LMFDB - Embedded newform 972.2.m.a.289.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [972,2,Mod(37,972)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(972, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("972.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.m (of order $27$, degree $18$, not 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:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$9$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 324)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			289.6
Character	$\chi$	$=$	972.289
Dual form			972.2.m.a.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.101566 - 0.235457i) q^{5} +(0.0645556 - 1.10838i) q^{7} +O(q^{10})$	$q+(-0.101566 - 0.235457i) q^{5} +(0.0645556 - 1.10838i) q^{7} +(2.61611 + 3.51405i) q^{11} +(-0.112256 - 0.118984i) q^{13} +(0.676180 + 3.83481i) q^{17} +(0.862985 - 4.89423i) q^{19} +(0.206233 + 3.54089i) q^{23} +(3.38608 - 3.58904i) q^{25} +(4.32976 + 1.02617i) q^{29} +(2.25761 + 1.13382i) q^{31} +(-0.267532 + 0.0973736i) q^{35} +(-0.682668 - 0.248471i) q^{37} +(2.28815 - 7.64295i) q^{41} +(2.86218 - 0.334541i) q^{43} +(3.94249 - 1.97999i) q^{47} +(5.72834 + 0.669546i) q^{49} +(1.43458 + 2.48476i) q^{53} +(0.561699 - 0.972892i) q^{55} +(2.10464 - 2.82703i) q^{59} +(12.2580 + 8.06224i) q^{61} +(-0.0166143 + 0.0385162i) q^{65} +(-10.5184 + 2.49291i) q^{67} +(-7.47705 + 6.27399i) q^{71} +(-1.39879 - 1.17372i) q^{73} +(4.06378 - 2.67279i) q^{77} +(2.34765 + 7.84168i) q^{79} +(0.543921 + 1.81682i) q^{83} +(0.834256 - 0.548699i) q^{85} +(-5.12706 - 4.30211i) q^{89} +(-0.139126 + 0.116741i) q^{91} +(-1.24003 + 0.293893i) q^{95} +(5.07129 - 11.7566i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q+O(q^{10}) $ 162 * q	$ 162 q - 27 q^{23} - 27 q^{29} - 27 q^{35} + 18 q^{41} + 54 q^{47} + 54 q^{53} + 63 q^{59} + 90 q^{65} + 27 q^{67} + 72 q^{71} + 144 q^{77} + 54 q^{79} + 72 q^{83} + 54 q^{85} + 99 q^{89} + 126 q^{95} + 27 q^{97}+O(q^{100}) $ 162 * q - 27 * q^23 - 27 * q^29 - 27 * q^35 + 18 * q^41 + 54 * q^47 + 54 * q^53 + 63 * q^59 + 90 * q^65 + 27 * q^67 + 72 * q^71 + 144 * q^77 + 54 * q^79 + 72 * q^83 + 54 * q^85 + 99 * q^89 + 126 * q^95 + 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{11}{27}\right)$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.101566	−	0.235457i	−0.0454218	−	0.105300i	0.893995	−	0.448078i	$-0.147891\pi$
$5$	−0.101566	−	0.235457i	−0.0454218	−	0.105300i	−0.939416	+	0.342778i	$0.888632\pi$
$6$		0			0
$7$	0.0645556	−	1.10838i	0.0243997	−	0.418927i	−0.963886	−	0.266314i	$-0.914194\pi$
$7$	0.0645556	−	1.10838i	0.0243997	−	0.418927i	0.988286	−	0.152613i	$-0.0487688\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.61611	+	3.51405i	0.788788	+	1.05953i	0.996684	+	0.0813752i	$0.0259312\pi$
$11$	2.61611	+	3.51405i	0.788788	+	1.05953i	−0.207896	+	0.978151i	$0.566661\pi$
$12$		0			0
$13$	−0.112256	−	0.118984i	−0.0311342	−	0.0330003i	0.711619	−	0.702565i	$-0.247962\pi$
$13$	−0.112256	−	0.118984i	−0.0311342	−	0.0330003i	−0.742754	+	0.669565i	$0.766481\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.676180	+	3.83481i	0.163998	+	0.930078i	0.950092	+	0.311971i	$0.100989\pi$
$17$	0.676180	+	3.83481i	0.163998	+	0.930078i	−0.786094	+	0.618107i	$0.787900\pi$
$18$		0			0
$19$	0.862985	−	4.89423i	0.197982	−	1.12281i	−0.710125	−	0.704076i	$-0.751362\pi$
$19$	0.862985	−	4.89423i	0.197982	−	1.12281i	0.908107	−	0.418738i	$-0.137527\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.206233	+	3.54089i	0.0430026	+	0.738326i	0.949045	+	0.315140i	$0.102051\pi$
$23$	0.206233	+	3.54089i	0.0430026	+	0.738326i	−0.906043	+	0.423187i	$0.860912\pi$
$24$		0			0
$25$	3.38608	−	3.58904i	0.677217	−	0.717808i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.32976	+	1.02617i	0.804016	+	0.190555i	0.612022	−	0.790841i	$-0.290356\pi$
$29$	4.32976	+	1.02617i	0.804016	+	0.190555i	0.191994	+	0.981396i	$0.438505\pi$
$30$		0			0
$31$	2.25761	+	1.13382i	0.405479	+	0.203639i	0.639836	−	0.768511i	$-0.279002\pi$
$31$	2.25761	+	1.13382i	0.405479	+	0.203639i	−0.234357	+	0.972151i	$0.575298\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.267532	+	0.0973736i	−0.0452211	+	0.0164591i
$36$		0			0
$37$	−0.682668	−	0.248471i	−0.112230	−	0.0408483i	0.285295	−	0.958440i	$-0.407908\pi$
$37$	−0.682668	−	0.248471i	−0.112230	−	0.0408483i	−0.397525	+	0.917591i	$0.630131\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.28815	−	7.64295i	0.357349	−	1.19363i	−0.570696	−	0.821161i	$-0.693327\pi$
$41$	2.28815	−	7.64295i	0.357349	−	1.19363i	0.928045	−	0.372467i	$-0.121488\pi$
$42$		0			0
$43$	2.86218	−	0.334541i	0.436479	−	0.0510171i	0.104984	−	0.994474i	$-0.466521\pi$
$43$	2.86218	−	0.334541i	0.436479	−	0.0510171i	0.331495	+	0.943457i	$0.392447\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.94249	−	1.97999i	0.575072	−	0.288812i	−0.137397	−	0.990516i	$-0.543874\pi$
$47$	3.94249	−	1.97999i	0.575072	−	0.288812i	0.712468	+	0.701704i	$0.247577\pi$
$48$		0			0
$49$	5.72834	+	0.669546i	0.818334	+	0.0956495i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.43458	+	2.48476i	0.197054	+	0.341308i	0.947572	−	0.319542i	$-0.103529\pi$
$53$	1.43458	+	2.48476i	0.197054	+	0.341308i	−0.750518	+	0.660850i	$0.770196\pi$
$54$		0			0
$55$	0.561699	−	0.972892i	0.0757395	−	0.131185i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.10464	−	2.82703i	0.274001	−	0.368048i	−0.643728	−	0.765255i	$-0.722613\pi$
$59$	2.10464	−	2.82703i	0.274001	−	0.368048i	0.917729	+	0.397207i	$0.130020\pi$
$60$		0			0
$61$	12.2580	+	8.06224i	1.56948	+	1.03226i	0.973335	+	0.229388i	$0.0736725\pi$
$61$	12.2580	+	8.06224i	1.56948	+	1.03226i	0.596146	+	0.802876i	$0.296698\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0166143	+	0.0385162i	−0.00206075	+	0.00477735i
