LMFDB - Embedded newform 882.2.h.i.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(67,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [2,1,3,-1,-6,0,0,-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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} -1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{10} -3.00000 q^{11} +(-1.50000 - 0.866025i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-4.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} -9.00000 q^{23} +(-1.50000 + 0.866025i) q^{24} +4.00000 q^{25} +(0.500000 + 0.866025i) q^{26} -5.19615i q^{27} +(-1.50000 - 2.59808i) q^{29} +5.19615i q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +(-1.50000 - 2.59808i) q^{34} -3.00000 q^{36} +(0.500000 + 0.866025i) q^{37} -7.00000 q^{38} +1.73205i q^{39} +3.00000 q^{40} +(1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{44} +(-4.50000 + 7.79423i) q^{45} +(-4.50000 + 7.79423i) q^{46} +1.73205i q^{48} +(2.00000 - 3.46410i) q^{50} -5.19615i q^{51} +1.00000 q^{52} +(-1.50000 + 2.59808i) q^{53} +(-4.50000 - 2.59808i) q^{54} +9.00000 q^{55} +(-10.5000 - 6.06218i) q^{57} -3.00000 q^{58} +(4.50000 + 2.59808i) q^{60} +(1.00000 - 1.73205i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +5.19615i q^{66} +(2.00000 + 3.46410i) q^{67} -3.00000 q^{68} +(-13.5000 + 7.79423i) q^{69} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(5.50000 - 9.52628i) q^{73} +1.00000 q^{74} +(6.00000 - 3.46410i) q^{75} +(-3.50000 + 6.06218i) q^{76} +(1.50000 + 0.866025i) q^{78} +(8.00000 - 13.8564i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(-4.50000 + 7.79423i) q^{85} +1.00000 q^{86} +(-4.50000 - 2.59808i) q^{87} +3.00000 q^{88} +(1.50000 + 2.59808i) q^{89} +(4.50000 + 7.79423i) q^{90} +(4.50000 + 7.79423i) q^{92} +(12.0000 + 6.92820i) q^{93} +(10.5000 + 18.1865i) q^{95} +(1.50000 + 0.866025i) q^{96} +(-0.500000 - 0.866025i) q^{97} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} - 6 q^{5} - 2 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} - 3 q^{12} - q^{13} - 9 q^{15} - q^{16} + 3 q^{17} - 3 q^{18} - 7 q^{19} + 3 q^{20} - 3 q^{22} - 18 q^{23} - 3 q^{24}+ \cdots - 9 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 - 6 * q^5 - 2 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 - 3 * q^12 - q^13 - 9 * q^15 - q^16 + 3 * q^17 - 3 * q^18 - 7 * q^19 + 3 * q^20 - 3 * q^22 - 18 * q^23 - 3 * q^24 + 8 * q^25 + q^26 - 3 * q^29 + 8 * q^31 + q^32 - 9 * q^33 - 3 * q^34 - 6 * q^36 + q^37 - 14 * q^38 + 6 * q^40 + 3 * q^41 + q^43 + 3 * q^44 - 9 * q^45 - 9 * q^46 + 4 * q^50 + 2 * q^52 - 3 * q^53 - 9 * q^54 + 18 * q^55 - 21 * q^57 - 6 * q^58 + 9 * q^60 + 2 * q^61 + 16 * q^62 + 2 * q^64 + 3 * q^65 + 4 * q^67 - 6 * q^68 - 27 * q^69 + 24 * q^71 - 3 * q^72 + 11 * q^73 + 2 * q^74 + 12 * q^75 - 7 * q^76 + 3 * q^78 + 16 * q^79 + 3 * q^80 - 9 * q^81 - 3 * q^82 - 9 * q^83 - 9 * q^85 + 2 * q^86 - 9 * q^87 + 6 * q^88 + 3 * q^89 + 9 * q^90 + 9 * q^92 + 24 * q^93 + 21 * q^95 + 3 * q^96 - q^97 - 9 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		−	1.73205i		−	0.707107i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		0			0
$15$	−4.50000	+	2.59808i	−1.16190	+	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	−9.00000			−1.87663			−0.938315	−	0.345782i	$-0.887614\pi$
$23$	−9.00000			−1.87663			−0.938315	+	0.345782i	$0.887614\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	4.00000			0.800000
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$			5.19615i			0.948683i
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$		0			0
$36$	−3.00000			−0.500000
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−7.00000			−1.13555
$39$			1.73205i			0.277350i
$40$	3.00000			0.474342
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	−4.50000	+	7.79423i	−0.670820	+	1.16190i
$46$	−4.50000	+	7.79423i	−0.663489	+	1.14920i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$			1.73205i			0.250000i
$49$		0			0
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		−	5.19615i		−	0.727607i
$52$	1.00000			0.138675
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	9.00000			1.21356
$56$		0			0
$57$	−10.5000	−	6.06218i	−1.39076	−	0.802955i
$58$	−3.00000			−0.393919
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	4.50000	+	2.59808i	0.580948	+	0.335410i
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	1.50000	−	2.59808i	0.186052	−	0.322252i
$66$			5.19615i			0.639602i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−3.00000			−0.363803
$69$	−13.5000	+	7.79423i	−1.62521	+	0.938315i
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	−0.340868	−	0.940111i	$-0.610721\pi$
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	0.984594	−	0.174855i	$-0.0559458\pi$
$74$	1.00000			0.116248
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$	−3.50000	+	6.06218i	−0.401478	+	0.695379i
$77$		0			0
$78$	1.50000	+	0.866025i	0.169842	+	0.0980581i
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	1.00000			0.107833
$87$	−4.50000	−	2.59808i	−0.482451	−	0.278543i
$88$	3.00000			0.319801
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	0.934508	−	0.355942i	$-0.115840\pi$
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	−0.775509	+	0.631337i	$0.782506\pi$
$90$	4.50000	+	7.79423i	0.474342	+	0.821584i
$91$		0			0
$92$	4.50000	+	7.79423i	0.469157	+	0.812605i
$93$	12.0000	+	6.92820i	1.24434	+	0.718421i
$94$		0			0
$95$	10.5000	+	18.1865i	1.07728	+	1.86590i
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	0.839525	−	0.543321i	$-0.182833\pi$
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	−0.890292	+	0.455389i	$0.849500\pi$
$98$		0			0
$99$	−4.50000	+	7.79423i	−0.452267	+	0.783349i
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$	−4.50000	−	2.59808i	−0.445566	−	0.257248i
$103$	13.0000			1.28093			0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000			1.28093			0.640464	+	0.767988i	$0.278742\pi$
$104$	0.500000	−	0.866025i	0.0490290	−	0.0849208i
$105$		0			0
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	0.562267	−	0.826956i	$-0.309929\pi$
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	−0.997298	+	0.0734594i	$0.976596\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	−0.366415	−	0.930451i	$-0.619415\pi$
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	0.989002	−	0.147901i	$-0.0472517\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$	1.50000	+	0.866025i	0.142374	+	0.0821995i
$112$		0			0
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	−0.572938	−	0.819599i	$-0.694196\pi$
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	0.996262	+	0.0863794i	$0.0275297\pi$
