LMFDB - Embedded newform 572.2.bh.a.369.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [572,2,Mod(57,572)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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

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			369.10
Character	$\chi$	$=$	572.369
Dual form			572.2.bh.a.541.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.762321 + 0.553859i) q^{3} +(-0.773316 - 1.51772i) q^{5} +(0.0988384 - 0.624041i) q^{7} +(-0.652677 - 2.00873i) q^{9} +(3.25122 + 0.655404i) q^{11} +(2.45808 + 2.63777i) q^{13} +(0.251086 - 1.58530i) q^{15} +(-0.170180 + 0.523759i) q^{17} +(-1.10553 - 6.98002i) q^{19} +(0.420977 - 0.420977i) q^{21} -5.78393i q^{23} +(1.23348 - 1.69774i) q^{25} +(1.48855 - 4.58128i) q^{27} +(0.177236 + 0.243944i) q^{29} +(6.42937 + 3.27593i) q^{31} +(2.11548 + 2.30035i) q^{33} +(-1.02355 + 0.332572i) q^{35} +(0.106966 + 0.0169418i) q^{37} +(0.412898 + 3.37226i) q^{39} +(0.470737 + 2.97212i) q^{41} -4.09351 q^{43} +(-2.54396 + 2.54396i) q^{45} +(1.38701 + 8.75722i) q^{47} +(6.27774 + 2.03976i) q^{49} +(-0.419820 + 0.305017i) q^{51} +(-0.849567 - 2.61470i) q^{53} +(-1.51950 - 5.44127i) q^{55} +(3.02318 - 5.93333i) q^{57} +(-12.8745 - 2.03913i) q^{59} +(8.45691 + 2.74782i) q^{61} +(-1.31804 + 0.208757i) q^{63} +(2.10251 - 5.77050i) q^{65} +(-7.50198 + 7.50198i) q^{67} +(3.20348 - 4.40921i) q^{69} +(0.0459906 + 0.0902617i) q^{71} +(-1.26046 + 7.95823i) q^{73} +(1.88061 - 0.611048i) q^{75} +(0.730344 - 1.96412i) q^{77} +(2.57604 - 0.837005i) q^{79} +(-1.45406 + 1.05643i) q^{81} +(-1.40214 + 0.714428i) q^{83} +(0.926520 - 0.146746i) q^{85} +0.284127i q^{87} +(-9.60592 - 9.60592i) q^{89} +(1.88903 - 1.27323i) q^{91} +(3.08685 + 6.05828i) q^{93} +(-9.73878 + 7.07564i) q^{95} +(-1.92011 - 0.978345i) q^{97} +(-0.805466 - 6.95860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{10}\right)$

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	0.785685	−	0.618627i	$-0.212311\pi$
$3$	0.762321	+	0.553859i	0.440126	+	0.319771i	−0.345559	+	0.938397i	$0.612311\pi$
$4$		0			0
$5$	−0.773316	−	1.51772i	−0.345837	−	0.678744i	0.650926	−	0.759142i	$-0.274381\pi$
$5$	−0.773316	−	1.51772i	−0.345837	−	0.678744i	−0.996763	+	0.0803976i	$0.974381\pi$
$6$		0			0
$7$	0.0988384	−	0.624041i	0.0373574	−	0.235865i	−0.961944	−	0.273248i	$-0.911902\pi$
$7$	0.0988384	−	0.624041i	0.0373574	−	0.235865i	0.999301	+	0.0373826i	$0.0119020\pi$
$8$		0			0
$9$	−0.652677	−	2.00873i	−0.217559	−	0.669578i
$10$		0			0
$11$	3.25122	+	0.655404i	0.980280	+	0.197612i
$11$	3.25122	+	0.655404i	0.980280	+	0.197612i
$12$		0			0
$13$	2.45808	+	2.63777i	0.681750	+	0.731586i
$13$	2.45808	+	2.63777i	0.681750	+	0.731586i
$14$		0			0
$15$	0.251086	−	1.58530i	0.0648302	−	0.409322i
$16$		0			0
$17$	−0.170180	+	0.523759i	−0.0412746	+	0.127030i	−0.969571	−	0.244812i	$-0.921274\pi$
$17$	−0.170180	+	0.523759i	−0.0412746	+	0.127030i	0.928296	+	0.371842i	$0.121274\pi$
$18$		0			0
$19$	−1.10553	−	6.98002i	−0.253625	−	1.60133i	−0.705143	−	0.709065i	$-0.749117\pi$
$19$	−1.10553	−	6.98002i	−0.253625	−	1.60133i	0.451518	−	0.892262i	$-0.350883\pi$
$20$		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	0.825156	−	0.564905i	$-0.191087\pi$
$29$	0.177236	+	0.243944i	0.0329119	+	0.0452993i	−0.792244	+	0.610204i	$0.791087\pi$
$30$		0			0
$31$	6.42937	+	3.27593i	1.15475	+	0.588374i	0.923151	−	0.384437i	$-0.125604\pi$
$31$	6.42937	+	3.27593i	1.15475	+	0.588374i	0.231599	+	0.972811i	$0.425604\pi$
$32$		0			0
$33$	2.11548	+	2.30035i	0.368257	+	0.400439i
$34$		0			0
$35$	−1.02355	+	0.332572i	−0.173012	+	0.0562149i
$36$		0			0
$37$	0.106966	+	0.0169418i	0.0175851	+	0.00278521i	0.165221	−	0.986257i	$-0.447166\pi$
$37$	0.106966	+	0.0169418i	0.0175851	+	0.00278521i	−0.147636	+	0.989042i	$0.547166\pi$
$38$		0			0
$39$	0.412898	+	3.37226i	0.0661166	+	0.539994i
$40$		0			0
$41$	0.470737	+	2.97212i	0.0735168	+	0.464167i	0.996793	+	0.0800288i	$0.0255012\pi$
$41$	0.470737	+	2.97212i	0.0735168	+	0.464167i	−0.923276	+	0.384138i	$0.874499\pi$
$42$		0			0
$43$	−4.09351			−0.624255			−0.312127	−	0.950040i	$-0.601042\pi$
$43$	−4.09351			−0.624255			−0.312127	+	0.950040i	$0.601042\pi$
$44$		0			0
$45$	−2.54396	+	2.54396i	−0.379232	+	0.379232i
$46$		0			0
$47$	1.38701	+	8.75722i	0.202316	+	1.27737i	0.854556	+	0.519360i	$0.173829\pi$
$47$	1.38701	+	8.75722i	0.202316	+	1.27737i	−0.652240	+	0.758013i	$0.726171\pi$
$48$		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	0.875600	−	0.483037i	$-0.160466\pi$
$53$	−0.849567	−	2.61470i	−0.116697	−	0.359156i	−0.992297	+	0.123880i	$0.960466\pi$
$54$		0			0
$55$	−1.51950	−	5.44127i	−0.204890	−	0.733701i
$56$		0			0
$57$	3.02318	−	5.93333i	0.400430	−	0.785888i
$58$		0			0
$59$	−12.8745	−	2.03913i	−1.67612	−	0.265472i	−0.755278	−	0.655404i	$-0.772498\pi$
$59$	−12.8745	−	2.03913i	−1.67612	−	0.265472i	−0.920843	+	0.389933i	$0.872498\pi$
$60$		0			0
$61$	8.45691	+	2.74782i	1.08280	+	0.351822i	0.795459	−	0.606007i	$-0.207230\pi$
$61$	8.45691	+	2.74782i	1.08280	+	0.351822i	0.287338	+	0.957829i	$0.407230\pi$
$62$		0			0
$63$	−1.31804	+	0.208757i	−0.166058	+	0.0263009i
$64$		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
$71$	0.0459906	+	0.0902617i	0.00545808	+	0.0107121i	0.893719	−	0.448626i	$-0.148087\pi$
$71$	0.0459906	+	0.0902617i	0.00545808	+	0.0107121i	−0.888261	+	0.459338i	$0.848087\pi$
$72$		0			0
$73$	−1.26046	+	7.95823i	−0.147526	+	0.931441i	0.797232	+	0.603673i	$0.206297\pi$
$73$	−1.26046	+	7.95823i	−0.147526	+	0.931441i	−0.944758	+	0.327768i	$0.893703\pi$
$74$		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	−0.160495	−	0.987037i	$-0.551309\pi$