$66$		0			0
$67$	−10.5184	+	2.49291i	−1.28503	+	0.304557i	−0.815704	−	0.578470i	$-0.803650\pi$
$67$	−10.5184	+	2.49291i	−1.28503	+	0.304557i	−0.469323	+	0.883027i	$0.655502\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.47705	+	6.27399i	−0.887363	+	0.744586i	−0.967679	−	0.252184i	$-0.918851\pi$
$71$	−7.47705	+	6.27399i	−0.887363	+	0.744586i	0.0803167	+	0.996769i	$0.474407\pi$
$72$		0			0
$73$	−1.39879	−	1.17372i	−0.163716	−	0.137374i	0.557249	−	0.830345i	$-0.311857\pi$
$73$	−1.39879	−	1.17372i	−0.163716	−	0.137374i	−0.720965	+	0.692972i	$0.756301\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.06378	−	2.67279i	0.463110	−	0.304593i
$78$		0			0
$79$	2.34765	+	7.84168i	0.264131	+	0.882258i	0.982447	+	0.186542i	$0.0597279\pi$
$79$	2.34765	+	7.84168i	0.264131	+	0.882258i	−0.718316	+	0.695717i	$0.755087\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.543921	+	1.81682i	0.0597031	+	0.199422i	0.982638	−	0.185534i	$-0.0594016\pi$
$83$	0.543921	+	1.81682i	0.0597031	+	0.199422i	−0.922935	+	0.384957i	$0.874216\pi$
$84$		0			0
$85$	0.834256	−	0.548699i	0.0904877	−	0.0595147i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.12706	−	4.30211i	−0.543467	−	0.456023i	0.329255	−	0.944241i	$-0.393203\pi$
$89$	−5.12706	−	4.30211i	−0.543467	−	0.456023i	−0.872722	+	0.488218i	$0.837647\pi$
$90$		0			0
$91$	−0.139126	+	0.116741i	−0.0145844	+	0.0122377i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.24003	+	0.293893i	−0.127225	+	0.0301528i
$96$		0			0
$97$	5.07129	−	11.7566i	0.514912	−	1.19370i	−0.440320	−	0.897841i	$-0.645135\pi$
$97$	5.07129	−	11.7566i	0.514912	−	1.19370i	0.955232	−	0.295859i	$-0.0956058\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.89152	+	5.19034i	0.785236	+	0.516458i	0.877673	−	0.479261i	$-0.159095\pi$
$101$	7.89152	+	5.19034i	0.785236	+	0.516458i	−0.0924366	+	0.995719i	$0.529466\pi$
$102$		0			0
$103$	−8.61511	+	11.5721i	−0.848872	+	1.14023i	0.139806	+	0.990179i	$0.455352\pi$
$103$	−8.61511	+	11.5721i	−0.848872	+	1.14023i	−0.988678	+	0.150054i	$0.952055\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.39527	+	2.41667i	−0.134886	+	0.233629i	−0.925554	−	0.378616i	$-0.876400\pi$
$107$	−1.39527	+	2.41667i	−0.134886	+	0.233629i	0.790668	+	0.612245i	$0.209733\pi$
$108$		0			0
$109$	−9.26041	−	16.0395i	−0.886987	−	1.53631i	−0.843420	−	0.537255i	$-0.819461\pi$
$109$	−9.26041	−	16.0395i	−0.886987	−	1.53631i	−0.0435668	−	0.999051i	$-0.513872\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.93727	+	1.04462i	0.840747	+	0.0982693i	0.525556	−	0.850759i	$-0.323857\pi$
$113$	8.93727	+	1.04462i	0.840747	+	0.0982693i	0.315191	+	0.949028i	$0.397931\pi$
$114$		0			0
$115$	0.812781	−	0.408194i	0.0757922	−	0.0380643i
$116$		0			0
$117$		0			0
$118$		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
$123$		0			0
$124$		0			0
$125$	−2.39380	−	0.871271i	−0.214108	−	0.0779289i
$126$		0			0
$127$	10.4592	−	3.80685i	0.928107	−	0.337803i	0.166648	−	0.986016i	$-0.446706\pi$
$127$	10.4592	−	3.80685i	0.928107	−	0.337803i	0.761459	+	0.648213i	$0.224483\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−19.1007	−	9.59275i	−1.66884	−	0.838123i	−0.995069	−	0.0991819i	$-0.968377\pi$
$131$	−19.1007	−	9.59275i	−1.66884	−	0.838123i	−0.673770	−	0.738941i	$-0.735326\pi$
$132$		0			0
$133$	−5.36894	−	1.27246i	−0.465546	−	0.110337i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.92085	+	2.03598i	−0.164110	+	0.173946i	−0.804210	−	0.594345i	$-0.797411\pi$
$137$	−1.92085	+	2.03598i	−0.164110	+	0.173946i	0.640100	+	0.768291i	$0.278893\pi$
$138$		0			0
$139$	−0.260028	−	4.46450i	−0.0220552	−	0.378674i	−0.991217	−	0.132247i	$-0.957781\pi$
$139$	−0.260028	−	4.46450i	−0.0220552	−	0.378674i	0.969161	−	0.246427i	$-0.0792564\pi$
$140$		0			0
$141$		0			0
$142$		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
$147$		0			0
$148$		0			0
$149$	−10.6262	−	11.2631i	−0.870530	−	0.922707i	0.127074	−	0.991893i	$-0.459441\pi$
$149$	−10.6262	−	11.2631i	−0.870530	−	0.922707i	−0.997604	+	0.0691858i	$0.977960\pi$
$150$		0			0
$151$	3.39467	+	4.55984i	0.276254	+	0.371074i	0.918497	−	0.395427i	$-0.129403\pi$
$151$	3.39467	+	4.55984i	0.276254	+	0.371074i	−0.642243	+	0.766501i	$0.721996\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.0376676	−	0.646729i	0.00302554	−	0.0519465i
$156$		0			0
$157$	5.78989	+	13.4225i	0.462083	+	1.07123i	0.976855	+	0.213902i	$0.0686175\pi$
$157$	5.78989	+	13.4225i	0.462083	+	1.07123i	−0.514772	+	0.857327i	$0.672123\pi$
$158$		0			0
$159$		0			0
$160$		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
$165$		0			0
$166$		0			0
$167$	−2.13058	−	4.93924i	−0.164869	−	0.382210i	0.815674	−	0.578511i	$-0.196366\pi$
$167$	−2.13058	−	4.93924i	−0.164869	−	0.382210i	−0.980544	+	0.196301i	$0.937107\pi$
$168$		0			0
$169$	0.754327	−	12.9513i	0.0580251	−	0.996253i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.7048	+	17.0655i	0.965928	+	1.29747i	0.954713	+	0.297529i	$0.0961624\pi$
$173$	12.7048	+	17.0655i	0.965928	+	1.29747i	0.0112147	+	0.999937i	$0.496430\pi$
$174$		0			0
$175$	−3.75942	−	3.98475i	−0.284185	−	0.301219i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.32585	+	7.51929i	0.0990989	+	0.562018i	0.993414	+	0.114580i	$0.0365523\pi$
$179$	1.32585	+	7.51929i	0.0990989	+	0.562018i	−0.894315	+	0.447438i	$0.852337\pi$
$180$		0			0
$181$	0.00732463	−	0.0415400i	0.000544435	−	0.00308765i	−0.984534	−	0.175192i	$-0.943945\pi$
$181$	0.00732463	−	0.0415400i	0.000544435	−	0.00308765i	0.985079	+	0.172104i	$0.0550566\pi$
$182$		0			0
$183$		0			0
$184$		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
$189$		0			0
$190$		0			0
$191$	−25.5630	−	6.05855i	−1.84968	−	0.438381i	−0.853150	−	0.521666i	$-0.825311\pi$
$191$	−25.5630	−	6.05855i	−1.84968	−	0.438381i	−0.996526	+	0.0832852i	$0.973459\pi$
