LMFDB - Embedded newform 294.2.f.b.215.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(215,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("294.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.f (of order $6$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	294.215
Dual form			294.2.f.b.227.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(1.22474 + 1.22474i) q^{6} -1.00000i q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(1.22474 + 1.22474i) q^{6} -1.00000i q^{8} +(2.59808 + 1.50000i) q^{9} +(-2.12132 + 1.22474i) q^{10} +(-0.448288 - 1.67303i) q^{12} -2.44949i q^{13} +(-3.00000 + 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.44949 - 4.24264i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(-2.12132 - 1.22474i) q^{19} +2.44949 q^{20} +(-5.19615 - 3.00000i) q^{23} +(-0.448288 + 1.67303i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.22474 + 2.12132i) q^{26} +(-3.67423 - 3.67423i) q^{27} -6.00000i q^{29} +(4.09808 - 1.09808i) q^{30} +(0.866025 - 0.500000i) q^{32} +4.89898i q^{34} +3.00000i q^{36} +(1.00000 - 1.73205i) q^{37} +(1.22474 + 2.12132i) q^{38} +(-1.09808 + 4.09808i) q^{39} +(-2.12132 - 1.22474i) q^{40} -4.89898 q^{41} +4.00000 q^{43} +(6.36396 - 3.67423i) q^{45} +(3.00000 + 5.19615i) q^{46} +(-2.44949 + 4.24264i) q^{47} +(1.22474 - 1.22474i) q^{48} +1.00000i q^{50} +(2.19615 + 8.19615i) q^{51} +(2.12132 - 1.22474i) q^{52} +(5.19615 - 3.00000i) q^{53} +(1.34486 + 5.01910i) q^{54} +(3.00000 + 3.00000i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(6.12372 + 10.6066i) q^{59} +(-4.09808 - 1.09808i) q^{60} +(10.6066 + 6.12372i) q^{61} -1.00000 q^{64} +(-5.19615 - 3.00000i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(2.44949 - 4.24264i) q^{68} +(7.34847 + 7.34847i) q^{69} +(1.50000 - 2.59808i) q^{72} +(8.48528 - 4.89898i) q^{73} +(-1.73205 + 1.00000i) q^{74} +(0.448288 + 1.67303i) q^{75} -2.44949i q^{76} +(3.00000 - 3.00000i) q^{78} +(5.00000 - 8.66025i) q^{79} +(1.22474 + 2.12132i) q^{80} +(4.50000 + 7.79423i) q^{81} +(4.24264 + 2.44949i) q^{82} +2.44949 q^{83} -12.0000 q^{85} +(-3.46410 - 2.00000i) q^{86} +(-2.68973 + 10.0382i) q^{87} -7.34847 q^{90} -6.00000i q^{92} +(4.24264 - 2.44949i) q^{94} +(-5.19615 + 3.00000i) q^{95} +(-1.67303 + 0.448288i) q^{96} +4.89898i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 24 q^{15} - 4 q^{16} - 12 q^{18} - 4 q^{25} + 12 q^{30} + 8 q^{37} + 12 q^{39} + 32 q^{43} + 24 q^{46} - 24 q^{51} + 24 q^{57} - 24 q^{58} - 12 q^{60} - 8 q^{64} - 32 q^{67} + 12 q^{72} + 24 q^{78} + 40 q^{79} + 36 q^{81} - 96 q^{85}+O(q^{100}) $ 8 * q + 4 * q^4 - 24 * q^15 - 4 * q^16 - 12 * q^18 - 4 * q^25 + 12 * q^30 + 8 * q^37 + 12 * q^39 + 32 * q^43 + 24 * q^46 - 24 * q^51 + 24 * q^57 - 24 * q^58 - 12 * q^60 - 8 * q^64 - 32 * q^67 + 12 * q^72 + 24 * q^78 + 40 * q^79 + 36 * q^81 - 96 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	−0.450708	−	0.892672i	$-0.648828\pi$
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	0.998430	−	0.0560116i	$-0.0178384\pi$
$6$	1.22474	+	1.22474i	0.500000	+	0.500000i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$	−2.12132	+	1.22474i	−0.670820	+	0.387298i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	−0.448288	−	1.67303i	−0.129410	−	0.482963i
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$		0			0
$15$	−3.00000	+	3.00000i	−0.774597	+	0.774597i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.44949	−	4.24264i	−0.594089	−	1.02899i	−0.993675	−	0.112296i	$-0.964180\pi$
$17$	−2.44949	−	4.24264i	−0.594089	−	1.02899i	0.399586	−	0.916696i	$-0.369154\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	−2.12132	−	1.22474i	−0.486664	−	0.280976i	0.236525	−	0.971625i	$-0.423991\pi$
$19$	−2.12132	−	1.22474i	−0.486664	−	0.280976i	−0.723190	+	0.690650i	$0.757325\pi$
$20$	2.44949			0.547723
$21$		0			0
$22$		0			0
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.151642	−	0.988436i	$-0.548456\pi$
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.931831	+	0.362892i	$0.881789\pi$
$24$	−0.448288	+	1.67303i	−0.0915064	+	0.341506i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.22474	+	2.12132i	−0.240192	+	0.416025i
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$		0			0
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$	4.09808	−	1.09808i	0.748203	−	0.200480i
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			4.89898i			0.840168i
$35$		0			0
$36$			3.00000i			0.500000i
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	1.22474	+	2.12132i	0.198680	+	0.344124i
$39$	−1.09808	+	4.09808i	−0.175833	+	0.656217i
$40$	−2.12132	−	1.22474i	−0.335410	−	0.193649i
$41$	−4.89898			−0.765092			−0.382546	−	0.923936i	$-0.624953\pi$
$41$	−4.89898			−0.765092			−0.382546	+	0.923936i	$0.624953\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	6.36396	−	3.67423i	0.948683	−	0.547723i
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	−2.44949	+	4.24264i	−0.357295	+	0.618853i	−0.987508	−	0.157569i	$-0.949634\pi$
$47$	−2.44949	+	4.24264i	−0.357295	+	0.618853i	0.630213	+	0.776422i	$0.282968\pi$
$48$	1.22474	−	1.22474i	0.176777	−	0.176777i
$49$		0			0
$50$			1.00000i			0.141421i
$51$	2.19615	+	8.19615i	0.307523	+	1.14769i
$52$	2.12132	−	1.22474i	0.294174	−	0.169842i
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	−0.0987002	−	0.995117i	$-0.531468\pi$
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	0.812447	+	0.583036i	$0.198135\pi$
$54$	1.34486	+	5.01910i	0.183013	+	0.683013i
$55$		0			0
$56$		0			0
$57$	3.00000	+	3.00000i	0.397360	+	0.397360i
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	6.12372	+	10.6066i	0.797241	+	1.38086i	0.921406	+	0.388600i	$0.127041\pi$
$59$	6.12372	+	10.6066i	0.797241	+	1.38086i	−0.124165	+	0.992262i	$0.539625\pi$
$60$	−4.09808	−	1.09808i	−0.529059	−	0.141761i
$61$	10.6066	+	6.12372i	1.35804	+	0.784063i	0.989359	−	0.145495i	$-0.0464774\pi$
$61$	10.6066	+	6.12372i	1.35804	+	0.784063i	0.368677	+	0.929557i	$0.379811\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.19615	−	3.00000i	−0.644503	−	0.372104i
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	2.44949	−	4.24264i	0.297044	−	0.514496i
$69$	7.34847	+	7.34847i	0.884652	+	0.884652i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	8.48528	−	4.89898i	0.993127	−	0.573382i	0.0869195	−	0.996215i	$-0.472298\pi$
$73$	8.48528	−	4.89898i	0.993127	−	0.573382i	0.906208	+	0.422833i	$0.138964\pi$
$74$	−1.73205	+	1.00000i	−0.201347	+	0.116248i
$75$	0.448288	+	1.67303i	0.0517638	+	0.193185i
$76$		−	2.44949i		−	0.280976i
$77$		0			0
$78$	3.00000	−	3.00000i	0.339683	−	0.339683i
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	1.22474	+	2.12132i	0.136931	+	0.237171i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	4.24264	+	2.44949i	0.468521	+	0.270501i
$83$	2.44949			0.268866			0.134433	−	0.990923i	$-0.457079\pi$
$83$	2.44949			0.268866			0.134433	+	0.990923i	$0.457079\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	−3.46410	−	2.00000i	−0.373544	−	0.215666i
$87$	−2.68973	+	10.0382i	−0.288369	+	1.07621i
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	−7.34847			−0.774597
$91$		0			0
$92$		−	6.00000i		−	0.625543i
$93$		0			0
$94$	4.24264	−	2.44949i	0.437595	−	0.252646i
