LMFDB - Embedded newform 1470.2.i.v.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1470,2,Mod(361,1470)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1470, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 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("1470.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,2,-2,2,-4,0,4,-2,2,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1470.361
Dual form			1470.2.i.v.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.70711 + 2.95680i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.707107 + 1.22474i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.41421 + 2.44949i) q^{19} -1.00000 q^{20} +3.41421 q^{22} +(0.414214 + 0.717439i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -0.242641 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-4.53553 + 7.85578i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.70711 + 2.95680i) q^{33} +1.41421 q^{34} +1.00000 q^{36} +(-0.707107 - 1.22474i) q^{37} +(1.41421 - 2.44949i) q^{38} +(0.500000 + 0.866025i) q^{40} +3.17157 q^{41} +7.41421 q^{43} +(-1.70711 - 2.95680i) q^{44} +(0.500000 - 0.866025i) q^{45} +(0.414214 - 0.717439i) q^{46} +(2.53553 + 4.39167i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(0.707107 + 1.22474i) q^{51} +(-6.65685 + 11.5300i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.41421 q^{55} +2.82843 q^{57} +(0.121320 + 0.210133i) q^{58} +(-7.24264 + 12.5446i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-0.171573 - 0.297173i) q^{61} +9.07107 q^{62} +1.00000 q^{64} +(1.70711 - 2.95680i) q^{66} +(5.94975 - 10.3053i) q^{67} +(-0.707107 - 1.22474i) q^{68} +0.828427 q^{69} +5.17157 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.82843 + 3.16693i) q^{73} +(-0.707107 + 1.22474i) q^{74} +(0.500000 + 0.866025i) q^{75} -2.82843 q^{76} +(-5.65685 - 9.79796i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.58579 - 2.74666i) q^{82} +10.8284 q^{83} -1.41421 q^{85} +(-3.70711 - 6.42090i) q^{86} +(-0.121320 + 0.210133i) q^{87} +(-1.70711 + 2.95680i) q^{88} +(5.24264 + 9.08052i) q^{89} -1.00000 q^{90} -0.828427 q^{92} +(4.53553 + 7.85578i) q^{93} +(2.53553 - 4.39167i) q^{94} +(-1.41421 + 2.44949i) q^{95} +(0.500000 + 0.866025i) q^{96} -3.17157 q^{97} +3.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 4 q^{15} - 2 q^{16} - 2 q^{18} - 4 q^{20} + 8 q^{22} - 4 q^{23} + 2 q^{24} - 2 q^{25} - 4 q^{27}+ \cdots + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 4 * q^15 - 2 * q^16 - 2 * q^18 - 4 * q^20 + 8 * q^22 - 4 * q^23 + 2 * q^24 - 2 * q^25 - 4 * q^27 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^36 + 2 * q^40 + 24 * q^41 + 24 * q^43 - 4 * q^44 + 2 * q^45 - 4 * q^46 - 4 * q^47 - 4 * q^48 + 4 * q^50 - 4 * q^53 + 2 * q^54 - 8 * q^55 - 8 * q^58 - 12 * q^59 - 2 * q^60 - 12 * q^61 + 8 * q^62 + 4 * q^64 + 4 * q^66 + 4 * q^67 - 8 * q^69 + 32 * q^71 - 2 * q^72 + 4 * q^73 + 2 * q^75 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 32 * q^83 - 12 * q^86 + 8 * q^87 - 4 * q^88 + 4 * q^89 - 4 * q^90 + 8 * q^92 + 4 * q^93 - 4 * q^94 + 2 * q^96 - 24 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.70711	+	2.95680i	−0.514712	+	0.891507i	0.485142	+	0.874435i	$0.338768\pi$
$11$	−1.70711	+	2.95680i	−0.514712	+	0.891507i	−0.999854	+	0.0170722i	$0.994565\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.707107	+	1.22474i	−0.171499	+	0.297044i	−0.938944	−	0.344070i	$-0.888194\pi$
$17$	−0.707107	+	1.22474i	−0.171499	+	0.297044i	0.767445	+	0.641114i	$0.221528\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	0.981399	−	0.191977i	$-0.0614899\pi$
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	−0.656957	+	0.753928i	$0.728157\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	3.41421			0.727913
$23$	0.414214	+	0.717439i	0.0863695	+	0.149596i	0.905974	−	0.423333i	$-0.139140\pi$
$23$	0.414214	+	0.717439i	0.0863695	+	0.149596i	−0.819604	+	0.572930i	$0.805807\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−0.242641			−0.0450572			−0.0225286	−	0.999746i	$-0.507172\pi$
$29$	−0.242641			−0.0450572			−0.0225286	+	0.999746i	$0.507172\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−4.53553	+	7.85578i	−0.814606	+	1.41094i	0.0950046	+	0.995477i	$0.469713\pi$
$31$	−4.53553	+	7.85578i	−0.814606	+	1.41094i	−0.909611	+	0.415462i	$0.863620\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.70711	+	2.95680i	0.297169	+	0.514712i
$34$	1.41421			0.242536
$35$		0			0
$36$	1.00000			0.166667
$37$	−0.707107	−	1.22474i	−0.116248	−	0.201347i	0.802030	−	0.597284i	$-0.203753\pi$
$37$	−0.707107	−	1.22474i	−0.116248	−	0.201347i	−0.918278	+	0.395937i	$0.870420\pi$
$38$	1.41421	−	2.44949i	0.229416	−	0.397360i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	3.17157			0.495316			0.247658	−	0.968847i	$-0.420339\pi$
$41$	3.17157			0.495316			0.247658	+	0.968847i	$0.420339\pi$
$42$		0			0
$43$	7.41421			1.13066			0.565328	−	0.824866i	$-0.308749\pi$
$43$	7.41421			1.13066			0.565328	+	0.824866i	$0.308749\pi$
$44$	−1.70711	−	2.95680i	−0.257356	−	0.445754i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	0.414214	−	0.717439i	0.0610725	−	0.105781i
$47$	2.53553	+	4.39167i	0.369846	+	0.640591i	0.989541	−	0.144251i	$-0.0460772\pi$
$47$	2.53553	+	4.39167i	0.369846	+	0.640591i	−0.619696	+	0.784842i	$0.712744\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	1.00000			0.141421
$51$	0.707107	+	1.22474i	0.0990148	+	0.171499i
$52$		0			0
$53$	−6.65685	+	11.5300i	−0.914389	+	1.58377i	−0.106596	+	0.994302i	$0.533995\pi$
$53$	−6.65685	+	11.5300i	−0.914389	+	1.58377i	−0.807793	+	0.589466i	$0.799338\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−3.41421			−0.460372
$56$		0			0
$57$	2.82843			0.374634
$58$	0.121320	+	0.210133i	0.0159301	+	0.0275918i
$59$	−7.24264	+	12.5446i	−0.942912	+	1.63317i	−0.183032	+	0.983107i	$0.558591\pi$
$59$	−7.24264	+	12.5446i	−0.942912	+	1.63317i	−0.759880	+	0.650064i	$0.774742\pi$
$60$	−0.500000	+	0.866025i	−0.0645497	+	0.111803i
$61$	−0.171573	−	0.297173i	−0.0219677	−	0.0380491i	0.854833	−	0.518904i	$-0.173660\pi$
$61$	−0.171573	−	0.297173i	−0.0219677	−	0.0380491i	−0.876800	+	0.480855i	$0.840326\pi$
$62$	9.07107			1.15203
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	1.70711	−	2.95680i	0.210130	−	0.363956i
$67$	5.94975	−	10.3053i	0.726877	−	1.25899i	−0.231319	−	0.972878i	$-0.574304\pi$
$67$	5.94975	−	10.3053i	0.726877	−	1.25899i	0.958197	−	0.286111i	$-0.0923625\pi$
$68$	−0.707107	−	1.22474i	−0.0857493	−	0.148522i
$69$	0.828427			0.0997309
$70$		0			0
$71$	5.17157			0.613753			0.306876	−	0.951749i	$-0.400716\pi$
$71$	5.17157			0.613753			0.306876	+	0.951749i	$0.400716\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−1.82843	+	3.16693i	−0.214001	+	0.370661i	−0.952963	−	0.303086i	$-0.901983\pi$
$73$	−1.82843	+	3.16693i	−0.214001	+	0.370661i	0.738962	+	0.673747i	$0.235316\pi$
$74$	−0.707107	+	1.22474i	−0.0821995	+	0.142374i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−2.82843			−0.324443
$77$		0			0
$78$		0			0
$79$	−5.65685	−	9.79796i	−0.636446	−	1.10236i	−0.986207	−	0.165518i	$-0.947071\pi$
$79$	−5.65685	−	9.79796i	−0.636446	−	1.10236i	0.349761	−	0.936839i	$-0.386263\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.58579	−	2.74666i	−0.175121	−	0.303318i
$83$	10.8284			1.18857			0.594287	−	0.804253i	$-0.297434\pi$
$83$	10.8284			1.18857			0.594287	+	0.804253i	$0.297434\pi$
$84$		0			0
