LMFDB - Embedded newform 882.2.e.f.655.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(373,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [2,2,-3,2,-1,-3,0,2,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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:	yes
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.f.373.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(1.50000 - 0.866025i) q^{15} +1.00000 q^{16} +(1.50000 + 2.59808i) q^{18} +(3.50000 + 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(4.00000 - 6.92820i) q^{29} +(1.50000 - 0.866025i) q^{30} +4.00000 q^{31} +1.00000 q^{32} -3.46410i q^{33} +(1.50000 + 2.59808i) q^{36} +(3.00000 + 5.19615i) q^{37} +(3.50000 + 6.06218i) q^{38} +3.46410i q^{39} +(-0.500000 + 0.866025i) q^{40} +(6.00000 + 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +(1.00000 + 1.73205i) q^{44} -3.00000 q^{45} +(-1.50000 + 2.59808i) q^{46} -8.00000 q^{47} +(-1.50000 - 0.866025i) q^{48} +(2.00000 + 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(-2.00000 + 3.46410i) q^{53} -5.19615i q^{54} -2.00000 q^{55} -12.1244i q^{57} +(4.00000 - 6.92820i) q^{58} +4.00000 q^{59} +(1.50000 - 0.866025i) q^{60} +13.0000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} -3.46410i q^{66} -2.00000 q^{67} +(4.50000 - 2.59808i) q^{69} -5.00000 q^{71} +(1.50000 + 2.59808i) q^{72} +(7.00000 - 12.1244i) q^{73} +(3.00000 + 5.19615i) q^{74} -6.92820i q^{75} +(3.50000 + 6.06218i) q^{76} +3.46410i q^{78} -11.0000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 + 10.3923i) q^{82} +(-6.00000 + 10.3923i) q^{83} +(4.00000 - 6.92820i) q^{86} +(-12.0000 + 6.92820i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-7.00000 - 12.1244i) q^{89} -3.00000 q^{90} +(-1.50000 + 2.59808i) q^{92} +(-6.00000 - 3.46410i) q^{93} -8.00000 q^{94} -7.00000 q^{95} +(-1.50000 - 0.866025i) q^{96} +(1.00000 - 1.73205i) q^{97} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 2 q^{8} + 3 q^{9} - q^{10} + 2 q^{11} - 3 q^{12} - 2 q^{13} + 3 q^{15} + 2 q^{16} + 3 q^{18} + 7 q^{19} - q^{20} + 2 q^{22} - 3 q^{23} - 3 q^{24}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 2 * q^8 + 3 * q^9 - q^10 + 2 * q^11 - 3 * q^12 - 2 * q^13 + 3 * q^15 + 2 * q^16 + 3 * q^18 + 7 * q^19 - q^20 + 2 * q^22 - 3 * q^23 - 3 * q^24 + 4 * q^25 - 2 * q^26 + 8 * q^29 + 3 * q^30 + 8 * q^31 + 2 * q^32 + 3 * q^36 + 6 * q^37 + 7 * q^38 - q^40 + 12 * q^41 + 8 * q^43 + 2 * q^44 - 6 * q^45 - 3 * q^46 - 16 * q^47 - 3 * q^48 + 4 * q^50 - 2 * q^52 - 4 * q^53 - 4 * q^55 + 8 * q^58 + 8 * q^59 + 3 * q^60 + 26 * q^61 + 8 * q^62 + 2 * q^64 + 4 * q^65 - 4 * q^67 + 9 * q^69 - 10 * q^71 + 3 * q^72 + 14 * q^73 + 6 * q^74 + 7 * q^76 - 22 * q^79 - q^80 - 9 * q^81 + 12 * q^82 - 12 * q^83 + 8 * q^86 - 24 * q^87 + 2 * q^88 - 14 * q^89 - 6 * q^90 - 3 * q^92 - 12 * q^93 - 16 * q^94 - 14 * q^95 - 3 * q^96 + 2 * q^97 - 6 * q^99

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
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−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
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	−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
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	0.917663	+	0.397360i	$0.130073\pi$
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	−0.208443	−	0.978035i	$-0.566840\pi$
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	0.951224	−	0.308500i	$-0.0998271\pi$
$30$	1.50000	−	0.866025i	0.273861	−	0.158114i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000			0.176777
$33$		−	3.46410i		−	0.603023i
$34$		0			0
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	3.00000	+	5.19615i	0.493197	+	0.854242i	0.999969	−	0.00783774i	$-0.00249486\pi$
$37$	3.00000	+	5.19615i	0.493197	+	0.854242i	−0.506772	+	0.862080i	$0.669162\pi$
$38$	3.50000	+	6.06218i	0.567775	+	0.983415i
$39$			3.46410i			0.554700i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.770950	+	0.636895i	$0.219782\pi$
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.166092	+	0.986110i	$0.446885\pi$
$42$		0			0
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	−3.00000			−0.447214
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$		0			0
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$		−	5.19615i		−	0.707107i
$55$	−2.00000			−0.269680
$56$		0			0
$57$		−	12.1244i		−	1.60591i
$58$	4.00000	−	6.92820i	0.525226	−	0.909718i
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$	1.50000	−	0.866025i	0.193649	−	0.111803i
$61$	13.0000			1.66448			0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000			1.66448			0.832240	+	0.554416i	$0.187058\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000			0.248069
$66$		−	3.46410i		−	0.426401i
$67$	−2.00000			−0.244339			−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000			−0.244339			−0.122169	+	0.992509i	$0.538985\pi$
$68$		0			0
$69$	4.50000	−	2.59808i	0.541736	−	0.312772i
$70$		0			0
$71$	−5.00000			−0.593391			−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000			−0.593391			−0.296695	+	0.954972i	$0.595885\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$	3.00000	+	5.19615i	0.348743	+	0.604040i
$75$		−	6.92820i		−	0.800000i
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$		0			0
$78$			3.46410i			0.392232i
$79$	−11.0000			−1.23760			−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000			−1.23760			−0.618798	+	0.785550i	$0.712380\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	6.00000	+	10.3923i	0.662589	+	1.14764i
$83$	−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
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	−12.0000	+	6.92820i	−1.28654	+	0.742781i
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$	−3.00000			−0.316228
$91$		0			0
$92$	−1.50000	+	2.59808i	−0.156386	+	0.270868i
$93$	−6.00000	−	3.46410i	−0.622171	−	0.359211i
$94$	−8.00000			−0.825137
$95$	−7.00000			−0.718185
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$		0			0
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	5.50000	+	9.52628i	0.547270	+	0.947900i	0.998460	+	0.0554722i	$0.0176664\pi$
$101$	5.50000	+	9.52628i	0.547270	+	0.947900i	−0.451190	+	0.892428i	$0.649000\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	−2.00000	+	3.46410i	−0.194257	+	0.336463i
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$		−	5.19615i		−	0.500000i
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	−0.945769	−	0.324840i	$-0.894690\pi$
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	0.754204	+	0.656640i	$0.228023\pi$
