LMFDB - Embedded newform 576.2.bb.e.529.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (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:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			529.18
Character	$\chi$	$=$	576.529
Dual form			576.2.bb.e.49.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71859 - 0.215523i) q^{3} +(2.73721 + 0.733432i) q^{5} +(1.14487 + 0.660988i) q^{7} +(2.90710 - 0.740791i) q^{9} +O(q^{10})$	\(q+(1.71859 - 0.215523i) q^{3} +(2.73721 + 0.733432i) q^{5} +(1.14487 + 0.660988i) q^{7} +(2.90710 - 0.740791i) q^{9} +(0.343957 + 1.28367i) q^{11} +(-0.902174 + 3.36696i) q^{13} +(4.86220 + 0.670538i) q^{15} -7.60772 q^{17} +(-4.32297 - 4.32297i) q^{19} +(2.11001 + 0.889223i) q^{21} +(3.46087 - 1.99814i) q^{23} +(2.62424 + 1.51511i) q^{25} +(4.83645 - 1.89966i) q^{27} +(-3.54658 + 0.950303i) q^{29} +(-0.569129 - 0.985760i) q^{31} +(0.867781 + 2.13197i) q^{33} +(2.64894 + 2.64894i) q^{35} +(2.26014 - 2.26014i) q^{37} +(-0.824810 + 5.98086i) q^{39} +(-1.42311 + 0.821634i) q^{41} +(-1.65438 - 6.17424i) q^{43} +(8.50065 + 0.104463i) q^{45} +(-4.58731 + 7.94546i) q^{47} +(-2.62619 - 4.54869i) q^{49} +(-13.0746 + 1.63964i) q^{51} +(7.72215 - 7.72215i) q^{53} +3.76593i q^{55} +(-8.36111 - 6.49771i) q^{57} +(4.80982 + 1.28879i) q^{59} +(9.92979 - 2.66068i) q^{61} +(3.81789 + 1.07345i) q^{63} +(-4.93887 + 8.55438i) q^{65} +(3.73189 - 13.9276i) q^{67} +(5.51718 - 4.17987i) q^{69} +7.87498i q^{71} -0.577222i q^{73} +(4.83654 + 2.03826i) q^{75} +(-0.454704 + 1.69698i) q^{77} +(-0.716890 + 1.24169i) q^{79} +(7.90246 - 4.30711i) q^{81} +(-3.30414 + 0.885341i) q^{83} +(-20.8239 - 5.57975i) q^{85} +(-5.89030 + 2.39755i) q^{87} +16.2114i q^{89} +(-3.25839 + 3.25839i) q^{91} +(-1.19055 - 1.57146i) q^{93} +(-8.66225 - 15.0035i) q^{95} +(-0.648931 + 1.12398i) q^{97} +(1.95085 + 3.47695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.71859	−	0.215523i	0.992228	−	0.124432i
$3$	1.71859	−	0.215523i	0.992228	−	0.124432i
$4$		0			0
$5$	2.73721	+	0.733432i	1.22412	+	0.328001i	0.812286	−	0.583260i	$-0.198223\pi$
$5$	2.73721	+	0.733432i	1.22412	+	0.328001i	0.411830	+	0.911261i	$0.364890\pi$
$6$		0			0
$7$	1.14487	+	0.660988i	0.432718	+	0.249830i	0.700504	−	0.713648i	$-0.252959\pi$
$7$	1.14487	+	0.660988i	0.432718	+	0.249830i	−0.267786	+	0.963479i	$0.586292\pi$
$8$		0			0
$9$	2.90710	−	0.740791i	0.969033	−	0.246930i
$10$		0			0
$11$	0.343957	+	1.28367i	0.103707	+	0.387040i	0.998195	−	0.0600515i	$-0.0191265\pi$
$11$	0.343957	+	1.28367i	0.103707	+	0.387040i	−0.894488	+	0.447092i	$0.852460\pi$
$12$		0			0
$13$	−0.902174	+	3.36696i	−0.250218	+	0.933827i	0.720470	+	0.693486i	$0.243926\pi$
$13$	−0.902174	+	3.36696i	−0.250218	+	0.933827i	−0.970689	+	0.240341i	$0.922741\pi$
$14$		0			0
$15$	4.86220	+	0.670538i	1.25542	+	0.173132i
$16$		0			0
$17$	−7.60772			−1.84514			−0.922572	−	0.385825i	$-0.873917\pi$
$17$	−7.60772			−1.84514			−0.922572	+	0.385825i	$0.873917\pi$
$18$		0			0
$19$	−4.32297	−	4.32297i	−0.991757	−	0.991757i	0.00820954	−	0.999966i	$-0.497387\pi$
$19$	−4.32297	−	4.32297i	−0.991757	−	0.991757i	−0.999966	+	0.00820954i	$0.997387\pi$
$20$		0			0
$21$	2.11001	+	0.889223i	0.460442	+	0.194044i
$22$		0			0
$23$	3.46087	−	1.99814i	0.721642	−	0.416640i	−0.0937148	−	0.995599i	$-0.529874\pi$
$23$	3.46087	−	1.99814i	0.721642	−	0.416640i	0.815357	+	0.578959i	$0.196541\pi$
$24$		0			0
$25$	2.62424	+	1.51511i	0.524849	+	0.303021i
$26$		0			0
$27$	4.83645	−	1.89966i	0.930776	−	0.365590i
$28$		0			0
$29$	−3.54658	+	0.950303i	−0.658583	+	0.176467i	−0.572606	−	0.819830i	$-0.694068\pi$
$29$	−3.54658	+	0.950303i	−0.658583	+	0.176467i	−0.0859765	+	0.996297i	$0.527401\pi$
$30$		0			0
$31$	−0.569129	−	0.985760i	−0.102219	−	0.177048i	0.810380	−	0.585905i	$-0.199261\pi$
$31$	−0.569129	−	0.985760i	−0.102219	−	0.177048i	−0.912598	+	0.408857i	$0.865927\pi$
$32$		0			0
$33$	0.867781	+	2.13197i	0.151061	+	0.371128i
$34$		0			0
$35$	2.64894	+	2.64894i	0.447753	+	0.447753i
$36$		0			0
$37$	2.26014	−	2.26014i	0.371565	−	0.371565i	−0.496482	−	0.868047i	$-0.665375\pi$
$37$	2.26014	−	2.26014i	0.371565	−	0.371565i	0.868047	+	0.496482i	$0.165375\pi$
$38$		0			0
$39$	−0.824810	+	5.98086i	−0.132075	+	0.957704i
$40$		0			0
$41$	−1.42311	+	0.821634i	−0.222253	+	0.128318i	−0.606993	−	0.794707i	$-0.707624\pi$
$41$	−1.42311	+	0.821634i	−0.222253	+	0.128318i	0.384740	+	0.923025i	$0.374291\pi$
$42$		0			0
$43$	−1.65438	−	6.17424i	−0.252291	−	0.941563i	−0.969578	−	0.244784i	$-0.921283\pi$
$43$	−1.65438	−	6.17424i	−0.252291	−	0.941563i	0.717287	−	0.696778i	$-0.245384\pi$
$44$		0			0
$45$	8.50065	+	0.104463i	1.26720	+	0.0155724i
$46$		0			0
$47$	−4.58731	+	7.94546i	−0.669129	+	1.15896i	0.309020	+	0.951056i	$0.399999\pi$
$47$	−4.58731	+	7.94546i	−0.669129	+	1.15896i	−0.978148	+	0.207909i	$0.933334\pi$
$48$		0			0
$49$	−2.62619	−	4.54869i	−0.375170	−	0.649813i
$50$		0			0
$51$	−13.0746	+	1.63964i	−1.83080	+	0.229595i
$52$		0			0
$53$	7.72215	−	7.72215i	1.06072	−	1.06072i	0.0626852	−	0.998033i	$-0.480034\pi$
$53$	7.72215	−	7.72215i	1.06072	−	1.06072i	0.998033	−	0.0626852i	$-0.0199664\pi$
$54$		0			0
$55$			3.76593i			0.507798i
$56$		0			0
$57$	−8.36111	−	6.49771i	−1.10746	−	0.860642i
$58$		0			0
$59$	4.80982	+	1.28879i	0.626185	+	0.167786i	0.557938	−	0.829883i	$-0.311593\pi$
$59$	4.80982	+	1.28879i	0.626185	+	0.167786i	0.0682473	+	0.997668i	$0.478259\pi$
$60$		0			0
$61$	9.92979	−	2.66068i	1.27138	−	0.340665i	0.440820	−	0.897596i	$-0.354688\pi$
$61$	9.92979	−	2.66068i	1.27138	−	0.340665i	0.830559	+	0.556931i	$0.188021\pi$
$62$		0			0
$63$	3.81789	+	1.07345i	0.481009	+	0.135242i
$64$		0			0
$65$	−4.93887	+	8.55438i	−0.612592	+	1.06104i
$66$		0			0
$67$	3.73189	−	13.9276i	0.455923	−	1.70153i	−0.229436	−	0.973324i	$-0.573688\pi$
$67$	3.73189	−	13.9276i	0.455923	−	1.70153i	0.685359	−	0.728205i	$-0.259645\pi$
$68$		0			0
$69$	5.51718	−	4.17987i	0.664190	−	0.503198i
$70$		0			0
$71$			7.87498i			0.934588i	0.884102	+	0.467294i	$0.154771\pi$
$71$			7.87498i			0.934588i	−0.884102	+	0.467294i	$0.845229\pi$
$72$		0			0
$73$		−	0.577222i		−	0.0675588i	−0.999429	−	0.0337794i	$-0.989246\pi$
$73$		−	0.577222i		−	0.0675588i	0.999429	−	0.0337794i	$-0.0107544\pi$
$74$		0			0
$75$	4.83654	+	2.03826i	0.558475	+	0.235358i
$76$		0			0
$77$	−0.454704	+	1.69698i	−0.0518183	+	0.193389i
$78$		0			0
$79$	−0.716890	+	1.24169i	−0.0806564	+	0.139701i	−0.903532	−	0.428521i	$-0.859035\pi$
$79$	−0.716890	+	1.24169i	−0.0806564	+	0.139701i	0.822876	+	0.568221i	$0.192368\pi$
$80$		0			0
$81$	7.90246	−	4.30711i	0.878051	−	0.478567i
$82$		0			0
$83$	−3.30414	+	0.885341i	−0.362676	+	0.0971788i	−0.435555	−	0.900162i	$-0.643448\pi$
$83$	−3.30414	+	0.885341i	−0.362676	+	0.0971788i	0.0728790	+	0.997341i	$0.476781\pi$