$192$		0			0
$193$	−7.36687	−	3.69978i	−0.530279	−	0.266316i	0.163451	−	0.986551i	$-0.447738\pi$
$193$	−7.36687	−	3.69978i	−0.530279	−	0.266316i	−0.693730	+	0.720235i	$0.744034\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−25.4783	+	9.27334i	−1.81525	+	0.660698i	−0.819041	+	0.573735i	$0.805494\pi$
$197$	−25.4783	+	9.27334i	−1.81525	+	0.660698i	−0.996212	+	0.0869634i	$0.972284\pi$
$198$		0			0
$199$	−5.87208	−	2.13726i	−0.416261	−	0.151506i	0.125395	−	0.992107i	$-0.459980\pi$
$199$	−5.87208	−	2.13726i	−0.416261	−	0.151506i	−0.541656	+	0.840600i	$0.682202\pi$
$200$		0			0
$201$		0			0
$202$		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
$207$		0			0
$208$		0			0
$209$	19.4562	−	9.77129i	1.34582	−	0.675894i
$210$		0			0
$211$	−10.1737	−	1.18914i	−0.700387	−	0.0818634i	−0.241556	−	0.970387i	$-0.577658\pi$
$211$	−10.1737	−	1.18914i	−0.700387	−	0.0818634i	−0.458831	+	0.888524i	$0.651732\pi$
$212$		0			0
$213$		0			0
$214$		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
$219$		0			0
$220$		0			0
$221$	0.380377	−	0.510934i	0.0255869	−	0.0343692i
$222$		0			0
$223$	13.3231	+	8.76274i	0.892181	+	0.586797i	0.910717	−	0.413032i	$-0.135530\pi$
$223$	13.3231	+	8.76274i	0.892181	+	0.586797i	−0.0185357	+	0.999828i	$0.505900\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.170392	−	0.395014i	0.0113093	−	0.0262180i	−0.912468	−	0.409148i	$-0.865826\pi$
$227$	0.170392	−	0.395014i	0.0113093	−	0.0262180i	0.923777	+	0.382930i	$0.125085\pi$
$228$		0			0
$229$	−6.65426	+	1.57709i	−0.439726	+	0.104217i	−0.444515	−	0.895772i	$-0.646624\pi$
$229$	−6.65426	+	1.57709i	−0.439726	+	0.104217i	0.00478884	+	0.999989i	$0.498476\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.08896	+	7.62654i	−0.595437	+	0.499631i	−0.889975	−	0.456009i	$-0.849279\pi$
$233$	−9.08896	+	7.62654i	−0.595437	+	0.499631i	0.294538	+	0.955640i	$0.404834\pi$
$234$		0			0
$235$	−0.866628	−	0.727187i	−0.0565326	−	0.0474365i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.89896	+	5.85294i	−0.575626	+	0.378595i	−0.803687	−	0.595052i	$-0.797132\pi$
$239$	−8.89896	+	5.85294i	−0.575626	+	0.378595i	0.228062	+	0.973647i	$0.426761\pi$
$240$		0			0
$241$	1.08582	+	3.62689i	0.0699438	+	0.233628i	0.985813	−	0.167849i	$-0.0536821\pi$
$241$	1.08582	+	3.62689i	0.0699438	+	0.233628i	−0.915869	+	0.401477i	$0.868497\pi$
$242$		0			0
$243$		0			0
$244$		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			0
$250$		0			0
$251$	−14.4677	−	12.1398i	−0.913193	−	0.766260i	0.0595305	−	0.998226i	$-0.481040\pi$
$251$	−14.4677	−	12.1398i	−0.913193	−	0.766260i	−0.972724	+	0.231966i	$0.925484\pi$
$252$		0			0
$253$	−11.9033	+	9.98808i	−0.748356	+	0.627945i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	19.4349	−	4.60616i	1.21232	−	0.287325i	0.425757	−	0.904837i	$-0.360008\pi$
$257$	19.4349	−	4.60616i	1.21232	−	0.287325i	0.786561	+	0.617513i	$0.211860\pi$
$258$		0			0
$259$	−0.319469	+	0.740613i	−0.0198509	+	0.0460195i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.8612	−	10.4320i	−0.978041	−	0.643267i	−0.0434736	−	0.999055i	$-0.513842\pi$
$263$	−15.8612	−	10.4320i	−0.978041	−	0.643267i	−0.934567	+	0.355787i	$0.884213\pi$
$264$		0			0
$265$	0.439350	−	0.590149i	0.0269890	−	0.0362526i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.22935	−	10.7896i	0.379810	−	0.657851i	−0.611224	−	0.791458i	$-0.709323\pi$
$269$	6.22935	−	10.7896i	0.379810	−	0.657851i	0.991034	+	0.133607i	$0.0426559\pi$
$270$		0			0
$271$	0.439706	+	0.761593i	0.0267102	+	0.0462635i	0.879072	−	0.476690i	$-0.158164\pi$
$271$	0.439706	+	0.761593i	0.0267102	+	0.0462635i	−0.852361	+	0.522953i	$0.824830\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	21.4704	+	2.50954i	1.29472	+	0.151331i
$276$		0			0
$277$	11.8732	−	5.96296i	0.713393	−	0.358279i	−0.0548004	−	0.998497i	$-0.517452\pi$
$277$	11.8732	−	5.96296i	0.713393	−	0.358279i	0.768193	+	0.640218i	$0.221156\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.76049	−	0.673305i	0.343642	−	0.0401660i	0.0574784	−	0.998347i	$-0.481694\pi$
$281$	5.76049	−	0.673305i	0.343642	−	0.0401660i	0.286164	+	0.958181i	$0.407620\pi$
$282$		0			0
$283$	−2.01769	+	6.73957i	−0.119939	+	0.400626i	−0.996783	−	0.0801505i	$-0.974460\pi$
$283$	−2.01769	+	6.73957i	−0.119939	+	0.400626i	0.876843	+	0.480776i	$0.159645\pi$
$284$		0			0
$285$		0			0
$286$		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
$291$		0			0
$292$		0			0
$293$	−16.9396	−	8.50740i	−0.989623	−	0.497008i	−0.121092	−	0.992641i	$-0.538640\pi$
$293$	−16.9396	−	8.50740i	−0.989623	−	0.497008i	−0.868532	+	0.495634i	$0.834936\pi$
$294$		0			0
$295$	−0.879404	−	0.208423i	−0.0512009	−	0.0121348i
$296$		0			0
$297$		0			0
$298$		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
$303$		0			0
$304$		0			0
$305$	0.653308	−	3.70509i	0.0374083	−	0.212153i
$306$		0			0
$307$	5.10196	+	28.9347i	0.291184	+	1.65139i	0.682319	+	0.731055i	$0.260972\pi$
$307$	5.10196	+	28.9347i	0.291184	+	1.65139i	−0.391134	+	0.920334i	$0.627917\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−22.2653	−	23.5998i	−1.26255	−	1.33822i	−0.916515	−	0.400000i	$-0.869010\pi$
$311$	−22.2653	−	23.5998i	−1.26255	−	1.33822i	−0.346032	−	0.938223i	$-0.612471\pi$
$312$		0			0
$313$	−17.9867	−	24.1603i	−1.01667	−	1.36562i	−0.929251	−	0.369449i	$-0.879546\pi$
$313$	−17.9867	−	24.1603i	−1.01667	−	1.36562i	−0.0874160	−	0.996172i	$-0.527861\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.03348	−	17.7442i	0.0580462	−	0.996616i	−0.836025	−	0.548691i	$-0.815126\pi$
$317$	1.03348	−	17.7442i	0.0580462	−	0.996616i	0.894071	−	0.447924i	$-0.147837\pi$
$318$		0			0
$319$	7.72112	+	17.8996i	0.432300	+	1.00218i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	19.3520			1.07677
$324$		0			0
$325$	−0.807147			−0.0447724
