LMFDB - Embedded newform 666.2.f.c.343.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(343,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.343"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,0,-1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 222)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			343.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	666.343
Dual form			666.2.f.c.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -1.00000 q^{10} -2.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} -8.00000 q^{23} +(2.00000 - 3.46410i) q^{25} +6.00000 q^{26} +(-1.00000 + 1.73205i) q^{28} -1.00000 q^{29} +2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{34} +(1.00000 - 1.73205i) q^{35} +(-5.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(0.500000 + 0.866025i) q^{40} +(-4.50000 - 7.79423i) q^{41} +10.0000 q^{43} +(1.00000 + 1.73205i) q^{44} +(4.00000 - 6.92820i) q^{46} -2.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-3.00000 + 5.19615i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-1.00000 - 1.73205i) q^{55} +(-1.00000 - 1.73205i) q^{56} +(0.500000 - 0.866025i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(-1.00000 + 1.73205i) q^{62} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(-1.00000 - 1.73205i) q^{67} -3.00000 q^{68} +(1.00000 + 1.73205i) q^{70} +(3.00000 + 5.19615i) q^{71} -2.00000 q^{73} +(5.00000 - 3.46410i) q^{74} +(1.00000 - 1.73205i) q^{76} +(2.00000 + 3.46410i) q^{77} +(5.00000 + 8.66025i) q^{79} -1.00000 q^{80} +9.00000 q^{82} +3.00000 q^{85} +(-5.00000 + 8.66025i) q^{86} -2.00000 q^{88} +(-0.500000 + 0.866025i) q^{89} +(-6.00000 + 10.3923i) q^{91} +(4.00000 + 6.92820i) q^{92} +(1.00000 - 1.73205i) q^{94} +(-1.00000 + 1.73205i) q^{95} -17.0000 q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 2 q^{8} - 2 q^{10} - 4 q^{11} - 6 q^{13} + 4 q^{14} - q^{16} + 3 q^{17} + 2 q^{19} + q^{20} + 2 q^{22} - 16 q^{23} + 4 q^{25} + 12 q^{26} - 2 q^{28} - 2 q^{29}+ \cdots + 3 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + q^5 - 2 * q^7 + 2 * q^8 - 2 * q^10 - 4 * q^11 - 6 * q^13 + 4 * q^14 - q^16 + 3 * q^17 + 2 * q^19 + q^20 + 2 * q^22 - 16 * q^23 + 4 * q^25 + 12 * q^26 - 2 * q^28 - 2 * q^29 + 4 * q^31 - q^32 + 3 * q^34 + 2 * q^35 - 11 * q^37 - 4 * q^38 + q^40 - 9 * q^41 + 20 * q^43 + 2 * q^44 + 8 * q^46 - 4 * q^47 + 3 * q^49 + 4 * q^50 - 6 * q^52 - 2 * q^53 - 2 * q^55 - 2 * q^56 + q^58 + 12 * q^59 - q^61 - 2 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^67 - 6 * q^68 + 2 * q^70 + 6 * q^71 - 4 * q^73 + 10 * q^74 + 2 * q^76 + 4 * q^77 + 10 * q^79 - 2 * q^80 + 18 * q^82 + 6 * q^85 - 10 * q^86 - 4 * q^88 - q^89 - 12 * q^91 + 8 * q^92 + 2 * q^94 - 2 * q^95 - 34 * q^97 + 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$	2.00000			0.534522
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	6.00000			1.17670
$27$		0			0
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	1.50000	+	2.59808i	0.257248	+	0.445566i
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$		0			0
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$38$	−2.00000			−0.324443
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	4.00000	−	6.92820i	0.589768	−	1.02151i
$47$	−2.00000			−0.291730			−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000			−0.291730			−0.145865	+	0.989305i	$0.546597\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		0			0
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$		0			0
$55$	−1.00000	−	1.73205i	−0.134840	−	0.233550i
$56$	−1.00000	−	1.73205i	−0.133631	−	0.231455i
$57$		0			0
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−1.00000	+	1.73205i	−0.127000	+	0.219971i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−3.00000			−0.363803
$69$		0			0
$70$	1.00000	+	1.73205i	0.119523	+	0.207020i
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	5.00000	−	3.46410i	0.581238	−	0.402694i
$75$		0			0
$76$	1.00000	−	1.73205i	0.114708	−	0.198680i
$77$	2.00000	+	3.46410i	0.227921	+	0.394771i
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$	9.00000			0.993884
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$		0			0
$85$	3.00000			0.325396
$86$	−5.00000	+	8.66025i	−0.539164	+	0.933859i
$87$		0			0
$88$	−2.00000			−0.213201
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	−0.891308	−	0.453398i	$-0.850212\pi$
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	0.838308	+	0.545197i	$0.183545\pi$
$90$		0			0
$91$	−6.00000	+	10.3923i	−0.628971	+	1.08941i
$92$	4.00000	+	6.92820i	0.417029	+	0.722315i
$93$		0			0
$94$	1.00000	−	1.73205i	0.103142	−	0.178647i
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$		0			0
$97$	−17.0000			−1.72609			−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000			−1.72609			−0.863044	+	0.505128i	$0.831445\pi$
$98$	1.50000	+	2.59808i	0.151523	+	0.262445i
$99$		0			0
$100$	−4.00000			−0.400000
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$		0			0
$103$	−2.00000			−0.197066			−0.0985329	−	0.995134i	$-0.531415\pi$
$103$	−2.00000			−0.197066			−0.0985329	+	0.995134i	$0.531415\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	−1.00000	−	1.73205i	−0.0971286	−	0.168232i
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$		0			0
$109$	1.50000	−	2.59808i	0.143674	−	0.248851i	−0.785203	−	0.619238i	$-0.787442\pi$
$109$	1.50000	−	2.59808i	0.143674	−	0.248851i	0.928877	+	0.370387i	$0.120775\pi$
$110$	2.00000			0.190693
$111$		0			0
$112$	2.00000			0.188982
$113$	7.00000	−	12.1244i	0.658505	−	1.14056i	−0.322498	−	0.946570i	$-0.604523\pi$
$113$	7.00000	−	12.1244i	0.658505	−	1.14056i	0.981003	−	0.193993i	$-0.0621440\pi$
$114$		0			0
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$		0			0
$118$	6.00000	+	10.3923i	0.552345	+	0.956689i
$119$	−6.00000			−0.550019
$120$		0			0
$121$	−7.00000			−0.636364
$122$	1.00000			0.0905357
$123$		0			0
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$	9.00000			0.804984
$126$		0			0
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	0.466870	+	0.884326i	$0.345382\pi$
