LMFDB - Embedded newform 722.2.c.e.653.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(429,722)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("722.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			653.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	722.653
Dual form			722.2.c.e.429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} -6.00000 q^{11} +1.00000 q^{12} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +2.00000 q^{18} +(0.500000 + 0.866025i) q^{21} +(-3.00000 - 5.19615i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} -5.00000 q^{26} -5.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-4.50000 + 7.79423i) q^{29} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} +(1.50000 - 2.59808i) q^{34} +(1.00000 + 1.73205i) q^{36} +2.00000 q^{37} +5.00000 q^{39} +(-0.500000 + 0.866025i) q^{42} +(-4.00000 - 6.92820i) q^{43} +(3.00000 - 5.19615i) q^{44} -3.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +5.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(1.50000 - 2.59808i) q^{53} +(-2.50000 - 4.33013i) q^{54} +1.00000 q^{56} -9.00000 q^{58} +(-4.50000 - 7.79423i) q^{59} +(5.00000 - 8.66025i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(-2.50000 + 4.33013i) q^{67} +3.00000 q^{68} +3.00000 q^{69} +(3.00000 + 5.19615i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(3.50000 + 6.06218i) q^{73} +(1.00000 + 1.73205i) q^{74} -5.00000 q^{75} +6.00000 q^{77} +(2.50000 + 4.33013i) q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -6.00000 q^{83} -1.00000 q^{84} +(4.00000 - 6.92820i) q^{86} +9.00000 q^{87} +6.00000 q^{88} +(6.00000 - 10.3923i) q^{89} +(2.50000 - 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} +(2.00000 + 3.46410i) q^{93} -1.00000 q^{96} +(5.00000 + 8.66025i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(-6.00000 + 10.3923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 12 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} - q^{16} - 3 q^{17} + 4 q^{18} + q^{21} - 6 q^{22} - 3 q^{23} + q^{24} + 5 q^{25} - 10 q^{26} - 10 q^{27} + q^{28} - 9 q^{29} - 8 q^{31} + q^{32} + 6 q^{33} + 3 q^{34} + 2 q^{36} + 4 q^{37} + 10 q^{39} - q^{42} - 8 q^{43} + 6 q^{44} - 6 q^{46} - q^{48} - 12 q^{49} + 10 q^{50} - 3 q^{51} - 5 q^{52} + 3 q^{53} - 5 q^{54} + 2 q^{56} - 18 q^{58} - 9 q^{59} + 10 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} - 6 q^{66} - 5 q^{67} + 6 q^{68} + 6 q^{69} + 6 q^{71} - 2 q^{72} + 7 q^{73} + 2 q^{74} - 10 q^{75} + 12 q^{77} + 5 q^{78} + 10 q^{79} - q^{81} - 12 q^{83} - 2 q^{84} + 8 q^{86} + 18 q^{87} + 12 q^{88} + 12 q^{89} + 5 q^{91} - 3 q^{92} + 4 q^{93} - 2 q^{96} + 10 q^{97} - 6 q^{98} - 12 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 12 * q^11 + 2 * q^12 - 5 * q^13 - q^14 - q^16 - 3 * q^17 + 4 * q^18 + q^21 - 6 * q^22 - 3 * q^23 + q^24 + 5 * q^25 - 10 * q^26 - 10 * q^27 + q^28 - 9 * q^29 - 8 * q^31 + q^32 + 6 * q^33 + 3 * q^34 + 2 * q^36 + 4 * q^37 + 10 * q^39 - q^42 - 8 * q^43 + 6 * q^44 - 6 * q^46 - q^48 - 12 * q^49 + 10 * q^50 - 3 * q^51 - 5 * q^52 + 3 * q^53 - 5 * q^54 + 2 * q^56 - 18 * q^58 - 9 * q^59 + 10 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 - 6 * q^66 - 5 * q^67 + 6 * q^68 + 6 * q^69 + 6 * q^71 - 2 * q^72 + 7 * q^73 + 2 * q^74 - 10 * q^75 + 12 * q^77 + 5 * q^78 + 10 * q^79 - q^81 - 12 * q^83 - 2 * q^84 + 8 * q^86 + 18 * q^87 + 12 * q^88 + 12 * q^89 + 5 * q^91 - 3 * q^92 + 4 * q^93 - 2 * q^96 + 10 * q^97 - 6 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−6.00000			−1.80907			−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000			−1.80907			−0.904534	+	0.426401i	$0.859781\pi$
$12$	1.00000			0.288675
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	2.00000			0.471405
$19$		0			0
$19$		0			0
$20$		0			0
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	−5.00000			−0.980581
$27$	−5.00000			−0.962250
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$		0			0
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	5.00000			0.800641
$40$		0			0
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$		0			0
$46$	−3.00000			−0.442326
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−6.00000			−0.857143
$50$	5.00000			0.707107
$51$	−1.50000	+	2.59808i	−0.210042	+	0.363803i
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$		0			0
$56$	1.00000			0.133631
$57$		0			0
$58$	−9.00000			−1.18176
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$		0			0
