LMFDB - Embedded newform 572.2.bg.a.9.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

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

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

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, 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 $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.9
Character	$\chi$	$=$	572.9
Dual form			572.2.bg.a.445.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0911637 + 0.867364i) q^{3} +(0.671959 + 2.06808i) q^{5} +(0.257245 - 2.44753i) q^{7} +(2.19043 - 0.465591i) q^{9} +O(q^{10})$	\(q+(0.0911637 + 0.867364i) q^{3} +(0.671959 + 2.06808i) q^{5} +(0.257245 - 2.44753i) q^{7} +(2.19043 - 0.465591i) q^{9} +(0.897761 + 3.19281i) q^{11} +(1.77872 - 3.13626i) q^{13} +(-1.73252 + 0.771367i) q^{15} +(-0.356820 + 0.396288i) q^{17} +(3.20430 + 1.42665i) q^{19} +2.14635 q^{21} +(-3.68853 + 6.38872i) q^{23} +(0.219667 - 0.159598i) q^{25} +(1.41204 + 4.34583i) q^{27} +(-2.05949 + 0.916946i) q^{29} +(-0.0412443 + 0.126937i) q^{31} +(-2.68748 + 1.06975i) q^{33} +(5.23453 - 1.11263i) q^{35} +(0.200524 - 0.0892791i) q^{37} +(2.88244 + 1.25689i) q^{39} +(0.349180 + 3.32222i) q^{41} +(-0.847571 - 1.46804i) q^{43} +(2.43476 + 4.21713i) q^{45} +(-9.03762 + 6.56621i) q^{47} +(0.922822 + 0.196152i) q^{49} +(-0.376255 - 0.273365i) q^{51} +(1.29404 - 3.98264i) q^{53} +(-5.99972 + 4.00208i) q^{55} +(-0.945306 + 2.90935i) q^{57} +(1.41530 - 13.4657i) q^{59} +(7.03253 - 7.81042i) q^{61} +(-0.576067 - 5.48091i) q^{63} +(7.68127 + 1.57110i) q^{65} +(-1.48399 + 2.57034i) q^{67} +(-5.87761 - 2.61688i) q^{69} +(-4.43537 + 4.92598i) q^{71} +(5.65610 + 4.10940i) q^{73} +(0.158455 + 0.175982i) q^{75} +(8.04543 - 1.37596i) q^{77} +(3.65500 - 11.2489i) q^{79} +(2.49661 - 1.11156i) q^{81} +(-0.431255 - 1.32727i) q^{83} +(-1.05932 - 0.471641i) q^{85} +(-0.983077 - 1.70274i) q^{87} +(2.73825 - 4.74279i) q^{89} +(-7.21852 - 5.16026i) q^{91} +(-0.113861 - 0.0242018i) q^{93} +(-0.797257 + 7.58539i) q^{95} +(-6.83542 + 1.45291i) q^{97} +(3.45303 + 6.57564i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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
$3$	0.0911637	+	0.867364i	0.0526334	+	0.500773i	0.988803	+	0.149225i	$0.0476779\pi$
$3$	0.0911637	+	0.867364i	0.0526334	+	0.500773i	−0.936170	+	0.351548i	$0.885655\pi$
$4$		0			0
$5$	0.671959	+	2.06808i	0.300509	+	0.924873i	0.981315	+	0.192408i	$0.0616299\pi$
$5$	0.671959	+	2.06808i	0.300509	+	0.924873i	−0.680806	+	0.732464i	$0.738370\pi$
$6$		0			0
$7$	0.257245	−	2.44753i	0.0972296	−	0.925078i	−0.831801	−	0.555074i	$-0.812690\pi$
$7$	0.257245	−	2.44753i	0.0972296	−	0.925078i	0.929030	−	0.370004i	$-0.120644\pi$
$8$		0			0
$9$	2.19043	−	0.465591i	0.730144	−	0.155197i
$10$		0			0
$11$	0.897761	+	3.19281i	0.270685	+	0.962668i
$11$	0.897761	+	3.19281i	0.270685	+	0.962668i
$12$		0			0
$13$	1.77872	−	3.13626i	0.493329	−	0.869843i
$13$	1.77872	−	3.13626i	0.493329	−	0.869843i
$14$		0			0
$15$	−1.73252	+	0.771367i	−0.447334	+	0.199166i
$16$		0			0
$17$	−0.356820	+	0.396288i	−0.0865414	+	0.0961140i	−0.784860	−	0.619673i	$-0.787265\pi$
$17$	−0.356820	+	0.396288i	−0.0865414	+	0.0961140i	0.698319	+	0.715787i	$0.253932\pi$
$18$		0			0
$19$	3.20430	+	1.42665i	0.735117	+	0.327295i	0.739921	−	0.672693i	$-0.234863\pi$
$19$	3.20430	+	1.42665i	0.735117	+	0.327295i	−0.00480444	+	0.999988i	$0.501529\pi$
$20$		0			0
$21$	2.14635			0.468372
$22$		0			0
$23$	−3.68853	+	6.38872i	−0.769112	+	1.33214i	0.168933	+	0.985628i	$0.445968\pi$
$23$	−3.68853	+	6.38872i	−0.769112	+	1.33214i	−0.938045	+	0.346514i	$0.887365\pi$
$24$		0			0
$25$	0.219667	−	0.159598i	0.0439335	−	0.0319195i
$26$		0			0
$27$	1.41204	+	4.34583i	0.271748	+	0.836355i
$28$		0			0
$29$	−2.05949	+	0.916946i	−0.382439	+	0.170273i	−0.588946	−	0.808172i	$-0.700457\pi$
$29$	−2.05949	+	0.916946i	−0.382439	+	0.170273i	0.206507	+	0.978445i	$0.433790\pi$
$30$		0			0
$31$	−0.0412443	+	0.126937i	−0.00740770	+	0.0227986i	−0.954692	−	0.297596i	$-0.903815\pi$
$31$	−0.0412443	+	0.126937i	−0.00740770	+	0.0227986i	0.947284	+	0.320394i	$0.103815\pi$
$32$		0			0
$33$	−2.68748	+	1.06975i	−0.467831	+	0.186220i
$34$		0			0
$35$	5.23453	−	1.11263i	0.884798	−	0.188070i
$36$		0			0
$37$	0.200524	−	0.0892791i	0.0329660	−	0.0146774i	−0.390187	−	0.920735i	$-0.627590\pi$
$37$	0.200524	−	0.0892791i	0.0329660	−	0.0146774i	0.423153	+	0.906058i	$0.360923\pi$
$38$		0			0
$39$	2.88244	+	1.25689i	0.461559	+	0.201263i
$40$		0			0
$41$	0.349180	+	3.32222i	0.0545327	+	0.518844i	0.987357	+	0.158513i	$0.0506698\pi$
$41$	0.349180	+	3.32222i	0.0545327	+	0.518844i	−0.932824	+	0.360332i	$0.882664\pi$
$42$		0			0
$43$	−0.847571	−	1.46804i	−0.129253	−	0.223873i	0.794134	−	0.607742i	$-0.207925\pi$
$43$	−0.847571	−	1.46804i	−0.129253	−	0.223873i	−0.923388	+	0.383869i	$0.874591\pi$
$44$		0			0
$45$	2.43476	+	4.21713i	0.362953	+	0.628652i
$46$		0			0
$47$	−9.03762	+	6.56621i	−1.31827	+	0.957781i	−0.318320	+	0.947983i	$0.603119\pi$
$47$	−9.03762	+	6.56621i	−1.31827	+	0.957781i	−0.999952	+	0.00979714i	$0.996881\pi$
$48$		0			0
$49$	0.922822	+	0.196152i	0.131832	+	0.0280217i
$50$		0			0
$51$	−0.376255	−	0.273365i	−0.0526863	−	0.0382788i
$52$		0			0
$53$	1.29404	−	3.98264i	0.177750	−	0.547058i	−0.821998	−	0.569490i	$-0.807141\pi$
$53$	1.29404	−	3.98264i	0.177750	−	0.547058i	0.999748	+	0.0224315i	$0.00714078\pi$
$54$		0			0
$55$	−5.99972	+	4.00208i	−0.809002	+	0.539640i
$56$		0			0
$57$	−0.945306	+	2.90935i	−0.125209	+	0.385353i
$58$		0			0
$59$	1.41530	−	13.4657i	0.184256	−	1.75308i	−0.377712	−	0.925923i	$-0.623289\pi$
$59$	1.41530	−	13.4657i	0.184256	−	1.75308i	0.561968	−	0.827159i	$-0.310044\pi$
$60$		0			0
$61$	7.03253	−	7.81042i	0.900424	−	1.00002i	−0.0995639	−	0.995031i	$-0.531745\pi$
$61$	7.03253	−	7.81042i	0.900424	−	1.00002i	0.999988	−	0.00499064i	$-0.00158858\pi$
$62$		0			0
$63$	−0.576067	−	5.48091i	−0.0725777	−	0.690530i
$64$		0			0
$65$	7.68127	+	1.57110i	0.952744	+	0.194871i
$66$		0			0
$67$	−1.48399	+	2.57034i	−0.181298	+	0.314017i	−0.942323	−	0.334706i	$-0.891363\pi$
$67$	−1.48399	+	2.57034i	−0.181298	+	0.314017i	0.761025	+	0.648723i	$0.224696\pi$
$68$		0			0
$69$	−5.87761	−	2.61688i	−0.707581	−	0.315035i
$70$		0			0
$71$	−4.43537	+	4.92598i	−0.526382	+	0.584606i	−0.946435	−	0.322893i	$-0.895345\pi$
$71$	−4.43537	+	4.92598i	−0.526382	+	0.584606i	0.420054	+	0.907499i	$0.362011\pi$
$72$		0			0
$73$	5.65610	+	4.10940i	0.661996	+	0.480968i	0.867337	−	0.497722i	$-0.165830\pi$
$73$	5.65610	+	4.10940i	0.661996	+	0.480968i	−0.205340	+	0.978691i	$0.565830\pi$
$74$		0			0
$75$	0.158455	+	0.175982i	0.0182968	+	0.0203207i
$76$		0			0
$77$	8.04543	−	1.37596i	0.916862	−	0.156805i
$78$		0			0
$79$	3.65500	−	11.2489i	0.411220	−	1.26560i	−0.504369	−	0.863488i	$-0.668275\pi$
