LMFDB - Embedded newform 40.2.f.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,2,Mod(29,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, 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("40.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	40.f (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:	$0.319401608085$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.3
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	40.29
Dual form			40.2.f.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} -1.41421 q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.41421 + 1.73205i) q^{5} +(-1.00000 + 1.73205i) q^{6} +2.44949i q^{7} -2.82843 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} -1.41421 q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.41421 + 1.73205i) q^{5} +(-1.00000 + 1.73205i) q^{6} +2.44949i q^{7} -2.82843 q^{8} -1.00000 q^{9} +(3.12132 - 0.507306i) q^{10} -3.46410i q^{11} +(1.41421 + 2.44949i) q^{12} +(3.00000 + 1.73205i) q^{14} +(-2.00000 - 2.44949i) q^{15} +(-2.00000 + 3.46410i) q^{16} -4.89898i q^{17} +(-0.707107 + 1.22474i) q^{18} +3.46410i q^{19} +(1.58579 - 4.18154i) q^{20} -3.46410i q^{21} +(-4.24264 - 2.44949i) q^{22} -2.44949i q^{23} +4.00000 q^{24} +(-1.00000 + 4.89898i) q^{25} +5.65685 q^{27} +(4.24264 - 2.44949i) q^{28} +(-4.41421 + 0.717439i) q^{30} +4.00000 q^{31} +(2.82843 + 4.89898i) q^{32} +4.89898i q^{33} +(-6.00000 - 3.46410i) q^{34} +(-4.24264 + 3.46410i) q^{35} +(1.00000 + 1.73205i) q^{36} -8.48528 q^{37} +(4.24264 + 2.44949i) q^{38} +(-4.00000 - 4.89898i) q^{40} +(-4.24264 - 2.44949i) q^{42} +4.24264 q^{43} +(-6.00000 + 3.46410i) q^{44} +(-1.41421 - 1.73205i) q^{45} +(-3.00000 - 1.73205i) q^{46} +7.34847i q^{47} +(2.82843 - 4.89898i) q^{48} +1.00000 q^{49} +(5.29289 + 4.68885i) q^{50} +6.92820i q^{51} +5.65685 q^{53} +(4.00000 - 6.92820i) q^{54} +(6.00000 - 4.89898i) q^{55} -6.92820i q^{56} -4.89898i q^{57} -10.3923i q^{59} +(-2.24264 + 5.91359i) q^{60} +3.46410i q^{61} +(2.82843 - 4.89898i) q^{62} -2.44949i q^{63} +8.00000 q^{64} +(6.00000 + 3.46410i) q^{66} -4.24264 q^{67} +(-8.48528 + 4.89898i) q^{68} +3.46410i q^{69} +(1.24264 + 7.64564i) q^{70} -12.0000 q^{71} +2.82843 q^{72} -4.89898i q^{73} +(-6.00000 + 10.3923i) q^{74} +(1.41421 - 6.92820i) q^{75} +(6.00000 - 3.46410i) q^{76} +8.48528 q^{77} -4.00000 q^{79} +(-8.82843 + 1.43488i) q^{80} -5.00000 q^{81} -9.89949 q^{83} +(-6.00000 + 3.46410i) q^{84} +(8.48528 - 6.92820i) q^{85} +(3.00000 - 5.19615i) q^{86} +9.79796i q^{88} +6.00000 q^{89} +(-3.12132 + 0.507306i) q^{90} +(-4.24264 + 2.44949i) q^{92} -5.65685 q^{93} +(9.00000 + 5.19615i) q^{94} +(-6.00000 + 4.89898i) q^{95} +(-4.00000 - 6.92820i) q^{96} +4.89898i q^{97} +(0.707107 - 1.22474i) q^{98} +3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 4 q^{10} + 12 q^{14} - 8 q^{15} - 8 q^{16} + 12 q^{20} + 16 q^{24} - 4 q^{25} - 12 q^{30} + 16 q^{31} - 24 q^{34} + 4 q^{36} - 16 q^{40} - 24 q^{44} - 12 q^{46} + 4 q^{49} + 24 q^{50} + 16 q^{54} + 24 q^{55} + 8 q^{60} + 32 q^{64} + 24 q^{66} - 12 q^{70} - 48 q^{71} - 24 q^{74} + 24 q^{76} - 16 q^{79} - 24 q^{80} - 20 q^{81} - 24 q^{84} + 12 q^{86} + 24 q^{89} - 4 q^{90} + 36 q^{94} - 24 q^{95} - 16 q^{96}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 4 * q^10 + 12 * q^14 - 8 * q^15 - 8 * q^16 + 12 * q^20 + 16 * q^24 - 4 * q^25 - 12 * q^30 + 16 * q^31 - 24 * q^34 + 4 * q^36 - 16 * q^40 - 24 * q^44 - 12 * q^46 + 4 * q^49 + 24 * q^50 + 16 * q^54 + 24 * q^55 + 8 * q^60 + 32 * q^64 + 24 * q^66 - 12 * q^70 - 48 * q^71 - 24 * q^74 + 24 * q^76 - 16 * q^79 - 24 * q^80 - 20 * q^81 - 24 * q^84 + 12 * q^86 + 24 * q^89 - 4 * q^90 + 36 * q^94 - 24 * q^95 - 16 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$3$	−1.41421			−0.816497			−0.408248	−	0.912871i	$-0.633860\pi$
$3$	−1.41421			−0.816497			−0.408248	+	0.912871i	$0.633860\pi$
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	1.41421	+	1.73205i	0.632456	+	0.774597i
$5$	1.41421	+	1.73205i	0.632456	+	0.774597i
$6$	−1.00000	+	1.73205i	−0.408248	+	0.707107i
$7$			2.44949i			0.925820i	0.886405	+	0.462910i	$0.153195\pi$
$7$			2.44949i			0.925820i	−0.886405	+	0.462910i	$0.846805\pi$
$8$	−2.82843			−1.00000
$9$	−1.00000			−0.333333
$10$	3.12132	−	0.507306i	0.987048	−	0.160424i
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$	1.41421	+	2.44949i	0.408248	+	0.707107i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	3.00000	+	1.73205i	0.801784	+	0.462910i
$15$	−2.00000	−	2.44949i	−0.516398	−	0.632456i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$		−	4.89898i		−	1.18818i	−0.804400	−	0.594089i	$-0.797513\pi$
$17$		−	4.89898i		−	1.18818i	0.804400	−	0.594089i	$-0.202487\pi$
$18$	−0.707107	+	1.22474i	−0.166667	+	0.288675i
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	1.58579	−	4.18154i	0.354593	−	0.935021i
$21$		−	3.46410i		−	0.755929i
$22$	−4.24264	−	2.44949i	−0.904534	−	0.522233i
$23$		−	2.44949i		−	0.510754i	−0.966842	−	0.255377i	$-0.917800\pi$
$23$		−	2.44949i		−	0.510754i	0.966842	−	0.255377i	$-0.0821996\pi$
$24$	4.00000			0.816497
$25$	−1.00000	+	4.89898i	−0.200000	+	0.979796i
$26$		0			0
$27$	5.65685			1.08866
$28$	4.24264	−	2.44949i	0.801784	−	0.462910i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	−4.41421	+	0.717439i	−0.805921	+	0.130986i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	2.82843	+	4.89898i	0.500000	+	0.866025i
$33$			4.89898i			0.852803i
$34$	−6.00000	−	3.46410i	−1.02899	−	0.594089i
$35$	−4.24264	+	3.46410i	−0.717137	+	0.585540i
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	−8.48528			−1.39497			−0.697486	−	0.716599i	$-0.745698\pi$
$37$	−8.48528			−1.39497			−0.697486	+	0.716599i	$0.745698\pi$
$38$	4.24264	+	2.44949i	0.688247	+	0.397360i
$39$		0			0
$40$	−4.00000	−	4.89898i	−0.632456	−	0.774597i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−4.24264	−	2.44949i	−0.654654	−	0.377964i
$43$	4.24264			0.646997			0.323498	−	0.946229i	$-0.395141\pi$
$43$	4.24264			0.646997			0.323498	+	0.946229i	$0.395141\pi$
$44$	−6.00000	+	3.46410i	−0.904534	+	0.522233i
$45$	−1.41421	−	1.73205i	−0.210819	−	0.258199i
$46$	−3.00000	−	1.73205i	−0.442326	−	0.255377i
$47$			7.34847i			1.07188i	0.844255	+	0.535942i	$0.180044\pi$
$47$			7.34847i			1.07188i	−0.844255	+	0.535942i	$0.819956\pi$
$48$	2.82843	−	4.89898i	0.408248	−	0.707107i
$49$	1.00000			0.142857
$50$	5.29289	+	4.68885i	0.748528	+	0.663103i
$51$			6.92820i			0.970143i
$52$		0			0
$53$	5.65685			0.777029			0.388514	−	0.921443i	$-0.372988\pi$
$53$	5.65685			0.777029			0.388514	+	0.921443i	$0.372988\pi$
$54$	4.00000	−	6.92820i	0.544331	−	0.942809i
$55$	6.00000	−	4.89898i	0.809040	−	0.660578i
$56$		−	6.92820i		−	0.925820i
$57$		−	4.89898i		−	0.648886i
$58$		0			0
$59$		−	10.3923i		−	1.35296i	−0.736460	−	0.676481i	$-0.763504\pi$
$59$		−	10.3923i		−	1.35296i	0.736460	−	0.676481i	$-0.236496\pi$
$60$	−2.24264	+	5.91359i	−0.289524	+	0.763441i
$61$			3.46410i			0.443533i	0.975100	+	0.221766i	$0.0711822\pi$
$61$			3.46410i			0.443533i	−0.975100	+	0.221766i	$0.928818\pi$
$62$	2.82843	−	4.89898i	0.359211	−	0.622171i
$63$		−	2.44949i		−	0.308607i
$64$	8.00000			1.00000
$65$		0			0
$66$	6.00000	+	3.46410i	0.738549	+	0.426401i
$67$	−4.24264			−0.518321			−0.259161	−	0.965834i	$-0.583446\pi$
$67$	−4.24264			−0.518321			−0.259161	+	0.965834i	$0.583446\pi$
$68$	−8.48528	+	4.89898i	−1.02899	+	0.594089i
$69$			3.46410i			0.417029i
