LMFDB - Embedded newform 572.2.bc.a.197.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(197,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 1]))

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

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

chi := DirichletCharacter("572.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bc (of order $12$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.12
Character	$\chi$	$=$	572.197
Dual form			572.2.bc.a.241.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26462 + 2.19039i) q^{3} +(-2.02978 + 2.02978i) q^{5} +(0.531478 + 1.98350i) q^{7} +(-1.69853 + 2.94193i) q^{9} +O(q^{10})$	\(q+(1.26462 + 2.19039i) q^{3} +(-2.02978 + 2.02978i) q^{5} +(0.531478 + 1.98350i) q^{7} +(-1.69853 + 2.94193i) q^{9} +(2.90356 + 1.60292i) q^{11} +(2.33081 - 2.75088i) q^{13} +(-7.01289 - 1.87910i) q^{15} +(2.26694 - 3.92646i) q^{17} +(-7.10628 + 1.90412i) q^{19} +(-3.67252 + 3.67252i) q^{21} +(-6.29301 + 3.63327i) q^{23} -3.23998i q^{25} -1.00424 q^{27} +(0.274080 - 0.158240i) q^{29} +(-0.786368 + 0.786368i) q^{31} +(0.160875 + 8.38700i) q^{33} +(-5.10484 - 2.94728i) q^{35} +(0.846685 - 3.15987i) q^{37} +(8.97307 + 1.62655i) q^{39} +(-1.33024 + 4.96454i) q^{41} +(3.58914 - 6.21656i) q^{43} +(-2.52384 - 9.41909i) q^{45} +(2.07971 + 2.07971i) q^{47} +(2.41037 - 1.39163i) q^{49} +11.4673 q^{51} -2.49105 q^{53} +(-9.14714 + 2.63999i) q^{55} +(-13.1575 - 13.1575i) q^{57} +(10.3192 - 2.76501i) q^{59} +(-1.95816 - 1.13055i) q^{61} +(-6.73806 - 1.80546i) q^{63} +(0.852653 + 10.3147i) q^{65} +(10.4665 + 2.80448i) q^{67} +(-15.9165 - 9.18941i) q^{69} +(3.96957 + 14.8146i) q^{71} +(6.53364 - 6.53364i) q^{73} +(7.09680 - 4.09734i) q^{75} +(-1.63623 + 6.61112i) q^{77} -12.6659i q^{79} +(3.82560 + 6.62613i) q^{81} +(9.00716 + 9.00716i) q^{83} +(3.36845 + 12.5712i) q^{85} +(0.693214 + 0.400227i) q^{87} +(-2.51893 + 9.40078i) q^{89} +(6.69514 + 3.16113i) q^{91} +(-2.71691 - 0.727993i) q^{93} +(10.5592 - 18.2891i) q^{95} +(-1.82938 - 6.82732i) q^{97} +(-9.64746 + 5.81946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^9	$ 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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
$3$	1.26462	+	2.19039i	0.730129	+	1.26462i	0.956828	+	0.290655i	$0.0938732\pi$
$3$	1.26462	+	2.19039i	0.730129	+	1.26462i	−0.226699	+	0.973965i	$0.572794\pi$
$4$		0			0
$5$	−2.02978	+	2.02978i	−0.907743	+	0.907743i	−0.996090	−	0.0883465i	$-0.971842\pi$
$5$	−2.02978	+	2.02978i	−0.907743	+	0.907743i	0.0883465	+	0.996090i	$0.471842\pi$
$6$		0			0
$7$	0.531478	+	1.98350i	0.200880	+	0.749693i	0.990666	+	0.136311i	$0.0435247\pi$
$7$	0.531478	+	1.98350i	0.200880	+	0.749693i	−0.789786	+	0.613382i	$0.789809\pi$
$8$		0			0
$9$	−1.69853	+	2.94193i	−0.566175	+	0.980644i
$10$		0			0
$11$	2.90356	+	1.60292i	0.875455	+	0.483299i
$11$	2.90356	+	1.60292i	0.875455	+	0.483299i
$12$		0			0
$13$	2.33081	−	2.75088i	0.646450	−	0.762957i
$13$	2.33081	−	2.75088i	0.646450	−	0.762957i
$14$		0			0
$15$	−7.01289	−	1.87910i	−1.81072	−	0.485181i
$16$		0			0
$17$	2.26694	−	3.92646i	0.549814	−	0.952306i	−0.448473	−	0.893796i	$-0.648032\pi$
$17$	2.26694	−	3.92646i	0.549814	−	0.952306i	0.998287	−	0.0585093i	$-0.0186347\pi$
$18$		0			0
$19$	−7.10628	+	1.90412i	−1.63029	+	0.436836i	−0.954002	−	0.299799i	$-0.903080\pi$
$19$	−7.10628	+	1.90412i	−1.63029	+	0.436836i	−0.676290	+	0.736635i	$0.736414\pi$
$20$		0			0
$21$	−3.67252	+	3.67252i	−0.801409	+	0.801409i
$22$		0			0
$23$	−6.29301	+	3.63327i	−1.31218	+	0.757589i	−0.982457	−	0.186487i	$-0.940290\pi$
$23$	−6.29301	+	3.63327i	−1.31218	+	0.757589i	−0.329726	+	0.944077i	$0.606956\pi$
$24$		0			0
$25$		−	3.23998i		−	0.647996i
$26$		0			0
$27$	−1.00424			−0.193266
$28$		0			0
$29$	0.274080	−	0.158240i	0.0508954	−	0.0293845i	−0.474336	−	0.880344i	$-0.657312\pi$
$29$	0.274080	−	0.158240i	0.0508954	−	0.0293845i	0.525232	+	0.850959i	$0.323979\pi$
$30$		0			0
$31$	−0.786368	+	0.786368i	−0.141236	+	0.141236i	−0.774190	−	0.632954i	$-0.781842\pi$
$31$	−0.786368	+	0.786368i	−0.141236	+	0.141236i	0.632954	+	0.774190i	$0.281842\pi$
$32$		0			0
$33$	0.160875	+	8.38700i	0.0280047	+	1.45999i
$34$		0			0
$35$	−5.10484	−	2.94728i	−0.862876	−	0.498182i
$36$		0			0
$37$	0.846685	−	3.15987i	0.139194	−	0.519480i	−0.860751	−	0.509026i	$-0.830006\pi$
$37$	0.846685	−	3.15987i	0.139194	−	0.519480i	0.999945	−	0.0104539i	$-0.00332765\pi$
$38$		0			0
$39$	8.97307	+	1.62655i	1.43684	+	0.260456i
$40$		0			0
$41$	−1.33024	+	4.96454i	−0.207749	+	0.775331i	0.780845	+	0.624725i	$0.214789\pi$
$41$	−1.33024	+	4.96454i	−0.207749	+	0.775331i	−0.988594	+	0.150606i	$0.951878\pi$
$42$		0			0
$43$	3.58914	−	6.21656i	0.547338	−	0.948017i	−0.451118	−	0.892464i	$-0.648975\pi$
$43$	3.58914	−	6.21656i	0.547338	−	0.948017i	0.998456	−	0.0555528i	$-0.0176921\pi$
$44$		0			0
$45$	−2.52384	−	9.41909i	−0.376232	−	1.40412i
$46$		0			0
$47$	2.07971	+	2.07971i	0.303357	+	0.303357i	0.842326	−	0.538969i	$-0.181186\pi$
$47$	2.07971	+	2.07971i	0.303357	+	0.303357i	−0.538969	+	0.842326i	$0.681186\pi$
$48$		0			0
$49$	2.41037	−	1.39163i	0.344338	−	0.198804i
$50$		0			0
$51$	11.4673			1.60574
$52$		0			0
$53$	−2.49105			−0.342173			−0.171086	−	0.985256i	$-0.554728\pi$
$53$	−2.49105			−0.342173			−0.171086	+	0.985256i	$0.554728\pi$
$54$		0			0
$55$	−9.14714	+	2.63999i	−1.23340	+	0.355977i
$56$		0			0
$57$	−13.1575	−	13.1575i	−1.74275	−	1.74275i
$58$		0			0
$59$	10.3192	−	2.76501i	1.34344	−	0.359974i	0.485730	−	0.874109i	$-0.338554\pi$
$59$	10.3192	−	2.76501i	1.34344	−	0.359974i	0.857709	+	0.514135i	$0.171887\pi$
$60$		0			0
$61$	−1.95816	−	1.13055i	−0.250717	−	0.144752i	0.369375	−	0.929280i	$-0.379572\pi$
$61$	−1.95816	−	1.13055i	−0.250717	−	0.144752i	−0.620093	+	0.784529i	$0.712905\pi$
$62$		0			0
$63$	−6.73806	−	1.80546i	−0.848915	−	0.227466i
$64$		0			0
$65$	0.852653	+	10.3147i	0.105759	+	1.27938i
$66$		0			0
$67$	10.4665	+	2.80448i	1.27868	+	0.342622i	0.833351	−	0.552744i	$-0.186419\pi$
$67$	10.4665	+	2.80448i	1.27868	+	0.342622i	0.445331	+	0.895366i	$0.353086\pi$
$68$		0			0
$69$	−15.9165	−	9.18941i	−1.91612	−	1.10628i
$70$		0			0
$71$	3.96957	+	14.8146i	0.471101	+	1.75817i	0.635826	+	0.771832i	$0.280660\pi$
$71$	3.96957	+	14.8146i	0.471101	+	1.75817i	−0.164725	+	0.986339i	$0.552674\pi$
$72$		0			0
$73$	6.53364	−	6.53364i	0.764705	−	0.764705i	−0.212464	−	0.977169i	$-0.568149\pi$
$73$	6.53364	−	6.53364i	0.764705	−	0.764705i	0.977169	+	0.212464i	$0.0681487\pi$
$74$		0			0
$75$	7.09680	−	4.09734i	0.819468	−	0.473120i
$76$		0			0
$77$	−1.63623	+	6.61112i	−0.186465	+	0.753408i
$78$		0			0
