LMFDB - Embedded newform 1050.2.i.b.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(151,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, 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("1050.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.i (of order $3$, degree $2$, 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:	$8.38429221223$
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			751.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.751
Dual form			1050.2.i.b.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{18} +(1.50000 - 2.59808i) q^{19} +(2.50000 + 0.866025i) q^{21} -1.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{26} +1.00000 q^{27} +(2.50000 + 0.866025i) q^{28} -8.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +1.00000 q^{36} +(5.50000 - 9.52628i) q^{37} +(1.50000 + 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{39} -11.0000 q^{41} +(-2.00000 + 1.73205i) q^{42} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(3.50000 + 6.06218i) q^{46} +(-2.50000 + 4.33013i) q^{47} +1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +(0.500000 + 0.866025i) q^{52} +(-5.50000 - 9.52628i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} -3.00000 q^{57} +(4.00000 - 6.92820i) q^{58} +(-2.00000 - 3.46410i) q^{59} -2.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} -7.00000 q^{69} -6.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(5.50000 + 9.52628i) q^{74} -3.00000 q^{76} +(-2.50000 - 0.866025i) q^{77} -1.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.50000 - 9.52628i) q^{82} -8.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} +(4.00000 + 6.92820i) q^{87} +(0.500000 + 0.866025i) q^{88} +(5.00000 - 8.66025i) q^{89} +(2.00000 - 1.73205i) q^{91} -7.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(-2.50000 - 4.33013i) q^{94} +(-0.500000 + 0.866025i) q^{96} +16.0000 q^{97} +(5.50000 + 4.33013i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + q^{11} - q^{12} - 2 q^{13} - q^{14} - q^{16} - q^{18} + 3 q^{19} + 5 q^{21} - 2 q^{22} + 7 q^{23} - q^{24} + q^{26} + 2 q^{27} + 5 q^{28} - 16 q^{29} + 2 q^{31} - q^{32} + q^{33} + 2 q^{36} + 11 q^{37} + 3 q^{38} + q^{39} - 22 q^{41} - 4 q^{42} - 16 q^{43} + q^{44} + 7 q^{46} - 5 q^{47} + 2 q^{48} + 2 q^{49} + q^{52} - 11 q^{53} - q^{54} - 4 q^{56} - 6 q^{57} + 8 q^{58} - 4 q^{59} - 4 q^{62} - q^{63} + 2 q^{64} + q^{66} - 14 q^{69} - 12 q^{71} - q^{72} - 6 q^{73} + 11 q^{74} - 6 q^{76} - 5 q^{77} - 2 q^{78} + 8 q^{79} - q^{81} + 11 q^{82} - 16 q^{83} - q^{84} + 8 q^{86} + 8 q^{87} + q^{88} + 10 q^{89} + 4 q^{91} - 14 q^{92} + 2 q^{93} - 5 q^{94} - q^{96} + 32 q^{97} + 11 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - q^9 + q^11 - q^12 - 2 * q^13 - q^14 - q^16 - q^18 + 3 * q^19 + 5 * q^21 - 2 * q^22 + 7 * q^23 - q^24 + q^26 + 2 * q^27 + 5 * q^28 - 16 * q^29 + 2 * q^31 - q^32 + q^33 + 2 * q^36 + 11 * q^37 + 3 * q^38 + q^39 - 22 * q^41 - 4 * q^42 - 16 * q^43 + q^44 + 7 * q^46 - 5 * q^47 + 2 * q^48 + 2 * q^49 + q^52 - 11 * q^53 - q^54 - 4 * q^56 - 6 * q^57 + 8 * q^58 - 4 * q^59 - 4 * q^62 - q^63 + 2 * q^64 + q^66 - 14 * q^69 - 12 * q^71 - q^72 - 6 * q^73 + 11 * q^74 - 6 * q^76 - 5 * q^77 - 2 * q^78 + 8 * q^79 - q^81 + 11 * q^82 - 16 * q^83 - q^84 + 8 * q^86 + 8 * q^87 + q^88 + 10 * q^89 + 4 * q^91 - 14 * q^92 + 2 * q^93 - 5 * q^94 - q^96 + 32 * q^97 + 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$5$		0			0
$6$	1.00000			0.408248
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	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	$0.544284\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$		0			0
$16$	−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	−0.641071	−	0.767482i	$-0.721509\pi$
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	0.985194	+	0.171442i	$0.0548427\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$	−1.00000			−0.213201
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	−0.227167	−	0.973856i	$-0.572946\pi$
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	0.956967	−	0.290196i	$-0.0937204\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	1.00000			0.192450
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	−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			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−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	$-0.473806\pi$
$37$	5.50000	−	9.52628i	0.904194	−	1.56611i	0.821995	−	0.569495i	$-0.192861\pi$
