LMFDB - Embedded newform 576.2.y.a.335.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [576,2,Mod(47,576)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			335.15
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

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

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
$3$	0.800065	−	1.53620i	0.461918	−	0.886923i
$3$	0.800065	−	1.53620i	0.461918	−	0.886923i
$4$		0			0
$5$	3.73424	+	1.00059i	1.67000	+	0.447476i	0.965111	−	0.261839i	$-0.0843291\pi$
$5$	3.73424	+	1.00059i	1.67000	+	0.447476i	0.704891	+	0.709315i	$0.250996\pi$
$6$		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
$11$	−0.211428	+	0.0566521i	−0.0637480	+	0.0170812i	−0.290552	−	0.956859i	$-0.593839\pi$
$11$	−0.211428	+	0.0566521i	−0.0637480	+	0.0170812i	0.226804	+	0.973940i	$0.427172\pi$
$12$		0			0
$13$	−2.71526	−	0.727551i	−0.753076	−	0.201786i	−0.138194	−	0.990405i	$-0.544130\pi$
$13$	−2.71526	−	0.727551i	−0.753076	−	0.201786i	−0.614882	+	0.788619i	$0.710796\pi$
$14$		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	0.824152	−	0.566369i	$-0.191652\pi$
$19$	1.12365	+	1.12365i	0.257782	+	0.257782i	−0.566369	+	0.824152i	$0.691652\pi$
$20$		0			0
$21$	−3.13037	−	4.91577i	−0.683104	−	1.07271i
$22$		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
$27$	−5.15209	+	0.675290i	−0.991519	+	0.129960i
$28$		0			0
$29$	2.03634	−	0.545635i	0.378138	−	0.101322i	−0.0647434	−	0.997902i	$-0.520623\pi$
$29$	2.03634	−	0.545635i	0.378138	−	0.101322i	0.442882	+	0.896580i	$0.353956\pi$
$30$		0			0
$31$	−7.21206	+	4.16388i	−1.29532	+	0.747856i	−0.979593	−	0.200993i	$-0.935583\pi$
$31$	−7.21206	+	4.16388i	−1.29532	+	0.747856i	−0.315731	+	0.948849i	$0.602250\pi$
$32$		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	0.453187	−	0.891416i	$-0.350287\pi$
$37$	−2.66564	−	2.66564i	−0.438229	−	0.438229i	−0.891416	+	0.453187i	$0.850287\pi$
$38$		0			0
$39$	−3.29004	+	3.58908i	−0.526828	+	0.574712i
$40$		0			0
$41$	1.70386	+	2.95117i	0.266098	+	0.460895i	0.967851	−	0.251526i	$-0.0809323\pi$
$41$	1.70386	+	2.95117i	0.266098	+	0.460895i	−0.701753	+	0.712420i	$0.747599\pi$
$42$		0			0
$43$	1.25664	+	4.68985i	0.191636	+	0.715195i	0.993112	+	0.117168i	$0.0373817\pi$
$43$	1.25664	+	4.68985i	0.191636	+	0.715195i	−0.801476	+	0.598027i	$0.795952\pi$
$44$		0			0
$45$	−3.96257	−	10.9000i	−0.590704	−	1.62487i
$46$		0			0
$47$	2.34998	−	4.07028i	0.342779	−	0.593711i	−0.642168	−	0.766564i	$-0.721965\pi$
$47$	2.34998	−	4.07028i	0.342779	−	0.593711i	0.984948	+	0.172852i	$0.0552984\pi$
$48$		0			0
$49$	−2.16067	−	3.74239i	−0.308667	−	0.534628i
$50$		0			0
$51$	6.51251	+	3.39177i	0.911933	+	0.474943i
$52$		0			0
$53$	7.58271	−	7.58271i	1.04157	−	1.04157i	0.0424680	−	0.999098i	$-0.486478\pi$
$53$	7.58271	−	7.58271i	1.04157	−	1.04157i	0.999098	−	0.0424680i	$-0.0135220\pi$
$54$		0			0
$55$	−0.846209			−0.114103
$56$		0			0
$57$	2.62513	−	0.827151i	0.347707	−	0.109559i
$58$		0			0
$59$	1.43167	−	5.34305i	0.186387	−	0.695605i	−0.807942	−	0.589261i	$-0.799419\pi$
$59$	1.43167	−	5.34305i	0.186387	−	0.695605i	0.994329	−	0.106344i	$-0.0339145\pi$
$60$		0			0
$61$	−2.33105	−	8.69958i	−0.298460	−	1.11387i	−0.938431	−	0.345468i	$-0.887720\pi$
$61$	−2.33105	−	8.69958i	−0.298460	−	1.11387i	0.639971	−	0.768399i	$-0.278946\pi$
$62$		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
$67$	−1.38665	+	5.17504i	−0.169406	+	0.632231i	0.828031	+	0.560682i	$0.189461\pi$
$67$	−1.38665	+	5.17504i	−0.169406	+	0.632231i	−0.997437	+	0.0715493i	$0.977206\pi$
$68$		0			0
$69$	0.289558	+	6.66110i	0.0348587	+	0.801902i
$70$		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	$0.0604644\pi$
$73$			3.22646i			0.377629i	−0.982013	+	0.188814i	$0.939536\pi$
$74$		0			0
$75$	14.5304	−	9.25302i	1.67783	−	1.06845i
$76$		0			0
$77$	−0.190618	+	0.711397i	−0.0217230	+	0.0810712i
$78$		0			0
$79$	−4.98587	−	2.87859i	−0.560954	−	0.323867i	0.192574	−	0.981282i	$-0.438316\pi$
$79$	−4.98587	−	2.87859i	−0.560954	−	0.323867i	−0.753528	+	0.657415i	$0.771650\pi$
$80$		0			0
$81$	−3.08462	+	8.45489i	−0.342736	+	0.939432i
$82$		0			0
$83$	−1.20739	−	4.50604i	−0.132528	−	0.494602i	0.867468	−	0.497494i	$-0.165746\pi$
$83$	−1.20739	−	4.50604i	−0.132528	−	0.494602i	−0.999996	+	0.00289160i	$0.999080\pi$
$84$		0			0
$85$	−4.24186	+	15.8308i	−0.460094	+	1.71710i
$86$		0			0
$87$	0.790999	−	3.56475i	0.0848040	−	0.382182i
$88$		0			0
$89$	2.96157			0.313926			0.156963	−	0.987605i	$-0.449830\pi$
$89$	2.96157			0.313926			0.156963	+	0.987605i	$0.449830\pi$
$90$		0			0
$91$	−6.68807	+	6.68807i	−0.701100	+	0.701100i
$92$		0			0
$93$	0.626426	+	14.4105i	0.0649573	+	1.49430i
