LMFDB - Embedded newform 828.2.k.a.137.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(137,828)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("828.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.2
Character	$\chi$	$=$	828.137
Dual form			828.2.k.a.689.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72869 + 0.107863i) q^{3} +(0.921249 + 1.59565i) q^{5} +(4.26677 + 2.46342i) q^{7} +(2.97673 - 0.372924i) q^{9} +O(q^{10})$	\(q+(-1.72869 + 0.107863i) q^{3} +(0.921249 + 1.59565i) q^{5} +(4.26677 + 2.46342i) q^{7} +(2.97673 - 0.372924i) q^{9} +(-0.542236 + 0.939180i) q^{11} +(-0.216403 - 0.374821i) q^{13} +(-1.76466 - 2.65901i) q^{15} +0.955596 q^{17} -2.23508i q^{19} +(-7.64163 - 3.79826i) q^{21} +(-4.62959 + 1.25177i) q^{23} +(0.802602 - 1.39015i) q^{25} +(-5.10562 + 0.965748i) q^{27} +(2.48447 + 1.43441i) q^{29} +(4.10853 + 7.11618i) q^{31} +(0.836054 - 1.68204i) q^{33} +9.07769i q^{35} -2.89752i q^{37} +(0.414522 + 0.624606i) q^{39} +(-2.06515 + 1.19231i) q^{41} +(4.29946 + 2.48229i) q^{43} +(3.33736 + 4.40626i) q^{45} +(-2.00476 - 1.15745i) q^{47} +(8.63688 + 14.9595i) q^{49} +(-1.65193 + 0.103074i) q^{51} +9.13609 q^{53} -1.99814 q^{55} +(0.241083 + 3.86376i) q^{57} +(-8.20007 + 4.73431i) q^{59} +(-7.72175 - 4.45815i) q^{61} +(13.6197 + 5.74176i) q^{63} +(0.398722 - 0.690606i) q^{65} +(-7.97045 + 4.60174i) q^{67} +(7.86809 - 2.66328i) q^{69} +7.27620i q^{71} +8.59659 q^{73} +(-1.23750 + 2.48970i) q^{75} +(-4.62719 + 2.67151i) q^{77} +(7.30210 + 4.21587i) q^{79} +(8.72186 - 2.22019i) q^{81} +(-0.667479 + 1.15611i) q^{83} +(0.880342 + 1.52480i) q^{85} +(-4.44959 - 2.21166i) q^{87} +7.47049 q^{89} -2.13236i q^{91} +(-7.86995 - 11.8585i) q^{93} +(3.56640 - 2.05906i) q^{95} +(-6.85638 - 3.95853i) q^{97} +(-1.26385 + 2.99790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{3} + 6 q^{9}+O(q^{10}) $ 48 * q - 2 * q^3 + 6 * q^9	$ 48 q - 2 q^{3} + 6 q^{9} + 21 q^{23} - 30 q^{25} - 2 q^{27} - 6 q^{29} - 6 q^{31} - 18 q^{39} - 12 q^{41} - 48 q^{47} + 12 q^{49} - 12 q^{55} - 36 q^{59} + 11 q^{69} + 64 q^{75} + 30 q^{77} - 26 q^{81} - 4 q^{87} + 38 q^{93} - 84 q^{95}+O(q^{100}) $ 48 * q - 2 * q^3 + 6 * q^9 + 21 * q^23 - 30 * q^25 - 2 * q^27 - 6 * q^29 - 6 * q^31 - 18 * q^39 - 12 * q^41 - 48 * q^47 + 12 * q^49 - 12 * q^55 - 36 * q^59 + 11 * q^69 + 64 * q^75 + 30 * q^77 - 26 * q^81 - 4 * q^87 + 38 * q^93 - 84 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	−1.72869	+	0.107863i	−0.998059	+	0.0622748i
$3$	−1.72869	+	0.107863i	−0.998059	+	0.0622748i
$4$		0			0
$5$	0.921249	+	1.59565i	0.411995	+	0.713596i	0.995108	−	0.0987950i	$-0.0314988\pi$
$5$	0.921249	+	1.59565i	0.411995	+	0.713596i	−0.583113	+	0.812391i	$0.698165\pi$
$6$		0			0
$7$	4.26677	+	2.46342i	1.61269	+	0.931085i	0.988744	+	0.149615i	$0.0478035\pi$
$7$	4.26677	+	2.46342i	1.61269	+	0.931085i	0.623943	+	0.781470i	$0.285530\pi$
$8$		0			0
$9$	2.97673	−	0.372924i	0.992244	−	0.124308i
$10$		0			0
$11$	−0.542236	+	0.939180i	−0.163490	+	0.283173i	−0.936118	−	0.351686i	$-0.885609\pi$
$11$	−0.542236	+	0.939180i	−0.163490	+	0.283173i	0.772628	+	0.634859i	$0.218942\pi$
$12$		0			0
$13$	−0.216403	−	0.374821i	−0.0600193	−	0.103957i	0.834454	−	0.551077i	$-0.185783\pi$
$13$	−0.216403	−	0.374821i	−0.0600193	−	0.103957i	−0.894474	+	0.447120i	$0.852450\pi$
$14$		0			0
$15$	−1.76466	−	2.65901i	−0.455634	−	0.686554i
$16$		0			0
$17$	0.955596			0.231766			0.115883	−	0.993263i	$-0.463030\pi$
$17$	0.955596			0.231766			0.115883	+	0.993263i	$0.463030\pi$
$18$		0			0
$19$		−	2.23508i		−	0.512762i	−0.966576	−	0.256381i	$-0.917470\pi$
$19$		−	2.23508i		−	0.512762i	0.966576	−	0.256381i	$-0.0825302\pi$
$20$		0			0
$21$	−7.64163	−	3.79826i	−1.66754	−	0.828848i
$22$		0			0
$23$	−4.62959	+	1.25177i	−0.965335	+	0.261012i
$23$	−4.62959	+	1.25177i	−0.965335	+	0.261012i
$24$		0			0
$25$	0.802602	−	1.39015i	0.160520	−	0.278029i
$26$		0			0
$27$	−5.10562	+	0.965748i	−0.982577	+	0.185858i
$28$		0			0
$29$	2.48447	+	1.43441i	0.461354	+	0.266363i	0.712614	−	0.701557i	$-0.247511\pi$
$29$	2.48447	+	1.43441i	0.461354	+	0.266363i	−0.251259	+	0.967920i	$0.580845\pi$
$30$		0			0
$31$	4.10853	+	7.11618i	0.737914	+	1.27810i	0.953433	+	0.301605i	$0.0975223\pi$
$31$	4.10853	+	7.11618i	0.737914	+	1.27810i	−0.215519	+	0.976500i	$0.569144\pi$
$32$		0			0
$33$	0.836054	−	1.68204i	0.145538	−	0.292805i
$34$		0			0
$35$			9.07769i			1.53441i
$36$		0			0
$37$		−	2.89752i		−	0.476349i	−0.971222	−	0.238175i	$-0.923451\pi$
$37$		−	2.89752i		−	0.476349i	0.971222	−	0.238175i	$-0.0765491\pi$
$38$		0			0
$39$	0.414522	+	0.624606i	0.0663767	+	0.100017i
$40$		0			0
$41$	−2.06515	+	1.19231i	−0.322522	+	0.186208i	−0.652516	−	0.757775i	$-0.726287\pi$
$41$	−2.06515	+	1.19231i	−0.322522	+	0.186208i	0.329994	+	0.943983i	$0.392953\pi$
$42$		0			0
$43$	4.29946	+	2.48229i	0.655662	+	0.378546i	0.790622	−	0.612305i	$-0.209757\pi$
$43$	4.29946	+	2.48229i	0.655662	+	0.378546i	−0.134960	+	0.990851i	$0.543091\pi$
$44$		0			0
$45$	3.33736	+	4.40626i	0.497505	+	0.656847i
$46$		0			0
$47$	−2.00476	−	1.15745i	−0.292425	−	0.168832i	0.346610	−	0.938009i	$-0.387333\pi$
$47$	−2.00476	−	1.15745i	−0.292425	−	0.168832i	−0.639035	+	0.769178i	$0.720666\pi$
$48$		0			0
$49$	8.63688	+	14.9595i	1.23384	+	2.13707i
$50$		0			0
$51$	−1.65193	+	0.103074i	−0.231316	+	0.0144332i
$52$		0			0
$53$	9.13609			1.25494			0.627469	−	0.778641i	$-0.284091\pi$
$53$	9.13609			1.25494			0.627469	+	0.778641i	$0.284091\pi$
$54$		0			0
$55$	−1.99814			−0.269429
$56$		0			0
$57$	0.241083	+	3.86376i	0.0319322	+	0.511767i
$58$		0			0
$59$	−8.20007	+	4.73431i	−1.06756	+	0.616355i	−0.927513	−	0.373791i	$-0.878058\pi$
$59$	−8.20007	+	4.73431i	−1.06756	+	0.616355i	−0.140044	+	0.990145i	$0.544725\pi$
$60$		0			0
$61$	−7.72175	−	4.45815i	−0.988669	−	0.570808i	−0.0837927	−	0.996483i	$-0.526703\pi$
$61$	−7.72175	−	4.45815i	−0.988669	−	0.570808i	−0.904876	+	0.425675i	$0.860037\pi$
$62$		0			0
$63$	13.6197	+	5.74176i	1.71592	+	0.723394i
$64$		0			0
$65$	0.398722	−	0.690606i	0.0494553	−	0.0856591i
$66$		0			0
$67$	−7.97045	+	4.60174i	−0.973745	+	0.562192i	−0.900376	−	0.435113i	$-0.856708\pi$
$67$	−7.97045	+	4.60174i	−0.973745	+	0.562192i	−0.0733692	+	0.997305i	$0.523375\pi$
$68$		0			0
$69$	7.86809	−	2.66328i	0.947207	−	0.320622i
$70$		0			0
$71$			7.27620i			0.863526i	0.901987	+	0.431763i	$0.142108\pi$
$71$			7.27620i			0.863526i	−0.901987	+	0.431763i	$0.857892\pi$
$72$		0			0
$73$	8.59659			1.00615			0.503077	−	0.864241i	$-0.332201\pi$
$73$	8.59659			1.00615			0.503077	+	0.864241i	$0.332201\pi$
$74$		0			0
$75$	−1.23750	+	2.48970i	−0.142895	+	0.287486i
$76$		0			0