$38$	1.50000	+	2.59808i	0.243332	+	0.421464i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	−11.0000			−1.71791			−0.858956	−	0.512050i	$-0.828886\pi$
$41$	−11.0000			−1.71791			−0.858956	+	0.512050i	$0.828886\pi$
$42$	−2.00000	+	1.73205i	−0.308607	+	0.267261i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	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
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−5.50000	−	9.52628i	−0.755483	−	1.30854i	−0.945134	−	0.326683i	$-0.894069\pi$
$53$	−5.50000	−	9.52628i	−0.755483	−	1.30854i	0.189651	−	0.981852i	$-0.439264\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$	−3.00000			−0.397360
$58$	4.00000	−	6.92820i	0.525226	−	0.909718i
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	−2.00000			−0.254000
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	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			0
$76$	−3.00000			−0.344124
$77$	−2.50000	−	0.866025i	−0.284901	−	0.0986928i
$78$	−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			0
$81$	−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	$0.644687\pi$
$84$	−0.500000	−	2.59808i	−0.0545545	−	0.283473i
$85$		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	$-0.655526\pi$
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	0.999388	−	0.0349934i	$-0.0111410\pi$
$90$		0			0
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	−7.00000			−0.729800
$93$	1.00000	−	1.73205i	0.103695	−	0.179605i
$94$	−2.50000	−	4.33013i	−0.257855	−	0.446619i
$95$		0			0
$96$	−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	$0.198228\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$	−1.00000			−0.100504
$100$		0			0
$101$		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	−0.999818	−	0.0190994i	$-0.993920\pi$
$107$	−5.00000	+	8.66025i	−0.483368	+	0.837218i	0.516449	+	0.856318i	$0.327253\pi$
$108$	−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			0
$111$	−11.0000			−1.04407
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.50000	−	2.59808i	0.140488	−	0.243332i
$115$		0			0
$116$	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
$120$		0			0
$121$	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
$125$		0			0
$126$	2.50000	+	0.866025i	0.222718	+	0.0771517i
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$		0			0
$131$	2.50000	−	4.33013i	0.218426	−	0.378325i	−0.735901	−	0.677089i	$-0.763241\pi$
$131$	2.50000	−	4.33013i	0.218426	−	0.378325i	0.954327	+	0.298764i	$0.0965744\pi$
$132$	−1.00000			−0.0870388
$133$	1.50000	+	7.79423i	0.130066	+	0.675845i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$	3.50000	−	6.06218i	0.297940	−	0.516047i
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$		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
$145$		0			0
$146$	6.00000			0.496564
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$	−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			0
$151$	−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
$154$	2.00000	−	1.73205i	0.161165	−	0.139573i
$155$		0			0
$156$	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
$160$		0			0
$161$	3.50000	+	18.1865i	0.275839	+	1.43330i
$162$	1.00000			0.0785674
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	5.50000	+	9.52628i	0.429478	+	0.743877i
$165$		0			0
$166$	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	$0.462969\pi$
$168$	2.50000	+	0.866025i	0.192879	+	0.0668153i
$169$	−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			0
$181$	−24.0000			−1.78391			−0.891953	−	0.452128i	$-0.850665\pi$
$181$	−24.0000			−1.78391			−0.891953	+	0.452128i	$0.850665\pi$
$182$	0.500000	+	2.59808i	0.0370625	+	0.192582i
$183$		0			0
$184$	3.50000	−	6.06218i	0.258023	−	0.446910i
$185$		0			0
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$		0			0
$188$	5.00000			0.364662
$189$	−2.00000	+	1.73205i	−0.145479	+	0.125988i
$190$		0			0
$191$	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	$0.124188\pi$
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	−0.133056	+	0.991109i	$0.542479\pi$
$194$	−8.00000	+	13.8564i	−0.574367	+	0.994832i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	1.00000			0.0712470			0.0356235	−	0.999365i	$-0.488658\pi$
$197$	1.00000			0.0712470			0.0356235	+	0.999365i	$0.488658\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	0.880616	+	0.473831i	$0.157129\pi$
