LMFDB - Embedded newform 544.2.bx.g.159.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(31,544)] 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("544.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 0, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.bx (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,8,0,-8,0,8,0,-8,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			159.1
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	544.159
Dual form			544.2.bx.g.479.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.292893 + 1.47247i) q^{3} +(-0.451406 + 0.675577i) q^{5} +(1.70711 - 1.14065i) q^{7} +(0.689246 - 0.285495i) q^{9} +(5.86143 + 1.16591i) q^{11} +(-2.87302 + 2.87302i) q^{13} +(-1.12698 - 0.466811i) q^{15} +(-3.14065 - 2.67139i) q^{17} +(0.555992 - 1.34228i) q^{19} +(2.17958 + 2.17958i) q^{21} +(-0.447215 + 2.24830i) q^{23} +(1.66078 + 4.00948i) q^{25} +(3.12453 + 4.67619i) q^{27} +(2.52814 + 1.68925i) q^{29} +(4.42788 - 0.880761i) q^{31} +8.97229i q^{33} +1.66818i q^{35} +(-9.45349 + 1.88042i) q^{37} +(-5.07193 - 3.38896i) q^{39} +(-0.822155 - 1.23044i) q^{41} +(1.82929 + 4.41629i) q^{43} +(-0.118256 + 0.594513i) q^{45} +(-7.90244 - 7.90244i) q^{47} +(-1.06566 + 2.57273i) q^{49} +(3.01367 - 5.40696i) q^{51} +(-2.40262 - 0.995200i) q^{53} +(-3.43355 + 3.43355i) q^{55} +(2.13932 + 0.425538i) q^{57} +(-0.0912618 + 0.0378019i) q^{59} +(9.64194 - 6.44254i) q^{61} +(0.850966 - 1.27356i) q^{63} +(-0.644047 - 3.23784i) q^{65} +8.34731 q^{67} -3.44155 q^{69} +(-0.472474 - 2.37529i) q^{71} +(4.36335 - 6.53022i) q^{73} +(-5.41742 + 3.61980i) q^{75} +(11.3360 - 4.69552i) q^{77} +(0.654509 + 0.130190i) q^{79} +(-4.38783 + 4.38783i) q^{81} +(-0.243503 - 0.100862i) q^{83} +(3.22243 - 0.915872i) q^{85} +(-1.74690 + 4.21738i) q^{87} +(-7.80317 - 7.80317i) q^{89} +(-1.62743 + 8.18166i) q^{91} +(2.59379 + 6.26197i) q^{93} +(0.655837 + 0.981530i) q^{95} +(-9.48083 - 6.33489i) q^{97} +(4.37283 - 0.869810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 16 q^{11} - 16 q^{13} - 16 q^{15} - 16 q^{17} + 16 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{29} + 8 q^{31} - 40 q^{37} - 24 q^{39} + 32 q^{43} + 24 q^{45} + 16 q^{47}+ \cdots - 16 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 16 * q^11 - 16 * q^13 - 16 * q^15 - 16 * q^17 + 16 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^29 + 8 * q^31 - 40 * q^37 - 24 * q^39 + 32 * q^43 + 24 * q^45 + 16 * q^47 - 8 * q^49 + 8 * q^51 + 16 * q^53 - 24 * q^55 - 24 * q^57 + 8 * q^59 + 24 * q^61 - 32 * q^63 - 16 * q^65 + 32 * q^67 + 16 * q^69 + 8 * q^71 + 24 * q^73 - 8 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^83 + 48 * q^85 - 40 * q^87 - 32 * q^89 - 40 * q^91 - 8 * q^93 + 56 * q^95 - 8 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$1$	$-1$	$e\left(\frac{15}{16}\right)$

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
$3$	0.292893	+	1.47247i	0.169102	+	0.850133i	0.968439	+	0.249250i	$0.0801842\pi$
$3$	0.292893	+	1.47247i	0.169102	+	0.850133i	−0.799337	+	0.600883i	$0.794816\pi$
$4$		0			0
$5$	−0.451406	+	0.675577i	−0.201875	+	0.302127i	−0.918569	−	0.395260i	$-0.870654\pi$
$5$	−0.451406	+	0.675577i	−0.201875	+	0.302127i	0.716694	+	0.697388i	$0.245654\pi$
$6$		0			0
$7$	1.70711	−	1.14065i	0.645226	−	0.431126i	−0.189433	−	0.981894i	$-0.560665\pi$
$7$	1.70711	−	1.14065i	0.645226	−	0.431126i	0.834659	+	0.550768i	$0.185665\pi$
$8$		0			0
$9$	0.689246	−	0.285495i	0.229749	−	0.0951651i
$10$		0			0
$11$	5.86143	+	1.16591i	1.76729	+	0.351535i	0.968296	−	0.249807i	$-0.0803671\pi$
$11$	5.86143	+	1.16591i	1.76729	+	0.351535i	0.798992	+	0.601342i	$0.205367\pi$
$12$		0			0
$13$	−2.87302	+	2.87302i	−0.796832	+	0.796832i	−0.982595	−	0.185763i	$-0.940524\pi$
$13$	−2.87302	+	2.87302i	−0.796832	+	0.796832i	0.185763	+	0.982595i	$0.440524\pi$
$14$		0			0
$15$	−1.12698	−	0.466811i	−0.290986	−	0.120530i
$16$		0			0
$17$	−3.14065	−	2.67139i	−0.761720	−	0.647906i
$17$	−3.14065	−	2.67139i	−0.761720	−	0.647906i
$18$		0			0
$19$	0.555992	−	1.34228i	0.127553	−	0.307941i	−0.847182	−	0.531302i	$-0.821703\pi$
$19$	0.555992	−	1.34228i	0.127553	−	0.307941i	0.974736	+	0.223361i	$0.0717029\pi$
$20$		0			0
$21$	2.17958	+	2.17958i	0.475623	+	0.475623i
$22$		0			0
$23$	−0.447215	+	2.24830i	−0.0932508	+	0.468804i	0.905738	+	0.423839i	$0.139318\pi$
$23$	−0.447215	+	2.24830i	−0.0932508	+	0.468804i	−0.998989	+	0.0449650i	$0.985682\pi$
$24$		0			0
$25$	1.66078	+	4.00948i	0.332156	+	0.801896i
$26$		0			0
$27$	3.12453	+	4.67619i	0.601316	+	0.899932i
$28$		0			0
$29$	2.52814	+	1.68925i	0.469463	+	0.313685i	0.767703	−	0.640806i	$-0.221400\pi$
$29$	2.52814	+	1.68925i	0.469463	+	0.313685i	−0.298240	+	0.954491i	$0.596400\pi$
$30$		0			0
$31$	4.42788	−	0.880761i	0.795271	−	0.158189i	0.219298	−	0.975658i	$-0.429623\pi$
$31$	4.42788	−	0.880761i	0.795271	−	0.158189i	0.575973	+	0.817469i	$0.304623\pi$
$32$		0			0
$33$			8.97229i			1.56187i
$34$		0			0
$35$			1.66818i			0.281974i
$36$		0			0
$37$	−9.45349	+	1.88042i	−1.55414	+	0.309138i	−0.896104	−	0.443845i	$-0.853614\pi$
$37$	−9.45349	+	1.88042i	−1.55414	+	0.309138i	−0.658040	+	0.752983i	$0.728614\pi$
$38$		0			0
$39$	−5.07193	−	3.38896i	−0.812159	−	0.542667i
$40$		0			0
$41$	−0.822155	−	1.23044i	−0.128399	−	0.192163i	0.761700	−	0.647930i	$-0.224365\pi$
$41$	−0.822155	−	1.23044i	−0.128399	−	0.192163i	−0.890099	+	0.455767i	$0.849365\pi$
$42$		0			0
$43$	1.82929	+	4.41629i	0.278964	+	0.673479i	0.999808	−	0.0196192i	$-0.00624538\pi$
$43$	1.82929	+	4.41629i	0.278964	+	0.673479i	−0.720844	+	0.693098i	$0.756245\pi$
$44$		0			0
$45$	−0.118256	+	0.594513i	−0.0176286	+	0.0886248i
$46$		0			0
$47$	−7.90244	−	7.90244i	−1.15269	−	1.15269i	−0.986011	−	0.166678i	$-0.946696\pi$
$47$	−7.90244	−	7.90244i	−1.15269	−	1.15269i	−0.166678	−	0.986011i	$-0.553304\pi$
$48$		0			0
$49$	−1.06566	+	2.57273i	−0.152237	+	0.367532i
$50$		0			0
$51$	3.01367	−	5.40696i	0.421998	−	0.757126i
$52$		0			0
$53$	−2.40262	−	0.995200i	−0.330026	−	0.136701i	0.211517	−	0.977374i	$-0.432160\pi$
$53$	−2.40262	−	0.995200i	−0.330026	−	0.136701i	−0.541543	+	0.840673i	$0.682160\pi$
$54$		0			0
$55$	−3.43355	+	3.43355i	−0.462979	+	0.462979i
$56$		0			0
$57$	2.13932	+	0.425538i	0.283360	+	0.0563639i
$58$		0			0
$59$	−0.0912618	+	0.0378019i	−0.0118813	+	0.00492138i	−0.388616	−	0.921400i	$-0.627047\pi$
$59$	−0.0912618	+	0.0378019i	−0.0118813	+	0.00492138i	0.376735	+	0.926321i	$0.377047\pi$
$60$		0			0
$61$	9.64194	−	6.44254i	1.23452	−	0.824882i	0.245038	−	0.969513i	$-0.421200\pi$
$61$	9.64194	−	6.44254i	1.23452	−	0.824882i	0.989486	+	0.144631i	$0.0461996\pi$
$62$		0			0
$63$	0.850966	−	1.27356i	0.107212	−	0.160454i
$64$		0			0
$65$	−0.644047	−	3.23784i	−0.0798841	−	0.401605i
$66$		0			0
$67$	8.34731			1.01979			0.509893	−	0.860238i	$-0.329685\pi$
$67$	8.34731			1.01979			0.509893	+	0.860238i	$0.329685\pi$
