LMFDB - Embedded newform 666.2.f.d.433.1

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,-1,3] 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 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			433.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	666.433
Dual form			666.2.f.d.343.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(2.00000 - 3.46410i) q^{7} +1.00000 q^{8} -3.00000 q^{10} +6.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} -4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} -6.00000 q^{23} +(-2.00000 - 3.46410i) q^{25} +2.00000 q^{26} +(2.00000 + 3.46410i) q^{28} -3.00000 q^{29} +2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{34} +(-6.00000 - 10.3923i) q^{35} +(5.50000 - 2.59808i) q^{37} +2.00000 q^{38} +(1.50000 - 2.59808i) q^{40} +(1.50000 - 2.59808i) q^{41} -4.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +(3.00000 + 5.19615i) q^{46} +6.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(9.00000 - 15.5885i) q^{55} +(2.00000 - 3.46410i) q^{56} +(1.50000 + 2.59808i) q^{58} +(0.500000 - 0.866025i) q^{61} +(-1.00000 - 1.73205i) q^{62} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-1.00000 + 1.73205i) q^{67} -3.00000 q^{68} +(-6.00000 + 10.3923i) q^{70} +(-6.00000 + 10.3923i) q^{71} -10.0000 q^{73} +(-5.00000 - 3.46410i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(12.0000 - 20.7846i) q^{77} +(-7.00000 + 12.1244i) q^{79} -3.00000 q^{80} -3.00000 q^{82} +(3.00000 + 5.19615i) q^{83} +9.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +6.00000 q^{88} +(1.50000 + 2.59808i) q^{89} +(4.00000 + 6.92820i) q^{91} +(3.00000 - 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(3.00000 + 5.19615i) q^{95} -13.0000 q^{97} +(-4.50000 + 7.79423i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 3 q^{5} + 4 q^{7} + 2 q^{8} - 6 q^{10} + 12 q^{11} - 2 q^{13} - 8 q^{14} - q^{16} + 3 q^{17} - 2 q^{19} + 3 q^{20} - 6 q^{22} - 12 q^{23} - 4 q^{25} + 4 q^{26} + 4 q^{28} - 6 q^{29}+ \cdots - 9 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 3 * q^5 + 4 * q^7 + 2 * q^8 - 6 * q^10 + 12 * q^11 - 2 * q^13 - 8 * q^14 - q^16 + 3 * q^17 - 2 * q^19 + 3 * q^20 - 6 * q^22 - 12 * q^23 - 4 * q^25 + 4 * q^26 + 4 * q^28 - 6 * q^29 + 4 * q^31 - q^32 + 3 * q^34 - 12 * q^35 + 11 * q^37 + 4 * q^38 + 3 * q^40 + 3 * q^41 - 8 * q^43 - 6 * q^44 + 6 * q^46 + 12 * q^47 - 9 * q^49 - 4 * q^50 - 2 * q^52 - 6 * q^53 + 18 * q^55 + 4 * q^56 + 3 * q^58 + q^61 - 2 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^67 - 6 * q^68 - 12 * q^70 - 12 * q^71 - 20 * q^73 - 10 * q^74 - 2 * q^76 + 24 * q^77 - 14 * q^79 - 6 * q^80 - 6 * q^82 + 6 * q^83 + 18 * q^85 + 4 * q^86 + 12 * q^88 + 3 * q^89 + 8 * q^91 + 6 * q^92 - 6 * q^94 + 6 * q^95 - 26 * q^97 - 9 * q^98

Character values

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

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

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
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−3.00000			−0.948683
$11$	6.00000			1.80907			0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000			1.80907			0.904534	+	0.426401i	$0.140219\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−4.00000			−1.06904
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$		0			0
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	2.00000			0.392232
$27$		0			0
$28$	2.00000	+	3.46410i	0.377964	+	0.654654i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		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
$35$	−6.00000	−	10.3923i	−1.01419	−	1.75662i
$36$		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
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−3.00000	+	5.19615i	−0.452267	+	0.783349i
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$		0			0
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	9.00000	−	15.5885i	1.21356	−	2.10195i
$56$	2.00000	−	3.46410i	0.267261	−	0.462910i
$57$		0			0
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−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	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	−3.00000			−0.363803
$69$		0			0
$70$	−6.00000	+	10.3923i	−0.717137	+	1.24212i
$71$	−6.00000	+	10.3923i	−0.712069	+	1.23334i	0.252010	+	0.967725i	$0.418908\pi$
$71$	−6.00000	+	10.3923i	−0.712069	+	1.23334i	−0.964079	+	0.265615i	$0.914425\pi$
$72$		0			0
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$	−5.00000	−	3.46410i	−0.581238	−	0.402694i
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	12.0000	−	20.7846i	1.36753	−	2.36863i
$78$		0			0
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$	−3.00000			−0.335410
$81$		0			0
$82$	−3.00000			−0.331295
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$		0			0
$85$	9.00000			0.976187
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$		0			0
$88$	6.00000			0.639602
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	0.934508	−	0.355942i	$-0.115840\pi$
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	−0.775509	+	0.631337i	$0.782506\pi$
$90$		0			0
$91$	4.00000	+	6.92820i	0.419314	+	0.726273i
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$		0			0
$97$	−13.0000			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$98$	−4.50000	+	7.79423i	−0.454569	+	0.787336i
$99$		0			0
$100$	4.00000			0.400000
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	0.888977	−	0.457951i	$-0.151417\pi$
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	−0.841086	+	0.540901i	$0.818083\pi$
$110$	−18.0000			−1.71623
$111$		0			0
$112$	−4.00000			−0.377964
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	−0.884182	−	0.467143i	$-0.845283\pi$
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	0.0375328	−	0.999295i	$-0.488050\pi$
$114$		0			0
$115$	−9.00000	+	15.5885i	−0.839254	+	1.45363i
