LMFDB - Embedded newform 507.2.e.b.22.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(22,507)] 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("507.22"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,1,1,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	507.22
Dual form			507.2.e.b.484.1

$q$-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} -2.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +1.00000 q^{12} -4.00000 q^{14} +(-1.00000 + 1.73205i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} -1.00000 q^{18} +(-1.00000 - 1.73205i) q^{20} -4.00000 q^{21} +(-2.00000 - 3.46410i) q^{22} +(1.50000 - 2.59808i) q^{24} -1.00000 q^{25} -1.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +(5.00000 - 8.66025i) q^{29} +(1.00000 + 1.73205i) q^{30} -4.00000 q^{31} +(2.50000 + 4.33013i) q^{32} +(-2.00000 - 3.46410i) q^{33} -2.00000 q^{34} +(4.00000 + 6.92820i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-1.00000 + 1.73205i) q^{37} -6.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(-2.00000 + 3.46410i) q^{42} +(6.00000 + 10.3923i) q^{43} +4.00000 q^{44} +(1.00000 + 1.73205i) q^{45} +(-0.500000 - 0.866025i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} -2.00000 q^{51} +6.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-4.00000 + 6.92820i) q^{55} +(-6.00000 - 10.3923i) q^{56} +(-5.00000 - 8.66025i) q^{58} +(6.00000 + 10.3923i) q^{59} -2.00000 q^{60} +(1.00000 + 1.73205i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-2.00000 + 3.46410i) q^{63} +7.00000 q^{64} -4.00000 q^{66} +(-4.00000 + 6.92820i) q^{67} +(1.00000 - 1.73205i) q^{68} +8.00000 q^{70} +(-1.50000 - 2.59808i) q^{72} -2.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} -16.0000 q^{77} +8.00000 q^{79} +(-1.00000 + 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} -4.00000 q^{83} +(-2.00000 - 3.46410i) q^{84} +(2.00000 + 3.46410i) q^{85} +12.0000 q^{86} +(-5.00000 - 8.66025i) q^{87} +(6.00000 - 10.3923i) q^{88} +(-1.00000 + 1.73205i) q^{89} +2.00000 q^{90} +(-2.00000 + 3.46410i) q^{93} +5.00000 q^{96} +(5.00000 + 8.66025i) q^{97} +(4.50000 + 7.79423i) q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} + q^{4} - 4 q^{5} - q^{6} - 4 q^{7} + 6 q^{8} - q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{12} - 8 q^{14} - 2 q^{15} + q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{20} - 8 q^{21} - 4 q^{22} + 3 q^{24}+ \cdots - 8 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 + q^4 - 4 * q^5 - q^6 - 4 * q^7 + 6 * q^8 - q^9 - 2 * q^10 + 4 * q^11 + 2 * q^12 - 8 * q^14 - 2 * q^15 + q^16 - 2 * q^17 - 2 * q^18 - 2 * q^20 - 8 * q^21 - 4 * q^22 + 3 * q^24 - 2 * q^25 - 2 * q^27 + 4 * q^28 + 10 * q^29 + 2 * q^30 - 8 * q^31 + 5 * q^32 - 4 * q^33 - 4 * q^34 + 8 * q^35 + q^36 - 2 * q^37 - 12 * q^40 + 6 * q^41 - 4 * q^42 + 12 * q^43 + 8 * q^44 + 2 * q^45 - q^48 - 9 * q^49 - q^50 - 4 * q^51 + 12 * q^53 - q^54 - 8 * q^55 - 12 * q^56 - 10 * q^58 + 12 * q^59 - 4 * q^60 + 2 * q^61 - 4 * q^62 - 4 * q^63 + 14 * q^64 - 8 * q^66 - 8 * q^67 + 2 * q^68 + 16 * q^70 - 3 * q^72 - 4 * q^73 + 2 * q^74 - q^75 - 32 * q^77 + 16 * q^79 - 2 * q^80 - q^81 - 6 * q^82 - 8 * q^83 - 4 * q^84 + 4 * q^85 + 24 * q^86 - 10 * q^87 + 12 * q^88 - 2 * q^89 + 4 * q^90 - 4 * q^93 + 10 * q^96 + 10 * q^97 + 9 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$	3.00000			1.06066
$9$	−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	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	−4.00000			−1.06904
$15$	−1.00000	+	1.73205i	−0.258199	+	0.447214i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−1.00000			−0.235702
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−1.00000	−	1.73205i	−0.223607	−	0.387298i
$21$	−4.00000			−0.872872
$22$	−2.00000	−	3.46410i	−0.426401	−	0.738549i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	2.00000	−	3.46410i	0.377964	−	0.654654i
$29$	5.00000	−	8.66025i	0.928477	−	1.60817i	0.142605	−	0.989780i	$-0.454452\pi$
$29$	5.00000	−	8.66025i	0.928477	−	1.60817i	0.785872	−	0.618389i	$-0.212214\pi$
$30$	1.00000	+	1.73205i	0.182574	+	0.316228i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$	−2.00000	−	3.46410i	−0.348155	−	0.603023i
$34$	−2.00000			−0.342997
$35$	4.00000	+	6.92820i	0.676123	+	1.17108i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$		0			0
$40$	−6.00000			−0.948683
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$	−2.00000	+	3.46410i	−0.308607	+	0.534522i
$43$	6.00000	+	10.3923i	0.914991	+	1.58481i	0.806914	+	0.590669i	$0.201136\pi$
$43$	6.00000	+	10.3923i	0.914991	+	1.58481i	0.108078	+	0.994142i	$0.465531\pi$
$44$	4.00000			0.603023
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−2.00000			−0.280056
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−4.00000	+	6.92820i	−0.539360	+	0.934199i
$56$	−6.00000	−	10.3923i	−0.801784	−	1.38873i
$57$		0			0
$58$	−5.00000	−	8.66025i	−0.656532	−	1.13715i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$	−2.00000			−0.258199
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	−2.00000	+	3.46410i	−0.251976	+	0.436436i
$64$	7.00000			0.875000
$65$		0			0
$66$	−4.00000			−0.492366
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$		0			0
$70$	8.00000			0.956183
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$	−16.0000			−1.82337
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$	−2.00000	−	3.46410i	−0.218218	−	0.377964i
$85$	2.00000	+	3.46410i	0.216930	+	0.375735i
$86$	12.0000			1.29399
$87$	−5.00000	−	8.66025i	−0.536056	−	0.928477i
$88$	6.00000	−	10.3923i	0.639602	−	1.10782i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$		0			0
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$		0			0
$95$		0			0
$96$	5.00000			0.510310
$97$	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	$0.663839\pi$
$98$	4.50000	+	7.79423i	0.454569	+	0.787336i
$99$	−4.00000			−0.402015
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$	−1.00000	+	1.73205i	−0.0990148	+	0.171499i
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$	8.00000			0.780720
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	4.00000	+	6.92820i	0.381385	+	0.660578i
$111$	1.00000	+	1.73205i	0.0949158	+	0.164399i
$112$	−4.00000			−0.377964
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$		0			0
$115$		0			0
$116$	10.0000			0.928477
$117$		0			0
$118$	12.0000			1.10469
