LMFDB - Embedded newform 200.2.d.f.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,2,Mod(101,200)]

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, 0]))

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

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

chi := DirichletCharacter("200.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.d (of order $2$, degree $1$, 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			101.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.2.d.f.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} -0.732051i q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{6} +2.73205 q^{7} +(2.00000 - 2.00000i) q^{8} +2.46410 q^{9} +O(q^{10})$	\(q+(-0.366025 + 1.36603i) q^{2} -0.732051i q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{6} +2.73205 q^{7} +(2.00000 - 2.00000i) q^{8} +2.46410 q^{9} +2.00000i q^{11} +(-0.732051 + 1.26795i) q^{12} +3.46410i q^{13} +(-1.00000 + 3.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} +3.46410 q^{17} +(-0.901924 + 3.36603i) q^{18} -7.46410i q^{19} -2.00000i q^{21} +(-2.73205 - 0.732051i) q^{22} -4.19615 q^{23} +(-1.46410 - 1.46410i) q^{24} +(-4.73205 - 1.26795i) q^{26} -4.00000i q^{27} +(-4.73205 - 2.73205i) q^{28} +6.92820i q^{29} +1.46410 q^{31} +(-5.46410 + 1.46410i) q^{32} +1.46410 q^{33} +(-1.26795 + 4.73205i) q^{34} +(-4.26795 - 2.46410i) q^{36} -2.00000i q^{37} +(10.1962 + 2.73205i) q^{38} +2.53590 q^{39} -5.46410 q^{41} +(2.73205 + 0.732051i) q^{42} -8.73205i q^{43} +(2.00000 - 3.46410i) q^{44} +(1.53590 - 5.73205i) q^{46} -6.73205 q^{47} +(2.53590 - 1.46410i) q^{48} +0.464102 q^{49} -2.53590i q^{51} +(3.46410 - 6.00000i) q^{52} +4.53590i q^{53} +(5.46410 + 1.46410i) q^{54} +(5.46410 - 5.46410i) q^{56} -5.46410 q^{57} +(-9.46410 - 2.53590i) q^{58} +0.535898i q^{59} -4.92820i q^{61} +(-0.535898 + 2.00000i) q^{62} +6.73205 q^{63} -8.00000i q^{64} +(-0.535898 + 2.00000i) q^{66} +7.26795i q^{67} +(-6.00000 - 3.46410i) q^{68} +3.07180i q^{69} -1.46410 q^{71} +(4.92820 - 4.92820i) q^{72} -0.535898 q^{73} +(2.73205 + 0.732051i) q^{74} +(-7.46410 + 12.9282i) q^{76} +5.46410i q^{77} +(-0.928203 + 3.46410i) q^{78} -14.9282 q^{79} +4.46410 q^{81} +(2.00000 - 7.46410i) q^{82} +4.73205i q^{83} +(-2.00000 + 3.46410i) q^{84} +(11.9282 + 3.19615i) q^{86} +5.07180 q^{87} +(4.00000 + 4.00000i) q^{88} -4.92820 q^{89} +9.46410i q^{91} +(7.26795 + 4.19615i) q^{92} -1.07180i q^{93} +(2.46410 - 9.19615i) q^{94} +(1.07180 + 4.00000i) q^{96} -6.39230 q^{97} +(-0.169873 + 0.633975i) q^{98} +4.92820i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{6} + 4 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^6 + 4 * q^7 + 8 * q^8 - 4 * q^9	$ 4 q + 2 q^{2} + 4 q^{6} + 4 q^{7} + 8 q^{8} - 4 q^{9} + 4 q^{12} - 4 q^{14} + 8 q^{16} - 14 q^{18} - 4 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 12 q^{28} - 8 q^{31} - 8 q^{32} - 8 q^{33} - 12 q^{34} - 24 q^{36} + 20 q^{38} + 24 q^{39} - 8 q^{41} + 4 q^{42} + 8 q^{44} + 20 q^{46} - 20 q^{47} + 24 q^{48} - 12 q^{49} + 8 q^{54} + 8 q^{56} - 8 q^{57} - 24 q^{58} - 16 q^{62} + 20 q^{63} - 16 q^{66} - 24 q^{68} + 8 q^{71} - 8 q^{72} - 16 q^{73} + 4 q^{74} - 16 q^{76} + 24 q^{78} - 32 q^{79} + 4 q^{81} + 8 q^{82} - 8 q^{84} + 20 q^{86} + 48 q^{87} + 16 q^{88} + 8 q^{89} + 36 q^{92} - 4 q^{94} + 32 q^{96} + 16 q^{97} - 18 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^6 + 4 * q^7 + 8 * q^8 - 4 * q^9 + 4 * q^12 - 4 * q^14 + 8 * q^16 - 14 * q^18 - 4 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 12 * q^28 - 8 * q^31 - 8 * q^32 - 8 * q^33 - 12 * q^34 - 24 * q^36 + 20 * q^38 + 24 * q^39 - 8 * q^41 + 4 * q^42 + 8 * q^44 + 20 * q^46 - 20 * q^47 + 24 * q^48 - 12 * q^49 + 8 * q^54 + 8 * q^56 - 8 * q^57 - 24 * q^58 - 16 * q^62 + 20 * q^63 - 16 * q^66 - 24 * q^68 + 8 * q^71 - 8 * q^72 - 16 * q^73 + 4 * q^74 - 16 * q^76 + 24 * q^78 - 32 * q^79 + 4 * q^81 + 8 * q^82 - 8 * q^84 + 20 * q^86 + 48 * q^87 + 16 * q^88 + 8 * q^89 + 36 * q^92 - 4 * q^94 + 32 * q^96 + 16 * q^97 - 18 * 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
$3$		−	0.732051i		−	0.422650i	−0.977416	−	0.211325i	$-0.932222\pi$
$3$		−	0.732051i		−	0.422650i	0.977416	−	0.211325i	$-0.0677778\pi$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$	1.00000	+	0.267949i	0.408248	+	0.109390i
$7$	2.73205			1.03262			0.516309	−	0.856402i	$-0.327306\pi$
$7$	2.73205			1.03262			0.516309	+	0.856402i	$0.327306\pi$
$8$	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	$0.902509\pi$
$12$	−0.732051	+	1.26795i	−0.211325	+	0.366025i
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$	−1.00000	+	3.73205i	−0.267261	+	0.997433i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	3.46410			0.840168			0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410			0.840168			0.420084	+	0.907485i	$0.362001\pi$
$18$	−0.901924	+	3.36603i	−0.212585	+	0.793380i
$19$		−	7.46410i		−	1.71238i	−0.516659	−	0.856191i	$-0.672825\pi$
$19$		−	7.46410i		−	1.71238i	0.516659	−	0.856191i	$-0.327175\pi$
$20$		0			0
$21$		−	2.00000i		−	0.436436i
$22$	−2.73205	−	0.732051i	−0.582475	−	0.156074i
$23$	−4.19615			−0.874958			−0.437479	−	0.899229i	$-0.644129\pi$
$23$	−4.19615			−0.874958			−0.437479	+	0.899229i	$0.644129\pi$
$24$	−1.46410	−	1.46410i	−0.298858	−	0.298858i
$25$		0			0
$26$	−4.73205	−	1.26795i	−0.928032	−	0.248665i
$27$		−	4.00000i		−	0.769800i
$28$	−4.73205	−	2.73205i	−0.894274	−	0.516309i
$29$			6.92820i			1.28654i	0.765641	+	0.643268i	$0.222422\pi$
$29$			6.92820i			1.28654i	−0.765641	+	0.643268i	$0.777578\pi$
$30$		0			0
$31$	1.46410			0.262960			0.131480	−	0.991319i	$-0.458027\pi$
$31$	1.46410			0.262960			0.131480	+	0.991319i	$0.458027\pi$
$32$	−5.46410	+	1.46410i	−0.965926	+	0.258819i
$33$	1.46410			0.254867
$34$	−1.26795	+	4.73205i	−0.217451	+	0.811540i
$35$		0			0
$36$	−4.26795	−	2.46410i	−0.711325	−	0.410684i
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	10.1962	+	2.73205i	1.65403	+	0.443197i
$39$	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	$0.640315\pi$
$42$	2.73205	+	0.732051i	0.421565	+	0.112958i
$43$		−	8.73205i		−	1.33163i	−0.746119	−	0.665813i	$-0.768085\pi$
$43$		−	8.73205i		−	1.33163i	0.746119	−	0.665813i	$-0.231915\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$		0			0
$46$	1.53590	−	5.73205i	0.226456	−	0.845145i
$47$	−6.73205			−0.981971			−0.490985	−	0.871168i	$-0.663363\pi$
$47$	−6.73205			−0.981971			−0.490985	+	0.871168i	$0.663363\pi$