$114$	−10.5000	+	6.06218i	−0.983415	+	0.567775i
$115$	27.0000			2.51776
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$	1.50000	+	2.59808i	0.138675	+	0.240192i
$118$		0			0
$119$		0			0
$120$	4.50000	−	2.59808i	0.410792	−	0.237171i
$121$	−2.00000			−0.181818
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$		−	5.19615i		−	0.468521i
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	3.00000			0.268328
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	1.50000	+	0.866025i	0.132068	+	0.0762493i
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$	4.50000	+	2.59808i	0.391675	+	0.226134i
$133$		0			0
$134$	4.00000			0.345547
$135$			15.5885i			1.34164i
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−9.00000			−0.768922			−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000			−0.768922			−0.384461	+	0.923141i	$0.625613\pi$
$138$			15.5885i			1.32698i
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	1.50000	−	2.59808i	0.125436	−	0.217262i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$	−5.50000	−	9.52628i	−0.455183	−	0.788400i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−9.00000			−0.737309			−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000			−0.737309			−0.368654	+	0.929567i	$0.620181\pi$
$150$		−	6.92820i		−	0.565685i
$151$	−7.00000			−0.569652			−0.284826	−	0.958579i	$-0.591936\pi$
$151$	−7.00000			−0.569652			−0.284826	+	0.958579i	$0.591936\pi$
$152$	3.50000	+	6.06218i	0.283887	+	0.491708i
$153$	−4.50000	−	7.79423i	−0.363803	−	0.630126i
$154$		0			0
$155$	−12.0000	−	20.7846i	−0.963863	−	1.66946i
$156$	1.50000	−	0.866025i	0.120096	−	0.0693375i
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.0242497	−	0.999706i	$-0.507720\pi$
$158$	−8.00000	−	13.8564i	−0.636446	−	1.10236i
$159$			5.19615i			0.412082i
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$		0			0
$162$	−9.00000			−0.707107
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	0.950615	+	0.310372i	$0.100454\pi$
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	−0.206518	+	0.978443i	$0.566213\pi$
$164$	−3.00000			−0.234261
$165$	13.5000	−	7.79423i	1.05097	−	0.606780i
$166$	−9.00000			−0.698535
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	0.415068	+	0.909790i	$0.363758\pi$
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	−0.995436	+	0.0954356i	$0.969576\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	4.50000	+	7.79423i	0.345134	+	0.597790i
$171$	−21.0000			−1.60591
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−4.50000	+	2.59808i	−0.341144	+	0.196960i
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$		0			0
$178$	3.00000			0.224860
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	−0.144308	−	0.989533i	$-0.546095\pi$
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	0.929114	−	0.369792i	$-0.120571\pi$
$180$	9.00000			0.670820
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		−	3.46410i		−	0.256074i
$184$	9.00000			0.663489
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$	12.0000	−	6.92820i	0.879883	−	0.508001i
$187$	−4.50000	+	7.79423i	−0.329073	+	0.569970i
$188$		0			0
$189$		0			0
$190$	21.0000			1.52350
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	1.50000	−	0.866025i	0.108253	−	0.0625000i
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	−1.00000			−0.0717958
$195$		−	5.19615i		−	0.372104i
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	4.50000	+	7.79423i	0.319801	+	0.553912i
$199$	−12.5000	+	21.6506i	−0.886102	+	1.53477i	−0.0416556	+	0.999132i	$0.513263\pi$
$199$	−12.5000	+	21.6506i	−0.886102	+	1.53477i	−0.844446	+	0.535641i	$0.820070\pi$
$200$	−4.00000			−0.282843
$201$	6.00000	+	3.46410i	0.423207	+	0.244339i
$202$	−1.50000	+	2.59808i	−0.105540	+	0.182800i
$203$		0			0
$204$	−4.50000	+	2.59808i	−0.315063	+	0.181902i
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	6.50000	−	11.2583i	0.452876	−	0.784405i
$207$	−13.5000	+	23.3827i	−0.938315	+	1.62521i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	10.5000	+	18.1865i	0.726300	+	1.25799i
$210$		0			0
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	−0.939156	−	0.343490i	$-0.888391\pi$
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	0.767049	+	0.641588i	$0.221724\pi$
$212$	3.00000			0.206041
$213$	18.0000	−	10.3923i	1.23334	−	0.712069i
$214$	−9.00000			−0.615227
$215$	−1.50000	−	2.59808i	−0.102299	−	0.177187i
$216$			5.19615i			0.353553i
$217$		0			0
$218$	−6.50000	−	11.2583i	−0.440236	−	0.762510i
$219$		−	19.0526i		−	1.28745i
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$	1.50000	+	2.59808i	0.100901	+	0.174766i
$222$	1.50000	−	0.866025i	0.100673	−	0.0581238i
$223$	−0.500000	−	0.866025i	−0.0334825	−	0.0579934i	0.848799	−	0.528716i	$-0.177326\pi$
$223$	−0.500000	−	0.866025i	−0.0334825	−	0.0579934i	−0.882281	+	0.470723i	$0.843993\pi$
$224$		0			0
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$	−4.50000	−	7.79423i	−0.299336	−	0.518464i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$			12.1244i			0.802955i
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$	13.5000	−	23.3827i	0.890164	−	1.54181i
$231$		0			0
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$	3.00000			0.196116
$235$		0			0
$236$		0			0
$237$		−	27.7128i		−	1.80014i
$238$		0			0
$239$	1.50000	−	2.59808i	0.0970269	−	0.168056i	−0.813426	−	0.581669i	$-0.802400\pi$
$239$	1.50000	−	2.59808i	0.0970269	−	0.168056i	0.910453	+	0.413613i	$0.135733\pi$
$240$		−	5.19615i		−	0.335410i
$241$	13.0000			0.837404			0.418702	−	0.908124i	$-0.362485\pi$
$241$	13.0000			0.837404			0.418702	+	0.908124i	$0.362485\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	−4.50000	−	2.59808i	−0.286910	−	0.165647i
$247$	7.00000			0.445399
$248$	−4.00000	−	6.92820i	−0.254000	−	0.439941i
$249$	−13.5000	−	7.79423i	−0.855528	−	0.493939i
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	27.0000			1.69748
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$			15.5885i			0.976187i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	21.0000			1.30994			0.654972	−	0.755653i	$-0.272680\pi$
$257$	21.0000			1.30994			0.654972	+	0.755653i	$0.272680\pi$
$258$	1.50000	−	0.866025i	0.0933859	−	0.0539164i
$259$		0			0
$260$	−3.00000			−0.186052
$261$	−9.00000			−0.557086
$262$	−7.50000	+	12.9904i	−0.463352	+	0.802548i
$263$	9.00000			0.554964			0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000			0.554964			0.277482	+	0.960731i	$0.410500\pi$
$264$	4.50000	−	2.59808i	0.276956	−	0.159901i
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$		0			0
$267$	4.50000	+	2.59808i	0.275396	+	0.159000i
