275	+	0.372330i	−0.878784	−	0.477220i	$-0.841645\pi$
$337$	−6.44855	+	6.83506i	−0.351275	+	0.372330i	0.527509	+	0.849549i	$0.323126\pi$
$338$		0			0
$339$	15.0003	−	4.22954i	0.814704	−	0.229717i
$340$		0			0
$341$	−1.92189	+	10.8996i	−0.104076	+	0.590244i
$342$		0			0
$343$	2.46146	+	13.9597i	0.132907	+	0.753750i
$344$		0			0
$345$	−1.50171	−	0.475990i	−0.0808495	−	0.0256265i
$346$		0			0
$347$	−2.08593	+	35.8140i	−0.111979	+	1.92260i	0.213312	+	0.976984i	$0.431575\pi$
$347$	−2.08593	+	35.8140i	−0.111979	+	1.92260i	−0.325291	+	0.945614i	$0.605462\pi$
$348$		0			0
$349$	−9.58971	−	10.1645i	−0.513325	−	0.544093i	0.417921	−	0.908483i	$-0.362759\pi$
$349$	−9.58971	−	10.1645i	−0.513325	−	0.544093i	−0.931246	+	0.364390i	$0.881277\pi$
$350$		0			0
$351$	0.235625	−	0.816678i	0.0125768	−	0.0435911i
$352$		0			0
$353$	1.37937	−	0.326917i	0.0734166	−	0.0174001i	−0.193743	−	0.981052i	$-0.562063\pi$
$353$	1.37937	−	0.326917i	0.0734166	−	0.0174001i	0.267160	+	0.963652i	$0.413915\pi$
$354$		0			0
$355$	2.23667	−	1.12330i	0.118710	−	0.0596185i
$356$		0			0
$357$	7.48153	−	0.315295i	0.395965	−	0.0166872i
$358$		0			0
$359$	−24.9076	−	9.06563i	−1.31457	−	0.478466i	−0.412858	−	0.910795i	$-0.635469\pi$
$359$	−24.9076	−	9.06563i	−1.31457	−	0.478466i	−0.901716	+	0.432330i	$0.857692\pi$
$360$		0			0
$361$	−5.35460	+	1.94891i	−0.281821	+	0.102574i
$362$		0			0
$363$	6.16401	+	12.7813i	0.323527	+	0.670844i
$364$		0			0
$365$	0.134291	+	0.448564i	0.00702913	+	0.0234789i
$366$		0			0
$367$	−3.61811	−	0.422896i	−0.188864	−	0.0220750i	0.0211353	−	0.999777i	$-0.493272\pi$
$367$	−3.61811	−	0.422896i	−0.188864	−	0.0220750i	−0.209999	+	0.977702i	$0.567346\pi$
$368$		0			0
$369$	−13.6687	−	19.6474i	−0.711565	−	1.02280i
$370$		0			0
$371$	−2.84666	−	1.42965i	−0.147791	−	0.0742236i
$372$		0			0
$373$	19.6589	−	2.29780i	1.01790	−	0.118975i	0.409257	−	0.912419i	$-0.365788\pi$
$373$	19.6589	−	2.29780i	1.01790	−	0.118975i	0.608643	+	0.793444i	$0.291714\pi$
$374$		0			0
$375$	−3.85607	+	2.14449i	−0.199127	+	0.110741i
$376$		0			0
$377$	0.363942	−	0.630367i	0.0187440	−	0.0324655i
$378$		0			0
$379$	9.55738	+	16.5539i	0.490929	+	0.850315i	0.999945	−	0.0104423i	$-0.00332394\pi$
$379$	9.55738	+	16.5539i	0.490929	+	0.850315i	−0.509016	+	0.860757i	$0.669991\pi$
$380$		0			0
$381$	−18.9295	−	3.65214i	−0.969787	−	0.187105i
$382$		0			0
$383$	20.3010	+	27.2690i	1.03733	+	1.39338i	0.916190	+	0.400744i	$0.131248\pi$
$383$	20.3010	+	27.2690i	1.03733	+	1.39338i	0.121143	+	0.992635i	$0.461344\pi$
$384$		0			0
$385$	−1.04207	+	0.685380i	−0.0531088	+	0.0349302i
$386$		0			0
$387$	8.47167	−	1.72251i	0.430639	−	0.0875602i
$388$		0			0
$389$	14.3604	+	33.2911i	0.728101	+	1.68793i	0.725776	+	0.687931i	$0.241481\pi$
$389$	14.3604	+	33.2911i	0.728101	+	1.68793i	0.00232490	+	0.999997i	$0.499260\pi$
$390$		0			0
$391$	−13.4392	−	3.18514i	−0.679649	−	0.161080i
$392$		0			0
$393$	−30.0468	+	21.6279i	−1.51566	+	1.09098i
$394$		0			0
$395$	−1.60794	−	1.34922i	−0.0809042	−	0.0678867i
$396$		0			0
$397$	17.7111	−	14.8614i	0.888894	−	0.745871i	−0.0790940	−	0.996867i	$-0.525203\pi$
$397$	17.7111	−	14.8614i	0.888894	−	0.745871i	0.967988	+	0.250997i	$0.0807583\pi$
$398$		0			0
$399$	8.83494	−	3.64388i	0.442300	−	0.182422i
$400$		0			0
$401$	−16.9377	−	11.1401i	−0.845827	−	0.556309i	0.0509962	−	0.998699i	$-0.483760\pi$
$401$	−16.9377	−	11.1401i	−0.845827	−	0.556309i	−0.896823	+	0.442390i	$0.854131\pi$
$402$		0			0
$403$	−0.118524	+	0.395898i	−0.00590410	+	0.0197211i
$404$		0			0
$405$	−0.518611	−	2.24883i	−0.0257700	−	0.111745i
$406$		0			0
$407$	0.912798	−	3.04896i	0.0452457	−	0.151131i
$408$		0			0
$409$	26.0391	+	17.1262i	1.28755	+	0.846835i	0.994029	−	0.109118i	$-0.0348026\pi$
$409$	26.0391	+	17.1262i	1.28755	+	0.846835i	0.293521	+	0.955953i	$0.405173\pi$
$410$		0			0
$411$	−3.84183	−	2.95720i	−0.189504	−	0.145868i
$412$		0			0
$413$	2.99755	−	2.51524i	0.147500	−	0.123767i
$414$		0			0
$415$	0.372540	+	0.312598i	0.0182873	+	0.0153448i
$416$		0			0
$417$	−0.775575	−	7.70692i	−0.0379800	−	0.377410i
$418$		0			0
$419$	−10.8193	−	2.56423i	−0.528559	−	0.125271i	−0.0423322	−	0.999104i	$-0.513479\pi$
$419$	−10.8193	−	2.56423i	−0.528559	−	0.125271i	−0.486226	+	0.873833i	$0.661627\pi$
$420$		0			0
$421$	8.91500	+	20.6673i	0.434491	+	1.00726i	0.985019	+	0.172446i	$0.0551670\pi$
$421$	8.91500	+	20.6673i	0.434491	+	1.00726i	−0.550528	+	0.834816i	$0.685574\pi$
$422$		0			0
