LMFDB - Embedded newform 567.2.g.l.541.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(109,567)] 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("567.109"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-6,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 14x^{12} - 39x^{10} + 77x^{8} - 156x^{6} + 224x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 14x^12 - 39x^10 + 77x^8 - 156x^6 + 224x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.5
Root			$-1.04779 + 0.949812i$ of defining polynomial
Character	$\chi$	$=$	567.541
Dual form			567.2.g.l.109.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.298668 + 0.517308i) q^{2} +(0.821595 - 1.42304i) q^{4} +2.09557 q^{5} +(-1.51053 - 2.17216i) q^{7} +2.17621 q^{8} +(0.625881 + 1.08406i) q^{10} +1.65141 q^{11} +(0.213022 + 0.368965i) q^{13} +(0.672530 - 1.43017i) q^{14} +(-0.993225 - 1.72032i) q^{16} +(-3.03819 - 5.26230i) q^{17} +(-2.70625 + 4.68736i) q^{19} +(1.72171 - 2.98209i) q^{20} +(0.493225 + 0.854291i) q^{22} +7.63457 q^{23} -0.608573 q^{25} +(-0.127246 + 0.220396i) q^{26} +(-4.33213 + 0.364918i) q^{28} +(-1.82688 + 3.16426i) q^{29} +(2.65372 - 4.59638i) q^{31} +(2.76950 - 4.79691i) q^{32} +(1.81482 - 3.14336i) q^{34} +(-3.16543 - 4.55193i) q^{35} +(2.33890 - 4.05110i) q^{37} -3.23308 q^{38} +4.56041 q^{40} +(0.742827 + 1.28661i) q^{41} +(-4.24499 + 7.35253i) q^{43} +(1.35679 - 2.35004i) q^{44} +(2.28020 + 3.94943i) q^{46} +(5.66624 + 9.81422i) q^{47} +(-2.43658 + 6.56225i) q^{49} +(-0.181761 - 0.314820i) q^{50} +0.700071 q^{52} +(2.74496 + 4.75441i) q^{53} +3.46066 q^{55} +(-3.28724 - 4.72708i) q^{56} -2.18253 q^{58} +(-0.779098 + 1.34944i) q^{59} +(-2.52408 - 4.37184i) q^{61} +3.17033 q^{62} -0.664256 q^{64} +(0.446403 + 0.773193i) q^{65} +(2.61498 - 4.52928i) q^{67} -9.98464 q^{68} +(1.40933 - 2.99702i) q^{70} +12.5604 q^{71} +(-0.793753 - 1.37482i) q^{73} +2.79422 q^{74} +(4.44688 + 7.70222i) q^{76} +(-2.49452 - 3.58714i) q^{77} +(3.81482 + 6.60746i) q^{79} +(-2.08138 - 3.60505i) q^{80} +(-0.443717 + 0.768541i) q^{82} +(2.62806 - 4.55193i) q^{83} +(-6.36674 - 11.0275i) q^{85} -5.07137 q^{86} +3.59382 q^{88} +(-9.27808 + 16.0701i) q^{89} +(0.479675 - 1.02005i) q^{91} +(6.27252 - 10.8643i) q^{92} +(-3.38465 + 5.86239i) q^{94} +(-5.67114 + 9.82270i) q^{95} +(-6.87728 + 11.9118i) q^{97} +(-4.12243 + 0.699472i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} - 14 q^{10} - 6 q^{13} - 6 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} + 72 q^{40} - 10 q^{43} + 36 q^{46} + 4 q^{49} + 68 q^{52} + 8 q^{55} - 44 q^{58} - 36 q^{61} + 76 q^{64}+ \cdots - 14 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 - 14 * q^10 - 6 * q^13 - 6 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 + 72 * q^40 - 10 * q^43 + 36 * q^46 + 4 * q^49 + 68 * q^52 + 8 * q^55 - 44 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 + 104 * q^70 - 32 * q^73 - 58 * q^76 + 32 * q^79 + 2 * q^82 - 30 * q^85 - 144 * q^88 - 22 * q^91 - 54 * q^94 - 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.298668	+	0.517308i	0.211190	+	0.365792i	0.952087	−	0.305826i	$-0.0989327\pi$
$2$	0.298668	+	0.517308i	0.211190	+	0.365792i	−0.740897	+	0.671619i	$0.765599\pi$
$3$		0			0
$3$		0			0
$4$	0.821595	−	1.42304i	0.410797	−	0.711522i
$5$	2.09557			0.937169			0.468584	−	0.883419i	$-0.344764\pi$
$5$	2.09557			0.937169			0.468584	+	0.883419i	$0.344764\pi$
$6$		0			0
$7$	−1.51053	−	2.17216i	−0.570928	−	0.821000i
$7$	−1.51053	−	2.17216i	−0.570928	−	0.821000i
$8$	2.17621			0.769406
$9$		0			0
$10$	0.625881	+	1.08406i	0.197921	+	0.342809i
$11$	1.65141			0.497920			0.248960	−	0.968514i	$-0.419911\pi$
$11$	1.65141			0.497920			0.248960	+	0.968514i	$0.419911\pi$
$12$		0			0
$13$	0.213022	+	0.368965i	0.0590817	+	0.102333i	0.894053	−	0.447960i	$-0.147849\pi$
$13$	0.213022	+	0.368965i	0.0590817	+	0.102333i	−0.834972	+	0.550293i	$0.814516\pi$
$14$	0.672530	−	1.43017i	0.179741	−	0.382228i
$15$		0			0
$16$	−0.993225	−	1.72032i	−0.248306	−	0.430079i
$17$	−3.03819	−	5.26230i	−0.736869	−	1.27629i	−0.953899	−	0.300129i	$-0.902970\pi$
$17$	−3.03819	−	5.26230i	−0.736869	−	1.27629i	0.217030	−	0.976165i	$-0.430363\pi$
$18$		0			0
$19$	−2.70625	+	4.68736i	−0.620856	+	1.07535i	0.368471	+	0.929639i	$0.379881\pi$
$19$	−2.70625	+	4.68736i	−0.620856	+	1.07535i	−0.989327	+	0.145714i	$0.953452\pi$
$20$	1.72171	−	2.98209i	0.384986	−	0.666816i
$21$		0			0
$22$	0.493225	+	0.854291i	0.105156	+	0.182135i
$23$	7.63457			1.59192			0.795959	−	0.605351i	$-0.206967\pi$
$23$	7.63457			1.59192			0.795959	+	0.605351i	$0.206967\pi$
$24$		0			0
$25$	−0.608573			−0.121715
$26$	−0.127246	+	0.220396i	−0.0249550	+	0.0432233i
$27$		0			0
$28$	−4.33213	+	0.364918i	−0.818695	+	0.0689631i
$29$	−1.82688	+	3.16426i	−0.339244	+	0.587588i	−0.984291	−	0.176555i	$-0.943505\pi$
$29$	−1.82688	+	3.16426i	−0.339244	+	0.587588i	0.645047	+	0.764143i	$0.276838\pi$
$30$		0			0
$31$	2.65372	−	4.59638i	0.476623	−	0.825535i	−0.523018	−	0.852321i	$-0.675194\pi$
$31$	2.65372	−	4.59638i	0.476623	−	0.825535i	0.999641	+	0.0267866i	$0.00852747\pi$
$32$	2.76950	−	4.79691i	0.489583	−	0.847982i
$33$		0			0
$34$	1.81482	−	3.14336i	0.311239	−	0.539082i
$35$	−3.16543	−	4.55193i	−0.535056	−	0.769416i
$36$		0			0
$37$	2.33890	−	4.05110i	0.384513	−	0.665997i	−0.607188	−	0.794558i	$-0.707703\pi$
$37$	2.33890	−	4.05110i	0.384513	−	0.665997i	0.991702	+	0.128561i	$0.0410360\pi$
$38$	−3.23308			−0.524475
$39$		0			0
$40$	4.56041			0.721063
$41$	0.742827	+	1.28661i	0.116010	+	0.200935i	0.918183	−	0.396156i	$-0.129656\pi$
$41$	0.742827	+	1.28661i	0.116010	+	0.200935i	−0.802173	+	0.597092i	$0.796323\pi$
$42$		0			0
$43$	−4.24499	+	7.35253i	−0.647354	+	1.12125i	0.336398	+	0.941720i	$0.390791\pi$
$43$	−4.24499	+	7.35253i	−0.647354	+	1.12125i	−0.983752	+	0.179531i	$0.942542\pi$
$44$	1.35679	−	2.35004i	0.204544	−	0.354281i
$45$		0			0
$46$	2.28020	+	3.94943i	0.336198	+	0.582311i
$47$	5.66624	+	9.81422i	0.826506	+	1.43155i	0.900763	+	0.434312i	$0.143008\pi$
$47$	5.66624	+	9.81422i	0.826506	+	1.43155i	−0.0742560	+	0.997239i	$0.523658\pi$
$48$		0			0
$49$	−2.43658	+	6.56225i	−0.348083	+	0.937464i
$50$	−0.181761	−	0.314820i	−0.0257049	−	0.0445222i
$51$		0			0
$52$	0.700071			0.0970824
$53$	2.74496	+	4.75441i	0.377050	+	0.653069i	0.990632	−	0.136562i	$-0.0436053\pi$
$53$	2.74496	+	4.75441i	0.377050	+	0.653069i	−0.613582	+	0.789631i	$0.710272\pi$
$54$		0			0
$55$	3.46066			0.466635
$56$	−3.28724	−	4.72708i	−0.439275	−	0.631683i
$57$		0			0
$58$	−2.18253			−0.286580
$59$	−0.779098	+	1.34944i	−0.101430	+	0.175682i	−0.912274	−	0.409581i	$-0.865675\pi$
$59$	−0.779098	+	1.34944i	−0.101430	+	0.175682i	0.810844	+	0.585262i	$0.199008\pi$
$60$		0			0
$61$	−2.52408	−	4.37184i	−0.323176	−	0.559757i	0.657966	−	0.753048i	$-0.271417\pi$
$61$	−2.52408	−	4.37184i	−0.323176	−	0.559757i	−0.981141	+	0.193291i	$0.938084\pi$
$62$	3.17033			0.402632
$63$		0			0
$64$	−0.664256			−0.0830320
$65$	0.446403	+	0.773193i	0.0553695	+	0.0959028i
$66$		0			0
$67$	2.61498	−	4.52928i	0.319471	−	0.553340i	−0.660907	−	0.750468i	$-0.729828\pi$
$67$	2.61498	−	4.52928i	0.319471	−	0.553340i	0.980378	+	0.197128i	$0.0631615\pi$
$68$	−9.98464			−1.21081
$69$		0			0
$70$	1.40933	−	2.99702i	0.168448	−	0.358212i