$110$	−2.00000			−0.190693
$111$		−	10.3923i		−	0.986394i
$112$		0			0
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	0.888585	−	0.458712i	$-0.151689\pi$
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$114$		−	12.1244i		−	1.13555i
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$	4.00000	−	6.92820i	0.371391	−	0.643268i
$117$	3.00000	−	5.19615i	0.277350	−	0.480384i
$118$	4.00000			0.368230
$119$		0			0
$120$	1.50000	−	0.866025i	0.136931	−	0.0790569i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	13.0000			1.17696
$123$		−	20.7846i		−	1.87409i
$124$	4.00000			0.359211
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−19.0000			−1.68598			−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	1.00000			0.0883883
$129$	−12.0000	+	6.92820i	−1.05654	+	0.609994i
$130$	2.00000			0.175412
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$		−	3.46410i		−	0.301511i
$133$		0			0
$134$	−2.00000			−0.172774
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$		0			0
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	4.50000	−	2.59808i	0.383065	−	0.221163i
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	0.609618	−	0.792695i	$-0.291323\pi$
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	−0.991303	+	0.131597i	$0.957989\pi$
$140$		0			0
$141$	12.0000	+	6.92820i	1.01058	+	0.583460i
$142$	−5.00000			−0.419591
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	4.00000	+	6.92820i	0.332182	+	0.575356i
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$		0			0
$148$	3.00000	+	5.19615i	0.246598	+	0.427121i
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$		−	6.92820i		−	0.565685i
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$	3.50000	+	6.06218i	0.283887	+	0.491708i
$153$		0			0
$154$		0			0
$155$	−2.00000	+	3.46410i	−0.160644	+	0.278243i
$156$			3.46410i			0.277350i
$157$	11.0000			0.877896			0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000			0.877896			0.438948	+	0.898513i	$0.355351\pi$
$158$	−11.0000			−0.875113
$159$	6.00000	−	3.46410i	0.475831	−	0.274721i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		0			0
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	3.00000	+	5.19615i	0.234978	+	0.406994i	0.959266	−	0.282503i	$-0.0911648\pi$
$163$	3.00000	+	5.19615i	0.234978	+	0.406994i	−0.724288	+	0.689497i	$0.757831\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$	3.00000	+	1.73205i	0.233550	+	0.134840i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	0.824737	−	0.565516i	$-0.191323\pi$
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	−0.902120	+	0.431486i	$0.857990\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−10.5000	+	18.1865i	−0.802955	+	1.39076i
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	−22.0000			−1.67263			−0.836315	−	0.548250i	$-0.815294\pi$
$173$	−22.0000			−1.67263			−0.836315	+	0.548250i	$0.815294\pi$
$174$	−12.0000	+	6.92820i	−0.909718	+	0.525226i
$175$		0			0
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$	−6.00000	−	3.46410i	−0.450988	−	0.260378i
$178$	−7.00000	−	12.1244i	−0.524672	−	0.908759i
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.0655145	−	0.997852i	$-0.479131\pi$
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.831408	−	0.555663i	$-0.187536\pi$
$180$	−3.00000			−0.223607
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$	−19.5000	−	11.2583i	−1.44148	−	0.832240i
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$	−6.00000			−0.441129
$186$	−6.00000	−	3.46410i	−0.439941	−	0.254000i
$187$		0			0
$188$	−8.00000			−0.583460
$189$		0			0
$190$	−7.00000			−0.507833
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	−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	$0.442405\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$	−3.00000	−	1.73205i	−0.214834	−	0.124035i
$196$		0			0
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	3.00000	+	1.73205i	0.211604	+	0.122169i
$202$	5.50000	+	9.52628i	0.386979	+	0.670267i
$203$		0			0
$204$		0			0
$205$	−12.0000			−0.838116
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$	−9.00000			−0.625543
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−7.00000	+	12.1244i	−0.484200	+	0.838659i
$210$		0			0
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$	−2.00000	+	3.46410i	−0.137361	+	0.237915i
$213$	7.50000	+	4.33013i	0.513892	+	0.296695i
$214$	−4.00000	−	6.92820i	−0.273434	−	0.473602i
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$		−	5.19615i		−	0.353553i
$217$		0			0
$218$	−2.00000	+	3.46410i	−0.135457	+	0.234619i
$219$	−21.0000	+	12.1244i	−1.41905	+	0.819288i
$220$	−2.00000			−0.134840
$221$		0			0
$222$		−	10.3923i		−	0.697486i
$223$	1.00000	−	1.73205i	0.0669650	−	0.115987i	−0.830599	−	0.556871i	$-0.812002\pi$
$223$	1.00000	−	1.73205i	0.0669650	−	0.115987i	0.897564	+	0.440884i	$0.145335\pi$
$224$		0			0
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$	0.500000	+	0.866025i	0.0332595	+	0.0576072i
$227$	−8.50000	−	14.7224i	−0.564165	−	0.977162i	−0.997127	−	0.0757500i	$-0.975865\pi$
$227$	−8.50000	−	14.7224i	−0.564165	−	0.977162i	0.432962	−	0.901412i	$-0.357468\pi$
$228$		−	12.1244i		−	0.802955i
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$	−1.50000	−	2.59808i	−0.0989071	−	0.171312i
$231$		0			0
$232$	4.00000	−	6.92820i	0.262613	−	0.454859i
$233$	−0.500000	−	0.866025i	−0.0327561	−	0.0567352i	0.849183	−	0.528099i	$-0.177095\pi$
$233$	−0.500000	−	0.866025i	−0.0327561	−	0.0567352i	−0.881939	+	0.471364i	$0.843762\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	4.00000			0.260378
$237$	16.5000	+	9.52628i	1.07179	+	0.618798i
$238$		0			0
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	0.999854	−	0.0170808i	$-0.00543724\pi$
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	−0.514719	+	0.857359i	$0.672104\pi$
$240$	1.50000	−	0.866025i	0.0968246	−	0.0559017i
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	13.0000			0.832240
$245$		0			0
$246$		−	20.7846i		−	1.32518i
$247$	7.00000	−	12.1244i	0.445399	−	0.771454i
$248$	4.00000			0.254000
$249$	18.0000	−	10.3923i	1.14070	−	0.658586i
$250$	−9.00000			−0.569210
$251$	7.00000			0.441836			0.220918	−	0.975292i	$-0.429095\pi$
$251$	7.00000			0.441836			0.220918	+	0.975292i	$0.429095\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	−19.0000			−1.19217
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	−0.963391	−	0.268101i	$-0.913604\pi$
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	0.713878	+	0.700270i	$0.246937\pi$
$258$	−12.0000	+	6.92820i	−0.747087	+	0.431331i
$259$		0			0