$68$		0			0
$69$	−3.44155			−0.414314
$70$		0			0
$71$	−0.472474	−	2.37529i	−0.0560723	−	0.281895i	0.942569	−	0.334013i	$-0.108403\pi$
$71$	−0.472474	−	2.37529i	−0.0560723	−	0.281895i	−0.998641	+	0.0521180i	$0.983403\pi$
$72$		0			0
$73$	4.36335	−	6.53022i	0.510692	−	0.764304i	−0.483100	−	0.875565i	$-0.660489\pi$
$73$	4.36335	−	6.53022i	0.510692	−	0.764304i	0.993791	+	0.111261i	$0.0354891\pi$
$74$		0			0
$75$	−5.41742	+	3.61980i	−0.625550	+	0.417979i
$76$		0			0
$77$	11.3360	−	4.69552i	1.29186	−	0.535104i
$78$		0			0
$79$	0.654509	+	0.130190i	0.0736380	+	0.0146475i	0.231772	−	0.972770i	$-0.425548\pi$
$79$	0.654509	+	0.130190i	0.0736380	+	0.0146475i	−0.158134	+	0.987418i	$0.550548\pi$
$80$		0			0
$81$	−4.38783	+	4.38783i	−0.487537	+	0.487537i
$82$		0			0
$83$	−0.243503	−	0.100862i	−0.0267279	−	0.0110711i	0.369279	−	0.929318i	$-0.379605\pi$
$83$	−0.243503	−	0.100862i	−0.0267279	−	0.0110711i	−0.396007	+	0.918247i	$0.629605\pi$
$84$		0			0
$85$	3.22243	−	0.915872i	0.349522	−	0.0993403i
$86$		0			0
$87$	−1.74690	+	4.21738i	−0.187287	+	0.452151i
$88$		0			0
$89$	−7.80317	−	7.80317i	−0.827134	−	0.827134i	0.159985	−	0.987119i	$-0.448855\pi$
$89$	−7.80317	−	7.80317i	−0.827134	−	0.827134i	−0.987119	+	0.159985i	$0.948855\pi$
$90$		0			0
$91$	−1.62743	+	8.18166i	−0.170601	+	0.857671i
$92$		0			0
$93$	2.59379	+	6.26197i	0.268964	+	0.649336i
$94$		0			0
$95$	0.655837	+	0.981530i	0.0672875	+	0.100703i
$96$		0			0
$97$	−9.48083	−	6.33489i	−0.962632	−	0.643210i	−0.0282946	−	0.999600i	$-0.509008\pi$
$97$	−9.48083	−	6.33489i	−0.962632	−	0.643210i	−0.934338	+	0.356389i	$0.884008\pi$
$98$		0			0
$99$	4.37283	−	0.869810i	0.439486	−	0.0874192i
$100$		0			0
$101$		−	18.1355i		−	1.80455i	−0.431164	−	0.902274i	$-0.641897\pi$
$101$		−	18.1355i		−	1.80455i	0.431164	−	0.902274i	$-0.358103\pi$
$102$		0			0
$103$			3.56767i			0.351533i	0.984432	+	0.175767i	$0.0562404\pi$
$103$			3.56767i			0.351533i	−0.984432	+	0.175767i	$0.943760\pi$
$104$		0			0
$105$	−2.45635	+	0.488598i	−0.239715	+	0.0476823i
$106$		0			0
$107$	−12.1953	−	8.14866i	−1.17897	−	0.787761i	−0.197672	−	0.980268i	$-0.563338\pi$
$107$	−12.1953	−	8.14866i	−1.17897	−	0.787761i	−0.981295	+	0.192508i	$0.938338\pi$
$108$		0			0
$109$	1.47666	+	2.20998i	0.141439	+	0.211678i	0.895425	−	0.445212i	$-0.146872\pi$
$109$	1.47666	+	2.20998i	0.141439	+	0.211678i	−0.753987	+	0.656890i	$0.771872\pi$
$110$		0			0
$111$	−5.53772	−	13.3692i	−0.525618	−	1.26895i
$112$		0			0
$113$	2.89088	−	14.5334i	0.271951	−	1.36719i	−0.567330	−	0.823491i	$-0.692023\pi$
$113$	2.89088	−	14.5334i	0.271951	−	1.36719i	0.839280	−	0.543699i	$-0.182977\pi$
$114$		0			0
$115$	−1.31703	−	1.31703i	−0.122813	−	0.122813i
$116$		0			0
$117$	−1.15998	+	2.80045i	−0.107241	+	0.258902i
$118$		0			0
$119$	−8.40855	−	0.977949i	−0.770811	−	0.0896484i
$120$		0			0
$121$	22.8343	+	9.45829i	2.07585	+	0.859844i
$122$		0			0
$123$	1.57099	−	1.57099i	0.141651	−	0.141651i
$124$		0			0
$125$	−7.44288	−	1.48048i	−0.665712	−	0.132418i
$126$		0			0
$127$	13.1749	−	5.45721i	1.16908	−	0.484249i	0.288192	−	0.957573i	$-0.406946\pi$
$127$	13.1749	−	5.45721i	1.16908	−	0.484249i	0.880889	+	0.473323i	$0.156946\pi$
$128$		0			0
$129$	−5.96709	+	3.98708i	−0.525373	+	0.351043i
$130$		0			0
$131$	−7.71511	+	11.5465i	−0.674073	+	1.00882i	0.323957	+	0.946072i	$0.394987\pi$
$131$	−7.71511	+	11.5465i	−0.674073	+	1.00882i	−0.998029	+	0.0627491i	$0.980013\pi$
$132$		0			0
$133$	−0.581941	−	2.92562i	−0.0504607	−	0.253683i
$134$		0			0
$135$	−4.56955			−0.393284
$136$		0			0
$137$	15.8174			1.35137			0.675687	−	0.737189i	$-0.263847\pi$
$137$	15.8174			1.35137			0.675687	+	0.737189i	$0.263847\pi$
$138$		0			0
$139$	−1.03594	−	5.20805i	−0.0878677	−	0.441741i	−0.999526	−	0.0307913i	$-0.990197\pi$
$139$	−1.03594	−	5.20805i	−0.0878677	−	0.441741i	0.911658	−	0.410949i	$-0.134803\pi$
$140$		0			0
$141$	9.32156	−	13.9507i	0.785017	−	1.17486i
$142$		0			0
$143$	−20.1897	+	13.4903i	−1.68834	+	1.12812i
$144$		0			0
$145$	−2.28243	+	0.945414i	−0.189546	+	0.0785123i
$146$		0			0
$147$	−4.10040	−	0.815619i	−0.338195	−	0.0672712i
$148$		0			0
$149$	−5.49661	+	5.49661i	−0.450299	+	0.450299i	−0.895454	−	0.445154i	$-0.853149\pi$
$149$	−5.49661	+	5.49661i	−0.450299	+	0.450299i	0.445154	+	0.895454i	$0.353149\pi$
$150$		0			0
$151$	0.568536	+	0.235495i	0.0462668	+	0.0191643i	0.405697	−	0.914008i	$-0.367029\pi$
$151$	0.568536	+	0.235495i	0.0462668	+	0.0191643i	−0.359430	+	0.933172i	$0.617029\pi$
$152$		0			0
$153$	−2.92735	−	0.944602i	−0.236662	−	0.0763665i
$154$		0			0
$155$	−1.40375	+	3.38896i	−0.112752	+	0.272207i
$156$		0			0
$157$	−4.04373	−	4.04373i	−0.322725	−	0.322725i	0.527087	−	0.849811i	$-0.323284\pi$
$157$	−4.04373	−	4.04373i	−0.322725	−	0.322725i	−0.849811	+	0.527087i	$0.823284\pi$
$158$		0			0
$159$	0.761693	−	3.82929i	0.0604062	−	0.303682i
$160$		0			0
$161$	1.80109	+	4.34821i	0.141946	+	0.342687i
$162$		0			0
$163$	−7.64318	−	11.4388i	−0.598660	−	0.895959i	0.401138	−	0.916017i	$-0.368615\pi$
$163$	−7.64318	−	11.4388i	−0.598660	−	0.895959i	−0.999799	+	0.0200588i	$0.993615\pi$
$164$		0			0
$165$	−6.06147	−	4.05014i	−0.471885	−	0.315303i
$166$		0			0
$167$	12.5062	−	2.48764i	0.967761	−	0.192500i	0.314186	−	0.949361i	$-0.398268\pi$
$167$	12.5062	−	2.48764i	0.967761	−	0.192500i	0.653575	+	0.756862i	$0.273268\pi$
$168$		0			0
$169$		−	3.50846i		−	0.269881i
$170$		0			0
$171$		−	1.08390i		−	0.0828877i
$172$		0			0
$173$	−8.51608	+	1.69395i	−0.647466	+	0.128789i	−0.507889	−	0.861422i	$-0.669574\pi$
$173$	−8.51608	+	1.69395i	−0.647466	+	0.128789i	−0.139576	+	0.990211i	$0.544574\pi$
$174$		0			0
$175$	7.40855	+	4.95024i	0.560034	+	0.374203i
$176$		0			0
$177$	−0.0823922	−	0.123309i	−0.00619298	−	0.00926845i
$178$		0			0
$179$	−6.00208	−	14.4903i	−0.448617	−	1.08306i	−0.972841	−	0.231476i	$-0.925645\pi$
$179$	−6.00208	−	14.4903i	−0.448617	−	1.08306i	0.524224	−	0.851580i	$-0.324355\pi$
$180$		0			0
$181$	−3.56706	+	17.9328i	−0.265138	+	1.33294i	0.586986	+	0.809597i	$0.300314\pi$
$181$	−3.56706	+	17.9328i	−0.265138	+	1.33294i	−0.852124	+	0.523340i	$0.824686\pi$
$182$		0			0
$183$	12.3105	+	12.3105i	0.910020	+	0.910020i
$184$		0			0
$185$	2.99699	−	7.23539i	0.220343	−	0.531956i
$186$		0			0
$187$	−15.2941	−	19.3199i	−1.11842	−	1.41281i
$188$		0			0
$189$	10.6678	+	4.41875i	0.775969	+	0.321417i
$190$		0			0
$191$	−6.58995	+	6.58995i	−0.476832	+	0.476832i	−0.904117	−	0.427285i	$-0.859470\pi$
$191$	−6.58995	+	6.58995i	−0.476832	+	0.476832i	0.427285	+	0.904117i	$0.359470\pi$
$192$		0			0
$193$	−18.5551	−	3.69084i	−1.33563	−	0.265672i	−0.524932	−	0.851144i	$-0.675909\pi$
$193$	−18.5551	−	3.69084i	−1.33563	−	0.265672i	−0.810693	+	0.585471i	$0.800909\pi$
$194$		0			0
$195$	4.57900	−	1.89668i	0.327909	−	0.135824i
$196$		0			0
$197$	−19.4824	+	13.0178i	−1.38807	+	0.927476i	−0.388084	+	0.921624i	$0.626863\pi$