$48$	2.53590	−	1.46410i	0.366025	−	0.211325i
$49$	0.464102			0.0663002
$50$		0			0
$51$		−	2.53590i		−	0.355097i
$52$	3.46410	−	6.00000i	0.480384	−	0.832050i
$53$			4.53590i			0.623054i	0.950237	+	0.311527i	$0.100840\pi$
$53$			4.53590i			0.623054i	−0.950237	+	0.311527i	$0.899160\pi$
$54$	5.46410	+	1.46410i	0.743570	+	0.199239i
$55$		0			0
$56$	5.46410	−	5.46410i	0.730171	−	0.730171i
$57$	−5.46410			−0.723738
$58$	−9.46410	−	2.53590i	−1.24270	−	0.332980i
$59$			0.535898i			0.0697680i	0.999391	+	0.0348840i	$0.0111062\pi$
$59$			0.535898i			0.0697680i	−0.999391	+	0.0348840i	$0.988894\pi$
$60$		0			0
$61$		−	4.92820i		−	0.630992i	−0.948927	−	0.315496i	$-0.897829\pi$
$61$		−	4.92820i		−	0.630992i	0.948927	−	0.315496i	$-0.102171\pi$
$62$	−0.535898	+	2.00000i	−0.0680592	+	0.254000i
$63$	6.73205			0.848159
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	−0.535898	+	2.00000i	−0.0659645	+	0.246183i
$67$			7.26795i			0.887921i	0.896046	+	0.443961i	$0.146427\pi$
$67$			7.26795i			0.887921i	−0.896046	+	0.443961i	$0.853573\pi$
$68$	−6.00000	−	3.46410i	−0.727607	−	0.420084i
$69$			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
$73$	−0.535898			−0.0627222			−0.0313611	−	0.999508i	$-0.509984\pi$
$73$	−0.535898			−0.0627222			−0.0313611	+	0.999508i	$0.509984\pi$
$74$	2.73205	+	0.732051i	0.317594	+	0.0850992i
$75$		0			0
$76$	−7.46410	+	12.9282i	−0.856191	+	1.48297i
$77$			5.46410i			0.622692i
$78$	−0.928203	+	3.46410i	−0.105098	+	0.392232i
$79$	−14.9282			−1.67955			−0.839777	−	0.542931i	$-0.817314\pi$
$79$	−14.9282			−1.67955			−0.839777	+	0.542931i	$0.817314\pi$
$80$		0			0
$81$	4.46410			0.496011
$82$	2.00000	−	7.46410i	0.220863	−	0.824272i
$83$			4.73205i			0.519410i	0.965688	+	0.259705i	$0.0836253\pi$
$83$			4.73205i			0.519410i	−0.965688	+	0.259705i	$0.916375\pi$
$84$	−2.00000	+	3.46410i	−0.218218	+	0.377964i
$85$		0			0
$86$	11.9282	+	3.19615i	1.28625	+	0.344650i
$87$	5.07180			0.543754
$88$	4.00000	+	4.00000i	0.426401	+	0.426401i
$89$	−4.92820			−0.522388			−0.261194	−	0.965286i	$-0.584116\pi$
$89$	−4.92820			−0.522388			−0.261194	+	0.965286i	$0.584116\pi$
$90$		0			0
$91$			9.46410i			0.992107i
$92$	7.26795	+	4.19615i	0.757736	+	0.437479i
$93$		−	1.07180i		−	0.111140i
$94$	2.46410	−	9.19615i	0.254153	−	0.948511i
$95$		0			0
$96$	1.07180	+	4.00000i	0.109390	+	0.408248i
$97$	−6.39230			−0.649040			−0.324520	−	0.945879i	$-0.605203\pi$
$97$	−6.39230			−0.649040			−0.324520	+	0.945879i	$0.605203\pi$
$98$	−0.169873	+	0.633975i	−0.0171598	+	0.0640411i
$99$			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	$0.817024\pi$
$102$	3.46410	+	0.928203i	0.342997	+	0.0919058i
$103$	1.66025			0.163590			0.0817948	−	0.996649i	$-0.473935\pi$
$103$	1.66025			0.163590			0.0817948	+	0.996649i	$0.473935\pi$
$104$	6.92820	+	6.92820i	0.679366	+	0.679366i
$105$		0			0
$106$	−6.19615	−	1.66025i	−0.601824	−	0.161258i
$107$		−	0.732051i		−	0.0707700i	−0.999374	−	0.0353850i	$-0.988734\pi$
$107$		−	0.732051i		−	0.0707700i	0.999374	−	0.0353850i	$-0.0112658\pi$
$108$	−4.00000	+	6.92820i	−0.384900	+	0.666667i
$109$		−	3.07180i		−	0.294225i	−0.989120	−	0.147112i	$-0.953002\pi$
$109$		−	3.07180i		−	0.294225i	0.989120	−	0.147112i	$-0.0469979\pi$
$110$		0			0
$111$	−1.46410			−0.138966
$112$	5.46410	+	9.46410i	0.516309	+	0.894274i
$113$	−0.928203			−0.0873180			−0.0436590	−	0.999046i	$-0.513902\pi$
$113$	−0.928203			−0.0873180			−0.0436590	+	0.999046i	$0.513902\pi$
$114$	2.00000	−	7.46410i	0.187317	−	0.699077i
$115$		0			0
$116$	6.92820	−	12.0000i	0.643268	−	1.11417i
$117$			8.53590i			0.789144i
$118$	−0.732051	−	0.196152i	−0.0673907	−	0.0180573i
$119$	9.46410			0.867573
$120$		0			0
$121$	7.00000			0.636364
$122$	6.73205	+	1.80385i	0.609491	+	0.163313i
$123$			4.00000i			0.360668i
$124$	−2.53590	−	1.46410i	−0.227730	−	0.131480i
$125$		0			0
$126$	−2.46410	+	9.19615i	−0.219520	+	0.819258i
$127$	−13.2679			−1.17734			−0.588670	−	0.808373i	$-0.700348\pi$
$127$	−13.2679			−1.17734			−0.588670	+	0.808373i	$0.700348\pi$
$128$	10.9282	+	2.92820i	0.965926	+	0.258819i
$129$	−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	$-0.111514\pi$
$132$	−2.53590	−	1.46410i	−0.220722	−	0.127434i
$133$		−	20.3923i		−	1.76824i
$134$	−9.92820	−	2.66025i	−0.857666	−	0.229811i
$135$		0			0
$136$	6.92820	−	6.92820i	0.594089	−	0.594089i
$137$	8.92820			0.762788			0.381394	−	0.924413i	$-0.375444\pi$
$137$	8.92820			0.762788			0.381394	+	0.924413i	$0.375444\pi$
$138$	−4.19615	−	1.12436i	−0.357200	−	0.0957115i
$139$			7.46410i			0.633097i	0.948576	+	0.316548i	$0.102524\pi$
$139$			7.46410i			0.633097i	−0.948576	+	0.316548i	$0.897476\pi$
$140$		0			0
$141$			4.92820i			0.415030i
$142$	0.535898	−	2.00000i	0.0449716	−	0.167836i
$143$	−6.92820			−0.579365
$144$	4.92820	+	8.53590i	0.410684	+	0.711325i
$145$		0			0
$146$	0.196152	−	0.732051i	0.0162337	−	0.0605850i
$147$		−	0.339746i		−	0.0280218i
$148$	−2.00000	+	3.46410i	−0.164399	+	0.284747i
$149$		−	19.8564i		−	1.62670i	−0.581775	−	0.813350i	$-0.697641\pi$
$149$		−	19.8564i		−	1.62670i	0.581775	−	0.813350i	$-0.302359\pi$
$150$		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
$153$	8.53590			0.690086
$154$	−7.46410	−	2.00000i	−0.601474	−	0.161165i
$155$		0			0
$156$	−4.39230	−	2.53590i	−0.351666	−	0.203034i
$157$		−	16.9282i		−	1.35102i	−0.737352	−	0.675509i	$-0.763924\pi$
$157$		−	16.9282i		−	1.35102i	0.737352	−	0.675509i	$-0.236076\pi$
$158$	5.46410	−	20.3923i	0.434701	−	1.62232i
$159$	3.32051			0.263333
$160$		0			0
$161$	−11.4641			−0.903498
$162$	−1.63397	+	6.09808i	−0.128377	+	0.479110i
$163$			10.1962i			0.798624i	0.916815	+	0.399312i	$0.130751\pi$
$163$			10.1962i			0.798624i	−0.916815	+	0.399312i	$0.869249\pi$
$164$	9.46410	+	5.46410i	0.739022	+	0.426675i
$165$		0			0
$166$	−6.46410	−	1.73205i	−0.501712	−	0.134433i
$167$	20.1962			1.56283			0.781413	−	0.624015i	$-0.214499\pi$
$167$	20.1962			1.56283			0.781413	+	0.624015i	$0.214499\pi$
$168$	−4.00000	−	4.00000i	−0.308607	−	0.308607i
$169$	1.00000			0.0769231
$170$		0			0
$171$		−	18.3923i		−	1.40649i
$172$	−8.73205	+	15.1244i	−0.665813	+	1.15322i
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$	−1.85641	+	6.92820i	−0.140734	+	0.525226i
$175$		0			0
$176$	−6.92820	+	4.00000i	−0.522233	+	0.301511i
$177$	0.392305			0.0294874
$178$	1.80385	−	6.73205i	0.135204	−	0.504589i
$179$			15.4641i			1.15584i	0.816093	+	0.577921i	$0.196136\pi$