$85$	−1.41421			−0.153393
$86$	−3.70711	−	6.42090i	−0.399748	−	0.692383i
$87$	−0.121320	+	0.210133i	−0.0130069	+	0.0225286i
$88$	−1.70711	+	2.95680i	−0.181978	+	0.315195i
$89$	5.24264	+	9.08052i	0.555719	+	0.962533i	0.997847	+	0.0655814i	$0.0208902\pi$
$89$	5.24264	+	9.08052i	0.555719	+	0.962533i	−0.442128	+	0.896952i	$0.645776\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−0.828427			−0.0863695
$93$	4.53553	+	7.85578i	0.470313	+	0.814606i
$94$	2.53553	−	4.39167i	0.261520	−	0.452967i
$95$	−1.41421	+	2.44949i	−0.145095	+	0.251312i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−3.17157			−0.322024			−0.161012	−	0.986952i	$-0.551476\pi$
$97$	−3.17157			−0.322024			−0.161012	+	0.986952i	$0.551476\pi$
$98$		0			0
$99$	3.41421			0.343141
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−8.82843	+	15.2913i	−0.878461	+	1.52154i	−0.0254321	+	0.999677i	$0.508096\pi$
$101$	−8.82843	+	15.2913i	−0.878461	+	1.52154i	−0.853029	+	0.521863i	$0.825237\pi$
$102$	0.707107	−	1.22474i	0.0700140	−	0.121268i
$103$	9.07107	+	15.7116i	0.893799	+	1.54811i	0.835284	+	0.549819i	$0.185303\pi$
$103$	9.07107	+	15.7116i	0.893799	+	1.54811i	0.0585147	+	0.998287i	$0.481364\pi$
$104$		0			0
$105$		0			0
$106$	13.3137			1.29314
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	8.65685	−	14.9941i	0.829176	−	1.43618i	−0.0695090	−	0.997581i	$-0.522143\pi$
$109$	8.65685	−	14.9941i	0.829176	−	1.43618i	0.898685	−	0.438594i	$-0.144523\pi$
$110$	1.70711	+	2.95680i	0.162766	+	0.281919i
$111$	−1.41421			−0.134231
$112$		0			0
$113$	−13.3137			−1.25245			−0.626224	−	0.779643i	$-0.715401\pi$
$113$	−13.3137			−1.25245			−0.626224	+	0.779643i	$0.715401\pi$
$114$	−1.41421	−	2.44949i	−0.132453	−	0.229416i
$115$	−0.414214	+	0.717439i	−0.0386256	+	0.0669015i
$116$	0.121320	−	0.210133i	0.0112643	−	0.0195104i
$117$		0			0
$118$	14.4853			1.33348
$119$		0			0
$120$	1.00000			0.0912871
$121$	−0.328427	−	0.568852i	−0.0298570	−	0.0517139i
$122$	−0.171573	+	0.297173i	−0.0155335	+	0.0269048i
$123$	1.58579	−	2.74666i	0.142986	−	0.247658i
$124$	−4.53553	−	7.85578i	−0.407303	−	0.705469i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	14.1421			1.25491			0.627456	−	0.778652i	$-0.284096\pi$
$127$	14.1421			1.25491			0.627456	+	0.778652i	$0.284096\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	3.70711	−	6.42090i	0.326393	−	0.565328i
$130$		0			0
$131$	−5.58579	−	9.67487i	−0.488032	−	0.845297i	0.511873	−	0.859061i	$-0.328952\pi$
$131$	−5.58579	−	9.67487i	−0.488032	−	0.845297i	−0.999905	+	0.0137643i	$0.995619\pi$
$132$	−3.41421			−0.297169
$133$		0			0
$134$	−11.8995			−1.02796
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−0.707107	+	1.22474i	−0.0606339	+	0.105021i
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	−0.290424	−	0.956898i	$-0.593796\pi$
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	0.973910	−	0.226935i	$-0.0728704\pi$
$138$	−0.414214	−	0.717439i	−0.0352602	−	0.0610725i
$139$	−6.34315			−0.538019			−0.269009	−	0.963138i	$-0.586696\pi$
$139$	−6.34315			−0.538019			−0.269009	+	0.963138i	$0.586696\pi$
$140$		0			0
$141$	5.07107			0.427061
$142$	−2.58579	−	4.47871i	−0.216994	−	0.375845i
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.121320	−	0.210133i	−0.0100751	−	0.0174506i
$146$	3.65685			0.302643
$147$		0			0
$148$	1.41421			0.116248
$149$	−2.94975	−	5.10911i	−0.241653	−	0.418555i	0.719532	−	0.694459i	$-0.244356\pi$
$149$	−2.94975	−	5.10911i	−0.241653	−	0.418555i	−0.961185	+	0.275904i	$0.911023\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	10.8995	−	18.8785i	0.886988	−	1.53631i	0.0435707	−	0.999050i	$-0.486127\pi$
$151$	10.8995	−	18.8785i	0.886988	−	1.53631i	0.843418	−	0.537258i	$-0.180540\pi$
$152$	1.41421	+	2.44949i	0.114708	+	0.198680i
$153$	1.41421			0.114332
$154$		0			0
$155$	−9.07107			−0.728606
$156$		0			0
$157$	5.82843	−	10.0951i	0.465159	−	0.805679i	−0.534050	−	0.845453i	$-0.679330\pi$
$157$	5.82843	−	10.0951i	0.465159	−	0.805679i	0.999209	+	0.0397739i	$0.0126638\pi$
$158$	−5.65685	+	9.79796i	−0.450035	+	0.779484i
$159$	6.65685	+	11.5300i	0.527923	+	0.914389i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	1.00000			0.0785674
$163$	5.36396	+	9.29065i	0.420138	+	0.727700i	0.995953	−	0.0898801i	$-0.0286484\pi$
$163$	5.36396	+	9.29065i	0.420138	+	0.727700i	−0.575815	+	0.817580i	$0.695315\pi$
$164$	−1.58579	+	2.74666i	−0.123829	+	0.214478i
$165$	−1.70711	+	2.95680i	−0.132898	+	0.230186i
$166$	−5.41421	−	9.37769i	−0.420224	−	0.727850i
$167$	13.0711			1.01147			0.505735	−	0.862689i	$-0.331221\pi$
$167$	13.0711			1.01147			0.505735	+	0.862689i	$0.331221\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	0.707107	+	1.22474i	0.0542326	+	0.0939336i
$171$	1.41421	−	2.44949i	0.108148	−	0.187317i
$172$	−3.70711	+	6.42090i	−0.282664	+	0.489589i
$173$	0.757359	+	1.31178i	0.0575810	+	0.0997332i	0.893379	−	0.449304i	$-0.148328\pi$
$173$	0.757359	+	1.31178i	0.0575810	+	0.0997332i	−0.835798	+	0.549037i	$0.814995\pi$
$174$	0.242641			0.0183945
$175$		0			0
$176$	3.41421			0.257356
$177$	7.24264	+	12.5446i	0.544390	+	0.942912i
$178$	5.24264	−	9.08052i	0.392953	−	0.680614i
$179$	−1.70711	+	2.95680i	−0.127595	+	0.221001i	−0.922744	−	0.385413i	$-0.874059\pi$
$179$	−1.70711	+	2.95680i	−0.127595	+	0.221001i	0.795149	+	0.606414i	$0.207392\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	3.17157			0.235741			0.117871	−	0.993029i	$-0.462393\pi$
$181$	3.17157			0.235741			0.117871	+	0.993029i	$0.462393\pi$
$182$		0			0
$183$	−0.343146			−0.0253661
$184$	0.414214	+	0.717439i	0.0305362	+	0.0528903i
$185$	0.707107	−	1.22474i	0.0519875	−	0.0900450i
$186$	4.53553	−	7.85578i	0.332561	−	0.576013i
$187$	−2.41421	−	4.18154i	−0.176545	−	0.305785i
$188$	−5.07107			−0.369846
$189$		0			0
$190$	2.82843			0.205196
$191$	−5.65685	−	9.79796i	−0.409316	−	0.708955i	0.585498	−	0.810674i	$-0.300899\pi$
$191$	−5.65685	−	9.79796i	−0.409316	−	0.708955i	−0.994813	+	0.101719i	$0.967566\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−8.89949	+	15.4144i	−0.640600	+	1.10955i	0.344699	+	0.938713i	$0.387981\pi$
$193$	−8.89949	+	15.4144i	−0.640600	+	1.10955i	−0.985299	+	0.170838i	$0.945353\pi$
$194$	1.58579	+	2.74666i	0.113853	+	0.197199i
$195$		0			0
$196$		0			0
$197$	−15.1716			−1.08093			−0.540465	−	0.841367i	$-0.681752\pi$
$197$	−15.1716			−1.08093			−0.540465	+	0.841367i	$0.681752\pi$
$198$	−1.70711	−	2.95680i	−0.121319	−	0.210130i
$199$	8.53553	−	14.7840i	0.605068	−	1.04801i	−0.386973	−	0.922091i	$-0.626479\pi$
$199$	8.53553	−	14.7840i	0.605068	−	1.04801i	0.992041	−	0.125917i	$-0.0401874\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−5.94975	−	10.3053i	−0.419663	−	0.726877i
$202$	17.6569			1.24233
$203$		0			0
$204$	−1.41421			−0.0990148
$205$	1.58579	+	2.74666i	0.110756	+	0.191835i
$206$	9.07107	−	15.7116i	0.632011	−	1.09468i
$207$	0.414214	−	0.717439i	0.0287898	−	0.0498655i
$208$		0			0
$209$	−9.65685			−0.667979
$210$		0			0
$211$	9.65685			0.664805			0.332403	−	0.943138i	$-0.392141\pi$
$211$	9.65685			0.664805			0.332403	+	0.943138i	$0.392141\pi$
$212$	−6.65685	−	11.5300i	−0.457195	−	0.791884i
$213$	2.58579	−	4.47871i	0.177175	−	0.306876i
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	3.70711	+	6.42090i	0.252823	+	0.437902i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−17.3137			−1.17263
$219$	1.82843	+	3.16693i	0.123554	+	0.214001i
$220$	1.70711	−	2.95680i	0.115093	−	0.199347i