$94$		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
$99$	0.502870	+	0.422285i	0.0505403	+	0.0424412i
$100$		0			0
$101$	0.0347486	+	0.129684i	0.00345762	+	0.0129040i	0.967633	−	0.252361i	$-0.0812071\pi$
$101$	0.0347486	+	0.129684i	0.00345762	+	0.0129040i	−0.964175	+	0.265265i	$0.914540\pi$
$102$		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	$-0.0582658\pi$
$107$	8.28837	+	8.28837i	0.801267	+	0.801267i	−0.182027	+	0.983294i	$0.558266\pi$
$108$		0			0
$109$	6.31291	−	6.31291i	0.604667	−	0.604667i	−0.336881	−	0.941547i	$-0.609372\pi$
$109$	6.31291	−	6.31291i	0.604667	−	0.604667i	0.941547	+	0.336881i	$0.109372\pi$
$110$		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
$115$	−14.3746	+	3.85167i	−1.34044	+	0.359171i
$116$		0			0
$117$	2.88128	+	7.92564i	0.266374	+	0.732725i
$118$		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
$123$	5.89676	−	0.256333i	0.531693	−	0.0231128i
$124$		0			0
$125$	13.5199	+	13.5199i	1.20926	+	1.20926i
$126$		0			0
$127$			13.4028i			1.18931i	0.803981	+	0.594654i	$0.202711\pi$
$127$			13.4028i			1.18931i	−0.803981	+	0.594654i	$0.797289\pi$
$128$		0			0
$129$	8.20992	+	1.82174i	0.722843	+	0.160395i
$130$		0			0
$131$	−0.632708	−	0.169534i	−0.0552800	−	0.0148122i	0.231073	−	0.972936i	$-0.425776\pi$
$131$	−0.632708	−	0.169534i	−0.0552800	−	0.0148122i	−0.286353	+	0.958124i	$0.592443\pi$
$132$		0			0
$133$	5.16461	−	1.38385i	0.447829	−	0.119995i
$134$		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	$0.522399\pi$
$137$	−10.5230	+	18.2263i	−0.899037	+	1.55718i	−0.828727	+	0.559652i	$0.810935\pi$
$138$		0			0
$139$	−6.44400	−	1.72666i	−0.546573	−	0.146454i	−0.0250423	−	0.999686i	$-0.507972\pi$
$139$	−6.44400	−	1.72666i	−0.546573	−	0.146454i	−0.521530	+	0.853233i	$0.674639\pi$
$140$		0			0
$141$	−4.37261	−	6.86651i	−0.368240	−	0.578264i
$142$		0			0
$143$	0.615299			0.0514539
$144$		0			0
$145$	8.15012			0.676831
$146$		0			0
$147$	−7.47772	+	0.325057i	−0.616752	+	0.0268103i
$148$		0			0
$149$	−21.5773	−	5.78161i	−1.76768	−	0.473648i	−0.779428	−	0.626492i	$-0.784490\pi$
$149$	−21.5773	−	5.78161i	−1.76768	−	0.473648i	−0.988250	+	0.152844i	$0.951157\pi$
$150$		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
$155$	−31.0979	+	8.33265i	−2.49784	+	0.669295i
$156$		0			0
$157$	−14.3943	−	3.85693i	−1.14879	−	0.307817i	−0.366308	−	0.930494i	$-0.619378\pi$
$157$	−14.3943	−	3.85693i	−1.14879	−	0.307817i	−0.782479	+	0.622677i	$0.786045\pi$
$158$		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	0.856863	−	0.515545i	$-0.172410\pi$
$163$	4.35766	+	4.35766i	0.341318	+	0.341318i	−0.515545	+	0.856863i	$0.672410\pi$
$164$		0			0
$165$	−0.677022	+	1.29994i	−0.0527061	+	0.101200i
$166$		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
$171$	0.829610	−	4.69449i	0.0634418	−	0.358997i
$172$		0			0
$173$	5.24342	−	1.40497i	0.398650	−	0.106818i	−0.0539235	−	0.998545i	$-0.517173\pi$
$173$	5.24342	−	1.40497i	0.398650	−	0.106818i	0.452573	+	0.891727i	$0.350506\pi$
$174$		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	$-0.743605\pi$
$179$	0.380130	−	0.380130i	0.0284123	−	0.0284123i	0.721170	+	0.692758i	$0.243605\pi$
$180$		0			0
$181$	−4.98992	−	4.98992i	−0.370898	−	0.370898i	0.496906	−	0.867804i	$-0.334469\pi$
$181$	−4.98992	−	4.98992i	−0.370898	−	0.370898i	−0.867804	+	0.496906i	$0.834469\pi$
$182$		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
$187$	−0.240169	−	0.896324i	−0.0175629	−	0.0655457i
$188$		0			0
$189$	−6.69991	+	16.1489i	−0.487347	+	1.17466i
$190$		0			0
$191$	−5.40555	+	9.36269i	−0.391132	+	0.677461i	−0.992599	−	0.121437i	$-0.961250\pi$
$191$	−5.40555	+	9.36269i	−0.391132	+	0.677461i	0.601467	+	0.798898i	$0.294583\pi$
$192$		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
$195$	−15.8770	+	10.1105i	−1.13697	+	0.724028i
$196$		0			0
$197$	2.94550	−	2.94550i	0.209858	−	0.209858i	−0.594349	−	0.804207i	$-0.702590\pi$
$197$	2.94550	−	2.94550i	0.209858	−	0.209858i	0.804207	+	0.594349i	$0.202590\pi$
$198$		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
$203$	1.83591	−	6.85170i	0.128856	−	0.480895i
$204$		0			0
$205$	3.40971	+	12.7252i	0.238145	+	0.888768i
$206$		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
$211$	4.70786	−	17.5700i	0.324103	−	1.20957i	−0.591108	−	0.806592i	$-0.701309\pi$
$211$	4.70786	−	17.5700i	0.324103	−	1.20957i	0.915211	−	0.402975i	$-0.132024\pi$
$212$		0			0
$213$	11.5770	+	6.02940i	0.793242	+	0.413127i
$214$		0			0
$215$			18.7704i			1.28013i
$216$		0			0
$217$			28.0206i			1.90216i
$218$		0			0
$219$	4.95647	+	2.58138i	0.334927	+	0.174433i
$220$		0			0
$221$	3.08436	−	11.5110i	0.207476	−	0.774312i
$222$		0			0
