LMFDB - Embedded newform 882.2.e.i.655.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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, 2]))

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.i.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 - 0.866025i) q^{6} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 - 0.866025i) q^{6} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.50000 + 2.59808i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{17} +(1.50000 - 2.59808i) q^{18} +(0.500000 + 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(1.50000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-1.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} -4.00000 q^{31} +1.00000 q^{32} +(4.50000 + 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} +(2.00000 + 3.46410i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-3.00000 - 1.73205i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(0.500000 - 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{44} +(3.00000 - 5.19615i) q^{46} -6.00000 q^{47} +(1.50000 - 0.866025i) q^{48} +(2.50000 + 4.33013i) q^{50} -5.19615i q^{51} +(-1.00000 - 1.73205i) q^{52} +(-6.00000 + 10.3923i) q^{53} -5.19615i q^{54} +(1.50000 + 0.866025i) q^{57} +(-3.00000 + 5.19615i) q^{58} +3.00000 q^{59} +8.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +(4.50000 + 2.59808i) q^{66} +5.00000 q^{67} +(1.50000 - 2.59808i) q^{68} -10.3923i q^{69} -12.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(-5.50000 + 9.52628i) q^{73} +(2.00000 + 3.46410i) q^{74} +(7.50000 + 4.33013i) q^{75} +(0.500000 + 0.866025i) q^{76} +(-3.00000 - 1.73205i) q^{78} -4.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{82} +(-6.00000 + 10.3923i) q^{83} +(0.500000 - 0.866025i) q^{86} +10.3923i q^{87} +(1.50000 + 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(3.00000 - 5.19615i) q^{92} +(-6.00000 + 3.46410i) q^{93} -6.00000 q^{94} +(1.50000 - 0.866025i) q^{96} +(-2.50000 + 4.33013i) q^{97} +9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 + 3 * q^9	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} + 3 q^{9} + 3 q^{11} + 3 q^{12} - 2 q^{13} + 2 q^{16} + 3 q^{17} + 3 q^{18} + q^{19} + 3 q^{22} + 6 q^{23} + 3 q^{24} + 5 q^{25} - 2 q^{26} - 6 q^{29} - 8 q^{31} + 2 q^{32} + 9 q^{33} + 3 q^{34} + 3 q^{36} + 4 q^{37} + q^{38} - 6 q^{39} - 9 q^{41} + q^{43} + 3 q^{44} + 6 q^{46} - 12 q^{47} + 3 q^{48} + 5 q^{50} - 2 q^{52} - 12 q^{53} + 3 q^{57} - 6 q^{58} + 6 q^{59} + 16 q^{61} - 8 q^{62} + 2 q^{64} + 9 q^{66} + 10 q^{67} + 3 q^{68} - 24 q^{71} + 3 q^{72} - 11 q^{73} + 4 q^{74} + 15 q^{75} + q^{76} - 6 q^{78} - 8 q^{79} - 9 q^{81} - 9 q^{82} - 12 q^{83} + q^{86} + 3 q^{88} - 6 q^{89} + 6 q^{92} - 12 q^{93} - 12 q^{94} + 3 q^{96} - 5 q^{97} + 18 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 + 3 * q^9 + 3 * q^11 + 3 * q^12 - 2 * q^13 + 2 * q^16 + 3 * q^17 + 3 * q^18 + q^19 + 3 * q^22 + 6 * q^23 + 3 * q^24 + 5 * q^25 - 2 * q^26 - 6 * q^29 - 8 * q^31 + 2 * q^32 + 9 * q^33 + 3 * q^34 + 3 * q^36 + 4 * q^37 + q^38 - 6 * q^39 - 9 * q^41 + q^43 + 3 * q^44 + 6 * q^46 - 12 * q^47 + 3 * q^48 + 5 * q^50 - 2 * q^52 - 12 * q^53 + 3 * q^57 - 6 * q^58 + 6 * q^59 + 16 * q^61 - 8 * q^62 + 2 * q^64 + 9 * q^66 + 10 * q^67 + 3 * q^68 - 24 * q^71 + 3 * q^72 - 11 * q^73 + 4 * q^74 + 15 * q^75 + q^76 - 6 * q^78 - 8 * q^79 - 9 * q^81 - 9 * q^82 - 12 * q^83 + q^86 + 3 * q^88 - 6 * q^89 + 6 * q^92 - 12 * q^93 - 12 * 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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	1.00000			0.500000
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	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
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	−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
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000			0.176777
$33$	4.50000	+	2.59808i	0.783349	+	0.452267i
$34$	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	$0.726690\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	−3.00000	−	1.73205i	−0.480384	−	0.277350i
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		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
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$		0			0
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$		−	5.19615i		−	0.727607i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−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	$0.858312\pi$
$54$		−	5.19615i		−	0.707107i
$55$		0			0
$56$		0			0
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	3.00000			0.390567			0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000			0.390567			0.195283	+	0.980747i	$0.437437\pi$
$60$		0			0
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	4.50000	+	2.59808i	0.553912	+	0.319801i
$67$	5.00000			0.610847			0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000			0.610847			0.305424	+	0.952217i	$0.401202\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		−	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	$0.752242\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	−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	$0.944054\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	7.50000	+	4.33013i	0.866025	+	0.500000i
