LMFDB - Embedded newform 572.2.bh.a.57.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, degree $8$, 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:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.10
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.762321 - 0.553859i) q^{3} +(1.51772 + 0.773316i) q^{5} +(-0.624041 + 0.0988384i) q^{7} +(-0.652677 + 2.00873i) q^{9} +O(q^{10})$	\(q+(0.762321 - 0.553859i) q^{3} +(1.51772 + 0.773316i) q^{5} +(-0.624041 + 0.0988384i) q^{7} +(-0.652677 + 2.00873i) q^{9} +(0.655404 + 3.25122i) q^{11} +(0.438190 + 3.57883i) q^{13} +(1.58530 - 0.251086i) q^{15} +(0.170180 + 0.523759i) q^{17} +(6.98002 + 1.10553i) q^{19} +(-0.420977 + 0.420977i) q^{21} -5.78393i q^{23} +(-1.23348 - 1.69774i) q^{25} +(1.48855 + 4.58128i) q^{27} +(0.177236 - 0.243944i) q^{29} +(-3.27593 - 6.42937i) q^{31} +(2.30035 + 2.11548i) q^{33} +(-1.02355 - 0.332572i) q^{35} +(0.0169418 + 0.106966i) q^{37} +(2.31621 + 2.48552i) q^{39} +(-2.97212 - 0.470737i) q^{41} +4.09351 q^{43} +(-2.54396 + 2.54396i) q^{45} +(8.75722 + 1.38701i) q^{47} +(-6.27774 + 2.03976i) q^{49} +(0.419820 + 0.305017i) q^{51} +(-0.849567 + 2.61470i) q^{53} +(-1.51950 + 5.44127i) q^{55} +(5.93333 - 3.02318i) q^{57} +(-2.03913 - 12.8745i) q^{59} +(8.45691 - 2.74782i) q^{61} +(0.208757 - 1.31804i) q^{63} +(-2.10251 + 5.77050i) q^{65} +(-7.50198 + 7.50198i) q^{67} +(-3.20348 - 4.40921i) q^{69} +(-0.0902617 - 0.0459906i) q^{71} +(7.95823 - 1.26046i) q^{73} +(-1.88061 - 0.611048i) q^{75} +(-0.730344 - 1.96412i) q^{77} +(2.57604 + 0.837005i) q^{79} +(-1.45406 - 1.05643i) q^{81} +(-0.714428 + 1.40214i) q^{83} +(-0.146746 + 0.926520i) q^{85} -0.284127i q^{87} +(-9.60592 - 9.60592i) q^{89} +(-0.627174 - 2.19002i) q^{91} +(-6.05828 - 3.08685i) q^{93} +(9.73878 + 7.07564i) q^{95} +(0.978345 + 1.92011i) q^{97} +(-6.95860 - 0.805466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	0.762321	−	0.553859i	0.440126	−	0.319771i	−0.345559	−	0.938397i	$-0.612311\pi$
$3$	0.762321	−	0.553859i	0.440126	−	0.319771i	0.785685	+	0.618627i	$0.212311\pi$
$4$		0			0
$5$	1.51772	+	0.773316i	0.678744	+	0.345837i	0.759142	−	0.650926i	$-0.225619\pi$
$5$	1.51772	+	0.773316i	0.678744	+	0.345837i	−0.0803976	+	0.996763i	$0.525619\pi$
$6$		0			0
$7$	−0.624041	+	0.0988384i	−0.235865	+	0.0373574i	−0.273248	−	0.961944i	$-0.588098\pi$
$7$	−0.624041	+	0.0988384i	−0.235865	+	0.0373574i	0.0373826	+	0.999301i	$0.488098\pi$
$8$		0			0
$9$	−0.652677	+	2.00873i	−0.217559	+	0.669578i
$10$		0			0
$11$	0.655404	+	3.25122i	0.197612	+	0.980280i
$11$	0.655404	+	3.25122i	0.197612	+	0.980280i
$12$		0			0
$13$	0.438190	+	3.57883i	0.121532	+	0.992588i
$13$	0.438190	+	3.57883i	0.121532	+	0.992588i
$14$		0			0
$15$	1.58530	−	0.251086i	0.409322	−	0.0648302i
$16$		0			0
$17$	0.170180	+	0.523759i	0.0412746	+	0.127030i	0.969571	−	0.244812i	$-0.0787262\pi$
$17$	0.170180	+	0.523759i	0.0412746	+	0.127030i	−0.928296	+	0.371842i	$0.878726\pi$
$18$		0			0
$19$	6.98002	+	1.10553i	1.60133	+	0.253625i	0.892262	−	0.451518i	$-0.149117\pi$
$19$	6.98002	+	1.10553i	1.60133	+	0.253625i	0.709065	+	0.705143i	$0.249117\pi$
$20$		0			0
$21$	−0.420977	+	0.420977i	−0.0918648	+	0.0918648i
$22$		0			0
$23$		−	5.78393i		−	1.20603i	−0.797729	−	0.603016i	$-0.793965\pi$
$23$		−	5.78393i		−	1.20603i	0.797729	−	0.603016i	$-0.206035\pi$
$24$		0			0
$25$	−1.23348	−	1.69774i	−0.246695	−	0.339547i
$26$		0			0
$27$	1.48855	+	4.58128i	0.286471	+	0.881667i
$28$		0			0
$29$	0.177236	−	0.243944i	0.0329119	−	0.0452993i	−0.792244	−	0.610204i	$-0.791087\pi$
$29$	0.177236	−	0.243944i	0.0329119	−	0.0452993i	0.825156	+	0.564905i	$0.191087\pi$
$30$		0			0
$31$	−3.27593	−	6.42937i	−0.588374	−	1.15475i	−0.972811	−	0.231599i	$-0.925604\pi$
$31$	−3.27593	−	6.42937i	−0.588374	−	1.15475i	0.384437	−	0.923151i	$-0.374396\pi$
$32$		0			0
$33$	2.30035	+	2.11548i	0.400439	+	0.368257i
$34$		0			0
$35$	−1.02355	−	0.332572i	−0.173012	−	0.0562149i
$36$		0			0
$37$	0.0169418	+	0.106966i	0.00278521	+	0.0175851i	0.989042	−	0.147636i	$-0.0471663\pi$
$37$	0.0169418	+	0.106966i	0.00278521	+	0.0175851i	−0.986257	+	0.165221i	$0.947166\pi$
$38$		0			0
$39$	2.31621	+	2.48552i	0.370890	+	0.398002i
$40$		0			0
$41$	−2.97212	−	0.470737i	−0.464167	−	0.0735168i	−0.0800288	−	0.996793i	$-0.525501\pi$
$41$	−2.97212	−	0.470737i	−0.464167	−	0.0735168i	−0.384138	+	0.923276i	$0.625501\pi$
$42$		0			0
$43$	4.09351			0.624255			0.312127	−	0.950040i	$-0.398958\pi$
$43$	4.09351			0.624255			0.312127	+	0.950040i	$0.398958\pi$
$44$		0			0
$45$	−2.54396	+	2.54396i	−0.379232	+	0.379232i
$46$		0			0
$47$	8.75722	+	1.38701i	1.27737	+	0.202316i	0.758013	−	0.652240i	$-0.226171\pi$
$47$	8.75722	+	1.38701i	1.27737	+	0.202316i	0.519360	+	0.854556i	$0.326171\pi$
$48$		0			0
$49$	−6.27774	+	2.03976i	−0.896820	+	0.291394i
$50$		0			0
$51$	0.419820	+	0.305017i	0.0587866	+	0.0427109i
$52$		0			0
$53$	−0.849567	+	2.61470i	−0.116697	+	0.359156i	−0.992297	−	0.123880i	$-0.960466\pi$
$53$	−0.849567	+	2.61470i	−0.116697	+	0.359156i	0.875600	+	0.483037i	$0.160466\pi$
$54$		0			0
$55$	−1.51950	+	5.44127i	−0.204890	+	0.733701i
$56$		0			0
$57$	5.93333	−	3.02318i	0.785888	−	0.400430i
$58$		0			0
$59$	−2.03913	−	12.8745i	−0.265472	−	1.67612i	−0.655404	−	0.755278i	$-0.727502\pi$
$59$	−2.03913	−	12.8745i	−0.265472	−	1.67612i	0.389933	−	0.920843i	$-0.372498\pi$
$60$		0			0
$61$	8.45691	−	2.74782i	1.08280	−	0.351822i	0.287338	−	0.957829i	$-0.407230\pi$
$61$	8.45691	−	2.74782i	1.08280	−	0.351822i	0.795459	+	0.606007i	$0.207230\pi$
$62$		0			0
$63$	0.208757	−	1.31804i	0.0263009	−	0.166058i
$64$		0			0
$65$	−2.10251	+	5.77050i	−0.260785	+	0.715743i
$66$		0			0
$67$	−7.50198	+	7.50198i	−0.916513	+	0.916513i	−0.996774	−	0.0802612i	$-0.974425\pi$
$67$	−7.50198	+	7.50198i	−0.916513	+	0.916513i	0.0802612	+	0.996774i	$0.474425\pi$
$68$		0			0
$69$	−3.20348	−	4.40921i	−0.385654	−	0.530807i
$70$		0			0
$71$	−0.0902617	−	0.0459906i	−0.0107121	−	0.00545808i	0.448626	−	0.893719i	$-0.351913\pi$
$71$	−0.0902617	−	0.0459906i	−0.0107121	−	0.00545808i	−0.459338	+	0.888261i	$0.651913\pi$
$72$		0			0
$73$	7.95823	−	1.26046i	0.931441	−	0.147526i	0.327768	−	0.944758i	$-0.393703\pi$
$73$	7.95823	−	1.26046i	0.931441	−	0.147526i	0.603673	+	0.797232i	$0.293703\pi$
$74$		0			0
$75$	−1.88061	−	0.611048i	−0.217154	−	0.0705577i
$76$		0			0
$77$	−0.730344	−	1.96412i	−0.0832305	−	0.223832i
$78$		0			0
$79$	2.57604	+	0.837005i	0.289827	+	0.0941704i	0.450322	−	0.892866i	$-0.351309\pi$
$79$	2.57604	+	0.837005i	0.289827	+	0.0941704i	−0.160495	+	0.987037i	$0.551309\pi$
$80$		0			0
$81$	−1.45406	−	1.05643i	−0.161562	−	0.117382i
$82$		0			0
$83$	−0.714428	+	1.40214i	−0.0784186	+	0.153905i	−0.926887	−	0.375342i	$-0.877525\pi$
