LMFDB - Embedded newform 399.2.j.a.172.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(58,399)] 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("399.58"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,-1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18603104065$
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			172.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	399.172
Dual form			399.2.j.a.58.1

$q$-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 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-2.00000 + 3.46410i) q^{11} +(-1.00000 - 1.73205i) q^{12} +4.00000 q^{13} +(1.00000 - 5.19615i) q^{14} +1.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{18} +(0.500000 + 0.866025i) q^{19} +2.00000 q^{20} +(-2.50000 + 0.866025i) q^{21} +8.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-4.00000 - 6.92820i) q^{26} +1.00000 q^{27} +(-5.00000 + 1.73205i) q^{28} +10.0000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(4.00000 - 6.92820i) q^{32} +(-2.00000 - 3.46410i) q^{33} +6.00000 q^{34} +(0.500000 - 2.59808i) q^{35} +2.00000 q^{36} +(3.00000 + 5.19615i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-2.00000 + 3.46410i) q^{39} +2.00000 q^{41} +(4.00000 + 3.46410i) q^{42} -7.00000 q^{43} +(-4.00000 - 6.92820i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{46} -4.00000 q^{48} +(1.00000 + 6.92820i) q^{49} -8.00000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(-4.00000 + 6.92820i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-1.00000 - 1.73205i) q^{54} +4.00000 q^{55} -1.00000 q^{57} +(-10.0000 - 17.3205i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(-5.00000 - 8.66025i) q^{61} +(0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-4.00000 + 6.92820i) q^{66} +(-5.00000 + 8.66025i) q^{67} +(-3.00000 - 5.19615i) q^{68} -3.00000 q^{69} +(-5.00000 + 1.73205i) q^{70} +6.00000 q^{71} +(-3.00000 + 5.19615i) q^{73} +(6.00000 - 10.3923i) q^{74} +(2.00000 + 3.46410i) q^{75} -2.00000 q^{76} +(-10.0000 + 3.46410i) q^{77} +8.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.00000 - 3.46410i) q^{82} +3.00000 q^{83} +(1.00000 - 5.19615i) q^{84} +3.00000 q^{85} +(7.00000 + 12.1244i) q^{86} +(-5.00000 + 8.66025i) q^{87} +(7.00000 + 12.1244i) q^{89} +2.00000 q^{90} +(8.00000 + 6.92820i) q^{91} -6.00000 q^{92} +(0.500000 - 0.866025i) q^{95} +(4.00000 + 6.92820i) q^{96} -12.0000 q^{97} +(11.0000 - 8.66025i) q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 4 q^{6} + 4 q^{7} - q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 8 q^{13} + 2 q^{14} + 2 q^{15} + 4 q^{16} - 3 q^{17} - 2 q^{18} + q^{19} + 4 q^{20} - 5 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 - 2 * q^4 - q^5 + 4 * q^6 + 4 * q^7 - q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 + 8 * q^13 + 2 * q^14 + 2 * q^15 + 4 * q^16 - 3 * q^17 - 2 * q^18 + q^19 + 4 * q^20 - 5 * q^21 + 16 * q^22 + 3 * q^23 + 4 * q^25 - 8 * q^26 + 2 * q^27 - 10 * q^28 + 20 * q^29 - 2 * q^30 + 8 * q^32 - 4 * q^33 + 12 * q^34 + q^35 + 4 * q^36 + 6 * q^37 + 2 * q^38 - 4 * q^39 + 4 * q^41 + 8 * q^42 - 14 * q^43 - 8 * q^44 - q^45 + 6 * q^46 - 8 * q^48 + 2 * q^49 - 16 * q^50 - 3 * q^51 - 8 * q^52 + 12 * q^53 - 2 * q^54 + 8 * q^55 - 2 * q^57 - 20 * q^58 - 12 * q^59 - 2 * q^60 - 10 * q^61 + q^63 - 16 * q^64 - 4 * q^65 - 8 * q^66 - 10 * q^67 - 6 * q^68 - 6 * q^69 - 10 * q^70 + 12 * q^71 - 6 * q^73 + 12 * q^74 + 4 * q^75 - 4 * q^76 - 20 * q^77 + 16 * q^78 + 10 * q^79 + 4 * q^80 - q^81 - 4 * q^82 + 6 * q^83 + 2 * q^84 + 6 * q^85 + 14 * q^86 - 10 * q^87 + 14 * q^89 + 4 * q^90 + 16 * q^91 - 12 * q^92 + q^95 + 8 * q^96 - 24 * q^97 + 22 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	2.00000			0.816497
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	1.00000	−	5.19615i	0.267261	−	1.38873i
$15$	1.00000			0.258199
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	−1.00000	+	1.73205i	−0.235702	+	0.408248i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$20$	2.00000			0.447214
$21$	−2.50000	+	0.866025i	−0.545545	+	0.188982i
$22$	8.00000			1.70561
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−4.00000	−	6.92820i	−0.784465	−	1.35873i
$27$	1.00000			0.192450
$28$	−5.00000	+	1.73205i	−0.944911	+	0.327327i
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$	−1.00000	−	1.73205i	−0.182574	−	0.316228i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$	−2.00000	−	3.46410i	−0.348155	−	0.603023i
$34$	6.00000			1.02899
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$	2.00000			0.333333
$37$	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	$0.669162\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$	−2.00000	+	3.46410i	−0.320256	+	0.554700i
$40$		0			0
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$	4.00000	+	3.46410i	0.617213	+	0.534522i
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$	−4.00000	−	6.92820i	−0.603023	−	1.04447i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−4.00000			−0.577350
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−8.00000			−1.13137
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$	−4.00000	+	6.92820i	−0.554700	+	0.960769i
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$	−1.00000	−	1.73205i	−0.136083	−	0.235702i
$55$	4.00000			0.539360
$56$		0			0
$57$	−1.00000			−0.132453
$58$	−10.0000	−	17.3205i	−1.31306	−	2.27429i
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$	−1.00000	+	1.73205i	−0.129099	+	0.223607i
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$		0			0
$63$	0.500000	−	2.59808i	0.0629941	−	0.327327i
$64$	−8.00000			−1.00000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$	−4.00000	+	6.92820i	−0.492366	+	0.852803i
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	−3.00000			−0.361158
$70$	−5.00000	+	1.73205i	−0.597614	+	0.207020i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	0.635323	+	0.772246i	$0.280867\pi$
$74$	6.00000	−	10.3923i	0.697486	−	1.20808i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	−2.00000			−0.229416
$77$	−10.0000	+	3.46410i	−1.13961	+	0.394771i
$78$	8.00000			0.905822
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.00000	−	3.46410i	−0.220863	−	0.382546i
$83$	3.00000			0.329293			0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000			0.329293			0.164646	+	0.986353i	$0.447352\pi$
$84$	1.00000	−	5.19615i	0.109109	−	0.566947i
$85$	3.00000			0.325396
$86$	7.00000	+	12.1244i	0.754829	+	1.30740i
$87$	−5.00000	+	8.66025i	−0.536056	+	0.928477i
$88$		0			0
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	0.951584	+	0.307389i	$0.0994552\pi$
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	−0.209585	+	0.977790i	$0.567211\pi$
$90$	2.00000			0.210819
$91$	8.00000	+	6.92820i	0.838628	+	0.726273i
$92$	−6.00000			−0.625543
$93$		0			0
$94$		0			0
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$	4.00000	+	6.92820i	0.408248	+	0.707107i
$97$	−12.0000			−1.21842			−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000			−1.21842			−0.609208	+	0.793011i	$0.708512\pi$
$98$	11.0000	−	8.66025i	1.11117	−	0.874818i
$99$	4.00000			0.402015
$100$	4.00000	+	6.92820i	0.400000	+	0.692820i
