LMFDB - Embedded newform 532.2.l.b.429.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [532,2,Mod(429,532)] 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("532.429"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(532, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 532 = 2^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	532.l (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			429.11
Character	$\chi$	$=$	532.429
Dual form			532.2.l.b.501.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.98364 q^{3} +(-0.223039 - 0.386315i) q^{5} +(1.18643 + 2.36482i) q^{7} +5.90209 q^{9} +(2.04785 + 3.54698i) q^{11} +(-2.40524 - 4.16600i) q^{13} +(-0.665468 - 1.15262i) q^{15} -5.31563 q^{17} +(-3.73139 + 2.25316i) q^{19} +(3.53989 + 7.05576i) q^{21} +4.90255 q^{23} +(2.40051 - 4.15780i) q^{25} +8.65879 q^{27} +(-1.24190 - 2.15103i) q^{29} +(-1.90744 - 3.30379i) q^{31} +(6.11005 + 10.5829i) q^{33} +(0.648944 - 0.985784i) q^{35} +(3.07344 - 5.32335i) q^{37} +(-7.17637 - 12.4298i) q^{39} +(2.73014 - 4.72874i) q^{41} +(-5.79221 + 10.0324i) q^{43} +(-1.31640 - 2.28007i) q^{45} -6.71365 q^{47} +(-4.18475 + 5.61141i) q^{49} -15.8599 q^{51} +(3.83682 - 6.64557i) q^{53} +(0.913501 - 1.58223i) q^{55} +(-11.1331 + 6.72263i) q^{57} +9.29294 q^{59} -6.96595 q^{61} +(7.00245 + 13.9574i) q^{63} +(-1.07293 + 1.85836i) q^{65} +(-2.53937 + 4.39833i) q^{67} +14.6274 q^{69} +(3.79529 - 6.57364i) q^{71} -2.96434 q^{73} +(7.16224 - 12.4054i) q^{75} +(-5.95833 + 9.05106i) q^{77} +(-6.48566 - 11.2335i) q^{79} +8.12841 q^{81} +14.5111 q^{83} +(1.18559 + 2.05351i) q^{85} +(-3.70537 - 6.41788i) q^{87} -3.69090 q^{89} +(6.99818 - 10.6306i) q^{91} +(-5.69111 - 9.85730i) q^{93} +(1.70268 + 0.938947i) q^{95} +(-5.62889 + 9.74952i) q^{97} +(12.0866 + 20.9346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 6 q^{5} - 6 q^{7} + 30 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} - 6 q^{17} + 17 q^{19} - 18 q^{21} - 16 q^{23} - 8 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} + 7 q^{33} - 21 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 - 6 * q^5 - 6 * q^7 + 30 * q^9 + q^11 - 7 * q^13 - 2 * q^15 - 6 * q^17 + 17 * q^19 - 18 * q^21 - 16 * q^23 - 8 * q^25 + 20 * q^27 - 22 * q^29 - 7 * q^31 + 7 * q^33 - 21 * q^35 + 9 * q^37 + 12 * q^39 - 11 * q^41 - 9 * q^43 - 28 * q^45 - 22 * q^47 - 32 * q^49 - 16 * q^51 - 7 * q^53 - 11 * q^55 + 11 * q^57 + 16 * q^59 + 12 * q^61 + 20 * q^63 + 3 * q^65 - 27 * q^67 + 108 * q^69 - 13 * q^71 + 20 * q^73 + 25 * q^75 + 2 * q^77 - 14 * q^79 + 80 * q^81 - 12 * q^83 - 19 * q^85 + 19 * q^87 + 74 * q^89 - 21 * q^91 + 5 * q^93 + 47 * q^95 - 21 * q^97 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$.

$n$	$267$	$381$	$477$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	2.98364			1.72260			0.861302	−	0.508094i	$-0.169650\pi$
$3$	2.98364			1.72260			0.861302	+	0.508094i	$0.169650\pi$
$4$		0			0
$5$	−0.223039	−	0.386315i	−0.0997461	−	0.172765i	0.811833	−	0.583889i	$-0.198470\pi$
$5$	−0.223039	−	0.386315i	−0.0997461	−	0.172765i	−0.911580	+	0.411124i	$0.865136\pi$
$6$		0			0
$7$	1.18643	+	2.36482i	0.448430	+	0.893818i
$7$	1.18643	+	2.36482i	0.448430	+	0.893818i
$8$		0			0
$9$	5.90209			1.96736
$10$		0			0
$11$	2.04785	+	3.54698i	0.617450	+	1.06946i	0.989949	+	0.141423i	$0.0451677\pi$
$11$	2.04785	+	3.54698i	0.617450	+	1.06946i	−0.372499	+	0.928033i	$0.621499\pi$
$12$		0			0
$13$	−2.40524	−	4.16600i	−0.667094	−	1.15544i	−0.978713	−	0.205233i	$-0.934205\pi$
$13$	−2.40524	−	4.16600i	−0.667094	−	1.15544i	0.311619	−	0.950207i	$-0.399129\pi$
$14$		0			0
$15$	−0.665468	−	1.15262i	−0.171823	−	0.297606i
$16$		0			0
$17$	−5.31563			−1.28923			−0.644615	−	0.764508i	$-0.722982\pi$
$17$	−5.31563			−1.28923			−0.644615	+	0.764508i	$0.722982\pi$
$18$		0			0
$19$	−3.73139	+	2.25316i	−0.856039	+	0.516911i
$19$	−3.73139	+	2.25316i	−0.856039	+	0.516911i
$20$		0			0
$21$	3.53989	+	7.05576i	0.772467	+	1.53969i
$22$		0			0
$23$	4.90255			1.02225			0.511126	−	0.859506i	$-0.329229\pi$
$23$	4.90255			1.02225			0.511126	+	0.859506i	$0.329229\pi$
$24$		0			0
$25$	2.40051	−	4.15780i	0.480101	−	0.831560i
$26$		0			0
$27$	8.65879			1.66638
$28$		0			0
$29$	−1.24190	−	2.15103i	−0.230614	−	0.399436i	0.727375	−	0.686240i	$-0.240740\pi$
$29$	−1.24190	−	2.15103i	−0.230614	−	0.399436i	−0.957989	+	0.286805i	$0.907407\pi$
$30$		0			0
$31$	−1.90744	−	3.30379i	−0.342587	−	0.593378i	0.642326	−	0.766432i	$-0.277970\pi$
$31$	−1.90744	−	3.30379i	−0.342587	−	0.593378i	−0.984912	+	0.173054i	$0.944636\pi$
$32$		0			0
$33$	6.11005	+	10.5829i	1.06362	+	1.84225i
$34$		0			0
$35$	0.648944	−	0.985784i	0.109692	−	0.166628i
$36$		0			0
$37$	3.07344	−	5.32335i	0.505270	−	0.875153i	−0.494711	−	0.869057i	$-0.664726\pi$
$37$	3.07344	−	5.32335i	0.505270	−	0.875153i	0.999981	−	0.00609591i	$-0.00194040\pi$
$38$		0			0
$39$	−7.17637	−	12.4298i	−1.14914	−	1.99037i
$40$		0			0
$41$	2.73014	−	4.72874i	0.426376	−	0.738506i	−0.570171	−	0.821526i	$-0.693123\pi$
$41$	2.73014	−	4.72874i	0.426376	−	0.738506i	0.996548	+	0.0830200i	$0.0264565\pi$
$42$		0			0
$43$	−5.79221	+	10.0324i	−0.883303	+	1.52993i	−0.0356574	+	0.999364i	$0.511353\pi$
$43$	−5.79221	+	10.0324i	−0.883303	+	1.52993i	−0.847646	+	0.530562i	$0.821981\pi$
$44$		0			0
$45$	−1.31640	−	2.28007i	−0.196237	−	0.339892i
$46$		0			0
$47$	−6.71365			−0.979286			−0.489643	−	0.871923i	$-0.662873\pi$
$47$	−6.71365			−0.979286			−0.489643	+	0.871923i	$0.662873\pi$
$48$		0			0
$49$	−4.18475	+	5.61141i	−0.597821	+	0.801630i
$50$		0			0
$51$	−15.8599			−2.22083
$52$		0			0
$53$	3.83682	−	6.64557i	0.527028	−	0.912839i	−0.472476	−	0.881344i	$-0.656640\pi$
$53$	3.83682	−	6.64557i	0.527028	−	0.912839i	0.999504	−	0.0314955i	$-0.0100270\pi$
$54$		0			0
$55$	0.913501	−	1.58223i	0.123177	−	0.213348i
$56$		0			0
$57$	−11.1331	+	6.72263i	−1.47462	+	0.890434i
$58$		0			0
$59$	9.29294			1.20984			0.604919	−	0.796287i	$-0.293205\pi$
$59$	9.29294			1.20984			0.604919	+	0.796287i	$0.293205\pi$
$60$		0			0
$61$	−6.96595			−0.891899			−0.445950	−	0.895058i	$-0.647134\pi$
$61$	−6.96595			−0.891899			−0.445950	+	0.895058i	$0.647134\pi$
$62$		0			0
$63$	7.00245	+	13.9574i	0.882225	+	1.75847i
$64$		0			0
$65$	−1.07293	+	1.85836i	−0.133080	+	0.230501i
$66$		0			0
$67$	−2.53937	+	4.39833i	−0.310234	+	0.537341i	−0.978413	−	0.206660i	$-0.933741\pi$
$67$	−2.53937	+	4.39833i	−0.310234	+	0.537341i	0.668179	+	0.744001i	$0.267074\pi$
$68$		0			0
$69$	14.6274			1.76094
$70$		0			0