$84$		0			0
$85$	−20.8239	−	5.57975i	−2.25867	−	0.605208i
$86$		0			0
$87$	−5.89030	+	2.39755i	−0.631506	+	0.257044i
$88$		0			0
$89$			16.2114i			1.71841i	0.511635	+	0.859203i	$0.329040\pi$
$89$			16.2114i			1.71841i	−0.511635	+	0.859203i	$0.670960\pi$
$90$		0			0
$91$	−3.25839	+	3.25839i	−0.341572	+	0.341572i
$92$		0			0
$93$	−1.19055	−	1.57146i	−0.123455	−	0.162952i
$94$		0			0
$95$	−8.66225	−	15.0035i	−0.888728	−	1.53932i
$96$		0			0
$97$	−0.648931	+	1.12398i	−0.0658889	+	0.114123i	−0.897088	−	0.441852i	$-0.854322\pi$
$97$	−0.648931	+	1.12398i	−0.0658889	+	0.114123i	0.831199	+	0.555975i	$0.187655\pi$
$98$		0			0
$99$	1.95085	+	3.47695i	0.196068	+	0.349446i
$100$		0			0
$101$	2.60956	+	9.73900i	0.259661	+	0.969067i	0.965438	+	0.260633i	$0.0839313\pi$
$101$	2.60956	+	9.73900i	0.259661	+	0.969067i	−0.705777	+	0.708434i	$0.749402\pi$
$102$		0			0
$103$	−8.04850	+	4.64680i	−0.793042	+	0.457863i	−0.841033	−	0.540985i	$-0.818052\pi$
$103$	−8.04850	+	4.64680i	−0.793042	+	0.457863i	0.0479901	+	0.998848i	$0.484718\pi$
$104$		0			0
$105$	5.12335	+	3.98154i	0.499988	+	0.388558i
$106$		0			0
$107$	−1.89502	+	1.89502i	−0.183199	+	0.183199i	−0.792748	−	0.609549i	$-0.791350\pi$
$107$	−1.89502	+	1.89502i	−0.183199	+	0.183199i	0.609549	+	0.792748i	$0.291350\pi$
$108$		0			0
$109$	−8.63272	−	8.63272i	−0.826864	−	0.826864i	0.160217	−	0.987082i	$-0.448780\pi$
$109$	−8.63272	−	8.63272i	−0.826864	−	0.826864i	−0.987082	+	0.160217i	$0.948780\pi$
$110$		0			0
$111$	3.39715	−	4.37137i	0.322443	−	0.414912i
$112$		0			0
$113$	−1.70180	−	2.94761i	−0.160092	−	0.277288i	0.774809	−	0.632195i	$-0.217846\pi$
$113$	−1.70180	−	2.94761i	−0.160092	−	0.277288i	−0.934902	+	0.354907i	$0.884512\pi$
$114$		0			0
$115$	10.9386	−	2.93099i	1.02003	−	0.273317i
$116$		0			0
$117$	−0.128497	+	10.4564i	−0.0118796	+	0.966695i
$118$		0			0
$119$	−8.70982	−	5.02862i	−0.798428	−	0.460972i
$120$		0			0
$121$	7.99679	−	4.61695i	0.726981	−	0.419722i
$122$		0			0
$123$	−2.26866	+	1.71877i	−0.204559	+	0.154976i
$124$		0			0
$125$	−3.94700	−	3.94700i	−0.353031	−	0.353031i
$126$		0			0
$127$	5.24504			0.465422			0.232711	−	0.972546i	$-0.425240\pi$
$127$	5.24504			0.465422			0.232711	+	0.972546i	$0.425240\pi$
$128$		0			0
$129$	−4.17390	−	10.2544i	−0.367491	−	0.902852i
$130$		0			0
$131$	−1.68026	+	6.27080i	−0.146805	+	0.547883i	0.852864	+	0.522134i	$0.174864\pi$
$131$	−1.68026	+	6.27080i	−0.146805	+	0.547883i	−0.999668	+	0.0257490i	$0.991803\pi$
$132$		0			0
$133$	−2.09178	−	7.80665i	−0.181381	−	0.676922i
$134$		0			0
$135$	14.6316	−	1.65256i	1.25929	−	0.142229i
$136$		0			0
$137$	−6.16622	−	3.56007i	−0.526816	−	0.304157i	0.212903	−	0.977073i	$-0.431708\pi$
$137$	−6.16622	−	3.56007i	−0.526816	−	0.304157i	−0.739719	+	0.672916i	$0.765042\pi$
$138$		0			0
$139$	−4.07133	−	1.09091i	−0.345326	−	0.0925298i	0.0819876	−	0.996633i	$-0.473873\pi$
$139$	−4.07133	−	1.09091i	−0.345326	−	0.0925298i	−0.427313	+	0.904104i	$0.640540\pi$
$140$		0			0
$141$	−6.17128	+	14.6437i	−0.519716	+	1.23322i
$142$		0			0
$143$	−4.63236			−0.387378
$144$		0			0
$145$	−10.4047			−0.864063
$146$		0			0
$147$	−5.49369	−	7.25133i	−0.453112	−	0.598080i
$148$		0			0
$149$	−8.40971	−	2.25338i	−0.688950	−	0.184604i	−0.102674	−	0.994715i	$-0.532740\pi$
$149$	−8.40971	−	2.25338i	−0.688950	−	0.184604i	−0.586276	+	0.810111i	$0.699407\pi$
$150$		0			0
$151$	−17.8103	−	10.2828i	−1.44938	−	0.836803i	−0.450940	−	0.892554i	$-0.648911\pi$
$151$	−17.8103	−	10.2828i	−1.44938	−	0.836803i	−0.998445	+	0.0557515i	$0.982245\pi$
$152$		0			0
$153$	−22.1164	+	5.63573i	−1.78801	+	0.455622i
$154$		0			0
$155$	−0.834834	−	3.11564i	−0.0670555	−	0.250255i
$156$		0			0
$157$	−2.38710	+	8.90879i	−0.190512	+	0.710999i	0.802872	+	0.596152i	$0.203304\pi$
$157$	−2.38710	+	8.90879i	−0.190512	+	0.710999i	−0.993383	+	0.114847i	$0.963362\pi$
$158$		0			0
$159$	11.6069	−	14.9355i	0.920487	−	1.18446i
$160$		0			0
$161$	5.28298			0.416357
$162$		0			0
$163$	10.4053	+	10.4053i	0.815004	+	0.815004i	0.985379	−	0.170375i	$-0.0544981\pi$
$163$	10.4053	+	10.4053i	0.815004	+	0.815004i	−0.170375	+	0.985379i	$0.554498\pi$
$164$		0			0
$165$	0.811644	+	6.47209i	0.0631864	+	0.503851i
$166$		0			0
$167$	5.95392	−	3.43750i	0.460728	−	0.266001i	−0.251622	−	0.967826i	$-0.580964\pi$
$167$	5.95392	−	3.43750i	0.460728	−	0.266001i	0.712350	+	0.701824i	$0.247631\pi$
$168$		0			0
$169$	0.735830	+	0.424832i	0.0566023	+	0.0326794i
$170$		0			0
$171$	−15.7697	−	9.36488i	−1.20594	−	0.716150i
$172$		0			0
$173$	−3.07494	+	0.823927i	−0.233783	+	0.0626420i	−0.373808	−	0.927506i	$-0.621948\pi$
$173$	−3.07494	+	0.823927i	−0.233783	+	0.0626420i	0.140025	+	0.990148i	$0.455282\pi$
$174$		0			0
$175$	2.00294	+	3.46919i	0.151408	+	0.262246i
$176$		0			0
$177$	8.54387	+	1.17827i	0.642197	+	0.0885642i
$178$		0			0
$179$	3.73648	+	3.73648i	0.279278	+	0.279278i	0.832821	−	0.553543i	$-0.186725\pi$
$179$	3.73648	+	3.73648i	0.279278	+	0.279278i	−0.553543	+	0.832821i	$0.686725\pi$
$180$		0			0
$181$	0.169132	−	0.169132i	0.0125715	−	0.0125715i	−0.700793	−	0.713365i	$-0.747170\pi$
$181$	0.169132	−	0.169132i	0.0125715	−	0.0125715i	0.713365	+	0.700793i	$0.247170\pi$
$182$		0			0
$183$	16.4918	−	6.71271i	1.21911	−	0.496218i
$184$		0			0
$185$	7.84414	−	4.52882i	0.576713	−	0.332965i
$186$		0			0
$187$	−2.61673	−	9.76578i	−0.191354	−	0.714145i
$188$		0			0
$189$	6.79274	+	1.02198i	0.494099	+	0.0743383i
$190$		0			0
$191$	−11.0451	+	19.1306i	−0.799194	+	1.38424i	0.120947	+	0.992659i	$0.461407\pi$
$191$	−11.0451	+	19.1306i	−0.799194	+	1.38424i	−0.920142	+	0.391586i	$0.871927\pi$
$192$		0			0
$193$	7.90683	+	13.6950i	0.569146	+	0.985790i	0.996651	+	0.0817767i	$0.0260594\pi$
$193$	7.90683	+	13.6950i	0.569146	+	0.985790i	−0.427505	+	0.904013i	$0.640607\pi$
$194$		0			0
$195$	−6.64423	+	15.7659i	−0.475803	+	1.12902i
$196$		0			0
$197$	1.19611	−	1.19611i	0.0852196	−	0.0852196i	−0.663212	−	0.748432i	$-0.730807\pi$
$197$	1.19611	−	1.19611i	0.0852196	−	0.0852196i	0.748432	+	0.663212i	$0.230807\pi$
$198$		0			0
$199$			6.39170i			0.453095i	0.974000	+	0.226548i	$0.0727439\pi$
$199$			6.39170i			0.453095i	−0.974000	+	0.226548i	$0.927256\pi$
$200$		0			0
$201$	3.41187	−	24.7402i	0.240655	−	1.74504i
$202$		0			0
$203$	−4.68849	−	1.25628i	−0.329068	−	0.0881734i
$204$		0			0
$205$	−4.49796	+	1.20523i	−0.314151	+	0.0841766i
$206$		0			0
$207$	8.58090	−	8.37256i	0.596414	−	0.581933i
$208$		0			0
$209$	4.06233	−	7.03617i	0.280997	−	0.486702i
$210$		0			0
$211$	−0.539586	+	2.01376i	−0.0371466	+	0.138633i	−0.982009	−	0.188835i	$-0.939529\pi$
$211$	−0.539586	+	2.01376i	−0.0371466	+	0.138633i	0.944862	+	0.327468i	$0.106195\pi$
$212$		0			0
$213$	1.69724	+	13.5339i	0.116293	+	0.927324i