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$		0			0
$118$		0			0
$119$	12.0000			1.10004
$120$		0			0
$121$	25.0000			2.27273
$122$	−1.00000			−0.0905357
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	3.00000			0.268328
$126$		0			0
$127$	5.00000	+	8.66025i	0.443678	+	0.768473i	0.997959	−	0.0638564i	$-0.0203400\pi$
$127$	5.00000	+	8.66025i	0.443678	+	0.768473i	−0.554281	+	0.832330i	$0.687007\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	3.00000	−	5.19615i	0.263117	−	0.455733i
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	0.928199	+	0.372084i	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$		0			0
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$	2.00000			0.172774
$135$		0			0
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	−3.00000			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$138$		0			0
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	0.820495	−	0.571654i	$-0.193698\pi$
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	−0.905314	+	0.424743i	$0.860365\pi$
$140$	12.0000			1.01419
$141$		0			0
$142$	12.0000			1.00702
$143$	−6.00000	+	10.3923i	−0.501745	+	0.869048i
$144$		0			0
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	5.00000	+	8.66025i	0.413803	+	0.716728i
$147$		0			0
$148$	−0.500000	+	6.06218i	−0.0410997	+	0.498308i
$149$	21.0000			1.72039			0.860194	−	0.509968i	$-0.170343\pi$
$149$	21.0000			1.72039			0.860194	+	0.509968i	$0.170343\pi$
$150$		0			0
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.0615699	−	0.998103i	$-0.480389\pi$
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.833597	−	0.552372i	$-0.186277\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$		0			0
$154$	−24.0000			−1.93398
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	0.558661	−	0.829396i	$-0.311315\pi$
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	14.0000			1.11378
$159$		0			0
$160$	1.50000	+	2.59808i	0.118585	+	0.205396i
$161$	−12.0000	+	20.7846i	−0.945732	+	1.63806i
$162$		0			0
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−4.50000	−	7.79423i	−0.345134	−	0.597790i
$171$		0			0
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	−0.920722	−	0.390218i	$-0.872399\pi$
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	0.122422	−	0.992478i	$-0.460934\pi$
$174$		0			0
$175$	−16.0000			−1.20949
$176$	−3.00000	−	5.19615i	−0.226134	−	0.391675i
$177$		0			0
$178$	1.50000	−	2.59808i	0.112430	−	0.194734i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	0.500000	−	0.866025i	0.0371647	−	0.0643712i	−0.846845	−	0.531840i	$-0.821501\pi$
$181$	0.500000	−	0.866025i	0.0371647	−	0.0643712i	0.884009	+	0.467469i	$0.154834\pi$
$182$	4.00000	−	6.92820i	0.296500	−	0.513553i
$183$		0			0
$184$	−6.00000			−0.442326
$185$	1.50000	−	18.1865i	0.110282	−	1.33710i
$186$		0			0
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$		0			0
$190$	3.00000	−	5.19615i	0.217643	−	0.376969i
$191$	6.00000			0.434145			0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000			0.434145			0.217072	+	0.976156i	$0.430349\pi$
$192$		0			0
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$	6.50000	+	11.2583i	0.466673	+	0.808301i
$195$		0			0
$196$	9.00000			0.642857
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	0.914501	−	0.404584i	$-0.132584\pi$
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	−0.807630	+	0.589689i	$0.799250\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$		0			0
$202$	1.50000	+	2.59808i	0.105540	+	0.182800i
$203$	−6.00000	+	10.3923i	−0.421117	+	0.729397i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$		0			0
$208$	2.00000			0.138675
$209$	−6.00000	+	10.3923i	−0.415029	+	0.718851i
$210$		0			0
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$	6.00000			0.412082
$213$		0			0
$214$	12.0000			0.820303
$215$	−6.00000	+	10.3923i	−0.409197	+	0.708749i
$216$		0			0
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$	0.500000	−	0.866025i	0.0338643	−	0.0586546i
$219$		0			0
$220$	9.00000	+	15.5885i	0.606780	+	1.05097i
$221$	−6.00000			−0.403604
$222$		0			0
$223$	14.0000			0.937509			0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000			0.937509			0.468755	+	0.883328i	$0.344703\pi$
$224$	2.00000	+	3.46410i	0.133631	+	0.231455i
$225$		0			0
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	0.395860	+	0.918311i	$0.370447\pi$
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	−0.993210	+	0.116331i	$0.962887\pi$
$228$		0			0
$229$	−5.50000	+	9.52628i	−0.363450	+	0.629514i	−0.988526	−	0.151050i	$-0.951735\pi$
$229$	−5.50000	+	9.52628i	−0.363450	+	0.629514i	0.625076	+	0.780564i	$0.285068\pi$
$230$	18.0000			1.18688
$231$		0			0
$232$	−3.00000			−0.196960
$233$	9.00000			0.589610			0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000			0.589610			0.294805	+	0.955557i	$0.404745\pi$
$234$		0			0
$235$	9.00000	−	15.5885i	0.587095	−	1.01688i
$236$		0			0
$237$		0			0
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	−12.5000	−	21.6506i	−0.803530	−	1.39176i
$243$		0			0
$244$	0.500000	+	0.866025i	0.0320092	+	0.0554416i
$245$	−27.0000			−1.72497
$246$		0			0
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$	2.00000			0.127000
$249$		0			0
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−36.0000			−2.26330
$254$	5.00000	−	8.66025i	0.313728	−	0.543393i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	0.888110	+	0.459631i	$0.152018\pi$
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	−0.0460033	+	0.998941i	$0.514648\pi$
$258$		0			0
$259$	2.00000	−	24.2487i	0.124274	−	1.50674i
$260$	−6.00000			−0.372104
$261$		0			0
$262$	9.00000	−	15.5885i	0.556022	−	0.963058i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	−18.0000			−1.10573
$266$	4.00000	−	6.92820i	0.245256	−	0.424795i
$267$		0			0
$268$	−1.00000	−	1.73205i	−0.0610847	−	0.105802i