$79$	3.65500	−	11.2489i	0.411220	−	1.26560i	0.915589	−	0.402116i	$-0.131725\pi$
$80$		0			0
$81$	2.49661	−	1.11156i	0.277401	−	0.123507i
$82$		0			0
$83$	−0.431255	−	1.32727i	−0.0473364	−	0.145686i	0.924595	−	0.380952i	$-0.124404\pi$
$83$	−0.431255	−	1.32727i	−0.0473364	−	0.145686i	−0.971931	+	0.235266i	$0.924404\pi$
$84$		0			0
$85$	−1.05932	−	0.471641i	−0.114900	−	0.0511567i
$86$		0			0
$87$	−0.983077	−	1.70274i	−0.105397	−	0.182553i
$88$		0			0
$89$	2.73825	−	4.74279i	0.290254	−	0.502735i	−0.683616	−	0.729842i	$-0.739594\pi$
$89$	2.73825	−	4.74279i	0.290254	−	0.502735i	0.973870	+	0.227107i	$0.0729268\pi$
$90$		0			0
$91$	−7.21852	−	5.16026i	−0.756706	−	0.540942i
$92$		0			0
$93$	−0.113861	−	0.0242018i	−0.0118068	−	0.00250961i
$94$		0			0
$95$	−0.797257	+	7.58539i	−0.0817968	+	0.778245i
$96$		0			0
$97$	−6.83542	+	1.45291i	−0.694032	+	0.147521i	−0.541404	−	0.840763i	$-0.682107\pi$
$97$	−6.83542	+	1.45291i	−0.694032	+	0.147521i	−0.152628	+	0.988284i	$0.548774\pi$
$98$		0			0
$99$	3.45303	+	6.57564i	0.347042	+	0.660877i
$100$		0			0
$101$	−3.42696	−	3.80602i	−0.340995	−	0.378713i	0.548118	−	0.836401i	$-0.315344\pi$
$101$	−3.42696	−	3.80602i	−0.340995	−	0.378713i	−0.889113	+	0.457688i	$0.848678\pi$
$102$		0			0
$103$	−7.37307	−	5.35685i	−0.726490	−	0.527826i	0.161961	−	0.986797i	$-0.448218\pi$
$103$	−7.37307	−	5.35685i	−0.726490	−	0.527826i	−0.888451	+	0.458971i	$0.848218\pi$
$104$		0			0
$105$	1.44226	+	4.43882i	0.140750	+	0.433184i
$106$		0			0
$107$	−1.11796	−	10.6367i	−0.108077	−	1.02828i	−0.905350	−	0.424666i	$-0.860392\pi$
$107$	−1.11796	−	10.6367i	−0.108077	−	1.02828i	0.797273	−	0.603619i	$-0.206275\pi$
$108$		0			0
$109$	−2.30512			−0.220790			−0.110395	−	0.993888i	$-0.535212\pi$
$109$	−2.30512			−0.220790			−0.110395	+	0.993888i	$0.535212\pi$
$110$		0			0
$111$	0.0957181	+	0.165789i	0.00908516	+	0.0157360i
$112$		0			0
$113$	−8.17786	−	3.64102i	−0.769308	−	0.342518i	−0.0157298	−	0.999876i	$-0.505007\pi$
$113$	−8.17786	−	3.64102i	−0.769308	−	0.342518i	−0.753578	+	0.657358i	$0.771674\pi$
$114$		0			0
$115$	−15.6909	−	3.33521i	−1.46319	−	0.311010i
$116$		0			0
$117$	2.43596	−	7.69793i	0.225204	−	0.711674i
$118$		0			0
$119$	0.878136	+	0.975269i	0.0804986	+	0.0894027i
$120$		0			0
$121$	−9.38805	+	5.73276i	−0.853459	+	0.521160i
$122$		0			0
$123$	−2.84975	+	0.605732i	−0.256953	+	0.0546170i
$124$		0			0
$125$	9.27373	+	6.73776i	0.829468	+	0.602643i
$126$		0			0
$127$	−14.2243	−	3.02347i	−1.26221	−	0.268290i	−0.472256	−	0.881462i	$-0.656560\pi$
$127$	−14.2243	−	3.02347i	−1.26221	−	0.268290i	−0.789950	+	0.613172i	$0.789893\pi$
$128$		0			0
$129$	1.19605	−	0.868984i	0.105307	−	0.0765098i
$130$		0			0
$131$	−5.75790			−0.503070			−0.251535	−	0.967848i	$-0.580935\pi$
$131$	−5.75790			−0.503070			−0.251535	+	0.967848i	$0.580935\pi$
$132$		0			0
$133$	4.31605	−	7.47561i	0.374249	−	0.648218i
$134$		0			0
$135$	−8.03867	+	5.84044i	−0.691859	+	0.502665i
$136$		0			0
$137$	2.30512	−	2.56009i	0.196939	−	0.218723i	−0.636584	−	0.771207i	$-0.719653\pi$
$137$	2.30512	−	2.56009i	0.196939	−	0.218723i	0.833524	+	0.552484i	$0.186320\pi$
$138$		0			0
$139$	−0.192025	+	1.82700i	−0.0162874	+	0.154964i	−0.999643	−	0.0267288i	$-0.991491\pi$
$139$	−0.192025	+	1.82700i	−0.0162874	+	0.154964i	0.983355	+	0.181693i	$0.0581576\pi$
$140$		0			0
$141$	−6.51920	−	7.24030i	−0.549016	−	0.609744i
$142$		0			0
$143$	11.6104	+	2.86351i	0.970907	+	0.239458i
$144$		0			0
$145$	−3.28021	−	3.64305i	−0.272407	−	0.302538i
$146$		0			0
$147$	−0.0860073	+	0.818305i	−0.00709376	+	0.0674927i
$148$		0			0
$149$	13.9911	−	15.5387i	1.14620	−	1.27298i	0.189506	−	0.981879i	$-0.439311\pi$
$149$	13.9911	−	15.5387i	1.14620	−	1.27298i	0.956692	−	0.291103i	$-0.0940221\pi$
$150$		0			0
$151$	−4.13246	+	3.00241i	−0.336295	+	0.244333i	−0.743097	−	0.669184i	$-0.766644\pi$
$151$	−4.13246	+	3.00241i	−0.336295	+	0.244333i	0.406802	+	0.913516i	$0.366644\pi$
$152$		0			0
$153$	−0.597081	+	1.03417i	−0.0482711	+	0.0836081i
$154$		0			0
$155$	−0.290230			−0.0233118
$156$		0			0
$157$	−1.06885	+	0.776568i	−0.0853039	+	0.0619769i	−0.629620	−	0.776903i	$-0.716789\pi$
$157$	−1.06885	+	0.776568i	−0.0853039	+	0.0619769i	0.544316	+	0.838880i	$0.316789\pi$
$158$		0			0
$159$	3.57237	+	0.759331i	0.283308	+	0.0602189i
$160$		0			0
$161$	14.6877	+	10.6713i	1.15755	+	0.841012i
$162$		0			0
$163$	10.2297	−	2.17439i	0.801251	−	0.170311i	0.210953	−	0.977496i	$-0.432343\pi$
$163$	10.2297	−	2.17439i	0.801251	−	0.170311i	0.590298	+	0.807185i	$0.299010\pi$
$164$		0			0
$165$	−4.01822	−	4.83910i	−0.312818	−	0.376723i
$166$		0			0
$167$	−0.667874	−	0.741749i	−0.0516816	−	0.0573983i	0.716750	−	0.697331i	$-0.245629\pi$
$167$	−0.667874	−	0.741749i	−0.0516816	−	0.0573983i	−0.768431	+	0.639932i	$0.778962\pi$
$168$		0			0
$169$	−6.67229	−	11.1571i	−0.513253	−	0.858237i
$170$		0			0
$171$	7.68304	+	1.63308i	0.587537	+	0.124885i
$172$		0			0
$173$	−14.5267	−	6.46769i	−1.10444	−	0.491729i	−0.228207	−	0.973613i	$-0.573286\pi$
$173$	−14.5267	−	6.46769i	−1.10444	−	0.491729i	−0.876235	+	0.481884i	$0.839953\pi$
$174$		0			0
$175$	−0.334111	−	0.578698i	−0.0252564	−	0.0437454i
$176$		0			0
$177$	11.8087			0.887594
$178$		0			0
$179$	0.274730	+	2.61389i	0.0205343	+	0.195371i	0.999980	−	0.00633752i	$-0.00201731\pi$
$179$	0.274730	+	2.61389i	0.0205343	+	0.195371i	−0.979446	+	0.201708i	$0.935351\pi$
$180$		0			0
$181$	−7.69086	−	23.6700i	−0.571657	−	1.75938i	−0.647289	−	0.762245i	$-0.724097\pi$
$181$	−7.69086	−	23.6700i	−0.571657	−	1.75938i	0.0756314	−	0.997136i	$-0.475903\pi$
$182$		0			0
$183$	7.41559	+	5.38774i	0.548176	+	0.398273i
$184$		0			0
$185$	0.319380	+	0.354708i	0.0234813	+	0.0260786i
$186$		0			0
$187$	−1.58561	−	0.783484i	−0.115951	−	0.0572940i
$188$		0			0
$189$	10.9998	−	2.33807i	0.800115	−	0.170070i
$190$		0			0
$191$	1.44079	−	13.7082i	0.104252	−	0.991889i	−0.809914	−	0.586548i	$-0.800486\pi$
$191$	1.44079	−	13.7082i	0.104252	−	0.991889i	0.914166	−	0.405340i	$-0.132847\pi$
$192$		0			0
$193$	−21.1060	−	4.48622i	−1.51924	−	0.322925i	−0.628637	−	0.777699i	$-0.716387\pi$
$193$	−21.1060	−	4.48622i	−1.51924	−	0.322925i	−0.890607	+	0.454774i	$0.849720\pi$
$194$		0			0
$195$	−0.662462	+	6.80568i	−0.0474399	+	0.487365i
$196$		0			0
$197$	−5.47120	+	9.47639i	−0.389807	+	0.675165i	−0.992423	−	0.122866i	$-0.960792\pi$
$197$	−5.47120	+	9.47639i	−0.389807	+	0.675165i	0.602617	+	0.798031i	$0.294125\pi$
$198$		0			0
$199$	12.3605	+	21.4090i	0.876211	+	1.51764i	0.855467	+	0.517858i	$0.173270\pi$
$199$	12.3605	+	21.4090i	0.876211	+	1.51764i	0.0207445	+	0.999785i	$0.493396\pi$
$200$		0			0
$201$	−2.36471	−	1.05284i	−0.166794	−	0.0742613i
$202$		0			0
$203$	1.71445	+	5.27655i	0.120331	+	0.370341i
$204$		0			0
$205$	−6.63598	+	2.95453i	−0.463477	+	0.206353i
$206$		0			0