$95$	−5.19615	+	3.00000i	−0.533114	+	0.307794i
$96$	−1.67303	+	0.448288i	−0.170753	+	0.0457532i
$97$			4.89898i			0.497416i	0.968579	+	0.248708i	$0.0800060\pi$
$97$			4.89898i			0.497416i	−0.968579	+	0.248708i	$0.919994\pi$
$98$		0			0
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−3.67423	−	6.36396i	−0.365600	−	0.633238i	0.623272	−	0.782005i	$-0.285803\pi$
$101$	−3.67423	−	6.36396i	−0.365600	−	0.633238i	−0.988872	+	0.148767i	$0.952470\pi$
$102$	2.19615	−	8.19615i	0.217451	−	0.811540i
$103$	−8.48528	−	4.89898i	−0.836080	−	0.482711i	0.0198501	−	0.999803i	$-0.493681\pi$
$103$	−8.48528	−	4.89898i	−0.836080	−	0.482711i	−0.855930	+	0.517092i	$0.827014\pi$
$104$	−2.44949			−0.240192
$105$		0			0
$106$	−6.00000			−0.582772
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.909624	−	0.415432i	$-0.136370\pi$
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.0950377	+	0.995474i	$0.469703\pi$
$108$	1.34486	−	5.01910i	0.129410	−	0.482963i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$		0			0
$111$	−2.44949	+	2.44949i	−0.232495	+	0.232495i
$112$		0			0
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	−1.09808	−	4.09808i	−0.102844	−	0.383820i
$115$	−12.7279	+	7.34847i	−1.18688	+	0.685248i
$116$	5.19615	−	3.00000i	0.482451	−	0.278543i
$117$	3.67423	−	6.36396i	0.339683	−	0.588348i
$118$		−	12.2474i		−	1.12747i
$119$		0			0
$120$	3.00000	+	3.00000i	0.273861	+	0.273861i
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$	−6.12372	−	10.6066i	−0.554416	−	0.960277i
$123$	8.19615	+	2.19615i	0.739022	+	0.198020i
$124$		0			0
$125$	9.79796			0.876356
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−6.69213	−	1.79315i	−0.589209	−	0.157878i
$130$	3.00000	+	5.19615i	0.263117	+	0.455733i
$131$	−3.67423	+	6.36396i	−0.321019	+	0.556022i	−0.980699	−	0.195525i	$-0.937359\pi$
$131$	−3.67423	+	6.36396i	−0.321019	+	0.556022i	0.659679	+	0.751547i	$0.270692\pi$
$132$		0			0
$133$		0			0
$134$			8.00000i			0.691095i
$135$	−12.2942	+	3.29423i	−1.05812	+	0.283522i
$136$	−4.24264	+	2.44949i	−0.363803	+	0.210042i
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.873247	−	0.487278i	$-0.837990\pi$
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.0146279	+	0.999893i	$0.504656\pi$
$138$	−2.68973	−	10.0382i	−0.228965	−	0.854508i
$139$			2.44949i			0.207763i	0.994590	+	0.103882i	$0.0331263\pi$
$139$			2.44949i			0.207763i	−0.994590	+	0.103882i	$0.966874\pi$
$140$		0			0
$141$	6.00000	−	6.00000i	0.505291	−	0.505291i
$142$		0			0
$143$		0			0
$144$	−2.59808	+	1.50000i	−0.216506	+	0.125000i
$145$	−12.7279	−	7.34847i	−1.05700	−	0.610257i
$146$	−9.79796			−0.810885
$147$		0			0
$148$	2.00000			0.164399
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	0.697507	−	0.716578i	$-0.254293\pi$
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	−0.271821	+	0.962348i	$0.587626\pi$
$150$	0.448288	−	1.67303i	0.0366025	−	0.136603i
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	−1.22474	+	2.12132i	−0.0993399	+	0.172062i
$153$		−	14.6969i		−	1.18818i
$154$		0			0
$155$		0			0
$156$	−4.09808	+	1.09808i	−0.328109	+	0.0879165i
$157$	−6.36396	+	3.67423i	−0.507899	+	0.293236i	−0.731970	−	0.681337i	$-0.761399\pi$
$157$	−6.36396	+	3.67423i	−0.507899	+	0.293236i	0.224070	+	0.974573i	$0.428065\pi$
$158$	−8.66025	+	5.00000i	−0.688973	+	0.397779i
$159$	−10.0382	+	2.68973i	−0.796081	+	0.213309i
$160$		−	2.44949i		−	0.193649i
$161$		0			0
$162$		−	9.00000i		−	0.707107i
$163$	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	$-0.0488907\pi$
$164$	−2.44949	−	4.24264i	−0.191273	−	0.331295i
$165$		0			0
$166$	−2.12132	−	1.22474i	−0.164646	−	0.0950586i
$167$	4.89898			0.379094			0.189547	−	0.981872i	$-0.439298\pi$
$167$	4.89898			0.379094			0.189547	+	0.981872i	$0.439298\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$	10.3923	+	6.00000i	0.797053	+	0.460179i
$171$	−3.67423	−	6.36396i	−0.280976	−	0.486664i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	11.0227	−	19.0919i	0.838041	−	1.45153i	−0.0534899	−	0.998568i	$-0.517034\pi$
$173$	11.0227	−	19.0919i	0.838041	−	1.45153i	0.891531	−	0.452961i	$-0.149632\pi$
$174$	7.34847	−	7.34847i	0.557086	−	0.557086i
$175$		0			0
$176$		0			0
$177$	−5.49038	−	20.4904i	−0.412682	−	1.54015i
$178$		0			0
$179$	20.7846	−	12.0000i	1.55351	−	0.896922i	0.555663	−	0.831408i	$-0.312464\pi$
$179$	20.7846	−	12.0000i	1.55351	−	0.896922i	0.997852	−	0.0655145i	$-0.0208689\pi$
$180$	6.36396	+	3.67423i	0.474342	+	0.273861i
$181$			12.2474i			0.910346i	0.890403	+	0.455173i	$0.150423\pi$
$181$			12.2474i			0.910346i	−0.890403	+	0.455173i	$0.849577\pi$
$182$		0			0
$183$	−15.0000	−	15.0000i	−1.10883	−	1.10883i
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	−2.44949	−	4.24264i	−0.180090	−	0.311925i
$186$		0			0
$187$		0			0
$188$	−4.89898			−0.357295
$189$		0			0
$190$	6.00000			0.435286
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	1.67303	+	0.448288i	0.120741	+	0.0323524i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	2.44949	−	4.24264i	0.175863	−	0.304604i
$195$	7.34847	+	7.34847i	0.526235	+	0.526235i
$196$		0			0
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		0			0
$199$	−8.48528	+	4.89898i	−0.601506	+	0.347279i	−0.769634	−	0.638486i	$-0.779561\pi$
$199$	−8.48528	+	4.89898i	−0.601506	+	0.347279i	0.168128	+	0.985765i	$0.446228\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	3.58630	+	13.3843i	0.252958	+	0.944053i
$202$			7.34847i			0.517036i
$203$		0			0
$204$	−6.00000	+	6.00000i	−0.420084	+	0.420084i
$205$	−6.00000	+	10.3923i	−0.419058	+	0.725830i
$206$	4.89898	+	8.48528i	0.341328	+	0.591198i
$207$	−9.00000	−	15.5885i	−0.625543	−	1.08347i
$208$	2.12132	+	1.22474i	0.147087	+	0.0849208i
$209$		0			0
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	5.19615	+	3.00000i	0.356873	+	0.206041i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	4.89898	−	8.48528i	0.334108	−	0.578691i
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$		0			0
$218$			10.0000i			0.677285i
$219$	−16.3923	+	4.39230i	−1.10769	+	0.296804i
$220$		0			0
$221$	−10.3923	+	6.00000i	−0.699062	+	0.403604i
$222$	3.34607	−	0.896575i	0.224573	−	0.0601742i
$223$		−	14.6969i		−	0.984180i	−0.870544	−	0.492090i	$-0.836233\pi$
$223$		−	14.6969i		−	0.984180i	0.870544	−	0.492090i	$-0.163767\pi$
$224$		0			0
$225$		−	3.00000i		−	0.200000i
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	3.67423	+	6.36396i	0.243868	+	0.422391i	0.961813	−	0.273709i	$-0.0882505\pi$
$227$	3.67423	+	6.36396i	0.243868	+	0.422391i	−0.717945	+	0.696100i	$0.754917\pi$
$228$	−1.09808	+	4.09808i	−0.0727219	+	0.271402i
$229$	19.0919	+	11.0227i	1.26163	+	0.728401i	0.973389	−	0.229158i	$-0.0735973\pi$
$229$	19.0919	+	11.0227i	1.26163	+	0.728401i	0.288238	+	0.957559i	$0.406931\pi$
$230$	14.6969			0.969087
$231$		0			0
$232$	−6.00000			−0.393919
$233$	20.7846	+	12.0000i	1.36165	+	0.786146i	0.989843	−	0.142166i	$-0.0454066\pi$
$233$	20.7846	+	12.0000i	1.36165	+	0.786146i	0.371802	+	0.928312i	$0.378740\pi$
$234$	−6.36396	+	3.67423i	−0.416025	+	0.240192i
$235$	6.00000	+	10.3923i	0.391397	+	0.677919i
$236$	−6.12372	+	10.6066i	−0.398621	+	0.690431i
$237$	−12.2474	+	12.2474i	−0.795557	+	0.795557i
$238$		0			0
