LMFDB - Embedded newform 966.2.be.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	966.19
Dual form			966.2.be.a.661.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.995472 + 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-1.41181 + 0.727837i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.71541 + 2.01429i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(0.995472 + 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-1.41181 + 0.727837i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.71541 + 2.01429i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-1.47460 + 0.590341i) q^{10} +(0.284588 + 2.98034i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(0.805109 + 0.115757i) q^{13} +(1.51617 + 2.16823i) q^{14} +(0.447498 - 1.52404i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-0.425212 + 1.22857i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(-2.26573 - 6.54639i) q^{19} +(-1.52404 + 0.447498i) q^{20} +(-2.64158 - 0.148522i) q^{21} +2.99390i q^{22} +(-1.41246 + 4.58312i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.43683 + 2.01775i) q^{25} +(0.790460 + 0.191763i) q^{26} +(0.755750 + 0.654861i) q^{27} +(1.30320 + 2.30254i) q^{28} +(4.34570 + 5.01520i) q^{29} +(0.590341 - 1.47460i) q^{30} +(-8.42539 + 2.04398i) q^{31} +(0.888835 + 0.458227i) q^{32} +(-2.35336 - 1.85070i) q^{33} +(-0.540069 + 1.18259i) q^{34} +(-3.88790 - 1.59526i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-1.39287 + 0.0663504i) q^{37} +(-1.63320 - 6.73212i) q^{38} +(-0.639366 + 0.502803i) q^{39} +(-1.55967 + 0.300603i) q^{40} +(-1.77403 + 2.76045i) q^{41} +(-2.61550 - 0.398948i) q^{42} +(-0.668427 - 2.27645i) q^{43} +(-0.284588 + 2.98034i) q^{44} +(0.794189 + 1.37558i) q^{45} +(-1.84172 + 4.42810i) q^{46} +(8.34400 + 4.81741i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(-1.11475 + 6.91067i) q^{49} +(-1.62212 + 1.87203i) q^{50} +(-0.595727 - 1.15555i) q^{51} +(0.768652 + 0.266033i) q^{52} +(4.82461 + 6.13500i) q^{53} +(0.690079 + 0.723734i) q^{54} +(-2.57099 - 4.00053i) q^{55} +(1.07843 + 2.41599i) q^{56} +(6.30138 + 2.87774i) q^{57} +(3.84930 + 5.40558i) q^{58} +(-0.798089 - 1.99353i) q^{59} +(0.727837 - 1.41181i) q^{60} +(2.53902 - 2.42095i) q^{61} +(-8.58153 + 1.23384i) q^{62} +(1.93039 - 1.80931i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-1.22091 + 0.422561i) q^{65} +(-2.16678 - 2.06603i) q^{66} +(1.45495 + 1.03606i) q^{67} +(-0.650036 + 1.12589i) q^{68} +(-2.34225 - 4.18496i) q^{69} +(-3.71866 - 1.95760i) q^{70} +(-0.801764 - 1.75562i) q^{71} +(0.235759 - 0.971812i) q^{72} +(1.71636 - 8.90535i) q^{73} +(-1.39287 - 0.0663504i) q^{74} +(-0.468785 - 2.43229i) q^{75} +(-0.985871 - 6.85689i) q^{76} +(-5.51509 + 5.68574i) q^{77} +(-0.684265 + 0.439751i) q^{78} +(0.629462 - 0.800426i) q^{79} +(-1.58119 + 0.150985i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-2.02840 + 2.57932i) q^{82} +(-1.11275 + 0.715120i) q^{83} +(-2.56573 - 0.645760i) q^{84} +(-0.293881 - 2.04399i) q^{85} +(-0.449009 - 2.32968i) q^{86} +(-6.62855 - 0.315757i) q^{87} +(-0.566599 + 2.93979i) q^{88} +(2.47434 - 10.1994i) q^{89} +(0.659836 + 1.44484i) q^{90} +(1.14792 + 1.82030i) q^{91} +(-2.25429 + 4.23298i) q^{92} +(4.33489 - 7.50825i) q^{93} +(7.84829 + 5.58874i) q^{94} +(7.96348 + 7.59317i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(2.15713 + 1.38630i) q^{97} +(-1.76660 + 6.77341i) q^{98} +(2.96342 - 0.426076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	−1.41181	+	0.727837i	−0.631379	+	0.325499i	−0.744040	−	0.668135i	$-0.767093\pi$
$5$	−1.41181	+	0.727837i	−0.631379	+	0.325499i	0.112661	+	0.993633i	$0.464063\pi$
$6$	−0.755750	+	0.654861i	−0.308533	+	0.267346i
$7$	1.71541	+	2.01429i	0.648363	+	0.761331i
$7$	1.71541	+	2.01429i	0.648363	+	0.761331i
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	−1.47460	+	0.590341i	−0.466309	+	0.186682i
$11$	0.284588	+	2.98034i	0.0858065	+	0.898606i	0.931211	+	0.364480i	$0.118753\pi$
$11$	0.284588	+	2.98034i	0.0858065	+	0.898606i	−0.845405	+	0.534126i	$0.820641\pi$
$12$	−0.814576	+	0.580057i	−0.235148	+	0.167448i
$13$	0.805109	+	0.115757i	0.223297	+	0.0321053i	0.253055	−	0.967452i	$-0.418565\pi$
$13$	0.805109	+	0.115757i	0.223297	+	0.0321053i	−0.0297581	+	0.999557i	$0.509474\pi$
$14$	1.51617	+	2.16823i	0.405213	+	0.579484i
$15$	0.447498	−	1.52404i	0.115543	−	0.393505i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	−0.425212	+	1.22857i	−0.103129	+	0.297972i	−0.984747	−	0.173992i	$-0.944333\pi$
$17$	−0.425212	+	1.22857i	−0.103129	+	0.297972i	0.881618	+	0.471963i	$0.156455\pi$
$18$	0.0475819	−	0.998867i	0.0112152	−	0.235435i
$19$	−2.26573	−	6.54639i	−0.519794	−	1.50185i	−0.833605	−	0.552361i	$-0.813727\pi$
$19$	−2.26573	−	6.54639i	−0.519794	−	1.50185i	0.313811	−	0.949485i	$-0.398394\pi$
$20$	−1.52404	+	0.447498i	−0.340785	+	0.100064i
$21$	−2.64158	−	0.148522i	−0.576440	−	0.0324102i
$22$			2.99390i			0.638301i
$23$	−1.41246	+	4.58312i	−0.294518	+	0.955646i
$23$	−1.41246	+	4.58312i	−0.294518	+	0.955646i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−1.43683	+	2.01775i	−0.287366	+	0.403550i
$26$	0.790460	+	0.191763i	0.155022	+	0.0376079i
$27$	0.755750	+	0.654861i	0.145444	+	0.126028i
$28$	1.30320	+	2.30254i	0.246282	+	0.435138i
$29$	4.34570	+	5.01520i	0.806976	+	0.931300i	0.998742	−	0.0501407i	$-0.0159670\pi$
$29$	4.34570	+	5.01520i	0.806976	+	0.931300i	−0.191766	+	0.981441i	$0.561422\pi$
$30$	0.590341	−	1.47460i	0.107781	−	0.269224i
$31$	−8.42539	+	2.04398i	−1.51324	+	0.367109i	−0.904575	−	0.426315i	$-0.859812\pi$
$31$	−8.42539	+	2.04398i	−1.51324	+	0.367109i	−0.608669	+	0.793424i	$0.708296\pi$
$32$	0.888835	+	0.458227i	0.157125	+	0.0810038i
$33$	−2.35336	−	1.85070i	−0.409668	−	0.322166i
$34$	−0.540069	+	1.18259i	−0.0926211	+	0.202812i
$35$	−3.88790	−	1.59526i	−0.657175	−	0.269647i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	−1.39287	+	0.0663504i	−0.228986	+	0.0109079i	−0.161761	−	0.986830i	$-0.551717\pi$
$37$	−1.39287	+	0.0663504i	−0.228986	+	0.0109079i	−0.0672246	+	0.997738i	$0.521414\pi$
$38$	−1.63320	−	6.73212i	−0.264939	−	1.09209i
$39$	−0.639366	+	0.502803i	−0.102380	+	0.0805129i
$40$	−1.55967	+	0.300603i	−0.246606	+	0.0475294i
$41$	−1.77403	+	2.76045i	−0.277058	+	0.431110i	−0.951698	−	0.307037i	$-0.900663\pi$
$41$	−1.77403	+	2.76045i	−0.277058	+	0.431110i	0.674640	+	0.738147i	$0.264299\pi$
$42$	−2.61550	−	0.398948i	−0.403580	−	0.0615590i
$43$	−0.668427	−	2.27645i	−0.101934	−	0.347156i	0.892695	−	0.450662i	$-0.148812\pi$
$43$	−0.668427	−	2.27645i	−0.101934	−	0.347156i	−0.994629	+	0.103506i	$0.966994\pi$
$44$	−0.284588	+	2.98034i	−0.0429033	+	0.449303i
$45$	0.794189	+	1.37558i	0.118391	+	0.205059i
$46$	−1.84172	+	4.42810i	−0.271546	+	0.652888i
$47$	8.34400	+	4.81741i	1.21710	+	0.702692i	0.964296	−	0.264827i	$-0.0853147\pi$
$47$	8.34400	+	4.81741i	1.21710	+	0.702692i	0.252801	+	0.967518i	$0.418648\pi$
$48$	−0.909632	+	0.415415i	−0.131294	+	0.0599600i
$49$	−1.11475	+	6.91067i	−0.159250	+	0.987238i
$50$	−1.62212	+	1.87203i	−0.229403	+	0.264745i
$51$	−0.595727	−	1.15555i	−0.0834185	−	0.161809i
$52$	0.768652	+	0.266033i	0.106593	+	0.0368921i
$53$	4.82461	+	6.13500i	0.662712	+	0.842706i	0.994938	−	0.100493i	$-0.0320421\pi$
$53$	4.82461	+	6.13500i	0.662712	+	0.842706i	−0.332226	+	0.943200i	$0.607800\pi$
$54$	0.690079	+	0.723734i	0.0939079	+	0.0984877i
$55$	−2.57099	−	4.00053i	−0.346672	−	0.539432i
$56$	1.07843	+	2.41599i	0.144111	+	0.322850i
$57$	6.30138	+	2.87774i	0.834638	+	0.381167i
$58$	3.84930	+	5.40558i	0.505437	+	0.709787i
$59$	−0.798089	−	1.99353i	−0.103902	−	0.259535i	0.867303	−	0.497781i	$-0.165852\pi$
$59$	−0.798089	−	1.99353i	−0.103902	−	0.259535i	−0.971205	+	0.238246i	$0.923428\pi$
$60$	0.727837	−	1.41181i	0.0939634	−	0.182264i
$61$	2.53902	−	2.42095i	0.325089	−	0.309971i	−0.509905	−	0.860231i	$-0.670320\pi$
$61$	2.53902	−	2.42095i	0.325089	−	0.309971i	0.834994	+	0.550259i	$0.185471\pi$
$62$	−8.58153	+	1.23384i	−1.08986	+	0.156698i
$63$	1.93039	−	1.80931i	0.243206	−	0.227951i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−1.22091	+	0.422561i	−0.151435	+	0.0524123i
$66$	−2.16678	−	2.06603i	−0.266713	−	0.254310i
$67$	1.45495	+	1.03606i	0.177750	+	0.126575i	0.665469	−	0.746425i	$-0.268232\pi$
$67$	1.45495	+	1.03606i	0.177750	+	0.126575i	−0.487719	+	0.873001i	$0.662171\pi$
$68$	−0.650036	+	1.12589i	−0.0788284	+	0.136535i
$69$	−2.34225	−	4.18496i	−0.281974	−	0.503810i
$70$	−3.71866	−	1.95760i	−0.444465	−	0.233978i
$71$	−0.801764	−	1.75562i	−0.0951519	−	0.208354i	0.856071	−	0.516858i	$-0.172899\pi$
$71$	−0.801764	−	1.75562i	−0.0951519	−	0.208354i	−0.951223	+	0.308505i	$0.900171\pi$
$72$	0.235759	−	0.971812i	0.0277845	−	0.114529i
$73$	1.71636	−	8.90535i	0.200885	−	1.04229i	−0.731778	−	0.681543i	$-0.761309\pi$
$73$	1.71636	−	8.90535i	0.200885	−	1.04229i	0.932663	−	0.360749i	$-0.117479\pi$
$74$	−1.39287	−	0.0663504i	−0.161917	−	0.00771308i
$75$	−0.468785	−	2.43229i	−0.0541307	−	0.280857i
$76$	−0.985871	−	6.85689i	−0.113087	−	0.786539i
$77$	−5.51509	+	5.68574i	−0.628503	+	0.647951i
$78$	−0.684265	+	0.439751i	−0.0774778	+	0.0497920i
$79$	0.629462	−	0.800426i	0.0708200	−	0.0900549i	−0.749352	−	0.662171i	$-0.769635\pi$
$79$	0.629462	−	0.800426i	0.0708200	−	0.0900549i	0.820172	+	0.572116i	$0.193877\pi$
$80$	−1.58119	+	0.150985i	−0.176782	+	0.0168806i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	−2.02840	+	2.57932i	−0.223999	+	0.284838i
