LMFDB - Embedded newform 1338.2.e.c.1075.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(931,1338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1338.931"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1075.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1338.1075
Dual form			1338.2.e.c.931.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} -1.00000 q^{27} +1.00000 q^{28} +(0.500000 - 0.866025i) q^{29} -1.00000 q^{30} +(2.00000 + 3.46410i) q^{31} +1.00000 q^{32} +3.00000 q^{33} +4.00000 q^{34} +(-0.500000 + 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.00000 - 3.46410i) q^{37} +(-0.500000 + 0.866025i) q^{40} +(0.500000 + 0.866025i) q^{42} +(-3.00000 - 5.19615i) q^{43} +(1.50000 - 2.59808i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{46} +(-4.00000 + 6.92820i) q^{47} +(0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +(2.00000 + 3.46410i) q^{50} +(2.00000 + 3.46410i) q^{51} +(-5.50000 + 9.52628i) q^{53} -1.00000 q^{54} +(1.50000 + 2.59808i) q^{55} +1.00000 q^{56} +(0.500000 - 0.866025i) q^{58} -3.00000 q^{59} -1.00000 q^{60} +(2.00000 + 3.46410i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(1.00000 + 1.73205i) q^{67} +4.00000 q^{68} +(-3.00000 + 5.19615i) q^{69} +(-0.500000 + 0.866025i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(1.50000 - 2.59808i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(0.500000 + 0.866025i) q^{84} +(-2.00000 + 3.46410i) q^{85} +(-3.00000 - 5.19615i) q^{86} +1.00000 q^{87} +(1.50000 - 2.59808i) q^{88} +(-0.500000 - 0.866025i) q^{90} +(3.00000 + 5.19615i) q^{92} +(-2.00000 + 3.46410i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(0.500000 + 0.866025i) q^{96} +(4.50000 - 7.79423i) q^{97} -6.00000 q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + q^{12} + 2 q^{14} - 2 q^{15} + 2 q^{16} + 8 q^{17} - q^{18} - q^{20} + q^{21} + 3 q^{22} + 6 q^{23}+ \cdots + 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^7 + 2 * q^8 - q^9 - q^10 + 3 * q^11 + q^12 + 2 * q^14 - 2 * q^15 + 2 * q^16 + 8 * q^17 - q^18 - q^20 + q^21 + 3 * q^22 + 6 * q^23 + q^24 + 4 * q^25 - 2 * q^27 + 2 * q^28 + q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 6 * q^33 + 8 * q^34 - q^35 - q^36 + 4 * q^37 - q^40 + q^42 - 6 * q^43 + 3 * q^44 - q^45 + 6 * q^46 - 8 * q^47 + q^48 - 12 * q^49 + 4 * q^50 + 4 * q^51 - 11 * q^53 - 2 * q^54 + 3 * q^55 + 2 * q^56 + q^58 - 6 * q^59 - 2 * q^60 + 4 * q^62 - q^63 + 2 * q^64 + 6 * q^66 + 2 * q^67 + 8 * q^68 - 6 * q^69 - q^70 - 6 * q^71 - q^72 + 14 * q^73 + 4 * q^74 - 4 * q^75 + 3 * q^77 + 11 * q^79 - q^80 - q^81 - 12 * q^83 + q^84 - 4 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 - q^90 + 6 * q^92 - 4 * q^93 - 8 * q^94 + q^96 + 9 * q^97 - 12 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times$.

$n$	$893$	$895$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	1.00000			0.267261
$15$	−1.00000			−0.258199
$16$	1.00000			0.250000
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	−1.00000			−0.192450
$28$	1.00000			0.188982
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$	−1.00000			−0.182574
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	1.00000			0.176777
$33$	3.00000			0.522233
$34$	4.00000			0.685994
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$		0			0
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−6.00000			−0.857143
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	2.00000	+	3.46410i	0.280056	+	0.485071i
$52$		0			0
$53$	−5.50000	+	9.52628i	−0.755483	+	1.30854i	0.189651	+	0.981852i	$0.439264\pi$
$53$	−5.50000	+	9.52628i	−0.755483	+	1.30854i	−0.945134	+	0.326683i	$0.894069\pi$
$54$	−1.00000			−0.136083
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$	1.00000			0.133631
$57$		0			0
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	−3.00000			−0.390567			−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000			−0.390567			−0.195283	+	0.980747i	$0.562563\pi$
$60$	−1.00000			−0.129099
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	4.00000			0.485071
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$		0			0
$77$	1.50000	−	2.59808i	0.170941	−	0.296078i
$78$		0			0
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	−0.370907	−	0.928670i	$-0.620953\pi$
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	0.989705	−	0.143120i	$-0.0457135\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	−2.00000	+	3.46410i	−0.216930	+	0.375735i
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$	1.00000			0.107211
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$		0			0
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	4.50000	−	7.79423i	0.456906	−	0.791384i	−0.541890	−	0.840450i	$-0.682291\pi$
$97$	4.50000	−	7.79423i	0.456906	−	0.791384i	0.998796	+	0.0490655i	$0.0156243\pi$
$98$	−6.00000			−0.606092
$99$	1.50000	+	2.59808i	0.150756	+	0.261116i
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$		0			0
$105$	−1.00000			−0.0975900
$106$	−5.50000	+	9.52628i	−0.534207	+	0.925274i
$107$	5.50000	−	9.52628i	0.531705	−	0.920940i	−0.467610	−	0.883935i	$-0.654885\pi$
$107$	5.50000	−	9.52628i	0.531705	−	0.920940i	0.999315	−	0.0370053i	$-0.0117818\pi$
$108$	−1.00000			−0.0962250
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	4.00000			0.379663
$112$	1.00000			0.0944911
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$		0			0
$115$	−6.00000			−0.559503
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$		0			0
$118$	−3.00000			−0.276172
$119$	4.00000			0.366679
$120$	−1.00000			−0.0912871
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−9.00000			−0.804984
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	0.500000	+	0.866025i	0.0443678	+	0.0768473i	0.887357	−	0.461084i	$-0.152539\pi$
$127$	0.500000	+	0.866025i	0.0443678	+	0.0768473i	−0.842989	+	0.537931i	$0.819206\pi$
$128$	1.00000			0.0883883
$129$	3.00000	−	5.19615i	0.264135	−	0.457496i
$130$		0			0
$131$	−3.50000	−	6.06218i	−0.305796	−	0.529655i	0.671642	−	0.740876i	$-0.265589\pi$
$131$	−3.50000	−	6.06218i	−0.305796	−	0.529655i	−0.977438	+	0.211221i	$0.932256\pi$
$132$	3.00000			0.261116
$133$		0			0
$134$	1.00000	+	1.73205i	0.0863868	+	0.149626i
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	4.00000			0.342997
