LMFDB - Embedded newform 666.2.e.b.223.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(223,666)] 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("666.223"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			223.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	666.223
Dual form			666.2.e.b.445.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(1.50000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +4.00000 q^{10} +(0.500000 - 0.866025i) q^{11} -1.73205i q^{12} +(-3.00000 - 5.19615i) q^{13} +6.92820i q^{15} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +3.00000 q^{18} -1.00000 q^{19} +(2.00000 - 3.46410i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} -6.00000 q^{26} +5.19615i q^{27} +(6.00000 + 3.46410i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 0.866025i) q^{33} +(1.50000 - 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} +1.00000 q^{37} +(-0.500000 + 0.866025i) q^{38} -10.3923i q^{39} +(-2.00000 - 3.46410i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(2.50000 - 4.33013i) q^{43} -1.00000 q^{44} +(-6.00000 + 10.3923i) q^{45} +6.00000 q^{46} +(2.00000 - 3.46410i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(3.50000 + 6.06218i) q^{49} +(5.50000 + 9.52628i) q^{50} +(4.50000 + 2.59808i) q^{51} +(-3.00000 + 5.19615i) q^{52} -12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +4.00000 q^{55} +(-1.50000 - 0.866025i) q^{57} +(-5.50000 - 9.52628i) q^{59} +(6.00000 - 3.46410i) q^{60} +(1.00000 - 1.73205i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(12.0000 - 20.7846i) q^{65} -1.73205i q^{66} +(-7.50000 - 12.9904i) q^{67} +(-1.50000 - 2.59808i) q^{68} +10.3923i q^{69} +12.0000 q^{71} +(-1.50000 - 2.59808i) q^{72} -5.00000 q^{73} +(0.500000 - 0.866025i) q^{74} +(-16.5000 + 9.52628i) q^{75} +(0.500000 + 0.866025i) q^{76} +(-9.00000 - 5.19615i) q^{78} +(3.00000 - 5.19615i) q^{79} -4.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -9.00000 q^{82} +(2.00000 - 3.46410i) q^{83} +(6.00000 + 10.3923i) q^{85} +(-2.50000 - 4.33013i) q^{86} +(-0.500000 + 0.866025i) q^{88} -10.0000 q^{89} +(6.00000 + 10.3923i) q^{90} +(3.00000 - 5.19615i) q^{92} +3.46410i q^{93} +(-2.00000 - 3.46410i) q^{94} +(-2.00000 - 3.46410i) q^{95} +1.73205i q^{96} +(-1.50000 + 2.59808i) q^{97} +7.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9} + 8 q^{10} + q^{11} - 6 q^{13} - q^{16} + 6 q^{17} + 6 q^{18} - 2 q^{19} + 4 q^{20} - q^{22} + 6 q^{23} - 3 q^{24} - 11 q^{25}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9 + 8 * q^10 + q^11 - 6 * q^13 - q^16 + 6 * q^17 + 6 * q^18 - 2 * q^19 + 4 * q^20 - q^22 + 6 * q^23 - 3 * q^24 - 11 * q^25 - 12 * q^26 + 12 * q^30 + 2 * q^31 + q^32 + 3 * q^33 + 3 * q^34 + 3 * q^36 + 2 * q^37 - q^38 - 4 * q^40 - 9 * q^41 + 5 * q^43 - 2 * q^44 - 12 * q^45 + 12 * q^46 + 4 * q^47 - 3 * q^48 + 7 * q^49 + 11 * q^50 + 9 * q^51 - 6 * q^52 - 24 * q^53 + 9 * q^54 + 8 * q^55 - 3 * q^57 - 11 * q^59 + 12 * q^60 + 2 * q^61 + 4 * q^62 + 2 * q^64 + 24 * q^65 - 15 * q^67 - 3 * q^68 + 24 * q^71 - 3 * q^72 - 10 * q^73 + q^74 - 33 * q^75 + q^76 - 18 * q^78 + 6 * q^79 - 8 * q^80 - 9 * q^81 - 18 * q^82 + 4 * q^83 + 12 * q^85 - 5 * q^86 - q^88 - 20 * q^89 + 12 * q^90 + 6 * q^92 - 4 * q^94 - 4 * q^95 - 3 * q^97 + 14 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.834512	+	0.550990i	$0.185750\pi$
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.0599153	+	0.998203i	$0.480917\pi$
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	4.00000			1.26491
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$		−	1.73205i		−	0.500000i
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$		0			0
$15$			6.92820i			1.78885i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	3.00000			0.707107
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$	2.00000	−	3.46410i	0.447214	−	0.774597i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	−6.00000			−1.17670
$27$			5.19615i			1.00000i
$28$		0			0
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$	6.00000	+	3.46410i	1.09545	+	0.632456i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.50000	−	0.866025i	0.261116	−	0.150756i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	1.00000			0.164399
$37$	1.00000			0.164399
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$		−	10.3923i		−	1.66410i
$40$	−2.00000	−	3.46410i	−0.316228	−	0.547723i
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		0			0
$43$	2.50000	−	4.33013i	0.381246	−	0.660338i	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	2.50000	−	4.33013i	0.381246	−	0.660338i	0.991241	+	0.132068i	$0.0421616\pi$
$44$	−1.00000			−0.150756
$45$	−6.00000	+	10.3923i	−0.894427	+	1.54919i
$46$	6.00000			0.884652
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	−0.682489	−	0.730896i	$-0.739102\pi$
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	0.974219	+	0.225605i	$0.0724358\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$	5.50000	+	9.52628i	0.777817	+	1.34722i
$51$	4.50000	+	2.59808i	0.630126	+	0.363803i
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	4.00000			0.539360