$260$	2.00000			0.124035
$261$	24.0000			1.48556
$262$	−7.50000	+	12.9904i	−0.463352	+	0.802548i
$263$	−9.50000	−	16.4545i	−0.585795	−	1.01463i	−0.994776	−	0.102084i	$-0.967449\pi$
$263$	−9.50000	−	16.4545i	−0.585795	−	1.01463i	0.408981	−	0.912543i	$-0.365884\pi$
$264$		−	3.46410i		−	0.213201i
$265$	−2.00000	−	3.46410i	−0.122859	−	0.212798i
$266$		0			0
$267$			24.2487i			1.48400i
$268$	−2.00000			−0.122169
$269$	−3.50000	+	6.06218i	−0.213399	+	0.369618i	−0.952776	−	0.303674i	$-0.901787\pi$
$269$	−3.50000	+	6.06218i	−0.213399	+	0.369618i	0.739377	+	0.673291i	$0.235120\pi$
$270$	4.50000	+	2.59808i	0.273861	+	0.158114i
$271$	−7.00000	−	12.1244i	−0.425220	−	0.736502i	0.571221	−	0.820796i	$-0.306470\pi$
$271$	−7.00000	−	12.1244i	−0.425220	−	0.736502i	−0.996441	+	0.0842940i	$0.973137\pi$
$272$		0			0
$273$		0			0
$274$	1.00000	+	1.73205i	0.0604122	+	0.104637i
$275$	−4.00000	+	6.92820i	−0.241209	+	0.417786i
$276$	4.50000	−	2.59808i	0.270868	−	0.156386i
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−4.50000	−	7.79423i	−0.269892	−	0.467467i
$279$	6.00000	+	10.3923i	0.359211	+	0.622171i
$280$		0			0
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	−0.550804	−	0.834634i	$-0.685679\pi$
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	0.998217	+	0.0596933i	$0.0190123\pi$
$282$	12.0000	+	6.92820i	0.714590	+	0.412568i
$283$	25.0000			1.48610			0.743048	−	0.669238i	$-0.233379\pi$
$283$	25.0000			1.48610			0.743048	+	0.669238i	$0.233379\pi$
$284$	−5.00000			−0.296695
$285$	10.5000	+	6.06218i	0.621966	+	0.359092i
$286$	2.00000	−	3.46410i	0.118262	−	0.204837i
$287$		0			0
$288$	1.50000	+	2.59808i	0.0883883	+	0.153093i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	4.00000	+	6.92820i	0.234888	+	0.406838i
$291$	−3.00000	+	1.73205i	−0.175863	+	0.101535i
$292$	7.00000	−	12.1244i	0.409644	−	0.709524i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$	−2.00000	+	3.46410i	−0.116445	+	0.201688i
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$	9.00000	−	5.19615i	0.522233	−	0.301511i
$298$	−5.00000	+	8.66025i	−0.289642	+	0.501675i
$299$	6.00000			0.346989
$300$		−	6.92820i		−	0.400000i
$301$		0			0
$302$	−9.50000	−	16.4545i	−0.546664	−	0.946849i
$303$		−	19.0526i		−	1.09454i
$304$	3.50000	+	6.06218i	0.200739	+	0.347690i
$305$	−6.50000	+	11.2583i	−0.372189	+	0.644650i
$306$		0			0
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$		0			0
$309$	12.0000	−	6.92820i	0.682656	−	0.394132i
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	−10.0000			−0.567048			−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000			−0.567048			−0.283524	+	0.958965i	$0.591504\pi$
$312$			3.46410i			0.196116i
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	11.0000			0.620766
$315$		0			0
$316$	−11.0000			−0.618798
$317$	24.0000			1.34797			0.673987	−	0.738743i	$-0.264580\pi$
$317$	24.0000			1.34797			0.673987	+	0.738743i	$0.264580\pi$
$318$	6.00000	−	3.46410i	0.336463	−	0.194257i
$319$	16.0000			0.895828
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$			13.8564i			0.773389i
$322$		0			0
$323$		0			0
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	4.00000	−	6.92820i	0.221880	−	0.384308i
$326$	3.00000	+	5.19615i	0.166155	+	0.287788i
$327$	6.00000	−	3.46410i	0.331801	−	0.191565i
$328$	6.00000	+	10.3923i	0.331295	+	0.573819i
$329$		0			0
$330$	3.00000	+	1.73205i	0.165145	+	0.0953463i
$331$	−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
$333$	−9.00000	+	15.5885i	−0.493197	+	0.854242i
$334$	−1.00000	−	1.73205i	−0.0547176	−	0.0947736i
$335$	1.00000	−	1.73205i	0.0546358	−	0.0946320i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		−	1.73205i		−	0.0940721i
$340$		0			0
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	−10.5000	+	18.1865i	−0.567775	+	0.983415i
$343$		0			0
$344$	4.00000	−	6.92820i	0.215666	−	0.373544i
$345$			5.19615i			0.279751i
$346$	−22.0000			−1.18273
$347$	12.0000			0.644194			0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000			0.644194			0.322097	+	0.946707i	$0.395612\pi$
$348$	−12.0000	+	6.92820i	−0.643268	+	0.371391i
$349$	15.0000	−	25.9808i	0.802932	−	1.39072i	−0.114747	−	0.993395i	$-0.536606\pi$
$349$	15.0000	−	25.9808i	0.802932	−	1.39072i	0.917679	−	0.397324i	$-0.130061\pi$
$350$		0			0
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$	−6.00000	−	3.46410i	−0.318896	−	0.184115i
$355$	2.50000	−	4.33013i	0.132686	−	0.229819i
$356$	−7.00000	−	12.1244i	−0.370999	−	0.642590i
$357$		0			0
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	−14.5000	−	25.1147i	−0.765281	−	1.32551i	−0.940098	−	0.340904i	$-0.889267\pi$
$359$	−14.5000	−	25.1147i	−0.765281	−	1.32551i	0.174817	−	0.984601i	$-0.444067\pi$
$360$	−3.00000			−0.158114
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	7.00000			0.367912
$363$	−10.5000	+	6.06218i	−0.551107	+	0.318182i
$364$		0			0
$365$	7.00000	+	12.1244i	0.366397	+	0.634618i
$366$	−19.5000	−	11.2583i	−1.01928	−	0.588482i
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	0.893873	+	0.448320i	$0.147978\pi$
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	−0.0586798	+	0.998277i	$0.518689\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$	−18.0000	+	31.1769i	−0.937043	+	1.62301i
$370$	−6.00000			−0.311925
$371$		0			0
$372$	−6.00000	−	3.46410i	−0.311086	−	0.179605i
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	−0.0708063	−	0.997490i	$-0.522557\pi$
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	0.899255	−	0.437425i	$-0.144109\pi$
$374$		0			0
$375$	13.5000	+	7.79423i	0.697137	+	0.402492i
$376$	−8.00000			−0.412568
$377$	−16.0000			−0.824042
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	−7.00000			−0.359092
$381$	28.5000	+	16.4545i	1.46010	+	0.842989i
$382$	3.00000			0.153493
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$		0			0
$386$	5.00000			0.254493
$387$	24.0000			1.21999
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	0.942578	+	0.333987i	$0.108394\pi$
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	−0.182047	+	0.983290i	$0.558272\pi$
$390$	−3.00000	−	1.73205i	−0.151911	−	0.0877058i
$391$		0			0
$392$		0			0
$393$	22.5000	−	12.9904i	1.13497	−	0.655278i
$394$	−12.0000			−0.604551
$395$	5.50000	−	9.52628i	0.276735	−	0.479319i
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$	7.00000	−	12.1244i	0.350878	−	0.607739i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$	3.00000	+	1.73205i	0.149626	+	0.0863868i
$403$	−4.00000	−	6.92820i	−0.199254	−	0.345118i
$404$	5.50000	+	9.52628i	0.273635	+	0.473950i