$83$	−0.714428	+	1.40214i	−0.0784186	+	0.153905i	0.848468	+	0.529247i	$0.177525\pi$
$84$		0			0
$85$	−0.146746	+	0.926520i	−0.0159169	+	0.100495i
$86$		0			0
$87$		−	0.284127i		−	0.0304617i
$88$		0			0
$89$	−9.60592	−	9.60592i	−1.01823	−	1.01823i	−0.999831	−	0.0183948i	$-0.994144\pi$
$89$	−9.60592	−	9.60592i	−1.01823	−	1.01823i	−0.0183948	−	0.999831i	$-0.505856\pi$
$90$		0			0
$91$	−0.627174	−	2.19002i	−0.0657457	−	0.229577i
$92$		0			0
$93$	−6.05828	−	3.08685i	−0.628214	−	0.320091i
$94$		0			0
$95$	9.73878	+	7.07564i	0.999178	+	0.725945i
$96$		0			0
$97$	0.978345	+	1.92011i	0.0993359	+	0.194958i	0.935326	−	0.353787i	$-0.115106\pi$
$97$	0.978345	+	1.92011i	0.0993359	+	0.194958i	−0.835990	+	0.548744i	$0.815106\pi$
$98$		0			0
$99$	−6.95860	−	0.805466i	−0.699366	−	0.0809524i
$100$		0			0
$101$	−5.90211	+	18.1648i	−0.587282	+	1.80747i	0.00262646	+	0.999997i	$0.499164\pi$
$101$	−5.90211	+	18.1648i	−0.587282	+	1.80747i	−0.589908	+	0.807470i	$0.700836\pi$
$102$		0			0
$103$	6.13566	−	8.44502i	0.604565	−	0.832112i	−0.391552	−	0.920156i	$-0.628062\pi$
$103$	6.13566	−	8.44502i	0.604565	−	0.832112i	0.996117	+	0.0880440i	$0.0280616\pi$
$104$		0			0
$105$	−0.964473	+	0.313376i	−0.0941229	+	0.0305824i
$106$		0			0
$107$	−6.27656	−	8.63895i	−0.606778	−	0.835159i	0.389529	−	0.921014i	$-0.372638\pi$
$107$	−6.27656	−	8.63895i	−0.606778	−	0.835159i	−0.996308	+	0.0858554i	$0.972638\pi$
$108$		0			0
$109$	−9.72306	−	9.72306i	−0.931300	−	0.931300i	0.0664871	−	0.997787i	$-0.478821\pi$
$109$	−9.72306	−	9.72306i	−0.931300	−	0.931300i	−0.997787	+	0.0664871i	$0.978821\pi$
$110$		0			0
$111$	0.0721592	+	0.0721592i	0.00684905	+	0.00684905i
$112$		0			0
$113$	−13.1167	+	9.52985i	−1.23392	+	0.896493i	−0.997177	−	0.0750805i	$-0.976079\pi$
$113$	−13.1167	+	9.52985i	−1.23392	+	0.896493i	−0.236739	+	0.971573i	$0.576079\pi$
$114$		0			0
$115$	4.47280	−	8.77837i	0.417091	−	0.818587i
$116$		0			0
$117$	−7.47490	−	1.45561i	−0.691055	−	0.134571i
$118$		0			0
$119$	−0.157967	−	0.310027i	−0.0144808	−	0.0284201i
$120$		0			0
$121$	−10.1409	+	4.26173i	−0.921899	+	0.387430i
$122$		0			0
$123$	−2.52643	+	1.28728i	−0.227800	+	0.116070i
$124$		0			0
$125$	−1.89152	−	11.9426i	−0.169182	−	1.06818i
$126$		0			0
$127$	−1.28354	−	3.95033i	−0.113896	−	0.350535i	0.877819	−	0.478992i	$-0.158998\pi$
$127$	−1.28354	−	3.95033i	−0.113896	−	0.350535i	−0.991715	+	0.128457i	$0.958998\pi$
$128$		0			0
$129$	3.12057	−	2.26723i	0.274751	−	0.199618i
$130$		0			0
$131$			19.2710i			1.68372i	0.539698	+	0.841859i	$0.318539\pi$
$131$			19.2710i			1.68372i	−0.539698	+	0.841859i	$0.681461\pi$
$132$		0			0
$133$	−4.46509			−0.387172
$134$		0			0
$135$	−1.28358	+	8.10420i	−0.110473	+	0.697499i
$136$		0			0
$137$	1.32487	−	2.60020i	0.113191	−	0.222150i	−0.827460	−	0.561524i	$-0.810215\pi$
$137$	1.32487	−	2.60020i	0.113191	−	0.222150i	0.940651	+	0.339374i	$0.110215\pi$
$138$		0			0
$139$	6.45125	−	8.87938i	0.547188	−	0.753139i	−0.442440	−	0.896798i	$-0.645887\pi$
$139$	6.45125	−	8.87938i	0.547188	−	0.753139i	0.989627	+	0.143659i	$0.0458869\pi$
$140$		0			0
$141$	7.44402	−	3.79292i	0.626900	−	0.319421i
$142$		0			0
$143$	−11.3484	+	3.77023i	−0.948998	+	0.315282i
$144$		0			0
$145$	0.457640	−	0.233179i	0.0380049	−	0.0193645i
$146$		0			0
$147$	−3.65591	+	5.03193i	−0.301535	+	0.415027i
$148$		0			0
$149$	3.03725	−	5.96094i	0.248821	−	0.488339i	−0.732487	−	0.680781i	$-0.761641\pi$
$149$	3.03725	−	5.96094i	0.248821	−	0.488339i	0.981308	+	0.192441i	$0.0616406\pi$
$150$		0			0
$151$	3.30915	−	20.8932i	0.269295	−	1.70026i	−0.368151	−	0.929766i	$-0.620009\pi$
$151$	3.30915	−	20.8932i	0.269295	−	1.70026i	0.637446	−	0.770495i	$-0.279991\pi$
$152$		0			0
$153$	−1.16316			−0.0940362
$154$		0			0
$155$		−	12.2913i		−	0.987261i
$156$		0			0
$157$	14.8997	−	10.8253i	1.18913	−	0.863951i	0.195954	−	0.980613i	$-0.437220\pi$
$157$	14.8997	−	10.8253i	1.18913	−	0.863951i	0.993172	+	0.116662i	$0.0372195\pi$
$158$		0			0
$159$	0.800531	+	2.46378i	0.0634862	+	0.195390i
$160$		0			0
$161$	0.571674	+	3.60941i	0.0450542	+	0.284461i
$162$		0			0
$163$	14.7914	−	7.53657i	1.15855	−	0.590310i	0.234324	−	0.972159i	$-0.424712\pi$
$163$	14.7914	−	7.53657i	1.15855	−	0.590310i	0.924225	+	0.381849i	$0.124712\pi$
$164$		0			0
$165$	1.85535	+	4.98959i	0.144439	+	0.388439i
$166$		0			0
$167$	2.57262	+	5.04905i	0.199075	+	0.390707i	0.968865	−	0.247591i	$-0.0796389\pi$
$167$	2.57262	+	5.04905i	0.199075	+	0.390707i	−0.769790	+	0.638298i	$0.779639\pi$
$168$		0			0
$169$	−12.6160	+	3.13641i	−0.970460	+	0.241262i
$170$		0			0
$171$	−6.77641	+	13.2994i	−0.518205	+	1.01703i
$172$		0			0
$173$	−9.80945	+	7.12698i	−0.745799	+	0.541855i	−0.894522	−	0.447024i	$-0.852484\pi$
$173$	−9.80945	+	7.12698i	−0.745799	+	0.541855i	0.148723	+	0.988879i	$0.452484\pi$
$174$		0			0
$175$	0.937542	+	0.937542i	0.0708715	+	0.0708715i
$176$		0			0
$177$	−8.68515	−	8.68515i	−0.652816	−	0.652816i
$178$		0			0
$179$	3.03532	+	4.17776i	0.226871	+	0.312261i	0.907244	−	0.420605i	$-0.138182\pi$
$179$	3.03532	+	4.17776i	0.226871	+	0.312261i	−0.680373	+	0.732866i	$0.738182\pi$
$180$		0			0
$181$	−3.78421	+	1.22956i	−0.281278	+	0.0913928i	−0.446259	−	0.894904i	$-0.647244\pi$
$181$	−3.78421	+	1.22956i	−0.281278	+	0.0913928i	0.164981	+	0.986297i	$0.447244\pi$
$182$		0			0
$183$	4.92498	−	6.77866i	0.364065	−	0.501093i
$184$		0			0
$185$	−0.0570058	+	0.175446i	−0.00419115	+	0.0128990i
$186$		0			0
$187$	−1.59132	+	0.896565i	−0.116369	+	0.0655633i
$188$		0			0
$189$	−1.38172	−	2.71178i	−0.100505	−	0.197253i
$190$		0			0
$191$	−9.30149	−	6.75793i	−0.673032	−	0.488986i	0.198007	−	0.980201i	$-0.436553\pi$
$191$	−9.30149	−	6.75793i	−0.673032	−	0.488986i	−0.871039	+	0.491214i	$0.836553\pi$
$192$		0			0
$193$	10.8762	+	5.54171i	0.782887	+	0.398901i	0.799275	−	0.600965i	$-0.205217\pi$
$193$	10.8762	+	5.54171i	0.782887	+	0.398901i	−0.0163886	+	0.999866i	$0.505217\pi$
$194$		0			0
$195$	1.59325	+	5.56347i	0.114095	+	0.398409i
$196$		0			0
$197$	−12.4171	−	12.4171i	−0.884680	−	0.884680i	0.109326	−	0.994006i	$-0.465131\pi$
$197$	−12.4171	−	12.4171i	−0.884680	−	0.884680i	−0.994006	+	0.109326i	$0.965131\pi$
$198$		0			0
$199$		−	20.8880i		−	1.48071i	−0.672215	−	0.740356i	$-0.734657\pi$
$199$		−	20.8880i		−	1.48071i	0.672215	−	0.740356i	$-0.265343\pi$
$200$		0			0
$201$	−1.56388	+	9.87396i	−0.110308	+	0.696455i
$202$		0			0
$203$	−0.0864913	+	0.169749i	−0.00607050	+	0.0119140i
$204$		0			0
$205$	−4.14680	−	3.01283i	−0.289625	−	0.210425i
$206$		0			0
$207$	11.6184	+	3.77503i	0.807532	+	0.262383i
$208$		0			0
$209$	0.980419	+	23.4182i	0.0678170	+	1.61987i
$210$		0			0
$211$	10.7576	+	3.49535i	0.740583	+	0.240630i	0.654924	−	0.755695i	$-0.272701\pi$
$211$	10.7576	+	3.49535i	0.740583	+	0.240630i	0.0856587	+	0.996325i	$0.472701\pi$
