LMFDB - Embedded newform 882.2.h.b.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$1$
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 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.79
Dual form			882.2.h.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{8} -3.00000 q^{9} -3.00000 q^{11} +(1.50000 + 0.866025i) q^{12} +(1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{22} -6.00000 q^{23} -1.73205i q^{24} -5.00000 q^{25} +(1.00000 - 1.73205i) q^{26} +5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +5.19615i q^{33} +(-1.50000 + 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} +(2.00000 - 3.46410i) q^{37} +1.00000 q^{38} +(3.00000 - 1.73205i) q^{39} +(4.50000 + 7.79423i) q^{41} +(0.500000 - 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(2.50000 + 4.33013i) q^{50} +(-4.50000 + 2.59808i) q^{51} -2.00000 q^{52} +(-6.00000 - 10.3923i) q^{53} +(4.50000 - 2.59808i) q^{54} +(1.50000 + 0.866025i) q^{57} +6.00000 q^{58} +(1.50000 - 2.59808i) q^{59} +(4.00000 + 6.92820i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(4.50000 - 2.59808i) q^{66} +(-2.50000 + 4.33013i) q^{67} +3.00000 q^{68} +10.3923i q^{69} -12.0000 q^{71} -3.00000 q^{72} +(5.50000 + 9.52628i) q^{73} -4.00000 q^{74} +8.66025i q^{75} +(-0.500000 - 0.866025i) q^{76} +(-3.00000 - 1.73205i) q^{78} +(2.00000 + 3.46410i) q^{79} +9.00000 q^{81} +(4.50000 - 7.79423i) q^{82} +(6.00000 - 10.3923i) q^{83} -1.00000 q^{86} +(9.00000 + 5.19615i) q^{87} -3.00000 q^{88} +(3.00000 - 5.19615i) q^{89} +(3.00000 - 5.19615i) q^{92} +(6.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(1.50000 + 0.866025i) q^{96} +(2.50000 - 4.33013i) q^{97} +9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 3 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 - 3 * q^6 + 2 * q^8 - 6 * q^9	$ 2 q - q^{2} - q^{4} - 3 q^{6} + 2 q^{8} - 6 q^{9} - 6 q^{11} + 3 q^{12} + 2 q^{13} - q^{16} - 3 q^{17} + 3 q^{18} - q^{19} + 3 q^{22} - 12 q^{23} - 10 q^{25} + 2 q^{26} - 6 q^{29} - 4 q^{31} - q^{32} - 3 q^{34} + 3 q^{36} + 4 q^{37} + 2 q^{38} + 6 q^{39} + 9 q^{41} + q^{43} + 3 q^{44} + 6 q^{46} - 6 q^{47} - 3 q^{48} + 5 q^{50} - 9 q^{51} - 4 q^{52} - 12 q^{53} + 9 q^{54} + 3 q^{57} + 12 q^{58} + 3 q^{59} + 8 q^{61} + 8 q^{62} + 2 q^{64} + 9 q^{66} - 5 q^{67} + 6 q^{68} - 24 q^{71} - 6 q^{72} + 11 q^{73} - 8 q^{74} - q^{76} - 6 q^{78} + 4 q^{79} + 18 q^{81} + 9 q^{82} + 12 q^{83} - 2 q^{86} + 18 q^{87} - 6 q^{88} + 6 q^{89} + 6 q^{92} + 12 q^{93} - 6 q^{94} + 3 q^{96} + 5 q^{97} + 18 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 - 3 * q^6 + 2 * q^8 - 6 * q^9 - 6 * q^11 + 3 * q^12 + 2 * q^13 - q^16 - 3 * q^17 + 3 * q^18 - q^19 + 3 * q^22 - 12 * q^23 - 10 * q^25 + 2 * q^26 - 6 * q^29 - 4 * q^31 - q^32 - 3 * q^34 + 3 * q^36 + 4 * q^37 + 2 * q^38 + 6 * q^39 + 9 * q^41 + q^43 + 3 * q^44 + 6 * q^46 - 6 * q^47 - 3 * q^48 + 5 * q^50 - 9 * q^51 - 4 * q^52 - 12 * q^53 + 9 * q^54 + 3 * q^57 + 12 * q^58 + 3 * q^59 + 8 * q^61 + 8 * q^62 + 2 * q^64 + 9 * q^66 - 5 * q^67 + 6 * q^68 - 24 * q^71 - 6 * q^72 + 11 * q^73 - 8 * q^74 - q^76 - 6 * q^78 + 4 * q^79 + 18 * q^81 + 9 * q^82 + 12 * q^83 - 2 * q^86 + 18 * q^87 - 6 * q^88 + 6 * q^89 + 6 * q^92 + 12 * q^93 - 6 * q^94 + 3 * q^96 + 5 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−3.00000			−1.00000
$10$		0			0
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$		−	1.73205i		−	0.353553i
$25$	−5.00000			−1.00000
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$			5.19615i			0.904534i
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	1.00000			0.162221
$39$	3.00000	−	1.73205i	0.480384	−	0.277350i
$40$		0			0
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$		0			0
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$	−2.00000			−0.277350
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	−0.902557	−	0.430570i	$-0.858312\pi$
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	0.0783936	−	0.996922i	$-0.475021\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$		0			0
$56$		0			0
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$	6.00000			0.787839
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	4.50000	−	2.59808i	0.553912	−	0.319801i
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$	3.00000			0.363803
$69$			10.3923i			1.25109i
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	−3.00000			−0.353553
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$	−4.00000			−0.464991
$75$			8.66025i			1.00000i
$76$	−0.500000	−	0.866025i	−0.0573539	−	0.0993399i
$77$		0			0
$78$	−3.00000	−	1.73205i	−0.339683	−	0.196116i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	−0.322396	−	0.946605i	$-0.604488\pi$
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	0.980982	−	0.194099i	$-0.0621783\pi$
$84$		0			0
$85$		0			0
$86$	−1.00000			−0.107833
$87$	9.00000	+	5.19615i	0.964901	+	0.557086i
$88$	−3.00000			−0.319801
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$		0			0
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$	6.00000	+	3.46410i	0.622171	+	0.359211i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	0.964579	+	0.263795i	$0.0849741\pi$
$98$		0			0
$99$	9.00000			0.904534
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$	4.50000	+	2.59808i	0.445566	+	0.257248i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$		0			0
$111$	−6.00000	−	3.46410i	−0.569495	−	0.328798i
$112$		0			0
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$		−	1.73205i		−	0.162221i
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$	−3.00000			−0.276172
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$	4.00000	−	6.92820i	0.362143	−	0.627250i
$123$	13.5000	−	7.79423i	1.21725	−	0.702782i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$		0			0
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.50000	−	0.866025i	−0.132068	−	0.0762493i
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−4.50000	−	2.59808i	−0.391675	−	0.226134i
$133$		0			0
$134$	5.00000			0.431934
$135$		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	$0.540905\pi$
$138$	9.00000	−	5.19615i	0.766131	−	0.442326i