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$		0			0
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$		0			0
$409$	−24.0000			−1.18672			−0.593362	−	0.804936i	$-0.702200\pi$
$409$	−24.0000			−1.18672			−0.593362	+	0.804936i	$0.702200\pi$
$410$	−12.0000			−0.592638
$411$		−	3.46410i		−	0.170872i
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$		0			0
$414$	−9.00000			−0.442326
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$			15.5885i			0.763370i
$418$	−7.00000	+	12.1244i	−0.342381	+	0.593022i
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	0.920609	−	0.390487i	$-0.127693\pi$
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	−0.798476	+	0.602027i	$0.794360\pi$
$420$		0			0
$421$	18.0000	−	31.1769i	0.877266	−	1.51947i	0.0229375	−	0.999737i	$-0.492698\pi$
$421$	18.0000	−	31.1769i	0.877266	−	1.51947i	0.854329	−	0.519733i	$-0.173969\pi$
$422$	11.0000	+	19.0526i	0.535472	+	0.927464i
$423$	−12.0000	−	20.7846i	−0.583460	−	1.01058i
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$		0			0
$426$	7.50000	+	4.33013i	0.363376	+	0.209795i
$427$		0			0
$428$	−4.00000	−	6.92820i	−0.193347	−	0.334887i
$429$	−6.00000	+	3.46410i	−0.289683	+	0.167248i
$430$	4.00000	+	6.92820i	0.192897	+	0.334108i
$431$	−16.0000	+	27.7128i	−0.770693	+	1.33488i	0.166491	+	0.986043i	$0.446756\pi$
$431$	−16.0000	+	27.7128i	−0.770693	+	1.33488i	−0.937184	+	0.348836i	$0.886577\pi$
$432$		−	5.19615i		−	0.250000i
$433$	−28.0000			−1.34559			−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000			−1.34559			−0.672797	+	0.739827i	$0.734907\pi$
$434$		0			0
$435$		−	13.8564i		−	0.664364i
$436$	−2.00000	+	3.46410i	−0.0957826	+	0.165900i
$437$	−21.0000			−1.00457
$438$	−21.0000	+	12.1244i	−1.00342	+	0.579324i
$439$	−36.0000			−1.71819			−0.859093	−	0.511819i	$-0.828972\pi$
$439$	−36.0000			−1.71819			−0.859093	+	0.511819i	$0.828972\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$		0			0
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$		−	10.3923i		−	0.493197i
$445$	14.0000			0.663664
$446$	1.00000	−	1.73205i	0.0473514	−	0.0820150i
$447$	15.0000	−	8.66025i	0.709476	−	0.409616i
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	−6.00000	+	10.3923i	−0.282843	+	0.489898i
$451$	−12.0000	+	20.7846i	−0.565058	+	0.978709i
$452$	0.500000	+	0.866025i	0.0235180	+	0.0407344i
$453$			32.9090i			1.54620i
$454$	−8.50000	−	14.7224i	−0.398925	−	0.690958i
$455$		0			0
$456$		−	12.1244i		−	0.567775i
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	6.50000	−	11.2583i	0.303725	−	0.526067i
$459$		0			0
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	0.877410	−	0.479741i	$-0.159269\pi$
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	−0.854173	+	0.519989i	$0.825936\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$	6.00000	−	3.46410i	0.278243	−	0.160644i
$466$	−0.500000	−	0.866025i	−0.0231621	−	0.0401179i
$467$	14.0000	+	24.2487i	0.647843	+	1.12210i	0.983637	+	0.180161i	$0.0576619\pi$
$467$	14.0000	+	24.2487i	0.647843	+	1.12210i	−0.335794	+	0.941935i	$0.609005\pi$
$468$	3.00000	−	5.19615i	0.138675	−	0.240192i
$469$		0			0
$470$	4.00000	−	6.92820i	0.184506	−	0.319574i
$471$	−16.5000	−	9.52628i	−0.760280	−	0.438948i
$472$	4.00000			0.184115
$473$	16.0000			0.735681
$474$	16.5000	+	9.52628i	0.757870	+	0.437557i
$475$	−14.0000	+	24.2487i	−0.642364	+	1.11261i
$476$		0			0
$477$	−12.0000			−0.549442
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$	1.50000	−	0.866025i	0.0684653	−	0.0395285i
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	−5.00000	−	8.66025i	−0.227744	−	0.394464i
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	−12.5000	+	21.6506i	−0.566429	+	0.981084i	0.430486	+	0.902597i	$0.358342\pi$
$487$	−12.5000	+	21.6506i	−0.566429	+	0.981084i	−0.996915	+	0.0784867i	$0.974991\pi$
$488$	13.0000			0.588482
$489$		−	10.3923i		−	0.469956i
$490$		0			0
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	0.790358	−	0.612646i	$-0.209895\pi$
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	−0.925746	+	0.378147i	$0.876561\pi$
$492$		−	20.7846i		−	0.937043i
$493$		0			0
$494$	7.00000	−	12.1244i	0.314945	−	0.545501i
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$	4.00000			0.179605
$497$		0			0
$498$	18.0000	−	10.3923i	0.806599	−	0.465690i
$499$	−12.0000	+	20.7846i	−0.537194	+	0.930447i	0.461860	+	0.886953i	$0.347182\pi$
$499$	−12.0000	+	20.7846i	−0.537194	+	0.930447i	−0.999054	+	0.0434940i	$0.986151\pi$
$500$	−9.00000			−0.402492
$501$			3.46410i			0.154765i
$502$	7.00000			0.312425
$503$	14.0000			0.624229			0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000			0.624229			0.312115	+	0.950044i	$0.398963\pi$
$504$		0			0
$505$	−11.0000			−0.489494
$506$	−6.00000			−0.266733
$507$	−13.5000	+	7.79423i	−0.599556	+	0.346154i
$508$	−19.0000			−0.842989
$509$	17.0000	−	29.4449i	0.753512	−	1.30512i	−0.192599	−	0.981278i	$-0.561692\pi$
$509$	17.0000	−	29.4449i	0.753512	−	1.30512i	0.946111	−	0.323843i	$-0.104975\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$	31.5000	−	18.1865i	1.39076	−	0.802955i
$514$	−4.00000	+	6.92820i	−0.176432	+	0.305590i
$515$	−4.00000	−	6.92820i	−0.176261	−	0.305293i
$516$	−12.0000	+	6.92820i	−0.528271	+	0.304997i
$517$	−8.00000	−	13.8564i	−0.351840	−	0.609404i
$518$		0			0
$519$	33.0000	+	19.0526i	1.44854	+	0.836315i
$520$	2.00000			0.0877058
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	−0.977633	−	0.210318i	$-0.932550\pi$
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	0.670957	+	0.741496i	$0.265883\pi$
$522$	24.0000			1.05045
$523$	−17.5000	−	30.3109i	−0.765222	−	1.32540i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$	−17.5000	−	30.3109i	−0.765222	−	1.32540i	0.174908	−	0.984585i	$-0.444037\pi$
$524$	−7.50000	+	12.9904i	−0.327639	+	0.567487i
$525$		0			0
$526$	−9.50000	−	16.4545i	−0.414220	−	0.717450i
$527$		0			0
$528$		−	3.46410i		−	0.150756i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−2.00000	−	3.46410i	−0.0868744	−	0.150471i
$531$	6.00000	+	10.3923i	0.260378	+	0.450988i
$532$		0			0
$533$	12.0000	−	20.7846i	0.519778	−	0.900281i
$534$			24.2487i			1.04934i
$535$	8.00000			0.345870
$536$	−2.00000			−0.0863868
$537$	−36.0000	+	20.7846i	−1.55351	+	0.896922i
$538$	−3.50000	+	6.06218i	−0.150896	+	0.261359i
$539$		0			0
$540$	4.50000	+	2.59808i	0.193649	+	0.111803i
$541$	10.0000	+	17.3205i	0.429934	+	0.744667i	0.996867	−	0.0790969i	$-0.0252036\pi$
$541$	10.0000	+	17.3205i	0.429934	+	0.744667i	−0.566933	+	0.823764i	$0.691870\pi$
$542$	−7.00000	−	12.1244i	−0.300676	−	0.520786i
