LMFDB - Embedded newform 819.2.s.g.289.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(289,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,44,0,0,4,0,0,8,0] 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.13
Character	$\chi$	$=$	819.289
Dual form			819.2.s.g.802.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.14867 q^{2} -0.680564 q^{4} +(-0.912102 + 1.57981i) q^{5} +(0.248536 - 2.63405i) q^{7} -3.07908 q^{8} +(-1.04770 + 1.81467i) q^{10} +(-0.248306 + 0.430078i) q^{11} +(-2.92318 - 2.11069i) q^{13} +(0.285485 - 3.02565i) q^{14} -2.17570 q^{16} +0.327463 q^{17} +(-2.30843 - 3.99832i) q^{19} +(0.620744 - 1.07516i) q^{20} +(-0.285221 + 0.494016i) q^{22} -4.71380 q^{23} +(0.836140 + 1.44824i) q^{25} +(-3.35776 - 2.42448i) q^{26} +(-0.169145 + 1.79264i) q^{28} +(-4.87261 - 8.43961i) q^{29} +(-2.01021 - 3.48178i) q^{31} +3.65899 q^{32} +0.376146 q^{34} +(3.93460 + 2.79516i) q^{35} -8.86196 q^{37} +(-2.65162 - 4.59274i) q^{38} +(2.80843 - 4.86435i) q^{40} +(3.37948 + 5.85344i) q^{41} +(-0.285886 + 0.495170i) q^{43} +(0.168988 - 0.292696i) q^{44} -5.41459 q^{46} +(3.64243 - 6.30887i) q^{47} +(-6.87646 - 1.30931i) q^{49} +(0.960446 + 1.66354i) q^{50} +(1.98941 + 1.43646i) q^{52} +(6.74741 + 11.6869i) q^{53} +(-0.452960 - 0.784550i) q^{55} +(-0.765261 + 8.11045i) q^{56} +(-5.59701 - 9.69430i) q^{58} -0.421318 q^{59} +(-2.02321 - 3.50430i) q^{61} +(-2.30906 - 3.99940i) q^{62} +8.55437 q^{64} +(6.00072 - 2.69289i) q^{65} +(3.30454 - 5.72363i) q^{67} -0.222860 q^{68} +(4.51955 + 3.21071i) q^{70} +(-5.61749 + 9.72977i) q^{71} +(-3.47946 - 6.02659i) q^{73} -10.1794 q^{74} +(1.57104 + 2.72111i) q^{76} +(1.07113 + 0.760940i) q^{77} +(-0.921823 + 1.59664i) q^{79} +(1.98446 - 3.43719i) q^{80} +(3.88190 + 6.72365i) q^{82} +16.4203 q^{83} +(-0.298680 + 0.517329i) q^{85} +(-0.328388 + 0.568785i) q^{86} +(0.764552 - 1.32424i) q^{88} -0.00916326 q^{89} +(-6.28619 + 7.17522i) q^{91} +3.20805 q^{92} +(4.18393 - 7.24679i) q^{94} +8.42210 q^{95} +(0.162372 - 0.281237i) q^{97} +(-7.89876 - 1.50397i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) $ 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.14867			0.812230			0.406115	−	0.913822i	$-0.366883\pi$
$2$	1.14867			0.812230			0.406115	+	0.913822i	$0.366883\pi$
$3$		0			0
$3$		0			0
$4$	−0.680564			−0.340282
$5$	−0.912102	+	1.57981i	−0.407904	+	0.706511i	−0.994655	−	0.103257i	$-0.967074\pi$
$5$	−0.912102	+	1.57981i	−0.407904	+	0.706511i	0.586750	+	0.809768i	$0.300407\pi$
$6$		0			0
$7$	0.248536	−	2.63405i	0.0939378	−	0.995578i
$7$	0.248536	−	2.63405i	0.0939378	−	0.995578i
$8$	−3.07908			−1.08862
$9$		0			0
$10$	−1.04770	+	1.81467i	−0.331312	+	0.573850i
$11$	−0.248306	+	0.430078i	−0.0748670	+	0.129673i	−0.901028	−	0.433760i	$-0.857187\pi$
$11$	−0.248306	+	0.430078i	−0.0748670	+	0.129673i	0.826161	+	0.563433i	$0.190520\pi$
$12$		0			0
$13$	−2.92318	−	2.11069i	−0.810744	−	0.585401i
$13$	−2.92318	−	2.11069i	−0.810744	−	0.585401i
$14$	0.285485	−	3.02565i	0.0762991	−	0.808639i
$15$		0			0
$16$	−2.17570			−0.543926
$17$	0.327463			0.0794215			0.0397108	−	0.999211i	$-0.487356\pi$
$17$	0.327463			0.0794215			0.0397108	+	0.999211i	$0.487356\pi$
$18$		0			0
$19$	−2.30843	−	3.99832i	−0.529590	−	0.917277i	−0.999404	−	0.0345120i	$-0.989012\pi$
$19$	−2.30843	−	3.99832i	−0.529590	−	0.917277i	0.469814	−	0.882765i	$-0.344321\pi$
$20$	0.620744	−	1.07516i	0.138803	−	0.240413i
$21$		0			0
$22$	−0.285221	+	0.494016i	−0.0608092	+	0.105325i
$23$	−4.71380			−0.982896			−0.491448	−	0.870907i	$-0.663532\pi$
$23$	−4.71380			−0.982896			−0.491448	+	0.870907i	$0.663532\pi$
$24$		0			0
$25$	0.836140	+	1.44824i	0.167228	+	0.289647i
$26$	−3.35776	−	2.42448i	−0.658511	−	0.475480i
$27$		0			0
$28$	−0.169145	+	1.79264i	−0.0319654	+	0.338777i
$29$	−4.87261	−	8.43961i	−0.904821	−	1.56720i	−0.821157	−	0.570702i	$-0.806671\pi$
$29$	−4.87261	−	8.43961i	−0.904821	−	1.56720i	−0.0836643	−	0.996494i	$-0.526662\pi$
$30$		0			0
$31$	−2.01021	−	3.48178i	−0.361043	−	0.625346i	0.627089	−	0.778947i	$-0.284246\pi$
$31$	−2.01021	−	3.48178i	−0.361043	−	0.625346i	−0.988133	+	0.153602i	$0.950913\pi$
$32$	3.65899			0.646824
$33$		0			0
$34$	0.376146			0.0645086
$35$	3.93460	+	2.79516i	0.665069	+	0.472469i
$36$		0			0
$37$	−8.86196			−1.45690			−0.728448	−	0.685101i	$-0.759758\pi$
$37$	−8.86196			−1.45690			−0.728448	+	0.685101i	$0.759758\pi$
$38$	−2.65162	−	4.59274i	−0.430149	−	0.745040i
$39$		0			0
$40$	2.80843	−	4.86435i	0.444052	−	0.769120i
$41$	3.37948	+	5.85344i	0.527787	+	0.914154i	0.999475	+	0.0323883i	$0.0103113\pi$
$41$	3.37948	+	5.85344i	0.527787	+	0.914154i	−0.471689	+	0.881765i	$0.656355\pi$
$42$		0			0
$43$	−0.285886	+	0.495170i	−0.0435973	+	0.0755127i	−0.887001	−	0.461768i	$-0.847215\pi$
$43$	−0.285886	+	0.495170i	−0.0435973	+	0.0755127i	0.843403	+	0.537281i	$0.180549\pi$
$44$	0.168988	−	0.292696i	0.0254759	−	0.0441255i
$45$		0			0
$46$	−5.41459			−0.798338
$47$	3.64243	−	6.30887i	0.531303	−	0.920243i	−0.468030	−	0.883713i	$-0.655036\pi$
$47$	3.64243	−	6.30887i	0.531303	−	0.920243i	0.999333	−	0.0365304i	$-0.0116306\pi$
$48$		0			0
$49$	−6.87646	−	1.30931i	−0.982351	−	0.187045i
$50$	0.960446	+	1.66354i	0.135828	+	0.235260i
$51$		0			0
$52$	1.98941	+	1.43646i	0.275882	+	0.199201i
$53$	6.74741	+	11.6869i	0.926828	+	1.60531i	0.788595	+	0.614913i	$0.210809\pi$
$53$	6.74741	+	11.6869i	0.926828	+	1.60531i	0.138233	+	0.990400i	$0.455858\pi$
$54$		0			0
$55$	−0.452960	−	0.784550i	−0.0610771	−	0.105789i
$56$	−0.765261	+	8.11045i	−0.102262	+	1.08380i
$57$		0			0
$58$	−5.59701	−	9.69430i	−0.734923	−	1.27292i
$59$	−0.421318			−0.0548509			−0.0274255	−	0.999624i	$-0.508731\pi$
$59$	−0.421318			−0.0548509			−0.0274255	+	0.999624i	$0.508731\pi$
$60$		0			0
$61$	−2.02321	−	3.50430i	−0.259046	−	0.448680i	0.706941	−	0.707273i	$-0.250075\pi$
$61$	−2.02321	−	3.50430i	−0.259046	−	0.448680i	−0.965986	+	0.258593i	$0.916741\pi$
$62$	−2.30906	−	3.99940i	−0.293250	−	0.507925i
$63$		0			0
$64$	8.55437			1.06930
$65$	6.00072	−	2.69289i	0.744298	−	0.334012i
$66$		0			0
$67$	3.30454	−	5.72363i	0.403713	−	0.699252i	−0.590457	−	0.807069i	$-0.701053\pi$
$67$	3.30454	−	5.72363i	0.403713	−	0.699252i	0.994171	+	0.107817i	$0.0343859\pi$
$68$	−0.222860			−0.0270257
$69$		0			0
$70$	4.51955	+	3.21071i	0.540189	+	0.383753i
$71$	−5.61749	+	9.72977i	−0.666673	+	1.15471i	0.312156	+	0.950031i	$0.398949\pi$
$71$	−5.61749	+	9.72977i	−0.666673	+	1.15471i	−0.978829	+	0.204681i	$0.934384\pi$
$72$		0			0
$73$	−3.47946	−	6.02659i	−0.407240	−	0.705360i	0.587340	−	0.809340i	$-0.300175\pi$
$73$	−3.47946	−	6.02659i	−0.407240	−	0.705360i	−0.994579	+	0.103981i	$0.966842\pi$
$74$	−10.1794			−1.18334
$75$		0			0
$76$	1.57104	+	2.72111i	0.180210	+	0.312133i
$77$	1.07113	+	0.760940i	0.122067	+	0.0867172i
$78$		0			0
$79$	−0.921823	+	1.59664i	−0.103713	+	0.179637i	−0.913212	−	0.407485i	$-0.866406\pi$
$79$	−0.921823	+	1.59664i	−0.103713	+	0.179637i	0.809499	+	0.587122i	$0.199739\pi$
$80$	1.98446	−	3.43719i	0.221870	−	0.384290i
$81$		0			0
$82$	3.88190	+	6.72365i	0.428684	+	0.742503i