$79$	2.57604	−	0.837005i	0.289827	−	0.0941704i	0.450322	+	0.892866i	$0.351309\pi$
$80$		0			0
$81$	−1.45406	+	1.05643i	−0.161562	+	0.117382i
$82$		0			0
$83$	−1.40214	+	0.714428i	−0.153905	+	0.0784186i	−0.529247	−	0.848468i	$-0.677525\pi$
$83$	−1.40214	+	0.714428i	−0.153905	+	0.0784186i	0.375342	+	0.926887i	$0.377525\pi$
$84$		0			0
$85$	0.926520	−	0.146746i	0.100495	−	0.0159169i
$86$		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
$91$	1.88903	−	1.27323i	0.198024	−	0.133471i
$92$		0			0
$93$	3.08685	+	6.05828i	0.320091	+	0.628214i
$94$		0			0
$95$	−9.73878	+	7.07564i	−0.999178	+	0.725945i
$96$		0			0
$97$	−1.92011	−	0.978345i	−0.194958	−	0.0993359i	0.353787	−	0.935326i	$-0.384894\pi$
$97$	−1.92011	−	0.978345i	−0.194958	−	0.0993359i	−0.548744	+	0.835990i	$0.684894\pi$
$98$		0			0
$99$	−0.805466	−	6.95860i	−0.0809524	−	0.699366i
$100$		0			0
$101$	5.90211	+	18.1648i	0.587282	+	1.80747i	0.589908	+	0.807470i	$0.299164\pi$
$101$	5.90211	+	18.1648i	0.587282	+	1.80747i	−0.00262646	+	0.999997i	$0.500836\pi$
$102$		0			0
$103$	−6.13566	−	8.44502i	−0.604565	−	0.832112i	0.391552	−	0.920156i	$-0.371938\pi$
$103$	−6.13566	−	8.44502i	−0.604565	−	0.832112i	−0.996117	+	0.0880440i	$0.971938\pi$
$104$		0			0
$105$	−0.964473	−	0.313376i	−0.0941229	−	0.0305824i
$106$		0			0
$107$	−6.27656	+	8.63895i	−0.606778	+	0.835159i	−0.996308	−	0.0858554i	$-0.972638\pi$
$107$	−6.27656	+	8.63895i	−0.606778	+	0.835159i	0.389529	+	0.921014i	$0.372638\pi$
$108$		0			0
$109$	9.72306	+	9.72306i	0.931300	+	0.931300i	0.997787	−	0.0664871i	$-0.0211791\pi$
$109$	9.72306	+	9.72306i	0.931300	+	0.931300i	−0.0664871	+	0.997787i	$0.521179\pi$
$110$		0			0
$111$	0.0721592	+	0.0721592i	0.00684905	+	0.00684905i
$112$		0			0
$113$	−13.1167	−	9.52985i	−1.23392	−	0.896493i	−0.236739	−	0.971573i	$-0.576079\pi$
$113$	−13.1167	−	9.52985i	−1.23392	−	0.896493i	−0.997177	+	0.0750805i	$0.976079\pi$
$114$		0			0
$115$	−8.77837	+	4.47280i	−0.818587	+	0.417091i
$116$		0			0
$117$	3.69424	−	6.65924i	0.341532	−	0.615647i
$118$		0			0
$119$	0.310027	+	0.157967i	0.0284201	+	0.0144808i
$120$		0			0
$121$	10.1409	+	4.26173i	0.921899	+	0.387430i
$122$		0			0
$123$	−1.28728	+	2.52643i	−0.116070	+	0.227800i
$124$		0			0
$125$	−11.9426	−	1.89152i	−1.06818	−	0.169182i
$126$		0			0
$127$	1.28354	−	3.95033i	0.113896	−	0.350535i	−0.877819	−	0.478992i	$-0.841002\pi$
$127$	1.28354	−	3.95033i	0.113896	−	0.350535i	0.991715	+	0.128457i	$0.0410024\pi$
$128$		0			0
$129$	−3.12057	−	2.26723i	−0.274751	−	0.199618i
$130$		0			0
$131$		−	19.2710i		−	1.68372i	−0.539698	−	0.841859i	$-0.681461\pi$
$131$		−	19.2710i		−	1.68372i	0.539698	−	0.841859i	$-0.318539\pi$
$132$		0			0
$133$	−4.46509			−0.387172
$134$		0			0
$135$	−8.10420	+	1.28358i	−0.697499	+	0.110473i
$136$		0			0
$137$	−2.60020	+	1.32487i	−0.222150	+	0.113191i	−0.561524	−	0.827460i	$-0.689785\pi$
$137$	−2.60020	+	1.32487i	−0.222150	+	0.113191i	0.339374	+	0.940651i	$0.389785\pi$
$138$		0			0
$139$	6.45125	+	8.87938i	0.547188	+	0.753139i	0.989627	−	0.143659i	$-0.0458869\pi$
$139$	6.45125	+	8.87938i	0.547188	+	0.753139i	−0.442440	+	0.896798i	$0.645887\pi$
$140$		0			0
$141$	−3.79292	+	7.44402i	−0.319421	+	0.626900i
$142$		0			0
$143$	6.26297	+	10.1870i	0.523736	+	0.851881i
$144$		0			0
$145$	0.233179	−	0.457640i	0.0193645	−	0.0380049i
$146$		0			0
$147$	3.65591	+	5.03193i	0.301535	+	0.415027i
$148$		0			0
$149$	5.96094	−	3.03725i	0.488339	−	0.248821i	−0.192441	−	0.981308i	$-0.561641\pi$
$149$	5.96094	−	3.03725i	0.488339	−	0.248821i	0.680781	+	0.732487i	$0.261641\pi$
$150$		0			0
$151$	−20.8932	+	3.30915i	−1.70026	+	0.269295i	−0.929766	−	0.368151i	$-0.879991\pi$
$151$	−20.8932	+	3.30915i	−1.70026	+	0.269295i	−0.770495	+	0.637446i	$0.779991\pi$
$152$		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	0.993172	−	0.116662i	$-0.0372195\pi$
$157$	14.8997	+	10.8253i	1.18913	+	0.863951i	0.195954	+	0.980613i	$0.437220\pi$
$158$		0			0
$159$	0.800531	−	2.46378i	0.0634862	−	0.195390i
$160$		0			0
$161$	−3.60941	−	0.571674i	−0.284461	−	0.0450542i
$162$		0			0
$163$	−7.53657	+	14.7914i	−0.590310	+	1.15855i	0.381849	+	0.924225i	$0.375288\pi$
$163$	−7.53657	+	14.7914i	−0.590310	+	1.15855i	−0.972159	+	0.234324i	$0.924712\pi$
$164$		0			0
$165$	1.85535	−	4.98959i	0.144439	−	0.388439i
$166$		0			0
$167$	5.04905	+	2.57262i	0.390707	+	0.199075i	0.638298	−	0.769790i	$-0.279639\pi$
$167$	5.04905	+	2.57262i	0.390707	+	0.199075i	−0.247591	+	0.968865i	$0.579639\pi$
$168$		0			0
$169$	−0.915651	+	12.9677i	−0.0704347	+	0.997516i
$170$		0			0
$171$	−13.2994	+	6.77641i	−1.01703	+	0.518205i
$172$		0			0
$173$	9.80945	+	7.12698i	0.745799	+	0.541855i	0.894522	−	0.447024i	$-0.147516\pi$
$173$	9.80945	+	7.12698i	0.745799	+	0.541855i	−0.148723	+	0.988879i	$0.547516\pi$
$174$		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	$-0.861818\pi$
$179$	−3.03532	+	4.17776i	−0.226871	+	0.312261i	0.680373	+	0.732866i	$0.261818\pi$
$180$		0			0
$181$	3.78421	+	1.22956i	0.281278	+	0.0913928i	0.446259	−	0.894904i	$-0.352756\pi$
$181$	3.78421	+	1.22956i	0.281278	+	0.0913928i	−0.164981	+	0.986297i	$0.552756\pi$
$182$		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
$187$	−0.896565	+	1.59132i	−0.0655633	+	0.116369i
$188$		0			0
$189$	−2.71178	−	1.38172i	−0.197253	−	0.100505i
$190$		0			0
$191$	−9.30149	+	6.75793i	−0.673032	+	0.488986i	−0.871039	−	0.491214i	$-0.836553\pi$
$191$	−9.30149	+	6.75793i	−0.673032	+	0.488986i	0.198007	+	0.980201i	$0.436553\pi$
$192$		0			0
$193$	5.54171	+	10.8762i	0.398901	+	0.782887i	0.999866	−	0.0163886i	$-0.00521690\pi$
$193$	5.54171	+	10.8762i	0.398901	+	0.782887i	−0.600965	+	0.799275i	$0.705217\pi$
