LMFDB - Embedded newform 1550.2.p.a.749.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1550,2,Mod(149,1550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1550, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1550.149"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1550 = 2 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1550.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4,0,-6,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$12.3768123133$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 62)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1550.749
Dual form			1550.2.p.a.149.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-2.59808 - 1.50000i) q^{3} -1.00000 q^{4} +(-1.50000 + 2.59808i) q^{6} +(-2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(3.00000 + 5.19615i) q^{9} +(1.50000 + 2.59808i) q^{11} +(2.59808 + 1.50000i) q^{12} +(4.33013 - 2.50000i) q^{13} +(-1.50000 + 2.59808i) q^{14} +1.00000 q^{16} +(2.59808 + 1.50000i) q^{17} +(5.19615 - 3.00000i) q^{18} +(3.50000 - 6.06218i) q^{19} +(4.50000 + 7.79423i) q^{21} +(2.59808 - 1.50000i) q^{22} -4.00000i q^{23} +(1.50000 - 2.59808i) q^{24} +(-2.50000 - 4.33013i) q^{26} -9.00000i q^{27} +(2.59808 + 1.50000i) q^{28} -2.00000 q^{29} +(2.00000 - 5.19615i) q^{31} -1.00000i q^{32} -9.00000i q^{33} +(1.50000 - 2.59808i) q^{34} +(-3.00000 - 5.19615i) q^{36} +(0.866025 + 0.500000i) q^{37} +(-6.06218 - 3.50000i) q^{38} -15.0000 q^{39} +(4.50000 + 7.79423i) q^{41} +(7.79423 - 4.50000i) q^{42} +(0.866025 + 0.500000i) q^{43} +(-1.50000 - 2.59808i) q^{44} -4.00000 q^{46} +8.00000i q^{47} +(-2.59808 - 1.50000i) q^{48} +(1.00000 + 1.73205i) q^{49} +(-4.50000 - 7.79423i) q^{51} +(-4.33013 + 2.50000i) q^{52} +(-2.59808 + 1.50000i) q^{53} -9.00000 q^{54} +(1.50000 - 2.59808i) q^{56} +(-18.1865 + 10.5000i) q^{57} +2.00000i q^{58} +(1.50000 - 2.59808i) q^{59} +6.00000 q^{61} +(-5.19615 - 2.00000i) q^{62} -18.0000i q^{63} -1.00000 q^{64} -9.00000 q^{66} +(2.59808 - 1.50000i) q^{67} +(-2.59808 - 1.50000i) q^{68} +(-6.00000 + 10.3923i) q^{69} +(0.500000 + 0.866025i) q^{71} +(-5.19615 + 3.00000i) q^{72} +(6.06218 - 3.50000i) q^{73} +(0.500000 - 0.866025i) q^{74} +(-3.50000 + 6.06218i) q^{76} -9.00000i q^{77} +15.0000i q^{78} +(0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(7.79423 - 4.50000i) q^{82} +(4.33013 - 2.50000i) q^{83} +(-4.50000 - 7.79423i) q^{84} +(0.500000 - 0.866025i) q^{86} +(5.19615 + 3.00000i) q^{87} +(-2.59808 + 1.50000i) q^{88} -6.00000 q^{89} -15.0000 q^{91} +4.00000i q^{92} +(-12.9904 + 10.5000i) q^{93} +8.00000 q^{94} +(-1.50000 + 2.59808i) q^{96} -14.0000i q^{97} +(1.73205 - 1.00000i) q^{98} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 6 q^{6} + 12 q^{9} + 6 q^{11} - 6 q^{14} + 4 q^{16} + 14 q^{19} + 18 q^{21} + 6 q^{24} - 10 q^{26} - 8 q^{29} + 8 q^{31} + 6 q^{34} - 12 q^{36} - 60 q^{39} + 18 q^{41} - 6 q^{44} - 16 q^{46}+ \cdots - 36 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 6 * q^6 + 12 * q^9 + 6 * q^11 - 6 * q^14 + 4 * q^16 + 14 * q^19 + 18 * q^21 + 6 * q^24 - 10 * q^26 - 8 * q^29 + 8 * q^31 + 6 * q^34 - 12 * q^36 - 60 * q^39 + 18 * q^41 - 6 * q^44 - 16 * q^46 + 4 * q^49 - 18 * q^51 - 36 * q^54 + 6 * q^56 + 6 * q^59 + 24 * q^61 - 4 * q^64 - 36 * q^66 - 24 * q^69 + 2 * q^71 + 2 * q^74 - 14 * q^76 + 2 * q^79 - 18 * q^81 - 18 * q^84 + 2 * q^86 - 24 * q^89 - 60 * q^91 + 32 * q^94 - 6 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1550\mathbb{Z}\right)^\times$.

$n$	$251$	$1427$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−2.59808	−	1.50000i	−1.50000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	−2.59808	−	1.50000i	−1.50000	−	0.866025i	−1.00000			$\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.50000	+	2.59808i	−0.612372	+	1.06066i
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.0791130	−	0.996866i	$-0.525209\pi$
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.902867	+	0.429919i	$0.858542\pi$
$8$			1.00000i			0.353553i
$9$	3.00000	+	5.19615i	1.00000	+	1.73205i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	2.59808	+	1.50000i	0.750000	+	0.433013i
$13$	4.33013	−	2.50000i	1.20096	−	0.693375i	0.240192	−	0.970725i	$-0.422790\pi$
$13$	4.33013	−	2.50000i	1.20096	−	0.693375i	0.960769	+	0.277350i	$0.0894562\pi$
$14$	−1.50000	+	2.59808i	−0.400892	+	0.694365i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.59808	+	1.50000i	0.630126	+	0.363803i	0.780801	−	0.624780i	$-0.214811\pi$
$17$	2.59808	+	1.50000i	0.630126	+	0.363803i	−0.150675	+	0.988583i	$0.548145\pi$
$18$	5.19615	−	3.00000i	1.22474	−	0.707107i
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$	4.50000	+	7.79423i	0.981981	+	1.70084i
$22$	2.59808	−	1.50000i	0.553912	−	0.319801i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$		0			0
$26$	−2.50000	−	4.33013i	−0.490290	−	0.849208i
$27$		−	9.00000i		−	1.73205i
$28$	2.59808	+	1.50000i	0.490990	+	0.283473i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	2.00000	−	5.19615i	0.359211	−	0.933257i
$31$	2.00000	−	5.19615i	0.359211	−	0.933257i
$32$		−	1.00000i		−	0.176777i
$33$		−	9.00000i		−	1.56670i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$		0			0
$36$	−3.00000	−	5.19615i	−0.500000	−	0.866025i
$37$	0.866025	+	0.500000i	0.142374	+	0.0821995i	0.569495	−	0.821995i	$-0.307139\pi$
$37$	0.866025	+	0.500000i	0.142374	+	0.0821995i	−0.427121	+	0.904194i	$0.640472\pi$
$38$	−6.06218	−	3.50000i	−0.983415	−	0.567775i
$39$	−15.0000			−2.40192
$40$		0			0
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$	7.79423	−	4.50000i	1.20268	−	0.694365i
$43$	0.866025	+	0.500000i	0.132068	+	0.0762493i	0.564578	−	0.825380i	$-0.309039\pi$
$43$	0.866025	+	0.500000i	0.132068	+	0.0762493i	−0.432511	+	0.901629i	$0.642372\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$		0			0
$46$	−4.00000			−0.589768
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$	−2.59808	−	1.50000i	−0.375000	−	0.216506i
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$		0			0
$51$	−4.50000	−	7.79423i	−0.630126	−	1.09141i
$52$	−4.33013	+	2.50000i	−0.600481	+	0.346688i
$53$	−2.59808	+	1.50000i	−0.356873	+	0.206041i	−0.667708	−	0.744423i	$-0.732725\pi$
$53$	−2.59808	+	1.50000i	−0.356873	+	0.206041i	0.310835	+	0.950464i	$0.399391\pi$
$54$	−9.00000			−1.22474
$55$		0			0
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	−18.1865	+	10.5000i	−2.40887	+	1.39076i
$58$			2.00000i			0.262613i
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$	−5.19615	−	2.00000i	−0.659912	−	0.254000i
$63$		−	18.0000i		−	2.26779i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−9.00000			−1.10782
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	−0.332830	−	0.942987i	$-0.608004\pi$
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	0.650236	+	0.759733i	$0.274670\pi$
$68$	−2.59808	−	1.50000i	−0.315063	−	0.181902i
$69$	−6.00000	+	10.3923i	−0.722315	+	1.25109i
$70$		0			0
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	0.894169	−	0.447730i	$-0.147767\pi$
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	−0.834830	+	0.550508i	$0.814434\pi$
$72$	−5.19615	+	3.00000i	−0.612372	+	0.353553i
$73$	6.06218	−	3.50000i	0.709524	−	0.409644i	−0.101361	−	0.994850i	$-0.532320\pi$