$83$	16.4203			1.80237			0.901184	−	0.433438i	$-0.142700\pi$
$83$	16.4203			1.80237			0.901184	+	0.433438i	$0.142700\pi$
$84$		0			0
$85$	−0.298680	+	0.517329i	−0.0323964	+	0.0561122i
$86$	−0.328388	+	0.568785i	−0.0354110	+	0.0613337i
$87$		0			0
$88$	0.764552	−	1.32424i	0.0815015	−	0.141165i
$89$	−0.00916326			−0.000971304			−0.000485652	−	1.00000i	$-0.500155\pi$
$89$	−0.00916326			−0.000971304			−0.000485652		1.00000i	$0.500155\pi$
$90$		0			0
$91$	−6.28619	+	7.17522i	−0.658971	+	0.752168i
$92$	3.20805			0.334462
$93$		0			0
$94$	4.18393	−	7.24679i	0.431540	−	0.747449i
$95$	8.42210			0.864089
$96$		0			0
$97$	0.162372	−	0.281237i	0.0164864	−	0.0285553i	−0.857665	−	0.514210i	$-0.828085\pi$
$97$	0.162372	−	0.281237i	0.0164864	−	0.0285553i	0.874151	+	0.485654i	$0.161419\pi$
$98$	−7.89876	−	1.50397i	−0.797895	−	0.151923i
$99$		0			0
$100$	−0.569047	−	0.985618i	−0.0569047	−	0.0985618i
$101$	−2.07095	+	3.58699i	−0.206067	+	0.356919i	−0.950472	−	0.310809i	$-0.899400\pi$
$101$	−2.07095	+	3.58699i	−0.206067	+	0.356919i	0.744405	+	0.667728i	$0.232733\pi$
$102$		0			0
$103$	−5.15653	+	8.93137i	−0.508088	+	0.880034i	0.491868	+	0.870670i	$0.336314\pi$
$103$	−5.15653	+	8.93137i	−0.508088	+	0.880034i	−0.999956	+	0.00936420i	$0.997019\pi$
$104$	9.00069	+	6.49898i	0.882590	+	0.637277i
$105$		0			0
$106$	7.75052	+	13.4243i	0.752798	+	1.30388i
$107$	−10.7439			−1.03865			−0.519326	−	0.854576i	$-0.673817\pi$
$107$	−10.7439			−1.03865			−0.519326	+	0.854576i	$0.673817\pi$
$108$		0			0
$109$	0.992640	+	1.71930i	0.0950777	+	0.164679i	0.909641	−	0.415395i	$-0.136357\pi$
$109$	0.992640	+	1.71930i	0.0950777	+	0.164679i	−0.814563	+	0.580075i	$0.803023\pi$
$110$	−0.520300	−	0.901187i	−0.0496087	−	0.0859248i
$111$		0			0
$112$	−0.540741	+	5.73092i	−0.0510952	+	0.541521i
$113$	−6.12608	+	10.6107i	−0.576293	+	0.998170i	0.419606	+	0.907706i	$0.362168\pi$
$113$	−6.12608	+	10.6107i	−0.576293	+	0.998170i	−0.995900	+	0.0904633i	$0.971165\pi$
$114$		0			0
$115$	4.29947	−	7.44690i	0.400928	−	0.694427i
$116$	3.31612	+	5.74370i	0.307894	+	0.533289i
$117$		0			0
$118$	−0.483954			−0.0445516
$119$	0.0813865	−	0.862556i	0.00746069	−	0.0790703i
$120$		0			0
$121$	5.37669	+	9.31270i	0.488790	+	0.846609i
$122$	−2.32399	−	4.02528i	−0.210405	−	0.364431i
$123$		0			0
$124$	1.36807	+	2.36957i	0.122857	+	0.212794i
$125$	−12.1716			−1.08866
$126$		0			0
$127$	2.59497	+	4.49461i	0.230266	+	0.398833i	0.957886	−	0.287148i	$-0.0927070\pi$
$127$	2.59497	+	4.49461i	0.230266	+	0.398833i	−0.727620	+	0.685980i	$0.759374\pi$
$128$	2.50814			0.221690
$129$		0			0
$130$	6.89283	−	3.09324i	0.604541	−	0.271295i
$131$	9.40287	−	16.2863i	0.821533	−	1.42294i	−0.0830079	−	0.996549i	$-0.526453\pi$
$131$	9.40287	−	16.2863i	0.821533	−	1.42294i	0.904541	−	0.426388i	$-0.140214\pi$
$132$		0			0
$133$	−11.1055	+	5.08680i	−0.962970	+	0.441082i
$134$	3.79581	−	6.57454i	0.327908	−	0.567954i
$135$		0			0
$136$	−1.00828			−0.0864597
$137$	8.66474			0.740279			0.370140	−	0.928976i	$-0.379310\pi$
$137$	8.66474			0.740279			0.370140	+	0.928976i	$0.379310\pi$
$138$		0			0
$139$	4.94885	−	8.57165i	0.419756	−	0.727038i	−0.576159	−	0.817338i	$-0.695449\pi$
$139$	4.94885	−	8.57165i	0.419756	−	0.727038i	0.995915	+	0.0902994i	$0.0287824\pi$
$140$	−2.67775	−	1.90229i	−0.226311	−	0.160773i
$141$		0			0
$142$	−6.45262	+	11.1763i	−0.541492	+	0.937892i
$143$	1.63360	−	0.733099i	0.136609	−	0.0613048i
$144$		0			0
$145$	17.7773			1.47632
$146$	−3.99674	−	6.92255i	−0.330772	−	0.572914i
$147$		0			0
$148$	6.03113			0.495756
$149$	3.99337	+	6.91671i	0.327149	+	0.566639i	0.981945	−	0.189167i	$-0.0605787\pi$
$149$	3.99337	+	6.91671i	0.327149	+	0.566639i	−0.654796	+	0.755806i	$0.727245\pi$
$150$		0			0
$151$	2.45028	+	4.24402i	0.199401	+	0.345373i	0.948334	−	0.317272i	$-0.102767\pi$
$151$	2.45028	+	4.24402i	0.199401	+	0.345373i	−0.748933	+	0.662646i	$0.769434\pi$
$152$	7.10783	+	12.3111i	0.576521	+	0.998564i
$153$		0			0
$154$	1.23038	+	0.874067i	0.0991466	+	0.0704343i
$155$	7.33405			0.589085
$156$		0			0
$157$	−10.2163	−	17.6952i	−0.815350	−	1.41223i	−0.909076	−	0.416630i	$-0.863211\pi$
$157$	−10.2163	−	17.6952i	−0.815350	−	1.41223i	0.0937259	−	0.995598i	$-0.470122\pi$
$158$	−1.05887	+	1.83401i	−0.0842390	+	0.145906i
$159$		0			0
$160$	−3.33737	+	5.78050i	−0.263843	+	0.456989i
$161$	−1.17155	+	12.4164i	−0.0923311	+	0.978550i
$162$		0			0
$163$	0.599918	+	1.03909i	0.0469892	+	0.0813877i	0.888563	−	0.458754i	$-0.151704\pi$
$163$	0.599918	+	1.03909i	0.0469892	+	0.0813877i	−0.841574	+	0.540142i	$0.818371\pi$
$164$	−2.29996	−	3.98364i	−0.179596	−	0.311070i
$165$		0			0
$166$	18.8615			1.46394
$167$	−8.84735	−	15.3241i	−0.684628	−	1.18581i	−0.973553	−	0.228460i	$-0.926631\pi$
$167$	−8.84735	−	15.3241i	−0.684628	−	1.18581i	0.288925	−	0.957352i	$-0.406702\pi$
$168$		0			0
$169$	4.08996	+	12.3399i	0.314612	+	0.949220i
$170$	−0.343084	+	0.594239i	−0.0263133	+	0.0455760i
$171$		0			0
$172$	0.194564	−	0.336995i	0.0148354	−	0.0256956i
$173$	−8.83439	−	15.3016i	−0.671666	−	1.16336i	−0.977431	−	0.211253i	$-0.932246\pi$
$173$	−8.83439	−	15.3016i	−0.671666	−	1.16336i	0.305765	−	0.952107i	$-0.401088\pi$
$174$		0			0
$175$	4.02254	−	1.84250i	0.304076	−	0.139280i
$176$	0.540240	−	0.935722i	0.0407221	−	0.0705327i
$177$		0			0
$178$	−0.0105255			−0.000788923
$179$	6.30863	−	10.9269i	0.471529	−	0.816712i	−0.527940	−	0.849281i	$-0.677036\pi$
$179$	6.30863	−	10.9269i	0.471529	−	0.816712i	0.999469	+	0.0325690i	$0.0103689\pi$
$180$		0			0
$181$	−16.3943			−1.21858			−0.609288	−	0.792949i	$-0.708545\pi$
$181$	−16.3943			−1.21858			−0.609288	+	0.792949i	$0.708545\pi$
$182$	−7.22074	+	8.24194i	−0.535237	+	0.610934i
$183$		0			0
$184$	14.5142			1.07000
$185$	8.08301	−	14.0002i	0.594275	−	1.02931i
$186$		0			0
$187$	−0.0813110	+	0.140835i	−0.00594605	+	0.0102989i
$188$	−2.47891	+	4.29359i	−0.180793	+	0.313142i
$189$		0			0
$190$	9.67419			0.701839
$191$	−4.06797	−	7.04593i	−0.294348	−	0.509825i	0.680485	−	0.732762i	$-0.261769\pi$
$191$	−4.06797	−	7.04593i	−0.294348	−	0.509825i	−0.974833	+	0.222937i	$0.928436\pi$
$192$		0			0
$193$	13.0818	−	22.6584i	0.941650	−	1.63099i	0.179326	−	0.983790i	$-0.442608\pi$
$193$	13.0818	−	22.6584i	0.941650	−	1.63099i	0.762324	−	0.647196i	$-0.224058\pi$
$194$	0.186511	−	0.323047i	0.0133907	−	0.0231934i
$195$		0			0
$196$	4.67987	+	0.891072i	0.334277	+	0.0636480i
$197$	2.28537	+	3.95838i	0.162826	+	0.282023i	0.935881	−	0.352316i	$-0.114606\pi$
$197$	2.28537	+	3.95838i	0.162826	+	0.282023i	−0.773055	+	0.634339i	$0.781272\pi$
$198$		0			0
$199$	20.7656			1.47204			0.736019	−	0.676961i	$-0.236704\pi$
$199$	20.7656			1.47204			0.736019	+	0.676961i	$0.236704\pi$
$200$	−2.57454	−	4.45923i	−0.182047	−	0.315315i
$201$		0			0
$202$	−2.37883	+	4.12026i	−0.167374	+	0.289900i
$203$	−23.4414	+	10.7372i	−1.64526	+	0.753601i
$204$		0			0
$205$	−12.3297			−0.861146
$206$	−5.92313	+	10.2592i	−0.412684	+	0.714790i
$207$		0			0
$208$	6.35997	+	4.59224i	0.440985	+	0.318415i
$209$	2.29279			0.158595
$210$		0			0
$211$	1.42574	+	2.46945i	0.0981517	+	0.170004i	0.910920	−	0.412584i	$-0.135374\pi$
