LMFDB - Embedded newform 200.2.f.e.149.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,2,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.4
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.2.f.e.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +0.732051 q^{3} +(1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{6} -2.73205i q^{7} +(2.00000 + 2.00000i) q^{8} -2.46410 q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +0.732051 q^{3} +(1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{6} -2.73205i q^{7} +(2.00000 + 2.00000i) q^{8} -2.46410 q^{9} +2.00000i q^{11} +(1.26795 + 0.732051i) q^{12} -3.46410 q^{13} +(1.00000 - 3.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} -3.46410i q^{17} +(-3.36603 - 0.901924i) q^{18} +7.46410i q^{19} -2.00000i q^{21} +(-0.732051 + 2.73205i) q^{22} -4.19615i q^{23} +(1.46410 + 1.46410i) q^{24} +(-4.73205 - 1.26795i) q^{26} -4.00000 q^{27} +(2.73205 - 4.73205i) q^{28} -6.92820i q^{29} +1.46410 q^{31} +(1.46410 + 5.46410i) q^{32} +1.46410i q^{33} +(1.26795 - 4.73205i) q^{34} +(-4.26795 - 2.46410i) q^{36} -2.00000 q^{37} +(-2.73205 + 10.1962i) q^{38} -2.53590 q^{39} -5.46410 q^{41} +(0.732051 - 2.73205i) q^{42} +8.73205 q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.53590 - 5.73205i) q^{46} +6.73205i q^{47} +(1.46410 + 2.53590i) q^{48} -0.464102 q^{49} -2.53590i q^{51} +(-6.00000 - 3.46410i) q^{52} -4.53590 q^{53} +(-5.46410 - 1.46410i) q^{54} +(5.46410 - 5.46410i) q^{56} +5.46410i q^{57} +(2.53590 - 9.46410i) q^{58} -0.535898i q^{59} -4.92820i q^{61} +(2.00000 + 0.535898i) q^{62} +6.73205i q^{63} +8.00000i q^{64} +(-0.535898 + 2.00000i) q^{66} +7.26795 q^{67} +(3.46410 - 6.00000i) q^{68} -3.07180i q^{69} -1.46410 q^{71} +(-4.92820 - 4.92820i) q^{72} -0.535898i q^{73} +(-2.73205 - 0.732051i) q^{74} +(-7.46410 + 12.9282i) q^{76} +5.46410 q^{77} +(-3.46410 - 0.928203i) q^{78} +14.9282 q^{79} +4.46410 q^{81} +(-7.46410 - 2.00000i) q^{82} -4.73205 q^{83} +(2.00000 - 3.46410i) q^{84} +(11.9282 + 3.19615i) q^{86} -5.07180i q^{87} +(-4.00000 + 4.00000i) q^{88} +4.92820 q^{89} +9.46410i q^{91} +(4.19615 - 7.26795i) q^{92} +1.07180 q^{93} +(-2.46410 + 9.19615i) q^{94} +(1.07180 + 4.00000i) q^{96} +6.39230i q^{97} +(-0.633975 - 0.169873i) q^{98} -4.92820i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} + 4 q^{6} + 8 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^6 + 8 * q^8 + 4 * q^9	$ 4 q + 2 q^{2} - 4 q^{3} + 4 q^{6} + 8 q^{8} + 4 q^{9} + 12 q^{12} + 4 q^{14} + 8 q^{16} - 10 q^{18} + 4 q^{22} - 8 q^{24} - 12 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{31} - 8 q^{32} + 12 q^{34} - 24 q^{36} - 8 q^{37} - 4 q^{38} - 24 q^{39} - 8 q^{41} - 4 q^{42} + 28 q^{43} - 8 q^{44} + 20 q^{46} - 8 q^{48} + 12 q^{49} - 24 q^{52} - 32 q^{53} - 8 q^{54} + 8 q^{56} + 24 q^{58} + 8 q^{62} - 16 q^{66} + 36 q^{67} + 8 q^{71} + 8 q^{72} - 4 q^{74} - 16 q^{76} + 8 q^{77} + 32 q^{79} + 4 q^{81} - 16 q^{82} - 12 q^{83} + 8 q^{84} + 20 q^{86} - 16 q^{88} - 8 q^{89} - 4 q^{92} + 32 q^{93} + 4 q^{94} + 32 q^{96} - 6 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^6 + 8 * q^8 + 4 * q^9 + 12 * q^12 + 4 * q^14 + 8 * q^16 - 10 * q^18 + 4 * q^22 - 8 * q^24 - 12 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^31 - 8 * q^32 + 12 * q^34 - 24 * q^36 - 8 * q^37 - 4 * q^38 - 24 * q^39 - 8 * q^41 - 4 * q^42 + 28 * q^43 - 8 * q^44 + 20 * q^46 - 8 * q^48 + 12 * q^49 - 24 * q^52 - 32 * q^53 - 8 * q^54 + 8 * q^56 + 24 * q^58 + 8 * q^62 - 16 * q^66 + 36 * q^67 + 8 * q^71 + 8 * q^72 - 4 * q^74 - 16 * q^76 + 8 * q^77 + 32 * q^79 + 4 * q^81 - 16 * q^82 - 12 * q^83 + 8 * q^84 + 20 * q^86 - 16 * q^88 - 8 * q^89 - 4 * q^92 + 32 * q^93 + 4 * q^94 + 32 * q^96 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$3$	0.732051			0.422650			0.211325	−	0.977416i	$-0.432222\pi$
$3$	0.732051			0.422650			0.211325	+	0.977416i	$0.432222\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$		0			0
$5$		0			0
$6$	1.00000	+	0.267949i	0.408248	+	0.109390i
$7$		−	2.73205i		−	1.03262i	−0.856402	−	0.516309i	$-0.827306\pi$
$7$		−	2.73205i		−	1.03262i	0.856402	−	0.516309i	$-0.172694\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−2.46410			−0.821367
$10$		0			0
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	1.26795	+	0.732051i	0.366025	+	0.211325i
$13$	−3.46410			−0.960769			−0.480384	−	0.877058i	$-0.659503\pi$
$13$	−3.46410			−0.960769			−0.480384	+	0.877058i	$0.659503\pi$
$14$	1.00000	−	3.73205i	0.267261	−	0.997433i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		−	3.46410i		−	0.840168i	−0.907485	−	0.420084i	$-0.862001\pi$
$17$		−	3.46410i		−	0.840168i	0.907485	−	0.420084i	$-0.137999\pi$
$18$	−3.36603	−	0.901924i	−0.793380	−	0.212585i
$19$			7.46410i			1.71238i	0.516659	+	0.856191i	$0.327175\pi$
$19$			7.46410i			1.71238i	−0.516659	+	0.856191i	$0.672825\pi$
$20$		0			0
$21$		−	2.00000i		−	0.436436i
$22$	−0.732051	+	2.73205i	−0.156074	+	0.582475i
$23$		−	4.19615i		−	0.874958i	−0.899229	−	0.437479i	$-0.855871\pi$
$23$		−	4.19615i		−	0.874958i	0.899229	−	0.437479i	$-0.144129\pi$
$24$	1.46410	+	1.46410i	0.298858	+	0.298858i
$25$		0			0
$26$	−4.73205	−	1.26795i	−0.928032	−	0.248665i
$27$	−4.00000			−0.769800
$28$	2.73205	−	4.73205i	0.516309	−	0.894274i
$29$		−	6.92820i		−	1.28654i	−0.765641	−	0.643268i	$-0.777578\pi$
$29$		−	6.92820i		−	1.28654i	0.765641	−	0.643268i	$-0.222422\pi$
$30$		0			0
$31$	1.46410			0.262960			0.131480	−	0.991319i	$-0.458027\pi$
$31$	1.46410			0.262960			0.131480	+	0.991319i	$0.458027\pi$
$32$	1.46410	+	5.46410i	0.258819	+	0.965926i
$33$			1.46410i			0.254867i
$34$	1.26795	−	4.73205i	0.217451	−	0.811540i
$35$		0			0
$36$	−4.26795	−	2.46410i	−0.711325	−	0.410684i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	−2.73205	+	10.1962i	−0.443197	+	1.65403i
$39$	−2.53590			−0.406069
$40$		0			0
$41$	−5.46410			−0.853349			−0.426675	−	0.904405i	$-0.640315\pi$
$41$	−5.46410			−0.853349			−0.426675	+	0.904405i	$0.640315\pi$
$42$	0.732051	−	2.73205i	0.112958	−	0.421565i
$43$	8.73205			1.33163			0.665813	−	0.746119i	$-0.268085\pi$
$43$	8.73205			1.33163			0.665813	+	0.746119i	$0.268085\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$		0			0
$46$	1.53590	−	5.73205i	0.226456	−	0.845145i
$47$			6.73205i			0.981971i	0.871168	+	0.490985i	$0.163363\pi$
$47$			6.73205i			0.981971i	−0.871168	+	0.490985i	$0.836637\pi$
$48$	1.46410	+	2.53590i	0.211325	+	0.366025i
$49$	−0.464102			−0.0663002
$50$		0			0
$51$		−	2.53590i		−	0.355097i
$52$	−6.00000	−	3.46410i	−0.832050	−	0.480384i
$53$	−4.53590			−0.623054			−0.311527	−	0.950237i	$-0.600840\pi$
$53$	−4.53590			−0.623054			−0.311527	+	0.950237i	$0.600840\pi$
$54$	−5.46410	−	1.46410i	−0.743570	−	0.199239i
$55$		0			0
$56$	5.46410	−	5.46410i	0.730171	−	0.730171i
$57$			5.46410i			0.723738i
$58$	2.53590	−	9.46410i	0.332980	−	1.24270i
$59$		−	0.535898i		−	0.0697680i	−0.999391	−	0.0348840i	$-0.988894\pi$
$59$		−	0.535898i		−	0.0697680i	0.999391	−	0.0348840i	$-0.0111062\pi$
$60$		0			0
$61$		−	4.92820i		−	0.630992i	−0.948927	−	0.315496i	$-0.897829\pi$
$61$		−	4.92820i		−	0.630992i	0.948927	−	0.315496i	$-0.102171\pi$
$62$	2.00000	+	0.535898i	0.254000	+	0.0680592i
$63$			6.73205i			0.848159i
$64$			8.00000i			1.00000i
$65$		0			0
$66$	−0.535898	+	2.00000i	−0.0659645	+	0.246183i
$67$	7.26795			0.887921			0.443961	−	0.896046i	$-0.353573\pi$
$67$	7.26795			0.887921			0.443961	+	0.896046i	$0.353573\pi$