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$		0			0
$271$	5.00000	+	8.66025i	0.303728	+	0.526073i	0.976977	−	0.213343i	$-0.0684351\pi$
$271$	5.00000	+	8.66025i	0.303728	+	0.526073i	−0.673249	+	0.739416i	$0.735102\pi$
$272$	1.50000	−	2.59808i	0.0909509	−	0.157532i
$273$		0			0
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$	−12.0000	−	20.7846i	−0.723627	−	1.25336i
$276$		0			0
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$	−1.00000	+	1.73205i	−0.0599760	+	0.103882i
$279$		0			0
$280$	−6.00000	−	10.3923i	−0.358569	−	0.621059i
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	0.998217	−	0.0596933i	$-0.0190123\pi$
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	−0.550804	+	0.834634i	$0.685679\pi$
$282$		0			0
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	−0.524057	−	0.851683i	$-0.675582\pi$
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	0.999608	+	0.0280052i	$0.00891551\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	12.0000			0.709575
$287$	−6.00000	−	10.3923i	−0.354169	−	0.613438i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	9.00000			0.528498
$291$		0			0
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	−0.818878	−	0.573967i	$-0.805404\pi$
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	0.906509	+	0.422186i	$0.138737\pi$
$294$		0			0
$295$		0			0
$296$	5.50000	−	2.59808i	0.319681	−	0.151010i
$297$		0			0
$298$	−10.5000	−	18.1865i	−0.608249	−	1.05352i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$		0			0
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$	−22.0000			−1.26596
$303$		0			0
$304$	2.00000			0.114708
$305$	−1.50000	−	2.59808i	−0.0858898	−	0.148765i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	12.0000	+	20.7846i	0.683763	+	1.18431i
$309$		0			0
$310$	−6.00000			−0.340777
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	6.50000	+	11.2583i	0.367402	+	0.636358i	0.989158	−	0.146852i	$-0.0469141\pi$
$313$	6.50000	+	11.2583i	0.367402	+	0.636358i	−0.621757	+	0.783210i	$0.713581\pi$
$314$	−5.50000	+	9.52628i	−0.310383	+	0.537599i
$315$		0			0
$316$	−7.00000	−	12.1244i	−0.393781	−	0.682048i
$317$	−10.5000	−	18.1865i	−0.589739	−	1.02146i	−0.994266	−	0.106932i	$-0.965897\pi$
$317$	−10.5000	−	18.1865i	−0.589739	−	1.02146i	0.404528	−	0.914526i	$-0.367436\pi$
$318$		0			0
$319$	−18.0000			−1.00781
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$		0			0
$322$	24.0000			1.33747
$323$	−6.00000			−0.333849
$324$		0			0
$325$	8.00000			0.443760
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		0			0
$328$	1.50000	−	2.59808i	0.0828236	−	0.143455i
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−6.00000			−0.329293
$333$		0			0
$334$	−12.0000			−0.656611
$335$	3.00000	+	5.19615i	0.163908	+	0.283896i
$336$		0			0
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	−0.293783	−	0.955872i	$-0.594914\pi$
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	0.974701	−	0.223513i	$-0.0717525\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$	−4.50000	+	7.79423i	−0.244047	+	0.422701i
$341$	12.0000			0.649836
$342$		0			0
$343$	−8.00000			−0.431959
$344$	−4.00000			−0.215666
$345$		0			0
$346$	−10.5000	+	18.1865i	−0.564483	+	0.977714i
$347$	−6.00000			−0.322097			−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000			−0.322097			−0.161048	+	0.986947i	$0.551488\pi$
$348$		0			0
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	0.879097	−	0.476642i	$-0.158146\pi$
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	−0.852333	+	0.523000i	$0.824813\pi$
$350$	8.00000	+	13.8564i	0.427618	+	0.740656i
$351$		0			0
$352$	−3.00000	+	5.19615i	−0.159901	+	0.276956i
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	−0.997592	−	0.0693543i	$-0.977906\pi$
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	0.438733	−	0.898617i	$-0.355427\pi$
$354$		0			0
$355$	18.0000	+	31.1769i	0.955341	+	1.65470i
$356$	−3.00000			−0.159000
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−1.00000			−0.0525588
$363$		0			0
$364$	−8.00000			−0.419314
$365$	−15.0000	+	25.9808i	−0.785136	+	1.35990i
$366$		0			0
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	0.913493	+	0.406855i	$0.133375\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$	−16.5000	+	7.79423i	−0.857794	+	0.405203i
$371$	−24.0000			−1.24602
$372$		0			0
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$	9.00000	−	15.5885i	0.465379	−	0.806060i
$375$		0			0
$376$	6.00000			0.309426
$377$	3.00000	−	5.19615i	0.154508	−	0.267615i
$378$		0			0
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	0.994992	−	0.0999550i	$-0.0318699\pi$
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	−0.584060	+	0.811711i	$0.698537\pi$
$380$	−6.00000			−0.307794
$381$		0			0
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	−0.671027	−	0.741433i	$-0.734147\pi$
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	0.977613	+	0.210411i	$0.0674801\pi$
$384$		0			0
$385$	−36.0000	−	62.3538i	−1.83473	−	3.17785i
$386$	−5.50000	−	9.52628i	−0.279943	−	0.484875i
$387$		0			0
$388$	6.50000	−	11.2583i	0.329988	−	0.571555i
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	−0.957263	−	0.289220i	$-0.906604\pi$
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	0.729103	+	0.684403i	$0.239937\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	−4.50000	−	7.79423i	−0.227284	−	0.393668i
$393$		0			0
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$	21.0000	+	36.3731i	1.05662	+	1.83013i
$396$		0			0
$397$	35.0000			1.75660			0.878300	−	0.478110i	$-0.158678\pi$
$397$	35.0000			1.75660			0.878300	+	0.478110i	$0.158678\pi$
$398$	−4.00000	−	6.92820i	−0.200502	−	0.347279i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−6.00000			−0.299626			−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000			−0.299626			−0.149813	+	0.988714i	$0.547867\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	1.50000	−	2.59808i	0.0746278	−	0.129259i
