LMFDB - Embedded newform 200.2.f.e.149.2

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			149.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.2.f.e.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} -2.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.00000 - 3.73205i) q^{6} -0.732051i q^{7} +(2.00000 - 2.00000i) q^{8} +4.46410 q^{9} +O(q^{10})$	\(q+(-0.366025 + 1.36603i) q^{2} -2.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.00000 - 3.73205i) q^{6} -0.732051i q^{7} +(2.00000 - 2.00000i) q^{8} +4.46410 q^{9} -2.00000i q^{11} +(4.73205 + 2.73205i) q^{12} +3.46410 q^{13} +(1.00000 + 0.267949i) q^{14} +(2.00000 + 3.46410i) q^{16} -3.46410i q^{17} +(-1.63397 + 6.09808i) q^{18} -0.535898i q^{19} +2.00000i q^{21} +(2.73205 + 0.732051i) q^{22} -6.19615i q^{23} +(-5.46410 + 5.46410i) q^{24} +(-1.26795 + 4.73205i) q^{26} -4.00000 q^{27} +(-0.732051 + 1.26795i) q^{28} -6.92820i q^{29} -5.46410 q^{31} +(-5.46410 + 1.46410i) q^{32} +5.46410i q^{33} +(4.73205 + 1.26795i) q^{34} +(-7.73205 - 4.46410i) q^{36} -2.00000 q^{37} +(0.732051 + 0.196152i) q^{38} -9.46410 q^{39} +1.46410 q^{41} +(-2.73205 - 0.732051i) q^{42} +5.26795 q^{43} +(-2.00000 + 3.46410i) q^{44} +(8.46410 + 2.26795i) q^{46} -3.26795i q^{47} +(-5.46410 - 9.46410i) q^{48} +6.46410 q^{49} +9.46410i q^{51} +(-6.00000 - 3.46410i) q^{52} -11.4641 q^{53} +(1.46410 - 5.46410i) q^{54} +(-1.46410 - 1.46410i) q^{56} +1.46410i q^{57} +(9.46410 + 2.53590i) q^{58} +7.46410i q^{59} -8.92820i q^{61} +(2.00000 - 7.46410i) q^{62} -3.26795i q^{63} -8.00000i q^{64} +(-7.46410 - 2.00000i) q^{66} +10.7321 q^{67} +(-3.46410 + 6.00000i) q^{68} +16.9282i q^{69} +5.46410 q^{71} +(8.92820 - 8.92820i) q^{72} +7.46410i q^{73} +(0.732051 - 2.73205i) q^{74} +(-0.535898 + 0.928203i) q^{76} -1.46410 q^{77} +(3.46410 - 12.9282i) q^{78} +1.07180 q^{79} -2.46410 q^{81} +(-0.535898 + 2.00000i) q^{82} -1.26795 q^{83} +(2.00000 - 3.46410i) q^{84} +(-1.92820 + 7.19615i) q^{86} +18.9282i q^{87} +(-4.00000 - 4.00000i) q^{88} -8.92820 q^{89} -2.53590i q^{91} +(-6.19615 + 10.7321i) q^{92} +14.9282 q^{93} +(4.46410 + 1.19615i) q^{94} +(14.9282 - 4.00000i) q^{96} +14.3923i q^{97} +(-2.36603 + 8.83013i) q^{98} -8.92820i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$3$	−2.73205			−1.57735			−0.788675	−	0.614810i	$-0.789233\pi$
$3$	−2.73205			−1.57735			−0.788675	+	0.614810i	$0.789233\pi$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$	1.00000	−	3.73205i	0.408248	−	1.52360i
$7$		−	0.732051i		−	0.276689i	−0.990384	−	0.138345i	$-0.955822\pi$
$7$		−	0.732051i		−	0.276689i	0.990384	−	0.138345i	$-0.0441781\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	4.46410			1.48803
$10$		0			0
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	4.73205	+	2.73205i	1.36603	+	0.788675i
$13$	3.46410			0.960769			0.480384	−	0.877058i	$-0.340497\pi$
$13$	3.46410			0.960769			0.480384	+	0.877058i	$0.340497\pi$
$14$	1.00000	+	0.267949i	0.267261	+	0.0716124i
$15$		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	$-0.137999\pi$
$18$	−1.63397	+	6.09808i	−0.385132	+	1.43733i
$19$		−	0.535898i		−	0.122944i	−0.998109	−	0.0614718i	$-0.980421\pi$
$19$		−	0.535898i		−	0.122944i	0.998109	−	0.0614718i	$-0.0195794\pi$
$20$		0			0
$21$			2.00000i			0.436436i
$22$	2.73205	+	0.732051i	0.582475	+	0.156074i
$23$		−	6.19615i		−	1.29199i	−0.763343	−	0.645994i	$-0.776443\pi$
$23$		−	6.19615i		−	1.29199i	0.763343	−	0.645994i	$-0.223557\pi$
$24$	−5.46410	+	5.46410i	−1.11536	+	1.11536i
$25$		0			0
$26$	−1.26795	+	4.73205i	−0.248665	+	0.928032i
$27$	−4.00000			−0.769800
$28$	−0.732051	+	1.26795i	−0.138345	+	0.239620i
$29$		−	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
$31$	−5.46410			−0.981382			−0.490691	−	0.871334i	$-0.663256\pi$
$31$	−5.46410			−0.981382			−0.490691	+	0.871334i	$0.663256\pi$
$32$	−5.46410	+	1.46410i	−0.965926	+	0.258819i
$33$			5.46410i			0.951178i
$34$	4.73205	+	1.26795i	0.811540	+	0.217451i
$35$		0			0
$36$	−7.73205	−	4.46410i	−1.28868	−	0.744017i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	0.732051	+	0.196152i	0.118754	+	0.0318201i
$39$	−9.46410			−1.51547
$40$		0			0
$41$	1.46410			0.228654			0.114327	−	0.993443i	$-0.463529\pi$
$41$	1.46410			0.228654			0.114327	+	0.993443i	$0.463529\pi$
$42$	−2.73205	−	0.732051i	−0.421565	−	0.112958i
$43$	5.26795			0.803355			0.401677	−	0.915781i	$-0.368427\pi$
$43$	5.26795			0.803355			0.401677	+	0.915781i	$0.368427\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$		0			0
$46$	8.46410	+	2.26795i	1.24796	+	0.334391i
$47$		−	3.26795i		−	0.476679i	−0.971182	−	0.238340i	$-0.923397\pi$
$47$		−	3.26795i		−	0.476679i	0.971182	−	0.238340i	$-0.0766032\pi$
$48$	−5.46410	−	9.46410i	−0.788675	−	1.36603i
$49$	6.46410			0.923443
$50$		0			0
$51$			9.46410i			1.32524i
$52$	−6.00000	−	3.46410i	−0.832050	−	0.480384i
$53$	−11.4641			−1.57472			−0.787358	−	0.616496i	$-0.788551\pi$
$53$	−11.4641			−1.57472			−0.787358	+	0.616496i	$0.788551\pi$
$54$	1.46410	−	5.46410i	0.199239	−	0.743570i
$55$		0			0
$56$	−1.46410	−	1.46410i	−0.195649	−	0.195649i
$57$			1.46410i			0.193925i
$58$	9.46410	+	2.53590i	1.24270	+	0.332980i
$59$			7.46410i			0.971743i	0.874030	+	0.485872i	$0.161498\pi$
$59$			7.46410i			0.971743i	−0.874030	+	0.485872i	$0.838502\pi$
$60$		0			0
$61$		−	8.92820i		−	1.14314i	−0.820554	−	0.571570i	$-0.806335\pi$
$61$		−	8.92820i		−	1.14314i	0.820554	−	0.571570i	$-0.193665\pi$
$62$	2.00000	−	7.46410i	0.254000	−	0.947942i
$63$		−	3.26795i		−	0.411723i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	−7.46410	−	2.00000i	−0.918767	−	0.246183i
$67$	10.7321			1.31113			0.655564	−	0.755139i	$-0.272431\pi$
$67$	10.7321			1.31113			0.655564	+	0.755139i	$0.272431\pi$
$68$	−3.46410	+	6.00000i	−0.420084	+	0.727607i
$69$			16.9282i			2.03792i
$70$		0			0
$71$	5.46410			0.648470			0.324235	−	0.945977i	$-0.394893\pi$
$71$	5.46410			0.648470			0.324235	+	0.945977i	$0.394893\pi$
$72$	8.92820	−	8.92820i	1.05220	−	1.05220i
$73$			7.46410i			0.873607i	0.899557	+	0.436804i	$0.143889\pi$
$73$			7.46410i			0.873607i	−0.899557	+	0.436804i	$0.856111\pi$
$74$	0.732051	−	2.73205i	0.0850992	−	0.317594i
$75$		0			0
$76$	−0.535898	+	0.928203i	−0.0614718	+	0.106472i
$77$	−1.46410			−0.166850
$78$	3.46410	−	12.9282i	0.392232	−	1.46383i
$79$	1.07180			0.120587			0.0602933	−	0.998181i	$-0.480796\pi$
$79$	1.07180			0.120587			0.0602933	+	0.998181i	$0.480796\pi$
$80$		0			0
$81$	−2.46410			−0.273789
$82$	−0.535898	+	2.00000i	−0.0591801	+	0.220863i
$83$	−1.26795			−0.139176			−0.0695878	−	0.997576i	$-0.522168\pi$
$83$	−1.26795			−0.139176			−0.0695878	+	0.997576i	$0.522168\pi$
$84$	2.00000	−	3.46410i	0.218218	−	0.377964i
$85$		0			0
$86$	−1.92820	+	7.19615i	−0.207924	+	0.775981i
$87$			18.9282i			2.02932i
$88$	−4.00000	−	4.00000i	−0.426401	−	0.426401i
$89$	−8.92820			−0.946388			−0.473194	−	0.880958i	$-0.656899\pi$
$89$	−8.92820			−0.946388			−0.473194	+	0.880958i	$0.656899\pi$
$90$		0			0
$91$		−	2.53590i		−	0.265834i
$92$	−6.19615	+	10.7321i	−0.645994	+	1.11889i
$93$	14.9282			1.54798