$212$		0			0
$213$	−0.0942807	+	0.0149326i	−0.00646001	+	0.00102316i
$214$		0			0
$215$	6.21279	+	3.16558i	0.423709	+	0.215891i
$216$		0			0
$217$	2.67978	+	3.68841i	0.181916	+	0.250385i
$218$		0			0
$219$	5.36861	−	5.36861i	0.362777	−	0.362777i
$220$		0			0
$221$	−1.79987	+	0.838549i	−0.121072	+	0.0564069i
$222$		0			0
$223$	1.95232	−	12.3264i	0.130737	−	0.825439i	−0.831956	−	0.554842i	$-0.812779\pi$
$223$	1.95232	−	12.3264i	0.130737	−	0.825439i	0.962693	−	0.270597i	$-0.0872212\pi$
$224$		0			0
$225$	4.21536	−	1.36965i	0.281024	−	0.0913102i
$226$		0			0
$227$	−0.315101	−	1.98947i	−0.0209140	−	0.132046i	0.975022	−	0.222108i	$-0.0712936\pi$
$227$	−0.315101	−	1.98947i	−0.0209140	−	0.132046i	−0.995936	+	0.0900616i	$0.971294\pi$
$228$		0			0
$229$	17.1348	−	8.73061i	1.13230	−	0.576935i	0.215587	−	0.976485i	$-0.430834\pi$
$229$	17.1348	−	8.73061i	1.13230	−	0.576935i	0.916711	+	0.399550i	$0.130834\pi$
$230$		0			0
$231$	−1.64460	−	1.09278i	−0.108207	−	0.0718997i
$232$		0			0
$233$	3.51290	−	10.8116i	0.230138	−	0.708291i	−0.767592	−	0.640939i	$-0.778545\pi$
$233$	3.51290	−	10.8116i	0.230138	−	0.708291i	0.997729	−	0.0673518i	$-0.0214550\pi$
$234$		0			0
$235$	12.2184	+	8.87718i	0.797040	+	0.579084i
$236$		0			0
$237$	2.42735	−	0.788694i	0.157673	−	0.0512312i
$238$		0			0
$239$	1.27648	+	0.202175i	0.0825687	+	0.0130776i	0.197582	−	0.980286i	$-0.436691\pi$
$239$	1.27648	+	0.202175i	0.0825687	+	0.0130776i	−0.115013	+	0.993364i	$0.536691\pi$
$240$		0			0
$241$	−18.1635	+	18.1635i	−1.17002	+	1.17002i	−0.187811	+	0.982205i	$0.560139\pi$
$241$	−18.1635	+	18.1635i	−1.17002	+	1.17002i	−0.982205	+	0.187811i	$0.939861\pi$
$242$		0			0
$243$	−16.1447			−1.03568
$244$		0			0
$245$	−11.1052	−	1.75889i	−0.709486	−	0.112372i
$246$		0			0
$247$	−0.897915	+	25.4647i	−0.0571329	+	1.62028i
$248$		0			0
$249$	0.231966	+	1.46458i	0.0147003	+	0.0928137i
$250$		0			0
$251$	−7.35569	−	2.39001i	−0.464287	−	0.150856i	0.0675266	−	0.997717i	$-0.478489\pi$
$251$	−7.35569	−	2.39001i	−0.464287	−	0.150856i	−0.531813	+	0.846862i	$0.678489\pi$
$252$		0			0
$253$	18.8048	−	3.79081i	1.18225	−	0.238326i
$254$		0			0
$255$	0.401294	+	0.787583i	0.0251300	+	0.0493204i
$256$		0			0
$257$	−4.60860	+	6.34319i	−0.287476	+	0.395677i	−0.928192	−	0.372101i	$-0.878638\pi$
$257$	−4.60860	+	6.34319i	−0.287476	+	0.395677i	0.640716	+	0.767778i	$0.278638\pi$
$258$		0			0
$259$	−0.0211447	−	0.0650768i	−0.00131387	−	0.00404368i
$260$		0			0
$261$	0.374341	+	0.515236i	0.0231711	+	0.0318923i
$262$		0			0
$263$			24.6567i			1.52040i	0.649691	+	0.760199i	$0.274898\pi$
$263$			24.6567i			1.52040i	−0.649691	+	0.760199i	$0.725102\pi$
$264$		0			0
$265$	−3.31139	+	3.31139i	−0.203417	+	0.203417i
$266$		0			0
$267$	−12.6431	−	2.00247i	−0.773747	−	0.122549i
$268$		0			0
$269$	4.01453	+	12.3555i	0.244770	+	0.753326i	0.995674	+	0.0929143i	$0.0296182\pi$
$269$	4.01453	+	12.3555i	0.244770	+	0.753326i	−0.750904	+	0.660412i	$0.770382\pi$
$270$		0			0
$271$	11.1765	−	1.77018i	0.678923	−	0.107531i	0.192556	−	0.981286i	$-0.438322\pi$
$271$	11.1765	−	1.77018i	0.678923	−	0.107531i	0.486366	+	0.873755i	$0.338322\pi$
$272$		0			0
$273$	−1.69107	−	1.32214i	−0.102348	−	0.0800193i
$274$		0			0
$275$	4.71129	−	5.12301i	0.284101	−	0.308929i
$276$		0			0
$277$	−2.76271	+	8.50275i	−0.165995	+	0.510881i	−0.999108	−	0.0422219i	$-0.986556\pi$
$277$	−2.76271	+	8.50275i	−0.165995	+	0.510881i	0.833113	+	0.553103i	$0.186556\pi$
$278$		0			0
$279$	15.0530	−	2.38416i	0.901201	−	0.142736i
$280$		0			0
$281$	−4.23247	−	2.15655i	−0.252488	−	0.128649i	0.323167	−	0.946342i	$-0.395253\pi$
$281$	−4.23247	−	2.15655i	−0.252488	−	0.128649i	−0.575654	+	0.817693i	$0.695253\pi$
$282$		0			0
$283$	−11.0516	+	8.02943i	−0.656947	+	0.477300i	−0.865631	−	0.500683i	$-0.833082\pi$
$283$	−11.0516	+	8.02943i	−0.656947	+	0.477300i	0.208683	+	0.977983i	$0.433082\pi$
$284$		0			0
$285$	11.3430			0.671901
$286$		0			0
$287$	1.90125			0.112227
$288$		0			0
$289$	13.5079	−	9.81408i	0.794584	−	0.577299i
$290$		0			0
$291$	1.80928	+	0.921876i	0.106062	+	0.0540413i
$292$		0			0
$293$	30.9579	−	4.90325i	1.80858	−	0.286451i	0.841375	−	0.540452i	$-0.181747\pi$
$293$	30.9579	−	4.90325i	1.80858	−	0.286451i	0.967204	+	0.254001i	$0.0817467\pi$
$294$		0			0
$295$	6.86126	−	21.1168i	0.399478	−	1.22947i
$296$		0			0
$297$	−13.9192	+	7.84219i	−0.807671	+	0.455050i
$298$		0			0
$299$	20.6997	−	2.53446i	1.19709	−	0.146571i
$300$		0			0
$301$	−2.55452	+	0.404596i	−0.147240	+	0.0233205i
$302$		0			0
$303$	5.56144	+	17.1164i	0.319497	+	0.983309i
$304$		0			0
$305$	14.9601	+	2.36945i	0.856615	+	0.135674i
$306$		0			0
$307$	−8.64938	+	8.64938i	−0.493646	+	0.493646i	−0.909453	−	0.415807i	$-0.863499\pi$
$307$	−8.64938	+	8.64938i	−0.493646	+	0.493646i	0.415807	+	0.909453i	$0.363499\pi$
$308$		0			0
$309$		−	9.83611i		−	0.559557i
$310$		0			0
$311$	7.75476	+	10.6735i	0.439732	+	0.605240i	0.970153	−	0.242495i	$-0.0779659\pi$
$311$	7.75476	+	10.6735i	0.439732	+	0.605240i	−0.530420	+	0.847735i	$0.677966\pi$
$312$		0			0
$313$	9.24447	+	28.4516i	0.522529	+	1.60818i	0.769152	+	0.639066i	$0.220679\pi$
$313$	9.24447	+	28.4516i	0.522529	+	1.60818i	−0.246623	+	0.969111i	$0.579321\pi$
$314$		0			0
$315$	1.33610	−	1.83898i	0.0752805	−	0.103615i
$316$		0			0
$317$	3.97407	+	7.79955i	0.223206	+	0.438066i	0.975268	−	0.221026i	$-0.0709406\pi$
$317$	3.97407	+	7.79955i	0.223206	+	0.438066i	−0.752062	+	0.659092i	$0.770941\pi$
$318$		0			0
$319$	0.909277	+	0.416351i	0.0509098	+	0.0233112i
$320$		0			0
$321$	−9.56952	−	3.10932i	−0.534118	−	0.173546i
$322$		0			0
$323$	0.608828	+	3.84399i	0.0338761	+	0.213885i
$324$		0			0
$325$	5.53540	−	5.15833i	0.307049	−	0.286133i
$326$		0			0
$327$	−12.7973	−	2.02689i	−0.707692	−	0.112087i
$328$		0			0
$329$	−5.60196			−0.308846
$330$		0			0
$331$	13.8726	−	13.8726i	0.762505	−	0.762505i	−0.214270	−	0.976775i	$-0.568737\pi$
$331$	13.8726	−	13.8726i	0.762505	−	0.762505i	0.976775	+	0.214270i	$0.0687372\pi$
$332$		0			0
$333$	−0.225924	−	0.0357828i	−0.0123806	−	0.00196089i
$334$		0			0
$335$	−17.1873	+	5.58449i	−0.939042	+	0.305113i
$336$		0			0
$337$	23.2007	+	16.8563i	1.26382	+	0.918219i	0.998939	−	0.0460616i	$-0.0146671\pi$
$337$	23.2007	+	16.8563i	1.26382	+	0.918219i	0.264882	+	0.964281i	$0.414667\pi$
$338$		0			0
$339$	−4.72096	+	14.5296i	−0.256407	+	0.789140i
$340$		0			0
$341$	18.7563	−	14.8646i	1.01571	−	0.804964i
$342$		0			0
$343$	7.65665	−	3.90126i	0.413420	−	0.210648i
$344$		0			0
$345$	−1.45226	−	9.16924i	−0.0781873	−	0.493655i
$346$		0			0
$347$	1.00745	−	0.327339i	0.0540825	−	0.0175725i	−0.281851	−	0.959458i	$-0.590948\pi$
$347$	1.00745	−	0.327339i	0.0540825	−	0.0175725i	0.335933	+	0.941886i	$0.390948\pi$