$101$	−5.50000	+	9.52628i	−0.547270	+	0.947900i	0.451190	+	0.892428i	$0.351000\pi$
$101$	−5.50000	+	9.52628i	−0.547270	+	0.947900i	−0.998460	+	0.0554722i	$0.982334\pi$
$102$	−3.00000	+	5.19615i	−0.297044	+	0.514496i
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$	2.00000	+	1.73205i	0.195180	+	0.169031i
$106$	−24.0000			−2.33109
$107$	−5.00000	−	8.66025i	−0.483368	−	0.837218i	0.516449	−	0.856318i	$-0.327253\pi$
$107$	−5.00000	−	8.66025i	−0.483368	−	0.837218i	−0.999818	+	0.0190994i	$0.993920\pi$
$108$	−1.00000	+	1.73205i	−0.0962250	+	0.166667i
$109$	3.00000	−	5.19615i	0.287348	−	0.497701i	−0.685828	−	0.727764i	$-0.740560\pi$
$109$	3.00000	−	5.19615i	0.287348	−	0.497701i	0.973176	+	0.230063i	$0.0738931\pi$
$110$	−4.00000	−	6.92820i	−0.381385	−	0.660578i
$111$	−6.00000			−0.569495
$112$	−2.00000	+	10.3923i	−0.188982	+	0.981981i
$113$	−8.00000			−0.752577			−0.376288	−	0.926503i	$-0.622800\pi$
$113$	−8.00000			−0.752577			−0.376288	+	0.926503i	$0.622800\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	−10.0000	+	17.3205i	−0.928477	+	1.60817i
$117$	−2.00000	−	3.46410i	−0.184900	−	0.320256i
$118$	24.0000			2.20938
$119$	−7.50000	+	2.59808i	−0.687524	+	0.238165i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−10.0000	+	17.3205i	−0.905357	+	1.56813i
$123$	−1.00000	+	1.73205i	−0.0901670	+	0.156174i
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−5.00000	+	1.73205i	−0.445435	+	0.154303i
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$		0			0
$129$	3.50000	−	6.06218i	0.308158	−	0.533745i
$130$	−4.00000	+	6.92820i	−0.350823	+	0.607644i
$131$	2.50000	+	4.33013i	0.218426	+	0.378325i	0.954327	−	0.298764i	$-0.0965744\pi$
$131$	2.50000	+	4.33013i	0.218426	+	0.378325i	−0.735901	+	0.677089i	$0.763241\pi$
$132$	8.00000			0.696311
$133$	−0.500000	+	2.59808i	−0.0433555	+	0.225282i
$134$	20.0000			1.72774
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$	3.00000	+	5.19615i	0.255377	+	0.442326i
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$	4.00000	+	3.46410i	0.338062	+	0.292770i
$141$		0			0
$142$	−6.00000	−	10.3923i	−0.503509	−	0.872103i
$143$	−8.00000	+	13.8564i	−0.668994	+	1.15873i
$144$	2.00000	−	3.46410i	0.166667	−	0.288675i
$145$	−5.00000	−	8.66025i	−0.415227	−	0.719195i
$146$	12.0000			0.993127
$147$	−6.50000	−	2.59808i	−0.536111	−	0.214286i
$148$	−12.0000			−0.986394
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$	4.00000	−	6.92820i	0.326599	−	0.565685i
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$		0			0
$153$	3.00000			0.242536
$154$	16.0000	+	13.8564i	1.28932	+	1.11658i
$155$		0			0
$156$	−4.00000	−	6.92820i	−0.320256	−	0.554700i
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	−0.885288	−	0.465044i	$-0.846039\pi$
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	0.845383	+	0.534160i	$0.179372\pi$
$158$	10.0000	−	17.3205i	0.795557	−	1.37795i
$159$	6.00000	+	10.3923i	0.475831	+	0.824163i
$160$	−8.00000			−0.632456
$161$	−1.50000	+	7.79423i	−0.118217	+	0.614271i
$162$	2.00000			0.157135
$163$	−9.50000	−	16.4545i	−0.744097	−	1.28881i	−0.950615	−	0.310372i	$-0.899546\pi$
$163$	−9.50000	−	16.4545i	−0.744097	−	1.28881i	0.206518	−	0.978443i	$-0.433787\pi$
$164$	−2.00000	+	3.46410i	−0.156174	+	0.270501i
$165$	−2.00000	+	3.46410i	−0.155700	+	0.269680i
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	−2.00000			−0.154765			−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000			−0.154765			−0.0773823	+	0.997001i	$0.524656\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$	−3.00000	−	5.19615i	−0.230089	−	0.398527i
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$	7.00000	−	12.1244i	0.533745	−	0.924473i
$173$	−7.00000	−	12.1244i	−0.532200	−	0.921798i	−0.999293	−	0.0375896i	$-0.988032\pi$
$173$	−7.00000	−	12.1244i	−0.532200	−	0.921798i	0.467093	−	0.884208i	$-0.345301\pi$
$174$	20.0000			1.51620
$175$	10.0000	−	3.46410i	0.755929	−	0.261861i
$176$	−16.0000			−1.20605
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$	14.0000	−	24.2487i	1.04934	−	1.81752i
$179$	8.00000	−	13.8564i	0.597948	−	1.03568i	−0.395175	−	0.918606i	$-0.629316\pi$
$179$	8.00000	−	13.8564i	0.597948	−	1.03568i	0.993124	−	0.117071i	$-0.0373504\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	4.00000	−	20.7846i	0.296500	−	1.54066i
$183$	10.0000			0.739221
$184$		0			0
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$		0			0
$187$	−6.00000	−	10.3923i	−0.438763	−	0.759961i
$188$		0			0
$189$	2.00000	+	1.73205i	0.145479	+	0.125988i
$190$	−2.00000			−0.145095
$191$	8.50000	+	14.7224i	0.615038	+	1.06528i	0.990378	+	0.138390i	$0.0441928\pi$
$191$	8.50000	+	14.7224i	0.615038	+	1.06528i	−0.375339	+	0.926887i	$0.622474\pi$
$192$	4.00000	−	6.92820i	0.288675	−	0.500000i
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	−0.420096	−	0.907480i	$-0.638004\pi$
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	0.995948	−	0.0899262i	$-0.0286631\pi$
$194$	12.0000	+	20.7846i	0.861550	+	1.49225i
$195$	4.00000			0.286446
$196$	−13.0000	−	5.19615i	−0.928571	−	0.371154i
$197$	−11.0000			−0.783718			−0.391859	−	0.920025i	$-0.628168\pi$
$197$	−11.0000			−0.783718			−0.391859	+	0.920025i	$0.628168\pi$
$198$	−4.00000	−	6.92820i	−0.284268	−	0.492366i
$199$	13.5000	−	23.3827i	0.956990	−	1.65755i	0.227242	−	0.973838i	$-0.427029\pi$
$199$	13.5000	−	23.3827i	0.956990	−	1.65755i	0.729748	−	0.683716i	$-0.239637\pi$
$200$		0			0
$201$	−5.00000	−	8.66025i	−0.352673	−	0.610847i
$202$	22.0000			1.54791
$203$	20.0000	+	17.3205i	1.40372	+	1.21566i
$204$	6.00000			0.420084
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$	−8.00000	+	13.8564i	−0.557386	+	0.965422i
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$	8.00000	+	13.8564i	0.554700	+	0.960769i
$209$	−4.00000			−0.276686
$210$	1.00000	−	5.19615i	0.0690066	−	0.358569i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	12.0000	+	20.7846i	0.824163	+	1.42749i
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$	−10.0000	+	17.3205i	−0.683586	+	1.18401i
$215$	3.50000	+	6.06218i	0.238698	+	0.413437i
$216$		0			0
$217$		0			0
$218$	−12.0000			−0.812743
$219$	−3.00000	−	5.19615i	−0.202721	−	0.351123i
$220$	−4.00000	+	6.92820i	−0.269680	+	0.467099i
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$	6.00000	+	10.3923i	0.402694	+	0.697486i
$223$	10.0000			0.669650			0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000			0.669650			0.334825	+	0.942280i	$0.391323\pi$
$224$	20.0000	−	6.92820i	1.33631	−	0.462910i
$225$	−4.00000			−0.266667
$226$	8.00000	+	13.8564i	0.532152	+	0.921714i
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	1.00000	−	1.73205i	0.0662266	−	0.114708i
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	−0.726900	+	0.686743i	$0.759040\pi$
$230$	−6.00000			−0.395628
$231$	2.00000	−	10.3923i	0.131590	−	0.683763i
$232$		0			0
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	0.680135	−	0.733087i	$-0.261921\pi$
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	−0.974939	+	0.222470i	$0.928588\pi$
$234$	−4.00000	+	6.92820i	−0.261488	+	0.452911i
$235$		0			0
$236$	−12.0000	−	20.7846i	−0.781133	−	1.35296i
$237$	−10.0000			−0.649570
