LMFDB - Embedded newform 216.2.t.a.157.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			157.9
Character	$\chi$	$=$	216.157
Dual form			216.2.t.a.205.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03448 - 0.964291i) q^{2} +(-0.759610 + 1.55660i) q^{3} +(0.140286 + 1.99507i) q^{4} +(-0.857221 - 2.35519i) q^{5} +(2.28681 - 0.877779i) q^{6} +(0.442985 + 2.51229i) q^{7} +(1.77871 - 2.19914i) q^{8} +(-1.84598 - 2.36481i) q^{9} +O(q^{10})$	\(q+(-1.03448 - 0.964291i) q^{2} +(-0.759610 + 1.55660i) q^{3} +(0.140286 + 1.99507i) q^{4} +(-0.857221 - 2.35519i) q^{5} +(2.28681 - 0.877779i) q^{6} +(0.442985 + 2.51229i) q^{7} +(1.77871 - 2.19914i) q^{8} +(-1.84598 - 2.36481i) q^{9} +(-1.38432 + 3.26301i) q^{10} +(-1.32995 + 3.65402i) q^{11} +(-3.21209 - 1.29711i) q^{12} +(-1.81187 + 2.15930i) q^{13} +(1.96432 - 3.02608i) q^{14} +(4.31724 + 0.454683i) q^{15} +(-3.96064 + 0.559764i) q^{16} +(-3.79287 + 6.56945i) q^{17} +(-0.370738 + 4.22641i) q^{18} +(-4.25574 + 2.45705i) q^{19} +(4.57853 - 2.04062i) q^{20} +(-4.24712 - 1.21881i) q^{21} +(4.89934 - 2.49753i) q^{22} +(0.488755 - 2.77187i) q^{23} +(2.07204 + 4.43922i) q^{24} +(-0.981892 + 0.823905i) q^{25} +(3.95653 - 0.486580i) q^{26} +(5.08329 - 1.07712i) q^{27} +(-4.95007 + 1.23623i) q^{28} +(1.68216 + 2.00472i) q^{29} +(-4.02764 - 4.63344i) q^{30} +(0.605101 - 3.43170i) q^{31} +(4.63697 + 3.24015i) q^{32} +(-4.67758 - 4.84583i) q^{33} +(10.2585 - 3.13851i) q^{34} +(5.53721 - 3.19691i) q^{35} +(4.45901 - 4.01463i) q^{36} +(6.91267 + 3.99103i) q^{37} +(6.77178 + 1.56201i) q^{38} +(-1.98485 - 4.46058i) q^{39} +(-6.70414 - 2.30406i) q^{40} +(-7.68334 - 6.44709i) q^{41} +(3.21826 + 5.35630i) q^{42} +(-1.38824 + 3.81417i) q^{43} +(-7.47660 - 2.14075i) q^{44} +(-3.98718 + 6.37482i) q^{45} +(-3.17849 + 2.39613i) q^{46} +(1.48461 + 8.41962i) q^{47} +(2.13722 - 6.59032i) q^{48} +(0.462463 - 0.168323i) q^{49} +(1.81023 + 0.0945182i) q^{50} +(-7.34487 - 10.8942i) q^{51} +(-4.56215 - 3.31189i) q^{52} -11.8427i q^{53} +(-6.29720 - 3.78751i) q^{54} +9.74598 q^{55} +(6.31282 + 3.49445i) q^{56} +(-0.591936 - 8.49088i) q^{57} +(0.192977 - 3.69593i) q^{58} +(-0.584688 - 1.60642i) q^{59} +(-0.301476 + 8.67700i) q^{60} +(-0.343677 + 0.0605995i) q^{61} +(-3.93512 + 2.96652i) q^{62} +(5.12336 - 5.68523i) q^{63} +(-1.67239 - 7.82324i) q^{64} +(6.63875 + 2.41631i) q^{65} +(0.166065 + 9.52345i) q^{66} +(1.45040 - 1.72852i) q^{67} +(-13.6386 - 6.64546i) q^{68} +(3.94342 + 2.86633i) q^{69} +(-8.81086 - 2.03235i) q^{70} +(-2.53118 + 4.38413i) q^{71} +(-8.48401 - 0.146742i) q^{72} +(1.34818 + 2.33512i) q^{73} +(-3.30248 - 10.7945i) q^{74} +(-0.536633 - 2.15426i) q^{75} +(-5.49903 - 8.14583i) q^{76} +(-9.76911 - 1.72256i) q^{77} +(-2.24801 + 6.52834i) q^{78} +(-0.652898 + 0.547847i) q^{79} +(4.71349 + 8.84824i) q^{80} +(-2.18468 + 8.73082i) q^{81} +(1.73137 + 14.0783i) q^{82} +(5.59873 + 6.67230i) q^{83} +(1.83581 - 8.64431i) q^{84} +(18.7237 + 3.30149i) q^{85} +(5.11408 - 2.60700i) q^{86} +(-4.39832 + 1.09564i) q^{87} +(5.67008 + 9.42417i) q^{88} +(3.02691 + 5.24277i) q^{89} +(10.2718 - 2.74981i) q^{90} +(-6.22743 - 3.59541i) q^{91} +(5.59865 + 0.586247i) q^{92} +(4.88213 + 3.54865i) q^{93} +(6.58317 - 10.1415i) q^{94} +(9.43495 + 7.91686i) q^{95} +(-8.56589 + 4.75664i) q^{96} +(4.71115 + 1.71472i) q^{97} +(-0.640719 - 0.271823i) q^{98} +(11.0961 - 3.60017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.03448	−	0.964291i	−0.731486	−	0.681857i
$2$	−1.03448	−	0.964291i	−0.731486	−	0.681857i
$3$	−0.759610	+	1.55660i	−0.438561	+	0.898701i
$3$	−0.759610	+	1.55660i	−0.438561	+	0.898701i
$4$	0.140286	+	1.99507i	0.0701432	+	0.997537i
$5$	−0.857221	−	2.35519i	−0.383361	−	1.05328i	−0.969932	−	0.243377i	$-0.921745\pi$
$5$	−0.857221	−	2.35519i	−0.383361	−	1.05328i	0.586571	−	0.809898i	$-0.300478\pi$
$6$	2.28681	−	0.877779i	0.933587	−	0.358352i
$7$	0.442985	+	2.51229i	0.167433	+	0.949558i	0.946521	+	0.322643i	$0.104571\pi$
$7$	0.442985	+	2.51229i	0.167433	+	0.949558i	−0.779088	+	0.626915i	$0.784317\pi$
$8$	1.77871	−	2.19914i	0.628868	−	0.777512i
$9$	−1.84598	−	2.36481i	−0.615328	−	0.788271i
$10$	−1.38432	+	3.26301i	−0.437760	+	1.03185i
$11$	−1.32995	+	3.65402i	−0.400996	+	1.10173i	0.560798	+	0.827953i	$0.310494\pi$
$11$	−1.32995	+	3.65402i	−0.400996	+	1.10173i	−0.961794	+	0.273774i	$0.911728\pi$
$12$	−3.21209	−	1.29711i	−0.927250	−	0.374443i
$13$	−1.81187	+	2.15930i	−0.502522	+	0.598883i	−0.956356	−	0.292204i	$-0.905612\pi$
$13$	−1.81187	+	2.15930i	−0.502522	+	0.598883i	0.453834	+	0.891086i	$0.350056\pi$
$14$	1.96432	−	3.02608i	0.524988	−	0.808753i
$15$	4.31724	+	0.454683i	1.11471	+	0.117399i
$16$	−3.96064	+	0.559764i	−0.990160	+	0.139941i
$17$	−3.79287	+	6.56945i	−0.919907	+	1.59333i	−0.120352	+	0.992731i	$0.538402\pi$
$17$	−3.79287	+	6.56945i	−0.919907	+	1.59333i	−0.799554	+	0.600594i	$0.794931\pi$
$18$	−0.370738	+	4.22641i	−0.0873838	+	0.996175i
$19$	−4.25574	+	2.45705i	−0.976334	+	0.563687i	−0.901161	−	0.433484i	$-0.857284\pi$
$19$	−4.25574	+	2.45705i	−0.976334	+	0.563687i	−0.0751728	+	0.997171i	$0.523951\pi$
$20$	4.57853	−	2.04062i	1.02379	−	0.456297i
$21$	−4.24712	−	1.21881i	−0.926798	−	0.265967i
$22$	4.89934	−	2.49753i	1.04454	−	0.532476i
$23$	0.488755	−	2.77187i	0.101912	−	0.577974i	−0.890496	−	0.454991i	$-0.849643\pi$
$23$	0.488755	−	2.77187i	0.101912	−	0.577974i	0.992409	−	0.122984i	$-0.0392463\pi$
$24$	2.07204	+	4.43922i	0.422954	+	0.906151i
$25$	−0.981892	+	0.823905i	−0.196378	+	0.164781i
$26$	3.95653	−	0.486580i	0.775940	−	0.0954262i
$27$	5.08329	−	1.07712i	0.978279	−	0.207291i
$28$	−4.95007	+	1.23623i	−0.935475	+	0.233625i
$29$	1.68216	+	2.00472i	0.312369	+	0.372267i	0.899272	−	0.437391i	$-0.144097\pi$
$29$	1.68216	+	2.00472i	0.312369	+	0.372267i	−0.586903	+	0.809658i	$0.699653\pi$
$30$	−4.02764	−	4.63344i	−0.735343	−	0.845946i
$31$	0.605101	−	3.43170i	0.108679	−	0.616351i	−0.881007	−	0.473103i	$-0.843134\pi$
$31$	0.605101	−	3.43170i	0.108679	−	0.616351i	0.989687	−	0.143249i	$-0.0457549\pi$
$32$	4.63697	+	3.24015i	0.819708	+	0.572782i
$33$	−4.67758	−	4.84583i	−0.814262	−	0.843550i
$34$	10.2585	−	3.13851i	1.75932	−	0.538250i
$35$	5.53721	−	3.19691i	0.935958	−	0.540376i
$36$	4.45901	−	4.01463i	0.743168	−	0.669105i
$37$	6.91267	+	3.99103i	1.13644	+	0.656121i	0.945545	−	0.325490i	$-0.105529\pi$
$37$	6.91267	+	3.99103i	1.13644	+	0.656121i	0.190890	+	0.981611i	$0.438863\pi$
$38$	6.77178	+	1.56201i	1.09853	+	0.253391i
$39$	−1.98485	−	4.46058i	−0.317830	−	0.714264i
$40$	−6.70414	−	2.30406i	−1.06002	−	0.364304i
$41$	−7.68334	−	6.44709i	−1.19994	−	1.00687i	−0.999632	−	0.0271328i	$-0.991362\pi$
$41$	−7.68334	−	6.44709i	−1.19994	−	1.00687i	−0.200305	−	0.979734i	$-0.564193\pi$
$42$	3.21826	+	5.35630i	0.496588	+	0.826495i
$43$	−1.38824	+	3.81417i	−0.211705	+	0.581655i	−0.999408	−	0.0343999i	$-0.989048\pi$
$43$	−1.38824	+	3.81417i	−0.211705	+	0.581655i	0.787703	+	0.616055i	$0.211270\pi$
$44$	−7.47660	−	2.14075i	−1.12714	−	0.322729i
$45$	−3.98718	+	6.37482i	−0.594373	+	0.950302i
$46$	−3.17849	+	2.39613i	−0.468643	+	0.353290i
$47$	1.48461	+	8.41962i	0.216552	+	1.22813i	0.878193	+	0.478307i	$0.158749\pi$
$47$	1.48461	+	8.41962i	0.216552	+	1.22813i	−0.661641	+	0.749821i	$0.730140\pi$
$48$	2.13722	−	6.59032i	0.308481	−	0.951231i
$49$	0.462463	−	0.168323i	0.0660661	−	0.0240461i
$50$	1.81023	+	0.0945182i	0.256005	+	0.0133669i
$51$	−7.34487	−	10.8942i	−1.02849	−	1.52549i
$52$	−4.56215	−	3.31189i	−0.632656	−	0.459277i
$53$		−	11.8427i		−	1.62672i	−0.581762	−	0.813359i	$-0.697637\pi$
$53$		−	11.8427i		−	1.62672i	0.581762	−	0.813359i	$-0.302363\pi$
$54$	−6.29720	−	3.78751i	−0.856940	−	0.515415i
$55$	9.74598			1.31415
$56$	6.31282	+	3.49445i	0.843586	+	0.466966i
$57$	−0.591936	−	8.49088i	−0.0784039	−	1.12464i
$58$	0.192977	−	3.69593i	0.0253391	−	0.485299i
$59$	−0.584688	−	1.60642i	−0.0761199	−	0.209138i	0.895796	−	0.444465i	$-0.146606\pi$
$59$	−0.584688	−	1.60642i	−0.0761199	−	0.209138i	−0.971916	+	0.235327i	$0.924384\pi$
$60$	−0.301476	+	8.67700i	−0.0389204	+	1.12020i
$61$	−0.343677	+	0.0605995i	−0.0440033	+	0.00775897i	−0.195606	−	0.980682i	$-0.562668\pi$
$61$	−0.343677	+	0.0605995i	−0.0440033	+	0.00775897i	0.151603	+	0.988441i	$0.451556\pi$
$62$	−3.93512	+	2.96652i	−0.499761	+	0.376748i
$63$	5.12336	−	5.68523i	0.645483	−	0.716272i
$64$	−1.67239	−	7.82324i	−0.209049	−	0.977905i
$65$	6.63875	+	2.41631i	0.823436	+	0.299706i
$66$	0.166065	+	9.52345i	0.0204412	+	1.17226i
$67$	1.45040	−	1.72852i	0.177195	−	0.211173i	−0.670135	−	0.742239i	$-0.733764\pi$
$67$	1.45040	−	1.72852i	0.177195	−	0.211173i	0.847330	+	0.531066i	$0.178208\pi$
$68$	−13.6386	−	6.64546i	−1.65393	−	0.805880i
$69$	3.94342	+	2.86633i	0.474731	+	0.345066i
$70$	−8.81086	−	2.03235i	−1.05310	−	0.242912i
$71$	−2.53118	+	4.38413i	−0.300396	+	0.520301i	−0.976226	−	0.216757i	$-0.930452\pi$
$71$	−2.53118	+	4.38413i	−0.300396	+	0.520301i	0.675830	+	0.737058i	$0.263785\pi$
$72$	−8.48401	−	0.146742i	−0.999850	−	0.0172937i
$73$	1.34818	+	2.33512i	0.157793	+	0.273305i	0.934072	−	0.357083i	$-0.116229\pi$
$73$	1.34818	+	2.33512i	0.157793	+	0.273305i	−0.776280	+	0.630389i	$0.782895\pi$
$74$	−3.30248	−	10.7945i	−0.383906	−	1.25483i
$75$	−0.536633	−	2.15426i	−0.0619650	−	0.248752i
$76$	−5.49903	−	8.14583i	−0.630782	−	0.934391i
$77$	−9.76911	−	1.72256i	−1.11329	−	0.196304i