$56$		0			0
$57$	−1.50000	−	0.866025i	−0.198680	−	0.114708i
$58$		0			0
$59$	−5.50000	−	9.52628i	−0.716039	−	1.24022i	−0.962557	−	0.271078i	$-0.912620\pi$
$59$	−5.50000	−	9.52628i	−0.716039	−	1.24022i	0.246518	−	0.969138i	$-0.420713\pi$
$60$	6.00000	−	3.46410i	0.774597	−	0.447214i
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	12.0000	−	20.7846i	1.48842	−	2.57801i
$66$		−	1.73205i		−	0.213201i
$67$	−7.50000	−	12.9904i	−0.916271	−	1.58703i	−0.805030	−	0.593234i	$-0.797851\pi$
$67$	−7.50000	−	12.9904i	−0.916271	−	1.58703i	−0.111241	−	0.993793i	$-0.535483\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$			10.3923i			1.25109i
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−5.00000			−0.585206			−0.292603	−	0.956234i	$-0.594521\pi$
$73$	−5.00000			−0.585206			−0.292603	+	0.956234i	$0.594521\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$	−16.5000	+	9.52628i	−1.90526	+	1.10000i
$76$	0.500000	+	0.866025i	0.0573539	+	0.0993399i
$77$		0			0
$78$	−9.00000	−	5.19615i	−1.01905	−	0.588348i
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$	−4.00000			−0.447214
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−9.00000			−0.993884
$83$	2.00000	−	3.46410i	0.219529	−	0.380235i	−0.735135	−	0.677920i	$-0.762881\pi$
$83$	2.00000	−	3.46410i	0.219529	−	0.380235i	0.954664	+	0.297686i	$0.0962148\pi$
$84$		0			0
$85$	6.00000	+	10.3923i	0.650791	+	1.12720i
$86$	−2.50000	−	4.33013i	−0.269582	−	0.466930i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$	6.00000	+	10.3923i	0.632456	+	1.09545i
$91$		0			0
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$			3.46410i			0.359211i
$94$	−2.00000	−	3.46410i	−0.206284	−	0.357295i
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$			1.73205i			0.176777i
$97$	−1.50000	+	2.59808i	−0.152302	+	0.263795i	−0.932073	−	0.362270i	$-0.882002\pi$
$97$	−1.50000	+	2.59808i	−0.152302	+	0.263795i	0.779771	+	0.626064i	$0.215335\pi$
$98$	7.00000			0.707107
$99$	3.00000			0.301511
$100$	11.0000			1.10000
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	−0.273138	−	0.961975i	$-0.588061\pi$
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	0.969664	−	0.244443i	$-0.0786053\pi$
$102$	4.50000	−	2.59808i	0.445566	−	0.257248i
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	3.00000	+	5.19615i	0.294174	+	0.509525i
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	17.0000			1.64345			0.821726	−	0.569883i	$-0.193011\pi$
$107$	17.0000			1.64345			0.821726	+	0.569883i	$0.193011\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$	1.50000	+	0.866025i	0.142374	+	0.0821995i
$112$		0			0
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	−0.981003	−	0.193993i	$-0.937856\pi$
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	0.322498	−	0.946570i	$-0.395477\pi$
$114$	−1.50000	+	0.866025i	−0.140488	+	0.0811107i
$115$	−12.0000	+	20.7846i	−1.11901	+	1.93817i
$116$		0			0
$117$	9.00000	−	15.5885i	0.832050	−	1.44115i
$118$	−11.0000			−1.01263
$119$		0			0
$120$		−	6.92820i		−	0.632456i
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$		−	15.5885i		−	1.40556i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	−24.0000			−2.14663
$126$		0			0
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	7.50000	−	4.33013i	0.660338	−	0.381246i
$130$	−12.0000	−	20.7846i	−1.05247	−	1.82293i
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$	−1.50000	−	0.866025i	−0.130558	−	0.0753778i
$133$		0			0
$134$	−15.0000			−1.29580
$135$	−18.0000	+	10.3923i	−1.54919	+	0.894427i
$136$	−3.00000			−0.257248
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	−0.344493	−	0.938789i	$-0.611949\pi$
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	0.985262	−	0.171054i	$-0.0547174\pi$
$138$	9.00000	+	5.19615i	0.766131	+	0.442326i
$139$	0.500000	+	0.866025i	0.0424094	+	0.0734553i	0.886451	−	0.462822i	$-0.153163\pi$
$139$	0.500000	+	0.866025i	0.0424094	+	0.0734553i	−0.844042	+	0.536278i	$0.819830\pi$
$140$		0			0
$141$	6.00000	−	3.46410i	0.505291	−	0.291730i
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−6.00000			−0.501745
$144$	−3.00000			−0.250000
$145$		0			0
$146$	−2.50000	+	4.33013i	−0.206901	+	0.358364i
$147$			12.1244i			1.00000i
$148$	−0.500000	−	0.866025i	−0.0410997	−	0.0711868i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$			19.0526i			1.55563i
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	−0.999909	−	0.0134886i	$-0.995706\pi$
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	0.511636	+	0.859202i	$0.329040\pi$
$152$	1.00000			0.0811107
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$		0			0
$155$	−4.00000	+	6.92820i	−0.321288	+	0.556487i
$156$	−9.00000	+	5.19615i	−0.720577	+	0.416025i
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	0.594565	−	0.804048i	$-0.297324\pi$
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	−0.993608	+	0.112884i	$0.963991\pi$
$158$	−3.00000	−	5.19615i	−0.238667	−	0.413384i
$159$	−18.0000	−	10.3923i	−1.42749	−	0.824163i
$160$	−2.00000	+	3.46410i	−0.158114	+	0.273861i
$161$		0			0