$238$	12.0000	+	10.3923i	0.777844	+	0.673633i
$239$	9.00000			0.582162			0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000			0.582162			0.291081	+	0.956698i	$0.405985\pi$
$240$	2.00000	+	3.46410i	0.129099	+	0.223607i
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.0766885	−	0.997055i	$-0.475565\pi$
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.825131	−	0.564942i	$-0.191101\pi$
$242$	−5.00000	+	8.66025i	−0.321412	+	0.556702i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	20.0000			1.28037
$245$	5.50000	−	4.33013i	0.351382	−	0.276642i
$246$	4.00000			0.255031
$247$	2.00000	+	3.46410i	0.127257	+	0.220416i
$248$		0			0
$249$	−1.50000	+	2.59808i	−0.0950586	+	0.164646i
$250$	9.00000	+	15.5885i	0.569210	+	0.985901i
$251$	−23.0000			−1.45175			−0.725874	−	0.687828i	$-0.758564\pi$
$251$	−23.0000			−1.45175			−0.725874	+	0.687828i	$0.758564\pi$
$252$	4.00000	+	3.46410i	0.251976	+	0.218218i
$253$	−12.0000			−0.754434
$254$	−12.0000	−	20.7846i	−0.752947	−	1.30414i
$255$	−1.50000	+	2.59808i	−0.0939336	+	0.162698i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	0.833150	−	0.553047i	$-0.186535\pi$
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	−0.895528	+	0.445005i	$0.853202\pi$
$258$	−14.0000			−0.871602
$259$	−3.00000	+	15.5885i	−0.186411	+	0.968620i
$260$	8.00000			0.496139
$261$	−5.00000	−	8.66025i	−0.309492	−	0.536056i
$262$	5.00000	−	8.66025i	0.308901	−	0.535032i
$263$	8.50000	−	14.7224i	0.524132	−	0.907824i	−0.475473	−	0.879730i	$-0.657723\pi$
$263$	8.50000	−	14.7224i	0.524132	−	0.907824i	0.999605	−	0.0280936i	$-0.00894366\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$	5.00000	−	1.73205i	0.306570	−	0.106199i
$267$	−14.0000			−0.856786
$268$	−10.0000	−	17.3205i	−0.610847	−	1.05802i
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$	−1.00000	+	1.73205i	−0.0608581	+	0.105409i
$271$	11.5000	+	19.9186i	0.698575	+	1.20997i	0.968960	+	0.247216i	$0.0795156\pi$
$271$	11.5000	+	19.9186i	0.698575	+	1.20997i	−0.270385	+	0.962752i	$0.587151\pi$
$272$	−12.0000			−0.727607
$273$	−10.0000	+	3.46410i	−0.605228	+	0.209657i
$274$	−36.0000			−2.17484
$275$	8.00000	+	13.8564i	0.482418	+	0.835573i
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	12.0000	+	20.7846i	0.719712	+	1.24658i
$279$		0			0
$280$		0			0
$281$	20.0000			1.19310			0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000			1.19310			0.596550	+	0.802576i	$0.296538\pi$
$282$		0			0
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	−0.880504	−	0.474039i	$-0.842796\pi$
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	0.850782	+	0.525519i	$0.176129\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$	0.500000	+	0.866025i	0.0296174	+	0.0512989i
$286$	32.0000			1.89220
$287$	4.00000	+	3.46410i	0.236113	+	0.204479i
$288$	−8.00000			−0.471405
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−10.0000	+	17.3205i	−0.587220	+	1.01710i
$291$	6.00000	−	10.3923i	0.351726	−	0.609208i
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	−16.0000			−0.934730			−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000			−0.934730			−0.467365	+	0.884064i	$0.654797\pi$
$294$	2.00000	+	13.8564i	0.116642	+	0.808122i
$295$	12.0000			0.698667
$296$		0			0
$297$	−2.00000	+	3.46410i	−0.116052	+	0.201008i
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$	−8.00000			−0.461880
$301$	−14.0000	−	12.1244i	−0.806947	−	0.698836i
$302$	−20.0000			−1.15087
$303$	−5.50000	−	9.52628i	−0.315967	−	0.547270i
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	−5.00000	+	8.66025i	−0.286299	+	0.495885i
$306$	−3.00000	−	5.19615i	−0.171499	−	0.297044i
$307$	22.0000			1.25561			0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$308$	4.00000	−	20.7846i	0.227921	−	1.18431i
$309$	8.00000			0.455104
$310$		0			0
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	−0.905416	−	0.424526i	$-0.860441\pi$
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	0.820358	+	0.571850i	$0.193774\pi$
$312$		0			0
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	0.667674	−	0.744453i	$-0.267290\pi$
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	−0.978553	+	0.205996i	$0.933957\pi$
$314$	2.00000			0.112867
$315$	−2.50000	+	0.866025i	−0.140859	+	0.0487950i
$316$	−20.0000			−1.12509
$317$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$317$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$318$	12.0000	−	20.7846i	0.672927	−	1.16554i
$319$	−20.0000	+	34.6410i	−1.11979	+	1.93952i
$320$	4.00000	+	6.92820i	0.223607	+	0.387298i
$321$	10.0000			0.558146
$322$	15.0000	−	5.19615i	0.835917	−	0.289570i
$323$	−3.00000			−0.166924
$324$	−1.00000	−	1.73205i	−0.0555556	−	0.0962250i
$325$	8.00000	−	13.8564i	0.443760	−	0.768615i
$326$	−19.0000	+	32.9090i	−1.05231	+	1.82266i
$327$	3.00000	+	5.19615i	0.165900	+	0.287348i
$328$		0			0
$329$		0			0
$330$	8.00000			0.440386
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	0.992112	+	0.125353i	$0.0400062\pi$
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	−0.387498	+	0.921871i	$0.626660\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	3.00000	−	5.19615i	0.164399	−	0.284747i
$334$	2.00000	+	3.46410i	0.109435	+	0.189547i
$335$	10.0000			0.546358
$336$	−8.00000	−	6.92820i	−0.436436	−	0.377964i
$337$	−8.00000			−0.435788			−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000			−0.435788			−0.217894	+	0.975972i	$0.569919\pi$
$338$	−3.00000	−	5.19615i	−0.163178	−	0.282633i
$339$	4.00000	−	6.92820i	0.217250	−	0.376288i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$		0			0
$342$	−2.00000			−0.108148
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	1.50000	+	2.59808i	0.0807573	+	0.139876i
$346$	−14.0000	+	24.2487i	−0.752645	+	1.30362i
$347$	−14.5000	+	25.1147i	−0.778401	+	1.34823i	0.154462	+	0.987999i	$0.450635\pi$
$347$	−14.5000	+	25.1147i	−0.778401	+	1.34823i	−0.932863	+	0.360231i	$0.882698\pi$
$348$	−10.0000	−	17.3205i	−0.536056	−	0.928477i
$349$	13.0000			0.695874			0.347937	−	0.937518i	$-0.386882\pi$
$349$	13.0000			0.695874			0.347937	+	0.937518i	$0.386882\pi$
$350$	−16.0000	−	13.8564i	−0.855236	−	0.740656i
$351$	4.00000			0.213504
$352$	16.0000	+	27.7128i	0.852803	+	1.47710i
$353$	13.0000	−	22.5167i	0.691920	−	1.19844i	−0.279288	−	0.960207i	$-0.590098\pi$
$353$	13.0000	−	22.5167i	0.691920	−	1.19844i	0.971208	−	0.238233i	$-0.0765683\pi$
$354$	−12.0000	+	20.7846i	−0.637793	+	1.10469i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	−28.0000			−1.48400
$357$	1.50000	−	7.79423i	0.0793884	−	0.412514i
$358$	−32.0000			−1.69125
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	14.0000	+	24.2487i	0.735824	+	1.27448i
$363$	5.00000			0.262432
$364$	−20.0000	+	6.92820i	−1.04828	+	0.363137i
$365$	6.00000			0.314054
$366$	−10.0000	−	17.3205i	−0.522708	−	0.905357i
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$	−6.00000	+	10.3923i	−0.312772	+	0.541736i
$369$	−1.00000	−	1.73205i	−0.0520579	−	0.0901670i
$370$	−12.0000			−0.623850
$371$	30.0000	−	10.3923i	1.55752	−	0.539542i
$372$		0			0
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	−0.899255	−	0.437425i	$-0.855891\pi$