$70$	1.24264	+	7.64564i	0.148524	+	0.913829i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	2.82843			0.333333
$73$		−	4.89898i		−	0.573382i	−0.958023	−	0.286691i	$-0.907445\pi$
$73$		−	4.89898i		−	0.573382i	0.958023	−	0.286691i	$-0.0925553\pi$
$74$	−6.00000	+	10.3923i	−0.697486	+	1.20808i
$75$	1.41421	−	6.92820i	0.163299	−	0.800000i
$76$	6.00000	−	3.46410i	0.688247	−	0.397360i
$77$	8.48528			0.966988
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−8.82843	+	1.43488i	−0.987048	+	0.160424i
$81$	−5.00000			−0.555556
$82$		0			0
$83$	−9.89949			−1.08661			−0.543305	−	0.839535i	$-0.682827\pi$
$83$	−9.89949			−1.08661			−0.543305	+	0.839535i	$0.682827\pi$
$84$	−6.00000	+	3.46410i	−0.654654	+	0.377964i
$85$	8.48528	−	6.92820i	0.920358	−	0.751469i
$86$	3.00000	−	5.19615i	0.323498	−	0.560316i
$87$		0			0
$88$			9.79796i			1.04447i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	−3.12132	+	0.507306i	−0.329016	+	0.0534747i
$91$		0			0
$92$	−4.24264	+	2.44949i	−0.442326	+	0.255377i
$93$	−5.65685			−0.586588
$94$	9.00000	+	5.19615i	0.928279	+	0.535942i
$95$	−6.00000	+	4.89898i	−0.615587	+	0.502625i
$96$	−4.00000	−	6.92820i	−0.408248	−	0.707107i
$97$			4.89898i			0.497416i	0.968579	+	0.248708i	$0.0800060\pi$
$97$			4.89898i			0.497416i	−0.968579	+	0.248708i	$0.919994\pi$
$98$	0.707107	−	1.22474i	0.0714286	−	0.123718i
$99$			3.46410i			0.348155i
$100$	9.48528	−	3.16693i	0.948528	−	0.316693i
$101$			13.8564i			1.37876i	0.724398	+	0.689382i	$0.242118\pi$
$101$			13.8564i			1.37876i	−0.724398	+	0.689382i	$0.757882\pi$
$102$	8.48528	+	4.89898i	0.840168	+	0.485071i
$103$			7.34847i			0.724066i	0.932165	+	0.362033i	$0.117917\pi$
$103$			7.34847i			0.724066i	−0.932165	+	0.362033i	$0.882083\pi$
$104$		0			0
$105$	6.00000	−	4.89898i	0.585540	−	0.478091i
$106$	4.00000	−	6.92820i	0.388514	−	0.672927i
$107$	1.41421			0.136717			0.0683586	−	0.997661i	$-0.478224\pi$
$107$	1.41421			0.136717			0.0683586	+	0.997661i	$0.478224\pi$
$108$	−5.65685	−	9.79796i	−0.544331	−	0.942809i
$109$		−	3.46410i		−	0.331801i	−0.986143	−	0.165900i	$-0.946947\pi$
$109$		−	3.46410i		−	0.331801i	0.986143	−	0.165900i	$-0.0530530\pi$
$110$	−1.75736	−	10.8126i	−0.167558	−	1.03094i
$111$	12.0000			1.13899
$112$	−8.48528	−	4.89898i	−0.801784	−	0.462910i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	−6.00000	−	3.46410i	−0.561951	−	0.324443i
$115$	4.24264	−	3.46410i	0.395628	−	0.323029i
$116$		0			0
$117$		0			0
$118$	−12.7279	−	7.34847i	−1.17170	−	0.676481i
$119$	12.0000			1.10004
$120$	5.65685	+	6.92820i	0.516398	+	0.632456i
$121$	−1.00000			−0.0909091
$122$	4.24264	+	2.44949i	0.384111	+	0.221766i
$123$		0			0
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$	−9.89949	+	5.19615i	−0.885438	+	0.464758i
$126$	−3.00000	−	1.73205i	−0.267261	−	0.154303i
$127$		−	17.1464i		−	1.52150i	−0.649045	−	0.760750i	$-0.724831\pi$
$127$		−	17.1464i		−	1.52150i	0.649045	−	0.760750i	$-0.275169\pi$
$128$	5.65685	−	9.79796i	0.500000	−	0.866025i
$129$	−6.00000			−0.528271
$130$		0			0
$131$			3.46410i			0.302660i	0.988483	+	0.151330i	$0.0483556\pi$
$131$			3.46410i			0.302660i	−0.988483	+	0.151330i	$0.951644\pi$
$132$	8.48528	−	4.89898i	0.738549	−	0.426401i
$133$	−8.48528			−0.735767
$134$	−3.00000	+	5.19615i	−0.259161	+	0.448879i
$135$	8.00000	+	9.79796i	0.688530	+	0.843274i
$136$			13.8564i			1.18818i
$137$			9.79796i			0.837096i	0.908195	+	0.418548i	$0.137461\pi$
$137$			9.79796i			0.837096i	−0.908195	+	0.418548i	$0.862539\pi$
$138$	4.24264	+	2.44949i	0.361158	+	0.208514i
$139$			10.3923i			0.881464i	0.897639	+	0.440732i	$0.145281\pi$
$139$			10.3923i			0.881464i	−0.897639	+	0.440732i	$0.854719\pi$
$140$	10.2426	+	3.88437i	0.865661	+	0.328289i
$141$		−	10.3923i		−	0.875190i
$142$	−8.48528	+	14.6969i	−0.712069	+	1.23334i
$143$		0			0
$144$	2.00000	−	3.46410i	0.166667	−	0.288675i
$145$		0			0
$146$	−6.00000	−	3.46410i	−0.496564	−	0.286691i
$147$	−1.41421			−0.116642
$148$	8.48528	+	14.6969i	0.697486	+	1.20808i
$149$		−	17.3205i		−	1.41895i	−0.704730	−	0.709476i	$-0.748932\pi$
$149$		−	17.3205i		−	1.41895i	0.704730	−	0.709476i	$-0.251068\pi$
$150$	−7.48528	−	6.63103i	−0.611171	−	0.541421i
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		−	9.79796i		−	0.794719i
$153$			4.89898i			0.396059i
$154$	6.00000	−	10.3923i	0.483494	−	0.837436i
$155$	5.65685	+	6.92820i	0.454369	+	0.556487i
$156$		0			0
$157$	8.48528			0.677199			0.338600	−	0.940931i	$-0.390047\pi$
$157$	8.48528			0.677199			0.338600	+	0.940931i	$0.390047\pi$
$158$	−2.82843	+	4.89898i	−0.225018	+	0.389742i
$159$	−8.00000			−0.634441
$160$	−4.48528	+	11.8272i	−0.354593	+	0.935021i
$161$	6.00000			0.472866
$162$	−3.53553	+	6.12372i	−0.277778	+	0.481125i
$163$	21.2132			1.66155			0.830773	−	0.556611i	$-0.187899\pi$
$163$	21.2132			1.66155			0.830773	+	0.556611i	$0.187899\pi$
$164$		0			0
$165$	−8.48528	+	6.92820i	−0.660578	+	0.539360i
$166$	−7.00000	+	12.1244i	−0.543305	+	0.941033i
$167$		−	12.2474i		−	0.947736i	−0.880596	−	0.473868i	$-0.842857\pi$
$167$		−	12.2474i		−	0.947736i	0.880596	−	0.473868i	$-0.157143\pi$
$168$			9.79796i			0.755929i
$169$	−13.0000			−1.00000
$170$	−2.48528	−	15.2913i	−0.190612	−	1.17279i
$171$		−	3.46410i		−	0.264906i
$172$	−4.24264	−	7.34847i	−0.323498	−	0.560316i
$173$	2.82843			0.215041			0.107521	−	0.994203i	$-0.465709\pi$
$173$	2.82843			0.215041			0.107521	+	0.994203i	$0.465709\pi$
$174$		0			0
$175$	−12.0000	−	2.44949i	−0.907115	−	0.185164i
$176$	12.0000	+	6.92820i	0.904534	+	0.522233i
$177$			14.6969i			1.10469i
$178$	4.24264	−	7.34847i	0.317999	−	0.550791i
$179$		−	3.46410i		−	0.258919i	−0.991585	−	0.129460i	$-0.958676\pi$
$179$		−	3.46410i		−	0.258919i	0.991585	−	0.129460i	$-0.0413242\pi$
$180$	−1.58579	+	4.18154i	−0.118198	+	0.311674i
$181$		−	13.8564i		−	1.02994i	−0.857209	−	0.514969i	$-0.827803\pi$
$181$		−	13.8564i		−	1.02994i	0.857209	−	0.514969i	$-0.172197\pi$
$182$		0			0
$183$		−	4.89898i		−	0.362143i
$184$			6.92820i			0.510754i
$185$	−12.0000	−	14.6969i	−0.882258	−	1.08054i
$186$	−4.00000	+	6.92820i	−0.293294	+	0.508001i
$187$	−16.9706			−1.24101
$188$	12.7279	−	7.34847i	0.928279	−	0.535942i
$189$			13.8564i			1.00791i
$190$	1.75736	+	10.8126i	0.127492	+	0.784426i
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$	−11.3137			−0.816497
$193$		−	24.4949i		−	1.76318i	−0.472015	−	0.881591i	$-0.656473\pi$
$193$		−	24.4949i		−	1.76318i	0.472015	−	0.881591i	$-0.343527\pi$
$194$	6.00000	+	3.46410i	0.430775	+	0.248708i
$195$		0			0
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	−5.65685			−0.403034			−0.201517	−	0.979485i	$-0.564587\pi$
$197$	−5.65685			−0.403034			−0.201517	+	0.979485i	$0.564587\pi$
$198$	4.24264	+	2.44949i	0.301511	+	0.174078i
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$	2.82843	−	13.8564i	0.200000	−	0.979796i
$201$	6.00000			0.423207
$202$	16.9706	+	9.79796i	1.19404	+	0.689382i
$203$		0			0
$204$	12.0000	−	6.92820i	0.840168	−	0.485071i
$205$		0			0
$206$	9.00000	+	5.19615i	0.627060	+	0.362033i
$207$			2.44949i			0.170251i
$208$		0			0
$209$	12.0000			0.830057
$210$	−1.75736	−	10.8126i	−0.121269	−	0.746138i
$211$		−	24.2487i		−	1.66935i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$		−	24.2487i		−	1.66935i	0.550743	−	0.834675i	$-0.314345\pi$
$212$	−5.65685	−	9.79796i	−0.388514	−	0.672927i
$213$	16.9706			1.16280
$214$	1.00000	−	1.73205i	0.0683586	−	0.118401i
$215$	6.00000	+	7.34847i	0.409197	+	0.501161i