$179$			15.4641i			1.15584i	−0.816093	+	0.577921i	$0.803864\pi$
$180$		0			0
$181$		−	16.0000i		−	1.18927i	−0.803996	−	0.594635i	$-0.797296\pi$
$181$		−	16.0000i		−	1.18927i	0.803996	−	0.594635i	$-0.202704\pi$
$182$	−12.9282	−	3.46410i	−0.958302	−	0.256776i
$183$	−3.60770			−0.266688
$184$	−8.39230	+	8.39230i	−0.618689	+	0.618689i
$185$		0			0
$186$	1.46410	+	0.392305i	0.107353	+	0.0287652i
$187$			6.92820i			0.506640i
$188$	11.6603	+	6.73205i	0.850411	+	0.490985i
$189$		−	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	$0.746367\pi$
$192$	−5.85641			−0.422650
$193$	−7.46410			−0.537278			−0.268639	−	0.963241i	$-0.586574\pi$
$193$	−7.46410			−0.537278			−0.268639	+	0.963241i	$0.586574\pi$
$194$	2.33975	−	8.73205i	0.167984	−	0.626925i
$195$		0			0
$196$	−0.803848	−	0.464102i	−0.0574177	−	0.0331501i
$197$		−	12.5359i		−	0.893146i	−0.894747	−	0.446573i	$-0.852644\pi$
$197$		−	12.5359i		−	0.893146i	0.894747	−	0.446573i	$-0.147356\pi$
$198$	−6.73205	−	1.80385i	−0.478426	−	0.128194i
$199$	25.8564			1.83291			0.916456	−	0.400135i	$-0.131037\pi$
$199$	25.8564			1.83291			0.916456	+	0.400135i	$0.131037\pi$
$200$		0			0
$201$	5.32051			0.375280
$202$	−14.9282	−	4.00000i	−1.05034	−	0.281439i
$203$			18.9282i			1.32850i
$204$	−2.53590	+	4.39230i	−0.177548	+	0.307523i
$205$		0			0
$206$	−0.607695	+	2.26795i	−0.0423401	+	0.158016i
$207$	−10.3397			−0.718662
$208$	−12.0000	+	6.92820i	−0.832050	+	0.480384i
$209$	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	$0.830050\pi$
$212$	4.53590	−	7.85641i	0.311527	−	0.539580i
$213$			1.07180i			0.0734383i
$214$	1.00000	+	0.267949i	0.0683586	+	0.0183166i
$215$		0			0
$216$	−8.00000	−	8.00000i	−0.544331	−	0.544331i
$217$	4.00000			0.271538
$218$	4.19615	+	1.12436i	0.284199	+	0.0761510i
$219$			0.392305i			0.0265095i
$220$		0			0
$221$			12.0000i			0.807207i
$222$	0.535898	−	2.00000i	0.0359671	−	0.134231i
$223$	16.1962			1.08457			0.542287	−	0.840193i	$-0.317558\pi$
$223$	16.1962			1.08457			0.542287	+	0.840193i	$0.317558\pi$
$224$	−14.9282	+	4.00000i	−0.997433	+	0.267261i
$225$		0			0
$226$	0.339746	−	1.26795i	0.0225996	−	0.0843427i
$227$		−	28.0526i		−	1.86191i	−0.365129	−	0.930957i	$-0.618975\pi$
$227$		−	28.0526i		−	1.86191i	0.365129	−	0.930957i	$-0.381025\pi$
$228$	9.46410	+	5.46410i	0.626775	+	0.361869i
$229$			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
$233$	−29.3205			−1.92085			−0.960425	−	0.278538i	$-0.910150\pi$
$233$	−29.3205			−1.92085			−0.960425	+	0.278538i	$0.910150\pi$
$234$	−11.6603	−	3.12436i	−0.762255	−	0.204246i
$235$		0			0
$236$	0.535898	−	0.928203i	0.0348840	−	0.0604209i
$237$			10.9282i			0.709863i
$238$	−3.46410	+	12.9282i	−0.224544	+	0.838011i
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		0			0
$241$	−4.39230			−0.282933			−0.141467	−	0.989943i	$-0.545182\pi$
$241$	−4.39230			−0.282933			−0.141467	+	0.989943i	$0.545182\pi$
$242$	−2.56218	+	9.56218i	−0.164703	+	0.614680i
$243$		−	15.2679i		−	0.979439i
$244$	−4.92820	+	8.53590i	−0.315496	+	0.546455i
$245$		0			0
$246$	−5.46410	−	1.46410i	−0.348378	−	0.0933477i
$247$	25.8564			1.64520
$248$	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	$-0.113622\pi$
$252$	−11.6603	−	6.73205i	−0.734527	−	0.424079i
$253$		−	8.39230i		−	0.527620i
$254$	4.85641	−	18.1244i	0.304718	−	1.13722i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	2.00000			0.124757			0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000			0.124757			0.0623783	+	0.998053i	$0.480131\pi$
$258$	2.33975	−	8.73205i	0.145666	−	0.543634i
$259$		−	5.46410i		−	0.339523i
$260$		0			0
$261$			17.0718i			1.05672i
$262$	10.7321	+	2.87564i	0.663028	+	0.177658i
$263$	−5.66025			−0.349026			−0.174513	−	0.984655i	$-0.555835\pi$
$263$	−5.66025			−0.349026			−0.174513	+	0.984655i	$0.555835\pi$
$264$	2.92820	−	2.92820i	0.180218	−	0.180218i
$265$		0			0
$266$	27.8564	+	7.46410i	1.70799	+	0.457653i
$267$			3.60770i			0.220787i
$268$	7.26795	−	12.5885i	0.443961	−	0.768962i
$269$		−	4.92820i		−	0.300478i	−0.988650	−	0.150239i	$-0.951996\pi$
$269$		−	4.92820i		−	0.300478i	0.988650	−	0.150239i	$-0.0480043\pi$
$270$		0			0
$271$	15.3205			0.930655			0.465327	−	0.885139i	$-0.345937\pi$
$271$	15.3205			0.930655			0.465327	+	0.885139i	$0.345937\pi$
$272$	6.92820	+	12.0000i	0.420084	+	0.727607i
$273$	6.92820			0.419314
$274$	−3.26795	+	12.1962i	−0.197424	+	0.736797i
$275$		0			0
$276$	3.07180	−	5.32051i	0.184900	−	0.320257i
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$	−10.1962	−	2.73205i	−0.611525	−	0.163858i
$279$	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	$0.325593\pi$
$282$	−6.73205	−	1.80385i	−0.400888	−	0.107418i
$283$			7.66025i			0.455355i	0.973737	+	0.227677i	$0.0731132\pi$
$283$			7.66025i			0.455355i	−0.973737	+	0.227677i	$0.926887\pi$
$284$	2.53590	+	1.46410i	0.150478	+	0.0868784i
$285$		0			0
$286$	2.53590	−	9.46410i	0.149951	−	0.559624i
$287$	−14.9282			−0.881184
$288$	−13.4641	+	3.60770i	−0.793380	+	0.212585i
$289$	−5.00000			−0.294118
$290$		0			0
$291$			4.67949i			0.274317i
$292$	0.928203	+	0.535898i	0.0543190	+	0.0313611i
$293$			11.8564i			0.692659i	0.938113	+	0.346329i	$0.112572\pi$
$293$			11.8564i			0.692659i	−0.938113	+	0.346329i	$0.887428\pi$
$294$	0.464102	+	0.124356i	0.0270670	+	0.00725257i
$295$		0			0
$296$	−4.00000	−	4.00000i	−0.232495	−	0.232495i
$297$	8.00000			0.464207
$298$	27.1244	+	7.26795i	1.57127	+	0.421021i
$299$		−	14.5359i		−	0.840633i
$300$		0			0
$301$		−	23.8564i		−	1.37506i
$302$	−3.07180	+	11.4641i	−0.176762	+	0.659685i
$303$	8.00000			0.459588
$304$	25.8564	−	14.9282i	1.48297	−	0.856191i
$305$		0			0
$306$	−3.12436	+	11.6603i	−0.178608	+	0.666572i
$307$			26.9808i			1.53987i	0.638120	+	0.769937i	$0.279712\pi$
$307$			26.9808i			1.53987i	−0.638120	+	0.769937i	$0.720288\pi$
$308$	5.46410	−	9.46410i	0.311346	−	0.539267i
$309$		−	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
$313$	31.8564			1.80063			0.900315	−	0.435238i	$-0.143336\pi$
$313$	31.8564			1.80063			0.900315	+	0.435238i	$0.143336\pi$
$314$	23.1244	+	6.19615i	1.30498	+	0.349669i
$315$		0			0
$316$	25.8564	+	14.9282i	1.45454	+	0.839777i
$317$			15.4641i			0.868550i	0.900780	+	0.434275i	$0.142995\pi$
$317$			15.4641i			0.868550i	−0.900780	+	0.434275i	$0.857005\pi$
$318$	−1.21539	+	4.53590i	−0.0681557	+	0.254361i
$319$	−13.8564			−0.775810
$320$		0			0
$321$	−0.535898			−0.0299109
$322$	4.19615	−	15.6603i	0.233842	−	0.872712i
