LMFDB - Embedded newform 1470.2.i.m.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(361,1470)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.7380090971$
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 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1470.961
Dual form			1470.2.i.m.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(-1.50000 + 2.59808i) q^{19} +1.00000 q^{20} +1.00000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +1.00000 q^{36} +(-5.50000 + 9.52628i) q^{37} +(1.50000 + 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +11.0000 q^{41} +8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.50000 + 6.06218i) q^{46} +(-2.50000 + 4.33013i) q^{47} +1.00000 q^{48} -1.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(5.50000 + 9.52628i) q^{53} +(0.500000 - 0.866025i) q^{54} -1.00000 q^{55} +3.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} -2.00000 q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(-0.500000 - 0.866025i) q^{66} +7.00000 q^{69} -6.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(5.50000 + 9.52628i) q^{74} +(-0.500000 + 0.866025i) q^{75} +3.00000 q^{76} +1.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.50000 - 9.52628i) q^{82} -8.00000 q^{83} +(4.00000 - 6.92820i) q^{86} +(4.00000 + 6.92820i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} -1.00000 q^{90} +7.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(2.50000 + 4.33013i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(0.500000 - 0.866025i) q^{96} +16.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{8} - q^{9} + q^{10} + q^{11} - q^{12} - 2 q^{13} + 2 q^{15} - q^{16} + q^{18} - 3 q^{19} + 2 q^{20} + 2 q^{22} - 7 q^{23} + q^{24} - q^{25} - q^{26} + 2 q^{27} - 16 q^{29} + q^{30} - 2 q^{31} + q^{32} + q^{33} + 2 q^{36} - 11 q^{37} + 3 q^{38} + q^{39} + q^{40} + 22 q^{41} + 16 q^{43} + q^{44} - q^{45} + 7 q^{46} - 5 q^{47} + 2 q^{48} - 2 q^{50} + q^{52} + 11 q^{53} + q^{54} - 2 q^{55} + 6 q^{57} - 8 q^{58} + 4 q^{59} - q^{60} - 4 q^{62} + 2 q^{64} + q^{65} - q^{66} + 14 q^{69} - 12 q^{71} + q^{72} - 6 q^{73} + 11 q^{74} - q^{75} + 6 q^{76} + 2 q^{78} + 8 q^{79} - q^{80} - q^{81} + 11 q^{82} - 16 q^{83} + 8 q^{86} + 8 q^{87} - q^{88} - 10 q^{89} - 2 q^{90} + 14 q^{92} - 2 q^{93} + 5 q^{94} - 3 q^{95} + q^{96} + 32 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^8 - q^9 + q^10 + q^11 - q^12 - 2 * q^13 + 2 * q^15 - q^16 + q^18 - 3 * q^19 + 2 * q^20 + 2 * q^22 - 7 * q^23 + q^24 - q^25 - q^26 + 2 * q^27 - 16 * q^29 + q^30 - 2 * q^31 + q^32 + q^33 + 2 * q^36 - 11 * q^37 + 3 * q^38 + q^39 + q^40 + 22 * q^41 + 16 * q^43 + q^44 - q^45 + 7 * q^46 - 5 * q^47 + 2 * q^48 - 2 * q^50 + q^52 + 11 * q^53 + q^54 - 2 * q^55 + 6 * q^57 - 8 * q^58 + 4 * q^59 - q^60 - 4 * q^62 + 2 * q^64 + q^65 - q^66 + 14 * q^69 - 12 * q^71 + q^72 - 6 * q^73 + 11 * q^74 - q^75 + 6 * q^76 + 2 * q^78 + 8 * q^79 - q^80 - q^81 + 11 * q^82 - 16 * q^83 + 8 * q^86 + 8 * q^87 - q^88 - 10 * q^89 - 2 * q^90 + 14 * q^92 - 2 * q^93 + 5 * q^94 - 3 * q^95 + q^96 + 32 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	−0.985194	−	0.171442i	$-0.945157\pi$
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	0.641071	+	0.767482i	$0.278491\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	1.00000			0.213201
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	0.227167	+	0.973856i	$0.427054\pi$
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	−0.956967	+	0.290196i	$0.906280\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	1.00000			0.192450
$28$		0			0
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$		0			0
$35$		0			0
$36$	1.00000			0.166667
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.0821995	+	0.996616i	$0.526194\pi$
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	1.50000	+	2.59808i	0.243332	+	0.421464i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	11.0000			1.71791			0.858956	−	0.512050i	$-0.171114\pi$
$41$	11.0000			1.71791			0.858956	+	0.512050i	$0.171114\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	3.50000	+	6.06218i	0.516047	+	0.893819i
$47$	−2.50000	+	4.33013i	−0.364662	+	0.631614i	−0.988722	−	0.149763i	$-0.952149\pi$
$47$	−2.50000	+	4.33013i	−0.364662	+	0.631614i	0.624059	+	0.781377i	$0.285482\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	5.50000	+	9.52628i	0.755483	+	1.30854i	0.945134	+	0.326683i	$0.105931\pi$
$53$	5.50000	+	9.52628i	0.755483	+	1.30854i	−0.189651	+	0.981852i	$0.560736\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−1.00000			−0.134840
$56$		0			0
$57$	3.00000			0.397360
$58$	−4.00000	+	6.92820i	−0.525226	+	0.909718i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	−0.500000	−	0.866025i	−0.0615457	−	0.106600i
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$		0			0
$69$	7.00000			0.842701
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	−0.986447	+	0.164083i	$0.947534\pi$
$74$	5.50000	+	9.52628i	0.639362	+	1.10741i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	3.00000			0.344124
$77$		0			0
$78$	1.00000			0.113228
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.50000	−	9.52628i	0.607373	−	1.05200i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$		0			0
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	4.00000	+	6.92820i	0.428845	+	0.742781i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	7.00000			0.729800
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$	2.50000	+	4.33013i	0.257855	+	0.446619i
$95$	−1.50000	−	2.59808i	−0.153897	−	0.266557i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	16.0000			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$98$		0			0
$99$	−1.00000			−0.100504
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	0.138767	+	0.990325i	$0.455686\pi$
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	−0.927030	+	0.374987i	$0.877647\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	11.0000			1.06841
$107$	5.00000	−	8.66025i	0.483368	−	0.837218i	−0.516449	−	0.856318i	$-0.672747\pi$
$107$	5.00000	−	8.66025i	0.483368	−	0.837218i	0.999818	+	0.0190994i	$0.00607989\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	0.685828	−	0.727764i	$-0.259440\pi$
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	−0.973176	+	0.230063i	$0.926107\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	11.0000			1.04407