$71$	12.5604			1.49065			0.745324	−	0.666703i	$-0.232295\pi$
$71$	12.5604			1.49065			0.745324	+	0.666703i	$0.232295\pi$
$72$		0			0
$73$	−0.793753	−	1.37482i	−0.0929017	−	0.160911i	0.815829	−	0.578293i	$-0.196281\pi$
$73$	−0.793753	−	1.37482i	−0.0929017	−	0.160911i	−0.908731	+	0.417382i	$0.862948\pi$
$74$	2.79422			0.324822
$75$		0			0
$76$	4.44688	+	7.70222i	0.510092	+	0.883505i
$77$	−2.49452	−	3.58714i	−0.284277	−	0.408793i
$78$		0			0
$79$	3.81482	+	6.60746i	0.429201	+	0.743398i	0.996802	−	0.0799058i	$-0.0254620\pi$
$79$	3.81482	+	6.60746i	0.429201	+	0.743398i	−0.567602	+	0.823303i	$0.692129\pi$
$80$	−2.08138	−	3.60505i	−0.232705	−	0.403057i
$81$		0			0
$82$	−0.443717	+	0.768541i	−0.0490004	+	0.0848711i
$83$	2.62806	−	4.55193i	0.288467	−	0.499639i	−0.684977	−	0.728564i	$-0.740188\pi$
$83$	2.62806	−	4.55193i	0.288467	−	0.499639i	0.973444	+	0.228926i	$0.0735213\pi$
$84$		0			0
$85$	−6.36674	−	11.0275i	−0.690570	−	1.19610i
$86$	−5.07137			−0.546860
$87$		0			0
$88$	3.59382			0.383103
$89$	−9.27808	+	16.0701i	−0.983474	+	1.70343i	−0.334946	+	0.942237i	$0.608718\pi$
$89$	−9.27808	+	16.0701i	−0.983474	+	1.70343i	−0.648528	+	0.761191i	$0.724615\pi$
$90$		0			0
$91$	0.479675	−	1.02005i	0.0502836	−	0.106931i
$92$	6.27252	−	10.8643i	0.653956	−	1.13268i
$93$		0			0
$94$	−3.38465	+	5.86239i	−0.349100	+	0.604659i
$95$	−5.67114	+	9.82270i	−0.581847	+	1.00779i
$96$		0			0
$97$	−6.87728	+	11.9118i	−0.698282	+	1.20946i	0.270780	+	0.962641i	$0.412718\pi$
$97$	−6.87728	+	11.9118i	−0.698282	+	1.20946i	−0.969062	+	0.246818i	$0.920615\pi$
$98$	−4.12243	+	0.699472i	−0.416429	+	0.0706574i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−15.9885			−1.59091			−0.795456	−	0.606011i	$-0.792769\pi$
$101$	−15.9885			−1.59091			−0.795456	+	0.606011i	$0.792769\pi$
$102$		0			0
$103$	−2.36313			−0.232846			−0.116423	−	0.993200i	$-0.537143\pi$
$103$	−2.36313			−0.232846			−0.116423	+	0.993200i	$0.537143\pi$
$104$	0.463581	+	0.802945i	0.0454578	+	0.0787353i
$105$		0			0
$106$	−1.63967	+	2.83998i	−0.159258	+	0.275844i
$107$	−2.27104	+	3.93356i	−0.219550	+	0.380272i	−0.954670	−	0.297665i	$-0.903792\pi$
$107$	−2.27104	+	3.93356i	−0.219550	+	0.380272i	0.735120	+	0.677936i	$0.237126\pi$
$108$		0			0
$109$	−8.62227	−	14.9342i	−0.825863	−	1.43044i	−0.901258	−	0.433283i	$-0.857355\pi$
$109$	−8.62227	−	14.9342i	−0.825863	−	1.43044i	0.0753945	−	0.997154i	$-0.475978\pi$
$110$	1.03359	+	1.79023i	0.0985489	+	0.170692i
$111$		0			0
$112$	−2.23651	+	4.75604i	−0.211330	+	0.449404i
$113$	5.33760	+	9.24499i	0.502119	+	0.869695i	0.999997	+	0.00244827i	$0.000779310\pi$
$113$	5.33760	+	9.24499i	0.502119	+	0.869695i	−0.497878	+	0.867247i	$0.665887\pi$
$114$		0			0
$115$	15.9988			1.49190
$116$	3.00192	+	5.19947i	0.278721	+	0.482759i
$117$		0			0
$118$	−0.930766			−0.0856840
$119$	−6.84128	+	14.5483i	−0.627139	+	1.33364i
$120$		0			0
$121$	−8.27283			−0.752075
$122$	1.50773	−	2.61146i	0.136503	−	0.236430i
$123$		0			0
$124$	−4.36057	−	7.55273i	−0.391591	−	0.678255i
$125$	−11.7532			−1.05124
$126$		0			0
$127$	14.4060			1.27833			0.639163	−	0.769072i	$-0.279281\pi$
$127$	14.4060			1.27833			0.639163	+	0.769072i	$0.279281\pi$
$128$	−5.73739	−	9.93745i	−0.507118	−	0.878355i
$129$		0			0
$130$	−0.266653	+	0.461856i	−0.0233870	+	0.0405075i
$131$	−10.1852			−0.889884			−0.444942	−	0.895559i	$-0.646776\pi$
$131$	−10.1852			−0.889884			−0.444942	+	0.895559i	$0.646776\pi$
$132$		0			0
$133$	14.2696	−	1.20200i	1.23733	−	0.104227i
$134$	3.12405			0.269877
$135$		0			0
$136$	−6.61173	−	11.4519i	−0.566951	−	0.981989i
$137$	−2.06231			−0.176195			−0.0880976	−	0.996112i	$-0.528079\pi$
$137$	−2.06231			−0.176195			−0.0880976	+	0.996112i	$0.528079\pi$
$138$		0			0
$139$	−3.31894	−	5.74858i	−0.281509	−	0.487588i	0.690248	−	0.723573i	$-0.257502\pi$
$139$	−3.31894	−	5.74858i	−0.281509	−	0.487588i	−0.971757	+	0.235985i	$0.924168\pi$
$140$	−9.07829	+	0.764713i	−0.767256	+	0.0646300i
$141$		0			0
$142$	3.75140	+	6.49761i	0.314810	+	0.545267i
$143$	0.351788	+	0.609314i	0.0294180	+	0.0509534i
$144$		0			0
$145$	−3.82837	+	6.63093i	−0.317929	+	0.550669i
$146$	0.474137	−	0.821230i	0.0392399	−	0.0679655i
$147$		0			0
$148$	−3.84326	−	6.65672i	−0.315914	−	0.547179i
$149$	−9.51701			−0.779664			−0.389832	−	0.920886i	$-0.627467\pi$
$149$	−9.51701			−0.779664			−0.389832	+	0.920886i	$0.627467\pi$
$150$		0			0
$151$	−11.0978			−0.903128			−0.451564	−	0.892239i	$-0.649134\pi$
$151$	−11.0978			−0.903128			−0.451564	+	0.892239i	$0.649134\pi$
$152$	−5.88936	+	10.2007i	−0.477690	+	0.827384i
$153$		0			0
$154$	1.11063	−	2.36180i	0.0894967	−	0.190319i
$155$	5.56107	−	9.63206i	0.446676	−	0.773665i
$156$		0			0
$157$	−12.1264	+	21.0035i	−0.967791	+	1.67626i	−0.265870	+	0.964009i	$0.585659\pi$
$157$	−12.1264	+	21.0035i	−0.967791	+	1.67626i	−0.701921	+	0.712255i	$0.747674\pi$
$158$	−2.27873	+	3.94688i	−0.181286	+	0.313997i
$159$		0			0
$160$	5.80369	−	10.0523i	0.458822	−	0.794703i
$161$	−11.5323	−	16.5835i	−0.908870	−	1.30696i
$162$		0			0
$163$	5.54515	−	9.60448i	0.434330	−	0.752281i	−0.562911	−	0.826518i	$-0.690319\pi$
$163$	5.54515	−	9.60448i	0.434330	−	0.752281i	0.997241	+	0.0742364i	$0.0236520\pi$
$164$	2.44121			0.190626
$165$		0			0
$166$	3.13967			0.243685
$167$	1.22550	+	2.12263i	0.0948321	+	0.164254i	0.909539	−	0.415620i	$-0.136435\pi$
$167$	1.22550	+	2.12263i	0.0948321	+	0.164254i	−0.814706	+	0.579874i	$0.803102\pi$
$168$		0			0
$169$	6.40924	−	11.1011i	0.493019	−	0.853933i
$170$	3.80309	−	6.58714i	0.291684	−	0.505211i
$171$		0			0
$172$	6.97532	+	12.0816i	0.531863	+	0.921214i
$173$	4.64053	+	8.03763i	0.352813	+	0.611090i	0.986741	−	0.162302i	$-0.0518919\pi$
$173$	4.64053	+	8.03763i	0.352813	+	0.611090i	−0.633928	+	0.773392i	$0.718559\pi$
$174$		0			0
$175$	0.919269	+	1.32192i	0.0694902	+	0.0999276i
$176$	−1.64023	−	2.84096i	−0.123637	−	0.214145i
$177$		0			0
$178$	−11.0843			−0.830801
$179$	9.27808	+	16.0701i	0.693476	+	1.20114i	0.970692	+	0.240328i	$0.0772551\pi$
$179$	9.27808	+	16.0701i	0.693476	+	1.20114i	−0.277215	+	0.960808i	$0.589412\pi$
$180$		0			0
$181$	13.2382			0.983989			0.491994	−	0.870598i	$-0.336268\pi$
$181$	13.2382			0.983989			0.491994	+	0.870598i	$0.336268\pi$
$182$	0.670945	−	0.0565173i	0.0497338	−	0.00418934i
$183$		0			0
$184$	16.6144			1.22483
$185$	4.90134	−	8.48937i	0.360354	−	0.624151i
$186$		0			0
$187$	−5.01731	−	8.69023i	−0.366902	−	0.635493i
$188$	18.6214			1.35811
$189$		0			0
$190$	−6.77515			−0.491521
$191$	−5.29867	−	9.17757i	−0.383399	−	0.664066i	0.608147	−	0.793824i	$-0.291913\pi$
$191$	−5.29867	−	9.17757i	−0.383399	−	0.664066i	−0.991546	+	0.129759i	$0.958580\pi$
$192$		0			0
$193$	4.05981	−	7.03179i	0.292231	−	0.506159i	−0.682106	−	0.731254i	$-0.738936\pi$
$193$	4.05981	−	7.03179i	0.292231	−	0.506159i	0.974337	+	0.225094i	$0.0722690\pi$
$194$	−8.21610			−0.589881
$195$		0			0
$196$	7.33649	+	8.85886i	0.524035	+	0.632776i
$197$	9.05534			0.645166			0.322583	−	0.946541i	$-0.395449\pi$
$197$	9.05534			0.645166			0.322583	+	0.946541i	$0.395449\pi$
$198$		0			0
$199$	−3.71302	−	6.43114i	−0.263209	−	0.455892i	0.703884	−	0.710315i	$-0.251448\pi$
$199$	−3.71302	−	6.43114i	−0.263209	−	0.455892i	−0.967093	+	0.254424i	$0.918114\pi$
$200$	−1.32438			−0.0936479