$207$	−5.10495	+	15.7114i	−0.354819	+	1.09202i
$208$		0			0
$209$	−1.67831	+	11.5115i	−0.116091	+	0.796268i
$210$		0			0
$211$	10.8368	+	12.0355i	0.746036	+	0.828557i	0.989976	−	0.141234i	$-0.0451068\pi$
$211$	10.8368	+	12.0355i	0.746036	+	0.828557i	−0.243941	+	0.969790i	$0.578440\pi$
$212$		0			0
$213$	−4.67696	−	3.39801i	−0.320460	−	0.232828i
$214$		0			0
$215$	2.46648	−	2.73930i	0.168213	−	0.186819i
$216$		0			0
$217$	0.300072	+	0.133601i	0.0203702	+	0.00906939i
$218$		0			0
$219$	−3.04871	+	5.28053i	−0.206013	+	0.356825i
$220$		0			0
$221$	0.608181	+	1.82397i	0.0409107	+	0.122693i
$222$		0			0
$223$	−2.32671	−	22.1372i	−0.155808	−	1.48242i	−0.740991	−	0.671515i	$-0.765644\pi$
$223$	−2.32671	−	22.1372i	−0.155808	−	1.48242i	0.585183	−	0.810901i	$-0.301023\pi$
$224$		0			0
$225$	0.406859	−	0.451863i	0.0271240	−	0.0301242i
$226$		0			0
$227$	−2.21147	+	21.0408i	−0.146781	+	1.39652i	0.634779	+	0.772694i	$0.281091\pi$
$227$	−2.21147	+	21.0408i	−0.146781	+	1.39652i	−0.781560	+	0.623831i	$0.785576\pi$
$228$		0			0
$229$	−6.93453	+	21.3423i	−0.458247	+	1.41034i	0.409035	+	0.912519i	$0.365866\pi$
$229$	−6.93453	+	21.3423i	−0.458247	+	1.41034i	−0.867281	+	0.497819i	$0.834134\pi$
$230$		0			0
$231$	1.92691	+	6.85288i	0.126781	+	0.450886i
$232$		0			0
$233$	6.27531	−	19.3134i	0.411109	−	1.26526i	−0.504576	−	0.863367i	$-0.668351\pi$
$233$	6.27531	−	19.3134i	0.411109	−	1.26526i	0.915685	−	0.401896i	$-0.131649\pi$
$234$		0			0
$235$	−19.6524	−	14.2783i	−1.28198	−	0.931412i
$236$		0			0
$237$	10.0901	+	2.14472i	0.655425	+	0.139315i
$238$		0			0
$239$	0.300880	−	0.218602i	0.0194623	−	0.0141402i	−0.578012	−	0.816029i	$-0.696171\pi$
$239$	0.300880	−	0.218602i	0.0194623	−	0.0141402i	0.597474	+	0.801888i	$0.296171\pi$
$240$		0			0
$241$	12.9713	+	22.4670i	0.835555	+	1.44722i	0.893578	+	0.448908i	$0.148187\pi$
$241$	12.9713	+	22.4670i	0.835555	+	1.44722i	−0.0580228	+	0.998315i	$0.518480\pi$
$242$		0			0
$243$	8.04594	+	13.9360i	0.516147	+	0.893993i
$244$		0			0
$245$	0.214442	+	2.04027i	0.0137002	+	0.130348i
$246$		0			0
$247$	10.1739	−	7.51192i	0.647350	−	0.477972i
$248$		0			0
$249$	1.11191	−	0.495054i	0.0704644	−	0.0313728i
$250$		0			0
$251$	−19.5527	+	4.15605i	−1.23415	+	0.262327i	−0.778394	−	0.627776i	$-0.783966\pi$
$251$	−19.5527	+	4.15605i	−1.23415	+	0.262327i	−0.455759	+	0.890103i	$0.650632\pi$
$252$		0			0
$253$	−23.7094	−	6.04122i	−1.49060	−	0.379809i
$254$		0			0
$255$	0.312513	−	0.961816i	0.0195703	−	0.0602312i
$256$		0			0
$257$	9.54679	−	4.25050i	0.595512	−	0.265139i	−0.0867696	−	0.996228i	$-0.527654\pi$
$257$	9.54679	−	4.25050i	0.595512	−	0.265139i	0.682282	+	0.731089i	$0.260988\pi$
$258$		0			0
$259$	−0.166929	−	0.513755i	−0.0103725	−	0.0319232i
$260$		0			0
$261$	−4.08426	+	2.96739i	−0.252810	+	0.183677i
$262$		0			0
$263$	11.6097	−	20.1086i	0.715883	−	1.23995i	−0.246734	−	0.969083i	$-0.579358\pi$
$263$	11.6097	−	20.1086i	0.715883	−	1.23995i	0.962618	−	0.270863i	$-0.0873092\pi$
$264$		0			0
$265$	9.10596			0.559375
$266$		0			0
$267$	4.36336	+	1.94269i	0.267033	+	0.118891i
$268$		0			0
$269$	12.7052	−	14.1105i	0.774648	−	0.860334i	−0.218663	−	0.975800i	$-0.570170\pi$
$269$	12.7052	−	14.1105i	0.774648	−	0.860334i	0.993311	+	0.115466i	$0.0368363\pi$
$270$		0			0
$271$	−16.9340	+	7.53952i	−1.02867	+	0.457993i	−0.850482	−	0.526004i	$-0.823690\pi$
$271$	−16.9340	+	7.53952i	−1.02867	+	0.457993i	−0.178187	+	0.983997i	$0.557023\pi$
$272$		0			0
$273$	3.81776	−	6.73151i	0.231061	−	0.407410i
$274$		0			0
$275$	0.706774	+	0.558075i	0.0426201	+	0.0336532i
$276$		0			0
$277$	24.6324	−	5.23577i	1.48002	−	0.314587i	0.604045	−	0.796950i	$-0.293555\pi$
$277$	24.6324	−	5.23577i	1.48002	−	0.314587i	0.875971	+	0.482363i	$0.160221\pi$
$278$		0			0
$279$	−0.0312422	+	0.297250i	−0.00187042	+	0.0177959i
$280$		0			0
$281$	4.14710	+	12.7635i	0.247395	+	0.761405i	0.995233	+	0.0975232i	$0.0310920\pi$
$281$	4.14710	+	12.7635i	0.247395	+	0.761405i	−0.747838	+	0.663881i	$0.768908\pi$
$282$		0			0
$283$	−0.967710	−	9.20715i	−0.0575244	−	0.547308i	−0.984894	−	0.173161i	$-0.944602\pi$
$283$	−0.967710	−	9.20715i	−0.0575244	−	0.547308i	0.927369	−	0.374148i	$-0.122065\pi$
$284$		0			0
$285$	−6.65198			−0.394029
$286$		0			0
$287$	8.22106			0.485274
$288$		0			0
$289$	1.74726	+	16.6241i	0.102780	+	0.977886i
$290$		0			0
$291$	−1.88335	−	5.79634i	−0.110404	−	0.339788i
$292$		0			0
$293$	−2.97099	+	28.2670i	−0.173567	+	1.65138i	0.467573	+	0.883954i	$0.345128\pi$
$293$	−2.97099	+	28.2670i	−0.173567	+	1.65138i	−0.641140	+	0.767424i	$0.721538\pi$
$294$		0			0
$295$	28.7991	−	6.12144i	1.67675	−	0.356404i
$296$		0			0
$297$	−12.6077	+	8.40990i	−0.731574	+	0.487992i
$298$		0			0
$299$	13.4758	+	22.9320i	0.779328	+	1.32619i
$300$		0			0
$301$	−3.81109	+	1.69681i	−0.219668	+	0.0978023i
$302$		0			0
$303$	2.98879	−	3.31939i	0.171702	−	0.190694i
$304$		0			0
$305$	20.8781	+	9.29554i	1.19548	+	0.532261i
$306$		0			0
$307$	2.12198			0.121108			0.0605540	−	0.998165i	$-0.480713\pi$
$307$	2.12198			0.121108			0.0605540	+	0.998165i	$0.480713\pi$
$308$		0			0
$309$	3.97418	−	6.88348i	0.226083	−	0.391588i
$310$		0			0
$311$	−15.2110	+	11.0515i	−0.862538	+	0.626671i	−0.928574	−	0.371147i	$-0.878965\pi$
$311$	−15.2110	+	11.0515i	−0.862538	+	0.626671i	0.0660361	+	0.997817i	$0.478965\pi$
$312$		0			0
$313$	−0.168896	−	0.519810i	−0.00954659	−	0.0293814i	0.946170	−	0.323671i	$-0.104917\pi$
$313$	−0.168896	−	0.519810i	−0.00954659	−	0.0293814i	−0.955716	+	0.294289i	$0.904917\pi$
$314$		0			0
$315$	10.9479	−	4.87430i	0.616842	−	0.274636i
$316$		0			0
$317$	−2.49143	+	7.66783i	−0.139933	+	0.430668i	−0.996325	−	0.0856579i	$-0.972701\pi$
$317$	−2.49143	+	7.66783i	−0.139933	+	0.430668i	0.856392	+	0.516326i	$0.172701\pi$
$318$		0			0
$319$	−4.77657	−	5.75237i	−0.267436	−	0.322071i
$320$		0			0
$321$	9.12394	−	1.93935i	0.509249	−	0.108244i
$322$		0			0
$323$	−1.70872	+	0.760771i	−0.0950757	+	0.0423304i
$324$		0			0
$325$	−0.109813	−	0.972815i	−0.00609132	−	0.0539621i
$326$		0			0
$327$	−0.210143	−	1.99937i	−0.0116209	−	0.110566i
$328$		0			0
$329$	13.7461	+	23.8089i	0.757847	+	1.31263i
$330$		0			0
$331$	−1.65852	−	2.87263i	−0.0911602	−	0.157894i	0.816839	−	0.576865i	$-0.195724\pi$
$331$	−1.65852	−	2.87263i	−0.0911602	−	0.157894i	−0.908000	+	0.418971i	$0.862391\pi$
$332$		0			0
$333$	0.397667	−	0.288922i	0.0217920	−	0.0158328i
$334$		0			0
$335$	−6.31285	−	1.34184i	−0.344908	−	0.0733124i
$336$		0			0
$337$	0.0421568	+	0.0306287i	0.00229643	+	0.00166845i	0.588933	−	0.808182i	$-0.299548\pi$
$337$	0.0421568	+	0.0306287i	0.00229643	+	0.00166845i	−0.586636	+	0.809850i	$0.699548\pi$
$338$		0			0
$339$	2.41256	−	7.42511i	0.131032	−	0.403276i
$340$		0			0
$341$	−0.442313	−	0.0177261i	−0.0239526	−	0.000959922i
$342$		0			0
$343$	6.04093	−	18.5921i	0.326180	−	1.00388i
$344$		0			0
