LMFDB - Embedded newform 576.2.y.a.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53620 - 0.800065i) q^{3} +(1.00059 - 3.73424i) q^{5} +(1.68236 - 2.91393i) q^{7} +(1.71979 + 2.45811i) q^{9} +O(q^{10})$	\(q+(-1.53620 - 0.800065i) q^{3} +(1.00059 - 3.73424i) q^{5} +(1.68236 - 2.91393i) q^{7} +(1.71979 + 2.45811i) q^{9} +(-0.0566521 - 0.211428i) q^{11} +(0.727551 - 2.71526i) q^{13} +(-4.52473 + 4.93599i) q^{15} +4.23937i q^{17} +(1.12365 - 1.12365i) q^{19} +(-4.91577 + 3.13037i) q^{21} +(-3.33369 + 1.92471i) q^{23} +(-8.61325 - 4.97286i) q^{25} +(-0.675290 - 5.15209i) q^{27} +(0.545635 + 2.03634i) q^{29} +(7.21206 - 4.16388i) q^{31} +(-0.0821277 + 0.370121i) q^{33} +(-9.19798 - 9.19798i) q^{35} +(-2.66564 + 2.66564i) q^{37} +(-3.29004 + 3.58908i) q^{39} +(-1.70386 - 2.95117i) q^{41} +(-4.68985 + 1.25664i) q^{43} +(10.9000 - 3.96257i) q^{45} +(-2.34998 + 4.07028i) q^{47} +(-2.16067 - 3.74239i) q^{49} +(3.39177 - 6.51251i) q^{51} +(-7.58271 - 7.58271i) q^{53} -0.846209 q^{55} +(-2.62513 + 0.827151i) q^{57} +(5.34305 + 1.43167i) q^{59} +(8.69958 - 2.33105i) q^{61} +(10.0561 - 0.875933i) q^{63} +(-9.41144 - 5.43370i) q^{65} +(5.17504 + 1.38665i) q^{67} +(6.66110 - 0.289558i) q^{69} +7.53614i q^{71} -3.22646i q^{73} +(9.25302 + 14.5304i) q^{75} +(-0.711397 - 0.190618i) q^{77} +(4.98587 + 2.87859i) q^{79} +(-3.08462 + 8.45489i) q^{81} +(-4.50604 + 1.20739i) q^{83} +(15.8308 + 4.24186i) q^{85} +(0.790999 - 3.56475i) q^{87} -2.96157 q^{89} +(-6.68807 - 6.68807i) q^{91} +(-14.4105 + 0.626426i) q^{93} +(-3.07166 - 5.32027i) q^{95} +(-7.63883 + 13.2308i) q^{97} +(0.422285 - 0.502870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.53620	−	0.800065i	−0.886923	−	0.461918i
$3$	−1.53620	−	0.800065i	−0.886923	−	0.461918i
$4$		0			0
$5$	1.00059	−	3.73424i	0.447476	−	1.67000i	−0.261839	−	0.965111i	$-0.584329\pi$
$5$	1.00059	−	3.73424i	0.447476	−	1.67000i	0.709315	−	0.704891i	$-0.249004\pi$
$6$		0			0
$7$	1.68236	−	2.91393i	0.635872	−	1.10136i	−0.350457	−	0.936579i	$-0.613974\pi$
$7$	1.68236	−	2.91393i	0.635872	−	1.10136i	0.986330	−	0.164785i	$-0.0526929\pi$
$8$		0			0
$9$	1.71979	+	2.45811i	0.573264	+	0.819371i
$10$		0			0
$11$	−0.0566521	−	0.211428i	−0.0170812	−	0.0637480i	0.956859	−	0.290552i	$-0.0938390\pi$
$11$	−0.0566521	−	0.211428i	−0.0170812	−	0.0637480i	−0.973940	+	0.226804i	$0.927172\pi$
$12$		0			0
$13$	0.727551	−	2.71526i	0.201786	−	0.753076i	−0.788619	−	0.614882i	$-0.789204\pi$
$13$	0.727551	−	2.71526i	0.201786	−	0.753076i	0.990405	−	0.138194i	$-0.0441298\pi$
$14$		0			0
$15$	−4.52473	+	4.93599i	−1.16828	+	1.27447i
$16$		0			0
$17$			4.23937i			1.02820i	0.857731	+	0.514100i	$0.171874\pi$
$17$			4.23937i			1.02820i	−0.857731	+	0.514100i	$0.828126\pi$
$18$		0			0
$19$	1.12365	−	1.12365i	0.257782	−	0.257782i	−0.566369	−	0.824152i	$-0.691652\pi$
$19$	1.12365	−	1.12365i	0.257782	−	0.257782i	0.824152	+	0.566369i	$0.191652\pi$
$20$		0			0
$21$	−4.91577	+	3.13037i	−1.07271	+	0.683104i
$22$		0			0
$23$	−3.33369	+	1.92471i	−0.695123	+	0.401329i	−0.805528	−	0.592557i	$-0.798118\pi$
$23$	−3.33369	+	1.92471i	−0.695123	+	0.401329i	0.110405	+	0.993887i	$0.464785\pi$
$24$		0			0
$25$	−8.61325	−	4.97286i	−1.72265	−	0.994572i
$26$		0			0
$27$	−0.675290	−	5.15209i	−0.129960	−	0.991519i
$28$		0			0
$29$	0.545635	+	2.03634i	0.101322	+	0.378138i	0.997902	−	0.0647434i	$-0.0206229\pi$
$29$	0.545635	+	2.03634i	0.101322	+	0.378138i	−0.896580	+	0.442882i	$0.853956\pi$
$30$		0			0
$31$	7.21206	−	4.16388i	1.29532	−	0.747856i	0.315731	−	0.948849i	$-0.397750\pi$
$31$	7.21206	−	4.16388i	1.29532	−	0.747856i	0.979593	+	0.200993i	$0.0644169\pi$
$32$		0			0
$33$	−0.0821277	+	0.370121i	−0.0142966	+	0.0644297i
$34$		0			0
$35$	−9.19798	−	9.19798i	−1.55474	−	1.55474i
$36$		0			0
$37$	−2.66564	+	2.66564i	−0.438229	+	0.438229i	−0.891416	−	0.453187i	$-0.850287\pi$
$37$	−2.66564	+	2.66564i	−0.438229	+	0.438229i	0.453187	+	0.891416i	$0.350287\pi$
$38$		0			0
$39$	−3.29004	+	3.58908i	−0.526828	+	0.574712i
$40$		0			0
$41$	−1.70386	−	2.95117i	−0.266098	−	0.460895i	0.701753	−	0.712420i	$-0.252401\pi$
$41$	−1.70386	−	2.95117i	−0.266098	−	0.460895i	−0.967851	+	0.251526i	$0.919068\pi$
$42$		0			0
$43$	−4.68985	+	1.25664i	−0.715195	+	0.191636i	−0.598027	−	0.801476i	$-0.704048\pi$
$43$	−4.68985	+	1.25664i	−0.715195	+	0.191636i	−0.117168	+	0.993112i	$0.537382\pi$
$44$		0			0
$45$	10.9000	−	3.96257i	1.62487	−	0.590704i
$46$		0			0
$47$	−2.34998	+	4.07028i	−0.342779	+	0.593711i	−0.984948	−	0.172852i	$-0.944702\pi$
$47$	−2.34998	+	4.07028i	−0.342779	+	0.593711i	0.642168	+	0.766564i	$0.278035\pi$
$48$		0			0
$49$	−2.16067	−	3.74239i	−0.308667	−	0.534628i
$50$		0			0
$51$	3.39177	−	6.51251i	0.474943	−	0.911933i
$52$		0			0
$53$	−7.58271	−	7.58271i	−1.04157	−	1.04157i	−0.999098	−	0.0424680i	$-0.986478\pi$
$53$	−7.58271	−	7.58271i	−1.04157	−	1.04157i	−0.0424680	−	0.999098i	$-0.513522\pi$
$54$		0			0
$55$	−0.846209			−0.114103
$56$		0			0
$57$	−2.62513	+	0.827151i	−0.347707	+	0.109559i
$58$		0			0
$59$	5.34305	+	1.43167i	0.695605	+	0.186387i	0.589261	−	0.807942i	$-0.299419\pi$
$59$	5.34305	+	1.43167i	0.695605	+	0.186387i	0.106344	+	0.994329i	$0.466085\pi$
$60$		0			0
$61$	8.69958	−	2.33105i	1.11387	−	0.298460i	0.345468	−	0.938431i	$-0.387720\pi$
$61$	8.69958	−	2.33105i	1.11387	−	0.298460i	0.768399	+	0.639971i	$0.221054\pi$
$62$		0			0
$63$	10.0561	−	0.875933i	1.26695	−	0.110357i
$64$		0			0
$65$	−9.41144	−	5.43370i	−1.16735	−	0.673967i
$66$		0			0
$67$	5.17504	+	1.38665i	0.632231	+	0.169406i	0.560682	−	0.828031i	$-0.310539\pi$
$67$	5.17504	+	1.38665i	0.632231	+	0.169406i	0.0715493	+	0.997437i	$0.477206\pi$
$68$		0			0
$69$	6.66110	−	0.289558i	0.801902	−	0.0348587i
$70$		0			0
$71$			7.53614i			0.894375i	0.894440	+	0.447187i	$0.147574\pi$
$71$			7.53614i			0.894375i	−0.894440	+	0.447187i	$0.852426\pi$
$72$		0			0
$73$		−	3.22646i		−	0.377629i	−0.982013	−	0.188814i	$-0.939536\pi$
$73$		−	3.22646i		−	0.377629i	0.982013	−	0.188814i	$-0.0604644\pi$
$74$		0			0
$75$	9.25302	+	14.5304i	1.06845	+	1.67783i
$76$		0			0
$77$	−0.711397	−	0.190618i	−0.0810712	−	0.0217230i
$78$		0			0
$79$	4.98587	+	2.87859i	0.560954	+	0.323867i	0.753528	−	0.657415i	$-0.228350\pi$
$79$	4.98587	+	2.87859i	0.560954	+	0.323867i	−0.192574	+	0.981282i	$0.561684\pi$
$80$		0			0
$81$	−3.08462	+	8.45489i	−0.342736	+	0.939432i
$82$		0			0
$83$	−4.50604	+	1.20739i	−0.494602	+	0.132528i	−0.497494	−	0.867468i	$-0.665746\pi$
$83$	−4.50604	+	1.20739i	−0.494602	+	0.132528i	0.00289160	+	0.999996i	$0.499080\pi$
$84$		0			0
$85$	15.8308	+	4.24186i	1.71710	+	0.460094i
$86$		0			0
$87$	0.790999	−	3.56475i	0.0848040	−	0.382182i
$88$		0			0
$89$	−2.96157			−0.313926			−0.156963	−	0.987605i	$-0.550170\pi$