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$	6.00000	+	3.46410i	0.467099	+	0.269680i
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	0.998808	+	0.0488118i	$0.0155435\pi$
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	−0.457132	+	0.889399i	$0.651123\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	12.0000			0.920358
$171$	−1.50000	−	2.59808i	−0.114708	−	0.198680i
$172$	−5.00000			−0.381246
$173$	−8.00000	+	13.8564i	−0.608229	+	1.05348i	0.383304	+	0.923622i	$0.374786\pi$
$173$	−8.00000	+	13.8564i	−0.608229	+	1.05348i	−0.991532	+	0.129861i	$0.958547\pi$
$174$		0			0
$175$		0			0
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$		−	19.0526i		−	1.43208i
$178$	−5.00000	+	8.66025i	−0.374766	+	0.649113i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	12.0000			0.894427
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$	3.00000	−	1.73205i	0.221766	−	0.128037i
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	3.00000	+	1.73205i	0.219971	+	0.127000i
$187$	1.50000	−	2.59808i	0.109691	−	0.189990i
$188$	−4.00000			−0.291730
$189$		0			0
$190$	−4.00000			−0.290191
$191$	−11.0000	+	19.0526i	−0.795932	+	1.37859i	0.126314	+	0.991990i	$0.459685\pi$
$191$	−11.0000	+	19.0526i	−0.795932	+	1.37859i	−0.922246	+	0.386604i	$0.873648\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$	1.50000	+	2.59808i	0.107694	+	0.186531i
$195$	36.0000	−	20.7846i	2.57801	−	1.48842i
$196$	3.50000	−	6.06218i	0.250000	−	0.433013i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$	5.50000	−	9.52628i	0.388909	−	0.673610i
$201$		−	25.9808i		−	1.83254i
$202$	−7.00000	−	12.1244i	−0.492518	−	0.853067i
$203$		0			0
$204$		−	5.19615i		−	0.363803i
$205$	18.0000	−	31.1769i	1.25717	−	2.17749i
$206$	8.00000			0.557386
$207$	−9.00000	+	15.5885i	−0.625543	+	1.08347i
$208$	6.00000			0.416025
$209$	−0.500000	+	0.866025i	−0.0345857	+	0.0599042i
$210$		0			0
$211$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$211$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$	18.0000	+	10.3923i	1.23334	+	0.712069i
$214$	8.50000	−	14.7224i	0.581048	−	1.00640i
$215$	20.0000			1.36399
$216$		−	5.19615i		−	0.353553i
$217$		0			0
$218$	−8.00000	+	13.8564i	−0.541828	+	0.938474i
$219$	−7.50000	−	4.33013i	−0.506803	−	0.292603i
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$	−9.00000	−	15.5885i	−0.605406	−	1.04859i
$222$	1.50000	−	0.866025i	0.100673	−	0.0581238i
$223$	−7.00000	+	12.1244i	−0.468755	+	0.811907i	−0.999362	−	0.0357107i	$-0.988630\pi$
$223$	−7.00000	+	12.1244i	−0.468755	+	0.811907i	0.530607	+	0.847618i	$0.321964\pi$
$224$		0			0
$225$	−33.0000			−2.20000
$226$	−14.0000			−0.931266
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$			1.73205i			0.114708i
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	0.897173	−	0.441679i	$-0.145617\pi$
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	−0.831092	+	0.556136i	$0.812283\pi$
$230$	12.0000	+	20.7846i	0.791257	+	1.37050i
$231$		0			0
$232$		0			0
$233$	−1.00000			−0.0655122			−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000			−0.0655122			−0.0327561	+	0.999463i	$0.510428\pi$
$234$	−9.00000	−	15.5885i	−0.588348	−	1.01905i
$235$	16.0000			1.04372
$236$	−5.50000	+	9.52628i	−0.358020	+	0.620108i
$237$	9.00000	−	5.19615i	0.584613	−	0.337526i
$238$		0			0
$239$	−8.00000	−	13.8564i	−0.517477	−	0.896296i	−0.999794	−	0.0202996i	$-0.993538\pi$
$239$	−8.00000	−	13.8564i	−0.517477	−	0.896296i	0.482317	−	0.875997i	$-0.339795\pi$
$240$	−6.00000	−	3.46410i	−0.387298	−	0.223607i
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	10.0000			0.642824
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−2.00000			−0.128037
$245$	−14.0000	+	24.2487i	−0.894427	+	1.54919i
$246$	−13.5000	−	7.79423i	−0.860729	−	0.496942i
$247$	3.00000	+	5.19615i	0.190885	+	0.330623i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	6.00000	−	3.46410i	0.380235	−	0.219529i
$250$	−12.0000	+	20.7846i	−0.758947	+	1.31453i
$251$	17.0000			1.07303			0.536515	−	0.843891i	$-0.319740\pi$
$251$	17.0000			1.07303			0.536515	+	0.843891i	$0.319740\pi$
$252$		0			0
$253$	6.00000			0.377217
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$			20.7846i			1.30158i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.50000	−	11.2583i	−0.405459	−	0.702275i	0.588916	−	0.808194i	$-0.299555\pi$
$257$	−6.50000	−	11.2583i	−0.405459	−	0.702275i	−0.994375	+	0.105919i	$0.966222\pi$
$258$		−	8.66025i		−	0.539164i
$259$		0			0
$260$	−24.0000			−1.48842
$261$		0			0
$262$	4.00000			0.247121
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.133281	+	0.991078i	$0.542551\pi$
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.791658	+	0.610964i	$0.790782\pi$
$264$	−1.50000	+	0.866025i	−0.0923186	+	0.0533002i
$265$	−24.0000	−	41.5692i	−1.47431	−	2.55358i
$266$		0			0
$267$	−15.0000	−	8.66025i	−0.917985	−	0.529999i
$268$	−7.50000	+	12.9904i	−0.458135	+	0.793514i
$269$	26.0000			1.58525			0.792624	−	0.609711i	$-0.208714\pi$
$269$	26.0000			1.58525			0.792624	+	0.609711i	$0.208714\pi$
$270$			20.7846i			1.26491i
