LMFDB - Embedded newform 572.2.bc.a.197.11

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			197.11
Character	$\chi$	$=$	572.197
Dual form			572.2.bc.a.241.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26462 + 2.19039i) q^{3} +(-2.02978 + 2.02978i) q^{5} +(-0.531478 - 1.98350i) q^{7} +(-1.69853 + 2.94193i) q^{9} +O(q^{10})$	\(q+(1.26462 + 2.19039i) q^{3} +(-2.02978 + 2.02978i) q^{5} +(-0.531478 - 1.98350i) q^{7} +(-1.69853 + 2.94193i) q^{9} +(-3.31601 - 0.0636059i) q^{11} +(-2.33081 + 2.75088i) q^{13} +(-7.01289 - 1.87910i) q^{15} +(-2.26694 + 3.92646i) q^{17} +(7.10628 - 1.90412i) q^{19} +(3.67252 - 3.67252i) q^{21} +(-6.29301 + 3.63327i) q^{23} -3.23998i q^{25} -1.00424 q^{27} +(-0.274080 + 0.158240i) q^{29} +(-0.786368 + 0.786368i) q^{31} +(-4.05418 - 7.34379i) q^{33} +(5.10484 + 2.94728i) q^{35} +(0.846685 - 3.15987i) q^{37} +(-8.97307 - 1.62655i) q^{39} +(1.33024 - 4.96454i) q^{41} +(-3.58914 + 6.21656i) q^{43} +(-2.52384 - 9.41909i) q^{45} +(2.07971 + 2.07971i) q^{47} +(2.41037 - 1.39163i) q^{49} -11.4673 q^{51} -2.49105 q^{53} +(6.85987 - 6.60166i) q^{55} +(13.1575 + 13.1575i) q^{57} +(10.3192 - 2.76501i) q^{59} +(1.95816 + 1.13055i) q^{61} +(6.73806 + 1.80546i) q^{63} +(-0.852653 - 10.3147i) q^{65} +(10.4665 + 2.80448i) q^{67} +(-15.9165 - 9.18941i) q^{69} +(3.96957 + 14.8146i) q^{71} +(-6.53364 + 6.53364i) q^{73} +(7.09680 - 4.09734i) q^{75} +(1.63623 + 6.61112i) q^{77} +12.6659i q^{79} +(3.82560 + 6.62613i) q^{81} +(-9.00716 - 9.00716i) q^{83} +(-3.36845 - 12.5712i) q^{85} +(-0.693214 - 0.400227i) q^{87} +(-2.51893 + 9.40078i) q^{89} +(6.69514 + 3.16113i) q^{91} +(-2.71691 - 0.727993i) q^{93} +(-10.5592 + 18.2891i) q^{95} +(-1.82938 - 6.82732i) q^{97} +(5.81946 - 9.64746i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.956475\pi$
$7$	−0.531478	−	1.98350i	−0.200880	−	0.749693i	0.789786	−	0.613382i	$-0.210191\pi$
$8$		0			0
$9$	−1.69853	+	2.94193i	−0.566175	+	0.980644i
$10$		0			0
$11$	−3.31601	−	0.0636059i	−0.999816	−	0.0191779i
$11$	−3.31601	−	0.0636059i	−0.999816	−	0.0191779i
$12$		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	$0.351968\pi$
$17$	−2.26694	+	3.92646i	−0.549814	+	0.952306i	−0.998287	+	0.0585093i	$0.981365\pi$
$18$		0			0
$19$	7.10628	−	1.90412i	1.63029	−	0.436836i	0.676290	−	0.736635i	$-0.263586\pi$
$19$	7.10628	−	1.90412i	1.63029	−	0.436836i	0.954002	+	0.299799i	$0.0969198\pi$
$20$		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	−0.525232	−	0.850959i	$-0.676021\pi$
$29$	−0.274080	+	0.158240i	−0.0508954	+	0.0293845i	0.474336	+	0.880344i	$0.342688\pi$
$30$		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
$33$	−4.05418	−	7.34379i	−0.705741	−	1.27839i
$34$		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	$-0.785211\pi$
$41$	1.33024	−	4.96454i	0.207749	−	0.775331i	0.988594	−	0.150606i	$-0.0481224\pi$
$42$		0			0
$43$	−3.58914	+	6.21656i	−0.547338	+	0.948017i	0.451118	+	0.892464i	$0.351025\pi$
$43$	−3.58914	+	6.21656i	−0.547338	+	0.948017i	−0.998456	+	0.0555528i	$0.982308\pi$
$44$		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
$55$	6.85987	−	6.60166i	0.924985	−	0.890168i
$56$		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	0.620093	−	0.784529i	$-0.287095\pi$