$214$		0			0
$215$		−	18.1135i		−	1.23533i
$216$		0			0
$217$		−	1.50475i		−	0.102149i
$218$		0			0
$219$	−0.124405	−	0.992008i	−0.00840649	−	0.0670337i
$220$		0			0
$221$	6.86349	−	25.6149i	0.461688	−	1.72304i
$222$		0			0
$223$	−13.6496	+	23.6417i	−0.914042	+	1.58317i	−0.105745	+	0.994393i	$0.533723\pi$
$223$	−13.6496	+	23.6417i	−0.914042	+	1.58317i	−0.808297	+	0.588775i	$0.799611\pi$
$224$		0			0
$225$	8.75131	+	2.46055i	0.583421	+	0.164037i
$226$		0			0
$227$	−2.80787	+	0.752368i	−0.186365	+	0.0499364i	−0.350794	−	0.936452i	$-0.614088\pi$
$227$	−2.80787	+	0.752368i	−0.186365	+	0.0499364i	0.164429	+	0.986389i	$0.447422\pi$
$228$		0			0
$229$	−6.48583	−	1.73787i	−0.428596	−	0.114842i	0.0380710	−	0.999275i	$-0.487879\pi$
$229$	−6.48583	−	1.73787i	−0.428596	−	0.114842i	−0.466667	+	0.884433i	$0.654545\pi$
$230$		0			0
$231$	−0.415712	+	3.01441i	−0.0273518	+	0.198333i
$232$		0			0
$233$			11.8159i			0.774086i	0.922062	+	0.387043i	$0.126503\pi$
$233$			11.8159i			0.774086i	−0.922062	+	0.387043i	$0.873497\pi$
$234$		0			0
$235$	−18.3839	+	18.3839i	−1.19923	+	1.19923i
$236$		0			0
$237$	−0.964426	+	2.28846i	−0.0626462	+	0.148651i
$238$		0			0
$239$	1.75364	+	3.03739i	0.113433	+	0.196472i	0.917152	−	0.398537i	$-0.130482\pi$
$239$	1.75364	+	3.03739i	0.113433	+	0.196472i	−0.803719	+	0.595009i	$0.797148\pi$
$240$		0			0
$241$	−4.35635	+	7.54543i	−0.280617	+	0.486044i	−0.971537	−	0.236888i	$-0.923873\pi$
$241$	−4.35635	+	7.54543i	−0.280617	+	0.486044i	0.690920	+	0.722932i	$0.257206\pi$
$242$		0			0
$243$	12.6528	−	9.10531i	0.811678	−	0.584106i
$244$		0			0
$245$	−3.85226	−	14.3768i	−0.246112	−	0.918502i
$246$		0			0
$247$	18.4553	−	10.6552i	1.17428	−	0.677973i
$248$		0			0
$249$	−5.48765	+	2.23366i	−0.347766	+	0.141552i
$250$		0			0
$251$	9.70213	−	9.70213i	0.612393	−	0.612393i	−0.331176	−	0.943569i	$-0.607445\pi$
$251$	9.70213	−	9.70213i	0.612393	−	0.612393i	0.943569	+	0.331176i	$0.107445\pi$
$252$		0			0
$253$	3.75533	+	3.75533i	0.236096	+	0.236096i
$254$		0			0
$255$	−36.9903	−	5.10127i	−2.31642	−	0.319454i
$256$		0			0
$257$	−9.26857	−	16.0536i	−0.578158	−	1.00140i	−0.995691	−	0.0927366i	$-0.970439\pi$
$257$	−9.26857	−	16.0536i	−0.578158	−	1.00140i	0.417533	−	0.908662i	$-0.362895\pi$
$258$		0			0
$259$	4.08149	−	1.09363i	0.253611	−	0.0679550i
$260$		0			0
$261$	−9.60628	+	5.38990i	−0.594614	+	0.333626i
$262$		0			0
$263$	−3.42692	−	1.97853i	−0.211313	−	0.122002i	0.390608	−	0.920557i	$-0.372265\pi$
$263$	−3.42692	−	1.97853i	−0.211313	−	0.122002i	−0.601922	+	0.798555i	$0.705598\pi$
$264$		0			0
$265$	26.8008	−	15.4734i	1.64636	−	0.950525i
$266$		0			0
$267$	3.49393	+	27.8608i	0.213825	+	1.70505i
$268$		0			0
$269$	17.6742	+	17.6742i	1.07762	+	1.07762i	0.996723	+	0.0808951i	$0.0257779\pi$
$269$	17.6742	+	17.6742i	1.07762	+	1.07762i	0.0808951	+	0.996723i	$0.474222\pi$
$270$		0			0
$271$	26.9563			1.63748			0.818738	−	0.574167i	$-0.194674\pi$
$271$	26.9563			1.63748			0.818738	+	0.574167i	$0.194674\pi$
$272$		0			0
$273$	−4.89758	+	6.30209i	−0.296415	+	0.381420i
$274$		0			0
$275$	−1.04226	+	3.88979i	−0.0628509	+	0.234563i
$276$		0			0
$277$	2.47723	+	9.24514i	0.148842	+	0.555487i	0.999554	+	0.0298548i	$0.00950449\pi$
$277$	2.47723	+	9.24514i	0.148842	+	0.555487i	−0.850712	+	0.525632i	$0.823829\pi$
$278$		0			0
$279$	−2.38476	−	2.44410i	−0.142772	−	0.146324i
$280$		0			0
$281$	8.51476	+	4.91600i	0.507948	+	0.293264i	0.731990	−	0.681316i	$-0.238592\pi$
$281$	8.51476	+	4.91600i	0.507948	+	0.293264i	−0.224042	+	0.974580i	$0.571925\pi$
$282$		0			0
$283$	30.0988	+	8.06496i	1.78919	+	0.479412i	0.992208	−	0.124591i	$-0.0397617\pi$
$283$	30.0988	+	8.06496i	1.78919	+	0.479412i	0.796982	+	0.604003i	$0.206428\pi$
$284$		0			0
$285$	−18.1204	−	23.9179i	−1.07336	−	1.41677i
$286$		0			0
$287$	−2.17236			−0.128231
$288$		0			0
$289$	40.8774			2.40456
$290$		0			0
$291$	−0.873002	+	2.07152i	−0.0511763	+	0.121435i
$292$		0			0
$293$	30.6204	+	8.20472i	1.78886	+	0.479325i	0.992152	−	0.125035i	$-0.0399044\pi$
$293$	30.6204	+	8.20472i	1.78886	+	0.479325i	0.796711	+	0.604360i	$0.206571\pi$
$294$		0			0
$295$	12.2202	+	7.05535i	0.711489	+	0.410778i
$296$		0			0
$297$	4.10207	+	5.55499i	0.238026	+	0.322333i
$298$		0			0
$299$	3.60533	+	13.4553i	0.208502	+	0.778139i
$300$		0			0
$301$	2.18706	−	8.16220i	0.126060	−	0.470462i
$302$		0			0
$303$	6.58374	+	16.1749i	0.378226	+	0.929225i
$304$		0			0
$305$	29.1313			1.66805
$306$		0			0
$307$	−17.2513	−	17.2513i	−0.984581	−	0.984581i	0.0153018	−	0.999883i	$-0.495129\pi$
$307$	−17.2513	−	17.2513i	−0.984581	−	0.984581i	−0.999883	+	0.0153018i	$0.995129\pi$
$308$		0			0
$309$	−12.8306	+	9.72059i	−0.729906	+	0.552985i
$310$		0			0
$311$	8.53625	−	4.92841i	0.484046	−	0.279464i	−0.238055	−	0.971252i	$-0.576510\pi$
$311$	8.53625	−	4.92841i	0.484046	−	0.279464i	0.722101	+	0.691787i	$0.243176\pi$
$312$		0			0
$313$	−8.45774	−	4.88308i	−0.478060	−	0.276008i	0.241548	−	0.970389i	$-0.422345\pi$
$313$	−8.45774	−	4.88308i	−0.478060	−	0.276008i	−0.719608	+	0.694381i	$0.755678\pi$
$314$		0			0
$315$	9.66305	+	5.73843i	0.544451	+	0.323324i
$316$		0			0
$317$	−12.8098	+	3.43237i	−0.719469	+	0.192781i	−0.599935	−	0.800049i	$-0.704807\pi$
$317$	−12.8098	+	3.43237i	−0.719469	+	0.192781i	−0.119534	+	0.992830i	$0.538140\pi$
$318$		0			0
$319$	−2.43974	−	4.22576i	−0.136599	−	0.236597i
$320$		0			0
$321$	−2.84834	+	3.66519i	−0.158979	+	0.204571i
$322$		0			0
$323$	32.8879	+	32.8879i	1.82993	+	1.82993i
$324$		0			0
$325$	−7.46883	+	7.46883i	−0.414296	+	0.414296i
$326$		0			0
$327$	−16.6966	−	12.9756i	−0.923327	−	0.717550i
$328$		0			0
$329$	−10.5037	+	6.06432i	−0.579089	+	0.334337i
$330$		0			0
$331$	−0.274151	−	1.02314i	−0.0150687	−	0.0562371i	0.957982	−	0.286828i	$-0.0926008\pi$
$331$	−0.274151	−	1.02314i	−0.0150687	−	0.0562371i	−0.973051	+	0.230591i	$0.925934\pi$
$332$		0			0
$333$	4.89617	−	8.24476i	0.268308	−	0.451810i
$334$		0			0
$335$	20.4299	−	35.3857i	1.11621	−	1.93332i
$336$		0			0
$337$	−2.50387	−	4.33683i	−0.136395	−	0.236242i	0.789735	−	0.613448i	$-0.210218\pi$
$337$	−2.50387	−	4.33683i	−0.136395	−	0.236242i	−0.926129	+	0.377206i	$0.876885\pi$
$338$		0			0
$339$	−3.55998	−	4.69895i	−0.193351	−	0.255212i
$340$		0			0
$341$	1.06963	−	1.06963i	0.0579238	−	0.0579238i
$342$		0			0
$343$		−	16.1974i		−	0.874575i
$344$		0			0
$345$	18.1673	−	7.39470i	0.978094	−	0.398117i
$346$		0			0
$347$	−5.88711	−	1.57745i	−0.316036	−	0.0846817i	0.0973140	−	0.995254i	$-0.468975\pi$
$347$	−5.88711	−	1.57745i	−0.316036	−	0.0846817i	−0.413350	+	0.910572i	$0.635642\pi$
$348$		0			0
$349$	−5.42227	+	1.45289i	−0.290247	+	0.0777715i	−0.401005	−	0.916076i	$-0.631339\pi$
$349$	−5.42227	+	1.45289i	−0.290247	+	0.0777715i	0.110758	+	0.993847i	$0.464672\pi$