$405$		0			0
$406$	12.0000			0.595550
$407$	33.0000	−	15.5885i	1.63575	−	0.772691i
$408$		0			0
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$		0			0
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$		0			0
$414$		0			0
$415$	18.0000			0.883585
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		0			0
$418$	12.0000			0.586939
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	−37.0000			−1.80327			−0.901635	−	0.432498i	$-0.857632\pi$
$421$	−37.0000			−1.80327			−0.901635	+	0.432498i	$0.857632\pi$
$422$	8.00000	+	13.8564i	0.389434	+	0.674519i
$423$		0			0
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	−2.00000	−	3.46410i	−0.0967868	−	0.167640i
$428$	−6.00000	−	10.3923i	−0.290021	−	0.502331i
$429$		0			0
$430$	12.0000			0.578691
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	−0.784683	−	0.619897i	$-0.787174\pi$
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	0.929188	+	0.369607i	$0.120508\pi$
$432$		0			0
$433$	−25.0000			−1.20142			−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000			−1.20142			−0.600712	+	0.799466i	$0.705116\pi$
$434$	−8.00000			−0.384012
$435$		0			0
$436$	−1.00000			−0.0478913
$437$	6.00000	−	10.3923i	0.287019	−	0.497131i
$438$		0			0
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	0.177325	+	0.984152i	$0.443256\pi$
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	−0.940963	+	0.338508i	$0.890078\pi$
$440$	9.00000	−	15.5885i	0.429058	−	0.743151i
$441$		0			0
$442$	3.00000	+	5.19615i	0.142695	+	0.247156i
$443$	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
$445$	9.00000			0.426641
$446$	−7.00000	−	12.1244i	−0.331460	−	0.574105i
$447$		0			0
$448$	2.00000	−	3.46410i	0.0944911	−	0.163663i
$449$	3.00000	−	5.19615i	0.141579	−	0.245222i	−0.786513	−	0.617574i	$-0.788115\pi$
$449$	3.00000	−	5.19615i	0.141579	−	0.245222i	0.928091	+	0.372353i	$0.121449\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	18.0000			0.846649
$453$		0			0
$454$	18.0000			0.844782
$455$	24.0000			1.12514
$456$		0			0
$457$	18.5000	−	32.0429i	0.865393	−	1.49891i	−0.00126243	−	0.999999i	$-0.500402\pi$
$457$	18.5000	−	32.0429i	0.865393	−	1.49891i	0.866656	−	0.498906i	$-0.166265\pi$
$458$	11.0000			0.513996
$459$		0			0
$460$	−9.00000	−	15.5885i	−0.419627	−	0.726816i
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	−0.968945	−	0.247276i	$-0.920465\pi$
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	0.270326	−	0.962769i	$-0.412869\pi$
$462$		0			0
$463$	8.00000	−	13.8564i	0.371792	−	0.643962i	−0.618050	−	0.786139i	$-0.712077\pi$
$463$	8.00000	−	13.8564i	0.371792	−	0.643962i	0.989841	+	0.142177i	$0.0454103\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$		0			0
$466$	−4.50000	−	7.79423i	−0.208458	−	0.361061i
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$		0			0
$469$	4.00000	+	6.92820i	0.184703	+	0.319915i
$470$	−18.0000			−0.830278
$471$		0			0
$472$		0			0
$473$	−24.0000			−1.10352
$474$		0			0
$475$	8.00000			0.367065
$476$	−6.00000	+	10.3923i	−0.275010	+	0.476331i
$477$		0			0
$478$		0			0
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	−1.00000	+	12.1244i	−0.0455961	+	0.552823i
$482$	14.0000			0.637683
$483$		0			0
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	−19.5000	+	33.7750i	−0.885449	+	1.53364i
$486$		0			0
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	0.500000	−	0.866025i	0.0226339	−	0.0392031i
$489$		0			0
$490$	13.5000	+	23.3827i	0.609868	+	1.05632i
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$		0			0
$493$	−4.50000	−	7.79423i	−0.202670	−	0.351034i
$494$	−2.00000	+	3.46410i	−0.0899843	+	0.155857i
$495$		0			0
$496$	−1.00000	−	1.73205i	−0.0449013	−	0.0777714i
$497$	24.0000	+	41.5692i	1.07655	+	1.86463i
$498$		0			0
$499$	−7.00000	+	12.1244i	−0.313363	+	0.542761i	−0.979088	−	0.203436i	$-0.934789\pi$
$499$	−7.00000	+	12.1244i	−0.313363	+	0.542761i	0.665725	+	0.746197i	$0.268122\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$		0			0
$502$		0			0
$503$	15.0000	+	25.9808i	0.668817	+	1.15842i	0.978235	+	0.207499i	$0.0665323\pi$
$503$	15.0000	+	25.9808i	0.668817	+	1.15842i	−0.309418	+	0.950926i	$0.600134\pi$
$504$		0			0
$505$	−4.50000	+	7.79423i	−0.200247	+	0.346839i
$506$	18.0000	+	31.1769i	0.800198	+	1.38598i
$507$		0			0
$508$	−10.0000			−0.443678
$509$	13.5000	+	23.3827i	0.598377	+	1.03642i	0.993061	+	0.117602i	$0.0375208\pi$
$509$	13.5000	+	23.3827i	0.598377	+	1.03642i	−0.394684	+	0.918817i	$0.629146\pi$
$510$		0			0
$511$	−20.0000	+	34.6410i	−0.884748	+	1.53243i
$512$	1.00000			0.0441942
$513$		0			0
$514$	13.5000	−	23.3827i	0.595459	−	1.03137i
$515$	−6.00000	+	10.3923i	−0.264392	+	0.457940i
$516$		0			0
$517$	36.0000			1.58328
$518$	−22.0000	+	10.3923i	−0.966625	+	0.456612i
$519$		0			0
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	0.924229	+	0.381839i	$0.124709\pi$
$522$		0			0
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	0.428269	+	0.903651i	$0.359124\pi$
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	−0.996719	+	0.0809336i	$0.974210\pi$
$524$	−18.0000			−0.786334
$525$		0			0
$526$		0			0
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$		0			0
$529$	13.0000			0.565217
$530$	9.00000	+	15.5885i	0.390935	+	0.677119i
$531$		0			0
$532$	−8.00000			−0.346844
$533$	3.00000	+	5.19615i	0.129944	+	0.225070i
$534$		0			0
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$		0			0
$538$	9.00000	+	15.5885i	0.388018	+	0.672066i
$539$	−27.0000	−	46.7654i	−1.16297	−	2.01433i
$540$		0			0
$541$	35.0000			1.50477			0.752384	−	0.658725i	$-0.228904\pi$
$541$	35.0000			1.50477			0.752384	+	0.658725i	$0.228904\pi$
$542$	5.00000	−	8.66025i	0.214768	−	0.371990i
$543$		0			0
$544$	−3.00000			−0.128624
$545$	3.00000			0.128506
$546$		0			0