$223$	2.82059	+	1.62847i	0.188881	+	0.109050i	0.591458	−	0.806336i	$-0.298552\pi$
$223$	2.82059	+	1.62847i	0.188881	+	0.109050i	−0.402578	+	0.915386i	$0.631886\pi$
$224$		0			0
$225$	−2.58916	−	29.7246i	−0.172610	−	1.98164i
$226$		0			0
$227$	2.36663	+	8.83238i	0.157079	+	0.586226i	0.998918	+	0.0464979i	$0.0148061\pi$
$227$	2.36663	+	8.83238i	0.157079	+	0.586226i	−0.841840	+	0.539728i	$0.818527\pi$
$228$		0			0
$229$	1.36053	−	5.07755i	0.0899061	−	0.335534i	−0.906292	−	0.422652i	$-0.861099\pi$
$229$	1.36053	−	5.07755i	0.0899061	−	0.335534i	0.996198	+	0.0871183i	$0.0277658\pi$
$230$		0			0
$231$	0.940338	+	0.861991i	0.0618697	+	0.0567148i
$232$		0			0
$233$	−14.1506			−0.927034			−0.463517	−	0.886088i	$-0.653413\pi$
$233$	−14.1506			−0.927034			−0.463517	+	0.886088i	$0.653413\pi$
$234$		0			0
$235$	12.8480	−	12.8480i	0.838114	−	0.838114i
$236$		0			0
$237$	−8.41110	+	5.35621i	−0.546360	+	0.347923i
$238$		0			0
$239$	−7.51536	−	13.0170i	−0.486128	−	0.841999i	0.513745	−	0.857943i	$-0.328258\pi$
$239$	−7.51536	−	13.0170i	−0.486128	−	0.841999i	−0.999873	+	0.0159444i	$0.994925\pi$
$240$		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
$243$	10.5205	+	11.5030i	0.674888	+	0.737921i
$244$		0			0
$245$	−4.32388	−	16.1369i	−0.276242	−	1.03095i
$246$		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	$-0.301333\pi$
$251$	−3.59758	−	3.59758i	−0.227077	−	0.227077i	−0.811471	+	0.584393i	$0.801333\pi$
$252$		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
$259$	−12.2521	+	3.28294i	−0.761307	+	0.203992i
$260$		0			0
$261$	−4.84331	−	4.06716i	−0.299793	−	0.251751i
$262$		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
$267$	2.36945	−	4.54955i	0.145008	−	0.278428i
$268$		0			0
$269$	7.43467	+	7.43467i	0.453300	+	0.453300i	0.896448	−	0.443148i	$-0.146139\pi$
$269$	7.43467	+	7.43467i	0.453300	+	0.453300i	−0.443148	+	0.896448i	$0.646139\pi$
$270$		0			0
$271$			11.8875i			0.722111i	0.932544	+	0.361056i	$0.117584\pi$
$271$			11.8875i			0.722111i	−0.932544	+	0.361056i	$0.882416\pi$
$272$		0			0
$273$	4.92329	+	15.6251i	0.297971	+	0.945673i
$274$		0			0
$275$	−2.10281	−	0.563445i	−0.126804	−	0.0339770i
$276$		0			0
$277$	−10.0081	+	2.68166i	−0.601329	+	0.161126i	−0.546626	−	0.837377i	$-0.684088\pi$
$277$	−10.0081	+	2.68166i	−0.601329	+	0.161126i	−0.0547032	+	0.998503i	$0.517421\pi$
$278$		0			0
$279$	22.6385	+	10.5670i	1.35533	+	0.632631i
$280$		0			0
$281$	7.05630	−	12.2219i	0.420944	−	0.729096i	−0.575088	−	0.818091i	$-0.695032\pi$
$281$	7.05630	−	12.2219i	0.420944	−	0.729096i	0.996032	+	0.0889955i	$0.0283657\pi$
$282$		0			0
$283$	12.7951	+	3.42843i	0.760588	+	0.203799i	0.618209	−	0.786013i	$-0.287858\pi$
$283$	12.7951	+	3.42843i	0.760588	+	0.203799i	0.142378	+	0.989812i	$0.454525\pi$
$284$		0			0
$285$	10.6305	−	0.462109i	0.629697	−	0.0273730i
$286$		0			0
$287$	11.4660			0.676817
$288$		0			0
$289$	−0.972286			−0.0571933
$290$		0			0
$291$	14.2136	+	22.3203i	0.833216	+	1.30844i
$292$		0			0
$293$	29.7073	+	7.96005i	1.73552	+	0.465031i	0.981443	−	0.191756i	$-0.0614181\pi$
$293$	29.7073	+	7.96005i	1.73552	+	0.465031i	0.754077	+	0.656787i	$0.228085\pi$
$294$		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
$299$	10.4522	−	2.80065i	0.604463	−	0.161965i
$300$		0			0
$301$	15.7800	+	4.22825i	0.909546	+	0.243712i
$302$		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	−0.875202	−	0.483758i	$-0.839272\pi$
$307$	−23.8109	−	23.8109i	−1.35896	−	1.35896i	−0.483758	−	0.875202i	$-0.660728\pi$
$308$		0			0
$309$	14.1588	−	0.615486i	0.805469	−	0.0350138i
$310$		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	−0.0435750	−	0.999050i	$-0.513875\pi$
$313$	−16.4634	−	9.50514i	−0.930565	−	0.537262i	−0.886990	+	0.461788i	$0.847208\pi$
$314$		0			0
$315$	−38.4283	−	6.79104i	−2.16519	−	0.382632i
$316$		0			0
$317$	−11.8751	+	3.18193i	−0.666972	+	0.178715i	−0.576391	−	0.817174i	$-0.695539\pi$
$317$	−11.8751	+	3.18193i	−0.666972	+	0.178715i	−0.0905818	+	0.995889i	$0.528873\pi$
$318$		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
$331$	8.94844	+	33.3960i	0.491851	+	1.83561i	0.546998	+	0.837134i	$0.315771\pi$
$331$	8.94844	+	33.3960i	0.491851	+	1.83561i	−0.0551468	+	0.998478i	$0.517563\pi$
$332$		0			0
$333$	−1.96809	+	11.1368i	−0.107851	+	0.610293i
$334$		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
$339$	−1.27301	−	29.2848i	−0.0691406	−	1.59053i
$340$		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
$347$	2.92992	−	10.9346i	0.157287	−	0.587002i	−0.841612	−	0.540082i	$-0.818393\pi$
$347$	2.92992	−	10.9346i	0.157287	−	0.587002i	0.998899	−	0.0469191i	$-0.0149403\pi$
$348$		0			0
$349$	−2.90715	−	10.8496i	−0.155616	−	0.580767i	−0.999052	−	0.0435372i	$-0.986137\pi$