$323$		−	25.8564i		−	1.43869i
$324$	−7.73205	−	4.46410i	−0.429558	−	0.248006i
$325$		0			0
$326$	−13.9282	−	3.73205i	−0.771412	−	0.206699i
$327$	−2.24871			−0.124354
$328$	−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	$0.874286\pi$
$332$	4.73205	−	8.19615i	0.259705	−	0.449822i
$333$		−	4.92820i		−	0.270064i
$334$	−7.39230	+	27.5885i	−0.404489	+	1.50957i
$335$		0			0
$336$	6.92820	−	4.00000i	0.377964	−	0.218218i
$337$	−7.85641			−0.427966			−0.213983	−	0.976837i	$-0.568644\pi$
$337$	−7.85641			−0.427966			−0.213983	+	0.976837i	$0.568644\pi$
$338$	−0.366025	+	1.36603i	−0.0199092	+	0.0743020i
$339$			0.679492i			0.0369049i
$340$		0			0
$341$			2.92820i			0.158571i
$342$	25.1244	+	6.73205i	1.35857	+	0.364028i
$343$	−17.8564			−0.964155
$344$	−17.4641	−	17.4641i	−0.941601	−	0.941601i
$345$		0			0
$346$	−2.73205	−	0.732051i	−0.146876	−	0.0393553i
$347$			15.6603i			0.840686i	0.907365	+	0.420343i	$0.138090\pi$
$347$			15.6603i			0.840686i	−0.907365	+	0.420343i	$0.861910\pi$
$348$	−8.78461	−	5.07180i	−0.470905	−	0.271877i
$349$			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
$353$	0.928203			0.0494033			0.0247016	−	0.999695i	$-0.492136\pi$
$353$	0.928203			0.0494033			0.0247016	+	0.999695i	$0.492136\pi$
$354$	−0.143594	+	0.535898i	−0.00763191	+	0.0284827i
$355$		0			0
$356$	8.53590	+	4.92820i	0.452402	+	0.261194i
$357$		−	6.92820i		−	0.366679i
$358$	−21.1244	−	5.66025i	−1.11646	−	0.299154i
$359$	5.07180			0.267679			0.133840	−	0.991003i	$-0.457269\pi$
$359$	5.07180			0.267679			0.133840	+	0.991003i	$0.457269\pi$
$360$		0			0
$361$	−36.7128			−1.93225
$362$	21.8564	+	5.85641i	1.14875	+	0.307806i
$363$		−	5.12436i		−	0.268959i
$364$	9.46410	−	16.3923i	0.496054	−	0.859190i
$365$		0			0
$366$	1.32051	−	4.92820i	0.0690241	−	0.257601i
$367$	−27.1244			−1.41588			−0.707940	−	0.706273i	$-0.750375\pi$
$367$	−27.1244			−1.41588			−0.707940	+	0.706273i	$0.750375\pi$
$368$	−8.39230	−	14.5359i	−0.437479	−	0.757736i
$369$	−13.4641			−0.700913
$370$		0			0
$371$			12.3923i			0.643376i
$372$	−1.07180	+	1.85641i	−0.0555701	+	0.0962502i
$373$			29.7128i			1.53847i	0.638965	+	0.769236i	$0.279363\pi$
$373$			29.7128i			1.53847i	−0.638965	+	0.769236i	$0.720637\pi$
$374$	−9.46410	−	2.53590i	−0.489377	−	0.131128i
$375$		0			0
$376$	−13.4641	+	13.4641i	−0.694358	+	0.694358i
$377$	−24.0000			−1.23606
$378$	14.9282	+	4.00000i	0.767824	+	0.205738i
$379$		−	12.2487i		−	0.629174i	−0.949229	−	0.314587i	$-0.898134\pi$
$379$		−	12.2487i		−	0.629174i	0.949229	−	0.314587i	$-0.101866\pi$
$380$		0			0
$381$			9.71281i			0.497602i
$382$	7.07180	−	26.3923i	0.361825	−	1.35035i
$383$	3.12436			0.159647			0.0798236	−	0.996809i	$-0.474564\pi$
$383$	3.12436			0.159647			0.0798236	+	0.996809i	$0.474564\pi$
$384$	2.14359	−	8.00000i	0.109390	−	0.408248i
$385$		0			0
$386$	2.73205	−	10.1962i	0.139058	−	0.518970i
$387$		−	21.5167i		−	1.09375i
$388$	11.0718	+	6.39230i	0.562085	+	0.324520i
$389$			34.7846i			1.76365i	0.471577	+	0.881825i	$0.343685\pi$
$389$			34.7846i			1.76365i	−0.471577	+	0.881825i	$0.656315\pi$
$390$		0			0
$391$	−14.5359			−0.735112
$392$	0.928203	−	0.928203i	0.0468813	−	0.0468813i
$393$	−5.75129			−0.290114
$394$	17.1244	+	4.58846i	0.862713	+	0.231163i
$395$		0			0
$396$	4.92820	−	8.53590i	0.247652	−	0.428945i
$397$		−	16.2487i		−	0.815499i	−0.913094	−	0.407750i	$-0.866314\pi$
$397$		−	16.2487i		−	0.815499i	0.913094	−	0.407750i	$-0.133686\pi$
$398$	−9.46410	+	35.3205i	−0.474393	+	1.77046i
$399$	−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	$0.334878\pi$
$402$	−1.94744	+	7.26795i	−0.0971295	+	0.362492i
$403$			5.07180i			0.252644i
$404$	10.9282	−	18.9282i	0.543698	−	0.941713i
$405$		0			0
$406$	−25.8564	−	6.92820i	−1.28323	−	0.343841i
$407$	4.00000			0.198273
$408$	−5.07180	−	5.07180i	−0.251091	−	0.251091i
$409$	23.3205			1.15312			0.576562	−	0.817053i	$-0.304394\pi$
$409$	23.3205			1.15312			0.576562	+	0.817053i	$0.304394\pi$
$410$		0			0
$411$		−	6.53590i		−	0.322392i
$412$	−2.87564	−	1.66025i	−0.141673	−	0.0817948i
$413$			1.46410i			0.0720437i
$414$	3.78461	−	14.1244i	0.186003	−	0.694174i
$415$		0			0
$416$	−5.07180	−	18.9282i	−0.248665	−	0.928032i
$417$	5.46410			0.267578
$418$	−5.46410	+	20.3923i	−0.267258	+	0.997420i
$419$			2.39230i			0.116872i	0.998291	+	0.0584359i	$0.0186113\pi$
$419$			2.39230i			0.116872i	−0.998291	+	0.0584359i	$0.981389\pi$
$420$		0			0
$421$		−	27.8564i		−	1.35764i	−0.734306	−	0.678819i	$-0.762492\pi$
$421$		−	27.8564i		−	1.35764i	0.734306	−	0.678819i	$-0.237508\pi$
$422$	−20.1962	−	5.41154i	−0.983133	−	0.263430i
$423$	−16.5885			−0.806558
$424$	9.07180	+	9.07180i	0.440565	+	0.440565i
$425$		0			0
$426$	−1.46410	−	0.392305i	−0.0709360	−	0.0190072i
$427$		−	13.4641i		−	0.651574i
$428$	−0.732051	+	1.26795i	−0.0353850	+	0.0612886i
$429$			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	$0.613847\pi$
$432$	13.8564	−	8.00000i	0.666667	−	0.384900i
$433$	12.5359			0.602437			0.301218	−	0.953555i	$-0.402607\pi$
$433$	12.5359			0.602437			0.301218	+	0.953555i	$0.402607\pi$
$434$	−1.46410	+	5.46410i	−0.0702791	+	0.262285i
$435$		0			0
$436$	−3.07180	+	5.32051i	−0.147112	+	0.254806i
$437$			31.3205i			1.49826i
$438$	−0.535898	−	0.143594i	−0.0256062	−	0.00686116i
$439$	−0.784610			−0.0374474			−0.0187237	−	0.999825i	$-0.505960\pi$
$439$	−0.784610			−0.0374474			−0.0187237	+	0.999825i	$0.505960\pi$
$440$		0			0
$441$	1.14359			0.0544568
$442$	−16.3923	−	4.39230i	−0.779702	−	0.208921i
$443$		−	30.9808i		−	1.47194i	−0.677014	−	0.735970i	$-0.736726\pi$
$443$		−	30.9808i		−	1.47194i	0.677014	−	0.735970i	$-0.263274\pi$
$444$	2.53590	+	1.46410i	0.120348	+	0.0694832i
$445$		0			0
$446$	−5.92820	+	22.1244i	−0.280709	+	1.04762i
$447$	−14.5359			−0.687524
$448$		−	21.8564i		−	1.03262i
$449$	11.3205			0.534248			0.267124	−	0.963662i	$-0.413927\pi$
$449$	11.3205			0.534248			0.267124	+	0.963662i	$0.413927\pi$
$450$		0			0
$451$		−	10.9282i		−	0.514589i
$452$	1.60770	+	0.928203i	0.0756196	+	0.0436590i
$453$		−	6.14359i		−	0.288651i
$454$	38.3205	+	10.2679i	1.79847	+	0.481899i
$455$		0			0
$456$	−10.9282	+	10.9282i	−0.511760	+	0.511760i
$457$	−14.7846			−0.691595			−0.345797	−	0.938309i	$-0.612392\pi$
$457$	−14.7846			−0.691595			−0.345797	+	0.938309i	$0.612392\pi$
$458$	−5.46410	−	1.46410i	−0.255321	−	0.0684130i
$459$		−	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	$-0.0217224\pi$
$462$	−1.46410	+	5.46410i	−0.0681162	+	0.254213i
