LMFDB - Embedded newform 552.2.bb.a.469.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.47
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41419 - 0.00887069i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.99984 - 0.0250896i) q^{4} +(2.01890 - 0.290274i) q^{5} +(1.06296 - 0.932799i) q^{6} +(0.214664 - 0.470048i) q^{7} +(2.82793 - 0.0532214i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(1.41419 - 0.00887069i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.99984 - 0.0250896i) q^{4} +(2.01890 - 0.290274i) q^{5} +(1.06296 - 0.932799i) q^{6} +(0.214664 - 0.470048i) q^{7} +(2.82793 - 0.0532214i) q^{8} +(0.142315 - 0.989821i) q^{9} +(2.85253 - 0.428411i) q^{10} +(-0.754084 + 2.56817i) q^{11} +(1.49495 - 1.32858i) q^{12} +(-5.11019 + 2.33374i) q^{13} +(0.299405 - 0.666640i) q^{14} +(1.33570 - 1.54147i) q^{15} +(3.99874 - 0.100351i) q^{16} +(-3.23560 - 2.07940i) q^{17} +(0.192479 - 1.40105i) q^{18} +(0.853390 + 1.32790i) q^{19} +(4.03020 - 0.631156i) q^{20} +(-0.145584 - 0.495814i) q^{21} +(-1.04363 + 3.63856i) q^{22} +(-2.90764 - 3.81387i) q^{23} +(2.10235 - 1.89212i) q^{24} +(-0.805758 + 0.236592i) q^{25} +(-7.20605 + 3.34568i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(0.417501 - 0.945408i) q^{28} +(-1.80210 + 2.80412i) q^{29} +(1.87525 - 2.19178i) q^{30} +(2.62274 - 3.02681i) q^{31} +(5.65407 - 0.177386i) q^{32} +(1.11190 + 2.43472i) q^{33} +(-4.59419 - 2.91195i) q^{34} +(0.296942 - 1.01129i) q^{35} +(0.259773 - 1.98306i) q^{36} +(-6.67926 - 0.960332i) q^{37} +(1.21863 + 1.87033i) q^{38} +(-2.33374 + 5.11019i) q^{39} +(5.69386 - 0.928323i) q^{40} +(0.979178 + 6.81033i) q^{41} +(-0.210281 - 0.699881i) q^{42} +(7.51004 - 6.50749i) q^{43} +(-1.44361 + 5.15486i) q^{44} -2.03966i q^{45} +(-4.14578 - 5.36773i) q^{46} +7.60726 q^{47} +(2.95633 - 2.69446i) q^{48} +(4.40916 + 5.08844i) q^{49} +(-1.13739 + 0.341732i) q^{50} +(-3.80702 + 0.547367i) q^{51} +(-10.1610 + 4.79533i) q^{52} +(-1.29655 - 0.592116i) q^{53} +(-0.772029 - 1.18489i) q^{54} +(-0.776947 + 5.40378i) q^{55} +(0.582037 - 1.34069i) q^{56} +(1.51454 + 0.444709i) q^{57} +(-2.52363 + 3.98153i) q^{58} +(-0.925840 + 0.422817i) q^{59} +(2.63251 - 3.11622i) q^{60} +(-4.46843 - 3.87191i) q^{61} +(3.68220 - 4.30373i) q^{62} +(-0.434714 - 0.279374i) q^{63} +(7.99433 - 0.301012i) q^{64} +(-9.63954 + 6.19496i) q^{65} +(1.59403 + 3.43328i) q^{66} +(-0.456590 - 1.55500i) q^{67} +(-6.52287 - 4.07728i) q^{68} +(-4.69500 - 0.978231i) q^{69} +(0.410961 - 1.43279i) q^{70} +(-14.2043 + 4.17075i) q^{71} +(0.349776 - 2.80672i) q^{72} +(10.3050 - 6.62265i) q^{73} +(-9.45423 - 1.29884i) q^{74} +(-0.454016 + 0.706463i) q^{75} +(1.73996 + 2.63418i) q^{76} +(1.04529 + 0.905749i) q^{77} +(-3.25502 + 7.24746i) q^{78} +(-3.77937 - 8.27566i) q^{79} +(8.04394 - 1.36333i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(1.44515 + 9.62239i) q^{82} +(5.36142 + 0.770855i) q^{83} +(-0.303585 - 0.987897i) q^{84} +(-7.13596 - 3.25888i) q^{85} +(10.5629 - 9.26942i) q^{86} +(0.474372 + 3.29933i) q^{87} +(-1.99581 + 7.30274i) q^{88} +(8.92759 + 10.3030i) q^{89} +(-0.0180932 - 2.88446i) q^{90} +2.90300i q^{91} +(-5.91052 - 7.55419i) q^{92} -4.00504i q^{93} +(10.7581 - 0.0674817i) q^{94} +(2.10837 + 2.43319i) q^{95} +(4.15690 - 3.83669i) q^{96} +(-0.0860829 - 0.598720i) q^{97} +(6.28051 + 7.15689i) q^{98} +(2.43472 + 1.11190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	1.41419	−	0.00887069i	0.999980	−	0.00627253i
$2$	1.41419	−	0.00887069i	0.999980	−	0.00627253i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$4$	1.99984	−	0.0250896i	0.999921	−	0.0125448i
$5$	2.01890	−	0.290274i	0.902881	−	0.129815i	0.324789	−	0.945787i	$-0.394707\pi$
$5$	2.01890	−	0.290274i	0.902881	−	0.129815i	0.578092	+	0.815972i	$0.303798\pi$
$6$	1.06296	−	0.932799i	0.433952	−	0.380813i
$7$	0.214664	−	0.470048i	0.0811353	−	0.177662i	−0.864717	−	0.502260i	$-0.832502\pi$
$7$	0.214664	−	0.470048i	0.0811353	−	0.177662i	0.945852	+	0.324599i	$0.105229\pi$
$8$	2.82793	−	0.0532214i	0.999823	−	0.0188166i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	2.85253	−	0.428411i	0.902049	−	0.135475i
$11$	−0.754084	+	2.56817i	−0.227365	+	0.774333i	0.764229	+	0.644945i	$0.223120\pi$
$11$	−0.754084	+	2.56817i	−0.227365	+	0.774333i	−0.991594	+	0.129389i	$0.958699\pi$
$12$	1.49495	−	1.32858i	0.431555	−	0.383528i
$13$	−5.11019	+	2.33374i	−1.41731	+	0.647264i	−0.969101	−	0.246664i	$-0.920666\pi$
$13$	−5.11019	+	2.33374i	−1.41731	+	0.647264i	−0.448210	+	0.893928i	$0.647938\pi$
$14$	0.299405	−	0.666640i	0.0800193	−	0.178167i
$15$	1.33570	−	1.54147i	0.344875	−	0.398007i
$16$	3.99874	−	0.100351i	0.999685	−	0.0250876i
$17$	−3.23560	−	2.07940i	−0.784749	−	0.504327i	0.0858577	−	0.996307i	$-0.472637\pi$
$17$	−3.23560	−	2.07940i	−0.784749	−	0.504327i	−0.870607	+	0.491980i	$0.836273\pi$
$18$	0.192479	−	1.40105i	0.0453678	−	0.330232i
$19$	0.853390	+	1.32790i	0.195781	+	0.304641i	0.925239	−	0.379384i	$-0.123864\pi$
$19$	0.853390	+	1.32790i	0.195781	+	0.304641i	−0.729458	+	0.684025i	$0.760228\pi$
$20$	4.03020	−	0.631156i	0.901181	−	0.141131i
$21$	−0.145584	−	0.495814i	−0.0317690	−	0.108195i
$22$	−1.04363	+	3.63856i	−0.222503	+	0.775744i
$23$	−2.90764	−	3.81387i	−0.606285	−	0.795247i
$23$	−2.90764	−	3.81387i	−0.606285	−	0.795247i
$24$	2.10235	−	1.89212i	0.429141	−	0.386227i
$25$	−0.805758	+	0.236592i	−0.161152	+	0.0473184i
$26$	−7.20605	+	3.34568i	−1.41322	+	0.656142i
$27$	−0.540641	−	0.841254i	−0.104046	−	0.161899i
$28$	0.417501	−	0.945408i	0.0789002	−	0.178665i
$29$	−1.80210	+	2.80412i	−0.334641	+	0.520712i	−0.967272	−	0.253742i	$-0.918339\pi$
$29$	−1.80210	+	2.80412i	−0.334641	+	0.520712i	0.632631	+	0.774453i	$0.281975\pi$
$30$	1.87525	−	2.19178i	0.342372	−	0.400162i
$31$	2.62274	−	3.02681i	0.471059	−	0.543631i	−0.469647	−	0.882854i	$-0.655619\pi$
$31$	2.62274	−	3.02681i	0.471059	−	0.543631i	0.940706	+	0.339223i	$0.110164\pi$
$32$	5.65407	−	0.177386i	0.999508	−	0.0313577i
$33$	1.11190	+	2.43472i	0.193556	+	0.423830i
$34$	−4.59419	−	2.91195i	−0.787897	−	0.499395i
$35$	0.296942	−	1.01129i	0.0501924	−	0.170940i
$36$	0.259773	−	1.98306i	0.0432955	−	0.330510i
$37$	−6.67926	−	0.960332i	−1.09806	−	0.157878i	−0.430616	−	0.902535i	$-0.641704\pi$
$37$	−6.67926	−	0.960332i	−1.09806	−	0.157878i	−0.667447	+	0.744658i	$0.732613\pi$
$38$	1.21863	+	1.87033i	0.197688	+	0.303407i
$39$	−2.33374	+	5.11019i	−0.373698	+	0.818285i
$40$	5.69386	−	0.928323i	0.900278	−	0.146781i
$41$	0.979178	+	6.81033i	0.152922	+	1.06360i	0.911289	+	0.411768i	$0.135088\pi$
$41$	0.979178	+	6.81033i	0.152922	+	1.06360i	−0.758367	+	0.651828i	$0.774002\pi$
$42$	−0.210281	−	0.699881i	−0.0324471	−	0.107994i
$43$	7.51004	−	6.50749i	1.14527	−	0.992383i	0.145275	−	0.989391i	$-0.453593\pi$
$43$	7.51004	−	6.50749i	1.14527	−	0.992383i	0.999996	−	0.00299165i	$-0.000952272\pi$
$44$	−1.44361	+	5.15486i	−0.217633	+	0.777125i
$45$		−	2.03966i		−	0.304055i
$46$	−4.14578	−	5.36773i	−0.611262	−	0.791429i
$47$	7.60726			1.10963			0.554816	−	0.831973i	$-0.312789\pi$
$47$	7.60726			1.10963			0.554816	+	0.831973i	$0.312789\pi$
$48$	2.95633	−	2.69446i	0.426710	−	0.388912i
$49$	4.40916	+	5.08844i	0.629880	+	0.726920i
$50$	−1.13739	+	0.341732i	−0.160852	+	0.0483283i
$51$	−3.80702	+	0.547367i	−0.533089	+	0.0766467i
$52$	−10.1610	+	4.79533i	−1.40908	+	0.664993i
$53$	−1.29655	−	0.592116i	−0.178095	−	0.0813334i	0.324372	−	0.945930i	$-0.394847\pi$
$53$	−1.29655	−	0.592116i	−0.178095	−	0.0813334i	−0.502467	+	0.864596i	$0.667574\pi$
$54$	−0.772029	−	1.18489i	−0.105060	−	0.161243i
$55$	−0.776947	+	5.40378i	−0.104763	+	0.728646i
$56$	0.582037	−	1.34069i	0.0777779	−	0.179157i
$57$	1.51454	+	0.444709i	0.200606	+	0.0589032i
$58$	−2.52363	+	3.98153i	−0.331368	+	0.522800i
$59$	−0.925840	+	0.422817i	−0.120534	+	0.0550461i	−0.474769	−	0.880110i	$-0.657469\pi$
$59$	−0.925840	+	0.422817i	−0.120534	+	0.0550461i	0.354235	+	0.935156i	$0.384741\pi$
$60$	2.63251	−	3.11622i	0.339855	−	0.402302i
$61$	−4.46843	−	3.87191i	−0.572124	−	0.495748i	0.320074	−	0.947392i	$-0.396292\pi$
$61$	−4.46843	−	3.87191i	−0.572124	−	0.495748i	−0.892198	+	0.451645i	$0.850838\pi$
$62$	3.68220	−	4.30373i	0.467640	−	0.546575i
$63$	−0.434714	−	0.279374i	−0.0547688	−	0.0351978i
$64$	7.99433	−	0.301012i	0.999292	−	0.0376265i
$65$	−9.63954	+	6.19496i	−1.19564	+	0.768390i
$66$	1.59403	+	3.43328i	0.196211	+	0.422607i
$67$	−0.456590	−	1.55500i	−0.0557813	−	0.189974i	0.926889	−	0.375336i	$-0.122473\pi$
$67$	−0.456590	−	1.55500i	−0.0557813	−	0.189974i	−0.982670	+	0.185362i	$0.940654\pi$
$68$	−6.52287	−	4.07728i	−0.791014	−	0.494443i
$69$	−4.69500	−	0.978231i	−0.565212	−	0.117765i
$70$	0.410961	−	1.43279i	0.0491192	−	0.171251i
$71$	−14.2043	+	4.17075i	−1.68574	+	0.494977i	−0.977489	−	0.210986i	$-0.932332\pi$
$71$	−14.2043	+	4.17075i	−1.68574	+	0.494977i	−0.708248	+	0.705963i	$0.750514\pi$
$72$	0.349776	−	2.80672i	0.0412215	−	0.330775i
$73$	10.3050	−	6.62265i	1.20611	−	0.775123i	0.226111	−	0.974102i	$-0.427399\pi$
$73$	10.3050	−	6.62265i	1.20611	−	0.775123i	0.980004	+	0.198979i	$0.0637625\pi$
$74$	−9.45423	−	1.29884i	−1.09903	−	0.150987i
$75$	−0.454016	+	0.706463i	−0.0524253	+	0.0815753i
$76$	1.73996	+	2.63418i	0.199587	+	0.302161i
$77$	1.04529	+	0.905749i	0.119122	+	0.103220i
$78$	−3.25502	+	7.24746i	−0.368558	+	0.820613i