$94$	4.46410	+	1.19615i	0.460437	+	0.123374i
$95$		0			0
$96$	14.9282	−	4.00000i	1.52360	−	0.408248i
$97$			14.3923i			1.46132i	0.682743	+	0.730659i	$0.260787\pi$
$97$			14.3923i			1.46132i	−0.682743	+	0.730659i	$0.739213\pi$
$98$	−2.36603	+	8.83013i	−0.239005	+	0.891978i
$99$		−	8.92820i		−	0.897318i
$100$		0			0
$101$			2.92820i			0.291367i	0.989331	+	0.145684i	$0.0465381\pi$
$101$			2.92820i			0.291367i	−0.989331	+	0.145684i	$0.953462\pi$
$102$	−12.9282	−	3.46410i	−1.28008	−	0.342997i
$103$			15.6603i			1.54305i	0.636199	+	0.771525i	$0.280506\pi$
$103$			15.6603i			1.54305i	−0.636199	+	0.771525i	$0.719494\pi$
$104$	6.92820	−	6.92820i	0.679366	−	0.679366i
$105$		0			0
$106$	4.19615	−	15.6603i	0.407566	−	1.52106i
$107$	2.73205			0.264117			0.132059	−	0.991242i	$-0.457841\pi$
$107$	2.73205			0.264117			0.132059	+	0.991242i	$0.457841\pi$
$108$	6.92820	+	4.00000i	0.666667	+	0.384900i
$109$		−	16.9282i		−	1.62143i	−0.585443	−	0.810714i	$-0.699079\pi$
$109$		−	16.9282i		−	1.62143i	0.585443	−	0.810714i	$-0.300921\pi$
$110$		0			0
$111$	5.46410			0.518630
$112$	2.53590	−	1.46410i	0.239620	−	0.138345i
$113$		−	12.9282i		−	1.21618i	−0.793867	−	0.608092i	$-0.791935\pi$
$113$		−	12.9282i		−	1.21618i	0.793867	−	0.608092i	$-0.208065\pi$
$114$	−2.00000	−	0.535898i	−0.187317	−	0.0501915i
$115$		0			0
$116$	−6.92820	+	12.0000i	−0.643268	+	1.11417i
$117$	15.4641			1.42966
$118$	−10.1962	−	2.73205i	−0.938632	−	0.251506i
$119$	−2.53590			−0.232465
$120$		0			0
$121$	7.00000			0.636364
$122$	12.1962	+	3.26795i	1.10419	+	0.295866i
$123$	−4.00000			−0.360668
$124$	9.46410	+	5.46410i	0.849901	+	0.490691i
$125$		0			0
$126$	4.46410	+	1.19615i	0.397694	+	0.106562i
$127$		−	16.7321i		−	1.48473i	−0.669996	−	0.742365i	$-0.733704\pi$
$127$		−	16.7321i		−	1.48473i	0.669996	−	0.742365i	$-0.266296\pi$
$128$	10.9282	+	2.92820i	0.965926	+	0.258819i
$129$	−14.3923			−1.26717
$130$		0			0
$131$		−	19.8564i		−	1.73486i	−0.497557	−	0.867431i	$-0.665770\pi$
$131$		−	19.8564i		−	1.73486i	0.497557	−	0.867431i	$-0.334230\pi$
$132$	5.46410	−	9.46410i	0.475589	−	0.823744i
$133$	−0.392305			−0.0340171
$134$	−3.92820	+	14.6603i	−0.339345	+	1.26645i
$135$		0			0
$136$	−6.92820	−	6.92820i	−0.594089	−	0.594089i
$137$		−	4.92820i		−	0.421045i	−0.977589	−	0.210522i	$-0.932484\pi$
$137$		−	4.92820i		−	0.421045i	0.977589	−	0.210522i	$-0.0675165\pi$
$138$	−23.1244	−	6.19615i	−1.96848	−	0.527452i
$139$			0.535898i			0.0454543i	0.999742	+	0.0227272i	$0.00723490\pi$
$139$			0.535898i			0.0454543i	−0.999742	+	0.0227272i	$0.992765\pi$
$140$		0			0
$141$			8.92820i			0.751890i
$142$	−2.00000	+	7.46410i	−0.167836	+	0.626373i
$143$		−	6.92820i		−	0.579365i
$144$	8.92820	+	15.4641i	0.744017	+	1.28868i
$145$		0			0
$146$	−10.1962	−	2.73205i	−0.843840	−	0.226106i
$147$	−17.6603			−1.45659
$148$	3.46410	+	2.00000i	0.284747	+	0.164399i
$149$			7.85641i			0.643622i	0.946804	+	0.321811i	$0.104292\pi$
$149$			7.85641i			0.643622i	−0.946804	+	0.321811i	$0.895708\pi$
$150$		0			0
$151$	−12.3923			−1.00847			−0.504236	−	0.863566i	$-0.668226\pi$
$151$	−12.3923			−1.00847			−0.504236	+	0.863566i	$0.668226\pi$
$152$	−1.07180	−	1.07180i	−0.0869342	−	0.0869342i
$153$		−	15.4641i		−	1.25020i
$154$	0.535898	−	2.00000i	0.0431839	−	0.161165i
$155$		0			0
$156$	16.3923	+	9.46410i	1.31243	+	0.757735i
$157$	−3.07180			−0.245156			−0.122578	−	0.992459i	$-0.539116\pi$
$157$	−3.07180			−0.245156			−0.122578	+	0.992459i	$0.539116\pi$
$158$	−0.392305	+	1.46410i	−0.0312101	+	0.116478i
$159$	31.3205			2.48388
$160$		0			0
$161$	−4.53590			−0.357479
$162$	0.901924	−	3.36603i	0.0708618	−	0.264460i
$163$	0.196152			0.0153638			0.00768192	−	0.999970i	$-0.497555\pi$
$163$	0.196152			0.0153638			0.00768192	+	0.999970i	$0.497555\pi$
$164$	−2.53590	−	1.46410i	−0.198020	−	0.114327i
$165$		0			0
$166$	0.464102	−	1.73205i	0.0360213	−	0.134433i
$167$			9.80385i			0.758645i	0.925265	+	0.379322i	$0.123843\pi$
$167$			9.80385i			0.758645i	−0.925265	+	0.379322i	$0.876157\pi$
$168$	4.00000	+	4.00000i	0.308607	+	0.308607i
$169$	−1.00000			−0.0769231
$170$		0			0
$171$		−	2.39230i		−	0.182944i
$172$	−9.12436	−	5.26795i	−0.695726	−	0.401677i
$173$	−2.00000			−0.152057			−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000			−0.152057			−0.0760286	+	0.997106i	$0.524224\pi$
$174$	−25.8564	−	6.92820i	−1.96017	−	0.525226i
$175$		0			0
$176$	6.92820	−	4.00000i	0.522233	−	0.301511i
$177$		−	20.3923i		−	1.53278i
$178$	3.26795	−	12.1962i	0.244943	−	0.914140i
$179$			8.53590i			0.638003i	0.947754	+	0.319002i	$0.103348\pi$
$179$			8.53590i			0.638003i	−0.947754	+	0.319002i	$0.896652\pi$
$180$		0			0
$181$			16.0000i			1.18927i	0.803996	+	0.594635i	$0.202704\pi$
$181$			16.0000i			1.18927i	−0.803996	+	0.594635i	$0.797296\pi$
$182$	3.46410	+	0.928203i	0.256776	+	0.0688030i
$183$			24.3923i			1.80313i
$184$	−12.3923	−	12.3923i	−0.913573	−	0.913573i
$185$		0			0
$186$	−5.46410	+	20.3923i	−0.400647	+	1.49524i
$187$	−6.92820			−0.506640
$188$	−3.26795	+	5.66025i	−0.238340	+	0.412816i
$189$			2.92820i			0.212995i
$190$		0			0
$191$	15.3205			1.10855			0.554277	−	0.832333i	$-0.312995\pi$
$191$	15.3205			1.10855			0.554277	+	0.832333i	$0.312995\pi$
$192$			21.8564i			1.57735i
$193$			0.535898i			0.0385748i	0.999814	+	0.0192874i	$0.00613975\pi$
$193$			0.535898i			0.0385748i	−0.999814	+	0.0192874i	$0.993860\pi$
$194$	−19.6603	−	5.26795i	−1.41152	−	0.378217i
$195$		0			0
$196$	−11.1962	−	6.46410i	−0.799725	−	0.461722i
$197$	−19.4641			−1.38676			−0.693380	−	0.720572i	$-0.743879\pi$
$197$	−19.4641			−1.38676			−0.693380	+	0.720572i	$0.743879\pi$
$198$	12.1962	+	3.26795i	0.866743	+	0.232243i
$199$	1.85641			0.131597			0.0657986	−	0.997833i	$-0.479041\pi$
$199$	1.85641			0.131597			0.0657986	+	0.997833i	$0.479041\pi$
$200$		0			0
$201$	−29.3205			−2.06811
$202$	−4.00000	−	1.07180i	−0.281439	−	0.0754114i
$203$	−5.07180			−0.355970
$204$	9.46410	−	16.3923i	0.662620	−	1.14769i
$205$		0			0
$206$	−21.3923	−	5.73205i	−1.49047	−	0.399371i
$207$		−	27.6603i		−	1.92252i
$208$	6.92820	+	12.0000i	0.480384	+	0.832050i
$209$	−1.07180			−0.0741377
$210$		0			0
$211$			26.7846i			1.84393i	0.387275	+	0.921964i	$0.373416\pi$
$211$			26.7846i			1.84393i	−0.387275	+	0.921964i	$0.626584\pi$
$212$	19.8564	+	11.4641i	1.36374	+	0.787358i
$213$	−14.9282			−1.02286
$214$	−1.00000	+	3.73205i	−0.0683586	+	0.255118i
$215$		0			0
$216$	−8.00000	+	8.00000i	−0.544331	+	0.544331i
$217$			4.00000i			0.271538i
$218$	23.1244	+	6.19615i	1.56618	+	0.419656i
$219$		−	20.3923i		−	1.37798i
$220$		0			0
$221$		−	12.0000i		−	0.807207i
$222$	−2.00000	+	7.46410i	−0.134231	+	0.500958i
$223$		−	5.80385i		−	0.388654i	−0.980937	−	0.194327i	$-0.937748\pi$
$223$		−	5.80385i		−	0.388654i	0.980937	−	0.194327i	$-0.0622523\pi$
$224$	1.07180	+	4.00000i	0.0716124	+	0.267261i
$225$		0			0
$226$	17.6603	+	4.73205i	1.17474	+	0.314771i
$227$	10.0526			0.667212			0.333606	−	0.942713i	$-0.391735\pi$
$227$	10.0526			0.667212			0.333606	+	0.942713i	$0.391735\pi$
$228$	1.46410	−	2.53590i	0.0969625	−	0.167944i