$139$	−9.50000	−	16.4545i	−0.805779	−	1.39565i	−0.915764	−	0.401718i	$-0.868413\pi$
$139$	−9.50000	−	16.4545i	−0.805779	−	1.39565i	0.109984	−	0.993933i	$-0.464920\pi$
$140$		0			0
$141$	−9.00000	+	5.19615i	−0.757937	+	0.437595i
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$		0			0
$146$	5.50000	−	9.52628i	0.455183	−	0.788400i
$147$		0			0
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$	7.50000	−	4.33013i	0.612372	−	0.353553i
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$		0			0
$155$		0			0
$156$			3.46410i			0.277350i
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	−0.934731	−	0.355357i	$-0.884359\pi$
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	0.775113	+	0.631822i	$0.217693\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	−18.0000	+	10.3923i	−1.42749	+	0.824163i
$160$		0			0
$161$		0			0
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	−9.00000			−0.702782
$165$		0			0
$166$	−12.0000			−0.931381
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	1.50000	−	2.59808i	0.114708	−	0.198680i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		−	10.3923i		−	0.787839i
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	−4.50000	−	2.59808i	−0.338241	−	0.195283i
$178$	−6.00000			−0.449719
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$	12.0000	−	6.92820i	0.887066	−	0.512148i
$184$	−6.00000			−0.442326
$185$		0			0
$186$		−	6.92820i		−	0.508001i
$187$	4.50000	+	7.79423i	0.329073	+	0.569970i
$188$	6.00000			0.437595
$189$		0			0
$190$		0			0
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$		−	1.73205i		−	0.125000i
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$	−5.00000			−0.358979
$195$		0			0
$196$		0			0
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	−4.50000	−	7.79423i	−0.319801	−	0.553912i
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	0.632581	−	0.774494i	$-0.281995\pi$
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	−0.987022	+	0.160585i	$0.948662\pi$
$200$	−5.00000			−0.353553
$201$	7.50000	+	4.33013i	0.529009	+	0.305424i
$202$		0			0
$203$		0			0
$204$		−	5.19615i		−	0.363803i
$205$		0			0
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$	18.0000			1.25109
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$	1.50000	−	2.59808i	0.103757	−	0.179713i
$210$		0			0
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	12.0000			0.824163
$213$			20.7846i			1.42414i
$214$	3.00000			0.205076
$215$		0			0
$216$			5.19615i			0.353553i
$217$		0			0
$218$	8.00000	−	13.8564i	0.541828	−	0.938474i
$219$	16.5000	−	9.52628i	1.11497	−	0.643726i
$220$		0			0
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$			6.92820i			0.464991i
$223$	13.0000	−	22.5167i	0.870544	−	1.50783i	0.00910984	−	0.999959i	$-0.497100\pi$
$223$	13.0000	−	22.5167i	0.870544	−	1.50783i	0.861435	−	0.507869i	$-0.169566\pi$
$224$		0			0
$225$	15.0000			1.00000
$226$	−3.00000	+	5.19615i	−0.199557	+	0.345643i
$227$	−21.0000			−1.39382			−0.696909	−	0.717159i	$-0.745442\pi$
$227$	−21.0000			−1.39382			−0.696909	+	0.717159i	$0.745442\pi$
$228$	−1.50000	+	0.866025i	−0.0993399	+	0.0573539i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$		0			0
$231$		0			0
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	−0.910968	−	0.412477i	$-0.864664\pi$
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	0.812700	+	0.582683i	$0.197997\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$		0			0
$236$	1.50000	+	2.59808i	0.0976417	+	0.169120i
$237$	6.00000	−	3.46410i	0.389742	−	0.225018i
$238$		0			0
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$		0			0
$241$	7.00000			0.450910			0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000			0.450910			0.225455	+	0.974254i	$0.427613\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$		−	15.5885i		−	1.00000i
$244$	−8.00000			−0.512148
$245$		0			0
$246$	−13.5000	−	7.79423i	−0.860729	−	0.496942i
$247$	−2.00000			−0.127257
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	−18.0000	−	10.3923i	−1.14070	−	0.658586i
$250$		0			0
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	21.0000			1.30994			0.654972	−	0.755653i	$-0.272680\pi$
$257$	21.0000			1.30994			0.654972	+	0.755653i	$0.272680\pi$
$258$			1.73205i			0.107833i
$259$		0			0
$260$		0			0
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$		0			0
$263$	18.0000			1.10993			0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000			1.10993			0.554964	+	0.831875i	$0.312732\pi$
$264$			5.19615i			0.319801i
$265$		0			0
$266$		0			0
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	−2.50000	−	4.33013i	−0.152712	−	0.264505i
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$		0			0
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$		0			0
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$	15.0000			0.904534
$276$	−9.00000	−	5.19615i	−0.541736	−	0.312772i
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$	−9.50000	+	16.4545i	−0.569772	+	0.986874i
$279$	6.00000	−	10.3923i	0.359211	−	0.622171i
$280$		0			0
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	−0.941526	−	0.336939i	$-0.890608\pi$
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	0.762561	+	0.646916i	$0.223942\pi$
$282$	9.00000	+	5.19615i	0.535942	+	0.309426i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$	−3.00000	+	5.19615i	−0.177394	+	0.307255i
$287$		0			0
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−7.50000	−	4.33013i	−0.439658	−	0.253837i
$292$	−11.0000			−0.643726
$293$	15.0000	+	25.9808i	0.876309	+	1.51781i	0.855361	+	0.518032i	$0.173335\pi$
$293$	15.0000	+	25.9808i	0.876309	+	1.51781i	0.0209480	+	0.999781i	$0.493332\pi$
$294$		0			0
$295$		0			0
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$		−	15.5885i		−	0.904534i
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$	−7.50000	−	4.33013i	−0.433013	−	0.250000i
$301$		0			0
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$		0			0
$304$	1.00000			0.0573539
$305$		0			0
$306$	4.50000	−	7.79423i	0.257248	−	0.445566i
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$		0			0
$309$			24.2487i			1.37946i
$310$		0			0