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	0.820495	−	0.571654i	$-0.193698\pi$
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	−0.905314	+	0.424743i	$0.860365\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$	−8.00000			−0.673722
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.500000	+	0.866025i	0.0415227	+	0.0719195i
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$	−2.00000	+	3.46410i	−0.163299	+	0.282843i
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	−0.279554	−	0.960130i	$-0.590186\pi$
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	0.971274	−	0.237964i	$-0.0764802\pi$
$152$		0			0
$153$	−2.00000	+	3.46410i	−0.161690	+	0.280056i
$154$	1.50000	−	2.59808i	0.120873	−	0.209359i
$155$	−4.00000			−0.321288
$156$		0			0
$157$	4.00000			0.319235			0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000			0.319235			0.159617	+	0.987179i	$0.448974\pi$
$158$	5.50000	−	9.52628i	0.437557	−	0.757870i
$159$	−11.0000			−0.872357
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	3.00000	+	5.19615i	0.236433	+	0.409514i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−18.0000			−1.40987			−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000			−1.40987			−0.704934	+	0.709273i	$0.749024\pi$
$164$		0			0
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$	0.500000	+	0.866025i	0.0385758	+	0.0668153i
$169$	−13.0000			−1.00000
$170$	−2.00000	+	3.46410i	−0.153393	+	0.265684i
$171$		0			0
$172$	−3.00000	−	5.19615i	−0.228748	−	0.396203i
$173$	3.50000	+	6.06218i	0.266100	+	0.460899i	0.967851	−	0.251523i	$-0.0809315\pi$
$173$	3.50000	+	6.06218i	0.266100	+	0.460899i	−0.701751	+	0.712422i	$0.747598\pi$
$174$	1.00000			0.0758098
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−1.50000	−	2.59808i	−0.112747	−	0.195283i
$178$		0			0
$179$	8.50000	−	14.7224i	0.635320	−	1.10041i	−0.351127	−	0.936328i	$-0.614202\pi$
$179$	8.50000	−	14.7224i	0.635320	−	1.10041i	0.986447	−	0.164079i	$-0.0524651\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−8.00000	−	13.8564i	−0.594635	−	1.02994i	−0.993598	−	0.112972i	$-0.963963\pi$
$181$	−8.00000	−	13.8564i	−0.594635	−	1.02994i	0.398963	−	0.916967i	$-0.369370\pi$
$182$		0			0
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$	6.00000	−	10.3923i	0.438763	−	0.759961i
$188$	−4.00000	+	6.92820i	−0.291730	+	0.505291i
$189$	−1.00000			−0.0727393
$190$		0			0
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	4.50000	−	7.79423i	0.323081	−	0.559593i
$195$		0			0
$196$	−6.00000			−0.428571
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	1.50000	+	2.59808i	0.106600	+	0.184637i
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	0.807950	−	0.589252i	$-0.200577\pi$
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	−0.914282	+	0.405079i	$0.867244\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$	−1.50000	−	2.59808i	−0.105540	−	0.182800i
$203$	0.500000	−	0.866025i	0.0350931	−	0.0607831i
$204$	2.00000	+	3.46410i	0.140028	+	0.242536i
$205$		0			0
$206$	−1.00000			−0.0696733
$207$	−6.00000			−0.417029
$208$		0			0
$209$		0			0
$210$	−1.00000			−0.0690066
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	−5.50000	+	9.52628i	−0.377742	+	0.654268i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$	5.50000	−	9.52628i	0.375972	−	0.651203i
$215$	6.00000			0.409197
$216$	−1.00000			−0.0680414
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$	14.0000			0.946032
$220$	1.50000	+	2.59808i	0.101130	+	0.175162i
$221$		0			0
$222$	4.00000			0.268462
$223$	−14.0000	−	5.19615i	−0.937509	−	0.347960i
$223$	−14.0000	−	5.19615i	−0.937509	−	0.347960i
$224$	1.00000			0.0668153
$225$	−4.00000			−0.266667
$226$	−3.00000	−	5.19615i	−0.199557	−	0.345643i
$227$	−24.0000			−1.59294			−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000			−1.59294			−0.796468	+	0.604681i	$0.793301\pi$
$228$		0			0
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$	−6.00000			−0.395628
$231$	3.00000			0.197386
$232$	0.500000	−	0.866025i	0.0328266	−	0.0568574i
$233$	−5.00000	+	8.66025i	−0.327561	+	0.567352i	−0.982027	−	0.188739i	$-0.939560\pi$
$233$	−5.00000	+	8.66025i	−0.327561	+	0.567352i	0.654466	+	0.756091i	$0.272893\pi$
$234$		0			0
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$	−3.00000			−0.195283
$237$	11.0000			0.714527
$238$	4.00000			0.259281
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	−1.00000			−0.0645497
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	3.00000	−	5.19615i	0.191663	−	0.331970i
$246$		0			0
$247$		0			0
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$	−12.0000			−0.760469
$250$	−9.00000			−0.569210
$251$	7.00000			0.441836			0.220918	−	0.975292i	$-0.429095\pi$
$251$	7.00000			0.441836			0.220918	+	0.975292i	$0.429095\pi$
$252$	−0.500000	+	0.866025i	−0.0314970	+	0.0545545i
$253$	18.0000			1.13165
$254$	0.500000	+	0.866025i	0.0313728	+	0.0543393i
$255$	−4.00000			−0.250490
$256$	1.00000			0.0625000
$257$	−8.00000			−0.499026			−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000			−0.499026			−0.249513	+	0.968371i	$0.580271\pi$
$258$	3.00000	−	5.19615i	0.186772	−	0.323498i
$259$	2.00000	−	3.46410i	0.124274	−	0.215249i
$260$		0			0
$261$	0.500000	+	0.866025i	0.0309492	+	0.0536056i
$262$	−3.50000	−	6.06218i	−0.216231	−	0.374523i
$263$	5.00000	−	8.66025i	0.308313	−	0.534014i	−0.669680	−	0.742650i	$-0.733569\pi$
$263$	5.00000	−	8.66025i	0.308313	−	0.534014i	0.977993	+	0.208635i	$0.0669022\pi$
$264$	3.00000			0.184637
$265$	−5.50000	−	9.52628i	−0.337862	−	0.585195i
$266$		0			0
$267$		0			0
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$	0.500000	−	0.866025i	0.0304290	−	0.0527046i
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	1.00000	+	1.73205i	0.0604122	+	0.104637i
$275$	12.0000			0.723627
$276$	−3.00000	+	5.19615i	−0.180579	+	0.312772i
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$	−1.00000	−	1.73205i	−0.0599760	−	0.103882i
$279$	−4.00000			−0.239474
$280$	−0.500000	+	0.866025i	−0.0298807	+	0.0517549i
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	−0.941526	−	0.336939i	$-0.890608\pi$
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	0.762561	+	0.646916i	$0.223942\pi$
$282$	−8.00000			−0.476393
$283$	18.0000			1.06999			0.534994	−	0.844856i	$-0.320314\pi$