$76$	0.500000	+	0.866025i	0.0573539	+	0.0993399i
$77$		0			0
$78$	−3.00000	−	1.73205i	−0.339683	−	0.196116i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$		0			0
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$			10.3923i			1.11417i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−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
$94$	−6.00000			−0.618853
$95$		0			0
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$	9.00000			0.904534
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		−	5.19615i		−	0.514496i
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$	−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	$0.879655\pi$
$108$		−	5.19615i		−	0.500000i
$109$	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	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$	1.50000	+	0.866025i	0.140488	+	0.0811107i
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	−6.00000			−0.554700
$118$	3.00000			0.276172
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	8.00000			0.724286
$123$	−13.5000	−	7.79423i	−1.21725	−	0.702782i
$124$	−4.00000			−0.359211
$125$		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	$0.471717\pi$
$128$	1.00000			0.0883883
$129$		−	1.73205i		−	0.152499i
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	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
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		−	10.3923i		−	0.884652i
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	0.915764	+	0.401718i	$0.131587\pi$
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	−0.109984	+	0.993933i	$0.535080\pi$
$140$		0			0
$141$	−9.00000	+	5.19615i	−0.757937	+	0.437595i
$142$	−12.0000			−1.00702
$143$	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
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	7.50000	+	4.33013i	0.612372	+	0.353553i
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$	0.500000	+	0.866025i	0.0405554	+	0.0702439i
$153$	−4.50000	−	7.79423i	−0.363803	−	0.630126i
$154$		0			0
$155$		0			0
$156$	−3.00000	−	1.73205i	−0.240192	−	0.138675i
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$	−4.00000			−0.318223
$159$			20.7846i			1.64833i
$160$		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	$0.783263\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	3.00000			0.229416
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$			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
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−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
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$		0			0
$186$	−6.00000	+	3.46410i	−0.439941	+	0.254000i
$187$	9.00000			0.658145
$188$	−6.00000			−0.437595
$189$		0			0
$190$		0			0
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$	1.50000	−	0.866025i	0.108253	−	0.0625000i
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	−2.50000	+	4.33013i	−0.179490	+	0.310885i
$195$		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	$0.640599\pi$
$198$	9.00000			0.639602
$199$	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	$0.0513380\pi$
$200$	2.50000	+	4.33013i	0.176777	+	0.306186i
$201$	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
$207$	−9.00000	−	15.5885i	−0.625543	−	1.08347i
$208$	−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	$-0.408366\pi$
$212$	−6.00000	+	10.3923i	−0.412082	+	0.713746i
$213$	−18.0000	+	10.3923i	−1.23334	+	0.712069i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$		0			0
$216$		−	5.19615i		−	0.353553i
$217$		0			0
$218$	8.00000	−	13.8564i	0.541828	−	0.938474i
$219$			19.0526i			1.28745i
$220$		0			0
$221$	−6.00000			−0.403604
$222$	6.00000	+	3.46410i	0.402694	+	0.232495i
$223$	−13.0000	+	22.5167i	−0.870544	+	1.50783i	−0.00910984	+	0.999959i	$0.502900\pi$
$223$	−13.0000	+	22.5167i	−0.870544	+	1.50783i	−0.861435	+	0.507869i	$0.830434\pi$
$224$		0			0
$225$	15.0000			1.00000
$226$	−3.00000	−	5.19615i	−0.199557	−	0.345643i
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	−0.969533	−	0.244962i	$-0.921225\pi$
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	0.272623	−	0.962121i	$-0.412109\pi$
$228$	1.50000	+	0.866025i	0.0993399	+	0.0573539i
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		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	$0.864664\pi$
$234$	−6.00000			−0.392232
$235$		0			0
$236$	3.00000			0.195283
$237$	−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
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	8.00000			0.512148
$245$		0			0
$246$	−13.5000	−	7.79423i	−0.860729	−	0.496942i
$247$	1.00000	−	1.73205i	0.0636285	−	0.110208i
$248$	−4.00000			−0.254000
$249$			20.7846i			1.31717i
$250$		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
$254$	2.00000			0.125491
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	−0.326929	−	0.945049i	$-0.606014\pi$
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	0.981901	−	0.189396i	$-0.0606529\pi$