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−1.00000	+	1.73205i	−0.125988	+	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.00000	+	5.19615i	−0.369274	+	0.639602i
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$	3.00000			0.363803
$69$	3.00000			0.361158
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	0.994850	−	0.101361i	$-0.0323196\pi$
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−5.00000			−0.577350
$76$		0			0
$77$	6.00000			0.683763
$78$	2.50000	+	4.33013i	0.283069	+	0.490290i
$79$	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	$0.643156\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−1.00000			−0.109109
$85$		0			0
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	9.00000			0.964901
$88$	6.00000			0.639602
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$		0			0
$91$	2.50000	−	4.33013i	0.262071	−	0.453921i
$92$	−1.50000	−	2.59808i	−0.156386	−	0.270868i
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	0.999961	+	0.00888289i	$0.00282755\pi$
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	−0.492287	+	0.870433i	$0.663839\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$	−6.00000	+	10.3923i	−0.603023	+	1.04447i
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$	−3.00000			−0.297044
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	2.50000	−	4.33013i	0.245145	−	0.424604i
$105$		0			0
$106$	3.00000			0.291386
$107$	−9.00000			−0.870063			−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000			−0.870063			−0.435031	+	0.900415i	$0.643263\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$		0			0
$111$	−1.00000	−	1.73205i	−0.0949158	−	0.164399i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$		0			0
$116$	−4.50000	−	7.79423i	−0.417815	−	0.723676i
$117$	5.00000	+	8.66025i	0.462250	+	0.800641i
$118$	4.50000	−	7.79423i	0.414259	−	0.717517i
$119$	1.50000	+	2.59808i	0.137505	+	0.238165i
$120$		0			0
$121$	25.0000			2.27273
$122$	10.0000			0.905357
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$		0			0
$126$	−2.00000			−0.178174
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$	−5.00000			−0.431934
$135$		0			0
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	−0.607233	−	0.794524i	$-0.707721\pi$
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	0.991694	+	0.128618i	$0.0410540\pi$
$138$	1.50000	+	2.59808i	0.127688	+	0.221163i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	15.0000	−	25.9808i	1.25436	−	2.17262i
$144$	−2.00000			−0.166667
$145$		0			0
$146$	−3.50000	+	6.06218i	−0.289662	+	0.501709i
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$	−2.50000	−	4.33013i	−0.204124	−	0.353553i
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	3.00000	+	5.19615i	0.241747	+	0.418718i
$155$		0			0
$156$	−2.50000	+	4.33013i	−0.200160	+	0.346688i
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.853646	+	0.520854i	$0.174386\pi$
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.0242497	+	0.999706i	$0.492280\pi$
$158$	−5.00000	+	8.66025i	−0.397779	+	0.688973i
$159$	−3.00000			−0.237915
$160$		0			0
$161$	1.50000	−	2.59808i	0.118217	−	0.204757i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$		0			0
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$	−0.500000	−	0.866025i	−0.0385758	−	0.0668153i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$	8.00000			0.609994
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	4.50000	+	7.79423i	0.341144	+	0.590879i
$175$	−2.50000	+	4.33013i	−0.188982	+	0.327327i
$176$	3.00000	+	5.19615i	0.226134	+	0.391675i
$177$	−4.50000	+	7.79423i	−0.338241	+	0.585850i
$178$	12.0000			0.899438
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$	5.00000			0.370625
$183$	−10.0000			−0.739221
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$		0			0
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$		0			0
$189$	5.00000			0.363696
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	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	$-0.334758\pi$
$194$	−5.00000	+	8.66025i	−0.358979	+	0.621770i
$195$		0			0
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−12.0000			−0.852803
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	0.602549	+	0.798082i	$0.294152\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$	5.00000			0.352673
$202$	−18.0000			−1.26648
$203$	4.50000	−	7.79423i	0.315838	−	0.547048i
$204$	−1.50000	−	2.59808i	−0.105021	−	0.181902i
$205$		0			0
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	5.00000			0.346688
$209$		0			0