$79$	−3.77937	−	8.27566i	−0.425212	−	0.931085i	−0.994079	−	0.108656i	$-0.965345\pi$
$79$	−3.77937	−	8.27566i	−0.425212	−	0.931085i	0.568867	−	0.822429i	$-0.307382\pi$
$80$	8.04394	−	1.36333i	0.899340	−	0.152425i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	1.44515	+	9.62239i	0.159590	+	1.06262i
$83$	5.36142	+	0.770855i	0.588492	+	0.0846124i	0.430127	−	0.902768i	$-0.358469\pi$
$83$	5.36142	+	0.770855i	0.588492	+	0.0846124i	0.158365	+	0.987381i	$0.449378\pi$
$84$	−0.303585	−	0.987897i	−0.0331238	−	0.107788i
$85$	−7.13596	−	3.25888i	−0.774004	−	0.353476i
$86$	10.5629	−	9.26942i	1.13902	−	0.999547i
$87$	0.474372	+	3.29933i	0.0508581	+	0.353726i
$88$	−1.99581	+	7.30274i	−0.212754	+	0.778474i
$89$	8.92759	+	10.3030i	0.946322	+	1.09211i	0.995635	+	0.0933307i	$0.0297514\pi$
$89$	8.92759	+	10.3030i	0.946322	+	1.09211i	−0.0493129	+	0.998783i	$0.515703\pi$
$90$	−0.0180932	−	2.88446i	−0.00190719	−	0.304049i
$91$			2.90300i			0.304318i
$92$	−5.91052	−	7.55419i	−0.616214	−	0.787579i
$93$		−	4.00504i		−	0.415303i
$94$	10.7581	−	0.0674817i	1.10961	−	0.00696020i
$95$	2.10837	+	2.43319i	0.216314	+	0.249640i
$96$	4.15690	−	3.83669i	0.424262	−	0.391580i
$97$	−0.0860829	−	0.598720i	−0.00874040	−	0.0607908i	0.984984	−	0.172643i	$-0.0552307\pi$
$97$	−0.0860829	−	0.598720i	−0.00874040	−	0.0607908i	−0.993725	+	0.111852i	$0.964322\pi$
$98$	6.28051	+	7.15689i	0.634427	+	0.722955i
$99$	2.43472	+	1.11190i	0.244698	+	0.111750i
$100$	−1.60545	+	0.493362i	−0.160545	+	0.0493362i
$101$	−10.9578	−	1.57550i	−1.09035	−	0.156768i	−0.426389	−	0.904540i	$-0.640215\pi$
$101$	−10.9578	−	1.57550i	−1.09035	−	0.156768i	−0.663956	+	0.747772i	$0.731124\pi$
$102$	−5.37898	+	0.807849i	−0.532598	+	0.0799890i
$103$	−3.57440	−	1.04954i	−0.352197	−	0.103414i	0.100849	−	0.994902i	$-0.467844\pi$
$103$	−3.57440	−	1.04954i	−0.352197	−	0.103414i	−0.453045	+	0.891488i	$0.649662\pi$
$104$	−14.3270	+	6.87163i	−1.40488	+	0.673819i
$105$	−0.437842	−	0.958740i	−0.0427290	−	0.0935634i
$106$	−1.83882	−	0.825861i	−0.178602	−	0.0802147i
$107$	−0.348630	−	0.302090i	−0.0337033	−	0.0292041i	0.637846	−	0.770164i	$-0.279826\pi$
$107$	−0.348630	−	0.302090i	−0.0337033	−	0.0292041i	−0.671550	+	0.740960i	$0.734371\pi$
$108$	−1.10230	−	1.66881i	−0.106069	−	0.160581i
$109$	−2.26020	+	3.51695i	−0.216488	+	0.336862i	−0.932464	−	0.361263i	$-0.882346\pi$
$109$	−2.26020	+	3.51695i	−0.216488	+	0.336862i	0.715976	+	0.698125i	$0.245982\pi$
$110$	−1.05081	+	7.64884i	−0.100191	+	0.729289i
$111$	−5.67673	+	3.64821i	−0.538811	+	0.346273i
$112$	0.811215	−	1.90114i	0.0766526	−	0.179641i
$113$	−11.5184	+	3.38210i	−1.08356	+	0.318162i	−0.774301	−	0.632817i	$-0.781899\pi$
$113$	−11.5184	+	3.38210i	−1.08356	+	0.318162i	−0.309257	+	0.950978i	$0.600080\pi$
$114$	2.14579	+	0.615466i	0.200971	+	0.0576437i
$115$	−6.97731	−	6.85582i	−0.650638	−	0.639308i
$116$	−3.53356	+	5.65301i	−0.328082	+	0.524869i
$117$	1.58273	+	5.39030i	0.146324	+	0.498333i
$118$	−1.30556	+	0.606155i	−0.120186	+	0.0558011i
$119$	−1.67198	+	1.07452i	−0.153270	+	0.0985009i
$120$	3.69521	−	4.43026i	0.337325	−	0.404426i
$121$	3.22692	+	2.07381i	0.293356	+	0.188529i
$122$	−6.35353	−	5.43597i	−0.575222	−	0.492149i
$123$	5.19983	+	4.50568i	0.468853	+	0.406264i
$124$	5.16913	−	6.11894i	0.464202	−	0.549497i
$125$	−10.8348	+	4.94808i	−0.969092	+	0.442570i
$126$	−0.617244	−	0.391230i	−0.0549885	−	0.0348535i
$127$	14.4025	+	4.22896i	1.27802	+	0.375260i	0.849171	−	0.528118i	$-0.177102\pi$
$127$	14.4025	+	4.22896i	1.27802	+	0.375260i	0.428846	+	0.903378i	$0.358920\pi$
$128$	11.3028	−	0.496603i	0.999036	−	0.0438939i
$129$	1.41421	−	9.83607i	0.124514	−	0.866017i
$130$	−13.5772	+	8.84633i	−1.19079	+	0.775875i
$131$	17.5620	+	8.02030i	1.53440	+	0.700737i	0.990385	−	0.138339i	$-0.0441764\pi$
$131$	17.5620	+	8.02030i	1.53440	+	0.700737i	0.544014	+	0.839076i	$0.316904\pi$
$132$	2.28471	+	4.84115i	0.198858	+	0.421368i
$133$	0.807370	−	0.116082i	0.0700078	−	0.0100656i
$134$	−0.659497	−	2.19501i	−0.0569719	−	0.189620i
$135$	−1.33570	−	1.54147i	−0.114958	−	0.132669i
$136$	−9.26071	−	5.70817i	−0.794100	−	0.489472i
$137$	−11.0872			−0.947242			−0.473621	−	0.880729i	$-0.657053\pi$
$137$	−11.0872			−0.947242			−0.473621	+	0.880729i	$0.657053\pi$
$138$	−6.64829	−	1.34175i	−0.565940	−	0.114218i
$139$		−	12.6389i		−	1.07202i	−0.844211	−	0.536010i	$-0.819931\pi$
$139$		−	12.6389i		−	1.07202i	0.844211	−	0.536010i	$-0.180069\pi$
$140$	0.568465	−	2.02988i	0.0480441	−	0.171556i
$141$	5.74918	−	4.98169i	0.484168	−	0.419534i
$142$	−20.0505	+	6.02422i	−1.68260	+	0.505541i
$143$	−2.13995	−	14.8837i	−0.178952	−	1.24464i
$144$	0.469751	−	3.97232i	0.0391459	−	0.331027i
$145$	−2.82429	+	6.18434i	−0.234545	+	0.513582i
$146$	14.5145	−	9.45707i	1.20123	−	0.782673i
$147$	6.66444	+	0.958202i	0.549674	+	0.0790312i
$148$	−13.3816	−	1.75293i	−1.09996	−	0.144090i
$149$	−3.58066	+	12.1946i	−0.293339	+	0.999022i	0.672547	+	0.740055i	$0.265200\pi$
$149$	−3.58066	+	12.1946i	−0.293339	+	0.999022i	−0.965886	+	0.258967i	$0.916618\pi$
$150$	−0.635797	+	1.00310i	−0.0519126	+	0.0819026i
$151$	2.85780	+	6.25771i	0.232565	+	0.509246i	0.989551	−	0.144185i	$-0.0460562\pi$
$151$	2.85780	+	6.25771i	0.232565	+	0.509246i	−0.756986	+	0.653431i	$0.773329\pi$
$152$	2.48400	+	3.70979i	0.201479	+	0.300904i
$153$	−2.51870	+	2.90674i	−0.203625	+	0.234996i
$154$	1.48627	+	1.27163i	0.119767	+	0.102471i
$155$	4.41646	−	6.87215i	0.354739	−	0.551984i
$156$	−4.53891	+	10.2781i	−0.363404	+	0.822908i
$157$	−7.88633	−	12.2714i	−0.629398	−	0.979362i	−0.998746	−	0.0500708i	$-0.984055\pi$
$157$	−7.88633	−	12.2714i	−0.629398	−	0.979362i	0.369348	−	0.929291i	$-0.379581\pi$
$158$	−5.41814	−	11.6698i	−0.431044	−	0.928399i
$159$	−1.36762	+	0.401571i	−0.108460	+	0.0318466i
$160$	11.3635	−	1.99936i	0.898366	−	0.158063i
$161$	−2.41687	+	0.548032i	−0.190476	+	0.0431910i
$162$	−1.35940	−	0.389911i	−0.106805	−	0.0306343i
$163$	2.49635	+	8.50179i	0.195529	+	0.665911i	0.997635	+	0.0687298i	$0.0218946\pi$
$163$	2.49635	+	8.50179i	0.195529	+	0.665911i	−0.802106	+	0.597182i	$0.796287\pi$
$164$	2.12907	+	13.5950i	0.166253	+	1.06159i
$165$	2.95155	+	4.59270i	0.229778	+	0.357541i
$166$	7.58888	+	1.04257i	0.589011	+	0.0809194i
$167$	14.3689	+	9.23435i	1.11190	+	0.714575i	0.961707	−	0.274081i	$-0.0883737\pi$
$167$	14.3689	+	9.23435i	1.11190	+	0.714575i	0.150194	+	0.988656i	$0.452010\pi$
$168$	−0.438089	−	1.39438i	−0.0337993	−	0.107578i
$169$	12.1545	−	14.0270i	0.934959	−	1.07900i
$170$	−10.1205	−	4.54537i	−0.776206	−	0.348614i
$171$	1.43584	−	0.655724i	0.109801	−	0.0501445i
$172$	14.8556	−	13.2024i	1.13273	−	1.00667i
$173$	−1.79624	+	6.11742i	−0.136565	+	0.465099i	−0.999168	−	0.0407831i	$-0.987015\pi$
$173$	−1.79624	+	6.11742i	−0.136565	+	0.465099i	0.862603	+	0.505882i	$0.168833\pi$
$174$	0.700118	+	4.66166i	0.0530758	+	0.353400i
$175$	−0.0617575	+	0.429533i	−0.00466843	+	0.0324696i
$176$	−2.75767	+	10.3451i	−0.207867	+	0.779794i
$177$	−0.422817	+	0.925840i	−0.0317809	+	0.0695904i
$178$	12.7167	+	14.4911i	0.953154	+	1.08616i
$179$	−9.60657	+	1.38122i	−0.718029	+	0.103237i	−0.491638	−	0.870800i	$-0.663602\pi$
$179$	−9.60657	+	1.38122i	−0.718029	+	0.103237i	−0.226391	+	0.974037i	$0.572693\pi$
$180$	−0.0511744	−	4.07901i	−0.00381431	−	0.304031i
$181$	10.0306	−	8.69160i	0.745571	−	0.646041i	−0.196864	−	0.980431i	$-0.563076\pi$
$181$	10.0306	−	8.69160i	0.745571	−	0.646041i	0.942435	+	0.334390i	$0.108530\pi$
$182$	0.0257517	+	4.10539i	0.00190884	+	0.304312i
$183$	−5.91258			−0.437070
$184$	−8.42558	−	10.6306i	−0.621142	−	0.783698i
$185$	−13.7635			−1.01191
$186$	−0.0355275	−	5.66387i	−0.00260500	−	0.415295i
$187$	7.78016	−	6.74155i	0.568942	−	0.492991i
$188$	15.2133	−	0.190863i	1.10955	−	0.0139201i
$189$	−0.511486	+	0.0735405i	−0.0372051	+	0.00534929i
$190$	3.00321	+	3.42227i	0.217876	+	0.248278i
$191$	8.37301	−	18.3343i	0.605850	−	1.32663i	−0.319527	−	0.947577i	$-0.603524\pi$
$191$	8.37301	−	18.3343i	0.605850	−	1.32663i	0.925377	−	0.379049i	$-0.123749\pi$
$192$	5.84459	−	5.46267i	0.421797	−	0.394234i
$193$	3.39679	−	23.6252i	0.244506	−	1.70058i	−0.384458	−	0.923142i	$-0.625612\pi$
$193$	3.39679	−	23.6252i	0.244506	−	1.70058i	0.628964	−	0.777434i	$-0.283479\pi$
$194$	−0.127048	−	0.845938i	−0.00912154	−	0.0607348i
$195$	−3.22825	+	10.9944i	−0.231179	+	0.787325i
$196$	8.94529	+	10.0655i	0.638950	+	0.718961i
$197$	4.34657	−	1.98501i	0.309681	−	0.141426i	−0.254512	−	0.967070i	$-0.581915\pi$
$197$	4.34657	−	1.98501i	0.309681	−	0.141426i	0.564193	+	0.825643i	$0.309188\pi$
$198$	3.45300	+	1.55083i	0.245394	+	0.110213i
$199$	6.14112	−	7.08723i	0.435332	−	0.502400i	−0.495114	−	0.868828i	$-0.664874\pi$
$199$	6.14112	−	7.08723i	0.435332	−	0.502400i	0.930447	+	0.366427i	$0.119419\pi$
$200$	−2.26603	+	0.711948i	−0.160233	+	0.0503423i
$201$	−1.36338	−	0.876190i	−0.0961653	−	0.0618017i
$202$	−15.5104	−	2.13084i	−1.09131	−	0.149926i
$203$	0.931225	+	1.44901i	0.0653592	+	0.101701i
$204$	−7.59971	+	1.19016i	−0.532086	+	0.0833282i
$205$	3.95373	+	13.4652i	0.276140	+	0.940448i
$206$	−5.06418	−	1.45254i	−0.352838	−	0.101203i
$207$	−4.18885	+	2.33528i	−0.291145	+	0.162313i
$208$	−20.2001	+	9.84485i	−1.40063	+	0.682617i
$209$	−4.05381	+	1.19031i	−0.280408	+	0.0823352i
$210$	−0.627694	−	1.35195i	−0.0433150	−	0.0932936i