$79$		−	12.6659i		−	1.42502i	−0.701662	−	0.712510i	$-0.747558\pi$
$79$		−	12.6659i		−	1.42502i	0.701662	−	0.712510i	$-0.252442\pi$
$80$		0			0
$81$	3.82560	+	6.62613i	0.425066	+	0.736236i
$82$		0			0
$83$	9.00716	+	9.00716i	0.988664	+	0.988664i	0.999936	−	0.0112725i	$-0.00358822\pi$
$83$	9.00716	+	9.00716i	0.988664	+	0.988664i	−0.0112725	+	0.999936i	$0.503588\pi$
$84$		0			0
$85$	3.36845	+	12.5712i	0.365359	+	1.36354i
$86$		0			0
$87$	0.693214	+	0.400227i	0.0743204	+	0.0429089i
$88$		0			0
$89$	−2.51893	+	9.40078i	−0.267006	+	0.996481i	0.694005	+	0.719970i	$0.255845\pi$
$89$	−2.51893	+	9.40078i	−0.267006	+	0.996481i	−0.961011	+	0.276510i	$0.910822\pi$
$90$		0			0
$91$	6.69514	+	3.16113i	0.701842	+	0.331376i
$92$		0			0
$93$	−2.71691	−	0.727993i	−0.281730	−	0.0754894i
$94$		0			0
$95$	10.5592	−	18.2891i	1.08335	−	1.87642i
$96$		0			0
$97$	−1.82938	−	6.82732i	−0.185745	−	0.693210i	−0.994470	−	0.105023i	$-0.966509\pi$
$97$	−1.82938	−	6.82732i	−0.185745	−	0.693210i	0.808725	−	0.588187i	$-0.200158\pi$
$98$		0			0
$99$	−9.64746	+	5.81946i	−0.969606	+	0.584878i
$100$		0			0
$101$	2.57150	+	4.45396i	0.255874	+	0.443186i	0.965132	−	0.261762i	$-0.0843036\pi$
$101$	2.57150	+	4.45396i	0.255874	+	0.443186i	−0.709259	+	0.704948i	$0.750970\pi$
$102$		0			0
$103$			7.37981i			0.727154i	0.931564	+	0.363577i	$0.118445\pi$
$103$			7.37981i			0.727154i	−0.931564	+	0.363577i	$0.881555\pi$
$104$		0			0
$105$		−	14.9088i		−	1.45495i
$106$		0			0
$107$	−8.41606	+	4.85901i	−0.813611	+	0.469739i	−0.848208	−	0.529663i	$-0.822318\pi$
$107$	−8.41606	+	4.85901i	−0.813611	+	0.469739i	0.0345972	+	0.999401i	$0.488985\pi$
$108$		0			0
$109$	−7.32628	−	7.32628i	−0.701731	−	0.701731i	0.263051	−	0.964782i	$-0.415271\pi$
$109$	−7.32628	−	7.32628i	−0.701731	−	0.701731i	−0.964782	+	0.263051i	$0.915271\pi$
$110$		0			0
$111$	7.99208	−	2.14147i	0.758574	−	0.203259i
$112$		0			0
$113$	−1.64324	+	2.84617i	−0.154583	+	0.267745i	−0.932907	−	0.360117i	$-0.882737\pi$
$113$	−1.64324	+	2.84617i	−0.154583	+	0.267745i	0.778324	+	0.627863i	$0.216070\pi$
$114$		0			0
$115$	5.39867	−	20.1481i	0.503429	−	1.87882i
$116$		0			0
$117$	4.13397	+	11.5295i	0.382185	+	1.06590i
$118$		0			0
$119$	8.99296	+	2.40966i	0.824383	+	0.220893i
$120$		0			0
$121$	5.86128	+	9.30835i	0.532843	+	0.846214i
$122$		0			0
$123$	−12.5565	+	3.36451i	−1.13218	+	0.303367i
$124$		0			0
$125$	−3.57245	−	3.57245i	−0.319529	−	0.319529i
$126$		0			0
$127$	6.73808	+	11.6707i	0.597908	+	1.03561i	0.993129	+	0.117021i	$0.0373345\pi$
$127$	6.73808	+	11.6707i	0.597908	+	1.03561i	−0.395221	+	0.918586i	$0.629332\pi$
$128$		0			0
$129$	18.1556			1.59851
$130$		0			0
$131$		−	19.6735i		−	1.71888i	−0.511233	−	0.859442i	$-0.670811\pi$
$131$		−	19.6735i		−	1.71888i	0.511233	−	0.859442i	$-0.329189\pi$
$132$		0			0
$133$	−7.55366	−	13.0833i	−0.654985	−	1.13447i
$134$		0			0
$135$	2.03838	−	2.03838i	0.175436	−	0.175436i
$136$		0			0
$137$	−4.36687	+	1.17010i	−0.373087	+	0.0999683i	−0.440490	−	0.897758i	$-0.645195\pi$
$137$	−4.36687	+	1.17010i	−0.373087	+	0.0999683i	0.0674032	+	0.997726i	$0.478529\pi$
$138$		0			0
$139$	−8.12319	−	4.68993i	−0.689000	−	0.397794i	0.114237	−	0.993454i	$-0.463558\pi$
$139$	−8.12319	−	4.68993i	−0.689000	−	0.397794i	−0.803237	+	0.595659i	$0.796891\pi$
$140$		0			0
$141$	−1.92533	+	7.18541i	−0.162142	+	0.605121i
$142$		0			0
$143$	11.1771	−	4.25123i	0.934674	−	0.355506i
$144$		0			0
$145$	−0.235129	+	0.877513i	−0.0195264	+	0.0728735i
$146$		0			0
$147$	6.09640	+	3.51976i	0.502823	+	0.290305i
$148$		0			0
$149$	5.60582	−	1.50208i	0.459247	−	0.123055i	−0.0217759	−	0.999763i	$-0.506932\pi$
$149$	5.60582	−	1.50208i	0.459247	−	0.123055i	0.481023	+	0.876708i	$0.340265\pi$
$150$		0			0
$151$	−10.5401	+	10.5401i	−0.857741	+	0.857741i	−0.991072	−	0.133331i	$-0.957433\pi$
$151$	−10.5401	+	10.5401i	−0.857741	+	0.857741i	0.133331	+	0.991072i	$0.457433\pi$
$152$		0			0
$153$	7.70092	+	13.3384i	0.622582	+	1.07834i
$154$		0			0
$155$		−	3.19230i		−	0.256412i
$156$		0			0
$157$	8.98932			0.717426			0.358713	−	0.933448i	$-0.383216\pi$
$157$	8.98932			0.717426			0.358713	+	0.933448i	$0.383216\pi$
$158$		0			0
$159$	−3.15024	−	5.45637i	−0.249830	−	0.432718i
$160$		0			0
$161$	−10.5512	−	10.5512i	−0.831550	−	0.831550i
$162$		0			0
$163$	−5.61458	+	1.50442i	−0.439768	+	0.117835i	−0.471908	−	0.881648i	$-0.656434\pi$
$163$	−5.61458	+	1.50442i	−0.439768	+	0.117835i	0.0321398	+	0.999483i	$0.489768\pi$
$164$		0			0
$165$	−17.3503	−	16.6972i	−1.35072	−	1.29987i
$166$		0			0
$167$	−0.690976	−	0.185147i	−0.0534694	−	0.0143271i	0.231985	−	0.972719i	$-0.425478\pi$
$167$	−0.690976	−	0.185147i	−0.0534694	−	0.0143271i	−0.285455	+	0.958392i	$0.592145\pi$
$168$		0			0
$169$	−2.13468	−	12.8235i	−0.164206	−	0.986426i
$170$		0			0
$171$	6.46840	−	24.1404i	0.494651	−	1.84606i
$172$		0			0
$173$	−1.68670	+	2.92146i	−0.128238	+	0.222114i	−0.922994	−	0.384815i	$-0.874265\pi$
$173$	−1.68670	+	2.92146i	−0.128238	+	0.222114i	0.794756	+	0.606929i	$0.207599\pi$
$174$		0			0
$175$	6.42650	−	1.72198i	0.485798	−	0.130169i
$176$		0			0
$177$	19.1062	+	19.1062i	1.43611	+	1.43611i
$178$		0			0
$179$	23.1511	−	13.3663i	1.73039	−	0.999042i	0.843320	−	0.537412i	$-0.180598\pi$
$179$	23.1511	−	13.3663i	1.73039	−	0.999042i	0.887072	−	0.461631i	$-0.152736\pi$
$180$		0			0
$181$		−	18.0605i		−	1.34242i	−0.741266	−	0.671211i	$-0.765774\pi$
$181$		−	18.0605i		−	1.34242i	0.741266	−	0.671211i	$-0.234226\pi$
$182$		0			0
$183$		−	5.71885i		−	0.422749i
$184$		0			0
$185$	4.69525	+	8.13242i	0.345202	+	0.597907i
$186$		0			0
$187$	12.8760	−	7.76696i	0.941586	−	0.567976i
$188$		0			0
$189$	−0.533731	−	1.99191i	−0.0388232	−	0.144890i
$190$		0			0
$191$	8.17760	−	14.1640i	0.591710	−	1.02487i	−0.402292	−	0.915512i	$-0.631786\pi$
$191$	8.17760	−	14.1640i	0.591710	−	1.02487i	0.994002	−	0.109361i	$-0.0348804\pi$
$192$		0			0
$193$	14.6397	+	3.92269i	1.05379	+	0.282361i	0.743816	−	0.668385i	$-0.233014\pi$
$193$	14.6397	+	3.92269i	1.05379	+	0.282361i	0.309971	+	0.950746i	$0.399681\pi$
$194$		0			0
$195$	−21.5149	+	14.9118i	−1.54071	+	1.06786i
$196$		0			0
$197$	−1.16396	+	4.34397i	−0.0829290	+	0.309495i	−0.994914	−	0.100728i	$-0.967883\pi$
$197$	−1.16396	+	4.34397i	−0.0829290	+	0.309495i	0.911985	+	0.410224i	$0.134549\pi$
$198$		0			0
$199$	−2.56131	−	1.47877i	−0.181566	−	0.104827i	0.406462	−	0.913668i	$-0.366762\pi$
$199$	−2.56131	−	1.47877i	−0.181566	−	0.104827i	−0.588028	+	0.808840i	$0.700096\pi$
$200$		0			0
$201$	7.09320	+	26.4722i	0.500316	+	1.86720i
$202$		0			0
$203$	0.459537	+	0.459537i	0.0322532	+	0.0322532i
$204$		0			0