$283$	18.0000			1.06999			0.534994	+	0.844856i	$0.320314\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−1.00000			−0.0588235
$290$	0.500000	+	0.866025i	0.0293610	+	0.0508548i
$291$	9.00000			0.527589
$292$	7.00000	−	12.1244i	0.409644	−	0.709524i
$293$	−9.50000	+	16.4545i	−0.554996	+	0.961281i	0.442908	+	0.896567i	$0.353947\pi$
$293$	−9.50000	+	16.4545i	−0.554996	+	0.961281i	−0.997904	+	0.0647140i	$0.979386\pi$
$294$	−3.00000	−	5.19615i	−0.174964	−	0.303046i
$295$	1.50000	−	2.59808i	0.0873334	−	0.151266i
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	−1.50000	+	2.59808i	−0.0870388	+	0.150756i
$298$	−5.00000	+	8.66025i	−0.289642	+	0.501675i
$299$		0			0
$300$	−2.00000	+	3.46410i	−0.115470	+	0.200000i
$301$	−3.00000	−	5.19615i	−0.172917	−	0.299501i
$302$	8.50000	−	14.7224i	0.489120	−	0.847181i
$303$	1.50000	−	2.59808i	0.0861727	−	0.149256i
$304$		0			0
$305$		0			0
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	0.542194	−	0.840254i	$-0.317594\pi$
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	−0.998778	+	0.0494267i	$0.984261\pi$
$308$	1.50000	−	2.59808i	0.0854704	−	0.148039i
$309$	−0.500000	−	0.866025i	−0.0284440	−	0.0492665i
$310$	−4.00000			−0.227185
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	0.129689	+	0.991555i	$0.458602\pi$
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	−0.923556	+	0.383464i	$0.874731\pi$
$312$		0			0
$313$	3.50000	+	6.06218i	0.197832	+	0.342655i	0.947825	−	0.318791i	$-0.103277\pi$
$313$	3.50000	+	6.06218i	0.197832	+	0.342655i	−0.749993	+	0.661445i	$0.769943\pi$
$314$	4.00000			0.225733
$315$	−0.500000	−	0.866025i	−0.0281718	−	0.0487950i
$316$	5.50000	−	9.52628i	0.309399	−	0.535895i
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	−0.905071	−	0.425261i	$-0.860182\pi$
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	0.820822	+	0.571184i	$0.193516\pi$
$318$	−11.0000			−0.616849
$319$	−1.50000	−	2.59808i	−0.0839839	−	0.145464i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	11.0000			0.613960
$322$	3.00000	+	5.19615i	0.167183	+	0.289570i
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−18.0000			−0.996928
$327$	10.0000			0.553001
$328$		0			0
$329$	−4.00000	+	6.92820i	−0.220527	+	0.381964i
$330$	−1.50000	+	2.59808i	−0.0825723	+	0.143019i
$331$	−32.0000			−1.75888			−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−32.0000			−1.75888			−0.879440	+	0.476011i	$0.842082\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$	14.0000			0.766046
$335$	−2.00000			−0.109272
$336$	0.500000	+	0.866025i	0.0272772	+	0.0472456i
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	−0.986960	−	0.160968i	$-0.948538\pi$
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	0.632882	+	0.774248i	$0.281872\pi$
$338$	−13.0000			−0.707107
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$	12.0000			0.649836
$342$		0			0
$343$	−13.0000			−0.701934
$344$	−3.00000	−	5.19615i	−0.161749	−	0.280158i
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$	3.50000	+	6.06218i	0.188161	+	0.325905i
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.844833	−	0.535031i	$-0.820300\pi$
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.0409337	−	0.999162i	$-0.513033\pi$
$348$	1.00000			0.0536056
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	−0.568486	−	0.822693i	$-0.692471\pi$
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	0.996716	+	0.0809766i	$0.0258039\pi$
$350$	2.00000	+	3.46410i	0.106904	+	0.185164i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	−0.989960	−	0.141344i	$-0.954858\pi$
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	0.617388	+	0.786659i	$0.288191\pi$
$354$	−1.50000	−	2.59808i	−0.0797241	−	0.138086i
$355$	6.00000			0.318447
$356$		0			0
$357$	2.00000	+	3.46410i	0.105851	+	0.183340i
$358$	8.50000	−	14.7224i	0.449239	−	0.778105i
$359$	−4.00000			−0.211112			−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000			−0.211112			−0.105556	+	0.994413i	$0.533662\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	−8.00000	−	13.8564i	−0.420471	−	0.728277i
$363$	−1.00000	+	1.73205i	−0.0524864	+	0.0909091i
$364$		0			0
$365$	7.00000	+	12.1244i	0.366397	+	0.634618i
$366$		0			0
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$	2.00000	+	3.46410i	0.103975	+	0.180090i
$371$	−5.50000	+	9.52628i	−0.285546	+	0.494580i
$372$	−2.00000	+	3.46410i	−0.103695	+	0.179605i
$373$	9.00000	−	15.5885i	0.466002	−	0.807140i	−0.533244	−	0.845962i	$-0.679027\pi$
$373$	9.00000	−	15.5885i	0.466002	−	0.807140i	0.999246	+	0.0388219i	$0.0123605\pi$
$374$	6.00000	−	10.3923i	0.310253	−	0.537373i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$		0			0
$378$	−1.00000			−0.0514344
$379$	−17.0000	−	29.4449i	−0.873231	−	1.51248i	−0.858635	−	0.512588i	$-0.828687\pi$
$379$	−17.0000	−	29.4449i	−0.873231	−	1.51248i	−0.0145964	−	0.999893i	$-0.504646\pi$
$380$		0			0
$381$	−0.500000	+	0.866025i	−0.0256158	+	0.0443678i
$382$	−4.00000			−0.204658
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	−0.949938	−	0.312437i	$-0.898855\pi$
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	0.745548	+	0.666452i	$0.232188\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	1.50000	+	2.59808i	0.0764471	+	0.132410i
$386$	5.00000			0.254493
$387$	6.00000			0.304997
$388$	4.50000	−	7.79423i	0.228453	−	0.395692i
$389$	−12.5000	+	21.6506i	−0.633775	+	1.09773i	0.352998	+	0.935624i	$0.385162\pi$
$389$	−12.5000	+	21.6506i	−0.633775	+	1.09773i	−0.986773	+	0.162107i	$0.948171\pi$
$390$		0			0
$391$	12.0000	+	20.7846i	0.606866	+	1.05112i
$392$	−6.00000			−0.303046
$393$	3.50000	−	6.06218i	0.176552	−	0.305796i
$394$	2.00000			0.100759
$395$	5.50000	+	9.52628i	0.276735	+	0.479319i
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−8.00000			−0.401508			−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000			−0.401508			−0.200754	+	0.979642i	$0.564339\pi$
$398$	−1.50000	−	2.59808i	−0.0751882	−	0.130230i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	10.0000	+	17.3205i	0.499376	+	0.864945i	1.00000		0.000720188i	$-0.000229243\pi$
$401$	10.0000	+	17.3205i	0.499376	+	0.864945i	−0.500624	+	0.865665i	$0.666896\pi$
$402$	−1.00000	+	1.73205i	−0.0498755	+	0.0863868i
$403$		0			0
