LMFDB - Embedded newform 490.2.e.h.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,2,Mod(361,490)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("490.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,1,-1,-1,2,0,-2,2,1,6] 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.361
Dual form			490.2.e.h.471.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{10} +(3.00000 - 5.19615i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{18} +(1.00000 + 1.73205i) q^{19} +1.00000 q^{20} +6.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{26} +5.00000 q^{27} -3.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(4.00000 - 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -2.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(2.00000 - 3.46410i) q^{39} +(0.500000 + 0.866025i) q^{40} -9.00000 q^{41} -7.00000 q^{43} +(3.00000 + 5.19615i) q^{44} +(1.00000 - 1.73205i) q^{45} +(-1.50000 + 2.59808i) q^{46} -1.00000 q^{48} -1.00000 q^{50} +(-2.00000 + 3.46410i) q^{52} +(3.00000 - 5.19615i) q^{53} +(2.50000 + 4.33013i) q^{54} -6.00000 q^{55} +2.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{60} +(2.50000 + 4.33013i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(3.00000 - 5.19615i) q^{66} +(-2.50000 + 4.33013i) q^{67} +3.00000 q^{69} -6.00000 q^{71} +(-1.00000 - 1.73205i) q^{72} +(-8.00000 + 13.8564i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(0.500000 + 0.866025i) q^{75} -2.00000 q^{76} +4.00000 q^{78} +(-1.00000 - 1.73205i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{82} -3.00000 q^{83} +(-3.50000 - 6.06218i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-7.50000 - 12.9904i) q^{89} +2.00000 q^{90} -3.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(1.00000 - 1.73205i) q^{95} +(-0.500000 - 0.866025i) q^{96} -14.0000 q^{97} +12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + 6 q^{11} + q^{12} + 8 q^{13} - 2 q^{15} - q^{16} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 12 q^{22} + 3 q^{23} - q^{24} - q^{25}+ \cdots + 24 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + 6 * q^11 + q^12 + 8 * q^13 - 2 * q^15 - q^16 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 12 * q^22 + 3 * q^23 - q^24 - q^25 + 4 * q^26 + 10 * q^27 - 6 * q^29 - q^30 + 8 * q^31 + q^32 - 6 * q^33 - 4 * q^36 + 4 * q^37 - 2 * q^38 + 4 * q^39 + q^40 - 18 * q^41 - 14 * q^43 + 6 * q^44 + 2 * q^45 - 3 * q^46 - 2 * q^48 - 2 * q^50 - 4 * q^52 + 6 * q^53 + 5 * q^54 - 12 * q^55 + 4 * q^57 - 3 * q^58 - 6 * q^59 + q^60 + 5 * q^61 + 16 * q^62 + 2 * q^64 - 4 * q^65 + 6 * q^66 - 5 * q^67 + 6 * q^69 - 12 * q^71 - 2 * q^72 - 16 * q^73 - 4 * q^74 + q^75 - 4 * q^76 + 8 * q^78 - 2 * q^79 - q^80 - q^81 - 9 * q^82 - 6 * q^83 - 7 * q^86 - 3 * q^87 - 6 * q^88 - 15 * q^89 + 4 * q^90 - 6 * q^92 - 8 * q^93 + 2 * q^95 - q^96 - 28 * q^97 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	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	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−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
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−1.00000	+	1.73205i	−0.235702	+	0.408248i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	6.00000			1.27920
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$	5.00000			0.962250
$28$		0			0
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$		0			0
$35$		0			0
$36$	−2.00000			−0.333333
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$	3.00000	+	5.19615i	0.452267	+	0.783349i
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$	2.50000	+	4.33013i	0.340207	+	0.589256i
$55$	−6.00000			−0.809040
$56$		0			0
$57$	2.00000			0.264906
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$	3.00000			0.361158
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.00000	−	1.73205i	−0.117851	−	0.204124i
$73$	−8.00000	+	13.8564i	−0.936329	+	1.62177i	−0.164083	+	0.986447i	$0.552466\pi$
$73$	−8.00000	+	13.8564i	−0.936329	+	1.62177i	−0.772246	+	0.635323i	$0.780867\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	4.00000			0.452911
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$		0			0
$85$		0			0
$86$	−3.50000	−	6.06218i	−0.377415	−	0.653701i
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$	−3.00000			−0.312772
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$		0			0
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$	12.0000			1.20605
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	−0.203317	−	0.979113i	$-0.565172\pi$
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	0.949595	−	0.313478i	$-0.101494\pi$
$102$		0			0
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	0.840341	−	0.542059i	$-0.182355\pi$
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	−0.889607	+	0.456727i	$0.849022\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	6.00000			0.582772
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	0.958952	+	0.283567i	$0.0915178\pi$
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	−0.233900	+	0.972261i	$0.575149\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$	−3.00000	−	5.19615i	−0.286039	−	0.495434i
$111$	4.00000			0.379663
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	4.00000	+	6.92820i	0.369800	+	0.640513i
$118$	−6.00000			−0.552345
$119$		0			0
$120$	1.00000			0.0912871
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	−2.50000	+	4.33013i	−0.226339	+	0.392031i
$123$	−4.50000	+	7.79423i	−0.405751	+	0.702782i
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−3.50000	+	6.06218i	−0.308158	+	0.533745i
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$	−5.00000			−0.431934