$205$	−7.37680	−	12.7770i	−0.515218	−	0.892384i
$206$		0			0
$207$		−	24.6848i		−	1.71571i
$208$		0			0
$209$	−23.6856	−	5.86210i	−1.63837	−	0.405490i
$210$		0			0
$211$	22.2739	−	12.8598i	1.53340	−	0.885308i	0.534196	−	0.845361i	$-0.320614\pi$
$211$	22.2739	−	12.8598i	1.53340	−	0.885308i	0.999202	−	0.0399471i	$-0.0127190\pi$
$212$		0			0
$213$	−27.4297	+	27.4297i	−1.87945	+	1.87945i
$214$		0			0
$215$	5.33309	+	19.9034i	0.363714	+	1.35740i
$216$		0			0
$217$	−1.97770	−	1.14183i	−0.134255	−	0.0775122i
$218$		0			0
$219$	22.5738	+	6.04863i	1.52539	+	0.408728i
$220$		0			0
$221$	−5.51741	−	15.3879i	−0.371141	−	1.03510i
$222$		0			0
$223$	−19.0057	−	5.09257i	−1.27272	−	0.341024i	−0.441646	−	0.897189i	$-0.645605\pi$
$223$	−19.0057	−	5.09257i	−1.27272	−	0.341024i	−0.831072	+	0.556165i	$0.812272\pi$
$224$		0			0
$225$	9.53180	+	5.50319i	0.635454	+	0.366879i
$226$		0			0
$227$	−20.0730	+	5.37855i	−1.33229	+	0.356987i	−0.853569	−	0.520979i	$-0.825567\pi$
$227$	−20.0730	+	5.37855i	−1.33229	+	0.356987i	−0.478723	+	0.877966i	$0.658900\pi$
$228$		0			0
$229$	−17.6301	−	17.6301i	−1.16503	−	1.16503i	−0.983360	−	0.181669i	$-0.941850\pi$
$229$	−17.6301	−	17.6301i	−1.16503	−	1.16503i	−0.181669	−	0.983360i	$-0.558150\pi$
$230$		0			0
$231$	−16.5501	+	4.77659i	−1.08892	+	0.314277i
$232$		0			0
$233$	−18.5673			−1.21638			−0.608191	−	0.793791i	$-0.708104\pi$
$233$	−18.5673			−1.21638			−0.608191	+	0.793791i	$0.708104\pi$
$234$		0			0
$235$	−8.44270			−0.550741
$236$		0			0
$237$	27.7431	−	16.0175i	1.80211	−	1.04045i
$238$		0			0
$239$	0.791909	+	0.791909i	0.0512243	+	0.0512243i	0.732255	−	0.681031i	$-0.238468\pi$
$239$	0.791909	+	0.791909i	0.0512243	+	0.0512243i	−0.681031	+	0.732255i	$0.738468\pi$
$240$		0			0
$241$	4.38963	+	16.3823i	0.282761	+	1.05528i	0.950460	+	0.310847i	$0.100613\pi$
$241$	4.38963	+	16.3823i	0.282761	+	1.05528i	−0.667699	+	0.744432i	$0.732721\pi$
$242$		0			0
$243$	−11.1822	+	19.3682i	−0.717339	+	1.24247i
$244$		0			0
$245$	−2.06782	+	7.71720i	−0.132108	+	0.493034i
$246$		0			0
$247$	−11.3254	+	23.9867i	−0.720615	+	1.52623i
$248$		0			0
$249$	−8.33852	+	31.1198i	−0.528432	+	1.97214i
$250$		0			0
$251$	14.0713	+	8.12410i	0.888176	+	0.512788i	0.873345	−	0.487102i	$-0.161946\pi$
$251$	14.0713	+	8.12410i	0.888176	+	0.512788i	0.0148304	+	0.999890i	$0.495279\pi$
$252$		0			0
$253$	−24.0960	+	0.462195i	−1.51490	+	0.0290579i
$254$		0			0
$255$	−23.2760	+	23.2760i	−1.45760	+	1.45760i
$256$		0			0
$257$	−7.44450	+	4.29808i	−0.464375	+	0.268107i	−0.713882	−	0.700266i	$-0.753065\pi$
$257$	−7.44450	+	4.29808i	−0.464375	+	0.268107i	0.249507	+	0.968373i	$0.419731\pi$
$258$		0			0
$259$	6.71761			0.417412
$260$		0			0
$261$			1.07510i			0.0665470i
$262$		0			0
$263$	11.5757	−	6.68325i	0.713790	−	0.412107i	−0.0986729	−	0.995120i	$-0.531460\pi$
$263$	11.5757	−	6.68325i	0.713790	−	0.412107i	0.812463	+	0.583013i	$0.198126\pi$
$264$		0			0
$265$	5.05628	−	5.05628i	0.310605	−	0.310605i
$266$		0			0
$267$	−23.7768	+	6.37098i	−1.45512	+	0.389898i
$268$		0			0
$269$	−3.52820	+	6.11102i	−0.215118	+	0.372596i	−0.953309	−	0.301996i	$-0.902347\pi$
$269$	−3.52820	+	6.11102i	−0.215118	+	0.372596i	0.738191	+	0.674592i	$0.235680\pi$
$270$		0			0
$271$	−4.28297	−	1.14762i	−0.260172	−	0.0697128i	0.126375	−	0.991983i	$-0.459666\pi$
$271$	−4.28297	−	1.14762i	−0.260172	−	0.0697128i	−0.386547	+	0.922270i	$0.626332\pi$
$272$		0			0
$273$	1.54272	+	18.6626i	0.0933698	+	1.12951i
$274$		0			0
$275$	5.19344	−	9.40746i	0.313176	−	0.567291i
$276$		0			0
$277$	−7.36097	+	12.7496i	−0.442278	+	0.766047i	−0.997858	−	0.0654153i	$-0.979163\pi$
$277$	−7.36097	+	12.7496i	−0.442278	+	0.766047i	0.555580	+	0.831463i	$0.312496\pi$
$278$		0			0
$279$	−0.977776	−	3.64911i	−0.0585379	−	0.218467i
$280$		0			0
$281$	20.5824	−	20.5824i	1.22784	−	1.22784i	0.263066	−	0.964778i	$-0.415266\pi$
$281$	20.5824	−	20.5824i	1.22784	−	1.22784i	0.964778	−	0.263066i	$-0.0847339\pi$
$282$		0			0
$283$	−9.38571	−	16.2565i	−0.557923	−	0.966351i	−0.997670	−	0.0682289i	$-0.978265\pi$
$283$	−9.38571	−	16.2565i	−0.557923	−	0.966351i	0.439747	−	0.898122i	$-0.355068\pi$
$284$		0			0
$285$	53.4136			3.16395
$286$		0			0
$287$	−10.5542			−0.622993
$288$		0			0
$289$	−1.77804	−	3.07966i	−0.104591	−	0.181157i
$290$		0			0
$291$	12.6410	−	12.6410i	0.741029	−	0.741029i
$292$		0			0
$293$	0.272681	+	1.01766i	0.0159302	+	0.0594524i	0.973433	−	0.228970i	$-0.0735359\pi$
$293$	0.272681	+	1.01766i	0.0159302	+	0.0594524i	−0.957503	+	0.288423i	$0.906869\pi$
$294$		0			0
$295$	−15.3332	+	26.5579i	−0.892735	+	1.54626i
$296$		0			0
$297$	−2.91587	−	1.60972i	−0.169196	−	0.0934053i
$298$		0			0
$299$	−4.67310	+	25.7798i	−0.270252	+	1.49088i
$300$		0			0
$301$	14.2381	+	3.81509i	0.820671	+	0.219898i
$302$		0			0
$303$	−6.50393	+	11.2651i	−0.373641	+	0.647166i
$304$		0			0
$305$	6.26939	−	1.67988i	0.358984	−	0.0961895i
$306$		0			0
$307$	9.42385	−	9.42385i	0.537847	−	0.537847i	−0.385049	−	0.922896i	$-0.625815\pi$
$307$	9.42385	−	9.42385i	0.537847	−	0.537847i	0.922896	+	0.385049i	$0.125815\pi$
$308$		0			0
$309$	−16.1646	+	9.33265i	−0.919573	+	0.530916i
$310$		0			0
$311$			21.8393i			1.23839i	0.785236	+	0.619197i	$0.212542\pi$
$311$			21.8393i			1.23839i	−0.785236	+	0.619197i	$0.787458\pi$
$312$		0			0
$313$	11.0248			0.623161			0.311581	−	0.950220i	$-0.399142\pi$
$313$	11.0248			0.623161			0.311581	+	0.950220i	$0.399142\pi$
$314$		0			0
$315$	17.3414	−	10.0121i	0.977078	−	0.564116i
$316$		0			0
$317$	0.779791	−	0.779791i	0.0437974	−	0.0437974i	−0.684869	−	0.728666i	$-0.740141\pi$
$317$	0.779791	−	0.779791i	0.0437974	−	0.0437974i	0.728666	+	0.684869i	$0.240141\pi$
$318$		0			0
$319$	1.04945	−	0.0201300i	0.0587581	−	0.00112706i
$320$		0			0
$321$	−21.2862	−	12.2896i	−1.18808	−	0.685939i
$322$		0			0
$323$	−8.63307	+	32.2190i	−0.480357	+	1.79272i
$324$		0			0
$325$	−8.91279	−	7.55177i	−0.494393	−	0.418897i
$326$		0			0
$327$	6.78242	−	25.3123i	0.375069	−	1.39978i
$328$		0			0
$329$	−3.01979	+	5.23043i	−0.166486	+	0.288363i
$330$		0			0
$331$	−2.16819	−	8.09180i	−0.119175	−	0.444766i	0.880391	−	0.474249i	$-0.157280\pi$
$331$	−2.16819	−	8.09180i	−0.119175	−	0.444766i	−0.999565	+	0.0294836i	$0.990614\pi$
$332$		0			0
$333$	7.85802	+	7.85802i	0.430617	+	0.430617i
$334$		0			0
$335$	−26.9370	+	15.5521i	−1.47173	+	0.849702i
$336$		0			0
$337$	14.6335			0.797136			0.398568	−	0.917139i	$-0.369507\pi$
$337$	14.6335			0.797136			0.398568	+	0.917139i	$0.369507\pi$
$338$		0			0
$339$	−8.31228			−0.451461
$340$		0			0
$341$	−3.54375	+	1.02278i	−0.191905	+	0.0553865i
$342$		0			0
$343$	14.2055	+	14.2055i	0.767026	+	0.767026i