$68$	3.46410	−	6.00000i	0.420084	−	0.727607i
$69$		−	3.07180i		−	0.369801i
$70$		0			0
$71$	−1.46410			−0.173757			−0.0868784	−	0.996219i	$-0.527689\pi$
$71$	−1.46410			−0.173757			−0.0868784	+	0.996219i	$0.527689\pi$
$72$	−4.92820	−	4.92820i	−0.580794	−	0.580794i
$73$		−	0.535898i		−	0.0627222i	−0.999508	−	0.0313611i	$-0.990016\pi$
$73$		−	0.535898i		−	0.0627222i	0.999508	−	0.0313611i	$-0.00998418\pi$
$74$	−2.73205	−	0.732051i	−0.317594	−	0.0850992i
$75$		0			0
$76$	−7.46410	+	12.9282i	−0.856191	+	1.48297i
$77$	5.46410			0.622692
$78$	−3.46410	−	0.928203i	−0.392232	−	0.105098i
$79$	14.9282			1.67955			0.839777	−	0.542931i	$-0.182686\pi$
$79$	14.9282			1.67955			0.839777	+	0.542931i	$0.182686\pi$
$80$		0			0
$81$	4.46410			0.496011
$82$	−7.46410	−	2.00000i	−0.824272	−	0.220863i
$83$	−4.73205			−0.519410			−0.259705	−	0.965688i	$-0.583625\pi$
$83$	−4.73205			−0.519410			−0.259705	+	0.965688i	$0.583625\pi$
$84$	2.00000	−	3.46410i	0.218218	−	0.377964i
$85$		0			0
$86$	11.9282	+	3.19615i	1.28625	+	0.344650i
$87$		−	5.07180i		−	0.543754i
$88$	−4.00000	+	4.00000i	−0.426401	+	0.426401i
$89$	4.92820			0.522388			0.261194	−	0.965286i	$-0.415884\pi$
$89$	4.92820			0.522388			0.261194	+	0.965286i	$0.415884\pi$
$90$		0			0
$91$			9.46410i			0.992107i
$92$	4.19615	−	7.26795i	0.437479	−	0.757736i
$93$	1.07180			0.111140
$94$	−2.46410	+	9.19615i	−0.254153	+	0.948511i
$95$		0			0
$96$	1.07180	+	4.00000i	0.109390	+	0.408248i
$97$			6.39230i			0.649040i	0.945879	+	0.324520i	$0.105203\pi$
$97$			6.39230i			0.649040i	−0.945879	+	0.324520i	$0.894797\pi$
$98$	−0.633975	−	0.169873i	−0.0640411	−	0.0171598i
$99$		−	4.92820i		−	0.495303i
$100$		0			0
$101$			10.9282i			1.08740i	0.839281	+	0.543698i	$0.182976\pi$
$101$			10.9282i			1.08740i	−0.839281	+	0.543698i	$0.817024\pi$
$102$	0.928203	−	3.46410i	0.0919058	−	0.342997i
$103$			1.66025i			0.163590i	0.996649	+	0.0817948i	$0.0260652\pi$
$103$			1.66025i			0.163590i	−0.996649	+	0.0817948i	$0.973935\pi$
$104$	−6.92820	−	6.92820i	−0.679366	−	0.679366i
$105$		0			0
$106$	−6.19615	−	1.66025i	−0.601824	−	0.161258i
$107$	−0.732051			−0.0707700			−0.0353850	−	0.999374i	$-0.511266\pi$
$107$	−0.732051			−0.0707700			−0.0353850	+	0.999374i	$0.511266\pi$
$108$	−6.92820	−	4.00000i	−0.666667	−	0.384900i
$109$			3.07180i			0.294225i	0.989120	+	0.147112i	$0.0469979\pi$
$109$			3.07180i			0.294225i	−0.989120	+	0.147112i	$0.953002\pi$
$110$		0			0
$111$	−1.46410			−0.138966
$112$	9.46410	−	5.46410i	0.894274	−	0.516309i
$113$		−	0.928203i		−	0.0873180i	−0.999046	−	0.0436590i	$-0.986098\pi$
$113$		−	0.928203i		−	0.0873180i	0.999046	−	0.0436590i	$-0.0139015\pi$
$114$	−2.00000	+	7.46410i	−0.187317	+	0.699077i
$115$		0			0
$116$	6.92820	−	12.0000i	0.643268	−	1.11417i
$117$	8.53590			0.789144
$118$	0.196152	−	0.732051i	0.0180573	−	0.0673907i
$119$	−9.46410			−0.867573
$120$		0			0
$121$	7.00000			0.636364
$122$	1.80385	−	6.73205i	0.163313	−	0.609491i
$123$	−4.00000			−0.360668
$124$	2.53590	+	1.46410i	0.227730	+	0.131480i
$125$		0			0
$126$	−2.46410	+	9.19615i	−0.219520	+	0.819258i
$127$			13.2679i			1.17734i	0.808373	+	0.588670i	$0.200348\pi$
$127$			13.2679i			1.17734i	−0.808373	+	0.588670i	$0.799652\pi$
$128$	−2.92820	+	10.9282i	−0.258819	+	0.965926i
$129$	6.39230			0.562811
$130$		0			0
$131$		−	7.85641i		−	0.686417i	−0.939259	−	0.343209i	$-0.888486\pi$
$131$		−	7.85641i		−	0.686417i	0.939259	−	0.343209i	$-0.111514\pi$
$132$	−1.46410	+	2.53590i	−0.127434	+	0.220722i
$133$	20.3923			1.76824
$134$	9.92820	+	2.66025i	0.857666	+	0.229811i
$135$		0			0
$136$	6.92820	−	6.92820i	0.594089	−	0.594089i
$137$		−	8.92820i		−	0.762788i	−0.924413	−	0.381394i	$-0.875444\pi$
$137$		−	8.92820i		−	0.762788i	0.924413	−	0.381394i	$-0.124556\pi$
$138$	1.12436	−	4.19615i	0.0957115	−	0.357200i
$139$		−	7.46410i		−	0.633097i	−0.948576	−	0.316548i	$-0.897476\pi$
$139$		−	7.46410i		−	0.633097i	0.948576	−	0.316548i	$-0.102524\pi$
$140$		0			0
$141$			4.92820i			0.415030i
$142$	−2.00000	−	0.535898i	−0.167836	−	0.0449716i
$143$		−	6.92820i		−	0.579365i
$144$	−4.92820	−	8.53590i	−0.410684	−	0.711325i
$145$		0			0
$146$	0.196152	−	0.732051i	0.0162337	−	0.0605850i
$147$	−0.339746			−0.0280218
$148$	−3.46410	−	2.00000i	−0.284747	−	0.164399i
$149$			19.8564i			1.62670i	0.581775	+	0.813350i	$0.302359\pi$
$149$			19.8564i			1.62670i	−0.581775	+	0.813350i	$0.697641\pi$
$150$		0			0
$151$	8.39230			0.682956			0.341478	−	0.939890i	$-0.389073\pi$
$151$	8.39230			0.682956			0.341478	+	0.939890i	$0.389073\pi$
$152$	−14.9282	+	14.9282i	−1.21084	+	1.21084i
$153$			8.53590i			0.690086i
$154$	7.46410	+	2.00000i	0.601474	+	0.161165i
$155$		0			0
$156$	−4.39230	−	2.53590i	−0.351666	−	0.203034i
$157$	−16.9282			−1.35102			−0.675509	−	0.737352i	$-0.736076\pi$
$157$	−16.9282			−1.35102			−0.675509	+	0.737352i	$0.736076\pi$
$158$	20.3923	+	5.46410i	1.62232	+	0.434701i
$159$	−3.32051			−0.263333
$160$		0			0
$161$	−11.4641			−0.903498
$162$	6.09808	+	1.63397i	0.479110	+	0.128377i
$163$	−10.1962			−0.798624			−0.399312	−	0.916815i	$-0.630751\pi$
$163$	−10.1962			−0.798624			−0.399312	+	0.916815i	$0.630751\pi$
$164$	−9.46410	−	5.46410i	−0.739022	−	0.426675i
$165$		0			0
$166$	−6.46410	−	1.73205i	−0.501712	−	0.134433i
$167$		−	20.1962i		−	1.56283i	−0.624015	−	0.781413i	$-0.714499\pi$
$167$		−	20.1962i		−	1.56283i	0.624015	−	0.781413i	$-0.285501\pi$
$168$	4.00000	−	4.00000i	0.308607	−	0.308607i
$169$	−1.00000			−0.0769231
$170$		0			0
$171$		−	18.3923i		−	1.40649i
$172$	15.1244	+	8.73205i	1.15322	+	0.665813i
$173$	−2.00000			−0.152057			−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000			−0.152057			−0.0760286	+	0.997106i	$0.524224\pi$
$174$	1.85641	−	6.92820i	0.140734	−	0.525226i
$175$		0			0
$176$	−6.92820	+	4.00000i	−0.522233	+	0.301511i
$177$		−	0.392305i		−	0.0294874i
$178$	6.73205	+	1.80385i	0.504589	+	0.135204i
$179$		−	15.4641i		−	1.15584i	−0.816093	−	0.577921i	$-0.803864\pi$
$179$		−	15.4641i		−	1.15584i	0.816093	−	0.577921i	$-0.196136\pi$
$180$		0			0
$181$		−	16.0000i		−	1.18927i	−0.803996	−	0.594635i	$-0.797296\pi$
$181$		−	16.0000i		−	1.18927i	0.803996	−	0.594635i	$-0.202704\pi$
$182$	−3.46410	+	12.9282i	−0.256776	+	0.958302i
$183$		−	3.60770i		−	0.266688i
$184$	8.39230	−	8.39230i	0.618689	−	0.618689i
$185$		0			0
$186$	1.46410	+	0.392305i	0.107353	+	0.0287652i
$187$	6.92820			0.506640
$188$	−6.73205	+	11.6603i	−0.490985	+	0.850411i
$189$			10.9282i			0.794910i
$190$		0			0
$191$	−19.3205			−1.39798			−0.698991	−	0.715130i	$-0.746367\pi$
$191$	−19.3205			−1.39798			−0.698991	+	0.715130i	$0.746367\pi$
$192$			5.85641i			0.422650i
$193$		−	7.46410i		−	0.537278i	−0.963241	−	0.268639i	$-0.913426\pi$
$193$		−	7.46410i		−	0.537278i	0.963241	−	0.268639i	$-0.0865738\pi$
$194$	−2.33975	+	8.73205i	−0.167984	+	0.626925i
$195$		0			0
$196$	−0.803848	−	0.464102i	−0.0574177	−	0.0331501i
$197$	−12.5359			−0.893146			−0.446573	−	0.894747i	$-0.647356\pi$
$197$	−12.5359			−0.893146			−0.446573	+	0.894747i	$0.647356\pi$
$198$	1.80385	−	6.73205i	0.128194	−	0.478426i
$199$	−25.8564			−1.83291			−0.916456	−	0.400135i	$-0.868963\pi$
$199$	−25.8564			−1.83291			−0.916456	+	0.400135i	$0.868963\pi$
$200$		0			0
$201$	5.32051			0.375280
$202$	−4.00000	+	14.9282i	−0.281439	+	1.05034i
$203$	−18.9282			−1.32850
$204$	2.53590	−	4.39230i	0.177548	−	0.307523i
$205$		0			0
$206$	−0.607695	+	2.26795i	−0.0423401	+	0.158016i
$207$			10.3397i			0.718662i
$208$	−6.92820	−	12.0000i	−0.480384	−	0.832050i