$197$	−19.4824	+	13.0178i	−1.38807	+	0.927476i	−0.999983	+	0.00585217i	$0.998137\pi$
$198$		0			0
$199$	10.7961	−	16.1575i	0.765316	−	1.14538i	−0.220143	−	0.975468i	$-0.570653\pi$
$199$	10.7961	−	16.1575i	0.765316	−	1.14538i	0.985460	−	0.169909i	$-0.0543475\pi$
$200$		0			0
$201$	2.44487	+	12.2912i	0.172448	+	0.866954i
$202$		0			0
$203$	6.24264			0.438147
$204$		0			0
$205$	1.20238			0.0839781
$206$		0			0
$207$	0.333638	+	1.67731i	0.0231895	+	0.116581i
$208$		0			0
$209$	4.82389	−	7.21946i	0.333676	−	0.499381i
$210$		0			0
$211$	−12.4136	+	8.29449i	−0.854586	+	0.571016i	−0.903889	−	0.427768i	$-0.859300\pi$
$211$	−12.4136	+	8.29449i	−0.854586	+	0.571016i	0.0493028	+	0.998784i	$0.484300\pi$
$212$		0			0
$213$	3.35916	−	1.39141i	0.230166	−	0.0953378i
$214$		0			0
$215$	−3.80930	−	0.757716i	−0.259792	−	0.0516758i
$216$		0			0
$217$	6.55423	−	6.55423i	0.444930	−	0.444930i
$218$		0			0
$219$	10.8936	+	4.51226i	0.736119	+	0.304911i
$220$		0			0
$221$	16.6981	−	1.34821i	1.12323	−	0.0906904i
$222$		0			0
$223$	−0.583332	+	1.40829i	−0.0390628	+	0.0943059i	−0.942207	−	0.335032i	$-0.891253\pi$
$223$	−0.583332	+	1.40829i	−0.0390628	+	0.0943059i	0.903144	+	0.429338i	$0.141253\pi$
$224$		0			0
$225$	2.28937	+	2.28937i	0.152625	+	0.152625i
$226$		0			0
$227$	−0.753047	+	3.78583i	−0.0499815	+	0.251274i	−0.997696	−	0.0678460i	$-0.978387\pi$
$227$	−0.753047	+	3.78583i	−0.0499815	+	0.251274i	0.947714	+	0.319120i	$0.103387\pi$
$228$		0			0
$229$	6.65440	+	16.0651i	0.439735	+	1.06161i	0.976040	+	0.217590i	$0.0698196\pi$
$229$	6.65440	+	16.0651i	0.439735	+	1.06161i	−0.536305	+	0.844024i	$0.680180\pi$
$230$		0			0
$231$	10.2343	+	15.3167i	0.673365	+	1.00776i
$232$		0			0
$233$	3.28943	+	2.19793i	0.215498	+	0.143991i	0.658635	−	0.752463i	$-0.271134\pi$
$233$	3.28943	+	2.19793i	0.215498	+	0.143991i	−0.443137	+	0.896454i	$0.646134\pi$
$234$		0			0
$235$	8.90591	−	1.77150i	0.580957	−	0.115560i
$236$		0			0
$237$			1.00188i			0.0650790i
$238$		0			0
$239$			29.4189i			1.90295i	0.307725	+	0.951475i	$0.400432\pi$
$239$			29.4189i			1.90295i	−0.307725	+	0.951475i	$0.599568\pi$
$240$		0			0
$241$	−18.9570	+	3.77078i	−1.22113	+	0.242897i	−0.763241	−	0.646114i	$-0.776393\pi$
$241$	−18.9570	+	3.77078i	−1.22113	+	0.242897i	−0.457885	+	0.889011i	$0.651393\pi$
$242$		0			0
$243$	6.28243	+	4.19779i	0.403018	+	0.269288i
$244$		0			0
$245$	−1.25703	−	1.88128i	−0.0803087	−	0.120190i
$246$		0			0
$247$	2.25903	+	5.45378i	0.143739	+	0.347016i
$248$		0			0
$249$	0.0771965	−	0.388093i	0.00489213	−	0.0245944i
$250$		0			0
$251$	−6.70769	−	6.70769i	−0.423386	−	0.423386i	0.462982	−	0.886368i	$-0.346779\pi$
$251$	−6.70769	−	6.70769i	−0.423386	−	0.423386i	−0.886368	+	0.462982i	$0.846779\pi$
$252$		0			0
$253$	−5.24264	+	12.6569i	−0.329602	+	0.795730i
$254$		0			0
$255$	2.29243	+	4.47670i	0.143557	+	0.280342i
$256$		0			0
$257$	4.53666	+	1.87915i	0.282989	+	0.117218i	0.519663	−	0.854371i	$-0.326057\pi$
$257$	4.53666	+	1.87915i	0.282989	+	0.117218i	−0.236674	+	0.971589i	$0.576057\pi$
$258$		0			0
$259$	−13.9932	+	13.9932i	−0.869496	+	0.869496i
$260$		0			0
$261$	2.22478	+	0.442536i	0.137710	+	0.0273923i
$262$		0			0
$263$	24.8112	−	10.2771i	1.52992	−	0.633715i	0.550373	−	0.834919i	$-0.314485\pi$
$263$	24.8112	−	10.2771i	1.52992	−	0.633715i	0.979549	+	0.201204i	$0.0644854\pi$
$264$		0			0
$265$	1.75689	−	1.17392i	0.107925	−	0.0721132i
$266$		0			0
$267$	9.20447	−	13.7755i	0.563304	−	0.843044i
$268$		0			0
$269$	−0.609085	−	3.06208i	−0.0371366	−	0.186698i	0.957765	−	0.287554i	$-0.0928420\pi$
$269$	−0.609085	−	3.06208i	−0.0371366	−	0.186698i	−0.994901	+	0.100856i	$0.967842\pi$
$270$		0			0
$271$	31.5213			1.91478			0.957392	−	0.288792i	$-0.0932536\pi$
$271$	31.5213			1.91478			0.957392	+	0.288792i	$0.0932536\pi$
$272$		0			0
$273$	−12.5239			−0.757984
$274$		0			0
$275$	5.05985	+	25.4376i	0.305121	+	1.53394i
$276$		0			0
$277$	2.07019	−	3.09826i	0.124386	−	0.186157i	−0.764050	−	0.645157i	$-0.776792\pi$
$277$	2.07019	−	3.09826i	0.124386	−	0.186157i	0.888436	+	0.459000i	$0.151792\pi$
$278$		0			0
$279$	2.80045	−	1.87120i	0.167659	−	0.112026i
$280$		0			0
$281$	6.44092	−	2.66791i	0.384233	−	0.159154i	−0.182202	−	0.983261i	$-0.558322\pi$
$281$	6.44092	−	2.66791i	0.384233	−	0.159154i	0.566435	+	0.824107i	$0.308322\pi$
$282$		0			0
$283$	14.0201	+	2.78877i	0.833408	+	0.165775i	0.593310	−	0.804974i	$-0.297821\pi$
$283$	14.0201	+	2.78877i	0.833408	+	0.165775i	0.240097	+	0.970749i	$0.422821\pi$
$284$		0			0
$285$	−1.25319	+	1.25319i	−0.0742324	+	0.0742324i
$286$		0			0
$287$	−2.80701	−	1.16270i	−0.165693	−	0.0686322i
$288$		0			0
$289$	2.72739	+	16.7798i	0.160435	+	0.987046i
$290$		0			0
$291$	6.55108	−	15.8157i	0.384031	−	0.927133i
$292$		0			0
$293$	−23.6925	−	23.6925i	−1.38413	−	1.38413i	−0.837134	−	0.546997i	$-0.815771\pi$
$293$	−23.6925	−	23.6925i	−1.38413	−	1.38413i	−0.546997	−	0.837134i	$-0.684229\pi$
$294$		0			0
$295$	0.0156580	−	0.0787183i	0.000911647	−	0.00458316i
$296$		0			0
$297$	12.8622	+	31.0521i	0.746339	+	1.80182i
$298$		0			0
$299$	−5.17456	−	7.74427i	−0.299252	−	0.447863i
$300$		0			0
$301$	8.16025	+	5.45250i	0.470349	+	0.314277i
$302$		0			0
$303$	26.7040	−	5.31176i	1.53411	−	0.305153i
$304$		0			0
$305$			9.42207i			0.539506i
$306$		0			0
$307$		−	26.6961i		−	1.52363i	−0.647797	−	0.761813i	$-0.724310\pi$
$307$		−	26.6961i		−	1.52363i	0.647797	−	0.761813i	$-0.275690\pi$
$308$		0			0
$309$	−5.25331	+	1.04495i	−0.298850	+	0.0594450i
$310$		0			0
$311$	−26.8467	−	17.9384i	−1.52234	−	1.01719i	−0.984748	−	0.173989i	$-0.944334\pi$
$311$	−26.8467	−	17.9384i	−1.52234	−	1.01719i	−0.537592	−	0.843205i	$-0.680666\pi$
$312$		0			0
$313$	−8.56680	−	12.8211i	−0.484224	−	0.724693i	0.506251	−	0.862386i	$-0.331031\pi$
$313$	−8.56680	−	12.8211i	−0.484224	−	0.724693i	−0.990475	+	0.137694i	$0.956031\pi$
$314$		0			0
$315$	0.476257	+	1.14979i	0.0268340	+	0.0647831i
$316$		0			0
$317$	0.445744	−	2.24090i	0.0250355	−	0.125862i	−0.966247	−	0.257619i	$-0.917062\pi$
$317$	0.445744	−	2.24090i	0.0250355	−	0.125862i	0.991282	+	0.131757i	$0.0420620\pi$
$318$		0			0
$319$	12.8490	+	12.8490i	0.719405	+	0.719405i
$320$		0			0
$321$	8.42676	−	20.3440i	0.470336	−	1.13549i
$322$		0			0
$323$	−5.33194	+	2.73038i	−0.296677	+	0.151922i
$324$		0			0
$325$	−16.2908	−	6.74785i	−0.903649	−	0.374303i
$326$		0			0
$327$	−2.82164	+	2.82164i	−0.156037	+	0.156037i
$328$		0			0
$329$	−22.5042	−	4.47637i	−1.24070	−	0.246790i
$330$		0			0
$331$	−20.1510	+	8.34682i	−1.10760	+	0.458783i	−0.860110	−	0.510108i	$-0.829605\pi$
$331$	−20.1510	+	8.34682i	−1.10760	+	0.458783i	−0.247489	+	0.968891i	$0.579605\pi$
$332$		0			0
$333$	−5.97893	+	3.99499i	−0.327643	+	0.218924i
$334$		0			0
$335$	−3.76802	+	5.63925i	−0.205869	+	0.308105i
$336$		0			0
$337$	4.43095	+	22.2759i	0.241369	+	1.21344i	0.891287	+	0.453440i	$0.149803\pi$
