LMFDB - Embedded newform 504.2.t.d.193.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(193,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.193"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$504 = 2^{3} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	504.t (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	504.193
Dual form			504.2.t.d.457.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61774 - 0.618811i) q^{3} -1.83657 q^{5} +(2.45061 + 0.997255i) q^{7} +(2.23415 + 2.00215i) q^{9} -3.09719 q^{11} +(2.40225 - 4.16081i) q^{13} +(2.97109 + 1.13649i) q^{15} +(1.87185 - 3.24214i) q^{17} +(-2.71408 - 4.70093i) q^{19} +(-3.34733 - 3.12976i) q^{21} -7.95829 q^{23} -1.62701 q^{25} +(-2.37531 - 4.62146i) q^{27} +(-0.325267 - 0.563379i) q^{29} +(-0.518342 - 0.897795i) q^{31} +(5.01044 + 1.91658i) q^{33} +(-4.50072 - 1.83153i) q^{35} +(0.873712 + 1.51331i) q^{37} +(-6.46096 + 5.24456i) q^{39} +(2.52260 - 4.36927i) q^{41} +(-6.09645 - 10.5594i) q^{43} +(-4.10317 - 3.67709i) q^{45} +(2.30691 - 3.99569i) q^{47} +(5.01096 + 4.88776i) q^{49} +(-5.03443 + 4.08660i) q^{51} +(4.55082 - 7.88226i) q^{53} +5.68821 q^{55} +(1.48168 + 9.28438i) q^{57} +(2.89863 + 5.02058i) q^{59} +(2.40623 - 4.16771i) q^{61} +(3.47836 + 7.13449i) q^{63} +(-4.41190 + 7.64163i) q^{65} +(7.23870 + 12.5378i) q^{67} +(12.8744 + 4.92468i) q^{69} -5.00714 q^{71} +(-1.81364 + 3.14131i) q^{73} +(2.63207 + 1.00681i) q^{75} +(-7.59000 - 3.08869i) q^{77} +(7.17904 - 12.4345i) q^{79} +(0.982810 + 8.94618i) q^{81} +(3.83139 + 6.63616i) q^{83} +(-3.43778 + 5.95441i) q^{85} +(0.177571 + 1.11268i) q^{87} +(-5.76798 - 9.99043i) q^{89} +(10.0364 - 7.80087i) q^{91} +(0.282976 + 1.77315i) q^{93} +(4.98461 + 8.63360i) q^{95} +(-1.04480 - 1.80964i) q^{97} +(-6.91957 - 6.20103i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39}+ \cdots - 56 q^{99}+O(q^{100})$ 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9 + 6 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 - 15 * q^21 - 4 * q^23 + 20 * q^25 - 4 * q^27 + 9 * q^29 - 4 * q^31 - 31 * q^33 + 14 * q^35 + 2 * q^37 + 8 * q^39 + 16 * q^41 + 22 * q^45 + 5 * q^47 - 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 - 19 * q^59 - 13 * q^61 + 21 * q^63 + 13 * q^65 + 26 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 8 * q^75 - 4 * q^77 + 10 * q^79 - 8 * q^81 - 28 * q^83 - 20 * q^85 + 9 * q^87 + 6 * q^89 - 37 * q^91 - 32 * q^93 + 12 * q^95 - 29 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$ .

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$		0			0
$2$		0			0
$3$	−1.61774	−	0.618811i	−0.934001	−	0.357271i
$3$	−1.61774	−	0.618811i	−0.934001	−	0.357271i
$4$		0			0
$5$	−1.83657			−0.821340			−0.410670	−	0.911784i	$-0.634705\pi$
$5$	−1.83657			−0.821340			−0.410670	+	0.911784i	$0.634705\pi$
$6$		0			0
$7$	2.45061	+	0.997255i	0.926243	+	0.376927i
$7$	2.45061	+	0.997255i	0.926243	+	0.376927i
$8$		0			0
$9$	2.23415	+	2.00215i	0.744715	+	0.667383i
$10$		0			0
$11$	−3.09719			−0.933838			−0.466919	−	0.884300i	$-0.654636\pi$
$11$	−3.09719			−0.933838			−0.466919	+	0.884300i	$0.654636\pi$
$12$		0			0
$13$	2.40225	−	4.16081i	0.666263	−	1.15400i	−0.312678	−	0.949859i	$-0.601226\pi$
$13$	2.40225	−	4.16081i	0.666263	−	1.15400i	0.978941	−	0.204143i	$-0.0654406\pi$
$14$		0			0
$15$	2.97109	+	1.13649i	0.767132	+	0.293441i
$16$		0			0
$17$	1.87185	−	3.24214i	0.453990	−	0.786333i	−0.544640	−	0.838670i	$-0.683334\pi$
$17$	1.87185	−	3.24214i	0.453990	−	0.786333i	0.998629	+	0.0523367i	$0.0166669\pi$
$18$		0			0
$19$	−2.71408	−	4.70093i	−0.622654	−	1.07847i	−0.988990	−	0.147985i	$-0.952721\pi$
$19$	−2.71408	−	4.70093i	−0.622654	−	1.07847i	0.366336	−	0.930483i	$-0.380612\pi$
$20$		0			0
$21$	−3.34733	−	3.12976i	−0.730447	−	0.682970i
$22$		0			0
$23$	−7.95829			−1.65942			−0.829709	−	0.558197i	$-0.811493\pi$
$23$	−7.95829			−1.65942			−0.829709	+	0.558197i	$0.811493\pi$
$24$		0			0
$25$	−1.62701			−0.325401
$26$		0			0
$27$	−2.37531	−	4.62146i	−0.457128	−	0.889401i
$28$		0			0
$29$	−0.325267	−	0.563379i	−0.0604006	−	0.104617i	0.834244	−	0.551396i	$-0.185904\pi$
$29$	−0.325267	−	0.563379i	−0.0604006	−	0.104617i	−0.894645	+	0.446779i	$0.852571\pi$
$30$		0			0
$31$	−0.518342	−	0.897795i	−0.0930970	−	0.161249i	0.815716	−	0.578453i	$-0.196343\pi$
$31$	−0.518342	−	0.897795i	−0.0930970	−	0.161249i	−0.908813	+	0.417204i	$0.863010\pi$
$32$		0			0
$33$	5.01044	+	1.91658i	0.872206	+	0.333633i
$34$		0			0
$35$	−4.50072	−	1.83153i	−0.760760	−	0.309585i
$36$		0			0
$37$	0.873712	+	1.51331i	0.143637	+	0.248787i	0.928864	−	0.370422i	$-0.120787\pi$
$37$	0.873712	+	1.51331i	0.143637	+	0.248787i	−0.785226	+	0.619209i	$0.787453\pi$
$38$		0			0
$39$	−6.46096	+	5.24456i	−1.03458	+	0.839802i
$40$		0			0
$41$	2.52260	−	4.36927i	0.393964	−	0.682365i	−0.599005	−	0.800745i	$-0.704437\pi$
$41$	2.52260	−	4.36927i	0.393964	−	0.682365i	0.992968	+	0.118381i	$0.0377703\pi$
$42$		0			0
$43$	−6.09645	−	10.5594i	−0.929699	−	1.61029i	−0.783824	−	0.620984i	$-0.786733\pi$
$43$	−6.09645	−	10.5594i	−0.929699	−	1.61029i	−0.145876	−	0.989303i	$-0.546600\pi$
$44$		0			0
$45$	−4.10317	−	3.67709i	−0.611664	−	0.548148i
$46$		0			0
$47$	2.30691	−	3.99569i	0.336498	−	0.582832i	−0.647273	−	0.762258i	$-0.724091\pi$
$47$	2.30691	−	3.99569i	0.336498	−	0.582832i	0.983771	+	0.179426i	$0.0574241\pi$
$48$		0			0
$49$	5.01096	+	4.88776i	0.715852	+	0.698252i
$50$		0			0
$51$	−5.03443	+	4.08660i	−0.704961	+	0.572239i
$52$		0			0
$53$	4.55082	−	7.88226i	0.625104	−	1.08271i	−0.363417	−	0.931626i	$-0.618390\pi$
$53$	4.55082	−	7.88226i	0.625104	−	1.08271i	0.988521	−	0.151085i	$-0.0482766\pi$
$54$		0			0
$55$	5.68821			0.766998
$56$		0			0
$57$	1.48168	+	9.28438i	0.196254	+	1.22975i
$58$		0			0
$59$	2.89863	+	5.02058i	0.377370	+	0.653624i	0.990679	−	0.136219i	$-0.0434952\pi$
$59$	2.89863	+	5.02058i	0.377370	+	0.653624i	−0.613309	+	0.789843i	$0.710162\pi$
$60$		0			0
$61$	2.40623	−	4.16771i	0.308086	−	0.533620i	−0.669858	−	0.742489i	$-0.733645\pi$
$61$	2.40623	−	4.16771i	0.308086	−	0.533620i	0.977944	+	0.208869i	$0.0669783\pi$
$62$		0			0
$63$	3.47836	+	7.13449i	0.438233	+	0.898862i
$64$		0			0
$65$	−4.41190	+	7.64163i	−0.547228	+	0.947827i
$66$		0			0
$67$	7.23870	+	12.5378i	0.884348	+	1.53174i	0.846459	+	0.532454i	$0.178730\pi$
$67$	7.23870	+	12.5378i	0.884348	+	1.53174i	0.0378895	+	0.999282i	$0.487937\pi$
$68$		0			0
$69$	12.8744	+	4.92468i	1.54990	+	0.592861i