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	−0.999284	+	0.0378419i	$0.987952\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	3.00000	+	5.19615i	0.263117	+	0.455733i
$131$	−10.0000	+	17.3205i	−0.873704	+	1.51330i	−0.0155672	+	0.999879i	$0.504955\pi$
$131$	−10.0000	+	17.3205i	−0.873704	+	1.51330i	−0.858137	+	0.513421i	$0.828378\pi$
$132$		0			0
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$	2.00000			0.172774
$135$		0			0
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	1.00000			0.0854358			0.0427179	−	0.999087i	$-0.486398\pi$
$137$	1.00000			0.0854358			0.0427179	+	0.999087i	$0.486398\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$	−2.00000			−0.169031
$141$		0			0
$142$	−6.00000			−0.503509
$143$	6.00000	+	10.3923i	0.501745	+	0.869048i
$144$		0			0
$145$	−0.500000	−	0.866025i	−0.0415227	−	0.0719195i
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$		0			0
$148$	0.500000	+	6.06218i	0.0410997	+	0.498308i
$149$	−5.00000			−0.409616			−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000			−0.409616			−0.204808	+	0.978802i	$0.565657\pi$
$150$		0			0
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$		0			0
$154$	−4.00000			−0.322329
$155$	1.00000	+	1.73205i	0.0803219	+	0.139122i
$156$		0			0
$157$	7.50000	−	12.9904i	0.598565	−	1.03675i	−0.394468	−	0.918910i	$-0.629071\pi$
$157$	7.50000	−	12.9904i	0.598565	−	1.03675i	0.993033	−	0.117836i	$-0.0375956\pi$
$158$	−10.0000			−0.795557
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	8.00000	+	13.8564i	0.630488	+	1.09204i
$162$		0			0
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	−0.724288	−	0.689497i	$-0.757831\pi$
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	0.959266	+	0.282503i	$0.0911648\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$		0			0
$167$	−10.0000	−	17.3205i	−0.773823	−	1.34030i	−0.935454	−	0.353450i	$-0.885009\pi$
$167$	−10.0000	−	17.3205i	−0.773823	−	1.34030i	0.161630	−	0.986851i	$-0.448325\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	−1.50000	+	2.59808i	−0.115045	+	0.199263i
$171$		0			0
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	−9.50000	+	16.4545i	−0.722272	+	1.25101i	0.237816	+	0.971310i	$0.423569\pi$
$173$	−9.50000	+	16.4545i	−0.722272	+	1.25101i	−0.960087	+	0.279701i	$0.909765\pi$
$174$		0			0
$175$	−8.00000			−0.604743
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$		0			0
$178$	−0.500000	−	0.866025i	−0.0374766	−	0.0649113i
$179$	−4.00000			−0.298974			−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000			−0.298974			−0.149487	+	0.988764i	$0.547762\pi$
$180$		0			0
$181$	9.50000	+	16.4545i	0.706129	+	1.22305i	0.966282	+	0.257485i	$0.0828937\pi$
$181$	9.50000	+	16.4545i	0.706129	+	1.22305i	−0.260153	+	0.965567i	$0.583773\pi$
$182$	−6.00000	−	10.3923i	−0.444750	−	0.770329i
$183$		0			0
$184$	−8.00000			−0.589768
$185$	−0.500000	−	6.06218i	−0.0367607	−	0.445700i
$186$		0			0
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	1.00000	+	1.73205i	0.0729325	+	0.126323i
$189$		0			0
$190$	−1.00000	−	1.73205i	−0.0725476	−	0.125656i
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$		0			0
$193$	27.0000			1.94350			0.971751	−	0.236007i	$-0.0758390\pi$
$193$	27.0000			1.94350			0.971751	+	0.236007i	$0.0758390\pi$
$194$	8.50000	−	14.7224i	0.610264	−	1.05701i
$195$		0			0
$196$	−3.00000			−0.214286
$197$	0.500000	−	0.866025i	0.0356235	−	0.0617018i	−0.847664	−	0.530534i	$-0.821992\pi$
$197$	0.500000	−	0.866025i	0.0356235	−	0.0617018i	0.883287	+	0.468832i	$0.155325\pi$
$198$		0			0
$199$	−26.0000			−1.84309			−0.921546	−	0.388270i	$-0.873073\pi$
$199$	−26.0000			−1.84309			−0.921546	+	0.388270i	$0.873073\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$		0			0
$202$	−1.50000	+	2.59808i	−0.105540	+	0.182800i
$203$	1.00000	+	1.73205i	0.0701862	+	0.121566i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	1.00000	−	1.73205i	0.0696733	−	0.120678i
$207$		0			0
$208$	6.00000			0.416025
$209$	−2.00000	−	3.46410i	−0.138343	−	0.239617i
$210$		0			0
$211$	−6.00000			−0.413057			−0.206529	−	0.978441i	$-0.566217\pi$
$211$	−6.00000			−0.413057			−0.206529	+	0.978441i	$0.566217\pi$
$212$	2.00000			0.137361
$213$		0			0
$214$	−6.00000			−0.410152
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$	1.50000	+	2.59808i	0.101593	+	0.175964i
$219$		0			0
$220$	−1.00000	+	1.73205i	−0.0674200	+	0.116775i
$221$	−18.0000			−1.21081
$222$		0			0
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$		0			0
$226$	7.00000	+	12.1244i	0.465633	+	0.806500i
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	−0.999184	+	0.0403978i	$0.987137\pi$
$228$		0			0
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$	−1.00000			−0.0656532
$233$	−19.0000			−1.24473			−0.622366	−	0.782727i	$-0.713828\pi$
$233$	−19.0000			−1.24473			−0.622366	+	0.782727i	$0.713828\pi$
$234$		0			0
$235$	−1.00000	−	1.73205i	−0.0652328	−	0.112987i
$236$	−12.0000			−0.781133
$237$		0			0
$238$	3.00000	−	5.19615i	0.194461	−	0.336817i
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	−0.752536	−	0.658551i	$-0.771170\pi$
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	0.946590	+	0.322440i	$0.104503\pi$
$240$		0			0
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	0.892058	+	0.451920i	$0.149261\pi$
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	−0.0546547	+	0.998505i	$0.517406\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$		0			0
$244$	−0.500000	+	0.866025i	−0.0320092	+	0.0554416i
$245$	3.00000			0.191663
$246$		0			0
$247$	6.00000	−	10.3923i	0.381771	−	0.661247i
$248$	2.00000			0.127000
$249$		0			0
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	30.0000			1.89358			0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000			1.89358			0.946792	+	0.321847i	$0.104304\pi$
$252$		0			0
$253$	16.0000			1.00591
$254$	−6.00000	−	10.3923i	−0.376473	−	0.652071i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	−0.0460033	−	0.998941i	$-0.514648\pi$
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	0.888110	−	0.459631i	$-0.152018\pi$
$258$		0			0
$259$	1.00000	+	12.1244i	0.0621370	+	0.753371i