$83$	−1.11275	+	0.715120i	−0.122140	+	0.0784946i	−0.600284	−	0.799787i	$-0.704946\pi$
$83$	−1.11275	+	0.715120i	−0.122140	+	0.0784946i	0.478144	+	0.878281i	$0.341310\pi$
$84$	−2.56573	−	0.645760i	−0.279945	−	0.0704582i
$85$	−0.293881	−	2.04399i	−0.0318759	−	0.221701i
$86$	−0.449009	−	2.32968i	−0.0484179	−	0.251216i
$87$	−6.62855	−	0.315757i	−0.710655	−	0.0338527i
$88$	−0.566599	+	2.93979i	−0.0603996	+	0.313383i
$89$	2.47434	−	10.1994i	0.262280	−	1.08113i	−0.676453	−	0.736486i	$-0.736484\pi$
$89$	2.47434	−	10.1994i	0.262280	−	1.08113i	0.938733	−	0.344646i	$-0.112001\pi$
$90$	0.659836	+	1.44484i	0.0695529	+	0.152300i
$91$	1.14792	+	1.82030i	0.120335	+	0.190819i
$92$	−2.25429	+	4.23298i	−0.235026	+	0.441319i
$93$	4.33489	−	7.50825i	0.449507	−	0.778569i
$94$	7.84829	+	5.58874i	0.809490	+	0.576435i
$95$	7.96348	+	7.59317i	0.817036	+	0.779042i
$96$	−0.945001	+	0.327068i	−0.0964487	+	0.0333812i
$97$	2.15713	+	1.38630i	0.219023	+	0.140758i	0.645552	−	0.763716i	$-0.276627\pi$
$97$	2.15713	+	1.38630i	0.219023	+	0.140758i	−0.426529	+	0.904474i	$0.640264\pi$
$98$	−1.76660	+	6.77341i	−0.178454	+	0.684218i
$99$	2.96342	−	0.426076i	0.297835	−	0.0428222i
$100$	−1.79273	+	1.70936i	−0.179273	+	0.170936i
$101$	−0.840675	+	1.63068i	−0.0836503	+	0.162259i	−0.926950	−	0.375184i	$-0.877579\pi$
$101$	−0.840675	+	1.63068i	−0.0836503	+	0.162259i	0.843300	+	0.537443i	$0.180610\pi$
$102$	−0.483188	−	1.20694i	−0.0478427	−	0.119505i
$103$	−2.01442	−	2.82886i	−0.198487	−	0.278736i	0.703322	−	0.710872i	$-0.251699\pi$
$103$	−2.01442	−	2.82886i	−0.198487	−	0.278736i	−0.901808	+	0.432136i	$0.857760\pi$
$104$	0.739883	+	0.337893i	0.0725515	+	0.0331332i
$105$	3.83750	−	1.71296i	0.374502	−	0.167167i
$106$	4.21960	+	6.56582i	0.409844	+	0.637729i
$107$	−3.83405	−	4.02104i	−0.370652	−	0.388729i	0.511821	−	0.859092i	$-0.328971\pi$
$107$	−3.83405	−	4.02104i	−0.370652	−	0.388729i	−0.882473	+	0.470364i	$0.844123\pi$
$108$	0.618159	+	0.786053i	0.0594824	+	0.0756380i
$109$	8.39857	+	2.90678i	0.804438	+	0.278419i	0.698182	−	0.715920i	$-0.253993\pi$
$109$	8.39857	+	2.90678i	0.804438	+	0.278419i	0.106256	+	0.994339i	$0.466114\pi$
$110$	−2.17907	−	4.22681i	−0.207766	−	0.403010i
$111$	0.913168	−	1.05385i	0.0866741	−	0.100027i
$112$	0.843893	+	2.50756i	0.0797404	+	0.236942i
$113$	5.55135	−	2.53522i	0.522227	−	0.238493i	−0.136819	−	0.990596i	$-0.543688\pi$
$113$	5.55135	−	2.53522i	0.522227	−	0.238493i	0.659045	+	0.752103i	$0.270960\pi$
$114$	5.99930	+	3.46370i	0.561886	+	0.324405i
$115$	−1.34164	−	7.49852i	−0.125109	−	0.699240i
$116$	3.31803	+	5.74700i	0.308072	+	0.533596i
$117$	0.0773174	−	0.809705i	0.00714800	−	0.0748572i
$118$	−0.604978	−	2.06037i	−0.0556927	−	0.189672i
$119$	−3.20411	+	1.25100i	−0.293720	+	0.114679i
$120$	0.858742	−	1.33623i	0.0783921	−	0.121980i
$121$	1.99978	−	0.385426i	0.181798	−	0.0350387i
$122$	2.75765	−	2.16864i	0.249666	−	0.196340i
$123$	−0.773609	−	3.18886i	−0.0697539	−	0.287530i
$124$	−8.65995	+	0.412524i	−0.777687	+	0.0370458i
$125$	1.69019	−	11.7555i	0.151175	−	1.05144i
$126$	2.09363	−	1.61762i	0.186516	−	0.144109i
$127$	7.25928	−	15.8956i	0.644157	−	1.41051i	−0.252419	−	0.967618i	$-0.581226\pi$
$127$	7.25928	−	15.8956i	0.644157	−	1.41051i	0.896576	−	0.442889i	$-0.146047\pi$
$128$	0.786053	+	0.618159i	0.0694779	+	0.0546381i
$129$	2.10881	+	1.08717i	0.185671	+	0.0957198i
$130$	−1.25555	+	0.304593i	−0.110119	+	0.0267146i
$131$	−0.559878	+	1.39851i	−0.0489168	+	0.122188i	−0.950814	−	0.309763i	$-0.899750\pi$
$131$	−0.559878	+	1.39851i	−0.0489168	+	0.122188i	0.901897	+	0.431951i	$0.142175\pi$
$132$	−1.96059	−	2.26264i	−0.170647	−	0.196937i
$133$	9.29971	−	15.7936i	0.806387	−	1.36948i
$134$	1.34987	+	1.16967i	0.116611	+	0.101044i
$135$	−1.54360	−	0.374474i	−0.132852	−	0.0322296i
$136$	−0.754115	+	1.05901i	−0.0646649	+	0.0908091i
$137$	5.55866	−	3.20929i	0.474908	−	0.274188i	−0.243384	−	0.969930i	$-0.578257\pi$
$137$	5.55866	−	3.20929i	0.474908	−	0.274188i	0.718292	+	0.695742i	$0.244924\pi$
$138$	−1.93384	−	4.38865i	−0.164619	−	0.373587i
$139$			12.9007i			1.09422i	0.837060	+	0.547111i	$0.184272\pi$
$139$			12.9007i			1.09422i	−0.837060	+	0.547111i	$0.815728\pi$
$140$	−3.51574	−	2.30222i	−0.297134	−	0.194573i
$141$	−9.24454	+	2.71444i	−0.778531	+	0.228597i
$142$	−0.631251	−	1.82388i	−0.0529734	−	0.153057i
$143$	−0.115871	+	2.43244i	−0.00968966	+	0.203411i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	−9.78554	−	3.91754i	−0.812645	−	0.325334i
$146$	2.55510	−	8.70187i	0.211462	−	0.720172i
$147$	−4.23222	−	5.57569i	−0.349068	−	0.459875i
$148$	−1.38025	−	0.198450i	−0.113456	−	0.0163125i
$149$	19.5846	−	13.9461i	1.60443	−	1.14251i	0.701553	−	0.712617i	$-0.252490\pi$
$149$	19.5846	−	13.9461i	1.60443	−	1.14251i	0.902879	−	0.429894i	$-0.141449\pi$
$150$	−0.235459	−	2.46584i	−0.0192251	−	0.201335i
$151$	−8.66760	+	3.46998i	−0.705359	+	0.282383i	−0.696479	−	0.717577i	$-0.745251\pi$
$151$	−8.66760	+	3.46998i	−0.705359	+	0.282383i	−0.00888031	+	0.999961i	$0.502827\pi$
$152$	−0.329619	−	6.91955i	−0.0267356	−	0.561250i
$153$	1.24741	+	0.366272i	0.100847	+	0.0296114i
$154$	−6.03058	+	5.13575i	−0.485958	+	0.413851i
$155$	10.4073	−	9.01801i	0.835938	−	0.724344i
$156$	−0.722968	+	0.372716i	−0.0578838	+	0.0298411i
$157$	15.1020	+	2.91068i	1.20527	+	0.232297i	0.752053	−	0.659102i	$-0.229063\pi$
$157$	15.1020	+	2.91068i	1.20527	+	0.232297i	0.453219	+	0.891399i	$0.350276\pi$
$158$	0.702697	−	0.736967i	0.0559036	−	0.0586300i
$159$	−7.76947	−	0.741894i	−0.616159	−	0.0588361i
$160$	−1.58838			−0.125572
$161$	−11.6547	+	5.01681i	−0.918518	+	0.395380i
$162$	−1.00000			−0.0785674
$163$	25.0361	+	2.39066i	1.96098	+	0.187251i	0.996920	−	0.0784249i	$-0.0249891\pi$
$163$	25.0361	+	2.39066i	1.96098	+	0.187251i	0.964062	+	0.265676i	$0.0855951\pi$
$164$	−2.26439	+	2.37483i	−0.176819	+	0.185443i
$165$	4.66950	+	0.899973i	0.363520	+	0.0700628i
$166$	−1.17569	+	0.606108i	−0.0912509	+	0.0470431i
$167$	−10.9068	+	9.45080i	−0.843993	+	0.731325i	−0.965259	−	0.261296i	$-0.915850\pi$
$167$	−10.9068	+	9.45080i	−0.843993	+	0.731325i	0.121265	+	0.992620i	$0.461305\pi$
$168$	−2.49273	−	0.886725i	−0.192319	−	0.0684123i
$169$	−11.8386	−	3.47613i	−0.910662	−	0.267395i
$170$	−0.0982569	−	2.06267i	−0.00753596	−	0.158199i
$171$	−6.43117	+	2.57465i	−0.491804	+	0.196889i
$172$	−0.225526	−	2.36181i	−0.0171962	−	0.180087i
$173$	−2.56634	+	1.82748i	−0.195115	+	0.138941i	−0.673439	−	0.739242i	$-0.735184\pi$
$173$	−2.56634	+	1.82748i	−0.195115	+	0.138941i	0.478324	+	0.878183i	$0.341244\pi$
$174$	−6.56852	−	0.944411i	−0.497958	−	0.0715956i
$175$	−6.52909	+	0.567061i	−0.493553	+	0.0428658i
$176$	−0.843478	+	2.87262i	−0.0635796	+	0.216532i
$177$	1.99353	+	0.798089i	0.149843	+	0.0599880i
$178$	3.43265	−	9.91799i	0.257288	−	0.743385i
$179$	−0.573556	+	12.0404i	−0.0428696	+	0.899944i	0.870339	+	0.492452i	$0.163899\pi$
$179$	−0.573556	+	12.0404i	−0.0428696	+	0.899944i	−0.913209	+	0.407491i	$0.866404\pi$
$180$	0.519508	+	1.50102i	0.0387218	+	0.111879i
$181$	6.10473	−	1.79251i	0.453761	−	0.133236i	−0.0468626	−	0.998901i	$-0.514922\pi$
$181$	6.10473	−	1.79251i	0.453761	−	0.133236i	0.500624	+	0.865665i	$0.333104\pi$
$182$	0.969693	+	1.92117i	0.0718784	+	0.142407i
$183$			3.50823i			0.259336i
$184$	−2.64646	+	3.99953i	−0.195099	+	0.294849i
$185$	1.91817	−	1.10745i	0.141026	−	0.0814217i
$186$	5.02896	−	7.06219i	0.368741	−	0.517825i
$187$	−3.78256	−	0.917640i	−0.276608	−	0.0671045i
$188$	7.28151	+	6.30947i	0.531059	+	0.460165i
$189$	−0.0226624	+	2.64565i	−0.00164845	+	0.192443i
$190$	7.20565	+	8.31576i	0.522753	+	0.603289i
$191$	−0.482105	+	1.20424i	−0.0348839	+	0.0871357i	−0.944787	−	0.327685i	$-0.893731\pi$
$191$	−0.482105	+	1.20424i	−0.0348839	+	0.0871357i	0.909903	+	0.414821i	$0.136156\pi$
$192$	−0.971812	+	0.235759i	−0.0701345	+	0.0170144i
$193$	−14.9634	−	7.71417i	−1.07709	−	0.555278i	−0.174006	−	0.984745i	$-0.555671\pi$
$193$	−14.9634	−	7.71417i	−1.07709	−	0.555278i	−0.903083	+	0.429467i	$0.858702\pi$
$194$	2.01558	+	1.58507i	0.144710	+	0.113802i
$195$	0.536703	−	1.17522i	0.0384341	−	0.0841589i
$196$	−2.40246	+	6.57482i	−0.171604	+	0.469630i
$197$	2.53313	−	17.6183i	0.180478	−	1.25525i	−0.675159	−	0.737673i	$-0.735925\pi$
$197$	2.53313	−	17.6183i	0.180478	−	1.25525i	0.855636	−	0.517578i	$-0.173166\pi$
$198$	2.99051	−	0.142455i	0.212526	−	0.0101239i
$199$	2.35002	+	9.68690i	0.166588	+	0.686686i	0.992433	+	0.122788i	$0.0391836\pi$
$199$	2.35002	+	9.68690i	0.166588	+	0.686686i	−0.825845	+	0.563898i	$0.809301\pi$
$200$	−1.94710	+	1.53121i	−0.137680	+	0.108273i
$201$	−1.75386	+	0.338029i	−0.123708	+	0.0238427i
$202$	−0.991875	+	1.54339i	−0.0697881	+	0.108592i
$203$	−2.64744	+	17.3566i	−0.185814	+	1.21820i
$204$	−0.366272	−	1.24741i	−0.0256442	−	0.0873361i
$205$	0.495435	−	5.18843i	0.0346027	−	0.362376i
$206$	−1.73640	−	3.00753i	−0.120981	−	0.209545i
$207$	4.64513	+	1.19279i	0.322859	+	0.0829043i
$208$	0.704414	+	0.406694i	0.0488424	+	0.0281991i
$209$	18.8657	−	8.61567i	1.30497	−	0.595958i
$210$	3.98295	−	1.34042i	0.274850	−	0.0924978i
$211$	14.7895	−	17.0680i	1.01815	−	1.17501i	0.0336833	−	0.999433i	$-0.489276\pi$
$211$	14.7895	−	17.0680i	1.01815	−	1.17501i	0.984466	−	0.175574i	$-0.0561783\pi$
$212$	3.57637	+	6.93719i	0.245626	+	0.476448i
$213$	1.82388	+	0.631251i	0.124970	+	0.0432526i
