LMFDB - Embedded newform 882.2.h.c.67.1

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			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.c.79.1

$q$-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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

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
$3$		−	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	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		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	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		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	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−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	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	−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	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	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	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$	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	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$	−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	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−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	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−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	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$	−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	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		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	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		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	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		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	$-0.248359\pi$
$97$	−2.50000	−	4.33013i	−0.253837	−	0.439658i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		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	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	−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	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	−0.173316	−	0.984866i	$-0.555448\pi$
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	0.939577	−	0.342337i	$-0.111218\pi$
$110$		0			0
$111$	6.00000	−	3.46410i	0.569495	−	0.328798i
$112$		0			0
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$			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	−0.109984	−	0.993933i	$-0.535080\pi$
$139$	9.50000	−	16.4545i	0.805779	−	1.39565i	0.915764	−	0.401718i	$-0.131587\pi$
$140$		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	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	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	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	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	$-0.679641\pi$
$167$	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
$170$		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	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		−	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	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		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	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$		−	1.73205i		−	0.125000i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	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	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$	−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	0.283918	+	0.958849i	$0.408366\pi$
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	−0.972346	+	0.233544i	$0.924968\pi$
$212$	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	−0.861435	−	0.507869i	$-0.830434\pi$
$223$	−13.0000	−	22.5167i	−0.870544	−	1.50783i	−0.00910984	−	0.999959i	$-0.502900\pi$
$224$		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	$-0.254558\pi$
$227$	21.0000			1.39382			0.696909	+	0.717159i	$0.254558\pi$
$228$	−1.50000	−	0.866025i	−0.0993399	−	0.0573539i
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$		0			0
$231$		0			0
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$	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	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$		0			0
$241$	−7.00000			−0.450910			−0.225455	−	0.974254i	$-0.572387\pi$
$241$	−7.00000			−0.450910			−0.225455	+	0.974254i	$0.572387\pi$
$242$	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	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$		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	$-0.727320\pi$