$216$	−16.0000			−1.08866
$217$			9.79796i			0.665129i
$218$	−4.24264	−	2.44949i	−0.287348	−	0.165900i
$219$			6.92820i			0.468165i
$220$	−14.4853	−	5.49333i	−0.976597	−	0.370360i
$221$		0			0
$222$	8.48528	−	14.6969i	0.569495	−	0.986394i
$223$			22.0454i			1.47627i	0.674653	+	0.738135i	$0.264293\pi$
$223$			22.0454i			1.47627i	−0.674653	+	0.738135i	$0.735707\pi$
$224$	−12.0000	+	6.92820i	−0.801784	+	0.462910i
$225$	1.00000	−	4.89898i	0.0666667	−	0.326599i
$226$		0			0
$227$	−1.41421			−0.0938647			−0.0469323	−	0.998898i	$-0.514945\pi$
$227$	−1.41421			−0.0938647			−0.0469323	+	0.998898i	$0.514945\pi$
$228$	−8.48528	+	4.89898i	−0.561951	+	0.324443i
$229$			27.7128i			1.83131i	0.401960	+	0.915657i	$0.368329\pi$
$229$			27.7128i			1.83131i	−0.401960	+	0.915657i	$0.631671\pi$
$230$	−1.24264	−	7.64564i	−0.0819373	−	0.504139i
$231$	−12.0000			−0.789542
$232$		0			0
$233$			14.6969i			0.962828i	0.876493	+	0.481414i	$0.159877\pi$
$233$			14.6969i			0.962828i	−0.876493	+	0.481414i	$0.840123\pi$
$234$		0			0
$235$	−12.7279	+	10.3923i	−0.830278	+	0.677919i
$236$	−18.0000	+	10.3923i	−1.17170	+	0.676481i
$237$	5.65685			0.367452
$238$	8.48528	−	14.6969i	0.550019	−	0.952661i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	12.4853	−	2.02922i	0.805921	−	0.130986i
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$	−0.707107	+	1.22474i	−0.0454545	+	0.0787296i
$243$	−9.89949			−0.635053
$244$	6.00000	−	3.46410i	0.384111	−	0.221766i
$245$	1.41421	+	1.73205i	0.0903508	+	0.110657i
$246$		0			0
$247$		0			0
$248$	−11.3137			−0.718421
$249$	14.0000			0.887214
$250$	−0.636039	+	15.7986i	−0.0402266	+	0.999191i
$251$			10.3923i			0.655956i	0.944685	+	0.327978i	$0.106367\pi$
$251$			10.3923i			0.655956i	−0.944685	+	0.327978i	$0.893633\pi$
$252$	−4.24264	+	2.44949i	−0.267261	+	0.154303i
$253$	−8.48528			−0.533465
$254$	−21.0000	−	12.1244i	−1.31766	−	0.760750i
$255$	−12.0000	+	9.79796i	−0.751469	+	0.613572i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		−	9.79796i		−	0.611180i	−0.952163	−	0.305590i	$-0.901146\pi$
$257$		−	9.79796i		−	0.611180i	0.952163	−	0.305590i	$-0.0988537\pi$
$258$	−4.24264	+	7.34847i	−0.264135	+	0.457496i
$259$		−	20.7846i		−	1.29149i
$260$		0			0
$261$		0			0
$262$	4.24264	+	2.44949i	0.262111	+	0.151330i
$263$		−	7.34847i		−	0.453126i	−0.973997	−	0.226563i	$-0.927251\pi$
$263$		−	7.34847i		−	0.453126i	0.973997	−	0.226563i	$-0.0727489\pi$
$264$		−	13.8564i		−	0.852803i
$265$	8.00000	+	9.79796i	0.491436	+	0.601884i
$266$	−6.00000	+	10.3923i	−0.367884	+	0.637193i
$267$	−8.48528			−0.519291
$268$	4.24264	+	7.34847i	0.259161	+	0.448879i
$269$		−	10.3923i		−	0.633630i	−0.948487	−	0.316815i	$-0.897387\pi$
$269$		−	10.3923i		−	0.633630i	0.948487	−	0.316815i	$-0.102613\pi$
$270$	17.6569	−	2.86976i	1.07456	−	0.174648i
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	16.9706	+	9.79796i	1.02899	+	0.594089i
$273$		0			0
$274$	12.0000	+	6.92820i	0.724947	+	0.418548i
$275$	16.9706	+	3.46410i	1.02336	+	0.208893i
$276$	6.00000	−	3.46410i	0.361158	−	0.208514i
$277$	25.4558			1.52949			0.764747	−	0.644331i	$-0.222864\pi$
$277$	25.4558			1.52949			0.764747	+	0.644331i	$0.222864\pi$
$278$	12.7279	+	7.34847i	0.763370	+	0.440732i
$279$	−4.00000			−0.239474
$280$	12.0000	−	9.79796i	0.717137	−	0.585540i
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	−12.7279	−	7.34847i	−0.757937	−	0.437595i
$283$	−21.2132			−1.26099			−0.630497	−	0.776192i	$-0.717149\pi$
$283$	−21.2132			−1.26099			−0.630497	+	0.776192i	$0.717149\pi$
$284$	12.0000	+	20.7846i	0.712069	+	1.23334i
$285$	8.48528	−	6.92820i	0.502625	−	0.410391i
$286$		0			0
$287$		0			0
$288$	−2.82843	−	4.89898i	−0.166667	−	0.288675i
$289$	−7.00000			−0.411765
$290$		0			0
$291$		−	6.92820i		−	0.406138i
$292$	−8.48528	+	4.89898i	−0.496564	+	0.286691i
$293$	−19.7990			−1.15667			−0.578335	−	0.815800i	$-0.696297\pi$
$293$	−19.7990			−1.15667			−0.578335	+	0.815800i	$0.696297\pi$
$294$	−1.00000	+	1.73205i	−0.0583212	+	0.101015i
$295$	18.0000	−	14.6969i	1.04800	−	0.855689i
$296$	24.0000			1.39497
$297$		−	19.5959i		−	1.13707i
$298$	−21.2132	−	12.2474i	−1.22885	−	0.709476i
$299$		0			0
$300$	−13.4142	+	4.47871i	−0.774470	+	0.258579i
$301$			10.3923i			0.599002i
$302$	−11.3137	+	19.5959i	−0.651031	+	1.12762i
$303$		−	19.5959i		−	1.12576i
$304$	−12.0000	−	6.92820i	−0.688247	−	0.397360i
$305$	−6.00000	+	4.89898i	−0.343559	+	0.280515i
$306$	6.00000	+	3.46410i	0.342997	+	0.198030i
$307$	29.6985			1.69498			0.847491	−	0.530810i	$-0.178112\pi$
$307$	29.6985			1.69498			0.847491	+	0.530810i	$0.178112\pi$
$308$	−8.48528	−	14.6969i	−0.483494	−	0.837436i
$309$		−	10.3923i		−	0.591198i
$310$	12.4853	−	2.02922i	0.709116	−	0.115252i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$		−	9.79796i		−	0.553813i	−0.960897	−	0.276907i	$-0.910691\pi$
$313$		−	9.79796i		−	0.553813i	0.960897	−	0.276907i	$-0.0893093\pi$
$314$	6.00000	−	10.3923i	0.338600	−	0.586472i
$315$	4.24264	−	3.46410i	0.239046	−	0.195180i
$316$	4.00000	+	6.92820i	0.225018	+	0.389742i
$317$	−28.2843			−1.58860			−0.794301	−	0.607524i	$-0.792163\pi$
$317$	−28.2843			−1.58860			−0.794301	+	0.607524i	$0.792163\pi$
$318$	−5.65685	+	9.79796i	−0.317221	+	0.549442i
$319$		0			0
$320$	11.3137	+	13.8564i	0.632456	+	0.774597i
$321$	−2.00000			−0.111629
$322$	4.24264	−	7.34847i	0.236433	−	0.409514i
$323$	16.9706			0.944267
$324$	5.00000	+	8.66025i	0.277778	+	0.481125i
$325$		0			0
$326$	15.0000	−	25.9808i	0.830773	−	1.43894i
$327$			4.89898i			0.270914i
$328$		0			0
$329$	−18.0000			−0.992372
$330$	2.48528	+	15.2913i	0.136810	+	0.841757i
$331$			31.1769i			1.71364i	0.515617	+	0.856819i	$0.327563\pi$
$331$			31.1769i			1.71364i	−0.515617	+	0.856819i	$0.672437\pi$
$332$	9.89949	+	17.1464i	0.543305	+	0.941033i
$333$	8.48528			0.464991
$334$	−15.0000	−	8.66025i	−0.820763	−	0.473868i
$335$	−6.00000	−	7.34847i	−0.327815	−	0.401490i
$336$	12.0000	+	6.92820i	0.654654	+	0.377964i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	−9.19239	+	15.9217i	−0.500000	+	0.866025i
$339$		0			0
$340$	−20.4853	−	7.76874i	−1.11097	−	0.421319i
$341$		−	13.8564i		−	0.750366i
$342$	−4.24264	−	2.44949i	−0.229416	−	0.132453i
$343$			19.5959i			1.05808i
$344$	−12.0000			−0.646997
$345$	−6.00000	+	4.89898i	−0.323029	+	0.263752i
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	15.5563			0.835109			0.417554	−	0.908652i	$-0.362887\pi$
$347$	15.5563			0.835109			0.417554	+	0.908652i	$0.362887\pi$
$348$		0			0
$349$		−	13.8564i		−	0.741716i	−0.928689	−	0.370858i	$-0.879064\pi$
$349$		−	13.8564i		−	0.741716i	0.928689	−	0.370858i	$-0.120936\pi$
$350$	−11.4853	+	12.9649i	−0.613914	+	0.693002i
$351$		0			0
$352$	16.9706	−	9.79796i	0.904534	−	0.522233i
$353$			29.3939i			1.56448i	0.622978	+	0.782239i	$0.285922\pi$
$353$			29.3939i			1.56448i	−0.622978	+	0.782239i	$0.714078\pi$
$354$	18.0000	+	10.3923i	0.956689	+	0.552345i
$355$	−16.9706	−	20.7846i	−0.900704	−	1.10313i
$356$	−6.00000	−	10.3923i	−0.317999	−	0.550791i
$357$	−16.9706			−0.898177
$358$	−4.24264	−	2.44949i	−0.224231	−	0.129460i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	4.00000	+	4.89898i	0.210819	+	0.258199i
$361$	7.00000			0.368421
$362$	−16.9706	−	9.79796i	−0.891953	−	0.514969i
$363$	1.41421			0.0742270
$364$		0			0
$365$	8.48528	−	6.92820i	0.444140	−	0.362639i
$366$	−6.00000	−	3.46410i	−0.313625	−	0.181071i
$367$			12.2474i			0.639312i	0.947534	+	0.319656i	$0.103567\pi$