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	1.50000	−	2.59808i	0.140488	−	0.243332i
$115$	−3.50000	−	6.06218i	−0.326377	−	0.565301i
$116$	4.00000	+	6.92820i	0.371391	+	0.643268i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	4.00000			0.368230
$119$		0			0
$120$	−1.00000			−0.0912871
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$	−5.50000	−	9.52628i	−0.495918	−	0.858956i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−17.0000			−1.50851			−0.754253	−	0.656584i	$-0.772001\pi$
$127$	−17.0000			−1.50851			−0.754253	+	0.656584i	$0.772001\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	−2.50000	+	4.33013i	−0.218426	+	0.378325i	−0.954327	−	0.298764i	$-0.903426\pi$
$131$	−2.50000	+	4.33013i	−0.218426	+	0.378325i	0.735901	+	0.677089i	$0.236759\pi$
$132$	−1.00000			−0.0870388
$133$		0			0
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$	3.50000	−	6.06218i	0.297940	−	0.516047i
$139$	−20.0000			−1.69638			−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000			−1.69638			−0.848189	+	0.529694i	$0.822307\pi$
$140$		0			0
$141$	5.00000			0.421076
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−0.500000	−	0.866025i	−0.0418121	−	0.0724207i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.00000	−	6.92820i	0.332182	−	0.575356i
$146$	−6.00000			−0.496564
$147$		0			0
$148$	11.0000			0.904194
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	0.717752	−	0.696299i	$-0.245171\pi$
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	−0.961888	+	0.273442i	$0.911838\pi$
$152$	1.50000	−	2.59808i	0.121666	−	0.210732i
$153$		0			0
$154$		0			0
$155$	2.00000			0.160644
$156$	0.500000	−	0.866025i	0.0400320	−	0.0693375i
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	5.50000	−	9.52628i	0.436178	−	0.755483i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	0.361619	+	0.932326i	$0.382224\pi$
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	−0.988227	+	0.152992i	$0.951109\pi$
$164$	−5.50000	−	9.52628i	−0.429478	−	0.743877i
$165$	0.500000	+	0.866025i	0.0389249	+	0.0674200i
$166$	−4.00000	+	6.92820i	−0.310460	+	0.537733i
$167$	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
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−1.50000	−	2.59808i	−0.114708	−	0.198680i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	0.426329	+	0.904568i	$0.359807\pi$
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	−0.996544	+	0.0830722i	$0.973527\pi$
$174$	8.00000			0.606478
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$	5.00000	+	8.66025i	0.374766	+	0.649113i
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	0.964833	+	0.262864i	$0.0846670\pi$
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	−0.254770	+	0.967002i	$0.582000\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	24.0000			1.78391			0.891953	−	0.452128i	$-0.149335\pi$
$181$	24.0000			1.78391			0.891953	+	0.452128i	$0.149335\pi$
$182$		0			0
$183$		0			0
$184$	3.50000	−	6.06218i	0.258023	−	0.446910i
$185$	−5.50000	−	9.52628i	−0.404368	−	0.700386i
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$		0			0
$188$	5.00000			0.364662
$189$		0			0
$190$	−3.00000			−0.217643
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−11.0000	−	19.0526i	−0.791797	−	1.37143i	−0.924853	−	0.380325i	$-0.875812\pi$
$193$	−11.0000	−	19.0526i	−0.791797	−	1.37143i	0.133056	−	0.991109i	$-0.457521\pi$
$194$	8.00000	−	13.8564i	0.574367	−	0.994832i
$195$	−1.00000			−0.0716115
$196$		0			0
$197$	−1.00000			−0.0712470			−0.0356235	−	0.999365i	$-0.511342\pi$
$197$	−1.00000			−0.0712470			−0.0356235	+	0.999365i	$0.511342\pi$
$198$	−0.500000	+	0.866025i	−0.0355335	+	0.0615457i
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	−0.880616	−	0.473831i	$-0.842871\pi$
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	0.0299585	−	0.999551i	$-0.490462\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.50000	+	9.52628i	−0.384137	+	0.665344i
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$	−3.50000	−	6.06218i	−0.243267	−	0.421350i
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$	5.50000	−	9.52628i	0.377742	−	0.654268i
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$	−5.00000	−	8.66025i	−0.341793	−	0.592003i
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−6.00000			−0.406371
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$	0.500000	+	0.866025i	0.0337100	+	0.0583874i
$221$		0			0
$222$	5.50000	−	9.52628i	0.369136	−	0.639362i
$223$	−12.0000			−0.803579			−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000			−0.803579			−0.401790	+	0.915732i	$0.631612\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	0.967692	−	0.252136i	$-0.0811332\pi$
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	−0.702202	+	0.711977i	$0.747800\pi$
$228$	−1.50000	−	2.59808i	−0.0993399	−	0.172062i
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$	−7.00000			−0.461566
$231$		0			0
$232$	8.00000			0.525226
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	0.404674	+	0.914461i	$0.367385\pi$
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	−0.994283	+	0.106773i	$0.965948\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	−2.50000	−	4.33013i	−0.163082	−	0.282466i
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$	−8.00000			−0.519656
$238$		0			0
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$	−5.00000	−	8.66025i	−0.321412	−	0.556702i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$	−11.0000			−0.701334
$247$	1.50000	−	2.59808i	0.0954427	−	0.165312i
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$	4.00000	+	6.92820i	0.253490	+	0.439057i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−13.0000			−0.820553			−0.410276	−	0.911961i	$-0.634568\pi$
$251$	−13.0000			−0.820553			−0.410276	+	0.911961i	$0.634568\pi$
$252$		0			0
$253$	−7.00000			−0.440086
$254$	−8.50000	+	14.7224i	−0.533337	+	0.923768i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.0000	+	17.3205i	−0.623783	+	1.08042i	0.364992	+	0.931011i	$0.381072\pi$
$257$	−10.0000	+	17.3205i	−0.623783	+	1.08042i	−0.988775	+	0.149413i	$0.952262\pi$
$258$	−8.00000			−0.498058
$259$		0			0
$260$	−1.00000			−0.0620174
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	2.50000	+	4.33013i	0.154451	+	0.267516i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	−11.0000			−0.675725
$266$		0			0