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$	1.00000			0.0496904
$406$	0.500000	−	0.866025i	0.0248146	−	0.0429801i
$407$	−6.00000	−	10.3923i	−0.297409	−	0.515127i
$408$	2.00000	+	3.46410i	0.0990148	+	0.171499i
$409$	−3.50000	+	6.06218i	−0.173064	+	0.299755i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−3.50000	+	6.06218i	−0.173064	+	0.299755i	0.766426	+	0.642333i	$0.222033\pi$
$410$		0			0
$411$	−1.00000	+	1.73205i	−0.0493264	+	0.0854358i
$412$	−1.00000			−0.0492665
$413$	−3.00000			−0.147620
$414$	−6.00000			−0.294884
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$		0			0
$417$	1.00000	−	1.73205i	0.0489702	−	0.0848189i
$418$		0			0
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$	−1.00000			−0.0487950
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	0.946883	−	0.321577i	$-0.104213\pi$
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	−0.751935	+	0.659237i	$0.770879\pi$
$422$	−10.0000	−	17.3205i	−0.486792	−	0.843149i
$423$	−4.00000	−	6.92820i	−0.194487	−	0.336861i
$424$	−5.50000	+	9.52628i	−0.267104	+	0.462637i
$425$	8.00000	+	13.8564i	0.388057	+	0.672134i
$426$	3.00000	−	5.19615i	0.145350	−	0.251754i
$427$		0			0
$428$	5.50000	−	9.52628i	0.265853	−	0.460470i
$429$		0			0
$430$	6.00000			0.289346
$431$	−2.00000			−0.0963366			−0.0481683	−	0.998839i	$-0.515338\pi$
$431$	−2.00000			−0.0963366			−0.0481683	+	0.998839i	$0.515338\pi$
$432$	−1.00000			−0.0481125
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$	2.00000	+	3.46410i	0.0960031	+	0.166282i
$435$	−0.500000	+	0.866025i	−0.0239732	+	0.0415227i
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$		0			0
$438$	14.0000			0.668946
$439$	−15.0000			−0.715911			−0.357955	−	0.933739i	$-0.616526\pi$
$439$	−15.0000			−0.715911			−0.357955	+	0.933739i	$0.616526\pi$
$440$	1.50000	+	2.59808i	0.0715097	+	0.123858i
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$		0			0
$443$	−14.5000	−	25.1147i	−0.688916	−	1.19324i	−0.972189	−	0.234198i	$-0.924754\pi$
$443$	−14.5000	−	25.1147i	−0.688916	−	1.19324i	0.283273	−	0.959039i	$-0.408580\pi$
$444$	4.00000			0.189832
$445$		0			0
$446$	−14.0000	−	5.19615i	−0.662919	−	0.246045i
$447$	−10.0000			−0.472984
$448$	1.00000			0.0472456
$449$	18.0000	+	31.1769i	0.849473	+	1.47133i	0.881680	+	0.471848i	$0.156413\pi$
$449$	18.0000	+	31.1769i	0.849473	+	1.47133i	−0.0322072	+	0.999481i	$0.510254\pi$
$450$	−4.00000			−0.188562
$451$		0			0
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	17.0000			0.798730
$454$	−24.0000			−1.12638
$455$		0			0
$456$		0			0
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	−0.575036	−	0.818128i	$-0.695012\pi$
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	0.996038	+	0.0889312i	$0.0283451\pi$
$458$	7.00000	+	12.1244i	0.327089	+	0.566534i
$459$	−4.00000			−0.186704
$460$	−6.00000			−0.279751
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$	3.00000			0.139573
$463$	23.0000			1.06890			0.534450	−	0.845200i	$-0.320519\pi$
$463$	23.0000			1.06890			0.534450	+	0.845200i	$0.320519\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$	−5.00000	+	8.66025i	−0.231621	+	0.401179i
$467$	10.5000	+	18.1865i	0.485882	+	0.841572i	0.999868	−	0.0162260i	$-0.00516512\pi$
$467$	10.5000	+	18.1865i	0.485882	+	0.841572i	−0.513986	+	0.857798i	$0.671832\pi$
$468$		0			0
$469$	1.00000	+	1.73205i	0.0461757	+	0.0799787i
$470$	−4.00000	−	6.92820i	−0.184506	−	0.319574i
$471$	2.00000	+	3.46410i	0.0921551	+	0.159617i
$472$	−3.00000			−0.138086
$473$	−18.0000			−0.827641
$474$	11.0000			0.505247
$475$		0			0
$476$	4.00000			0.183340
$477$	−5.50000	−	9.52628i	−0.251828	−	0.436178i
$478$	−12.0000			−0.548867
$479$	−24.0000			−1.09659			−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000			−1.09659			−0.548294	+	0.836286i	$0.684723\pi$
$480$	−1.00000			−0.0456435
$481$		0			0
$482$	−7.00000	+	12.1244i	−0.318841	+	0.552249i
$483$	−3.00000	+	5.19615i	−0.136505	+	0.236433i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	4.50000	+	7.79423i	0.204334	+	0.353918i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	5.00000			0.226572			0.113286	−	0.993562i	$-0.463862\pi$
$487$	5.00000			0.226572			0.113286	+	0.993562i	$0.463862\pi$
$488$		0			0
$489$	−9.00000	−	15.5885i	−0.406994	−	0.704934i
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	−10.0000	−	17.3205i	−0.451294	−	0.781664i	0.547173	−	0.837020i	$-0.315704\pi$
$491$	−10.0000	−	17.3205i	−0.451294	−	0.781664i	−0.998467	+	0.0553560i	$0.982371\pi$
$492$		0			0
$493$	2.00000	−	3.46410i	0.0900755	−	0.156015i
$494$		0			0
$495$	−3.00000			−0.134840
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$	−12.0000			−0.537733
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$	−9.00000			−0.402492
$501$	7.00000	+	12.1244i	0.312737	+	0.541676i
$502$	7.00000			0.312425
$503$	1.00000	−	1.73205i	0.0445878	−	0.0772283i	−0.842870	−	0.538117i	$-0.819136\pi$
$503$	1.00000	−	1.73205i	0.0445878	−	0.0772283i	0.887458	+	0.460889i	$0.152469\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	3.00000			0.133498
$506$	18.0000			0.800198
$507$	−6.50000	−	11.2583i	−0.288675	−	0.500000i
$508$	0.500000	+	0.866025i	0.0221839	+	0.0384237i
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$	−4.00000			−0.177123
$511$	7.00000	−	12.1244i	0.309662	−	0.536350i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−8.00000			−0.352865
$515$	0.500000	−	0.866025i	0.0220326	−	0.0381616i
$516$	3.00000	−	5.19615i	0.132068	−	0.228748i
$517$	12.0000	+	20.7846i	0.527759	+	0.914106i
$518$	2.00000	−	3.46410i	0.0878750	−	0.152204i
$519$	−3.50000	+	6.06218i	−0.153633	+	0.266100i
$520$		0			0
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$	0.500000	+	0.866025i	0.0218844	+	0.0379049i
$523$	−18.0000	+	31.1769i	−0.787085	+	1.36327i	0.140660	+	0.990058i	$0.455077\pi$
$523$	−18.0000	+	31.1769i	−0.787085	+	1.36327i	−0.927746	+	0.373213i	$0.878256\pi$
$524$	−3.50000	−	6.06218i	−0.152898	−	0.264827i
$525$	−2.00000	+	3.46410i	−0.0872872	+	0.151186i
$526$	5.00000	−	8.66025i	0.218010	−	0.377605i
$527$	8.00000	+	13.8564i	0.348485	+	0.603595i
$528$	3.00000			0.130558
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−5.50000	−	9.52628i	−0.238905	−	0.413795i