$89$	−2.96157			−0.313926			−0.156963	+	0.987605i	$0.550170\pi$
$90$		0			0
$91$	−6.68807	−	6.68807i	−0.701100	−	0.701100i
$92$		0			0
$93$	−14.4105	+	0.626426i	−1.49430	+	0.0649573i
$94$		0			0
$95$	−3.07166	−	5.32027i	−0.315146	−	0.545849i
$96$		0			0
$97$	−7.63883	+	13.2308i	−0.775606	+	1.34339i	0.158848	+	0.987303i	$0.449222\pi$
$97$	−7.63883	+	13.2308i	−0.775606	+	1.34339i	−0.934453	+	0.356085i	$0.884111\pi$
$98$		0			0
$99$	0.422285	−	0.502870i	0.0424412	−	0.0505403i
$100$		0			0
$101$	0.129684	−	0.0347486i	0.0129040	−	0.00345762i	−0.252361	−	0.967633i	$-0.581207\pi$
$101$	0.129684	−	0.0347486i	0.0129040	−	0.00345762i	0.265265	+	0.964175i	$0.414540\pi$
$102$		0			0
$103$	4.09117	+	7.08611i	0.403115	+	0.698215i	0.994100	−	0.108467i	$-0.0345942\pi$
$103$	4.09117	+	7.08611i	0.403115	+	0.698215i	−0.590985	+	0.806682i	$0.701261\pi$
$104$		0			0
$105$	6.77091	+	21.4889i	0.660774	+	2.09710i
$106$		0			0
$107$	−8.28837	+	8.28837i	−0.801267	+	0.801267i	−0.983294	−	0.182027i	$-0.941734\pi$
$107$	−8.28837	+	8.28837i	−0.801267	+	0.801267i	0.182027	+	0.983294i	$0.441734\pi$
$108$		0			0
$109$	6.31291	+	6.31291i	0.604667	+	0.604667i	0.941547	−	0.336881i	$-0.109372\pi$
$109$	6.31291	+	6.31291i	0.604667	+	0.604667i	−0.336881	+	0.941547i	$0.609372\pi$
$110$		0			0
$111$	6.22764	−	1.96226i	0.591101	−	0.186250i
$112$		0			0
$113$	14.6562	−	8.46178i	1.37874	−	0.796017i	0.386735	−	0.922191i	$-0.373603\pi$
$113$	14.6562	−	8.46178i	1.37874	−	0.796017i	0.992008	+	0.126174i	$0.0402696\pi$
$114$		0			0
$115$	3.85167	+	14.3746i	0.359171	+	1.34044i
$116$		0			0
$117$	7.92564	−	2.88128i	0.732725	−	0.266374i
$118$		0			0
$119$	12.3533	+	7.13215i	1.13242	+	0.653803i
$120$		0			0
$121$	9.48479	−	5.47604i	0.862253	−	0.497822i
$122$		0			0
$123$	0.256333	+	5.89676i	0.0231128	+	0.531693i
$124$		0			0
$125$	−13.5199	+	13.5199i	−1.20926	+	1.20926i
$126$		0			0
$127$		−	13.4028i		−	1.18931i	−0.803981	−	0.594654i	$-0.797289\pi$
$127$		−	13.4028i		−	1.18931i	0.803981	−	0.594654i	$-0.202711\pi$
$128$		0			0
$129$	8.20992	+	1.82174i	0.722843	+	0.160395i
$130$		0			0
$131$	−0.169534	+	0.632708i	−0.0148122	+	0.0552800i	−0.972936	−	0.231073i	$-0.925776\pi$
$131$	−0.169534	+	0.632708i	−0.0148122	+	0.0552800i	0.958124	+	0.286353i	$0.0924430\pi$
$132$		0			0
$133$	−1.38385	−	5.16461i	−0.119995	−	0.447829i
$134$		0			0
$135$	−19.9148	−	2.63341i	−1.71399	−	0.226648i
$136$		0			0
$137$	10.5230	−	18.2263i	0.899037	−	1.55718i	0.0703095	−	0.997525i	$-0.477601\pi$
$137$	10.5230	−	18.2263i	0.899037	−	1.55718i	0.828727	−	0.559652i	$-0.189065\pi$
$138$		0			0
$139$	1.72666	−	6.44400i	0.146454	−	0.546573i	−0.853233	−	0.521530i	$-0.825361\pi$
$139$	1.72666	−	6.44400i	0.146454	−	0.546573i	0.999686	−	0.0250423i	$-0.00797204\pi$
$140$		0			0
$141$	6.86651	−	4.37261i	0.578264	−	0.368240i
$142$		0			0
$143$	−0.615299			−0.0514539
$144$		0			0
$145$	8.15012			0.676831
$146$		0			0
$147$	0.325057	+	7.47772i	0.0268103	+	0.616752i
$148$		0			0
$149$	−5.78161	+	21.5773i	−0.473648	+	1.76768i	0.152844	+	0.988250i	$0.451157\pi$
$149$	−5.78161	+	21.5773i	−0.473648	+	1.76768i	−0.626492	+	0.779428i	$0.715510\pi$
$150$		0			0
$151$	9.97506	−	17.2773i	0.811759	−	1.40601i	−0.0998734	−	0.995000i	$-0.531844\pi$
$151$	9.97506	−	17.2773i	0.811759	−	1.40601i	0.911632	−	0.411007i	$-0.134823\pi$
$152$		0			0
$153$	−10.4209	+	7.29084i	−0.842476	+	0.589430i
$154$		0			0
$155$	−8.33265	−	31.0979i	−0.669295	−	2.49784i
$156$		0			0
$157$	3.85693	−	14.3943i	0.307817	−	1.14879i	−0.622677	−	0.782479i	$-0.713955\pi$
$157$	3.85693	−	14.3943i	0.307817	−	1.14879i	0.930494	−	0.366308i	$-0.119378\pi$
$158$		0			0
$159$	5.58187	+	17.7152i	0.442671	+	1.40491i
$160$		0			0
$161$			12.9522i			1.02078i
$162$		0			0
$163$	4.35766	−	4.35766i	0.341318	−	0.341318i	−0.515545	−	0.856863i	$-0.672410\pi$
$163$	4.35766	−	4.35766i	0.341318	−	0.341318i	0.856863	+	0.515545i	$0.172410\pi$
$164$		0			0
$165$	1.29994	+	0.677022i	0.101200	+	0.0527061i
$166$		0			0
$167$	11.8952	−	6.86770i	0.920479	−	0.531439i	0.0366910	−	0.999327i	$-0.488318\pi$
$167$	11.8952	−	6.86770i	0.920479	−	0.531439i	0.883788	+	0.467888i	$0.154985\pi$
$168$		0			0
$169$	4.41505	+	2.54903i	0.339619	+	0.196079i
$170$		0			0
$171$	4.69449	+	0.829610i	0.358997	+	0.0634418i
$172$		0			0
$173$	1.40497	+	5.24342i	0.106818	+	0.398650i	0.998545	−	0.0539235i	$-0.0171727\pi$
$173$	1.40497	+	5.24342i	0.106818	+	0.398650i	−0.891727	+	0.452573i	$0.850506\pi$
$174$		0			0
$175$	−28.9812	+	16.7323i	−2.19077	+	1.26484i
$176$		0			0
$177$	−7.06254	−	6.47410i	−0.530853	−	0.486623i
$178$		0			0
$179$	−0.380130	−	0.380130i	−0.0284123	−	0.0284123i	0.692758	−	0.721170i	$-0.256395\pi$
$179$	−0.380130	−	0.380130i	−0.0284123	−	0.0284123i	−0.721170	+	0.692758i	$0.756395\pi$
$180$		0			0
$181$	−4.98992	+	4.98992i	−0.370898	+	0.370898i	−0.867804	−	0.496906i	$-0.834469\pi$
$181$	−4.98992	+	4.98992i	−0.370898	+	0.370898i	0.496906	+	0.867804i	$0.334469\pi$
$182$		0			0
$183$	−15.2292	−	3.37929i	−1.12578	−	0.249804i
$184$		0			0
$185$	7.28695	+	12.6214i	0.535747	+	0.927941i
$186$		0			0
$187$	0.896324	−	0.240169i	0.0655457	−	0.0175629i
$188$		0			0
$189$	−16.1489	−	6.69991i	−1.17466	−	0.487347i
$190$		0			0
$191$	5.40555	−	9.36269i	0.391132	−	0.677461i	−0.601467	−	0.798898i	$-0.705417\pi$
$191$	5.40555	−	9.36269i	0.391132	−	0.677461i	0.992599	+	0.121437i	$0.0387502\pi$
$192$		0			0
$193$	2.60044	+	4.50410i	0.187184	+	0.324212i	0.944310	−	0.329056i	$-0.106731\pi$
$193$	2.60044	+	4.50410i	0.187184	+	0.324212i	−0.757126	+	0.653268i	$0.773397\pi$
$194$		0			0
$195$	10.1105	+	15.8770i	0.724028	+	1.13697i
$196$		0			0
$197$	−2.94550	−	2.94550i	−0.209858	−	0.209858i	0.594349	−	0.804207i	$-0.297410\pi$
$197$	−2.94550	−	2.94550i	−0.209858	−	0.209858i	−0.804207	+	0.594349i	$0.797410\pi$
$198$		0			0
$199$	−2.57285			−0.182384			−0.0911921	−	0.995833i	$-0.529068\pi$
$199$	−2.57285			−0.182384			−0.0911921	+	0.995833i	$0.529068\pi$
$200$		0			0
$201$	−6.84046	−	6.27053i	−0.482489	−	0.442289i
$202$		0			0
$203$	6.85170	+	1.83591i	0.480895	+	0.128856i
$204$		0			0
$205$	−12.7252	+	3.40971i	−0.888768	+	0.238145i
$206$		0			0
$207$	−10.4644	−	4.88449i	−0.727327	−	0.339495i
$208$		0			0
$209$	−0.301228	−	0.173914i	−0.0208364	−	0.0120299i
$210$		0			0
$211$	−17.5700	−	4.70786i	−1.20957	−	0.324103i	−0.402975	−	0.915211i	$-0.632024\pi$
$211$	−17.5700	−	4.70786i	−1.20957	−	0.324103i	−0.806592	+	0.591108i	$0.798691\pi$
$212$		0			0
$213$	6.02940	−	11.5770i	0.413127	−	0.793242i
$214$		0			0
$215$			18.7704i			1.28013i
$216$		0			0
$217$		−	28.0206i		−	1.90216i
$218$		0			0
$219$	−2.58138	+	4.95647i	−0.174433	+	0.334927i
$220$		0			0