$267$	10.0000			0.611990
$268$		0			0
$269$	10.0000	+	17.3205i	0.609711	+	1.05605i	0.991288	+	0.131713i	$0.0420477\pi$
$269$	10.0000	+	17.3205i	0.609711	+	1.05605i	−0.381577	+	0.924337i	$0.624619\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	16.0000	−	27.7128i	0.971931	−	1.68343i	0.282218	−	0.959350i	$-0.408930\pi$
$271$	16.0000	−	27.7128i	0.971931	−	1.68343i	0.689713	−	0.724083i	$-0.257737\pi$
$272$		0			0
$273$		0			0
$274$	18.0000			1.08742
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−3.50000	−	6.06218i	−0.210675	−	0.364900i
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	0.980373	+	0.197153i	$0.0631696\pi$
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	−0.319447	+	0.947604i	$0.603497\pi$
$278$	−10.0000	+	17.3205i	−0.599760	+	1.03882i
$279$	2.00000			0.119737
$280$		0			0
$281$	−1.00000			−0.0596550			−0.0298275	−	0.999555i	$-0.509496\pi$
$281$	−1.00000			−0.0596550			−0.0298275	+	0.999555i	$0.509496\pi$
$282$	2.50000	−	4.33013i	0.148873	−	0.257855i
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$	−1.50000	+	2.59808i	−0.0888523	+	0.153897i
$286$	−1.00000			−0.0591312
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−4.00000	−	6.92820i	−0.234888	−	0.406838i
$291$	−8.00000	−	13.8564i	−0.468968	−	0.812277i
$292$	−3.00000	+	5.19615i	−0.175562	+	0.304082i
$293$	−27.0000			−1.57736			−0.788678	−	0.614806i	$-0.789234\pi$
$293$	−27.0000			−1.57736			−0.788678	+	0.614806i	$0.789234\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	5.50000	−	9.52628i	0.319681	−	0.553704i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$		0			0
$299$	3.50000	−	6.06218i	0.202410	−	0.350585i
$300$	1.00000			0.0577350
$301$		0			0
$302$	−6.00000			−0.345261
$303$		0			0
$304$	−1.50000	−	2.59808i	−0.0860309	−	0.149010i
$305$		0			0
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	−6.00000	+	10.3923i	−0.339140	+	0.587408i	−0.984271	−	0.176664i	$-0.943469\pi$
$313$	−6.00000	+	10.3923i	−0.339140	+	0.587408i	0.645131	+	0.764072i	$0.276803\pi$
$314$	−7.00000			−0.395033
$315$		0			0
$316$	−8.00000			−0.450035
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	−5.50000	−	9.52628i	−0.308425	−	0.534207i
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−10.0000			−0.558146
$322$		0			0
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$	8.00000	+	13.8564i	0.443079	+	0.767435i
$327$	−3.00000	+	5.19615i	−0.165900	+	0.287348i
$328$	−11.0000			−0.607373
$329$		0			0
$330$	1.00000			0.0550482
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	−0.630232	−	0.776407i	$-0.717040\pi$
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	0.987504	+	0.157593i	$0.0503735\pi$
$332$	4.00000	+	6.92820i	0.219529	+	0.380235i
$333$	−5.50000	−	9.52628i	−0.301398	−	0.522037i
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$		0			0
$336$		0			0
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$	1.00000	−	1.73205i	0.0541530	−	0.0937958i
$342$	−3.00000			−0.162221
$343$		0			0
$344$	−8.00000			−0.431331
$345$	−3.50000	+	6.06218i	−0.188434	+	0.326377i
$346$	7.50000	+	12.9904i	0.403202	+	0.698367i
$347$	−7.00000	−	12.1244i	−0.375780	−	0.650870i	0.614664	−	0.788789i	$-0.289292\pi$
$347$	−7.00000	−	12.1244i	−0.375780	−	0.650870i	−0.990443	+	0.137920i	$0.955958\pi$
$348$	4.00000	−	6.92820i	0.214423	−	0.371391i
$349$	−12.0000			−0.642345			−0.321173	−	0.947021i	$-0.604077\pi$
$349$	−12.0000			−0.642345			−0.321173	+	0.947021i	$0.604077\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$	−2.00000	−	3.46410i	−0.106299	−	0.184115i
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$	10.0000			0.529999
$357$		0			0
$358$	19.0000			1.00418
$359$	−2.00000	+	3.46410i	−0.105556	+	0.182828i	−0.913965	−	0.405793i	$-0.866996\pi$
$359$	−2.00000	+	3.46410i	−0.105556	+	0.182828i	0.808409	+	0.588621i	$0.200329\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	12.0000	−	20.7846i	0.630706	−	1.09241i
$363$	−10.0000			−0.524864
$364$		0			0
$365$	6.00000			0.314054
$366$		0			0
$367$	12.5000	+	21.6506i	0.652495	+	1.13015i	0.982516	+	0.186180i	$0.0596109\pi$
$367$	12.5000	+	21.6506i	0.652495	+	1.13015i	−0.330021	+	0.943974i	$0.607056\pi$
$368$	−3.50000	−	6.06218i	−0.182450	−	0.316013i
$369$	−5.50000	+	9.52628i	−0.286319	+	0.495918i
$370$	−11.0000			−0.571863
$371$		0			0
$372$	2.00000			0.103695
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	2.50000	−	4.33013i	0.128928	−	0.223309i
$377$	8.00000			0.412021
$378$		0			0
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$	−1.50000	+	2.59808i	−0.0769484	+	0.133278i
$381$	8.50000	+	14.7224i	0.435468	+	0.754253i
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	17.5000	−	30.3109i	0.894208	−	1.54881i	0.0594268	−	0.998233i	$-0.481073\pi$
$383$	17.5000	−	30.3109i	0.894208	−	1.54881i	0.834781	−	0.550581i	$-0.185594\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−22.0000			−1.11977
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$	−8.00000	−	13.8564i	−0.406138	−	0.703452i
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$	−0.500000	+	0.866025i	−0.0253185	+	0.0438529i
$391$		0			0
$392$		0			0
$393$	5.00000			0.252217
$394$	−0.500000	+	0.866025i	−0.0251896	+	0.0436297i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$	−24.0000			−1.20301
$399$		0			0
$400$	1.00000			0.0500000
$401$	2.50000	−	4.33013i	0.124844	−	0.216236i	−0.796828	−	0.604206i	$-0.793490\pi$
$401$	2.50000	−	4.33013i	0.124844	−	0.216236i	0.921672	+	0.387970i	$0.126824\pi$
$402$		0			0
$403$	1.00000	+	1.73205i	0.0498135	+	0.0862796i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−11.0000			−0.545250
$408$		0			0
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	0.889689	−	0.456566i	$-0.150921\pi$
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	−0.840243	+	0.542211i	$0.817588\pi$
$410$	5.50000	+	9.52628i	0.271626	+	0.470469i
$411$	9.00000	−	15.5885i	0.443937	−	0.768922i
$412$	16.0000			0.788263
$413$		0			0
$414$	−7.00000			−0.344031
$415$	4.00000	−	6.92820i	0.196352	−	0.340092i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	10.0000	+	17.3205i	0.489702	+	0.848189i
$418$	−1.50000	+	2.59808i	−0.0733674	+	0.127076i
$419$	5.00000			0.244266			0.122133	−	0.992514i	$-0.461027\pi$
$419$	5.00000			0.244266			0.122133	+	0.992514i	$0.461027\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	2.50000	−	4.33013i	0.121698	−	0.210787i