$214$	−3.43447	−	4.36728i	−0.234775	−	0.298541i
$215$	2.60058	+	2.72741i	0.177358	+	0.186007i
$216$	0.540641	+	0.841254i	0.0367859	+	0.0572401i
$217$	−18.5701	−	13.4649i	−1.26062	−	0.914060i
$218$	8.08424	+	3.69195i	0.547534	+	0.250050i
$219$	5.26068	+	7.38758i	0.355483	+	0.499207i
$220$	−1.76742	−	4.41480i	−0.119159	−	0.297646i
$221$	−0.484557	+	0.939910i	−0.0325948	+	0.0632252i
$222$	1.00921	−	0.962278i	0.0677336	−	0.0645839i
$223$	1.97590	−	0.284091i	0.132316	−	0.0190242i	−0.0758387	−	0.997120i	$-0.524163\pi$
$223$	1.97590	−	0.284091i	0.132316	−	0.0190242i	0.208155	+	0.978096i	$0.433254\pi$
$224$	0.601713	+	2.57642i	0.0402036	+	0.172144i
$225$	2.08383	+	1.33920i	0.138922	+	0.0892797i
$226$	5.76720	−	1.99605i	0.383628	−	0.132775i
$227$	20.2040	+	19.2645i	1.34099	+	1.27863i	0.930274	+	0.366866i	$0.119569\pi$
$227$	20.2040	+	19.2645i	1.34099	+	1.27863i	0.410714	+	0.911764i	$0.365279\pi$
$228$	5.64289	+	4.01828i	0.373710	+	0.266117i
$229$	11.3157	−	19.5994i	0.747762	−	1.29516i	−0.201131	−	0.979564i	$-0.564462\pi$
$229$	11.3157	−	19.5994i	0.747762	−	1.29516i	0.948893	−	0.315598i	$-0.102205\pi$
$230$	−0.622790	−	7.59210i	−0.0410655	−	0.500608i
$231$	−0.309115	−	7.91507i	−0.0203383	−	0.520774i
$232$	2.75672	+	6.03638i	0.180988	+	0.396308i
$233$	−3.43012	+	14.1391i	−0.224714	+	0.926285i	0.741994	+	0.670406i	$0.233880\pi$
$233$	−3.43012	+	14.1391i	−0.224714	+	0.926285i	−0.966709	+	0.255879i	$0.917635\pi$
$234$	0.153935	−	0.798689i	0.0100630	−	0.0522119i
$235$	−15.2864	−	0.728181i	−0.997175	−	0.0475013i
$236$	−0.406388	−	2.10854i	−0.0264536	−	0.137254i
$237$	0.144917	+	1.00792i	0.00941337	+	0.0654714i
$238$	−3.30851	+	0.940761i	−0.214459	+	0.0609805i
$239$	−17.3160	+	11.1283i	−1.12008	+	0.719831i	−0.963466	−	0.267830i	$-0.913694\pi$
$239$	−17.3160	+	11.1283i	−1.12008	+	0.719831i	−0.156612	+	0.987660i	$0.550057\pi$
$240$	0.981871	−	1.24855i	0.0633795	−	0.0805936i
$241$	−6.14590	+	0.586862i	−0.395892	+	0.0378031i	−0.291104	−	0.956691i	$-0.594023\pi$
$241$	−6.14590	+	0.586862i	−0.395892	+	0.0378031i	−0.104788	+	0.994495i	$0.533416\pi$
$242$	2.02736	−	0.193589i	0.130324	−	0.0124444i
$243$	0.618159	−	0.786053i	0.0396549	−	0.0504253i
$244$	2.95131	−	1.89669i	0.188938	−	0.121423i
$245$	−3.45603	−	10.5679i	−0.220798	−	0.675158i
$246$	−0.466985	−	3.24796i	−0.0297739	−	0.207082i
$247$	−1.06637	−	5.53283i	−0.0678513	−	0.352046i
$248$	−8.65995	−	0.412524i	−0.549908	−	0.0261953i
$249$	0.250328	−	1.29882i	0.0158639	−	0.0823095i
$250$	2.79997	−	11.5416i	0.177085	−	0.729956i
$251$	−1.21326	−	2.65666i	−0.0765800	−	0.167687i	0.867470	−	0.497490i	$-0.165745\pi$
$251$	−1.21326	−	2.65666i	−0.0765800	−	0.167687i	−0.944050	+	0.329803i	$0.893018\pi$
$252$	2.23792	−	1.41128i	0.140976	−	0.0889025i
$253$	−14.0612	−	2.90531i	−0.884021	−	0.182655i
$254$	8.73738	−	15.1336i	0.548232	−	0.949566i
$255$	1.68210	+	1.19782i	0.105337	+	0.0750104i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	9.64849	−	3.33937i	0.601856	−	0.208304i	−0.00911351	−	0.999958i	$-0.502901\pi$
$257$	9.64849	−	3.33937i	0.601856	−	0.208304i	0.610970	+	0.791654i	$0.290780\pi$
$258$	1.99592	+	1.28270i	0.124261	+	0.0798575i
$259$	−2.52298	−	2.69182i	−0.156771	−	0.167262i
$260$	−1.27882	+	0.183866i	−0.0793089	+	0.0114029i
$261$	4.80275	−	4.57941i	0.297283	−	0.283458i
$262$	−0.690280	+	1.33896i	−0.0426456	+	0.0827210i
$263$	−2.40830	−	6.01563i	−0.148502	−	0.370940i	0.835402	−	0.549640i	$-0.185235\pi$
$263$	−2.40830	−	6.01563i	−0.148502	−	0.370940i	−0.983904	+	0.178700i	$0.942811\pi$
$264$	−1.73663	−	2.43876i	−0.106882	−	0.150095i
$265$	−11.2767	−	5.14990i	−0.692722	−	0.316356i
$266$	10.7589	−	14.8381i	0.659669	−	0.909781i
$267$	5.67415	+	8.82914i	0.347252	+	0.540335i
$268$	1.23258	+	1.29269i	0.0752917	+	0.0789636i
$269$	18.7620	+	23.8578i	1.14394	+	1.45464i	0.870109	+	0.492860i	$0.164048\pi$
$269$	18.7620	+	23.8578i	1.14394	+	1.45464i	0.273831	+	0.961778i	$0.411709\pi$
$270$	−1.50102	−	0.519508i	−0.0913491	−	0.0316162i
$271$	−7.52999	−	14.6061i	−0.457414	−	0.887260i	−0.998916	−	0.0465597i	$-0.985174\pi$
$271$	−7.52999	−	14.6061i	−0.457414	−	0.887260i	0.541501	−	0.840700i	$-0.317856\pi$
$272$	−0.851366	+	0.982528i	−0.0516216	+	0.0595745i
$273$	−2.10957	−	0.425358i	−0.127677	−	0.0257438i
$274$	5.83855	−	2.66638i	0.352720	−	0.161082i
$275$	−6.42248	−	3.70802i	−0.387290	−	0.223602i
$276$	−1.50791	−	4.55260i	−0.0907658	−	0.274035i
$277$	12.4898	+	21.6330i	0.750441	+	1.29980i	0.947609	+	0.319433i	$0.103492\pi$
$277$	12.4898	+	21.6330i	0.750441	+	1.29980i	−0.197168	+	0.980370i	$0.563174\pi$
$278$	−1.22629	+	12.8423i	−0.0735479	+	0.770228i
$279$	2.44256	+	8.31859i	0.146232	+	0.498021i
$280$	−3.28098	−	2.62599i	−0.196076	−	0.156933i
$281$	2.28584	−	3.55683i	0.136362	−	0.212183i	−0.766356	−	0.642416i	$-0.777932\pi$
$281$	2.28584	−	3.55683i	0.136362	−	0.212183i	0.902718	+	0.430233i	$0.141569\pi$
$282$	−9.46071	+	1.82340i	−0.563377	+	0.108582i
$283$	−4.44239	+	3.49353i	−0.264072	+	0.207669i	−0.741412	−	0.671050i	$-0.765844\pi$
$283$	−4.44239	+	3.49353i	−0.264072	+	0.207669i	0.477340	+	0.878719i	$0.341601\pi$
$284$	−0.455022	−	1.87563i	−0.0270006	−	0.111298i
$285$	−10.9909	+	0.523559i	−0.651043	+	0.0310130i
$286$	−0.346565	+	2.41041i	−0.0204928	+	0.142531i
$287$	−8.60355	+	1.16188i	−0.507851	+	0.0685833i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	12.0343	+	9.46390i	0.707902	+	0.556700i
$290$	−9.36885	−	4.82998i	−0.550158	−	0.283626i
$291$	−2.49190	+	0.604529i	−0.146078	+	0.0354381i
$292$	3.37070	−	8.41959i	0.197255	−	0.492719i
$293$	−17.8042	−	20.5471i	−1.04013	−	1.20037i	−0.979339	−	0.202224i	$-0.935183\pi$
$293$	−17.8042	−	20.5471i	−1.04013	−	1.20037i	−0.0607916	−	0.998150i	$-0.519363\pi$
$294$	−3.68305	−	5.95274i	−0.214800	−	0.347171i
$295$	2.57771	+	2.23360i	0.150080	+	0.130045i
$296$	−1.35514	−	0.328753i	−0.0787658	−	0.0191084i
$297$	−1.73663	+	2.43876i	−0.100770	+	0.141511i
$298$	20.8216	−	12.0213i	1.20616	−	0.696378i
$299$	−1.66771	+	3.52640i	−0.0964462	+	0.203937i
$300$		−	2.47705i		−	0.143013i
$301$	3.43882	−	5.25145i	0.198210	−	0.302689i
$302$	−8.95819	+	2.63036i	−0.515486	+	0.151360i
$303$	−0.600048	−	1.73372i	−0.0344719	−	0.0995999i
$304$	0.329619	−	6.91955i	0.0189049	−	0.396863i
$305$	−1.82255	+	5.26592i	−0.104359	+	0.301525i
$306$	1.20694	+	0.483188i	0.0689964	+	0.0276220i
$307$	−0.640097	+	2.17997i	−0.0365323	+	0.124417i	−0.975740	−	0.218931i	$-0.929743\pi$
$307$	−0.640097	+	2.17997i	−0.0365323	+	0.124417i	0.939208	+	0.343349i	$0.111561\pi$
$308$	−6.49146	+	4.53926i	−0.369885	+	0.258648i
$309$	3.43745	+	0.494231i	0.195550	+	0.0281158i
$310$	11.2174	−	7.98790i	0.637107	−	0.453682i
$311$	1.20184	+	12.5863i	0.0681502	+	0.713701i	0.963388	+	0.268112i	$0.0863997\pi$
$311$	1.20184	+	12.5863i	0.0681502	+	0.713701i	−0.895238	+	0.445589i	$0.852994\pi$
$312$	−0.755123	+	0.302306i	−0.0427504	+	0.0171147i
$313$	−0.668853	−	14.0410i	−0.0378058	−	0.793642i	−0.935565	−	0.353155i	$-0.885109\pi$
$313$	−0.668853	−	14.0410i	−0.0378058	−	0.793642i	0.897759	−	0.440487i	$-0.145194\pi$
$314$	14.7570	+	4.33303i	0.832783	+	0.244527i
$315$	−1.40845	+	3.95940i	−0.0793574	+	0.223087i
$316$	0.769568	−	0.666835i	0.0432916	−	0.0375124i
$317$	12.9527	−	6.67759i	0.727497	−	0.375051i	−0.0543492	−	0.998522i	$-0.517308\pi$
$317$	12.9527	−	6.67759i	0.727497	−	0.375051i	0.781846	+	0.623471i	$0.214278\pi$
$318$	−7.66377	−	1.47707i	−0.429763	−	0.0828300i
$319$	−13.7103	+	14.3789i	−0.767628	+	0.805065i
$320$	−1.58119	−	0.150985i	−0.0883910	−	0.00844032i
$321$	5.55596			0.310104
$322$	−12.0788	+	3.88625i	−0.673124	+	0.216572i
$323$	9.00611			0.501113
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	−1.39037	+	1.45818i	−0.0771241	+	0.0808854i
$326$	24.6955	+	4.75967i	1.36776	+	0.263614i
$327$	−7.89941	+	4.07243i	−0.436839	+	0.225206i
$328$	−2.47988	+	2.14883i	−0.136929	+	0.118649i
$329$	4.60969	+	25.0711i	0.254140	+	1.38221i
$330$	4.56281	+	1.33976i	0.251175	+	0.0737515i
$331$	−0.760469	−	15.9642i	−0.0417992	−	0.877473i	−0.918255	−	0.395990i	$-0.870401\pi$
$331$	−0.760469	−	15.9642i	−0.0417992	−	0.877473i	0.876456	−	0.481483i	$-0.159902\pi$
$332$	−1.22798	+	0.491608i	−0.0673940	+	0.0269805i
$333$	0.132551	+	1.38813i	0.00726372	+	0.0760692i
$334$	−11.7558	+	8.37124i	−0.643247	+	0.458054i
$335$	−2.80819	−	0.403757i	−0.153428	−	0.0220596i
$336$	−2.39716	−	1.11966i	−0.130776	−	0.0610824i
$337$	3.14360	−	10.7061i	0.171243	−	0.583199i	−0.828488	−	0.560006i	$-0.810799\pi$
$337$	3.14360	−	10.7061i	0.171243	−	0.583199i	0.999731	−	0.0231927i	$-0.00738314\pi$
$338$	−11.4546	−	4.58572i	−0.623047	−	0.249430i
$339$	−1.99605	+	5.76720i	−0.108410	+	0.313231i
$340$	0.0982569	−	2.06267i	0.00532873	−	0.111864i
$341$	−8.48951	−	24.5288i	−0.459733	−	1.32831i
$342$	−6.64679	+	1.95167i	−0.359417	+	0.105534i
$343$	−15.8324	+	9.60918i	−0.854867	+	0.518847i
$344$		−	2.37256i		−	0.127920i
$345$	6.35277	+	4.20358i	0.342022	+	0.226313i
$346$	−2.72843	+	1.57526i	−0.146682	+	0.0846866i
$347$	−10.8036	+	15.1716i	−0.579970	+	0.814454i	−0.995464	−	0.0951423i	$-0.969669\pi$
$347$	−10.8036	+	15.1716i	−0.579970	+	0.814454i	0.415494	+	0.909596i	$0.363609\pi$
$348$	−6.44901	−	1.56451i	−0.345703	−	0.0838666i
$349$	11.7336	+	10.1672i	0.628086	+	0.544240i	0.909688	−	0.415291i	$-0.136320\pi$
$349$	11.7336	+	10.1672i	0.628086	+	0.544240i	−0.281602	+	0.959531i	$0.590866\pi$
$350$	−6.55343	−	0.0561361i	−0.350295	−	0.00300060i