$201$		0			0
$202$	−4.77525	−	8.27097i	−0.335985	−	0.581943i
$203$	9.63285	−	0.811426i	0.676093	−	0.0569509i
$204$		0			0
$205$	1.55665	+	2.69619i	0.108721	+	0.188310i
$206$	−0.705791	−	1.22247i	−0.0491748	−	0.0851733i
$207$		0			0
$208$	0.423158	−	0.732931i	0.0293407	−	0.0508196i
$209$	−4.46914	+	7.74077i	−0.309137	+	0.535440i
$210$		0			0
$211$	−1.33890	−	2.31905i	−0.0921739	−	0.159650i	0.816252	−	0.577696i	$-0.196048\pi$
$211$	−1.33890	−	2.31905i	−0.0921739	−	0.159650i	−0.908426	+	0.418047i	$0.862715\pi$
$212$	9.02099			0.619564
$213$		0			0
$214$	−2.71315			−0.185467
$215$	−8.89568	+	15.4078i	−0.606680	+	1.05080i
$216$		0			0
$217$	−13.9926	+	1.17867i	−0.949881	+	0.0800136i
$218$	5.15039	−	8.92074i	0.348829	−	0.604189i
$219$		0			0
$220$	2.84326	−	4.92467i	0.191693	−	0.332021i
$221$	1.29440	−	2.24197i	0.0870709	−	0.150811i
$222$		0			0
$223$	−10.7685	+	18.6515i	−0.721110	+	1.24900i	0.239445	+	0.970910i	$0.423035\pi$
$223$	−10.7685	+	18.6515i	−0.721110	+	1.24900i	−0.960555	+	0.278090i	$0.910299\pi$
$224$	−14.6031	+	1.23010i	−0.975710	+	0.0821892i
$225$		0			0
$226$	−3.18834	+	5.52237i	−0.212085	+	0.367342i
$227$	13.1010			0.869546			0.434773	−	0.900540i	$-0.356829\pi$
$227$	13.1010			0.869546			0.434773	+	0.900540i	$0.356829\pi$
$228$		0			0
$229$	16.8245			1.11180			0.555898	−	0.831251i	$-0.312375\pi$
$229$	16.8245			1.11180			0.555898	+	0.831251i	$0.312375\pi$
$230$	4.77833	+	8.27631i	0.315074	+	0.545724i
$231$		0			0
$232$	−3.97568	+	6.88608i	−0.261016	+	0.452094i
$233$	11.3842	−	19.7180i	0.745804	−	1.29177i	−0.204014	−	0.978968i	$-0.565399\pi$
$233$	11.3842	−	19.7180i	0.745804	−	1.29177i	0.949818	−	0.312803i	$-0.101268\pi$
$234$		0			0
$235$	11.8740	+	20.5664i	0.774576	+	1.34161i
$236$	1.28020	+	2.21738i	0.0833342	+	0.144339i
$237$		0			0
$238$	−9.56923	+	0.806067i	−0.620281	+	0.0522496i
$239$	4.75905	+	8.24292i	0.307837	+	0.533190i	0.977889	−	0.209125i	$-0.0670614\pi$
$239$	4.75905	+	8.24292i	0.307837	+	0.533190i	−0.670052	+	0.742314i	$0.733728\pi$
$240$		0			0
$241$	1.17308			0.0755650			0.0377825	−	0.999286i	$-0.487971\pi$
$241$	1.17308			0.0755650			0.0377825	+	0.999286i	$0.487971\pi$
$242$	−2.47083	−	4.27960i	−0.158831	−	0.275103i
$243$		0			0
$244$	−8.29509			−0.531039
$245$	−5.10603	+	13.7517i	−0.326212	+	0.878562i
$246$		0			0
$247$	−2.30596			−0.146725
$248$	5.77506	−	10.0027i	0.366716	−	0.635171i
$249$		0			0
$250$	−3.51030	−	6.08002i	−0.222011	−	0.384534i
$251$	7.59042			0.479103			0.239552	−	0.970884i	$-0.423000\pi$
$251$	7.59042			0.479103			0.239552	+	0.970884i	$0.423000\pi$
$252$		0			0
$253$	12.6078			0.792648
$254$	4.30261	+	7.45234i	0.269970	+	0.467601i
$255$		0			0
$256$	2.76289	−	4.78547i	0.172681	−	0.299092i
$257$	23.2862			1.45255			0.726277	−	0.687402i	$-0.241249\pi$
$257$	23.2862			1.45255			0.726277	+	0.687402i	$0.241249\pi$
$258$		0			0
$259$	−12.3326	+	1.03884i	−0.766313	+	0.0645506i
$260$	1.46705			0.0909826
$261$		0			0
$262$	−3.04199	−	5.26888i	−0.187935	−	0.325513i
$263$	10.4446			0.644042			0.322021	−	0.946733i	$-0.395638\pi$
$263$	10.4446			0.644042			0.322021	+	0.946733i	$0.395638\pi$
$264$		0			0
$265$	5.75227	+	9.96322i	0.353359	+	0.612036i
$266$	4.88367	+	7.02277i	0.299437	+	0.430594i
$267$		0			0
$268$	−4.29691	−	7.44247i	−0.262476	−	0.454621i
$269$	−14.2349	−	24.6556i	−0.867917	−	1.50328i	−0.864122	−	0.503283i	$-0.832125\pi$
$269$	−14.2349	−	24.6556i	−0.867917	−	1.50328i	−0.00379485	−	0.999993i	$-0.501208\pi$
$270$		0			0
$271$	−13.6962	+	23.7226i	−0.831986	+	1.44104i	0.0644746	+	0.997919i	$0.479463\pi$
$271$	−13.6962	+	23.7226i	−0.831986	+	1.44104i	−0.896461	+	0.443123i	$0.853870\pi$
$272$	−6.03521	+	10.4533i	−0.365938	+	0.633824i
$273$		0			0
$274$	−0.615947	−	1.06685i	−0.0372107	−	0.0644508i
$275$	−1.00501			−0.0606041
$276$		0			0
$277$	4.11257			0.247100			0.123550	−	0.992338i	$-0.460572\pi$
$277$	4.11257			0.247100			0.123550	+	0.992338i	$0.460572\pi$
$278$	1.98252	−	3.43383i	0.118904	−	0.205948i
$279$		0			0
$280$	−6.88865	−	9.90594i	−0.411675	−	0.591993i
$281$	3.63063	−	6.28843i	0.216585	−	0.375136i	−0.737177	−	0.675700i	$-0.763841\pi$
$281$	3.63063	−	6.28843i	0.216585	−	0.375136i	0.953762	+	0.300564i	$0.0971748\pi$
$282$		0			0
$283$	0.640173	−	1.10881i	0.0380543	−	0.0659120i	−0.846371	−	0.532594i	$-0.821217\pi$
$283$	0.640173	−	1.10881i	0.0380543	−	0.0659120i	0.884425	+	0.466682i	$0.154551\pi$
$284$	10.3196	−	17.8740i	0.612354	−	1.06063i
$285$		0			0
$286$	−0.210136	+	0.363966i	−0.0124256	+	0.0215217i
$287$	1.67267	−	3.55701i	0.0987345	−	0.209964i
$288$		0			0
$289$	−9.96117	+	17.2532i	−0.585951	+	1.01490i
$290$	−4.57365			−0.268574
$291$		0			0
$292$	−2.60857			−0.152655
$293$	−10.0067	−	17.3321i	−0.584598	−	1.01255i	−0.994925	−	0.100615i	$-0.967919\pi$
$293$	−10.0067	−	17.3321i	−0.584598	−	1.01255i	0.410327	−	0.911938i	$-0.365414\pi$
$294$		0			0
$295$	−1.63266	+	2.82784i	−0.0950569	+	0.164643i
$296$	5.08994	−	8.81604i	0.295847	−	0.512422i
$297$		0			0
$298$	−2.84243	−	4.92323i	−0.164657	−	0.285195i
$299$	1.62633	+	2.81689i	0.0940532	+	0.162905i
$300$		0			0
$301$	22.3831	−	1.88545i	1.29014	−	0.108675i
$302$	−3.31456	−	5.74099i	−0.190732	−	0.330357i
$303$		0			0
$304$	10.7516			0.616649
$305$	−5.28940	−	9.16151i	−0.302870	−	0.524587i
$306$		0			0
$307$	−2.19415			−0.125227			−0.0626134	−	0.998038i	$-0.519944\pi$
$307$	−2.19415			−0.125227			−0.0626134	+	0.998038i	$0.519944\pi$
$308$	−7.15414	+	0.602631i	−0.407645	+	0.0343381i
$309$		0			0
$310$	6.64366			0.377334
$311$	4.25439	−	7.36882i	0.241244	−	0.417847i	−0.719825	−	0.694156i	$-0.755778\pi$
$311$	4.25439	−	7.36882i	0.241244	−	0.417847i	0.961069	+	0.276309i	$0.0891112\pi$
$312$		0			0
$313$	−1.51731	−	2.62806i	−0.0857633	−	0.148546i	0.819953	−	0.572431i	$-0.194000\pi$
$313$	−1.51731	−	2.62806i	−0.0857633	−	0.148546i	−0.905716	+	0.423885i	$0.860666\pi$
$314$	−14.4871			−0.817552
$315$		0			0
$316$	12.5369			0.705258
$317$	−2.64225	−	4.57652i	−0.148404	−	0.257043i	0.782234	−	0.622985i	$-0.214080\pi$
$317$	−2.64225	−	4.57652i	−0.148404	−	0.257043i	−0.930638	+	0.365942i	$0.880747\pi$
$318$		0			0
$319$	−3.01694	+	5.22550i	−0.168916	+	0.292572i
$320$	−1.39200			−0.0778150
$321$		0			0
$322$	5.13447	−	10.9187i	0.286133	−	0.608476i
$323$	32.8883			1.82996
$324$		0			0
$325$	−0.129639	−	0.224542i	−0.00719110	−	0.0124554i
$326$	6.62464			0.366905
$327$		0			0
$328$	1.61655	+	2.79994i	0.0892588	+	0.154601i
$329$	12.7590	−	27.1327i	0.703428	−	1.49587i
$330$		0			0
$331$	−10.6008	−	18.3612i	−0.582675	−	1.00922i	−0.995161	−	0.0982581i	$-0.968673\pi$
$331$	−10.6008	−	18.3612i	−0.582675	−	1.00922i	0.412486	−	0.910964i	$-0.364660\pi$
$332$	−4.31839	−	7.47968i	−0.237003	−	0.410500i
$333$		0			0
$334$	−0.732036	+	1.26792i	−0.0400552	+	0.0693777i
$335$	5.47989	−	9.49145i	0.299398	−	0.518573i
$336$		0			0
$337$	7.02483	+	12.1674i	0.382667	+	0.662798i	0.991442	−	0.130544i	$-0.0416725\pi$
$337$	7.02483	+	12.1674i	0.382667	+	0.662798i	−0.608776	+	0.793342i	$0.708339\pi$
$338$	7.65695			0.416483
$339$		0			0
$340$	−20.9235			−1.13474
$341$	4.38240	−	7.59053i	0.237320	−	0.411051i
$342$		0			0
$343$	17.9348	−	4.61985i	0.968388	−	0.249449i
$344$	−9.23798	+	16.0007i	−0.498078	+	0.862697i
$345$		0			0
$346$	−2.77196	+	4.80117i	−0.149021	+	0.258112i