$423$	−2.50000	−	4.33013i	−0.121554	−	0.210538i
$424$	−5.50000	−	9.52628i	−0.267104	−	0.462637i
$425$		0			0
$426$	6.00000			0.290701
$427$		0			0
$428$	−10.0000			−0.483368
$429$	−0.500000	+	0.866025i	−0.0241402	+	0.0418121i
$430$	4.00000	+	6.92820i	0.192897	+	0.334108i
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	32.0000			1.53782			0.768911	−	0.639356i	$-0.220799\pi$
$433$	32.0000			1.53782			0.768911	+	0.639356i	$0.220799\pi$
$434$		0			0
$435$	−8.00000			−0.383571
$436$	−3.00000	+	5.19615i	−0.143674	+	0.248851i
$437$	−10.5000	−	18.1865i	−0.502283	−	0.869980i
$438$	3.00000	+	5.19615i	0.143346	+	0.248282i
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	0.940963	−	0.338508i	$-0.109922\pi$
$440$	1.00000			0.0476731
$441$		0			0
$442$		0			0
$443$	−8.00000	+	13.8564i	−0.380091	+	0.658338i	−0.991075	−	0.133306i	$-0.957441\pi$
$443$	−8.00000	+	13.8564i	−0.380091	+	0.658338i	0.610984	+	0.791643i	$0.290774\pi$
$444$	−5.50000	−	9.52628i	−0.261018	−	0.452097i
$445$	−5.00000	−	8.66025i	−0.237023	−	0.410535i
$446$	−6.00000	+	10.3923i	−0.284108	+	0.492090i
$447$		0			0
$448$		0			0
$449$	11.0000			0.519122			0.259561	−	0.965727i	$-0.416422\pi$
$449$	11.0000			0.519122			0.259561	+	0.965727i	$0.416422\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$	5.50000	+	9.52628i	0.258985	+	0.448575i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	−3.00000	+	5.19615i	−0.140952	+	0.244137i
$454$	8.00000			0.375459
$455$		0			0
$456$	−3.00000			−0.140488
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	−0.575036	−	0.818128i	$-0.695012\pi$
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	0.996038	+	0.0889312i	$0.0283451\pi$
$458$	−7.00000	−	12.1244i	−0.327089	−	0.566534i
$459$		0			0
$460$	−3.50000	+	6.06218i	−0.163188	+	0.282650i
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$	−13.0000			−0.604161			−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000			−0.604161			−0.302081	+	0.953282i	$0.597681\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$	−1.00000	−	1.73205i	−0.0463739	−	0.0803219i
$466$	9.00000	+	15.5885i	0.416917	+	0.722121i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$	−1.00000			−0.0462250
$469$		0			0
$470$	−5.00000			−0.230633
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$	−4.00000	+	6.92820i	−0.183726	+	0.318223i
$475$	3.00000			0.137649
$476$		0			0
$477$	−11.0000			−0.503655
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	11.0000	+	19.0526i	0.502603	+	0.870534i	0.999995	+	0.00300810i	$0.000957509\pi$
$479$	11.0000	+	19.0526i	0.502603	+	0.870534i	−0.497393	+	0.867526i	$0.665709\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	5.50000	−	9.52628i	0.250778	−	0.434361i
$482$	7.00000			0.318841
$483$		0			0
$484$	−10.0000			−0.454545
$485$	−8.00000	+	13.8564i	−0.363261	+	0.629187i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	0.988374	−	0.152042i	$-0.0485850\pi$
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	−0.625859	+	0.779936i	$0.715252\pi$
$488$		0			0
$489$	16.0000			0.723545
$490$		0			0
$491$	20.0000			0.902587			0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000			0.902587			0.451294	+	0.892375i	$0.350963\pi$
$492$	−5.50000	+	9.52628i	−0.247959	+	0.429478i
$493$		0			0
$494$	−1.50000	−	2.59808i	−0.0674882	−	0.116893i
$495$	0.500000	−	0.866025i	0.0224733	−	0.0389249i
$496$	2.00000			0.0898027
$497$		0			0
$498$	8.00000			0.358489
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−1.50000	−	2.59808i	−0.0670151	−	0.116073i
$502$	−6.50000	+	11.2583i	−0.290109	+	0.502484i
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$		0			0
$506$	−3.50000	+	6.06218i	−0.155594	+	0.269497i
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$	8.50000	+	14.7224i	0.377127	+	0.653202i
$509$	−17.0000	+	29.4449i	−0.753512	+	1.30512i	0.192599	+	0.981278i	$0.438308\pi$
$509$	−17.0000	+	29.4449i	−0.753512	+	1.30512i	−0.946111	+	0.323843i	$0.895025\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−1.50000	+	2.59808i	−0.0662266	+	0.114708i
$514$	10.0000	+	17.3205i	0.441081	+	0.763975i
$515$	−8.00000	−	13.8564i	−0.352522	−	0.610586i
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$	−5.00000			−0.219900
$518$		0			0
$519$	15.0000			0.658427
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	−16.5000	−	28.5788i	−0.722878	−	1.25206i	−0.959841	−	0.280543i	$-0.909485\pi$
$521$	−16.5000	−	28.5788i	−0.722878	−	1.25206i	0.236963	−	0.971519i	$-0.423848\pi$
$522$	−4.00000	−	6.92820i	−0.175075	−	0.303239i
$523$	1.00000	−	1.73205i	0.0437269	−	0.0757373i	−0.843334	−	0.537390i	$-0.819410\pi$
$523$	1.00000	−	1.73205i	0.0437269	−	0.0757373i	0.887061	+	0.461653i	$0.152744\pi$
$524$	5.00000			0.218426
$525$		0			0
$526$	−24.0000			−1.04645
$527$		0			0
$528$	0.500000	+	0.866025i	0.0217597	+	0.0376889i
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$	−5.50000	+	9.52628i	−0.238905	+	0.413795i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	−11.0000			−0.476463
$534$	5.00000	−	8.66025i	0.216371	−	0.374766i
$535$	5.00000	+	8.66025i	0.216169	+	0.374415i
$536$		0			0
$537$	9.50000	−	16.4545i	0.409955	−	0.710063i
$538$	20.0000			0.862261
$539$		0			0
$540$	1.00000			0.0430331
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−16.0000	−	27.7128i	−0.687259	−	1.19037i
$543$	−12.0000	−	20.7846i	−0.514969	−	0.891953i
$544$		0			0
$545$	6.00000			0.257012
$546$		0			0
$547$	16.0000			0.684111			0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000			0.684111			0.342055	+	0.939680i	$0.388877\pi$
$548$	9.00000	−	15.5885i	0.384461	−	0.665906i
$549$		0			0
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$	12.0000	−	20.7846i	0.511217	−	0.885454i
$552$	−7.00000			−0.297940
$553$		0			0
$554$	22.0000			0.934690
$555$	−5.50000	+	9.52628i	−0.233462	+	0.404368i
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	16.5000	+	28.5788i	0.699127	+	1.21092i	0.968769	+	0.247964i	$0.0797613\pi$
$557$	16.5000	+	28.5788i	0.699127	+	1.21092i	−0.269642	+	0.962961i	$0.586905\pi$
$558$	1.00000	−	1.73205i	0.0423334	−	0.0733236i
$559$	−8.00000			−0.338364
$560$		0			0
$561$		0			0
$562$	−0.500000	+	0.866025i	−0.0210912	+	0.0365311i
$563$	−19.0000	−	32.9090i	−0.800755	−	1.38695i	−0.919120	−	0.393977i	$-0.871099\pi$
$563$	−19.0000	−	32.9090i	−0.800755	−	1.38695i	0.118366	−	0.992970i	$-0.462235\pi$
$564$	−2.50000	−	4.33013i	−0.105269	−	0.182331i