$351$	0.532656	+	0.614717i	0.0284311	+	0.0328112i
$352$	−1.11272	+	2.77944i	−0.0593081	+	0.148145i
$353$	−2.16925	+	0.526255i	−0.115458	+	0.0280097i	−0.293071	−	0.956091i	$-0.594677\pi$
$353$	−2.16925	+	0.526255i	−0.115458	+	0.0280097i	0.177614	+	0.984100i	$0.443162\pi$
$354$	1.90864	+	0.983972i	0.101443	+	0.0522975i
$355$	2.40974	+	1.89504i	0.127896	+	0.100578i
$356$	4.35987	−	9.54679i	0.231073	−	0.505979i
$357$	1.30570	−	3.18221i	0.0691050	−	0.168420i
$358$	−1.71547	+	11.9314i	−0.0906656	+	0.630593i
$359$	−18.7193	+	0.891710i	−0.987966	+	0.0470626i	−0.535339	−	0.844637i	$-0.679816\pi$
$359$	−18.7193	+	0.891710i	−0.987966	+	0.0470626i	−0.452627	+	0.891700i	$0.649513\pi$
$360$	0.374474	+	1.54360i	0.0197365	+	0.0813551i
$361$	−22.7867	+	17.9197i	−1.19930	+	0.943142i
$362$	6.24748	−	1.20410i	0.328360	−	0.0632862i
$363$	−1.10106	+	1.71328i	−0.0577906	+	0.0899240i
$364$	0.782683	+	2.00465i	0.0410238	+	0.105072i
$365$	4.05847	+	13.8219i	0.212430	+	0.723470i
$366$	−0.333478	+	3.49234i	−0.0174312	+	0.182548i
$367$	−12.5482	−	21.7341i	−0.655010	−	1.13451i	−0.981891	−	0.189446i	$-0.939331\pi$
$367$	−12.5482	−	21.7341i	−0.655010	−	1.13451i	0.326881	−	0.945066i	$-0.394002\pi$
$368$	−3.01465	+	3.72986i	−0.157150	+	0.194432i
$369$	2.84174	+	1.64068i	0.147935	+	0.0854103i
$370$	2.01475	−	0.920106i	0.104742	−	0.0478340i
$371$	−4.08150	+	20.2422i	−0.211901	+	1.05092i
$372$	5.67749	−	6.55218i	0.294364	−	0.339715i
$373$	−15.5697	−	30.2010i	−0.806167	−	1.56375i	−0.825816	−	0.563940i	$-0.809285\pi$
$373$	−15.5697	−	30.2010i	−0.806167	−	1.56375i	0.0196486	−	0.999807i	$-0.493745\pi$
$374$	−3.67821	−	1.27304i	−0.190196	−	0.0658273i
$375$	7.34150	+	9.33547i	0.379113	+	0.482082i
$376$	6.64879	+	6.97305i	0.342885	+	0.359607i
$377$	2.91821	+	4.54083i	0.150296	+	0.233865i
$378$	−0.274045	+	2.63152i	−0.0140954	+	0.135351i
$379$	−7.43347	−	3.39475i	−0.381832	−	0.174377i	0.215246	−	0.976560i	$-0.430945\pi$
$379$	−7.43347	−	3.39475i	−0.381832	−	0.174377i	−0.597078	+	0.802183i	$0.703672\pi$
$380$	6.38256	+	8.96305i	0.327418	+	0.459795i
$381$	6.49472	+	16.2230i	0.332734	+	0.831130i
$382$	−0.594392	+	1.15296i	−0.0304117	+	0.0589905i
$383$	−18.4589	+	17.6005i	−0.943204	+	0.899344i	−0.995056	−	0.0993113i	$-0.968336\pi$
$383$	−18.4589	+	17.6005i	−0.943204	+	0.899344i	0.0518521	+	0.998655i	$0.483488\pi$
$384$	−0.989821	+	0.142315i	−0.0505116	+	0.00726247i
$385$	3.64795	−	12.0413i	0.185917	−	0.613680i
$386$	−14.1624	−	9.10160i	−0.720845	−	0.463259i
$387$	−2.24207	+	0.775987i	−0.113971	+	0.0394457i
$388$	1.85579	+	1.76949i	0.0942132	+	0.0898321i
$389$	3.95719	+	2.81791i	0.200638	+	0.142873i	0.675960	−	0.736938i	$-0.263729\pi$
$389$	3.95719	+	2.81791i	0.200638	+	0.142873i	−0.475322	+	0.879812i	$0.657669\pi$
$390$	0.645984	−	1.11888i	0.0327107	−	0.0566565i
$391$	−5.03008	−	3.68410i	−0.254382	−	0.186313i
$392$	−3.01656	+	6.31668i	−0.152359	+	0.319040i
$393$	−0.625788	−	1.37028i	−0.0315668	−	0.0691217i
$394$	4.19638	−	17.2977i	0.211411	−	0.871446i
$395$	−0.306099	+	1.58819i	−0.0154015	+	0.0799106i
$396$	2.99051	+	0.142455i	0.150279	+	0.00715865i
$397$	4.32710	+	22.4511i	0.217171	+	1.12679i	0.912806	+	0.408394i	$0.133911\pi$
$397$	4.32710	+	22.4511i	0.217171	+	1.12679i	−0.695635	+	0.718395i	$0.744877\pi$
$398$	1.41858	+	9.86642i	0.0711068	+	0.494559i
$399$	5.01282	+	17.6293i	0.250955	+	0.882571i
$400$	−2.08383	+	1.33920i	−0.104191	+	0.0669598i
$401$	6.36419	−	8.09272i	0.317812	−	0.404131i	−0.600731	−	0.799451i	$-0.705124\pi$
$401$	6.36419	−	8.09272i	0.317812	−	0.404131i	0.918544	+	0.395320i	$0.129366\pi$
$402$	−1.77805	+	0.169783i	−0.0886812	+	0.00846803i
$403$	−7.01996	+	0.670325i	−0.349689	+	0.0333912i
$404$	−1.13409	+	1.44211i	−0.0564232	+	0.0717479i
$405$	1.33623	−	0.858742i	0.0663978	−	0.0426712i
$406$	−4.28531	+	17.0264i	−0.212676	+	0.845005i
$407$	−0.594140	−	4.13233i	−0.0294504	−	0.204832i
$408$	−0.246040	−	1.27658i	−0.0121808	−	0.0632000i
$409$	27.6206	+	1.31573i	1.36575	+	0.0650588i	0.717602	−	0.696454i	$-0.245240\pi$
$409$	27.6206	+	1.31573i	1.36575	+	0.0650588i	0.648150	+	0.761512i	$0.275543\pi$
$410$	0.986384	−	5.11785i	0.0487140	−	0.252752i
$411$	−1.51324	+	6.23766i	−0.0746426	+	0.307681i
$412$	−1.44265	−	3.15897i	−0.0710744	−	0.155631i
$413$	2.64650	−	5.02730i	0.130226	−	0.247377i
$414$	4.51072	+	1.62893i	0.221690	+	0.0800576i
$415$	1.05049	−	1.81951i	0.0515668	−	0.0893163i
$416$	0.662566	+	0.471811i	0.0324850	+	0.0231324i
$417$	−9.33667	−	8.90249i	−0.457218	−	0.435957i
$418$	19.5992	−	6.78336i	0.958630	−	0.331785i
$419$	−22.0842	−	14.1927i	−1.07888	−	0.693357i	−0.124585	−	0.992209i	$-0.539760\pi$
$419$	−22.0842	−	14.1927i	−1.07888	−	0.693357i	−0.954300	+	0.298852i	$0.903396\pi$
$420$	4.09233	−	0.955748i	0.199685	−	0.0466357i
$421$	22.6922	−	3.26265i	1.10595	−	0.159012i	0.434940	−	0.900459i	$-0.356770\pi$
$421$	22.6922	−	3.26265i	1.10595	−	0.159012i	0.671011	+	0.741448i	$0.265861\pi$
$422$	16.3449	−	15.5848i	0.795658	−	0.758659i
$423$	4.41493	−	8.56377i	0.214661	−	0.416385i
$424$	2.90075	+	7.24574i	0.140873	+	0.351884i
$425$	−1.86798	−	2.62322i	−0.0906105	−	0.127245i
$426$	1.75562	+	0.801764i	0.0850600	+	0.0388456i
$427$	9.23197	+	0.961413i	0.446766	+	0.0465260i
$428$	−3.00378	−	4.67397i	−0.145193	−	0.225925i
$429$	−1.68048	−	1.76244i	−0.0811343	−	0.0850912i
$430$	2.32954	+	2.96226i	0.112341	+	0.142853i
$431$	−21.9670	−	7.60286i	−1.05811	−	0.366217i	−0.258050	−	0.966131i	$-0.583080\pi$
$431$	−21.9670	−	7.60286i	−1.05811	−	0.366217i	−0.800064	+	0.599914i	$0.795201\pi$
$432$	0.458227	+	0.888835i	0.0220464	+	0.0427641i
$433$	−20.2970	+	23.4240i	−0.975411	+	1.12568i	0.0166417	+	0.999862i	$0.494703\pi$
$433$	−20.2970	+	23.4240i	−0.975411	+	1.12568i	−0.992053	+	0.125823i	$0.959843\pi$
$434$	−17.2061	−	15.1692i	−0.825921	−	0.728144i
$435$	9.58805	−	4.37872i	0.459712	−	0.209943i
$436$	7.69669	+	4.44369i	0.368605	+	0.212814i
$437$	33.2031	−	1.13759i	1.58832	−	0.0544184i
$438$	4.53462	+	7.85419i	0.216673	+	0.375288i
$439$	−1.64527	+	17.2300i	−0.0785242	+	0.822343i	0.867326	+	0.497740i	$0.165837\pi$
$439$	−1.64527	+	17.2300i	−0.0785242	+	0.822343i	−0.945850	+	0.324603i	$0.894769\pi$
$440$	−1.33976	−	4.56281i	−0.0638707	−	0.217524i
$441$	6.95588	+	0.784666i	0.331232	+	0.0373650i
$442$	−0.571707	+	0.889594i	−0.0271933	+	0.0423137i
$443$	9.38744	−	1.80928i	0.446011	−	0.0859615i	0.0386994	−	0.999251i	$-0.487679\pi$
$443$	9.38744	−	1.80928i	0.446011	−	0.0859615i	0.407311	+	0.913289i	$0.366466\pi$
$444$	1.09611	−	0.861989i	0.0520190	−	0.0409082i
$445$	3.93019	+	16.2005i	0.186309	+	0.767976i
$446$	1.99395	−	0.0949838i	0.0944165	−	0.00449761i
$447$	−3.42163	+	23.7980i	−0.161838	+	1.12561i
$448$	0.354084	+	2.62195i	0.0167289	+	0.123876i
$449$	−11.0998	+	24.3052i	−0.523833	+	1.14703i	0.444135	+	0.895960i	$0.353511\pi$
$449$	−11.0998	+	24.3052i	−0.523833	+	1.14703i	−0.967968	+	0.251074i	$0.919216\pi$
$450$	1.94710	+	1.53121i	0.0917870	+	0.0721821i
$451$	−8.73195	−	4.50163i	−0.411172	−	0.211974i
$452$	5.93082	−	1.43880i	0.278962	−	0.0676755i
$453$	3.46998	−	8.66760i	0.163034	−	0.407239i
$454$	18.2813	+	21.0978i	0.857986	+	0.990168i
$455$	−2.94552	−	1.73441i	−0.138088	−	0.0813102i
$456$	5.23538	+	4.53648i	0.245169	+	0.212440i
$457$	−9.73017	−	2.36051i	−0.455158	−	0.110420i	0.00162406	−	0.999999i	$-0.499483\pi$
$457$	−9.73017	−	2.36051i	−0.455158	−	0.110420i	−0.456782	+	0.889578i	$0.650998\pi$
$458$	13.1275	−	18.4350i	0.613407	−	0.861410i
$459$	−1.12589	+	0.650036i	−0.0525523	+	0.0303411i
$460$	0.101705	−	7.61692i	0.00474202	−	0.355141i
$461$		−	4.21696i		−	0.196404i	−0.995167	−	0.0982018i	$-0.968691\pi$
$461$		−	4.21696i		−	0.196404i	0.995167	−	0.0982018i	$-0.0313091\pi$
$462$	0.444660	−	7.90862i	0.0206874	−	0.367942i
$463$	33.3165	−	9.78262i	1.54835	−	0.454637i	0.607743	−	0.794133i	$-0.292075\pi$
$463$	33.3165	−	9.78262i	1.54835	−	0.454637i	0.940607	+	0.339497i	$0.110257\pi$
$464$	2.17044	+	6.27109i	0.100760	+	0.291128i
$465$	−0.655245	+	13.7553i	−0.0303863	+	0.637886i
$466$	−4.75859	+	13.7491i	−0.220438	+	0.636913i
$467$	11.8725	+	4.75304i	0.549394	+	0.219944i	0.629717	−	0.776825i	$-0.283171\pi$
$467$	11.8725	+	4.75304i	0.549394	+	0.219944i	−0.0803227	+	0.996769i	$0.525595\pi$
$468$	0.229158	−	0.780440i	0.0105928	−	0.0360758i
$469$	0.408893	+	4.70796i	0.0188809	+	0.217393i
$470$	−15.1480	−	2.17795i	−0.698724	−	0.100461i
$471$	−12.5281	+	8.92125i	−0.577266	+	0.411069i
$472$	−0.204118	−	2.13762i	−0.00939531	−	0.0983921i
$473$	6.59437	−	2.63999i	0.303210	−	0.121387i
$474$	0.0484519	+	1.01713i	0.00222547	+	0.0467184i
$475$	16.4644	+	4.83440i	0.755441	+	0.221817i
$476$	−3.38296	+	0.622007i	−0.155058	+	0.0285096i
$477$	5.89848	−	5.11106i	0.270073	−	0.234020i
$478$	−18.2954	+	9.43193i	−0.836812	+	0.431406i
$479$	16.8323	+	3.24416i	0.769088	+	0.148230i	0.558679	−	0.829384i	$-0.311308\pi$
$479$	16.8323	+	3.24416i	0.769088	+	0.148230i	0.210409	+	0.977613i	$0.432520\pi$
$480$	1.09611	−	1.14956i	0.0500302	−	0.0524702i
$481$	−1.12909	−	0.107815i	−0.0514821	−	0.00491594i
$482$	−6.17385			−0.281211
$483$	4.41182	−	11.8969i	0.200745	−	0.541327i
$484$	2.03658			0.0925719
$485$	−4.05445	−	0.387153i	−0.184103	−	0.0175797i
$486$	0.690079	−	0.723734i	0.0313026	−	0.0328292i
$487$	−5.25997	−	1.01378i	−0.238352	−	0.0459386i	0.0686763	−	0.997639i	$-0.478122\pi$
$487$	−5.25997	−	1.01378i	−0.238352	−	0.0459386i	−0.307028	+	0.951700i	$0.599335\pi$