$221$		0			0
$222$	0.707107	+	1.22474i	0.0474579	+	0.0821995i
$223$	−6.34315			−0.424768			−0.212384	−	0.977186i	$-0.568123\pi$
$223$	−6.34315			−0.424768			−0.212384	+	0.977186i	$0.568123\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	6.65685	+	11.5300i	0.442807	+	0.766965i
$227$	−1.17157	+	2.02922i	−0.0777600	+	0.134684i	−0.902283	−	0.431144i	$-0.858110\pi$
$227$	−1.17157	+	2.02922i	−0.0777600	+	0.134684i	0.824523	+	0.565828i	$0.191443\pi$
$228$	−1.41421	+	2.44949i	−0.0936586	+	0.162221i
$229$	−6.89949	−	11.9503i	−0.455931	−	0.789696i	0.542810	−	0.839856i	$-0.317360\pi$
$229$	−6.89949	−	11.9503i	−0.455931	−	0.789696i	−0.998741	+	0.0501592i	$0.984027\pi$
$230$	0.828427			0.0546249
$231$		0			0
$232$	−0.242641			−0.0159301
$233$	13.4853	+	23.3572i	0.883450	+	1.53018i	0.847480	+	0.530828i	$0.178119\pi$
$233$	13.4853	+	23.3572i	0.883450	+	1.53018i	0.0359704	+	0.999353i	$0.488548\pi$
$234$		0			0
$235$	−2.53553	+	4.39167i	−0.165400	+	0.286481i
$236$	−7.24264	−	12.5446i	−0.471456	−	0.816585i
$237$	−11.3137			−0.734904
$238$		0			0
$239$	0.686292			0.0443925			0.0221963	−	0.999754i	$-0.492934\pi$
$239$	0.686292			0.0443925			0.0221963	+	0.999754i	$0.492934\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	−3.87868	+	6.71807i	−0.249848	+	0.432749i	−0.963483	−	0.267768i	$-0.913714\pi$
$241$	−3.87868	+	6.71807i	−0.249848	+	0.432749i	0.713636	+	0.700517i	$0.247047\pi$
$242$	−0.328427	+	0.568852i	−0.0211121	+	0.0365672i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.343146			0.0219677
$245$		0			0
$246$	−3.17157			−0.202212
$247$		0			0
$248$	−4.53553	+	7.85578i	−0.288007	+	0.498842i
$249$	5.41421	−	9.37769i	0.343112	−	0.594287i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	6.34315			0.400376			0.200188	−	0.979758i	$-0.435845\pi$
$251$	6.34315			0.400376			0.200188	+	0.979758i	$0.435845\pi$
$252$		0			0
$253$	−2.82843			−0.177822
$254$	−7.07107	−	12.2474i	−0.443678	−	0.768473i
$255$	−0.707107	+	1.22474i	−0.0442807	+	0.0766965i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.94975	−	15.5014i	−0.558270	−	0.966952i	−0.997641	−	0.0686462i	$-0.978132\pi$
$257$	−8.94975	−	15.5014i	−0.558270	−	0.966952i	0.439371	−	0.898306i	$-0.355201\pi$
$258$	−7.41421			−0.461589
$259$		0			0
$260$		0			0
$261$	0.121320	+	0.210133i	0.00750954	+	0.0130069i
$262$	−5.58579	+	9.67487i	−0.345091	+	0.597715i
$263$	−8.89949	+	15.4144i	−0.548766	+	0.950491i	0.449593	+	0.893233i	$0.351569\pi$
$263$	−8.89949	+	15.4144i	−0.548766	+	0.950491i	−0.998359	+	0.0572577i	$0.981764\pi$
$264$	1.70711	+	2.95680i	0.105065	+	0.181978i
$265$	−13.3137			−0.817855
$266$		0			0
$267$	10.4853			0.641689
$268$	5.94975	+	10.3053i	0.363439	+	0.629494i
$269$	−1.82843	+	3.16693i	−0.111481	+	0.193091i	−0.916368	−	0.400338i	$-0.868893\pi$
$269$	−1.82843	+	3.16693i	−0.111481	+	0.193091i	0.804886	+	0.593429i	$0.202226\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−2.87868	−	4.98602i	−0.174867	−	0.302879i	0.765248	−	0.643736i	$-0.222616\pi$
$271$	−2.87868	−	4.98602i	−0.174867	−	0.302879i	−0.940115	+	0.340856i	$0.889283\pi$
$272$	1.41421			0.0857493
$273$		0			0
$274$	−16.0000			−0.966595
$275$	−1.70711	−	2.95680i	−0.102942	−	0.178301i
$276$	−0.414214	+	0.717439i	−0.0249327	+	0.0431847i
$277$	−1.05025	+	1.81909i	−0.0631036	+	0.109299i	−0.895851	−	0.444354i	$-0.853433\pi$
$277$	−1.05025	+	1.81909i	−0.0631036	+	0.109299i	0.832748	+	0.553653i	$0.186767\pi$
$278$	3.17157	+	5.49333i	0.190218	+	0.329468i
$279$	9.07107			0.543071
$280$		0			0
$281$	−30.4853			−1.81860			−0.909300	−	0.416142i	$-0.863382\pi$
$281$	−30.4853			−1.81860			−0.909300	+	0.416142i	$0.863382\pi$
$282$	−2.53553	−	4.39167i	−0.150989	−	0.261520i
$283$	6.75736	−	11.7041i	0.401683	−	0.695736i	−0.592246	−	0.805757i	$-0.701759\pi$
$283$	6.75736	−	11.7041i	0.401683	−	0.695736i	0.993929	+	0.110021i	$0.0350919\pi$
$284$	−2.58579	+	4.47871i	−0.153438	+	0.265763i
$285$	1.41421	+	2.44949i	0.0837708	+	0.145095i
$286$		0			0
$287$		0			0
$288$	1.00000			0.0589256
$289$	7.50000	+	12.9904i	0.441176	+	0.764140i
$290$	−0.121320	+	0.210133i	−0.00712418	+	0.0123394i
$291$	−1.58579	+	2.74666i	−0.0929604	+	0.161012i
$292$	−1.82843	−	3.16693i	−0.107001	−	0.185330i
$293$	−16.6274			−0.971384			−0.485692	−	0.874130i	$-0.661432\pi$
$293$	−16.6274			−0.971384			−0.485692	+	0.874130i	$0.661432\pi$
$294$		0			0
$295$	−14.4853			−0.843366
$296$	−0.707107	−	1.22474i	−0.0410997	−	0.0711868i
$297$	1.70711	−	2.95680i	0.0990564	−	0.171571i
$298$	−2.94975	+	5.10911i	−0.170874	+	0.295963i
$299$		0			0
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	−21.7990			−1.25439
$303$	8.82843	+	15.2913i	0.507180	+	0.878461i
$304$	1.41421	−	2.44949i	0.0811107	−	0.140488i
$305$	0.171573	−	0.297173i	0.00982423	−	0.0170161i
$306$	−0.707107	−	1.22474i	−0.0404226	−	0.0700140i
$307$	−15.3137			−0.874000			−0.437000	−	0.899462i	$-0.643959\pi$
$307$	−15.3137			−0.874000			−0.437000	+	0.899462i	$0.643959\pi$
$308$		0			0
$309$	18.1421			1.03207
$310$	4.53553	+	7.85578i	0.257601	+	0.446178i
$311$	−17.4142	+	30.1623i	−0.987469	+	1.71035i	−0.357067	+	0.934079i	$0.616223\pi$
$311$	−17.4142	+	30.1623i	−0.987469	+	1.71035i	−0.630402	+	0.776269i	$0.717110\pi$
$312$		0			0
$313$	11.5858	+	20.0672i	0.654867	+	1.13426i	0.981927	+	0.189260i	$0.0606089\pi$
$313$	11.5858	+	20.0672i	0.654867	+	1.13426i	−0.327060	+	0.945004i	$0.606058\pi$
$314$	−11.6569			−0.657834
$315$		0			0
$316$	11.3137			0.636446
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$	6.65685	−	11.5300i	0.373298	−	0.646571i
$319$	0.414214	−	0.717439i	0.0231915	−	0.0401689i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	4.00000			0.223258
$322$		0			0
$323$	−4.00000			−0.222566
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	5.36396	−	9.29065i	0.297082	−	0.514562i
$327$	−8.65685	−	14.9941i	−0.478725	−	0.829176i
$328$	3.17157			0.175121
$329$		0			0
$330$	3.41421			0.187946
$331$	−13.3137	−	23.0600i	−0.731788	−	1.26749i	−0.956118	−	0.292980i	$-0.905353\pi$
$331$	−13.3137	−	23.0600i	−0.731788	−	1.26749i	0.224331	−	0.974513i	$-0.427980\pi$
$332$	−5.41421	+	9.37769i	−0.297144	+	0.514668i
$333$	−0.707107	+	1.22474i	−0.0387492	+	0.0671156i
$334$	−6.53553	−	11.3199i	−0.357609	−	0.619396i
$335$	11.8995			0.650139
$336$		0			0
$337$	−8.82843			−0.480915			−0.240458	−	0.970660i	$-0.577297\pi$
$337$	−8.82843			−0.480915			−0.240458	+	0.970660i	$0.577297\pi$
$338$	6.50000	+	11.2583i	0.353553	+	0.612372i
$339$	−6.65685	+	11.5300i	−0.361551	+	0.626224i
$340$	0.707107	−	1.22474i	0.0383482	−	0.0664211i
$341$	−15.4853	−	26.8213i	−0.838575	−	1.45245i
$342$	−2.82843			−0.152944
$343$		0			0
$344$	7.41421			0.399748
$345$	0.414214	+	0.717439i	0.0223005	+	0.0386256i
$346$	0.757359	−	1.31178i	0.0407159	−	0.0705220i
$347$	4.82843	−	8.36308i	0.259204	−	0.448954i	−0.706825	−	0.707388i	$-0.749873\pi$
$347$	4.82843	−	8.36308i	0.259204	−	0.448954i	0.966029	+	0.258435i	$0.0832066\pi$
$348$	−0.121320	−	0.210133i	−0.00650345	−	0.0112643i
$349$	−33.7990			−1.80922			−0.904609	−	0.426242i	$-0.859837\pi$
$349$	−33.7990			−1.80922			−0.904609	+	0.426242i	$0.859837\pi$
$350$		0			0
$351$		0			0
$352$	−1.70711	−	2.95680i	−0.0909891	−	0.157598i
$353$	12.3640	−	21.4150i	0.658067	−	1.13981i	−0.323048	−	0.946383i	$-0.604708\pi$
$353$	12.3640	−	21.4150i	0.658067	−	1.13981i	0.981115	−	0.193423i	$-0.0619591\pi$
$354$	7.24264	−	12.5446i	0.384942	−	0.666739i