$349$	−2.90715	−	10.8496i	−0.155616	−	0.580767i	0.843436	−	0.537230i	$-0.180529\pi$
$350$		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
$355$	−7.54056	+	28.1417i	−0.400211	+	1.49361i
$356$		0			0
$357$	20.8398	−	13.2708i	1.10296	−	0.702366i
$358$		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
$363$	0.823831	+	18.9517i	0.0432399	+	0.994705i
$364$		0			0
$365$	−3.22835	+	12.0484i	−0.168980	+	0.630641i
$366$		0			0
$367$	−20.1365	−	11.6258i	−1.05112	−	0.606863i	−0.128156	−	0.991754i	$-0.540906\pi$
$367$	−20.1365	−	11.6258i	−1.05112	−	0.606863i	−0.922962	+	0.384891i	$0.874239\pi$
$368$		0			0
$369$	4.32402	−	9.26366i	0.225099	−	0.482247i
$370$		0			0
$371$	−9.33867	−	34.8524i	−0.484839	−	1.80945i
$372$		0			0
$373$	−2.66079	+	9.93021i	−0.137771	+	0.514167i	0.862201	+	0.506567i	$0.169086\pi$
$373$	−2.66079	+	9.93021i	−0.137771	+	0.514167i	−0.999971	+	0.00759967i	$0.997581\pi$
$374$		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	−0.531345	−	0.847156i	$-0.678313\pi$
$379$	6.14819	−	6.14819i	0.315811	−	0.315811i	0.847156	+	0.531345i	$0.178313\pi$
$380$		0			0
$381$	20.5894	+	10.7231i	1.05483	+	0.549363i
$382$		0			0
$383$	−1.40170	−	2.42782i	−0.0716238	−	0.124056i	0.827989	−	0.560744i	$-0.189485\pi$
$383$	−1.40170	−	2.42782i	−0.0716238	−	0.124056i	−0.899613	+	0.436688i	$0.856151\pi$
$384$		0			0
$385$	−1.42363	+	2.46580i	−0.0725548	+	0.125669i
$386$		0			0
$387$	9.36701	−	11.1545i	0.476152	−	0.567017i
$388$		0			0
$389$	7.82350	+	29.1977i	0.396667	+	1.48038i	0.818922	+	0.573905i	$0.194572\pi$
$389$	7.82350	+	29.1977i	0.396667	+	1.48038i	−0.422255	+	0.906477i	$0.638761\pi$
$390$		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	−0.656266	−	0.754530i	$-0.727865\pi$
$397$	1.95789	−	1.95789i	0.0982636	−	0.0982636i	0.754530	+	0.656266i	$0.227865\pi$
$398$		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
$403$	22.6120	−	6.05887i	1.12638	−	0.301814i
$404$		0			0
$405$	−19.9786	+	28.4861i	−0.992743	+	1.41549i
$406$		0			0
$407$	0.714607	+	0.412578i	0.0354217	+	0.0204508i
$408$		0			0
$409$	22.8959	−	13.2190i	1.13213	−	0.653636i	0.187660	−	0.982234i	$-0.439910\pi$
$409$	22.8959	−	13.2190i	1.13213	−	0.653636i	0.944470	+	0.328598i	$0.106576\pi$
$410$		0			0
$411$	19.5801	+	30.7475i	0.965816	+	1.51666i
$412$		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
$419$	0.499479	+	0.133835i	0.0244012	+	0.00653827i	0.270999	−	0.962580i	$-0.412646\pi$
$419$	0.499479	+	0.133835i	0.0244012	+	0.00653827i	−0.246598	+	0.969118i	$0.579313\pi$
$420$		0			0
$421$	12.8514	−	3.44352i	0.626339	−	0.167827i	0.0683313	−	0.997663i	$-0.478233\pi$
$421$	12.8514	−	3.44352i	0.626339	−	0.167827i	0.558008	+	0.829836i	$0.311566\pi$
$422$		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
$427$	−29.2717	−	7.84332i	−1.41655	−	0.379565i
$428$		0			0
$429$	0.492279	−	0.945220i	0.0237675	−	0.0456356i
$430$		0			0
$431$	8.61129			0.414791			0.207396	−	0.978257i	$-0.433501\pi$
$431$	8.61129			0.414791			0.207396	+	0.978257i	$0.433501\pi$
$432$		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
$435$	6.52063	−	12.5202i	0.312640	−	0.600297i
$436$		0			0
$437$	−5.90859	−	1.58320i	−0.282646	−	0.0757348i
$438$		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
$443$	31.1860	−	8.35627i	1.48169	−	0.397018i	0.574770	−	0.818315i	$-0.305092\pi$
$443$	31.1860	−	8.35627i	1.48169	−	0.397018i	0.906923	+	0.421297i	$0.138425\pi$
$444$		0			0
$445$	11.0592	+	2.96330i	0.524257	+	0.140474i
$446$		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
$453$	−18.5606	−	29.1466i	−0.872054	−	1.36943i
$454$		0			0
$455$	−31.6669	+	18.2829i	−1.48457	+	0.857114i
$456$		0			0
$457$	13.1358	+	7.58393i	0.614465	+	0.354761i	0.774711	−	0.632316i	$-0.217895\pi$
$457$	13.1358	+	7.58393i	0.614465	+	0.354761i	−0.160246	+	0.987077i	$0.551229\pi$
$458$		0			0
$459$	−2.86281	−	21.8416i	−0.133624	−	1.01948i
$460$		0			0
$461$	−11.5696	+	3.10006i	−0.538849	+	0.144384i	−0.517971	−	0.855398i	$-0.673313\pi$
$461$	−11.5696	+	3.10006i	−0.538849	+	0.144384i	−0.0208774	+	0.999782i	$0.506646\pi$
$462$		0			0
$463$	2.03363	−	1.17412i	0.0945107	−	0.0545658i	−0.452000	−	0.892018i	$-0.649289\pi$
$463$	2.03363	−	1.17412i	0.0945107	−	0.0545658i	0.546510	+	0.837452i	$0.315956\pi$
$464$		0			0
$465$	−12.0797	+	54.4391i	−0.560184	+	2.52455i
$466$		0			0
$467$	−24.1509	+	24.1509i	−1.11757	+	1.11757i	−0.125473	+	0.992097i	$0.540045\pi$
$467$	−24.1509	+	24.1509i	−1.11757	+	1.11757i	−0.992097	+	0.125473i	$0.959955\pi$
$468$		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
$475$	4.09051	+	15.2660i	0.187685	+	0.700452i
$476$		0			0
$477$	−31.6799	−	5.59846i	−1.45052	−	0.256336i