$73$	6.06218	−	3.50000i	0.709524	−	0.409644i	0.810885	+	0.585206i	$0.198986\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	−3.50000	+	6.06218i	−0.401478	+	0.695379i
$77$		−	9.00000i		−	1.02565i
$78$			15.0000i			1.69842i
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	7.79423	−	4.50000i	0.860729	−	0.496942i
$83$	4.33013	−	2.50000i	0.475293	−	0.274411i	−0.243160	−	0.969986i	$-0.578184\pi$
$83$	4.33013	−	2.50000i	0.475293	−	0.274411i	0.718453	+	0.695576i	$0.244851\pi$
$84$	−4.50000	−	7.79423i	−0.490990	−	0.850420i
$85$		0			0
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$	5.19615	+	3.00000i	0.557086	+	0.321634i
$88$	−2.59808	+	1.50000i	−0.276956	+	0.159901i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	−15.0000			−1.57243
$92$			4.00000i			0.417029i
$93$	−12.9904	+	10.5000i	−1.34704	+	1.08880i
$94$	8.00000			0.825137
$95$		0			0
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$		−	14.0000i		−	1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$		−	14.0000i		−	1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$	1.73205	−	1.00000i	0.174964	−	0.101015i
$99$	−9.00000	+	15.5885i	−0.904534	+	1.56670i
$100$		0			0
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$	−7.79423	+	4.50000i	−0.771744	+	0.445566i
$103$	−11.2583	+	6.50000i	−1.10932	+	0.640464i	−0.938652	−	0.344865i	$-0.887925\pi$
$103$	−11.2583	+	6.50000i	−1.10932	+	0.640464i	−0.170664	+	0.985329i	$0.554591\pi$
$104$	2.50000	+	4.33013i	0.245145	+	0.424604i
$105$		0			0
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	−11.2583	−	6.50000i	−1.08838	−	0.628379i	−0.155238	−	0.987877i	$-0.549614\pi$
$107$	−11.2583	−	6.50000i	−1.08838	−	0.628379i	−0.933146	+	0.359498i	$0.882948\pi$
$108$			9.00000i			0.866025i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	−1.50000	−	2.59808i	−0.142374	−	0.246598i
$112$	−2.59808	−	1.50000i	−0.245495	−	0.141737i
$113$	−0.866025	+	0.500000i	−0.0814688	+	0.0470360i	−0.540181	−	0.841549i	$-0.681644\pi$
$113$	−0.866025	+	0.500000i	−0.0814688	+	0.0470360i	0.458712	+	0.888585i	$0.348311\pi$
$114$	10.5000	+	18.1865i	0.983415	+	1.70332i
$115$		0			0
$116$	2.00000			0.185695
$117$	25.9808	+	15.0000i	2.40192	+	1.38675i
$118$	−2.59808	−	1.50000i	−0.239172	−	0.138086i
$119$	−4.50000	−	7.79423i	−0.412514	−	0.714496i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		−	6.00000i		−	0.543214i
$123$		−	27.0000i		−	2.43451i
$124$	−2.00000	+	5.19615i	−0.179605	+	0.466628i
$125$		0			0
$126$	−18.0000			−1.60357
$127$	11.2583	+	6.50000i	0.999015	+	0.576782i	0.907957	−	0.419064i	$-0.137642\pi$
$127$	11.2583	+	6.50000i	0.999015	+	0.576782i	0.0910585	+	0.995846i	$0.470975\pi$
$128$			1.00000i			0.0883883i
$129$	−1.50000	−	2.59808i	−0.132068	−	0.228748i
$130$		0			0
$131$	10.5000	−	18.1865i	0.917389	−	1.58896i	0.114024	−	0.993478i	$-0.463626\pi$
$131$	10.5000	−	18.1865i	0.917389	−	1.58896i	0.803365	−	0.595487i	$-0.203041\pi$
$132$			9.00000i			0.783349i
$133$	−18.1865	+	10.5000i	−1.57697	+	0.910465i
$134$	−1.50000	−	2.59808i	−0.129580	−	0.224440i
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−9.52628	+	5.50000i	−0.813885	+	0.469897i	−0.848303	−	0.529511i	$-0.822376\pi$
$137$	−9.52628	+	5.50000i	−0.813885	+	0.469897i	0.0344182	+	0.999408i	$0.489042\pi$
$138$	10.3923	+	6.00000i	0.884652	+	0.510754i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	12.0000	−	20.7846i	1.01058	−	1.75038i
$142$	0.866025	−	0.500000i	0.0726752	−	0.0419591i
$143$	12.9904	+	7.50000i	1.08631	+	0.627182i
$144$	3.00000	+	5.19615i	0.250000	+	0.433013i
$145$		0			0
$146$	−3.50000	−	6.06218i	−0.289662	−	0.501709i
$147$		−	6.00000i		−	0.494872i
$148$	−0.866025	−	0.500000i	−0.0711868	−	0.0410997i
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	6.06218	+	3.50000i	0.491708	+	0.283887i
$153$			18.0000i			1.45521i
$154$	−9.00000			−0.725241
$155$		0			0
$156$	15.0000			1.20096
$157$			10.0000i			0.798087i	0.916932	+	0.399043i	$0.130658\pi$
$157$			10.0000i			0.798087i	−0.916932	+	0.399043i	$0.869342\pi$
$158$	−0.866025	−	0.500000i	−0.0688973	−	0.0397779i
$159$	9.00000			0.713746
$160$		0			0
$161$	−6.00000	+	10.3923i	−0.472866	+	0.819028i
$162$	7.79423	+	4.50000i	0.612372	+	0.353553i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$	−2.50000	−	4.33013i	−0.194038	−	0.336083i
$167$	−16.4545	−	9.50000i	−1.27329	−	0.735132i	−0.297681	−	0.954665i	$-0.596213\pi$
$167$	−16.4545	−	9.50000i	−1.27329	−	0.735132i	−0.975605	+	0.219533i	$0.929547\pi$
$168$	−7.79423	+	4.50000i	−0.601338	+	0.347183i
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	42.0000			3.21182
$172$	−0.866025	−	0.500000i	−0.0660338	−	0.0381246i
$173$	0.866025	−	0.500000i	0.0658427	−	0.0380143i	−0.466717	−	0.884407i	$-0.654563\pi$
$173$	0.866025	−	0.500000i	0.0658427	−	0.0380143i	0.532560	+	0.846392i	$0.321230\pi$
$174$	3.00000	−	5.19615i	0.227429	−	0.393919i
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	−7.79423	+	4.50000i	−0.585850	+	0.338241i
$178$			6.00000i			0.449719i
$179$	9.50000	−	16.4545i	0.710063	−	1.22987i	−0.254770	−	0.967002i	$-0.582000\pi$
$179$	9.50000	−	16.4545i	0.710063	−	1.22987i	0.964833	−	0.262864i	$-0.0846670\pi$
$180$		0			0
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	0.758030	−	0.652219i	$-0.226162\pi$
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	−0.943854	+	0.330364i	$0.892829\pi$
$182$			15.0000i			1.11187i
$183$	−15.5885	−	9.00000i	−1.15233	−	0.665299i
$184$	4.00000			0.294884
$185$		0			0
$186$	10.5000	+	12.9904i	0.769897	+	0.952501i
$187$			9.00000i			0.658145i
$188$		−	8.00000i		−	0.583460i
$189$	−13.5000	+	23.3827i	−0.981981	+	1.70084i
$190$		0			0
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	0.806641	−	0.591041i	$-0.201283\pi$
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	−0.915177	+	0.403051i	$0.867950\pi$
$192$	2.59808	+	1.50000i	0.187500	+	0.108253i
$193$	−16.4545	−	9.50000i	−1.18442	−	0.683825i	−0.227387	−	0.973805i	$-0.573018\pi$
$193$	−16.4545	−	9.50000i	−1.18442	−	0.683825i	−0.957033	+	0.289980i	$0.906351\pi$
$194$	−14.0000			−1.00514
$195$		0			0
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	12.9904	−	7.50000i	0.925526	−	0.534353i	0.0401324	−	0.999194i	$-0.487222\pi$
$197$	12.9904	−	7.50000i	0.925526	−	0.534353i	0.885394	+	0.464841i	$0.153889\pi$
$198$	15.5885	+	9.00000i	1.10782	+	0.639602i
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	−0.950509	−	0.310696i	$-0.899438\pi$
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	0.206184	−	0.978513i	$-0.433895\pi$
$200$		0			0
$201$	−9.00000			−0.634811
$202$			10.0000i			0.703598i
$203$	5.19615	+	3.00000i	0.364698	+	0.210559i
$204$	4.50000	+	7.79423i	0.315063	+	0.545705i
$205$		0			0
$206$	6.50000	+	11.2583i	0.452876	+	0.784405i
$207$	20.7846	−	12.0000i	1.44463	−	0.834058i
$208$	4.33013	−	2.50000i	0.300240	−	0.173344i
$209$	21.0000			1.45260
$210$		0			0
$211$	0.500000	−	0.866025i	0.0344214	−	0.0596196i	−0.848301	−	0.529514i	$-0.822374\pi$
$211$	0.500000	−	0.866025i	0.0344214	−	0.0596196i	0.882723	+	0.469894i	$0.155708\pi$
$212$	2.59808	−	1.50000i	0.178437	−	0.103020i
$213$		−	3.00000i		−	0.205557i
$214$	−6.50000	+	11.2583i	−0.444331	+	0.769604i
$215$		0			0
$216$	9.00000			0.612372
$217$	−12.9904	+	10.5000i	−0.881845	+	0.712786i