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	−14.0000			−0.588464
$567$		0			0
$568$	6.00000			0.251754
$569$	4.50000	−	7.79423i	0.188650	−	0.326751i	−0.756151	−	0.654398i	$-0.772922\pi$
$569$	4.50000	−	7.79423i	0.188650	−	0.326751i	0.944800	+	0.327647i	$0.106256\pi$
$570$	1.50000	+	2.59808i	0.0628281	+	0.108821i
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	0.978022	+	0.208502i	$0.0668588\pi$
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	−0.308443	+	0.951243i	$0.599808\pi$
$572$	−0.500000	+	0.866025i	−0.0209061	+	0.0362103i
$573$	−6.00000			−0.250654
$574$		0			0
$575$	7.00000			0.291920
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	0.682730	−	0.730670i	$-0.260792\pi$
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	−0.974144	+	0.225927i	$0.927459\pi$
$578$	−8.50000	−	14.7224i	−0.353553	−	0.612372i
$579$	−11.0000	+	19.0526i	−0.457144	+	0.791797i
$580$	−8.00000			−0.332182
$581$		0			0
$582$	−16.0000			−0.663221
$583$	−5.50000	+	9.52628i	−0.227787	+	0.394538i
$584$	3.00000	+	5.19615i	0.124141	+	0.215018i
$585$	0.500000	+	0.866025i	0.0206725	+	0.0358057i
$586$	−13.5000	+	23.3827i	−0.557680	+	0.965930i
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$	−2.00000	+	3.46410i	−0.0823387	+	0.142615i
$591$	0.500000	+	0.866025i	0.0205673	+	0.0356235i
$592$	−5.50000	−	9.52628i	−0.226049	−	0.391528i
$593$	8.00000	−	13.8564i	0.328521	−	0.569014i	−0.653698	−	0.756756i	$-0.726783\pi$
$593$	8.00000	−	13.8564i	0.328521	−	0.569014i	0.982219	+	0.187741i	$0.0601166\pi$
$594$	1.00000			0.0410305
$595$		0			0
$596$		0			0
$597$	−12.0000	+	20.7846i	−0.491127	+	0.850657i
$598$	−3.50000	−	6.06218i	−0.143126	−	0.247901i
$599$	−1.00000	−	1.73205i	−0.0408589	−	0.0707697i	0.844873	−	0.534967i	$-0.179676\pi$
$599$	−1.00000	−	1.73205i	−0.0408589	−	0.0707697i	−0.885732	+	0.464198i	$0.846343\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$		0			0
$604$	−3.00000	+	5.19615i	−0.122068	+	0.211428i
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$		0			0
$607$	−18.5000	+	32.0429i	−0.750892	+	1.30058i	0.196499	+	0.980504i	$0.437043\pi$
$607$	−18.5000	+	32.0429i	−0.750892	+	1.30058i	−0.947391	+	0.320079i	$0.896291\pi$
$608$	−3.00000			−0.121666
$609$		0			0
$610$		0			0
$611$	2.50000	−	4.33013i	0.101139	−	0.175178i
$612$		0			0
$613$	20.5000	+	35.5070i	0.827987	+	1.43412i	0.899615	+	0.436684i	$0.143847\pi$
$613$	20.5000	+	35.5070i	0.827987	+	1.43412i	−0.0716275	+	0.997431i	$0.522819\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$	11.0000			0.443563
$616$		0			0
$617$	28.0000			1.12724			0.563619	−	0.826035i	$-0.309409\pi$
$617$	28.0000			1.12724			0.563619	+	0.826035i	$0.309409\pi$
$618$	8.00000	−	13.8564i	0.321807	−	0.557386i
$619$	14.5000	+	25.1147i	0.582804	+	1.00945i	0.995145	+	0.0984169i	$0.0313779\pi$
$619$	14.5000	+	25.1147i	0.582804	+	1.00945i	−0.412341	+	0.911030i	$0.635289\pi$
$620$	−1.00000	−	1.73205i	−0.0401610	−	0.0695608i
$621$	−3.50000	+	6.06218i	−0.140450	+	0.243267i
$622$	12.0000			0.481156
$623$		0			0
$624$	−1.00000			−0.0400320
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.00000	+	10.3923i	0.239808	+	0.415360i
$627$	1.50000	+	2.59808i	0.0599042	+	0.103757i
$628$	−3.50000	+	6.06218i	−0.139665	+	0.241907i
$629$		0			0
$630$		0			0
$631$	−26.0000			−1.03504			−0.517522	−	0.855670i	$-0.673145\pi$
$631$	−26.0000			−1.03504			−0.517522	+	0.855670i	$0.673145\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	−2.50000	−	4.33013i	−0.0993661	−	0.172107i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	8.50000	−	14.7224i	0.337312	−	0.584242i
$636$	−11.0000			−0.436178
$637$		0			0
$638$	−8.00000			−0.316723
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	0.894127	−	0.447813i	$-0.147797\pi$
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	−0.834881	+	0.550431i	$0.814464\pi$
$642$	−5.00000	+	8.66025i	−0.197334	+	0.341793i
$643$	10.0000			0.394362			0.197181	−	0.980367i	$-0.436821\pi$
$643$	10.0000			0.394362			0.197181	+	0.980367i	$0.436821\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	−8.50000	−	14.7224i	−0.334169	−	0.578799i	0.649155	−	0.760656i	$-0.275122\pi$
$647$	−8.50000	−	14.7224i	−0.334169	−	0.578799i	−0.983325	+	0.181857i	$0.941789\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−2.00000	+	3.46410i	−0.0785069	+	0.135978i
$650$	1.00000			0.0392232
$651$		0			0
$652$	16.0000			0.626608
$653$	−3.50000	+	6.06218i	−0.136966	+	0.237231i	−0.926347	−	0.376672i	$-0.877068\pi$
$653$	−3.50000	+	6.06218i	−0.136966	+	0.237231i	0.789381	+	0.613904i	$0.210402\pi$
$654$	3.00000	+	5.19615i	0.117309	+	0.203186i
$655$	−2.50000	−	4.33013i	−0.0976831	−	0.169192i
$656$	−5.50000	+	9.52628i	−0.214739	+	0.371939i
$657$	6.00000			0.234082
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	0.500000	−	0.866025i	0.0194625	−	0.0337100i
$661$	−12.0000	−	20.7846i	−0.466746	−	0.808428i	0.532533	−	0.846410i	$-0.321240\pi$
$661$	−12.0000	−	20.7846i	−0.466746	−	0.808428i	−0.999278	+	0.0379819i	$0.987907\pi$
$662$	−6.50000	−	11.2583i	−0.252630	−	0.437567i
$663$		0			0
$664$	8.00000			0.310460
$665$		0			0
$666$	−11.0000			−0.426241
$667$	28.0000	−	48.4974i	1.08416	−	1.87783i
$668$	−1.50000	−	2.59808i	−0.0580367	−	0.100523i
$669$	6.00000	+	10.3923i	0.231973	+	0.401790i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	28.0000			1.07932			0.539660	−	0.841883i	$-0.318553\pi$
$673$	28.0000			1.07932			0.539660	+	0.841883i	$0.318553\pi$
$674$	−6.00000	+	10.3923i	−0.231111	+	0.400297i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	−6.50000	+	11.2583i	−0.249815	+	0.432693i	−0.963474	−	0.267800i	$-0.913703\pi$
$677$	−6.50000	+	11.2583i	−0.249815	+	0.432693i	0.713659	+	0.700493i	$0.247037\pi$
$678$	−6.00000			−0.230429
$679$		0			0
$680$		0			0
$681$	4.00000	−	6.92820i	0.153280	−	0.265489i
$682$	−1.00000	−	1.73205i	−0.0382920	−	0.0663237i
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	0.825222	−	0.564809i	$-0.191050\pi$
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	−0.901750	+	0.432259i	$0.857717\pi$
$684$	−1.50000	+	2.59808i	−0.0573539	+	0.0993399i
$685$	−18.0000			−0.687745
$686$		0			0
$687$	−14.0000			−0.534133
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−5.50000	−	9.52628i	−0.209533	−	0.362922i
$690$	3.50000	+	6.06218i	0.133243	+	0.230783i
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	−0.957290	−	0.289130i	$-0.906634\pi$