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$	−1.09808	−	4.09808i	−0.0708805	−	0.264530i
$241$	21.2132	−	12.2474i	1.36646	−	0.788928i	0.375988	−	0.926624i	$-0.377303\pi$
$241$	21.2132	−	12.2474i	1.36646	−	0.788928i	0.990474	+	0.137697i	$0.0439700\pi$
$242$	9.52628	−	5.50000i	0.612372	−	0.353553i
$243$	−4.03459	−	15.0573i	−0.258819	−	0.965926i
$244$			12.2474i			0.784063i
$245$		0			0
$246$	−6.00000	−	6.00000i	−0.382546	−	0.382546i
$247$	−3.00000	+	5.19615i	−0.190885	+	0.330623i
$248$		0			0
$249$	−4.09808	−	1.09808i	−0.259705	−	0.0695878i
$250$	−8.48528	−	4.89898i	−0.536656	−	0.309839i
$251$	−17.1464			−1.08227			−0.541136	−	0.840935i	$-0.682006\pi$
$251$	−17.1464			−1.08227			−0.541136	+	0.840935i	$0.682006\pi$
$252$		0			0
$253$		0			0
$254$	−6.92820	−	4.00000i	−0.434714	−	0.250982i
$255$	20.0764	+	5.37945i	1.25723	+	0.336874i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.6969	+	25.4558i	−0.916770	+	1.58789i	−0.112481	+	0.993654i	$0.535880\pi$
$257$	−14.6969	+	25.4558i	−0.916770	+	1.58789i	−0.804289	+	0.594238i	$0.797454\pi$
$258$	4.89898	+	4.89898i	0.304997	+	0.304997i
$259$		0			0
$260$		−	6.00000i		−	0.372104i
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$	6.36396	−	3.67423i	0.393167	−	0.226995i
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.977147	−	0.212565i	$-0.931818\pi$
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.304487	+	0.952517i	$0.598485\pi$
$264$		0			0
$265$		−	14.6969i		−	0.902826i
$266$		0			0
$267$		0			0
$268$	4.00000	−	6.92820i	0.244339	−	0.423207i
$269$	6.12372	+	10.6066i	0.373370	+	0.646696i	0.990082	−	0.140493i	$-0.0448688\pi$
$269$	6.12372	+	10.6066i	0.373370	+	0.646696i	−0.616712	+	0.787189i	$0.711536\pi$
$270$	12.2942	+	3.29423i	0.748203	+	0.200480i
$271$	21.2132	+	12.2474i	1.28861	+	0.743980i	0.978406	−	0.206691i	$-0.0662693\pi$
$271$	21.2132	+	12.2474i	1.28861	+	0.743980i	0.310204	+	0.950670i	$0.399603\pi$
$272$	4.89898			0.297044
$273$		0			0
$274$	12.0000			0.724947
$275$		0			0
$276$	−2.68973	+	10.0382i	−0.161903	+	0.604228i
$277$	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	$0.603497\pi$
$278$	1.22474	−	2.12132i	0.0734553	−	0.127228i
$279$		0			0
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−8.19615	+	2.19615i	−0.488074	+	0.130779i
$283$	19.0919	−	11.0227i	1.13489	−	0.655232i	0.189733	−	0.981836i	$-0.439238\pi$
$283$	19.0919	−	11.0227i	1.13489	−	0.655232i	0.945161	+	0.326604i	$0.105904\pi$
$284$		0			0
$285$	10.0382	−	2.68973i	0.594611	−	0.159326i
$286$		0			0
$287$		0			0
$288$	3.00000			0.176777
$289$	−3.50000	+	6.06218i	−0.205882	+	0.356599i
$290$	7.34847	+	12.7279i	0.431517	+	0.747409i
$291$	2.19615	−	8.19615i	0.128741	−	0.480467i
$292$	8.48528	+	4.89898i	0.496564	+	0.286691i
$293$	2.44949			0.143101			0.0715504	−	0.997437i	$-0.477205\pi$
$293$	2.44949			0.143101			0.0715504	+	0.997437i	$0.477205\pi$
$294$		0			0
$295$	30.0000			1.74667
$296$	−1.73205	−	1.00000i	−0.100673	−	0.0581238i
$297$		0			0
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−7.34847	+	12.7279i	−0.424973	+	0.736075i
$300$	−1.22474	+	1.22474i	−0.0707107	+	0.0707107i
$301$		0			0
$302$		−	8.00000i		−	0.460348i
$303$	3.29423	+	12.2942i	0.189248	+	0.706285i
$304$	2.12132	−	1.22474i	0.121666	−	0.0702439i
$305$	25.9808	−	15.0000i	1.48765	−	0.858898i
$306$	−7.34847	+	12.7279i	−0.420084	+	0.727607i
$307$		−	7.34847i		−	0.419399i	−0.977766	−	0.209700i	$-0.932751\pi$
$307$		−	7.34847i		−	0.419399i	0.977766	−	0.209700i	$-0.0672486\pi$
$308$		0			0
$309$	12.0000	+	12.0000i	0.682656	+	0.682656i
$310$		0			0
$311$	−9.79796	−	16.9706i	−0.555591	−	0.962312i	−0.997857	−	0.0654284i	$-0.979159\pi$
$311$	−9.79796	−	16.9706i	−0.555591	−	0.962312i	0.442266	−	0.896884i	$-0.354175\pi$
$312$	4.09808	+	1.09808i	0.232008	+	0.0621663i
$313$	−29.6985	−	17.1464i	−1.67866	−	0.969173i	−0.962519	−	0.271216i	$-0.912574\pi$
$313$	−29.6985	−	17.1464i	−1.67866	−	0.969173i	−0.716139	−	0.697958i	$-0.754092\pi$
$314$	7.34847			0.414698
$315$		0			0
$316$	10.0000			0.562544
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.00635137	−	0.999980i	$-0.502022\pi$
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.869184	+	0.494489i	$0.835355\pi$
$318$	10.0382	+	2.68973i	0.562914	+	0.150832i
$319$		0			0
$320$	−1.22474	+	2.12132i	−0.0684653	+	0.118585i
$321$	−14.6969	−	14.6969i	−0.820303	−	0.820303i
$322$		0			0
$323$			12.0000i			0.667698i
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−2.12132	+	1.22474i	−0.117670	+	0.0679366i
$326$	−13.8564	+	8.00000i	−0.767435	+	0.443079i
$327$	4.48288	+	16.7303i	0.247904	+	0.925189i
$328$			4.89898i			0.270501i
$329$		0			0
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	1.22474	+	2.12132i	0.0672166	+	0.116423i
$333$	5.19615	−	3.00000i	0.284747	−	0.164399i
$334$	−4.24264	−	2.44949i	−0.232147	−	0.134030i
$335$	−19.5959			−1.07064
$336$		0			0
$337$	−32.0000			−1.74315			−0.871576	−	0.490261i	$-0.836901\pi$
$337$	−32.0000			−1.74315			−0.871576	+	0.490261i	$0.836901\pi$
$338$	−6.06218	−	3.50000i	−0.329739	−	0.190375i
$339$	2.68973	−	10.0382i	0.146086	−	0.545200i
$340$	−6.00000	−	10.3923i	−0.325396	−	0.563602i
$341$		0			0
$342$			7.34847i			0.397360i
$343$		0			0
$344$		−	4.00000i		−	0.215666i
$345$	24.5885	−	6.58846i	1.32380	−	0.354711i
$346$	−19.0919	+	11.0227i	−1.02639	+	0.592584i
$347$	−10.3923	+	6.00000i	−0.557888	+	0.322097i	−0.752297	−	0.658824i	$-0.771054\pi$
$347$	−10.3923	+	6.00000i	−0.557888	+	0.322097i	0.194409	+	0.980921i	$0.437721\pi$
$348$	−10.0382	+	2.68973i	−0.538104	+	0.144184i
$349$			2.44949i			0.131118i	0.997849	+	0.0655591i	$0.0208831\pi$
$349$			2.44949i			0.131118i	−0.997849	+	0.0655591i	$0.979117\pi$
$350$		0			0
$351$	−9.00000	+	9.00000i	−0.480384	+	0.480384i
$352$		0			0
$353$	4.89898	+	8.48528i	0.260746	+	0.451626i	0.966440	−	0.256891i	$-0.0826980\pi$
$353$	4.89898	+	8.48528i	0.260746	+	0.451626i	−0.705694	+	0.708517i	$0.749365\pi$
$354$	−5.49038	+	20.4904i	−0.291810	+	1.08905i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−24.0000			−1.26844
$359$	5.19615	+	3.00000i	0.274242	+	0.158334i	0.630814	−	0.775934i	$-0.282721\pi$
$359$	5.19615	+	3.00000i	0.274242	+	0.158334i	−0.356572	+	0.934268i	$0.616054\pi$
$360$	−3.67423	−	6.36396i	−0.193649	−	0.335410i
$361$	−6.50000	−	11.2583i	−0.342105	−	0.592544i
$362$	6.12372	−	10.6066i	0.321856	−	0.557471i
$363$	13.4722	−	13.4722i	0.707107	−	0.707107i
$364$		0			0
$365$		−	24.0000i		−	1.25622i
$366$	5.49038	+	20.4904i	0.286987	+	1.07105i
$367$	4.24264	−	2.44949i	0.221464	−	0.127862i	−0.385164	−	0.922848i	$-0.625855\pi$
$367$	4.24264	−	2.44949i	0.221464	−	0.127862i	0.606628	+	0.794986i	$0.292522\pi$
$368$	5.19615	−	3.00000i	0.270868	−	0.156386i
$369$	−12.7279	−	7.34847i	−0.662589	−	0.382546i
$370$			4.89898i			0.254686i
$371$		0			0
$372$		0			0
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$		0			0
$375$	−16.3923	−	4.39230i	−0.846495	−	0.226818i
$376$	4.24264	+	2.44949i	0.218797	+	0.126323i
$377$	−14.6969			−0.756931
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−5.19615	−	3.00000i	−0.266557	−	0.153897i
$381$	−13.3843	−	3.58630i	−0.685696	−	0.183732i
$382$		0			0
$383$	17.1464	−	29.6985i	0.876142	−	1.51752i	0.0205998	−	0.999788i	$-0.493442\pi$