$257$	−21.0000			−1.30994			−0.654972	+	0.755653i	$0.727320\pi$
$258$			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	−0.224523	−	0.974469i	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$		0			0
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	−0.991658	−	0.128897i	$-0.958856\pi$
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	0.384201	−	0.923249i	$-0.374477\pi$
$272$	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	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$	9.00000	−	5.19615i	0.535942	−	0.309426i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	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	−0.0209480	+	0.999781i	$0.506668\pi$
$293$	−15.0000	+	25.9808i	−0.876309	+	1.51781i	−0.855361	+	0.518032i	$0.826665\pi$
$294$		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	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$		−	24.2487i		−	1.37946i
$310$		0			0
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$	3.00000	+	1.73205i	0.169842	+	0.0980581i
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	0.0863973	+	0.996261i	$0.472465\pi$
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	−0.905986	+	0.423308i	$0.860869\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−4.00000			−0.225018
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	−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	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−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	−0.852086	−	0.523402i	$-0.824663\pi$
$337$	0.500000	−	0.866025i	0.0272367	−	0.0471754i	0.879322	+	0.476227i	$0.157996\pi$
$338$	−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	−0.844833	−	0.535031i	$-0.820300\pi$
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.0409337	−	0.999162i	$-0.513033\pi$
$348$	9.00000	+	5.19615i	0.482451	+	0.278543i
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	0.996716	−	0.0809766i	$-0.0258039\pi$
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	−0.568486	+	0.822693i	$0.692471\pi$
$350$		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	$-0.688761\pi$
$353$	−21.0000			−1.11772			−0.558859	+	0.829263i	$0.688761\pi$
$354$		−	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	0.999590	−	0.0286287i	$-0.00911406\pi$
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	−0.524588	+	0.851356i	$0.675781\pi$
$360$		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	$-0.760850\pi$
$367$	−28.0000			−1.46159			−0.730794	+	0.682598i	$0.760850\pi$
$368$	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	−0.999998	−	0.00217869i	$-0.999307\pi$
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	0.498112	−	0.867113i	$-0.334027\pi$
$398$	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	$-0.304741\pi$
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	−0.995968	+	0.0897044i	$0.971408\pi$
$410$		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	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$	−10.0000	−	17.3205i	−0.487370	−	0.844150i	0.512524	−	0.858673i	$-0.328710\pi$
$421$	−10.0000	−	17.3205i	−0.487370	−	0.844150i	−0.999895	+	0.0145228i	$0.995377\pi$
$422$	−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	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$		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	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$		0			0
$442$	−6.00000			−0.285391
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	−0.899457	−	0.437009i	$-0.856038\pi$
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	0.828190	+	0.560448i	$0.189371\pi$
$444$	−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	−0.993431	−	0.114433i	$-0.963495\pi$
$457$	−8.50000	+	14.7224i	−0.397613	+	0.688686i	0.595818	+	0.803120i	$0.296828\pi$
$458$	−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	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$	−10.0000	+	17.3205i	−0.464739	+	0.804952i	−0.999190	−	0.0402476i	$-0.987185\pi$
$463$	−10.0000	+	17.3205i	−0.464739	+	0.804952i	0.534450	+	0.845200i	$0.320519\pi$
$464$	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	$-0.0538472\pi$
$467$	7.50000	+	12.9904i	0.347059	+	0.601123i	−0.638667	+	0.769483i	$0.720514\pi$
$468$	−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	$-0.909115\pi$
$479$	−42.0000			−1.91903			−0.959514	+	0.281659i	$0.909115\pi$