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$	13.5000	+	7.79423i	0.821584	+	0.474342i
$271$	2.50000	+	4.33013i	0.151864	+	0.263036i	0.931913	−	0.362682i	$-0.118139\pi$
$271$	2.50000	+	4.33013i	0.151864	+	0.263036i	−0.780049	+	0.625719i	$0.784806\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		0			0
$274$	−4.50000	+	7.79423i	−0.271855	+	0.470867i
$275$	−12.0000			−0.723627
$276$	13.5000	+	7.79423i	0.812605	+	0.469157i
$277$	−1.00000			−0.0600842			−0.0300421	−	0.999549i	$-0.509564\pi$
$277$	−1.00000			−0.0600842			−0.0300421	+	0.999549i	$0.509564\pi$
$278$	3.50000	+	6.06218i	0.209916	+	0.363585i
$279$	24.0000			1.43684
$280$		0			0
$281$	10.5000	+	18.1865i	0.626377	+	1.08492i	0.988273	+	0.152699i	$0.0487965\pi$
$281$	10.5000	+	18.1865i	0.626377	+	1.08492i	−0.361895	+	0.932219i	$0.617870\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	31.5000	+	18.1865i	1.86590	+	1.07728i
$286$	−1.50000	−	2.59808i	−0.0886969	−	0.153627i
$287$		0			0
$288$	3.00000			0.176777
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	9.00000			0.528498
$291$	−1.50000	−	0.866025i	−0.0879316	−	0.0507673i
$292$	−11.0000			−0.643726
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$		0			0
$295$		0			0
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$			15.5885i			0.904534i
$298$	−4.50000	+	7.79423i	−0.260678	+	0.451508i
$299$	4.50000	−	7.79423i	0.260242	−	0.450752i
$300$	−6.00000	−	3.46410i	−0.346410	−	0.200000i
$301$		0			0
$302$	−3.50000	+	6.06218i	−0.201402	+	0.348839i
$303$	−4.50000	+	2.59808i	−0.258518	+	0.149256i
$304$	7.00000			0.401478
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$	−9.00000			−0.514496
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$	19.5000	−	11.2583i	1.10932	−	0.640464i
$310$	−24.0000			−1.36311
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		−	1.73205i		−	0.0980581i
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	−0.972028	−	0.234863i	$-0.924536\pi$
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	0.689412	+	0.724370i	$0.257869\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	−16.0000			−0.900070
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	4.50000	+	2.59808i	0.252347	+	0.145693i
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$	−3.00000			−0.167705
$321$	−13.5000	−	7.79423i	−0.753497	−	0.435031i
$322$		0			0
$323$	−21.0000			−1.16847
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−2.00000	+	3.46410i	−0.110940	+	0.192154i
$326$	19.0000			1.05231
$327$		−	22.5167i		−	1.24517i
$328$	−1.50000	+	2.59808i	−0.0828236	+	0.143455i
$329$		0			0
$330$		−	15.5885i		−	0.858116i
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$	3.00000			0.164399
$334$	7.50000	+	12.9904i	0.410382	+	0.710802i
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$		0			0
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	−0.632882	−	0.774248i	$-0.718128\pi$
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	0.986960	+	0.160968i	$0.0514616\pi$
$338$	12.0000			0.652714
$339$		−	15.5885i		−	0.846649i
$340$	9.00000			0.488094
$341$	−12.0000	−	20.7846i	−0.649836	−	1.12555i
$342$	−10.5000	+	18.1865i	−0.567775	+	0.983415i
$343$		0			0
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$	40.5000	−	23.3827i	2.18045	−	1.25888i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$			5.19615i			0.278543i
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	0.990282	+	0.139072i	$0.0444119\pi$
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	4.50000	+	2.59808i	0.240192	+	0.138675i
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$		0			0
$355$	−36.0000			−1.91068
$356$	1.50000	−	2.59808i	0.0794998	−	0.137698i
$357$		0			0
$358$	−10.5000	−	18.1865i	−0.554942	−	0.961188i
$359$	−4.50000	−	7.79423i	−0.237501	−	0.411364i	0.722496	−	0.691375i	$-0.242995\pi$
$359$	−4.50000	−	7.79423i	−0.237501	−	0.411364i	−0.959997	+	0.280012i	$0.909662\pi$
$360$	4.50000	−	7.79423i	0.237171	−	0.410792i
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$	−3.00000	+	1.73205i	−0.157459	+	0.0909091i
$364$		0			0
$365$	−16.5000	+	28.5788i	−0.863649	+	1.49588i
$366$	−3.00000	−	1.73205i	−0.156813	−	0.0905357i
$367$	−17.0000			−0.887393			−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000			−0.887393			−0.443696	+	0.896177i	$0.646333\pi$
$368$	4.50000	−	7.79423i	0.234579	−	0.406302i
$369$	−4.50000	−	7.79423i	−0.234261	−	0.405751i
$370$	−3.00000			−0.155963
$371$		0			0
$372$		−	13.8564i		−	0.718421i
$373$	−13.0000			−0.673114			−0.336557	−	0.941663i	$-0.609263\pi$
$373$	−13.0000			−0.673114			−0.336557	+	0.941663i	$0.609263\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$	4.50000	−	2.59808i	0.232379	−	0.134164i
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	10.5000	−	18.1865i	0.538639	−	0.932949i
$381$	−6.00000	+	3.46410i	−0.307389	+	0.177471i
$382$		0			0
$383$	−15.0000			−0.766464			−0.383232	−	0.923652i	$-0.625189\pi$
$383$	−15.0000			−0.766464			−0.383232	+	0.923652i	$0.625189\pi$
$384$		−	1.73205i		−	0.0883883i
$385$		0			0
$386$	−14.0000			−0.712581
$387$	3.00000			0.152499
$388$	−0.500000	+	0.866025i	−0.0253837	+	0.0439658i
$389$	27.0000			1.36895			0.684477	−	0.729034i	$-0.260031\pi$
$389$	27.0000			1.36895			0.684477	+	0.729034i	$0.260031\pi$
$390$	−4.50000	−	2.59808i	−0.227866	−	0.131559i
$391$	−13.5000	+	23.3827i	−0.682724	+	1.18251i
$392$		0			0
$393$	−22.5000	+	12.9904i	−1.13497	+	0.655278i
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	−24.0000	+	41.5692i	−1.20757	+	2.09157i
$396$	9.00000			0.452267
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	0.655534	−	0.755166i	$-0.272444\pi$
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	−0.981760	+	0.190126i	$0.939110\pi$
$398$	12.5000	+	21.6506i	0.626568	+	1.08525i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	27.0000			1.34832			0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000			1.34832			0.674158	+	0.738587i	$0.264507\pi$
$402$	6.00000	−	3.46410i	0.299253	−	0.172774i
$403$	−8.00000			−0.398508
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$	13.5000	+	23.3827i	0.670820	+	1.16190i
$406$		0			0
$407$	−1.50000	−	2.59808i	−0.0743522	−	0.128782i
$408$			5.19615i			0.257248i
$409$	−17.0000	−	29.4449i	−0.840596	−	1.45595i	−0.889392	−	0.457146i	$-0.848872\pi$
$409$	−17.0000	−	29.4449i	−0.840596	−	1.45595i	0.0487958	−	0.998809i	$-0.484462\pi$
$410$	4.50000	+	7.79423i	0.222239	+	0.384930i
$411$	−13.5000	+	7.79423i	−0.665906	+	0.384461i
$412$	−6.50000	−	11.2583i	−0.320232	−	0.554658i
$413$		0			0
$414$	13.5000	+	23.3827i	0.663489	+	1.14920i
$415$	13.5000	+	23.3827i	0.662689	+	1.14781i
$416$	−1.00000			−0.0490290
$417$			12.1244i			0.593732i