$70$		0			0
$71$	−5.00714			−0.594238			−0.297119	−	0.954840i	$-0.596026\pi$
$71$	−5.00714			−0.594238			−0.297119	+	0.954840i	$0.596026\pi$
$72$		0			0
$73$	−1.81364	+	3.14131i	−0.212270	+	0.367662i	−0.952425	−	0.304774i	$-0.901419\pi$
$73$	−1.81364	+	3.14131i	−0.212270	+	0.367662i	0.740155	+	0.672437i	$0.234752\pi$
$74$		0			0
$75$	2.63207	+	1.00681i	0.303925	+	0.116256i
$76$		0			0
$77$	−7.59000	−	3.08869i	−0.864961	−	0.351989i
$78$		0			0
$79$	7.17904	−	12.4345i	0.807705	−	1.39899i	−0.106745	−	0.994286i	$-0.534043\pi$
$79$	7.17904	−	12.4345i	0.807705	−	1.39899i	0.914450	−	0.404699i	$-0.132624\pi$
$80$		0			0
$81$	0.982810	+	8.94618i	0.109201	+	0.994020i
$82$		0			0
$83$	3.83139	+	6.63616i	0.420550	+	0.728414i	0.995993	−	0.0894279i	$-0.0285038\pi$
$83$	3.83139	+	6.63616i	0.420550	+	0.728414i	−0.575443	+	0.817842i	$0.695171\pi$
$84$		0			0
$85$	−3.43778	+	5.95441i	−0.372880	+	0.645847i
$86$		0			0
$87$	0.177571	+	1.11268i	0.0190376	+	0.119292i
$88$		0			0
$89$	−5.76798	−	9.99043i	−0.611405	−	1.05898i	−0.991004	−	0.133833i	$-0.957271\pi$
$89$	−5.76798	−	9.99043i	−0.611405	−	1.05898i	0.379599	−	0.925151i	$-0.376062\pi$
$90$		0			0
$91$	10.0364	−	7.80087i	1.05210	−	0.817753i
$92$		0			0
$93$	0.282976	+	1.77315i	0.0293432	+	0.183867i
$94$		0			0
$95$	4.98461	+	8.63360i	0.511410	+	0.885788i
$96$		0			0
$97$	−1.04480	−	1.80964i	−0.106083	−	0.183741i	0.808097	−	0.589049i	$-0.200498\pi$
$97$	−1.04480	−	1.80964i	−0.106083	−	0.183741i	−0.914180	+	0.405308i	$0.867164\pi$
$98$		0			0
$99$	−6.91957	−	6.20103i	−0.695443	−	0.623227i
$100$		0			0
$101$	−16.4532			−1.63716			−0.818578	−	0.574395i	$-0.805237\pi$
$101$	−16.4532			−1.63716			−0.818578	+	0.574395i	$0.805237\pi$
$102$		0			0
$103$	−7.74692			−0.763327			−0.381663	−	0.924301i	$-0.624649\pi$
$103$	−7.74692			−0.763327			−0.381663	+	0.924301i	$0.624649\pi$
$104$		0			0
$105$	6.14760	+	5.74803i	0.599945	+	0.560950i
$106$		0			0
$107$	3.74746	+	6.49080i	0.362281	+	0.627489i	0.988336	−	0.152290i	$-0.0486647\pi$
$107$	3.74746	+	6.49080i	0.362281	+	0.627489i	−0.626055	+	0.779779i	$0.715331\pi$
$108$		0			0
$109$	−4.30644	+	7.45897i	−0.412482	+	0.714440i	−0.995160	−	0.0982628i	$-0.968671\pi$
$109$	−4.30644	+	7.45897i	−0.412482	+	0.714440i	0.582678	+	0.812703i	$0.302005\pi$
$110$		0			0
$111$	−0.476981	−	2.98881i	−0.0452730	−	0.283685i
$112$		0			0
$113$	−1.55747	+	2.69762i	−0.146514	+	0.253771i	−0.929937	−	0.367719i	$-0.880139\pi$
$113$	−1.55747	+	2.69762i	−0.146514	+	0.253771i	0.783422	+	0.621490i	$0.213472\pi$
$114$		0			0
$115$	14.6160			1.36295
$116$		0			0
$117$	13.6975	−	4.48621i	1.26634	−	0.414750i
$118$		0			0
$119$	7.82040	−	6.07850i	0.716895	−	0.557215i
$120$		0			0
$121$	−1.40741			−0.127946
$122$		0			0
$123$	−6.78465	+	5.50731i	−0.611751	+	0.496578i
$124$		0			0
$125$	12.1710			1.08860
$126$		0			0
$127$	10.8866			0.966033			0.483017	−	0.875611i	$-0.339541\pi$
$127$	10.8866			0.966033			0.483017	+	0.875611i	$0.339541\pi$
$128$		0			0
$129$	3.32820	+	20.8548i	0.293032	+	1.83616i
$130$		0			0
$131$	−16.0558			−1.40280			−0.701401	−	0.712767i	$-0.747442\pi$
$131$	−16.0558			−1.40280			−0.701401	+	0.712767i	$0.747442\pi$
$132$		0			0
$133$	−1.96313	−	14.2268i	−0.170225	−	1.23362i
$134$		0			0
$135$	4.36242	+	8.48764i	0.375457	+	0.730500i
$136$		0			0
$137$	13.4406			1.14831			0.574155	−	0.818747i	$-0.305331\pi$
$137$	13.4406			1.14831			0.574155	+	0.818747i	$0.305331\pi$
$138$		0			0
$139$	−4.06953	+	7.04863i	−0.345173	+	0.597857i	−0.985385	−	0.170341i	$-0.945513\pi$
$139$	−4.06953	+	7.04863i	−0.345173	+	0.597857i	0.640212	+	0.768198i	$0.278846\pi$
$140$		0			0
$141$	−6.20456	+	5.03644i	−0.522518	+	0.424144i
$142$		0			0
$143$	−7.44022	+	12.8868i	−0.622182	+	1.07765i
$144$		0			0
$145$	0.597376	+	1.03469i	0.0496094	+	0.0859260i
$146$		0			0
$147$	−5.08182	−	11.0080i	−0.419141	−	0.907921i
$148$		0			0
$149$	7.52958			0.616847			0.308424	−	0.951249i	$-0.400199\pi$
$149$	7.52958			0.616847			0.308424	+	0.951249i	$0.400199\pi$
$150$		0			0
$151$	−5.67232			−0.461607			−0.230803	−	0.973000i	$-0.574135\pi$
$151$	−5.67232			−0.461607			−0.230803	+	0.973000i	$0.574135\pi$
$152$		0			0
$153$	10.6732	−	3.49569i	0.862878	−	0.282610i
$154$		0			0
$155$	0.951973	+	1.64886i	0.0764643	+	0.132440i
$156$		0			0
$157$	−0.218381	−	0.378248i	−0.0174287	−	0.0301875i	0.857179	−	0.515018i	$-0.172215\pi$
$157$	−0.218381	−	0.378248i	−0.0174287	−	0.0301875i	−0.874608	+	0.484830i	$0.838881\pi$
$158$		0			0
$159$	−12.2397	+	9.93532i	−0.970668	+	0.787922i
$160$		0			0
$161$	−19.5026	−	7.93644i	−1.53702	−	0.625479i
$162$		0			0
$163$	9.12649	+	15.8076i	0.714842	+	1.23814i	0.963020	+	0.269429i	$0.0868348\pi$
$163$	9.12649	+	15.8076i	0.714842	+	1.23814i	−0.248178	+	0.968714i	$0.579832\pi$
$164$		0			0
$165$	−9.20203	−	3.51993i	−0.716377	−	0.274026i
$166$		0			0
$167$	0.765108	−	1.32521i	0.0592058	−	0.102548i	−0.834903	−	0.550397i	$-0.814477\pi$
$167$	0.765108	−	1.32521i	0.0592058	−	0.102548i	0.894109	+	0.447849i	$0.147810\pi$
$168$		0			0
$169$	−5.04157	−	8.73226i	−0.387813	−	0.671713i
$170$		0			0
$171$	3.34830	−	15.9366i	0.256051	−	1.21870i
$172$		0			0
$173$	−1.08474	+	1.87883i	−0.0824716	+	0.142845i	−0.904311	−	0.426874i	$-0.859615\pi$
$173$	−1.08474	+	1.87883i	−0.0824716	+	0.142845i	0.821839	+	0.569719i	$0.192948\pi$
$174$		0			0
$175$	−3.98716	−	1.62254i	−0.301401	−	0.122653i
$176$		0			0
$177$	−1.58244	−	9.91569i	−0.118943	−	0.745309i
$178$		0			0
$179$	−1.08263	+	1.87517i	−0.0809195	+	0.140157i	−0.903645	−	0.428282i	$-0.859119\pi$
$179$	−1.08263	+	1.87517i	−0.0809195	+	0.140157i	0.822726	+	0.568439i	$0.192452\pi$
$180$		0			0
$181$	0.557838			0.0414638			0.0207319	−	0.999785i	$-0.493400\pi$
$181$	0.557838			0.0414638			0.0207319	+	0.999785i	$0.493400\pi$
$182$		0			0
$183$	−6.47167	+	5.25325i	−0.478399	+	0.388332i
$184$		0			0
$185$	−1.60463	−	2.77931i	−0.117975	−	0.204339i
$186$		0			0
$187$	−5.79747	+	10.0415i	−0.423953	+	0.734308i
$188$		0			0
$189$	−1.21217	−	13.6942i	−0.0881725	−	0.996105i
$190$		0			0
$191$	11.9998	−	20.7843i	0.868277	−	1.50390i	0.00452179	−	0.999990i	$-0.498561\pi$
$191$	11.9998	−	20.7843i	0.868277	−	1.50390i	0.863756	−	0.503911i	$-0.168106\pi$
$192$		0			0
$193$	10.6397	+	18.4285i	0.765862	+	1.32651i	0.939790	+	0.341753i	$0.111021\pi$
$193$	10.6397	+	18.4285i	0.765862	+	1.32651i	−0.173928	+	0.984758i	$0.555646\pi$
$194$		0			0
$195$	11.8660	−	9.63201i	0.849743	−	0.689763i