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$		0			0
$231$	4.00000			0.263181
$232$	−13.8564	−	13.8564i	−0.909718	−	0.909718i
$233$		−	5.32051i		−	0.348558i	−0.984696	−	0.174279i	$-0.944241\pi$
$233$		−	5.32051i		−	0.348558i	0.984696	−	0.174279i	$-0.0557595\pi$
$234$	−5.66025	+	21.1244i	−0.370022	+	1.38094i
$235$		0			0
$236$	7.46410	−	12.9282i	0.485872	−	0.841554i
$237$	−2.92820			−0.190207
$238$	0.928203	−	3.46410i	0.0601665	−	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
$241$	16.3923			1.05592			0.527961	−	0.849269i	$-0.322957\pi$
$241$	16.3923			1.05592			0.527961	+	0.849269i	$0.322957\pi$
$242$	−2.56218	+	9.56218i	−0.164703	+	0.614680i
$243$	18.7321			1.20166
$244$	−8.92820	+	15.4641i	−0.571570	+	0.989988i
$245$		0			0
$246$	1.46410	−	5.46410i	0.0933477	−	0.348378i
$247$		−	1.85641i		−	0.118120i
$248$	−10.9282	+	10.9282i	−0.693942	+	0.693942i
$249$	3.46410			0.219529
$250$		0			0
$251$			24.9282i			1.57345i	0.617301	+	0.786727i	$0.288226\pi$
$251$			24.9282i			1.57345i	−0.617301	+	0.786727i	$0.711774\pi$
$252$	−3.26795	+	5.66025i	−0.205861	+	0.356562i
$253$	−12.3923			−0.779098
$254$	22.8564	+	6.12436i	1.43414	+	0.384276i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$			2.00000i			0.124757i	0.998053	+	0.0623783i	$0.0198685\pi$
$257$			2.00000i			0.124757i	−0.998053	+	0.0623783i	$0.980131\pi$
$258$	5.26795	−	19.6603i	0.327968	−	1.22399i
$259$			1.46410i			0.0909748i
$260$		0			0
$261$		−	30.9282i		−	1.91441i
$262$	27.1244	+	7.26795i	1.67575	+	0.449015i
$263$		−	11.6603i		−	0.719002i	−0.933145	−	0.359501i	$-0.882947\pi$
$263$		−	11.6603i		−	0.719002i	0.933145	−	0.359501i	$-0.117053\pi$
$264$	10.9282	+	10.9282i	0.672584	+	0.672584i
$265$		0			0
$266$	0.143594	−	0.535898i	0.00880428	−	0.0328580i
$267$	24.3923			1.49278
$268$	−18.5885	−	10.7321i	−1.13547	−	0.655564i
$269$			8.92820i			0.544362i	0.962246	+	0.272181i	$0.0877450\pi$
$269$			8.92820i			0.544362i	−0.962246	+	0.272181i	$0.912255\pi$
$270$		0			0
$271$	−19.3205			−1.17364			−0.586819	−	0.809718i	$-0.699620\pi$
$271$	−19.3205			−1.17364			−0.586819	+	0.809718i	$0.699620\pi$
$272$	12.0000	−	6.92820i	0.727607	−	0.420084i
$273$			6.92820i			0.419314i
$274$	6.73205	+	1.80385i	0.406698	+	0.108974i
$275$		0			0
$276$	16.9282	−	29.3205i	1.01896	−	1.76489i
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$	−0.732051	−	0.196152i	−0.0439055	−	0.0117644i
$279$	−24.3923			−1.46033
$280$		0			0
$281$	10.5359			0.628519			0.314260	−	0.949337i	$-0.398244\pi$
$281$	10.5359			0.628519			0.314260	+	0.949337i	$0.398244\pi$
$282$	−12.1962	−	3.26795i	−0.726270	−	0.194604i
$283$	9.66025			0.574242			0.287121	−	0.957894i	$-0.407302\pi$
$283$	9.66025			0.574242			0.287121	+	0.957894i	$0.407302\pi$
$284$	−9.46410	−	5.46410i	−0.561591	−	0.324235i
$285$		0			0
$286$	9.46410	+	2.53590i	0.559624	+	0.149951i
$287$		−	1.07180i		−	0.0632662i
$288$	−24.3923	+	6.53590i	−1.43733	+	0.385132i
$289$	5.00000			0.294118
$290$		0			0
$291$		−	39.3205i		−	2.30501i
$292$	7.46410	−	12.9282i	0.436804	−	0.756566i
$293$	15.8564			0.926341			0.463171	−	0.886269i	$-0.346712\pi$
$293$	15.8564			0.926341			0.463171	+	0.886269i	$0.346712\pi$
$294$	6.46410	−	24.1244i	0.376994	−	1.40696i
$295$		0			0
$296$	−4.00000	+	4.00000i	−0.232495	+	0.232495i
$297$			8.00000i			0.464207i
$298$	−10.7321	−	2.87564i	−0.621691	−	0.166582i
$299$		−	21.4641i		−	1.24130i
$300$		0			0
$301$		−	3.85641i		−	0.222280i
$302$	4.53590	−	16.9282i	0.261012	−	0.974109i
$303$		−	8.00000i		−	0.459588i
$304$	1.85641	−	1.07180i	0.106472	−	0.0614718i
$305$		0			0
$306$	21.1244	+	5.66025i	1.20760	+	0.323575i
$307$	−24.9808			−1.42573			−0.712864	−	0.701303i	$-0.752602\pi$
$307$	−24.9808			−1.42573			−0.712864	+	0.701303i	$0.752602\pi$
$308$	2.53590	+	1.46410i	0.144496	+	0.0834249i
$309$		−	42.7846i		−	2.43393i
$310$		0			0
$311$	31.3205			1.77602			0.888012	−	0.459821i	$-0.152086\pi$
$311$	31.3205			1.77602			0.888012	+	0.459821i	$0.152086\pi$
$312$	−18.9282	+	18.9282i	−1.07160	+	1.07160i
$313$		−	4.14359i		−	0.234210i	−0.993120	−	0.117105i	$-0.962639\pi$
$313$		−	4.14359i		−	0.234210i	0.993120	−	0.117105i	$-0.0373614\pi$
$314$	1.12436	−	4.19615i	0.0634511	−	0.236803i
$315$		0			0
$316$	−1.85641	−	1.07180i	−0.104431	−	0.0602933i
$317$	8.53590			0.479424			0.239712	−	0.970844i	$-0.422947\pi$
$317$	8.53590			0.479424			0.239712	+	0.970844i	$0.422947\pi$
$318$	−11.4641	+	42.7846i	−0.642875	+	2.39924i
$319$	−13.8564			−0.775810
$320$		0			0
$321$	−7.46410			−0.416606
$322$	1.66025	−	6.19615i	0.0925223	−	0.345298i
$323$	−1.85641			−0.103293
$324$	4.26795	+	2.46410i	0.237108	+	0.136895i
$325$		0			0
$326$	−0.0717968	+	0.267949i	−0.00397646	+	0.0148403i
$327$			46.2487i			2.55756i
$328$	2.92820	−	2.92820i	0.161683	−	0.161683i
$329$	−2.39230			−0.131892
$330$		0			0
$331$		−	14.0000i		−	0.769510i	−0.923019	−	0.384755i	$-0.874286\pi$
$331$		−	14.0000i		−	0.769510i	0.923019	−	0.384755i	$-0.125714\pi$
$332$	2.19615	+	1.26795i	0.120530	+	0.0695878i
$333$	−8.92820			−0.489263
$334$	−13.3923	−	3.58846i	−0.732794	−	0.196352i
$335$		0			0
$336$	−6.92820	+	4.00000i	−0.377964	+	0.218218i
$337$			19.8564i			1.08165i	0.841136	+	0.540824i	$0.181887\pi$
$337$			19.8564i			1.08165i	−0.841136	+	0.540824i	$0.818113\pi$
$338$	0.366025	−	1.36603i	0.0199092	−	0.0743020i
$339$			35.3205i			1.91835i
$340$		0			0
$341$			10.9282i			0.591795i
$342$	3.26795	+	0.875644i	0.176710	+	0.0473494i
$343$		−	9.85641i		−	0.532196i
$344$	10.5359	−	10.5359i	0.568058	−	0.568058i
$345$		0			0
$346$	0.732051	−	2.73205i	0.0393553	−	0.146876i
$347$	−1.66025			−0.0891271			−0.0445636	−	0.999007i	$-0.514190\pi$
$347$	−1.66025			−0.0891271			−0.0445636	+	0.999007i	$0.514190\pi$
$348$	18.9282	−	32.7846i	1.01466	−	1.75744i
$349$			28.0000i			1.49881i	0.662114	+	0.749403i	$0.269659\pi$
$349$			28.0000i			1.49881i	−0.662114	+	0.749403i	$0.730341\pi$
$350$		0			0
$351$	−13.8564			−0.739600
$352$	2.92820	+	10.9282i	0.156074	+	0.582475i
$353$			12.9282i			0.688099i	0.938952	+	0.344049i	$0.111799\pi$
$353$			12.9282i			0.688099i	−0.938952	+	0.344049i	$0.888201\pi$
$354$	27.8564	+	7.46410i	1.48055	+	0.396713i
$355$		0			0
$356$	15.4641	+	8.92820i	0.819596	+	0.473194i
$357$	6.92820			0.366679
$358$	−11.6603	−	3.12436i	−0.616264	−	0.165127i
$359$	−18.9282			−0.998992			−0.499496	−	0.866316i	$-0.666482\pi$
$359$	−18.9282			−0.998992			−0.499496	+	0.866316i	$0.666482\pi$
$360$		0			0
$361$	18.7128			0.984885
$362$	−21.8564	−	5.85641i	−1.14875	−	0.307806i
$363$	−19.1244			−1.00377
$364$	−2.53590	+	4.39230i	−0.132917	+	0.230219i
$365$		0			0
$366$	−33.3205	−	8.92820i	−1.74169	−	0.466685i
$367$		−	2.87564i		−	0.150107i	−0.997179	−	0.0750537i	$-0.976087\pi$
$367$		−	2.87564i		−	0.150107i	0.997179	−	0.0750537i	$-0.0239128\pi$
$368$	21.4641	−	12.3923i	1.11889	−	0.645994i
$369$	6.53590			0.340245
$370$		0			0
$371$			8.39230i			0.435707i
$372$	−25.8564	−	14.9282i	−1.34059	−	0.773991i
$373$	25.7128			1.33136			0.665679	−	0.746238i	$-0.268142\pi$
$373$	25.7128			1.33136			0.665679	+	0.746238i	$0.268142\pi$