$271$	−6.00000			−0.364474			−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000			−0.364474			−0.182237	+	0.983255i	$0.558334\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$		0			0
$274$	−7.50000	−	12.9904i	−0.453092	−	0.784778i
$275$	5.50000	+	9.52628i	0.331662	+	0.574456i
$276$	9.00000	−	5.19615i	0.541736	−	0.312772i
$277$	−12.0000	+	20.7846i	−0.721010	+	1.24883i	0.239585	+	0.970875i	$0.422989\pi$
$277$	−12.0000	+	20.7846i	−0.721010	+	1.24883i	−0.960595	+	0.277951i	$0.910345\pi$
$278$	1.00000			0.0599760
$279$	−3.00000	+	5.19615i	−0.179605	+	0.311086i
$280$		0			0
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	0.462174	+	0.886789i	$0.347070\pi$
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	−0.999069	+	0.0431402i	$0.986264\pi$
$282$		−	6.92820i		−	0.412568i
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	0.993626	+	0.112728i	$0.0359589\pi$
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	−0.399188	+	0.916869i	$0.630708\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		−	6.92820i		−	0.410391i
$286$	−3.00000	+	5.19615i	−0.177394	+	0.307255i
$287$		0			0
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	−8.00000			−0.470588
$290$		0			0
$291$	−4.50000	+	2.59808i	−0.263795	+	0.152302i
$292$	2.50000	+	4.33013i	0.146301	+	0.253402i
$293$	7.00000	+	12.1244i	0.408944	+	0.708312i	0.994772	−	0.102123i	$-0.0325637\pi$
$293$	7.00000	+	12.1244i	0.408944	+	0.708312i	−0.585827	+	0.810436i	$0.699230\pi$
$294$	10.5000	+	6.06218i	0.612372	+	0.353553i
$295$	22.0000	−	38.1051i	1.28089	−	2.21857i
$296$	−1.00000			−0.0581238
$297$	4.50000	+	2.59808i	0.261116	+	0.150756i
$298$	6.00000			0.347571
$299$	18.0000	−	31.1769i	1.04097	−	1.80301i
$300$	16.5000	+	9.52628i	0.952628	+	0.550000i
$301$		0			0
$302$	6.00000	+	10.3923i	0.345261	+	0.598010i
$303$	21.0000	−	12.1244i	1.20642	−	0.696526i
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	8.00000			0.458079
$306$	9.00000			0.514496
$307$	35.0000			1.99756			0.998778	−	0.0494267i	$-0.0157394\pi$
$307$	35.0000			1.99756			0.998778	+	0.0494267i	$0.0157394\pi$
$308$		0			0
$309$			13.8564i			0.788263i
$310$	4.00000	+	6.92820i	0.227185	+	0.393496i
$311$	−9.00000	−	15.5885i	−0.510343	−	0.883940i	−0.999928	−	0.0119847i	$-0.996185\pi$
$311$	−9.00000	−	15.5885i	−0.510343	−	0.883940i	0.489585	−	0.871956i	$-0.337148\pi$
$312$			10.3923i			0.588348i
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	0.462093	+	0.886831i	$0.347098\pi$
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	−0.999065	+	0.0432311i	$0.986235\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	−6.00000			−0.337526
$317$	7.00000	−	12.1244i	0.393159	−	0.680972i	−0.599705	−	0.800221i	$-0.704715\pi$
$317$	7.00000	−	12.1244i	0.393159	−	0.680972i	0.992864	+	0.119249i	$0.0380488\pi$
$318$	−18.0000	+	10.3923i	−1.00939	+	0.582772i
$319$		0			0
$320$	2.00000	+	3.46410i	0.111803	+	0.193649i
$321$	25.5000	+	14.7224i	1.42327	+	0.821726i
$322$		0			0
$323$	−3.00000			−0.166924
$324$	9.00000			0.500000
$325$	66.0000			3.66102
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	−24.0000	−	13.8564i	−1.32720	−	0.766261i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$	6.00000	−	3.46410i	0.330289	−	0.190693i
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$	−4.00000			−0.219529
$333$	1.50000	+	2.59808i	0.0821995	+	0.142374i
$334$	14.0000			0.766046
$335$	30.0000	−	51.9615i	1.63908	−	2.83896i
$336$		0			0
$337$	−13.5000	−	23.3827i	−0.735392	−	1.27374i	−0.954551	−	0.298047i	$-0.903665\pi$
$337$	−13.5000	−	23.3827i	−0.735392	−	1.27374i	0.219159	−	0.975689i	$-0.429669\pi$
$338$	11.5000	+	19.9186i	0.625518	+	1.08343i
$339$		−	24.2487i		−	1.31701i
$340$	6.00000	−	10.3923i	0.325396	−	0.563602i
$341$	2.00000			0.108306
$342$	−3.00000			−0.162221
$343$		0			0
$344$	−2.50000	+	4.33013i	−0.134791	+	0.233465i
$345$	−36.0000	+	20.7846i	−1.93817	+	1.11901i
$346$	8.00000	+	13.8564i	0.430083	+	0.744925i
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	0.719590	−	0.694399i	$-0.244330\pi$
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	−0.961162	+	0.275983i	$0.910997\pi$
$348$		0			0
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$		0			0
$351$	27.0000	−	15.5885i	1.44115	−	0.832050i
$352$	1.00000			0.0533002
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	−0.594441	−	0.804139i	$-0.702627\pi$
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	0.993626	+	0.112731i	$0.0359599\pi$
$354$	−16.5000	−	9.52628i	−0.876965	−	0.506316i
$355$	24.0000	+	41.5692i	1.27379	+	2.20627i
$356$	5.00000	+	8.66025i	0.264999	+	0.458993i
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	22.0000			1.16112			0.580558	−	0.814219i	$-0.302835\pi$
$359$	22.0000			1.16112			0.580558	+	0.814219i	$0.302835\pi$
$360$	6.00000	−	10.3923i	0.316228	−	0.547723i
$361$	−18.0000			−0.947368
$362$	7.00000	−	12.1244i	0.367912	−	0.637242i
$363$			17.3205i			0.909091i
$364$		0			0
$365$	−10.0000	−	17.3205i	−0.523424	−	0.906597i
$366$		−	3.46410i		−	0.181071i
$367$	−1.00000	+	1.73205i	−0.0521996	+	0.0904123i	−0.890945	−	0.454112i	$-0.849957\pi$