$194$		0			0
$195$	4.79884	−	3.23448i	0.343652	−	0.231626i
$196$		0			0
$197$	12.4171	+	12.4171i	0.884680	+	0.884680i	0.994006	−	0.109326i	$-0.0348692\pi$
$197$	12.4171	+	12.4171i	0.884680	+	0.884680i	−0.109326	+	0.994006i	$0.534869\pi$
$198$		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
$201$	−9.87396	+	1.56388i	−0.696455	+	0.110308i
$202$		0			0
$203$	0.169749	−	0.0864913i	0.0119140	−	0.00607050i
$204$		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	0.0856587	−	0.996325i	$-0.472701\pi$
$211$	10.7576	−	3.49535i	0.740583	−	0.240630i	0.654924	+	0.755695i	$0.272701\pi$
$212$		0			0
$213$	−0.0149326	+	0.0942807i	−0.00102316	+	0.00646001i
$214$		0			0
$215$	3.16558	+	6.21279i	0.215891	+	0.423709i
$216$		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
$223$	12.3264	−	1.95232i	0.825439	−	0.130737i	0.270597	−	0.962693i	$-0.412779\pi$
$223$	12.3264	−	1.95232i	0.825439	−	0.130737i	0.554842	+	0.831956i	$0.312779\pi$
$224$		0			0
$225$	−4.21536	−	1.36965i	−0.281024	−	0.0913102i
$226$		0			0
$227$	1.98947	+	0.315101i	0.132046	+	0.0209140i	0.222108	−	0.975022i	$-0.428706\pi$
$227$	1.98947	+	0.315101i	0.132046	+	0.0209140i	−0.0900616	+	0.995936i	$0.528706\pi$
$228$		0			0
$229$	−8.73061	+	17.1348i	−0.576935	+	1.13230i	0.399550	+	0.916711i	$0.369166\pi$
$229$	−8.73061	+	17.1348i	−0.576935	+	1.13230i	−0.976485	+	0.215587i	$0.930834\pi$
$230$		0			0
$231$	1.64460	−	1.09278i	0.108207	−	0.0718997i
$232$		0			0
$233$	−3.51290	−	10.8116i	−0.230138	−	0.708291i	−0.997729	−	0.0673518i	$-0.978545\pi$
$233$	−3.51290	−	10.8116i	−0.230138	−	0.708291i	0.767592	−	0.640939i	$-0.221455\pi$
$234$		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
$239$	−0.202175	−	1.27648i	−0.0130776	−	0.0825687i	0.980286	−	0.197582i	$-0.0633089\pi$
$239$	−0.202175	−	1.27648i	−0.0130776	−	0.0825687i	−0.993364	+	0.115013i	$0.963309\pi$
$240$		0			0
$241$	18.1635	−	18.1635i	1.17002	−	1.17002i	0.187811	−	0.982205i	$-0.439861\pi$
$241$	18.1635	−	18.1635i	1.17002	−	1.17002i	0.982205	−	0.187811i	$-0.0601392\pi$
$242$		0			0
$243$	−16.1447			−1.03568
$244$		0			0
$245$	−1.75889	−	11.1052i	−0.112372	−	0.709486i
$246$		0			0
$247$	15.6942	−	20.0736i	0.998599	−	1.27725i
$248$		0			0
$249$	−1.46458	−	0.231966i	−0.0928137	−	0.0147003i
$250$		0			0
$251$	7.35569	−	2.39001i	0.464287	−	0.150856i	−0.0675266	−	0.997717i	$-0.521511\pi$
$251$	7.35569	−	2.39001i	0.464287	−	0.150856i	0.531813	+	0.846862i	$0.321511\pi$
$252$		0			0
$253$	3.79081	−	18.8048i	0.238326	−	1.18225i
$254$		0			0
$255$	0.787583	+	0.401294i	0.0493204	+	0.0251300i
$256$		0			0
$257$	4.60860	+	6.34319i	0.287476	+	0.395677i	0.928192	−	0.372101i	$-0.121362\pi$
$257$	4.60860	+	6.34319i	0.287476	+	0.395677i	−0.640716	+	0.767778i	$0.721362\pi$
$258$		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	$-0.725102\pi$
$263$		−	24.6567i		−	1.52040i	0.649691	−	0.760199i	$-0.274898\pi$
$264$		0			0
$265$	−3.31139	+	3.31139i	−0.203417	+	0.203417i
$266$		0			0
$267$	−2.00247	−	12.6431i	−0.122549	−	0.773747i
$268$		0			0
$269$	4.01453	−	12.3555i	0.244770	−	0.753326i	−0.750904	−	0.660412i	$-0.770382\pi$
$269$	4.01453	−	12.3555i	0.244770	−	0.753326i	0.995674	−	0.0929143i	$-0.0296182\pi$
$270$		0			0
$271$	−1.77018	+	11.1765i	−0.107531	+	0.678923i	0.873755	+	0.486366i	$0.161678\pi$
$271$	−1.77018	+	11.1765i	−0.107531	+	0.678923i	−0.981286	+	0.192556i	$0.938322\pi$
$272$		0			0
$273$	2.14524	+	0.0756435i	0.129836	+	0.00457816i
$274$		0			0
$275$	5.12301	−	4.71129i	0.308929	−	0.284101i
$276$		0			0
$277$	2.76271	+	8.50275i	0.165995	+	0.510881i	0.999108	−	0.0422219i	$-0.0134437\pi$
$277$	2.76271	+	8.50275i	0.165995	+	0.510881i	−0.833113	+	0.553103i	$0.813444\pi$
$278$		0			0
$279$	2.38416	−	15.0530i	0.142736	−	0.901201i
$280$		0			0
$281$	−2.15655	−	4.23247i	−0.128649	−	0.252488i	0.817693	−	0.575654i	$-0.195253\pi$
$281$	−2.15655	−	4.23247i	−0.128649	−	0.252488i	−0.946342	+	0.323167i	$0.895253\pi$
$282$		0			0
$283$	11.0516	+	8.02943i	0.656947	+	0.477300i	0.865631	−	0.500683i	$-0.166918\pi$
$283$	11.0516	+	8.02943i	0.656947	+	0.477300i	−0.208683	+	0.977983i	$0.566918\pi$
$284$		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
$291$	−0.921876	−	1.80928i	−0.0540413	−	0.106062i
$292$		0			0
$293$	−4.90325	+	30.9579i	−0.286451	+	1.80858i	0.254001	+	0.967204i	$0.418253\pi$
$293$	−4.90325	+	30.9579i	−0.286451	+	1.80858i	−0.540452	+	0.841375i	$0.681747\pi$
$294$		0			0
$295$	6.86126	+	21.1168i	0.399478	+	1.22947i
$296$		0			0
$297$	7.84219	−	13.9192i	0.455050	−	0.807671i
$298$		0			0
$299$	15.2567	−	14.2174i	0.882316	−	0.822212i
$300$		0			0
$301$	−0.404596	+	2.55452i	−0.0233205	+	0.147240i
$302$		0			0
$303$	−5.56144	+	17.1164i	−0.319497	+	0.983309i
$304$		0			0
$305$	−2.36945	−	14.9601i	−0.135674	−	0.856615i
$306$		0			0
$307$	8.64938	−	8.64938i	0.493646	−	0.493646i	−0.415807	−	0.909453i	$-0.636501\pi$
$307$	8.64938	−	8.64938i	0.493646	−	0.493646i	0.909453	+	0.415807i	$0.136501\pi$
$308$		0			0
$309$		−	9.83611i		−	0.559557i
$310$		0			0
$311$	−7.75476	+	10.6735i	−0.439732	+	0.605240i	−0.970153	−	0.242495i	$-0.922034\pi$
$311$	−7.75476	+	10.6735i	−0.439732	+	0.605240i	0.530420	+	0.847735i	$0.322034\pi$
$312$		0			0
$313$	9.24447	−	28.4516i	0.522529	−	1.60818i	−0.246623	−	0.969111i	$-0.579321\pi$
$313$	9.24447	−	28.4516i	0.522529	−	1.60818i	0.769152	−	0.639066i	$-0.220679\pi$
$314$		0			0
$315$	1.33610	+	1.83898i	0.0752805	+	0.103615i
$316$		0			0
$317$	−7.79955	−	3.97407i	−0.438066	−	0.223206i	0.221026	−	0.975268i	$-0.429059\pi$
$317$	−7.79955	−	3.97407i	−0.438066	−	0.223206i	−0.659092	+	0.752062i	$0.729059\pi$
$318$		0			0
$319$	0.416351	+	0.909277i	0.0233112	+	0.0509098i