$258$		−	1.73205i		−	0.107833i
$259$		0			0
$260$		0			0
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$		0			0
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	−0.997906	−	0.0646755i	$-0.979399\pi$
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	0.442943	−	0.896550i	$-0.353935\pi$
$264$	4.50000	+	2.59808i	0.276956	+	0.159901i
$265$		0			0
$266$		0			0
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	5.00000			0.305424
$269$	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
$275$	−7.50000	+	12.9904i	−0.452267	+	0.783349i
$276$		−	10.3923i		−	0.625543i
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	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
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$	−12.0000			−0.712069
$285$		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
$291$			8.66025i			0.507673i
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	−15.0000	−	25.9808i	−0.876309	−	1.51781i	−0.855361	−	0.518032i	$-0.826665\pi$
$293$	−15.0000	−	25.9808i	−0.876309	−	1.51781i	−0.0209480	−	0.999781i	$-0.506668\pi$
$294$		0			0
$295$		0			0
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−12.0000			−0.693978
$300$	7.50000	+	4.33013i	0.433013	+	0.250000i
$301$		0			0
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$		0			0
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$		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
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$	−3.00000	−	1.73205i	−0.169842	−	0.0980581i
$313$	29.0000			1.63918			0.819588	−	0.572953i	$-0.194202\pi$
$313$	29.0000			1.63918			0.819588	+	0.572953i	$0.194202\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$			20.7846i			1.16554i
$319$	−18.0000			−1.00781
$320$		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
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$		−	27.7128i		−	1.53252i
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$		0			0
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	12.0000			0.657596
$334$	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	$0.824663\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	−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
$346$	−6.00000			−0.322562
$347$	33.0000			1.77153			0.885766	−	0.464131i	$-0.153633\pi$
$347$	33.0000			1.77153			0.885766	+	0.464131i	$0.153633\pi$
$348$			10.3923i			0.557086i
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	−0.568486	−	0.822693i	$-0.692471\pi$
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	0.996716	+	0.0809766i	$0.0258039\pi$
$350$		0			0
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	0.997592	+	0.0693543i	$0.0220939\pi$
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	−0.438733	+	0.898617i	$0.644573\pi$
$354$	4.50000	−	2.59808i	0.239172	−	0.138086i
$355$		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
$362$	14.0000			0.735824
$363$		−	3.46410i		−	0.181818i
$364$		0			0
$365$		0			0
$366$	12.0000	−	6.92820i	0.627250	−	0.362143i
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$	−27.0000			−1.40556
$370$		0			0
$371$		0			0
$372$	−6.00000	+	3.46410i	−0.311086	+	0.179605i
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.0291379	−	0.999575i	$-0.490724\pi$
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.851089	−	0.525022i	$-0.175943\pi$
$374$	9.00000			0.465379
$375$		0			0
$376$	−6.00000			−0.309426
$377$	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
$381$	3.00000	−	1.73205i	0.153695	−	0.0887357i
$382$	−18.0000			−0.920960
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$	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
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$		0			0
$393$		0			0
$394$	−12.0000			−0.604551
$395$		0			0
$396$	9.00000			0.452267
$397$	−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
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$	7.50000	−	4.33013i	0.374066	−	0.215967i
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$		−	5.19615i		−	0.257248i
$409$	17.0000			0.840596			0.420298	−	0.907386i	$-0.361926\pi$
$409$	17.0000			0.840596			0.420298	+	0.907386i	$0.361926\pi$
$410$		0			0
$411$	4.50000	+	2.59808i	0.221969	+	0.128154i
$412$	−7.00000	+	12.1244i	−0.344865	+	0.597324i
$413$		0			0
$414$	−9.00000	−	15.5885i	−0.442326	−	0.766131i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	28.5000	+	16.4545i	1.39565	+	0.805779i
$418$	−1.50000	+	2.59808i	−0.0733674	+	0.127076i
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$		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
$425$	15.0000			0.727607
$426$	−18.0000	+	10.3923i	−0.872103	+	0.503509i
$427$		0			0
$428$	−1.50000	−	2.59808i	−0.0725052	−	0.125583i
$429$		−	10.3923i		−	0.501745i
$430$		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	$-0.0903517\pi$
$432$		−	5.19615i		−	0.250000i
$433$	−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
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$	6.00000			0.287019
$438$			19.0526i			0.910366i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$		0			0