$367$			12.2474i			0.639312i	−0.947534	+	0.319656i	$0.896433\pi$
$368$	8.48528	+	4.89898i	0.442326	+	0.255377i
$369$		0			0
$370$	−26.4853	+	4.30463i	−1.37690	+	0.223787i
$371$			13.8564i			0.719389i
$372$	5.65685	+	9.79796i	0.293294	+	0.508001i
$373$	−8.48528			−0.439351			−0.219676	−	0.975573i	$-0.570500\pi$
$373$	−8.48528			−0.439351			−0.219676	+	0.975573i	$0.570500\pi$
$374$	−12.0000	+	20.7846i	−0.620505	+	1.07475i
$375$	14.0000	−	7.34847i	0.722957	−	0.379473i
$376$		−	20.7846i		−	1.07188i
$377$		0			0
$378$	16.9706	+	9.79796i	0.872872	+	0.503953i
$379$			24.2487i			1.24557i	0.782392	+	0.622786i	$0.213999\pi$
$379$			24.2487i			1.24557i	−0.782392	+	0.622786i	$0.786001\pi$
$380$	14.4853	+	5.49333i	0.743079	+	0.281802i
$381$			24.2487i			1.24230i
$382$	16.9706	−	29.3939i	0.868290	−	1.50392i
$383$		−	26.9444i		−	1.37679i	−0.725334	−	0.688397i	$-0.758315\pi$
$383$		−	26.9444i		−	1.37679i	0.725334	−	0.688397i	$-0.241685\pi$
$384$	−8.00000	+	13.8564i	−0.408248	+	0.707107i
$385$	12.0000	+	14.6969i	0.611577	+	0.749025i
$386$	−30.0000	−	17.3205i	−1.52696	−	0.881591i
$387$	−4.24264			−0.215666
$388$	8.48528	−	4.89898i	0.430775	−	0.248708i
$389$		−	3.46410i		−	0.175637i	−0.996136	−	0.0878185i	$-0.972010\pi$
$389$		−	3.46410i		−	0.175637i	0.996136	−	0.0878185i	$-0.0279895\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	−2.82843			−0.142857
$393$		−	4.89898i		−	0.247121i
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	−5.65685	−	6.92820i	−0.284627	−	0.348596i
$396$	6.00000	−	3.46410i	0.301511	−	0.174078i
$397$	−16.9706			−0.851728			−0.425864	−	0.904787i	$-0.640030\pi$
$397$	−16.9706			−0.851728			−0.425864	+	0.904787i	$0.640030\pi$
$398$	2.82843	−	4.89898i	0.141776	−	0.245564i
$399$	12.0000			0.600751
$400$	−14.9706	−	13.2621i	−0.748528	−	0.663103i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$	4.24264	−	7.34847i	0.211604	−	0.366508i
$403$		0			0
$404$	24.0000	−	13.8564i	1.19404	−	0.689382i
$405$	−7.07107	−	8.66025i	−0.351364	−	0.430331i
$406$		0			0
$407$			29.3939i			1.45700i
$408$		−	19.5959i		−	0.970143i
$409$	32.0000			1.58230			0.791149	−	0.611623i	$-0.209483\pi$
$409$	32.0000			1.58230			0.791149	+	0.611623i	$0.209483\pi$
$410$		0			0
$411$		−	13.8564i		−	0.683486i
$412$	12.7279	−	7.34847i	0.627060	−	0.362033i
$413$	25.4558			1.25260
$414$	3.00000	+	1.73205i	0.147442	+	0.0851257i
$415$	−14.0000	−	17.1464i	−0.687233	−	0.841685i
$416$		0			0
$417$		−	14.6969i		−	0.719712i
$418$	8.48528	−	14.6969i	0.415029	−	0.718851i
$419$			10.3923i			0.507697i	0.967244	+	0.253849i	$0.0816965\pi$
$419$			10.3923i			0.507697i	−0.967244	+	0.253849i	$0.918303\pi$
$420$	−14.4853	−	5.49333i	−0.706809	−	0.268047i
$421$			24.2487i			1.18181i	0.806741	+	0.590905i	$0.201229\pi$
$421$			24.2487i			1.18181i	−0.806741	+	0.590905i	$0.798771\pi$
$422$	−29.6985	−	17.1464i	−1.44570	−	0.834675i
$423$		−	7.34847i		−	0.357295i
$424$	−16.0000			−0.777029
$425$	24.0000	+	4.89898i	1.16417	+	0.237635i
$426$	12.0000	−	20.7846i	0.581402	−	1.00702i
$427$	−8.48528			−0.410632
$428$	−1.41421	−	2.44949i	−0.0683586	−	0.118401i
$429$		0			0
$430$	13.2426	−	2.15232i	0.638617	−	0.103794i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$	−11.3137	+	19.5959i	−0.544331	+	0.942809i
$433$			4.89898i			0.235430i	0.993047	+	0.117715i	$0.0375569\pi$
$433$			4.89898i			0.235430i	−0.993047	+	0.117715i	$0.962443\pi$
$434$	12.0000	+	6.92820i	0.576018	+	0.332564i
$435$		0			0
$436$	−6.00000	+	3.46410i	−0.287348	+	0.165900i
$437$	8.48528			0.405906
$438$	8.48528	+	4.89898i	0.405442	+	0.234082i
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$	−16.9706	+	13.8564i	−0.809040	+	0.660578i
$441$	−1.00000			−0.0476190
$442$		0			0
$443$	1.41421			0.0671913			0.0335957	−	0.999436i	$-0.489304\pi$
$443$	1.41421			0.0671913			0.0335957	+	0.999436i	$0.489304\pi$
$444$	−12.0000	−	20.7846i	−0.569495	−	0.986394i
$445$	8.48528	+	10.3923i	0.402241	+	0.492642i
$446$	27.0000	+	15.5885i	1.27849	+	0.738135i
$447$			24.4949i			1.15857i
$448$			19.5959i			0.925820i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$	−5.29289	−	4.68885i	−0.249509	−	0.221034i
$451$		0			0
$452$		0			0
$453$	22.6274			1.06313
$454$	−1.00000	+	1.73205i	−0.0469323	+	0.0812892i
$455$		0			0
$456$			13.8564i			0.648886i
$457$		−	19.5959i		−	0.916658i	−0.888783	−	0.458329i	$-0.848448\pi$
$457$		−	19.5959i		−	0.916658i	0.888783	−	0.458329i	$-0.151552\pi$
$458$	33.9411	+	19.5959i	1.58596	+	0.915657i
$459$		−	27.7128i		−	1.29352i
$460$	−10.2426	−	3.88437i	−0.477566	−	0.181110i
$461$		−	13.8564i		−	0.645357i	−0.946509	−	0.322679i	$-0.895417\pi$
$461$		−	13.8564i		−	0.645357i	0.946509	−	0.322679i	$-0.104583\pi$
$462$	−8.48528	+	14.6969i	−0.394771	+	0.683763i
$463$			17.1464i			0.796862i	0.917198	+	0.398431i	$0.130445\pi$
$463$			17.1464i			0.796862i	−0.917198	+	0.398431i	$0.869555\pi$
$464$		0			0
$465$	−8.00000	−	9.79796i	−0.370991	−	0.454369i
$466$	18.0000	+	10.3923i	0.833834	+	0.481414i
$467$	−7.07107			−0.327210			−0.163605	−	0.986526i	$-0.552312\pi$
$467$	−7.07107			−0.327210			−0.163605	+	0.986526i	$0.552312\pi$
$468$		0			0
$469$		−	10.3923i		−	0.479872i
$470$	3.72792	+	22.9369i	0.171956	+	1.05800i
$471$	−12.0000			−0.552931
$472$			29.3939i			1.35296i
$473$		−	14.6969i		−	0.675766i
$474$	4.00000	−	6.92820i	0.183726	−	0.318223i
$475$	−16.9706	−	3.46410i	−0.778663	−	0.158944i
$476$	−12.0000	−	20.7846i	−0.550019	−	0.952661i
$477$	−5.65685			−0.259010
$478$	−8.48528	+	14.6969i	−0.388108	+	0.672222i
$479$	−24.0000			−1.09659			−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000			−1.09659			−0.548294	+	0.836286i	$0.684723\pi$
$480$	6.34315	−	16.7262i	0.289524	−	0.763441i
$481$		0			0
$482$	2.82843	−	4.89898i	0.128831	−	0.223142i
$483$	−8.48528			−0.386094
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−8.48528	+	6.92820i	−0.385297	+	0.314594i
$486$	−7.00000	+	12.1244i	−0.317526	+	0.549972i
$487$		−	7.34847i		−	0.332991i	−0.986042	−	0.166495i	$-0.946755\pi$
$487$		−	7.34847i		−	0.332991i	0.986042	−	0.166495i	$-0.0532451\pi$
$488$		−	9.79796i		−	0.443533i
$489$	−30.0000			−1.35665
$490$	3.12132	−	0.507306i	0.141007	−	0.0229177i
$491$		−	24.2487i		−	1.09433i	−0.837025	−	0.547165i	$-0.815707\pi$
$491$		−	24.2487i		−	1.09433i	0.837025	−	0.547165i	$-0.184293\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−6.00000	+	4.89898i	−0.269680	+	0.220193i
$496$	−8.00000	+	13.8564i	−0.359211	+	0.622171i
$497$		−	29.3939i		−	1.31850i
$498$	9.89949	−	17.1464i	0.443607	−	0.768350i
$499$		−	17.3205i		−	0.775372i	−0.921791	−	0.387686i	$-0.873274\pi$
$499$		−	17.3205i		−	0.775372i	0.921791	−	0.387686i	$-0.126726\pi$
$500$	18.8995	+	11.9503i	0.845211	+	0.534433i
$501$			17.3205i			0.773823i
$502$	12.7279	+	7.34847i	0.568075	+	0.327978i
$503$		−	12.2474i		−	0.546087i	−0.962002	−	0.273043i	$-0.911970\pi$
$503$		−	12.2474i		−	0.546087i	0.962002	−	0.273043i	$-0.0880303\pi$
$504$			6.92820i			0.308607i
$505$	−24.0000	+	19.5959i	−1.06799	+	0.872007i
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$	18.3848			0.816497
$508$	−29.6985	+	17.1464i	−1.31766	+	0.760750i
$509$			27.7128i			1.22835i	0.789170	+	0.614174i	$0.210511\pi$
$509$			27.7128i			1.22835i	−0.789170	+	0.614174i	$0.789489\pi$
$510$	3.51472	+	21.6251i	0.155634	+	0.957577i
$511$	12.0000			0.530849
$512$	−22.6274			−1.00000
$513$			19.5959i			0.865181i
$514$	−12.0000	−	6.92820i	−0.529297	−	0.305590i