$119$	−4.00000	+	6.92820i	−0.366679	+	0.635107i
$120$	−3.00000	+	5.19615i	−0.273861	+	0.474342i
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	2.00000			0.181071
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	12.0000			1.07331
$126$	2.00000	+	3.46410i	0.178174	+	0.308607i
$127$	8.00000	−	13.8564i	0.709885	−	1.22956i	−0.255014	−	0.966937i	$-0.582080\pi$
$127$	8.00000	−	13.8564i	0.709885	−	1.22956i	0.964899	−	0.262620i	$-0.0845865\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	12.0000			1.05654
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$	2.00000	−	3.46410i	0.174078	−	0.301511i
$133$		0			0
$134$	4.00000	+	6.92820i	0.345547	+	0.598506i
$135$	2.00000			0.172133
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	−0.999947	−	0.0103230i	$-0.996714\pi$
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	0.491033	−	0.871141i	$-0.336619\pi$
$140$	−4.00000	+	6.92820i	−0.338062	+	0.585540i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−10.0000	+	17.3205i	−0.830455	+	1.43839i
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$	4.50000	+	7.79423i	0.371154	+	0.642857i
$148$	−2.00000			−0.164399
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−4.00000			−0.325515			−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000			−0.325515			−0.162758	+	0.986666i	$0.552039\pi$
$152$		0			0
$153$	−1.00000	+	1.73205i	−0.0808452	+	0.140028i
$154$	−8.00000	+	13.8564i	−0.644658	+	1.11658i
$155$	8.00000			0.642575
$156$		0			0
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	−5.00000	−	8.66025i	−0.395285	−	0.684653i
$161$		0			0
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$	6.00000			0.468521
$165$	4.00000	+	6.92820i	0.311400	+	0.539360i
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	−0.978259	−	0.207385i	$-0.933505\pi$
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	0.668730	+	0.743505i	$0.266838\pi$
$168$	−12.0000			−0.925820
$169$		0			0
$170$	4.00000			0.306786
$171$		0			0
$172$	−6.00000	+	10.3923i	−0.457496	+	0.792406i
$173$	−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	$0.906580\pi$
$174$	−10.0000			−0.758098
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$	12.0000			0.901975
$178$	1.00000	+	1.73205i	0.0749532	+	0.129823i
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$	−1.00000	+	1.73205i	−0.0745356	+	0.129099i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	−8.00000			−0.585018
$188$		0			0
$189$	2.00000	+	3.46410i	0.145479	+	0.251976i
$190$		0			0
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$	3.50000	−	6.06218i	0.252591	−	0.437500i
$193$	9.00000	−	15.5885i	0.647834	−	1.12208i	−0.335805	−	0.941932i	$-0.609008\pi$
$193$	9.00000	−	15.5885i	0.647834	−	1.12208i	0.983639	−	0.180150i	$-0.0576584\pi$
$194$	10.0000			0.717958
$195$		0			0
$196$	−9.00000			−0.642857
$197$	9.00000	−	15.5885i	0.641223	−	1.11063i	−0.343937	−	0.938993i	$-0.611761\pi$
$197$	9.00000	−	15.5885i	0.641223	−	1.11063i	0.985160	−	0.171639i	$-0.0549062\pi$
$198$	−2.00000	+	3.46410i	−0.142134	+	0.246183i
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	−3.00000			−0.212132
$201$	4.00000	+	6.92820i	0.282138	+	0.488678i
$202$	−9.00000	−	15.5885i	−0.633238	−	1.09680i
$203$	−40.0000			−2.80745
$204$	−1.00000	−	1.73205i	−0.0700140	−	0.121268i
$205$	−6.00000	+	10.3923i	−0.419058	+	0.725830i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$	4.00000	−	6.92820i	0.276026	−	0.478091i
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	−0.283918	−	0.958849i	$-0.591634\pi$
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	0.972346	−	0.233544i	$-0.0750324\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−12.0000	−	20.7846i	−0.818393	−	1.41750i
$216$	−3.00000			−0.204124
$217$	8.00000	+	13.8564i	0.543075	+	0.940634i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$	−8.00000			−0.539360
$221$		0			0
$222$	2.00000			0.134231
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	−0.791258	−	0.611482i	$-0.790574\pi$
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	0.925188	+	0.379509i	$0.123907\pi$
$224$	10.0000	−	17.3205i	0.668153	−	1.15728i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	6.00000			0.399114
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$		0			0
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$		0			0
$231$	−8.00000	+	13.8564i	−0.526361	+	0.911685i
$232$	15.0000	−	25.9808i	0.984798	−	1.70572i
$233$	−14.0000			−0.917170			−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000			−0.917170			−0.458585	+	0.888650i	$0.651644\pi$
$234$		0			0
$235$		0			0
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$	4.00000	−	6.92820i	0.259828	−	0.450035i
$238$	4.00000	+	6.92820i	0.259281	+	0.449089i
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$	1.00000	+	1.73205i	0.0645497	+	0.111803i
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	−5.00000			−0.321412
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$	9.00000	−	15.5885i	0.574989	−	0.995910i
$246$	−6.00000			−0.382546
$247$		0			0
$248$	−12.0000			−0.762001
$249$	−2.00000	+	3.46410i	−0.126745	+	0.219529i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$	−4.00000			−0.251976
$253$		0			0
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$	4.00000			0.250490
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	0.101305	+	0.994855i	$0.467698\pi$
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	−0.912222	+	0.409695i	$0.865635\pi$
$258$	6.00000	−	10.3923i	0.373544	−	0.646997i
$259$	8.00000			0.497096
$260$		0			0
$261$	−10.0000			−0.618984
$262$	2.00000	−	3.46410i	0.123560	−	0.214013i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$	−6.00000	−	10.3923i	−0.369274	−	0.639602i
$265$	−12.0000			−0.737154
$266$		0			0
$267$	1.00000	+	1.73205i	0.0611990	+	0.106000i
$268$	−8.00000			−0.488678
$269$	−11.0000	−	19.0526i	−0.670682	−	1.16166i	−0.977711	−	0.209955i	$-0.932668\pi$
$269$	−11.0000	−	19.0526i	−0.670682	−	1.16166i	0.307029	−	0.951700i	$-0.400665\pi$
$270$	1.00000	−	1.73205i	0.0608581	−	0.105409i
$271$	−6.00000	+	10.3923i	−0.364474	+	0.631288i	−0.988692	−	0.149963i	$-0.952085\pi$
$271$	−6.00000	+	10.3923i	−0.364474	+	0.631288i	0.624218	+	0.781251i	$0.285418\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	6.00000			0.362473
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	−12.0000			−0.719712