$211$	−1.44925	−	2.25508i	−0.0997706	−	0.155246i	0.787779	−	0.615957i	$-0.211231\pi$
$211$	−1.44925	−	2.25508i	−0.0997706	−	0.155246i	−0.887550	+	0.460711i	$0.847594\pi$
$212$	−2.60776	−	1.15161i	−0.179102	−	0.0790928i
$213$	−8.00361	+	12.4539i	−0.548399	+	0.853325i
$214$	−0.495707	−	0.424118i	−0.0338859	−	0.0289921i
$215$	13.2731	−	15.3180i	0.905217	−	1.04468i
$216$	−1.57367	−	2.35023i	−0.107074	−	0.159913i
$217$	−0.859737	−	1.88256i	−0.0583628	−	0.127797i
$218$	−3.16515	+	4.99366i	−0.214371	+	0.338214i
$219$	3.45112	−	11.7534i	0.233205	−	0.794224i
$220$	−1.41819	+	10.8262i	−0.0956145	+	0.729903i
$221$	21.3873	+	3.07503i	1.43867	+	0.206849i
$222$	−7.99559	+	5.20961i	−0.536629	+	0.349646i
$223$	2.65631	−	5.81651i	0.177880	−	0.389502i	−0.799600	−	0.600534i	$-0.794955\pi$
$223$	2.65631	−	5.81651i	0.177880	−	0.389502i	0.977479	+	0.211031i	$0.0676821\pi$
$224$	1.13034	−	2.69576i	0.0755243	−	0.180118i
$225$	0.119512	+	0.831227i	0.00796749	+	0.0554151i
$226$	−16.2591	+	4.88510i	−1.08154	+	0.324952i
$227$	−13.2020	+	11.4396i	−0.876245	+	0.759270i	−0.971714	−	0.236162i	$-0.924110\pi$
$227$	−13.2020	+	11.4396i	−0.876245	+	0.759270i	0.0954690	+	0.995432i	$0.469565\pi$
$228$	3.04000	+	0.851349i	0.201329	+	0.0563820i
$229$		−	20.5469i		−	1.35778i	−0.734240	−	0.678890i	$-0.762461\pi$
$229$		−	20.5469i		−	1.35778i	0.734240	−	0.678890i	$-0.237539\pi$
$230$	−9.92804	−	9.63351i	−0.654635	−	0.635215i
$231$	1.38312			0.0910025
$232$	−4.94696	+	8.02575i	−0.324784	+	0.526916i
$233$	1.75321	+	2.02331i	0.114857	+	0.132552i	0.810266	−	0.586062i	$-0.199322\pi$
$233$	1.75321	+	2.02331i	0.114857	+	0.132552i	−0.695410	+	0.718614i	$0.744777\pi$
$234$	2.28610	+	7.60884i	0.149447	+	0.497406i
$235$	15.3583	−	2.20819i	1.00187	−	0.144047i
$236$	−1.84093	+	0.868797i	−0.119834	+	0.0565538i
$237$	−8.27566	−	3.77937i	−0.537562	−	0.245496i
$238$	−2.35496	+	1.53440i	−0.152650	+	0.0994604i
$239$	−1.51784	+	10.5568i	−0.0981806	+	0.682861i	0.879980	+	0.475011i	$0.157556\pi$
$239$	−1.51784	+	10.5568i	−0.0981806	+	0.682861i	−0.978161	+	0.207850i	$0.933353\pi$
$240$	5.18641	−	6.29800i	0.334781	−	0.406534i
$241$	11.4679	+	3.36729i	0.738714	+	0.216906i	0.629378	−	0.777099i	$-0.283310\pi$
$241$	11.4679	+	3.36729i	0.738714	+	0.216906i	0.109335	+	0.994005i	$0.465128\pi$
$242$	4.58186	+	2.90413i	0.294533	+	0.186685i
$243$	−0.909632	+	0.415415i	−0.0583529	+	0.0266489i
$244$	−9.03330	−	7.63111i	−0.578298	−	0.488532i
$245$	10.3787	+	8.99320i	0.663071	+	0.574555i
$246$	7.39350	+	6.32574i	0.471392	+	0.403315i
$247$	−7.45997	−	4.79423i	−0.474666	−	0.305050i
$248$	7.25584	−	8.69918i	0.460746	−	0.552398i
$249$	4.55669	−	2.92841i	0.288769	−	0.185580i
$250$	−15.2785	+	7.09362i	−0.966297	+	0.448640i
$251$	−4.73784	−	16.1356i	−0.299050	−	1.01847i	−0.962732	−	0.270455i	$-0.912826\pi$
$251$	−4.73784	−	16.1356i	−0.299050	−	1.01847i	0.663683	−	0.748014i	$-0.268992\pi$
$252$	−0.876369	−	0.547797i	−0.0552060	−	0.0345079i
$253$	11.9873	−	4.59135i	0.753634	−	0.288656i
$254$	20.4054	+	5.85278i	1.28035	+	0.367236i
$255$	−7.52711	+	2.21016i	−0.471366	+	0.138406i
$256$	15.9799	−	0.802552i	0.998741	−	0.0501595i
$257$	−3.07254	+	1.97460i	−0.191660	+	0.123172i	−0.632952	−	0.774191i	$-0.718157\pi$
$257$	−3.07254	+	1.97460i	−0.191660	+	0.123172i	0.441292	+	0.897364i	$0.354520\pi$
$258$	1.91271	−	13.9226i	0.119080	−	0.866781i
$259$	−1.88520	+	2.93342i	−0.117140	+	0.182274i
$260$	−19.1221	+	12.6308i	−1.18590	+	0.783329i
$261$	2.51911	+	2.18282i	0.155929	+	0.135113i
$262$	24.9071	+	11.1864i	1.53876	+	0.691098i
$263$	−3.06878	−	6.71969i	−0.189229	−	0.414354i	0.791110	−	0.611674i	$-0.209503\pi$
$263$	−3.06878	−	6.71969i	−0.189229	−	0.414354i	−0.980339	+	0.197320i	$0.936776\pi$
$264$	3.27394	+	6.82602i	0.201497	+	0.420112i
$265$	−2.78949	−	0.819069i	−0.171357	−	0.0503150i
$266$	1.14074	−	0.171324i	0.0699433	−	0.0105045i
$267$	13.4940	+	1.94015i	0.825822	+	0.118735i
$268$	−0.952123	−	3.09830i	−0.0581601	−	0.189259i
$269$	5.43388	+	2.48157i	0.331310	+	0.151304i	0.574123	−	0.818769i	$-0.305343\pi$
$269$	5.43388	+	2.48157i	0.331310	+	0.151304i	−0.242813	+	0.970073i	$0.578070\pi$
$270$	−1.90260	−	2.16808i	−0.115788	−	0.131945i
$271$	2.25768	+	15.7025i	0.137144	+	0.953859i	0.935916	+	0.352224i	$0.114575\pi$
$271$	2.25768	+	15.7025i	0.137144	+	0.953859i	−0.798772	+	0.601634i	$0.794516\pi$
$272$	−13.1470	−	7.99027i	−0.797154	−	0.484481i
$273$	1.90106	+	2.19394i	0.115058	+	0.132784i
$274$	−15.6793	+	0.0983510i	−0.947224	+	0.00594160i
$275$		−	2.24774i		−	0.135544i
$276$	−9.41381	−	1.83851i	−0.566645	−	0.110665i
$277$			18.8452i			1.13230i	0.824303	+	0.566148i	$0.191567\pi$
$277$			18.8452i			1.13230i	−0.824303	+	0.566148i	$0.808433\pi$
$278$	−0.112116	−	17.8738i	−0.00672428	−	1.07200i
$279$	−2.62274	−	3.02681i	−0.157020	−	0.181210i
$280$	0.785909	−	2.87567i	0.0469670	−	0.171854i
$281$	2.41163	+	16.7733i	0.143866	+	1.00061i	0.926007	+	0.377507i	$0.123219\pi$
$281$	2.41163	+	16.7733i	0.143866	+	1.00061i	−0.782141	+	0.623101i	$0.785872\pi$
$282$	8.08622	−	7.09604i	0.481527	−	0.422563i
$283$	12.3344	+	5.63292i	0.733203	+	0.334842i	0.746785	−	0.665065i	$-0.231596\pi$
$283$	12.3344	+	5.63292i	0.733203	+	0.334842i	−0.0135825	+	0.999908i	$0.504324\pi$
$284$	−28.3017	+	8.69723i	−1.67940	+	0.516085i
$285$	3.18680	+	0.458192i	0.188769	+	0.0271410i
$286$	−3.15832	−	21.0293i	−0.186755	−	1.24349i
$287$	3.41138	+	1.00167i	0.201367	+	0.0591268i
$288$	0.629078	−	5.62177i	0.0370688	−	0.331266i
$289$	−0.916817	−	2.00755i	−0.0539304	−	0.118091i
$290$	−3.93922	+	8.77086i	−0.231319	+	0.515043i
$291$	−0.457135	−	0.396110i	−0.0267978	−	0.0232204i
$292$	20.4423	−	13.5028i	1.19630	−	0.790192i
$293$	10.7413	−	16.7138i	0.627515	−	0.976432i	−0.371336	−	0.928499i	$-0.621100\pi$
$293$	10.7413	−	16.7138i	0.627515	−	0.976432i	0.998851	−	0.0479334i	$-0.0152635\pi$
$294$	9.43326	+	1.29596i	0.550159	+	0.0755818i
$295$	−1.74645	+	1.12237i	−0.101682	+	0.0653471i
$296$	−18.9396	−	2.36027i	−1.10084	−	0.137188i
$297$	2.56817	−	0.754084i	0.149021	−	0.0437564i
$298$	−4.95555	+	17.2772i	−0.287067	+	1.00084i
$299$	23.7592	+	12.7039i	1.37403	+	0.734686i
$300$	−0.890236	+	1.42421i	−0.0513978	+	0.0822266i
$301$	−1.44670	−	4.92700i	−0.0833864	−	0.283988i
$302$	4.09697	+	8.82422i	0.235754	+	0.507777i
$303$	−9.31311	+	5.98517i	−0.535024	+	0.343839i
$304$	3.54574	+	5.22430i	0.203362	+	0.299634i
$305$	−10.1452	−	6.51995i	−0.580915	−	0.373331i
$306$	−3.53613	+	4.13301i	−0.202147	+	0.236269i
$307$	18.5242	+	16.0513i	1.05723	+	0.916095i	0.996627	−	0.0820670i	$-0.0261521\pi$
$307$	18.5242	+	16.0513i	1.05723	+	0.916095i	0.0606031	+	0.998162i	$0.480698\pi$
$308$	2.11314	+	1.78513i	0.120407	+	0.101717i
$309$	−3.38866	+	1.54755i	−0.192774	+	0.0880369i
$310$	6.18473	−	9.75767i	0.351269	−	0.554198i
$311$	10.6769	+	3.13501i	0.605430	+	0.177770i	0.570059	−	0.821604i	$-0.306920\pi$
$311$	10.6769	+	3.13501i	0.605430	+	0.177770i	0.0353712	+	0.999374i	$0.488739\pi$
$312$	−6.32769	+	14.5754i	−0.358235	+	0.825172i
$313$	3.94994	−	27.4725i	0.223264	−	1.55284i	−0.502308	−	0.864689i	$-0.667515\pi$
$313$	3.94994	−	27.4725i	0.223264	−	1.55284i	0.725572	−	0.688147i	$-0.241575\pi$
$314$	−11.2616	−	17.2840i	−0.635528	−	0.975395i
$315$	−0.958740	−	0.437842i	−0.0540189	−	0.0246696i
$316$	−7.76578	−	16.4552i	−0.436859	−	0.925677i
$317$	0.871027	−	0.125235i	0.0489217	−	0.00703388i	−0.117811	−	0.993036i	$-0.537588\pi$
$317$	0.871027	−	0.125235i	0.0489217	−	0.00703388i	0.166732	+	0.986002i	$0.446678\pi$
$318$	−1.93051	+	0.580027i	−0.108258	+	0.0325263i
$319$	−5.84253	−	6.74264i	−0.327119	−	0.377515i
$320$	16.0524	−	2.92826i	0.897357	−	0.163695i
$321$	−0.461304			−0.0257475
$322$	−3.41304	+	0.796458i	−0.190201	+	0.0443849i
$323$		−	6.07110i		−	0.337805i
$324$	−1.92590	−	0.539347i	−0.106995	−	0.0299637i
$325$	3.56543	−	3.08946i	0.197774	−	0.171372i
$326$	3.60572	+	12.0010i	0.199702	+	0.664672i
$327$	0.594962	+	4.13805i	0.0329014	+	0.228835i
$328$	3.13150	+	19.2070i	0.172908	+	1.06053i
$329$	1.63300	−	3.57578i	0.0900304	−	0.197139i
$330$	4.21478	+	6.46875i	0.232016	+	0.356093i
$331$	−27.7790	−	3.99401i	−1.52687	−	0.219531i	−0.672853	−	0.739776i	$-0.734931\pi$
$331$	−27.7790	−	3.99401i	−1.52687	−	0.219531i	−0.854017	+	0.520246i	$0.825840\pi$
$332$	10.7413	+	1.40707i	0.589507	+	0.0772232i
$333$	−1.90111	+	6.47460i	−0.104180	+	0.354806i
$334$	20.4022	+	12.9316i	1.11636	+	0.707587i
$335$	−1.37319	−	3.00686i	−0.0750253	−	0.164282i
$336$	−0.631908	−	1.96802i	−0.0344734	−	0.107364i
$337$	−20.4827	+	23.6383i	−1.11576	+	1.28766i	−0.162102	+	0.986774i	$0.551827\pi$
$337$	−20.4827	+	23.6383i	−1.11576	+	1.28766i	−0.953660	+	0.300885i	$0.902718\pi$
$338$	17.0642	−	19.9446i	0.928172	−	1.08484i
$339$	−6.49021	+	10.0990i	−0.352500	+	0.548500i
$340$	−14.3526	−	6.33822i	−0.778377	−	0.343738i
$341$	5.79560	+	9.01813i	0.313849	+	0.488359i
$342$	2.02472	−	0.940052i	0.109484	−	0.0508322i
$343$	6.80900	−	1.99930i	0.367651	−	0.107952i
$344$	20.8915	−	18.8024i	1.12639	−	1.01376i
$345$	−9.76271	−	0.612113i	−0.525607	−	0.0329551i
$346$	−2.48595	+	8.66710i	−0.133645	+	0.465946i
$347$	−6.96813	−	23.7313i	−0.374069	−	1.27396i	−0.904588	−	0.426288i	$-0.859821\pi$
$347$	−6.96813	−	23.7313i	−0.374069	−	1.27396i	0.530519	−	0.847673i	$-0.321997\pi$
$348$	1.03145	+	6.58625i	0.0552915	+	0.353060i