$515$	−12.7279	+	10.3923i	−0.560859	+	0.457940i
$516$	6.00000	+	10.3923i	0.264135	+	0.457496i
$517$	25.4558			1.11955
$518$	−25.4558	−	14.6969i	−1.11847	−	0.645746i
$519$	−4.00000			−0.175581
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		0			0
$523$	12.7279			0.556553			0.278277	−	0.960501i	$-0.410237\pi$
$523$	12.7279			0.556553			0.278277	+	0.960501i	$0.410237\pi$
$524$	6.00000	−	3.46410i	0.262111	−	0.151330i
$525$	16.9706	+	3.46410i	0.740656	+	0.151186i
$526$	−9.00000	−	5.19615i	−0.392419	−	0.226563i
$527$		−	19.5959i		−	0.853612i
$528$	−16.9706	−	9.79796i	−0.738549	−	0.426401i
$529$	17.0000			0.739130
$530$	17.6569	−	2.86976i	0.766965	−	0.124654i
$531$			10.3923i			0.450988i
$532$	8.48528	+	14.6969i	0.367884	+	0.637193i
$533$		0			0
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$	2.00000	+	2.44949i	0.0864675	+	0.105901i
$536$	12.0000			0.518321
$537$			4.89898i			0.211407i
$538$	−12.7279	−	7.34847i	−0.548740	−	0.316815i
$539$		−	3.46410i		−	0.149209i
$540$	8.97056	−	23.6544i	0.386032	−	1.01792i
$541$		−	41.5692i		−	1.78720i	−0.448864	−	0.893600i	$-0.648171\pi$
$541$		−	41.5692i		−	1.78720i	0.448864	−	0.893600i	$-0.351829\pi$
$542$	14.1421	−	24.4949i	0.607457	−	1.05215i
$543$			19.5959i			0.840941i
$544$	24.0000	−	13.8564i	1.02899	−	0.594089i
$545$	6.00000	−	4.89898i	0.257012	−	0.209849i
$546$		0			0
$547$	4.24264			0.181402			0.0907011	−	0.995878i	$-0.471089\pi$
$547$	4.24264			0.181402			0.0907011	+	0.995878i	$0.471089\pi$
$548$	16.9706	−	9.79796i	0.724947	−	0.418548i
$549$		−	3.46410i		−	0.147844i
$550$	16.2426	−	18.3351i	0.692589	−	0.781812i
$551$		0			0
$552$		−	9.79796i		−	0.417029i
$553$		−	9.79796i		−	0.416652i
$554$	18.0000	−	31.1769i	0.764747	−	1.32458i
$555$	16.9706	+	20.7846i	0.720360	+	0.882258i
$556$	18.0000	−	10.3923i	0.763370	−	0.440732i
$557$	−14.1421			−0.599222			−0.299611	−	0.954062i	$-0.596857\pi$
$557$	−14.1421			−0.599222			−0.299611	+	0.954062i	$0.596857\pi$
$558$	−2.82843	+	4.89898i	−0.119737	+	0.207390i
$559$		0			0
$560$	−3.51472	−	21.6251i	−0.148524	−	0.913829i
$561$	24.0000			1.01328
$562$	−8.48528	+	14.6969i	−0.357930	+	0.619953i
$563$	−41.0122			−1.72846			−0.864229	−	0.503099i	$-0.832193\pi$
$563$	−41.0122			−1.72846			−0.864229	+	0.503099i	$0.832193\pi$
$564$	−18.0000	+	10.3923i	−0.757937	+	0.437595i
$565$		0			0
$566$	−15.0000	+	25.9808i	−0.630497	+	1.09205i
$567$		−	12.2474i		−	0.514344i
$568$	33.9411			1.42414
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$	−2.48528	−	15.2913i	−0.104097	−	0.640481i
$571$		−	3.46410i		−	0.144968i	−0.997370	−	0.0724841i	$-0.976907\pi$
$571$		−	3.46410i		−	0.144968i	0.997370	−	0.0724841i	$-0.0230926\pi$
$572$		0			0
$573$	−33.9411			−1.41791
$574$		0			0
$575$	12.0000	+	2.44949i	0.500435	+	0.102151i
$576$	−8.00000			−0.333333
$577$			29.3939i			1.22368i	0.790980	+	0.611842i	$0.209571\pi$
$577$			29.3939i			1.22368i	−0.790980	+	0.611842i	$0.790429\pi$
$578$	−4.94975	+	8.57321i	−0.205882	+	0.356599i
$579$			34.6410i			1.43963i
$580$		0			0
$581$		−	24.2487i		−	1.00601i
$582$	−8.48528	−	4.89898i	−0.351726	−	0.203069i
$583$		−	19.5959i		−	0.811580i
$584$			13.8564i			0.573382i
$585$		0			0
$586$	−14.0000	+	24.2487i	−0.578335	+	1.00171i
$587$	9.89949			0.408596			0.204298	−	0.978909i	$-0.434509\pi$
$587$	9.89949			0.408596			0.204298	+	0.978909i	$0.434509\pi$
$588$	1.41421	+	2.44949i	0.0583212	+	0.101015i
$589$			13.8564i			0.570943i
$590$	−5.27208	−	32.4377i	−0.217048	−	1.33544i
$591$	8.00000			0.329076
$592$	16.9706	−	29.3939i	0.697486	−	1.20808i
$593$		−	9.79796i		−	0.402354i	−0.979555	−	0.201177i	$-0.935523\pi$
$593$		−	9.79796i		−	0.402354i	0.979555	−	0.201177i	$-0.0644766\pi$
$594$	−24.0000	−	13.8564i	−0.984732	−	0.568535i
$595$	16.9706	+	20.7846i	0.695725	+	0.852086i
$596$	−30.0000	+	17.3205i	−1.22885	+	0.709476i
$597$	−5.65685			−0.231520
$598$		0			0
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$	−4.00000	+	19.5959i	−0.163299	+	0.800000i
$601$	−28.0000			−1.14214			−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000			−1.14214			−0.571072	+	0.820900i	$0.693472\pi$
$602$	12.7279	+	7.34847i	0.518751	+	0.299501i
$603$	4.24264			0.172774
$604$	16.0000	+	27.7128i	0.651031	+	1.12762i
$605$	−1.41421	−	1.73205i	−0.0574960	−	0.0704179i
$606$	−24.0000	−	13.8564i	−0.974933	−	0.562878i
$607$			7.34847i			0.298265i	0.988817	+	0.149133i	$0.0476481\pi$
$607$			7.34847i			0.298265i	−0.988817	+	0.149133i	$0.952352\pi$
$608$	−16.9706	+	9.79796i	−0.688247	+	0.397360i
$609$		0			0
$610$	1.75736	+	10.8126i	0.0711534	+	0.437788i
$611$		0			0
$612$	8.48528	−	4.89898i	0.342997	−	0.198030i
$613$	−33.9411			−1.37087			−0.685435	−	0.728134i	$-0.740388\pi$
$613$	−33.9411			−1.37087			−0.685435	+	0.728134i	$0.740388\pi$
$614$	21.0000	−	36.3731i	0.847491	−	1.46790i
$615$		0			0
$616$	−24.0000			−0.966988
$617$			34.2929i			1.38058i	0.723534	+	0.690289i	$0.242517\pi$
$617$			34.2929i			1.38058i	−0.723534	+	0.690289i	$0.757483\pi$
$618$	−12.7279	−	7.34847i	−0.511992	−	0.295599i
$619$		−	10.3923i		−	0.417702i	−0.977947	−	0.208851i	$-0.933028\pi$
$619$		−	10.3923i		−	0.417702i	0.977947	−	0.208851i	$-0.0669724\pi$
$620$	6.34315	−	16.7262i	0.254747	−	0.671739i
$621$		−	13.8564i		−	0.556038i
$622$	−16.9706	+	29.3939i	−0.680458	+	1.17859i
$623$			14.6969i			0.588820i
$624$		0			0
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	−12.0000	−	6.92820i	−0.479616	−	0.276907i
$627$	−16.9706			−0.677739
$628$	−8.48528	−	14.6969i	−0.338600	−	0.586472i
$629$			41.5692i			1.65747i
$630$	−1.24264	−	7.64564i	−0.0495080	−	0.304610i
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	11.3137			0.450035
$633$			34.2929i			1.36302i
$634$	−20.0000	+	34.6410i	−0.794301	+	1.37577i
$635$	29.6985	−	24.2487i	1.17855	−	0.962281i
$636$	8.00000	+	13.8564i	0.317221	+	0.549442i
$637$		0			0
$638$		0			0
$639$	12.0000			0.474713
$640$	24.9706	−	4.05845i	0.987048	−	0.160424i
$641$	12.0000			0.473972			0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000			0.473972			0.236986	+	0.971513i	$0.423841\pi$
$642$	−1.41421	+	2.44949i	−0.0558146	+	0.0966736i
$643$	29.6985			1.17119			0.585597	−	0.810602i	$-0.300860\pi$
$643$	29.6985			1.17119			0.585597	+	0.810602i	$0.300860\pi$
$644$	−6.00000	−	10.3923i	−0.236433	−	0.409514i
$645$	−8.48528	−	10.3923i	−0.334108	−	0.409197i
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$			12.2474i			0.481497i	0.970588	+	0.240748i	$0.0773929\pi$
$647$			12.2474i			0.481497i	−0.970588	+	0.240748i	$0.922607\pi$
$648$	14.1421			0.555556
$649$	−36.0000			−1.41312
$650$		0			0
$651$		−	13.8564i		−	0.543075i
$652$	−21.2132	−	36.7423i	−0.830773	−	1.43894i
$653$	11.3137			0.442740			0.221370	−	0.975190i	$-0.428947\pi$
$653$	11.3137			0.442740			0.221370	+	0.975190i	$0.428947\pi$
$654$	6.00000	+	3.46410i	0.234619	+	0.135457i
$655$	−6.00000	+	4.89898i	−0.234439	+	0.191419i
$656$		0			0
$657$			4.89898i			0.191127i
$658$	−12.7279	+	22.0454i	−0.496186	+	0.859419i
$659$			24.2487i			0.944596i	0.881439	+	0.472298i	$0.156575\pi$
$659$			24.2487i			0.944596i	−0.881439	+	0.472298i	$0.843425\pi$
$660$	20.4853	+	7.76874i	0.797388	+	0.302398i
$661$		−	10.3923i		−	0.404214i	−0.979363	−	0.202107i	$-0.935221\pi$
$661$		−	10.3923i		−	0.404214i	0.979363	−	0.202107i	$-0.0647788\pi$
$662$	38.1838	+	22.0454i	1.48405	+	0.856819i
$663$		0			0
$664$	28.0000			1.08661
$665$	−12.0000	−	14.6969i	−0.465340	−	0.569923i