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$	12.0000	+	20.7846i	0.717137	+	1.24212i
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	−6.00000	+	10.3923i	−0.356663	+	0.617758i	−0.987401	−	0.158237i	$-0.949419\pi$
$283$	−6.00000	+	10.3923i	−0.356663	+	0.617758i	0.630738	+	0.775996i	$0.282752\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−24.0000			−1.41668
$288$	2.50000	−	4.33013i	0.147314	−	0.255155i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	10.0000	+	17.3205i	0.587220	+	1.01710i
$291$	10.0000			0.586210
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	0.764990	−	0.644042i	$-0.222744\pi$
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	−0.940252	+	0.340480i	$0.889411\pi$
$294$	9.00000			0.524891
$295$	−12.0000	−	20.7846i	−0.698667	−	1.21013i
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$	−2.00000	+	3.46410i	−0.116052	+	0.201008i
$298$	−6.00000			−0.347571
$299$		0			0
$300$	−1.00000			−0.0577350
$301$	24.0000	−	41.5692i	1.38334	−	2.39601i
$302$	−2.00000	+	3.46410i	−0.115087	+	0.199337i
$303$	−9.00000	−	15.5885i	−0.517036	−	0.895533i
$304$		0			0
$305$	−2.00000	−	3.46410i	−0.114520	−	0.198354i
$306$	1.00000	+	1.73205i	0.0571662	+	0.0990148i
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$	−8.00000	−	13.8564i	−0.455842	−	0.789542i
$309$		0			0
$310$	4.00000	−	6.92820i	0.227185	−	0.393496i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−9.00000	+	15.5885i	−0.507899	+	0.879708i
$315$	4.00000	−	6.92820i	0.225374	−	0.390360i
$316$	4.00000	+	6.92820i	0.225018	+	0.389742i
$317$	−26.0000			−1.46031			−0.730153	−	0.683284i	$-0.760551\pi$
$317$	−26.0000			−1.46031			−0.730153	+	0.683284i	$0.760551\pi$
$318$	−3.00000	−	5.19615i	−0.168232	−	0.291386i
$319$	−20.0000	−	34.6410i	−1.11979	−	1.93952i
$320$	−14.0000			−0.782624
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$		0			0
$323$		0			0
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	8.00000			0.443079
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	9.00000	−	15.5885i	0.496942	−	0.860729i
$329$		0			0
$330$	8.00000			0.440386
$331$	−8.00000	−	13.8564i	−0.439720	−	0.761617i	0.557948	−	0.829876i	$-0.311589\pi$
$331$	−8.00000	−	13.8564i	−0.439720	−	0.761617i	−0.997668	+	0.0682590i	$0.978256\pi$
$332$	−2.00000	−	3.46410i	−0.109764	−	0.190117i
$333$	2.00000			0.109599
$334$	4.00000	+	6.92820i	0.218870	+	0.379094i
$335$	8.00000	−	13.8564i	0.437087	−	0.757056i
$336$	−2.00000	+	3.46410i	−0.109109	+	0.188982i
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$		0			0
$339$	6.00000			0.325875
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$	−8.00000	+	13.8564i	−0.433224	+	0.750366i
$342$		0			0
$343$	8.00000			0.431959
$344$	18.0000	+	31.1769i	0.970495	+	1.68095i
$345$		0			0
$346$	−6.00000			−0.322562
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	5.00000	−	8.66025i	0.268028	−	0.464238i
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	20.0000			1.06600
$353$	−1.00000	+	1.73205i	−0.0532246	+	0.0921878i	−0.891410	−	0.453197i	$-0.850283\pi$
$353$	−1.00000	+	1.73205i	−0.0532246	+	0.0921878i	0.838186	+	0.545385i	$0.183617\pi$
$354$	6.00000	−	10.3923i	0.318896	−	0.552345i
$355$		0			0
$356$	−2.00000			−0.106000
$357$	4.00000	+	6.92820i	0.211702	+	0.366679i
$358$	2.00000	+	3.46410i	0.105703	+	0.183083i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$	3.00000	+	5.19615i	0.158114	+	0.273861i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	−5.00000	+	8.66025i	−0.262794	+	0.455173i
$363$	−5.00000			−0.262432
$364$		0			0
$365$	4.00000			0.209370
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$		0			0
$369$	−6.00000			−0.312348
$370$	−2.00000	−	3.46410i	−0.103975	−	0.180090i
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$	−4.00000			−0.207390
$373$	13.0000	+	22.5167i	0.673114	+	1.16587i	0.977016	+	0.213165i	$0.0683772\pi$
$373$	13.0000	+	22.5167i	0.673114	+	1.16587i	−0.303902	+	0.952703i	$0.598289\pi$
$374$	−4.00000	+	6.92820i	−0.206835	+	0.358249i
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$		0			0
$377$		0			0
$378$	4.00000			0.205738
$379$	−12.0000	+	20.7846i	−0.616399	+	1.06763i	0.373739	+	0.927534i	$0.378076\pi$
$379$	−12.0000	+	20.7846i	−0.616399	+	1.06763i	−0.990137	+	0.140100i	$0.955258\pi$
$380$		0			0
$381$	−8.00000	−	13.8564i	−0.409852	−	0.709885i
$382$	−8.00000			−0.409316
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$	1.50000	+	2.59808i	0.0765466	+	0.132583i
$385$	32.0000			1.63087
$386$	−9.00000	−	15.5885i	−0.458088	−	0.793432i
$387$	6.00000	−	10.3923i	0.304997	−	0.528271i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	22.0000			1.11544			0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000			1.11544			0.557722	+	0.830028i	$0.311675\pi$
$390$		0			0
$391$		0			0
$392$	−13.5000	+	23.3827i	−0.681853	+	1.18100i
$393$	2.00000	−	3.46410i	0.100887	−	0.174741i
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	−16.0000			−0.805047
$396$	−2.00000	−	3.46410i	−0.100504	−	0.174078i
$397$	19.0000	+	32.9090i	0.953583	+	1.65165i	0.737579	+	0.675261i	$0.235969\pi$
$397$	19.0000	+	32.9090i	0.953583	+	1.65165i	0.216004	+	0.976392i	$0.430698\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	−0.449008	−	0.893528i	$-0.648223\pi$
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	0.998322	−	0.0579116i	$-0.0184442\pi$
$402$	8.00000			0.399004
$403$		0			0
$404$	18.0000			0.895533
$405$	1.00000	−	1.73205i	0.0496904	−	0.0860663i
$406$	−20.0000	+	34.6410i	−0.992583	+	1.71920i
$407$	4.00000	+	6.92820i	0.198273	+	0.343418i
$408$	−6.00000			−0.297044
$409$	17.0000	+	29.4449i	0.840596	+	1.45595i	0.889392	+	0.457146i	$0.151128\pi$
$409$	17.0000	+	29.4449i	0.840596	+	1.45595i	−0.0487958	+	0.998809i	$0.515538\pi$
$410$	6.00000	+	10.3923i	0.296319	+	0.513239i
$411$	6.00000			0.295958
$412$		0			0
$413$	24.0000	−	41.5692i	1.18096	−	2.04549i
$414$		0			0
$415$	8.00000			0.392705
$416$		0			0
$417$	−12.0000			−0.587643
$418$		0			0
$419$	−2.00000	+	3.46410i	−0.0977064	+	0.169232i	−0.910735	−	0.412991i	$-0.864484\pi$
$419$	−2.00000	+	3.46410i	−0.0977064	+	0.169232i	0.813029	+	0.582224i	$0.197817\pi$
$420$	4.00000	+	6.92820i	0.195180	+	0.338062i
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	−10.0000	−	17.3205i	−0.486792	−	0.843149i
$423$		0			0
$424$	18.0000			0.874157