$196$		0			0
$197$	−14.8768			−1.05993			−0.529964	−	0.848020i	$-0.677795\pi$
$197$	−14.8768			−1.05993			−0.529964	+	0.848020i	$0.677795\pi$
$198$		0			0
$199$	6.17884	−	10.7021i	0.438006	−	0.758649i	−0.559530	−	0.828810i	$-0.689018\pi$
$199$	6.17884	−	10.7021i	0.438006	−	0.758649i	0.997536	+	0.0701616i	$0.0223515\pi$
$200$		0			0
$201$	−3.95178	−	24.7623i	−0.278737	−	1.74659i
$202$		0			0
$203$	−0.235270	−	1.70500i	−0.0165127	−	0.119667i
$204$		0			0
$205$	−4.63293	+	8.02447i	−0.323578	+	0.560453i
$206$		0			0
$207$	−17.7800	−	15.9337i	−1.23579	−	1.10747i
$208$		0			0
$209$	8.40604	+	14.5597i	0.581458	+	1.00711i
$210$		0			0
$211$	8.65802	−	14.9961i	0.596043	−	1.03238i	−0.397356	−	0.917664i	$-0.630072\pi$
$211$	8.65802	−	14.9961i	0.596043	−	1.03238i	0.993399	−	0.114712i	$-0.0365944\pi$
$212$		0			0
$213$	8.10023	+	3.09847i	0.555019	+	0.212304i
$214$		0			0
$215$	11.1966	+	19.3930i	0.763599	+	1.32259i
$216$		0			0
$217$	−0.374923	−	2.71706i	−0.0254514	−	0.184446i
$218$		0			0
$219$	4.87786	−	3.95951i	0.329615	−	0.267559i
$220$		0			0
$221$	−8.99328	−	15.5768i	−0.604953	−	1.04781i
$222$		0			0
$223$	1.14489	+	1.98301i	0.0766677	+	0.132792i	0.901810	−	0.432132i	$-0.142239\pi$
$223$	1.14489	+	1.98301i	0.0766677	+	0.132792i	−0.825143	+	0.564925i	$0.808905\pi$
$224$		0			0
$225$	−3.63497	−	3.25751i	−0.242331	−	0.217167i
$226$		0			0
$227$	−3.56026			−0.236303			−0.118152	−	0.992996i	$-0.537697\pi$
$227$	−3.56026			−0.236303			−0.118152	+	0.992996i	$0.537697\pi$
$228$		0			0
$229$	−26.9597			−1.78155			−0.890775	−	0.454445i	$-0.849837\pi$
$229$	−26.9597			−1.78155			−0.890775	+	0.454445i	$0.849837\pi$
$230$		0			0
$231$	10.3673	+	9.69347i	0.682119	+	0.637783i
$232$		0			0
$233$	10.7321	+	18.5885i	0.703081	+	1.21777i	0.967380	+	0.253332i	$0.0815264\pi$
$233$	10.7321	+	18.5885i	0.703081	+	1.21777i	−0.264298	+	0.964441i	$0.585140\pi$
$234$		0			0
$235$	−4.23681	+	7.33837i	−0.276379	+	0.478703i
$236$		0			0
$237$	−19.3084	+	15.6732i	−1.25421	+	1.01808i
$238$		0			0
$239$	4.65970	−	8.07083i	0.301411	−	0.522059i	−0.675045	−	0.737777i	$-0.735876\pi$
$239$	4.65970	−	8.07083i	0.301411	−	0.522059i	0.976456	+	0.215718i	$0.0692091\pi$
$240$		0			0
$241$	−20.2007			−1.30124			−0.650620	−	0.759404i	$-0.725491\pi$
$241$	−20.2007			−1.30124			−0.650620	+	0.759404i	$0.725491\pi$
$242$		0			0
$243$	3.94607	−	15.0807i	0.253140	−	0.967430i
$244$		0			0
$245$	−9.20299	−	8.97673i	−0.587958	−	0.573502i
$246$		0			0
$247$	−26.0796			−1.65940
$248$		0			0
$249$	−2.09165	−	13.1065i	−0.132553	−	0.830589i
$250$		0			0
$251$	27.1837			1.71582			0.857910	−	0.513800i	$-0.171762\pi$
$251$	27.1837			1.71582			0.857910	+	0.513800i	$0.171762\pi$
$252$		0			0
$253$	24.6483			1.54963
$254$		0			0
$255$	9.24608	−	7.50534i	0.579012	−	0.470002i
$256$		0			0
$257$	28.4821			1.77667			0.888333	−	0.459200i	$-0.151864\pi$
$257$	28.4821			1.77667			0.888333	+	0.459200i	$0.151864\pi$
$258$		0			0
$259$	0.631966	+	4.57985i	0.0392685	+	0.284578i
$260$		0			0
$261$	0.401274	−	1.90990i	0.0248383	−	0.118220i
$262$		0			0
$263$	3.59814			0.221871			0.110935	−	0.993828i	$-0.464615\pi$
$263$	3.59814			0.221871			0.110935	+	0.993828i	$0.464615\pi$
$264$		0			0
$265$	−8.35791	+	14.4763i	−0.513422	+	0.889274i
$266$		0			0
$267$	3.14888	+	19.7312i	0.192708	+	1.20753i
$268$		0			0
$269$	11.2261	−	19.4443i	0.684470	−	1.18554i	−0.289133	−	0.957289i	$-0.593367\pi$
$269$	11.2261	−	19.4443i	0.684470	−	1.18554i	0.973603	−	0.228248i	$-0.0732997\pi$
$270$		0			0
$271$	−14.7935	−	25.6231i	−0.898642	−	1.55649i	−0.829231	−	0.558906i	$-0.811221\pi$
$271$	−14.7935	−	25.6231i	−0.898642	−	1.55649i	−0.0694115	−	0.997588i	$-0.522112\pi$
$272$		0			0
$273$	−21.0635	+	6.40914i	−1.27482	+	0.387899i
$274$		0			0
$275$	5.03915			0.303872
$276$		0			0
$277$	−20.3867			−1.22492			−0.612459	−	0.790503i	$-0.709819\pi$
$277$	−20.3867			−1.22492			−0.612459	+	0.790503i	$0.709819\pi$
$278$		0			0
$279$	0.639467	−	3.04360i	0.0382839	−	0.182216i
$280$		0			0
$281$	−2.23968	−	3.87924i	−0.133608	−	0.231416i	0.791457	−	0.611225i	$-0.209323\pi$
$281$	−2.23968	−	3.87924i	−0.133608	−	0.231416i	−0.925065	+	0.379809i	$0.875990\pi$
$282$		0			0
$283$	−1.03840	−	1.79856i	−0.0617264	−	0.106913i	0.833511	−	0.552503i	$-0.186327\pi$
$283$	−1.03840	−	1.79856i	−0.0617264	−	0.106913i	−0.895237	+	0.445590i	$0.852994\pi$
$284$		0			0
$285$	−2.72122	−	17.0514i	−0.161191	−	1.01004i
$286$		0			0
$287$	10.5392	−	8.19169i	0.622108	−	0.483540i
$288$		0			0
$289$	1.49237	+	2.58486i	0.0877865	+	0.152051i
$290$		0			0
$291$	0.570380	+	3.57405i	0.0334362	+	0.209515i
$292$		0			0
$293$	−0.887340	+	1.53692i	−0.0518389	+	0.0897877i	−0.890780	−	0.454434i	$-0.849842\pi$
$293$	−0.887340	+	1.53692i	−0.0518389	+	0.0897877i	0.838942	+	0.544222i	$0.183175\pi$
$294$		0			0
$295$	−5.32355	−	9.22066i	−0.309949	−	0.536847i
$296$		0			0
$297$	7.35678	+	14.3136i	0.426884	+	0.830556i
$298$		0			0
$299$	−19.1178	+	33.1129i	−1.10561	+	1.91497i
$300$		0			0
$301$	−4.40963	−	31.9566i	−0.254167	−	1.84195i
$302$		0			0
$303$	26.6170	+	10.1814i	1.52911	+	0.584908i
$304$		0			0
$305$	−4.41921	+	7.65429i	−0.253043	+	0.438283i
$306$		0			0
$307$	19.6315			1.12043			0.560215	−	0.828347i	$-0.310718\pi$
$307$	19.6315			1.12043			0.560215	+	0.828347i	$0.310718\pi$
$308$		0			0
$309$	12.5325	+	4.79388i	0.712948	+	0.272714i
$310$		0			0
$311$	6.65795	+	11.5319i	0.377538	+	0.653915i	0.990703	−	0.136040i	$-0.0434375\pi$
$311$	6.65795	+	11.5319i	0.377538	+	0.653915i	−0.613166	+	0.789954i	$0.710104\pi$
$312$		0			0
$313$	−2.32641	+	4.02945i	−0.131496	+	0.227758i	−0.924254	−	0.381779i	$-0.875311\pi$
$313$	−2.32641	+	4.02945i	−0.131496	+	0.227758i	0.792757	+	0.609537i	$0.208645\pi$
$314$		0			0
$315$	−6.38826	−	13.1030i	−0.359938	−	0.738271i
$316$		0			0
$317$	2.06276	−	3.57281i	0.115856	−	0.200669i	−0.802265	−	0.596967i	$-0.796372\pi$
$317$	2.06276	−	3.57281i	0.115856	−	0.200669i	0.918122	+	0.396299i	$0.129705\pi$
$318$		0			0
$319$	1.00741	+	1.74489i	0.0564044	+	0.0976953i
$320$		0			0
$321$	−2.04583	−	12.8194i	−0.114187	−	0.715508i
$322$		0			0
$323$	−20.3214			−1.13071
$324$		0			0
$325$	−3.90847	+	6.76967i	−0.216803	+	0.375514i
$326$		0			0
$327$	11.5824	−	9.40178i	0.640507	−	0.519920i
$328$		0			0
$329$	9.63807	−	7.49130i	0.531364	−	0.413009i
$330$		0			0
$331$	−0.0220297	+	0.0381566i	−0.00121086	+	0.00209727i	−0.866630	−	0.498951i	$-0.833719\pi$