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$	1.50000	+	2.59808i	0.127688	+	0.221163i
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	12.0000	−	20.7846i	1.00349	−	1.73810i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	1.50000	+	2.59808i	0.124568	+	0.215758i
$146$	−16.0000			−1.32417
$147$		0			0
$148$	−4.00000			−0.328798
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	−0.990485	−	0.137619i	$-0.956055\pi$
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	0.376061	−	0.926595i	$-0.377278\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	0.935857	+	0.352381i	$0.114628\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$		0			0
$154$		0			0
$155$	−8.00000			−0.642575
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.0242497	+	0.999706i	$0.507720\pi$
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.853646	+	0.520854i	$0.825614\pi$
$158$	1.00000	−	1.73205i	0.0795557	−	0.137795i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	−1.50000	−	2.59808i	−0.116423	−	0.201650i
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$	3.50000	−	6.06218i	0.266872	−	0.462237i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	−3.00000			−0.227429
$175$		0			0
$176$	−6.00000			−0.452267
$177$	3.00000	+	5.19615i	0.225494	+	0.390567i
$178$	7.50000	−	12.9904i	0.562149	−	0.973670i
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.0655145	−	0.997852i	$-0.479131\pi$
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.831408	−	0.555663i	$-0.187536\pi$
$180$	1.00000	+	1.73205i	0.0745356	+	0.129099i
$181$	−11.0000			−0.817624			−0.408812	−	0.912619i	$-0.634057\pi$
$181$	−11.0000			−0.817624			−0.408812	+	0.912619i	$0.634057\pi$
$182$		0			0
$183$	5.00000			0.369611
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$		0			0
$188$		0			0
$189$		0			0
$190$	2.00000			0.145095
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$	−4.00000			−0.286446
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	6.00000	+	10.3923i	0.426401	+	0.738549i
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	2.50000	+	4.33013i	0.176336	+	0.305424i
$202$	15.0000			1.05540
$203$		0			0
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	0.500000	−	0.866025i	0.0348367	−	0.0603388i
$207$	−3.00000	+	5.19615i	−0.208514	+	0.361158i
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$	12.0000			0.830057
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$	−7.50000	+	12.9904i	−0.512689	+	0.888004i
$215$	3.50000	+	6.06218i	0.238698	+	0.413437i
$216$	−5.00000			−0.340207
$217$		0			0
$218$	−11.0000			−0.745014
$219$	8.00000	+	13.8564i	0.540590	+	0.936329i
$220$	3.00000	−	5.19615i	0.202260	−	0.350325i
$221$		0			0
$222$	2.00000	+	3.46410i	0.134231	+	0.232495i
$223$	28.0000			1.87502			0.937509	−	0.347960i	$-0.113126\pi$
$223$	28.0000			1.87502			0.937509	+	0.347960i	$0.113126\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$	3.00000			0.197814
$231$		0			0
$232$	3.00000			0.196960
$233$	6.00000	+	10.3923i	0.393073	+	0.680823i	0.992853	−	0.119342i	$-0.0380786\pi$
$233$	6.00000	+	10.3923i	0.393073	+	0.680823i	−0.599780	+	0.800165i	$0.704745\pi$
$234$	−4.00000	+	6.92820i	−0.261488	+	0.452911i
$235$		0			0
$236$	−3.00000	−	5.19615i	−0.195283	−	0.338241i
$237$	−2.00000			−0.129914
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	−0.832019	−	0.554747i	$-0.812815\pi$
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	0.896435	+	0.443176i	$0.146148\pi$
$242$	12.5000	−	21.6506i	0.803530	−	1.39176i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	−5.00000			−0.320092
$245$		0			0
$246$	−9.00000			−0.573819
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$	−4.00000	+	6.92820i	−0.254000	+	0.439941i
$249$	−1.50000	+	2.59808i	−0.0950586	+	0.164646i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$	−7.00000			−0.435801
$259$		0			0
$260$	4.00000			0.248069
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	−0.336270	−	0.941766i	$-0.609166\pi$
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	0.983728	−	0.179664i	$-0.0575011\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$	−6.00000			−0.368577
$266$		0			0
$267$	−15.0000			−0.917985
$268$	−2.50000	−	4.33013i	−0.152712	−	0.264505i
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$	2.50000	−	4.33013i	0.152145	−	0.263523i
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	0.894799	−	0.446469i	$-0.147319\pi$
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	−0.834053	+	0.551684i	$0.813985\pi$
$272$		0			0
$273$		0			0
$274$	−12.0000			−0.724947
$275$	3.00000	+	5.19615i	0.180907	+	0.313340i
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	5.00000	+	8.66025i	0.299880	+	0.519408i
$279$	16.0000			0.957895
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	−1.00000	−	1.73205i	−0.0592349	−	0.102598i
$286$	24.0000			1.41915
$287$		0			0
$288$	2.00000			0.117851
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−1.50000	+	2.59808i	−0.0880830	+	0.152564i
$291$	−7.00000	+	12.1244i	−0.410347	+	0.710742i
$292$	−8.00000	−	13.8564i	−0.468165	−	0.810885i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$	−2.00000	−	3.46410i	−0.116248	−	0.201347i
$297$	15.0000	−	25.9808i	0.870388	−	1.50756i
$298$	7.50000	−	12.9904i	0.434463	−	0.752513i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	4.00000			0.230174
$303$	−7.50000	−	12.9904i	−0.430864	−	0.746278i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$	2.50000	−	4.33013i	0.143150	−	0.247942i
$306$		0			0
$307$	−5.00000			−0.285365			−0.142683	−	0.989769i	$-0.545573\pi$
$307$	−5.00000			−0.285365			−0.142683	+	0.989769i	$0.545573\pi$
$308$		0			0
$309$	−1.00000			−0.0568880