$423$	−13.0897	−	1.95788i	−0.636441	−	0.0951956i
$424$		0			0
$425$	−16.0529	+	10.5581i	−0.778679	+	0.512145i
$426$		0			0
$427$	9.72733	+	13.0661i	0.470738	+	0.632311i
$428$		0			0
$429$	0.405747	+	1.17306i	0.0195897	+	0.0566359i
$430$		0			0
$431$	−5.01255	−	8.68200i	−0.241446	−	0.418197i	0.719680	−	0.694306i	$-0.244288\pi$
$431$	−5.01255	−	8.68200i	−0.241446	−	0.418197i	−0.961126	+	0.276109i	$0.910955\pi$
$432$		0			0
$433$	−8.52034	+	14.7577i	−0.409462	+	0.709208i	−0.994829	−	0.101560i	$-0.967617\pi$
$433$	−8.52034	+	14.7577i	−0.409462	+	0.709208i	0.585368	+	0.810768i	$0.300950\pi$
$434$		0			0
$435$	0.0317373	−	1.97607i	0.00152169	−	0.0947453i
$436$		0			0
$437$	−17.5079	+	2.04638i	−0.837517	+	0.0978917i
$438$		0			0
$439$	18.5691	+	9.32574i	0.886253	+	0.445093i	0.832862	−	0.553480i	$-0.186701\pi$
$439$	18.5691	+	9.32574i	0.886253	+	0.445093i	0.0533913	+	0.998574i	$0.482997\pi$
$440$		0			0
$441$	15.7030	−	7.26459i	0.747763	−	0.345933i
$442$		0			0
$443$	12.2621	+	1.43324i	0.582590	+	0.0680951i	0.402283	−	0.915515i	$-0.368217\pi$
$443$	12.2621	+	1.43324i	0.582590	+	0.0680951i	0.180307	+	0.983610i	$0.442291\pi$
$444$		0			0
$445$	−0.492227	−	1.64415i	−0.0233338	−	0.0779402i
$446$		0			0
$447$	−15.0958	+	22.1683i	−0.714008	+	1.04852i
$448$		0			0
$449$	−26.4864	+	9.64028i	−1.24997	+	0.454953i	−0.880392	−	0.474246i	$-0.842721\pi$
$449$	−26.4864	+	9.64028i	−1.24997	+	0.454953i	−0.369580	+	0.929199i	$0.620498\pi$
$450$		0			0
$451$	32.8438	+	11.9542i	1.54655	+	0.562899i
$452$		0			0
$453$	−4.55970	+	8.72679i	−0.214233	+	0.410020i
$454$		0			0
$455$	−0.0416179	+	0.0209013i	−0.00195108	+	0.000979869i
$456$		0			0
$457$	−8.31914	+	1.97167i	−0.389153	+	0.0922310i	−0.420535	−	0.907277i	$-0.638157\pi$
$457$	−8.31914	+	1.97167i	−0.389153	+	0.0922310i	0.0313815	+	0.999507i	$0.490009\pi$
$458$		0			0
$459$	−5.99661	−	19.3246i	−0.279898	−	0.901996i
$460$		0			0
$461$	17.1596	+	18.1881i	0.799200	+	0.847103i	0.990935	−	0.134344i	$-0.0428927\pi$
$461$	17.1596	+	18.1881i	0.799200	+	0.847103i	−0.191735	+	0.981447i	$0.561411\pi$
$462$		0			0
$463$	−1.10894	+	19.0397i	−0.0515367	+	0.884851i	0.869150	+	0.494549i	$0.164667\pi$
$463$	−1.10894	+	19.0397i	−0.0515367	+	0.884851i	−0.920687	+	0.390303i	$0.872370\pi$
$464$		0			0
$465$	0.241199	+	1.09583i	0.0111854	+	0.0508181i
$466$		0			0
$467$	−4.29929	−	24.3825i	−0.198947	−	1.12829i	−0.906684	−	0.421810i	$-0.861395\pi$
$467$	−4.29929	−	24.3825i	−0.198947	−	1.12829i	0.707737	−	0.706476i	$-0.249716\pi$
$468$		0			0
$469$	2.08406	−	11.8193i	0.0962329	−	0.545764i
$470$		0			0
$471$	−6.23387	+	24.5397i	−0.287241	+	1.13073i
$472$		0			0
$473$	−8.66340	+	9.18266i	−0.398343	+	0.422219i
$474$		0			0
$475$	−14.6434	+	19.6696i	−0.671887	+	0.902502i
$476$		0			0
$477$	−1.76611	+	8.42433i	−0.0808648	+	0.385723i
$478$		0			0
$479$	−1.12152	−	19.2557i	−0.0512433	−	0.879814i	−0.921781	−	0.387712i	$-0.873266\pi$
$479$	−1.12152	−	19.2557i	−0.0512433	−	0.879814i	0.870537	−	0.492102i	$-0.163771\pi$
$480$		0			0
$481$	0.0470693	−	0.109119i	0.00214618	−	0.00497540i
$482$		0			0
$483$	6.73527	−	1.07639i	0.306465	−	0.0489773i
$484$		0			0
$485$	3.28324			0.149084
$486$		0			0
$487$	2.79299			0.126562			0.0632811	−	0.997996i	$-0.479844\pi$
$487$	2.79299			0.126562			0.0632811	+	0.997996i	$0.479844\pi$
$488$		0			0
$489$	34.7058	−	5.54646i	1.56945	−	0.250820i
$490$		0			0
$491$	−13.0099	+	30.1602i	−0.587127	+	1.36111i	0.322849	+	0.946451i	$0.395359\pi$
$491$	−13.0099	+	30.1602i	−0.587127	+	1.36111i	−0.909975	+	0.414662i	$0.863900\pi$
$492$		0			0
$493$	−1.00747	−	17.2977i	−0.0453744	−	0.779048i
$494$		0			0
$495$	2.51082	+	2.24811i	0.112853	+	0.101045i
$496$		0			0
$497$	−6.47126	+	8.69241i	−0.290276	+	0.389908i
$498$		0			0
$499$	−22.4207	+	23.7646i	−1.00369	+	1.06385i	−0.00573037	+	0.999984i	$0.501824\pi$
$499$	−22.4207	+	23.7646i	−1.00369	+	1.06385i	−0.997959	+	0.0638645i	$0.979657\pi$
$500$		0			0
$501$	−2.29396	+	9.03019i	−0.102486	+	0.403439i
$502$		0			0
$503$	−3.02284	+	17.1434i	−0.134782	+	0.764384i	0.840230	+	0.542230i	$0.182420\pi$
$503$	−3.02284	+	17.1434i	−0.134782	+	0.764384i	−0.975012	+	0.222154i	$0.928691\pi$
$504$		0			0
$505$	0.420589	+	2.38528i	0.0187160	+	0.106143i
$506$		0			0
$507$	−4.83022	−	21.9450i	−0.214518	−	0.974613i
$508$		0			0
$509$	−1.94524	+	33.3985i	−0.0862212	+	1.48036i	0.626779	+	0.779197i	$0.284373\pi$
$509$	−1.94524	+	33.3985i	−0.0862212	+	1.48036i	−0.713000	+	0.701164i	$0.752664\pi$