$367$	−1.00000	+	1.73205i	−0.0521996	+	0.0904123i	0.838745	+	0.544524i	$0.183290\pi$
$368$	−6.00000			−0.312772
$369$	13.5000	−	23.3827i	0.702782	−	1.21725i
$370$	4.00000			0.207950
$371$		0			0
$372$	3.00000	−	1.73205i	0.155543	−	0.0898027i
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	−1.50000	−	2.59808i	−0.0775632	−	0.134343i
$375$	−36.0000	−	20.7846i	−1.85903	−	1.07331i
$376$	−2.00000	+	3.46410i	−0.103142	+	0.178647i
$377$		0			0
$378$		0			0
$379$	25.0000			1.28416			0.642082	−	0.766636i	$-0.278071\pi$
$379$	25.0000			1.28416			0.642082	+	0.766636i	$0.278071\pi$
$380$	−2.00000	+	3.46410i	−0.102598	+	0.177705i
$381$	−3.00000	−	1.73205i	−0.153695	−	0.0887357i
$382$	11.0000	+	19.0526i	0.562809	+	0.974814i
$383$	14.0000	+	24.2487i	0.715367	+	1.23905i	0.962818	+	0.270151i	$0.0870736\pi$
$383$	14.0000	+	24.2487i	0.715367	+	1.23905i	−0.247451	+	0.968900i	$0.579593\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$		0			0
$386$	−11.0000			−0.559885
$387$	15.0000			0.762493
$388$	3.00000			0.152302
$389$	−16.0000	+	27.7128i	−0.811232	+	1.40510i	0.100770	+	0.994910i	$0.467869\pi$
$389$	−16.0000	+	27.7128i	−0.811232	+	1.40510i	−0.912002	+	0.410186i	$0.865464\pi$
$390$		−	41.5692i		−	2.10494i
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$	−3.50000	−	6.06218i	−0.176777	−	0.306186i
$393$			6.92820i			0.349482i
$394$	−6.00000	+	10.3923i	−0.302276	+	0.523557i
$395$	24.0000			1.20757
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	38.0000			1.90717			0.953583	−	0.301131i	$-0.0973643\pi$
$397$	38.0000			1.90717			0.953583	+	0.301131i	$0.0973643\pi$
$398$	−7.00000	+	12.1244i	−0.350878	+	0.607739i
$399$		0			0
$400$	−5.50000	−	9.52628i	−0.275000	−	0.476314i
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	0.902703	+	0.430263i	$0.141579\pi$
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	−0.0787327	+	0.996896i	$0.525087\pi$
$402$	−22.5000	−	12.9904i	−1.12220	−	0.647901i
$403$	6.00000	−	10.3923i	0.298881	−	0.517678i
$404$	−14.0000			−0.696526
$405$	−36.0000			−1.78885
$406$		0			0
$407$	0.500000	−	0.866025i	0.0247841	−	0.0429273i
$408$	−4.50000	−	2.59808i	−0.222783	−	0.128624i
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	0.826555	−	0.562856i	$-0.190297\pi$
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	−0.900725	+	0.434389i	$0.856964\pi$
$410$	−18.0000	−	31.1769i	−0.888957	−	1.53972i
$411$	22.5000	−	12.9904i	1.10984	−	0.640768i
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$		0			0
$414$	9.00000	+	15.5885i	0.442326	+	0.766131i
$415$	16.0000			0.785409
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$			1.73205i			0.0848189i
$418$	0.500000	+	0.866025i	0.0244558	+	0.0423587i
$419$	8.00000	+	13.8564i	0.390826	+	0.676930i	0.992559	−	0.121768i	$-0.0388562\pi$
$419$	8.00000	+	13.8564i	0.390826	+	0.676930i	−0.601733	+	0.798697i	$0.705523\pi$
$420$		0			0
$421$	2.00000	−	3.46410i	0.0974740	−	0.168830i	−0.813164	−	0.582034i	$-0.802257\pi$
$421$	2.00000	−	3.46410i	0.0974740	−	0.168830i	0.910638	+	0.413204i	$0.135590\pi$
$422$		0			0
$423$	12.0000			0.583460
$424$	12.0000			0.582772
$425$	−16.5000	+	28.5788i	−0.800368	+	1.38628i
$426$	18.0000	−	10.3923i	0.872103	−	0.503509i
$427$		0			0
$428$	−8.50000	−	14.7224i	−0.410863	−	0.711636i
$429$	−9.00000	−	5.19615i	−0.434524	−	0.250873i
$430$	10.0000	−	17.3205i	0.482243	−	0.835269i
$431$	−8.00000			−0.385346			−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000			−0.385346			−0.192673	+	0.981263i	$0.561716\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−15.0000			−0.720854			−0.360427	−	0.932787i	$-0.617369\pi$
$433$	−15.0000			−0.720854			−0.360427	+	0.932787i	$0.617369\pi$
$434$		0			0
$435$		0			0
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$	−7.50000	+	4.33013i	−0.358364	+	0.206901i
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	−0.909798	−	0.415051i	$-0.863764\pi$
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	0.814344	+	0.580383i	$0.197097\pi$
$440$	−4.00000			−0.190693
$441$	−10.5000	+	18.1865i	−0.500000	+	0.866025i
$442$	−18.0000			−0.856173
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	−0.952901	−	0.303281i	$-0.901918\pi$
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	0.739100	+	0.673596i	$0.235251\pi$
$444$		−	1.73205i		−	0.0821995i
$445$	−20.0000	−	34.6410i	−0.948091	−	1.64214i
$446$	7.00000	+	12.1244i	0.331460	+	0.574105i
$447$			10.3923i			0.491539i
$448$		0			0
$449$	−25.0000			−1.17982			−0.589911	−	0.807468i	$-0.700837\pi$
$449$	−25.0000			−1.17982			−0.589911	+	0.807468i	$0.700837\pi$
$450$	−16.5000	+	28.5788i	−0.777817	+	1.34722i
$451$	−9.00000			−0.423793
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$	−18.0000	+	10.3923i	−0.845714	+	0.488273i
$454$	−1.50000	−	2.59808i	−0.0703985	−	0.121934i
$455$		0			0
$456$	1.50000	+	0.866025i	0.0702439	+	0.0405554i
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	−0.741370	−	0.671096i	$-0.765824\pi$
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	0.951871	+	0.306497i	$0.0991571\pi$
$458$	2.00000			0.0934539
$459$			15.5885i			0.727607i
$460$	24.0000			1.11901