$347$	−10.0290	+	17.3707i	−0.538385	+	0.932510i	0.460606	+	0.887605i	$0.347632\pi$
$347$	−10.0290	+	17.3707i	−0.538385	+	0.932510i	−0.998991	+	0.0449055i	$0.985701\pi$
$348$		0			0
$349$	13.9647	−	24.1876i	0.747513	−	1.29473i	−0.201499	−	0.979489i	$-0.564581\pi$
$349$	13.9647	−	24.1876i	0.747513	−	1.29473i	0.949012	−	0.315241i	$-0.102085\pi$
$350$	−0.409283	+	0.870361i	−0.0218771	+	0.0465227i
$351$		0			0
$352$	4.57359	−	7.92169i	0.243773	−	0.422228i
$353$	−5.99251			−0.318949			−0.159475	−	0.987202i	$-0.550980\pi$
$353$	−5.99251			−0.318949			−0.159475	+	0.987202i	$0.550980\pi$
$354$		0			0
$355$	26.3213			1.39699
$356$	15.2456	+	26.4062i	0.808017	+	1.39953i
$357$		0			0
$358$	−5.54213	+	9.59926i	−0.292911	+	0.507337i
$359$	−8.30710	+	14.3883i	−0.438432	+	0.759386i	−0.997569	−	0.0696890i	$-0.977799\pi$
$359$	−8.30710	+	14.3883i	−0.438432	+	0.759386i	0.559137	+	0.829075i	$0.311133\pi$
$360$		0			0
$361$	−5.14755	−	8.91581i	−0.270924	−	0.469253i
$362$	3.95383	+	6.84824i	0.207809	+	0.359935i
$363$		0			0
$364$	−1.05748	−	1.52067i	−0.0554271	−	0.0797047i
$365$	−1.66337	−	2.88104i	−0.0870646	−	0.150800i
$366$		0			0
$367$	6.49528			0.339051			0.169525	−	0.985526i	$-0.445777\pi$
$367$	6.49528			0.339051			0.169525	+	0.985526i	$0.445777\pi$
$368$	−7.58285	−	13.1339i	−0.395283	−	0.684651i
$369$		0			0
$370$	5.85550			0.304413
$371$	6.18100	−	13.1442i	0.320902	−	0.682413i
$372$		0			0
$373$	−20.1610			−1.04390			−0.521949	−	0.852977i	$-0.674795\pi$
$373$	−20.1610			−1.04390			−0.521949	+	0.852977i	$0.674795\pi$
$374$	2.99702	−	5.19099i	0.154972	−	0.268420i
$375$		0			0
$376$	12.3309	+	21.3578i	0.635919	+	1.10144i
$377$	−1.55667			−0.0801724
$378$		0			0
$379$	−15.3014			−0.785981			−0.392990	−	0.919543i	$-0.628559\pi$
$379$	−15.3014			−0.785981			−0.392990	+	0.919543i	$0.628559\pi$
$380$	9.31876	+	16.1406i	0.478042	+	0.827993i
$381$		0			0
$382$	3.16509	−	5.48210i	0.161940	−	0.280488i
$383$	6.78591			0.346744			0.173372	−	0.984856i	$-0.444534\pi$
$383$	6.78591			0.346744			0.173372	+	0.984856i	$0.444534\pi$
$384$		0			0
$385$	−5.22744	−	7.51712i	−0.266415	−	0.383108i
$386$	4.85014			0.246866
$387$		0			0
$388$	11.3007	+	19.5733i	0.573705	+	0.993686i
$389$	−5.75913			−0.292000			−0.146000	−	0.989285i	$-0.546640\pi$
$389$	−5.75913			−0.292000			−0.146000	+	0.989285i	$0.546640\pi$
$390$		0			0
$391$	−23.1953	−	40.1754i	−1.17303	−	2.03176i
$392$	−5.30250	+	14.2808i	−0.267817	+	0.721290i
$393$		0			0
$394$	2.70454	+	4.68440i	0.136253	+	0.235997i
$395$	7.99423	+	13.8464i	0.402234	+	0.696689i
$396$		0			0
$397$	0.247873	−	0.429329i	0.0124404	−	0.0215474i	−0.859738	−	0.510735i	$-0.829373\pi$
$397$	0.247873	−	0.429329i	0.0124404	−	0.0215474i	0.872179	+	0.489188i	$0.162707\pi$
$398$	2.21792	−	3.84155i	0.111174	−	0.192560i
$399$		0			0
$400$	0.604450	+	1.04694i	0.0302225	+	0.0523469i
$401$	10.3829			0.518500			0.259250	−	0.965810i	$-0.416525\pi$
$401$	10.3829			0.518500			0.259250	+	0.965810i	$0.416525\pi$
$402$		0			0
$403$	2.26121			0.112639
$404$	−13.1360	+	22.7523i	−0.653542	+	1.13197i
$405$		0			0
$406$	3.29678	+	4.74081i	0.163617	+	0.235282i
$407$	3.86250	−	6.69005i	0.191457	−	0.331613i
$408$		0			0
$409$	15.0097	−	25.9976i	0.742182	−	1.28550i	−0.209318	−	0.977848i	$-0.567124\pi$
$409$	15.0097	−	25.9976i	0.742182	−	1.28550i	0.951500	−	0.307649i	$-0.0995423\pi$
$410$	−0.929842	+	1.61053i	−0.0459216	+	0.0795386i
$411$		0			0
$412$	−1.94153	+	3.36284i	−0.0956525	+	0.165675i
$413$	4.10805	−	0.346043i	0.202144	−	0.0170276i
$414$		0			0
$415$	5.50728	−	9.53889i	0.270342	−	0.468246i
$416$	2.35986			0.115702
$417$		0			0
$418$	−5.33916			−0.261147
$419$	−13.8248	−	23.9452i	−0.675384	−	1.16980i	−0.976357	−	0.216166i	$-0.930645\pi$
$419$	−13.8248	−	23.9452i	−0.675384	−	1.16980i	0.300973	−	0.953633i	$-0.402689\pi$
$420$		0			0
$421$	−6.23107	+	10.7925i	−0.303684	+	0.525996i	−0.976967	−	0.213388i	$-0.931550\pi$
$421$	−6.23107	+	10.7925i	−0.303684	+	0.525996i	0.673284	+	0.739384i	$0.264883\pi$
$422$	0.799775	−	1.38525i	0.0389325	−	0.0674330i
$423$		0			0
$424$	5.97361	+	10.3466i	0.290104	+	0.502475i
$425$	1.84896	+	3.20249i	0.0896876	+	0.155344i
$426$		0			0
$427$	−5.68363	+	12.0865i	−0.275050	+	0.584908i
$428$	3.73175	+	6.46359i	0.180381	+	0.312429i
$429$		0			0
$430$	−10.6274			−0.512500
$431$	7.05162	+	12.2138i	0.339665	+	0.588316i	0.984370	−	0.176115i	$-0.0563531\pi$
$431$	7.05162	+	12.2138i	0.339665	+	0.588316i	−0.644705	+	0.764431i	$0.723020\pi$
$432$		0			0
$433$	−15.3684			−0.738560			−0.369280	−	0.929318i	$-0.620396\pi$
$433$	−15.3684			−0.738560			−0.369280	+	0.929318i	$0.620396\pi$
$434$	−4.78889	−	6.88647i	−0.229874	−	0.330561i
$435$		0			0
$436$	−28.3360			−1.35705
$437$	−20.6610	+	35.7860i	−0.988351	+	1.71187i
$438$		0			0
$439$	−9.62286	−	16.6673i	−0.459274	−	0.795486i	0.539648	−	0.841890i	$-0.318557\pi$
$439$	−9.62286	−	16.6673i	−0.459274	−	0.795486i	−0.998923	+	0.0464041i	$0.985224\pi$
$440$	7.53112			0.359032
$441$		0			0
$442$	1.54639			0.0735541
$443$	−12.2849	−	21.2781i	−0.583673	−	1.01095i	−0.995039	−	0.0994811i	$-0.968282\pi$
$443$	−12.2849	−	21.2781i	−0.583673	−	1.01095i	0.411367	−	0.911470i	$-0.365052\pi$
$444$		0			0
$445$	−19.4429	+	33.6761i	−0.921682	+	1.59640i
$446$	−12.8648			−0.609166
$447$		0			0
$448$	1.00338	+	1.44287i	0.0474053	+	0.0681693i
$449$	−40.0045			−1.88793			−0.943965	−	0.330046i	$-0.892936\pi$
$449$	−40.0045			−1.88793			−0.943965	+	0.330046i	$0.892936\pi$
$450$		0			0
$451$	1.22671	+	2.12473i	0.0577637	+	0.100050i
$452$	17.5414			0.825076
$453$		0			0
$454$	3.91286	+	6.77727i	0.183640	+	0.318073i
$455$	1.00519	−	2.13760i	0.0471242	−	0.100212i
$456$		0			0
$457$	5.31807	+	9.21117i	0.248769	+	0.430880i	0.963184	−	0.268841i	$-0.0866407\pi$
$457$	5.31807	+	9.21117i	0.248769	+	0.430880i	−0.714416	+	0.699722i	$0.753307\pi$
$458$	5.02495	+	8.70347i	0.234800	+	0.406686i
$459$		0			0
$460$	13.1445	−	22.7670i	0.612867	−	1.06152i
$461$	8.20458	−	14.2107i	0.382125	−	0.661860i	−0.609241	−	0.792986i	$-0.708526\pi$
$461$	8.20458	−	14.2107i	0.382125	−	0.661860i	0.991366	+	0.131125i	$0.0418589\pi$
$462$		0			0
$463$	−3.03196	−	5.25152i	−0.140907	−	0.244059i	0.786931	−	0.617041i	$-0.211669\pi$
$463$	−3.03196	−	5.25152i	−0.140907	−	0.244059i	−0.927839	+	0.372982i	$0.878335\pi$
$464$	7.25803			0.336946
$465$		0			0
$466$	13.6004			0.630027
$467$	12.6433	−	21.8988i	0.585062	−	1.01336i	−0.409805	−	0.912173i	$-0.634403\pi$
$467$	12.6433	−	21.8988i	0.585062	−	1.01336i	0.994868	−	0.101185i	$-0.0322632\pi$
$468$		0			0
$469$	−13.7884	+	1.16147i	−0.636687	+	0.0536315i
$470$	−7.09279	+	12.2851i	−0.327166	+	0.566668i
$471$		0			0
$472$	−1.69548	+	2.93666i	−0.0780408	+	0.135171i
$473$	−7.01023	+	12.1421i	−0.322331	+	0.558294i
$474$		0			0
$475$	1.64695	−	2.85260i	0.0755671	−	0.130886i
$476$	15.0821	+	21.6882i	0.691288	+	0.994079i
$477$		0			0
$478$	−2.84275	+	4.92379i	−0.130025	+	0.225209i
$479$	3.34249			0.152722			0.0763611	−	0.997080i	$-0.475670\pi$
$479$	3.34249			0.152722			0.0763611	+	0.997080i	$0.475670\pi$
$480$		0			0
$481$	1.99295			0.0908708
$482$	0.350363	+	0.606846i	0.0159586	+	0.0276411i
$483$		0			0
$484$	−6.79691	+	11.7726i	−0.308951	+	0.535118i
$485$	−14.4118	+	24.9620i	−0.654408	+	1.13347i