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$	−4.50000	−	7.79423i	−0.307614	−	0.532803i
$215$		0			0
$216$	5.00000			0.340207
$217$	4.00000			0.271538
$218$	5.50000	−	9.52628i	0.372507	−	0.645201i
$219$	3.50000	−	6.06218i	0.236508	−	0.409644i
$220$		0			0
$221$	15.0000			1.00901
$222$	1.00000	−	1.73205i	0.0671156	−	0.116248i
$223$	−13.0000	−	22.5167i	−0.870544	−	1.50783i	−0.861435	−	0.507869i	$-0.830434\pi$
$223$	−13.0000	−	22.5167i	−0.870544	−	1.50783i	−0.00910984	−	0.999959i	$-0.502900\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−5.00000	−	8.66025i	−0.333333	−	0.577350i
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	−15.0000			−0.995585			−0.497792	−	0.867296i	$-0.665856\pi$
$227$	−15.0000			−0.995585			−0.497792	+	0.867296i	$0.665856\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	−3.00000	−	5.19615i	−0.197386	−	0.341882i
$232$	4.50000	−	7.79423i	0.295439	−	0.511716i
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	−5.00000	+	8.66025i	−0.326860	+	0.566139i
$235$		0			0
$236$	9.00000			0.585850
$237$	5.00000	−	8.66025i	0.324785	−	0.562544i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	−21.0000			−1.35838			−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000			−1.35838			−0.679189	+	0.733964i	$0.737668\pi$
$240$		0			0
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	0.707953	+	0.706260i	$0.249619\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	5.00000	+	8.66025i	0.320092	+	0.554416i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	4.00000			0.254000
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$		0			0
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	−0.945036	−	0.326965i	$-0.893974\pi$
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	0.755678	+	0.654943i	$0.227307\pi$
$252$	−1.00000	−	1.73205i	−0.0629941	−	0.109109i
$253$	9.00000	−	15.5885i	0.565825	−	0.980038i
$254$	−2.00000			−0.125491
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$	−8.00000			−0.498058
$259$	−2.00000			−0.124274
$260$		0			0
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$		0			0
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$		0			0
$266$		0			0
$267$	−12.0000			−0.734388
$268$	−2.50000	−	4.33013i	−0.152712	−	0.264505i
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$		0			0
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	0.649211	−	0.760609i	$-0.275099\pi$
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	−0.983312	+	0.181928i	$0.941766\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	−5.00000			−0.302614
$274$	9.00000			0.543710
$275$	−15.0000	+	25.9808i	−0.904534	+	1.56670i
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	8.00000			0.480673			0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000			0.480673			0.240337	+	0.970690i	$0.422742\pi$
$278$	4.00000			0.239904
$279$	−4.00000	+	6.92820i	−0.239474	+	0.414781i
$280$		0			0
$281$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$281$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$282$		0			0
$283$	11.0000	+	19.0526i	0.653882	+	1.13256i	0.982173	+	0.187980i	$0.0601941\pi$
$283$	11.0000	+	19.0526i	0.653882	+	1.13256i	−0.328291	+	0.944577i	$0.606473\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	30.0000			1.77394
$287$		0			0
$288$	−1.00000	−	1.73205i	−0.0589256	−	0.102062i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$	−7.00000			−0.409644
$293$	−21.0000			−1.22683			−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000			−1.22683			−0.613417	+	0.789760i	$0.710205\pi$
$294$	−3.00000	+	5.19615i	−0.174964	+	0.303046i
$295$		0			0
$296$	−2.00000			−0.116248
$297$	30.0000			1.74078
$298$		0			0
$299$	−7.50000	−	12.9904i	−0.433736	−	0.751253i
$300$	2.50000	−	4.33013i	0.144338	−	0.250000i
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	−5.00000	−	8.66025i	−0.287718	−	0.498342i
$303$	18.0000			1.03407
$304$		0			0
$305$		0			0
$306$	−3.00000	−	5.19615i	−0.171499	−	0.297044i
$307$	−10.0000	−	17.3205i	−0.570730	−	0.988534i	−0.996491	−	0.0836980i	$-0.973327\pi$
$307$	−10.0000	−	17.3205i	−0.570730	−	0.988534i	0.425761	−	0.904836i	$-0.360006\pi$
$308$	−3.00000	+	5.19615i	−0.170941	+	0.296078i
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$		0			0
$311$	−21.0000			−1.19080			−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000			−1.19080			−0.595400	+	0.803429i	$0.703007\pi$
$312$	−5.00000			−0.283069
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$	−11.0000	+	19.0526i	−0.620766	+	1.07520i