$442$	−6.00000			−0.285391
$443$	3.00000			0.142534			0.0712672	−	0.997457i	$-0.477296\pi$
$443$	3.00000			0.142534			0.0712672	+	0.997457i	$0.477296\pi$
$444$	6.00000	+	3.46410i	0.284747	+	0.164399i
$445$		0			0
$446$	−13.0000	+	22.5167i	−0.615568	+	1.06619i
$447$		−	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	$0.431882\pi$
$450$	15.0000			0.707107
$451$	13.5000	−	23.3827i	0.635690	−	1.10105i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	15.0000	+	8.66025i	0.704761	+	0.406894i
$454$	−10.5000	−	18.1865i	−0.492789	−	0.853536i
$455$		0			0
$456$	1.50000	+	0.866025i	0.0702439	+	0.0405554i
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	−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	$-0.587131\pi$
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	0.968945	−	0.247276i	$-0.0795353\pi$
$462$		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	$0.987185\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	−1.50000	−	2.59808i	−0.0694862	−	0.120354i
$467$	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
$472$	3.00000			0.138086
$473$	3.00000			0.137940
$474$	−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
$479$	21.0000	+	36.3731i	0.959514	+	1.66193i	0.723681	+	0.690134i	$0.242449\pi$
$479$	21.0000	+	36.3731i	0.959514	+	1.66193i	0.235833	+	0.971794i	$0.424218\pi$
$480$		0			0
$481$	4.00000	−	6.92820i	0.182384	−	0.315899i
$482$	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	$0.966154\pi$
$488$	8.00000			0.362143
$489$	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	$0.723424\pi$
$492$	−13.5000	−	7.79423i	−0.608627	−	0.351391i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	1.00000	−	1.73205i	0.0449921	−	0.0779287i
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$			20.7846i			0.931381i
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	−0.683062	−	0.730361i	$-0.739352\pi$
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	0.974042	+	0.226369i	$0.0726854\pi$
$500$		0			0
$501$	18.0000	+	10.3923i	0.804181	+	0.464294i
$502$	21.0000			0.937276
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$	18.0000			0.800198
$507$		−	15.5885i		−	0.692308i
$508$	2.00000			0.0887357
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		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
$516$		−	1.73205i		−	0.0762493i
$517$	−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	$0.145733\pi$
$522$	9.00000	+	15.5885i	0.393919	+	0.682288i
$523$	−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
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	4.50000	+	2.59808i	0.195837	+	0.113067i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	4.50000	−	7.79423i	0.195283	−	0.338241i
$532$		0			0
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$	−9.00000	−	5.19615i	−0.389468	−	0.224860i
$535$		0			0
$536$	5.00000			0.215967
$537$			20.7846i			0.896922i
$538$	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	$0.805929\pi$
$542$	−10.0000	−	17.3205i	−0.429537	−	0.743980i
$543$	21.0000	−	12.1244i	0.901196	−	0.520306i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$		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
$551$	−6.00000			−0.255609
$552$		−	10.3923i		−	0.442326i
$553$		0			0
$554$	5.00000	+	8.66025i	0.212430	+	0.367939i
$555$		0			0
$556$	9.50000	+	16.4545i	0.402890	+	0.697826i
$557$	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	$-0.0525683\pi$
$558$	−6.00000	+	10.3923i	−0.254000	+	0.439941i
$559$	−2.00000			−0.0845910
$560$		0			0
$561$	13.5000	−	7.79423i	0.569970	−	0.329073i
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	−39.0000			−1.64365			−0.821827	−	0.569737i	$-0.807045\pi$
$563$	−39.0000			−1.64365			−0.821827	+	0.569737i	$0.807045\pi$
$564$	−9.00000	+	5.19615i	−0.378968	+	0.218797i
$565$		0			0
$566$	−4.00000			−0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$	45.0000			1.88650			0.943249	−	0.332086i	$-0.107752\pi$
$569$	45.0000			1.88650			0.943249	+	0.332086i	$0.107752\pi$
$570$		0			0
$571$	−37.0000			−1.54840			−0.774201	−	0.632940i	$-0.781848\pi$
$571$	−37.0000			−1.54840			−0.774201	+	0.632940i	$0.781848\pi$
$572$	3.00000	−	5.19615i	0.125436	−	0.217262i
$573$	−27.0000	+	15.5885i	−1.12794	+	0.651217i
$574$		0			0
$575$	30.0000			1.25109
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−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	$0.240202\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	7.50000	−	4.33013i	0.311689	−	0.179954i
$580$		0			0
$581$		0			0
$582$			8.66025i			0.358979i
$583$	−36.0000			−1.49097
$584$	−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	−0.758089	−	0.652151i	$-0.773867\pi$
$587$	4.50000	−	7.79423i	0.185735	−	0.321702i	0.943824	+	0.330449i	$0.107200\pi$
$588$		0			0
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$		0			0
$591$	−18.0000	+	10.3923i	−0.740421	+	0.427482i
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	−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
$597$		−	17.3205i		−	0.708881i
$598$	−12.0000			−0.490716
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$	7.50000	+	4.33013i	0.306186	+	0.176777i