$71$	3.79529	−	6.57364i	0.450419	−	0.780148i	−0.547993	−	0.836483i	$-0.684608\pi$
$71$	3.79529	−	6.57364i	0.450419	−	0.780148i	0.998412	+	0.0563348i	$0.0179414\pi$
$72$		0			0
$73$	−2.96434			−0.346950			−0.173475	−	0.984838i	$-0.555500\pi$
$73$	−2.96434			−0.346950			−0.173475	+	0.984838i	$0.555500\pi$
$74$		0			0
$75$	7.16224	−	12.4054i	0.827025	−	1.43245i
$76$		0			0
$77$	−5.95833	+	9.05106i	−0.679015	+	1.03146i
$78$		0			0
$79$	−6.48566	−	11.2335i	−0.729694	−	1.26387i	−0.957013	−	0.290046i	$-0.906329\pi$
$79$	−6.48566	−	11.2335i	−0.729694	−	1.26387i	0.227319	−	0.973820i	$-0.427004\pi$
$80$		0			0
$81$	8.12841			0.903157
$82$		0			0
$83$	14.5111			1.59280			0.796400	−	0.604770i	$-0.206735\pi$
$83$	14.5111			1.59280			0.796400	+	0.604770i	$0.206735\pi$
$84$		0			0
$85$	1.18559	+	2.05351i	0.128596	+	0.222734i
$86$		0			0
$87$	−3.70537	−	6.41788i	−0.397257	−	0.688069i
$88$		0			0
$89$	−3.69090			−0.391234			−0.195617	−	0.980680i	$-0.562671\pi$
$89$	−3.69090			−0.391234			−0.195617	+	0.980680i	$0.562671\pi$
$90$		0			0
$91$	6.99818	−	10.6306i	0.733608	−	1.11439i
$92$		0			0
$93$	−5.69111	−	9.85730i	−0.590141	−	1.02215i
$94$		0			0
$95$	1.70268	+	0.938947i	0.174691	+	0.0963339i
$96$		0			0
$97$	−5.62889	+	9.74952i	−0.571527	+	0.989914i	0.424882	+	0.905249i	$0.360316\pi$
$97$	−5.62889	+	9.74952i	−0.571527	+	0.989914i	−0.996409	+	0.0846656i	$0.973018\pi$
$98$		0			0
$99$	12.0866	+	20.9346i	1.21475	+	2.10401i
$100$		0			0
$101$	−7.30193	+	12.6473i	−0.726569	+	1.25846i	0.231755	+	0.972774i	$0.425553\pi$
$101$	−7.30193	+	12.6473i	−0.726569	+	1.25846i	−0.958325	+	0.285681i	$0.907780\pi$
$102$		0			0
$103$	−8.42694	+	14.5959i	−0.830331	+	1.43818i	0.0674443	+	0.997723i	$0.478516\pi$
$103$	−8.42694	+	14.5959i	−0.830331	+	1.43818i	−0.897776	+	0.440453i	$0.854818\pi$
$104$		0			0
$105$	1.93621	−	2.94122i	0.188955	−	0.287034i
$106$		0			0
$107$	−5.03741	+	8.72505i	−0.486985	+	0.843482i	−0.999888	−	0.0149640i	$-0.995237\pi$
$107$	−5.03741	+	8.72505i	−0.486985	+	0.843482i	0.512903	+	0.858446i	$0.328570\pi$
$108$		0			0
$109$	1.05871			0.101406			0.0507030	−	0.998714i	$-0.483854\pi$
$109$	1.05871			0.101406			0.0507030	+	0.998714i	$0.483854\pi$
$110$		0			0
$111$	9.17002	−	15.8829i	0.870380	−	1.50754i
$112$		0			0
$113$	9.24954			0.870124			0.435062	−	0.900401i	$-0.356726\pi$
$113$	9.24954			0.870124			0.435062	+	0.900401i	$0.356726\pi$
$114$		0			0
$115$	−1.09346	−	1.89393i	−0.101966	−	0.176610i
$116$		0			0
$117$	−14.1960	−	24.5881i	−1.31242	−	2.27317i
$118$		0			0
$119$	−6.30664	−	12.5705i	−0.578129	−	1.15234i
$120$		0			0
$121$	−2.88739	+	5.00110i	−0.262490	+	0.454646i
$122$		0			0
$123$	8.14575	−	14.1089i	0.734478	−	1.27215i
$124$		0			0
$125$	−4.37202			−0.391045
$126$		0			0
$127$	−2.70638	−	4.68759i	−0.240153	−	0.415957i	0.720605	−	0.693346i	$-0.243864\pi$
$127$	−2.70638	−	4.68759i	−0.240153	−	0.415957i	−0.960758	+	0.277389i	$0.910531\pi$
$128$		0			0
$129$	−17.2818	+	29.9330i	−1.52158	+	2.63546i
$130$		0			0
$131$	−1.16548	−	2.01867i	−0.101828	−	0.176372i	0.810610	−	0.585587i	$-0.199136\pi$
$131$	−1.16548	−	2.01867i	−0.101828	−	0.176372i	−0.912438	+	0.409215i	$0.865803\pi$
$132$		0			0
$133$	−9.75537	−	6.15083i	−0.845898	−	0.533344i
$134$		0			0
$135$	−1.93125	−	3.34502i	−0.166215	−	0.287893i
$136$		0			0
$137$	−0.713078	+	1.23509i	−0.0609223	+	0.105521i	−0.894878	−	0.446311i	$-0.852738\pi$
$137$	−0.713078	+	1.23509i	−0.0609223	+	0.105521i	0.833956	+	0.551832i	$0.186071\pi$
$138$		0			0
$139$	−5.35101	−	9.26821i	−0.453866	−	0.786120i	0.544756	−	0.838595i	$-0.316622\pi$
$139$	−5.35101	−	9.26821i	−0.453866	−	0.786120i	−0.998622	+	0.0524751i	$0.983289\pi$
$140$		0			0
$141$	−20.0311			−1.68692
$142$		0			0
$143$	9.85115	−	17.0627i	0.823795	−	1.42685i
$144$		0			0
$145$	−0.553982	+	0.959525i	−0.0460057	+	0.0796843i
$146$		0			0
$147$	−12.4858	+	16.7424i	−1.02981	+	1.38089i
$148$		0			0
$149$	3.73021	+	6.46091i	0.305590	+	0.529298i	0.977393	−	0.211433i	$-0.0678129\pi$
$149$	3.73021	+	6.46091i	0.305590	+	0.529298i	−0.671802	+	0.740731i	$0.734480\pi$
$150$		0			0
$151$	4.31419	+	7.47240i	0.351084	+	0.608095i	0.986440	−	0.164124i	$-0.0524798\pi$
$151$	4.31419	+	7.47240i	0.351084	+	0.608095i	−0.635356	+	0.772220i	$0.719146\pi$
$152$		0			0
$153$	−31.3733			−2.53638
$154$		0			0
$155$	−0.850868	+	1.47375i	−0.0683434	+	0.118374i
$156$		0			0
$157$	−5.81573			−0.464145			−0.232073	−	0.972698i	$-0.574551\pi$
$157$	−5.81573			−0.464145			−0.232073	+	0.972698i	$0.574551\pi$
$158$		0			0
$159$	11.4477	−	19.8280i	0.907860	−	1.57246i
$160$		0			0
$161$	5.81655	+	11.5936i	0.458409	+	0.913707i
$162$		0			0
$163$	10.9228	−	18.9188i	0.855539	−	1.48184i	−0.0206055	−	0.999788i	$-0.506559\pi$
$163$	10.9228	−	18.9188i	0.855539	−	1.48184i	0.876144	−	0.482049i	$-0.160107\pi$
$164$		0			0
$165$	2.72556	−	4.72080i	0.212184	−	0.367514i
$166$		0			0
$167$	4.28434	+	7.42070i	0.331533	+	0.574231i	0.982813	−	0.184606i	$-0.0591010\pi$
$167$	4.28434	+	7.42070i	0.331533	+	0.574231i	−0.651280	+	0.758837i	$0.725768\pi$
$168$		0			0
$169$	−5.07037	+	8.78214i	−0.390029	+	0.675549i
$170$		0			0
$171$	−22.0230	+	13.2984i	−1.68414	+	1.01695i
$172$		0			0
$173$	−3.10119	−	5.37141i	−0.235779	−	0.408381i	0.723720	−	0.690094i	$-0.242431\pi$
$173$	−3.10119	−	5.37141i	−0.235779	−	0.408381i	−0.959499	+	0.281713i	$0.909097\pi$
$174$		0			0
$175$	12.6805	+	0.743809i	0.958555	+	0.0562267i
$176$		0			0
$177$	27.7268			2.08407
$178$		0			0
$179$	−0.902405	−	1.56301i	−0.0674489	−	0.116825i	0.830329	−	0.557274i	$-0.188153\pi$
$179$	−0.902405	−	1.56301i	−0.0674489	−	0.116825i	−0.897778	+	0.440449i	$0.854819\pi$
$180$		0			0
$181$	0.803537	+	1.39177i	0.0597264	+	0.103449i	0.894343	−	0.447383i	$-0.147644\pi$
$181$	0.803537	+	1.39177i	0.0597264	+	0.103449i	−0.834616	+	0.550832i	$0.814311\pi$
$182$		0			0
$183$	−20.7839			−1.53639
$184$		0			0
$185$	−2.74199			−0.201595
$186$		0			0
$187$	−10.8856	−	18.8544i	−0.796035	−	1.37877i
$188$		0			0
$189$	10.2731	+	20.4765i	0.747257	+	1.48944i
$190$		0			0
$191$	−12.6875	+	21.9754i	−0.918035	+	1.59008i	−0.115639	+	0.993291i	$0.536891\pi$
$191$	−12.6875	+	21.9754i	−0.918035	+	1.59008i	−0.802396	+	0.596792i	$0.796442\pi$
$192$		0			0
$193$	−15.0283			−1.08176			−0.540880	−	0.841100i	$-0.681909\pi$
$193$	−15.0283			−1.08176			−0.540880	+	0.841100i	$0.681909\pi$
$194$		0			0
$195$	−3.20122	+	5.54468i	−0.229244	+	0.397062i
$196$		0			0
$197$	16.3688			1.16623			0.583114	−	0.812390i	$-0.301834\pi$
$197$	16.3688			1.16623			0.583114	+	0.812390i	$0.301834\pi$