$315$		0			0
$316$	−10.0000			−0.562544
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	−0.711535	−	0.702650i	$-0.752000\pi$
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	0.964281	+	0.264883i	$0.0853332\pi$
$318$	−1.50000	−	2.59808i	−0.0841158	−	0.145693i
$319$	27.0000	−	46.7654i	1.51171	−	2.61836i
$320$		0			0
$321$	4.50000	+	7.79423i	0.251166	+	0.435031i
$322$	3.00000			0.167183
$323$		0			0
$324$	1.00000			0.0555556
$325$	12.5000	+	21.6506i	0.693375	+	1.20096i
$326$	10.0000	+	17.3205i	0.553849	+	0.959294i
$327$	−5.50000	+	9.52628i	−0.304151	+	0.526804i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.00000			−0.0549650			−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	−1.00000			−0.0549650			−0.0274825	+	0.999622i	$0.508749\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	2.00000	−	3.46410i	0.109599	−	0.189832i
$334$	−12.0000			−0.656611
$335$		0			0
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	2.00000	+	3.46410i	0.108947	+	0.188702i	0.915344	−	0.402673i	$-0.131919\pi$
$337$	2.00000	+	3.46410i	0.108947	+	0.188702i	−0.806397	+	0.591375i	$0.798585\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$	24.0000			1.29967
$342$		0			0
$343$	13.0000			0.701934
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	0.516667	−	0.856186i	$-0.327172\pi$
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	−0.999813	+	0.0193540i	$0.993839\pi$
$348$	−4.50000	+	7.79423i	−0.241225	+	0.417815i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	−5.00000			−0.267261
$351$	12.5000	−	21.6506i	0.667201	−	1.15563i
$352$	−3.00000	+	5.19615i	−0.159901	+	0.276956i
$353$	−15.0000			−0.798369			−0.399185	−	0.916871i	$-0.630707\pi$
$353$	−15.0000			−0.798369			−0.399185	+	0.916871i	$0.630707\pi$
$354$	−9.00000			−0.478345
$355$		0			0
$356$	6.00000	+	10.3923i	0.317999	+	0.550791i
$357$	1.50000	−	2.59808i	0.0793884	−	0.137505i
$358$		0			0
$359$	−10.5000	−	18.1865i	−0.554169	−	0.959849i	−0.997968	−	0.0637221i	$-0.979703\pi$
$359$	−10.5000	−	18.1865i	−0.554169	−	0.959849i	0.443799	−	0.896126i	$-0.353630\pi$
$360$		0			0
$361$		0			0
$362$	−2.00000			−0.105118
$363$	−12.5000	−	21.6506i	−0.656080	−	1.13636i
$364$	2.50000	+	4.33013i	0.131036	+	0.226960i
$365$		0			0
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$	3.00000			0.156386
$369$		0			0
$370$		0			0
$371$	−1.50000	+	2.59808i	−0.0778761	+	0.134885i
$372$	−4.00000			−0.207390
$373$	23.0000			1.19089			0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000			1.19089			0.595447	+	0.803394i	$0.296975\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$		0			0
$376$		0			0
$377$	−22.5000	−	38.9711i	−1.15881	−	2.00712i
$378$	2.50000	+	4.33013i	0.128586	+	0.222718i
$379$	−7.00000			−0.359566			−0.179783	−	0.983706i	$-0.557540\pi$
$379$	−7.00000			−0.359566			−0.179783	+	0.983706i	$0.557540\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	1.50000	+	2.59808i	0.0767467	+	0.132929i
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	7.00000	−	12.1244i	0.356291	−	0.617113i
$387$	−16.0000			−0.813326
$388$	−10.0000			−0.507673
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	9.00000			0.455150
$392$	6.00000			0.303046
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−6.00000	−	10.3923i	−0.301511	−	0.522233i
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	−0.999998	−	0.00217869i	$-0.999307\pi$
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	0.498112	−	0.867113i	$-0.334027\pi$
$398$	−11.0000			−0.551380
$399$		0			0
$400$	−5.00000			−0.250000
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$	2.50000	+	4.33013i	0.124689	+	0.215967i
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	−9.00000	−	15.5885i	−0.447767	−	0.775555i
$405$		0			0
$406$	9.00000			0.446663
$407$	−12.0000			−0.594818
$408$	1.50000	−	2.59808i	0.0742611	−	0.128624i
$409$	−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	$0.876150\pi$
$410$		0			0
$411$	−9.00000			−0.443937
$412$	−7.00000	+	12.1244i	−0.344865	+	0.597324i
$413$	4.50000	+	7.79423i	0.221431	+	0.383529i
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$		0			0
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$	−4.00000			−0.195881
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	0.581086	−	0.813842i	$-0.302628\pi$
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	−0.995351	+	0.0963145i	$0.969295\pi$
$422$	2.50000	−	4.33013i	0.121698	−	0.210787i
$423$		0			0
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$	−15.0000			−0.727607