$218$		−	2.00000i		−	0.135457i
$219$	−21.0000			−1.41905
$220$		0			0
$221$	15.0000			1.00901
$222$	−2.59808	+	1.50000i	−0.174371	+	0.100673i
$223$	16.4545	+	9.50000i	1.10187	+	0.636167i	0.936713	−	0.350100i	$-0.113852\pi$
$223$	16.4545	+	9.50000i	1.10187	+	0.636167i	0.165161	+	0.986267i	$0.447186\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$		0			0
$226$	0.500000	+	0.866025i	0.0332595	+	0.0576072i
$227$	−18.1865	+	10.5000i	−1.20708	+	0.696909i	−0.962121	−	0.272623i	$-0.912109\pi$
$227$	−18.1865	+	10.5000i	−1.20708	+	0.696909i	−0.244962	+	0.969533i	$0.578775\pi$
$228$	18.1865	−	10.5000i	1.20443	−	0.695379i
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	−13.5000	+	23.3827i	−0.888235	+	1.53847i
$232$		−	2.00000i		−	0.131306i
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$	15.0000	−	25.9808i	0.980581	−	1.69842i
$235$		0			0
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	−2.59808	+	1.50000i	−0.168763	+	0.0974355i
$238$	−7.79423	+	4.50000i	−0.505225	+	0.291692i
$239$	−0.500000	−	0.866025i	−0.0323423	−	0.0560185i	0.849401	−	0.527748i	$-0.176963\pi$
$239$	−0.500000	−	0.866025i	−0.0323423	−	0.0560185i	−0.881743	+	0.471729i	$0.843630\pi$
$240$		0			0
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$	−1.73205	−	1.00000i	−0.111340	−	0.0642824i
$243$		0			0
$244$	−6.00000			−0.384111
$245$		0			0
$246$	−27.0000			−1.72146
$247$		−	35.0000i		−	2.22700i
$248$	5.19615	+	2.00000i	0.329956	+	0.127000i
$249$	−15.0000			−0.950586
$250$		0			0
$251$	−11.5000	+	19.9186i	−0.725874	+	1.25725i	0.232740	+	0.972539i	$0.425231\pi$
$251$	−11.5000	+	19.9186i	−0.725874	+	1.25725i	−0.958613	+	0.284711i	$0.908102\pi$
$252$			18.0000i			1.13389i
$253$	10.3923	−	6.00000i	0.653359	−	0.377217i
$254$	6.50000	−	11.2583i	0.407846	−	0.706410i
$255$		0			0
$256$	1.00000			0.0625000
$257$	11.2583	−	6.50000i	0.702275	−	0.405459i	−0.105919	−	0.994375i	$-0.533778\pi$
$257$	11.2583	−	6.50000i	0.702275	−	0.405459i	0.808194	+	0.588916i	$0.200445\pi$
$258$	−2.59808	+	1.50000i	−0.161749	+	0.0933859i
$259$	−1.50000	−	2.59808i	−0.0932055	−	0.161437i
$260$		0			0
$261$	−6.00000	−	10.3923i	−0.371391	−	0.643268i
$262$	−18.1865	−	10.5000i	−1.12357	−	0.648692i
$263$		−	16.0000i		−	0.986602i	−0.869859	−	0.493301i	$-0.835790\pi$
$263$		−	16.0000i		−	0.986602i	0.869859	−	0.493301i	$-0.164210\pi$
$264$	9.00000			0.553912
$265$		0			0
$266$	10.5000	+	18.1865i	0.643796	+	1.11509i
$267$	15.5885	+	9.00000i	0.953998	+	0.550791i
$268$	−2.59808	+	1.50000i	−0.158703	+	0.0916271i
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	2.59808	+	1.50000i	0.157532	+	0.0909509i
$273$	38.9711	+	22.5000i	2.35864	+	1.36176i
$274$	5.50000	+	9.52628i	0.332267	+	0.575504i
$275$		0			0
$276$	6.00000	−	10.3923i	0.361158	−	0.625543i
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$		0			0
$279$	33.0000	−	5.19615i	1.97566	−	0.311086i
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	−20.7846	−	12.0000i	−1.23771	−	0.714590i
$283$			4.00000i			0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$			4.00000i			0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$	−0.500000	−	0.866025i	−0.0296695	−	0.0513892i
$285$		0			0
$286$	7.50000	−	12.9904i	0.443484	−	0.768137i
$287$		−	27.0000i		−	1.59376i
$288$	5.19615	−	3.00000i	0.306186	−	0.176777i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$	−21.0000	+	36.3731i	−1.23104	+	2.13223i
$292$	−6.06218	+	3.50000i	−0.354762	+	0.204822i
$293$	16.4545	+	9.50000i	0.961281	+	0.554996i	0.896567	−	0.442908i	$-0.146053\pi$
$293$	16.4545	+	9.50000i	0.961281	+	0.554996i	0.0647140	+	0.997904i	$0.479386\pi$
$294$	−6.00000			−0.349927
$295$		0			0
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$	23.3827	−	13.5000i	1.35680	−	0.783349i
$298$	−0.866025	−	0.500000i	−0.0501675	−	0.0289642i
$299$	−10.0000	−	17.3205i	−0.578315	−	1.00167i
$300$		0			0
$301$	−1.50000	−	2.59808i	−0.0864586	−	0.149751i
$302$			16.0000i			0.920697i
$303$	25.9808	+	15.0000i	1.49256	+	0.861727i
$304$	3.50000	−	6.06218i	0.200739	−	0.347690i
$305$		0			0
$306$	18.0000			1.02899
$307$	−4.33013	−	2.50000i	−0.247133	−	0.142683i	0.371318	−	0.928506i	$-0.378906\pi$
$307$	−4.33013	−	2.50000i	−0.247133	−	0.142683i	−0.618451	+	0.785823i	$0.712239\pi$
$308$			9.00000i			0.512823i
$309$	39.0000			2.21863
$310$		0			0
$311$	32.0000			1.81455			0.907277	−	0.420534i	$-0.138157\pi$
$311$	32.0000			1.81455			0.907277	+	0.420534i	$0.138157\pi$
$312$		−	15.0000i		−	0.849208i
$313$	−6.06218	−	3.50000i	−0.342655	−	0.197832i	0.318791	−	0.947825i	$-0.396723\pi$
$313$	−6.06218	−	3.50000i	−0.342655	−	0.197832i	−0.661445	+	0.749993i	$0.730057\pi$
$314$	10.0000			0.564333
$315$		0			0
$316$	−0.500000	+	0.866025i	−0.0281272	+	0.0487177i
$317$	25.1147	+	14.5000i	1.41058	+	0.814401i	0.995443	−	0.0953560i	$-0.0303989\pi$
$317$	25.1147	+	14.5000i	1.41058	+	0.814401i	0.415141	+	0.909757i	$0.363732\pi$
$318$		−	9.00000i		−	0.504695i
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$	19.5000	+	33.7750i	1.08838	+	1.88514i
$322$	10.3923	+	6.00000i	0.579141	+	0.334367i
$323$	18.1865	−	10.5000i	1.01193	−	0.584236i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$		0			0
$326$	−4.00000			−0.221540
$327$	−5.19615	−	3.00000i	−0.287348	−	0.165900i
$328$	−7.79423	+	4.50000i	−0.430364	+	0.248471i
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$332$	−4.33013	+	2.50000i	−0.237647	+	0.137205i
$333$			6.00000i			0.328798i
$334$	−9.50000	+	16.4545i	−0.519817	+	0.900349i
$335$		0			0
$336$	4.50000	+	7.79423i	0.245495	+	0.425210i
$337$		−	30.0000i		−	1.63420i	−0.576493	−	0.817102i	$-0.695579\pi$
$337$		−	30.0000i		−	1.63420i	0.576493	−	0.817102i	$-0.304421\pi$
$338$	−10.3923	−	6.00000i	−0.565267	−	0.326357i
$339$	3.00000			0.162938
$340$		0			0
$341$	16.5000	−	2.59808i	0.893525	−	0.140694i
$342$		−	42.0000i		−	2.27110i
$343$			15.0000i			0.809924i
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$		0			0
$346$	−0.500000	−	0.866025i	−0.0268802	−	0.0465578i
$347$	−7.79423	−	4.50000i	−0.418416	−	0.241573i	0.275983	−	0.961162i	$-0.410997\pi$
$347$	−7.79423	−	4.50000i	−0.418416	−	0.241573i	−0.694399	+	0.719590i	$0.744330\pi$
$348$	−5.19615	−	3.00000i	−0.278543	−	0.160817i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	−22.5000	−	38.9711i	−1.20096	−	2.08013i
$352$	2.59808	−	1.50000i	0.138478	−	0.0799503i
$353$	−26.8468	−	15.5000i	−1.42891	−	0.824982i	−0.431875	−	0.901933i	$-0.642148\pi$
$353$	−26.8468	−	15.5000i	−1.42891	−	0.824982i	−0.997035	+	0.0769515i	$0.975481\pi$
$354$	4.50000	+	7.79423i	0.239172	+	0.414259i
$355$		0			0
$356$	6.00000			0.317999
$357$			27.0000i			1.42899i
$358$	−16.4545	−	9.50000i	−0.869646	−	0.502091i
$359$	15.5000	+	26.8468i	0.818059	+	1.41692i	0.907111	+	0.420892i	$0.138283\pi$
$359$	15.5000	+	26.8468i	0.818059	+	1.41692i	−0.0890519	+	0.996027i	$0.528384\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	−4.33013	+	2.50000i	−0.227586	+	0.131397i
$363$	−5.19615	+	3.00000i	−0.272727	+	0.157459i
$364$	15.0000			0.786214
$365$		0			0
$366$	−9.00000	+	15.5885i	−0.470438	+	0.814822i
$367$	−6.06218	+	3.50000i	−0.316443	+	0.182699i	−0.649806	−	0.760100i	$-0.725150\pi$
$367$	−6.06218	+	3.50000i	−0.316443	+	0.182699i	0.333363	+	0.942799i	$0.391817\pi$