$478$		0			0
$479$	2.40917	−	4.17281i	0.110078	−	0.190660i	−0.805724	−	0.592292i	$-0.798223\pi$
$479$	2.40917	−	4.17281i	0.110078	−	0.190660i	0.915801	+	0.401631i	$0.131557\pi$
$480$		0			0
$481$	5.29851	+	9.17730i	0.241591	+	0.418449i
$482$		0			0
$483$	19.8971	+	10.3626i	0.905351	+	0.471515i
$484$		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
$491$	0.504576	−	1.88310i	0.0227712	−	0.0849832i	−0.953605	−	0.301060i	$-0.902660\pi$
$491$	0.504576	−	1.88310i	0.0227712	−	0.0849832i	0.976376	+	0.216077i	$0.0693262\pi$
$492$		0			0
$493$	2.31315	+	8.63279i	0.104179	+	0.388801i
$494$		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
$499$	2.91509	−	10.8793i	0.130497	−	0.487023i	−0.869478	−	0.493971i	$-0.835545\pi$
$499$	2.91509	−	10.8793i	0.130497	−	0.487023i	0.999976	+	0.00694794i	$0.00221162\pi$
$500$		0			0
$501$	−1.03320	−	23.7680i	−0.0461598	−	1.06187i
$502$		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
$507$	−7.44813	+	4.74299i	−0.330783	+	0.210644i
$508$		0			0
$509$	8.59758	−	32.0866i	0.381081	−	1.42221i	−0.463172	−	0.886269i	$-0.653289\pi$
$509$	8.59758	−	32.0866i	0.381081	−	1.42221i	0.844253	−	0.535945i	$-0.180045\pi$
$510$		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
$515$	8.18713	+	30.5548i	0.360768	+	1.34641i
$516$		0			0
$517$	−0.266262	+	0.993703i	−0.0117102	+	0.0437030i
$518$		0			0
$519$	2.03677	−	9.17899i	0.0894042	−	0.402913i
$520$		0			0
$521$	20.5032			0.898262			0.449131	−	0.893466i	$-0.351734\pi$
$521$	20.5032			0.898262			0.449131	+	0.893466i	$0.351734\pi$
$522$		0			0
$523$	29.2406	−	29.2406i	1.27860	−	1.27860i	0.337151	−	0.941451i	$-0.390537\pi$
$523$	29.2406	−	29.2406i	1.27860	−	1.27860i	0.941451	−	0.337151i	$-0.109463\pi$
$524$		0			0
$525$	−2.51725	−	57.9076i	−0.109862	−	2.52730i
$526$		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
$531$	−15.5960	+	5.66974i	−0.676808	+	0.246046i
$532$		0			0
$533$	−2.47928	−	9.25281i	−0.107390	−	0.400784i
$534$		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	−0.109077	−	0.994033i	$-0.534790\pi$
$541$	20.5836	−	20.5836i	0.884956	−	0.884956i	0.994033	+	0.109077i	$0.0347895\pi$
$542$		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
$547$	38.0779	−	10.2029i	1.62809	−	0.436246i	0.674728	−	0.738067i	$-0.264261\pi$
$547$	38.0779	−	10.2029i	1.62809	−	0.436246i	0.953365	+	0.301821i	$0.0975945\pi$
$548$		0			0
$549$	−17.3756	+	20.6914i	−0.741574	+	0.883089i
$550$		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
$555$	−25.2189	+	1.09627i	−1.07048	+	0.0465340i
$556$		0			0
$557$	1.52288	+	1.52288i	0.0645265	+	0.0645265i	0.738634	−	0.674107i	$-0.235471\pi$
$557$	1.52288	+	1.52288i	0.0645265	+	0.0645265i	−0.674107	+	0.738634i	$0.735471\pi$
$558$		0			0
$559$		−	13.6484i		−	0.577266i
$560$		0			0
$561$	−1.56908	−	0.348170i	−0.0662466	−	0.0146998i
$562$		0			0
$563$	4.85715	+	1.30147i	0.204705	+	0.0548504i	0.359714	−	0.933063i	$-0.382874\pi$
$563$	4.85715	+	1.30147i	0.204705	+	0.0548504i	−0.155010	+	0.987913i	$0.549541\pi$
$564$		0			0
$565$	63.1966	−	16.9335i	2.65870	−	0.712397i
$566$		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	$-0.571724\pi$
$569$	17.4710	−	30.2606i	0.732421	−	1.26859i	0.955846	−	0.293869i	$-0.0949430\pi$
$570$		0			0
$571$	−34.1869	−	9.16034i	−1.43068	−	0.383348i	−0.541417	−	0.840754i	$-0.682112\pi$
$571$	−34.1869	−	9.16034i	−1.43068	−	0.383348i	−0.889258	+	0.457406i	$0.848779\pi$
$572$		0			0
$573$	10.0581	+	15.7947i	0.420185	+	0.659835i
$574$		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
$579$	8.99970	−	0.391218i	0.374015	−	0.0162584i
$580$		0			0
$581$	−15.1616	−	4.06253i	−0.629008	−	0.168542i
$582$		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
$587$	−12.3561	+	3.31081i	−0.509991	+	0.136652i	−0.504633	−	0.863334i	$-0.668372\pi$
$587$	−12.3561	+	3.31081i	−0.509991	+	0.136652i	−0.00535825	+	0.999986i	$0.501706\pi$
$588$		0			0
$589$	−12.7825	−	3.42507i	−0.526696	−	0.141128i
$590$		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
$597$	−2.05844	+	3.95239i	−0.0842465	+	0.161761i
$598$		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	−0.0592656	−	0.998242i	$-0.518876\pi$
$601$	−23.3729	−	13.4944i	−0.953401	−	0.550447i	−0.894136	+	0.447796i	$0.852209\pi$
$602$		0			0
$603$	15.1056	−	5.49146i	0.615146	−	0.223630i
$604$		0			0
$605$	−40.8977	+	10.9585i	−1.66273	+	0.445527i
$606$		0			0
$607$	−21.2314	+	12.2579i	−0.861755	+	0.497534i	−0.864600	−	0.502462i	$-0.832428\pi$
$607$	−21.2314	+	12.2579i	−0.861755	+	0.497534i	0.00284471	+	0.999996i	$0.499095\pi$
$608$		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	−0.964937	−	0.262481i	$-0.915459\pi$