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	−0.0299585	+	0.999551i	$0.509538\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	16.0000	−	13.8564i	1.12298	−	0.972529i
$204$		0			0
$205$		0			0
$206$	−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
$215$		0			0
$216$	1.00000			0.0680414
$217$	−5.00000	−	1.73205i	−0.339422	−	0.117579i
$218$	6.00000			0.406371
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$		0			0
$221$		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	$0.631612\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$	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	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$	0.500000	+	2.59808i	0.0328976	+	0.170941i
$232$	−8.00000			−0.525226
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$	0.500000	+	0.866025i	0.0326860	+	0.0566139i
$235$		0			0
$236$	−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			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	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			0
$251$	13.0000			0.820553			0.410276	−	0.911961i	$-0.365432\pi$
$251$	13.0000			0.820553			0.410276	+	0.911961i	$0.365432\pi$
$252$	−2.00000	+	1.73205i	−0.125988	+	0.109109i
$253$	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
$259$	5.50000	+	28.5788i	0.341753	+	1.77580i
$260$		0			0
$261$	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	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$	0.500000	−	0.866025i	0.0307729	−	0.0533002i
$265$		0			0
$266$	−7.50000	−	2.59808i	−0.459855	−	0.159298i
$267$	−10.0000			−0.611990
$268$		0			0
$269$	−10.0000	−	17.3205i	−0.609711	−	1.05605i	−0.991288	−	0.131713i	$-0.957952\pi$
$269$	−10.0000	−	17.3205i	−0.609711	−	1.05605i	0.381577	−	0.924337i	$-0.375381\pi$
$270$		0			0
$271$	−16.0000	+	27.7128i	−0.971931	+	1.68343i	−0.282218	+	0.959350i	$0.591070\pi$
$271$	−16.0000	+	27.7128i	−0.971931	+	1.68343i	−0.689713	+	0.724083i	$0.742263\pi$
$272$		0			0
$273$	−2.50000	−	0.866025i	−0.151307	−	0.0524142i
$274$	18.0000			1.08742
$275$		0			0
$276$	3.50000	+	6.06218i	0.210675	+	0.364900i
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	−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
$285$		0			0
$286$	1.00000			0.0591312
$287$	22.0000	−	19.0526i	1.29862	−	1.12464i
$288$	1.00000			0.0589256
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	−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	$0.789234\pi$
$294$	1.00000	−	6.92820i	0.0583212	−	0.404061i
$295$		0			0
$296$	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
$300$		0			0
$301$	16.0000	−	13.8564i	0.922225	−	0.798670i
$302$	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	$0.693340\pi$
$308$	0.500000	+	2.59808i	0.0284901	+	0.148039i
$309$	16.0000			0.910208
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$	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	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	−5.50000	−	9.52628i	−0.308425	−	0.534207i
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$		0			0
$321$	10.0000			0.558146
$322$	−17.5000	−	6.06218i	−0.975237	−	0.337832i
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	8.00000	+	13.8564i	0.443079	+	0.767435i
$327$	−3.00000	+	5.19615i	−0.165900	+	0.287348i
$328$	−11.0000			−0.607373
$329$	−2.50000	−	12.9904i	−0.137829	−	0.716183i
$330$		0			0
$331$	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
$336$	−2.00000	+	1.73205i	−0.109109	+	0.0944911i
$337$	12.0000			0.653682			0.326841	−	0.945079i	$-0.394016\pi$
$337$	12.0000			0.653682			0.326841	+	0.945079i	$0.394016\pi$
$338$	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
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−8.00000			−0.431331
$345$		0			0
$346$	−7.50000	−	12.9904i	−0.403202	−	0.698367i
$347$	7.00000	+	12.1244i	0.375780	+	0.650870i	0.990443	−	0.137920i	$-0.0440416\pi$
$347$	7.00000	+	12.1244i	0.375780	+	0.650870i	−0.614664	+	0.788789i	$0.710708\pi$
$348$	4.00000	−	6.92820i	0.214423	−	0.371391i
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$		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
$355$		0			0
$356$	−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			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	12.0000	−	20.7846i	0.630706	−	1.09241i
$363$	−10.0000			−0.524864
$364$	−2.50000	−	0.866025i	−0.131036	−	0.0453921i
$365$		0			0
$366$		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
$370$		0			0
$371$	27.5000	+	9.52628i	1.42773	+	0.494580i
$372$	−2.00000			−0.103695