$78$	−2.24801	+	6.52834i	−0.254538	+	0.739189i
$79$	−0.652898	+	0.547847i	−0.0734568	+	0.0616376i	−0.678777	−	0.734345i	$-0.737490\pi$
$79$	−0.652898	+	0.547847i	−0.0734568	+	0.0616376i	0.605320	+	0.795982i	$0.293045\pi$
$80$	4.71349	+	8.84824i	0.526985	+	0.989263i
$81$	−2.18468	+	8.73082i	−0.242742	+	0.970091i
$82$	1.73137	+	14.0783i	0.191198	+	1.55469i
$83$	5.59873	+	6.67230i	0.614540	+	0.732380i	0.980121	−	0.198399i	$-0.0635742\pi$
$83$	5.59873	+	6.67230i	0.614540	+	0.732380i	−0.365581	+	0.930779i	$0.619130\pi$
$84$	1.83581	−	8.64431i	0.200303	−	0.943171i
$85$	18.7237	+	3.30149i	2.03087	+	0.358096i
$86$	5.11408	−	2.60700i	0.551465	−	0.281120i
$87$	−4.39832	+	1.09564i	−0.471550	+	0.117465i
$88$	5.67008	+	9.42417i	0.604432	+	1.00462i
$89$	3.02691	+	5.24277i	0.320852	+	0.555732i	0.980664	−	0.195698i	$-0.0626974\pi$
$89$	3.02691	+	5.24277i	0.320852	+	0.555732i	−0.659812	+	0.751431i	$0.729364\pi$
$90$	10.2718	−	2.74981i	1.08275	−	0.289855i
$91$	−6.22743	−	3.59541i	−0.652812	−	0.376901i
$92$	5.59865	+	0.586247i	0.583699	+	0.0611205i
$93$	4.88213	+	3.54865i	0.506253	+	0.367978i
$94$	6.58317	−	10.1415i	0.679002	−	1.04602i
$95$	9.43495	+	7.91686i	0.968006	+	0.812253i
$96$	−8.56589	+	4.75664i	−0.874252	+	0.485472i
$97$	4.71115	+	1.71472i	0.478344	+	0.174103i	0.569929	−	0.821694i	$-0.306971\pi$
$97$	4.71115	+	1.71472i	0.478344	+	0.174103i	−0.0915842	+	0.995797i	$0.529193\pi$
$98$	−0.640719	−	0.271823i	−0.0647224	−	0.0274582i
$99$	11.0961	−	3.60017i	1.11520	−	0.361830i
$100$	−1.78150	−	1.84336i	−0.178150	−	0.184336i
$101$	1.06482	−	0.187757i	0.105954	−	0.0186825i	−0.120420	−	0.992723i	$-0.538424\pi$
$101$	1.06482	−	0.187757i	0.105954	−	0.0186825i	0.226374	+	0.974041i	$0.427313\pi$
$102$	−2.90706	+	18.3524i	−0.287842	+	1.81716i
$103$	10.4356	−	3.79825i	1.02825	−	0.374252i	0.227836	−	0.973700i	$-0.426835\pi$
$103$	10.4356	−	3.79825i	1.02825	−	0.374252i	0.800414	+	0.599447i	$0.204613\pi$
$104$	1.52581	+	7.82532i	0.149618	+	0.767335i
$105$	0.770176	+	11.0476i	0.0751615	+	1.07814i
$106$	−11.4198	+	12.2510i	−1.10919	+	1.18992i
$107$			12.1144i			1.17114i	0.810622	+	0.585570i	$0.199129\pi$
$107$			12.1144i			1.17114i	−0.810622	+	0.585570i	$0.800871\pi$
$108$	2.86205	+	9.99043i	0.275400	+	0.961330i
$109$		−	19.5560i		−	1.87312i	−0.350502	−	0.936562i	$-0.613989\pi$
$109$		−	19.5560i		−	1.87312i	0.350502	−	0.936562i	$-0.386011\pi$
$110$	−10.0820	−	9.39796i	−0.961281	−	0.896060i
$111$	−11.4634	+	7.72861i	−1.08805	+	0.733567i
$112$	−3.16080	−	9.70232i	−0.298667	−	0.916783i
$113$	−5.58697	+	2.03349i	−0.525578	+	0.191295i	−0.591163	−	0.806552i	$-0.701331\pi$
$113$	−5.58697	+	2.03349i	−0.525578	+	0.191295i	0.0655850	+	0.997847i	$0.479109\pi$
$114$	−7.57533	+	9.35442i	−0.709495	+	0.876121i
$115$	−6.94726	+	1.22499i	−0.647835	+	0.114231i
$116$	−3.76358	+	3.63727i	−0.349440	+	0.337712i
$117$	8.45103	+	0.298694i	0.781298	+	0.0276143i
$118$	−0.944206	+	2.22561i	−0.0869212	+	0.204884i
$119$	−18.1846	−	6.61864i	−1.66698	−	0.606730i
$120$	8.67902	−	8.68545i	0.792283	−	0.792869i
$121$	−3.15656	−	2.64867i	−0.286960	−	0.240788i
$122$	0.413961	+	0.268715i	0.0374783	+	0.0243284i
$123$	15.8719	−	7.06259i	1.43112	−	0.636812i
$124$	6.93138	+	0.725800i	0.622456	+	0.0651788i
$125$	−8.07064	−	4.65959i	−0.721860	−	0.416766i
$126$	−10.7822	+	0.940835i	−0.960556	+	0.0838162i
$127$	6.21113	+	10.7580i	0.551148	+	0.954617i	0.998192	+	0.0601050i	$0.0191435\pi$
$127$	6.21113	+	10.7580i	0.551148	+	0.954617i	−0.447044	+	0.894512i	$0.647523\pi$
$128$	−5.81383	+	9.70564i	−0.513874	+	0.857865i
$129$	−4.88260	−	5.05822i	−0.429889	−	0.445351i
$130$	−4.53761	−	8.90130i	−0.397975	−	0.780696i
$131$	−0.306951	−	0.0541237i	−0.0268184	−	0.00472881i	0.160223	−	0.987081i	$-0.448779\pi$
$131$	−0.306951	−	0.0541237i	−0.0268184	−	0.00472881i	−0.187041	+	0.982352i	$0.559890\pi$
$132$	9.01158	−	10.0119i	0.784357	−	0.871426i
$133$	−8.05807	−	9.60324i	−0.698724	−	0.832706i
$134$	−3.16721	+	0.389507i	−0.273605	+	0.0336483i
$135$	−6.89432	−	11.0488i	−0.593369	−	0.950930i
$136$	7.70069	+	20.0262i	0.660329	+	1.71723i
$137$	4.88568	−	4.09957i	0.417412	−	0.350250i	−0.409766	−	0.912191i	$-0.634390\pi$
$137$	4.88568	−	4.09957i	0.417412	−	0.350250i	0.827177	+	0.561941i	$0.189945\pi$
$138$	−1.31540	−	6.76776i	−0.111974	−	0.576110i
$139$	−5.04955	−	0.890371i	−0.428297	−	0.0755203i	−0.0446555	−	0.999002i	$-0.514219\pi$
$139$	−5.04955	−	0.890371i	−0.428297	−	0.0755203i	−0.383641	+	0.923482i	$0.625330\pi$
$140$	7.15486	+	10.5987i	0.604696	+	0.895749i
$141$	−14.2337	−	4.08470i	−1.19869	−	0.343994i
$142$	6.84603	−	2.09449i	0.574506	−	0.175766i
$143$	−5.48042	−	9.49237i	−0.458296	−	0.793792i
$144$	8.63502	+	8.33286i	0.719585	+	0.694405i
$145$	3.27952	−	5.68030i	0.272350	−	0.471723i
$146$	0.857071	−	3.71567i	0.0709317	−	0.307511i
$147$	−0.0892810	+	0.847728i	−0.00736377	+	0.0699194i
$148$	−6.99265	+	14.3512i	−0.574792	+	1.17966i
$149$	−1.33347	+	1.58917i	−0.109242	+	0.130190i	−0.817895	−	0.575368i	$-0.804859\pi$
$149$	−1.33347	+	1.58917i	−0.109242	+	0.130190i	0.708653	+	0.705558i	$0.249303\pi$
$150$	−1.52219	+	2.74600i	−0.124287	+	0.224210i
$151$	−22.6819	−	8.25555i	−1.84583	−	0.671827i	−0.987257	−	0.159134i	$-0.949130\pi$
$151$	−22.6819	−	8.25555i	−1.84583	−	0.671827i	−0.858572	−	0.512693i	$-0.828648\pi$
$152$	−2.16633	+	13.7293i	−0.175713	+	1.11360i
$153$	22.5371	−	3.15767i	1.82202	−	0.255282i
$154$	8.44488	+	11.2022i	0.680508	+	0.902700i
$155$	−8.60102	+	1.51659i	−0.690851	+	0.121816i
$156$	8.62074	−	4.58568i	0.690211	−	0.367148i
$157$	2.97797	+	8.18190i	0.237668	+	0.652987i	0.999983	+	0.00578127i	$0.00184025\pi$
$157$	2.97797	+	8.18190i	0.237668	+	0.652987i	−0.762316	+	0.647206i	$0.775938\pi$
$158$	1.20369	+	0.0628488i	0.0957606	+	0.00499998i
$159$	18.4343	+	8.99582i	1.46193	+	0.713415i
$160$	3.65627	−	13.6985i	0.289053	−	1.08296i
$161$	7.18026			0.565883
$162$	10.6790	−	6.92517i	0.839025	−	0.544092i
$163$		−	6.44084i		−	0.504485i	−0.967664	−	0.252243i	$-0.918832\pi$
$163$		−	6.44084i		−	0.504485i	0.967664	−	0.252243i	$-0.0811681\pi$
$164$	11.7846	−	16.2333i	0.920219	−	1.26761i
$165$	−7.40315	+	15.1706i	−0.576334	+	1.18103i
$166$	0.642285	−	12.3011i	0.0498510	−	0.954754i
$167$	−13.4013	+	4.87768i	−1.03703	+	0.377446i	−0.803752	−	0.594965i	$-0.797166\pi$
$167$	−13.4013	+	4.87768i	−1.03703	+	0.377446i	−0.233273	+	0.972411i	$0.574944\pi$
$168$	−10.2347	+	7.17209i	−0.789627	+	0.553338i
$169$	0.877712	+	4.97775i	0.0675163	+	0.382904i
$170$	−16.1856	−	21.4704i	−1.24138	−	1.64670i
$171$	13.6665	+	5.52835i	1.04510	+	0.422764i
$172$	−7.80430	−	2.23457i	−0.595072	−	0.170385i
$173$	−3.39321	+	9.32276i	−0.257981	+	0.708796i	0.741311	+	0.671162i	$0.234204\pi$
$173$	−3.39321	+	9.32276i	−0.257981	+	0.708796i	−0.999292	+	0.0376343i	$0.988018\pi$
$174$	5.60648	+	3.10785i	0.425026	+	0.235606i
$175$	−2.50486	−	2.10182i	−0.189349	−	0.158883i
$176$	3.22208	−	15.2167i	0.242873	−	1.14700i
$177$	2.94468	+	0.310127i	0.221335	+	0.0233106i
$178$	1.92428	−	8.34235i	0.144231	−	0.625286i
$179$	8.28116	+	4.78113i	0.618963	+	0.357359i	0.776465	−	0.630160i	$-0.217011\pi$
$179$	8.28116	+	4.78113i	0.618963	+	0.357359i	−0.157502	+	0.987519i	$0.550344\pi$
$180$	−13.2776	−	7.06041i	−0.989653	−	0.526252i
$181$	4.60888	−	2.66094i	0.342575	−	0.197786i	−0.318835	−	0.947810i	$-0.603292\pi$
$181$	4.60888	−	2.66094i	0.342575	−	0.197786i	0.661410	+	0.750024i	$0.269958\pi$
$182$	2.97512	+	9.72443i	0.220530	+	0.720823i
$183$	0.166731	−	0.580998i	0.0123251	−	0.0429486i
$184$	−5.22636	−	6.00518i	−0.385292	−	0.442708i
$185$	3.47397	−	19.7019i	0.255411	−	1.44851i
$186$	−1.62852	−	8.37879i	−0.119409	−	0.614363i
$187$	−18.9605	−	22.5963i	−1.38653	−	1.65240i
$188$	−16.5895	+	4.14306i	−1.20991	+	0.302164i
$189$	4.95786	+	12.2936i	0.360631	+	0.894225i
$190$	−2.12608	−	17.2879i	−0.154242	−	1.25419i
$191$	3.17518	−	2.66429i	0.229748	−	0.192781i	−0.520645	−	0.853773i	$-0.674309\pi$
$191$	3.17518	−	2.66429i	0.229748	−	0.192781i	0.750393	+	0.660992i	$0.229864\pi$
$192$	13.4480	+	3.33937i	0.970526	+	0.240998i
$193$	−3.12735	+	17.7361i	−0.225112	+	1.27667i	0.637360	+	0.770566i	$0.280027\pi$
$193$	−3.12735	+	17.7361i	−0.225112	+	1.27667i	−0.862472	+	0.506106i	$0.831085\pi$
$194$	−3.22009	−	6.31675i	−0.231189	−	0.453516i
$195$	−8.80408	+	8.49840i	−0.630473	+	0.608583i
$196$	0.400694	+	0.899034i	0.0286210	+	0.0642167i
$197$	13.4165	−	7.74604i	0.955888	−	0.551882i	0.0609831	−	0.998139i	$-0.480576\pi$
$197$	13.4165	−	7.74604i	0.955888	−	0.551882i	0.894905	+	0.446256i	$0.147243\pi$
$198$	−14.9503	−	6.97561i	−1.06247	−	0.495735i
$199$	−8.79403	+	15.2317i	−0.623392	+	1.07975i	0.365457	+	0.930828i	$0.380913\pi$
$199$	−8.79403	+	15.2317i	−0.623392	+	1.07975i	−0.988849	+	0.148919i	$0.952421\pi$
$200$	0.0653798	+	3.62480i	0.00462305	+	0.256312i
$201$	1.58887	+	3.57070i	0.112070	+	0.251857i
$202$	−1.28259	−	0.832567i	−0.0902424	−	0.0585792i
$203$	−4.29127	+	5.11414i	−0.301188	+	0.358942i
$204$	20.7043	−	16.1819i	1.44959	−	1.13296i
$205$	−8.59783	+	23.6223i	−0.600499	+	1.64986i
$206$	−14.4580	−	6.13375i	−1.00734	−	0.427359i
$207$	−7.45718	+	3.96101i	−0.518310	+	0.275309i
$208$	5.96746	−	9.56644i	0.413769	−	0.663313i
$209$	−3.31818	−	18.8183i	−0.229523	−	1.30169i
$210$	9.85637	−	12.1712i	0.680154	−	0.839890i
$211$	8.41203	+	23.1119i	0.579108	+	1.59109i	0.789687	+	0.613510i	$0.210243\pi$