$348$		0			0
$349$	3.68369	−	23.2579i	0.197183	−	1.24497i	−0.668248	−	0.743938i	$-0.732956\pi$
$349$	3.68369	−	23.2579i	0.197183	−	1.24497i	0.865432	−	0.501027i	$-0.167044\pi$
$350$		0			0
$351$	−15.7433	+	7.33472i	−0.840317	+	0.391498i
$352$		0			0
$353$	−7.29264	+	7.29264i	−0.388148	+	0.388148i	−0.874026	−	0.485878i	$-0.838500\pi$
$353$	−7.29264	+	7.29264i	−0.388148	+	0.388148i	0.485878	+	0.874026i	$0.338500\pi$
$354$		0			0
$355$	−0.101426	−	0.139602i	−0.00538316	−	0.00740928i
$356$		0			0
$357$	−0.292132	−	0.148849i	−0.0154613	−	0.00787792i
$358$		0			0
$359$	−22.0350	+	3.49000i	−1.16296	+	0.184195i	−0.707932	−	0.706281i	$-0.750372\pi$
$359$	−22.0350	+	3.49000i	−1.16296	+	0.184195i	−0.455031	+	0.890476i	$0.650372\pi$
$360$		0			0
$361$	29.4284	+	9.56188i	1.54887	+	0.503257i
$362$		0			0
$363$	−5.37022	+	8.86543i	−0.281864	+	0.465314i
$364$		0			0
$365$	13.0531	+	4.24120i	0.683230	+	0.221995i
$366$		0			0
$367$	6.00687	+	4.36424i	0.313556	+	0.227812i	0.733421	−	0.679775i	$-0.237923\pi$
$367$	6.00687	+	4.36424i	0.313556	+	0.227812i	−0.419865	+	0.907587i	$0.637923\pi$
$368$		0			0
$369$	2.88542	−	5.66295i	0.150209	−	0.294801i
$370$		0			0
$371$	0.271732	−	1.71565i	0.0141076	−	0.0890721i
$372$		0			0
$373$		−	11.9799i		−	0.620293i	−0.950689	−	0.310147i	$-0.899622\pi$
$373$		−	11.9799i		−	0.620293i	0.950689	−	0.310147i	$-0.100378\pi$
$374$		0			0
$375$	−8.05644	−	8.05644i	−0.416033	−	0.416033i
$376$		0			0
$377$	0.950696	+	0.527402i	0.0489633	+	0.0271626i
$378$		0			0
$379$	−24.1408	−	12.3003i	−1.24003	−	0.631826i	−0.293968	−	0.955815i	$-0.594976\pi$
$379$	−24.1408	−	12.3003i	−1.24003	−	0.631826i	−0.946061	+	0.323989i	$0.894976\pi$
$380$		0			0
$381$	−3.16639	−	2.30052i	−0.162219	−	0.117859i
$382$		0			0
$383$	−1.33016	−	2.61058i	−0.0679679	−	0.133395i	0.854523	−	0.519414i	$-0.173850\pi$
$383$	−1.33016	−	2.61058i	−0.0679679	−	0.133395i	−0.922491	+	0.386019i	$0.873850\pi$
$384$		0			0
$385$	0.410426	−	3.54576i	0.0209173	−	0.180709i
$386$		0			0
$387$	−2.67174	+	8.22277i	−0.135812	+	0.417987i
$388$		0			0
$389$	8.12218	−	11.1792i	0.411811	−	0.566809i	−0.551848	−	0.833945i	$-0.686077\pi$
$389$	8.12218	−	11.1792i	0.411811	−	0.566809i	0.963659	+	0.267136i	$0.0860771\pi$
$390$		0			0
$391$	3.02938	−	0.984306i	0.153202	−	0.0497785i
$392$		0			0
$393$	10.6734	+	14.6907i	0.538403	+	0.741049i
$394$		0			0
$395$	3.26243	+	3.26243i	0.164150	+	0.164150i
$396$		0			0
$397$	−16.4577	−	16.4577i	−0.825991	−	0.825991i	0.160969	−	0.986959i	$-0.448538\pi$
$397$	−16.4577	−	16.4577i	−0.825991	−	0.825991i	−0.986959	+	0.160969i	$0.948538\pi$
$398$		0			0
$399$	−3.40383	+	2.47303i	−0.170405	+	0.123806i
$400$		0			0
$401$	−5.24191	+	10.2878i	−0.261768	+	0.513749i	−0.984059	−	0.177840i	$-0.943089\pi$
$401$	−5.24191	+	10.2878i	−0.261768	+	0.513749i	0.722291	+	0.691589i	$0.243089\pi$
$402$		0			0
$403$	21.5741	−	14.5413i	1.07468	−	0.724352i
$404$		0			0
$405$	−1.38989	−	2.72781i	−0.0690642	−	0.135546i
$406$		0			0
$407$	−0.336667	+	0.125188i	−0.0166880	+	0.00620531i
$408$		0			0
$409$	14.0631	−	7.16549i	0.695374	−	0.354310i	−0.0703125	−	0.997525i	$-0.522400\pi$
$409$	14.0631	−	7.16549i	0.695374	−	0.354310i	0.765686	+	0.643215i	$0.222400\pi$
$410$		0			0
$411$	−0.430168	−	2.71598i	−0.0212186	−	0.133969i
$412$		0			0
$413$	2.54500	+	7.83270i	0.125231	+	0.385422i
$414$		0			0
$415$	−2.16860	+	1.57558i	−0.106452	+	0.0773421i
$416$		0			0
$417$		−	10.3420i		−	0.506451i
$418$		0			0
$419$	−19.6143			−0.958222			−0.479111	−	0.877754i	$-0.659041\pi$
$419$	−19.6143			−0.958222			−0.479111	+	0.877754i	$0.659041\pi$
$420$		0			0
$421$	−1.69823	+	10.7222i	−0.0827666	+	0.522568i	0.911118	+	0.412145i	$0.135220\pi$
$421$	−1.69823	+	10.7222i	−0.0827666	+	0.522568i	−0.993885	+	0.110423i	$0.964780\pi$
$422$		0			0
$423$	−8.50176	+	16.6857i	−0.413370	+	0.811284i
$424$		0			0
$425$	0.679291	−	0.934964i	0.0329505	−	0.0453524i
$426$		0			0
$427$	−5.00587	+	2.55062i	−0.242251	+	0.123433i
$428$		0			0
$429$	−6.56293	+	9.15952i	−0.316861	+	0.442226i
$430$		0			0
$431$	−31.4541	+	16.0267i	−1.51509	+	0.771978i	−0.996544	−	0.0830694i	$-0.973528\pi$
$431$	−31.4541	+	16.0267i	−1.51509	+	0.771978i	−0.518549	+	0.855048i	$0.673528\pi$
$432$		0			0
$433$	−15.8569	+	21.8251i	−0.762033	+	1.04885i	0.235010	+	0.971993i	$0.424488\pi$
$433$	−15.8569	+	21.8251i	−0.762033	+	1.04885i	−0.997042	+	0.0768549i	$0.975512\pi$
$434$		0			0
$435$	0.219720	−	0.431225i	0.0105348	−	0.0206757i
$436$		0			0
$437$	6.39429	−	40.3719i	0.305880	−	1.93125i
$438$		0			0
$439$	−15.5074			−0.740129			−0.370065	−	0.929006i	$-0.620664\pi$
$439$	−15.5074			−0.740129			−0.370065	+	0.929006i	$0.620664\pi$
$440$		0			0
$441$		−	13.9416i		−	0.663886i
$442$		0			0
$443$	−8.48176	+	6.16236i	−0.402981	+	0.292783i	−0.770754	−	0.637133i	$-0.780120\pi$
$443$	−8.48176	+	6.16236i	−0.402981	+	0.292783i	0.367773	+	0.929915i	$0.380120\pi$
$444$		0			0
$445$	−7.15067	−	22.0075i	−0.338974	−	1.04325i
$446$		0			0
$447$	−0.986159	−	6.22636i	−0.0466437	−	0.294497i
$448$		0			0
$449$	−3.22183	+	1.64160i	−0.152047	+	0.0774720i	−0.528359	−	0.849021i	$-0.677192\pi$
$449$	−3.22183	+	1.64160i	−0.152047	+	0.0774720i	0.376311	+	0.926493i	$0.377192\pi$
$450$		0			0
$451$	−0.417466	−	9.97153i	−0.0196577	−	0.469541i
$452$		0			0
$453$	−9.04922	−	17.7601i	−0.425170	−	0.834442i
$454$		0			0
$455$	0.741708	−	3.80884i	0.0347718	−	0.178561i
$456$		0			0
$457$	3.36204	−	6.59838i	0.157270	−	0.308659i	−0.798904	−	0.601458i	$-0.794587\pi$
$457$	3.36204	−	6.59838i	0.157270	−	0.308659i	0.956174	+	0.292799i	$0.0945866\pi$
$458$		0			0
$459$	−2.14616	+	1.55928i	−0.100174	+	0.0727809i
$460$		0			0
$461$	13.8339	+	13.8339i	0.644311	+	0.644311i	0.951612	−	0.307302i	$-0.0994260\pi$
$461$	13.8339	+	13.8339i	0.644311	+	0.644311i	−0.307302	+	0.951612i	$0.599426\pi$
$462$		0			0
$463$	−3.96836	−	3.96836i	−0.184425	−	0.184425i	0.608856	−	0.793281i	$-0.291629\pi$
$463$	−3.96836	−	3.96836i	−0.184425	−	0.184425i	−0.793281	+	0.608856i	$0.791629\pi$
$464$		0			0
$465$	−6.80765	−	9.36992i	−0.315697	−	0.434520i
$466$		0			0
$467$	12.8094	−	4.16203i	0.592748	−	0.192596i	0.00274479	−	0.999996i	$-0.499126\pi$
$467$	12.8094	−	4.16203i	0.592748	−	0.192596i	0.590004	+	0.807401i	$0.299126\pi$
$468$		0			0
$469$	3.94006	−	5.42303i	0.181935	−	0.250412i
$470$		0			0
$471$	5.36269	−	16.5047i	0.247100	−	0.760495i
$472$		0			0
$473$	2.68290	+	13.3089i	0.123360	+	0.611945i
$474$		0			0
$475$	−6.73280	−	13.2139i	−0.308922	−	0.606294i
$476$		0			0
$477$	−4.69774	−	3.41311i	−0.215095	−	0.156275i
$478$		0			0
$479$	−11.3328	−	5.77437i	−0.517811	−	0.263838i	0.175496	−	0.984480i	$-0.443847\pi$
$479$	−11.3328	−	5.77437i	−0.517811	−	0.263838i	−0.693307	+	0.720642i	$0.743847\pi$