$488$	3.11824	−	1.60756i	0.141156	−	0.0727709i
$489$	−19.0071	+	16.4698i	−0.859532	+	0.744789i
$490$	−2.43584	−	10.8486i	−0.110040	−	0.490088i
$491$	−27.7816	−	8.15740i	−1.25376	−	0.368138i	−0.413594	−	0.910461i	$-0.635727\pi$
$491$	−27.7816	−	8.15740i	−1.25376	−	0.368138i	−0.840170	+	0.542323i	$0.817545\pi$
$492$	−0.156133	−	3.27764i	−0.00703903	−	0.147767i
$493$	−8.00936	+	3.20647i	−0.360724	+	0.144412i
$494$	−0.535608	−	5.60914i	−0.0240982	−	0.252367i
$495$	−3.87367	+	2.75843i	−0.174108	+	0.123982i
$496$	−8.58153	−	1.23384i	−0.385322	−	0.0554009i
$497$	2.16098	−	4.62659i	0.0969330	−	0.207531i
$498$	0.372655	−	1.26915i	0.0166991	−	0.0568718i
$499$	−12.5334	−	5.01762i	−0.561072	−	0.224620i	0.0737511	−	0.997277i	$-0.476503\pi$
$499$	−12.5334	−	5.01762i	−0.561072	−	0.224620i	−0.634824	+	0.772657i	$0.718927\pi$
$500$	3.88439	−	11.2232i	0.173715	−	0.501917i
$501$	0.686691	−	14.4154i	0.0306791	−	0.644033i
$502$	−0.955230	−	2.75996i	−0.0426340	−	0.123183i
$503$	19.1169	−	5.61324i	0.852382	−	0.250282i	0.173777	−	0.984785i	$-0.444403\pi$
$503$	19.1169	−	5.61324i	0.852382	−	0.250282i	0.678605	+	0.734503i	$0.262585\pi$
$504$	2.36194	−	1.19217i	0.105209	−	0.0531033i
$505$		−	2.91408i		−	0.129675i
$506$	−13.7214	−	4.22875i	−0.609990	−	0.187991i
$507$	10.6854	−	6.16920i	0.474554	−	0.273984i
$508$	10.1364	−	14.2345i	0.449728	−	0.631555i
$509$	−40.5270	−	9.83174i	−1.79633	−	0.435784i	−0.808134	−	0.588998i	$-0.799523\pi$
$509$	−40.5270	−	9.83174i	−1.79633	−	0.435784i	−0.988193	+	0.153214i	$0.951038\pi$
$510$	1.56063	+	1.35229i	0.0691057	+	0.0598805i
$511$	20.8822	−	11.8190i	0.923776	−	0.522844i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	2.57465	−	6.43117i	0.113674	−	0.283943i
$514$	9.92223	−	2.40711i	0.437651	−	0.106173i
$515$	4.90292	+	2.52763i	0.216049	+	0.111381i
$516$	1.86496	+	1.46662i	0.0821001	+	0.0645642i
$517$	−11.9829	+	26.2389i	−0.527008	+	1.15399i
$518$	−2.25569	−	2.91946i	−0.0991091	−	0.128274i
$519$	0.448366	−	3.11846i	0.0196811	−	0.136885i
$520$	−1.29050	+	0.0614743i	−0.0565924	+	0.00269583i
$521$	−5.72172	−	23.5853i	−0.250673	−	1.03329i	−0.948438	−	0.316962i	$-0.897337\pi$
$521$	−5.72172	−	23.5853i	−0.250673	−	1.03329i	0.697765	−	0.716327i	$-0.254178\pi$
$522$	5.21630	−	4.10214i	0.228311	−	0.179546i
$523$	−30.7025	+	5.91743i	−1.34253	+	0.258751i	−0.809387	−	0.587276i	$-0.800200\pi$
$523$	−30.7025	+	5.91743i	−1.34253	+	0.258751i	−0.533141	+	0.846027i	$0.678988\pi$
$524$	−0.814430	+	1.26728i	−0.0355785	+	0.0553613i
$525$	4.09519	−	5.11664i	0.178729	−	0.223308i
$526$	−1.82557	−	6.21732i	−0.0795986	−	0.271088i
$527$	1.07141	−	11.2203i	0.0466712	−	0.488763i
$528$	−1.49695	−	2.59279i	−0.0651463	−	0.112837i
$529$	−19.0099	−	12.9469i	−0.826518	−	0.562910i
$530$	−10.7361	−	6.19850i	−0.466347	−	0.269246i
$531$	−1.95330	+	0.892041i	−0.0847658	+	0.0387113i
$532$	12.1206	−	13.7482i	0.525495	−	0.596060i
$533$	−1.74783	+	2.01711i	−0.0757070	+	0.0873706i
$534$	4.80919	+	9.32853i	0.208114	+	0.403685i
$535$	8.33961	+	2.88637i	0.360553	+	0.124789i
$536$	1.10412	+	1.40400i	0.0476907	+	0.0606436i
$537$	−8.31827	−	8.72395i	−0.358960	−	0.376466i
$538$	16.4092	+	25.5332i	0.707452	+	1.10082i
$539$	−20.9134	−	1.35564i	−0.900803	−	0.0583917i
$540$	−1.44484	−	0.659836i	−0.0621760	−	0.0283948i
$541$	24.0850	+	33.8226i	1.03549	+	1.45415i	0.885030	+	0.465533i	$0.154137\pi$
$541$	24.0850	+	33.8226i	1.03549	+	1.45415i	0.150464	+	0.988615i	$0.451923\pi$
$542$	−6.10749	−	15.2558i	−0.262339	−	0.655291i
$543$	−2.91544	+	5.65517i	−0.125114	+	0.242687i
$544$	−0.940906	+	0.897152i	−0.0403410	+	0.0384651i
$545$	−13.9728	+	2.00899i	−0.598530	+	0.0860556i
$546$	−2.05958	−	0.623959i	−0.0881419	−	0.0267030i
$547$	−9.83375	−	6.31977i	−0.420461	−	0.270214i	0.313257	−	0.949669i	$-0.398580\pi$
$547$	−9.83375	−	6.31977i	−0.420461	−	0.270214i	−0.733717	+	0.679455i	$0.762216\pi$
$548$	6.06557	−	2.09931i	0.259108	−	0.0896782i
$549$	−2.53902	−	2.42095i	−0.108363	−	0.103324i
$550$	−6.04093	−	4.30173i	−0.257586	−	0.183426i
$551$	22.9853	−	39.8118i	0.979208	−	1.69604i
$552$	−1.06833	−	4.67532i	−0.0454713	−	0.198995i
$553$	2.69208	−	0.105136i	0.114479	−	0.00447085i
$554$	10.3769	+	22.7223i	0.440873	+	0.965378i
$555$	−0.522184	+	2.15247i	−0.0221655	+	0.0913674i
$556$	−2.44147	+	12.6676i	−0.103541	+	0.537224i
$557$	20.1044	+	0.957690i	0.851850	+	0.0405786i	0.468965	−	0.883217i	$-0.344627\pi$
$557$	20.1044	+	0.957690i	0.851850	+	0.0405786i	0.382886	+	0.923796i	$0.374930\pi$
$558$	1.64077	+	8.51310i	0.0694591	+	0.360388i
$559$	−0.274640	−	1.91017i	−0.0116161	−	0.0807914i
$560$	−3.01651	−	2.92597i	−0.127471	−	0.123645i
$561$	3.27439	−	2.10432i	0.138245	−	0.0888447i
$562$	2.61359	−	3.32345i	0.110247	−	0.140191i
$563$	7.47074	−	0.713370i	0.314854	−	0.0300649i	0.0635673	−	0.997978i	$-0.479752\pi$
$563$	7.47074	−	0.713370i	0.314854	−	0.0300649i	0.251287	+	0.967913i	$0.419146\pi$
$564$	−9.59119	+	0.915848i	−0.403862	+	0.0385642i
$565$	−5.99221	+	7.61971i	−0.252094	+	0.320564i
$566$	−4.75435	+	3.05544i	−0.199840	+	0.128430i
$567$	−1.89911	−	1.84211i	−0.0797552	−	0.0773614i
$568$	−0.274672	−	1.91039i	−0.0115250	−	0.0801580i
$569$	4.98024	+	25.8399i	0.208782	+	1.08327i	0.923426	+	0.383777i	$0.125377\pi$
$569$	4.98024	+	25.8399i	0.208782	+	1.08327i	−0.714643	+	0.699489i	$0.753411\pi$
$570$	−10.9909	−	0.523559i	−0.460357	−	0.0219295i
$571$	−0.808071	+	4.19267i	−0.0338167	+	0.175458i	−0.994910	−	0.100766i	$-0.967871\pi$
$571$	−0.808071	+	4.19267i	−0.0338167	+	0.175458i	0.961093	+	0.276223i	$0.0890829\pi$
$572$	−0.574120	+	2.36655i	−0.0240052	+	0.0989506i
$573$	−0.538858	−	1.17994i	−0.0225111	−	0.0492925i
$574$	−8.67504	+	0.338795i	−0.362089	+	0.0141410i
$575$	−7.21811	−	9.43515i	−0.301016	−	0.393473i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−20.7344	−	14.7649i	−0.863186	−	0.614672i	0.0603525	−	0.998177i	$-0.480778\pi$
$577$	−20.7344	−	14.7649i	−0.863186	−	0.614672i	−0.923539	+	0.383505i	$0.874717\pi$
$578$	11.0802	+	10.5650i	0.460877	+	0.439445i
$579$	15.9089	−	5.50613i	0.661153	−	0.228827i
$580$	−8.86730	−	5.69867i	−0.368195	−	0.236624i
$581$	−3.34928	−	1.01468i	−0.138951	−	0.0420959i
$582$	−2.53808	+	0.364921i	−0.105207	+	0.0151265i
$583$	−16.9113	+	16.1249i	−0.700396	+	0.667827i
$584$	4.15577	−	8.06106i	0.171967	−	0.333569i
$585$	0.480176	+	1.19942i	0.0198528	+	0.0495900i
$586$	−15.7704	−	22.1465i	−0.651470	−	0.914862i
$587$	−1.13584	−	0.518723i	−0.0468813	−	0.0214100i	0.391836	−	0.920035i	$-0.371840\pi$
$587$	−1.13584	−	0.518723i	−0.0468813	−	0.0214100i	−0.438718	+	0.898625i	$0.644567\pi$
$588$	−3.10053	−	6.27588i	−0.127864	−	0.258813i
$589$	32.4703	+	50.5248i	1.33792	+	2.08184i
$590$	2.35372	+	2.46851i	0.0969012	+	0.101627i
$591$	11.0029	+	13.9913i	0.452598	+	0.575526i
$592$	−1.31775	−	0.456079i	−0.0541593	−	0.0187447i
$593$	0.986256	+	1.91307i	0.0405007	+	0.0785604i	0.908217	−	0.418499i	$-0.137444\pi$
$593$	0.986256	+	1.91307i	0.0405007	+	0.0785604i	−0.867717	+	0.497059i	$0.834413\pi$
$594$	−1.96059	+	2.26264i	−0.0804438	+	0.0928371i
$595$	3.61306	−	4.09823i	0.148121	−	0.168011i
$596$	21.8700	−	9.98769i	0.895830	−	0.409112i
$597$	−8.63243	−	4.98394i	−0.353302	−	0.203979i
$598$	−1.99537	+	3.35191i	−0.0815966	+	0.137070i
$599$	19.6621	+	34.0558i	0.803373	+	1.39148i	0.917384	+	0.398004i	$0.130297\pi$
$599$	19.6621	+	34.0558i	0.803373	+	1.39148i	−0.114010	+	0.993480i	$0.536370\pi$
$600$	0.235459	−	2.46584i	0.00961257	−	0.100667i
$601$	10.9461	+	37.2789i	0.446500	+	1.52064i	0.808521	+	0.588468i	$0.200269\pi$
$601$	10.9461	+	37.2789i	0.446500	+	1.52064i	−0.362021	+	0.932170i	$0.617913\pi$
$602$	3.92243	−	4.90079i	0.159866	−	0.199741i
$603$	0.965660	−	1.50260i	0.0393247	−	0.0611905i
$604$	−9.16766	+	1.76692i	−0.373027	+	0.0718950i
$605$	−2.54277	+	1.99966i	−0.103378	+	0.0812977i
$606$	−0.432530	−	1.78291i	−0.0175703	−	0.0724259i
$607$	−10.6635	+	0.507966i	−0.432819	+	0.0206177i	−0.262861	−	0.964834i	$-0.584666\pi$
$607$	−10.6635	+	0.507966i	−0.432819	+	0.0206177i	−0.169958	+	0.985451i	$0.554363\pi$
$608$	0.985871	−	6.85689i	0.0399824	−	0.278083i
$609$	−10.7346	−	13.8935i	−0.434990	−	0.562993i
$610$	−2.31486	+	5.06883i	−0.0937258	+	0.205231i
$611$	6.16018	+	4.84442i	0.249214	+	0.195984i
$612$	1.15555	+	0.595727i	0.0467103	+	0.0240808i
$613$	4.76910	−	1.15697i	0.192622	−	0.0467296i	−0.138287	−	0.990392i	$-0.544160\pi$
$613$	4.76910	−	1.15697i	0.192622	−	0.0467296i	0.330909	+	0.943663i	$0.392645\pi$
$614$	−0.844418	+	2.10925i	−0.0340779	+	0.0851226i
$615$	3.41316	+	3.93899i	0.137632	+	0.158835i
$616$	−6.89355	+	3.90165i	−0.277749	+	0.157202i
$617$	−15.7934	−	13.6850i	−0.635818	−	0.550939i	0.276195	−	0.961102i	$-0.410927\pi$
$617$	−15.7934	−	13.6850i	−0.635818	−	0.550939i	−0.912013	+	0.410162i	$0.865472\pi$
$618$	3.37491	+	0.818743i	0.135759	+	0.0329347i
$619$	−20.7248	+	29.1040i	−0.833002	+	1.16979i	0.150450	+	0.988618i	$0.451928\pi$
$619$	−20.7248	+	29.1040i	−0.833002	+	1.16979i	−0.983452	+	0.181170i	$0.942012\pi$
$620$	11.9259	−	6.88544i	0.478957	−	0.276526i
$621$	−4.06877	+	2.53873i	−0.163274	+	0.101876i
$622$			12.6435i			0.506958i
$623$	24.7890	−	12.5120i	0.993152	−	0.501284i
$624$	−0.780440	+	0.229158i	−0.0312426	+	0.00917365i
$625$	2.11905	+	6.12260i	0.0847622	+	0.244904i
$626$	0.668853	−	14.0410i	0.0267327	−	0.561189i
$627$	−6.78336	+	19.5992i	−0.270901	+	0.782718i
$628$	14.2783	+	5.71615i	0.569764	+	0.228099i