$463$	14.7321			0.684656			0.342328	−	0.939580i	$-0.388785\pi$
$463$	14.7321			0.684656			0.342328	+	0.939580i	$0.388785\pi$
$464$	−24.0000	+	13.8564i	−1.11417	+	0.643268i
$465$		0			0
$466$	10.7321	−	40.0526i	0.497153	−	1.85540i
$467$		−	8.33975i		−	0.385917i	−0.981207	−	0.192959i	$-0.938192\pi$
$467$		−	8.33975i		−	0.385917i	0.981207	−	0.192959i	$-0.0618083\pi$
$468$	8.53590	−	14.7846i	0.394572	−	0.683419i
$469$			19.8564i			0.916884i
$470$		0			0
$471$	−12.3923			−0.571007
$472$	1.07180	+	1.07180i	0.0493334	+	0.0493334i
$473$	17.4641			0.803000
$474$	−14.9282	−	4.00000i	−0.685675	−	0.183726i
$475$		0			0
$476$	−16.3923	−	9.46410i	−0.751340	−	0.433786i
$477$			11.1769i			0.511756i
$478$	7.32051	−	27.3205i	0.334832	−	1.24961i
$479$	−21.8564			−0.998645			−0.499322	−	0.866416i	$-0.666418\pi$
$479$	−21.8564			−0.998645			−0.499322	+	0.866416i	$0.666418\pi$
$480$		0			0
$481$	6.92820			0.315899
$482$	1.60770	−	6.00000i	0.0732285	−	0.273293i
$483$			8.39230i			0.381863i
$484$	−12.1244	−	7.00000i	−0.551107	−	0.318182i
$485$		0			0
$486$	20.8564	+	5.58846i	0.946066	+	0.253498i
$487$	24.5885			1.11421			0.557105	−	0.830442i	$-0.311912\pi$
$487$	24.5885			1.11421			0.557105	+	0.830442i	$0.311912\pi$
$488$	−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	$0.977919\pi$
$492$	4.00000	−	6.92820i	0.180334	−	0.312348i
$493$			24.0000i			1.08091i
$494$	−9.46410	+	35.3205i	−0.425810	+	1.58914i
$495$		0			0
$496$	2.92820	+	5.07180i	0.131480	+	0.227730i
$497$	−4.00000			−0.179425
$498$	−1.26795	+	4.73205i	−0.0568182	+	0.212048i
$499$		−	24.5359i		−	1.09838i	−0.835698	−	0.549189i	$-0.814937\pi$
$499$		−	24.5359i		−	1.09838i	0.835698	−	0.549189i	$-0.185063\pi$
$500$		0			0
$501$		−	14.7846i		−	0.660528i
$502$	15.1244	+	4.05256i	0.675033	+	0.180875i
$503$	17.6603			0.787432			0.393716	−	0.919232i	$-0.371189\pi$
$503$	17.6603			0.787432			0.393716	+	0.919232i	$0.371189\pi$
$504$	13.4641	−	13.4641i	0.599739	−	0.599739i
$505$		0			0
$506$	11.4641	+	3.07180i	0.509641	+	0.136558i
$507$		−	0.732051i		−	0.0325115i
$508$	22.9808	+	13.2679i	1.01961	+	0.588670i
$509$		−	25.8564i		−	1.14607i	−0.819533	−	0.573033i	$-0.805767\pi$
$509$		−	25.8564i		−	1.14607i	0.819533	−	0.573033i	$-0.194233\pi$
$510$		0			0
$511$	−1.46410			−0.0647680
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−29.8564			−1.31819
$514$	−0.732051	+	2.73205i	−0.0322894	+	0.120506i
$515$		0			0
$516$	11.0718	+	6.39230i	0.487409	+	0.281406i
$517$		−	13.4641i		−	0.592151i
$518$	7.46410	+	2.00000i	0.327954	+	0.0878750i
$519$	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	$0.615053\pi$
$522$	−23.3205	−	6.24871i	−1.02071	−	0.273499i
$523$		−	22.1962i		−	0.970570i	−0.874356	−	0.485285i	$-0.838716\pi$
$523$		−	22.1962i		−	0.970570i	0.874356	−	0.485285i	$-0.161284\pi$
$524$	−7.85641	+	13.6077i	−0.343209	+	0.594455i
$525$		0			0
$526$	2.07180	−	7.73205i	0.0903346	−	0.337133i
$527$	5.07180			0.220931
$528$	2.92820	+	5.07180i	0.127434	+	0.220722i
$529$	−5.39230			−0.234448
$530$		0			0
$531$			1.32051i			0.0573052i
$532$	−20.3923	+	35.3205i	−0.884119	+	1.53134i
$533$		−	18.9282i		−	0.819871i
$534$	−4.92820	−	1.32051i	−0.213264	−	0.0571440i
$535$		0			0
$536$	14.5359	+	14.5359i	0.627855	+	0.627855i
$537$	11.3205			0.488516
$538$	6.73205	+	1.80385i	0.290239	+	0.0777694i
$539$			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	$0.909334\pi$
$542$	−5.60770	+	20.9282i	−0.240871	+	0.898943i
$543$	−11.7128			−0.502645
$544$	−18.9282	+	5.07180i	−0.811540	+	0.217451i
$545$		0			0
$546$	−2.53590	+	9.46410i	−0.108526	+	0.405026i
$547$			36.7321i			1.57055i	0.619148	+	0.785275i	$0.287478\pi$
$547$			36.7321i			1.57055i	−0.619148	+	0.785275i	$0.712522\pi$
$548$	−15.4641	−	8.92820i	−0.660594	−	0.381394i
$549$		−	12.1436i		−	0.518276i
$550$		0			0
$551$	51.7128			2.20304
$552$	6.14359	+	6.14359i	0.261489	+	0.261489i
$553$	−40.7846			−1.73434
$554$	−2.73205	−	0.732051i	−0.116074	−	0.0311019i
$555$		0			0
$556$	7.46410	−	12.9282i	0.316548	−	0.548278i
$557$		−	26.7846i		−	1.13490i	−0.823408	−	0.567450i	$-0.807930\pi$
$557$		−	26.7846i		−	1.13490i	0.823408	−	0.567450i	$-0.192070\pi$
$558$	−1.32051	+	4.92820i	−0.0559016	+	0.208627i
$559$	30.2487			1.27938
$560$		0			0
$561$	5.07180			0.214131
$562$	−6.39230	+	23.8564i	−0.269643	+	1.00632i
$563$			16.0526i			0.676535i	0.941050	+	0.338267i	$0.109841\pi$
$563$			16.0526i			0.676535i	−0.941050	+	0.338267i	$0.890159\pi$
$564$	4.92820	−	8.53590i	0.207515	−	0.359426i
$565$		0			0
$566$	−10.4641	−	2.80385i	−0.439839	−	0.117855i
$567$	12.1962			0.512190
$568$	−2.92820	+	2.92820i	−0.122865	+	0.122865i
$569$	−6.53590			−0.273999			−0.137000	−	0.990571i	$-0.543746\pi$
$569$	−6.53590			−0.273999			−0.137000	+	0.990571i	$0.543746\pi$
$570$		0			0
$571$			34.7846i			1.45569i	0.685741	+	0.727845i	$0.259478\pi$
$571$			34.7846i			1.45569i	−0.685741	+	0.727845i	$0.740522\pi$
$572$	12.0000	+	6.92820i	0.501745	+	0.289683i
$573$			14.1436i			0.590857i
$574$	5.46410	−	20.3923i	0.228067	−	0.851158i
$575$		0			0
$576$		−	19.7128i		−	0.821367i
$577$	43.5692			1.81381			0.906905	−	0.421335i	$-0.138438\pi$
$577$	43.5692			1.81381			0.906905	+	0.421335i	$0.138438\pi$
$578$	1.83013	−	6.83013i	0.0761232	−	0.284096i
$579$			5.46410i			0.227080i
$580$		0			0
$581$			12.9282i			0.536352i
$582$	−6.39230	−	1.71281i	−0.264970	−	0.0709984i
$583$	−9.07180			−0.375715
$584$	−1.07180	+	1.07180i	−0.0443513	+	0.0443513i
$585$		0			0
$586$	−16.1962	−	4.33975i	−0.669057	−	0.179273i
$587$		−	14.1962i		−	0.585938i	−0.956122	−	0.292969i	$-0.905357\pi$
$587$		−	14.1962i		−	0.585938i	0.956122	−	0.292969i	$-0.0946433\pi$
$588$	−0.339746	+	0.588457i	−0.0140109	+	0.0242676i
$589$		−	10.9282i		−	0.450289i
$590$		0			0
$591$	−9.17691			−0.377488
$592$	6.92820	−	4.00000i	0.284747	−	0.164399i
$593$	36.6410			1.50467			0.752333	−	0.658783i	$-0.228928\pi$
$593$	36.6410			1.50467			0.752333	+	0.658783i	$0.228928\pi$
$594$	−2.92820	+	10.9282i	−0.120146	+	0.448390i
$595$		0			0
$596$	−19.8564	+	34.3923i	−0.813350	+	1.40876i
$597$		−	18.9282i		−	0.774680i
$598$	19.8564	+	5.32051i	0.811989	+	0.217572i
$599$	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
$601$	25.4641			1.03870			0.519351	−	0.854561i	$-0.326174\pi$
$601$	25.4641			1.03870			0.519351	+	0.854561i	$0.326174\pi$
$602$	32.5885	+	8.73205i	1.32821	+	0.355892i
$603$			17.9090i			0.729309i
$604$	−14.5359	−	8.39230i	−0.591457	−	0.341478i