$543$	−10.5000	−	6.06218i	−0.450598	−	0.260153i
$544$		0			0
$545$	−2.00000	−	3.46410i	−0.0856706	−	0.148386i
$546$		0			0
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	−0.767752	−	0.640747i	$-0.778625\pi$
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	0.938779	+	0.344519i	$0.111958\pi$
$548$	1.00000	+	1.73205i	0.0427179	+	0.0739895i
$549$	19.5000	+	33.7750i	0.832240	+	1.44148i
$550$	−4.00000	+	6.92820i	−0.170561	+	0.295420i
$551$	56.0000			2.38568
$552$	4.50000	−	2.59808i	0.191533	−	0.110581i
$553$		0			0
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$	9.00000	+	5.19615i	0.382029	+	0.220564i
$556$	−4.50000	−	7.79423i	−0.190843	−	0.330549i
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	−0.991254	−	0.131965i	$-0.957871\pi$
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	0.609912	+	0.792469i	$0.291205\pi$
$558$	6.00000	+	10.3923i	0.254000	+	0.439941i
$559$	−16.0000			−0.676728
$560$		0			0
$561$		0			0
$562$	7.50000	−	12.9904i	0.316368	−	0.547966i
$563$	11.0000			0.463595			0.231797	−	0.972764i	$-0.425539\pi$
$563$	11.0000			0.463595			0.231797	+	0.972764i	$0.425539\pi$
$564$	12.0000	+	6.92820i	0.505291	+	0.291730i
$565$	−1.00000			−0.0420703
$566$	25.0000			1.05083
$567$		0			0
$568$	−5.00000			−0.209795
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$	10.5000	+	6.06218i	0.439797	+	0.253917i
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	−4.50000	−	2.59808i	−0.187990	−	0.108536i
$574$		0			0
$575$	−12.0000			−0.500435
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−14.0000	+	24.2487i	−0.582828	+	1.00949i	0.412315	+	0.911041i	$0.364720\pi$
$577$	−14.0000	+	24.2487i	−0.582828	+	1.00949i	−0.995142	+	0.0984456i	$0.968613\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	−7.50000	−	4.33013i	−0.311689	−	0.179954i
$580$	4.00000	+	6.92820i	0.166091	+	0.287678i
$581$		0			0
$582$	−3.00000	+	1.73205i	−0.124354	+	0.0717958i
$583$	−8.00000			−0.331326
$584$	7.00000	−	12.1244i	0.289662	−	0.501709i
$585$	3.00000	+	5.19615i	0.124035	+	0.214834i
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	11.5000	−	19.9186i	0.474656	−	0.822128i	−0.524923	−	0.851150i	$-0.675906\pi$
$587$	11.5000	−	19.9186i	0.474656	−	0.822128i	0.999579	+	0.0290218i	$0.00923921\pi$
$588$		0			0
$589$	14.0000	+	24.2487i	0.576860	+	0.999151i
$590$	−2.00000	+	3.46410i	−0.0823387	+	0.142615i
$591$	18.0000	+	10.3923i	0.740421	+	0.427482i
$592$	3.00000	+	5.19615i	0.123299	+	0.213561i
$593$	−21.0000	−	36.3731i	−0.862367	−	1.49366i	−0.869638	−	0.493689i	$-0.835648\pi$
$593$	−21.0000	−	36.3731i	−0.862367	−	1.49366i	0.00727173	−	0.999974i	$-0.497685\pi$
$594$	9.00000	−	5.19615i	0.369274	−	0.213201i
$595$		0			0
$596$	−5.00000	+	8.66025i	−0.204808	+	0.354738i
$597$	−21.0000	+	12.1244i	−0.859473	+	0.496217i
$598$	6.00000			0.245358
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		−	6.92820i		−	0.282843i
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	0.469095	+	0.883148i	$0.344580\pi$
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	−3.00000	−	5.19615i	−0.122169	−	0.211604i
$604$	−9.50000	−	16.4545i	−0.386550	−	0.669523i
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$		−	19.0526i		−	0.773957i
$607$	3.00000	−	5.19615i	0.121766	−	0.210905i	−0.798698	−	0.601732i	$-0.794478\pi$
$607$	3.00000	−	5.19615i	0.121766	−	0.210905i	0.920464	+	0.390827i	$0.127811\pi$
$608$	3.50000	+	6.06218i	0.141944	+	0.245854i
$609$		0			0
$610$	−6.50000	+	11.2583i	−0.263177	+	0.455836i
$611$	8.00000	+	13.8564i	0.323645	+	0.560570i
$612$		0			0
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$614$	7.00000			0.282497
$615$	18.0000	+	10.3923i	0.725830	+	0.419058i
$616$		0			0
$617$	11.0000	+	19.0526i	0.442843	+	0.767027i	0.997899	−	0.0647859i	$-0.0206365\pi$
$617$	11.0000	+	19.0526i	0.442843	+	0.767027i	−0.555056	+	0.831813i	$0.687303\pi$
$618$	12.0000	−	6.92820i	0.482711	−	0.278693i
$619$	5.50000	+	9.52628i	0.221064	+	0.382893i	0.955131	−	0.296183i	$-0.0957138\pi$
$619$	5.50000	+	9.52628i	0.221064	+	0.382893i	−0.734068	+	0.679076i	$0.762380\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$	−10.0000			−0.400963
$623$		0			0
$624$			3.46410i			0.138675i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	6.00000			0.239808
$627$	21.0000	−	12.1244i	0.838659	−	0.484200i
$628$	11.0000			0.438948
$629$		0			0
$630$		0			0
$631$	9.00000			0.358284			0.179142	−	0.983823i	$-0.442668\pi$
$631$	9.00000			0.358284			0.179142	+	0.983823i	$0.442668\pi$
$632$	−11.0000			−0.437557
$633$		−	38.1051i		−	1.51454i
$634$	24.0000			0.953162
$635$	9.50000	−	16.4545i	0.376996	−	0.652976i
$636$	6.00000	−	3.46410i	0.237915	−	0.137361i
$637$		0			0
$638$	16.0000			0.633446
$639$	−7.50000	−	12.9904i	−0.296695	−	0.513892i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−23.5000	−	40.7032i	−0.928194	−	1.60768i	−0.786342	−	0.617792i	$-0.788027\pi$
$641$	−23.5000	−	40.7032i	−0.928194	−	1.60768i	−0.141852	−	0.989888i	$-0.545306\pi$
$642$			13.8564i			0.546869i
$643$	6.00000	+	10.3923i	0.236617	+	0.409832i	0.959741	−	0.280885i	$-0.0906280\pi$
$643$	6.00000	+	10.3923i	0.236617	+	0.409832i	−0.723124	+	0.690718i	$0.757295\pi$
$644$		0			0
$645$		−	13.8564i		−	0.545595i
$646$		0			0
$647$	21.0000	−	36.3731i	0.825595	−	1.42997i	−0.0758684	−	0.997118i	$-0.524173\pi$
$647$	21.0000	−	36.3731i	0.825595	−	1.42997i	0.901464	−	0.432855i	$-0.142494\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	4.00000	+	6.92820i	0.157014	+	0.271956i
$650$	4.00000	−	6.92820i	0.156893	−	0.271746i
$651$		0			0
$652$	3.00000	+	5.19615i	0.117489	+	0.203497i
$653$	16.0000	−	27.7128i	0.626128	−	1.08449i	−0.362193	−	0.932103i	$-0.617972\pi$
$653$	16.0000	−	27.7128i	0.626128	−	1.08449i	0.988322	−	0.152383i	$-0.0486948\pi$
$654$	6.00000	−	3.46410i	0.234619	−	0.135457i
$655$	−7.50000	−	12.9904i	−0.293049	−	0.507576i
$656$	6.00000	+	10.3923i	0.234261	+	0.405751i
$657$	42.0000			1.63858
$658$		0			0
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	−0.992388	−	0.123148i	$-0.960701\pi$
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	0.602844	+	0.797859i	$0.294034\pi$
$660$	3.00000	+	1.73205i	0.116775	+	0.0674200i
$661$	−31.0000			−1.20576			−0.602880	−	0.797832i	$-0.705980\pi$
$661$	−31.0000			−1.20576			−0.602880	+	0.797832i	$0.705980\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$		0			0
$666$	−9.00000	+	15.5885i	−0.348743	+	0.604040i
$667$	12.0000	+	20.7846i	0.464642	+	0.804783i
$668$	−1.00000	−	1.73205i	−0.0386912	−	0.0670151i
$669$	−3.00000	+	1.73205i	−0.115987	+	0.0669650i