$461$	8.00000	−	13.8564i	0.372597	−	0.645357i	−0.617367	−	0.786675i	$-0.711801\pi$
$461$	8.00000	−	13.8564i	0.372597	−	0.645357i	0.989964	+	0.141318i	$0.0451340\pi$
$462$		0			0
$463$	7.00000	+	12.1244i	0.325318	+	0.563467i	0.981577	−	0.191069i	$-0.0611955\pi$
$463$	7.00000	+	12.1244i	0.325318	+	0.563467i	−0.656259	+	0.754536i	$0.727862\pi$
$464$		0			0
$465$	−12.0000	+	6.92820i	−0.556487	+	0.321288i
$466$	−0.500000	+	0.866025i	−0.0231621	+	0.0401179i
$467$	9.00000			0.416470			0.208235	−	0.978079i	$-0.433228\pi$
$467$	9.00000			0.416470			0.208235	+	0.978079i	$0.433228\pi$
$468$	−18.0000			−0.832050
$469$		0			0
$470$	8.00000	−	13.8564i	0.369012	−	0.639148i
$471$		−	17.3205i		−	0.798087i
$472$	5.50000	+	9.52628i	0.253158	+	0.438483i
$473$	−2.50000	−	4.33013i	−0.114950	−	0.199099i
$474$		−	10.3923i		−	0.477334i
$475$	5.50000	−	9.52628i	0.252357	−	0.437096i
$476$		0			0
$477$	−18.0000	−	31.1769i	−0.824163	−	1.42749i
$478$	−16.0000			−0.731823
$479$	−16.0000	+	27.7128i	−0.731059	+	1.26623i	0.225372	+	0.974273i	$0.427640\pi$
$479$	−16.0000	+	27.7128i	−0.731059	+	1.26623i	−0.956431	+	0.291958i	$0.905693\pi$
$480$	−6.00000	+	3.46410i	−0.273861	+	0.158114i
$481$	−3.00000	−	5.19615i	−0.136788	−	0.236924i
$482$	−0.500000	−	0.866025i	−0.0227744	−	0.0394464i
$483$		0			0
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−12.0000			−0.544892
$486$			15.5885i			0.707107i
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$	6.00000	+	3.46410i	0.271329	+	0.156652i
$490$	14.0000	+	24.2487i	0.632456	+	1.09545i
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	0.645675	−	0.763612i	$-0.276576\pi$
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	−0.984145	+	0.177365i	$0.943243\pi$
$492$	−13.5000	+	7.79423i	−0.608627	+	0.351391i
$493$		0			0
$494$	6.00000			0.269953
$495$	6.00000	+	10.3923i	0.269680	+	0.467099i
$496$	−2.00000			−0.0898027
$497$		0			0
$498$		−	6.92820i		−	0.310460i
$499$	−19.5000	−	33.7750i	−0.872940	−	1.51198i	−0.858941	−	0.512074i	$-0.828877\pi$
$499$	−19.5000	−	33.7750i	−0.872940	−	1.51198i	−0.0139987	−	0.999902i	$-0.504456\pi$
$500$	12.0000	+	20.7846i	0.536656	+	0.929516i
$501$			24.2487i			1.08335i
$502$	8.50000	−	14.7224i	0.379374	−	0.657094i
$503$	20.0000			0.891756			0.445878	−	0.895094i	$-0.352892\pi$
$503$	20.0000			0.891756			0.445878	+	0.895094i	$0.352892\pi$
$504$		0			0
$505$	56.0000			2.49197
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$	−34.5000	+	19.9186i	−1.53220	+	0.884615i
$508$	1.00000	+	1.73205i	0.0443678	+	0.0768473i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$	18.0000	+	10.3923i	0.797053	+	0.460179i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		−	5.19615i		−	0.229416i
$514$	−13.0000			−0.573405
$515$	−16.0000	+	27.7128i	−0.705044	+	1.22117i
$516$	−7.50000	−	4.33013i	−0.330169	−	0.190623i
$517$	−2.00000	−	3.46410i	−0.0879599	−	0.152351i
$518$		0			0
$519$	−24.0000	+	13.8564i	−1.05348	+	0.608229i
$520$	−12.0000	+	20.7846i	−0.526235	+	0.911465i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		0			0
$523$	−36.0000			−1.57417			−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000			−1.57417			−0.787085	+	0.616844i	$0.788411\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$		0			0
$526$	15.0000	+	25.9808i	0.654031	+	1.13282i
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$			1.73205i			0.0753778i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−48.0000			−2.08499
$531$	16.5000	−	28.5788i	0.716039	−	1.24022i
$532$		0			0
$533$	−27.0000	+	46.7654i	−1.16950	+	2.02563i
$534$	−15.0000	+	8.66025i	−0.649113	+	0.374766i
$535$	34.0000	+	58.8897i	1.46995	+	2.54602i
$536$	7.50000	+	12.9904i	0.323951	+	0.561099i
$537$	18.0000	+	10.3923i	0.776757	+	0.448461i
$538$	13.0000	−	22.5167i	0.560470	−	0.970762i
$539$	7.00000			0.301511
$540$	18.0000	+	10.3923i	0.774597	+	0.447214i
$541$	−42.0000			−1.80572			−0.902861	−	0.429934i	$-0.858537\pi$
$541$	−42.0000			−1.80572			−0.902861	+	0.429934i	$0.858537\pi$
$542$	−3.00000	+	5.19615i	−0.128861	+	0.223194i
$543$	21.0000	+	12.1244i	0.901196	+	0.520306i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	−32.0000	−	55.4256i	−1.37073	−	2.37417i
$546$		0			0
$547$	−7.50000	+	12.9904i	−0.320677	+	0.555429i	−0.980628	−	0.195880i	$-0.937244\pi$
$547$	−7.50000	+	12.9904i	−0.320677	+	0.555429i	0.659951	+	0.751309i	$0.270577\pi$
$548$	−15.0000			−0.640768
$549$	6.00000			0.256074
$550$	11.0000			0.469042
$551$		0			0
$552$		−	10.3923i		−	0.442326i
$553$		0			0
$554$	12.0000	+	20.7846i	0.509831	+	0.883053i
$555$			6.92820i			0.294086i
$556$	0.500000	−	0.866025i	0.0212047	−	0.0367277i
$557$	−10.0000			−0.423714			−0.211857	−	0.977301i	$-0.567951\pi$
$557$	−10.0000			−0.423714			−0.211857	+	0.977301i	$0.567951\pi$
$558$	3.00000	+	5.19615i	0.127000	+	0.219971i
$559$	−30.0000			−1.26886
$560$		0			0
$561$	4.50000	−	2.59808i	0.189990	−	0.109691i
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−12.5000	−	21.6506i	−0.526812	−	0.912465i	−0.999512	−	0.0312419i	$-0.990054\pi$
$563$	−12.5000	−	21.6506i	−0.526812	−	0.912465i	0.472700	−	0.881224i	$-0.343280\pi$