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	−0.777847	−	0.628454i	$-0.783688\pi$
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	0.933181	+	0.359408i	$0.117021\pi$
$374$		0			0
$375$		0			0
$376$	−2.50000	+	4.33013i	−0.128928	+	0.223309i
$377$	8.00000			0.412021
$378$	−0.500000	−	2.59808i	−0.0257172	−	0.133631i
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$		0			0
$381$	−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			0
$391$		0			0
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$	−5.00000			−0.252217
$394$	−0.500000	+	0.866025i	−0.0251896	+	0.0436297i
$395$		0			0
$396$	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
$399$	6.00000	−	5.19615i	0.300376	−	0.260133i
$400$		0			0
$401$	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
$405$		0			0
$406$	4.00000	+	20.7846i	0.198517	+	1.03152i
$407$	11.0000			0.545250
$408$		0			0
$409$	−1.00000	−	1.73205i	−0.0494468	−	0.0856444i	0.840243	−	0.542211i	$-0.182412\pi$
$409$	−1.00000	−	1.73205i	−0.0494468	−	0.0856444i	−0.889689	+	0.456566i	$0.849079\pi$
$410$		0			0
$411$	−9.00000	+	15.5885i	−0.443937	+	0.768922i
$412$	16.0000			0.788263
$413$	10.0000	+	3.46410i	0.492068	+	0.170457i
$414$	−7.00000			−0.344031
$415$		0			0
$416$	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	$-0.538973\pi$
$419$	−5.00000			−0.244266			−0.122133	+	0.992514i	$0.538973\pi$
$420$		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
$430$		0			0
$431$		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	$0.220799\pi$
$434$	4.00000	−	3.46410i	0.192006	−	0.166282i
$435$		0			0
$436$	−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	$0.443256\pi$
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	−0.940963	+	0.338508i	$0.890078\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$		0			0
$443$	8.00000	−	13.8564i	0.380091	−	0.658338i	−0.610984	−	0.791643i	$-0.709226\pi$
$443$	8.00000	−	13.8564i	0.380091	−	0.658338i	0.991075	+	0.133306i	$0.0425592\pi$
$444$	5.50000	+	9.52628i	0.261018	+	0.452097i
$445$		0			0
$446$	6.00000	−	10.3923i	0.284108	−	0.492090i
$447$		0			0
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$	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			0
$451$	−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	−0.996038	−	0.0889312i	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$	−7.00000	−	12.1244i	−0.327089	−	0.566534i
$459$		0			0
$460$		0			0
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$	−2.50000	−	0.866025i	−0.116311	−	0.0402911i
$463$	13.0000			0.604161			0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000			0.604161			0.302081	+	0.953282i	$0.402319\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$		0			0
$466$	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
$470$		0			0
$471$	−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
$475$		0			0
$476$		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	$-0.999042\pi$
$479$	−11.0000	−	19.0526i	−0.502603	−	0.870534i	0.497393	−	0.867526i	$-0.334291\pi$
$480$		0			0
$481$	−5.50000	+	9.52628i	−0.250778	+	0.434361i
$482$	7.00000			0.318841
$483$	14.0000	−	12.1244i	0.637022	−	0.551677i
$484$	−10.0000			−0.454545
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$		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			0
$496$	−2.00000			−0.0898027
$497$	12.0000	−	10.3923i	0.538274	−	0.466159i
$498$	−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			0
$501$	−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	$0.796540\pi$
$504$	−0.500000	−	2.59808i	−0.0222718	−	0.115728i
$505$		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	$-0.561692\pi$
$509$	17.0000	−	29.4449i	0.753512	−	1.30512i	0.946111	−	0.323843i	$-0.104975\pi$
$510$		0			0
$511$	15.0000	+	5.19615i	0.663561	+	0.229864i
$512$	1.00000			0.0441942
$513$	1.50000	−	2.59808i	0.0662266	−	0.114708i
$514$	−10.0000	−	17.3205i	−0.441081	−	0.763975i
$515$		0			0
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$	−5.00000			−0.219900
$518$	−27.5000	−	9.52628i	−1.20828	−	0.418561i
$519$	15.0000			0.658427
$520$		0			0
$521$	16.5000	+	28.5788i	0.722878	+	1.25206i	0.959841	+	0.280543i	$0.0905145\pi$
$521$	16.5000	+	28.5788i	0.722878	+	1.25206i	−0.236963	+	0.971519i	$0.576152\pi$
$522$	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
$530$		0			0
$531$	4.00000			0.173585
$532$	6.00000	−	5.19615i	0.260133	−	0.225282i
$533$	11.0000			0.476463
$534$	5.00000	−	8.66025i	0.216371	−	0.374766i