$418$	21.0000			1.02714
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	−0.734919	−	0.678155i	$-0.762780\pi$
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	0.954759	+	0.297382i	$0.0961133\pi$
$420$		0			0
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	−0.878582	−	0.477592i	$-0.841510\pi$
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	0.0256838	−	0.999670i	$-0.491824\pi$
$422$	2.50000	+	4.33013i	0.121698	+	0.210787i
$423$		0			0
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		−	20.7846i		−	1.00702i
$427$		0			0
$428$	−4.50000	+	7.79423i	−0.217516	+	0.376748i
$429$		−	5.19615i		−	0.250873i
$430$	−3.00000			−0.144673
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	0.332785	+	0.943003i	$0.392012\pi$
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	−0.983057	+	0.183301i	$0.941322\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	13.5000	+	7.79423i	0.647275	+	0.373705i
$436$	−13.0000			−0.622587
$437$	31.5000	+	54.5596i	1.50685	+	2.60994i
$438$	−16.5000	−	9.52628i	−0.788400	−	0.455183i
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	3.00000			0.142695
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$		−	1.73205i		−	0.0821995i
$445$	−4.50000	−	7.79423i	−0.213320	−	0.369482i
$446$	−1.00000			−0.0473514
$447$	−13.5000	+	7.79423i	−0.638528	+	0.368654i
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	−6.00000	−	10.3923i	−0.282843	−	0.489898i
$451$	−4.50000	+	7.79423i	−0.211897	+	0.367016i
$452$	−9.00000			−0.423324
$453$	−10.5000	+	6.06218i	−0.493333	+	0.284826i
$454$	1.50000	−	2.59808i	0.0703985	−	0.121934i
$455$		0			0
$456$	10.5000	+	6.06218i	0.491708	+	0.283887i
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	6.50000	−	11.2583i	0.303725	−	0.526067i
$459$	−13.5000	−	7.79423i	−0.630126	−	0.363803i
$460$	−13.5000	−	23.3827i	−0.629441	−	1.09022i
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	0.741998	−	0.670402i	$-0.233878\pi$
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	−0.951584	+	0.307388i	$0.900545\pi$
$462$		0			0
$463$	−20.5000	+	35.5070i	−0.952716	+	1.65015i	−0.213205	+	0.977007i	$0.568390\pi$
$463$	−20.5000	+	35.5070i	−0.952716	+	1.65015i	−0.739511	+	0.673145i	$0.764943\pi$
$464$	3.00000			0.139272
$465$	−36.0000	−	20.7846i	−1.66946	−	0.963863i
$466$	−3.00000			−0.138972
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	0.829231	−	0.558906i	$-0.188779\pi$
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	−0.898642	+	0.438682i	$0.855446\pi$
$468$	1.50000	−	2.59808i	0.0693375	−	0.120096i
$469$		0			0
$470$		0			0
$471$	−33.0000	−	19.0526i	−1.52056	−	0.877896i
$472$		0			0
$473$	−1.50000	−	2.59808i	−0.0689701	−	0.119460i
$474$	−24.0000	−	13.8564i	−1.10236	−	0.636446i
$475$	−14.0000	−	24.2487i	−0.642364	−	1.11261i
$476$		0			0
$477$	4.50000	+	7.79423i	0.206041	+	0.356873i
$478$	−1.50000	−	2.59808i	−0.0686084	−	0.118833i
$479$	3.00000			0.137073			0.0685367	−	0.997649i	$-0.478167\pi$
$479$	3.00000			0.137073			0.0685367	+	0.997649i	$0.478167\pi$
$480$	−4.50000	−	2.59808i	−0.205396	−	0.118585i
$481$	−1.00000			−0.0455961
$482$	6.50000	−	11.2583i	0.296067	−	0.512803i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	1.50000	+	2.59808i	0.0681115	+	0.117973i
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	12.5000	−	21.6506i	0.566429	−	0.981084i	−0.430486	−	0.902597i	$-0.641658\pi$
$487$	12.5000	−	21.6506i	0.566429	−	0.981084i	0.996915	−	0.0784867i	$-0.0250088\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$	28.5000	+	16.4545i	1.28881	+	0.744097i
$490$		0			0
$491$	−10.5000	+	18.1865i	−0.473858	+	0.820747i	−0.999552	−	0.0299272i	$-0.990472\pi$
$491$	−10.5000	+	18.1865i	−0.473858	+	0.820747i	0.525694	+	0.850674i	$0.323806\pi$
$492$	−4.50000	+	2.59808i	−0.202876	+	0.117130i
$493$	−9.00000			−0.405340
$494$	3.50000	−	6.06218i	0.157472	−	0.272750i
$495$	13.5000	−	23.3827i	0.606780	−	1.05097i
$496$	−8.00000			−0.359211
$497$		0			0
$498$	−13.5000	+	7.79423i	−0.604949	+	0.349268i
$499$	−25.0000			−1.11915			−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000			−1.11915			−0.559577	+	0.828778i	$0.689036\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$			25.9808i			1.16073i
$502$	−6.00000	+	10.3923i	−0.267793	+	0.463831i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	13.5000	−	23.3827i	0.600148	−	1.03949i
$507$	18.0000	+	10.3923i	0.799408	+	0.461538i
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$	9.00000			0.398918			0.199459	−	0.979906i	$-0.436082\pi$
$509$	9.00000			0.398918			0.199459	+	0.979906i	$0.436082\pi$
$510$	13.5000	+	7.79423i	0.597790	+	0.345134i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−31.5000	+	18.1865i	−1.39076	+	0.802955i
$514$	10.5000	−	18.1865i	0.463135	−	0.802174i
$515$	−39.0000			−1.71855
$516$		−	1.73205i		−	0.0762493i
$517$		0			0
$518$		0			0
$519$			10.3923i			0.456172i
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$	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	$0.145733\pi$
$522$	−4.50000	+	7.79423i	−0.196960	+	0.341144i
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	0.779301	−	0.626650i	$-0.215574\pi$
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	−0.932345	+	0.361569i	$0.882241\pi$
$524$	7.50000	+	12.9904i	0.327639	+	0.567487i
$525$		0			0
$526$	4.50000	−	7.79423i	0.196209	−	0.339845i
$527$	24.0000			1.04546
$528$		−	5.19615i		−	0.226134i
$529$	58.0000			2.52174
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$		0			0
$532$		0			0
$533$	1.50000	+	2.59808i	0.0649722	+	0.112535i
$534$	4.50000	−	2.59808i	0.194734	−	0.112430i
$535$	13.5000	+	23.3827i	0.583656	+	1.01092i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$		−	36.3731i		−	1.56961i
$538$	−7.50000	−	12.9904i	−0.323348	−	0.560055i
$539$		0			0
$540$	13.5000	−	7.79423i	0.580948	−	0.335410i
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	0.723234	−	0.690604i	$-0.242655\pi$
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	−0.959697	+	0.281037i	$0.909322\pi$
$542$	5.00000			0.214768
$543$	−3.00000	+	1.73205i	−0.128742	+	0.0743294i
$544$	3.00000			0.128624
$545$	−19.5000	+	33.7750i	−0.835288	+	1.44676i
$546$		0			0
$547$	−5.50000	−	9.52628i	−0.235163	−	0.407314i	0.724157	−	0.689635i	$-0.242229\pi$
$547$	−5.50000	−	9.52628i	−0.235163	−	0.407314i	−0.959320	+	0.282321i	$0.908896\pi$
$548$	4.50000	+	7.79423i	0.192230	+	0.332953i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	−6.00000	+	10.3923i	−0.255841	+	0.443129i
$551$	−10.5000	+	18.1865i	−0.447315	+	0.774772i
$552$	13.5000	−	7.79423i	0.574598	−	0.331744i
$553$		0			0
$554$	−0.500000	+	0.866025i	−0.0212430	+	0.0367939i
$555$	−4.50000	−	2.59808i	−0.191014	−	0.110282i