$368$		−	4.00000i		−	0.208514i
$369$	−27.0000	+	46.7654i	−1.40556	+	2.43451i
$370$		0			0
$371$	9.00000			0.467257
$372$	12.9904	−	10.5000i	0.673520	−	0.544400i
$373$			10.0000i			0.517780i	0.965907	+	0.258890i	$0.0833568\pi$
$373$			10.0000i			0.517780i	−0.965907	+	0.258890i	$0.916643\pi$
$374$	9.00000			0.465379
$375$		0			0
$376$	−8.00000			−0.412568
$377$	−8.66025	+	5.00000i	−0.446026	+	0.257513i
$378$	23.3827	+	13.5000i	1.20268	+	0.694365i
$379$	−0.500000	+	0.866025i	−0.0256833	+	0.0444847i	−0.878581	−	0.477593i	$-0.841509\pi$
$379$	−0.500000	+	0.866025i	−0.0256833	+	0.0444847i	0.852898	+	0.522077i	$0.174843\pi$
$380$		0			0
$381$	−19.5000	−	33.7750i	−0.999015	−	1.73035i
$382$	−2.59808	+	1.50000i	−0.132929	+	0.0767467i
$383$	12.9904	−	7.50000i	0.663777	−	0.383232i	−0.129937	−	0.991522i	$-0.541478\pi$
$383$	12.9904	−	7.50000i	0.663777	−	0.383232i	0.793715	+	0.608290i	$0.208144\pi$
$384$	1.50000	−	2.59808i	0.0765466	−	0.132583i
$385$		0			0
$386$	−9.50000	+	16.4545i	−0.483537	+	0.837511i
$387$			6.00000i			0.304997i
$388$			14.0000i			0.710742i
$389$	−11.5000	+	19.9186i	−0.583073	+	1.00991i	0.412039	+	0.911166i	$0.364817\pi$
$389$	−11.5000	+	19.9186i	−0.583073	+	1.00991i	−0.995113	+	0.0987463i	$0.968517\pi$
$390$		0			0
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$	−1.73205	+	1.00000i	−0.0874818	+	0.0505076i
$393$	−54.5596	+	31.5000i	−2.75217	+	1.58896i
$394$	−7.50000	−	12.9904i	−0.377845	−	0.654446i
$395$		0			0
$396$	9.00000	−	15.5885i	0.452267	−	0.783349i
$397$	18.1865	+	10.5000i	0.912756	+	0.526980i	0.881317	−	0.472526i	$-0.156658\pi$
$397$	18.1865	+	10.5000i	0.912756	+	0.526980i	0.0314391	+	0.999506i	$0.489991\pi$
$398$	−18.1865	+	10.5000i	−0.911609	+	0.526317i
$399$	63.0000			3.15394
$400$		0			0
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$			9.00000i			0.448879i
$403$	−4.33013	−	27.5000i	−0.215699	−	1.36987i
$404$	10.0000			0.497519
$405$		0			0
$406$	3.00000	−	5.19615i	0.148888	−	0.257881i
$407$			3.00000i			0.148704i
$408$	7.79423	−	4.50000i	0.385872	−	0.222783i
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	0.939490	−	0.342578i	$-0.111300\pi$
$410$		0			0
$411$	33.0000			1.62777
$412$	11.2583	−	6.50000i	0.554658	−	0.320232i
$413$	−7.79423	+	4.50000i	−0.383529	+	0.221431i
$414$	−12.0000	−	20.7846i	−0.589768	−	1.02151i
$415$		0			0
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$		0			0
$418$		−	21.0000i		−	1.02714i
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	0.988861	−	0.148844i	$-0.0475552\pi$
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	−0.623333	+	0.781956i	$0.714222\pi$
$422$	−0.866025	−	0.500000i	−0.0421575	−	0.0243396i
$423$	−41.5692	+	24.0000i	−2.02116	+	1.16692i
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$		0			0
$426$	−3.00000			−0.145350
$427$	−15.5885	−	9.00000i	−0.754378	−	0.435541i
$428$	11.2583	+	6.50000i	0.544192	+	0.314189i
$429$	−22.5000	−	38.9711i	−1.08631	−	1.88154i
$430$		0			0
$431$	−2.50000	+	4.33013i	−0.120421	+	0.208575i	−0.919934	−	0.392074i	$-0.871758\pi$
$431$	−2.50000	+	4.33013i	−0.120421	+	0.208575i	0.799513	+	0.600649i	$0.205091\pi$
$432$		−	9.00000i		−	0.433013i
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	10.5000	+	12.9904i	0.504016	+	0.623558i
$435$		0			0
$436$	−2.00000			−0.0957826
$437$	−24.2487	−	14.0000i	−1.15997	−	0.669711i
$438$			21.0000i			1.00342i
$439$	−6.50000	−	11.2583i	−0.310228	−	0.537331i	0.668184	−	0.743996i	$-0.267072\pi$
$439$	−6.50000	−	11.2583i	−0.310228	−	0.537331i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$	−6.00000	+	10.3923i	−0.285714	+	0.494872i
$442$		−	15.0000i		−	0.713477i
$443$	−9.52628	+	5.50000i	−0.452607	+	0.261313i	−0.708931	−	0.705278i	$-0.750822\pi$
$443$	−9.52628	+	5.50000i	−0.452607	+	0.261313i	0.256323	+	0.966591i	$0.417489\pi$
$444$	1.50000	+	2.59808i	0.0711868	+	0.123299i
$445$		0			0
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$	−2.59808	+	1.50000i	−0.122885	+	0.0709476i
$448$	2.59808	+	1.50000i	0.122748	+	0.0708683i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	−13.5000	+	23.3827i	−0.635690	+	1.10105i
$452$	0.866025	−	0.500000i	0.0407344	−	0.0235180i
$453$	41.5692	+	24.0000i	1.95309	+	1.12762i
$454$	10.5000	+	18.1865i	0.492789	+	0.853536i
$455$		0			0
$456$	−10.5000	−	18.1865i	−0.491708	−	0.851662i
$457$		−	10.0000i		−	0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$		−	10.0000i		−	0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$	6.06218	+	3.50000i	0.283267	+	0.163544i
$459$	13.5000	−	23.3827i	0.630126	−	1.09141i
$460$		0			0
$461$	−42.0000			−1.95614			−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000			−1.95614			−0.978068	+	0.208288i	$0.933211\pi$
$462$	23.3827	+	13.5000i	1.08786	+	0.628077i
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$	−2.00000			−0.0928477
$465$		0			0
$466$	−18.0000			−0.833834
$467$			8.00000i			0.370196i	0.982720	+	0.185098i	$0.0592602\pi$
$467$			8.00000i			0.370196i	−0.982720	+	0.185098i	$0.940740\pi$
$468$	−25.9808	−	15.0000i	−1.20096	−	0.693375i
$469$	−9.00000			−0.415581
$470$		0			0
$471$	15.0000	−	25.9808i	0.691164	−	1.19713i
$472$	2.59808	+	1.50000i	0.119586	+	0.0690431i
$473$			3.00000i			0.137940i
$474$	1.50000	+	2.59808i	0.0688973	+	0.119334i
$475$		0			0
$476$	4.50000	+	7.79423i	0.206257	+	0.357248i
$477$	−15.5885	−	9.00000i	−0.713746	−	0.412082i
$478$	−0.866025	+	0.500000i	−0.0396111	+	0.0228695i
$479$	−5.50000	+	9.52628i	−0.251301	+	0.435267i	−0.963884	−	0.266321i	$-0.914192\pi$
$479$	−5.50000	+	9.52628i	−0.251301	+	0.435267i	0.712583	+	0.701588i	$0.247525\pi$
$480$		0			0
$481$	5.00000			0.227980
$482$	−21.6506	−	12.5000i	−0.986159	−	0.569359i
$483$	31.1769	−	18.0000i	1.41860	−	0.819028i
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$		0			0
$486$		0			0
$487$	−9.52628	+	5.50000i	−0.431677	+	0.249229i	−0.700061	−	0.714083i	$-0.746844\pi$
$487$	−9.52628	+	5.50000i	−0.431677	+	0.249229i	0.268384	+	0.963312i	$0.413510\pi$
$488$			6.00000i			0.271607i
$489$	−6.00000	+	10.3923i	−0.271329	+	0.469956i
$490$		0			0
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	0.984145	−	0.177365i	$-0.0567572\pi$
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	−0.645675	+	0.763612i	$0.723424\pi$
$492$			27.0000i			1.21725i
$493$	−5.19615	−	3.00000i	−0.234023	−	0.135113i
$494$	−35.0000			−1.57472
$495$		0			0
$496$	2.00000	−	5.19615i	0.0898027	−	0.233314i
$497$		−	3.00000i		−	0.134568i
$498$			15.0000i			0.672166i
$499$	7.50000	−	12.9904i	0.335746	−	0.581529i	−0.647882	−	0.761741i	$-0.724345\pi$
$499$	7.50000	−	12.9904i	0.335746	−	0.581529i	0.983628	+	0.180212i	$0.0576783\pi$
$500$		0			0
$501$	28.5000	+	49.3634i	1.27329	+	2.20540i
$502$	19.9186	+	11.5000i	0.889010	+	0.513270i
$503$	−7.79423	−	4.50000i	−0.347527	−	0.200645i	0.316068	−	0.948736i	$-0.397637\pi$
$503$	−7.79423	−	4.50000i	−0.347527	−	0.200645i	−0.663596	+	0.748091i	$0.730970\pi$
$504$	18.0000			0.801784
$505$		0			0
$506$	−6.00000	−	10.3923i	−0.266733	−	0.461994i
$507$	−31.1769	+	18.0000i	−1.38462	+	0.799408i
$508$	−11.2583	−	6.50000i	−0.499508	−	0.288391i
$509$	0.500000	+	0.866025i	0.0221621	+	0.0383859i	0.876894	−	0.480684i	$-0.159612\pi$
