LMFDB - Embedded newform 294.2.f.b.215.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,2,Mod(215,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			215.3
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	294.215
Dual form			294.2.f.b.227.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

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
$3$	−0.448288	+	1.67303i	−0.258819	+	0.965926i
$3$	−0.448288	+	1.67303i	−0.258819	+	0.965926i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.22474	+	2.12132i	−0.547723	+	0.948683i	0.450708	+	0.892672i	$0.351172\pi$
$5$	−1.22474	+	2.12132i	−0.547723	+	0.948683i	−0.998430	+	0.0560116i	$0.982162\pi$
$6$	−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	$0.333333\pi$
$12$	−1.67303	+	0.448288i	−0.482963	+	0.129410i
$13$		−	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	$0.0358205\pi$
$17$	2.44949	+	4.24264i	0.594089	+	1.02899i	−0.399586	+	0.916696i	$0.630846\pi$
$18$	−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	0.931831	−	0.362892i	$-0.118211\pi$
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.151642	+	0.988436i	$0.451544\pi$
$24$	−1.67303	−	0.448288i	−0.341506	−	0.0915064i
$25$	−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	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$	−1.09808	−	4.09808i	−0.200480	−	0.748203i
$31$		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
$39$	4.09808	+	1.09808i	0.656217	+	0.175833i
$40$	−2.12132	−	1.22474i	−0.335410	−	0.193649i
$41$	4.89898			0.765092			0.382546	−	0.923936i	$-0.375047\pi$
$41$	4.89898			0.765092			0.382546	+	0.923936i	$0.375047\pi$
$42$		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	−0.630213	−	0.776422i	$-0.717032\pi$
$47$	2.44949	−	4.24264i	0.357295	−	0.618853i	0.987508	+	0.157569i	$0.0503658\pi$
$48$	−1.22474	−	1.22474i	−0.176777	−	0.176777i
$49$		0			0
$50$		−	1.00000i		−	0.141421i
$51$	−8.19615	+	2.19615i	−1.14769	+	0.307523i
$52$	2.12132	−	1.22474i	0.294174	−	0.169842i
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	−0.812447	−	0.583036i	$-0.801865\pi$
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	0.0987002	+	0.995117i	$0.468532\pi$
$54$	5.01910	−	1.34486i	0.683013	−	0.183013i
$55$		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	$-0.872959\pi$
$59$	−6.12372	−	10.6066i	−0.797241	−	1.38086i	0.124165	−	0.992262i	$-0.460375\pi$
$60$	1.09808	−	4.09808i	0.141761	−	0.529059i
$61$	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
$75$	1.67303	−	0.448288i	0.193185	−	0.0517638i
$76$		−	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	$-0.542921\pi$
$83$	−2.44949			−0.268866			−0.134433	+	0.990923i	$0.542921\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	3.46410	+	2.00000i	0.373544	+	0.215666i
$87$	−10.0382	−	2.68973i	−1.07621	−	0.288369i
$88$		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
$96$	−0.448288	−	1.67303i	−0.0457532	−	0.170753i
$97$			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	0.988872	−	0.148767i	$-0.0475305\pi$
$101$	3.67423	+	6.36396i	0.365600	+	0.633238i	−0.623272	+	0.782005i	$0.714197\pi$
$102$	−8.19615	−	2.19615i	−0.811540	−	0.217451i
$103$	−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	−0.0950377	−	0.995474i	$-0.530297\pi$
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.909624	+	0.415432i	$0.863630\pi$
$108$	5.01910	+	1.34486i	0.482963	+	0.129410i
$109$	−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	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	4.09808	−	1.09808i	0.383820	−	0.102844i
$115$	−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
$123$	−2.19615	+	8.19615i	−0.198020	+	0.739022i
$124$		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
$129$	−1.79315	+	6.69213i	−0.157878	+	0.589209i