$221$	11.5110	+	3.08436i	0.774312	+	0.207476i
$222$		0			0
$223$	−2.82059	−	1.62847i	−0.188881	−	0.109050i	0.402578	−	0.915386i	$-0.368114\pi$
$223$	−2.82059	−	1.62847i	−0.188881	−	0.109050i	−0.591458	+	0.806336i	$0.701448\pi$
$224$		0			0
$225$	−2.58916	−	29.7246i	−0.172610	−	1.98164i
$226$		0			0
$227$	8.83238	−	2.36663i	0.586226	−	0.157079i	0.0464979	−	0.998918i	$-0.485194\pi$
$227$	8.83238	−	2.36663i	0.586226	−	0.157079i	0.539728	+	0.841840i	$0.318527\pi$
$228$		0			0
$229$	−5.07755	−	1.36053i	−0.335534	−	0.0899061i	0.0871183	−	0.996198i	$-0.472234\pi$
$229$	−5.07755	−	1.36053i	−0.335534	−	0.0899061i	−0.422652	+	0.906292i	$0.638901\pi$
$230$		0			0
$231$	0.940338	+	0.861991i	0.0618697	+	0.0567148i
$232$		0			0
$233$	14.1506			0.927034			0.463517	−	0.886088i	$-0.346587\pi$
$233$	14.1506			0.927034			0.463517	+	0.886088i	$0.346587\pi$
$234$		0			0
$235$	12.8480	+	12.8480i	0.838114	+	0.838114i
$236$		0			0
$237$	−5.35621	−	8.41110i	−0.347923	−	0.546360i
$238$		0			0
$239$	7.51536	+	13.0170i	0.486128	+	0.841999i	0.999873	−	0.0159444i	$-0.00507546\pi$
$239$	7.51536	+	13.0170i	0.486128	+	0.841999i	−0.513745	+	0.857943i	$0.671742\pi$
$240$		0			0
$241$	7.18920	−	12.4521i	0.463097	−	0.802108i	−0.536016	−	0.844208i	$-0.680071\pi$
$241$	7.18920	−	12.4521i	0.463097	−	0.802108i	0.999113	+	0.0420996i	$0.0134047\pi$
$242$		0			0
$243$	11.5030	−	10.5205i	0.737921	−	0.674888i
$244$		0			0
$245$	−16.1369	+	4.32388i	−1.03095	+	0.276242i
$246$		0			0
$247$	−2.23348	−	3.86850i	−0.142113	−	0.246147i
$248$		0			0
$249$	7.88815	+	1.75034i	0.499891	+	0.110923i
$250$		0			0
$251$	3.59758	−	3.59758i	0.227077	−	0.227077i	−0.584393	−	0.811471i	$-0.698667\pi$
$251$	3.59758	−	3.59758i	0.227077	−	0.227077i	0.811471	+	0.584393i	$0.198667\pi$
$252$		0			0
$253$	0.595798	+	0.595798i	0.0374575	+	0.0374575i
$254$		0			0
$255$	−20.9255	−	19.1820i	−1.31041	−	1.20122i
$256$		0			0
$257$	−4.92640	+	2.84426i	−0.307300	+	0.177420i	−0.645718	−	0.763576i	$-0.723442\pi$
$257$	−4.92640	+	2.84426i	−0.307300	+	0.177420i	0.338418	+	0.940996i	$0.390108\pi$
$258$		0			0
$259$	3.28294	+	12.2521i	0.203992	+	0.761307i
$260$		0			0
$261$	−4.06716	+	4.84331i	−0.251751	+	0.299793i
$262$		0			0
$263$	−18.8392	−	10.8768i	−1.16167	−	0.670693i	−0.209970	−	0.977708i	$-0.567337\pi$
$263$	−18.8392	−	10.8768i	−1.16167	−	0.670693i	−0.951705	+	0.307015i	$0.900670\pi$
$264$		0			0
$265$	−35.9028	+	20.7285i	−2.20549	+	1.27334i
$266$		0			0
$267$	4.54955	+	2.36945i	0.278428	+	0.145008i
$268$		0			0
$269$	−7.43467	+	7.43467i	−0.453300	+	0.453300i	−0.896448	−	0.443148i	$-0.853861\pi$
$269$	−7.43467	+	7.43467i	−0.453300	+	0.453300i	0.443148	+	0.896448i	$0.353861\pi$
$270$		0			0
$271$		−	11.8875i		−	0.722111i	−0.932544	−	0.361056i	$-0.882416\pi$
$271$		−	11.8875i		−	0.722111i	0.932544	−	0.361056i	$-0.117584\pi$
$272$		0			0
$273$	4.92329	+	15.6251i	0.297971	+	0.945673i
$274$		0			0
$275$	−0.563445	+	2.10281i	−0.0339770	+	0.126804i
$276$		0			0
$277$	2.68166	+	10.0081i	0.161126	+	0.601329i	0.998503	+	0.0547032i	$0.0174213\pi$
$277$	2.68166	+	10.0081i	0.161126	+	0.601329i	−0.837377	+	0.546626i	$0.815912\pi$
$278$		0			0
$279$	22.6385	+	10.5670i	1.35533	+	0.632631i
$280$		0			0
$281$	−7.05630	+	12.2219i	−0.420944	+	0.729096i	−0.996032	−	0.0889955i	$-0.971634\pi$
$281$	−7.05630	+	12.2219i	−0.420944	+	0.729096i	0.575088	+	0.818091i	$0.304968\pi$
$282$		0			0
$283$	−3.42843	+	12.7951i	−0.203799	+	0.760588i	0.786013	+	0.618209i	$0.212142\pi$
$283$	−3.42843	+	12.7951i	−0.203799	+	0.760588i	−0.989812	+	0.142378i	$0.954525\pi$
$284$		0			0
$285$	0.462109	+	10.6305i	0.0273730	+	0.629697i
$286$		0			0
$287$	−11.4660			−0.676817
$288$		0			0
$289$	−0.972286			−0.0571933
$290$		0			0
$291$	22.3203	−	14.2136i	1.30844	−	0.833216i
$292$		0			0
$293$	7.96005	−	29.7073i	0.465031	−	1.73552i	−0.191756	−	0.981443i	$-0.561418\pi$
$293$	7.96005	−	29.7073i	0.465031	−	1.73552i	0.656787	−	0.754077i	$-0.271915\pi$
$294$		0			0
$295$	10.6924	−	18.5197i	0.622533	−	1.07826i
$296$		0			0
$297$	−1.05104	+	0.434652i	−0.0609875	+	0.0252210i
$298$		0			0
$299$	2.80065	+	10.4522i	0.161965	+	0.604463i
$300$		0			0
$301$	−4.22825	+	15.7800i	−0.243712	+	0.909546i
$302$		0			0
$303$	−0.227020	−	0.0503746i	−0.0130420	−	0.00289395i
$304$		0			0
$305$		−	34.8187i		−	1.99371i
$306$		0			0
$307$	−23.8109	+	23.8109i	−1.35896	+	1.35896i	−0.483758	+	0.875202i	$0.660728\pi$
$307$	−23.8109	+	23.8109i	−1.35896	+	1.35896i	−0.875202	+	0.483758i	$0.839272\pi$
$308$		0			0
$309$	−0.615486	−	14.1588i	−0.0350138	−	0.805469i
$310$		0			0
$311$	9.20941	−	5.31706i	0.522218	−	0.301503i	−0.215624	−	0.976477i	$-0.569178\pi$
$311$	9.20941	−	5.31706i	0.522218	−	0.301503i	0.737842	+	0.674974i	$0.235845\pi$
$312$		0			0
$313$	16.4634	+	9.50514i	0.930565	+	0.537262i	0.886990	−	0.461788i	$-0.152792\pi$
$313$	16.4634	+	9.50514i	0.930565	+	0.537262i	0.0435750	+	0.999050i	$0.486125\pi$
$314$		0			0
$315$	6.79104	−	38.4283i	0.382632	−	2.16519i
$316$		0			0
$317$	−3.18193	−	11.8751i	−0.178715	−	0.666972i	−0.995889	−	0.0905818i	$-0.971127\pi$
$317$	−3.18193	−	11.8751i	−0.178715	−	0.666972i	0.817174	−	0.576391i	$-0.195539\pi$
$318$		0			0
$319$	0.399628	−	0.230725i	0.0223749	−	0.0129181i
$320$		0			0
$321$	19.3638	−	6.10132i	1.08078	−	0.340543i
$322$		0			0
$323$	4.76356	+	4.76356i	0.265052	+	0.265052i
$324$		0			0
$325$	−19.7692	+	19.7692i	−1.09660	+	1.09660i
$326$		0			0
$327$	−4.64712	−	14.7486i	−0.256987	−	0.815599i
$328$		0			0
$329$	7.90701	+	13.6953i	0.435928	+	0.755049i
$330$		0			0
$331$	−33.3960	+	8.94844i	−1.83561	+	0.491851i	−0.998478	−	0.0551468i	$-0.982437\pi$
$331$	−33.3960	+	8.94844i	−1.83561	+	0.491851i	−0.837134	+	0.546998i	$0.815771\pi$
$332$		0			0
$333$	−11.1368	−	1.96809i	−0.610293	−	0.107851i
$334$		0			0
$335$	10.3561	−	17.9374i	0.565817	−	0.980023i
$336$		0			0
$337$	−14.3693	−	24.8884i	−0.782746	−	1.35576i	−0.930336	−	0.366707i	$-0.880485\pi$
$337$	−14.3693	−	24.8884i	−0.782746	−	1.35576i	0.147591	−	0.989049i	$-0.452848\pi$
$338$		0			0
$339$	−29.2848	+	1.27301i	−1.59053	+	0.0691406i
$340$		0			0
$341$	−1.28894	−	1.28894i	−0.0698001	−	0.0698001i
$342$		0			0
$343$	9.01293			0.486653
$344$		0			0
$345$	5.58372	−	25.1639i	0.300617	−	1.35478i
$346$		0			0
$347$	10.9346	+	2.92992i	0.587002	+	0.157287i	0.540082	−	0.841612i	$-0.318393\pi$
$347$	10.9346	+	2.92992i	0.587002	+	0.157287i	0.0469191	+	0.998899i	$0.485060\pi$
$348$		0			0
$349$	10.8496	−	2.90715i	0.580767	−	0.155616i	0.0435372	−	0.999052i	$-0.486137\pi$
$349$	10.8496	−	2.90715i	0.580767	−	0.155616i	0.537230	+	0.843436i	$0.319471\pi$
$350$		0			0
$351$	−14.4805	−	1.91482i	−0.772914	−	0.102205i
$352$		0			0
$353$	1.85946	+	1.07356i	0.0989689	+	0.0571397i	0.548668	−	0.836041i	$-0.315135\pi$