$260$	−6.00000			−0.372104
$261$		0			0
$262$	−10.0000	−	17.3205i	−0.617802	−	1.07006i
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$		0			0
$265$	−2.00000			−0.122859
$266$	2.00000	+	3.46410i	0.122628	+	0.212398i
$267$		0			0
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	30.0000			1.82913			0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000			1.82913			0.914566	+	0.404436i	$0.132532\pi$
$270$		0			0
$271$	11.0000	−	19.0526i	0.668202	−	1.15736i	−0.310204	−	0.950670i	$-0.600397\pi$
$271$	11.0000	−	19.0526i	0.668202	−	1.15736i	0.978406	−	0.206691i	$-0.0662693\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		0			0
$274$	−0.500000	+	0.866025i	−0.0302061	+	0.0523185i
$275$	−4.00000	+	6.92820i	−0.241209	+	0.417786i
$276$		0			0
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	0.601975	−	0.798515i	$-0.294381\pi$
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	−0.992522	+	0.122068i	$0.961047\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$		0			0
$280$	1.00000	−	1.73205i	0.0597614	−	0.103510i
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	−0.110717	−	0.993852i	$-0.535315\pi$
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	0.916060	−	0.401042i	$-0.131352\pi$
$282$		0			0
$283$	3.00000	+	5.19615i	0.178331	+	0.308879i	0.941309	−	0.337546i	$-0.109597\pi$
$283$	3.00000	+	5.19615i	0.178331	+	0.308879i	−0.762978	+	0.646425i	$0.776263\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−12.0000			−0.709575
$287$	−9.00000	+	15.5885i	−0.531253	+	0.920158i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	1.00000			0.0587220
$291$		0			0
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$		0			0
$295$	12.0000			0.698667
$296$	−5.50000	−	2.59808i	−0.319681	−	0.151010i
$297$		0			0
$298$	2.50000	−	4.33013i	0.144821	−	0.250838i
$299$	24.0000	+	41.5692i	1.38796	+	2.40401i
$300$		0			0
$301$	−10.0000	−	17.3205i	−0.576390	−	0.998337i
$302$	−16.0000			−0.920697
$303$		0			0
$304$	−2.00000			−0.114708
$305$	0.500000	−	0.866025i	0.0286299	−	0.0495885i
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$		0			0
$310$	−2.00000			−0.113592
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	−0.972250	−	0.233944i	$-0.924837\pi$
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	0.688726	+	0.725022i	$0.258170\pi$
$312$		0			0
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$	7.50000	+	12.9904i	0.423249	+	0.733090i
$315$		0			0
$316$	5.00000	−	8.66025i	0.281272	−	0.487177i
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	−0.711535	−	0.702650i	$-0.752000\pi$
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	0.964281	+	0.264883i	$0.0853332\pi$
$318$		0			0
$319$	2.00000			0.111979
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	−16.0000			−0.891645
$323$	6.00000			0.333849
$324$		0			0
$325$	−24.0000			−1.33128
$326$	3.00000	+	5.19615i	0.166155	+	0.287788i
$327$		0			0
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$	2.00000	+	3.46410i	0.110264	+	0.190982i
$330$		0			0
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$		0			0
$333$		0			0
$334$	20.0000			1.09435
$335$	1.00000	−	1.73205i	0.0546358	−	0.0946320i
$336$		0			0
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	−0.988260	−	0.152784i	$-0.951176\pi$
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	0.361815	−	0.932250i	$-0.382157\pi$
$338$	−11.5000	−	19.9186i	−0.625518	−	1.08343i
$339$		0			0
$340$	−1.50000	−	2.59808i	−0.0813489	−	0.140900i
$341$	−4.00000			−0.216612
$342$		0			0
$343$	−20.0000			−1.07990
$344$	10.0000			0.539164
$345$		0			0
$346$	−9.50000	−	16.4545i	−0.510723	−	0.884598i
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$		0			0
$349$	7.50000	−	12.9904i	0.401466	−	0.695359i	−0.592437	−	0.805617i	$-0.701834\pi$
$349$	7.50000	−	12.9904i	0.401466	−	0.695359i	0.993903	+	0.110257i	$0.0351675\pi$
$350$	4.00000	−	6.92820i	0.213809	−	0.370328i
$351$		0			0
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	15.5000	−	26.8468i	0.824982	−	1.42891i	−0.0769515	−	0.997035i	$-0.524519\pi$
$353$	15.5000	−	26.8468i	0.824982	−	1.42891i	0.901933	−	0.431875i	$-0.142148\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	1.00000			0.0529999
$357$		0			0
$358$	2.00000	−	3.46410i	0.105703	−	0.183083i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−19.0000			−0.998618
$363$		0			0
$364$	12.0000			0.628971
$365$	−1.00000	−	1.73205i	−0.0523424	−	0.0906597i
$366$		0			0
$367$	−18.0000	−	31.1769i	−0.939592	−	1.62742i	−0.766233	−	0.642563i	$-0.777871\pi$
$367$	−18.0000	−	31.1769i	−0.939592	−	1.62742i	−0.173360	−	0.984859i	$-0.555462\pi$
$368$	4.00000	−	6.92820i	0.208514	−	0.361158i
$369$		0			0
$370$	5.50000	+	2.59808i	0.285931	+	0.135068i
$371$	4.00000			0.207670
$372$		0			0
$373$	3.50000	+	6.06218i	0.181223	+	0.313888i	0.942297	−	0.334777i	$-0.108661\pi$
$373$	3.50000	+	6.06218i	0.181223	+	0.313888i	−0.761074	+	0.648665i	$0.775328\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$		0			0
$376$	−2.00000			−0.103142
$377$	3.00000	+	5.19615i	0.154508	+	0.267615i
$378$		0			0
$379$	1.00000	−	1.73205i	0.0513665	−	0.0889695i	−0.839199	−	0.543825i	$-0.816976\pi$
$379$	1.00000	−	1.73205i	0.0513665	−	0.0889695i	0.890565	+	0.454855i	$0.150309\pi$
$380$	2.00000			0.102598
$381$		0			0
$382$	12.0000	−	20.7846i	0.613973	−	1.06343i
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		0			0
$385$	−2.00000	+	3.46410i	−0.101929	+	0.176547i
$386$	−13.5000	+	23.3827i	−0.687132	+	1.19015i
$387$		0			0
$388$	8.50000	+	14.7224i	0.431522	+	0.747418i
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$		0			0
$391$	−12.0000	+	20.7846i	−0.606866	+	1.05112i
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$		0			0
$394$	0.500000	+	0.866025i	0.0251896	+	0.0436297i
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$		0			0
$397$	37.0000			1.85698			0.928488	−	0.371361i	$-0.121109\pi$
$397$	37.0000			1.85698			0.928488	+	0.371361i	$0.121109\pi$
$398$	13.0000	−	22.5167i	0.651631	−	1.12866i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−22.0000			−1.09863			−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000			−1.09863			−0.549314	+	0.835616i	$0.685111\pi$