$509$	0.500000	+	0.866025i	0.0221621	+	0.0383859i	−0.854732	+	0.519070i	$0.826278\pi$
$510$		0			0
$511$	−21.0000			−0.928985
$512$		−	1.00000i		−	0.0441942i
$513$	−54.5596	−	31.5000i	−2.40887	−	1.39076i
$514$	−6.50000	−	11.2583i	−0.286703	−	0.496584i
$515$		0			0
$516$	1.50000	+	2.59808i	0.0660338	+	0.114374i
$517$	−20.7846	+	12.0000i	−0.914106	+	0.527759i
$518$	−2.59808	+	1.50000i	−0.114153	+	0.0659062i
$519$	−3.00000			−0.131685
$520$		0			0
$521$	−15.5000	+	26.8468i	−0.679067	+	1.17618i	0.296195	+	0.955128i	$0.404282\pi$
$521$	−15.5000	+	26.8468i	−0.679067	+	1.17618i	−0.975262	+	0.221052i	$0.929051\pi$
$522$	−10.3923	+	6.00000i	−0.454859	+	0.262613i
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	−10.5000	+	18.1865i	−0.458695	+	0.794482i
$525$		0			0
$526$	−16.0000			−0.697633
$527$	12.9904	−	10.5000i	0.565870	−	0.457387i
$528$		−	9.00000i		−	0.391675i
$529$	7.00000			0.304348
$530$		0			0
$531$	18.0000			0.781133
$532$	18.1865	−	10.5000i	0.788486	−	0.455233i
$533$	38.9711	+	22.5000i	1.68803	+	0.974583i
$534$	9.00000	−	15.5885i	0.389468	−	0.674579i
$535$		0			0
$536$	1.50000	+	2.59808i	0.0647901	+	0.112220i
$537$	−49.3634	+	28.5000i	−2.13019	+	1.22987i
$538$	18.1865	−	10.5000i	0.784077	−	0.452687i
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$		0			0
$541$	−14.5000	+	25.1147i	−0.623404	+	1.07977i	0.365444	+	0.930834i	$0.380917\pi$
$541$	−14.5000	+	25.1147i	−0.623404	+	1.07977i	−0.988847	+	0.148933i	$0.952416\pi$
$542$			8.00000i			0.343629i
$543$			15.0000i			0.643712i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$		0			0
$546$	22.5000	−	38.9711i	0.962911	−	1.66781i
$547$	−11.2583	+	6.50000i	−0.481371	+	0.277920i	−0.720988	−	0.692948i	$-0.756312\pi$
$547$	−11.2583	+	6.50000i	−0.481371	+	0.277920i	0.239616	+	0.970868i	$0.422978\pi$
$548$	9.52628	−	5.50000i	0.406942	−	0.234948i
$549$	18.0000	+	31.1769i	0.768221	+	1.33060i
$550$		0			0
$551$	−7.00000	+	12.1244i	−0.298210	+	0.516515i
$552$	−10.3923	−	6.00000i	−0.442326	−	0.255377i
$553$	−2.59808	+	1.50000i	−0.110481	+	0.0637865i
$554$	2.00000			0.0849719
$555$		0			0
$556$		0			0
$557$			2.00000i			0.0847427i	0.999102	+	0.0423714i	$0.0134913\pi$
$557$			2.00000i			0.0847427i	−0.999102	+	0.0423714i	$0.986509\pi$
$558$	−5.19615	−	33.0000i	−0.219971	−	1.39700i
$559$	5.00000			0.211477
$560$		0			0
$561$	13.5000	−	23.3827i	0.569970	−	0.987218i
$562$		−	30.0000i		−	1.26547i
$563$	18.1865	−	10.5000i	0.766471	−	0.442522i	−0.0651433	−	0.997876i	$-0.520750\pi$
$563$	18.1865	−	10.5000i	0.766471	−	0.442522i	0.831614	+	0.555354i	$0.187417\pi$
$564$	−12.0000	+	20.7846i	−0.505291	+	0.875190i
$565$		0			0
$566$	4.00000			0.168133
$567$	23.3827	−	13.5000i	0.981981	−	0.566947i
$568$	−0.866025	+	0.500000i	−0.0363376	+	0.0209795i
$569$	−12.5000	−	21.6506i	−0.524027	−	0.907642i	−0.999609	−	0.0279702i	$-0.991096\pi$
$569$	−12.5000	−	21.6506i	−0.524027	−	0.907642i	0.475581	−	0.879672i	$-0.342238\pi$
$570$		0			0
$571$	−12.5000	−	21.6506i	−0.523109	−	0.906051i	−0.999638	−	0.0268925i	$-0.991439\pi$
$571$	−12.5000	−	21.6506i	−0.523109	−	0.906051i	0.476530	−	0.879158i	$-0.341895\pi$
$572$	−12.9904	−	7.50000i	−0.543155	−	0.313591i
$573$			9.00000i			0.375980i
$574$	−27.0000			−1.12696
$575$		0			0
$576$	−3.00000	−	5.19615i	−0.125000	−	0.216506i
$577$	2.59808	+	1.50000i	0.108159	+	0.0624458i	0.553104	−	0.833112i	$-0.313443\pi$
$577$	2.59808	+	1.50000i	0.108159	+	0.0624458i	−0.444945	+	0.895558i	$0.646777\pi$
$578$	−6.92820	+	4.00000i	−0.288175	+	0.166378i
$579$	28.5000	+	49.3634i	1.18442	+	2.05147i
$580$		0			0
$581$	−15.0000			−0.622305
$582$	36.3731	+	21.0000i	1.50771	+	0.870478i
$583$	−7.79423	−	4.50000i	−0.322804	−	0.186371i
$584$	3.50000	+	6.06218i	0.144831	+	0.250855i
$585$		0			0
$586$	9.50000	−	16.4545i	0.392441	−	0.679728i
$587$			28.0000i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$587$			28.0000i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$588$			6.00000i			0.247436i
$589$	−24.5000	−	30.3109i	−1.00950	−	1.24894i
$590$		0			0
$591$	−45.0000			−1.85105
$592$	0.866025	+	0.500000i	0.0355934	+	0.0205499i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$	−13.5000	−	23.3827i	−0.553912	−	0.959403i
$595$		0			0
$596$	−0.500000	+	0.866025i	−0.0204808	+	0.0354738i
$597$			63.0000i			2.57842i
$598$	−17.3205	+	10.0000i	−0.708288	+	0.408930i
$599$	−8.50000	−	14.7224i	−0.347301	−	0.601542i	0.638468	−	0.769648i	$-0.279568\pi$
$599$	−8.50000	−	14.7224i	−0.347301	−	0.601542i	−0.985769	+	0.168106i	$0.946235\pi$
$600$		0			0
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	−0.303986	−	0.952676i	$-0.598318\pi$
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	0.977035	−	0.213079i	$-0.0683491\pi$
$602$	−2.59808	+	1.50000i	−0.105890	+	0.0611354i
$603$	15.5885	+	9.00000i	0.634811	+	0.366508i
$604$	16.0000			0.651031
$605$		0			0
$606$	15.0000	−	25.9808i	0.609333	−	1.05540i
$607$	35.5070	−	20.5000i	1.44119	−	0.832069i	0.443257	−	0.896394i	$-0.353823\pi$
$607$	35.5070	−	20.5000i	1.44119	−	0.832069i	0.997929	+	0.0643251i	$0.0204895\pi$
$608$	−6.06218	−	3.50000i	−0.245854	−	0.141944i
$609$	−9.00000	−	15.5885i	−0.364698	−	0.631676i
$610$		0			0
$611$	20.0000	+	34.6410i	0.809113	+	1.40143i
$612$		−	18.0000i		−	0.727607i
$613$	−4.33013	−	2.50000i	−0.174892	−	0.100974i	0.409998	−	0.912086i	$-0.365529\pi$
$613$	−4.33013	−	2.50000i	−0.174892	−	0.100974i	−0.584891	+	0.811112i	$0.698863\pi$
$614$	−2.50000	+	4.33013i	−0.100892	+	0.174750i
$615$		0			0
$616$	9.00000			0.362620
$617$	23.3827	+	13.5000i	0.941351	+	0.543490i	0.890384	−	0.455211i	$-0.150436\pi$
$617$	23.3827	+	13.5000i	0.941351	+	0.543490i	0.0509678	+	0.998700i	$0.483769\pi$
$618$		−	39.0000i		−	1.56881i
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$		0			0
$621$	−36.0000			−1.44463
$622$		−	32.0000i		−	1.28308i
$623$	15.5885	+	9.00000i	0.624538	+	0.360577i
$624$	−15.0000			−0.600481
$625$		0			0
$626$	−3.50000	+	6.06218i	−0.139888	+	0.242293i
$627$	−54.5596	−	31.5000i	−2.17890	−	1.25799i
$628$		−	10.0000i		−	0.399043i
$629$	1.50000	+	2.59808i	0.0598089	+	0.103592i
$630$		0			0
$631$	−13.5000	−	23.3827i	−0.537427	−	0.930850i	−0.999042	−	0.0437697i	$-0.986063\pi$
$631$	−13.5000	−	23.3827i	−0.537427	−	0.930850i	0.461615	−	0.887080i	$-0.347270\pi$
$632$	0.866025	+	0.500000i	0.0344486	+	0.0198889i
$633$	−2.59808	+	1.50000i	−0.103264	+	0.0596196i
$634$	14.5000	−	25.1147i	0.575869	−	0.997434i
$635$		0			0
$636$	−9.00000			−0.356873
$637$	8.66025	+	5.00000i	0.343132	+	0.198107i
$638$	−5.19615	+	3.00000i	−0.205718	+	0.118771i
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	−5.50000	−	9.52628i	−0.217237	−	0.376265i	0.736725	−	0.676192i	$-0.236371\pi$
$641$	−5.50000	−	9.52628i	−0.217237	−	0.376265i	−0.953962	+	0.299927i	$0.903038\pi$
$642$	33.7750	−	19.5000i	1.33299	−	0.769604i
$643$			28.0000i			1.10421i	0.833774	+	0.552106i	$0.186176\pi$
$643$			28.0000i			1.10421i	−0.833774	+	0.552106i	$0.813824\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$		0			0
$646$	−10.5000	−	18.1865i	−0.413117	−	0.715540i
$647$		−	4.00000i		−	0.157256i	−0.996904	−	0.0786281i	$-0.974946\pi$
$647$		−	4.00000i		−	0.157256i	0.996904	−	0.0786281i	$-0.0250540\pi$
$648$	−7.79423	−	4.50000i	−0.306186	−	0.176777i
$649$	9.00000			0.353281
$650$		0			0