$480$		0			0
$481$	−0.375390	+	0.107503i	−0.0171163	+	0.00490172i
$482$		0			0
$483$	2.43490	+	2.43490i	0.110792	+	0.110792i
$484$		0			0
$485$			3.67075i			0.166680i
$486$		0			0
$487$	−1.95326	+	12.3324i	−0.0885104	+	0.558833i	0.903086	+	0.429461i	$0.141296\pi$
$487$	−1.95326	+	12.3324i	−0.0885104	+	0.558833i	−0.991596	+	0.129372i	$0.958704\pi$
$488$		0			0
$489$	7.10157	−	13.9376i	0.321144	−	0.630281i
$490$		0			0
$491$	−26.5282	−	19.2738i	−1.19720	−	0.869816i	−0.203193	−	0.979139i	$-0.565132\pi$
$491$	−26.5282	−	19.2738i	−1.19720	−	0.869816i	−0.994006	+	0.109323i	$0.965132\pi$
$492$		0			0
$493$	0.157930	+	0.0513145i	0.00711280	+	0.00231109i
$494$		0			0
$495$	−9.93831	−	6.60367i	−0.446694	−	0.296813i
$496$		0			0
$497$	0.0608726	+	0.0197787i	0.00273051	+	0.000887197i
$498$		0			0
$499$	3.39218	−	0.537268i	0.151855	−	0.0240514i	−0.0800442	−	0.996791i	$-0.525506\pi$
$499$	3.39218	−	0.537268i	0.151855	−	0.0240514i	0.231899	+	0.972740i	$0.425506\pi$
$500$		0			0
$501$	4.75762	+	2.42413i	0.212555	+	0.108302i
$502$		0			0
$503$	−19.3545	−	26.6392i	−0.862976	−	1.18778i	−0.980852	−	0.194756i	$-0.937608\pi$
$503$	−19.3545	−	26.6392i	−0.862976	−	1.18778i	0.117876	−	0.993028i	$-0.462392\pi$
$504$		0			0
$505$	−23.0049	+	23.0049i	−1.02370	+	1.02370i
$506$		0			0
$507$	−7.88030	+	9.37842i	−0.349977	+	0.416510i
$508$		0			0
$509$	2.89659	−	18.2884i	0.128389	−	0.810618i	−0.836501	−	0.547965i	$-0.815403\pi$
$509$	2.89659	−	18.2884i	0.128389	−	0.810618i	0.964890	−	0.262653i	$-0.0845973\pi$
$510$		0			0
$511$	−4.84168	+	1.57316i	−0.214183	+	0.0695924i
$512$		0			0
$513$	5.32537	+	33.6231i	0.235121	+	1.48449i
$514$		0			0
$515$	15.8429	−	8.07234i	0.698120	−	0.355710i
$516$		0			0
$517$	1.23005	+	29.3807i	0.0540973	+	1.29216i
$518$		0			0
$519$	−3.53061	+	10.8661i	−0.154977	+	0.476969i
$520$		0			0
$521$	10.2889	+	7.47534i	0.450766	+	0.327500i	0.789898	−	0.613238i	$-0.210133\pi$
$521$	10.2889	+	7.47534i	0.450766	+	0.327500i	−0.339132	+	0.940739i	$0.610133\pi$
$522$		0			0
$523$	−17.1203	+	5.56273i	−0.748619	+	0.243241i	−0.658387	−	0.752680i	$-0.728761\pi$
$523$	−17.1203	+	5.56273i	−0.748619	+	0.243241i	−0.0902320	+	0.995921i	$0.528761\pi$
$524$		0			0
$525$	1.23397	+	0.195442i	0.0538550	+	0.00852980i
$526$		0			0
$527$	2.80995	−	2.80995i	0.122403	−	0.122403i
$528$		0			0
$529$	−10.4538			−0.454514
$530$		0			0
$531$	27.1924	+	4.30685i	1.18005	+	0.186901i
$532$		0			0
$533$	0.382335	−	10.8430i	0.0165608	−	0.469661i
$534$		0			0
$535$	−2.84542	−	17.9652i	−0.123018	−	0.776705i
$536$		0			0
$537$	4.62778	+	1.50366i	0.199704	+	0.0648876i
$538$		0			0
$539$	−10.7462	−	19.0735i	−0.462870	−	0.821552i
$540$		0			0
$541$	3.28199	+	6.44126i	0.141104	+	0.276931i	0.950734	−	0.310009i	$-0.100332\pi$
$541$	3.28199	+	6.44126i	0.141104	+	0.276931i	−0.809630	+	0.586941i	$0.800332\pi$
$542$		0			0
$543$	−2.20378	+	3.03324i	−0.0945732	+	0.130169i
$544$		0			0
$545$	−7.23786	−	22.2759i	−0.310036	−	0.954193i
$546$		0			0
$547$	15.5802	+	21.4443i	0.666161	+	0.916892i	0.999666	−	0.0258563i	$-0.00823122\pi$
$547$	15.5802	+	21.4443i	0.666161	+	0.916892i	−0.333504	+	0.942749i	$0.608231\pi$
$548$		0			0
$549$			18.7811i			0.801558i
$550$		0			0
$551$	1.50680	−	1.50680i	0.0641917	−	0.0641917i
$552$		0			0
$553$	−1.69028	−	0.267714i	−0.0718781	−	0.0113844i
$554$		0			0
$555$	0.0537155	+	0.165319i	0.00228009	+	0.00701741i
$556$		0			0
$557$	39.6483	−	6.27967i	1.67995	−	0.266078i	0.757681	−	0.652625i	$-0.226332\pi$
$557$	39.6483	−	6.27967i	1.67995	−	0.266078i	0.922270	+	0.386546i	$0.126332\pi$
$558$		0			0
$559$	1.79373	+	14.6500i	0.0758669	+	0.619627i
$560$		0			0
$561$	−0.716527	+	1.56484i	−0.0302518	+	0.0660675i
$562$		0			0
$563$	−9.99083	+	30.7486i	−0.421063	+	1.29590i	0.485651	+	0.874153i	$0.338583\pi$
$563$	−9.99083	+	30.7486i	−0.421063	+	1.29590i	−0.906714	+	0.421746i	$0.861417\pi$
$564$		0			0
$565$	−27.2770	+	4.32026i	−1.14755	+	0.181755i
$566$		0			0
$567$	1.01181	+	0.515542i	0.0424919	+	0.0216507i
$568$		0			0
$569$	26.9755	−	19.5989i	1.13087	−	0.821628i	0.145052	−	0.989424i	$-0.453665\pi$
$569$	26.9755	−	19.5989i	1.13087	−	0.821628i	0.985822	+	0.167797i	$0.0536652\pi$
$570$		0			0
$571$	15.2464			0.638043			0.319022	−	0.947747i	$-0.396646\pi$
$571$	15.2464			0.638043			0.319022	+	0.947747i	$0.396646\pi$
$572$		0			0
$573$	−10.8337			−0.452583
$574$		0			0
$575$	−9.81958	+	7.13434i	−0.409505	+	0.297523i
$576$		0			0
$577$	−1.19312	−	0.607927i	−0.0496704	−	0.0253083i	0.428979	−	0.903315i	$-0.358873\pi$
$577$	−1.19312	−	0.607927i	−0.0496704	−	0.0253083i	−0.478649	+	0.878006i	$0.658873\pi$
$578$		0			0
$579$	11.3605	−	1.79932i	0.472126	−	0.0747774i
$580$		0			0
$581$	0.307247	−	0.945608i	0.0127467	−	0.0392304i
$582$		0			0
$583$	−9.05777	−	1.04845i	−0.375135	−	0.0434223i
$584$		0			0
$585$	−10.2191	−	7.98966i	−0.422509	−	0.330332i
$586$		0			0
$587$	2.03504	−	0.322319i	0.0839951	−	0.0133035i	−0.114295	−	0.993447i	$-0.536461\pi$
$587$	2.03504	−	0.322319i	0.0839951	−	0.0133035i	0.198291	+	0.980143i	$0.436461\pi$
$588$		0			0
$589$	−15.7582	−	48.4988i	−0.649306	−	1.99836i
$590$		0			0
$591$	−16.3431	−	2.58849i	−0.672266	−	0.106476i
$592$		0			0
$593$	17.0326	−	17.0326i	0.699447	−	0.699447i	−0.264844	−	0.964291i	$-0.585321\pi$
$593$	17.0326	−	17.0326i	0.699447	−	0.699447i	0.964291	+	0.264844i	$0.0853206\pi$
$594$		0			0
$595$		−	0.592691i		−	0.0242980i
$596$		0			0
$597$	−11.5690	−	15.9234i	−0.473488	−	0.651701i
$598$		0			0
$599$	3.52161	+	10.8384i	0.143889	+	0.442845i	0.996866	−	0.0791029i	$-0.0252056\pi$
$599$	3.52161	+	10.8384i	0.143889	+	0.442845i	−0.852977	+	0.521948i	$0.825206\pi$
$600$		0			0
$601$	−7.85959	+	10.8178i	−0.320599	+	0.441267i	−0.938650	−	0.344871i	$-0.887923\pi$
$601$	−7.85959	+	10.8178i	−0.320599	+	0.441267i	0.618051	+	0.786138i	$0.287923\pi$
$602$		0			0
$603$	−10.1731	−	19.9658i	−0.414281	−	0.813072i
$604$		0			0
$605$	−18.6867	−	1.37401i	−0.759721	−	0.0558616i
$606$		0			0
$607$	21.4490	+	6.96922i	0.870590	+	0.282872i	0.710045	−	0.704157i	$-0.248675\pi$
$607$	21.4490	+	6.96922i	0.870590	+	0.282872i	0.160545	+	0.987028i	$0.448675\pi$
$608$		0			0
$609$	0.0280827	+	0.177307i	0.00113797	+	0.00718485i
$610$		0			0
$611$	−1.12653	+	31.9483i	−0.0455747	+	1.29249i
$612$		0			0
$613$	−18.6745	−	2.95775i	−0.754257	−	0.119463i	−0.232546	−	0.972585i	$-0.574706\pi$
$613$	−18.6745	−	2.95775i	−0.754257	−	0.119463i	−0.521710	+	0.853123i	$0.674706\pi$
$614$		0			0
$615$	−4.82988			−0.194760
$616$		0			0
$617$	−20.2508	+	20.2508i	−0.815268	+	0.815268i	−0.985418	−	0.170150i	$-0.945575\pi$
$617$	−20.2508	+	20.2508i	−0.815268	+	0.815268i	0.170150	+	0.985418i	$0.445575\pi$
$618$		0			0
$619$	−47.7565	−	7.56389i	−1.91950	−	0.304018i	−0.922802	−	0.385274i	$-0.874107\pi$