$355$	2.58579	+	4.47871i	0.137239	+	0.237705i
$356$	−10.4853			−0.555719
$357$		0			0
$358$	3.41421			0.180447
$359$	−6.58579	−	11.4069i	−0.347585	−	0.602034i	0.638235	−	0.769841i	$-0.279665\pi$
$359$	−6.58579	−	11.4069i	−0.347585	−	0.602034i	−0.985820	+	0.167807i	$0.946331\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$	−1.58579	−	2.74666i	−0.0833471	−	0.144361i
$363$	−0.656854			−0.0344759
$364$		0			0
$365$	−3.65685			−0.191408
$366$	0.171573	+	0.297173i	0.00896826	+	0.0155335i
$367$	−0.242641	+	0.420266i	−0.0126657	+	0.0219377i	−0.872289	−	0.488991i	$-0.837365\pi$
$367$	−0.242641	+	0.420266i	−0.0126657	+	0.0219377i	0.859623	+	0.510929i	$0.170698\pi$
$368$	0.414214	−	0.717439i	0.0215924	−	0.0373991i
$369$	−1.58579	−	2.74666i	−0.0825527	−	0.142986i
$370$	−1.41421			−0.0735215
$371$		0			0
$372$	−9.07107			−0.470313
$373$	1.53553	+	2.65962i	0.0795069	+	0.137710i	0.903037	−	0.429562i	$-0.141332\pi$
$373$	1.53553	+	2.65962i	0.0795069	+	0.137710i	−0.823530	+	0.567272i	$0.807999\pi$
$374$	−2.41421	+	4.18154i	−0.124836	+	0.216222i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	2.53553	+	4.39167i	0.130760	+	0.226483i
$377$		0			0
$378$		0			0
$379$	−7.51472			−0.386005			−0.193003	−	0.981198i	$-0.561823\pi$
$379$	−7.51472			−0.386005			−0.193003	+	0.981198i	$0.561823\pi$
$380$	−1.41421	−	2.44949i	−0.0725476	−	0.125656i
$381$	7.07107	−	12.2474i	0.362262	−	0.627456i
$382$	−5.65685	+	9.79796i	−0.289430	+	0.501307i
$383$	−1.94975	−	3.37706i	−0.0996274	−	0.172560i	0.811903	−	0.583792i	$-0.198432\pi$
$383$	−1.94975	−	3.37706i	−0.0996274	−	0.172560i	−0.911530	+	0.411233i	$0.865098\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	17.7990			0.905945
$387$	−3.70711	−	6.42090i	−0.188443	−	0.326393i
$388$	1.58579	−	2.74666i	0.0805061	−	0.139441i
$389$	−6.46447	+	11.1968i	−0.327761	+	0.567699i	−0.982067	−	0.188531i	$-0.939628\pi$
$389$	−6.46447	+	11.1968i	−0.327761	+	0.567699i	0.654306	+	0.756230i	$0.272961\pi$
$390$		0			0
$391$	−1.17157			−0.0592490
$392$		0			0
$393$	−11.1716			−0.563531
$394$	7.58579	+	13.1390i	0.382166	+	0.661932i
$395$	5.65685	−	9.79796i	0.284627	−	0.492989i
$396$	−1.70711	+	2.95680i	−0.0857853	+	0.148585i
$397$	−12.3137	−	21.3280i	−0.618007	−	1.07042i	−0.989849	−	0.142124i	$-0.954607\pi$
$397$	−12.3137	−	21.3280i	−0.618007	−	1.07042i	0.371842	−	0.928296i	$-0.378726\pi$
$398$	−17.0711			−0.855695
$399$		0			0
$400$	1.00000			0.0500000
$401$	1.34315	+	2.32640i	0.0670735	+	0.116175i	0.897612	−	0.440787i	$-0.145300\pi$
$401$	1.34315	+	2.32640i	0.0670735	+	0.116175i	−0.830538	+	0.556961i	$0.811967\pi$
$402$	−5.94975	+	10.3053i	−0.296746	+	0.513980i
$403$		0			0
$404$	−8.82843	−	15.2913i	−0.439231	−	0.760770i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	4.82843			0.239336
$408$	0.707107	+	1.22474i	0.0350070	+	0.0606339i
$409$	9.19239	−	15.9217i	0.454534	−	0.787277i	−0.544127	−	0.839003i	$-0.683139\pi$
$409$	9.19239	−	15.9217i	0.454534	−	0.787277i	0.998661	+	0.0517263i	$0.0164724\pi$
$410$	1.58579	−	2.74666i	0.0783164	−	0.135648i
$411$	−8.00000	−	13.8564i	−0.394611	−	0.683486i
$412$	−18.1421			−0.893799
$413$		0			0
$414$	−0.828427			−0.0407150
$415$	5.41421	+	9.37769i	0.265773	+	0.460333i
$416$		0			0
$417$	−3.17157	+	5.49333i	−0.155313	+	0.269009i
$418$	4.82843	+	8.36308i	0.236166	+	0.409052i
$419$	6.34315			0.309883			0.154941	−	0.987924i	$-0.450481\pi$
$419$	6.34315			0.309883			0.154941	+	0.987924i	$0.450481\pi$
$420$		0			0
$421$	−28.6274			−1.39521			−0.697607	−	0.716480i	$-0.745752\pi$
$421$	−28.6274			−1.39521			−0.697607	+	0.716480i	$0.745752\pi$
$422$	−4.82843	−	8.36308i	−0.235044	−	0.407108i
$423$	2.53553	−	4.39167i	0.123282	−	0.213530i
$424$	−6.65685	+	11.5300i	−0.323285	+	0.559947i
$425$	−0.707107	−	1.22474i	−0.0342997	−	0.0594089i
$426$	−5.17157			−0.250564
$427$		0			0
$428$	−4.00000			−0.193347
$429$		0			0
$430$	3.70711	−	6.42090i	0.178773	−	0.309643i
$431$	7.07107	−	12.2474i	0.340601	−	0.589939i	−0.643943	−	0.765073i	$-0.722703\pi$
$431$	7.07107	−	12.2474i	0.340601	−	0.589939i	0.984545	+	0.175134i	$0.0560360\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−3.17157			−0.152416			−0.0762080	−	0.997092i	$-0.524281\pi$
$433$	−3.17157			−0.152416			−0.0762080	+	0.997092i	$0.524281\pi$
$434$		0			0
$435$	−0.242641			−0.0116337
$436$	8.65685	+	14.9941i	0.414588	+	0.718088i
$437$	−1.17157	+	2.02922i	−0.0560439	+	0.0970709i
$438$	1.82843	−	3.16693i	0.0873656	−	0.151322i
$439$	1.22183	+	2.11626i	0.0583145	+	0.101004i	0.893709	−	0.448647i	$-0.148094\pi$
$439$	1.22183	+	2.11626i	0.0583145	+	0.101004i	−0.835394	+	0.549651i	$0.814761\pi$
$440$	−3.41421			−0.162766
$441$		0			0
$442$		0			0
$443$	−1.17157	−	2.02922i	−0.0556631	−	0.0964113i	0.836851	−	0.547430i	$-0.184394\pi$
$443$	−1.17157	−	2.02922i	−0.0556631	−	0.0964113i	−0.892514	+	0.451019i	$0.851061\pi$
$444$	0.707107	−	1.22474i	0.0335578	−	0.0581238i
$445$	−5.24264	+	9.08052i	−0.248525	+	0.430458i
$446$	3.17157	+	5.49333i	0.150178	+	0.260116i
$447$	−5.89949			−0.279037
$448$		0			0
$449$	37.1127			1.75146			0.875728	−	0.482804i	$-0.160382\pi$
$449$	37.1127			1.75146			0.875728	+	0.482804i	$0.160382\pi$
$450$	−0.500000	−	0.866025i	−0.0235702	−	0.0408248i
$451$	−5.41421	+	9.37769i	−0.254945	+	0.441578i
$452$	6.65685	−	11.5300i	0.313112	−	0.542326i
$453$	−10.8995	−	18.8785i	−0.512103	−	0.886988i
$454$	2.34315			0.109969
$455$		0			0
$456$	2.82843			0.132453
$457$	−14.8995	−	25.8067i	−0.696969	−	1.20719i	−0.969512	−	0.245042i	$-0.921198\pi$
$457$	−14.8995	−	25.8067i	−0.696969	−	1.20719i	0.272543	−	0.962143i	$-0.412135\pi$
$458$	−6.89949	+	11.9503i	−0.322392	+	0.558400i
$459$	0.707107	−	1.22474i	0.0330049	−	0.0571662i
$460$	−0.414214	−	0.717439i	−0.0193128	−	0.0334508i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	22.3431			1.03837			0.519187	−	0.854661i	$-0.326235\pi$
$463$	22.3431			1.03837			0.519187	+	0.854661i	$0.326235\pi$
$464$	0.121320	+	0.210133i	0.00563216	+	0.00975518i
$465$	−4.53553	+	7.85578i	−0.210330	+	0.364303i
$466$	13.4853	−	23.3572i	0.624694	−	1.08200i
$467$	−1.75736	−	3.04384i	−0.0813209	−	0.140852i	0.822497	−	0.568770i	$-0.192581\pi$
$467$	−1.75736	−	3.04384i	−0.0813209	−	0.140852i	−0.903818	+	0.427918i	$0.859247\pi$
$468$		0			0
$469$		0			0
$470$	5.07107			0.233911
$471$	−5.82843	−	10.0951i	−0.268560	−	0.465159i
$472$	−7.24264	+	12.5446i	−0.333370	+	0.577413i
$473$	−12.6569	+	21.9223i	−0.581963	+	1.00799i
$474$	5.65685	+	9.79796i	0.259828	+	0.450035i
$475$	−2.82843			−0.129777
$476$		0			0
$477$	13.3137			0.609593
$478$	−0.343146	−	0.594346i	−0.0156951	−	0.0271847i
$479$	−0.242641	+	0.420266i	−0.0110865	+	0.0192024i	−0.871515	−	0.490368i	$-0.836862\pi$
$479$	−0.242641	+	0.420266i	−0.0110865	+	0.0192024i	0.860429	+	0.509570i	$0.170196\pi$
$480$	−0.500000	+	0.866025i	−0.0228218	+	0.0395285i
$481$		0			0
$482$	7.75736			0.353338
$483$		0			0
$484$	0.656854			0.0298570
$485$	−1.58579	−	2.74666i	−0.0720069	−	0.124720i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−3.75736	+	6.50794i	−0.170262	+	0.294903i	−0.938511	−	0.345248i	$-0.887795\pi$
$487$	−3.75736	+	6.50794i	−0.170262	+	0.294903i	0.768249	+	0.640151i	$0.221128\pi$
$488$	−0.171573	−	0.297173i	−0.00776674	−	0.0134524i
$489$	10.7279			0.485133
$490$		0			0
$491$	−7.89949			−0.356499			−0.178250	−	0.983985i	$-0.557043\pi$
$491$	−7.89949			−0.356499			−0.178250	+	0.983985i	$0.557043\pi$
$492$	1.58579	+	2.74666i	0.0714928	+	0.123829i