$531$	1.50000	−	2.59808i	0.0650945	−	0.112747i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	5.50000	+	9.52628i	0.237786	+	0.411857i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	17.0000			0.733604
$538$	−5.00000	−	8.66025i	−0.215565	−	0.373370i
$539$	−9.00000	+	15.5885i	−0.387657	+	0.671442i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$		0			0
$543$	8.00000	−	13.8564i	0.343313	−	0.594635i
$544$	4.00000			0.171499
$545$	5.00000	+	8.66025i	0.214176	+	0.370965i
$546$		0			0
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	0.938779	−	0.344519i	$-0.111958\pi$
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	−0.767752	+	0.640747i	$0.778625\pi$
$548$	1.00000	+	1.73205i	0.0427179	+	0.0739895i
$549$		0			0
$550$	12.0000			0.511682
$551$		0			0
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	5.50000	−	9.52628i	0.233884	−	0.405099i
$554$	26.0000			1.10463
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	−2.00000			−0.0847427			−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000			−0.0847427			−0.0423714	+	0.999102i	$0.513491\pi$
$558$	−4.00000			−0.169334
$559$		0			0
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$	12.0000			0.506640
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	0.404198	+	0.914671i	$0.367551\pi$
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	−0.994228	+	0.107290i	$0.965783\pi$
$564$	−8.00000			−0.336861
$565$	6.00000			0.252422
$566$	18.0000			0.756596
$567$	−0.500000	−	0.866025i	−0.0209980	−	0.0363696i
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$		0			0
$573$	−2.00000	−	3.46410i	−0.0835512	−	0.144715i
$574$		0			0
$575$	−12.0000	+	20.7846i	−0.500435	+	0.866778i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−1.50000	−	2.59808i	−0.0624458	−	0.108159i	0.833112	−	0.553104i	$-0.186557\pi$
$577$	−1.50000	−	2.59808i	−0.0624458	−	0.108159i	−0.895558	+	0.444945i	$0.853223\pi$
$578$	−1.00000			−0.0415945
$579$	2.50000	+	4.33013i	0.103896	+	0.179954i
$580$	0.500000	+	0.866025i	0.0207614	+	0.0359597i
$581$	−6.00000	+	10.3923i	−0.248922	+	0.431145i
$582$	9.00000			0.373062
$583$	16.5000	+	28.5788i	0.683360	+	1.18361i
$584$	7.00000	−	12.1244i	0.289662	−	0.501709i
$585$		0			0
$586$	−9.50000	+	16.4545i	−0.392441	+	0.679728i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$	−3.00000	−	5.19615i	−0.123718	−	0.214286i
$589$		0			0
$590$	1.50000	−	2.59808i	0.0617540	−	0.106961i
$591$	1.00000	+	1.73205i	0.0411345	+	0.0712470i
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	0.973202	−	0.229953i	$-0.0738573\pi$
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	−0.685746	+	0.727841i	$0.740524\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$	−2.00000	+	3.46410i	−0.0819920	+	0.142014i
$596$	−5.00000	+	8.66025i	−0.204808	+	0.354738i
$597$	1.50000	−	2.59808i	0.0613909	−	0.106332i
$598$		0			0
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$	−2.00000	+	3.46410i	−0.0816497	+	0.141421i
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$	−3.00000	−	5.19615i	−0.122271	−	0.211779i
$603$	−2.00000			−0.0814463
$604$	8.50000	−	14.7224i	0.345860	−	0.599047i
$605$	−2.00000			−0.0813116
$606$	1.50000	−	2.59808i	0.0609333	−	0.105540i
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	0.928272	−	0.371901i	$-0.121294\pi$
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	−0.786212	+	0.617957i	$0.787961\pi$
$608$		0			0
$609$	1.00000			0.0405220
$610$		0			0
$611$		0			0
$612$	−2.00000	+	3.46410i	−0.0808452	+	0.140028i
$613$	−30.0000			−1.21169			−0.605844	−	0.795583i	$-0.707165\pi$
$613$	−30.0000			−1.21169			−0.605844	+	0.795583i	$0.707165\pi$
$614$	−8.00000	−	13.8564i	−0.322854	−	0.559199i
$615$		0			0
$616$	1.50000	−	2.59808i	0.0604367	−	0.104679i
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$	−0.500000	−	0.866025i	−0.0201129	−	0.0348367i
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$	−4.00000			−0.160644
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$	−14.0000	+	24.2487i	−0.561349	+	0.972285i
$623$		0			0
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	3.50000	+	6.06218i	0.139888	+	0.242293i
$627$		0			0
$628$	4.00000			0.159617
$629$	8.00000	−	13.8564i	0.318981	−	0.552491i
$630$	−0.500000	−	0.866025i	−0.0199205	−	0.0345033i
$631$	7.50000	+	12.9904i	0.298570	+	0.517139i	0.975809	−	0.218624i	$-0.0701569\pi$
$631$	7.50000	+	12.9904i	0.298570	+	0.517139i	−0.677239	+	0.735763i	$0.736824\pi$
$632$	5.50000	−	9.52628i	0.218778	−	0.378935i
$633$	10.0000	−	17.3205i	0.397464	−	0.688428i
$634$	−1.50000	+	2.59808i	−0.0595726	+	0.103183i
$635$	−1.00000			−0.0396838
$636$	−11.0000			−0.436178
$637$		0			0
$638$	−1.50000	−	2.59808i	−0.0593856	−	0.102859i
$639$	6.00000			0.237356
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	12.0000			0.473972			0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000			0.473972			0.236986	+	0.971513i	$0.423841\pi$
$642$	11.0000			0.434135
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$	3.00000	+	5.19615i	0.118125	+	0.204598i
$646$		0			0
$647$	7.00000	−	12.1244i	0.275198	−	0.476658i	−0.694987	−	0.719023i	$-0.744590\pi$
$647$	7.00000	−	12.1244i	0.275198	−	0.476658i	0.970185	+	0.242365i	$0.0779231\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$		0			0
$651$	−2.00000	+	3.46410i	−0.0783862	+	0.135769i
$652$	−18.0000			−0.704934
$653$	17.0000			0.665261			0.332631	−	0.943057i	$-0.392064\pi$
$653$	17.0000			0.665261			0.332631	+	0.943057i	$0.392064\pi$
$654$	10.0000			0.391031
$655$	7.00000			0.273513
$656$		0			0
$657$	7.00000	+	12.1244i	0.273096	+	0.473016i
$658$	−4.00000	+	6.92820i	−0.155936	+	0.270089i
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$	−1.50000	+	2.59808i	−0.0583874	+	0.101130i
$661$	−10.0000			−0.388955			−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000			−0.388955			−0.194477	+	0.980907i	$0.562301\pi$
$662$	−32.0000			−1.24372
$663$		0			0
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$		0			0
$666$	2.00000	+	3.46410i	0.0774984	+	0.134231i
$667$	6.00000			0.232321
$668$	14.0000			0.541676
$669$	−2.50000	−	14.7224i	−0.0966556	−	0.569202i
$670$	−2.00000			−0.0772667
$671$		0			0
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	9.00000			0.346925			0.173462	−	0.984841i	$-0.444505\pi$
$673$	9.00000			0.346925			0.173462	+	0.984841i	$0.444505\pi$