$198$		0			0
$199$	4.25409	−	7.36831i	0.301565	−	0.522325i	−0.674926	−	0.737886i	$-0.735824\pi$
$199$	4.25409	−	7.36831i	0.301565	−	0.522325i	0.976491	+	0.215560i	$0.0691577\pi$
$200$		0			0
$201$	−7.57657	+	13.1230i	−0.534410	+	0.925626i
$202$		0			0
$203$	3.61336	−	5.48891i	0.253608	−	0.385246i
$204$		0			0
$205$	−2.43571			−0.170118
$206$		0			0
$207$	28.9353			2.01114
$208$		0			0
$209$	−15.6333	−	8.62102i	−1.08138	−	0.596328i
$210$		0			0
$211$	4.64083	−	8.03815i	0.319488	−	0.553369i	−0.660893	−	0.750480i	$-0.729823\pi$
$211$	4.64083	−	8.03815i	0.319488	−	0.553369i	0.980381	+	0.197111i	$0.0631558\pi$
$212$		0			0
$213$	11.3238	−	19.6134i	0.775893	−	1.34389i
$214$		0			0
$215$	5.16755			0.352424
$216$		0			0
$217$	5.54980	−	8.43048i	0.376745	−	0.572298i
$218$		0			0
$219$	−8.84452			−0.597658
$220$		0			0
$221$	12.7854	+	22.1449i	0.860037	+	1.48963i
$222$		0			0
$223$	−1.01709	+	1.76165i	−0.0681095	+	0.117969i	−0.898069	−	0.439854i	$-0.855030\pi$
$223$	−1.01709	+	1.76165i	−0.0681095	+	0.117969i	0.829960	+	0.557823i	$0.188363\pi$
$224$		0			0
$225$	14.1680	−	24.5397i	0.944534	−	1.63598i
$226$		0			0
$227$	2.71486	+	4.70227i	0.180191	+	0.312101i	0.941946	−	0.335766i	$-0.108995\pi$
$227$	2.71486	+	4.70227i	0.180191	+	0.312101i	−0.761754	+	0.647866i	$0.775662\pi$
$228$		0			0
$229$	0.406958	−	0.704872i	0.0268926	−	0.0465793i	−0.852266	−	0.523109i	$-0.824772\pi$
$229$	0.406958	−	0.704872i	0.0268926	−	0.0465793i	0.879158	+	0.476530i	$0.158105\pi$
$230$		0			0
$231$	−17.7775	+	27.0051i	−1.16967	+	1.77680i
$232$		0			0
$233$	−1.43338	−	2.48269i	−0.0939039	−	0.162646i	0.815247	−	0.579114i	$-0.196601\pi$
$233$	−1.43338	−	2.48269i	−0.0939039	−	0.162646i	−0.909151	+	0.416467i	$0.863268\pi$
$234$		0			0
$235$	1.49741	+	2.59358i	0.0976799	+	0.169187i
$236$		0			0
$237$	−19.3509	−	33.5167i	−1.25697	−	2.17714i
$238$		0			0
$239$	11.2031			0.724668			0.362334	−	0.932048i	$-0.381980\pi$
$239$	11.2031			0.724668			0.362334	+	0.932048i	$0.381980\pi$
$240$		0			0
$241$	10.7191	−	18.5661i	0.690480	−	1.19595i	−0.281200	−	0.959649i	$-0.590733\pi$
$241$	10.7191	−	18.5661i	0.690480	−	1.19595i	0.971681	−	0.236298i	$-0.0759341\pi$
$242$		0			0
$243$	−1.72413			−0.110603
$244$		0			0
$245$	3.10113	+	0.365067i	0.198124	+	0.0233233i
$246$		0			0
$247$	18.3616	+	10.1256i	1.16832	+	0.644274i
$248$		0			0
$249$	43.2958			2.74376
$250$		0			0
$251$	13.3601	+	23.1403i	0.843281	+	1.46061i	0.887106	+	0.461566i	$0.152712\pi$
$251$	13.3601	+	23.1403i	0.843281	+	1.46061i	−0.0438250	+	0.999039i	$0.513954\pi$
$252$		0			0
$253$	10.0397	+	17.3893i	0.631190	+	1.09325i
$254$		0			0
$255$	3.53738	+	6.12692i	0.221519	+	0.383682i
$256$		0			0
$257$	−12.3086			−0.767791			−0.383896	−	0.923377i	$-0.625418\pi$
$257$	−12.3086			−0.767791			−0.383896	+	0.923377i	$0.625418\pi$
$258$		0			0
$259$	16.2352	+	0.952320i	1.00881	+	0.0591743i
$260$		0			0
$261$	−7.32978	−	12.6956i	−0.453702	−	0.785835i
$262$		0			0
$263$	13.7384			0.847146			0.423573	−	0.905862i	$-0.360776\pi$
$263$	13.7384			0.847146			0.423573	+	0.905862i	$0.360776\pi$
$264$		0			0
$265$	−3.42304			−0.210276
$266$		0			0
$267$	−11.0123			−0.673942
$268$		0			0
$269$	25.0299			1.52610			0.763050	−	0.646339i	$-0.223701\pi$
$269$	25.0299			1.52610			0.763050	+	0.646339i	$0.223701\pi$
$270$		0			0
$271$	3.52930	+	6.11293i	0.214390	+	0.371334i	0.953084	−	0.302707i	$-0.0978904\pi$
$271$	3.52930	+	6.11293i	0.214390	+	0.371334i	−0.738694	+	0.674041i	$0.764557\pi$
$272$		0			0
$273$	20.8800	−	31.7180i	1.26372	−	1.91966i
$274$		0			0
$275$	19.6635			1.18576
$276$		0			0
$277$	9.56431	+	16.5659i	0.574664	+	0.995346i	0.996078	+	0.0884783i	$0.0282004\pi$
$277$	9.56431	+	16.5659i	0.574664	+	0.995346i	−0.421415	+	0.906868i	$0.638466\pi$
$278$		0			0
$279$	−11.2579	−	19.4992i	−0.673993	−	1.16739i
$280$		0			0
$281$	15.2351	+	26.3880i	0.908850	+	1.57417i	0.815664	+	0.578526i	$0.196372\pi$
$281$	15.2351	+	26.3880i	0.908850	+	1.57417i	0.0931859	+	0.995649i	$0.470295\pi$
$282$		0			0
$283$	8.46324			0.503087			0.251544	−	0.967846i	$-0.419062\pi$
$283$	8.46324			0.503087			0.251544	+	0.967846i	$0.419062\pi$
$284$		0			0
$285$	5.08017	+	2.80148i	0.300923	+	0.165945i
$286$		0			0
$287$	14.4218	+	0.845948i	0.851290	+	0.0499347i
$288$		0			0
$289$	11.2559			0.662112
$290$		0			0
$291$	−16.7946	+	29.0890i	−0.984515	+	1.70523i
$292$		0			0
$293$	5.50012			0.321321			0.160660	−	0.987010i	$-0.448638\pi$
$293$	5.50012			0.321321			0.160660	+	0.987010i	$0.448638\pi$
$294$		0			0
$295$	−2.07269	−	3.59000i	−0.120677	−	0.209018i
$296$		0			0
$297$	17.7319	+	30.7126i	1.02891	+	1.78212i
$298$		0			0
$299$	−11.7918	−	20.4240i	−0.681938	−	1.18115i
$300$		0			0
$301$	−30.5969	−	1.79474i	−1.76358	−	0.103447i
$302$		0			0
$303$	−21.7863	+	37.7350i	−1.25159	+	2.16782i
$304$		0			0
$305$	1.55368	+	2.69105i	0.0889634	+	0.154089i
$306$		0			0
$307$	−2.80966	+	4.86648i	−0.160356	+	0.277745i	−0.934996	−	0.354657i	$-0.884598\pi$
$307$	−2.80966	+	4.86648i	−0.160356	+	0.277745i	0.774640	+	0.632402i	$0.217931\pi$
$308$		0			0
$309$	−25.1429	+	43.5489i	−1.43033	+	2.47741i
$310$		0			0
$311$	−15.8006	−	27.3675i	−0.895971	−	1.55187i	−0.832598	−	0.553877i	$-0.813148\pi$
$311$	−15.8006	−	27.3675i	−0.895971	−	1.55187i	−0.0633727	−	0.997990i	$-0.520186\pi$
$312$		0			0
$313$	27.1943			1.53711			0.768557	−	0.639781i	$-0.220975\pi$
$313$	27.1943			1.53711			0.768557	+	0.639781i	$0.220975\pi$
$314$		0			0
$315$	3.83013	−	5.81819i	0.215803	−	0.327818i
$316$		0			0
$317$	3.17458			0.178302			0.0891512	−	0.996018i	$-0.471585\pi$
$317$	3.17458			0.178302			0.0891512	+	0.996018i	$0.471585\pi$
$318$		0			0
$319$	5.08643	−	8.80996i	0.284786	−	0.493263i
$320$		0			0
$321$	−15.0298	+	26.0324i	−0.838882	+	1.45299i
$322$		0			0
$323$	19.8347	−	11.9770i	1.10363	−	0.666417i
$324$		0			0
$325$	−23.0952			−1.28109
$326$		0			0
$327$	3.15881			0.174682
$328$		0			0
$329$	−7.96530	−	15.8766i	−0.439141	−	0.875303i
$330$		0			0
$331$	−15.7716	+	27.3172i	−0.866885	+	1.50149i	−0.00172246	+	0.999999i	$0.500548\pi$
$331$	−15.7716	+	27.3172i	−0.866885	+	1.50149i	−0.865163	+	0.501491i	$0.832785\pi$
$332$		0			0
$333$	18.1397	−	31.4189i	0.994050	−	1.72174i
$334$		0			0
$335$	2.26552			0.123779
$336$		0			0
$337$	0.252791	−	0.437848i	0.0137704	−	0.0238511i	−0.859058	−	0.511878i	$-0.828950\pi$
$337$	0.252791	−	0.437848i	0.0137704	−	0.0238511i	0.872829	+	0.488027i	$0.162283\pi$
$338$		0			0
$339$	27.5973			1.49888
$340$		0			0
$341$	7.81231	−	13.5313i	0.423061	−	0.732762i