$493$	0.171573	−	0.297173i	0.00772725	−	0.0133840i
$494$		0			0
$495$	1.70711	+	2.95680i	0.0767287	+	0.132898i
$496$	9.07107			0.407303
$497$		0			0
$498$	−10.8284			−0.485233
$499$	11.8995	+	20.6105i	0.532695	+	0.922654i	0.999271	+	0.0381732i	$0.0121539\pi$
$499$	11.8995	+	20.6105i	0.532695	+	0.922654i	−0.466577	+	0.884481i	$0.654513\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	6.53553	−	11.3199i	0.291986	−	0.505735i
$502$	−3.17157	−	5.49333i	−0.141554	−	0.245179i
$503$	−4.10051			−0.182832			−0.0914162	−	0.995813i	$-0.529139\pi$
$503$	−4.10051			−0.182832			−0.0914162	+	0.995813i	$0.529139\pi$
$504$		0			0
$505$	−17.6569			−0.785720
$506$	1.41421	+	2.44949i	0.0628695	+	0.108893i
$507$	−6.50000	+	11.2583i	−0.288675	+	0.500000i
$508$	−7.07107	+	12.2474i	−0.313728	+	0.543393i
$509$	−14.8284	−	25.6836i	−0.657258	−	1.13841i	−0.981322	−	0.192370i	$-0.938383\pi$
$509$	−14.8284	−	25.6836i	−0.657258	−	1.13841i	0.324064	−	0.946035i	$-0.394951\pi$
$510$	1.41421			0.0626224
$511$		0			0
$512$	1.00000			0.0441942
$513$	−1.41421	−	2.44949i	−0.0624391	−	0.108148i
$514$	−8.94975	+	15.5014i	−0.394756	+	0.683738i
$515$	−9.07107	+	15.7116i	−0.399719	+	0.692334i
$516$	3.70711	+	6.42090i	0.163196	+	0.282664i
$517$	−17.3137			−0.761456
$518$		0			0
$519$	1.51472			0.0664888
$520$		0			0
$521$	8.07107	−	13.9795i	0.353600	−	0.612453i	−0.633277	−	0.773925i	$-0.718291\pi$
$521$	8.07107	−	13.9795i	0.353600	−	0.612453i	0.986877	+	0.161472i	$0.0516241\pi$
$522$	0.121320	−	0.210133i	0.00531005	−	0.00919727i
$523$	20.5563	+	35.6046i	0.898866	+	1.55688i	0.828945	+	0.559330i	$0.188941\pi$
$523$	20.5563	+	35.6046i	0.898866	+	1.55688i	0.0699211	+	0.997553i	$0.477725\pi$
$524$	11.1716			0.488032
$525$		0			0
$526$	17.7990			0.776073
$527$	−6.41421	−	11.1097i	−0.279408	−	0.483948i
$528$	1.70711	−	2.95680i	0.0742923	−	0.128678i
$529$	11.1569	−	19.3242i	0.485081	−	0.840184i
$530$	6.65685	+	11.5300i	0.289155	+	0.500832i
$531$	14.4853			0.628608
$532$		0			0
$533$		0			0
$534$	−5.24264	−	9.08052i	−0.226871	−	0.392953i
$535$	−2.00000	+	3.46410i	−0.0864675	+	0.149766i
$536$	5.94975	−	10.3053i	0.256990	−	0.445120i
$537$	1.70711	+	2.95680i	0.0736671	+	0.127595i
$538$	3.65685			0.157658
$539$		0			0
$540$	1.00000			0.0430331
$541$	−7.24264	−	12.5446i	−0.311385	−	0.539335i	0.667277	−	0.744810i	$-0.267460\pi$
$541$	−7.24264	−	12.5446i	−0.311385	−	0.539335i	−0.978663	+	0.205474i	$0.934126\pi$
$542$	−2.87868	+	4.98602i	−0.123650	+	0.214168i
$543$	1.58579	−	2.74666i	0.0680526	−	0.117871i
$544$	−0.707107	−	1.22474i	−0.0303170	−	0.0525105i
$545$	17.3137			0.741638
$546$		0			0
$547$	24.5858			1.05121			0.525606	−	0.850728i	$-0.323839\pi$
$547$	24.5858			1.05121			0.525606	+	0.850728i	$0.323839\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$	−0.171573	+	0.297173i	−0.00732255	+	0.0126830i
$550$	−1.70711	+	2.95680i	−0.0727913	+	0.126078i
$551$	−0.343146	−	0.594346i	−0.0146185	−	0.0253200i
$552$	0.828427			0.0352602
$553$		0			0
$554$	2.10051			0.0892419
$555$	−0.707107	−	1.22474i	−0.0300150	−	0.0519875i
$556$	3.17157	−	5.49333i	0.134505	−	0.232969i
$557$	16.3137	−	28.2562i	0.691234	−	1.19725i	−0.280200	−	0.959942i	$-0.590401\pi$
$557$	16.3137	−	28.2562i	0.691234	−	1.19725i	0.971434	−	0.237311i	$-0.0762660\pi$
$558$	−4.53553	−	7.85578i	−0.192004	−	0.332561i
$559$		0			0
$560$		0			0
$561$	−4.82843			−0.203856
$562$	15.2426	+	26.4010i	0.642972	+	1.11366i
$563$	1.07107	−	1.85514i	0.0451401	−	0.0781850i	−0.842573	−	0.538583i	$-0.818960\pi$
$563$	1.07107	−	1.85514i	0.0451401	−	0.0781850i	0.887713	+	0.460398i	$0.152293\pi$
$564$	−2.53553	+	4.39167i	−0.106765	+	0.184923i
$565$	−6.65685	−	11.5300i	−0.280056	−	0.485071i
$566$	−13.5147			−0.568066
$567$		0			0
$568$	5.17157			0.216994
$569$	−0.514719	−	0.891519i	−0.0215781	−	0.0373744i	0.855035	−	0.518571i	$-0.173536\pi$
$569$	−0.514719	−	0.891519i	−0.0215781	−	0.0373744i	−0.876613	+	0.481196i	$0.840202\pi$
$570$	1.41421	−	2.44949i	0.0592349	−	0.102598i
$571$	−13.6569	+	23.6544i	−0.571522	+	0.989904i	0.424888	+	0.905246i	$0.360313\pi$
$571$	−13.6569	+	23.6544i	−0.571522	+	0.989904i	−0.996410	+	0.0846587i	$0.973020\pi$
$572$		0			0
$573$	−11.3137			−0.472637
$574$		0			0
$575$	−0.828427			−0.0345478
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	8.07107	−	13.9795i	0.336003	−	0.581974i	−0.647674	−	0.761918i	$-0.724258\pi$
$577$	8.07107	−	13.9795i	0.336003	−	0.581974i	0.983677	+	0.179943i	$0.0575915\pi$
$578$	7.50000	−	12.9904i	0.311959	−	0.540329i
$579$	8.89949	+	15.4144i	0.369850	+	0.640600i
$580$	0.242641			0.0100751
$581$		0			0
$582$	3.17157			0.131466
$583$	−22.7279	−	39.3659i	−0.941294	−	1.63037i
$584$	−1.82843	+	3.16693i	−0.0756609	+	0.131048i
$585$		0			0
$586$	8.31371	+	14.3998i	0.343436	+	0.594849i
$587$	19.7990			0.817192			0.408596	−	0.912715i	$-0.366019\pi$
$587$	19.7990			0.817192			0.408596	+	0.912715i	$0.366019\pi$
$588$		0			0
$589$	−25.6569			−1.05717
$590$	7.24264	+	12.5446i	0.298175	+	0.516454i
$591$	−7.58579	+	13.1390i	−0.312038	+	0.540465i
$592$	−0.707107	+	1.22474i	−0.0290619	+	0.0503367i
$593$	−2.60660	−	4.51477i	−0.107040	−	0.185399i	0.807530	−	0.589827i	$-0.200804\pi$
$593$	−2.60660	−	4.51477i	−0.107040	−	0.185399i	−0.914570	+	0.404428i	$0.867471\pi$
$594$	−3.41421			−0.140087
$595$		0			0
$596$	5.89949			0.241653
$597$	−8.53553	−	14.7840i	−0.349336	−	0.605068i
$598$		0			0
$599$	−13.6569	+	23.6544i	−0.558004	+	0.966491i	0.439659	+	0.898165i	$0.355099\pi$
$599$	−13.6569	+	23.6544i	−0.558004	+	0.966491i	−0.997663	+	0.0683264i	$0.978234\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	34.1838			1.39438			0.697192	−	0.716884i	$-0.254432\pi$
$601$	34.1838			1.39438			0.697192	+	0.716884i	$0.254432\pi$
$602$		0			0
$603$	−11.8995			−0.484585
$604$	10.8995	+	18.8785i	0.443494	+	0.768154i
$605$	0.328427	−	0.568852i	0.0133525	−	0.0231271i
$606$	8.82843	−	15.2913i	0.358630	−	0.621166i
$607$	14.4853	+	25.0892i	0.587939	+	1.01834i	0.994502	+	0.104718i	$0.0333940\pi$
$607$	14.4853	+	25.0892i	0.587939	+	1.01834i	−0.406563	+	0.913623i	$0.633273\pi$
$608$	−2.82843			−0.114708
$609$		0			0
$610$	−0.343146			−0.0138936
$611$		0			0
$612$	−0.707107	+	1.22474i	−0.0285831	+	0.0495074i
$613$	−18.6066	+	32.2276i	−0.751514	+	1.30166i	0.195575	+	0.980689i	$0.437343\pi$
$613$	−18.6066	+	32.2276i	−0.751514	+	1.30166i	−0.947089	+	0.320971i	$0.895991\pi$
$614$	7.65685	+	13.2621i	0.309005	+	0.535213i
$615$	3.17157			0.127890
$616$		0			0
$617$	12.2843			0.494546			0.247273	−	0.968946i	$-0.420466\pi$
$617$	12.2843			0.494546			0.247273	+	0.968946i	$0.420466\pi$
$618$	−9.07107	−	15.7116i	−0.364892	−	0.632011i
$619$	15.0711	−	26.1039i	0.605757	−	1.04920i	−0.386174	−	0.922426i	$-0.626204\pi$
$619$	15.0711	−	26.1039i	0.605757	−	1.04920i	0.991931	−	0.126777i	$-0.0404631\pi$
$620$	4.53553	−	7.85578i	0.182151	−	0.315496i
$621$	−0.414214	−	0.717439i	−0.0166218	−	0.0287898i
$622$	34.8284			1.39649
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	11.5858	−	20.0672i	0.463061	−	0.802045i
$627$	−4.82843	+	8.36308i	−0.192829	+	0.333989i
$628$	5.82843	+	10.0951i	0.232580	+	0.402840i
$629$	2.00000			0.0797452
$630$		0			0
$631$	19.1716			0.763208			0.381604	−	0.924326i	$-0.375372\pi$
$631$	19.1716			0.763208			0.381604	+	0.924326i	$0.375372\pi$
$632$	−5.65685	−	9.79796i	−0.225018	−	0.389742i
$633$	4.82843	−	8.36308i	0.191913	−	0.332403i
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$	7.07107	+	12.2474i	0.280607	+	0.486025i