$353$	1.85946	+	1.07356i	0.0989689	+	0.0571397i	−0.449699	+	0.893180i	$0.648469\pi$
$354$		0			0
$355$	28.1417	+	7.54056i	1.49361	+	0.400211i
$356$		0			0
$357$	−13.2708	−	20.8398i	−0.702366	−	1.10296i
$358$		0			0
$359$		−	11.0166i		−	0.581435i	−0.956809	−	0.290718i	$-0.906106\pi$
$359$		−	11.0166i		−	0.581435i	0.956809	−	0.290718i	$-0.0938941\pi$
$360$		0			0
$361$			16.4748i			0.867097i
$362$		0			0
$363$	−18.9517	+	0.823831i	−0.994705	+	0.0432399i
$364$		0			0
$365$	−12.0484	−	3.22835i	−0.630641	−	0.168980i
$366$		0			0
$367$	20.1365	+	11.6258i	1.05112	+	0.606863i	0.922962	−	0.384891i	$-0.125761\pi$
$367$	20.1365	+	11.6258i	1.05112	+	0.606863i	0.128156	+	0.991754i	$0.459094\pi$
$368$		0			0
$369$	4.32402	−	9.26366i	0.225099	−	0.482247i
$370$		0			0
$371$	−34.8524	+	9.33867i	−1.80945	+	0.484839i
$372$		0			0
$373$	9.93021	+	2.66079i	0.514167	+	0.137771i	0.506567	−	0.862201i	$-0.330914\pi$
$373$	9.93021	+	2.66079i	0.514167	+	0.137771i	0.00759967	+	0.999971i	$0.497581\pi$
$374$		0			0
$375$	31.5860	−	9.95240i	1.63109	−	0.513940i
$376$		0			0
$377$	5.92615			0.305212
$378$		0			0
$379$	6.14819	+	6.14819i	0.315811	+	0.315811i	0.847156	−	0.531345i	$-0.178313\pi$
$379$	6.14819	+	6.14819i	0.315811	+	0.315811i	−0.531345	+	0.847156i	$0.678313\pi$
$380$		0			0
$381$	−10.7231	+	20.5894i	−0.549363	+	1.05483i
$382$		0			0
$383$	1.40170	+	2.42782i	0.0716238	+	0.124056i	0.899613	−	0.436688i	$-0.143849\pi$
$383$	1.40170	+	2.42782i	0.0716238	+	0.124056i	−0.827989	+	0.560744i	$0.810515\pi$
$384$		0			0
$385$	−1.42363	+	2.46580i	−0.0725548	+	0.125669i
$386$		0			0
$387$	−11.1545	−	9.36701i	−0.567017	−	0.476152i
$388$		0			0
$389$	29.1977	−	7.82350i	1.48038	−	0.396667i	0.573905	−	0.818922i	$-0.305428\pi$
$389$	29.1977	−	7.82350i	1.48038	−	0.396667i	0.906477	+	0.422255i	$0.138761\pi$
$390$		0			0
$391$	−8.15956	−	14.1328i	−0.412647	−	0.714725i
$392$		0			0
$393$	0.766644	−	0.836325i	0.0386721	−	0.0421870i
$394$		0			0
$395$	15.7382	−	15.7382i	0.791873	−	0.791873i
$396$		0			0
$397$	1.95789	+	1.95789i	0.0982636	+	0.0982636i	0.754530	−	0.656266i	$-0.227865\pi$
$397$	1.95789	+	1.95789i	0.0982636	+	0.0982636i	−0.656266	+	0.754530i	$0.727865\pi$
$398$		0			0
$399$	−2.00615	+	9.04103i	−0.100433	+	0.452617i
$400$		0			0
$401$	−28.7356	+	16.5905i	−1.43499	+	0.828489i	−0.997495	−	0.0707337i	$-0.977466\pi$
$401$	−28.7356	+	16.5905i	−1.43499	+	0.828489i	−0.437490	+	0.899223i	$0.644133\pi$
$402$		0			0
$403$	−6.05887	−	22.6120i	−0.301814	−	1.12638i
$404$		0			0
$405$	28.4861	+	19.9786i	1.41549	+	0.992743i
$406$		0			0
$407$	0.714607	+	0.412578i	0.0354217	+	0.0204508i
$408$		0			0
$409$	−22.8959	+	13.2190i	−1.13213	+	0.653636i	−0.944470	−	0.328598i	$-0.893424\pi$
$409$	−22.8959	+	13.2190i	−1.13213	+	0.653636i	−0.187660	+	0.982234i	$0.560090\pi$
$410$		0			0
$411$	−30.7475	+	19.5801i	−1.51666	+	0.965816i
$412$		0			0
$413$	13.1607	−	13.1607i	0.647596	−	0.647596i
$414$		0			0
$415$			18.0347i			0.885290i
$416$		0			0
$417$	−7.80811	+	8.51780i	−0.382365	+	0.417118i
$418$		0			0
$419$	0.133835	−	0.499479i	0.00653827	−	0.0244012i	−0.962580	−	0.270999i	$-0.912646\pi$
$419$	0.133835	−	0.499479i	0.00653827	−	0.0244012i	0.969118	+	0.246598i	$0.0793127\pi$
$420$		0			0
$421$	−3.44352	−	12.8514i	−0.167827	−	0.626339i	−0.997663	−	0.0683313i	$-0.978233\pi$
$421$	−3.44352	−	12.8514i	−0.167827	−	0.626339i	0.829836	−	0.558008i	$-0.188434\pi$
$422$		0			0
$423$	−14.0467	+	1.22353i	−0.682972	+	0.0594902i
$424$		0			0
$425$	21.0818	−	36.5148i	1.02262	−	1.77123i
$426$		0			0
$427$	7.84332	−	29.2717i	0.379565	−	1.41655i
$428$		0			0
$429$	0.945220	+	0.492279i	0.0456356	+	0.0237675i
$430$		0			0
$431$	−8.61129			−0.414791			−0.207396	−	0.978257i	$-0.566499\pi$
$431$	−8.61129			−0.414791			−0.207396	+	0.978257i	$0.566499\pi$
$432$		0			0
$433$	6.43973			0.309474			0.154737	−	0.987956i	$-0.450547\pi$
$433$	6.43973			0.309474			0.154737	+	0.987956i	$0.450547\pi$
$434$		0			0
$435$	−12.5202	−	6.52063i	−0.600297	−	0.312640i
$436$		0			0
$437$	−1.58320	+	5.90859i	−0.0757348	+	0.282646i
$438$		0			0
$439$	−14.4510	+	25.0298i	−0.689707	+	1.19461i	0.282225	+	0.959348i	$0.408927\pi$
$439$	−14.4510	+	25.0298i	−0.689707	+	1.19461i	−0.971933	+	0.235260i	$0.924406\pi$
$440$		0			0
$441$	5.48331	−	11.7473i	0.261110	−	0.559396i
$442$		0			0
$443$	8.35627	+	31.1860i	0.397018	+	1.48169i	0.818315	+	0.574770i	$0.194908\pi$
$443$	8.35627	+	31.1860i	0.397018	+	1.48169i	−0.421297	+	0.906923i	$0.638425\pi$
$444$		0			0
$445$	−2.96330	+	11.0592i	−0.140474	+	0.524257i
$446$		0			0
$447$	26.1449	−	28.5212i	1.23661	−	1.34901i
$448$		0			0
$449$			10.7097i			0.505423i	0.967542	+	0.252711i	$0.0813223\pi$
$449$			10.7097i			0.505423i	−0.967542	+	0.252711i	$0.918678\pi$
$450$		0			0
$451$	−0.527433	+	0.527433i	−0.0248359	+	0.0248359i
$452$		0			0
$453$	−29.1466	+	18.5606i	−1.36943	+	0.872054i
$454$		0			0
$455$	−31.6669	+	18.2829i	−1.48457	+	0.857114i
$456$		0			0
$457$	−13.1358	−	7.58393i	−0.614465	−	0.354761i	0.160246	−	0.987077i	$-0.448771\pi$
$457$	−13.1358	−	7.58393i	−0.614465	−	0.354761i	−0.774711	+	0.632316i	$0.782105\pi$
$458$		0			0
$459$	21.8416	−	2.86281i	1.01948	−	0.133624i
$460$		0			0
$461$	−3.10006	−	11.5696i	−0.144384	−	0.538849i	−0.999782	−	0.0208774i	$-0.993354\pi$
$461$	−3.10006	−	11.5696i	−0.144384	−	0.538849i	0.855398	−	0.517971i	$-0.173313\pi$
$462$		0			0
$463$	−2.03363	+	1.17412i	−0.0945107	+	0.0545658i	−0.546510	−	0.837452i	$-0.684044\pi$
$463$	−2.03363	+	1.17412i	−0.0945107	+	0.0545658i	0.452000	+	0.892018i	$0.350711\pi$
$464$		0			0
$465$	−12.0797	+	54.4391i	−0.560184	+	2.52455i
$466$		0			0
$467$	24.1509	+	24.1509i	1.11757	+	1.11757i	0.992097	+	0.125473i	$0.0400449\pi$
$467$	24.1509	+	24.1509i	1.11757	+	1.11757i	0.125473	+	0.992097i	$0.459955\pi$
$468$		0			0
$469$	12.7469	−	12.7469i	0.588596	−	0.588596i
$470$		0			0
$471$	−17.4413	+	19.0266i	−0.803654	+	0.876700i
$472$		0			0
$473$	0.531379	+	0.920376i	0.0244328	+	0.0423189i
$474$		0			0
$475$	−15.2660	+	4.09051i	−0.700452	+	0.187685i
$476$		0			0
$477$	5.59846	−	31.6799i	0.256336	−	1.45052i
$478$		0			0
$479$	−2.40917	+	4.17281i	−0.110078	+	0.190660i	−0.915801	−	0.401631i	$-0.868443\pi$
$479$	−2.40917	+	4.17281i	−0.110078	+	0.190660i	0.805724	+	0.592292i	$0.201777\pi$
$480$		0			0
$481$	5.29851	+	9.17730i	0.241591	+	0.418449i
$482$		0			0
$483$	10.3626	−	19.8971i	0.471515	−	0.905351i
$484$		0			0
$485$	41.7638	+	41.7638i	1.89640	+	1.89640i
$486$		0			0
$487$	−37.5042			−1.69948			−0.849739	−	0.527204i	$-0.823240\pi$
$487$	−37.5042			−1.69948			−0.849739	+	0.527204i	$0.823240\pi$
$488$		0			0
$489$	−10.1806	+	3.20781i	−0.460384	+	0.145062i