$510$		0			0
$511$	−1.39122	−	1.47461i	−0.0615441	−	0.0652330i
$512$		0			0
$513$	−15.6271	−	20.5584i	−0.689952	−	0.907675i
$514$		0			0
$515$	−3.59974	+	0.853153i	−0.158623	+	0.0375944i
$516$		0			0
$517$	17.2718	−	8.67423i	0.759613	−	0.381492i
$518$		0			0
$519$	17.0650	−	32.6606i	0.749069	−	1.43364i
$520$		0			0
$521$	1.53032	+	0.556990i	0.0670444	+	0.0244022i	0.375325	−	0.926893i	$-0.377531\pi$
$521$	1.53032	+	0.556990i	0.0670444	+	0.0244022i	−0.308280	+	0.951296i	$0.599753\pi$
$522$		0			0
$523$	35.7374	−	13.0073i	1.56269	−	0.568771i	0.591336	−	0.806425i	$-0.298601\pi$
$523$	35.7374	−	13.0073i	1.56269	−	0.568771i	0.971350	+	0.237654i	$0.0763783\pi$
$524$		0			0
$525$	5.34073	−	7.84289i	0.233089	−	0.342292i
$526$		0			0
$527$	2.82141	+	9.42418i	0.122903	+	0.410524i
$528$		0			0
$529$	10.3491	+	1.20964i	0.449962	+	0.0525930i
$530$		0			0
$531$	−8.64272	−	6.09081i	−0.375062	−	0.264318i
$532$		0			0
$533$	1.16625	+	0.585712i	0.0505158	+	0.0253700i
$534$		0			0
$535$	0.710735	−	0.0830730i	0.0307277	−	0.00359156i
$536$		0			0
$537$	0.212372	−	13.2230i	0.00916452	−	0.570614i
$538$		0			0
$539$	−12.6332	+	21.8813i	−0.544149	+	0.942493i
$540$		0			0
$541$	−17.1456	−	29.6971i	−0.737147	−	1.27678i	−0.953775	−	0.300522i	$-0.902839\pi$
$541$	−17.1456	−	29.6971i	−0.737147	−	1.27678i	0.216627	−	0.976254i	$-0.430494\pi$
$542$		0			0
$543$	−0.0238821	−	0.0690458i	−0.00102488	−	0.00296304i
$544$		0			0
$545$	2.83607	+	3.80950i	0.121484	+	0.163181i
$546$		0			0
$547$	−24.1693	+	15.8964i	−1.03341	+	0.679682i	−0.948523	−	0.316709i	$-0.897422\pi$
$547$	−24.1693	+	15.8964i	−1.03341	+	0.679682i	−0.0848838	+	0.996391i	$0.527052\pi$
$548$		0			0
$549$	27.4042	−	34.4433i	1.16958	−	1.47000i
$550$		0			0
$551$	−8.75884	−	20.3053i	−0.373139	−	0.865034i
$552$		0			0
$553$	8.84310	+	2.09585i	0.376047	+	0.0891247i
$554$		0			0
$555$	−0.0323077	−	0.321043i	−0.00137138	−	0.0136275i
$556$		0			0
$557$	14.4591	+	12.1326i	0.612651	+	0.514075i	0.895484	−	0.445094i	$-0.146830\pi$
$557$	14.4591	+	12.1326i	0.612651	+	0.514075i	−0.282833	+	0.959169i	$0.591274\pi$
$558$		0			0
$559$	−0.361102	+	0.303001i	−0.0152730	+	0.0128156i
$560$		0			0
$561$	23.4143	+	18.0228i	0.988552	+	0.760925i
$562$		0			0
$563$	−4.55867	−	2.99828i	−0.192125	−	0.126363i	0.449802	−	0.893128i	$-0.351494\pi$
$563$	−4.55867	−	2.99828i	−0.192125	−	0.126363i	−0.641927	+	0.766766i	$0.721865\pi$
$564$		0			0
$565$	−0.661762	+	2.21044i	−0.0278406	+	0.0929939i
$566$		0			0
$567$	6.37642	+	7.69333i	0.267785	+	0.323089i
$568$		0			0
$569$	8.96143	−	29.9332i	0.375683	−	1.25487i	−0.536086	−	0.844163i	$-0.680098\pi$
$569$	8.96143	−	29.9332i	0.375683	−	1.25487i	0.911769	−	0.410704i	$-0.134717\pi$
$570$		0			0
$571$	36.0668	+	23.7215i	1.50935	+	0.992714i	0.990449	+	0.137878i	$0.0440281\pi$
$571$	36.0668	+	23.7215i	1.50935	+	0.992714i	0.518898	+	0.854836i	$0.326342\pi$
$572$		0			0
$573$	−42.0656	+	17.3495i	−1.75732	+	0.724787i
$574$		0			0
$575$	−13.4067	+	11.2496i	−0.559099	+	0.469139i
$576$		0			0
$577$	−21.1557	−	17.7518i	−0.880725	−	0.739016i	0.0856030	−	0.996329i	$-0.472718\pi$
$577$	−21.1557	−	17.7518i	−0.880725	−	0.739016i	−0.966328	+	0.257313i	$0.917163\pi$
$578$		0			0
$579$	11.5886	−	8.34155i	0.481607	−	0.346663i
$580$		0			0
$581$	−2.04884	−	0.485584i	−0.0850001	−	0.0201454i
$582$		0			0
$583$	−4.97856	−	11.5416i	−0.206191	−	0.478004i
$584$		0			0
$585$	0.0833729	+	0.0942589i	0.00344705	+	0.00389713i
$586$		0			0
$587$	14.4192	−	9.48365i	0.595144	−	0.391432i	−0.215902	−	0.976415i	$-0.569269\pi$
$587$	14.4192	−	9.48365i	0.595144	−	0.391432i	0.811046	+	0.584983i	$0.198899\pi$
$588$		0			0
$589$	7.49745	+	10.0708i	0.308927	+	0.414961i
$590$		0			0
$591$	−46.1115	−	8.89648i	−1.89677	−	0.365952i
$592$		0			0
$593$	−14.0107	−	24.2673i	−0.575352	−	0.996539i	−0.996003	−	0.0893165i	$-0.971532\pi$
$593$	−14.0107	−	24.2673i	−0.575352	−	0.996539i	0.420651	−	0.907222i	$-0.361802\pi$
$594$		0			0
$595$	−0.554309	+	0.960091i	−0.0227245	+	0.0393599i
$596$		0			0
$597$	9.45910	−	5.26051i	0.387135	−	0.215298i
$598$		0			0
$599$	−43.4131	+	5.07427i	−1.77381	+	0.207329i	−0.939168	−	0.343459i	$-0.888401\pi$
$599$	−43.4131	+	5.07427i	−1.77381	+	0.207329i	−0.834645	+	0.550788i	$0.814327\pi$
$600$		0			0
$601$	11.5276	+	5.78938i	0.470221	+	0.236154i	0.668098	−	0.744073i	$-0.267109\pi$
$601$	11.5276	+	5.78938i	0.470221	+	0.236154i	−0.197877	+	0.980227i	$0.563405\pi$