$77$	−4.62719	+	2.67151i	−0.527317	+	0.304447i
$78$		0			0
$79$	7.30210	+	4.21587i	0.821550	+	0.474322i	0.850951	−	0.525245i	$-0.176026\pi$
$79$	7.30210	+	4.21587i	0.821550	+	0.474322i	−0.0294005	+	0.999568i	$0.509360\pi$
$80$		0			0
$81$	8.72186	−	2.22019i	0.969095	−	0.246687i
$82$		0			0
$83$	−0.667479	+	1.15611i	−0.0732654	+	0.126899i	−0.900331	−	0.435207i	$-0.856675\pi$
$83$	−0.667479	+	1.15611i	−0.0732654	+	0.126899i	0.827065	+	0.562106i	$0.190009\pi$
$84$		0			0
$85$	0.880342	+	1.52480i	0.0954865	+	0.165387i
$86$		0			0
$87$	−4.44959	−	2.21166i	−0.477046	−	0.237115i
$88$		0			0
$89$	7.47049			0.791871			0.395935	−	0.918278i	$-0.370420\pi$
$89$	7.47049			0.791871			0.395935	+	0.918278i	$0.370420\pi$
$90$		0			0
$91$		−	2.13236i		−	0.223533i
$92$		0			0
$93$	−7.86995	−	11.8585i	−0.816075	−	1.22967i
$94$		0			0
$95$	3.56640	−	2.05906i	0.365905	−	0.211256i
$96$		0			0
$97$	−6.85638	−	3.95853i	−0.696160	−	0.401928i	0.109756	−	0.993959i	$-0.464993\pi$
$97$	−6.85638	−	3.95853i	−0.696160	−	0.401928i	−0.805915	+	0.592031i	$0.798326\pi$
$98$		0			0
$99$	−1.26385	+	2.99790i	−0.127021	+	0.301300i
$100$		0			0
$101$	−12.4184	−	7.16979i	−1.23568	−	0.713420i	−0.267472	−	0.963566i	$-0.586188\pi$
$101$	−12.4184	−	7.16979i	−1.23568	−	0.713420i	−0.968208	+	0.250145i	$0.919522\pi$
$102$		0			0
$103$	5.49095	−	3.17020i	0.541039	−	0.312369i	−0.204461	−	0.978875i	$-0.565544\pi$
$103$	5.49095	−	3.17020i	0.541039	−	0.312369i	0.745500	+	0.666506i	$0.232211\pi$
$104$		0			0
$105$	−0.979148	−	15.6925i	−0.0955551	−	1.53143i
$106$		0			0
$107$	−13.3189			−1.28759			−0.643794	−	0.765199i	$-0.722641\pi$
$107$	−13.3189			−1.28759			−0.643794	+	0.765199i	$0.722641\pi$
$108$		0			0
$109$		−	12.1331i		−	1.16214i	−0.813852	−	0.581072i	$-0.802633\pi$
$109$		−	12.1331i		−	1.16214i	0.813852	−	0.581072i	$-0.197367\pi$
$110$		0			0
$111$	0.312536	+	5.00891i	0.0296646	+	0.475425i
$112$		0			0
$113$	−8.52815	−	14.7712i	−0.802261	−	1.38956i	−0.918125	−	0.396292i	$-0.870297\pi$
$113$	−8.52815	−	14.7712i	−0.802261	−	1.38956i	0.115864	−	0.993265i	$-0.463036\pi$
$114$		0			0
$115$	−6.26239	−	6.23400i	−0.583971	−	0.581324i
$116$		0			0
$117$	−0.783952	−	1.03504i	−0.0724764	−	0.0956894i
$118$		0			0
$119$	4.07731	+	2.35404i	0.373766	+	0.215794i
$120$		0			0
$121$	4.91196	+	8.50777i	0.446542	+	0.773433i
$122$		0			0
$123$	3.44139	−	2.28389i	0.310300	−	0.205932i
$124$		0			0
$125$	12.1701			1.08852
$126$		0			0
$127$	−0.146102			−0.0129645			−0.00648223	−	0.999979i	$-0.502063\pi$
$127$	−0.146102			−0.0129645			−0.00648223	+	0.999979i	$0.502063\pi$
$128$		0			0
$129$	−7.70018	−	3.82736i	−0.677963	−	0.336980i
$130$		0			0
$131$	−7.91761	+	4.57124i	−0.691765	+	0.399391i	−0.804273	−	0.594260i	$-0.797445\pi$
$131$	−7.91761	+	4.57124i	−0.691765	+	0.399391i	0.112508	+	0.993651i	$0.464112\pi$
$132$		0			0
$133$	5.50594	−	9.53657i	0.477426	−	0.826925i
$134$		0			0
$135$	−6.24454	−	7.25708i	−0.537444	−	0.624590i
$136$		0			0
$137$	−5.16890	+	8.95279i	−0.441609	+	0.764888i	−0.997809	−	0.0661597i	$-0.978925\pi$
$137$	−5.16890	+	8.95279i	−0.441609	+	0.764888i	0.556201	+	0.831048i	$0.312259\pi$
$138$		0			0
$139$	−2.43522	−	4.21793i	−0.206553	−	0.357760i	0.744073	−	0.668098i	$-0.232891\pi$
$139$	−2.43522	−	4.21793i	−0.206553	−	0.357760i	−0.950626	+	0.310337i	$0.899558\pi$
$140$		0			0
$141$	3.59046	+	1.78463i	0.302371	+	0.150293i
$142$		0			0
$143$	0.469365			0.0392503
$144$		0			0
$145$			5.28579i			0.438961i
$146$		0			0
$147$	−16.5441	−	24.9287i	−1.36453	−	2.05609i
$148$		0			0
$149$	10.4847	+	18.1600i	0.858940	+	1.48773i	0.872941	+	0.487825i	$0.162210\pi$
$149$	10.4847	+	18.1600i	0.858940	+	1.48773i	−0.0140018	+	0.999902i	$0.504457\pi$
$150$		0			0
$151$	6.71278	−	11.6269i	0.546279	−	0.946182i	−0.452247	−	0.891893i	$-0.649377\pi$
$151$	6.71278	−	11.6269i	0.546279	−	0.946182i	0.998525	−	0.0542894i	$-0.0172894\pi$
$152$		0			0
$153$	2.84455	−	0.356364i	0.229968	−	0.0288104i
$154$		0			0
$155$	−7.56996	+	13.1116i	−0.608034	+	1.05315i
$156$		0			0
$157$	16.0010	−	9.23817i	1.27702	−	0.737287i	0.300719	−	0.953713i	$-0.402773\pi$
$157$	16.0010	−	9.23817i	1.27702	−	0.737287i	0.976299	+	0.216426i	$0.0694401\pi$
$158$		0			0
$159$	−15.7935	+	0.985448i	−1.25250	+	0.0781511i
$160$		0			0
$161$	−22.8370	−	6.06360i	−1.79981	−	0.477879i
$162$		0			0
$163$	0.244848			0.0191779			0.00958897	−	0.999954i	$-0.496948\pi$
$163$	0.244848			0.0191779			0.00958897	+	0.999954i	$0.496948\pi$
$164$		0			0
$165$	3.45416	−	0.215525i	0.268906	−	0.0167786i
$166$		0			0
$167$	−8.20746	+	4.73858i	−0.635113	+	0.366682i	−0.782729	−	0.622362i	$-0.786173\pi$
$167$	−8.20746	+	4.73858i	−0.635113	+	0.366682i	0.147617	+	0.989045i	$0.452840\pi$
$168$		0			0
$169$	6.40634	−	11.0961i	0.492795	−	0.853547i
$170$		0			0
$171$	−0.833514	−	6.65323i	−0.0637404	−	0.508785i
$172$		0			0
$173$	−4.97961	−	2.87498i	−0.378593	−	0.218581i	0.298613	−	0.954374i	$-0.403476\pi$
$173$	−4.97961	−	2.87498i	−0.378593	−	0.218581i	−0.677206	+	0.735793i	$0.736809\pi$
$174$		0			0
$175$	6.84903	−	3.95429i	0.517738	−	0.298916i
$176$		0			0
$177$	13.6647	−	9.06863i	1.02710	−	0.681640i
$178$		0			0
$179$		−	9.15470i		−	0.684254i	−0.939654	−	0.342127i	$-0.888853\pi$
$179$		−	9.15470i		−	0.684254i	0.939654	−	0.342127i	$-0.111147\pi$
$180$		0			0
$181$			18.0992i			1.34530i	0.739961	+	0.672650i	$0.234844\pi$
$181$			18.0992i			1.34530i	−0.739961	+	0.672650i	$0.765156\pi$
$182$		0			0
$183$	13.8294	+	6.87387i	1.02230	+	0.508131i
$184$		0			0
$185$	4.62343	−	2.66934i	0.339921	−	0.196254i
$186$		0			0
$187$	−0.518159	+	0.897477i	−0.0378915	+	0.0656300i
$188$		0			0
$189$	−24.1635	−	8.45666i	−1.75764	−	0.615131i
$190$		0			0
$191$	0.482975	−	0.836538i	0.0349469	−	0.0605297i	−0.848023	−	0.529959i	$-0.822207\pi$
$191$	0.482975	−	0.836538i	0.0349469	−	0.0605297i	0.882970	+	0.469430i	$0.155540\pi$
$192$		0			0
$193$	−0.629455	−	1.09025i	−0.0453092	−	0.0784778i	0.842481	−	0.538725i	$-0.181094\pi$
$193$	−0.629455	−	1.09025i	−0.0453092	−	0.0784778i	−0.887791	+	0.460248i	$0.847761\pi$
$194$		0			0
$195$	−0.614775	+	1.23685i	−0.0440249	+	0.0885727i
$196$		0			0
$197$		−	25.2040i		−	1.79571i	−0.440289	−	0.897856i	$-0.645124\pi$
$197$		−	25.2040i		−	1.79571i	0.440289	−	0.897856i	$-0.354876\pi$
$198$		0			0
$199$		−	15.6286i		−	1.10788i	−0.832555	−	0.553942i	$-0.813123\pi$
$199$		−	15.6286i		−	1.10788i	0.832555	−	0.553942i	$-0.186877\pi$
$200$		0			0
$201$	13.2821	−	8.81469i	0.936845	−	0.621741i
$202$		0			0
$203$	7.06710	+	12.2406i	0.496013	+	0.859120i
$204$		0			0
$205$	−3.80503	−	2.19684i	−0.265755	−	0.153434i
$206$		0			0
$207$	−13.3142	+	5.45267i	−0.925402	+	0.378987i