$383$	17.1464	−	29.6985i	0.876142	−	1.51752i	0.855542	−	0.517734i	$-0.173224\pi$
$384$	−1.22474	−	1.22474i	−0.0625000	−	0.0625000i
$385$		0			0
$386$			4.00000i			0.203595i
$387$	10.3923	+	6.00000i	0.528271	+	0.304997i
$388$	−4.24264	+	2.44949i	−0.215387	+	0.124354i
$389$	−5.19615	+	3.00000i	−0.263455	+	0.152106i	−0.625910	−	0.779895i	$-0.715272\pi$
$389$	−5.19615	+	3.00000i	−0.263455	+	0.152106i	0.362454	+	0.932002i	$0.381939\pi$
$390$	−2.68973	−	10.0382i	−0.136200	−	0.508304i
$391$			29.3939i			1.48651i
$392$		0			0
$393$	9.00000	−	9.00000i	0.453990	−	0.453990i
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	−12.2474	−	21.2132i	−0.616236	−	1.06735i
$396$		0			0
$397$	6.36396	+	3.67423i	0.319398	+	0.184405i	0.651124	−	0.758971i	$-0.274298\pi$
$397$	6.36396	+	3.67423i	0.319398	+	0.184405i	−0.331726	+	0.943376i	$0.607631\pi$
$398$	9.79796			0.491127
$399$		0			0
$400$	1.00000			0.0500000
$401$	−25.9808	−	15.0000i	−1.29742	−	0.749064i	−0.317460	−	0.948272i	$-0.602830\pi$
$401$	−25.9808	−	15.0000i	−1.29742	−	0.749064i	−0.979957	+	0.199207i	$0.936163\pi$
$402$	3.58630	−	13.3843i	0.178868	−	0.667546i
$403$		0			0
$404$	3.67423	−	6.36396i	0.182800	−	0.316619i
$405$	22.0454			1.09545
$406$		0			0
$407$		0			0
$408$	8.19615	−	2.19615i	0.405770	−	0.108726i
$409$	−29.6985	+	17.1464i	−1.46850	+	0.847836i	−0.999377	−	0.0352988i	$-0.988762\pi$
$409$	−29.6985	+	17.1464i	−1.46850	+	0.847836i	−0.469119	+	0.883135i	$0.655428\pi$
$410$	10.3923	−	6.00000i	0.513239	−	0.296319i
$411$	20.0764	−	5.37945i	0.990295	−	0.265349i
$412$		−	9.79796i		−	0.482711i
$413$		0			0
$414$			18.0000i			0.884652i
$415$	3.00000	−	5.19615i	0.147264	−	0.255069i
$416$	−1.22474	−	2.12132i	−0.0600481	−	0.104006i
$417$	1.09808	−	4.09808i	0.0537730	−	0.200684i
$418$		0			0
$419$	12.2474			0.598327			0.299164	−	0.954202i	$-0.403292\pi$
$419$	12.2474			0.598327			0.299164	+	0.954202i	$0.403292\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	6.92820	+	4.00000i	0.337260	+	0.194717i
$423$	−12.7279	+	7.34847i	−0.618853	+	0.357295i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	−2.44949	+	4.24264i	−0.118818	+	0.205798i
$426$		0			0
$427$		0			0
$428$			12.0000i			0.580042i
$429$		0			0
$430$	−8.48528	+	4.89898i	−0.409197	+	0.236250i
$431$	25.9808	−	15.0000i	1.25145	−	0.722525i	0.280052	−	0.959985i	$-0.409648\pi$
$431$	25.9808	−	15.0000i	1.25145	−	0.722525i	0.971397	+	0.237460i	$0.0763149\pi$
$432$	5.01910	−	1.34486i	0.241481	−	0.0647048i
$433$		−	14.6969i		−	0.706290i	−0.935569	−	0.353145i	$-0.885112\pi$
$433$		−	14.6969i		−	0.706290i	0.935569	−	0.353145i	$-0.114888\pi$
$434$		0			0
$435$	18.0000	+	18.0000i	0.863034	+	0.863034i
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	7.34847	+	12.7279i	0.351525	+	0.608859i
$438$	16.3923	+	4.39230i	0.783255	+	0.209872i
$439$	−12.7279	−	7.34847i	−0.607471	−	0.350723i	0.164504	−	0.986376i	$-0.447398\pi$
$439$	−12.7279	−	7.34847i	−0.607471	−	0.350723i	−0.771975	+	0.635653i	$0.780731\pi$
$440$		0			0
$441$		0			0
$442$	12.0000			0.570782
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.481486	−	0.876454i	$-0.659903\pi$
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.999774	+	0.0212481i	$0.993236\pi$
$444$	−3.34607	−	0.896575i	−0.158797	−	0.0425496i
$445$		0			0
$446$	−7.34847	+	12.7279i	−0.347960	+	0.602685i
$447$	−7.34847	−	7.34847i	−0.347571	−	0.347571i
$448$		0			0
$449$		−	36.0000i		−	1.69895i	−0.527633	−	0.849473i	$-0.676920\pi$
$449$		−	36.0000i		−	1.69895i	0.527633	−	0.849473i	$-0.323080\pi$
$450$	−1.50000	+	2.59808i	−0.0707107	+	0.122474i
$451$		0			0
$452$	−5.19615	+	3.00000i	−0.244406	+	0.141108i
$453$	−3.58630	−	13.3843i	−0.168499	−	0.628847i
$454$		−	7.34847i		−	0.344881i
$455$		0			0
$456$	3.00000	−	3.00000i	0.140488	−	0.140488i
$457$	−14.0000	+	24.2487i	−0.654892	+	1.13431i	0.327028	+	0.945015i	$0.393953\pi$
$457$	−14.0000	+	24.2487i	−0.654892	+	1.13431i	−0.981921	+	0.189292i	$0.939381\pi$
$458$	−11.0227	−	19.0919i	−0.515057	−	0.892105i
$459$	−6.58846	+	24.5885i	−0.307523	+	1.14769i
$460$	−12.7279	−	7.34847i	−0.593442	−	0.342624i
$461$	31.8434			1.48309			0.741547	−	0.670901i	$-0.234093\pi$
$461$	31.8434			1.48309			0.741547	+	0.670901i	$0.234093\pi$
$462$		0			0
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	5.19615	+	3.00000i	0.241225	+	0.139272i
$465$		0			0
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$	3.67423	−	6.36396i	0.170023	−	0.294489i	−0.768404	−	0.639965i	$-0.778949\pi$
$467$	3.67423	−	6.36396i	0.170023	−	0.294489i	0.938428	+	0.345476i	$0.112282\pi$
$468$	7.34847			0.339683
$469$		0			0
$470$		−	12.0000i		−	0.553519i
$471$	12.2942	−	3.29423i	0.566488	−	0.151790i
$472$	10.6066	−	6.12372i	0.488208	−	0.281867i
$473$		0			0
$474$	16.7303	−	4.48288i	0.768449	−	0.205905i
$475$			2.44949i			0.112390i
$476$		0			0
$477$	18.0000			0.824163
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	−12.2474	−	21.2132i	−0.559600	−	0.969256i	−0.997530	−	0.0702467i	$-0.977621\pi$
$479$	−12.2474	−	21.2132i	−0.559600	−	0.969256i	0.437929	−	0.899009i	$-0.355712\pi$
$480$	−1.09808	+	4.09808i	−0.0501201	+	0.187051i
$481$	−4.24264	−	2.44949i	−0.193448	−	0.111687i
$482$	−24.4949			−1.11571
$483$		0			0
$484$	−11.0000			−0.500000
$485$	10.3923	+	6.00000i	0.471890	+	0.272446i
$486$	−4.03459	+	15.0573i	−0.183013	+	0.683013i
$487$	16.0000	+	27.7128i	0.725029	+	1.25579i	0.958962	+	0.283535i	$0.0915071\pi$
$487$	16.0000	+	27.7128i	0.725029	+	1.25579i	−0.233933	+	0.972253i	$0.575160\pi$
$488$	6.12372	−	10.6066i	0.277208	−	0.480138i
$489$	−19.5959	+	19.5959i	−0.886158	+	0.886158i
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	2.19615	+	8.19615i	0.0990102	+	0.369511i
$493$	−25.4558	+	14.6969i	−1.14647	+	0.661917i
$494$	5.19615	−	3.00000i	0.233786	−	0.134976i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	3.00000	+	3.00000i	0.134433	+	0.134433i
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	−0.550572	−	0.834788i	$-0.685590\pi$
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	0.998233	+	0.0594153i	$0.0189236\pi$
$500$	4.89898	+	8.48528i	0.219089	+	0.379473i
$501$	−8.19615	−	2.19615i	−0.366177	−	0.0981169i
$502$	14.8492	+	8.57321i	0.662754	+	0.382641i
$503$	39.1918			1.74748			0.873739	−	0.486395i	$-0.161689\pi$
$503$	39.1918			1.74748			0.873739	+	0.486395i	$0.161689\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$	−11.7112	−	3.13801i	−0.520114	−	0.139364i
$508$	4.00000	+	6.92820i	0.177471	+	0.307389i
$509$	6.12372	−	10.6066i	0.271429	−	0.470129i	−0.697799	−	0.716294i	$-0.745837\pi$
$509$	6.12372	−	10.6066i	0.271429	−	0.470129i	0.969228	+	0.246165i	$0.0791704\pi$
$510$	−14.6969	−	14.6969i	−0.650791	−	0.650791i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	3.29423	+	12.2942i	0.145444	+	0.542803i
$514$	25.4558	−	14.6969i	1.12281	−	0.648254i
$515$	−20.7846	+	12.0000i	−0.915879	+	0.528783i
$516$	−1.79315	−	6.69213i	−0.0789391	−	0.294605i
$517$		0			0
$518$		0			0
$519$	−27.0000	+	27.0000i	−1.18517	+	1.18517i
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	2.44949	+	4.24264i	0.107314	+	0.185873i	0.914681	−	0.404176i	$-0.132442\pi$
$521$	2.44949	+	4.24264i	0.107314	+	0.185873i	−0.807367	+	0.590049i	$0.799108\pi$