$345$	1.46240	−	13.9138i	0.0787329	−	0.749094i
$346$		0			0
$347$	19.4329	−	21.5824i	1.04321	−	1.15860i	0.0561248	−	0.998424i	$-0.482126\pi$
$347$	19.4329	−	21.5824i	1.04321	−	1.15860i	0.987088	−	0.160181i	$-0.0512078\pi$
$348$		0			0
$349$	3.16938	+	30.1546i	0.169653	+	1.61414i	0.665956	+	0.745991i	$0.268024\pi$
$349$	3.16938	+	30.1546i	0.169653	+	1.61414i	−0.496303	+	0.868149i	$0.665310\pi$
$350$		0			0
$351$	16.1413	+	3.30148i	0.861558	+	0.176220i
$352$		0			0
$353$	−2.49808	+	4.32680i	−0.132959	+	0.230293i	−0.924816	−	0.380414i	$-0.875781\pi$
$353$	−2.49808	+	4.32680i	−0.132959	+	0.230293i	0.791857	+	0.610707i	$0.209115\pi$
$354$		0			0
$355$	−13.1677	−	5.86264i	−0.698869	−	0.311156i
$356$		0			0
$357$	−0.765859	+	0.850573i	−0.0405336	+	0.0450171i
$358$		0			0
$359$	20.2269	+	14.6957i	1.06753	+	0.775609i	0.975468	−	0.220143i	$-0.0706526\pi$
$359$	20.2269	+	14.6957i	1.06753	+	0.775609i	0.0920672	+	0.995753i	$0.470653\pi$
$360$		0			0
$361$	−4.48126	−	4.97694i	−0.235856	−	0.261944i
$362$		0			0
$363$	−5.82824	−	7.62024i	−0.305903	−	0.399959i
$364$		0			0
$365$	−4.69788	+	14.4586i	−0.245899	+	0.756798i
$366$		0			0
$367$	−11.5011	+	5.12061i	−0.600351	+	0.267293i	−0.684328	−	0.729174i	$-0.739904\pi$
$367$	−11.5011	+	5.12061i	−0.600351	+	0.267293i	0.0839772	+	0.996468i	$0.473238\pi$
$368$		0			0
$369$	2.31165	+	7.11453i	0.120340	+	0.370368i
$370$		0			0
$371$	−9.41474	−	4.19171i	−0.488789	−	0.217623i
$372$		0			0
$373$	−12.4315	−	21.5321i	−0.643681	−	1.11489i	−0.984604	−	0.174797i	$-0.944073\pi$
$373$	−12.4315	−	21.5321i	−0.643681	−	1.11489i	0.340923	−	0.940091i	$-0.389260\pi$
$374$		0			0
$375$	−4.99866	+	8.65794i	−0.258130	+	0.447094i
$376$		0			0
$377$	−0.787487	+	8.09011i	−0.0405577	+	0.416662i
$378$		0			0
$379$	24.9440	+	5.30201i	1.28129	+	0.272346i	0.797756	−	0.602981i	$-0.206020\pi$
$379$	24.9440	+	5.30201i	1.28129	+	0.272346i	0.483532	+	0.875327i	$0.339354\pi$
$380$		0			0
$381$	1.32571	−	12.6133i	0.0679183	−	0.646199i
$382$		0			0
$383$	−11.5318	+	2.45115i	−0.589246	+	0.125248i	−0.492879	−	0.870098i	$-0.664055\pi$
$383$	−11.5318	+	2.45115i	−0.589246	+	0.125248i	−0.0963666	+	0.995346i	$0.530722\pi$
$384$		0			0
$385$	8.25179	+	15.7140i	0.420550	+	0.800859i
$386$		0			0
$387$	−2.54005	−	2.82101i	−0.129118	−	0.143400i
$388$		0			0
$389$	−30.8705	−	22.4288i	−1.56520	−	1.13718i	−0.931580	−	0.363537i	$-0.881569\pi$
$389$	−30.8705	−	22.4288i	−1.56520	−	1.13718i	−0.633619	−	0.773646i	$-0.718431\pi$
$390$		0			0
$391$	−1.21564	−	3.74134i	−0.0614774	−	0.189208i
$392$		0			0
$393$	−0.524911	−	4.99420i	−0.0264783	−	0.251924i
$394$		0			0
$395$	25.7197			1.29410
$396$		0			0
$397$	−11.4802	−	19.8843i	−0.576174	−	0.997962i	−0.995913	−	0.0903173i	$-0.971212\pi$
$397$	−11.4802	−	19.8843i	−0.576174	−	0.997962i	0.419739	−	0.907645i	$-0.362121\pi$
$398$		0			0
$399$	6.87755	+	3.06208i	0.344308	+	0.153296i
$400$		0			0
$401$	15.9915	+	3.39910i	0.798577	+	0.169743i	0.589089	−	0.808068i	$-0.299487\pi$
$401$	15.9915	+	3.39910i	0.798577	+	0.169743i	0.209488	+	0.977811i	$0.432820\pi$
$402$		0			0
$403$	0.324745	+	0.355139i	0.0161767	+	0.0176907i
$404$		0			0
$405$	3.97641	+	4.41625i	0.197590	+	0.219445i
$406$		0			0
$407$	0.465074	+	0.560084i	0.0230529	+	0.0277623i
$408$		0			0
$409$	−2.93933	+	0.624773i	−0.145340	+	0.0308931i	−0.280007	−	0.959998i	$-0.590337\pi$
$409$	−2.93933	+	0.624773i	−0.145340	+	0.0308931i	0.134667	+	0.990891i	$0.457004\pi$
$410$		0			0
$411$	2.43067	+	1.76599i	0.119896	+	0.0871098i
$412$		0			0
$413$	−32.5935	−	6.92797i	−1.60382	−	0.340903i
$414$		0			0
$415$	2.45511	−	1.78374i	0.120516	−	0.0875603i
$416$		0			0
$417$	−1.60218			−0.0784590
$418$		0			0
$419$	−5.66677	+	9.81514i	−0.276840	+	0.479501i	−0.970598	−	0.240707i	$-0.922621\pi$
$419$	−5.66677	+	9.81514i	−0.276840	+	0.479501i	0.693758	+	0.720209i	$0.255954\pi$
$420$		0			0
$421$	−20.3846	+	14.8103i	−0.993485	+	0.721809i	−0.960681	−	0.277653i	$-0.910443\pi$
$421$	−20.3846	+	14.8103i	−0.993485	+	0.721809i	−0.0328031	+	0.999462i	$0.510443\pi$
$422$		0			0
$423$	−16.7391	+	18.5907i	−0.813884	+	0.903910i
$424$		0			0
$425$	−0.0151349	+	0.143999i	−0.000734152	+	0.00698499i
$426$		0			0
$427$	−17.3071	−	19.2215i	−0.837550	−	0.930194i
$428$		0			0
$429$	−1.42526	+	10.3315i	−0.0688123	+	0.498807i
$430$		0			0
$431$	−25.2468	−	28.0394i	−1.21610	−	1.35061i	−0.918253	−	0.395995i	$-0.870400\pi$
$431$	−25.2468	−	28.0394i	−1.21610	−	1.35061i	−0.297842	−	0.954615i	$-0.596267\pi$
$432$		0			0
$433$	−4.21566	+	40.1093i	−0.202591	+	1.92753i	0.144126	+	0.989559i	$0.453963\pi$
$433$	−4.21566	+	40.1093i	−0.202591	+	1.92753i	−0.346717	+	0.937970i	$0.612704\pi$
$434$		0			0
$435$	2.86081	−	3.17725i	0.137165	−	0.152338i
$436$		0			0
$437$	−20.9336	+	15.2092i	−1.00139	+	0.727553i
$438$		0			0
$439$	1.84588	−	3.19716i	0.0880991	−	0.152592i	−0.818609	−	0.574352i	$-0.805254\pi$
$439$	1.84588	−	3.19716i	0.0880991	−	0.152592i	0.906708	+	0.421760i	$0.138587\pi$
$440$		0			0
$441$	2.11271			0.100605
$442$		0			0
$443$	−0.510762	+	0.371090i	−0.0242670	+	0.0176310i	−0.599853	−	0.800110i	$-0.704774\pi$
$443$	−0.510762	+	0.371090i	−0.0242670	+	0.0176310i	0.575586	+	0.817742i	$0.304774\pi$
$444$		0			0
$445$	11.6485	+	2.47596i	0.552190	+	0.117372i
$446$		0			0
$447$	14.7532	+	10.7188i	0.697803	+	0.506984i
$448$		0			0
$449$	16.6122	−	3.53103i	0.783977	−	0.166639i	0.201502	−	0.979488i	$-0.435418\pi$
$449$	16.6122	−	3.53103i	0.783977	−	0.166639i	0.582475	+	0.812849i	$0.302084\pi$
$450$		0			0
$451$	−10.2937	+	4.09743i	−0.484714	+	0.192940i
$452$		0			0
$453$	−2.98091	−	3.31064i	−0.140056	−	0.155547i
$454$		0			0
$455$	5.82127	−	18.3959i	0.272906	−	0.862415i
$456$		0			0
$457$	−34.1022	−	7.24864i	−1.59523	−	0.339077i	−0.677267	−	0.735737i	$-0.736836\pi$
$457$	−34.1022	−	7.24864i	−1.59523	−	0.339077i	−0.917965	+	0.396660i	$0.870169\pi$
$458$		0			0
$459$	−2.22605	−	0.991099i	−0.103903	−	0.0462605i
$460$		0			0
$461$	−4.81973	−	8.34803i	−0.224477	−	0.388806i	0.731685	−	0.681643i	$-0.238734\pi$
$461$	−4.81973	−	8.34803i	−0.224477	−	0.388806i	−0.956163	+	0.292836i	$0.905401\pi$
$462$		0			0
$463$	4.75824			0.221134			0.110567	−	0.993869i	$-0.464733\pi$
$463$	4.75824			0.221134			0.110567	+	0.993869i	$0.464733\pi$
$464$		0			0
$465$	−0.0264584	−	0.251735i	−0.00122698	−	0.0116739i
$466$		0			0
$467$	−7.04296	−	21.6760i	−0.325909	−	1.00305i	−0.971028	−	0.238964i	$-0.923192\pi$
$467$	−7.04296	−	21.6760i	−0.325909	−	1.00305i	0.645119	−	0.764082i	$-0.276808\pi$
$468$		0			0
$469$	5.90923	+	4.29331i	0.272863	+	0.198246i
$470$		0			0
$471$	−0.771008	−	0.856291i	−0.0355262	−	0.0394558i
$472$		0			0
$473$	3.92624	−	4.02408i	0.180529	−	0.185027i
$474$		0			0
$475$	0.931570	−	0.198011i	0.0427434	−	0.00908538i
$476$		0			0
$477$	0.980224	−	9.32621i	0.0448814	−	0.427018i