$670$	1.00000	−	1.73205i	0.0386334	−	0.0669150i
$671$	13.0000	+	22.5167i	0.501859	+	0.869246i
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	11.0000	+	19.0526i	0.423704	+	0.733877i
$675$	18.0000	−	10.3923i	0.692820	−	0.400000i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		−	1.73205i		−	0.0665190i
$679$		0			0
$680$		0			0
$681$			29.4449i			1.12833i
$682$	4.00000	+	6.92820i	0.153168	+	0.265295i
$683$	5.00000	−	8.66025i	0.191320	−	0.331375i	−0.754368	−	0.656452i	$-0.772057\pi$
$683$	5.00000	−	8.66025i	0.191320	−	0.331375i	0.945688	+	0.325076i	$0.105390\pi$
$684$	−10.5000	+	18.1865i	−0.401478	+	0.695379i
$685$	−2.00000			−0.0764161
$686$		0			0
$687$	−19.5000	+	11.2583i	−0.743971	+	0.429532i
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	8.00000			0.304776
$690$			5.19615i			0.197814i
$691$	−29.0000			−1.10321			−0.551606	−	0.834105i	$-0.685985\pi$
$691$	−29.0000			−1.10321			−0.551606	+	0.834105i	$0.685985\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	9.00000			0.341389
$696$	−12.0000	+	6.92820i	−0.454859	+	0.262613i
$697$		0			0
$698$	15.0000	−	25.9808i	0.567758	−	0.983386i
$699$			1.73205i			0.0655122i
$700$		0			0
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$	−9.00000	+	5.19615i	−0.339683	+	0.196116i
$703$	−21.0000	+	36.3731i	−0.792030	+	1.37184i
$704$	1.00000	+	1.73205i	0.0376889	+	0.0652791i
$705$	−12.0000	+	6.92820i	−0.451946	+	0.260931i
$706$	−12.0000	−	20.7846i	−0.451626	−	0.782239i
$707$		0			0
$708$	−6.00000	−	3.46410i	−0.225494	−	0.130189i
$709$	−32.0000			−1.20179			−0.600893	−	0.799330i	$-0.705188\pi$
$709$	−32.0000			−1.20179			−0.600893	+	0.799330i	$0.705188\pi$
$710$	2.50000	−	4.33013i	0.0938233	−	0.162507i
$711$	−16.5000	−	28.5788i	−0.618798	−	1.07179i
$712$	−7.00000	−	12.1244i	−0.262336	−	0.454379i
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$		0			0
$715$	2.00000	+	3.46410i	0.0747958	+	0.129550i
$716$	12.0000	−	20.7846i	0.448461	−	0.776757i
$717$		−	25.9808i		−	0.970269i
$718$	−14.5000	−	25.1147i	−0.541135	−	0.937274i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−3.00000			−0.111803
$721$		0			0
$722$	−15.0000	+	25.9808i	−0.558242	+	0.966904i
$723$			17.3205i			0.644157i
$724$	7.00000			0.260153
$725$	32.0000			1.18845
$726$	−10.5000	+	6.06218i	−0.389692	+	0.224989i
$727$	−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
$730$	7.00000	+	12.1244i	0.259082	+	0.448743i
$731$		0			0
$732$	−19.5000	−	11.2583i	−0.720741	−	0.416120i
$733$	−0.500000	+	0.866025i	−0.0184679	+	0.0319874i	−0.875112	−	0.483921i	$-0.839212\pi$
$733$	−0.500000	+	0.866025i	−0.0184679	+	0.0319874i	0.856644	+	0.515908i	$0.172546\pi$
$734$	16.0000	+	27.7128i	0.590571	+	1.02290i
$735$		0			0
$736$	−1.50000	+	2.59808i	−0.0552907	+	0.0957664i
$737$	−2.00000	−	3.46410i	−0.0736709	−	0.127602i
$738$	−18.0000	+	31.1769i	−0.662589	+	1.14764i
$739$	19.0000	−	32.9090i	0.698926	−	1.21058i	−0.269913	−	0.962885i	$-0.586995\pi$
$739$	19.0000	−	32.9090i	0.698926	−	1.21058i	0.968839	−	0.247691i	$-0.0796718\pi$
$740$	−6.00000			−0.220564
$741$	−21.0000	+	12.1244i	−0.771454	+	0.445399i
$742$		0			0
$743$	−24.0000	−	41.5692i	−0.880475	−	1.52503i	−0.850814	−	0.525467i	$-0.823891\pi$
$743$	−24.0000	−	41.5692i	−0.880475	−	1.52503i	−0.0296605	−	0.999560i	$-0.509443\pi$
$744$	−6.00000	−	3.46410i	−0.219971	−	0.127000i
$745$	−5.00000	−	8.66025i	−0.183186	−	0.317287i
$746$	16.0000	−	27.7128i	0.585802	−	1.01464i
$747$	−36.0000			−1.31717
$748$		0			0
$749$		0			0
$750$	13.5000	+	7.79423i	0.492950	+	0.284605i
$751$	19.5000	−	33.7750i	0.711565	−	1.23247i	−0.252704	−	0.967544i	$-0.581320\pi$
$751$	19.5000	−	33.7750i	0.711565	−	1.23247i	0.964269	−	0.264923i	$-0.0853467\pi$
$752$	−8.00000			−0.291730
$753$	−10.5000	−	6.06218i	−0.382641	−	0.220918i
$754$	−16.0000			−0.582686
$755$	19.0000			0.691481
$756$		0			0
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$	−12.0000			−0.435860
$759$	9.00000	+	5.19615i	0.326679	+	0.188608i
$760$	−7.00000			−0.253917
$761$	10.0000	−	17.3205i	0.362500	−	0.627868i	−0.625872	−	0.779926i	$-0.715257\pi$
$761$	10.0000	−	17.3205i	0.362500	−	0.627868i	0.988372	+	0.152058i	$0.0485900\pi$
$762$	28.5000	+	16.4545i	1.03245	+	0.596083i
$763$		0			0
$764$	3.00000			0.108536
$765$		0			0
$766$	3.00000	−	5.19615i	0.108394	−	0.187745i
$767$	−4.00000	−	6.92820i	−0.144432	−	0.250163i
$768$	−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
$771$	12.0000	−	6.92820i	0.432169	−	0.249513i
$772$	5.00000			0.179954
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	−0.990721	−	0.135910i	$-0.956604\pi$
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	0.613062	+	0.790034i	$0.289937\pi$
$774$	24.0000			0.862662
$775$	8.00000	+	13.8564i	0.287368	+	0.497737i
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$		0			0
$778$	15.0000	+	25.9808i	0.537776	+	0.931455i
$779$	−42.0000	+	72.7461i	−1.50481	+	2.60640i
$780$	−3.00000	−	1.73205i	−0.107417	−	0.0620174i
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$		0			0
$783$	−36.0000	−	20.7846i	−1.28654	−	0.742781i
$784$		0			0
$785$	−5.50000	+	9.52628i	−0.196303	+	0.340007i
$786$	22.5000	−	12.9904i	0.802548	−	0.463352i
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$	−12.0000			−0.427482
$789$			32.9090i			1.17159i
$790$	5.50000	−	9.52628i	0.195681	−	0.338930i
$791$		0			0
$792$	−3.00000	+	5.19615i	−0.106600	+	0.184637i
$793$	−13.0000	−	22.5167i	−0.461644	−	0.799590i
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$			6.92820i			0.245718i
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	−25.5000	−	44.1673i	−0.903256	−	1.56449i	−0.823241	−	0.567692i	$-0.807836\pi$
$797$	−25.5000	−	44.1673i	−0.903256	−	1.56449i	−0.0800155	−	0.996794i	$-0.525497\pi$
$798$		0			0
$799$		0			0
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	21.0000	−	36.3731i	0.741999	−	1.28518i
$802$	−1.50000	+	2.59808i	−0.0529668	+	0.0917413i
$803$	28.0000			0.988099
$804$	3.00000	+	1.73205i	0.105802	+	0.0610847i
$805$		0			0
$806$	−4.00000	−	6.92820i	−0.140894	−	0.244036i
$807$	10.5000	−	6.06218i	0.369618	−	0.213399i
$808$	5.50000	+	9.52628i	0.193489	+	0.335133i
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	−0.979739	−	0.200279i	$-0.935815\pi$
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	0.663316	+	0.748340i	$0.269149\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$		0			0
$813$			24.2487i			0.850439i
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$	−6.00000			−0.210171
$816$		0			0
$817$	56.0000			1.95919
$818$	−24.0000			−0.839140