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	0.0708063	−	0.997490i	$-0.477443\pi$
$374$	−12.0000	+	20.7846i	−0.620505	+	1.07475i
$375$	4.50000	−	7.79423i	0.232379	−	0.402492i
$376$		0			0
$377$	40.0000			2.06010
$378$	1.00000	−	5.19615i	0.0514344	−	0.267261i
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$	1.00000	+	1.73205i	0.0512989	+	0.0888523i
$381$	−6.00000	+	10.3923i	−0.307389	+	0.532414i
$382$	17.0000	−	29.4449i	0.869796	−	1.50653i
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$		0			0
$385$	8.00000	+	6.92820i	0.407718	+	0.353094i
$386$	−32.0000			−1.62876
$387$	3.50000	+	6.06218i	0.177915	+	0.308158i
$388$	12.0000	−	20.7846i	0.609208	−	1.05518i
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	−0.825491	−	0.564416i	$-0.809102\pi$
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$390$	−4.00000	−	6.92820i	−0.202548	−	0.350823i
$391$	−9.00000			−0.455150
$392$		0			0
$393$	−5.00000			−0.252217
$394$	11.0000	+	19.0526i	0.554172	+	0.959854i
$395$	5.00000	−	8.66025i	0.251577	−	0.435745i
$396$	−4.00000	+	6.92820i	−0.201008	+	0.348155i
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	0.990538	−	0.137241i	$-0.0438236\pi$
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	−0.614123	+	0.789210i	$0.710490\pi$
$398$	−54.0000			−2.70678
$399$	−2.00000	−	1.73205i	−0.100125	−	0.0867110i
$400$	16.0000			0.800000
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	0.976050	−	0.217545i	$-0.0698049\pi$
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	−0.676425	+	0.736512i	$0.736472\pi$
$402$	−10.0000	+	17.3205i	−0.498755	+	0.863868i
$403$		0			0
$404$	−11.0000	−	19.0526i	−0.547270	−	0.947900i
$405$	1.00000			0.0496904
$406$	10.0000	−	51.9615i	0.496292	−	2.57881i
$407$	−24.0000			−1.18964
$408$		0			0
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	0.134107	+	0.990967i	$0.457183\pi$
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	−0.925256	+	0.379344i	$0.876150\pi$
$410$	−2.00000	+	3.46410i	−0.0987730	+	0.171080i
$411$	9.00000	+	15.5885i	0.443937	+	0.768922i
$412$	16.0000			0.788263
$413$	−30.0000	+	10.3923i	−1.47620	+	0.511372i
$414$	−6.00000			−0.294884
$415$	−1.50000	−	2.59808i	−0.0736321	−	0.127535i
$416$	16.0000	−	27.7128i	0.784465	−	1.35873i
$417$	6.00000	−	10.3923i	0.293821	−	0.508913i
$418$	4.00000	+	6.92820i	0.195646	+	0.338869i
$419$	−9.00000			−0.439679			−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000			−0.439679			−0.219839	+	0.975536i	$0.570553\pi$
$420$	−5.00000	+	1.73205i	−0.243975	+	0.0845154i
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$		0			0
$424$		0			0
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$	12.0000			0.581402
$427$	5.00000	−	25.9808i	0.241967	−	1.25730i
$428$	20.0000			0.966736
$429$	−8.00000	−	13.8564i	−0.386244	−	0.668994i
$430$	7.00000	−	12.1244i	0.337570	−	0.584688i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	10.0000			0.479463
$436$	6.00000	+	10.3923i	0.287348	+	0.497701i
$437$	−1.50000	+	2.59808i	−0.0717547	+	0.124283i
$438$	−6.00000	+	10.3923i	−0.286691	+	0.496564i
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	−0.962607	−	0.270901i	$-0.912678\pi$
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	0.246696	−	0.969093i	$-0.420655\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$	24.0000			1.14156
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	0.999999	−	0.00130426i	$-0.000415158\pi$
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	−0.501129	+	0.865373i	$0.667082\pi$
$444$	6.00000	−	10.3923i	0.284747	−	0.493197i
$445$	7.00000	−	12.1244i	0.331832	−	0.574750i
$446$	−10.0000	−	17.3205i	−0.473514	−	0.820150i
$447$	−9.00000			−0.425685
$448$	−16.0000	−	13.8564i	−0.755929	−	0.654654i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	4.00000	+	6.92820i	0.188562	+	0.326599i
$451$	−4.00000	+	6.92820i	−0.188353	+	0.326236i
$452$	8.00000	−	13.8564i	0.376288	−	0.651751i
$453$	5.00000	+	8.66025i	0.234920	+	0.406894i
$454$		0			0
$455$	2.00000	−	10.3923i	0.0937614	−	0.487199i
$456$		0			0
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	−0.999857	−	0.0168929i	$-0.994623\pi$
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	0.485299	−	0.874348i	$-0.338711\pi$
$458$	7.00000	−	12.1244i	0.327089	−	0.566534i
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$	3.00000	+	5.19615i	0.139876	+	0.242272i
$461$	26.0000			1.21094			0.605470	−	0.795868i	$-0.292985\pi$
$461$	26.0000			1.21094			0.605470	+	0.795868i	$0.292985\pi$
$462$	−20.0000	+	6.92820i	−0.930484	+	0.322329i
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	20.0000	+	34.6410i	0.928477	+	1.60817i
$465$		0			0
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	−0.895696	−	0.444667i	$-0.853322\pi$
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	0.0627555	−	0.998029i	$-0.480011\pi$
$468$	8.00000			0.369800
$469$	−25.0000	+	8.66025i	−1.15439	+	0.399893i
$470$		0			0
$471$	−0.500000	−	0.866025i	−0.0230388	−	0.0399043i
$472$		0			0
$473$	14.0000	−	24.2487i	0.643721	−	1.11496i
$474$	10.0000	+	17.3205i	0.459315	+	0.795557i
$475$	4.00000			0.183533
$476$	3.00000	−	15.5885i	0.137505	−	0.714496i
$477$	−12.0000			−0.549442
$478$	−9.00000	−	15.5885i	−0.411650	−	0.712999i
$479$	−5.50000	+	9.52628i	−0.251301	+	0.435267i	−0.963884	−	0.266321i	$-0.914192\pi$
$479$	−5.50000	+	9.52628i	−0.251301	+	0.435267i	0.712583	+	0.701588i	$0.247525\pi$
$480$	4.00000	−	6.92820i	0.182574	−	0.316228i
$481$	12.0000	+	20.7846i	0.547153	+	0.947697i
$482$	−56.0000			−2.55073
$483$	−6.00000	−	5.19615i	−0.273009	−	0.236433i
$484$	10.0000			0.454545
$485$	6.00000	+	10.3923i	0.272446	+	0.471890i
$486$	−1.00000	+	1.73205i	−0.0453609	+	0.0785674i
$487$	16.0000	−	27.7128i	0.725029	−	1.25579i	−0.233933	−	0.972253i	$-0.575160\pi$
$487$	16.0000	−	27.7128i	0.725029	−	1.25579i	0.958962	−	0.283535i	$-0.0915071\pi$
$488$		0			0
$489$	19.0000			0.859210
$490$	−13.0000	−	5.19615i	−0.587280	−	0.234738i
$491$	−1.00000			−0.0451294			−0.0225647	−	0.999745i	$-0.507183\pi$
$491$	−1.00000			−0.0451294			−0.0225647	+	0.999745i	$0.507183\pi$
$492$	−2.00000	−	3.46410i	−0.0901670	−	0.156174i
$493$	−15.0000	+	25.9808i	−0.675566	+	1.17011i
$494$	4.00000	−	6.92820i	0.179969	−	0.311715i
$495$	−2.00000	−	3.46410i	−0.0898933	−	0.155700i
$496$		0			0
$497$	12.0000	+	10.3923i	0.538274	+	0.466159i
$498$	6.00000			0.268866
$499$	−3.50000	−	6.06218i	−0.156682	−	0.271380i	0.776989	−	0.629515i	$-0.216746\pi$
$499$	−3.50000	−	6.06218i	−0.156682	−	0.271380i	−0.933670	+	0.358134i	$0.883413\pi$
$500$	9.00000	−	15.5885i	0.402492	−	0.697137i
$501$	1.00000	−	1.73205i	0.0446767	−	0.0773823i
$502$	23.0000	+	39.8372i	1.02654	+	1.77802i
$503$	−3.00000			−0.133763			−0.0668817	−	0.997761i	$-0.521305\pi$
$503$	−3.00000			−0.133763			−0.0668817	+	0.997761i	$0.521305\pi$
$504$		0			0
$505$	11.0000			0.489494
$506$	12.0000	+	20.7846i	0.533465	+	0.923989i
$507$	−1.50000	+	2.59808i	−0.0666173	+	0.115385i
$508$	−12.0000	+	20.7846i	−0.532414	+	0.922168i
$509$	−19.0000	−	32.9090i	−0.842160	−	1.45866i	−0.888065	−	0.459718i	$-0.847950\pi$
$509$	−19.0000	−	32.9090i	−0.842160	−	1.45866i	0.0459045	−	0.998946i	$-0.485383\pi$
$510$	6.00000			0.265684