$478$		0			0
$479$	4.95016	+	1.05219i	0.226179	+	0.0480757i	0.319607	−	0.947550i	$-0.396449\pi$
$479$	4.95016	+	1.05219i	0.226179	+	0.0480757i	−0.0934281	+	0.995626i	$0.529783\pi$
$480$		0			0
$481$	0.0766743	−	0.787700i	0.00349605	−	0.0359160i
$482$		0			0
$483$	−7.91687	+	13.7124i	−0.360230	+	0.623937i
$484$		0			0
$485$	−7.59786	−	13.1599i	−0.345001	−	0.597559i
$486$		0			0
$487$	−17.3672	−	7.73238i	−0.786983	−	0.350388i	−0.0264198	−	0.999651i	$-0.508411\pi$
$487$	−17.3672	−	7.73238i	−0.786983	−	0.350388i	−0.760564	+	0.649263i	$0.775077\pi$
$488$		0			0
$489$	2.81856	+	8.67464i	0.127460	+	0.392281i
$490$		0			0
$491$	−13.6226	+	6.06516i	−0.614778	+	0.273717i	−0.690409	−	0.723419i	$-0.742569\pi$
$491$	−13.6226	+	6.06516i	−0.614778	+	0.273717i	0.0756313	+	0.997136i	$0.475903\pi$
$492$		0			0
$493$	0.371493	−	1.14334i	0.0167312	−	0.0514933i
$494$		0			0
$495$	−11.2786	+	11.5597i	−0.506938	+	0.519570i
$496$		0			0
$497$	10.9155	+	12.1229i	0.489626	+	0.543785i
$498$		0			0
$499$	12.4611	+	9.05348i	0.557833	+	0.405290i	0.830665	−	0.556772i	$-0.187960\pi$
$499$	12.4611	+	9.05348i	0.557833	+	0.405290i	−0.272832	+	0.962062i	$0.587960\pi$
$500$		0			0
$501$	0.582481	−	0.646911i	0.0260233	−	0.0289018i
$502$		0			0
$503$	−4.38324	−	1.95155i	−0.195439	−	0.0870152i	0.306683	−	0.951812i	$-0.400781\pi$
$503$	−4.38324	−	1.95155i	−0.195439	−	0.0870152i	−0.502123	+	0.864796i	$0.667447\pi$
$504$		0			0
$505$	5.56837	−	9.64470i	0.247789	−	0.429184i
$506$		0			0
$507$	9.06899	−	6.80442i	0.402768	−	0.302195i
$508$		0			0
$509$	−1.01744	−	9.68033i	−0.0450974	−	0.429073i	−0.993655	−	0.112469i	$-0.964124\pi$
$509$	−1.01744	−	9.68033i	−0.0450974	−	0.429073i	0.948558	−	0.316604i	$-0.102543\pi$
$510$		0			0
$511$	11.5129	−	12.7863i	0.509299	−	0.565634i
$512$		0			0
$513$	−1.67534	+	15.9398i	−0.0739682	+	0.703760i
$514$		0			0
$515$	6.12398	−	18.8477i	0.269855	−	0.830527i
$516$		0			0
$517$	−29.0783	−	22.9605i	−1.27886	−	1.00980i
$518$		0			0
$519$	4.28554	−	13.1895i	0.188114	−	0.578956i
$520$		0			0
$521$	12.2128	+	8.87309i	0.535051	+	0.388737i	0.822244	−	0.569136i	$-0.192722\pi$
$521$	12.2128	+	8.87309i	0.535051	+	0.388737i	−0.287193	+	0.957873i	$0.592722\pi$
$522$		0			0
$523$	17.9211	+	3.80924i	0.783634	+	0.166567i	0.582319	−	0.812960i	$-0.302145\pi$
$523$	17.9211	+	3.80924i	0.783634	+	0.166567i	0.201315	+	0.979527i	$0.435479\pi$
$524$		0			0
$525$	0.471483	−	0.342552i	0.0205772	−	0.0149502i
$526$		0			0
$527$	−0.0355868	−	0.0616382i	−0.00155019	−	0.00268500i
$528$		0			0
$529$	−15.7105	−	27.2114i	−0.683067	−	1.18311i
$530$		0			0
$531$	−3.16938	−	30.1546i	−0.137539	−	1.30860i
$532$		0			0
$533$	11.0405	+	4.81420i	0.478215	+	0.208526i
$534$		0			0
$535$	21.2462	−	9.45943i	0.918554	−	0.408967i
$536$		0			0
$537$	−2.24215	+	0.476583i	−0.0967557	+	0.0205661i
$538$		0			0
$539$	0.202199	+	3.12249i	0.00870932	+	0.134495i
$540$		0			0
$541$	10.2892	−	31.6670i	0.442369	−	1.36147i	−0.442975	−	0.896534i	$-0.646077\pi$
$541$	10.2892	−	31.6670i	0.442369	−	1.36147i	0.885344	−	0.464937i	$-0.153923\pi$
$542$		0			0
$543$	19.8294	−	8.82863i	0.850962	−	0.378873i
$544$		0			0
$545$	−1.54894	−	4.76716i	−0.0663495	−	0.204203i
$546$		0			0
$547$	26.9608	−	19.5882i	1.15276	−	0.837531i	0.163916	−	0.986474i	$-0.447587\pi$
$547$	26.9608	−	19.5882i	1.15276	−	0.837531i	0.988846	+	0.148944i	$0.0475873\pi$
$548$		0			0
$549$	11.7678	−	20.3825i	0.502239	−	0.869903i
$550$		0			0
$551$	−7.90740			−0.336866
$552$		0			0
$553$	−26.5919	−	11.8395i	−1.13080	−	0.503465i
$554$		0			0
$555$	−0.278545	+	0.309356i	−0.0118236	+	0.0131314i
$556$		0			0
$557$	−6.26704	+	2.79027i	−0.265543	+	0.118227i	−0.535189	−	0.844732i	$-0.679760\pi$
$557$	−6.26704	+	2.79027i	−0.265543	+	0.118227i	0.269647	+	0.962959i	$0.413093\pi$
$558$		0			0
$559$	−6.11174	+	0.0469753i	−0.258499	+	0.00198684i
$560$		0			0
$561$	0.535016	−	1.44673i	0.0225884	−	0.0610809i
$562$		0			0
$563$	−27.1431	+	5.76944i	−1.14395	+	0.243153i	−0.740633	−	0.671910i	$-0.765474\pi$
$563$	−27.1431	+	5.76944i	−1.14395	+	0.243153i	−0.403312	+	0.915063i	$0.632141\pi$
$564$		0			0
$565$	2.03472	−	19.3591i	0.0856013	−	0.814442i
$566$		0			0
$567$	−2.07833	−	6.39646i	−0.0872818	−	0.268626i
$568$		0			0
$569$	0.369192	+	3.51263i	0.0154773	+	0.147257i	0.999531	−	0.0306130i	$-0.00974596\pi$
$569$	0.369192	+	3.51263i	0.0154773	+	0.147257i	−0.984054	+	0.177870i	$0.943079\pi$
$570$		0			0
$571$	9.24223			0.386775			0.193388	−	0.981122i	$-0.438053\pi$
$571$	9.24223			0.386775			0.193388	+	0.981122i	$0.438053\pi$
$572$		0			0
$573$	12.0213			0.502198
$574$		0			0
$575$	0.209376	+	1.99208i	0.00873157	+	0.0830753i
$576$		0			0
$577$	9.04902	+	27.8500i	0.376716	+	1.15941i	0.942314	+	0.334731i	$0.108645\pi$
$577$	9.04902	+	27.8500i	0.376716	+	1.15941i	−0.565598	+	0.824681i	$0.691355\pi$
$578$		0			0
$579$	1.96709	−	18.7156i	0.0817493	−	0.777793i
$580$		0			0
$581$	−3.35946	+	0.714075i	−0.139374	+	0.0296248i
$582$		0			0
$583$	13.8776	+	0.556156i	0.574750	+	0.0230336i
$584$		0			0
$585$	17.5568	−	0.134943i	0.725884	−	0.00557919i
$586$		0			0
$587$	9.34000	−	4.15843i	0.385503	−	0.171637i	−0.204829	−	0.978798i	$-0.565664\pi$
$587$	9.34000	−	4.15843i	0.385503	−	0.171637i	0.590332	+	0.807161i	$0.298997\pi$
$588$		0			0
$589$	−0.313253	+	0.347903i	−0.0129074	+	0.0143351i
$590$		0			0
$591$	−8.71826	−	3.88162i	−0.358621	−	0.159668i
$592$		0			0
$593$	−37.0097			−1.51981			−0.759903	−	0.650037i	$-0.774754\pi$
$593$	−37.0097			−1.51981			−0.759903	+	0.650037i	$0.774754\pi$
$594$		0			0
$595$	−1.42686	+	2.47139i	−0.0584956	+	0.101317i
$596$		0			0
$597$	−17.4426	+	12.6728i	−0.713876	+	0.518662i
$598$		0			0
$599$	1.37860	+	4.24289i	0.0563280	+	0.173360i	0.975262	−	0.221051i	$-0.0709487\pi$
$599$	1.37860	+	4.24289i	0.0563280	+	0.173360i	−0.918934	+	0.394411i	$0.870949\pi$
$600$		0			0
$601$	−28.5953	+	12.7315i	−1.16643	+	0.519327i	−0.896279	−	0.443492i	$-0.853740\pi$
$601$	−28.5953	+	12.7315i	−1.16643	+	0.519327i	−0.270149	+	0.962819i	$0.587073\pi$
$602$		0			0
$603$	−2.05385	+	6.32109i	−0.0836391	+	0.257415i
$604$		0			0
$605$	−18.1642	−	15.5630i	−0.738479	−	0.632727i
$606$		0			0
$607$	17.3784	−	3.69389i	0.705367	−	0.149930i	0.158757	−	0.987318i	$-0.449251\pi$
$607$	17.3784	−	3.69389i	0.705367	−	0.149930i	0.546610	+	0.837387i	$0.315918\pi$
$608$		0			0
$609$	−4.42039	+	1.96809i	−0.179123	+	0.0797509i
$610$		0			0
$611$	4.51795	+	40.0238i	0.182777	+	1.61919i
$612$		0			0
$613$	2.96665	+	28.2258i	0.119822	+	1.14003i	0.874869	+	0.484360i	$0.160947\pi$
$613$	2.96665	+	28.2258i	0.119822	+	1.14003i	−0.755047	+	0.655671i	$0.772386\pi$
$614$		0			0
$615$	−3.16761	−	5.48647i	−0.127731	−	0.221236i
$616$		0			0
$617$	12.2619	+	21.2382i	0.493646	+	0.855020i	0.999973	−	0.00732176i	$-0.00233061\pi$