$535$		0			0
$536$		0			0
$537$	9.50000	−	16.4545i	0.409955	−	0.710063i
$538$	20.0000			0.862261
$539$	6.50000	−	2.59808i	0.279975	−	0.111907i
$540$		0			0
$541$	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
$545$		0			0
$546$	2.00000	−	1.73205i	0.0855921	−	0.0741249i
$547$	−16.0000			−0.684111			−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000			−0.684111			−0.342055	+	0.939680i	$0.611123\pi$
$548$	−9.00000	+	15.5885i	−0.384461	+	0.665906i
$549$		0			0
$550$		0			0
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$	−7.00000			−0.297940
$553$	4.00000	+	20.7846i	0.170097	+	0.883852i
$554$	22.0000			0.934690
$555$		0			0
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	−0.968769	−	0.247964i	$-0.920239\pi$
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	0.269642	−	0.962961i	$-0.413095\pi$
$558$	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
$565$		0			0
$566$	14.0000			0.588464
$567$	2.50000	+	0.866025i	0.104990	+	0.0363696i
$568$	−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	$0.106256\pi$
$570$		0			0
$571$	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
$574$	5.50000	+	28.5788i	0.229566	+	1.19286i
$575$		0			0
$576$	−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
$580$		0			0
$581$	16.0000	−	13.8564i	0.663792	−	0.574861i
$582$	16.0000			0.663221
$583$	5.50000	−	9.52628i	0.227787	−	0.394538i
$584$	−3.00000	−	5.19615i	−0.124141	−	0.215018i
$585$		0			0
$586$	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	$0.378854\pi$
$588$	5.50000	+	4.33013i	0.226816	+	0.178571i
$589$	6.00000			0.247226
$590$		0			0
$591$	−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			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$	4.00000	+	20.7846i	0.163028	+	0.847117i
$603$		0			0
$604$	−3.00000	+	5.19615i	−0.122068	+	0.211428i
$605$		0			0
$606$		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
$609$	−20.0000	−	6.92820i	−0.810441	−	0.280745i
$610$		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	$-0.856153\pi$
$613$	−20.5000	−	35.5070i	−0.827987	−	1.43412i	0.0716275	−	0.997431i	$-0.477181\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$		0			0
$616$	−2.50000	−	0.866025i	−0.100728	−	0.0348932i
$617$	−28.0000			−1.12724			−0.563619	−	0.826035i	$-0.690591\pi$
$617$	−28.0000			−1.12724			−0.563619	+	0.826035i	$0.690591\pi$
$618$	−8.00000	+	13.8564i	−0.321807	+	0.557386i
$619$	−14.5000	−	25.1147i	−0.582804	−	1.00945i	−0.995145	−	0.0984169i	$-0.968622\pi$
$619$	−14.5000	−	25.1147i	−0.582804	−	1.00945i	0.412341	−	0.911030i	$-0.364711\pi$
$620$		0			0
$621$	3.50000	−	6.06218i	0.140450	−	0.243267i
$622$	12.0000			0.481156
$623$	5.00000	+	25.9808i	0.200321	+	1.04090i
$624$	−1.00000			−0.0400320
$625$		0			0
$626$	−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
$635$		0			0
$636$	11.0000			0.436178
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$	8.00000			0.316723
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$	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	$0.436821\pi$
$644$	14.0000	−	12.1244i	0.551677	−	0.477767i
$645$		0			0
$646$		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
$650$		0			0
$651$	1.00000	+	5.19615i	0.0391931	+	0.203653i
$652$	−16.0000			−0.626608
$653$	3.50000	−	6.06218i	0.136966	−	0.237231i	−0.789381	−	0.613904i	$-0.789598\pi$
$653$	3.50000	−	6.06218i	0.136966	−	0.237231i	0.926347	+	0.376672i	$0.122932\pi$
$654$	−3.00000	−	5.19615i	−0.117309	−	0.203186i
$655$		0			0
$656$	5.50000	−	9.52628i	0.214739	−	0.371939i
$657$	6.00000			0.234082
$658$	12.5000	+	4.33013i	0.487301	+	0.168806i
$659$	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			0
$661$	12.0000	+	20.7846i	0.466746	+	0.808428i	0.999278	−	0.0379819i	$-0.0120929\pi$
$661$	12.0000	+	20.7846i	0.466746	+	0.808428i	−0.532533	+	0.846410i	$0.678760\pi$
$662$	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
$672$	−0.500000	−	2.59808i	−0.0192879	−	0.100223i
$673$	−28.0000			−1.07932			−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000			−1.07932			−0.539660	+	0.841883i	$0.681447\pi$
$674$	−6.00000	+	10.3923i	−0.231111	+	0.400297i
$675$		0			0
$676$	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
$679$	−32.0000	+	27.7128i	−1.22805	+	1.06352i
$680$		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	0.901750	−	0.432259i	$-0.142283\pi$
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	−0.825222	+	0.564809i	$0.808950\pi$