$601$	18.5000	−	32.0429i	0.754631	−	1.30706i	−0.190927	−	0.981604i	$-0.561149\pi$
$601$	18.5000	−	32.0429i	0.754631	−	1.30706i	0.945558	−	0.325455i	$-0.105517\pi$
$602$		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
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	−0.428497	−	0.903543i	$-0.640957\pi$
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	0.996740	−	0.0806818i	$-0.0257098\pi$
$608$	0.500000	+	0.866025i	0.0202777	+	0.0351220i
$609$		0			0
$610$		0			0
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$	−4.50000	−	7.79423i	−0.181902	−	0.315063i
$613$	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	$0.0619359\pi$
$614$	−7.00000			−0.282497
$615$		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	$-0.349564\pi$
$618$			24.2487i			0.975426i
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	−0.967271	−	0.253744i	$-0.918338\pi$
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	0.263887	−	0.964554i	$-0.414995\pi$
$620$		0			0
$621$	−27.0000	−	15.5885i	−1.08347	−	0.625543i
$622$	−18.0000			−0.721734
$623$		0			0
$624$	−3.00000	−	1.73205i	−0.120096	−	0.0693375i
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	29.0000			1.15907
$627$			5.19615i			0.207514i
$628$	−4.00000			−0.159617
$629$	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	$0.793153\pi$
$632$	−4.00000			−0.159111
$633$	−30.0000	−	17.3205i	−1.19239	−	0.688428i
$634$	−18.0000			−0.714871
$635$		0			0
$636$			20.7846i			0.824163i
$637$		0			0
$638$	−18.0000			−0.712627
$639$	−18.0000	+	31.1769i	−0.712069	+	1.23334i
$640$		0			0
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	0.894127	−	0.447813i	$-0.147797\pi$
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	−0.834881	+	0.550431i	$0.814464\pi$
$642$	−4.50000	−	2.59808i	−0.177601	−	0.102538i
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	0.545086	−	0.838380i	$-0.316497\pi$
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	−0.998602	+	0.0528680i	$0.983164\pi$
$644$		0			0
$645$		0			0
$646$	3.00000			0.118033
$647$	−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	$0.281786\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	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
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$		−	27.7128i		−	1.08366i
$655$		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
$661$	−4.00000			−0.155582			−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000			−0.155582			−0.0777910	+	0.996970i	$0.524787\pi$
$662$	−4.00000			−0.155464
$663$	−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
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$			45.0333i			1.74109i
$670$		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
$675$	22.5000	−	12.9904i	0.866025	−	0.500000i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	36.0000			1.38359			0.691796	−	0.722093i	$-0.256820\pi$
$677$	36.0000			1.38359			0.691796	+	0.722093i	$0.256820\pi$
$678$	−9.00000	−	5.19615i	−0.345643	−	0.199557i
$679$		0			0
$680$		0			0
$681$	−31.5000	−	18.1865i	−1.20708	−	0.696909i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	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	$0.111583\pi$
$684$	3.00000			0.114708
$685$		0			0
$686$		0			0
$687$			24.2487i			0.925146i
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	24.0000			0.914327
$690$		0			0
$691$	8.00000			0.304334			0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000			0.304334			0.152167	+	0.988355i	$0.451375\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	33.0000			1.25266
$695$		0			0
$696$			10.3923i			0.393919i
$697$	−27.0000			−1.02270
$698$	8.00000	−	13.8564i	0.302804	−	0.524473i
$699$	−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
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	10.5000	+	18.1865i	0.395173	+	0.684459i
$707$		0			0
$708$	4.50000	−	2.59808i	0.169120	−	0.0976417i
$709$	−4.00000			−0.150223			−0.0751116	−	0.997175i	$-0.523931\pi$
$709$	−4.00000			−0.150223			−0.0751116	+	0.997175i	$0.523931\pi$
$710$		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
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	−9.00000	−	5.19615i	−0.336111	−	0.194054i
$718$	9.00000	+	15.5885i	0.335877	+	0.581756i
$719$	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
$723$	10.5000	+	6.06218i	0.390499	+	0.225455i
$724$	14.0000			0.520306
$725$	−30.0000			−1.11417
$726$		−	3.46410i		−	0.128565i
$727$	−13.0000	+	22.5167i	−0.482143	+	0.835097i	−0.999790	−	0.0204978i	$-0.993475\pi$
$727$	−13.0000	+	22.5167i	−0.482143	+	0.835097i	0.517647	+	0.855595i	$0.326808\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$	12.0000	−	6.92820i	0.443533	−	0.256074i
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	−0.965854	−	0.259087i	$-0.916578\pi$
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	0.707303	+	0.706910i	$0.249912\pi$
$734$	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
$738$	−27.0000			−0.993884
$739$	−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	0.805735	−	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