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$	3.00000	−	1.73205i	0.169842	−	0.0980581i
$313$	14.5000	+	25.1147i	0.819588	+	1.41957i	0.905986	+	0.423308i	$0.139131\pi$
$313$	14.5000	+	25.1147i	0.819588	+	1.41957i	−0.0863973	+	0.996261i	$0.527535\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−4.00000			−0.225018
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$	18.0000	+	10.3923i	1.00939	+	0.582772i
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	4.50000	+	2.59808i	0.251166	+	0.145010i
$322$		0			0
$323$	3.00000			0.166924
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−5.00000	−	8.66025i	−0.277350	−	0.480384i
$326$	−4.00000			−0.221540
$327$	24.0000	−	13.8564i	1.32720	−	0.766261i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$		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	+	10.3923i	0.329293	+	0.570352i
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$		0			0
$336$		0			0
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	0.879322	−	0.476227i	$-0.157996\pi$
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	−0.852086	+	0.523402i	$0.824663\pi$
$338$	−9.00000			−0.489535
$339$	−9.00000	+	5.19615i	−0.488813	+	0.282216i
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	−3.00000			−0.162221
$343$		0			0
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.0409337	+	0.999162i	$0.513033\pi$
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.844833	+	0.535031i	$0.820300\pi$
$348$	−9.00000	+	5.19615i	−0.482451	+	0.278543i
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	−0.996716	−	0.0809766i	$-0.974196\pi$
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	0.568486	+	0.822693i	$0.307529\pi$
$350$		0			0
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	21.0000			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$354$			5.19615i			0.276172i
$355$		0			0
$356$	3.00000	+	5.19615i	0.159000	+	0.275396i
$357$		0			0
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	−0.524588	−	0.851356i	$-0.675781\pi$
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	0.999590	+	0.0286287i	$0.00911406\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	7.00000	+	12.1244i	0.367912	+	0.637242i
$363$			3.46410i			0.181818i
$364$		0			0
$365$		0			0
$366$	−12.0000	−	6.92820i	−0.627250	−	0.362143i
$367$	28.0000			1.46159			0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000			1.46159			0.730794	+	0.682598i	$0.239150\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	−13.5000	−	23.3827i	−0.702782	−	1.21725i
$370$		0			0
$371$		0			0
$372$	−6.00000	+	3.46410i	−0.311086	+	0.179605i
$373$	−34.0000			−1.76045			−0.880227	−	0.474554i	$-0.842610\pi$
$373$	−34.0000			−1.76045			−0.880227	+	0.474554i	$0.842610\pi$
$374$	4.50000	−	7.79423i	0.232689	−	0.403030i
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	−12.0000			−0.618031
$378$		0			0
$379$	23.0000			1.18143			0.590715	−	0.806880i	$-0.298846\pi$
$379$	23.0000			1.18143			0.590715	+	0.806880i	$0.298846\pi$
$380$		0			0
$381$		−	3.46410i		−	0.177471i
$382$	9.00000	−	15.5885i	0.460480	−	0.797575i
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$		0			0
$386$	5.00000			0.254493
$387$	−1.50000	+	2.59808i	−0.0762493	+	0.132068i
$388$	2.50000	+	4.33013i	0.126918	+	0.219829i
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$		0			0
$393$		0			0
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$		0			0
$396$	−4.50000	+	7.79423i	−0.226134	+	0.391675i
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	−0.498112	−	0.867113i	$-0.665973\pi$
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	0.999998	−	0.00217869i	$-0.000693499\pi$
$398$	−5.00000	+	8.66025i	−0.250627	+	0.434099i
$399$		0			0
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	−27.0000			−1.34832			−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000			−1.34832			−0.674158	+	0.738587i	$0.735493\pi$
$402$		−	8.66025i		−	0.431934i
$403$	−8.00000			−0.398508
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$	−4.50000	+	2.59808i	−0.222783	+	0.128624i
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	−0.575670	−	0.817682i	$-0.695259\pi$
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	0.995968	+	0.0897044i	$0.0285922\pi$
$410$		0			0
$411$			5.19615i			0.256307i
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$		0			0
$414$	−9.00000	−	15.5885i	−0.442326	−	0.766131i
$415$		0			0
$416$	−2.00000			−0.0980581
$417$	−28.5000	+	16.4545i	−1.39565	+	0.805779i
$418$	−3.00000			−0.146735
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	−0.999895	−	0.0145228i	$-0.995377\pi$
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	0.512524	+	0.858673i	$0.328710\pi$
$422$	−10.0000	+	17.3205i	−0.486792	+	0.843149i
$423$	9.00000	+	15.5885i	0.437595	+	0.757937i
$424$	−6.00000	−	10.3923i	−0.291386	−	0.504695i
$425$	7.50000	+	12.9904i	0.363803	+	0.630126i
$426$	18.0000	−	10.3923i	0.872103	−	0.503509i
$427$		0			0
$428$	−1.50000	−	2.59808i	−0.0725052	−	0.125583i
$429$	−9.00000	+	5.19615i	−0.434524	+	0.250873i
$430$		0			0
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	7.00000			0.336399			0.168199	−	0.985753i	$-0.446205\pi$
$433$	7.00000			0.336399			0.168199	+	0.985753i	$0.446205\pi$
$434$		0			0
$435$		0			0
$436$	−16.0000			−0.766261
$437$	3.00000	−	5.19615i	0.143509	−	0.248566i
$438$	−16.5000	−	9.52628i	−0.788400	−	0.455183i
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$		0			0
$442$	−6.00000			−0.285391
$443$	−1.50000	−	2.59808i	−0.0712672	−	0.123438i	0.828190	−	0.560448i	$-0.189371\pi$
$443$	−1.50000	−	2.59808i	−0.0712672	−	0.123438i	−0.899457	+	0.437009i	$0.856038\pi$
$444$	6.00000	−	3.46410i	0.284747	−	0.164399i
$445$		0			0
$446$	−26.0000			−1.23114
$447$			10.3923i			0.491539i
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	−7.50000	−	12.9904i	−0.353553	−	0.612372i
$451$	−13.5000	−	23.3827i	−0.635690	−	1.10105i
$452$	6.00000			0.282216
$453$			17.3205i			0.813788i
$454$	10.5000	+	18.1865i	0.492789	+	0.853536i
$455$		0			0
$456$	1.50000	+	0.866025i	0.0702439	+	0.0405554i
$457$	−8.50000	−	14.7224i	−0.397613	−	0.688686i	0.595818	−	0.803120i	$-0.296828\pi$