$426$	6.00000			0.290701
$427$	−5.00000	+	8.66025i	−0.241967	+	0.419099i
$428$	4.50000	−	7.79423i	0.217516	−	0.376748i
$429$	−30.0000			−1.44841
$430$		0			0
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	−0.929188	−	0.369607i	$-0.879492\pi$
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	0.784683	+	0.619897i	$0.212826\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	−1.00000	+	1.73205i	−0.0480569	+	0.0832370i	−0.889053	−	0.457804i	$-0.848636\pi$
$433$	−1.00000	+	1.73205i	−0.0480569	+	0.0832370i	0.840996	+	0.541041i	$0.181970\pi$
$434$	2.00000	+	3.46410i	0.0960031	+	0.166282i
$435$		0			0
$436$	11.0000			0.526804
$437$		0			0
$438$	7.00000			0.334473
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$	−6.00000	+	10.3923i	−0.285714	+	0.494872i
$442$	7.50000	+	12.9904i	0.356739	+	0.617889i
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	−0.569057	−	0.822298i	$-0.692691\pi$
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	0.996660	+	0.0816684i	$0.0260248\pi$
$444$	2.00000			0.0949158
$445$		0			0
$446$	13.0000	−	22.5167i	0.615568	−	1.06619i
$447$		0			0
$448$	−1.00000			−0.0472456
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$	5.00000	−	8.66025i	0.235702	−	0.408248i
$451$		0			0
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	5.00000	+	8.66025i	0.234920	+	0.406894i
$454$	−7.50000	−	12.9904i	−0.351992	−	0.609669i
$455$		0			0
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	−11.0000	−	19.0526i	−0.513996	−	0.890268i
$459$	7.50000	+	12.9904i	0.350070	+	0.606339i
$460$		0			0
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	0.971248	−	0.238071i	$-0.0765153\pi$
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	−0.691800	+	0.722089i	$0.743182\pi$
$462$	3.00000	−	5.19615i	0.139573	−	0.241747i
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	9.00000			0.417815
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$	−10.0000			−0.462250
$469$	2.50000	−	4.33013i	0.115439	−	0.199947i
$470$		0			0
$471$	11.0000	−	19.0526i	0.506853	−	0.877896i
$472$	4.50000	+	7.79423i	0.207129	+	0.358758i
$473$	24.0000	+	41.5692i	1.10352	+	1.91135i
$474$	10.0000			0.459315
$475$		0			0
$476$	−3.00000			−0.137505
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$	−10.5000	−	18.1865i	−0.480259	−	0.831833i
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$		0			0
$481$	−5.00000	+	8.66025i	−0.227980	+	0.394874i
$482$	−8.00000			−0.364390
$483$	−3.00000			−0.136505
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$		0			0
$486$	−16.0000			−0.725775
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−5.00000	+	8.66025i	−0.226339	+	0.392031i
$489$	−10.0000	−	17.3205i	−0.452216	−	0.783260i
$490$		0			0
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	0.911230	+	0.411897i	$0.135134\pi$
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	−0.0989017	+	0.995097i	$0.531533\pi$
$492$		0			0
$493$	27.0000			1.21602
$494$		0			0
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$		0			0
$501$	12.0000			0.536120
$502$	−6.00000			−0.267793
$503$	10.5000	−	18.1865i	0.468172	−	0.810897i	−0.531167	−	0.847267i	$-0.678246\pi$
$503$	10.5000	−	18.1865i	0.468172	−	0.810897i	0.999338	+	0.0363700i	$0.0115795\pi$
$504$	1.00000	−	1.73205i	0.0445435	−	0.0771517i
$505$		0			0
$506$	18.0000			0.800198
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$		0			0
$511$	−3.50000	−	6.06218i	−0.154831	−	0.268175i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−12.0000			−0.529297
$515$		0			0
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$		0			0
$518$	−1.00000	−	1.73205i	−0.0439375	−	0.0761019i
$519$	−3.00000	+	5.19615i	−0.131685	+	0.228086i
$520$		0			0
$521$	−36.0000			−1.57719			−0.788594	−	0.614914i	$-0.789191\pi$
$521$	−36.0000			−1.57719			−0.788594	+	0.614914i	$0.789191\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	−5.50000	+	9.52628i	−0.240498	+	0.416555i	−0.960856	−	0.277047i	$-0.910644\pi$
$523$	−5.50000	+	9.52628i	−0.240498	+	0.416555i	0.720358	+	0.693602i	$0.243977\pi$
$524$		0			0
$525$	5.00000			0.218218
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$	3.00000	−	5.19615i	0.130558	−	0.226134i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$		0			0
$534$	−6.00000	−	10.3923i	−0.259645	−	0.449719i
$535$		0			0
$536$	2.50000	−	4.33013i	0.107984	−	0.187033i
$537$		0			0
$538$	−3.00000	+	5.19615i	−0.129339	+	0.224022i
$539$	36.0000			1.55063
$540$		0			0