$613$	−30.3894	−	30.3894i	−1.22742	−	1.22742i	−0.262481	−	0.964937i	$-0.584541\pi$
$614$		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	$0.0534341\pi$
$617$	15.8393	+	27.4345i	0.637668	+	1.10447i	−0.348275	+	0.937392i	$0.613233\pi$
$618$		0			0
$619$	−5.39413	−	20.1312i	−0.216809	−	0.809141i	−0.985522	−	0.169547i	$-0.945769\pi$
$619$	−5.39413	−	20.1312i	−0.216809	−	0.809141i	0.768713	−	0.639593i	$-0.220897\pi$
$620$		0			0
$621$	15.8757	−	12.1675i	0.637071	−	0.488264i
$622$		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
$627$	−0.508167	+	0.323602i	−0.0202943	+	0.0129234i
$628$		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
$635$	−13.4107	+	50.0494i	−0.532187	+	1.98615i
$636$		0			0
$637$	3.14400	+	11.7335i	0.124570	+	0.464900i
$638$		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
$643$	3.45056	−	12.8777i	0.136077	−	0.507846i	−0.863914	−	0.503639i	$-0.831994\pi$
$643$	3.45056	−	12.8777i	0.136077	−	0.507846i	0.999991	−	0.00420705i	$-0.00133915\pi$
$644$		0			0
$645$	28.8350	+	15.0175i	1.13538	+	0.591315i
$646$		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
$651$	43.0451	+	22.4183i	1.68707	+	0.878642i
$652$		0			0
$653$	5.39824	−	20.1465i	0.211249	−	0.788394i	−0.776204	−	0.630482i	$-0.782857\pi$
$653$	5.39824	−	20.1465i	0.211249	−	0.788394i	0.987453	−	0.157912i	$-0.0504761\pi$
$654$		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
$659$	3.90477	+	14.5728i	0.152108	+	0.567676i	0.999336	+	0.0364452i	$0.0116034\pi$
$659$	3.90477	+	14.5728i	0.152108	+	0.567676i	−0.847227	+	0.531230i	$0.821730\pi$
$660$		0			0
$661$	2.44325	−	9.11835i	0.0950316	−	0.354663i	−0.901993	−	0.431751i	$-0.857896\pi$
$661$	2.44325	−	9.11835i	0.0950316	−	0.354663i	0.997024	+	0.0770887i	$0.0245625\pi$
$662$		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
$669$	4.75830	−	3.03010i	0.183966	−	0.117150i
$670$		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
$675$	−47.7343	−	19.8042i	−1.83729	−	0.762263i
$676$		0			0
$677$	−4.16296	−	15.5364i	−0.159996	−	0.597111i	−0.998626	−	0.0524101i	$-0.983310\pi$
$677$	−4.16296	−	15.5364i	−0.159996	−	0.597111i	0.838630	−	0.544701i	$-0.183357\pi$
$678$		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	0.994742	+	0.102416i	$0.0326571\pi$
$683$	28.6734	+	28.6734i	1.09716	+	1.09716i	0.102416	+	0.994742i	$0.467343\pi$
$684$		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
$691$	−44.0504	+	11.8033i	−1.67575	+	0.449017i	−0.966653	−	0.256089i	$-0.917566\pi$
$691$	−44.0504	+	11.8033i	−1.67575	+	0.449017i	−0.709102	+	0.705106i	$0.750899\pi$
$692$		0			0
$693$	2.07652	−	0.754895i	0.0788804	−	0.0286761i
$694$		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
$699$	−11.3214	+	21.7380i	−0.428213	+	0.822208i
$700$		0			0
$701$	−13.0178	−	13.0178i	−0.491676	−	0.491676i	0.417158	−	0.908834i	$-0.363026\pi$
$701$	−13.0178	−	13.0178i	−0.491676	−	0.491676i	−0.908834	+	0.417158i	$0.863026\pi$
$702$		0			0
$703$		−	5.99049i		−	0.225935i
$704$		0			0
$705$	−9.45784	−	30.0164i	−0.356203	−	1.13048i
$706$		0			0
$707$	0.436349	+	0.116919i	0.0164106	+	0.00439721i
$708$		0			0
$709$	−16.3841	+	4.39011i	−0.615319	+	0.164874i	−0.552999	−	0.833182i	$-0.686517\pi$
$709$	−16.3841	+	4.39011i	−0.615319	+	0.164874i	−0.0623199	+	0.998056i	$0.519850\pi$
$710$		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
$715$	2.29767	+	0.615660i	0.0859282	+	0.0230244i
$716$		0			0
$717$	−26.0094	+	1.13063i	−0.971339	+	0.0422242i
$718$		0			0
$719$	43.0731			1.60635			0.803177	−	0.595740i	$-0.203141\pi$
$719$	43.0731			1.60635			0.803177	+	0.595740i	$0.203141\pi$
$720$		0			0
$721$	27.5313			1.02532
$722$		0			0
$723$	−13.3770	−	21.0065i	−0.497495	−	0.781240i
$724$		0			0
$725$	20.2528	+	5.42673i	0.752171	+	0.201544i
$726$		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
$731$	−19.8820	+	5.32737i	−0.735363	+	0.197040i
$732$		0			0
$733$	−2.53658	−	0.679676i	−0.0936909	−	0.0251044i	0.211669	−	0.977341i	$-0.432110\pi$
$733$	−2.53658	−	0.679676i	−0.0936909	−	0.0251044i	−0.305360	+	0.952237i	$0.598777\pi$
$734$		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	0.422836	−	0.906206i	$-0.361035\pi$
$739$	−13.1402	−	13.1402i	−0.483370	−	0.483370i	−0.906206	+	0.422836i	$0.861035\pi$
$740$		0			0
$741$	−7.72970	+	0.336011i	−0.283958	+	0.0123437i
$742$		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
$747$	−8.99989	+	10.7174i	−0.329289	+	0.392127i
$748$		0			0
$749$	38.0958	−	10.2077i	1.39199	−	0.372982i
$750$		0			0
$751$	−7.86676	+	4.54188i	−0.287062	+	0.165735i	−0.636616	−	0.771181i	$-0.719666\pi$
$751$	−7.86676	+	4.54188i	−0.287062	+	0.165735i	0.349554	+	0.936916i	$0.386333\pi$