$619$	−47.7565	−	7.56389i	−1.91950	−	0.304018i	−0.996693	+	0.0812555i	$0.974107\pi$
$620$		0			0
$621$	26.4978	−	8.60965i	1.06332	−	0.345493i
$622$		0			0
$623$	6.94392	+	5.04506i	0.278202	+	0.202126i
$624$		0			0
$625$	3.12220	−	9.60914i	0.124888	−	0.384366i
$626$		0			0
$627$	13.7178	+	17.3092i	0.547834	+	0.691261i
$628$		0			0
$629$	−0.0531413	+	0.0270769i	−0.00211888	+	0.00107963i
$630$		0			0
$631$	−1.49819	−	9.45921i	−0.0596421	−	0.376565i	−0.999397	−	0.0347168i	$-0.988947\pi$
$631$	−1.49819	−	9.45921i	−0.0596421	−	0.376565i	0.939755	−	0.341848i	$-0.111053\pi$
$632$		0			0
$633$	10.1367	−	3.29360i	0.402896	−	0.130909i
$634$		0			0
$635$	1.10680	−	6.98807i	0.0439221	−	0.277313i
$636$		0			0
$637$	−10.0508	−	21.5731i	−0.398227	−	0.854758i
$638$		0			0
$639$	0.151295	−	0.151295i	0.00598512	−	0.00598512i
$640$		0			0
$641$	−1.02165	−	1.40618i	−0.0403526	−	0.0555406i	0.788364	−	0.615209i	$-0.210928\pi$
$641$	−1.02165	−	1.40618i	−0.0403526	−	0.0555406i	−0.828717	+	0.559669i	$0.810928\pi$
$642$		0			0
$643$	3.64153	+	1.85545i	0.143608	+	0.0731719i	0.524318	−	0.851523i	$-0.324320\pi$
$643$	3.64153	+	1.85545i	0.143608	+	0.0731719i	−0.380710	+	0.924695i	$0.624320\pi$
$644$		0			0
$645$	6.48943	−	1.02782i	0.255521	−	0.0404705i
$646$		0			0
$647$	−21.6038	−	7.01949i	−0.849332	−	0.275965i	−0.148166	−	0.988963i	$-0.547337\pi$
$647$	−21.6038	−	7.01949i	−0.849332	−	0.275965i	−0.701166	+	0.712998i	$0.747337\pi$
$648$		0			0
$649$	40.5215	−	15.0677i	1.59061	−	0.591458i
$650$		0			0
$651$	4.08571	+	1.32753i	0.160132	+	0.0520300i
$652$		0			0
$653$	−22.1955	−	16.1259i	−0.868575	−	0.631057i	0.0616290	−	0.998099i	$-0.480370\pi$
$653$	−22.1955	−	16.1259i	−0.868575	−	0.631057i	−0.930204	+	0.367042i	$0.880370\pi$
$654$		0			0
$655$	−14.9026	+	29.2480i	−0.582292	+	1.14281i
$656$		0			0
$657$	−2.66223	+	16.8086i	−0.103863	+	0.655767i
$658$		0			0
$659$		−	15.2954i		−	0.595826i	−0.954593	−	0.297913i	$-0.903710\pi$
$659$		−	15.2954i		−	0.595826i	0.954593	−	0.297913i	$-0.0962905\pi$
$660$		0			0
$661$	16.7732	+	16.7732i	0.652401	+	0.652401i	0.953570	−	0.301170i	$-0.0973771\pi$
$661$	16.7732	+	16.7732i	0.652401	+	0.652401i	−0.301170	+	0.953570i	$0.597377\pi$
$662$		0			0
$663$	−0.907642	+	1.63612i	−0.0352499	+	0.0635415i
$664$		0			0
$665$	−6.77674	−	3.45292i	−0.262791	−	0.133899i
$666$		0			0
$667$	−1.41095	−	1.02512i	−0.0546324	−	0.0396928i
$668$		0			0
$669$	−5.33882	−	10.4780i	−0.206411	−	0.405103i
$670$		0			0
$671$	14.4765	+	25.6944i	0.558857	+	0.991920i
$672$		0			0
$673$	−6.91806	+	21.2916i	−0.266671	+	0.820730i	0.724632	+	0.689136i	$0.242010\pi$
$673$	−6.91806	+	21.2916i	−0.266671	+	0.820730i	−0.991304	+	0.131595i	$0.957990\pi$
$674$		0			0
$675$	5.94171	−	8.17806i	0.228696	−	0.314774i
$676$		0			0
$677$	−1.56380	+	0.508110i	−0.0601018	+	0.0195283i	−0.338914	−	0.940818i	$-0.610059\pi$
$677$	−1.56380	+	0.508110i	−0.0601018	+	0.0195283i	0.278812	+	0.960346i	$0.410059\pi$
$678$		0			0
$679$	−0.800308	−	1.10153i	−0.0307130	−	0.0422728i
$680$		0			0
$681$	−1.34210	−	1.34210i	−0.0514292	−	0.0514292i
$682$		0			0
$683$	33.8286	+	33.8286i	1.29441	+	1.29441i	0.932028	+	0.362387i	$0.118038\pi$
$683$	33.8286	+	33.8286i	1.29441	+	1.29441i	0.362387	+	0.932028i	$0.381962\pi$
$684$		0			0
$685$	4.02155	−	2.92182i	0.153655	−	0.111637i
$686$		0			0
$687$	8.22669	−	16.1458i	0.313868	−	0.616000i
$688$		0			0
$689$	−9.72982	−	1.89472i	−0.370677	−	0.0721830i
$690$		0			0
$691$	−5.10230	−	10.0138i	−0.194101	−	0.380944i	0.773359	−	0.633968i	$-0.218575\pi$
$691$	−5.10230	−	10.0138i	−0.194101	−	0.380944i	−0.967460	+	0.253024i	$0.918575\pi$
$692$		0			0
$693$	4.42207	−	0.185133i	0.167980	−	0.00703262i
$694$		0			0
$695$	16.6577	−	8.48754i	0.631864	−	0.321951i
$696$		0			0
$697$	−0.259241	−	1.63678i	−0.00981945	−	0.0619975i
$698$		0			0
$699$	−3.31014	−	10.1876i	−0.125201	−	0.385329i
$700$		0			0
$701$	−7.99950	+	5.81198i	−0.302137	+	0.219515i	−0.728515	−	0.685030i	$-0.759789\pi$
$701$	−7.99950	+	5.81198i	−0.302137	+	0.219515i	0.426378	+	0.904545i	$0.359789\pi$
$702$		0			0
$703$			0.765356i			0.0288659i
$704$		0			0
$705$	14.2311			0.535972
$706$		0			0
$707$	1.88778	−	11.9189i	0.0709971	−	0.448258i
$708$		0			0
$709$	0.0953457	−	0.187127i	0.00358078	−	0.00702769i	−0.889209	−	0.457501i	$-0.848745\pi$
$709$	0.0953457	−	0.187127i	0.00358078	−	0.00702769i	0.892790	+	0.450473i	$0.148745\pi$
$710$		0			0
$711$	−3.36264	+	4.62827i	−0.126109	+	0.173574i
$712$		0			0
$713$	−37.1870	+	18.9477i	−1.39267	+	0.709598i
$714$		0			0
$715$	−20.1392	−	3.05373i	−0.753163	−	0.114203i
$716$		0			0
$717$	1.08507	−	0.552869i	0.0405225	−	0.0206473i
$718$		0			0
$719$	25.7344	−	35.4203i	0.959730	−	1.32095i	0.0126622	−	0.999920i	$-0.495969\pi$
$719$	25.7344	−	35.4203i	0.959730	−	1.32095i	0.947067	−	0.321035i	$-0.104031\pi$
$720$		0			0
$721$	−2.99421	+	5.87648i	−0.111510	+	0.218851i
$722$		0			0
$723$	−3.78642	+	23.9065i	−0.140818	+	0.889092i
$724$		0			0
$725$	−0.632769			−0.0235004
$726$		0			0
$727$		−	31.8042i		−	1.17955i	−0.807567	−	0.589776i	$-0.799216\pi$
$727$		−	31.8042i		−	1.17955i	0.807567	−	0.589776i	$-0.200784\pi$
$728$		0			0
$729$	−7.94528	+	5.77258i	−0.294270	+	0.213799i
$730$		0			0
$731$	0.696632	+	2.14401i	0.0257659	+	0.0792992i
$732$		0			0
$733$	6.39608	+	40.3832i	0.236244	+	1.49159i	0.765671	+	0.643233i	$0.222407\pi$
$733$	6.39608	+	40.3832i	0.236244	+	1.49159i	−0.529426	+	0.848356i	$0.677593\pi$
$734$		0			0
$735$	−9.43992	+	4.80988i	−0.348197	+	0.177415i
$736$		0			0
$737$	−29.3074	−	19.4738i	−1.07955	−	0.717326i
$738$		0			0
$739$	−20.8582	−	40.9365i	−0.767280	−	1.50587i	−0.860064	−	0.510185i	$-0.829577\pi$
$739$	−20.8582	−	40.9365i	−0.767280	−	1.50587i	0.0927845	−	0.995686i	$-0.470423\pi$
$740$		0			0
$741$	13.4194	+	19.9096i	0.492972	+	0.731398i
$742$		0			0
$743$	−6.13423	+	12.0391i	−0.225043	+	0.441672i	−0.975727	−	0.218989i	$-0.929724\pi$
$743$	−6.13423	+	12.0391i	−0.225043	+	0.441672i	0.750684	+	0.660661i	$0.229724\pi$
$744$		0			0
$745$	9.21938	−	6.69827i	0.337772	−	0.245406i
$746$		0			0
$747$	−2.35024	−	2.35024i	−0.0859908	−	0.0859908i
$748$		0			0
$749$	4.77069	+	4.77069i	0.174317	+	0.174317i
$750$		0			0
$751$	8.76370	+	12.0622i	0.319792	+	0.440156i	0.938404	−	0.345541i	$-0.112305\pi$
$751$	8.76370	+	12.0622i	0.319792	+	0.440156i	−0.618612	+	0.785697i	$0.712305\pi$
$752$		0			0
$753$	−6.93112	+	2.25206i	−0.252584	+	0.0820696i
$754$		0			0
$755$	21.1794	−	29.1509i	0.770796	−	1.06091i
$756$		0			0
$757$	−4.13550	+	12.7277i	−0.150307	+	0.462598i	−0.997655	−	0.0684400i	$-0.978198\pi$
$757$	−4.13550	+	12.7277i	−0.150307	+	0.462598i	0.847348	+	0.531038i	$0.178198\pi$
$758$		0			0
$759$	12.2358	−	13.3050i	0.444130	−	0.482942i