$564$	−6.00000	−	3.46410i	−0.252646	−	0.145865i
$565$	28.0000	−	48.4974i	1.17797	−	2.04030i
$566$	20.0000			0.840663
$567$		0			0
$568$	−12.0000			−0.503509
$569$	0.500000	−	0.866025i	0.0209611	−	0.0363057i	−0.855355	−	0.518043i	$-0.826661\pi$
$569$	0.500000	−	0.866025i	0.0209611	−	0.0363057i	0.876316	+	0.481737i	$0.159994\pi$
$570$	−6.00000	−	3.46410i	−0.251312	−	0.145095i
$571$	−22.5000	−	38.9711i	−0.941596	−	1.63089i	−0.762428	−	0.647073i	$-0.775993\pi$
$571$	−22.5000	−	38.9711i	−0.941596	−	1.63089i	−0.179168	−	0.983819i	$-0.557340\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	−33.0000	+	19.0526i	−1.37859	+	0.795932i
$574$		0			0
$575$	−66.0000			−2.75239
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−23.0000			−0.957503			−0.478751	−	0.877951i	$-0.658910\pi$
$577$	−23.0000			−0.957503			−0.478751	+	0.877951i	$0.658910\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$		−	19.0526i		−	0.791797i
$580$		0			0
$581$		0			0
$582$			5.19615i			0.215387i
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	5.00000			0.206901
$585$	72.0000			2.97683
$586$	14.0000			0.578335
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	−0.293640	−	0.955916i	$-0.594867\pi$
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	0.974668	−	0.223659i	$-0.0718001\pi$
$588$	10.5000	−	6.06218i	0.433013	−	0.250000i
$589$	−1.00000	−	1.73205i	−0.0412043	−	0.0713679i
$590$	−22.0000	−	38.1051i	−0.905726	−	1.56876i
$591$	−18.0000	−	10.3923i	−0.740421	−	0.427482i
$592$	−0.500000	+	0.866025i	−0.0205499	+	0.0355934i
$593$	−2.00000			−0.0821302			−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000			−0.0821302			−0.0410651	+	0.999156i	$0.513075\pi$
$594$	4.50000	−	2.59808i	0.184637	−	0.106600i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	−21.0000	−	12.1244i	−0.859473	−	0.496217i
$598$	−18.0000	−	31.1769i	−0.736075	−	1.27492i
$599$	13.0000	+	22.5167i	0.531166	+	0.920006i	0.999338	+	0.0363689i	$0.0115791\pi$
$599$	13.0000	+	22.5167i	0.531166	+	0.920006i	−0.468173	+	0.883637i	$0.655088\pi$
$600$	16.5000	−	9.52628i	0.673610	−	0.388909i
$601$	−15.5000	+	26.8468i	−0.632258	+	1.09510i	0.354831	+	0.934931i	$0.384538\pi$
$601$	−15.5000	+	26.8468i	−0.632258	+	1.09510i	−0.987089	+	0.160173i	$0.948795\pi$
$602$		0			0
$603$	22.5000	−	38.9711i	0.916271	−	1.58703i
$604$	12.0000			0.488273
$605$	−20.0000	+	34.6410i	−0.813116	+	1.40836i
$606$		−	24.2487i		−	0.985037i
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	0.656744	−	0.754114i	$-0.271933\pi$
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	−0.981454	+	0.191700i	$0.938600\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$		0			0
$610$	4.00000	−	6.92820i	0.161955	−	0.280515i
$611$	−24.0000			−0.970936
$612$	4.50000	−	7.79423i	0.181902	−	0.315063i
$613$	44.0000			1.77714			0.888572	−	0.458738i	$-0.151698\pi$
$613$	44.0000			1.77714			0.888572	+	0.458738i	$0.151698\pi$
$614$	17.5000	−	30.3109i	0.706243	−	1.22325i
$615$	54.0000	−	31.1769i	2.17749	−	1.25717i
$616$		0			0
$617$	0.500000	+	0.866025i	0.0201292	+	0.0348649i	0.875915	−	0.482466i	$-0.160259\pi$
$617$	0.500000	+	0.866025i	0.0201292	+	0.0348649i	−0.855785	+	0.517331i	$0.826926\pi$
$618$	12.0000	+	6.92820i	0.482711	+	0.278693i
$619$	−12.5000	+	21.6506i	−0.502417	+	0.870212i	0.497579	+	0.867419i	$0.334223\pi$
$619$	−12.5000	+	21.6506i	−0.502417	+	0.870212i	−0.999996	+	0.00279365i	$0.999111\pi$
$620$	8.00000			0.321288
$621$	−27.0000	+	15.5885i	−1.08347	+	0.625543i
$622$	−18.0000			−0.721734
$623$		0			0
$624$	9.00000	+	5.19615i	0.360288	+	0.208013i
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	9.50000	+	16.4545i	0.379696	+	0.657653i
$627$	−1.50000	+	0.866025i	−0.0599042	+	0.0345857i
$628$	−5.00000	+	8.66025i	−0.199522	+	0.345582i
$629$	3.00000			0.119618
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$	−3.00000	+	5.19615i	−0.119334	+	0.206692i
$633$		0			0
$634$	−7.00000	−	12.1244i	−0.278006	−	0.481520i
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$			20.7846i			0.824163i
$637$	21.0000	−	36.3731i	0.832050	−	1.44115i
$638$		0			0
$639$	18.0000	+	31.1769i	0.712069	+	1.23334i
$640$	4.00000			0.158114
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	−0.736725	−	0.676192i	$-0.763629\pi$
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	0.953962	+	0.299927i	$0.0969622\pi$
$642$	25.5000	−	14.7224i	1.00640	−	0.581048i
$643$	−5.50000	−	9.52628i	−0.216899	−	0.375680i	0.736959	−	0.675937i	$-0.236261\pi$
$643$	−5.50000	−	9.52628i	−0.216899	−	0.375680i	−0.953858	+	0.300257i	$0.902928\pi$
$644$		0			0
$645$	30.0000	+	17.3205i	1.18125	+	0.681994i
$646$	−1.50000	+	2.59808i	−0.0590167	+	0.102220i
$647$	28.0000			1.10079			0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000			1.10079			0.550397	+	0.834903i	$0.314476\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−11.0000			−0.431788
$650$	33.0000	−	57.1577i	1.29437	−	2.24191i
$651$		0			0
$652$	−2.00000	−	3.46410i	−0.0783260	−	0.135665i
$653$	−6.00000	−	10.3923i	−0.234798	−	0.406682i	0.724416	−	0.689363i	$-0.242110\pi$