$337$	4.43095	+	22.2759i	0.241369	+	1.21344i	−0.649918	+	0.760005i	$0.725197\pi$
$338$		0			0
$339$	22.2468			1.20828
$340$		0			0
$341$	26.9806			1.46108
$342$		0			0
$343$	3.91920	+	19.7032i	0.211617	+	1.06387i
$344$		0			0
$345$	1.55354	−	2.32503i	0.0836396	−	0.125176i
$346$		0			0
$347$	15.8449	−	10.5872i	0.850599	−	0.568352i	−0.0520914	−	0.998642i	$-0.516589\pi$
$347$	15.8449	−	10.5872i	0.850599	−	0.568352i	0.902691	+	0.430290i	$0.141589\pi$
$348$		0			0
$349$	26.6494	−	11.0386i	1.42651	−	0.590880i	0.470024	−	0.882654i	$-0.344245\pi$
$349$	26.6494	−	11.0386i	1.42651	−	0.590880i	0.956487	+	0.291774i	$0.0942454\pi$
$350$		0			0
$351$	−22.4116	−	4.45794i	−1.19624	−	0.237947i
$352$		0			0
$353$	−17.3428	+	17.3428i	−0.923063	+	0.923063i	−0.997245	−	0.0741821i	$-0.976365\pi$
$353$	−17.3428	+	17.3428i	−0.923063	+	0.923063i	0.0741821	+	0.997245i	$0.476365\pi$
$354$		0			0
$355$	1.81796	+	0.753026i	0.0964876	+	0.0399665i
$356$		0			0
$357$	−1.02280	−	12.6678i	−0.0541325	−	0.670451i
$358$		0			0
$359$	2.90036	−	7.00208i	0.153075	−	0.369556i	−0.828675	−	0.559729i	$-0.810905\pi$
$359$	2.90036	−	7.00208i	0.153075	−	0.369556i	0.981750	+	0.190174i	$0.0609051\pi$
$360$		0			0
$361$	11.9424	+	11.9424i	0.628549	+	0.628549i
$362$		0			0
$363$	−7.23906	+	36.3932i	−0.379952	+	1.91015i
$364$		0			0
$365$	2.44202	+	5.89556i	0.127821	+	0.308588i
$366$		0			0
$367$	13.5738	+	20.3147i	0.708548	+	1.06042i	0.994759	+	0.102250i	$0.0326042\pi$
$367$	13.5738	+	20.3147i	0.708548	+	1.06042i	−0.286211	+	0.958167i	$0.592396\pi$
$368$		0			0
$369$	−0.917953	−	0.613357i	−0.0477867	−	0.0319301i
$370$		0			0
$371$	−5.23671	+	1.04165i	−0.271877	+	0.0540796i
$372$		0			0
$373$			32.6500i			1.69055i	0.534329	+	0.845277i	$0.320564\pi$
$373$			32.6500i			1.69055i	−0.534329	+	0.845277i	$0.679436\pi$
$374$		0			0
$375$		−	11.3931i		−	0.588336i
$376$		0			0
$377$	−12.1166	+	2.41014i	−0.624037	+	0.124129i
$378$		0			0
$379$	−28.3478	−	18.9414i	−1.45613	−	0.972953i	−0.996390	−	0.0848974i	$-0.972944\pi$
$379$	−28.3478	−	18.9414i	−1.45613	−	0.972953i	−0.459737	−	0.888055i	$-0.652056\pi$
$380$		0			0
$381$	11.8944	+	17.8013i	0.609370	+	0.911987i
$382$		0			0
$383$	−9.14594	−	22.0803i	−0.467336	−	1.12825i	−0.965322	−	0.261063i	$-0.915927\pi$
$383$	−9.14594	−	22.0803i	−0.467336	−	1.12825i	0.497986	−	0.867185i	$-0.334073\pi$
$384$		0			0
$385$	−1.94495	+	9.77791i	−0.0991237	+	0.498328i
$386$		0			0
$387$	2.52166	+	2.52166i	0.128183	+	0.128183i
$388$		0			0
$389$	3.33304	−	8.04667i	0.168992	−	0.407982i	−0.816582	−	0.577230i	$-0.804134\pi$
$389$	3.33304	−	8.04667i	0.168992	−	0.407982i	0.985574	+	0.169247i	$0.0541337\pi$
$390$		0			0
$391$	7.41063	−	5.86645i	0.374772	−	0.296679i
$392$		0			0
$393$	−19.2616	−	7.97842i	−0.971619	−	0.402458i
$394$		0			0
$395$	−0.383402	+	0.383402i	−0.0192911	+	0.0192911i
$396$		0			0
$397$	1.39635	+	0.277752i	0.0700810	+	0.0139400i	0.230006	−	0.973189i	$-0.426125\pi$
$397$	1.39635	+	0.277752i	0.0700810	+	0.0139400i	−0.159925	+	0.987129i	$0.551125\pi$
$398$		0			0
$399$	4.13744	−	1.71379i	0.207131	−	0.0857966i
$400$		0			0
$401$	6.27920	−	4.19562i	0.313568	−	0.209519i	−0.388820	−	0.921314i	$-0.627117\pi$
$401$	6.27920	−	4.19562i	0.313568	−	0.209519i	0.702388	+	0.711794i	$0.252117\pi$
$402$		0			0
$403$	−10.1909	+	15.2518i	−0.507647	+	0.759748i
$404$		0			0
$405$	−0.983623	−	4.94501i	−0.0488766	−	0.245719i
$406$		0			0
$407$	−57.6033			−2.85529
$408$		0			0
$409$	2.27542			0.112512			0.0562561	−	0.998416i	$-0.482084\pi$
$409$	2.27542			0.112512			0.0562561	+	0.998416i	$0.482084\pi$
$410$		0			0
$411$	4.63281	+	23.2907i	0.228520	+	1.14885i
$412$		0			0
$413$	−0.112675	+	0.168630i	−0.00554436	+	0.00829773i
$414$		0			0
$415$	0.178059	−	0.118975i	0.00874056	−	0.00584025i
$416$		0			0
$417$	7.36529	−	3.05080i	0.360680	−	0.149398i
$418$		0			0
$419$	11.8423	+	2.35558i	0.578534	+	0.115078i	0.475679	−	0.879619i	$-0.342202\pi$
$419$	11.8423	+	2.35558i	0.578534	+	0.115078i	0.102855	+	0.994696i	$0.467202\pi$
$420$		0			0
$421$	−12.6612	+	12.6612i	−0.617069	+	0.617069i	−0.944778	−	0.327710i	$-0.893723\pi$
$421$	−12.6612	+	12.6612i	−0.617069	+	0.617069i	0.327710	+	0.944778i	$0.393723\pi$
$422$		0			0
$423$	−7.70284	−	3.19062i	−0.374525	−	0.155133i
$424$		0			0
$425$	5.49493	−	17.0290i	0.266543	−	0.826026i
$426$		0			0
$427$	9.11112	−	21.9962i	0.440918	−	1.06447i
$428$		0			0
$429$	−25.7775	−	25.7775i	−1.24455	−	1.24455i
$430$		0			0
$431$	5.64894	−	28.3991i	0.272100	−	1.36794i	−0.566891	−	0.823793i	$-0.691854\pi$
$431$	5.64894	−	28.3991i	0.272100	−	1.36794i	0.838991	−	0.544145i	$-0.183146\pi$
$432$		0			0
$433$	−3.21946	−	7.77247i	−0.154718	−	0.373521i	0.827447	−	0.561543i	$-0.189792\pi$
$433$	−3.21946	−	7.77247i	−0.154718	−	0.373521i	−0.982165	+	0.188022i	$0.939792\pi$
$434$		0			0
$435$	−2.06061	−	3.08391i	−0.0987985	−	0.147862i
$436$		0			0
$437$	2.76921	+	1.85033i	0.132469	+	0.0885132i
$438$		0			0
$439$	3.01800	−	0.600318i	0.144041	−	0.0286516i	−0.122543	−	0.992463i	$-0.539105\pi$
$439$	3.01800	−	0.600318i	0.144041	−	0.0286516i	0.266584	+	0.963812i	$0.414105\pi$
$440$		0			0
$441$			2.07748i			0.0989277i
$442$		0			0
$443$			0.275866i			0.0131068i	0.999979	+	0.00655340i	$0.00208603\pi$
$443$			0.275866i			0.0131068i	−0.999979	+	0.00655340i	$0.997914\pi$
$444$		0			0
$445$	8.79403	−	1.74924i	0.416877	−	0.0829220i
$446$		0			0
$447$	−9.70353	−	6.48369i	−0.458961	−	0.306668i
$448$		0			0
$449$	−16.0469	−	24.0159i	−0.757300	−	1.13338i	−0.987094	−	0.160141i	$-0.948805\pi$
$449$	−16.0469	−	24.0159i	−0.757300	−	1.13338i	0.229794	−	0.973239i	$-0.426195\pi$
$450$		0			0
$451$	−3.38442	−	8.17071i	−0.159366	−	0.384744i
$452$		0			0
$453$	−0.180240	+	0.906129i	−0.00846842	+	0.0425736i
$454$		0			0
$455$	−4.79271	−	4.79271i	−0.224686	−	0.224686i
$456$		0			0
$457$	2.67532	−	6.45880i	0.125146	−	0.302130i	−0.848872	−	0.528598i	$-0.822718\pi$
$457$	2.67532	−	6.45880i	0.125146	−	0.302130i	0.974019	+	0.226468i	$0.0727179\pi$
$458$		0			0
$459$	2.67884	−	23.0331i	0.125038	−	1.07509i
$460$		0			0
$461$	−15.4068	−	6.38170i	−0.717566	−	0.297225i	−0.00613444	−	0.999981i	$-0.501953\pi$
$461$	−15.4068	−	6.38170i	−0.717566	−	0.297225i	−0.711431	+	0.702756i	$0.751953\pi$
$462$		0			0
$463$	−26.1409	+	26.1409i	−1.21487	+	1.21487i	−0.245463	+	0.969406i	$0.578940\pi$
$463$	−26.1409	+	26.1409i	−1.21487	+	1.21487i	−0.969406	+	0.245463i	$0.921060\pi$
$464$		0			0
$465$	−5.40130	−	1.07438i	−0.250479	−	0.0498234i
$466$		0			0
$467$	4.94703	−	2.04913i	0.228921	−	0.0948223i	−0.265275	−	0.964173i	$-0.585463\pi$
$467$	4.94703	−	2.04913i	0.228921	−	0.0948223i	0.494196	+	0.869351i	$0.335463\pi$
$468$		0			0
$469$	14.2497	−	9.52138i	0.657992	−	0.439656i
$470$		0			0
$471$	4.76990	−	7.13866i	0.219786	−	0.328932i
$472$		0			0
$473$	5.57324	+	28.0186i	0.256258	+	1.28830i
$474$		0			0
$475$	6.30524			0.289304
$476$		0			0
$477$	−1.94013			−0.0888322