$211$	1.42574	+	2.46945i	0.0981517	+	0.170004i	−0.812768	+	0.582588i	$0.802040\pi$
$212$	−4.59204	−	7.95365i	−0.315383	−	0.546259i
$213$		0			0
$214$	−12.3412			−0.843625
$215$	−0.521515	−	0.903291i	−0.0355670	−	0.0616039i
$216$		0			0
$217$	−9.67079	+	4.42964i	−0.656496	+	0.300703i
$218$	1.14021	+	1.97491i	0.0772249	+	0.133758i
$219$		0			0
$220$	0.308268	+	0.533937i	0.0207835	+	0.0359980i
$221$	−0.957234	−	0.691174i	−0.0643906	−	0.0464934i
$222$		0			0
$223$	−5.62612	−	9.74472i	−0.376753	−	0.652555i	0.613835	−	0.789434i	$-0.289626\pi$
$223$	−5.62612	−	9.74472i	−0.376753	−	0.652555i	−0.990588	+	0.136879i	$0.956293\pi$
$224$	0.909392	−	9.63797i	0.0607613	−	0.643964i
$225$		0			0
$226$	−7.03683	+	12.1881i	−0.468083	+	0.810743i
$227$	−21.6594			−1.43759			−0.718793	−	0.695224i	$-0.755305\pi$
$227$	−21.6594			−1.43759			−0.718793	+	0.695224i	$0.755305\pi$
$228$		0			0
$229$	4.42401	−	7.66262i	0.292347	−	0.506360i	−0.682017	−	0.731336i	$-0.738897\pi$
$229$	4.42401	−	7.66262i	0.292347	−	0.506360i	0.974364	+	0.224976i	$0.0722304\pi$
$230$	4.93866	−	8.55401i	0.325646	−	0.564035i
$231$		0			0
$232$	15.0031	+	25.9862i	0.985004	+	1.70608i
$233$	0.892952	−	1.54664i	0.0584992	−	0.101324i	−0.835293	−	0.549806i	$-0.814702\pi$
$233$	0.892952	−	1.54664i	0.0584992	−	0.101324i	0.893792	+	0.448482i	$0.148035\pi$
$234$		0			0
$235$	6.64453	+	11.5087i	0.433441	+	0.750742i
$236$	0.286734			0.0186648
$237$		0			0
$238$	0.0934860	−	0.990789i	0.00605979	−	0.0642233i
$239$	−10.0734			−0.651592			−0.325796	−	0.945440i	$-0.605632\pi$
$239$	−10.0734			−0.651592			−0.325796	+	0.945440i	$0.605632\pi$
$240$		0			0
$241$	−0.0318609			−0.00205234			−0.00102617	−	0.999999i	$-0.500327\pi$
$241$	−0.0318609			−0.00205234			−0.00102617	+	0.999999i	$0.500327\pi$
$242$	6.17602	+	10.6972i	0.397010	+	0.687641i
$243$		0			0
$244$	1.37692	+	2.38490i	0.0881486	+	0.152678i
$245$	8.34050	−	9.66925i	0.532855	−	0.617746i
$246$		0			0
$247$	−1.69126	+	16.5602i	−0.107612	+	1.05370i
$248$	6.18957	+	10.7207i	0.393038	+	0.680762i
$249$		0			0
$250$	−13.9811			−0.884243
$251$	−8.02759	+	13.9042i	−0.506697	+	0.877625i	0.493273	+	0.869875i	$0.335800\pi$
$251$	−8.02759	+	13.9042i	−0.506697	+	0.877625i	−0.999970	+	0.00775047i	$0.997533\pi$
$252$		0			0
$253$	1.17046	−	2.02730i	0.0735865	−	0.127455i
$254$	2.98075	+	5.16281i	0.187029	+	0.323944i
$255$		0			0
$256$	−14.2277			−0.889233
$257$	−7.50163			−0.467939			−0.233969	−	0.972244i	$-0.575172\pi$
$257$	−7.50163			−0.467939			−0.233969	+	0.972244i	$0.575172\pi$
$258$		0			0
$259$	−2.20252	+	23.3429i	−0.136858	+	1.45045i
$260$	−4.08388	+	1.83269i	−0.253271	+	0.113658i
$261$		0			0
$262$	10.8008	−	18.7075i	0.667274	−	1.15575i
$263$	−5.44106	+	9.42419i	−0.335510	+	0.581120i	−0.983583	−	0.180458i	$-0.942242\pi$
$263$	−5.44106	+	9.42419i	−0.335510	+	0.581120i	0.648073	+	0.761579i	$0.275575\pi$
$264$		0			0
$265$	−24.6173			−1.51223
$266$	−12.7565	+	5.84304i	−0.782153	+	0.358260i
$267$		0			0
$268$	−2.24895	+	3.89529i	−0.137376	+	0.237943i
$269$	0.664410			0.0405098			0.0202549	−	0.999795i	$-0.493552\pi$
$269$	0.664410			0.0405098			0.0202549	+	0.999795i	$0.493552\pi$
$270$		0			0
$271$	10.5923			0.643436			0.321718	−	0.946836i	$-0.395740\pi$
$271$	10.5923			0.643436			0.321718	+	0.946836i	$0.395740\pi$
$272$	−0.712463			−0.0431994
$273$		0			0
$274$	9.95291			0.601277
$275$	−0.830473			−0.0500794
$276$		0			0
$277$	−5.40947			−0.325024			−0.162512	−	0.986707i	$-0.551960\pi$
$277$	−5.40947			−0.325024			−0.162512	+	0.986707i	$0.551960\pi$
$278$	5.68458	−	9.84598i	0.340938	−	0.590522i
$279$		0			0
$280$	−12.1149	−	8.60652i	−0.724006	−	0.514338i
$281$	−18.0294			−1.07554			−0.537772	−	0.843091i	$-0.680734\pi$
$281$	−18.0294			−1.07554			−0.537772	+	0.843091i	$0.680734\pi$
$282$		0			0
$283$	11.4478	−	19.8282i	0.680504	−	1.17867i	−0.294324	−	0.955706i	$-0.595094\pi$
$283$	11.4478	−	19.8282i	0.680504	−	1.17867i	0.974827	−	0.222961i	$-0.0715723\pi$
$284$	3.82306	−	6.62174i	0.226857	−	0.392928i
$285$		0			0
$286$	1.87647	−	0.842086i	0.110958	−	0.0497936i
$287$	16.2582	−	7.44695i	0.959690	−	0.439579i
$288$		0			0
$289$	−16.8928			−0.993692
$290$	20.4202			1.19911
$291$		0			0
$292$	2.36799	+	4.10148i	0.138576	+	0.240021i
$293$	6.98624	−	12.1005i	0.408141	−	0.706920i	−0.586541	−	0.809920i	$-0.699511\pi$
$293$	6.98624	−	12.1005i	0.408141	−	0.706920i	0.994681	+	0.102999i	$0.0328440\pi$
$294$		0			0
$295$	0.384285	−	0.665601i	0.0223739	−	0.0387528i
$296$	27.2866			1.58600
$297$		0			0
$298$	4.58705	+	7.94500i	0.265720	+	0.460241i
$299$	13.7793	+	9.94939i	0.796877	+	0.575388i
$300$		0			0
$301$	1.23325	+	0.876107i	0.0710833	+	0.0504980i
$302$	2.81456	+	4.87496i	0.161960	+	0.280523i
$303$		0			0
$304$	5.02246	+	8.69916i	0.288058	+	0.498931i
$305$	7.38150			0.422663
$306$		0			0
$307$	26.2965			1.50082			0.750409	−	0.660973i	$-0.229856\pi$
$307$	26.2965			1.50082			0.750409	+	0.660973i	$0.229856\pi$
$308$	−0.728976	−	0.517868i	−0.0415373	−	0.0295083i
$309$		0			0
$310$	8.42438			0.478473
$311$	9.81974	+	17.0083i	0.556827	+	0.964452i	0.997759	+	0.0669116i	$0.0213145\pi$
$311$	9.81974	+	17.0083i	0.556827	+	0.964452i	−0.440932	+	0.897540i	$0.645352\pi$
$312$		0			0
$313$	15.0427	−	26.0547i	0.850264	−	1.47270i	−0.0307058	−	0.999528i	$-0.509775\pi$
$313$	15.0427	−	26.0547i	0.850264	−	1.47270i	0.880970	−	0.473172i	$-0.156891\pi$
$314$	−11.7351	−	20.3259i	−0.662252	−	1.14705i
$315$		0			0
$316$	0.627360	−	1.08662i	0.0352917	−	0.0611271i
$317$	7.30518	−	12.6529i	0.410300	−	0.710660i	−0.584623	−	0.811305i	$-0.698757\pi$
$317$	7.30518	−	12.6529i	0.410300	−	0.710660i	0.994922	+	0.100646i	$0.0320908\pi$
$318$		0			0
$319$	4.83959			0.270965
$320$	−7.80246	+	13.5143i	−0.436171	+	0.755470i
$321$		0			0
$322$	−1.34572	+	14.2623i	−0.0749941	+	0.794808i
$323$	−0.755927	−	1.30930i	−0.0420609	−	0.0728516i
$324$		0			0
$325$	0.612594	−	5.99829i	0.0339806	−	0.332725i
$326$	0.689106	+	1.19357i	0.0381661	+	0.0661056i
$327$		0			0
$328$	−10.4057	−	18.0232i	−0.574558	−	0.995164i
$329$	−15.7126	−	11.1623i	−0.866264	−	0.615399i
$330$		0			0
$331$	−11.2112	−	19.4183i	−0.616221	−	1.06733i	−0.990169	−	0.139876i	$-0.955329\pi$
$331$	−11.2112	−	19.4183i	−0.616221	−	1.06733i	0.373948	−	0.927450i	$-0.378004\pi$
$332$	−11.1751			−0.613313
$333$		0			0
$334$	−10.1627	−	17.6022i	−0.556076	−	0.963152i
$335$	6.02815	+	10.4411i	0.329353	+	0.570456i
$336$		0			0
$337$	−17.9465			−0.977606			−0.488803	−	0.872394i	$-0.662566\pi$
$337$	−17.9465			−0.977606			−0.488803	+	0.872394i	$0.662566\pi$
$338$	4.69800	+	14.1744i	0.255538	+	0.770985i
$339$		0			0
$340$	0.203271	−	0.352076i	0.0110239	−	0.0190940i
$341$	1.99658			0.108121
$342$		0			0
$343$	−5.15785	+	17.7875i	−0.278498	+	0.960437i
$344$	0.880266	−	1.52466i	0.0474607	−	0.0822044i
$345$		0			0
$346$	−10.1478	−	17.5765i	−0.545548	−	0.944916i
$347$	−14.4532			−0.775887			−0.387943	−	0.921683i	$-0.626814\pi$
$347$	−14.4532			−0.775887			−0.387943	+	0.921683i	$0.626814\pi$
$348$		0			0
$349$	4.41584	+	7.64846i	0.236375	+	0.409413i	0.959671	−	0.281125i	$-0.0907074\pi$