$617$	12.2619	+	21.2382i	0.493646	+	0.855020i	−0.506327	+	0.862341i	$0.668997\pi$
$618$		0			0
$619$	23.7860	−	17.2816i	0.956042	−	0.694605i	0.00381374	−	0.999993i	$-0.498786\pi$
$619$	23.7860	−	17.2816i	0.956042	−	0.694605i	0.952228	+	0.305388i	$0.0987860\pi$
$620$		0			0
$621$	−32.9727	−	7.00856i	−1.32315	−	0.281244i
$622$		0			0
$623$	−10.9037	−	7.92200i	−0.436848	−	0.317388i
$624$		0			0
$625$	−7.28312	+	22.4151i	−0.291325	+	0.896605i
$626$		0			0
$627$	−10.1377	−	0.406276i	−0.404860	−	0.0162251i
$628$		0			0
$629$	−0.0361707	+	0.111322i	−0.00144222	+	0.00443870i
$630$		0			0
$631$	1.12902	−	10.7419i	0.0449454	−	0.427627i	−0.948793	−	0.315898i	$-0.897694\pi$
$631$	1.12902	−	10.7419i	0.0449454	−	0.427627i	0.993739	−	0.111729i	$-0.0356390\pi$
$632$		0			0
$633$	−9.45122	+	10.4966i	−0.375652	+	0.417204i
$634$		0			0
$635$	−3.30539	−	31.4487i	−0.131170	−	1.24800i
$636$		0			0
$637$	2.25663	−	2.54531i	0.0894109	−	0.100849i
$638$		0			0
$639$	−7.42189	+	12.8551i	−0.293606	+	0.508540i
$640$		0			0
$641$	−33.4127	−	14.8763i	−1.31972	−	0.587579i	−0.378574	−	0.925571i	$-0.623586\pi$
$641$	−33.4127	−	14.8763i	−1.31972	−	0.587579i	−0.941149	+	0.337992i	$0.890252\pi$
$642$		0			0
$643$	−31.8872	+	35.4143i	−1.25751	+	1.39661i	−0.374515	+	0.927221i	$0.622191\pi$
$643$	−31.8872	+	35.4143i	−1.25751	+	1.39661i	−0.882994	+	0.469385i	$0.844476\pi$
$644$		0			0
$645$	2.60083	+	1.88961i	0.102407	+	0.0744034i
$646$		0			0
$647$	16.0458	+	17.8206i	0.630825	+	0.700602i	0.970816	−	0.239827i	$-0.0770907\pi$
$647$	16.0458	+	17.8206i	0.630825	+	0.700602i	−0.339991	+	0.940429i	$0.610424\pi$
$648$		0			0
$649$	44.2639	−	7.57018i	1.73751	−	0.297156i
$650$		0			0
$651$	−0.0885247	+	0.272451i	−0.00346956	+	0.0106782i
$652$		0			0
$653$	−25.0503	+	11.1531i	−0.980293	+	0.436455i	−0.833384	−	0.552695i	$-0.813599\pi$
$653$	−25.0503	+	11.1531i	−0.980293	+	0.436455i	−0.146910	+	0.989150i	$0.546933\pi$
$654$		0			0
$655$	−3.86908	−	11.9078i	−0.151177	−	0.465276i
$656$		0			0
$657$	14.3026	+	6.36793i	0.557998	+	0.248437i
$658$		0			0
$659$	0.612602	+	1.06106i	0.0238636	+	0.0413330i	0.877711	−	0.479191i	$-0.159070\pi$
$659$	0.612602	+	1.06106i	0.0238636	+	0.0413330i	−0.853847	+	0.520524i	$0.825737\pi$
$660$		0			0
$661$	0.655022	−	1.13453i	0.0254774	−	0.0441282i	−0.853006	−	0.521902i	$-0.825223\pi$
$661$	0.655022	−	1.13453i	0.0254774	−	0.0441282i	0.878483	+	0.477774i	$0.158556\pi$
$662$		0			0
$663$	−1.52660	+	0.693794i	−0.0592882	+	0.0269447i
$664$		0			0
$665$	18.3604	+	3.90261i	0.711984	+	0.151337i
$666$		0			0
$667$	1.73840	−	16.5397i	0.0673109	−	0.640421i
$668$		0			0
$669$	18.9889	−	4.03621i	0.734153	−	0.156049i
$670$		0			0
$671$	31.2507	+	15.4416i	1.20642	+	0.596118i
$672$		0			0
$673$	−4.39407	−	4.88011i	−0.169379	−	0.188114i	0.652479	−	0.757807i	$-0.273729\pi$
$673$	−4.39407	−	4.88011i	−0.169379	−	0.188114i	−0.821858	+	0.569692i	$0.807062\pi$
$674$		0			0
$675$	1.00376	+	0.729277i	0.0386349	+	0.0280699i
$676$		0			0
$677$	−12.1331	−	37.3418i	−0.466313	−	1.43516i	−0.857324	−	0.514777i	$-0.827875\pi$
$677$	−12.1331	−	37.3418i	−0.466313	−	1.43516i	0.391011	−	0.920386i	$-0.372125\pi$
$678$		0			0
$679$	1.79766	+	17.1036i	0.0689880	+	0.656377i
$680$		0			0
$681$	−18.4516			−0.707067
$682$		0			0
$683$	5.01114	+	8.67955i	0.191746	+	0.332114i	0.945829	−	0.324665i	$-0.105252\pi$
$683$	5.01114	+	8.67955i	0.191746	+	0.332114i	−0.754083	+	0.656779i	$0.771918\pi$
$684$		0			0
$685$	6.84341	+	3.04688i	0.261473	+	0.116415i
$686$		0			0
$687$	−19.1437	−	4.06912i	−0.730378	−	0.155247i
$688$		0			0
$689$	−10.1889	−	11.1425i	−0.388165	−	0.424494i
$690$		0			0
$691$	−15.6861	−	17.4212i	−0.596729	−	0.662734i	0.366812	−	0.930295i	$-0.380449\pi$
$691$	−15.6861	−	17.4212i	−0.596729	−	0.662734i	−0.963541	+	0.267561i	$0.913782\pi$
$692$		0			0
$693$	16.9823	−	6.75983i	0.645106	−	0.256785i
$694$		0			0
$695$	−3.90741	+	0.830545i	−0.148216	+	0.0315044i
$696$		0			0
$697$	−1.44115	−	1.04706i	−0.0545875	−	0.0396602i
$698$		0			0
$699$	17.3238	+	3.68229i	0.655248	+	0.139277i
$700$		0			0
$701$	29.9910	−	21.7898i	1.13275	−	0.822988i	0.146654	−	0.989188i	$-0.453150\pi$
$701$	29.9910	−	21.7898i	1.13275	−	0.822988i	0.986092	+	0.166200i	$0.0531497\pi$
$702$		0			0
$703$	0.769910			0.0290377
$704$		0			0
$705$	10.5929	−	18.3474i	0.398951	−	0.691003i
$706$		0			0
$707$	−10.1969	+	7.40849i	−0.383494	+	0.278625i
$708$		0			0
$709$	−1.21467	+	1.34903i	−0.0456181	+	0.0506640i	−0.765522	−	0.643410i	$-0.777519\pi$
$709$	−1.21467	+	1.34903i	−0.0456181	+	0.0506640i	0.719904	+	0.694074i	$0.244186\pi$
$710$		0			0
$711$	2.76863	−	26.3418i	0.103832	−	0.987894i
$712$		0			0
$713$	−0.658834	−	0.731710i	−0.0246735	−	0.0274027i
$714$		0			0
$715$	1.87973	+	25.9353i	0.0702979	+	0.969924i
$716$		0			0
$717$	0.217037	+	0.241044i	0.00810539	+	0.00900194i
$718$		0			0
$719$	−2.73825	+	26.0527i	−0.102119	+	0.971600i	0.816738	+	0.577009i	$0.195780\pi$
$719$	−2.73825	+	26.0527i	−0.102119	+	0.971600i	−0.918857	+	0.394591i	$0.870886\pi$
$720$		0			0
$721$	−15.0077	+	16.6678i	−0.558916	+	0.620740i
$722$		0			0
$723$	−18.3045	+	13.2990i	−0.680752	+	0.494596i
$724$		0			0
$725$	−0.306061	+	0.530114i	−0.0113668	+	0.0196879i
$726$		0			0
$727$	22.0782			0.818835			0.409417	−	0.912347i	$-0.365732\pi$
$727$	22.0782			0.818835			0.409417	+	0.912347i	$0.365732\pi$
$728$		0			0
$729$	−4.72124	+	3.43018i	−0.174861	+	0.127044i
$730$		0			0
$731$	0.884195	+	0.187941i	0.0327031	+	0.00695127i
$732$		0			0
$733$	−14.4683	−	10.5119i	−0.534400	−	0.388264i	0.287601	−	0.957750i	$-0.407142\pi$
$733$	−14.4683	−	10.5119i	−0.534400	−	0.388264i	−0.822001	+	0.569486i	$0.807142\pi$
$734$		0			0
$735$	−1.75011	+	0.371998i	−0.0645539	+	0.0137213i
$736$		0			0
$737$	−9.53887	−	2.43053i	−0.351369	−	0.0895298i
$738$		0			0
$739$	13.3343	+	14.8093i	0.490510	+	0.544767i	0.936682	−	0.350180i	$-0.113880\pi$
$739$	13.3343	+	14.8093i	0.490510	+	0.544767i	−0.446172	+	0.894947i	$0.647213\pi$
$740$		0			0
$741$	7.44306	+	8.13967i	0.273428	+	0.299018i
$742$		0			0
$743$	−2.06518	−	0.438968i	−0.0757642	−	0.0161042i	0.169874	−	0.985466i	$-0.445664\pi$
$743$	−2.06518	−	0.438968i	−0.0757642	−	0.0161042i	−0.245638	+	0.969362i	$0.578997\pi$
$744$		0			0
$745$	41.5368	+	18.4934i	1.52179	+	0.677544i
$746$		0			0
$747$	−1.56260	−	2.70650i	−0.0571725	−	0.0990257i
$748$		0			0
$749$	−26.3211			−0.961752
$750$		0			0
$751$	5.51180	+	52.4413i	0.201129	+	1.91361i	0.371854	+	0.928291i	$0.378722\pi$
$751$	5.51180	+	52.4413i	0.201129	+	1.91361i	−0.170725	+	0.985319i	$0.554611\pi$
$752$		0			0
$753$	−5.38730	−	16.5804i	−0.196324	−	0.604224i
$754$		0			0
$755$	−8.98607	−	6.52876i	−0.327036	−	0.237606i
$756$		0			0
$757$	23.4369	+	26.0294i	0.851830	+	0.946053i	0.999073	−	0.0430470i	$-0.0137065\pi$
$757$	23.4369	+	26.0294i	0.851830	+	0.946053i	−0.147243	+	0.989100i	$0.547040\pi$