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	0.729039	+	0.684472i	$0.239967\pi$
$692$	15.0000			0.570214
$693$		0			0
$694$	−14.0000			−0.531433
$695$	10.0000	−	17.3205i	0.379322	−	0.657004i
$696$	−4.00000	−	6.92820i	−0.151620	−	0.262613i
$697$		0			0
$698$	−6.00000	+	10.3923i	−0.227103	+	0.393355i
$699$	18.0000			0.680823
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	−0.500000	+	0.866025i	−0.0188713	+	0.0326860i
$703$	−16.5000	−	28.5788i	−0.622309	−	1.07787i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−2.50000	+	4.33013i	−0.0941554	+	0.163082i
$706$	24.0000			0.903252
$707$		0			0
$708$	−4.00000			−0.150329
$709$	−22.0000	+	38.1051i	−0.826227	+	1.43107i	0.0747503	+	0.997202i	$0.476184\pi$
$709$	−22.0000	+	38.1051i	−0.826227	+	1.43107i	−0.900978	+	0.433865i	$0.857149\pi$
$710$	−3.00000	−	5.19615i	−0.112588	−	0.195008i
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$	5.00000	−	8.66025i	0.187383	−	0.324557i
$713$	14.0000			0.524304
$714$		0			0
$715$	1.00000			0.0373979
$716$	9.50000	−	16.4545i	0.355032	−	0.614933i
$717$	9.00000	+	15.5885i	0.336111	+	0.582162i
$718$	2.00000	+	3.46410i	0.0746393	+	0.129279i
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	−0.846776	−	0.531949i	$-0.821460\pi$
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	0.884070	+	0.467355i	$0.154793\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	10.0000			0.372161
$723$	3.50000	−	6.06218i	0.130166	−	0.225455i
$724$	−12.0000	−	20.7846i	−0.445976	−	0.772454i
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$	−5.00000	+	8.66025i	−0.185567	+	0.321412i
$727$	−11.0000			−0.407967			−0.203984	−	0.978974i	$-0.565389\pi$
$727$	−11.0000			−0.407967			−0.203984	+	0.978974i	$0.565389\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$		0			0
$732$		0			0
$733$	5.50000	−	9.52628i	0.203147	−	0.351861i	−0.746394	−	0.665505i	$-0.768216\pi$
$733$	5.50000	−	9.52628i	0.203147	−	0.351861i	0.949541	+	0.313644i	$0.101550\pi$
$734$	25.0000			0.922767
$735$		0			0
$736$	−7.00000			−0.258023
$737$		0			0
$738$	5.50000	+	9.52628i	0.202458	+	0.350667i
$739$	9.50000	+	16.4545i	0.349463	+	0.605288i	0.986154	−	0.165831i	$-0.0530307\pi$
$739$	9.50000	+	16.4545i	0.349463	+	0.605288i	−0.636691	+	0.771119i	$0.719697\pi$
$740$	−5.50000	+	9.52628i	−0.202184	+	0.350193i
$741$	−3.00000			−0.110208
$742$		0			0
$743$	49.0000			1.79764			0.898818	−	0.438322i	$-0.144427\pi$
$743$	49.0000			1.79764			0.898818	+	0.438322i	$0.144427\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$		0			0
$746$	3.00000	+	5.19615i	0.109838	+	0.190245i
$747$	4.00000	−	6.92820i	0.146352	−	0.253490i
$748$		0			0
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	−0.999570	−	0.0293387i	$-0.990660\pi$
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	0.525193	+	0.850983i	$0.323993\pi$
$752$	−2.50000	−	4.33013i	−0.0911656	−	0.157903i
$753$	6.50000	+	11.2583i	0.236873	+	0.410276i
$754$	4.00000	−	6.92820i	0.145671	−	0.252310i
$755$	6.00000			0.218362
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−9.50000	+	16.4545i	−0.345056	+	0.597654i
$759$	3.50000	+	6.06218i	0.127042	+	0.220043i
$760$	1.50000	+	2.59808i	0.0544107	+	0.0942421i
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	−0.510551	−	0.859848i	$-0.670558\pi$
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	0.999925	+	0.0122260i	$0.00389175\pi$
$762$	17.0000			0.615845
$763$		0			0
$764$	−6.00000			−0.217072
$765$		0			0
$766$	−17.5000	−	30.3109i	−0.632301	−	1.09518i
$767$	−2.00000	−	3.46410i	−0.0722158	−	0.125081i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	5.00000			0.180305			0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000			0.180305			0.0901523	+	0.995928i	$0.471265\pi$
$770$		0			0
$771$	20.0000			0.720282
$772$	−11.0000	+	19.0526i	−0.395899	+	0.685717i
$773$	16.5000	+	28.5788i	0.593464	+	1.02791i	0.993762	+	0.111524i	$0.0355733\pi$
$773$	16.5000	+	28.5788i	0.593464	+	1.02791i	−0.400298	+	0.916385i	$0.631093\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$	−1.00000	+	1.73205i	−0.0359211	+	0.0622171i
$776$	−16.0000			−0.574367
$777$		0			0
$778$	−10.0000			−0.358517
$779$	−16.5000	+	28.5788i	−0.591174	+	1.02394i
$780$	0.500000	+	0.866025i	0.0179029	+	0.0310087i
$781$	−3.00000	−	5.19615i	−0.107348	−	0.185933i
$782$		0			0
$783$	−8.00000			−0.285897
$784$		0			0
$785$	7.00000			0.249841
$786$	2.50000	−	4.33013i	0.0891720	−	0.154451i
$787$	11.0000	+	19.0526i	0.392108	+	0.679150i	0.992727	−	0.120384i	$-0.0384127\pi$
$787$	11.0000	+	19.0526i	0.392108	+	0.679150i	−0.600620	+	0.799535i	$0.705079\pi$
$788$	0.500000	+	0.866025i	0.0178118	+	0.0308509i
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$	8.00000			0.284627
$791$		0			0
$792$	1.00000			0.0355335
$793$		0			0
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$	5.50000	+	9.52628i	0.195065	+	0.337862i
$796$	−12.0000	+	20.7846i	−0.425329	+	0.736691i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−5.00000	−	8.66025i	−0.176666	−	0.305995i
$802$	−2.50000	−	4.33013i	−0.0882781	−	0.152902i
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$		0			0
$806$	2.00000			0.0704470
$807$	10.0000	−	17.3205i	0.352017	−	0.609711i
$808$		0			0
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	0.973253	+	0.229736i	$0.0737862\pi$
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	−0.287670	+	0.957730i	$0.592880\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−9.00000			−0.316033			−0.158016	−	0.987436i	$-0.550510\pi$
$811$	−9.00000			−0.316033			−0.158016	+	0.987436i	$0.550510\pi$
$812$		0			0
$813$	−32.0000			−1.12229
$814$	−5.50000	+	9.52628i	−0.192775	+	0.333896i
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$		0			0
$817$	−12.0000	+	20.7846i	−0.419827	+	0.727161i
$818$	2.00000			0.0699284
$819$		0			0
$820$	11.0000			0.384137
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	0.222731	+	0.974880i	$0.428503\pi$
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	−0.955636	+	0.294549i	$0.904831\pi$
$822$	−9.00000	−	15.5885i	−0.313911	−	0.543710i
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$	−1.00000			−0.0348155
$826$		0			0
$827$	−10.0000			−0.347734			−0.173867	−	0.984769i	$-0.555626\pi$
$827$	−10.0000			−0.347734			−0.173867	+	0.984769i	$0.555626\pi$
$828$	−3.50000	+	6.06218i	−0.121633	+	0.210675i