$331$	−0.0220297	+	0.0381566i	−0.00121086	+	0.00209727i	0.865419	+	0.501048i	$0.167052\pi$
$332$		0			0
$333$	−1.07788	+	5.13026i	−0.0590673	+	0.281137i
$334$		0			0
$335$	−13.2944	−	23.0266i	−0.726350	−	1.25808i
$336$		0			0
$337$	−13.3351	+	23.0970i	−0.726407	+	1.25817i	0.231986	+	0.972719i	$0.425478\pi$
$337$	−13.3351	+	23.0970i	−0.726407	+	1.25817i	−0.958392	+	0.285454i	$0.907856\pi$
$338$		0			0
$339$	4.18889	−	3.40026i	0.227509	−	0.184677i
$340$		0			0
$341$	1.60541	+	2.78064i	0.0869376	+	0.150580i
$342$		0			0
$343$	7.40556	+	16.9752i	0.399863	+	0.916575i
$344$		0			0
$345$	−23.6448	−	9.04452i	−1.27299	−	0.486941i
$346$		0			0
$347$	−5.41259	−	9.37488i	−0.290563	−	0.503270i	0.683380	−	0.730063i	$-0.260509\pi$
$347$	−5.41259	−	9.37488i	−0.290563	−	0.503270i	−0.973943	+	0.226793i	$0.927176\pi$
$348$		0			0
$349$	−2.69555	−	4.66884i	−0.144290	−	0.249917i	0.784818	−	0.619726i	$-0.212756\pi$
$349$	−2.69555	−	4.66884i	−0.144290	−	0.249917i	−0.929108	+	0.369809i	$0.879423\pi$
$350$		0			0
$351$	−24.9351	−	1.21868i	−1.33094	−	0.0650483i
$352$		0			0
$353$	−8.94614			−0.476155			−0.238078	−	0.971246i	$-0.576517\pi$
$353$	−8.94614			−0.476155			−0.238078	+	0.971246i	$0.576517\pi$
$354$		0			0
$355$	9.19596			0.488071
$356$		0			0
$357$	−16.4128	+	4.99405i	−0.868657	+	0.264313i
$358$		0			0
$359$	1.84157	+	3.18969i	0.0971942	+	0.168345i	0.910522	−	0.413460i	$-0.135680\pi$
$359$	1.84157	+	3.18969i	0.0971942	+	0.168345i	−0.813328	+	0.581805i	$0.802347\pi$
$360$		0			0
$361$	−5.23251	+	9.06297i	−0.275395	+	0.476998i
$362$		0			0
$363$	2.27682	+	0.870920i	0.119502	+	0.0457114i
$364$		0			0
$365$	3.33087	−	5.76924i	0.174346	−	0.301976i
$366$		0			0
$367$	−7.49976			−0.391484			−0.195742	−	0.980655i	$-0.562712\pi$
$367$	−7.49976			−0.391484			−0.195742	+	0.980655i	$0.562712\pi$
$368$		0			0
$369$	14.3838	−	4.71096i	0.748789	−	0.245243i
$370$		0			0
$371$	19.0129	−	14.7780i	0.987101	−	0.767235i
$372$		0			0
$373$	8.23833			0.426565			0.213282	−	0.976991i	$-0.431585\pi$
$373$	8.23833			0.426565			0.213282	+	0.976991i	$0.431585\pi$
$374$		0			0
$375$	−19.6894	−	7.53153i	−1.01676	−	0.388927i
$376$		0			0
$377$	−3.12549			−0.160971
$378$		0			0
$379$	−3.92853			−0.201795			−0.100897	−	0.994897i	$-0.532171\pi$
$379$	−3.92853			−0.201795			−0.100897	+	0.994897i	$0.532171\pi$
$380$		0			0
$381$	−17.6117	−	6.73678i	−0.902276	−	0.345136i
$382$		0			0
$383$	23.9265			1.22259			0.611293	−	0.791404i	$-0.290650\pi$
$383$	23.9265			1.22259			0.611293	+	0.791404i	$0.290650\pi$
$384$		0			0
$385$	13.9396	+	5.67260i	0.710427	+	0.289102i
$386$		0			0
$387$	7.52104	−	35.7971i	0.382316	−	1.81967i
$388$		0			0
$389$	12.6575			0.641761			0.320881	−	0.947120i	$-0.396021\pi$
$389$	12.6575			0.641761			0.320881	+	0.947120i	$0.396021\pi$
$390$		0			0
$391$	−14.8967	+	25.8018i	−0.753359	+	1.30486i
$392$		0			0
$393$	25.9741	+	9.93551i	1.31022	+	0.501180i
$394$		0			0
$395$	−13.1848	+	22.8368i	−0.663400	+	1.14904i
$396$		0			0
$397$	−17.7703	−	30.7791i	−0.891866	−	1.54476i	−0.837636	−	0.546229i	$-0.816063\pi$
$397$	−17.7703	−	30.7791i	−0.891866	−	1.54476i	−0.0542297	−	0.998528i	$-0.517270\pi$
$398$		0			0
$399$	−5.62786	+	24.2300i	−0.281746	+	1.21302i
$400$		0			0
$401$	−3.32332			−0.165959			−0.0829794	−	0.996551i	$-0.526444\pi$
$401$	−3.32332			−0.165959			−0.0829794	+	0.996551i	$0.526444\pi$
$402$		0			0
$403$	−4.98074			−0.248109
$404$		0			0
$405$	−1.80500	−	16.4303i	−0.0896912	−	0.816428i
$406$		0			0
$407$	−2.70605	−	4.68702i	−0.134134	−	0.232327i
$408$		0			0
$409$	−11.2564	−	19.4967i	−0.556595	−	0.964051i	−0.997777	−	0.0666338i	$-0.978774\pi$
$409$	−11.2564	−	19.4967i	−0.556595	−	0.964051i	0.441182	−	0.897418i	$-0.354559\pi$
$410$		0			0
$411$	−21.7434	−	8.31720i	−1.07252	−	0.410257i
$412$		0			0
$413$	2.09662	+	15.1942i	0.103168	+	0.747656i
$414$		0			0
$415$	−7.03662	−	12.1878i	−0.345414	−	0.598275i
$416$		0			0
$417$	10.9452	−	8.88456i	0.535989	−	0.435079i
$418$		0			0
$419$	−3.59772	+	6.23144i	−0.175760	+	0.304426i	−0.940424	−	0.340004i	$-0.889572\pi$
$419$	−3.59772	+	6.23144i	−0.175760	+	0.304426i	0.764664	+	0.644429i	$0.222905\pi$
$420$		0			0
$421$	16.8121	+	29.1193i	0.819370	+	1.41919i	0.906147	+	0.422962i	$0.139010\pi$
$421$	16.8121	+	29.1193i	0.819370	+	1.41919i	−0.0867773	+	0.996228i	$0.527657\pi$
$422$		0			0
$423$	13.1539	−	4.30818i	0.639567	−	0.209471i
$424$		0			0
$425$	−3.04551	+	5.27498i	−0.147729	+	0.255874i
$426$		0			0
$427$	10.0530	−	7.81380i	0.486498	−	0.378136i
$428$		0			0
$429$	20.0108	−	16.2434i	0.966132	−	0.784239i
$430$		0			0
$431$	16.4871	−	28.5565i	0.794156	−	1.37552i	−0.129217	−	0.991616i	$-0.541246\pi$
$431$	16.4871	−	28.5565i	0.794156	−	1.37552i	0.923373	−	0.383903i	$-0.125420\pi$
$432$		0			0
$433$	19.8977			0.956221			0.478110	−	0.878300i	$-0.341322\pi$
$433$	19.8977			0.956221			0.478110	+	0.878300i	$0.341322\pi$
$434$		0			0
$435$	−0.326122	−	2.04351i	−0.0156364	−	0.0979789i
$436$		0			0
$437$	21.5995	+	37.4114i	1.03324	+	1.78963i
$438$		0			0
$439$	−14.5634	+	25.2246i	−0.695074	+	1.20390i	0.275082	+	0.961421i	$0.411295\pi$
$439$	−14.5634	+	25.2246i	−0.695074	+	1.20390i	−0.970156	+	0.242482i	$0.922038\pi$
$440$		0			0
$441$	1.40920	+	20.9527i	0.0671046	+	0.997746i
$442$		0			0
$443$	−6.88317	+	11.9220i	−0.327029	+	0.566431i	−0.981921	−	0.189292i	$-0.939381\pi$
$443$	−6.88317	+	11.9220i	−0.327029	+	0.566431i	0.654892	+	0.755723i	$0.272714\pi$
$444$		0			0
$445$	10.5933	+	18.3481i	0.502171	+	0.869785i
$446$		0			0
$447$	−12.1809	−	4.65939i	−0.576136	−	0.220382i
$448$		0			0
$449$	−12.0958			−0.570838			−0.285419	−	0.958403i	$-0.592133\pi$
$449$	−12.0958			−0.570838			−0.285419	+	0.958403i	$0.592133\pi$
$450$		0			0
$451$	−7.81297	+	13.5325i	−0.367898	+	0.637218i
$452$		0			0
$453$	9.17632	+	3.51009i	0.431141	+	0.164919i
$454$		0			0
$455$	−18.4325	+	14.3269i	−0.864128	+	0.671653i
$456$		0			0
$457$	4.17738	−	7.23544i	0.195410	−	0.338459i	−0.751625	−	0.659591i	$-0.770730\pi$
$457$	4.17738	−	7.23544i	0.195410	−	0.338459i	0.947035	+	0.321131i	$0.104063\pi$
$458$		0			0
$459$	−19.4296	−	0.949604i	−0.906897	−	0.0443237i
$460$		0			0
$461$	11.1673	+	19.3423i	0.520112	+	0.900860i	0.999727	+	0.0233807i	$0.00744299\pi$
$461$	11.1673	+	19.3423i	0.520112	+	0.900860i	−0.479615	+	0.877479i	$0.659224\pi$
$462$		0			0
$463$	−0.0370790	+	0.0642228i	−0.00172321	+	0.00298469i	−0.866886	−	0.498507i	$-0.833882\pi$