$602$		0			0
$603$	−32.3143	+	2.72850i	−1.31594	+	0.111113i
$604$		0			0
$605$	−2.08662	−	0.243890i	−0.0848330	−	0.00991555i
$606$		0			0
$607$	8.30773	+	27.7498i	0.337201	+	1.12633i	0.943578	+	0.331151i	$0.107437\pi$
$607$	8.30773	+	27.7498i	0.337201	+	1.12633i	−0.606377	+	0.795177i	$0.707378\pi$
$608$		0			0
$609$	3.71702	+	7.70737i	0.150621	+	0.312319i
$610$		0			0
$611$	0.678156	−	0.246829i	0.0274352	−	0.00998561i
$612$		0			0
$613$	−9.37562	−	3.41245i	−0.378678	−	0.137827i	0.145667	−	0.989334i	$-0.453467\pi$
$613$	−9.37562	−	3.41245i	−0.378678	−	0.137827i	−0.524344	+	0.851506i	$0.675690\pi$
$614$		0			0
$615$	3.54032	−	0.149200i	0.142759	−	0.00601633i
$616$		0			0
$617$	42.2946	−	21.2412i	1.70272	−	0.855137i	0.714956	−	0.699170i	$-0.246447\pi$
$617$	42.2946	−	21.2412i	1.70272	−	0.855137i	0.987762	−	0.155968i	$-0.0498496\pi$
$618$		0			0
$619$	0.748495	−	0.177397i	0.0300846	−	0.00713017i	−0.215546	−	0.976494i	$-0.569153\pi$
$619$	0.748495	−	0.177397i	0.0300846	−	0.00713017i	0.245631	+	0.969364i	$0.421005\pi$
$620$		0			0
$621$	−7.46867	−	16.8491i	−0.299708	−	0.676129i
$622$		0			0
$623$	5.09934	+	5.40499i	0.204301	+	0.216546i
$624$		0			0
$625$	−1.39652	+	23.9774i	−0.0558609	+	0.959094i
$626$		0			0
$627$	35.9478	+	11.3942i	1.43562	+	0.455040i
$628$		0			0
$629$	−0.491231	−	2.78591i	−0.0195867	−	0.111082i
$630$		0			0
$631$	1.29424	−	7.34001i	0.0515230	−	0.292201i	−0.948149	−	0.317827i	$-0.897047\pi$
$631$	1.29424	−	7.34001i	0.0515230	−	0.292201i	0.999672	+	0.0256260i	$0.00815790\pi$
$632$		0			0
$633$	17.0755	−	4.81468i	0.678691	−	0.191366i
$634$		0			0
$635$	1.95866	−	2.07605i	0.0777269	−	0.0823857i
$636$		0			0
$637$	−0.563374	+	0.756742i	−0.0223217	+	0.0299832i
$638$		0			0
$639$	27.1801	+	10.8934i	1.07523	+	0.430937i
$640$		0			0
$641$	0.212140	+	3.64229i	0.00837901	+	0.143862i	0.999903	+	0.0139373i	$0.00443652\pi$
$641$	0.212140	+	3.64229i	0.00837901	+	0.143862i	−0.991524	+	0.129925i	$0.958526\pi$
$642$		0			0
$643$	−0.626343	+	1.45203i	−0.0247006	+	0.0572623i	−0.930120	−	0.367256i	$-0.880297\pi$
$643$	−0.626343	+	1.45203i	−0.0247006	+	0.0572623i	0.905419	+	0.424518i	$0.139557\pi$
$644$		0			0
$645$	−0.457005	+	1.19552i	−0.0179945	+	0.0470734i
$646$		0			0
$647$	−46.1899			−1.81591			−0.907956	−	0.419066i	$-0.862358\pi$
$647$	−46.1899			−1.81591			−0.907956	+	0.419066i	$0.862358\pi$
$648$		0			0
$649$	15.4403			0.606085
$650$		0			0
$651$	−3.06261	−	3.77125i	−0.120033	−	0.147807i
$652$		0			0
$653$	9.49766	−	22.0180i	0.371672	−	0.861633i	−0.625039	−	0.780594i	$-0.714917\pi$
$653$	9.49766	−	22.0180i	0.371672	−	0.861633i	0.996711	−	0.0810390i	$-0.0258238\pi$
$654$		0			0
$655$	−0.318691	−	5.47171i	−0.0124523	−	0.213797i
$656$		0			0
$657$	−2.88991	+	4.65364i	−0.112746	+	0.181556i
$658$		0			0
$659$	0.541245	−	0.727018i	0.0210839	−	0.0283206i	−0.791456	−	0.611226i	$-0.790677\pi$
$659$	0.541245	−	0.727018i	0.0210839	−	0.0283206i	0.812540	+	0.582905i	$0.198084\pi$
$660$		0			0
$661$	27.6434	−	29.3003i	1.07520	−	1.13965i	0.0855263	−	0.996336i	$-0.472743\pi$
$661$	27.6434	−	29.3003i	1.07520	−	1.13965i	0.989677	−	0.143313i	$-0.0457757\pi$
$662$		0			0
$663$	0.790233	+	0.769904i	0.0306901	+	0.0299006i
$664$		0			0
$665$	−0.245693	+	1.39339i	−0.00952757	+	0.0540335i
$666$		0			0
$667$	−2.74062	−	15.5428i	−0.106117	−	0.601821i
$668$		0			0
$669$	−20.3920	+	18.6290i	−0.788398	+	0.720240i
$670$		0			0
$671$	−3.73731	+	64.1671i	−0.144277	+	2.47714i
$672$		0			0
$673$	−27.8513	−	29.5206i	−1.07359	−	1.13794i	−0.989947	−	0.141441i	$-0.954826\pi$
$673$	−27.8513	−	29.5206i	−1.07359	−	1.13794i	−0.0836419	−	0.996496i	$-0.526655\pi$
$674$		0			0
$675$	−24.1793	−	8.52774i	−0.930663	−	0.328233i
$676$		0			0
$677$	38.0410	−	9.01587i	1.46203	−	0.346508i	0.578810	−	0.815462i	$-0.303517\pi$
$677$	38.0410	−	9.01587i	1.46203	−	0.346508i	0.883222	+	0.468954i	$0.155369\pi$
$678$		0			0
$679$	−12.7033	+	6.37986i	−0.487510	+	0.244836i
$680$		0			0
$681$	0.399402	+	0.629036i	0.0153051	+	0.0241047i
$682$		0			0
$683$	3.73261	+	1.35856i	0.142824	+	0.0519838i	0.412443	−	0.910983i	$-0.364676\pi$
$683$	3.73261	+	1.35856i	0.142824	+	0.0519838i	−0.269619	+	0.962967i	$0.586898\pi$
$684$		0			0
$685$	0.674481	−	0.245491i	0.0257706	−	0.00937973i
$686$		0			0
$687$	11.8122	+	0.878515i	0.450662	+	0.0335174i
$688$		0			0
$689$	−0.134608	−	0.449621i	−0.00512814	−	0.0171292i
$690$		0			0