$666$	6.00000	−	10.3923i	0.232495	−	0.402694i
$667$		0			0
$668$	−21.2132	+	12.2474i	−0.820763	+	0.473868i
$669$		−	31.1769i		−	1.20537i
$670$	−13.2426	+	2.15232i	−0.511608	+	0.0831513i
$671$	12.0000			0.463255
$672$	16.9706	−	9.79796i	0.654654	−	0.377964i
$673$		−	34.2929i		−	1.32189i	−0.750433	−	0.660946i	$-0.770155\pi$
$673$		−	34.2929i		−	1.32189i	0.750433	−	0.660946i	$-0.229845\pi$
$674$		0			0
$675$	−5.65685	+	27.7128i	−0.217732	+	1.06667i
$676$	13.0000	+	22.5167i	0.500000	+	0.866025i
$677$	22.6274			0.869642			0.434821	−	0.900517i	$-0.356812\pi$
$677$	22.6274			0.869642			0.434821	+	0.900517i	$0.356812\pi$
$678$		0			0
$679$	−12.0000			−0.460518
$680$	−24.0000	+	19.5959i	−0.920358	+	0.751469i
$681$	2.00000			0.0766402
$682$	−16.9706	−	9.79796i	−0.649836	−	0.375183i
$683$	15.5563			0.595247			0.297624	−	0.954683i	$-0.403806\pi$
$683$	15.5563			0.595247			0.297624	+	0.954683i	$0.403806\pi$
$684$	−6.00000	+	3.46410i	−0.229416	+	0.132453i
$685$	−16.9706	+	13.8564i	−0.648412	+	0.529426i
$686$	24.0000	+	13.8564i	0.916324	+	0.529040i
$687$		−	39.1918i		−	1.49526i
$688$	−8.48528	+	14.6969i	−0.323498	+	0.560316i
$689$		0			0
$690$	1.75736	+	10.8126i	0.0669015	+	0.411628i
$691$			3.46410i			0.131781i	0.997827	+	0.0658903i	$0.0209887\pi$
$691$			3.46410i			0.131781i	−0.997827	+	0.0658903i	$0.979011\pi$
$692$	−2.82843	−	4.89898i	−0.107521	−	0.186231i
$693$	−8.48528			−0.322329
$694$	11.0000	−	19.0526i	0.417554	−	0.723225i
$695$	−18.0000	+	14.6969i	−0.682779	+	0.557487i
$696$		0			0
$697$		0			0
$698$	−16.9706	−	9.79796i	−0.642345	−	0.370858i
$699$		−	20.7846i		−	0.786146i
$700$	7.75736	+	23.2341i	0.293201	+	0.878166i
$701$			24.2487i			0.915861i	0.888988	+	0.457931i	$0.151409\pi$
$701$			24.2487i			0.915861i	−0.888988	+	0.457931i	$0.848591\pi$
$702$		0			0
$703$		−	29.3939i		−	1.10861i
$704$		−	27.7128i		−	1.04447i
$705$	18.0000	−	14.6969i	0.677919	−	0.553519i
$706$	36.0000	+	20.7846i	1.35488	+	0.782239i
$707$	−33.9411			−1.27649
$708$	25.4558	−	14.6969i	0.956689	−	0.552345i
$709$		−	41.5692i		−	1.56116i	−0.625053	−	0.780582i	$-0.714923\pi$
$709$		−	41.5692i		−	1.56116i	0.625053	−	0.780582i	$-0.285077\pi$
$710$	−37.4558	+	6.08767i	−1.40569	+	0.228466i
$711$	4.00000			0.150012
$712$	−16.9706			−0.635999
$713$		−	9.79796i		−	0.366936i
$714$	−12.0000	+	20.7846i	−0.449089	+	0.777844i
$715$		0			0
$716$	−6.00000	+	3.46410i	−0.224231	+	0.129460i
$717$	16.9706			0.633777
$718$	16.9706	−	29.3939i	0.633336	−	1.09697i
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$	8.82843	−	1.43488i	0.329016	−	0.0534747i
$721$	−18.0000			−0.670355
$722$	4.94975	−	8.57321i	0.184211	−	0.319062i
$723$	−5.65685			−0.210381
$724$	−24.0000	+	13.8564i	−0.891953	+	0.514969i
$725$		0			0
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$		−	46.5403i		−	1.72608i	−0.505132	−	0.863042i	$-0.668556\pi$
$727$		−	46.5403i		−	1.72608i	0.505132	−	0.863042i	$-0.331444\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−2.48528	−	15.2913i	−0.0919844	−	0.565956i
$731$		−	20.7846i		−	0.768747i
$732$	−8.48528	+	4.89898i	−0.313625	+	0.181071i
$733$	42.4264			1.56706			0.783528	−	0.621357i	$-0.213418\pi$
$733$	42.4264			1.56706			0.783528	+	0.621357i	$0.213418\pi$
$734$	15.0000	+	8.66025i	0.553660	+	0.319656i
$735$	−2.00000	−	2.44949i	−0.0737711	−	0.0903508i
$736$	12.0000	−	6.92820i	0.442326	−	0.255377i
$737$			14.6969i			0.541369i
$738$		0			0
$739$		−	3.46410i		−	0.127429i	−0.997968	−	0.0637145i	$-0.979705\pi$
$739$		−	3.46410i		−	0.127429i	0.997968	−	0.0637145i	$-0.0202947\pi$
$740$	−13.4558	+	35.4815i	−0.494647	+	1.30433i
$741$		0			0
$742$	16.9706	+	9.79796i	0.623009	+	0.359694i
$743$			51.4393i			1.88712i	0.331195	+	0.943562i	$0.392548\pi$
$743$			51.4393i			1.88712i	−0.331195	+	0.943562i	$0.607452\pi$
$744$	16.0000			0.586588
$745$	30.0000	−	24.4949i	1.09911	−	0.897424i
$746$	−6.00000	+	10.3923i	−0.219676	+	0.380489i
$747$	9.89949			0.362204
$748$	16.9706	+	29.3939i	0.620505	+	1.07475i
$749$			3.46410i			0.126576i
$750$	0.899495	−	22.3426i	0.0328449	−	0.815836i
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$	−25.4558	−	14.6969i	−0.928279	−	0.535942i
$753$		−	14.6969i		−	0.535586i
$754$		0			0
$755$	−22.6274	−	27.7128i	−0.823496	−	1.00857i
$756$	24.0000	−	13.8564i	0.872872	−	0.503953i
$757$	−25.4558			−0.925208			−0.462604	−	0.886565i	$-0.653085\pi$
$757$	−25.4558			−0.925208			−0.462604	+	0.886565i	$0.653085\pi$
$758$	29.6985	+	17.1464i	1.07870	+	0.622786i
$759$	12.0000			0.435572
$760$	16.9706	−	13.8564i	0.615587	−	0.502625i
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$	29.6985	+	17.1464i	1.07586	+	0.621150i
$763$	8.48528			0.307188
$764$	−24.0000	−	41.5692i	−0.868290	−	1.50392i
$765$	−8.48528	+	6.92820i	−0.306786	+	0.250490i
$766$	−33.0000	−	19.0526i	−1.19234	−	0.688397i
$767$		0			0
$768$	11.3137	+	19.5959i	0.408248	+	0.707107i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$	26.4853	−	4.30463i	0.954463	−	0.155128i
$771$			13.8564i			0.499026i
$772$	−42.4264	+	24.4949i	−1.52696	+	0.881591i
$773$	28.2843			1.01731			0.508657	−	0.860969i	$-0.330142\pi$
$773$	28.2843			1.01731			0.508657	+	0.860969i	$0.330142\pi$
$774$	−3.00000	+	5.19615i	−0.107833	+	0.186772i
$775$	−4.00000	+	19.5959i	−0.143684	+	0.703906i
$776$		−	13.8564i		−	0.497416i
$777$			29.3939i			1.05450i
$778$	−4.24264	−	2.44949i	−0.152106	−	0.0878185i
$779$		0			0
$780$		0			0
$781$			41.5692i			1.48746i
$782$	−8.48528	+	14.6969i	−0.303433	+	0.525561i
$783$		0			0
$784$	−2.00000	+	3.46410i	−0.0714286	+	0.123718i
$785$	12.0000	+	14.6969i	0.428298	+	0.524556i
$786$	−6.00000	−	3.46410i	−0.214013	−	0.123560i
$787$	−21.2132			−0.756169			−0.378085	−	0.925771i	$-0.623417\pi$
$787$	−21.2132			−0.756169			−0.378085	+	0.925771i	$0.623417\pi$
$788$	5.65685	+	9.79796i	0.201517	+	0.349038i
$789$			10.3923i			0.369976i
$790$	−12.4853	+	2.02922i	−0.444206	+	0.0721965i
$791$		0			0
$792$		−	9.79796i		−	0.348155i
$793$		0			0
$794$	−12.0000	+	20.7846i	−0.425864	+	0.737618i
$795$	−11.3137	−	13.8564i	−0.401256	−	0.491436i
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	39.5980			1.40263			0.701316	−	0.712850i	$-0.252596\pi$
$797$	39.5980			1.40263			0.701316	+	0.712850i	$0.252596\pi$
$798$	8.48528	−	14.6969i	0.300376	−	0.520266i
$799$	36.0000			1.27359
$800$	−26.8284	+	8.95743i	−0.948528	+	0.316693i
$801$	−6.00000			−0.212000
$802$	−12.7279	+	22.0454i	−0.449439	+	0.778450i
$803$	−16.9706			−0.598878
$804$	−6.00000	−	10.3923i	−0.211604	−	0.366508i
$805$	8.48528	+	10.3923i	0.299067	+	0.366281i
$806$		0			0
$807$			14.6969i			0.517357i
$808$		−	39.1918i		−	1.37876i
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$	−15.6066	+	2.53653i	−0.548360	+	0.0891246i
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$		0			0
$813$	−28.2843			−0.991973
$814$	36.0000	+	20.7846i	1.26180	+	0.728500i
$815$	30.0000	+	36.7423i	1.05085	+	1.28703i
$816$	−24.0000	−	13.8564i	−0.840168	−	0.485071i
$817$			14.6969i			0.514181i
$818$	22.6274	−	39.1918i	0.791149	−	1.37031i
$819$		0			0
$820$		0			0
$821$			31.1769i			1.08808i	0.839059	+	0.544041i	$0.183106\pi$
$821$			31.1769i			1.08808i	−0.839059	+	0.544041i	$0.816894\pi$
$822$	−16.9706	−	9.79796i	−0.591916	−	0.341743i
$823$			26.9444i			0.939222i	0.882873	+	0.469611i	$0.155606\pi$
$823$			26.9444i			0.939222i	−0.882873	+	0.469611i	$0.844394\pi$
$824$		−	20.7846i		−	0.724066i
$825$	−24.0000	−	4.89898i	−0.835573	−	0.170561i