$636$	−13.3137			−0.527923
$637$		0			0
$638$	−0.828427			−0.0327977
$639$	−2.58579	−	4.47871i	−0.102292	−	0.177175i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−2.00000	−	3.46410i	−0.0789337	−	0.136717i
$643$	36.4264			1.43652			0.718259	−	0.695776i	$-0.244939\pi$
$643$	36.4264			1.43652			0.718259	+	0.695776i	$0.244939\pi$
$644$		0			0
$645$	7.41421			0.291934
$646$	2.00000	+	3.46410i	0.0786889	+	0.136293i
$647$	9.46447	−	16.3929i	0.372087	−	0.644473i	−0.617800	−	0.786335i	$-0.711976\pi$
$647$	9.46447	−	16.3929i	0.372087	−	0.644473i	0.989886	+	0.141863i	$0.0453091\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−24.7279	−	42.8300i	−0.970656	−	1.68123i
$650$		0			0
$651$		0			0
$652$	−10.7279			−0.420138
$653$	−13.5858	−	23.5313i	−0.531653	−	0.920850i	−0.999317	−	0.0369438i	$-0.988238\pi$
$653$	−13.5858	−	23.5313i	−0.531653	−	0.920850i	0.467664	−	0.883906i	$-0.345096\pi$
$654$	−8.65685	+	14.9941i	−0.338510	+	0.586316i
$655$	5.58579	−	9.67487i	0.218255	−	0.378028i
$656$	−1.58579	−	2.74666i	−0.0619146	−	0.107239i
$657$	3.65685			0.142667
$658$		0			0
$659$	39.8995			1.55426			0.777132	−	0.629338i	$-0.216674\pi$
$659$	39.8995			1.55426			0.777132	+	0.629338i	$0.216674\pi$
$660$	−1.70711	−	2.95680i	−0.0664490	−	0.115093i
$661$	−8.17157	+	14.1536i	−0.317837	+	0.550510i	−0.980037	−	0.198817i	$-0.936290\pi$
$661$	−8.17157	+	14.1536i	−0.317837	+	0.550510i	0.662199	+	0.749328i	$0.269623\pi$
$662$	−13.3137	+	23.0600i	−0.517452	+	0.896253i
$663$		0			0
$664$	10.8284			0.420224
$665$		0			0
$666$	1.41421			0.0547997
$667$	−0.100505	−	0.174080i	−0.00389157	−	0.00674040i
$668$	−6.53553	+	11.3199i	−0.252867	+	0.437979i
$669$	−3.17157	+	5.49333i	−0.122620	+	0.212384i
$670$	−5.94975	−	10.3053i	−0.229859	−	0.398127i
$671$	1.17157			0.0452281
$672$		0			0
$673$	−37.5980			−1.44930			−0.724648	−	0.689119i	$-0.757998\pi$
$673$	−37.5980			−1.44930			−0.724648	+	0.689119i	$0.757998\pi$
$674$	4.41421	+	7.64564i	0.170029	+	0.294499i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	8.41421	+	14.5738i	0.323384	+	0.560118i	0.981184	−	0.193075i	$-0.0618460\pi$
$677$	8.41421	+	14.5738i	0.323384	+	0.560118i	−0.657800	+	0.753193i	$0.728513\pi$
$678$	13.3137			0.511310
$679$		0			0
$680$	−1.41421			−0.0542326
$681$	1.17157	+	2.02922i	0.0448948	+	0.0777600i
$682$	−15.4853	+	26.8213i	−0.592962	+	1.02704i
$683$	3.89949	−	6.75412i	0.149210	−	0.258439i	−0.781726	−	0.623622i	$-0.785660\pi$
$683$	3.89949	−	6.75412i	0.149210	−	0.258439i	0.930936	+	0.365183i	$0.118994\pi$
$684$	1.41421	+	2.44949i	0.0540738	+	0.0936586i
$685$	16.0000			0.611329
$686$		0			0
$687$	−13.7990			−0.526464
$688$	−3.70711	−	6.42090i	−0.141332	−	0.244794i
$689$		0			0
$690$	0.414214	−	0.717439i	0.0157688	−	0.0273124i
$691$	22.1421	+	38.3513i	0.842327	+	1.45895i	0.887923	+	0.459992i	$0.152148\pi$
$691$	22.1421	+	38.3513i	0.842327	+	1.45895i	−0.0455963	+	0.998960i	$0.514519\pi$
$692$	−1.51472			−0.0575810
$693$		0			0
$694$	−9.65685			−0.366569
$695$	−3.17157	−	5.49333i	−0.120305	−	0.208374i
$696$	−0.121320	+	0.210133i	−0.00459864	+	0.00796507i
$697$	−2.24264	+	3.88437i	−0.0849461	+	0.147131i
$698$	16.8995	+	29.2708i	0.639655	+	1.10792i
$699$	26.9706			1.02012
$700$		0			0
$701$	19.5563			0.738633			0.369317	−	0.929304i	$-0.379592\pi$
$701$	19.5563			0.738633			0.369317	+	0.929304i	$0.379592\pi$
$702$		0			0
$703$	2.00000	−	3.46410i	0.0754314	−	0.130651i
$704$	−1.70711	+	2.95680i	−0.0643390	+	0.111438i
$705$	2.53553	+	4.39167i	0.0954937	+	0.165400i
$706$	−24.7279			−0.930648
$707$		0			0
$708$	−14.4853			−0.544390
$709$	−8.55635	−	14.8200i	−0.321340	−	0.556578i	0.659424	−	0.751771i	$-0.270800\pi$
$709$	−8.55635	−	14.8200i	−0.321340	−	0.556578i	−0.980765	+	0.195193i	$0.937467\pi$
$710$	2.58579	−	4.47871i	0.0970428	−	0.168083i
$711$	−5.65685	+	9.79796i	−0.212149	+	0.367452i
$712$	5.24264	+	9.08052i	0.196476	+	0.340307i
$713$	−7.51472			−0.281428
$714$		0			0
$715$		0			0
$716$	−1.70711	−	2.95680i	−0.0637976	−	0.110501i
$717$	0.343146	−	0.594346i	0.0128150	−	0.0221963i
$718$	−6.58579	+	11.4069i	−0.245779	+	0.425702i
$719$	22.1421	+	38.3513i	0.825762	+	1.43026i	0.901335	+	0.433122i	$0.142588\pi$
$719$	22.1421	+	38.3513i	0.825762	+	1.43026i	−0.0755730	+	0.997140i	$0.524079\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	−11.0000			−0.409378
$723$	3.87868	+	6.71807i	0.144250	+	0.249848i
$724$	−1.58579	+	2.74666i	−0.0589353	+	0.102079i
$725$	0.121320	−	0.210133i	0.00450572	−	0.00780414i
$726$	0.328427	+	0.568852i	0.0121891	+	0.0211121i
$727$	−34.3431			−1.27372			−0.636858	−	0.770981i	$-0.719766\pi$
$727$	−34.3431			−1.27372			−0.636858	+	0.770981i	$0.719766\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	1.82843	+	3.16693i	0.0676731	+	0.117213i
$731$	−5.24264	+	9.08052i	−0.193906	+	0.335855i
$732$	0.171573	−	0.297173i	0.00634152	−	0.0109838i
$733$	25.9706	+	44.9823i	0.959245	+	1.66146i	0.724341	+	0.689442i	$0.242144\pi$
$733$	25.9706	+	44.9823i	0.959245	+	1.66146i	0.234903	+	0.972019i	$0.424523\pi$
$734$	0.485281			0.0179121
$735$		0			0
$736$	−0.828427			−0.0305362
$737$	20.3137	+	35.1844i	0.748265	+	1.29603i
$738$	−1.58579	+	2.74666i	−0.0583736	+	0.101106i
$739$	−9.55635	+	16.5521i	−0.351536	+	0.608878i	−0.986519	−	0.163648i	$-0.947674\pi$
$739$	−9.55635	+	16.5521i	−0.351536	+	0.608878i	0.634983	+	0.772526i	$0.281007\pi$
$740$	0.707107	+	1.22474i	0.0259938	+	0.0450225i
$741$		0			0
$742$		0			0
$743$	−5.65685			−0.207530			−0.103765	−	0.994602i	$-0.533089\pi$
$743$	−5.65685			−0.207530			−0.103765	+	0.994602i	$0.533089\pi$
$744$	4.53553	+	7.85578i	0.166281	+	0.288007i
$745$	2.94975	−	5.10911i	0.108070	−	0.187183i
$746$	1.53553	−	2.65962i	0.0562199	−	0.0973757i
$747$	−5.41421	−	9.37769i	−0.198096	−	0.343112i
$748$	4.82843			0.176545
$749$		0			0
$750$	1.00000			0.0365148
$751$	−21.2426	−	36.7933i	−0.775155	−	1.34261i	−0.934707	−	0.355418i	$-0.884338\pi$
$751$	−21.2426	−	36.7933i	−0.775155	−	1.34261i	0.159552	−	0.987189i	$-0.448995\pi$
$752$	2.53553	−	4.39167i	0.0924614	−	0.160148i
$753$	3.17157	−	5.49333i	0.115579	−	0.200188i
$754$		0			0
$755$	21.7990			0.793346
$756$		0			0
$757$	32.2426			1.17188			0.585939	−	0.810355i	$-0.300726\pi$
$757$	32.2426			1.17188			0.585939	+	0.810355i	$0.300726\pi$
$758$	3.75736	+	6.50794i	0.136473	+	0.236379i
$759$	−1.41421	+	2.44949i	−0.0513327	+	0.0889108i
$760$	−1.41421	+	2.44949i	−0.0512989	+	0.0888523i
$761$	7.48528	+	12.9649i	0.271341	+	0.469977i	0.969206	−	0.246253i	$-0.0791995\pi$
$761$	7.48528	+	12.9649i	0.271341	+	0.469977i	−0.697864	+	0.716230i	$0.745866\pi$
$762$	−14.1421			−0.512316
$763$		0			0
$764$	11.3137			0.409316
$765$	0.707107	+	1.22474i	0.0255655	+	0.0442807i
$766$	−1.94975	+	3.37706i	−0.0704472	+	0.122018i
$767$		0			0
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	33.4142			1.20495			0.602474	−	0.798139i	$-0.294182\pi$
$769$	33.4142			1.20495			0.602474	+	0.798139i	$0.294182\pi$
$770$		0			0
$771$	−17.8995			−0.644635
$772$	−8.89949	−	15.4144i	−0.320300	−	0.554776i
$773$	19.8284	−	34.3438i	0.713179	−	1.23526i	−0.250479	−	0.968122i	$-0.580588\pi$
$773$	19.8284	−	34.3438i	0.713179	−	1.23526i	0.963658	−	0.267140i	$-0.0860786\pi$
$774$	−3.70711	+	6.42090i	−0.133249	+	0.230794i
$775$	−4.53553	−	7.85578i	−0.162921	−	0.282188i
$776$	−3.17157			−0.113853
$777$		0			0
$778$	12.9289			0.463525
$779$	4.48528	+	7.76874i	0.160702	+	0.278344i