$310$	−4.00000	−	6.92820i	−0.227185	−	0.393496i
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$	−2.00000	+	3.46410i	−0.113228	+	0.196116i
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	0.956647	−	0.291250i	$-0.0940712\pi$
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	−0.730554	+	0.682855i	$0.760738\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	2.00000			0.112509
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$	3.00000	−	5.19615i	0.168232	−	0.291386i
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	15.0000			0.837218
$322$		0			0
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−2.00000	+	3.46410i	−0.110940	+	0.192154i
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$	5.50000	+	9.52628i	0.304151	+	0.526804i
$328$	9.00000			0.496942
$329$		0			0
$330$	−6.00000			−0.330289
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	1.50000	−	2.59808i	0.0823232	−	0.142588i
$333$	−4.00000	+	6.92820i	−0.219199	+	0.379663i
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$	5.00000			0.273179
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$		0			0
$341$	−24.0000	−	41.5692i	−1.29967	−	2.25110i
$342$	−4.00000			−0.216295
$343$		0			0
$344$	7.00000			0.377415
$345$	−1.50000	−	2.59808i	−0.0807573	−	0.139876i
$346$		0			0
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	−0.961162	−	0.275983i	$-0.910997\pi$
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	0.719590	+	0.694399i	$0.244330\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−17.0000			−0.909989			−0.454995	−	0.890494i	$-0.650359\pi$
$349$	−17.0000			−0.909989			−0.454995	+	0.890494i	$0.650359\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$	−3.00000	−	5.19615i	−0.159901	−	0.276956i
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	15.0000			0.794998
$357$		0			0
$358$	24.0000			1.26844
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$	−1.00000	+	1.73205i	−0.0527046	+	0.0912871i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−5.50000	−	9.52628i	−0.289074	−	0.500690i
$363$	−25.0000			−1.31216
$364$		0			0
$365$	16.0000			0.837478
$366$	2.50000	+	4.33013i	0.130677	+	0.226339i
$367$	17.5000	−	30.3109i	0.913493	−	1.58222i	0.104399	−	0.994535i	$-0.466708\pi$
$367$	17.5000	−	30.3109i	0.913493	−	1.58222i	0.809093	−	0.587680i	$-0.199959\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$	4.00000			0.207950
$371$		0			0
$372$	8.00000			0.414781
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−34.0000			−1.74646			−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000			−1.74646			−0.873231	+	0.487306i	$0.837980\pi$
$380$	1.00000	+	1.73205i	0.0512989	+	0.0888523i
$381$	4.00000	−	6.92820i	0.204926	−	0.354943i
$382$	−3.00000	+	5.19615i	−0.153493	+	0.265858i
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	0.608290	−	0.793715i	$-0.291856\pi$
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	−0.991522	+	0.129937i	$0.958522\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−2.00000			−0.101797
$387$	−7.00000	−	12.1244i	−0.355830	−	0.616316i
$388$	7.00000	−	12.1244i	0.355371	−	0.615521i
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$	−2.00000	−	3.46410i	−0.101274	−	0.175412i
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	−1.00000	+	1.73205i	−0.0503155	+	0.0871489i
$396$	−6.00000	+	10.3923i	−0.301511	+	0.522233i
$397$	7.00000	+	12.1244i	0.351320	+	0.608504i	0.986481	−	0.163876i	$-0.0523996\pi$
$397$	7.00000	+	12.1244i	0.351320	+	0.608504i	−0.635161	+	0.772380i	$0.719066\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	1.00000			0.0500000
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$	−2.50000	+	4.33013i	−0.124689	+	0.215967i
$403$	16.0000	−	27.7128i	0.797017	−	1.38047i
$404$	7.50000	+	12.9904i	0.373139	+	0.646296i
$405$	1.00000			0.0496904
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	−6.50000	+	11.2583i	−0.321404	+	0.556689i	−0.980778	−	0.195127i	$-0.937488\pi$
$409$	−6.50000	+	11.2583i	−0.321404	+	0.556689i	0.659374	+	0.751815i	$0.270822\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$	6.00000	+	10.3923i	0.295958	+	0.512615i
$412$	1.00000			0.0492665
$413$		0			0
$414$	−6.00000			−0.294884
$415$	1.50000	+	2.59808i	0.0736321	+	0.127535i
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$	5.00000	−	8.66025i	0.244851	−	0.424094i
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$	−5.00000	−	8.66025i	−0.243396	−	0.421575i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$		0			0
$426$	−6.00000			−0.290701
$427$		0			0
$428$	−15.0000			−0.725052
$429$	−12.0000	−	20.7846i	−0.579365	−	1.00349i
$430$	−3.50000	+	6.06218i	−0.168785	+	0.292344i
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	22.0000			1.05725			0.528626	−	0.848855i	$-0.322707\pi$
$433$	22.0000			1.05725			0.528626	+	0.848855i	$0.322707\pi$
$434$		0			0
$435$	3.00000			0.143839
$436$	−5.50000	−	9.52628i	−0.263402	−	0.456226i
$437$	−3.00000	+	5.19615i	−0.143509	+	0.248566i
$438$	−8.00000	+	13.8564i	−0.382255	+	0.662085i
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$		0			0
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	0.501129	−	0.865373i	$-0.332918\pi$
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	−0.999999	+	0.00130426i	$0.999585\pi$
$444$	−2.00000	+	3.46410i	−0.0949158	+	0.164399i
$445$	−7.50000	+	12.9904i	−0.355534	+	0.615803i
$446$	14.0000	+	24.2487i	0.662919	+	1.14821i
$447$	−15.0000			−0.709476
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$	−1.00000	−	1.73205i	−0.0471405	−	0.0816497i
$451$	−27.0000	+	46.7654i	−1.27138	+	2.20210i
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	−2.00000	−	3.46410i	−0.0939682	−	0.162758i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	−0.948566	−	0.316579i	$-0.897466\pi$