$211$	8.41203	+	23.1119i	0.579108	+	1.59109i	−0.210579	+	0.977577i	$0.567535\pi$
$212$	23.6270	−	1.66137i	1.62271	−	0.114103i
$213$	−4.90162	−	7.27026i	−0.335853	−	0.498150i
$214$	11.6818	−	12.5320i	0.798549	−	0.856672i
$215$	10.1731			0.693803
$216$	6.67296	−	13.0947i	0.454037	−	0.890983i
$217$	8.88949			0.603458
$218$	−18.8577	+	20.2302i	−1.27720	+	1.37016i
$219$	−4.65894	+	0.324795i	−0.314822	+	0.0219476i
$220$	1.36723	+	19.4440i	0.0921786	+	1.31091i
$221$	−7.31323	−	20.0929i	−0.491941	−	1.35160i
$222$	19.3112	+	3.05894i	1.29608	+	0.205303i
$223$	−2.95087	−	16.7352i	−0.197605	−	1.12067i	−0.908660	−	0.417537i	$-0.862893\pi$
$223$	−2.95087	−	16.7352i	−0.197605	−	1.12067i	0.711055	−	0.703136i	$-0.248218\pi$
$224$	−6.08609	+	13.0848i	−0.406644	+	0.874262i
$225$	3.76094	+	0.801074i	0.250729	+	0.0534050i
$226$	7.74046	+	3.28386i	0.514888	+	0.218439i
$227$	−3.04973	+	8.37907i	−0.202418	+	0.556138i	−0.998817	−	0.0486333i	$-0.984513\pi$
$227$	−3.04973	+	8.37907i	−0.202418	+	0.556138i	0.796399	+	0.604772i	$0.206736\pi$
$228$	16.8569	−	2.37211i	1.11637	−	0.157097i
$229$	−1.06473	+	1.26890i	−0.0703594	+	0.0838511i	−0.800076	−	0.599899i	$-0.795208\pi$
$229$	−1.06473	+	1.26890i	−0.0703594	+	0.0838511i	0.729717	+	0.683750i	$0.239652\pi$
$230$	8.36803	+	5.43195i	0.551771	+	0.358172i
$231$	10.1020	−	13.8981i	0.664666	−	0.914427i
$232$	7.40072	−	0.133485i	0.485881	−	0.00876374i
$233$	−7.11806	+	12.3288i	−0.466320	+	0.807689i	−0.999260	−	0.0384635i	$-0.987754\pi$
$233$	−7.11806	+	12.3288i	−0.466320	+	0.807689i	0.532940	+	0.846153i	$0.321087\pi$
$234$	−8.45437	−	8.45824i	−0.552680	−	0.552933i
$235$	18.5572	−	10.7140i	1.21054	−	0.698905i
$236$	3.12290	−	1.39185i	0.203283	−	0.0906020i
$237$	−0.356828	−	1.43245i	−0.0231785	−	0.0930475i
$238$	12.4292	+	24.3820i	0.805667	+	1.58045i
$239$	3.00714	−	17.0544i	0.194516	−	1.10316i	−0.718590	−	0.695434i	$-0.755212\pi$
$239$	3.00714	−	17.0544i	0.194516	−	1.10316i	0.913106	−	0.407722i	$-0.133677\pi$
$240$	−17.3535	+	0.615799i	−1.12017	+	0.0397497i
$241$	16.9856	−	14.2526i	1.09414	−	0.918090i	0.0971195	−	0.995273i	$-0.469037\pi$
$241$	16.9856	−	14.2526i	1.09414	−	0.918090i	0.997017	+	0.0771832i	$0.0245926\pi$
$242$	0.711304	+	5.78384i	0.0457244	+	0.371799i
$243$	−11.9309	−	10.0327i	−0.765365	−	0.643597i
$244$	−0.169114	−	0.677159i	−0.0108264	−	0.0433507i
$245$	−0.792866	−	0.944900i	−0.0506543	−	0.0603675i
$246$	−23.2295	−	7.99900i	−1.48106	−	0.509998i
$247$	2.40533	−	13.6413i	0.153047	−	0.867975i
$248$	−6.47047	−	7.43469i	−0.410875	−	0.472103i
$249$	−14.6389	+	3.64661i	−0.927705	+	0.231094i
$250$	3.85570	+	12.6027i	0.243856	+	0.797064i
$251$	5.87413	−	3.39143i	0.370772	−	0.214065i	−0.303024	−	0.952983i	$-0.597996\pi$
$251$	5.87413	−	3.39143i	0.370772	−	0.214065i	0.673796	+	0.738918i	$0.264663\pi$
$252$	12.0612	+	9.42392i	0.759784	+	0.593651i
$253$	9.47842	+	5.47237i	0.595903	+	0.344045i
$254$	3.94856	−	17.1182i	0.247755	−	1.07409i
$255$	−19.3618	+	26.6373i	−1.21248	+	1.66809i
$256$	15.3733	−	4.43404i	0.960833	−	0.277128i
$257$	17.7134	+	14.8633i	1.10493	+	0.927148i	0.997747	−	0.0670910i	$-0.0213718\pi$
$257$	17.7134	+	14.8633i	1.10493	+	0.927148i	0.107185	+	0.994239i	$0.465816\pi$
$258$	0.173344	+	9.94086i	0.0107919	+	0.618891i
$259$	−6.96443	+	19.1346i	−0.432749	+	1.18897i
$260$	−3.88938	+	13.5838i	−0.241209	+	0.842430i
$261$	1.63555	−	7.67867i	0.101238	−	0.475298i
$262$	0.265342	+	0.351979i	0.0163929	+	0.0217454i
$263$	0.367614	+	2.08484i	0.0226680	+	0.128557i	0.994042	−	0.108999i	$-0.0347647\pi$
$263$	0.367614	+	2.08484i	0.0226680	+	0.128557i	−0.971374	+	0.237556i	$0.923654\pi$
$264$	−18.9767	+	1.66732i	−1.16793	+	0.102617i
$265$	−27.8918	+	10.1518i	−1.71338	+	0.623620i
$266$	−0.924420	+	17.7047i	−0.0566798	+	1.08554i
$267$	−10.4602	+	0.729223i	−0.640151	+	0.0446277i
$268$	3.65200	+	2.65117i	0.223082	+	0.161946i
$269$			25.6896i			1.56632i	0.621820	+	0.783161i	$0.286394\pi$
$269$			25.6896i			1.56632i	−0.621820	+	0.783161i	$0.713606\pi$
$270$	−3.52224	+	18.0779i	−0.214357	+	1.10018i
$271$	−27.3036			−1.65857			−0.829287	−	0.558823i	$-0.811253\pi$
$271$	−27.3036			−1.65857			−0.829287	+	0.558823i	$0.811253\pi$
$272$	11.3449	−	28.1423i	0.687883	−	1.70638i
$273$	10.3270	−	6.96249i	0.625020	−	0.421389i
$274$	−9.00730	−	0.470302i	−0.544151	−	0.0284120i
$275$	−1.70469	−	4.68360i	−0.102797	−	0.282432i
$276$	−5.16534	+	8.26951i	−0.310917	+	0.497766i
$277$	16.2093	−	2.85814i	0.973923	−	0.171729i	0.336028	−	0.941852i	$-0.390916\pi$
$277$	16.2093	−	2.85814i	0.973923	−	0.171729i	0.637895	+	0.770123i	$0.279805\pi$
$278$	4.36506	+	5.79030i	0.261799	+	0.347279i
$279$	−9.23233	+	4.90391i	−0.552725	+	0.293590i
$280$	2.81864	−	17.8634i	0.168446	−	1.06754i
$281$	27.1438	+	9.87955i	1.61927	+	0.589364i	0.983242	−	0.182305i	$-0.0583560\pi$
$281$	27.1438	+	9.87955i	1.61927	+	0.589364i	0.636023	+	0.771670i	$0.280578\pi$
$282$	10.7856	+	17.9509i	0.642272	+	1.06896i
$283$	−2.37158	+	2.82634i	−0.140976	+	0.168009i	−0.831913	−	0.554907i	$-0.812754\pi$
$283$	−2.37158	+	2.82634i	−0.140976	+	0.168009i	0.690937	+	0.722915i	$0.257198\pi$
$284$	−9.10176	−	4.43486i	−0.540090	−	0.263160i
$285$	−19.4902	+	8.67268i	−1.15450	+	0.513725i
$286$	−3.48403	+	15.1044i	−0.206015	+	0.893140i
$287$	12.7934	−	22.1588i	0.755169	−	1.30799i
$288$	−0.897432	−	16.9468i	−0.0528817	−	0.998601i
$289$	−20.2718	−	35.1117i	−1.19246	−	2.06540i
$290$	−8.87005	+	2.71373i	−0.520867	+	0.159356i
$291$	−6.24776	+	6.03084i	−0.366250	+	0.353534i
$292$	−4.46961	+	3.01731i	−0.261564	+	0.176575i
$293$	12.6127	+	2.22395i	0.736840	+	0.129925i	0.529459	−	0.848336i	$-0.322395\pi$
$293$	12.6127	+	2.22395i	0.736840	+	0.129925i	0.207381	+	0.978260i	$0.433506\pi$
$294$	0.909815	−	0.790862i	0.0530615	−	0.0461240i
$295$	−3.28222	+	2.75411i	−0.191098	+	0.160350i
$296$	21.0724	−	8.10301i	1.22481	−	0.470978i
$297$	−2.82473	+	20.0069i	−0.163907	+	1.16092i
$298$	2.91186	−	0.358105i	0.168680	−	0.0207445i
$299$	5.09974	+	6.07763i	0.294926	+	0.351479i
$300$	4.22262	−	1.37283i	0.243793	−	0.0792607i
$301$	−10.1973	−	1.79806i	−0.587762	−	0.103638i
$302$	15.5032	+	30.4121i	0.892108	+	1.75002i
$303$	−0.516588	+	1.80012i	−0.0296772	+	0.103414i
$304$	15.4801	−	12.1137i	0.887844	−	0.694769i
$305$	0.437330	+	0.757478i	0.0250415	+	0.0433731i
$306$	−26.3590	−	18.4658i	−1.50685	−	1.05562i
$307$	−16.6782	−	9.62914i	−0.951873	−	0.549564i	−0.0582108	−	0.998304i	$-0.518540\pi$
$307$	−16.6782	−	9.62914i	−0.951873	−	0.549564i	−0.893662	+	0.448740i	$0.851873\pi$
$308$	2.06616	−	19.7317i	0.117730	−	1.12432i
$309$	−2.01465	+	19.1292i	−0.114609	+	1.08822i
$310$	10.3600	+	6.72501i	0.588408	+	0.381955i
$311$	24.4635	+	20.5273i	1.38720	+	1.16400i	0.966460	+	0.256818i	$0.0826740\pi$
$311$	24.4635	+	20.5273i	1.38720	+	1.16400i	0.420740	+	0.907181i	$0.361770\pi$
$312$	−13.3399	−	3.56912i	−0.755222	−	0.202062i
$313$	5.47887	+	1.99414i	0.309684	+	0.112716i	0.492187	−	0.870490i	$-0.336198\pi$
$313$	5.47887	+	1.99414i	0.309684	+	0.112716i	−0.182503	+	0.983205i	$0.558420\pi$
$314$	4.80909	−	11.3356i	0.271393	−	0.639706i
$315$	−17.7817	−	7.19301i	−1.00188	−	0.405280i
$316$	−1.18459	−	1.22572i	−0.0666382	−	0.0689524i
$317$	−10.5865	+	1.86668i	−0.594595	+	0.104843i	−0.462844	−	0.886440i	$-0.653171\pi$
$317$	−10.5865	+	1.86668i	−0.594595	+	0.104843i	−0.131751	+	0.991283i	$0.542060\pi$
$318$	−10.3953	−	27.0820i	−0.582937	−	1.51868i
$319$	−9.56247	+	3.48045i	−0.535395	+	0.194868i
$320$	−16.9916	+	10.6451i	−0.949862	+	0.595077i
$321$	−18.8572	−	9.20220i	−1.05251	−	0.513616i
$322$	−7.42781	−	6.92386i	−0.413936	−	0.385851i
$323$		−	37.2772i		−	2.07416i
$324$	−17.7251	−	3.13378i	−0.984728	−	0.174099i
$325$		−	3.61301i		−	0.200414i
$326$	−6.21084	+	6.66290i	−0.343987	+	0.369024i
$327$	30.4408	+	14.8549i	1.68338	+	0.821479i
$328$	−27.8445	+	5.42922i	−1.53745	+	0.299779i
$329$	−20.4949	+	7.45953i	−1.12992	+	0.411257i
$330$	22.2872	−	8.55481i	1.22687	−	0.470927i
$331$	17.6652	−	3.11484i	0.970965	−	0.171207i	0.334400	−	0.942431i	$-0.391466\pi$
$331$	17.6652	−	3.11484i	0.970965	−	0.171207i	0.636564	+	0.771224i	$0.280355\pi$
$332$	−12.5263	+	12.1059i	−0.687471	+	0.664398i
$333$	−3.32264	−	23.7145i	−0.182079	−	1.29955i
$334$	18.5669	+	7.87692i	1.01593	+	0.431006i
$335$	−5.31432	−	1.93426i	−0.290353	−	0.105680i
$336$	17.5036	+	2.44990i	0.954898	+	0.133653i
$337$	1.36202	+	1.14287i	0.0741941	+	0.0622562i	0.679130	−	0.734018i	$-0.262357\pi$
$337$	1.36202	+	1.14287i	0.0741941	+	0.0622562i	−0.604936	+	0.796274i	$0.706801\pi$
$338$	3.89203	−	5.99574i	0.211698	−	0.326125i
$339$	1.07859	−	10.2413i	0.0585812	−	0.556232i
$340$	−3.96003	+	37.8182i	−0.214763	+	2.05098i
$341$	11.7347	+	6.77505i	0.635471	+	0.366889i
$342$	−8.80676	−	18.8974i	−0.476215	−	1.02186i
$343$	9.55642	+	16.5522i	0.515998	+	0.893735i
$344$	5.91859	+	9.83723i	0.319109	+	0.530388i
$345$	3.37039	−	11.7446i	0.181456	−	0.632307i
$346$	12.5000	−	6.37214i	0.672007	−	0.342569i
$347$	−3.34069	−	0.589055i	−0.179338	−	0.0316221i	0.0832579	−	0.996528i	$-0.473467\pi$
$347$	−3.34069	−	0.589055i	−0.179338	−	0.0316221i	−0.262596	+	0.964906i	$0.584579\pi$
$348$	−2.80290	−	8.62128i	−0.150251	−	0.462149i
$349$	−1.19141	−	1.41987i	−0.0637747	−	0.0760038i	0.733214	−	0.679998i	$-0.238019\pi$
$349$	−1.19141	−	1.41987i	−0.0637747	−	0.0760038i	−0.796989	+	0.603994i	$0.793575\pi$