$691$	−12.5915	−	1.47174i	−0.479003	−	0.0559875i	−0.126834	−	0.991924i	$-0.540482\pi$
$691$	−12.5915	−	1.47174i	−0.479003	−	0.0559875i	−0.352169	+	0.935936i	$0.614556\pi$
$692$		0			0
$693$	−14.0832	−	3.81934i	−0.534975	−	0.145085i
$694$		0			0
$695$	1.02479	+	0.514668i	0.0388724	+	0.0195225i
$696$		0			0
$697$	30.8565	−	3.60660i	1.16877	−	0.136610i
$698$		0			0
$699$	−17.6299	−	10.5597i	−0.666823	−	0.399404i
$700$		0			0
$701$	10.9161	−	18.9072i	0.412295	−	0.714116i	−0.582845	−	0.812583i	$-0.698061\pi$
$701$	10.9161	−	18.9072i	0.412295	−	0.714116i	0.995140	+	0.0984671i	$0.0313939\pi$
$702$		0			0
$703$	−1.80521	−	3.12671i	−0.0680846	−	0.117926i
$704$		0			0
$705$	1.28347	−	1.48062i	0.0483382	−	0.0557635i
$706$		0			0
$707$	−6.26229	−	8.41172i	−0.235518	−	0.316355i
$708$		0			0
$709$	0.0836438	−	0.0550134i	0.00314131	−	0.00206607i	−0.547937	−	0.836519i	$-0.684587\pi$
$709$	0.0836438	−	0.0550134i	0.00314131	−	0.00206607i	0.551079	+	0.834453i	$0.314216\pi$
$710$		0			0
$711$	−0.639846	−	24.5484i	−0.0239961	−	0.920635i
$712$		0			0
$713$	3.54912	+	8.22779i	0.132916	+	0.308133i
$714$		0			0
$715$	−0.178813	−	0.0423794i	−0.00668722	−	0.00158490i
$716$		0			0
$717$	−16.8201	−	7.57814i	−0.628159	−	0.283011i
$718$		0			0
$719$	−26.8168	−	22.5019i	−1.00010	−	0.839180i	−0.0130985	−	0.999914i	$-0.504169\pi$
$719$	−26.8168	−	22.5019i	−1.00010	−	0.839180i	−0.986998	+	0.160734i	$0.948614\pi$
$720$		0			0
$721$	12.2701	−	10.2958i	0.456962	−	0.383437i
$722$		0			0
$723$	−0.865766	+	6.50003i	−0.0321982	+	0.241739i
$724$		0			0
$725$	−18.3439	−	12.0650i	−0.681275	−	0.448082i
$726$		0			0
$727$	−5.50176	+	18.3772i	−0.204049	+	0.681571i	0.793302	+	0.608829i	$0.208360\pi$
$727$	−5.50176	+	18.3772i	−0.204049	+	0.681571i	−0.997351	+	0.0727425i	$0.976825\pi$
$728$		0			0
$729$	15.6870	−	21.9754i	0.580999	−	0.813904i
$730$		0			0
$731$	−3.21825	+	10.7497i	−0.119031	+	0.397593i
$732$		0			0
$733$	−34.6638	−	22.7987i	−1.28033	−	0.842090i	−0.287065	−	0.957911i	$-0.592680\pi$
$733$	−34.6638	−	22.7987i	−1.28033	−	0.842090i	−0.993270	+	0.115822i	$0.963050\pi$
$734$		0			0
$735$	−0.338196	+	2.53912i	−0.0124746	+	0.0936570i
$736$		0			0
$737$	36.2775	−	30.4405i	1.33630	−	1.12129i
$738$		0			0
$739$	18.9744	+	15.9214i	0.697983	+	0.585677i	0.921199	−	0.389092i	$-0.127211\pi$
$739$	18.9744	+	15.9214i	0.697983	+	0.585677i	−0.223216	+	0.974769i	$0.571656\pi$
$740$		0			0
$741$	1.28379	+	0.578400i	0.0471613	+	0.0212481i
$742$		0			0
$743$	19.1931	+	4.54884i	0.704125	+	0.166881i	0.567054	−	0.823681i	$-0.308083\pi$
$743$	19.1931	+	4.54884i	0.704125	+	0.166881i	0.137071	+	0.990561i	$0.456231\pi$
$744$		0			0
$745$	−1.57271	−	3.64596i	−0.0576197	−	0.133577i
$746$		0			0
$747$	0.148244	+	5.68756i	0.00542398	+	0.208097i
$748$		0			0
$749$	−2.58851	+	1.70249i	−0.0945822	+	0.0622077i
$750$		0			0
$751$	−23.3182	−	31.3218i	−0.850894	−	1.14295i	−0.988313	−	0.152436i	$-0.951288\pi$
$751$	−23.3182	−	31.3218i	−0.850894	−	1.14295i	0.137419	−	0.990513i	$-0.456119\pi$
$752$		0			0
$753$	−21.4265	+	24.7179i	−0.780826	+	0.900770i
$754$		0			0
$755$	−0.728861	−	1.26243i	−0.0265260	−	0.0459444i
$756$		0			0
$757$	14.4054	−	24.9509i	0.523574	−	0.906857i	−0.476049	−	0.879419i	$-0.657932\pi$
$757$	14.4054	−	24.9509i	0.523574	−	0.906857i	0.999623	−	0.0274384i	$-0.00873501\pi$
$758$		0			0
$759$	23.0889	+	13.8295i	0.838076	+	0.501978i
$760$		0			0
$761$	−2.66068	+	0.310989i	−0.0964495	+	0.0112733i	−0.164181	−	0.986430i	$-0.552498\pi$
$761$	−2.66068	+	0.310989i	−0.0964495	+	0.0112733i	0.0677313	+	0.997704i	$0.478424\pi$
$762$		0			0
$763$	−18.3756	−	9.22859i	−0.665242	−	0.334097i
$764$		0			0
$765$	2.89114	+	0.784076i	0.104529	+	0.0283483i
$766$		0			0
$767$	0.572630	+	0.0669309i	0.0206765	+	0.00241673i
$768$		0			0
$769$	−2.32359	−	7.76133i	−0.0837908	−	0.279881i	0.905818	−	0.423667i	$-0.139257\pi$
$769$	−2.32359	−	7.76133i	−0.0837908	−	0.279881i	−0.989609	+	0.143786i	$0.954072\pi$
$770$		0			0
$771$	34.4995	+	2.56586i	1.24247	+	0.0924071i
$772$		0			0
$773$	18.3195	−	6.66776i	0.658908	−	0.239823i	0.00914295	−	0.999958i	$-0.497090\pi$
$773$	18.3195	−	6.66776i	0.658908	−	0.239823i	0.649765	+	0.760135i	$0.274867\pi$
$774$		0			0
$775$	11.7138	+	4.26347i	0.420771	+	0.153148i
$776$		0			0
$777$	0.748840	+	1.17938i	0.0268645	+	0.0423101i
$778$		0			0
$779$	35.4317	−	17.7945i	1.26947	−	0.637554i
$780$		0			0
$781$	−41.6079	+	9.86126i	−1.48885	+	0.352864i
$782$		0			0
$783$	17.5625	−	15.0385i	0.627631	−	0.537431i