$556$	7.00000			0.296866
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	−0.754802	−	0.655953i	$-0.772267\pi$
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	0.945473	+	0.325701i	$0.105600\pi$
$558$	12.0000	−	20.7846i	0.508001	−	0.879883i
$559$	−1.00000			−0.0422955
$560$		0			0
$561$			15.5885i			0.658145i
$562$	21.0000			0.885832
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$	−13.5000	+	23.3827i	−0.567949	+	0.983717i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$	31.5000	−	18.1865i	1.31939	−	0.761750i
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	−3.00000			−0.125436
$573$		0			0
$574$		0			0
$575$	−36.0000			−1.50130
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−12.5000	+	21.6506i	−0.520382	+	0.901328i	0.479337	+	0.877631i	$0.340877\pi$
$577$	−12.5000	+	21.6506i	−0.520382	+	0.901328i	−0.999719	+	0.0236970i	$0.992456\pi$
$578$	8.00000			0.332756
$579$	−21.0000	−	12.1244i	−0.872730	−	0.503871i
$580$	4.50000	−	7.79423i	0.186852	−	0.323638i
$581$		0			0
$582$	−1.50000	+	0.866025i	−0.0621770	+	0.0358979i
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$	−5.50000	+	9.52628i	−0.227592	+	0.394200i
$585$	−4.50000	−	7.79423i	−0.186052	−	0.322252i
$586$	4.50000	+	7.79423i	0.185893	+	0.321977i
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	0.895320	−	0.445424i	$-0.146947\pi$
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	−0.833408	+	0.552658i	$0.813614\pi$
$588$		0			0
$589$	28.0000	−	48.4974i	1.15372	−	1.99830i
$590$		0			0
$591$	27.0000	−	15.5885i	1.11063	−	0.641223i
$592$	−1.00000			−0.0410997
$593$	19.5000	+	33.7750i	0.800769	+	1.38697i	0.919111	+	0.394000i	$0.128909\pi$
$593$	19.5000	+	33.7750i	0.800769	+	1.38697i	−0.118342	+	0.992973i	$0.537758\pi$
$594$	13.5000	+	7.79423i	0.553912	+	0.319801i
$595$		0			0
$596$	4.50000	+	7.79423i	0.184327	+	0.319264i
$597$			43.3013i			1.77220i
$598$	−4.50000	−	7.79423i	−0.184019	−	0.318730i
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$	−6.00000	+	3.46410i	−0.244949	+	0.141421i
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	−0.999934	−	0.0114528i	$-0.996354\pi$
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	0.490049	−	0.871695i	$-0.336979\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	3.50000	+	6.06218i	0.142413	+	0.246667i
$605$	6.00000			0.243935
$606$			5.19615i			0.211079i
$607$	13.0000			0.527654			0.263827	−	0.964570i	$-0.415015\pi$
$607$	13.0000			0.527654			0.263827	+	0.964570i	$0.415015\pi$
$608$	3.50000	−	6.06218i	0.141944	−	0.245854i
$609$		0			0
$610$	3.00000	+	5.19615i	0.121466	+	0.210386i
$611$		0			0
$612$	−4.50000	+	7.79423i	−0.181902	+	0.315063i
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	−0.999178	−	0.0405396i	$-0.987092\pi$
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	0.534697	+	0.845044i	$0.320426\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$			15.5885i			0.628587i
$616$		0			0
$617$	22.5000	−	38.9711i	0.905816	−	1.56892i	0.0859976	−	0.996295i	$-0.472592\pi$
$617$	22.5000	−	38.9711i	0.905816	−	1.56892i	0.819818	−	0.572624i	$-0.194074\pi$
$618$		−	22.5167i		−	0.905753i
$619$	−17.0000			−0.683288			−0.341644	−	0.939829i	$-0.610984\pi$
$619$	−17.0000			−0.683288			−0.341644	+	0.939829i	$0.610984\pi$
$620$	−12.0000	+	20.7846i	−0.481932	+	0.834730i
$621$			46.7654i			1.87663i
$622$	−24.0000			−0.962312
$623$		0			0
$624$	−1.50000	−	0.866025i	−0.0600481	−	0.0346688i
$625$	−29.0000			−1.16000
$626$	5.00000	+	8.66025i	0.199840	+	0.346133i
$627$	31.5000	+	18.1865i	1.25799	+	0.726300i
$628$	−11.0000	+	19.0526i	−0.438948	+	0.760280i
$629$	3.00000			0.119618
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−8.00000	+	13.8564i	−0.318223	+	0.551178i
$633$			8.66025i			0.344214i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	12.0000			0.476205
$636$	4.50000	−	2.59808i	0.178437	−	0.103020i
$637$		0			0
$638$	9.00000			0.356313
$639$	18.0000	−	31.1769i	0.712069	−	1.23334i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−33.0000			−1.30342			−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000			−1.30342			−0.651711	+	0.758468i	$0.725948\pi$
$642$	−13.5000	+	7.79423i	−0.532803	+	0.307614i
$643$	14.5000	−	25.1147i	0.571824	−	0.990429i	−0.424555	−	0.905402i	$-0.639569\pi$
$643$	14.5000	−	25.1147i	0.571824	−	0.990429i	0.996379	−	0.0850262i	$-0.0270974\pi$
$644$		0			0
$645$	−4.50000	−	2.59808i	−0.177187	−	0.102299i
$646$	−10.5000	+	18.1865i	−0.413117	+	0.715540i
$647$	−10.5000	+	18.1865i	−0.412798	+	0.714986i	−0.995194	−	0.0979182i	$-0.968782\pi$
$647$	−10.5000	+	18.1865i	−0.412798	+	0.714986i	0.582397	+	0.812905i	$0.302115\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$		0			0
$650$	2.00000	+	3.46410i	0.0784465	+	0.135873i
$651$		0			0
$652$	9.50000	−	16.4545i	0.372049	−	0.644407i
$653$	15.0000			0.586995			0.293498	−	0.955960i	$-0.405181\pi$
$653$	15.0000			0.586995			0.293498	+	0.955960i	$0.405181\pi$
$654$	−19.5000	−	11.2583i	−0.762510	−	0.440236i
$655$	45.0000			1.75830
$656$	1.50000	+	2.59808i	0.0585652	+	0.101438i
$657$	−16.5000	−	28.5788i	−0.643726	−	1.11497i
$658$		0			0
$659$	−1.50000	−	2.59808i	−0.0584317	−	0.101207i	0.835330	−	0.549749i	$-0.185277\pi$
$659$	−1.50000	−	2.59808i	−0.0584317	−	0.101207i	−0.893762	+	0.448542i	$0.851943\pi$
$660$	−13.5000	−	7.79423i	−0.525487	−	0.303390i
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	0.568831	−	0.822454i	$-0.307396\pi$
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	−0.996682	+	0.0813955i	$0.974062\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$	4.50000	+	2.59808i	0.174766	+	0.100901i
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$		0			0
$666$	1.50000	−	2.59808i	0.0581238	−	0.100673i
$667$	13.5000	+	23.3827i	0.522722	+	0.905381i
$668$	15.0000			0.580367
$669$	−1.50000	−	0.866025i	−0.0579934	−	0.0334825i
$670$	−12.0000			−0.463600
$671$	−3.00000	+	5.19615i	−0.115814	+	0.200595i
$672$		0			0
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	−0.976593	−	0.215096i	$-0.930993\pi$
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	0.302017	−	0.953302i	$-0.402340\pi$
$674$	−6.50000	−	11.2583i	−0.250371	−	0.433655i
$675$		−	20.7846i		−	0.800000i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	0.419380	+	0.907811i	$0.362247\pi$
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	−0.995877	+	0.0907112i	$0.971086\pi$
$678$	−13.5000	−	7.79423i	−0.518464	−	0.299336i
$679$		0			0
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$	4.50000	−	2.59808i	0.172440	−	0.0995585i
$682$	−24.0000			−0.919007
$683$	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	$0.111583\pi$