$463$	−0.0370790	+	0.0642228i	−0.00172321	+	0.00298469i	0.865163	+	0.501492i	$0.167215\pi$
$464$		0			0
$465$	−0.519705	−	3.25652i	−0.0241007	−	0.151018i
$466$		0			0
$467$	14.5828	+	25.2581i	0.674810	+	1.16880i	0.976524	+	0.215407i	$0.0691077\pi$
$467$	14.5828	+	25.2581i	0.674810	+	1.16880i	−0.301715	+	0.953398i	$0.597559\pi$
$468$		0			0
$469$	5.23584	+	37.9441i	0.241769	+	1.75209i
$470$		0			0
$471$	0.119220	+	0.747042i	0.00549336	+	0.0344219i
$472$		0			0
$473$	18.8819	+	32.7043i	0.868189	+	1.50375i
$474$		0			0
$475$	4.41583	+	7.64845i	0.202612	+	0.350935i
$476$		0			0
$477$	25.9486	−	8.49869i	1.18811	−	0.389128i
$478$		0			0
$479$	27.9103			1.27525			0.637626	−	0.770346i	$-0.279917\pi$
$479$	27.9103			1.27525			0.637626	+	0.770346i	$0.279917\pi$
$480$		0			0
$481$	8.39548			0.382801
$482$		0			0
$483$	26.6390	+	24.9075i	1.21212	+	1.13333i
$484$		0			0
$485$	1.91884	+	3.32353i	0.0871301	+	0.150914i
$486$		0			0
$487$	−2.14409	+	3.71367i	−0.0971580	+	0.168283i	−0.910507	−	0.413493i	$-0.864309\pi$
$487$	−2.14409	+	3.71367i	−0.0971580	+	0.168283i	0.813349	+	0.581776i	$0.197642\pi$
$488$		0			0
$489$	−4.98238	−	31.2200i	−0.225311	−	1.41182i
$490$		0			0
$491$	−5.22215	+	9.04503i	−0.235672	+	0.408196i	−0.959468	−	0.281818i	$-0.909063\pi$
$491$	−5.22215	+	9.04503i	−0.235672	+	0.408196i	0.723796	+	0.690015i	$0.242396\pi$
$492$		0			0
$493$	−2.43540			−0.109685
$494$		0			0
$495$	12.7083	+	11.3886i	0.571195	+	0.511881i
$496$		0			0
$497$	−12.2705	−	4.99339i	−0.550409	−	0.223984i
$498$		0			0
$499$	−6.12624			−0.274248			−0.137124	−	0.990554i	$-0.543786\pi$
$499$	−6.12624			−0.274248			−0.137124	+	0.990554i	$0.543786\pi$
$500$		0			0
$501$	−2.05780	+	1.67038i	−0.0919355	+	0.0746270i
$502$		0			0
$503$	−12.4469			−0.554982			−0.277491	−	0.960728i	$-0.589503\pi$
$503$	−12.4469			−0.554982			−0.277491	+	0.960728i	$0.589503\pi$
$504$		0			0
$505$	30.2175			1.34466
$506$		0			0
$507$	2.75232	+	17.2463i	0.122235	+	0.765935i
$508$		0			0
$509$	11.8090			0.523425			0.261712	−	0.965146i	$-0.415713\pi$
$509$	11.8090			0.523425			0.261712	+	0.965146i	$0.415713\pi$
$510$		0			0
$511$	−7.57720	+	5.88946i	−0.335195	+	0.260534i
$512$		0			0
$513$	−15.2784	+	23.7092i	−0.674558	+	1.04679i
$514$		0			0
$515$	14.2278			0.626950
$516$		0			0
$517$	−7.14495	+	12.3754i	−0.314235	+	0.544271i
$518$		0			0
$519$	2.91748	−	2.36821i	0.128063	−	0.103953i
$520$		0			0
$521$	5.54828	−	9.60991i	0.243075	−	0.421018i	−0.718514	−	0.695513i	$-0.755177\pi$
$521$	5.54828	−	9.60991i	0.243075	−	0.421018i	0.961589	+	0.274495i	$0.0885107\pi$
$522$		0			0
$523$	10.6209	+	18.3960i	0.464421	+	0.804401i	0.999175	−	0.0406065i	$-0.0129290\pi$
$523$	10.6209	+	18.3960i	0.464421	+	0.804401i	−0.534754	+	0.845008i	$0.679596\pi$
$524$		0			0
$525$	5.44612	+	5.09214i	0.237688	+	0.222239i
$526$		0			0
$527$	−3.88103			−0.169060
$528$		0			0
$529$	40.3343			1.75367
$530$		0			0
$531$	−3.57598	+	17.0202i	−0.155184	+	0.738614i
$532$		0			0
$533$	−12.1198	−	20.9921i	−0.524967	−	0.909269i
$534$		0			0
$535$	−6.88248	−	11.9208i	−0.297556	−	0.515382i
$536$		0			0
$537$	2.91178	−	2.36359i	0.125653	−	0.101996i
$538$		0			0
$539$	−15.5199	−	15.1383i	−0.668490	−	0.652054i
$540$		0			0
$541$	−6.33567	−	10.9737i	−0.272392	−	0.471796i	0.697082	−	0.716991i	$-0.254481\pi$
$541$	−6.33567	−	10.9737i	−0.272392	−	0.471796i	−0.969474	+	0.245195i	$0.921148\pi$
$542$		0			0
$543$	−0.902436	−	0.345197i	−0.0387272	−	0.0148138i
$544$		0			0
$545$	7.90908	−	13.6989i	0.338788	−	0.586798i
$546$		0			0
$547$	−21.4805	−	37.2053i	−0.918438	−	1.59078i	−0.801788	−	0.597609i	$-0.796117\pi$
$547$	−21.4805	−	37.2053i	−0.918438	−	1.59078i	−0.116651	−	0.993173i	$-0.537216\pi$
$548$		0			0
$549$	13.7202	−	4.49364i	0.585565	−	0.191784i
$550$		0			0
$551$	−1.76560	+	3.05812i	−0.0752173	+	0.130280i
$552$		0			0
$553$	29.9933	−	23.3126i	1.27545	−	0.991355i
$554$		0			0
$555$	0.876009	+	5.48915i	0.0371845	+	0.233002i
$556$		0			0
$557$	16.5129	−	28.6012i	0.699673	−	1.21187i	−0.268906	−	0.963166i	$-0.586662\pi$
$557$	16.5129	−	28.6012i	0.699673	−	1.21187i	0.968580	−	0.248703i	$-0.0800044\pi$
$558$		0			0
$559$	−58.5807			−2.47770
$560$		0			0
$561$	15.5926	−	12.6570i	0.658319	−	0.534378i
$562$		0			0
$563$	−18.4066	−	31.8812i	−0.775746	−	1.34363i	−0.934374	−	0.356293i	$-0.884041\pi$
$563$	−18.4066	−	31.8812i	−0.775746	−	1.34363i	0.158629	−	0.987338i	$-0.449293\pi$
$564$		0			0
$565$	2.86040	−	4.95437i	0.120338	−	0.208432i
$566$		0			0
$567$	−6.51314	+	22.9037i	−0.273526	+	0.961865i
$568$		0			0
$569$	−22.1786	+	38.4144i	−0.929774	+	1.61042i	−0.146075	+	0.989273i	$0.546664\pi$
$569$	−22.1786	+	38.4144i	−0.929774	+	1.61042i	−0.783698	+	0.621142i	$0.786669\pi$
$570$		0			0
$571$	21.2936	+	36.8816i	0.891110	+	1.54345i	0.838546	+	0.544831i	$0.183406\pi$
$571$	21.2936	+	36.8816i	0.891110	+	1.54345i	0.0525644	+	0.998618i	$0.483261\pi$
$572$		0			0
$573$	−32.2741	+	26.1979i	−1.34827	+	1.09443i
$574$		0			0
$575$	12.9482			0.539977
$576$		0			0
$577$	16.3209	−	28.2687i	0.679450	−	1.17684i	−0.295697	−	0.955282i	$-0.595552\pi$
$577$	16.3209	−	28.2687i	0.679450	−	1.17684i	0.975147	−	0.221559i	$-0.0711147\pi$
$578$		0			0
$579$	−5.80847	−	36.3964i	−0.241392	−	1.51258i
$580$		0			0
$581$	2.77129	+	20.0835i	0.114973	+	0.833205i
$582$		0			0
$583$	−14.0948	+	24.4129i	−0.583746	+	1.01108i
$584$		0			0
$585$	−25.1565	+	8.23924i	−1.04009	+	0.340651i
$586$		0			0
$587$	−13.1270	−	22.7366i	−0.541809	−	0.938441i	−0.998800	−	0.0489701i	$-0.984406\pi$
$587$	−13.1270	−	22.7366i	−0.541809	−	0.938441i	0.456991	−	0.889471i	$-0.348927\pi$
$588$		0			0
$589$	−2.81365	+	4.87338i	−0.115934	+	0.200804i
$590$		0			0
$591$	24.0667	+	9.20593i	0.989974	+	0.378681i
$592$		0			0
$593$	−2.59998	−	4.50330i	−0.106768	−	0.184928i	0.807691	−	0.589606i	$-0.200717\pi$
$593$	−2.59998	−	4.50330i	−0.106768	−	0.184928i	−0.914459	+	0.404678i	$0.867384\pi$
$594$		0			0
$595$	−14.3627	+	11.1636i	−0.588814	+	0.457663i
$596$		0			0
$597$	−16.6183	+	13.4896i	−0.680141	+	0.552092i
$598$		0			0
$599$	−13.1837	−	22.8349i	−0.538673	−	0.933008i	−0.998976	−	0.0452465i	$-0.985593\pi$
$599$	−13.1837	−	22.8349i	−0.538673	−	0.933008i	0.460303	−	0.887762i	$-0.347741\pi$
$600$		0			0
$601$	−15.4505	−	26.7611i	−0.630239	−	1.09161i	−0.987503	−	0.157603i	$-0.949623\pi$
$601$	−15.4505	−	26.7611i	−0.630239	−	1.09161i	0.357263	−	0.934004i	$-0.383710\pi$
$602$		0			0