$342$		0			0
$343$	−18.2349	−	3.23860i	−0.984592	−	0.174868i
$344$		0			0
$345$	−3.26249	−	5.65079i	−0.175646	−	0.304228i
$346$		0			0
$347$	18.3650			0.985884			0.492942	−	0.870062i	$-0.335921\pi$
$347$	18.3650			0.985884			0.492942	+	0.870062i	$0.335921\pi$
$348$		0			0
$349$	13.1178			0.702178			0.351089	−	0.936342i	$-0.385811\pi$
$349$	13.1178			0.702178			0.351089	+	0.936342i	$0.385811\pi$
$350$		0			0
$351$	−20.8265	−	36.0725i	−1.11164	−	1.92541i
$352$		0			0
$353$	4.06185	+	7.03533i	0.216190	+	0.374453i	0.953640	−	0.300949i	$-0.0973035\pi$
$353$	4.06185	+	7.03533i	0.216190	+	0.374453i	−0.737450	+	0.675402i	$0.763970\pi$
$354$		0			0
$355$	−3.38599			−0.179710
$356$		0			0
$357$	−18.8167	−	37.5058i	−0.995887	−	1.98502i
$358$		0			0
$359$	−18.2269	−	31.5700i	−0.961981	−	1.66620i	−0.717515	−	0.696543i	$-0.754721\pi$
$359$	−18.2269	−	31.5700i	−0.961981	−	1.66620i	−0.244466	−	0.969658i	$-0.578613\pi$
$360$		0			0
$361$	8.84650	−	16.8149i	0.465605	−	0.884993i
$362$		0			0
$363$	−8.61492	+	14.9215i	−0.452166	+	0.783175i
$364$		0			0
$365$	0.661164	+	1.14517i	0.0346069	+	0.0599409i
$366$		0			0
$367$	−15.6431	+	27.0946i	−0.816562	+	1.41433i	0.0916389	+	0.995792i	$0.470789\pi$
$367$	−15.6431	+	27.0946i	−0.816562	+	1.41433i	−0.908201	+	0.418535i	$0.862544\pi$
$368$		0			0
$369$	16.1135	−	27.9095i	0.838838	−	1.45291i
$370$		0			0
$371$	20.2677	+	1.18886i	1.05225	+	0.0617224i
$372$		0			0
$373$	−1.37440	+	2.38053i	−0.0711638	+	0.123259i	−0.899412	−	0.437103i	$-0.856005\pi$
$373$	−1.37440	+	2.38053i	−0.0711638	+	0.123259i	0.828248	+	0.560362i	$0.189338\pi$
$374$		0			0
$375$	−13.0445			−0.673616
$376$		0			0
$377$	−5.97412	+	10.3475i	−0.307683	+	0.532922i
$378$		0			0
$379$	−4.80918			−0.247031			−0.123515	−	0.992343i	$-0.539417\pi$
$379$	−4.80918			−0.247031			−0.123515	+	0.992343i	$0.539417\pi$
$380$		0			0
$381$	−8.07487	−	13.9861i	−0.413688	−	0.716528i
$382$		0			0
$383$	−1.11911	−	1.93835i	−0.0571837	−	0.0990450i	0.836016	−	0.548704i	$-0.184879\pi$
$383$	−1.11911	−	1.93835i	−0.0571837	−	0.0990450i	−0.893200	+	0.449659i	$0.851545\pi$
$384$		0			0
$385$	4.82550	+	0.283053i	0.245930	+	0.0144257i
$386$		0			0
$387$	−34.1861	+	59.2121i	−1.73778	+	3.00992i
$388$		0			0
$389$	−2.14684	+	3.71844i	−0.108849	+	0.188532i	−0.915304	−	0.402763i	$-0.868050\pi$
$389$	−2.14684	+	3.71844i	−0.108849	+	0.188532i	0.806455	+	0.591295i	$0.201383\pi$
$390$		0			0
$391$	−26.0601			−1.31792
$392$		0			0
$393$	−3.47737	−	6.02298i	−0.175410	−	0.303819i
$394$		0			0
$395$	−2.89311	+	5.01101i	−0.145568	+	0.252132i
$396$		0			0
$397$	2.47300	+	4.28335i	0.124116	+	0.214975i	0.921387	−	0.388646i	$-0.127057\pi$
$397$	2.47300	+	4.28335i	0.124116	+	0.214975i	−0.797271	+	0.603622i	$0.793724\pi$
$398$		0			0
$399$	−29.1065	−	18.3518i	−1.45715	−	0.918741i
$400$		0			0
$401$	−15.6678	−	27.1375i	−0.782414	−	1.35518i	−0.930532	−	0.366212i	$-0.880655\pi$
$401$	−15.6678	−	27.1375i	−0.782414	−	1.35518i	0.148117	−	0.988970i	$-0.452679\pi$
$402$		0			0
$403$	−9.17572	+	15.8928i	−0.457075	+	0.791677i
$404$		0			0
$405$	−1.81295	−	3.14013i	−0.0900864	−	0.156034i
$406$		0			0
$407$	25.1758			1.24792
$408$		0			0
$409$	3.76470	−	6.52065i	0.186152	−	0.322425i	−0.757812	−	0.652473i	$-0.773732\pi$
$409$	3.76470	−	6.52065i	0.186152	−	0.322425i	0.943964	+	0.330048i	$0.107065\pi$
$410$		0			0
$411$	−2.12757	+	3.68505i	−0.104945	+	0.181770i
$412$		0			0
$413$	11.0255	+	21.9761i	0.542528	+	1.08137i
$414$		0			0
$415$	−3.23654	−	5.60585i	−0.158876	−	0.275180i
$416$		0			0
$417$	−15.9655	−	27.6530i	−0.781832	−	1.35417i
$418$		0			0
$419$	20.0188			0.977982			0.488991	−	0.872289i	$-0.337365\pi$
$419$	20.0188			0.977982			0.488991	+	0.872289i	$0.337365\pi$
$420$		0			0
$421$	−8.84394	+	15.3181i	−0.431027	+	0.746561i	−0.996962	−	0.0778891i	$-0.975182\pi$
$421$	−8.84394	+	15.3181i	−0.431027	+	0.746561i	0.565935	+	0.824450i	$0.308515\pi$
$422$		0			0
$423$	−39.6246			−1.92661
$424$		0			0
$425$	−12.7602	+	22.1013i	−0.618961	+	1.07207i
$426$		0			0
$427$	−8.26465	−	16.4732i	−0.399954	−	0.797195i
$428$		0			0
$429$	29.3923	−	50.9089i	1.41907	−	2.45790i
$430$		0			0
$431$	1.96614	−	3.40546i	0.0947057	−	0.164035i	−0.814780	−	0.579770i	$-0.803142\pi$
$431$	1.96614	−	3.40546i	0.0947057	−	0.164035i	0.909486	+	0.415735i	$0.136476\pi$
$432$		0			0
$433$	7.61657	+	13.1923i	0.366029	+	0.633981i	0.988941	−	0.148311i	$-0.0473838\pi$
$433$	7.61657	+	13.1923i	0.366029	+	0.633981i	−0.622912	+	0.782292i	$0.714050\pi$
$434$		0			0
$435$	−1.65288	+	2.86288i	−0.0792496	+	0.137264i
$436$		0			0
$437$	−18.2933	+	11.0462i	−0.875087	+	0.528414i
$438$		0			0
$439$	6.32590	+	10.9568i	0.301919	+	0.522939i	0.976571	−	0.215197i	$-0.0690395\pi$
$439$	6.32590	+	10.9568i	0.301919	+	0.522939i	−0.674652	+	0.738136i	$0.735706\pi$
$440$		0			0
$441$	−24.6988	+	33.1190i	−1.17613	+	1.57710i
$442$		0			0
$443$	23.9279			1.13685			0.568424	−	0.822735i	$-0.307553\pi$
$443$	23.9279			1.13685			0.568424	+	0.822735i	$0.307553\pi$
$444$		0			0
$445$	0.823214	+	1.42585i	0.0390241	+	0.0675917i
$446$		0			0
$447$	11.1296	+	19.2770i	0.526411	+	0.911771i
$448$		0			0
$449$	34.3080			1.61909			0.809547	−	0.587055i	$-0.199713\pi$
$449$	34.3080			1.61909			0.809547	+	0.587055i	$0.199713\pi$
$450$		0			0
$451$	22.3637			1.05307
$452$		0			0
$453$	12.8720	+	22.2949i	0.604779	+	1.04751i
$454$		0			0
$455$	−5.66765	−	0.332451i	−0.265703	−	0.0155856i
$456$		0			0
$457$	15.4671	−	26.7899i	0.723522	−	1.25318i	−0.236057	−	0.971739i	$-0.575855\pi$
$457$	15.4671	−	26.7899i	0.723522	−	1.25318i	0.959579	−	0.281438i	$-0.0908115\pi$
$458$		0			0
$459$	−46.0269			−2.14835
$460$		0			0
$461$	6.34056	−	10.9822i	0.295309	−	0.511491i	−0.679748	−	0.733446i	$-0.737911\pi$
$461$	6.34056	−	10.9822i	0.295309	−	0.511491i	0.975057	+	0.221956i	$0.0712440\pi$
$462$		0			0
$463$	−9.58072			−0.445254			−0.222627	−	0.974904i	$-0.571463\pi$
$463$	−9.58072			−0.445254			−0.222627	+	0.974904i	$0.571463\pi$
$464$		0			0
$465$	−2.53868	+	4.39713i	−0.117729	+	0.203912i
$466$		0			0
$467$	−6.72199	+	11.6428i	−0.311057	+	0.538766i	−0.978591	−	0.205813i	$-0.934016\pi$
$467$	−6.72199	+	11.6428i	−0.311057	+	0.538766i	0.667535	+	0.744579i	$0.267350\pi$
$468$		0			0
$469$	−13.4141	−	0.786838i	−0.619403	−	0.0363328i
$470$		0			0
$471$	−17.3520			−0.799539
$472$		0			0
$473$	−47.4463			−2.18158
$474$		0			0
$475$	0.410987	+	20.9231i	0.0188574	+	0.960018i
$476$		0			0
$477$	22.6453	−	39.2228i	1.03686	−	1.79589i
$478$		0			0