$684$	1.50000	−	2.59808i	0.0573539	−	0.0993399i
$685$		0			0
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$	14.0000			0.534133
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	5.50000	+	9.52628i	0.209533	+	0.362922i
$690$		0			0
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$	15.0000			0.570214
$693$	2.00000	−	1.73205i	0.0759737	−	0.0657952i
$694$	−14.0000			−0.531433
$695$		0			0
$696$	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
$705$		0			0
$706$	−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	$0.857149\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	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	−0.884070	−	0.467355i	$-0.845207\pi$
$719$	−1.00000	+	1.73205i	−0.0372937	+	0.0645946i	0.846776	+	0.531949i	$0.178540\pi$
$720$		0			0
$721$	−8.00000	−	41.5692i	−0.297936	−	1.54812i
$722$	−10.0000			−0.372161
$723$	−3.50000	+	6.06218i	−0.130166	+	0.225455i
$724$	12.0000	+	20.7846i	0.445976	+	0.772454i
$725$		0			0
$726$	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	$0.565389\pi$
$728$	2.00000	−	1.73205i	0.0741249	−	0.0641941i
$729$	1.00000			0.0370370
$730$		0			0
$731$		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	$0.719697\pi$
$740$		0			0
$741$	3.00000			0.110208
$742$	−22.0000	+	19.0526i	−0.807645	+	0.699441i
$743$	−49.0000			−1.79764			−0.898818	−	0.438322i	$-0.855573\pi$
$743$	−49.0000			−1.79764			−0.898818	+	0.438322i	$0.855573\pi$
$744$	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
$749$	−5.00000	−	25.9808i	−0.182696	−	0.949316i
$750$		0			0
$751$	−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
$755$		0			0
$756$	2.50000	+	0.866025i	0.0909241	+	0.0314970i
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	9.50000	−	16.4545i	0.345056	−	0.597654i
$759$	−3.50000	−	6.06218i	−0.127042	−	0.220043i
$760$		0			0
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$	17.0000			0.615845
$763$	15.0000	+	5.19615i	0.543036	+	0.188113i
$764$	−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	$-0.528735\pi$
$769$	−5.00000			−0.180305			−0.0901523	+	0.995928i	$0.528735\pi$
$770$		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
$775$		0			0
$776$	16.0000			0.574367
$777$	22.0000	−	19.0526i	0.789246	−	0.683507i
$778$	10.0000			0.358517
$779$	−16.5000	+	28.5788i	−0.591174	+	1.02394i
$780$		0			0
$781$	−3.00000	−	5.19615i	−0.107348	−	0.185933i
$782$		0			0
$783$	−8.00000			−0.285897
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$		0			0
$786$	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
$790$		0			0
$791$	12.0000	−	10.3923i	0.426671	−	0.369508i
$792$	−1.00000			−0.0355335
$793$		0			0
$794$	7.00000	+	12.1244i	0.248421	+	0.430277i
$795$		0			0
$796$	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	$0.396721\pi$
$798$	1.50000	+	7.79423i	0.0530994	+	0.275913i
$799$		0			0
$800$		0			0
$801$	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			0
$811$	9.00000			0.316033			0.158016	−	0.987436i	$-0.449490\pi$
$811$	9.00000			0.316033			0.158016	+	0.987436i	$0.449490\pi$
$812$	−20.0000	−	6.92820i	−0.701862	−	0.243132i
$813$	32.0000			1.12229
$814$	−5.50000	+	9.52628i	−0.192775	+	0.333896i
$815$		0			0
$816$		0			0
$817$	−12.0000	+	20.7846i	−0.419827	+	0.727161i
$818$	2.00000			0.0699284
$819$	0.500000	+	2.59808i	0.0174714	+	0.0907841i
$820$		0			0
$821$	−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	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$	−8.00000	+	13.8564i	−0.278693	+	0.482711i
$825$		0			0
$826$	−8.00000	+	6.92820i	−0.278356	+	0.241063i
$827$	10.0000			0.347734			0.173867	−	0.984769i	$-0.444374\pi$
$827$	10.0000			0.347734			0.173867	+	0.984769i	$0.444374\pi$
$828$	3.50000	−	6.06218i	0.121633	−	0.210675i
$829$	4.00000	+	6.92820i	0.138926	+	0.240626i	0.927090	−	0.374838i	$-0.122302\pi$
$829$	4.00000	+	6.92820i	0.138926	+	0.240626i	−0.788165	+	0.615465i	$0.788968\pi$
$830$		0			0
$831$	−11.0000	+	19.0526i	−0.381586	+	0.660926i
$832$	−1.00000			−0.0346688
$833$		0			0
$834$	20.0000			0.692543
$835$		0			0
$836$	−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	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$		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
$845$		0			0
$846$	5.00000			0.171904
$847$	5.00000	+	25.9808i	0.171802	+	0.892710i
$848$	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
$855$		0			0
$856$	−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	−0.950043	−	0.312120i	$-0.898961\pi$