$320$		0			0
$321$	−9.56952	+	3.10932i	−0.534118	+	0.173546i
$322$		0			0
$323$	3.84399	+	0.608828i	0.213885	+	0.0338761i
$324$		0			0
$325$	7.51022	−	0.919548i	0.416592	−	0.0510073i
$326$		0			0
$327$	2.02689	+	12.7973i	0.112087	+	0.707692i
$328$		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
$333$	−0.0357828	−	0.225924i	−0.00196089	−	0.0123806i
$334$		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	$-0.985333\pi$
$337$	−23.2007	+	16.8563i	−1.26382	+	0.918219i	−0.264882	+	0.964281i	$0.585333\pi$
$338$		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
$343$	3.90126	−	7.65665i	0.210648	−	0.413420i
$344$		0			0
$345$	−9.16924	−	1.45226i	−0.493655	−	0.0781873i
$346$		0			0
$347$	1.00745	+	0.327339i	0.0540825	+	0.0175725i	0.335933	−	0.941886i	$-0.390948\pi$
$347$	1.00745	+	0.327339i	0.0540825	+	0.0175725i	−0.281851	+	0.959458i	$0.590948\pi$
$348$		0			0
$349$	−23.2579	+	3.68369i	−1.24497	+	0.197183i	−0.743938	−	0.668248i	$-0.767044\pi$
$349$	−23.2579	+	3.68369i	−1.24497	+	0.197183i	−0.501027	+	0.865432i	$0.667044\pi$
$350$		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
$357$	0.148849	+	0.292132i	0.00787792	+	0.0154613i
$358$		0			0
$359$	3.49000	−	22.0350i	0.184195	−	1.16296i	−0.706281	−	0.707932i	$-0.749628\pi$
$359$	3.49000	−	22.0350i	0.184195	−	1.16296i	0.890476	−	0.455031i	$-0.150372\pi$
$360$		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	−0.419865	−	0.907587i	$-0.637923\pi$
$367$	6.00687	−	4.36424i	0.313556	−	0.227812i	0.733421	+	0.679775i	$0.237923\pi$
$368$		0			0
$369$	5.66295	−	2.88542i	0.294801	−	0.150209i
$370$		0			0
$371$	−1.71565	+	0.271732i	−0.0890721	+	0.0141076i
$372$		0			0
$373$			11.9799i			0.620293i	0.950689	+	0.310147i	$0.100378\pi$
$373$			11.9799i			0.620293i	−0.950689	+	0.310147i	$0.899622\pi$
$374$		0			0
$375$	−8.05644	−	8.05644i	−0.416033	−	0.416033i
$376$		0			0
$377$	−0.207808	+	1.06714i	−0.0107026	+	0.0549606i
$378$		0			0
$379$	12.3003	+	24.1408i	0.631826	+	1.24003i	0.955815	+	0.293968i	$0.0949759\pi$
$379$	12.3003	+	24.1408i	0.631826	+	1.24003i	−0.323989	+	0.946061i	$0.605024\pi$
$380$		0			0
$381$	3.16639	−	2.30052i	0.162219	−	0.117859i
$382$		0			0
$383$	2.61058	+	1.33016i	0.133395	+	0.0679679i	0.519414	−	0.854523i	$-0.326150\pi$
$383$	2.61058	+	1.33016i	0.133395	+	0.0679679i	−0.386019	+	0.922491i	$0.626150\pi$
$384$		0			0
$385$	−3.54576	+	0.410426i	−0.180709	+	0.0209173i
$386$		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	$-0.313923\pi$
$389$	−8.12218	−	11.1792i	−0.411811	−	0.566809i	−0.963659	+	0.267136i	$0.913923\pi$
$390$		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
$401$	10.2878	−	5.24191i	0.513749	−	0.261768i	−0.177840	−	0.984059i	$-0.556911\pi$
$401$	10.2878	−	5.24191i	0.513749	−	0.261768i	0.691589	+	0.722291i	$0.256911\pi$
$402$		0			0
$403$	7.16279	+	25.0117i	0.356804	+	1.24592i
$404$		0			0
$405$	2.72781	+	1.38989i	0.135546	+	0.0690642i
$406$		0			0
$407$	0.336667	+	0.125188i	0.0166880	+	0.00620531i
$408$		0			0
$409$	7.16549	−	14.0631i	0.354310	−	0.695374i	−0.643215	−	0.765686i	$-0.722400\pi$
$409$	7.16549	−	14.0631i	0.354310	−	0.695374i	0.997525	+	0.0703125i	$0.0223997\pi$
$410$		0			0
$411$	−2.71598	−	0.430168i	−0.133969	−	0.0212186i
$412$		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
$421$	−10.7222	+	1.69823i	−0.522568	+	0.0827666i	−0.412145	−	0.911118i	$-0.635220\pi$
$421$	−10.7222	+	1.69823i	−0.522568	+	0.0827666i	−0.110423	+	0.993885i	$0.535220\pi$
$422$		0			0
$423$	16.6857	−	8.50176i	0.811284	−	0.413370i
$424$		0			0
$425$	0.679291	+	0.934964i	0.0329505	+	0.0453524i
$426$		0			0
$427$	2.55062	−	5.00587i	0.123433	−	0.242251i
$428$		0			0
$429$	−0.867769	+	11.2346i	−0.0418963	+	0.542411i
$430$		0			0
$431$	−16.0267	+	31.4541i	−0.771978	+	1.51509i	0.0830694	+	0.996544i	$0.473528\pi$
$431$	−16.0267	+	31.4541i	−0.771978	+	1.51509i	−0.855048	+	0.518549i	$0.826472\pi$
$432$		0			0
$433$	15.8569	+	21.8251i	0.762033	+	1.04885i	0.997042	+	0.0768549i	$0.0244878\pi$
$433$	15.8569	+	21.8251i	0.762033	+	1.04885i	−0.235010	+	0.971993i	$0.575512\pi$
$434$		0			0
$435$	0.431225	−	0.219720i	0.0206757	−	0.0105348i
$436$		0			0
$437$	−40.3719	+	6.39429i	−1.93125	+	0.305880i
$438$		0			0
$439$	15.5074			0.740129			0.370065	−	0.929006i	$-0.379336\pi$
$439$	15.5074			0.740129			0.370065	+	0.929006i	$0.379336\pi$
$440$		0			0
$441$		−	13.9416i		−	0.663886i
$442$		0			0
$443$	−8.48176	−	6.16236i	−0.402981	−	0.292783i	0.367773	−	0.929915i	$-0.380120\pi$
$443$	−8.48176	−	6.16236i	−0.402981	−	0.292783i	−0.770754	+	0.637133i	$0.780120\pi$
$444$		0			0
$445$	−7.15067	+	22.0075i	−0.338974	+	1.04325i
$446$		0			0
$447$	6.22636	+	0.986159i	0.294497	+	0.0466437i
$448$		0			0
$449$	1.64160	−	3.22183i	0.0774720	−	0.152047i	−0.849021	−	0.528359i	$-0.822808\pi$
$449$	1.64160	−	3.22183i	0.0774720	−	0.152047i	0.926493	+	0.376311i	$0.122808\pi$
$450$		0			0
$451$	−0.417466	+	9.97153i	−0.0196577	+	0.469541i
$452$		0			0
$453$	−17.7601	−	9.04922i	−0.834442	−	0.425170i
$454$		0			0
$455$	−3.39322	−	1.88240i	−0.159077	−	0.0882484i
$456$		0			0
$457$	6.59838	−	3.36204i	0.308659	−	0.157270i	−0.292799	−	0.956174i	$-0.594587\pi$
$457$	6.59838	−	3.36204i	0.308659	−	0.157270i	0.601458	+	0.798904i	$0.294587\pi$
$458$		0			0
$459$	2.14616	+	1.55928i	0.100174	+	0.0727809i
$460$		0			0
$461$	−13.8339	−	13.8339i	−0.644311	−	0.644311i	0.307302	−	0.951612i	$-0.400574\pi$
$461$	−13.8339	−	13.8339i	−0.644311	−	0.644311i	−0.951612	+	0.307302i	$0.900574\pi$
$462$		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	$-0.500874\pi$
$467$	−12.8094	−	4.16203i	−0.592748	−	0.192596i	−0.590004	+	0.807401i	$0.700874\pi$