$349$	4.41584	+	7.64846i	0.236375	+	0.409413i	−0.723297	+	0.690537i	$0.757374\pi$
$350$	4.62056	−	2.11642i	0.246979	−	0.113127i
$351$		0			0
$352$	−0.908548	+	1.57365i	−0.0484258	+	0.0838759i
$353$	−17.8226	+	30.8696i	−0.948599	+	1.64302i	−0.200219	+	0.979751i	$0.564165\pi$
$353$	−17.8226	+	30.8696i	−0.948599	+	1.64302i	−0.748380	+	0.663271i	$0.769168\pi$
$354$		0			0
$355$	−10.2474	−	17.7491i	−0.543878	−	0.942024i
$356$	0.00623619			0.000330517
$357$		0			0
$358$	7.24651	−	12.5513i	0.382990	−	0.663359i
$359$	10.3638	−	17.9506i	0.546980	−	0.947398i	−0.451499	−	0.892272i	$-0.649111\pi$
$359$	10.3638	−	17.9506i	0.546980	−	0.947398i	0.998479	−	0.0551261i	$-0.0175561\pi$
$360$		0			0
$361$	−1.15771	+	2.00521i	−0.0609319	+	0.105537i
$362$	−18.8316			−0.989765
$363$		0			0
$364$	4.27815	−	4.88320i	0.224236	−	0.255949i
$365$	12.6945			0.664459
$366$		0			0
$367$	−8.16891	+	14.1490i	−0.426414	+	0.738570i	−0.996551	−	0.0829792i	$-0.973556\pi$
$367$	−8.16891	+	14.1490i	−0.426414	+	0.738570i	0.570138	+	0.821549i	$0.306890\pi$
$368$	10.2558			0.534623
$369$		0			0
$370$	9.28469	−	16.0815i	0.482688	−	0.836040i
$371$	32.4608	−	14.8684i	1.68528	−	0.771930i
$372$		0			0
$373$	−17.8600	−	30.9344i	−0.924755	−	1.60172i	−0.791955	−	0.610579i	$-0.790937\pi$
$373$	−17.8600	−	30.9344i	−0.924755	−	1.60172i	−0.132799	−	0.991143i	$-0.542397\pi$
$374$	−0.0933993	+	0.161772i	−0.00482956	+	0.00836505i
$375$		0			0
$376$	−11.2153	+	19.4255i	−0.578385	+	1.00179i
$377$	−3.56990	+	34.9551i	−0.183859	+	1.80028i
$378$		0			0
$379$	13.5707	+	23.5051i	0.697078	+	1.20738i	0.969475	+	0.245190i	$0.0788504\pi$
$379$	13.5707	+	23.5051i	0.697078	+	1.20738i	−0.272397	+	0.962185i	$0.587816\pi$
$380$	−5.73178			−0.294034
$381$		0			0
$382$	−4.67274	−	8.09342i	−0.239078	−	0.414095i
$383$	6.24995	+	10.8252i	0.319357	+	0.553143i	0.980354	−	0.197246i	$-0.0631996\pi$
$383$	6.24995	+	10.8252i	0.319357	+	0.553143i	−0.660997	+	0.750389i	$0.729866\pi$
$384$		0			0
$385$	−2.17912	+	0.998132i	−0.111058	+	0.0508695i
$386$	15.0267	−	26.0269i	0.764837	−	1.32474i
$387$		0			0
$388$	−0.110505	+	0.191400i	−0.00561002	+	0.00971684i
$389$	−15.8307	−	27.4196i	−0.802648	−	1.39023i	−0.917868	−	0.396886i	$-0.870091\pi$
$389$	−15.8307	−	27.4196i	−0.802648	−	1.39023i	0.115220	−	0.993340i	$-0.463243\pi$
$390$		0			0
$391$	−1.54360			−0.0780631
$392$	21.1731	+	4.03148i	1.06940	+	0.203620i
$393$		0			0
$394$	2.62513	+	4.54685i	0.132252	+	0.229067i
$395$	−1.68159	−	2.91260i	−0.0846101	−	0.146549i
$396$		0			0
$397$	−6.03390	−	10.4510i	−0.302833	−	0.524521i	0.673944	−	0.738783i	$-0.264599\pi$
$397$	−6.03390	−	10.4510i	−0.302833	−	0.524521i	−0.976776	+	0.214261i	$0.931266\pi$
$398$	23.8528			1.19563
$399$		0			0
$400$	−1.81919	−	3.15093i	−0.0909596	−	0.157547i
$401$	−20.7929			−1.03835			−0.519173	−	0.854669i	$-0.673760\pi$
$401$	−20.7929			−1.03835			−0.519173	+	0.854669i	$0.673760\pi$
$402$		0			0
$403$	−1.47277	+	14.4208i	−0.0733637	+	0.718350i
$404$	1.40941	−	2.44118i	0.0701210	−	0.121453i
$405$		0			0
$406$	−26.9264	+	12.3334i	−1.33633	+	0.612098i
$407$	2.20047	−	3.81133i	0.109073	−	0.188921i
$408$		0			0
$409$	−25.8758			−1.27948			−0.639738	−	0.768593i	$-0.720957\pi$
$409$	−25.8758			−1.27948			−0.639738	+	0.768593i	$0.720957\pi$
$410$	−14.1628			−0.699449
$411$		0			0
$412$	3.50935	−	6.07837i	0.172893	−	0.299460i
$413$	−0.104713	+	1.10977i	−0.00515257	+	0.0546084i
$414$		0			0
$415$	−14.9770	+	25.9410i	−0.735194	+	1.27339i
$416$	−10.6959	−	7.72300i	−0.524409	−	0.378651i
$417$		0			0
$418$	2.63365			0.128816
$419$	−1.57424	−	2.72667i	−0.0769068	−	0.133207i	0.825007	−	0.565122i	$-0.191171\pi$
$419$	−1.57424	−	2.72667i	−0.0769068	−	0.133207i	−0.901914	+	0.431916i	$0.857838\pi$
$420$		0			0
$421$	3.38102			0.164781			0.0823905	−	0.996600i	$-0.473745\pi$
$421$	3.38102			0.164781			0.0823905	+	0.996600i	$0.473745\pi$
$422$	1.63770	+	2.83657i	0.0797218	+	0.138082i
$423$		0			0
$424$	−20.7758	−	35.9847i	−1.00896	−	1.74757i
$425$	0.273805	+	0.474245i	0.0132815	+	0.0230042i
$426$		0			0
$427$	−9.73336	+	4.45830i	−0.471030	+	0.215752i
$428$	7.31192			0.353435
$429$		0			0
$430$	−0.599047	−	1.03758i	−0.0288886	−	0.0500365i
$431$	−9.61470	+	16.6531i	−0.463124	+	0.802154i	−0.999115	−	0.0420699i	$-0.986605\pi$
$431$	−9.61470	+	16.6531i	−0.463124	+	0.802154i	0.535991	+	0.844224i	$0.319938\pi$
$432$		0			0
$433$	9.58693	−	16.6050i	0.460718	−	0.797988i	−0.538279	−	0.842767i	$-0.680925\pi$
$433$	9.58693	−	16.6050i	0.460718	−	0.797988i	0.998997	+	0.0447794i	$0.0142585\pi$
$434$	−11.1085	+	5.08818i	−0.533226	+	0.244240i
$435$		0			0
$436$	−0.675555	−	1.17010i	−0.0323532	−	0.0560374i
$437$	10.8815	+	18.8473i	0.520532	+	0.901588i
$438$		0			0
$439$	−7.92306			−0.378147			−0.189074	−	0.981963i	$-0.560548\pi$
$439$	−7.92306			−0.378147			−0.189074	+	0.981963i	$0.560548\pi$
$440$	1.39470	+	2.41569i	0.0664896	+	0.115163i
$441$		0			0
$442$	−1.09954	−	0.793929i	−0.0523000	−	0.0377634i
$443$	−5.63224	+	9.75532i	−0.267596	+	0.463489i	−0.968240	−	0.250021i	$-0.919562\pi$
$443$	−5.63224	+	9.75532i	−0.267596	+	0.463489i	0.700645	+	0.713510i	$0.252896\pi$
$444$		0			0
$445$	0.00835783	−	0.0144762i	0.000396199	−	0.000686237i
$446$	−6.46254	−	11.1934i	−0.306010	−	0.530025i
$447$		0			0
$448$	2.12607	−	22.5327i	0.100447	−	1.06457i
$449$	0.249038	−	0.431347i	0.0117528	−	0.0203565i	−0.860089	−	0.510144i	$-0.829592\pi$
$449$	0.249038	−	0.431347i	0.0117528	−	0.0203565i	0.871842	+	0.489787i	$0.162926\pi$
$450$		0			0
$451$	−3.35658			−0.158055
$452$	4.16919	−	7.22125i	0.196102	−	0.339659i
$453$		0			0
$454$	−24.8795			−1.16765
$455$	−5.60183	−	16.4755i	−0.262618	−	0.772383i
$456$		0			0
$457$	18.6139			0.870723			0.435361	−	0.900256i	$-0.356621\pi$
$457$	18.6139			0.870723			0.435361	+	0.900256i	$0.356621\pi$
$458$	5.08172	−	8.80180i	0.237453	−	0.411281i
$459$		0			0
$460$	−2.92607	+	5.06809i	−0.136429	+	0.236301i
$461$	−2.92514	+	5.06650i	−0.136237	+	0.235970i	−0.926069	−	0.377353i	$-0.876834\pi$
$461$	−2.92514	+	5.06650i	−0.136237	+	0.235970i	0.789832	+	0.613323i	$0.210168\pi$
$462$		0			0
$463$	23.3439			1.08488			0.542441	−	0.840094i	$-0.317500\pi$
$463$	23.3439			1.08488			0.542441	+	0.840094i	$0.317500\pi$
$464$	10.6014	+	18.3621i	0.492156	+	0.852439i
$465$		0			0
$466$	1.02570	−	1.77657i	0.0475148	−	0.0822981i
$467$	−5.90061	+	10.2202i	−0.273048	+	0.472933i	−0.969641	−	0.244534i	$-0.921365\pi$
$467$	−5.90061	+	10.2202i	−0.273048	+	0.472933i	0.696593	+	0.717467i	$0.254698\pi$
$468$		0			0
$469$	−14.2550	−	10.1268i	−0.658236	−	0.467614i
$470$	7.63235	+	13.2196i	0.352054	+	0.609776i
$471$		0			0
$472$	1.29727			0.0597117
$473$	−0.141974	−	0.245907i	−0.00652799	−	0.0113068i
$474$		0			0
$475$	3.86034	−	6.68631i	0.177125	−	0.306789i
$476$	−0.0553887	+	0.587024i	−0.00253874	+	0.0269062i
$477$		0			0
$478$	−11.5709			−0.529243
$479$	17.0841	−	29.5905i	0.780592	−	1.35203i	−0.151005	−	0.988533i	$-0.548251\pi$
$479$	17.0841	−	29.5905i	0.780592	−	1.35203i	0.931597	−	0.363492i	$-0.118416\pi$
$480$		0			0
$481$	25.9051	+	18.7049i	1.18117	+	0.852868i
$482$	−0.0365976			−0.00166697