$511$	−15.0000	+	5.19615i	−0.663561	+	0.229864i
$512$	32.0000			1.41421
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$	−2.00000	+	3.46410i	−0.0882162	+	0.152795i
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$	7.00000	+	12.1244i	0.308158	+	0.533745i
$517$		0			0
$518$	30.0000	−	10.3923i	1.31812	−	0.456612i
$519$	14.0000			0.614532
$520$		0			0
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$	−10.0000	+	17.3205i	−0.437688	+	0.758098i
$523$	−20.0000	−	34.6410i	−0.874539	−	1.51475i	−0.857253	−	0.514895i	$-0.827831\pi$
$523$	−20.0000	−	34.6410i	−0.874539	−	1.51475i	−0.0172859	−	0.999851i	$-0.505503\pi$
$524$	−10.0000			−0.436852
$525$	−2.00000	+	10.3923i	−0.0872872	+	0.453557i
$526$	−34.0000			−1.48247
$527$		0			0
$528$	8.00000	−	13.8564i	0.348155	−	0.603023i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	12.0000	+	20.7846i	0.521247	+	0.902826i
$531$	12.0000			0.520756
$532$	−4.00000	−	3.46410i	−0.173422	−	0.150188i
$533$	8.00000			0.346518
$534$	14.0000	+	24.2487i	0.605839	+	1.04934i
$535$	−5.00000	+	8.66025i	−0.216169	+	0.374415i
$536$		0			0
$537$	8.00000	+	13.8564i	0.345225	+	0.597948i
$538$	−36.0000			−1.55207
$539$	−26.0000	−	10.3923i	−1.11990	−	0.447628i
$540$	2.00000			0.0860663
$541$	−17.5000	−	30.3109i	−0.752384	−	1.30317i	−0.946664	−	0.322221i	$-0.895571\pi$
$541$	−17.5000	−	30.3109i	−0.752384	−	1.30317i	0.194281	−	0.980946i	$-0.437763\pi$
$542$	23.0000	−	39.8372i	0.987935	−	1.71115i
$543$	7.00000	−	12.1244i	0.300399	−	0.520306i
$544$	12.0000	+	20.7846i	0.514496	+	0.891133i
$545$	−6.00000			−0.257012
$546$	16.0000	+	13.8564i	0.684737	+	0.592999i
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	18.0000	+	31.1769i	0.768922	+	1.33181i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$	16.0000	−	27.7128i	0.682242	−	1.18168i
$551$	5.00000	+	8.66025i	0.213007	+	0.368939i
$552$		0			0
$553$	−5.00000	+	25.9808i	−0.212622	+	1.10481i
$554$	44.0000			1.86938
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	12.0000	−	20.7846i	0.508913	−	0.881464i
$557$	−3.50000	+	6.06218i	−0.148300	+	0.256863i	−0.930599	−	0.366040i	$-0.880713\pi$
$557$	−3.50000	+	6.06218i	−0.148300	+	0.256863i	0.782299	+	0.622903i	$0.214047\pi$
$558$		0			0
$559$	−28.0000			−1.18427
$560$	10.0000	−	3.46410i	0.422577	−	0.146385i
$561$	12.0000			0.506640
$562$	−20.0000	−	34.6410i	−0.843649	−	1.46124i
$563$	−5.00000	+	8.66025i	−0.210725	+	0.364986i	−0.951942	−	0.306280i	$-0.900916\pi$
$563$	−5.00000	+	8.66025i	−0.210725	+	0.364986i	0.741217	+	0.671266i	$0.234249\pi$
$564$		0			0
$565$	4.00000	+	6.92820i	0.168281	+	0.291472i
$566$	2.00000			0.0840663
$567$	−2.50000	+	0.866025i	−0.104990	+	0.0363696i
$568$		0			0
$569$	10.0000	+	17.3205i	0.419222	+	0.726113i	0.995861	−	0.0908852i	$-0.0289696\pi$
$569$	10.0000	+	17.3205i	0.419222	+	0.726113i	−0.576640	+	0.816999i	$0.695636\pi$
$570$	1.00000	−	1.73205i	0.0418854	−	0.0725476i
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	−0.913584	−	0.406651i	$-0.866697\pi$
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	0.808962	+	0.587861i	$0.200030\pi$
$572$	−16.0000	−	27.7128i	−0.668994	−	1.15873i
$573$	−17.0000			−0.710185
$574$	2.00000	−	10.3923i	0.0834784	−	0.433766i
$575$	12.0000			0.500435
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	−0.844459	−	0.535620i	$-0.820078\pi$
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	0.886090	+	0.463513i	$0.153411\pi$
$578$	8.00000	−	13.8564i	0.332756	−	0.576351i
$579$	8.00000	+	13.8564i	0.332469	+	0.575853i
$580$	20.0000			0.830455
$581$	6.00000	+	5.19615i	0.248922	+	0.215573i
$582$	−24.0000			−0.994832
$583$	24.0000	+	41.5692i	0.993978	+	1.72162i
$584$		0			0
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$	16.0000	+	27.7128i	0.660954	+	1.14481i
$587$	7.00000			0.288921			0.144460	−	0.989511i	$-0.453855\pi$
$587$	7.00000			0.288921			0.144460	+	0.989511i	$0.453855\pi$
$588$	11.0000	−	8.66025i	0.453632	−	0.357143i
$589$		0			0
$590$	−12.0000	−	20.7846i	−0.494032	−	0.855689i
$591$	5.50000	−	9.52628i	0.226240	−	0.391859i
$592$	−12.0000	+	20.7846i	−0.493197	+	0.854242i
$593$	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	$0.537758\pi$
$594$	8.00000			0.328244
$595$	6.00000	+	5.19615i	0.245976	+	0.213021i
$596$	−18.0000			−0.737309
$597$	13.5000	+	23.3827i	0.552518	+	0.956990i
$598$	12.0000	−	20.7846i	0.490716	−	0.849946i
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	−30.0000			−1.22373			−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000			−1.22373			−0.611863	+	0.790964i	$0.709580\pi$
$602$	−7.00000	+	36.3731i	−0.285299	+	1.48246i
$603$	10.0000			0.407231
$604$	10.0000	+	17.3205i	0.406894	+	0.704761i
$605$	−2.50000	+	4.33013i	−0.101639	+	0.176045i
$606$	−11.0000	+	19.0526i	−0.446844	+	0.773957i
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	8.00000			0.324443
$609$	−25.0000	+	8.66025i	−1.01305	+	0.350931i
$610$	20.0000			0.809776
$611$		0			0
$612$	−3.00000	+	5.19615i	−0.121268	+	0.210042i
$613$	−12.5000	+	21.6506i	−0.504870	+	0.874461i	0.495114	+	0.868828i	$0.335126\pi$
$613$	−12.5000	+	21.6506i	−0.504870	+	0.874461i	−0.999984	+	0.00563283i	$0.998207\pi$
$614$	−22.0000	−	38.1051i	−0.887848	−	1.53780i
$615$	2.00000			0.0806478
$616$		0			0
$617$	27.0000			1.08698			0.543490	−	0.839416i	$-0.317103\pi$
$617$	27.0000			1.08698			0.543490	+	0.839416i	$0.317103\pi$
$618$	−8.00000	−	13.8564i	−0.321807	−	0.557386i
$619$	17.5000	−	30.3109i	0.703384	−	1.21830i	−0.263887	−	0.964554i	$-0.585005\pi$
$619$	17.5000	−	30.3109i	0.703384	−	1.21830i	0.967271	−	0.253744i	$-0.0816620\pi$
$620$		0			0
$621$	1.50000	+	2.59808i	0.0601929	+	0.104257i
$622$	6.00000			0.240578
$623$	−7.00000	+	36.3731i	−0.280449	+	1.45726i
$624$	−16.0000			−0.640513
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−11.0000	+	19.0526i	−0.439648	+	0.761493i
$627$	2.00000	−	3.46410i	0.0798723	−	0.138343i
$628$	−1.00000	−	1.73205i	−0.0399043	−	0.0691164i
$629$	−18.0000			−0.717707
$630$	4.00000	+	3.46410i	0.159364	+	0.138013i
$631$	5.00000			0.199047			0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000			0.199047			0.0995234	+	0.995035i	$0.468268\pi$
$632$		0			0
$633$	−2.00000	+	3.46410i	−0.0794929	+	0.137686i
$634$		0			0
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$	−24.0000			−0.951662
$637$	4.00000	+	27.7128i	0.158486	+	1.09802i
$638$	80.0000			3.16723
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−10.0000	−	17.3205i	−0.394669	−	0.683586i
$643$	11.0000			0.433798			0.216899	−	0.976194i	$-0.430406\pi$
$643$	11.0000			0.433798			0.216899	+	0.976194i	$0.430406\pi$
$644$	−12.0000	−	10.3923i	−0.472866	−	0.409514i
$645$	−7.00000			−0.275625
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	−11.5000	+	19.9186i	−0.452112	+	0.783080i	−0.998517	−	0.0544405i	$-0.982662\pi$
$647$	−11.5000	+	19.9186i	−0.452112	+	0.783080i	0.546405	+	0.837521i	$0.315996\pi$
$648$		0			0
$649$	−24.0000	−	41.5692i	−0.942082	−	1.63173i
$650$	−32.0000			−1.25514
$651$		0			0
$652$	38.0000			1.48819
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	0.994988	−	0.0999939i	$-0.0318823\pi$
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	−0.584091	+	0.811688i	$0.698549\pi$