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$	−6.00000			−0.218797
$753$	31.5000	−	18.1865i	1.14792	−	0.662754i
$754$	12.0000			0.437014
$755$		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	$0.488428\pi$
$758$	23.0000			0.835398
$759$	27.0000	−	15.5885i	0.980038	−	0.565825i
$760$		0			0
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$	3.00000	−	1.73205i	0.108679	−	0.0627456i
$763$		0			0
$764$	−18.0000			−0.651217
$765$		0			0
$766$		0			0
$767$	−3.00000	−	5.19615i	−0.108324	−	0.187622i
$768$	1.50000	−	0.866025i	0.0541266	−	0.0312500i
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$		−	36.3731i		−	1.30994i
$772$	5.00000			0.179954
$773$	−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	$0.271596\pi$
$774$	−1.50000	−	2.59808i	−0.0539164	−	0.0933859i
$775$	−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
$779$	4.50000	−	7.79423i	0.161229	−	0.279257i
$780$		0			0
$781$	−18.0000	−	31.1769i	−0.644091	−	1.11560i
$782$	−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
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−12.0000			−0.427482
$789$	−27.0000	−	15.5885i	−0.961225	−	0.554964i
$790$		0			0
$791$		0			0
$792$	9.00000			0.319801
$793$	−8.00000	−	13.8564i	−0.284088	−	0.492055i
$794$	−10.0000	−	17.3205i	−0.354887	−	0.614682i
$795$		0			0
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	0.952506	−	0.304520i	$-0.0984960\pi$
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	−0.739975	+	0.672634i	$0.765163\pi$
$798$		0			0
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$	2.50000	+	4.33013i	0.0883883	+	0.153093i
$801$	−18.0000			−0.635999
$802$	13.5000	−	23.3827i	0.476702	−	0.825671i
$803$	−33.0000			−1.16454
$804$	7.50000	−	4.33013i	0.264505	−	0.152712i
$805$		0			0
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$		−	41.5692i		−	1.46331i
$808$		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
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$		0			0
$816$		−	5.19615i		−	0.181902i
$817$	1.00000			0.0349856
$818$	17.0000			0.594391
$819$		0			0
$820$		0			0
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$	4.50000	+	2.59808i	0.156956	+	0.0906183i
$823$	−16.0000			−0.557725			−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000			−0.557725			−0.278862	+	0.960331i	$0.589957\pi$
$824$	−7.00000	+	12.1244i	−0.243857	+	0.422372i
$825$			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
$831$	15.0000	+	8.66025i	0.520344	+	0.300421i
$832$	−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
$837$			20.7846i			0.718421i
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	−0.950813	−	0.309764i	$-0.899750\pi$
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	0.743670	+	0.668546i	$0.233083\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−10.0000	+	17.3205i	−0.344623	+	0.596904i
$843$			10.3923i			0.357930i
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$		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
$850$	15.0000			0.514496
$851$	24.0000			0.822709
$852$	−18.0000	+	10.3923i	−0.616670	+	0.356034i
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	−0.998060	−	0.0622597i	$-0.980169\pi$
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	0.552948	+	0.833215i	$0.313503\pi$
$854$		0			0
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		−	10.3923i		−	0.354787i
$859$	−17.5000	+	30.3109i	−0.597092	+	1.03419i	0.396156	+	0.918183i	$0.370344\pi$
$859$	−17.5000	+	30.3109i	−0.597092	+	1.03419i	−0.993248	+	0.116011i	$0.962989\pi$
$860$		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	$0.967276\pi$
$864$		−	5.19615i		−	0.176777i
$865$		0			0
$866$	−7.00000			−0.237870
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$		0			0
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	−5.00000	−	8.66025i	−0.169419	−	0.293442i
$872$	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
$877$	−4.00000	+	6.92820i	−0.135070	+	0.233949i	−0.925624	−	0.378444i	$-0.876459\pi$
$877$	−4.00000	+	6.92820i	−0.135070	+	0.233949i	0.790554	+	0.612392i	$0.209793\pi$
$878$	8.00000			0.269987
$879$	−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	$0.603582\pi$
$884$	−6.00000			−0.201802
$885$		0			0
$886$	3.00000			0.100787
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$	6.00000	+	3.46410i	0.201347	+	0.116248i
$889$		0			0
$890$		0			0
$891$	13.5000	−	23.3827i	0.452267	−	0.783349i
$892$	−13.0000	+	22.5167i	−0.435272	+	0.753914i
$893$	−3.00000	−	5.19615i	−0.100391	−	0.173883i
$894$		−	10.3923i		−	0.347571i
$895$		0			0
$896$		0			0
$897$	−18.0000	+	10.3923i	−0.601003	+	0.346989i
$898$	9.00000			0.300334
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$	15.0000			0.500000
$901$	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
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	0.999855	+	0.0170220i	$0.00541854\pi$
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	−0.485186	+	0.874411i	$0.661248\pi$
$908$	−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	$0.874056\pi$
$912$	1.50000	+	0.866025i	0.0496700	+	0.0286770i
$913$	−36.0000			−1.19143