$522$	−15.5885	+	9.00000i	−0.682288	+	0.393919i
$523$	2.12132	+	1.22474i	0.0927589	+	0.0535544i	0.545662	−	0.838005i	$-0.316278\pi$
$523$	2.12132	+	1.22474i	0.0927589	+	0.0535544i	−0.452903	+	0.891560i	$0.649612\pi$
$524$	−7.34847			−0.321019
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$		0			0
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$	−7.34847	+	12.7279i	−0.319197	+	0.552866i
$531$			36.7423i			1.59448i
$532$		0			0
$533$			12.0000i			0.519778i
$534$		0			0
$535$	25.4558	−	14.6969i	1.10055	−	0.635404i
$536$	−6.92820	+	4.00000i	−0.299253	+	0.172774i
$537$	−40.1528	+	10.7589i	−1.73272	+	0.464281i
$538$		−	12.2474i		−	0.528025i
$539$		0			0
$540$	−9.00000	−	9.00000i	−0.387298	−	0.387298i
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$	−12.2474	−	21.2132i	−0.526073	−	0.911185i
$543$	5.49038	−	20.4904i	0.235615	−	0.879326i
$544$	−4.24264	−	2.44949i	−0.181902	−	0.105021i
$545$	−24.4949			−1.04925
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−10.3923	−	6.00000i	−0.443937	−	0.256307i
$549$	18.3712	+	31.8198i	0.784063	+	1.35804i
$550$		0			0
$551$	−7.34847	+	12.7279i	−0.313055	+	0.542228i
$552$	7.34847	−	7.34847i	0.312772	−	0.312772i
$553$		0			0
$554$		−	22.0000i		−	0.934690i
$555$	2.19615	+	8.19615i	0.0932215	+	0.347907i
$556$	−2.12132	+	1.22474i	−0.0899640	+	0.0519408i
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	−0.131965	−	0.991254i	$-0.542129\pi$
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	0.792469	+	0.609912i	$0.208795\pi$
$558$		0			0
$559$		−	9.79796i		−	0.414410i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.0227	+	19.0919i	0.464552	+	0.804627i	0.999181	−	0.0404596i	$-0.0128822\pi$
$563$	11.0227	+	19.0919i	0.464552	+	0.804627i	−0.534630	+	0.845087i	$0.679549\pi$
$564$	8.19615	+	2.19615i	0.345120	+	0.0924747i
$565$	12.7279	+	7.34847i	0.535468	+	0.309152i
$566$	−22.0454			−0.926638
$567$		0			0
$568$		0			0
$569$	5.19615	+	3.00000i	0.217834	+	0.125767i	0.604947	−	0.796266i	$-0.293194\pi$
$569$	5.19615	+	3.00000i	0.217834	+	0.125767i	−0.387113	+	0.922032i	$0.626528\pi$
$570$	−10.0382	−	2.68973i	−0.420454	−	0.112660i
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			6.00000i			0.250217i
$576$	−2.59808	−	1.50000i	−0.108253	−	0.0625000i
$577$	−16.9706	+	9.79796i	−0.706494	+	0.407894i	−0.809761	−	0.586759i	$-0.800404\pi$
$577$	−16.9706	+	9.79796i	−0.706494	+	0.407894i	0.103268	+	0.994654i	$0.467070\pi$
$578$	6.06218	−	3.50000i	0.252153	−	0.145581i
$579$	1.79315	+	6.69213i	0.0745208	+	0.278115i
$580$		−	14.6969i		−	0.610257i
$581$		0			0
$582$	−6.00000	+	6.00000i	−0.248708	+	0.248708i
$583$		0			0
$584$	−4.89898	−	8.48528i	−0.202721	−	0.351123i
$585$	−9.00000	−	15.5885i	−0.372104	−	0.644503i
$586$	−2.12132	−	1.22474i	−0.0876309	−	0.0505937i
$587$	−7.34847			−0.303304			−0.151652	−	0.988434i	$-0.548459\pi$
$587$	−7.34847			−0.303304			−0.151652	+	0.988434i	$0.548459\pi$
$588$		0			0
$589$		0			0
$590$	−25.9808	−	15.0000i	−1.06961	−	0.617540i
$591$	8.06918	−	30.1146i	0.331922	−	1.23875i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	−19.5959	+	33.9411i	−0.804708	+	1.39379i	0.111780	+	0.993733i	$0.464345\pi$
$593$	−19.5959	+	33.9411i	−0.804708	+	1.39379i	−0.916488	+	0.400062i	$0.868989\pi$
$594$		0			0
$595$		0			0
$596$			6.00000i			0.245770i
$597$	16.3923	−	4.39230i	0.670892	−	0.179765i
$598$	12.7279	−	7.34847i	0.520483	−	0.300501i
$599$	20.7846	−	12.0000i	0.849236	−	0.490307i	−0.0111569	−	0.999938i	$-0.503551\pi$
$599$	20.7846	−	12.0000i	0.849236	−	0.490307i	0.860393	+	0.509631i	$0.170218\pi$
$600$	1.67303	−	0.448288i	0.0683013	−	0.0183013i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		−	24.0000i		−	0.977356i
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	13.4722	+	23.3345i	0.547723	+	0.948683i
$606$	3.29423	−	12.2942i	0.133819	−	0.499419i
$607$	−4.24264	−	2.44949i	−0.172203	−	0.0994217i	0.411421	−	0.911445i	$-0.365033\pi$
$607$	−4.24264	−	2.44949i	−0.172203	−	0.0994217i	−0.583624	+	0.812024i	$0.698366\pi$
$608$	−2.44949			−0.0993399
$609$		0			0
$610$	−30.0000			−1.21466
$611$	10.3923	+	6.00000i	0.420428	+	0.242734i
$612$	12.7279	−	7.34847i	0.514496	−	0.297044i
$613$	−7.00000	−	12.1244i	−0.282727	−	0.489698i	0.689328	−	0.724449i	$-0.257906\pi$
$613$	−7.00000	−	12.1244i	−0.282727	−	0.489698i	−0.972056	+	0.234751i	$0.924572\pi$
$614$	−3.67423	+	6.36396i	−0.148280	+	0.256829i
$615$	14.6969	−	14.6969i	0.592638	−	0.592638i
$616$		0			0
$617$			18.0000i			0.724653i	0.932051	+	0.362326i	$0.118017\pi$
$617$			18.0000i			0.724653i	−0.932051	+	0.362326i	$0.881983\pi$
$618$	−4.39230	−	16.3923i	−0.176684	−	0.659395i
$619$	23.3345	−	13.4722i	0.937894	−	0.541493i	0.0485943	−	0.998819i	$-0.484526\pi$
$619$	23.3345	−	13.4722i	0.937894	−	0.541493i	0.889299	+	0.457325i	$0.151193\pi$
$620$		0			0
$621$	8.06918	+	30.1146i	0.323805	+	1.20846i
$622$			19.5959i			0.785725i
$623$		0			0
$624$	−3.00000	−	3.00000i	−0.120096	−	0.120096i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	17.1464	+	29.6985i	0.685309	+	1.18699i
$627$		0			0
$628$	−6.36396	−	3.67423i	−0.253950	−	0.146618i
$629$	−9.79796			−0.390670
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	−8.66025	−	5.00000i	−0.344486	−	0.198889i
$633$	13.3843	+	3.58630i	0.531977	+	0.142543i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	9.79796	−	16.9706i	0.388820	−	0.673456i
$636$	−7.34847	−	7.34847i	−0.291386	−	0.291386i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	2.12132	−	1.22474i	0.0838525	−	0.0484123i
$641$	−25.9808	+	15.0000i	−1.02618	+	0.592464i	−0.915888	−	0.401435i	$-0.868512\pi$
$641$	−25.9808	+	15.0000i	−1.02618	+	0.592464i	−0.110291	+	0.993899i	$0.535178\pi$
$642$	5.37945	+	20.0764i	0.212310	+	0.792352i
$643$			22.0454i			0.869386i	0.900579	+	0.434693i	$0.143143\pi$
$643$			22.0454i			0.869386i	−0.900579	+	0.434693i	$0.856857\pi$
$644$		0			0
$645$	−12.0000	+	12.0000i	−0.472500	+	0.472500i
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	22.0454	+	38.1838i	0.866694	+	1.50116i	0.865355	+	0.501160i	$0.167093\pi$
$647$	22.0454	+	38.1838i	0.866694	+	1.50116i	0.00133956	+	0.999999i	$0.499574\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$		0			0
$650$	2.44949			0.0960769
$651$		0			0
$652$	16.0000			0.626608
$653$	−5.19615	−	3.00000i	−0.203341	−	0.117399i	0.394872	−	0.918736i	$-0.370789\pi$
$653$	−5.19615	−	3.00000i	−0.203341	−	0.117399i	−0.598213	+	0.801337i	$0.704122\pi$
$654$	4.48288	−	16.7303i	0.175294	−	0.654208i
$655$	9.00000	+	15.5885i	0.351659	+	0.609091i
$656$	2.44949	−	4.24264i	0.0956365	−	0.165647i
$657$	29.3939			1.14676
$658$		0			0
$659$		−	36.0000i		−	1.40236i	−0.712984	−	0.701180i	$-0.752657\pi$
$659$		−	36.0000i		−	1.40236i	0.712984	−	0.701180i	$-0.247343\pi$
$660$		0			0
$661$	10.6066	−	6.12372i	0.412549	−	0.238185i	−0.279335	−	0.960194i	$-0.590114\pi$
$661$	10.6066	−	6.12372i	0.412549	−	0.238185i	0.691884	+	0.722008i	$0.256781\pi$
$662$	−6.92820	+	4.00000i	−0.269272	+	0.155464i
$663$	20.0764	−	5.37945i	0.779702	−	0.208921i
$664$		−	2.44949i		−	0.0950586i
$665$		0			0
$666$	−6.00000			−0.232495
$667$	−18.0000	+	31.1769i	−0.696963	+	1.20717i
$668$	2.44949	+	4.24264i	0.0947736	+	0.164153i
$669$	−6.58846	+	24.5885i	−0.254724	+	0.950645i