$684$	10.5000	+	18.1865i	0.401478	+	0.695379i
$685$	27.0000			1.03162
$686$		0			0
$687$	19.5000	−	11.2583i	0.743971	−	0.429532i
$688$	−1.00000			−0.0381246
$689$	−1.50000	−	2.59808i	−0.0571454	−	0.0989788i
$690$		−	46.7654i		−	1.78033i
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	−0.0555386	−	0.998457i	$-0.517688\pi$
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	0.892458	−	0.451130i	$-0.148979\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	10.5000	−	18.1865i	0.398288	−	0.689855i
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$	23.0000			0.870563
$699$	−4.50000	−	2.59808i	−0.170206	−	0.0982683i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	4.50000	−	2.59808i	0.169842	−	0.0980581i
$703$	3.50000	−	6.06218i	0.132005	−	0.228639i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	−1.50000	+	2.59808i	−0.0564532	+	0.0977799i
$707$		0			0
$708$		0			0
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$	−18.0000	+	31.1769i	−0.675528	+	1.17005i
$711$	−24.0000	−	41.5692i	−0.900070	−	1.55897i
$712$	−1.50000	−	2.59808i	−0.0562149	−	0.0973670i
$713$	−36.0000	−	62.3538i	−1.34821	−	2.33517i
$714$		0			0
$715$	−4.50000	+	7.79423i	−0.168290	+	0.291488i
$716$	−21.0000			−0.784807
$717$		−	5.19615i		−	0.194054i
$718$	−9.00000			−0.335877
$719$	−7.50000	−	12.9904i	−0.279703	−	0.484459i	0.691608	−	0.722273i	$-0.256903\pi$
$719$	−7.50000	−	12.9904i	−0.279703	−	0.484459i	−0.971311	+	0.237814i	$0.923569\pi$
$720$	−4.50000	−	7.79423i	−0.167705	−	0.290474i
$721$		0			0
$722$	15.0000	+	25.9808i	0.558242	+	0.966904i
$723$	19.5000	−	11.2583i	0.725213	−	0.418702i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$			3.46410i			0.128565i
$727$	−6.50000	−	11.2583i	−0.241072	−	0.417548i	0.719948	−	0.694028i	$-0.244166\pi$
$727$	−6.50000	−	11.2583i	−0.241072	−	0.417548i	−0.961020	+	0.276479i	$0.910832\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	16.5000	+	28.5788i	0.610692	+	1.05775i
$731$	3.00000			0.110959
$732$	−3.00000	+	1.73205i	−0.110883	+	0.0640184i
$733$	1.00000			0.0369358			0.0184679	−	0.999829i	$-0.494121\pi$
$733$	1.00000			0.0369358			0.0184679	+	0.999829i	$0.494121\pi$
$734$	−8.50000	+	14.7224i	−0.313741	+	0.543415i
$735$		0			0
$736$	−4.50000	−	7.79423i	−0.165872	−	0.287299i
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	−9.00000			−0.331295
$739$	−11.5000	+	19.9186i	−0.423034	+	0.732717i	−0.996235	−	0.0866983i	$-0.972368\pi$
$739$	−11.5000	+	19.9186i	−0.423034	+	0.732717i	0.573200	+	0.819415i	$0.305702\pi$
$740$	−1.50000	+	2.59808i	−0.0551411	+	0.0955072i
$741$	10.5000	−	6.06218i	0.385727	−	0.222700i
$742$		0			0
$743$	−10.5000	+	18.1865i	−0.385208	+	0.667199i	−0.991798	−	0.127815i	$-0.959204\pi$
$743$	−10.5000	+	18.1865i	−0.385208	+	0.667199i	0.606590	+	0.795015i	$0.292537\pi$
$744$	−12.0000	−	6.92820i	−0.439941	−	0.254000i
$745$	27.0000			0.989203
$746$	−6.50000	+	11.2583i	−0.237982	+	0.412197i
$747$	−27.0000			−0.987878
$748$	9.00000			0.329073
$749$		0			0
$750$		−	5.19615i		−	0.189737i
$751$	−13.0000			−0.474377			−0.237188	−	0.971464i	$-0.576226\pi$
$751$	−13.0000			−0.474377			−0.237188	+	0.971464i	$0.576226\pi$
$752$		0			0
$753$	−18.0000	+	10.3923i	−0.655956	+	0.378717i
$754$	1.50000	−	2.59808i	0.0546268	−	0.0946164i
$755$	21.0000			0.764268
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$	40.5000	−	23.3827i	1.47006	−	0.848738i
$760$	−10.5000	−	18.1865i	−0.380875	−	0.659695i
$761$	45.0000			1.63125			0.815624	−	0.578582i	$-0.196394\pi$
$761$	45.0000			1.63125			0.815624	+	0.578582i	$0.196394\pi$
$762$			6.92820i			0.250982i
$763$		0			0
$764$		0			0
$765$	13.5000	+	23.3827i	0.488094	+	0.845403i
$766$	−7.50000	+	12.9904i	−0.270986	+	0.469362i
$767$		0			0
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	−0.580696	−	0.814120i	$-0.697220\pi$
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	0.995397	+	0.0958377i	$0.0305530\pi$
$770$		0			0
$771$	31.5000	−	18.1865i	1.13444	−	0.654972i
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	−0.514301	−	0.857610i	$-0.671949\pi$
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	0.999862	+	0.0165929i	$0.00528194\pi$
$774$	1.50000	−	2.59808i	0.0539164	−	0.0933859i
$775$	16.0000	+	27.7128i	0.574737	+	0.995474i
$776$	0.500000	+	0.866025i	0.0179490	+	0.0310885i
$777$		0			0
$778$	13.5000	−	23.3827i	0.483998	−	0.838310i
$779$	−21.0000			−0.752403
$780$	−4.50000	+	2.59808i	−0.161126	+	0.0930261i
$781$	−36.0000			−1.28818
$782$	13.5000	+	23.3827i	0.482759	+	0.836163i
$783$	−13.5000	+	7.79423i	−0.482451	+	0.278543i
$784$		0			0
$785$	33.0000	+	57.1577i	1.17782	+	2.04004i
$786$			25.9808i			0.926703i
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$	13.5000	−	7.79423i	0.480613	−	0.277482i
$790$	24.0000	+	41.5692i	0.853882	+	1.47897i
$791$		0			0
$792$	4.50000	−	7.79423i	0.159901	−	0.276956i
$793$	1.00000	+	1.73205i	0.0355110	+	0.0615069i
$794$	−13.0000			−0.461353
$795$		−	15.5885i		−	0.552866i
$796$	25.0000			0.886102
$797$	−10.5000	+	18.1865i	−0.371929	+	0.644200i	−0.989862	−	0.142031i	$-0.954637\pi$
$797$	−10.5000	+	18.1865i	−0.371929	+	0.644200i	0.617933	+	0.786231i	$0.287970\pi$
$798$		0			0
$799$		0			0
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	9.00000			0.317999
$802$	13.5000	−	23.3827i	0.476702	−	0.825671i
$803$	−16.5000	+	28.5788i	−0.582272	+	1.00853i
$804$		−	6.92820i		−	0.244339i
$805$		0			0
$806$	−4.00000	+	6.92820i	−0.140894	+	0.244036i
$807$		−	25.9808i		−	0.914566i
$808$	3.00000			0.105540
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	−0.415357	−	0.909659i	$-0.636343\pi$
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	0.995466	−	0.0951198i	$-0.0303234\pi$
$810$	27.0000			0.948683
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	7.50000	+	4.33013i	0.263036	+	0.151864i
$814$	−3.00000			−0.105150
$815$	−28.5000	−	49.3634i	−0.998311	−	1.72913i
$816$	4.50000	+	2.59808i	0.157532	+	0.0909509i
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$	−34.0000			−1.18878
$819$		0			0
$820$	9.00000			0.314294
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$			15.5885i			0.543710i
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$	−13.0000			−0.452876
$825$	−18.0000	+	10.3923i	−0.626680	+	0.361814i
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	27.0000			0.938315
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	−0.754567	−	0.656223i	$-0.772153\pi$
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	0.945589	+	0.325362i	$0.105486\pi$
$830$	27.0000			0.937184
$831$	−1.50000	+	0.866025i	−0.0520344	+	0.0300421i
$832$	−0.500000	+	0.866025i	−0.0173344	+	0.0300240i
$833$		0			0