$468$		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
$473$	−13.3089	−	2.68290i	−0.611945	−	0.123360i
$474$		0			0
$475$	−13.2139	−	6.73280i	−0.606294	−	0.308922i
$476$		0			0
$477$	−4.69774	+	3.41311i	−0.215095	+	0.156275i
$478$		0			0
$479$	−5.77437	−	11.3328i	−0.263838	−	0.517811i	0.720642	−	0.693307i	$-0.243847\pi$
$479$	−5.77437	−	11.3328i	−0.263838	−	0.517811i	−0.984480	+	0.175496i	$0.943847\pi$
$480$		0			0
$481$	0.218243	+	0.323796i	0.00995104	+	0.0147638i
$482$		0			0
$483$	−2.43490	−	2.43490i	−0.110792	−	0.110792i
$484$		0			0
$485$			3.67075i			0.166680i
$486$		0			0
$487$	−12.3324	+	1.95326i	−0.558833	+	0.0885104i	−0.429461	−	0.903086i	$-0.641296\pi$
$487$	−12.3324	+	1.95326i	−0.558833	+	0.0885104i	−0.129372	+	0.991596i	$0.541296\pi$
$488$		0			0
$489$	−13.9376	+	7.10157i	−0.630281	+	0.321144i
$490$		0			0
$491$	26.5282	−	19.2738i	1.19720	−	0.869816i	0.203193	−	0.979139i	$-0.434868\pi$
$491$	26.5282	−	19.2738i	1.19720	−	0.869816i	0.994006	+	0.109323i	$0.0348681\pi$
$492$		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
$499$	0.537268	−	3.39218i	0.0240514	−	0.151855i	−0.972740	−	0.231899i	$-0.925506\pi$
$499$	0.537268	−	3.39218i	0.0240514	−	0.151855i	0.996791	+	0.0800442i	$0.0255061\pi$
$500$		0			0
$501$	2.42413	+	4.75762i	0.108302	+	0.212555i
$502$		0			0
$503$	−19.3545	+	26.6392i	−0.862976	+	1.18778i	0.117876	+	0.993028i	$0.462392\pi$
$503$	−19.3545	+	26.6392i	−0.862976	+	1.18778i	−0.980852	+	0.194756i	$0.937608\pi$
$504$		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
$509$	18.2884	−	2.89659i	0.810618	−	0.128389i	0.262653	−	0.964890i	$-0.415403\pi$
$509$	18.2884	−	2.89659i	0.810618	−	0.128389i	0.547965	+	0.836501i	$0.315403\pi$
$510$		0			0
$511$	4.84168	+	1.57316i	0.214183	+	0.0695924i
$512$		0			0
$513$	−33.6231	−	5.32537i	−1.48449	−	0.235121i
$514$		0			0
$515$	−8.07234	+	15.8429i	−0.355710	+	0.698120i
$516$		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	−0.339132	−	0.940739i	$-0.610133\pi$
$521$	10.2889	−	7.47534i	0.450766	−	0.327500i	0.789898	+	0.613238i	$0.210133\pi$
$522$		0			0
$523$	−17.1203	−	5.56273i	−0.748619	−	0.243241i	−0.0902320	−	0.995921i	$-0.528761\pi$
$523$	−17.1203	−	5.56273i	−0.748619	−	0.243241i	−0.658387	+	0.752680i	$0.728761\pi$
$524$		0			0
$525$	−0.195442	−	1.23397i	−0.00852980	−	0.0538550i
$526$		0			0
$527$	−2.80995	+	2.80995i	−0.122403	+	0.122403i
$528$		0			0
$529$	−10.4538			−0.454514
$530$		0			0
$531$	4.30685	+	27.1924i	0.186901	+	1.18005i
$532$		0			0
$533$	−6.68265	+	8.54741i	−0.289458	+	0.370229i
$534$		0			0
$535$	17.9652	+	2.84542i	0.776705	+	0.123018i
$536$		0			0
$537$	−4.62778	+	1.50366i	−0.199704	+	0.0648876i
$538$		0			0
$539$	19.0735	+	10.7462i	0.821552	+	0.462870i
$540$		0			0
$541$	6.44126	+	3.28199i	0.276931	+	0.141104i	0.586941	−	0.809630i	$-0.300332\pi$
$541$	6.44126	+	3.28199i	0.276931	+	0.141104i	−0.310009	+	0.950734i	$0.600332\pi$
$542$		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	−0.333504	−	0.942749i	$-0.608231\pi$
$547$	15.5802	−	21.4443i	0.666161	−	0.916892i	0.999666	+	0.0258563i	$0.00823122\pi$
$548$		0			0
$549$		−	18.7811i		−	0.801558i
$550$		0			0
$551$	1.50680	−	1.50680i	0.0641917	−	0.0641917i
$552$		0			0
$553$	−0.267714	−	1.69028i	−0.0113844	−	0.0718781i
$554$		0			0
$555$	0.0537155	−	0.165319i	0.00228009	−	0.00701741i
$556$		0			0
$557$	−6.27967	+	39.6483i	−0.266078	+	1.67995i	0.386546	+	0.922270i	$0.373668\pi$
$557$	−6.27967	+	39.6483i	−0.266078	+	1.67995i	−0.652625	+	0.757681i	$0.726332\pi$
$558$		0			0
$559$	−10.0622	−	10.7977i	−0.425585	−	0.456696i
$560$		0			0
$561$	−1.56484	+	0.716527i	−0.0660675	+	0.0302518i
$562$		0			0
$563$	9.99083	+	30.7486i	0.421063	+	1.29590i	0.906714	+	0.421746i	$0.138583\pi$
$563$	9.99083	+	30.7486i	0.421063	+	1.29590i	−0.485651	+	0.874153i	$0.661417\pi$
$564$		0			0
$565$	−4.32026	+	27.2770i	−0.181755	+	1.14755i
$566$		0			0
$567$	0.515542	+	1.01181i	0.0216507	+	0.0424919i
$568$		0			0
$569$	−26.9755	−	19.5989i	−1.13087	−	0.821628i	−0.145052	−	0.989424i	$-0.546335\pi$
$569$	−26.9755	−	19.5989i	−1.13087	−	0.821628i	−0.985822	+	0.167797i	$0.946335\pi$
$570$		0			0
$571$	−15.2464			−0.638043			−0.319022	−	0.947747i	$-0.603354\pi$
$571$	−15.2464			−0.638043			−0.319022	+	0.947747i	$0.603354\pi$
$572$		0			0
$573$	−10.8337			−0.452583
$574$		0			0
$575$	−9.81958	−	7.13434i	−0.409505	−	0.297523i
$576$		0			0
$577$	0.607927	+	1.19312i	0.0253083	+	0.0496704i	0.903315	−	0.428979i	$-0.141127\pi$
$577$	0.607927	+	1.19312i	0.0253083	+	0.0496704i	−0.878006	+	0.478649i	$0.841127\pi$
$578$		0			0
$579$	−1.79932	+	11.3605i	−0.0747774	+	0.472126i
$580$		0			0
$581$	0.307247	+	0.945608i	0.0127467	+	0.0392304i
$582$		0			0
$583$	−1.04845	−	9.05777i	−0.0434223	−	0.375135i
$584$		0			0
$585$	−12.9637	−	0.457113i	−0.535981	−	0.0188993i
$586$		0			0
$587$	0.322319	−	2.03504i	0.0133035	−	0.0839951i	−0.980143	−	0.198291i	$-0.936461\pi$
$587$	0.322319	−	2.03504i	0.0133035	−	0.0839951i	0.993447	+	0.114295i	$0.0364611\pi$
$588$		0			0
$589$	15.7582	−	48.4988i	0.649306	−	1.99836i
$590$		0			0
$591$	2.58849	+	16.3431i	0.106476	+	0.672266i
$592$		0			0
$593$	−17.0326	+	17.0326i	−0.699447	+	0.699447i	−0.964291	−	0.264844i	$-0.914679\pi$
$593$	−17.0326	+	17.0326i	−0.699447	+	0.699447i	0.264844	+	0.964291i	$0.414679\pi$
$594$		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	−0.852977	−	0.521948i	$-0.825206\pi$
$599$	3.52161	−	10.8384i	0.143889	−	0.442845i	0.996866	+	0.0791029i	$0.0252056\pi$
$600$		0			0
$601$	−7.85959	−	10.8178i	−0.320599	−	0.441267i	0.618051	−	0.786138i	$-0.287923\pi$
$601$	−7.85959	−	10.8178i	−0.320599	−	0.441267i	−0.938650	+	0.344871i	$0.887923\pi$