$130$	3.00000	+	5.19615i	0.263117	+	0.455733i
$131$	3.67423	−	6.36396i	0.321019	−	0.556022i	−0.659679	−	0.751547i	$-0.729308\pi$
$131$	3.67423	−	6.36396i	0.321019	−	0.556022i	0.980699	+	0.195525i	$0.0626412\pi$
$132$		0			0
$133$		0			0
$134$		−	8.00000i		−	0.691095i
$135$	3.29423	+	12.2942i	0.283522	+	1.05812i
$136$	−4.24264	+	2.44949i	−0.363803	+	0.210042i
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.0146279	−	0.999893i	$-0.495344\pi$
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.873247	+	0.487278i	$0.162010\pi$
$138$	−10.0382	+	2.68973i	−0.854508	+	0.228965i
$139$			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	0.271821	−	0.962348i	$-0.412374\pi$
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	−0.697507	+	0.716578i	$0.745707\pi$
$150$	1.67303	+	0.448288i	0.136603	+	0.0366025i
$151$	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
$156$	1.09808	+	4.09808i	0.0879165	+	0.328109i
$157$	−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
$159$	−2.68973	−	10.0382i	−0.213309	−	0.796081i
$160$		−	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	$-0.560702\pi$
$167$	−4.89898			−0.379094			−0.189547	+	0.981872i	$0.560702\pi$
$168$		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	$0.482966\pi$
$173$	−11.0227	+	19.0919i	−0.838041	+	1.45153i	−0.891531	+	0.452961i	$0.850368\pi$
$174$	−7.34847	−	7.34847i	−0.557086	−	0.557086i
$175$		0			0
$176$		0			0
$177$	20.4904	−	5.49038i	1.54015	−	0.412682i
$178$		0			0
$179$	−20.7846	+	12.0000i	−1.55351	+	0.896922i	−0.555663	+	0.831408i	$0.687536\pi$
$179$	−20.7846	+	12.0000i	−1.55351	+	0.896922i	−0.997852	+	0.0655145i	$0.979131\pi$
$180$	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	$0.666667\pi$
$192$	0.448288	−	1.67303i	0.0323524	−	0.120741i
$193$	−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	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		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
$201$	13.3843	−	3.58630i	0.944053	−	0.252958i
$202$			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
$219$	4.39230	+	16.3923i	0.296804	+	1.10769i
$220$		0			0
$221$	10.3923	−	6.00000i	0.699062	−	0.403604i
$222$	0.896575	+	3.34607i	0.0601742	+	0.224573i
$223$		−	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	0.717945	−	0.696100i	$-0.245083\pi$
$227$	−3.67423	−	6.36396i	−0.243868	−	0.422391i	−0.961813	+	0.273709i	$0.911750\pi$
$228$	4.09808	+	1.09808i	0.271402	+	0.0727219i
$229$	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	−0.371802	−	0.928312i	$-0.621260\pi$
$233$	−20.7846	−	12.0000i	−1.36165	−	0.786146i	−0.989843	+	0.142166i	$0.954593\pi$
$234$	−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	$0.0621637\pi$
$239$			6.00000i			0.388108i	−0.980991	+	0.194054i	$0.937836\pi$
$240$	4.09808	−	1.09808i	0.264530	−	0.0708805i
$241$	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
$243$	−15.0573	+	4.03459i	−0.965926	+	0.258819i
$244$			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
$249$	1.09808	−	4.09808i	0.0695878	−	0.259705i
$250$	−8.48528	−	4.89898i	−0.536656	−	0.309839i
$251$	17.1464			1.08227			0.541136	−	0.840935i	$-0.317994\pi$
$251$	17.1464			1.08227			0.541136	+	0.840935i	$0.317994\pi$
$252$		0			0
$253$		0			0
$254$	6.92820	+	4.00000i	0.434714	+	0.250982i
$255$	5.37945	−	20.0764i	0.336874	−	1.25723i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.6969	−	25.4558i	0.916770	−	1.58789i	0.112481	−	0.993654i	$-0.464120\pi$
$257$	14.6969	−	25.4558i	0.916770	−	1.58789i	0.804289	−	0.594238i	$-0.202546\pi$
$258$	−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	0.304487	−	0.952517i	$-0.401515\pi$
$263$	20.7846	−	12.0000i	1.28163	−	0.739952i	0.977147	+	0.212565i	$0.0681817\pi$