$457$	−8.50000	−	14.7224i	−0.397613	−	0.688686i	−0.993431	+	0.114433i	$0.963495\pi$
$458$	7.00000	+	12.1244i	0.327089	+	0.566534i
$459$	13.5000	−	7.79423i	0.630126	−	0.363803i
$460$		0			0
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	0.270326	+	0.962769i	$0.412869\pi$
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	−0.968945	+	0.247276i	$0.920465\pi$
$462$		0			0
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	0.534450	−	0.845200i	$-0.320519\pi$
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$	3.00000			0.138972
$467$	−7.50000	+	12.9904i	−0.347059	+	0.601123i	−0.985726	−	0.168360i	$-0.946153\pi$
$467$	−7.50000	+	12.9904i	−0.347059	+	0.601123i	0.638667	+	0.769483i	$0.279486\pi$
$468$	6.00000			0.277350
$469$		0			0
$470$		0			0
$471$	6.00000	+	3.46410i	0.276465	+	0.159617i
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$	−1.50000	+	2.59808i	−0.0689701	+	0.119460i
$474$	−6.00000	−	3.46410i	−0.275589	−	0.159111i
$475$	2.50000	−	4.33013i	0.114708	−	0.198680i
$476$		0			0
$477$	18.0000	+	31.1769i	0.824163	+	1.42749i
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	42.0000			1.91903			0.959514	−	0.281659i	$-0.0908848\pi$
$479$	42.0000			1.91903			0.959514	+	0.281659i	$0.0908848\pi$
$480$		0			0
$481$	8.00000			0.364769
$482$	−3.50000	−	6.06218i	−0.159421	−	0.276125i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	−13.0000	−	22.5167i	−0.589086	−	1.02033i	−0.994352	−	0.106129i	$-0.966154\pi$
$487$	−13.0000	−	22.5167i	−0.589086	−	1.02033i	0.405266	−	0.914199i	$-0.367179\pi$
$488$	4.00000	+	6.92820i	0.181071	+	0.313625i
$489$	−6.00000	−	3.46410i	−0.271329	−	0.156652i
$490$		0			0
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	0.984145	−	0.177365i	$-0.0567572\pi$
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	−0.645675	+	0.763612i	$0.723424\pi$
$492$			15.5885i			0.702782i
$493$	18.0000			0.810679
$494$	1.00000	+	1.73205i	0.0449921	+	0.0779287i
$495$		0			0
$496$	4.00000			0.179605
$497$		0			0
$498$			20.7846i			0.931381i
$499$	−13.0000			−0.581960			−0.290980	−	0.956729i	$-0.593981\pi$
$499$	−13.0000			−0.581960			−0.290980	+	0.956729i	$0.593981\pi$
$500$		0			0
$501$	−18.0000	+	10.3923i	−0.804181	+	0.464294i
$502$	10.5000	+	18.1865i	0.468638	+	0.811705i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$	−13.5000	−	7.79423i	−0.599556	−	0.346154i
$508$	−1.00000	+	1.73205i	−0.0443678	+	0.0768473i
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$	−4.50000	−	2.59808i	−0.198680	−	0.114708i
$514$	−10.5000	−	18.1865i	−0.463135	−	0.802174i
$515$		0			0
$516$	1.50000	−	0.866025i	0.0660338	−	0.0381246i
$517$	9.00000	+	15.5885i	0.395820	+	0.685580i
$518$		0			0
$519$	−9.00000	+	5.19615i	−0.395056	+	0.228086i
$520$		0			0
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$	−18.0000			−0.787839
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	−0.560208	−	0.828352i	$-0.689279\pi$
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	0.997478	+	0.0709788i	$0.0226123\pi$
$524$		0			0
$525$		0			0
$526$	−9.00000	−	15.5885i	−0.392419	−	0.679689i
$527$	12.0000			0.522728
$528$	4.50000	−	2.59808i	0.195837	−	0.113067i
$529$	13.0000			0.565217
$530$		0			0
$531$	−4.50000	+	7.79423i	−0.195283	+	0.338241i
$532$		0			0
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$			10.3923i			0.449719i
$535$		0			0
$536$	−2.50000	+	4.33013i	−0.107984	+	0.187033i
$537$	−18.0000	+	10.3923i	−0.776757	+	0.448461i
$538$	−12.0000	+	20.7846i	−0.517357	+	0.896088i
$539$		0			0
$540$		0			0
$541$	2.00000	−	3.46410i	0.0859867	−	0.148933i	−0.819825	−	0.572615i	$-0.805929\pi$
$541$	2.00000	−	3.46410i	0.0859867	−	0.148933i	0.905811	+	0.423681i	$0.139262\pi$
$542$	−20.0000			−0.859074
$543$			24.2487i			1.04061i
$544$	3.00000			0.128624
$545$		0			0
$546$		0			0
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	0.876517	+	0.481371i	$0.159861\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$	−12.0000	−	20.7846i	−0.512148	−	0.887066i
$550$	−7.50000	−	12.9904i	−0.319801	−	0.553912i
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$			10.3923i			0.442326i
$553$		0			0
$554$	5.00000	+	8.66025i	0.212430	+	0.367939i
$555$		0			0
$556$	19.0000			0.805779
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	0.986394	+	0.164399i	$0.0525683\pi$
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	−0.350824	+	0.936442i	$0.614098\pi$
$558$	−12.0000			−0.508001
$559$	2.00000			0.0845910
$560$		0			0
$561$	13.5000	−	7.79423i	0.569970	−	0.329073i
$562$	6.00000			0.253095
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	0.0824933	+	0.996592i	$0.473712\pi$
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	−0.904320	+	0.426855i	$0.859622\pi$
$564$		−	10.3923i		−	0.437595i
$565$		0			0
$566$	4.00000			0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.759220	−	0.650835i	$-0.774419\pi$
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.184030	−	0.982921i	$-0.558914\pi$
$570$		0			0
$571$	18.5000	−	32.0429i	0.774201	−	1.34096i	−0.161042	−	0.986948i	$-0.551485\pi$
$571$	18.5000	−	32.0429i	0.774201	−	1.34096i	0.935243	−	0.354008i	$-0.115181\pi$
$572$	6.00000			0.250873
$573$	27.0000	−	15.5885i	1.12794	−	0.651217i
$574$		0			0
$575$	30.0000			1.25109
$576$	−3.00000			−0.125000
$577$	5.50000	+	9.52628i	0.228968	+	0.396584i	0.957503	−	0.288425i	$-0.0931316\pi$
$577$	5.50000	+	9.52628i	0.228968	+	0.396584i	−0.728535	+	0.685009i	$0.759798\pi$
$578$	−8.00000			−0.332756
$579$	7.50000	+	4.33013i	0.311689	+	0.179954i
$580$		0			0
$581$		0			0
$582$			8.66025i			0.358979i
$583$	18.0000	+	31.1769i	0.745484	+	1.29122i
$584$	5.50000	+	9.52628i	0.227592	+	0.394200i
$585$		0			0
$586$	15.0000	−	25.9808i	0.619644	−	1.07326i
$587$	−4.50000	+	7.79423i	−0.185735	+	0.321702i	−0.943824	−	0.330449i	$-0.892800\pi$
$587$	−4.50000	+	7.79423i	−0.185735	+	0.321702i	0.758089	+	0.652151i	$0.226133\pi$
$588$		0			0
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$		0			0
$591$			20.7846i			0.854965i
$592$	−4.00000			−0.164399