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.94007	−	4.49759i	−0.106960	−	0.247960i
$330$		0			0
$331$	−1.64835	+	28.3011i	−0.0906017	+	1.55557i	0.580534	+	0.814236i	$0.302844\pi$
$331$	−1.64835	+	28.3011i	−0.0906017	+	1.55557i	−0.671136	+	0.741334i	$0.734193\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.65529	+	2.22344i	0.0904380	+	0.121479i
$336$		0			0
$337$	−6.44855	−	6.83506i	−0.351275	−	0.372330i	0.527509	−	0.849549i	$-0.323126\pi$
$337$	−6.44855	−	6.83506i	−0.351275	−	0.372330i	−0.878784	+	0.477220i	$0.841645\pi$
$338$		0			0
$339$		0			0
$340$		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
$345$		0			0
$346$		0			0
$347$	2.08593	+	35.8140i	0.111979	+	1.92260i	0.325291	+	0.945614i	$0.394538\pi$
$347$	2.08593	+	35.8140i	0.111979	+	1.92260i	−0.213312	+	0.976984i	$0.568425\pi$
$348$		0			0
$349$	−9.58971	+	10.1645i	−0.513325	+	0.544093i	−0.931246	−	0.364390i	$-0.881277\pi$
$349$	−9.58971	+	10.1645i	−0.513325	+	0.544093i	0.417921	+	0.908483i	$0.362759\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.37937	−	0.326917i	−0.0734166	−	0.0174001i	0.193743	−	0.981052i	$-0.437937\pi$
$353$	−1.37937	−	0.326917i	−0.0734166	−	0.0174001i	−0.267160	+	0.963652i	$0.586085\pi$
$354$		0			0
$355$	2.23667	+	1.12330i	0.118710	+	0.0596185i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	24.9076	−	9.06563i	1.31457	−	0.478466i	0.412858	−	0.910795i	$-0.364531\pi$
$359$	24.9076	−	9.06563i	1.31457	−	0.478466i	0.901716	+	0.432330i	$0.142308\pi$
$360$		0			0
$361$	−5.35460	−	1.94891i	−0.281821	−	0.102574i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.134291	+	0.448564i	−0.00702913	+	0.0234789i
$366$		0			0
$367$	−3.61811	+	0.422896i	−0.188864	+	0.0220750i	−0.209999	−	0.977702i	$-0.567346\pi$
$367$	−3.61811	+	0.422896i	−0.188864	+	0.0220750i	0.0211353	+	0.999777i	$0.493272\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.84666	−	1.42965i	0.147791	−	0.0742236i
$372$		0			0
$373$	19.6589	+	2.29780i	1.01790	+	0.118975i	0.608643	−	0.793444i	$-0.291714\pi$
$373$	19.6589	+	2.29780i	1.01790	+	0.118975i	0.409257	+	0.912419i	$0.365788\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.363942	−	0.630367i	−0.0187440	−	0.0324655i
$378$		0			0
$379$	9.55738	−	16.5539i	0.490929	−	0.850315i	−0.509016	−	0.860757i	$-0.669991\pi$
$379$	9.55738	−	16.5539i	0.490929	−	0.850315i	0.999945	+	0.0104423i	$0.00332394\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−20.3010	+	27.2690i	−1.03733	+	1.39338i	−0.121143	+	0.992635i	$0.538656\pi$
$383$	−20.3010	+	27.2690i	−1.03733	+	1.39338i	−0.916190	+	0.400744i	$0.868752\pi$
$384$		0			0
$385$	−1.04207	−	0.685380i	−0.0531088	−	0.0349302i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.3604	+	33.2911i	−0.728101	+	1.68793i	−0.00232490	+	0.999997i	$0.500740\pi$
$389$	−14.3604	+	33.2911i	−0.728101	+	1.68793i	−0.725776	+	0.687931i	$0.758519\pi$
$390$		0			0
$391$	−13.4392	+	3.18514i	−0.679649	+	0.161080i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.60794	−	1.34922i	0.0809042	−	0.0678867i
$396$		0			0
$397$	17.7111	+	14.8614i	0.888894	+	0.745871i	0.967988	−	0.250997i	$-0.0807583\pi$
$397$	17.7111	+	14.8614i	0.888894	+	0.745871i	−0.0790940	+	0.996867i	$0.525203\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	16.9377	−	11.1401i	0.845827	−	0.556309i	−0.0509962	−	0.998699i	$-0.516240\pi$
$401$	16.9377	−	11.1401i	0.845827	−	0.556309i	0.896823	+	0.442390i	$0.145869\pi$
$402$		0			0
$403$	−0.118524	−	0.395898i	−0.00590410	−	0.0197211i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.912798	−	3.04896i	−0.0452457	−	0.151131i
$408$		0			0
$409$	26.0391	−	17.1262i	1.28755	−	0.846835i	0.293521	−	0.955953i	$-0.405173\pi$
$409$	26.0391	−	17.1262i	1.28755	−	0.846835i	0.994029	+	0.109118i	$0.0348026\pi$
$410$		0			0
$411$		0			0
$412$		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			0
$418$		0			0
$419$	10.8193	−	2.56423i	0.528559	−	0.125271i	0.0423322	−	0.999104i	$-0.486521\pi$
$419$	10.8193	−	2.56423i	0.528559	−	0.125271i	0.486226	+	0.873833i	$0.338373\pi$
$420$		0			0
$421$	8.91500	−	20.6673i	0.434491	−	1.00726i	−0.550528	−	0.834816i	$-0.685574\pi$
$421$	8.91500	−	20.6673i	0.434491	−	1.00726i	0.985019	−	0.172446i	$-0.0551670\pi$
$422$		0			0
$423$		0			0
$424$		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			0
$430$		0			0
$431$	5.01255	−	8.68200i	0.241446	−	0.418197i	−0.719680	−	0.694306i	$-0.755712\pi$
$431$	5.01255	−	8.68200i	0.241446	−	0.418197i	0.961126	+	0.276109i	$0.0890449\pi$
$432$		0			0
$433$	−8.52034	−	14.7577i	−0.409462	−	0.709208i	0.585368	−	0.810768i	$-0.300950\pi$
$433$	−8.52034	−	14.7577i	−0.409462	−	0.709208i	−0.994829	+	0.101560i	$0.967617\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.5079	+	2.04638i	0.837517	+	0.0978917i
$438$		0			0
$439$	18.5691	−	9.32574i	0.886253	−	0.445093i	0.0533913	−	0.998574i	$-0.482997\pi$
$439$	18.5691	−	9.32574i	0.886253	−	0.445093i	0.832862	+	0.553480i	$0.186701\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.2621	+	1.43324i	−0.582590	+	0.0680951i	−0.402283	−	0.915515i	$-0.631783\pi$
$443$	−12.2621	+	1.43324i	−0.582590	+	0.0680951i	−0.180307	+	0.983610i	$0.557709\pi$
$444$		0			0
$445$	−0.492227	+	1.64415i	−0.0233338	+	0.0779402i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	26.4864	+	9.64028i	1.24997	+	0.454953i	0.880392	−	0.474246i	$-0.157279\pi$
$449$	26.4864	+	9.64028i	1.24997	+	0.454953i	0.369580	+	0.929199i	$0.379502\pi$
$450$		0			0
$451$	32.8438	−	11.9542i	1.54655	−	0.562899i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.0416179	+	0.0209013i	0.00195108	+	0.000979869i
$456$		0			0
$457$	−8.31914	−	1.97167i	−0.389153	−	0.0922310i	0.0313815	−	0.999507i	$-0.490009\pi$