$264$		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	0.616712	−	0.787189i	$-0.288464\pi$
$269$	−6.12372	−	10.6066i	−0.373370	−	0.646696i	−0.990082	+	0.140493i	$0.955131\pi$
$270$	−3.29423	+	12.2942i	−0.200480	+	0.748203i
$271$	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
$276$	−10.0382	−	2.68973i	−0.604228	−	0.161903i
$277$	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			$\pi$
$282$	2.19615	+	8.19615i	0.130779	+	0.488074i
$283$	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
$285$	2.68973	+	10.0382i	0.159326	+	0.594611i
$286$		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
$291$	−8.19615	−	2.19615i	−0.480467	−	0.128741i
$292$	8.48528	+	4.89898i	0.496564	+	0.286691i
$293$	−2.44949			−0.143101			−0.0715504	−	0.997437i	$-0.522795\pi$
$293$	−2.44949			−0.143101			−0.0715504	+	0.997437i	$0.522795\pi$
$294$		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
$303$	−12.2942	+	3.29423i	−0.706285	+	0.189248i
$304$	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	$0.0208414\pi$
$311$	9.79796	+	16.9706i	0.555591	+	0.962312i	−0.442266	+	0.896884i	$0.645825\pi$
$312$	−1.09808	+	4.09808i	−0.0621663	+	0.232008i
$313$	−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	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$	2.68973	−	10.0382i	0.150832	−	0.562914i
$319$		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
$327$	16.7303	−	4.48288i	0.925189	−	0.247904i
$328$			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
$339$	10.0382	+	2.68973i	0.545200	+	0.146086i
$340$	−6.00000	−	10.3923i	−0.325396	−	0.563602i
$341$		0			0
$342$			7.34847i			0.397360i
$343$		0			0
$344$			4.00000i			0.215666i
$345$	−6.58846	−	24.5885i	−0.354711	−	1.32380i
$346$	−19.0919	+	11.0227i	−1.02639	+	0.592584i
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	−0.194409	−	0.980921i	$-0.562279\pi$
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	0.752297	+	0.658824i	$0.228946\pi$
$348$	−2.68973	−	10.0382i	−0.144184	−	0.538104i
$349$			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	0.705694	−	0.708517i	$-0.250635\pi$
$353$	−4.89898	−	8.48528i	−0.260746	−	0.451626i	−0.966440	+	0.256891i	$0.917302\pi$
$354$	20.4904	+	5.49038i	1.08905	+	0.291810i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−24.0000			−1.26844
$359$	−5.19615	−	3.00000i	−0.274242	−	0.158334i	0.356572	−	0.934268i	$-0.383946\pi$
$359$	−5.19615	−	3.00000i	−0.274242	−	0.158334i	−0.630814	+	0.775934i	$0.717279\pi$
$360$	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
$366$	−20.4904	+	5.49038i	−1.07105	+	0.286987i
$367$	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
$375$	4.39230	−	16.3923i	0.226818	−	0.846495i
$376$	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
$381$	−3.58630	+	13.3843i	−0.183732	+	0.685696i
$382$		0			0
$383$	−17.1464	+	29.6985i	−0.876142	+	1.51752i	−0.0205998	+	0.999788i	$0.506558\pi$
$383$	−17.1464	+	29.6985i	−0.876142	+	1.51752i	−0.855542	+	0.517734i	$0.826776\pi$
$384$	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	−0.362454	−	0.932002i	$-0.618061\pi$
$389$	5.19615	−	3.00000i	0.263455	−	0.152106i	0.625910	+	0.779895i	$0.284728\pi$
$390$	−10.0382	+	2.68973i	−0.508304	+	0.136200i
$391$			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	0.979957	−	0.199207i	$-0.0638367\pi$
$401$	25.9808	+	15.0000i	1.29742	+	0.749064i	0.317460	+	0.948272i	$0.397170\pi$
$402$	13.3843	+	3.58630i	0.667546	+	0.178868i
$403$		0			0
$404$	−3.67423	+	6.36396i	−0.182800	+	0.316619i
$405$	−22.0454			−1.09545
$406$		0			0
$407$		0			0
$408$	−2.19615	−	8.19615i	−0.108726	−	0.405770i
$409$	−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
$411$	5.37945	+	20.0764i	0.265349	+	0.990295i