$483$		0			0
$484$	−3.65918	−	6.33789i	−0.166326	−	0.288086i
$485$	0.296200	+	0.513033i	0.0134497	+	0.0232956i
$486$		0			0
$487$	−16.5891			−0.751723			−0.375861	−	0.926676i	$-0.622653\pi$
$487$	−16.5891			−0.751723			−0.375861	+	0.926676i	$0.622653\pi$
$488$	6.22962	+	10.7900i	0.282002	+	0.488441i
$489$		0			0
$490$	9.58045	−	11.1067i	0.432801	−	0.501752i
$491$	6.06699	+	10.5083i	0.273799	+	0.474234i	0.969831	−	0.243776i	$-0.0783863\pi$
$491$	6.06699	+	10.5083i	0.273799	+	0.474234i	−0.696032	+	0.718011i	$0.745053\pi$
$492$		0			0
$493$	−1.59560	−	2.76366i	−0.0718623	−	0.124469i
$494$	−1.94270	+	19.0221i	−0.0874060	+	0.855847i
$495$		0			0
$496$	4.37361	+	7.57532i	0.196381	+	0.340142i
$497$	24.2326	+	17.2150i	1.08698	+	0.772196i
$498$		0			0
$499$	8.06176	−	13.9634i	0.360894	−	0.625087i	−0.627214	−	0.778847i	$-0.715805\pi$
$499$	8.06176	−	13.9634i	0.360894	−	0.625087i	0.988108	+	0.153760i	$0.0491383\pi$
$500$	8.28355			0.370452
$501$		0			0
$502$	−9.22103	+	15.9713i	−0.411555	+	0.712834i
$503$	−12.7570	+	22.0958i	−0.568806	+	0.985201i	0.427878	+	0.903836i	$0.359261\pi$
$503$	−12.7570	+	22.0958i	−0.568806	+	0.985201i	−0.996684	+	0.0813649i	$0.974072\pi$
$504$		0			0
$505$	−3.77783	−	6.54340i	−0.168111	−	0.291178i
$506$	1.34447	−	2.32870i	0.0597691	−	0.103523i
$507$		0			0
$508$	−1.76604	−	3.05887i	−0.0783554	−	0.135716i
$509$	27.1284			1.20244			0.601222	−	0.799082i	$-0.294681\pi$
$509$	27.1284			1.20244			0.601222	+	0.799082i	$0.294681\pi$
$510$		0			0
$511$	−16.7391	+	7.66724i	−0.740496	+	0.339179i
$512$	−21.3592			−0.943952
$513$		0			0
$514$	−8.61688			−0.380074
$515$	−9.40656	−	16.2926i	−0.414502	−	0.717939i
$516$		0			0
$517$	1.80887	+	3.13306i	0.0795540	+	0.137792i
$518$	−2.52996	+	26.8132i	−0.111160	+	1.17810i
$519$		0			0
$520$	−18.4767	+	8.29162i	−0.810256	+	0.363612i
$521$	−11.1918	−	19.3847i	−0.490320	−	0.849260i	0.509618	−	0.860401i	$-0.329787\pi$
$521$	−11.1918	−	19.3847i	−0.490320	−	0.849260i	−0.999938	+	0.0111412i	$0.996454\pi$
$522$		0			0
$523$	−21.7523			−0.951163			−0.475581	−	0.879672i	$-0.657762\pi$
$523$	−21.7523			−0.951163			−0.475581	+	0.879672i	$0.657762\pi$
$524$	−6.39926	+	11.0838i	−0.279553	+	0.484200i
$525$		0			0
$526$	−6.24996	+	10.8253i	−0.272511	+	0.472004i
$527$	−0.658269	−	1.14015i	−0.0286746	−	0.0496659i
$528$		0			0
$529$	−0.780048			−0.0339151
$530$	−28.2771			−1.22828
$531$		0			0
$532$	7.55801	−	3.46189i	0.327681	−	0.150092i
$533$	2.47596	−	24.2437i	0.107246	−	1.05011i
$534$		0			0
$535$	9.79954	−	16.9733i	0.423671	−	0.733820i
$536$	−10.1749	+	17.6235i	−0.439490	+	0.761218i
$537$		0			0
$538$	0.763186			0.0329033
$539$	2.27057	−	2.63230i	0.0978004	−	0.113381i
$540$		0			0
$541$	10.5424	−	18.2599i	0.453252	−	0.785056i	−0.545334	−	0.838219i	$-0.683597\pi$
$541$	10.5424	−	18.2599i	0.453252	−	0.785056i	0.998586	+	0.0531634i	$0.0169304\pi$
$542$	12.1670			0.522618
$543$		0			0
$544$	1.19819			0.0513718
$545$	−3.62156			−0.155130
$546$		0			0
$547$	17.6882			0.756293			0.378146	−	0.925746i	$-0.376562\pi$
$547$	17.6882			0.756293			0.378146	+	0.925746i	$0.376562\pi$
$548$	−5.89691			−0.251904
$549$		0			0
$550$	−0.953937			−0.0406760
$551$	−22.4962	+	38.9645i	−0.958369	+	1.65994i
$552$		0			0
$553$	3.97654	+	2.82495i	0.169100	+	0.120129i
$554$	−6.21368			−0.263994
$555$		0			0
$556$	−3.36801	+	5.83356i	−0.142835	+	0.247398i
$557$	20.6726	−	35.8060i	0.875926	−	1.51715i	0.0201523	−	0.999797i	$-0.493585\pi$
$557$	20.6726	−	35.8060i	0.875926	−	1.51715i	0.855773	−	0.517351i	$-0.173082\pi$
$558$		0			0
$559$	1.88085	−	0.844052i	0.0795514	−	0.0356996i
$560$	−8.56053	−	6.08145i	−0.361749	−	0.256988i
$561$		0			0
$562$	−20.7098			−0.873589
$563$	4.33402			0.182657			0.0913287	−	0.995821i	$-0.470889\pi$
$563$	4.33402			0.182657			0.0913287	+	0.995821i	$0.470889\pi$
$564$		0			0
$565$	−11.1752	−	19.3561i	−0.470145	−	0.814315i
$566$	13.1498	−	22.7761i	0.552726	−	0.957349i
$567$		0			0
$568$	17.2967	−	29.9587i	0.725752	−	1.25704i
$569$	−17.4873			−0.733105			−0.366553	−	0.930397i	$-0.619462\pi$
$569$	−17.4873			−0.733105			−0.366553	+	0.930397i	$0.619462\pi$
$570$		0			0
$571$	21.9017	+	37.9348i	0.916557	+	1.58752i	0.804606	+	0.593809i	$0.202377\pi$
$571$	21.9017	+	37.9348i	0.916557	+	1.58752i	0.111951	+	0.993714i	$0.464290\pi$
$572$	−1.11177	+	0.498921i	−0.0464855	+	0.0208609i
$573$		0			0
$574$	18.6752	−	8.55406i	0.779489	−	0.357040i
$575$	−3.94140	−	6.82671i	−0.164368	−	0.284693i
$576$		0			0
$577$	−5.53294	−	9.58333i	−0.230339	−	0.398959i	0.727569	−	0.686035i	$-0.240650\pi$
$577$	−5.53294	−	9.58333i	−0.230339	−	0.398959i	−0.957908	+	0.287076i	$0.907317\pi$
$578$	−19.4042			−0.807107
$579$		0			0
$580$	−12.0986			−0.502366
$581$	4.08105	−	43.2520i	0.169310	−	1.79440i
$582$		0			0
$583$	−6.70168			−0.277555
$584$	10.7135	+	18.5563i	0.443328	+	0.767867i
$585$		0			0
$586$	8.02486	−	13.8995i	0.331504	−	0.574182i
$587$	−16.7991	−	29.0970i	−0.693375	−	1.20096i	−0.970726	−	0.240191i	$-0.922790\pi$
$587$	−16.7991	−	29.0970i	−0.693375	−	1.20096i	0.277351	−	0.960769i	$-0.410544\pi$
$588$		0			0
$589$	−9.28084	+	16.0749i	−0.382410	+	0.662354i
$590$	0.441415	−	0.764554i	0.0181728	−	0.0314762i
$591$		0			0
$592$	19.2810			0.792444
$593$	12.6657	−	21.9376i	0.520118	−	0.900870i	−0.479609	−	0.877482i	$-0.659221\pi$
$593$	12.6657	−	21.9376i	0.520118	−	0.900870i	0.999726	−	0.0233879i	$-0.00744528\pi$
$594$		0			0
$595$	1.28844	+	0.915314i	0.0528208	+	0.0375242i
$596$	−2.71774	−	4.70727i	−0.111323	−	0.192817i
$597$		0			0
$598$	15.8278	+	11.4285i	0.647248	+	0.467347i
$599$	0.0951740	+	0.164846i	0.00388870	+	0.00673543i	0.867963	−	0.496629i	$-0.165429\pi$
$599$	0.0951740	+	0.164846i	0.00388870	+	0.00673543i	−0.864075	+	0.503364i	$0.832096\pi$
$600$		0			0
$601$	14.2066	+	24.6066i	0.579501	+	1.00372i	0.995537	+	0.0943767i	$0.0300858\pi$
$601$	14.2066	+	24.6066i	0.579501	+	1.00372i	−0.416036	+	0.909348i	$0.636581\pi$
$602$	1.41659	+	1.00636i	0.0577360	+	0.0410160i
$603$		0			0
$604$	−1.66758	−	2.88833i	−0.0678527	−	0.117524i
$605$	−19.6164			−0.797518
$606$		0			0
$607$	3.76150	+	6.51512i	0.152675	+	0.264440i	0.932210	−	0.361918i	$-0.117878\pi$
$607$	3.76150	+	6.51512i	0.152675	+	0.264440i	−0.779535	+	0.626358i	$0.784545\pi$
$608$	−8.44653	−	14.6298i	−0.342552	−	0.593318i
$609$		0			0
$610$	8.47888			0.343300
$611$	−23.9635	+	10.7539i	−0.969461	+	0.435057i
$612$		0			0
$613$	−0.0687133	+	0.119015i	−0.00277530	+	0.00480696i	−0.867410	−	0.497595i	$-0.834217\pi$
$613$	−0.0687133	+	0.119015i	−0.00277530	+	0.00480696i	0.864634	+	0.502402i	$0.167550\pi$
$614$	30.2059			1.21901
$615$		0			0
$616$	−3.29811	−	2.34299i	−0.132884	−	0.0944018i
$617$	−3.53171	+	6.11709i	−0.142181	+	0.246265i	−0.928318	−	0.371788i	$-0.878745\pi$
$617$	−3.53171	+	6.11709i	−0.142181	+	0.246265i	0.786137	+	0.618053i	$0.212078\pi$
$618$		0			0
$619$	1.01040	+	1.75007i	0.0406115	+	0.0703412i	0.885617	−	0.464417i	$-0.153736\pi$
$619$	1.01040	+	1.75007i	0.0406115	+	0.0703412i	−0.845005	+	0.534758i	$0.820403\pi$
$620$	−4.99129			−0.200455
$621$		0			0