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$	4.00000	−	6.92820i	0.193574	−	0.335279i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	−24.0000			−1.15738
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	−0.907906	−	0.419173i	$-0.862320\pi$
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	0.0909384	−	0.995857i	$-0.471013\pi$
$434$	16.0000			0.768025
$435$	10.0000	+	17.3205i	0.479463	+	0.830455i
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$		0			0
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	0.177325	+	0.984152i	$0.443256\pi$
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	−0.940963	+	0.338508i	$0.890078\pi$
$440$	−12.0000	+	20.7846i	−0.572078	+	0.990867i
$441$	9.00000			0.428571
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$	2.00000	−	3.46410i	0.0948091	−	0.164214i
$446$	−2.00000	−	3.46410i	−0.0947027	−	0.164030i
$447$	−6.00000			−0.283790
$448$	−14.0000	−	24.2487i	−0.661438	−	1.14564i
$449$	11.0000	+	19.0526i	0.519122	+	0.899146i	0.999753	+	0.0222229i	$0.00707434\pi$
$449$	11.0000	+	19.0526i	0.519122	+	0.899146i	−0.480631	+	0.876923i	$0.659592\pi$
$450$	1.00000			0.0471405
$451$	−12.0000	−	20.7846i	−0.565058	−	0.978709i
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	−2.00000	+	3.46410i	−0.0939682	+	0.162758i
$454$	−20.0000			−0.938647
$455$		0			0
$456$		0			0
$457$	1.00000	−	1.73205i	0.0467780	−	0.0810219i	−0.841688	−	0.539964i	$-0.818438\pi$
$457$	1.00000	−	1.73205i	0.0467780	−	0.0810219i	0.888466	+	0.458942i	$0.151771\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$		0			0
$461$	−19.0000	−	32.9090i	−0.884918	−	1.53272i	−0.845807	−	0.533488i	$-0.820881\pi$
$461$	−19.0000	−	32.9090i	−0.884918	−	1.53272i	−0.0391109	−	0.999235i	$-0.512453\pi$
$462$	8.00000	+	13.8564i	0.372194	+	0.644658i
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−5.00000	−	8.66025i	−0.232119	−	0.402042i
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	32.0000			1.47762
$470$		0			0
$471$	−9.00000	+	15.5885i	−0.414698	+	0.718278i
$472$	18.0000	+	31.1769i	0.828517	+	1.43503i
$473$	48.0000			2.20704
$474$	−4.00000	−	6.92820i	−0.183726	−	0.318223i
$475$		0			0
$476$	−8.00000			−0.366679
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$	12.0000	−	20.7846i	0.548867	−	0.950666i
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$	−10.0000			−0.456435
$481$		0			0
$482$	10.0000			0.455488
$483$		0			0
$484$	2.50000	−	4.33013i	0.113636	−	0.196824i
$485$	−10.0000	−	17.3205i	−0.454077	−	0.786484i
$486$	1.00000			0.0453609
$487$	6.00000	+	10.3923i	0.271886	+	0.470920i	0.969345	−	0.245705i	$-0.0790193\pi$
$487$	6.00000	+	10.3923i	0.271886	+	0.470920i	−0.697459	+	0.716625i	$0.745686\pi$
$488$	3.00000	+	5.19615i	0.135804	+	0.235219i
$489$	8.00000			0.361773
$490$	−9.00000	−	15.5885i	−0.406579	−	0.704215i
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	−20.0000			−0.900755
$494$		0			0
$495$	8.00000			0.359573
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$		0			0
$498$	2.00000	+	3.46410i	0.0896221	+	0.155230i
$499$	24.0000			1.07439			0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000			1.07439			0.537194	+	0.843459i	$0.319484\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$	4.00000	+	6.92820i	0.178707	+	0.309529i
$502$	12.0000			0.535586
$503$	4.00000	+	6.92820i	0.178351	+	0.308913i	0.941316	−	0.337527i	$-0.109590\pi$
$503$	4.00000	+	6.92820i	0.178351	+	0.308913i	−0.762965	+	0.646440i	$0.776257\pi$
$504$	−6.00000	+	10.3923i	−0.267261	+	0.462910i
$505$	−18.0000	+	31.1769i	−0.800989	+	1.38735i
$506$		0			0
$507$		0			0
$508$	16.0000			0.709885
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$	2.00000	−	3.46410i	0.0885615	−	0.153393i
$511$	4.00000	+	6.92820i	0.176950	+	0.306486i
$512$	11.0000			0.486136
$513$		0			0
$514$	13.0000	+	22.5167i	0.573405	+	0.993167i
$515$		0			0
$516$	6.00000	+	10.3923i	0.264135	+	0.457496i
$517$		0			0
$518$	4.00000	−	6.92820i	0.175750	−	0.304408i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	−5.00000	+	8.66025i	−0.218844	+	0.379049i
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.244507	+	0.969648i	$0.578626\pi$
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.717486	+	0.696573i	$0.754707\pi$
$524$	2.00000	+	3.46410i	0.0873704	+	0.151330i
$525$	4.00000			0.174574
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$	4.00000	+	6.92820i	0.174243	+	0.301797i
$528$	−4.00000			−0.174078
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−6.00000	+	10.3923i	−0.260623	+	0.451413i
$531$	6.00000	−	10.3923i	0.260378	−	0.450988i
$532$		0			0
$533$		0			0
$534$	2.00000			0.0865485
$535$	12.0000	−	20.7846i	0.518805	−	0.898597i
$536$	−12.0000	+	20.7846i	−0.518321	+	0.897758i
$537$	2.00000	+	3.46410i	0.0863064	+	0.149487i
$538$	−22.0000			−0.948487
$539$	18.0000	+	31.1769i	0.775315	+	1.34288i
$540$	1.00000	+	1.73205i	0.0430331	+	0.0745356i
$541$	−30.0000			−1.28980			−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000			−1.28980			−0.644900	+	0.764267i	$0.723101\pi$
$542$	6.00000	+	10.3923i	0.257722	+	0.446388i
$543$	−5.00000	+	8.66025i	−0.214571	+	0.371647i
$544$	5.00000	−	8.66025i	0.214373	−	0.371305i
$545$	−4.00000			−0.171341
$546$		0			0
$547$	4.00000			0.171028			0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000			0.171028			0.0855138	+	0.996337i	$0.472747\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$		0			0
$552$		0			0
$553$	−16.0000	−	27.7128i	−0.680389	−	1.17847i
$554$	10.0000			0.424859
$555$	−2.00000	−	3.46410i	−0.0848953	−	0.147043i
$556$	6.00000	−	10.3923i	0.254457	−	0.440732i
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	−0.609912	−	0.792469i	$-0.708795\pi$
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	0.991254	+	0.131965i	$0.0421286\pi$
$558$	4.00000			0.169334
$559$		0			0
$560$	8.00000			0.338062
$561$	−4.00000	+	6.92820i	−0.168880	+	0.292509i
$562$	5.00000	−	8.66025i	0.210912	−	0.365311i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$	−6.00000	−	10.3923i	−0.252422	−	0.437208i
$566$	6.00000	+	10.3923i	0.252199	+	0.436821i
$567$	4.00000			0.167984
$568$		0			0
$569$	−17.0000	+	29.4449i	−0.712677	+	1.23439i	0.251172	+	0.967943i	$0.419184\pi$
$569$	−17.0000	+	29.4449i	−0.712677	+	1.23439i	−0.963849	+	0.266450i	$0.914149\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		0			0
$573$	−8.00000			−0.334205
$574$	−12.0000	+	20.7846i	−0.500870	+	0.867533i
$575$		0			0