$674$	−6.50000	+	11.2583i	−0.250371	+	0.433655i
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$	−13.0000			−0.500000
$677$	41.0000			1.57576			0.787879	−	0.615830i	$-0.211179\pi$
$677$	41.0000			1.57576			0.787879	+	0.615830i	$0.211179\pi$
$678$	3.00000	−	5.19615i	0.115214	−	0.199557i
$679$	4.50000	−	7.79423i	0.172694	−	0.299115i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$	−12.0000	−	20.7846i	−0.459841	−	0.796468i
$682$	12.0000			0.459504
$683$	−9.00000			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$	−13.0000			−0.496342
$687$	−7.00000	+	12.1244i	−0.267067	+	0.462573i
$688$	−3.00000	−	5.19615i	−0.114374	−	0.198101i
$689$		0			0
$690$	−3.00000	−	5.19615i	−0.114208	−	0.197814i
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	−0.995785	−	0.0917209i	$-0.970763\pi$
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	0.577325	+	0.816514i	$0.304097\pi$
$692$	3.50000	+	6.06218i	0.133050	+	0.230449i
$693$	1.50000	+	2.59808i	0.0569803	+	0.0986928i
$694$	−16.5000	−	28.5788i	−0.626331	−	1.08484i
$695$	2.00000			0.0758643
$696$	1.00000			0.0379049
$697$		0			0
$698$	8.00000	−	13.8564i	0.302804	−	0.524473i
$699$	−10.0000			−0.378235
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	−5.00000			−0.188847			−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$		0			0
$703$		0			0
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$	4.00000	−	6.92820i	0.150649	−	0.260931i
$706$	−7.00000	+	12.1244i	−0.263448	+	0.456306i
$707$	−1.50000	−	2.59808i	−0.0564133	−	0.0977107i
$708$	−1.50000	−	2.59808i	−0.0563735	−	0.0976417i
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$	6.00000			0.225176
$711$	5.50000	+	9.52628i	0.206266	+	0.357263i
$712$		0			0
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$	2.00000	+	3.46410i	0.0748481	+	0.129641i
$715$		0			0
$716$	8.50000	−	14.7224i	0.317660	−	0.550203i
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$	−4.00000			−0.149279
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	−1.00000			−0.0372419
$722$	9.50000	−	16.4545i	0.353553	−	0.612372i
$723$	−14.0000			−0.520666
$724$	−8.00000	−	13.8564i	−0.297318	−	0.514969i
$725$	4.00000			0.148556
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	−0.678676	−	0.734438i	$-0.737446\pi$
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	0.975380	+	0.220532i	$0.0707793\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	7.00000	+	12.1244i	0.259082	+	0.448743i
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	34.0000			1.25582			0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000			1.25582			0.627909	+	0.778287i	$0.283911\pi$
$734$		0			0
$735$	6.00000			0.221313
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	6.00000			0.221013
$738$		0			0
$739$	12.0000	−	20.7846i	0.441427	−	0.764574i	−0.556369	−	0.830936i	$-0.687806\pi$
$739$	12.0000	−	20.7846i	0.441427	−	0.764574i	0.997796	+	0.0663614i	$0.0211390\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$	−5.50000	+	9.52628i	−0.201911	+	0.349721i
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$	−5.00000	−	8.66025i	−0.183186	−	0.317287i
$746$	9.00000	−	15.5885i	0.329513	−	0.570734i
$747$	−6.00000	−	10.3923i	−0.219529	−	0.380235i
$748$	6.00000	−	10.3923i	0.219382	−	0.379980i
$749$	5.50000	−	9.52628i	0.200966	−	0.348083i
$750$	−4.50000	−	7.79423i	−0.164317	−	0.284605i
$751$	17.0000			0.620339			0.310169	−	0.950681i	$-0.399614\pi$
$751$	17.0000			0.620339			0.310169	+	0.950681i	$0.399614\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$	3.50000	+	6.06218i	0.127547	+	0.220918i
$754$		0			0
$755$	8.50000	+	14.7224i	0.309347	+	0.535804i
$756$	−1.00000			−0.0363696
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	−0.593899	−	0.804539i	$-0.702412\pi$
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	0.993701	+	0.112062i	$0.0357456\pi$
$758$	−17.0000	−	29.4449i	−0.617468	−	1.06949i
$759$	9.00000	+	15.5885i	0.326679	+	0.565825i
$760$		0			0
$761$	−7.00000	−	12.1244i	−0.253750	−	0.439508i	0.710805	−	0.703389i	$-0.248331\pi$
$761$	−7.00000	−	12.1244i	−0.253750	−	0.439508i	−0.964555	+	0.263881i	$0.914997\pi$
$762$	−0.500000	+	0.866025i	−0.0181131	+	0.0313728i
$763$	5.00000	−	8.66025i	0.181012	−	0.313522i
$764$	−4.00000			−0.144715
$765$	−2.00000	−	3.46410i	−0.0723102	−	0.125245i
$766$	−4.00000	+	6.92820i	−0.144526	+	0.250326i
$767$		0			0
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	27.0000	+	46.7654i	0.973645	+	1.68640i	0.684336	+	0.729167i	$0.260092\pi$
$769$	27.0000	+	46.7654i	0.973645	+	1.68640i	0.289309	+	0.957236i	$0.406575\pi$
$770$	1.50000	+	2.59808i	0.0540562	+	0.0936282i
$771$	−4.00000	−	6.92820i	−0.144056	−	0.249513i
$772$	5.00000			0.179954
$773$	39.0000			1.40273			0.701366	−	0.712801i	$-0.252574\pi$
$773$	39.0000			1.40273			0.701366	+	0.712801i	$0.252574\pi$
$774$	6.00000			0.215666
$775$	−8.00000	+	13.8564i	−0.287368	+	0.497737i
$776$	4.50000	−	7.79423i	0.161541	−	0.279797i
$777$	4.00000			0.143499
$778$	−12.5000	+	21.6506i	−0.448147	+	0.776213i
$779$		0			0
$780$		0			0
$781$	−18.0000			−0.644091
$782$	12.0000	+	20.7846i	0.429119	+	0.743256i
$783$	−0.500000	+	0.866025i	−0.0178685	+	0.0309492i
$784$	−6.00000			−0.214286
$785$	−2.00000	+	3.46410i	−0.0713831	+	0.123639i
$786$	3.50000	−	6.06218i	0.124841	−	0.216231i
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$	2.00000			0.0712470
$789$	10.0000			0.356009
$790$	5.50000	+	9.52628i	0.195681	+	0.338930i
$791$	−3.00000	−	5.19615i	−0.106668	−	0.184754i
$792$	1.50000	+	2.59808i	0.0533002	+	0.0923186i
$793$		0			0
$794$	−8.00000			−0.283909
$795$	5.50000	−	9.52628i	0.195065	−	0.337862i
$796$	−1.50000	−	2.59808i	−0.0531661	−	0.0920864i
$797$	21.0000			0.743858			0.371929	−	0.928261i	$-0.378696\pi$
$797$	21.0000			0.743858			0.371929	+	0.928261i	$0.378696\pi$
$798$		0			0
$799$	−16.0000	+	27.7128i	−0.566039	+	0.980409i
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$		0			0
$802$	10.0000	+	17.3205i	0.353112	+	0.611608i
$803$	−21.0000	−	36.3731i	−0.741074	−	1.28358i
$804$	−1.00000	+	1.73205i	−0.0352673	+	0.0610847i
$805$	−6.00000			−0.211472
$806$		0			0
$807$	5.00000	−	8.66025i	0.176008	−	0.304855i
$808$	−1.50000	−	2.59808i	−0.0527698	−	0.0914000i
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	−0.979739	−	0.200279i	$-0.935815\pi$