$834$	10.5000	+	6.06218i	0.363585	+	0.209916i
$835$	22.5000	−	38.9711i	0.778645	−	1.34865i
$836$	10.5000	−	18.1865i	0.363150	−	0.628994i
$837$	36.0000	−	20.7846i	1.24434	−	0.718421i
$838$	−4.50000	−	7.79423i	−0.155450	−	0.269247i
$839$	7.50000	+	12.9904i	0.258929	+	0.448478i	0.965955	−	0.258709i	$-0.0832972\pi$
$839$	7.50000	+	12.9904i	0.258929	+	0.448478i	−0.707026	+	0.707187i	$0.749964\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−35.0000			−1.20618
$843$	31.5000	+	18.1865i	1.08492	+	0.626377i
$844$	5.00000			0.172107
$845$	−18.0000	−	31.1769i	−0.619219	−	1.07252i
$846$		0			0
$847$		0			0
$848$	−1.50000	−	2.59808i	−0.0515102	−	0.0892183i
$849$	−6.00000	−	3.46410i	−0.205919	−	0.118888i
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$	−4.50000	−	7.79423i	−0.154258	−	0.267183i
$852$	−18.0000	−	10.3923i	−0.616670	−	0.356034i
$853$	−0.500000	−	0.866025i	−0.0171197	−	0.0296521i	0.857339	−	0.514753i	$-0.172116\pi$
$853$	−0.500000	−	0.866025i	−0.0171197	−	0.0296521i	−0.874458	+	0.485101i	$0.838783\pi$
$854$		0			0
$855$	63.0000			2.15455
$856$	4.50000	+	7.79423i	0.153807	+	0.266401i
$857$	−3.00000			−0.102478			−0.0512390	−	0.998686i	$-0.516317\pi$
$857$	−3.00000			−0.102478			−0.0512390	+	0.998686i	$0.516317\pi$
$858$	−4.50000	−	2.59808i	−0.153627	−	0.0886969i
$859$	25.0000			0.852989			0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000			0.852989			0.426494	+	0.904490i	$0.359748\pi$
$860$	−1.50000	+	2.59808i	−0.0511496	+	0.0885937i
$861$		0			0
$862$	13.5000	+	23.3827i	0.459812	+	0.796417i
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.864007	+	0.503480i	$0.167947\pi$
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.00402340	+	0.999992i	$0.498719\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	−1.00000	+	1.73205i	−0.0339814	+	0.0588575i
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$		0			0
$869$	−24.0000	+	41.5692i	−0.814144	+	1.41014i
$870$	13.5000	−	7.79423i	0.457693	−	0.264249i
$871$	−4.00000			−0.135535
$872$	−6.50000	+	11.2583i	−0.220118	+	0.381255i
$873$	−3.00000			−0.101535
$874$	63.0000			2.13101
$875$		0			0
$876$	−16.5000	+	9.52628i	−0.557483	+	0.321863i
$877$	47.0000			1.58708			0.793539	−	0.608520i	$-0.208236\pi$
$877$	47.0000			1.58708			0.793539	+	0.608520i	$0.208236\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$			15.5885i			0.525786i
$880$	−4.50000	+	7.79423i	−0.151695	+	0.262743i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	1.50000	−	2.59808i	0.0504505	−	0.0873828i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	33.0000			1.10803			0.554016	−	0.832506i	$-0.313095\pi$
$887$	33.0000			1.10803			0.554016	+	0.832506i	$0.313095\pi$
$888$	−1.50000	−	0.866025i	−0.0503367	−	0.0290619i
$889$		0			0
$890$	−9.00000			−0.301681
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$	−0.500000	+	0.866025i	−0.0167412	+	0.0289967i
$893$		0			0
$894$			15.5885i			0.521356i
$895$	−31.5000	+	54.5596i	−1.05293	+	1.82373i
$896$		0			0
$897$		−	15.5885i		−	0.520483i
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$	−12.0000			−0.400000
$901$	4.50000	+	7.79423i	0.149917	+	0.259663i
$902$	4.50000	+	7.79423i	0.149834	+	0.259519i
$903$		0			0
$904$	−4.50000	+	7.79423i	−0.149668	+	0.259232i
$905$	6.00000			0.199447
$906$			12.1244i			0.402805i
$907$	−43.0000			−1.42779			−0.713896	−	0.700252i	$-0.753071\pi$
$907$	−43.0000			−1.42779			−0.713896	+	0.700252i	$0.753071\pi$
$908$	−1.50000	−	2.59808i	−0.0497792	−	0.0862202i
$909$	−4.50000	+	7.79423i	−0.149256	+	0.258518i
$910$		0			0
$911$	−19.5000	−	33.7750i	−0.646064	−	1.11902i	−0.984055	−	0.177866i	$-0.943081\pi$
$911$	−19.5000	−	33.7750i	−0.646064	−	1.11902i	0.337991	−	0.941149i	$-0.390253\pi$
$912$	10.5000	−	6.06218i	0.347690	−	0.200739i
$913$	13.5000	+	23.3827i	0.446785	+	0.773854i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$			10.3923i			0.343559i
$916$	−6.50000	−	11.2583i	−0.214766	−	0.371986i
$917$		0			0
$918$	−13.5000	+	7.79423i	−0.445566	+	0.257248i
$919$	−26.5000	−	45.8993i	−0.874154	−	1.51408i	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−26.5000	−	45.8993i	−0.874154	−	1.51408i	−0.0164935	−	0.999864i	$-0.505250\pi$
$920$	−27.0000			−0.890164
$921$	42.0000	−	24.2487i	1.38395	−	0.799022i
$922$	−9.00000			−0.296399
$923$	−6.00000	+	10.3923i	−0.197492	+	0.342067i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	20.5000	+	35.5070i	0.673672	+	1.16683i
$927$	19.5000	−	33.7750i	0.640464	−	1.10932i
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$	−36.0000	+	20.7846i	−1.18049	+	0.681554i
$931$		0			0
$932$	−1.50000	+	2.59808i	−0.0491341	+	0.0851028i
$933$	−36.0000	−	20.7846i	−1.17859	−	0.680458i
$934$	−3.00000			−0.0981630
$935$	13.5000	−	23.3827i	0.441497	−	0.764696i
$936$	−1.50000	−	2.59808i	−0.0490290	−	0.0849208i
$937$	−26.0000			−0.849383			−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000			−0.849383			−0.424691	+	0.905338i	$0.639617\pi$
$938$		0			0
$939$			17.3205i			0.565233i
$940$		0			0
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	0.812975	−	0.582298i	$-0.197846\pi$
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	−0.910773	+	0.412908i	$0.864513\pi$
$942$	−33.0000	+	19.0526i	−1.07520	+	0.620766i
$943$	−13.5000	+	23.3827i	−0.439620	+	0.761445i
$944$		0			0
$945$		0			0
$946$	−3.00000			−0.0975384
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	−24.0000	+	13.8564i	−0.779484	+	0.450035i
$949$	5.50000	+	9.52628i	0.178538	+	0.309236i
$950$	−28.0000			−0.908440
$951$			31.1769i			1.01098i
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	9.00000			0.291386
$955$		0			0
$956$	−3.00000			−0.0970269
$957$	13.5000	+	7.79423i	0.436393	+	0.251952i
$958$	1.50000	−	2.59808i	0.0484628	−	0.0839400i
$959$		0			0
$960$	−4.50000	+	2.59808i	−0.145237	+	0.0838525i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−0.500000	+	0.866025i	−0.0161206	+	0.0279218i
$963$	−27.0000			−0.870063
$964$	−6.50000	−	11.2583i	−0.209351	−	0.362606i
$965$	21.0000	+	36.3731i	0.676014	+	1.17089i
$966$		0			0
$967$	−20.5000	+	35.5070i	−0.659236	+	1.14183i	0.321578	+	0.946883i	$0.395787\pi$
$967$	−20.5000	+	35.5070i	−0.659236	+	1.14183i	−0.980814	+	0.194946i	$0.937547\pi$
$968$	2.00000			0.0642824
$969$	−31.5000	+	18.1865i	−1.01193	+	0.584236i
$970$	3.00000			0.0963242
$971$	16.5000	+	28.5788i	0.529510	+	0.917139i	0.999408	+	0.0344175i	$0.0109576\pi$
$971$	16.5000	+	28.5788i	0.529510	+	0.917139i	−0.469897	+	0.882721i	$0.655709\pi$
$972$			15.5885i			0.500000i
$973$		0			0
$974$	−12.5000	−	21.6506i	−0.400526	−	0.693731i
$975$			6.92820i			0.221880i
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$	28.5000	−	16.4545i	0.911330	−	0.526156i