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	0.200118	−	0.979772i	$-0.435868\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$		0			0
$460$	1.50000	+	2.59808i	0.0699379	+	0.121136i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	−13.0000			−0.604161			−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000			−0.604161			−0.302081	+	0.953282i	$0.597681\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$	−4.00000	+	6.92820i	−0.185496	+	0.321288i
$466$	−6.00000	+	10.3923i	−0.277945	+	0.481414i
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	0.638667	−	0.769483i	$-0.279486\pi$
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	−0.985726	+	0.168360i	$0.946153\pi$
$468$	−8.00000			−0.369800
$469$		0			0
$470$		0			0
$471$	11.0000	+	19.0526i	0.506853	+	0.877896i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$	−21.0000	+	36.3731i	−0.965581	+	1.67244i
$474$	−1.00000	−	1.73205i	−0.0459315	−	0.0795557i
$475$	−2.00000			−0.0917663
$476$		0			0
$477$	12.0000			0.549442
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	−0.695773	−	0.718262i	$-0.744938\pi$
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	0.969920	+	0.243426i	$0.0782712\pi$
$480$	−0.500000	+	0.866025i	−0.0228218	+	0.0395285i
$481$	8.00000	+	13.8564i	0.364769	+	0.631798i
$482$	2.00000			0.0910975
$483$		0			0
$484$	25.0000			1.13636
$485$	7.00000	+	12.1244i	0.317854	+	0.550539i
$486$	−8.00000	+	13.8564i	−0.362887	+	0.628539i
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	−2.50000	−	4.33013i	−0.113170	−	0.196016i
$489$	4.00000			0.180886
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	−4.50000	−	7.79423i	−0.202876	−	0.351391i
$493$		0			0
$494$	−4.00000	+	6.92820i	−0.179969	+	0.311715i
$495$	−6.00000	−	10.3923i	−0.269680	−	0.467099i
$496$	−8.00000			−0.359211
$497$		0			0
$498$	−3.00000			−0.134433
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	0.999962	−	0.00872186i	$-0.00277629\pi$
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	−0.507534	+	0.861632i	$0.669443\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$	6.00000	+	10.3923i	0.267793	+	0.463831i
$503$	−21.0000			−0.936344			−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000			−0.936344			−0.468172	+	0.883637i	$0.655087\pi$
$504$		0			0
$505$	−15.0000			−0.667491
$506$	9.00000	+	15.5885i	0.400099	+	0.692991i
$507$	1.50000	−	2.59808i	0.0666173	−	0.115385i
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	0.999220	−	0.0394971i	$-0.0125756\pi$
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	−0.533815	+	0.845601i	$0.679242\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	5.00000	+	8.66025i	0.220755	+	0.382360i
$514$		0			0
$515$	−0.500000	+	0.866025i	−0.0220326	+	0.0381616i
$516$	−3.50000	−	6.06218i	−0.154079	−	0.266872i
$517$		0			0
$518$		0			0
$519$		0			0
$520$	2.00000	+	3.46410i	0.0877058	+	0.151911i
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	−0.990873	−	0.134801i	$-0.956961\pi$
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	0.378695	−	0.925521i	$-0.376373\pi$
$524$		0			0
$525$		0			0
$526$	21.0000			0.915644
$527$		0			0
$528$	−3.00000	+	5.19615i	−0.130558	+	0.226134i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−3.00000	−	5.19615i	−0.130312	−	0.225706i
$531$	−12.0000			−0.520756
$532$		0			0
$533$	−36.0000			−1.55933
$534$	−7.50000	−	12.9904i	−0.324557	−	0.562149i
$535$	7.50000	−	12.9904i	0.324253	−	0.561623i
$536$	2.50000	−	4.33013i	0.107984	−	0.187033i
$537$	−12.0000	−	20.7846i	−0.517838	−	0.896922i
$538$	15.0000			0.646696
$539$		0			0
$540$	5.00000			0.215166
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$	−1.00000	+	1.73205i	−0.0429537	+	0.0743980i
$543$	−5.50000	+	9.52628i	−0.236028	+	0.408812i
$544$		0			0
$545$	11.0000			0.471188
$546$		0			0
$547$	−19.0000			−0.812381			−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000			−0.812381			−0.406191	+	0.913788i	$0.633143\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$	−3.00000	+	5.19615i	−0.127920	+	0.221565i
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$	−3.00000			−0.127688
$553$		0			0
$554$	−8.00000			−0.339887
$555$	−2.00000	−	3.46410i	−0.0848953	−	0.147043i
$556$	−5.00000	+	8.66025i	−0.212047	+	0.367277i
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	−0.609912	−	0.792469i	$-0.708795\pi$
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	0.991254	+	0.131965i	$0.0421286\pi$
$558$	8.00000	+	13.8564i	0.338667	+	0.586588i
$559$	−28.0000			−1.18427
$560$		0			0
$561$		0			0
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	13.5000	−	23.3827i	0.568957	−	0.985463i	−0.427712	−	0.903915i	$-0.640680\pi$
$563$	13.5000	−	23.3827i	0.568957	−	0.985463i	0.996669	−	0.0815478i	$-0.0259863\pi$
$564$		0			0
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	6.00000			0.251754
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$	1.00000	−	1.73205i	0.0418854	−	0.0725476i
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	−0.538642	−	0.842535i	$-0.681062\pi$
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	0.998978	+	0.0452101i	$0.0143957\pi$
$572$	12.0000	+	20.7846i	0.501745	+	0.869048i
$573$	6.00000			0.250654
$574$		0			0
$575$	−3.00000			−0.125109
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	13.0000	−	22.5167i	0.541197	−	0.937381i	−0.457639	−	0.889138i	$-0.651305\pi$
$577$	13.0000	−	22.5167i	0.541197	−	0.937381i	0.998836	−	0.0482425i	$-0.0153620\pi$
$578$	−8.50000	+	14.7224i	−0.353553	+	0.612372i
$579$	1.00000	+	1.73205i	0.0415586	+	0.0719816i
$580$	−3.00000			−0.124568