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$		0			0
$550$	−12.0000	+	20.7846i	−0.511682	+	0.886259i
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$		0			0
$553$	28.0000	+	48.4974i	1.19068	+	2.06232i
$554$	−1.00000			−0.0424859
$555$		0			0
$556$	2.00000			0.0848189
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	−0.968769	−	0.247964i	$-0.920239\pi$
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	0.269642	−	0.962961i	$-0.413095\pi$
$558$		0			0
$559$	4.00000	−	6.92820i	0.169182	−	0.293032i
$560$	−6.00000	+	10.3923i	−0.253546	+	0.439155i
$561$		0			0
$562$	7.50000	−	12.9904i	0.316368	−	0.547966i
$563$	−6.00000			−0.252870			−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000			−0.252870			−0.126435	+	0.991975i	$0.540353\pi$
$564$		0			0
$565$	−54.0000			−2.27180
$566$	−16.0000			−0.672530
$567$		0			0
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	−3.00000			−0.125767			−0.0628833	−	0.998021i	$-0.520030\pi$
$569$	−3.00000			−0.125767			−0.0628833	+	0.998021i	$0.520030\pi$
$570$		0			0
$571$	−19.0000	−	32.9090i	−0.795125	−	1.37720i	−0.922760	−	0.385376i	$-0.874072\pi$
$571$	−19.0000	−	32.9090i	−0.795125	−	1.37720i	0.127634	−	0.991821i	$-0.459262\pi$
$572$	−6.00000	−	10.3923i	−0.250873	−	0.434524i
$573$		0			0
$574$	−6.00000	+	10.3923i	−0.250435	+	0.433766i
$575$	12.0000	+	20.7846i	0.500435	+	0.866778i
$576$		0			0
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	0.965701	+	0.259656i	$0.0836092\pi$
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	−0.257982	+	0.966150i	$0.583058\pi$
$578$	−8.00000			−0.332756
$579$		0			0
$580$	−4.50000	−	7.79423i	−0.186852	−	0.323638i
$581$	24.0000			0.995688
$582$		0			0
$583$	−18.0000	−	31.1769i	−0.745484	−	1.29122i
$584$	−10.0000			−0.413803
$585$		0			0
$586$	−3.00000			−0.123929
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	−0.618322	−	0.785925i	$-0.712187\pi$
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	0.989792	+	0.142520i	$0.0455206\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$		0			0
$592$	−5.00000	−	3.46410i	−0.205499	−	0.142374i
$593$	−27.0000			−1.10876			−0.554379	−	0.832265i	$-0.687044\pi$
$593$	−27.0000			−1.10876			−0.554379	+	0.832265i	$0.687044\pi$
$594$		0			0
$595$	18.0000	−	31.1769i	0.737928	−	1.27813i
$596$	−10.5000	+	18.1865i	−0.430097	+	0.744949i
$597$		0			0
$598$	−12.0000			−0.490716
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	−0.920783	−	0.390075i	$-0.872449\pi$
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	0.798206	+	0.602384i	$0.205782\pi$
$600$		0			0
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	0.967600	−	0.252486i	$-0.0812483\pi$
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	−0.702460	+	0.711723i	$0.747915\pi$
$602$	16.0000			0.652111
$603$		0			0
$604$	11.0000	+	19.0526i	0.447584	+	0.775238i
$605$	37.5000	−	64.9519i	1.52459	−	2.64067i
$606$		0			0
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$		0			0
$610$	−1.50000	+	2.59808i	−0.0607332	+	0.105193i
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$		0			0
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$		0			0
$616$	12.0000	−	20.7846i	0.483494	−	0.837436i
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	0.626017	−	0.779809i	$-0.284684\pi$
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	−0.988343	+	0.152242i	$0.951351\pi$
$618$		0			0
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$	3.00000	+	5.19615i	0.120483	+	0.208683i
$621$		0			0
$622$		0			0
$623$	12.0000			0.480770
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	6.50000	−	11.2583i	0.259792	−	0.449973i
$627$		0			0
$628$	11.0000			0.438948
$629$	15.0000	+	10.3923i	0.598089	+	0.414368i
$630$		0			0
$631$	5.00000	+	8.66025i	0.199047	+	0.344759i	0.948220	−	0.317615i	$-0.102882\pi$
$631$	5.00000	+	8.66025i	0.199047	+	0.344759i	−0.749173	+	0.662375i	$0.769549\pi$
$632$	−7.00000	+	12.1244i	−0.278445	+	0.482281i
$633$		0			0
$634$	−10.5000	+	18.1865i	−0.417008	+	0.722280i
$635$	30.0000			1.19051
$636$		0			0
$637$	18.0000			0.713186
$638$	9.00000	+	15.5885i	0.356313	+	0.617153i
$639$		0			0
$640$	−3.00000			−0.118585
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	0.580674	−	0.814136i	$-0.302789\pi$
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	−0.995400	+	0.0958109i	$0.969456\pi$
$642$		0			0
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$	−12.0000	−	20.7846i	−0.472866	−	0.819028i
$645$		0			0
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$		0			0
$649$		0			0
$650$	−4.00000	−	6.92820i	−0.156893	−	0.271746i
$651$		0			0
$652$	−16.0000			−0.626608
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	−0.835182	−	0.549973i	$-0.814638\pi$
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	0.893882	+	0.448303i	$0.147971\pi$
$654$		0			0
$655$	54.0000			2.10995
$656$	−3.00000			−0.117130
$657$		0			0
$658$	−24.0000			−0.935617
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$		0			0
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	−0.513680	−	0.857982i	$-0.671718\pi$
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	0.999874	+	0.0158695i	$0.00505163\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$		0			0
$664$	3.00000	+	5.19615i	0.116423	+	0.201650i
$665$	24.0000			0.930680
$666$		0			0
$667$	18.0000			0.696963
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$		0			0
$670$	3.00000	−	5.19615i	0.115900	−	0.200745i
$671$	3.00000	−	5.19615i	0.115814	−	0.200595i
$672$		0			0
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	−0.753420	−	0.657539i	$-0.771597\pi$
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	0.946156	+	0.323711i	$0.104931\pi$
$674$	−25.0000			−0.962964
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−3.00000			−0.115299			−0.0576497	−	0.998337i	$-0.518361\pi$