$350$		0			0
$351$	2.03276	+	17.9980i	0.108501	+	0.960661i
$352$		0			0
$353$	−5.06146	+	8.76671i	−0.269395	+	0.466605i	−0.968706	−	0.248212i	$-0.920157\pi$
$353$	−5.06146	+	8.76671i	−0.269395	+	0.466605i	0.699311	+	0.714817i	$0.253490\pi$
$354$		0			0
$355$	−5.77576	+	21.5554i	−0.306546	+	1.14404i
$356$		0			0
$357$	−16.0524	−	6.76496i	−0.849582	−	0.358040i
$358$		0			0
$359$		−	5.28081i		−	0.278710i	−0.990242	−	0.139355i	$-0.955497\pi$
$359$		−	5.28081i		−	0.278710i	0.990242	−	0.139355i	$-0.0445030\pi$
$360$		0			0
$361$			18.3761i			0.967163i
$362$		0			0
$363$	12.7481	−	9.65813i	0.669104	−	0.506920i
$364$		0			0
$365$	0.423353	−	1.57998i	0.0221593	−	0.0826997i
$366$		0			0
$367$	−5.01941	+	8.69388i	−0.262011	+	0.453817i	−0.966776	−	0.255624i	$-0.917719\pi$
$367$	−5.01941	+	8.69388i	−0.262011	+	0.453817i	0.704765	+	0.709441i	$0.251052\pi$
$368$		0			0
$369$	−3.52847	+	3.44280i	−0.183685	+	0.179225i
$370$		0			0
$371$	13.9451	−	3.73657i	0.723992	−	0.193993i
$372$		0			0
$373$	25.1865	+	6.74869i	1.30411	+	0.349434i	0.843001	−	0.537912i	$-0.180787\pi$
$373$	25.1865	+	6.74869i	1.30411	+	0.349434i	0.461105	+	0.887346i	$0.347453\pi$
$374$		0			0
$375$	−7.63395	−	5.93261i	−0.394215	−	0.306359i
$376$		0			0
$377$		−	12.7985i		−	0.659157i
$378$		0			0
$379$	11.3259	−	11.3259i	0.581771	−	0.581771i	−0.353619	−	0.935390i	$-0.615049\pi$
$379$	11.3259	−	11.3259i	0.581771	−	0.581771i	0.935390	+	0.353619i	$0.115049\pi$
$380$		0			0
$381$	9.01407	−	1.13043i	0.461805	−	0.0579135i
$382$		0			0
$383$	−2.50076	−	4.33145i	−0.127783	−	0.221327i	0.795034	−	0.606564i	$-0.207453\pi$
$383$	−2.50076	−	4.33145i	−0.127783	−	0.221327i	−0.922817	+	0.385238i	$0.874119\pi$
$384$		0			0
$385$	−2.48924	+	4.31148i	−0.126863	+	0.219733i
$386$		0			0
$387$	−9.38328	−	16.7236i	−0.476979	−	0.850107i
$388$		0			0
$389$	−3.45749	−	12.9035i	−0.175302	−	0.654235i	−0.996500	−	0.0835921i	$-0.973361\pi$
$389$	−3.45749	−	12.9035i	−0.175302	−	0.654235i	0.821198	−	0.570643i	$-0.193306\pi$
$390$		0			0
$391$	−26.3294	+	15.2013i	−1.33153	+	0.768761i
$392$		0			0
$393$	−1.53617	+	11.1391i	−0.0774895	+	0.561892i
$394$		0			0
$395$	−2.87297	+	2.87297i	−0.144555	+	0.144555i
$396$		0			0
$397$	−18.7165	−	18.7165i	−0.939356	−	0.939356i	0.0589078	−	0.998263i	$-0.481238\pi$
$397$	−18.7165	−	18.7165i	−0.939356	−	0.939356i	−0.998263	+	0.0589078i	$0.981238\pi$
$398$		0			0
$399$	−5.27743	−	12.9656i	−0.264202	−	0.649092i
$400$		0			0
$401$	6.66124	+	11.5376i	0.332647	+	0.576161i	0.983030	−	0.183445i	$-0.0587250\pi$
$401$	6.66124	+	11.5376i	0.332647	+	0.576161i	−0.650383	+	0.759606i	$0.725392\pi$
$402$		0			0
$403$	3.83247	−	1.02691i	0.190909	−	0.0511538i
$404$		0			0
$405$	24.7896	−	5.99352i	1.23181	−	0.297820i
$406$		0			0
$407$	3.67866	+	2.12388i	0.182345	+	0.105277i
$408$		0			0
$409$	−10.6037	+	6.12206i	−0.524320	+	0.302717i	−0.738701	−	0.674034i	$-0.764560\pi$
$409$	−10.6037	+	6.12206i	−0.524320	+	0.302717i	0.214380	+	0.976750i	$0.431227\pi$
$410$		0			0
$411$	−11.3645	−	4.78934i	−0.560568	−	0.236241i
$412$		0			0
$413$	4.65472	+	4.65472i	0.229044	+	0.229044i
$414$		0			0
$415$	−9.69344			−0.475832
$416$		0			0
$417$	−7.23206	−	0.997361i	−0.354156	−	0.0488410i
$418$		0			0
$419$	8.58573	−	32.0424i	0.419440	−	1.56537i	−0.356332	−	0.934360i	$-0.615973\pi$
$419$	8.58573	−	32.0424i	0.419440	−	1.56537i	0.775772	−	0.631013i	$-0.217361\pi$
$420$		0			0
$421$	6.61930	+	24.7035i	0.322605	+	1.20398i	0.916698	+	0.399581i	$0.130844\pi$
$421$	6.61930	+	24.7035i	0.322605	+	1.20398i	−0.594093	+	0.804396i	$0.702489\pi$
$422$		0			0
$423$	−7.44985	+	26.4965i	−0.362224	+	1.28830i
$424$		0			0
$425$	−19.9645	−	11.5265i	−0.968421	−	0.559118i
$426$		0			0
$427$	13.1269	+	3.51736i	0.635258	+	0.170217i
$428$		0			0
$429$	−7.96113	+	0.998381i	−0.384367	+	0.0482023i
$430$		0			0
$431$	10.3041			0.496332			0.248166	−	0.968717i	$-0.420172\pi$
$431$	10.3041			0.496332			0.248166	+	0.968717i	$0.420172\pi$
$432$		0			0
$433$	−11.7692			−0.565591			−0.282795	−	0.959180i	$-0.591262\pi$
$433$	−11.7692			−0.565591			−0.282795	+	0.959180i	$0.591262\pi$
$434$		0			0
$435$	−17.8814	+	2.24245i	−0.857347	+	0.107517i
$436$		0			0
$437$	−23.5991	−	6.32337i	−1.12890	−	0.302488i
$438$		0			0
$439$	23.9893	+	13.8502i	1.14494	+	0.661034i	0.947650	−	0.319310i	$-0.103451\pi$
$439$	23.9893	+	13.8502i	1.14494	+	0.661034i	0.197294	+	0.980344i	$0.436785\pi$
$440$		0			0
$441$	−11.0042	−	11.2780i	−0.524011	−	0.537050i
$442$		0			0
$443$	−6.50677	−	24.2836i	−0.309146	−	1.15375i	−0.929317	−	0.369282i	$-0.879604\pi$
$443$	−6.50677	−	24.2836i	−0.309146	−	1.15375i	0.620172	−	0.784466i	$-0.287063\pi$
$444$		0			0
$445$	−11.8900	+	44.3739i	−0.563638	+	2.10353i
$446$		0			0
$447$	−14.9385	−	2.06014i	−0.706567	−	0.0974413i
$448$		0			0
$449$	−20.0988			−0.948522			−0.474261	−	0.880384i	$-0.657285\pi$
$449$	−20.0988			−0.948522			−0.474261	+	0.880384i	$0.657285\pi$
$450$		0			0
$451$	−1.54419	−	1.54419i	−0.0727133	−	0.0727133i
$452$		0			0
$453$	−32.8248	−	13.8334i	−1.54225	−	0.649949i
$454$		0			0
$455$	−11.3087	+	6.52907i	−0.530159	+	0.306088i
$456$		0			0
$457$	−20.8270	−	12.0245i	−0.974244	−	0.562480i	−0.0737167	−	0.997279i	$-0.523486\pi$
$457$	−20.8270	−	12.0245i	−0.974244	−	0.562480i	−0.900527	+	0.434799i	$0.856819\pi$
$458$		0			0
$459$	−36.7944	+	14.4521i	−1.71742	+	0.674566i
$460$		0			0
$461$	−3.90967	+	1.04759i	−0.182092	+	0.0487913i	−0.348713	−	0.937230i	$-0.613381\pi$
$461$	−3.90967	+	1.04759i	−0.182092	+	0.0487913i	0.166621	+	0.986021i	$0.446714\pi$
$462$		0			0
$463$	−5.16489	−	8.94585i	−0.240033	−	0.415749i	0.720691	−	0.693257i	$-0.243825\pi$
$463$	−5.16489	−	8.94585i	−0.240033	−	0.415749i	−0.960723	+	0.277508i	$0.910492\pi$
$464$		0			0
$465$	−2.10623	−	5.17459i	−0.0976741	−	0.239966i
$466$		0			0
$467$	−11.8966	−	11.8966i	−0.550509	−	0.550509i	0.376079	−	0.926588i	$-0.377272\pi$
$467$	−11.8966	−	11.8966i	−0.550509	−	0.550509i	−0.926588	+	0.376079i	$0.877272\pi$
$468$		0			0
$469$	13.4785	−	13.4785i	0.622380	−	0.622380i
$470$		0			0
$471$	−2.18240	+	15.8250i	−0.100560	+	0.729179i
$472$		0			0
$473$	7.35663	−	4.24735i	0.338258	−	0.195293i
$474$		0			0
$475$	−4.79476	−	17.8943i	−0.219999	−	0.821046i
$476$		0			0
$477$	16.7286	−	28.1695i	0.765948	−	1.28980i
$478$		0			0
$479$	7.47878	−	12.9536i	0.341714	−	0.591866i	−0.643037	−	0.765835i	$-0.722326\pi$
$479$	7.47878	−	12.9536i	0.341714	−	0.591866i	0.984751	+	0.173969i	$0.0556593\pi$
$480$		0			0
$481$	5.57077	+	9.64886i	0.254005	+	0.439950i
$482$		0			0
$483$	9.07927	−	1.13860i	0.413121	−	0.0518082i
$484$		0			0
$485$	−2.60062	+	2.60062i	−0.118088	+	0.118088i
$486$		0			0
$487$		−	27.0362i		−	1.22513i	−0.790420	−	0.612565i	$-0.790138\pi$