$784$		0			0
$785$	−2.57236	−	2.72654i	−0.0918114	−	0.0973144i
$786$		0			0
$787$	−0.692188	+	11.8844i	−0.0246738	+	0.423633i	0.963241	+	0.268638i	$0.0865734\pi$
$787$	−0.692188	+	11.8844i	−0.0246738	+	0.423633i	−0.987915	+	0.154996i	$0.950464\pi$
$788$		0			0
$789$	−24.2766	+	22.1779i	−0.864270	+	0.789553i
$790$		0			0
$791$	−1.73478	−	9.83842i	−0.0616817	−	0.349814i
$792$		0			0
$793$	−0.416757	+	2.36355i	−0.0147995	+	0.0839320i
$794$		0			0
$795$	−0.912750	−	0.889269i	−0.0323719	−	0.0315391i
$796$		0			0
$797$	4.97388	−	5.27200i	0.176184	−	0.186744i	−0.633264	−	0.773936i	$-0.718285\pi$
$797$	4.97388	−	5.27200i	0.176184	−	0.186744i	0.809448	+	0.587192i	$0.199767\pi$
$798$		0			0
$799$	10.2587	−	13.7799i	0.362928	−	0.487497i
$800$		0			0
$801$	10.5926	−	17.0573i	0.374270	−	0.602690i
$802$		0			0
$803$	−0.465131	−	7.98599i	−0.0164141	−	0.281820i
$804$		0			0
$805$	−0.399963	+	0.927219i	−0.0140969	+	0.0326802i
$806$		0			0
$807$	13.6035	+	16.7512i	0.478867	+	0.589669i
$808$		0			0
$809$	−22.0334			−0.774654			−0.387327	−	0.921942i	$-0.626602\pi$
$809$	−22.0334			−0.774654			−0.387327	+	0.921942i	$0.626602\pi$
$810$		0			0
$811$	−33.9166			−1.19097			−0.595486	−	0.803365i	$-0.703041\pi$
$811$	−33.9166			−1.19097			−0.595486	+	0.803365i	$0.703041\pi$
$812$		0			0
$813$	−0.543878	+	1.42278i	−0.0190746	+	0.0498989i
$814$		0			0
$815$	−2.06095	+	4.77782i	−0.0721919	+	0.167360i
$816$		0			0
$817$	0.832699	+	14.2969i	0.0291325	+	0.500185i
$818$		0			0
$819$	−0.505742	−	0.202695i	−0.0176721	−	0.00708273i
$820$		0			0
$821$	22.3580	−	30.0320i	0.780299	−	1.04812i	−0.217107	−	0.976148i	$-0.569662\pi$
$821$	22.3580	−	30.0320i	0.780299	−	1.04812i	0.997406	−	0.0719757i	$-0.0229304\pi$
$822$		0			0
$823$	−17.0015	+	18.0206i	−0.592636	+	0.628157i	−0.952387	−	0.304891i	$-0.901380\pi$
$823$	−17.0015	+	18.0206i	−0.592636	+	0.628157i	0.359751	+	0.933048i	$0.382862\pi$
$824$		0			0
$825$	36.0360	−	10.1608i	1.25461	−	0.353755i
$826$		0			0
$827$	6.86252	−	38.9193i	0.238633	−	1.35336i	−0.596192	−	0.802842i	$-0.703320\pi$
$827$	6.86252	−	38.9193i	0.238633	−	1.35336i	0.834825	−	0.550515i	$-0.185569\pi$
$828$		0			0
$829$	−3.16118	−	17.9280i	−0.109792	−	0.622664i	−0.989197	−	0.146589i	$-0.953170\pi$
$829$	−3.16118	−	17.9280i	−0.109792	−	0.622664i	0.879405	−	0.476074i	$-0.157941\pi$
$830$		0			0
$831$	−21.9372	−	6.95334i	−0.760994	−	0.241209i
$832$		0			0
$833$	−1.30581	+	22.4198i	−0.0452435	+	0.776800i
$834$		0			0
$835$	−0.946584	−	1.00332i	−0.0327579	−	0.0347214i
$836$		0			0
$837$	−7.73335	+	10.6075i	−0.267304	+	0.366649i
$838$		0			0
$839$	3.91312	−	0.927427i	0.135096	−	0.0320184i	−0.162512	−	0.986707i	$-0.551959\pi$
$839$	3.91312	−	0.927427i	0.135096	−	0.0320184i	0.297608	+	0.954688i	$0.403811\pi$
$840$		0			0
$841$	−8.22156	+	4.12902i	−0.283502	+	0.142380i
$842$		0			0
$843$	10.0365	−	0.422969i	0.345675	−	0.0145678i
$844$		0			0
$845$	3.12609	+	1.13780i	0.107541	+	0.0391416i
$846$		0			0
$847$	8.54734	−	3.11098i	0.293690	−	0.106894i
$848$		0			0
$849$	5.29313	+	10.9755i	0.181660	+	0.376678i
$850$		0			0
$851$	−0.739018	−	2.46849i	−0.0253332	−	0.0846189i
$852$		0			0
$853$	−13.5263	−	1.58100i	−0.463132	−	0.0541324i	−0.118673	−	0.992933i	$-0.537864\pi$
$853$	−13.5263	−	1.58100i	−0.463132	−	0.0541324i	−0.344460	+	0.938801i	$0.611938\pi$
$854$		0			0
$855$	3.80959	−	0.321668i	0.130285	−	0.0110008i
$856$		0			0
$857$	23.6796	+	11.8924i	0.808881	+	0.406235i	0.804645	−	0.593756i	$-0.202355\pi$
$857$	23.6796	+	11.8924i	0.808881	+	0.406235i	0.00423566	+	0.999991i	$0.498652\pi$
$858$		0			0
$859$	10.9611	−	1.28117i	0.373987	−	0.0437128i	0.0729765	−	0.997334i	$-0.476750\pi$
$859$	10.9611	−	1.28117i	0.373987	−	0.0437128i	0.301010	+	0.953621i	$0.402676\pi$
$860$		0			0
$861$	−13.4081	+	7.45668i	−0.456947	+	0.254123i
$862$		0			0
$863$	−10.9478	+	18.9621i	−0.372667	+	0.645477i	−0.989975	−	0.141244i	$-0.954890\pi$
$863$	−10.9478	+	18.9621i	−0.372667	+	0.645477i	0.617308	+	0.786721i	$0.288223\pi$
$864$		0			0
$865$	2.72781	+	4.72471i	0.0927485	+	0.160645i
$866$		0			0
$867$	−3.12420	−	0.602766i	−0.106104	−	0.0204710i
$868$		0			0
$869$	21.4144	+	28.7645i	0.726433	+	0.975768i
$870$		0			0
$871$	1.47737	−	0.971680i	0.0500587	−	0.0329241i
$872$		0			0
$873$	25.4485	+	28.7713i	0.861302	+	0.973762i
$874$		0			0
$875$	1.12023	+	2.59699i	0.0378707	+	0.0877941i
$876$		0			0
$877$	−11.5896	−	2.74678i	−0.391352	−	0.0927522i	0.0302285	−	0.999543i	$-0.490376\pi$