$914$	17.0000			0.562310
$915$		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
$921$	−10.5000	+	6.06218i	−0.345987	+	0.199756i
$922$	15.0000	−	25.9808i	0.493999	−	0.855631i
$923$	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
$927$	21.0000	+	36.3731i	0.689730	+	1.19465i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	−6.00000			−0.196854			−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000			−0.196854			−0.0984268	+	0.995144i	$0.531381\pi$
$930$		0			0
$931$		0			0
$932$	−1.50000	−	2.59808i	−0.0491341	−	0.0851028i
$933$	−27.0000	+	15.5885i	−0.883940	+	0.510343i
$934$	7.50000	+	12.9904i	0.245407	+	0.425058i
$935$		0			0
$936$	−6.00000			−0.196116
$937$	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
$941$	−60.0000			−1.95594			−0.977972	−	0.208736i	$-0.933065\pi$
$941$	−60.0000			−1.95594			−0.977972	+	0.208736i	$0.933065\pi$
$942$	−6.00000	+	3.46410i	−0.195491	+	0.112867i
$943$	−54.0000			−1.75848
$944$	3.00000			0.0976417
$945$		0			0
$946$	3.00000			0.0975384
$947$	3.00000			0.0974869			0.0487435	−	0.998811i	$-0.484478\pi$
$947$	3.00000			0.0974869			0.0487435	+	0.998811i	$0.484478\pi$
$948$	−6.00000	+	3.46410i	−0.194871	+	0.112509i
$949$	22.0000			0.714150
$950$	−2.50000	+	4.33013i	−0.0811107	+	0.140488i
$951$	−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
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$	−27.0000	+	15.5885i	−0.872786	+	0.503903i
$958$	21.0000	+	36.3731i	0.678479	+	1.17516i
$959$		0			0
$960$		0			0
$961$	−15.0000			−0.483871
$962$	4.00000	−	6.92820i	0.128965	−	0.223374i
$963$	−9.00000			−0.290021
$964$	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	$0.718244\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$	4.50000	−	2.59808i	0.144561	−	0.0834622i
$970$		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
$975$		−	17.3205i		−	0.554700i
$976$	8.00000			0.256074
$977$	−51.0000			−1.63163			−0.815817	−	0.578310i	$-0.803713\pi$
$977$	−51.0000			−1.63163			−0.815817	+	0.578310i	$0.803713\pi$
$978$	6.00000	+	3.46410i	0.191859	+	0.110770i
$979$	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		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$	−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	$0.0848781\pi$
$992$	−4.00000			−0.127000
$993$	−6.00000	+	3.46410i	−0.190404	+	0.109930i
$994$		0			0
$995$		0			0
$996$			20.7846i			0.658586i
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	0.997938	−	0.0641836i	$-0.0204443\pi$
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	−0.554554	+	0.832148i	$0.687111\pi$
$998$	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.e.i.655.1		2
3.2	odd	2		2646.2.e.b.2125.1		2
7.2	even	3		882.2.h.c.79.1		2
7.3	odd	6		882.2.f.d.295.1		2
7.4	even	3		18.2.c.a.7.1	✓	2
7.5	odd	6		882.2.h.b.79.1		2
7.6	odd	2		882.2.e.g.655.1		2
9.4	even	3		882.2.h.c.67.1		2
9.5	odd	6		2646.2.h.h.361.1		2
21.2	odd	6		2646.2.h.h.667.1		2
21.5	even	6		2646.2.h.i.667.1		2
21.11	odd	6		54.2.c.a.19.1		2
21.17	even	6		2646.2.f.g.883.1		2
21.20	even	2		2646.2.e.c.2125.1		2
28.11	odd	6		144.2.i.c.97.1		2
35.4	even	6		450.2.e.i.151.1		2
35.18	odd	12		450.2.j.e.349.2		4
35.32	odd	12		450.2.j.e.349.1		4
56.11	odd	6		576.2.i.a.385.1		2
56.53	even	6		576.2.i.g.385.1		2
63.4	even	3		18.2.c.a.13.1	yes	2
63.5	even	6		2646.2.e.c.1549.1		2
63.11	odd	6		162.2.a.b.1.1		1
63.13	odd	6		882.2.h.b.67.1		2
63.23	odd	6		2646.2.e.b.1549.1		2
63.25	even	3		162.2.a.c.1.1		1
63.31	odd	6		882.2.f.d.589.1		2
63.32	odd	6		54.2.c.a.37.1		2
63.38	even	6		7938.2.a.i.1.1		1
63.40	odd	6		882.2.e.g.373.1		2
63.41	even	6		2646.2.h.i.361.1		2
63.52	odd	6		7938.2.a.x.1.1		1
63.58	even	3	inner	882.2.e.i.373.1		2
63.59	even	6		2646.2.f.g.1765.1		2
84.11	even	6		432.2.i.b.289.1		2
105.32	even	12		1350.2.j.a.1099.2		4
105.53	even	12		1350.2.j.a.1099.1		4
105.74	odd	6		1350.2.e.c.451.1		2
168.11	even	6		1728.2.i.f.1153.1		2
168.53	odd	6		1728.2.i.e.1153.1		2
252.11	even	6		1296.2.a.f.1.1		1
252.67	odd	6		144.2.i.c.49.1		2
252.95	even	6		432.2.i.b.145.1		2
252.151	odd	6		1296.2.a.g.1.1		1
315.4	even	6		450.2.e.i.301.1		2
315.32	even	12		1350.2.j.a.199.1		4
315.67	odd	12		450.2.j.e.49.2		4
315.74	odd	6		4050.2.a.v.1.1		1
315.88	odd	12		4050.2.c.c.649.1		2
315.137	even	12		4050.2.c.r.649.1		2
315.158	even	12		1350.2.j.a.199.2		4
315.193	odd	12		450.2.j.e.49.1		4
315.214	even	6		4050.2.a.c.1.1		1
315.263	even	12		4050.2.c.r.649.2		2
315.277	odd	12		4050.2.c.c.649.2		2
315.284	odd	6		1350.2.e.c.901.1		2
504.11	even	6		5184.2.a.p.1.1		1
504.67	odd	6		576.2.i.a.193.1		2
504.221	odd	6		1728.2.i.e.577.1		2
504.277	even	6		5184.2.a.r.1.1		1
504.347	even	6		1728.2.i.f.577.1		2
504.389	odd	6		5184.2.a.q.1.1		1
504.403	odd	6		5184.2.a.o.1.1		1
504.445	even	6		576.2.i.g.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.2.c.a.7.1	✓	2	7.4	even	3
18.2.c.a.13.1	yes	2	63.4	even	3
54.2.c.a.19.1		2	21.11	odd	6
54.2.c.a.37.1		2	63.32	odd	6
144.2.i.c.49.1		2	252.67	odd	6
144.2.i.c.97.1		2	28.11	odd	6
162.2.a.b.1.1		1	63.11	odd	6
162.2.a.c.1.1		1	63.25	even	3
432.2.i.b.145.1		2	252.95	even	6
432.2.i.b.289.1		2	84.11	even	6