$576$	−3.50000	−	6.06218i	−0.145833	−	0.252591i
$577$	46.0000			1.91501			0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000			1.91501			0.957503	+	0.288425i	$0.0931316\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	−9.00000	−	15.5885i	−0.374027	−	0.647834i
$580$	−20.0000			−0.830455
$581$	8.00000	+	13.8564i	0.331896	+	0.574861i
$582$	5.00000	−	8.66025i	0.207257	−	0.358979i
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$	−6.00000			−0.248282
$585$		0			0
$586$	−6.00000			−0.247858
$587$	14.0000	−	24.2487i	0.577842	−	1.00085i	−0.417885	−	0.908500i	$-0.637228\pi$
$587$	14.0000	−	24.2487i	0.577842	−	1.00085i	0.995726	−	0.0923513i	$-0.0294383\pi$
$588$	−4.50000	+	7.79423i	−0.185577	+	0.321429i
$589$		0			0
$590$	−24.0000			−0.988064
$591$	−9.00000	−	15.5885i	−0.370211	−	0.641223i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	26.0000			1.06769			0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000			1.06769			0.533846	+	0.845582i	$0.320746\pi$
$594$	2.00000	+	3.46410i	0.0820610	+	0.142134i
$595$	8.00000	−	13.8564i	0.327968	−	0.568057i
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	−8.00000			−0.327418
$598$		0			0
$599$	−40.0000			−1.63436			−0.817178	−	0.576386i	$-0.804463\pi$
$599$	−40.0000			−1.63436			−0.817178	+	0.576386i	$0.804463\pi$
$600$	−1.50000	+	2.59808i	−0.0612372	+	0.106066i
$601$	19.0000	−	32.9090i	0.775026	−	1.34238i	−0.159754	−	0.987157i	$-0.551070\pi$
$601$	19.0000	−	32.9090i	0.775026	−	1.34238i	0.934780	−	0.355228i	$-0.115597\pi$
$602$	−24.0000	−	41.5692i	−0.978167	−	1.69423i
$603$	8.00000			0.325785
$604$	−2.00000	−	3.46410i	−0.0813788	−	0.140952i
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$	−18.0000			−0.731200
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$		0			0
$609$	−20.0000	+	34.6410i	−0.810441	+	1.40372i
$610$	−4.00000			−0.161955
$611$		0			0
$612$	−2.00000			−0.0808452
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	8.00000	−	13.8564i	0.322854	−	0.559199i
$615$	6.00000	+	10.3923i	0.241943	+	0.419058i
$616$	−48.0000			−1.93398
$617$	11.0000	+	19.0526i	0.442843	+	0.767027i	0.997899	−	0.0647859i	$-0.0206365\pi$
$617$	11.0000	+	19.0526i	0.442843	+	0.767027i	−0.555056	+	0.831813i	$0.687303\pi$
$618$		0			0
$619$	−24.0000			−0.964641			−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000			−0.964641			−0.482321	+	0.875995i	$0.660206\pi$
$620$	4.00000	+	6.92820i	0.160644	+	0.278243i
$621$		0			0
$622$		0			0
$623$	8.00000			0.320513
$624$		0			0
$625$	−19.0000			−0.760000
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$		0			0
$628$	−9.00000	−	15.5885i	−0.359139	−	0.622047i
$629$	4.00000			0.159490
$630$	−4.00000	−	6.92820i	−0.159364	−	0.276026i
$631$	10.0000	+	17.3205i	0.398094	+	0.689519i	0.993491	−	0.113913i	$-0.0363385\pi$
$631$	10.0000	+	17.3205i	0.398094	+	0.689519i	−0.595397	+	0.803432i	$0.703005\pi$
$632$	24.0000			0.954669
$633$	−10.0000	−	17.3205i	−0.397464	−	0.688428i
$634$	−13.0000	+	22.5167i	−0.516296	+	0.894251i
$635$	−16.0000	+	27.7128i	−0.634941	+	1.09975i
$636$	6.00000			0.237915
$637$		0			0
$638$	−40.0000			−1.58362
$639$		0			0
$640$	3.00000	−	5.19615i	0.118585	−	0.205396i
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	0.845601	−	0.533816i	$-0.179242\pi$
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	−0.885098	+	0.465404i	$0.845909\pi$
$642$	12.0000			0.473602
$643$	−20.0000	−	34.6410i	−0.788723	−	1.36611i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$	−20.0000	−	34.6410i	−0.788723	−	1.36611i	0.138027	−	0.990429i	$-0.455924\pi$
$644$		0			0
$645$	−24.0000			−0.944999
$646$		0			0
$647$	4.00000	−	6.92820i	0.157256	−	0.272376i	−0.776622	−	0.629967i	$-0.783068\pi$
$647$	4.00000	−	6.92820i	0.157256	−	0.272376i	0.933878	+	0.357591i	$0.116402\pi$
$648$	−1.50000	+	2.59808i	−0.0589256	+	0.102062i
$649$	48.0000			1.88416
$650$		0			0
$651$	16.0000			0.627089
$652$	−4.00000	+	6.92820i	−0.156652	+	0.271329i
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$	−8.00000			−0.312586
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	1.00000	+	1.73205i	0.0390137	+	0.0675737i
$658$		0			0
$659$	−14.0000	−	24.2487i	−0.545363	−	0.944596i	−0.998584	−	0.0531977i	$-0.983059\pi$
$659$	−14.0000	−	24.2487i	−0.545363	−	0.944596i	0.453221	−	0.891398i	$-0.350275\pi$
$660$	−4.00000	+	6.92820i	−0.155700	+	0.269680i
$661$	15.0000	−	25.9808i	0.583432	−	1.01053i	−0.411636	−	0.911348i	$-0.635043\pi$
$661$	15.0000	−	25.9808i	0.583432	−	1.01053i	0.995069	−	0.0991864i	$-0.0316240\pi$
$662$	−16.0000			−0.621858
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$	1.00000	−	1.73205i	0.0387492	−	0.0671156i
$667$		0			0
$668$	−8.00000			−0.309529
$669$	−2.00000	−	3.46410i	−0.0773245	−	0.133930i
$670$	−8.00000	−	13.8564i	−0.309067	−	0.535320i
$671$	8.00000			0.308837
$672$	−10.0000	−	17.3205i	−0.385758	−	0.668153i
$673$	7.00000	−	12.1244i	0.269830	−	0.467360i	−0.698988	−	0.715134i	$-0.746366\pi$
$673$	7.00000	−	12.1244i	0.269830	−	0.467360i	0.968818	+	0.247774i	$0.0796991\pi$
$674$	9.00000	−	15.5885i	0.346667	−	0.600445i
$675$	1.00000			0.0384900
$676$		0			0
$677$	22.0000			0.845529			0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000			0.845529			0.422764	+	0.906240i	$0.361060\pi$
$678$	3.00000	−	5.19615i	0.115214	−	0.199557i
$679$	20.0000	−	34.6410i	0.767530	−	1.32940i
$680$	6.00000	+	10.3923i	0.230089	+	0.398527i
$681$	−20.0000			−0.766402
$682$	8.00000	+	13.8564i	0.306336	+	0.530589i
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$		0			0
$685$	−6.00000	−	10.3923i	−0.229248	−	0.397070i
$686$	4.00000	−	6.92820i	0.152721	−	0.264520i
$687$	5.00000	−	8.66025i	0.190762	−	0.330409i
$688$	12.0000			0.457496
$689$		0			0
$690$		0			0
$691$	−12.0000	+	20.7846i	−0.456502	+	0.790684i	−0.998773	−	0.0495194i	$-0.984231\pi$
$691$	−12.0000	+	20.7846i	−0.456502	+	0.790684i	0.542272	+	0.840203i	$0.317564\pi$
$692$	3.00000	−	5.19615i	0.114043	−	0.197528i
$693$	8.00000	+	13.8564i	0.303895	+	0.526361i
$694$	12.0000			0.455514
$695$	12.0000	+	20.7846i	0.455186	+	0.788405i
$696$	−15.0000	−	25.9808i	−0.568574	−	0.984798i
$697$	−12.0000			−0.454532
$698$	13.0000	+	22.5167i	0.492057	+	0.852268i
$699$	−7.00000	+	12.1244i	−0.264764	+	0.458585i
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$		0			0
$703$		0			0
$704$	14.0000	−	24.2487i	0.527645	−	0.913908i
$705$		0			0
$706$	1.00000	+	1.73205i	0.0376355	+	0.0651866i