$677$	−3.00000			−0.115299			−0.0576497	+	0.998337i	$0.518361\pi$
$678$		0			0
$679$	−26.0000	+	45.0333i	−0.997788	+	1.72822i
$680$	9.00000			0.345134
$681$		0			0
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$		0			0
$685$	−4.50000	+	7.79423i	−0.171936	+	0.297802i
$686$	4.00000	+	6.92820i	0.152721	+	0.264520i
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	12.0000			0.457164
$690$		0			0
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.743170	−	0.669102i	$-0.766679\pi$
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.207875	−	0.978155i	$-0.566655\pi$
$692$	21.0000			0.798300
$693$		0			0
$694$	3.00000	+	5.19615i	0.113878	+	0.197243i
$695$	−6.00000			−0.227593
$696$		0			0
$697$	9.00000			0.340899
$698$	0.500000	−	0.866025i	0.0189253	−	0.0327795i
$699$		0			0
$700$	8.00000	−	13.8564i	0.302372	−	0.523723i
$701$	15.0000	+	25.9808i	0.566542	+	0.981280i	0.996904	+	0.0786236i	$0.0250525\pi$
$701$	15.0000	+	25.9808i	0.566542	+	0.981280i	−0.430362	+	0.902656i	$0.641614\pi$
$702$		0			0
$703$	−1.00000	+	12.1244i	−0.0377157	+	0.457279i
$704$	6.00000			0.226134
$705$		0			0
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$	−6.00000	+	10.3923i	−0.225653	+	0.390843i
$708$		0			0
$709$	−22.0000			−0.826227			−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000			−0.826227			−0.413114	+	0.910679i	$0.635559\pi$
$710$	18.0000	−	31.1769i	0.675528	−	1.17005i
$711$		0			0
$712$	1.50000	+	2.59808i	0.0562149	+	0.0973670i
$713$	−12.0000			−0.449404
$714$		0			0
$715$	18.0000	+	31.1769i	0.673162	+	1.16595i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−21.0000	−	36.3731i	−0.783168	−	1.35649i	−0.930087	−	0.367338i	$-0.880269\pi$
$719$	−21.0000	−	36.3731i	−0.783168	−	1.35649i	0.146920	−	0.989148i	$-0.453064\pi$
$720$		0			0
$721$	−8.00000	+	13.8564i	−0.297936	+	0.516040i
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$		0			0
$724$	0.500000	+	0.866025i	0.0185824	+	0.0321856i
$725$	6.00000	+	10.3923i	0.222834	+	0.385961i
$726$		0			0
$727$	2.00000	−	3.46410i	0.0741759	−	0.128476i	−0.826552	−	0.562861i	$-0.809701\pi$
$727$	2.00000	−	3.46410i	0.0741759	−	0.128476i	0.900728	+	0.434384i	$0.143034\pi$
$728$	4.00000	+	6.92820i	0.148250	+	0.256776i
$729$		0			0
$730$	30.0000			1.11035
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$		0			0
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	−0.883902	−	0.467671i	$-0.845093\pi$
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	0.846967	+	0.531646i	$0.178426\pi$
$734$	−4.00000			−0.147643
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	−6.00000	+	10.3923i	−0.221013	+	0.382805i
$738$		0			0
$739$	38.0000			1.39785			0.698926	−	0.715194i	$-0.253662\pi$
$739$	38.0000			1.39785			0.698926	+	0.715194i	$0.253662\pi$
$740$	15.0000	+	10.3923i	0.551411	+	0.382029i
$741$		0			0
$742$	12.0000	+	20.7846i	0.440534	+	0.763027i
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	−0.915794	−	0.401648i	$-0.868437\pi$
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	0.805735	+	0.592277i	$0.201771\pi$
$744$		0			0
$745$	31.5000	−	54.5596i	1.15407	−	1.99891i
$746$	−25.0000			−0.915315
$747$		0			0
$748$	−18.0000			−0.658145
$749$	24.0000	+	41.5692i	0.876941	+	1.51891i
$750$		0			0
$751$	−16.0000			−0.583848			−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000			−0.583848			−0.291924	+	0.956441i	$0.594295\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$		0			0
$754$	−6.00000			−0.218507
$755$	−33.0000	−	57.1577i	−1.20099	−	2.08018i
$756$		0			0
$757$	−17.5000	−	30.3109i	−0.636048	−	1.10167i	−0.986292	−	0.165009i	$-0.947235\pi$
$757$	−17.5000	−	30.3109i	−0.636048	−	1.10167i	0.350244	−	0.936659i	$-0.386099\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$		0			0
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	0.999925	−	0.0122260i	$-0.00389175\pi$
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	−0.510551	+	0.859848i	$0.670558\pi$
$762$		0			0
$763$	4.00000			0.144810
$764$	−3.00000	+	5.19615i	−0.108536	+	0.187990i
$765$		0			0
$766$	−12.0000			−0.433578
$767$		0			0
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$	−36.0000	+	62.3538i	−1.29735	+	2.24708i
$771$		0			0
$772$	−5.50000	+	9.52628i	−0.197949	+	0.342858i
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	−0.990721	−	0.135910i	$-0.956604\pi$
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	0.613062	+	0.790034i	$0.289937\pi$
$774$		0			0
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$	−13.0000			−0.466673
$777$		0			0
$778$	9.00000			0.322666
$779$	3.00000	+	5.19615i	0.107486	+	0.186171i
$780$		0			0
$781$	−36.0000	+	62.3538i	−1.28818	+	2.23120i
$782$	−9.00000	+	15.5885i	−0.321839	+	0.557442i
$783$		0			0
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$	−33.0000			−1.17782
$786$		0			0
$787$	20.0000			0.712923			0.356462	−	0.934310i	$-0.383983\pi$
$787$	20.0000			0.712923			0.356462	+	0.934310i	$0.383983\pi$
$788$	−3.00000			−0.106871
$789$		0			0
$790$	21.0000	−	36.3731i	0.747146	−	1.29410i
$791$	−72.0000			−2.56003
$792$		0			0
$793$	1.00000	+	1.73205i	0.0355110	+	0.0615069i
$794$	−17.5000	−	30.3109i	−0.621052	−	1.07569i
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	0.661441	−	0.749997i	$-0.269945\pi$
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	−0.980237	+	0.197826i	$0.936612\pi$
$798$		0			0
$799$	9.00000	+	15.5885i	0.318397	+	0.551480i
$800$	4.00000			0.141421
$801$		0			0
$802$	3.00000	+	5.19615i	0.105934	+	0.183483i
$803$	−60.0000			−2.11735
$804$		0			0
$805$	36.0000	+	62.3538i	1.26883	+	2.19768i
$806$	4.00000			0.140894
$807$		0			0
$808$	−3.00000			−0.105540
$809$	21.0000	−	36.3731i	0.738321	−	1.27881i	−0.214930	−	0.976629i	$-0.568952\pi$
$809$	21.0000	−	36.3731i	0.738321	−	1.27881i	0.953251	−	0.302180i	$-0.0977142\pi$
$810$		0			0