$61$	1.95816	+	1.13055i	0.250717	+	0.144752i	−0.369375	+	0.929280i	$0.620428\pi$
$62$		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	−0.977169	−	0.212464i	$-0.931851\pi$
$73$	−6.53364	+	6.53364i	−0.764705	+	0.764705i	0.212464	+	0.977169i	$0.431851\pi$
$74$		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	$0.252442\pi$
$79$			12.6659i			1.42502i	−0.701662	+	0.712510i	$0.747558\pi$
$80$		0			0
$81$	3.82560	+	6.62613i	0.425066	+	0.736236i
$82$		0			0
$83$	−9.00716	−	9.00716i	−0.988664	−	0.988664i	0.0112725	−	0.999936i	$-0.496412\pi$
$83$	−9.00716	−	9.00716i	−0.988664	−	0.988664i	−0.999936	+	0.0112725i	$0.996412\pi$
$84$		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
$99$	5.81946	−	9.64746i	0.584878	−	0.969606i
$100$		0			0
$101$	−2.57150	−	4.45396i	−0.255874	−	0.443186i	0.709259	−	0.704948i	$-0.249030\pi$
$101$	−2.57150	−	4.45396i	−0.255874	−	0.443186i	−0.965132	+	0.261762i	$0.915696\pi$
$102$		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	−0.0345972	−	0.999401i	$-0.511015\pi$
$107$	8.41606	−	4.85901i	0.813611	−	0.469739i	0.848208	+	0.529663i	$0.177682\pi$
$108$		0			0
$109$	7.32628	+	7.32628i	0.701731	+	0.701731i	0.964782	−	0.263051i	$-0.0847288\pi$
$109$	7.32628	+	7.32628i	0.701731	+	0.701731i	−0.263051	+	0.964782i	$0.584729\pi$
$110$		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
$121$	10.9919	+	0.421836i	0.999264	+	0.0383487i
$122$		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	$-0.962665\pi$
$127$	−6.73808	−	11.6707i	−0.597908	−	1.03561i	0.395221	−	0.918586i	$-0.370668\pi$
$128$		0			0
$129$	−18.1556			−1.59851
$130$		0			0
$131$			19.6735i			1.71888i	0.511233	+	0.859442i	$0.329189\pi$
$131$			19.6735i			1.71888i	−0.511233	+	0.859442i	$0.670811\pi$
$132$		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	0.803237	−	0.595659i	$-0.203109\pi$
$139$	8.12319	+	4.68993i	0.689000	+	0.397794i	−0.114237	+	0.993454i	$0.536442\pi$
$140$		0			0
$141$	−1.92533	+	7.18541i	−0.162142	+	0.605121i
$142$		0			0
$143$	7.90396	−	8.97370i	0.660963	−	0.750419i
$144$		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	−0.481023	−	0.876708i	$-0.659735\pi$
$149$	−5.60582	+	1.50208i	−0.459247	+	0.123055i	0.0217759	+	0.999763i	$0.493068\pi$
$150$		0			0
$151$	10.5401	−	10.5401i	0.857741	−	0.857741i	−0.133331	−	0.991072i	$-0.542567\pi$
$151$	10.5401	−	10.5401i	0.857741	−	0.857741i	0.991072	+	0.133331i	$0.0425673\pi$
$152$		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
$165$	23.1353	+	6.67717i	1.80108	+	0.519817i
$166$		0			0
$167$	0.690976	+	0.185147i	0.0534694	+	0.0143271i	0.285455	−	0.958392i	$-0.407855\pi$
$167$	0.690976	+	0.185147i	0.0534694	+	0.0143271i	−0.231985	+	0.972719i	$0.574522\pi$
$168$		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	−0.794756	−	0.606929i	$-0.792401\pi$
$173$	1.68670	−	2.92146i	0.128238	−	0.222114i	0.922994	+	0.384815i	$0.125735\pi$
$174$		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
$187$	7.76696	−	12.8760i	0.567976	−	0.941586i
$188$		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	−0.309971	−	0.950746i	$-0.600319\pi$
$193$	−14.6397	−	3.92269i	−1.05379	−	0.282361i	−0.743816	+	0.668385i	$0.766986\pi$
$194$		0			0
$195$	21.5149	−	14.9118i	1.54071	−	1.06786i
$196$		0			0