$605$		0			0
$606$	−2.92820	+	10.9282i	−0.118950	+	0.443928i
$607$	20.9808			0.851583			0.425791	−	0.904821i	$-0.359996\pi$
$607$	20.9808			0.851583			0.425791	+	0.904821i	$0.359996\pi$
$608$	10.9282	+	40.7846i	0.443197	+	1.65403i
$609$	13.8564			0.561490
$610$		0			0
$611$		−	23.3205i		−	0.943447i
$612$	−14.7846	−	8.53590i	−0.597632	−	0.345043i
$613$			5.60770i			0.226493i	0.993567	+	0.113246i	$0.0361249\pi$
$613$			5.60770i			0.226493i	−0.993567	+	0.113246i	$0.963875\pi$
$614$	−36.8564	−	9.87564i	−1.48740	−	0.398549i
$615$		0			0
$616$	10.9282	+	10.9282i	0.440310	+	0.440310i
$617$	27.4641			1.10566			0.552832	−	0.833293i	$-0.313547\pi$
$617$	27.4641			1.10566			0.552832	+	0.833293i	$0.313547\pi$
$618$	1.66025	+	0.444864i	0.0667852	+	0.0178950i
$619$			33.3205i			1.33926i	0.742693	+	0.669632i	$0.233548\pi$
$619$			33.3205i			1.33926i	−0.742693	+	0.669632i	$0.766452\pi$
$620$		0			0
$621$			16.7846i			0.673543i
$622$	1.21539	−	4.53590i	0.0487327	−	0.181873i
$623$	−13.4641			−0.539428
$624$	5.07180	+	8.78461i	0.203034	+	0.351666i
$625$		0			0
$626$	−11.6603	+	43.5167i	−0.466037	+	1.73928i
$627$		−	10.9282i		−	0.436430i
$628$	−16.9282	+	29.3205i	−0.675509	+	1.17002i
$629$		−	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
$633$	10.8231			0.430179
$634$	−21.1244	−	5.66025i	−0.838955	−	0.224797i
$635$		0			0
$636$	−5.75129	−	3.32051i	−0.228053	−	0.131667i
$637$			1.60770i			0.0636992i
$638$	5.07180	−	18.9282i	0.200794	−	0.749375i
$639$	−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	$0.631936\pi$
$642$	0.196152	−	0.732051i	0.00774152	−	0.0288917i
$643$			14.8756i			0.586638i	0.956015	+	0.293319i	$0.0947598\pi$
$643$			14.8756i			0.586638i	−0.956015	+	0.293319i	$0.905240\pi$
$644$	19.8564	+	11.4641i	0.782452	+	0.451749i
$645$		0			0
$646$	35.3205	+	9.46410i	1.38967	+	0.372360i
$647$	−13.2679			−0.521617			−0.260808	−	0.965391i	$-0.583989\pi$
$647$	−13.2679			−0.521617			−0.260808	+	0.965391i	$0.583989\pi$
$648$	8.92820	−	8.92820i	0.350733	−	0.350733i
$649$	−1.07180			−0.0420717
$650$		0			0
$651$		−	2.92820i		−	0.114765i
$652$	10.1962	−	17.6603i	0.399312	−	0.691629i
$653$		−	36.2487i		−	1.41852i	−0.704946	−	0.709261i	$-0.749029\pi$
$653$		−	36.2487i		−	1.41852i	0.704946	−	0.709261i	$-0.250971\pi$
$654$	0.823085	−	3.07180i	0.0321852	−	0.120117i
$655$		0			0
$656$	−10.9282	−	18.9282i	−0.426675	−	0.739022i
$657$	−1.32051			−0.0515179
$658$	6.73205	−	25.1244i	0.262443	−	0.979449i
$659$		−	17.3205i		−	0.674711i	−0.941377	−	0.337356i	$-0.890468\pi$
$659$		−	17.3205i		−	0.674711i	0.941377	−	0.337356i	$-0.109532\pi$
$660$		0			0
$661$			35.8564i			1.39465i	0.716754	+	0.697326i	$0.245627\pi$
$661$			35.8564i			1.39465i	−0.716754	+	0.697326i	$0.754373\pi$
$662$	−19.1244	−	5.12436i	−0.743289	−	0.199164i
$663$	8.78461			0.341166
$664$	9.46410	+	9.46410i	0.367278	+	0.367278i
$665$		0			0
$666$	6.73205	+	1.80385i	0.260862	+	0.0698977i
$667$		−	29.0718i		−	1.12566i
$668$	−34.9808	−	20.1962i	−1.35345	−	0.781413i
$669$		−	11.8564i		−	0.458395i
$670$		0			0
$671$	9.85641			0.380502
$672$	2.92820	+	10.9282i	0.112958	+	0.421565i
$673$	−19.4641			−0.750286			−0.375143	−	0.926967i	$-0.622406\pi$
$673$	−19.4641			−0.750286			−0.375143	+	0.926967i	$0.622406\pi$
$674$	2.87564	−	10.7321i	0.110766	−	0.413383i
$675$		0			0
$676$	−1.73205	−	1.00000i	−0.0666173	−	0.0384615i
$677$			38.3923i			1.47554i	0.675054	+	0.737768i	$0.264120\pi$
$677$			38.3923i			1.47554i	−0.675054	+	0.737768i	$0.735880\pi$
$678$	−0.928203	−	0.248711i	−0.0356474	−	0.00955170i
$679$	−17.4641			−0.670211
$680$		0			0
$681$	−20.5359			−0.786937
$682$	−4.00000	−	1.07180i	−0.153168	−	0.0410412i
$683$			34.9808i			1.33850i	0.743037	+	0.669251i	$0.233385\pi$
$683$			34.9808i			1.33850i	−0.743037	+	0.669251i	$0.766615\pi$
$684$	−18.3923	+	31.8564i	−0.703247	+	1.21806i
$685$		0			0
$686$	6.53590	−	24.3923i	0.249542	−	0.931303i
$687$	2.92820			0.111718
$688$	30.2487	−	17.4641i	1.15322	−	0.665813i
$689$	−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	$-0.111232\pi$
$692$	2.00000	−	3.46410i	0.0760286	−	0.131685i
$693$			13.4641i			0.511459i
$694$	−21.3923	−	5.73205i	−0.812041	−	0.217586i
$695$		0			0
$696$	10.1436	−	10.1436i	0.384492	−	0.384492i
$697$	−18.9282			−0.716957
$698$	−38.2487	−	10.2487i	−1.44774	−	0.387919i
$699$			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	$-0.213615\pi$
$702$	−5.07180	+	18.9282i	−0.191423	+	0.714399i
$703$	−14.9282			−0.563028
$704$	16.0000			0.603023
$705$		0			0
$706$	−0.339746	+	1.26795i	−0.0127865	+	0.0477199i
$707$			29.8564i			1.12287i
$708$	−0.679492	−	0.392305i	−0.0255369	−	0.0147437i
$709$		−	28.7846i		−	1.08103i	−0.841335	−	0.540514i	$-0.818230\pi$
$709$		−	28.7846i		−	1.08103i	0.841335	−	0.540514i	$-0.181770\pi$
$710$		0			0
$711$	−36.7846			−1.37953
$712$	−9.85641	+	9.85641i	−0.369384	+	0.369384i
$713$	−6.14359			−0.230079
$714$	9.46410	+	2.53590i	0.354185	+	0.0949036i
$715$		0			0
$716$	15.4641	−	26.7846i	0.577921	−	1.00099i
$717$			14.6410i			0.546779i
$718$	−1.85641	+	6.92820i	−0.0692805	+	0.258558i
$719$	25.8564			0.964281			0.482141	−	0.876094i	$-0.339859\pi$
$719$	25.8564			0.964281			0.482141	+	0.876094i	$0.339859\pi$
$720$		0			0
$721$	4.53590			0.168926
$722$	13.4378	−	50.1506i	0.500104	−	1.86641i
$723$			3.21539i			0.119582i
$724$	−16.0000	+	27.7128i	−0.594635	+	1.02994i
$725$		0			0
$726$	7.00000	+	1.87564i	0.259794	+	0.0696117i
$727$	−14.0526			−0.521181			−0.260590	−	0.965449i	$-0.583917\pi$
$727$	−14.0526			−0.521181			−0.260590	+	0.965449i	$0.583917\pi$
$728$	18.9282	+	18.9282i	0.701526	+	0.701526i
$729$	2.21539			0.0820515
$730$		0			0
$731$		−	30.2487i		−	1.11879i
$732$	6.24871	+	3.60770i	0.230959	+	0.133344i
$733$		−	48.9282i		−	1.80720i	−0.428373	−	0.903602i	$-0.640913\pi$
$733$		−	48.9282i		−	1.80720i	0.428373	−	0.903602i	$-0.359087\pi$
$734$	9.92820	−	37.0526i	0.366457	−	1.36763i
$735$		0			0
$736$	22.9282	−	6.14359i	0.845145	−	0.226456i
$737$	−14.5359			−0.535437
$738$	4.92820	−	18.3923i	0.181410	−	0.677030i
$739$			5.32051i			0.195718i	0.995200	+	0.0978590i	$0.0311994\pi$
$739$			5.32051i			0.195718i	−0.995200	+	0.0978590i	$0.968801\pi$
$740$		0			0
$741$		−	18.9282i		−	0.695345i
$742$	−16.9282	−	4.53590i	−0.621454	−	0.166518i
$743$	40.9808			1.50344			0.751719	−	0.659483i	$-0.229225\pi$
$743$	40.9808			1.50344			0.751719	+	0.659483i	$0.229225\pi$
$744$	−2.14359	−	2.14359i	−0.0785880	−	0.0785880i