$487$		−	27.0362i		−	1.22513i	0.790420	−	0.612565i	$-0.209862\pi$
$488$		0			0
$489$	20.1250	+	15.6398i	0.910082	+	0.707257i
$490$		0			0
$491$	−5.41853	−	1.45189i	−0.244535	−	0.0655229i	0.134470	−	0.990918i	$-0.457067\pi$
$491$	−5.41853	−	1.45189i	−0.244535	−	0.0655229i	−0.379005	+	0.925395i	$0.623734\pi$
$492$		0			0
$493$	26.9814	−	7.22964i	1.21518	−	0.325607i
$494$		0			0
$495$	2.78977	+	10.9479i	0.125391	+	0.492073i
$496$		0			0
$497$	−5.20527	+	9.01579i	−0.233488	+	0.404413i
$498$		0			0
$499$	−5.68146	+	21.2035i	−0.254337	+	0.949198i	0.714121	+	0.700022i	$0.246826\pi$
$499$	−5.68146	+	21.2035i	−0.254337	+	0.949198i	−0.968458	+	0.249176i	$0.919840\pi$
$500$		0			0
$501$	9.49148	−	7.19085i	0.424048	−	0.321264i
$502$		0			0
$503$			23.1955i			1.03423i	0.855915	+	0.517117i	$0.172995\pi$
$503$			23.1955i			1.03423i	−0.855915	+	0.517117i	$0.827005\pi$
$504$		0			0
$505$			28.5716i			1.27142i
$506$		0			0
$507$	1.35615	+	0.571523i	0.0602288	+	0.0253822i
$508$		0			0
$509$	−3.37049	+	12.5788i	−0.149394	+	0.557547i	0.850126	+	0.526579i	$0.176526\pi$
$509$	−3.37049	+	12.5788i	−0.149394	+	0.557547i	−0.999520	+	0.0309681i	$0.990141\pi$
$510$		0			0
$511$	0.381537	−	0.660842i	0.0168782	−	0.0292339i
$512$		0			0
$513$	−29.1200	−	12.6957i	−1.28568	−	0.560527i
$514$		0			0
$515$	−25.4385	+	6.81623i	−1.12095	+	0.300359i
$516$		0			0
$517$	−11.7772	−	3.15568i	−0.517959	−	0.138787i
$518$		0			0
$519$	−5.10698	+	2.07871i	−0.224171	+	0.0912453i
$520$		0			0
$521$		−	21.4547i		−	0.939949i	−0.882680	−	0.469974i	$-0.844263\pi$
$521$		−	21.4547i		−	0.939949i	0.882680	−	0.469974i	$-0.155737\pi$
$522$		0			0
$523$	−2.07495	+	2.07495i	−0.0907314	+	0.0907314i	−0.751016	−	0.660284i	$-0.770436\pi$
$523$	−2.07495	+	2.07495i	−0.0907314	+	0.0907314i	0.660284	+	0.751016i	$0.270436\pi$
$524$		0			0
$525$	4.18992	+	5.53043i	0.182863	+	0.241368i
$526$		0			0
$527$	4.32977	+	7.49939i	0.188608	+	0.326678i
$528$		0			0
$529$	−3.51490	+	6.08799i	−0.152822	+	0.264695i
$530$		0			0
$531$	14.9374	+	0.183562i	0.648226	+	0.00796593i
$532$		0			0
$533$	−1.48251	−	5.53282i	−0.0642148	−	0.239653i
$534$		0			0
$535$	−6.57693	+	3.79719i	−0.284346	+	0.164167i
$536$		0			0
$537$	7.22677	+	5.61618i	0.311858	+	0.242356i
$538$		0			0
$539$	4.93571	−	4.93571i	0.212596	−	0.212596i
$540$		0			0
$541$	22.7947	+	22.7947i	0.980022	+	0.980022i	0.999804	−	0.0197819i	$-0.00629719\pi$
$541$	22.7947	+	22.7947i	0.980022	+	0.980022i	−0.0197819	+	0.999804i	$0.506297\pi$
$542$		0			0
$543$	0.254217	−	0.327121i	0.0109095	−	0.0140381i
$544$		0			0
$545$	−17.2980	−	29.9610i	−0.740965	−	1.28339i
$546$		0			0
$547$	−13.3804	+	3.58528i	−0.572106	+	0.153295i	−0.533262	−	0.845950i	$-0.679034\pi$
$547$	−13.3804	+	3.58528i	−0.572106	+	0.153295i	−0.0388438	+	0.999245i	$0.512367\pi$
$548$		0			0
$549$	26.8959	−	15.0908i	1.14789	−	0.644058i
$550$		0			0
$551$	19.4399	+	11.2236i	0.828166	+	0.478142i
$552$		0			0
$553$	−1.64148	+	0.947711i	−0.0698030	+	0.0403008i
$554$		0			0
$555$	12.5048	−	9.47377i	0.530799	−	0.402139i
$556$		0			0
$557$	−8.62660	−	8.62660i	−0.365521	−	0.365521i	0.500320	−	0.865841i	$-0.333216\pi$
$557$	−8.62660	−	8.62660i	−0.365521	−	0.365521i	−0.865841	+	0.500320i	$0.833216\pi$
$558$		0			0
$559$	22.2810			0.942384
$560$		0			0
$561$	−6.60184	−	16.2194i	−0.278730	−	0.684784i
$562$		0			0
$563$	5.46409	−	20.3923i	0.230284	−	0.859432i	−0.749934	−	0.661513i	$-0.769915\pi$
$563$	5.46409	−	20.3923i	0.230284	−	0.859432i	0.980218	−	0.197920i	$-0.0634185\pi$
$564$		0			0
$565$	−2.49631	−	9.31636i	−0.105021	−	0.391942i
$566$		0			0
$567$	11.8942	+	0.292376i	0.499509	+	0.0122786i
$568$		0			0
$569$	21.4776	+	12.4001i	0.900389	+	0.519840i	0.877326	−	0.479894i	$-0.159325\pi$
$569$	21.4776	+	12.4001i	0.900389	+	0.519840i	0.0230625	+	0.999734i	$0.492658\pi$
$570$		0			0
$571$	−17.7063	−	4.74438i	−0.740985	−	0.198546i	−0.131469	−	0.991320i	$-0.541969\pi$
$571$	−17.7063	−	4.74438i	−0.740985	−	0.198546i	−0.609516	+	0.792774i	$0.708636\pi$
$572$		0			0
$573$	−14.8589	+	35.2582i	−0.620738	+	1.47293i
$574$		0			0
$575$	12.1096			0.505004
$576$		0			0
$577$	−23.4462			−0.976078			−0.488039	−	0.872822i	$-0.662288\pi$
$577$	−23.4462			−0.976078			−0.488039	+	0.872822i	$0.662288\pi$
$578$		0			0
$579$	16.5402	+	21.8320i	0.687387	+	0.907308i
$580$		0			0
$581$	−4.36800	−	1.17040i	−0.181215	−	0.0485564i
$582$		0			0
$583$	12.5688	+	7.25657i	0.520545	+	0.300537i
$584$		0			0
$585$	−8.02079	+	28.5271i	−0.331619	+	1.17945i
$586$		0			0
$587$	−4.33159	−	16.1657i	−0.178784	−	0.667230i	−0.995876	−	0.0907235i	$-0.971082\pi$
$587$	−4.33159	−	16.1657i	−0.178784	−	0.667230i	0.817092	−	0.576507i	$-0.195585\pi$
$588$		0			0
$589$	−1.80108	+	6.72173i	−0.0742123	+	0.276964i
$590$		0			0
$591$	1.79784	−	2.31342i	0.0739532	−	0.0951613i
$592$		0			0
$593$	6.18675			0.254059			0.127030	−	0.991899i	$-0.459456\pi$
$593$	6.18675			0.254059			0.127030	+	0.991899i	$0.459456\pi$
$594$		0			0
$595$	−20.1524	−	20.1524i	−0.826168	−	0.826168i
$596$		0			0
$597$	1.37756	+	10.9847i	0.0563797	+	0.449574i
$598$		0			0
$599$	−7.98730	+	4.61147i	−0.326352	+	0.188420i	−0.654220	−	0.756304i	$-0.727003\pi$
$599$	−7.98730	+	4.61147i	−0.326352	+	0.188420i	0.327868	+	0.944723i	$0.393670\pi$
$600$		0			0
$601$	−15.0097	−	8.66586i	−0.612259	−	0.353488i	0.161590	−	0.986858i	$-0.448338\pi$
$601$	−15.0097	−	8.66586i	−0.612259	−	0.353488i	−0.773849	+	0.633370i	$0.781671\pi$
$602$		0			0
$603$	0.531535	−	43.2535i	0.0216458	−	1.76142i
$604$		0			0
$605$	25.2751	−	6.77243i	1.02758	−	0.275339i
$606$		0			0
$607$	−11.8418	−	20.5106i	−0.480643	−	0.832498i	0.519110	−	0.854707i	$-0.326263\pi$
$607$	−11.8418	−	20.5106i	−0.480643	−	0.832498i	−0.999753	+	0.0222090i	$0.992930\pi$
$608$		0			0
$609$	−8.32835	−	1.14855i	−0.337482	−	0.0465415i
$610$		0			0
$611$	−22.6135	−	22.6135i	−0.914844	−	0.914844i
$612$		0			0
$613$	15.4110	−	15.4110i	0.622445	−	0.622445i	−0.323711	−	0.946156i	$-0.604930\pi$
$613$	15.4110	−	15.4110i	0.622445	−	0.622445i	0.946156	+	0.323711i	$0.104930\pi$
$614$		0			0
$615$	−7.47040	+	3.04070i	−0.301236	+	0.122613i
$616$		0			0
$617$	−11.9979	+	6.92700i	−0.483018	+	0.278870i	−0.721673	−	0.692234i	$-0.756627\pi$
$617$	−11.9979	+	6.92700i	−0.483018	+	0.278870i	0.238655	+	0.971104i	$0.423293\pi$
$618$		0			0
$619$	10.3518	+	38.6333i	0.416072	+	1.55280i	0.782678	+	0.622427i	$0.213853\pi$
$619$	10.3518	+	38.6333i	0.416072	+	1.55280i	−0.366606	+	0.930376i	$0.619480\pi$
$620$		0			0
$621$	12.9426	−	16.2384i	0.519367	−	0.651624i
$622$		0			0
$623$	−10.7156	+	18.5599i	−0.429310	+	0.743586i
$624$		0			0
$625$	−15.4844	−	26.8198i	−0.619377	−	1.07279i
$626$		0			0
$627$	5.46503	−	12.9678i	0.218252	−	0.517884i
$628$		0			0
$629$	−17.1945	+	17.1945i	−0.685591	+	0.685591i