$412$		−	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
$417$	−4.09808	−	1.09808i	−0.200684	−	0.0537730i
$418$		0			0
$419$	−12.2474			−0.598327			−0.299164	−	0.954202i	$-0.596708\pi$
$419$	−12.2474			−0.598327			−0.299164	+	0.954202i	$0.596708\pi$
$420$		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	−0.971397	−	0.237460i	$-0.923685\pi$
$431$	−25.9808	+	15.0000i	−1.25145	+	0.722525i	−0.280052	+	0.959985i	$0.590352\pi$
$432$	1.34486	+	5.01910i	0.0647048	+	0.241481i
$433$		−	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
$438$	−4.39230	+	16.3923i	−0.209872	+	0.783255i
$439$	−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	0.999774	−	0.0212481i	$-0.00676401\pi$
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.481486	+	0.876454i	$0.340097\pi$
$444$	−0.896575	+	3.34607i	−0.0425496	+	0.158797i
$445$		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	$0.323080\pi$
$449$			36.0000i			1.69895i	−0.527633	+	0.849473i	$0.676920\pi$
$450$	−1.50000	+	2.59808i	−0.0707107	+	0.122474i
$451$		0			0
$452$	5.19615	−	3.00000i	0.244406	−	0.141108i
$453$	−13.3843	+	3.58630i	−0.628847	+	0.168499i
$454$		−	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
$459$	24.5885	+	6.58846i	1.14769	+	0.307523i
$460$	−12.7279	−	7.34847i	−0.593442	−	0.342624i
$461$	−31.8434			−1.48309			−0.741547	−	0.670901i	$-0.765907\pi$
$461$	−31.8434			−1.48309			−0.741547	+	0.670901i	$0.765907\pi$
$462$		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	−0.938428	−	0.345476i	$-0.887718\pi$
$467$	−3.67423	+	6.36396i	−0.170023	+	0.294489i	0.768404	+	0.639965i	$0.221051\pi$
$468$	−7.34847			−0.339683
$469$		0			0
$470$			12.0000i			0.553519i
$471$	−3.29423	−	12.2942i	−0.151790	−	0.566488i
$472$	10.6066	−	6.12372i	0.488208	−	0.281867i
$473$		0			0
$474$	4.48288	+	16.7303i	0.205905	+	0.768449i
$475$			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	$0.0223786\pi$
$479$	12.2474	+	21.2132i	0.559600	+	0.969256i	−0.437929	+	0.899009i	$0.644288\pi$
$480$	4.09808	+	1.09808i	0.187051	+	0.0501201i
$481$	−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
$486$	−15.0573	−	4.03459i	−0.683013	−	0.183013i
$487$	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			$\pi$
$492$	−8.19615	+	2.19615i	−0.369511	+	0.0990102i
$493$	−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
$501$	2.19615	−	8.19615i	0.0981169	−	0.366177i
$502$	14.8492	+	8.57321i	0.662754	+	0.382641i
$503$	−39.1918			−1.74748			−0.873739	−	0.486395i	$-0.838311\pi$
$503$	−39.1918			−1.74748			−0.873739	+	0.486395i	$0.838311\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$	−3.13801	+	11.7112i	−0.139364	+	0.520114i
$508$	4.00000	+	6.92820i	0.177471	+	0.307389i
$509$	−6.12372	+	10.6066i	−0.271429	+	0.470129i	−0.969228	−	0.246165i	$-0.920830\pi$
$509$	−6.12372	+	10.6066i	−0.271429	+	0.470129i	0.697799	+	0.716294i	$0.254163\pi$
$510$	14.6969	−	14.6969i	0.650791	−	0.650791i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−12.2942	+	3.29423i	−0.542803	+	0.145444i
$514$	25.4558	−	14.6969i	1.12281	−	0.648254i
$515$	20.7846	−	12.0000i	0.915879	−	0.528783i
$516$	−6.69213	+	1.79315i	−0.294605	+	0.0789391i
$517$		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	0.807367	−	0.590049i	$-0.200892\pi$
$521$	−2.44949	−	4.24264i	−0.107314	−	0.185873i	−0.914681	+	0.404176i	$0.867558\pi$
$522$	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
$537$	−10.7589	−	40.1528i	−0.464281	−	1.73272i
$538$		−	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
$543$	−20.4904	−	5.49038i	−0.879326	−	0.235615i
$544$	−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
$555$	−8.19615	+	2.19615i	−0.347907	+	0.0932215i
$556$	−2.12132	+	1.22474i	−0.0899640	+	0.0519408i
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	−0.792469	−	0.609912i	$-0.791205\pi$