$490$		0			0
$491$	1.88310	+	0.504576i	0.0849832	+	0.0227712i	0.301060	−	0.953605i	$-0.402660\pi$
$491$	1.88310	+	0.504576i	0.0849832	+	0.0227712i	−0.216077	+	0.976376i	$0.569326\pi$
$492$		0			0
$493$	−8.63279	+	2.31315i	−0.388801	+	0.104179i
$494$		0			0
$495$	−1.45530	−	2.08008i	−0.0654111	−	0.0934925i
$496$		0			0
$497$	21.9598	+	12.6785i	0.985032	+	0.568708i
$498$		0			0
$499$	−10.8793	−	2.91509i	−0.487023	−	0.130497i	0.00694794	−	0.999976i	$-0.497788\pi$
$499$	−10.8793	−	2.91509i	−0.487023	−	0.130497i	−0.493971	+	0.869478i	$0.664455\pi$
$500$		0			0
$501$	−23.7680	+	1.03320i	−1.06187	+	0.0461598i
$502$		0			0
$503$			15.3339i			0.683706i	0.939753	+	0.341853i	$0.111055\pi$
$503$			15.3339i			0.683706i	−0.939753	+	0.341853i	$0.888945\pi$
$504$		0			0
$505$		−	0.519039i		−	0.0230969i
$506$		0			0
$507$	−4.74299	−	7.44813i	−0.210644	−	0.330783i
$508$		0			0
$509$	32.0866	+	8.59758i	1.42221	+	0.381081i	0.886269	−	0.463172i	$-0.153289\pi$
$509$	32.0866	+	8.59758i	1.42221	+	0.381081i	0.535945	+	0.844253i	$0.319955\pi$
$510$		0			0
$511$	−9.40169	−	5.42807i	−0.415906	−	0.240124i
$512$		0			0
$513$	−6.54791	−	5.03034i	−0.289097	−	0.222095i
$514$		0			0
$515$	30.5548	−	8.18713i	1.34641	−	0.360768i
$516$		0			0
$517$	0.993703	+	0.266262i	0.0437030	+	0.0117102i
$518$		0			0
$519$	2.03677	−	9.17899i	0.0894042	−	0.402913i
$520$		0			0
$521$	−20.5032			−0.898262			−0.449131	−	0.893466i	$-0.648266\pi$
$521$	−20.5032			−0.898262			−0.449131	+	0.893466i	$0.648266\pi$
$522$		0			0
$523$	29.2406	+	29.2406i	1.27860	+	1.27860i	0.941451	+	0.337151i	$0.109463\pi$
$523$	29.2406	+	29.2406i	1.27860	+	1.27860i	0.337151	+	0.941451i	$0.390537\pi$
$524$		0			0
$525$	57.9076	−	2.51725i	2.52730	−	0.109862i
$526$		0			0
$527$	17.6523	+	30.5746i	0.768944	+	1.33185i
$528$		0			0
$529$	−4.09099	+	7.08581i	−0.177869	+	0.308079i
$530$		0			0
$531$	5.66974	+	15.5960i	0.246046	+	0.676808i
$532$		0			0
$533$	−9.25281	+	2.47928i	−0.400784	+	0.107390i
$534$		0			0
$535$	22.6575	+	39.2440i	0.979570	+	1.69667i
$536$		0			0
$537$	0.279825	+	0.888083i	0.0120754	+	0.0383236i
$538$		0			0
$539$	−0.668841	+	0.668841i	−0.0288090	+	0.0288090i
$540$		0			0
$541$	20.5836	+	20.5836i	0.884956	+	0.884956i	0.994033	−	0.109077i	$-0.0347895\pi$
$541$	20.5836	+	20.5836i	0.884956	+	0.884956i	−0.109077	+	0.994033i	$0.534790\pi$
$542$		0			0
$543$	11.6578	−	3.67324i	0.500282	−	0.157634i
$544$		0			0
$545$	29.8905	−	17.2573i	1.28037	−	0.739221i
$546$		0			0
$547$	−10.2029	−	38.0779i	−0.436246	−	1.62809i	−0.738067	−	0.674728i	$-0.764261\pi$
$547$	−10.2029	−	38.0779i	−0.436246	−	1.62809i	0.301821	−	0.953365i	$-0.402406\pi$
$548$		0			0
$549$	20.6914	+	17.3756i	0.883089	+	0.741574i
$550$		0			0
$551$	2.90122	+	1.67502i	0.123596	+	0.0713584i
$552$		0			0
$553$	16.7761	−	9.68566i	0.713391	−	0.411876i
$554$		0			0
$555$	−1.09627	−	25.2189i	−0.0465340	−	1.07048i
$556$		0			0
$557$	−1.52288	+	1.52288i	−0.0645265	+	0.0645265i	−0.738634	−	0.674107i	$-0.764529\pi$
$557$	−1.52288	+	1.52288i	−0.0645265	+	0.0645265i	0.674107	+	0.738634i	$0.264529\pi$
$558$		0			0
$559$			13.6484i			0.577266i
$560$		0			0
$561$	−1.56908	−	0.348170i	−0.0662466	−	0.0146998i
$562$		0			0
$563$	1.30147	−	4.85715i	0.0548504	−	0.204705i	−0.933063	−	0.359714i	$-0.882874\pi$
$563$	1.30147	−	4.85715i	0.0548504	−	0.204705i	0.987913	+	0.155010i	$0.0495409\pi$
$564$		0			0
$565$	−16.9335	−	63.1966i	−0.712397	−	2.65870i
$566$		0			0
$567$	19.4475	+	23.2126i	0.816719	+	0.974836i
$568$		0			0
$569$	−17.4710	+	30.2606i	−0.732421	+	1.26859i	0.223425	+	0.974721i	$0.428276\pi$
$569$	−17.4710	+	30.2606i	−0.732421	+	1.26859i	−0.955846	+	0.293869i	$0.905057\pi$
$570$		0			0
$571$	9.16034	−	34.1869i	0.383348	−	1.43068i	−0.457406	−	0.889258i	$-0.651221\pi$
$571$	9.16034	−	34.1869i	0.383348	−	1.43068i	0.840754	−	0.541417i	$-0.182112\pi$
$572$		0			0
$573$	−15.7947	+	10.0581i	−0.659835	+	0.420185i
$574$		0			0
$575$	38.2852			1.59660
$576$		0			0
$577$	−17.4865			−0.727972			−0.363986	−	0.931404i	$-0.618584\pi$
$577$	−17.4865			−0.727972			−0.363986	+	0.931404i	$0.618584\pi$
$578$		0			0
$579$	−0.391218	−	8.99970i	−0.0162584	−	0.374015i
$580$		0			0
$581$	−4.06253	+	15.1616i	−0.168542	+	0.629008i
$582$		0			0
$583$	−1.17362	+	2.03278i	−0.0486065	+	0.0841890i
$584$		0			0
$585$	−2.82909	−	32.4792i	−0.116969	−	1.34285i
$586$		0			0
$587$	−3.31081	−	12.3561i	−0.136652	−	0.509991i	−0.999986	−	0.00535825i	$-0.998294\pi$
$587$	−3.31081	−	12.3561i	−0.136652	−	0.509991i	0.863334	−	0.504633i	$-0.168372\pi$
$588$		0			0
$589$	3.42507	−	12.7825i	0.141128	−	0.526696i
$590$		0			0
$591$	2.16827	+	6.88145i	0.0891907	+	0.283065i
$592$		0			0
$593$			25.7816i			1.05872i	0.848397	+	0.529361i	$0.177568\pi$
$593$			25.7816i			1.05872i	−0.848397	+	0.529361i	$0.822432\pi$
$594$		0			0
$595$	38.9937	−	38.9937i	1.59858	−	1.59858i
$596$		0			0
$597$	3.95239	+	2.05844i	0.161761	+	0.0842465i
$598$		0			0
$599$	27.3647	−	15.7990i	1.11809	−	0.645531i	0.177180	−	0.984179i	$-0.443303\pi$
$599$	27.3647	−	15.7990i	1.11809	−	0.645531i	0.940913	+	0.338647i	$0.109969\pi$
$600$		0			0
$601$	23.3729	+	13.4944i	0.953401	+	0.550447i	0.894136	−	0.447796i	$-0.147791\pi$
$601$	23.3729	+	13.4944i	0.953401	+	0.550447i	0.0592656	+	0.998242i	$0.481124\pi$
$602$		0			0
$603$	5.49146	+	15.1056i	0.223630	+	0.615146i
$604$		0			0
$605$	−10.9585	−	40.8977i	−0.445527	−	1.66273i
$606$		0			0
$607$	21.2314	−	12.2579i	0.861755	−	0.497534i	−0.00284471	−	0.999996i	$-0.500905\pi$
$607$	21.2314	−	12.2579i	0.861755	−	0.497534i	0.864600	+	0.502462i	$0.167572\pi$
$608$		0			0
$609$	−9.05671	−	8.30212i	−0.366996	−	0.336419i
$610$		0			0
$611$	9.34212	+	9.34212i	0.377942	+	0.377942i
$612$		0			0
$613$	−30.3894	+	30.3894i	−1.22742	+	1.22742i	−0.262481	+	0.964937i	$0.584541\pi$
$613$	−30.3894	+	30.3894i	−1.22742	+	1.22742i	−0.964937	+	0.262481i	$0.915459\pi$
$614$		0			0
$615$	22.2764	+	4.94301i	0.898272	+	0.199322i
$616$		0			0
$617$	−15.8393	−	27.4345i	−0.637668	−	1.10447i	−0.985943	−	0.167081i	$-0.946566\pi$
$617$	−15.8393	−	27.4345i	−0.637668	−	1.10447i	0.348275	−	0.937392i	$-0.386767\pi$
$618$		0			0
$619$	20.1312	−	5.39413i	0.809141	−	0.216809i	0.169547	−	0.985522i	$-0.445769\pi$
$619$	20.1312	−	5.39413i	0.809141	−	0.216809i	0.639593	+	0.768713i	$0.279103\pi$
$620$		0			0
$621$	12.1675	+	15.8757i	0.488264	+	0.637071i
$622$		0			0
$623$	−4.98242	+	8.62981i	−0.199617	+	0.345746i
$624$		0			0
$625$	12.0944	+	20.9481i	0.483775	+	0.837923i
$626$		0			0
$627$	0.323602	+	0.508167i	0.0129234	+	0.0202943i
$628$		0			0
$629$	−11.3007	−	11.3007i	−0.450587	−	0.450587i
$630$		0			0
$631$	19.9953			0.796002			0.398001	−	0.917385i	$-0.369704\pi$