$479$	7.99069	−	13.8403i	0.365104	−	0.632379i	−0.623689	−	0.781673i	$-0.714367\pi$
$479$	7.99069	−	13.8403i	0.365104	−	0.632379i	0.988793	+	0.149294i	$0.0477001\pi$
$480$		0			0
$481$	−29.5694			−1.34825
$482$		0			0
$483$	17.3545	+	34.5912i	0.789656	+	1.57396i
$484$		0			0
$485$	5.02185			0.228030
$486$		0			0
$487$	−11.9653	−	20.7245i	−0.542200	−	0.939119i	−0.998777	−	0.0494347i	$-0.984258\pi$
$487$	−11.9653	−	20.7245i	−0.542200	−	0.939119i	0.456577	−	0.889684i	$-0.349075\pi$
$488$		0			0
$489$	32.5896	−	56.4469i	1.47375	−	2.55262i
$490$		0			0
$491$	−14.2944	+	24.7586i	−0.645097	+	1.11734i	0.339182	+	0.940721i	$0.389850\pi$
$491$	−14.2944	+	24.7586i	−0.645097	+	1.11734i	−0.984279	+	0.176621i	$0.943483\pi$
$492$		0			0
$493$	6.60145	+	11.4341i	0.297315	+	0.514964i
$494$		0			0
$495$	5.39157	−	9.33847i	0.242333	−	0.419733i
$496$		0			0
$497$	20.0483	+	1.17599i	0.899291	+	0.0527504i
$498$		0			0
$499$	3.09614	+	5.36268i	0.138602	+	0.240066i	0.926968	−	0.375141i	$-0.122406\pi$
$499$	3.09614	+	5.36268i	0.138602	+	0.240066i	−0.788365	+	0.615207i	$0.789072\pi$
$500$		0			0
$501$	12.7829	+	22.1407i	0.571099	+	0.989173i
$502$		0			0
$503$	−21.5797	−	37.3771i	−0.962190	−	1.66656i	−0.716983	−	0.697090i	$-0.754478\pi$
$503$	−21.5797	−	37.3771i	−0.962190	−	1.66656i	−0.245206	−	0.969471i	$-0.578856\pi$
$504$		0			0
$505$	6.51446			0.289890
$506$		0			0
$507$	−15.1281	+	26.2027i	−0.671865	+	1.16370i
$508$		0			0
$509$	33.2599			1.47422			0.737110	−	0.675773i	$-0.236190\pi$
$509$	33.2599			1.47422			0.737110	+	0.675773i	$0.236190\pi$
$510$		0			0
$511$	−3.51700	−	7.01014i	−0.155583	−	0.310110i
$512$		0			0
$513$	−32.3093	+	19.5097i	−1.42649	+	0.861373i
$514$		0			0
$515$	7.51815			0.331289
$516$		0			0
$517$	−13.7485	−	23.8132i	−0.604660	−	1.04730i
$518$		0			0
$519$	−9.25281	−	16.0263i	−0.406153	−	0.703478i
$520$		0			0
$521$	−1.82562	−	3.16206i	−0.0799818	−	0.138533i	0.823260	−	0.567664i	$-0.192153\pi$
$521$	−1.82562	−	3.16206i	−0.0799818	−	0.138533i	−0.903242	+	0.429132i	$0.858820\pi$
$522$		0			0
$523$	−31.5693			−1.38043			−0.690214	−	0.723605i	$-0.742484\pi$
$523$	−31.5693			−1.38043			−0.690214	+	0.723605i	$0.742484\pi$
$524$		0			0
$525$	37.8340	+	2.21926i	1.65121	+	0.0968563i
$526$		0			0
$527$	10.1393	+	17.5617i	0.441673	+	0.765000i
$528$		0			0
$529$	1.03498			0.0449992
$530$		0			0
$531$	54.8478			2.38019
$532$		0			0
$533$	−26.2666			−1.13773
$534$		0			0
$535$	4.49416			0.194299
$536$		0			0
$537$	−2.69245	−	4.66346i	−0.116188	−	0.201243i
$538$		0			0
$539$	−28.4733	−	3.35189i	−1.22643	−	0.144376i
$540$		0			0
$541$	13.2634			0.570238			0.285119	−	0.958492i	$-0.407967\pi$
$541$	13.2634			0.570238			0.285119	+	0.958492i	$0.407967\pi$
$542$		0			0
$543$	2.39746	+	4.15253i	0.102885	+	0.178202i
$544$		0			0
$545$	−0.236134	−	0.408996i	−0.0101149	−	0.0175194i
$546$		0			0
$547$	9.82026	+	17.0092i	0.419884	+	0.727260i	0.995927	−	0.0901589i	$-0.0287375\pi$
$547$	9.82026	+	17.0092i	0.419884	+	0.727260i	−0.576044	+	0.817419i	$0.695404\pi$
$548$		0			0
$549$	−41.1137			−1.75469
$550$		0			0
$551$	9.48061	+	5.22812i	0.403887	+	0.222725i
$552$		0			0
$553$	18.8704	−	28.6652i	0.802450	−	1.21897i
$554$		0			0
$555$	−8.18109			−0.347268
$556$		0			0
$557$	−16.5501	+	28.6657i	−0.701252	+	1.21460i	0.266775	+	0.963759i	$0.414042\pi$
$557$	−16.5501	+	28.6657i	−0.701252	+	1.21460i	−0.968027	+	0.250845i	$0.919292\pi$
$558$		0			0
$559$	55.7266			2.35699
$560$		0			0
$561$	−32.4787	−	56.2548i	−1.37125	−	2.37508i
$562$		0			0
$563$	−16.6164	−	28.7804i	−0.700297	−	1.21295i	−0.968362	−	0.249549i	$-0.919717\pi$
$563$	−16.6164	−	28.7804i	−0.700297	−	1.21295i	0.268065	−	0.963401i	$-0.413616\pi$
$564$		0			0
$565$	−2.06301	−	3.57324i	−0.0867914	−	0.150327i
$566$		0			0
$567$	9.64383	+	19.2222i	0.405003	+	0.807258i
$568$		0			0
$569$	13.9270	−	24.1223i	0.583850	−	1.01126i	−0.411167	−	0.911560i	$-0.634879\pi$
$569$	13.9270	−	24.1223i	0.583850	−	1.01126i	0.995018	−	0.0996985i	$-0.0317878\pi$
$570$		0			0
$571$	−10.2213	−	17.7037i	−0.427746	−	0.740878i	0.568926	−	0.822388i	$-0.307359\pi$
$571$	−10.2213	−	17.7037i	−0.427746	−	0.740878i	−0.996672	+	0.0815105i	$0.974026\pi$
$572$		0			0
$573$	−37.8549	+	65.5666i	−1.58141	+	2.73908i
$574$		0			0
$575$	11.7686	−	20.3838i	0.490785	−	0.850064i
$576$		0			0
$577$	1.06635	+	1.84697i	0.0443927	+	0.0768904i	0.887368	−	0.461062i	$-0.152531\pi$
$577$	1.06635	+	1.84697i	0.0443927	+	0.0768904i	−0.842975	+	0.537952i	$0.819198\pi$
$578$		0			0
$579$	−44.8390			−1.86344
$580$		0			0
$581$	17.2165	+	34.3161i	0.714259	+	1.42367i
$582$		0			0
$583$	31.4290			1.30165
$584$		0			0
$585$	−6.33250	+	10.9682i	−0.261817	+	0.453480i
$586$		0			0
$587$	−8.56695	+	14.8384i	−0.353596	+	0.612446i	−0.986877	−	0.161476i	$-0.948374\pi$
$587$	−8.56695	+	14.8384i	−0.353596	+	0.612446i	0.633281	+	0.773922i	$0.281708\pi$
$588$		0			0
$589$	14.5614	+	8.02992i	0.599991	+	0.330867i
$590$		0			0
$591$	48.8386			2.00895
$592$		0			0
$593$	−45.3910			−1.86398			−0.931992	−	0.362479i	$-0.881931\pi$
$593$	−45.3910			−1.86398			−0.931992	+	0.362479i	$0.881931\pi$
$594$		0			0
$595$	−3.44954	+	5.24006i	−0.141418	+	0.214822i
$596$		0			0
$597$	12.6927	−	21.9844i	0.519477	−	0.899760i
$598$		0			0
$599$	−16.5039	+	28.5856i	−0.674331	+	1.16798i	0.302333	+	0.953202i	$0.402235\pi$
$599$	−16.5039	+	28.5856i	−0.674331	+	1.16798i	−0.976664	+	0.214773i	$0.931099\pi$
$600$		0			0
$601$	30.5198			1.24493			0.622465	−	0.782648i	$-0.286131\pi$
$601$	30.5198			1.24493			0.622465	+	0.782648i	$0.286131\pi$
$602$		0			0
$603$	−14.9876	+	25.9593i	−0.610343	+	1.05715i
$604$		0			0
$605$	2.57600			0.104729
$606$		0			0
$607$	1.89631	−	3.28450i	0.0769688	−	0.133314i	−0.824972	−	0.565174i	$-0.808809\pi$
$607$	1.89631	−	3.28450i	0.0769688	−	0.133314i	0.901941	+	0.431860i	$0.142142\pi$
$608$		0			0
$609$	10.7810	−	16.3769i	0.436867	−	0.663626i
$610$		0			0
$611$	16.1479	+	27.9690i	0.653276	+	1.13151i
$612$		0			0
$613$	−6.10037			−0.246392			−0.123196	−	0.992382i	$-0.539314\pi$
$613$	−6.10037			−0.246392			−0.123196	+	0.992382i	$0.539314\pi$
$614$		0			0
$615$	−7.26728			−0.293045
$616$		0			0
$617$	−6.65647	−	11.5294i	−0.267980	−	0.464154i	0.700360	−	0.713789i	$-0.253023\pi$
$617$	−6.65647	−	11.5294i	−0.267980	−	0.464154i	−0.968340	+	0.249635i	$0.919689\pi$
$618$		0			0
$619$	8.97040	+	15.5372i	0.360551	+	0.624492i	0.988052	−	0.154124i	$-0.0492554\pi$
$619$	8.97040	+	15.5372i	0.360551	+	0.624492i	−0.627501	+	0.778616i	$0.715922\pi$
$620$		0			0