$402$		0			0
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$		0			0
$406$	−2.00000			−0.0992583
$407$	11.0000	+	5.19615i	0.545250	+	0.257564i
$408$		0			0
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	4.50000	+	7.79423i	0.222239	+	0.384930i
$411$		0			0
$412$	1.00000	+	1.73205i	0.0492665	+	0.0853320i
$413$	−24.0000			−1.18096
$414$		0			0
$415$		0			0
$416$	−3.00000	+	5.19615i	−0.147087	+	0.254762i
$417$		0			0
$418$	4.00000			0.195646
$419$	7.00000	−	12.1244i	0.341972	−	0.592314i	−0.642827	−	0.766012i	$-0.722238\pi$
$419$	7.00000	−	12.1244i	0.341972	−	0.592314i	0.984799	+	0.173698i	$0.0555717\pi$
$420$		0			0
$421$	−15.0000			−0.731055			−0.365528	−	0.930800i	$-0.619111\pi$
$421$	−15.0000			−0.731055			−0.365528	+	0.930800i	$0.619111\pi$
$422$	3.00000	−	5.19615i	0.146038	−	0.252945i
$423$		0			0
$424$	−1.00000	+	1.73205i	−0.0485643	+	0.0841158i
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$		0			0
$427$	−1.00000	+	1.73205i	−0.0483934	+	0.0838198i
$428$	3.00000	−	5.19615i	0.145010	−	0.251166i
$429$		0			0
$430$	−10.0000			−0.482243
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	0.563658	−	0.826008i	$-0.309393\pi$
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	−0.997173	+	0.0751385i	$0.976060\pi$
$432$		0			0
$433$	−13.0000			−0.624740			−0.312370	−	0.949960i	$-0.601123\pi$
$433$	−13.0000			−0.624740			−0.312370	+	0.949960i	$0.601123\pi$
$434$	4.00000			0.192006
$435$		0			0
$436$	−3.00000			−0.143674
$437$	−8.00000	−	13.8564i	−0.382692	−	0.662842i
$438$		0			0
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	0.814344	−	0.580383i	$-0.197097\pi$
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	−0.909798	+	0.415051i	$0.863764\pi$
$440$	−1.00000	−	1.73205i	−0.0476731	−	0.0825723i
$441$		0			0
$442$	9.00000	−	15.5885i	0.428086	−	0.741467i
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$		0			0
$445$	−1.00000			−0.0474045
$446$	−12.0000	+	20.7846i	−0.568216	+	0.984180i
$447$		0			0
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	7.00000	+	12.1244i	0.330350	+	0.572184i	0.982581	−	0.185837i	$-0.0594997\pi$
$449$	7.00000	+	12.1244i	0.330350	+	0.572184i	−0.652230	+	0.758021i	$0.726166\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	−14.0000			−0.658505
$453$		0			0
$454$	14.0000			0.657053
$455$	−12.0000			−0.562569
$456$		0			0
$457$	2.50000	+	4.33013i	0.116945	+	0.202555i	0.918556	−	0.395292i	$-0.129357\pi$
$457$	2.50000	+	4.33013i	0.116945	+	0.202555i	−0.801611	+	0.597847i	$0.796023\pi$
$458$	1.00000			0.0467269
$459$		0			0
$460$	−4.00000	+	6.92820i	−0.186501	+	0.323029i
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	−0.487577	−	0.873080i	$-0.662119\pi$
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	0.999898	−	0.0142861i	$-0.00454755\pi$
$462$		0			0
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	0.999916	+	0.0129968i	$0.00413714\pi$
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	−0.488702	+	0.872451i	$0.662530\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$		0			0
$466$	9.50000	−	16.4545i	0.440079	−	0.762239i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$	−2.00000	+	3.46410i	−0.0923514	+	0.159957i
$470$	2.00000			0.0922531
$471$		0			0
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$	−20.0000			−0.919601
$474$		0			0
$475$	8.00000			0.367065
$476$	3.00000	+	5.19615i	0.137505	+	0.238165i
$477$		0			0
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	−0.969920	−	0.243426i	$-0.921729\pi$
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	0.695773	+	0.718262i	$0.255062\pi$
$480$		0			0
$481$	3.00000	+	36.3731i	0.136788	+	1.65847i
$482$	−26.0000			−1.18427
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−8.50000	−	14.7224i	−0.385965	−	0.668511i
$486$		0			0
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	−0.500000	−	0.866025i	−0.0226339	−	0.0392031i
$489$		0			0
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	26.0000			1.17336			0.586682	−	0.809818i	$-0.300434\pi$
$491$	26.0000			1.17336			0.586682	+	0.809818i	$0.300434\pi$
$492$		0			0
$493$	−1.50000	+	2.59808i	−0.0675566	+	0.117011i
$494$	6.00000	+	10.3923i	0.269953	+	0.467572i
$495$		0			0
$496$	−1.00000	+	1.73205i	−0.0449013	+	0.0777714i
$497$	6.00000	−	10.3923i	0.269137	−	0.466159i
$498$		0			0
$499$	3.00000	+	5.19615i	0.134298	+	0.232612i	0.925329	−	0.379165i	$-0.123789\pi$
$499$	3.00000	+	5.19615i	0.134298	+	0.232612i	−0.791031	+	0.611776i	$0.790455\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$		0			0
$502$	−15.0000	+	25.9808i	−0.669483	+	1.15958i
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	−0.925124	−	0.379664i	$-0.876040\pi$
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	0.791361	+	0.611349i	$0.209373\pi$
$504$		0			0
$505$	1.50000	+	2.59808i	0.0667491	+	0.115613i
$506$	−8.00000	+	13.8564i	−0.355643	+	0.615992i
$507$		0			0
$508$	12.0000			0.532414
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$	1.00000			0.0441942
$513$		0			0
$514$	13.5000	+	23.3827i	0.595459	+	1.03137i
$515$	−1.00000	−	1.73205i	−0.0440653	−	0.0763233i
$516$		0			0
$517$	4.00000			0.175920
$518$	−11.0000	−	5.19615i	−0.483312	−	0.228306i
$519$		0			0
$520$	3.00000	−	5.19615i	0.131559	−	0.227866i
$521$	7.00000	+	12.1244i	0.306676	+	0.531178i	0.977633	−	0.210318i	$-0.0674500\pi$
$521$	7.00000	+	12.1244i	0.306676	+	0.531178i	−0.670957	+	0.741496i	$0.734117\pi$
$522$		0			0
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$	20.0000			0.873704
$525$		0			0
$526$	−12.0000			−0.523225
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$		0			0
$529$	41.0000			1.78261
$530$	1.00000	−	1.73205i	0.0434372	−	0.0752355i
$531$		0			0
$532$	−4.00000			−0.173422
$533$	−27.0000	+	46.7654i	−1.16950	+	2.02563i
$534$		0			0
$535$	−3.00000	+	5.19615i	−0.129701	+	0.224649i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$		0			0
$538$	−15.0000	+	25.9808i	−0.646696	+	1.12011i
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$		0			0