$629$	0.510747	−	1.73945i	0.0203648	−	0.0693562i
$630$	−1.77844	+	3.80759i	−0.0708548	+	0.151698i
$631$	−29.1948	−	4.19758i	−1.16223	−	0.167103i	−0.465906	−	0.884834i	$-0.654272\pi$
$631$	−29.1948	−	4.19758i	−1.16223	−	0.167103i	−0.696320	+	0.717731i	$0.745181\pi$
$632$	0.829470	−	0.590663i	0.0329945	−	0.0234953i
$633$	2.14676	+	22.4819i	0.0853261	+	0.893575i
$634$	13.5288	−	5.41612i	0.537298	−	0.215102i
$635$	1.32071	+	27.7251i	0.0524108	+	1.10024i
$636$	−7.48866	−	2.19887i	−0.296945	−	0.0871908i
$637$	−1.69745	+	5.43480i	−0.0672556	+	0.215335i
$638$	−15.0150	+	13.0106i	−0.594450	+	0.515094i
$639$	−1.71548	+	0.884391i	−0.0678633	+	0.0349860i
$640$	−1.55967	−	0.300603i	−0.0616516	−	0.0118824i
$641$	−11.1690	+	11.7137i	−0.441149	+	0.462663i	−0.906342	−	0.422546i	$-0.861137\pi$
$641$	−11.1690	+	11.7137i	−0.441149	+	0.462663i	0.465193	+	0.885209i	$0.345985\pi$
$642$	5.53081	+	0.528128i	0.218284	+	0.0208435i
$643$	21.7253			0.856764			0.428382	−	0.903598i	$-0.359084\pi$
$643$	21.7253			0.856764			0.428382	+	0.903598i	$0.359084\pi$
$644$	−12.3935	+	2.72049i	−0.488372	+	0.107202i
$645$	−3.76852			−0.148385
$646$	8.96533	+	0.856085i	0.352736	+	0.0336822i
$647$	14.9452	−	15.6741i	0.587557	−	0.616212i	−0.361097	−	0.932528i	$-0.617598\pi$
$647$	14.9452	−	15.6741i	0.587557	−	0.616212i	0.948654	+	0.316316i	$0.102446\pi$
$648$	−0.981929	−	0.189251i	−0.0385738	−	0.00743449i
$649$	5.71427	−	2.94591i	0.224305	−	0.115637i
$650$	−1.52269	+	1.31942i	−0.0597247	+	0.0517518i
$651$	22.5599	−	4.14797i	0.884192	−	0.162572i
$652$	24.1313	+	7.08558i	0.945054	+	0.277493i
$653$	−2.30903	−	48.4726i	−0.0903595	−	1.89688i	−0.358546	−	0.933512i	$-0.616727\pi$
$653$	−2.30903	−	48.4726i	−0.0903595	−	1.89688i	0.268187	−	0.963367i	$-0.413576\pi$
$654$	−8.25075	+	3.30310i	−0.322630	+	0.129162i
$655$	−0.227446	−	2.38192i	−0.00888706	−	0.0930695i
$656$	−2.67291	+	1.90337i	−0.104360	+	0.0743142i
$657$	−8.97693	−	1.29069i	−0.350223	−	0.0503545i
$658$	2.20566	+	25.3957i	0.0859855	+	0.990029i
$659$	−5.53065	+	18.8357i	−0.215444	+	0.733734i	0.778865	+	0.627192i	$0.215796\pi$
$659$	−5.53065	+	18.8357i	−0.215444	+	0.733734i	−0.994308	+	0.106542i	$0.966022\pi$
$660$	4.41480	+	1.76742i	0.171846	+	0.0687967i
$661$	10.8630	−	31.3866i	0.422522	−	1.22080i	−0.510155	−	0.860082i	$-0.670412\pi$
$661$	10.8630	−	31.3866i	0.422522	−	1.22080i	0.932677	−	0.360713i	$-0.117467\pi$
$662$	0.760469	−	15.9642i	0.0295565	−	0.620467i
$663$	−0.345862	−	0.999302i	−0.0134322	−	0.0388097i
$664$	−1.26915	+	0.372655i	−0.0492524	+	0.0144618i
$665$	−1.63424	+	29.0662i	−0.0633730	+	1.12714i
$666$			1.39445i			0.0540337i
$667$	−29.1234	+	12.8331i	−1.12766	+	0.496899i
$668$	−12.4983	+	7.21588i	−0.483573	+	0.279191i
$669$	−1.15792	+	1.62607i	−0.0447677	+	0.0628675i
$670$	−2.75709	−	0.668864i	−0.106516	−	0.0258405i
$671$	7.93784	+	6.87818i	0.306437	+	0.265529i
$672$	−2.27987	−	1.34245i	−0.0879480	−	0.0517863i
$673$	24.9187	+	28.7577i	0.960546	+	1.10853i	0.994032	+	0.109090i	$0.0347938\pi$
$673$	24.9187	+	28.7577i	0.960546	+	1.10853i	−0.0334856	+	0.999439i	$0.510661\pi$
$674$	4.14704	−	10.3588i	0.159738	−	0.399007i
$675$	−2.40723	+	0.583987i	−0.0926543	+	0.0224777i
$676$	−10.9668	−	5.65378i	−0.421800	−	0.217453i
$677$	−28.1940	−	22.1720i	−1.08358	−	0.852139i	−0.0939235	−	0.995579i	$-0.529941\pi$
$677$	−28.1940	−	22.1720i	−1.08358	−	0.852139i	−0.989659	+	0.143441i	$0.954183\pi$
$678$	−2.53522	+	5.55135i	−0.0973644	+	0.213198i
$679$	0.907936	+	6.72316i	0.0348434	+	0.258011i
$680$	0.293881	−	2.04399i	0.0112698	−	0.0783833i
$681$	−27.8847	+	1.32831i	−1.06855	+	0.0509011i
$682$	−6.11946	−	25.2247i	−0.234326	−	0.965905i
$683$	−7.38865	+	5.81050i	−0.282719	+	0.222332i	−0.749440	−	0.662072i	$-0.769677\pi$
$683$	−7.38865	+	5.81050i	−0.282719	+	0.222332i	0.466722	+	0.884404i	$0.345435\pi$
$684$	−6.80221	+	1.31102i	−0.260089	+	0.0501280i
$685$	−5.51191	+	8.57670i	−0.210599	+	0.327699i
$686$	−16.6741	+	8.06071i	−0.636619	+	0.307759i
$687$	6.37600	+	21.7147i	0.243260	+	0.828466i
$688$	0.225526	−	2.36181i	0.00859809	−	0.0900433i
$689$	3.17417	+	5.49782i	0.120926	+	0.209450i
$690$	5.92443	+	4.78841i	0.225539	+	0.182292i
$691$	31.2647	+	18.0507i	1.18936	+	0.686679i	0.958162	−	0.286226i	$-0.0924009\pi$
$691$	31.2647	+	18.0507i	1.18936	+	0.686679i	0.231202	+	0.972906i	$0.425734\pi$
$692$	−2.86582	+	1.30878i	−0.108942	+	0.0497522i
$693$	5.94172	+	5.23831i	0.225707	+	0.198987i
$694$	−12.1969	+	14.0759i	−0.462987	+	0.534315i
$695$	−9.38960	−	18.2133i	−0.356168	−	0.690869i
$696$	−6.27109	−	2.17044i	−0.237705	−	0.0822705i
$697$	−2.63706	−	3.35330i	−0.0998859	−	0.127015i
$698$	10.7140	+	11.2366i	0.405532	+	0.425310i
$699$	−7.86592	−	12.2396i	−0.297516	−	0.462944i
$700$	−6.51842	−	0.678825i	−0.246373	−	0.0256572i
$701$	−37.5158	−	17.1329i	−1.41695	−	0.647100i	−0.447928	−	0.894070i	$-0.647838\pi$
$701$	−37.5158	−	17.1329i	−1.41695	−	0.647100i	−0.969023	+	0.246970i	$0.920565\pi$
$702$	0.471811	+	0.662566i	0.0178074	+	0.0250069i
$703$	3.59021	+	8.96792i	0.135408	+	0.338232i
$704$	−1.37188	+	2.66108i	−0.0517048	+	0.100293i
$705$	11.0758	−	10.5608i	0.417140	−	0.397742i
$706$	−2.20946	+	0.317672i	−0.0831539	+	0.0119557i
$707$	−4.72677	+	1.10392i	−0.177769	+	0.0415172i
$708$	1.80646	+	1.16094i	0.0678911	+	0.0436309i
$709$	24.3827	−	8.43893i	0.915711	−	0.316931i	0.171740	−	0.985142i	$-0.445061\pi$
$709$	24.3827	−	8.43893i	0.915711	−	0.316931i	0.743971	+	0.668212i	$0.232940\pi$
$710$	2.21869	+	2.11552i	0.0832661	+	0.0793940i
$711$	−0.829470	−	0.590663i	−0.0311076	−	0.0221516i
$712$	5.24761	−	9.08913i	0.196663	−	0.340630i
$713$	2.53272	−	41.5016i	0.0948513	−	1.55425i
$714$	1.60228	−	3.04368i	0.0599637	−	0.113907i
$715$	−1.60683	−	3.51847i	−0.0600921	−	0.131583i
$716$	−2.84186	+	11.7143i	−0.106205	+	0.437784i
$717$	3.89546	−	20.2116i	0.145479	−	0.754815i
$718$	−18.7193	−	0.891710i	−0.698598	−	0.0332783i
$719$	9.56415	+	49.6235i	0.356683	+	1.85065i	0.506916	+	0.861995i	$0.330785\pi$
$719$	9.56415	+	49.6235i	0.356683	+	1.85065i	−0.150234	+	0.988651i	$0.548003\pi$
$720$	0.226050	+	1.57221i	0.00842438	+	0.0585929i
$721$	2.24260	−	8.91028i	0.0835186	−	0.331836i
$722$	−24.3869	+	15.6725i	−0.907588	+	0.583271i
$723$	3.81642	−	4.85298i	0.141934	−	0.180484i
$724$	6.33364	−	0.604790i	0.235388	−	0.0224768i
$725$	−16.3635	+	1.56252i	−0.607724	+	0.0580306i
$726$	−1.25893	+	1.60086i	−0.0467233	+	0.0594136i
$727$	11.7184	−	7.53095i	0.434611	−	0.279308i	−0.304987	−	0.952357i	$-0.598652\pi$
$727$	11.7184	−	7.53095i	0.434611	−	0.279308i	0.739598	+	0.673049i	$0.235016\pi$
$728$	0.588586	+	2.06997i	0.0218144	+	0.0767181i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	2.72624	+	14.1451i	0.100903	+	0.523532i
$731$	3.08100	+	0.146766i	0.113955	+	0.00542834i
$732$	−0.663936	+	3.44483i	−0.0245398	+	0.127325i
$733$	2.54371	−	10.4853i	0.0939542	−	0.387284i	−0.905347	−	0.424673i	$-0.860389\pi$
$733$	2.54371	−	10.4853i	0.0939542	−	0.387284i	0.999301	+	0.0373890i	$0.0119041\pi$
$734$	−10.4254	−	22.8285i	−0.384809	−	0.842614i
$735$	10.0333	+	4.79143i	0.370083	+	0.176735i
$736$	−3.35555	+	3.42641i	−0.123687	+	0.126299i
$737$	−2.67376	+	4.63109i	−0.0984892	+	0.170588i
$738$	2.67291	+	1.90337i	0.0983913	+	0.0700641i
$739$	−8.97777	−	8.56029i	−0.330253	−	0.314895i	0.506751	−	0.862092i	$-0.330846\pi$
$739$	−8.97777	−	8.56029i	−0.330253	−	0.314895i	−0.837004	+	0.547197i	$0.815695\pi$
$740$	2.09309	−	0.724426i	0.0769435	−	0.0266304i
$741$	4.74018	+	3.04633i	0.174135	+	0.111910i
$742$	−5.98716	+	19.7626i	−0.219796	+	0.725507i
$743$	−39.8650	+	5.73172i	−1.46250	+	0.210276i	−0.827166	−	0.561957i	$-0.810049\pi$
$743$	−39.8650	+	5.73172i	−1.46250	+	0.210276i	−0.635339	+	0.772234i	$0.719139\pi$
$744$	6.27461	−	5.98283i	0.230038	−	0.219341i
$745$	−17.4992	+	33.9436i	−0.641120	+	1.24360i
$746$	−12.6284	−	31.5442i	−0.462358	−	1.15492i
$747$	0.767256	+	1.07746i	0.0280724	+	0.0394222i
$748$	−3.54054	−	1.61691i	−0.129455	−	0.0591201i
$749$	1.52259	−	14.6206i	0.0556341	−	0.534226i
$750$	6.42086	+	9.99106i	0.234457	+	0.364822i
$751$	25.9983	+	27.2662i	0.948690	+	0.994957i	0.999993	−	0.00372603i	$-0.00118604\pi$
$751$	25.9983	+	27.2662i	0.948690	+	0.994957i	−0.0513034	+	0.998683i	$0.516338\pi$
$752$	5.95585	+	7.57348i	0.217188	+	0.276176i
$753$	2.75996	+	0.955230i	0.100578	+	0.0348105i
$754$	2.47337	+	4.79766i	0.0900747	+	0.174721i
$755$	9.71139	−	11.2075i	0.353434	−	0.407884i
$756$	−0.522946	+	2.59355i	−0.0190194	+	0.0943267i
$757$	22.8942	−	10.4554i	0.832104	−	0.380009i	0.0466361	−	0.998912i	$-0.485150\pi$
$757$	22.8942	−	10.4554i	0.832104	−	0.380009i	0.785467	+	0.618903i	$0.212423\pi$
$758$	−7.07712	−	4.08598i	−0.257053	−	0.148409i
$759$	11.8060	−	8.17169i	0.428531	−	0.296614i
$760$	5.50166	+	9.52916i	0.199566	+	0.345659i
$761$	3.03245	−	31.7572i	0.109926	−	1.15120i	−0.757225	−	0.653154i	$-0.773446\pi$
$761$	3.03245	−	31.7572i	0.109926	−	1.15120i	0.867152	−	0.498044i	$-0.165948\pi$
$762$	4.92321	+	16.7669i	0.178349	+	0.607401i
$763$	8.55189	+	21.9035i	0.309599	+	0.792960i
$764$	−0.701296	+	1.09124i	−0.0253720	+	0.0394796i
$765$	−2.02769	+	0.390805i	−0.0733112	+	0.0141296i
$766$	−20.0483	+	15.7662i	−0.724375	+	0.569655i
$767$	−0.411783	−	1.69739i	−0.0148686	−	0.0612893i
$768$	−0.998867	+	0.0475819i	−0.0360435	+	0.00171696i
$769$	−3.59512	+	25.0046i	−0.129644	+	0.901690i	0.816362	+	0.577540i	$0.195987\pi$