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	0.131965	+	0.991254i	$0.457871\pi$
$558$		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	0.534630	−	0.845087i	$-0.320451\pi$
$563$	−11.0227	−	19.0919i	−0.464552	−	0.804627i	−0.999181	+	0.0404596i	$0.987118\pi$
$564$	−2.19615	+	8.19615i	−0.0924747	+	0.345120i
$565$	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	0.387113	−	0.922032i	$-0.373472\pi$
$569$	−5.19615	−	3.00000i	−0.217834	−	0.125767i	−0.604947	+	0.796266i	$0.706806\pi$
$570$	−2.68973	+	10.0382i	−0.112660	+	0.420454i
$571$	−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
$579$	6.69213	−	1.79315i	0.278115	−	0.0745208i
$580$		−	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	$-0.451541\pi$
$587$	7.34847			0.303304			0.151652	+	0.988434i	$0.451541\pi$
$588$		0			0
$589$		0			0
$590$	25.9808	+	15.0000i	1.06961	+	0.617540i
$591$	30.1146	+	8.06918i	1.23875	+	0.331922i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	19.5959	−	33.9411i	0.804708	−	1.39379i	−0.111780	−	0.993733i	$-0.535655\pi$
$593$	19.5959	−	33.9411i	0.804708	−	1.39379i	0.916488	−	0.400062i	$-0.131011\pi$
$594$		0			0
$595$		0			0
$596$		−	6.00000i		−	0.245770i
$597$	−4.39230	−	16.3923i	−0.179765	−	0.670892i
$598$	12.7279	−	7.34847i	0.520483	−	0.300501i
$599$	−20.7846	+	12.0000i	−0.849236	+	0.490307i	−0.860393	−	0.509631i	$-0.829782\pi$
$599$	−20.7846	+	12.0000i	−0.849236	+	0.490307i	0.0111569	+	0.999938i	$0.496449\pi$
$600$	0.448288	+	1.67303i	0.0183013	+	0.0683013i
$601$		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
$606$	−12.2942	−	3.29423i	−0.499419	−	0.133819i
$607$	−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	$-0.881983\pi$
$617$		−	18.0000i		−	0.724653i	0.932051	−	0.362326i	$-0.118017\pi$
$618$	16.3923	−	4.39230i	0.659395	−	0.176684i
$619$	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
$621$	30.1146	−	8.06918i	1.20846	−	0.323805i
$622$			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
$633$	3.58630	−	13.3843i	0.142543	−	0.531977i
$634$	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	0.110291	−	0.993899i	$-0.464822\pi$
$641$	25.9808	−	15.0000i	1.02618	−	0.592464i	0.915888	+	0.401435i	$0.131488\pi$
$642$	20.0764	−	5.37945i	0.792352	−	0.212310i
$643$			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	$-0.832907\pi$
$647$	−22.0454	−	38.1838i	−0.866694	−	1.50116i	−0.00133956	−	0.999999i	$-0.500426\pi$
$648$	−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	0.598213	−	0.801337i	$-0.295878\pi$
$653$	5.19615	+	3.00000i	0.203341	+	0.117399i	−0.394872	+	0.918736i	$0.629211\pi$
$654$	16.7303	+	4.48288i	0.654208	+	0.175294i
$655$	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	$0.247343\pi$
$659$			36.0000i			1.40236i	−0.712984	+	0.701180i	$0.752657\pi$
$660$		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
$663$	5.37945	+	20.0764i	0.208921	+	0.779702i
$664$		−	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
$669$	24.5885	+	6.58846i	0.950645	+	0.254724i
$670$	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
$675$	−5.01910	−	1.34486i	−0.193185	−	0.0517638i
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	−3.67423	+	6.36396i	−0.141212	+	0.244587i	−0.927953	−	0.372696i	$-0.878433\pi$
$677$	−3.67423	+	6.36396i	−0.141212	+	0.244587i	0.786741	+	0.617283i	$0.211767\pi$
$678$	7.34847	+	7.34847i	0.282216	+	0.282216i
$679$		0			0
$680$		−	12.0000i		−	0.460179i
$681$	12.2942	−	3.29423i	0.471116	−	0.126235i
$682$		0			0
$683$	20.7846	−	12.0000i	0.795301	−	0.459167i	−0.0465244	−	0.998917i	$-0.514815\pi$
$683$	20.7846	−	12.0000i	0.795301	−	0.459167i	0.841825	+	0.539750i	$0.181481\pi$
$684$	−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