$486$		0			0
$487$	−3.63943	−	6.30368i	−0.164918	−	0.285647i	0.771708	−	0.635977i	$-0.219403\pi$
$487$	−3.63943	−	6.30368i	−0.164918	−	0.285647i	−0.936626	+	0.350330i	$0.886069\pi$
$488$	−5.49293	−	9.51404i	−0.248653	−	0.430680i
$489$		0			0
$490$	−8.63886	+	1.46580i	−0.390264	+	0.0662179i
$491$	−1.48565	−	2.57323i	−0.0670466	−	0.116128i	0.830553	−	0.556939i	$-0.188024\pi$
$491$	−1.48565	−	2.57323i	−0.0670466	−	0.116128i	−0.897600	+	0.440811i	$0.854691\pi$
$492$		0			0
$493$	22.2017			0.999913
$494$	−0.688717	−	1.19289i	−0.0309869	−	0.0536708i
$495$		0			0
$496$	−10.5430			−0.473394
$497$	−18.9729	−	27.2833i	−0.851052	−	1.22382i
$498$		0			0
$499$	12.4859			0.558944			0.279472	−	0.960154i	$-0.409841\pi$
$499$	12.4859			0.558944			0.279472	+	0.960154i	$0.409841\pi$
$500$	−9.65635	+	16.7253i	−0.431845	+	0.747977i
$501$		0			0
$502$	2.26702	+	3.92659i	0.101182	+	0.175252i
$503$	17.4657			0.778755			0.389377	−	0.921078i	$-0.372690\pi$
$503$	17.4657			0.778755			0.389377	+	0.921078i	$0.372690\pi$
$504$		0			0
$505$	−33.5050			−1.49095
$506$	3.76556	+	6.52214i	0.167400	+	0.289945i
$507$		0			0
$508$	11.8359	−	20.5004i	0.525133	−	0.909556i
$509$	−27.5341			−1.22043			−0.610215	−	0.792236i	$-0.708917\pi$
$509$	−27.5341			−1.22043			−0.610215	+	0.792236i	$0.708917\pi$
$510$		0			0
$511$	−1.78734	+	3.80087i	−0.0790674	+	0.168141i
$512$	−19.6488			−0.868363
$513$		0			0
$514$	6.95485	+	12.0462i	0.306765	+	0.531333i
$515$	−4.95211			−0.218216
$516$		0			0
$517$	9.35732	+	16.2074i	0.411534	+	0.712798i
$518$	−4.22077	−	6.06951i	−0.185450	−	0.266679i
$519$		0			0
$520$	0.971467	+	1.68263i	0.0426017	+	0.0737882i
$521$	−3.46252	−	5.99726i	−0.151696	−	0.262745i	0.780155	−	0.625586i	$-0.215140\pi$
$521$	−3.46252	−	5.99726i	−0.151696	−	0.262745i	−0.931851	+	0.362841i	$0.881807\pi$
$522$		0			0
$523$	20.7968	−	36.0211i	0.909381	−	1.57509i	0.0944561	−	0.995529i	$-0.469889\pi$
$523$	20.7968	−	36.0211i	0.909381	−	1.57509i	0.814925	−	0.579566i	$-0.196778\pi$
$524$	−8.36810	+	14.4940i	−0.365562	+	0.633172i
$525$		0			0
$526$	3.11947	+	5.40308i	0.136015	+	0.235586i
$527$	−32.2500			−1.40483
$528$		0			0
$529$	35.2867			1.53420
$530$	−3.43604	+	5.95139i	−0.149252	+	0.258512i
$531$		0			0
$532$	10.0133	−	21.2938i	0.434132	−	0.923203i
$533$	−0.316477	+	0.548154i	−0.0137081	+	0.0237432i
$534$		0			0
$535$	−4.75914	+	8.24307i	−0.205755	+	0.356379i
$536$	5.69075	−	9.85667i	0.245803	−	0.425743i
$537$		0			0
$538$	8.50302	−	14.7277i	0.366591	−	0.634954i
$539$	−4.02380	+	10.8370i	−0.173317	+	0.466782i
$540$		0			0
$541$	16.8944	−	29.2619i	0.726345	−	1.25807i	−0.232073	−	0.972698i	$-0.574551\pi$
$541$	16.8944	−	29.2619i	0.726345	−	1.25807i	0.958418	−	0.285368i	$-0.0921158\pi$
$542$	−16.3625			−0.702830
$543$		0			0
$544$	−33.6570			−1.44303
$545$	−18.0686	−	31.2957i	−0.773973	−	1.34056i
$546$		0			0
$547$	7.06548	−	12.2378i	0.302098	−	0.523249i	−0.674513	−	0.738263i	$-0.735646\pi$
$547$	7.06548	−	12.2378i	0.302098	−	0.523249i	0.976611	+	0.215014i	$0.0689797\pi$
$548$	−1.69438	+	2.93476i	−0.0723805	+	0.125367i
$549$		0			0
$550$	−0.300163	−	0.519898i	−0.0127990	−	0.0221685i
$551$	−9.88800	−	17.1265i	−0.421243	−	0.729614i
$552$		0			0
$553$	8.59007	−	18.2672i	0.365287	−	0.776800i
$554$	1.22829	+	2.12746i	0.0521851	+	0.0903873i
$555$		0			0
$556$	−10.9073			−0.462573
$557$	3.74784	+	6.49145i	0.158801	+	0.275051i	0.934437	−	0.356130i	$-0.115904\pi$
$557$	3.74784	+	6.49145i	0.158801	+	0.275051i	−0.775636	+	0.631181i	$0.782571\pi$
$558$		0			0
$559$	−3.61710			−0.152987
$560$	−4.68676	+	9.96663i	−0.198052	+	0.421167i
$561$		0			0
$562$	4.33741			0.182963
$563$	−5.21120	+	9.02606i	−0.219626	+	0.380403i	−0.954694	−	0.297591i	$-0.903817\pi$
$563$	−5.21120	+	9.02606i	−0.219626	+	0.380403i	0.735068	+	0.677994i	$0.237150\pi$
$564$		0			0
$565$	11.1853	+	19.3735i	0.470570	+	0.815051i
$566$	0.764797			0.0321468
$567$		0			0
$568$	27.3341			1.14691
$569$	14.9832	+	25.9517i	0.628130	+	1.08795i	0.987927	+	0.154923i	$0.0495129\pi$
$569$	14.9832	+	25.9517i	0.628130	+	1.08795i	−0.359796	+	0.933031i	$0.617154\pi$
$570$		0			0
$571$	−15.7168	+	27.2223i	−0.657727	+	1.13922i	0.323476	+	0.946236i	$0.395149\pi$
$571$	−15.7168	+	27.2223i	−0.657727	+	1.13922i	−0.981203	+	0.192980i	$0.938185\pi$
$572$	1.15611			0.0483393
$573$		0			0
$574$	2.33964	−	0.197081i	0.0976549	−	0.00822599i
$575$	−4.64619			−0.193760
$576$		0			0
$577$	1.35570	+	2.34815i	0.0564387	+	0.0977547i	0.892864	−	0.450326i	$-0.148692\pi$
$577$	1.35570	+	2.34815i	0.0564387	+	0.0977547i	−0.836426	+	0.548080i	$0.815359\pi$
$578$	−11.9003			−0.494989
$579$		0			0
$580$	6.29074	+	10.8959i	0.261209	+	0.452427i
$581$	−13.8573	+	1.16727i	−0.574897	+	0.0484266i
$582$		0			0
$583$	4.53307	+	7.85151i	0.187741	+	0.325176i
$584$	−1.72737	−	2.99190i	−0.0714792	−	0.123806i
$585$		0			0
$586$	5.97737	−	10.3531i	0.246923	−	0.427683i
$587$	−5.35198	+	9.26990i	−0.220900	+	0.382610i	−0.955081	−	0.296343i	$-0.904233\pi$
$587$	−5.35198	+	9.26990i	−0.220900	+	0.382610i	0.734182	+	0.678953i	$0.237566\pi$
$588$		0			0
$589$	14.3633	+	24.8779i	0.591828	+	1.02508i
$590$	−1.95049			−0.0803004
$591$		0			0
$592$	−9.29223			−0.381908
$593$	14.8489	−	25.7191i	0.609773	−	1.05616i	−0.381505	−	0.924367i	$-0.624594\pi$
$593$	14.8489	−	25.7191i	0.609773	−	1.05616i	0.991278	−	0.131791i	$-0.0420727\pi$
$594$		0			0
$595$	−14.3364	+	30.4870i	−0.587735	+	1.24985i
$596$	−7.81912	+	13.5431i	−0.320284	+	0.554748i
$597$		0			0
$598$	−0.971467	+	1.68263i	−0.0397262	+	0.0688079i
$599$	−7.19914	+	12.4693i	−0.294149	+	0.509481i	−0.974787	−	0.223140i	$-0.928369\pi$
$599$	−7.19914	+	12.4693i	−0.294149	+	0.509481i	0.680638	+	0.732620i	$0.261703\pi$
$600$		0			0
$601$	−8.85598	+	15.3390i	−0.361243	+	0.625691i	−0.988166	−	0.153390i	$-0.950981\pi$
$601$	−8.85598	+	15.3390i	−0.361243	+	0.625691i	0.626923	+	0.779081i	$0.284314\pi$
$602$	7.66047	+	11.0158i	0.312218	+	0.448972i
$603$		0			0
$604$	−9.11791	+	15.7927i	−0.371002	+	0.642595i
$605$	−17.3363			−0.704822
$606$		0			0
$607$	−5.15543			−0.209252			−0.104626	−	0.994512i	$-0.533365\pi$
$607$	−5.15543			−0.209252			−0.104626	+	0.994512i	$0.533365\pi$
$608$	14.9899	+	25.9633i	0.607921	+	1.05295i
$609$		0			0
$610$	3.15955	−	5.47250i	0.127927	−	0.221575i
$611$	−2.41407	+	4.18129i	−0.0976628	+	0.169157i
$612$		0			0
$613$	−5.62940	−	9.75042i	−0.227370	−	0.393816i	0.729658	−	0.683812i	$-0.239679\pi$
$613$	−5.62940	−	9.75042i	−0.227370	−	0.393816i	−0.957028	+	0.289996i	$0.906346\pi$
$614$	−0.655323	−	1.13505i	−0.0264467	−	0.0458070i
$615$		0			0
$616$	−5.42859	−	7.80637i	−0.218724	−	0.314528i
$617$	0.260152	+	0.450597i	0.0104733	+	0.0181403i	0.871215	−	0.490902i	$-0.163333\pi$
$617$	0.260152	+	0.450597i	0.0104733	+	0.0181403i	−0.860741	+	0.509043i	$0.830000\pi$
$618$		0			0
$619$	−37.4740			−1.50621			−0.753104	−	0.657901i	$-0.771444\pi$
$619$	−37.4740			−1.50621			−0.753104	+	0.657901i	$0.771444\pi$
$620$	−9.13789	−	15.8273i	−0.366987	−	0.635639i
$621$		0			0
$622$	5.08260			0.203794
$623$	48.9217	−	4.12094i	1.96001	−	0.165102i
$624$		0			0
$625$	−21.5868			−0.863471
$626$	0.906343	−	1.56983i	0.0362248	−	0.0627431i
$627$		0			0
$628$	19.9260	+	34.5128i	0.795132	+	1.37721i
$629$	−28.4241			−1.13334
$630$		0			0