$780$		0			0
$781$	−8.82843	+	15.2913i	−0.315906	+	0.547165i
$782$	0.585786	+	1.01461i	0.0209477	+	0.0362824i
$783$	0.242641			0.00867127
$784$		0			0
$785$	11.6569			0.416051
$786$	5.58579	+	9.67487i	0.199238	+	0.345091i
$787$	−2.48528	+	4.30463i	−0.0885907	+	0.153444i	−0.906916	−	0.421312i	$-0.861570\pi$
$787$	−2.48528	+	4.30463i	−0.0885907	+	0.153444i	0.818325	+	0.574756i	$0.194903\pi$
$788$	7.58579	−	13.1390i	0.270232	−	0.468056i
$789$	8.89949	+	15.4144i	0.316830	+	0.548766i
$790$	−11.3137			−0.402524
$791$		0			0
$792$	3.41421			0.121319
$793$		0			0
$794$	−12.3137	+	21.3280i	−0.436997	+	0.756901i
$795$	−6.65685	+	11.5300i	−0.236094	+	0.408927i
$796$	8.53553	+	14.7840i	0.302534	+	0.524004i
$797$	−9.51472			−0.337029			−0.168514	−	0.985699i	$-0.553897\pi$
$797$	−9.51472			−0.337029			−0.168514	+	0.985699i	$0.553897\pi$
$798$		0			0
$799$	−7.17157			−0.253712
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	5.24264	−	9.08052i	0.185240	−	0.320844i
$802$	1.34315	−	2.32640i	0.0474281	−	0.0821479i
$803$	−6.24264	−	10.8126i	−0.220298	−	0.381567i
$804$	11.8995			0.419663
$805$		0			0
$806$		0			0
$807$	1.82843	+	3.16693i	0.0643637	+	0.111481i
$808$	−8.82843	+	15.2913i	−0.310583	+	0.537946i
$809$	18.5563	−	32.1405i	0.652406	−	1.13000i	−0.330131	−	0.943935i	$-0.607093\pi$
$809$	18.5563	−	32.1405i	0.652406	−	1.13000i	0.982537	−	0.186066i	$-0.0595738\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	36.9706			1.29821			0.649106	−	0.760698i	$-0.275143\pi$
$811$	36.9706			1.29821			0.649106	+	0.760698i	$0.275143\pi$
$812$		0			0
$813$	−5.75736			−0.201919
$814$	−2.41421	−	4.18154i	−0.0846181	−	0.146563i
$815$	−5.36396	+	9.29065i	−0.187891	+	0.325437i
$816$	0.707107	−	1.22474i	0.0247537	−	0.0428746i
$817$	10.4853	+	18.1610i	0.366834	+	0.635374i
$818$	−18.3848			−0.642809
$819$		0			0
$820$	−3.17157			−0.110756
$821$	17.7782	+	30.7927i	0.620463	+	1.07467i	0.989400	+	0.145218i	$0.0463885\pi$
$821$	17.7782	+	30.7927i	0.620463	+	1.07467i	−0.368937	+	0.929454i	$0.620278\pi$
$822$	−8.00000	+	13.8564i	−0.279032	+	0.483298i
$823$	20.1421	−	34.8872i	0.702111	−	1.21609i	−0.265613	−	0.964080i	$-0.585574\pi$
$823$	20.1421	−	34.8872i	0.702111	−	1.21609i	0.967724	−	0.252012i	$-0.0810922\pi$
$824$	9.07107	+	15.7116i	0.316006	+	0.547338i
$825$	−3.41421			−0.118868
$826$		0			0
$827$	51.1127			1.77736			0.888681	−	0.458525i	$-0.151622\pi$
$827$	51.1127			1.77736			0.888681	+	0.458525i	$0.151622\pi$
$828$	0.414214	+	0.717439i	0.0143949	+	0.0249327i
$829$	−11.3431	+	19.6469i	−0.393964	+	0.682365i	−0.992968	−	0.118380i	$-0.962230\pi$
$829$	−11.3431	+	19.6469i	−0.393964	+	0.682365i	0.599005	+	0.800746i	$0.295563\pi$
$830$	5.41421	−	9.37769i	0.187930	−	0.325504i
$831$	1.05025	+	1.81909i	0.0364329	+	0.0631036i
$832$		0			0
$833$		0			0
$834$	6.34315			0.219645
$835$	6.53553	+	11.3199i	0.226171	+	0.391740i
$836$	4.82843	−	8.36308i	0.166995	−	0.289243i
$837$	4.53553	−	7.85578i	0.156771	−	0.271535i
$838$	−3.17157	−	5.49333i	−0.109560	−	0.189764i
$839$	−10.8284			−0.373839			−0.186919	−	0.982375i	$-0.559850\pi$
$839$	−10.8284			−0.373839			−0.186919	+	0.982375i	$0.559850\pi$
$840$		0			0
$841$	−28.9411			−0.997970
$842$	14.3137	+	24.7921i	0.493283	+	0.854391i
$843$	−15.2426	+	26.4010i	−0.524984	+	0.909300i
$844$	−4.82843	+	8.36308i	−0.166201	+	0.287869i
$845$	−6.50000	−	11.2583i	−0.223607	−	0.387298i
$846$	−5.07107			−0.174347
$847$		0			0
$848$	13.3137			0.457195
$849$	−6.75736	−	11.7041i	−0.231912	−	0.401683i
$850$	−0.707107	+	1.22474i	−0.0242536	+	0.0420084i
$851$	0.585786	−	1.01461i	0.0200805	−	0.0347804i
$852$	2.58579	+	4.47871i	0.0885876	+	0.153438i
$853$	−29.3137			−1.00368			−0.501841	−	0.864960i	$-0.667344\pi$
$853$	−29.3137			−1.00368			−0.501841	+	0.864960i	$0.667344\pi$
$854$		0			0
$855$	2.82843			0.0967302
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$	26.3640	−	45.6637i	0.900576	−	1.55984i	0.0738274	−	0.997271i	$-0.476479\pi$
$857$	26.3640	−	45.6637i	0.900576	−	1.55984i	0.826748	−	0.562572i	$-0.190188\pi$
$858$		0			0
$859$	−8.48528	−	14.6969i	−0.289514	−	0.501453i	0.684180	−	0.729313i	$-0.260160\pi$
$859$	−8.48528	−	14.6969i	−0.289514	−	0.501453i	−0.973694	+	0.227860i	$0.926827\pi$
$860$	−7.41421			−0.252823
$861$		0			0
$862$	−14.1421			−0.481683
$863$	−16.4853	−	28.5533i	−0.561166	−	0.971967i	−0.997395	−	0.0721318i	$-0.977020\pi$
$863$	−16.4853	−	28.5533i	−0.561166	−	0.971967i	0.436230	−	0.899835i	$-0.356314\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−0.757359	+	1.31178i	−0.0257510	+	0.0446020i
$866$	1.58579	+	2.74666i	0.0538872	+	0.0933354i
$867$	15.0000			0.509427
$868$		0			0
$869$	38.6274			1.31035
$870$	0.121320	+	0.210133i	0.00411314	+	0.00712418i
$871$		0			0
$872$	8.65685	−	14.9941i	0.293158	−	0.507765i
$873$	1.58579	+	2.74666i	0.0536707	+	0.0929604i
$874$	2.34315			0.0792581
$875$		0			0
$876$	−3.65685			−0.123554
$877$	−9.29289	−	16.0958i	−0.313799	−	0.543515i	0.665383	−	0.746502i	$-0.268268\pi$
$877$	−9.29289	−	16.0958i	−0.313799	−	0.543515i	−0.979181	+	0.202987i	$0.934935\pi$
$878$	1.22183	−	2.11626i	0.0412346	−	0.0714204i
$879$	−8.31371	+	14.3998i	−0.280414	+	0.485692i
$880$	1.70711	+	2.95680i	0.0575466	+	0.0996736i
$881$	−20.3431			−0.685378			−0.342689	−	0.939449i	$-0.611338\pi$
$881$	−20.3431			−0.685378			−0.342689	+	0.939449i	$0.611338\pi$
$882$		0			0
$883$	38.0416			1.28020			0.640101	−	0.768290i	$-0.278892\pi$
$883$	38.0416			1.28020			0.640101	+	0.768290i	$0.278892\pi$
$884$		0			0
$885$	−7.24264	+	12.5446i	−0.243459	+	0.421683i
$886$	−1.17157	+	2.02922i	−0.0393598	+	0.0681731i
$887$	17.8492	+	30.9158i	0.599319	+	1.03805i	0.992922	+	0.118770i	$0.0378952\pi$
$887$	17.8492	+	30.9158i	0.599319	+	1.03805i	−0.393603	+	0.919281i	$0.628771\pi$
$888$	−1.41421			−0.0474579
$889$		0			0
$890$	10.4853			0.351467
$891$	−1.70711	−	2.95680i	−0.0571902	−	0.0990564i
$892$	3.17157	−	5.49333i	0.106192	−	0.183930i
$893$	−7.17157	+	12.4215i	−0.239988	+	0.415671i
$894$	2.94975	+	5.10911i	0.0986543	+	0.170874i
$895$	−3.41421			−0.114125
$896$		0			0
$897$		0			0
$898$	−18.5563	−	32.1405i	−0.619233	−	1.07254i
$899$	1.10051	−	1.90613i	0.0367039	−	0.0635730i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−9.41421	−	16.3059i	−0.313633	−	0.543228i
$902$	10.8284			0.360547
$903$		0			0
$904$	−13.3137			−0.442807
$905$	1.58579	+	2.74666i	0.0527133	+	0.0913022i
$906$	−10.8995	+	18.8785i	−0.362111	+	0.627195i
$907$	−0.393398	+	0.681386i	−0.0130626	+	0.0226250i	−0.872483	−	0.488645i	$-0.837491\pi$
$907$	−0.393398	+	0.681386i	−0.0130626	+	0.0226250i	0.859420	+	0.511270i	$0.170825\pi$
$908$	−1.17157	−	2.02922i	−0.0388800	−	0.0673422i
$909$	17.6569			0.585641
$910$		0			0
$911$	−5.65685			−0.187420			−0.0937100	−	0.995600i	$-0.529873\pi$
$911$	−5.65685			−0.187420			−0.0937100	+	0.995600i	$0.529873\pi$
$912$	−1.41421	−	2.44949i	−0.0468293	−	0.0811107i
$913$	−18.4853	+	32.0174i	−0.611774	+	1.05962i
$914$	−14.8995	+	25.8067i	−0.492831	+	0.853609i
$915$	−0.171573	−	0.297173i	−0.00567202	−	0.00982423i
$916$	13.7990			0.455931
$917$		0			0
$918$	−1.41421			−0.0466760
$919$	23.3848	+	40.5036i	0.771393	+	1.33609i	0.936800	+	0.349866i	$0.113773\pi$
$919$	23.3848	+	40.5036i	0.771393	+	1.33609i	−0.165407	+	0.986225i	$0.552894\pi$
$920$	−0.414214	+	0.717439i	−0.0136562	+	0.0236533i
$921$	−7.65685	+	13.2621i	−0.252302	+	0.437000i
$922$	−7.00000	−	12.1244i	−0.230533	−	0.399294i
$923$		0			0