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−32.0000			−1.11681			−0.558404	−	0.829569i	$-0.688586\pi$
$821$	−32.0000			−1.11681			−0.558404	+	0.829569i	$0.688586\pi$
$822$		−	3.46410i		−	0.120824i
$823$	−44.0000			−1.53374			−0.766872	−	0.641800i	$-0.778188\pi$
$823$	−44.0000			−1.53374			−0.766872	+	0.641800i	$0.778188\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$	12.0000	−	6.92820i	0.417786	−	0.241209i
$826$		0			0
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$	−9.00000			−0.312772
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$		−	3.46410i		−	0.120168i
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$		0			0
$834$			15.5885i			0.539784i
$835$	2.00000			0.0692129
$836$	−7.00000	+	12.1244i	−0.242100	+	0.419330i
$837$		−	20.7846i		−	0.718421i
$838$	2.50000	+	4.33013i	0.0863611	+	0.149582i
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	−0.481927	−	0.876211i	$-0.660063\pi$
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	0.999785	−	0.0207443i	$-0.00660359\pi$
$840$		0			0
$841$	−17.5000	−	30.3109i	−0.603448	−	1.04520i
$842$	18.0000	−	31.1769i	0.620321	−	1.07443i
$843$	−22.5000	+	12.9904i	−0.774941	+	0.447412i
$844$	11.0000	+	19.0526i	0.378636	+	0.655816i
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$	−12.0000	−	20.7846i	−0.412568	−	0.714590i
$847$		0			0
$848$	−2.00000	+	3.46410i	−0.0686803	+	0.118958i
$849$	−37.5000	−	21.6506i	−1.28700	−	0.743048i
$850$		0			0
$851$	−18.0000			−0.617032
$852$	7.50000	+	4.33013i	0.256946	+	0.148348i
$853$	18.5000	−	32.0429i	0.633428	−	1.09713i	−0.353418	−	0.935466i	$-0.614981\pi$
$853$	18.5000	−	32.0429i	0.633428	−	1.09713i	0.986846	−	0.161664i	$-0.0516860\pi$
$854$		0			0
$855$	−10.5000	−	18.1865i	−0.359092	−	0.621966i
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$	−6.00000	+	3.46410i	−0.204837	+	0.118262i
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	0.376381	+	0.926465i	$0.377169\pi$
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	−0.990533	+	0.137277i	$0.956165\pi$
$860$	4.00000	+	6.92820i	0.136399	+	0.236250i
$861$		0			0
$862$	−16.0000	+	27.7128i	−0.544962	+	0.943902i
$863$	−28.5000	−	49.3634i	−0.970151	−	1.68035i	−0.695087	−	0.718925i	$-0.744634\pi$
$863$	−28.5000	−	49.3634i	−0.970151	−	1.68035i	−0.275064	−	0.961426i	$-0.588699\pi$
$864$		−	5.19615i		−	0.176777i
$865$	11.0000	−	19.0526i	0.374011	−	0.647806i
$866$	−28.0000			−0.951479
$867$		−	29.4449i		−	1.00000i
$868$		0			0
$869$	−11.0000	−	19.0526i	−0.373149	−	0.646314i
$870$		−	13.8564i		−	0.469776i
$871$	2.00000	+	3.46410i	0.0677674	+	0.117377i
$872$	−2.00000	+	3.46410i	−0.0677285	+	0.117309i
$873$	6.00000			0.203069
$874$	−21.0000			−0.710336
$875$		0			0
$876$	−21.0000	+	12.1244i	−0.709524	+	0.409644i
$877$	−12.0000	+	20.7846i	−0.405211	+	0.701846i	−0.994346	−	0.106188i	$-0.966135\pi$
$877$	−12.0000	+	20.7846i	−0.405211	+	0.701846i	0.589135	+	0.808035i	$0.299469\pi$
$878$	−36.0000			−1.21494
$879$			15.5885i			0.525786i
$880$	−2.00000			−0.0674200
$881$	28.0000			0.943344			0.471672	−	0.881774i	$-0.343651\pi$
$881$	28.0000			0.943344			0.471672	+	0.881774i	$0.343651\pi$
$882$		0			0
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$		0			0
$885$	6.00000	−	3.46410i	0.201688	−	0.116445i
$886$	24.0000			0.806296
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$		−	10.3923i		−	0.348743i
$889$		0			0
$890$	14.0000			0.469281
$891$	−18.0000			−0.603023
$892$	1.00000	−	1.73205i	0.0334825	−	0.0579934i
$893$	−28.0000	−	48.4974i	−0.936984	−	1.62290i
$894$	15.0000	−	8.66025i	0.501675	−	0.289642i
$895$	12.0000	+	20.7846i	0.401116	+	0.694753i
$896$		0			0
$897$	−9.00000	−	5.19615i	−0.300501	−	0.173494i
$898$	9.00000			0.300334
$899$	16.0000	−	27.7128i	0.533630	−	0.924274i
$900$	−6.00000	+	10.3923i	−0.200000	+	0.346410i
$901$		0			0
$902$	−12.0000	+	20.7846i	−0.399556	+	0.692052i
$903$		0			0
$904$	0.500000	+	0.866025i	0.0166298	+	0.0288036i
$905$	−3.50000	+	6.06218i	−0.116344	+	0.201514i
$906$			32.9090i			1.09333i
$907$	1.00000	+	1.73205i	0.0332045	+	0.0575118i	0.882150	−	0.470968i	$-0.156095\pi$
$907$	1.00000	+	1.73205i	0.0332045	+	0.0575118i	−0.848946	+	0.528480i	$0.822762\pi$
$908$	−8.50000	−	14.7224i	−0.282082	−	0.488581i
$909$	−16.5000	+	28.5788i	−0.547270	+	0.947900i
$910$		0			0
$911$	0.500000	−	0.866025i	0.0165657	−	0.0286927i	−0.857624	−	0.514278i	$-0.828060\pi$
$911$	0.500000	−	0.866025i	0.0165657	−	0.0286927i	0.874189	+	0.485585i	$0.161393\pi$
$912$		−	12.1244i		−	0.401478i
$913$	−24.0000			−0.794284
$914$	17.0000			0.562310
$915$	19.5000	−	11.2583i	0.644650	−	0.372189i
$916$	6.50000	−	11.2583i	0.214766	−	0.371986i
$917$		0			0
$918$		0			0
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	0.715402	−	0.698713i	$-0.246244\pi$
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	−0.962804	+	0.270200i	$0.912910\pi$
$920$	−1.50000	−	2.59808i	−0.0494535	−	0.0856560i
$921$	−10.5000	−	6.06218i	−0.345987	−	0.199756i
$922$	4.50000	−	7.79423i	0.148200	−	0.256689i
$923$	5.00000	+	8.66025i	0.164577	+	0.285056i
$924$		0			0
$925$	−12.0000	+	20.7846i	−0.394558	+	0.683394i
$926$	0.500000	+	0.866025i	0.0164310	+	0.0284594i
$927$	−24.0000			−0.788263
$928$	4.00000	−	6.92820i	0.131306	−	0.227429i
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$	6.00000	−	3.46410i	0.196748	−	0.113592i
$931$		0			0
$932$	−0.500000	−	0.866025i	−0.0163780	−	0.0283676i
$933$	15.0000	+	8.66025i	0.491078	+	0.283524i
$934$	14.0000	+	24.2487i	0.458094	+	0.793442i
$935$		0			0
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$	−9.00000	−	5.19615i	−0.293704	−	0.169570i
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$	−3.00000			−0.0977972			−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000			−0.0977972			−0.0488986	+	0.998804i	$0.515571\pi$
$942$	−16.5000	−	9.52628i	−0.537599	−	0.310383i
$943$	−36.0000			−1.17232
$944$	4.00000			0.130189
$945$		0			0
$946$	16.0000			0.520205
$947$	10.0000			0.324956			0.162478	−	0.986712i	$-0.448051\pi$
$947$	10.0000			0.324956			0.162478	+	0.986712i	$0.448051\pi$
$948$	16.5000	+	9.52628i	0.535895	+	0.309399i
$949$	−28.0000			−0.908918
$950$	−14.0000	+	24.2487i	−0.454220	+	0.786732i
$951$	−36.0000	−	20.7846i	−1.16738	−	0.673987i
$952$		0			0
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$	−12.0000			−0.388514
$955$	−1.50000	+	2.59808i	−0.0485389	+	0.0840718i
$956$	7.50000	+	12.9904i	0.242567	+	0.420139i
$957$	−24.0000	−	13.8564i	−0.775810	−	0.447914i
$958$	−12.0000	−	20.7846i	−0.387702	−	0.671520i
$959$		0			0
$960$	1.50000	−	0.866025i	0.0484123	−	0.0279508i
$961$	−15.0000			−0.483871