$877$	−11.5896	−	2.74678i	−0.391352	−	0.0927522i	−0.421581	+	0.906791i	$0.638525\pi$
$878$		0			0
$879$	−26.6472	+	19.1808i	−0.898789	+	0.646953i
$880$		0			0
$881$	3.05584	+	2.56415i	0.102954	+	0.0863885i	0.692812	−	0.721119i	$-0.256372\pi$
$881$	3.05584	+	2.56415i	0.102954	+	0.0863885i	−0.589858	+	0.807507i	$0.700816\pi$
$882$		0			0
$883$	8.66860	−	7.27382i	0.291722	−	0.244783i	−0.485167	−	0.874421i	$-0.661241\pi$
$883$	8.66860	−	7.27382i	0.291722	−	0.244783i	0.776889	+	0.629638i	$0.216797\pi$
$884$		0			0
$885$	1.44712	−	0.596849i	0.0486443	−	0.0200628i
$886$		0			0
$887$	−19.9234	−	13.1038i	−0.668962	−	0.439983i	0.169070	−	0.985604i	$-0.445923\pi$
$887$	−19.9234	−	13.1038i	−0.668962	−	0.439983i	−0.838032	+	0.545621i	$0.816294\pi$
$888$		0			0
$889$	−3.54422	+	11.8385i	−0.118869	+	0.397052i
$890$		0			0
$891$	−0.238936	+	39.4277i	−0.00800467	+	1.32088i
$892$		0			0
$893$	6.28824	−	21.0042i	0.210428	−	0.702878i
$894$		0			0
$895$	1.63581	+	1.07589i	0.0546790	+	0.0359629i
$896$		0			0
$897$	0.796345	+	0.612976i	0.0265892	+	0.0204667i
$898$		0			0
$899$	−8.61143	+	7.22585i	−0.287207	+	0.240996i
$900$		0			0
$901$	−8.55855	−	7.18147i	−0.285127	−	0.239250i
$902$		0			0
$903$	−0.554859	−	5.51366i	−0.0184645	−	0.183483i
$904$		0			0
$905$	0.0105248	+	0.00249443i	0.000349857	+	8.29176e-5i
$906$		0			0
$907$	−5.23639	−	12.1393i	−0.173872	−	0.403080i	0.808889	−	0.587961i	$-0.200069\pi$
$907$	−5.23639	−	12.1393i	−0.173872	−	0.403080i	−0.982761	+	0.184881i	$0.940810\pi$
$908$		0			0
$909$	−17.6424	+	22.1740i	−0.585162	+	0.735466i
$910$		0			0
$911$	5.81470	−	3.82439i	0.192650	−	0.126708i	−0.449520	−	0.893270i	$-0.648405\pi$
$911$	5.81470	−	3.82439i	0.192650	−	0.126708i	0.642169	+	0.766563i	$0.278035\pi$
$912$		0			0
$913$	−4.96145	−	6.66438i	−0.164200	−	0.220559i
$914$		0			0
$915$	2.13012	+	6.15842i	0.0704196	+	0.203591i
$916$		0			0
$917$	11.8654	+	20.5516i	0.391832	+	0.678672i
$918$		0			0
$919$	−13.3747	+	23.1657i	−0.441191	+	0.764165i	−0.997778	−	0.0666241i	$-0.978777\pi$
$919$	−13.3747	+	23.1657i	−0.441191	+	0.764165i	0.556587	+	0.830789i	$0.312110\pi$
$920$		0			0
$921$	−0.817220	+	50.8829i	−0.0269283	+	1.67665i
$922$		0			0
$923$	−1.58585	+	0.185359i	−0.0521988	+	0.00610117i
$924$		0			0
$925$	−3.20334	−	1.60878i	−0.105325	−	0.0528963i
$926$		0			0
$927$	−35.3779	−	24.9320i	−1.16196	−	0.818874i
$928$		0			0
$929$	−30.8542	−	3.60634i	−1.01229	−	0.118320i	−0.406258	−	0.913758i	$-0.633167\pi$
$929$	−30.8542	−	3.60634i	−1.01229	−	0.118320i	−0.606035	+	0.795438i	$0.707241\pi$
$930$		0			0
$931$	8.22038	+	27.4580i	0.269412	+	0.899899i
$932$		0			0
$933$	−31.6306	+	46.4498i	−1.03554	+	1.52070i
$934$		0			0
$935$	−4.11066	+	1.49616i	−0.134433	+	0.0489296i
$936$		0			0
$937$	−35.4347	−	12.8972i	−1.15760	−	0.421332i	−0.309361	−	0.950945i	$-0.600115\pi$
$937$	−35.4347	−	12.8972i	−1.15760	−	0.421332i	−0.848240	+	0.529612i	$0.822337\pi$
$938$		0			0
$939$	24.1596	−	46.2389i	0.788418	−	1.50895i
$940$		0			0
$941$	10.3910	−	5.21854i	0.338736	−	0.170119i	−0.271297	−	0.962496i	$-0.587453\pi$
$941$	10.3910	−	5.21854i	0.338736	−	0.170119i	0.610033	+	0.792376i	$0.291156\pi$
$942$		0			0
$943$	27.5347	−	6.52585i	0.896654	−	0.212511i
$944$		0			0
$945$	−1.46756	+	0.186426i	−0.0477397	+	0.00606444i
$946$		0			0
$947$	7.36355	+	7.80490i	0.239283	+	0.253625i	0.835875	−	0.548919i	$-0.184961\pi$
$947$	7.36355	+	7.80490i	0.239283	+	0.253625i	−0.596592	+	0.802544i	$0.703479\pi$
$948$		0			0
$949$	0.0173676	−	0.298190i	0.000563777	−	0.00967967i
$950$		0			0
$951$	6.61777	+	30.0663i	0.214596	+	0.974967i
$952$		0			0
$953$	2.54335	+	14.4240i	0.0823871	+	0.467241i	0.997890	+	0.0649290i	$0.0206821\pi$
$953$	2.54335	+	14.4240i	0.0823871	+	0.467241i	−0.915503	+	0.402312i	$0.868207\pi$
$954$		0			0
$955$	1.16981	−	6.63434i	0.0378543	−	0.214682i
$956$		0			0
$957$	−8.31319	+	32.7250i	−0.268727	+	1.05785i
$958$		0			0
$959$	−2.13264	+	2.26046i	−0.0688664	+	0.0729942i
$960$		0			0
$961$	−14.7006	+	19.7464i	−0.474214	+	0.636980i
$962$		0			0
$963$	6.23690	+	5.58433i	0.200981	+	0.179953i
$964$		0			0
$965$	0.122914	+	2.11036i	0.00395675	+	0.0679347i
$966$		0			0
$967$	−5.12115	+	11.8722i	−0.164685	+	0.381783i	−0.980497	−	0.196534i	$-0.937031\pi$
$967$	−5.12115	+	11.8722i	−0.164685	+	0.381783i	0.815812	+	0.578318i	$0.196291\pi$
$968$		0			0
$969$	33.0986	−	5.28960i	1.06328	−	0.169927i
$970$		0			0