$707$	−72.0000			−2.70784
$708$	6.00000	+	10.3923i	0.225494	+	0.390567i
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	0.511683	−	0.859174i	$-0.329022\pi$
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	−0.999908	+	0.0135434i	$0.995689\pi$
$710$		0			0
$711$	−4.00000	−	6.92820i	−0.150012	−	0.259828i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$		0			0
$714$	8.00000			0.299392
$715$		0			0
$716$	−4.00000			−0.149487
$717$	12.0000	−	20.7846i	0.448148	−	0.776215i
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	0.998224	−	0.0595683i	$-0.0189724\pi$
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	−0.550700	+	0.834703i	$0.685639\pi$
$720$	2.00000			0.0745356
$721$		0			0
$722$	−9.50000	−	16.4545i	−0.353553	−	0.612372i
$723$	10.0000			0.371904
$724$	−5.00000	−	8.66025i	−0.185824	−	0.321856i
$725$	−5.00000	+	8.66025i	−0.185695	+	0.321634i
$726$	−2.50000	+	4.33013i	−0.0927837	+	0.160706i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	2.00000	−	3.46410i	0.0740233	−	0.128212i
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	1.00000	+	1.73205i	0.0369611	+	0.0640184i
$733$	−30.0000			−1.10808			−0.554038	−	0.832492i	$-0.686914\pi$
$733$	−30.0000			−1.10808			−0.554038	+	0.832492i	$0.686914\pi$
$734$	8.00000	+	13.8564i	0.295285	+	0.511449i
$735$	−9.00000	−	15.5885i	−0.331970	−	0.574989i
$736$		0			0
$737$	16.0000	+	27.7128i	0.589368	+	1.02081i
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	16.0000	−	27.7128i	0.588570	−	1.01943i	−0.405851	−	0.913939i	$-0.633025\pi$
$739$	16.0000	−	27.7128i	0.588570	−	1.01943i	0.994420	−	0.105493i	$-0.0336420\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$	−24.0000			−0.881068
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.0296605	−	0.999560i	$-0.490557\pi$
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.850814	−	0.525467i	$-0.176109\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$	6.00000	+	10.3923i	0.219823	+	0.380745i
$746$	26.0000			0.951928
$747$	2.00000	+	3.46410i	0.0731762	+	0.126745i
$748$	−4.00000	−	6.92820i	−0.146254	−	0.253320i
$749$	48.0000			1.75388
$750$	−6.00000	−	10.3923i	−0.219089	−	0.379473i
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$		0			0
$753$	12.0000			0.437304
$754$		0			0
$755$	8.00000			0.291150
$756$	−2.00000	+	3.46410i	−0.0727393	+	0.125988i
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	−0.993701	−	0.112062i	$-0.964254\pi$
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	0.593899	+	0.804539i	$0.297588\pi$
$758$	12.0000	+	20.7846i	0.435860	+	0.754931i
$759$		0			0
$760$		0			0
$761$	−5.00000	−	8.66025i	−0.181250	−	0.313934i	0.761057	−	0.648686i	$-0.224681\pi$
$761$	−5.00000	−	8.66025i	−0.181250	−	0.313934i	−0.942306	+	0.334752i	$0.891348\pi$
$762$	−16.0000			−0.579619
$763$	−4.00000	−	6.92820i	−0.144810	−	0.250818i
$764$	4.00000	−	6.92820i	0.144715	−	0.250654i
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$	−16.0000			−0.578103
$767$		0			0
$768$	17.0000			0.613435
$769$	−15.0000	+	25.9808i	−0.540914	+	0.936890i	0.457938	+	0.888984i	$0.348588\pi$
$769$	−15.0000	+	25.9808i	−0.540914	+	0.936890i	−0.998852	+	0.0479061i	$0.984745\pi$
$770$	16.0000	−	27.7128i	0.576600	−	0.998700i
$771$	13.0000	+	22.5167i	0.468184	+	0.810918i
$772$	18.0000			0.647834
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	0.941825	−	0.336104i	$-0.109109\pi$
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	−0.761987	+	0.647592i	$0.775776\pi$
$774$	−6.00000	−	10.3923i	−0.215666	−	0.373544i
$775$	4.00000			0.143684
$776$	15.0000	+	25.9808i	0.538469	+	0.932655i
$777$	4.00000	−	6.92820i	0.143499	−	0.248548i
$778$	11.0000	−	19.0526i	0.394369	−	0.683067i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−5.00000	+	8.66025i	−0.178685	+	0.309492i
$784$	4.50000	+	7.79423i	0.160714	+	0.278365i
$785$	36.0000			1.28490
$786$	−2.00000	−	3.46410i	−0.0713376	−	0.123560i
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	18.0000			0.641223
$789$	12.0000	+	20.7846i	0.427211	+	0.739952i
$790$	−8.00000	+	13.8564i	−0.284627	+	0.492989i
$791$	12.0000	−	20.7846i	0.426671	−	0.739016i
$792$	−12.0000			−0.426401
$793$		0			0
$794$	38.0000			1.34857
$795$	−6.00000	+	10.3923i	−0.212798	+	0.368577i
$796$	4.00000	−	6.92820i	0.141776	−	0.245564i
$797$	−23.0000	−	39.8372i	−0.814702	−	1.41110i	−0.909542	−	0.415612i	$-0.863567\pi$
$797$	−23.0000	−	39.8372i	−0.814702	−	1.41110i	0.0948400	−	0.995493i	$-0.469766\pi$
$798$		0			0
$799$		0			0
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	2.00000			0.0706665
$802$	−11.0000	−	19.0526i	−0.388424	−	0.672769i
$803$	−4.00000	+	6.92820i	−0.141157	+	0.244491i
$804$	−4.00000	+	6.92820i	−0.141069	+	0.244339i
$805$		0			0
$806$		0			0
$807$	−22.0000			−0.774437
$808$	27.0000	−	46.7654i	0.949857	−	1.64520i
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$	−1.00000	−	1.73205i	−0.0351364	−	0.0608581i
$811$	−8.00000			−0.280918			−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000			−0.280918			−0.140459	+	0.990086i	$0.544858\pi$
$812$	−20.0000	−	34.6410i	−0.701862	−	1.21566i
$813$	6.00000	+	10.3923i	0.210429	+	0.364474i
$814$	8.00000			0.280400
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$	−1.00000	+	1.73205i	−0.0350070	+	0.0606339i
$817$		0			0
$818$	34.0000			1.18878
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$	3.00000	−	5.19615i	0.104637	−	0.181237i
$823$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$823$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$	2.00000	+	3.46410i	0.0696311	+	0.120605i
$826$	−24.0000	−	41.5692i	−0.835067	−	1.44638i
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$		0			0
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	−0.403739	−	0.914874i	$-0.632290\pi$
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	0.994174	−	0.107788i	$-0.0343769\pi$
$830$	4.00000	−	6.92820i	0.138842	−	0.240481i
$831$	10.0000			0.346896
$832$		0			0
$833$	18.0000			0.623663
$834$	−6.00000	+	10.3923i	−0.207763	+	0.359856i
$835$	8.00000	−	13.8564i	0.276851	−	0.479521i
$836$		0			0
$837$	4.00000			0.138260
$838$	2.00000	+	3.46410i	0.0690889	+	0.119665i
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	0.899158	+	0.437623i	$0.144180\pi$
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	−0.0705865	+	0.997506i	$0.522487\pi$
$840$	24.0000			0.828079