$622$	11.2796	+	19.5369i	0.452271	+	0.783357i
$623$	−0.00227740	+	0.0241365i	−9.12422e−5	+	0.000967009i
$624$		0			0
$625$	6.92104	−	11.9876i	0.276842	−	0.479504i
$626$	17.2791	−	29.9282i	0.690610	−	1.19617i
$627$		0			0
$628$	6.95285	+	12.0427i	0.277449	+	0.480556i
$629$	−2.90197			−0.115709
$630$		0			0
$631$	−10.3447	+	17.9176i	−0.411816	+	0.713287i	−0.995088	−	0.0989901i	$-0.968439\pi$
$631$	−10.3447	+	17.9176i	−0.411816	+	0.713287i	0.583272	+	0.812277i	$0.301772\pi$
$632$	2.83836	−	4.91619i	0.112904	−	0.195555i
$633$		0			0
$634$	8.39121	−	14.5340i	0.333258	−	0.577219i
$635$	−9.46750			−0.375706
$636$		0			0
$637$	17.3376	+	18.3414i	0.686940	+	0.726715i
$638$	5.55907			0.220086
$639$		0			0
$640$	−2.28768	+	3.96238i	−0.0904285	+	0.156627i
$641$	16.6246			0.656632			0.328316	−	0.944568i	$-0.393519\pi$
$641$	16.6246			0.656632			0.328316	+	0.944568i	$0.393519\pi$
$642$		0			0
$643$	19.4799	−	33.7401i	0.768212	−	1.33058i	−0.170320	−	0.985389i	$-0.554480\pi$
$643$	19.4799	−	33.7401i	0.768212	−	1.33058i	0.938532	−	0.345193i	$-0.112186\pi$
$644$	0.797315	−	8.45016i	0.0314186	−	0.332983i
$645$		0			0
$646$	−0.868308	−	1.50395i	−0.0341631	−	0.0591723i
$647$	−3.91165	+	6.77518i	−0.153783	+	0.266360i	−0.932615	−	0.360872i	$-0.882479\pi$
$647$	−3.91165	+	6.77518i	−0.153783	+	0.266360i	0.778832	+	0.627232i	$0.215812\pi$
$648$		0			0
$649$	0.104616	−	0.181200i	0.00410652	−	0.00711270i
$650$	0.703666	−	6.89004i	0.0276001	−	0.270250i
$651$		0			0
$652$	−0.408283	−	0.707167i	−0.0159896	−	0.0276948i
$653$	−38.1430			−1.49265			−0.746326	−	0.665580i	$-0.768184\pi$
$653$	−38.1430			−1.49265			−0.746326	+	0.665580i	$0.768184\pi$
$654$		0			0
$655$	17.1528	+	29.7094i	0.670214	+	1.16084i
$656$	−7.35276	−	12.7353i	−0.287077	−	0.497232i
$657$		0			0
$658$	−18.0486	−	12.8218i	−0.703606	−	0.499845i
$659$	4.06002	−	7.03216i	0.158156	−	0.273934i	−0.776048	−	0.630674i	$-0.782778\pi$
$659$	4.06002	−	7.03216i	0.158156	−	0.273934i	0.934204	+	0.356740i	$0.116112\pi$
$660$		0			0
$661$	7.74977	−	13.4230i	0.301431	−	0.522094i	−0.675029	−	0.737791i	$-0.735869\pi$
$661$	7.74977	−	13.4230i	0.301431	−	0.522094i	0.976460	+	0.215697i	$0.0692024\pi$
$662$	−12.8779	−	22.3052i	−0.500513	−	0.866915i
$663$		0			0
$664$	−50.5595			−1.96209
$665$	2.09320	−	22.1842i	0.0811706	−	0.860268i
$666$		0			0
$667$	22.9685	+	39.7827i	0.889345	+	1.54039i
$668$	6.02119	+	10.4290i	0.232967	+	0.403510i
$669$		0			0
$670$	6.92434	+	11.9933i	0.267510	+	0.463342i
$671$	2.00950			0.0775758
$672$		0			0
$673$	−0.244034	−	0.422680i	−0.00940684	−	0.0162931i	0.861284	−	0.508124i	$-0.169661\pi$
$673$	−0.244034	−	0.422680i	−0.00940684	−	0.0162931i	−0.870691	+	0.491831i	$0.836328\pi$
$674$	−20.6145			−0.794041
$675$		0			0
$676$	−2.78348	−	8.39807i	−0.107057	−	0.323003i
$677$	−22.8264	+	39.5366i	−0.877292	+	1.51951i	−0.0229904	+	0.999736i	$0.507319\pi$
$677$	−22.8264	+	39.5366i	−0.877292	+	1.51951i	−0.854301	+	0.519778i	$0.826015\pi$
$678$		0			0
$679$	−0.700437	−	0.497594i	−0.0268803	−	0.0190959i
$680$	0.919658	−	1.59290i	0.0352673	−	0.0610847i
$681$		0			0
$682$	2.29341			0.0878191
$683$	−23.1964			−0.887585			−0.443793	−	0.896130i	$-0.646367\pi$
$683$	−23.1964			−0.887585			−0.443793	+	0.896130i	$0.646367\pi$
$684$		0			0
$685$	−7.90313	+	13.6886i	−0.301963	+	0.523015i
$686$	−5.92465	+	20.4320i	−0.226204	+	0.780096i
$687$		0			0
$688$	0.622004	−	1.07734i	0.0237137	−	0.0410733i
$689$	4.94346	−	48.4045i	0.188331	−	1.84406i
$690$		0			0
$691$	42.7318			1.62559			0.812796	−	0.582548i	$-0.197944\pi$
$691$	42.7318			1.62559			0.812796	+	0.582548i	$0.197944\pi$
$692$	6.01237	+	10.4137i	0.228556	+	0.395871i
$693$		0			0
$694$	−16.6019			−0.630199
$695$	9.02771	+	15.6364i	0.342440	+	0.593124i
$696$		0			0
$697$	1.10666	+	1.91679i	0.0419176	+	0.0726035i
$698$	5.07233	+	8.78554i	0.191991	+	0.332537i
$699$		0			0
$700$	−2.73760	+	1.25394i	−0.103471	+	0.0473944i
$701$	35.9248			1.35686			0.678430	−	0.734665i	$-0.262661\pi$
$701$	35.9248			1.35686			0.678430	+	0.734665i	$0.262661\pi$
$702$		0			0
$703$	20.4572	+	35.4329i	0.771559	+	1.33638i
$704$	−2.12410	+	3.67905i	−0.0800550	+	0.138659i
$705$		0			0
$706$	−20.4722	+	35.4589i	−0.770481	+	1.33451i
$707$	8.93361	+	6.34649i	0.335983	+	0.238684i
$708$		0			0
$709$	−2.85298	−	4.94150i	−0.107146	−	0.185582i	0.807467	−	0.589913i	$-0.200838\pi$
$709$	−2.85298	−	4.94150i	−0.107146	−	0.185582i	−0.914613	+	0.404331i	$0.867504\pi$
$710$	−11.7709	−	20.3878i	−0.441754	−	0.765140i
$711$		0			0
$712$	0.0282144			0.00105738
$713$	9.47571	+	16.4124i	0.354868	+	0.614650i
$714$		0			0
$715$	−0.331859	+	3.24944i	−0.0124108	+	0.121522i
$716$	−4.29343	+	7.43644i	−0.160453	+	0.277913i
$717$		0			0
$718$	11.9046	−	20.6193i	0.444274	−	0.769505i
$719$	0.427075	+	0.739715i	0.0159272	+	0.0275867i	0.873879	−	0.486143i	$-0.161597\pi$
$719$	0.427075	+	0.739715i	0.0159272	+	0.0275867i	−0.857952	+	0.513730i	$0.828263\pi$
$720$		0			0
$721$	22.2441	+	15.8023i	0.828414	+	0.588509i
$722$	−1.32982	+	2.30332i	−0.0494908	+	0.0857205i
$723$		0			0
$724$	11.1574			0.414660
$725$	8.14837	−	14.1134i	0.302623	−	0.524158i
$726$		0			0
$727$	−15.2191			−0.564444			−0.282222	−	0.959349i	$-0.591071\pi$
$727$	−15.2191			−0.564444			−0.282222	+	0.959349i	$0.591071\pi$
$728$	19.3556	−	22.0931i	0.717368	−	0.818823i
$729$		0			0
$730$	14.5817			0.539694
$731$	−0.0936173	+	0.162150i	−0.00346256	+	0.00599733i
$732$		0			0
$733$	7.18875	−	12.4513i	0.265523	−	0.459899i	−0.702178	−	0.712002i	$-0.747789\pi$
$733$	7.18875	−	12.4513i	0.265523	−	0.459899i	0.967700	+	0.252103i	$0.0811222\pi$
$734$	−9.38336	+	16.2524i	−0.346346	+	0.599889i
$735$		0			0
$736$	−17.2478			−0.635761
$737$	1.64107	+	2.84242i	0.0604496	+	0.104702i
$738$		0			0
$739$	−2.53508	+	4.39089i	−0.0932544	+	0.161521i	−0.908879	−	0.417060i	$-0.863060\pi$
$739$	−2.53508	+	4.39089i	−0.0932544	+	0.161521i	0.815624	+	0.578582i	$0.196394\pi$
$740$	−5.50101	+	9.52802i	−0.202221	+	0.350257i
$741$		0			0
$742$	37.2866	−	17.0789i	1.36883	−	0.626985i
$743$	10.6129	+	18.3820i	0.389348	+	0.674371i	0.992362	−	0.123360i	$-0.0393670\pi$
$743$	10.6129	+	18.3820i	0.389348	+	0.674371i	−0.603014	+	0.797731i	$0.706034\pi$
$744$		0			0
$745$	−14.5694			−0.533782
$746$	−20.5152	−	35.5333i	−0.751114	−	1.30097i
$747$		0			0
$748$	0.0553374	−	0.0958471i	0.00202333	−	0.00350452i
$749$	−2.67025	+	28.3000i	−0.0975688	+	1.03406i
$750$		0			0
$751$	33.1636			1.21016			0.605079	−	0.796166i	$-0.293142\pi$
$751$	33.1636			1.21016			0.605079	+	0.796166i	$0.293142\pi$
$752$	−7.92484	+	13.7262i	−0.288989	+	0.500544i
$753$		0			0
$754$	−4.10062	+	40.1517i	−0.149336	+	1.46224i
$755$	−8.93964			−0.325347
$756$		0			0
$757$	−10.2642	−	17.7781i	−0.373059	−	0.646157i	0.616976	−	0.786982i	$-0.288358\pi$
$757$	−10.2642	−	17.7781i	−0.373059	−	0.646157i	−0.990034	+	0.140825i	$0.955024\pi$
$758$	15.5882	+	26.9995i	0.566188	+	0.980667i
$759$		0			0
$760$	−25.9323			−0.940662
$761$	18.4562	+	31.9671i	0.669036	+	1.15881i	0.978174	+	0.207788i	$0.0666263\pi$
$761$	18.4562	+	31.9671i	0.669036	+	1.15881i	−0.309137	+	0.951017i	$0.600040\pi$