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	0.788165	−	0.615465i	$-0.211032\pi$
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	−0.927090	+	0.374838i	$0.877698\pi$
$830$	−4.00000	−	6.92820i	−0.138842	−	0.240481i
$831$	11.0000	−	19.0526i	0.381586	−	0.660926i
$832$	−1.00000			−0.0346688
$833$		0			0
$834$	20.0000			0.692543
$835$	−1.50000	+	2.59808i	−0.0519096	+	0.0899101i
$836$	1.50000	+	2.59808i	0.0518786	+	0.0898563i
$837$	−1.00000	−	1.73205i	−0.0345651	−	0.0598684i
$838$	2.50000	−	4.33013i	0.0863611	−	0.149582i
$839$	40.0000			1.38095			0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000			1.38095			0.690477	+	0.723355i	$0.257401\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	11.0000	−	19.0526i	0.379085	−	0.656595i
$843$	0.500000	+	0.866025i	0.0172209	+	0.0298275i
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	6.00000	−	10.3923i	0.206406	−	0.357506i
$846$	−5.00000			−0.171904
$847$		0			0
$848$	−11.0000			−0.377742
$849$	−7.00000	+	12.1244i	−0.240239	+	0.416107i
$850$		0			0
$851$	−38.5000	−	66.6840i	−1.31976	−	2.28590i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	41.0000			1.40381			0.701907	−	0.712269i	$-0.252332\pi$
$853$	41.0000			1.40381			0.701907	+	0.712269i	$0.252332\pi$
$854$		0			0
$855$	3.00000			0.102598
$856$	−5.00000	+	8.66025i	−0.170896	+	0.296001i
$857$	−7.00000	−	12.1244i	−0.239115	−	0.414160i	0.721345	−	0.692576i	$-0.243524\pi$
$857$	−7.00000	−	12.1244i	−0.239115	−	0.414160i	−0.960461	+	0.278416i	$0.910191\pi$
$858$	0.500000	+	0.866025i	0.0170697	+	0.0295656i
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	−0.745325	−	0.666701i	$-0.767706\pi$
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	0.950043	+	0.312120i	$0.101039\pi$
$860$	8.00000			0.272798
$861$		0			0
$862$		0			0
$863$	26.5000	−	45.8993i	0.902070	−	1.56243i	0.0772684	−	0.997010i	$-0.475380\pi$
$863$	26.5000	−	45.8993i	0.902070	−	1.56243i	0.824802	−	0.565422i	$-0.191287\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−7.50000	−	12.9904i	−0.255008	−	0.441686i
$866$	16.0000	−	27.7128i	0.543702	−	0.941720i
$867$	−17.0000			−0.577350
$868$		0			0
$869$	8.00000			0.271381
$870$	−4.00000	+	6.92820i	−0.135613	+	0.234888i
$871$		0			0
$872$	3.00000	+	5.19615i	0.101593	+	0.175964i
$873$	−8.00000	+	13.8564i	−0.270759	+	0.468968i
$874$	−21.0000			−0.710336
$875$		0			0
$876$	6.00000			0.202721
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	−0.973098	−	0.230391i	$-0.925999\pi$
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	0.686074	+	0.727532i	$0.259333\pi$
$878$	−16.0000	−	27.7128i	−0.539974	−	0.935262i
$879$	13.5000	+	23.3827i	0.455344	+	0.788678i
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	53.0000			1.78562			0.892808	−	0.450438i	$-0.148732\pi$
$881$	53.0000			1.78562			0.892808	+	0.450438i	$0.148732\pi$
$882$		0			0
$883$	−42.0000			−1.41341			−0.706706	−	0.707507i	$-0.749820\pi$
$883$	−42.0000			−1.41341			−0.706706	+	0.707507i	$0.749820\pi$
$884$		0			0
$885$	2.00000	+	3.46410i	0.0672293	+	0.116445i
$886$	8.00000	+	13.8564i	0.268765	+	0.465515i
$887$	22.0000	−	38.1051i	0.738688	−	1.27944i	−0.214399	−	0.976746i	$-0.568779\pi$
$887$	22.0000	−	38.1051i	0.738688	−	1.27944i	0.953086	−	0.302698i	$-0.0978875\pi$
$888$	−11.0000			−0.369136
$889$		0			0
$890$	−10.0000			−0.335201
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	6.00000	+	10.3923i	0.200895	+	0.347960i
$893$	−7.50000	−	12.9904i	−0.250978	−	0.434707i
$894$		0			0
$895$	−19.0000			−0.635100
$896$		0			0
$897$	−7.00000			−0.233723
$898$	5.50000	−	9.52628i	0.183537	−	0.317896i
$899$	8.00000	+	13.8564i	0.266815	+	0.462137i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$		0			0
$902$	11.0000			0.366260
$903$		0			0
$904$	−6.00000			−0.199557
$905$	−12.0000	+	20.7846i	−0.398893	+	0.690904i
$906$	3.00000	+	5.19615i	0.0996683	+	0.172631i
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	4.00000	−	6.92820i	0.132745	−	0.229920i
$909$		0			0
$910$		0			0
$911$	−2.00000			−0.0662630			−0.0331315	−	0.999451i	$-0.510548\pi$
$911$	−2.00000			−0.0662630			−0.0331315	+	0.999451i	$0.510548\pi$
$912$	−1.50000	+	2.59808i	−0.0496700	+	0.0860309i
$913$	−4.00000	−	6.92820i	−0.132381	−	0.229290i
$914$	−9.00000	−	15.5885i	−0.297694	−	0.515620i
$915$		0			0
$916$	−14.0000			−0.462573
$917$		0			0
$918$		0			0
$919$	18.0000	−	31.1769i	0.593765	−	1.02843i	−0.399955	−	0.916535i	$-0.630974\pi$
$919$	18.0000	−	31.1769i	0.593765	−	1.02843i	0.993720	−	0.111897i	$-0.0356925\pi$
$920$	3.50000	+	6.06218i	0.115392	+	0.199864i
$921$	10.0000	+	17.3205i	0.329511	+	0.570730i
$922$	6.00000	−	10.3923i	0.197599	−	0.342252i
$923$	6.00000			0.197492
$924$		0			0
$925$	11.0000			0.361678
$926$	−6.50000	+	11.2583i	−0.213603	+	0.369972i
$927$	−8.00000	−	13.8564i	−0.262754	−	0.455104i
$928$	−4.00000	−	6.92820i	−0.131306	−	0.227429i
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$	−2.00000			−0.0655826
$931$		0			0
$932$	18.0000			0.589610
$933$	6.00000	−	10.3923i	0.196431	−	0.340229i
$934$		0			0
$935$		0			0
$936$	−0.500000	+	0.866025i	−0.0163430	+	0.0283069i
$937$	−12.0000			−0.392023			−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000			−0.392023			−0.196011	+	0.980602i	$0.562799\pi$
$938$		0			0
$939$	12.0000			0.391605
$940$	−2.50000	+	4.33013i	−0.0815410	+	0.141233i
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.851146	+	0.524929i	$0.175908\pi$
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.0290288	+	0.999579i	$0.490759\pi$
$942$	3.50000	+	6.06218i	0.114036	+	0.197516i
$943$	−38.5000	+	66.6840i	−1.25373	+	2.17153i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	8.00000			0.260102
$947$	−11.0000	+	19.0526i	−0.357452	+	0.619125i	−0.987534	−	0.157403i	$-0.949688\pi$
$947$	−11.0000	+	19.0526i	−0.357452	+	0.619125i	0.630082	+	0.776528i	$0.283021\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	3.00000	+	5.19615i	0.0973841	+	0.168674i
$950$	1.50000	−	2.59808i	0.0486664	−	0.0842927i
$951$	−18.0000			−0.583690
$952$		0			0
$953$	−20.0000			−0.647864			−0.323932	−	0.946080i	$-0.605005\pi$
$953$	−20.0000			−0.647864			−0.323932	+	0.946080i	$0.605005\pi$
$954$	−5.50000	+	9.52628i	−0.178069	+	0.308425i
$955$	3.00000	+	5.19615i	0.0970777	+	0.168144i
$956$	9.00000	+	15.5885i	0.291081	+	0.504167i
$957$	−4.00000	+	6.92820i	−0.129302	+	0.223957i
$958$	22.0000			0.710788
$959$		0			0