$631$	0.502795			0.0200159			0.0100080	−	0.999950i	$-0.496814\pi$
$631$	0.502795			0.0200159			0.0100080	+	0.999950i	$0.496814\pi$
$632$	8.30185	+	14.3792i	0.330230	+	0.571975i
$633$		0			0
$634$	1.57831	−	2.73372i	0.0626828	−	0.108570i
$635$	30.1888			1.19801
$636$		0			0
$637$	−2.94029	+	0.498892i	−0.116498	+	0.0197668i
$638$	−3.60426			−0.142694
$639$		0			0
$640$	−12.0231	−	20.8247i	−0.475256	−	0.823167i
$641$	−9.96117			−0.393442			−0.196721	−	0.980459i	$-0.563029\pi$
$641$	−9.96117			−0.393442			−0.196721	+	0.980459i	$0.563029\pi$
$642$		0			0
$643$	−10.8118	−	18.7266i	−0.426376	−	0.738505i	0.570172	−	0.821525i	$-0.306877\pi$
$643$	−10.8118	−	18.7266i	−0.426376	−	0.738505i	−0.996548	+	0.0830207i	$0.973543\pi$
$644$	−33.0739	+	2.78599i	−1.30330	+	0.109784i
$645$		0			0
$646$	9.82270	+	17.0134i	0.386469	+	0.669384i
$647$	19.3679	+	33.5462i	0.761430	+	1.31884i	0.942113	+	0.335294i	$0.108836\pi$
$647$	19.3679	+	33.5462i	0.761430	+	1.31884i	−0.180683	+	0.983541i	$0.557831\pi$
$648$		0			0
$649$	−1.28661	+	2.22848i	−0.0505040	+	0.0874755i
$650$	0.0774383	−	0.134127i	0.00303738	−	0.00526090i
$651$		0			0
$652$	−9.11173	−	15.7820i	−0.356843	−	0.618070i
$653$	−21.7978			−0.853013			−0.426506	−	0.904485i	$-0.640256\pi$
$653$	−21.7978			−0.853013			−0.426506	+	0.904485i	$0.640256\pi$
$654$		0			0
$655$	−21.3438			−0.833972
$656$	1.47559	−	2.55579i	0.0576120	−	0.0997870i
$657$		0			0
$658$	17.8467	−	1.50332i	0.695737	−	0.0586056i
$659$	−2.56810	+	4.44807i	−0.100039	+	0.173272i	−0.911700	−	0.410856i	$-0.865230\pi$
$659$	−2.56810	+	4.44807i	−0.100039	+	0.173272i	0.811662	+	0.584128i	$0.198563\pi$
$660$		0			0
$661$	−6.58087	+	11.3984i	−0.255966	+	0.443347i	−0.965158	−	0.261670i	$-0.915727\pi$
$661$	−6.58087	+	11.3984i	−0.255966	+	0.443347i	0.709191	+	0.705016i	$0.249060\pi$
$662$	6.33226	−	10.9678i	0.246110	−	0.426276i
$663$		0			0
$664$	5.71920	−	9.90594i	0.221948	−	0.384425i
$665$	29.9029	−	2.51888i	1.15959	−	0.0976781i
$666$		0			0
$667$	−13.9475	+	24.1577i	−0.540048	+	0.935391i
$668$	4.02746			0.155827
$669$		0			0
$670$	6.54667			0.252920
$671$	−4.16831	−	7.21972i	−0.160916	−	0.278714i
$672$		0			0
$673$	3.50605	−	6.07265i	0.135148	−	0.234083i	−0.790506	−	0.612454i	$-0.790182\pi$
$673$	3.50605	−	6.07265i	0.135148	−	0.234083i	0.925654	+	0.378371i	$0.123516\pi$
$674$	−4.19618	+	7.26800i	−0.161631	+	0.279953i
$675$		0			0
$676$	−10.5316	−	18.2413i	−0.405062	−	0.701587i
$677$	−18.4481	−	31.9531i	−0.709018	−	1.22806i	−0.965222	−	0.261433i	$-0.915805\pi$
$677$	−18.4481	−	31.9531i	−0.709018	−	1.22806i	0.256203	−	0.966623i	$-0.417528\pi$
$678$		0			0
$679$	36.2627	−	3.05460i	1.39164	−	0.117225i
$680$	−13.8554	−	23.9982i	−0.531329	−	0.920289i
$681$		0			0
$682$	5.23553			0.200479
$683$	2.79970	+	4.84921i	0.107127	+	0.185550i	0.914605	−	0.404348i	$-0.132501\pi$
$683$	2.79970	+	4.84921i	0.107127	+	0.185550i	−0.807478	+	0.589898i	$0.799168\pi$
$684$		0			0
$685$	−4.32172			−0.165125
$686$	7.74644	+	7.89802i	0.295760	+	0.301548i
$687$		0			0
$688$	16.8649			0.642969
$689$	−1.16948	+	2.02559i	−0.0445535	+	0.0771689i
$690$		0			0
$691$	3.19219	+	5.52903i	0.121437	+	0.210334i	0.920334	−	0.391132i	$-0.127917\pi$
$691$	3.19219	+	5.52903i	0.121437	+	0.210334i	−0.798898	+	0.601467i	$0.794583\pi$
$692$	15.2505			0.579738
$693$		0			0
$694$	−11.9814			−0.454807
$695$	−6.95509	−	12.0466i	−0.263822	−	0.456952i
$696$		0			0
$697$	4.51369	−	7.81795i	0.170968	−	0.296126i
$698$	16.6832			0.631470
$699$		0			0
$700$	2.63641	−	0.222079i	0.0996471	−	0.00839380i
$701$	−10.9860			−0.414937			−0.207468	−	0.978242i	$-0.566522\pi$
$701$	−10.9860			−0.414937			−0.207468	+	0.978242i	$0.566522\pi$
$702$		0			0
$703$	12.6593	+	21.9265i	0.477455	+	0.826975i
$704$	−1.09696			−0.0413433
$705$		0			0
$706$	−1.78977	−	3.09998i	−0.0673590	−	0.116669i
$707$	24.1511	+	34.7295i	0.908296	+	1.30614i
$708$		0			0
$709$	−13.2658	−	22.9771i	−0.498208	−	0.862922i	0.501790	−	0.864990i	$-0.332675\pi$
$709$	−13.2658	−	22.9771i	−0.498208	−	0.862922i	−0.999998	+	0.00206764i	$0.999342\pi$
$710$	7.86133	+	13.6162i	0.295030	+	0.511008i
$711$		0			0
$712$	−20.1910	+	34.9719i	−0.756691	+	1.31063i
$713$	20.2600	−	35.0914i	0.758744	−	1.31418i
$714$		0			0
$715$	0.737197	+	1.27686i	0.0275696	+	0.0477520i
$716$	30.4913			1.13951
$717$		0			0
$718$	−9.92426			−0.370370
$719$	10.4980	−	18.1831i	0.391510	−	0.678116i	−0.601139	−	0.799145i	$-0.705286\pi$
$719$	10.4980	−	18.1831i	0.391510	−	0.678116i	0.992649	+	0.121029i	$0.0386194\pi$
$720$		0			0
$721$	3.56959	+	5.13310i	0.132938	+	0.191167i
$722$	3.07482	−	5.32574i	0.114433	−	0.198203i
$723$		0			0
$724$	10.8764	−	18.8386i	0.404220	−	0.700129i
$725$	1.11179	−	1.92568i	0.0412909	−	0.0715179i
$726$		0			0
$727$	−8.53160	+	14.7772i	−0.316420	+	0.548055i	−0.979738	−	0.200282i	$-0.935814\pi$
$727$	−8.53160	+	14.7772i	−0.316420	+	0.548055i	0.663319	+	0.748337i	$0.269147\pi$
$728$	1.04387	−	2.21985i	0.0386885	−	0.0822730i
$729$		0			0
$730$	0.993590	−	1.72095i	0.0367744	−	0.0636951i
$731$	51.5883			1.90806
$732$		0			0
$733$	−34.4805			−1.27357			−0.636784	−	0.771042i	$-0.719736\pi$
$733$	−34.4805			−1.27357			−0.636784	+	0.771042i	$0.719736\pi$
$734$	1.93993	+	3.36006i	0.0716042	+	0.124022i
$735$		0			0
$736$	21.1439	−	36.6224i	0.779376	−	1.34992i
$737$	4.31842	−	7.47973i	0.159071	−	0.275519i
$738$		0			0
$739$	0.685922	+	1.18805i	0.0252321	+	0.0437032i	0.878366	−	0.477989i	$-0.158634\pi$
$739$	0.685922	+	1.18805i	0.0252321	+	0.0437032i	−0.853134	+	0.521692i	$0.825301\pi$
$740$	−8.05383	−	13.9497i	−0.296065	−	0.512799i
$741$		0			0
$742$	8.64568	−	0.728271i	0.317393	−	0.0267357i
$743$	4.47124	+	7.74442i	0.164034	+	0.284115i	0.936312	−	0.351170i	$-0.114216\pi$
$743$	4.47124	+	7.74442i	0.164034	+	0.284115i	−0.772278	+	0.635285i	$0.780883\pi$
$744$		0			0
$745$	−19.9436			−0.730676
$746$	−6.02145	−	10.4295i	−0.220461	−	0.381850i
$747$		0			0
$748$	−16.4888			−0.602889
$749$	11.9748	−	1.00870i	0.437550	−	0.0368572i
$750$		0			0
$751$	50.5711			1.84537			0.922683	−	0.385559i	$-0.125991\pi$
$751$	50.5711			1.84537			0.922683	+	0.385559i	$0.125991\pi$
$752$	11.2557	−	19.4955i	0.410453	−	0.710926i
$753$		0			0
$754$	−0.464927	−	0.805277i	−0.0169316	−	0.0293265i
$755$	−23.2563			−0.846383
$756$		0			0
$757$	9.56041			0.347479			0.173739	−	0.984792i	$-0.444415\pi$
$757$	9.56041			0.347479			0.173739	+	0.984792i	$0.444415\pi$
$758$	−4.57004	−	7.91555i	−0.165991	−	0.287506i
$759$		0			0
$760$	−12.3416	+	21.3763i	−0.447676	+	0.775398i
$761$	37.8812			1.37319			0.686595	−	0.727040i	$-0.259104\pi$
$761$	37.8812			1.37319			0.686595	+	0.727040i	$0.259104\pi$
$762$		0			0
$763$	−19.4153	+	41.2876i	−0.702881	+	1.49471i
$764$	−17.4134			−0.629996
$765$		0			0
$766$	2.02674	+	3.51041i	0.0732289	+	0.126836i
$767$	−0.663860			−0.0239706
$768$		0			0
$769$	14.2794	+	24.7326i	0.514928	+	0.891881i	0.999850	+	0.0173236i	$0.00551456\pi$
$769$	14.2794	+	24.7326i	0.514928	+	0.891881i	−0.484922	+	0.874557i	$0.661152\pi$
$770$	2.32740	−	4.94932i	0.0838736	−	0.178361i
$771$		0			0
$772$	−6.67103	−	11.5546i	−0.240096	−	0.415858i
$773$	5.35149	+	9.26905i	0.192480	+	0.333385i	0.946071	−	0.323958i	$-0.105014\pi$
$773$	5.35149	+	9.26905i	0.192480	+	0.333385i	−0.753592	+	0.657343i	$0.771680\pi$