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$	5.50000	−	9.52628i	0.236245	−	0.409189i
$543$	2.00000			0.0858282
$544$	−3.00000			−0.128624
$545$		0			0
$546$	−2.50000	−	4.33013i	−0.106990	−	0.185312i
$547$	−22.0000	+	38.1051i	−0.940652	+	1.62926i	−0.176421	+	0.984315i	$0.556452\pi$
$547$	−22.0000	+	38.1051i	−0.940652	+	1.62926i	−0.764231	+	0.644942i	$0.776881\pi$
$548$	4.50000	+	7.79423i	0.192230	+	0.332953i
$549$	−10.0000	−	17.3205i	−0.426790	−	0.739221i
$550$	−30.0000			−1.27920
$551$		0			0
$552$	−3.00000			−0.127688
$553$	−5.00000	−	8.66025i	−0.212622	−	0.368271i
$554$	4.00000	+	6.92820i	0.169944	+	0.294351i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	0.491496	+	0.870880i	$0.336450\pi$
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	−0.999952	+	0.00979220i	$0.996883\pi$
$558$	−8.00000			−0.338667
$559$	40.0000			1.69182
$560$		0			0
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$		0			0
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$		0			0
$566$	−11.0000	+	19.0526i	−0.462364	+	0.800839i
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	15.0000	+	25.9808i	0.627182	+	1.08631i
$573$	−1.50000	−	2.59808i	−0.0626634	−	0.108536i
$574$		0			0
$575$	7.50000	+	12.9904i	0.312772	+	0.541736i
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$	8.00000			0.332756
$579$	−7.00000	+	12.1244i	−0.290910	+	0.503871i
$580$		0			0
$581$	6.00000			0.248922
$582$	10.0000			0.414513
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$	−3.50000	−	6.06218i	−0.144831	−	0.250855i
$585$		0			0
$586$	−10.5000	−	18.1865i	−0.433751	−	0.751279i
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$	−6.00000			−0.247436
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	15.0000	−	25.9808i	0.615976	−	1.06690i	−0.374236	−	0.927333i	$-0.622095\pi$
$593$	15.0000	−	25.9808i	0.615976	−	1.06690i	0.990212	−	0.139569i	$-0.0445716\pi$
$594$	15.0000	+	25.9808i	0.615457	+	1.06600i
$595$		0			0
$596$		0			0
$597$	11.0000			0.450200
$598$	7.50000	−	12.9904i	0.306698	−	0.531216i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$	5.00000			0.204124
$601$	−28.0000			−1.14214			−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000			−1.14214			−0.571072	+	0.820900i	$0.693472\pi$
$602$	−4.00000	+	6.92820i	−0.163028	+	0.282372i
$603$	5.00000	+	8.66025i	0.203616	+	0.352673i
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$		0			0
$606$	9.00000	+	15.5885i	0.365600	+	0.633238i
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$		0			0
$609$	−9.00000			−0.364698
$610$		0			0
$611$		0			0
$612$	3.00000	−	5.19615i	0.121268	−	0.210042i
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$		0			0
$616$	−6.00000			−0.241747
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	−0.799298	−	0.600935i	$-0.794795\pi$
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	0.920074	+	0.391745i	$0.128129\pi$
$618$	7.00000	−	12.1244i	0.281581	−	0.487713i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$		0			0
$621$	7.50000	−	12.9904i	0.300965	−	0.521286i
$622$	−10.5000	−	18.1865i	−0.421012	−	0.729214i
$623$	−6.00000	+	10.3923i	−0.240385	+	0.416359i
$624$	−2.50000	−	4.33013i	−0.100080	−	0.173344i
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	19.0000			0.759393
$627$		0			0
$628$	−22.0000			−0.877896
$629$	−3.00000	−	5.19615i	−0.119618	−	0.207184i
$630$		0			0
$631$	8.00000	−	13.8564i	0.318475	−	0.551615i	−0.661695	−	0.749773i	$-0.730163\pi$
$631$	8.00000	−	13.8564i	0.318475	−	0.551615i	0.980170	+	0.198158i	$0.0634960\pi$
$632$	−5.00000	−	8.66025i	−0.198889	−	0.344486i
$633$	−2.50000	+	4.33013i	−0.0993661	+	0.172107i
$634$	9.00000			0.357436
$635$		0			0
$636$	1.50000	−	2.59808i	0.0594789	−	0.103020i
$637$	15.0000	−	25.9808i	0.594322	−	1.02940i
$638$	54.0000			2.13788
$639$	12.0000			0.474713
$640$		0			0
$641$	−3.00000	−	5.19615i	−0.118493	−	0.205236i	0.800678	−	0.599095i	$-0.204473\pi$
$641$	−3.00000	−	5.19615i	−0.118493	−	0.205236i	−0.919171	+	0.393860i	$0.871140\pi$
$642$	−4.50000	+	7.79423i	−0.177601	+	0.307614i
$643$	11.0000	+	19.0526i	0.433798	+	0.751360i	0.997197	−	0.0748254i	$-0.0238399\pi$
$643$	11.0000	+	19.0526i	0.433798	+	0.751360i	−0.563399	+	0.826185i	$0.690507\pi$
$644$	1.50000	+	2.59808i	0.0591083	+	0.102379i
$645$		0			0
$646$		0			0
$647$	27.0000			1.06148			0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000			1.06148			0.530740	+	0.847535i	$0.321914\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	27.0000	+	46.7654i	1.05984	+	1.83570i