$602$		0			0
$603$	19.9658	+	10.1731i	0.813072	+	0.414281i
$604$		0			0
$605$	−1.37401	−	18.6867i	−0.0558616	−	0.759721i
$606$		0			0
$607$	21.4490	−	6.96922i	0.870590	−	0.282872i	0.160545	−	0.987028i	$-0.448675\pi$
$607$	21.4490	−	6.96922i	0.870590	−	0.282872i	0.710045	+	0.704157i	$0.248675\pi$
$608$		0			0
$609$	0.177307	+	0.0280827i	0.00718485	+	0.00113797i
$610$		0			0
$611$	−19.6901	+	25.1846i	−0.796578	+	1.01886i
$612$		0			0
$613$	2.95775	+	18.6745i	0.119463	+	0.754257i	0.972585	+	0.232546i	$0.0747058\pi$
$613$	2.95775	+	18.6745i	0.119463	+	0.754257i	−0.853123	+	0.521710i	$0.825294\pi$
$614$		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
$619$	−7.56389	−	47.7565i	−0.304018	−	1.91950i	−0.385274	−	0.922802i	$-0.625893\pi$
$619$	−7.56389	−	47.7565i	−0.304018	−	1.91950i	0.0812555	−	0.996693i	$-0.474107\pi$
$620$		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
$629$	−0.0270769	+	0.0531413i	−0.00107963	+	0.00211888i
$630$		0			0
$631$	−9.45921	−	1.49819i	−0.376565	−	0.0596421i	−0.0347168	−	0.999397i	$-0.511053\pi$
$631$	−9.45921	−	1.49819i	−0.376565	−	0.0596421i	−0.341848	+	0.939755i	$0.611053\pi$
$632$		0			0
$633$	10.1367	+	3.29360i	0.402896	+	0.130909i
$634$		0			0
$635$	−6.98807	+	1.10680i	−0.277313	+	0.0439221i
$636$		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	$-0.789072\pi$
$641$	1.02165	−	1.40618i	0.0403526	−	0.0555406i	0.828717	+	0.559669i	$0.189072\pi$
$642$		0			0
$643$	−1.85545	−	3.64153i	−0.0731719	−	0.143608i	0.851523	−	0.524318i	$-0.175680\pi$
$643$	−1.85545	−	3.64153i	−0.0731719	−	0.143608i	−0.924695	+	0.380710i	$0.875680\pi$
$644$		0			0
$645$	−1.02782	+	6.48943i	−0.0404705	+	0.255521i
$646$		0			0
$647$	21.6038	−	7.01949i	0.849332	−	0.275965i	0.148166	−	0.988963i	$-0.452663\pi$
$647$	21.6038	−	7.01949i	0.849332	−	0.275965i	0.701166	+	0.712998i	$0.252663\pi$
$648$		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	−0.930204	−	0.367042i	$-0.880370\pi$
$653$	−22.1955	+	16.1259i	−0.868575	+	0.631057i	0.0616290	+	0.998099i	$0.480370\pi$
$654$		0			0
$655$	−29.2480	+	14.9026i	−1.14281	+	0.582292i
$656$		0			0
$657$	16.8086	−	2.66223i	0.655767	−	0.103863i
$658$		0			0
$659$			15.2954i			0.595826i	0.954593	+	0.297913i	$0.0962905\pi$
$659$			15.2954i			0.595826i	−0.954593	+	0.297913i	$0.903710\pi$
$660$		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
$663$	−1.83652	−	0.357631i	−0.0713244	−	0.0138892i
$664$		0			0
$665$	3.45292	+	6.77674i	0.133899	+	0.262791i
$666$		0			0
$667$	1.41095	−	1.02512i	0.0546324	−	0.0396928i
$668$		0			0
$669$	10.4780	+	5.33882i	0.405103	+	0.206411i
$670$		0			0
$671$	25.6944	+	14.4765i	0.991920	+	0.558857i
$672$		0			0
$673$	6.91806	+	21.2916i	0.266671	+	0.820730i	0.991304	+	0.131595i	$0.0420097\pi$
$673$	6.91806	+	21.2916i	0.266671	+	0.820730i	−0.724632	+	0.689136i	$0.757990\pi$
$674$		0			0
$675$	−5.94171	−	8.17806i	−0.228696	−	0.314774i
$676$		0			0
$677$	−1.56380	−	0.508110i	−0.0601018	−	0.0195283i	0.278812	−	0.960346i	$-0.410059\pi$
$677$	−1.56380	−	0.508110i	−0.0601018	−	0.0195283i	−0.338914	+	0.940818i	$0.610059\pi$
$678$		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
$687$	−16.1458	+	8.22669i	−0.616000	+	0.313868i
$688$		0			0
$689$	4.80866	−	8.66811i	0.183195	−	0.330229i
$690$		0			0
$691$	10.0138	+	5.10230i	0.380944	+	0.194101i	0.633968	−	0.773359i	$-0.281425\pi$
$691$	10.0138	+	5.10230i	0.380944	+	0.194101i	−0.253024	+	0.967460i	$0.581425\pi$
$692$		0			0
$693$	−4.42207	−	0.185133i	−0.167980	−	0.00703262i
$694$		0			0
$695$	8.48754	−	16.6577i	0.321951	−	0.631864i
$696$		0			0
$697$	−1.63678	−	0.259241i	−0.0619975	−	0.00981945i
$698$		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	$-0.240211\pi$
$701$	7.99950	+	5.81198i	0.302137	+	0.219515i	−0.426378	+	0.904545i	$0.640211\pi$
$702$		0			0
$703$		−	0.765356i		−	0.0288659i
$704$		0			0
$705$	14.2311			0.535972
$706$		0			0
$707$	11.9189	−	1.88778i	0.448258	−	0.0709971i
$708$		0			0
$709$	−0.187127	+	0.0953457i	−0.00702769	+	0.00358078i	−0.457501	−	0.889209i	$-0.651255\pi$
$709$	−0.187127	+	0.0953457i	−0.00702769	+	0.00358078i	0.450473	+	0.892790i	$0.351255\pi$
$710$		0			0
$711$	−3.36264	−	4.62827i	−0.126109	−	0.173574i
$712$		0			0
$713$	18.9477	−	37.1870i	0.709598	−	1.39267i
$714$		0			0
$715$	10.6177	−	17.3832i	0.397081	−	0.650095i
$716$		0			0
$717$	0.552869	−	1.08507i	0.0206473	−	0.0405225i
$718$		0			0
$719$	−25.7344	−	35.4203i	−0.959730	−	1.32095i	−0.947067	−	0.321035i	$-0.895969\pi$
$719$	−25.7344	−	35.4203i	−0.959730	−	1.32095i	−0.0126622	−	0.999920i	$-0.504031\pi$
$720$		0			0
$721$	−5.87648	+	2.99421i	−0.218851	+	0.111510i
$722$		0			0
$723$	23.9065	−	3.78642i	0.889092	−	0.140818i
$724$		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
$733$	−40.3832	−	6.39608i	−1.49159	−	0.236244i	−0.643233	−	0.765671i	$-0.722407\pi$
$733$	−40.3832	−	6.39608i	−1.49159	−	0.236244i	−0.848356	+	0.529426i	$0.822407\pi$
$734$		0			0
$735$	4.80988	−	9.43992i	0.177415	−	0.348197i
$736$		0			0
$737$	−29.3074	+	19.4738i	−1.07955	+	0.717326i
$738$		0			0
$739$	−40.9365	−	20.8582i	−1.50587	−	0.767280i	−0.510185	−	0.860064i	$-0.670423\pi$
$739$	−40.9365	−	20.8582i	−1.50587	−	0.767280i	−0.995686	+	0.0927845i	$0.970423\pi$
$740$		0			0
$741$	23.0820	−	6.61016i	0.847938	−	0.242830i
$742$		0			0
$743$	−12.0391	+	6.13423i	−0.441672	+	0.225043i	−0.660661	−	0.750684i	$-0.729724\pi$
$743$	−12.0391	+	6.13423i	−0.441672	+	0.225043i	0.218989	+	0.975727i	$0.429724\pi$
$744$		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	$-0.887695\pi$
$751$	−8.76370	+	12.0622i	−0.319792	+	0.440156i	0.618612	+	0.785697i	$0.287695\pi$