$774$		0			0
$775$	−1.61498	+	2.79723i	−0.0580119	+	0.100480i
$776$	−14.9664	+	25.9226i	−0.537262	+	0.930566i
$777$		0			0
$778$	−1.72007	−	2.97925i	−0.0616675	−	0.106811i
$779$	−8.04109			−0.288102
$780$		0			0
$781$	20.7425			0.742224
$782$	13.8554	−	23.9982i	0.495467	−	0.858174i
$783$		0			0
$784$	13.7092	−	2.32610i	0.489615	−	0.0830752i
$785$	−25.4117	+	44.0144i	−0.906984	+	1.57094i
$786$		0			0
$787$	18.3183	−	31.7283i	0.652978	−	1.13099i	−0.329418	−	0.944184i	$-0.606853\pi$
$787$	18.3183	−	31.7283i	0.652978	−	1.13099i	0.982397	−	0.186808i	$-0.0598141\pi$
$788$	7.43982	−	12.8861i	0.265033	−	0.459050i
$789$		0			0
$790$	−4.77525	+	8.27097i	−0.169896	+	0.294268i
$791$	12.0190	−	25.5590i	0.427346	−	0.908773i
$792$		0			0
$793$	1.07537	−	1.86260i	0.0381875	−	0.0661428i
$794$	0.296128			0.0105092
$795$		0			0
$796$	−12.2024			−0.432502
$797$	−9.52403	−	16.4961i	−0.337359	−	0.584322i	0.646576	−	0.762849i	$-0.276200\pi$
$797$	−9.52403	−	16.4961i	−0.337359	−	0.584322i	−0.983935	+	0.178527i	$0.942867\pi$
$798$		0			0
$799$	34.4302	−	59.6349i	1.21805	−	2.10973i
$800$	−1.68544	+	2.91927i	−0.0595893	+	0.103212i
$801$		0			0
$802$	3.10106	+	5.37119i	0.109502	+	0.189663i
$803$	−1.31082	−	2.27040i	−0.0462577	−	0.0801206i
$804$		0			0
$805$	−24.1667	−	34.7520i	−0.851765	−	1.22485i
$806$	0.675350	+	1.16974i	0.0237882	+	0.0412024i
$807$		0			0
$808$	−34.7943			−1.22406
$809$	−9.24567	−	16.0140i	−0.325060	−	0.563021i	0.656464	−	0.754357i	$-0.272051\pi$
$809$	−9.24567	−	16.0140i	−0.325060	−	0.563021i	−0.981525	+	0.191336i	$0.938718\pi$
$810$		0			0
$811$	41.5033			1.45738			0.728690	−	0.684844i	$-0.240130\pi$
$811$	41.5033			1.45738			0.728690	+	0.684844i	$0.240130\pi$
$812$	6.75960	−	14.3746i	0.237216	−	0.504450i
$813$		0			0
$814$	4.61442			0.161735
$815$	11.6203	−	20.1269i	0.407040	−	0.705014i
$816$		0			0
$817$	−22.9760	−	39.7955i	−0.803827	−	1.39227i
$818$	17.9317			0.626966
$819$		0			0
$820$	5.11573			0.178649
$821$	16.2444	+	28.1360i	0.566932	+	0.981955i	0.996867	+	0.0790951i	$0.0252031\pi$
$821$	16.2444	+	28.1360i	0.566932	+	0.981955i	−0.429935	+	0.902860i	$0.641464\pi$
$822$		0			0
$823$	7.86963	−	13.6306i	0.274318	−	0.475133i	−0.695645	−	0.718386i	$-0.744881\pi$
$823$	7.86963	−	13.6306i	0.274318	−	0.475133i	0.969963	+	0.243253i	$0.0782145\pi$
$824$	−5.14266			−0.179153
$825$		0			0
$826$	1.40595	+	2.02178i	0.0489194	+	0.0703466i
$827$	−40.6095			−1.41213			−0.706066	−	0.708146i	$-0.749532\pi$
$827$	−40.6095			−1.41213			−0.706066	+	0.708146i	$0.749532\pi$
$828$		0			0
$829$	−12.7290	−	22.0473i	−0.442097	−	0.765734i	0.555748	−	0.831351i	$-0.312432\pi$
$829$	−12.7290	−	22.0473i	−0.442097	−	0.765734i	−0.997845	+	0.0656169i	$0.979098\pi$
$830$	6.57940			0.228374
$831$		0			0
$832$	−0.141501	−	0.245087i	−0.00490567	−	0.00849688i
$833$	41.9353	−	7.11535i	1.45297	−	0.246532i
$834$		0			0
$835$	2.56813	+	4.44813i	0.0888737	+	0.153934i
$836$	7.34364	+	12.7196i	0.253985	+	0.439915i
$837$		0			0
$838$	8.25803	−	14.3033i	0.285269	−	0.494100i
$839$	−24.1746	+	41.8717i	−0.834600	+	1.44557i	0.0597550	+	0.998213i	$0.480968\pi$
$839$	−24.1746	+	41.8717i	−0.834600	+	1.44557i	−0.894355	+	0.447357i	$0.852365\pi$
$840$		0			0
$841$	7.82499	+	13.5533i	0.269827	+	0.467354i
$842$	−7.44409			−0.256540
$843$		0			0
$844$	−4.40014			−0.151459
$845$	13.4310	−	23.2632i	0.462042	−	0.800280i
$846$		0			0
$847$	12.4964	+	17.9699i	0.429381	+	0.617454i
$848$	5.45273	−	9.44441i	0.187248	−	0.324322i
$849$		0			0
$850$	−1.10445	+	1.91296i	−0.0378823	+	0.0656141i
$851$	17.8565	−	30.9284i	0.612114	−	1.06021i
$852$		0			0
$853$	1.32933	−	2.30247i	0.0455155	−	0.0788352i	−0.842370	−	0.538899i	$-0.818840\pi$
$853$	1.32933	−	2.30247i	0.0455155	−	0.0788352i	0.887886	+	0.460064i	$0.152174\pi$
$854$	−7.94998	+	0.669669i	−0.272043	+	0.0229156i
$855$		0			0
$856$	−4.94226	+	8.56025i	−0.168923	+	0.292583i
$857$	14.0664			0.480498			0.240249	−	0.970711i	$-0.422771\pi$
$857$	14.0664			0.480498			0.240249	+	0.970711i	$0.422771\pi$
$858$		0			0
$859$	−19.2927			−0.658258			−0.329129	−	0.944285i	$-0.606755\pi$
$859$	−19.2927			−0.658258			−0.329129	+	0.944285i	$0.606755\pi$
$860$	14.6173	+	25.3179i	0.498445	+	0.863333i
$861$		0			0
$862$	−4.21219	+	7.29572i	−0.143468	+	0.248493i
$863$	21.1692	−	36.6661i	0.720608	−	1.24813i	−0.240149	−	0.970736i	$-0.577196\pi$
$863$	21.1692	−	36.6661i	0.720608	−	1.24813i	0.960756	−	0.277393i	$-0.0894705\pi$
$864$		0			0
$865$	9.72457	+	16.8434i	0.330645	+	0.572694i
$866$	−4.59006	−	7.95022i	−0.155977	−	0.270159i
$867$		0			0
$868$	−9.81896	+	20.8805i	−0.333277	+	0.708731i
$869$	6.29985	+	10.9117i	0.213708	+	0.370153i
$870$		0			0
$871$	2.22820			0.0754996
$872$	−18.7639	−	32.4999i	−0.635424	−	1.10059i
$873$		0			0
$874$	−24.6832			−0.834921
$875$	17.7536	+	25.5298i	0.600180	+	0.863065i
$876$		0			0
$877$	−10.0508			−0.339393			−0.169697	−	0.985496i	$-0.554279\pi$
$877$	−10.0508			−0.339393			−0.169697	+	0.985496i	$0.554279\pi$
$878$	5.74809	−	9.95598i	0.193989	−	0.335998i
$879$		0			0
$880$	−3.43722	−	5.95343i	−0.115868	−	0.200690i
$881$	−25.7602			−0.867885			−0.433942	−	0.900941i	$-0.642878\pi$
$881$	−25.7602			−0.867885			−0.433942	+	0.900941i	$0.642878\pi$
$882$		0			0
$883$	−53.1876			−1.78991			−0.894953	−	0.446160i	$-0.852791\pi$
$883$	−53.1876			−1.78991			−0.894953	+	0.446160i	$0.852791\pi$
$884$	−2.12695	−	3.68398i	−0.0715370	−	0.123906i
$885$		0			0
$886$	7.33821	−	12.7102i	0.246532	−	0.427006i
$887$	20.9517			0.703489			0.351745	−	0.936096i	$-0.385589\pi$
$887$	20.9517			0.703489			0.351745	+	0.936096i	$0.385589\pi$
$888$		0			0
$889$	−21.7607	−	31.2922i	−0.729832	−	1.04951i
$890$	−23.2279			−0.778601
$891$		0			0
$892$	17.6946	+	30.6480i	0.592460	+	1.02617i
$893$	−61.3370			−2.05256
$894$		0			0
$895$	19.4429	+	33.6761i	0.649904	+	1.12567i
$896$	−12.9192	+	27.4734i	−0.431601	+	0.917822i
$897$		0			0
$898$	−11.9481	−	20.6947i	−0.398712	−	0.690590i
$899$	9.69609	+	16.7941i	0.323383	+	0.560115i
$900$		0			0
$901$	16.6794	−	28.8896i	0.555672	−	0.962452i
$902$	−0.732761	+	1.26918i	−0.0243983	+	0.0422591i
$903$		0			0
$904$	11.6157	+	20.1190i	0.386333	+	0.669149i
$905$	27.7416			0.922163
$906$		0			0
$907$	47.5854			1.58005			0.790024	−	0.613077i	$-0.210068\pi$
$907$	47.5854			1.58005			0.790024	+	0.613077i	$0.210068\pi$
$908$	10.7637	−	18.6433i	0.357207	−	0.618701i
$909$		0			0
$910$	1.40602	−	0.118436i	0.0466090	−	0.00392612i
$911$	14.8860	−	25.7833i	0.493194	−	0.854238i	−0.506775	−	0.862078i	$-0.669162\pi$
$911$	14.8860	−	25.7833i	0.493194	−	0.854238i	0.999969	+	0.00784062i	$0.00249577\pi$
$912$		0			0
$913$	4.34001	−	7.51712i	0.143633	−	0.248780i
$914$	−3.17668	+	5.50217i	−0.105075	+	0.181995i
$915$		0			0
$916$	13.8229	−	23.9420i	0.456723	−	0.791067i
$917$	15.3851	+	22.1239i	0.508060	+	0.730595i
$918$		0			0
$919$	−15.2293	+	26.3779i	−0.502367	+	0.870126i	0.497629	+	0.867390i	$0.334204\pi$
$919$	−15.2293	+	26.3779i	−0.502367	+	0.870126i	−0.999996	+	0.00273583i	$0.999129\pi$
$920$	34.8167			1.14787
$921$		0			0
$922$	9.80179			0.322805
$923$	2.67565	+	4.63436i	0.0880700	+	0.152542i
$924$		0			0
$925$	−1.42339	+	2.46539i	−0.0468009	+	0.0810615i
$926$	1.81110	−	3.13692i	0.0595165	−	0.103086i
$927$		0			0