$209$	−14.9282			−1.03261
$210$		0			0
$211$			14.7846i			1.01781i	0.860821	+	0.508907i	$0.169950\pi$
$211$			14.7846i			1.01781i	−0.860821	+	0.508907i	$0.830050\pi$
$212$	−7.85641	−	4.53590i	−0.539580	−	0.311527i
$213$	−1.07180			−0.0734383
$214$	−1.00000	−	0.267949i	−0.0683586	−	0.0183166i
$215$		0			0
$216$	−8.00000	−	8.00000i	−0.544331	−	0.544331i
$217$		−	4.00000i		−	0.271538i
$218$	−1.12436	+	4.19615i	−0.0761510	+	0.284199i
$219$		−	0.392305i		−	0.0265095i
$220$		0			0
$221$			12.0000i			0.807207i
$222$	−2.00000	−	0.535898i	−0.134231	−	0.0359671i
$223$			16.1962i			1.08457i	0.840193	+	0.542287i	$0.182442\pi$
$223$			16.1962i			1.08457i	−0.840193	+	0.542287i	$0.817558\pi$
$224$	14.9282	−	4.00000i	0.997433	−	0.267261i
$225$		0			0
$226$	0.339746	−	1.26795i	0.0225996	−	0.0843427i
$227$	−28.0526			−1.86191			−0.930957	−	0.365129i	$-0.881025\pi$
$227$	−28.0526			−1.86191			−0.930957	+	0.365129i	$0.881025\pi$
$228$	−5.46410	+	9.46410i	−0.361869	+	0.626775i
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$		0			0
$231$	4.00000			0.263181
$232$	13.8564	−	13.8564i	0.909718	−	0.909718i
$233$		−	29.3205i		−	1.92085i	−0.278538	−	0.960425i	$-0.589850\pi$
$233$		−	29.3205i		−	1.92085i	0.278538	−	0.960425i	$-0.410150\pi$
$234$	11.6603	+	3.12436i	0.762255	+	0.204246i
$235$		0			0
$236$	0.535898	−	0.928203i	0.0348840	−	0.0604209i
$237$	10.9282			0.709863
$238$	−12.9282	−	3.46410i	−0.838011	−	0.224544i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	−4.39230			−0.282933			−0.141467	−	0.989943i	$-0.545182\pi$
$241$	−4.39230			−0.282933			−0.141467	+	0.989943i	$0.545182\pi$
$242$	9.56218	+	2.56218i	0.614680	+	0.164703i
$243$	15.2679			0.979439
$244$	4.92820	−	8.53590i	0.315496	−	0.546455i
$245$		0			0
$246$	−5.46410	−	1.46410i	−0.348378	−	0.0933477i
$247$		−	25.8564i		−	1.64520i
$248$	2.92820	+	2.92820i	0.185941	+	0.185941i
$249$	−3.46410			−0.219529
$250$		0			0
$251$		−	11.0718i		−	0.698846i	−0.936965	−	0.349423i	$-0.886378\pi$
$251$		−	11.0718i		−	0.698846i	0.936965	−	0.349423i	$-0.113622\pi$
$252$	−6.73205	+	11.6603i	−0.424079	+	0.734527i
$253$	8.39230			0.527620
$254$	−4.85641	+	18.1244i	−0.304718	+	1.13722i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		−	2.00000i		−	0.124757i	−0.998053	−	0.0623783i	$-0.980131\pi$
$257$		−	2.00000i		−	0.124757i	0.998053	−	0.0623783i	$-0.0198685\pi$
$258$	8.73205	+	2.33975i	0.543634	+	0.145666i
$259$			5.46410i			0.339523i
$260$		0			0
$261$			17.0718i			1.05672i
$262$	2.87564	−	10.7321i	0.177658	−	0.663028i
$263$		−	5.66025i		−	0.349026i	−0.984655	−	0.174513i	$-0.944165\pi$
$263$		−	5.66025i		−	0.349026i	0.984655	−	0.174513i	$-0.0558351\pi$
$264$	−2.92820	+	2.92820i	−0.180218	+	0.180218i
$265$		0			0
$266$	27.8564	+	7.46410i	1.70799	+	0.457653i
$267$	3.60770			0.220787
$268$	12.5885	+	7.26795i	0.768962	+	0.443961i
$269$			4.92820i			0.300478i	0.988650	+	0.150239i	$0.0480043\pi$
$269$			4.92820i			0.300478i	−0.988650	+	0.150239i	$0.951996\pi$
$270$		0			0
$271$	15.3205			0.930655			0.465327	−	0.885139i	$-0.345937\pi$
$271$	15.3205			0.930655			0.465327	+	0.885139i	$0.345937\pi$
$272$	12.0000	−	6.92820i	0.727607	−	0.420084i
$273$			6.92820i			0.419314i
$274$	3.26795	−	12.1962i	0.197424	−	0.736797i
$275$		0			0
$276$	3.07180	−	5.32051i	0.184900	−	0.320257i
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$	2.73205	−	10.1962i	0.163858	−	0.611525i
$279$	−3.60770			−0.215987
$280$		0			0
$281$	17.4641			1.04182			0.520910	−	0.853611i	$-0.325593\pi$
$281$	17.4641			1.04182			0.520910	+	0.853611i	$0.325593\pi$
$282$	−1.80385	+	6.73205i	−0.107418	+	0.400888i
$283$	−7.66025			−0.455355			−0.227677	−	0.973737i	$-0.573113\pi$
$283$	−7.66025			−0.455355			−0.227677	+	0.973737i	$0.573113\pi$
$284$	−2.53590	−	1.46410i	−0.150478	−	0.0868784i
$285$		0			0
$286$	2.53590	−	9.46410i	0.149951	−	0.559624i
$287$			14.9282i			0.881184i
$288$	−3.60770	−	13.4641i	−0.212585	−	0.793380i
$289$	5.00000			0.294118
$290$		0			0
$291$			4.67949i			0.274317i
$292$	0.535898	−	0.928203i	0.0313611	−	0.0543190i
$293$	−11.8564			−0.692659			−0.346329	−	0.938113i	$-0.612572\pi$
$293$	−11.8564			−0.692659			−0.346329	+	0.938113i	$0.612572\pi$
$294$	−0.464102	−	0.124356i	−0.0270670	−	0.00725257i
$295$		0			0
$296$	−4.00000	−	4.00000i	−0.232495	−	0.232495i
$297$		−	8.00000i		−	0.464207i
$298$	−7.26795	+	27.1244i	−0.421021	+	1.57127i
$299$			14.5359i			0.840633i
$300$		0			0
$301$		−	23.8564i		−	1.37506i
$302$	11.4641	+	3.07180i	0.659685	+	0.176762i
$303$			8.00000i			0.459588i
$304$	−25.8564	+	14.9282i	−1.48297	+	0.856191i
$305$		0			0
$306$	−3.12436	+	11.6603i	−0.178608	+	0.666572i
$307$	26.9808			1.53987			0.769937	−	0.638120i	$-0.220288\pi$
$307$	26.9808			1.53987			0.769937	+	0.638120i	$0.220288\pi$
$308$	9.46410	+	5.46410i	0.539267	+	0.311346i
$309$			1.21539i			0.0691411i
$310$		0			0
$311$	−3.32051			−0.188289			−0.0941444	−	0.995559i	$-0.530012\pi$
$311$	−3.32051			−0.188289			−0.0941444	+	0.995559i	$0.530012\pi$
$312$	−5.07180	−	5.07180i	−0.287134	−	0.287134i
$313$			31.8564i			1.80063i	0.435238	+	0.900315i	$0.356664\pi$
$313$			31.8564i			1.80063i	−0.435238	+	0.900315i	$0.643336\pi$
$314$	−23.1244	−	6.19615i	−1.30498	−	0.349669i
$315$		0			0
$316$	25.8564	+	14.9282i	1.45454	+	0.839777i
$317$	15.4641			0.868550			0.434275	−	0.900780i	$-0.357005\pi$
$317$	15.4641			0.868550			0.434275	+	0.900780i	$0.357005\pi$
$318$	−4.53590	−	1.21539i	−0.254361	−	0.0681557i
$319$	13.8564			0.775810
$320$		0			0
$321$	−0.535898			−0.0299109
$322$	−15.6603	−	4.19615i	−0.872712	−	0.233842i
$323$	25.8564			1.43869
$324$	7.73205	+	4.46410i	0.429558	+	0.248006i
$325$		0			0
$326$	−13.9282	−	3.73205i	−0.771412	−	0.206699i
$327$			2.24871i			0.124354i
$328$	−10.9282	−	10.9282i	−0.603409	−	0.603409i
$329$	18.3923			1.01400
$330$		0			0
$331$			14.0000i			0.769510i	0.923019	+	0.384755i	$0.125714\pi$
$331$			14.0000i			0.769510i	−0.923019	+	0.384755i	$0.874286\pi$
$332$	−8.19615	−	4.73205i	−0.449822	−	0.259705i
$333$	4.92820			0.270064
$334$	7.39230	−	27.5885i	0.404489	−	1.50957i
$335$		0			0
$336$	6.92820	−	4.00000i	0.377964	−	0.218218i
$337$			7.85641i			0.427966i	0.976837	+	0.213983i	$0.0686437\pi$
$337$			7.85641i			0.427966i	−0.976837	+	0.213983i	$0.931356\pi$
$338$	−1.36603	−	0.366025i	−0.0743020	−	0.0199092i
$339$		−	0.679492i		−	0.0369049i
$340$		0			0
$341$			2.92820i			0.158571i
$342$	6.73205	−	25.1244i	0.364028	−	1.35857i
$343$		−	17.8564i		−	0.964155i
$344$	17.4641	+	17.4641i	0.941601	+	0.941601i
$345$		0			0
$346$	−2.73205	−	0.732051i	−0.146876	−	0.0393553i
$347$	15.6603			0.840686			0.420343	−	0.907365i	$-0.361910\pi$
$347$	15.6603			0.840686			0.420343	+	0.907365i	$0.361910\pi$
$348$	5.07180	−	8.78461i	0.271877	−	0.470905i
$349$		−	28.0000i		−	1.49881i	−0.662114	−	0.749403i	$-0.730341\pi$
$349$		−	28.0000i		−	1.49881i	0.662114	−	0.749403i	$-0.269659\pi$
$350$		0			0
$351$	13.8564			0.739600
$352$	−10.9282	+	2.92820i	−0.582475	+	0.156074i
$353$			0.928203i			0.0494033i	0.999695	+	0.0247016i	$0.00786357\pi$
$353$			0.928203i			0.0494033i	−0.999695	+	0.0247016i	$0.992136\pi$
$354$	0.143594	−	0.535898i	0.00763191	−	0.0284827i
$355$		0			0
$356$	8.53590	+	4.92820i	0.452402	+	0.261194i
$357$	−6.92820			−0.366679
$358$	5.66025	−	21.1244i	0.299154	−	1.11646i
$359$	−5.07180			−0.267679			−0.133840	−	0.991003i	$-0.542731\pi$
$359$	−5.07180			−0.267679			−0.133840	+	0.991003i	$0.542731\pi$
$360$		0			0