$350$	0.564447	+	4.58970i	0.0301710	+	0.245330i
$351$	−6.88443	+	12.9280i	−0.367464	+	0.690043i
$352$	−18.0065	+	12.6343i	−0.959749	+	0.673411i
$353$	−10.5282	+	8.83425i	−0.560362	+	0.470200i	−0.878432	−	0.477868i	$-0.841410\pi$
$353$	−10.5282	+	8.83425i	−0.560362	+	0.470200i	0.318070	+	0.948067i	$0.396965\pi$
$354$	−2.74715	−	3.16034i	−0.146009	−	0.167970i
$355$	12.4953	+	2.20325i	0.663180	+	0.116937i
$356$	−10.0351	+	6.77441i	−0.531858	+	0.359043i
$357$	24.1157	−	23.2784i	1.27634	−	1.23203i
$358$	−3.95627	−	12.9314i	−0.209096	−	0.683447i
$359$	−5.37668	−	9.31267i	−0.283770	−	0.491504i	0.688540	−	0.725198i	$-0.258252\pi$
$359$	−5.37668	−	9.31267i	−0.283770	−	0.491504i	−0.972310	+	0.233694i	$0.924919\pi$
$360$	6.92707	+	20.1073i	0.365088	+	1.05975i
$361$	2.57423	−	4.45870i	0.135486	−	0.234668i
$362$	−7.33370	−	1.69162i	−0.385451	−	0.0889096i
$363$	6.52067	−	2.90154i	0.342247	−	0.152291i
$364$	6.29949	−	12.9286i	0.330183	−	0.677642i
$365$	4.34397	−	5.17695i	0.227374	−	0.270974i
$366$	−0.732731	+	0.440251i	−0.0383004	+	0.0230123i
$367$	−10.2024	−	3.71337i	−0.532562	−	0.193837i	0.0617202	−	0.998093i	$-0.480341\pi$
$367$	−10.2024	−	3.71337i	−0.532562	−	0.193837i	−0.594282	+	0.804257i	$0.702564\pi$
$368$	−0.384192	+	11.2520i	−0.0200274	+	0.586549i
$369$	−1.06283	+	30.0709i	−0.0553286	+	1.56543i
$370$	−22.5921	+	17.0312i	−1.17451	+	0.885411i
$371$	29.7523	−	5.24613i	1.54466	−	0.272366i
$372$	−6.39492	+	10.2380i	−0.331561	+	0.530817i
$373$	−7.89812	−	21.6999i	−0.408949	−	1.12358i	−0.957744	−	0.287621i	$-0.907135\pi$
$373$	−7.89812	−	21.6999i	−0.408949	−	1.12358i	0.548795	−	0.835957i	$-0.315087\pi$
$374$	−2.17515	+	41.6588i	−0.112474	+	2.15412i
$375$	13.3836	−	9.02326i	0.691128	−	0.465959i
$376$	21.1566	+	11.7112i	1.09107	+	0.603959i
$377$	−7.37665			−0.379917
$378$	6.72578	−	17.4982i	0.345937	−	0.900012i
$379$			19.1947i			0.985963i	0.870040	+	0.492982i	$0.164093\pi$
$379$			19.1947i			0.985963i	−0.870040	+	0.492982i	$0.835907\pi$
$380$	−14.4711	+	19.9341i	−0.742353	+	1.02260i
$381$	−21.4639	+	1.49634i	−1.09963	+	0.0766599i
$382$	−5.85380	−	0.305647i	−0.299506	−	0.0156382i
$383$	23.4828	−	8.54705i	1.19992	−	0.436734i	0.336722	−	0.941604i	$-0.390682\pi$
$383$	23.4828	−	8.54705i	1.19992	−	0.436734i	0.863195	+	0.504870i	$0.168460\pi$
$384$	−10.6915	−	16.4223i	−0.545599	−	0.838046i
$385$	4.31733	+	24.4848i	0.220031	+	1.24786i
$386$	20.3379	−	15.3319i	1.03517	−	0.780374i
$387$	11.5825	−	3.75796i	0.588770	−	0.191028i
$388$	−2.76008	+	9.63964i	−0.140122	+	0.489378i
$389$	−0.272464	+	0.748588i	−0.0138145	+	0.0379549i	−0.946408	−	0.322973i	$-0.895318\pi$
$389$	−0.272464	+	0.748588i	−0.0138145	+	0.0379549i	0.932594	+	0.360928i	$0.117540\pi$
$390$	17.3025	−	0.301714i	0.876149	−	0.0152779i
$391$	16.3559	+	13.7242i	0.827151	+	0.694062i
$392$	0.452422	−	1.31642i	0.0228508	−	0.0664890i
$393$	0.317412	−	0.436685i	0.0160113	−	0.0220279i
$394$	−21.3485	−	4.92434i	−1.07552	−	0.248085i
$395$	1.84996	+	1.06808i	0.0930817	+	0.0537408i
$396$	8.73924	+	21.6326i	0.439163	+	1.08708i
$397$	−26.8054	+	15.4761i	−1.34532	+	0.776723i	−0.987583	−	0.157099i	$-0.949786\pi$
$397$	−26.8054	+	15.4761i	−1.34532	+	0.776723i	−0.357740	+	0.933821i	$0.616453\pi$
$398$	23.7850	−	7.27685i	1.19223	−	0.364756i
$399$	21.0694	−	5.24845i	1.05479	−	0.262751i
$400$	3.42773	−	3.81282i	0.171386	−	0.190641i
$401$	5.68481	−	32.2401i	0.283886	−	1.61000i	−0.425353	−	0.905028i	$-0.639850\pi$
$401$	5.68481	−	32.2401i	0.283886	−	1.61000i	0.709239	−	0.704968i	$-0.249039\pi$
$402$	1.79954	−	5.22594i	0.0897528	−	0.260646i
$403$	6.31371	+	7.52439i	0.314508	+	0.374816i
$404$	0.523969	+	2.09806i	0.0260684	+	0.104382i
$405$	22.4355	−	2.33889i	1.11483	−	0.116220i
$406$	9.37074	−	1.15243i	0.465062	−	0.0571940i
$407$	−23.7768	+	19.9511i	−1.17857	+	0.988940i
$408$	−37.0222	−	3.22521i	−1.83287	−	0.159672i
$409$	0.478133	−	2.71163i	0.0236422	−	0.134081i	−0.970702	−	0.240286i	$-0.922759\pi$
$409$	0.478133	−	2.71163i	0.0236422	−	0.134081i	0.994344	+	0.106205i	$0.0338699\pi$
$410$	31.6731	−	16.1460i	1.56422	−	0.797393i
$411$	2.67017	+	10.7191i	0.131710	+	0.528735i
$412$	9.04175	+	20.2869i	0.445455	+	0.999466i
$413$	3.77678	−	2.18053i	0.185843	−	0.107297i
$414$	11.5339	+	3.09332i	0.566858	+	0.152028i
$415$	10.9152	−	18.9057i	0.535807	−	0.928046i
$416$	−15.3980	+	4.14189i	−0.754951	+	0.203073i
$417$	5.22163	−	7.18377i	0.255705	−	0.351791i
$418$	−14.7137	+	22.6668i	−0.719673	+	1.10867i
$419$	−16.1377	+	19.2321i	−0.788376	+	0.939551i	−0.999279	−	0.0379565i	$-0.987915\pi$
$419$	−16.1377	+	19.2321i	−0.788376	+	0.939551i	0.210903	+	0.977507i	$0.432360\pi$
$420$	−21.9327	+	3.08639i	−1.07021	+	0.150600i
$421$	2.33021	−	6.40219i	0.113567	−	0.312024i	−0.869868	−	0.493285i	$-0.835796\pi$
$421$	2.33021	−	6.40219i	0.113567	−	0.312024i	0.983435	+	0.181262i	$0.0580181\pi$
$422$	13.5845	−	32.0203i	0.661283	−	1.55873i
$423$	17.1703	−	19.0533i	0.834847	−	0.926404i
$424$	−26.0437	−	21.0647i	−1.26479	−	1.02299i
$425$	−1.68841	−	9.57545i	−0.0819000	−	0.464478i
$426$	−1.94003	+	12.2475i	−0.0939950	+	0.593394i
$427$	−0.304487	−	0.836572i	−0.0147352	−	0.0404846i
$428$	−24.1691	+	1.69948i	−1.16826	+	0.0821475i
$429$	18.9388	−	1.32031i	0.914373	−	0.0637449i
$430$	−10.5239	−	9.80987i	−0.507507	−	0.473074i
$431$	2.93816			0.141526			0.0707631	−	0.997493i	$-0.477457\pi$
$431$	2.93816			0.141526			0.0707631	+	0.997493i	$0.477457\pi$
$432$	−19.5301	+	7.11151i	−0.939644	+	0.342153i
$433$	−31.2403			−1.50131			−0.750656	−	0.660694i	$-0.770262\pi$
$433$	−31.2403			−1.50131			−0.750656	+	0.660694i	$0.770262\pi$
$434$	−9.19597	−	8.57205i	−0.441421	−	0.411472i
$435$	6.35078	+	9.41971i	0.304496	+	0.451640i
$436$	39.0156	−	2.74344i	1.86851	−	0.131387i
$437$	4.73061	+	12.9972i	0.226296	+	0.621743i
$438$	5.13276	+	4.15658i	0.245253	+	0.198609i
$439$	1.21855	+	6.91073i	0.0581581	+	0.329831i	0.999980	−	0.00628055i	$-0.00199917\pi$
$439$	1.21855	+	6.91073i	0.0581581	+	0.329831i	−0.941822	+	0.336112i	$0.890888\pi$
$440$	17.3353	−	21.4327i	0.826426	−	1.02177i
$441$	−1.25175	−	0.782917i	−0.0596072	−	0.0372818i
$442$	−11.8101	+	27.8378i	−0.561748	+	1.32411i
$443$	7.15814	−	19.6668i	0.340093	−	0.934399i	−0.645273	−	0.763952i	$-0.723257\pi$
$443$	7.15814	−	19.6668i	0.340093	−	0.934399i	0.985367	−	0.170447i	$-0.0545213\pi$
$444$	−17.0273	−	21.7860i	−0.808080	−	1.03392i
$445$	9.75301	−	11.6232i	0.462337	−	0.550992i
$446$	−13.0850	+	20.1577i	−0.619593	+	0.954495i
$447$	−1.46077	−	3.28282i	−0.0690923	−	0.155272i
$448$	18.9134	−	7.66713i	0.893576	−	0.362238i
$449$	7.57475	−	13.1198i	0.357474	−	0.619164i	−0.630064	−	0.776543i	$-0.716971\pi$
$449$	7.57475	−	13.1198i	0.357474	−	0.619164i	0.987538	+	0.157380i	$0.0503046\pi$
$450$	−3.11814	−	4.45533i	−0.146990	−	0.210026i
$451$	33.7763	−	19.5007i	1.59046	−	0.918253i
$452$	−4.84074	−	10.8611i	−0.227689	−	0.510865i
$453$	30.0800	−	29.0356i	1.41328	−	1.36421i
$454$	11.2347	−	5.72713i	0.527272	−	0.268787i
$455$	−3.12961	+	17.7489i	−0.146718	+	0.832080i
$456$	−19.7255	−	13.8010i	−0.923730	−	0.646293i
$457$	0.729228	−	0.611895i	0.0341118	−	0.0286232i	−0.625572	−	0.780166i	$-0.715134\pi$
$457$	0.729228	−	0.611895i	0.0341118	−	0.0286232i	0.659684	+	0.751543i	$0.270690\pi$
$458$	2.32503	−	0.285935i	0.108641	−	0.0133609i
$459$	−12.2042	+	37.4798i	−0.569643	+	1.74941i
$460$	−3.41855	−	13.6884i	−0.159391	−	0.638227i
$461$	−2.82485	−	3.36653i	−0.131567	−	0.156795i	0.696239	−	0.717810i	$-0.254855\pi$
$461$	−2.82485	−	3.36653i	−0.131567	−	0.156795i	−0.827806	+	0.561015i	$0.810411\pi$
$462$	−23.8521	+	4.63595i	−1.10970	+	0.215684i
$463$	−0.0157534	+	0.0893420i	−0.000732123	+	0.00415207i	−0.985172	−	0.171572i	$-0.945115\pi$
$463$	−0.0157534	+	0.0893420i	−0.000732123	+	0.00415207i	0.984440	+	0.175724i	$0.0562266\pi$
$464$	−7.78460	−	6.99836i	−0.361391	−	0.324891i
$465$	4.17270	−	14.5403i	0.193504	−	0.674292i
$466$	19.2521	−	5.89003i	0.891834	−	0.272850i
$467$	−8.84291	+	5.10545i	−0.409201	+	0.236252i	−0.690446	−	0.723384i	$-0.742586\pi$
$467$	−8.84291	+	5.10545i	−0.409201	+	0.236252i	0.281245	+	0.959636i	$0.409252\pi$
$468$	0.589649	+	16.9023i	0.0272565	+	0.781311i
$469$	4.98507	+	2.87813i	0.230189	+	0.132900i
$470$	−29.5284	−	6.81115i	−1.36205	−	0.314175i
$471$	−14.9980	−	1.57956i	−0.691072	−	0.0727823i
$472$	−4.57272	−	1.57154i	−0.210476	−	0.0723359i
$473$	−12.0907	−	10.1453i	−0.555933	−	0.466483i
$474$	−1.01217	+	1.82592i	−0.0464904	+	0.0838674i
$475$	2.15430	−	5.91889i	0.0988460	−	0.271577i
$476$	10.6536	−	37.2081i	0.488308	−	1.70543i
$477$	−28.0057	+	21.8614i	−1.28229	+	1.00097i
$478$	−19.5562	+	14.7426i	−0.894479	+	0.674310i
$479$	0.385466	+	2.18609i	0.0176124	+	0.0998848i	0.992347	−	0.123482i	$-0.0394062\pi$
$479$	0.385466	+	2.18609i	0.0176124	+	0.0998848i	−0.974734	+	0.223367i	$0.928295\pi$
$480$	18.5457	+	16.0968i	0.846490	+	0.734717i
$481$	−21.1427	+	7.69531i	−0.964024	+	0.350876i
$482$	−31.3148	−	1.63505i	−1.42635	−	0.0744746i
$483$	−5.45420	+	11.1768i	−0.248175	+	0.508560i
$484$	4.84147	−	6.66915i	0.220067	−	0.303143i
$485$		−	12.5656i		−	0.570573i
$486$	2.66777	+	21.8834i	0.121013	+	0.992651i
$487$	41.4817			1.87971			0.939857	−	0.341569i	$-0.110958\pi$
$487$	41.4817			1.87971			0.939857	+	0.341569i	$0.110958\pi$
$488$	−0.478034	+	0.863580i	−0.0216396	+	0.0390924i
$489$	10.0258	+	4.89252i	0.453382	+	0.221248i