$208$		0			0
$209$	2.09914	+	1.21194i	0.145201	+	0.0838316i
$210$		0			0
$211$	2.02579	+	3.50876i	0.139461	+	0.241553i	0.927293	−	0.374337i	$-0.122130\pi$
$211$	2.02579	+	3.50876i	0.139461	+	0.241553i	−0.787832	+	0.615890i	$0.788796\pi$
$212$		0			0
$213$	−0.784833	−	12.5783i	−0.0537759	−	0.861849i
$214$		0			0
$215$			9.14724i			0.623837i
$216$		0			0
$217$			40.4842i			2.74824i
$218$		0			0
$219$	−14.8608	+	0.927255i	−1.00420	+	0.0626581i
$220$		0			0
$221$	−0.206794	−	0.358177i	−0.0139105	−	0.0240936i
$222$		0			0
$223$	2.85828	−	4.95068i	0.191404	−	0.331522i	−0.754311	−	0.656517i	$-0.772029\pi$
$223$	2.85828	−	4.95068i	0.191404	−	0.331522i	0.945716	+	0.324995i	$0.105362\pi$
$224$		0			0
$225$	1.87071	−	4.43740i	0.124714	−	0.295827i
$226$		0			0
$227$	13.1068	−	22.7016i	0.869926	−	1.50676i	0.00785561	−	0.999969i	$-0.497499\pi$
$227$	13.1068	−	22.7016i	0.869926	−	1.50676i	0.862071	−	0.506788i	$-0.169167\pi$
$228$		0			0
$229$	14.7020	−	8.48822i	0.971537	−	0.560917i	0.0718329	−	0.997417i	$-0.477115\pi$
$229$	14.7020	−	8.48822i	0.971537	−	0.560917i	0.899705	+	0.436499i	$0.143782\pi$
$230$		0			0
$231$	7.71081	−	5.11731i	0.507334	−	0.336694i
$232$		0			0
$233$			27.2635i			1.78609i	0.449963	+	0.893047i	$0.351437\pi$
$233$			27.2635i			1.78609i	−0.449963	+	0.893047i	$0.648563\pi$
$234$		0			0
$235$		−	4.26520i		−	0.278231i
$236$		0			0
$237$	−13.0778	−	6.50030i	−0.849494	−	0.422240i
$238$		0			0
$239$	17.3616	−	10.0237i	1.12303	−	0.648382i	0.180858	−	0.983509i	$-0.442113\pi$
$239$	17.3616	−	10.0237i	1.12303	−	0.648382i	0.942173	+	0.335127i	$0.108779\pi$
$240$		0			0
$241$	−4.91062	−	2.83515i	−0.316321	−	0.182628i	0.333431	−	0.942775i	$-0.391794\pi$
$241$	−4.91062	−	2.83515i	−0.316321	−	0.182628i	−0.649752	+	0.760147i	$0.725127\pi$
$242$		0			0
$243$	−14.8379	+	4.77878i	−0.951852	+	0.306559i
$244$		0			0
$245$	−15.9134	+	27.5629i	−1.01667	+	1.76093i
$246$		0			0
$247$	−0.837754	+	0.483677i	−0.0533050	+	0.0307757i
$248$		0			0
$249$	1.02916	−	2.07055i	0.0652205	−	0.131216i
$250$		0			0
$251$	19.2420			1.21455			0.607273	−	0.794493i	$-0.292263\pi$
$251$	19.2420			1.21455			0.607273	+	0.794493i	$0.292263\pi$
$252$		0			0
$253$	1.33469	−	5.02677i	0.0839112	−	0.316030i
$254$		0			0
$255$	−1.68631	−	2.54094i	−0.105601	−	0.159120i
$256$		0			0
$257$	−18.0813	+	10.4392i	−1.12788	+	0.651181i	−0.943400	−	0.331656i	$-0.892393\pi$
$257$	−18.0813	+	10.4392i	−1.12788	+	0.651181i	−0.184478	+	0.982837i	$0.559059\pi$
$258$		0			0
$259$	7.13781	−	12.3630i	0.443522	−	0.768203i
$260$		0			0
$261$	7.93052	+	3.34333i	0.490887	+	0.206947i
$262$		0			0
$263$	15.3685	−	26.6190i	0.947660	−	1.64140i	0.197326	−	0.980338i	$-0.436774\pi$
$263$	15.3685	−	26.6190i	0.947660	−	1.64140i	0.750335	−	0.661058i	$-0.229892\pi$
$264$		0			0
$265$	8.41661	+	14.5780i	0.517028	+	0.895520i
$266$		0			0
$267$	−12.9142	+	0.805791i	−0.790334	+	0.0493136i
$268$		0			0
$269$			13.9455i			0.850275i	0.905129	+	0.425138i	$0.139774\pi$
$269$			13.9455i			0.850275i	−0.905129	+	0.425138i	$0.860226\pi$
$270$		0			0
$271$	−15.7101			−0.954322			−0.477161	−	0.878816i	$-0.658334\pi$
$271$	−15.7101			−0.954322			−0.477161	+	0.878816i	$0.658334\pi$
$272$		0			0
$273$	0.230003	+	3.68619i	0.0139204	+	0.223099i
$274$		0			0
$275$	0.870399	+	1.50757i	0.0524870	+	0.0909102i
$276$		0			0
$277$	−7.10881	+	12.3128i	−0.427127	+	0.739806i	−0.996616	−	0.0821927i	$-0.973808\pi$
$277$	−7.10881	+	12.3128i	−0.427127	+	0.739806i	0.569489	+	0.821999i	$0.307141\pi$
$278$		0			0
$279$	14.8838	+	19.6508i	0.891069	+	1.17646i
$280$		0			0
$281$	10.4110	−	18.0323i	0.621066	−	1.07572i	−0.368221	−	0.929738i	$-0.620033\pi$
$281$	10.4110	−	18.0323i	0.621066	−	1.07572i	0.989288	−	0.145980i	$-0.0466335\pi$
$282$		0			0
$283$	−10.7469	+	6.20473i	−0.638837	+	0.368833i	−0.784166	−	0.620551i	$-0.786909\pi$
$283$	−10.7469	+	6.20473i	−0.638837	+	0.368833i	0.145329	+	0.989383i	$0.453576\pi$
$284$		0			0
$285$	−5.94310	+	3.94416i	−0.352039	+	0.233632i
$286$		0			0
$287$	−11.7487			−0.693503
$288$		0			0
$289$	−16.0868			−0.946284
$290$		0			0
$291$	12.2795	+	6.10352i	0.719838	+	0.357795i
$292$		0			0
$293$	−5.50548	−	9.53577i	−0.321634	−	0.557086i	0.659192	−	0.751975i	$-0.270899\pi$
$293$	−5.50548	−	9.53577i	−0.321634	−	0.557086i	−0.980825	+	0.194889i	$0.937565\pi$
$294$		0			0
$295$	−15.1086	−	8.72295i	−0.879657	−	0.507870i
$296$		0			0
$297$	1.86144	−	5.31876i	0.108012	−	0.308626i
$298$		0			0
$299$	1.47105	+	1.46438i	0.0850727	+	0.0846872i
$300$		0			0
$301$	12.2299	+	21.1828i	0.704918	+	1.22095i
$302$		0			0
$303$	22.2410	+	11.0548i	1.27771	+	0.635084i
$304$		0			0
$305$		−	16.4283i		−	0.940680i
$306$		0			0
$307$	−13.8912			−0.792813			−0.396407	−	0.918075i	$-0.629743\pi$
$307$	−13.8912			−0.792813			−0.396407	+	0.918075i	$0.629743\pi$
$308$		0			0
$309$	−9.15019	+	6.07256i	−0.520536	+	0.345456i
$310$		0			0
$311$	16.5301	−	9.54363i	0.937334	−	0.541170i	0.0482101	−	0.998837i	$-0.484648\pi$
$311$	16.5301	−	9.54363i	0.937334	−	0.541170i	0.889123	+	0.457667i	$0.151315\pi$
$312$		0			0
$313$	5.69064	+	3.28549i	0.321654	+	0.185707i	0.652130	−	0.758107i	$-0.273876\pi$
$313$	5.69064	+	3.28549i	0.321654	+	0.185707i	−0.330476	+	0.943815i	$0.607209\pi$
$314$		0			0
$315$	3.38528	+	27.0218i	0.190739	+	1.52251i
$316$		0			0
$317$	−25.9054	−	14.9565i	−1.45499	−	0.840040i	−0.456234	−	0.889860i	$-0.650802\pi$
$317$	−25.9054	−	14.9565i	−1.45499	−	0.840040i	−0.998758	+	0.0498193i	$0.984135\pi$
$318$		0			0
$319$	−2.69434	+	1.55558i	−0.150854	+	0.0870955i
$320$		0			0
$321$	23.0243	−	1.43662i	1.28509	−	0.0801843i
$322$		0			0
$323$		−	2.13583i		−	0.118841i
$324$		0			0
$325$	−0.694741			−0.0385373
$326$		0			0
$327$	1.30872	+	20.9744i	0.0723723	+	1.15989i
$328$		0			0
$329$	−5.70257	−	9.87715i	−0.314393	−	0.544545i
$330$		0			0
$331$	5.38910	−	9.33419i	0.296212	−	0.513054i	−0.679054	−	0.734088i	$-0.737610\pi$
$331$	5.38910	−	9.33419i	0.296212	−	0.513054i	0.975266	+	0.221034i	$0.0709433\pi$
$332$		0			0
$333$	−1.08055	−	8.62514i	−0.0592140	−	0.472655i
$334$		0			0
$335$	−14.6855	−	8.47869i	−0.802356	−	0.463241i
$336$		0			0
$337$	7.64835	−	4.41578i	0.416632	−	0.240543i	−0.277003	−	0.960869i	$-0.589341\pi$
$337$	7.64835	−	4.41578i	0.416632	−	0.240543i	0.693635	+	0.720326i	$0.256008\pi$
$338$		0			0
$339$	16.3358	+	24.6149i	0.887238	+	1.33690i
$340$		0			0
$341$	−8.91117			−0.482567
$342$		0			0
$343$			50.6172i			2.73307i
$344$		0			0
$345$	11.4981	+	10.1012i	0.619039	+	0.543829i
$346$		0			0
$347$	12.0323	−	6.94688i	0.645930	−	0.372928i	−0.140965	−	0.990015i	$-0.545021\pi$
$347$	12.0323	−	6.94688i	0.645930	−	0.372928i	0.786895	+	0.617087i	$0.211687\pi$