$374$	2.53590	−	9.46410i	0.131128	−	0.489377i
$375$		0			0
$376$	−6.53590	−	6.53590i	−0.337063	−	0.337063i
$377$		−	24.0000i		−	1.23606i
$378$	−4.00000	−	1.07180i	−0.205738	−	0.0551273i
$379$			36.2487i			1.86197i	0.365056	+	0.930986i	$0.381050\pi$
$379$			36.2487i			1.86197i	−0.365056	+	0.930986i	$0.618950\pi$
$380$		0			0
$381$			45.7128i			2.34194i
$382$	−5.60770	+	20.9282i	−0.286915	+	1.07078i
$383$			21.1244i			1.07940i	0.841856	+	0.539702i	$0.181463\pi$
$383$			21.1244i			1.07940i	−0.841856	+	0.539702i	$0.818537\pi$
$384$	−29.8564	−	8.00000i	−1.52360	−	0.408248i
$385$		0			0
$386$	−0.732051	−	0.196152i	−0.0372604	−	0.00998390i
$387$	23.5167			1.19542
$388$	14.3923	−	24.9282i	0.730659	−	1.26554i
$389$		−	6.78461i		−	0.343993i	−0.985098	−	0.171997i	$-0.944978\pi$
$389$		−	6.78461i		−	0.343993i	0.985098	−	0.171997i	$-0.0550218\pi$
$390$		0			0
$391$	−21.4641			−1.08549
$392$	12.9282	−	12.9282i	0.652973	−	0.652973i
$393$			54.2487i			2.73649i
$394$	7.12436	−	26.5885i	0.358920	−	1.33951i
$395$		0			0
$396$	−8.92820	+	15.4641i	−0.448659	+	0.777100i
$397$	32.2487			1.61852			0.809258	−	0.587453i	$-0.199869\pi$
$397$	32.2487			1.61852			0.809258	+	0.587453i	$0.199869\pi$
$398$	−0.679492	+	2.53590i	−0.0340599	+	0.127113i
$399$	1.07180			0.0536570
$400$		0			0
$401$	−7.85641			−0.392330			−0.196165	−	0.980571i	$-0.562849\pi$
$401$	−7.85641			−0.392330			−0.196165	+	0.980571i	$0.562849\pi$
$402$	10.7321	−	40.0526i	0.535266	−	1.99764i
$403$	−18.9282			−0.942881
$404$	2.92820	−	5.07180i	0.145684	−	0.252331i
$405$		0			0
$406$	1.85641	−	6.92820i	0.0921319	−	0.343841i
$407$			4.00000i			0.198273i
$408$	18.9282	+	18.9282i	0.937086	+	0.937086i
$409$	11.3205			0.559763			0.279882	−	0.960035i	$-0.409705\pi$
$409$	11.3205			0.559763			0.279882	+	0.960035i	$0.409705\pi$
$410$		0			0
$411$			13.4641i			0.664135i
$412$	15.6603	−	27.1244i	0.771525	−	1.33632i
$413$	5.46410			0.268871
$414$	37.7846	+	10.1244i	1.85701	+	0.497585i
$415$		0			0
$416$	−18.9282	+	5.07180i	−0.928032	+	0.248665i
$417$		−	1.46410i		−	0.0716974i
$418$	0.392305	−	1.46410i	0.0191883	−	0.0716116i
$419$		−	18.3923i		−	0.898523i	−0.893400	−	0.449261i	$-0.851687\pi$
$419$		−	18.3923i		−	0.898523i	0.893400	−	0.449261i	$-0.148313\pi$
$420$		0			0
$421$			0.143594i			0.00699832i	0.999994	+	0.00349916i	$0.00111382\pi$
$421$			0.143594i			0.00699832i	−0.999994	+	0.00349916i	$0.998886\pi$
$422$	−36.5885	−	9.80385i	−1.78110	−	0.477244i
$423$		−	14.5885i		−	0.709315i
$424$	−22.9282	+	22.9282i	−1.11349	+	1.11349i
$425$		0			0
$426$	5.46410	−	20.3923i	0.264737	−	0.988010i
$427$	−6.53590			−0.316294
$428$	−4.73205	−	2.73205i	−0.228732	−	0.132059i
$429$			18.9282i			0.913862i
$430$		0			0
$431$	−21.4641			−1.03389			−0.516945	−	0.856019i	$-0.672931\pi$
$431$	−21.4641			−1.03389			−0.516945	+	0.856019i	$0.672931\pi$
$432$	−8.00000	−	13.8564i	−0.384900	−	0.666667i
$433$		−	19.4641i		−	0.935385i	−0.883891	−	0.467693i	$-0.845085\pi$
$433$		−	19.4641i		−	0.935385i	0.883891	−	0.467693i	$-0.154915\pi$
$434$	−5.46410	−	1.46410i	−0.262285	−	0.0702791i
$435$		0			0
$436$	−16.9282	+	29.3205i	−0.810714	+	1.40420i
$437$	−3.32051			−0.158841
$438$	27.8564	+	7.46410i	1.33103	+	0.356649i
$439$	−40.7846			−1.94654			−0.973272	−	0.229657i	$-0.926240\pi$
$439$	−40.7846			−1.94654			−0.973272	+	0.229657i	$0.926240\pi$
$440$		0			0
$441$	28.8564			1.37411
$442$	16.3923	+	4.39230i	0.779702	+	0.208921i
$443$	−20.9808			−0.996826			−0.498413	−	0.866940i	$-0.666084\pi$
$443$	−20.9808			−0.996826			−0.498413	+	0.866940i	$0.666084\pi$
$444$	−9.46410	−	5.46410i	−0.449146	−	0.259315i
$445$		0			0
$446$	7.92820	+	2.12436i	0.375411	+	0.100591i
$447$		−	21.4641i		−	1.01522i
$448$	−5.85641			−0.276689
$449$	23.3205			1.10056			0.550281	−	0.834979i	$-0.314520\pi$
$449$	23.3205			1.10056			0.550281	+	0.834979i	$0.314520\pi$
$450$		0			0
$451$		−	2.92820i		−	0.137884i
$452$	−12.9282	+	22.3923i	−0.608092	+	1.05325i
$453$	33.8564			1.59071
$454$	−3.67949	+	13.7321i	−0.172687	+	0.644477i
$455$		0			0
$456$	2.92820	+	2.92820i	0.137126	+	0.137126i
$457$			26.7846i			1.25293i	0.779449	+	0.626466i	$0.215499\pi$
$457$			26.7846i			1.25293i	−0.779449	+	0.626466i	$0.784501\pi$
$458$	−5.46410	−	1.46410i	−0.255321	−	0.0684130i
$459$			13.8564i			0.646762i
$460$		0			0
$461$		−	10.9282i		−	0.508977i	−0.967076	−	0.254489i	$-0.918093\pi$
$461$		−	10.9282i		−	0.508977i	0.967076	−	0.254489i	$-0.0819071\pi$
$462$	−1.46410	+	5.46410i	−0.0681162	+	0.254213i
$463$		−	11.2679i		−	0.523666i	−0.965113	−	0.261833i	$-0.915673\pi$
$463$		−	11.2679i		−	0.523666i	0.965113	−	0.261833i	$-0.0843270\pi$
$464$	24.0000	−	13.8564i	1.11417	−	0.643268i
$465$		0			0
$466$	7.26795	+	1.94744i	0.336681	+	0.0902135i
$467$	−25.6603			−1.18741			−0.593707	−	0.804681i	$-0.702336\pi$
$467$	−25.6603			−1.18741			−0.593707	+	0.804681i	$0.702336\pi$
$468$	−26.7846	−	15.4641i	−1.23812	−	0.714828i
$469$		−	7.85641i		−	0.362775i
$470$		0			0
$471$	8.39230			0.386697
$472$	14.9282	+	14.9282i	0.687126	+	0.687126i
$473$		−	10.5359i		−	0.484441i
$474$	1.07180	−	4.00000i	0.0492293	−	0.183726i
$475$		0			0
$476$	4.39230	+	2.53590i	0.201321	+	0.116233i
$477$	−51.1769			−2.34323
$478$	−7.32051	+	27.3205i	−0.334832	+	1.24961i
$479$	−5.85641			−0.267586			−0.133793	−	0.991009i	$-0.542716\pi$
$479$	−5.85641			−0.267586			−0.133793	+	0.991009i	$0.542716\pi$
$480$		0			0
$481$	−6.92820			−0.315899
$482$	−6.00000	+	22.3923i	−0.273293	+	1.01994i
$483$	12.3923			0.563869
$484$	−12.1244	−	7.00000i	−0.551107	−	0.318182i
$485$		0			0
$486$	−6.85641	+	25.5885i	−0.311013	+	1.16072i
$487$		−	6.58846i		−	0.298551i	−0.988796	−	0.149276i	$-0.952306\pi$
$487$		−	6.58846i		−	0.298551i	0.988796	−	0.149276i	$-0.0476942\pi$
$488$	−17.8564	−	17.8564i	−0.808322	−	0.808322i
$489$	−0.535898			−0.0242342
$490$		0			0
$491$		−	16.9282i		−	0.763959i	−0.924171	−	0.381980i	$-0.875242\pi$
$491$		−	16.9282i		−	0.763959i	0.924171	−	0.381980i	$-0.124758\pi$
$492$	6.92820	+	4.00000i	0.312348	+	0.180334i
$493$	−24.0000			−1.08091
$494$	2.53590	+	0.679492i	0.114095	+	0.0305718i
$495$		0			0
$496$	−10.9282	−	18.9282i	−0.490691	−	0.849901i
$497$		−	4.00000i		−	0.179425i
$498$	−1.26795	+	4.73205i	−0.0568182	+	0.212048i
$499$		−	31.4641i		−	1.40853i	−0.709939	−	0.704263i	$-0.751277\pi$
$499$		−	31.4641i		−	1.40853i	0.709939	−	0.704263i	$-0.248723\pi$
$500$		0			0
$501$		−	26.7846i		−	1.19665i
$502$	−34.0526	−	9.12436i	−1.51984	−	0.407240i
$503$		−	0.339746i		−	0.0151485i	−0.999971	−	0.00757426i	$-0.997589\pi$
$503$		−	0.339746i		−	0.0151485i	0.999971	−	0.00757426i	$-0.00241099\pi$
$504$	−6.53590	−	6.53590i	−0.291132	−	0.291132i
$505$		0			0
$506$	4.53590	−	16.9282i	0.201645	−	0.752550i
$507$	2.73205			0.121335
$508$	−16.7321	+	28.9808i	−0.742365	+	1.28581i
$509$			1.85641i			0.0822838i	0.999153	+	0.0411419i	$0.0130996\pi$
$509$			1.85641i			0.0822838i	−0.999153	+	0.0411419i	$0.986900\pi$
$510$		0			0
$511$	5.46410			0.241718
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$			2.14359i			0.0946420i
$514$	−2.73205	−	0.732051i	−0.120506	−	0.0322894i