$490$	−0.0909574	+	1.74203i	−0.00410903	+	0.0786969i
$491$	−1.96933	−	5.41068i	−0.0888745	−	0.244181i	0.887290	−	0.461211i	$-0.152585\pi$
$491$	−1.96933	−	5.41068i	−0.0888745	−	0.244181i	−0.976165	+	0.217031i	$0.930363\pi$
$492$	16.3170	+	30.6748i	0.735627	+	1.38292i
$493$	−19.5501	+	3.44721i	−0.880493	+	0.155255i
$494$	−15.6424	+	11.7922i	−0.703786	+	0.530555i
$495$	−17.9909	−	23.0474i	−0.808632	−	1.03590i
$496$	−0.475647	+	13.9304i	−0.0213572	+	0.625495i
$497$	−12.1355	−	4.41696i	−0.544352	−	0.198128i
$498$	18.6600	+	10.3439i	0.836176	+	0.463519i
$499$	8.64536	−	10.3031i	0.387019	−	0.461232i	−0.536997	−	0.843584i	$-0.680441\pi$
$499$	8.64536	−	10.3031i	0.387019	−	0.461232i	0.924017	+	0.382352i	$0.124886\pi$
$500$	8.16402	−	16.7552i	0.365106	−	0.749315i
$501$	2.58720	−	24.5656i	0.115587	−	1.09751i
$502$	−9.34698	−	2.15601i	−0.417176	−	0.0962275i
$503$	9.82946	−	17.0251i	0.438274	−	0.759113i	−0.559282	−	0.828977i	$-0.688923\pi$
$503$	9.82946	−	17.0251i	0.438274	−	0.759113i	0.997557	+	0.0698643i	$0.0222566\pi$
$504$	−3.38963	−	21.3793i	−0.150986	−	0.952311i
$505$	−1.35499	−	2.34691i	−0.0602963	−	0.104436i
$506$	−4.52826	−	14.8010i	−0.201306	−	0.657985i
$507$	−8.41507	−	2.41491i	−0.373726	−	0.107250i
$508$	−20.5916	+	13.9009i	−0.913606	+	0.616751i
$509$	8.99761	+	1.58652i	0.398812	+	0.0703213i	0.369457	−	0.929248i	$-0.379544\pi$
$509$	8.99761	+	1.58652i	0.398812	+	0.0703213i	0.0293547	+	0.999569i	$0.490655\pi$
$510$	45.7154	−	8.88535i	2.02431	−	0.393450i
$511$	−5.26929	+	4.42146i	−0.233100	+	0.195594i
$512$	−20.1791	−	10.2374i	−0.891797	−	0.452435i
$513$	−18.9866	+	17.0738i	−0.838280	+	0.753829i
$514$	−3.99156	−	32.4566i	−0.176060	−	1.43160i
$515$	−17.8912	−	21.3219i	−0.788381	−	0.939556i
$516$	9.40656	−	10.4507i	0.414101	−	0.460068i
$517$	−32.7399	−	5.77292i	−1.43990	−	0.253893i
$518$	25.6559	−	13.0786i	1.12725	−	0.574640i
$519$	−11.9343	−	12.3635i	−0.523856	−	0.542698i
$520$	17.1222	−	10.3016i	0.750858	−	0.451755i
$521$	13.8130	+	23.9247i	0.605157	+	1.04816i	0.992027	+	0.126028i	$0.0402229\pi$
$521$	13.8130	+	23.9247i	0.605157	+	1.04816i	−0.386870	+	0.922134i	$0.626444\pi$
$522$	−9.09641	+	6.36627i	−0.398139	+	0.278644i
$523$	−2.64626	−	1.52782i	−0.115713	−	0.0668068i	0.441027	−	0.897494i	$-0.354614\pi$
$523$	−2.64626	−	1.52782i	−0.115713	−	0.0668068i	−0.556739	+	0.830687i	$0.687948\pi$
$524$	0.0649197	−	0.619982i	0.00283603	−	0.0270840i
$525$	5.17440	−	2.30248i	0.225830	−	0.100489i
$526$	1.63011	−	2.51121i	0.0710760	−	0.109494i
$527$	20.2493	+	16.9912i	0.882073	+	0.740147i
$528$	21.2387	+	16.5742i	0.924297	+	0.721301i
$529$	14.1686	+	5.15694i	0.616025	+	0.224215i
$530$	38.6427	+	16.3940i	1.67853	+	0.712111i
$531$	−2.71955	+	4.34810i	−0.118018	+	0.188691i
$532$	18.0287	−	17.4237i	0.781645	−	0.755411i
$533$	27.8424	−	4.90937i	1.20599	−	0.212649i
$534$	11.5240	+	9.33226i	0.498691	+	0.403847i
$535$	28.5317	−	10.3847i	1.23353	−	0.448969i
$536$	−1.22141	−	6.26417i	−0.0527570	−	0.270571i
$537$	−13.7327	+	9.25863i	−0.592612	+	0.399539i
$538$	24.7722	−	26.5753i	1.06801	−	1.14574i
$539$			1.91371i			0.0824292i
$540$	21.0760	−	15.3047i	0.906967	−	0.658608i
$541$		−	12.4110i		−	0.533592i	−0.963753	−	0.266796i	$-0.914035\pi$
$541$		−	12.4110i		−	0.533592i	0.963753	−	0.266796i	$-0.0859650\pi$
$542$	28.2449	+	26.3286i	1.21322	+	1.13091i
$543$	0.641054	+	9.19544i	0.0275103	+	0.394614i
$544$	−38.8734	+	18.1728i	−1.66668	+	0.779154i
$545$	−46.0581	+	16.7638i	−1.97291	+	0.718082i
$546$	−17.3969	−	2.75572i	−0.744520	−	0.117934i
$547$	−0.791575	+	0.139576i	−0.0338453	+	0.00596784i	−0.190545	−	0.981678i	$-0.561026\pi$
$547$	−0.791575	+	0.139576i	−0.0338453	+	0.00596784i	0.156700	+	0.987646i	$0.449914\pi$
$548$	8.86434	+	9.17218i	0.378666	+	0.391816i
$549$	0.777728	+	0.700865i	0.0331926	+	0.0299122i
$550$	−2.75289	+	6.48890i	−0.117384	+	0.276688i
$551$	−12.0845	−	4.39841i	−0.514819	−	0.187379i
$552$	13.3176	−	3.57373i	0.566836	−	0.152108i
$553$	−1.66558	−	1.39758i	−0.0708275	−	0.0594313i
$554$	−19.5242	−	12.6738i	−0.829506	−	0.538459i
$555$	28.0290	+	20.3733i	1.18976	+	0.864799i
$556$	1.06797	−	10.1991i	0.0452922	−	0.432539i
$557$	15.6214	+	9.01902i	0.661900	+	0.382148i	0.793000	−	0.609221i	$-0.208518\pi$
$557$	15.6214	+	9.01902i	0.661900	+	0.382148i	−0.131101	+	0.991369i	$0.541851\pi$
$558$	14.2794	+	3.82967i	0.604497	+	0.162123i
$559$	−5.72063	−	9.90842i	−0.241957	−	0.419081i
$560$	−20.1414	+	15.7613i	−0.851128	+	0.666037i
$561$	49.5759	−	12.3495i	2.09310	−	0.521397i
$562$	−18.5529	−	36.3947i	−0.782608	−	1.53522i
$563$	−20.6986	−	3.64973i	−0.872344	−	0.153818i	−0.280484	−	0.959859i	$-0.590495\pi$
$563$	−20.6986	−	3.64973i	−0.872344	−	0.153818i	−0.591860	+	0.806041i	$0.701606\pi$
$564$	6.15248	−	28.9703i	0.259066	−	1.21987i
$565$	9.57853	+	11.4152i	0.402972	+	0.480243i
$566$	5.17876	−	0.636891i	0.217680	−	0.0267705i
$567$	−22.9022	−	1.62094i	−0.961800	−	0.0680729i
$568$	5.13907	+	13.3645i	0.215631	+	0.560762i
$569$	18.1237	−	15.2076i	0.759785	−	0.637535i	−0.178286	−	0.983979i	$-0.557055\pi$
$569$	18.1237	−	15.2076i	0.759785	−	0.637535i	0.938071	+	0.346444i	$0.112611\pi$
$570$	28.5252	+	9.82257i	1.19479	+	0.411422i
$571$	3.45440	+	0.609103i	0.144562	+	0.0254902i	0.245461	−	0.969407i	$-0.421061\pi$
$571$	3.45440	+	0.609103i	0.144562	+	0.0254902i	−0.100899	+	0.994897i	$0.532172\pi$
$572$	18.1692	−	12.2655i	0.759690	−	0.512846i
$573$	1.73533	+	6.96629i	0.0724943	+	0.291021i
$574$	−34.6020	+	10.5862i	−1.44426	+	0.441860i
$575$	1.80385	+	3.12436i	0.0752258	+	0.130295i
$576$	−15.4133	+	18.3965i	−0.642220	+	0.766520i
$577$	8.52365	−	14.7634i	0.354844	−	0.614608i	−0.632247	−	0.774767i	$-0.717867\pi$
$577$	8.52365	−	14.7634i	0.354844	−	0.614608i	0.987091	+	0.160159i	$0.0512006\pi$
$578$	−12.8872	+	55.8701i	−0.536038	+	2.32389i
$579$	−25.2324	−	18.3405i	−1.04862	−	0.762207i
$580$	11.7927	+	5.74602i	0.489665	+	0.238591i
$581$	−14.2826	+	17.0214i	−0.592543	+	0.706166i
$582$	12.2786	−	0.214109i	0.508966	−	0.00887511i
$583$	43.2733	+	15.7502i	1.79220	+	0.652307i
$584$	7.53327	+	1.18866i	0.311729	+	0.0491872i
$585$	−6.54092	−	20.1599i	−0.270434	−	0.833508i
$586$	−10.9030	−	14.4629i	−0.450398	−	0.597457i
$587$	−36.9148	+	6.50908i	−1.52364	+	0.268658i	−0.871861	−	0.489753i	$-0.837087\pi$
$587$	−36.9148	+	6.50908i	−1.52364	+	0.268658i	−0.651776	+	0.758412i	$0.725976\pi$
$588$	−1.70380	−	0.0591974i	−0.0702637	−	0.00244126i
$589$	5.85671	+	16.0912i	0.241322	+	0.663026i
$590$	6.05114	+	0.315951i	0.249121	+	0.0130075i
$591$	1.86612	+	26.7681i	0.0767620	+	1.10109i
$592$	−29.6126	−	11.9376i	−1.21707	−	0.490631i
$593$	−16.4642			−0.676103			−0.338051	−	0.941128i	$-0.609768\pi$
$593$	−16.4642			−0.676103			−0.338051	+	0.941128i	$0.609768\pi$
$594$	22.2146	−	17.9729i	0.911477	−	0.737435i
$595$			48.5018i			1.98838i
$596$	−3.35757	−	2.43743i	−0.137532	−	0.0998411i
$597$	−17.0296	−	25.2589i	−0.696974	−	1.03378i
$598$	0.585041	−	11.2048i	0.0239241	−	0.458199i
$599$	−20.2683	+	7.37705i	−0.828139	+	0.301418i	−0.721095	−	0.692836i	$-0.756361\pi$
$599$	−20.2683	+	7.37705i	−0.828139	+	0.301418i	−0.107044	+	0.994254i	$0.534139\pi$
$600$	−5.69201	−	2.65166i	−0.232375	−	0.108254i
$601$	−3.05008	−	17.2979i	−0.124415	−	0.705595i	−0.981653	−	0.190674i	$-0.938933\pi$
$601$	−3.05008	−	17.2979i	−0.124415	−	0.705595i	0.857238	−	0.514920i	$-0.172179\pi$
$602$	8.81501	+	11.6932i	0.359273	+	0.476579i
$603$	−6.76506	−	0.239105i	−0.275494	−	0.00973709i
$604$	13.2885	−	46.4103i	0.540700	−	1.88841i
$605$	−3.53227	+	9.70482i	−0.143607	+	0.394557i
$606$	2.27024	−	1.36404i	0.0922221	−	0.0554104i
$607$	−17.1550	−	14.3947i	−0.696299	−	0.584264i	0.224419	−	0.974493i	$-0.427951\pi$
$607$	−17.1550	−	14.3947i	−0.696299	−	0.584264i	−0.920718	+	0.390229i	$0.872396\pi$
$608$	−27.6949	−	2.39595i	−1.12318	−	0.0971685i
$609$	−4.70096	−	10.5645i	−0.190492	−	0.428096i
$610$	0.278021	−	1.20531i	0.0112567	−	0.0488015i
$611$	−20.8704	−	12.0495i	−0.844327	−	0.487472i
$612$	9.46143	+	44.5202i	0.382456	+	1.79962i
$613$	−20.3462	+	11.7469i	−0.821774	+	0.474451i	−0.851028	−	0.525121i	$-0.824020\pi$
$613$	−20.3462	+	11.7469i	−0.821774	+	0.474451i	0.0292540	+	0.999572i	$0.490687\pi$
$614$	7.96789	+	26.0437i	0.321558	+	1.05104i
$615$	−30.2395	−	31.3271i	−1.21937	−	1.26323i
$616$	−21.1645	+	18.4197i	−0.852743	+	0.742150i
$617$	−0.911711	+	5.17057i	−0.0367041	+	0.208159i	−0.997645	−	0.0685961i	$-0.978148\pi$
$617$	−0.911711	+	5.17057i	−0.0367041	+	0.208159i	0.960940	+	0.276755i	$0.0892591\pi$
$618$	20.5302	−	17.8460i	0.825846	−	0.717872i
$619$	14.0073	+	16.6933i	0.563001	+	0.670958i	0.970179	−	0.242390i	$-0.0779315\pi$
$619$	14.0073	+	16.6933i	0.563001	+	0.670958i	−0.407178	+	0.913349i	$0.633487\pi$
$620$	−4.23232	−	16.9469i	−0.169974	−	0.680605i
$621$	−0.501144	−	14.6166i	−0.0201102	−	0.586546i
$622$	−5.51264	−	44.8250i	−0.221037	−	1.79732i
$623$	−11.8305	+	9.92697i	−0.473979	+	0.397716i
$624$	10.3581	+	16.5557i	0.414657	+	0.662758i
$625$	−5.16880	+	29.3137i	−0.206752	+	1.17255i
$626$	−3.74483	−	7.34612i	−0.149673	−	0.293610i
$627$	31.8130	+	9.12952i	1.27049	+	0.364598i
$628$	−15.9057	+	7.08908i	−0.634708	+	0.282885i
$629$	−52.4377	+	30.2749i	−2.09083	+	1.20714i
$630$	11.4586	+	24.5877i	0.456521	+	0.979598i
$631$	−18.2913	+	31.6814i	−0.728164	+	1.26122i	0.229494	+	0.973310i	$0.426293\pi$