$349$	2.57513	+	4.00697i	0.137843	+	0.214488i	0.903311	−	0.428986i	$-0.141129\pi$
$349$	2.57513	+	4.00697i	0.137843	+	0.214488i	−0.765468	+	0.643474i	$0.777493\pi$
$350$	−0.0835263	+	0.607987i	−0.00446467	+	0.0324983i
$351$	4.72605	+	3.03725i	0.252258	+	0.162116i
$352$	−3.80809	+	14.6544i	−0.202972	+	0.781082i
$353$	18.2894	−	21.1071i	0.973446	−	1.12342i	−0.0188865	−	0.999822i	$-0.506012\pi$
$353$	18.2894	−	21.1071i	0.973446	−	1.12342i	0.992333	−	0.123595i	$-0.0394424\pi$
$354$	−0.589729	+	1.31306i	−0.0313437	+	0.0697884i
$355$	−27.4664	+	12.5435i	−1.45776	+	0.665739i
$356$	18.1123	+	20.3804i	0.959948	+	1.08016i
$357$	−0.559941	+	1.90698i	−0.0296352	+	0.100928i
$358$	−13.5732	+	2.03851i	−0.717367	+	0.107739i
$359$	3.36682	−	23.4167i	0.177694	−	1.23589i	−0.684388	−	0.729118i	$-0.739930\pi$
$359$	3.36682	−	23.4167i	0.177694	−	1.23589i	0.862082	−	0.506769i	$-0.169160\pi$
$360$	−0.108554	−	5.76802i	−0.00572128	−	0.304001i
$361$	6.85784	−	15.0166i	0.360939	−	0.790346i
$362$	14.1081	−	12.3805i	0.741504	−	0.650705i
$363$	3.79680	−	0.545898i	0.199280	−	0.0286522i
$364$	0.0728353	+	5.80555i	0.00381761	+	0.304294i
$365$	18.8825	−	16.3618i	0.988355	−	0.856415i
$366$	−8.36148	+	0.0524487i	−0.437062	+	0.00274154i
$367$	−19.9636			−1.04209			−0.521046	−	0.853529i	$-0.674458\pi$
$367$	−19.9636			−1.04209			−0.521046	+	0.853529i	$0.674458\pi$
$368$	−12.0096	−	14.9589i	−0.626045	−	0.779787i
$369$	6.88037			0.358178
$370$	−19.4642	+	0.122092i	−1.01189	+	0.00634726i
$371$	−0.556646	+	0.482337i	−0.0288996	+	0.0250417i
$372$	−0.100485	−	8.00945i	−0.00520990	−	0.415271i
$373$	30.0606	−	4.32206i	1.55648	−	0.223788i	0.690300	−	0.723523i	$-0.257478\pi$
$373$	30.0606	−	4.32206i	1.55648	−	0.223788i	0.866178	+	0.499735i	$0.166569\pi$
$374$	10.9428	−	9.60282i	0.565838	−	0.496550i
$375$	−4.94808	+	10.8348i	−0.255518	+	0.559506i
$376$	21.5128	−	0.404869i	1.10944	−	0.0208795i
$377$	2.66496	−	18.5352i	0.137252	−	0.954611i
$378$	−0.722683	+	0.108537i	−0.0371708	+	0.00558255i
$379$	−7.14274	+	24.3259i	−0.366898	+	1.24954i	0.544761	+	0.838591i	$0.316620\pi$
$379$	−7.14274	+	24.3259i	−0.366898	+	1.24954i	−0.911659	+	0.410948i	$0.865198\pi$
$380$	4.27745	+	4.81309i	0.219429	+	0.246906i
$381$	13.6541	−	6.23561i	0.699520	−	0.319460i
$382$	11.6784	−	26.0024i	0.597517	−	1.33040i
$383$	9.29738	−	10.7297i	0.475074	−	0.548264i	−0.466742	−	0.884393i	$-0.654572\pi$
$383$	9.29738	−	10.7297i	0.475074	−	0.548264i	0.941816	+	0.336129i	$0.109118\pi$
$384$	8.21688	−	7.77707i	0.419316	−	0.396872i
$385$	2.37326	+	1.52520i	0.120952	+	0.0777313i
$386$	4.59412	−	33.4405i	0.233834	−	1.70208i
$387$	−5.37246	−	8.35971i	−0.273098	−	0.424948i
$388$	−0.187174	−	1.19519i	−0.00950232	−	0.0606764i
$389$	−5.93379	−	20.2086i	−0.300855	−	1.02462i	−0.961702	−	0.274098i	$-0.911621\pi$
$389$	−5.93379	−	20.2086i	−0.300855	−	1.02462i	0.660846	−	0.750521i	$-0.270197\pi$
$390$	−4.46781	+	15.5768i	−0.226236	+	0.788760i
$391$	1.47743	+	18.3863i	0.0747167	+	0.929836i
$392$	12.7396	+	14.1551i	0.643447	+	0.714939i
$393$	18.5247	−	5.43933i	0.934445	−	0.274378i
$394$	6.12925	−	2.84573i	0.308787	−	0.143366i
$395$	−10.0324	−	15.6107i	−0.504784	−	0.785460i
$396$	4.89695	+	2.16253i	0.246081	+	0.108671i
$397$	−9.89176	+	15.3919i	−0.496453	+	0.772496i	−0.995568	−	0.0940393i	$-0.970022\pi$
$397$	−9.89176	+	15.3919i	−0.496453	+	0.772496i	0.499115	+	0.866536i	$0.333658\pi$
$398$	8.62182	−	10.0771i	0.432173	−	0.505121i
$399$	0.534152	−	0.616444i	0.0267410	−	0.0308608i
$400$	−3.19827	+	1.02693i	−0.159914	+	0.0513464i
$401$	15.0980	+	33.0600i	0.753958	+	1.65094i	0.759120	+	0.650951i	$0.225630\pi$
$401$	15.0980	+	33.0600i	0.753958	+	1.65094i	−0.00516189	+	0.999987i	$0.501643\pi$
$402$	−1.93584	−	1.22700i	−0.0965510	−	0.0611972i
$403$	−6.33892	+	21.5884i	−0.315764	+	1.07539i
$404$	−21.9535	−	2.87582i	−1.09223	−	0.143077i
$405$	−2.01890	−	0.290274i	−0.100320	−	0.0144238i
$406$	1.32978	+	2.04092i	0.0659958	+	0.101289i
$407$	7.50302	−	16.4293i	0.371911	−	0.814371i
$408$	−10.7368	+	1.75053i	−0.531553	+	0.0866640i
$409$	4.06636	+	28.2821i	0.201068	+	1.39846i	0.801122	+	0.598501i	$0.204237\pi$
$409$	4.06636	+	28.2821i	0.201068	+	1.39846i	−0.600054	+	0.799960i	$0.704854\pi$
$410$	5.71075	+	19.0072i	0.282034	+	0.938698i
$411$	−8.37914	+	7.26056i	−0.413312	+	0.358137i
$412$	−7.17458	−	2.00923i	−0.353466	−	0.0989879i
$413$			0.525953i			0.0258805i
$414$	−5.90310	+	3.33967i	−0.290122	+	0.164136i
$415$	11.0479			0.542322
$416$	−28.4794	+	14.1016i	−1.39632	+	0.691390i
$417$	−8.27674	−	9.55187i	−0.405314	−	0.467757i
$418$	−5.72228	+	1.71927i	−0.279886	+	0.0840924i
$419$	−3.42952	+	0.493091i	−0.167543	+	0.0240891i	−0.225576	−	0.974226i	$-0.572426\pi$
$419$	−3.42952	+	0.493091i	−0.167543	+	0.0240891i	0.0580326	+	0.998315i	$0.481517\pi$
$420$	−0.899669	−	1.90634i	−0.0438994	−	0.0930200i
$421$	−16.3495	−	7.46657i	−0.796826	−	0.363898i	−0.0249641	−	0.999688i	$-0.507947\pi$
$421$	−16.3495	−	7.46657i	−0.796826	−	0.363898i	−0.771862	+	0.635790i	$0.780674\pi$
$422$	−2.06951	−	3.17624i	−0.100742	−	0.154617i
$423$	1.08263	−	7.52983i	0.0526391	−	0.366113i
$424$	−3.69807	−	1.60546i	−0.179594	−	0.0779679i
$425$	3.09908	+	0.909972i	0.150327	+	0.0441401i
$426$	−11.2081	+	17.6831i	−0.543035	+	0.856748i
$427$	−2.77920	+	1.26922i	−0.134495	+	0.0614217i
$428$	−0.704785	−	0.595385i	−0.0340671	−	0.0287790i
$429$	−11.3640	−	9.84697i	−0.548659	−	0.475416i
$430$	18.6347	−	21.7802i	0.898646	−	1.05033i
$431$	3.74242	+	2.40511i	0.180266	+	0.115850i	0.627662	−	0.778486i	$-0.284012\pi$
$431$	3.74242	+	2.40511i	0.180266	+	0.115850i	−0.447396	+	0.894336i	$0.647648\pi$
$432$	−2.24630	−	3.30970i	−0.108075	−	0.159238i
$433$	−3.14167	+	2.01903i	−0.150979	+	0.0970282i	−0.613949	−	0.789346i	$-0.710420\pi$
$433$	−3.14167	+	2.01903i	−0.150979	+	0.0970282i	0.462970	+	0.886374i	$0.346784\pi$
$434$	−1.23253	−	2.65467i	−0.0591632	−	0.127428i
$435$	1.91542	+	6.52333i	0.0918375	+	0.312770i
$436$	−4.43181	+	7.09004i	−0.212245	+	0.339552i
$437$	2.58309	−	7.11578i	0.123566	−	0.340394i
$438$	4.77626	−	16.6522i	0.228219	−	0.795671i
$439$	−27.0062	+	7.92972i	−1.28893	+	0.378465i	−0.853187	−	0.521605i	$-0.825334\pi$
$439$	−27.0062	+	7.92972i	−1.28893	+	0.378465i	−0.435746	+	0.900070i	$0.643515\pi$
$440$	−1.90955	+	15.3228i	−0.0910343	+	0.730488i
$441$	5.66414	−	3.64012i	0.269721	−	0.173339i
$442$	30.2729	+	4.15894i	1.43994	+	0.197821i
$443$	4.29701	−	6.68627i	0.204157	−	0.317674i	−0.724044	−	0.689754i	$-0.757719\pi$
$443$	4.29701	−	6.68627i	0.204157	−	0.317674i	0.928201	+	0.372079i	$0.121355\pi$
$444$	−11.2610	+	7.43828i	−0.534425	+	0.353005i
$445$	21.0146	+	18.2093i	0.996188	+	0.863202i
$446$	3.70492	−	8.24919i	0.175433	−	0.390611i
$447$	5.27969	+	11.5609i	0.249721	+	0.546812i
$448$	1.57460	−	3.82234i	0.0743931	−	0.180589i
$449$	−5.66006	−	1.66194i	−0.267115	−	0.0784319i	0.145433	−	0.989368i	$-0.453543\pi$
$449$	−5.66006	−	1.66194i	−0.267115	−	0.0784319i	−0.412547	+	0.910936i	$0.635361\pi$
$450$	0.176386	+	1.17445i	0.00831493	+	0.0553640i
$451$	−18.2285	−	2.62086i	−0.858346	−	0.123412i
$452$	−22.9501	+	7.05267i	−1.07948	+	0.331730i
$453$	6.25771	+	2.85780i	0.294013	+	0.134271i
$454$	−18.5685	+	16.2948i	−0.871465	+	0.764752i
$455$	0.842668	+	5.86088i	0.0395049	+	0.274762i
$456$	4.30668	+	1.17700i	0.201679	+	0.0551180i
$457$	0.232393	+	0.268195i	0.0108709	+	0.0125457i	0.761159	−	0.648565i	$-0.224631\pi$
$457$	0.232393	+	0.268195i	0.0108709	+	0.0125457i	−0.750288	+	0.661111i	$0.770085\pi$
$458$	−0.182266	−	29.0572i	−0.00851672	−	1.35775i
$459$			3.84617i			0.179524i
$460$	−14.1255	−	13.5355i	−0.658607	−	0.631096i
$461$			9.49749i			0.442342i	0.975235	+	0.221171i	$0.0709879\pi$
$461$			9.49749i			0.442342i	−0.975235	+	0.221171i	$0.929012\pi$
$462$	1.95599	−	0.0122692i	0.0910007	−	0.000570816i
$463$	−12.9762	−	14.9753i	−0.603054	−	0.695962i	0.369343	−	0.929293i	$-0.379583\pi$
$463$	−12.9762	−	14.9753i	−0.603054	−	0.695962i	−0.972397	+	0.233332i	$0.925037\pi$
$464$	−6.92472	+	11.3938i	−0.321472	+	0.528943i
$465$	−1.16256	−	8.08579i	−0.0539125	−	0.374969i
$466$	2.49731	+	2.84579i	0.115686	+	0.131829i
$467$	−28.0694	−	12.8189i	−1.29890	−	0.593187i	−0.358584	−	0.933497i	$-0.616740\pi$
$467$	−28.0694	−	12.8189i	−1.29890	−	0.593187i	−0.940313	+	0.340311i	$0.889468\pi$
$468$	3.30046	+	10.7400i	0.152564	+	0.496459i
$469$	−0.828940	−	0.119184i	−0.0382769	−	0.00550338i
$470$	21.6999	−	3.25903i	1.00094	−	0.150328i
$471$	−13.9961	−	4.10963i	−0.644908	−	0.189362i
$472$	−2.59570	+	1.24497i	−0.119477	+	0.0573044i
$473$	11.0492	+	24.1943i	0.508041	+	1.11245i
$474$	−11.7369	−	5.27132i	−0.539091	−	0.242120i
$475$	−1.00180	−	0.868062i	−0.0459656	−	0.0398294i
$476$	−3.31674	+	2.19082i	−0.152023	+	0.100416i
$477$	−0.770608	+	1.19909i	−0.0352837	+	0.0549025i
$478$	−2.05286	+	14.9427i	−0.0938954	+	0.683464i
$479$	−17.1188	+	11.0016i	−0.782177	+	0.502675i	−0.869755	−	0.493483i	$-0.835724\pi$
$479$	−17.1188	+	11.0016i	−0.782177	+	0.502675i	0.0875785	+	0.996158i	$0.472087\pi$
$480$	7.27868	−	8.95254i	0.332225	−	0.408626i
$481$	36.3734	−	10.6802i	1.65849	−	0.486975i
$482$	16.2476	+	4.66024i	0.740060	+	0.212268i
$483$	−1.46766	+	1.99689i	−0.0667810	+	0.0908615i
$484$	6.50536	+	4.06634i	0.295698	+	0.184834i
$485$	−0.347586	−	1.18377i	−0.0157831	−	0.0537522i
$486$	−1.28270	+	0.595543i	−0.0581846	+	0.0270144i