$344$		0			0
$345$	50.9594	−	13.6545i	2.74356	−	0.735136i
$346$		0			0
$347$	−21.7467	−	12.5555i	−1.16743	−	0.674014i	−0.214354	−	0.976756i	$-0.568765\pi$
$347$	−21.7467	−	12.5555i	−1.16743	−	0.674014i	−0.953073	+	0.302742i	$0.902098\pi$
$348$		0			0
$349$	−27.3181	−	7.31987i	−1.46231	−	0.391824i	−0.562021	−	0.827123i	$-0.689976\pi$
$349$	−27.3181	−	7.31987i	−1.46231	−	0.391824i	−0.900286	+	0.435299i	$0.856643\pi$
$350$		0			0
$351$	−2.34069	+	2.76254i	−0.124937	+	0.147454i
$352$		0			0
$353$	−9.14142	−	2.44944i	−0.486549	−	0.130370i	0.00720150	−	0.999974i	$-0.497708\pi$
$353$	−9.14142	−	2.44944i	−0.486549	−	0.130370i	−0.493750	+	0.869604i	$0.664374\pi$
$354$		0			0
$355$	−38.1277	−	22.0130i	−2.02361	−	1.16833i
$356$		0			0
$357$	6.09460	+	22.7454i	0.322560	+	1.20381i
$358$		0			0
$359$	12.3498	−	12.3498i	0.651798	−	0.651798i	−0.301628	−	0.953426i	$-0.597530\pi$
$359$	12.3498	−	12.3498i	0.651798	−	0.651798i	0.953426	+	0.301628i	$0.0975300\pi$
$360$		0			0
$361$	30.4191	−	17.5625i	1.60100	−	0.924340i
$362$		0			0
$363$	−12.9766	+	24.6100i	−0.681095	+	1.29169i
$364$		0			0
$365$			26.5237i			1.38831i
$366$		0			0
$367$	−1.95311	−	3.38288i	−0.101951	−	0.176585i	0.810537	−	0.585687i	$-0.199175\pi$
$367$	−1.95311	−	3.38288i	−0.101951	−	0.176585i	−0.912489	+	0.409102i	$0.865842\pi$
$368$		0			0
$369$	−12.3459	−	12.3459i	−0.642701	−	0.642701i
$370$		0			0
$371$	−1.32394	−	4.94101i	−0.0687355	−	0.256524i
$372$		0			0
$373$	−0.320902	−	0.185273i	−0.0166157	−	0.00959308i	0.491669	−	0.870782i	$-0.336387\pi$
$373$	−0.320902	−	0.185273i	−0.0166157	−	0.00959308i	−0.508285	+	0.861189i	$0.669720\pi$
$374$		0			0
$375$	3.30725	−	12.3428i	0.170786	−	0.637381i
$376$		0			0
$377$	0.203528	−	1.12279i	0.0104822	−	0.0578266i
$378$		0			0
$379$	3.11026	+	0.833390i	0.159763	+	0.0428084i	0.337814	−	0.941213i	$-0.390313\pi$
$379$	3.11026	+	0.833390i	0.159763	+	0.0428084i	−0.178051	+	0.984021i	$0.556979\pi$
$380$		0			0
$381$	−17.0422	+	29.5180i	−0.873099	+	1.51225i
$382$		0			0
$383$	−3.32735	−	12.4179i	−0.170020	−	0.634523i	−0.997346	−	0.0728014i	$-0.976806\pi$
$383$	−3.32735	−	12.4179i	−0.170020	−	0.634523i	0.827327	−	0.561721i	$-0.189861\pi$
$384$		0			0
$385$	−10.0979	−	16.7403i	−0.514638	−	0.853163i
$386$		0			0
$387$	12.1925	+	21.1180i	0.619779	+	1.07349i
$388$		0			0
$389$		−	20.8818i		−	1.05875i	−0.848388	−	0.529374i	$-0.822427\pi$
$389$		−	20.8818i		−	1.05875i	0.848388	−	0.529374i	$-0.177573\pi$
$390$		0			0
$391$			32.9456i			1.66613i
$392$		0			0
$393$	43.0926	−	24.8795i	2.17373	−	1.25501i
$394$		0			0
$395$	25.7088	+	25.7088i	1.29355	+	1.29355i
$396$		0			0
$397$	−0.394337	+	0.105662i	−0.0197912	+	0.00530304i	−0.268701	−	0.963224i	$-0.586594\pi$
$397$	−0.394337	+	0.105662i	−0.0197912	+	0.00530304i	0.248910	+	0.968527i	$0.419928\pi$
$398$		0			0
$399$	19.1050	−	33.0908i	0.956447	−	1.65661i
$400$		0			0
$401$	7.43588	−	27.7511i	0.371330	−	1.38582i	−0.487303	−	0.873233i	$-0.662019\pi$
$401$	7.43588	−	27.7511i	0.371330	−	1.38582i	0.858633	−	0.512590i	$-0.171314\pi$
$402$		0			0
$403$	0.330332	+	3.99608i	0.0164550	+	0.199059i
$404$		0			0
$405$	−21.2147	−	5.68445i	−1.05416	−	0.282463i
$406$		0			0
$407$	7.52343	−	7.81770i	0.372923	−	0.387509i
$408$		0			0
$409$	−34.3032	+	9.19152i	−1.69618	+	0.454491i	−0.971974	−	0.235088i	$-0.924462\pi$
$409$	−34.3032	+	9.19152i	−1.69618	+	0.454491i	−0.724210	+	0.689579i	$0.757796\pi$
$410$		0			0
$411$	−8.08540	−	8.08540i	−0.398823	−	0.398823i
$412$		0			0
$413$	10.9688	+	18.9985i	0.539739	+	0.934856i
$414$		0			0
$415$	−36.5650			−1.79491
$416$		0			0
$417$		−	23.7239i		−	1.16176i
$418$		0			0
$419$	−6.63389	−	11.4902i	−0.324087	−	0.561335i	0.657240	−	0.753681i	$-0.271724\pi$
$419$	−6.63389	−	11.4902i	−0.324087	−	0.561335i	−0.981327	+	0.192346i	$0.938390\pi$
$420$		0			0
$421$	18.5206	−	18.5206i	0.902638	−	0.902638i	−0.0930260	−	0.995664i	$-0.529654\pi$
$421$	18.5206	−	18.5206i	0.902638	−	0.902638i	0.995664	+	0.0930260i	$0.0296540\pi$
$422$		0			0
$423$	−9.65082	+	2.58593i	−0.469239	+	0.125732i
$424$		0			0
$425$	−12.7216	−	7.34484i	−0.617090	−	0.356277i
$426$		0			0
$427$	1.20172	−	4.48488i	0.0581553	−	0.217039i
$428$		0			0
$429$	23.4466	+	19.1059i	1.13201	+	0.922443i
$430$		0			0
$431$	0.0382190	−	0.142635i	0.00184095	−	0.00687051i	−0.964999	−	0.262253i	$-0.915535\pi$
$431$	0.0382190	−	0.142635i	0.00184095	−	0.00687051i	0.966840	+	0.255382i	$0.0822013\pi$
$432$		0			0
$433$	−21.3323	−	12.3162i	−1.02517	−	0.591880i	−0.109570	−	0.993979i	$-0.534947\pi$
$433$	−21.3323	−	12.3162i	−1.02517	−	0.591880i	−0.915596	+	0.402099i	$0.868281\pi$
$434$		0			0
$435$	−2.21944	+	0.594697i	−0.106414	+	0.0285136i
$436$		0			0
$437$	37.8017	−	37.8017i	1.80830	−	1.80830i
$438$		0			0
$439$	−12.1180	−	20.9890i	−0.578361	−	1.00175i	−0.995668	−	0.0929850i	$-0.970359\pi$
$439$	−12.1180	−	20.9890i	−0.578361	−	1.00175i	0.417306	−	0.908766i	$-0.362974\pi$
$440$		0			0
$441$			9.45486i			0.450231i
$442$		0			0
$443$	10.9271			0.519163			0.259581	−	0.965721i	$-0.416415\pi$
$443$	10.9271			0.519163			0.259581	+	0.965721i	$0.416415\pi$
$444$		0			0
$445$	−13.9686	−	24.1943i	−0.662176	−	1.14692i
$446$		0			0
$447$	10.3794	+	10.3794i	0.490927	+	0.490927i
$448$		0			0
$449$	−9.67205	+	2.59162i	−0.456452	+	0.122306i	−0.479717	−	0.877423i	$-0.659261\pi$
$449$	−9.67205	+	2.59162i	−0.456452	+	0.122306i	0.0232646	+	0.999729i	$0.492594\pi$
$450$		0			0
$451$	−11.8202	+	12.2825i	−0.556592	+	0.578362i
$452$		0			0
$453$	−36.4161	−	9.75766i	−1.71098	−	0.458455i
$454$		0			0
$455$	−20.0060	+	7.17326i	−0.937897	+	0.336288i
$456$		0			0
$457$	3.86394	−	14.4204i	0.180748	−	0.674559i	−0.814753	−	0.579808i	$-0.803128\pi$
$457$	3.86394	−	14.4204i	0.180748	−	0.674559i	0.995501	−	0.0947515i	$-0.0302057\pi$
$458$		0			0
$459$	−2.27655	+	3.94310i	−0.106260	+	0.184048i
$460$		0			0
$461$	2.39970	−	0.642997i	0.111765	−	0.0299474i	−0.202503	−	0.979282i	$-0.564908\pi$
$461$	2.39970	−	0.642997i	0.111765	−	0.0299474i	0.314268	+	0.949334i	$0.398241\pi$
$462$		0			0
$463$	25.5311	+	25.5311i	1.18653	+	1.18653i	0.978020	+	0.208511i	$0.0668616\pi$
$463$	25.5311	+	25.5311i	1.18653	+	1.18653i	0.208511	+	0.978020i	$0.433138\pi$
$464$		0			0
$465$	6.99237	−	4.03705i	0.324264	−	0.187214i
$466$		0			0
$467$		−	4.30741i		−	0.199323i	−0.995021	−	0.0996617i	$-0.968224\pi$
$467$		−	4.30741i		−	0.199323i	0.995021	−	0.0996617i	$-0.0317761\pi$
$468$		0			0
$469$			22.2508i			1.02744i
$470$		0			0
$471$	11.3681	+	19.6901i	0.523813	+	0.907271i
$472$		0			0
$473$	20.3859	−	12.2970i	0.937346	−	0.565418i
$474$		0			0
$475$	6.16932	+	23.0242i	0.283068	+	1.05642i