$361$	−36.7128			−1.93225
$362$	5.85641	−	21.8564i	0.307806	−	1.14875i
$363$	5.12436			0.268959
$364$	−9.46410	+	16.3923i	−0.496054	+	0.859190i
$365$		0			0
$366$	1.32051	−	4.92820i	0.0690241	−	0.257601i
$367$			27.1244i			1.41588i	0.706273	+	0.707940i	$0.250375\pi$
$367$			27.1244i			1.41588i	−0.706273	+	0.707940i	$0.749625\pi$
$368$	14.5359	−	8.39230i	0.757736	−	0.437479i
$369$	13.4641			0.700913
$370$		0			0
$371$			12.3923i			0.643376i
$372$	1.85641	+	1.07180i	0.0962502	+	0.0555701i
$373$	−29.7128			−1.53847			−0.769236	−	0.638965i	$-0.779363\pi$
$373$	−29.7128			−1.53847			−0.769236	+	0.638965i	$0.779363\pi$
$374$	9.46410	+	2.53590i	0.489377	+	0.131128i
$375$		0			0
$376$	−13.4641	+	13.4641i	−0.694358	+	0.694358i
$377$			24.0000i			1.23606i
$378$	−4.00000	+	14.9282i	−0.205738	+	0.767824i
$379$			12.2487i			0.629174i	0.949229	+	0.314587i	$0.101866\pi$
$379$			12.2487i			0.629174i	−0.949229	+	0.314587i	$0.898134\pi$
$380$		0			0
$381$			9.71281i			0.497602i
$382$	−26.3923	−	7.07180i	−1.35035	−	0.361825i
$383$			3.12436i			0.159647i	0.996809	+	0.0798236i	$0.0254357\pi$
$383$			3.12436i			0.159647i	−0.996809	+	0.0798236i	$0.974564\pi$
$384$	−2.14359	+	8.00000i	−0.109390	+	0.408248i
$385$		0			0
$386$	2.73205	−	10.1962i	0.139058	−	0.518970i
$387$	−21.5167			−1.09375
$388$	−6.39230	+	11.0718i	−0.324520	+	0.562085i
$389$		−	34.7846i		−	1.76365i	−0.471577	−	0.881825i	$-0.656315\pi$
$389$		−	34.7846i		−	1.76365i	0.471577	−	0.881825i	$-0.343685\pi$
$390$		0			0
$391$	−14.5359			−0.735112
$392$	−0.928203	−	0.928203i	−0.0468813	−	0.0468813i
$393$		−	5.75129i		−	0.290114i
$394$	−17.1244	−	4.58846i	−0.862713	−	0.231163i
$395$		0			0
$396$	4.92820	−	8.53590i	0.247652	−	0.428945i
$397$	−16.2487			−0.815499			−0.407750	−	0.913094i	$-0.633686\pi$
$397$	−16.2487			−0.815499			−0.407750	+	0.913094i	$0.633686\pi$
$398$	−35.3205	−	9.46410i	−1.77046	−	0.474393i
$399$	14.9282			0.747345
$400$		0			0
$401$	19.8564			0.991582			0.495791	−	0.868442i	$-0.334878\pi$
$401$	19.8564			0.991582			0.495791	+	0.868442i	$0.334878\pi$
$402$	7.26795	+	1.94744i	0.362492	+	0.0971295i
$403$	−5.07180			−0.252644
$404$	−10.9282	+	18.9282i	−0.543698	+	0.941713i
$405$		0			0
$406$	−25.8564	−	6.92820i	−1.28323	−	0.343841i
$407$		−	4.00000i		−	0.198273i
$408$	5.07180	−	5.07180i	0.251091	−	0.251091i
$409$	−23.3205			−1.15312			−0.576562	−	0.817053i	$-0.695606\pi$
$409$	−23.3205			−1.15312			−0.576562	+	0.817053i	$0.695606\pi$
$410$		0			0
$411$		−	6.53590i		−	0.322392i
$412$	−1.66025	+	2.87564i	−0.0817948	+	0.141673i
$413$	−1.46410			−0.0720437
$414$	−3.78461	+	14.1244i	−0.186003	+	0.694174i
$415$		0			0
$416$	−5.07180	−	18.9282i	−0.248665	−	0.928032i
$417$		−	5.46410i		−	0.267578i
$418$	−20.3923	−	5.46410i	−0.997420	−	0.267258i
$419$		−	2.39230i		−	0.116872i	−0.998291	−	0.0584359i	$-0.981389\pi$
$419$		−	2.39230i		−	0.116872i	0.998291	−	0.0584359i	$-0.0186113\pi$
$420$		0			0
$421$		−	27.8564i		−	1.35764i	−0.734306	−	0.678819i	$-0.762492\pi$
$421$		−	27.8564i		−	1.35764i	0.734306	−	0.678819i	$-0.237508\pi$
$422$	−5.41154	+	20.1962i	−0.263430	+	0.983133i
$423$		−	16.5885i		−	0.806558i
$424$	−9.07180	−	9.07180i	−0.440565	−	0.440565i
$425$		0			0
$426$	−1.46410	−	0.392305i	−0.0709360	−	0.0190072i
$427$	−13.4641			−0.651574
$428$	−1.26795	−	0.732051i	−0.0612886	−	0.0353850i
$429$		−	5.07180i		−	0.244869i
$430$		0			0
$431$	−14.5359			−0.700170			−0.350085	−	0.936718i	$-0.613847\pi$
$431$	−14.5359			−0.700170			−0.350085	+	0.936718i	$0.613847\pi$
$432$	−8.00000	−	13.8564i	−0.384900	−	0.666667i
$433$			12.5359i			0.602437i	0.953555	+	0.301218i	$0.0973933\pi$
$433$			12.5359i			0.602437i	−0.953555	+	0.301218i	$0.902607\pi$
$434$	1.46410	−	5.46410i	0.0702791	−	0.262285i
$435$		0			0
$436$	−3.07180	+	5.32051i	−0.147112	+	0.254806i
$437$	31.3205			1.49826
$438$	0.143594	−	0.535898i	0.00686116	−	0.0256062i
$439$	0.784610			0.0374474			0.0187237	−	0.999825i	$-0.494040\pi$
$439$	0.784610			0.0374474			0.0187237	+	0.999825i	$0.494040\pi$
$440$		0			0
$441$	1.14359			0.0544568
$442$	−4.39230	+	16.3923i	−0.208921	+	0.779702i
$443$	30.9808			1.47194			0.735970	−	0.677014i	$-0.236726\pi$
$443$	30.9808			1.47194			0.735970	+	0.677014i	$0.236726\pi$
$444$	−2.53590	−	1.46410i	−0.120348	−	0.0694832i
$445$		0			0
$446$	−5.92820	+	22.1244i	−0.280709	+	1.04762i
$447$			14.5359i			0.687524i
$448$	21.8564			1.03262
$449$	−11.3205			−0.534248			−0.267124	−	0.963662i	$-0.586073\pi$
$449$	−11.3205			−0.534248			−0.267124	+	0.963662i	$0.586073\pi$
$450$		0			0
$451$		−	10.9282i		−	0.514589i
$452$	0.928203	−	1.60770i	0.0436590	−	0.0756196i
$453$	6.14359			0.288651
$454$	−38.3205	−	10.2679i	−1.79847	−	0.481899i
$455$		0			0
$456$	−10.9282	+	10.9282i	−0.511760	+	0.511760i
$457$			14.7846i			0.691595i	0.938309	+	0.345797i	$0.112392\pi$
$457$			14.7846i			0.691595i	−0.938309	+	0.345797i	$0.887608\pi$
$458$	1.46410	−	5.46410i	0.0684130	−	0.255321i
$459$			13.8564i			0.646762i
$460$		0			0
$461$		−	2.92820i		−	0.136380i	−0.997672	−	0.0681900i	$-0.978278\pi$
$461$		−	2.92820i		−	0.136380i	0.997672	−	0.0681900i	$-0.0217224\pi$
$462$	5.46410	+	1.46410i	0.254213	+	0.0681162i
$463$			14.7321i			0.684656i	0.939580	+	0.342328i	$0.111215\pi$
$463$			14.7321i			0.684656i	−0.939580	+	0.342328i	$0.888785\pi$
$464$	24.0000	−	13.8564i	1.11417	−	0.643268i
$465$		0			0
$466$	10.7321	−	40.0526i	0.497153	−	1.85540i
$467$	−8.33975			−0.385917			−0.192959	−	0.981207i	$-0.561808\pi$
$467$	−8.33975			−0.385917			−0.192959	+	0.981207i	$0.561808\pi$
$468$	14.7846	+	8.53590i	0.683419	+	0.394572i
$469$		−	19.8564i		−	0.916884i
$470$		0			0
$471$	−12.3923			−0.571007
$472$	1.07180	−	1.07180i	0.0493334	−	0.0493334i
$473$			17.4641i			0.803000i
$474$	14.9282	+	4.00000i	0.685675	+	0.183726i
$475$		0			0
$476$	−16.3923	−	9.46410i	−0.751340	−	0.433786i
$477$	11.1769			0.511756
$478$	27.3205	+	7.32051i	1.24961	+	0.334832i
$479$	21.8564			0.998645			0.499322	−	0.866416i	$-0.333582\pi$
$479$	21.8564			0.998645			0.499322	+	0.866416i	$0.333582\pi$
$480$		0			0
$481$	6.92820			0.315899
$482$	−6.00000	−	1.60770i	−0.273293	−	0.0732285i
$483$	−8.39230			−0.381863
$484$	12.1244	+	7.00000i	0.551107	+	0.318182i
$485$		0			0
$486$	20.8564	+	5.58846i	0.946066	+	0.253498i
$487$		−	24.5885i		−	1.11421i	−0.830442	−	0.557105i	$-0.811912\pi$
$487$		−	24.5885i		−	1.11421i	0.830442	−	0.557105i	$-0.188088\pi$
$488$	9.85641	−	9.85641i	0.446179	−	0.446179i
$489$	−7.46410			−0.337538
$490$		0			0
$491$			3.07180i			0.138628i	0.997595	+	0.0693141i	$0.0220811\pi$
$491$			3.07180i			0.138628i	−0.997595	+	0.0693141i	$0.977919\pi$
$492$	−6.92820	−	4.00000i	−0.312348	−	0.180334i
$493$	−24.0000			−1.08091
$494$	9.46410	−	35.3205i	0.425810	−	1.58914i
$495$		0			0
$496$	2.92820	+	5.07180i	0.131480	+	0.227730i
$497$			4.00000i			0.179425i
$498$	−4.73205	−	1.26795i	−0.212048	−	0.0568182i
$499$			24.5359i			1.09838i	0.835698	+	0.549189i	$0.185063\pi$
$499$			24.5359i			1.09838i	−0.835698	+	0.549189i	$0.814937\pi$
$500$		0			0
$501$		−	14.7846i		−	0.660528i
$502$	4.05256	−	15.1244i	0.180875	−	0.675033i
$503$			17.6603i			0.787432i	0.919232	+	0.393716i	$0.128811\pi$
$503$			17.6603i			0.787432i	−0.919232	+	0.393716i	$0.871189\pi$
$504$	−13.4641	+	13.4641i	−0.599739	+	0.599739i
$505$		0			0
$506$	11.4641	+	3.07180i	0.509641	+	0.136558i
$507$	−0.732051			−0.0325115
$508$	−13.2679	+	22.9808i	−0.588670	+	1.01961i
$509$			25.8564i			1.14607i	0.819533	+	0.573033i	$0.194233\pi$