$752$		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	0.847348	−	0.531038i	$-0.178198\pi$
$757$	−4.13550	−	12.7277i	−0.150307	−	0.462598i	−0.997655	+	0.0684400i	$0.978198\pi$
$758$		0			0
$759$	13.3050	−	12.2358i	0.482942	−	0.444130i
$760$		0			0
$761$	3.36731	+	1.71573i	0.122065	+	0.0621952i	0.513957	−	0.857816i	$-0.328179\pi$
$761$	3.36731	+	1.71573i	0.122065	+	0.0621952i	−0.391892	+	0.920011i	$0.628179\pi$
$762$		0			0
$763$	7.02860	−	5.10658i	0.254452	−	0.184871i
$764$		0			0
$765$	−0.899493	−	1.76535i	−0.0325212	−	0.0638265i
$766$		0			0
$767$	−26.2679	−	38.9724i	−0.948480	−	1.40721i
$768$		0			0
$769$	−19.2017	−	19.2017i	−0.692430	−	0.692430i	0.270336	−	0.962766i	$-0.412865\pi$
$769$	−19.2017	−	19.2017i	−0.692430	−	0.692430i	−0.962766	+	0.270336i	$0.912865\pi$
$770$		0			0
$771$			7.38806i			0.266075i
$772$		0			0
$773$	40.1354	−	6.35682i	1.44357	−	0.228639i	0.615001	−	0.788526i	$-0.289156\pi$
$773$	40.1354	−	6.35682i	1.44357	−	0.228639i	0.828569	+	0.559887i	$0.189156\pi$
$774$		0			0
$775$	13.4921	−	6.87459i	0.484652	−	0.246943i
$776$		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
$785$	4.90753	−	30.9849i	0.175157	−	1.10590i
$786$		0			0
$787$	−8.18104	−	16.0562i	−0.291622	−	0.572341i	0.697989	−	0.716108i	$-0.254078\pi$
$787$	−8.18104	−	16.0562i	−0.291622	−	0.572341i	−0.989612	+	0.143767i	$0.954078\pi$
$788$		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
$795$	−4.35839	+	0.690300i	−0.154576	+	0.0244824i
$796$		0			0
$797$	44.8289	+	14.5658i	1.58792	+	0.515947i	0.964081	−	0.265607i	$-0.0855723\pi$
$797$	44.8289	+	14.5658i	1.58792	+	0.515947i	0.623839	+	0.781553i	$0.285572\pi$
$798$		0			0
$799$	−4.82271	−	0.763843i	−0.170615	−	0.0270228i
$800$		0			0
$801$	−13.0262	+	25.5653i	−0.460257	+	0.903305i
$802$		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	0.274316	−	0.961640i	$-0.411549\pi$
$809$	−1.96243	−	0.637631i	−0.0689952	−	0.0224179i	−0.343311	+	0.939222i	$0.611549\pi$
$810$		0			0
$811$	3.10548	+	19.6072i	0.109048	+	0.688503i	0.980277	+	0.197627i	$0.0633234\pi$
$811$	3.10548	+	19.6072i	0.109048	+	0.688503i	−0.871229	+	0.490877i	$0.836677\pi$
$812$		0			0
$813$	−7.53964	+	7.53964i	−0.264427	+	0.264427i
$814$		0			0
$815$	28.2773			0.990509
$816$		0			0
$817$	4.52549	+	28.5728i	0.158327	+	0.999636i
$818$		0			0
$819$	−3.79051	−	2.96355i	−0.132451	−	0.103555i
$820$		0			0
$821$	−24.5719	−	3.89181i	−0.857566	−	0.135825i	−0.287859	−	0.957673i	$-0.592943\pi$
$821$	−24.5719	−	3.89181i	−0.857566	−	0.135825i	−0.569707	+	0.821848i	$0.692943\pi$
$822$		0			0
$823$	−25.0931	+	8.15325i	−0.874691	+	0.284204i	−0.711751	−	0.702431i	$-0.752098\pi$
$823$	−25.0931	+	8.15325i	−0.874691	+	0.284204i	−0.162940	+	0.986636i	$0.552098\pi$
$824$		0			0
$825$	6.51477	−	0.754092i	0.226815	−	0.0262541i
$826$		0			0
$827$	21.1422	+	10.7725i	0.735185	+	0.374596i	0.781147	−	0.624348i	$-0.214635\pi$
$827$	21.1422	+	10.7725i	0.735185	+	0.374596i	−0.0459613	+	0.998943i	$0.514635\pi$
$828$		0			0
$829$	12.3290	+	16.9694i	0.428202	+	0.589370i	0.967539	−	0.252720i	$-0.0813251\pi$
$829$	12.3290	+	16.9694i	0.428202	+	0.589370i	−0.539337	+	0.842090i	$0.681325\pi$
$830$		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
$839$	0.654048	+	4.12950i	0.0225802	+	0.142566i	0.996403	−	0.0847435i	$-0.0270071\pi$
$839$	0.654048	+	4.12950i	0.0225802	+	0.142566i	−0.973823	+	0.227310i	$0.927007\pi$
$840$		0			0
$841$	8.93340	−	27.4942i	0.308048	−	0.948075i
$842$		0			0
$843$	0.700206	−	4.42092i	0.0241164	−	0.152265i
$844$		0			0
$845$	20.3894	−	8.63844i	0.701417	−	0.297171i
$846$		0			0
$847$	3.66180	−	5.90711i	0.125821	−	0.202971i
$848$		0			0
$849$	3.97767	+	12.2420i	0.136513	+	0.420145i
$850$		0			0
$851$	0.0979900	−	0.618685i	0.00335905	−	0.0212082i
$852$		0			0
$853$	17.4226	+	34.1938i	0.596539	+	1.17077i	0.969995	+	0.243126i	$0.0781730\pi$
$853$	17.4226	+	34.1938i	0.596539	+	1.17077i	−0.373455	+	0.927648i	$0.621827\pi$
$854$		0			0
$855$	20.5693	+	14.9445i	0.703457	+	0.511091i
$856$		0			0
$857$	27.5703			0.941785			0.470892	−	0.882191i	$-0.343932\pi$
$857$	27.5703			0.941785			0.470892	+	0.882191i	$0.343932\pi$
$858$		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
$863$	−1.92808	−	3.78408i	−0.0656327	−	0.128812i	0.855859	−	0.517209i	$-0.173029\pi$
$863$	−1.92808	−	3.78408i	−0.0656327	−	0.128812i	−0.921492	+	0.388397i	$0.873029\pi$
$864$		0			0
$865$	3.23095	−	20.3994i	0.109855	−	0.693600i
$866$		0			0
$867$	4.86176	+	14.9630i	0.165114	+	0.508169i
$868$		0			0
$869$	8.92384	−	1.03295i	0.302721	−	0.0350403i
$870$		0			0
$871$	−38.2290	−	1.34800i	−1.29534	−	0.0456751i
$872$		0			0
$873$	−0.712022	+	4.49553i	−0.0240983	+	0.152151i
$874$		0			0
$875$	−2.36077	+	7.26570i	−0.0798085	+	0.245625i
$876$		0			0
$877$	−5.47235	−	34.5511i	−0.184788	−	1.16671i	−0.889405	−	0.457119i	$-0.848881\pi$
$877$	−5.47235	−	34.5511i	−0.184788	−	1.16671i	0.704617	−	0.709588i	$-0.251119\pi$
$878$		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	$-0.949424\pi$
$883$	−15.8027	+	21.7505i	−0.531803	+	0.731963i	0.455601	+	0.890184i	$0.349424\pi$
$884$		0			0
$885$	−6.46524	+	19.8980i	−0.217327	+	0.668863i
$886$		0			0
$887$	−9.00441	−	12.3935i	−0.302338	−	0.416133i	0.630634	−	0.776080i	$-0.282795\pi$
$887$	−9.00441	−	12.3935i	−0.302338	−	0.416133i	−0.932973	+	0.359947i	$0.882795\pi$
$888$		0			0
$889$	−2.33830	−	1.19143i	−0.0784242	−	0.0399591i
$890$		0			0
$891$	−5.41985	+	2.48171i	−0.181572	+	0.0831403i
$892$		0			0
$893$	59.5922	−	19.3627i	1.99418	−	0.647948i
$894$		0			0
$895$	8.68792	+	1.37603i	0.290405	+	0.0459957i
$896$		0			0
$897$	19.5049	−	2.38817i	0.651250	−	0.0797387i
$898$		0			0