$197$	1.16396	−	4.34397i	0.0829290	−	0.309495i	−0.911985	−	0.410224i	$-0.865451\pi$
$197$	1.16396	−	4.34397i	0.0829290	−	0.309495i	0.994914	+	0.100728i	$0.0321173\pi$
$198$		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	$0.679386\pi$
$211$	−22.2739	+	12.8598i	−1.53340	+	0.885308i	−0.999202	+	0.0399471i	$0.987281\pi$
$212$		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	0.478723	−	0.877966i	$-0.341100\pi$
$227$	20.0730	−	5.37855i	1.33229	−	0.356987i	0.853569	+	0.520979i	$0.174433\pi$
$228$		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
$231$	−12.4117	+	11.9445i	−0.816631	+	0.785892i
$232$		0			0
$233$	18.5673			1.21638			0.608191	−	0.793791i	$-0.291896\pi$
$233$	18.5673			1.21638			0.608191	+	0.793791i	$0.291896\pi$
$234$		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	0.681031	−	0.732255i	$-0.261532\pi$
$239$	−0.791909	−	0.791909i	−0.0512243	−	0.0512243i	−0.732255	+	0.681031i	$0.761532\pi$
$240$		0			0
$241$	−4.38963	−	16.3823i	−0.282761	−	1.05528i	−0.950460	−	0.310847i	$-0.899387\pi$
$241$	−4.38963	−	16.3823i	−0.282761	−	1.05528i	0.667699	−	0.744432i	$-0.267279\pi$
$242$		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
$253$	21.0988	−	11.6477i	1.32647	−	0.732285i
$254$		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	−0.812463	−	0.583013i	$-0.801874\pi$
$263$	−11.5757	+	6.68325i	−0.713790	+	0.412107i	0.0986729	+	0.995120i	$0.468540\pi$
$264$		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	0.386547	−	0.922270i	$-0.373668\pi$
$271$	4.28297	+	1.14762i	0.260172	+	0.0697128i	−0.126375	+	0.991983i	$0.540334\pi$
$272$		0			0
$273$	1.54272	+	18.6626i	0.0933698	+	1.12951i
$274$		0			0
$275$	−0.206082	+	10.7438i	−0.0124272	+	0.647877i
$276$		0			0
$277$	7.36097	−	12.7496i	0.442278	−	0.766047i	−0.555580	−	0.831463i	$-0.687504\pi$
$277$	7.36097	−	12.7496i	0.442278	−	0.766047i	0.997858	+	0.0654153i	$0.0208372\pi$
$278$		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	$0.584734\pi$
$281$	−20.5824	+	20.5824i	−1.22784	+	1.22784i	−0.964778	+	0.263066i	$0.915266\pi$
$282$		0			0
$283$	9.38571	+	16.2565i	0.557923	+	0.966351i	0.997670	+	0.0682289i	$0.0217348\pi$
$283$	9.38571	+	16.2565i	0.557923	+	0.966351i	−0.439747	+	0.898122i	$0.644932\pi$
$284$		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	0.957503	−	0.288423i	$-0.0931308\pi$
$293$	−0.272681	−	1.01766i	−0.0159302	−	0.0594524i	−0.973433	+	0.228970i	$0.926464\pi$
$294$		0			0
$295$	−15.3332	+	26.5579i	−0.892735	+	1.54626i
$296$		0			0
$297$	3.33007	+	0.0638755i	0.193230	+	0.00370644i
$298$		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	−0.922896	−	0.385049i	$-0.874185\pi$
$307$	−9.42385	+	9.42385i	−0.537847	+	0.537847i	0.385049	+	0.922896i	$0.374185\pi$
$308$		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
$319$	0.918919	−	0.507294i	0.0514496	−	0.0284030i
$320$		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	$-0.630493\pi$
$337$	−14.6335			−0.797136			−0.398568	+	0.917139i	$0.630493\pi$
$338$		0			0
$339$	−8.31228			−0.451461
$340$		0			0
$341$	2.65763	−	2.55759i	0.143919	−	0.138501i
$342$		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	0.953073	−	0.302742i	$-0.0979021\pi$
$347$	21.7467	+	12.5555i	1.16743	+	0.674014i	0.214354	+	0.976756i	$0.431235\pi$