$541$	−23.0000			−0.988847			−0.494424	−	0.869221i	$-0.664621\pi$
$541$	−23.0000			−0.988847			−0.494424	+	0.869221i	$0.664621\pi$
$542$	11.0000	+	19.0526i	0.472490	+	0.818377i
$543$		0			0
$544$	−3.00000			−0.128624
$545$	3.00000			0.128506
$546$		0			0
$547$	38.0000			1.62476			0.812381	−	0.583127i	$-0.198171\pi$
$547$	38.0000			1.62476			0.812381	+	0.583127i	$0.198171\pi$
$548$	−0.500000	−	0.866025i	−0.0213589	−	0.0369948i
$549$		0			0
$550$	−4.00000	−	6.92820i	−0.170561	−	0.295420i
$551$	−1.00000	−	1.73205i	−0.0426014	−	0.0737878i
$552$		0			0
$553$	10.0000	−	17.3205i	0.425243	−	0.736543i
$554$	13.0000			0.552317
$555$		0			0
$556$	4.00000			0.169638
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	−0.754802	−	0.655953i	$-0.772267\pi$
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	0.945473	+	0.325701i	$0.105600\pi$
$558$		0			0
$559$	−30.0000	−	51.9615i	−1.26886	−	2.19774i
$560$	1.00000	+	1.73205i	0.0422577	+	0.0731925i
$561$		0			0
$562$	13.5000	+	23.3827i	0.569463	+	0.986339i
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$	14.0000			0.588984
$566$	−6.00000			−0.252199
$567$		0			0
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−27.0000			−1.13190			−0.565949	−	0.824440i	$-0.691490\pi$
$569$	−27.0000			−1.13190			−0.565949	+	0.824440i	$0.691490\pi$
$570$		0			0
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	−0.937503	−	0.347977i	$-0.886869\pi$
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	0.770108	+	0.637913i	$0.220202\pi$
$572$	6.00000	−	10.3923i	0.250873	−	0.434524i
$573$		0			0
$574$	−9.00000	−	15.5885i	−0.375653	−	0.650650i
$575$	−16.0000	+	27.7128i	−0.667246	+	1.15570i
$576$		0			0
$577$	−7.00000	+	12.1244i	−0.291414	+	0.504744i	−0.974144	−	0.225927i	$-0.927459\pi$
$577$	−7.00000	+	12.1244i	−0.291414	+	0.504744i	0.682730	+	0.730670i	$0.260792\pi$
$578$	−8.00000			−0.332756
$579$		0			0
$580$	−0.500000	+	0.866025i	−0.0207614	+	0.0359597i
$581$		0			0
$582$		0			0
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	−9.00000			−0.371787
$587$	−10.0000	−	17.3205i	−0.412744	−	0.714894i	0.582445	−	0.812870i	$-0.302096\pi$
$587$	−10.0000	−	17.3205i	−0.412744	−	0.714894i	−0.995189	+	0.0979766i	$0.968763\pi$
$588$		0			0
$589$	2.00000	+	3.46410i	0.0824086	+	0.142736i
$590$	−6.00000	+	10.3923i	−0.247016	+	0.427844i
$591$		0			0
$592$	5.00000	−	3.46410i	0.205499	−	0.142374i
$593$	29.0000			1.19089			0.595444	−	0.803397i	$-0.296976\pi$
$593$	29.0000			1.19089			0.595444	+	0.803397i	$0.296976\pi$
$594$		0			0
$595$	−3.00000	−	5.19615i	−0.122988	−	0.213021i
$596$	2.50000	+	4.33013i	0.102404	+	0.177369i
$597$		0			0
$598$	−48.0000			−1.96287
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	0.621480	−	0.783430i	$-0.286532\pi$
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	−0.989210	+	0.146503i	$0.953198\pi$
$600$		0			0
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	−0.303986	−	0.952676i	$-0.598318\pi$
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	0.977035	−	0.213079i	$-0.0683491\pi$
$602$	20.0000			0.815139
$603$		0			0
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$		0			0
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$		0			0
$610$	0.500000	+	0.866025i	0.0202444	+	0.0350643i
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$		0			0
$613$	−8.50000	+	14.7224i	−0.343312	+	0.594633i	−0.985046	−	0.172294i	$-0.944882\pi$
$613$	−8.50000	+	14.7224i	−0.343312	+	0.594633i	0.641734	+	0.766927i	$0.278215\pi$
$614$	−1.00000	+	1.73205i	−0.0403567	+	0.0698999i
$615$		0			0
$616$	2.00000	+	3.46410i	0.0805823	+	0.139573i
$617$	13.0000	−	22.5167i	0.523360	−	0.906487i	−0.476270	−	0.879299i	$-0.658012\pi$
$617$	13.0000	−	22.5167i	0.523360	−	0.906487i	0.999630	−	0.0271876i	$-0.00865514\pi$
$618$		0			0
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$	1.00000	−	1.73205i	0.0401610	−	0.0695608i
$621$		0			0
$622$	−5.00000	−	8.66025i	−0.200482	−	0.347245i
$623$	2.00000			0.0801283
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	8.50000	+	14.7224i	0.339728	+	0.588427i
$627$		0			0
$628$	−15.0000			−0.598565
$629$	−15.0000	+	10.3923i	−0.598089	+	0.414368i
$630$		0			0
$631$	−16.0000	+	27.7128i	−0.636950	+	1.10323i	0.349148	+	0.937067i	$0.386471\pi$
$631$	−16.0000	+	27.7128i	−0.636950	+	1.10323i	−0.986098	+	0.166162i	$0.946862\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$		0			0
$634$	4.50000	+	7.79423i	0.178718	+	0.309548i
$635$	−12.0000			−0.476205
$636$		0			0
$637$	−18.0000			−0.713186
$638$	−1.00000	+	1.73205i	−0.0395904	+	0.0685725i
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	−22.5000	+	38.9711i	−0.888697	+	1.53927i	−0.0472793	+	0.998882i	$0.515055\pi$
$641$	−22.5000	+	38.9711i	−0.888697	+	1.53927i	−0.841417	+	0.540386i	$0.818278\pi$
$642$		0			0
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$	8.00000	−	13.8564i	0.315244	−	0.546019i
$645$		0			0
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	−7.00000	−	12.1244i	−0.275198	−	0.476658i	0.694987	−	0.719023i	$-0.255410\pi$
$647$	−7.00000	−	12.1244i	−0.275198	−	0.476658i	−0.970185	+	0.242365i	$0.922077\pi$
$648$		0			0
$649$	−12.0000	+	20.7846i	−0.471041	+	0.815867i
$650$	12.0000	−	20.7846i	0.470679	−	0.815239i
$651$		0			0
$652$	−6.00000			−0.234978
$653$	24.5000	+	42.4352i	0.958759	+	1.66062i	0.725521	+	0.688200i	$0.241599\pi$
$653$	24.5000	+	42.4352i	0.958759	+	1.66062i	0.233238	+	0.972420i	$0.425068\pi$
$654$		0			0
$655$	−20.0000			−0.781465
$656$	9.00000			0.351391
$657$		0			0
$658$	−4.00000			−0.155936
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	0.602844	−	0.797859i	$-0.294034\pi$
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	−0.992388	+	0.123148i	$0.960701\pi$
$660$		0			0
$661$	−8.50000	−	14.7224i	−0.330612	−	0.572636i	0.652020	−	0.758202i	$-0.273922\pi$
$661$	−8.50000	−	14.7224i	−0.330612	−	0.572636i	−0.982632	+	0.185565i	$0.940588\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$		0			0
$664$		0			0
$665$	4.00000			0.155113
$666$		0			0
$667$	8.00000			0.309761
$668$	−10.0000	+	17.3205i	−0.386912	+	0.670151i
$669$		0			0
$670$	1.00000	+	1.73205i	0.0386334	+	0.0669150i