$631$	−18.2913	+	31.6814i	−0.728164	+	1.26122i	−0.957658	+	0.287908i	$0.907040\pi$
$632$	0.0434736	+	2.41027i	0.00172929	+	0.0958754i
$633$	−42.3657	−	4.46187i	−1.68389	−	0.177343i
$634$	12.7515	+	8.27739i	0.506426	+	0.328737i
$635$	20.0128	−	23.8504i	0.794186	−	0.946474i
$636$	−15.3613	+	38.0397i	−0.609113	+	1.50837i
$637$	−0.474463	+	1.30358i	−0.0187989	+	0.0516496i
$638$	13.2483	+	5.62055i	0.524506	+	0.222520i
$639$	15.0402	−	2.10728i	0.594980	−	0.0833625i
$640$	27.8424	+	5.37282i	1.10057	+	0.212379i
$641$	2.53575	+	14.3809i	0.100156	+	0.568012i	0.993045	+	0.117736i	$0.0375636\pi$
$641$	2.53575	+	14.3809i	0.100156	+	0.568012i	−0.892889	+	0.450277i	$0.851325\pi$
$642$	10.6337	+	27.7033i	0.419680	+	1.09336i
$643$	−16.8828	−	46.3851i	−0.665793	−	1.82925i	−0.548494	−	0.836155i	$-0.684798\pi$
$643$	−16.8828	−	46.3851i	−0.665793	−	1.82925i	−0.117300	−	0.993097i	$-0.537424\pi$
$644$	1.00729	+	14.3251i	0.0396929	+	0.564490i
$645$	−7.72762	+	15.8355i	−0.304275	+	0.623521i
$646$	−35.9460	+	38.5624i	−1.41428	+	1.51722i
$647$	−23.5483			−0.925778			−0.462889	−	0.886416i	$-0.653187\pi$
$647$	−23.5483			−0.925778			−0.462889	+	0.886416i	$0.653187\pi$
$648$	15.3143	+	20.3340i	0.601604	+	0.798794i
$649$	6.64748			0.260936
$650$	−3.48399	+	3.73758i	−0.136653	+	0.146600i
$651$	−6.75254	+	13.8373i	−0.264653	+	0.542328i
$652$	12.8499	−	0.903562i	0.503243	−	0.0353862i
$653$	9.17895	+	25.2190i	0.359200	+	0.986894i	0.979308	+	0.202377i	$0.0648667\pi$
$653$	9.17895	+	25.2190i	0.359200	+	0.986894i	−0.620108	+	0.784517i	$0.712911\pi$
$654$	−17.1658	−	44.7208i	−0.671237	−	1.74872i
$655$	0.135653	+	0.769324i	0.00530039	+	0.0300600i
$656$	34.0398	+	21.2337i	1.32903	+	0.829039i
$657$	3.03340	−	7.49880i	0.118344	−	0.292556i
$658$	28.3947	+	12.0463i	1.10694	+	0.469615i
$659$	2.27329	−	6.24582i	0.0885548	−	0.243302i	−0.887508	−	0.460793i	$-0.847565\pi$
$659$	2.27329	−	6.24582i	0.0885548	−	0.243302i	0.976062	+	0.217491i	$0.0697872\pi$
$660$	−31.3049	−	12.6416i	−1.21854	−	0.492074i
$661$	−19.3288	+	23.0352i	−0.751803	+	0.895964i	−0.997300	−	0.0734332i	$-0.976604\pi$
$661$	−19.3288	+	23.0352i	−0.751803	+	0.895964i	0.245497	+	0.969397i	$0.421049\pi$
$662$	−21.2778	−	13.8121i	−0.826986	−	0.536823i
$663$	36.8318	+	3.87905i	1.43043	+	0.150650i
$664$	24.6318	−	0.444279i	0.955899	−	0.0172414i
$665$	−15.7099	+	27.2104i	−0.609206	+	1.05517i
$666$	−19.4305	+	27.7362i	−0.752918	+	1.07475i
$667$	6.37898	−	3.68291i	0.246995	−	0.142603i
$668$	−11.6114	−	26.0523i	−0.449257	−	1.00800i
$669$	28.2915	+	8.11893i	1.09381	+	0.313896i
$670$	3.63236	+	7.12550i	0.140330	+	0.275282i
$671$	0.235642	−	1.33639i	0.00909687	−	0.0515909i
$672$	−15.7446	−	19.4129i	−0.607362	−	0.748869i
$673$	17.8623	−	14.9883i	0.688543	−	0.577756i	−0.229946	−	0.973203i	$-0.573855\pi$
$673$	17.8623	−	14.9883i	0.688543	−	0.577756i	0.918489	+	0.395447i	$0.129410\pi$
$674$	−0.306920	−	2.49566i	−0.0118221	−	0.0961293i
$675$	−4.10380	+	5.24576i	−0.157955	+	0.201909i
$676$	−9.80785	+	2.44941i	−0.377225	+	0.0942081i
$677$	27.4963	+	32.7688i	1.05677	+	1.25941i	0.964614	+	0.263665i	$0.0849312\pi$
$677$	27.4963	+	32.7688i	1.05677	+	1.25941i	0.0921554	+	0.995745i	$0.470624\pi$
$678$	−10.9914	+	9.55433i	−0.422122	+	0.366932i
$679$	−2.22091	+	12.5954i	−0.0852305	+	0.483366i
$680$	40.5643	−	35.3035i	1.55557	−	1.35383i
$681$	−10.7262	−	11.1120i	−0.411030	−	0.425814i
$682$	−5.60619	−	18.3243i	−0.214672	−	0.701674i
$683$	−9.59344	+	5.53878i	−0.367083	+	0.211935i	−0.672183	−	0.740385i	$-0.734643\pi$
$683$	−9.59344	+	5.53878i	−0.367083	+	0.211935i	0.305100	+	0.952320i	$0.401310\pi$
$684$	−9.11224	+	28.0412i	−0.348415	+	1.07218i
$685$	−13.8434	−	7.99249i	−0.528929	−	0.305377i
$686$	6.07524	−	26.3380i	0.231954	−	1.00559i
$687$	−1.16638	−	2.62122i	−0.0445002	−	0.100006i
$688$	3.36330	−	15.8836i	0.128225	−	0.605558i
$689$	25.5719	+	21.4574i	0.974213	+	0.817462i
$690$	−14.8118	+	8.89947i	−0.563875	+	0.338797i
$691$	15.4467	−	42.4396i	0.587622	−	1.61448i	−0.187218	−	0.982318i	$-0.559947\pi$
$691$	15.4467	−	42.4396i	0.587622	−	1.61448i	0.774839	−	0.632158i	$-0.217831\pi$
$692$	−19.0756	−	5.46184i	−0.725146	−	0.207628i
$693$	13.9601	+	26.2819i	0.530300	+	0.998368i
$694$	2.88785	+	3.83076i	0.109621	+	0.145414i
$695$	2.23158	+	12.6559i	0.0846486	+	0.480066i
$696$	−5.41388	+	11.6213i	−0.205213	+	0.440505i
$697$	71.4958	−	26.0223i	2.70810	−	0.985666i
$698$	−0.136678	+	2.61769i	−0.00517335	+	0.0990809i
$699$	−13.7841	−	20.4451i	−0.521362	−	0.773303i
$700$	3.84190	−	5.29223i	0.145210	−	0.200027i
$701$		−	10.1103i		−	0.381863i	−0.981603	−	0.190931i	$-0.938849\pi$
$701$		−	10.1103i		−	0.381863i	0.981603	−	0.190931i	$-0.0611508\pi$
$702$	19.5881	−	6.73508i	0.739305	−	0.254199i
$703$	−39.2247			−1.47939
$704$	30.8104	+	4.29359i	1.16121	+	0.161821i
$705$	2.58114	+	37.0246i	0.0972115	+	1.39443i
$706$	19.4100	+	1.01346i	0.730506	+	0.0381422i
$707$	0.943400	+	2.59197i	0.0354802	+	0.0974811i
$708$	−0.205629	+	5.91835i	−0.00772800	+	0.222425i
$709$	9.89080	−	1.74401i	0.371457	−	0.0654978i	0.0151963	−	0.999885i	$-0.495163\pi$
$709$	9.89080	−	1.74401i	0.371457	−	0.0654978i	0.356260	+	0.934387i	$0.384052\pi$
$710$	−10.8015	−	14.3283i	−0.405373	−	0.537731i
$711$	2.50079	+	0.532665i	0.0937871	+	0.0199765i
$712$	16.9136	+	2.66876i	0.633862	+	0.100016i
$713$	−9.21647	−	3.35452i	−0.345159	−	0.125628i
$714$	−47.3944	+	0.826440i	−1.77369	+	0.0309288i
$715$	−17.6584	+	21.0445i	−0.660389	+	0.787020i
$716$	−8.37698	+	17.1923i	−0.313062	+	0.642505i
$717$	24.2625	+	17.6356i	0.906100	+	0.658613i
$718$	−3.41808	+	14.8184i	−0.127562	+	0.553019i
$719$	12.6792	−	21.9611i	0.472856	−	0.819010i	−0.526662	−	0.850075i	$-0.676557\pi$
$719$	12.6792	−	21.9611i	0.472856	−	0.819010i	0.999517	+	0.0310648i	$0.00988984\pi$
$720$	12.2234	−	27.4802i	0.455539	−	1.02413i
$721$	14.1651	+	24.5347i	0.527537	+	0.913721i
$722$	−6.96246	+	2.13011i	−0.259116	+	0.0792746i
$723$	9.28311	+	37.2661i	0.345243	+	1.38594i
$724$	5.95533	+	8.82176i	0.221328	+	0.327858i
$725$	−3.30340	−	0.582478i	−0.122685	−	0.0216327i
$726$	−9.54342	−	3.28625i	−0.354189	−	0.121964i
$727$	10.0163	−	8.40466i	0.371483	−	0.311712i	−0.437865	−	0.899041i	$-0.644265\pi$
$727$	10.0163	−	8.40466i	0.371483	−	0.311712i	0.809348	+	0.587329i	$0.199821\pi$
$728$	−18.9836	+	7.29978i	−0.703578	+	0.270548i
$729$	24.6796	−	10.9506i	0.914061	−	0.405578i
$730$	−9.48583	+	1.16658i	−0.351086	+	0.0431770i
$731$	−19.7916	−	23.5867i	−0.732017	−	0.872384i
$732$	1.18252	+	0.251135i	0.0437073	+	0.00928222i
$733$	−8.57953	−	1.51280i	−0.316892	−	0.0558766i	0.0129398	−	0.999916i	$-0.495881\pi$
$733$	−8.57953	−	1.51280i	−0.316892	−	0.0558766i	−0.329832	+	0.944040i	$0.606992\pi$
$734$	6.97339	+	13.6795i	0.257393	+	0.504919i
$735$	2.07310	−	0.516416i	0.0764673	−	0.0190483i
$736$	11.2476	−	11.2694i	0.414592	−	0.415396i
$737$	4.38708	+	7.59865i	0.161600	+	0.279900i
$738$	30.0966	−	30.0828i	1.10787	−	1.10736i
$739$	−36.1627	−	20.8786i	−1.33027	−	0.768031i	−0.344927	−	0.938629i	$-0.612096\pi$
$739$	−36.1627	−	20.8786i	−1.33027	−	0.768031i	−0.985341	+	0.170599i	$0.945430\pi$
$740$	39.7940	+	4.16692i	1.46286	+	0.153179i
$741$	19.4069	+	14.1062i	0.712930	+	0.518204i
$742$	−35.8369	−	23.2629i	−1.31561	−	0.854007i
$743$	−9.46740	−	7.94409i	−0.347325	−	0.291441i	0.452390	−	0.891820i	$-0.350572\pi$
$743$	−9.46740	−	7.94409i	−0.347325	−	0.291441i	−0.799715	+	0.600380i	$0.795016\pi$
$744$	16.4878	−	4.42445i	0.604474	−	0.162208i
$745$	4.88588	+	1.77831i	0.179005	+	0.0651524i
$746$	−12.7546	+	30.0641i	−0.466979	+	1.10073i
$747$	5.44358	−	25.5569i	0.199170	−	0.935078i
$748$	42.4213	−	40.9976i	1.55108	−	1.49902i
$749$	−30.4348	+	5.36648i	−1.11207	+	0.196087i
$750$	−22.5461	−	3.57136i	−0.823268	−	0.130408i
$751$	23.4602	−	8.53880i	0.856074	−	0.311585i	0.123560	−	0.992337i	$-0.460569\pi$
$751$	23.4602	−	8.53880i	0.856074	−	0.311585i	0.732514	+	0.680752i	$0.238347\pi$
$752$	−10.5930	−	32.5161i	−0.386287	−	1.18574i
$753$	0.817040	+	11.7198i	0.0297746	+	0.427094i
$754$	7.63098	+	7.11324i	0.277904	+	0.259049i
$755$			60.4972i			2.20172i
$756$	−23.8311	+	11.6159i	−0.866727	+	0.422467i
$757$		−	8.24126i		−	0.299534i	−0.988721	−	0.149767i	$-0.952148\pi$
$757$		−	8.24126i		−	0.299534i	0.988721	−	0.149767i	$-0.0478523\pi$
$758$	18.5092	−	19.8564i	0.672286	−	0.721218i
$759$	−15.7182	+	10.5972i	−0.570534	+	0.384654i
$760$	34.1923	−	6.66694i	1.24028	−	0.241835i
$761$	6.01155	−	2.18802i	0.217918	−	0.0793158i	−0.230754	−	0.973012i	$-0.574119\pi$
$761$	6.01155	−	2.18802i	0.217918	−	0.0793158i	0.448672	+	0.893696i	$0.351897\pi$
$762$	23.6468	+	19.1495i	0.856633	+	0.693713i
$763$	49.1304	−	8.66301i	1.77864	−	0.313622i
$764$	5.76089	+	5.96095i	0.208422	+	0.215660i
$765$	−26.7562	−	50.3724i	−0.967372	−	1.82122i
$766$	−32.5343	−	13.8026i	−1.17551	−	0.498707i
$767$	4.52812	+	1.64810i	0.163501	+	0.0595094i
$768$	−4.77572	+	27.2982i	−0.172329	+	0.985039i
$769$	22.1762	+	18.6080i	0.799693	+	0.671022i	0.948124	−	0.317900i	$-0.102978\pi$
$769$	22.1762	+	18.6080i	0.799693	+	0.671022i	−0.148431	+	0.988923i	$0.547422\pi$
$770$	19.1443	−	29.4921i	0.689911	−	1.06282i
$771$	−36.5915	+	16.2823i	−1.31781	+	0.586393i
$772$	−35.8235	−	3.75116i	−1.28932	−	0.135007i
$773$	−20.3275	−	11.7361i	−0.731130	−	0.422118i	0.0877057	−	0.996146i	$-0.472046\pi$
$773$	−20.3275	−	11.7361i	−0.731130	−	0.422118i	−0.818835	+	0.574029i	$0.805380\pi$