$762$		0			0
$763$	4.77544	−	2.18736i	0.172883	−	0.0791876i
$764$	2.76851	+	4.79520i	0.100161	+	0.173484i
$765$		0			0
$766$	7.17911	+	12.4346i	0.259392	+	0.449280i
$767$	1.23159	+	0.889272i	0.0444701	+	0.0321097i
$768$		0			0
$769$	12.7516	+	22.0865i	0.459836	+	0.796460i	0.998952	−	0.0457720i	$-0.0145748\pi$
$769$	12.7516	+	22.0865i	0.459836	+	0.796460i	−0.539116	+	0.842232i	$0.681241\pi$
$770$	−2.50309	+	1.14652i	−0.0902050	+	0.0413177i
$771$		0			0
$772$	−8.90302	+	15.4205i	−0.320427	+	0.554995i
$773$	22.9043			0.823811			0.411905	−	0.911227i	$-0.364863\pi$
$773$	22.9043			0.823811			0.411905	+	0.911227i	$0.364863\pi$
$774$		0			0
$775$	3.36163	−	5.82251i	0.120753	−	0.209151i
$776$	−0.499956	+	0.865949i	−0.0179474	+	0.0310858i
$777$		0			0
$778$	−18.1842	−	31.4959i	−0.651935	−	1.12918i
$779$	15.6026	−	27.0245i	0.559022	−	0.968254i
$780$		0			0
$781$	−2.78971	−	4.83192i	−0.0998236	−	0.172900i
$782$	−1.77308			−0.0634052
$783$		0			0
$784$	14.9611	+	2.84868i	0.534326	+	0.101739i
$785$	37.2733			1.33034
$786$		0			0
$787$	−0.829312			−0.0295618			−0.0147809	−	0.999891i	$-0.504705\pi$
$787$	−0.829312			−0.0295618			−0.0147809	+	0.999891i	$0.504705\pi$
$788$	−1.55534	−	2.69393i	−0.0554067	−	0.0959672i
$789$		0			0
$790$	−1.93159	−	3.34561i	−0.0687229	−	0.119032i
$791$	26.4265	+	18.7736i	0.939620	+	0.667511i
$792$		0			0
$793$	−1.48230	+	14.5141i	−0.0526378	+	0.515410i
$794$	−6.93094	−	12.0047i	−0.245970	−	0.426032i
$795$		0			0
$796$	−14.1324			−0.500908
$797$	−15.8043	+	27.3738i	−0.559815	+	0.969629i	0.437696	+	0.899123i	$0.355795\pi$
$797$	−15.8043	+	27.3738i	−0.559815	+	0.969629i	−0.997511	+	0.0705057i	$0.977539\pi$
$798$		0			0
$799$	1.19276	−	2.06592i	0.0421969	−	0.0730871i
$800$	3.05943	+	5.29909i	0.108167	+	0.187351i
$801$		0			0
$802$	−23.8841			−0.843376
$803$	3.45587			0.121955
$804$		0			0
$805$	−18.5470	−	13.1759i	−0.653694	−	0.464388i
$806$	−1.69172	+	16.5647i	−0.0595882	+	0.583466i
$807$		0			0
$808$	6.37661	−	11.0446i	0.224328	−	0.388548i
$809$	−17.9240	+	31.0453i	−0.630176	+	1.09150i	0.357340	+	0.933974i	$0.383684\pi$
$809$	−17.9240	+	31.0453i	−0.630176	+	1.09150i	−0.987515	+	0.157522i	$0.949650\pi$
$810$		0			0
$811$	32.5379			1.14256			0.571279	−	0.820756i	$-0.306447\pi$
$811$	32.5379			1.14256			0.571279	+	0.820756i	$0.306447\pi$
$812$	15.9534	−	7.30733i	0.559854	−	0.256437i
$813$		0			0
$814$	2.52761	−	4.37795i	0.0885928	−	0.153447i
$815$	−2.18875			−0.0766684
$816$		0			0
$817$	2.63980			0.0923548
$818$	−29.7227			−1.03923
$819$		0			0
$820$	8.39118			0.293033
$821$	3.79577			0.132473			0.0662366	−	0.997804i	$-0.478901\pi$
$821$	3.79577			0.132473			0.0662366	+	0.997804i	$0.478901\pi$
$822$		0			0
$823$	47.3353			1.65000			0.825002	−	0.565130i	$-0.191174\pi$
$823$	47.3353			1.65000			0.825002	+	0.565130i	$0.191174\pi$
$824$	15.8773	−	27.5004i	0.553113	−	0.958020i
$825$		0			0
$826$	−0.120280	+	1.27476i	−0.00418508	+	0.0443546i
$827$	41.4999			1.44309			0.721546	−	0.692367i	$-0.243432\pi$
$827$	41.4999			1.44309			0.721546	+	0.692367i	$0.243432\pi$
$828$		0			0
$829$	−13.5276	+	23.4304i	−0.469831	+	0.813772i	−0.999405	−	0.0344923i	$-0.989019\pi$
$829$	−13.5276	+	23.4304i	−0.469831	+	0.813772i	0.529574	+	0.848264i	$0.322352\pi$
$830$	−17.2036	+	29.7975i	−0.597146	+	1.03429i
$831$		0			0
$832$	−25.0060	−	18.0556i	−0.866926	−	0.625967i
$833$	−2.25179	−	0.428752i	−0.0780199	−	0.0148554i
$834$		0			0
$835$	32.2787			1.11705
$836$	−1.56039			−0.0539671
$837$		0			0
$838$	−1.80828	−	3.13203i	−0.0624660	−	0.108194i
$839$	4.19837	−	7.27179i	0.144944	−	0.251050i	−0.784408	−	0.620245i	$-0.787033\pi$
$839$	4.19837	−	7.27179i	0.144944	−	0.251050i	0.929352	+	0.369195i	$0.120367\pi$
$840$		0			0
$841$	−32.9847	+	57.1312i	−1.13740	+	1.97004i
$842$	3.88367			0.133840
$843$		0			0
$844$	−0.970305	−	1.68062i	−0.0333993	−	0.0578492i
$845$	−23.2251	−	4.79386i	−0.798966	−	0.164914i
$846$		0			0
$847$	25.8664	−	11.8479i	0.888781	−	0.407100i
$848$	−14.6804	−	25.4271i	−0.504126	−	0.873171i
$849$		0			0
$850$	0.314511	+	0.544749i	0.0107876	+	0.0186847i
$851$	41.7735			1.43198
$852$		0			0
$853$	47.6418			1.63122			0.815611	−	0.578600i	$-0.196401\pi$
$853$	47.6418			1.63122			0.815611	+	0.578600i	$0.196401\pi$
$854$	−11.1804	+	5.12110i	−0.382585	+	0.175240i
$855$		0			0
$856$	33.0813			1.13070
$857$	15.6312	+	27.0740i	0.533952	+	0.924832i	0.999213	+	0.0396584i	$0.0126270\pi$
$857$	15.6312	+	27.0740i	0.533952	+	0.924832i	−0.465261	+	0.885173i	$0.654040\pi$
$858$		0			0
$859$	1.08936	−	1.88682i	0.0371684	−	0.0643776i	−0.846843	−	0.531843i	$-0.821500\pi$
$859$	1.08936	−	1.88682i	0.0371684	−	0.0643776i	0.884011	+	0.467466i	$0.154833\pi$
$860$	0.354924	+	0.614747i	0.0121028	+	0.0209627i
$861$		0			0
$862$	−11.0441	+	19.1289i	−0.376163	+	0.651534i
$863$	−3.14358	+	5.44484i	−0.107009	+	0.185345i	−0.914557	−	0.404457i	$-0.867461\pi$
$863$	−3.14358	+	5.44484i	−0.107009	+	0.185345i	0.807548	+	0.589801i	$0.200794\pi$
$864$		0			0
$865$	32.2315			1.09590
$866$	11.0122	−	19.0737i	0.374209	−	0.648150i
$867$		0			0
$868$	6.58159	−	3.01465i	0.223394	−	0.102324i
$869$	−0.457788	−	0.792912i	−0.0155294	−	0.0268977i
$870$		0			0
$871$	−21.7406	+	9.75633i	−0.736651	+	0.330581i
$872$	−3.05641	−	5.29386i	−0.103503	−	0.179273i
$873$		0			0
$874$	12.4992	+	21.6493i	0.422792	+	0.732297i
$875$	−3.02508	+	32.0606i	−0.102266	+	1.08385i
$876$		0			0
$877$	−23.4247	−	40.5727i	−0.790995	−	1.37004i	−0.925351	−	0.379111i	$-0.876230\pi$
$877$	−23.4247	−	40.5727i	−0.790995	−	1.37004i	0.134356	−	0.990933i	$-0.457103\pi$
$878$	−9.10096			−0.307143
$879$		0			0
$880$	0.985507	+	1.70695i	0.0332214	+	0.0575412i
$881$	0.866498	+	1.50082i	0.0291931	+	0.0505639i	0.880253	−	0.474505i	$-0.157373\pi$
$881$	0.866498	+	1.50082i	0.0291931	+	0.0505639i	−0.851060	+	0.525069i	$0.824040\pi$
$882$		0			0
$883$	−24.9808			−0.840672			−0.420336	−	0.907369i	$-0.638088\pi$
$883$	−24.9808			−0.840672			−0.420336	+	0.907369i	$0.638088\pi$
$884$	0.651460	+	0.470388i	0.0219110	+	0.0158209i
$885$		0			0
$886$	−6.46956	+	11.2056i	−0.217349	+	0.376460i
$887$	1.51742			0.0509499			0.0254750	−	0.999675i	$-0.491890\pi$
$887$	1.51742			0.0509499			0.0254750	+	0.999675i	$0.491890\pi$
$888$		0			0
$889$	12.4840	−	5.71820i	0.418700	−	0.191782i
$890$	0.00960037	−	0.0166283i	0.000321805	−	0.000557383i
$891$		0			0
$892$	3.82894	+	6.63191i	0.128202	+	0.222053i
$893$	−33.6332			−1.12549
$894$		0			0
$895$	11.5082	+	19.9328i	0.384678	+	0.666281i
$896$	0.623363	−	6.60657i	0.0208251	−	0.220710i
$897$		0			0
$898$	0.286062	−	0.495474i	0.00954601	−	0.0165342i
$899$	−19.5899	+	33.9307i	−0.653360	+	1.13165i
$900$		0			0
$901$	2.20953	+	3.82702i	0.0736101	+	0.127496i
$902$	−3.85559			−0.128377
$903$		0			0
$904$	18.8627	−	32.6711i	0.627363	−	1.08662i
$905$	14.9532	−	25.8998i	0.497063	−	0.860938i
$906$		0			0
$907$	16.0723	−	27.8380i	0.533672	−	0.924347i	−0.465555	−	0.885019i	$-0.654145\pi$
$907$	16.0723	−	27.8380i	0.533672	−	0.924347i	0.999226	−	0.0393276i	$-0.0125216\pi$
$908$	14.7406			0.489185
$909$		0			0
$910$	−6.43463	−	18.9249i	−0.213306	−	0.627353i