$476$		0			0
$477$	4.23112	−	7.32851i	0.193730	−	0.335550i
$478$		0			0
$479$	−11.0789	−	2.96859i	−0.506209	−	0.135638i	−0.00332894	−	0.999994i	$-0.501060\pi$
$479$	−11.0789	−	2.96859i	−0.506209	−	0.135638i	−0.502880	+	0.864356i	$0.667726\pi$
$480$		0			0
$481$	−6.71897	−	9.69418i	−0.306359	−	0.442017i
$482$		0			0
$483$	9.76793	−	36.4544i	0.444456	−	1.65873i
$484$		0			0
$485$	17.5712	+	10.1447i	0.797865	+	0.460648i
$486$		0			0
$487$	−1.27897	−	4.77317i	−0.0579556	−	0.216293i	0.930875	−	0.365338i	$-0.119047\pi$
$487$	−1.27897	−	4.77317i	−0.0579556	−	0.216293i	−0.988830	+	0.149045i	$0.952380\pi$
$488$		0			0
$489$	−10.3956	−	10.3956i	−0.470104	−	0.470104i
$490$		0			0
$491$	15.4686	+	26.7924i	0.698087	+	1.20912i	0.969129	+	0.246555i	$0.0792985\pi$
$491$	15.4686	+	26.7924i	0.698087	+	1.20912i	−0.271042	+	0.962568i	$0.587368\pi$
$492$		0			0
$493$		−	1.43488i		−	0.0646240i
$494$		0			0
$495$	7.76997	−	31.3944i	0.349234	−	1.41107i
$496$		0			0
$497$	−27.2751	+	15.7473i	−1.22345	+	0.706362i
$498$		0			0
$499$	−6.06953	+	6.06953i	−0.271710	+	0.271710i	−0.829788	−	0.558079i	$-0.811539\pi$
$499$	−6.06953	+	6.06953i	−0.271710	+	0.271710i	0.558079	+	0.829788i	$0.311539\pi$
$500$		0			0
$501$	−0.468280	−	1.74764i	−0.0209212	−	0.0780790i
$502$		0			0
$503$	−16.6000	−	9.58401i	−0.740157	−	0.427330i	0.0819696	−	0.996635i	$-0.473879\pi$
$503$	−16.6000	−	9.58401i	−0.740157	−	0.427330i	−0.822126	+	0.569305i	$0.807212\pi$
$504$		0			0
$505$	−14.2601	−	3.82099i	−0.634567	−	0.170032i
$506$		0			0
$507$	25.3889	−	20.8927i	1.12756	−	0.927876i
$508$		0			0
$509$	−11.2005	−	3.00116i	−0.496453	−	0.133024i	0.00190029	−	0.999998i	$-0.499395\pi$
$509$	−11.2005	−	3.00116i	−0.496453	−	0.133024i	−0.498353	+	0.866974i	$0.666062\pi$
$510$		0			0
$511$	16.4320	+	9.48701i	0.726908	+	0.419681i
$512$		0			0
$513$	7.13641	−	1.91219i	0.315080	−	0.0844255i
$514$		0			0
$515$	−14.9794	−	14.9794i	−0.660069	−	0.660069i
$516$		0			0
$517$	2.70494	+	9.37218i	0.118963	+	0.412188i
$518$		0			0
$519$	−8.53215			−0.374520
$520$		0			0
$521$	−1.42406			−0.0623891			−0.0311945	−	0.999513i	$-0.509931\pi$
$521$	−1.42406			−0.0623891			−0.0311945	+	0.999513i	$0.509931\pi$
$522$		0			0
$523$	35.2237	−	20.3364i	1.54023	−	0.889250i	0.541403	−	0.840763i	$-0.317893\pi$
$523$	35.2237	−	20.3364i	1.54023	−	0.889250i	0.998824	−	0.0484869i	$-0.0154399\pi$
$524$		0			0
$525$	11.8989	+	11.8989i	0.519309	+	0.519309i
$526$		0			0
$527$	1.30499	+	4.87029i	0.0568463	+	0.212153i
$528$		0			0
$529$	14.9013	−	25.8098i	0.647883	−	1.12217i
$530$		0			0
$531$	−9.39288	+	35.0547i	−0.407616	+	1.52124i
$532$		0			0
$533$	10.5563	+	15.2307i	0.457244	+	0.659716i
$534$		0			0
$535$	7.22000	−	26.9454i	0.312148	−	1.16495i
$536$		0			0
$537$	58.5546	+	33.8065i	2.52682	+	1.45886i
$538$		0			0
$539$	9.22931	−	0.177031i	0.397535	−	0.00762528i
$540$		0			0
$541$	30.4180	−	30.4180i	1.30777	−	1.30777i	0.384753	−	0.923019i	$-0.374286\pi$
$541$	30.4180	−	30.4180i	1.30777	−	1.30777i	0.923019	−	0.384753i	$-0.125714\pi$
$542$		0			0
$543$	39.5594	−	22.8396i	1.69765	−	0.980141i
$544$		0			0
$545$	29.7414			1.27398
$546$		0			0
$547$			25.2405i			1.07921i	0.841919	+	0.539604i	$0.181426\pi$
$547$			25.2405i			1.07921i	−0.841919	+	0.539604i	$0.818574\pi$
$548$		0			0
$549$	6.65199	−	3.84053i	0.283900	−	0.163910i
$550$		0			0
$551$	−1.64638	+	1.64638i	−0.0701382	+	0.0701382i
$552$		0			0
$553$	25.1227	−	6.73162i	1.06833	−	0.286257i
$554$		0			0
$555$	−11.8754	+	20.5688i	−0.504083	+	0.873098i
$556$		0			0
$557$	−25.6178	−	6.86428i	−1.08546	−	0.290849i	−0.328631	−	0.944458i	$-0.606587\pi$
$557$	−25.6178	−	6.86428i	−1.08546	−	0.290849i	−0.756832	+	0.653609i	$0.773254\pi$
$558$		0			0
$559$	−8.73544	−	24.3629i	−0.369470	−	1.03044i
$560$		0			0
$561$	33.2959	+	18.3812i	1.40575	+	0.776053i
$562$		0			0
$563$	−15.0848	+	26.1277i	−0.635751	+	1.10115i	0.350605	+	0.936523i	$0.385976\pi$
$563$	−15.0848	+	26.1277i	−0.635751	+	1.10115i	−0.986356	+	0.164629i	$0.947357\pi$
$564$		0			0
$565$	−2.44168	−	9.11249i	−0.102722	−	0.383365i
$566$		0			0
$567$	−11.1097	+	11.1097i	−0.466564	+	0.466564i
$568$		0			0
$569$	1.89037	+	3.27422i	0.0792485	+	0.137262i	0.902926	−	0.429796i	$-0.141415\pi$
$569$	1.89037	+	3.27422i	0.0792485	+	0.137262i	−0.823677	+	0.567059i	$0.808081\pi$
$570$		0			0
$571$	−29.7561			−1.24525			−0.622627	−	0.782519i	$-0.713935\pi$
$571$	−29.7561			−1.24525			−0.622627	+	0.782519i	$0.713935\pi$
$572$		0			0
$573$	41.3662			1.72810
$574$		0			0
$575$	11.7717	+	20.3892i	0.490915	+	0.850289i
$576$		0			0
$577$	−21.4116	+	21.4116i	−0.891376	+	0.891376i	−0.994653	−	0.103277i	$-0.967067\pi$
$577$	−21.4116	+	21.4116i	−0.891376	+	0.891376i	0.103277	+	0.994653i	$0.467067\pi$
$578$		0			0
$579$	9.92142	+	37.0272i	0.412320	+	1.53880i
$580$		0			0
$581$	−13.0786	+	22.6528i	−0.542592	+	0.939797i
$582$		0			0
$583$	−7.23292	−	3.99297i	−0.299557	−	0.165372i
$584$		0			0
$585$	−31.7934	−	15.0113i	−1.31449	−	0.620641i
$586$		0			0
$587$	−25.1366	−	6.73532i	−1.03750	−	0.277996i	−0.300421	−	0.953807i	$-0.597127\pi$
$587$	−25.1366	−	6.73532i	−1.03750	−	0.277996i	−0.737076	+	0.675810i	$0.763794\pi$
$588$		0			0
$589$	4.09081	−	7.08550i	0.168559	−	0.291953i
$590$		0			0
$591$	−10.9870	+	2.94394i	−0.451943	+	0.121098i
$592$		0			0
$593$	−10.2975	+	10.2975i	−0.422868	+	0.422868i	−0.886190	−	0.463322i	$-0.846657\pi$
$593$	−10.2975	+	10.2975i	−0.422868	+	0.422868i	0.463322	+	0.886190i	$0.346657\pi$
$594$		0			0
$595$	−23.1448	+	13.3626i	−0.948843	+	0.547814i
$596$		0			0
$597$		−	7.48034i		−	0.306150i
$598$		0			0
$599$	27.4714			1.12245			0.561226	−	0.827662i	$-0.310330\pi$
$599$	27.4714			1.12245			0.561226	+	0.827662i	$0.310330\pi$
$600$		0			0
$601$	15.3942	−	8.88787i	0.627944	−	0.362544i	−0.152011	−	0.988379i	$-0.548575\pi$
$601$	15.3942	−	8.88787i	0.627944	−	0.362544i	0.779955	+	0.625835i	$0.215242\pi$
$602$		0			0
$603$	−26.0281	+	26.0281i	−1.05995	+	1.05995i
$604$		0			0
$605$	−30.7909	−	6.99680i	−1.25183	−	0.284460i
$606$		0			0
$607$	16.1266	+	9.31072i	0.654560	+	0.377911i	0.790201	−	0.612847i	$-0.209976\pi$
$607$	16.1266	+	9.31072i	0.654560	+	0.377911i	−0.135641	+	0.990758i	$0.543309\pi$
$608$		0			0
$609$	−0.425424	+	1.58770i	−0.0172390	+	0.0643370i
$610$		0			0
$611$	10.5684	−	0.873629i	0.427553	−	0.0353433i
$612$		0			0
$613$	8.27168	−	30.8703i	0.334090	−	1.24684i	−0.570762	−	0.821115i	$-0.693352\pi$
$613$	8.27168	−	30.8703i	0.334090	−	1.24684i	0.904852	−	0.425726i	$-0.139981\pi$
$614$		0			0
$615$	18.6577	−	32.3161i	0.752351	−	1.30311i
$616$		0			0
$617$	7.41310	+	27.6661i	0.298440	+	1.11379i	0.938447	+	0.345424i	$0.112265\pi$