$509$			25.8564i			1.14607i	−0.819533	+	0.573033i	$0.805767\pi$
$510$		0			0
$511$	−1.46410			−0.0647680
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		−	29.8564i		−	1.31819i
$514$	0.732051	−	2.73205i	0.0322894	−	0.120506i
$515$		0			0
$516$	11.0718	+	6.39230i	0.487409	+	0.281406i
$517$	−13.4641			−0.592151
$518$	−2.00000	+	7.46410i	−0.0878750	+	0.327954i
$519$	−1.46410			−0.0642669
$520$		0			0
$521$	−16.1436			−0.707264			−0.353632	−	0.935385i	$-0.615053\pi$
$521$	−16.1436			−0.707264			−0.353632	+	0.935385i	$0.615053\pi$
$522$	−6.24871	+	23.3205i	−0.273499	+	1.02071i
$523$	22.1962			0.970570			0.485285	−	0.874356i	$-0.338716\pi$
$523$	22.1962			0.970570			0.485285	+	0.874356i	$0.338716\pi$
$524$	7.85641	−	13.6077i	0.343209	−	0.594455i
$525$		0			0
$526$	2.07180	−	7.73205i	0.0903346	−	0.337133i
$527$		−	5.07180i		−	0.220931i
$528$	−5.07180	+	2.92820i	−0.220722	+	0.127434i
$529$	5.39230			0.234448
$530$		0			0
$531$			1.32051i			0.0573052i
$532$	35.3205	+	20.3923i	1.53134	+	0.884119i
$533$	18.9282			0.819871
$534$	4.92820	+	1.32051i	0.213264	+	0.0571440i
$535$		0			0
$536$	14.5359	+	14.5359i	0.627855	+	0.627855i
$537$		−	11.3205i		−	0.488516i
$538$	−1.80385	+	6.73205i	−0.0777694	+	0.290239i
$539$		−	0.928203i		−	0.0399805i
$540$		0			0
$541$			13.0718i			0.562000i	0.959708	+	0.281000i	$0.0906662\pi$
$541$			13.0718i			0.562000i	−0.959708	+	0.281000i	$0.909334\pi$
$542$	20.9282	+	5.60770i	0.898943	+	0.240871i
$543$		−	11.7128i		−	0.502645i
$544$	18.9282	−	5.07180i	0.811540	−	0.217451i
$545$		0			0
$546$	−2.53590	+	9.46410i	−0.108526	+	0.405026i
$547$	36.7321			1.57055			0.785275	−	0.619148i	$-0.212522\pi$
$547$	36.7321			1.57055			0.785275	+	0.619148i	$0.212522\pi$
$548$	8.92820	−	15.4641i	0.381394	−	0.660594i
$549$			12.1436i			0.518276i
$550$		0			0
$551$	51.7128			2.20304
$552$	6.14359	−	6.14359i	0.261489	−	0.261489i
$553$		−	40.7846i		−	1.73434i
$554$	2.73205	+	0.732051i	0.116074	+	0.0311019i
$555$		0			0
$556$	7.46410	−	12.9282i	0.316548	−	0.548278i
$557$	−26.7846			−1.13490			−0.567450	−	0.823408i	$-0.692070\pi$
$557$	−26.7846			−1.13490			−0.567450	+	0.823408i	$0.692070\pi$
$558$	−4.92820	−	1.32051i	−0.208627	−	0.0559016i
$559$	−30.2487			−1.27938
$560$		0			0
$561$	5.07180			0.214131
$562$	23.8564	+	6.39230i	1.00632	+	0.269643i
$563$	−16.0526			−0.676535			−0.338267	−	0.941050i	$-0.609841\pi$
$563$	−16.0526			−0.676535			−0.338267	+	0.941050i	$0.609841\pi$
$564$	−4.92820	+	8.53590i	−0.207515	+	0.359426i
$565$		0			0
$566$	−10.4641	−	2.80385i	−0.439839	−	0.117855i
$567$		−	12.1962i		−	0.512190i
$568$	−2.92820	−	2.92820i	−0.122865	−	0.122865i
$569$	6.53590			0.273999			0.137000	−	0.990571i	$-0.456254\pi$
$569$	6.53590			0.273999			0.137000	+	0.990571i	$0.456254\pi$
$570$		0			0
$571$			34.7846i			1.45569i	0.685741	+	0.727845i	$0.259478\pi$
$571$			34.7846i			1.45569i	−0.685741	+	0.727845i	$0.740522\pi$
$572$	6.92820	−	12.0000i	0.289683	−	0.501745i
$573$	−14.1436			−0.590857
$574$	−5.46410	+	20.3923i	−0.228067	+	0.851158i
$575$		0			0
$576$		−	19.7128i		−	0.821367i
$577$		−	43.5692i		−	1.81381i	−0.421335	−	0.906905i	$-0.638438\pi$
$577$		−	43.5692i		−	1.81381i	0.421335	−	0.906905i	$-0.361562\pi$
$578$	6.83013	+	1.83013i	0.284096	+	0.0761232i
$579$		−	5.46410i		−	0.227080i
$580$		0			0
$581$			12.9282i			0.536352i
$582$	−1.71281	+	6.39230i	−0.0709984	+	0.264970i
$583$		−	9.07180i		−	0.375715i
$584$	1.07180	−	1.07180i	0.0443513	−	0.0443513i
$585$		0			0
$586$	−16.1962	−	4.33975i	−0.669057	−	0.179273i
$587$	−14.1962			−0.585938			−0.292969	−	0.956122i	$-0.594643\pi$
$587$	−14.1962			−0.585938			−0.292969	+	0.956122i	$0.594643\pi$
$588$	−0.588457	−	0.339746i	−0.0242676	−	0.0140109i
$589$			10.9282i			0.450289i
$590$		0			0
$591$	−9.17691			−0.377488
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$			36.6410i			1.50467i	0.658783	+	0.752333i	$0.271072\pi$
$593$			36.6410i			1.50467i	−0.658783	+	0.752333i	$0.728928\pi$
$594$	2.92820	−	10.9282i	0.120146	−	0.448390i
$595$		0			0
$596$	−19.8564	+	34.3923i	−0.813350	+	1.40876i
$597$	−18.9282			−0.774680
$598$	−5.32051	+	19.8564i	−0.217572	+	0.811989i
$599$	−34.6410			−1.41539			−0.707697	−	0.706516i	$-0.750266\pi$
$599$	−34.6410			−1.41539			−0.707697	+	0.706516i	$0.750266\pi$
$600$		0			0
$601$	25.4641			1.03870			0.519351	−	0.854561i	$-0.326174\pi$
$601$	25.4641			1.03870			0.519351	+	0.854561i	$0.326174\pi$
$602$	8.73205	−	32.5885i	0.355892	−	1.32821i
$603$	−17.9090			−0.729309
$604$	14.5359	+	8.39230i	0.591457	+	0.341478i
$605$		0			0
$606$	−2.92820	+	10.9282i	−0.118950	+	0.443928i
$607$		−	20.9808i		−	0.851583i	−0.904821	−	0.425791i	$-0.859996\pi$
$607$		−	20.9808i		−	0.851583i	0.904821	−	0.425791i	$-0.140004\pi$
$608$	−40.7846	+	10.9282i	−1.65403	+	0.443197i
$609$	−13.8564			−0.561490
$610$		0			0
$611$		−	23.3205i		−	0.943447i
$612$	−8.53590	+	14.7846i	−0.345043	+	0.597632i
$613$	−5.60770			−0.226493			−0.113246	−	0.993567i	$-0.536125\pi$
$613$	−5.60770			−0.226493			−0.113246	+	0.993567i	$0.536125\pi$
$614$	36.8564	+	9.87564i	1.48740	+	0.398549i
$615$		0			0
$616$	10.9282	+	10.9282i	0.440310	+	0.440310i
$617$		−	27.4641i		−	1.10566i	−0.833293	−	0.552832i	$-0.813547\pi$
$617$		−	27.4641i		−	1.10566i	0.833293	−	0.552832i	$-0.186453\pi$
$618$	−0.444864	+	1.66025i	−0.0178950	+	0.0667852i
$619$		−	33.3205i		−	1.33926i	−0.742693	−	0.669632i	$-0.766452\pi$
$619$		−	33.3205i		−	1.33926i	0.742693	−	0.669632i	$-0.233548\pi$
$620$		0			0
$621$			16.7846i			0.673543i
$622$	−4.53590	−	1.21539i	−0.181873	−	0.0487327i
$623$		−	13.4641i		−	0.539428i
$624$	−5.07180	−	8.78461i	−0.203034	−	0.351666i
$625$		0			0
$626$	−11.6603	+	43.5167i	−0.466037	+	1.73928i
$627$	−10.9282			−0.436430
$628$	−29.3205	−	16.9282i	−1.17002	−	0.675509i
$629$			6.92820i			0.276246i
$630$		0			0
$631$	11.3205			0.450662			0.225331	−	0.974282i	$-0.427654\pi$
$631$	11.3205			0.450662			0.225331	+	0.974282i	$0.427654\pi$
$632$	29.8564	+	29.8564i	1.18762	+	1.18762i
$633$			10.8231i			0.430179i
$634$	21.1244	+	5.66025i	0.838955	+	0.224797i
$635$		0			0
$636$	−5.75129	−	3.32051i	−0.228053	−	0.131667i
$637$	1.60770			0.0636992
$638$	18.9282	+	5.07180i	0.749375	+	0.200794i
$639$	3.60770			0.142718
$640$		0			0
$641$	−20.3923			−0.805448			−0.402724	−	0.915322i	$-0.631936\pi$
$641$	−20.3923			−0.805448			−0.402724	+	0.915322i	$0.631936\pi$
$642$	−0.732051	−	0.196152i	−0.0288917	−	0.00774152i
$643$	−14.8756			−0.586638			−0.293319	−	0.956015i	$-0.594760\pi$
$643$	−14.8756			−0.586638			−0.293319	+	0.956015i	$0.594760\pi$
$644$	−19.8564	−	11.4641i	−0.782452	−	0.451749i
$645$		0			0
$646$	35.3205	+	9.46410i	1.38967	+	0.372360i
$647$			13.2679i			0.521617i	0.965391	+	0.260808i	$0.0839891\pi$
$647$			13.2679i			0.521617i	−0.965391	+	0.260808i	$0.916011\pi$
$648$	8.92820	+	8.92820i	0.350733	+	0.350733i
$649$	1.07180			0.0420717
$650$		0			0
$651$		−	2.92820i		−	0.114765i
$652$	−17.6603	−	10.1962i	−0.691629	−	0.399312i
$653$	36.2487			1.41852			0.709261	−	0.704946i	$-0.249029\pi$
$653$	36.2487			1.41852			0.709261	+	0.704946i	$0.249029\pi$
$654$	−0.823085	+	3.07180i	−0.0321852	+	0.120117i
$655$		0			0
$656$	−10.9282	−	18.9282i	−0.426675	−	0.739022i
$657$			1.32051i			0.0515179i
$658$	25.1244	+	6.73205i	0.979449	+	0.262443i
$659$			17.3205i			0.674711i	0.941377	+	0.337356i	$0.109532\pi$
$659$			17.3205i			0.674711i	−0.941377	+	0.337356i	$0.890468\pi$
$660$		0			0
$661$			35.8564i			1.39465i	0.716754	+	0.697326i	$0.245627\pi$