$841$	−35.5000	−	61.4878i	−1.22414	−	2.12027i
$842$	5.00000	−	8.66025i	0.172311	−	0.298452i
$843$	5.00000	−	8.66025i	0.172209	−	0.298275i
$844$	20.0000			0.688428
$845$		0			0
$846$		0			0
$847$	−10.0000	+	17.3205i	−0.343604	+	0.595140i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$	6.00000	+	10.3923i	0.205919	+	0.356663i
$850$	2.00000			0.0685994
$851$		0			0
$852$		0			0
$853$	−30.0000			−1.02718			−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000			−1.02718			−0.513590	+	0.858036i	$0.671685\pi$
$854$	−4.00000	−	6.92820i	−0.136877	−	0.237078i
$855$		0			0
$856$	−18.0000	+	31.1769i	−0.615227	+	1.06561i
$857$	−46.0000			−1.57133			−0.785665	−	0.618652i	$-0.787679\pi$
$857$	−46.0000			−1.57133			−0.785665	+	0.618652i	$0.787679\pi$
$858$		0			0
$859$	−44.0000			−1.50126			−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000			−1.50126			−0.750630	+	0.660722i	$0.770250\pi$
$860$	12.0000	−	20.7846i	0.409197	−	0.708749i
$861$	−12.0000	+	20.7846i	−0.408959	+	0.708338i
$862$		0			0
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$	6.00000	+	10.3923i	0.204006	+	0.353349i
$866$	−34.0000			−1.15537
$867$	−6.50000	−	11.2583i	−0.220752	−	0.382353i
$868$	−8.00000	+	13.8564i	−0.271538	+	0.470317i
$869$	16.0000	−	27.7128i	0.542763	−	0.940093i
$870$	20.0000			0.678064
$871$		0			0
$872$	6.00000			0.203186
$873$	5.00000	−	8.66025i	0.169224	−	0.293105i
$874$		0			0
$875$	−24.0000	−	41.5692i	−0.811348	−	1.40530i
$876$	−2.00000			−0.0675737
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	0.769174	−	0.639040i	$-0.220668\pi$
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	−0.938012	+	0.346604i	$0.887335\pi$
$878$	16.0000	+	27.7128i	0.539974	+	0.935262i
$879$	−6.00000			−0.202375
$880$	4.00000	+	6.92820i	0.134840	+	0.233550i
$881$	−29.0000	+	50.2295i	−0.977035	+	1.69227i	−0.303985	+	0.952677i	$0.598317\pi$
$881$	−29.0000	+	50.2295i	−0.977035	+	1.69227i	−0.673050	+	0.739597i	$0.735016\pi$
$882$	4.50000	−	7.79423i	0.151523	−	0.262445i
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$	−24.0000			−0.806751
$886$	−2.00000	+	3.46410i	−0.0671913	+	0.116379i
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	−0.109881	−	0.993945i	$-0.535047\pi$
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	0.915722	−	0.401813i	$-0.131620\pi$
$888$	3.00000	+	5.19615i	0.100673	+	0.174371i
$889$	−64.0000			−2.14649
$890$	−2.00000	−	3.46410i	−0.0670402	−	0.116117i
$891$	2.00000	+	3.46410i	0.0670025	+	0.116052i
$892$	4.00000			0.133930
$893$		0			0
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$	4.00000	−	6.92820i	0.133705	−	0.231584i
$896$	12.0000			0.400892
$897$		0			0
$898$	22.0000			0.734150
$899$	−20.0000	+	34.6410i	−0.667037	+	1.15534i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$	−24.0000			−0.799113
$903$	−24.0000	−	41.5692i	−0.798670	−	1.38334i
$904$	9.00000	+	15.5885i	0.299336	+	0.518464i
$905$	20.0000			0.664822
$906$	2.00000	+	3.46410i	0.0664455	+	0.115087i
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	10.0000	−	17.3205i	0.331862	−	0.574801i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$		0			0
$913$	−8.00000	+	13.8564i	−0.264761	+	0.458580i
$914$	−1.00000	−	1.73205i	−0.0330771	−	0.0572911i
$915$	−4.00000			−0.132236
$916$	5.00000	+	8.66025i	0.165205	+	0.286143i
$917$	−8.00000	−	13.8564i	−0.264183	−	0.457579i
$918$	2.00000			0.0660098
$919$	24.0000	+	41.5692i	0.791687	+	1.37124i	0.924922	+	0.380158i	$0.124130\pi$
$919$	24.0000	+	41.5692i	0.791687	+	1.37124i	−0.133235	+	0.991084i	$0.542536\pi$
$920$		0			0
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$	−38.0000			−1.25146
$923$		0			0
$924$	−16.0000			−0.526361
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	−2.00000	+	3.46410i	−0.0657241	+	0.113837i
$927$		0			0
$928$	50.0000			1.64133
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$	−4.00000	−	6.92820i	−0.131165	−	0.227185i
$931$		0			0
$932$	−7.00000	−	12.1244i	−0.229293	−	0.397146i
$933$		0			0
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$	16.0000			0.523256
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	16.0000	−	27.7128i	0.522419	−	0.904855i
$939$	−3.00000	+	5.19615i	−0.0979013	+	0.169570i
$940$		0			0
$941$	14.0000			0.456387			0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000			0.456387			0.228193	+	0.973616i	$0.426718\pi$
$942$	9.00000	+	15.5885i	0.293236	+	0.507899i
$943$		0			0
$944$	12.0000			0.390567
$945$	−4.00000	−	6.92820i	−0.130120	−	0.225374i
$946$	24.0000	−	41.5692i	0.780307	−	1.35153i
$947$	−30.0000	+	51.9615i	−0.974869	+	1.68852i	−0.294502	+	0.955651i	$0.595154\pi$
$947$	−30.0000	+	51.9615i	−0.974869	+	1.68852i	−0.680367	+	0.732872i	$0.738179\pi$
$948$	8.00000			0.259828
$949$		0			0
$950$		0			0
$951$	−13.0000	+	22.5167i	−0.421554	+	0.730153i
$952$	−12.0000	+	20.7846i	−0.388922	+	0.673633i
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	0.999869	−	0.0162081i	$-0.00515944\pi$
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	−0.513971	+	0.857808i	$0.671826\pi$
$954$	−6.00000			−0.194257
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$	−40.0000			−1.29302
$958$	12.0000	+	20.7846i	0.387702	+	0.671520i
$959$	12.0000	−	20.7846i	0.387500	−	0.671170i
$960$	−7.00000	+	12.1244i	−0.225924	+	0.391312i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	12.0000			0.386695
$964$	−5.00000	+	8.66025i	−0.161039	+	0.278928i
$965$	−18.0000	+	31.1769i	−0.579441	+	1.00362i
$966$		0			0
$967$	52.0000			1.67221			0.836104	−	0.548572i	$-0.184828\pi$
$967$	52.0000			1.67221			0.836104	+	0.548572i	$0.184828\pi$
$968$	−7.50000	−	12.9904i	−0.241059	−	0.417527i
$969$		0			0
$970$	−20.0000			−0.642161
$971$	30.0000	+	51.9615i	0.962746	+	1.66752i	0.715553	+	0.698558i	$0.246175\pi$
$971$	30.0000	+	51.9615i	0.962746	+	1.66752i	0.247193	+	0.968966i	$0.420492\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−24.0000	+	41.5692i	−0.769405	+	1.33265i
$974$	12.0000			0.384505
$975$		0			0
$976$	2.00000			0.0640184
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	0.305530	+	0.952183i	$0.401167\pi$
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	−0.977379	+	0.211495i	$0.932167\pi$
$978$	4.00000	−	6.92820i	0.127906	−	0.221540i
$979$	4.00000	+	6.92820i	0.127841	+	0.221426i
$980$	18.0000			0.574989
$981$	−1.00000	−	1.73205i	−0.0319275	−	0.0553001i