$630$		0			0
$631$			16.7956i			0.668624i	0.942462	+	0.334312i	$0.108504\pi$
$631$			16.7956i			0.668624i	−0.942462	+	0.334312i	$0.891496\pi$
$632$		0			0
$633$	−0.493315	+	3.57712i	−0.0196075	+	0.142178i
$634$		0			0
$635$	14.3567	+	3.84688i	0.569730	+	0.152659i
$636$		0			0
$637$	17.6845	−	4.73856i	0.700687	−	0.187749i
$638$		0			0
$639$	5.83371	+	22.8933i	0.230778	+	0.905647i
$640$		0			0
$641$	20.0246	−	34.6837i	0.790925	−	1.36992i	−0.134470	−	0.990918i	$-0.542933\pi$
$641$	20.0246	−	34.6837i	0.790925	−	1.36992i	0.925395	−	0.379005i	$-0.123734\pi$
$642$		0			0
$643$	0.289008	−	1.07859i	0.0113974	−	0.0425356i	−0.959993	−	0.280024i	$-0.909658\pi$
$643$	0.289008	−	1.07859i	0.0113974	−	0.0425356i	0.971390	+	0.237489i	$0.0763242\pi$
$644$		0			0
$645$	−3.90388	−	31.1297i	−0.153715	−	1.22573i
$646$		0			0
$647$			31.9272i			1.25519i	0.778541	+	0.627594i	$0.215960\pi$
$647$			31.9272i			1.25519i	−0.778541	+	0.627594i	$0.784040\pi$
$648$		0			0
$649$			6.61750i			0.259759i
$650$		0			0
$651$	−0.324308	−	2.58605i	−0.0127106	−	0.101355i
$652$		0			0
$653$	−3.36682	+	12.5651i	−0.131754	+	0.491712i	−0.999990	−	0.00443888i	$-0.998587\pi$
$653$	−3.36682	+	12.5651i	−0.131754	+	0.491712i	0.868236	+	0.496151i	$0.165254\pi$
$654$		0			0
$655$	−9.19841	+	15.9321i	−0.359412	+	0.622519i
$656$		0			0
$657$	−0.427601	−	1.67804i	−0.0166823	−	0.0654667i
$658$		0			0
$659$	−15.4883	+	4.15007i	−0.603337	+	0.161664i	−0.547541	−	0.836779i	$-0.684436\pi$
$659$	−15.4883	+	4.15007i	−0.603337	+	0.161664i	−0.0557954	+	0.998442i	$0.517769\pi$
$660$		0			0
$661$	21.9923	+	5.89283i	0.855403	+	0.229204i	0.659765	−	0.751472i	$-0.270656\pi$
$661$	21.9923	+	5.89283i	0.855403	+	0.229204i	0.195637	+	0.980676i	$0.437322\pi$
$662$		0			0
$663$	6.27493	−	45.5007i	0.243698	−	1.76710i
$664$		0			0
$665$		−	22.9026i		−	0.888124i
$666$		0			0
$667$	−10.3754	+	10.3754i	−0.401738	+	0.401738i
$668$		0			0
$669$	−18.3627	+	43.5722i	−0.709941	+	1.68460i
$670$		0			0
$671$	6.83085	+	11.8314i	0.263702	+	0.456745i
$672$		0			0
$673$	16.3212	−	28.2692i	0.629136	−	1.08970i	−0.358589	−	0.933496i	$-0.616742\pi$
$673$	16.3212	−	28.2692i	0.629136	−	1.08970i	0.987725	−	0.156201i	$-0.0499246\pi$
$674$		0			0
$675$	15.5702	+	2.34257i	0.599298	+	0.0901656i
$676$		0			0
$677$	3.84993	+	14.3681i	0.147965	+	0.552212i	0.999606	+	0.0280861i	$0.00894127\pi$
$677$	3.84993	+	14.3681i	0.147965	+	0.552212i	−0.851641	+	0.524126i	$0.824392\pi$
$678$		0			0
$679$	−1.48588	+	0.857871i	−0.0570227	+	0.0329221i
$680$		0			0
$681$	−4.66343	+	1.89817i	−0.178703	+	0.0727381i
$682$		0			0
$683$	−21.4912	+	21.4912i	−0.822338	+	0.822338i	−0.986443	−	0.164105i	$-0.947526\pi$
$683$	−21.4912	+	21.4912i	−0.822338	+	0.822338i	0.164105	+	0.986443i	$0.447526\pi$
$684$		0			0
$685$	−14.2671	−	14.2671i	−0.545120	−	0.545120i
$686$		0			0
$687$	−11.5210	−	1.58885i	−0.439555	−	0.0606183i
$688$		0			0
$689$	19.0334	+	32.9669i	0.725116	+	1.25594i
$690$		0			0
$691$	8.83775	−	2.36807i	0.336204	−	0.0900855i	−0.0867676	−	0.996229i	$-0.527654\pi$
$691$	8.83775	−	2.36807i	0.336204	−	0.0900855i	0.422971	+	0.906143i	$0.360987\pi$
$692$		0			0
$693$	−0.0647636	+	5.27012i	−0.00246017	+	0.200195i
$694$		0			0
$695$	−10.3440	−	5.97209i	−0.392369	−	0.226534i
$696$		0			0
$697$	10.8266	−	6.25077i	0.410088	−	0.236765i
$698$		0			0
$699$	2.54660	+	20.3067i	0.0963212	+	0.768070i
$700$		0			0
$701$	−4.05144	−	4.05144i	−0.153021	−	0.153021i	0.626445	−	0.779466i	$-0.284509\pi$
$701$	−4.05144	−	4.05144i	−0.153021	−	0.153021i	−0.779466	+	0.626445i	$0.784509\pi$
$702$		0			0
$703$	−19.5411			−0.737005
$704$		0			0
$705$	−27.6322	+	35.5565i	−1.04069	+	1.33913i
$706$		0			0
$707$	−3.44978	+	12.8747i	−0.129742	+	0.484204i
$708$		0			0
$709$	−1.00775	−	3.76098i	−0.0378469	−	0.141247i	0.944417	−	0.328750i	$-0.106627\pi$
$709$	−1.00775	−	3.76098i	−0.0378469	−	0.141247i	−0.982264	+	0.187503i	$0.939961\pi$
$710$		0			0
$711$	−1.16424	+	4.14078i	−0.0436623	+	0.155291i
$712$		0			0
$713$	−3.93936	−	2.27439i	−0.147530	−	0.0851767i
$714$		0			0
$715$	−12.6797	−	3.39752i	−0.474195	−	0.127060i
$716$		0			0
$717$	3.66841	+	4.84208i	0.136999	+	0.180831i
$718$		0			0
$719$	37.0063			1.38010			0.690050	−	0.723761i	$-0.257588\pi$
$719$	37.0063			1.38010			0.690050	+	0.723761i	$0.257588\pi$
$720$		0			0
$721$	−12.2859			−0.457552
$722$		0			0
$723$	−5.86057	+	13.9064i	−0.217957	+	0.517184i
$724$		0			0
$725$	−10.7469	−	2.87962i	−0.399129	−	0.106946i
$726$		0			0
$727$	−28.4066	−	16.4006i	−1.05354	−	0.608264i	−0.129905	−	0.991526i	$-0.541467\pi$
$727$	−28.4066	−	16.4006i	−1.05354	−	0.608264i	−0.923640	+	0.383262i	$0.874801\pi$
$728$		0			0
$729$	19.7826	−	18.3753i	0.732688	−	0.680565i
$730$		0			0
$731$	12.5861	+	46.9719i	0.465513	+	1.73732i
$732$		0			0
$733$	10.9743	−	40.9566i	0.405345	−	1.51277i	−0.398075	−	0.917353i	$-0.630322\pi$
$733$	10.9743	−	40.9566i	0.405345	−	1.51277i	0.803419	−	0.595413i	$-0.203012\pi$
$734$		0			0
$735$	−9.71899	−	23.8776i	−0.358490	−	0.880740i
$736$		0			0
$737$	19.1620			0.705842
$738$		0			0
$739$	15.3761	+	15.3761i	0.565620	+	0.565620i	0.930898	−	0.365278i	$-0.119026\pi$
$739$	15.3761	+	15.3761i	0.565620	+	0.565620i	−0.365278	+	0.930898i	$0.619026\pi$
$740$		0			0
$741$	29.4207	−	22.2894i	1.08080	−	0.818823i
$742$		0			0
$743$	−40.4824	+	23.3725i	−1.48516	+	0.857456i	−0.999857	−	0.0168926i	$-0.994623\pi$
$743$	−40.4824	+	23.3725i	−1.48516	+	0.857456i	−0.485299	+	0.874348i	$0.661289\pi$
$744$		0			0
$745$	−21.3664	−	12.3359i	−0.782805	−	0.451952i
$746$		0			0
$747$	−8.94961	+	5.02145i	−0.327449	+	0.183725i
$748$		0			0
$749$	−3.42213	+	0.916958i	−0.125042	+	0.0335049i
$750$		0			0
$751$	−25.7074	−	44.5265i	−0.938077	−	1.62480i	−0.769054	−	0.639184i	$-0.779272\pi$
$751$	−25.7074	−	44.5265i	−0.938077	−	1.62480i	−0.169023	−	0.985612i	$-0.554061\pi$
$752$		0			0
$753$	14.5829	−	18.7650i	0.531432	−	0.683835i
$754$		0			0
$755$	−41.2088	−	41.2088i	−1.49974	−	1.49974i
$756$		0			0
$757$	25.4143	−	25.4143i	0.923698	−	0.923698i	−0.0735910	−	0.997289i	$-0.523446\pi$
$757$	25.4143	−	25.4143i	0.923698	−	0.923698i	0.997289	+	0.0735910i	$0.0234459\pi$
$758$		0			0
$759$	7.26324	+	5.64452i	0.263639	+	0.204883i
$760$		0			0
$761$	20.2336	−	11.6819i	0.733467	−	0.423467i	−0.0862220	−	0.996276i	$-0.527479\pi$
$761$	20.2336	−	11.6819i	0.733467	−	0.423467i	0.819689	+	0.572808i	$0.194146\pi$
$762$		0			0
$763$	−4.17717	−	15.5894i	−0.151224	−	0.564375i
$764$		0			0
$765$	−64.6706	−	0.794725i	−2.33817	−	0.0287334i
$766$		0			0
$767$	−8.67859	+	15.0318i	−0.313366	+	0.542765i
$768$		0			0
$769$	−12.7645	−	22.1087i	−0.460299	−	0.797261i	0.538677	−	0.842513i	$-0.318924\pi$
$769$	−12.7645	−	22.1087i	−0.460299	−	0.797261i	−0.998976	+	0.0452513i	$0.985591\pi$