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	0.663316	+	0.748340i	$0.269149\pi$
$810$	1.00000			0.0351364
$811$	13.0000	+	22.5167i	0.456492	+	0.790667i	0.998773	−	0.0495304i	$-0.0157725\pi$
$811$	13.0000	+	22.5167i	0.456492	+	0.790667i	−0.542281	+	0.840197i	$0.682439\pi$
$812$	0.500000	−	0.866025i	0.0175466	−	0.0303915i
$813$		0			0
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	9.00000	−	15.5885i	0.315256	−	0.546040i
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$		0			0
$818$	−3.50000	+	6.06218i	−0.122375	+	0.211959i
$819$		0			0
$820$		0			0
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$	−1.00000	+	1.73205i	−0.0348790	+	0.0604122i
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$	−1.00000			−0.0348367
$825$	6.00000	+	10.3923i	0.208893	+	0.361814i
$826$	−3.00000			−0.104383
$827$	0.500000	−	0.866025i	0.0173867	−	0.0301147i	−0.857201	−	0.514982i	$-0.827799\pi$
$827$	0.500000	−	0.866025i	0.0173867	−	0.0301147i	0.874588	+	0.484867i	$0.161132\pi$
$828$	−6.00000			−0.208514
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	−0.513635	−	0.858009i	$-0.671701\pi$
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	0.999875	+	0.0158163i	$0.00503471\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$	13.0000	+	22.5167i	0.450965	+	0.781094i
$832$		0			0
$833$	−24.0000			−0.831551
$834$	1.00000	−	1.73205i	0.0346272	−	0.0599760i
$835$	−7.00000	+	12.1244i	−0.242245	+	0.419581i
$836$		0			0
$837$	−2.00000	−	3.46410i	−0.0691301	−	0.119737i
$838$	28.0000			0.967244
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	−0.950813	−	0.309764i	$-0.899750\pi$
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	0.743670	+	0.668546i	$0.233083\pi$
$840$	−1.00000			−0.0345033
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	4.00000	+	6.92820i	0.137849	+	0.238762i
$843$	−6.00000			−0.206651
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	6.50000	−	11.2583i	0.223607	−	0.387298i
$846$	−4.00000	−	6.92820i	−0.137523	−	0.238197i
$847$	1.00000	+	1.73205i	0.0343604	+	0.0595140i
$848$	−5.50000	+	9.52628i	−0.188871	+	0.327134i
$849$	9.00000	+	15.5885i	0.308879	+	0.534994i
$850$	8.00000	+	13.8564i	0.274398	+	0.475271i
$851$	24.0000			0.822709
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	13.0000	+	22.5167i	0.445112	+	0.770956i	0.998060	−	0.0622597i	$-0.0198307\pi$
$853$	13.0000	+	22.5167i	0.445112	+	0.770956i	−0.552948	+	0.833215i	$0.686497\pi$
$854$		0			0
$855$		0			0
$856$	5.50000	−	9.52628i	0.187986	−	0.325602i
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$		0			0
$859$	−22.0000			−0.750630			−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000			−0.750630			−0.375315	+	0.926897i	$0.622466\pi$
$860$	6.00000			0.204598
$861$		0			0
$862$	−2.00000			−0.0681203
$863$	−19.0000	+	32.9090i	−0.646768	+	1.12023i	0.337123	+	0.941461i	$0.390546\pi$
$863$	−19.0000	+	32.9090i	−0.646768	+	1.12023i	−0.983890	+	0.178774i	$0.942787\pi$
$864$	−1.00000			−0.0340207
$865$	−7.00000			−0.238007
$866$	−7.00000			−0.237870
$867$	−0.500000	−	0.866025i	−0.0169809	−	0.0294118i
$868$	2.00000	+	3.46410i	0.0678844	+	0.117579i
$869$	−16.5000	−	28.5788i	−0.559724	−	0.969471i
$870$	−0.500000	+	0.866025i	−0.0169516	+	0.0293610i
$871$		0			0
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$	4.50000	+	7.79423i	0.152302	+	0.263795i
$874$		0			0
$875$	−9.00000			−0.304256
$876$	14.0000			0.473016
$877$	−4.00000			−0.135070			−0.0675352	−	0.997717i	$-0.521513\pi$
$877$	−4.00000			−0.135070			−0.0675352	+	0.997717i	$0.521513\pi$
$878$	−15.0000			−0.506225
$879$	−19.0000			−0.640854
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	−27.0000	+	46.7654i	−0.909653	+	1.57557i	−0.0951067	+	0.995467i	$0.530319\pi$
$881$	−27.0000	+	46.7654i	−0.909653	+	1.57557i	−0.814546	+	0.580098i	$0.803014\pi$
$882$	3.00000	−	5.19615i	0.101015	−	0.174964i
$883$	−10.0000	+	17.3205i	−0.336527	+	0.582882i	−0.983777	−	0.179396i	$-0.942586\pi$
$883$	−10.0000	+	17.3205i	−0.336527	+	0.582882i	0.647250	+	0.762278i	$0.275919\pi$
$884$		0			0
$885$	3.00000			0.100844
$886$	−14.5000	−	25.1147i	−0.487137	−	0.843746i
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	−0.109881	−	0.993945i	$-0.535047\pi$
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	0.915722	−	0.401813i	$-0.131620\pi$
$888$	4.00000			0.134231
$889$	0.500000	+	0.866025i	0.0167695	+	0.0290456i
$890$		0			0
$891$	−3.00000			−0.100504
$892$	−14.0000	−	5.19615i	−0.468755	−	0.173980i
$893$		0			0
$894$	−10.0000			−0.334450
$895$	8.50000	+	14.7224i	0.284124	+	0.492117i
$896$	1.00000			0.0334077
$897$		0			0
$898$	18.0000	+	31.1769i	0.600668	+	1.04039i
$899$	4.00000			0.133407
$900$	−4.00000			−0.133333
$901$	−22.0000	+	38.1051i	−0.732926	+	1.26947i
$902$		0			0
$903$	3.00000	−	5.19615i	0.0998337	−	0.172917i
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	16.0000			0.531858
$906$	17.0000			0.564787
$907$	12.0000			0.398453			0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000			0.398453			0.199227	+	0.979953i	$0.436157\pi$
$908$	−24.0000			−0.796468
$909$	3.00000			0.0995037
$910$		0			0
$911$	11.0000	+	19.0526i	0.364446	+	0.631239i	0.988687	−	0.149992i	$-0.0479250\pi$
$911$	11.0000	+	19.0526i	0.364446	+	0.631239i	−0.624241	+	0.781232i	$0.714592\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	9.00000	−	15.5885i	0.297694	−	0.515620i
$915$		0			0
$916$	7.00000	+	12.1244i	0.231287	+	0.400600i
$917$	−3.50000	−	6.06218i	−0.115580	−	0.200191i
$918$	−4.00000			−0.132020
$919$	−39.0000			−1.28649			−0.643246	−	0.765660i	$-0.722413\pi$
$919$	−39.0000			−1.28649			−0.643246	+	0.765660i	$0.722413\pi$
$920$	−6.00000			−0.197814
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$	14.0000			0.461065
$923$		0			0
$924$	3.00000			0.0986928
$925$	16.0000			0.526077
$926$	23.0000			0.755827
$927$	0.500000	−	0.866025i	0.0164222	−	0.0284440i
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	10.0000	−	17.3205i	0.328089	−	0.568267i	−0.654043	−	0.756457i	$-0.726929\pi$
$929$	10.0000	−	17.3205i	0.328089	−	0.568267i	0.982133	+	0.188190i	$0.0602620\pi$
$930$	−2.00000	−	3.46410i	−0.0655826	−	0.113592i
$931$		0			0
$932$	−5.00000	+	8.66025i	−0.163780	+	0.283676i
$933$	−28.0000			−0.916679
$934$	10.5000	+	18.1865i	0.343570	+	0.595082i