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$	−13.5000	+	7.79423i	−0.553912	+	0.319801i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	−15.0000	+	8.66025i	−0.613909	+	0.354441i
$598$	−6.00000	+	10.3923i	−0.245358	+	0.424973i
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$			8.66025i			0.353553i
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	0.190927	+	0.981604i	$0.438851\pi$
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	−0.945558	+	0.325455i	$0.894483\pi$
$602$		0			0
$603$	7.50000	−	12.9904i	0.305424	−	0.529009i
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$		0			0
$606$		0			0
$607$	28.0000			1.13648			0.568242	−	0.822861i	$-0.307624\pi$
$607$	28.0000			1.13648			0.568242	+	0.822861i	$0.307624\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$		0			0
$610$		0			0
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$	−9.00000			−0.363803
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$		0			0
$616$		0			0
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	−0.998700	−	0.0509678i	$-0.983769\pi$
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	0.455211	−	0.890384i	$-0.349564\pi$
$618$	21.0000	−	12.1244i	0.844744	−	0.487713i
$619$	−35.0000			−1.40677			−0.703384	−	0.710810i	$-0.748329\pi$
$619$	−35.0000			−1.40677			−0.703384	+	0.710810i	$0.748329\pi$
$620$		0			0
$621$		−	31.1769i		−	1.25109i
$622$	18.0000			0.721734
$623$		0			0
$624$	−3.00000	−	1.73205i	−0.120096	−	0.0693375i
$625$	25.0000			1.00000
$626$	14.5000	−	25.1147i	0.579537	−	1.00379i
$627$	−4.50000	−	2.59808i	−0.179713	−	0.103757i
$628$	−2.00000	−	3.46410i	−0.0798087	−	0.138233i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$	−30.0000	+	17.3205i	−1.19239	+	0.688428i
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$		0			0
$636$		−	20.7846i		−	0.824163i
$637$		0			0
$638$	−18.0000			−0.712627
$639$	36.0000			1.42414
$640$		0			0
$641$	−3.00000			−0.118493			−0.0592464	−	0.998243i	$-0.518870\pi$
$641$	−3.00000			−0.118493			−0.0592464	+	0.998243i	$0.518870\pi$
$642$		−	5.19615i		−	0.205076i
$643$	11.5000	+	19.9186i	0.453516	+	0.785512i	0.998602	−	0.0528680i	$-0.0168363\pi$
$643$	11.5000	+	19.9186i	0.453516	+	0.785512i	−0.545086	+	0.838380i	$0.683503\pi$
$644$		0			0
$645$		0			0
$646$	−1.50000	−	2.59808i	−0.0590167	−	0.102220i
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	0.986916	−	0.161233i	$-0.0515470\pi$
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	−0.633090	+	0.774078i	$0.718214\pi$
$648$	9.00000			0.353553
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$	−5.00000	+	8.66025i	−0.196116	+	0.339683i
$651$		0			0
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$	−24.0000	−	13.8564i	−0.938474	−	0.541828i
$655$		0			0
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	−16.5000	−	28.5788i	−0.643726	−	1.11497i
$658$		0			0
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		0			0
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	−0.902297	−	0.431116i	$-0.858120\pi$
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	0.824506	+	0.565854i	$0.191453\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$	−9.00000	−	5.19615i	−0.349531	−	0.201802i
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$		0			0
$666$	12.0000			0.464991
$667$	18.0000	−	31.1769i	0.696963	−	1.20717i
$668$	12.0000			0.464294
$669$	−39.0000	−	22.5167i	−1.50783	−	0.870544i
$670$		0			0
$671$	−12.0000	−	20.7846i	−0.463255	−	0.802381i
$672$		0			0
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	−0.572309	−	0.820038i	$-0.693952\pi$
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	0.996328	+	0.0856156i	$0.0272857\pi$
$674$	0.500000	−	0.866025i	0.0192593	−	0.0333581i
$675$		−	25.9808i		−	1.00000i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	18.0000	+	31.1769i	0.691796	+	1.19823i	0.971249	+	0.238067i	$0.0765137\pi$
$677$	18.0000	+	31.1769i	0.691796	+	1.19823i	−0.279453	+	0.960159i	$0.590153\pi$
$678$	9.00000	+	5.19615i	0.345643	+	0.199557i
$679$		0			0
$680$		0			0
$681$			36.3731i			1.39382i
$682$	−12.0000			−0.459504
$683$	4.50000	+	7.79423i	0.172188	+	0.298238i	0.939184	−	0.343413i	$-0.111583\pi$
$683$	4.50000	+	7.79423i	0.172188	+	0.298238i	−0.766997	+	0.641651i	$0.778250\pi$
$684$	1.50000	+	2.59808i	0.0573539	+	0.0993399i
$685$		0			0
$686$		0			0
$687$			24.2487i			0.925146i
$688$	−1.00000			−0.0381246
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	33.0000			1.25266
$695$		0			0
$696$	9.00000	+	5.19615i	0.341144	+	0.196960i
$697$	13.5000	−	23.3827i	0.511349	−	0.885682i
$698$	16.0000			0.605609
$699$	4.50000	+	2.59808i	0.170206	+	0.0982683i
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	9.00000	+	5.19615i	0.339683	+	0.196116i
$703$	2.00000	+	3.46410i	0.0754314	+	0.130651i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	−10.5000	−	18.1865i	−0.395173	−	0.684459i
$707$		0			0
$708$	4.50000	−	2.59808i	0.169120	−	0.0976417i
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	0.901135	−	0.433539i	$-0.142735\pi$
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	−0.826023	+	0.563636i	$0.809402\pi$
$710$		0			0
$711$	−6.00000	−	10.3923i	−0.225018	−	0.389742i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	12.0000	−	20.7846i	0.449404	−	0.778390i
$714$		0			0
$715$		0			0
$716$	12.0000			0.448461
$717$	−9.00000	+	5.19615i	−0.336111	+	0.194054i
$718$	−18.0000			−0.671754
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$		0			0
$722$	9.00000	−	15.5885i	0.334945	−	0.580142i
$723$		−	12.1244i		−	0.450910i
$724$	7.00000	−	12.1244i	0.260153	−	0.450598i
$725$	15.0000	−	25.9808i	0.557086	−	0.964901i
$726$	3.00000	−	1.73205i	0.111340	−	0.0642824i
$727$	13.0000	−	22.5167i	0.482143	−	0.835097i	−0.517647	−	0.855595i	$-0.673192\pi$
$727$	13.0000	−	22.5167i	0.482143	−	0.835097i	0.999790	+	0.0204978i	$0.00652512\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−3.00000			−0.110959
$732$			13.8564i			0.512148i
$733$	−14.0000			−0.517102			−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000			−0.517102			−0.258551	+	0.965998i	$0.583245\pi$
$734$	−14.0000	−	24.2487i	−0.516749	−	0.895036i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	7.50000	−	12.9904i	0.276266	−	0.478507i