$478$		0			0
$479$	1.84210	+	9.26085i	0.0841676	+	0.423139i	0.999778	+	0.0210722i	$0.00670799\pi$
$479$	1.84210	+	9.26085i	0.0841676	+	0.423139i	−0.915610	+	0.402067i	$0.868292\pi$
$480$		0			0
$481$	21.7576	−	32.5625i	0.992060	−	1.48472i
$482$		0			0
$483$	−5.87510	+	3.92562i	−0.267326	+	0.178622i
$484$		0			0
$485$	8.55940	−	3.54542i	0.388662	−	0.160989i
$486$		0			0
$487$	−0.144124	−	0.0286680i	−0.00653088	−	0.00129907i	0.191824	−	0.981429i	$-0.438560\pi$
$487$	−0.144124	−	0.0286680i	−0.00653088	−	0.00129907i	−0.198355	+	0.980130i	$0.563560\pi$
$488$		0			0
$489$	14.6047	−	14.6047i	0.660449	−	0.660449i
$490$		0			0
$491$	−5.79184	−	2.39906i	−0.261382	−	0.108268i	0.248144	−	0.968723i	$-0.420179\pi$
$491$	−5.79184	−	2.39906i	−0.261382	−	0.108268i	−0.509526	+	0.860455i	$0.670179\pi$
$492$		0			0
$493$	−3.42737	−	12.0590i	−0.154361	−	0.543108i
$494$		0			0
$495$	−1.38630	+	3.34682i	−0.0623095	+	0.150428i
$496$		0			0
$497$	−3.51594	−	3.51594i	−0.157711	−	0.157711i
$498$		0			0
$499$	−4.94943	+	24.8825i	−0.221567	+	1.11389i	0.696527	+	0.717530i	$0.254727\pi$
$499$	−4.94943	+	24.8825i	−0.221567	+	1.11389i	−0.918094	+	0.396362i	$0.870273\pi$
$500$		0			0
$501$	7.32598	+	17.6865i	0.327301	+	0.790174i
$502$		0			0
$503$	10.4418	+	15.6273i	0.465578	+	0.696786i	0.987748	−	0.156055i	$-0.0498776\pi$
$503$	10.4418	+	15.6273i	0.465578	+	0.696786i	−0.522171	+	0.852841i	$0.674878\pi$
$504$		0			0
$505$	12.2519	+	8.18646i	0.545203	+	0.364293i
$506$		0			0
$507$	5.16611	−	1.02760i	0.229435	−	0.0456375i
$508$		0			0
$509$			14.0438i			0.622479i	0.950332	+	0.311239i	$0.100744\pi$
$509$			14.0438i			0.622479i	−0.950332	+	0.311239i	$0.899256\pi$
$510$		0			0
$511$		−	16.1248i		−	0.713321i
$512$		0			0
$513$	8.01398	−	1.59408i	0.353826	−	0.0703804i
$514$		0			0
$515$	−2.41024	−	1.61047i	−0.106208	−	0.0709657i
$516$		0			0
$517$	−37.1060	−	55.5331i	−1.63192	−	2.44234i
$518$		0			0
$519$	−4.98860	−	12.0436i	−0.218975	−	0.528653i
$520$		0			0
$521$	4.50770	−	22.6617i	0.197486	−	0.992829i	−0.747137	−	0.664670i	$-0.768572\pi$
$521$	4.50770	−	22.6617i	0.197486	−	0.992829i	0.944623	−	0.328158i	$-0.106428\pi$
$522$		0			0
$523$	16.4969	+	16.4969i	0.721359	+	0.721359i	0.968882	−	0.247523i	$-0.0796167\pi$
$523$	16.4969	+	16.4969i	0.721359	+	0.721359i	−0.247523	+	0.968882i	$0.579617\pi$
$524$		0			0
$525$	−5.11918	+	12.3588i	−0.223419	+	0.539382i
$526$		0			0
$527$	−16.2593	−	9.06242i	−0.708266	−	0.394765i
$528$		0			0
$529$	16.3944	+	6.79077i	0.712798	+	0.295251i
$530$		0			0
$531$	−0.0521096	+	0.0521096i	−0.00226136	+	0.00226136i
$532$		0			0
$533$	5.89715	+	1.17302i	0.255434	+	0.0508090i
$534$		0			0
$535$	11.0101	−	4.56053i	0.476008	−	0.197169i
$536$		0			0
$537$	19.5786	−	13.0820i	0.844880	−	0.564531i
$538$		0			0
$539$	−9.24585	+	13.8374i	−0.398247	+	0.596019i
$540$		0			0
$541$	2.18195	+	10.9694i	0.0938095	+	0.471612i	0.998921	+	0.0464384i	$0.0147871\pi$
$541$	2.18195	+	10.9694i	0.0938095	+	0.471612i	−0.905112	+	0.425174i	$0.860213\pi$
$542$		0			0
$543$	−27.4504			−1.17801
$544$		0			0
$545$	−2.15959			−0.0925066
$546$		0			0
$547$	0.783986	+	3.94137i	0.0335208	+	0.168521i	0.993920	−	0.110109i	$-0.0351199\pi$
$547$	0.783986	+	3.94137i	0.0335208	+	0.168521i	−0.960399	+	0.278629i	$0.910120\pi$
$548$		0			0
$549$	4.80636	−	7.19322i	0.205130	−	0.306999i
$550$		0			0
$551$	3.67307	−	2.45427i	0.156478	−	0.104555i
$552$		0			0
$553$	1.26582	−	0.524319i	0.0538281	−	0.0222963i
$554$		0			0
$555$	11.5317	+	2.29380i	0.489494	+	0.0973664i
$556$		0			0
$557$	27.3910	−	27.3910i	1.16059	−	1.16059i	0.176249	−	0.984346i	$-0.443604\pi$
$557$	27.3910	−	27.3910i	1.16059	−	1.16059i	0.984346	−	0.176249i	$-0.0563964\pi$
$558$		0			0
$559$	−17.9437	−	7.43251i	−0.758936	−	0.314362i
$560$		0			0
$561$	23.9684	−	28.1788i	1.01195	−	1.18971i
$562$		0			0
$563$	−4.44883	+	10.7404i	−0.187496	+	0.452655i	−0.989476	−	0.144695i	$-0.953780\pi$
$563$	−4.44883	+	10.7404i	−0.187496	+	0.452655i	0.801980	+	0.597350i	$0.203780\pi$
$564$		0			0
$565$	8.51348	+	8.51348i	0.358165	+	0.358165i
$566$		0			0
$567$	−2.48551	+	12.4955i	−0.104381	+	0.524761i
$568$		0			0
$569$	−4.58727	−	11.0746i	−0.192308	−	0.464273i	0.798086	−	0.602543i	$-0.205846\pi$
$569$	−4.58727	−	11.0746i	−0.192308	−	0.464273i	−0.990395	+	0.138270i	$0.955846\pi$
$570$		0			0
$571$	−7.09451	−	10.6177i	−0.296896	−	0.444336i	0.652790	−	0.757539i	$-0.273598\pi$
$571$	−7.09451	−	10.6177i	−0.296896	−	0.444336i	−0.949686	+	0.313202i	$0.898598\pi$
$572$		0			0
$573$	−11.6337	−	7.77337i	−0.486004	−	0.324737i
$574$		0			0
$575$	−9.75725	+	1.94084i	−0.406905	+	0.0809385i
$576$		0			0
$577$		−	5.19597i		−	0.216311i	−0.994134	−	0.108156i	$-0.965506\pi$
$577$		−	5.19597i		−	0.216311i	0.994134	−	0.108156i	$-0.0344944\pi$
$578$		0			0
$579$		−	28.4029i		−	1.18039i
$580$		0			0
$581$	−0.530734	+	0.105570i	−0.0220185	+	0.00437976i
$582$		0			0
$583$	−12.9225	−	8.63454i	−0.535195	−	0.357606i
$584$		0			0
$585$	−1.36829	−	2.04780i	−0.0565720	−	0.0846660i
$586$		0			0
$587$	9.13915	+	22.0639i	0.377213	+	0.910673i	0.992486	+	0.122359i	$0.0390459\pi$
$587$	9.13915	+	22.0639i	0.377213	+	0.910673i	−0.615273	+	0.788314i	$0.710954\pi$
$588$		0			0
$589$	1.27964	−	6.43317i	0.0527265	−	0.265074i
$590$		0			0
$591$	−24.8746	−	24.8746i	−1.02320	−	1.02320i
$592$		0			0
$593$	−7.01228	+	16.9291i	−0.287960	+	0.695196i	−0.999976	−	0.00696686i	$-0.997782\pi$
$593$	−7.01228	+	16.9291i	−0.287960	+	0.695196i	0.712016	+	0.702163i	$0.247782\pi$
$594$		0			0
$595$	4.45635	−	5.23917i	0.182693	−	0.214785i
$596$		0			0
$597$	26.9536	+	11.1646i	1.10314	+	0.456935i
$598$		0			0
$599$	−3.47924	+	3.47924i	−0.142158	+	0.142158i	−0.774604	−	0.632446i	$-0.782051\pi$
$599$	−3.47924	+	3.47924i	−0.142158	+	0.142158i	0.632446	+	0.774604i	$0.282051\pi$
$600$		0			0
$601$	−34.4497	−	6.85248i	−1.40523	−	0.279518i	−0.566501	−	0.824061i	$-0.691703\pi$
$601$	−34.4497	−	6.85248i	−1.40523	−	0.279518i	−0.838733	+	0.544543i	$0.816703\pi$
$602$		0			0
$603$	5.75335	−	2.38312i	0.234295	−	0.0970480i
$604$		0			0
$605$	−16.6973	+	11.1568i	−0.678844	+	0.453589i
$606$		0			0
$607$	7.98248	−	11.9466i	0.323999	−	0.484899i	−0.633337	−	0.773876i	$-0.718315\pi$
$607$	7.98248	−	11.9466i	0.323999	−	0.484899i	0.957336	+	0.288977i	$0.0933152\pi$
$608$		0			0
$609$	1.82843	+	9.19212i	0.0740916	+	0.372484i
$610$		0			0
$611$	45.4077			1.83700
$612$		0			0
$613$	−28.3888			−1.14661			−0.573305	−	0.819342i	$-0.694339\pi$
$613$	−28.3888			−1.14661			−0.573305	+	0.819342i	$0.694339\pi$
$614$		0			0
$615$	0.352170	+	1.77048i	0.0142009	+	0.0713926i
$616$		0			0
$617$	−10.8921	+	16.3011i	−0.438498	+	0.656258i	−0.983234	−	0.182349i	$-0.941630\pi$
$617$	−10.8921	+	16.3011i	−0.438498	+	0.656258i	0.544736	+	0.838608i	$0.316630\pi$
$618$		0			0
$619$	−9.04157	+	6.04138i	−0.363411	+	0.242824i	−0.723847	−	0.689960i	$-0.757628\pi$