$515$		0			0
$516$	24.9282	+	14.3923i	1.09740	+	0.633586i
$517$	−6.53590			−0.287448
$518$	−2.00000	−	0.535898i	−0.0878750	−	0.0235460i
$519$	5.46410			0.239847
$520$		0			0
$521$	−43.8564			−1.92138			−0.960692	−	0.277616i	$-0.910456\pi$
$521$	−43.8564			−1.92138			−0.960692	+	0.277616i	$0.910456\pi$
$522$	42.2487	+	11.3205i	1.84918	+	0.495485i
$523$	11.8038			0.516146			0.258073	−	0.966125i	$-0.416912\pi$
$523$	11.8038			0.516146			0.258073	+	0.966125i	$0.416912\pi$
$524$	−19.8564	+	34.3923i	−0.867431	+	1.50243i
$525$		0			0
$526$	15.9282	+	4.26795i	0.694503	+	0.186091i
$527$			18.9282i			0.824525i
$528$	−18.9282	+	10.9282i	−0.823744	+	0.475589i
$529$	−15.3923			−0.669231
$530$		0			0
$531$			33.3205i			1.44599i
$532$	0.679492	+	0.392305i	0.0294597	+	0.0170086i
$533$	5.07180			0.219684
$534$	−8.92820	+	33.3205i	−0.386361	+	1.44192i
$535$		0			0
$536$	21.4641	−	21.4641i	0.927108	−	0.927108i
$537$		−	23.3205i		−	1.00635i
$538$	−12.1962	−	3.26795i	−0.525813	−	0.140891i
$539$		−	12.9282i		−	0.556857i
$540$		0			0
$541$		−	26.9282i		−	1.15773i	−0.815422	−	0.578867i	$-0.803495\pi$
$541$		−	26.9282i		−	1.15773i	0.815422	−	0.578867i	$-0.196505\pi$
$542$	7.07180	−	26.3923i	0.303760	−	1.13365i
$543$		−	43.7128i		−	1.87590i
$544$	5.07180	+	18.9282i	0.217451	+	0.811540i
$545$		0			0
$546$	−9.46410	−	2.53590i	−0.405026	−	0.108526i
$547$	33.2679			1.42243			0.711217	−	0.702972i	$-0.248144\pi$
$547$	33.2679			1.42243			0.711217	+	0.702972i	$0.248144\pi$
$548$	−4.92820	+	8.53590i	−0.210522	+	0.364636i
$549$		−	39.8564i		−	1.70103i
$550$		0			0
$551$	−3.71281			−0.158171
$552$	33.8564	+	33.8564i	1.44102	+	1.44102i
$553$		−	0.784610i		−	0.0333650i
$554$	−0.732051	+	2.73205i	−0.0311019	+	0.116074i
$555$		0			0
$556$	0.535898	−	0.928203i	0.0227272	−	0.0393646i
$557$	14.7846			0.626444			0.313222	−	0.949680i	$-0.398592\pi$
$557$	14.7846			0.626444			0.313222	+	0.949680i	$0.398592\pi$
$558$	8.92820	−	33.3205i	0.377961	−	1.41057i
$559$	18.2487			0.771838
$560$		0			0
$561$	18.9282			0.799149
$562$	−3.85641	+	14.3923i	−0.162673	+	0.607103i
$563$	22.0526			0.929405			0.464702	−	0.885467i	$-0.346161\pi$
$563$	22.0526			0.929405			0.464702	+	0.885467i	$0.346161\pi$
$564$	8.92820	−	15.4641i	0.375945	−	0.651156i
$565$		0			0
$566$	−3.53590	+	13.1962i	−0.148625	+	0.554676i
$567$			1.80385i			0.0757545i
$568$	10.9282	−	10.9282i	0.458537	−	0.458537i
$569$	13.4641			0.564445			0.282222	−	0.959349i	$-0.408928\pi$
$569$	13.4641			0.564445			0.282222	+	0.959349i	$0.408928\pi$
$570$		0			0
$571$			6.78461i			0.283927i	0.989872	+	0.141964i	$0.0453416\pi$
$571$			6.78461i			0.283927i	−0.989872	+	0.141964i	$0.954658\pi$
$572$	−6.92820	+	12.0000i	−0.289683	+	0.501745i
$573$	−41.8564			−1.74858
$574$	1.46410	+	0.392305i	0.0611104	+	0.0163745i
$575$		0			0
$576$		−	35.7128i		−	1.48803i
$577$		−	39.5692i		−	1.64729i	−0.567107	−	0.823644i	$-0.691937\pi$
$577$		−	39.5692i		−	1.64729i	0.567107	−	0.823644i	$-0.308063\pi$
$578$	−1.83013	+	6.83013i	−0.0761232	+	0.284096i
$579$		−	1.46410i		−	0.0608460i
$580$		0			0
$581$			0.928203i			0.0385084i
$582$	53.7128	+	14.3923i	2.22647	+	0.596580i
$583$			22.9282i			0.949589i
$584$	14.9282	+	14.9282i	0.617733	+	0.617733i
$585$		0			0
$586$	−5.80385	+	21.6603i	−0.239755	+	0.894777i
$587$	−3.80385			−0.157002			−0.0785008	−	0.996914i	$-0.525013\pi$
$587$	−3.80385			−0.157002			−0.0785008	+	0.996914i	$0.525013\pi$
$588$	30.5885	+	17.6603i	1.26145	+	0.728297i
$589$			2.92820i			0.120655i
$590$		0			0
$591$	53.1769			2.18741
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$			32.6410i			1.34041i	0.742178	+	0.670203i	$0.233793\pi$
$593$			32.6410i			1.34041i	−0.742178	+	0.670203i	$0.766207\pi$
$594$	−10.9282	−	2.92820i	−0.448390	−	0.120146i
$595$		0			0
$596$	7.85641	−	13.6077i	0.321811	−	0.557393i
$597$	−5.07180			−0.207575
$598$	29.3205	+	7.85641i	1.19900	+	0.321272i
$599$	34.6410			1.41539			0.707697	−	0.706516i	$-0.249734\pi$
$599$	34.6410			1.41539			0.707697	+	0.706516i	$0.249734\pi$
$600$		0			0
$601$	18.5359			0.756095			0.378048	−	0.925786i	$-0.376596\pi$
$601$	18.5359			0.756095			0.378048	+	0.925786i	$0.376596\pi$
$602$	5.26795	+	1.41154i	0.214706	+	0.0575302i
$603$	47.9090			1.95100
$604$	21.4641	+	12.3923i	0.873362	+	0.504236i
$605$		0			0
$606$	10.9282	+	2.92820i	0.443928	+	0.118950i
$607$		−	30.9808i		−	1.25747i	−0.777619	−	0.628735i	$-0.783573\pi$
$607$		−	30.9808i		−	1.25747i	0.777619	−	0.628735i	$-0.216427\pi$
$608$	0.784610	+	2.92820i	0.0318201	+	0.118754i
$609$	13.8564			0.561490
$610$		0			0
$611$		−	11.3205i		−	0.457979i
$612$	−15.4641	+	26.7846i	−0.625099	+	1.08270i
$613$	−26.3923			−1.06598			−0.532988	−	0.846123i	$-0.678931\pi$
$613$	−26.3923			−1.06598			−0.532988	+	0.846123i	$0.678931\pi$
$614$	9.14359	−	34.1244i	0.369005	−	1.37715i
$615$		0			0
$616$	−2.92820	+	2.92820i	−0.117981	+	0.117981i
$617$			20.5359i			0.826744i	0.910562	+	0.413372i	$0.135649\pi$
$617$			20.5359i			0.826744i	−0.910562	+	0.413372i	$0.864351\pi$
$618$	58.4449	+	15.6603i	2.35100	+	0.629948i
$619$		−	1.32051i		−	0.0530757i	−0.999648	−	0.0265379i	$-0.991552\pi$
$619$		−	1.32051i		−	0.0530757i	0.999648	−	0.0265379i	$-0.00844825\pi$
$620$		0			0
$621$			24.7846i			0.994572i
$622$	−11.4641	+	42.7846i	−0.459669	+	1.71551i
$623$			6.53590i			0.261855i
$624$	−18.9282	−	32.7846i	−0.757735	−	1.31243i
$625$		0			0
$626$	5.66025	+	1.51666i	0.226229	+	0.0606179i
$627$	2.92820			0.116941
$628$	5.32051	+	3.07180i	0.212311	+	0.122578i
$629$			6.92820i			0.276246i
$630$		0			0
$631$	−23.3205			−0.928375			−0.464187	−	0.885737i	$-0.653654\pi$
$631$	−23.3205			−0.928375			−0.464187	+	0.885737i	$0.653654\pi$
$632$	2.14359	−	2.14359i	0.0852676	−	0.0852676i
$633$		−	73.1769i		−	2.90852i
$634$	−3.12436	+	11.6603i	−0.124084	+	0.463088i
$635$		0			0
$636$	−54.2487	−	31.3205i	−2.15110	−	1.24194i
$637$	22.3923			0.887215
$638$	5.07180	−	18.9282i	0.200794	−	0.749375i
$639$	24.3923			0.964945
$640$		0			0
$641$	0.392305			0.0154951			0.00774755	−	0.999970i	$-0.497534\pi$
$641$	0.392305			0.0154951			0.00774755	+	0.999970i	$0.497534\pi$
$642$	2.73205	−	10.1962i	0.107825	−	0.402410i
$643$	−39.1244			−1.54291			−0.771457	−	0.636281i	$-0.780472\pi$
$643$	−39.1244			−1.54291			−0.771457	+	0.636281i	$0.780472\pi$
$644$	7.85641	+	4.53590i	0.309586	+	0.178739i
$645$		0			0
$646$	0.679492	−	2.53590i	0.0267343	−	0.0997736i
$647$		−	16.7321i		−	0.657805i	−0.944364	−	0.328902i	$-0.893321\pi$
$647$		−	16.7321i		−	0.657805i	0.944364	−	0.328902i	$-0.106679\pi$
$648$	−4.92820	+	4.92820i	−0.193598	+	0.193598i
$649$	14.9282			0.585983
$650$		0			0
$651$		−	10.9282i		−	0.428310i
$652$	−0.339746	−	0.196152i	−0.0133055	−	0.00768192i
$653$	−12.2487			−0.479329			−0.239665	−	0.970856i	$-0.577037\pi$
$653$	−12.2487			−0.479329			−0.239665	+	0.970856i	$0.577037\pi$
$654$	−63.1769	−	16.9282i	−2.47041	−	0.661945i
$655$		0			0
$656$	2.92820	+	5.07180i	0.114327	+	0.198020i
$657$			33.3205i			1.29996i
$658$	0.875644	−	3.26795i	0.0341362	−	0.127398i