$650$	−12.5000	+	21.6506i	−0.490290	+	0.849208i
$651$	−2.00000	−	3.46410i	−0.0783862	−	0.135769i
$652$	−10.0000	+	17.3205i	−0.391630	+	0.678323i
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$	−11.0000			−0.430134
$655$		0			0
$656$		0			0
$657$	14.0000			0.546192
$658$		0			0
$659$	22.5000	−	38.9711i	0.876476	−	1.51810i	0.0212930	−	0.999773i	$-0.493222\pi$
$659$	22.5000	−	38.9711i	0.876476	−	1.51810i	0.855183	−	0.518327i	$-0.173445\pi$
$660$		0			0
$661$	6.50000	−	11.2583i	0.252821	−	0.437898i	−0.711481	−	0.702706i	$-0.751975\pi$
$661$	6.50000	−	11.2583i	0.252821	−	0.437898i	0.964301	+	0.264807i	$0.0853084\pi$
$662$	−0.500000	−	0.866025i	−0.0194331	−	0.0336590i
$663$	−7.50000	−	12.9904i	−0.291276	−	0.504505i
$664$	6.00000			0.232845
$665$		0			0
$666$	4.00000			0.154997
$667$	−13.5000	−	23.3827i	−0.522722	−	0.905381i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$	−13.0000	+	22.5167i	−0.502609	+	0.870544i
$670$		0			0
$671$	−30.0000	+	51.9615i	−1.15814	+	2.00595i
$672$	1.00000			0.0385758
$673$	44.0000			1.69608			0.848038	−	0.529936i	$-0.177784\pi$
$673$	44.0000			1.69608			0.848038	+	0.529936i	$0.177784\pi$
$674$	−2.00000	+	3.46410i	−0.0770371	+	0.133432i
$675$	−12.5000	+	21.6506i	−0.481125	+	0.833333i
$676$	12.0000			0.461538
$677$	−33.0000			−1.26829			−0.634147	−	0.773213i	$-0.718648\pi$
$677$	−33.0000			−1.26829			−0.634147	+	0.773213i	$0.718648\pi$
$678$	3.00000	−	5.19615i	0.115214	−	0.199557i
$679$	−5.00000	−	8.66025i	−0.191882	−	0.332350i
$680$		0			0
$681$	7.50000	+	12.9904i	0.287401	+	0.497792i
$682$	12.0000	+	20.7846i	0.459504	+	0.795884i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$		0			0
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$	11.0000	+	19.0526i	0.419676	+	0.726900i
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	7.50000	+	12.9904i	0.285727	+	0.494894i
$690$		0			0
$691$	−10.0000			−0.380418			−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000			−0.380418			−0.190209	+	0.981744i	$0.560917\pi$
$692$	6.00000			0.228086
$693$	6.00000	−	10.3923i	0.227921	−	0.394771i
$694$	9.00000	−	15.5885i	0.341635	−	0.591730i
$695$		0			0
$696$	−9.00000			−0.341144
$697$		0			0
$698$	−5.00000	−	8.66025i	−0.189253	−	0.327795i
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$	−2.50000	−	4.33013i	−0.0944911	−	0.163663i
$701$	−6.00000	−	10.3923i	−0.226617	−	0.392512i	0.730186	−	0.683248i	$-0.239433\pi$
$701$	−6.00000	−	10.3923i	−0.226617	−	0.392512i	−0.956803	+	0.290736i	$0.906100\pi$
$702$	25.0000			0.943564
$703$		0			0
$704$	−6.00000			−0.226134
$705$		0			0
$706$	−7.50000	−	12.9904i	−0.282266	−	0.488899i
$707$	9.00000	−	15.5885i	0.338480	−	0.586264i
$708$	−4.50000	−	7.79423i	−0.169120	−	0.292925i
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$		0			0
$711$	20.0000			0.750059
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$	3.00000			0.112272
$715$		0			0
$716$		0			0
$717$	10.5000	+	18.1865i	0.392130	+	0.679189i
$718$	10.5000	−	18.1865i	0.391857	−	0.678715i
$719$	−19.5000	−	33.7750i	−0.727227	−	1.25959i	−0.958051	−	0.286599i	$-0.907475\pi$
$719$	−19.5000	−	33.7750i	−0.727227	−	1.25959i	0.230823	−	0.972996i	$-0.425858\pi$
$720$		0			0
$721$	−14.0000			−0.521387
$722$		0			0
$723$	8.00000			0.297523
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	22.5000	+	38.9711i	0.835629	+	1.44735i
$726$	12.5000	−	21.6506i	0.463919	−	0.803530i
$727$	18.5000	+	32.0429i	0.686127	+	1.18841i	0.973081	+	0.230463i	$0.0740239\pi$
$727$	18.5000	+	32.0429i	0.686127	+	1.18841i	−0.286954	+	0.957944i	$0.592643\pi$
$728$	−2.50000	+	4.33013i	−0.0926562	+	0.160485i
$729$	13.0000			0.481481
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$	5.00000	−	8.66025i	0.184805	−	0.320092i
$733$	32.0000			1.18195			0.590973	−	0.806691i	$-0.298744\pi$
$733$	32.0000			1.18195			0.590973	+	0.806691i	$0.298744\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$	1.50000	+	2.59808i	0.0552907	+	0.0957664i
$737$	15.0000	−	25.9808i	0.552532	−	0.957014i
$738$		0			0
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		0			0
$741$		0			0
$742$	−3.00000			−0.110133
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	0.980522	+	0.196409i	$0.0629279\pi$
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	−0.320166	+	0.947361i	$0.603739\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$		0			0
$746$	11.5000	+	19.9186i	0.421045	+	0.729271i
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$	−18.0000			−0.658145
$749$	9.00000			0.328853
$750$		0			0