$769$	−3.59512	+	25.0046i	−0.129644	+	0.901690i	−0.946006	+	0.324150i	$0.894922\pi$
$770$	4.77603	−	11.6400i	0.172116	−	0.419476i
$771$	−4.24140	+	9.28737i	−0.152750	+	0.334476i
$772$	−13.2331	−	10.4066i	−0.476269	−	0.374542i
$773$	24.2365	+	12.4948i	0.871726	+	0.449406i	0.835213	−	0.549927i	$-0.185345\pi$
$773$	24.2365	+	12.4948i	0.871726	+	0.449406i	0.0365134	+	0.999333i	$0.488375\pi$
$774$	−2.30568	+	0.559351i	−0.0828759	+	0.0201055i
$775$	7.98163	−	19.9372i	0.286709	−	0.716164i
$776$	1.67918	+	1.93788i	0.0602791	+	0.0695658i
$777$	3.68922	+	0.0316016i	0.132350	+	0.00113370i
$778$	3.67142	+	3.18130i	0.131627	+	0.114055i
$779$	22.0905	+	5.35909i	0.791474	+	0.192009i
$780$	0.749415	−	1.05241i	0.0268334	−	0.0376822i
$781$	5.00417	−	2.88916i	0.179063	−	0.103382i
$782$	−4.65711	−	4.14555i	−0.166538	−	0.148245i
$783$			6.63607i			0.237154i
$784$	−3.60333	+	6.00133i	−0.128691	+	0.214333i
$785$	−23.4396	+	6.88250i	−0.836597	+	0.245647i
$786$	−0.492700	−	1.42356i	−0.0175740	−	0.0507769i
$787$	2.47519	−	51.9607i	0.0882311	−	1.85220i	−0.330152	−	0.943928i	$-0.607100\pi$
$787$	2.47519	−	51.9607i	0.0882311	−	1.85220i	0.418383	−	0.908270i	$-0.362597\pi$
$788$	5.82163	−	16.8205i	0.207387	−	0.599205i
$789$	6.01563	+	2.40830i	0.214162	+	0.0857376i
$790$	−0.455680	+	1.55190i	−0.0162124	+	0.0552143i
$791$	14.6295	+	6.83311i	0.520165	+	0.242957i
$792$	2.96342	+	0.426076i	0.105301	+	0.0151399i
$793$	2.32443	−	1.65522i	0.0825430	−	0.0587786i
$794$	2.17339	+	22.7608i	0.0771307	+	0.807750i
$795$	11.5090	−	4.60750i	0.408181	−	0.163411i
$796$	0.474291	+	9.95658i	0.0168108	+	0.352902i
$797$	−41.2687	−	12.1176i	−1.46181	−	0.429227i	−0.548385	−	0.836226i	$-0.684757\pi$
$797$	−41.2687	−	12.1176i	−1.46181	−	0.429227i	−0.913429	+	0.406999i	$0.866575\pi$
$798$	3.31435	+	18.0260i	0.117327	+	0.638114i
$799$	−9.46648	+	8.20276i	−0.334900	+	0.290193i
$800$	−2.20169	+	1.13505i	−0.0778416	+	0.0401301i
$801$	−10.3056	−	1.98623i	−0.364129	−	0.0701801i
$802$	7.10463	−	7.45112i	0.250873	−	0.263108i
$803$	27.0294	+	2.58100i	0.953848	+	0.0910814i
$804$	−1.78614			−0.0629923
$805$	12.8027	−	15.5655i	0.451237	−	0.548611i
$806$	−7.05189			−0.248392
$807$	−30.2140	−	2.88509i	−1.06358	−	0.101560i
$808$	−1.26604	+	1.32778i	−0.0445391	+	0.0467112i
$809$	−33.0957	−	6.37867i	−1.16358	−	0.224262i	−0.429335	−	0.903145i	$-0.641252\pi$
$809$	−33.0957	−	6.37867i	−1.16358	−	0.224262i	−0.734246	+	0.678883i	$0.762464\pi$
$810$	1.41181	−	0.727837i	0.0496058	−	0.0255736i
$811$	13.8292	−	11.9831i	0.485610	−	0.420784i	−0.377338	−	0.926076i	$-0.623161\pi$
$811$	13.8292	−	11.9831i	0.485610	−	0.420784i	0.862949	+	0.505292i	$0.168615\pi$
$812$	−5.88436	+	16.5419i	−0.206501	+	0.580508i
$813$	15.7672	+	4.62968i	0.552981	+	0.162370i
$814$	−0.198646	−	4.17010i	−0.00696255	−	0.146162i
$815$	−37.0862	+	14.8471i	−1.29907	+	0.520071i
$816$	−0.123580	−	1.29418i	−0.00432615	−	0.0453055i
$817$	−13.3881	+	9.53361i	−0.468390	+	0.333539i
$818$	27.3705	+	3.93528i	0.956987	+	0.137594i
$819$	1.76361	−	1.23323i	0.0616256	−	0.0430927i
$820$	1.46840	−	5.00091i	0.0512787	−	0.174639i
$821$	−6.20829	−	2.48543i	−0.216671	−	0.0867419i	0.260788	−	0.965396i	$-0.416018\pi$
$821$	−6.20829	−	2.48543i	−0.216671	−	0.0867419i	−0.477459	+	0.878654i	$0.658442\pi$
$822$	−2.09931	+	6.06557i	−0.0732220	+	0.211561i
$823$	2.43122	−	51.0375i	0.0847469	−	1.77906i	−0.412022	−	0.911174i	$-0.635177\pi$
$823$	2.43122	−	51.0375i	0.0847469	−	1.77906i	0.496769	−	0.867883i	$-0.334520\pi$
$824$	−1.13584	−	3.28180i	−0.0395689	−	0.114327i
$825$	7.11564	−	2.08934i	0.247735	−	0.0727415i
$826$	3.11240	−	4.75297i	0.108294	−	0.165377i
$827$		−	53.8225i		−	1.87159i	−0.352543	−	0.935796i	$-0.614683\pi$
$827$		−	53.8225i		−	1.87159i	0.352543	−	0.935796i	$-0.385317\pi$
$828$	4.33545	+	2.05033i	0.150667	+	0.0712538i
$829$	28.5140	−	16.4625i	0.990331	−	0.571768i	0.0849578	−	0.996385i	$-0.472924\pi$
$829$	28.5140	−	16.4625i	0.990331	−	0.571768i	0.905373	+	0.424617i	$0.139591\pi$
$830$	1.21869	−	1.71142i	0.0423015	−	0.0594041i
$831$	−24.2755	−	5.88918i	−0.842109	−	0.204293i
$832$	0.614717	+	0.532656i	0.0213115	+	0.0184665i
$833$	−8.01622	−	4.30804i	−0.277746	−	0.149265i
$834$	−8.44815	−	9.74969i	−0.292536	−	0.337604i
$835$	8.51966	−	21.2811i	0.294835	−	0.736462i
$836$	20.1553	−	4.88962i	0.697085	−	0.169111i
$837$	−7.70600	−	3.97272i	−0.266358	−	0.137317i
$838$	−20.6351	−	16.2276i	−0.712829	−	0.560575i
$839$	12.6905	−	27.7884i	0.438126	−	0.959363i	−0.553812	−	0.832642i	$-0.686827\pi$
$839$	12.6905	−	27.7884i	0.438126	−	0.959363i	0.991938	−	0.126721i	$-0.0404454\pi$
$840$	4.16465	−	0.562420i	0.143694	−	0.0194053i
$841$	−2.14004	+	14.8843i	−0.0737945	+	0.513252i
$842$	22.8996	−	1.09084i	0.789172	−	0.0375929i
$843$	0.996793	+	4.10884i	0.0343314	+	0.141516i
$844$	17.7523	−	13.9606i	0.611061	−	0.480544i
$845$	19.2439	−	3.70896i	0.662010	−	0.127592i
$846$	5.20898	−	8.10533i	0.179088	−	0.278667i
$847$	4.20680	+	3.36698i	0.144547	+	0.115691i
$848$	2.19887	+	7.48866i	0.0755095	+	0.257162i
$849$	0.537210	−	5.62592i	0.0184370	−	0.193081i
$850$	−1.61017	−	2.78890i	−0.0552285	−	0.0956585i
$851$	1.66327	−	6.47739i	0.0570163	−	0.222042i
$852$	1.67146	+	0.965015i	0.0572631	+	0.0330609i
$853$	−43.4351	+	19.8361i	−1.48719	+	0.679176i	−0.982863	−	0.184338i	$-0.940986\pi$
$853$	−43.4351	+	19.8361i	−1.48719	+	0.679176i	−0.504325	+	0.863514i	$0.668259\pi$
$854$	9.09878	+	1.83461i	0.311354	+	0.0627792i
$855$	7.20565	−	8.31576i	0.246428	−	0.284393i
$856$	−2.54589	−	4.93834i	−0.0870167	−	0.168789i
$857$	−6.93032	−	2.39861i	−0.236735	−	0.0819348i	0.206125	−	0.978526i	$-0.433915\pi$
$857$	−6.93032	−	2.39861i	−0.236735	−	0.0819348i	−0.442860	+	0.896591i	$0.646036\pi$
$858$	−1.50534	−	1.91420i	−0.0513915	−	0.0653496i
$859$	−0.918878	−	0.963692i	−0.0313517	−	0.0328807i	0.707871	−	0.706341i	$-0.249656\pi$
$859$	−0.918878	−	0.963692i	−0.0313517	−	0.0328807i	−0.739223	+	0.673461i	$0.764807\pi$
$860$	2.03741	+	3.17028i	0.0694753	+	0.108106i
$861$	5.09624	−	7.02847i	0.173679	−	0.239530i
$862$	−21.1449	−	9.65654i	−0.720197	−	0.328903i
$863$	−21.4269	−	30.0899i	−0.729382	−	1.02427i	−0.998134	−	0.0610639i	$-0.980551\pi$
$863$	−21.4269	−	30.0899i	−0.729382	−	1.02427i	0.268752	−	0.963209i	$-0.413389\pi$
$864$	0.371662	+	0.928368i	0.0126442	+	0.0315837i
$865$	2.29307	−	4.44793i	0.0779667	−	0.151234i
$866$	−22.4317	+	21.3886i	−0.762259	+	0.726813i
$867$	−15.1540	+	2.17881i	−0.514656	+	0.0739964i
$868$	−15.6863	−	16.7360i	−0.532428	−	0.568058i
$869$	2.56468	+	1.64822i	0.0870007	+	0.0559120i
$870$	9.96086	−	3.44749i	0.337705	−	0.116881i
$871$	1.05146	+	1.00256i	0.0356273	+	0.0339706i
$872$	7.23944	+	5.15518i	0.245158	+	0.174576i
$873$	1.28209	−	2.22065i	0.0433922	−	0.0751575i
$874$	33.1609	+	2.02372i	1.12169	+	0.0684533i
$875$	26.5784	−	16.7610i	0.898514	−	0.566624i
$876$	3.76750	+	8.24967i	0.127292	+	0.278731i
$877$	1.44400	−	5.95224i	0.0487603	−	0.200993i	−0.942221	−	0.334991i	$-0.891267\pi$
$877$	1.44400	−	5.95224i	0.0487603	−	0.200993i	0.990982	+	0.133999i	$0.0427817\pi$
$878$	−3.27563	+	16.9956i	−0.110547	+	0.573573i
$879$	27.1569	+	1.29364i	0.915980	+	0.0436335i
$880$	−0.899973	−	4.66950i	−0.0303381	−	0.157409i
$881$	−0.371500	−	2.58384i	−0.0125162	−	0.0870518i	0.982606	−	0.185703i	$-0.0594563\pi$
$881$	−0.371500	−	2.58384i	−0.0125162	−	0.0870518i	−0.995122	+	0.0986513i	$0.968547\pi$
$882$	6.84980	+	1.44231i	0.230645	+	0.0485651i
$883$	−29.8330	+	19.1725i	−1.00396	+	0.645206i	−0.935823	−	0.352470i	$-0.885342\pi$
$883$	−29.8330	+	19.1725i	−1.00396	+	0.645206i	−0.0681374	+	0.997676i	$0.521706\pi$
$884$	−0.653680	+	0.831221i	−0.0219856	+	0.0279570i
$885$	−3.39536	+	0.324217i	−0.114134	+	0.0108984i
$886$	9.51692	−	0.908755i	0.319727	−	0.0305302i
$887$	28.3668	−	36.0713i	0.952463	−	1.21116i	−0.0249223	−	0.999689i	$-0.507934\pi$
$887$	28.3668	−	36.0713i	0.952463	−	1.21116i	0.977385	−	0.211466i	$-0.0678237\pi$
$888$	1.17308	−	0.753895i	0.0393661	−	0.0252990i
$889$	44.4710	−	12.6451i	1.49151	−	0.424104i
$890$	2.37244	+	16.5007i	0.0795245	+	0.553105i
$891$	−0.566599	−	2.93979i	−0.0189818	−	0.0984868i
$892$	1.99395	+	0.0949838i	0.0667625	+	0.00318029i
$893$	12.6314	−	65.5381i	0.422695	−	2.19315i
$894$	−5.66828	+	23.3650i	−0.189576	+	0.781441i
$895$	−7.95372	−	17.4162i	−0.265864	−	0.582160i
$896$	0.103249	+	2.64374i	0.00344929	+	0.0883210i
$897$	−1.40133	−	3.64048i	−0.0467889	−	0.121552i
$898$	−13.3599	+	23.1401i	−0.445826	+	0.772194i
$899$	−46.8652	−	33.3725i	−1.56304	−	1.11304i
$900$	1.79273	+	1.70936i	0.0597576	+	0.0569787i
$901$	−9.58874	+	3.31870i	−0.319447	+	0.110562i
$902$	−8.26451	−	5.31128i	−0.275178	−	0.176846i
$903$	1.42760	+	6.11270i	0.0475075	+	0.203418i
$904$	6.04073	−	0.868526i	0.200912	−	0.0288867i
$905$	−7.31405	+	6.97393i	−0.243127	+	0.231821i
$906$	4.27818	−	8.29851i	0.142133	−	0.275699i
$907$	−7.06212	−	17.6403i	−0.234494	−	0.585737i	0.763716	−	0.645553i	$-0.223373\pi$
$907$	−7.06212	−	17.6403i	−0.234494	−	0.585737i	−0.998209	+	0.0598155i	$0.980949\pi$
$908$	16.1931	+	22.7400i	0.537386	+	0.754654i
$909$	1.66884	+	0.762132i	0.0553518	+	0.0252783i
$910$	−2.76732	−	2.00654i	−0.0917357	−	0.0665162i
$911$	−2.30160	−	3.58135i	−0.0762553	−	0.118656i	0.801031	−	0.598622i	$-0.204285\pi$
$911$	−2.30160	−	3.58135i	−0.0762553	−	0.118656i	−0.877287	+	0.479967i	$0.840649\pi$
$912$	4.78045	+	5.01359i	0.158297	+	0.166017i
$913$	−2.44797	−	3.11285i	−0.0810161	−	0.103020i