$774$	−15.6056	−	7.28135i	−0.560931	−	0.261723i
$775$	2.23325	+	3.86810i	0.0802207	+	0.138946i
$776$	12.1507	−	7.31047i	0.436183	−	0.262431i
$777$	−24.4946	−	25.3757i	−0.878740	−	0.910347i
$778$	1.00371	−	0.511663i	0.0359849	−	0.0183440i
$779$	48.5392	+	8.55877i	1.73910	+	0.306650i
$780$	−18.1900	−	16.3726i	−0.651308	−	0.586232i
$781$	−12.6533	−	15.0797i	−0.452772	−	0.539593i
$782$	−3.68565	−	29.9692i	−0.131798	−	1.07169i
$783$	10.7102	+	8.37868i	0.382752	+	0.299430i
$784$	−1.73743	+	0.925536i	−0.0620510	+	0.0330548i
$785$	16.7172	−	14.0274i	0.596662	−	0.500659i
$786$	−0.749447	+	0.145664i	−0.0267319	+	0.00519566i
$787$	6.50488	+	1.14699i	0.231874	+	0.0408856i	0.288378	−	0.957517i	$-0.406884\pi$
$787$	6.50488	+	1.14699i	0.231874	+	0.0408856i	−0.0565038	+	0.998402i	$0.517995\pi$
$788$	17.3361	+	25.6803i	0.617572	+	0.914823i
$789$	−3.52450	−	1.01144i	−0.125476	−	0.0360082i
$790$	−0.883808	−	2.88880i	−0.0314445	−	0.102779i
$791$	−7.58367	−	13.1353i	−0.269644	−	0.467037i
$792$	11.8195	−	30.8056i	0.419989	−	1.09463i
$793$	0.491845	−	0.851900i	0.0174659	−	0.0302519i
$794$	42.6530	+	9.83851i	1.51370	+	0.349156i
$795$	5.38467	−	51.1277i	0.190974	−	1.81331i
$796$	−31.6221	−	15.4079i	−1.12081	−	0.546120i
$797$	−8.42383	+	10.0391i	−0.298387	+	0.355604i	−0.894318	−	0.447432i	$-0.852339\pi$
$797$	−8.42383	+	10.0391i	−0.298387	+	0.355604i	0.595931	+	0.803036i	$0.296783\pi$
$798$	−26.8568	−	14.8876i	−0.950721	−	0.527015i
$799$	−60.9432	−	22.1815i	−2.15601	−	0.784725i
$800$	−7.22257	+	0.638948i	−0.255356	+	0.0225902i
$801$	6.81053	−	16.8362i	0.240638	−	0.594876i
$802$	−36.9697	+	27.8699i	−1.30544	+	0.984120i
$803$	−10.3256	+	1.82068i	−0.364382	+	0.0642504i
$804$	−6.90090	+	3.67084i	−0.243376	+	0.129460i
$805$	−6.15506	−	16.9109i	−0.216938	−	0.596031i
$806$	0.724307	−	13.8721i	0.0255126	−	0.488622i
$807$	−39.9883	−	19.5141i	−1.40765	−	0.686928i
$808$	1.48110	−	2.67565i	0.0521051	−	0.0941291i
$809$	−2.66482			−0.0936902			−0.0468451	−	0.998902i	$-0.514917\pi$
$809$	−2.66482			−0.0936902			−0.0468451	+	0.998902i	$0.514917\pi$
$810$	−25.4644	−	19.2148i	−0.894728	−	0.675141i
$811$			55.4951i			1.94870i	0.225042	+	0.974349i	$0.427748\pi$
$811$			55.4951i			1.94870i	−0.225042	+	0.974349i	$0.572252\pi$
$812$	−10.8051	−	7.84396i	−0.379184	−	0.275269i
$813$	20.7401	−	42.5006i	0.727386	−	1.49056i
$814$	43.8352	+	2.28879i	1.53642	+	0.0802219i
$815$	−15.1694	+	5.52122i	−0.531362	+	0.193400i
$816$	35.1886	+	39.0366i	1.23185	+	1.36655i
$817$	−3.46361	−	19.6431i	−0.121176	−	0.687226i
$818$	−3.10942	+	2.34406i	−0.108718	+	0.0819581i
$819$	2.99327	+	21.3638i	0.104593	+	0.746511i
$820$	−48.3345	−	13.8394i	−1.68791	−	0.483293i
$821$	17.2927	−	47.5113i	0.603519	−	1.65815i	−0.140568	−	0.990071i	$-0.544893\pi$
$821$	17.2927	−	47.5113i	0.603519	−	1.65815i	0.744086	−	0.668083i	$-0.232885\pi$
$822$	7.57411	−	13.6635i	0.264177	−	0.476569i
$823$	7.96652	+	6.68471i	0.277696	+	0.233014i	0.770989	−	0.636849i	$-0.219763\pi$
$823$	7.96652	+	6.68471i	0.277696	+	0.233014i	−0.493293	+	0.869863i	$0.664207\pi$
$824$	10.2090	−	29.7053i	0.355648	−	1.03483i
$825$	8.58538	+	0.904195i	0.298905	+	0.0314800i
$826$	−6.00966	−	1.38621i	−0.209103	−	0.0482325i
$827$	−2.28479	−	1.31912i	−0.0794498	−	0.0458703i	0.459749	−	0.888049i	$-0.347939\pi$
$827$	−2.28479	−	1.31912i	−0.0794498	−	0.0458703i	−0.539199	+	0.842179i	$0.681273\pi$
$828$	−8.94865	−	14.3220i	−0.310987	−	0.497722i
$829$	−12.8874	+	7.44056i	−0.447599	+	0.258421i	−0.706816	−	0.707398i	$-0.749869\pi$
$829$	−12.8874	+	7.44056i	−0.447599	+	0.258421i	0.259217	+	0.965819i	$0.416536\pi$
$830$	−29.5222	+	9.03209i	−1.02473	+	0.313508i
$831$	−7.86379	+	27.4024i	−0.272792	+	0.950580i
$832$	19.9229	+	10.5635i	0.690702	+	0.366223i
$833$	−0.648275	+	3.67655i	−0.0224614	+	0.127385i
$834$	−12.3289	+	2.39627i	−0.426915	+	0.0829761i
$835$	22.9758	+	27.3815i	0.795109	+	0.947574i
$836$	37.0784	−	9.25996i	1.28238	−	0.320262i
$837$	−0.620439	−	18.0961i	−0.0214455	−	0.625492i
$838$	35.2394	−	4.33379i	1.21732	−	0.149708i
$839$	3.12853	−	2.62515i	0.108009	−	0.0906302i	−0.587184	−	0.809454i	$-0.699763\pi$
$839$	3.12853	−	2.62515i	0.108009	−	0.0906302i	0.695193	+	0.718823i	$0.255319\pi$
$840$	25.6651	+	17.9567i	0.885529	+	0.619566i
$841$	3.84656	−	21.8149i	0.132640	−	0.752238i
$842$	−8.58412	+	4.37593i	−0.295828	+	0.150804i
$843$	−35.9972	+	34.7474i	−1.23981	+	1.19676i
$844$	−44.9298	+	20.0249i	−1.54655	+	0.689286i
$845$	10.9712	−	6.33421i	0.377420	−	0.217904i
$846$	−36.1352	+	3.15308i	−1.24235	+	0.108405i
$847$	5.25593	−	9.10354i	0.180596	−	0.312801i
$848$	6.62910	+	46.9046i	0.227644	+	1.61071i
$849$	−2.59800	−	5.83851i	−0.0891630	−	0.200377i
$850$	−7.48690	+	11.5337i	−0.256799	+	0.395603i
$851$	14.4412	−	17.2104i	0.495038	−	0.589964i
$852$	13.8171	−	10.7990i	0.473365	−	0.369968i
$853$	6.86679	−	18.8664i	0.235115	−	0.645972i	−0.764884	−	0.644168i	$-0.777204\pi$
$853$	6.86679	−	18.8664i	0.235115	−	0.645972i	0.999998	−	0.00180361i	$-0.000574106\pi$
$854$	−0.491713	+	1.15903i	−0.0168261	+	0.0396612i
$855$	1.30513	−	36.9263i	0.0446344	−	1.26285i
$856$	26.6411	+	21.5479i	0.910575	+	0.736493i
$857$	7.94304	+	45.0472i	0.271329	+	1.53878i	0.750386	+	0.661000i	$0.229868\pi$
$857$	7.94304	+	45.0472i	0.271329	+	1.53878i	−0.479057	+	0.877784i	$0.659021\pi$
$858$	−20.8649	−	16.8967i	−0.712316	−	0.576843i
$859$	−4.92364	−	13.5276i	−0.167992	−	0.461555i	0.826918	−	0.562323i	$-0.190092\pi$
$859$	−4.92364	−	13.5276i	−0.167992	−	0.461555i	−0.994910	+	0.100768i	$0.967870\pi$
$860$	1.42715	+	20.2962i	0.0486656	+	0.692094i
$861$	24.7743	+	36.7462i	0.844306	+	1.25231i
$862$	−3.03946	−	2.83324i	−0.103524	−	0.0965006i
$863$	−6.80168			−0.231532			−0.115766	−	0.993277i	$-0.536932\pi$
$863$	−6.80168			−0.231532			−0.115766	+	0.993277i	$0.536932\pi$
$864$	27.0611	+	11.4760i	0.920636	+	0.390423i
$865$	24.8656			0.845457
$866$	32.3173	+	30.1247i	1.09819	+	1.02368i
$867$	70.0534	−	4.88373i	2.37914	−	0.165860i
$868$	1.24707	+	17.7352i	0.0423285	+	0.601971i
$869$	−1.13352	−	3.11431i	−0.0384519	−	0.105646i
$870$	2.51360	−	15.8685i	0.0852191	−	0.537991i
$871$	1.10446	+	6.26372i	0.0374233	+	0.212238i
$872$	−43.0063	−	34.7844i	−1.45638	−	1.17795i
$873$	−4.64172	−	14.3063i	−0.157098	−	0.484196i
$874$	7.63942	−	18.0070i	0.258407	−	0.609097i
$875$	8.13108	−	22.3399i	0.274881	−	0.755228i
$876$	−1.30158	−	9.24936i	−0.0439761	−	0.312507i
$877$	26.6118	−	31.7147i	0.898615	−	1.07093i	−0.0985084	−	0.995136i	$-0.531407\pi$
$877$	26.6118	−	31.7147i	0.898615	−	1.07093i	0.997124	−	0.0757918i	$-0.0241484\pi$
$878$	5.40339	−	8.32403i	0.182356	−	0.280922i
$879$	−13.0425	+	17.9435i	−0.439913	+	0.605219i
$880$	−38.6003	+	5.45545i	−1.30122	+	0.183903i
$881$	14.8677	−	25.7517i	0.500907	−	0.867596i	−0.499093	−	0.866549i	$-0.666333\pi$
$881$	14.8677	−	25.7517i	0.500907	−	0.867596i	0.999999	−	0.00104741i	$-0.000333401\pi$
$882$	0.539949	+	2.01696i	0.0181810	+	0.0679146i
$883$	2.83903	−	1.63911i	0.0955408	−	0.0551605i	−0.451468	−	0.892287i	$-0.649100\pi$
$883$	2.83903	−	1.63911i	0.0955408	−	0.0551605i	0.547009	+	0.837127i	$0.315766\pi$
$884$	39.0610	−	17.4092i	1.31376	−	0.585535i
$885$	−1.79383	−	7.20113i	−0.0602989	−	0.242063i
$886$	−26.3695	+	13.4424i	−0.885900	+	0.451605i
$887$	2.48943	−	14.1182i	0.0835867	−	0.474044i	−0.914066	−	0.405566i	$-0.867075\pi$
$887$	2.48943	−	14.1182i	0.0835867	−	0.474044i	0.997653	−	0.0684782i	$-0.0218144\pi$
$888$	−3.39371	+	38.9564i	−0.113886	+	1.30729i
$889$	−24.2758	+	20.3698i	−0.814184	+	0.683181i
$890$	−21.2974	+	2.61918i	−0.713890	+	0.0877952i
$891$	−28.9970	−	19.5944i	−0.971437	−	0.656438i
$892$	32.9740	−	8.23493i	1.10405	−	0.275726i
$893$	−27.0056	−	32.1840i	−0.903707	−	1.07700i
$894$	−1.65446	+	4.80462i	−0.0553333	+	0.160690i
$895$	4.16171	−	23.6022i	0.139111	−	0.788936i
$896$	−26.9589	−	10.3066i	−0.900632	−	0.344319i
$897$	−13.3342	+	3.32160i	−0.445217	+	0.110905i
$898$	−20.4873	+	6.26792i	−0.683668	+	0.209163i
$899$	7.89747	−	4.55961i	0.263395	−	0.152071i
$900$	−1.07059	+	7.61573i	−0.0356865	+	0.253858i
$901$	77.7999	+	44.9178i	2.59189	+	1.49643i
$902$	−53.7451	−	12.3971i	−1.78952	−	0.412777i
$903$	10.5448	−	14.5072i	0.350909	−	0.482771i
$904$	−5.46566	+	15.9035i	−0.181785	+	0.528942i
$905$	−10.2179	−	8.57380i	−0.339653	−	0.285003i
$906$	−59.1158	+	1.03083i	−1.96399	+	0.0342471i
$907$	−9.86338	+	27.0994i	−0.327508	+	0.899822i	0.661232	+	0.750181i	$0.270034\pi$
$907$	−9.86338	+	27.0994i	−0.327508	+	0.899822i	−0.988741	+	0.149640i	$0.952188\pi$
$908$	−17.1447	−	4.90897i	−0.568967	−	0.162910i
$909$	−2.40965	−	2.17151i	−0.0799232	−	0.0720244i
$910$	20.3526	−	15.3430i	0.674682	−	0.508614i
$911$	−8.43557	−	47.8405i	−0.279483	−	1.58503i	−0.724352	−	0.689430i	$-0.757861\pi$
$911$	−8.43557	−	47.8405i	−0.279483	−	1.58503i	0.444869	−	0.895595i	$-0.353250\pi$
$912$	7.09733	+	33.2980i	0.235016	+	1.10261i
$913$	−31.8267	+	11.5840i	−1.05331	+	0.383374i
$914$	−1.34441	−	0.0701964i	−0.0444693	−	0.00232189i
$915$	−1.51129	+	0.105359i	−0.0499616	+	0.00348305i
$916$	−2.68091	−	1.94621i	−0.0885798	−	0.0643045i
$917$		−	0.795126i		−	0.0262574i
$918$	48.7664	−	27.0036i	1.60953	−	0.891251i
$919$	3.55196			0.117168			0.0585842	−	0.998282i	$-0.481341\pi$
$919$	3.55196			0.117168			0.0585842	+	0.998282i	$0.481341\pi$
$920$	−9.66323	+	17.4569i	−0.318587	+	0.575536i