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	−0.690693	−	0.723148i	$-0.742694\pi$
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	0.971611	+	0.236584i	$0.0760278\pi$
$812$	−6.00000	−	10.3923i	−0.210559	−	0.364698i
$813$		0			0
$814$	−30.0000	−	20.7846i	−1.05150	−	0.728500i
$815$	48.0000			1.68137
$816$		0			0
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$	−5.50000	+	9.52628i	−0.192303	+	0.333079i
$819$		0			0
$820$	9.00000			0.314294
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$		0			0
$823$	17.0000	+	29.4449i	0.592583	+	1.02638i	0.993883	+	0.110437i	$0.0352250\pi$
$823$	17.0000	+	29.4449i	0.592583	+	1.02638i	−0.401300	+	0.915947i	$0.631442\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$		0			0
$827$	12.0000	−	20.7846i	0.417281	−	0.722752i	−0.578384	−	0.815765i	$-0.696316\pi$
$827$	12.0000	−	20.7846i	0.417281	−	0.722752i	0.995665	+	0.0930129i	$0.0296498\pi$
$828$		0			0
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	0.546971	−	0.837151i	$-0.315781\pi$
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	−0.998480	+	0.0551154i	$0.982447\pi$
$830$	−9.00000	−	15.5885i	−0.312395	−	0.541083i
$831$		0			0
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	13.5000	−	23.3827i	0.467747	−	0.810162i
$834$		0			0
$835$	−18.0000	−	31.1769i	−0.622916	−	1.07892i
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$		0			0
$838$		0			0
$839$	3.00000	+	5.19615i	0.103572	+	0.179391i	0.913154	−	0.407615i	$-0.133640\pi$
$839$	3.00000	+	5.19615i	0.103572	+	0.179391i	−0.809582	+	0.587007i	$0.800306\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	18.5000	+	32.0429i	0.637552	+	1.10427i
$843$		0			0
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	27.0000			0.928828
$846$		0			0
$847$	50.0000	−	86.6025i	1.71802	−	2.97570i
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$		0			0
$850$	−12.0000			−0.411597
$851$	−33.0000	+	15.5885i	−1.13123	+	0.534365i
$852$		0			0
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	0.986846	+	0.161664i	$0.0516860\pi$
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	−0.353418	+	0.935466i	$0.614981\pi$
$854$	−2.00000	+	3.46410i	−0.0684386	+	0.118539i
$855$		0			0
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	−3.00000			−0.102478			−0.0512390	−	0.998686i	$-0.516317\pi$
$857$	−3.00000			−0.102478			−0.0512390	+	0.998686i	$0.516317\pi$
$858$		0			0
$859$	−52.0000			−1.77422			−0.887109	−	0.461561i	$-0.847290\pi$
$859$	−52.0000			−1.77422			−0.887109	+	0.461561i	$0.847290\pi$
$860$	−6.00000	−	10.3923i	−0.204598	−	0.354375i
$861$		0			0
$862$	−6.00000			−0.204361
$863$	24.0000	+	41.5692i	0.816970	+	1.41503i	0.907905	+	0.419176i	$0.137681\pi$
$863$	24.0000	+	41.5692i	0.816970	+	1.41503i	−0.0909355	+	0.995857i	$0.528986\pi$
$864$		0			0
$865$	−63.0000			−2.14206
$866$	12.5000	+	21.6506i	0.424767	+	0.735719i
$867$		0			0
$868$	4.00000	+	6.92820i	0.135769	+	0.235159i
$869$	−42.0000	+	72.7461i	−1.42475	+	2.46774i
$870$		0			0
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	0.500000	+	0.866025i	0.0169321	+	0.0293273i
$873$		0			0
$874$	−12.0000			−0.405906
$875$	6.00000	−	10.3923i	0.202837	−	0.351324i
$876$		0			0
$877$	−25.0000			−0.844190			−0.422095	−	0.906552i	$-0.638705\pi$
$877$	−25.0000			−0.844190			−0.422095	+	0.906552i	$0.638705\pi$
$878$	32.0000			1.07995
$879$		0			0
$880$	−18.0000			−0.606780
$881$	25.5000	−	44.1673i	0.859117	−	1.48803i	−0.0136556	−	0.999907i	$-0.504347\pi$
$881$	25.5000	−	44.1673i	0.859117	−	1.48803i	0.872772	−	0.488127i	$-0.162320\pi$
$882$		0			0
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	−0.882361	−	0.470573i	$-0.844047\pi$
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	0.848709	+	0.528861i	$0.177381\pi$
$884$	3.00000	−	5.19615i	0.100901	−	0.174766i
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	−6.00000			−0.201460			−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000			−0.201460			−0.100730	+	0.994914i	$0.532118\pi$
$888$		0			0
$889$	40.0000			1.34156
$890$	−4.50000	−	7.79423i	−0.150840	−	0.261263i
$891$		0			0
$892$	−7.00000	+	12.1244i	−0.234377	+	0.405953i
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$		0			0
$895$		0			0
$896$	−4.00000			−0.133631
$897$		0			0
$898$	−6.00000			−0.200223
$899$	−6.00000			−0.200111
$900$		0			0
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$	−18.0000			−0.599334
$903$		0			0
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$	−1.50000	−	2.59808i	−0.0498617	−	0.0863630i
$906$		0			0
$907$	29.0000	−	50.2295i	0.962929	−	1.66784i	0.247851	−	0.968798i	$-0.420276\pi$
$907$	29.0000	−	50.2295i	0.962929	−	1.66784i	0.715079	−	0.699044i	$-0.246391\pi$
$908$	−9.00000	−	15.5885i	−0.298675	−	0.517321i
$909$		0			0
$910$	−12.0000	−	20.7846i	−0.397796	−	0.689003i
$911$	42.0000			1.39152			0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000			1.39152			0.695761	+	0.718273i	$0.255067\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	−37.0000			−1.22385
$915$		0			0
$916$	−5.50000	−	9.52628i	−0.181725	−	0.314757i
$917$	72.0000			2.37765
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$	−9.00000	+	15.5885i	−0.296721	+	0.513936i
$921$		0			0
$922$	−15.0000	+	25.9808i	−0.493999	+	0.855631i
$923$	−12.0000	−	20.7846i	−0.394985	−	0.684134i
$924$		0			0
$925$	−20.0000	−	13.8564i	−0.657596	−	0.455596i
$926$	−16.0000			−0.525793
$927$		0			0
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	−4.50000	+	7.79423i	−0.147640	+	0.255720i	−0.930355	−	0.366660i	$-0.880501\pi$
$929$	−4.50000	+	7.79423i	−0.147640	+	0.255720i	0.782715	+	0.622381i	$0.213834\pi$
$930$		0			0
$931$	18.0000			0.589926
$932$	−4.50000	+	7.79423i	−0.147402	+	0.255308i
$933$		0			0
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$	54.0000			1.76599
$936$		0			0
$937$	0.500000	+	0.866025i	0.0163343	+	0.0282918i	0.874077	−	0.485787i	$-0.161467\pi$