$758$		0			0
$759$	3.07851	−	21.1154i	0.111743	−	0.766441i
$760$		0			0
$761$	14.9438	−	3.17640i	0.541712	−	0.115144i	0.0710742	−	0.997471i	$-0.477357\pi$
$761$	14.9438	−	3.17640i	0.541712	−	0.115144i	0.470638	+	0.882327i	$0.344024\pi$
$762$		0			0
$763$	−0.592980	+	5.64183i	−0.0214673	+	0.204248i
$764$		0			0
$765$	−2.53997	−	0.539887i	−0.0918327	−	0.0195197i
$766$		0			0
$767$	−39.7145	−	28.3905i	−1.43401	−	1.02512i
$768$		0			0
$769$	−14.0224	+	24.2874i	−0.505659	+	0.875827i	0.494320	+	0.869280i	$0.335417\pi$
$769$	−14.0224	+	24.2874i	−0.505659	+	0.875827i	−0.999979	+	0.00654675i	$0.997916\pi$
$770$		0			0
$771$	4.55705	+	7.89305i	0.164118	+	0.284261i
$772$		0			0
$773$	41.1825	+	18.3356i	1.48123	+	0.659486i	0.978742	−	0.205097i	$-0.0657511\pi$
$773$	41.1825	+	18.3356i	1.48123	+	0.659486i	0.502489	+	0.864584i	$0.332418\pi$
$774$		0			0
$775$	0.0111988	+	0.0344664i	0.000402273	+	0.00123807i
$776$		0			0
$777$	0.430395	−	0.191624i	0.0154403	−	0.00687448i
$778$		0			0
$779$	−3.62076	+	11.1436i	−0.129727	+	0.399260i
$780$		0			0
$781$	−19.7096	−	9.73894i	−0.705265	−	0.348487i
$782$		0			0
$783$	−6.89299	−	7.65544i	−0.246335	−	0.273583i
$784$		0			0
$785$	−2.32423	−	1.68865i	−0.0829553	−	0.0602706i
$786$		0			0
$787$	−11.1668	+	12.4020i	−0.398054	+	0.442084i	−0.908537	−	0.417804i	$-0.862800\pi$
$787$	−11.1668	+	12.4020i	−0.398054	+	0.442084i	0.510483	+	0.859888i	$0.329467\pi$
$788$		0			0
$789$	18.4998	+	8.23665i	0.658611	+	0.293233i
$790$		0			0
$791$	−11.0152	+	19.0789i	−0.391655	+	0.678367i
$792$		0			0
$793$	−11.9866	−	35.9484i	−0.425657	−	1.27657i
$794$		0			0
$795$	0.830133	+	7.89819i	0.0294418	+	0.280120i
$796$		0			0
$797$	13.1785	−	14.6362i	0.466806	−	0.518440i	−0.463066	−	0.886324i	$-0.653251\pi$
$797$	13.1785	−	14.6362i	0.466806	−	0.518440i	0.929872	+	0.367883i	$0.119917\pi$
$798$		0			0
$799$	0.622685	−	5.92445i	0.0220290	−	0.209592i
$800$		0			0
$801$	3.78976	−	11.6637i	0.133904	−	0.412116i
$802$		0			0
$803$	−8.04269	+	21.7481i	−0.283820	+	0.767474i
$804$		0			0
$805$	−12.1994	+	37.5460i	−0.429973	+	1.32332i
$806$		0			0
$807$	13.3972	+	9.73365i	0.471604	+	0.342641i
$808$		0			0
$809$	27.1526	+	5.77146i	0.954635	+	0.202914i	0.658794	−	0.752323i	$-0.271067\pi$
$809$	27.1526	+	5.77146i	0.954635	+	0.202914i	0.295841	+	0.955237i	$0.404400\pi$
$810$		0			0
$811$	12.8730	−	9.35279i	0.452032	−	0.328421i	−0.338365	−	0.941015i	$-0.609874\pi$
$811$	12.8730	−	9.35279i	0.452032	−	0.328421i	0.790398	+	0.612594i	$0.209874\pi$
$812$		0			0
$813$	−8.08328	−	14.0006i	−0.283493	−	0.491024i
$814$		0			0
$815$	11.3707	+	19.6947i	0.398300	+	0.689875i
$816$		0			0
$817$	−0.621504	−	5.91321i	−0.0217437	−	0.206877i
$818$		0			0
$819$	−18.2142	−	7.94233i	−0.636457	−	0.277528i
$820$		0			0
$821$	17.7087	−	7.88442i	0.618038	−	0.275168i	−0.0737413	−	0.997277i	$-0.523494\pi$
$821$	17.7087	−	7.88442i	0.618038	−	0.275168i	0.691779	+	0.722109i	$0.256827\pi$
$822$		0			0
$823$	10.6822	−	2.27057i	0.372357	−	0.0791470i	−0.0179321	−	0.999839i	$-0.505708\pi$
$823$	10.6822	−	2.27057i	0.372357	−	0.0791470i	0.390289	+	0.920692i	$0.372375\pi$
$824$		0			0
$825$	−0.419622	+	0.663906i	−0.0146094	+	0.0231143i
$826$		0			0
$827$	1.51952	−	4.67660i	0.0528389	−	0.162621i	−0.921155	−	0.389196i	$-0.872753\pi$
$827$	1.51952	−	4.67660i	0.0528389	−	0.162621i	0.973994	+	0.226575i	$0.0727528\pi$
$828$		0			0
$829$	4.90362	−	2.18323i	0.170310	−	0.0758268i	−0.319811	−	0.947481i	$-0.603619\pi$
$829$	4.90362	−	2.18323i	0.170310	−	0.0758268i	0.490121	+	0.871655i	$0.336953\pi$
$830$		0			0
$831$	6.78690	+	20.8879i	0.235435	+	0.724594i
$832$		0			0
$833$	−0.407014	+	0.295713i	−0.0141022	+	0.0102458i
$834$		0			0
$835$	1.08521	−	1.87964i	0.0375553	−	0.0650476i
$836$		0			0
$837$	−0.609885			−0.0210807
$838$		0			0
$839$	33.4229	+	14.8808i	1.15389	+	0.513743i	0.892303	−	0.451437i	$-0.149089\pi$
$839$	33.4229	+	14.8808i	1.15389	+	0.513743i	0.261584	+	0.965181i	$0.415755\pi$
$840$		0			0
$841$	−16.0041	+	17.7743i	−0.551864	+	0.612907i
$842$		0			0
$843$	−10.6925	+	4.76061i	−0.368270	+	0.163964i
$844$		0			0
$845$	18.5902	−	21.2959i	0.639523	−	0.732602i
$846$		0			0
$847$	11.6161	+	24.4522i	0.399132	+	0.840188i
$848$		0			0
$849$	7.89773	−	1.67871i	0.271049	−	0.0576133i
$850$		0			0
$851$	−0.169260	+	1.61040i	−0.00580217	+	0.0552039i
$852$		0			0
$853$	15.2711	+	46.9997i	0.522874	+	1.60924i	0.768482	+	0.639871i	$0.221012\pi$
$853$	15.2711	+	46.9997i	0.522874	+	1.60924i	−0.245609	+	0.969369i	$0.578988\pi$
$854$		0			0
$855$	1.78535	+	16.9865i	0.0610577	+	0.580926i
$856$		0			0
$857$	−2.66255			−0.0909511			−0.0454756	−	0.998965i	$-0.514480\pi$
$857$	−2.66255			−0.0909511			−0.0454756	+	0.998965i	$0.514480\pi$
$858$		0			0
$859$	6.49678			0.221667			0.110834	−	0.993839i	$-0.464648\pi$
$859$	6.49678			0.221667			0.110834	+	0.993839i	$0.464648\pi$
$860$		0			0
$861$	0.749462	+	7.13065i	0.0255416	+	0.243012i
$862$		0			0
$863$	−7.88056	−	24.2539i	−0.268257	−	0.825611i	−0.990925	−	0.134416i	$-0.957084\pi$
$863$	−7.88056	−	24.2539i	−0.268257	−	0.825611i	0.722668	−	0.691196i	$-0.242916\pi$
$864$		0			0
$865$	3.61436	−	34.3883i	0.122892	−	1.16924i
$866$		0			0
$867$	−14.2598	+	3.03102i	−0.484289	+	0.102939i
$868$		0			0
$869$	39.1970	+	1.57086i	1.32967	+	0.0532877i
$870$		0			0
$871$	5.42166	+	9.22610i	0.183706	+	0.312614i
$872$		0			0
$873$	−14.2961	+	6.36502i	−0.483848	+	0.215423i
$874$		0			0
$875$	18.8765	−	20.9644i	0.638141	−	0.708727i
$876$		0			0
$877$	21.7025	+	9.66256i	0.732841	+	0.326282i	0.739006	−	0.673699i	$-0.235296\pi$
$877$	21.7025	+	9.66256i	0.732841	+	0.326282i	−0.00616498	+	0.999981i	$0.501962\pi$
$878$		0			0
$879$	−24.7887			−0.836101
$880$		0			0
$881$	−5.97627	+	10.3512i	−0.201346	+	0.348741i	−0.948962	−	0.315390i	$-0.897865\pi$
$881$	−5.97627	+	10.3512i	−0.201346	+	0.348741i	0.747617	+	0.664131i	$0.231198\pi$
$882$		0			0
$883$	26.3537	−	19.1471i	0.886871	−	0.644350i	−0.0481890	−	0.998838i	$-0.515345\pi$
$883$	26.3537	−	19.1471i	0.886871	−	0.644350i	0.935060	+	0.354488i	$0.115345\pi$
$884$		0			0
$885$	7.93495	+	24.4213i	0.266730	+	0.820911i
$886$		0			0
$887$	5.33154	−	2.37375i	0.179016	−	0.0797029i	−0.315272	−	0.949001i	$-0.602096\pi$
$887$	5.33154	−	2.37375i	0.179016	−	0.0797029i	0.494287	+	0.869299i	$0.335429\pi$
$888$		0			0
$889$	−11.0592	+	34.0367i	−0.370913	+	1.14155i
$890$		0			0
$891$	5.79036	+	6.97327i	0.193984	+	0.233613i
$892$		0			0
$893$	−38.3269	+	8.14664i	−1.28256	+	0.272617i
$894$		0			0
$895$	−5.22111	+	2.32459i	−0.174523	+	0.0777024i
$896$		0			0
$897$	−18.6619	+	13.7790i	−0.623102	+	0.460068i
$898$		0			0
$899$	−0.0314519	−	0.299245i	−0.00104898	−	0.00998037i
$900$		0			0
$901$	1.11654	+	1.93390i	0.0371972	+	0.0644275i
$902$		0			0
$903$	−1.81918	−	3.15092i	−0.0605386	−	0.104856i