$752$		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	0.957353	−	0.288920i	$-0.0932961\pi$
$757$	18.3910	+	18.3910i	0.668433	+	0.668433i	−0.288920	+	0.957353i	$0.593296\pi$
$758$		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	$0.00421194\pi$
$761$	14.1080	+	24.4358i	0.511415	+	0.885797i	−0.488497	+	0.872565i	$0.662455\pi$
$762$		0			0
$763$	−7.77481	−	29.0160i	−0.281467	−	1.05045i
$764$		0			0
$765$	46.2091	−	16.7988i	1.67069	−	0.607362i
$766$		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
$771$	0.427898	+	9.84350i	0.0154104	+	0.354505i
$772$		0			0
$773$	10.5491	−	10.5491i	0.379425	−	0.379425i	−0.491470	−	0.870895i	$-0.663540\pi$
$773$	10.5491	−	10.5491i	0.379425	−	0.379425i	0.870895	+	0.491470i	$0.163540\pi$
$774$		0			0
$775$	−82.8256			−2.97518
$776$		0			0
$777$	−4.75923	+	21.4482i	−0.170736	+	0.769448i
$778$		0			0
$779$	−1.40154	+	5.23060i	−0.0502152	+	0.187406i
$780$		0			0
$781$	−0.426938	−	1.59335i	−0.0152770	−	0.0570146i
$782$		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
$787$	9.05729	−	33.8023i	0.322857	−	1.20492i	−0.593591	−	0.804767i	$-0.702290\pi$
$787$	9.05729	−	33.8023i	0.322857	−	1.20492i	0.916448	−	0.400153i	$-0.131043\pi$
$788$		0			0
$789$	−31.7815	+	20.2385i	−1.13145	+	0.720511i
$790$		0			0
$791$		−	56.9431i		−	2.02466i
$792$		0			0
$793$			25.3175i			0.899052i
$794$		0			0
$795$	−3.11845	−	71.7379i	−0.110600	−	2.54428i
$796$		0			0
$797$	−7.41329	+	27.6668i	−0.262592	+	0.980007i	0.701116	+	0.713048i	$0.252686\pi$
$797$	−7.41329	+	27.6668i	−0.262592	+	0.980007i	−0.963708	+	0.266959i	$0.913981\pi$
$798$		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
$803$	−0.182786	−	0.682165i	−0.00645036	−	0.0240731i
$804$		0			0
$805$	−12.9598	+	48.3667i	−0.456773	+	1.70470i
$806$		0			0
$807$	17.3693	−	5.47289i	0.611429	−	0.192655i
$808$		0			0
$809$	39.9831			1.40573			0.702865	−	0.711323i	$-0.251904\pi$
$809$	39.9831			1.40573			0.702865	+	0.711323i	$0.251904\pi$
$810$		0			0
$811$	33.5121	−	33.5121i	1.17677	−	1.17677i	0.196204	−	0.980563i	$-0.437138\pi$
$811$	33.5121	−	33.5121i	1.17677	−	1.17677i	0.980563	−	0.196204i	$-0.0628616\pi$
$812$		0			0
$813$	18.2614	+	9.51073i	0.640457	+	0.333556i
$814$		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
$819$	27.9421	+	4.93793i	0.976377	+	0.172545i
$820$		0			0
$821$	−2.91908	−	10.8942i	−0.101877	−	0.380209i	0.896096	−	0.443861i	$-0.146392\pi$
$821$	−2.91908	−	10.8942i	−0.101877	−	0.380209i	−0.997972	+	0.0636527i	$0.979725\pi$
$822$		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	$-0.136381\pi$
$827$	14.2104	+	14.2104i	0.494144	+	0.494144i	−0.415465	+	0.909609i	$0.636381\pi$
$828$		0			0
$829$	6.15512	−	6.15512i	0.213776	−	0.213776i	−0.592093	−	0.805869i	$-0.701698\pi$
$829$	6.15512	−	6.15512i	0.213776	−	0.213776i	0.805869	+	0.592093i	$0.201698\pi$
$830$		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
$835$	51.2913	−	13.7435i	1.77501	−	0.475612i
$836$		0			0
$837$	34.3453	−	26.3229i	1.18715	−	0.909853i
$838$		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
$843$	−13.1297	−	20.6181i	−0.452210	−	0.710127i
$844$		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
$851$	14.0170	+	3.75585i	0.480497	+	0.128749i
$852$		0			0
$853$	18.8477	−	5.05023i	0.645334	−	0.172917i	0.0787157	−	0.996897i	$-0.474918\pi$
$853$	18.8477	−	5.05023i	0.645334	−	0.172917i	0.566618	+	0.823980i	$0.308251\pi$
$854$		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	$-0.612799\pi$
$857$	18.6982	−	32.3862i	0.638717	−	1.10629i	0.985715	−	0.168424i	$-0.0538679\pi$
$858$		0			0
$859$	−26.5180	−	7.10549i	−0.904784	−	0.242436i	−0.223714	−	0.974655i	$-0.571818\pi$
$859$	−26.5180	−	7.10549i	−0.904784	−	0.242436i	−0.681070	+	0.732219i	$0.738485\pi$
$860$		0			0
$861$	9.17354	−	17.6140i	0.312634	−	0.600284i
$862$		0			0
$863$	−10.1797			−0.346520			−0.173260	−	0.984876i	$-0.555430\pi$
$863$	−10.1797			−0.346520			−0.173260	+	0.984876i	$0.555430\pi$
$864$		0			0
$865$	20.9860			0.713545
$866$		0			0
$867$	−0.777892	+	1.49362i	−0.0264186	+	0.0507261i
$868$		0			0
$869$	1.21723	+	0.326156i	0.0412918	+	0.0110641i
$870$		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
$875$	62.1414	−	16.6507i	2.10076	−	0.562897i
$876$		0			0
$877$	25.7779	+	6.90717i	0.870458	+	0.233239i	0.666286	−	0.745696i	$-0.267883\pi$
$877$	25.7779	+	6.90717i	0.870458	+	0.233239i	0.204172	+	0.978935i	$0.434550\pi$
$878$		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	0.956933	−	0.290310i	$-0.0937586\pi$
$883$	19.8089	+	19.8089i	0.666622	+	0.666622i	−0.290310	+	0.956933i	$0.593759\pi$
$884$		0			0
$885$	−19.8953	−	31.2425i	−0.668774	−	1.05021i
$886$		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