$480$		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	0.405266	+	0.914199i	$0.367179\pi$
$487$	−13.0000	+	22.5167i	−0.589086	+	1.02033i	−0.994352	+	0.106129i	$0.966154\pi$
$488$	−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	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$		−	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	$-0.812400\pi$
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	0.897011	+	0.442007i	$0.145733\pi$
$522$	−18.0000			−0.787839
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$		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	0.905811	−	0.423681i	$-0.139262\pi$
$541$	2.00000	+	3.46410i	0.0859867	+	0.148933i	−0.819825	+	0.572615i	$0.805929\pi$
$542$	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	0.876517	−	0.481371i	$-0.159861\pi$
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	−0.855138	+	0.518400i	$0.826528\pi$
$548$	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	−0.350824	−	0.936442i	$-0.614098\pi$
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	0.986394	−	0.164399i	$-0.0525683\pi$
$558$	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	0.904320	+	0.426855i	$0.140378\pi$
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	−0.0824933	+	0.996592i	$0.526288\pi$
$564$			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	−0.184030	+	0.982921i	$0.558914\pi$
$569$	−22.5000	+	38.9711i	−0.943249	+	1.63376i	−0.759220	+	0.650835i	$0.774419\pi$
$570$		0			0
$571$	18.5000	+	32.0429i	0.774201	+	1.34096i	0.935243	+	0.354008i	$0.115181\pi$
$571$	18.5000	+	32.0429i	0.774201	+	1.34096i	−0.161042	+	0.986948i	$0.551485\pi$
$572$	−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	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$	−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	$-0.107200\pi$
$587$	4.50000	+	7.79423i	0.185735	+	0.321702i	−0.758089	+	0.652151i	$0.773867\pi$
$588$		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	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$	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	0.717021	−	0.697051i	$-0.245505\pi$
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	−0.962175	+	0.272433i	$0.912172\pi$
$600$			8.66025i			0.353553i
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	0.945558	+	0.325455i	$0.105517\pi$
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	−0.190927	+	0.981604i	$0.561149\pi$
$602$		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	$-0.692376\pi$
$607$	−28.0000			−1.13648			−0.568242	+	0.822861i	$0.692376\pi$
$608$	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	−0.658012	−	0.753007i	$-0.728603\pi$
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	0.981129	+	0.193352i	$0.0619359\pi$
$614$	3.50000	−	6.06218i	0.141249	−	0.244650i
$615$		0			0
$616$		0			0
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$	21.0000	+	12.1244i	0.844744	+	0.487713i
$619$	35.0000			1.40677			0.703384	−	0.710810i	$-0.251671\pi$
$619$	35.0000			1.40677			0.703384	+	0.710810i	$0.251671\pi$
$620$		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	$-0.983164\pi$
$643$	−11.5000	+	19.9186i	−0.453516	+	0.785512i	0.545086	+	0.838380i	$0.316497\pi$
$644$		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	$-0.948453\pi$
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	0.633090	+	0.774078i	$0.281786\pi$
$648$	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	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	0.902297	−	0.431116i	$-0.141880\pi$
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	−0.824506	+	0.565854i	$0.808547\pi$
$662$	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	0.996328	−	0.0856156i	$-0.0272857\pi$
$673$	11.0000	+	19.0526i	0.424019	+	0.734422i	−0.572309	+	0.820038i	$0.693952\pi$
$674$	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	0.279453	+	0.960159i	$0.409847\pi$
$677$	−18.0000	+	31.1769i	−0.691796	+	1.19823i	−0.971249	+	0.238067i	$0.923486\pi$
$678$	−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	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$	−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	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	−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	−0.826023	−	0.563636i	$-0.809402\pi$
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	0.901135	+	0.433539i	$0.142735\pi$
$710$		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	0.977539	+	0.210752i	$0.0675914\pi$
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	−0.306253	+	0.951950i	$0.599075\pi$