$899$	0.340371	+	2.14902i	0.0113520	+	0.0716738i
$900$		0			0
$901$	1.51405			0.0504403
$902$		0			0
$903$	−1.72328	+	1.72328i	−0.0573470	+	0.0573470i
$904$		0			0
$905$	−1.06026	−	6.69420i	−0.0352442	−	0.222523i
$906$		0			0
$907$	−51.0410	−	16.5842i	−1.69479	−	0.550670i	−0.707100	−	0.707113i	$-0.749997\pi$
$907$	−51.0410	−	16.5842i	−1.69479	−	0.550670i	−0.987687	+	0.156444i	$0.949997\pi$
$908$		0			0
$909$	32.6361	−	23.7115i	1.08247	−	0.786461i
$910$		0			0
$911$	−16.2555	−	50.0294i	−0.538570	−	1.65755i	−0.735807	−	0.677191i	$-0.763197\pi$
$911$	−16.2555	−	50.0294i	−0.538570	−	1.65755i	0.197238	−	0.980356i	$-0.436803\pi$
$912$		0			0
$913$	−5.02692	+	1.40379i	−0.166367	+	0.0464588i
$914$		0			0
$915$	6.47952	−	12.7168i	0.214206	−	0.420404i
$916$		0			0
$917$	−12.0259	−	1.90472i	−0.397131	−	0.0628993i
$918$		0			0
$919$	18.1452	+	5.89574i	0.598556	+	0.194483i	0.592596	−	0.805500i	$-0.298103\pi$
$919$	18.1452	+	5.89574i	0.598556	+	0.194483i	0.00595960	+	0.999982i	$0.498103\pi$
$920$		0			0
$921$	11.3841	−	1.80307i	0.375120	−	0.0594132i
$922$		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
$929$	−7.14455	−	14.0220i	−0.234405	−	0.460046i	0.743601	−	0.668624i	$-0.233116\pi$
$929$	−7.14455	−	14.0220i	−0.234405	−	0.460046i	−0.978006	+	0.208578i	$0.933116\pi$
$930$		0			0
$931$	7.29737	−	46.0738i	0.239162	−	1.51001i
$932$		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	−0.920170	−	0.391520i	$-0.871949\pi$
$937$	−43.9099	+	14.2672i	−1.43447	+	0.466089i	−0.514303	+	0.857608i	$0.671949\pi$
$938$		0			0
$939$	22.8054	−	16.5691i	0.744227	−	0.540712i
$940$		0			0
$941$	33.3853	−	17.0106i	1.08833	−	0.554531i	0.184677	−	0.982799i	$-0.440876\pi$
$941$	33.3853	−	17.0106i	1.08833	−	0.554531i	0.903652	+	0.428268i	$0.140876\pi$
$942$		0			0
$943$	17.1905	−	2.72271i	0.559800	−	0.0886636i
$944$		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
$949$	−24.0903	+	16.2372i	−0.782004	+	0.527082i
$950$		0			0
$951$	−3.74469	−	7.34937i	−0.121430	−	0.238320i
$952$		0			0
$953$	41.4118	−	30.0874i	1.34146	−	0.974627i	0.342070	−	0.939675i	$-0.388872\pi$
$953$	41.4118	−	30.0874i	1.34146	−	0.974627i	0.999389	−	0.0349521i	$-0.0111279\pi$
$954$		0			0
$955$	17.4496	+	8.89102i	0.564656	+	0.287707i
$956$		0			0
$957$	−0.186218	+	0.923761i	−0.00601958	+	0.0298610i
$958$		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	0.708045	−	0.706167i	$-0.249577\pi$
$967$	0.0583856	+	0.0583856i	0.00187756	+	0.00187756i	−0.706167	+	0.708045i	$0.749577\pi$
$968$		0			0
$969$	2.59315	+	2.59315i	0.0833039	+	0.0833039i
$970$		0			0
$971$	−21.5435	−	15.6523i	−0.691364	−	0.502305i	0.185744	−	0.982598i	$-0.440530\pi$
$971$	−21.5435	−	15.6523i	−0.691364	−	0.502305i	−0.877108	+	0.480293i	$0.840530\pi$
$972$		0			0
$973$	6.17873	−	3.14822i	0.198081	−	0.100927i
$974$		0			0
$975$	6.23450	+	3.45861i	0.199664	+	0.110764i
$976$		0			0
$977$	−53.8824	−	27.4544i	−1.72385	−	0.878345i	−0.976967	−	0.213389i	$-0.931550\pi$
$977$	−53.8824	−	27.4544i	−1.72385	−	0.878345i	−0.746883	−	0.664956i	$-0.768450\pi$
$978$		0			0
$979$	−24.9352	−	37.5267i	−0.796933	−	1.19936i
$980$		0			0
$981$	13.1850	−	25.8770i	0.420965	−	0.826190i
$982$		0			0
$983$	32.5785	+	5.15993i	1.03909	+	0.164576i	0.652589	−	0.757712i	$-0.273683\pi$
$983$	32.5785	+	5.15993i	1.03909	+	0.164576i	0.386503	+	0.922288i	$0.373683\pi$
$984$		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
$993$	18.2588	−	2.89191i	0.579425	−	0.0917719i
$994$		0			0
$995$	−31.7021	+	16.1530i	−1.00502	+	0.512086i
$996$		0			0
$997$	−32.4968	−	44.7280i	−1.02918	−	1.41655i	−0.905558	−	0.424222i	$-0.860548\pi$
$997$	−32.4968	−	44.7280i	−1.02918	−	1.41655i	−0.123626	−	0.992329i	$-0.539452\pi$
$998$		0			0
$999$	0.236839	−	0.464823i	0.00749326	−	0.0147064i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.10	✓	112	11.2	odd	10	inner
572.2.bh.a.281.10	yes	112	13.8	odd	4	inner
572.2.bh.a.369.10	yes	112	1.1	even	1	trivial
572.2.bh.a.541.10	yes	112	143.112	even	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.762321 + 0.553859i) q^{3} +(-0.773316 - 1.51772i) q^{5} +(0.0988384 - 0.624041i) q^{7} +(-0.652677 - 2.00873i) q^{9} +(3.25122 + 0.655404i) q^{11} +(2.45808 + 2.63777i) q^{13} +(0.251086 - 1.58530i) q^{15} +(-0.170180 + 0.523759i) q^{17} +(-1.10553 - 6.98002i) q^{19} +(0.420977 - 0.420977i) q^{21} -5.78393i q^{23} +(1.23348 - 1.69774i) q^{25} +(1.48855 - 4.58128i) q^{27} +(0.177236 + 0.243944i) q^{29} +(6.42937 + 3.27593i) q^{31} +(2.11548 + 2.30035i) q^{33} +(-1.02355 + 0.332572i) q^{35} +(0.106966 + 0.0169418i) q^{37} +(0.412898 + 3.37226i) q^{39} +(0.470737 + 2.97212i) q^{41} -4.09351 q^{43} +(-2.54396 + 2.54396i) q^{45} +(1.38701 + 8.75722i) q^{47} +(6.27774 + 2.03976i) q^{49} +(-0.419820 + 0.305017i) q^{51} +(-0.849567 - 2.61470i) q^{53} +(-1.51950 - 5.44127i) q^{55} +(3.02318 - 5.93333i) q^{57} +(-12.8745 - 2.03913i) q^{59} +(8.45691 + 2.74782i) q^{61} +(-1.31804 + 0.208757i) q^{63} +(2.10251 - 5.77050i) q^{65} +(-7.50198 + 7.50198i) q^{67} +(3.20348 - 4.40921i) q^{69} +(0.0459906 + 0.0902617i) q^{71} +(-1.26046 + 7.95823i) q^{73} +(1.88061 - 0.611048i) q^{75} +(0.730344 - 1.96412i) q^{77} +(2.57604 - 0.837005i) q^{79} +(-1.45406 + 1.05643i) q^{81} +(-1.40214 + 0.714428i) q^{83} +(0.926520 - 0.146746i) q^{85} +0.284127i q^{87} +(-9.60592 - 9.60592i) q^{89} +(1.88903 - 1.27323i) q^{91} +(3.08685 + 6.05828i) q^{93} +(-9.73878 + 7.07564i) q^{95} +(-1.92011 - 0.978345i) q^{97} +(-0.805466 - 6.95860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59}+ \cdots - 90 q^{99}+O(q^{100}) \) 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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