$581$		0			0
$582$	−14.0000			−0.580319
$583$	−18.0000	−	31.1769i	−0.745484	−	1.29122i
$584$	8.00000	−	13.8564i	0.331042	−	0.573382i
$585$	4.00000	−	6.92820i	0.165380	−	0.286446i
$586$	−6.00000	−	10.3923i	−0.247858	−	0.429302i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$	3.00000	+	5.19615i	0.123508	+	0.213922i
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$	30.0000			1.23091
$595$		0			0
$596$	15.0000			0.614424
$597$	2.00000	+	3.46410i	0.0818546	+	0.141776i
$598$	−6.00000	+	10.3923i	−0.245358	+	0.424973i
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	46.0000			1.87638			0.938190	−	0.346122i	$-0.112502\pi$
$601$	46.0000			1.87638			0.938190	+	0.346122i	$0.112502\pi$
$602$		0			0
$603$	−10.0000			−0.407231
$604$	2.00000	+	3.46410i	0.0813788	+	0.140952i
$605$	−12.5000	+	21.6506i	−0.508197	+	0.880223i
$606$	7.50000	−	12.9904i	0.304667	−	0.527698i
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$	5.00000			0.202444
$611$		0			0
$612$		0			0
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	−0.658012	−	0.753007i	$-0.728603\pi$
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	0.981129	+	0.193352i	$0.0619359\pi$
$614$	−2.50000	−	4.33013i	−0.100892	−	0.174750i
$615$	9.00000			0.362915
$616$		0			0
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$	−0.500000	−	0.866025i	−0.0201129	−	0.0348367i
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	−0.690365	−	0.723462i	$-0.742550\pi$
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	0.971718	+	0.236143i	$0.0758832\pi$
$620$	4.00000	−	6.92820i	0.160644	−	0.278243i
$621$	7.50000	+	12.9904i	0.300965	+	0.521286i
$622$	−18.0000			−0.721734
$623$		0			0
$624$	−4.00000			−0.160128
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.00000	+	6.92820i	−0.159872	+	0.276907i
$627$	6.00000	−	10.3923i	0.239617	−	0.415029i
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$		0			0
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	1.00000	+	1.73205i	0.0397779	+	0.0688973i
$633$	−5.00000	+	8.66025i	−0.198732	+	0.344214i
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$	6.00000			0.237915
$637$		0			0
$638$	−18.0000			−0.712627
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	−0.834881	−	0.550431i	$-0.814464\pi$
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	0.894127	+	0.447813i	$0.147797\pi$
$642$	7.50000	+	12.9904i	0.296001	+	0.512689i
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$		0			0
$645$	7.00000			0.275625
$646$		0			0
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	−0.835033	−	0.550200i	$-0.814551\pi$
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	0.894004	+	0.448059i	$0.147885\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	18.0000	+	31.1769i	0.706562	+	1.22380i
$650$	−4.00000			−0.156893
$651$		0			0
$652$	−4.00000			−0.156652
$653$	24.0000	+	41.5692i	0.939193	+	1.62673i	0.766982	+	0.641669i	$0.221758\pi$
$653$	24.0000	+	41.5692i	0.939193	+	1.62673i	0.172211	+	0.985060i	$0.444909\pi$
$654$	−5.50000	+	9.52628i	−0.215067	+	0.372507i
$655$		0			0
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$	−32.0000			−1.24844
$658$		0			0
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	−0.123974	−	0.992286i	$-0.539564\pi$
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	0.921331	−	0.388778i	$-0.127103\pi$
$662$	−14.0000	+	24.2487i	−0.544125	+	0.942453i
$663$		0			0
$664$	3.00000			0.116423
$665$		0			0
$666$	−8.00000			−0.309994
$667$	−4.50000	−	7.79423i	−0.174241	−	0.301794i
$668$	−1.50000	+	2.59808i	−0.0580367	+	0.100523i
$669$	14.0000	−	24.2487i	0.541271	−	0.937509i
$670$	2.50000	+	4.33013i	0.0965834	+	0.167287i
$671$	30.0000			1.15814
$672$		0			0
$673$	8.00000			0.308377			0.154189	−	0.988041i	$-0.450724\pi$
$673$	8.00000			0.308377			0.154189	+	0.988041i	$0.450724\pi$
$674$	−11.0000	−	19.0526i	−0.423704	−	0.733877i
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	0.957984	−	0.286820i	$-0.0925982\pi$
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	−0.727386	+	0.686229i	$0.759265\pi$
$678$	6.00000			0.230429
$679$		0			0
$680$		0			0
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$	24.0000	−	41.5692i	0.919007	−	1.59177i
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	−0.939184	−	0.343413i	$-0.888417\pi$
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	0.766997	+	0.641651i	$0.221750\pi$
$684$	−2.00000	−	3.46410i	−0.0764719	−	0.132453i
$685$	12.0000			0.458496
$686$		0			0
$687$	14.0000			0.534133
$688$	3.50000	+	6.06218i	0.133436	+	0.231118i
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$	1.50000	−	2.59808i	0.0571040	−	0.0989071i
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	0.577325	−	0.816514i	$-0.304097\pi$
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	−0.995785	+	0.0917209i	$0.970763\pi$
$692$		0			0
$693$		0			0
$694$	−9.00000			−0.341635
$695$	−5.00000	−	8.66025i	−0.189661	−	0.328502i
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$		0			0
$698$	−8.50000	−	14.7224i	−0.321730	−	0.557252i
$699$	12.0000			0.453882
$700$		0			0
$701$	−3.00000			−0.113308			−0.0566542	−	0.998394i	$-0.518043\pi$
$701$	−3.00000			−0.113308			−0.0566542	+	0.998394i	$0.518043\pi$
$702$	10.0000	+	17.3205i	0.377426	+	0.653720i
$703$	−4.00000	+	6.92820i	−0.150863	+	0.261302i
$704$	3.00000	−	5.19615i	0.113067	−	0.195837i
$705$		0			0
$706$	−6.00000			−0.225813
$707$		0			0
$708$	−6.00000			−0.225494
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	0.995228	+	0.0975728i	$0.0311079\pi$
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	−0.413114	+	0.910679i	$0.635559\pi$
$710$	−3.00000	+	5.19615i	−0.112588	+	0.195008i