$859$	−6.00000	+	10.3923i	−0.204717	+	0.354581i	0.745325	+	0.666701i	$0.232294\pi$
$860$		0			0
$861$	−27.5000	−	9.52628i	−0.937197	−	0.324655i
$862$		0			0
$863$	−26.5000	+	45.8993i	−0.902070	+	1.56243i	−0.0772684	+	0.997010i	$0.524620\pi$
$863$	−26.5000	+	45.8993i	−0.902070	+	1.56243i	−0.824802	+	0.565422i	$0.808713\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	−16.0000	+	27.7128i	−0.543702	+	0.941720i
$867$	−17.0000			−0.577350
$868$	1.00000	+	5.19615i	0.0339422	+	0.176369i
$869$	8.00000			0.271381
$870$		0			0
$871$		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	−0.686074	−	0.727532i	$-0.740667\pi$
$877$	8.50000	−	14.7224i	0.287025	−	0.497141i	0.973098	+	0.230391i	$0.0740005\pi$
$878$	−16.0000	−	27.7128i	−0.539974	−	0.935262i
$879$	13.5000	+	23.3827i	0.455344	+	0.788678i
$880$		0			0
$881$	−53.0000			−1.78562			−0.892808	−	0.450438i	$-0.851268\pi$
$881$	−53.0000			−1.78562			−0.892808	+	0.450438i	$0.851268\pi$
$882$	−6.50000	+	2.59808i	−0.218866	+	0.0874818i
$883$	42.0000			1.41341			0.706706	−	0.707507i	$-0.250180\pi$
$883$	42.0000			1.41341			0.706706	+	0.707507i	$0.250180\pi$
$884$		0			0
$885$		0			0
$886$	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
$889$	−34.0000	+	29.4449i	−1.14032	+	0.987549i
$890$		0			0
$891$	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
$895$		0			0
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$	7.00000			0.233723
$898$	−5.50000	+	9.52628i	−0.183537	+	0.317896i
$899$	−8.00000	−	13.8564i	−0.266815	−	0.462137i
$900$		0			0
$901$		0			0
$902$	11.0000			0.366260
$903$	−20.0000	−	6.92820i	−0.665558	−	0.230556i
$904$	−6.00000			−0.199557
$905$		0			0
$906$	−3.00000	−	5.19615i	−0.0996683	−	0.172631i
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	0.770996	−	0.636841i	$-0.219759\pi$
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	−0.937018	+	0.349281i	$0.886426\pi$
$908$	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
$917$	2.50000	+	12.9904i	0.0825573	+	0.428980i
$918$		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	$-0.0356925\pi$
$920$		0			0
$921$	10.0000	+	17.3205i	0.329511	+	0.570730i
$922$	6.00000	−	10.3923i	0.197599	−	0.342252i
$923$	6.00000			0.197492
$924$	2.00000	−	1.73205i	0.0657952	−	0.0569803i
$925$		0			0
$926$	−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	−0.640768	−	0.767735i	$-0.721384\pi$
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	0.985262	+	0.171054i	$0.0547172\pi$
$930$		0			0
$931$	−16.5000	−	12.9904i	−0.540766	−	0.425743i
$932$	−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
$940$		0			0
$941$	−27.0000	−	46.7654i	−0.880175	−	1.52451i	−0.851146	−	0.524929i	$-0.824092\pi$
$941$	−27.0000	−	46.7654i	−0.880175	−	1.52451i	−0.0290288	−	0.999579i	$-0.509241\pi$
$942$	−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	−0.630082	−	0.776528i	$-0.716979\pi$
$947$	11.0000	−	19.0526i	0.357452	−	0.619125i	0.987534	+	0.157403i	$0.0503122\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	3.00000	+	5.19615i	0.0973841	+	0.168674i
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$	20.0000			0.647864			0.323932	−	0.946080i	$-0.394995\pi$
$953$	20.0000			0.647864			0.323932	+	0.946080i	$0.394995\pi$
$954$	−5.50000	+	9.52628i	−0.178069	+	0.308425i
$955$		0			0
$956$	9.00000	+	15.5885i	0.291081	+	0.504167i
$957$	−4.00000	+	6.92820i	−0.129302	+	0.223957i
$958$	22.0000			0.710788
$959$	45.0000	+	15.5885i	1.45313	+	0.503378i
$960$		0			0
$961$	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
$965$		0			0
$966$	3.50000	+	18.1865i	0.112611	+	0.585142i
$967$	20.0000			0.643157			0.321578	−	0.946883i	$-0.395787\pi$
$967$	20.0000			0.643157			0.321578	+	0.946883i	$0.395787\pi$
$968$	5.00000	−	8.66025i	0.160706	−	0.278351i
$969$		0			0
$970$		0			0
$971$	22.5000	−	38.9711i	0.722059	−	1.25064i	−0.238114	−	0.971237i	$-0.576529\pi$
$971$	22.5000	−	38.9711i	0.722059	−	1.25064i	0.960173	−	0.279406i	$-0.0901376\pi$
$972$	1.00000			0.0320750
$973$	−40.0000	+	34.6410i	−1.28234	+	1.11054i
$974$	16.0000			0.512673
$975$		0			0
$976$		0			0
$977$	27.0000	+	46.7654i	0.863807	+	1.49616i	0.868227	+	0.496167i	$0.165259\pi$
$977$	27.0000	+	46.7654i	0.863807	+	1.49616i	−0.00442082	+	0.999990i	$0.501407\pi$
$978$	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			0
$986$		0			0
$987$	−10.0000	+	8.66025i	−0.318304	+	0.275659i
$988$	3.00000			0.0954427
$989$	−28.0000	+	48.4974i	−0.890348	+	1.54213i
$990$		0			0