$617$	7.41310	+	27.6661i	0.298440	+	1.11379i	−0.640007	+	0.768369i	$0.721068\pi$
$618$		0			0
$619$	15.2173	+	15.2173i	0.611636	+	0.611636i	0.943372	−	0.331736i	$-0.107634\pi$
$619$	15.2173	+	15.2173i	0.611636	+	0.611636i	−0.331736	+	0.943372i	$0.607634\pi$
$620$		0			0
$621$	6.31969	−	3.64867i	0.253600	−	0.146416i
$622$		0			0
$623$	−19.9852			−0.800691
$624$		0			0
$625$	30.7024			1.22810
$626$		0			0
$627$	−17.1131	−	59.2940i	−0.683431	−	2.36798i
$628$		0			0
$629$	−10.4877	−	10.4877i	−0.418173	−	0.418173i
$630$		0			0
$631$	43.7887	−	11.7332i	1.74320	−	0.467090i	0.760048	−	0.649867i	$-0.225176\pi$
$631$	43.7887	−	11.7332i	1.74320	−	0.467090i	0.983154	+	0.182778i	$0.0585089\pi$
$632$		0			0
$633$	56.3360	+	32.5256i	2.23916	+	1.29278i
$634$		0			0
$635$	−37.3657	−	10.0121i	−1.48281	−	0.397318i
$636$		0			0
$637$	1.78991	−	9.87425i	0.0709187	−	0.391232i
$638$		0			0
$639$	−50.3260	−	13.4848i	−1.99087	−	0.533451i
$640$		0			0
$641$	−34.9593	−	20.1838i	−1.38081	−	0.797212i	−0.388555	−	0.921425i	$-0.627026\pi$
$641$	−34.9593	−	20.1838i	−1.38081	−	0.797212i	−0.992255	+	0.124214i	$0.960359\pi$
$642$		0			0
$643$	−2.13662	−	7.97398i	−0.0842602	−	0.314463i	0.910913	−	0.412599i	$-0.135379\pi$
$643$	−2.13662	−	7.97398i	−0.0842602	−	0.314463i	−0.995173	+	0.0981355i	$0.968712\pi$
$644$		0			0
$645$	−36.8517	+	36.8517i	−1.45104	+	1.45104i
$646$		0			0
$647$	10.8897	−	6.28719i	0.428119	−	0.247175i	−0.270426	−	0.962741i	$-0.587164\pi$
$647$	10.8897	−	6.28719i	0.428119	−	0.247175i	0.698545	+	0.715566i	$0.253831\pi$
$648$		0			0
$649$	34.3943	+	8.51245i	1.35010	+	0.334143i
$650$		0			0
$651$		−	5.77590i		−	0.226375i
$652$		0			0
$653$	22.6431	+	39.2189i	0.886091	+	1.53476i	0.844458	+	0.535622i	$0.179923\pi$
$653$	22.6431	+	39.2189i	0.886091	+	1.53476i	0.0416335	+	0.999133i	$0.486744\pi$
$654$		0			0
$655$	39.9328	+	39.9328i	1.56031	+	1.56031i
$656$		0			0
$657$	8.12398	+	30.3191i	0.316947	+	1.18286i
$658$		0			0
$659$	−29.5689	−	17.0716i	−1.15184	−	0.665016i	−0.202506	−	0.979281i	$-0.564909\pi$
$659$	−29.5689	−	17.0716i	−1.15184	−	0.665016i	−0.949335	+	0.314265i	$0.898242\pi$
$660$		0			0
$661$	−10.2538	+	38.2678i	−0.398827	+	1.48844i	0.416335	+	0.909211i	$0.363314\pi$
$661$	−10.2538	+	38.2678i	−0.398827	+	1.48844i	−0.815162	+	0.579233i	$0.803352\pi$
$662$		0			0
$663$	26.7280	−	31.5451i	1.03803	−	1.22511i
$664$		0			0
$665$	41.8884	+	11.2240i	1.62436	+	0.435247i
$666$		0			0
$667$	−1.14986	+	1.99161i	−0.0445227	+	0.0771156i
$668$		0			0
$669$	−12.8803	−	48.0700i	−0.497982	−	1.85850i
$670$		0			0
$671$	−3.87346	−	6.42139i	−0.149533	−	0.247895i
$672$		0			0
$673$	−12.5597	−	21.7540i	−0.484139	−	0.838554i	0.515695	−	0.856772i	$-0.327534\pi$
$673$	−12.5597	−	21.7540i	−0.484139	−	0.838554i	−0.999834	+	0.0182186i	$0.994201\pi$
$674$		0			0
$675$			3.25371i			0.125236i
$676$		0			0
$677$			13.5226i			0.519717i	0.965647	+	0.259859i	$0.0836760\pi$
$677$			13.5226i			0.519717i	−0.965647	+	0.259859i	$0.916324\pi$
$678$		0			0
$679$	12.5697	−	7.25714i	0.482382	−	0.278503i
$680$		0			0
$681$	−37.1658	−	37.1658i	−1.42420	−	1.42420i
$682$		0			0
$683$	−4.60290	+	1.23334i	−0.176125	+	0.0471925i	−0.345804	−	0.938307i	$-0.612394\pi$
$683$	−4.60290	+	1.23334i	−0.176125	+	0.0471925i	0.169679	+	0.985499i	$0.445727\pi$
$684$		0			0
$685$	6.48873	−	11.2388i	0.247922	−	0.429413i
$686$		0			0
$687$	16.3213	−	60.9120i	0.622697	−	2.32394i
$688$		0			0
$689$	−5.80617	+	6.85259i	−0.221197	+	0.261063i
$690$		0			0
$691$	2.95030	+	0.790531i	0.112235	+	0.0300732i	0.314499	−	0.949258i	$-0.398163\pi$
$691$	2.95030	+	0.790531i	0.112235	+	0.0300732i	−0.202265	+	0.979331i	$0.564830\pi$
$692$		0			0
$693$	−16.6703	−	16.0428i	−0.633253	−	0.609417i
$694$		0			0
$695$	26.0078	−	6.96876i	0.986531	−	0.264340i
$696$		0			0
$697$	16.4775	+	16.4775i	0.624129	+	0.624129i
$698$		0			0
$699$	−23.4805	−	40.6695i	−0.888115	−	1.53826i
$700$		0			0
$701$	25.8956			0.978063			0.489032	−	0.872266i	$-0.337350\pi$
$701$	25.8956			0.978063			0.489032	+	0.872266i	$0.337350\pi$
$702$		0			0
$703$			24.0671i			0.907709i
$704$		0			0
$705$	−10.6768	−	18.4928i	−0.402112	−	0.696478i
$706$		0			0
$707$	−7.46775	+	7.46775i	−0.280854	+	0.280854i
$708$		0			0
$709$	−8.47285	+	2.27029i	−0.318205	+	0.0852627i	−0.414386	−	0.910101i	$-0.636004\pi$
$709$	−8.47285	+	2.27029i	−0.318205	+	0.0852627i	0.0961816	+	0.995364i	$0.469337\pi$
$710$		0			0
$711$	37.2621	+	21.5133i	1.39744	+	0.806811i
$712$		0			0
$713$	2.09153	−	7.80571i	0.0783286	−	0.292326i
$714$		0			0
$715$	−14.0579	+	31.3160i	−0.525736	+	1.17115i
$716$		0			0
$717$	−0.733122	+	2.73605i	−0.0273789	+	0.102180i
$718$		0			0
$719$	−23.1209	−	13.3489i	−0.862265	−	0.497829i	0.00250481	−	0.999997i	$-0.499203\pi$
$719$	−23.1209	−	13.3489i	−0.862265	−	0.497829i	−0.864770	+	0.502168i	$0.832536\pi$
$720$		0			0
$721$	−14.6379	+	3.92220i	−0.545142	+	0.146070i
$722$		0			0
$723$	−30.3324	+	30.3324i	−1.12807	+	1.12807i
$724$		0			0
$725$	−0.512695	−	0.888014i	−0.0190410	−	0.0329800i
$726$		0			0
$727$		−	35.8793i		−	1.33069i	−0.746536	−	0.665345i	$-0.768284\pi$
$727$		−	35.8793i		−	1.33069i	0.746536	−	0.665345i	$-0.231716\pi$
$728$		0			0
$729$	−33.6114			−1.24487
$730$		0			0
$731$	−16.2727	−	28.1852i	−0.601868	−	1.04247i
$732$		0			0
$733$	−9.22356	−	9.22356i	−0.340680	−	0.340680i	0.515943	−	0.856623i	$-0.327442\pi$
$733$	−9.22356	−	9.22356i	−0.340680	−	0.340680i	−0.856623	+	0.515943i	$0.827442\pi$
$734$		0			0
$735$	−19.5186	+	5.23000i	−0.719956	+	0.192912i
$736$		0			0
$737$	25.8946	+	24.9199i	0.953839	+	0.917936i
$738$		0			0
$739$	−13.9170	−	3.72905i	−0.511945	−	0.137175i	−0.00640660	−	0.999979i	$-0.502039\pi$
$739$	−13.9170	−	3.72905i	−0.511945	−	0.137175i	−0.505538	+	0.862804i	$0.668706\pi$
$740$		0			0
$741$	−66.8623	+	5.52710i	−2.45625	+	0.203043i
$742$		0			0
$743$	−1.65786	+	6.18721i	−0.0608209	+	0.226987i	−0.989646	−	0.143533i	$-0.954154\pi$
$743$	−1.65786	+	6.18721i	−0.0608209	+	0.226987i	0.928825	+	0.370520i	$0.120820\pi$
$744$		0			0
$745$	−8.32969	+	14.4274i	−0.305176	+	0.528581i
$746$		0			0
$747$	−41.7973	+	11.1996i	−1.52928	+	0.409771i
$748$		0			0
$749$	−14.1108	−	14.1108i	−0.515598	−	0.515598i
$750$		0			0
$751$	−32.2455	+	18.6169i	−1.17665	+	0.679341i	−0.955238	−	0.295838i	$-0.904401\pi$
$751$	−32.2455	+	18.6169i	−1.17665	+	0.679341i	−0.221415	+	0.975180i	$0.571068\pi$
$752$		0			0
$753$			41.0956i			1.49761i
$754$		0			0
$755$		−	42.7881i		−	1.55722i
$756$		0			0
$757$	2.20430	+	3.81795i	0.0801165	+	0.138766i	0.903300	−	0.429010i	$-0.141137\pi$