$621$	42.4501			1.70347
$622$		0			0
$623$	−4.37901	−	8.72831i	−0.175441	−	0.349692i
$624$		0			0
$625$	−11.0274	−	19.1000i	−0.441096	−	0.764001i
$626$		0			0
$627$	−46.6440	−	25.7220i	−1.86278	−	1.02724i
$628$		0			0
$629$	−16.3372	+	28.2969i	−0.651409	+	1.12827i
$630$		0			0
$631$	−12.0857	−	20.9330i	−0.481123	−	0.833329i	0.518643	−	0.854991i	$-0.326438\pi$
$631$	−12.0857	−	20.9330i	−0.481123	−	0.833329i	−0.999765	+	0.0216621i	$0.993104\pi$
$632$		0			0
$633$	13.8465	−	23.9829i	0.550351	−	0.953236i
$634$		0			0
$635$	−1.20726	+	2.09103i	−0.0479086	+	0.0829801i
$636$		0			0
$637$	33.4425	+	3.93686i	1.32504	+	0.155984i
$638$		0			0
$639$	22.4002	−	38.7982i	0.886137	−	1.53483i
$640$		0			0
$641$	−26.3479			−1.04068			−0.520340	−	0.853959i	$-0.674195\pi$
$641$	−26.3479			−1.04068			−0.520340	+	0.853959i	$0.674195\pi$
$642$		0			0
$643$	12.6746	−	21.9531i	0.499839	−	0.865747i	−0.500161	−	0.865933i	$-0.666726\pi$
$643$	12.6746	−	21.9531i	0.499839	−	0.865747i	1.00000		0.000185699i	$5.91099e-5\pi$
$644$		0			0
$645$	15.4181			0.607087
$646$		0			0
$647$	−15.8823	−	27.5090i	−0.624399	−	1.08149i	−0.988657	−	0.150192i	$-0.952011\pi$
$647$	−15.8823	−	27.5090i	−0.624399	−	1.08149i	0.364258	−	0.931298i	$-0.381323\pi$
$648$		0			0
$649$	19.0306	+	32.9619i	0.747015	+	1.29387i
$650$		0			0
$651$	16.5586	−	25.1535i	0.648983	−	0.985843i
$652$		0			0
$653$	−16.9097	+	29.2885i	−0.661730	+	1.14615i	0.318431	+	0.947946i	$0.396844\pi$
$653$	−16.9097	+	29.2885i	−0.661730	+	1.14615i	−0.980161	+	0.198203i	$0.936489\pi$
$654$		0			0
$655$	−0.519895	+	0.900485i	−0.0203140	+	0.0351849i
$656$		0			0
$657$	−17.4958			−0.682577
$658$		0			0
$659$	11.0517	+	19.1421i	0.430513	+	0.745670i	0.996917	−	0.0784575i	$-0.0249995\pi$
$659$	11.0517	+	19.1421i	0.430513	+	0.745670i	−0.566405	+	0.824127i	$0.691666\pi$
$660$		0			0
$661$	20.9063	−	36.2108i	0.813161	−	1.40844i	−0.0974793	−	0.995238i	$-0.531078\pi$
$661$	20.9063	−	36.2108i	0.813161	−	1.40844i	0.910641	−	0.413199i	$-0.135589\pi$
$662$		0			0
$663$	38.1469	+	66.0724i	1.48150	+	2.56604i
$664$		0			0
$665$	−0.200327	+	5.14052i	−0.00776833	+	0.199341i
$666$		0			0
$667$	−6.08845	−	10.5455i	−0.235746	−	0.408324i
$668$		0			0
$669$	−3.03463	+	5.25613i	−0.117326	+	0.203214i
$670$		0			0
$671$	−14.2652	−	24.7081i	−0.550703	−	0.953846i
$672$		0			0
$673$	−24.8724			−0.958761			−0.479381	−	0.877607i	$-0.659139\pi$
$673$	−24.8724			−0.958761			−0.479381	+	0.877607i	$0.659139\pi$
$674$		0			0
$675$	20.7855	−	36.0015i	0.800034	−	1.38570i
$676$		0			0
$677$	−16.1566	+	27.9840i	−0.620947	+	1.07551i	0.368363	+	0.929682i	$0.379919\pi$
$677$	−16.1566	+	27.9840i	−0.620947	+	1.07551i	−0.989310	+	0.145830i	$0.953415\pi$
$678$		0			0
$679$	−29.7342	−	1.74414i	−1.14109	−	0.0669339i
$680$		0			0
$681$	8.10015	+	14.0299i	0.310398	+	0.537626i
$682$		0			0
$683$	−9.51782	−	16.4854i	−0.364189	−	0.630794i	0.624456	−	0.781060i	$-0.285321\pi$
$683$	−9.51782	−	16.4854i	−0.364189	−	0.630794i	−0.988646	+	0.150265i	$0.951987\pi$
$684$		0			0
$685$	0.636177			0.0243071
$686$		0			0
$687$	1.21422	−	2.10308i	0.0463252	−	0.0802376i
$688$		0			0
$689$	−36.9139			−1.40631
$690$		0			0
$691$	7.98499	−	13.8304i	0.303763	−	0.526134i	−0.673222	−	0.739441i	$-0.735090\pi$
$691$	7.98499	−	13.8304i	0.303763	−	0.526134i	0.976985	+	0.213307i	$0.0684234\pi$
$692$		0			0
$693$	−35.1666	+	53.4202i	−1.33587	+	2.02927i
$694$		0			0
$695$	−2.38697	+	4.13435i	−0.0905428	+	0.156825i
$696$		0			0
$697$	−14.5124	+	25.1362i	−0.549697	+	0.952103i
$698$		0			0
$699$	−4.27669	−	7.40744i	−0.161759	−	0.280175i
$700$		0			0
$701$	3.15311	−	5.46134i	0.119091	−	0.206272i	−0.800317	−	0.599578i	$-0.795335\pi$
$701$	3.15311	−	5.46134i	0.119091	−	0.206272i	0.919408	+	0.393306i	$0.128669\pi$
$702$		0			0
$703$	0.526199	+	26.7884i	0.0198460	+	1.01034i
$704$		0			0
$705$	4.46771	+	7.73831i	0.168264	+	0.291441i
$706$		0			0
$707$	−38.5719	−	2.26254i	−1.45065	−	0.0850916i
$708$		0			0
$709$	−35.3475			−1.32750			−0.663751	−	0.747953i	$-0.731037\pi$
$709$	−35.3475			−1.32750			−0.663751	+	0.747953i	$0.731037\pi$
$710$		0			0
$711$	−38.2790	−	66.3011i	−1.43557	−	2.48649i
$712$		0			0
$713$	−9.35133	−	16.1970i	−0.350210	−	0.606581i
$714$		0			0
$715$	−8.78877			−0.328681
$716$		0			0
$717$	33.4260			1.24832
$718$		0			0
$719$	13.0258	+	22.5614i	0.485780	+	0.841396i	0.999866	−	0.0163422i	$-0.00520211\pi$
$719$	13.0258	+	22.5614i	0.485780	+	0.841396i	−0.514086	+	0.857739i	$0.671869\pi$
$720$		0			0
$721$	−44.5147	−	2.61113i	−1.65781	−	0.0972436i
$722$		0			0
$723$	31.9820	−	55.3945i	1.18942	−	2.06014i
$724$		0			0
$725$	−11.9247			−0.442873
$726$		0			0
$727$	−5.81912	+	10.0790i	−0.215819	+	0.373810i	−0.953526	−	0.301312i	$-0.902576\pi$
$727$	−5.81912	+	10.0790i	−0.215819	+	0.373810i	0.737706	+	0.675122i	$0.235909\pi$
$728$		0			0
$729$	−29.5294			−1.09368
$730$		0			0
$731$	30.7892	−	53.3285i	1.13878	−	1.97243i
$732$		0			0
$733$	−13.7782	+	23.8645i	−0.508909	+	0.881456i	0.491038	+	0.871138i	$0.336618\pi$
$733$	−13.7782	+	23.8645i	−0.508909	+	0.881456i	−0.999947	+	0.0103179i	$0.996716\pi$
$734$		0			0
$735$	9.25265	+	1.08923i	0.341289	+	0.0401768i
$736$		0			0
$737$	−20.8010			−0.766216
$738$		0			0
$739$	22.6077			0.831636			0.415818	−	0.909448i	$-0.363495\pi$
$739$	22.6077			0.831636			0.415818	+	0.909448i	$0.363495\pi$
$740$		0			0
$741$	54.7843	+	30.2110i	2.01255	+	1.10983i
$742$		0			0
$743$	0.867573	−	1.50268i	0.0318282	−	0.0551280i	−0.849673	−	0.527311i	$-0.823200\pi$
$743$	0.867573	−	1.50268i	0.0318282	−	0.0551280i	0.881501	+	0.472183i	$0.156534\pi$
$744$		0			0
$745$	1.66396	−	2.88207i	0.0609629	−	0.105591i
$746$		0			0
$747$	85.6458			3.13362
$748$		0			0
$749$	−26.6097	−	1.56087i	−0.972298	−	0.0570328i
$750$		0			0
$751$	−40.4676			−1.47669			−0.738343	−	0.674426i	$-0.764391\pi$
$751$	−40.4676			−1.47669			−0.738343	+	0.674426i	$0.764391\pi$
$752$		0			0
$753$	39.8616	+	69.0424i	1.45264	+	2.51604i
$754$		0			0
$755$	1.92447	−	3.33327i	0.0700385	−	0.121310i
$756$		0			0
$757$	−3.56111	+	6.16803i	−0.129431	+	0.224181i	−0.923456	−	0.383704i	$-0.874648\pi$
$757$	−3.56111	+	6.16803i	−0.129431	+	0.224181i	0.794025	+	0.607885i	$0.207982\pi$
$758$		0			0
$759$	29.9548	+	51.8832i	1.08729	+	1.88324i
$760$		0			0
$761$	1.46387	−	2.53549i	0.0530652	−	0.0919116i	−0.838273	−	0.545251i	$-0.816434\pi$
$761$	1.46387	−	2.53549i	0.0530652	−	0.0919116i	0.891338	+	0.453340i	$0.149768\pi$
$762$		0			0
$763$	1.25609	+	2.50366i	0.0454735	+	0.0906386i
$764$		0			0