$457$	−8.31914	−	1.97167i	−0.389153	−	0.0922310i	−0.420535	+	0.907277i	$0.638157\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−17.1596	+	18.1881i	−0.799200	+	0.847103i	−0.990935	−	0.134344i	$-0.957107\pi$
$461$	−17.1596	+	18.1881i	−0.799200	+	0.847103i	0.191735	+	0.981447i	$0.438589\pi$
$462$		0			0
$463$	−1.10894	−	19.0397i	−0.0515367	−	0.884851i	−0.920687	−	0.390303i	$-0.872370\pi$
$463$	−1.10894	−	19.0397i	−0.0515367	−	0.884851i	0.869150	−	0.494549i	$-0.164667\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.29929	−	24.3825i	0.198947	−	1.12829i	−0.707737	−	0.706476i	$-0.750284\pi$
$467$	4.29929	−	24.3825i	0.198947	−	1.12829i	0.906684	−	0.421810i	$-0.138605\pi$
$468$		0			0
$469$	2.08406	+	11.8193i	0.0962329	+	0.545764i
$470$		0			0
$471$		0			0
$472$		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
$477$		0			0
$478$		0			0
$479$	1.12152	−	19.2557i	0.0512433	−	0.879814i	−0.870537	−	0.492102i	$-0.836229\pi$
$479$	1.12152	−	19.2557i	0.0512433	−	0.879814i	0.921781	−	0.387712i	$-0.126734\pi$
$480$		0			0
$481$	0.0470693	+	0.109119i	0.00214618	+	0.00497540i
$482$		0			0
$483$		0			0
$484$		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
$489$		0			0
$490$		0			0
$491$	13.0099	+	30.1602i	0.587127	+	1.36111i	0.909975	+	0.414662i	$0.136100\pi$
$491$	13.0099	+	30.1602i	0.587127	+	1.36111i	−0.322849	+	0.946451i	$0.604641\pi$
$492$		0			0
$493$	−1.00747	+	17.2977i	−0.0453744	+	0.779048i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.47126	+	8.69241i	0.290276	+	0.389908i
$498$		0			0
$499$	−22.4207	−	23.7646i	−1.00369	−	1.06385i	−0.997959	−	0.0638645i	$-0.979657\pi$
$499$	−22.4207	−	23.7646i	−1.00369	−	1.06385i	−0.00573037	−	0.999984i	$-0.501824\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.02284	+	17.1434i	0.134782	+	0.764384i	0.975012	+	0.222154i	$0.0713088\pi$
$503$	3.02284	+	17.1434i	0.134782	+	0.764384i	−0.840230	+	0.542230i	$0.817580\pi$
$504$		0			0
$505$	0.420589	−	2.38528i	0.0187160	−	0.106143i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.94524	+	33.3985i	0.0862212	+	1.48036i	0.713000	+	0.701164i	$0.247336\pi$
$509$	1.94524	+	33.3985i	0.0862212	+	1.48036i	−0.626779	+	0.779197i	$0.715627\pi$
$510$		0			0
$511$	−1.39122	+	1.47461i	−0.0615441	+	0.0652330i
$512$		0			0
$513$		0			0
$514$		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
$519$		0			0
$520$		0			0
$521$	−1.53032	+	0.556990i	−0.0670444	+	0.0244022i	−0.375325	−	0.926893i	$-0.622469\pi$
$521$	−1.53032	+	0.556990i	−0.0670444	+	0.0244022i	0.308280	+	0.951296i	$0.400247\pi$
$522$		0			0
$523$	35.7374	+	13.0073i	1.56269	+	0.568771i	0.971350	−	0.237654i	$-0.0763783\pi$
$523$	35.7374	+	13.0073i	1.56269	+	0.568771i	0.591336	+	0.806425i	$0.298601\pi$
$524$		0			0
$525$		0			0
$526$		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
$531$		0			0
$532$		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			0
$538$		0			0
$539$	12.6332	+	21.8813i	0.544149	+	0.942493i
$540$		0			0
$541$	−17.1456	+	29.6971i	−0.737147	+	1.27678i	0.216627	+	0.976254i	$0.430494\pi$
$541$	−17.1456	+	29.6971i	−0.737147	+	1.27678i	−0.953775	+	0.300522i	$0.902839\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.83607	+	3.80950i	−0.121484	+	0.163181i
$546$		0			0
$547$	−24.1693	−	15.8964i	−1.03341	−	0.679682i	−0.0848838	−	0.996391i	$-0.527052\pi$
$547$	−24.1693	−	15.8964i	−1.03341	−	0.679682i	−0.948523	+	0.316709i	$0.897422\pi$
$548$		0			0
$549$		0			0
$550$		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			0
$556$		0			0
$557$	−14.4591	+	12.1326i	−0.612651	+	0.514075i	−0.895484	−	0.445094i	$-0.853170\pi$
$557$	−14.4591	+	12.1326i	−0.612651	+	0.514075i	0.282833	+	0.959169i	$0.408726\pi$
$558$		0			0
$559$	−0.361102	−	0.303001i	−0.0152730	−	0.0128156i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.55867	−	2.99828i	0.192125	−	0.126363i	−0.449802	−	0.893128i	$-0.648506\pi$
$563$	4.55867	−	2.99828i	0.192125	−	0.126363i	0.641927	+	0.766766i	$0.278135\pi$
$564$		0			0
$565$	−0.661762	−	2.21044i	−0.0278406	−	0.0929939i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.96143	−	29.9332i	−0.375683	−	1.25487i	−0.911769	−	0.410704i	$-0.865283\pi$
$569$	−8.96143	−	29.9332i	−0.375683	−	1.25487i	0.536086	−	0.844163i	$-0.319902\pi$
$570$		0			0
$571$	36.0668	−	23.7215i	1.50935	−	0.992714i	0.518898	−	0.854836i	$-0.326342\pi$
$571$	36.0668	−	23.7215i	1.50935	−	0.992714i	0.990449	−	0.137878i	$-0.0440281\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	13.4067	+	11.2496i	0.559099	+	0.469139i
$576$		0			0
$577$	−21.1557	+	17.7518i	−0.880725	+	0.739016i	−0.966328	−	0.257313i	$-0.917163\pi$
$577$	−21.1557	+	17.7518i	−0.880725	+	0.739016i	0.0856030	+	0.996329i	$0.472718\pi$
$578$		0			0
$579$		0			0
$580$		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			0
$586$		0			0
$587$	−14.4192	−	9.48365i	−0.595144	−	0.391432i	0.215902	−	0.976415i	$-0.430731\pi$
$587$	−14.4192	−	9.48365i	−0.595144	−	0.391432i	−0.811046	+	0.584983i	$0.801101\pi$
$588$		0			0
$589$	7.49745	−	10.0708i	0.308927	−	0.414961i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.0107	−	24.2673i	0.575352	−	0.996539i	−0.420651	−	0.907222i	$-0.638198\pi$
$593$	14.0107	−	24.2673i	0.575352	−	0.996539i	0.996003	−	0.0893165i	$-0.0284683\pi$
$594$		0			0
$595$	−0.554309	−	0.960091i	−0.0227245	−	0.0393599i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	43.4131	+	5.07427i	1.77381	+	0.207329i	0.939168	−	0.343459i	$-0.111599\pi$
$599$	43.4131	+	5.07427i	1.77381	+	0.207329i	0.834645	+	0.550788i	$0.185673\pi$
$600$		0			0
$601$	11.5276	−	5.78938i	0.470221	−	0.236154i	−0.197877	−	0.980227i	$-0.563405\pi$
$601$	11.5276	−	5.78938i	0.470221	−	0.236154i	0.668098	+	0.744073i	$0.267109\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.08662	−	0.243890i	0.0848330	−	0.00991555i
$606$		0			0
$607$	8.30773	−	27.7498i	0.337201	−	1.12633i	−0.606377	−	0.795177i	$-0.707378\pi$