$619$	−9.04157	+	6.04138i	−0.363411	+	0.242824i	0.360436	+	0.932784i	$0.382628\pi$
$620$		0			0
$621$	−11.9108	+	4.93362i	−0.477965	+	0.197979i
$622$		0			0
$623$	−22.2215	−	4.42014i	−0.890287	−	0.177089i
$624$		0			0
$625$	−10.9837	+	10.9837i	−0.439347	+	0.439347i
$626$		0			0
$627$	12.0434	+	4.98852i	0.480965	+	0.199222i
$628$		0			0
$629$	34.7134	+	19.3482i	1.38412	+	0.771463i
$630$		0			0
$631$	17.1253	−	41.3441i	0.681747	−	1.64588i	−0.0790322	−	0.996872i	$-0.525183\pi$
$631$	17.1253	−	41.3441i	0.681747	−	1.64588i	0.760779	−	0.649011i	$-0.224817\pi$
$632$		0			0
$633$	−15.8493	−	15.8493i	−0.629952	−	0.629952i
$634$		0			0
$635$	−2.26045	+	11.3641i	−0.0897033	+	0.450969i
$636$		0			0
$637$	−4.32983	−	10.4531i	−0.171554	−	0.414169i
$638$		0			0
$639$	−1.00378	−	1.50227i	−0.0397091	−	0.0594288i
$640$		0			0
$641$	22.2117	+	14.8414i	0.877309	+	0.586199i	0.910619	−	0.413246i	$-0.135605\pi$
$641$	22.2117	+	14.8414i	0.877309	+	0.586199i	−0.0333104	+	0.999445i	$0.510605\pi$
$642$		0			0
$643$	−44.7690	+	8.90512i	−1.76552	+	0.351184i	−0.967776	−	0.251814i	$-0.918973\pi$
$643$	−44.7690	+	8.90512i	−1.76552	+	0.351184i	−0.797743	+	0.602997i	$0.793973\pi$
$644$		0			0
$645$		−	5.83102i		−	0.229596i
$646$		0			0
$647$			16.3446i			0.642573i	0.946982	+	0.321286i	$0.104115\pi$
$647$			16.3446i			0.642573i	−0.946982	+	0.321286i	$0.895885\pi$
$648$		0			0
$649$	−0.578998	+	0.115170i	−0.0227277	+	0.00452081i
$650$		0			0
$651$	11.5706	+	7.73124i	0.453488	+	0.303011i
$652$		0			0
$653$	−1.59099	−	2.38109i	−0.0622604	−	0.0931793i	0.799033	−	0.601287i	$-0.205345\pi$
$653$	−1.59099	−	2.38109i	−0.0622604	−	0.0931793i	−0.861294	+	0.508108i	$0.830345\pi$
$654$		0			0
$655$	−4.31789	−	10.4243i	−0.168714	−	0.407311i
$656$		0			0
$657$	1.14308	−	5.74664i	0.0445957	−	0.224198i
$658$		0			0
$659$	27.4487	+	27.4487i	1.06925	+	1.06925i	0.997417	+	0.0718311i	$0.0228843\pi$
$659$	27.4487	+	27.4487i	1.06925	+	1.06925i	0.0718311	+	0.997417i	$0.477116\pi$
$660$		0			0
$661$	2.69700	−	6.51114i	0.104901	−	0.253254i	−0.862710	−	0.505699i	$-0.831235\pi$
$661$	2.69700	−	6.51114i	0.104901	−	0.253254i	0.967611	+	0.252445i	$0.0812347\pi$
$662$		0			0
$663$	6.87596	+	24.1926i	0.267040	+	0.939563i
$664$		0			0
$665$	2.23917	+	0.927494i	0.0868313	+	0.0359667i
$666$		0			0
$667$	−4.92856	+	4.92856i	−0.190835	+	0.190835i
$668$		0			0
$669$	−2.24452	−	0.446463i	−0.0867781	−	0.0172612i
$670$		0			0
$671$	64.0269	−	26.5208i	2.47173	−	1.02383i
$672$		0			0
$673$	−30.0915	+	20.1065i	−1.15994	+	0.775048i	−0.978071	−	0.208274i	$-0.933215\pi$
$673$	−30.0915	+	20.1065i	−1.15994	+	0.775048i	−0.181871	+	0.983322i	$0.558215\pi$
$674$		0			0
$675$	−13.5599	+	20.2938i	−0.521921	+	0.781111i
$676$		0			0
$677$	2.86033	+	14.3799i	0.109931	+	0.552663i	0.996019	+	0.0891443i	$0.0284132\pi$
$677$	2.86033	+	14.3799i	0.109931	+	0.552663i	−0.886087	+	0.463518i	$0.846587\pi$
$678$		0			0
$679$	−23.4107			−0.898420
$680$		0			0
$681$	−5.79509			−0.222068
$682$		0			0
$683$	3.11209	+	15.6456i	0.119081	+	0.598660i	0.993533	+	0.113548i	$0.0362215\pi$
$683$	3.11209	+	15.6456i	0.119081	+	0.598660i	−0.874452	+	0.485113i	$0.838779\pi$
$684$		0			0
$685$	−7.14008	+	10.6859i	−0.272808	+	0.408286i
$686$		0			0
$687$	−21.7065	+	14.5038i	−0.828153	+	0.553354i
$688$		0			0
$689$	9.76201	−	4.04356i	0.371903	−	0.154047i
$690$		0			0
$691$	2.10927	+	0.419559i	0.0802402	+	0.0159608i	0.235047	−	0.971984i	$-0.424476\pi$
$691$	2.10927	+	0.419559i	0.0802402	+	0.0159608i	−0.154807	+	0.987945i	$0.549476\pi$
$692$		0			0
$693$	6.47274	−	6.47274i	0.245879	−	0.245879i
$694$		0			0
$695$	3.98607	+	1.65108i	0.151200	+	0.0626291i
$696$		0			0
$697$	−0.704883	+	6.06069i	−0.0266993	+	0.229565i
$698$		0			0
$699$	−2.27294	+	5.48736i	−0.0859705	+	0.207551i
$700$		0			0
$701$	4.67789	+	4.67789i	0.176682	+	0.176682i	0.789908	−	0.613226i	$-0.210128\pi$
$701$	4.67789	+	4.67789i	0.176682	+	0.176682i	−0.613226	+	0.789908i	$0.710128\pi$
$702$		0			0
$703$	−2.73201	+	13.7348i	−0.103040	+	0.518016i
$704$		0			0
$705$	5.21696	+	12.5949i	0.196482	+	0.474350i
$706$		0			0
$707$	−20.6863	−	30.9592i	−0.777987	−	1.16434i
$708$		0			0
$709$	−6.89041	−	4.60403i	−0.258775	−	0.172908i	0.419415	−	0.907795i	$-0.362235\pi$
$709$	−6.89041	−	4.60403i	−0.258775	−	0.172908i	−0.678190	+	0.734887i	$0.737235\pi$
$710$		0			0
$711$	0.488286	−	0.0971262i	0.0183122	−	0.00364252i
$712$		0			0
$713$			10.3491i			0.387577i
$714$		0			0
$715$		−	19.7293i		−	0.737833i
$716$		0			0
$717$	−43.3186	+	8.61660i	−1.61776	+	0.321793i
$718$		0			0
$719$	13.1429	+	8.78181i	0.490148	+	0.327506i	0.775963	−	0.630779i	$-0.217264\pi$
$719$	13.1429	+	8.78181i	0.490148	+	0.327506i	−0.285815	+	0.958285i	$0.592264\pi$
$720$		0			0
$721$	4.06948	+	6.09040i	0.151555	+	0.226818i
$722$		0			0
$723$	−11.1047	−	26.8092i	−0.412990	−	0.997045i
$724$		0			0
$725$	−2.57432	+	12.9420i	−0.0956078	+	0.480653i
$726$		0			0
$727$	22.7318	+	22.7318i	0.843076	+	0.843076i	0.989258	−	0.146182i	$-0.0466985\pi$
$727$	22.7318	+	22.7318i	0.843076	+	0.843076i	−0.146182	+	0.989258i	$0.546699\pi$
$728$		0			0
$729$	−11.4651	+	27.6791i	−0.424632	+	1.02515i
$730$		0			0
$731$	6.05247	−	18.7568i	0.223859	−	0.693745i
$732$		0			0
$733$	20.7512	+	8.59541i	0.766461	+	0.317479i	0.731438	−	0.681908i	$-0.238849\pi$
$733$	20.7512	+	8.59541i	0.766461	+	0.317479i	0.0350232	+	0.999387i	$0.488849\pi$
$734$		0			0
$735$	2.40196	−	2.40196i	0.0885975	−	0.0885975i
$736$		0			0
$737$	48.9272	+	9.73222i	1.80225	+	0.358491i
$738$		0			0
$739$	43.4870	−	18.0129i	1.59969	−	0.662615i	0.608322	−	0.793690i	$-0.291843\pi$
$739$	43.4870	−	18.0129i	1.59969	−	0.662615i	0.991372	+	0.131075i	$0.0418428\pi$
$740$		0			0
$741$	−7.36889	+	4.92374i	−0.270703	+	0.180878i
$742$		0			0
$743$	−8.19762	+	12.2686i	−0.300742	+	0.450092i	−0.950806	−	0.309788i	$-0.899742\pi$
$743$	−8.19762	+	12.2686i	−0.300742	+	0.450092i	0.650064	+	0.759879i	$0.274742\pi$
$744$		0			0
$745$	−1.23218	−	6.19458i	−0.0451435	−	0.226952i
$746$		0			0
$747$	−0.196629			−0.00719428
$748$		0			0
$749$	−30.1135			−1.10032
$750$		0			0
$751$	−8.76165	−	44.0478i	−0.319717	−	1.60733i	−0.722055	−	0.691836i	$-0.756802\pi$
$751$	−8.76165	−	44.0478i	−0.319717	−	1.60733i	0.402337	−	0.915491i	$-0.368198\pi$
$752$		0			0
$753$	7.91226	−	11.8415i	0.288339	−	0.431529i
$754$		0			0
$755$	−0.415735	+	0.277785i	−0.0151302	+	0.0101096i
$756$		0			0
$757$	25.2396	−	10.4546i	0.917349	−	0.379978i	0.126484	−	0.991969i	$-0.459631\pi$
$757$	25.2396	−	10.4546i	0.917349	−	0.379978i	0.790865	+	0.611990i	$0.209631\pi$
$758$		0			0
$759$	−20.1724	−	4.01254i	−0.732212	−	0.145646i
$760$		0			0
$761$	−12.4584	+	12.4584i	−0.451618	+	0.451618i	−0.895891	−	0.444273i	$-0.853462\pi$
$761$	−12.4584	+	12.4584i	−0.451618	+	0.451618i	0.444273	+	0.895891i	$0.353462\pi$
$762$		0			0
$763$	5.04165	+	2.08832i	0.182520	+	0.0756022i