$661$			35.8564i			1.39465i	−0.716754	+	0.697326i	$0.754373\pi$
$662$	−5.12436	+	19.1244i	−0.199164	+	0.743289i
$663$			8.78461i			0.341166i
$664$	−9.46410	−	9.46410i	−0.367278	−	0.367278i
$665$		0			0
$666$	6.73205	+	1.80385i	0.260862	+	0.0698977i
$667$	−29.0718			−1.12566
$668$	20.1962	−	34.9808i	0.781413	−	1.35345i
$669$			11.8564i			0.458395i
$670$		0			0
$671$	9.85641			0.380502
$672$	10.9282	−	2.92820i	0.421565	−	0.112958i
$673$		−	19.4641i		−	0.750286i	−0.926967	−	0.375143i	$-0.877594\pi$
$673$		−	19.4641i		−	0.750286i	0.926967	−	0.375143i	$-0.122406\pi$
$674$	−2.87564	+	10.7321i	−0.110766	+	0.413383i
$675$		0			0
$676$	−1.73205	−	1.00000i	−0.0666173	−	0.0384615i
$677$	38.3923			1.47554			0.737768	−	0.675054i	$-0.235880\pi$
$677$	38.3923			1.47554			0.737768	+	0.675054i	$0.235880\pi$
$678$	0.248711	−	0.928203i	0.00955170	−	0.0356474i
$679$	17.4641			0.670211
$680$		0			0
$681$	−20.5359			−0.786937
$682$	−1.07180	+	4.00000i	−0.0410412	+	0.153168i
$683$	−34.9808			−1.33850			−0.669251	−	0.743037i	$-0.733385\pi$
$683$	−34.9808			−1.33850			−0.669251	+	0.743037i	$0.733385\pi$
$684$	18.3923	−	31.8564i	0.703247	−	1.21806i
$685$		0			0
$686$	6.53590	−	24.3923i	0.249542	−	0.931303i
$687$		−	2.92820i		−	0.111718i
$688$	17.4641	+	30.2487i	0.665813	+	1.15322i
$689$	15.7128			0.598610
$690$		0			0
$691$		−	18.0000i		−	0.684752i	−0.939563	−	0.342376i	$-0.888768\pi$
$691$		−	18.0000i		−	0.684752i	0.939563	−	0.342376i	$-0.111232\pi$
$692$	−3.46410	−	2.00000i	−0.131685	−	0.0760286i
$693$	−13.4641			−0.511459
$694$	21.3923	+	5.73205i	0.812041	+	0.217586i
$695$		0			0
$696$	10.1436	−	10.1436i	0.384492	−	0.384492i
$697$			18.9282i			0.716957i
$698$	10.2487	−	38.2487i	0.387919	−	1.44774i
$699$		−	21.4641i		−	0.811847i
$700$		0			0
$701$		−	32.9282i		−	1.24368i	−0.783144	−	0.621841i	$-0.786385\pi$
$701$		−	32.9282i		−	1.24368i	0.783144	−	0.621841i	$-0.213615\pi$
$702$	18.9282	+	5.07180i	0.714399	+	0.191423i
$703$		−	14.9282i		−	0.563028i
$704$	−16.0000			−0.603023
$705$		0			0
$706$	−0.339746	+	1.26795i	−0.0127865	+	0.0477199i
$707$	29.8564			1.12287
$708$	0.392305	−	0.679492i	0.0147437	−	0.0255369i
$709$			28.7846i			1.08103i	0.841335	+	0.540514i	$0.181770\pi$
$709$			28.7846i			1.08103i	−0.841335	+	0.540514i	$0.818230\pi$
$710$		0			0
$711$	−36.7846			−1.37953
$712$	9.85641	+	9.85641i	0.369384	+	0.369384i
$713$		−	6.14359i		−	0.230079i
$714$	−9.46410	−	2.53590i	−0.354185	−	0.0949036i
$715$		0			0
$716$	15.4641	−	26.7846i	0.577921	−	1.00099i
$717$	14.6410			0.546779
$718$	−6.92820	−	1.85641i	−0.258558	−	0.0692805i
$719$	−25.8564			−0.964281			−0.482141	−	0.876094i	$-0.660141\pi$
$719$	−25.8564			−0.964281			−0.482141	+	0.876094i	$0.660141\pi$
$720$		0			0
$721$	4.53590			0.168926
$722$	−50.1506	−	13.4378i	−1.86641	−	0.500104i
$723$	−3.21539			−0.119582
$724$	16.0000	−	27.7128i	0.594635	−	1.02994i
$725$		0			0
$726$	7.00000	+	1.87564i	0.259794	+	0.0696117i
$727$			14.0526i			0.521181i	0.965449	+	0.260590i	$0.0839172\pi$
$727$			14.0526i			0.521181i	−0.965449	+	0.260590i	$0.916083\pi$
$728$	−18.9282	+	18.9282i	−0.701526	+	0.701526i
$729$	−2.21539			−0.0820515
$730$		0			0
$731$		−	30.2487i		−	1.11879i
$732$	3.60770	−	6.24871i	0.133344	−	0.230959i
$733$	48.9282			1.80720			0.903602	−	0.428373i	$-0.140913\pi$
$733$	48.9282			1.80720			0.903602	+	0.428373i	$0.140913\pi$
$734$	−9.92820	+	37.0526i	−0.366457	+	1.36763i
$735$		0			0
$736$	22.9282	−	6.14359i	0.845145	−	0.226456i
$737$			14.5359i			0.535437i
$738$	18.3923	+	4.92820i	0.677030	+	0.181410i
$739$		−	5.32051i		−	0.195718i	−0.995200	−	0.0978590i	$-0.968801\pi$
$739$		−	5.32051i		−	0.195718i	0.995200	−	0.0978590i	$-0.0311994\pi$
$740$		0			0
$741$		−	18.9282i		−	0.695345i
$742$	−4.53590	+	16.9282i	−0.166518	+	0.621454i
$743$			40.9808i			1.50344i	0.659483	+	0.751719i	$0.270775\pi$
$743$			40.9808i			1.50344i	−0.659483	+	0.751719i	$0.729225\pi$
$744$	2.14359	+	2.14359i	0.0785880	+	0.0785880i
$745$		0			0
$746$	−40.5885	−	10.8756i	−1.48605	−	0.398186i
$747$	11.6603			0.426626
$748$	12.0000	+	6.92820i	0.438763	+	0.253320i
$749$			2.00000i			0.0730784i
$750$		0			0
$751$	−22.2487			−0.811867			−0.405934	−	0.913903i	$-0.633054\pi$
$751$	−22.2487			−0.811867			−0.405934	+	0.913903i	$0.633054\pi$
$752$	−23.3205	+	13.4641i	−0.850411	+	0.490985i
$753$		−	8.10512i		−	0.295367i
$754$	−8.78461	+	32.7846i	−0.319917	+	1.19395i
$755$		0			0
$756$	−10.9282	+	18.9282i	−0.397455	+	0.688412i
$757$	−32.9282			−1.19680			−0.598398	−	0.801199i	$-0.704196\pi$
$757$	−32.9282			−1.19680			−0.598398	+	0.801199i	$0.704196\pi$
$758$	−4.48334	+	16.7321i	−0.162842	+	0.607735i
$759$	6.14359			0.222998
$760$		0			0
$761$	49.7128			1.80209			0.901044	−	0.433728i	$-0.142802\pi$
$761$	49.7128			1.80209			0.901044	+	0.433728i	$0.142802\pi$
$762$	−3.55514	+	13.2679i	−0.128789	+	0.480647i
$763$	8.39230			0.303822
$764$	−33.4641	−	19.3205i	−1.21069	−	0.698991i
$765$		0			0
$766$	−1.14359	+	4.26795i	−0.0413197	+	0.154207i
$767$			1.85641i			0.0670310i
$768$	−5.85641	+	10.1436i	−0.211325	+	0.366025i
$769$	0.928203			0.0334719			0.0167359	−	0.999860i	$-0.494673\pi$
$769$	0.928203			0.0334719			0.0167359	+	0.999860i	$0.494673\pi$
$770$		0			0
$771$		−	1.46410i		−	0.0527283i
$772$	7.46410	−	12.9282i	0.268639	−	0.465296i
$773$	1.60770			0.0578248			0.0289124	−	0.999582i	$-0.490796\pi$
$773$	1.60770			0.0578248			0.0289124	+	0.999582i	$0.490796\pi$
$774$	−29.3923	−	7.87564i	−1.05648	−	0.283084i
$775$		0			0
$776$	−12.7846	+	12.7846i	−0.458941	+	0.458941i
$777$			4.00000i			0.143499i
$778$	12.7321	−	47.5167i	0.456466	−	1.70355i
$779$		−	40.7846i		−	1.46126i
$780$		0			0
$781$		−	2.92820i		−	0.104779i
$782$	−19.8564	−	5.32051i	−0.710064	−	0.190261i
$783$			27.7128i			0.990375i
$784$	−0.928203	−	1.60770i	−0.0331501	−	0.0574177i
$785$		0			0
$786$	2.10512	−	7.85641i	0.0750871	−	0.280229i
$787$	−14.5885			−0.520022			−0.260011	−	0.965606i	$-0.583726\pi$
$787$	−14.5885			−0.520022			−0.260011	+	0.965606i	$0.583726\pi$
$788$	−21.7128	−	12.5359i	−0.773487	−	0.446573i
$789$		−	4.14359i		−	0.147516i
$790$		0			0
$791$	−2.53590			−0.0901662
$792$	9.85641	−	9.85641i	0.350232	−	0.350232i
$793$			17.0718i			0.606237i
$794$	−22.1962	−	5.94744i	−0.787712	−	0.211067i
$795$		0			0
$796$	−44.7846	−	25.8564i	−1.58735	−	0.916456i
$797$	−26.1051			−0.924691			−0.462345	−	0.886700i	$-0.652992\pi$
$797$	−26.1051			−0.924691			−0.462345	+	0.886700i	$0.652992\pi$
$798$	20.3923	+	5.46410i	0.721880	+	0.193427i
$799$	23.3205			0.825020
$800$		0			0
$801$	−12.1436			−0.429073
$802$	27.1244	+	7.26795i	0.957794	+	0.256640i
$803$	1.07180			0.0378229
$804$	9.21539	+	5.32051i	0.325002	+	0.187640i
$805$		0			0
$806$	−6.92820	−	1.85641i	−0.244036	−	0.0653891i
$807$			3.60770i			0.126997i
$808$	−21.8564	+	21.8564i	−0.768906	+	0.768906i
$809$	3.85641			0.135584			0.0677920	−	0.997699i	$-0.478405\pi$
$809$	3.85641			0.135584			0.0677920	+	0.997699i	$0.478405\pi$
$810$		0			0
$811$			15.0718i			0.529242i	0.964352	+	0.264621i	$0.0852469\pi$
$811$			15.0718i			0.529242i	−0.964352	+	0.264621i	$0.914753\pi$
$812$	−32.7846	−	18.9282i	−1.15051	−	0.664250i
$813$	11.2154			0.393341
$814$	1.46410	−	5.46410i	0.0513167	−	0.191517i
$815$		0			0
$816$	8.78461	−	5.07180i	0.307523	−	0.177548i
$817$			65.1769i			2.28025i
$818$	−31.8564	−	8.53590i	−1.11383	−	0.298451i
$819$		−	23.3205i		−	0.814885i
$820$		0			0
$821$			6.78461i			0.236785i	0.992967	+	0.118392i	$0.0377740\pi$