$921$	27.6576	−	18.6468i	0.911349	−	0.614432i
$922$	−0.324067	+	6.20658i	−0.0106726	+	0.204403i
$923$	−4.88050	−	13.4091i	−0.160644	−	0.441365i
$924$	29.1449	+	18.2046i	0.958797	+	0.598888i
$925$	−10.0757	+	1.77662i	−0.331288	+	0.0584150i
$926$	0.102448	−	0.0772314i	0.00336666	−	0.00253798i
$927$	−28.2461	−	17.6667i	−0.927723	−	0.580251i
$928$	1.30453	+	14.7463i	0.0428234	+	0.484070i
$929$	−15.0376	−	5.47325i	−0.493369	−	0.179572i	0.0833403	−	0.996521i	$-0.473441\pi$
$929$	−15.0376	−	5.47325i	−0.493369	−	0.179572i	−0.576709	+	0.816950i	$0.695663\pi$
$930$	−18.3377	+	11.0180i	−0.601316	+	0.361293i
$931$	−1.55454	+	1.85263i	−0.0509482	+	0.0607176i
$932$	−25.5955	−	12.4715i	−0.838409	−	0.408517i
$933$	−50.5355	+	22.4871i	−1.65446	+	0.736194i
$934$	14.0709	+	3.24566i	0.460415	+	0.106201i
$935$	−36.9653	+	64.0257i	−1.20889	+	2.09386i
$936$	15.6888	−	18.0537i	0.512804	−	0.590103i
$937$	−3.30668	−	5.72734i	−0.108025	−	0.187104i	0.806945	−	0.590626i	$-0.201119\pi$
$937$	−3.30668	−	5.72734i	−0.108025	−	0.187104i	−0.914970	+	0.403522i	$0.867786\pi$
$938$	−2.38158	−	7.78441i	−0.0777615	−	0.254170i
$939$	−7.26588	+	7.01361i	−0.237113	+	0.228881i
$940$	23.9786	+	35.5200i	0.782095	+	1.15853i
$941$	55.8790	+	9.85298i	1.82160	+	0.321198i	0.976845	−	0.213950i	$-0.0686329\pi$
$941$	55.8790	+	9.85298i	1.82160	+	0.321198i	0.844759	+	0.535148i	$0.179744\pi$
$942$	13.9919	+	16.0965i	0.455882	+	0.524451i
$943$	−21.6258	+	18.1462i	−0.704231	+	0.590920i
$944$	3.21495	+	6.03515i	0.104638	+	0.196427i
$945$	24.7038	−	22.2150i	0.803614	−	0.722655i
$946$	2.72454	+	22.1541i	0.0885825	+	0.720292i
$947$	−1.48059	−	1.76450i	−0.0481128	−	0.0573386i	0.741451	−	0.671007i	$-0.234138\pi$
$947$	−1.48059	−	1.76450i	−0.0481128	−	0.0573386i	−0.789564	+	0.613668i	$0.789693\pi$
$948$	2.80778	−	0.912851i	0.0911926	−	0.0296480i
$949$	−7.48497	−	1.31980i	−0.242972	−	0.0428426i
$950$	−7.93610	+	4.04559i	−0.257481	+	0.131256i
$951$	5.13592	−	17.8968i	0.166543	−	0.580343i
$952$	−46.9003	+	28.2177i	−1.52005	+	0.914541i
$953$	−8.85341	−	15.3346i	−0.286790	−	0.496735i	0.686252	−	0.727364i	$-0.259255\pi$
$953$	−8.85341	−	15.3346i	−0.286790	−	0.496735i	−0.973042	+	0.230629i	$0.925922\pi$
$954$	50.0520	+	4.39053i	1.62049	+	0.142149i
$955$	−8.99675	−	5.19427i	−0.291128	−	0.168083i
$956$	34.4466	+	3.60698i	1.11408	+	0.116658i
$957$	1.84609	−	17.5287i	0.0596755	−	0.566622i
$958$	1.70927	−	2.63316i	0.0552239	−	0.0850735i
$959$	12.4636	+	10.4582i	0.402471	+	0.337713i
$960$	−3.66303	−	34.5352i	−0.118224	−	1.11462i
$961$	17.7201	+	6.44958i	0.571615	+	0.208051i
$962$	29.2922	+	12.4271i	0.944417	+	0.400665i
$963$	28.6482	−	22.3629i	0.923176	−	0.720635i
$964$	30.8178	+	31.8880i	0.992574	+	1.02704i
$965$	44.4528	−	7.83822i	1.43099	−	0.252321i
$966$	16.4199	−	6.30267i	0.528301	−	0.202785i
$967$	−40.5193	+	14.7478i	−1.30301	+	0.474257i	−0.897976	−	0.440044i	$-0.854963\pi$
$967$	−40.5193	+	14.7478i	−1.30301	+	0.474257i	−0.405035	+	0.914301i	$0.632741\pi$
$968$	−11.4394	+	2.23050i	−0.367676	+	0.0716909i
$969$	58.0255	+	28.3161i	1.86405	+	0.909645i
$970$	−12.1169	+	12.9988i	−0.389049	+	0.417366i
$971$		−	28.3313i		−	0.909195i	−0.890697	−	0.454598i	$-0.849783\pi$
$971$		−	28.3313i		−	0.909195i	0.890697	−	0.454598i	$-0.150217\pi$
$972$	18.3422	−	25.2104i	0.588327	−	0.808623i
$973$		−	13.0804i		−	0.419337i
$974$	−42.9118	−	40.0004i	−1.37498	−	1.28169i
$975$	5.62400	+	2.74448i	0.180112	+	0.0878937i
$976$	1.32726	−	0.432390i	0.0424845	−	0.0138405i
$977$	2.02803	−	0.738143i	0.0648824	−	0.0236153i	−0.309375	−	0.950940i	$-0.600120\pi$
$977$	2.02803	−	0.738143i	0.0648824	−	0.0236153i	0.374257	+	0.927325i	$0.377898\pi$
$978$	−5.65363	−	14.7290i	−0.180783	−	0.470981i
$979$	−23.1828	+	4.08776i	−0.740926	+	0.130645i
$980$	1.77392	−	1.71438i	0.0566657	−	0.0547639i
$981$	−46.2462	+	36.1001i	−1.47653	+	1.15259i
$982$	−3.18025	+	7.49623i	−0.101486	+	0.239214i
$983$	38.8354	+	14.1349i	1.23866	+	0.450834i	0.876554	−	0.481304i	$-0.159837\pi$
$983$	38.8354	+	14.1349i	1.23866	+	0.450834i	0.362103	+	0.932138i	$0.382059\pi$
$984$	12.6998	−	47.4667i	0.404856	−	1.51318i
$985$	−29.7444	−	24.9585i	−0.947734	−	0.795243i
$986$	23.5483	+	15.2859i	0.749929	+	0.486803i
$987$	3.95665	−	37.5686i	0.125942	−	1.19582i
$988$	27.5528	+	2.88512i	0.876572	+	0.0917879i
$989$	9.89386	+	5.71222i	0.314606	+	0.181638i
$990$	−3.61321	+	41.1905i	−0.114835	+	1.30912i
$991$	18.3797	+	31.8346i	0.583851	+	1.01126i	0.995018	+	0.0996989i	$0.0317880\pi$
$991$	18.3797	+	31.8346i	0.583851	+	1.01126i	−0.411167	+	0.911560i	$0.634879\pi$
$992$	13.9250	−	13.9521i	0.442120	−	0.442978i
$993$	−8.57008	+	29.8636i	−0.271963	+	0.947692i
$994$	8.29467	+	16.2714i	0.263091	+	0.516098i
$995$	43.4120	+	7.65472i	1.37625	+	0.242671i
$996$	−9.32890	−	28.6942i	−0.295597	−	0.909210i
$997$	1.91885	+	2.28679i	0.0607705	+	0.0724234i	0.795573	−	0.605857i	$-0.207170\pi$
$997$	1.91885	+	2.28679i	0.0607705	+	0.0724234i	−0.734803	+	0.678281i	$0.762725\pi$
$998$	−18.8786	+	2.32172i	−0.597593	+	0.0734928i
$999$	39.4379	+	12.8418i	1.24776	+	0.406297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.157.9	✓	204
3.2	odd	2		648.2.t.a.37.26		204
4.3	odd	2		864.2.bf.a.49.23		204
8.3	odd	2		864.2.bf.a.49.12		204
8.5	even	2	inner	216.2.t.a.157.24	yes	204
24.5	odd	2		648.2.t.a.37.11		204
27.11	odd	18		648.2.t.a.613.11		204
27.16	even	9	inner	216.2.t.a.205.24	yes	204
108.43	odd	18		864.2.bf.a.529.12		204
216.43	odd	18		864.2.bf.a.529.23		204
216.173	odd	18		648.2.t.a.613.26		204
216.205	even	18	inner	216.2.t.a.205.9	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.9	✓	204	1.1	even	1	trivial
216.2.t.a.157.24	yes	204	8.5	even	2	inner
216.2.t.a.205.9	yes	204	216.205	even	18	inner
216.2.t.a.205.24	yes	204	27.16	even	9	inner
648.2.t.a.37.11		204	24.5	odd	2
648.2.t.a.37.26		204	3.2	odd	2
648.2.t.a.613.11		204	27.11	odd	18
648.2.t.a.613.26		204	216.173	odd	18
864.2.bf.a.49.12		204	8.3	odd	2
864.2.bf.a.49.23		204	4.3	odd	2
864.2.bf.a.529.12		204	108.43	odd	18
864.2.bf.a.529.23		204	216.43	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03448 - 0.964291i) q^{2} +(-0.759610 + 1.55660i) q^{3} +(0.140286 + 1.99507i) q^{4} +(-0.857221 - 2.35519i) q^{5} +(2.28681 - 0.877779i) q^{6} +(0.442985 + 2.51229i) q^{7} +(1.77871 - 2.19914i) q^{8} +(-1.84598 - 2.36481i) q^{9} +O(q^{10})\)	\(q+(-1.03448 - 0.964291i) q^{2} +(-0.759610 + 1.55660i) q^{3} +(0.140286 + 1.99507i) q^{4} +(-0.857221 - 2.35519i) q^{5} +(2.28681 - 0.877779i) q^{6} +(0.442985 + 2.51229i) q^{7} +(1.77871 - 2.19914i) q^{8} +(-1.84598 - 2.36481i) q^{9} +(-1.38432 + 3.26301i) q^{10} +(-1.32995 + 3.65402i) q^{11} +(-3.21209 - 1.29711i) q^{12} +(-1.81187 + 2.15930i) q^{13} +(1.96432 - 3.02608i) q^{14} +(4.31724 + 0.454683i) q^{15} +(-3.96064 + 0.559764i) q^{16} +(-3.79287 + 6.56945i) q^{17} +(-0.370738 + 4.22641i) q^{18} +(-4.25574 + 2.45705i) q^{19} +(4.57853 - 2.04062i) q^{20} +(-4.24712 - 1.21881i) q^{21} +(4.89934 - 2.49753i) q^{22} +(0.488755 - 2.77187i) q^{23} +(2.07204 + 4.43922i) q^{24} +(-0.981892 + 0.823905i) q^{25} +(3.95653 - 0.486580i) q^{26} +(5.08329 - 1.07712i) q^{27} +(-4.95007 + 1.23623i) q^{28} +(1.68216 + 2.00472i) q^{29} +(-4.02764 - 4.63344i) q^{30} +(0.605101 - 3.43170i) q^{31} +(4.63697 + 3.24015i) q^{32} +(-4.67758 - 4.84583i) q^{33} +(10.2585 - 3.13851i) q^{34} +(5.53721 - 3.19691i) q^{35} +(4.45901 - 4.01463i) q^{36} +(6.91267 + 3.99103i) q^{37} +(6.77178 + 1.56201i) q^{38} +(-1.98485 - 4.46058i) q^{39} +(-6.70414 - 2.30406i) q^{40} +(-7.68334 - 6.44709i) q^{41} +(3.21826 + 5.35630i) q^{42} +(-1.38824 + 3.81417i) q^{43} +(-7.47660 - 2.14075i) q^{44} +(-3.98718 + 6.37482i) q^{45} +(-3.17849 + 2.39613i) q^{46} +(1.48461 + 8.41962i) q^{47} +(2.13722 - 6.59032i) q^{48} +(0.462463 - 0.168323i) q^{49} +(1.81023 + 0.0945182i) q^{50} +(-7.34487 - 10.8942i) q^{51} +(-4.56215 - 3.31189i) q^{52} -11.8427i q^{53} +(-6.29720 - 3.78751i) q^{54} +9.74598 q^{55} +(6.31282 + 3.49445i) q^{56} +(-0.591936 - 8.49088i) q^{57} +(0.192977 - 3.69593i) q^{58} +(-0.584688 - 1.60642i) q^{59} +(-0.301476 + 8.67700i) q^{60} +(-0.343677 + 0.0605995i) q^{61} +(-3.93512 + 2.96652i) q^{62} +(5.12336 - 5.68523i) q^{63} +(-1.67239 - 7.82324i) q^{64} +(6.63875 + 2.41631i) q^{65} +(0.166065 + 9.52345i) q^{66} +(1.45040 - 1.72852i) q^{67} +(-13.6386 - 6.64546i) q^{68} +(3.94342 + 2.86633i) q^{69} +(-8.81086 - 2.03235i) q^{70} +(-2.53118 + 4.38413i) q^{71} +(-8.48401 - 0.146742i) q^{72} +(1.34818 + 2.33512i) q^{73} +(-3.30248 - 10.7945i) q^{74} +(-0.536633 - 2.15426i) q^{75} +(-5.49903 - 8.14583i) q^{76} +(-9.76911 - 1.72256i) q^{77} +(-2.24801 + 6.52834i) q^{78} +(-0.652898 + 0.547847i) q^{79} +(4.71349 + 8.84824i) q^{80} +(-2.18468 + 8.73082i) q^{81} +(1.73137 + 14.0783i) q^{82} +(5.59873 + 6.67230i) q^{83} +(1.83581 - 8.64431i) q^{84} +(18.7237 + 3.30149i) q^{85} +(5.11408 - 2.60700i) q^{86} +(-4.39832 + 1.09564i) q^{87} +(5.67008 + 9.42417i) q^{88} +(3.02691 + 5.24277i) q^{89} +(10.2718 - 2.74981i) q^{90} +(-6.22743 - 3.59541i) q^{91} +(5.59865 + 0.586247i) q^{92} +(4.88213 + 3.54865i) q^{93} +(6.58317 - 10.1415i) q^{94} +(9.43495 + 7.91686i) q^{95} +(-8.56589 + 4.75664i) q^{96} +(4.71115 + 1.71472i) q^{97} +(-0.640719 - 0.271823i) q^{98} +(11.0961 - 3.60017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more