$348$		0			0
$349$	0.229918	−	0.398230i	0.0123072	−	0.0213167i	−0.859806	−	0.510621i	$-0.829416\pi$
$349$	0.229918	−	0.398230i	0.0123072	−	0.0213167i	0.872113	+	0.489304i	$0.162749\pi$
$350$		0			0
$351$	1.46685	+	1.70470i	0.0782948	+	0.0909902i
$352$		0			0
$353$	7.31534	+	4.22352i	0.389356	+	0.224795i	0.681881	−	0.731463i	$-0.261162\pi$
$353$	7.31534	+	4.22352i	0.389356	+	0.224795i	−0.292525	+	0.956258i	$0.594495\pi$
$354$		0			0
$355$	−11.6103	+	6.70319i	−0.616209	+	0.355768i
$356$		0			0
$357$	−7.30231	−	3.62960i	−0.386479	−	0.192099i
$358$		0			0
$359$	30.7440			1.62261			0.811304	−	0.584624i	$-0.198758\pi$
$359$	30.7440			1.62261			0.811304	+	0.584624i	$0.198758\pi$
$360$		0			0
$361$	14.0044			0.737075
$362$		0			0
$363$	−9.40893	−	14.1775i	−0.493841	−	0.744124i
$364$		0			0
$365$	7.91960	+	13.7171i	0.414531	+	0.717988i
$366$		0			0
$367$	−21.6685	−	12.5103i	−1.13109	−	0.653034i	−0.186880	−	0.982383i	$-0.559837\pi$
$367$	−21.6685	−	12.5103i	−1.13109	−	0.653034i	−0.944208	+	0.329349i	$0.893171\pi$
$368$		0			0
$369$	−5.70275	+	4.31934i	−0.296873	+	0.224856i
$370$		0			0
$371$	38.9816	+	22.5060i	2.02382	+	1.16846i
$372$		0			0
$373$	2.07102	−	1.19570i	0.107233	−	0.0619112i	−0.445424	−	0.895320i	$-0.646947\pi$
$373$	2.07102	−	1.19570i	0.107233	−	0.0619112i	0.552657	+	0.833408i	$0.313614\pi$
$374$		0			0
$375$	−21.0383	+	1.31270i	−1.08641	+	0.0677876i
$376$		0			0
$377$		−	1.24164i		−	0.0639477i
$378$		0			0
$379$		−	24.7721i		−	1.27246i	−0.771501	−	0.636228i	$-0.780494\pi$
$379$		−	24.7721i		−	1.27246i	0.771501	−	0.636228i	$-0.219506\pi$
$380$		0			0
$381$	0.252565	−	0.0157590i	0.0129393	−	0.000807359i
$382$		0			0
$383$	−8.45278	−	14.6406i	−0.431917	−	0.748102i	0.565122	−	0.825008i	$-0.308829\pi$
$383$	−8.45278	−	14.6406i	−0.431917	−	0.748102i	−0.997038	+	0.0769058i	$0.975496\pi$
$384$		0			0
$385$	−8.52559	−	4.92225i	−0.434504	−	0.250861i
$386$		0			0
$387$	13.7240	+	5.78575i	0.697632	+	0.294106i
$388$		0			0
$389$	14.2598	−	24.6987i	0.723001	−	1.25228i	−0.236790	−	0.971561i	$-0.576095\pi$
$389$	14.2598	−	24.6987i	0.723001	−	1.25228i	0.959791	−	0.280714i	$-0.0905713\pi$
$390$		0			0
$391$	−4.42402	+	1.19619i	−0.223732	+	0.0604938i
$392$		0			0
$393$	13.1940	−	8.75626i	0.665550	−	0.441695i
$394$		0			0
$395$			15.5355i			0.781673i
$396$		0			0
$397$	−33.2401			−1.66827			−0.834135	−	0.551560i	$-0.814033\pi$
$397$	−33.2401			−1.66827			−0.834135	+	0.551560i	$0.814033\pi$
$398$		0			0
$399$	−8.48941	+	17.0796i	−0.425002	+	0.855052i
$400$		0			0
$401$	−11.4668	−	19.8610i	−0.572623	−	0.991812i	−0.996295	−	0.0859963i	$-0.972593\pi$
$401$	−11.4668	−	19.8610i	−0.572623	−	0.991812i	0.423673	−	0.905815i	$-0.360741\pi$
$402$		0			0
$403$	1.77820	−	3.07992i	0.0885782	−	0.153422i
$404$		0			0
$405$	11.5776	+	11.8717i	0.575297	+	0.589909i
$406$		0			0
$407$	2.72129	+	1.57114i	0.134889	+	0.0778785i
$408$		0			0
$409$	−1.85688	−	3.21621i	−0.0918169	−	0.159031i	0.816459	−	0.577404i	$-0.195934\pi$
$409$	−1.85688	−	3.21621i	−0.0918169	−	0.159031i	−0.908276	+	0.418372i	$0.862601\pi$
$410$		0			0
$411$	7.96974	−	16.0341i	0.393118	−	0.790905i
$412$		0			0
$413$	−46.6504			−2.29552
$414$		0			0
$415$	−2.45966			−0.120740
$416$		0			0
$417$	4.66471	+	7.02882i	0.228432	+	0.344203i
$418$		0			0
$419$	17.7685	+	30.7759i	0.868047	+	1.50350i	0.863989	+	0.503510i	$0.167958\pi$
$419$	17.7685	+	30.7759i	0.868047	+	1.50350i	0.00405822	+	0.999992i	$0.498708\pi$
$420$		0			0
$421$	11.3341	+	6.54375i	0.552391	+	0.318923i	0.750086	−	0.661341i	$-0.230012\pi$
$421$	11.3341	+	6.54375i	0.552391	+	0.318923i	−0.197695	+	0.980264i	$0.563346\pi$
$422$		0			0
$423$	−6.39928	−	2.69780i	−0.311144	−	0.131171i
$424$		0			0
$425$	0.766963	−	1.32842i	0.0372032	−	0.0644378i
$426$		0			0
$427$	−21.9646	−	38.0438i	−1.06294	−	1.84107i
$428$		0			0
$429$	−0.811387	+	0.0506272i	−0.0391741	+	0.00244431i
$430$		0			0
$431$	−24.6577			−1.18772			−0.593859	−	0.804569i	$-0.702396\pi$
$431$	−24.6577			−1.18772			−0.593859	+	0.804569i	$0.702396\pi$
$432$		0			0
$433$		−	19.6989i		−	0.946667i	−0.880883	−	0.473334i	$-0.843050\pi$
$433$		−	19.6989i		−	0.946667i	0.880883	−	0.473334i	$-0.156950\pi$
$434$		0			0
$435$	−0.570142	−	9.13748i	−0.0273362	−	0.438109i
$436$		0			0
$437$	2.79781	+	10.3475i	0.133837	+	0.494988i
$438$		0			0
$439$	−13.9102	+	24.0932i	−0.663899	+	1.14991i	0.315684	+	0.948864i	$0.397766\pi$
$439$	−13.9102	+	24.0932i	−0.663899	+	1.14991i	−0.979583	+	0.201042i	$0.935567\pi$
$440$		0			0
$441$	31.2884	+	41.3095i	1.48992	+	1.96712i
$442$		0			0
$443$	3.74212	+	2.16052i	0.177794	+	0.102649i	0.586256	−	0.810126i	$-0.300601\pi$
$443$	3.74212	+	2.16052i	0.177794	+	0.102649i	−0.408462	+	0.912775i	$0.633935\pi$
$444$		0			0
$445$	6.88218	+	11.9203i	0.326247	+	0.565076i
$446$		0			0
$447$	−20.0836	−	30.2621i	−0.949920	−	1.43135i
$448$		0			0
$449$		−	17.2970i		−	0.816296i	−0.912916	−	0.408148i	$-0.866175\pi$
$449$		−	17.2970i		−	0.816296i	0.912916	−	0.408148i	$-0.133825\pi$
$450$		0			0
$451$		−	2.58606i		−	0.121773i
$452$		0			0
$453$	−10.3502	+	20.8233i	−0.486295	+	0.978365i
$454$		0			0
$455$	3.40251	−	1.96444i	0.159512	−	0.0920943i
$456$		0			0
$457$	16.6154	+	9.59288i	0.777233	+	0.448736i	0.835449	−	0.549568i	$-0.185208\pi$
$457$	16.6154	+	9.59288i	0.777233	+	0.448736i	−0.0582155	+	0.998304i	$0.518541\pi$
$458$		0			0
$459$	−4.87891	+	0.922866i	−0.227728	+	0.0430757i
$460$		0			0
$461$	23.2487	+	13.4227i	1.08280	+	0.625155i	0.931650	−	0.363356i	$-0.118369\pi$
$461$	23.2487	+	13.4227i	1.08280	+	0.625155i	0.151150	+	0.988511i	$0.451702\pi$
$462$		0			0
$463$	10.7508	+	18.6209i	0.499631	+	0.865386i	1.00000		0.000426422i	$-0.000135734\pi$
$463$	10.7508	+	18.6209i	0.499631	+	0.865386i	−0.500369	+	0.865812i	$0.666802\pi$
$464$		0			0
$465$	11.6718	−	23.4823i	0.541269	−	1.08897i
$466$		0			0
$467$	25.6491			1.18690			0.593450	−	0.804871i	$-0.297765\pi$
$467$	25.6491			1.18690			0.593450	+	0.804871i	$0.297765\pi$
$468$		0			0
$469$	−45.3441			−2.09379
$470$		0			0
$471$	−26.6643	+	17.6958i	−1.22862	+	0.815382i
$472$		0			0
$473$	−4.66264	+	2.69198i	−0.214389	+	0.123777i
$474$		0			0
$475$	−3.10709	−	1.79388i	−0.142563	−	0.0823088i
$476$		0			0
$477$	27.1957	−	3.40706i	1.24521	−	0.155999i
$478$		0			0
$479$	−11.1615	+	19.3324i	−0.509984	+	0.883318i	0.489949	+	0.871751i	$0.337015\pi$
$479$	−11.1615	+	19.3324i	−0.509984	+	0.883318i	−0.999933	+	0.0115671i	$0.996318\pi$
$480$		0			0
$481$	−1.08605	+	0.627032i	−0.0495196	+	0.0285902i
$482$		0			0
$483$	40.1321	+	8.01881i	1.82608	+	0.364868i
$484$		0			0
$485$		−	14.5872i		−	0.662369i
$486$		0			0