$654$	6.00000	−	10.3923i	0.234619	−	0.406371i
$655$	2.50000	−	4.33013i	0.0976831	−	0.169192i
$656$	4.00000	+	6.92820i	0.156174	+	0.270501i
$657$	6.00000			0.234082
$658$		0			0
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$	−4.00000	−	6.92820i	−0.155700	−	0.269680i
$661$	−20.0000	+	34.6410i	−0.777910	+	1.34738i	0.155235	+	0.987878i	$0.450387\pi$
$661$	−20.0000	+	34.6410i	−0.777910	+	1.34738i	−0.933144	+	0.359502i	$0.882947\pi$
$662$	22.0000	−	38.1051i	0.855054	−	1.48100i
$663$	−6.00000	−	10.3923i	−0.233021	−	0.403604i
$664$		0			0
$665$	2.50000	−	0.866025i	0.0969458	−	0.0335830i
$666$	−12.0000			−0.464991
$667$	15.0000	+	25.9808i	0.580802	+	1.00598i
$668$	2.00000	−	3.46410i	0.0773823	−	0.134030i
$669$	−5.00000	+	8.66025i	−0.193311	+	0.334825i
$670$	−10.0000	−	17.3205i	−0.386334	−	0.669150i
$671$	40.0000			1.54418
$672$	−4.00000	+	20.7846i	−0.154303	+	0.801784i
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$	8.00000	+	13.8564i	0.308148	+	0.533729i
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$	−3.00000	+	5.19615i	−0.115385	+	0.199852i
$677$	−15.0000	−	25.9808i	−0.576497	−	0.998522i	−0.995877	−	0.0907112i	$-0.971086\pi$
$677$	−15.0000	−	25.9808i	−0.576497	−	0.998522i	0.419380	−	0.907811i	$-0.362247\pi$
$678$	−16.0000			−0.614476
$679$	−24.0000	−	20.7846i	−0.921035	−	0.797640i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	−0.283491	−	0.958975i	$-0.591493\pi$
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	0.972242	−	0.233977i	$-0.0751739\pi$
$684$	1.00000	+	1.73205i	0.0382360	+	0.0662266i
$685$	−18.0000			−0.687745
$686$	37.0000	+	1.73205i	1.41267	+	0.0661300i
$687$	−7.00000			−0.267067
$688$	−14.0000	−	24.2487i	−0.533745	−	0.924473i
$689$	24.0000	−	41.5692i	0.914327	−	1.58366i
$690$	3.00000	−	5.19615i	0.114208	−	0.197814i
$691$	−20.5000	−	35.5070i	−0.779857	−	1.35075i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−20.5000	−	35.5070i	−0.779857	−	1.35075i	0.152167	−	0.988355i	$-0.451375\pi$
$692$	28.0000			1.06440
$693$	8.00000	+	6.92820i	0.303895	+	0.263181i
$694$	58.0000			2.20165
$695$	6.00000	+	10.3923i	0.227593	+	0.394203i
$696$		0			0
$697$	−3.00000	+	5.19615i	−0.113633	+	0.196818i
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$	9.00000			0.340411
$700$	−4.00000	+	20.7846i	−0.151186	+	0.785584i
$701$	−21.0000			−0.793159			−0.396580	−	0.918000i	$-0.629803\pi$
$701$	−21.0000			−0.793159			−0.396580	+	0.918000i	$0.629803\pi$
$702$	−4.00000	−	6.92820i	−0.150970	−	0.261488i
$703$	−3.00000	+	5.19615i	−0.113147	+	0.195977i
$704$	16.0000	−	27.7128i	0.603023	−	1.04447i
$705$		0			0
$706$	−52.0000			−1.95705
$707$	−27.5000	+	9.52628i	−1.03424	+	0.358273i
$708$	24.0000			0.901975
$709$	−10.5000	−	18.1865i	−0.394336	−	0.683010i	0.598680	−	0.800988i	$-0.295692\pi$
$709$	−10.5000	−	18.1865i	−0.394336	−	0.683010i	−0.993016	+	0.117978i	$0.962359\pi$
$710$	−6.00000	+	10.3923i	−0.225176	+	0.390016i
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$		0			0
$713$		0			0
$714$	−15.0000	+	5.19615i	−0.561361	+	0.194461i
$715$	16.0000			0.598366
$716$	16.0000	+	27.7128i	0.597948	+	1.03568i
$717$	−4.50000	+	7.79423i	−0.168056	+	0.291081i
$718$	−20.0000	+	34.6410i	−0.746393	+	1.29279i
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	0.601075	−	0.799193i	$-0.294739\pi$
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	−0.992659	+	0.120950i	$0.961406\pi$
$720$	−4.00000			−0.149071
$721$	4.00000	−	20.7846i	0.148968	−	0.774059i
$722$	2.00000			0.0744323
$723$	14.0000	+	24.2487i	0.520666	+	0.901819i
$724$	14.0000	−	24.2487i	0.520306	−	0.901196i
$725$	20.0000	−	34.6410i	0.742781	−	1.28654i
$726$	−5.00000	−	8.66025i	−0.185567	−	0.321412i
$727$	47.0000			1.74313			0.871567	−	0.490277i	$-0.163104\pi$
$727$	47.0000			1.74313			0.871567	+	0.490277i	$0.163104\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−6.00000	−	10.3923i	−0.222070	−	0.384636i
$731$	10.5000	−	18.1865i	0.388357	−	0.672653i
$732$	−10.0000	+	17.3205i	−0.369611	+	0.640184i
$733$	15.0000	+	25.9808i	0.554038	+	0.959621i	0.997978	+	0.0635649i	$0.0202470\pi$
$733$	15.0000	+	25.9808i	0.554038	+	0.959621i	−0.443940	+	0.896056i	$0.646420\pi$
$734$		0			0
$735$	1.00000	+	6.92820i	0.0368856	+	0.255551i
$736$	24.0000			0.884652
$737$	−20.0000	−	34.6410i	−0.736709	−	1.27602i
$738$	−2.00000	+	3.46410i	−0.0736210	+	0.127515i
$739$	−25.5000	+	44.1673i	−0.938033	+	1.62472i	−0.168898	+	0.985634i	$0.554021\pi$
$739$	−25.5000	+	44.1673i	−0.938033	+	1.62472i	−0.769135	+	0.639087i	$0.779313\pi$
$740$	6.00000	+	10.3923i	0.220564	+	0.382029i
$741$	−4.00000			−0.146944
$742$	−48.0000	−	41.5692i	−1.76214	−	1.52605i
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	4.50000	−	7.79423i	0.164867	−	0.285558i
$746$	−32.0000	+	55.4256i	−1.17160	+	2.02928i
$747$	−1.50000	−	2.59808i	−0.0548821	−	0.0950586i
$748$	24.0000			0.877527
$749$	5.00000	−	25.9808i	0.182696	−	0.949316i
$750$	−18.0000			−0.657267
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	0.965013	−	0.262201i	$-0.0844484\pi$
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	−0.709580	+	0.704625i	$0.751115\pi$
$752$		0			0
$753$	11.5000	−	19.9186i	0.419083	−	0.725874i
$754$	−40.0000	−	69.2820i	−1.45671	−	2.52310i
$755$	−10.0000			−0.363937
$756$	−5.00000	+	1.73205i	−0.181848	+	0.0629941i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−12.0000	−	20.7846i	−0.435860	−	0.754931i
$759$	6.00000	−	10.3923i	0.217786	−	0.377217i
$760$		0			0
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	0.991152	−	0.132734i	$-0.0423756\pi$
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	−0.610527	+	0.791995i	$0.709042\pi$
$762$	24.0000			0.869428
$763$	15.0000	−	5.19615i	0.543036	−	0.188113i
$764$	−34.0000			−1.23008
$765$	−1.50000	−	2.59808i	−0.0542326	−	0.0939336i
$766$	−12.0000	+	20.7846i	−0.433578	+	0.750978i
$767$	−24.0000	+	41.5692i	−0.866590	+	1.50098i
$768$	−8.00000	−	13.8564i	−0.288675	−	0.500000i
$769$	−37.0000			−1.33425			−0.667127	−	0.744944i	$-0.732476\pi$
$769$	−37.0000			−1.33425			−0.667127	+	0.744944i	$0.732476\pi$
$770$	4.00000	−	20.7846i	0.144150	−	0.749025i
$771$	2.00000			0.0720282
$772$	16.0000	+	27.7128i	0.575853	+	0.997406i
$773$	14.0000	−	24.2487i	0.503545	−	0.872166i	−0.496447	−	0.868067i	$-0.665362\pi$
$773$	14.0000	−	24.2487i	0.503545	−	0.872166i	0.999992	−	0.00409826i	$-0.00130452\pi$
$774$	7.00000	−	12.1244i	0.251610	−	0.435801i
$775$		0			0
$776$		0			0
$777$	−12.0000	−	10.3923i	−0.430498	−	0.372822i
$778$	−6.00000			−0.215110
$779$	1.00000	+	1.73205i	0.0358287	+	0.0620572i
$780$	−4.00000	+	6.92820i	−0.143223	+	0.248069i
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$	9.00000	+	15.5885i	0.321839	+	0.557442i
$783$	10.0000			0.357371
$784$	−22.0000	+	17.3205i	−0.785714	+	0.618590i
$785$	1.00000			0.0356915
$786$	5.00000	+	8.66025i	0.178344	+	0.308901i
$787$	−23.0000	+	39.8372i	−0.819861	+	1.42004i	0.0859225	+	0.996302i	$0.472616\pi$
$787$	−23.0000	+	39.8372i	−0.819861	+	1.42004i	−0.905784	+	0.423740i	$0.860717\pi$
$788$	11.0000	−	19.0526i	0.391859	−	0.678719i
$789$	8.50000	+	14.7224i	0.302608	+	0.524132i
$790$	−20.0000			−0.711568