$690$	6.58846	−	24.5885i	0.250818	−	0.936067i
$691$	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
$696$	2.68973	−	10.0382i	0.101954	−	0.380497i
$697$	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	$-0.808281\pi$
$701$		−	30.0000i		−	1.13308i	0.824033	−	0.566542i	$-0.191719\pi$
$702$	−3.29423	−	12.2942i	−0.124333	−	0.464016i
$703$	−4.24264	+	2.44949i	−0.160014	+	0.0923843i
$704$		0			0
$705$	−20.0764	+	5.37945i	−0.756121	+	0.202602i
$706$		−	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
$717$	−10.0382	−	2.68973i	−0.374883	−	0.100450i
$718$	−3.00000	−	5.19615i	−0.111959	−	0.193919i
$719$	12.2474	−	21.2132i	0.456753	−	0.791119i	−0.542034	−	0.840356i	$-0.682346\pi$
$719$	12.2474	−	21.2132i	0.456753	−	0.791119i	0.998787	+	0.0492373i	$0.0156791\pi$
$720$			7.34847i			0.273861i
$721$		0			0
$722$		−	13.0000i		−	0.483810i
$723$	10.9808	+	40.9808i	0.408379	+	1.52409i
$724$	−10.6066	+	6.12372i	−0.394191	+	0.227586i
$725$	5.19615	−	3.00000i	0.192980	−	0.111417i
$726$	−4.93117	−	18.4034i	−0.183013	−	0.683013i
$727$			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
$732$	−20.4904	−	5.49038i	−0.757346	−	0.202930i
$733$	−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	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$		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
$753$	−7.68653	+	28.6865i	−0.280113	+	1.04540i
$754$	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	−0.907002	−	0.421127i	$-0.861635\pi$
$761$	−2.44949	+	4.24264i	−0.0887939	+	0.153796i	0.818208	+	0.574923i	$0.194968\pi$
$762$	−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
$768$	1.67303	−	0.448288i	0.0603704	−	0.0161762i
$769$		−	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	0.999843	−	0.0177365i	$-0.00564599\pi$
$773$	13.4722	+	23.3345i	0.484561	+	0.839284i	−0.515282	+	0.857021i	$0.672313\pi$
$774$	−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
$780$	−10.0382	−	2.68973i	−0.359425	−	0.0963077i
$781$		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
$786$	3.29423	+	12.2942i	0.117501	+	0.438521i
$787$	−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
$789$	10.7589	+	40.1528i	0.383027	+	1.42948i
$790$			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
$795$	24.5885	+	6.58846i	0.872063	+	0.233668i
$796$	−8.48528	−	4.89898i	−0.300753	−	0.173640i
$797$	7.34847			0.260296			0.130148	−	0.991495i	$-0.458455\pi$
$797$	7.34847			0.260296			0.130148	+	0.991495i	$0.458455\pi$
$798$		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
$807$	20.4904	−	5.49038i	0.721296	−	0.193271i
$808$	−6.36396	+	3.67423i	−0.223883	+	0.129259i
$809$	5.19615	−	3.00000i	0.182687	−	0.105474i	−0.405868	−	0.913932i	$-0.633031\pi$
$809$	5.19615	−	3.00000i	0.182687	−	0.105474i	0.588555	+	0.808458i	$0.299697\pi$
$810$	−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
$816$	2.19615	−	8.19615i	0.0768807	−	0.286923i
$817$	−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	−0.0273557	−	0.999626i	$-0.508709\pi$
$821$	−25.9808	−	15.0000i	−0.906735	−	0.523504i	−0.879379	+	0.476122i	$0.842042\pi$
$822$	−5.37945	+	20.0764i	−0.187630	+	0.700245i
$823$	−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	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$	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
$831$	−36.8067	+	9.86233i	−1.27681	+	0.342120i
$832$			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	$-0.361037\pi$
$839$	24.4949			0.845658			0.422829	+	0.906210i	$0.361037\pi$
$840$		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
$849$	9.88269	+	36.8827i	0.339173	+	1.26581i
$850$	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	0.904825	−	0.425784i	$-0.140002\pi$