$960$	1.00000			0.0322749
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−5.50000	−	9.52628i	−0.177327	−	0.307140i
$963$	5.00000	+	8.66025i	0.161123	+	0.279073i
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$	22.0000			0.708205
$966$		0			0
$967$	−20.0000			−0.643157			−0.321578	−	0.946883i	$-0.604213\pi$
$967$	−20.0000			−0.643157			−0.321578	+	0.946883i	$0.604213\pi$
$968$	−5.00000	+	8.66025i	−0.160706	+	0.278351i
$969$		0			0
$970$	8.00000	+	13.8564i	0.256865	+	0.444902i
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	0.238114	+	0.971237i	$0.423471\pi$
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	−0.960173	+	0.279406i	$0.909862\pi$
$972$	1.00000			0.0320750
$973$		0			0
$974$	16.0000			0.512673
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$		0			0
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	−0.868227	−	0.496167i	$-0.834741\pi$
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	0.00442082	−	0.999990i	$-0.498593\pi$
$978$	8.00000	−	13.8564i	0.255812	−	0.443079i
$979$	−10.0000			−0.319601
$980$		0			0
$981$	6.00000			0.191565
$982$	10.0000	−	17.3205i	0.319113	−	0.552720i
$983$	24.5000	+	42.4352i	0.781429	+	1.35347i	0.931110	+	0.364740i	$0.118842\pi$
$983$	24.5000	+	42.4352i	0.781429	+	1.35347i	−0.149681	+	0.988734i	$0.547825\pi$
$984$	5.50000	+	9.52628i	0.175334	+	0.303687i
$985$	0.500000	−	0.866025i	0.0159313	−	0.0275939i
$986$		0			0
$987$		0			0
$988$	−3.00000			−0.0954427
$989$	−28.0000	+	48.4974i	−0.890348	+	1.54213i
$990$	−0.500000	−	0.866025i	−0.0158910	−	0.0275241i
$991$	−11.0000	−	19.0526i	−0.349427	−	0.605224i	0.636721	−	0.771094i	$-0.280290\pi$
$991$	−11.0000	−	19.0526i	−0.349427	−	0.605224i	−0.986148	+	0.165870i	$0.946957\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	−13.0000			−0.412543
$994$		0			0
$995$	24.0000			0.760851
$996$	4.00000	−	6.92820i	0.126745	−	0.219529i
$997$	7.00000	+	12.1244i	0.221692	+	0.383982i	0.955322	−	0.295567i	$-0.0955086\pi$
$997$	7.00000	+	12.1244i	0.221692	+	0.383982i	−0.733630	+	0.679549i	$0.762175\pi$
$998$	−16.0000	−	27.7128i	−0.506471	−	0.877234i
$999$	−5.50000	+	9.52628i	−0.174012	+	0.301398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.m.961.1		2
7.2	even	3		1470.2.a.h.1.1		1
7.3	odd	6		210.2.i.d.151.1	yes	2
7.4	even	3	inner	1470.2.i.m.361.1		2
7.5	odd	6		1470.2.a.a.1.1		1
7.6	odd	2		210.2.i.d.121.1	✓	2
21.2	odd	6		4410.2.a.ba.1.1		1
21.5	even	6		4410.2.a.bj.1.1		1
21.17	even	6		630.2.k.c.361.1		2
21.20	even	2		630.2.k.c.541.1		2
28.3	even	6		1680.2.bg.g.1201.1		2
28.27	even	2		1680.2.bg.g.961.1		2
35.3	even	12		1050.2.o.i.949.2		4
35.9	even	6		7350.2.a.bu.1.1		1
35.13	even	4		1050.2.o.i.499.1		4
35.17	even	12		1050.2.o.i.949.1		4
35.19	odd	6		7350.2.a.cp.1.1		1
35.24	odd	6		1050.2.i.b.151.1		2
35.27	even	4		1050.2.o.i.499.2		4
35.34	odd	2		1050.2.i.b.751.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.d.121.1	✓	2	7.6	odd	2
210.2.i.d.151.1	yes	2	7.3	odd	6
630.2.k.c.361.1		2	21.17	even	6
630.2.k.c.541.1		2	21.20	even	2
1050.2.i.b.151.1		2	35.24	odd	6
1050.2.i.b.751.1		2	35.34	odd	2
1050.2.o.i.499.1		4	35.13	even	4
1050.2.o.i.499.2		4	35.27	even	4
1050.2.o.i.949.1		4	35.17	even	12
1050.2.o.i.949.2		4	35.3	even	12
1470.2.a.a.1.1		1	7.5	odd	6
1470.2.a.h.1.1		1	7.2	even	3
1470.2.i.m.361.1		2	7.4	even	3	inner
1470.2.i.m.961.1		2	1.1	even	1	trivial
1680.2.bg.g.961.1		2	28.27	even	2
1680.2.bg.g.1201.1		2	28.3	even	6
4410.2.a.ba.1.1		1	21.2	odd	6
4410.2.a.bj.1.1		1	21.5	even	6
7350.2.a.bu.1.1		1	35.9	even	6
7350.2.a.cp.1.1		1	35.19	odd	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(-1.50000 + 2.59808i) q^{19} +1.00000 q^{20} +1.00000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +1.00000 q^{36} +(-5.50000 + 9.52628i) q^{37} +(1.50000 + 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +11.0000 q^{41} +8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.50000 + 6.06218i) q^{46} +(-2.50000 + 4.33013i) q^{47} +1.00000 q^{48} -1.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(5.50000 + 9.52628i) q^{53} +(0.500000 - 0.866025i) q^{54} -1.00000 q^{55} +3.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} -2.00000 q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(-0.500000 - 0.866025i) q^{66} +7.00000 q^{69} -6.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(5.50000 + 9.52628i) q^{74} +(-0.500000 + 0.866025i) q^{75} +3.00000 q^{76} +1.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.50000 - 9.52628i) q^{82} -8.00000 q^{83} +(4.00000 - 6.92820i) q^{86} +(4.00000 + 6.92820i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} -1.00000 q^{90} +7.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(2.50000 + 4.33013i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(0.500000 - 0.866025i) q^{96} +16.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{8} - q^{9} + q^{10} + q^{11} - q^{12} - 2 q^{13} + 2 q^{15} - q^{16} + q^{18} - 3 q^{19} + 2 q^{20} + 2 q^{22} - 7 q^{23} + q^{24} - q^{25} - q^{26} + 2 q^{27} - 16 q^{29} + q^{30} - 2 q^{31} + q^{32} + q^{33} + 2 q^{36} - 11 q^{37} + 3 q^{38} + q^{39} + q^{40} + 22 q^{41} + 16 q^{43} + q^{44} - q^{45} + 7 q^{46} - 5 q^{47} + 2 q^{48} - 2 q^{50} + q^{52} + 11 q^{53} + q^{54} - 2 q^{55} + 6 q^{57} - 8 q^{58} + 4 q^{59} - q^{60} - 4 q^{62} + 2 q^{64} + q^{65} - q^{66} + 14 q^{69} - 12 q^{71} + q^{72} - 6 q^{73} + 11 q^{74} - q^{75} + 6 q^{76} + 2 q^{78} + 8 q^{79} - q^{80} - q^{81} + 11 q^{82} - 16 q^{83} + 8 q^{86} + 8 q^{87} - q^{88} - 10 q^{89} - 2 q^{90} + 14 q^{92} - 2 q^{93} + 5 q^{94} - 3 q^{95} + q^{96} + 32 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^8 - q^9 + q^10 + q^11 - q^12 - 2 * q^13 + 2 * q^15 - q^16 + q^18 - 3 * q^19 + 2 * q^20 + 2 * q^22 - 7 * q^23 + q^24 - q^25 - q^26 + 2 * q^27 - 16 * q^29 + q^30 - 2 * q^31 + q^32 + q^33 + 2 * q^36 - 11 * q^37 + 3 * q^38 + q^39 + q^40 + 22 * q^41 + 16 * q^43 + q^44 - q^45 + 7 * q^46 - 5 * q^47 + 2 * q^48 - 2 * q^50 + q^52 + 11 * q^53 + q^54 - 2 * q^55 + 6 * q^57 - 8 * q^58 + 4 * q^59 - q^60 - 4 * q^62 + 2 * q^64 + q^65 - q^66 + 14 * q^69 - 12 * q^71 + q^72 - 6 * q^73 + 11 * q^74 - q^75 + 6 * q^76 + 2 * q^78 + 8 * q^79 - q^80 - q^81 + 11 * q^82 - 16 * q^83 + 8 * q^86 + 8 * q^87 - q^88 - 10 * q^89 - 2 * q^90 + 14 * q^92 - 2 * q^93 + 5 * q^94 - 3 * q^95 + q^96 + 32 * q^97 - 2 * q^99

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