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	7.50000	+	12.9904i	0.281074	+	0.486835i
$713$	24.0000			0.898807
$714$		0			0
$715$	−24.0000			−0.897549
$716$	12.0000	+	20.7846i	0.448461	+	0.776757i
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$	12.0000	−	20.7846i	0.447836	−	0.775675i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$	−2.00000			−0.0745356
$721$		0			0
$722$	15.0000			0.558242
$723$	−1.00000	−	1.73205i	−0.0371904	−	0.0644157i
$724$	5.50000	−	9.52628i	0.204406	−	0.354041i
$725$	1.50000	−	2.59808i	0.0557086	−	0.0964901i
$726$	−12.5000	−	21.6506i	−0.463919	−	0.803530i
$727$	19.0000			0.704671			0.352335	−	0.935874i	$-0.385388\pi$
$727$	19.0000			0.704671			0.352335	+	0.935874i	$0.385388\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	8.00000	+	13.8564i	0.296093	+	0.512849i
$731$		0			0
$732$	−2.50000	+	4.33013i	−0.0924027	+	0.160046i
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	−0.987971	−	0.154642i	$-0.950578\pi$
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	0.360061	−	0.932929i	$-0.382756\pi$
$734$	35.0000			1.29187
$735$		0			0
$736$	3.00000			0.110581
$737$	15.0000	+	25.9808i	0.552532	+	0.957014i
$738$	9.00000	−	15.5885i	0.331295	−	0.573819i
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	−0.999688	−	0.0249776i	$-0.992049\pi$
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	0.521475	+	0.853266i	$0.325382\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$	8.00000			0.293887
$742$		0			0
$743$	39.0000			1.43077			0.715386	−	0.698730i	$-0.246251\pi$
$743$	39.0000			1.43077			0.715386	+	0.698730i	$0.246251\pi$
$744$	4.00000	+	6.92820i	0.146647	+	0.254000i
$745$	−7.50000	+	12.9904i	−0.274779	+	0.475931i
$746$	−2.00000	+	3.46410i	−0.0732252	+	0.126830i
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$		0			0
$749$		0			0
$750$	1.00000			0.0365148
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$		0			0
$753$	6.00000	−	10.3923i	0.218652	−	0.378717i
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$	−4.00000			−0.145575
$756$		0			0
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	−17.0000	−	29.4449i	−0.617468	−	1.06949i
$759$	9.00000	−	15.5885i	0.326679	−	0.565825i
$760$	−1.00000	+	1.73205i	−0.0362738	+	0.0628281i
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	0.942207	+	0.335032i	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$	8.00000			0.289809
$763$		0			0
$764$	−6.00000			−0.217072
$765$		0			0
$766$	7.50000	−	12.9904i	0.270986	−	0.469362i
$767$	−12.0000	+	20.7846i	−0.433295	+	0.750489i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	−6.00000	+	10.3923i	−0.215805	+	0.373785i	−0.953521	−	0.301326i	$-0.902571\pi$
$773$	−6.00000	+	10.3923i	−0.215805	+	0.373785i	0.737716	+	0.675111i	$0.235904\pi$
$774$	7.00000	−	12.1244i	0.251610	−	0.435801i
$775$	4.00000	+	6.92820i	0.143684	+	0.248868i
$776$	14.0000			0.502571
$777$		0			0
$778$	30.0000			1.07555
$779$	−9.00000	−	15.5885i	−0.322458	−	0.558514i
$780$	2.00000	−	3.46410i	0.0716115	−	0.124035i
$781$	−18.0000	+	31.1769i	−0.644091	+	1.11560i
$782$		0			0
$783$	−15.0000			−0.536056
$784$		0			0
$785$	22.0000			0.785214
$786$		0			0
$787$	−21.5000	+	37.2391i	−0.766392	+	1.32743i	0.173115	+	0.984902i	$0.444617\pi$
$787$	−21.5000	+	37.2391i	−0.766392	+	1.32743i	−0.939507	+	0.342529i	$0.888717\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$	−10.5000	−	18.1865i	−0.373810	−	0.647458i
$790$	−2.00000			−0.0711568
$791$		0			0
$792$	−12.0000			−0.426401
$793$	10.0000	+	17.3205i	0.355110	+	0.615069i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$	−3.00000	+	5.19615i	−0.106399	+	0.184289i
$796$	−2.00000	−	3.46410i	−0.0708881	−	0.122782i
$797$	48.0000			1.70025			0.850124	−	0.526583i	$-0.176527\pi$
$797$	48.0000			1.70025			0.850124	+	0.526583i	$0.176527\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	15.0000	−	25.9808i	0.529999	−	0.917985i
$802$	7.50000	−	12.9904i	0.264834	−	0.458706i
$803$	48.0000	+	83.1384i	1.69388	+	2.93389i
$804$	−5.00000			−0.176336
$805$		0			0
$806$	32.0000			1.12715
$807$	−7.50000	−	12.9904i	−0.264013	−	0.457283i
$808$	−7.50000	+	12.9904i	−0.263849	+	0.457000i
$809$	−10.5000	+	18.1865i	−0.369160	+	0.639404i	−0.989434	−	0.144981i	$-0.953688\pi$
$809$	−10.5000	+	18.1865i	−0.369160	+	0.639404i	0.620274	+	0.784385i	$0.287021\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$	2.00000			0.0701431
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	−7.00000	−	12.1244i	−0.244899	−	0.424178i
$818$	−13.0000			−0.454534
$819$		0			0
$820$	−9.00000			−0.314294
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$	−6.00000	+	10.3923i	−0.209274	+	0.362473i
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	−0.651588	−	0.758573i	$-0.725897\pi$
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	0.982737	+	0.185006i	$0.0592303\pi$
$824$	0.500000	+	0.866025i	0.0174183	+	0.0301694i
$825$	6.00000			0.208893
$826$		0			0
$827$	15.0000			0.521601			0.260801	−	0.965393i	$-0.416014\pi$
$827$	15.0000			0.521601			0.260801	+	0.965393i	$0.416014\pi$
$828$	−3.00000	−	5.19615i	−0.104257	−	0.180579i
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$	−1.50000	+	2.59808i	−0.0520658	+	0.0901805i
$831$	4.00000	+	6.92820i	0.138758	+	0.240337i
$832$	4.00000			0.138675
$833$		0			0
$834$	10.0000			0.346272
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$	20.0000	−	34.6410i	0.691301	−	1.19737i
$838$		0			0
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	8.50000	+	14.7224i	0.292929	+	0.507369i
$843$	−3.00000	+	5.19615i	−0.103325	+	0.178965i
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$	−1.50000	−	2.59808i	−0.0516016	−	0.0893765i