$924$		0			0
$925$	1.41421			0.0464991
$926$	−11.1716	−	19.3497i	−0.367121	−	0.635872i
$927$	9.07107	−	15.7116i	0.297933	−	0.516035i
$928$	0.121320	−	0.210133i	0.00398254	−	0.00689795i
$929$	−0.171573	−	0.297173i	−0.00562912	−	0.00974993i	0.863197	−	0.504867i	$-0.168458\pi$
$929$	−0.171573	−	0.297173i	−0.00562912	−	0.00974993i	−0.868826	+	0.495117i	$0.835125\pi$
$930$	9.07107			0.297452
$931$		0			0
$932$	−26.9706			−0.883450
$933$	17.4142	+	30.1623i	0.570116	+	0.987469i
$934$	−1.75736	+	3.04384i	−0.0575026	+	0.0995973i
$935$	2.41421	−	4.18154i	0.0789532	−	0.136751i
$936$		0			0
$937$	50.9706			1.66514			0.832568	−	0.553923i	$-0.186870\pi$
$937$	50.9706			1.66514			0.832568	+	0.553923i	$0.186870\pi$
$938$		0			0
$939$	23.1716			0.756176
$940$	−2.53553	−	4.39167i	−0.0827000	−	0.143241i
$941$	−10.1421	+	17.5667i	−0.330624	+	0.572658i	−0.982634	−	0.185552i	$-0.940593\pi$
$941$	−10.1421	+	17.5667i	−0.330624	+	0.572658i	0.652010	+	0.758210i	$0.273926\pi$
$942$	−5.82843	+	10.0951i	−0.189900	+	0.328917i
$943$	1.31371	+	2.27541i	0.0427802	+	0.0740975i
$944$	14.4853			0.471456
$945$		0			0
$946$	25.3137			0.823020
$947$	−9.75736	−	16.9002i	−0.317072	−	0.549184i	0.662804	−	0.748793i	$-0.269366\pi$
$947$	−9.75736	−	16.9002i	−0.317072	−	0.549184i	−0.979876	+	0.199609i	$0.936033\pi$
$948$	5.65685	−	9.79796i	0.183726	−	0.318223i
$949$		0			0
$950$	1.41421	+	2.44949i	0.0458831	+	0.0794719i
$951$	18.0000			0.583690
$952$		0			0
$953$	55.5980			1.80100			0.900498	−	0.434861i	$-0.143202\pi$
$953$	55.5980			1.80100			0.900498	+	0.434861i	$0.143202\pi$
$954$	−6.65685	−	11.5300i	−0.215524	−	0.373298i
$955$	5.65685	−	9.79796i	0.183052	−	0.317055i
$956$	−0.343146	+	0.594346i	−0.0110981	+	0.0192225i
$957$	−0.414214	−	0.717439i	−0.0133896	−	0.0231915i
$958$	0.485281			0.0156787
$959$		0			0
$960$	1.00000			0.0322749
$961$	−25.6421	−	44.4135i	−0.827166	−	1.43269i
$962$		0			0
$963$	2.00000	−	3.46410i	0.0644491	−	0.111629i
$964$	−3.87868	−	6.71807i	−0.124924	−	0.216374i
$965$	−17.7990			−0.572970
$966$		0			0
$967$	12.2843			0.395036			0.197518	−	0.980299i	$-0.436712\pi$
$967$	12.2843			0.395036			0.197518	+	0.980299i	$0.436712\pi$
$968$	−0.328427	−	0.568852i	−0.0105560	−	0.0182836i
$969$	−2.00000	+	3.46410i	−0.0642493	+	0.111283i
$970$	−1.58579	+	2.74666i	−0.0509165	+	0.0881900i
$971$	5.51472	+	9.55177i	0.176976	+	0.306531i	0.940843	−	0.338842i	$-0.110035\pi$
$971$	5.51472	+	9.55177i	0.176976	+	0.306531i	−0.763868	+	0.645373i	$0.776702\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	7.51472			0.240787
$975$		0			0
$976$	−0.171573	+	0.297173i	−0.00549191	+	0.00951227i
$977$	8.65685	−	14.9941i	0.276957	−	0.479704i	−0.693670	−	0.720293i	$-0.744007\pi$
$977$	8.65685	−	14.9941i	0.276957	−	0.479704i	0.970627	+	0.240589i	$0.0773406\pi$
$978$	−5.36396	−	9.29065i	−0.171521	−	0.297082i
$979$	−35.7990			−1.14414
$980$		0			0
$981$	−17.3137			−0.552784
$982$	3.94975	+	6.84116i	0.126042	+	0.218310i
$983$	18.4350	−	31.9304i	0.587986	−	1.01842i	−0.406510	−	0.913646i	$-0.633254\pi$
$983$	18.4350	−	31.9304i	0.587986	−	1.01842i	0.994496	−	0.104775i	$-0.0334124\pi$
$984$	1.58579	−	2.74666i	0.0505530	−	0.0875604i
$985$	−7.58579	−	13.1390i	−0.241703	−	0.418642i
$986$	−0.343146			−0.0109280
$987$		0			0
$988$		0			0
$989$	3.07107	+	5.31925i	0.0976543	+	0.169142i
$990$	1.70711	−	2.95680i	0.0542554	−	0.0939731i
$991$	−7.58579	+	13.1390i	−0.240970	+	0.417373i	−0.960991	−	0.276580i	$-0.910799\pi$
$991$	−7.58579	+	13.1390i	−0.240970	+	0.417373i	0.720021	+	0.693953i	$0.244132\pi$
$992$	−4.53553	−	7.85578i	−0.144003	−	0.249421i
$993$	−26.6274			−0.844996
$994$		0			0
$995$	17.0711			0.541189
$996$	5.41421	+	9.37769i	0.171556	+	0.297144i
$997$	−12.6569	+	21.9223i	−0.400847	+	0.694287i	−0.993828	−	0.110929i	$-0.964617\pi$
$997$	−12.6569	+	21.9223i	−0.400847	+	0.694287i	0.592982	+	0.805216i	$0.297951\pi$
$998$	11.8995	−	20.6105i	0.376672	−	0.652415i
$999$	0.707107	+	1.22474i	0.0223719	+	0.0387492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.v.361.1		4
7.2	even	3	inner	1470.2.i.v.961.1		4
7.3	odd	6		1470.2.a.v.1.2	yes	2
7.4	even	3		1470.2.a.u.1.2	✓	2
7.5	odd	6		1470.2.i.u.961.1		4
7.6	odd	2		1470.2.i.u.361.1		4
21.11	odd	6		4410.2.a.br.1.1		2
21.17	even	6		4410.2.a.bn.1.1		2
35.4	even	6		7350.2.a.df.1.2		2
35.24	odd	6		7350.2.a.dd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.a.u.1.2	✓	2	7.4	even	3
1470.2.a.v.1.2	yes	2	7.3	odd	6
1470.2.i.u.361.1		4	7.6	odd	2
1470.2.i.u.961.1		4	7.5	odd	6
1470.2.i.v.361.1		4	1.1	even	1	trivial
1470.2.i.v.961.1		4	7.2	even	3	inner
4410.2.a.bn.1.1		2	21.17	even	6
4410.2.a.br.1.1		2	21.11	odd	6
7350.2.a.dd.1.2		2	35.24	odd	6
7350.2.a.df.1.2		2	35.4	even	6

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.70711 + 2.95680i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.707107 + 1.22474i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.41421 + 2.44949i) q^{19} -1.00000 q^{20} +3.41421 q^{22} +(0.414214 + 0.717439i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -0.242641 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-4.53553 + 7.85578i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.70711 + 2.95680i) q^{33} +1.41421 q^{34} +1.00000 q^{36} +(-0.707107 - 1.22474i) q^{37} +(1.41421 - 2.44949i) q^{38} +(0.500000 + 0.866025i) q^{40} +3.17157 q^{41} +7.41421 q^{43} +(-1.70711 - 2.95680i) q^{44} +(0.500000 - 0.866025i) q^{45} +(0.414214 - 0.717439i) q^{46} +(2.53553 + 4.39167i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(0.707107 + 1.22474i) q^{51} +(-6.65685 + 11.5300i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.41421 q^{55} +2.82843 q^{57} +(0.121320 + 0.210133i) q^{58} +(-7.24264 + 12.5446i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-0.171573 - 0.297173i) q^{61} +9.07107 q^{62} +1.00000 q^{64} +(1.70711 - 2.95680i) q^{66} +(5.94975 - 10.3053i) q^{67} +(-0.707107 - 1.22474i) q^{68} +0.828427 q^{69} +5.17157 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.82843 + 3.16693i) q^{73} +(-0.707107 + 1.22474i) q^{74} +(0.500000 + 0.866025i) q^{75} -2.82843 q^{76} +(-5.65685 - 9.79796i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.58579 - 2.74666i) q^{82} +10.8284 q^{83} -1.41421 q^{85} +(-3.70711 - 6.42090i) q^{86} +(-0.121320 + 0.210133i) q^{87} +(-1.70711 + 2.95680i) q^{88} +(5.24264 + 9.08052i) q^{89} -1.00000 q^{90} -0.828427 q^{92} +(4.53553 + 7.85578i) q^{93} +(2.53553 - 4.39167i) q^{94} +(-1.41421 + 2.44949i) q^{95} +(0.500000 + 0.866025i) q^{96} -3.17157 q^{97} +3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 4 q^{15} - 2 q^{16} - 2 q^{18} - 4 q^{20} + 8 q^{22} - 4 q^{23} + 2 q^{24} - 2 q^{25} - 4 q^{27}+ \cdots + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 4 * q^15 - 2 * q^16 - 2 * q^18 - 4 * q^20 + 8 * q^22 - 4 * q^23 + 2 * q^24 - 2 * q^25 - 4 * q^27 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^36 + 2 * q^40 + 24 * q^41 + 24 * q^43 - 4 * q^44 + 2 * q^45 - 4 * q^46 - 4 * q^47 - 4 * q^48 + 4 * q^50 - 4 * q^53 + 2 * q^54 - 8 * q^55 - 8 * q^58 - 12 * q^59 - 2 * q^60 - 12 * q^61 + 8 * q^62 + 4 * q^64 + 4 * q^66 + 4 * q^67 - 8 * q^69 + 32 * q^71 - 2 * q^72 + 4 * q^73 + 2 * q^75 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 32 * q^83 - 12 * q^86 + 8 * q^87 - 4 * q^88 + 4 * q^89 - 4 * q^90 + 8 * q^92 + 4 * q^93 - 4 * q^94 + 2 * q^96 - 24 * q^97 + 8 * q^99

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