$928$	10.1191	+	17.5268i	0.332176	+	0.575346i
$929$	10.5830	+	18.3304i	0.347218	+	0.601400i	0.985754	−	0.168192i	$-0.0537930\pi$
$929$	10.5830	+	18.3304i	0.347218	+	0.601400i	−0.638536	+	0.769592i	$0.720460\pi$
$930$		0			0
$931$	−24.1656	−	29.1802i	−0.791996	−	0.956342i
$932$	−18.7064	−	32.4005i	−0.612749	−	1.06131i
$933$		0			0
$934$	15.1046			0.494238
$935$	−10.5141	−	18.2110i	−0.343849	−	0.595564i
$936$		0			0
$937$	40.2779			1.31582			0.657912	−	0.753095i	$-0.271440\pi$
$937$	40.2779			1.31582			0.657912	+	0.753095i	$0.271440\pi$
$938$	−4.71898	−	6.78594i	−0.154080	−	0.221569i
$939$		0			0
$940$	39.0226			1.27278
$941$	−0.910476	+	1.57699i	−0.0296807	+	0.0514084i	−0.880484	−	0.474076i	$-0.842782\pi$
$941$	−0.910476	+	1.57699i	−0.0296807	+	0.0514084i	0.850804	+	0.525484i	$0.176116\pi$
$942$		0			0
$943$	5.67116	+	9.82274i	0.184678	+	0.319872i
$944$	3.09528			0.100743
$945$		0			0
$946$	−8.37494			−0.272293
$947$	−6.74590	−	11.6842i	−0.219212	−	0.379687i	0.735355	−	0.677682i	$-0.237015\pi$
$947$	−6.74590	−	11.6842i	−0.219212	−	0.379687i	−0.954567	+	0.297995i	$0.903682\pi$
$948$		0			0
$949$	0.338174	−	0.585734i	0.0109776	−	0.0190137i
$950$	1.96756			0.0638362
$951$		0			0
$952$	−14.8880	+	31.6602i	−0.482524	+	1.02611i
$953$	−4.95309			−0.160446			−0.0802232	−	0.996777i	$-0.525563\pi$
$953$	−4.95309			−0.160446			−0.0802232	+	0.996777i	$0.525563\pi$
$954$		0			0
$955$	−11.1038	−	19.2323i	−0.359309	−	0.622342i
$956$	15.6400			0.505835
$957$		0			0
$958$	0.998294	+	1.72910i	0.0322534	+	0.0558646i
$959$	3.11519	+	4.47968i	0.100595	+	0.144656i
$960$		0			0
$961$	1.41551	+	2.45174i	0.0456616	+	0.0790883i
$962$	0.595231	+	1.03097i	0.0191910	+	0.0332398i
$963$		0			0
$964$	0.963800	−	1.66935i	0.0310419	−	0.0537661i
$965$	8.50762	−	14.7356i	0.273870	−	0.474357i
$966$		0			0
$967$	−8.62831	−	14.9447i	−0.277468	−	0.480588i	0.693287	−	0.720662i	$-0.256162\pi$
$967$	−8.62831	−	14.9447i	−0.277468	−	0.480588i	−0.970755	+	0.240073i	$0.922829\pi$
$968$	−18.0034			−0.578651
$969$		0			0
$970$	−17.2174			−0.552818
$971$	23.4532	−	40.6221i	0.752649	−	1.30363i	−0.193886	−	0.981024i	$-0.562109\pi$
$971$	23.4532	−	40.6221i	0.752649	−	1.30363i	0.946535	−	0.322602i	$-0.104558\pi$
$972$		0			0
$973$	−7.47347	+	15.8927i	−0.239588	+	0.509497i
$974$	2.17396	−	3.76542i	0.0696583	−	0.120652i
$975$		0			0
$976$	−5.01397	+	8.68444i	−0.160493	+	0.277982i
$977$	17.5817	−	30.4524i	0.562488	−	0.974257i	−0.434791	−	0.900531i	$-0.643178\pi$
$977$	17.5817	−	30.4524i	0.562488	−	0.974257i	0.997279	−	0.0737259i	$-0.0234890\pi$
$978$		0			0
$979$	−15.3220	+	26.5384i	−0.489692	+	0.848171i
$980$	15.3741	+	18.5644i	0.491109	+	0.593018i
$981$		0			0
$982$	0.887434	−	1.53708i	0.0283192	−	0.0490502i
$983$	12.0860			0.385482			0.192741	−	0.981250i	$-0.438262\pi$
$983$	12.0860			0.385482			0.192741	+	0.981250i	$0.438262\pi$
$984$		0			0
$985$	18.9761			0.604630
$986$	6.63093	+	11.4851i	0.211172	+	0.365760i
$987$		0			0
$988$	−1.89457	+	3.28148i	−0.0602742	+	0.104398i
$989$	−32.4087	+	56.1334i	−1.03054	+	1.78494i
$990$		0			0
$991$	−16.1874	−	28.0374i	−0.514209	−	0.890636i	−0.999864	−	0.0164855i	$-0.994752\pi$
$991$	−16.1874	−	28.0374i	−0.514209	−	0.890636i	0.485655	−	0.874150i	$-0.338581\pi$
$992$	−14.6990	−	25.4594i	−0.466693	−	0.808335i
$993$		0			0
$994$	8.44725	−	17.9635i	0.267931	−	0.569768i
$995$	−7.78091	−	13.4769i	−0.246671	−	0.427247i
$996$		0			0
$997$	−14.7332			−0.466605			−0.233303	−	0.972404i	$-0.574953\pi$
$997$	−14.7332			−0.466605			−0.233303	+	0.972404i	$0.574953\pi$
$998$	3.72913	+	6.45904i	0.118044	+	0.204457i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.g.l.541.5		16
3.2	odd	2	inner	567.2.g.l.541.4		16
7.4	even	3		567.2.h.l.298.4		16
9.2	odd	6		567.2.e.g.163.4	✓	16
9.4	even	3		567.2.h.l.352.4		16
9.5	odd	6		567.2.h.l.352.5		16
9.7	even	3		567.2.e.g.163.5	yes	16
21.11	odd	6		567.2.h.l.298.5		16
63.2	odd	6		3969.2.a.bg.1.5		8
63.4	even	3	inner	567.2.g.l.109.5		16
63.11	odd	6		567.2.e.g.487.4	yes	16
63.16	even	3		3969.2.a.bg.1.4		8
63.25	even	3		567.2.e.g.487.5	yes	16
63.32	odd	6	inner	567.2.g.l.109.4		16
63.47	even	6		3969.2.a.bf.1.5		8
63.61	odd	6		3969.2.a.bf.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.4	✓	16	9.2	odd	6
567.2.e.g.163.5	yes	16	9.7	even	3
567.2.e.g.487.4	yes	16	63.11	odd	6
567.2.e.g.487.5	yes	16	63.25	even	3
567.2.g.l.109.4		16	63.32	odd	6	inner
567.2.g.l.109.5		16	63.4	even	3	inner
567.2.g.l.541.4		16	3.2	odd	2	inner
567.2.g.l.541.5		16	1.1	even	1	trivial
567.2.h.l.298.4		16	7.4	even	3
567.2.h.l.298.5		16	21.11	odd	6
567.2.h.l.352.4		16	9.4	even	3
567.2.h.l.352.5		16	9.5	odd	6
3969.2.a.bf.1.4		8	63.61	odd	6
3969.2.a.bf.1.5		8	63.47	even	6
3969.2.a.bg.1.4		8	63.16	even	3
3969.2.a.bg.1.5		8	63.2	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.298668 + 0.517308i) q^{2} +(0.821595 - 1.42304i) q^{4} +2.09557 q^{5} +(-1.51053 - 2.17216i) q^{7} +2.17621 q^{8} +(0.625881 + 1.08406i) q^{10} +1.65141 q^{11} +(0.213022 + 0.368965i) q^{13} +(0.672530 - 1.43017i) q^{14} +(-0.993225 - 1.72032i) q^{16} +(-3.03819 - 5.26230i) q^{17} +(-2.70625 + 4.68736i) q^{19} +(1.72171 - 2.98209i) q^{20} +(0.493225 + 0.854291i) q^{22} +7.63457 q^{23} -0.608573 q^{25} +(-0.127246 + 0.220396i) q^{26} +(-4.33213 + 0.364918i) q^{28} +(-1.82688 + 3.16426i) q^{29} +(2.65372 - 4.59638i) q^{31} +(2.76950 - 4.79691i) q^{32} +(1.81482 - 3.14336i) q^{34} +(-3.16543 - 4.55193i) q^{35} +(2.33890 - 4.05110i) q^{37} -3.23308 q^{38} +4.56041 q^{40} +(0.742827 + 1.28661i) q^{41} +(-4.24499 + 7.35253i) q^{43} +(1.35679 - 2.35004i) q^{44} +(2.28020 + 3.94943i) q^{46} +(5.66624 + 9.81422i) q^{47} +(-2.43658 + 6.56225i) q^{49} +(-0.181761 - 0.314820i) q^{50} +0.700071 q^{52} +(2.74496 + 4.75441i) q^{53} +3.46066 q^{55} +(-3.28724 - 4.72708i) q^{56} -2.18253 q^{58} +(-0.779098 + 1.34944i) q^{59} +(-2.52408 - 4.37184i) q^{61} +3.17033 q^{62} -0.664256 q^{64} +(0.446403 + 0.773193i) q^{65} +(2.61498 - 4.52928i) q^{67} -9.98464 q^{68} +(1.40933 - 2.99702i) q^{70} +12.5604 q^{71} +(-0.793753 - 1.37482i) q^{73} +2.79422 q^{74} +(4.44688 + 7.70222i) q^{76} +(-2.49452 - 3.58714i) q^{77} +(3.81482 + 6.60746i) q^{79} +(-2.08138 - 3.60505i) q^{80} +(-0.443717 + 0.768541i) q^{82} +(2.62806 - 4.55193i) q^{83} +(-6.36674 - 11.0275i) q^{85} -5.07137 q^{86} +3.59382 q^{88} +(-9.27808 + 16.0701i) q^{89} +(0.479675 - 1.02005i) q^{91} +(6.27252 - 10.8643i) q^{92} +(-3.38465 + 5.86239i) q^{94} +(-5.67114 + 9.82270i) q^{95} +(-6.87728 + 11.9118i) q^{97} +(-4.12243 + 0.699472i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} - 14 q^{10} - 6 q^{13} - 6 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} + 72 q^{40} - 10 q^{43} + 36 q^{46} + 4 q^{49} + 68 q^{52} + 8 q^{55} - 44 q^{58} - 36 q^{61} + 76 q^{64}+ \cdots - 14 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 - 14 * q^10 - 6 * q^13 - 6 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 + 72 * q^40 - 10 * q^43 + 36 * q^46 + 4 * q^49 + 68 * q^52 + 8 * q^55 - 44 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 + 104 * q^70 - 32 * q^73 - 58 * q^76 + 32 * q^79 + 2 * q^82 - 30 * q^85 - 144 * q^88 - 22 * q^91 - 54 * q^94 - 14 * q^97

Introduction

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