$846$		0			0
$847$		0			0
$848$	−6.00000			−0.206041
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$	−3.00000	−	5.19615i	−0.102778	−	0.178017i
$853$	46.0000			1.57501			0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	−7.50000	−	12.9904i	−0.256345	−	0.444002i
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$	12.0000	−	20.7846i	0.409673	−	0.709575i
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	0.998549	+	0.0538535i	$0.0171504\pi$
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	−0.452636	+	0.891695i	$0.649516\pi$
$860$	−7.00000			−0.238698
$861$		0			0
$862$	−30.0000			−1.02180
$863$	−13.5000	−	23.3827i	−0.459545	−	0.795956i	0.539392	−	0.842055i	$-0.318654\pi$
$863$	−13.5000	−	23.3827i	−0.459545	−	0.795956i	−0.998937	+	0.0460992i	$0.985321\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$		0			0
$866$	11.0000	+	19.0526i	0.373795	+	0.647432i
$867$	17.0000			0.577350
$868$		0			0
$869$	−12.0000			−0.407072
$870$	1.50000	+	2.59808i	0.0508548	+	0.0880830i
$871$	−10.0000	+	17.3205i	−0.338837	+	0.586883i
$872$	5.50000	−	9.52628i	0.186254	−	0.322601i
$873$	−14.0000	−	24.2487i	−0.473828	−	0.820695i
$874$	−6.00000			−0.202953
$875$		0			0
$876$	−16.0000			−0.540590
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	14.0000	−	24.2487i	0.472477	−	0.818354i
$879$	−6.00000	+	10.3923i	−0.202375	+	0.350524i
$880$	3.00000	+	5.19615i	0.101130	+	0.175162i
$881$	−57.0000			−1.92038			−0.960189	−	0.279350i	$-0.909881\pi$
$881$	−57.0000			−1.92038			−0.960189	+	0.279350i	$0.909881\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$	3.00000	−	5.19615i	0.100844	−	0.174667i
$886$	10.5000	−	18.1865i	0.352754	−	0.610989i
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	0.634141	−	0.773217i	$-0.281354\pi$
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	−0.986696	+	0.162573i	$0.948021\pi$
$888$	−4.00000			−0.134231
$889$		0			0
$890$	−15.0000			−0.502801
$891$	3.00000	+	5.19615i	0.100504	+	0.174078i
$892$	−14.0000	+	24.2487i	−0.468755	+	0.811907i
$893$		0			0
$894$	−7.50000	−	12.9904i	−0.250838	−	0.434463i
$895$	−24.0000			−0.802232
$896$		0			0
$897$	12.0000			0.400668
$898$	−4.50000	−	7.79423i	−0.150167	−	0.260097i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$	1.00000	−	1.73205i	0.0333333	−	0.0577350i
$901$		0			0
$902$	−54.0000			−1.79800
$903$		0			0
$904$	−6.00000			−0.199557
$905$	5.50000	+	9.52628i	0.182826	+	0.316664i
$906$	2.00000	−	3.46410i	0.0664455	−	0.115087i
$907$	12.5000	−	21.6506i	0.415056	−	0.718898i	−0.580379	−	0.814347i	$-0.697095\pi$
$907$	12.5000	−	21.6506i	0.415056	−	0.718898i	0.995434	+	0.0954492i	$0.0304288\pi$
$908$	−6.00000	−	10.3923i	−0.199117	−	0.344881i
$909$	30.0000			0.995037
$910$		0			0
$911$	18.0000			0.596367			0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000			0.596367			0.298183	+	0.954509i	$0.403619\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	−9.00000	+	15.5885i	−0.297857	+	0.515903i
$914$	16.0000	−	27.7128i	0.529233	−	0.916658i
$915$	−2.50000	−	4.33013i	−0.0826475	−	0.143150i
$916$	−14.0000			−0.462573
$917$		0			0
$918$		0			0
$919$	−7.00000	−	12.1244i	−0.230909	−	0.399946i	0.727167	−	0.686461i	$-0.240837\pi$
$919$	−7.00000	−	12.1244i	−0.230909	−	0.399946i	−0.958076	+	0.286515i	$0.907503\pi$
$920$	−1.50000	+	2.59808i	−0.0494535	+	0.0856560i
$921$	−2.50000	+	4.33013i	−0.0823778	+	0.142683i
$922$	−9.00000	−	15.5885i	−0.296399	−	0.513378i
$923$	−24.0000			−0.789970
$924$		0			0
$925$	−4.00000			−0.131519
$926$	−6.50000	−	11.2583i	−0.213603	−	0.369972i
$927$	1.00000	−	1.73205i	0.0328443	−	0.0568880i
$928$	−1.50000	+	2.59808i	−0.0492399	+	0.0852860i
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$	−8.00000			−0.262330
$931$		0			0
$932$	−12.0000			−0.393073
$933$	9.00000	+	15.5885i	0.294647	+	0.510343i
$934$	7.50000	−	12.9904i	0.245407	−	0.425058i
$935$		0			0
$936$	−4.00000	−	6.92820i	−0.130744	−	0.226455i
$937$	28.0000			0.914720			0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000			0.914720			0.457360	+	0.889282i	$0.348795\pi$
$938$		0			0
$939$	8.00000			0.261070
$940$		0			0
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	−0.910773	−	0.412908i	$-0.864513\pi$
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	0.812975	+	0.582298i	$0.197846\pi$
$942$	−11.0000	+	19.0526i	−0.358399	+	0.620766i
$943$	−13.5000	−	23.3827i	−0.439620	−	0.761445i
$944$	6.00000			0.195283
$945$		0			0
$946$	−42.0000			−1.36554
$947$	1.50000	+	2.59808i	0.0487435	+	0.0844261i	0.889368	−	0.457193i	$-0.151145\pi$
$947$	1.50000	+	2.59808i	0.0487435	+	0.0844261i	−0.840624	+	0.541619i	$0.817812\pi$
$948$	1.00000	−	1.73205i	0.0324785	−	0.0562544i
$949$	−32.0000	+	55.4256i	−1.03876	+	1.79919i
$950$	−1.00000	−	1.73205i	−0.0324443	−	0.0561951i
$951$	−12.0000			−0.389127
$952$		0			0
$953$	60.0000			1.94359			0.971795	−	0.235826i	$-0.0757795\pi$
$953$	60.0000			1.94359			0.971795	+	0.235826i	$0.0757795\pi$
$954$	6.00000	+	10.3923i	0.194257	+	0.336463i
$955$	3.00000	−	5.19615i	0.0970777	−	0.168144i
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$	9.00000	+	15.5885i	0.290929	+	0.503903i
$958$	12.0000			0.387702
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−8.00000	+	13.8564i	−0.257930	+	0.446748i
$963$	−15.0000	+	25.9808i	−0.483368	+	0.837218i
$964$	1.00000	+	1.73205i	0.0322078	+	0.0557856i
$965$	2.00000			0.0643823
$966$		0			0
$967$	35.0000			1.12552			0.562762	−	0.826619i	$-0.309739\pi$
$967$	35.0000			1.12552			0.562762	+	0.826619i	$0.309739\pi$
$968$	12.5000	+	21.6506i	0.401765	+	0.695878i
$969$		0			0
$970$	−7.00000	+	12.1244i	−0.224756	+	0.389290i
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$	−16.0000			−0.513200