$487$	−7.21710			−0.327038			−0.163519	−	0.986540i	$-0.552285\pi$
$487$	−7.21710			−0.327038			−0.163519	+	0.986540i	$0.552285\pi$
$488$		0			0
$489$	−0.423265	+	0.0264100i	−0.0191407	+	0.00119430i
$490$		0			0
$491$	22.9026	−	13.2228i	1.03358	−	0.596737i	0.115570	−	0.993299i	$-0.463130\pi$
$491$	22.9026	−	13.2228i	1.03358	−	0.596737i	0.918008	+	0.396563i	$0.129797\pi$
$492$		0			0
$493$	2.37415	+	1.37072i	0.106926	+	0.0617339i
$494$		0			0
$495$	−5.94791	+	0.745152i	−0.267339	+	0.0334921i
$496$		0			0
$497$	−17.9243	+	31.0458i	−0.804016	+	1.39260i
$498$		0			0
$499$	6.53279	+	11.3151i	0.292448	+	0.506534i	0.974388	−	0.224874i	$-0.0721969\pi$
$499$	6.53279	+	11.3151i	0.292448	+	0.506534i	−0.681940	+	0.731408i	$0.738864\pi$
$500$		0			0
$501$	13.6770	−	9.07681i	0.611045	−	0.405522i
$502$		0			0
$503$	−20.3826			−0.908815			−0.454407	−	0.890794i	$-0.650149\pi$
$503$	−20.3826			−0.908815			−0.454407	+	0.890794i	$0.650149\pi$
$504$		0			0
$505$		−	26.4206i		−	1.17570i
$506$		0			0
$507$	−9.87771	+	19.8727i	−0.438684	+	0.882579i
$508$		0			0
$509$	1.44218	−	0.832645i	0.0639236	−	0.0369063i	−0.467698	−	0.883889i	$-0.654916\pi$
$509$	1.44218	−	0.832645i	0.0639236	−	0.0369063i	0.531621	+	0.846982i	$0.321583\pi$
$510$		0			0
$511$	36.6797	+	21.1770i	1.62261	+	0.936816i
$512$		0			0
$513$	2.15852	+	11.4115i	0.0953012	+	0.503828i
$514$		0			0
$515$	10.1171	+	5.84109i	0.445811	+	0.257389i
$516$		0			0
$517$	2.17411	−	1.25522i	0.0956172	−	0.0552046i
$518$		0			0
$519$	8.91831	+	4.43283i	0.391470	+	0.194580i
$520$		0			0
$521$	26.6524			1.16766			0.583831	−	0.811875i	$-0.301553\pi$
$521$	26.6524			1.16766			0.583831	+	0.811875i	$0.301553\pi$
$522$		0			0
$523$		−	19.9223i		−	0.871141i	−0.900155	−	0.435570i	$-0.856547\pi$
$523$		−	19.9223i		−	0.871141i	0.900155	−	0.435570i	$-0.143453\pi$
$524$		0			0
$525$	−11.4133	+	7.57450i	−0.498118	+	0.330578i
$526$		0			0
$527$	3.92610	+	6.80020i	0.171023	+	0.296221i
$528$		0			0
$529$	19.8661	−	11.5904i	0.863745	−	0.503929i
$530$		0			0
$531$	−22.6439	+	17.1508i	−0.982660	+	0.744280i
$532$		0			0
$533$	0.893808	+	0.516040i	0.0387151	+	0.0223522i
$534$		0			0
$535$	−12.2700	−	21.2523i	−0.530480	−	0.918818i
$536$		0			0
$537$	0.987455	+	15.8256i	0.0426118	+	0.682926i
$538$		0			0
$539$	−18.7329			−0.806883
$540$		0			0
$541$	−31.3822			−1.34922			−0.674612	−	0.738172i	$-0.735689\pi$
$541$	−31.3822			−1.34922			−0.674612	+	0.738172i	$0.735689\pi$
$542$		0			0
$543$	−1.95223	−	31.2878i	−0.0837783	−	1.34269i
$544$		0			0
$545$	19.3602	−	11.1776i	0.829301	−	0.478797i
$546$		0			0
$547$	18.5521	−	32.1332i	0.793231	−	1.37392i	−0.130725	−	0.991419i	$-0.541730\pi$
$547$	18.5521	−	32.1332i	0.793231	−	1.37392i	0.923956	−	0.382498i	$-0.124936\pi$
$548$		0			0
$549$	−24.6481	−	10.3911i	−1.05196	−	0.443482i
$550$		0			0
$551$	3.20602	−	5.55298i	0.136581	−	0.236565i
$552$		0			0
$553$	20.7709	+	35.9763i	0.883269	+	1.52987i
$554$		0			0
$555$	−7.70454	+	5.11315i	−0.327040	+	0.217041i
$556$		0			0
$557$	10.2644			0.434916			0.217458	−	0.976070i	$-0.430223\pi$
$557$	10.2644			0.434916			0.217458	+	0.976070i	$0.430223\pi$
$558$		0			0
$559$		−	2.14870i		−	0.0908804i
$560$		0			0
$561$	0.798930	−	1.60735i	0.0337309	−	0.0678623i
$562$		0			0
$563$	−5.22787	−	9.05494i	−0.220329	−	0.381620i	0.734579	−	0.678523i	$-0.237380\pi$
$563$	−5.22787	−	9.05494i	−0.220329	−	0.381620i	−0.954908	+	0.296903i	$0.904046\pi$
$564$		0			0
$565$	15.7131	−	27.2159i	0.661055	−	1.14498i
$566$		0			0
$567$	42.6834	+	12.0126i	1.79253	+	0.504481i
$568$		0			0
$569$	−18.1663	+	31.4649i	−0.761570	+	1.31908i	0.180471	+	0.983580i	$0.442238\pi$
$569$	−18.1663	+	31.4649i	−0.761570	+	1.31908i	−0.942041	+	0.335497i	$0.891096\pi$
$570$		0			0
$571$	1.54410	−	0.891484i	0.0646184	−	0.0373074i	−0.467343	−	0.884076i	$-0.654789\pi$
$571$	1.54410	−	0.891484i	0.0646184	−	0.0373074i	0.531961	+	0.846769i	$0.321455\pi$
$572$		0			0
$573$	−0.744682	+	1.49821i	−0.0311096	+	0.0625886i
$574$		0			0
$575$	−1.97557	+	7.44048i	−0.0823869	+	0.310289i
$576$		0			0
$577$	−25.3256			−1.05432			−0.527158	−	0.849767i	$-0.676743\pi$
$577$	−25.3256			−1.05432			−0.527158	+	0.849767i	$0.676743\pi$
$578$		0			0
$579$	1.20573	+	1.81681i	0.0501084	+	0.0755039i
$580$		0			0
$581$	−5.69596	+	3.28856i	−0.236308	+	0.136433i
$582$		0			0
$583$	−4.95392	+	8.58044i	−0.205170	+	0.355365i
$584$		0			0
$585$	0.929344	−	2.20444i	0.0384236	−	0.0911424i
$586$		0			0
$587$	−12.4095	−	7.16461i	−0.512194	−	0.295715i	0.221541	−	0.975151i	$-0.428891\pi$
$587$	−12.4095	−	7.16461i	−0.512194	−	0.295715i	−0.733735	+	0.679436i	$0.762225\pi$
$588$		0			0
$589$	15.9052	−	9.18289i	0.655364	−	0.378375i
$590$		0			0
$591$	2.71858	+	43.5699i	0.111828	+	1.79223i
$592$		0			0
$593$			7.38543i			0.303283i	0.988436	+	0.151642i	$0.0484560\pi$
$593$			7.38543i			0.303283i	−0.988436	+	0.151642i	$0.951544\pi$
$594$		0			0
$595$			8.67461i			0.355624i
$596$		0			0
$597$	1.68575	+	27.0170i	0.0689933	+	1.10573i
$598$		0			0
$599$	23.5430	−	13.5925i	0.961940	−	0.555376i	0.0651703	−	0.997874i	$-0.479241\pi$
$599$	23.5430	−	13.5925i	0.961940	−	0.555376i	0.896770	+	0.442498i	$0.145908\pi$
$600$		0			0
$601$	−18.7460	+	32.4691i	−0.764666	+	1.32444i	0.175756	+	0.984434i	$0.443763\pi$
$601$	−18.7460	+	32.4691i	−0.764666	+	1.32444i	−0.940423	+	0.340007i	$0.889570\pi$
$602$		0			0
$603$	−22.0098	+	16.6705i	−0.896308	+	0.678876i
$604$		0			0
$605$	−9.05027	+	15.6755i	−0.367946	+	0.637301i
$606$		0			0
$607$	−18.7492	−	32.4746i	−0.761008	−	1.31810i	−0.942331	−	0.334681i	$-0.891371\pi$
$607$	−18.7492	−	32.4746i	−0.761008	−	1.31810i	0.181323	−	0.983424i	$-0.441962\pi$
$608$		0			0
$609$	−13.5371	−	20.3979i	−0.548552	−	0.826564i
$610$		0			0
$611$			1.00190i			0.0405326i
$612$		0			0
$613$			21.9808i			0.887795i	0.896078	+	0.443897i	$0.146405\pi$
$613$			21.9808i			0.887795i	−0.896078	+	0.443897i	$0.853595\pi$
$614$		0			0
$615$	6.81467	+	3.38722i	0.274794	+	0.136586i
$616$		0			0
$617$	−2.66744	−	4.62015i	−0.107387	−	0.186000i	0.807324	−	0.590109i	$-0.200915\pi$
$617$	−2.66744	−	4.62015i	−0.107387	−	0.186000i	−0.914711	+	0.404109i	$0.867582\pi$
$618$		0			0
$619$	32.5762	+	18.8079i	1.30935	+	0.755952i	0.981987	−	0.188948i	$-0.0605079\pi$
$619$	32.5762	+	18.8079i	1.30935	+	0.755952i	0.327359	+	0.944900i	$0.393841\pi$
$620$		0			0
$621$	22.4280	−	10.8621i	0.900005	−	0.435880i
$622$		0			0
$623$	31.8749	+	18.4030i	1.27704	+	0.737299i
$624$		0			0
$625$	7.19865	+	12.4684i	0.287946	+	0.498737i
$626$		0			0
$627$	−3.75949	−	1.86865i	−0.150139	−	0.0746266i
$628$		0			0
$629$		−	2.76886i		−	0.110402i
$630$		0			0