$738$	−13.5000	+	23.3827i	−0.496942	+	0.860729i
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	−0.867581	−	0.497296i	$-0.834326\pi$
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	0.00311943	−	0.999995i	$-0.499007\pi$
$740$		0			0
$741$			3.46410i			0.127257i
$742$		0			0
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	0.805735	−	0.592277i	$-0.201771\pi$
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	−0.915794	+	0.401648i	$0.868437\pi$
$744$	6.00000	+	3.46410i	0.219971	+	0.127000i
$745$		0			0
$746$	17.0000	+	29.4449i	0.622414	+	1.07805i
$747$	−18.0000	+	31.1769i	−0.658586	+	1.14070i
$748$	−9.00000			−0.329073
$749$		0			0
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$			36.3731i			1.32551i
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$		0			0
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−11.5000	−	19.9186i	−0.417699	−	0.723476i
$759$		−	31.1769i		−	1.13165i
$760$		0			0
$761$	−42.0000			−1.52250			−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000			−1.52250			−0.761249	+	0.648459i	$0.775414\pi$
$762$	−3.00000	+	1.73205i	−0.108679	+	0.0627456i
$763$		0			0
$764$	−18.0000			−0.651217
$765$		0			0
$766$		0			0
$767$	6.00000			0.216647
$768$	1.50000	+	0.866025i	0.0541266	+	0.0312500i
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	0.883493	−	0.468445i	$-0.155186\pi$
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	−0.847432	+	0.530904i	$0.821852\pi$
$770$		0			0
$771$		−	36.3731i		−	1.30994i
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	3.00000			0.107833
$775$	10.0000	−	17.3205i	0.359211	−	0.622171i
$776$	2.50000	−	4.33013i	0.0897448	−	0.155443i
$777$		0			0
$778$	−9.00000	−	15.5885i	−0.322666	−	0.558873i
$779$	−9.00000			−0.322458
$780$		0			0
$781$	36.0000			1.28818
$782$	9.00000	−	15.5885i	0.321839	−	0.557442i
$783$	−27.0000	−	15.5885i	−0.964901	−	0.557086i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$	6.00000	−	10.3923i	0.213741	−	0.370211i
$789$		−	31.1769i		−	1.10993i
$790$		0			0
$791$		0			0
$792$	9.00000			0.319801
$793$	−8.00000	+	13.8564i	−0.284088	+	0.492055i
$794$	−20.0000			−0.709773
$795$		0			0
$796$	10.0000			0.354441
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	0.739975	−	0.672634i	$-0.234837\pi$
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	−0.952506	+	0.304520i	$0.901504\pi$
$798$		0			0
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$	13.5000	+	23.3827i	0.476702	+	0.825671i
$803$	−16.5000	−	28.5788i	−0.582272	−	1.00853i
$804$	−7.50000	+	4.33013i	−0.264505	+	0.152712i
$805$		0			0
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$	−36.0000	+	20.7846i	−1.26726	+	0.731653i
$808$		0			0
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	−0.995466	−	0.0951198i	$-0.969677\pi$
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	0.415357	−	0.909659i	$-0.363657\pi$
$810$		0			0
$811$	7.00000			0.245803			0.122902	−	0.992419i	$-0.460780\pi$
$811$	7.00000			0.245803			0.122902	+	0.992419i	$0.460780\pi$
$812$		0			0
$813$	−30.0000	−	17.3205i	−1.05215	−	0.607457i
$814$	12.0000			0.420600
$815$		0			0
$816$	4.50000	+	2.59808i	0.157532	+	0.0909509i
$817$	0.500000	+	0.866025i	0.0174928	+	0.0302984i
$818$	−17.0000			−0.594391
$819$		0			0
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$	4.50000	−	2.59808i	0.156956	−	0.0906183i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	−14.0000			−0.487713
$825$		−	25.9808i		−	0.904534i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	−9.00000	+	15.5885i	−0.312772	+	0.541736i
$829$	−5.00000	−	8.66025i	−0.173657	−	0.300783i	0.766039	−	0.642795i	$-0.222225\pi$
$829$	−5.00000	−	8.66025i	−0.173657	−	0.300783i	−0.939696	+	0.342012i	$0.888892\pi$
$830$		0			0
$831$			17.3205i			0.600842i
$832$	1.00000	+	1.73205i	0.0346688	+	0.0600481i
$833$		0			0
$834$	28.5000	+	16.4545i	0.986874	+	0.569772i
$835$		0			0
$836$	1.50000	+	2.59808i	0.0518786	+	0.0898563i
$837$	−18.0000	−	10.3923i	−0.622171	−	0.359211i
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	20.0000			0.689246
$843$	9.00000	+	5.19615i	0.309976	+	0.178965i
$844$	20.0000			0.688428
$845$		0			0
$846$	9.00000	−	15.5885i	0.309426	−	0.535942i
$847$		0			0
$848$	−6.00000	+	10.3923i	−0.206041	+	0.356873i
$849$	6.00000	+	3.46410i	0.205919	+	0.118888i
$850$	7.50000	−	12.9904i	0.257248	−	0.445566i
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$	−18.0000	−	10.3923i	−0.616670	−	0.356034i
$853$	13.0000	−	22.5167i	0.445112	−	0.770956i	−0.552948	−	0.833215i	$-0.686497\pi$
$853$	13.0000	−	22.5167i	0.445112	−	0.770956i	0.998060	+	0.0622597i	$0.0198307\pi$
$854$		0			0
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	42.0000			1.43469			0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000			1.43469			0.717346	+	0.696717i	$0.245357\pi$
$858$	9.00000	+	5.19615i	0.307255	+	0.177394i
$859$	−35.0000			−1.19418			−0.597092	−	0.802173i	$-0.703677\pi$
$859$	−35.0000			−1.19418			−0.597092	+	0.802173i	$0.703677\pi$
$860$		0			0
$861$		0			0
$862$	15.0000	−	25.9808i	0.510902	−	0.884908i
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$		0			0
$866$	−3.50000	−	6.06218i	−0.118935	−	0.206001i
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$		0			0
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	−10.0000			−0.338837
$872$	8.00000	+	13.8564i	0.270914	+	0.469237i
$873$	−7.50000	+	12.9904i	−0.253837	+	0.439658i
$874$	−6.00000			−0.202953
$875$		0			0
$876$			19.0526i			0.643726i
$877$	8.00000			0.270141			0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000			0.270141			0.135070	+	0.990836i	$0.456874\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$	45.0000	−	25.9808i	1.51781	−	0.876309i
$880$		0			0
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$		0			0
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$		0			0
$886$	−1.50000	+	2.59808i	−0.0503935	+	0.0872841i
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$	−6.00000	−	3.46410i	−0.201347	−	0.116248i
$889$		0			0
$890$		0			0
$891$	−27.0000			−0.904534
$892$	13.0000	+	22.5167i	0.435272	+	0.753914i
$893$	6.00000			0.200782