$670$	16.9706	+	9.79796i	0.655630	+	0.378528i
$671$		0			0
$672$		0			0
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	27.7128	+	16.0000i	1.06746	+	0.616297i
$675$	−1.34486	+	5.01910i	−0.0517638	+	0.193185i
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	3.67423	−	6.36396i	0.141212	−	0.244587i	−0.786741	−	0.617283i	$-0.788233\pi$
$677$	3.67423	−	6.36396i	0.141212	−	0.244587i	0.927953	+	0.372696i	$0.121567\pi$
$678$	−7.34847	+	7.34847i	−0.282216	+	0.282216i
$679$		0			0
$680$			12.0000i			0.460179i
$681$	−3.29423	−	12.2942i	−0.126235	−	0.471116i
$682$		0			0
$683$	−20.7846	+	12.0000i	−0.795301	+	0.459167i	−0.841825	−	0.539750i	$-0.818519\pi$
$683$	−20.7846	+	12.0000i	−0.795301	+	0.459167i	0.0465244	+	0.998917i	$0.485185\pi$
$684$	3.67423	−	6.36396i	0.140488	−	0.243332i
$685$			29.3939i			1.12308i
$686$		0			0
$687$	−27.0000	−	27.0000i	−1.03011	−	1.03011i
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	−7.34847	−	12.7279i	−0.279954	−	0.484895i
$690$	−24.5885	−	6.58846i	−0.936067	−	0.250818i
$691$	31.8198	+	18.3712i	1.21048	+	0.698872i	0.962864	−	0.269985i	$-0.0870189\pi$
$691$	31.8198	+	18.3712i	1.21048	+	0.698872i	0.247618	+	0.968858i	$0.420352\pi$
$692$	22.0454			0.838041
$693$		0			0
$694$	12.0000			0.455514
$695$	5.19615	+	3.00000i	0.197101	+	0.113796i
$696$	10.0382	+	2.68973i	0.380497	+	0.101954i
$697$	12.0000	+	20.7846i	0.454532	+	0.787273i
$698$	1.22474	−	2.12132i	0.0463573	−	0.0802932i
$699$	−29.3939	−	29.3939i	−1.11178	−	1.11178i
$700$		0			0
$701$			30.0000i			1.13308i	0.824033	+	0.566542i	$0.191719\pi$
$701$			30.0000i			1.13308i	−0.824033	+	0.566542i	$0.808281\pi$
$702$	12.2942	−	3.29423i	0.464016	−	0.124333i
$703$	−4.24264	+	2.44949i	−0.160014	+	0.0923843i
$704$		0			0
$705$	−5.37945	−	20.0764i	−0.202602	−	0.756121i
$706$		−	9.79796i		−	0.368751i
$707$		0			0
$708$	15.0000	−	15.0000i	0.563735	−	0.563735i
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$		0			0
$711$	25.9808	−	15.0000i	0.974355	−	0.562544i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	20.7846	+	12.0000i	0.776757	+	0.448461i
$717$	−2.68973	+	10.0382i	−0.100450	+	0.374883i
$718$	−3.00000	−	5.19615i	−0.111959	−	0.193919i
$719$	−12.2474	+	21.2132i	−0.456753	+	0.791119i	−0.998787	−	0.0492373i	$-0.984321\pi$
$719$	−12.2474	+	21.2132i	−0.456753	+	0.791119i	0.542034	+	0.840356i	$0.317654\pi$
$720$			7.34847i			0.273861i
$721$		0			0
$722$			13.0000i			0.483810i
$723$	−40.9808	+	10.9808i	−1.52409	+	0.408379i
$724$	−10.6066	+	6.12372i	−0.394191	+	0.227586i
$725$	−5.19615	+	3.00000i	−0.192980	+	0.111417i
$726$	−18.4034	+	4.93117i	−0.683013	+	0.183013i
$727$			29.3939i			1.09016i	0.838385	+	0.545079i	$0.183500\pi$
$727$			29.3939i			1.09016i	−0.838385	+	0.545079i	$0.816500\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$	−12.0000	+	20.7846i	−0.444140	+	0.769273i
$731$	−9.79796	−	16.9706i	−0.362391	−	0.627679i
$732$	5.49038	−	20.4904i	0.202930	−	0.757346i
$733$	−19.0919	−	11.0227i	−0.705175	−	0.407133i	0.104097	−	0.994567i	$-0.466805\pi$
$733$	−19.0919	−	11.0227i	−0.705175	−	0.407133i	−0.809272	+	0.587434i	$0.800138\pi$
$734$	−4.89898			−0.180825
$735$		0			0
$736$	−6.00000			−0.221163
$737$		0			0
$738$	7.34847	+	12.7279i	0.270501	+	0.468521i
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	2.44949	−	4.24264i	0.0900450	−	0.155963i
$741$	7.34847	−	7.34847i	0.269953	−	0.269953i
$742$		0			0
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$		0			0
$745$	12.7279	−	7.34847i	0.466315	−	0.269227i
$746$	12.1244	−	7.00000i	0.443904	−	0.256288i
$747$	6.36396	+	3.67423i	0.232845	+	0.134433i
$748$		0			0
$749$		0			0
$750$	12.0000	+	12.0000i	0.438178	+	0.438178i
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	−0.783769	−	0.621052i	$-0.786706\pi$
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	0.929731	+	0.368238i	$0.120039\pi$
$752$	−2.44949	−	4.24264i	−0.0893237	−	0.154713i
$753$	28.6865	+	7.68653i	1.04540	+	0.280113i
$754$	12.7279	+	7.34847i	0.463524	+	0.267615i
$755$	19.5959			0.713168
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	17.3205	+	10.0000i	0.629109	+	0.363216i
$759$		0			0
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	2.44949	−	4.24264i	0.0887939	−	0.153796i	−0.818208	−	0.574923i	$-0.805032\pi$
$761$	2.44949	−	4.24264i	0.0887939	−	0.153796i	0.907002	+	0.421127i	$0.138365\pi$
$762$	9.79796	+	9.79796i	0.354943	+	0.354943i
$763$		0			0
$764$		0			0
$765$	−31.1769	−	18.0000i	−1.12720	−	0.650791i
$766$	−29.6985	+	17.1464i	−1.07305	+	0.619526i
$767$	25.9808	−	15.0000i	0.938111	−	0.541619i
$768$	0.448288	+	1.67303i	0.0161762	+	0.0603704i
$769$		−	34.2929i		−	1.23663i	−0.785930	−	0.618316i	$-0.787815\pi$
$769$		−	34.2929i		−	1.23663i	0.785930	−	0.618316i	$-0.212185\pi$
$770$		0			0
$771$	36.0000	−	36.0000i	1.29651	−	1.29651i
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	−13.4722	−	23.3345i	−0.484561	−	0.839284i	0.515282	−	0.857021i	$-0.327687\pi$
$773$	−13.4722	−	23.3345i	−0.484561	−	0.839284i	−0.999843	+	0.0177365i	$0.994354\pi$
$774$	−6.00000	−	10.3923i	−0.215666	−	0.373544i
$775$		0			0
$776$	4.89898			0.175863
$777$		0			0
$778$	6.00000			0.215110
$779$	10.3923	+	6.00000i	0.372343	+	0.214972i
$780$	−2.68973	+	10.0382i	−0.0963077	+	0.359425i
$781$		0			0
$782$	14.6969	−	25.4558i	0.525561	−	0.910299i
$783$	−22.0454	+	22.0454i	−0.787839	+	0.787839i
$784$		0			0
$785$			18.0000i			0.642448i
$786$	−12.2942	+	3.29423i	−0.438521	+	0.117501i
$787$	−27.5772	+	15.9217i	−0.983020	+	0.567547i	−0.903180	−	0.429261i	$-0.858774\pi$
$787$	−27.5772	+	15.9217i	−0.983020	+	0.567547i	−0.0798393	+	0.996808i	$0.525441\pi$
$788$	−15.5885	+	9.00000i	−0.555316	+	0.320612i
$789$	40.1528	−	10.7589i	1.42948	−	0.383027i
$790$			24.4949i			0.871489i
$791$		0			0
$792$		0			0
$793$	15.0000	−	25.9808i	0.532666	−	0.922604i
$794$	−3.67423	−	6.36396i	−0.130394	−	0.225849i
$795$	−6.58846	+	24.5885i	−0.233668	+	0.872063i
$796$	−8.48528	−	4.89898i	−0.300753	−	0.173640i
$797$	−7.34847			−0.260296			−0.130148	−	0.991495i	$-0.541545\pi$
$797$	−7.34847			−0.260296			−0.130148	+	0.991495i	$0.541545\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		0			0
$802$	15.0000	+	25.9808i	0.529668	+	0.917413i
$803$		0			0
$804$	−9.79796	+	9.79796i	−0.345547	+	0.345547i
$805$		0			0
$806$		0			0
$807$	−5.49038	−	20.4904i	−0.193271	−	0.721296i
$808$	−6.36396	+	3.67423i	−0.223883	+	0.129259i
$809$	−5.19615	+	3.00000i	−0.182687	+	0.105474i	−0.588555	−	0.808458i	$-0.700303\pi$
$809$	−5.19615	+	3.00000i	−0.182687	+	0.105474i	0.405868	+	0.913932i	$0.366969\pi$
$810$	−19.0919	−	11.0227i	−0.670820	−	0.387298i
$811$		−	36.7423i		−	1.29020i	−0.764099	−	0.645099i	$-0.776816\pi$
$811$		−	36.7423i		−	1.29020i	0.764099	−	0.645099i	$-0.223184\pi$
$812$		0			0
$813$	−30.0000	−	30.0000i	−1.05215	−	1.05215i
$814$		0			0
$815$	−19.5959	−	33.9411i	−0.686415	−	1.18891i
$816$	−8.19615	−	2.19615i	−0.286923	−	0.0768807i
$817$	−8.48528	−	4.89898i	−0.296862	−	0.171394i
$818$	34.2929			1.19902
$819$		0			0
$820$	−12.0000			−0.419058
$821$	25.9808	+	15.0000i	0.906735	+	0.523504i	0.879379	−	0.476122i	$-0.157958\pi$
$821$	25.9808	+	15.0000i	0.906735	+	0.523504i	0.0273557	+	0.999626i	$0.491291\pi$
$822$	−20.0764	−	5.37945i	−0.700245	−	0.187630i