$651$	49.5000	−	7.79423i	1.94006	−	0.305480i
$652$			4.00000i			0.156652i
$653$		−	18.0000i		−	0.704394i	−0.935926	−	0.352197i	$-0.885435\pi$
$653$		−	18.0000i		−	0.704394i	0.935926	−	0.352197i	$-0.114565\pi$
$654$	−3.00000	+	5.19615i	−0.117309	+	0.203186i
$655$		0			0
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$	36.3731	+	21.0000i	1.41905	+	0.819288i
$658$	−20.7846	−	12.0000i	−0.810268	−	0.467809i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−24.5000	−	42.4352i	−0.952940	−	1.65054i	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−24.5000	−	42.4352i	−0.952940	−	1.65054i	−0.213925	−	0.976850i	$-0.568625\pi$
$662$	−14.7224	+	8.50000i	−0.572204	+	0.330362i
$663$	−38.9711	−	22.5000i	−1.51351	−	0.873828i
$664$	2.50000	+	4.33013i	0.0970188	+	0.168042i
$665$		0			0
$666$	6.00000			0.232495
$667$			8.00000i			0.309761i
$668$	16.4545	+	9.50000i	0.636643	+	0.367566i
$669$	−28.5000	−	49.3634i	−1.10187	−	1.90850i
$670$		0			0
$671$	9.00000	+	15.5885i	0.347441	+	0.601786i
$672$	7.79423	−	4.50000i	0.300669	−	0.173591i
$673$	23.3827	−	13.5000i	0.901336	−	0.520387i	0.0237028	−	0.999719i	$-0.492454\pi$
$673$	23.3827	−	13.5000i	0.901336	−	0.520387i	0.877633	+	0.479332i	$0.159121\pi$
$674$	−30.0000			−1.15556
$675$		0			0
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	23.3827	−	13.5000i	0.898670	−	0.518847i	0.0219013	−	0.999760i	$-0.493028\pi$
$677$	23.3827	−	13.5000i	0.898670	−	0.518847i	0.876768	+	0.480913i	$0.159695\pi$
$678$		−	3.00000i		−	0.115214i
$679$	−21.0000	+	36.3731i	−0.805906	+	1.39587i
$680$		0			0
$681$	63.0000			2.41417
$682$	−2.59808	−	16.5000i	−0.0994855	−	0.631818i
$683$		−	16.0000i		−	0.612223i	−0.951996	−	0.306111i	$-0.900972\pi$
$683$		−	16.0000i		−	0.612223i	0.951996	−	0.306111i	$-0.0990280\pi$
$684$	−42.0000			−1.60591
$685$		0			0
$686$	15.0000			0.572703
$687$	18.1865	−	10.5000i	0.693860	−	0.400600i
$688$	0.866025	+	0.500000i	0.0330169	+	0.0190623i
$689$	−7.50000	+	12.9904i	−0.285727	+	0.494894i
$690$		0			0
$691$	13.5000	+	23.3827i	0.513564	+	0.889519i	0.999876	+	0.0157341i	$0.00500851\pi$
$691$	13.5000	+	23.3827i	0.513564	+	0.889519i	−0.486312	+	0.873785i	$0.661658\pi$
$692$	−0.866025	+	0.500000i	−0.0329213	+	0.0190071i
$693$	46.7654	−	27.0000i	1.77647	−	1.02565i
$694$	−4.50000	+	7.79423i	−0.170818	+	0.295865i
$695$		0			0
$696$	−3.00000	+	5.19615i	−0.113715	+	0.196960i
$697$			27.0000i			1.02270i
$698$		−	14.0000i		−	0.529908i
$699$	−27.0000	+	46.7654i	−1.02123	+	1.76883i
$700$		0			0
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	−0.688917	−	0.724840i	$-0.741914\pi$
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	0.972188	+	0.234200i	$0.0752470\pi$
$702$	−38.9711	+	22.5000i	−1.47087	+	0.849208i
$703$	6.06218	−	3.50000i	0.228639	−	0.132005i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	−15.5000	+	26.8468i	−0.583350	+	1.01039i
$707$	25.9808	+	15.0000i	0.977107	+	0.564133i
$708$	7.79423	−	4.50000i	0.292925	−	0.169120i
$709$	−38.0000			−1.42712			−0.713560	−	0.700594i	$-0.752918\pi$
$709$	−38.0000			−1.42712			−0.713560	+	0.700594i	$0.752918\pi$
$710$		0			0
$711$	6.00000			0.225018
$712$		−	6.00000i		−	0.224860i
$713$	−20.7846	−	8.00000i	−0.778390	−	0.299602i
$714$	27.0000			1.01045
$715$		0			0
$716$	−9.50000	+	16.4545i	−0.355032	+	0.614933i
$717$			3.00000i			0.112037i
$718$	26.8468	−	15.5000i	1.00191	−	0.578455i
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	−0.923880	−	0.382682i	$-0.875001\pi$
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	0.793352	+	0.608763i	$0.208334\pi$
$720$		0			0
$721$	39.0000			1.45244
$722$	−25.9808	+	15.0000i	−0.966904	+	0.558242i
$723$	−64.9519	+	37.5000i	−2.41559	+	1.39464i
$724$	2.50000	+	4.33013i	0.0929118	+	0.160928i
$725$		0			0
$726$	3.00000	+	5.19615i	0.111340	+	0.192847i
$727$	32.0429	+	18.5000i	1.18841	+	0.686127i	0.957944	−	0.286954i	$-0.0926427\pi$
$727$	32.0429	+	18.5000i	1.18841	+	0.686127i	0.230463	+	0.973081i	$0.425976\pi$
$728$		−	15.0000i		−	0.555937i
$729$	27.0000			1.00000
$730$		0			0
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$	15.5885	+	9.00000i	0.576166	+	0.332650i
$733$	0.866025	−	0.500000i	0.0319874	−	0.0184679i	−0.483921	−	0.875112i	$-0.660788\pi$
$733$	0.866025	−	0.500000i	0.0319874	−	0.0184679i	0.515908	+	0.856644i	$0.327454\pi$
$734$	3.50000	+	6.06218i	0.129187	+	0.223759i
$735$		0			0
$736$	−4.00000			−0.147442
$737$	7.79423	+	4.50000i	0.287104	+	0.165760i
$738$	46.7654	+	27.0000i	1.72146	+	0.993884i
$739$	12.5000	+	21.6506i	0.459820	+	0.796431i	0.998951	−	0.0457903i	$-0.0145806\pi$
$739$	12.5000	+	21.6506i	0.459820	+	0.796431i	−0.539131	+	0.842222i	$0.681247\pi$
$740$		0			0
$741$	−52.5000	+	90.9327i	−1.92864	+	3.34050i
$742$		−	9.00000i		−	0.330400i
$743$		−	40.0000i		−	1.46746i	−0.679442	−	0.733729i	$-0.737778\pi$
$743$		−	40.0000i		−	1.46746i	0.679442	−	0.733729i	$-0.262222\pi$
$744$	−10.5000	−	12.9904i	−0.384949	−	0.476250i
$745$		0			0
$746$	10.0000			0.366126
$747$	25.9808	+	15.0000i	0.950586	+	0.548821i
$748$		−	9.00000i		−	0.329073i
$749$	19.5000	+	33.7750i	0.712514	+	1.23411i
$750$		0			0
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$			8.00000i			0.291730i
$753$	59.7558	−	34.5000i	2.17762	−	1.25725i
$754$	5.00000	+	8.66025i	0.182089	+	0.315388i
$755$		0			0
$756$	13.5000	−	23.3827i	0.490990	−	0.850420i
$757$	37.2391	−	21.5000i	1.35348	−	0.781431i	0.364743	−	0.931108i	$-0.381157\pi$
$757$	37.2391	−	21.5000i	1.35348	−	0.781431i	0.988735	+	0.149677i	$0.0478235\pi$
$758$	0.866025	+	0.500000i	0.0314555	+	0.0181608i
$759$	−36.0000			−1.30672
$760$		0			0
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	−0.922464	−	0.386082i	$-0.873828\pi$
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	0.795589	+	0.605836i	$0.207161\pi$
$762$	−33.7750	+	19.5000i	−1.22354	+	0.706410i
$763$	−5.19615	−	3.00000i	−0.188113	−	0.108607i
$764$	1.50000	+	2.59808i	0.0542681	+	0.0939951i
$765$		0			0
$766$	−7.50000	−	12.9904i	−0.270986	−	0.469362i
$767$		−	15.0000i		−	0.541619i
$768$	−2.59808	−	1.50000i	−0.0937500	−	0.0541266i
$769$	−16.5000	+	28.5788i	−0.595005	+	1.03058i	0.398541	+	0.917151i	$0.369517\pi$
$769$	−16.5000	+	28.5788i	−0.595005	+	1.03058i	−0.993546	+	0.113429i	$0.963817\pi$
$770$		0			0
$771$	−39.0000			−1.40455
$772$	16.4545	+	9.50000i	0.592210	+	0.341912i
$773$			46.0000i			1.65451i	0.561830	+	0.827253i	$0.310097\pi$
$773$			46.0000i			1.65451i	−0.561830	+	0.827253i	$0.689903\pi$
$774$	6.00000			0.215666
$775$		0			0
$776$	14.0000			0.502571
$777$			9.00000i			0.322873i
$778$	19.9186	+	11.5000i	0.714116	+	0.412295i
$779$	63.0000			2.25721
$780$		0			0
$781$	−1.50000	+	2.59808i	−0.0536742	+	0.0929665i
$782$	−10.3923	−	6.00000i	−0.371628	−	0.214560i
$783$			18.0000i			0.643268i
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$		0			0
$786$	31.5000	+	54.5596i	1.12357	+	1.94608i
$787$	−45.8993	−	26.5000i	−1.63614	−	0.944623i	−0.982146	−	0.188119i	$-0.939761\pi$
$787$	−45.8993	−	26.5000i	−1.63614	−	0.944623i	−0.653989	−	0.756504i	$-0.726906\pi$
$788$	−12.9904	+	7.50000i	−0.462763	+	0.267176i
$789$	−24.0000	+	41.5692i	−0.854423	+	1.47990i
$790$		0			0
$791$	3.00000			0.106668
$792$	−15.5885	−	9.00000i	−0.553912	−	0.319801i
$793$	25.9808	−	15.0000i	0.922604	−	0.532666i