$487$	−20.0699	+	12.8982i	−0.909455	+	0.584471i	−0.909580	−	0.415529i	$-0.863597\pi$
$487$	−20.0699	+	12.8982i	−0.909455	+	0.584471i	0.000125165		1.00000i	$0.499960\pi$
$488$	−12.8425	−	10.7117i	−0.581351	−	0.484895i
$489$	7.45410	+	4.79046i	0.337086	+	0.216632i
$490$	14.7572	+	12.6260i	0.666662	+	0.570384i
$491$	−15.4721	−	13.4066i	−0.698244	−	0.605032i	0.231676	−	0.972793i	$-0.425579\pi$
$491$	−15.4721	−	13.4066i	−0.698244	−	0.605032i	−0.929920	+	0.367761i	$0.880125\pi$
$492$	10.5119	+	8.88019i	0.473913	+	0.400350i
$493$	11.6617	−	5.32574i	0.525218	−	0.239859i
$494$	−10.5923	−	6.71376i	−0.476570	−	0.302066i
$495$	5.23821	+	1.53808i	0.235440	+	0.0691314i
$496$	10.1839	−	12.3666i	0.457272	−	0.555277i
$497$	−1.08869	+	7.57200i	−0.0488344	+	0.339651i
$498$	6.41803	−	4.18173i	0.287599	−	0.187388i
$499$	−11.2018	−	5.11568i	−0.501460	−	0.229009i	0.148592	−	0.988899i	$-0.452526\pi$
$499$	−11.2018	−	5.11568i	−0.501460	−	0.229009i	−0.650053	+	0.759889i	$0.725253\pi$
$500$	−21.5437	+	10.1672i	−0.963464	+	0.454692i
$501$	16.9065	−	2.43079i	0.755328	−	0.108600i
$502$	−6.84332	−	22.7767i	−0.305432	−	1.01657i
$503$	22.4596	+	25.9197i	1.00142	+	1.15570i	0.987789	+	0.155796i	$0.0497944\pi$
$503$	22.4596	+	25.9197i	1.00142	+	1.15570i	0.0136335	+	0.999907i	$0.495660\pi$
$504$	−1.24421	−	0.766912i	−0.0554214	−	0.0341610i
$505$	−22.5801			−1.00480
$506$	16.9115	−	6.59936i	0.751809	−	0.293377i
$507$		−	18.5604i		−	0.824295i
$508$	28.9089	+	8.09590i	1.28262	+	0.359198i
$509$	−3.19111	+	2.76511i	−0.141443	+	0.122561i	−0.722709	−	0.691153i	$-0.757103\pi$
$509$	−3.19111	+	2.76511i	−0.141443	+	0.122561i	0.581265	+	0.813714i	$0.302558\pi$
$510$	−10.6251	+	3.19235i	−0.470489	+	0.141360i
$511$	−0.900845	−	6.26551i	−0.0398510	−	0.277170i
$512$	22.5914	−	1.27671i	0.998407	−	0.0564231i
$513$	0.655724	−	1.43584i	0.0289509	−	0.0633937i
$514$	−4.32763	+	2.81971i	−0.190883	+	0.124372i
$515$	−7.52103	−	1.08136i	−0.331416	−	0.0476504i
$516$	2.58142	−	19.7061i	0.113641	−	0.867511i
$517$	−5.73651	+	19.5368i	−0.252291	+	0.859225i
$518$	−2.64000	+	4.16513i	−0.115995	+	0.183005i
$519$	2.64855	+	5.79952i	0.116259	+	0.254571i
$520$	−26.9302	+	18.0319i	−1.18097	+	0.790752i
$521$	−5.54587	+	6.40028i	−0.242969	+	0.280401i	−0.864116	−	0.503293i	$-0.832122\pi$
$521$	−5.54587	+	6.40028i	−0.242969	+	0.280401i	0.621147	+	0.783694i	$0.286667\pi$
$522$	3.58185	+	3.06457i	0.156773	+	0.134133i
$523$	19.5121	−	30.3614i	0.853205	−	1.32761i	−0.0901840	−	0.995925i	$-0.528746\pi$
$523$	19.5121	−	30.3614i	0.853205	−	1.32761i	0.943389	−	0.331688i	$-0.107618\pi$
$524$	35.3225	+	15.5987i	1.54307	+	0.681433i
$525$	0.234611	+	0.365062i	0.0102393	+	0.0159326i
$526$	−4.39943	−	9.47567i	−0.191824	−	0.413159i
$527$	−14.7801	+	4.33983i	−0.643831	+	0.189046i
$528$	4.69051	+	9.62422i	0.204128	+	0.418840i
$529$	−6.09123	+	22.1787i	−0.264836	+	0.964293i
$530$	−3.95212	−	1.13357i	−0.171669	−	0.0492391i
$531$	0.286753	+	0.976590i	0.0124440	+	0.0423804i
$532$	1.61170	−	0.252403i	0.0698761	−	0.0109430i
$533$	−20.8974	−	32.5169i	−0.905165	−	1.40846i
$534$	19.1003	+	2.62403i	0.826550	+	0.113553i
$535$	−0.791539	−	0.508691i	−0.0342212	−	0.0219926i
$536$	−1.37396	−	4.37313i	−0.0593461	−	0.188891i
$537$	−6.35566	+	7.33482i	−0.274267	+	0.316521i
$538$	7.70654	+	3.46120i	0.332252	+	0.149223i
$539$	−16.3929	+	7.48638i	−0.706091	+	0.322461i
$540$	−2.70986	−	3.04919i	−0.116614	−	0.131216i
$541$	8.69532	−	29.6135i	0.373841	−	1.27319i	−0.530977	−	0.847386i	$-0.678175\pi$
$541$	8.69532	−	29.6135i	0.373841	−	1.27319i	0.904818	−	0.425799i	$-0.140007\pi$
$542$	3.33207	+	22.1862i	0.143125	+	0.952980i
$543$	1.88886	−	13.1373i	0.0810589	−	0.563777i
$544$	−18.6632	−	11.1831i	−0.800178	−	0.479472i
$545$	−3.54225	+	7.75645i	−0.151733	+	0.332250i
$546$	2.70792	+	3.08578i	0.115888	+	0.132059i
$547$	−28.7038	+	4.12699i	−1.22729	+	0.176457i	−0.725310	−	0.688423i	$-0.758303\pi$
$547$	−28.7038	+	4.12699i	−1.22729	+	0.176457i	−0.501978	+	0.864880i	$0.667394\pi$
$548$	−22.1726	+	0.278173i	−0.947168	+	0.0118830i
$549$	−4.46843	+	3.87191i	−0.190708	+	0.165249i
$550$	−0.0199390	−	3.17871i	−0.000850201	−	0.135541i
$551$	−5.26148			−0.224147
$552$	−13.3292	−	2.51649i	−0.567328	−	0.107109i
$553$	−4.70125			−0.199918
$554$	0.167170	+	26.6506i	0.00710236	+	1.13227i
$555$	−10.4018	+	9.01319i	−0.441531	+	0.382589i
$556$	−0.317106	−	25.2759i	−0.0134483	−	1.07194i
$557$	−45.5949	+	6.55556i	−1.93192	+	0.277768i	−0.997020	−	0.0771431i	$-0.975420\pi$
$557$	−45.5949	+	6.55556i	−1.93192	+	0.277768i	−0.934900	+	0.354911i	$0.884511\pi$
$558$	−3.73590	−	4.25720i	−0.158153	−	0.180222i
$559$	−23.1909	+	50.7810i	−0.980871	+	2.14781i
$560$	1.08591	−	4.07370i	0.0458881	−	0.172145i
$561$	1.46508	−	10.1898i	0.0618557	−	0.430216i
$562$	3.55928	+	23.6991i	0.150139	+	0.999686i
$563$	−5.05415	+	17.2128i	−0.213007	+	0.725435i	0.781789	+	0.623544i	$0.214308\pi$
$563$	−5.05415	+	17.2128i	−0.213007	+	0.725435i	−0.994796	+	0.101891i	$0.967511\pi$
$564$	11.3725	−	10.1068i	0.478867	−	0.425575i
$565$	−22.2728	+	10.1716i	−0.937022	+	0.427924i
$566$	17.4931	+	7.85658i	0.735289	+	0.330237i
$567$	−0.338396	+	0.390530i	−0.0142113	+	0.0164007i
$568$	−39.9467	+	12.5505i	−1.67613	+	0.526609i
$569$	−15.7142	−	10.0989i	−0.658774	−	0.423368i	0.168089	−	0.985772i	$-0.446240\pi$
$569$	−15.7142	−	10.0989i	−0.658774	−	0.423368i	−0.826863	+	0.562403i	$0.809877\pi$
$570$	4.51079	+	0.619700i	0.188936	+	0.0259564i
$571$	2.95467	+	4.59755i	0.123649	+	0.192402i	0.897559	−	0.440893i	$-0.145338\pi$
$571$	2.95467	+	4.59755i	0.123649	+	0.192402i	−0.773910	+	0.633295i	$0.781702\pi$
$572$	−4.65299	−	29.7113i	−0.194551	−	1.24229i
$573$	−5.67854	−	19.3393i	−0.237224	−	0.807912i
$574$	4.83321	+	1.38629i	0.201734	+	0.0578625i
$575$	3.24519	+	2.38513i	0.135334	+	0.0994669i
$576$	0.839764	−	7.95580i	0.0349902	−	0.331492i
$577$	−21.4206	+	6.28966i	−0.891752	+	0.261842i	−0.695341	−	0.718680i	$-0.744747\pi$
$577$	−21.4206	+	6.28966i	−0.891752	+	0.261842i	−0.196411	+	0.980522i	$0.562929\pi$
$578$	−1.31436	−	2.83092i	−0.0546701	−	0.117751i
$579$	−12.9041	−	20.0791i	−0.536275	−	0.834460i
$580$	−5.49298	+	12.4386i	−0.228084	+	0.516484i
$581$	1.51324	−	2.35465i	0.0627798	−	0.0976873i
$582$	−0.649988	−	0.556118i	−0.0269429	−	0.0230518i
$583$	2.49837	−	2.88327i	0.103472	−	0.119413i
$584$	28.7895	−	19.2768i	1.19132	−	0.797681i
$585$	4.76005	+	10.4231i	0.196804	+	0.430941i
$586$	15.0420	−	23.7317i	0.621378	−	0.980349i
$587$	−2.91461	+	9.92625i	−0.120299	+	0.409700i	−0.997520	−	0.0703867i	$-0.977577\pi$
$587$	−2.91461	+	9.92625i	−0.120299	+	0.409700i	0.877221	+	0.480087i	$0.159395\pi$
$588$	13.3519	+	1.74905i	0.550622	+	0.0721294i
$589$	6.25753	+	0.899697i	0.257837	+	0.0370714i
$590$	−2.45985	+	1.60274i	−0.101270	+	0.0659837i
$591$	1.98501	−	4.34657i	0.0816525	−	0.178794i
$592$	−26.8050	−	3.16985i	−1.10168	−	0.130280i
$593$	1.45495	+	10.1194i	0.0597476	+	0.415554i	0.997642	+	0.0686329i	$0.0218637\pi$
$593$	1.45495	+	10.1194i	0.0597476	+	0.415554i	−0.937894	+	0.346921i	$0.887227\pi$
$594$	3.62518	−	1.08920i	0.148743	−	0.0446902i
$595$	−3.06366	+	2.65468i	−0.125598	+	0.108831i
$596$	−6.85480	+	24.4772i	−0.280784	+	1.00262i
$597$		−	9.37775i		−	0.383806i
$598$	33.7126	+	17.7549i	1.37861	+	0.726053i
$599$	13.4538			0.549708			0.274854	−	0.961486i	$-0.411370\pi$
$599$	13.4538			0.549708			0.274854	+	0.961486i	$0.411370\pi$
$600$	−1.24633	+	2.02199i	−0.0508810	+	0.0825474i
$601$	−31.1854	−	35.9898i	−1.27208	−	1.46806i	−0.815929	−	0.578152i	$-0.803774\pi$
$601$	−31.1854	−	35.9898i	−1.27208	−	1.46806i	−0.456148	−	0.889904i	$-0.650771\pi$
$602$	−2.08961	−	6.95487i	−0.0851660	−	0.283459i
$603$	−1.60415	+	0.230643i	−0.0653262	+	0.00939249i
$604$	5.87216	+	12.4427i	0.238935	+	0.506288i
$605$	7.11681	+	3.25014i	0.289339	+	0.132137i
$606$	−13.1174	+	8.54676i	−0.532857	+	0.347188i
$607$	−4.77355	+	33.2008i	−0.193752	+	1.34758i	0.628214	+	0.778041i	$0.283786\pi$
$607$	−4.77355	+	33.2008i	−0.193752	+	1.34758i	−0.821966	+	0.569536i	$0.807123\pi$
$608$	5.06068	+	7.35667i	0.205238	+	0.298352i
$609$	1.65268	+	0.485269i	0.0669698	+	0.0196641i
$610$	−14.4051	−	9.13042i	−0.583245	−	0.369680i
$611$	−38.8745	+	17.7534i	−1.57269	+	0.718225i
$612$	−4.96408	+	5.87622i	−0.200661	+	0.237532i
$613$	32.6987	+	28.3336i	1.32069	+	1.14438i	0.978840	+	0.204629i	$0.0655987\pi$
$613$	32.6987	+	28.3336i	1.32069	+	1.14438i	0.341849	+	0.939755i	$0.388947\pi$
$614$	26.3390	+	22.5352i	1.06296	+	0.909445i
$615$	11.8058	+	7.58715i	0.476057	+	0.305944i
$616$	3.00421	+	2.50576i	0.121043	+	0.100960i
$617$	−14.9576	+	9.61265i	−0.602169	+	0.386991i	−0.805913	−	0.592033i	$-0.798325\pi$
$617$	−14.9576	+	9.61265i	−0.602169	+	0.386991i	0.203744	+	0.979024i	$0.434689\pi$
$618$	−4.77846	+	2.21858i	−0.192218	+	0.0892444i
$619$	−7.25273	−	24.7005i	−0.291512	−	0.992798i	−0.966862	−	0.255301i	$-0.917826\pi$
$619$	−7.25273	−	24.7005i	−0.291512	−	0.992798i	0.675350	−	0.737497i	$-0.263993\pi$
$620$	8.65980	−	13.8540i	0.347786	−	0.556391i
$621$	−1.63644	+	4.50800i	−0.0656682	+	0.180900i
$622$	15.1269	+	4.33878i	0.606533	+	0.173969i
$623$	6.75933	−	1.98472i	0.270807	−	0.0795160i
$624$	−8.81923	+	20.6685i	−0.353052	+	0.827403i
$625$	−16.9058	+	10.8647i	−0.676230	+	0.434587i
$626$	5.34226	−	38.8862i	0.213519	−	1.55421i
$627$	−2.28418	+	3.55425i	−0.0912214	+	0.141943i