$826$	18.0000	−	31.1769i	0.626300	−	1.08478i
$827$	−35.3553			−1.22943			−0.614713	−	0.788751i	$-0.710728\pi$
$827$	−35.3553			−1.22943			−0.614713	+	0.788751i	$0.710728\pi$
$828$	4.24264	−	2.44949i	0.147442	−	0.0851257i
$829$		−	10.3923i		−	0.360940i	−0.983581	−	0.180470i	$-0.942238\pi$
$829$		−	10.3923i		−	0.360940i	0.983581	−	0.180470i	$-0.0577618\pi$
$830$	−30.8995	+	5.02207i	−1.07254	+	0.174319i
$831$	−36.0000			−1.24883
$832$		0			0
$833$		−	4.89898i		−	0.169740i
$834$	−18.0000	−	10.3923i	−0.623289	−	0.359856i
$835$	21.2132	−	17.3205i	0.734113	−	0.599401i
$836$	−12.0000	−	20.7846i	−0.415029	−	0.718851i
$837$	22.6274			0.782118
$838$	12.7279	+	7.34847i	0.439679	+	0.253849i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	−16.9706	+	13.8564i	−0.585540	+	0.478091i
$841$	29.0000			1.00000
$842$	29.6985	+	17.1464i	1.02348	+	0.590905i
$843$	16.9706			0.584497
$844$	−42.0000	+	24.2487i	−1.44570	+	0.834675i
$845$	−18.3848	−	22.5167i	−0.632456	−	0.774597i
$846$	−9.00000	−	5.19615i	−0.309426	−	0.178647i
$847$		−	2.44949i		−	0.0841655i
$848$	−11.3137	+	19.5959i	−0.388514	+	0.672927i
$849$	30.0000			1.02960
$850$	22.9706	−	25.9298i	0.787884	−	0.889384i
$851$			20.7846i			0.712487i
$852$	−16.9706	−	29.3939i	−0.581402	−	1.00702i
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$	−6.00000	+	10.3923i	−0.205316	+	0.355617i
$855$	6.00000	−	4.89898i	0.205196	−	0.167542i
$856$	−4.00000			−0.136717
$857$		−	39.1918i		−	1.33877i	−0.742917	−	0.669384i	$-0.766558\pi$
$857$		−	39.1918i		−	1.33877i	0.742917	−	0.669384i	$-0.233442\pi$
$858$		0			0
$859$			3.46410i			0.118194i	0.998252	+	0.0590968i	$0.0188221\pi$
$859$			3.46410i			0.118194i	−0.998252	+	0.0590968i	$0.981178\pi$
$860$	6.72792	−	17.7408i	0.229420	−	0.604955i
$861$		0			0
$862$	8.48528	−	14.6969i	0.289010	−	0.500580i
$863$		−	2.44949i		−	0.0833816i	−0.999131	−	0.0416908i	$-0.986726\pi$
$863$		−	2.44949i		−	0.0833816i	0.999131	−	0.0416908i	$-0.0132744\pi$
$864$	16.0000	+	27.7128i	0.544331	+	0.942809i
$865$	4.00000	+	4.89898i	0.136004	+	0.166570i
$866$	6.00000	+	3.46410i	0.203888	+	0.117715i
$867$	9.89949			0.336204
$868$	16.9706	−	9.79796i	0.576018	−	0.332564i
$869$			13.8564i			0.470046i
$870$		0			0
$871$		0			0
$872$			9.79796i			0.331801i
$873$		−	4.89898i		−	0.165805i
$874$	6.00000	−	10.3923i	0.202953	−	0.351525i
$875$	−12.7279	−	24.2487i	−0.430282	−	0.819756i
$876$	12.0000	−	6.92820i	0.405442	−	0.234082i
$877$	−8.48528			−0.286528			−0.143264	−	0.989685i	$-0.545760\pi$
$877$	−8.48528			−0.286528			−0.143264	+	0.989685i	$0.545760\pi$
$878$	−5.65685	+	9.79796i	−0.190910	+	0.330665i
$879$	28.0000			0.944417
$880$	4.97056	+	30.5826i	0.167558	+	1.03094i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	−0.707107	+	1.22474i	−0.0238095	+	0.0412393i
$883$	4.24264			0.142776			0.0713881	−	0.997449i	$-0.477257\pi$
$883$	4.24264			0.142776			0.0713881	+	0.997449i	$0.477257\pi$
$884$		0			0
$885$	−25.4558	+	20.7846i	−0.855689	+	0.698667i
$886$	1.00000	−	1.73205i	0.0335957	−	0.0581894i
$887$		−	26.9444i		−	0.904704i	−0.891839	−	0.452352i	$-0.850585\pi$
$887$		−	26.9444i		−	0.904704i	0.891839	−	0.452352i	$-0.149415\pi$
$888$	−33.9411			−1.13899
$889$	42.0000			1.40863
$890$	18.7279	−	3.04384i	0.627761	−	0.102030i
$891$			17.3205i			0.580259i
$892$	38.1838	−	22.0454i	1.27849	−	0.738135i
$893$	−25.4558			−0.851847
$894$	30.0000	+	17.3205i	1.00335	+	0.579284i
$895$	6.00000	−	4.89898i	0.200558	−	0.163755i
$896$	24.0000	+	13.8564i	0.801784	+	0.462910i
$897$		0			0
$898$	−8.48528	+	14.6969i	−0.283158	+	0.490443i
$899$		0			0
$900$	−9.48528	+	3.16693i	−0.316176	+	0.105564i
$901$		−	27.7128i		−	0.923248i
$902$		0			0
$903$		−	14.6969i		−	0.489083i
$904$		0			0
$905$	24.0000	−	19.5959i	0.797787	−	0.651390i
$906$	16.0000	−	27.7128i	0.531564	−	0.920697i
$907$	−4.24264			−0.140875			−0.0704373	−	0.997516i	$-0.522439\pi$
$907$	−4.24264			−0.140875			−0.0704373	+	0.997516i	$0.522439\pi$
$908$	1.41421	+	2.44949i	0.0469323	+	0.0812892i
$909$		−	13.8564i		−	0.459588i
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	16.9706	+	9.79796i	0.561951	+	0.324443i
$913$			34.2929i			1.13493i
$914$	−24.0000	−	13.8564i	−0.793849	−	0.458329i
$915$	8.48528	−	6.92820i	0.280515	−	0.229039i
$916$	48.0000	−	27.7128i	1.58596	−	0.915657i
$917$	−8.48528			−0.280209
$918$	−33.9411	−	19.5959i	−1.12022	−	0.646762i
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$	−12.0000	+	9.79796i	−0.395628	+	0.323029i
$921$	−42.0000			−1.38395
$922$	−16.9706	−	9.79796i	−0.558896	−	0.322679i
$923$		0			0
$924$	12.0000	+	20.7846i	0.394771	+	0.683763i
$925$	8.48528	−	41.5692i	0.278994	−	1.36679i
$926$	21.0000	+	12.1244i	0.690103	+	0.398431i
$927$		−	7.34847i		−	0.241355i
$928$		0			0
$929$	−36.0000			−1.18112			−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−36.0000			−1.18112			−0.590561	+	0.806993i	$0.701093\pi$
$930$	−17.6569	+	2.86976i	−0.578991	+	0.0941030i
$931$			3.46410i			0.113531i
$932$	25.4558	−	14.6969i	0.833834	−	0.481414i
$933$	33.9411			1.11118
$934$	−5.00000	+	8.66025i	−0.163605	+	0.283372i
$935$	−24.0000	−	29.3939i	−0.784884	−	0.961283i
$936$		0			0
$937$			4.89898i			0.160043i	0.996793	+	0.0800213i	$0.0254988\pi$
$937$			4.89898i			0.160043i	−0.996793	+	0.0800213i	$0.974501\pi$
$938$	−12.7279	−	7.34847i	−0.415581	−	0.239936i
$939$			13.8564i			0.452187i
$940$	30.7279	+	11.6531i	1.00223	+	0.380082i
$941$			13.8564i			0.451706i	0.974161	+	0.225853i	$0.0725169\pi$
$941$			13.8564i			0.451706i	−0.974161	+	0.225853i	$0.927483\pi$
$942$	−8.48528	+	14.6969i	−0.276465	+	0.478852i
$943$		0			0
$944$	36.0000	+	20.7846i	1.17170	+	0.676481i
$945$	−24.0000	+	19.5959i	−0.780720	+	0.637455i
$946$	−18.0000	−	10.3923i	−0.585230	−	0.337883i
$947$	41.0122			1.33272			0.666359	−	0.745631i	$-0.267852\pi$
$947$	41.0122			1.33272			0.666359	+	0.745631i	$0.267852\pi$
$948$	−5.65685	−	9.79796i	−0.183726	−	0.318223i
$949$		0			0
$950$	−16.2426	+	18.3351i	−0.526981	+	0.594870i
$951$	40.0000			1.29709
$952$	−33.9411			−1.10004
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$	−4.00000	+	6.92820i	−0.129505	+	0.224309i
$955$	33.9411	+	41.5692i	1.09831	+	1.34515i
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$		0			0
$958$	−16.9706	+	29.3939i	−0.548294	+	0.949673i
$959$	−24.0000			−0.775000
$960$	−16.0000	−	19.5959i	−0.516398	−	0.632456i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−1.41421			−0.0455724
$964$	−4.00000	−	6.92820i	−0.128831	−	0.223142i
$965$	42.4264	−	34.6410i	1.36575	−	1.11513i
$966$	−6.00000	+	10.3923i	−0.193047	+	0.334367i
$967$			17.1464i			0.551392i	0.961245	+	0.275696i	$0.0889083\pi$
$967$			17.1464i			0.551392i	−0.961245	+	0.275696i	$0.911092\pi$
$968$	2.82843			0.0909091
$969$	−24.0000			−0.770991
$970$	2.48528	+	15.2913i	0.0797976	+	0.490974i
$971$			3.46410i			0.111168i	0.998454	+	0.0555842i	$0.0177021\pi$
$971$			3.46410i			0.111168i	−0.998454	+	0.0555842i	$0.982298\pi$
$972$	9.89949	+	17.1464i	0.317526	+	0.549972i
$973$	−25.4558			−0.816077
$974$	−9.00000	−	5.19615i	−0.288379	−	0.166495i
$975$		0			0
$976$	−12.0000	−	6.92820i	−0.384111	−	0.221766i
$977$			44.0908i			1.41059i	0.708914	+	0.705295i	$0.249185\pi$
$977$			44.0908i			1.41059i	−0.708914	+	0.705295i	$0.750815\pi$
$978$	−21.2132	+	36.7423i	−0.678323	+	1.17489i
$979$		−	20.7846i		−	0.664279i
$980$	1.58579	−	4.18154i	0.0506561	−	0.133574i
$981$			3.46410i			0.110600i