$745$		0			0
$746$	−40.5885	−	10.8756i	−1.48605	−	0.398186i
$747$			11.6603i			0.426626i
$748$	6.92820	−	12.0000i	0.253320	−	0.438763i
$749$		−	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	$0.633054\pi$
$752$	−13.4641	−	23.3205i	−0.490985	−	0.850411i
$753$	−8.10512			−0.295367
$754$	8.78461	−	32.7846i	0.319917	−	1.19395i
$755$		0			0
$756$	−10.9282	+	18.9282i	−0.397455	+	0.688412i
$757$		−	32.9282i		−	1.19680i	−0.801199	−	0.598398i	$-0.795804\pi$
$757$		−	32.9282i		−	1.19680i	0.801199	−	0.598398i	$-0.204196\pi$
$758$	16.7321	+	4.48334i	0.607735	+	0.162842i
$759$	−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	$0.142802\pi$
$762$	−13.2679	−	3.55514i	−0.480647	−	0.128789i
$763$		−	8.39230i		−	0.303822i
$764$	33.4641	+	19.3205i	1.21069	+	0.698991i
$765$		0			0
$766$	−1.14359	+	4.26795i	−0.0413197	+	0.154207i
$767$	−1.85641			−0.0670310
$768$	10.1436	+	5.85641i	0.366025	+	0.211325i
$769$	−0.928203			−0.0334719			−0.0167359	−	0.999860i	$-0.505327\pi$
$769$	−0.928203			−0.0334719			−0.0167359	+	0.999860i	$0.505327\pi$
$770$		0			0
$771$		−	1.46410i		−	0.0527283i
$772$	12.9282	+	7.46410i	0.465296	+	0.268639i
$773$		−	1.60770i		−	0.0578248i	−0.999582	−	0.0289124i	$-0.990796\pi$
$773$		−	1.60770i		−	0.0578248i	0.999582	−	0.0289124i	$-0.00920438\pi$
$774$	29.3923	+	7.87564i	1.05648	+	0.283084i
$775$		0			0
$776$	−12.7846	+	12.7846i	−0.458941	+	0.458941i
$777$	−4.00000			−0.143499
$778$	−47.5167	−	12.7321i	−1.70355	−	0.456466i
$779$			40.7846i			1.46126i
$780$		0			0
$781$		−	2.92820i		−	0.104779i
$782$	5.32051	−	19.8564i	0.190261	−	0.710064i
$783$	27.7128			0.990375
$784$	0.928203	+	1.60770i	0.0331501	+	0.0574177i
$785$		0			0
$786$	2.10512	−	7.85641i	0.0750871	−	0.280229i
$787$		−	14.5885i		−	0.520022i	−0.965606	−	0.260011i	$-0.916274\pi$
$787$		−	14.5885i		−	0.520022i	0.965606	−	0.260011i	$-0.0837262\pi$
$788$	−12.5359	+	21.7128i	−0.446573	+	0.773487i
$789$			4.14359i			0.147516i
$790$		0			0
$791$	−2.53590			−0.0901662
$792$	9.85641	+	9.85641i	0.350232	+	0.350232i
$793$	17.0718			0.606237
$794$	22.1962	+	5.94744i	0.787712	+	0.211067i
$795$		0			0
$796$	−44.7846	−	25.8564i	−1.58735	−	0.916456i
$797$		−	26.1051i		−	0.924691i	−0.886700	−	0.462345i	$-0.847008\pi$
$797$		−	26.1051i		−	0.924691i	0.886700	−	0.462345i	$-0.152992\pi$
$798$	5.46410	−	20.3923i	0.193427	−	0.721880i
$799$	−23.3205			−0.825020
$800$		0			0
$801$	−12.1436			−0.429073
$802$	−7.26795	+	27.1244i	−0.256640	+	0.957794i
$803$		−	1.07180i		−	0.0378229i
$804$	−9.21539	−	5.32051i	−0.325002	−	0.187640i
$805$		0			0
$806$	−6.92820	−	1.85641i	−0.244036	−	0.0653891i
$807$	−3.60770			−0.126997
$808$	21.8564	+	21.8564i	0.768906	+	0.768906i
$809$	−3.85641			−0.135584			−0.0677920	−	0.997699i	$-0.521595\pi$
$809$	−3.85641			−0.135584			−0.0677920	+	0.997699i	$0.521595\pi$
$810$		0			0
$811$			15.0718i			0.529242i	0.964352	+	0.264621i	$0.0852469\pi$
$811$			15.0718i			0.529242i	−0.964352	+	0.264621i	$0.914753\pi$
$812$	18.9282	−	32.7846i	0.664250	−	1.15051i
$813$		−	11.2154i		−	0.393341i
$814$	−1.46410	+	5.46410i	−0.0513167	+	0.191517i
$815$		0			0
$816$	8.78461	−	5.07180i	0.307523	−	0.177548i
$817$	−65.1769			−2.28025
$818$	−8.53590	+	31.8564i	−0.298451	+	1.11383i
$819$			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	$0.962226\pi$
$822$	8.92820	+	2.39230i	0.311407	+	0.0834412i
$823$	−15.1244			−0.527202			−0.263601	−	0.964632i	$-0.584910\pi$
$823$	−15.1244			−0.527202			−0.263601	+	0.964632i	$0.584910\pi$
$824$	3.32051	−	3.32051i	0.115675	−	0.115675i
$825$		0			0
$826$	−2.00000	−	0.535898i	−0.0695889	−	0.0186463i
$827$		−	1.12436i		−	0.0390977i	−0.999809	−	0.0195488i	$-0.993777\pi$
$827$		−	1.12436i		−	0.0390977i	0.999809	−	0.0195488i	$-0.00622298\pi$
$828$	17.9090	+	10.3397i	0.622380	+	0.359331i
$829$		−	15.0718i		−	0.523465i	−0.965140	−	0.261733i	$-0.915706\pi$
$829$		−	15.0718i		−	0.523465i	0.965140	−	0.261733i	$-0.0842938\pi$
$830$		0			0
$831$	1.46410			0.0507891
$832$	27.7128			0.960769
$833$	1.60770			0.0557033
$834$	−2.00000	+	7.46410i	−0.0692543	+	0.258461i
$835$		0			0
$836$	−25.8564	−	14.9282i	−0.894263	−	0.516303i
$837$		−	5.85641i		−	0.202427i
$838$	−3.26795	−	0.875644i	−0.112889	−	0.0302486i
$839$	−16.7846			−0.579469			−0.289735	−	0.957107i	$-0.593567\pi$
$839$	−16.7846			−0.579469			−0.289735	+	0.957107i	$0.593567\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$	38.0526	+	10.1962i	1.31138	+	0.351383i
$843$		−	12.7846i		−	0.440325i
$844$	14.7846	−	25.6077i	0.508907	−	0.881453i
$845$		0			0
$846$	6.07180	−	22.6603i	0.208753	−	0.779076i
$847$	19.1244			0.657121
$848$	−15.7128	+	9.07180i	−0.539580	+	0.311527i
$849$	5.60770			0.192456
$850$		0			0
$851$			8.39230i			0.287685i
$852$	1.07180	−	1.85641i	0.0367192	−	0.0635994i
$853$		−	42.3923i		−	1.45148i	−0.687967	−	0.725742i	$-0.741496\pi$
$853$		−	42.3923i		−	1.45148i	0.687967	−	0.725742i	$-0.258504\pi$
$854$	18.3923	+	4.92820i	0.629372	+	0.168640i
$855$		0			0
$856$	−1.46410	−	1.46410i	−0.0500420	−	0.0500420i
$857$	−7.85641			−0.268370			−0.134185	−	0.990956i	$-0.542842\pi$
$857$	−7.85641			−0.268370			−0.134185	+	0.990956i	$0.542842\pi$
$858$	−6.92820	−	1.85641i	−0.236525	−	0.0633767i
$859$			20.2487i			0.690877i	0.938441	+	0.345439i	$0.112270\pi$
$859$			20.2487i			0.690877i	−0.938441	+	0.345439i	$0.887730\pi$
$860$		0			0
$861$			10.9282i			0.372432i
$862$	5.32051	−	19.8564i	0.181217	−	0.676312i
$863$	−30.3397			−1.03278			−0.516388	−	0.856354i	$-0.672724\pi$
$863$	−30.3397			−1.03278			−0.516388	+	0.856354i	$0.672724\pi$
$864$	5.85641	+	21.8564i	0.199239	+	0.743570i
$865$		0			0
$866$	−4.58846	+	17.1244i	−0.155922	+	0.581909i
$867$			3.66025i			0.124309i
$868$	−6.92820	−	4.00000i	−0.235159	−	0.135769i
$869$		−	29.8564i		−	1.01281i
$870$		0			0
$871$	−25.1769			−0.853087
$872$	−6.14359	−	6.14359i	−0.208048	−	0.208048i
$873$	−15.7513			−0.533100
$874$	−42.7846	−	11.4641i	−1.44721	−	0.387779i
$875$		0			0
$876$	0.392305	−	0.679492i	0.0132548	−	0.0229579i
$877$			53.7128i			1.81375i	0.421397	+	0.906876i	$0.361540\pi$
$877$			53.7128i			1.81375i	−0.421397	+	0.906876i	$0.638460\pi$
$878$	0.287187	−	1.07180i	0.00969209	−	0.0361714i
$879$	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	$0.486398\pi$
$882$	−0.418584	+	1.56218i	−0.0140945	+	0.0526013i
$883$			37.9090i			1.27574i	0.770145	+	0.637869i	$0.220184\pi$
$883$			37.9090i			1.27574i	−0.770145	+	0.637869i	$0.779816\pi$