$348$		0			0
$349$	27.3181	+	7.31987i	1.46231	+	0.391824i	0.900286	−	0.435299i	$-0.143357\pi$
$349$	27.3181	+	7.31987i	1.46231	+	0.391824i	0.562021	+	0.827123i	$0.310024\pi$
$350$		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	−0.953426	−	0.301628i	$-0.902470\pi$
$359$	−12.3498	+	12.3498i	−0.651798	+	0.651798i	0.301628	+	0.953426i	$0.402470\pi$
$360$		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	0.508285	−	0.861189i	$-0.330280\pi$
$373$	0.320902	+	0.185273i	0.0166157	+	0.00959308i	−0.491669	+	0.870782i	$0.663613\pi$
$374$		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
$385$	−16.7403	−	10.0979i	−0.853163	−	0.514638i
$386$		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
$407$	−3.00861	+	10.4243i	−0.149131	+	0.516715i
$408$		0			0
$409$	34.3032	−	9.19152i	1.69618	−	0.454491i	0.724210	−	0.689579i	$-0.242204\pi$
$409$	34.3032	−	9.19152i	1.69618	−	0.454491i	0.971974	+	0.235088i	$0.0755378\pi$
$410$		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
$429$	29.6514	+	5.96440i	1.43158	+	0.287964i
$430$		0			0
$431$	−0.0382190	+	0.142635i	−0.00184095	+	0.00687051i	−0.966840	−	0.255382i	$-0.917799\pi$
$431$	−0.0382190	+	0.142635i	−0.00184095	+	0.00687051i	0.964999	+	0.262253i	$0.0844654\pi$
$432$		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	$0.0296409\pi$
$439$	12.1180	+	20.9890i	0.578361	+	1.00175i	−0.417306	+	0.908766i	$0.637026\pi$
$440$		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
$451$	−4.72688	+	16.3779i	−0.222580	+	0.771204i
$452$		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	$0.196872\pi$
$457$	−3.86394	+	14.4204i	−0.180748	+	0.674559i	−0.995501	+	0.0947515i	$0.969794\pi$
$458$		0			0
$459$	2.27655	−	3.94310i	0.106260	−	0.184048i
$460$		0			0
$461$	−2.39970	+	0.642997i	−0.111765	+	0.0299474i	−0.314268	−	0.949334i	$-0.601759\pi$
$461$	−2.39970	+	0.642997i	−0.111765	+	0.0299474i	0.202503	+	0.979282i	$0.435092\pi$
$462$		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
$473$	12.2970	−	20.3859i	0.565418	−	0.937346i
$474$		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	0.502880	−	0.864356i	$-0.332274\pi$
$479$	11.0789	+	2.96859i	0.506209	+	0.135638i	0.00332894	+	0.999994i	$0.498940\pi$
$480$		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	$-0.920702\pi$
$491$	−15.4686	−	26.7924i	−0.698087	−	1.20912i	0.271042	−	0.962568i	$-0.412632\pi$
$492$		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	0.822126	−	0.569305i	$-0.192788\pi$
$503$	16.6000	+	9.58401i	0.740157	+	0.427330i	−0.0819696	+	0.996635i	$0.526121\pi$
$504$		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
$517$	−6.76407	−	7.02864i	−0.297484	−	0.309119i
$518$		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	$0.682107\pi$
$523$	−35.2237	+	20.3364i	−1.54023	+	0.889250i	−0.998824	+	0.0484869i	$0.984560\pi$
$524$		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
$539$	−8.08133	+	4.46134i	−0.348088	+	0.192164i
$540$		0			0
$541$	−30.4180	+	30.4180i	−1.30777	+	1.30777i	−0.384753	+	0.923019i	$0.625714\pi$
$541$	−30.4180	+	30.4180i	−1.30777	+	1.30777i	−0.923019	+	0.384753i	$0.874286\pi$
$542$		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	$-0.818574\pi$