$764$		0			0
$765$	1.95957	−	1.55125i	0.0708486	−	0.0560856i
$766$		0			0
$767$	0.153591	−	0.370802i	0.00554586	−	0.0133889i
$768$		0			0
$769$	−10.5340	−	10.5340i	−0.379867	−	0.379867i	0.491187	−	0.871054i	$-0.336563\pi$
$769$	−10.5340	−	10.5340i	−0.379867	−	0.379867i	−0.871054	+	0.491187i	$0.836563\pi$
$770$		0			0
$771$	−1.43824	+	7.23050i	−0.0517968	+	0.260400i
$772$		0			0
$773$	−6.70315	−	16.1828i	−0.241096	−	0.582056i	0.756297	−	0.654229i	$-0.227007\pi$
$773$	−6.70315	−	16.1828i	−0.241096	−	0.582056i	−0.997392	+	0.0721727i	$0.977007\pi$
$774$		0			0
$775$	10.8851	+	16.2908i	0.391006	+	0.585181i
$776$		0			0
$777$	−24.7032	−	16.5061i	−0.886221	−	0.592154i
$778$		0			0
$779$	−2.10871	+	0.419449i	−0.0755526	+	0.0150283i
$780$		0			0
$781$		−	14.4734i		−	0.517900i
$782$		0			0
$783$			17.1001i			0.611109i
$784$		0			0
$785$	4.55721	−	0.906486i	0.162654	−	0.0323539i
$786$		0			0
$787$	2.24549	+	1.50039i	0.0800431	+	0.0534831i	0.594948	−	0.803764i	$-0.297173\pi$
$787$	2.24549	+	1.50039i	0.0800431	+	0.0534831i	−0.514905	+	0.857247i	$0.672173\pi$
$788$		0			0
$789$	22.3998	+	33.5237i	0.797455	+	1.19348i
$790$		0			0
$791$	−11.6425	−	28.1076i	−0.413961	−	0.999391i
$792$		0			0
$793$	−9.19193	+	46.2110i	−0.326415	+	1.64100i
$794$		0			0
$795$	2.24315	+	2.24315i	0.0795562	+	0.0795562i
$796$		0			0
$797$	−9.37385	+	22.6305i	−0.332039	+	0.801612i	0.666391	+	0.745602i	$0.267838\pi$
$797$	−9.37385	+	22.6305i	−0.332039	+	0.801612i	−0.998430	+	0.0560103i	$0.982162\pi$
$798$		0			0
$799$	3.70835	+	45.9293i	0.131192	+	1.62486i
$800$		0			0
$801$	−7.60607	−	3.15054i	−0.268747	−	0.111319i
$802$		0			0
$803$	33.1891	−	33.1891i	1.17122	−	1.17122i
$804$		0			0
$805$	−3.75057	−	0.746035i	−0.132190	−	0.0262943i
$806$		0			0
$807$	4.33043	−	1.79372i	0.152438	−	0.0631420i
$808$		0			0
$809$	−35.9588	+	24.0269i	−1.26424	+	0.844740i	−0.993039	−	0.117782i	$-0.962422\pi$
$809$	−35.9588	+	24.0269i	−1.26424	+	0.844740i	−0.271203	+	0.962522i	$0.587422\pi$
$810$		0			0
$811$	−20.8025	+	31.1332i	−0.730476	+	1.09323i	0.261302	+	0.965257i	$0.415848\pi$
$811$	−20.8025	+	31.1332i	−0.730476	+	1.09323i	−0.991777	+	0.127977i	$0.959152\pi$
$812$		0			0
$813$	9.23238	+	46.4143i	0.323794	+	1.62782i
$814$		0			0
$815$	11.1780			0.391548
$816$		0			0
$817$	6.94499			0.242974
$818$		0			0
$819$	1.21412	+	6.10381i	0.0424249	+	0.213284i
$820$		0			0
$821$	24.0701	−	36.0235i	0.840054	−	1.25723i	−0.124202	−	0.992257i	$-0.539637\pi$
$821$	24.0701	−	36.0235i	0.840054	−	1.25723i	0.964256	−	0.264972i	$-0.0853628\pi$
$822$		0			0
$823$	32.7295	−	21.8692i	1.14088	−	0.762311i	0.166238	−	0.986086i	$-0.446838\pi$
$823$	32.7295	−	21.8692i	1.14088	−	0.762311i	0.974641	+	0.223775i	$0.0718381\pi$
$824$		0			0
$825$	−35.9742	+	14.9010i	−1.25246	+	0.518786i
$826$		0			0
$827$	27.5139	+	5.47285i	0.956751	+	0.190310i	0.648686	−	0.761056i	$-0.275319\pi$
$827$	27.5139	+	5.47285i	0.956751	+	0.190310i	0.308064	+	0.951365i	$0.400319\pi$
$828$		0			0
$829$	−0.660040	+	0.660040i	−0.0229241	+	0.0229241i	−0.718476	−	0.695552i	$-0.755160\pi$
$829$	−0.660040	+	0.660040i	−0.0229241	+	0.0229241i	0.695552	+	0.718476i	$0.255160\pi$
$830$		0			0
$831$	5.16846	+	2.14085i	0.179292	+	0.0742651i
$832$		0			0
$833$	10.2196	−	5.23325i	0.354088	−	0.181322i
$834$		0			0
$835$	−3.96479	+	9.57185i	−0.137207	+	0.331248i
$836$		0			0
$837$	17.9536	+	17.9536i	0.620569	+	0.620569i
$838$		0			0
$839$	−3.38332	+	17.0091i	−0.116805	+	0.587220i	0.877403	+	0.479753i	$0.159274\pi$
$839$	−3.38332	+	17.0091i	−0.116805	+	0.587220i	−0.994209	+	0.107467i	$0.965726\pi$
$840$		0			0
$841$	−7.55990	−	18.2512i	−0.260686	−	0.629352i
$842$		0			0
$843$	5.81493	+	8.70266i	0.200277	+	0.299736i
$844$		0			0
$845$	2.37023	+	1.58374i	0.0815385	+	0.0544823i
$846$		0			0
$847$	49.7692	−	9.89972i	1.71009	−	0.340158i
$848$		0			0
$849$			21.4610i			0.736540i
$850$		0			0
$851$		−	22.0953i		−	0.757416i
$852$		0			0
$853$	8.62261	−	1.71514i	0.295232	−	0.0587254i	−0.0452518	−	0.998976i	$-0.514409\pi$
$853$	8.62261	−	1.71514i	0.295232	−	0.0587254i	0.340484	+	0.940250i	$0.389409\pi$
$854$		0			0
$855$	0.732256	+	0.489278i	0.0250426	+	0.0167329i
$856$		0			0
$857$	20.1122	+	30.1000i	0.687018	+	1.02820i	0.996996	+	0.0774517i	$0.0246783\pi$
$857$	20.1122	+	30.1000i	0.687018	+	1.02820i	−0.309978	+	0.950744i	$0.600322\pi$
$858$		0			0
$859$	−1.48067	−	3.57466i	−0.0505200	−	0.121966i	0.896605	−	0.442832i	$-0.146026\pi$
$859$	−1.48067	−	3.57466i	−0.0505200	−	0.121966i	−0.947125	+	0.320866i	$0.896026\pi$
$860$		0			0
$861$	0.889895	−	4.47380i	0.0303275	−	0.152467i
$862$		0			0
$863$	32.6793	+	32.6793i	1.11242	+	1.11242i	0.992823	+	0.119594i	$0.0381593\pi$
$863$	32.6793	+	32.6793i	1.11242	+	1.11242i	0.119594	+	0.992823i	$0.461841\pi$
$864$		0			0
$865$	2.69981	−	6.51793i	0.0917964	−	0.221616i
$866$		0			0
$867$	−23.9090	+	8.93070i	−0.811991	+	0.303303i
$868$		0			0
$869$	3.68457	+	1.52620i	0.124990	+	0.0517727i
$870$		0			0
$871$	−23.9820	+	23.9820i	−0.812598	+	0.812598i
$872$		0			0
$873$	−8.34320	−	1.65957i	−0.282375	−	0.0561678i
$874$		0			0
$875$	−14.3945	+	5.96240i	−0.486623	+	0.201566i
$876$		0			0
$877$	30.2817	−	20.2336i	1.02254	−	0.683240i	0.0731447	−	0.997321i	$-0.476697\pi$
$877$	30.2817	−	20.2336i	1.02254	−	0.683240i	0.949396	+	0.314081i	$0.101697\pi$
$878$		0			0
$879$	27.9472	−	41.8260i	0.942637	−	1.41076i
$880$		0			0
$881$	−4.93397	−	24.8047i	−0.166230	−	0.835693i	−0.970439	−	0.241347i	$-0.922411\pi$
$881$	−4.93397	−	24.8047i	−0.166230	−	0.835693i	0.804209	−	0.594346i	$-0.202589\pi$
$882$		0			0
$883$	14.0488			0.472780			0.236390	−	0.971658i	$-0.424036\pi$
$883$	14.0488			0.472780			0.236390	+	0.971658i	$0.424036\pi$
$884$		0			0
$885$	0.120497			0.00405045
$886$		0			0
$887$	5.67519	+	28.5311i	0.190554	+	0.957981i	0.951144	+	0.308748i	$0.0999100\pi$
$887$	5.67519	+	28.5311i	0.190554	+	0.957981i	−0.760590	+	0.649233i	$0.775090\pi$
$888$		0			0
$889$	16.2661	−	24.3440i	0.545549	−	0.816471i
$890$		0			0
$891$	−30.8348	+	20.6031i	−1.03300	+	0.690231i
$892$		0			0
$893$	−15.0010	+	6.21362i	−0.501990	+	0.207931i
$894$		0			0
$895$	12.4987	+	2.48614i	0.417785	+	0.0831026i
$896$		0			0
$897$	9.88764	−	9.88764i	0.330139	−	0.330139i
$898$		0			0
$899$	12.6821	+	5.25310i	0.422972	+	0.175201i
$900$		0			0
$901$	4.88725	+	9.54392i	0.162818	+	0.317954i
$902$		0			0
$903$	−5.63859	+	13.6128i	−0.187640	+	0.453004i
$904$		0			0
$905$	−10.5048	−	10.5048i	−0.349192	−	0.349192i
$906$		0			0
$907$	0.902376	−	4.53655i	0.0299629	−	0.150634i	−0.962908	−	0.269831i	$-0.913032\pi$
$907$	0.902376	−	4.53655i	0.0299629	−	0.150634i	0.992871	+	0.119197i	$0.0380321\pi$
$908$		0			0
$909$	−5.17759	−	12.4998i	−0.171730	−	0.414593i
$910$		0			0
$911$	2.26518	+	3.39008i	0.0750488	+	0.112318i	0.867095	−	0.498142i	$-0.165984\pi$
$911$	2.26518	+	3.39008i	0.0750488	+	0.112318i	−0.792047	+	0.610461i	$0.790984\pi$