$607$	8.30773	−	27.7498i	0.337201	−	1.12633i	0.943578	−	0.331151i	$-0.107437\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.678156	−	0.246829i	−0.0274352	−	0.00998561i
$612$		0			0
$613$	−9.37562	+	3.41245i	−0.378678	+	0.137827i	−0.524344	−	0.851506i	$-0.675690\pi$
$613$	−9.37562	+	3.41245i	−0.378678	+	0.137827i	0.145667	+	0.989334i	$0.453467\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−42.2946	−	21.2412i	−1.70272	−	0.855137i	−0.987762	−	0.155968i	$-0.950150\pi$
$617$	−42.2946	−	21.2412i	−1.70272	−	0.855137i	−0.714956	−	0.699170i	$-0.753553\pi$
$618$		0			0
$619$	0.748495	+	0.177397i	0.0300846	+	0.00713017i	0.245631	−	0.969364i	$-0.421005\pi$
$619$	0.748495	+	0.177397i	0.0300846	+	0.00713017i	−0.215546	+	0.976494i	$0.569153\pi$
$620$		0			0
$621$		0			0
$622$		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
$627$		0			0
$628$		0			0
$629$	0.491231	−	2.78591i	0.0195867	−	0.111082i
$630$		0			0
$631$	1.29424	+	7.34001i	0.0515230	+	0.292201i	0.999672	−	0.0256260i	$-0.00815790\pi$
$631$	1.29424	+	7.34001i	0.0515230	+	0.292201i	−0.948149	+	0.317827i	$0.897047\pi$
$632$		0			0
$633$		0			0
$634$		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
$639$		0			0
$640$		0			0
$641$	−0.212140	+	3.64229i	−0.00837901	+	0.143862i	0.991524	+	0.129925i	$0.0414736\pi$
$641$	−0.212140	+	3.64229i	−0.00837901	+	0.143862i	−0.999903	+	0.0139373i	$0.995563\pi$
$642$		0			0
$643$	−0.626343	−	1.45203i	−0.0247006	−	0.0572623i	0.905419	−	0.424518i	$-0.139557\pi$
$643$	−0.626343	−	1.45203i	−0.0247006	−	0.0572623i	−0.930120	+	0.367256i	$0.880297\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	46.1899			1.81591			0.907956	−	0.419066i	$-0.137642\pi$
$647$	46.1899			1.81591			0.907956	+	0.419066i	$0.137642\pi$
$648$		0			0
$649$	15.4403			0.606085
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.49766	−	22.0180i	−0.371672	−	0.861633i	−0.996711	−	0.0810390i	$-0.974176\pi$
$653$	−9.49766	−	22.0180i	−0.371672	−	0.861633i	0.625039	−	0.780594i	$-0.285083\pi$
$654$		0			0
$655$	−0.318691	+	5.47171i	−0.0124523	+	0.213797i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.541245	−	0.727018i	−0.0210839	−	0.0283206i	0.791456	−	0.611226i	$-0.209323\pi$
$659$	−0.541245	−	0.727018i	−0.0210839	−	0.0283206i	−0.812540	+	0.582905i	$0.801916\pi$
$660$		0			0
$661$	27.6434	+	29.3003i	1.07520	+	1.13965i	0.989677	+	0.143313i	$0.0457757\pi$
$661$	27.6434	+	29.3003i	1.07520	+	1.13965i	0.0855263	+	0.996336i	$0.472743\pi$
$662$		0			0
$663$		0			0
$664$		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
$669$		0			0
$670$		0			0
$671$	3.73731	+	64.1671i	0.144277	+	2.47714i
$672$		0			0
$673$	−27.8513	+	29.5206i	−1.07359	+	1.13794i	−0.0836419	+	0.996496i	$0.526655\pi$
$673$	−27.8513	+	29.5206i	−1.07359	+	1.13794i	−0.989947	+	0.141441i	$0.954826\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−38.0410	−	9.01587i	−1.46203	−	0.346508i	−0.578810	−	0.815462i	$-0.696483\pi$
$677$	−38.0410	−	9.01587i	−1.46203	−	0.346508i	−0.883222	+	0.468954i	$0.844631\pi$
$678$		0			0
$679$	−12.7033	−	6.37986i	−0.487510	−	0.244836i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.73261	+	1.35856i	−0.142824	+	0.0519838i	−0.412443	−	0.910983i	$-0.635324\pi$
$683$	−3.73261	+	1.35856i	−0.142824	+	0.0519838i	0.269619	+	0.962967i	$0.413102\pi$
$684$		0			0
$685$	0.674481	+	0.245491i	0.0257706	+	0.00937973i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.134608	−	0.449621i	0.00512814	−	0.0171292i
$690$		0			0
$691$	−12.5915	+	1.47174i	−0.479003	+	0.0559875i	−0.352169	−	0.935936i	$-0.614556\pi$
$691$	−12.5915	+	1.47174i	−0.479003	+	0.0559875i	−0.126834	+	0.991924i	$0.540482\pi$
$692$		0			0
$693$		0			0
$694$		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
$699$		0			0
$700$		0			0
$701$	−10.9161	−	18.9072i	−0.412295	−	0.714116i	0.582845	−	0.812583i	$-0.301939\pi$
$701$	−10.9161	−	18.9072i	−0.412295	−	0.714116i	−0.995140	+	0.0984671i	$0.968606\pi$
$702$		0			0
$703$	−1.80521	+	3.12671i	−0.0680846	+	0.117926i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.26229	−	8.41172i	0.235518	−	0.316355i
$708$		0			0
$709$	0.0836438	+	0.0550134i	0.00314131	+	0.00206607i	0.551079	−	0.834453i	$-0.314216\pi$
$709$	0.0836438	+	0.0550134i	0.00314131	+	0.00206607i	−0.547937	+	0.836519i	$0.684587\pi$
$710$		0			0
$711$		0			0
$712$		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
$717$		0			0
$718$		0			0
$719$	26.8168	−	22.5019i	1.00010	−	0.839180i	0.0130985	−	0.999914i	$-0.495831\pi$
$719$	26.8168	−	22.5019i	1.00010	−	0.839180i	0.986998	+	0.160734i	$0.0513861\pi$
$720$		0			0
$721$	12.2701	+	10.2958i	0.456962	+	0.383437i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	18.3439	−	12.0650i	0.681275	−	0.448082i
$726$		0			0
$727$	−5.50176	−	18.3772i	−0.204049	−	0.681571i	−0.997351	−	0.0727425i	$-0.976825\pi$
$727$	−5.50176	−	18.3772i	−0.204049	−	0.681571i	0.793302	−	0.608829i	$-0.208360\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.21825	+	10.7497i	0.119031	+	0.397593i
$732$		0			0
$733$	−34.6638	+	22.7987i	−1.28033	+	0.842090i	−0.993270	−	0.115822i	$-0.963050\pi$
$733$	−34.6638	+	22.7987i	−1.28033	+	0.842090i	−0.287065	+	0.957911i	$0.592680\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−36.2775	−	30.4405i	−1.33630	−	1.12129i
$738$		0			0
$739$	18.9744	−	15.9214i	0.697983	−	0.585677i	−0.223216	−	0.974769i	$-0.571656\pi$
$739$	18.9744	−	15.9214i	0.697983	−	0.585677i	0.921199	+	0.389092i	$0.127211\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−19.1931	+	4.54884i	−0.704125	+	0.166881i	−0.567054	−	0.823681i	$-0.691917\pi$
$743$	−19.1931	+	4.54884i	−0.704125	+	0.166881i	−0.137071	+	0.990561i	$0.543769\pi$
$744$		0			0
$745$	−1.57271	+	3.64596i	−0.0576197	+	0.133577i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.58851	+	1.70249i	0.0945822	+	0.0622077i