$884$	12.0000	−	20.7846i	0.403604	−	0.699062i
$885$		0			0
$886$	42.3205	+	11.3397i	1.42179	+	0.380966i
$887$	−51.9090			−1.74293			−0.871466	−	0.490455i	$-0.836830\pi$
$887$	−51.9090			−1.74293			−0.871466	+	0.490455i	$0.836830\pi$
$888$	−2.92820	+	2.92820i	−0.0982641	+	0.0982641i
$889$	−36.2487			−1.21574
$890$		0			0
$891$			8.92820i			0.299106i
$892$	−28.0526	−	16.1962i	−0.939269	−	0.542287i
$893$			50.2487i			1.68151i
$894$	5.32051	−	19.8564i	0.177944	−	0.664098i
$895$		0			0
$896$	29.8564	+	8.00000i	0.997433	+	0.267261i
$897$	−10.6410			−0.355293
$898$	−4.14359	+	15.4641i	−0.138274	+	0.516044i
$899$			10.1436i			0.338308i
$900$		0			0
$901$			15.7128i			0.523470i
$902$	14.9282	+	4.00000i	0.497055	+	0.133185i
$903$	−17.4641			−0.581169
$904$	−1.85641	+	1.85641i	−0.0617432	+	0.0617432i
$905$		0			0
$906$	8.39230	+	2.24871i	0.278816	+	0.0747084i
$907$			29.1244i			0.967058i	0.875328	+	0.483529i	$0.160645\pi$
$907$			29.1244i			0.967058i	−0.875328	+	0.483529i	$0.839355\pi$
$908$	−28.0526	+	48.5885i	−0.930957	+	1.61246i
$909$			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	$0.429954\pi$
$912$	−10.9282	−	18.9282i	−0.361869	−	0.626775i
$913$	−9.46410			−0.313216
$914$	5.41154	−	20.1962i	0.178998	−	0.668029i
$915$		0			0
$916$	4.00000	−	6.92820i	0.132164	−	0.228914i
$917$		−	21.4641i		−	0.708807i
$918$	18.9282	+	5.07180i	0.624724	+	0.167394i
$919$	−25.0718			−0.827042			−0.413521	−	0.910495i	$-0.635701\pi$
$919$	−25.0718			−0.827042			−0.413521	+	0.910495i	$0.635701\pi$
$920$		0			0
$921$	19.7513			0.650827
$922$	4.00000	+	1.07180i	0.131733	+	0.0352977i
$923$		−	5.07180i		−	0.166940i
$924$	−6.92820	−	4.00000i	−0.227921	−	0.131590i
$925$		0			0
$926$	−5.39230	+	20.1244i	−0.177202	+	0.661327i
$927$	4.09103			0.134367
$928$	−10.1436	−	37.8564i	−0.332980	−	1.24270i
$929$	−10.5359			−0.345672			−0.172836	−	0.984951i	$-0.555293\pi$
$929$	−10.5359			−0.345672			−0.172836	+	0.984951i	$0.555293\pi$
$930$		0			0
$931$		−	3.46410i		−	0.113531i
$932$	50.7846	+	29.3205i	1.66351	+	0.960425i
$933$			2.43078i			0.0795802i
$934$	11.3923	+	3.05256i	0.372768	+	0.0998828i
$935$		0			0
$936$	17.0718	+	17.0718i	0.558009	+	0.558009i
$937$	44.2487			1.44554			0.722771	−	0.691087i	$-0.242868\pi$
$937$	44.2487			1.44554			0.722771	+	0.691087i	$0.242868\pi$
$938$	−27.1244	−	7.26795i	−0.885642	−	0.237307i
$939$		−	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	$0.825341\pi$
$942$	4.53590	−	16.9282i	0.147788	−	0.551551i
$943$	22.9282			0.746645
$944$	−1.85641	+	1.07180i	−0.0604209	+	0.0348840i
$945$		0			0
$946$	−6.39230	+	23.8564i	−0.207832	+	0.775639i
$947$			21.1244i			0.686449i	0.939253	+	0.343225i	$0.111519\pi$
$947$			21.1244i			0.686449i	−0.939253	+	0.343225i	$0.888481\pi$
$948$	10.9282	−	18.9282i	0.354932	−	0.614759i
$949$		−	1.85641i		−	0.0602615i
$950$		0			0
$951$	11.3205			0.367093
$952$	18.9282	−	18.9282i	0.613467	−	0.613467i
$953$	58.7846			1.90422			0.952110	−	0.305755i	$-0.0989089\pi$
$953$	58.7846			1.90422			0.952110	+	0.305755i	$0.0989089\pi$
$954$	−15.2679	−	4.09103i	−0.494318	−	0.132452i
$955$		0			0
$956$	34.6410	+	20.0000i	1.12037	+	0.646846i
$957$			10.1436i			0.327896i
$958$	8.00000	−	29.8564i	0.258468	−	0.964617i
$959$	24.3923			0.787669
$960$		0			0
$961$	−28.8564			−0.930852
$962$	−2.53590	+	9.46410i	−0.0817606	+	0.305135i
$963$		−	1.80385i		−	0.0581282i
$964$	7.60770	+	4.39230i	0.245027	+	0.141467i
$965$		0			0
$966$	−11.4641	−	3.07180i	−0.368851	−	0.0988334i
$967$	−33.6603			−1.08244			−0.541220	−	0.840881i	$-0.682038\pi$
$967$	−33.6603			−1.08244			−0.541220	+	0.840881i	$0.682038\pi$
$968$	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	$-0.120712\pi$
$972$	−15.2679	+	26.4449i	−0.489720	+	0.848219i
$973$			20.3923i			0.653747i
$974$	−9.00000	+	33.5885i	−0.288379	+	1.07624i
$975$		0			0
$976$	17.0718	−	9.85641i	0.546455	−	0.315496i
$977$	31.4641			1.00663			0.503313	−	0.864104i	$-0.332114\pi$
$977$	31.4641			1.00663			0.503313	+	0.864104i	$0.332114\pi$
$978$	−2.73205	+	10.1962i	−0.0873614	+	0.326037i
$979$		−	9.85641i		−	0.315012i
$980$		0			0
$981$		−	7.56922i		−	0.241667i
$982$	−4.19615	−	1.12436i	−0.133905	−	0.0358796i
$983$	45.2679			1.44382			0.721912	−	0.691985i	$-0.243264\pi$
$983$	45.2679			1.44382			0.721912	+	0.691985i	$0.243264\pi$
$984$	8.00000	+	8.00000i	0.255031	+	0.255031i
$985$		0			0
$986$	−32.7846	−	8.78461i	−1.04407	−	0.279759i
$987$			13.4641i			0.428567i
$988$	−44.7846	−	25.8564i	−1.42479	−	0.822602i
$989$			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	$0.315186\pi$
$992$	−8.00000	+	2.14359i	−0.254000	+	0.0680592i
$993$	10.2487			0.325233
$994$	1.46410	−	5.46410i	0.0464385	−	0.173311i
$995$		0			0
$996$	−6.00000	−	3.46410i	−0.190117	−	0.109764i
$997$			51.1769i			1.62079i	0.585884	+	0.810395i	$0.300747\pi$
$997$			51.1769i			1.62079i	−0.585884	+	0.810395i	$0.699253\pi$
$998$	33.5167	+	8.98076i	1.06095	+	0.284281i
$999$	−8.00000			−0.253109

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.d.a.21.3	✓	4	5.4	even	2
40.2.d.a.21.4	yes	4	40.29	even	2
160.2.d.a.81.2		4	20.19	odd	2
160.2.d.a.81.3		4	40.19	odd	2
200.2.d.f.101.1		4	8.5	even	2	inner
200.2.d.f.101.2		4	1.1	even	1	trivial
200.2.f.c.149.1		4	5.2	odd	4
200.2.f.c.149.2		4	40.13	odd	4
200.2.f.e.149.3		4	40.37	odd	4
200.2.f.e.149.4		4	5.3	odd	4
360.2.k.e.181.1		4	120.29	odd	2
360.2.k.e.181.2		4	15.14	odd	2
800.2.d.e.401.2		4	8.3	odd	2
800.2.d.e.401.3		4	4.3	odd	2
800.2.f.c.49.3		4	20.7	even	4
800.2.f.c.49.4		4	40.3	even	4
800.2.f.e.49.1		4	40.27	even	4
800.2.f.e.49.2		4	20.3	even	4
1280.2.a.a.1.2		2	80.69	even	4
1280.2.a.d.1.2		2	80.19	odd	4
1280.2.a.n.1.1		2	80.59	odd	4
1280.2.a.o.1.1		2	80.29	even	4
1440.2.k.e.721.2		4	60.59	even	2
1440.2.k.e.721.4		4	120.59	even	2
1800.2.d.l.1549.1		4	15.8	even	4
1800.2.d.l.1549.2		4	120.77	even	4
1800.2.d.p.1549.3		4	120.53	even	4
1800.2.d.p.1549.4		4	15.2	even	4
1800.2.k.j.901.3		4	3.2	odd	2
1800.2.k.j.901.4		4	24.5	odd	2
6400.2.a.z.1.2		2	16.13	even	4
6400.2.a.be.1.2		2	16.11	odd	4
6400.2.a.ce.1.1		2	16.5	even	4
6400.2.a.cj.1.1		2	16.3	odd	4
7200.2.d.n.2449.1		4	120.107	odd	4
7200.2.d.n.2449.4		4	60.23	odd	4
7200.2.d.o.2449.1		4	60.47	odd	4
7200.2.d.o.2449.4		4	120.83	odd	4
7200.2.k.j.3601.1		4	24.11	even	2
7200.2.k.j.3601.2		4	12.11	even	2

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.d (of order \(2\), degree \(1\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more