$770$		0			0
$771$	−19.3888	−	25.5920i	−0.698270	−	0.921674i
$772$		0			0
$773$	−19.2256	+	19.2256i	−0.691496	+	0.691496i	−0.962561	−	0.271065i	$-0.912624\pi$
$773$	−19.2256	+	19.2256i	−0.691496	+	0.691496i	0.271065	+	0.962561i	$0.412624\pi$
$774$		0			0
$775$		−	3.44916i		−	0.123898i
$776$		0			0
$777$	6.77870	−	2.75916i	0.243185	−	0.0989843i
$778$		0			0
$779$	9.70397	+	2.60017i	0.347681	+	0.0931608i
$780$		0			0
$781$	−10.1088	+	2.70866i	−0.361723	+	0.0969234i
$782$		0			0
$783$	−15.3476	+	11.3334i	−0.548479	+	0.405022i
$784$		0			0
$785$	−13.0680	+	22.6344i	−0.466416	+	0.807857i
$786$		0			0
$787$	−5.16260	+	19.2671i	−0.184027	+	0.686797i	0.810810	+	0.585309i	$0.199027\pi$
$787$	−5.16260	+	19.2671i	−0.184027	+	0.686797i	−0.994837	+	0.101488i	$0.967640\pi$
$788$		0			0
$789$	−6.31589	−	2.66171i	−0.224852	−	0.0947593i
$790$		0			0
$791$		−	4.49949i		−	0.159983i
$792$		0			0
$793$			35.8336i			1.27249i
$794$		0			0
$795$	42.7246	−	32.3687i	1.51529	−	1.14800i
$796$		0			0
$797$	−3.02171	+	11.2772i	−0.107035	+	0.399458i	−0.998568	−	0.0534965i	$-0.982963\pi$
$797$	−3.02171	+	11.2772i	−0.107035	+	0.399458i	0.891534	+	0.452955i	$0.149630\pi$
$798$		0			0
$799$	34.8990	−	60.4469i	1.23464	−	2.13846i
$800$		0			0
$801$	12.0093	+	47.1282i	0.424326	+	1.66519i
$802$		0			0
$803$	0.740961	−	0.198540i	0.0261479	−	0.00700632i
$804$		0			0
$805$	14.4606	+	3.87471i	0.509669	+	0.136565i
$806$		0			0
$807$	34.1840	+	26.5656i	1.20333	+	0.935152i
$808$		0			0
$809$			13.1110i			0.460958i	0.973077	+	0.230479i	$0.0740292\pi$
$809$			13.1110i			0.460958i	−0.973077	+	0.230479i	$0.925971\pi$
$810$		0			0
$811$	34.1945	−	34.1945i	1.20073	−	1.20073i	0.226789	−	0.973944i	$-0.427177\pi$
$811$	34.1945	−	34.1945i	1.20073	−	1.20073i	0.973944	−	0.226789i	$-0.0728227\pi$
$812$		0			0
$813$	46.3267	−	5.80969i	1.62475	−	0.203755i
$814$		0			0
$815$	20.8498	+	36.1129i	0.730337	+	1.26498i
$816$		0			0
$817$	−19.5392	+	33.8429i	−0.683590	+	1.18401i
$818$		0			0
$819$	−7.05868	+	11.8862i	−0.246650	+	0.415339i
$820$		0			0
$821$	6.39631	+	23.8714i	0.223233	+	0.833116i	0.983105	+	0.183044i	$0.0585949\pi$
$821$	6.39631	+	23.8714i	0.223233	+	0.833116i	−0.759872	+	0.650073i	$0.774738\pi$
$822$		0			0
$823$	16.2152	−	9.36184i	0.565226	−	0.326333i	−0.190014	−	0.981781i	$-0.560853\pi$
$823$	16.2152	−	9.36184i	0.565226	−	0.326333i	0.755240	+	0.655448i	$0.227520\pi$
$824$		0			0
$825$	−0.952888	+	6.90958i	−0.0331753	+	0.240561i
$826$		0			0
$827$	24.1212	−	24.1212i	0.838775	−	0.838775i	−0.149923	−	0.988698i	$-0.547902\pi$
$827$	24.1212	−	24.1212i	0.838775	−	0.838775i	0.988698	+	0.149923i	$0.0479025\pi$
$828$		0			0
$829$	−20.8683	−	20.8683i	−0.724787	−	0.724787i	0.244789	−	0.969576i	$-0.421281\pi$
$829$	−20.8683	−	20.8683i	−0.724787	−	0.724787i	−0.969576	+	0.244789i	$0.921281\pi$
$830$		0			0
$831$	6.24988	+	15.3547i	0.216806	+	0.532649i
$832$		0			0
$833$	19.9793	+	34.6052i	0.692242	+	1.19900i
$834$		0			0
$835$	18.8183	−	5.04234i	0.651233	−	0.174497i
$836$		0			0
$837$	−4.62517	−	3.68643i	−0.159869	−	0.127422i
$838$		0			0
$839$	5.01977	+	2.89816i	0.173302	+	0.100056i	0.584142	−	0.811652i	$-0.301431\pi$
$839$	5.01977	+	2.89816i	0.173302	+	0.100056i	−0.410840	+	0.911707i	$0.634765\pi$
$840$		0			0
$841$	−13.4396	+	7.75936i	−0.463435	+	0.267564i
$842$		0			0
$843$	15.6929	+	6.61346i	0.540492	+	0.227780i
$844$		0			0
$845$	1.70253	+	1.70253i	0.0585689	+	0.0585689i
$846$		0			0
$847$	12.2070			0.419437
$848$		0			0
$849$	53.4657	+	7.37337i	1.83494	+	0.253053i
$850$		0			0
$851$	3.30600	−	12.3381i	0.113328	−	0.422946i
$852$		0			0
$853$	−0.461332	−	1.72171i	−0.0157957	−	0.0589504i	0.957578	−	0.288174i	$-0.0930481\pi$
$853$	−0.461332	−	1.72171i	−0.0157957	−	0.0589504i	−0.973374	+	0.229223i	$0.926381\pi$
$854$		0			0
$855$	−36.2964	−	37.1996i	−1.24131	−	1.27220i
$856$		0			0
$857$	12.6918	+	7.32760i	0.433543	+	0.250306i	0.700855	−	0.713304i	$-0.252802\pi$
$857$	12.6918	+	7.32760i	0.433543	+	0.250306i	−0.267312	+	0.963610i	$0.586135\pi$
$858$		0			0
$859$	51.3859	+	13.7688i	1.75327	+	0.469786i	0.985318	−	0.170727i	$-0.0546116\pi$
$859$	51.3859	+	13.7688i	1.75327	+	0.469786i	0.767947	+	0.640513i	$0.221278\pi$
$860$		0			0
$861$	−3.73340	+	0.468194i	−0.127234	+	0.0159560i
$862$		0			0
$863$	−23.9467			−0.815157			−0.407578	−	0.913170i	$-0.633627\pi$
$863$	−23.9467			−0.815157			−0.407578	+	0.913170i	$0.633627\pi$
$864$		0			0
$865$	−9.02103			−0.306724
$866$		0			0
$867$	70.2515	−	8.81003i	2.38587	−	0.299204i
$868$		0			0
$869$	−1.84049	−	0.493159i	−0.0624345	−	0.0167293i
$870$		0			0
$871$	43.5269	+	25.1303i	1.47485	+	0.851507i
$872$		0			0
$873$	−1.05387	+	3.74825i	−0.0356681	+	0.126859i
$874$		0			0
$875$	−1.90986	−	7.12771i	−0.0645652	−	0.240961i
$876$		0			0
$877$	10.6447	−	39.7266i	0.359446	−	1.34147i	−0.515349	−	0.856980i	$-0.672338\pi$
$877$	10.6447	−	39.7266i	0.359446	−	1.34147i	0.874796	−	0.484492i	$-0.160996\pi$
$878$		0			0
$879$	54.3922	+	7.50114i	1.83460	+	0.253007i
$880$		0			0
$881$	−41.2335			−1.38919			−0.694597	−	0.719399i	$-0.744417\pi$
$881$	−41.2335			−1.38919			−0.694597	+	0.719399i	$0.744417\pi$
$882$		0			0
$883$	11.9719	+	11.9719i	0.402885	+	0.402885i	0.879248	−	0.476364i	$-0.158045\pi$
$883$	11.9719	+	11.9719i	0.402885	+	0.402885i	−0.476364	+	0.879248i	$0.658045\pi$
$884$		0			0
$885$	22.5221	+	9.49151i	0.757074	+	0.319054i
$886$		0			0
$887$	26.7452	−	15.4413i	0.898016	−	0.518470i	0.0214599	−	0.999770i	$-0.493169\pi$
$887$	26.7452	−	15.4413i	0.898016	−	0.518470i	0.876556	+	0.481300i	$0.159835\pi$
$888$		0			0
$889$	6.00486	+	3.46691i	0.201397	+	0.116276i
$890$		0			0
$891$	8.24700	+	8.66266i	0.276285	+	0.290210i
$892$		0			0
$893$	54.1788	−	14.5172i	1.81302	−	0.485798i
$894$		0			0
$895$	7.48706	+	12.9680i	0.250265	+	0.433471i
$896$		0			0
$897$	9.09601	+	22.3471i	0.303707	+	0.746147i
$898$		0			0
$899$	2.95523	+	2.95523i	0.0985624	+	0.0985624i
$900$		0			0
$901$	−58.7480	+	58.7480i	−1.95718	+	1.95718i
$902$		0			0
$903$	1.99951	−	14.4988i	0.0665395	−	0.482491i
$904$		0			0
$905$	0.586997	−	0.338903i	0.0195125	−	0.0112655i
$906$		0			0
$907$	−7.16365	−	26.7351i	−0.237865	−	0.887725i	−0.976836	−	0.213988i	$-0.931355\pi$
$907$	−7.16365	−	26.7351i	−0.237865	−	0.887725i	0.738971	−	0.673737i	$-0.235312\pi$
$908$		0			0
$909$	14.8008	+	26.3791i	0.490912	+	0.874940i
$910$		0			0
$911$	4.83009	−	8.36596i	0.160028	−	0.277177i	−0.774850	−	0.632145i	$-0.782175\pi$
$911$	4.83009	−	8.36596i	0.160028	−	0.277177i	0.934878	+	0.354968i	$0.115508\pi$
$912$		0			0
$913$	−2.27297	−	3.93689i	−0.0752242	−	0.130292i
$914$		0			0
$915$	50.0647	−	6.27846i	1.65509	−	0.207560i
$916$		0			0
$917$	−6.06859	+	6.06859i	−0.200403	+	0.200403i
$918$		0			0