$894$	9.00000	−	5.19615i	0.301005	−	0.173785i
$895$		0			0
$896$		0			0
$897$	−18.0000	+	10.3923i	−0.601003	+	0.346989i
$898$	−4.50000	−	7.79423i	−0.150167	−	0.260097i
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$	−7.50000	+	12.9904i	−0.250000	+	0.433013i
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$	−13.5000	+	23.3827i	−0.449501	+	0.778558i
$903$		0			0
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$		0			0
$906$	15.0000	−	8.66025i	0.498342	−	0.287718i
$907$	−31.0000			−1.02934			−0.514669	−	0.857389i	$-0.672085\pi$
$907$	−31.0000			−1.02934			−0.514669	+	0.857389i	$0.672085\pi$
$908$	10.5000	−	18.1865i	0.348455	−	0.603541i
$909$		0			0
$910$		0			0
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	0.127585	+	0.991828i	$0.459277\pi$
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	−0.922740	+	0.385422i	$0.874056\pi$
$912$		−	1.73205i		−	0.0573539i
$913$	−18.0000	+	31.1769i	−0.595713	+	1.03181i
$914$	−8.50000	+	14.7224i	−0.281155	+	0.486975i
$915$		0			0
$916$	7.00000	−	12.1244i	0.231287	−	0.400600i
$917$		0			0
$918$	−13.5000	−	7.79423i	−0.445566	−	0.257248i
$919$	−19.0000	+	32.9090i	−0.626752	+	1.08557i	0.361447	+	0.932393i	$0.382283\pi$
$919$	−19.0000	+	32.9090i	−0.626752	+	1.08557i	−0.988199	+	0.153174i	$0.951051\pi$
$920$		0			0
$921$		−	12.1244i		−	0.399511i
$922$	30.0000			0.987997
$923$	−12.0000	−	20.7846i	−0.394985	−	0.684134i
$924$		0			0
$925$	−10.0000	+	17.3205i	−0.328798	+	0.569495i
$926$	−10.0000	+	17.3205i	−0.328620	+	0.569187i
$927$	42.0000			1.37946
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	0.812607	−	0.582812i	$-0.198048\pi$
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	−0.911034	+	0.412332i	$0.864714\pi$
$930$		0			0
$931$		0			0
$932$	−1.50000	−	2.59808i	−0.0491341	−	0.0851028i
$933$	27.0000	+	15.5885i	0.883940	+	0.510343i
$934$	15.0000			0.490815
$935$		0			0
$936$	−3.00000	−	5.19615i	−0.0980581	−	0.169842i
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$		0			0
$939$	43.5000	−	25.1147i	1.41957	−	0.819588i
$940$		0			0
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.308215	+	0.951317i	$0.599732\pi$
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.669757	+	0.742581i	$0.733602\pi$
$942$		−	6.92820i		−	0.225733i
$943$	−27.0000	−	46.7654i	−0.879241	−	1.52289i
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	3.00000			0.0975384
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	0.840624	−	0.541619i	$-0.182188\pi$
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	−0.889368	+	0.457193i	$0.848855\pi$
$948$			6.92820i			0.225018i
$949$	−11.0000	+	19.0526i	−0.357075	+	0.618472i
$950$	−5.00000			−0.162221
$951$	27.0000	−	15.5885i	0.875535	−	0.505490i
$952$		0			0
$953$	9.00000			0.291539			0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000			0.291539			0.145769	+	0.989319i	$0.453434\pi$
$954$	18.0000	−	31.1769i	0.582772	−	1.00939i
$955$		0			0
$956$	6.00000			0.194054
$957$	−27.0000	−	15.5885i	−0.872786	−	0.503903i
$958$	−21.0000	−	36.3731i	−0.678479	−	1.17516i
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−4.00000	−	6.92820i	−0.128965	−	0.223374i
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$	−3.50000	+	6.06218i	−0.112727	+	0.195250i
$965$		0			0
$966$		0			0
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515777\pi$
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$968$	−2.00000			−0.0642824
$969$		−	5.19615i		−	0.166924i
$970$		0			0
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	0.418101	+	0.908401i	$0.362696\pi$
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	−0.995748	+	0.0921142i	$0.970638\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$		0			0
$974$	−13.0000	+	22.5167i	−0.416547	+	0.721480i
$975$	−15.0000	+	8.66025i	−0.480384	+	0.277350i
$976$	4.00000	−	6.92820i	0.128037	−	0.221766i
$977$	25.5000	−	44.1673i	0.815817	−	1.41304i	−0.0929223	−	0.995673i	$-0.529621\pi$
$977$	25.5000	−	44.1673i	0.815817	−	1.41304i	0.908740	−	0.417364i	$-0.137046\pi$
$978$			6.92820i			0.221540i
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$		0			0
$981$	−24.0000	−	41.5692i	−0.766261	−	1.32720i
$982$	7.50000	−	12.9904i	0.239335	−	0.414540i
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$	13.5000	−	7.79423i	0.430364	−	0.248471i
$985$		0			0
$986$	−9.00000	−	15.5885i	−0.286618	−	0.496438i
$987$		0			0
$988$	1.00000	−	1.73205i	0.0318142	−	0.0551039i
$989$	−3.00000	+	5.19615i	−0.0953945	+	0.165228i
$990$		0			0
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	6.00000	−	3.46410i	0.190404	−	0.109930i
$994$		0			0
$995$		0			0
$996$	18.0000	−	10.3923i	0.570352	−	0.329293i
$997$	28.0000			0.886769			0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000			0.886769			0.443384	+	0.896332i	$0.353778\pi$
$998$	6.50000	+	11.2583i	0.205754	+	0.356376i
$999$	18.0000	+	10.3923i	0.569495	+	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.b.79.1		2
3.2	odd	2		2646.2.h.i.667.1		2
7.2	even	3		882.2.f.d.295.1		2
7.3	odd	6		882.2.e.i.655.1		2
7.4	even	3		882.2.e.g.655.1		2
7.5	odd	6		18.2.c.a.7.1	✓	2
7.6	odd	2		882.2.h.c.79.1		2
9.4	even	3		882.2.e.g.373.1		2
9.5	odd	6		2646.2.e.c.1549.1		2
21.2	odd	6		2646.2.f.g.883.1		2
21.5	even	6		54.2.c.a.19.1		2
21.11	odd	6		2646.2.e.c.2125.1		2
21.17	even	6		2646.2.e.b.2125.1		2
21.20	even	2		2646.2.h.h.667.1		2
28.19	even	6		144.2.i.c.97.1		2
35.12	even	12		450.2.j.e.349.1		4
35.19	odd	6		450.2.e.i.151.1		2
35.33	even	12		450.2.j.e.349.2		4
56.5	odd	6		576.2.i.g.385.1		2
56.19	even	6		576.2.i.a.385.1		2
63.2	odd	6		7938.2.a.i.1.1		1
63.4	even	3	inner	882.2.h.b.67.1		2
63.5	even	6		54.2.c.a.37.1		2
63.13	odd	6		882.2.e.i.373.1		2
63.16	even	3		7938.2.a.x.1.1		1
63.23	odd	6		2646.2.f.g.1765.1		2
63.31	odd	6		882.2.h.c.67.1		2
63.32	odd	6		2646.2.h.i.361.1		2
63.40	odd	6		18.2.c.a.13.1	yes	2
63.41	even	6		2646.2.e.b.1549.1		2
63.47	even	6		162.2.a.b.1.1		1
63.58	even	3		882.2.f.d.589.1		2
63.59	even	6		2646.2.h.h.361.1		2
63.61	odd	6		162.2.a.c.1.1		1
84.47	odd	6		432.2.i.b.289.1		2
105.47	odd	12		1350.2.j.a.1099.2		4
105.68	odd	12		1350.2.j.a.1099.1		4
105.89	even	6		1350.2.e.c.451.1		2