$904$		0			0
$905$	43.7836	−	31.8106i	1.45541	−	1.05742i
$906$		0			0
$907$	26.1329	+	5.55473i	0.867730	+	0.184442i	0.620205	−	0.784440i	$-0.287049\pi$
$907$	26.1329	+	5.55473i	0.867730	+	0.184442i	0.247525	+	0.968882i	$0.420383\pi$
$908$		0			0
$909$	−9.27857	−	6.74127i	−0.307751	−	0.223594i
$910$		0			0
$911$	2.46794	−	7.59553i	0.0817664	−	0.251651i	−0.901813	−	0.432126i	$-0.857763\pi$
$911$	2.46794	−	7.59553i	0.0817664	−	0.251651i	0.983580	+	0.180475i	$0.0577635\pi$
$912$		0			0
$913$	3.85054	−	2.56848i	0.127434	−	0.0850044i
$914$		0			0
$915$	−6.15930	+	18.9564i	−0.203620	+	0.626678i
$916$		0			0
$917$	−1.48119	+	14.0926i	−0.0489133	+	0.465379i
$918$		0			0
$919$	31.1509	−	34.5966i	1.02757	−	1.14124i	0.0376993	−	0.999289i	$-0.487997\pi$
$919$	31.1509	−	34.5966i	1.02757	−	1.14124i	0.989874	−	0.141947i	$-0.0453362\pi$
$920$		0			0
$921$	0.193448	+	1.84053i	0.00637432	+	0.0606476i
$922$		0			0
$923$	7.55987	+	22.6724i	0.248836	+	0.746273i
$924$		0			0
$925$	0.0297999	−	0.0516149i	0.000979814	−	0.00169709i
$926$		0			0
$927$	−18.6443	−	8.30098i	−0.612359	−	0.272640i
$928$		0			0
$929$	34.7180	−	38.5583i	1.13906	−	1.26506i	0.179439	−	0.983769i	$-0.442572\pi$
$929$	34.7180	−	38.5583i	1.13906	−	1.26506i	0.959624	−	0.281287i	$-0.0907614\pi$
$930$		0			0
$931$	2.67716	+	1.94507i	0.0877404	+	0.0637471i
$932$		0			0
$933$	−10.9723	−	12.1860i	−0.359218	−	0.398952i
$934$		0			0
$935$	0.554840	−	3.80564i	0.0181452	−	0.124458i
$936$		0			0
$937$	−14.8758	+	45.7831i	−0.485972	+	1.49567i	0.344596	+	0.938751i	$0.388016\pi$
$937$	−14.8758	+	45.7831i	−0.485972	+	1.49567i	−0.830568	+	0.556917i	$0.811984\pi$
$938$		0			0
$939$	0.435467	−	0.193883i	0.0142109	−	0.00632712i
$940$		0			0
$941$	−6.30443	−	19.4030i	−0.205518	−	0.632521i	−0.999692	−	0.0248294i	$-0.992096\pi$
$941$	−6.30443	−	19.4030i	−0.205518	−	0.632521i	0.794173	−	0.607691i	$-0.207904\pi$
$942$		0			0
$943$	−22.5127	−	10.0233i	−0.733116	−	0.326404i
$944$		0			0
$945$	12.2267	+	21.1773i	0.397735	+	0.688897i
$946$		0			0
$947$	6.28699	−	10.8894i	0.204300	−	0.353857i	−0.745610	−	0.666383i	$-0.767842\pi$
$947$	6.28699	−	10.8894i	0.204300	−	0.353857i	0.949909	+	0.312526i	$0.101175\pi$
$948$		0			0
$949$	22.9488	−	10.4295i	0.744949	−	0.338557i
$950$		0			0
$951$	−6.87793	−	1.46195i	−0.223032	−	0.0474069i
$952$		0			0
$953$	−1.67859	+	15.9708i	−0.0543750	+	0.517344i	0.933106	+	0.359603i	$0.117088\pi$
$953$	−1.67859	+	15.9708i	−0.0543750	+	0.517344i	−0.987481	+	0.157741i	$0.949579\pi$
$954$		0			0
$955$	29.3177	−	6.23167i	0.948699	−	0.201652i
$956$		0			0
$957$	4.55395	−	4.66743i	0.147208	−	0.150877i
$958$		0			0
$959$	−5.67291	−	6.30040i	−0.183188	−	0.203451i
$960$		0			0
$961$	25.0651	+	18.2109i	0.808552	+	0.587447i
$962$		0			0
$963$	−7.40115	−	22.7784i	−0.238499	−	0.734023i
$964$		0			0
$965$	−4.90453	−	46.6634i	−0.157882	−	1.50215i
$966$		0			0
$967$	36.3895			1.17021			0.585104	−	0.810958i	$-0.301054\pi$
$967$	36.3895			1.17021			0.585104	+	0.810958i	$0.301054\pi$
$968$		0			0
$969$	−0.815639	−	1.41273i	−0.0262021	−	0.0453834i
$970$		0			0
$971$	41.2715	+	18.3753i	1.32447	+	0.589690i	0.942413	−	0.334451i	$-0.108551\pi$
$971$	41.2715	+	18.3753i	1.32447	+	0.589690i	0.382052	+	0.924141i	$0.375217\pi$
$972$		0			0
$973$	4.42223	+	0.939973i	0.141770	+	0.0301342i
$974$		0			0
$975$	0.833774	−	0.183933i	0.0267021	−	0.00589057i
$976$		0			0
$977$	−9.07006	−	10.0733i	−0.290177	−	0.322274i	0.580376	−	0.814348i	$-0.302906\pi$
$977$	−9.07006	−	10.0733i	−0.290177	−	0.322274i	−0.870553	+	0.492074i	$0.836239\pi$
$978$		0			0
$979$	17.6011	+	4.48482i	0.562534	+	0.143335i
$980$		0			0
$981$	−5.04920	+	1.07324i	−0.161209	+	0.0342659i
$982$		0			0
$983$	−9.08803	−	6.60284i	−0.289863	−	0.210598i	0.433345	−	0.901228i	$-0.357333\pi$
$983$	−9.08803	−	6.60284i	−0.289863	−	0.210598i	−0.723208	+	0.690630i	$0.757333\pi$
$984$		0			0
$985$	−23.2743	−	4.94712i	−0.741582	−	0.157628i
$986$		0			0
$987$	−19.3979	+	14.0934i	−0.617441	+	0.448597i
$988$		0			0
$989$	12.5052			0.397641
$990$		0			0
$991$	−17.3924	+	30.1246i	−0.552489	+	0.956939i	0.445605	+	0.895230i	$0.352989\pi$
$991$	−17.3924	+	30.1246i	−0.552489	+	0.956939i	−0.998094	+	0.0617096i	$0.980345\pi$
$992$		0			0
$993$	2.34042	−	1.70042i	0.0742711	−	0.0539611i
$994$		0			0
$995$	−35.9697	+	39.9484i	−1.14032	+	1.26645i
$996$		0			0
$997$	−5.54243	+	52.7327i	−0.175531	+	1.67006i	0.452417	+	0.891807i	$0.350562\pi$
$997$	−5.54243	+	52.7327i	−0.175531	+	1.67006i	−0.627947	+	0.778256i	$0.716105\pi$
$998$		0			0
$999$	0.671141	+	0.745378i	0.0212340	+	0.0235827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.9.9	✓	112
11.5	even	5	inner	572.2.bg.a.269.6	yes	112
13.3	even	3	inner	572.2.bg.a.185.6	yes	112
143.16	even	15	inner	572.2.bg.a.445.9	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.9.9	✓	112	1.1	even	1	trivial
572.2.bg.a.185.6	yes	112	13.3	even	3	inner
572.2.bg.a.269.6	yes	112	11.5	even	5	inner
572.2.bg.a.445.9	yes	112	143.16	even	15	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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0911637 + 0.867364i) q^{3} +(0.671959 + 2.06808i) q^{5} +(0.257245 - 2.44753i) q^{7} +(2.19043 - 0.465591i) q^{9} +O(q^{10})\)	\(q+(0.0911637 + 0.867364i) q^{3} +(0.671959 + 2.06808i) q^{5} +(0.257245 - 2.44753i) q^{7} +(2.19043 - 0.465591i) q^{9} +(0.897761 + 3.19281i) q^{11} +(1.77872 - 3.13626i) q^{13} +(-1.73252 + 0.771367i) q^{15} +(-0.356820 + 0.396288i) q^{17} +(3.20430 + 1.42665i) q^{19} +2.14635 q^{21} +(-3.68853 + 6.38872i) q^{23} +(0.219667 - 0.159598i) q^{25} +(1.41204 + 4.34583i) q^{27} +(-2.05949 + 0.916946i) q^{29} +(-0.0412443 + 0.126937i) q^{31} +(-2.68748 + 1.06975i) q^{33} +(5.23453 - 1.11263i) q^{35} +(0.200524 - 0.0892791i) q^{37} +(2.88244 + 1.25689i) q^{39} +(0.349180 + 3.32222i) q^{41} +(-0.847571 - 1.46804i) q^{43} +(2.43476 + 4.21713i) q^{45} +(-9.03762 + 6.56621i) q^{47} +(0.922822 + 0.196152i) q^{49} +(-0.376255 - 0.273365i) q^{51} +(1.29404 - 3.98264i) q^{53} +(-5.99972 + 4.00208i) q^{55} +(-0.945306 + 2.90935i) q^{57} +(1.41530 - 13.4657i) q^{59} +(7.03253 - 7.81042i) q^{61} +(-0.576067 - 5.48091i) q^{63} +(7.68127 + 1.57110i) q^{65} +(-1.48399 + 2.57034i) q^{67} +(-5.87761 - 2.61688i) q^{69} +(-4.43537 + 4.92598i) q^{71} +(5.65610 + 4.10940i) q^{73} +(0.158455 + 0.175982i) q^{75} +(8.04543 - 1.37596i) q^{77} +(3.65500 - 11.2489i) q^{79} +(2.49661 - 1.11156i) q^{81} +(-0.431255 - 1.32727i) q^{83} +(-1.05932 - 0.471641i) q^{85} +(-0.983077 - 1.70274i) q^{87} +(2.73825 - 4.74279i) q^{89} +(-7.21852 - 5.16026i) q^{91} +(-0.113861 - 0.0242018i) q^{93} +(-0.797257 + 7.58539i) q^{95} +(-6.83542 + 1.45291i) q^{97} +(3.45303 + 6.57564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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