$671$	1.00000	+	1.73205i	0.0386046	+	0.0668651i
$672$		0			0
$673$	1.00000	+	1.73205i	0.0385472	+	0.0667657i	0.884655	−	0.466246i	$-0.154394\pi$
$673$	1.00000	+	1.73205i	0.0385472	+	0.0667657i	−0.846108	+	0.533011i	$0.821060\pi$
$674$	23.0000			0.885927
$675$		0			0
$676$	23.0000			0.884615
$677$	3.00000			0.115299			0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000			0.115299			0.0576497	+	0.998337i	$0.481639\pi$
$678$		0			0
$679$	17.0000	+	29.4449i	0.652400	+	1.12999i
$680$	3.00000			0.115045
$681$		0			0
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	25.0000	−	43.3013i	0.956598	−	1.65688i	0.225931	−	0.974143i	$-0.427458\pi$
$683$	25.0000	−	43.3013i	0.956598	−	1.65688i	0.730667	−	0.682734i	$-0.239209\pi$
$684$		0			0
$685$	0.500000	+	0.866025i	0.0191040	+	0.0330891i
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$		0			0
$688$	−5.00000	+	8.66025i	−0.190623	+	0.330169i
$689$	12.0000			0.457164
$690$		0			0
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	−0.755110	−	0.655598i	$-0.772417\pi$
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	0.945319	+	0.326146i	$0.105750\pi$
$692$	19.0000			0.722272
$693$		0			0
$694$	6.00000	−	10.3923i	0.227757	−	0.394486i
$695$	−4.00000			−0.151729
$696$		0			0
$697$	−27.0000			−1.02270
$698$	7.50000	+	12.9904i	0.283879	+	0.491693i
$699$		0			0
$700$	4.00000	+	6.92820i	0.151186	+	0.261861i
$701$	19.0000	−	32.9090i	0.717620	−	1.24295i	−0.244320	−	0.969695i	$-0.578565\pi$
$701$	19.0000	−	32.9090i	0.717620	−	1.24295i	0.961940	−	0.273260i	$-0.0881019\pi$
$702$		0			0
$703$	−1.00000	−	12.1244i	−0.0377157	−	0.457279i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$	15.5000	+	26.8468i	0.583350	+	1.01039i
$707$	−3.00000	−	5.19615i	−0.112827	−	0.195421i
$708$		0			0
$709$	26.0000			0.976450			0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000			0.976450			0.488225	+	0.872718i	$0.337644\pi$
$710$	−3.00000	−	5.19615i	−0.112588	−	0.195008i
$711$		0			0
$712$	−0.500000	+	0.866025i	−0.0187383	+	0.0324557i
$713$	−16.0000			−0.599205
$714$		0			0
$715$	−6.00000	+	10.3923i	−0.224387	+	0.388650i
$716$	2.00000	+	3.46410i	0.0747435	+	0.129460i
$717$		0			0
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	−0.990016	−	0.140955i	$-0.954983\pi$
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	0.617079	+	0.786901i	$0.288316\pi$
$720$		0			0
$721$	2.00000	+	3.46410i	0.0744839	+	0.129010i
$722$	7.50000	+	12.9904i	0.279121	+	0.483452i
$723$		0			0
$724$	9.50000	−	16.4545i	0.353065	−	0.611526i
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$		0			0
$727$	8.00000	+	13.8564i	0.296704	+	0.513906i	0.975380	−	0.220532i	$-0.0707793\pi$
$727$	8.00000	+	13.8564i	0.296704	+	0.513906i	−0.678676	+	0.734438i	$0.737446\pi$
$728$	−6.00000	+	10.3923i	−0.222375	+	0.385164i
$729$		0			0
$730$	2.00000			0.0740233
$731$	15.0000	−	25.9808i	0.554795	−	0.960933i
$732$		0			0
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$	36.0000			1.32878
$735$		0			0
$736$	4.00000	+	6.92820i	0.147442	+	0.255377i
$737$	2.00000	+	3.46410i	0.0736709	+	0.127602i
$738$		0			0
$739$	40.0000			1.47142			0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000			1.47142			0.735712	+	0.677295i	$0.236848\pi$
$740$	−5.00000	+	3.46410i	−0.183804	+	0.127343i
$741$		0			0
$742$	−2.00000	+	3.46410i	−0.0734223	+	0.127171i
$743$	13.0000	+	22.5167i	0.476924	+	0.826056i	0.999650	−	0.0264443i	$-0.00841845\pi$
$743$	13.0000	+	22.5167i	0.476924	+	0.826056i	−0.522727	+	0.852500i	$0.675085\pi$
$744$		0			0
$745$	−2.50000	−	4.33013i	−0.0915929	−	0.158644i
$746$	−7.00000			−0.256288
$747$		0			0
$748$	6.00000			0.219382
$749$	6.00000	−	10.3923i	0.219235	−	0.379727i
$750$		0			0
$751$	26.0000			0.948753			0.474377	−	0.880322i	$-0.342673\pi$
$751$	26.0000			0.948753			0.474377	+	0.880322i	$0.342673\pi$
$752$	1.00000	−	1.73205i	0.0364662	−	0.0631614i
$753$		0			0
$754$	−6.00000			−0.218507
$755$	−8.00000	+	13.8564i	−0.291150	+	0.504286i
$756$		0			0
$757$	1.50000	−	2.59808i	0.0545184	−	0.0944287i	−0.837478	−	0.546471i	$-0.815971\pi$
$757$	1.50000	−	2.59808i	0.0545184	−	0.0944287i	0.891997	+	0.452042i	$0.149304\pi$
$758$	1.00000	+	1.73205i	0.0363216	+	0.0629109i
$759$		0			0
$760$	−1.00000	+	1.73205i	−0.0362738	+	0.0628281i
$761$	−16.5000	+	28.5788i	−0.598125	+	1.03598i	0.394973	+	0.918693i	$0.370754\pi$
$761$	−16.5000	+	28.5788i	−0.598125	+	1.03598i	−0.993098	+	0.117289i	$0.962579\pi$
$762$		0			0
$763$	−6.00000			−0.217215
$764$	12.0000	+	20.7846i	0.434145	+	0.751961i
$765$		0			0
$766$	−6.00000			−0.216789
$767$	−72.0000			−2.59977
$768$		0			0
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$	−2.00000	−	3.46410i	−0.0720750	−	0.124838i
$771$		0			0
$772$	−13.5000	−	23.3827i	−0.485876	−	0.841561i
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	−0.613062	+	0.790034i	$0.710063\pi$
$774$		0			0
$775$	4.00000	−	6.92820i	0.143684	−	0.248868i
$776$	−17.0000			−0.610264
$777$		0			0
$778$	15.0000			0.537776
$779$	9.00000	−	15.5885i	0.322458	−	0.558514i
$780$		0			0
$781$	−6.00000	−	10.3923i	−0.214697	−	0.371866i
$782$	−12.0000	−	20.7846i	−0.429119	−	0.743256i
$783$		0			0
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$	15.0000			0.535373
$786$		0			0
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−1.00000			−0.0356235
$789$		0			0
$790$	−5.00000	−	8.66025i	−0.177892	−	0.308118i
$791$	−28.0000			−0.995565
$792$		0			0
$793$	−3.00000	+	5.19615i	−0.106533	+	0.184521i
$794$	−18.5000	+	32.0429i	−0.656540	+	1.13716i
$795$		0			0
$796$	13.0000	+	22.5167i	0.460773	+	0.798082i
$797$	11.0000	−	19.0526i	0.389640	−	0.674876i	−0.602761	−	0.797922i	$-0.705933\pi$
$797$	11.0000	−	19.0526i	0.389640	−	0.674876i	0.992401	+	0.123045i	$0.0392661\pi$
$798$		0			0
$799$	−3.00000	+	5.19615i	−0.106132	+	0.183827i
$800$	−4.00000			−0.141421
$801$		0			0
$802$	11.0000	−	19.0526i	0.388424	−	0.672769i
$803$	4.00000			0.141157
$804$		0			0
$805$	−8.00000	+	13.8564i	−0.281963	+	0.488374i
$806$	12.0000			0.422682
$807$		0			0
$808$	3.00000			0.105540