$971$	42.6173			1.36765			0.683827	−	0.729644i	$-0.260314\pi$
$971$	42.6173			1.36765			0.683827	+	0.729644i	$0.260314\pi$
$972$		0			0
$973$	−4.96514			−0.159175
$974$		0			0
$975$	1.38050	−	0.220623i	0.0442114	−	0.00706559i
$976$		0			0
$977$	12.8704	−	29.8369i	0.411760	−	0.954567i	−0.578544	−	0.815651i	$-0.696379\pi$
$977$	12.8704	−	29.8369i	0.411760	−	0.954567i	0.990304	−	0.138916i	$-0.0443618\pi$
$978$		0			0
$979$	1.70487	+	29.2716i	0.0544880	+	0.935523i
$980$		0			0
$981$	−11.4005	+	54.3803i	−0.363991	+	1.73623i
$982$		0			0
$983$	13.9767	−	18.7740i	0.445789	−	0.598799i	−0.521257	−	0.853400i	$-0.674537\pi$
$983$	13.9767	−	18.7740i	0.445789	−	0.598799i	0.967046	+	0.254601i	$0.0819442\pi$
$984$		0			0
$985$	4.77121	−	5.05718i	0.152023	−	0.161135i
$986$		0			0
$987$	−2.08884	+	8.22273i	−0.0664884	+	0.261732i
$988$		0			0
$989$	−1.77485	+	10.0657i	−0.0564370	+	0.320070i
$990$		0			0
$991$	6.15676	+	34.9167i	0.195576	+	1.10917i	0.911596	+	0.411087i	$0.134851\pi$
$991$	6.15676	+	34.9167i	0.195576	+	1.10917i	−0.716020	+	0.698080i	$0.754038\pi$
$992$		0			0
$993$	10.5550	+	47.9542i	0.334953	+	1.52178i
$994$		0			0
$995$	−0.0931717	+	1.59970i	−0.00295374	+	0.0507138i
$996$		0			0
$997$	−8.13233	−	8.61976i	−0.257553	−	0.272991i	0.585675	−	0.810546i	$-0.300829\pi$
$997$	−8.13233	−	8.61976i	−0.257553	−	0.272991i	−0.843229	+	0.537555i	$0.819348\pi$
$998$		0			0
$999$	2.56291	−	2.77153i	0.0810868	−	0.0876873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.m.a.49.1	✓	162
3.2	odd	2		972.2.m.a.37.6		162
81.38	odd	54		972.2.m.a.289.6		162
81.43	even	27	inner	324.2.m.a.205.1	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.m.a.49.1	✓	162	1.1	even	1	trivial
324.2.m.a.205.1	yes	162	81.43	even	27	inner
972.2.m.a.37.6		162	3.2	odd	2
972.2.m.a.289.6		162	81.38	odd	54

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.m (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71035 + 0.273337i) q^{3} +(0.101566 - 0.235457i) q^{5} +(0.0645556 + 1.10838i) q^{7} +(2.85057 - 0.935001i) q^{9} +O(q^{10})\)	\(q+(-1.71035 + 0.273337i) q^{3} +(0.101566 - 0.235457i) q^{5} +(0.0645556 + 1.10838i) q^{7} +(2.85057 - 0.935001i) q^{9} +(-2.61611 + 3.51405i) q^{11} +(-0.112256 + 0.118984i) q^{13} +(-0.109355 + 0.430475i) q^{15} +(-0.676180 + 3.83481i) q^{17} +(0.862985 + 4.89423i) q^{19} +(-0.413373 - 1.87806i) q^{21} +(-0.206233 + 3.54089i) q^{23} +(3.38608 + 3.58904i) q^{25} +(-4.61990 + 2.37834i) q^{27} +(-4.32976 + 1.02617i) q^{29} +(2.25761 - 1.13382i) q^{31} +(3.51394 - 6.72533i) q^{33} +(0.267532 + 0.0973736i) q^{35} +(-0.682668 + 0.248471i) q^{37} +(0.159474 - 0.234188i) q^{39} +(-2.28815 - 7.64295i) q^{41} +(2.86218 + 0.334541i) q^{43} +(0.0693695 - 0.766152i) q^{45} +(-3.94249 - 1.97999i) q^{47} +(5.72834 - 0.669546i) q^{49} +(0.108309 - 6.74368i) q^{51} +(-1.43458 + 2.48476i) q^{53} +(0.561699 + 0.972892i) q^{55} +(-2.81378 - 8.13495i) q^{57} +(-2.10464 - 2.82703i) q^{59} +(12.2580 - 8.06224i) q^{61} +(1.22035 + 3.09915i) q^{63} +(0.0166143 + 0.0385162i) q^{65} +(-10.5184 - 2.49291i) q^{67} +(-0.615124 - 6.11252i) q^{69} +(7.47705 + 6.27399i) q^{71} +(-1.39879 + 1.17372i) q^{73} +(-6.77239 - 5.21296i) q^{75} +(-4.06378 - 2.67279i) q^{77} +(2.34765 - 7.84168i) q^{79} +(7.25155 - 5.33058i) q^{81} +(-0.543921 + 1.81682i) q^{83} +(0.834256 + 0.548699i) q^{85} +(7.12490 - 2.93859i) q^{87} +(5.12706 - 4.30211i) q^{89} +(-0.139126 - 0.116741i) q^{91} +(-3.55139 + 2.55631i) q^{93} +(1.24003 + 0.293893i) q^{95} +(5.07129 + 11.7566i) q^{97} +(-4.17178 + 12.4631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q+O(q^{10}) \) 162 * q	\( 162 q + 27 q^{21} + 27 q^{23} + 27 q^{27} + 27 q^{29} + 27 q^{33} + 27 q^{35} - 18 q^{41} - 54 q^{45} - 54 q^{47} - 63 q^{51} - 54 q^{53} - 54 q^{57} - 63 q^{59} - 54 q^{63} - 90 q^{65} + 27 q^{67} - 90 q^{69} - 72 q^{71} - 90 q^{75} - 144 q^{77} + 54 q^{79} - 72 q^{81} - 72 q^{83} + 54 q^{85} - 144 q^{87} - 99 q^{89} - 90 q^{93} - 126 q^{95} + 27 q^{97} - 90 q^{99}+O(q^{100}) \) 162 * q + 27 * q^21 + 27 * q^23 + 27 * q^27 + 27 * q^29 + 27 * q^33 + 27 * q^35 - 18 * q^41 - 54 * q^45 - 54 * q^47 - 63 * q^51 - 54 * q^53 - 54 * q^57 - 63 * q^59 - 54 * q^63 - 90 * q^65 + 27 * q^67 - 90 * q^69 - 72 * q^71 - 90 * q^75 - 144 * q^77 + 54 * q^79 - 72 * q^81 - 72 * q^83 + 54 * q^85 - 144 * q^87 - 99 * q^89 - 90 * q^93 - 126 * q^95 + 27 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more