$603$	−8.93021	+	42.5042i	−0.363666	+	1.73091i
$604$		0			0
$605$	2.58480			0.105087
$606$		0			0
$607$	7.67321			0.311446			0.155723	−	0.987801i	$-0.450229\pi$
$607$	7.67321			0.311446			0.155723	+	0.987801i	$0.450229\pi$
$608$		0			0
$609$	−0.674467	+	2.90382i	−0.0273308	+	0.117669i
$610$		0			0
$611$	−11.0836	−	19.1973i	−0.448393	−	0.776639i
$612$		0			0
$613$	7.97498	−	13.8131i	0.322106	−	0.557905i	−0.658816	−	0.752304i	$-0.728942\pi$
$613$	7.97498	−	13.8131i	0.322106	−	0.557905i	0.980922	+	0.194399i	$0.0622758\pi$
$614$		0			0
$615$	12.4605	−	10.1146i	0.502456	−	0.407859i
$616$		0			0
$617$	−3.67011	+	6.35682i	−0.147753	+	0.255916i	−0.930397	−	0.366554i	$-0.880537\pi$
$617$	−3.67011	+	6.35682i	−0.147753	+	0.255916i	0.782644	+	0.622470i	$0.213871\pi$
$618$		0			0
$619$	20.5684			0.826713			0.413357	−	0.910569i	$-0.364356\pi$
$619$	20.5684			0.826713			0.413357	+	0.910569i	$0.364356\pi$
$620$		0			0
$621$	18.9034	+	36.7789i	0.758566	+	1.47589i
$622$		0			0
$623$	−4.17205	−	30.2348i	−0.167150	−	1.21133i
$624$		0			0
$625$	−14.2178			−0.568713
$626$		0			0
$627$	−4.58906	−	28.7555i	−0.183269	−	1.14838i
$628$		0			0
$629$	6.54182			0.260840
$630$		0			0
$631$	−5.09394			−0.202787			−0.101393	−	0.994846i	$-0.532330\pi$
$631$	−5.09394			−0.202787			−0.101393	+	0.994846i	$0.532330\pi$
$632$		0			0
$633$	−23.2862	+	18.9021i	−0.925542	+	0.751292i
$634$		0			0
$635$	−19.9941			−0.793442
$636$		0			0
$637$	32.3746	−	9.10807i	1.28273	−	0.360875i
$638$		0			0
$639$	−11.1867	−	10.0250i	−0.442538	−	0.396584i
$640$		0			0
$641$	12.6372			0.499140			0.249570	−	0.968357i	$-0.419711\pi$
$641$	12.6372			0.499140			0.249570	+	0.968357i	$0.419711\pi$
$642$		0			0
$643$	12.4329	−	21.5344i	0.490306	−	0.849235i	−0.509632	−	0.860393i	$-0.670218\pi$
$643$	12.4329	−	21.5344i	0.490306	−	0.849235i	0.999938	+	0.0111579i	$0.00355174\pi$
$644$		0			0
$645$	−6.11247	−	38.3013i	−0.240678	−	1.50811i
$646$		0			0
$647$	1.12339	−	1.94577i	0.0441650	−	0.0764960i	−0.843098	−	0.537760i	$-0.819271\pi$
$647$	1.12339	−	1.94577i	0.0441650	−	0.0764960i	0.887263	+	0.461264i	$0.152604\pi$
$648$		0			0
$649$	−8.97762	−	15.5497i	−0.352403	−	0.610379i
$650$		0			0
$651$	−1.07482	+	4.62750i	−0.0421256	+	0.181366i
$652$		0			0
$653$	2.05762			0.0805207			0.0402604	−	0.999189i	$-0.487181\pi$
$653$	2.05762			0.0805207			0.0402604	+	0.999189i	$0.487181\pi$
$654$		0			0
$655$	29.4876			1.15218
$656$		0			0
$657$	−10.3413	+	3.38697i	−0.403452	+	0.132138i
$658$		0			0
$659$	−4.16599	−	7.21571i	−0.162284	−	0.281084i	0.773403	−	0.633914i	$-0.218553\pi$
$659$	−4.16599	−	7.21571i	−0.162284	−	0.281084i	−0.935687	+	0.352830i	$0.885219\pi$
$660$		0			0
$661$	−17.0463	−	29.5251i	−0.663024	−	1.14839i	−0.979817	−	0.199897i	$-0.935939\pi$
$661$	−17.0463	−	29.5251i	−0.663024	−	1.14839i	0.316793	−	0.948495i	$-0.397394\pi$
$662$		0			0
$663$	4.90965	+	30.7643i	0.190675	+	1.19479i
$664$		0			0
$665$	3.60543	+	26.1285i	0.139812	+	1.01322i
$666$		0			0
$667$	2.58857	+	4.48353i	0.100230	+	0.173603i
$668$		0			0
$669$	−0.625025	−	3.91646i	−0.0241649	−	0.151419i
$670$		0			0
$671$	−7.45255	+	12.9082i	−0.287702	+	0.498315i
$672$		0			0
$673$	0.571008	+	0.989016i	0.0220108	+	0.0381237i	0.876821	−	0.480817i	$-0.159660\pi$
$673$	0.571008	+	0.989016i	0.0220108	+	0.0381237i	−0.854810	+	0.518941i	$0.826327\pi$
$674$		0			0
$675$	3.86464	+	7.51915i	0.148750	+	0.289412i
$676$		0			0
$677$	−18.1906	+	31.5070i	−0.699121	+	1.21091i	0.269651	+	0.962958i	$0.413092\pi$
$677$	−18.1906	+	31.5070i	−0.699121	+	1.21091i	−0.968772	+	0.247955i	$0.920242\pi$
$678$		0			0
$679$	−0.755713	−	5.47665i	−0.0290016	−	0.210174i
$680$		0			0
$681$	5.75957	+	2.20313i	0.220707	+	0.0844242i
$682$		0			0
$683$	3.11274	−	5.39142i	0.119106	−	0.206297i	−0.800308	−	0.599589i	$-0.795331\pi$
$683$	3.11274	−	5.39142i	0.119106	−	0.206297i	0.919414	+	0.393292i	$0.128664\pi$
$684$		0			0
$685$	−24.6846			−0.943152
$686$		0			0
$687$	43.6138	+	16.6830i	1.66397	+	0.636496i
$688$		0			0
$689$	−21.8644	−	37.8702i	−0.832967	−	1.44274i
$690$		0			0
$691$	19.9130	−	34.4903i	0.757525	−	1.31207i	−0.186584	−	0.982439i	$-0.559742\pi$
$691$	19.9130	−	34.4903i	0.757525	−	1.31207i	0.944109	−	0.329633i	$-0.106925\pi$
$692$		0			0
$693$	−10.7732	−	22.0969i	−0.409238	−	0.839391i
$694$		0			0
$695$	7.47398	−	12.9453i	0.283504	−	0.491044i
$696$		0			0
$697$	−9.44384	−	16.3572i	−0.357711	−	0.619573i
$698$		0			0
$699$	−5.85890	−	36.7124i	−0.221604	−	1.38859i
$700$		0			0
$701$	−48.3337			−1.82554			−0.912769	−	0.408477i	$-0.866060\pi$
$701$	−48.3337			−1.82554			−0.912769	+	0.408477i	$0.866060\pi$
$702$		0			0
$703$	4.74265	−	8.21452i	0.178873	−	0.309816i
$704$		0			0
$705$	11.3951	−	9.24977i	0.429165	−	0.348367i
$706$		0			0
$707$	−40.3204	−	16.4081i	−1.51640	−	0.617088i
$708$		0			0
$709$	8.04198	−	13.9291i	0.302023	−	0.523119i	−0.674571	−	0.738210i	$-0.735671\pi$
$709$	8.04198	−	13.9291i	0.302023	−	0.523119i	0.976594	+	0.215091i	$0.0690048\pi$
$710$		0			0
$711$	40.9346	−	13.4069i	1.53517	−	0.502798i
$712$		0			0
$713$	4.12512	+	7.14491i	0.154487	+	0.267579i
$714$		0			0
$715$	13.6645	−	23.6676i	0.511023	−	0.885117i
$716$		0			0
$717$	−12.5325	+	10.1730i	−0.468034	+	0.379918i
$718$		0			0
$719$	21.0734	+	36.5002i	0.785906	+	1.36123i	0.928456	+	0.371442i	$0.121136\pi$
$719$	21.0734	+	36.5002i	0.785906	+	1.36123i	−0.142550	+	0.989788i	$0.545530\pi$
$720$		0			0
$721$	−18.9847	−	7.72566i	−0.707026	−	0.287718i
$722$		0			0
$723$	32.6794	+	12.5004i	1.21536	+	0.464895i
$724$		0			0
$725$	0.529212	+	0.916622i	0.0196544	+	0.0340425i
$726$		0			0
$727$	−12.9548	−	22.4384i	−0.480467	−	0.832192i	0.519282	−	0.854603i	$-0.326199\pi$
$727$	−12.9548	−	22.4384i	−0.480467	−	0.832192i	−0.999749	+	0.0224103i	$0.992866\pi$
$728$		0			0
$729$	−15.7158	+	21.9548i	−0.582068	+	0.813140i
$730$		0			0
$731$	−45.6465			−1.68830
$732$		0			0
$733$	20.4054			0.753692			0.376846	−	0.926276i	$-0.377009\pi$
$733$	20.4054			0.753692			0.376846	+	0.926276i	$0.377009\pi$
$734$		0			0
$735$	9.33312	+	20.2169i	0.344257	+	0.745711i
$736$		0			0
$737$	−22.4196	−	38.8320i	−0.825838	−	1.43039i
$738$		0			0
$739$	−11.8953	+	20.6033i	−0.437576	+	0.757903i	−0.997502	−	0.0706392i	$-0.977496\pi$
$739$	−11.8953	+	20.6033i	−0.437576	+	0.757903i	0.559926	+	0.828542i	$0.310829\pi$
$740$		0			0
$741$	42.1899	+	16.1383i	1.54989	+	0.592857i
$742$		0			0
$743$	21.6320	−	37.4678i	0.793603	−	1.37456i	−0.130120	−	0.991498i	$-0.541536\pi$