$750$		0			0
$751$	−23.3182	+	31.3218i	−0.850894	+	1.14295i	0.137419	+	0.990513i	$0.456119\pi$
$751$	−23.3182	+	31.3218i	−0.850894	+	1.14295i	−0.988313	+	0.152436i	$0.951288\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.728861	−	1.26243i	0.0265260	−	0.0459444i
$756$		0			0
$757$	14.4054	+	24.9509i	0.523574	+	0.906857i	0.999623	+	0.0274384i	$0.00873501\pi$
$757$	14.4054	+	24.9509i	0.523574	+	0.906857i	−0.476049	+	0.879419i	$0.657932\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.66068	+	0.310989i	0.0964495	+	0.0112733i	0.164181	−	0.986430i	$-0.447502\pi$
$761$	2.66068	+	0.310989i	0.0964495	+	0.0112733i	−0.0677313	+	0.997704i	$0.521576\pi$
$762$		0			0
$763$	−18.3756	+	9.22859i	−0.665242	+	0.334097i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.572630	+	0.0669309i	−0.0206765	+	0.00241673i
$768$		0			0
$769$	−2.32359	+	7.76133i	−0.0837908	+	0.279881i	−0.989609	−	0.143786i	$-0.954072\pi$
$769$	−2.32359	+	7.76133i	−0.0837908	+	0.279881i	0.905818	+	0.423667i	$0.139257\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−18.3195	−	6.66776i	−0.658908	−	0.239823i	−0.00914295	−	0.999958i	$-0.502910\pi$
$773$	−18.3195	−	6.66776i	−0.658908	−	0.239823i	−0.649765	+	0.760135i	$0.725133\pi$
$774$		0			0
$775$	11.7138	−	4.26347i	0.420771	−	0.153148i
$776$		0			0
$777$		0			0
$778$		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
$783$		0			0
$784$		0			0
$785$	2.57236	−	2.72654i	0.0918114	−	0.0973144i
$786$		0			0
$787$	−0.692188	−	11.8844i	−0.0246738	−	0.423633i	−0.987915	−	0.154996i	$-0.950464\pi$
$787$	−0.692188	−	11.8844i	−0.0246738	−	0.423633i	0.963241	−	0.268638i	$-0.0865734\pi$
$788$		0			0
$789$		0			0
$790$		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			0
$796$		0			0
$797$	−4.97388	−	5.27200i	−0.176184	−	0.186744i	0.633264	−	0.773936i	$-0.281715\pi$
$797$	−4.97388	−	5.27200i	−0.176184	−	0.186744i	−0.809448	+	0.587192i	$0.800233\pi$
$798$		0			0
$799$	10.2587	+	13.7799i	0.362928	+	0.487497i
$800$		0			0
$801$		0			0
$802$		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
$807$		0			0
$808$		0			0
$809$	22.0334			0.774654			0.387327	−	0.921942i	$-0.373398\pi$
$809$	22.0334			0.774654			0.387327	+	0.921942i	$0.373398\pi$
$810$		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			0
$814$		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			0
$820$		0			0
$821$	−22.3580	−	30.0320i	−0.780299	−	1.04812i	−0.997406	−	0.0719757i	$-0.977070\pi$
$821$	−22.3580	−	30.0320i	−0.780299	−	1.04812i	0.217107	−	0.976148i	$-0.430338\pi$
$822$		0			0
$823$	−17.0015	−	18.0206i	−0.592636	−	0.628157i	0.359751	−	0.933048i	$-0.382862\pi$
$823$	−17.0015	−	18.0206i	−0.592636	−	0.628157i	−0.952387	+	0.304891i	$0.901380\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.86252	−	38.9193i	−0.238633	−	1.35336i	−0.834825	−	0.550515i	$-0.814431\pi$
$827$	−6.86252	−	38.9193i	−0.238633	−	1.35336i	0.596192	−	0.802842i	$-0.296680\pi$
$828$		0			0
$829$	−3.16118	+	17.9280i	−0.109792	+	0.622664i	0.879405	+	0.476074i	$0.157941\pi$
$829$	−3.16118	+	17.9280i	−0.109792	+	0.622664i	−0.989197	+	0.146589i	$0.953170\pi$
$830$		0			0
$831$		0			0
$832$		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
$837$		0			0
$838$		0			0
$839$	−3.91312	−	0.927427i	−0.135096	−	0.0320184i	0.162512	−	0.986707i	$-0.448041\pi$
$839$	−3.91312	−	0.927427i	−0.135096	−	0.0320184i	−0.297608	+	0.954688i	$0.596189\pi$
$840$		0			0
$841$	−8.22156	−	4.12902i	−0.283502	−	0.142380i
$842$		0			0
$843$		0			0
$844$		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
$849$		0			0
$850$		0			0
$851$	0.739018	−	2.46849i	0.0253332	−	0.0846189i
$852$		0			0
$853$	−13.5263	+	1.58100i	−0.463132	+	0.0541324i	−0.344460	−	0.938801i	$-0.611938\pi$
$853$	−13.5263	+	1.58100i	−0.463132	+	0.0541324i	−0.118673	+	0.992933i	$0.537864\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.6796	+	11.8924i	−0.808881	+	0.406235i	−0.804645	−	0.593756i	$-0.797645\pi$
$857$	−23.6796	+	11.8924i	−0.808881	+	0.406235i	−0.00423566	+	0.999991i	$0.501348\pi$
$858$		0			0
$859$	10.9611	+	1.28117i	0.373987	+	0.0437128i	0.301010	−	0.953621i	$-0.402676\pi$
$859$	10.9611	+	1.28117i	0.373987	+	0.0437128i	0.0729765	+	0.997334i	$0.476750\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.9478	+	18.9621i	0.372667	+	0.645477i	0.989975	−	0.141244i	$-0.0451102\pi$
$863$	10.9478	+	18.9621i	0.372667	+	0.645477i	−0.617308	+	0.786721i	$0.711777\pi$
$864$		0			0
$865$	2.72781	−	4.72471i	0.0927485	−	0.160645i
$866$		0			0
$867$		0			0
$868$		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
$873$		0			0
$874$		0			0
$875$	−1.12023	+	2.59699i	−0.0378707	+	0.0877941i
$876$		0			0
$877$	−11.5896	+	2.74678i	−0.391352	+	0.0927522i	−0.421581	−	0.906791i	$-0.638525\pi$
$877$	−11.5896	+	2.74678i	−0.391352	+	0.0927522i	0.0302285	+	0.999543i	$0.490376\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−3.05584	+	2.56415i	−0.102954	+	0.0863885i	−0.692812	−	0.721119i	$-0.743628\pi$
$881$	−3.05584	+	2.56415i	−0.102954	+	0.0863885i	0.589858	+	0.807507i	$0.299184\pi$
$882$		0			0
$883$	8.66860	+	7.27382i	0.291722	+	0.244783i	0.776889	−	0.629638i	$-0.216797\pi$
$883$	8.66860	+	7.27382i	0.291722	+	0.244783i	−0.485167	+	0.874421i	$0.661241\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.9234	−	13.1038i	0.668962	−	0.439983i	−0.169070	−	0.985604i	$-0.554077\pi$
$887$	19.9234	−	13.1038i	0.668962	−	0.439983i	0.838032	+	0.545621i	$0.183706\pi$
$888$		0			0
$889$	−3.54422	−	11.8385i	−0.118869	−	0.397052i
$890$		0			0
$891$		0			0
$892$		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			0
$898$		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			0
$904$		0			0
$905$	−0.0105248	+	0.00249443i	−0.000349857	+	8.29176e-5i
$906$		0			0