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	−4.89898	+	8.48528i	−0.170664	+	0.295599i
$825$		0			0
$826$		0			0
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$	9.00000	−	15.5885i	0.312772	−	0.541736i
$829$	23.3345	−	13.4722i	0.810442	−	0.467909i	−0.0366677	−	0.999328i	$-0.511674\pi$
$829$	23.3345	−	13.4722i	0.810442	−	0.467909i	0.847109	+	0.531419i	$0.178341\pi$
$830$	−5.19615	+	3.00000i	−0.180361	+	0.104132i
$831$	−9.86233	−	36.8067i	−0.342120	−	1.27681i
$832$			2.44949i			0.0849208i
$833$		0			0
$834$	−3.00000	+	3.00000i	−0.103882	+	0.103882i
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$		0			0
$837$		0			0
$838$	−10.6066	−	6.12372i	−0.366399	−	0.211541i
$839$	−24.4949			−0.845658			−0.422829	−	0.906210i	$-0.638963\pi$
$839$	−24.4949			−0.845658			−0.422829	+	0.906210i	$0.638963\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	−1.73205	−	1.00000i	−0.0596904	−	0.0344623i
$843$		0			0
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	8.57321	−	14.8492i	0.294928	−	0.510829i
$846$	14.6969			0.505291
$847$		0			0
$848$			6.00000i			0.206041i
$849$	−36.8827	+	9.88269i	−1.26581	+	0.339173i
$850$	4.24264	−	2.44949i	0.145521	−	0.0840168i
$851$	−10.3923	+	6.00000i	−0.356244	+	0.205677i
$852$		0			0
$853$		−	2.44949i		−	0.0838689i	−0.999120	−	0.0419345i	$-0.986648\pi$
$853$		−	2.44949i		−	0.0838689i	0.999120	−	0.0419345i	$-0.0133521\pi$
$854$		0			0
$855$	−18.0000			−0.615587
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	−2.44949	−	4.24264i	−0.0836730	−	0.144926i	0.821152	−	0.570710i	$-0.193332\pi$
$857$	−2.44949	−	4.24264i	−0.0836730	−	0.144926i	−0.904825	+	0.425784i	$0.859998\pi$
$858$		0			0
$859$	−23.3345	−	13.4722i	−0.796164	−	0.459665i	0.0459643	−	0.998943i	$-0.485364\pi$
$859$	−23.3345	−	13.4722i	−0.796164	−	0.459665i	−0.842128	+	0.539278i	$0.818697\pi$
$860$	9.79796			0.334108
$861$		0			0
$862$	−30.0000			−1.02180
$863$	20.7846	+	12.0000i	0.707516	+	0.408485i	0.810141	−	0.586235i	$-0.199391\pi$
$863$	20.7846	+	12.0000i	0.707516	+	0.408485i	−0.102624	+	0.994720i	$0.532724\pi$
$864$	−5.01910	−	1.34486i	−0.170753	−	0.0457532i
$865$	−27.0000	−	46.7654i	−0.918028	−	1.59007i
$866$	−7.34847	+	12.7279i	−0.249711	+	0.432512i
$867$	8.57321	−	8.57321i	0.291162	−	0.291162i
$868$		0			0
$869$		0			0
$870$	−6.58846	−	24.5885i	−0.223370	−	0.833627i
$871$	−16.9706	+	9.79796i	−0.575026	+	0.331991i
$872$	−8.66025	+	5.00000i	−0.293273	+	0.169321i
$873$	−7.34847	+	12.7279i	−0.248708	+	0.430775i
$874$		−	14.6969i		−	0.497131i
$875$		0			0
$876$	−12.0000	−	12.0000i	−0.405442	−	0.405442i
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	7.34847	+	12.7279i	0.247999	+	0.429547i
$879$	−4.09808	−	1.09808i	−0.138225	−	0.0370372i
$880$		0			0
$881$	−29.3939			−0.990305			−0.495152	−	0.868806i	$-0.664888\pi$
$881$	−29.3939			−0.990305			−0.495152	+	0.868806i	$0.664888\pi$
$882$		0			0
$883$	−56.0000			−1.88455			−0.942275	−	0.334840i	$-0.891318\pi$
$883$	−56.0000			−1.88455			−0.942275	+	0.334840i	$0.891318\pi$
$884$	−10.3923	−	6.00000i	−0.349531	−	0.201802i
$885$	−50.1910	−	13.4486i	−1.68715	−	0.452071i
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	−2.44949	+	4.24264i	−0.0822458	+	0.142454i	−0.904214	−	0.427079i	$-0.859543\pi$
$887$	−2.44949	+	4.24264i	−0.0822458	+	0.142454i	0.821968	+	0.569533i	$0.192876\pi$
$888$	2.44949	+	2.44949i	0.0821995	+	0.0821995i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	12.7279	−	7.34847i	0.426162	−	0.246045i
$893$	10.3923	−	6.00000i	0.347765	−	0.200782i
$894$	2.68973	+	10.0382i	0.0899579	+	0.335727i
$895$		−	58.7878i		−	1.96506i
$896$		0			0
$897$	18.0000	−	18.0000i	0.601003	−	0.601003i
$898$	−18.0000	+	31.1769i	−0.600668	+	1.04039i
$899$		0			0
$900$	2.59808	−	1.50000i	0.0866025	−	0.0500000i
$901$	−25.4558	−	14.6969i	−0.848057	−	0.489626i
$902$		0			0
$903$		0			0
$904$	6.00000			0.199557
$905$	25.9808	+	15.0000i	0.863630	+	0.498617i
$906$	−3.58630	+	13.3843i	−0.119147	+	0.444662i
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$	−3.67423	+	6.36396i	−0.121934	+	0.211195i
$909$		−	22.0454i		−	0.731200i
$910$		0			0
$911$			30.0000i			0.993944i	0.867766	+	0.496972i	$0.165555\pi$
$911$			30.0000i			0.993944i	−0.867766	+	0.496972i	$0.834445\pi$
$912$	−4.09808	+	1.09808i	−0.135701	+	0.0363609i
$913$		0			0
$914$	24.2487	−	14.0000i	0.802076	−	0.463079i
$915$	−50.1910	+	13.4486i	−1.65926	+	0.444598i
$916$			22.0454i			0.728401i
$917$		0			0
$918$	18.0000	−	18.0000i	0.594089	−	0.594089i
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	−0.936632	−	0.350315i	$-0.886075\pi$
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	0.771697	+	0.635990i	$0.219408\pi$
$920$	7.34847	+	12.7279i	0.242272	+	0.419627i
$921$	−3.29423	+	12.2942i	−0.108549	+	0.405109i
$922$	−27.5772	−	15.9217i	−0.908206	−	0.524353i
$923$		0			0
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	−12.1244	−	7.00000i	−0.398431	−	0.230034i
$927$	−14.6969	−	25.4558i	−0.482711	−	0.836080i
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	12.2474	−	21.2132i	0.401826	−	0.695983i	−0.592121	−	0.805849i	$-0.701709\pi$
$929$	12.2474	−	21.2132i	0.401826	−	0.695983i	0.993946	+	0.109867i	$0.0350424\pi$
$930$		0			0
$931$		0			0
$932$			24.0000i			0.786146i
$933$	8.78461	+	32.7846i	0.287595	+	1.07332i
$934$	−6.36396	+	3.67423i	−0.208235	+	0.120225i
$935$		0			0
$936$	−6.36396	−	3.67423i	−0.208013	−	0.120096i
$937$		−	19.5959i		−	0.640171i	−0.947389	−	0.320085i	$-0.896288\pi$
$937$		−	19.5959i		−	0.640171i	0.947389	−	0.320085i	$-0.103712\pi$
$938$		0			0
$939$	42.0000	+	42.0000i	1.37062	+	1.37062i
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$	−15.9217	−	27.5772i	−0.519032	−	0.898990i	−0.999755	−	0.0221175i	$-0.992959\pi$
$941$	−15.9217	−	27.5772i	−0.519032	−	0.898990i	0.480723	−	0.876872i	$-0.340374\pi$
$942$	−12.2942	−	3.29423i	−0.400568	−	0.107332i
$943$	25.4558	+	14.6969i	0.828956	+	0.478598i
$944$	−12.2474			−0.398621
$945$		0			0
$946$		0			0
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	0.659256	−	0.751918i	$-0.270871\pi$
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	−0.321552	+	0.946892i	$0.604204\pi$
$948$	−16.7303	−	4.48288i	−0.543376	−	0.145597i
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$	1.22474	−	2.12132i	0.0397360	−	0.0688247i
$951$	22.0454	+	22.0454i	0.714871	+	0.714871i
$952$		0			0
$953$			36.0000i			1.16615i	0.812417	+	0.583077i	$0.198151\pi$
$953$			36.0000i			1.16615i	−0.812417	+	0.583077i	$0.801849\pi$
$954$	−15.5885	−	9.00000i	−0.504695	−	0.291386i
$955$		0			0
$956$	5.19615	−	3.00000i	0.168056	−	0.0970269i
$957$		0			0
$958$			24.4949i			0.791394i
$959$		0			0
$960$	3.00000	−	3.00000i	0.0968246	−	0.0968246i
$961$	−15.5000	+	26.8468i	−0.500000	+	0.866025i
$962$	2.44949	+	4.24264i	0.0789747	+	0.136788i
$963$	18.0000	+	31.1769i	0.580042	+	1.00466i
$964$	21.2132	+	12.2474i	0.683231	+	0.394464i
$965$	−9.79796			−0.315407
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	9.52628	+	5.50000i	0.306186	+	0.176777i
$969$	5.37945	−	20.0764i	0.172813	−	0.644947i
$970$	−6.00000	−	10.3923i	−0.192648	−	0.333677i
$971$	20.8207	−	36.0624i	0.668167	−	1.15730i	−0.310249	−	0.950655i	$-0.600413\pi$