$659$			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
$661$		−	8.14359i		−	0.316749i	−0.987379	−	0.158375i	$-0.949375\pi$
$661$		−	8.14359i		−	0.316749i	0.987379	−	0.158375i	$-0.0506253\pi$
$662$	19.1244	+	5.12436i	0.743289	+	0.199164i
$663$			32.7846i			1.27325i
$664$	−2.53590	+	2.53590i	−0.0984119	+	0.0984119i
$665$		0			0
$666$	3.26795	−	12.1962i	0.126630	−	0.472591i
$667$	−42.9282			−1.66219
$668$	9.80385	−	16.9808i	0.379322	−	0.657005i
$669$			15.8564i			0.613044i
$670$		0			0
$671$	−17.8564			−0.689339
$672$	−2.92820	−	10.9282i	−0.112958	−	0.421565i
$673$			12.5359i			0.483223i	0.970373	+	0.241612i	$0.0776760\pi$
$673$			12.5359i			0.483223i	−0.970373	+	0.241612i	$0.922324\pi$
$674$	−27.1244	−	7.26795i	−1.04479	−	0.279951i
$675$		0			0
$676$	1.73205	+	1.00000i	0.0666173	+	0.0384615i
$677$	17.6077			0.676719			0.338359	−	0.941017i	$-0.390128\pi$
$677$	17.6077			0.676719			0.338359	+	0.941017i	$0.390128\pi$
$678$	−48.2487	−	12.9282i	−1.85298	−	0.496505i
$679$	10.5359			0.404331
$680$		0			0
$681$	−27.4641			−1.05243
$682$	−14.9282	−	4.00000i	−0.571630	−	0.153168i
$683$	16.9808			0.649751			0.324875	−	0.945757i	$-0.394678\pi$
$683$	16.9808			0.649751			0.324875	+	0.945757i	$0.394678\pi$
$684$	−2.39230	+	4.14359i	−0.0914721	+	0.158434i
$685$		0			0
$686$	13.4641	+	3.60770i	0.514062	+	0.137742i
$687$		−	10.9282i		−	0.416937i
$688$	10.5359	+	18.2487i	0.401677	+	0.695726i
$689$	−39.7128			−1.51294
$690$		0			0
$691$			18.0000i			0.684752i	0.939563	+	0.342376i	$0.111232\pi$
$691$			18.0000i			0.684752i	−0.939563	+	0.342376i	$0.888768\pi$
$692$	3.46410	+	2.00000i	0.131685	+	0.0760286i
$693$	−6.53590			−0.248278
$694$	0.607695	−	2.26795i	0.0230678	−	0.0860902i
$695$		0			0
$696$	37.8564	+	37.8564i	1.43494	+	1.43494i
$697$		−	5.07180i		−	0.192108i
$698$	−38.2487	−	10.2487i	−1.44774	−	0.387919i
$699$			14.5359i			0.549798i
$700$		0			0
$701$			19.0718i			0.720332i	0.932888	+	0.360166i	$0.117280\pi$
$701$			19.0718i			0.720332i	−0.932888	+	0.360166i	$0.882720\pi$
$702$	5.07180	−	18.9282i	0.191423	−	0.714399i
$703$			1.07180i			0.0404236i
$704$	−16.0000			−0.603023
$705$		0			0
$706$	−17.6603	−	4.73205i	−0.664652	−	0.178093i
$707$	2.14359			0.0806181
$708$	−20.3923	+	35.3205i	−0.766390	+	1.32743i
$709$			12.7846i			0.480136i	0.970756	+	0.240068i	$0.0771698\pi$
$709$			12.7846i			0.480136i	−0.970756	+	0.240068i	$0.922830\pi$
$710$		0			0
$711$	4.78461			0.179437
$712$	−17.8564	+	17.8564i	−0.669197	+	0.669197i
$713$			33.8564i			1.26793i
$714$	−2.53590	+	9.46410i	−0.0949036	+	0.354185i
$715$		0			0
$716$	8.53590	−	14.7846i	0.319002	−	0.552527i
$717$	−54.6410			−2.04061
$718$	6.92820	−	25.8564i	0.258558	−	0.964953i
$719$	1.85641			0.0692323			0.0346161	−	0.999401i	$-0.488979\pi$
$719$	1.85641			0.0692323			0.0346161	+	0.999401i	$0.488979\pi$
$720$		0			0
$721$	11.4641			0.426945
$722$	−6.84936	+	25.5622i	−0.254907	+	0.951326i
$723$	−44.7846			−1.66556
$724$	16.0000	−	27.7128i	0.594635	−	1.02994i
$725$		0			0
$726$	7.00000	−	26.1244i	0.259794	−	0.969566i
$727$			24.0526i			0.892060i	0.895018	+	0.446030i	$0.147163\pi$
$727$			24.0526i			0.892060i	−0.895018	+	0.446030i	$0.852837\pi$
$728$	−5.07180	−	5.07180i	−0.187973	−	0.187973i
$729$	−43.7846			−1.62165
$730$		0			0
$731$		−	18.2487i		−	0.674953i
$732$	24.3923	−	42.2487i	0.901566	−	1.56156i
$733$	35.0718			1.29541			0.647703	−	0.761893i	$-0.275730\pi$
$733$	35.0718			1.29541			0.647703	+	0.761893i	$0.275730\pi$
$734$	3.92820	+	1.05256i	0.144993	+	0.0388507i
$735$		0			0
$736$	9.07180	+	33.8564i	0.334391	+	1.24796i
$737$		−	21.4641i		−	0.790640i
$738$	−2.39230	+	8.92820i	−0.0880620	+	0.328652i
$739$		−	29.3205i		−	1.07857i	−0.842123	−	0.539286i	$-0.818694\pi$
$739$		−	29.3205i		−	1.07857i	0.842123	−	0.539286i	$-0.181306\pi$
$740$		0			0
$741$			5.07180i			0.186317i
$742$	−11.4641	−	3.07180i	−0.420860	−	0.112769i
$743$			10.9808i			0.402845i	0.979504	+	0.201423i	$0.0645564\pi$
$743$			10.9808i			0.402845i	−0.979504	+	0.201423i	$0.935444\pi$
$744$	29.8564	−	29.8564i	1.09459	−	1.09459i
$745$		0			0
$746$	−9.41154	+	35.1244i	−0.344581	+	1.28599i
$747$	−5.66025			−0.207098
$748$	12.0000	+	6.92820i	0.438763	+	0.253320i
$749$		−	2.00000i		−	0.0730784i
$750$		0			0
$751$	26.2487			0.957829			0.478915	−	0.877862i	$-0.341030\pi$
$751$	26.2487			0.957829			0.478915	+	0.877862i	$0.341030\pi$
$752$	11.3205	−	6.53590i	0.412816	−	0.238340i
$753$		−	68.1051i		−	2.48189i
$754$	32.7846	+	8.78461i	1.19395	+	0.319917i
$755$		0			0
$756$	2.92820	−	5.07180i	0.106498	−	0.184459i
$757$	−19.0718			−0.693176			−0.346588	−	0.938017i	$-0.612660\pi$
$757$	−19.0718			−0.693176			−0.346588	+	0.938017i	$0.612660\pi$
$758$	−49.5167	−	13.2679i	−1.79853	−	0.481914i
$759$	33.8564			1.22891
$760$		0			0
$761$	−5.71281			−0.207089			−0.103545	−	0.994625i	$-0.533018\pi$
$761$	−5.71281			−0.207089			−0.103545	+	0.994625i	$0.533018\pi$
$762$	−62.4449	−	16.7321i	−2.26214	−	0.606138i
$763$	−12.3923			−0.448632
$764$	−26.5359	−	15.3205i	−0.960035	−	0.554277i
$765$		0			0
$766$	−28.8564	−	7.73205i	−1.04262	−	0.279370i
$767$			25.8564i			0.933621i
$768$	21.8564	−	37.8564i	0.788675	−	1.36603i
$769$	−12.9282			−0.466203			−0.233101	−	0.972452i	$-0.574887\pi$
$769$	−12.9282			−0.466203			−0.233101	+	0.972452i	$0.574887\pi$
$770$		0			0
$771$		−	5.46410i		−	0.196785i
$772$	0.535898	−	0.928203i	0.0192874	−	0.0334068i
$773$	22.3923			0.805395			0.402698	−	0.915333i	$-0.368073\pi$
$773$	22.3923			0.805395			0.402698	+	0.915333i	$0.368073\pi$
$774$	−8.60770	+	32.1244i	−0.309397	+	1.15469i
$775$		0			0
$776$	28.7846	+	28.7846i	1.03331	+	1.03331i
$777$		−	4.00000i		−	0.143499i
$778$	9.26795	+	2.48334i	0.332272	+	0.0890320i
$779$		−	0.784610i		−	0.0281116i
$780$		0			0
$781$		−	10.9282i		−	0.391042i
$782$	7.85641	−	29.3205i	0.280945	−	1.04850i
$783$			27.7128i			0.990375i
$784$	12.9282	+	22.3923i	0.461722	+	0.799725i
$785$		0			0
$786$	−74.1051	−	19.8564i	−2.64324	−	0.708255i
$787$	16.5885			0.591315			0.295657	−	0.955294i	$-0.404461\pi$
$787$	16.5885			0.591315			0.295657	+	0.955294i	$0.404461\pi$
$788$	33.7128	+	19.4641i	1.20097	+	0.693380i
$789$			31.8564i			1.13412i
$790$		0			0
$791$	−9.46410			−0.336505
$792$	−17.8564	−	17.8564i	−0.634500	−	0.634500i
$793$		−	30.9282i		−	1.09829i
$794$	−11.8038	+	44.0526i	−0.418903	+	1.56337i
$795$		0			0
$796$	−3.21539	−	1.85641i	−0.113966	−	0.0657986i
$797$	50.1051			1.77481			0.887407	−	0.460986i	$-0.152504\pi$
$797$	50.1051			1.77481			0.887407	+	0.460986i	$0.152504\pi$
$798$	−0.392305	+	1.46410i	−0.0138874	+	0.0518286i
$799$	−11.3205			−0.400491
$800$		0			0
$801$	−39.8564			−1.40826
$802$	2.87564	−	10.7321i	0.101543	−	0.378962i
$803$	14.9282			0.526805
$804$	50.7846	+	29.3205i	1.79104	+	1.03405i
$805$		0			0
$806$	6.92820	−	25.8564i	0.244036	−	0.910753i
$807$		−	24.3923i		−	0.858650i
$808$	5.85641	+	5.85641i	0.206028	+	0.206028i
$809$	−23.8564			−0.838747			−0.419373	−	0.907814i	$-0.637750\pi$
$809$	−23.8564			−0.838747			−0.419373	+	0.907814i	$0.637750\pi$
$810$		0			0
$811$		−	28.9282i		−	1.01581i	−0.861414	−	0.507903i	$-0.830421\pi$