$757$	2.20430	+	3.81795i	0.0801165	+	0.138766i	−0.823183	+	0.567776i	$0.807804\pi$
$758$		0			0
$759$	−31.4846	−	52.1949i	−1.14282	−	1.89456i
$760$		0			0
$761$	7.58164	+	28.2951i	0.274834	+	1.02569i	0.955952	+	0.293522i	$0.0948272\pi$
$761$	7.58164	+	28.2951i	0.274834	+	1.02569i	−0.681118	+	0.732173i	$0.738506\pi$
$762$		0			0
$763$	10.6379	−	18.4254i	0.385119	−	0.667046i
$764$		0			0
$765$	−42.7051	−	11.4428i	−1.54400	−	0.413715i
$766$		0			0
$767$	16.4458	−	34.8315i	0.593822	−	1.25769i
$768$		0			0
$769$	−5.76085	+	21.4998i	−0.207742	+	0.775303i	0.780855	+	0.624713i	$0.214784\pi$
$769$	−5.76085	+	21.4998i	−0.207742	+	0.775303i	−0.988596	+	0.150590i	$0.951883\pi$
$770$		0			0
$771$	−18.8289	−	10.8709i	−0.678107	−	0.391505i
$772$		0			0
$773$	1.94677	+	7.26546i	0.0700206	+	0.261320i	0.992058	−	0.125780i	$-0.0401433\pi$
$773$	1.94677	+	7.26546i	0.0700206	+	0.261320i	−0.922038	+	0.387100i	$0.873477\pi$
$774$		0			0
$775$	2.54782	+	2.54782i	0.0915203	+	0.0915203i
$776$		0			0
$777$	8.49522	+	14.7141i	0.304764	+	0.527867i
$778$		0			0
$779$		−	37.8124i		−	1.35477i
$780$		0			0
$781$	−12.2208	+	49.3780i	−0.437296	+	1.76688i
$782$		0			0
$783$	−0.275242	+	0.158911i	−0.00983635	+	0.00567902i
$784$		0			0
$785$	−18.2463	+	18.2463i	−0.651239	+	0.651239i
$786$		0			0
$787$	−1.11681	−	4.16799i	−0.0398100	−	0.148573i	0.943160	−	0.332339i	$-0.107838\pi$
$787$	−1.11681	−	4.16799i	−0.0398100	−	0.148573i	−0.982970	+	0.183766i	$0.941171\pi$
$788$		0			0
$789$	29.2778	+	16.9035i	1.04232	+	0.601782i
$790$		0			0
$791$	−6.51873	−	1.74669i	−0.231779	−	0.0621051i
$792$		0			0
$793$	−7.67410	+	2.75159i	−0.272515	+	0.0977118i
$794$		0			0
$795$	17.4695	+	4.68093i	0.619579	+	0.166016i
$796$		0			0
$797$	18.1620	+	10.4859i	0.643332	+	0.371428i	0.785897	−	0.618358i	$-0.212202\pi$
$797$	18.1620	+	10.4859i	0.643332	+	0.371428i	−0.142565	+	0.989785i	$0.545535\pi$
$798$		0			0
$799$	12.8805	−	3.45131i	0.455679	−	0.122099i
$800$		0			0
$801$	−23.3780	−	23.3780i	−0.826021	−	0.826021i
$802$		0			0
$803$	29.4437	−	8.49787i	1.03905	−	0.299883i
$804$		0			0
$805$	42.8331			1.50967
$806$		0			0
$807$	−17.8473			−0.628256
$808$		0			0
$809$	−10.5651	+	6.09974i	−0.371448	+	0.214455i	−0.674091	−	0.738649i	$-0.735464\pi$
$809$	−10.5651	+	6.09974i	−0.371448	+	0.214455i	0.302643	+	0.953104i	$0.402131\pi$
$810$		0			0
$811$	−1.31277	−	1.31277i	−0.0460977	−	0.0460977i	0.683682	−	0.729780i	$-0.260377\pi$
$811$	−1.31277	−	1.31277i	−0.0460977	−	0.0460977i	−0.729780	+	0.683682i	$0.760377\pi$
$812$		0			0
$813$	−2.90260	−	10.8327i	−0.101799	−	0.379918i
$814$		0			0
$815$	8.34270	−	14.4500i	0.292232	−	0.506161i
$816$		0			0
$817$	−13.6683	+	51.0108i	−0.478193	+	1.78464i
$818$		0			0
$819$	−20.6717	+	14.3274i	−0.722328	+	0.500640i
$820$		0			0
$821$	13.1597	−	49.1127i	0.459277	−	1.71405i	−0.215923	−	0.976410i	$-0.569276\pi$
$821$	13.1597	−	49.1127i	0.459277	−	1.71405i	0.675200	−	0.737635i	$-0.264057\pi$
$822$		0			0
$823$	41.0853	+	23.7206i	1.43214	+	0.826849i	0.997284	−	0.0736489i	$-0.0234644\pi$
$823$	41.0853	+	23.7206i	1.43214	+	0.826849i	0.434860	+	0.900498i	$0.356798\pi$
$824$		0			0
$825$	27.1737	−	0.521230i	0.946066	−	0.0181469i
$826$		0			0
$827$	1.74243	−	1.74243i	0.0605901	−	0.0605901i	−0.676162	−	0.736753i	$-0.736358\pi$
$827$	1.74243	−	1.74243i	0.0605901	−	0.0605901i	0.736753	+	0.676162i	$0.236358\pi$
$828$		0			0
$829$	24.1607	−	13.9492i	0.839136	−	0.484476i	−0.0178342	−	0.999841i	$-0.505677\pi$
$829$	24.1607	−	13.9492i	0.839136	−	0.484476i	0.856971	+	0.515365i	$0.172344\pi$
$830$		0			0
$831$	−37.2353			−1.29168
$832$		0			0
$833$		−	12.6189i		−	0.437221i
$834$		0			0
$835$	1.77833	−	1.02672i	0.0615418	−	0.0355312i
$836$		0			0
$837$	0.789702	−	0.789702i	0.0272961	−	0.0272961i
$838$		0			0
$839$	12.3737	−	3.31552i	0.427187	−	0.114465i	−0.0388182	−	0.999246i	$-0.512359\pi$
$839$	12.3737	−	3.31552i	0.427187	−	0.114465i	0.466006	+	0.884782i	$0.345693\pi$
$840$		0			0
$841$	−14.4499	+	25.0280i	−0.498273	+	0.863034i
$842$		0			0
$843$	71.1124	+	19.0545i	2.44924	+	0.656272i
$844$		0			0
$845$	30.3618	+	21.6960i	1.04448	+	0.746365i
$846$		0			0
$847$	−15.3480	+	16.5730i	−0.527363	+	0.569456i
$848$		0			0
$849$	23.7387	−	41.1167i	0.814711	−	1.41112i
$850$		0			0
$851$	6.15248	+	22.9613i	0.210904	+	0.787105i
$852$		0			0
$853$	−17.5550	+	17.5550i	−0.601073	+	0.601073i	−0.940597	−	0.339525i	$-0.889734\pi$
$853$	−17.5550	+	17.5550i	−0.601073	+	0.601073i	0.339525	+	0.940597i	$0.389734\pi$
$854$		0			0
$855$	35.8702	+	62.1290i	1.22674	+	2.12477i
$856$		0			0
$857$	−23.9032			−0.816516			−0.408258	−	0.912867i	$-0.633864\pi$
$857$	−23.9032			−0.816516			−0.408258	+	0.912867i	$0.633864\pi$
$858$		0			0
$859$	4.27864			0.145985			0.0729927	−	0.997332i	$-0.476745\pi$
$859$	4.27864			0.145985			0.0729927	+	0.997332i	$0.476745\pi$
$860$		0			0
$861$	−13.3470	−	23.1177i	−0.454865	−	0.787849i
$862$		0			0
$863$	35.3912	−	35.3912i	1.20473	−	1.20473i	0.232019	−	0.972711i	$-0.425467\pi$
$863$	35.3912	−	35.3912i	1.20473	−	1.20473i	0.972711	−	0.232019i	$-0.0745332\pi$
$864$		0			0
$865$	−2.50627	−	9.35353i	−0.0852158	−	0.318030i
$866$		0			0
$867$	4.49710	−	7.78920i	0.152729	−	0.264535i
$868$		0			0
$869$	20.3024	−	36.7760i	0.688711	−	1.24754i
$870$		0			0
$871$	32.1101	−	22.2553i	1.08801	−	0.754091i
$872$		0			0
$873$	23.1928	+	6.21449i	0.784956	+	0.210328i
$874$		0			0
$875$	5.18728	−	8.98463i	0.175362	−	0.303736i
$876$		0			0
$877$	−3.86955	+	1.03684i	−0.130665	+	0.0350117i	−0.323559	−	0.946208i	$-0.604879\pi$
$877$	−3.86955	+	1.03684i	−0.130665	+	0.0350117i	0.192894	+	0.981220i	$0.438213\pi$
$878$		0			0
$879$	−1.88423	+	1.88423i	−0.0635535	+	0.0635535i
$880$		0			0
$881$	7.56373	−	4.36692i	0.254829	−	0.147125i	−0.367145	−	0.930164i	$-0.619665\pi$
$881$	7.56373	−	4.36692i	0.254829	−	0.147125i	0.621973	+	0.783038i	$0.286331\pi$
$882$		0			0
$883$			54.8144i			1.84465i	0.386413	+	0.922326i	$0.373714\pi$
$883$			54.8144i			1.84465i	−0.386413	+	0.922326i	$0.626286\pi$
$884$		0			0
$885$	−77.5628			−2.60724
$886$		0			0
$887$	−24.0330	+	13.8755i	−0.806949	+	0.465892i	−0.845895	−	0.533349i	$-0.820933\pi$
$887$	−24.0330	+	13.8755i	−0.806949	+	0.465892i	0.0389461	+	0.999241i	$0.487600\pi$
$888$		0			0
$889$	−19.5677	+	19.5677i	−0.656280	+	0.656280i
$890$		0			0
$891$	0.486661	+	25.3715i	0.0163038	+	0.849976i
$892$		0			0
$893$	−18.7390	−	10.8190i	−0.627078	−	0.362044i
$894$		0			0
$895$	−19.8609	+	74.1220i	−0.663878	+	2.47763i
$896$		0			0
$897$	−62.3773	+	22.3657i	−2.08272	+	0.746769i
$898$		0			0
$899$	−0.0910928	+	0.339963i	−0.00303812	+	0.0113384i
$900$		0			0
$901$	−5.64707	+	9.78102i	−0.188131	+	0.325853i