$937$	0.500000	+	0.866025i	0.0163343	+	0.0282918i	−0.857743	+	0.514079i	$0.828134\pi$
$938$	4.00000	−	6.92820i	0.130605	−	0.226214i
$939$		0			0
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	13.5000	+	23.3827i	0.440087	+	0.762254i	0.997695	−	0.0678506i	$-0.0216141\pi$
$941$	13.5000	+	23.3827i	0.440087	+	0.762254i	−0.557608	+	0.830104i	$0.688281\pi$
$942$		0			0
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$		0			0
$945$		0			0
$946$	12.0000	+	20.7846i	0.390154	+	0.675766i
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	−0.932002	−	0.362454i	$-0.881939\pi$
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	0.152106	−	0.988364i	$-0.451394\pi$
$948$		0			0
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$	−4.00000	−	6.92820i	−0.129777	−	0.224781i
$951$		0			0
$952$	12.0000			0.388922
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	0.813337	−	0.581793i	$-0.197649\pi$
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	−0.910516	+	0.413473i	$0.864315\pi$
$954$		0			0
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$		0			0
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	−6.00000	+	10.3923i	−0.193750	+	0.335585i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	11.0000	−	5.19615i	0.354654	−	0.167531i
$963$		0			0
$964$	−7.00000	−	12.1244i	−0.225455	−	0.390499i
$965$	16.5000	−	28.5788i	0.531154	−	0.919985i
$966$		0			0
$967$	26.0000	−	45.0333i	0.836104	−	1.44817i	−0.0570251	−	0.998373i	$-0.518161\pi$
$967$	26.0000	−	45.0333i	0.836104	−	1.44817i	0.893129	−	0.449801i	$-0.148505\pi$
$968$	25.0000			0.803530
$969$		0			0
$970$	39.0000			1.25221
$971$	15.0000	+	25.9808i	0.481373	+	0.833762i	0.999771	−	0.0213768i	$-0.00680496\pi$
$971$	15.0000	+	25.9808i	0.481373	+	0.833762i	−0.518399	+	0.855139i	$0.673472\pi$
$972$		0			0
$973$	−8.00000			−0.256468
$974$	−1.00000	−	1.73205i	−0.0320421	−	0.0554985i
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$		0			0
$979$	9.00000	+	15.5885i	0.287641	+	0.498209i
$980$	13.5000	−	23.3827i	0.431242	−	0.746933i
$981$		0			0
$982$	3.00000	+	5.19615i	0.0957338	+	0.165816i
$983$	−15.0000	−	25.9808i	−0.478426	−	0.828658i	0.521268	−	0.853393i	$-0.325459\pi$
$983$	−15.0000	−	25.9808i	−0.478426	−	0.828658i	−0.999694	+	0.0247352i	$0.992126\pi$
$984$		0			0
$985$	9.00000			0.286764
$986$	−4.50000	+	7.79423i	−0.143309	+	0.248219i
$987$		0			0
$988$	4.00000			0.127257
$989$	24.0000			0.763156
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$		0			0
$994$	24.0000	−	41.5692i	0.761234	−	1.31850i
$995$	12.0000	−	20.7846i	0.380426	−	0.658916i
$996$		0			0
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	14.0000			0.443162
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.f.d.433.1		2
3.2	odd	2		74.2.c.b.63.1	yes	2
12.11	even	2		592.2.i.a.433.1		2
37.10	even	3	inner	666.2.f.d.343.1		2
111.11	odd	6		2738.2.a.c.1.1		1
111.26	odd	6		2738.2.a.a.1.1		1
111.47	odd	6		74.2.c.b.47.1	✓	2
444.47	even	6		592.2.i.a.417.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.c.b.47.1	✓	2	111.47	odd	6
74.2.c.b.63.1	yes	2	3.2	odd	2
592.2.i.a.417.1		2	444.47	even	6
592.2.i.a.433.1		2	12.11	even	2
666.2.f.d.343.1		2	37.10	even	3	inner
666.2.f.d.433.1		2	1.1	even	1	trivial
2738.2.a.a.1.1		1	111.26	odd	6
2738.2.a.c.1.1		1	111.11	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(2.00000 - 3.46410i) q^{7} +1.00000 q^{8} -3.00000 q^{10} +6.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} -4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} -6.00000 q^{23} +(-2.00000 - 3.46410i) q^{25} +2.00000 q^{26} +(2.00000 + 3.46410i) q^{28} -3.00000 q^{29} +2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{34} +(-6.00000 - 10.3923i) q^{35} +(5.50000 - 2.59808i) q^{37} +2.00000 q^{38} +(1.50000 - 2.59808i) q^{40} +(1.50000 - 2.59808i) q^{41} -4.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +(3.00000 + 5.19615i) q^{46} +6.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(9.00000 - 15.5885i) q^{55} +(2.00000 - 3.46410i) q^{56} +(1.50000 + 2.59808i) q^{58} +(0.500000 - 0.866025i) q^{61} +(-1.00000 - 1.73205i) q^{62} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-1.00000 + 1.73205i) q^{67} -3.00000 q^{68} +(-6.00000 + 10.3923i) q^{70} +(-6.00000 + 10.3923i) q^{71} -10.0000 q^{73} +(-5.00000 - 3.46410i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(12.0000 - 20.7846i) q^{77} +(-7.00000 + 12.1244i) q^{79} -3.00000 q^{80} -3.00000 q^{82} +(3.00000 + 5.19615i) q^{83} +9.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +6.00000 q^{88} +(1.50000 + 2.59808i) q^{89} +(4.00000 + 6.92820i) q^{91} +(3.00000 - 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(3.00000 + 5.19615i) q^{95} -13.0000 q^{97} +(-4.50000 + 7.79423i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 3 q^{5} + 4 q^{7} + 2 q^{8} - 6 q^{10} + 12 q^{11} - 2 q^{13} - 8 q^{14} - q^{16} + 3 q^{17} - 2 q^{19} + 3 q^{20} - 6 q^{22} - 12 q^{23} - 4 q^{25} + 4 q^{26} + 4 q^{28} - 6 q^{29}+ \cdots - 9 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 3 * q^5 + 4 * q^7 + 2 * q^8 - 6 * q^10 + 12 * q^11 - 2 * q^13 - 8 * q^14 - q^16 + 3 * q^17 - 2 * q^19 + 3 * q^20 - 6 * q^22 - 12 * q^23 - 4 * q^25 + 4 * q^26 + 4 * q^28 - 6 * q^29 + 4 * q^31 - q^32 + 3 * q^34 - 12 * q^35 + 11 * q^37 + 4 * q^38 + 3 * q^40 + 3 * q^41 - 8 * q^43 - 6 * q^44 + 6 * q^46 + 12 * q^47 - 9 * q^49 - 4 * q^50 - 2 * q^52 - 6 * q^53 + 18 * q^55 + 4 * q^56 + 3 * q^58 + q^61 - 2 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^67 - 6 * q^68 - 12 * q^70 - 12 * q^71 - 20 * q^73 - 10 * q^74 - 2 * q^76 + 24 * q^77 - 14 * q^79 - 6 * q^80 - 6 * q^82 + 6 * q^83 + 18 * q^85 + 4 * q^86 + 12 * q^88 + 3 * q^89 + 8 * q^91 + 6 * q^92 - 6 * q^94 + 6 * q^95 - 26 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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