$765$	6.99747	+	12.1200i	0.252994	+	0.438199i
$766$		0			0
$767$	−22.3518	−	38.7144i	−0.807076	−	1.39790i
$768$		0			0
$769$	−9.11561	−	15.7887i	−0.328717	−	0.569355i	0.653540	−	0.756892i	$-0.273283\pi$
$769$	−9.11561	−	15.7887i	−0.328717	−	0.569355i	−0.982258	+	0.187537i	$0.939950\pi$
$770$		0			0
$771$	−36.7245			−1.32260
$772$		0			0
$773$	5.35847	−	9.28114i	0.192731	−	0.333819i	−0.753424	−	0.657536i	$-0.771599\pi$
$773$	5.35847	−	9.28114i	0.192731	−	0.333819i	0.946154	+	0.323716i	$0.104932\pi$
$774$		0			0
$775$	−18.3153			−0.657905
$776$		0			0
$777$	48.4399	+	2.84138i	1.73777	+	0.101934i
$778$		0			0
$779$	0.467423	+	23.7962i	0.0167472	+	0.852589i
$780$		0			0
$781$	31.0888			1.11244
$782$		0			0
$783$	−10.7533	−	18.6253i	−0.384292	−	0.665613i
$784$		0			0
$785$	1.29713	+	2.24670i	0.0462967	+	0.0801882i
$786$		0			0
$787$	9.50413	+	16.4616i	0.338786	+	0.586794i	0.984205	−	0.177035i	$-0.0566506\pi$
$787$	9.50413	+	16.4616i	0.338786	+	0.586794i	−0.645419	+	0.763829i	$0.723317\pi$
$788$		0			0
$789$	40.9904			1.45930
$790$		0			0
$791$	10.9740	+	21.8735i	0.390190	+	0.777732i
$792$		0			0
$793$	16.7548	+	29.0202i	0.594980	+	1.03054i
$794$		0			0
$795$	−10.2131			−0.362222
$796$		0			0
$797$	−7.67070			−0.271710			−0.135855	−	0.990729i	$-0.543378\pi$
$797$	−7.67070			−0.271710			−0.135855	+	0.990729i	$0.543378\pi$
$798$		0			0
$799$	35.6872			1.26252
$800$		0			0
$801$	−21.7840			−0.769700
$802$		0			0
$803$	−6.07053	−	10.5145i	−0.214224	−	0.371048i
$804$		0			0
$805$	3.18148	−	4.83286i	0.112132	−	0.170336i
$806$		0			0
$807$	74.6802			2.62887
$808$		0			0
$809$	−9.63335	−	16.6854i	−0.338690	−	0.586629i	0.645496	−	0.763763i	$-0.276651\pi$
$809$	−9.63335	−	16.6854i	−0.338690	−	0.586629i	−0.984187	+	0.177134i	$0.943317\pi$
$810$		0			0
$811$	11.6463	+	20.1720i	0.408957	+	0.708334i	0.994773	−	0.102110i	$-0.0325594\pi$
$811$	11.6463	+	20.1720i	0.408957	+	0.708334i	−0.585816	+	0.810444i	$0.699226\pi$
$812$		0			0
$813$	10.5302	+	18.2388i	0.369309	+	0.639662i
$814$		0			0
$815$	−9.74483			−0.341347
$816$		0			0
$817$	−0.991675	−	50.4856i	−0.0346943	−	1.76627i
$818$		0			0
$819$	41.3039	−	62.7431i	1.44327	−	2.19242i
$820$		0			0
$821$	−2.41760			−0.0843749			−0.0421874	−	0.999110i	$-0.513433\pi$
$821$	−2.41760			−0.0843749			−0.0421874	+	0.999110i	$0.513433\pi$
$822$		0			0
$823$	−6.65953	+	11.5346i	−0.232137	+	0.402073i	−0.958437	−	0.285305i	$-0.907905\pi$
$823$	−6.65953	+	11.5346i	−0.232137	+	0.402073i	0.726300	+	0.687378i	$0.241238\pi$
$824$		0			0
$825$	58.6688			2.04259
$826$		0			0
$827$	9.38209	+	16.2503i	0.326247	+	0.565077i	0.981764	−	0.190104i	$-0.0608824\pi$
$827$	9.38209	+	16.2503i	0.326247	+	0.565077i	−0.655517	+	0.755181i	$0.727549\pi$
$828$		0			0
$829$	−16.6185	−	28.7842i	−0.577186	−	0.999715i	−0.995800	−	0.0915510i	$-0.970818\pi$
$829$	−16.6185	−	28.7842i	−0.577186	−	0.999715i	0.418615	−	0.908164i	$-0.362516\pi$
$830$		0			0
$831$	28.5364	+	49.4265i	0.989918	+	1.71459i
$832$		0			0
$833$	22.2446	−	29.8282i	0.770728	−	1.03348i
$834$		0			0
$835$	1.91115	−	3.31021i	0.0661381	−	0.114555i
$836$		0			0
$837$	−16.5161	−	28.6068i	−0.570881	−	0.988795i
$838$		0			0
$839$	5.45416	−	9.44689i	0.188299	−	0.326143i	−0.756384	−	0.654127i	$-0.773036\pi$
$839$	5.45416	−	9.44689i	0.188299	−	0.326143i	0.944683	+	0.327984i	$0.106369\pi$
$840$		0			0
$841$	11.4154	−	19.7720i	0.393634	−	0.681794i
$842$		0			0
$843$	45.4560	+	78.7321i	1.56559	+	2.71168i
$844$		0			0
$845$	4.52356			0.155615
$846$		0			0
$847$	−15.2524	−	0.894672i	−0.524079	−	0.0307413i
$848$		0			0
$849$	25.2512			0.866620
$850$		0			0
$851$	15.0677	−	26.0980i	0.516513	−	0.894627i
$852$		0			0
$853$	1.56947	−	2.71841i	0.0537378	−	0.0930766i	−0.837905	−	0.545816i	$-0.816220\pi$
$853$	1.56947	−	2.71841i	0.0537378	−	0.0930766i	0.891643	+	0.452739i	$0.149553\pi$
$854$		0			0
$855$	10.0494	+	5.54175i	0.343681	+	0.189524i
$856$		0			0
$857$	−39.5202			−1.34999			−0.674993	−	0.737824i	$-0.735853\pi$
$857$	−39.5202			−1.34999			−0.674993	+	0.737824i	$0.735853\pi$
$858$		0			0
$859$	−9.08434			−0.309954			−0.154977	−	0.987918i	$-0.549530\pi$
$859$	−9.08434			−0.309954			−0.154977	+	0.987918i	$0.549530\pi$
$860$		0			0
$861$	43.0293	+	2.52400i	1.46643	+	0.0860178i
$862$		0			0
$863$	−11.5365	+	19.9818i	−0.392706	+	0.680187i	−0.992805	−	0.119738i	$-0.961794\pi$
$863$	−11.5365	+	19.9818i	−0.392706	+	0.680187i	0.600099	+	0.799926i	$0.295128\pi$
$864$		0			0
$865$	−1.38337	+	2.39607i	−0.0470360	+	0.0814688i
$866$		0			0
$867$	33.5835			1.14056
$868$		0			0
$869$	26.5633	−	46.0090i	0.901099	−	1.56075i
$870$		0			0
$871$	24.4312			0.827821
$872$		0			0
$873$	−33.2222	+	57.5426i	−1.12440	+	1.94752i
$874$		0			0
$875$	−5.18711	−	10.3390i	−0.175356	−	0.349523i
$876$		0			0
$877$	14.9654	+	25.9209i	0.505347	+	0.875287i	0.999981	+	0.00618527i	$0.00196884\pi$
$877$	14.9654	+	25.9209i	0.505347	+	0.875287i	−0.494634	+	0.869101i	$0.664698\pi$
$878$		0			0
$879$	16.4104			0.553508
$880$		0			0
$881$	20.3891			0.686925			0.343462	−	0.939166i	$-0.388400\pi$
$881$	20.3891			0.686925			0.343462	+	0.939166i	$0.388400\pi$
$882$		0			0
$883$	1.68307	+	2.91517i	0.0566399	+	0.0981032i	0.892955	−	0.450146i	$-0.148628\pi$
$883$	1.68307	+	2.91517i	0.0566399	+	0.0981032i	−0.836315	+	0.548249i	$0.815295\pi$
$884$		0			0
$885$	−6.18415	−	10.7113i	−0.207878	−	0.360055i
$886$		0			0
$887$	46.6068			1.56490			0.782452	−	0.622711i	$-0.213969\pi$
$887$	46.6068			1.56490			0.782452	+	0.622711i	$0.213969\pi$
$888$		0			0
$889$	7.87437	−	11.9616i	0.264098	−	0.401180i
$890$		0			0
$891$	16.6458	+	28.8313i	0.557655	+	0.965886i
$892$		0			0
$893$	25.0512	−	15.1269i	0.838307	−	0.506204i
$894$		0			0
$895$	−0.402543	+	0.697225i	−0.0134555	+	0.0233057i
$896$		0			0
$897$	−35.1825	−	60.9379i	−1.17471	−	2.03466i
$898$		0			0
$899$	−4.73769	+	8.20591i	−0.158011	+	0.273683i
$900$		0			0
$901$	−20.3951	+	35.3254i	−0.679460	+	1.17686i
$902$		0			0
$903$	−91.2900	−	5.35487i	−3.03794	−	0.178199i
$904$		0			0
$905$	0.358440	−	0.620837i	0.0119150	−	0.0206373i
$906$		0			0
$907$	−45.5901			−1.51379			−0.756897	−	0.653534i	$-0.773286\pi$
$907$	−45.5901			−1.51379			−0.756897	+	0.653534i	$0.773286\pi$
$908$		0			0
$909$	−43.0967	+	74.6456i	−1.42943	+	2.47584i
$910$		0			0
$911$	18.7178			0.620147			0.310073	−	0.950713i	$-0.399646\pi$
$911$	18.7178			0.620147			0.310073	+	0.950713i	$0.399646\pi$
$912$		0			0
$913$	29.7166	+	51.4706i	0.983475	+	1.70343i
$914$		0			0
$915$	4.63562	+	8.02912i	0.153249	+	0.265435i