$991$	−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
$994$	3.00000	+	15.5885i	0.0951542	+	0.494436i
$995$		0			0
$996$	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	1050.2.i.b.751.1		2
5.2	odd	4		1050.2.o.i.499.1		4
5.3	odd	4		1050.2.o.i.499.2		4
5.4	even	2		210.2.i.d.121.1	✓	2
7.2	even	3		7350.2.a.cp.1.1		1
7.4	even	3	inner	1050.2.i.b.151.1		2
7.5	odd	6		7350.2.a.bu.1.1		1
15.14	odd	2		630.2.k.c.541.1		2
20.19	odd	2		1680.2.bg.g.961.1		2
35.4	even	6		210.2.i.d.151.1	yes	2
35.9	even	6		1470.2.a.a.1.1		1
35.18	odd	12		1050.2.o.i.949.1		4
35.19	odd	6		1470.2.a.h.1.1		1
35.24	odd	6		1470.2.i.m.361.1		2
35.32	odd	12		1050.2.o.i.949.2		4
35.34	odd	2		1470.2.i.m.961.1		2
105.44	odd	6		4410.2.a.bj.1.1		1
105.74	odd	6		630.2.k.c.361.1		2
105.89	even	6		4410.2.a.ba.1.1		1
140.39	odd	6		1680.2.bg.g.1201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.d.121.1	✓	2	5.4	even	2
210.2.i.d.151.1	yes	2	35.4	even	6
630.2.k.c.361.1		2	105.74	odd	6
630.2.k.c.541.1		2	15.14	odd	2
1050.2.i.b.151.1		2	7.4	even	3	inner
1050.2.i.b.751.1		2	1.1	even	1	trivial
1050.2.o.i.499.1		4	5.2	odd	4
1050.2.o.i.499.2		4	5.3	odd	4
1050.2.o.i.949.1		4	35.18	odd	12
1050.2.o.i.949.2		4	35.32	odd	12
1470.2.a.a.1.1		1	35.9	even	6
1470.2.a.h.1.1		1	35.19	odd	6
1470.2.i.m.361.1		2	35.24	odd	6
1470.2.i.m.961.1		2	35.34	odd	2
1680.2.bg.g.961.1		2	20.19	odd	2
1680.2.bg.g.1201.1		2	140.39	odd	6
4410.2.a.ba.1.1		1	105.89	even	6
4410.2.a.bj.1.1		1	105.44	odd	6
7350.2.a.bu.1.1		1	7.5	odd	6
7350.2.a.cp.1.1		1	7.2	even	3

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{18} +(1.50000 - 2.59808i) q^{19} +(2.50000 + 0.866025i) q^{21} -1.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{26} +1.00000 q^{27} +(2.50000 + 0.866025i) q^{28} -8.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +1.00000 q^{36} +(5.50000 - 9.52628i) q^{37} +(1.50000 + 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{39} -11.0000 q^{41} +(-2.00000 + 1.73205i) q^{42} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(3.50000 + 6.06218i) q^{46} +(-2.50000 + 4.33013i) q^{47} +1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +(0.500000 + 0.866025i) q^{52} +(-5.50000 - 9.52628i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} -3.00000 q^{57} +(4.00000 - 6.92820i) q^{58} +(-2.00000 - 3.46410i) q^{59} -2.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} -7.00000 q^{69} -6.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(5.50000 + 9.52628i) q^{74} -3.00000 q^{76} +(-2.50000 - 0.866025i) q^{77} -1.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.50000 - 9.52628i) q^{82} -8.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} +(4.00000 + 6.92820i) q^{87} +(0.500000 + 0.866025i) q^{88} +(5.00000 - 8.66025i) q^{89} +(2.00000 - 1.73205i) q^{91} -7.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(-2.50000 - 4.33013i) q^{94} +(-0.500000 + 0.866025i) q^{96} +16.0000 q^{97} +(5.50000 + 4.33013i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + q^{11} - q^{12} - 2 q^{13} - q^{14} - q^{16} - q^{18} + 3 q^{19} + 5 q^{21} - 2 q^{22} + 7 q^{23} - q^{24} + q^{26} + 2 q^{27} + 5 q^{28} - 16 q^{29} + 2 q^{31} - q^{32} + q^{33} + 2 q^{36} + 11 q^{37} + 3 q^{38} + q^{39} - 22 q^{41} - 4 q^{42} - 16 q^{43} + q^{44} + 7 q^{46} - 5 q^{47} + 2 q^{48} + 2 q^{49} + q^{52} - 11 q^{53} - q^{54} - 4 q^{56} - 6 q^{57} + 8 q^{58} - 4 q^{59} - 4 q^{62} - q^{63} + 2 q^{64} + q^{66} - 14 q^{69} - 12 q^{71} - q^{72} - 6 q^{73} + 11 q^{74} - 6 q^{76} - 5 q^{77} - 2 q^{78} + 8 q^{79} - q^{81} + 11 q^{82} - 16 q^{83} - q^{84} + 8 q^{86} + 8 q^{87} + q^{88} + 10 q^{89} + 4 q^{91} - 14 q^{92} + 2 q^{93} - 5 q^{94} - q^{96} + 32 q^{97} + 11 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - q^9 + q^11 - q^12 - 2 * q^13 - q^14 - q^16 - q^18 + 3 * q^19 + 5 * q^21 - 2 * q^22 + 7 * q^23 - q^24 + q^26 + 2 * q^27 + 5 * q^28 - 16 * q^29 + 2 * q^31 - q^32 + q^33 + 2 * q^36 + 11 * q^37 + 3 * q^38 + q^39 - 22 * q^41 - 4 * q^42 - 16 * q^43 + q^44 + 7 * q^46 - 5 * q^47 + 2 * q^48 + 2 * q^49 + q^52 - 11 * q^53 - q^54 - 4 * q^56 - 6 * q^57 + 8 * q^58 - 4 * q^59 - 4 * q^62 - q^63 + 2 * q^64 + q^66 - 14 * q^69 - 12 * q^71 - q^72 - 6 * q^73 + 11 * q^74 - 6 * q^76 - 5 * q^77 - 2 * q^78 + 8 * q^79 - q^81 + 11 * q^82 - 16 * q^83 - q^84 + 8 * q^86 + 8 * q^87 + q^88 + 10 * q^89 + 4 * q^91 - 14 * q^92 + 2 * q^93 - 5 * q^94 - q^96 + 32 * q^97 + 11 * q^98 - 2 * q^99

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