$821$			6.78461i			0.236785i	−0.992967	+	0.118392i	$0.962226\pi$
$822$	2.39230	−	8.92820i	0.0834412	−	0.311407i
$823$		−	15.1244i		−	0.527202i	−0.964632	−	0.263601i	$-0.915090\pi$
$823$		−	15.1244i		−	0.527202i	0.964632	−	0.263601i	$-0.0849102\pi$
$824$	−3.32051	+	3.32051i	−0.115675	+	0.115675i
$825$		0			0
$826$	−2.00000	−	0.535898i	−0.0695889	−	0.0186463i
$827$	−1.12436			−0.0390977			−0.0195488	−	0.999809i	$-0.506223\pi$
$827$	−1.12436			−0.0390977			−0.0195488	+	0.999809i	$0.506223\pi$
$828$	−10.3397	+	17.9090i	−0.359331	+	0.622380i
$829$			15.0718i			0.523465i	0.965140	+	0.261733i	$0.0842938\pi$
$829$			15.0718i			0.523465i	−0.965140	+	0.261733i	$0.915706\pi$
$830$		0			0
$831$	1.46410			0.0507891
$832$		−	27.7128i		−	0.960769i
$833$			1.60770i			0.0557033i
$834$	2.00000	−	7.46410i	0.0692543	−	0.258461i
$835$		0			0
$836$	−25.8564	−	14.9282i	−0.894263	−	0.516303i
$837$	−5.85641			−0.202427
$838$	0.875644	−	3.26795i	0.0302486	−	0.112889i
$839$	16.7846			0.579469			0.289735	−	0.957107i	$-0.406433\pi$
$839$	16.7846			0.579469			0.289735	+	0.957107i	$0.406433\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$	10.1962	−	38.0526i	0.351383	−	1.31138i
$843$	12.7846			0.440325
$844$	−14.7846	+	25.6077i	−0.508907	+	0.881453i
$845$		0			0
$846$	6.07180	−	22.6603i	0.208753	−	0.779076i
$847$		−	19.1244i		−	0.657121i
$848$	−9.07180	−	15.7128i	−0.311527	−	0.539580i
$849$	−5.60770			−0.192456
$850$		0			0
$851$			8.39230i			0.287685i
$852$	−1.85641	−	1.07180i	−0.0635994	−	0.0367192i
$853$	42.3923			1.45148			0.725742	−	0.687967i	$-0.241496\pi$
$853$	42.3923			1.45148			0.725742	+	0.687967i	$0.241496\pi$
$854$	−18.3923	−	4.92820i	−0.629372	−	0.168640i
$855$		0			0
$856$	−1.46410	−	1.46410i	−0.0500420	−	0.0500420i
$857$			7.85641i			0.268370i	0.990956	+	0.134185i	$0.0428416\pi$
$857$			7.85641i			0.268370i	−0.990956	+	0.134185i	$0.957158\pi$
$858$	1.85641	−	6.92820i	0.0633767	−	0.236525i
$859$		−	20.2487i		−	0.690877i	−0.938441	−	0.345439i	$-0.887730\pi$
$859$		−	20.2487i		−	0.690877i	0.938441	−	0.345439i	$-0.112270\pi$
$860$		0			0
$861$			10.9282i			0.372432i
$862$	−19.8564	−	5.32051i	−0.676312	−	0.181217i
$863$		−	30.3397i		−	1.03278i	−0.856354	−	0.516388i	$-0.827276\pi$
$863$		−	30.3397i		−	1.03278i	0.856354	−	0.516388i	$-0.172724\pi$
$864$	−5.85641	−	21.8564i	−0.199239	−	0.743570i
$865$		0			0
$866$	−4.58846	+	17.1244i	−0.155922	+	0.581909i
$867$	3.66025			0.124309
$868$	4.00000	−	6.92820i	0.135769	−	0.235159i
$869$			29.8564i			1.01281i
$870$		0			0
$871$	−25.1769			−0.853087
$872$	−6.14359	+	6.14359i	−0.208048	+	0.208048i
$873$		−	15.7513i		−	0.533100i
$874$	42.7846	+	11.4641i	1.44721	+	0.387779i
$875$		0			0
$876$	0.392305	−	0.679492i	0.0132548	−	0.0229579i
$877$	53.7128			1.81375			0.906876	−	0.421397i	$-0.138460\pi$
$877$	53.7128			1.81375			0.906876	+	0.421397i	$0.138460\pi$
$878$	1.07180	+	0.287187i	0.0361714	+	0.00969209i
$879$	−8.67949			−0.292752
$880$		0			0
$881$	2.53590			0.0854366			0.0427183	−	0.999087i	$-0.486398\pi$
$881$	2.53590			0.0854366			0.0427183	+	0.999087i	$0.486398\pi$
$882$	1.56218	+	0.418584i	0.0526013	+	0.0140945i
$883$	−37.9090			−1.27574			−0.637869	−	0.770145i	$-0.720184\pi$
$883$	−37.9090			−1.27574			−0.637869	+	0.770145i	$0.720184\pi$
$884$	−12.0000	+	20.7846i	−0.403604	+	0.699062i
$885$		0			0
$886$	42.3205	+	11.3397i	1.42179	+	0.380966i
$887$			51.9090i			1.74293i	0.490455	+	0.871466i	$0.336830\pi$
$887$			51.9090i			1.74293i	−0.490455	+	0.871466i	$0.663170\pi$
$888$	−2.92820	−	2.92820i	−0.0982641	−	0.0982641i
$889$	36.2487			1.21574
$890$		0			0
$891$			8.92820i			0.299106i
$892$	−16.1962	+	28.0526i	−0.542287	+	0.939269i
$893$	−50.2487			−1.68151
$894$	−5.32051	+	19.8564i	−0.177944	+	0.664098i
$895$		0			0
$896$	29.8564	+	8.00000i	0.997433	+	0.267261i
$897$			10.6410i			0.355293i
$898$	−15.4641	−	4.14359i	−0.516044	−	0.138274i
$899$		−	10.1436i		−	0.338308i
$900$		0			0
$901$			15.7128i			0.523470i
$902$	4.00000	−	14.9282i	0.133185	−	0.497055i
$903$		−	17.4641i		−	0.581169i
$904$	1.85641	−	1.85641i	0.0617432	−	0.0617432i
$905$		0			0
$906$	8.39230	+	2.24871i	0.278816	+	0.0747084i
$907$	29.1244			0.967058			0.483529	−	0.875328i	$-0.339355\pi$
$907$	29.1244			0.967058			0.483529	+	0.875328i	$0.339355\pi$
$908$	−48.5885	−	28.0526i	−1.61246	−	0.930957i
$909$		−	26.9282i		−	0.893152i
$910$		0			0
$911$	13.1769			0.436571			0.218285	−	0.975885i	$-0.429954\pi$
$911$	13.1769			0.436571			0.218285	+	0.975885i	$0.429954\pi$
$912$	−18.9282	+	10.9282i	−0.626775	+	0.361869i
$913$		−	9.46410i		−	0.313216i
$914$	−5.41154	+	20.1962i	−0.178998	+	0.668029i
$915$		0			0
$916$	4.00000	−	6.92820i	0.132164	−	0.228914i
$917$	−21.4641			−0.708807
$918$	−5.07180	+	18.9282i	−0.167394	+	0.624724i
$919$	25.0718			0.827042			0.413521	−	0.910495i	$-0.364299\pi$
$919$	25.0718			0.827042			0.413521	+	0.910495i	$0.364299\pi$
$920$		0			0
$921$	19.7513			0.650827
$922$	1.07180	−	4.00000i	0.0352977	−	0.131733i
$923$	5.07180			0.166940
$924$	6.92820	+	4.00000i	0.227921	+	0.131590i
$925$		0			0
$926$	−5.39230	+	20.1244i	−0.177202	+	0.661327i
$927$		−	4.09103i		−	0.134367i
$928$	37.8564	−	10.1436i	1.24270	−	0.332980i
$929$	10.5359			0.345672			0.172836	−	0.984951i	$-0.444707\pi$
$929$	10.5359			0.345672			0.172836	+	0.984951i	$0.444707\pi$
$930$		0			0
$931$		−	3.46410i		−	0.113531i
$932$	29.3205	−	50.7846i	0.960425	−	1.66351i
$933$	−2.43078			−0.0795802
$934$	−11.3923	−	3.05256i	−0.372768	−	0.0998828i
$935$		0			0
$936$	17.0718	+	17.0718i	0.558009	+	0.558009i
$937$		−	44.2487i		−	1.44554i	−0.691087	−	0.722771i	$-0.742868\pi$
$937$		−	44.2487i		−	1.44554i	0.691087	−	0.722771i	$-0.257132\pi$
$938$	7.26795	−	27.1244i	0.237307	−	0.885642i
$939$			23.3205i			0.761036i
$940$		0			0
$941$			32.0000i			1.04317i	0.853199	+	0.521585i	$0.174659\pi$
$941$			32.0000i			1.04317i	−0.853199	+	0.521585i	$0.825341\pi$
$942$	−16.9282	−	4.53590i	−0.551551	−	0.147788i
$943$			22.9282i			0.746645i
$944$	1.85641	−	1.07180i	0.0604209	−	0.0348840i
$945$		0			0
$946$	−6.39230	+	23.8564i	−0.207832	+	0.775639i
$947$	21.1244			0.686449			0.343225	−	0.939253i	$-0.388481\pi$
$947$	21.1244			0.686449			0.343225	+	0.939253i	$0.388481\pi$
$948$	18.9282	+	10.9282i	0.614759	+	0.354932i
$949$			1.85641i			0.0602615i
$950$		0			0
$951$	11.3205			0.367093
$952$	−18.9282	−	18.9282i	−0.613467	−	0.613467i
$953$			58.7846i			1.90422i	0.305755	+	0.952110i	$0.401091\pi$
$953$			58.7846i			1.90422i	−0.305755	+	0.952110i	$0.598909\pi$
$954$	15.2679	+	4.09103i	0.494318	+	0.132452i
$955$		0			0
$956$	34.6410	+	20.0000i	1.12037	+	0.646846i
$957$	10.1436			0.327896
$958$	29.8564	+	8.00000i	0.964617	+	0.258468i
$959$	−24.3923			−0.787669
$960$		0			0
$961$	−28.8564			−0.930852
$962$	9.46410	+	2.53590i	0.305135	+	0.0817606i
$963$	1.80385			0.0581282
$964$	−7.60770	−	4.39230i	−0.245027	−	0.141467i
$965$		0			0
$966$	−11.4641	−	3.07180i	−0.368851	−	0.0988334i
$967$			33.6603i			1.08244i	0.840881	+	0.541220i	$0.182038\pi$
$967$			33.6603i			1.08244i	−0.840881	+	0.541220i	$0.817962\pi$
$968$	14.0000	+	14.0000i	0.449977	+	0.449977i
$969$	18.9282			0.608061
$970$		0			0
$971$		−	23.0718i		−	0.740409i	−0.928950	−	0.370205i	$-0.879288\pi$
$971$		−	23.0718i		−	0.740409i	0.928950	−	0.370205i	$-0.120712\pi$
$972$	26.4449	+	15.2679i	0.848219	+	0.489720i
$973$	−20.3923			−0.653747
$974$	9.00000	−	33.5885i	0.288379	−	1.07624i
$975$		0			0