$916$		0			0
$917$	3.39103	−	5.15117i	0.111982	−	0.170107i
$918$		0			0
$919$	−13.2959	+	23.0292i	−0.438592	+	0.759664i	−0.997581	−	0.0695113i	$-0.977856\pi$
$919$	−13.2959	+	23.0292i	−0.438592	+	0.759664i	0.558989	+	0.829175i	$0.311189\pi$
$920$		0			0
$921$	−8.38301	+	14.5198i	−0.276230	+	0.478444i
$922$		0			0
$923$	−36.5144			−1.20189
$924$		0			0
$925$	−14.7556	−	25.5575i	−0.485162	−	0.840325i
$926$		0			0
$927$	−49.7366	+	86.1463i	−1.63356	+	2.82942i
$928$		0			0
$929$	−2.46225	−	4.26474i	−0.0807838	−	0.139922i	0.822803	−	0.568327i	$-0.192409\pi$
$929$	−2.46225	−	4.26474i	−0.0807838	−	0.139922i	−0.903587	+	0.428405i	$0.859076\pi$
$930$		0			0
$931$	2.97148	−	30.3673i	0.0973864	−	0.995247i
$932$		0			0
$933$	−47.1433	−	81.6546i	−1.54340	−	2.67325i
$934$		0			0
$935$	−4.85583	+	8.41055i	−0.158803	+	0.275054i
$936$		0			0
$937$	−2.34076	−	4.05431i	−0.0764692	−	0.132449i	0.825255	−	0.564760i	$-0.191031\pi$
$937$	−2.34076	−	4.05431i	−0.0764692	−	0.132449i	−0.901724	+	0.432312i	$0.857698\pi$
$938$		0			0
$939$	81.1380			2.64784
$940$		0			0
$941$	13.2507	−	22.9510i	0.431962	−	0.748180i	−0.565080	−	0.825036i	$-0.691155\pi$
$941$	13.2507	−	22.9510i	0.431962	−	0.748180i	0.997042	+	0.0768561i	$0.0244882\pi$
$942$		0			0
$943$	13.3847	−	23.1829i	0.435864	−	0.754939i
$944$		0			0
$945$	5.61907	−	8.53570i	0.182788	−	0.277666i
$946$		0			0
$947$	2.87681	+	4.98278i	0.0934838	+	0.161919i	0.908975	−	0.416851i	$-0.136866\pi$
$947$	2.87681	+	4.98278i	0.0934838	+	0.161919i	−0.815491	+	0.578770i	$0.803533\pi$
$948$		0			0
$949$	7.12996	+	12.3495i	0.231448	+	0.400880i
$950$		0			0
$951$	9.47181			0.307144
$952$		0			0
$953$	−17.3933	+	30.1261i	−0.563425	+	0.975881i	0.433769	+	0.901024i	$0.357183\pi$
$953$	−17.3933	+	30.1261i	−0.563425	+	0.975881i	−0.997194	+	0.0748568i	$0.976150\pi$
$954$		0			0
$955$	11.3192			0.366282
$956$		0			0
$957$	15.1761	−	26.2857i	0.490573	−	0.849697i
$958$		0			0
$959$	−3.76678	−	0.220951i	−0.121636	−	0.00713487i
$960$		0			0
$961$	8.22333	−	14.2432i	0.265269	−	0.459459i
$962$		0			0
$963$	−29.7313	+	51.4960i	−0.958076	+	1.65944i
$964$		0			0
$965$	3.35190	+	5.80565i	0.107901	+	0.186891i
$966$		0			0
$967$	−12.2583	+	21.2320i	−0.394201	+	0.682776i	−0.992999	−	0.118124i	$-0.962312\pi$
$967$	−12.2583	+	21.2320i	−0.394201	+	0.682776i	0.598798	+	0.800900i	$0.295645\pi$
$968$		0			0
$969$	59.1794	−	35.7350i	1.90112	−	1.14797i
$970$		0			0
$971$	−22.1600	−	38.3822i	−0.711148	−	1.23174i	−0.964426	−	0.264351i	$-0.914842\pi$
$971$	−22.1600	−	38.3822i	−0.711148	−	1.23174i	0.253278	−	0.967393i	$-0.418491\pi$
$972$		0			0
$973$	15.5690	−	23.6503i	0.499120	−	0.758194i
$974$		0			0
$975$	−68.9077			−2.20681
$976$		0			0
$977$	6.95397	+	12.0446i	0.222477	+	0.385342i	0.955560	−	0.294798i	$-0.0952524\pi$
$977$	6.95397	+	12.0446i	0.222477	+	0.385342i	−0.733082	+	0.680140i	$0.761919\pi$
$978$		0			0
$979$	−7.55841	−	13.0915i	−0.241568	−	0.418408i
$980$		0			0
$981$	6.24861			0.199503
$982$		0			0
$983$	−35.1549			−1.12127			−0.560633	−	0.828065i	$-0.689442\pi$
$983$	−35.1549			−1.12127			−0.560633	+	0.828065i	$0.689442\pi$
$984$		0			0
$985$	−3.65088	−	6.32351i	−0.116327	−	0.201484i
$986$		0			0
$987$	−23.7656	−	47.3699i	−0.756466	−	1.50780i
$988$		0			0
$989$	−28.3966	+	49.1843i	−0.902959	+	1.56397i
$990$		0			0
$991$	26.8434			0.852710			0.426355	−	0.904556i	$-0.359797\pi$
$991$	26.8434			0.852710			0.426355	+	0.904556i	$0.359797\pi$
$992$		0			0
$993$	−47.0567	+	81.5046i	−1.49330	+	2.58647i
$994$		0			0
$995$	−3.79532			−0.120320
$996$		0			0
$997$	24.6954	−	42.7736i	0.782110	−	1.35465i	−0.148601	−	0.988897i	$-0.547477\pi$
$997$	24.6954	−	42.7736i	0.782110	−	1.35465i	0.930711	−	0.365756i	$-0.119190\pi$
$998$		0			0
$999$	26.6122	−	46.0938i	0.841974	−	1.45834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.l.b.429.11	yes	24
7.4	even	3		532.2.k.b.277.2	yes	24
19.7	even	3		532.2.k.b.121.2	✓	24
133.102	even	3	inner	532.2.l.b.501.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.k.b.121.2	✓	24	19.7	even	3
532.2.k.b.277.2	yes	24	7.4	even	3
532.2.l.b.429.11	yes	24	1.1	even	1	trivial
532.2.l.b.501.11	yes	24	133.102	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:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.98364 q^{3} +(-0.223039 - 0.386315i) q^{5} +(1.18643 + 2.36482i) q^{7} +5.90209 q^{9} +(2.04785 + 3.54698i) q^{11} +(-2.40524 - 4.16600i) q^{13} +(-0.665468 - 1.15262i) q^{15} -5.31563 q^{17} +(-3.73139 + 2.25316i) q^{19} +(3.53989 + 7.05576i) q^{21} +4.90255 q^{23} +(2.40051 - 4.15780i) q^{25} +8.65879 q^{27} +(-1.24190 - 2.15103i) q^{29} +(-1.90744 - 3.30379i) q^{31} +(6.11005 + 10.5829i) q^{33} +(0.648944 - 0.985784i) q^{35} +(3.07344 - 5.32335i) q^{37} +(-7.17637 - 12.4298i) q^{39} +(2.73014 - 4.72874i) q^{41} +(-5.79221 + 10.0324i) q^{43} +(-1.31640 - 2.28007i) q^{45} -6.71365 q^{47} +(-4.18475 + 5.61141i) q^{49} -15.8599 q^{51} +(3.83682 - 6.64557i) q^{53} +(0.913501 - 1.58223i) q^{55} +(-11.1331 + 6.72263i) q^{57} +9.29294 q^{59} -6.96595 q^{61} +(7.00245 + 13.9574i) q^{63} +(-1.07293 + 1.85836i) q^{65} +(-2.53937 + 4.39833i) q^{67} +14.6274 q^{69} +(3.79529 - 6.57364i) q^{71} -2.96434 q^{73} +(7.16224 - 12.4054i) q^{75} +(-5.95833 + 9.05106i) q^{77} +(-6.48566 - 11.2335i) q^{79} +8.12841 q^{81} +14.5111 q^{83} +(1.18559 + 2.05351i) q^{85} +(-3.70537 - 6.41788i) q^{87} -3.69090 q^{89} +(6.99818 - 10.6306i) q^{91} +(-5.69111 - 9.85730i) q^{93} +(1.70268 + 0.938947i) q^{95} +(-5.62889 + 9.74952i) q^{97} +(12.0866 + 20.9346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 6 q^{5} - 6 q^{7} + 30 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} - 6 q^{17} + 17 q^{19} - 18 q^{21} - 16 q^{23} - 8 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} + 7 q^{33} - 21 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 - 6 * q^5 - 6 * q^7 + 30 * q^9 + q^11 - 7 * q^13 - 2 * q^15 - 6 * q^17 + 17 * q^19 - 18 * q^21 - 16 * q^23 - 8 * q^25 + 20 * q^27 - 22 * q^29 - 7 * q^31 + 7 * q^33 - 21 * q^35 + 9 * q^37 + 12 * q^39 - 11 * q^41 - 9 * q^43 - 28 * q^45 - 22 * q^47 - 32 * q^49 - 16 * q^51 - 7 * q^53 - 11 * q^55 + 11 * q^57 + 16 * q^59 + 12 * q^61 + 20 * q^63 + 3 * q^65 - 27 * q^67 + 108 * q^69 - 13 * q^71 + 20 * q^73 + 25 * q^75 + 2 * q^77 - 14 * q^79 + 80 * q^81 - 12 * q^83 - 19 * q^85 + 19 * q^87 + 74 * q^89 - 21 * q^91 + 5 * q^93 + 47 * q^95 - 21 * q^97 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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