$971$	20.8207	−	36.0624i	0.668167	−	1.15730i	0.978416	−	0.206644i	$-0.0662541\pi$
$972$	11.0227	−	11.0227i	0.353553	−	0.353553i
$973$		0			0
$974$		−	32.0000i		−	1.02535i
$975$	4.09808	−	1.09808i	0.131243	−	0.0351666i
$976$	−10.6066	+	6.12372i	−0.339509	+	0.196016i
$977$	−10.3923	+	6.00000i	−0.332479	+	0.191957i	−0.656941	−	0.753942i	$-0.728150\pi$
$977$	−10.3923	+	6.00000i	−0.332479	+	0.191957i	0.324462	+	0.945899i	$0.394817\pi$
$978$	26.7685	−	7.17260i	0.855963	−	0.229355i
$979$		0			0
$980$		0			0
$981$		−	30.0000i		−	0.957826i
$982$		0			0
$983$	17.1464	+	29.6985i	0.546886	+	0.947235i	0.998486	+	0.0550138i	$0.0175203\pi$
$983$	17.1464	+	29.6985i	0.546886	+	0.947235i	−0.451599	+	0.892221i	$0.649146\pi$
$984$	2.19615	−	8.19615i	0.0700108	−	0.261284i
$985$	38.1838	+	22.0454i	1.21664	+	0.702425i
$986$	29.3939			0.936092
$987$		0			0
$988$	−6.00000			−0.190885
$989$	−20.7846	−	12.0000i	−0.660912	−	0.381578i
$990$		0			0
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	0.992278	+	0.124033i	$0.0395829\pi$
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	−0.388723	+	0.921355i	$0.627084\pi$
$992$		0			0
$993$	−9.79796	+	9.79796i	−0.310929	+	0.310929i
$994$		0			0
$995$			24.0000i			0.760851i
$996$	−1.09808	−	4.09808i	−0.0347939	−	0.129853i
$997$	−6.36396	+	3.67423i	−0.201549	+	0.116364i	−0.597378	−	0.801960i	$-0.703791\pi$
$997$	−6.36396	+	3.67423i	−0.201549	+	0.116364i	0.395829	+	0.918324i	$0.370457\pi$
$998$	−17.3205	+	10.0000i	−0.548271	+	0.316544i
$999$	−10.0382	+	2.68973i	−0.317594	+	0.0850992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.f.b.215.1		8
3.2	odd	2	inner	294.2.f.b.215.3		8
7.2	even	3		42.2.d.a.41.4	yes	4
7.3	odd	6	inner	294.2.f.b.227.3		8
7.4	even	3	inner	294.2.f.b.227.4		8
7.5	odd	6		42.2.d.a.41.3	yes	4
7.6	odd	2	inner	294.2.f.b.215.2		8
21.2	odd	6		42.2.d.a.41.1	✓	4
21.5	even	6		42.2.d.a.41.2	yes	4
21.11	odd	6	inner	294.2.f.b.227.2		8
21.17	even	6	inner	294.2.f.b.227.1		8
21.20	even	2	inner	294.2.f.b.215.4		8
28.19	even	6		336.2.k.b.209.3		4
28.23	odd	6		336.2.k.b.209.2		4
35.2	odd	12		1050.2.d.b.1049.1		4
35.9	even	6		1050.2.b.b.251.1		4
35.12	even	12		1050.2.d.b.1049.4		4
35.19	odd	6		1050.2.b.b.251.2		4
35.23	odd	12		1050.2.d.e.1049.4		4
35.33	even	12		1050.2.d.e.1049.1		4
56.5	odd	6		1344.2.k.c.1217.3		4
56.19	even	6		1344.2.k.d.1217.2		4
56.37	even	6		1344.2.k.c.1217.2		4
56.51	odd	6		1344.2.k.d.1217.3		4
63.2	odd	6		1134.2.m.g.377.1		8
63.5	even	6		1134.2.m.g.755.4		8
63.16	even	3		1134.2.m.g.377.4		8
63.23	odd	6		1134.2.m.g.755.3		8
63.40	odd	6		1134.2.m.g.755.1		8
63.47	even	6		1134.2.m.g.377.2		8
63.58	even	3		1134.2.m.g.755.2		8
63.61	odd	6		1134.2.m.g.377.3		8
84.23	even	6		336.2.k.b.209.4		4
84.47	odd	6		336.2.k.b.209.1		4
105.2	even	12		1050.2.d.e.1049.2		4
105.23	even	12		1050.2.d.b.1049.3		4
105.44	odd	6		1050.2.b.b.251.4		4
105.47	odd	12		1050.2.d.e.1049.3		4
105.68	odd	12		1050.2.d.b.1049.2		4
105.89	even	6		1050.2.b.b.251.3		4
168.5	even	6		1344.2.k.c.1217.1		4
168.107	even	6		1344.2.k.d.1217.1		4
168.131	odd	6		1344.2.k.d.1217.4		4
168.149	odd	6		1344.2.k.c.1217.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.d.a.41.1	✓	4	21.2	odd	6
42.2.d.a.41.2	yes	4	21.5	even	6
42.2.d.a.41.3	yes	4	7.5	odd	6
42.2.d.a.41.4	yes	4	7.2	even	3
294.2.f.b.215.1		8	1.1	even	1	trivial
294.2.f.b.215.2		8	7.6	odd	2	inner
294.2.f.b.215.3		8	3.2	odd	2	inner
294.2.f.b.215.4		8	21.20	even	2	inner
294.2.f.b.227.1		8	21.17	even	6	inner
294.2.f.b.227.2		8	21.11	odd	6	inner
294.2.f.b.227.3		8	7.3	odd	6	inner
294.2.f.b.227.4		8	7.4	even	3	inner
336.2.k.b.209.1		4	84.47	odd	6
336.2.k.b.209.2		4	28.23	odd	6
336.2.k.b.209.3		4	28.19	even	6
336.2.k.b.209.4		4	84.23	even	6
1050.2.b.b.251.1		4	35.9	even	6
1050.2.b.b.251.2		4	35.19	odd	6
1050.2.b.b.251.3		4	105.89	even	6
1050.2.b.b.251.4		4	105.44	odd	6
1050.2.d.b.1049.1		4	35.2	odd	12
1050.2.d.b.1049.2		4	105.68	odd	12
1050.2.d.b.1049.3		4	105.23	even	12
1050.2.d.b.1049.4		4	35.12	even	12
1050.2.d.e.1049.1		4	35.33	even	12
1050.2.d.e.1049.2		4	105.2	even	12
1050.2.d.e.1049.3		4	105.47	odd	12
1050.2.d.e.1049.4		4	35.23	odd	12
1134.2.m.g.377.1		8	63.2	odd	6
1134.2.m.g.377.2		8	63.47	even	6
1134.2.m.g.377.3		8	63.61	odd	6
1134.2.m.g.377.4		8	63.16	even	3
1134.2.m.g.755.1		8	63.40	odd	6
1134.2.m.g.755.2		8	63.58	even	3
1134.2.m.g.755.3		8	63.23	odd	6
1134.2.m.g.755.4		8	63.5	even	6
1344.2.k.c.1217.1		4	168.5	even	6
1344.2.k.c.1217.2		4	56.37	even	6
1344.2.k.c.1217.3		4	56.5	odd	6
1344.2.k.c.1217.4		4	168.149	odd	6
1344.2.k.d.1217.1		4	168.107	even	6
1344.2.k.d.1217.2		4	56.19	even	6
1344.2.k.d.1217.3		4	56.51	odd	6
1344.2.k.d.1217.4		4	168.131	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(1.22474 + 1.22474i) q^{6} -1.00000i q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(1.22474 + 1.22474i) q^{6} -1.00000i q^{8} +(2.59808 + 1.50000i) q^{9} +(-2.12132 + 1.22474i) q^{10} +(-0.448288 - 1.67303i) q^{12} -2.44949i q^{13} +(-3.00000 + 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.44949 - 4.24264i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(-2.12132 - 1.22474i) q^{19} +2.44949 q^{20} +(-5.19615 - 3.00000i) q^{23} +(-0.448288 + 1.67303i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.22474 + 2.12132i) q^{26} +(-3.67423 - 3.67423i) q^{27} -6.00000i q^{29} +(4.09808 - 1.09808i) q^{30} +(0.866025 - 0.500000i) q^{32} +4.89898i q^{34} +3.00000i q^{36} +(1.00000 - 1.73205i) q^{37} +(1.22474 + 2.12132i) q^{38} +(-1.09808 + 4.09808i) q^{39} +(-2.12132 - 1.22474i) q^{40} -4.89898 q^{41} +4.00000 q^{43} +(6.36396 - 3.67423i) q^{45} +(3.00000 + 5.19615i) q^{46} +(-2.44949 + 4.24264i) q^{47} +(1.22474 - 1.22474i) q^{48} +1.00000i q^{50} +(2.19615 + 8.19615i) q^{51} +(2.12132 - 1.22474i) q^{52} +(5.19615 - 3.00000i) q^{53} +(1.34486 + 5.01910i) q^{54} +(3.00000 + 3.00000i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(6.12372 + 10.6066i) q^{59} +(-4.09808 - 1.09808i) q^{60} +(10.6066 + 6.12372i) q^{61} -1.00000 q^{64} +(-5.19615 - 3.00000i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(2.44949 - 4.24264i) q^{68} +(7.34847 + 7.34847i) q^{69} +(1.50000 - 2.59808i) q^{72} +(8.48528 - 4.89898i) q^{73} +(-1.73205 + 1.00000i) q^{74} +(0.448288 + 1.67303i) q^{75} -2.44949i q^{76} +(3.00000 - 3.00000i) q^{78} +(5.00000 - 8.66025i) q^{79} +(1.22474 + 2.12132i) q^{80} +(4.50000 + 7.79423i) q^{81} +(4.24264 + 2.44949i) q^{82} +2.44949 q^{83} -12.0000 q^{85} +(-3.46410 - 2.00000i) q^{86} +(-2.68973 + 10.0382i) q^{87} -7.34847 q^{90} -6.00000i q^{92} +(4.24264 - 2.44949i) q^{94} +(-5.19615 + 3.00000i) q^{95} +(-1.67303 + 0.448288i) q^{96} +4.89898i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 24 q^{15} - 4 q^{16} - 12 q^{18} - 4 q^{25} + 12 q^{30} + 8 q^{37} + 12 q^{39} + 32 q^{43} + 24 q^{46} - 24 q^{51} + 24 q^{57} - 24 q^{58} - 12 q^{60} - 8 q^{64} - 32 q^{67} + 12 q^{72} + 24 q^{78} + 40 q^{79} + 36 q^{81} - 96 q^{85}+O(q^{100}) \) 8 * q + 4 * q^4 - 24 * q^15 - 4 * q^16 - 12 * q^18 - 4 * q^25 + 12 * q^30 + 8 * q^37 + 12 * q^39 + 32 * q^43 + 24 * q^46 - 24 * q^51 + 24 * q^57 - 24 * q^58 - 12 * q^60 - 8 * q^64 - 32 * q^67 + 12 * q^72 + 24 * q^78 + 40 * q^79 + 36 * q^81 - 96 * q^85

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