450.2.e.i.151.1		2	35.4	even	6
450.2.e.i.301.1		2	315.4	even	6
450.2.j.e.49.1		4	315.193	odd	12
450.2.j.e.49.2		4	315.67	odd	12
450.2.j.e.349.1		4	35.32	odd	12
450.2.j.e.349.2		4	35.18	odd	12
576.2.i.a.193.1		2	504.67	odd	6
576.2.i.a.385.1		2	56.11	odd	6
576.2.i.g.193.1		2	504.445	even	6
576.2.i.g.385.1		2	56.53	even	6
882.2.e.g.373.1		2	63.40	odd	6
882.2.e.g.655.1		2	7.6	odd	2
882.2.e.i.373.1		2	63.58	even	3	inner
882.2.e.i.655.1		2	1.1	even	1	trivial
882.2.f.d.295.1		2	7.3	odd	6
882.2.f.d.589.1		2	63.31	odd	6
882.2.h.b.67.1		2	63.13	odd	6
882.2.h.b.79.1		2	7.5	odd	6
882.2.h.c.67.1		2	9.4	even	3
882.2.h.c.79.1		2	7.2	even	3
1296.2.a.f.1.1		1	252.11	even	6
1296.2.a.g.1.1		1	252.151	odd	6
1350.2.e.c.451.1		2	105.74	odd	6
1350.2.e.c.901.1		2	315.284	odd	6
1350.2.j.a.199.1		4	315.32	even	12
1350.2.j.a.199.2		4	315.158	even	12
1350.2.j.a.1099.1		4	105.53	even	12
1350.2.j.a.1099.2		4	105.32	even	12
1728.2.i.e.577.1		2	504.221	odd	6
1728.2.i.e.1153.1		2	168.53	odd	6
1728.2.i.f.577.1		2	504.347	even	6
1728.2.i.f.1153.1		2	168.11	even	6
2646.2.e.b.1549.1		2	63.23	odd	6
2646.2.e.b.2125.1		2	3.2	odd	2
2646.2.e.c.1549.1		2	63.5	even	6
2646.2.e.c.2125.1		2	21.20	even	2
2646.2.f.g.883.1		2	21.17	even	6
2646.2.f.g.1765.1		2	63.59	even	6
2646.2.h.h.361.1		2	9.5	odd	6
2646.2.h.h.667.1		2	21.2	odd	6
2646.2.h.i.361.1		2	63.41	even	6
2646.2.h.i.667.1		2	21.5	even	6
4050.2.a.c.1.1		1	315.214	even	6
4050.2.a.v.1.1		1	315.74	odd	6
4050.2.c.c.649.1		2	315.88	odd	12
4050.2.c.c.649.2		2	315.277	odd	12
4050.2.c.r.649.1		2	315.137	even	12
4050.2.c.r.649.2		2	315.263	even	12
5184.2.a.o.1.1		1	504.403	odd	6
5184.2.a.p.1.1		1	504.11	even	6
5184.2.a.q.1.1		1	504.389	odd	6
5184.2.a.r.1.1		1	504.277	even	6
7938.2.a.i.1.1		1	63.38	even	6
7938.2.a.x.1.1		1	63.52	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 - 0.866025i) q^{6} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 - 0.866025i) q^{6} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.50000 + 2.59808i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{17} +(1.50000 - 2.59808i) q^{18} +(0.500000 + 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(1.50000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-1.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} -4.00000 q^{31} +1.00000 q^{32} +(4.50000 + 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} +(2.00000 + 3.46410i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-3.00000 - 1.73205i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(0.500000 - 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{44} +(3.00000 - 5.19615i) q^{46} -6.00000 q^{47} +(1.50000 - 0.866025i) q^{48} +(2.50000 + 4.33013i) q^{50} -5.19615i q^{51} +(-1.00000 - 1.73205i) q^{52} +(-6.00000 + 10.3923i) q^{53} -5.19615i q^{54} +(1.50000 + 0.866025i) q^{57} +(-3.00000 + 5.19615i) q^{58} +3.00000 q^{59} +8.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +(4.50000 + 2.59808i) q^{66} +5.00000 q^{67} +(1.50000 - 2.59808i) q^{68} -10.3923i q^{69} -12.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(-5.50000 + 9.52628i) q^{73} +(2.00000 + 3.46410i) q^{74} +(7.50000 + 4.33013i) q^{75} +(0.500000 + 0.866025i) q^{76} +(-3.00000 - 1.73205i) q^{78} -4.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{82} +(-6.00000 + 10.3923i) q^{83} +(0.500000 - 0.866025i) q^{86} +10.3923i q^{87} +(1.50000 + 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(3.00000 - 5.19615i) q^{92} +(-6.00000 + 3.46410i) q^{93} -6.00000 q^{94} +(1.50000 - 0.866025i) q^{96} +(-2.50000 + 4.33013i) q^{97} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 + 3 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} + 3 q^{9} + 3 q^{11} + 3 q^{12} - 2 q^{13} + 2 q^{16} + 3 q^{17} + 3 q^{18} + q^{19} + 3 q^{22} + 6 q^{23} + 3 q^{24} + 5 q^{25} - 2 q^{26} - 6 q^{29} - 8 q^{31} + 2 q^{32} + 9 q^{33} + 3 q^{34} + 3 q^{36} + 4 q^{37} + q^{38} - 6 q^{39} - 9 q^{41} + q^{43} + 3 q^{44} + 6 q^{46} - 12 q^{47} + 3 q^{48} + 5 q^{50} - 2 q^{52} - 12 q^{53} + 3 q^{57} - 6 q^{58} + 6 q^{59} + 16 q^{61} - 8 q^{62} + 2 q^{64} + 9 q^{66} + 10 q^{67} + 3 q^{68} - 24 q^{71} + 3 q^{72} - 11 q^{73} + 4 q^{74} + 15 q^{75} + q^{76} - 6 q^{78} - 8 q^{79} - 9 q^{81} - 9 q^{82} - 12 q^{83} + q^{86} + 3 q^{88} - 6 q^{89} + 6 q^{92} - 12 q^{93} - 12 q^{94} + 3 q^{96} - 5 q^{97} + 18 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 + 3 * q^9 + 3 * q^11 + 3 * q^12 - 2 * q^13 + 2 * q^16 + 3 * q^17 + 3 * q^18 + q^19 + 3 * q^22 + 6 * q^23 + 3 * q^24 + 5 * q^25 - 2 * q^26 - 6 * q^29 - 8 * q^31 + 2 * q^32 + 9 * q^33 + 3 * q^34 + 3 * q^36 + 4 * q^37 + q^38 - 6 * q^39 - 9 * q^41 + q^43 + 3 * q^44 + 6 * q^46 - 12 * q^47 + 3 * q^48 + 5 * q^50 - 2 * q^52 - 12 * q^53 + 3 * q^57 - 6 * q^58 + 6 * q^59 + 16 * q^61 - 8 * q^62 + 2 * q^64 + 9 * q^66 + 10 * q^67 + 3 * q^68 - 24 * q^71 + 3 * q^72 - 11 * q^73 + 4 * q^74 + 15 * q^75 + q^76 - 6 * q^78 - 8 * q^79 - 9 * q^81 - 9 * q^82 - 12 * q^83 + q^86 + 3 * q^88 - 6 * q^89 + 6 * q^92 - 12 * q^93 - 12 * q^94 + 3 * q^96 - 5 * q^97 + 18 * q^99

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