$811$		−	28.9282i		−	1.01581i	0.861414	−	0.507903i	$-0.169579\pi$
$812$	8.78461	+	5.07180i	0.308279	+	0.177985i
$813$	52.7846			1.85124
$814$	−5.46410	−	1.46410i	−0.191517	−	0.0513167i
$815$		0			0
$816$	−32.7846	+	18.9282i	−1.14769	+	0.662620i
$817$		−	2.82309i		−	0.0987673i
$818$	−4.14359	+	15.4641i	−0.144877	+	0.540690i
$819$		−	11.3205i		−	0.395571i
$820$		0			0
$821$			34.7846i			1.21399i	0.794705	+	0.606996i	$0.207625\pi$
$821$			34.7846i			1.21399i	−0.794705	+	0.606996i	$0.792375\pi$
$822$	−18.3923	−	4.92820i	−0.641505	−	0.171891i
$823$		−	9.12436i		−	0.318055i	−0.987274	−	0.159028i	$-0.949164\pi$
$823$		−	9.12436i		−	0.318055i	0.987274	−	0.159028i	$-0.0508359\pi$
$824$	31.3205	+	31.3205i	1.09110	+	1.09110i
$825$		0			0
$826$	−2.00000	+	7.46410i	−0.0695889	+	0.259709i
$827$	23.1244			0.804113			0.402056	−	0.915615i	$-0.368296\pi$
$827$	23.1244			0.804113			0.402056	+	0.915615i	$0.368296\pi$
$828$	−27.6603	+	47.9090i	−0.961260	+	1.66495i
$829$		−	28.9282i		−	1.00472i	−0.864659	−	0.502359i	$-0.832466\pi$
$829$		−	28.9282i		−	1.00472i	0.864659	−	0.502359i	$-0.167534\pi$
$830$		0			0
$831$	−5.46410			−0.189548
$832$		−	27.7128i		−	0.960769i
$833$		−	22.3923i		−	0.775847i
$834$	2.00000	+	0.535898i	0.0692543	+	0.0185566i
$835$		0			0
$836$	1.85641	+	1.07180i	0.0642052	+	0.0370689i
$837$	21.8564			0.755468
$838$	25.1244	+	6.73205i	0.867906	+	0.232555i
$839$	−24.7846			−0.855660			−0.427830	−	0.903859i	$-0.640722\pi$
$839$	−24.7846			−0.855660			−0.427830	+	0.903859i	$0.640722\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$	−0.196152	−	0.0525589i	−0.00675986	−	0.00181130i
$843$	−28.7846			−0.991395
$844$	26.7846	−	46.3923i	0.921964	−	1.59689i
$845$		0			0
$846$	19.9282	+	5.33975i	0.685146	+	0.183584i
$847$		−	5.12436i		−	0.176075i
$848$	−22.9282	−	39.7128i	−0.787358	−	1.36374i
$849$	−26.3923			−0.905782
$850$		0			0
$851$			12.3923i			0.424803i
$852$	25.8564	+	14.9282i	0.885826	+	0.511432i
$853$	21.6077			0.739833			0.369917	−	0.929065i	$-0.379386\pi$
$853$	21.6077			0.739833			0.369917	+	0.929065i	$0.379386\pi$
$854$	2.39230	−	8.92820i	0.0818630	−	0.305517i
$855$		0			0
$856$	5.46410	−	5.46410i	0.186759	−	0.186759i
$857$			19.8564i			0.678282i	0.940736	+	0.339141i	$0.110136\pi$
$857$			19.8564i			0.678282i	−0.940736	+	0.339141i	$0.889864\pi$
$858$	−25.8564	−	6.92820i	−0.882723	−	0.236525i
$859$		−	28.2487i		−	0.963834i	−0.876217	−	0.481917i	$-0.839941\pi$
$859$		−	28.2487i		−	0.963834i	0.876217	−	0.481917i	$-0.160059\pi$
$860$		0			0
$861$			2.92820i			0.0997929i
$862$	7.85641	−	29.3205i	0.267590	−	0.998660i
$863$			47.6603i			1.62237i	0.584787	+	0.811187i	$0.301178\pi$
$863$			47.6603i			1.62237i	−0.584787	+	0.811187i	$0.698822\pi$
$864$	21.8564	−	5.85641i	0.743570	−	0.199239i
$865$		0			0
$866$	26.5885	+	7.12436i	0.903513	+	0.242095i
$867$	−13.6603			−0.463927
$868$	4.00000	−	6.92820i	0.135769	−	0.235159i
$869$		−	2.14359i		−	0.0727164i
$870$		0			0
$871$	37.1769			1.25969
$872$	−33.8564	−	33.8564i	−1.14652	−	1.14652i
$873$			64.2487i			2.17449i
$874$	1.21539	−	4.53590i	0.0411112	−	0.153429i
$875$		0			0
$876$	−20.3923	+	35.3205i	−0.688992	+	1.19337i
$877$	−1.71281			−0.0578376			−0.0289188	−	0.999582i	$-0.509206\pi$
$877$	−1.71281			−0.0578376			−0.0289188	+	0.999582i	$0.509206\pi$
$878$	14.9282	−	55.7128i	0.503802	−	1.88022i
$879$	−43.3205			−1.46116
$880$		0			0
$881$	9.46410			0.318854			0.159427	−	0.987210i	$-0.449035\pi$
$881$	9.46410			0.318854			0.159427	+	0.987210i	$0.449035\pi$
$882$	−10.5622	+	39.4186i	−0.355647	+	1.32729i
$883$	27.9090			0.939211			0.469606	−	0.882876i	$-0.344396\pi$
$883$	27.9090			0.939211			0.469606	+	0.882876i	$0.344396\pi$
$884$	−12.0000	+	20.7846i	−0.403604	+	0.699062i
$885$		0			0
$886$	7.67949	−	28.6603i	0.257998	−	0.962860i
$887$			13.9090i			0.467017i	0.972355	+	0.233509i	$0.0750207\pi$
$887$			13.9090i			0.467017i	−0.972355	+	0.233509i	$0.924979\pi$
$888$	10.9282	−	10.9282i	0.366726	−	0.366726i
$889$	−12.2487			−0.410809
$890$		0			0
$891$			4.92820i			0.165101i
$892$	−5.80385	+	10.0526i	−0.194327	+	0.336585i
$893$	−1.75129			−0.0586046
$894$	29.3205	+	7.85641i	0.980624	+	0.262758i
$895$		0			0
$896$	2.14359	−	8.00000i	0.0716124	−	0.267261i
$897$			58.6410i			1.95797i
$898$	−8.53590	+	31.8564i	−0.284847	+	1.06306i
$899$			37.8564i			1.26258i
$900$		0			0
$901$			39.7128i			1.32303i
$902$	4.00000	+	1.07180i	0.133185	+	0.0356869i
$903$			10.5359i			0.350613i
$904$	−25.8564	−	25.8564i	−0.859971	−	0.859971i
$905$		0			0
$906$	−12.3923	+	46.2487i	−0.411707	+	1.53651i
$907$	4.87564			0.161893			0.0809466	−	0.996718i	$-0.474206\pi$
$907$	4.87564			0.161893			0.0809466	+	0.996718i	$0.474206\pi$
$908$	−17.4115	−	10.0526i	−0.577822	−	0.333606i
$909$			13.0718i			0.433564i
$910$		0			0
$911$	−49.1769			−1.62930			−0.814652	−	0.579950i	$-0.803072\pi$
$911$	−49.1769			−1.62930			−0.814652	+	0.579950i	$0.803072\pi$
$912$	−5.07180	+	2.92820i	−0.167944	+	0.0969625i
$913$			2.53590i			0.0839260i
$914$	−36.5885	−	9.80385i	−1.21024	−	0.324282i
$915$		0			0
$916$	4.00000	−	6.92820i	0.132164	−	0.228914i
$917$	−14.5359			−0.480018
$918$	−18.9282	−	5.07180i	−0.624724	−	0.167394i
$919$	38.9282			1.28412			0.642061	−	0.766653i	$-0.278079\pi$
$919$	38.9282			1.28412			0.642061	+	0.766653i	$0.278079\pi$
$920$		0			0
$921$	68.2487			2.24887
$922$	14.9282	+	4.00000i	0.491634	+	0.131733i
$923$	18.9282			0.623029
$924$	−6.92820	−	4.00000i	−0.227921	−	0.131590i
$925$		0			0
$926$	15.3923	+	4.12436i	0.505823	+	0.135535i
$927$			69.9090i			2.29611i
$928$	10.1436	+	37.8564i	0.332980	+	1.24270i
$929$	17.4641			0.572979			0.286489	−	0.958083i	$-0.407512\pi$
$929$	17.4641			0.572979			0.286489	+	0.958083i	$0.407512\pi$
$930$		0			0
$931$		−	3.46410i		−	0.113531i
$932$	−5.32051	+	9.21539i	−0.174279	+	0.301860i
$933$	−85.5692			−2.80141
$934$	9.39230	−	35.0526i	0.307326	−	1.14695i
$935$		0			0
$936$	30.9282	−	30.9282i	1.01092	−	1.01092i
$937$		−	4.24871i		−	0.138799i	−0.997589	−	0.0693997i	$-0.977892\pi$
$937$		−	4.24871i		−	0.138799i	0.997589	−	0.0693997i	$-0.0221084\pi$
$938$	10.7321	+	2.87564i	0.350414	+	0.0938931i
$939$			11.3205i			0.369431i
$940$		0			0
$941$		−	32.0000i		−	1.04317i	−0.853199	−	0.521585i	$-0.825341\pi$
$941$		−	32.0000i		−	1.04317i	0.853199	−	0.521585i	$-0.174659\pi$
$942$	−3.07180	+	11.4641i	−0.100085	+	0.373521i
$943$		−	9.07180i		−	0.295418i
$944$	−25.8564	+	14.9282i	−0.841554	+	0.485872i
$945$		0			0
$946$	14.3923	+	3.85641i	0.467934	+	0.125383i
$947$	−3.12436			−0.101528			−0.0507640	−	0.998711i	$-0.516166\pi$
$947$	−3.12436			−0.101528			−0.0507640	+	0.998711i	$0.516166\pi$
$948$	5.07180	+	2.92820i	0.164724	+	0.0951036i
$949$			25.8564i			0.839334i
$950$		0			0
$951$	−23.3205			−0.756219
$952$	−5.07180	+	5.07180i	−0.164378	+	0.164378i
$953$		−	17.2154i		−	0.557661i	−0.960340	−	0.278831i	$-0.910053\pi$
$953$		−	17.2154i		−	0.557661i	0.960340	−	0.278831i	$-0.0899468\pi$
$954$	18.7321	−	69.9090i	0.606473	−	2.26339i
$955$		0			0
$956$	−34.6410	−	20.0000i	−1.12037	−	0.646846i