$631$			16.6249i			0.661826i	0.943661	+	0.330913i	$0.107357\pi$
$631$			16.6249i			0.661826i	−0.943661	+	0.330913i	$0.892643\pi$
$632$		0			0
$633$	−3.88042	−	5.84705i	−0.154233	−	0.232400i
$634$		0			0
$635$	−0.134596	−	0.233128i	−0.00534129	−	0.00925139i
$636$		0			0
$637$	3.73809	−	6.47456i	0.148108	−	0.256531i
$638$		0			0
$639$	2.71346	+	21.6593i	0.107343	+	0.856828i
$640$		0			0
$641$	21.1099	−	36.5634i	0.833790	−	1.44417i	−0.0612220	−	0.998124i	$-0.519500\pi$
$641$	21.1099	−	36.5634i	0.833790	−	1.44417i	0.895012	−	0.446042i	$-0.147167\pi$
$642$		0			0
$643$	−39.4893	+	22.7991i	−1.55731	+	0.899111i	−0.559792	+	0.828633i	$0.689119\pi$
$643$	−39.4893	+	22.7991i	−1.55731	+	0.899111i	−0.997513	+	0.0704772i	$0.977548\pi$
$644$		0			0
$645$	−0.986650	−	15.8127i	−0.0388493	−	0.622626i
$646$		0			0
$647$		−	29.9477i		−	1.17736i	−0.808365	−	0.588682i	$-0.799647\pi$
$647$		−	29.9477i		−	1.17736i	0.808365	−	0.588682i	$-0.200353\pi$
$648$		0			0
$649$		−	10.2685i		−	0.403072i
$650$		0			0
$651$	−4.36675	−	69.9845i	−0.171146	−	2.74291i
$652$		0			0
$653$	−4.27805	+	2.46993i	−0.167413	+	0.0966559i	−0.581365	−	0.813643i	$-0.697481\pi$
$653$	−4.27805	+	2.46993i	−0.167413	+	0.0966559i	0.413953	+	0.910298i	$0.364148\pi$
$654$		0			0
$655$	−14.5882	−	8.42249i	−0.570007	−	0.329094i
$656$		0			0
$657$	25.5897	−	3.20587i	0.998351	−	0.125073i
$658$		0			0
$659$	2.62524	−	4.54705i	0.102265	−	0.177128i	−0.810353	−	0.585943i	$-0.800724\pi$
$659$	2.62524	−	4.54705i	0.102265	−	0.177128i	0.912617	+	0.408815i	$0.134058\pi$
$660$		0			0
$661$	−22.1890	+	12.8108i	−0.863053	+	0.498284i	−0.865033	−	0.501714i	$-0.832703\pi$
$661$	−22.1890	+	12.8108i	−0.863053	+	0.498284i	0.00198069	+	0.999998i	$0.499370\pi$
$662$		0			0
$663$	0.396116	+	0.596872i	0.0153839	+	0.0231806i
$664$		0			0
$665$	20.2894			0.786788
$666$		0			0
$667$	−13.2976	−	3.53073i	−0.514886	−	0.136711i
$668$		0			0
$669$	−4.40708	+	8.86649i	−0.170387	+	0.342798i
$670$		0			0
$671$	8.37402	−	4.83474i	0.323275	−	0.186643i
$672$		0			0
$673$	5.37031	−	9.30165i	0.207010	−	0.358552i	−0.743761	−	0.668446i	$-0.766960\pi$
$673$	5.37031	−	9.30165i	0.207010	−	0.358552i	0.950771	+	0.309893i	$0.100293\pi$
$674$		0			0
$675$	−2.75525	+	7.87267i	−0.106049	+	0.303019i
$676$		0			0
$677$	8.92497	−	15.4585i	0.343014	−	0.594118i	−0.641977	−	0.766724i	$-0.721885\pi$
$677$	8.92497	−	15.4585i	0.343014	−	0.594118i	0.984991	+	0.172606i	$0.0552187\pi$
$678$		0			0
$679$	−19.5031	−	33.7803i	−0.748458	−	1.29637i
$680$		0			0
$681$	−20.2089	+	40.6577i	−0.774405	+	1.55801i
$682$		0			0
$683$			19.4408i			0.743882i	0.928256	+	0.371941i	$0.121308\pi$
$683$			19.4408i			0.743882i	−0.928256	+	0.371941i	$0.878692\pi$
$684$		0			0
$685$	−19.0474			−0.727762
$686$		0			0
$687$	−24.4997	+	16.2593i	−0.934721	+	0.620331i
$688$		0			0
$689$	−1.97708	−	3.42440i	−0.0753206	−	0.130459i
$690$		0			0
$691$	−11.5890	+	20.0727i	−0.440865	+	0.763601i	−0.997754	−	0.0669859i	$-0.978662\pi$
$691$	−11.5890	+	20.0727i	−0.440865	+	0.763601i	0.556888	+	0.830587i	$0.311995\pi$
$692$		0			0
$693$	−12.7776	+	9.67795i	−0.485382	+	0.367635i
$694$		0			0
$695$	4.48690	−	7.77153i	0.170198	−	0.294791i
$696$		0			0
$697$	−1.97345	+	1.13937i	−0.0747497	+	0.0431568i
$698$		0			0
$699$	−2.94073	−	47.1302i	−0.111229	−	1.78263i
$700$		0			0
$701$	−4.72340			−0.178400			−0.0892001	−	0.996014i	$-0.528431\pi$
$701$	−4.72340			−0.178400			−0.0892001	+	0.996014i	$0.528431\pi$
$702$		0			0
$703$	−6.47619			−0.244254
$704$		0			0
$705$	0.460058	+	7.37320i	0.0173268	+	0.277691i
$706$		0			0
$707$	−35.3244	−	61.1836i	−1.32851	−	2.30105i
$708$		0			0
$709$	−17.0402	−	9.83814i	−0.639956	−	0.369479i	0.144641	−	0.989484i	$-0.453797\pi$
$709$	−17.0402	−	9.83814i	−0.639956	−	0.369479i	−0.784598	+	0.620005i	$0.787131\pi$
$710$		0			0
$711$	23.3086	+	9.82638i	0.874140	+	0.368518i
$712$		0			0
$713$	−27.9286	−	27.8021i	−1.04594	−	1.04120i
$714$		0			0
$715$	0.432402	+	0.748943i	0.0161709	+	0.0280089i
$716$		0			0
$717$	−28.9317	+	19.2006i	−1.08047	+	0.717060i
$718$		0			0
$719$		−	20.5383i		−	0.765950i	−0.923759	−	0.382975i	$-0.874899\pi$
$719$		−	20.5383i		−	0.765950i	0.923759	−	0.382975i	$-0.125101\pi$
$720$		0			0
$721$	31.2381			1.16337
$722$		0			0
$723$	8.79475	+	4.37142i	0.327080	+	0.162575i
$724$		0			0
$725$	3.98808	−	2.30252i	0.148113	−	0.0855134i
$726$		0			0
$727$	−23.0251	−	13.2935i	−0.853952	−	0.493030i	0.00803005	−	0.999968i	$-0.497444\pi$
$727$	−23.0251	−	13.2935i	−0.853952	−	0.493030i	−0.861982	+	0.506938i	$0.830777\pi$
$728$		0			0
$729$	25.1347	−	9.86148i	0.930913	−	0.365240i
$730$		0			0
$731$	4.10855	+	2.37207i	0.151960	+	0.0877342i
$732$		0			0
$733$	−40.5527	+	23.4131i	−1.49785	+	0.864782i	−0.999997	−	0.00248110i	$-0.999210\pi$
$733$	−40.5527	+	23.4131i	−1.49785	+	0.864782i	−0.497850	+	0.867263i	$0.665877\pi$
$734$		0			0
$735$	24.5363	−	49.3641i	0.905037	−	1.82082i
$736$		0			0
$737$		−	9.98091i		−	0.367652i
$738$		0			0
$739$	18.8551			0.693595			0.346797	−	0.937940i	$-0.387269\pi$
$739$	18.8551			0.693595			0.346797	+	0.937940i	$0.387269\pi$
$740$		0			0
$741$	1.39605	−	0.926491i	0.0512850	−	0.0340355i
$742$		0			0
$743$	−20.3583	−	35.2617i	−0.746875	−	1.29363i	−0.949313	−	0.314331i	$-0.898220\pi$
$743$	−20.3583	−	35.2617i	−0.746875	−	1.29363i	0.202438	−	0.979295i	$-0.435114\pi$
$744$		0			0
$745$	−19.3180	+	33.4598i	−0.707758	+	1.22587i
$746$		0			0
$747$	−1.55577	+	3.69034i	−0.0569225	+	0.135023i
$748$		0			0
$749$	−56.8287	−	32.8101i	−2.07648	−	1.19885i
$750$		0			0
$751$	38.4084	−	22.1751i	1.40154	−	0.809182i	0.406993	−	0.913431i	$-0.366577\pi$
$751$	38.4084	−	22.1751i	1.40154	−	0.809182i	0.994551	+	0.104249i	$0.0332440\pi$
$752$		0			0
$753$	−33.2635	+	2.07551i	−1.21219	+	0.0756356i
$754$		0			0
$755$	24.7366			0.900256
$756$		0			0
$757$			8.39380i			0.305078i	0.988297	+	0.152539i	$0.0487449\pi$
$757$			8.39380i			0.305078i	−0.988297	+	0.152539i	$0.951255\pi$
$758$		0			0
$759$	−1.76506	+	8.83369i	−0.0640676	+	0.320642i
$760$		0			0
$761$	24.4388	−	14.1097i	0.885904	−	0.511477i	0.0133037	−	0.999912i	$-0.495765\pi$
$761$	24.4388	−	14.1097i	0.885904	−	0.511477i	0.872601	+	0.488434i	$0.162432\pi$
$762$		0			0
$763$	29.8890	−	51.7693i	1.08206	−	1.87417i
$764$		0			0
$765$	3.18917	+	4.21061i	0.115305	+	0.152235i
$766$		0			0
$767$	3.54903	+	2.04904i	0.128148	+	0.0739864i
$768$		0			0
$769$	−24.4423	+	14.1118i	−0.881412	+	0.508884i	−0.871124	−	0.491063i	$-0.836608\pi$
$769$	−24.4423	+	14.1118i	−0.881412	+	0.508884i	−0.0102886	+	0.999947i	$0.503275\pi$
$770$		0			0
$771$	30.1309	−	19.9965i	1.08514	−	0.720155i
$772$		0			0
$773$	16.2443			0.584267			0.292134	−	0.956378i	$-0.405635\pi$