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	0.541748	−	0.840541i	$-0.317763\pi$
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	−0.998804	+	0.0488972i	$0.984429\pi$
$810$		0			0
$811$	−8.00000	−	13.8564i	−0.280918	−	0.486564i	0.690693	−	0.723148i	$-0.257306\pi$
$811$	−8.00000	−	13.8564i	−0.280918	−	0.486564i	−0.971611	+	0.236584i	$0.923972\pi$
$812$	1.00000	−	1.73205i	0.0350931	−	0.0607831i
$813$		0			0
$814$	−10.0000	+	6.92820i	−0.350500	+	0.242833i
$815$	6.00000			0.210171
$816$		0			0
$817$	10.0000	+	17.3205i	0.349856	+	0.605968i
$818$	−15.5000	−	26.8468i	−0.541945	−	0.938676i
$819$		0			0
$820$	−9.00000			−0.314294
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	0.955636	+	0.294549i	$0.0951694\pi$
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$822$		0			0
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	−0.360623	−	0.932712i	$-0.617436\pi$
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	0.988063	−	0.154047i	$-0.0492308\pi$
$824$	−2.00000			−0.0696733
$825$		0			0
$826$	12.0000	−	20.7846i	0.417533	−	0.723189i
$827$	−16.0000	−	27.7128i	−0.556375	−	0.963669i	−0.997795	−	0.0663686i	$-0.978859\pi$
$827$	−16.0000	−	27.7128i	−0.556375	−	0.963669i	0.441421	−	0.897300i	$-0.354475\pi$
$828$		0			0
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$		0			0
$831$		0			0
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$	−4.50000	−	7.79423i	−0.155916	−	0.270054i
$834$		0			0
$835$	10.0000	−	17.3205i	0.346064	−	0.599401i
$836$	−2.00000	+	3.46410i	−0.0691714	+	0.119808i
$837$		0			0
$838$	7.00000	+	12.1244i	0.241811	+	0.418829i
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	−0.898482	−	0.439010i	$-0.855329\pi$
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	0.829435	+	0.558604i	$0.188663\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	7.50000	−	12.9904i	0.258467	−	0.447678i
$843$		0			0
$844$	3.00000	+	5.19615i	0.103264	+	0.178859i
$845$	−23.0000			−0.791224
$846$		0			0
$847$	7.00000	+	12.1244i	0.240523	+	0.416598i
$848$	−1.00000	−	1.73205i	−0.0343401	−	0.0594789i
$849$		0			0
$850$	12.0000			0.411597
$851$	44.0000	+	20.7846i	1.50830	+	0.712487i
$852$		0			0
$853$	21.5000	−	37.2391i	0.736146	−	1.27504i	−0.218073	−	0.975933i	$-0.569977\pi$
$853$	21.5000	−	37.2391i	0.736146	−	1.27504i	0.954219	−	0.299110i	$-0.0966897\pi$
$854$	−1.00000	−	1.73205i	−0.0342193	−	0.0592696i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	21.0000			0.717346			0.358673	−	0.933463i	$-0.383229\pi$
$857$	21.0000			0.717346			0.358673	+	0.933463i	$0.383229\pi$
$858$		0			0
$859$	46.0000			1.56950			0.784750	−	0.619813i	$-0.212791\pi$
$859$	46.0000			1.56950			0.784750	+	0.619813i	$0.212791\pi$
$860$	5.00000	−	8.66025i	0.170499	−	0.295312i
$861$		0			0
$862$	18.0000			0.613082
$863$	22.0000	−	38.1051i	0.748889	−	1.29711i	−0.199467	−	0.979905i	$-0.563921\pi$
$863$	22.0000	−	38.1051i	0.748889	−	1.29711i	0.948356	−	0.317209i	$-0.102746\pi$
$864$		0			0
$865$	−19.0000			−0.646019
$866$	6.50000	−	11.2583i	0.220879	−	0.382574i
$867$		0			0
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$	−10.0000	−	17.3205i	−0.339227	−	0.587558i
$870$		0			0
$871$	−6.00000	+	10.3923i	−0.203302	+	0.352130i
$872$	1.50000	−	2.59808i	0.0507964	−	0.0879820i
$873$		0			0
$874$	16.0000			0.541208
$875$	−9.00000	−	15.5885i	−0.304256	−	0.526986i
$876$		0			0
$877$	−23.0000			−0.776655			−0.388327	−	0.921521i	$-0.626947\pi$
$877$	−23.0000			−0.776655			−0.388327	+	0.921521i	$0.626947\pi$
$878$	4.00000			0.134993
$879$		0			0
$880$	2.00000			0.0674200
$881$	−10.5000	−	18.1865i	−0.353754	−	0.612720i	0.633150	−	0.774029i	$-0.281762\pi$
$881$	−10.5000	−	18.1865i	−0.353754	−	0.612720i	−0.986904	+	0.161309i	$0.948428\pi$
$882$		0			0
$883$	10.0000	+	17.3205i	0.336527	+	0.582882i	0.983777	−	0.179396i	$-0.0574144\pi$
$883$	10.0000	+	17.3205i	0.336527	+	0.582882i	−0.647250	+	0.762278i	$0.724081\pi$
$884$	9.00000	+	15.5885i	0.302703	+	0.524297i
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	−36.0000			−1.20876			−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000			−1.20876			−0.604381	+	0.796696i	$0.706579\pi$
$888$		0			0
$889$	24.0000			0.804934
$890$	0.500000	−	0.866025i	0.0167600	−	0.0290292i
$891$		0			0
$892$	−12.0000	−	20.7846i	−0.401790	−	0.695920i
$893$	−2.00000	−	3.46410i	−0.0669274	−	0.115922i
$894$		0			0
$895$	−2.00000	−	3.46410i	−0.0668526	−	0.115792i
$896$	2.00000			0.0668153
$897$		0			0
$898$	−14.0000			−0.467186
$899$	−2.00000			−0.0667037
$900$		0			0
$901$	3.00000	+	5.19615i	0.0999445	+	0.173109i
$902$	−18.0000			−0.599334
$903$		0			0
$904$	7.00000	−	12.1244i	0.232817	−	0.403250i
$905$	−9.50000	+	16.4545i	−0.315791	+	0.546966i
$906$		0			0
$907$	−23.0000	−	39.8372i	−0.763702	−	1.32277i	−0.940930	−	0.338602i	$-0.890046\pi$
$907$	−23.0000	−	39.8372i	−0.763702	−	1.32277i	0.177227	−	0.984170i	$-0.443287\pi$
$908$	−7.00000	+	12.1244i	−0.232303	+	0.402361i
$909$		0			0
$910$	6.00000	−	10.3923i	0.198898	−	0.344502i
$911$	−28.0000			−0.927681			−0.463841	−	0.885919i	$-0.653529\pi$
$911$	−28.0000			−0.927681			−0.463841	+	0.885919i	$0.653529\pi$
$912$		0			0
$913$		0			0
$914$	−5.00000			−0.165385
$915$		0			0
$916$	−0.500000	+	0.866025i	−0.0165205	+	0.0286143i
$917$	40.0000			1.32092
$918$		0			0
$919$	−32.0000			−1.05558			−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000			−1.05558			−0.527791	+	0.849374i	$0.676980\pi$
$920$	−4.00000	−	6.92820i	−0.131876	−	0.228416i
$921$		0			0
$922$	11.0000	+	19.0526i	0.362266	+	0.627463i
$923$	18.0000	−	31.1769i	0.592477	−	1.02620i
$924$		0			0
$925$	−20.0000	+	13.8564i	−0.657596	+	0.455596i
$926$	−22.0000			−0.722965
$927$		0			0
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	0.985482	+	0.169779i	$0.0543055\pi$
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	−0.345708	+	0.938342i	$0.612361\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$	9.50000	+	16.4545i	0.311183	+	0.538985i
$933$		0			0
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$	−6.00000			−0.196221
$936$		0			0
$937$	−21.5000	+	37.2391i	−0.702374	+	1.21655i	0.265256	+	0.964178i	$0.414543\pi$