$794$	10.5000	−	18.1865i	0.372631	−	0.645416i
$795$		0			0
$796$	10.5000	+	18.1865i	0.372163	+	0.644605i
$797$	−28.5788	+	16.5000i	−1.01231	+	0.584460i	−0.911868	−	0.410483i	$-0.865360\pi$
$797$	−28.5788	+	16.5000i	−1.01231	+	0.584460i	−0.100446	+	0.994943i	$0.532027\pi$
$798$		−	63.0000i		−	2.23018i
$799$	−12.0000	+	20.7846i	−0.424529	+	0.735307i
$800$		0			0
$801$	−18.0000	−	31.1769i	−0.635999	−	1.10158i
$802$			18.0000i			0.635602i
$803$	18.1865	+	10.5000i	0.641789	+	0.370537i
$804$	9.00000			0.317406
$805$		0			0
$806$	−27.5000	+	4.33013i	−0.968646	+	0.152522i
$807$		−	63.0000i		−	2.21771i
$808$		−	10.0000i		−	0.351799i
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$		0			0
$811$	−2.50000	−	4.33013i	−0.0877869	−	0.152051i	0.818788	−	0.574095i	$-0.194646\pi$
$811$	−2.50000	−	4.33013i	−0.0877869	−	0.152051i	−0.906575	+	0.422044i	$0.861313\pi$
$812$	−5.19615	−	3.00000i	−0.182349	−	0.105279i
$813$	20.7846	+	12.0000i	0.728948	+	0.420858i
$814$	3.00000			0.105150
$815$		0			0
$816$	−4.50000	−	7.79423i	−0.157532	−	0.272853i
$817$	6.06218	−	3.50000i	0.212089	−	0.122449i
$818$	−26.8468	−	15.5000i	−0.938676	−	0.541945i
$819$	−45.0000	−	77.9423i	−1.57243	−	2.72352i
$820$		0			0
$821$	38.0000			1.32621			0.663105	−	0.748527i	$-0.269238\pi$
$821$	38.0000			1.32621			0.663105	+	0.748527i	$0.269238\pi$
$822$		−	33.0000i		−	1.15101i
$823$	−28.5788	−	16.5000i	−0.996196	−	0.575154i	−0.0890752	−	0.996025i	$-0.528391\pi$
$823$	−28.5788	−	16.5000i	−0.996196	−	0.575154i	−0.907120	+	0.420871i	$0.861724\pi$
$824$	−6.50000	−	11.2583i	−0.226438	−	0.392203i
$825$		0			0
$826$	4.50000	+	7.79423i	0.156575	+	0.271196i
$827$	37.2391	−	21.5000i	1.29493	−	0.747628i	0.315406	−	0.948957i	$-0.397859\pi$
$827$	37.2391	−	21.5000i	1.29493	−	0.747628i	0.979524	+	0.201328i	$0.0645259\pi$
$828$	−20.7846	+	12.0000i	−0.722315	+	0.417029i
$829$	−46.0000			−1.59765			−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000			−1.59765			−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$	3.00000	−	5.19615i	0.104069	−	0.180253i
$832$	−4.33013	+	2.50000i	−0.150120	+	0.0866719i
$833$			6.00000i			0.207888i
$834$		0			0
$835$		0			0
$836$	−21.0000			−0.726300
$837$	−46.7654	−	18.0000i	−1.61645	−	0.622171i
$838$		−	28.0000i		−	0.967244i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	12.9904	−	7.50000i	0.447678	−	0.258467i
$843$	−77.9423	−	45.0000i	−2.68447	−	1.54988i
$844$	−0.500000	+	0.866025i	−0.0172107	+	0.0298098i
$845$		0			0
$846$	24.0000	+	41.5692i	0.825137	+	1.42918i
$847$	−5.19615	+	3.00000i	−0.178542	+	0.103081i
$848$	−2.59808	+	1.50000i	−0.0892183	+	0.0515102i
$849$	6.00000	−	10.3923i	0.205919	−	0.356663i
$850$		0			0
$851$	2.00000	−	3.46410i	0.0685591	−	0.118748i
$852$			3.00000i			0.102778i
$853$			14.0000i			0.479351i	0.970853	+	0.239675i	$0.0770410\pi$
$853$			14.0000i			0.479351i	−0.970853	+	0.239675i	$0.922959\pi$
$854$	−9.00000	+	15.5885i	−0.307974	+	0.533426i
$855$		0			0
$856$	6.50000	−	11.2583i	0.222165	−	0.384802i
$857$	18.1865	−	10.5000i	0.621240	−	0.358673i	−0.156112	−	0.987739i	$-0.549896\pi$
$857$	18.1865	−	10.5000i	0.621240	−	0.358673i	0.777352	+	0.629066i	$0.216563\pi$
$858$	−38.9711	+	22.5000i	−1.33045	+	0.768137i
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	0.874429	−	0.485153i	$-0.161236\pi$
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	−0.857369	+	0.514701i	$0.827903\pi$
$860$		0			0
$861$	−40.5000	+	70.1481i	−1.38024	+	2.39064i
$862$	4.33013	+	2.50000i	0.147485	+	0.0851503i
$863$	2.59808	−	1.50000i	0.0884395	−	0.0510606i	−0.455128	−	0.890426i	$-0.650407\pi$
$863$	2.59808	−	1.50000i	0.0884395	−	0.0510606i	0.543568	+	0.839365i	$0.317073\pi$
$864$	−9.00000			−0.306186
$865$		0			0
$866$	14.0000			0.475739
$867$			24.0000i			0.815083i
$868$	12.9904	−	10.5000i	0.440922	−	0.356393i
$869$	3.00000			0.101768
$870$		0			0
$871$	7.50000	−	12.9904i	0.254128	−	0.440162i
$872$			2.00000i			0.0677285i
$873$	72.7461	−	42.0000i	2.46208	−	1.42148i
$874$	−14.0000	+	24.2487i	−0.473557	+	0.820225i
$875$		0			0
$876$	21.0000			0.709524
$877$	9.52628	−	5.50000i	0.321680	−	0.185722i	−0.330461	−	0.943820i	$-0.607204\pi$
$877$	9.52628	−	5.50000i	0.321680	−	0.185722i	0.652141	+	0.758098i	$0.273871\pi$
$878$	−11.2583	+	6.50000i	−0.379950	+	0.219364i
$879$	−28.5000	−	49.3634i	−0.961281	−	1.66499i
$880$		0			0
$881$	−9.50000	−	16.4545i	−0.320063	−	0.554366i	0.660438	−	0.750881i	$-0.270371\pi$
$881$	−9.50000	−	16.4545i	−0.320063	−	0.554366i	−0.980501	+	0.196515i	$0.937037\pi$
$882$	10.3923	+	6.00000i	0.349927	+	0.202031i
$883$			44.0000i			1.48072i	0.672212	+	0.740359i	$0.265344\pi$
$883$			44.0000i			1.48072i	−0.672212	+	0.740359i	$0.734656\pi$
$884$	−15.0000			−0.504505
$885$		0			0
$886$	5.50000	+	9.52628i	0.184776	+	0.320042i
$887$	18.1865	+	10.5000i	0.610644	+	0.352555i	0.773217	−	0.634141i	$-0.218646\pi$
$887$	18.1865	+	10.5000i	0.610644	+	0.352555i	−0.162573	+	0.986696i	$0.551979\pi$
$888$	2.59808	−	1.50000i	0.0871857	−	0.0503367i
$889$	−19.5000	−	33.7750i	−0.654009	−	1.13278i
$890$		0			0
$891$	−27.0000			−0.904534
$892$	−16.4545	−	9.50000i	−0.550937	−	0.318084i
$893$	48.4974	+	28.0000i	1.62290	+	0.936984i
$894$	1.50000	+	2.59808i	0.0501675	+	0.0868927i
$895$		0			0
$896$	1.50000	−	2.59808i	0.0501115	−	0.0867956i
$897$			60.0000i			2.00334i
$898$			30.0000i			1.00111i
$899$	−4.00000	+	10.3923i	−0.133407	+	0.346603i
$900$		0			0
$901$	−9.00000			−0.299833
$902$	23.3827	+	13.5000i	0.778558	+	0.449501i
$903$			9.00000i			0.299501i
$904$	−0.500000	−	0.866025i	−0.0166298	−	0.0288036i
$905$		0			0
$906$	24.0000	−	41.5692i	0.797347	−	1.38104i
$907$		−	12.0000i		−	0.398453i	−0.979953	−	0.199227i	$-0.936157\pi$
$907$		−	12.0000i		−	0.398453i	0.979953	−	0.199227i	$-0.0638430\pi$
$908$	18.1865	−	10.5000i	0.603541	−	0.348455i
$909$	−30.0000	−	51.9615i	−0.995037	−	1.72345i
$910$		0			0
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	−0.714620	−	0.699513i	$-0.753400\pi$
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	0.963106	+	0.269122i	$0.0867336\pi$
$912$	−18.1865	+	10.5000i	−0.602216	+	0.347690i
$913$	12.9904	+	7.50000i	0.429919	+	0.248214i
$914$	−10.0000			−0.330771
$915$		0			0
$916$	3.50000	−	6.06218i	0.115643	−	0.200300i
$917$	−54.5596	+	31.5000i	−1.80172	+	1.04022i
$918$	−23.3827	−	13.5000i	−0.771744	−	0.445566i
$919$	29.5000	+	51.0955i	0.973115	+	1.68548i	0.686020	+	0.727583i	$0.259356\pi$
$919$	29.5000	+	51.0955i	0.973115	+	1.68548i	0.287096	+	0.957902i	$0.407310\pi$
$920$		0			0
$921$	7.50000	+	12.9904i	0.247133	+	0.428048i
$922$			42.0000i			1.38320i
$923$	4.33013	+	2.50000i	0.142528	+	0.0822885i
$924$	13.5000	−	23.3827i	0.444117	−	0.769234i
$925$		0			0
$926$	16.0000			0.525793
$927$	−67.5500	−	39.0000i	−2.21863	−	1.28093i
$928$			2.00000i			0.0656532i
$929$	−34.0000			−1.11550			−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000			−1.11550			−0.557752	+	0.830008i	$0.688336\pi$
$930$		0			0
$931$	14.0000			0.458831
$932$			18.0000i			0.589610i
$933$	−83.1384	−	48.0000i	−2.72183	−	1.57145i
$934$	8.00000			0.261768
$935$		0			0
$936$	−15.0000	+	25.9808i	−0.490290	+	0.849208i
$937$	19.9186	+	11.5000i	0.650712	+	0.375689i	0.788729	−	0.614741i	$-0.210740\pi$