$911$	−33.3781			−1.10587			−0.552934	−	0.833225i	$-0.686492\pi$
$911$	−33.3781			−1.10587			−0.552934	+	0.833225i	$0.686492\pi$
$912$		0			0
$913$	−4.07727	+	7.06203i	−0.134938	+	0.233719i
$914$	21.3812			0.707227
$915$		0			0
$916$	−3.01083	+	5.21490i	−0.0994805	+	0.172305i
$917$	−40.5619	−	28.8154i	−1.33947	−	0.951568i
$918$		0			0
$919$	19.3034	+	33.4345i	0.636760	+	1.10290i	0.986139	+	0.165920i	$0.0530593\pi$
$919$	19.3034	+	33.4345i	0.636760	+	1.10290i	−0.349379	+	0.936982i	$0.613607\pi$
$920$	−13.2384	+	22.9296i	−0.436457	+	0.755966i
$921$		0			0
$922$	−3.36001	+	5.81972i	−0.110656	+	0.191662i
$923$	36.9575	−	16.5851i	1.21647	−	0.545905i
$924$		0			0
$925$	−7.40984	−	12.8342i	−0.243634	−	0.421986i
$926$	26.8143			0.881174
$927$		0			0
$928$	−17.8288	−	30.8805i	−0.585261	−	1.01370i
$929$	−20.8012	−	36.0287i	−0.682465	−	1.18206i	−0.974226	−	0.225573i	$-0.927575\pi$
$929$	−20.8012	−	36.0287i	−0.682465	−	1.18206i	0.291762	−	0.956491i	$-0.405759\pi$
$930$		0			0
$931$	10.6388	+	30.5167i	0.348672	+	1.00015i
$932$	−0.607711	+	1.05259i	−0.0199062	+	0.0344786i
$933$		0			0
$934$	−6.77784	+	11.7396i	−0.221778	+	0.384130i
$935$	−0.148328	−	0.256911i	−0.00485084	−	0.00840190i
$936$		0			0
$937$	2.73494			0.0893465			0.0446732	−	0.999002i	$-0.485775\pi$
$937$	2.73494			0.0893465			0.0446732	+	0.999002i	$0.485775\pi$
$938$	−16.3743	−	11.6324i	−0.534639	−	0.379811i
$939$		0			0
$940$	−4.52203	−	7.83238i	−0.147492	−	0.255464i
$941$	8.96190	+	15.5225i	0.292150	+	0.506018i	0.974318	−	0.225177i	$-0.0722961\pi$
$941$	8.96190	+	15.5225i	0.292150	+	0.506018i	−0.682168	+	0.731195i	$0.738963\pi$
$942$		0			0
$943$	−15.9302	−	27.5920i	−0.518760	−	0.898518i
$944$	0.916663			0.0298348
$945$		0			0
$946$	−0.163081	−	0.282465i	−0.00530223	−	0.00918373i
$947$	24.7653			0.804766			0.402383	−	0.915472i	$-0.368182\pi$
$947$	24.7653			0.804766			0.402383	+	0.915472i	$0.368182\pi$
$948$		0			0
$949$	−2.54921	+	24.9609i	−0.0827507	+	0.810264i
$950$	4.43425	−	7.68034i	0.143866	−	0.249183i
$951$		0			0
$952$	−0.250595	+	2.65587i	−0.00812183	+	0.0860774i
$953$	−1.24712	+	2.16007i	−0.0403981	+	0.0699715i	−0.885517	−	0.464606i	$-0.846196\pi$
$953$	−1.24712	+	2.16007i	−0.0403981	+	0.0699715i	0.845119	+	0.534578i	$0.179529\pi$
$954$		0			0
$955$	14.8416			0.480263
$956$	6.85557			0.221725
$957$		0			0
$958$	19.6239	−	33.9896i	0.634020	−	1.09816i
$959$	2.15350	−	22.8234i	0.0695402	−	0.737006i
$960$		0			0
$961$	7.41815	−	12.8486i	0.239295	−	0.414471i
$962$	29.7563	+	21.4857i	0.959383	+	0.692725i
$963$		0			0
$964$	0.0216834			0.000698375
$965$	23.8639	+	41.3335i	0.768206	+	1.33057i
$966$		0			0
$967$	−17.6660			−0.568102			−0.284051	−	0.958809i	$-0.591678\pi$
$967$	−17.6660			−0.568102			−0.284051	+	0.958809i	$0.591678\pi$
$968$	−16.5552	−	28.6745i	−0.532105	−	0.921633i
$969$		0			0
$970$	0.340235	+	0.589304i	0.0109243	+	0.0189214i
$971$	24.4539	+	42.3553i	0.784761	+	1.35925i	0.929141	+	0.369724i	$0.120548\pi$
$971$	24.4539	+	42.3553i	0.784761	+	1.35925i	−0.144380	+	0.989522i	$0.546119\pi$
$972$		0			0
$973$	−21.3482	−	15.1659i	−0.684392	−	0.486196i
$974$	−19.0553			−0.610572
$975$		0			0
$976$	4.40191	+	7.62433i	0.140902	+	0.244049i
$977$	15.3944	−	26.6639i	0.492511	−	0.853054i	−0.507452	−	0.861680i	$-0.669413\pi$
$977$	15.3944	−	26.6639i	0.492511	−	0.853054i	0.999963	+	0.00862628i	$0.00274586\pi$
$978$		0			0
$979$	0.00227529	−	0.00394092i	7.27186e−5	−	0.000125952i
$980$	−5.67624	+	6.58055i	−0.181321	+	0.210208i
$981$		0			0
$982$	6.96895	+	12.0706i	0.222388	+	0.385187i
$983$	12.6951	+	21.9885i	0.404910	+	0.701325i	0.994311	−	0.106516i	$-0.0339694\pi$
$983$	12.6951	+	21.9885i	0.404910	+	0.701325i	−0.589401	+	0.807841i	$0.700636\pi$
$984$		0			0
$985$	−8.33796			−0.265669
$986$	−1.83282	−	3.17453i	−0.0583687	−	0.101098i
$987$		0			0
$988$	1.15101	−	11.2703i	0.0366186	−	0.358555i
$989$	1.34761	−	2.33413i	0.0428516	−	0.0742211i
$990$		0			0
$991$	−15.7060	+	27.2036i	−0.498917	+	0.864150i	−0.999999	−	0.00124977i	$-0.999602\pi$
$991$	−15.7060	+	27.2036i	−0.498917	+	0.864150i	0.501082	+	0.865400i	$0.332936\pi$
$992$	−7.35532	−	12.7398i	−0.233532	−	0.404489i
$993$		0			0
$994$	27.8352	+	19.7743i	0.882878	+	0.627201i
$995$	−18.9404	+	32.8057i	−0.600450	+	1.04001i
$996$		0			0
$997$	−52.9958			−1.67840			−0.839198	−	0.543827i	$-0.816975\pi$
$997$	−52.9958			−1.67840			−0.839198	+	0.543827i	$0.816975\pi$
$998$	9.26028	−	16.0393i	0.293129	−	0.507714i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.g.289.13	yes	36
3.2	odd	2	inner	819.2.s.g.289.6	yes	36
7.4	even	3		819.2.n.g.172.6	yes	36
13.9	even	3		819.2.n.g.100.6	✓	36
21.11	odd	6		819.2.n.g.172.13	yes	36
39.35	odd	6		819.2.n.g.100.13	yes	36
91.74	even	3	inner	819.2.s.g.802.13	yes	36
273.74	odd	6	inner	819.2.s.g.802.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.n.g.100.6	✓	36	13.9	even	3
819.2.n.g.100.13	yes	36	39.35	odd	6
819.2.n.g.172.6	yes	36	7.4	even	3
819.2.n.g.172.13	yes	36	21.11	odd	6
819.2.s.g.289.6	yes	36	3.2	odd	2	inner
819.2.s.g.289.13	yes	36	1.1	even	1	trivial
819.2.s.g.802.6	yes	36	273.74	odd	6	inner
819.2.s.g.802.13	yes	36	91.74	even	3	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.14867 q^{2} -0.680564 q^{4} +(-0.912102 + 1.57981i) q^{5} +(0.248536 - 2.63405i) q^{7} -3.07908 q^{8} +(-1.04770 + 1.81467i) q^{10} +(-0.248306 + 0.430078i) q^{11} +(-2.92318 - 2.11069i) q^{13} +(0.285485 - 3.02565i) q^{14} -2.17570 q^{16} +0.327463 q^{17} +(-2.30843 - 3.99832i) q^{19} +(0.620744 - 1.07516i) q^{20} +(-0.285221 + 0.494016i) q^{22} -4.71380 q^{23} +(0.836140 + 1.44824i) q^{25} +(-3.35776 - 2.42448i) q^{26} +(-0.169145 + 1.79264i) q^{28} +(-4.87261 - 8.43961i) q^{29} +(-2.01021 - 3.48178i) q^{31} +3.65899 q^{32} +0.376146 q^{34} +(3.93460 + 2.79516i) q^{35} -8.86196 q^{37} +(-2.65162 - 4.59274i) q^{38} +(2.80843 - 4.86435i) q^{40} +(3.37948 + 5.85344i) q^{41} +(-0.285886 + 0.495170i) q^{43} +(0.168988 - 0.292696i) q^{44} -5.41459 q^{46} +(3.64243 - 6.30887i) q^{47} +(-6.87646 - 1.30931i) q^{49} +(0.960446 + 1.66354i) q^{50} +(1.98941 + 1.43646i) q^{52} +(6.74741 + 11.6869i) q^{53} +(-0.452960 - 0.784550i) q^{55} +(-0.765261 + 8.11045i) q^{56} +(-5.59701 - 9.69430i) q^{58} -0.421318 q^{59} +(-2.02321 - 3.50430i) q^{61} +(-2.30906 - 3.99940i) q^{62} +8.55437 q^{64} +(6.00072 - 2.69289i) q^{65} +(3.30454 - 5.72363i) q^{67} -0.222860 q^{68} +(4.51955 + 3.21071i) q^{70} +(-5.61749 + 9.72977i) q^{71} +(-3.47946 - 6.02659i) q^{73} -10.1794 q^{74} +(1.57104 + 2.72111i) q^{76} +(1.07113 + 0.760940i) q^{77} +(-0.921823 + 1.59664i) q^{79} +(1.98446 - 3.43719i) q^{80} +(3.88190 + 6.72365i) q^{82} +16.4203 q^{83} +(-0.298680 + 0.517329i) q^{85} +(-0.328388 + 0.568785i) q^{86} +(0.764552 - 1.32424i) q^{88} -0.00916326 q^{89} +(-6.28619 + 7.17522i) q^{91} +3.20805 q^{92} +(4.18393 - 7.24679i) q^{94} +8.42210 q^{95} +(0.162372 - 0.281237i) q^{97} +(-7.89876 - 1.50397i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) \) 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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