$743$	21.6320	−	37.4678i	0.793603	−	1.37456i	0.923723	−	0.383062i	$-0.125130\pi$
$744$		0			0
$745$	−13.8286			−0.506641
$746$		0			0
$747$	−4.72670	+	22.4972i	−0.172941	+	0.823128i
$748$		0			0
$749$	2.71058	+	19.6436i	0.0990426	+	0.717761i
$750$		0			0
$751$	−14.3693			−0.524343			−0.262172	−	0.965021i	$-0.584439\pi$
$751$	−14.3693			−0.524343			−0.262172	+	0.965021i	$0.584439\pi$
$752$		0			0
$753$	−43.9761	−	16.8216i	−1.60258	−	0.613013i
$754$		0			0
$755$	10.4176			0.379136
$756$		0			0
$757$	39.7854			1.44603			0.723013	−	0.690835i	$-0.242757\pi$
$757$	39.7854			1.44603			0.723013	+	0.690835i	$0.242757\pi$
$758$		0			0
$759$	−39.8745	−	15.2527i	−1.44735	−	0.553637i
$760$		0			0
$761$	−22.3933			−0.811756			−0.405878	−	0.913927i	$-0.633034\pi$
$761$	−22.3933			−0.811756			−0.405878	+	0.913927i	$0.633034\pi$
$762$		0			0
$763$	−17.9919	+	13.9844i	−0.651350	+	0.506269i
$764$		0			0
$765$	−19.6021	+	6.42008i	−0.708716	+	0.232118i
$766$		0			0
$767$	27.8529			1.00571
$768$		0			0
$769$	−1.45546	+	2.52093i	−0.0524853	+	0.0909071i	−0.891074	−	0.453857i	$-0.850048\pi$
$769$	−1.45546	+	2.52093i	−0.0524853	+	0.0909071i	0.838589	+	0.544764i	$0.183381\pi$
$770$		0			0
$771$	−46.0766	−	17.6251i	−1.65941	−	0.634751i
$772$		0			0
$773$	−6.68612	+	11.5807i	−0.240483	+	0.416529i	−0.960852	−	0.277062i	$-0.910639\pi$
$773$	−6.68612	+	11.5807i	−0.240483	+	0.416529i	0.720369	+	0.693591i	$0.243972\pi$
$774$		0			0
$775$	0.843347	+	1.46072i	0.0302939	+	0.0524706i
$776$		0			0
$777$	1.81171	−	7.80006i	0.0649947	−	0.279826i
$778$		0			0
$779$	−27.3862			−0.981211
$780$		0			0
$781$	15.5081			0.554922
$782$		0			0
$783$	−1.83103	+	2.84141i	−0.0654355	+	0.101544i
$784$		0			0
$785$	0.401073	+	0.694679i	0.0143149	+	0.0247941i
$786$		0			0
$787$	11.9264	+	20.6571i	0.425130	+	0.736347i	0.996433	−	0.0843925i	$-0.0268950\pi$
$787$	11.9264	+	20.6571i	0.425130	+	0.736347i	−0.571302	+	0.820740i	$0.693562\pi$
$788$		0			0
$789$	−5.82084	−	2.22657i	−0.207228	−	0.0792680i
$790$		0			0
$791$	−6.50696	+	5.05761i	−0.231361	+	0.179828i
$792$		0			0
$793$	−11.5607	−	20.0237i	−0.410533	−	0.711063i
$794$		0			0
$795$	22.4790	−	18.2469i	0.797248	−	0.647151i
$796$		0			0
$797$	−6.10559	+	10.5752i	−0.216271	+	0.374593i	−0.953665	−	0.300870i	$-0.902723\pi$
$797$	−6.10559	+	10.5752i	−0.216271	+	0.374593i	0.737394	+	0.675463i	$0.236056\pi$
$798$		0			0
$799$	−8.63639	−	14.9587i	−0.305533	−	0.529199i
$800$		0			0
$801$	7.11582	−	33.8684i	0.251425	−	1.19668i
$802$		0			0
$803$	5.61718	−	9.72923i	0.198226	−	0.343337i
$804$		0			0
$805$	35.8180	+	14.5758i	1.26242	+	0.513731i
$806$		0			0
$807$	−30.1933	+	24.5088i	−1.06285	+	0.862751i
$808$		0			0
$809$	26.7838	−	46.3910i	0.941669	−	1.63102i	0.179383	−	0.983779i	$-0.442590\pi$
$809$	26.7838	−	46.3910i	0.941669	−	1.63102i	0.762287	−	0.647240i	$-0.224077\pi$
$810$		0			0
$811$	1.81310			0.0636667			0.0318334	−	0.999493i	$-0.489865\pi$
$811$	1.81310			0.0636667			0.0318334	+	0.999493i	$0.489865\pi$
$812$		0			0
$813$	8.07614	+	50.6059i	0.283243	+	1.77483i
$814$		0			0
$815$	−16.7615	−	29.0317i	−0.587128	−	1.01694i
$816$		0			0
$817$	−33.0925	+	57.3180i	−1.15776	+	2.00530i
$818$		0			0
$819$	38.0412	+	2.66599i	1.32927	+	0.0931573i
$820$		0			0
$821$	19.8371	−	34.3589i	0.692321	−	1.19913i	−0.278755	−	0.960362i	$-0.589922\pi$
$821$	19.8371	−	34.3589i	0.692321	−	1.19913i	0.971076	−	0.238772i	$-0.0767450\pi$
$822$		0			0
$823$	−8.40656	−	14.5606i	−0.293034	−	0.507550i	0.681491	−	0.731826i	$-0.261332\pi$
$823$	−8.40656	−	14.5606i	−0.293034	−	0.507550i	−0.974526	+	0.224276i	$0.927998\pi$
$824$		0			0
$825$	−8.15202	−	3.11828i	−0.283817	−	0.108565i
$826$		0			0
$827$	37.2198			1.29426			0.647130	−	0.762379i	$-0.275969\pi$
$827$	37.2198			1.29426			0.647130	+	0.762379i	$0.275969\pi$
$828$		0			0
$829$	−11.4365	+	19.8086i	−0.397206	+	0.687981i	−0.993380	−	0.114874i	$-0.963354\pi$
$829$	−11.4365	+	19.8086i	−0.397206	+	0.687981i	0.596174	+	0.802855i	$0.296687\pi$
$830$		0			0
$831$	32.9803	+	12.6155i	1.14407	+	0.437627i
$832$		0			0
$833$	25.2266	−	7.09707i	0.874048	−	0.245899i
$834$		0			0
$835$	−1.40518	+	2.43384i	−0.0486281	+	0.0842263i
$836$		0			0
$837$	−2.91790	+	4.52804i	−0.100858	+	0.156512i
$838$		0			0
$839$	18.4071	+	31.8820i	0.635484	+	1.10069i	0.986412	+	0.164288i	$0.0525326\pi$
$839$	18.4071	+	31.8820i	0.635484	+	1.10069i	−0.350929	+	0.936402i	$0.614134\pi$
$840$		0			0
$841$	14.2884	−	24.7482i	0.492704	−	0.853388i
$842$		0			0
$843$	1.22270	+	7.66153i	0.0421119	+	0.263877i
$844$		0			0
$845$	9.25921	+	16.0374i	0.318527	+	0.551704i
$846$		0			0
$847$	−3.44901	−	1.40354i	−0.118509	−	0.0482264i
$848$		0			0
$849$	0.566887	+	3.55217i	0.0194555	+	0.121910i
$850$		0			0
$851$	−6.95325	−	12.0434i	−0.238354	−	0.412842i
$852$		0			0
$853$	6.98355	+	12.0959i	0.239112	+	0.414155i	0.960460	−	0.278419i	$-0.0898102\pi$
$853$	6.98355	+	12.0959i	0.239112	+	0.414155i	−0.721347	+	0.692573i	$0.756477\pi$
$854$		0			0
$855$	−6.14939	+	29.2686i	−0.210305	+	1.00097i
$856$		0			0
$857$	17.5677			0.600102			0.300051	−	0.953923i	$-0.402996\pi$
$857$	17.5677			0.600102			0.300051	+	0.953923i	$0.402996\pi$
$858$		0			0
$859$	2.84577			0.0970963			0.0485482	−	0.998821i	$-0.484541\pi$
$859$	2.84577			0.0970963			0.0485482	+	0.998821i	$0.484541\pi$
$860$		0			0
$861$	−22.1187	+	6.73024i	−0.753804	+	0.229366i
$862$		0			0
$863$	−27.7115	−	47.9977i	−0.943310	−	1.63386i	−0.759100	−	0.650974i	$-0.774361\pi$
$863$	−27.7115	−	47.9977i	−0.943310	−	1.63386i	−0.184210	−	0.982887i	$-0.558973\pi$
$864$		0			0
$865$	1.99221	−	3.45061i	0.0677372	−	0.117324i
$866$		0			0
$867$	−0.814721	−	5.10512i	−0.0276694	−	0.173379i
$868$		0			0
$869$	−22.2348	+	38.5119i	−0.754265	+	1.30643i
$870$		0			0
$871$	69.5566			2.35684
$872$		0			0
$873$	1.28894	−	6.13483i	0.0436240	−	0.207633i
$874$		0			0
$875$	29.8263	+	12.1376i	1.00831	+	0.410324i
$876$		0			0
$877$	54.8689			1.85279			0.926396	−	0.376552i	$-0.122890\pi$
$877$	54.8689			1.85279			0.926396	+	0.376552i	$0.122890\pi$
$878$		0			0
$879$	2.38654	−	1.93723i	0.0804961	−	0.0653412i
$880$		0			0
$881$	−51.1572			−1.72353			−0.861765	−	0.507307i	$-0.830641\pi$
$881$	−51.1572			−1.72353			−0.861765	+	0.507307i	$0.830641\pi$
$882$		0			0
$883$	38.6438			1.30047			0.650234	−	0.759734i	$-0.274671\pi$
$883$	38.6438			1.30047			0.650234	+	0.759734i	$0.274671\pi$
$884$		0			0