$982$	−29.6985	−	17.1464i	−0.947717	−	0.547165i
$983$		−	56.3383i		−	1.79691i	−0.439064	−	0.898456i	$-0.644690\pi$
$983$		−	56.3383i		−	1.79691i	0.439064	−	0.898456i	$-0.355310\pi$
$984$		0			0
$985$	−8.00000	−	9.79796i	−0.254901	−	0.312189i
$986$		0			0
$987$	25.4558			0.810268
$988$		0			0
$989$		−	10.3923i		−	0.330456i
$990$	1.75736	+	10.8126i	0.0558525	+	0.343646i
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	11.3137	+	19.5959i	0.359211	+	0.622171i
$993$		−	44.0908i		−	1.39918i
$994$	−36.0000	−	20.7846i	−1.14185	−	0.659248i
$995$	5.65685	+	6.92820i	0.179334	+	0.219639i
$996$	−14.0000	−	24.2487i	−0.443607	−	0.768350i
$997$	−50.9117			−1.61239			−0.806195	−	0.591650i	$-0.798477\pi$
$997$	−50.9117			−1.61239			−0.806195	+	0.591650i	$0.798477\pi$
$998$	−21.2132	−	12.2474i	−0.671492	−	0.387686i
$999$	−48.0000			−1.51865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.2.f.a.29.3	yes	4
3.2	odd	2		360.2.d.b.109.2		4
4.3	odd	2		160.2.f.a.49.4		4
5.2	odd	4		200.2.d.e.101.4		4
5.3	odd	4		200.2.d.e.101.1		4
5.4	even	2	inner	40.2.f.a.29.2	yes	4
8.3	odd	2		160.2.f.a.49.1		4
8.5	even	2	inner	40.2.f.a.29.1	✓	4
12.11	even	2		1440.2.d.c.1009.1		4
15.2	even	4		1800.2.k.m.901.1		4
15.8	even	4		1800.2.k.m.901.4		4
15.14	odd	2		360.2.d.b.109.3		4
16.3	odd	4		1280.2.c.k.769.4		4
16.5	even	4		1280.2.c.i.769.3		4
16.11	odd	4		1280.2.c.k.769.1		4
16.13	even	4		1280.2.c.i.769.2		4
20.3	even	4		800.2.d.f.401.3		4
20.7	even	4		800.2.d.f.401.2		4
20.19	odd	2		160.2.f.a.49.2		4
24.5	odd	2		360.2.d.b.109.4		4
24.11	even	2		1440.2.d.c.1009.4		4
40.3	even	4		800.2.d.f.401.1		4
40.13	odd	4		200.2.d.e.101.2		4
40.19	odd	2		160.2.f.a.49.3		4
40.27	even	4		800.2.d.f.401.4		4
40.29	even	2	inner	40.2.f.a.29.4	yes	4
40.37	odd	4		200.2.d.e.101.3		4
60.23	odd	4		7200.2.k.l.3601.1		4
60.47	odd	4		7200.2.k.l.3601.3		4
60.59	even	2		1440.2.d.c.1009.3		4
80.3	even	4		6400.2.a.cm.1.2		4
80.13	odd	4		6400.2.a.co.1.3		4
80.19	odd	4		1280.2.c.k.769.2		4
80.27	even	4		6400.2.a.cm.1.1		4
80.29	even	4		1280.2.c.i.769.4		4
80.37	odd	4		6400.2.a.co.1.4		4
80.43	even	4		6400.2.a.cm.1.4		4
80.53	odd	4		6400.2.a.co.1.1		4
80.59	odd	4		1280.2.c.k.769.3		4
80.67	even	4		6400.2.a.cm.1.3		4
80.69	even	4		1280.2.c.i.769.1		4
80.77	odd	4		6400.2.a.co.1.2		4
120.29	odd	2		360.2.d.b.109.1		4
120.53	even	4		1800.2.k.m.901.3		4
120.59	even	2		1440.2.d.c.1009.2		4
120.77	even	4		1800.2.k.m.901.2		4
120.83	odd	4		7200.2.k.l.3601.2		4
120.107	odd	4		7200.2.k.l.3601.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.f.a.29.1	✓	4	8.5	even	2	inner
40.2.f.a.29.2	yes	4	5.4	even	2	inner
40.2.f.a.29.3	yes	4	1.1	even	1	trivial
40.2.f.a.29.4	yes	4	40.29	even	2	inner
160.2.f.a.49.1		4	8.3	odd	2
160.2.f.a.49.2		4	20.19	odd	2
160.2.f.a.49.3		4	40.19	odd	2
160.2.f.a.49.4		4	4.3	odd	2
200.2.d.e.101.1		4	5.3	odd	4
200.2.d.e.101.2		4	40.13	odd	4
200.2.d.e.101.3		4	40.37	odd	4
200.2.d.e.101.4		4	5.2	odd	4
360.2.d.b.109.1		4	120.29	odd	2
360.2.d.b.109.2		4	3.2	odd	2
360.2.d.b.109.3		4	15.14	odd	2
360.2.d.b.109.4		4	24.5	odd	2
800.2.d.f.401.1		4	40.3	even	4
800.2.d.f.401.2		4	20.7	even	4
800.2.d.f.401.3		4	20.3	even	4
800.2.d.f.401.4		4	40.27	even	4
1280.2.c.i.769.1		4	80.69	even	4
1280.2.c.i.769.2		4	16.13	even	4
1280.2.c.i.769.3		4	16.5	even	4
1280.2.c.i.769.4		4	80.29	even	4
1280.2.c.k.769.1		4	16.11	odd	4
1280.2.c.k.769.2		4	80.19	odd	4
1280.2.c.k.769.3		4	80.59	odd	4
1280.2.c.k.769.4		4	16.3	odd	4
1440.2.d.c.1009.1		4	12.11	even	2
1440.2.d.c.1009.2		4	120.59	even	2
1440.2.d.c.1009.3		4	60.59	even	2
1440.2.d.c.1009.4		4	24.11	even	2
1800.2.k.m.901.1		4	15.2	even	4
1800.2.k.m.901.2		4	120.77	even	4
1800.2.k.m.901.3		4	120.53	even	4
1800.2.k.m.901.4		4	15.8	even	4
6400.2.a.cm.1.1		4	80.27	even	4
6400.2.a.cm.1.2		4	80.3	even	4
6400.2.a.cm.1.3		4	80.67	even	4
6400.2.a.cm.1.4		4	80.43	even	4
6400.2.a.co.1.1		4	80.53	odd	4
6400.2.a.co.1.2		4	80.77	odd	4
6400.2.a.co.1.3		4	80.13	odd	4
6400.2.a.co.1.4		4	80.37	odd	4
7200.2.k.l.3601.1		4	60.23	odd	4
7200.2.k.l.3601.2		4	120.83	odd	4
7200.2.k.l.3601.3		4	60.47	odd	4
7200.2.k.l.3601.4		4	120.107	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	40.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} -1.41421 q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.41421 + 1.73205i) q^{5} +(-1.00000 + 1.73205i) q^{6} +2.44949i q^{7} -2.82843 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} -1.41421 q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.41421 + 1.73205i) q^{5} +(-1.00000 + 1.73205i) q^{6} +2.44949i q^{7} -2.82843 q^{8} -1.00000 q^{9} +(3.12132 - 0.507306i) q^{10} -3.46410i q^{11} +(1.41421 + 2.44949i) q^{12} +(3.00000 + 1.73205i) q^{14} +(-2.00000 - 2.44949i) q^{15} +(-2.00000 + 3.46410i) q^{16} -4.89898i q^{17} +(-0.707107 + 1.22474i) q^{18} +3.46410i q^{19} +(1.58579 - 4.18154i) q^{20} -3.46410i q^{21} +(-4.24264 - 2.44949i) q^{22} -2.44949i q^{23} +4.00000 q^{24} +(-1.00000 + 4.89898i) q^{25} +5.65685 q^{27} +(4.24264 - 2.44949i) q^{28} +(-4.41421 + 0.717439i) q^{30} +4.00000 q^{31} +(2.82843 + 4.89898i) q^{32} +4.89898i q^{33} +(-6.00000 - 3.46410i) q^{34} +(-4.24264 + 3.46410i) q^{35} +(1.00000 + 1.73205i) q^{36} -8.48528 q^{37} +(4.24264 + 2.44949i) q^{38} +(-4.00000 - 4.89898i) q^{40} +(-4.24264 - 2.44949i) q^{42} +4.24264 q^{43} +(-6.00000 + 3.46410i) q^{44} +(-1.41421 - 1.73205i) q^{45} +(-3.00000 - 1.73205i) q^{46} +7.34847i q^{47} +(2.82843 - 4.89898i) q^{48} +1.00000 q^{49} +(5.29289 + 4.68885i) q^{50} +6.92820i q^{51} +5.65685 q^{53} +(4.00000 - 6.92820i) q^{54} +(6.00000 - 4.89898i) q^{55} -6.92820i q^{56} -4.89898i q^{57} -10.3923i q^{59} +(-2.24264 + 5.91359i) q^{60} +3.46410i q^{61} +(2.82843 - 4.89898i) q^{62} -2.44949i q^{63} +8.00000 q^{64} +(6.00000 + 3.46410i) q^{66} -4.24264 q^{67} +(-8.48528 + 4.89898i) q^{68} +3.46410i q^{69} +(1.24264 + 7.64564i) q^{70} -12.0000 q^{71} +2.82843 q^{72} -4.89898i q^{73} +(-6.00000 + 10.3923i) q^{74} +(1.41421 - 6.92820i) q^{75} +(6.00000 - 3.46410i) q^{76} +8.48528 q^{77} -4.00000 q^{79} +(-8.82843 + 1.43488i) q^{80} -5.00000 q^{81} -9.89949 q^{83} +(-6.00000 + 3.46410i) q^{84} +(8.48528 - 6.92820i) q^{85} +(3.00000 - 5.19615i) q^{86} +9.79796i q^{88} +6.00000 q^{89} +(-3.12132 + 0.507306i) q^{90} +(-4.24264 + 2.44949i) q^{92} -5.65685 q^{93} +(9.00000 + 5.19615i) q^{94} +(-6.00000 + 4.89898i) q^{95} +(-4.00000 - 6.92820i) q^{96} +4.89898i q^{97} +(0.707107 - 1.22474i) q^{98} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 4 q^{10} + 12 q^{14} - 8 q^{15} - 8 q^{16} + 12 q^{20} + 16 q^{24} - 4 q^{25} - 12 q^{30} + 16 q^{31} - 24 q^{34} + 4 q^{36} - 16 q^{40} - 24 q^{44} - 12 q^{46} + 4 q^{49} + 24 q^{50} + 16 q^{54} + 24 q^{55} + 8 q^{60} + 32 q^{64} + 24 q^{66} - 12 q^{70} - 48 q^{71} - 24 q^{74} + 24 q^{76} - 16 q^{79} - 24 q^{80} - 20 q^{81} - 24 q^{84} + 12 q^{86} + 24 q^{89} - 4 q^{90} + 36 q^{94} - 24 q^{95} - 16 q^{96}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 4 * q^10 + 12 * q^14 - 8 * q^15 - 8 * q^16 + 12 * q^20 + 16 * q^24 - 4 * q^25 - 12 * q^30 + 16 * q^31 - 24 * q^34 + 4 * q^36 - 16 * q^40 - 24 * q^44 - 12 * q^46 + 4 * q^49 + 24 * q^50 + 16 * q^54 + 24 * q^55 + 8 * q^60 + 32 * q^64 + 24 * q^66 - 12 * q^70 - 48 * q^71 - 24 * q^74 + 24 * q^76 - 16 * q^79 - 24 * q^80 - 20 * q^81 - 24 * q^84 + 12 * q^86 + 24 * q^89 - 4 * q^90 + 36 * q^94 - 24 * q^95 - 16 * q^96

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