$935$	6.00000	+	10.3923i	0.196221	+	0.339865i
$936$		0			0
$937$	2.50000	+	4.33013i	0.0816714	+	0.141459i	0.903968	−	0.427600i	$-0.140641\pi$
$937$	2.50000	+	4.33013i	0.0816714	+	0.141459i	−0.822297	+	0.569059i	$0.807308\pi$
$938$	1.00000	+	1.73205i	0.0326512	+	0.0565535i
$939$	−3.50000	+	6.06218i	−0.114218	+	0.197832i
$940$	−4.00000	−	6.92820i	−0.130466	−	0.225973i
$941$	−3.00000			−0.0977972			−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000			−0.0977972			−0.0488986	+	0.998804i	$0.515571\pi$
$942$	2.00000	+	3.46410i	0.0651635	+	0.112867i
$943$		0			0
$944$	−3.00000			−0.0976417
$945$	0.500000	−	0.866025i	0.0162650	−	0.0281718i
$946$	−18.0000			−0.585230
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.789741	−	0.613441i	$-0.789785\pi$
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.136385	−	0.990656i	$-0.543548\pi$
$948$	11.0000			0.357263
$949$		0			0
$950$		0			0
$951$	−3.00000			−0.0972817
$952$	4.00000			0.129641
$953$	18.0000	+	31.1769i	0.583077	+	1.00992i	0.995112	+	0.0987513i	$0.0314848\pi$
$953$	18.0000	+	31.1769i	0.583077	+	1.00992i	−0.412035	+	0.911168i	$0.635182\pi$
$954$	−5.50000	−	9.52628i	−0.178069	−	0.308425i
$955$	2.00000	−	3.46410i	0.0647185	−	0.112096i
$956$	−12.0000			−0.388108
$957$	1.50000	−	2.59808i	0.0484881	−	0.0839839i
$958$	−24.0000			−0.775405
$959$	1.00000	+	1.73205i	0.0322917	+	0.0559308i
$960$	−1.00000			−0.0322749
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	5.50000	+	9.52628i	0.177235	+	0.306980i
$964$	−7.00000	+	12.1244i	−0.225455	+	0.390499i
$965$	−2.50000	+	4.33013i	−0.0804778	+	0.139392i
$966$	−3.00000	+	5.19615i	−0.0965234	+	0.167183i
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	−0.794515	−	0.607244i	$-0.792275\pi$
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	0.923147	+	0.384448i	$0.125608\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$	4.50000	+	7.79423i	0.144486	+	0.250258i
$971$	6.50000	−	11.2583i	0.208595	−	0.361297i	−0.742677	−	0.669650i	$-0.766444\pi$
$971$	6.50000	−	11.2583i	0.208595	−	0.361297i	0.951272	+	0.308353i	$0.0997776\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−1.00000	−	1.73205i	−0.0320585	−	0.0555270i
$974$	5.00000			0.160210
$975$		0			0
$976$		0			0
$977$	12.0000	−	20.7846i	0.383914	−	0.664959i	−0.607704	−	0.794164i	$-0.707909\pi$
$977$	12.0000	−	20.7846i	0.383914	−	0.664959i	0.991618	+	0.129205i	$0.0412426\pi$
$978$	−9.00000	−	15.5885i	−0.287788	−	0.498464i
$979$		0			0
$980$	3.00000	−	5.19615i	0.0958315	−	0.165985i
$981$	5.00000	+	8.66025i	0.159638	+	0.276501i
$982$	−10.0000	−	17.3205i	−0.319113	−	0.552720i
$983$	18.0000			0.574111			0.287055	−	0.957914i	$-0.407324\pi$
$983$	18.0000			0.574111			0.287055	+	0.957914i	$0.407324\pi$
$984$		0			0
$985$	−1.00000	+	1.73205i	−0.0318626	+	0.0551877i
$986$	2.00000	−	3.46410i	0.0636930	−	0.110319i
$987$	−8.00000			−0.254643
$988$		0			0
$989$	18.0000	−	31.1769i	0.572367	−	0.991368i
$990$	−3.00000			−0.0953463
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	0.994537	+	0.104389i	$0.0332887\pi$
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	−0.406865	+	0.913488i	$0.633378\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	−16.0000	−	27.7128i	−0.507745	−	0.879440i
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$	3.00000			0.0951064
$996$	−12.0000			−0.380235
$997$	4.00000			0.126681			0.0633406	−	0.997992i	$-0.479825\pi$
$997$	4.00000			0.126681			0.0633406	+	0.997992i	$0.479825\pi$
$998$	−5.00000	+	8.66025i	−0.158272	+	0.274136i
$999$	−2.00000	+	3.46410i	−0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.e.c.1075.1	yes	2
223.39	even	3	inner	1338.2.e.c.931.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.e.c.931.1	✓	2	223.39	even	3	inner
1338.2.e.c.1075.1	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} -1.00000 q^{27} +1.00000 q^{28} +(0.500000 - 0.866025i) q^{29} -1.00000 q^{30} +(2.00000 + 3.46410i) q^{31} +1.00000 q^{32} +3.00000 q^{33} +4.00000 q^{34} +(-0.500000 + 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.00000 - 3.46410i) q^{37} +(-0.500000 + 0.866025i) q^{40} +(0.500000 + 0.866025i) q^{42} +(-3.00000 - 5.19615i) q^{43} +(1.50000 - 2.59808i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{46} +(-4.00000 + 6.92820i) q^{47} +(0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +(2.00000 + 3.46410i) q^{50} +(2.00000 + 3.46410i) q^{51} +(-5.50000 + 9.52628i) q^{53} -1.00000 q^{54} +(1.50000 + 2.59808i) q^{55} +1.00000 q^{56} +(0.500000 - 0.866025i) q^{58} -3.00000 q^{59} -1.00000 q^{60} +(2.00000 + 3.46410i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(1.00000 + 1.73205i) q^{67} +4.00000 q^{68} +(-3.00000 + 5.19615i) q^{69} +(-0.500000 + 0.866025i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(1.50000 - 2.59808i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(0.500000 + 0.866025i) q^{84} +(-2.00000 + 3.46410i) q^{85} +(-3.00000 - 5.19615i) q^{86} +1.00000 q^{87} +(1.50000 - 2.59808i) q^{88} +(-0.500000 - 0.866025i) q^{90} +(3.00000 + 5.19615i) q^{92} +(-2.00000 + 3.46410i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(0.500000 + 0.866025i) q^{96} +(4.50000 - 7.79423i) q^{97} -6.00000 q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + q^{12} + 2 q^{14} - 2 q^{15} + 2 q^{16} + 8 q^{17} - q^{18} - q^{20} + q^{21} + 3 q^{22} + 6 q^{23}+ \cdots + 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^7 + 2 * q^8 - q^9 - q^10 + 3 * q^11 + q^12 + 2 * q^14 - 2 * q^15 + 2 * q^16 + 8 * q^17 - q^18 - q^20 + q^21 + 3 * q^22 + 6 * q^23 + q^24 + 4 * q^25 - 2 * q^27 + 2 * q^28 + q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 6 * q^33 + 8 * q^34 - q^35 - q^36 + 4 * q^37 - q^40 + q^42 - 6 * q^43 + 3 * q^44 - q^45 + 6 * q^46 - 8 * q^47 + q^48 - 12 * q^49 + 4 * q^50 + 4 * q^51 - 11 * q^53 - 2 * q^54 + 3 * q^55 + 2 * q^56 + q^58 - 6 * q^59 - 2 * q^60 + 4 * q^62 - q^63 + 2 * q^64 + 6 * q^66 + 2 * q^67 + 8 * q^68 - 6 * q^69 - q^70 - 6 * q^71 - q^72 + 14 * q^73 + 4 * q^74 - 4 * q^75 + 3 * q^77 + 11 * q^79 - q^80 - q^81 - 12 * q^83 + q^84 - 4 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 - q^90 + 6 * q^92 - 4 * q^93 - 8 * q^94 + q^96 + 9 * q^97 - 12 * q^98 + 3 * q^99

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