$973$		0			0
$974$	16.0000			0.512673
$975$	2.00000	+	3.46410i	0.0640513	+	0.110940i
$976$	2.50000	−	4.33013i	0.0800230	−	0.138604i
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$	2.00000	+	3.46410i	0.0639529	+	0.110770i
$979$	−90.0000			−2.87641
$980$		0			0
$981$	−22.0000			−0.702406
$982$		0			0
$983$	19.5000	−	33.7750i	0.621953	−	1.07725i	−0.367168	−	0.930155i	$-0.619673\pi$
$983$	19.5000	−	33.7750i	0.621953	−	1.07725i	0.989122	−	0.147100i	$-0.0469940\pi$
$984$	4.50000	−	7.79423i	0.143455	−	0.248471i
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$		0			0
$987$		0			0
$988$	−8.00000			−0.254514
$989$	−10.5000	−	18.1865i	−0.333881	−	0.578298i
$990$	6.00000	−	10.3923i	0.190693	−	0.330289i
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	−0.553308	−	0.832977i	$-0.686635\pi$
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	0.998033	+	0.0626908i	$0.0199682\pi$
$992$	−4.00000	−	6.92820i	−0.127000	−	0.219971i
$993$	28.0000			0.888553
$994$		0			0
$995$	4.00000			0.126809
$996$	−1.50000	−	2.59808i	−0.0475293	−	0.0823232i
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	−0.733630	−	0.679549i	$-0.762175\pi$
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	0.955322	+	0.295567i	$0.0955086\pi$
$998$	−11.0000	+	19.0526i	−0.348199	+	0.603098i
$999$	10.0000	+	17.3205i	0.316386	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.e.h.361.1		2
7.2	even	3	inner	490.2.e.h.471.1		2
7.3	odd	6		490.2.a.c.1.1		1
7.4	even	3		490.2.a.b.1.1		1
7.5	odd	6		70.2.e.c.51.1	yes	2
7.6	odd	2		70.2.e.c.11.1	✓	2
21.5	even	6		630.2.k.b.541.1		2
21.11	odd	6		4410.2.a.bd.1.1		1
21.17	even	6		4410.2.a.bm.1.1		1
21.20	even	2		630.2.k.b.361.1		2
28.3	even	6		3920.2.a.p.1.1		1
28.11	odd	6		3920.2.a.bc.1.1		1
28.19	even	6		560.2.q.g.401.1		2
28.27	even	2		560.2.q.g.81.1		2
35.3	even	12		2450.2.c.g.99.2		2
35.4	even	6		2450.2.a.bc.1.1		1
35.12	even	12		350.2.j.b.149.2		4
35.13	even	4		350.2.j.b.249.2		4
35.17	even	12		2450.2.c.g.99.1		2
35.18	odd	12		2450.2.c.l.99.2		2
35.19	odd	6		350.2.e.e.51.1		2
35.24	odd	6		2450.2.a.w.1.1		1
35.27	even	4		350.2.j.b.249.1		4
35.32	odd	12		2450.2.c.l.99.1		2
35.33	even	12		350.2.j.b.149.1		4
35.34	odd	2		350.2.e.e.151.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.c.11.1	✓	2	7.6	odd	2
70.2.e.c.51.1	yes	2	7.5	odd	6
350.2.e.e.51.1		2	35.19	odd	6
350.2.e.e.151.1		2	35.34	odd	2
350.2.j.b.149.1		4	35.33	even	12
350.2.j.b.149.2		4	35.12	even	12
350.2.j.b.249.1		4	35.27	even	4
350.2.j.b.249.2		4	35.13	even	4
490.2.a.b.1.1		1	7.4	even	3
490.2.a.c.1.1		1	7.3	odd	6
490.2.e.h.361.1		2	1.1	even	1	trivial
490.2.e.h.471.1		2	7.2	even	3	inner
560.2.q.g.81.1		2	28.27	even	2
560.2.q.g.401.1		2	28.19	even	6
630.2.k.b.361.1		2	21.20	even	2
630.2.k.b.541.1		2	21.5	even	6
2450.2.a.w.1.1		1	35.24	odd	6
2450.2.a.bc.1.1		1	35.4	even	6
2450.2.c.g.99.1		2	35.17	even	12
2450.2.c.g.99.2		2	35.3	even	12
2450.2.c.l.99.1		2	35.32	odd	12
2450.2.c.l.99.2		2	35.18	odd	12
3920.2.a.p.1.1		1	28.3	even	6
3920.2.a.bc.1.1		1	28.11	odd	6
4410.2.a.bd.1.1		1	21.11	odd	6
4410.2.a.bm.1.1		1	21.17	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{10} +(3.00000 - 5.19615i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{18} +(1.00000 + 1.73205i) q^{19} +1.00000 q^{20} +6.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{26} +5.00000 q^{27} -3.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(4.00000 - 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -2.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(2.00000 - 3.46410i) q^{39} +(0.500000 + 0.866025i) q^{40} -9.00000 q^{41} -7.00000 q^{43} +(3.00000 + 5.19615i) q^{44} +(1.00000 - 1.73205i) q^{45} +(-1.50000 + 2.59808i) q^{46} -1.00000 q^{48} -1.00000 q^{50} +(-2.00000 + 3.46410i) q^{52} +(3.00000 - 5.19615i) q^{53} +(2.50000 + 4.33013i) q^{54} -6.00000 q^{55} +2.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{60} +(2.50000 + 4.33013i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(3.00000 - 5.19615i) q^{66} +(-2.50000 + 4.33013i) q^{67} +3.00000 q^{69} -6.00000 q^{71} +(-1.00000 - 1.73205i) q^{72} +(-8.00000 + 13.8564i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(0.500000 + 0.866025i) q^{75} -2.00000 q^{76} +4.00000 q^{78} +(-1.00000 - 1.73205i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{82} -3.00000 q^{83} +(-3.50000 - 6.06218i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-7.50000 - 12.9904i) q^{89} +2.00000 q^{90} -3.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(1.00000 - 1.73205i) q^{95} +(-0.500000 - 0.866025i) q^{96} -14.0000 q^{97} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + 6 q^{11} + q^{12} + 8 q^{13} - 2 q^{15} - q^{16} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 12 q^{22} + 3 q^{23} - q^{24} - q^{25}+ \cdots + 24 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + 6 * q^11 + q^12 + 8 * q^13 - 2 * q^15 - q^16 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 12 * q^22 + 3 * q^23 - q^24 - q^25 + 4 * q^26 + 10 * q^27 - 6 * q^29 - q^30 + 8 * q^31 + q^32 - 6 * q^33 - 4 * q^36 + 4 * q^37 - 2 * q^38 + 4 * q^39 + q^40 - 18 * q^41 - 14 * q^43 + 6 * q^44 + 2 * q^45 - 3 * q^46 - 2 * q^48 - 2 * q^50 - 4 * q^52 + 6 * q^53 + 5 * q^54 - 12 * q^55 + 4 * q^57 - 3 * q^58 - 6 * q^59 + q^60 + 5 * q^61 + 16 * q^62 + 2 * q^64 - 4 * q^65 + 6 * q^66 - 5 * q^67 + 6 * q^69 - 12 * q^71 - 2 * q^72 - 16 * q^73 - 4 * q^74 + q^75 - 4 * q^76 + 8 * q^78 - 2 * q^79 - q^80 - q^81 - 9 * q^82 - 6 * q^83 - 7 * q^86 - 3 * q^87 - 6 * q^88 - 15 * q^89 + 4 * q^90 - 6 * q^92 - 8 * q^93 + 2 * q^95 - q^96 - 28 * q^97 + 24 * q^99

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