$628$	−16.0793	−	24.3429i	−0.641634	−	0.971389i
$629$	19.6145	+	16.9961i	0.782082	+	0.677678i
$630$	−1.35972	−	0.610685i	−0.0541726	−	0.0243303i
$631$	7.33737	+	16.0666i	0.292096	+	0.639602i	0.997610	−	0.0690945i	$-0.0220110\pi$
$631$	7.33737	+	16.0666i	0.292096	+	0.639602i	−0.705514	+	0.708696i	$0.749284\pi$
$632$	−11.1282	−	23.2018i	−0.442657	−	0.922919i
$633$	−2.57203	−	0.755217i	−0.102229	−	0.0300172i
$634$	1.23068	−	0.184832i	0.0488766	−	0.00734061i
$635$	30.3048	+	4.35718i	1.20261	+	0.172909i
$636$	−2.72496	+	0.837391i	−0.108052	+	0.0332047i
$637$	−34.4068	−	15.7130i	−1.36325	−	0.622573i
$638$	−8.32223	−	9.48351i	−0.329480	−	0.375456i
$639$	2.10682	+	14.6533i	0.0833445	+	0.579674i
$640$	22.6751	−	4.28351i	0.896312	−	0.169320i
$641$	−23.6008	−	27.2368i	−0.932176	−	1.07579i	−0.996962	−	0.0778892i	$-0.975182\pi$
$641$	−23.6008	−	27.2368i	−0.932176	−	1.07579i	0.0647861	−	0.997899i	$-0.479363\pi$
$642$	−0.652369	+	0.00409208i	−0.0257470	+	0.000161502i
$643$			4.28058i			0.168810i	0.996432	+	0.0844049i	$0.0268989\pi$
$643$			4.28058i			0.168810i	−0.996432	+	0.0844049i	$0.973101\pi$
$644$	−4.81961	+	1.15662i	−0.189919	+	0.0455770i
$645$		−	20.2686i		−	0.798074i
$646$	−0.0538548	−	8.58566i	−0.00211889	−	0.337798i
$647$	1.18773	+	1.37071i	0.0466945	+	0.0538883i	0.778616	−	0.627500i	$-0.215922\pi$
$647$	1.18773	+	1.37071i	0.0466945	+	0.0538883i	−0.731922	+	0.681389i	$0.761376\pi$
$648$	−2.72837	−	0.745653i	−0.107180	−	0.0292920i
$649$	−0.387706	−	2.69656i	−0.0152188	−	0.105849i
$650$	5.01477	−	4.40070i	0.196696	−	0.172610i
$651$	−1.88256	−	0.859737i	−0.0737834	−	0.0336958i
$652$	5.20561	+	16.9396i	0.203868	+	0.663406i
$653$	17.1590	+	2.46709i	0.671484	+	0.0965448i	0.469620	−	0.882869i	$-0.344391\pi$
$653$	17.1590	+	2.46709i	0.671484	+	0.0965448i	0.201864	+	0.979414i	$0.435300\pi$
$654$	0.878093	+	5.84669i	0.0343362	+	0.228624i
$655$	37.7841	+	11.0944i	1.47635	+	0.433494i
$656$	4.59890	+	27.1345i	0.179557	+	1.05942i
$657$	−5.08868	−	11.1427i	−0.198528	−	0.434717i
$658$	2.27765	−	5.07130i	0.0887920	−	0.197700i
$659$	−24.7045	−	21.4065i	−0.962350	−	0.833881i	0.0238037	−	0.999717i	$-0.492422\pi$
$659$	−24.7045	−	21.4065i	−0.962350	−	0.833881i	−0.986153	+	0.165836i	$0.946968\pi$
$660$	6.01786	+	9.11062i	0.234245	+	0.354630i
$661$	−1.02006	+	1.58724i	−0.0396757	+	0.0617365i	−0.860525	−	0.509408i	$-0.829864\pi$
$661$	−1.02006	+	1.58724i	−0.0396757	+	0.0617365i	0.820849	+	0.571145i	$0.193501\pi$
$662$	−39.3200	−	5.40185i	−1.52822	−	0.209949i
$663$	18.1772	−	11.6818i	0.705943	−	0.453682i
$664$	15.2027	+	1.89458i	0.589980	+	0.0735240i
$665$	1.59630	−	0.468717i	0.0619020	−	0.0181761i
$666$	−2.63109	+	9.17315i	−0.101953	+	0.355452i
$667$	15.9344	−	1.28041i	0.616982	−	0.0495775i
$668$	28.9673	+	18.1067i	1.12078	+	0.700571i
$669$	−1.80150	−	6.13534i	−0.0696500	−	0.237206i
$670$	−1.96862	−	4.24008i	−0.0760543	−	0.163809i
$671$	13.3133	−	8.55595i	0.513955	−	0.330299i
$672$	−0.911093	−	2.77754i	−0.0351462	−	0.107146i
$673$	−19.4115	−	12.4750i	−0.748259	−	0.480877i	0.110104	−	0.993920i	$-0.464882\pi$
$673$	−19.4115	−	12.4750i	−0.748259	−	0.480877i	−0.858363	+	0.513043i	$0.828518\pi$
$674$	−28.7566	+	33.6106i	−1.10766	+	1.29463i
$675$	0.634659	+	0.549935i	0.0244280	+	0.0211670i
$676$	23.9551	−	28.3567i	0.921349	−	1.09064i
$677$	3.67614	−	1.67884i	0.141285	−	0.0645229i	−0.343518	−	0.939146i	$-0.611619\pi$
$677$	3.67614	−	1.67884i	0.141285	−	0.0645229i	0.484803	+	0.874623i	$0.338891\pi$
$678$	−9.08878	+	14.3394i	−0.349052	+	0.550701i
$679$	−0.299906	−	0.0880604i	−0.0115093	−	0.00337945i
$680$	−20.3534	−	8.83610i	−0.780518	−	0.338849i
$681$	−2.48605	+	17.2909i	−0.0952658	+	0.662588i
$682$	8.27605	+	12.7019i	0.316906	+	0.486381i
$683$	23.9588	+	10.9416i	0.916760	+	0.418670i	0.817195	−	0.576361i	$-0.195528\pi$
$683$	23.9588	+	10.9416i	0.916760	+	0.418670i	0.0995644	+	0.995031i	$0.468255\pi$
$684$	2.85499	−	1.34737i	0.109163	−	0.0515180i
$685$	−22.3839	+	3.21833i	−0.855247	+	0.122966i
$686$	9.61145	−	2.88778i	0.366967	−	0.110256i
$687$	−13.4554	−	15.5283i	−0.513355	−	0.592443i
$688$	29.3777	−	26.7754i	1.12001	−	1.02080i
$689$	8.00748			0.305061
$690$	−13.8117	−	0.779040i	−0.525803	−	0.0296575i
$691$			23.8911i			0.908861i	0.890782	+	0.454431i	$0.150157\pi$
$691$			23.8911i			0.908861i	−0.890782	+	0.454431i	$0.849843\pi$
$692$	−3.43871	+	12.2789i	−0.130720	+	0.466776i
$693$	1.04529	−	0.905749i	0.0397073	−	0.0344066i
$694$	−10.0647	−	33.4986i	−0.382052	−	1.27159i
$695$	−3.66876	−	25.5168i	−0.139164	−	0.967907i
$696$	1.51709	+	9.30502i	0.0575050	+	0.352706i
$697$	10.9931	−	24.0716i	0.416395	−	0.911778i
$698$	3.67725	+	5.64376i	0.139186	+	0.213620i
$699$	2.64998	+	0.381009i	0.100231	+	0.0144111i
$700$	−0.112728	+	0.860547i	−0.00426073	+	0.0325256i
$701$	−12.4878	+	42.5294i	−0.471656	+	1.60631i	0.289115	+	0.957294i	$0.406639\pi$
$701$	−12.4878	+	42.5294i	−0.471656	+	1.60631i	−0.760771	+	0.649020i	$0.775179\pi$
$702$	6.71045	+	4.25331i	0.253270	+	0.160531i
$703$	−4.42479	−	9.68893i	−0.166884	−	0.365425i
$704$	−5.25535	+	20.7578i	−0.198068	+	0.782340i
$705$	10.1610	−	11.7264i	0.382685	−	0.441641i
$706$	25.6774	−	30.0116i	0.966380	−	1.12950i
$707$	−3.09281	+	4.81251i	−0.116317	+	0.180993i
$708$	−0.822339	+	1.86214i	−0.0309054	+	0.0699836i
$709$	−3.52862	−	5.49065i	−0.132520	−	0.206206i	0.768651	−	0.639668i	$-0.220928\pi$
$709$	−3.52862	−	5.49065i	−0.132520	−	0.206206i	−0.901172	+	0.433462i	$0.857292\pi$
$710$	−38.7313	+	17.9825i	−1.45356	+	0.674869i
$711$	−8.72929	+	2.56315i	−0.327374	+	0.0961257i
$712$	25.7949	+	28.6609i	0.966705	+	1.07411i
$713$	−19.1699	−	1.20193i	−0.717917	−	0.0450128i
$714$	−0.774944	+	2.70179i	−0.0290015	+	0.101112i
$715$	−8.64070	−	29.4275i	−0.323144	−	1.10053i
$716$	−19.1770	+	3.00324i	−0.716677	+	0.112236i
$717$	5.76612	+	8.97225i	0.215340	+	0.335075i
$718$	4.55358	−	33.1455i	0.169938	−	1.23698i
$719$	16.1691	+	10.3913i	0.603006	+	0.387529i	0.806229	−	0.591604i	$-0.201505\pi$
$719$	16.1691	+	10.3913i	0.603006	+	0.387529i	−0.203222	+	0.979133i	$0.565141\pi$
$720$	−0.204681	−	8.15608i	−0.00762802	−	0.303959i
$721$	−1.26063	+	1.45484i	−0.0469483	+	0.0541812i
$722$	9.56505	−	21.2971i	0.355974	−	0.792594i
$723$	10.8720	−	4.96507i	0.404333	−	0.184653i
$724$	19.8416	−	17.6335i	0.737408	−	0.655344i
$725$	0.788622	−	2.68580i	0.0292887	−	0.0997481i
$726$	5.36454	−	0.805681i	0.199097	−	0.0299016i
$727$	3.70230	−	25.7501i	0.137311	−	0.955017i	−0.798370	−	0.602168i	$-0.794304\pi$
$727$	3.70230	−	25.7501i	0.137311	−	0.955017i	0.935680	−	0.352849i	$-0.114787\pi$
$728$	0.154502	+	8.20948i	0.00572622	+	0.304264i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	26.5582	−	23.3061i	0.982964	−	0.862597i
$731$	−37.8312	+	5.43930i	−1.39924	+	0.201180i
$732$	−11.8242	+	0.148344i	−0.437036	+	0.00548296i
$733$	3.92773	−	3.40340i	0.145074	−	0.125707i	−0.579300	−	0.815114i	$-0.696674\pi$
$733$	3.92773	−	3.40340i	0.145074	−	0.125707i	0.724374	+	0.689407i	$0.242129\pi$
$734$	−28.2322	+	0.177091i	−1.04207	+	0.00653655i
$735$	13.7330			0.506549
$736$	−17.1165	−	21.0481i	−0.630924	−	0.775844i
$737$	4.33782			0.159786
$738$	9.73012	−	0.0610336i	0.358170	−	0.00224668i
$739$	11.6762	−	10.1175i	0.429517	−	0.372178i	−0.413106	−	0.910683i	$-0.635556\pi$
$739$	11.6762	−	10.1175i	0.429517	−	0.372178i	0.842623	+	0.538505i	$0.181011\pi$
$740$	−27.5249	+	0.345322i	−1.01183	+	0.0126943i
$741$	−8.77742	+	1.26200i	−0.322447	+	0.0463608i
$742$	−0.782923	+	0.687052i	−0.0287420	+	0.0252225i
$743$	−15.8464	+	34.6988i	−0.581349	+	1.27298i	0.359182	+	0.933267i	$0.383056\pi$
$743$	−15.8464	+	34.6988i	−0.581349	+	1.27298i	−0.940531	+	0.339708i	$0.889672\pi$
$744$	−0.213154	−	11.3260i	−0.00781460	−	0.415230i
$745$	−3.68922	+	25.6591i	−0.135163	+	0.940077i
$746$	42.4729	−	6.37886i	1.55504	−	0.233547i
$747$	1.52602	−	5.19714i	0.0558341	−	0.190153i
$748$	15.3900	−	13.6772i	0.562713	−	0.500089i
$749$	−0.216835	+	0.0990252i	−0.00792298	+	0.00361830i
$750$	−6.90139	+	15.3663i	−0.252003	+	0.561098i
$751$	17.1121	−	19.7484i	0.624430	−	0.720631i	−0.352112	−	0.935958i	$-0.614536\pi$
$751$	17.1121	−	19.7484i	0.624430	−	0.720631i	0.976542	+	0.215327i	$0.0690818\pi$
$752$	30.4195	−	0.763393i	1.10928	−	0.0278381i
$753$	−14.1472	−	9.09184i	−0.515552	−	0.331325i
$754$	3.60433	−	26.2359i	0.131262	−	0.955453i
$755$	7.58608	+	11.8042i	0.276086	+	0.429598i
$756$	−1.02105	+	0.159902i	−0.0371351	+	0.00581560i
$757$	14.3747	+	48.9556i	0.522456	+	1.77932i	0.620577	+	0.784146i	$0.286899\pi$
$757$	14.3747	+	48.9556i	0.522456	+	1.77932i	−0.0981211	+	0.995174i	$0.531283\pi$
$758$	−9.88537	+	34.4648i	−0.359053	+	1.25182i
$759$	6.05269	−	11.3199i	0.219699	−	0.410887i
$760$	6.09181	+	6.76866i	0.220973	+	0.245525i
$761$	31.6116	−	9.28199i	1.14592	−	0.336472i	0.346973	−	0.937875i	$-0.387210\pi$
$761$	31.6116	−	9.28199i	1.14592	−	0.336472i	0.798946	+	0.601403i	$0.205392\pi$
$762$	19.2541	−	8.93943i	0.697502	−	0.323841i
$763$	1.16795	+	1.81737i	0.0422826	+	0.0657930i
$764$	16.2847	−	36.8759i	0.589160	−	1.33412i
$765$	−4.24127	+	6.59954i	−0.153343	+	0.238607i
$766$	13.0530	−	15.2563i	0.471625	−	0.551234i
$767$	3.74447	−	4.32135i	0.135205	−	0.156035i
$768$	11.5512	−	11.0711i	0.416818	−	0.399494i
$769$	16.2309	+	35.5406i	0.585300	+	1.28163i	0.938241	+	0.345982i	$0.112454\pi$