$912$		0			0
$913$	−1.30968	−	0.875099i	−0.0433440	−	0.0289615i
$914$		0			0
$915$	−13.8737	+	2.75966i	−0.458652	+	0.0912315i
$916$		0			0
$917$			28.5113i			0.941528i
$918$		0			0
$919$			42.9256i			1.41598i	0.706220	+	0.707992i	$0.250399\pi$
$919$			42.9256i			1.41598i	−0.706220	+	0.707992i	$0.749601\pi$
$920$		0			0
$921$	39.3093	−	7.81910i	1.29528	−	0.257648i
$922$		0			0
$923$	8.18166	+	5.46681i	0.269303	+	0.179942i
$924$		0			0
$925$	−23.2397	−	34.7806i	−0.764115	−	1.14358i
$926$		0			0
$927$	1.01855	+	2.45901i	0.0334537	+	0.0807644i
$928$		0			0
$929$	−0.857745	+	4.31217i	−0.0281417	+	0.141478i	−0.992302	−	0.123843i	$-0.960478\pi$
$929$	−0.857745	+	4.31217i	−0.0281417	+	0.141478i	0.964160	+	0.265321i	$0.0854780\pi$
$930$		0			0
$931$	2.86083	+	2.86083i	0.0937600	+	0.0937600i
$932$		0			0
$933$	18.5506	−	44.7852i	0.607320	−	1.46620i
$934$		0			0
$935$	19.9559	−	1.61125i	0.652628	−	0.0526934i
$936$		0			0
$937$	4.62312	+	1.91496i	0.151031	+	0.0625590i	0.456918	−	0.889509i	$-0.348953\pi$
$937$	4.62312	+	1.91496i	0.151031	+	0.0625590i	−0.305888	+	0.952068i	$0.598953\pi$
$938$		0			0
$939$	16.3696	−	16.3696i	0.534202	−	0.534202i
$940$		0			0
$941$	−26.2898	−	5.22937i	−0.857023	−	0.170473i	−0.253027	−	0.967459i	$-0.581426\pi$
$941$	−26.2898	−	5.22937i	−0.857023	−	0.170473i	−0.603997	+	0.796987i	$0.706426\pi$
$942$		0			0
$943$	3.13409	−	1.29818i	0.102060	−	0.0422746i
$944$		0			0
$945$	−7.80071	+	5.21227i	−0.253757	+	0.169555i
$946$		0			0
$947$	22.2935	−	33.3646i	0.724443	−	1.08420i	−0.268228	−	0.963355i	$-0.586438\pi$
$947$	22.2935	−	33.3646i	0.724443	−	1.08420i	0.992671	−	0.120850i	$-0.0385619\pi$
$948$		0			0
$949$	6.22544	+	31.2974i	0.202086	+	1.01596i
$950$		0			0
$951$	3.43023			0.111233
$952$		0			0
$953$	−18.5020			−0.599338			−0.299669	−	0.954043i	$-0.596876\pi$
$953$	−18.5020			−0.599338			−0.299669	+	0.954043i	$0.596876\pi$
$954$		0			0
$955$	−1.47727	−	7.42676i	−0.0478035	−	0.240324i
$956$		0			0
$957$	−15.1564	+	22.6832i	−0.489937	+	0.733242i
$958$		0			0
$959$	27.0020	−	18.0422i	0.871941	−	0.582612i
$960$		0			0
$961$	−9.80985	+	4.06337i	−0.316447	+	0.131077i
$962$		0			0
$963$	−10.7320	−	2.13473i	−0.345834	−	0.0687906i
$964$		0			0
$965$	10.8693	−	10.8693i	0.349896	−	0.349896i
$966$		0			0
$967$	−12.8978	−	5.34244i	−0.414765	−	0.171801i	0.165535	−	0.986204i	$-0.447065\pi$
$967$	−12.8978	−	5.34244i	−0.414765	−	0.171801i	−0.580300	+	0.814403i	$0.697065\pi$
$968$		0			0
$969$	−5.58210	−	7.05143i	−0.179323	−	0.226524i
$970$		0			0
$971$	−1.61277	+	3.89357i	−0.0517562	+	0.124951i	−0.947643	−	0.319332i	$-0.896541\pi$
$971$	−1.61277	+	3.89357i	−0.0517562	+	0.124951i	0.895887	+	0.444283i	$0.146541\pi$
$972$		0			0
$973$	−7.70904	−	7.70904i	−0.247140	−	0.247140i
$974$		0			0
$975$	5.16458	−	25.9641i	0.165399	−	0.831517i
$976$		0			0
$977$	14.6299	+	35.3198i	0.468053	+	1.12998i	0.965012	+	0.262206i	$0.0844501\pi$
$977$	14.6299	+	35.3198i	0.468053	+	1.12998i	−0.496959	+	0.867774i	$0.665550\pi$
$978$		0			0
$979$	−36.6399	−	54.8355i	−1.17102	−	1.75255i
$980$		0			0
$981$	1.64873	+	1.10164i	0.0526398	+	0.0351728i
$982$		0			0
$983$	18.9887	−	3.77709i	0.605645	−	0.120470i	0.117264	−	0.993101i	$-0.462588\pi$
$983$	18.9887	−	3.77709i	0.605645	−	0.120470i	0.488381	+	0.872630i	$0.337588\pi$
$984$		0			0
$985$		−	19.0382i		−	0.606607i
$986$		0			0
$987$		−	34.4480i		−	1.09649i
$988$		0			0
$989$	−10.7473	+	2.13776i	−0.341743	+	0.0679769i
$990$		0			0
$991$	−1.77414	−	1.18544i	−0.0563575	−	0.0376569i	0.527072	−	0.849820i	$-0.323290\pi$
$991$	−1.77414	−	1.18544i	−0.0563575	−	0.0376569i	−0.583430	+	0.812164i	$0.698290\pi$
$992$		0			0
$993$	−18.1926	−	27.2271i	−0.577324	−	0.864026i
$994$		0			0
$995$	6.04222	+	14.5872i	0.191551	+	0.462446i
$996$		0			0
$997$	3.81274	−	19.1679i	0.120751	−	0.607055i	−0.872261	−	0.489040i	$-0.837347\pi$
$997$	3.81274	−	19.1679i	0.120751	−	0.607055i	0.993012	−	0.118014i	$-0.0376529\pi$
$998$		0			0
$999$	−38.3309	−	38.3309i	−1.21273	−	1.21273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.bx.g.159.1	yes	8
4.3	odd	2		544.2.bx.a.159.1	✓	8
17.3	odd	16		544.2.bx.a.479.1	yes	8
68.3	even	16	inner	544.2.bx.g.479.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bx.a.159.1	✓	8	4.3	odd	2
544.2.bx.a.479.1	yes	8	17.3	odd	16
544.2.bx.g.159.1	yes	8	1.1	even	1	trivial
544.2.bx.g.479.1	yes	8	68.3	even	16	inner

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:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.bx (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.292893 + 1.47247i) q^{3} +(-0.451406 + 0.675577i) q^{5} +(1.70711 - 1.14065i) q^{7} +(0.689246 - 0.285495i) q^{9} +(5.86143 + 1.16591i) q^{11} +(-2.87302 + 2.87302i) q^{13} +(-1.12698 - 0.466811i) q^{15} +(-3.14065 - 2.67139i) q^{17} +(0.555992 - 1.34228i) q^{19} +(2.17958 + 2.17958i) q^{21} +(-0.447215 + 2.24830i) q^{23} +(1.66078 + 4.00948i) q^{25} +(3.12453 + 4.67619i) q^{27} +(2.52814 + 1.68925i) q^{29} +(4.42788 - 0.880761i) q^{31} +8.97229i q^{33} +1.66818i q^{35} +(-9.45349 + 1.88042i) q^{37} +(-5.07193 - 3.38896i) q^{39} +(-0.822155 - 1.23044i) q^{41} +(1.82929 + 4.41629i) q^{43} +(-0.118256 + 0.594513i) q^{45} +(-7.90244 - 7.90244i) q^{47} +(-1.06566 + 2.57273i) q^{49} +(3.01367 - 5.40696i) q^{51} +(-2.40262 - 0.995200i) q^{53} +(-3.43355 + 3.43355i) q^{55} +(2.13932 + 0.425538i) q^{57} +(-0.0912618 + 0.0378019i) q^{59} +(9.64194 - 6.44254i) q^{61} +(0.850966 - 1.27356i) q^{63} +(-0.644047 - 3.23784i) q^{65} +8.34731 q^{67} -3.44155 q^{69} +(-0.472474 - 2.37529i) q^{71} +(4.36335 - 6.53022i) q^{73} +(-5.41742 + 3.61980i) q^{75} +(11.3360 - 4.69552i) q^{77} +(0.654509 + 0.130190i) q^{79} +(-4.38783 + 4.38783i) q^{81} +(-0.243503 - 0.100862i) q^{83} +(3.22243 - 0.915872i) q^{85} +(-1.74690 + 4.21738i) q^{87} +(-7.80317 - 7.80317i) q^{89} +(-1.62743 + 8.18166i) q^{91} +(2.59379 + 6.26197i) q^{93} +(0.655837 + 0.981530i) q^{95} +(-9.48083 - 6.33489i) q^{97} +(4.37283 - 0.869810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 16 q^{11} - 16 q^{13} - 16 q^{15} - 16 q^{17} + 16 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{29} + 8 q^{31} - 40 q^{37} - 24 q^{39} + 32 q^{43} + 24 q^{45} + 16 q^{47}+ \cdots - 16 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 16 * q^11 - 16 * q^13 - 16 * q^15 - 16 * q^17 + 16 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^29 + 8 * q^31 - 40 * q^37 - 24 * q^39 + 32 * q^43 + 24 * q^45 + 16 * q^47 - 8 * q^49 + 8 * q^51 + 16 * q^53 - 24 * q^55 - 24 * q^57 + 8 * q^59 + 24 * q^61 - 32 * q^63 - 16 * q^65 + 32 * q^67 + 16 * q^69 + 8 * q^71 + 24 * q^73 - 8 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^83 + 48 * q^85 - 40 * q^87 - 32 * q^89 - 40 * q^91 - 8 * q^93 + 56 * q^95 - 8 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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