$937$	19.9186	+	11.5000i	0.650712	+	0.375689i	−0.138017	+	0.990430i	$0.544073\pi$
$938$			9.00000i			0.293860i
$939$	10.5000	+	18.1865i	0.342655	+	0.593495i
$940$		0			0
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	0.642567	−	0.766229i	$-0.277869\pi$
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	−0.984858	+	0.173365i	$0.944536\pi$
$942$	−25.9808	−	15.0000i	−0.846499	−	0.488726i
$943$	31.1769	−	18.0000i	1.01526	−	0.586161i
$944$	1.50000	−	2.59808i	0.0488208	−	0.0845602i
$945$		0			0
$946$	3.00000			0.0975384
$947$	−11.2583	−	6.50000i	−0.365847	−	0.211222i	0.305796	−	0.952097i	$-0.401078\pi$
$947$	−11.2583	−	6.50000i	−0.365847	−	0.211222i	−0.671642	+	0.740875i	$0.734411\pi$
$948$	2.59808	−	1.50000i	0.0843816	−	0.0487177i
$949$	17.5000	−	30.3109i	0.568074	−	0.983933i
$950$		0			0
$951$	−43.5000	−	75.3442i	−1.41058	−	2.44320i
$952$	7.79423	−	4.50000i	0.252612	−	0.145846i
$953$		−	26.0000i		−	0.842223i	−0.907009	−	0.421111i	$-0.861640\pi$
$953$		−	26.0000i		−	0.842223i	0.907009	−	0.421111i	$-0.138360\pi$
$954$	−9.00000	+	15.5885i	−0.291386	+	0.504695i
$955$		0			0
$956$	0.500000	+	0.866025i	0.0161712	+	0.0280093i
$957$			18.0000i			0.581857i
$958$	9.52628	+	5.50000i	0.307780	+	0.177697i
$959$	33.0000			1.06563
$960$		0			0
$961$	−23.0000	−	20.7846i	−0.741935	−	0.670471i
$962$		−	5.00000i		−	0.161206i
$963$		−	78.0000i		−	2.51351i
$964$	−12.5000	+	21.6506i	−0.402598	+	0.697320i
$965$		0			0
$966$	−18.0000	−	31.1769i	−0.579141	−	1.00310i
$967$	11.2583	+	6.50000i	0.362043	+	0.209026i	0.669977	−	0.742382i	$-0.266304\pi$
$967$	11.2583	+	6.50000i	0.362043	+	0.209026i	−0.307933	+	0.951408i	$0.599637\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$	−63.0000			−2.02385
$970$		0			0
$971$	−0.500000	−	0.866025i	−0.0160458	−	0.0277921i	0.857891	−	0.513832i	$-0.171774\pi$
$971$	−0.500000	−	0.866025i	−0.0160458	−	0.0277921i	−0.873937	+	0.486040i	$0.838441\pi$
$972$		0			0
$973$		0			0
$974$	5.50000	+	9.52628i	0.176231	+	0.305242i
$975$		0			0
$976$	6.00000			0.192055
$977$		−	54.0000i		−	1.72761i	−0.503824	−	0.863807i	$-0.668074\pi$
$977$		−	54.0000i		−	1.72761i	0.503824	−	0.863807i	$-0.331926\pi$
$978$	10.3923	+	6.00000i	0.332309	+	0.191859i
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$		0			0
$981$	6.00000	+	10.3923i	0.191565	+	0.331801i
$982$	12.9904	−	7.50000i	0.414540	−	0.239335i
$983$	−42.4352	+	24.5000i	−1.35347	+	0.781429i	−0.988734	−	0.149681i	$-0.952175\pi$
$983$	−42.4352	+	24.5000i	−1.35347	+	0.781429i	−0.364740	+	0.931110i	$0.618842\pi$
$984$	27.0000			0.860729
$985$		0			0
$986$	−3.00000	+	5.19615i	−0.0955395	+	0.165479i
$987$	−62.3538	+	36.0000i	−1.98474	+	1.14589i
$988$			35.0000i			1.11350i
$989$	2.00000	−	3.46410i	0.0635963	−	0.110152i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	−5.19615	−	2.00000i	−0.164978	−	0.0635001i
$993$			51.0000i			1.61844i
$994$	−3.00000			−0.0951542
$995$		0			0
$996$	15.0000			0.475293
$997$	30.3109	−	17.5000i	0.959955	−	0.554231i	0.0637961	−	0.997963i	$-0.479679\pi$
$997$	30.3109	−	17.5000i	0.959955	−	0.554231i	0.896159	+	0.443732i	$0.146346\pi$
$998$	−12.9904	−	7.50000i	−0.411203	−	0.237408i
$999$	4.50000	−	7.79423i	0.142374	−	0.246598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1550.2.p.a.749.1		4
5.2	odd	4		62.2.c.b.5.1	✓	2
5.3	odd	4		1550.2.e.d.501.1		2
5.4	even	2	inner	1550.2.p.a.749.2		4
15.2	even	4		558.2.e.b.253.1		2
20.7	even	4		496.2.i.g.129.1		2
31.25	even	3	inner	1550.2.p.a.149.1		4
155.57	even	12		1922.2.a.c.1.1		1
155.67	odd	12		1922.2.a.e.1.1		1
155.87	odd	12		62.2.c.b.25.1	yes	2
155.118	odd	12		1550.2.e.d.1451.1		2
155.149	even	6	inner	1550.2.p.a.149.2		4
465.242	even	12		558.2.e.b.397.1		2
620.87	even	12		496.2.i.g.273.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.c.b.5.1	✓	2	5.2	odd	4
62.2.c.b.25.1	yes	2	155.87	odd	12
496.2.i.g.129.1		2	20.7	even	4
496.2.i.g.273.1		2	620.87	even	12
558.2.e.b.253.1		2	15.2	even	4
558.2.e.b.397.1		2	465.242	even	12
1550.2.e.d.501.1		2	5.3	odd	4
1550.2.e.d.1451.1		2	155.118	odd	12
1550.2.p.a.149.1		4	31.25	even	3	inner
1550.2.p.a.149.2		4	155.149	even	6	inner
1550.2.p.a.749.1		4	1.1	even	1	trivial
1550.2.p.a.749.2		4	5.4	even	2	inner
1922.2.a.c.1.1		1	155.57	even	12
1922.2.a.e.1.1		1	155.67	odd	12

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:	\( N \)	\(=\)	\( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1550.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-2.59808 - 1.50000i) q^{3} -1.00000 q^{4} +(-1.50000 + 2.59808i) q^{6} +(-2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(3.00000 + 5.19615i) q^{9} +(1.50000 + 2.59808i) q^{11} +(2.59808 + 1.50000i) q^{12} +(4.33013 - 2.50000i) q^{13} +(-1.50000 + 2.59808i) q^{14} +1.00000 q^{16} +(2.59808 + 1.50000i) q^{17} +(5.19615 - 3.00000i) q^{18} +(3.50000 - 6.06218i) q^{19} +(4.50000 + 7.79423i) q^{21} +(2.59808 - 1.50000i) q^{22} -4.00000i q^{23} +(1.50000 - 2.59808i) q^{24} +(-2.50000 - 4.33013i) q^{26} -9.00000i q^{27} +(2.59808 + 1.50000i) q^{28} -2.00000 q^{29} +(2.00000 - 5.19615i) q^{31} -1.00000i q^{32} -9.00000i q^{33} +(1.50000 - 2.59808i) q^{34} +(-3.00000 - 5.19615i) q^{36} +(0.866025 + 0.500000i) q^{37} +(-6.06218 - 3.50000i) q^{38} -15.0000 q^{39} +(4.50000 + 7.79423i) q^{41} +(7.79423 - 4.50000i) q^{42} +(0.866025 + 0.500000i) q^{43} +(-1.50000 - 2.59808i) q^{44} -4.00000 q^{46} +8.00000i q^{47} +(-2.59808 - 1.50000i) q^{48} +(1.00000 + 1.73205i) q^{49} +(-4.50000 - 7.79423i) q^{51} +(-4.33013 + 2.50000i) q^{52} +(-2.59808 + 1.50000i) q^{53} -9.00000 q^{54} +(1.50000 - 2.59808i) q^{56} +(-18.1865 + 10.5000i) q^{57} +2.00000i q^{58} +(1.50000 - 2.59808i) q^{59} +6.00000 q^{61} +(-5.19615 - 2.00000i) q^{62} -18.0000i q^{63} -1.00000 q^{64} -9.00000 q^{66} +(2.59808 - 1.50000i) q^{67} +(-2.59808 - 1.50000i) q^{68} +(-6.00000 + 10.3923i) q^{69} +(0.500000 + 0.866025i) q^{71} +(-5.19615 + 3.00000i) q^{72} +(6.06218 - 3.50000i) q^{73} +(0.500000 - 0.866025i) q^{74} +(-3.50000 + 6.06218i) q^{76} -9.00000i q^{77} +15.0000i q^{78} +(0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(7.79423 - 4.50000i) q^{82} +(4.33013 - 2.50000i) q^{83} +(-4.50000 - 7.79423i) q^{84} +(0.500000 - 0.866025i) q^{86} +(5.19615 + 3.00000i) q^{87} +(-2.59808 + 1.50000i) q^{88} -6.00000 q^{89} -15.0000 q^{91} +4.00000i q^{92} +(-12.9904 + 10.5000i) q^{93} +8.00000 q^{94} +(-1.50000 + 2.59808i) q^{96} -14.0000i q^{97} +(1.73205 - 1.00000i) q^{98} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 6 q^{6} + 12 q^{9} + 6 q^{11} - 6 q^{14} + 4 q^{16} + 14 q^{19} + 18 q^{21} + 6 q^{24} - 10 q^{26} - 8 q^{29} + 8 q^{31} + 6 q^{34} - 12 q^{36} - 60 q^{39} + 18 q^{41} - 6 q^{44} - 16 q^{46}+ \cdots - 36 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 6 * q^6 + 12 * q^9 + 6 * q^11 - 6 * q^14 + 4 * q^16 + 14 * q^19 + 18 * q^21 + 6 * q^24 - 10 * q^26 - 8 * q^29 + 8 * q^31 + 6 * q^34 - 12 * q^36 - 60 * q^39 + 18 * q^41 - 6 * q^44 - 16 * q^46 + 4 * q^49 - 18 * q^51 - 36 * q^54 + 6 * q^56 + 6 * q^59 + 24 * q^61 - 4 * q^64 - 36 * q^66 - 24 * q^69 + 2 * q^71 + 2 * q^74 - 14 * q^76 + 2 * q^79 - 18 * q^81 - 18 * q^84 + 2 * q^86 - 24 * q^89 - 60 * q^91 + 32 * q^94 - 6 * q^96 - 36 * q^99

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