$631$	19.9953			0.796002			0.398001	+	0.917385i	$0.369704\pi$
$632$		0			0
$633$	23.2243	+	21.2893i	0.923084	+	0.846174i
$634$		0			0
$635$	−50.0494	−	13.4107i	−1.98615	−	0.532187i
$636$		0			0
$637$	−11.7335	+	3.14400i	−0.464900	+	0.124570i
$638$		0			0
$639$	−18.5247	+	12.9606i	−0.732824	+	0.512713i
$640$		0			0
$641$	12.6976	+	7.33098i	0.501526	+	0.289556i	0.729344	−	0.684148i	$-0.239826\pi$
$641$	12.6976	+	7.33098i	0.501526	+	0.289556i	−0.227818	+	0.973704i	$0.573159\pi$
$642$		0			0
$643$	−12.8777	−	3.45056i	−0.507846	−	0.136077i	−0.00420705	−	0.999991i	$-0.501339\pi$
$643$	−12.8777	−	3.45056i	−0.507846	−	0.136077i	−0.503639	+	0.863914i	$0.668006\pi$
$644$		0			0
$645$	15.0175	−	28.8350i	0.591315	−	1.13538i
$646$		0			0
$647$		−	30.5078i		−	1.19939i	−0.800231	−	0.599693i	$-0.795290\pi$
$647$		−	30.5078i		−	1.19939i	0.800231	−	0.599693i	$-0.204710\pi$
$648$		0			0
$649$		−	1.21078i		−	0.0475272i
$650$		0			0
$651$	−22.4183	+	43.0451i	−0.878642	+	1.68707i
$652$		0			0
$653$	20.1465	+	5.39824i	0.788394	+	0.211249i	0.630482	−	0.776204i	$-0.282857\pi$
$653$	20.1465	+	5.39824i	0.788394	+	0.211249i	0.157912	+	0.987453i	$0.449524\pi$
$654$		0			0
$655$	2.19305	+	1.26616i	0.0856896	+	0.0494729i
$656$		0			0
$657$	7.93100	−	5.54884i	0.309418	−	0.216481i
$658$		0			0
$659$	14.5728	−	3.90477i	0.567676	−	0.152108i	0.0364452	−	0.999336i	$-0.488397\pi$
$659$	14.5728	−	3.90477i	0.567676	−	0.152108i	0.531230	+	0.847227i	$0.321730\pi$
$660$		0			0
$661$	−9.11835	−	2.44325i	−0.354663	−	0.0950316i	0.0770887	−	0.997024i	$-0.475438\pi$
$661$	−9.11835	−	2.44325i	−0.354663	−	0.0950316i	−0.431751	+	0.901993i	$0.642104\pi$
$662$		0			0
$663$	−15.2154	−	13.9477i	−0.590918	−	0.541684i
$664$		0			0
$665$	−20.6706			−0.801570
$666$		0			0
$667$	−5.73833	−	5.73833i	−0.222189	−	0.222189i
$668$		0			0
$669$	3.03010	+	4.75830i	0.117150	+	0.183966i
$670$		0			0
$671$	−0.985698	−	1.70728i	−0.0380525	−	0.0659088i
$672$		0			0
$673$	−16.1140	+	27.9103i	−0.621149	+	1.07586i	0.368123	+	0.929777i	$0.380001\pi$
$673$	−16.1140	+	27.9103i	−0.621149	+	1.07586i	−0.989272	+	0.146085i	$0.953333\pi$
$674$		0			0
$675$	−19.8042	+	47.7343i	−0.762263	+	1.83729i
$676$		0			0
$677$	−15.5364	+	4.16296i	−0.597111	+	0.159996i	−0.544701	−	0.838630i	$-0.683357\pi$
$677$	−15.5364	+	4.16296i	−0.597111	+	0.159996i	−0.0524101	+	0.998626i	$0.516690\pi$
$678$		0			0
$679$	25.7025	+	44.5181i	0.986372	+	1.70845i
$680$		0			0
$681$	−15.4617	−	3.43087i	−0.592494	−	0.131471i
$682$		0			0
$683$	−28.6734	+	28.6734i	−1.09716	+	1.09716i	−0.102416	+	0.994742i	$0.532657\pi$
$683$	−28.6734	+	28.6734i	−1.09716	+	1.09716i	−0.994742	+	0.102416i	$0.967343\pi$
$684$		0			0
$685$	−57.5322	−	57.5322i	−2.19819	−	2.19819i
$686$		0			0
$687$	6.71160	+	6.15240i	0.256064	+	0.234729i
$688$		0			0
$689$	−26.1058	+	15.0722i	−0.994552	+	0.574205i
$690$		0			0
$691$	11.8033	+	44.0504i	0.449017	+	1.67575i	0.705106	+	0.709102i	$0.250899\pi$
$691$	11.8033	+	44.0504i	0.449017	+	1.67575i	−0.256089	+	0.966653i	$0.582434\pi$
$692$		0			0
$693$	−0.754895	−	2.07652i	−0.0286761	−	0.0788804i
$694$		0			0
$695$	−22.3358	−	12.8956i	−0.847243	−	0.489156i
$696$		0			0
$697$	12.5111	−	7.22328i	0.473892	−	0.273601i
$698$		0			0
$699$	−21.7380	−	11.3214i	−0.822208	−	0.428213i
$700$		0			0
$701$	13.0178	−	13.0178i	0.491676	−	0.491676i	−0.417158	−	0.908834i	$-0.636974\pi$
$701$	13.0178	−	13.0178i	0.491676	−	0.491676i	0.908834	+	0.417158i	$0.136974\pi$
$702$		0			0
$703$			5.99049i			0.225935i
$704$		0			0
$705$	−9.45784	−	30.0164i	−0.356203	−	1.13048i
$706$		0			0
$707$	0.116919	−	0.436349i	0.00439721	−	0.0164106i
$708$		0			0
$709$	4.39011	+	16.3841i	0.164874	+	0.615319i	0.998056	+	0.0623199i	$0.0198499\pi$
$709$	4.39011	+	16.3841i	0.164874	+	0.615319i	−0.833182	+	0.552999i	$0.813483\pi$
$710$		0			0
$711$	1.49876	+	17.2064i	0.0562079	+	0.645291i
$712$		0			0
$713$	−16.0285	+	27.7622i	−0.600273	+	1.03970i
$714$		0			0
$715$	−0.615660	+	2.29767i	−0.0230244	+	0.0859282i
$716$		0			0
$717$	−1.13063	−	26.0094i	−0.0422242	−	0.971339i
$718$		0			0
$719$	−43.0731			−1.60635			−0.803177	−	0.595740i	$-0.796859\pi$
$719$	−43.0731			−1.60635			−0.803177	+	0.595740i	$0.796859\pi$
$720$		0			0
$721$	27.5313			1.02532
$722$		0			0
$723$	−21.0065	+	13.3770i	−0.781240	+	0.497495i
$724$		0			0
$725$	5.42673	−	20.2528i	0.201544	−	0.752171i
$726$		0			0
$727$	−15.3101	+	26.5179i	−0.567821	+	0.983495i	0.428960	+	0.903324i	$0.358880\pi$
$727$	−15.3101	+	26.5179i	−0.567821	+	0.983495i	−0.996781	+	0.0801716i	$0.974453\pi$
$728$		0			0
$729$	−26.0880	+	6.95830i	−0.966221	+	0.257715i
$730$		0			0
$731$	−5.32737	−	19.8820i	−0.197040	−	0.735363i
$732$		0			0
$733$	0.679676	−	2.53658i	0.0251044	−	0.0936909i	−0.952237	−	0.305360i	$-0.901223\pi$
$733$	0.679676	−	2.53658i	0.0251044	−	0.0936909i	0.977341	+	0.211669i	$0.0678899\pi$
$734$		0			0
$735$	28.2489	+	6.26827i	1.04197	+	0.231209i
$736$		0			0
$737$		−	1.17271i		−	0.0431972i
$738$		0			0
$739$	−13.1402	+	13.1402i	−0.483370	+	0.483370i	−0.906206	−	0.422836i	$-0.861035\pi$
$739$	−13.1402	+	13.1402i	−0.483370	+	0.483370i	0.422836	+	0.906206i	$0.361035\pi$
$740$		0			0
$741$	0.336011	+	7.72970i	0.0123437	+	0.283958i
$742$		0			0
$743$	1.79055	−	1.03378i	0.0656890	−	0.0379255i	−0.466796	−	0.884365i	$-0.654592\pi$
$743$	1.79055	−	1.03378i	0.0656890	−	0.0379255i	0.532485	+	0.846440i	$0.321258\pi$
$744$		0			0
$745$	74.7897	+	43.1798i	2.74008	+	1.58199i
$746$		0			0
$747$	−10.7174	−	8.99989i	−0.392127	−	0.329289i
$748$		0			0
$749$	10.2077	+	38.0958i	0.372982	+	1.39199i
$750$		0			0
$751$	7.86676	−	4.54188i	0.287062	−	0.165735i	−0.349554	−	0.936916i	$-0.613667\pi$
$751$	7.86676	−	4.54188i	0.287062	−	0.165735i	0.636616	+	0.771181i	$0.280334\pi$
$752$		0			0
$753$	−8.40489	+	2.64829i	−0.306291	+	0.0965091i
$754$		0			0
$755$	−54.5367	−	54.5367i	−1.98479	−	1.98479i
$756$		0			0
$757$	18.3910	−	18.3910i	0.668433	−	0.668433i	−0.288920	−	0.957353i	$-0.593296\pi$
$757$	18.3910	−	18.3910i	0.668433	−	0.668433i	0.957353	+	0.288920i	$0.0932961\pi$
$758$		0			0
$759$	−0.438586	−	1.39194i	−0.0159196	−	0.0505242i
$760$		0			0
$761$	−14.1080	−	24.4358i	−0.511415	−	0.885797i	−0.999912	−	0.0132318i	$-0.995788\pi$
$761$	−14.1080	−	24.4358i	−0.511415	−	0.885797i	0.488497	−	0.872565i	$-0.337545\pi$
$762$		0			0
$763$	29.0160	−	7.77481i	1.05045	−	0.281467i
$764$		0			0
$765$	16.7988	+	46.2091i	0.607362	+	1.67069i
$766$		0			0
$767$	7.77467	−	13.4661i	0.280727	−	0.486234i
$768$		0			0
$769$	−14.6064	−	25.2991i	−0.526722	−	0.912309i	−0.999515	−	0.0311354i	$-0.990088\pi$
$769$	−14.6064	−	25.2991i	−0.526722	−	0.912309i	0.472794	−	0.881173i	$-0.343246\pi$
$770$		0			0
$771$	9.84350	−	0.427898i	0.354505	−	0.0154104i