$720$		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	$-0.326808\pi$
$727$	−13.0000	−	22.5167i	−0.482143	−	0.835097i	−0.999790	+	0.0204978i	$0.993475\pi$
$728$		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	$-0.416755\pi$
$733$	14.0000			0.517102			0.258551	+	0.965998i	$0.416755\pi$
$734$	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	0.00311943	+	0.999995i	$0.499007\pi$
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	−0.867581	+	0.497296i	$0.834326\pi$
$740$		0			0
$741$			3.46410i			0.127257i
$742$		0			0
$743$	−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	$0.201771\pi$
$744$	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	$-0.224586\pi$
$761$	42.0000			1.52250			0.761249	+	0.648459i	$0.224586\pi$
$762$	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	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$		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	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$	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	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	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	$-0.765163\pi$
$797$	6.00000	−	10.3923i	0.212531	−	0.368114i	0.952506	+	0.304520i	$0.0984960\pi$
$798$		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	0.415357	+	0.909659i	$0.363657\pi$
$809$	−16.5000	+	28.5788i	−0.580109	+	1.00478i	−0.995466	+	0.0951198i	$0.969677\pi$
$810$		0			0
$811$	−7.00000			−0.245803			−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000			−0.245803			−0.122902	+	0.992419i	$0.539220\pi$
$812$		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	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$	−4.50000	−	2.59808i	−0.156956	−	0.0906183i
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	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	$-0.777775\pi$
$829$	5.00000	−	8.66025i	0.173657	−	0.300783i	0.939696	+	0.342012i	$0.111108\pi$
$830$		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	$-0.233083\pi$
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	−0.950813	+	0.309764i	$0.899750\pi$
$840$		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	$-0.313503\pi$
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	−0.998060	+	0.0622597i	$0.980169\pi$
$854$		0			0
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$	9.00000	−	5.19615i	0.307255	−	0.177394i
$859$	35.0000			1.19418			0.597092	−	0.802173i	$-0.296323\pi$
$859$	35.0000			1.19418			0.597092	+	0.802173i	$0.296323\pi$
$860$		0			0
$861$		0			0
$862$	15.0000	+	25.9808i	0.510902	+	0.884908i
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$	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	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		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	−0.922740	−	0.385422i	$-0.874056\pi$
$911$	−24.0000	−	41.5692i	−0.795155	−	1.37725i	0.127585	−	0.991828i	$-0.459277\pi$
$912$			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	−0.988199	−	0.153174i	$-0.951051\pi$
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	0.361447	−	0.932393i	$-0.382283\pi$
$920$		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	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		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	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$		0			0
$939$	43.5000	+	25.1147i	1.41957	+	0.819588i
$940$		0			0
$941$	30.0000	+	51.9615i	0.977972	+	1.69390i	0.669757	+	0.742581i	$0.266398\pi$
$941$	30.0000	+	51.9615i	0.977972	+	1.69390i	0.308215	+	0.951317i	$0.400268\pi$
$942$			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	−0.889368	−	0.457193i	$-0.848855\pi$
$947$	−1.50000	+	2.59808i	−0.0487435	+	0.0844261i	0.840624	+	0.541619i	$0.182188\pi$
$948$			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	−0.633165	−	0.774017i	$-0.718244\pi$
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	0.986901	+	0.161328i	$0.0515777\pi$
$968$	−2.00000			−0.0642824
$969$		−	5.19615i		−	0.166924i
$970$		0			0
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$	−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	0.908740	+	0.417364i	$0.137046\pi$
$977$	25.5000	+	44.1673i	0.815817	+	1.41304i	−0.0929223	+	0.995673i	$0.529621\pi$
$978$			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	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	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	$-0.646222\pi$