$760$		0			0
$761$	1.71573	+	3.36731i	0.0621952	+	0.122065i	0.920011	−	0.391892i	$-0.128179\pi$
$761$	1.71573	+	3.36731i	0.0621952	+	0.122065i	−0.857816	+	0.513957i	$0.828179\pi$
$762$		0			0
$763$	7.02860	+	5.10658i	0.254452	+	0.184871i
$764$		0			0
$765$	−1.76535	−	0.899493i	−0.0638265	−	0.0325212i
$766$		0			0
$767$	45.1822	−	12.9392i	1.63143	−	0.467206i
$768$		0			0
$769$	19.2017	+	19.2017i	0.692430	+	0.692430i	0.962766	−	0.270336i	$-0.0871349\pi$
$769$	19.2017	+	19.2017i	0.692430	+	0.692430i	−0.270336	+	0.962766i	$0.587135\pi$
$770$		0			0
$771$			7.38806i			0.266075i
$772$		0			0
$773$	6.35682	−	40.1354i	0.228639	−	1.44357i	−0.559887	−	0.828569i	$-0.689156\pi$
$773$	6.35682	−	40.1354i	0.228639	−	1.44357i	0.788526	−	0.615001i	$-0.210844\pi$
$774$		0			0
$775$	−6.87459	+	13.4921i	−0.246943	+	0.484652i
$776$		0			0
$777$	−0.0521624	−	0.0378982i	−0.00187132	−	0.00135959i
$778$		0			0
$779$	−20.2250	−	6.57151i	−0.724637	−	0.235449i
$780$		0			0
$781$	0.0903679	−	0.323603i	0.00323362	−	0.0115794i
$782$		0			0
$783$	1.38140	+	0.448844i	0.0493672	+	0.0160404i
$784$		0			0
$785$	30.9849	−	4.90753i	1.10590	−	0.175157i
$786$		0			0
$787$	−16.0562	−	8.18104i	−0.572341	−	0.291622i	0.143767	−	0.989612i	$-0.454078\pi$
$787$	−16.0562	−	8.18104i	−0.572341	−	0.291622i	−0.716108	+	0.697989i	$0.754078\pi$
$788$		0			0
$789$	13.6563	+	18.7963i	0.486178	+	0.669167i
$790$		0			0
$791$	7.24345	−	7.24345i	0.257548	−	0.257548i
$792$		0			0
$793$	13.5397	+	29.0617i	0.480808	+	1.03201i
$794$		0			0
$795$	−0.690300	+	4.35839i	−0.0244824	+	0.154576i
$796$		0			0
$797$	−44.8289	+	14.5658i	−1.58792	+	0.515947i	−0.964081	−	0.265607i	$-0.914428\pi$
$797$	−44.8289	+	14.5658i	−1.58792	+	0.515947i	−0.623839	+	0.781553i	$0.714428\pi$
$798$		0			0
$799$	0.763843	+	4.82271i	0.0270228	+	0.170615i
$800$		0			0
$801$	25.5653	−	13.0262i	0.903305	−	0.460257i
$802$		0			0
$803$	9.31389	+	25.0479i	0.328680	+	0.883920i
$804$		0			0
$805$	−1.92357	+	5.92015i	−0.0677970	+	0.208658i
$806$		0			0
$807$	9.90355	+	7.19535i	0.348621	+	0.253288i
$808$		0			0
$809$	−1.96243	+	0.637631i	−0.0689952	+	0.0224179i	−0.343311	−	0.939222i	$-0.611549\pi$
$809$	−1.96243	+	0.637631i	−0.0689952	+	0.0224179i	0.274316	+	0.961640i	$0.411549\pi$
$810$		0			0
$811$	−19.6072	−	3.10548i	−0.688503	−	0.109048i	−0.197627	−	0.980277i	$-0.563323\pi$
$811$	−19.6072	−	3.10548i	−0.688503	−	0.109048i	−0.490877	+	0.871229i	$0.663323\pi$
$812$		0			0
$813$	7.53964	−	7.53964i	0.264427	−	0.264427i
$814$		0			0
$815$	28.2773			0.990509
$816$		0			0
$817$	28.5728	+	4.52549i	0.999636	+	0.158327i
$818$		0			0
$819$	4.80851	+	0.169554i	0.168023	+	0.00592468i
$820$		0			0
$821$	3.89181	+	24.5719i	0.135825	+	0.857566i	0.957673	+	0.287859i	$0.0929433\pi$
$821$	3.89181	+	24.5719i	0.135825	+	0.857566i	−0.821848	+	0.569707i	$0.807057\pi$
$822$		0			0
$823$	25.0931	+	8.15325i	0.874691	+	0.284204i	0.711751	−	0.702431i	$-0.247902\pi$
$823$	25.0931	+	8.15325i	0.874691	+	0.284204i	0.162940	+	0.986636i	$0.447902\pi$
$824$		0			0
$825$	0.754092	−	6.51477i	0.0262541	−	0.226815i
$826$		0			0
$827$	10.7725	+	21.1422i	0.374596	+	0.735185i	0.998943	−	0.0459613i	$-0.0146351\pi$
$827$	10.7725	+	21.1422i	0.374596	+	0.735185i	−0.624348	+	0.781147i	$0.714635\pi$
$828$		0			0
$829$	−12.3290	+	16.9694i	−0.428202	+	0.589370i	−0.967539	−	0.252720i	$-0.918675\pi$
$829$	−12.3290	+	16.9694i	−0.428202	+	0.589370i	0.539337	+	0.842090i	$0.318675\pi$
$830$		0			0
$831$	2.60325	+	8.01198i	0.0903058	+	0.277933i
$832$		0			0
$833$	−2.13669	−	2.94089i	−0.0740318	−	0.101896i
$834$		0			0
$835$			9.65247i			0.334038i
$836$		0			0
$837$	24.5784	−	24.5784i	0.849553	−	0.849553i
$838$		0			0
$839$	4.12950	+	0.654048i	0.142566	+	0.0225802i	0.227310	−	0.973823i	$-0.427007\pi$
$839$	4.12950	+	0.654048i	0.142566	+	0.0225802i	−0.0847435	+	0.996403i	$0.527007\pi$
$840$		0			0
$841$	8.93340	+	27.4942i	0.308048	+	0.948075i
$842$		0			0
$843$	−4.42092	+	0.700206i	−0.152265	+	0.0241164i
$844$		0			0
$845$	−21.5729	−	4.99595i	−0.742131	−	0.171866i
$846$		0			0
$847$	5.90711	−	3.66180i	0.202971	−	0.125821i
$848$		0			0
$849$	−3.97767	+	12.2420i	−0.136513	+	0.420145i
$850$		0			0
$851$	0.618685	−	0.0979900i	0.0212082	−	0.00335905i
$852$		0			0
$853$	34.1938	+	17.4226i	1.17077	+	0.596539i	0.927648	−	0.373455i	$-0.121827\pi$
$853$	34.1938	+	17.4226i	1.17077	+	0.596539i	0.243126	+	0.969995i	$0.421827\pi$
$854$		0			0
$855$	−20.5693	+	14.9445i	−0.703457	+	0.511091i
$856$		0			0
$857$	−27.5703			−0.941785			−0.470892	−	0.882191i	$-0.656068\pi$
$857$	−27.5703			−0.941785			−0.470892	+	0.882191i	$0.656068\pi$
$858$		0			0
$859$	11.6626			0.397923			0.198961	−	0.980007i	$-0.436243\pi$
$859$	11.6626			0.397923			0.198961	+	0.980007i	$0.436243\pi$
$860$		0			0
$861$	1.44936	−	1.05302i	0.0493942	−	0.0358870i
$862$		0			0
$863$	3.78408	+	1.92808i	0.128812	+	0.0656327i	0.517209	−	0.855859i	$-0.326971\pi$
$863$	3.78408	+	1.92808i	0.128812	+	0.0656327i	−0.388397	+	0.921492i	$0.626971\pi$
$864$		0			0
$865$	−20.3994	+	3.23095i	−0.693600	+	0.109855i
$866$		0			0
$867$	4.86176	−	14.9630i	0.165114	−	0.508169i
$868$		0			0
$869$	−1.03295	+	8.92384i	−0.0350403	+	0.302721i
$870$		0			0
$871$	−30.1356	−	23.5610i	−1.02110	−	0.798334i
$872$		0			0
$873$	−4.49553	+	0.712022i	−0.152151	+	0.0240983i
$874$		0			0
$875$	2.36077	+	7.26570i	0.0798085	+	0.245625i
$876$		0			0
$877$	34.5511	+	5.47235i	1.16671	+	0.184788i	0.709588	−	0.704617i	$-0.248881\pi$
$877$	34.5511	+	5.47235i	1.16671	+	0.184788i	0.457119	+	0.889405i	$0.348881\pi$
$878$		0			0
$879$	20.8841	−	20.8841i	0.704405	−	0.704405i
$880$		0			0
$881$		−	34.3197i		−	1.15626i	−0.815944	−	0.578131i	$-0.803782\pi$
$881$		−	34.3197i		−	1.15626i	0.815944	−	0.578131i	$-0.196218\pi$
$882$		0			0
$883$	15.8027	+	21.7505i	0.531803	+	0.731963i	0.987404	−	0.158221i	$-0.0505757\pi$
$883$	15.8027	+	21.7505i	0.531803	+	0.731963i	−0.455601	+	0.890184i	$0.650576\pi$
$884$		0			0
$885$	−6.46524	−	19.8980i	−0.217327	−	0.668863i
$886$		0			0
$887$	−9.00441	+	12.3935i	−0.302338	+	0.416133i	−0.932973	−	0.359947i	$-0.882795\pi$
$887$	−9.00441	+	12.3935i	−0.302338	+	0.416133i	0.630634	+	0.776080i	$0.282795\pi$
$888$		0			0
$889$	1.19143	+	2.33830i	0.0399591	+	0.0784242i
$890$		0			0
$891$	2.48171	−	5.41985i	0.0831403	−	0.181572i
$892$		0			0
$893$	59.5922	+	19.3627i	1.99418	+	0.647948i
$894$		0			0
$895$	1.37603	+	8.68792i	0.0459957	+	0.290405i
$896$		0			0
$897$	14.3761	−	13.3968i	0.480003	−	0.447305i
$898$		0			0
$899$	−2.14902	−	0.340371i	−0.0716738	−	0.0113520i
$900$		0			0
$901$	−1.51405			−0.0504403
$902$		0			0
$903$	−1.72328	+	1.72328i	−0.0573470	+	0.0573470i
$904$		0			0
$905$	−6.69420	−	1.06026i	−0.222523	−	0.0352442i