$772$		0			0
$773$	−10.5491	−	10.5491i	−0.379425	−	0.379425i	0.491470	−	0.870895i	$-0.336460\pi$
$773$	−10.5491	−	10.5491i	−0.379425	−	0.379425i	−0.870895	+	0.491470i	$0.836460\pi$
$774$		0			0
$775$	−82.8256			−2.97518
$776$		0			0
$777$	4.75923	−	21.4482i	0.170736	−	0.769448i
$778$		0			0
$779$	−5.23060	−	1.40154i	−0.187406	−	0.0502152i
$780$		0			0
$781$	1.59335	−	0.426938i	0.0570146	−	0.0152770i
$782$		0			0
$783$	10.1229	−	4.18627i	0.361764	−	0.149605i
$784$		0			0
$785$	−49.8924	−	28.8054i	−1.78074	−	1.02811i
$786$		0			0
$787$	−33.8023	−	9.05729i	−1.20492	−	0.322857i	−0.400153	−	0.916448i	$-0.631043\pi$
$787$	−33.8023	−	9.05729i	−1.20492	−	0.322857i	−0.804767	+	0.593591i	$0.797710\pi$
$788$		0			0
$789$	20.2385	+	31.7815i	0.720511	+	1.13145i
$790$		0			0
$791$		−	56.9431i		−	2.02466i
$792$		0			0
$793$		−	25.3175i		−	0.899052i
$794$		0			0
$795$	71.7379	−	3.11845i	2.54428	−	0.110600i
$796$		0			0
$797$	−27.6668	−	7.41329i	−0.980007	−	0.262592i	−0.266959	−	0.963708i	$-0.586019\pi$
$797$	−27.6668	−	7.41329i	−0.980007	−	0.262592i	−0.713048	+	0.701116i	$0.752686\pi$
$798$		0			0
$799$	−17.2554	−	9.96243i	−0.610453	−	0.352445i
$800$		0			0
$801$	−5.09328	−	7.27986i	−0.179962	−	0.257221i
$802$		0			0
$803$	−0.682165	+	0.182786i	−0.0240731	+	0.00645036i
$804$		0			0
$805$	48.3667	+	12.9598i	1.70470	+	0.456773i
$806$		0			0
$807$	17.3693	−	5.47289i	0.611429	−	0.192655i
$808$		0			0
$809$	−39.9831			−1.40573			−0.702865	−	0.711323i	$-0.748096\pi$
$809$	−39.9831			−1.40573			−0.702865	+	0.711323i	$0.748096\pi$
$810$		0			0
$811$	33.5121	+	33.5121i	1.17677	+	1.17677i	0.980563	+	0.196204i	$0.0628616\pi$
$811$	33.5121	+	33.5121i	1.17677	+	1.17677i	0.196204	+	0.980563i	$0.437138\pi$
$812$		0			0
$813$	−9.51073	+	18.2614i	−0.333556	+	0.640457i
$814$		0			0
$815$	−11.9123	−	20.6328i	−0.417271	−	0.722734i
$816$		0			0
$817$	−3.85771	+	6.68176i	−0.134964	+	0.233765i
$818$		0			0
$819$	4.93793	−	27.9421i	0.172545	−	0.976377i
$820$		0			0
$821$	−10.8942	+	2.91908i	−0.380209	+	0.101877i	−0.443861	−	0.896096i	$-0.646392\pi$
$821$	−10.8942	+	2.91908i	−0.380209	+	0.101877i	0.0636527	+	0.997972i	$0.479725\pi$
$822$		0			0
$823$	−27.4702	−	47.5798i	−0.957551	−	1.65853i	−0.728420	−	0.685131i	$-0.759745\pi$
$823$	−27.4702	−	47.5798i	−0.957551	−	1.65853i	−0.229131	−	0.973396i	$-0.573588\pi$
$824$		0			0
$825$	2.54794	−	2.77953i	0.0887080	−	0.0967708i
$826$		0			0
$827$	−14.2104	+	14.2104i	−0.494144	+	0.494144i	−0.909609	−	0.415465i	$-0.863619\pi$
$827$	−14.2104	+	14.2104i	−0.494144	+	0.494144i	0.415465	+	0.909609i	$0.363619\pi$
$828$		0			0
$829$	6.15512	+	6.15512i	0.213776	+	0.213776i	0.805869	−	0.592093i	$-0.201698\pi$
$829$	6.15512	+	6.15512i	0.213776	+	0.213776i	−0.592093	+	0.805869i	$0.701698\pi$
$830$		0			0
$831$	3.88757	−	17.5199i	0.134858	−	0.607759i
$832$		0			0
$833$	15.8654	−	9.15989i	0.549704	−	0.317371i
$834$		0			0
$835$	−13.7435	−	51.2913i	−0.475612	−	1.77501i
$836$		0			0
$837$	−26.3229	−	34.3453i	−0.909853	−	1.18715i
$838$		0			0
$839$	21.5384	+	12.4352i	0.743590	+	0.429312i	0.823373	−	0.567500i	$-0.192089\pi$
$839$	21.5384	+	12.4352i	0.743590	+	0.429312i	−0.0797833	+	0.996812i	$0.525423\pi$
$840$		0			0
$841$	21.2658	−	12.2778i	0.733303	−	0.423373i
$842$		0			0
$843$	20.6181	−	13.1297i	0.710127	−	0.452210i
$844$		0			0
$845$	13.9363	−	13.9363i	0.479424	−	0.479424i
$846$		0			0
$847$		−	36.8507i		−	1.26621i
$848$		0			0
$849$	15.5036	−	16.9128i	0.532083	−	0.580444i
$850$		0			0
$851$	3.75585	−	14.0170i	0.128749	−	0.480497i
$852$		0			0
$853$	−5.05023	−	18.8477i	−0.172917	−	0.645334i	−0.996897	−	0.0787157i	$-0.974918\pi$
$853$	−5.05023	−	18.8477i	−0.172917	−	0.645334i	0.823980	−	0.566618i	$-0.191749\pi$
$854$		0			0
$855$	7.79521	−	16.7003i	0.266590	−	0.571137i
$856$		0			0
$857$	−18.6982	+	32.3862i	−0.638717	+	1.10629i	0.346998	+	0.937866i	$0.387201\pi$
$857$	−18.6982	+	32.3862i	−0.638717	+	1.10629i	−0.985715	+	0.168424i	$0.946132\pi$
$858$		0			0
$859$	7.10549	−	26.5180i	0.242436	−	0.904784i	−0.732219	−	0.681070i	$-0.761515\pi$
$859$	7.10549	−	26.5180i	0.242436	−	0.904784i	0.974655	−	0.223714i	$-0.0718182\pi$
$860$		0			0
$861$	17.6140	+	9.17354i	0.600284	+	0.312634i
$862$		0			0
$863$	10.1797			0.346520			0.173260	−	0.984876i	$-0.444570\pi$
$863$	10.1797			0.346520			0.173260	+	0.984876i	$0.444570\pi$
$864$		0			0
$865$	20.9860			0.713545
$866$		0			0
$867$	1.49362	+	0.777892i	0.0507261	+	0.0264186i
$868$		0			0
$869$	0.326156	−	1.21723i	0.0110641	−	0.0412918i
$870$		0			0
$871$	7.53020	−	13.0427i	0.255151	−	0.441935i
$872$		0			0
$873$	−45.6601	+	3.97721i	−1.54536	+	0.134608i
$874$		0			0
$875$	16.6507	+	62.1414i	0.562897	+	2.10076i
$876$		0			0
$877$	−6.90717	+	25.7779i	−0.233239	+	0.870458i	0.745696	+	0.666286i	$0.232117\pi$
$877$	−6.90717	+	25.7779i	−0.233239	+	0.870458i	−0.978935	+	0.204172i	$0.934550\pi$
$878$		0			0
$879$	−35.9960	+	39.2677i	−1.21411	+	1.32447i
$880$		0			0
$881$		−	30.7798i		−	1.03700i	−0.855078	−	0.518499i	$-0.826491\pi$
$881$		−	30.7798i		−	1.03700i	0.855078	−	0.518499i	$-0.173509\pi$
$882$		0			0
$883$	19.8089	−	19.8089i	0.666622	−	0.666622i	−0.290310	−	0.956933i	$-0.593759\pi$
$883$	19.8089	−	19.8089i	0.666622	−	0.666622i	0.956933	+	0.290310i	$0.0937586\pi$
$884$		0			0
$885$	−31.2425	+	19.8953i	−1.05021	+	0.668774i
$886$		0			0
$887$	−21.0940	+	12.1786i	−0.708266	+	0.408918i	−0.810419	−	0.585851i	$-0.800760\pi$
$887$	−21.0940	+	12.1786i	−0.708266	+	0.408918i	0.102153	+	0.994769i	$0.467427\pi$
$888$		0			0
$889$	−39.0550	−	22.5484i	−1.30986	−	0.756249i
$890$		0			0
$891$	1.96235	+	0.173190i	0.0657413	+	0.00580210i
$892$		0			0
$893$	1.93301	+	7.21410i	0.0646858	+	0.241411i
$894$		0			0
$895$	−1.79985	+	1.03914i	−0.0601624	+	0.0347348i
$896$		0			0
$897$	4.06006	−	18.2972i	0.135561	−	0.610927i
$898$		0			0
$899$	12.4142	+	12.4142i	0.414037	+	0.414037i
$900$		0			0
$901$	32.1460	−	32.1460i	1.07094	−	1.07094i
$902$		0			0
$903$	19.1205	−	20.8583i	0.636289	−	0.694122i
$904$		0			0
$905$	13.6407	+	23.6264i	0.453433	+	0.785369i
$906$		0			0
$907$	−56.0698	+	15.0239i	−1.86177	+	0.498859i	−0.999965	−	0.00838605i	$-0.997331\pi$
$907$	−56.0698	+	15.0239i	−1.86177	+	0.498859i	−0.861802	+	0.507245i	$0.830664\pi$
$908$		0			0
$909$	0.308445	+	0.259016i	0.0102305	+	0.00859103i
$910$		0			0
$911$	−11.9347	+	20.6715i	−0.395414	+	0.684877i	−0.993154	−	0.116813i	$-0.962732\pi$
$911$	−11.9347	+	20.6715i	−0.395414	+	0.684877i	0.597740	+	0.801690i	$0.296066\pi$
$912$		0			0
$913$	0.510553	+	0.884303i	0.0168968	+	0.0292662i
$914$		0			0
$915$	−27.8572	+	53.4884i	−0.920932	+	1.76827i
$916$		0			0
$917$	1.55845	+	1.55845i	0.0514646	+	0.0514646i
$918$		0			0