$547$		−	25.2405i		−	1.07921i	0.841919	−	0.539604i	$-0.181426\pi$
$548$		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	0.756832	−	0.653609i	$-0.226746\pi$
$557$	25.6178	+	6.86428i	1.08546	+	0.290849i	0.328631	+	0.944458i	$0.393413\pi$
$558$		0			0
$559$	−8.73544	−	24.3629i	−0.369470	−	1.03044i
$560$		0			0
$561$	38.0256	+	0.729386i	1.60544	+	0.0307947i
$562$		0			0
$563$	15.0848	−	26.1277i	0.635751	−	1.10115i	−0.350605	−	0.936523i	$-0.614024\pi$
$563$	15.0848	−	26.1277i	0.635751	−	1.10115i	0.986356	−	0.164629i	$-0.0526426\pi$
$564$		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	0.823677	−	0.567059i	$-0.191919\pi$
$569$	−1.89037	−	3.27422i	−0.0792485	−	0.137262i	−0.902926	+	0.429796i	$0.858585\pi$
$570$		0			0
$571$	29.7561			1.24525			0.622627	−	0.782519i	$-0.286065\pi$
$571$	29.7561			1.24525			0.622627	+	0.782519i	$0.286065\pi$
$572$		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
$583$	8.26037	+	0.158446i	0.342110	+	0.00656215i
$584$		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	−0.463322	−	0.886190i	$-0.653343\pi$
$593$	10.2975	−	10.2975i	0.422868	−	0.422868i	0.886190	+	0.463322i	$0.153343\pi$
$594$		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	−0.779955	−	0.625835i	$-0.784758\pi$
$601$	−15.3942	+	8.88787i	−0.627944	+	0.362544i	0.152011	+	0.988379i	$0.451425\pi$
$602$		0			0
$603$	−26.0281	+	26.0281i	−1.05995	+	1.05995i
$604$		0			0
$605$	−23.1673	+	21.4549i	−0.941886	+	0.872265i
$606$		0			0
$607$	−16.1266	−	9.31072i	−0.654560	−	0.377911i	0.135641	−	0.990758i	$-0.456691\pi$
$607$	−16.1266	−	9.31072i	−0.654560	−	0.377911i	−0.790201	+	0.612847i	$0.790024\pi$
$608$		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	$0.306648\pi$
$613$	−8.27168	+	30.8703i	−0.334090	+	1.24684i	−0.904852	+	0.425726i	$0.860019\pi$
$614$		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
$627$	−42.7936	−	44.4674i	−1.70901	−	1.77586i
$628$		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	0.949335	−	0.314265i	$-0.101758\pi$
$659$	29.5689	+	17.0716i	1.15184	+	0.665016i	0.202506	+	0.979281i	$0.435091\pi$
$660$		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
$671$	−6.42139	−	3.87346i	−0.247895	−	0.149533i
$672$		0			0
$673$	12.5597	+	21.7540i	0.484139	+	0.838554i	0.999834	−	0.0182186i	$-0.00579947\pi$
$673$	12.5597	+	21.7540i	0.484139	+	0.838554i	−0.515695	+	0.856772i	$0.672466\pi$
$674$		0			0
$675$			3.25371i			0.125236i
$676$		0			0
$677$		−	13.5226i		−	0.519717i	−0.965647	−	0.259859i	$-0.916324\pi$
$677$		−	13.5226i		−	0.519717i	0.965647	−	0.259859i	$-0.0836760\pi$
$678$		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
$693$	−22.2287	−	6.41550i	−0.844397	−	0.243705i
$694$		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	$-0.662650\pi$
$701$	−25.8956			−0.978063			−0.489032	+	0.872266i	$0.662650\pi$
$702$		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
$715$	2.17133	+	34.2579i	0.0812033	+	1.28117i
$716$		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	0.856623	−	0.515943i	$-0.172558\pi$
$733$	9.22356	+	9.22356i	0.340680	+	0.340680i	−0.515943	+	0.856623i	$0.672558\pi$
$734$		0			0
$735$	−19.5186	+	5.23000i	−0.719956	+	0.192912i
$736$		0			0
$737$	−34.5286	−	9.96542i	−1.27188	−	0.367081i
$738$		0			0