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$	−9.00000	−	15.5885i	−0.286910	−	0.496942i
$985$	−18.0000	+	31.1769i	−0.573528	+	0.993379i
$986$	−10.0000	+	17.3205i	−0.318465	+	0.551597i
$987$		0			0
$988$		0			0
$989$		0			0
$990$	4.00000	−	6.92820i	0.127128	−	0.220193i
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	−0.964658	−	0.263504i	$-0.915122\pi$
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	0.710530	+	0.703667i	$0.248455\pi$
$992$	−10.0000	−	17.3205i	−0.317500	−	0.549927i
$993$	−16.0000			−0.507745
$994$		0			0
$995$	8.00000	+	13.8564i	0.253617	+	0.439278i
$996$	−4.00000			−0.126745
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	0.995077	−	0.0991016i	$-0.0315969\pi$
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	−0.583363	+	0.812211i	$0.698264\pi$
$998$	12.0000	−	20.7846i	0.379853	−	0.657925i
$999$	1.00000	−	1.73205i	0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.e.b.22.1		2
13.2	odd	12		507.2.j.e.361.2		4
13.3	even	3	inner	507.2.e.b.484.1		2
13.4	even	6		39.2.a.a.1.1	✓	1
13.5	odd	4		507.2.j.e.316.1		4
13.6	odd	12		507.2.b.a.337.2		2
13.7	odd	12		507.2.b.a.337.1		2
13.8	odd	4		507.2.j.e.316.2		4
13.9	even	3		507.2.a.a.1.1		1
13.10	even	6		507.2.e.a.484.1		2
13.11	odd	12		507.2.j.e.361.1		4
13.12	even	2		507.2.e.a.22.1		2
39.17	odd	6		117.2.a.a.1.1		1
39.20	even	12		1521.2.b.b.1351.2		2
39.32	even	12		1521.2.b.b.1351.1		2
39.35	odd	6		1521.2.a.e.1.1		1
52.35	odd	6		8112.2.a.s.1.1		1
52.43	odd	6		624.2.a.i.1.1		1
65.4	even	6		975.2.a.f.1.1		1
65.17	odd	12		975.2.c.f.274.2		2
65.43	odd	12		975.2.c.f.274.1		2
91.69	odd	6		1911.2.a.f.1.1		1
104.43	odd	6		2496.2.a.e.1.1		1
104.69	even	6		2496.2.a.q.1.1		1
117.4	even	6		1053.2.e.b.703.1		2
117.43	even	6		1053.2.e.b.352.1		2
117.56	odd	6		1053.2.e.d.352.1		2
117.95	odd	6		1053.2.e.d.703.1		2
143.43	odd	6		4719.2.a.c.1.1		1
156.95	even	6		1872.2.a.h.1.1		1
195.17	even	12		2925.2.c.e.2224.1		2
195.134	odd	6		2925.2.a.p.1.1		1
195.173	even	12		2925.2.c.e.2224.2		2
273.251	even	6		5733.2.a.e.1.1		1
312.173	odd	6		7488.2.a.bl.1.1		1
312.251	even	6		7488.2.a.by.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.a.a.1.1	✓	1	13.4	even	6
117.2.a.a.1.1		1	39.17	odd	6
507.2.a.a.1.1		1	13.9	even	3
507.2.b.a.337.1		2	13.7	odd	12
507.2.b.a.337.2		2	13.6	odd	12
507.2.e.a.22.1		2	13.12	even	2
507.2.e.a.484.1		2	13.10	even	6
507.2.e.b.22.1		2	1.1	even	1	trivial
507.2.e.b.484.1		2	13.3	even	3	inner
507.2.j.e.316.1		4	13.5	odd	4
507.2.j.e.316.2		4	13.8	odd	4
507.2.j.e.361.1		4	13.11	odd	12
507.2.j.e.361.2		4	13.2	odd	12
624.2.a.i.1.1		1	52.43	odd	6
975.2.a.f.1.1		1	65.4	even	6
975.2.c.f.274.1		2	65.43	odd	12
975.2.c.f.274.2		2	65.17	odd	12
1053.2.e.b.352.1		2	117.43	even	6
1053.2.e.b.703.1		2	117.4	even	6
1053.2.e.d.352.1		2	117.56	odd	6
1053.2.e.d.703.1		2	117.95	odd	6
1521.2.a.e.1.1		1	39.35	odd	6
1521.2.b.b.1351.1		2	39.32	even	12
1521.2.b.b.1351.2		2	39.20	even	12
1872.2.a.h.1.1		1	156.95	even	6
1911.2.a.f.1.1		1	91.69	odd	6
2496.2.a.e.1.1		1	104.43	odd	6
2496.2.a.q.1.1		1	104.69	even	6
2925.2.a.p.1.1		1	195.134	odd	6
2925.2.c.e.2224.1		2	195.17	even	12
2925.2.c.e.2224.2		2	195.173	even	12
4719.2.a.c.1.1		1	143.43	odd	6
5733.2.a.e.1.1		1	273.251	even	6
7488.2.a.bl.1.1		1	312.173	odd	6
7488.2.a.by.1.1		1	312.251	even	6
8112.2.a.s.1.1		1	52.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.e (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} -2.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +1.00000 q^{12} -4.00000 q^{14} +(-1.00000 + 1.73205i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} -1.00000 q^{18} +(-1.00000 - 1.73205i) q^{20} -4.00000 q^{21} +(-2.00000 - 3.46410i) q^{22} +(1.50000 - 2.59808i) q^{24} -1.00000 q^{25} -1.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +(5.00000 - 8.66025i) q^{29} +(1.00000 + 1.73205i) q^{30} -4.00000 q^{31} +(2.50000 + 4.33013i) q^{32} +(-2.00000 - 3.46410i) q^{33} -2.00000 q^{34} +(4.00000 + 6.92820i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-1.00000 + 1.73205i) q^{37} -6.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(-2.00000 + 3.46410i) q^{42} +(6.00000 + 10.3923i) q^{43} +4.00000 q^{44} +(1.00000 + 1.73205i) q^{45} +(-0.500000 - 0.866025i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} -2.00000 q^{51} +6.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-4.00000 + 6.92820i) q^{55} +(-6.00000 - 10.3923i) q^{56} +(-5.00000 - 8.66025i) q^{58} +(6.00000 + 10.3923i) q^{59} -2.00000 q^{60} +(1.00000 + 1.73205i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-2.00000 + 3.46410i) q^{63} +7.00000 q^{64} -4.00000 q^{66} +(-4.00000 + 6.92820i) q^{67} +(1.00000 - 1.73205i) q^{68} +8.00000 q^{70} +(-1.50000 - 2.59808i) q^{72} -2.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} -16.0000 q^{77} +8.00000 q^{79} +(-1.00000 + 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} -4.00000 q^{83} +(-2.00000 - 3.46410i) q^{84} +(2.00000 + 3.46410i) q^{85} +12.0000 q^{86} +(-5.00000 - 8.66025i) q^{87} +(6.00000 - 10.3923i) q^{88} +(-1.00000 + 1.73205i) q^{89} +2.00000 q^{90} +(-2.00000 + 3.46410i) q^{93} +5.00000 q^{96} +(5.00000 + 8.66025i) q^{97} +(4.50000 + 7.79423i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} + q^{4} - 4 q^{5} - q^{6} - 4 q^{7} + 6 q^{8} - q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{12} - 8 q^{14} - 2 q^{15} + q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{20} - 8 q^{21} - 4 q^{22} + 3 q^{24}+ \cdots - 8 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 + q^4 - 4 * q^5 - q^6 - 4 * q^7 + 6 * q^8 - q^9 - 2 * q^10 + 4 * q^11 + 2 * q^12 - 8 * q^14 - 2 * q^15 + q^16 - 2 * q^17 - 2 * q^18 - 2 * q^20 - 8 * q^21 - 4 * q^22 + 3 * q^24 - 2 * q^25 - 2 * q^27 + 4 * q^28 + 10 * q^29 + 2 * q^30 - 8 * q^31 + 5 * q^32 - 4 * q^33 - 4 * q^34 + 8 * q^35 + q^36 - 2 * q^37 - 12 * q^40 + 6 * q^41 - 4 * q^42 + 12 * q^43 + 8 * q^44 + 2 * q^45 - q^48 - 9 * q^49 - q^50 - 4 * q^51 + 12 * q^53 - q^54 - 8 * q^55 - 12 * q^56 - 10 * q^58 + 12 * q^59 - 4 * q^60 + 2 * q^61 - 4 * q^62 - 4 * q^63 + 14 * q^64 - 8 * q^66 - 8 * q^67 + 2 * q^68 + 16 * q^70 - 3 * q^72 - 4 * q^73 + 2 * q^74 - q^75 - 32 * q^77 + 16 * q^79 - 2 * q^80 - q^81 - 6 * q^82 - 8 * q^83 - 4 * q^84 + 4 * q^85 + 24 * q^86 - 10 * q^87 + 12 * q^88 - 2 * q^89 + 4 * q^90 - 4 * q^93 + 10 * q^96 + 10 * q^97 + 9 * q^98 - 8 * q^99

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