$773$	16.2443			0.584267			0.292134	+	0.956378i	$0.405635\pi$
$774$		0			0
$775$	13.1901			0.473801
$776$		0			0
$777$	−11.0055	+	22.1418i	−0.394821	+	0.794332i
$778$		0			0
$779$	2.66492	+	4.61577i	0.0954805	+	0.165377i
$780$		0			0
$781$	−6.83366	−	3.94541i	−0.244527	−	0.141178i
$782$		0			0
$783$	−14.0700	−	4.92417i	−0.502822	−	0.175975i
$784$		0			0
$785$	29.4818	+	17.0213i	1.05225	+	0.607517i
$786$		0			0
$787$	−5.69769	+	3.28956i	−0.203101	+	0.117260i	−0.598101	−	0.801421i	$-0.704078\pi$
$787$	−5.69769	+	3.28956i	−0.203101	+	0.117260i	0.395000	+	0.918681i	$0.370744\pi$
$788$		0			0
$789$	−23.6961	+	47.6736i	−0.843603	+	1.69723i
$790$		0			0
$791$		−	84.0337i		−	2.98789i
$792$		0			0
$793$			3.85903i			0.137038i
$794$		0			0
$795$	−16.1221	−	24.2930i	−0.571793	−	0.861584i
$796$		0			0
$797$	11.3647	+	19.6842i	0.402559	+	0.697252i	0.994034	−	0.109071i	$-0.0347876\pi$
$797$	11.3647	+	19.6842i	0.402559	+	0.697252i	−0.591475	+	0.806323i	$0.701454\pi$
$798$		0			0
$799$	−1.91574	−	1.10606i	−0.0677742	−	0.0391294i
$800$		0			0
$801$	22.2376	−	2.78592i	0.785729	−	0.0984358i
$802$		0			0
$803$	−4.66138	+	8.07375i	−0.164497	+	0.284916i
$804$		0			0
$805$	−11.3632	−	42.0260i	−0.400500	−	1.48122i
$806$		0			0
$807$	−1.50421	−	24.1075i	−0.0529507	−	0.848625i
$808$		0			0
$809$		−	5.61426i		−	0.197387i	−0.995118	−	0.0986935i	$-0.968534\pi$
$809$		−	5.61426i		−	0.197387i	0.995118	−	0.0986935i	$-0.0314663\pi$
$810$		0			0
$811$	28.9195			1.01550			0.507751	−	0.861504i	$-0.330477\pi$
$811$	28.9195			1.01550			0.507751	+	0.861504i	$0.330477\pi$
$812$		0			0
$813$	27.1579	−	1.69454i	0.952469	−	0.0594302i
$814$		0			0
$815$	0.225566	+	0.390691i	0.00790122	+	0.0136853i
$816$		0			0
$817$	5.54813	−	9.60964i	0.194104	−	0.336199i
$818$		0			0
$819$	−0.795209	−	6.34748i	−0.0277868	−	0.221799i
$820$		0			0
$821$	−30.5799	−	17.6553i	−1.06724	−	0.616174i	−0.139817	−	0.990177i	$-0.544652\pi$
$821$	−30.5799	−	17.6553i	−1.06724	−	0.616174i	−0.927427	+	0.374003i	$0.877985\pi$
$822$		0			0
$823$	−21.2580	−	36.8200i	−0.741009	−	1.28346i	−0.952036	−	0.305985i	$-0.901014\pi$
$823$	−21.2580	−	36.8200i	−0.741009	−	1.28346i	0.211028	−	0.977480i	$-0.432319\pi$
$824$		0			0
$825$	−1.66726	−	2.51224i	−0.0580466	−	0.0874651i
$826$		0			0
$827$	−9.50813			−0.330630			−0.165315	−	0.986241i	$-0.552864\pi$
$827$	−9.50813			−0.330630			−0.165315	+	0.986241i	$0.552864\pi$
$828$		0			0
$829$	−34.3799			−1.19406			−0.597031	−	0.802218i	$-0.703653\pi$
$829$	−34.3799			−1.19406			−0.597031	+	0.802218i	$0.703653\pi$
$830$		0			0
$831$	10.9608	−	22.0518i	0.380227	−	0.764969i
$832$		0			0
$833$	8.25337	+	14.2953i	0.285962	+	0.495301i
$834$		0			0
$835$	−15.1222	−	8.73082i	−0.523326	−	0.302143i
$836$		0			0
$837$	−27.8490	−	32.3647i	−0.962603	−	1.11869i
$838$		0			0
$839$	4.26310	−	7.38390i	0.147178	−	0.254921i	−0.783005	−	0.622015i	$-0.786314\pi$
$839$	4.26310	−	7.38390i	0.147178	−	0.254921i	0.930184	+	0.367095i	$0.119648\pi$
$840$		0			0
$841$	−10.3849	−	17.9873i	−0.358102	−	0.620250i
$842$		0			0
$843$	−16.0523	+	32.2952i	−0.552871	+	1.11231i
$844$		0			0
$845$	23.6073			0.812117
$846$		0			0
$847$			48.4009i			1.66307i
$848$		0			0
$849$	17.9088	−	11.8852i	0.614628	−	0.407900i
$850$		0			0
$851$	3.62703	+	13.4143i	0.124333	+	0.459837i
$852$		0			0
$853$	15.8507	−	27.4541i	0.542716	−	0.940012i	−0.456031	−	0.889964i	$-0.650729\pi$
$853$	15.8507	−	27.4541i	0.542716	−	0.940012i	0.998747	−	0.0500480i	$-0.0159374\pi$
$854$		0			0
$855$	9.84835	−	7.45928i	0.336806	−	0.255102i
$856$		0			0
$857$	−6.47887	−	3.74058i	−0.221314	−	0.127776i	0.385245	−	0.922814i	$-0.374117\pi$
$857$	−6.47887	−	3.74058i	−0.221314	−	0.127776i	−0.606558	+	0.795039i	$0.707450\pi$
$858$		0			0
$859$	8.63566	+	14.9574i	0.294645	+	0.510340i	0.974902	−	0.222633i	$-0.0714653\pi$
$859$	8.63566	+	14.9574i	0.294645	+	0.510340i	−0.680257	+	0.732973i	$0.738132\pi$
$860$		0			0
$861$	20.3098	−	1.26725i	0.692157	−	0.0431878i
$862$		0			0
$863$		−	4.89723i		−	0.166704i	−0.996520	−	0.0833518i	$-0.973437\pi$
$863$		−	4.89723i		−	0.166704i	0.996520	−	0.0833518i	$-0.0265625\pi$
$864$		0			0
$865$		−	10.5943i		−	0.360217i
$866$		0			0
$867$	27.8091	−	1.73518i	0.944448	−	0.0589297i
$868$		0			0
$869$	−7.91892	+	4.57199i	−0.268631	+	0.155094i
$870$		0			0
$871$	3.44965	+	1.99166i	0.116887	+	0.0674848i
$872$		0			0
$873$	−21.8858	−	9.22658i	−0.740723	−	0.312272i
$874$		0			0
$875$	51.9269	+	29.9800i	1.75545	+	1.01351i
$876$		0			0
$877$	16.4353	+	28.4668i	0.554981	+	0.961256i	0.997905	+	0.0646967i	$0.0206080\pi$
$877$	16.4353	+	28.4668i	0.554981	+	0.961256i	−0.442923	+	0.896559i	$0.646059\pi$
$878$		0			0
$879$	10.5458	+	15.8905i	0.355702	+	0.535975i
$880$		0			0
$881$	37.7311			1.27119			0.635596	−	0.772022i	$-0.280754\pi$
$881$	37.7311			1.27119			0.635596	+	0.772022i	$0.280754\pi$
$882$		0			0
$883$	22.0677			0.742638			0.371319	−	0.928505i	$-0.378906\pi$
$883$	22.0677			0.742638			0.371319	+	0.928505i	$0.378906\pi$
$884$		0			0
$885$	27.0590	+	13.4496i	0.909577	+	0.452104i
$886$		0			0
$887$	0.273783	−	0.158069i	0.00919273	−	0.00530742i	−0.495397	−	0.868667i	$-0.664977\pi$
$887$	0.273783	−	0.158069i	0.00919273	−	0.00530742i	0.504589	+	0.863359i	$0.331644\pi$
$888$		0			0
$889$	−0.623384	−	0.359911i	−0.0209076	−	0.0120710i
$890$		0			0
$891$	−2.64415	+	9.39526i	−0.0885823	+	0.314753i
$892$		0			0
$893$	−2.58699	+	4.48081i	−0.0865705	+	0.149944i
$894$		0			0
$895$	14.6077	−	8.43376i	0.488281	−	0.281909i
$896$		0			0
$897$	−2.70093	−	2.37278i	−0.0901815	−	0.0792249i
$898$		0			0
$899$			23.5732i			0.786212i
$900$		0			0
$901$	8.73042			0.290852
$902$		0			0
$903$	−23.4265	−	35.2992i	−0.779584	−	1.17469i
$904$		0			0
$905$	−28.8799	+	16.6738i	−0.960001	+	0.554257i
$906$		0			0
$907$	−19.0677	−	11.0087i	−0.633131	−	0.365539i	0.148832	−	0.988862i	$-0.452448\pi$
$907$	−19.0677	−	11.0087i	−0.633131	−	0.365539i	−0.781964	+	0.623324i	$0.785782\pi$
$908$		0			0
$909$	−39.6401	−	16.7114i	−1.31478	−	0.554282i
$910$		0			0
$911$	−10.7584	+	18.6341i	−0.356441	+	0.617374i	−0.987363	−	0.158472i	$-0.949343\pi$
$911$	−10.7584	+	18.6341i	−0.356441	+	0.617374i	0.630923	+	0.775846i	$0.282677\pi$
$912$		0			0
$913$	−0.723862	−	1.25377i	−0.0239563	−	0.0414936i
$914$		0			0
$915$	1.77201	+	28.3994i	0.0585807	+	0.938855i
$916$		0			0
$917$	−45.0435			−1.48747
$918$		0			0
$919$			26.4808i			0.873522i	0.899578	+	0.436761i	$0.143874\pi$
$919$			26.4808i			0.873522i	−0.899578	+	0.436761i	$0.856126\pi$
$920$		0			0
$921$	24.0136	−	1.49835i	0.791275	−	0.0493723i
$922$		0			0
$923$	2.72727	−	1.57459i	0.0897691	−	0.0518282i