$739$	13.9170	+	3.72905i	0.511945	+	0.137175i	0.505538	−	0.862804i	$-0.331294\pi$
$739$	13.9170	+	3.72905i	0.511945	+	0.137175i	0.00640660	+	0.999979i	$0.497961\pi$
$740$		0			0
$741$	−66.8623	+	5.52710i	−2.45625	+	0.203043i
$742$		0			0
$743$	1.65786	−	6.18721i	0.0608209	−	0.226987i	−0.928825	−	0.370520i	$-0.879180\pi$
$743$	1.65786	−	6.18721i	0.0608209	−	0.226987i	0.989646	+	0.143533i	$0.0458463\pi$
$744$		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
$759$	52.1949	+	31.4846i	1.89456	+	1.14282i
$760$		0			0
$761$	−7.58164	−	28.2951i	−0.274834	−	1.02569i	−0.955952	−	0.293522i	$-0.905173\pi$
$761$	−7.58164	−	28.2951i	−0.274834	−	1.02569i	0.681118	−	0.732173i	$-0.261494\pi$
$762$		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	$-0.785216\pi$
$769$	5.76085	−	21.4998i	0.207742	−	0.775303i	0.988596	−	0.150590i	$-0.0481173\pi$
$770$		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	0.982970	−	0.183766i	$-0.0588289\pi$
$787$	1.11681	+	4.16799i	0.0398100	+	0.148573i	−0.943160	+	0.332339i	$0.892162\pi$
$788$		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
$803$	22.0812	−	21.2501i	0.779230	−	0.749899i
$804$		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	−0.302643	−	0.953104i	$-0.597869\pi$
$809$	10.5651	−	6.09974i	0.371448	−	0.214455i	0.674091	+	0.738649i	$0.264536\pi$
$810$		0			0
$811$	1.31277	+	1.31277i	0.0460977	+	0.0460977i	0.729780	−	0.683682i	$-0.239623\pi$
$811$	1.31277	+	1.31277i	0.0460977	+	0.0460977i	−0.683682	+	0.729780i	$0.739623\pi$
$812$		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	$0.430724\pi$
$821$	−13.1597	+	49.1127i	−0.459277	+	1.71405i	−0.675200	+	0.737635i	$0.735943\pi$
$822$		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
$825$	−23.7937	+	13.1354i	−0.828391	+	0.457318i
$826$		0			0
$827$	−1.74243	+	1.74243i	−0.0605901	+	0.0605901i	−0.736753	−	0.676162i	$-0.763642\pi$
$827$	−1.74243	+	1.74243i	−0.0605901	+	0.0605901i	0.676162	+	0.736753i	$0.263642\pi$
$828$		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
$847$	−5.00524	−	22.0267i	−0.171982	−	0.756845i
$848$		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	−0.339525	−	0.940597i	$-0.610266\pi$
$853$	17.5550	−	17.5550i	0.601073	−	0.601073i	0.940597	+	0.339525i	$0.110266\pi$
$854$		0			0
$855$	−35.8702	−	62.1290i	−1.22674	−	2.12477i
$856$		0			0
$857$	23.9032			0.816516			0.408258	−	0.912867i	$-0.366136\pi$
$857$	23.9032			0.816516			0.408258	+	0.912867i	$0.366136\pi$
$858$		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
$869$	0.805623	−	42.0002i	0.0273289	−	1.42476i
$870$		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	−0.192894	−	0.981220i	$-0.561787\pi$
$877$	3.86955	−	1.03684i	0.130665	−	0.0350117i	0.323559	+	0.946208i	$0.395121\pi$
$878$		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	−0.0389461	−	0.999241i	$-0.512400\pi$
$887$	24.0330	−	13.8755i	0.806949	−	0.465892i	0.845895	+	0.533349i	$0.179067\pi$
$888$		0			0
$889$	−19.5677	+	19.5677i	−0.656280	+	0.656280i
$890$		0			0
$891$	−12.2643	−	22.2157i	−0.410869	−	0.744253i
$892$		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
$913$	29.2950	+	30.4408i	0.969522	+	1.00744i
$914$		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	0.212552	−	0.977150i	$-0.431823\pi$