$791$	−16.0000	−	13.8564i	−0.568895	−	0.492677i
$792$		0			0
$793$	−20.0000	−	34.6410i	−0.710221	−	1.23014i
$794$	15.0000	−	25.9808i	0.532330	−	0.922023i
$795$	6.00000	−	10.3923i	0.212798	−	0.368577i
$796$	27.0000	+	46.7654i	0.956990	+	1.65755i
$797$	4.00000			0.141687			0.0708436	−	0.997487i	$-0.477431\pi$
$797$	4.00000			0.141687			0.0708436	+	0.997487i	$0.477431\pi$
$798$	−1.00000	+	5.19615i	−0.0353996	+	0.183942i
$799$		0			0
$800$	−16.0000	−	27.7128i	−0.565685	−	0.979796i
$801$	7.00000	−	12.1244i	0.247333	−	0.428393i
$802$	12.0000	−	20.7846i	0.423735	−	0.733930i
$803$	−12.0000	−	20.7846i	−0.423471	−	0.733473i
$804$	20.0000			0.705346
$805$	7.50000	−	2.59808i	0.264340	−	0.0915702i
$806$		0			0
$807$	9.00000	+	15.5885i	0.316815	+	0.548740i
$808$		0			0
$809$	13.5000	−	23.3827i	0.474635	−	0.822091i	−0.524943	−	0.851137i	$-0.675914\pi$
$809$	13.5000	−	23.3827i	0.474635	−	0.822091i	0.999578	+	0.0290457i	$0.00924684\pi$
$810$	−1.00000	−	1.73205i	−0.0351364	−	0.0608581i
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	−50.0000	+	17.3205i	−1.75466	+	0.607831i
$813$	−23.0000			−0.806645
$814$	24.0000	+	41.5692i	0.841200	+	1.45700i
$815$	−9.50000	+	16.4545i	−0.332770	+	0.576375i
$816$	6.00000	−	10.3923i	0.210042	−	0.363803i
$817$	−3.50000	−	6.06218i	−0.122449	−	0.212089i
$818$	64.0000			2.23771
$819$	2.00000	−	10.3923i	0.0698857	−	0.363137i
$820$	4.00000			0.139686
$821$	5.00000	+	8.66025i	0.174501	+	0.302245i	0.939989	−	0.341206i	$-0.110835\pi$
$821$	5.00000	+	8.66025i	0.174501	+	0.302245i	−0.765487	+	0.643451i	$0.777502\pi$
$822$	18.0000	−	31.1769i	0.627822	−	1.08742i
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$		0			0
$825$	−16.0000			−0.557048
$826$	48.0000	+	41.5692i	1.67013	+	1.44638i
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$	3.00000	+	5.19615i	0.104257	+	0.180579i
$829$	26.0000	−	45.0333i	0.903017	−	1.56407i	0.0794606	−	0.996838i	$-0.474680\pi$
$829$	26.0000	−	45.0333i	0.903017	−	1.56407i	0.823557	−	0.567234i	$-0.191986\pi$
$830$	−3.00000	+	5.19615i	−0.104132	+	0.180361i
$831$	−11.0000	−	19.0526i	−0.381586	−	0.660926i
$832$	−32.0000			−1.10940
$833$	−19.5000	−	7.79423i	−0.675635	−	0.270054i
$834$	−24.0000			−0.831052
$835$	1.00000	+	1.73205i	0.0346064	+	0.0599401i
$836$	4.00000	−	6.92820i	0.138343	−	0.239617i
$837$		0			0
$838$	9.00000	+	15.5885i	0.310900	+	0.538494i
$839$	−56.0000			−1.93333			−0.966667	−	0.256036i	$-0.917584\pi$
$839$	−56.0000			−1.93333			−0.966667	+	0.256036i	$0.917584\pi$
$840$		0			0
$841$	71.0000			2.44828
$842$	−8.00000	−	13.8564i	−0.275698	−	0.477523i
$843$	−10.0000	+	17.3205i	−0.344418	+	0.596550i
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	−1.50000	−	2.59808i	−0.0516016	−	0.0893765i
$846$		0			0
$847$	2.50000	−	12.9904i	0.0859010	−	0.446355i
$848$	48.0000			1.64833
$849$	−0.500000	−	0.866025i	−0.0171600	−	0.0297219i
$850$	12.0000	−	20.7846i	0.411597	−	0.712906i
$851$	−9.00000	+	15.5885i	−0.308516	+	0.534365i
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$	−37.0000			−1.26686			−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000			−1.26686			−0.633428	+	0.773802i	$0.718353\pi$
$854$	−50.0000	+	17.3205i	−1.71096	+	0.592696i
$855$	−1.00000			−0.0341993
$856$		0			0
$857$	−20.0000	+	34.6410i	−0.683187	+	1.18331i	0.290816	+	0.956779i	$0.406073\pi$
$857$	−20.0000	+	34.6410i	−0.683187	+	1.18331i	−0.974003	+	0.226536i	$0.927260\pi$
$858$	−16.0000	+	27.7128i	−0.546231	+	0.946100i
$859$	−8.50000	−	14.7224i	−0.290016	−	0.502323i	0.683797	−	0.729672i	$-0.260327\pi$
$859$	−8.50000	−	14.7224i	−0.290016	−	0.502323i	−0.973813	+	0.227349i	$0.926994\pi$
$860$	−14.0000			−0.477396
$861$	−5.00000	+	1.73205i	−0.170400	+	0.0590281i
$862$	−24.0000			−0.817443
$863$	6.00000	+	10.3923i	0.204242	+	0.353758i	0.949891	−	0.312581i	$-0.101194\pi$
$863$	6.00000	+	10.3923i	0.204242	+	0.353758i	−0.745649	+	0.666339i	$0.767860\pi$
$864$	4.00000	−	6.92820i	0.136083	−	0.235702i
$865$	−7.00000	+	12.1244i	−0.238007	+	0.412240i
$866$	14.0000	+	24.2487i	0.475739	+	0.824005i
$867$	−8.00000			−0.271694
$868$		0			0
$869$	−40.0000			−1.35691
$870$	−10.0000	−	17.3205i	−0.339032	−	0.587220i
$871$	−20.0000	+	34.6410i	−0.677674	+	1.17377i
$872$		0			0
$873$	6.00000	+	10.3923i	0.203069	+	0.351726i
$874$	6.00000			0.202953
$875$	−18.0000	−	15.5885i	−0.608511	−	0.526986i
$876$	12.0000			0.405442
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$	−30.0000	+	51.9615i	−1.01245	+	1.75362i
$879$	8.00000	−	13.8564i	0.269833	−	0.467365i
$880$	8.00000	+	13.8564i	0.269680	+	0.467099i
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$	−13.0000	−	5.19615i	−0.437733	−	0.174964i
$883$	47.0000			1.58168			0.790838	−	0.612026i	$-0.209645\pi$
$883$	47.0000			1.58168			0.790838	+	0.612026i	$0.209645\pi$
$884$	−12.0000	−	20.7846i	−0.403604	−	0.699062i
$885$	−6.00000	+	10.3923i	−0.201688	+	0.349334i
$886$	21.0000	−	36.3731i	0.705509	−	1.22198i
$887$	−7.00000	−	12.1244i	−0.235037	−	0.407096i	0.724246	−	0.689541i	$-0.242188\pi$
$887$	−7.00000	−	12.1244i	−0.235037	−	0.407096i	−0.959283	+	0.282445i	$0.908854\pi$
$888$		0			0
$889$	24.0000	+	20.7846i	0.804934	+	0.697093i
$890$	−28.0000			−0.938562
$891$	−2.00000	−	3.46410i	−0.0670025	−	0.116052i
$892$	−10.0000	+	17.3205i	−0.334825	+	0.579934i
$893$		0			0
$894$	9.00000	+	15.5885i	0.301005	+	0.521356i
$895$	−16.0000			−0.534821
$896$		0			0
$897$	−12.0000			−0.400668
$898$	−6.00000	−	10.3923i	−0.200223	−	0.346796i
$899$		0			0
$900$	4.00000	−	6.92820i	0.133333	−	0.230940i
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$	16.0000			0.532742
$903$	17.5000	−	6.06218i	0.582364	−	0.201737i
$904$		0			0
$905$	7.00000	+	12.1244i	0.232688	+	0.403027i
$906$	10.0000	−	17.3205i	0.332228	−	0.575435i
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	−0.982913	−	0.184073i	$-0.941072\pi$
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	0.650868	+	0.759191i	$0.274405\pi$
$908$		0			0
$909$	11.0000			0.364847
$910$	−20.0000	+	6.92820i	−0.662994	+	0.229668i
$911$	−42.0000			−1.39152			−0.695761	−	0.718273i	$-0.744933\pi$
$911$	−42.0000			−1.39152			−0.695761	+	0.718273i	$0.744933\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$	−22.0000	+	38.1051i	−0.727695	+	1.26041i
$915$	−5.00000	−	8.66025i	−0.165295	−	0.286299i
$916$	−14.0000			−0.462573
$917$	−2.50000	+	12.9904i	−0.0825573	+	0.428980i
$918$	6.00000			0.198030
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	0.917961	−	0.396670i	$-0.129834\pi$
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	−0.802507	+	0.596643i	$0.796501\pi$
$920$		0			0
$921$	−11.0000	+	19.0526i	−0.362462	+	0.627803i
$922$	−26.0000	−	45.0333i	−0.856264	−	1.48309i
$923$	24.0000			0.789970
$924$	16.0000	+	13.8564i	0.526361	+	0.455842i
$925$	24.0000			0.789115
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$	−4.00000	+	6.92820i	−0.131377	+	0.227552i
$928$	40.0000	−	69.2820i	1.31306	−	2.27429i
$929$	27.5000	+	47.6314i	0.902246	+	1.56274i	0.824572	+	0.565757i	$0.191416\pi$
$929$	27.5000	+	47.6314i	0.902246	+	1.56274i	0.0776734	+	0.996979i	$0.475251\pi$
$930$		0			0
$931$	−5.50000	+	4.33013i	−0.180255	+	0.141914i
$932$	18.0000			0.589610