$914$	−9.46173	−	3.27474i	−0.312966	−	0.108319i
$915$	−2.55342	−	4.95294i	−0.0844134	−	0.163739i
$916$	14.8204	−	17.1037i	0.489680	−	0.565121i
$917$	−3.77742	+	1.27125i	−0.124742	+	0.0419805i
$918$	−1.18259	+	0.540069i	−0.0390312	+	0.0178249i
$919$	28.6324	+	16.5309i	0.944495	+	0.545304i	0.891366	−	0.453284i	$-0.149747\pi$
$919$	28.6324	+	16.5309i	0.944495	+	0.545304i	0.0531282	+	0.998588i	$0.483081\pi$
$920$	0.825279	−	7.57276i	0.0272086	−	0.249666i
$921$	−1.13600	−	1.96761i	−0.0374325	−	0.0648350i
$922$	0.400848	−	4.19787i	0.0132012	−	0.138249i
$923$	−0.442282	−	1.50627i	−0.0145579	−	0.0495796i
$924$	1.19441	−	7.83054i	0.0392931	−	0.257606i
$925$	1.86744	−	2.90579i	0.0614009	−	0.0955417i
$926$	34.0956	−	6.57138i	1.12045	−	0.215949i
$927$	−2.72980	+	2.14674i	−0.0896585	+	0.0705082i
$928$	1.56451	+	6.44901i	0.0513576	+	0.211699i
$929$	41.4557	−	1.97478i	1.36012	−	0.0647904i	0.645208	−	0.764007i	$-0.276771\pi$
$929$	41.4557	−	1.97478i	1.36012	−	0.0647904i	0.714910	+	0.699216i	$0.246467\pi$
$930$	−1.95980	+	13.6307i	−0.0642644	+	0.446969i
$931$	47.7657	−	8.36010i	1.56546	−	0.273991i
$932$	−6.04398	+	13.2345i	−0.197977	+	0.433509i
$933$	−9.93846	−	7.81569i	−0.325371	−	0.255874i
$934$	11.3669	+	5.86007i	0.371938	+	0.191747i
$935$	6.00814	−	1.45756i	0.196487	−	0.0476673i
$936$	0.302306	−	0.755123i	0.00988117	−	0.0246820i
$937$	10.4917	+	12.1081i	0.342749	+	0.395554i	0.900787	−	0.434262i	$-0.142991\pi$
$937$	10.4917	+	12.1081i	0.342749	+	0.395554i	−0.558037	+	0.829816i	$0.688445\pi$
$938$	−0.0404783	+	4.72551i	−0.00132166	+	0.154293i
$939$	10.6235	+	9.20529i	0.346684	+	0.300403i
$940$	−14.8724	−	3.60799i	−0.485083	−	0.117680i
$941$	3.38018	−	4.74679i	0.110191	−	0.154741i	−0.755798	−	0.654805i	$-0.772751\pi$
$941$	3.38018	−	4.74679i	0.110191	−	0.154741i	0.865989	+	0.500064i	$0.166690\pi$
$942$	−13.3194	+	7.68998i	−0.433971	+	0.250553i
$943$	−10.1457	−	12.0296i	−0.330390	−	0.391739i
$944$		−	2.14735i		−	0.0698902i
$945$	−1.89361	−	3.75165i	−0.0615992	−	0.122041i
$946$	6.81546	−	2.00120i	0.221590	−	0.0650646i
$947$	−5.08058	−	14.6794i	−0.165097	−	0.477015i	0.831859	−	0.554987i	$-0.187277\pi$
$947$	−5.08058	−	14.6794i	−0.165097	−	0.477015i	−0.996956	+	0.0779719i	$0.975156\pi$
$948$	−0.0484519	+	1.01713i	−0.00157365	+	0.0330349i
$949$	2.41272	−	6.97109i	0.0783201	−	0.226291i
$950$	15.9304	+	6.37755i	0.516849	+	0.206915i
$951$	−4.10560	+	13.9824i	−0.133133	+	0.453410i
$952$	−3.42677	+	0.297620i	−0.111062	+	0.00964591i
$953$	7.71498	+	1.10925i	0.249913	+	0.0359320i	0.266133	−	0.963936i	$-0.414254\pi$
$953$	7.71498	+	1.10925i	0.249913	+	0.0359320i	−0.0162198	+	0.999868i	$0.505163\pi$
$954$	6.35761	−	4.52723i	0.205835	−	0.146575i
$955$	−0.195851	−	2.05105i	−0.00633760	−	0.0663703i
$956$	−19.1091	+	7.65013i	−0.618033	+	0.247423i
$957$	−0.945343	−	19.8452i	−0.0305586	−	0.641504i
$958$	16.4477	+	4.82949i	0.531402	+	0.156034i
$959$	15.9998	+	5.69152i	0.516661	+	0.183789i
$960$	1.20042	−	1.04017i	0.0387433	−	0.0335712i
$961$	39.2554	−	20.2376i	1.26630	−	0.652825i
$962$	−1.11373	−	0.214654i	−0.0359080	−	0.00692071i
$963$	−3.83405	+	4.02104i	−0.123551	+	0.129576i
$964$	−6.14590	−	0.586862i	−0.197946	−	0.0189016i
$965$	26.7401			0.860794
$966$	5.52271	−	11.4236i	0.177690	−	0.367550i
$967$	29.4334			0.946515			0.473258	−	0.880924i	$-0.343078\pi$
$967$	29.4334			0.946515			0.473258	+	0.880924i	$0.343078\pi$
$968$	2.02736	+	0.193589i	0.0651618	+	0.00622220i
$969$	−6.21493	+	6.51803i	−0.199652	+	0.209389i
$970$	−3.99929	−	0.770800i	−0.128409	−	0.0247489i
$971$	−9.78231	+	5.04313i	−0.313929	+	0.161842i	−0.607989	−	0.793945i	$-0.708024\pi$
$971$	−9.78231	+	5.04313i	−0.313929	+	0.161842i	0.294060	+	0.955787i	$0.404993\pi$
$972$	0.755750	−	0.654861i	0.0242407	−	0.0210047i
$973$	−25.9858	+	22.1299i	−0.833065	+	0.709453i
$974$	−5.13978	−	1.50918i	−0.164689	−	0.0483571i
$975$	−0.0958683	−	2.01252i	−0.00307024	−	0.0644523i
$976$	3.25693	−	1.30388i	0.104252	−	0.0417361i
$977$	−2.52860	−	26.4807i	−0.0808970	−	0.847191i	−0.941299	−	0.337575i	$-0.890393\pi$
$977$	−2.52860	−	26.4807i	−0.0808970	−	0.847191i	0.860402	−	0.509616i	$-0.170213\pi$
$978$	−20.4866	+	14.5884i	−0.655090	+	0.466487i
$979$	31.1018	+	4.47176i	0.994017	+	0.142918i
$980$	−1.39359	−	11.0310i	−0.0445165	−	0.352371i
$981$	2.50386	−	8.52737i	0.0799422	−	0.272258i
$982$	−26.8804	−	10.7613i	−0.857787	−	0.343406i
$983$	−14.6497	+	42.3276i	−0.467254	+	1.35004i	0.427716	+	0.903913i	$0.359318\pi$
$983$	−14.6497	+	42.3276i	−0.467254	+	1.35004i	−0.894970	+	0.446127i	$0.852803\pi$
$984$	0.156133	−	3.27764i	0.00497734	−	0.104487i
$985$	9.24695	+	26.7173i	0.294632	+	0.851284i
$986$	−8.27789	+	2.43061i	−0.263622	+	0.0774063i
$987$	−21.3258	−	13.9648i	−0.678809	−	0.444506i
$988$		−	5.63466i		−	0.179262i
$989$	11.3774	+	0.151916i	0.361779	+	0.00483066i
$990$	−4.11833	+	2.37772i	−0.130889	+	0.0755689i
$991$	21.0347	−	29.5391i	0.668190	−	0.938342i	−0.331797	−	0.943351i	$-0.607655\pi$
$991$	21.0347	−	29.5391i	0.668190	−	0.938342i	0.999987	+	0.00500902i	$0.00159443\pi$
$992$	−8.42539	−	2.04398i	−0.267506	−	0.0648963i
$993$	12.0786	+	10.4662i	0.383304	+	0.332135i
$994$	2.59098	−	4.40022i	0.0821808	−	0.139567i
$995$	−10.3683	−	11.9656i	−0.328696	−	0.379335i
$996$	0.491608	−	1.22798i	0.0155772	−	0.0389099i
$997$	16.9370	−	4.10887i	0.536400	−	0.130129i	0.0415973	−	0.999134i	$-0.486755\pi$
$997$	16.9370	−	4.10887i	0.536400	−	0.130129i	0.494803	+	0.869005i	$0.335240\pi$
$998$	−11.9997	−	6.18628i	−0.379844	−	0.195823i
$999$	−1.09611	−	0.861989i	−0.0346793	−	0.0272721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.19.3	✓	320
7.3	odd	6	inner	966.2.be.a.157.3	yes	320
23.17	odd	22	inner	966.2.be.a.523.3	yes	320
161.17	even	66	inner	966.2.be.a.661.3	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.19.3	✓	320	1.1	even	1	trivial
966.2.be.a.157.3	yes	320	7.3	odd	6	inner
966.2.be.a.523.3	yes	320	23.17	odd	22	inner
966.2.be.a.661.3	yes	320	161.17	even	66	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.995472 + 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-1.41181 + 0.727837i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.71541 + 2.01429i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(0.995472 + 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-1.41181 + 0.727837i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.71541 + 2.01429i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-1.47460 + 0.590341i) q^{10} +(0.284588 + 2.98034i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(0.805109 + 0.115757i) q^{13} +(1.51617 + 2.16823i) q^{14} +(0.447498 - 1.52404i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-0.425212 + 1.22857i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(-2.26573 - 6.54639i) q^{19} +(-1.52404 + 0.447498i) q^{20} +(-2.64158 - 0.148522i) q^{21} +2.99390i q^{22} +(-1.41246 + 4.58312i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.43683 + 2.01775i) q^{25} +(0.790460 + 0.191763i) q^{26} +(0.755750 + 0.654861i) q^{27} +(1.30320 + 2.30254i) q^{28} +(4.34570 + 5.01520i) q^{29} +(0.590341 - 1.47460i) q^{30} +(-8.42539 + 2.04398i) q^{31} +(0.888835 + 0.458227i) q^{32} +(-2.35336 - 1.85070i) q^{33} +(-0.540069 + 1.18259i) q^{34} +(-3.88790 - 1.59526i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-1.39287 + 0.0663504i) q^{37} +(-1.63320 - 6.73212i) q^{38} +(-0.639366 + 0.502803i) q^{39} +(-1.55967 + 0.300603i) q^{40} +(-1.77403 + 2.76045i) q^{41} +(-2.61550 - 0.398948i) q^{42} +(-0.668427 - 2.27645i) q^{43} +(-0.284588 + 2.98034i) q^{44} +(0.794189 + 1.37558i) q^{45} +(-1.84172 + 4.42810i) q^{46} +(8.34400 + 4.81741i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(-1.11475 + 6.91067i) q^{49} +(-1.62212 + 1.87203i) q^{50} +(-0.595727 - 1.15555i) q^{51} +(0.768652 + 0.266033i) q^{52} +(4.82461 + 6.13500i) q^{53} +(0.690079 + 0.723734i) q^{54} +(-2.57099 - 4.00053i) q^{55} +(1.07843 + 2.41599i) q^{56} +(6.30138 + 2.87774i) q^{57} +(3.84930 + 5.40558i) q^{58} +(-0.798089 - 1.99353i) q^{59} +(0.727837 - 1.41181i) q^{60} +(2.53902 - 2.42095i) q^{61} +(-8.58153 + 1.23384i) q^{62} +(1.93039 - 1.80931i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-1.22091 + 0.422561i) q^{65} +(-2.16678 - 2.06603i) q^{66} +(1.45495 + 1.03606i) q^{67} +(-0.650036 + 1.12589i) q^{68} +(-2.34225 - 4.18496i) q^{69} +(-3.71866 - 1.95760i) q^{70} +(-0.801764 - 1.75562i) q^{71} +(0.235759 - 0.971812i) q^{72} +(1.71636 - 8.90535i) q^{73} +(-1.39287 - 0.0663504i) q^{74} +(-0.468785 - 2.43229i) q^{75} +(-0.985871 - 6.85689i) q^{76} +(-5.51509 + 5.68574i) q^{77} +(-0.684265 + 0.439751i) q^{78} +(0.629462 - 0.800426i) q^{79} +(-1.58119 + 0.150985i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-2.02840 + 2.57932i) q^{82} +(-1.11275 + 0.715120i) q^{83} +(-2.56573 - 0.645760i) q^{84} +(-0.293881 - 2.04399i) q^{85} +(-0.449009 - 2.32968i) q^{86} +(-6.62855 - 0.315757i) q^{87} +(-0.566599 + 2.93979i) q^{88} +(2.47434 - 10.1994i) q^{89} +(0.659836 + 1.44484i) q^{90} +(1.14792 + 1.82030i) q^{91} +(-2.25429 + 4.23298i) q^{92} +(4.33489 - 7.50825i) q^{93} +(7.84829 + 5.58874i) q^{94} +(7.96348 + 7.59317i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(2.15713 + 1.38630i) q^{97} +(-1.76660 + 6.77341i) q^{98} +(2.96342 - 0.426076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

Modular forms

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