$919$			12.5574i			0.414229i	0.978317	+	0.207115i	$0.0664073\pi$
$919$			12.5574i			0.414229i	−0.978317	+	0.207115i	$0.933593\pi$
$920$		0			0
$921$	−33.3659	−	25.9298i	−1.09944	−	0.854415i
$922$		0			0
$923$	−26.5147	−	7.10460i	−0.872743	−	0.233851i
$924$		0			0
$925$	9.35553	−	2.50681i	0.307608	−	0.0824233i
$926$		0			0
$927$	−19.9555	+	19.4710i	−0.655424	+	0.639511i
$928$		0			0
$929$	4.50031	−	7.79477i	0.147650	−	0.255738i	−0.782708	−	0.622389i	$-0.786162\pi$
$929$	4.50031	−	7.79477i	0.147650	−	0.255738i	0.930359	+	0.366651i	$0.119496\pi$
$930$		0			0
$931$	−8.31092	+	31.0168i	−0.272379	+	1.01653i
$932$		0			0
$933$	13.6081	−	10.3097i	0.445510	−	0.337523i
$934$		0			0
$935$		−	28.6501i		−	0.936960i
$936$		0			0
$937$		−	59.2265i		−	1.93485i	−0.253166	−	0.967423i	$-0.581472\pi$
$937$		−	59.2265i		−	1.93485i	0.253166	−	0.967423i	$-0.418528\pi$
$938$		0			0
$939$	−15.5878	−	6.56917i	−0.508689	−	0.214377i
$940$		0			0
$941$	−2.95446	+	11.0262i	−0.0963126	+	0.359443i	−0.997215	−	0.0745778i	$-0.976239\pi$
$941$	−2.95446	+	11.0262i	−0.0963126	+	0.359443i	0.900903	+	0.434021i	$0.142906\pi$
$942$		0			0
$943$	−3.28347	+	5.68714i	−0.106925	+	0.185199i
$944$		0			0
$945$	17.8436	+	7.77939i	0.580452	+	0.253064i
$946$		0			0
$947$	−8.32058	+	2.22949i	−0.270382	+	0.0724488i	−0.391463	−	0.920194i	$-0.628031\pi$
$947$	−8.32058	+	2.22949i	−0.270382	+	0.0724488i	0.121080	+	0.992643i	$0.461364\pi$
$948$		0			0
$949$	1.94348	+	0.520755i	0.0630882	+	0.0169044i
$950$		0			0
$951$	−21.2750	+	8.65964i	−0.689889	+	0.280808i
$952$		0			0
$953$		−	43.5260i		−	1.40995i	−0.709234	−	0.704973i	$-0.750959\pi$
$953$		−	43.5260i		−	1.40995i	0.709234	−	0.704973i	$-0.249041\pi$
$954$		0			0
$955$	−44.2637	+	44.2637i	−1.43234	+	1.43234i
$956$		0			0
$957$	−5.10367	−	6.73653i	−0.164978	−	0.217761i
$958$		0			0
$959$	−4.70633	−	8.15160i	−0.151975	−	0.263229i
$960$		0			0
$961$	14.8522	−	25.7247i	0.479103	−	0.829830i
$962$		0			0
$963$	−4.10520	+	6.91283i	−0.132288	+	0.222763i
$964$		0			0
$965$	11.5982	+	43.2852i	0.373361	+	1.39340i
$966$		0			0
$967$	26.2267	−	15.1420i	0.843393	−	0.486933i	−0.0150229	−	0.999887i	$-0.504782\pi$
$967$	26.2267	−	15.1420i	0.843393	−	0.486933i	0.858416	+	0.512954i	$0.171449\pi$
$968$		0			0
$969$	63.6090	+	49.4328i	2.04341	+	1.58801i
$970$		0			0
$971$	−9.06755	+	9.06755i	−0.290992	+	0.290992i	−0.837472	−	0.546480i	$-0.815967\pi$
$971$	−9.06755	+	9.06755i	−0.290992	+	0.290992i	0.546480	+	0.837472i	$0.315967\pi$
$972$		0			0
$973$	−3.94005	−	3.94005i	−0.126312	−	0.126312i
$974$		0			0
$975$	−11.2261	+	14.4456i	−0.359524	+	0.462628i
$976$		0			0
$977$	10.4475	+	18.0956i	0.334246	+	0.578931i	0.983340	−	0.181778i	$-0.0581851\pi$
$977$	10.4475	+	18.0956i	0.334246	+	0.578931i	−0.649094	+	0.760708i	$0.724852\pi$
$978$		0			0
$979$	−20.8100	+	5.57603i	−0.665092	+	0.178211i
$980$		0			0
$981$	−31.4912	−	18.7011i	−1.00544	−	0.597081i
$982$		0			0
$983$	1.14158	+	0.659092i	0.0364108	+	0.0210218i	0.518095	−	0.855323i	$-0.326641\pi$
$983$	1.14158	+	0.659092i	0.0364108	+	0.0210218i	−0.481684	+	0.876345i	$0.659975\pi$
$984$		0			0
$985$	4.15128	−	2.39674i	0.132271	−	0.0763665i
$986$		0			0
$987$	−16.7446	+	12.6859i	−0.532986	+	0.403796i
$988$		0			0
$989$	−18.0626	−	18.0626i	−0.574357	−	0.574357i
$990$		0			0
$991$	−2.51185			−0.0797914			−0.0398957	−	0.999204i	$-0.512703\pi$
$991$	−2.51185			−0.0797914			−0.0398957	+	0.999204i	$0.512703\pi$
$992$		0			0
$993$	−0.691664	−	1.69928i	−0.0219493	−	0.0539250i
$994$		0			0
$995$	−4.68788	+	17.4954i	−0.148616	+	0.554641i
$996$		0			0
$997$	11.9030	+	44.4227i	0.376973	+	1.40688i	0.850441	+	0.526071i	$0.176335\pi$
$997$	11.9030	+	44.4227i	0.376973	+	1.40688i	−0.473468	+	0.880811i	$0.656998\pi$
$998$		0			0
$999$	6.63757	−	15.2246i	0.210003	−	0.481685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.529.18		72
3.2	odd	2		1728.2.bc.e.721.5		72
4.3	odd	2		144.2.x.e.61.17	yes	72
9.4	even	3	inner	576.2.bb.e.337.11		72
9.5	odd	6		1728.2.bc.e.145.14		72
12.11	even	2		432.2.y.e.397.2		72
16.5	even	4	inner	576.2.bb.e.241.11		72
16.11	odd	4		144.2.x.e.133.7	yes	72
36.23	even	6		432.2.y.e.253.12		72
36.31	odd	6		144.2.x.e.13.7	✓	72
48.5	odd	4		1728.2.bc.e.1585.14		72
48.11	even	4		432.2.y.e.181.12		72
144.5	odd	12		1728.2.bc.e.1009.5		72
144.59	even	12		432.2.y.e.37.2		72
144.85	even	12	inner	576.2.bb.e.49.18		72
144.139	odd	12		144.2.x.e.85.17	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.7	✓	72	36.31	odd	6
144.2.x.e.61.17	yes	72	4.3	odd	2
144.2.x.e.85.17	yes	72	144.139	odd	12
144.2.x.e.133.7	yes	72	16.11	odd	4
432.2.y.e.37.2		72	144.59	even	12
432.2.y.e.181.12		72	48.11	even	4
432.2.y.e.253.12		72	36.23	even	6
432.2.y.e.397.2		72	12.11	even	2
576.2.bb.e.49.18		72	144.85	even	12	inner
576.2.bb.e.241.11		72	16.5	even	4	inner
576.2.bb.e.337.11		72	9.4	even	3	inner
576.2.bb.e.529.18		72	1.1	even	1	trivial
1728.2.bc.e.145.14		72	9.5	odd	6
1728.2.bc.e.721.5		72	3.2	odd	2
1728.2.bc.e.1009.5		72	144.5	odd	12
1728.2.bc.e.1585.14		72	48.5	odd	4

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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71859 - 0.215523i) q^{3} +(2.73721 + 0.733432i) q^{5} +(1.14487 + 0.660988i) q^{7} +(2.90710 - 0.740791i) q^{9} +O(q^{10})\)	\(q+(1.71859 - 0.215523i) q^{3} +(2.73721 + 0.733432i) q^{5} +(1.14487 + 0.660988i) q^{7} +(2.90710 - 0.740791i) q^{9} +(0.343957 + 1.28367i) q^{11} +(-0.902174 + 3.36696i) q^{13} +(4.86220 + 0.670538i) q^{15} -7.60772 q^{17} +(-4.32297 - 4.32297i) q^{19} +(2.11001 + 0.889223i) q^{21} +(3.46087 - 1.99814i) q^{23} +(2.62424 + 1.51511i) q^{25} +(4.83645 - 1.89966i) q^{27} +(-3.54658 + 0.950303i) q^{29} +(-0.569129 - 0.985760i) q^{31} +(0.867781 + 2.13197i) q^{33} +(2.64894 + 2.64894i) q^{35} +(2.26014 - 2.26014i) q^{37} +(-0.824810 + 5.98086i) q^{39} +(-1.42311 + 0.821634i) q^{41} +(-1.65438 - 6.17424i) q^{43} +(8.50065 + 0.104463i) q^{45} +(-4.58731 + 7.94546i) q^{47} +(-2.62619 - 4.54869i) q^{49} +(-13.0746 + 1.63964i) q^{51} +(7.72215 - 7.72215i) q^{53} +3.76593i q^{55} +(-8.36111 - 6.49771i) q^{57} +(4.80982 + 1.28879i) q^{59} +(9.92979 - 2.66068i) q^{61} +(3.81789 + 1.07345i) q^{63} +(-4.93887 + 8.55438i) q^{65} +(3.73189 - 13.9276i) q^{67} +(5.51718 - 4.17987i) q^{69} +7.87498i q^{71} -0.577222i q^{73} +(4.83654 + 2.03826i) q^{75} +(-0.454704 + 1.69698i) q^{77} +(-0.716890 + 1.24169i) q^{79} +(7.90246 - 4.30711i) q^{81} +(-3.30414 + 0.885341i) q^{83} +(-20.8239 - 5.57975i) q^{85} +(-5.89030 + 2.39755i) q^{87} +16.2114i q^{89} +(-3.25839 + 3.25839i) q^{91} +(-1.19055 - 1.57146i) q^{93} +(-8.66225 - 15.0035i) q^{95} +(-0.648931 + 1.12398i) q^{97} +(1.95085 + 3.47695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more