$962$	6.00000	−	10.3923i	0.193448	−	0.335061i
$963$	12.0000	−	20.7846i	0.386695	−	0.669775i
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$	−2.50000	+	4.33013i	−0.0804778	+	0.139392i
$966$		0			0
$967$	−6.50000	−	11.2583i	−0.209026	−	0.362043i	0.742382	−	0.669977i	$-0.233696\pi$
$967$	−6.50000	−	11.2583i	−0.209026	−	0.362043i	−0.951408	+	0.307933i	$0.900363\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$		0			0
$970$	1.00000	+	1.73205i	0.0321081	+	0.0556128i
$971$	17.5000	+	30.3109i	0.561602	+	0.972723i	0.997357	+	0.0726575i	$0.0231480\pi$
$971$	17.5000	+	30.3109i	0.561602	+	0.972723i	−0.435755	+	0.900065i	$0.643519\pi$
$972$	13.5000	−	7.79423i	0.433013	−	0.250000i
$973$		0			0
$974$	−12.5000	+	21.6506i	−0.400526	+	0.693731i
$975$	−12.0000	+	6.92820i	−0.384308	+	0.221880i
$976$	13.0000			0.416120
$977$	−2.00000			−0.0639857			−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000			−0.0639857			−0.0319928	+	0.999488i	$0.510185\pi$
$978$		−	10.3923i		−	0.332309i
$979$	14.0000	−	24.2487i	0.447442	−	0.774992i
$980$		0			0
$981$	−12.0000			−0.383131
$982$	−3.00000	−	5.19615i	−0.0957338	−	0.165816i
$983$	16.0000	+	27.7128i	0.510321	+	0.883901i	0.999928	+	0.0119587i	$0.00380665\pi$
$983$	16.0000	+	27.7128i	0.510321	+	0.883901i	−0.489608	+	0.871943i	$0.662860\pi$
$984$		−	20.7846i		−	0.662589i
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$		0			0
$987$		0			0
$988$	7.00000	−	12.1244i	0.222700	−	0.385727i
$989$	12.0000	+	20.7846i	0.381578	+	0.660912i
$990$	−3.00000	−	5.19615i	−0.0953463	−	0.165145i
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$	4.00000			0.127000
$993$	6.00000	+	3.46410i	0.190404	+	0.109930i
$994$		0			0
$995$	7.00000	+	12.1244i	0.221915	+	0.384368i
$996$	18.0000	−	10.3923i	0.570352	−	0.329293i
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	0.699457	−	0.714675i	$-0.253425\pi$
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	−0.968655	+	0.248410i	$0.920092\pi$
$998$	−12.0000	+	20.7846i	−0.379853	+	0.657925i
$999$	27.0000	−	15.5885i	0.854242	−	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.e.f.655.1		2
3.2	odd	2		2646.2.e.d.2125.1		2
7.2	even	3		882.2.h.d.79.1		2
7.3	odd	6		882.2.f.c.295.1	yes	2
7.4	even	3		882.2.f.b.295.1	✓	2
7.5	odd	6		882.2.h.a.79.1		2
7.6	odd	2		882.2.e.j.655.1		2
9.4	even	3		882.2.h.d.67.1		2
9.5	odd	6		2646.2.h.g.361.1		2
21.2	odd	6		2646.2.h.g.667.1		2
21.5	even	6		2646.2.h.j.667.1		2
21.11	odd	6		2646.2.f.h.883.1		2
21.17	even	6		2646.2.f.f.883.1		2
21.20	even	2		2646.2.e.a.2125.1		2
63.4	even	3		882.2.f.b.589.1	yes	2
63.5	even	6		2646.2.e.a.1549.1		2
63.11	odd	6		7938.2.a.f.1.1		1
63.13	odd	6		882.2.h.a.67.1		2
63.23	odd	6		2646.2.e.d.1549.1		2
63.25	even	3		7938.2.a.ba.1.1		1
63.31	odd	6		882.2.f.c.589.1	yes	2
63.32	odd	6		2646.2.f.h.1765.1		2
63.38	even	6		7938.2.a.k.1.1		1
63.40	odd	6		882.2.e.j.373.1		2
63.41	even	6		2646.2.h.j.361.1		2
63.52	odd	6		7938.2.a.v.1.1		1
63.58	even	3	inner	882.2.e.f.373.1		2
63.59	even	6		2646.2.f.f.1765.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.f.373.1		2	63.58	even	3	inner
882.2.e.f.655.1		2	1.1	even	1	trivial
882.2.e.j.373.1		2	63.40	odd	6
882.2.e.j.655.1		2	7.6	odd	2
882.2.f.b.295.1	✓	2	7.4	even	3
882.2.f.b.589.1	yes	2	63.4	even	3
882.2.f.c.295.1	yes	2	7.3	odd	6
882.2.f.c.589.1	yes	2	63.31	odd	6
882.2.h.a.67.1		2	63.13	odd	6
882.2.h.a.79.1		2	7.5	odd	6
882.2.h.d.67.1		2	9.4	even	3
882.2.h.d.79.1		2	7.2	even	3
2646.2.e.a.1549.1		2	63.5	even	6
2646.2.e.a.2125.1		2	21.20	even	2
2646.2.e.d.1549.1		2	63.23	odd	6
2646.2.e.d.2125.1		2	3.2	odd	2
2646.2.f.f.883.1		2	21.17	even	6
2646.2.f.f.1765.1		2	63.59	even	6
2646.2.f.h.883.1		2	21.11	odd	6
2646.2.f.h.1765.1		2	63.32	odd	6
2646.2.h.g.361.1		2	9.5	odd	6
2646.2.h.g.667.1		2	21.2	odd	6
2646.2.h.j.361.1		2	63.41	even	6
2646.2.h.j.667.1		2	21.5	even	6
7938.2.a.f.1.1		1	63.11	odd	6
7938.2.a.k.1.1		1	63.38	even	6
7938.2.a.v.1.1		1	63.52	odd	6
7938.2.a.ba.1.1		1	63.25	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(1.50000 - 0.866025i) q^{15} +1.00000 q^{16} +(1.50000 + 2.59808i) q^{18} +(3.50000 + 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(4.00000 - 6.92820i) q^{29} +(1.50000 - 0.866025i) q^{30} +4.00000 q^{31} +1.00000 q^{32} -3.46410i q^{33} +(1.50000 + 2.59808i) q^{36} +(3.00000 + 5.19615i) q^{37} +(3.50000 + 6.06218i) q^{38} +3.46410i q^{39} +(-0.500000 + 0.866025i) q^{40} +(6.00000 + 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +(1.00000 + 1.73205i) q^{44} -3.00000 q^{45} +(-1.50000 + 2.59808i) q^{46} -8.00000 q^{47} +(-1.50000 - 0.866025i) q^{48} +(2.00000 + 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(-2.00000 + 3.46410i) q^{53} -5.19615i q^{54} -2.00000 q^{55} -12.1244i q^{57} +(4.00000 - 6.92820i) q^{58} +4.00000 q^{59} +(1.50000 - 0.866025i) q^{60} +13.0000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} -3.46410i q^{66} -2.00000 q^{67} +(4.50000 - 2.59808i) q^{69} -5.00000 q^{71} +(1.50000 + 2.59808i) q^{72} +(7.00000 - 12.1244i) q^{73} +(3.00000 + 5.19615i) q^{74} -6.92820i q^{75} +(3.50000 + 6.06218i) q^{76} +3.46410i q^{78} -11.0000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 + 10.3923i) q^{82} +(-6.00000 + 10.3923i) q^{83} +(4.00000 - 6.92820i) q^{86} +(-12.0000 + 6.92820i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-7.00000 - 12.1244i) q^{89} -3.00000 q^{90} +(-1.50000 + 2.59808i) q^{92} +(-6.00000 - 3.46410i) q^{93} -8.00000 q^{94} -7.00000 q^{95} +(-1.50000 - 0.866025i) q^{96} +(1.00000 - 1.73205i) q^{97} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 2 q^{8} + 3 q^{9} - q^{10} + 2 q^{11} - 3 q^{12} - 2 q^{13} + 3 q^{15} + 2 q^{16} + 3 q^{18} + 7 q^{19} - q^{20} + 2 q^{22} - 3 q^{23} - 3 q^{24}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 2 * q^8 + 3 * q^9 - q^10 + 2 * q^11 - 3 * q^12 - 2 * q^13 + 3 * q^15 + 2 * q^16 + 3 * q^18 + 7 * q^19 - q^20 + 2 * q^22 - 3 * q^23 - 3 * q^24 + 4 * q^25 - 2 * q^26 + 8 * q^29 + 3 * q^30 + 8 * q^31 + 2 * q^32 + 3 * q^36 + 6 * q^37 + 7 * q^38 - q^40 + 12 * q^41 + 8 * q^43 + 2 * q^44 - 6 * q^45 - 3 * q^46 - 16 * q^47 - 3 * q^48 + 4 * q^50 - 2 * q^52 - 4 * q^53 - 4 * q^55 + 8 * q^58 + 8 * q^59 + 3 * q^60 + 26 * q^61 + 8 * q^62 + 2 * q^64 + 4 * q^65 - 4 * q^67 + 9 * q^69 - 10 * q^71 + 3 * q^72 + 14 * q^73 + 6 * q^74 + 7 * q^76 - 22 * q^79 - q^80 - 9 * q^81 + 12 * q^82 - 12 * q^83 + 8 * q^86 - 24 * q^87 + 2 * q^88 - 14 * q^89 - 6 * q^90 - 3 * q^92 - 12 * q^93 - 16 * q^94 - 14 * q^95 - 3 * q^96 + 2 * q^97 - 6 * q^99

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