$907$	−5.23639	+	12.1393i	−0.173872	+	0.403080i	−0.982761	−	0.184881i	$-0.940810\pi$
$907$	−5.23639	+	12.1393i	−0.173872	+	0.403080i	0.808889	+	0.587961i	$0.200069\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.81470	−	3.82439i	−0.192650	−	0.126708i	0.449520	−	0.893270i	$-0.351595\pi$
$911$	−5.81470	−	3.82439i	−0.192650	−	0.126708i	−0.642169	+	0.766563i	$0.721965\pi$
$912$		0			0
$913$	−4.96145	+	6.66438i	−0.164200	+	0.220559i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.8654	+	20.5516i	−0.391832	+	0.678672i
$918$		0			0
$919$	−13.3747	−	23.1657i	−0.441191	−	0.764165i	0.556587	−	0.830789i	$-0.312110\pi$
$919$	−13.3747	−	23.1657i	−0.441191	−	0.764165i	−0.997778	+	0.0666241i	$0.978777\pi$
$920$		0			0
$921$		0			0
$922$		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
$927$		0			0
$928$		0			0
$929$	30.8542	−	3.60634i	1.01229	−	0.118320i	0.406258	−	0.913758i	$-0.366833\pi$
$929$	30.8542	−	3.60634i	1.01229	−	0.118320i	0.606035	+	0.795438i	$0.292759\pi$
$930$		0			0
$931$	8.22038	−	27.4580i	0.269412	−	0.899899i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.11066	+	1.49616i	0.134433	+	0.0489296i
$936$		0			0
$937$	−35.4347	+	12.8972i	−1.15760	+	0.421332i	−0.848240	−	0.529612i	$-0.822337\pi$
$937$	−35.4347	+	12.8972i	−1.15760	+	0.421332i	−0.309361	+	0.950945i	$0.600115\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.3910	−	5.21854i	−0.338736	−	0.170119i	0.271297	−	0.962496i	$-0.412547\pi$
$941$	−10.3910	−	5.21854i	−0.338736	−	0.170119i	−0.610033	+	0.792376i	$0.708844\pi$
$942$		0			0
$943$	27.5347	+	6.52585i	0.896654	+	0.212511i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.36355	+	7.80490i	−0.239283	+	0.253625i	−0.835875	−	0.548919i	$-0.815039\pi$
$947$	−7.36355	+	7.80490i	−0.239283	+	0.253625i	0.596592	+	0.802544i	$0.296521\pi$
$948$		0			0
$949$	0.0173676	+	0.298190i	0.000563777	+	0.00967967i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−2.54335	+	14.4240i	−0.0823871	+	0.467241i	0.915503	+	0.402312i	$0.131793\pi$
$953$	−2.54335	+	14.4240i	−0.0823871	+	0.467241i	−0.997890	+	0.0649290i	$0.979318\pi$
$954$		0			0
$955$	1.16981	+	6.63434i	0.0378543	+	0.214682i
$956$		0			0
$957$		0			0
$958$		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
$963$		0			0
$964$		0			0
$965$	−0.122914	+	2.11036i	−0.00395675	+	0.0679347i
$966$		0			0
$967$	−5.12115	−	11.8722i	−0.164685	−	0.381783i	0.815812	−	0.578318i	$-0.196291\pi$
$967$	−5.12115	−	11.8722i	−0.164685	−	0.381783i	−0.980497	+	0.196534i	$0.937031\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−42.6173			−1.36765			−0.683827	−	0.729644i	$-0.739686\pi$
$971$	−42.6173			−1.36765			−0.683827	+	0.729644i	$0.739686\pi$
$972$		0			0
$973$	−4.96514			−0.159175
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.8704	−	29.8369i	−0.411760	−	0.954567i	−0.990304	−	0.138916i	$-0.955638\pi$
$977$	−12.8704	−	29.8369i	−0.411760	−	0.954567i	0.578544	−	0.815651i	$-0.303621\pi$
$978$		0			0
$979$	1.70487	−	29.2716i	0.0544880	−	0.935523i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−13.9767	−	18.7740i	−0.445789	−	0.598799i	0.521257	−	0.853400i	$-0.325463\pi$
$983$	−13.9767	−	18.7740i	−0.445789	−	0.598799i	−0.967046	+	0.254601i	$0.918056\pi$
$984$		0			0
$985$	4.77121	+	5.05718i	0.152023	+	0.161135i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.77485	+	10.0657i	0.0564370	+	0.320070i
$990$		0			0
$991$	6.15676	−	34.9167i	0.195576	−	1.10917i	−0.716020	−	0.698080i	$-0.754038\pi$
$991$	6.15676	−	34.9167i	0.195576	−	1.10917i	0.911596	−	0.411087i	$-0.134851\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.0931717	+	1.59970i	0.00295374	+	0.0507138i
$996$		0			0
$997$	−8.13233	+	8.61976i	−0.257553	+	0.272991i	−0.843229	−	0.537555i	$-0.819348\pi$
$997$	−8.13233	+	8.61976i	−0.257553	+	0.272991i	0.585675	+	0.810546i	$0.300829\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.m.a.49.1	✓	162	81.32	odd	54
324.2.m.a.205.1	yes	162	3.2	odd	2
972.2.m.a.37.6		162	81.49	even	27	inner
972.2.m.a.289.6		162	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.m (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.101566 - 0.235457i) q^{5} +(0.0645556 - 1.10838i) q^{7} +O(q^{10})\)	\(q+(-0.101566 - 0.235457i) q^{5} +(0.0645556 - 1.10838i) q^{7} +(2.61611 + 3.51405i) q^{11} +(-0.112256 - 0.118984i) q^{13} +(0.676180 + 3.83481i) q^{17} +(0.862985 - 4.89423i) q^{19} +(0.206233 + 3.54089i) q^{23} +(3.38608 - 3.58904i) q^{25} +(4.32976 + 1.02617i) q^{29} +(2.25761 + 1.13382i) q^{31} +(-0.267532 + 0.0973736i) q^{35} +(-0.682668 - 0.248471i) q^{37} +(2.28815 - 7.64295i) q^{41} +(2.86218 - 0.334541i) q^{43} +(3.94249 - 1.97999i) q^{47} +(5.72834 + 0.669546i) q^{49} +(1.43458 + 2.48476i) q^{53} +(0.561699 - 0.972892i) q^{55} +(2.10464 - 2.82703i) q^{59} +(12.2580 + 8.06224i) q^{61} +(-0.0166143 + 0.0385162i) q^{65} +(-10.5184 + 2.49291i) q^{67} +(-7.47705 + 6.27399i) q^{71} +(-1.39879 - 1.17372i) q^{73} +(4.06378 - 2.67279i) q^{77} +(2.34765 + 7.84168i) q^{79} +(0.543921 + 1.81682i) q^{83} +(0.834256 - 0.548699i) q^{85} +(-5.12706 - 4.30211i) q^{89} +(-0.139126 + 0.116741i) q^{91} +(-1.24003 + 0.293893i) q^{95} +(5.07129 - 11.7566i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q+O(q^{10}) \) 162 * q	\( 162 q - 27 q^{23} - 27 q^{29} - 27 q^{35} + 18 q^{41} + 54 q^{47} + 54 q^{53} + 63 q^{59} + 90 q^{65} + 27 q^{67} + 72 q^{71} + 144 q^{77} + 54 q^{79} + 72 q^{83} + 54 q^{85} + 99 q^{89} + 126 q^{95} + 27 q^{97}+O(q^{100}) \) 162 * q - 27 * q^23 - 27 * q^29 - 27 * q^35 + 18 * q^41 + 54 * q^47 + 54 * q^53 + 63 * q^59 + 90 * q^65 + 27 * q^67 + 72 * q^71 + 144 * q^77 + 54 * q^79 + 72 * q^83 + 54 * q^85 + 99 * q^89 + 126 * q^95 + 27 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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