$919$	−15.9884	−	9.23091i	−0.527409	−	0.304500i	−0.739961	+	0.672650i	$0.765156\pi$
$920$		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	$-0.962005\pi$
$937$		−	7.29029i		−	0.238164i	0.992884	−	0.119082i	$-0.0379951\pi$
$938$		0			0
$939$	13.9422	+	24.1487i	0.454988	+	0.788062i
$940$		0			0
$941$	25.4782	+	25.4782i	0.830566	+	0.830566i	0.987594	−	0.157028i	$-0.0501912\pi$
$941$	25.4782	+	25.4782i	0.830566	+	0.830566i	−0.157028	+	0.987594i	$0.550191\pi$
$942$		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	$0.604926\pi$
$953$	−30.2918	+	52.4669i	−0.981248	+	1.69957i	−0.657551	+	0.753410i	$0.728408\pi$
$954$		0			0
$955$	12.1511	+	45.3485i	0.393200	+	1.46744i
$956$		0			0
$957$	2.27325	+	1.37125i	0.0734838	+	0.0443263i
$958$		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	0.749161	−	0.662387i	$-0.230457\pi$
$967$	2.69838	+	2.69838i	0.0867741	+	0.0867741i	−0.662387	+	0.749161i	$0.730457\pi$
$968$		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
$979$	8.95076	−	31.0129i	0.286067	−	0.991177i
$980$		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	0.915894	−	0.401420i	$-0.131483\pi$
$997$	32.4026	+	18.7077i	1.02620	+	0.592478i	0.110307	+	0.993898i	$0.464817\pi$
$998$		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.197.11	✓	56
11.10	odd	2	inner	572.2.bc.a.197.12	yes	56
13.7	odd	12	inner	572.2.bc.a.241.12	yes	56
143.98	even	12	inner	572.2.bc.a.241.11	yes	56

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

\(f(q)\)	\(=\)	\(q+(1.26462 + 2.19039i) q^{3} +(-2.02978 + 2.02978i) q^{5} +(-0.531478 - 1.98350i) q^{7} +(-1.69853 + 2.94193i) q^{9} +O(q^{10})\)	\(q+(1.26462 + 2.19039i) q^{3} +(-2.02978 + 2.02978i) q^{5} +(-0.531478 - 1.98350i) q^{7} +(-1.69853 + 2.94193i) q^{9} +(-3.31601 - 0.0636059i) q^{11} +(-2.33081 + 2.75088i) q^{13} +(-7.01289 - 1.87910i) q^{15} +(-2.26694 + 3.92646i) q^{17} +(7.10628 - 1.90412i) q^{19} +(3.67252 - 3.67252i) q^{21} +(-6.29301 + 3.63327i) q^{23} -3.23998i q^{25} -1.00424 q^{27} +(-0.274080 + 0.158240i) q^{29} +(-0.786368 + 0.786368i) q^{31} +(-4.05418 - 7.34379i) q^{33} +(5.10484 + 2.94728i) q^{35} +(0.846685 - 3.15987i) q^{37} +(-8.97307 - 1.62655i) q^{39} +(1.33024 - 4.96454i) q^{41} +(-3.58914 + 6.21656i) q^{43} +(-2.52384 - 9.41909i) q^{45} +(2.07971 + 2.07971i) q^{47} +(2.41037 - 1.39163i) q^{49} -11.4673 q^{51} -2.49105 q^{53} +(6.85987 - 6.60166i) q^{55} +(13.1575 + 13.1575i) q^{57} +(10.3192 - 2.76501i) q^{59} +(1.95816 + 1.13055i) q^{61} +(6.73806 + 1.80546i) q^{63} +(-0.852653 - 10.3147i) q^{65} +(10.4665 + 2.80448i) q^{67} +(-15.9165 - 9.18941i) q^{69} +(3.96957 + 14.8146i) q^{71} +(-6.53364 + 6.53364i) q^{73} +(7.09680 - 4.09734i) q^{75} +(1.63623 + 6.61112i) q^{77} +12.6659i q^{79} +(3.82560 + 6.62613i) q^{81} +(-9.00716 - 9.00716i) q^{83} +(-3.36845 - 12.5712i) q^{85} +(-0.693214 - 0.400227i) q^{87} +(-2.51893 + 9.40078i) q^{89} +(6.69514 + 3.16113i) q^{91} +(-2.71691 - 0.727993i) q^{93} +(-10.5592 + 18.2891i) q^{95} +(-1.82938 - 6.82732i) q^{97} +(5.81946 - 9.64746i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{9}+O(q^{10}) \) 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

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