$924$		0			0
$925$	−4.02798	−	2.32555i	−0.132439	−	0.0764638i
$926$		0			0
$927$	15.1628	−	11.4845i	0.498013	−	0.377202i
$928$		0			0
$929$	20.2005	+	11.6628i	0.662756	+	0.382642i	0.793326	−	0.608797i	$-0.208347\pi$
$929$	20.2005	+	11.6628i	0.662756	+	0.382642i	−0.130570	+	0.991439i	$0.541681\pi$
$930$		0			0
$931$	33.4357	−	19.3041i	1.09581	−	0.632667i
$932$		0			0
$933$	−27.5459	+	18.2810i	−0.901813	+	0.598492i
$934$		0			0
$935$	−1.90941			−0.0624444
$936$		0			0
$937$			26.3411i			0.860526i	0.902704	+	0.430263i	$0.141579\pi$
$937$			26.3411i			0.860526i	−0.902704	+	0.430263i	$0.858421\pi$
$938$		0			0
$939$	−10.1917	−	5.06579i	−0.332595	−	0.165316i
$940$		0			0
$941$	−14.8591	−	25.7366i	−0.484391	−	0.838990i	0.515448	−	0.856921i	$-0.327626\pi$
$941$	−14.8591	−	25.7366i	−0.484391	−	0.838990i	−0.999839	+	0.0179305i	$0.994292\pi$
$942$		0			0
$943$	8.06828	−	8.10501i	0.262739	−	0.263936i
$944$		0			0
$945$	−8.76677	−	46.3472i	−0.285183	−	1.50768i
$946$		0			0
$947$	−19.1721	−	11.0690i	−0.623011	−	0.359695i	0.155030	−	0.987910i	$-0.450453\pi$
$947$	−19.1721	−	11.0690i	−0.623011	−	0.359695i	−0.778040	+	0.628215i	$0.783786\pi$
$948$		0			0
$949$	−1.86033	−	3.22218i	−0.0603888	−	0.104596i
$950$		0			0
$951$	46.3956	+	23.0609i	1.50448	+	0.747800i
$952$		0			0
$953$	12.6557			0.409958			0.204979	−	0.978766i	$-0.434287\pi$
$953$	12.6557			0.409958			0.204979	+	0.978766i	$0.434287\pi$
$954$		0			0
$955$	1.77976			0.0575917
$956$		0			0
$957$	4.48988	−	2.97973i	0.145137	−	0.0963208i
$958$		0			0
$959$	−44.1090	+	25.4663i	−1.42435	+	0.822350i
$960$		0			0
$961$	−18.2601	+	31.6273i	−0.589034	+	1.02024i
$962$		0			0
$963$	−39.6468	+	4.96694i	−1.27760	+	0.160057i
$964$		0			0
$965$	1.15977	−	2.00878i	0.0373343	−	0.0646649i
$966$		0			0
$967$	17.2809	+	29.9315i	0.555717	+	0.962531i	0.997847	+	0.0655798i	$0.0208897\pi$
$967$	17.2809	+	29.9315i	0.555717	+	0.962531i	−0.442130	+	0.896951i	$0.645777\pi$
$968$		0			0
$969$	0.230378	+	3.69219i	0.00740080	+	0.118610i
$970$		0			0
$971$	−49.9253			−1.60218			−0.801090	−	0.598545i	$-0.795746\pi$
$971$	−49.9253			−1.60218			−0.801090	+	0.598545i	$0.795746\pi$
$972$		0			0
$973$		−	23.9959i		−	0.769274i
$974$		0			0
$975$	1.20099	−	0.0749369i	0.0384625	−	0.00239990i
$976$		0			0
$977$	25.3322	+	43.8766i	0.810448	+	1.40374i	0.912551	+	0.408964i	$0.134110\pi$
$977$	25.3322	+	43.8766i	0.810448	+	1.40374i	−0.102102	+	0.994774i	$0.532557\pi$
$978$		0			0
$979$	−4.05077	+	7.01614i	−0.129463	+	0.224237i
$980$		0			0
$981$	−4.52473	−	36.1171i	−0.144464	−	1.15313i
$982$		0			0
$983$	−4.37990	+	7.58621i	−0.139697	+	0.241963i	−0.927382	−	0.374116i	$-0.877946\pi$
$983$	−4.37990	+	7.58621i	−0.139697	+	0.241963i	0.787685	+	0.616078i	$0.211280\pi$
$984$		0			0
$985$	40.2168	−	23.2192i	1.28141	−	0.739824i
$986$		0			0
$987$	10.9234	+	16.4594i	0.347694	+	0.523909i
$988$		0			0
$989$	−23.0120	−	6.11006i	−0.731739	−	0.194289i
$990$		0			0
$991$	−8.79842			−0.279491			−0.139746	−	0.990187i	$-0.544628\pi$
$991$	−8.79842			−0.279491			−0.139746	+	0.990187i	$0.544628\pi$
$992$		0			0
$993$	−8.30926	+	16.7172i	−0.263686	+	0.530504i
$994$		0			0
$995$	24.9378	−	14.3979i	0.790582	−	0.456443i
$996$		0			0
$997$	−17.7990	+	30.8288i	−0.563700	+	0.976358i	0.433469	+	0.901168i	$0.357289\pi$
$997$	−17.7990	+	30.8288i	−0.563700	+	0.976358i	−0.997169	+	0.0751891i	$0.976044\pi$
$998$		0			0
$999$	2.79828	+	14.7936i	0.0885335	+	0.468050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.k.a.137.2	yes	48
3.2	odd	2		2484.2.k.a.413.8		48
9.2	odd	6		7452.2.g.b.3725.33		48
9.4	even	3		2484.2.k.a.2069.17		48
9.5	odd	6	inner	828.2.k.a.689.1	yes	48
9.7	even	3		7452.2.g.b.3725.15		48
23.22	odd	2	inner	828.2.k.a.137.1	✓	48
69.68	even	2		2484.2.k.a.413.17		48
207.22	odd	6		2484.2.k.a.2069.8		48
207.68	even	6	inner	828.2.k.a.689.2	yes	48
207.137	even	6		7452.2.g.b.3725.16		48
207.160	odd	6		7452.2.g.b.3725.34		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
828.2.k.a.137.1	✓	48	23.22	odd	2	inner
828.2.k.a.137.2	yes	48	1.1	even	1	trivial
828.2.k.a.689.1	yes	48	9.5	odd	6	inner
828.2.k.a.689.2	yes	48	207.68	even	6	inner
2484.2.k.a.413.8		48	3.2	odd	2
2484.2.k.a.413.17		48	69.68	even	2
2484.2.k.a.2069.8		48	207.22	odd	6
2484.2.k.a.2069.17		48	9.4	even	3
7452.2.g.b.3725.15		48	9.7	even	3
7452.2.g.b.3725.16		48	207.137	even	6
7452.2.g.b.3725.33		48	9.2	odd	6
7452.2.g.b.3725.34		48	207.160	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72869 + 0.107863i) q^{3} +(0.921249 + 1.59565i) q^{5} +(4.26677 + 2.46342i) q^{7} +(2.97673 - 0.372924i) q^{9} +O(q^{10})\)	\(q+(-1.72869 + 0.107863i) q^{3} +(0.921249 + 1.59565i) q^{5} +(4.26677 + 2.46342i) q^{7} +(2.97673 - 0.372924i) q^{9} +(-0.542236 + 0.939180i) q^{11} +(-0.216403 - 0.374821i) q^{13} +(-1.76466 - 2.65901i) q^{15} +0.955596 q^{17} -2.23508i q^{19} +(-7.64163 - 3.79826i) q^{21} +(-4.62959 + 1.25177i) q^{23} +(0.802602 - 1.39015i) q^{25} +(-5.10562 + 0.965748i) q^{27} +(2.48447 + 1.43441i) q^{29} +(4.10853 + 7.11618i) q^{31} +(0.836054 - 1.68204i) q^{33} +9.07769i q^{35} -2.89752i q^{37} +(0.414522 + 0.624606i) q^{39} +(-2.06515 + 1.19231i) q^{41} +(4.29946 + 2.48229i) q^{43} +(3.33736 + 4.40626i) q^{45} +(-2.00476 - 1.15745i) q^{47} +(8.63688 + 14.9595i) q^{49} +(-1.65193 + 0.103074i) q^{51} +9.13609 q^{53} -1.99814 q^{55} +(0.241083 + 3.86376i) q^{57} +(-8.20007 + 4.73431i) q^{59} +(-7.72175 - 4.45815i) q^{61} +(13.6197 + 5.74176i) q^{63} +(0.398722 - 0.690606i) q^{65} +(-7.97045 + 4.60174i) q^{67} +(7.86809 - 2.66328i) q^{69} +7.27620i q^{71} +8.59659 q^{73} +(-1.23750 + 2.48970i) q^{75} +(-4.62719 + 2.67151i) q^{77} +(7.30210 + 4.21587i) q^{79} +(8.72186 - 2.22019i) q^{81} +(-0.667479 + 1.15611i) q^{83} +(0.880342 + 1.52480i) q^{85} +(-4.44959 - 2.21166i) q^{87} +7.47049 q^{89} -2.13236i q^{91} +(-7.86995 - 11.8585i) q^{93} +(3.56640 - 2.05906i) q^{95} +(-6.85638 - 3.95853i) q^{97} +(-1.26385 + 2.99790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 48 * q - 2 * q^3 + 6 * q^9	\( 48 q - 2 q^{3} + 6 q^{9} + 21 q^{23} - 30 q^{25} - 2 q^{27} - 6 q^{29} - 6 q^{31} - 18 q^{39} - 12 q^{41} - 48 q^{47} + 12 q^{49} - 12 q^{55} - 36 q^{59} + 11 q^{69} + 64 q^{75} + 30 q^{77} - 26 q^{81} - 4 q^{87} + 38 q^{93} - 84 q^{95}+O(q^{100}) \) 48 * q - 2 * q^3 + 6 * q^9 + 21 * q^23 - 30 * q^25 - 2 * q^27 - 6 * q^29 - 6 * q^31 - 18 * q^39 - 12 * q^41 - 48 * q^47 + 12 * q^49 - 12 * q^55 - 36 * q^59 + 11 * q^69 + 64 * q^75 + 30 * q^77 - 26 * q^81 - 4 * q^87 + 38 * q^93 - 84 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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