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$		0			0
$753$	6.00000			0.218652
$754$	22.5000	−	38.9711i	0.819402	−	1.41925i
$755$		0			0
$756$	−2.50000	+	4.33013i	−0.0909241	+	0.157485i
$757$	−1.00000	−	1.73205i	−0.0363456	−	0.0629525i	0.847280	−	0.531146i	$-0.178238\pi$
$757$	−1.00000	−	1.73205i	−0.0363456	−	0.0629525i	−0.883626	+	0.468193i	$0.844905\pi$
$758$	−3.50000	−	6.06218i	−0.127126	−	0.220188i
$759$	−18.0000			−0.653359
$760$		0			0
$761$	−21.0000			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$762$	1.00000	+	1.73205i	0.0362262	+	0.0627456i
$763$	5.50000	+	9.52628i	0.199113	+	0.344874i
$764$	−1.50000	+	2.59808i	−0.0542681	+	0.0939951i
$765$		0			0
$766$	9.00000	−	15.5885i	0.325183	−	0.563234i
$767$	45.0000			1.62486
$768$	1.00000			0.0360844
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$		0			0
$771$	12.0000			0.432169
$772$	14.0000			0.503871
$773$	−25.5000	+	44.1673i	−0.917171	+	1.58859i	−0.113480	+	0.993540i	$0.536200\pi$
$773$	−25.5000	+	44.1673i	−0.917171	+	1.58859i	−0.803691	+	0.595047i	$0.797133\pi$
$774$	−8.00000	−	13.8564i	−0.287554	−	0.498058i
$775$	−10.0000	+	17.3205i	−0.359211	+	0.622171i
$776$	−5.00000	−	8.66025i	−0.179490	−	0.310885i
$777$	1.00000	+	1.73205i	0.0358748	+	0.0621370i
$778$	−18.0000			−0.645331
$779$		0			0
$780$		0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} -6.00000 q^{11} +1.00000 q^{12} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +2.00000 q^{18} +(0.500000 + 0.866025i) q^{21} +(-3.00000 - 5.19615i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} -5.00000 q^{26} -5.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-4.50000 + 7.79423i) q^{29} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} +(1.50000 - 2.59808i) q^{34} +(1.00000 + 1.73205i) q^{36} +2.00000 q^{37} +5.00000 q^{39} +(-0.500000 + 0.866025i) q^{42} +(-4.00000 - 6.92820i) q^{43} +(3.00000 - 5.19615i) q^{44} -3.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +5.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(1.50000 - 2.59808i) q^{53} +(-2.50000 - 4.33013i) q^{54} +1.00000 q^{56} -9.00000 q^{58} +(-4.50000 - 7.79423i) q^{59} +(5.00000 - 8.66025i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(-2.50000 + 4.33013i) q^{67} +3.00000 q^{68} +3.00000 q^{69} +(3.00000 + 5.19615i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(3.50000 + 6.06218i) q^{73} +(1.00000 + 1.73205i) q^{74} -5.00000 q^{75} +6.00000 q^{77} +(2.50000 + 4.33013i) q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -6.00000 q^{83} -1.00000 q^{84} +(4.00000 - 6.92820i) q^{86} +9.00000 q^{87} +6.00000 q^{88} +(6.00000 - 10.3923i) q^{89} +(2.50000 - 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} +(2.00000 + 3.46410i) q^{93} -1.00000 q^{96} +(5.00000 + 8.66025i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(-6.00000 + 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 12 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} - q^{16} - 3 q^{17} + 4 q^{18} + q^{21} - 6 q^{22} - 3 q^{23} + q^{24} + 5 q^{25} - 10 q^{26} - 10 q^{27} + q^{28} - 9 q^{29} - 8 q^{31} + q^{32} + 6 q^{33} + 3 q^{34} + 2 q^{36} + 4 q^{37} + 10 q^{39} - q^{42} - 8 q^{43} + 6 q^{44} - 6 q^{46} - q^{48} - 12 q^{49} + 10 q^{50} - 3 q^{51} - 5 q^{52} + 3 q^{53} - 5 q^{54} + 2 q^{56} - 18 q^{58} - 9 q^{59} + 10 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} - 6 q^{66} - 5 q^{67} + 6 q^{68} + 6 q^{69} + 6 q^{71} - 2 q^{72} + 7 q^{73} + 2 q^{74} - 10 q^{75} + 12 q^{77} + 5 q^{78} + 10 q^{79} - q^{81} - 12 q^{83} - 2 q^{84} + 8 q^{86} + 18 q^{87} + 12 q^{88} + 12 q^{89} + 5 q^{91} - 3 q^{92} + 4 q^{93} - 2 q^{96} + 10 q^{97} - 6 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 12 * q^11 + 2 * q^12 - 5 * q^13 - q^14 - q^16 - 3 * q^17 + 4 * q^18 + q^21 - 6 * q^22 - 3 * q^23 + q^24 + 5 * q^25 - 10 * q^26 - 10 * q^27 + q^28 - 9 * q^29 - 8 * q^31 + q^32 + 6 * q^33 + 3 * q^34 + 2 * q^36 + 4 * q^37 + 10 * q^39 - q^42 - 8 * q^43 + 6 * q^44 - 6 * q^46 - q^48 - 12 * q^49 + 10 * q^50 - 3 * q^51 - 5 * q^52 + 3 * q^53 - 5 * q^54 + 2 * q^56 - 18 * q^58 - 9 * q^59 + 10 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 - 6 * q^66 - 5 * q^67 + 6 * q^68 + 6 * q^69 + 6 * q^71 - 2 * q^72 + 7 * q^73 + 2 * q^74 - 10 * q^75 + 12 * q^77 + 5 * q^78 + 10 * q^79 - q^81 - 12 * q^83 - 2 * q^84 + 8 * q^86 + 18 * q^87 + 12 * q^88 + 12 * q^89 + 5 * q^91 - 3 * q^92 + 4 * q^93 - 2 * q^96 + 10 * q^97 - 6 * q^98 - 12 * q^99

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