$906$		0			0
$907$	51.0410	−	16.5842i	1.69479	−	0.550670i	0.707100	−	0.707113i	$-0.250003\pi$
$907$	51.0410	−	16.5842i	1.69479	−	0.550670i	0.987687	+	0.156444i	$0.0500029\pi$
$908$		0			0
$909$	−32.6361	−	23.7115i	−1.08247	−	0.786461i
$910$		0			0
$911$	−16.2555	+	50.0294i	−0.538570	+	1.65755i	0.197238	+	0.980356i	$0.436803\pi$
$911$	−16.2555	+	50.0294i	−0.538570	+	1.65755i	−0.735807	+	0.677191i	$0.763197\pi$
$912$		0			0
$913$	−5.02692	−	1.40379i	−0.166367	−	0.0464588i
$914$		0			0
$915$	12.7168	−	6.47952i	0.420404	−	0.214206i
$916$		0			0
$917$	−1.90472	−	12.0259i	−0.0628993	−	0.397131i
$918$		0			0
$919$	18.1452	−	5.89574i	0.598556	−	0.194483i	0.00595960	−	0.999982i	$-0.498103\pi$
$919$	18.1452	−	5.89574i	0.598556	−	0.194483i	0.592596	+	0.805500i	$0.298103\pi$
$920$		0			0
$921$	−1.80307	+	11.3841i	−0.0594132	+	0.375120i
$922$		0			0
$923$	0.125041	−	0.343183i	0.00411576	−	0.0112960i
$924$		0			0
$925$	0.160703	−	0.160703i	0.00528388	−	0.00528388i
$926$		0			0
$927$	12.9592	+	17.8368i	0.425635	+	0.585836i
$928$		0			0
$929$	14.0220	+	7.14455i	0.460046	+	0.234405i	0.668624	−	0.743601i	$-0.266884\pi$
$929$	14.0220	+	7.14455i	0.460046	+	0.234405i	−0.208578	+	0.978006i	$0.566884\pi$
$930$		0			0
$931$	−46.0738	+	7.29737i	−1.51001	+	0.239162i
$932$		0			0
$933$	11.8232	+	3.84160i	0.387076	+	0.125768i
$934$		0			0
$935$	−3.10850	+	0.130140i	−0.101659	+	0.00425602i
$936$		0			0
$937$	−43.9099	−	14.2672i	−1.43447	−	0.466089i	−0.514303	−	0.857608i	$-0.671949\pi$
$937$	−43.9099	−	14.2672i	−1.43447	−	0.466089i	−0.920170	+	0.391520i	$0.871949\pi$
$938$		0			0
$939$	22.8054	+	16.5691i	0.744227	+	0.540712i
$940$		0			0
$941$	17.0106	−	33.3853i	0.554531	−	1.08833i	−0.428268	−	0.903652i	$-0.640876\pi$
$941$	17.0106	−	33.3853i	0.554531	−	1.08833i	0.982799	−	0.184677i	$-0.0591238\pi$
$942$		0			0
$943$	−2.72271	+	17.1905i	−0.0886636	+	0.559800i
$944$		0			0
$945$		−	5.18422i		−	0.168643i
$946$		0			0
$947$	26.6861	+	26.6861i	0.867180	+	0.867180i	0.992159	−	0.124979i	$-0.0398864\pi$
$947$	26.6861	+	26.6861i	0.867180	+	0.867180i	−0.124979	+	0.992159i	$0.539886\pi$
$948$		0			0
$949$	7.99818	+	27.9288i	0.259632	+	0.906607i
$950$		0			0
$951$	7.34937	+	3.74469i	0.238320	+	0.121430i
$952$		0			0
$953$	−41.4118	−	30.0874i	−1.34146	−	0.974627i	−0.999389	−	0.0349521i	$-0.988872\pi$
$953$	−41.4118	−	30.0874i	−1.34146	−	0.974627i	−0.342070	−	0.939675i	$-0.611128\pi$
$954$		0			0
$955$	−8.89102	−	17.4496i	−0.287707	−	0.564656i
$956$		0			0
$957$	0.923761	−	0.186218i	0.0298610	−	0.00601958i
$958$		0			0
$959$	−0.569772	+	1.75358i	−0.0183989	+	0.0566260i
$960$		0			0
$961$	−12.3838	+	17.0448i	−0.399477	+	0.549833i
$962$		0			0
$963$	21.4499	−	6.96950i	0.691213	−	0.224589i
$964$		0			0
$965$	12.2215	+	16.8215i	0.393425	+	0.541503i
$966$		0			0
$967$	−0.0583856	−	0.0583856i	−0.00187756	−	0.00187756i	0.706167	−	0.708045i	$-0.250423\pi$
$967$	−0.0583856	−	0.0583856i	−0.00187756	−	0.00187756i	−0.708045	+	0.706167i	$0.750423\pi$
$968$		0			0
$969$	2.59315	+	2.59315i	0.0833039	+	0.0833039i
$970$		0			0
$971$	−21.5435	+	15.6523i	−0.691364	+	0.502305i	−0.877108	−	0.480293i	$-0.840530\pi$
$971$	−21.5435	+	15.6523i	−0.691364	+	0.502305i	0.185744	+	0.982598i	$0.440530\pi$
$972$		0			0
$973$	−3.14822	+	6.17873i	−0.100927	+	0.198081i
$974$		0			0
$975$	1.36277	−	6.99814i	0.0436435	−	0.224120i
$976$		0			0
$977$	27.4544	+	53.8824i	0.878345	+	1.72385i	0.664956	+	0.746883i	$0.268450\pi$
$977$	27.4544	+	53.8824i	0.878345	+	1.72385i	0.213389	+	0.976967i	$0.431550\pi$
$978$		0			0
$979$	24.9352	−	37.5267i	0.796933	−	1.19936i
$980$		0			0
$981$	25.8770	−	13.1850i	0.826190	−	0.420965i
$982$		0			0
$983$	5.15993	+	32.5785i	0.164576	+	1.03909i	0.922288	+	0.386503i	$0.126317\pi$
$983$	5.15993	+	32.5785i	0.164576	+	1.03909i	−0.757712	+	0.652589i	$0.773683\pi$
$984$		0			0
$985$	−9.24329	−	28.4479i	−0.294516	−	0.906426i
$986$		0			0
$987$	−4.27049	+	3.10269i	−0.135931	+	0.0987598i
$988$		0			0
$989$		−	23.6766i		−	0.752871i
$990$		0			0
$991$	−38.5013			−1.22303			−0.611517	−	0.791231i	$-0.709440\pi$
$991$	−38.5013			−1.22303			−0.611517	+	0.791231i	$0.709440\pi$
$992$		0			0
$993$	2.89191	−	18.2588i	0.0917719	−	0.579425i
$994$		0			0
$995$	16.1530	−	31.7021i	0.512086	−	1.00502i
$996$		0			0
$997$	−32.4968	+	44.7280i	−1.02918	+	1.41655i	−0.123626	+	0.992329i	$0.539452\pi$
$997$	−32.4968	+	44.7280i	−1.02918	+	1.41655i	−0.905558	+	0.424222i	$0.860548\pi$
$998$		0			0
$999$	−0.464823	+	0.236839i	−0.0147064	+	0.00749326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.10	✓	112
11.6	odd	10	inner	572.2.bh.a.369.10	yes	112
13.8	odd	4	inner	572.2.bh.a.541.10	yes	112
143.138	even	20	inner	572.2.bh.a.281.10	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.10	✓	112	1.1	even	1	trivial
572.2.bh.a.281.10	yes	112	143.138	even	20	inner
572.2.bh.a.369.10	yes	112	11.6	odd	10	inner
572.2.bh.a.541.10	yes	112	13.8	odd	4	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.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.762321 - 0.553859i) q^{3} +(1.51772 + 0.773316i) q^{5} +(-0.624041 + 0.0988384i) q^{7} +(-0.652677 + 2.00873i) q^{9} +O(q^{10})\)	\(q+(0.762321 - 0.553859i) q^{3} +(1.51772 + 0.773316i) q^{5} +(-0.624041 + 0.0988384i) q^{7} +(-0.652677 + 2.00873i) q^{9} +(0.655404 + 3.25122i) q^{11} +(0.438190 + 3.57883i) q^{13} +(1.58530 - 0.251086i) q^{15} +(0.170180 + 0.523759i) q^{17} +(6.98002 + 1.10553i) q^{19} +(-0.420977 + 0.420977i) q^{21} -5.78393i q^{23} +(-1.23348 - 1.69774i) q^{25} +(1.48855 + 4.58128i) q^{27} +(0.177236 - 0.243944i) q^{29} +(-3.27593 - 6.42937i) q^{31} +(2.30035 + 2.11548i) q^{33} +(-1.02355 - 0.332572i) q^{35} +(0.0169418 + 0.106966i) q^{37} +(2.31621 + 2.48552i) q^{39} +(-2.97212 - 0.470737i) q^{41} +4.09351 q^{43} +(-2.54396 + 2.54396i) q^{45} +(8.75722 + 1.38701i) q^{47} +(-6.27774 + 2.03976i) q^{49} +(0.419820 + 0.305017i) q^{51} +(-0.849567 + 2.61470i) q^{53} +(-1.51950 + 5.44127i) q^{55} +(5.93333 - 3.02318i) q^{57} +(-2.03913 - 12.8745i) q^{59} +(8.45691 - 2.74782i) q^{61} +(0.208757 - 1.31804i) q^{63} +(-2.10251 + 5.77050i) q^{65} +(-7.50198 + 7.50198i) q^{67} +(-3.20348 - 4.40921i) q^{69} +(-0.0902617 - 0.0459906i) q^{71} +(7.95823 - 1.26046i) q^{73} +(-1.88061 - 0.611048i) q^{75} +(-0.730344 - 1.96412i) q^{77} +(2.57604 + 0.837005i) q^{79} +(-1.45406 - 1.05643i) q^{81} +(-0.714428 + 1.40214i) q^{83} +(-0.146746 + 0.926520i) q^{85} -0.284127i q^{87} +(-9.60592 - 9.60592i) q^{89} +(-0.627174 - 2.19002i) q^{91} +(-6.05828 - 3.08685i) q^{93} +(9.73878 + 7.07564i) q^{95} +(0.978345 + 1.92011i) q^{97} +(-6.95860 - 0.805466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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