$933$	−1.50000	−	2.59808i	−0.0491078	−	0.0850572i
$934$	−36.0000	+	62.3538i	−1.17796	+	2.04028i
$935$	−6.00000	+	10.3923i	−0.196221	+	0.339865i
$936$		0			0
$937$	57.0000			1.86211			0.931054	−	0.364880i	$-0.118890\pi$
$937$	57.0000			1.86211			0.931054	+	0.364880i	$0.118890\pi$
$938$	40.0000	+	34.6410i	1.30605	+	1.13107i
$939$	11.0000			0.358971
$940$		0			0
$941$	−10.0000	+	17.3205i	−0.325991	+	0.564632i	−0.981712	−	0.190370i	$-0.939031\pi$
$941$	−10.0000	+	17.3205i	−0.325991	+	0.564632i	0.655722	+	0.755003i	$0.272364\pi$
$942$	−1.00000	+	1.73205i	−0.0325818	+	0.0564333i
$943$	3.00000	+	5.19615i	0.0976934	+	0.169210i
$944$	−48.0000			−1.56227
$945$	0.500000	−	2.59808i	0.0162650	−	0.0845154i
$946$	−56.0000			−1.82072
$947$	14.0000	+	24.2487i	0.454939	+	0.787977i	0.998685	−	0.0512727i	$-0.0163278\pi$
$947$	14.0000	+	24.2487i	0.454939	+	0.787977i	−0.543746	+	0.839250i	$0.682994\pi$
$948$	10.0000	−	17.3205i	0.324785	−	0.562544i
$949$	−12.0000	+	20.7846i	−0.389536	+	0.674697i
$950$	−4.00000	−	6.92820i	−0.129777	−	0.224781i
$951$		0			0
$952$		0			0
$953$	−34.0000			−1.10137			−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000			−1.10137			−0.550684	+	0.834714i	$0.685633\pi$
$954$	12.0000	+	20.7846i	0.388514	+	0.672927i
$955$	8.50000	−	14.7224i	0.275054	−	0.476407i
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$	−20.0000	−	34.6410i	−0.646508	−	1.11979i
$958$	22.0000			0.710788
$959$	45.0000	−	15.5885i	1.45313	−	0.503378i
$960$	−8.00000			−0.258199
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	24.0000	−	41.5692i	0.773791	−	1.34025i
$963$	−5.00000	+	8.66025i	−0.161123	+	0.279073i
$964$	28.0000	+	48.4974i	0.901819	+	1.56200i
$965$	−16.0000			−0.515058
$966$	−3.00000	+	15.5885i	−0.0965234	+	0.501550i
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$		0			0
$969$	1.50000	−	2.59808i	0.0481869	−	0.0834622i
$970$	12.0000	−	20.7846i	0.385297	−	0.667354i
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$	2.00000			0.0641500
$973$	−24.0000	−	20.7846i	−0.769405	−	0.666324i
$974$	−64.0000			−2.05069
$975$	8.00000	+	13.8564i	0.256205	+	0.443760i
$976$	20.0000	−	34.6410i	0.640184	−	1.10883i
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$	−19.0000	−	32.9090i	−0.607553	−	1.05231i
$979$	−56.0000			−1.78977
$980$	2.00000	+	13.8564i	0.0638877	+	0.442627i
$981$	−6.00000			−0.191565
$982$	1.00000	+	1.73205i	0.0319113	+	0.0552720i
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	−0.991453	−	0.130465i	$-0.958353\pi$
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	0.608712	+	0.793391i	$0.291686\pi$
$984$		0			0
$985$	5.50000	+	9.52628i	0.175245	+	0.303533i
$986$	60.0000			1.91079
$987$		0			0
$988$	−8.00000			−0.254514
$989$	−10.5000	−	18.1865i	−0.333881	−	0.578298i
$990$	−4.00000	+	6.92820i	−0.127128	+	0.220193i
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$		0			0
$993$	−22.0000			−0.698149
$994$	6.00000	−	31.1769i	0.190308	−	0.988872i
$995$	−27.0000			−0.855958
$996$	−3.00000	−	5.19615i	−0.0950586	−	0.164646i
$997$	−12.5000	+	21.6506i	−0.395879	+	0.685682i	−0.993213	−	0.116310i	$-0.962893\pi$
$997$	−12.5000	+	21.6506i	−0.395879	+	0.685682i	0.597334	+	0.801993i	$0.296227\pi$
$998$	−7.00000	+	12.1244i	−0.221581	+	0.383790i
$999$	3.00000	+	5.19615i	0.0949158	+	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.j.a.172.1	yes	2
3.2	odd	2		1197.2.j.b.172.1		2
7.2	even	3	inner	399.2.j.a.58.1	✓	2
7.3	odd	6		2793.2.a.k.1.1		1
7.4	even	3		2793.2.a.l.1.1		1
21.2	odd	6		1197.2.j.b.856.1		2
21.11	odd	6		8379.2.a.b.1.1		1
21.17	even	6		8379.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.a.58.1	✓	2	7.2	even	3	inner
399.2.j.a.172.1	yes	2	1.1	even	1	trivial
1197.2.j.b.172.1		2	3.2	odd	2
1197.2.j.b.856.1		2	21.2	odd	6
2793.2.a.k.1.1		1	7.3	odd	6
2793.2.a.l.1.1		1	7.4	even	3
8379.2.a.b.1.1		1	21.11	odd	6
8379.2.a.c.1.1		1	21.17	even	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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-2.00000 + 3.46410i) q^{11} +(-1.00000 - 1.73205i) q^{12} +4.00000 q^{13} +(1.00000 - 5.19615i) q^{14} +1.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{18} +(0.500000 + 0.866025i) q^{19} +2.00000 q^{20} +(-2.50000 + 0.866025i) q^{21} +8.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-4.00000 - 6.92820i) q^{26} +1.00000 q^{27} +(-5.00000 + 1.73205i) q^{28} +10.0000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(4.00000 - 6.92820i) q^{32} +(-2.00000 - 3.46410i) q^{33} +6.00000 q^{34} +(0.500000 - 2.59808i) q^{35} +2.00000 q^{36} +(3.00000 + 5.19615i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-2.00000 + 3.46410i) q^{39} +2.00000 q^{41} +(4.00000 + 3.46410i) q^{42} -7.00000 q^{43} +(-4.00000 - 6.92820i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{46} -4.00000 q^{48} +(1.00000 + 6.92820i) q^{49} -8.00000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(-4.00000 + 6.92820i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-1.00000 - 1.73205i) q^{54} +4.00000 q^{55} -1.00000 q^{57} +(-10.0000 - 17.3205i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(-5.00000 - 8.66025i) q^{61} +(0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-4.00000 + 6.92820i) q^{66} +(-5.00000 + 8.66025i) q^{67} +(-3.00000 - 5.19615i) q^{68} -3.00000 q^{69} +(-5.00000 + 1.73205i) q^{70} +6.00000 q^{71} +(-3.00000 + 5.19615i) q^{73} +(6.00000 - 10.3923i) q^{74} +(2.00000 + 3.46410i) q^{75} -2.00000 q^{76} +(-10.0000 + 3.46410i) q^{77} +8.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.00000 - 3.46410i) q^{82} +3.00000 q^{83} +(1.00000 - 5.19615i) q^{84} +3.00000 q^{85} +(7.00000 + 12.1244i) q^{86} +(-5.00000 + 8.66025i) q^{87} +(7.00000 + 12.1244i) q^{89} +2.00000 q^{90} +(8.00000 + 6.92820i) q^{91} -6.00000 q^{92} +(0.500000 - 0.866025i) q^{95} +(4.00000 + 6.92820i) q^{96} -12.0000 q^{97} +(11.0000 - 8.66025i) q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 4 q^{6} + 4 q^{7} - q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 8 q^{13} + 2 q^{14} + 2 q^{15} + 4 q^{16} - 3 q^{17} - 2 q^{18} + q^{19} + 4 q^{20} - 5 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 - 2 * q^4 - q^5 + 4 * q^6 + 4 * q^7 - q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 + 8 * q^13 + 2 * q^14 + 2 * q^15 + 4 * q^16 - 3 * q^17 - 2 * q^18 + q^19 + 4 * q^20 - 5 * q^21 + 16 * q^22 + 3 * q^23 + 4 * q^25 - 8 * q^26 + 2 * q^27 - 10 * q^28 + 20 * q^29 - 2 * q^30 + 8 * q^32 - 4 * q^33 + 12 * q^34 + q^35 + 4 * q^36 + 6 * q^37 + 2 * q^38 - 4 * q^39 + 4 * q^41 + 8 * q^42 - 14 * q^43 - 8 * q^44 - q^45 + 6 * q^46 - 8 * q^48 + 2 * q^49 - 16 * q^50 - 3 * q^51 - 8 * q^52 + 12 * q^53 - 2 * q^54 + 8 * q^55 - 2 * q^57 - 20 * q^58 - 12 * q^59 - 2 * q^60 - 10 * q^61 + q^63 - 16 * q^64 - 4 * q^65 - 8 * q^66 - 10 * q^67 - 6 * q^68 - 6 * q^69 - 10 * q^70 + 12 * q^71 - 6 * q^73 + 12 * q^74 + 4 * q^75 - 4 * q^76 - 20 * q^77 + 16 * q^78 + 10 * q^79 + 4 * q^80 - q^81 - 4 * q^82 + 6 * q^83 + 2 * q^84 + 6 * q^85 + 14 * q^86 - 10 * q^87 + 14 * q^89 + 4 * q^90 + 16 * q^91 - 12 * q^92 + q^95 + 8 * q^96 - 24 * q^97 + 22 * q^98 + 8 * q^99

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