$976$	17.0718	−	9.85641i	0.546455	−	0.315496i
$977$		−	31.4641i		−	1.00663i	−0.864104	−	0.503313i	$-0.832114\pi$
$977$		−	31.4641i		−	1.00663i	0.864104	−	0.503313i	$-0.167886\pi$
$978$	−10.1962	−	2.73205i	−0.326037	−	0.0873614i
$979$			9.85641i			0.315012i
$980$		0			0
$981$		−	7.56922i		−	0.241667i
$982$	−1.12436	+	4.19615i	−0.0358796	+	0.133905i
$983$			45.2679i			1.44382i	0.691985	+	0.721912i	$0.256736\pi$
$983$			45.2679i			1.44382i	−0.691985	+	0.721912i	$0.743264\pi$
$984$	−8.00000	−	8.00000i	−0.255031	−	0.255031i
$985$		0			0
$986$	−32.7846	−	8.78461i	−1.04407	−	0.279759i
$987$	13.4641			0.428567
$988$	25.8564	−	44.7846i	0.822602	−	1.42479i
$989$		−	36.6410i		−	1.16512i
$990$		0			0
$991$	34.5359			1.09707			0.548534	−	0.836128i	$-0.315186\pi$
$991$	34.5359			1.09707			0.548534	+	0.836128i	$0.315186\pi$
$992$	2.14359	+	8.00000i	0.0680592	+	0.254000i
$993$			10.2487i			0.325233i
$994$	−1.46410	+	5.46410i	−0.0464385	+	0.173311i
$995$		0			0
$996$	−6.00000	−	3.46410i	−0.190117	−	0.109764i
$997$	51.1769			1.62079			0.810395	−	0.585884i	$-0.199253\pi$
$997$	51.1769			1.62079			0.810395	+	0.585884i	$0.199253\pi$
$998$	−8.98076	+	33.5167i	−0.284281	+	1.06095i
$999$	8.00000			0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.f.e.149.4		4
3.2	odd	2		1800.2.d.l.1549.1		4
4.3	odd	2		800.2.f.e.49.2		4
5.2	odd	4		200.2.d.f.101.2		4
5.3	odd	4		40.2.d.a.21.3	✓	4
5.4	even	2		200.2.f.c.149.1		4
8.3	odd	2		800.2.f.c.49.4		4
8.5	even	2		200.2.f.c.149.2		4
12.11	even	2		7200.2.d.n.2449.4		4
15.2	even	4		1800.2.k.j.901.3		4
15.8	even	4		360.2.k.e.181.2		4
15.14	odd	2		1800.2.d.p.1549.4		4
20.3	even	4		160.2.d.a.81.2		4
20.7	even	4		800.2.d.e.401.3		4
20.19	odd	2		800.2.f.c.49.3		4
24.5	odd	2		1800.2.d.p.1549.3		4
24.11	even	2		7200.2.d.o.2449.4		4
40.3	even	4		160.2.d.a.81.3		4
40.13	odd	4		40.2.d.a.21.4	yes	4
40.19	odd	2		800.2.f.e.49.1		4
40.27	even	4		800.2.d.e.401.2		4
40.29	even	2	inner	200.2.f.e.149.3		4
40.37	odd	4		200.2.d.f.101.1		4
60.23	odd	4		1440.2.k.e.721.2		4
60.47	odd	4		7200.2.k.j.3601.2		4
60.59	even	2		7200.2.d.o.2449.1		4
80.3	even	4		1280.2.a.d.1.2		2
80.13	odd	4		1280.2.a.o.1.1		2
80.27	even	4		6400.2.a.be.1.2		2
80.37	odd	4		6400.2.a.ce.1.1		2
80.43	even	4		1280.2.a.n.1.1		2
80.53	odd	4		1280.2.a.a.1.2		2
80.67	even	4		6400.2.a.cj.1.1		2
80.77	odd	4		6400.2.a.z.1.2		2
120.29	odd	2		1800.2.d.l.1549.2		4
120.53	even	4		360.2.k.e.181.1		4
120.59	even	2		7200.2.d.n.2449.1		4
120.77	even	4		1800.2.k.j.901.4		4
120.83	odd	4		1440.2.k.e.721.4		4
120.107	odd	4		7200.2.k.j.3601.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.d.a.21.3	✓	4	5.3	odd	4
40.2.d.a.21.4	yes	4	40.13	odd	4
160.2.d.a.81.2		4	20.3	even	4
160.2.d.a.81.3		4	40.3	even	4
200.2.d.f.101.1		4	40.37	odd	4
200.2.d.f.101.2		4	5.2	odd	4
200.2.f.c.149.1		4	5.4	even	2
200.2.f.c.149.2		4	8.5	even	2
200.2.f.e.149.3		4	40.29	even	2	inner
200.2.f.e.149.4		4	1.1	even	1	trivial
360.2.k.e.181.1		4	120.53	even	4
360.2.k.e.181.2		4	15.8	even	4
800.2.d.e.401.2		4	40.27	even	4
800.2.d.e.401.3		4	20.7	even	4
800.2.f.c.49.3		4	20.19	odd	2
800.2.f.c.49.4		4	8.3	odd	2
800.2.f.e.49.1		4	40.19	odd	2
800.2.f.e.49.2		4	4.3	odd	2
1280.2.a.a.1.2		2	80.53	odd	4
1280.2.a.d.1.2		2	80.3	even	4
1280.2.a.n.1.1		2	80.43	even	4
1280.2.a.o.1.1		2	80.13	odd	4
1440.2.k.e.721.2		4	60.23	odd	4
1440.2.k.e.721.4		4	120.83	odd	4
1800.2.d.l.1549.1		4	3.2	odd	2
1800.2.d.l.1549.2		4	120.29	odd	2
1800.2.d.p.1549.3		4	24.5	odd	2
1800.2.d.p.1549.4		4	15.14	odd	2
1800.2.k.j.901.3		4	15.2	even	4
1800.2.k.j.901.4		4	120.77	even	4
6400.2.a.z.1.2		2	80.77	odd	4
6400.2.a.be.1.2		2	80.27	even	4
6400.2.a.ce.1.1		2	80.37	odd	4
6400.2.a.cj.1.1		2	80.67	even	4
7200.2.d.n.2449.1		4	120.59	even	2
7200.2.d.n.2449.4		4	12.11	even	2
7200.2.d.o.2449.1		4	60.59	even	2
7200.2.d.o.2449.4		4	24.11	even	2
7200.2.k.j.3601.1		4	120.107	odd	4
7200.2.k.j.3601.2		4	60.47	odd	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +0.732051 q^{3} +(1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{6} -2.73205i q^{7} +(2.00000 + 2.00000i) q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +0.732051 q^{3} +(1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{6} -2.73205i q^{7} +(2.00000 + 2.00000i) q^{8} -2.46410 q^{9} +2.00000i q^{11} +(1.26795 + 0.732051i) q^{12} -3.46410 q^{13} +(1.00000 - 3.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} -3.46410i q^{17} +(-3.36603 - 0.901924i) q^{18} +7.46410i q^{19} -2.00000i q^{21} +(-0.732051 + 2.73205i) q^{22} -4.19615i q^{23} +(1.46410 + 1.46410i) q^{24} +(-4.73205 - 1.26795i) q^{26} -4.00000 q^{27} +(2.73205 - 4.73205i) q^{28} -6.92820i q^{29} +1.46410 q^{31} +(1.46410 + 5.46410i) q^{32} +1.46410i q^{33} +(1.26795 - 4.73205i) q^{34} +(-4.26795 - 2.46410i) q^{36} -2.00000 q^{37} +(-2.73205 + 10.1962i) q^{38} -2.53590 q^{39} -5.46410 q^{41} +(0.732051 - 2.73205i) q^{42} +8.73205 q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.53590 - 5.73205i) q^{46} +6.73205i q^{47} +(1.46410 + 2.53590i) q^{48} -0.464102 q^{49} -2.53590i q^{51} +(-6.00000 - 3.46410i) q^{52} -4.53590 q^{53} +(-5.46410 - 1.46410i) q^{54} +(5.46410 - 5.46410i) q^{56} +5.46410i q^{57} +(2.53590 - 9.46410i) q^{58} -0.535898i q^{59} -4.92820i q^{61} +(2.00000 + 0.535898i) q^{62} +6.73205i q^{63} +8.00000i q^{64} +(-0.535898 + 2.00000i) q^{66} +7.26795 q^{67} +(3.46410 - 6.00000i) q^{68} -3.07180i q^{69} -1.46410 q^{71} +(-4.92820 - 4.92820i) q^{72} -0.535898i q^{73} +(-2.73205 - 0.732051i) q^{74} +(-7.46410 + 12.9282i) q^{76} +5.46410 q^{77} +(-3.46410 - 0.928203i) q^{78} +14.9282 q^{79} +4.46410 q^{81} +(-7.46410 - 2.00000i) q^{82} -4.73205 q^{83} +(2.00000 - 3.46410i) q^{84} +(11.9282 + 3.19615i) q^{86} -5.07180i q^{87} +(-4.00000 + 4.00000i) q^{88} +4.92820 q^{89} +9.46410i q^{91} +(4.19615 - 7.26795i) q^{92} +1.07180 q^{93} +(-2.46410 + 9.19615i) q^{94} +(1.07180 + 4.00000i) q^{96} +6.39230i q^{97} +(-0.633975 - 0.169873i) q^{98} -4.92820i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{6} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^6 + 8 * q^8 + 4 * q^9	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{6} + 8 q^{8} + 4 q^{9} + 12 q^{12} + 4 q^{14} + 8 q^{16} - 10 q^{18} + 4 q^{22} - 8 q^{24} - 12 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{31} - 8 q^{32} + 12 q^{34} - 24 q^{36} - 8 q^{37} - 4 q^{38} - 24 q^{39} - 8 q^{41} - 4 q^{42} + 28 q^{43} - 8 q^{44} + 20 q^{46} - 8 q^{48} + 12 q^{49} - 24 q^{52} - 32 q^{53} - 8 q^{54} + 8 q^{56} + 24 q^{58} + 8 q^{62} - 16 q^{66} + 36 q^{67} + 8 q^{71} + 8 q^{72} - 4 q^{74} - 16 q^{76} + 8 q^{77} + 32 q^{79} + 4 q^{81} - 16 q^{82} - 12 q^{83} + 8 q^{84} + 20 q^{86} - 16 q^{88} - 8 q^{89} - 4 q^{92} + 32 q^{93} + 4 q^{94} + 32 q^{96} - 6 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^6 + 8 * q^8 + 4 * q^9 + 12 * q^12 + 4 * q^14 + 8 * q^16 - 10 * q^18 + 4 * q^22 - 8 * q^24 - 12 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^31 - 8 * q^32 + 12 * q^34 - 24 * q^36 - 8 * q^37 - 4 * q^38 - 24 * q^39 - 8 * q^41 - 4 * q^42 + 28 * q^43 - 8 * q^44 + 20 * q^46 - 8 * q^48 + 12 * q^49 - 24 * q^52 - 32 * q^53 - 8 * q^54 + 8 * q^56 + 24 * q^58 + 8 * q^62 - 16 * q^66 + 36 * q^67 + 8 * q^71 + 8 * q^72 - 4 * q^74 - 16 * q^76 + 8 * q^77 + 32 * q^79 + 4 * q^81 - 16 * q^82 - 12 * q^83 + 8 * q^84 + 20 * q^86 - 16 * q^88 - 8 * q^89 - 4 * q^92 + 32 * q^93 + 4 * q^94 + 32 * q^96 - 6 * q^98

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