$769$	16.2309	+	35.5406i	0.585300	+	1.28163i	−0.352941	+	0.935645i	$0.614819\pi$
$770$	3.36975	+	2.13586i	0.121437	+	0.0769711i
$771$	−1.02898	+	3.50439i	−0.0370579	+	0.126208i
$772$	6.20029	−	47.3318i	0.223153	−	1.70351i
$773$	41.1105	+	5.91080i	1.47864	+	0.212597i	0.833948	−	0.551844i	$-0.186076\pi$
$773$	41.1105	+	5.91080i	1.47864	+	0.212597i	0.644694	+	0.764440i	$0.276985\pi$
$774$	−7.67182	−	11.7745i	−0.275758	−	0.423227i
$775$	−1.39718	+	3.05939i	−0.0501881	+	0.109897i
$776$	−0.275301	−	1.68855i	−0.00988273	−	0.0606156i
$777$	0.496247	+	3.45147i	0.0178028	+	0.123821i
$778$	−8.57075	−	28.5261i	−0.307276	−	1.02271i
$779$	−8.20783	+	7.11213i	−0.294076	+	0.254818i
$780$	−6.18014	+	22.0681i	−0.221284	+	0.790163i
$781$		−	39.6241i		−	1.41786i
$782$	2.25246	+	25.9886i	0.0805477	+	0.929349i
$783$	3.33326			0.119121
$784$	18.1417	+	19.9049i	0.647919	+	0.710889i
$785$	−19.4838	−	22.4855i	−0.695407	−	0.802542i
$786$	26.1490	−	7.85655i	0.932706	−	0.280234i
$787$	46.3916	−	6.67011i	1.65368	−	0.237764i	0.748607	−	0.663014i	$-0.230723\pi$
$787$	46.3916	−	6.67011i	1.65368	−	0.237764i	0.905076	+	0.425251i	$0.139814\pi$
$788$	8.64266	−	4.07877i	0.307882	−	0.145300i
$789$	−6.71969	−	3.06878i	−0.239227	−	0.109251i
$790$	−14.3261	−	21.9874i	−0.509701	−	0.782278i
$791$	−0.882829	+	6.14021i	−0.0313898	+	0.218321i
$792$	6.94437	+	3.01478i	0.246758	+	0.107126i
$793$	31.8706	+	9.35804i	1.13176	+	0.332314i
$794$	−13.8522	+	21.8547i	−0.491598	+	0.775595i
$795$	−2.64453	+	1.20772i	−0.0937919	+	0.0428333i
$796$	12.1035	−	14.3274i	0.428996	−	0.507822i
$797$	−2.32053	−	2.01075i	−0.0821974	−	0.0712245i	0.612793	−	0.790243i	$-0.290046\pi$
$797$	−2.32053	−	2.01075i	−0.0821974	−	0.0712245i	−0.694990	+	0.719019i	$0.744591\pi$
$798$	0.749921	−	0.876504i	0.0265469	−	0.0310279i
$799$	−24.6141	−	15.8185i	−0.870783	−	0.559618i
$800$	−4.51384	+	1.48064i	−0.159588	+	0.0523484i
$801$	11.4686	−	7.37045i	0.405225	−	0.260422i
$802$	21.6446	+	46.6191i	0.764299	+	1.64618i
$803$	9.23725	+	31.4592i	0.325975	+	1.11017i
$804$	−2.74852	−	1.71803i	−0.0969330	−	0.0605904i
$805$	−4.72034	+	1.80798i	−0.166370	+	0.0637228i
$806$	−8.77290	+	30.5862i	−0.309012	+	1.07735i
$807$	5.73174	−	1.68299i	0.201767	−	0.0592441i
$808$	−31.0718	−	3.87220i	−1.09310	−	0.136224i
$809$	4.45876	−	2.86547i	0.156762	−	0.100745i	−0.459908	−	0.887966i	$-0.652118\pi$
$809$	4.45876	−	2.86547i	0.156762	−	0.100745i	0.616670	+	0.787222i	$0.288481\pi$
$810$	−2.85768	−	0.392593i	−0.100409	−	0.0137943i
$811$	20.4690	−	31.8505i	0.718765	−	1.11842i	−0.269100	−	0.963112i	$-0.586726\pi$
$811$	20.4690	−	31.8505i	0.718765	−	1.11842i	0.987866	−	0.155309i	$-0.0496373\pi$
$812$	1.89866	+	2.87444i	0.0666299	+	0.100873i
$813$	11.9892	+	10.3887i	0.420479	+	0.364347i
$814$	10.4649	−	23.3007i	0.366795	−	0.816688i
$815$	7.50774	+	16.4397i	0.262985	+	0.575856i
$816$	−15.1684	+	2.57081i	−0.530999	+	0.0899965i
$817$	15.0503	+	4.41917i	0.526543	+	0.154607i
$818$	6.00146	+	39.9601i	0.209836	+	1.39717i
$819$	2.87346	+	0.413141i	0.100407	+	0.0144363i
$820$	8.24467	+	26.8290i	0.287916	+	0.936910i
$821$	−36.6190	−	16.7233i	−1.27801	−	0.583648i	−0.343356	−	0.939205i	$-0.611564\pi$
$821$	−36.6190	−	16.7233i	−1.27801	−	0.583648i	−0.934654	+	0.355557i	$0.884291\pi$
$822$	−11.7852	+	10.3421i	−0.411058	+	0.360723i
$823$	−6.28217	−	43.6935i	−0.218983	−	1.52306i	−0.741805	−	0.670616i	$-0.766030\pi$
$823$	−6.28217	−	43.6935i	−0.218983	−	1.52306i	0.522822	−	0.852442i	$-0.324879\pi$
$824$	−10.1640	−	2.77779i	−0.354080	−	0.0967688i
$825$	−1.47195	−	1.69872i	−0.0512468	−	0.0591420i
$826$	0.00466557	+	0.743795i	0.000162336	+	0.0258799i
$827$		−	45.9955i		−	1.59942i	−0.600386	−	0.799710i	$-0.704986\pi$
$827$		−	45.9955i		−	1.59942i	0.600386	−	0.799710i	$-0.295014\pi$
$828$	−8.31845	+	4.77528i	−0.289086	+	0.165953i
$829$		−	7.92405i		−	0.275214i	−0.990487	−	0.137607i	$-0.956059\pi$
$829$		−	7.92405i		−	0.275214i	0.990487	−	0.137607i	$-0.0439411\pi$
$830$	15.6238	−	0.0980029i	0.542311	−	0.00340173i
$831$	12.3410	+	14.2422i	0.428103	+	0.494057i
$832$	−40.1501	+	20.1950i	−1.39195	+	0.700134i
$833$	−3.68541	−	25.6326i	−0.127692	−	0.888116i
$834$	−11.7896	−	13.4347i	−0.408240	−	0.465206i
$835$	31.6900	+	14.4723i	1.09668	+	0.500835i
$836$	−8.07711	+	2.48213i	−0.279353	+	0.0858463i
$837$	−3.96428	−	0.569977i	−0.137025	−	0.0197013i
$838$	−4.84561	+	0.727745i	−0.167389	+	0.0251395i
$839$	2.17195	+	0.637742i	0.0749841	+	0.0220173i	0.319009	−	0.947752i	$-0.396650\pi$
$839$	2.17195	+	0.637742i	0.0749841	+	0.0220173i	−0.244025	+	0.969769i	$0.578468\pi$
$840$	−1.28921	−	2.68794i	−0.0444820	−	0.0927429i
$841$	7.43151	+	16.2727i	0.256259	+	0.561129i
$842$	−23.1875	−	10.4141i	−0.799093	−	0.358893i
$843$	12.8067	+	11.0971i	0.441087	+	0.382204i
$844$	−2.95485	−	4.47344i	−0.101710	−	0.153982i
$845$	20.4670	−	31.8473i	0.704086	−	1.09558i
$846$	1.46424	−	10.6582i	0.0503416	−	0.366436i
$847$	1.66750	−	1.07163i	0.0572958	−	0.0368218i
$848$	−5.24400	−	2.23761i	−0.180080	−	0.0768398i
$849$	13.0105	−	3.82022i	0.446519	−	0.131110i
$850$	4.39075	+	1.25938i	0.150601	+	0.0431963i
$851$	15.7583	+	28.2661i	0.540188	+	0.968950i
$852$	−15.6935	+	25.1066i	−0.537651	+	0.860137i
$853$	−3.48871	−	11.8815i	−0.119451	−	0.406813i	0.877959	−	0.478736i	$-0.158905\pi$
$853$	−3.48871	−	11.8815i	−0.119451	−	0.406813i	−0.997410	+	0.0719225i	$0.977087\pi$
$854$	−3.91904	+	1.81956i	−0.134107	+	0.0622641i
$855$	2.70847	−	1.74063i	0.0926278	−	0.0595283i
$856$	−1.00198	−	0.835733i	−0.0342469	−	0.0285648i
$857$	35.8714	+	23.0531i	1.22534	+	0.787480i	0.983159	−	0.182750i	$-0.0585000\pi$
$857$	35.8714	+	23.0531i	1.22534	+	0.787480i	0.242184	+	0.970230i	$0.422136\pi$
$858$	−16.1582	−	13.8246i	−0.551631	−	0.471965i
$859$	42.5127	+	36.8375i	1.45052	+	1.25688i	0.909395	+	0.415934i	$0.136545\pi$
$859$	42.5127	+	36.8375i	1.45052	+	1.25688i	0.541121	+	0.840945i	$0.318000\pi$
$860$	26.1598	−	30.9665i	0.892041	−	1.05595i
$861$	3.23410	−	1.47697i	0.110218	−	0.0503349i
$862$	5.31381	+	3.36807i	0.180989	+	0.114717i
$863$	−39.0288	−	11.4599i	−1.32856	−	0.390099i	−0.460983	−	0.887409i	$-0.652503\pi$
$863$	−39.0288	−	11.4599i	−1.32856	−	0.390099i	−0.867573	+	0.497310i	$0.834321\pi$
$864$	−3.20605	−	4.66061i	−0.109072	−	0.158557i
$865$	−1.85070	+	12.8719i	−0.0629256	+	0.437657i
$866$	−4.42499	+	2.88315i	−0.150367	+	0.0979734i
$867$	−2.00755	−	0.916817i	−0.0681800	−	0.0311367i
$868$	−1.76657	−	3.74326i	−0.0599614	−	0.127054i
$869$	24.1033	−	3.46553i	0.817648	−	0.117560i
$870$	2.76663	+	9.20821i	0.0937976	+	0.312188i
$871$	5.96224	+	6.88079i	0.202023	+	0.233147i
$872$	−6.20451	+	10.0660i	−0.210111	+	0.340876i
$873$	−0.604877			−0.0204720
$874$	3.58985	−	10.0860i	0.121428	−	0.341162i
$875$			6.15504i			0.208078i
$876$	6.60681	−	23.5916i	0.223223	−	0.797087i
$877$	21.3154	−	18.4699i	0.719769	−	0.623684i	−0.215960	−	0.976402i	$-0.569288\pi$
$877$	21.3154	−	18.4699i	0.719769	−	0.623684i	0.935729	+	0.352719i	$0.114743\pi$
$878$	−38.1214	+	11.4537i	−1.28653	+	0.386542i
$879$	−2.82748	−	19.6655i	−0.0953684	−	0.663302i
$880$	−2.56454	+	21.6863i	−0.0864505	+	0.731045i
$881$	4.36675	−	9.56184i	0.147119	−	0.322147i	−0.821698	−	0.569924i	$-0.806973\pi$
$881$	4.36675	−	9.56184i	0.147119	−	0.322147i	0.968817	+	0.247777i	$0.0797000\pi$
$882$	7.97785	−	5.19805i	0.268628	−	0.175028i
$883$	−26.7644	−	3.84813i	−0.900692	−	0.129500i	−0.323614	−	0.946189i	$-0.604898\pi$
$883$	−26.7644	−	3.84813i	−0.900692	−	0.129500i	−0.577078	+	0.816689i	$0.695807\pi$
$884$	42.8484	+	5.61298i	1.44115	+	0.188785i
$885$	−0.584879	+	1.99191i	−0.0196605	+	0.0669574i
$886$	6.01745	−	9.49375i	0.202160	−	0.318949i
$887$	−0.461541	−	1.01063i	−0.0154970	−	0.0339338i	0.901725	−	0.432310i	$-0.142301\pi$
$887$	−0.461541	−	1.01063i	−0.0154970	−	0.0339338i	−0.917222	+	0.398376i	$0.869574\pi$
$888$	−15.8592	+	10.6190i	−0.532200	+	0.356350i
$889$	5.07952	−	5.86207i	0.170361	−	0.196608i
$890$	29.8801	+	25.5649i	1.00158	+	0.856937i
$891$	1.44708	−	2.25169i	0.0484789	−	0.0754346i
$892$	5.16627	−	11.6988i	0.172980	−	0.391703i
$893$	6.49196	+	10.1017i	0.217245	+	0.338040i
$894$	7.56902	+	16.3024i	0.253146	+	0.545235i
$895$	−18.9938	+	5.57708i	−0.634893	+	0.186421i
$896$	2.19288	−	5.41947i	0.0732588	−	0.181052i
$897$	26.2753	−	5.95800i	0.877306	−	0.198932i
$898$	−8.01912	−	2.30009i	−0.267601	−	0.0767549i
$899$	3.76109	+	12.8091i	0.125439	+	0.427207i
$900$	0.259861	+	1.65932i	0.00866204	+	0.0553108i
$901$	2.96389	+	4.61190i	0.0987414	+	0.153645i
$902$	−25.8017	−	3.54469i	−0.859104	−	0.118025i
$903$	−4.31984	−	2.77620i	−0.143755	−	0.0923860i
$904$	−32.3932	+	10.1774i	−1.07738	+	0.338494i
$905$	17.7279	−	20.4591i	0.589296	−	0.680084i
$906$	8.87492	+	3.98595i	0.294850	+	0.132424i
$907$	−14.9283	+	6.81753i	−0.495686	+	0.226372i	−0.647541	−	0.762031i	$-0.724203\pi$
$907$	−14.9283	+	6.81753i	−0.495686	+	0.226372i	0.151855	+	0.988403i	$0.451475\pi$
$908$	−26.1148	+	23.2086i	−0.866651	+	0.770203i
$909$	−3.11892	+	10.6221i	−0.103448	+	0.352312i
$910$	1.24368	+	8.28090i	0.0412276	+	0.274509i
$911$	−0.0598575	+	0.416318i	−0.00198317	+	0.0137932i	−0.990789	−	0.135415i	$-0.956763\pi$
$911$	−0.0598575	+	0.416318i	−0.00198317	+	0.0137932i	0.988806	+	0.149208i	$0.0476724\pi$
$912$	6.10088	+	1.62629i	0.202020	+	0.0538519i
$913$	−6.02265	+	13.1878i	−0.199320	+	0.436451i