$957$	37.8564			1.22372
$958$	2.14359	−	8.00000i	0.0692564	−	0.258468i
$959$	−3.60770			−0.116499
$960$		0			0
$961$	−1.14359			−0.0368901
$962$	2.53590	−	9.46410i	0.0817606	−	0.305135i
$963$	12.1962			0.393016
$964$	−28.3923	−	16.3923i	−0.914455	−	0.527961i
$965$		0			0
$966$	−4.53590	+	16.9282i	−0.145940	+	0.544656i
$967$		−	16.3397i		−	0.525451i	−0.964871	−	0.262725i	$-0.915379\pi$
$967$		−	16.3397i		−	0.525451i	0.964871	−	0.262725i	$-0.0846213\pi$
$968$	14.0000	−	14.0000i	0.449977	−	0.449977i
$969$	5.07180			0.162930
$970$		0			0
$971$			36.9282i			1.18508i	0.805540	+	0.592541i	$0.201875\pi$
$971$			36.9282i			1.18508i	−0.805540	+	0.592541i	$0.798125\pi$
$972$	−32.4449	−	18.7321i	−1.04067	−	0.600831i
$973$	0.392305			0.0125767
$974$	9.00000	+	2.41154i	0.288379	+	0.0772708i
$975$		0			0
$976$	30.9282	−	17.8564i	0.989988	−	0.571570i
$977$			24.5359i			0.784973i	0.919758	+	0.392486i	$0.128385\pi$
$977$			24.5359i			0.784973i	−0.919758	+	0.392486i	$0.871615\pi$
$978$	0.196152	−	0.732051i	0.00627226	−	0.0234084i
$979$			17.8564i			0.570693i
$980$		0			0
$981$		−	75.5692i		−	2.41274i
$982$	23.1244	+	6.19615i	0.737928	+	0.197727i
$983$		−	48.7321i		−	1.55431i	−0.629309	−	0.777156i	$-0.716662\pi$
$983$		−	48.7321i		−	1.55431i	0.629309	−	0.777156i	$-0.283338\pi$
$984$	−8.00000	+	8.00000i	−0.255031	+	0.255031i
$985$		0			0
$986$	8.78461	−	32.7846i	0.279759	−	1.04407i
$987$	6.53590			0.208040
$988$	−1.85641	+	3.21539i	−0.0590602	+	0.102295i
$989$		−	32.6410i		−	1.03792i
$990$		0			0
$991$	41.4641			1.31715			0.658575	−	0.752515i	$-0.271159\pi$
$991$	41.4641			1.31715			0.658575	+	0.752515i	$0.271159\pi$
$992$	29.8564	−	8.00000i	0.947942	−	0.254000i
$993$			38.2487i			1.21379i
$994$	5.46410	+	1.46410i	0.173311	+	0.0464385i
$995$		0			0
$996$	−6.00000	−	3.46410i	−0.190117	−	0.109764i
$997$	−11.1769			−0.353976			−0.176988	−	0.984213i	$-0.556635\pi$
$997$	−11.1769			−0.353976			−0.176988	+	0.984213i	$0.556635\pi$
$998$	42.9808	+	11.5167i	1.36053	+	0.364554i
$999$	8.00000			0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.f.e.149.2		4
3.2	odd	2		1800.2.d.l.1549.3		4
4.3	odd	2		800.2.f.e.49.4		4
5.2	odd	4		40.2.d.a.21.1	✓	4
5.3	odd	4		200.2.d.f.101.4		4
5.4	even	2		200.2.f.c.149.3		4
8.3	odd	2		800.2.f.c.49.2		4
8.5	even	2		200.2.f.c.149.4		4
12.11	even	2		7200.2.d.n.2449.3		4
15.2	even	4		360.2.k.e.181.4		4
15.8	even	4		1800.2.k.j.901.1		4
15.14	odd	2		1800.2.d.p.1549.2		4
20.3	even	4		800.2.d.e.401.4		4
20.7	even	4		160.2.d.a.81.1		4
20.19	odd	2		800.2.f.c.49.1		4
24.5	odd	2		1800.2.d.p.1549.1		4
24.11	even	2		7200.2.d.o.2449.3		4
40.3	even	4		800.2.d.e.401.1		4
40.13	odd	4		200.2.d.f.101.3		4
40.19	odd	2		800.2.f.e.49.3		4
40.27	even	4		160.2.d.a.81.4		4
40.29	even	2	inner	200.2.f.e.149.1		4
40.37	odd	4		40.2.d.a.21.2	yes	4
60.23	odd	4		7200.2.k.j.3601.3		4
60.47	odd	4		1440.2.k.e.721.3		4
60.59	even	2		7200.2.d.o.2449.2		4
80.3	even	4		6400.2.a.be.1.1		2
80.13	odd	4		6400.2.a.ce.1.2		2
80.27	even	4		1280.2.a.d.1.1		2
80.37	odd	4		1280.2.a.o.1.2		2
80.43	even	4		6400.2.a.cj.1.2		2
80.53	odd	4		6400.2.a.z.1.1		2
80.67	even	4		1280.2.a.n.1.2		2
80.77	odd	4		1280.2.a.a.1.1		2
120.29	odd	2		1800.2.d.l.1549.4		4
120.53	even	4		1800.2.k.j.901.2		4
120.59	even	2		7200.2.d.n.2449.2		4
120.77	even	4		360.2.k.e.181.3		4
120.83	odd	4		7200.2.k.j.3601.4		4
120.107	odd	4		1440.2.k.e.721.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.d.a.21.1	✓	4	5.2	odd	4
40.2.d.a.21.2	yes	4	40.37	odd	4
160.2.d.a.81.1		4	20.7	even	4
160.2.d.a.81.4		4	40.27	even	4
200.2.d.f.101.3		4	40.13	odd	4
200.2.d.f.101.4		4	5.3	odd	4
200.2.f.c.149.3		4	5.4	even	2
200.2.f.c.149.4		4	8.5	even	2
200.2.f.e.149.1		4	40.29	even	2	inner
200.2.f.e.149.2		4	1.1	even	1	trivial
360.2.k.e.181.3		4	120.77	even	4
360.2.k.e.181.4		4	15.2	even	4
800.2.d.e.401.1		4	40.3	even	4
800.2.d.e.401.4		4	20.3	even	4
800.2.f.c.49.1		4	20.19	odd	2
800.2.f.c.49.2		4	8.3	odd	2
800.2.f.e.49.3		4	40.19	odd	2
800.2.f.e.49.4		4	4.3	odd	2
1280.2.a.a.1.1		2	80.77	odd	4
1280.2.a.d.1.1		2	80.27	even	4
1280.2.a.n.1.2		2	80.67	even	4
1280.2.a.o.1.2		2	80.37	odd	4
1440.2.k.e.721.1		4	120.107	odd	4
1440.2.k.e.721.3		4	60.47	odd	4
1800.2.d.l.1549.3		4	3.2	odd	2
1800.2.d.l.1549.4		4	120.29	odd	2
1800.2.d.p.1549.1		4	24.5	odd	2
1800.2.d.p.1549.2		4	15.14	odd	2
1800.2.k.j.901.1		4	15.8	even	4
1800.2.k.j.901.2		4	120.53	even	4
6400.2.a.z.1.1		2	80.53	odd	4
6400.2.a.be.1.1		2	80.3	even	4
6400.2.a.ce.1.2		2	80.13	odd	4
6400.2.a.cj.1.2		2	80.43	even	4
7200.2.d.n.2449.2		4	120.59	even	2
7200.2.d.n.2449.3		4	12.11	even	2
7200.2.d.o.2449.2		4	60.59	even	2
7200.2.d.o.2449.3		4	24.11	even	2
7200.2.k.j.3601.3		4	60.23	odd	4
7200.2.k.j.3601.4		4	120.83	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)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} -2.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.00000 - 3.73205i) q^{6} -0.732051i q^{7} +(2.00000 - 2.00000i) q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q+(-0.366025 + 1.36603i) q^{2} -2.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.00000 - 3.73205i) q^{6} -0.732051i q^{7} +(2.00000 - 2.00000i) q^{8} +4.46410 q^{9} -2.00000i q^{11} +(4.73205 + 2.73205i) q^{12} +3.46410 q^{13} +(1.00000 + 0.267949i) q^{14} +(2.00000 + 3.46410i) q^{16} -3.46410i q^{17} +(-1.63397 + 6.09808i) q^{18} -0.535898i q^{19} +2.00000i q^{21} +(2.73205 + 0.732051i) q^{22} -6.19615i q^{23} +(-5.46410 + 5.46410i) q^{24} +(-1.26795 + 4.73205i) q^{26} -4.00000 q^{27} +(-0.732051 + 1.26795i) q^{28} -6.92820i q^{29} -5.46410 q^{31} +(-5.46410 + 1.46410i) q^{32} +5.46410i q^{33} +(4.73205 + 1.26795i) q^{34} +(-7.73205 - 4.46410i) q^{36} -2.00000 q^{37} +(0.732051 + 0.196152i) q^{38} -9.46410 q^{39} +1.46410 q^{41} +(-2.73205 - 0.732051i) q^{42} +5.26795 q^{43} +(-2.00000 + 3.46410i) q^{44} +(8.46410 + 2.26795i) q^{46} -3.26795i q^{47} +(-5.46410 - 9.46410i) q^{48} +6.46410 q^{49} +9.46410i q^{51} +(-6.00000 - 3.46410i) q^{52} -11.4641 q^{53} +(1.46410 - 5.46410i) q^{54} +(-1.46410 - 1.46410i) q^{56} +1.46410i q^{57} +(9.46410 + 2.53590i) q^{58} +7.46410i q^{59} -8.92820i q^{61} +(2.00000 - 7.46410i) q^{62} -3.26795i q^{63} -8.00000i q^{64} +(-7.46410 - 2.00000i) q^{66} +10.7321 q^{67} +(-3.46410 + 6.00000i) q^{68} +16.9282i q^{69} +5.46410 q^{71} +(8.92820 - 8.92820i) q^{72} +7.46410i q^{73} +(0.732051 - 2.73205i) q^{74} +(-0.535898 + 0.928203i) q^{76} -1.46410 q^{77} +(3.46410 - 12.9282i) q^{78} +1.07180 q^{79} -2.46410 q^{81} +(-0.535898 + 2.00000i) q^{82} -1.26795 q^{83} +(2.00000 - 3.46410i) q^{84} +(-1.92820 + 7.19615i) q^{86} +18.9282i q^{87} +(-4.00000 - 4.00000i) q^{88} -8.92820 q^{89} -2.53590i q^{91} +(-6.19615 + 10.7321i) q^{92} +14.9282 q^{93} +(4.46410 + 1.19615i) q^{94} +(14.9282 - 4.00000i) q^{96} +14.3923i q^{97} +(-2.36603 + 8.83013i) q^{98} -8.92820i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{6} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) 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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