$997$	−28.0000			−0.886769			−0.443384	+	0.896332i	$0.646222\pi$
$998$	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.c.67.1		2
3.2	odd	2		2646.2.h.h.361.1		2
7.2	even	3		882.2.e.i.373.1		2
7.3	odd	6		882.2.f.d.589.1		2
7.4	even	3		18.2.c.a.13.1	yes	2
7.5	odd	6		882.2.e.g.373.1		2
7.6	odd	2		882.2.h.b.67.1		2
9.2	odd	6		2646.2.e.b.2125.1		2
9.7	even	3		882.2.e.i.655.1		2
21.2	odd	6		2646.2.e.b.1549.1		2
21.5	even	6		2646.2.e.c.1549.1		2
21.11	odd	6		54.2.c.a.37.1		2
21.17	even	6		2646.2.f.g.1765.1		2
21.20	even	2		2646.2.h.i.361.1		2
28.11	odd	6		144.2.i.c.49.1		2
35.4	even	6		450.2.e.i.301.1		2
35.18	odd	12		450.2.j.e.49.1		4
35.32	odd	12		450.2.j.e.49.2		4
56.11	odd	6		576.2.i.a.193.1		2
56.53	even	6		576.2.i.g.193.1		2
63.2	odd	6		2646.2.h.h.667.1		2
63.4	even	3		162.2.a.c.1.1		1
63.11	odd	6		54.2.c.a.19.1		2
63.16	even	3	inner	882.2.h.c.79.1		2
63.20	even	6		2646.2.e.c.2125.1		2
63.25	even	3		18.2.c.a.7.1	✓	2
63.31	odd	6		7938.2.a.x.1.1		1
63.32	odd	6		162.2.a.b.1.1		1
63.34	odd	6		882.2.e.g.655.1		2
63.38	even	6		2646.2.f.g.883.1		2
63.47	even	6		2646.2.h.i.667.1		2
63.52	odd	6		882.2.f.d.295.1		2
63.59	even	6		7938.2.a.i.1.1		1
63.61	odd	6		882.2.h.b.79.1		2
84.11	even	6		432.2.i.b.145.1		2
105.32	even	12		1350.2.j.a.199.1		4
105.53	even	12		1350.2.j.a.199.2		4
105.74	odd	6		1350.2.e.c.901.1		2
168.11	even	6		1728.2.i.f.577.1		2
168.53	odd	6		1728.2.i.e.577.1		2
252.11	even	6		432.2.i.b.289.1		2
252.67	odd	6		1296.2.a.g.1.1		1
252.95	even	6		1296.2.a.f.1.1		1
252.151	odd	6		144.2.i.c.97.1		2
315.4	even	6		4050.2.a.c.1.1		1
315.32	even	12		4050.2.c.r.649.1		2
315.67	odd	12		4050.2.c.c.649.2		2
315.74	odd	6		1350.2.e.c.451.1		2
315.88	odd	12		450.2.j.e.349.2		4
315.137	even	12		1350.2.j.a.1099.2		4
315.158	even	12		4050.2.c.r.649.2		2
315.193	odd	12		4050.2.c.c.649.1		2
315.214	even	6		450.2.e.i.151.1		2
315.263	even	12		1350.2.j.a.1099.1		4
315.277	odd	12		450.2.j.e.349.1		4
315.284	odd	6		4050.2.a.v.1.1		1
504.11	even	6		1728.2.i.f.1153.1		2
504.67	odd	6		5184.2.a.o.1.1		1
504.221	odd	6		5184.2.a.q.1.1		1
504.277	even	6		576.2.i.g.385.1		2
504.347	even	6		5184.2.a.p.1.1		1
504.389	odd	6		1728.2.i.e.1153.1		2
504.403	odd	6		576.2.i.a.385.1		2
504.445	even	6		5184.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.2.c.a.7.1	✓	2	63.25	even	3
18.2.c.a.13.1	yes	2	7.4	even	3
54.2.c.a.19.1		2	63.11	odd	6
54.2.c.a.37.1		2	21.11	odd	6
144.2.i.c.49.1		2	28.11	odd	6
144.2.i.c.97.1		2	252.151	odd	6
162.2.a.b.1.1		1	63.32	odd	6
162.2.a.c.1.1		1	63.4	even	3
432.2.i.b.145.1		2	84.11	even	6
432.2.i.b.289.1		2	252.11	even	6
450.2.e.i.151.1		2	315.214	even	6
450.2.e.i.301.1		2	35.4	even	6
450.2.j.e.49.1		4	35.18	odd	12
450.2.j.e.49.2		4	35.32	odd	12
450.2.j.e.349.1		4	315.277	odd	12
450.2.j.e.349.2		4	315.88	odd	12
576.2.i.a.193.1		2	56.11	odd	6
576.2.i.a.385.1		2	504.403	odd	6
576.2.i.g.193.1		2	56.53	even	6
576.2.i.g.385.1		2	504.277	even	6
882.2.e.g.373.1		2	7.5	odd	6
882.2.e.g.655.1		2	63.34	odd	6
882.2.e.i.373.1		2	7.2	even	3
882.2.e.i.655.1		2	9.7	even	3
882.2.f.d.295.1		2	63.52	odd	6
882.2.f.d.589.1		2	7.3	odd	6
882.2.h.b.67.1		2	7.6	odd	2
882.2.h.b.79.1		2	63.61	odd	6
882.2.h.c.67.1		2	1.1	even	1	trivial
882.2.h.c.79.1		2	63.16	even	3	inner
1296.2.a.f.1.1		1	252.95	even	6
1296.2.a.g.1.1		1	252.67	odd	6
1350.2.e.c.451.1		2	315.74	odd	6
1350.2.e.c.901.1		2	105.74	odd	6
1350.2.j.a.199.1		4	105.32	even	12
1350.2.j.a.199.2		4	105.53	even	12
1350.2.j.a.1099.1		4	315.263	even	12
1350.2.j.a.1099.2		4	315.137	even	12
1728.2.i.e.577.1		2	168.53	odd	6
1728.2.i.e.1153.1		2	504.389	odd	6
1728.2.i.f.577.1		2	168.11	even	6
1728.2.i.f.1153.1		2	504.11	even	6
2646.2.e.b.1549.1		2	21.2	odd	6
2646.2.e.b.2125.1		2	9.2	odd	6
2646.2.e.c.1549.1		2	21.5	even	6
2646.2.e.c.2125.1		2	63.20	even	6
2646.2.f.g.883.1		2	63.38	even	6
2646.2.f.g.1765.1		2	21.17	even	6
2646.2.h.h.361.1		2	3.2	odd	2
2646.2.h.h.667.1		2	63.2	odd	6
2646.2.h.i.361.1		2	21.20	even	2
2646.2.h.i.667.1		2	63.47	even	6
4050.2.a.c.1.1		1	315.4	even	6
4050.2.a.v.1.1		1	315.284	odd	6
4050.2.c.c.649.1		2	315.193	odd	12
4050.2.c.c.649.2		2	315.67	odd	12
4050.2.c.r.649.1		2	315.32	even	12
4050.2.c.r.649.2		2	315.158	even	12
5184.2.a.o.1.1		1	504.67	odd	6
5184.2.a.p.1.1		1	504.347	even	6
5184.2.a.q.1.1		1	504.221	odd	6
5184.2.a.r.1.1		1	504.445	even	6
7938.2.a.i.1.1		1	63.59	even	6
7938.2.a.x.1.1		1	63.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
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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