$914$	0.331025	+	0.377217i	0.0109493	+	0.0124772i
$915$	−11.9369	+	1.71627i	−0.394622	+	0.0567381i
$916$	−0.515515	−	41.0907i	−0.0170331	−	1.35767i
$917$	7.53985	−	6.53332i	0.248988	−	0.215749i
$918$	0.0341182	+	5.43920i	0.00112607	+	0.179520i
$919$	41.3907			1.36535			0.682676	−	0.730721i	$-0.260816\pi$
$919$	41.3907			1.36535			0.682676	+	0.730721i	$0.260816\pi$
$920$	−20.0962	−	19.0164i	−0.662552	−	0.626953i
$921$	24.5110			0.807664
$922$	0.0842493	+	13.4312i	0.00277460	+	0.442333i
$923$	62.8530	−	54.4625i	2.06883	−	1.79265i
$924$	2.76602	−	0.0347019i	0.0909953	−	0.00114161i
$925$	5.60907	−	0.806462i	0.184425	−	0.0265163i
$926$	−18.4836	−	21.0628i	−0.607408	−	0.692165i
$927$	−1.54755	+	3.38866i	−0.0508281	+	0.111298i
$928$	−9.69178	+	16.1743i	−0.318148	+	0.530949i
$929$	−0.414287	+	2.88143i	−0.0135923	+	0.0945367i	−0.995488	−	0.0948841i	$-0.969752\pi$
$929$	−0.414287	+	2.88143i	−0.0135923	+	0.0945367i	0.981896	+	0.189421i	$0.0606610\pi$
$930$	−1.71580	−	11.4245i	−0.0562634	−	0.374624i
$931$	−2.99421	+	10.1974i	−0.0981314	+	0.334205i
$932$	3.55691	+	4.00232i	0.116510	+	0.131100i
$933$	10.1220	−	4.62258i	0.331381	−	0.151336i
$934$	−39.8091	−	17.8793i	−1.30259	−	0.585028i
$935$	13.7505	−	15.8689i	0.449689	−	0.518969i
$936$	4.76274	+	15.1591i	0.155675	+	0.495492i
$937$	−18.7784	−	12.0682i	−0.613465	−	0.394250i	0.196690	−	0.980466i	$-0.436981\pi$
$937$	−18.7784	−	12.0682i	−0.613465	−	0.394250i	−0.810155	+	0.586216i	$0.800617\pi$
$938$	−1.17333	−	0.161194i	−0.0383106	−	0.00526318i
$939$	−15.0055	−	23.3490i	−0.489685	−	0.761965i
$940$	30.6588	−	4.80137i	0.999980	−	0.156603i
$941$	13.6050	+	46.3342i	0.443509	+	1.51045i	0.813582	+	0.581450i	$0.197514\pi$
$941$	13.6050	+	46.3342i	0.443509	+	1.51045i	−0.370073	+	0.929003i	$0.620667\pi$
$942$	−19.8296	−	5.68763i	−0.646083	−	0.185313i
$943$	23.1266	−	23.5365i	0.753107	−	0.766453i
$944$	−3.65977	+	1.78364i	−0.119115	+	0.0580527i
$945$	−1.01129	+	0.296942i	−0.0328974	+	0.00965954i
$946$	15.8402	+	34.1172i	0.515009	+	1.10925i
$947$	13.3870	+	20.8306i	0.435020	+	0.676905i	0.987677	−	0.156504i	$-0.0500224\pi$
$947$	13.3870	+	20.8306i	0.435020	+	0.676905i	−0.552657	+	0.833409i	$0.686386\pi$
$948$	−16.6448	−	7.35051i	−0.540600	−	0.238733i
$949$	−37.2052	+	57.8923i	−1.20773	+	1.87927i
$950$	−1.42443	−	1.21871i	−0.0462145	−	0.0395403i
$951$	0.576267	−	0.665047i	0.0186867	−	0.0215656i
$952$	−4.67106	+	3.12764i	−0.151390	+	0.101368i
$953$	−20.4280	−	44.7311i	−0.661728	−	1.44898i	−0.880903	−	0.473297i	$-0.843064\pi$
$953$	−20.4280	−	44.7311i	−0.661728	−	1.44898i	0.219175	−	0.975686i	$-0.429663\pi$
$954$	−1.07915	+	1.70257i	−0.0349387	+	0.0551228i
$955$	11.5823	−	39.4457i	0.374795	−	1.27643i
$956$	−2.77057	+	21.1500i	−0.0896065	+	0.684039i
$957$	−8.83098	−	1.26970i	−0.285465	−	0.0410437i
$958$	−24.1115	+	15.7101i	−0.779009	+	0.507571i
$959$	−2.38002	+	5.21151i	−0.0768548	+	0.168288i
$960$	10.2140	−	12.7251i	0.329655	−	0.410702i
$961$	2.12898	+	14.8074i	0.0686768	+	0.477657i
$962$	51.3440	−	15.4264i	1.65540	−	0.497368i
$963$	−0.348630	+	0.302090i	−0.0112344	+	0.00973470i
$964$	23.0185	+	6.44632i	0.741377	+	0.207622i
$965$		−	48.6829i		−	1.56716i
$966$	−2.05783	+	2.83699i	−0.0662097	+	0.0912786i
$967$	−38.1596			−1.22713			−0.613566	−	0.789644i	$-0.710265\pi$
$967$	−38.1596			−1.22713			−0.613566	+	0.789644i	$0.710265\pi$
$968$	9.23586	+	5.69285i	0.296852	+	0.182975i
$969$	−3.97572	−	4.58823i	−0.127719	−	0.147395i
$970$	−0.502052	−	1.67099i	−0.0161199	−	0.0536521i
$971$	46.3993	−	6.67121i	1.48902	−	0.214089i	0.650731	−	0.759308i	$-0.274463\pi$
$971$	46.3993	−	6.67121i	1.48902	−	0.214089i	0.838294	+	0.545219i	$0.183553\pi$
$972$	−1.80870	+	0.853587i	−0.0580140	+	0.0273788i
$973$	−5.94091	−	2.71312i	−0.190457	−	0.0869787i
$974$	−28.2682	+	18.4184i	−0.905771	+	0.590164i
$975$	0.671404	−	4.66972i	0.0215021	−	0.149551i
$976$	−18.2566	−	15.0344i	−0.584381	−	0.481239i
$977$	35.0133	+	10.2808i	1.12017	+	0.328913i	0.788839	−	0.614600i	$-0.210683\pi$
$977$	35.0133	+	10.2808i	1.12017	+	0.328913i	0.331335	+	0.943513i	$0.392501\pi$
$978$	10.5840	+	6.70848i	0.338438	+	0.214513i
$979$	−33.1920	+	15.1583i	−1.06082	+	0.484461i
$980$	20.9814	+	17.7246i	0.670227	+	0.566191i
$981$	3.15949	+	2.73771i	0.100875	+	0.0874084i
$982$	−21.9993	−	18.8222i	−0.702026	−	0.600641i
$983$	−38.1383	−	24.5100i	−1.21642	−	0.781747i	−0.234700	−	0.972068i	$-0.575411\pi$
$983$	−38.1383	−	24.5100i	−1.21642	−	0.781747i	−0.981722	+	0.190321i	$0.939047\pi$
$984$	14.9445	+	12.4650i	0.476415	+	0.397369i
$985$	8.19911	−	5.26925i	0.261245	−	0.167892i
$986$	16.4446	−	7.63503i	0.523703	−	0.243149i
$987$	−1.10749	−	3.77178i	−0.0352520	−	0.120057i
$988$	−15.0390	−	9.40054i	−0.478456	−	0.299071i
$989$	−46.6553	−	9.72089i	−1.48355	−	0.309106i
$990$	7.42144	+	2.12866i	0.235869	+	0.0676532i
$991$	6.00886	−	1.76436i	0.190878	−	0.0560468i	−0.184897	−	0.982758i	$-0.559195\pi$
$991$	6.00886	−	1.76436i	0.190878	−	0.0560468i	0.375774	+	0.926711i	$0.377377\pi$
$992$	14.2923	−	17.5790i	0.453780	−	0.558135i
$993$	−23.6095	+	15.1729i	−0.749223	+	0.481497i
$994$	−1.47244	+	10.7179i	−0.0467030	+	0.339950i
$995$	10.3411	−	16.0910i	0.327834	−	0.510120i
$996$	9.03919	−	5.97068i	0.286418	−	0.189188i
$997$	−13.7807	−	11.9411i	−0.436441	−	0.378178i	0.408747	−	0.912648i	$-0.365966\pi$
$997$	−13.7807	−	11.9411i	−0.436441	−	0.378178i	−0.845188	+	0.534470i	$0.820511\pi$
$998$	−15.8868	−	7.13516i	−0.502887	−	0.225859i
$999$	2.80320	+	6.13814i	0.0886892	+	0.194202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.47	yes	480
8.5	even	2	inner	552.2.bb.a.469.39	yes	480
23.18	even	11	inner	552.2.bb.a.133.39	✓	480
184.133	even	22	inner	552.2.bb.a.133.47	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.39	✓	480	23.18	even	11	inner
552.2.bb.a.133.47	yes	480	184.133	even	22	inner
552.2.bb.a.469.39	yes	480	8.5	even	2	inner
552.2.bb.a.469.47	yes	480	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41419 - 0.00887069i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.99984 - 0.0250896i) q^{4} +(2.01890 - 0.290274i) q^{5} +(1.06296 - 0.932799i) q^{6} +(0.214664 - 0.470048i) q^{7} +(2.82793 - 0.0532214i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(1.41419 - 0.00887069i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.99984 - 0.0250896i) q^{4} +(2.01890 - 0.290274i) q^{5} +(1.06296 - 0.932799i) q^{6} +(0.214664 - 0.470048i) q^{7} +(2.82793 - 0.0532214i) q^{8} +(0.142315 - 0.989821i) q^{9} +(2.85253 - 0.428411i) q^{10} +(-0.754084 + 2.56817i) q^{11} +(1.49495 - 1.32858i) q^{12} +(-5.11019 + 2.33374i) q^{13} +(0.299405 - 0.666640i) q^{14} +(1.33570 - 1.54147i) q^{15} +(3.99874 - 0.100351i) q^{16} +(-3.23560 - 2.07940i) q^{17} +(0.192479 - 1.40105i) q^{18} +(0.853390 + 1.32790i) q^{19} +(4.03020 - 0.631156i) q^{20} +(-0.145584 - 0.495814i) q^{21} +(-1.04363 + 3.63856i) q^{22} +(-2.90764 - 3.81387i) q^{23} +(2.10235 - 1.89212i) q^{24} +(-0.805758 + 0.236592i) q^{25} +(-7.20605 + 3.34568i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(0.417501 - 0.945408i) q^{28} +(-1.80210 + 2.80412i) q^{29} +(1.87525 - 2.19178i) q^{30} +(2.62274 - 3.02681i) q^{31} +(5.65407 - 0.177386i) q^{32} +(1.11190 + 2.43472i) q^{33} +(-4.59419 - 2.91195i) q^{34} +(0.296942 - 1.01129i) q^{35} +(0.259773 - 1.98306i) q^{36} +(-6.67926 - 0.960332i) q^{37} +(1.21863 + 1.87033i) q^{38} +(-2.33374 + 5.11019i) q^{39} +(5.69386 - 0.928323i) q^{40} +(0.979178 + 6.81033i) q^{41} +(-0.210281 - 0.699881i) q^{42} +(7.51004 - 6.50749i) q^{43} +(-1.44361 + 5.15486i) q^{44} -2.03966i q^{45} +(-4.14578 - 5.36773i) q^{46} +7.60726 q^{47} +(2.95633 - 2.69446i) q^{48} +(4.40916 + 5.08844i) q^{49} +(-1.13739 + 0.341732i) q^{50} +(-3.80702 + 0.547367i) q^{51} +(-10.1610 + 4.79533i) q^{52} +(-1.29655 - 0.592116i) q^{53} +(-0.772029 - 1.18489i) q^{54} +(-0.776947 + 5.40378i) q^{55} +(0.582037 - 1.34069i) q^{56} +(1.51454 + 0.444709i) q^{57} +(-2.52363 + 3.98153i) q^{58} +(-0.925840 + 0.422817i) q^{59} +(2.63251 - 3.11622i) q^{60} +(-4.46843 - 3.87191i) q^{61} +(3.68220 - 4.30373i) q^{62} +(-0.434714 - 0.279374i) q^{63} +(7.99433 - 0.301012i) q^{64} +(-9.63954 + 6.19496i) q^{65} +(1.59403 + 3.43328i) q^{66} +(-0.456590 - 1.55500i) q^{67} +(-6.52287 - 4.07728i) q^{68} +(-4.69500 - 0.978231i) q^{69} +(0.410961 - 1.43279i) q^{70} +(-14.2043 + 4.17075i) q^{71} +(0.349776 - 2.80672i) q^{72} +(10.3050 - 6.62265i) q^{73} +(-9.45423 - 1.29884i) q^{74} +(-0.454016 + 0.706463i) q^{75} +(1.73996 + 2.63418i) q^{76} +(1.04529 + 0.905749i) q^{77} +(-3.25502 + 7.24746i) q^{78} +(-3.77937 - 8.27566i) q^{79} +(8.04394 - 1.36333i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(1.44515 + 9.62239i) q^{82} +(5.36142 + 0.770855i) q^{83} +(-0.303585 - 0.987897i) q^{84} +(-7.13596 - 3.25888i) q^{85} +(10.5629 - 9.26942i) q^{86} +(0.474372 + 3.29933i) q^{87} +(-1.99581 + 7.30274i) q^{88} +(8.92759 + 10.3030i) q^{89} +(-0.0180932 - 2.88446i) q^{90} +2.90300i q^{91} +(-5.91052 - 7.55419i) q^{92} -4.00504i q^{93} +(10.7581 - 0.0674817i) q^{94} +(2.10837 + 2.43319i) q^{95} +(4.15690 - 3.83669i) q^{96} +(-0.0860829 - 0.598720i) q^{97} +(6.28051 + 7.15689i) q^{98} +(2.43472 + 1.11190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

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