$857$	2.44949	+	4.24264i	0.0836730	+	0.144926i	−0.821152	+	0.570710i	$0.806668\pi$
$858$		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	0.102624	−	0.994720i	$-0.467276\pi$
$863$	−20.7846	−	12.0000i	−0.707516	−	0.408485i	−0.810141	+	0.586235i	$0.800609\pi$
$864$	−1.34486	+	5.01910i	−0.0457532	+	0.170753i
$865$	−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
$870$	24.5885	−	6.58846i	0.833627	−	0.223370i
$871$	−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
$879$	1.09808	−	4.09808i	0.0370372	−	0.138225i
$880$		0			0
$881$	29.3939			0.990305			0.495152	−	0.868806i	$-0.335112\pi$
$881$	29.3939			0.990305			0.495152	+	0.868806i	$0.335112\pi$
$882$		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
$885$	−13.4486	+	50.1910i	−0.452071	+	1.68715i
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	2.44949	−	4.24264i	0.0822458	−	0.142454i	−0.821968	−	0.569533i	$-0.807124\pi$
$887$	2.44949	−	4.24264i	0.0822458	−	0.142454i	0.904214	+	0.427079i	$0.140457\pi$
$888$	−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
$894$	10.0382	−	2.68973i	0.335727	−	0.0899579i
$895$		−	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
$906$	−13.3843	−	3.58630i	−0.444662	−	0.119147i
$907$	−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	$-0.834445\pi$
$911$		−	30.0000i		−	0.993944i	0.867766	−	0.496972i	$-0.165555\pi$
$912$	1.09808	+	4.09808i	0.0363609	+	0.135701i
$913$		0			0
$914$	−24.2487	+	14.0000i	−0.802076	+	0.463079i
$915$	−13.4486	−	50.1910i	−0.444598	−	1.65926i
$916$			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
$921$	12.2942	+	3.29423i	0.405109	+	0.108549i
$922$	−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	−0.993946	−	0.109867i	$-0.964958\pi$
$929$	−12.2474	+	21.2132i	−0.401826	+	0.695983i	0.592121	+	0.805849i	$0.298291\pi$
$930$		0			0
$931$		0			0
$932$		−	24.0000i		−	0.786146i
$933$	−32.7846	+	8.78461i	−1.07332	+	0.287595i
$934$	−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	$0.00704081\pi$
$941$	15.9217	+	27.5772i	0.519032	+	0.898990i	−0.480723	+	0.876872i	$0.659626\pi$
$942$	3.29423	−	12.2942i	0.107332	−	0.400568i
$943$	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	0.321552	−	0.946892i	$-0.395796\pi$
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	−0.659256	+	0.751918i	$0.729129\pi$
$948$	−4.48288	+	16.7303i	−0.145597	+	0.543376i
$949$	−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	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$	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
$969$	20.0764	+	5.37945i	0.644947	+	0.172813i
$970$	−6.00000	−	10.3923i	−0.192648	−	0.333677i
$971$	−20.8207	+	36.0624i	−0.668167	+	1.15730i	0.310249	+	0.950655i	$0.399587\pi$
$971$	−20.8207	+	36.0624i	−0.668167	+	1.15730i	−0.978416	+	0.206644i	$0.933746\pi$
$972$	−11.0227	−	11.0227i	−0.353553	−	0.353553i
$973$		0			0
$974$			32.0000i			1.02535i
$975$	−1.09808	−	4.09808i	−0.0351666	−	0.131243i
$976$	−10.6066	+	6.12372i	−0.339509	+	0.196016i
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	−0.324462	−	0.945899i	$-0.605183\pi$
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	0.656941	+	0.753942i	$0.271850\pi$
$978$	7.17260	+	26.7685i	0.229355	+	0.855963i
$979$		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	$-0.982480\pi$
$983$	−17.1464	−	29.6985i	−0.546886	−	0.947235i	0.451599	−	0.892221i	$-0.350854\pi$
$984$	−8.19615	−	2.19615i	−0.261284	−	0.0700108i
$985$	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
$996$	4.09808	−	1.09808i	0.129853	−	0.0347939i
$997$	−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
$999$	−2.68973	−	10.0382i	−0.0850992	−	0.317594i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.f (of order \(6\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more