$979$	−4.50000	−	7.79423i	−0.143821	−	0.249105i
$980$		0			0
$981$	−19.5000	−	33.7750i	−0.622587	−	1.07835i
$982$	10.5000	+	18.1865i	0.335068	+	0.580356i
$983$	15.0000			0.478426			0.239213	−	0.970967i	$-0.423111\pi$
$983$	15.0000			0.478426			0.239213	+	0.970967i	$0.423111\pi$
$984$			5.19615i			0.165647i
$985$	−54.0000			−1.72058
$986$	−4.50000	+	7.79423i	−0.143309	+	0.248219i
$987$		0			0
$988$	−3.50000	−	6.06218i	−0.111350	−	0.192864i
$989$	−4.50000	−	7.79423i	−0.143092	−	0.247842i
$990$	−13.5000	−	23.3827i	−0.429058	−	0.743151i
$991$	12.5000	−	21.6506i	0.397076	−	0.687755i	−0.596288	−	0.802771i	$-0.703358\pi$
$991$	12.5000	−	21.6506i	0.397076	−	0.687755i	0.993364	+	0.115015i	$0.0366917\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$			13.8564i			0.439720i
$994$		0			0
$995$	37.5000	−	64.9519i	1.18883	−	2.05911i
$996$			15.5885i			0.493939i
$997$	13.0000			0.411714			0.205857	−	0.978582i	$-0.434002\pi$
$997$	13.0000			0.411714			0.205857	+	0.978582i	$0.434002\pi$
$998$	−12.5000	+	21.6506i	−0.395681	+	0.685339i
$999$	4.50000	−	2.59808i	0.142374	−	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.i.67.1		2
3.2	odd	2		2646.2.h.d.361.1		2
7.2	even	3		882.2.e.c.373.1		2
7.3	odd	6		882.2.f.i.589.1		2
7.4	even	3		882.2.f.g.589.1		2
7.5	odd	6		126.2.e.a.121.1	yes	2
7.6	odd	2		126.2.h.b.67.1	yes	2
9.2	odd	6		2646.2.e.g.2125.1		2
9.7	even	3		882.2.e.c.655.1		2
21.2	odd	6		2646.2.e.g.1549.1		2
21.5	even	6		378.2.e.b.37.1		2
21.11	odd	6		2646.2.f.a.1765.1		2
21.17	even	6		2646.2.f.d.1765.1		2
21.20	even	2		378.2.h.a.361.1		2
28.19	even	6		1008.2.q.a.625.1		2
28.27	even	2		1008.2.t.f.193.1		2
63.2	odd	6		2646.2.h.d.667.1		2
63.4	even	3		7938.2.a.b.1.1		1
63.5	even	6		1134.2.g.c.163.1		2
63.11	odd	6		2646.2.f.a.883.1		2
63.13	odd	6		1134.2.g.e.487.1		2
63.16	even	3	inner	882.2.h.i.79.1		2
63.20	even	6		378.2.e.b.235.1		2
63.25	even	3		882.2.f.g.295.1		2
63.31	odd	6		7938.2.a.m.1.1		1
63.32	odd	6		7938.2.a.be.1.1		1
63.34	odd	6		126.2.e.a.25.1	✓	2
63.38	even	6		2646.2.f.d.883.1		2
63.40	odd	6		1134.2.g.e.163.1		2
63.41	even	6		1134.2.g.c.487.1		2
63.47	even	6		378.2.h.a.289.1		2
63.52	odd	6		882.2.f.i.295.1		2
63.59	even	6		7938.2.a.t.1.1		1
63.61	odd	6		126.2.h.b.79.1	yes	2
84.47	odd	6		3024.2.q.f.2305.1		2
84.83	odd	2		3024.2.t.a.1873.1		2
252.47	odd	6		3024.2.t.a.289.1		2
252.83	odd	6		3024.2.q.f.2881.1		2
252.187	even	6		1008.2.t.f.961.1		2
252.223	even	6		1008.2.q.a.529.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.a.25.1	✓	2	63.34	odd	6
126.2.e.a.121.1	yes	2	7.5	odd	6
126.2.h.b.67.1	yes	2	7.6	odd	2
126.2.h.b.79.1	yes	2	63.61	odd	6
378.2.e.b.37.1		2	21.5	even	6
378.2.e.b.235.1		2	63.20	even	6
378.2.h.a.289.1		2	63.47	even	6
378.2.h.a.361.1		2	21.20	even	2
882.2.e.c.373.1		2	7.2	even	3
882.2.e.c.655.1		2	9.7	even	3
882.2.f.g.295.1		2	63.25	even	3
882.2.f.g.589.1		2	7.4	even	3
882.2.f.i.295.1		2	63.52	odd	6
882.2.f.i.589.1		2	7.3	odd	6
882.2.h.i.67.1		2	1.1	even	1	trivial
882.2.h.i.79.1		2	63.16	even	3	inner
1008.2.q.a.529.1		2	252.223	even	6
1008.2.q.a.625.1		2	28.19	even	6
1008.2.t.f.193.1		2	28.27	even	2
1008.2.t.f.961.1		2	252.187	even	6
1134.2.g.c.163.1		2	63.5	even	6
1134.2.g.c.487.1		2	63.41	even	6
1134.2.g.e.163.1		2	63.40	odd	6
1134.2.g.e.487.1		2	63.13	odd	6
2646.2.e.g.1549.1		2	21.2	odd	6
2646.2.e.g.2125.1		2	9.2	odd	6
2646.2.f.a.883.1		2	63.11	odd	6
2646.2.f.a.1765.1		2	21.11	odd	6
2646.2.f.d.883.1		2	63.38	even	6
2646.2.f.d.1765.1		2	21.17	even	6
2646.2.h.d.361.1		2	3.2	odd	2
2646.2.h.d.667.1		2	63.2	odd	6
3024.2.q.f.2305.1		2	84.47	odd	6
3024.2.q.f.2881.1		2	252.83	odd	6
3024.2.t.a.289.1		2	252.47	odd	6
3024.2.t.a.1873.1		2	84.83	odd	2
7938.2.a.b.1.1		1	63.4	even	3
7938.2.a.m.1.1		1	63.31	odd	6
7938.2.a.t.1.1		1	63.59	even	6
7938.2.a.be.1.1		1	63.32	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} -1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{10} -3.00000 q^{11} +(-1.50000 - 0.866025i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-4.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} -9.00000 q^{23} +(-1.50000 + 0.866025i) q^{24} +4.00000 q^{25} +(0.500000 + 0.866025i) q^{26} -5.19615i q^{27} +(-1.50000 - 2.59808i) q^{29} +5.19615i q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +(-1.50000 - 2.59808i) q^{34} -3.00000 q^{36} +(0.500000 + 0.866025i) q^{37} -7.00000 q^{38} +1.73205i q^{39} +3.00000 q^{40} +(1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{44} +(-4.50000 + 7.79423i) q^{45} +(-4.50000 + 7.79423i) q^{46} +1.73205i q^{48} +(2.00000 - 3.46410i) q^{50} -5.19615i q^{51} +1.00000 q^{52} +(-1.50000 + 2.59808i) q^{53} +(-4.50000 - 2.59808i) q^{54} +9.00000 q^{55} +(-10.5000 - 6.06218i) q^{57} -3.00000 q^{58} +(4.50000 + 2.59808i) q^{60} +(1.00000 - 1.73205i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +5.19615i q^{66} +(2.00000 + 3.46410i) q^{67} -3.00000 q^{68} +(-13.5000 + 7.79423i) q^{69} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(5.50000 - 9.52628i) q^{73} +1.00000 q^{74} +(6.00000 - 3.46410i) q^{75} +(-3.50000 + 6.06218i) q^{76} +(1.50000 + 0.866025i) q^{78} +(8.00000 - 13.8564i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(-4.50000 + 7.79423i) q^{85} +1.00000 q^{86} +(-4.50000 - 2.59808i) q^{87} +3.00000 q^{88} +(1.50000 + 2.59808i) q^{89} +(4.50000 + 7.79423i) q^{90} +(4.50000 + 7.79423i) q^{92} +(12.0000 + 6.92820i) q^{93} +(10.5000 + 18.1865i) q^{95} +(1.50000 + 0.866025i) q^{96} +(-0.500000 - 0.866025i) q^{97} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} - 6 q^{5} - 2 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} - 3 q^{12} - q^{13} - 9 q^{15} - q^{16} + 3 q^{17} - 3 q^{18} - 7 q^{19} + 3 q^{20} - 3 q^{22} - 18 q^{23} - 3 q^{24}+ \cdots - 9 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 - 6 * q^5 - 2 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 - 3 * q^12 - q^13 - 9 * q^15 - q^16 + 3 * q^17 - 3 * q^18 - 7 * q^19 + 3 * q^20 - 3 * q^22 - 18 * q^23 - 3 * q^24 + 8 * q^25 + q^26 - 3 * q^29 + 8 * q^31 + q^32 - 9 * q^33 - 3 * q^34 - 6 * q^36 + q^37 - 14 * q^38 + 6 * q^40 + 3 * q^41 + q^43 + 3 * q^44 - 9 * q^45 - 9 * q^46 + 4 * q^50 + 2 * q^52 - 3 * q^53 - 9 * q^54 + 18 * q^55 - 21 * q^57 - 6 * q^58 + 9 * q^60 + 2 * q^61 + 16 * q^62 + 2 * q^64 + 3 * q^65 + 4 * q^67 - 6 * q^68 - 27 * q^69 + 24 * q^71 - 3 * q^72 + 11 * q^73 + 2 * q^74 + 12 * q^75 - 7 * q^76 + 3 * q^78 + 16 * q^79 + 3 * q^80 - 9 * q^81 - 3 * q^82 - 9 * q^83 - 9 * q^85 + 2 * q^86 - 9 * q^87 + 6 * q^88 + 3 * q^89 + 9 * q^90 + 9 * q^92 + 24 * q^93 + 21 * q^95 + 3 * q^96 - q^97 - 9 * q^99

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