$919$	15.7779			0.520466			0.260233	−	0.965546i	$-0.416201\pi$
$919$	15.7779			0.520466			0.260233	+	0.965546i	$0.416201\pi$
$920$		0			0
$921$	55.6284	−	17.5279i	1.83302	−	0.577565i
$922$		0			0
$923$	20.4625	+	5.48292i	0.673533	+	0.180473i
$924$		0			0
$925$	36.2157	−	9.70397i	1.19077	−	0.319065i
$926$		0			0
$927$	−10.3825	+	22.2432i	−0.341006	+	0.730562i
$928$		0			0
$929$	14.3132	+	8.26371i	0.469600	+	0.271123i	0.716072	−	0.698026i	$-0.245938\pi$
$929$	14.3132	+	8.26371i	0.469600	+	0.271123i	−0.246472	+	0.969150i	$0.579271\pi$
$930$		0			0
$931$	−6.63296	−	1.77730i	−0.217387	−	0.0582485i
$932$		0			0
$933$	−18.4014	+	0.799912i	−0.602436	+	0.0261879i
$934$		0			0
$935$		−	3.58740i		−	0.117320i
$936$		0			0
$937$			5.92940i			0.193705i	0.995299	+	0.0968526i	$0.0308775\pi$
$937$			5.92940i			0.193705i	−0.995299	+	0.0968526i	$0.969122\pi$
$938$		0			0
$939$	−17.6862	−	27.7735i	−0.577169	−	0.906354i
$940$		0			0
$941$	−20.6096	−	5.52232i	−0.671853	−	0.180022i	−0.0932635	−	0.995641i	$-0.529730\pi$
$941$	−20.6096	−	5.52232i	−0.671853	−	0.180022i	−0.578589	+	0.815619i	$0.696397\pi$
$942$		0			0
$943$	11.3603	+	6.55886i	0.369941	+	0.213586i
$944$		0			0
$945$	−41.1775	+	53.6001i	−1.33950	+	1.74361i
$946$		0			0
$947$	31.9863	−	8.57071i	1.03942	−	0.278511i	0.301545	−	0.953452i	$-0.402498\pi$
$947$	31.9863	−	8.57071i	1.03942	−	0.278511i	0.737871	+	0.674941i	$0.235831\pi$
$948$		0			0
$949$	−8.76066	−	2.34741i	−0.284383	−	0.0762002i
$950$		0			0
$951$	−4.61279	+	20.7882i	−0.149580	+	0.674105i
$952$		0			0
$953$	−0.546564			−0.0177049			−0.00885247	−	0.999961i	$-0.502818\pi$
$953$	−0.546564			−0.0177049			−0.00885247	+	0.999961i	$0.502818\pi$
$954$		0			0
$955$	−29.5538	−	29.5538i	−0.956339	−	0.956339i
$956$		0			0
$957$	−0.798502	+	0.0347109i	−0.0258119	+	0.00112205i
$958$		0			0
$959$	−35.4068	−	61.3264i	−1.14335	−	1.98033i
$960$		0			0
$961$	19.1758	−	33.2135i	0.618576	−	1.07140i
$962$		0			0
$963$	−34.6280	−	6.11946i	−1.11587	−	0.197197i
$964$		0			0
$965$	19.4213	−	5.20393i	0.625195	−	0.167521i
$966$		0			0
$967$	7.49046	+	12.9739i	0.240877	+	0.417211i	0.960964	−	0.276672i	$-0.0892316\pi$
$967$	7.49046	+	12.9739i	0.240877	+	0.417211i	−0.720087	+	0.693883i	$0.755898\pi$
$968$		0			0
$969$	−3.50660	−	11.1289i	−0.112648	−	0.357512i
$970$		0			0
$971$	29.4725	−	29.4725i	0.945816	−	0.945816i	−0.0527896	−	0.998606i	$-0.516811\pi$
$971$	29.4725	−	29.4725i	0.945816	−	0.945816i	0.998606	+	0.0527896i	$0.0168113\pi$
$972$		0			0
$973$	−15.8725	−	15.8725i	−0.508849	−	0.508849i
$974$		0			0
$975$	46.1859	−	14.5527i	1.47913	−	0.466059i
$976$		0			0
$977$	2.02199	−	1.16740i	0.0646892	−	0.0373483i	−0.467307	−	0.884095i	$-0.654776\pi$
$977$	2.02199	−	1.16740i	0.0646892	−	0.0373483i	0.531996	+	0.846747i	$0.321442\pi$
$978$		0			0
$979$	0.167779	+	0.626159i	0.00536224	+	0.0200121i
$980$		0			0
$981$	−4.66094	+	26.3747i	−0.148812	+	0.842080i
$982$		0			0
$983$	−21.5089	−	12.4182i	−0.686029	−	0.396079i	0.116094	−	0.993238i	$-0.462963\pi$
$983$	−21.5089	−	12.4182i	−0.686029	−	0.396079i	−0.802123	+	0.597159i	$0.796296\pi$
$984$		0			0
$985$	−13.9464	+	8.05197i	−0.444370	+	0.256557i
$986$		0			0
$987$	−1.18955	−	27.3649i	−0.0378639	−	0.871033i
$988$		0			0
$989$	13.2158	−	13.2158i	0.420240	−	0.420240i
$990$		0			0
$991$		−	7.12527i		−	0.226342i	−0.993576	−	0.113171i	$-0.963899\pi$
$991$		−	7.12527i		−	0.226342i	0.993576	−	0.113171i	$-0.0361008\pi$
$992$		0			0
$993$	58.4622	+	12.9724i	1.85524	+	0.411668i
$994$		0			0
$995$	−2.57436	+	9.60763i	−0.0816126	+	0.304582i
$996$		0			0
$997$	12.7516	+	47.5897i	0.403848	+	1.50718i	0.806170	+	0.591684i	$0.201537\pi$
$997$	12.7516	+	47.5897i	0.403848	+	1.50718i	−0.402322	+	0.915498i	$0.631797\pi$
$998$		0			0
$999$	15.5337	+	11.9335i	0.491465	+	0.377561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.47.3		88
3.2	odd	2		1728.2.z.a.1007.1		88
4.3	odd	2		144.2.u.a.83.14	yes	88
9.4	even	3		1728.2.z.a.1583.1		88
9.5	odd	6	inner	576.2.y.a.239.15		88
12.11	even	2		432.2.v.a.35.9		88
16.5	even	4		144.2.u.a.11.7	✓	88
16.11	odd	4	inner	576.2.y.a.335.15		88
36.23	even	6		144.2.u.a.131.7	yes	88
36.31	odd	6		432.2.v.a.179.16		88
48.5	odd	4		432.2.v.a.251.16		88
48.11	even	4		1728.2.z.a.143.1		88
144.5	odd	12		144.2.u.a.59.14	yes	88
144.59	even	12	inner	576.2.y.a.527.3		88
144.85	even	12		432.2.v.a.395.9		88
144.139	odd	12		1728.2.z.a.719.1		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.7	✓	88	16.5	even	4
144.2.u.a.59.14	yes	88	144.5	odd	12
144.2.u.a.83.14	yes	88	4.3	odd	2
144.2.u.a.131.7	yes	88	36.23	even	6
432.2.v.a.35.9		88	12.11	even	2
432.2.v.a.179.16		88	36.31	odd	6
432.2.v.a.251.16		88	48.5	odd	4
432.2.v.a.395.9		88	144.85	even	12
576.2.y.a.47.3		88	1.1	even	1	trivial
576.2.y.a.239.15		88	9.5	odd	6	inner
576.2.y.a.335.15		88	16.11	odd	4	inner
576.2.y.a.527.3		88	144.59	even	12	inner
1728.2.z.a.143.1		88	48.11	even	4
1728.2.z.a.719.1		88	144.139	odd	12
1728.2.z.a.1007.1		88	3.2	odd	2
1728.2.z.a.1583.1		88	9.4	even	3

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53620 - 0.800065i) q^{3} +(1.00059 - 3.73424i) q^{5} +(1.68236 - 2.91393i) q^{7} +(1.71979 + 2.45811i) q^{9} +O(q^{10})\)	\(q+(-1.53620 - 0.800065i) q^{3} +(1.00059 - 3.73424i) q^{5} +(1.68236 - 2.91393i) q^{7} +(1.71979 + 2.45811i) q^{9} +(-0.0566521 - 0.211428i) q^{11} +(0.727551 - 2.71526i) q^{13} +(-4.52473 + 4.93599i) q^{15} +4.23937i q^{17} +(1.12365 - 1.12365i) q^{19} +(-4.91577 + 3.13037i) q^{21} +(-3.33369 + 1.92471i) q^{23} +(-8.61325 - 4.97286i) q^{25} +(-0.675290 - 5.15209i) q^{27} +(0.545635 + 2.03634i) q^{29} +(7.21206 - 4.16388i) q^{31} +(-0.0821277 + 0.370121i) q^{33} +(-9.19798 - 9.19798i) q^{35} +(-2.66564 + 2.66564i) q^{37} +(-3.29004 + 3.58908i) q^{39} +(-1.70386 - 2.95117i) q^{41} +(-4.68985 + 1.25664i) q^{43} +(10.9000 - 3.96257i) q^{45} +(-2.34998 + 4.07028i) q^{47} +(-2.16067 - 3.74239i) q^{49} +(3.39177 - 6.51251i) q^{51} +(-7.58271 - 7.58271i) q^{53} -0.846209 q^{55} +(-2.62513 + 0.827151i) q^{57} +(5.34305 + 1.43167i) q^{59} +(8.69958 - 2.33105i) q^{61} +(10.0561 - 0.875933i) q^{63} +(-9.41144 - 5.43370i) q^{65} +(5.17504 + 1.38665i) q^{67} +(6.66110 - 0.289558i) q^{69} +7.53614i q^{71} -3.22646i q^{73} +(9.25302 + 14.5304i) q^{75} +(-0.711397 - 0.190618i) q^{77} +(4.98587 + 2.87859i) q^{79} +(-3.08462 + 8.45489i) q^{81} +(-4.50604 + 1.20739i) q^{83} +(15.8308 + 4.24186i) q^{85} +(0.790999 - 3.56475i) q^{87} -2.96157 q^{89} +(-6.68807 - 6.68807i) q^{91} +(-14.4105 + 0.626426i) q^{93} +(-3.07166 - 5.32027i) q^{95} +(-7.63883 + 13.2308i) q^{97} +(0.422285 - 0.502870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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