168.5	even	6		1728.2.i.e.1153.1		2
168.131	odd	6		1728.2.i.f.1153.1		2
252.47	odd	6		1296.2.a.f.1.1		1
252.103	even	6		144.2.i.c.49.1		2
252.131	odd	6		432.2.i.b.145.1		2
252.187	even	6		1296.2.a.g.1.1		1
315.47	odd	12		4050.2.c.r.649.1		2
315.68	odd	12		1350.2.j.a.199.2		4
315.103	even	12		450.2.j.e.49.1		4
315.124	odd	6		4050.2.a.c.1.1		1
315.173	odd	12		4050.2.c.r.649.2		2
315.187	even	12		4050.2.c.c.649.2		2
315.194	even	6		1350.2.e.c.901.1		2
315.229	odd	6		450.2.e.i.301.1		2
315.257	odd	12		1350.2.j.a.199.1		4
315.292	even	12		450.2.j.e.49.2		4
315.299	even	6		4050.2.a.v.1.1		1
315.313	even	12		4050.2.c.c.649.1		2
504.5	even	6		1728.2.i.e.577.1		2
504.61	odd	6		5184.2.a.r.1.1		1
504.131	odd	6		1728.2.i.f.577.1		2
504.173	even	6		5184.2.a.q.1.1		1
504.187	even	6		5184.2.a.o.1.1		1
504.229	odd	6		576.2.i.g.193.1		2
504.299	odd	6		5184.2.a.p.1.1		1
504.355	even	6		576.2.i.a.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.2.c.a.7.1	✓	2	7.5	odd	6
18.2.c.a.13.1	yes	2	63.40	odd	6
54.2.c.a.19.1		2	21.5	even	6
54.2.c.a.37.1		2	63.5	even	6
144.2.i.c.49.1		2	252.103	even	6
144.2.i.c.97.1		2	28.19	even	6
162.2.a.b.1.1		1	63.47	even	6
162.2.a.c.1.1		1	63.61	odd	6
432.2.i.b.145.1		2	252.131	odd	6
432.2.i.b.289.1		2	84.47	odd	6
450.2.e.i.151.1		2	35.19	odd	6
450.2.e.i.301.1		2	315.229	odd	6
450.2.j.e.49.1		4	315.103	even	12
450.2.j.e.49.2		4	315.292	even	12
450.2.j.e.349.1		4	35.12	even	12
450.2.j.e.349.2		4	35.33	even	12
576.2.i.a.193.1		2	504.355	even	6
576.2.i.a.385.1		2	56.19	even	6
576.2.i.g.193.1		2	504.229	odd	6
576.2.i.g.385.1		2	56.5	odd	6
882.2.e.g.373.1		2	9.4	even	3
882.2.e.g.655.1		2	7.4	even	3
882.2.e.i.373.1		2	63.13	odd	6
882.2.e.i.655.1		2	7.3	odd	6
882.2.f.d.295.1		2	7.2	even	3
882.2.f.d.589.1		2	63.58	even	3
882.2.h.b.67.1		2	63.4	even	3	inner
882.2.h.b.79.1		2	1.1	even	1	trivial
882.2.h.c.67.1		2	63.31	odd	6
882.2.h.c.79.1		2	7.6	odd	2
1296.2.a.f.1.1		1	252.47	odd	6
1296.2.a.g.1.1		1	252.187	even	6
1350.2.e.c.451.1		2	105.89	even	6
1350.2.e.c.901.1		2	315.194	even	6
1350.2.j.a.199.1		4	315.257	odd	12
1350.2.j.a.199.2		4	315.68	odd	12
1350.2.j.a.1099.1		4	105.68	odd	12
1350.2.j.a.1099.2		4	105.47	odd	12
1728.2.i.e.577.1		2	504.5	even	6
1728.2.i.e.1153.1		2	168.5	even	6
1728.2.i.f.577.1		2	504.131	odd	6
1728.2.i.f.1153.1		2	168.131	odd	6
2646.2.e.b.1549.1		2	63.41	even	6
2646.2.e.b.2125.1		2	21.17	even	6
2646.2.e.c.1549.1		2	9.5	odd	6
2646.2.e.c.2125.1		2	21.11	odd	6
2646.2.f.g.883.1		2	21.2	odd	6
2646.2.f.g.1765.1		2	63.23	odd	6
2646.2.h.h.361.1		2	63.59	even	6
2646.2.h.h.667.1		2	21.20	even	2
2646.2.h.i.361.1		2	63.32	odd	6
2646.2.h.i.667.1		2	3.2	odd	2
4050.2.a.c.1.1		1	315.124	odd	6
4050.2.a.v.1.1		1	315.299	even	6
4050.2.c.c.649.1		2	315.313	even	12
4050.2.c.c.649.2		2	315.187	even	12
4050.2.c.r.649.1		2	315.47	odd	12
4050.2.c.r.649.2		2	315.173	odd	12
5184.2.a.o.1.1		1	504.187	even	6
5184.2.a.p.1.1		1	504.299	odd	6
5184.2.a.q.1.1		1	504.173	even	6
5184.2.a.r.1.1		1	504.61	odd	6
7938.2.a.i.1.1		1	63.2	odd	6
7938.2.a.x.1.1		1	63.16	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{8} -3.00000 q^{9} -3.00000 q^{11} +(1.50000 + 0.866025i) q^{12} +(1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{22} -6.00000 q^{23} -1.73205i q^{24} -5.00000 q^{25} +(1.00000 - 1.73205i) q^{26} +5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +5.19615i q^{33} +(-1.50000 + 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} +(2.00000 - 3.46410i) q^{37} +1.00000 q^{38} +(3.00000 - 1.73205i) q^{39} +(4.50000 + 7.79423i) q^{41} +(0.500000 - 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(2.50000 + 4.33013i) q^{50} +(-4.50000 + 2.59808i) q^{51} -2.00000 q^{52} +(-6.00000 - 10.3923i) q^{53} +(4.50000 - 2.59808i) q^{54} +(1.50000 + 0.866025i) q^{57} +6.00000 q^{58} +(1.50000 - 2.59808i) q^{59} +(4.00000 + 6.92820i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(4.50000 - 2.59808i) q^{66} +(-2.50000 + 4.33013i) q^{67} +3.00000 q^{68} +10.3923i q^{69} -12.0000 q^{71} -3.00000 q^{72} +(5.50000 + 9.52628i) q^{73} -4.00000 q^{74} +8.66025i q^{75} +(-0.500000 - 0.866025i) q^{76} +(-3.00000 - 1.73205i) q^{78} +(2.00000 + 3.46410i) q^{79} +9.00000 q^{81} +(4.50000 - 7.79423i) q^{82} +(6.00000 - 10.3923i) q^{83} -1.00000 q^{86} +(9.00000 + 5.19615i) q^{87} -3.00000 q^{88} +(3.00000 - 5.19615i) q^{89} +(3.00000 - 5.19615i) q^{92} +(6.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(1.50000 + 0.866025i) q^{96} +(2.50000 - 4.33013i) q^{97} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 3 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 - 3 * q^6 + 2 * q^8 - 6 * q^9	\( 2 q - q^{2} - q^{4} - 3 q^{6} + 2 q^{8} - 6 q^{9} - 6 q^{11} + 3 q^{12} + 2 q^{13} - q^{16} - 3 q^{17} + 3 q^{18} - q^{19} + 3 q^{22} - 12 q^{23} - 10 q^{25} + 2 q^{26} - 6 q^{29} - 4 q^{31} - q^{32} - 3 q^{34} + 3 q^{36} + 4 q^{37} + 2 q^{38} + 6 q^{39} + 9 q^{41} + q^{43} + 3 q^{44} + 6 q^{46} - 6 q^{47} - 3 q^{48} + 5 q^{50} - 9 q^{51} - 4 q^{52} - 12 q^{53} + 9 q^{54} + 3 q^{57} + 12 q^{58} + 3 q^{59} + 8 q^{61} + 8 q^{62} + 2 q^{64} + 9 q^{66} - 5 q^{67} + 6 q^{68} - 24 q^{71} - 6 q^{72} + 11 q^{73} - 8 q^{74} - q^{76} - 6 q^{78} + 4 q^{79} + 18 q^{81} + 9 q^{82} + 12 q^{83} - 2 q^{86} + 18 q^{87} - 6 q^{88} + 6 q^{89} + 6 q^{92} + 12 q^{93} - 6 q^{94} + 3 q^{96} + 5 q^{97} + 18 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 - 3 * q^6 + 2 * q^8 - 6 * q^9 - 6 * q^11 + 3 * q^12 + 2 * q^13 - q^16 - 3 * q^17 + 3 * q^18 - q^19 + 3 * q^22 - 12 * q^23 - 10 * q^25 + 2 * q^26 - 6 * q^29 - 4 * q^31 - q^32 - 3 * q^34 + 3 * q^36 + 4 * q^37 + 2 * q^38 + 6 * q^39 + 9 * q^41 + q^43 + 3 * q^44 + 6 * q^46 - 6 * q^47 - 3 * q^48 + 5 * q^50 - 9 * q^51 - 4 * q^52 - 12 * q^53 + 9 * q^54 + 3 * q^57 + 12 * q^58 + 3 * q^59 + 8 * q^61 + 8 * q^62 + 2 * q^64 + 9 * q^66 - 5 * q^67 + 6 * q^68 - 24 * q^71 - 6 * q^72 + 11 * q^73 - 8 * q^74 - q^76 - 6 * q^78 + 4 * q^79 + 18 * q^81 + 9 * q^82 + 12 * q^83 - 2 * q^86 + 18 * q^87 - 6 * q^88 + 6 * q^89 + 6 * q^92 + 12 * q^93 - 6 * q^94 + 3 * q^96 + 5 * q^97 + 18 * q^99

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