$885$	2.90625	+	18.2109i	0.0976927	+	0.612152i
$886$		0			0
$887$	−17.8525			−0.599429			−0.299714	−	0.954029i	$-0.596891\pi$
$887$	−17.8525			−0.599429			−0.299714	+	0.954029i	$0.596891\pi$
$888$		0			0
$889$	26.6789	+	10.8568i	0.894782	+	0.364124i
$890$		0			0
$891$	−3.04395	−	27.7080i	−0.101976	−	0.928254i
$892$		0			0
$893$	−25.0446			−0.838087
$894$		0			0
$895$	1.98833	−	3.44388i	0.0664624	−	0.115116i
$896$		0			0
$897$	51.4182	−	41.7377i	1.71680	−	1.39358i
$898$		0			0
$899$	−0.337199	+	0.584047i	−0.0112462	+	0.0194790i
$900$		0			0
$901$	−17.0369	−	29.5088i	−0.567581	−	0.983080i
$902$		0			0
$903$	−12.6415	+	54.4260i	−0.420681	+	1.81118i
$904$		0			0
$905$	−1.02451			−0.0340559
$906$		0			0
$907$	−36.4663			−1.21084			−0.605422	−	0.795905i	$-0.706996\pi$
$907$	−36.4663			−1.21084			−0.605422	+	0.795905i	$0.706996\pi$
$908$		0			0
$909$	−36.7589	−	32.9418i	−1.21921	−	1.09261i
$910$		0			0
$911$	18.9847	+	32.8825i	0.628993	+	1.08945i	0.987754	+	0.156018i	$0.0498658\pi$
$911$	18.9847	+	32.8825i	0.628993	+	1.08945i	−0.358762	+	0.933429i	$0.616801\pi$
$912$		0			0
$913$	−11.8666	−	20.5535i	−0.392726	−	0.680221i
$914$		0			0
$915$	11.8857	−	9.64797i	0.392928	−	0.318952i
$916$		0			0
$917$	−39.3465	−	16.0117i	−1.29934	−	0.528754i
$918$		0			0
$919$	−1.21770	−	2.10911i	−0.0401681	−	0.0695732i	0.845242	−	0.534383i	$-0.179456\pi$
$919$	−1.21770	−	2.10911i	−0.0401681	−	0.0695732i	−0.885411	+	0.464810i	$0.846123\pi$
$920$		0			0
$921$	−31.7586	−	12.1482i	−1.04648	−	0.400297i
$922$		0			0
$923$	−12.0284	+	20.8338i	−0.395919	+	0.685752i
$924$		0			0
$925$	−1.42153	−	2.46217i	−0.0467398	−	0.0809557i
$926$		0			0
$927$	−17.3077	−	15.5105i	−0.568461	−	0.509431i
$928$		0			0
$929$	17.7404	−	30.7273i	0.582044	−	1.00813i	−0.413193	−	0.910644i	$-0.635586\pi$
$929$	17.7404	−	30.7273i	0.582044	−	1.00813i	0.995237	−	0.0974863i	$-0.0310802\pi$
$930$		0			0
$931$	9.37687	−	36.8220i	0.307314	−	1.20679i
$932$		0			0
$933$	−3.63474	−	22.7756i	−0.118996	−	0.745640i
$934$		0			0
$935$	10.6475	−	18.4420i	0.348209	−	0.603116i
$936$		0			0
$937$	−30.0427			−0.981452			−0.490726	−	0.871314i	$-0.663268\pi$
$937$	−30.0427			−0.981452			−0.490726	+	0.871314i	$0.663268\pi$
$938$		0			0
$939$	6.25698	−	5.07899i	0.204189	−	0.165746i
$940$		0			0
$941$	15.1250	+	26.1972i	0.493060	+	0.854004i	0.999968	−	0.00799565i	$-0.00254512\pi$
$941$	15.1250	+	26.1972i	0.493060	+	0.854004i	−0.506908	+	0.862000i	$0.669212\pi$
$942$		0			0
$943$	−20.0756	+	34.7719i	−0.653750	+	1.13233i
$944$		0			0
$945$	2.22624	+	25.1503i	0.0724196	+	0.818141i
$946$		0			0
$947$	−16.9944	+	29.4352i	−0.552245	+	0.956516i	0.445868	+	0.895099i	$0.352895\pi$
$947$	−16.9944	+	29.4352i	−0.552245	+	0.956516i	−0.998112	+	0.0614168i	$0.980438\pi$
$948$		0			0
$949$	8.71360	+	15.0924i	0.282855	+	0.489920i
$950$		0			0
$951$	−5.54790	+	4.50340i	−0.179903	+	0.146033i
$952$		0			0
$953$	−21.4324			−0.694265			−0.347132	−	0.937816i	$-0.612845\pi$
$953$	−21.4324			−0.694265			−0.347132	+	0.937816i	$0.612845\pi$
$954$		0			0
$955$	−22.0385	+	38.1719i	−0.713151	+	1.23521i
$956$		0			0
$957$	−0.549972	−	3.44618i	−0.0177781	−	0.111399i
$958$		0			0
$959$	32.9377	+	13.4037i	1.06361	+	0.432829i
$960$		0			0
$961$	14.9626	−	25.9161i	0.482666	−	0.836002i
$962$		0			0
$963$	−4.62316	+	22.0044i	−0.148979	+	0.709081i
$964$		0			0
$965$	−19.5406	−	33.8452i	−0.629033	−	1.08952i
$966$		0			0
$967$	12.4095	−	21.4938i	0.399061	−	0.691194i	−0.594549	−	0.804059i	$-0.702669\pi$
$967$	12.4095	−	21.4938i	0.399061	−	0.691194i	0.993610	+	0.112865i	$0.0360028\pi$
$968$		0			0
$969$	32.8747	+	12.5751i	1.05609	+	0.403971i
$970$		0			0
$971$	−13.9437	−	24.1512i	−0.447475	−	0.775050i	0.550746	−	0.834673i	$-0.314343\pi$
$971$	−13.9437	−	24.1512i	−0.447475	−	0.775050i	−0.998221	+	0.0596234i	$0.981010\pi$
$972$		0			0
$973$	−17.0021	+	13.2151i	−0.545062	+	0.423656i
$974$		0			0
$975$	10.5120	−	8.53294i	0.336654	−	0.273273i
$976$		0			0
$977$	−13.6237	−	23.5969i	−0.435859	−	0.754930i	0.561506	−	0.827473i	$-0.310222\pi$
$977$	−13.6237	−	23.5969i	−0.435859	−	0.754930i	−0.997365	+	0.0725422i	$0.976889\pi$
$978$		0			0
$979$	17.8645	+	30.9423i	0.570953	+	0.988920i
$980$		0			0
$981$	−24.5552	+	8.04230i	−0.783986	+	0.256771i
$982$		0			0
$983$	−13.8908			−0.443047			−0.221523	−	0.975155i	$-0.571103\pi$
$983$	−13.8908			−0.443047			−0.221523	+	0.975155i	$0.571103\pi$
$984$		0			0
$985$	27.3223			0.870561
$986$		0			0
$987$	−20.2276	+	6.15480i	−0.643850	+	0.195909i
$988$		0			0
$989$	48.5173	+	84.0344i	1.54276	+	2.67214i
$990$		0			0
$991$	21.3271	−	36.9397i	0.677479	−	1.17343i	−0.298259	−	0.954485i	$-0.596406\pi$
$991$	21.3271	−	36.9397i	0.677479	−	1.17343i	0.975738	−	0.218942i	$-0.0702607\pi$
$992$		0			0
$993$	0.0592500	−	0.0480950i	0.00188024	−	0.00152625i
$994$		0			0
$995$	−11.3479	+	19.6551i	−0.359752	+	0.623108i
$996$		0			0
$997$	43.1810			1.36756			0.683779	−	0.729690i	$-0.260335\pi$
$997$	43.1810			1.36756			0.683779	+	0.729690i	$0.260335\pi$
$998$		0			0
$999$	4.91839	−	7.63241i	0.155611	−	0.241479i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.d.193.1	yes	22
3.2	odd	2		1512.2.t.d.361.8		22
4.3	odd	2		1008.2.t.k.193.11		22
7.2	even	3		504.2.q.d.121.9	yes	22
9.2	odd	6		1512.2.q.c.1369.4		22
9.7	even	3		504.2.q.d.25.9	✓	22
12.11	even	2		3024.2.t.l.1873.8		22
21.2	odd	6		1512.2.q.c.793.4		22
28.23	odd	6		1008.2.q.k.625.3		22
36.7	odd	6		1008.2.q.k.529.3		22
36.11	even	6		3024.2.q.k.2881.4		22
63.2	odd	6		1512.2.t.d.289.8		22
63.16	even	3	inner	504.2.t.d.457.1	yes	22
84.23	even	6		3024.2.q.k.2305.4		22
252.79	odd	6		1008.2.t.k.961.11		22
252.191	even	6		3024.2.t.l.289.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.9	✓	22	9.7	even	3
504.2.q.d.121.9	yes	22	7.2	even	3
504.2.t.d.193.1	yes	22	1.1	even	1	trivial
504.2.t.d.457.1	yes	22	63.16	even	3	inner
1008.2.q.k.529.3		22	36.7	odd	6
1008.2.q.k.625.3		22	28.23	odd	6
1008.2.t.k.193.11		22	4.3	odd	2
1008.2.t.k.961.11		22	252.79	odd	6
1512.2.q.c.793.4		22	21.2	odd	6
1512.2.q.c.1369.4		22	9.2	odd	6
1512.2.t.d.289.8		22	63.2	odd	6
1512.2.t.d.361.8		22	3.2	odd	2
3024.2.q.k.2305.4		22	84.23	even	6
3024.2.q.k.2881.4		22	36.11	even	6
3024.2.t.l.289.8		22	252.191	even	6
3024.2.t.l.1873.8		22	12.11	even	2

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	504.2.t.d.193.1

Level	$504$
Weight	$2$
Character	504.193
Analytic conductor	$4.024$
Analytic rank	$0$
Dimension	$22$
Inner twists	$2$