$902$		0			0
$903$	9.64928	+	36.0116i	0.321108	+	1.19839i
$904$		0			0
$905$	36.6587	+	36.6587i	1.21858	+	1.21858i
$906$		0			0
$907$	−37.2908	+	21.5299i	−1.23822	+	0.714888i	−0.968730	−	0.248115i	$-0.920189\pi$
$907$	−37.2908	+	21.5299i	−1.23822	+	0.714888i	−0.269491	+	0.963003i	$0.586855\pi$
$908$		0			0
$909$	−17.4710			−0.579477
$910$		0			0
$911$	−26.6918			−0.884338			−0.442169	−	0.896932i	$-0.645791\pi$
$911$	−26.6918			−0.884338			−0.442169	+	0.896932i	$0.645791\pi$
$912$		0			0
$913$	11.7150	+	40.5906i	0.387710	+	1.34335i
$914$		0			0
$915$	11.6080	+	11.6080i	0.383748	+	0.383748i
$916$		0			0
$917$	39.0225	−	10.4560i	1.28864	−	0.345289i
$918$		0			0
$919$	15.9884	+	9.23091i	0.527409	+	0.304500i	0.739961	−	0.672650i	$-0.234844\pi$
$919$	15.9884	+	9.23091i	0.527409	+	0.304500i	−0.212552	+	0.977150i	$0.568177\pi$
$920$		0			0
$921$	32.5594	+	8.72427i	1.07287	+	0.287475i
$922$		0			0
$923$	50.0055	+	23.6102i	1.64595	+	0.777140i
$924$		0			0
$925$	−10.2379	−	2.74324i	−0.336621	−	0.0901973i
$926$		0			0
$927$	−21.7109	−	12.5348i	−0.713079	−	0.411697i
$928$		0			0
$929$	−10.2119	−	38.1112i	−0.335040	−	1.25039i	−0.903826	−	0.427901i	$-0.859253\pi$
$929$	−10.2119	−	38.1112i	−0.335040	−	1.25039i	0.568785	−	0.822486i	$-0.307414\pi$
$930$		0			0
$931$	−14.4789	+	14.4789i	−0.474528	+	0.474528i
$932$		0			0
$933$	−47.8365	+	27.6184i	−1.56610	+	0.904186i
$934$		0			0
$935$	−10.3702	+	41.9006i	−0.339142	+	1.37030i
$936$		0			0
$937$			7.29029i			0.238164i	0.992884	+	0.119082i	$0.0379951\pi$
$937$			7.29029i			0.238164i	−0.992884	+	0.119082i	$0.962005\pi$
$938$		0			0
$939$	13.9422	+	24.1487i	0.454988	+	0.788062i
$940$		0			0
$941$	−25.4782	−	25.4782i	−0.830566	−	0.830566i	0.157028	−	0.987594i	$-0.449809\pi$
$941$	−25.4782	−	25.4782i	−0.830566	−	0.830566i	−0.987594	+	0.157028i	$0.949809\pi$
$942$		0			0
$943$	−9.66628	−	36.0750i	−0.314777	−	1.17476i
$944$		0			0
$945$	5.12648	+	2.95978i	0.166765	+	0.0962816i
$946$		0			0
$947$	1.26752	−	4.73044i	0.0411888	−	0.153719i	−0.942269	−	0.334858i	$-0.891312\pi$
$947$	1.26752	−	4.73044i	0.0411888	−	0.153719i	0.983457	+	0.181139i	$0.0579784\pi$
$948$		0			0
$949$	−2.74460	−	33.2019i	−0.0890936	−	1.07778i
$950$		0			0
$951$	2.69418	+	0.721904i	0.0873649	+	0.0234093i
$952$		0			0
$953$	30.2918	−	52.4669i	0.981248	−	1.69957i	0.323697	−	0.946161i	$-0.395074\pi$
$953$	30.2918	−	52.4669i	0.981248	−	1.69957i	0.657551	−	0.753410i	$-0.271592\pi$
$954$		0			0
$955$	12.1511	+	45.3485i	0.393200	+	1.46744i
$956$		0			0
$957$	1.37125	+	2.27325i	0.0443263	+	0.0734838i
$958$		0			0
$959$	−4.64179	−	8.03981i	−0.149891	−	0.259619i
$960$		0			0
$961$			29.7632i			0.960105i
$962$		0			0
$963$		−	33.0126i		−	1.06382i
$964$		0			0
$965$	−37.6774	+	21.7531i	−1.21288	+	0.700256i
$966$		0			0
$967$	−2.69838	−	2.69838i	−0.0867741	−	0.0867741i	0.662387	−	0.749161i	$-0.269543\pi$
$967$	−2.69838	−	2.69838i	−0.0867741	−	0.0867741i	−0.749161	+	0.662387i	$0.769543\pi$
$968$		0			0
$969$	−81.4897	+	21.8351i	−2.61783	+	0.701444i
$970$		0			0
$971$	8.00634	−	13.8674i	0.256936	−	0.445026i	−0.708484	−	0.705727i	$-0.750621\pi$
$971$	8.00634	−	13.8674i	0.256936	−	0.445026i	0.965419	+	0.260702i	$0.0839538\pi$
$972$		0			0
$973$	4.98518	−	18.6050i	0.159818	−	0.596447i
$974$		0			0
$975$	5.26999	−	29.0726i	0.168775	−	0.931067i
$976$		0			0
$977$	−37.2520	−	9.98164i	−1.19180	−	0.319341i	−0.392201	−	0.919879i	$-0.628286\pi$
$977$	−37.2520	−	9.98164i	−1.19180	−	0.319341i	−0.799596	+	0.600538i	$0.794953\pi$
$978$		0			0
$979$	−22.3826	+	23.2580i	−0.715351	+	0.743330i
$980$		0			0
$981$	33.9973	−	9.10955i	1.08545	−	0.290846i
$982$		0			0
$983$	−23.6528	−	23.6528i	−0.754409	−	0.754409i	0.220890	−	0.975299i	$-0.429104\pi$
$983$	−23.6528	−	23.6528i	−0.754409	−	0.754409i	−0.975299	+	0.220890i	$0.929104\pi$
$984$		0			0
$985$	−6.45471	−	11.1799i	−0.205664	−	0.356221i
$986$		0			0
$987$	−15.2755			−0.486226
$988$		0			0
$989$			52.1612i			1.65863i
$990$		0			0
$991$	30.4308	+	52.7077i	0.966667	+	1.67432i	0.705069	+	0.709139i	$0.250916\pi$
$991$	30.4308	+	52.7077i	0.966667	+	1.67432i	0.261597	+	0.965177i	$0.415751\pi$
$992$		0			0
$993$	14.9822	−	14.9822i	0.475447	−	0.475447i
$994$		0			0
$995$	8.20046	−	2.19731i	0.259972	−	0.0696593i
$996$		0			0
$997$	−32.4026	−	18.7077i	−1.02620	−	0.592478i	−0.110307	−	0.993898i	$-0.535183\pi$
$997$	−32.4026	−	18.7077i	−1.02620	−	0.592478i	−0.915894	+	0.401420i	$0.868517\pi$
$998$		0			0
$999$	−0.850275	+	3.17327i	−0.0269015	+	0.100398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bc.a.197.12	yes	56
11.10	odd	2	inner	572.2.bc.a.197.11	✓	56
13.7	odd	12	inner	572.2.bc.a.241.11	yes	56
143.98	even	12	inner	572.2.bc.a.241.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bc.a.197.11	✓	56	11.10	odd	2	inner
572.2.bc.a.197.12	yes	56	1.1	even	1	trivial
572.2.bc.a.241.11	yes	56	13.7	odd	12	inner
572.2.bc.a.241.12	yes	56	143.98	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26462 + 2.19039i) q^{3} +(-2.02978 + 2.02978i) q^{5} +(0.531478 + 1.98350i) q^{7} +(-1.69853 + 2.94193i) q^{9} +O(q^{10})\)	\(q+(1.26462 + 2.19039i) q^{3} +(-2.02978 + 2.02978i) q^{5} +(0.531478 + 1.98350i) q^{7} +(-1.69853 + 2.94193i) q^{9} +(2.90356 + 1.60292i) q^{11} +(2.33081 - 2.75088i) q^{13} +(-7.01289 - 1.87910i) q^{15} +(2.26694 - 3.92646i) q^{17} +(-7.10628 + 1.90412i) q^{19} +(-3.67252 + 3.67252i) q^{21} +(-6.29301 + 3.63327i) q^{23} -3.23998i q^{25} -1.00424 q^{27} +(0.274080 - 0.158240i) q^{29} +(-0.786368 + 0.786368i) q^{31} +(0.160875 + 8.38700i) q^{33} +(-5.10484 - 2.94728i) q^{35} +(0.846685 - 3.15987i) q^{37} +(8.97307 + 1.62655i) q^{39} +(-1.33024 + 4.96454i) q^{41} +(3.58914 - 6.21656i) q^{43} +(-2.52384 - 9.41909i) q^{45} +(2.07971 + 2.07971i) q^{47} +(2.41037 - 1.39163i) q^{49} +11.4673 q^{51} -2.49105 q^{53} +(-9.14714 + 2.63999i) q^{55} +(-13.1575 - 13.1575i) q^{57} +(10.3192 - 2.76501i) q^{59} +(-1.95816 - 1.13055i) q^{61} +(-6.73806 - 1.80546i) q^{63} +(0.852653 + 10.3147i) q^{65} +(10.4665 + 2.80448i) q^{67} +(-15.9165 - 9.18941i) q^{69} +(3.96957 + 14.8146i) q^{71} +(6.53364 - 6.53364i) q^{73} +(7.09680 - 4.09734i) q^{75} +(-1.63623 + 6.61112i) q^{77} -12.6659i q^{79} +(3.82560 + 6.62613i) q^{81} +(9.00716 + 9.00716i) q^{83} +(3.36845 + 12.5712i) q^{85} +(0.693214 + 0.400227i) q^{87} +(-2.51893 + 9.40078i) q^{89} +(6.69514 + 3.16113i) q^{91} +(-2.71691 - 0.727993i) q^{93} +(10.5592 - 18.2891i) q^{95} +(-1.82938 - 6.82732i) q^{97} +(-9.64746 + 5.81946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^9	\( 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more