$891$	0.173190	−	1.96235i	0.00580210	−	0.0657413i
$892$		0			0
$893$	7.21410	−	1.93301i	0.241411	−	0.0646858i
$894$		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
$907$	15.0239	+	56.0698i	0.498859	+	1.86177i	0.507245	+	0.861802i	$0.330664\pi$
$907$	15.0239	+	56.0698i	0.498859	+	1.86177i	−0.00838605	+	0.999965i	$0.502669\pi$
$908$		0			0
$909$	0.259016	−	0.308445i	0.00859103	−	0.0102305i
$910$		0			0
$911$	11.9347	−	20.6715i	0.395414	−	0.684877i	−0.597740	−	0.801690i	$-0.703934\pi$
$911$	11.9347	−	20.6715i	0.395414	−	0.684877i	0.993154	+	0.116813i	$0.0372678\pi$
$912$		0			0
$913$	0.510553	+	0.884303i	0.0168968	+	0.0292662i
$914$		0			0
$915$	−53.4884	−	27.8572i	−1.76827	−	0.920932i
$916$		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
$923$	5.48292	−	20.4625i	0.180473	−	0.673533i
$924$		0			0
$925$	−9.70397	−	36.2157i	−0.319065	−	1.19077i
$926$		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
$931$	1.77730	−	6.63296i	0.0582485	−	0.217387i
$932$		0			0
$933$	−0.799912	−	18.4014i	−0.0261879	−	0.602436i
$934$		0			0
$935$		−	3.58740i		−	0.117320i
$936$		0			0
$937$		−	5.92940i		−	0.193705i	−0.995299	−	0.0968526i	$-0.969122\pi$
$937$		−	5.92940i		−	0.193705i	0.995299	−	0.0968526i	$-0.0308775\pi$
$938$		0			0
$939$	−27.7735	+	17.6862i	−0.906354	+	0.577169i
$940$		0			0
$941$	−5.52232	+	20.6096i	−0.180022	+	0.671853i	0.815619	+	0.578589i	$0.196397\pi$
$941$	−5.52232	+	20.6096i	−0.180022	+	0.671853i	−0.995641	+	0.0932635i	$0.970270\pi$
$942$		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
$947$	8.57071	+	31.9863i	0.278511	+	1.03942i	0.953452	+	0.301545i	$0.0975022\pi$
$947$	8.57071	+	31.9863i	0.278511	+	1.03942i	−0.674941	+	0.737871i	$0.735831\pi$
$948$		0			0
$949$	2.34741	−	8.76066i	0.0762002	−	0.284383i
$950$		0			0
$951$	−4.61279	+	20.7882i	−0.149580	+	0.674105i
$952$		0			0
$953$	0.546564			0.0177049			0.00885247	−	0.999961i	$-0.497182\pi$
$953$	0.546564			0.0177049			0.00885247	+	0.999961i	$0.497182\pi$
$954$		0			0
$955$	−29.5538	+	29.5538i	−0.956339	+	0.956339i
$956$		0			0
$957$	0.0347109	+	0.798502i	0.00112205	+	0.0258119i
$958$		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
$963$	6.11946	−	34.6280i	0.197197	−	1.11587i
$964$		0			0
$965$	5.20393	+	19.4213i	0.167521	+	0.625195i
$966$		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	$-0.483189\pi$
$971$	−29.4725	−	29.4725i	−0.945816	−	0.945816i	−0.998606	+	0.0527896i	$0.983189\pi$
$972$		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
$979$	−0.626159	+	0.167779i	−0.0200121	+	0.00536224i
$980$		0			0
$981$	−26.3747	−	4.66094i	−0.842080	−	0.148812i
$982$		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
$987$	−27.3649	+	1.18955i	−0.871033	+	0.0378639i
$988$		0			0
$989$	−13.2158	−	13.2158i	−0.420240	−	0.420240i
$990$		0			0
$991$			7.12527i			0.226342i	0.993576	+	0.113171i	$0.0361008\pi$
$991$			7.12527i			0.226342i	−0.993576	+	0.113171i	$0.963899\pi$
$992$		0			0
$993$	58.4622	+	12.9724i	1.85524	+	0.411668i
$994$		0			0
$995$	−9.60763	−	2.57436i	−0.304582	−	0.0816126i
$996$		0			0
$997$	−47.5897	+	12.7516i	−1.50718	+	0.403848i	−0.915498	−	0.402322i	$-0.868203\pi$
$997$	−47.5897	+	12.7516i	−1.50718	+	0.403848i	−0.591684	+	0.806170i	$0.701537\pi$
$998$		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.335.15		88
3.2	odd	2		1728.2.z.a.143.1		88
4.3	odd	2		144.2.u.a.11.7	✓	88
9.4	even	3		1728.2.z.a.719.1		88
9.5	odd	6	inner	576.2.y.a.527.3		88
12.11	even	2		432.2.v.a.251.16		88
16.3	odd	4	inner	576.2.y.a.47.3		88
16.13	even	4		144.2.u.a.83.14	yes	88
36.23	even	6		144.2.u.a.59.14	yes	88
36.31	odd	6		432.2.v.a.395.9		88
48.29	odd	4		432.2.v.a.35.9		88
48.35	even	4		1728.2.z.a.1007.1		88
144.13	even	12		432.2.v.a.179.16		88
144.67	odd	12		1728.2.z.a.1583.1		88
144.77	odd	12		144.2.u.a.131.7	yes	88
144.131	even	12	inner	576.2.y.a.239.15		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.7	✓	88	4.3	odd	2
144.2.u.a.59.14	yes	88	36.23	even	6
144.2.u.a.83.14	yes	88	16.13	even	4
144.2.u.a.131.7	yes	88	144.77	odd	12
432.2.v.a.35.9		88	48.29	odd	4
432.2.v.a.179.16		88	144.13	even	12
432.2.v.a.251.16		88	12.11	even	2
432.2.v.a.395.9		88	36.31	odd	6
576.2.y.a.47.3		88	16.3	odd	4	inner
576.2.y.a.239.15		88	144.131	even	12	inner
576.2.y.a.335.15		88	1.1	even	1	trivial
576.2.y.a.527.3		88	9.5	odd	6	inner
1728.2.z.a.143.1		88	3.2	odd	2
1728.2.z.a.719.1		88	9.4	even	3
1728.2.z.a.1007.1		88	48.35	even	4
1728.2.z.a.1583.1		88	144.67	odd	12

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 $\F_{q}$
Belyi maps

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

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