$937$	−21.5000	+	37.2391i	−0.702374	+	1.21655i	−0.967631	+	0.252370i	$0.918790\pi$
$938$	−2.00000	−	3.46410i	−0.0653023	−	0.113107i
$939$		0			0
$940$	−1.00000	+	1.73205i	−0.0326164	+	0.0564933i
$941$	8.50000	−	14.7224i	0.277092	−	0.479938i	−0.693569	−	0.720390i	$-0.743963\pi$
$941$	8.50000	−	14.7224i	0.277092	−	0.479938i	0.970661	+	0.240453i	$0.0772960\pi$
$942$		0			0
$943$	36.0000	+	62.3538i	1.17232	+	2.03052i
$944$	6.00000	+	10.3923i	0.195283	+	0.338241i
$945$		0			0
$946$	10.0000	−	17.3205i	0.325128	−	0.563138i
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	−0.543746	−	0.839250i	$-0.682994\pi$
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	0.998685	+	0.0512727i	$0.0163278\pi$
$948$		0			0
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$	−4.00000	+	6.92820i	−0.129777	+	0.224781i
$951$		0			0
$952$	−6.00000			−0.194461
$953$	−17.0000	+	29.4449i	−0.550684	+	0.953813i	0.447541	+	0.894263i	$0.352300\pi$
$953$	−17.0000	+	29.4449i	−0.550684	+	0.953813i	−0.998225	+	0.0595495i	$0.981034\pi$
$954$		0			0
$955$	−12.0000	−	20.7846i	−0.388311	−	0.672574i
$956$	−6.00000			−0.194054
$957$		0			0
$958$	−6.00000	−	10.3923i	−0.193851	−	0.335760i
$959$	−1.00000	−	1.73205i	−0.0322917	−	0.0559308i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	−33.0000	−	15.5885i	−1.06396	−	0.502592i
$963$		0			0
$964$	13.0000	−	22.5167i	0.418702	−	0.725213i
$965$	13.5000	+	23.3827i	0.434580	+	0.752715i
$966$		0			0
$967$	−12.0000	−	20.7846i	−0.385894	−	0.668388i	0.605999	−	0.795466i	$-0.292774\pi$
$967$	−12.0000	−	20.7846i	−0.385894	−	0.668388i	−0.991893	+	0.127078i	$0.959440\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	17.0000			0.545837
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	−0.167258	−	0.985913i	$-0.553491\pi$
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	0.937455	−	0.348107i	$-0.113175\pi$
$972$		0			0
$973$	8.00000			0.256468
$974$	16.0000	−	27.7128i	0.512673	−	0.887976i
$975$		0			0
$976$	1.00000			0.0320092
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	0.305530	+	0.952183i	$0.401167\pi$
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	−0.977379	+	0.211495i	$0.932167\pi$
$978$		0			0
$979$	1.00000	−	1.73205i	0.0319601	−	0.0553566i
$980$	−1.50000	−	2.59808i	−0.0479157	−	0.0829925i
$981$		0			0
$982$	−13.0000	+	22.5167i	−0.414847	+	0.718536i
$983$	17.0000	−	29.4449i	0.542216	−	0.939145i	−0.456561	−	0.889692i	$-0.650919\pi$
$983$	17.0000	−	29.4449i	0.542216	−	0.939145i	0.998776	−	0.0494530i	$-0.0157478\pi$
$984$		0			0
$985$	1.00000			0.0318626
$986$	−1.50000	−	2.59808i	−0.0477697	−	0.0827396i
$987$		0			0
$988$	−12.0000			−0.381771
$989$	−80.0000			−2.54385
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$		0			0
$994$	6.00000	+	10.3923i	0.190308	+	0.329624i
$995$	−13.0000	−	22.5167i	−0.412128	−	0.713826i
$996$		0			0
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	−0.314188	−	0.949361i	$-0.601732\pi$
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	0.979265	−	0.202586i	$-0.0649345\pi$
$998$	−6.00000			−0.189927
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.f.c.343.1		2
3.2	odd	2		222.2.e.b.121.1	✓	2
12.11	even	2		1776.2.q.e.1009.1		2
37.26	even	3	inner	666.2.f.c.433.1		2
111.26	odd	6		222.2.e.b.211.1	yes	2
111.47	odd	6		8214.2.a.e.1.1		1
111.101	odd	6		8214.2.a.k.1.1		1
444.359	even	6		1776.2.q.e.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.e.b.121.1	✓	2	3.2	odd	2
222.2.e.b.211.1	yes	2	111.26	odd	6
666.2.f.c.343.1		2	1.1	even	1	trivial
666.2.f.c.433.1		2	37.26	even	3	inner
1776.2.q.e.433.1		2	444.359	even	6
1776.2.q.e.1009.1		2	12.11	even	2
8214.2.a.e.1.1		1	111.47	odd	6
8214.2.a.k.1.1		1	111.101	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -1.00000 q^{10} -2.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} -8.00000 q^{23} +(2.00000 - 3.46410i) q^{25} +6.00000 q^{26} +(-1.00000 + 1.73205i) q^{28} -1.00000 q^{29} +2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{34} +(1.00000 - 1.73205i) q^{35} +(-5.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(0.500000 + 0.866025i) q^{40} +(-4.50000 - 7.79423i) q^{41} +10.0000 q^{43} +(1.00000 + 1.73205i) q^{44} +(4.00000 - 6.92820i) q^{46} -2.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-3.00000 + 5.19615i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-1.00000 - 1.73205i) q^{55} +(-1.00000 - 1.73205i) q^{56} +(0.500000 - 0.866025i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(-1.00000 + 1.73205i) q^{62} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(-1.00000 - 1.73205i) q^{67} -3.00000 q^{68} +(1.00000 + 1.73205i) q^{70} +(3.00000 + 5.19615i) q^{71} -2.00000 q^{73} +(5.00000 - 3.46410i) q^{74} +(1.00000 - 1.73205i) q^{76} +(2.00000 + 3.46410i) q^{77} +(5.00000 + 8.66025i) q^{79} -1.00000 q^{80} +9.00000 q^{82} +3.00000 q^{85} +(-5.00000 + 8.66025i) q^{86} -2.00000 q^{88} +(-0.500000 + 0.866025i) q^{89} +(-6.00000 + 10.3923i) q^{91} +(4.00000 + 6.92820i) q^{92} +(1.00000 - 1.73205i) q^{94} +(-1.00000 + 1.73205i) q^{95} -17.0000 q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 2 q^{8} - 2 q^{10} - 4 q^{11} - 6 q^{13} + 4 q^{14} - q^{16} + 3 q^{17} + 2 q^{19} + q^{20} + 2 q^{22} - 16 q^{23} + 4 q^{25} + 12 q^{26} - 2 q^{28} - 2 q^{29}+ \cdots + 3 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + q^5 - 2 * q^7 + 2 * q^8 - 2 * q^10 - 4 * q^11 - 6 * q^13 + 4 * q^14 - q^16 + 3 * q^17 + 2 * q^19 + q^20 + 2 * q^22 - 16 * q^23 + 4 * q^25 + 12 * q^26 - 2 * q^28 - 2 * q^29 + 4 * q^31 - q^32 + 3 * q^34 + 2 * q^35 - 11 * q^37 - 4 * q^38 + q^40 - 9 * q^41 + 20 * q^43 + 2 * q^44 + 8 * q^46 - 4 * q^47 + 3 * q^49 + 4 * q^50 - 6 * q^52 - 2 * q^53 - 2 * q^55 - 2 * q^56 + q^58 + 12 * q^59 - q^61 - 2 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^67 - 6 * q^68 + 2 * q^70 + 6 * q^71 - 4 * q^73 + 10 * q^74 + 2 * q^76 + 4 * q^77 + 10 * q^79 - 2 * q^80 + 18 * q^82 + 6 * q^85 - 10 * q^86 - 4 * q^88 - q^89 - 12 * q^91 + 8 * q^92 + 2 * q^94 - 2 * q^95 - 34 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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