$653$	−6.00000	−	10.3923i	−0.234798	−	0.406682i	−0.959214	+	0.282681i	$0.908776\pi$
$654$	−24.0000	+	13.8564i	−0.938474	+	0.541828i
$655$	−8.00000	+	13.8564i	−0.312586	+	0.541415i
$656$	9.00000			0.351391
$657$	−7.50000	−	12.9904i	−0.292603	−	0.506803i
$658$		0			0
$659$	−20.0000	+	34.6410i	−0.779089	+	1.34942i	0.153378	+	0.988168i	$0.450985\pi$
$659$	−20.0000	+	34.6410i	−0.779089	+	1.34942i	−0.932467	+	0.361255i	$0.882348\pi$
$660$		−	6.92820i		−	0.269680i
$661$	21.0000	+	36.3731i	0.816805	+	1.41475i	0.908024	+	0.418917i	$0.137590\pi$
$661$	21.0000	+	36.3731i	0.816805	+	1.41475i	−0.0912190	+	0.995831i	$0.529076\pi$
$662$	2.00000	+	3.46410i	0.0777322	+	0.134636i
$663$		−	31.1769i		−	1.21081i
$664$	−2.00000	+	3.46410i	−0.0776151	+	0.134433i
$665$		0			0
$666$	3.00000			0.116248
$667$		0			0
$668$	7.00000	−	12.1244i	0.270838	−	0.469105i
$669$	−21.0000	+	12.1244i	−0.811907	+	0.468755i
$670$	−30.0000	−	51.9615i	−1.15900	−	2.00745i
$671$	−1.00000	−	1.73205i	−0.0386046	−	0.0668651i
$672$		0			0
$673$	19.0000	−	32.9090i	0.732396	−	1.26855i	−0.223460	−	0.974713i	$-0.571735\pi$
$673$	19.0000	−	32.9090i	0.732396	−	1.26855i	0.955856	−	0.293834i	$-0.0949314\pi$
$674$	−27.0000			−1.04000
$675$	−49.5000	−	28.5788i	−1.90526	−	1.10000i
$676$	23.0000			0.884615
$677$	5.00000	−	8.66025i	0.192166	−	0.332841i	−0.753802	−	0.657102i	$-0.771782\pi$
$677$	5.00000	−	8.66025i	0.192166	−	0.332841i	0.945968	+	0.324261i	$0.105116\pi$
$678$	−21.0000	−	12.1244i	−0.806500	−	0.465633i
$679$		0			0
$680$	−6.00000	−	10.3923i	−0.230089	−	0.398527i
$681$	4.50000	−	2.59808i	0.172440	−	0.0995585i
$682$	1.00000	−	1.73205i	0.0382920	−	0.0663237i
$683$	−21.0000			−0.803543			−0.401771	−	0.915740i	$-0.631605\pi$
$683$	−21.0000			−0.803543			−0.401771	+	0.915740i	$0.631605\pi$
$684$	−1.50000	+	2.59808i	−0.0573539	+	0.0993399i
$685$	60.0000			2.29248
$686$		0			0
$687$			3.46410i			0.132164i
$688$	2.50000	+	4.33013i	0.0953116	+	0.165085i
$689$	36.0000	+	62.3538i	1.37149	+	2.37549i
$690$			41.5692i			1.58251i
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	−0.825473	−	0.564441i	$-0.809092\pi$
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	0.901557	+	0.432660i	$0.142425\pi$
$692$	16.0000			0.608229
$693$		0			0
$694$	−9.00000			−0.341635
$695$	−2.00000	+	3.46410i	−0.0758643	+	0.131401i
$696$		0			0
$697$	−13.5000	−	23.3827i	−0.511349	−	0.885682i
$698$	5.00000	+	8.66025i	0.189253	+	0.327795i
$699$	−1.50000	−	0.866025i	−0.0567352	−	0.0327561i
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		−	31.1769i		−	1.17670i
$703$	−1.00000			−0.0377157
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	24.0000	+	13.8564i	0.903892	+	0.521862i
$706$	−7.50000	−	12.9904i	−0.282266	−	0.488899i
$707$		0			0
$708$	−16.5000	+	9.52628i	−0.620108	+	0.358020i
$709$	−18.0000	+	31.1769i	−0.676004	+	1.17087i	0.300170	+	0.953886i	$0.402957\pi$
$709$	−18.0000	+	31.1769i	−0.676004	+	1.17087i	−0.976174	+	0.216988i	$0.930377\pi$
$710$	48.0000			1.80141
$711$	18.0000			0.675053
$712$	10.0000			0.374766
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$		0			0
$715$	−12.0000	−	20.7846i	−0.448775	−	0.777300i
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$		−	27.7128i		−	1.03495i
$718$	11.0000	−	19.0526i	0.410516	−	0.711035i
$719$	42.0000			1.56634			0.783168	−	0.621810i	$-0.213603\pi$
$719$	42.0000			1.56634			0.783168	+	0.621810i	$0.213603\pi$
$720$	−6.00000	−	10.3923i	−0.223607	−	0.387298i
$721$		0			0
$722$	−9.00000	+	15.5885i	−0.334945	+	0.580142i
$723$	1.50000	−	0.866025i	0.0557856	−	0.0322078i
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$		0			0
$726$	15.0000	+	8.66025i	0.556702	+	0.321412i
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−20.0000			−0.740233
$731$	7.50000	−	12.9904i	0.277398	−	0.480467i
$732$	−3.00000	−	1.73205i	−0.110883	−	0.0640184i
$733$	2.00000	+	3.46410i	0.0738717	+	0.127950i	0.900595	−	0.434659i	$-0.143131\pi$
$733$	2.00000	+	3.46410i	0.0738717	+	0.127950i	−0.826723	+	0.562609i	$0.809798\pi$
$734$	1.00000	+	1.73205i	0.0369107	+	0.0639312i
$735$	−42.0000	+	24.2487i	−1.54919	+	0.894427i
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	−15.0000			−0.552532
$738$	−13.5000	−	23.3827i	−0.496942	−	0.860729i
$739$	−11.0000			−0.404642			−0.202321	−	0.979319i	$-0.564848\pi$
$739$	−11.0000			−0.404642			−0.202321	+	0.979319i	$0.564848\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$			10.3923i			0.381771i
$742$		0			0
$743$	−24.0000	−	41.5692i	−0.880475	−	1.52503i	−0.850814	−	0.525467i	$-0.823891\pi$
$743$	−24.0000	−	41.5692i	−0.880475	−	1.52503i	−0.0296605	−	0.999560i	$-0.509443\pi$
$744$		−	3.46410i		−	0.127000i
$745$	−12.0000	+	20.7846i	−0.439646	+	0.761489i
$746$	4.00000			0.146450
$747$	12.0000			0.439057
$748$	−3.00000			−0.109691
$749$		0			0
$750$	−36.0000	+	20.7846i	−1.31453	+	0.758947i
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	0.993895	−	0.110333i	$-0.0351919\pi$
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	−0.592499	+	0.805571i	$0.701859\pi$
$752$	2.00000	+	3.46410i	0.0729325	+	0.126323i
$753$	25.5000	+	14.7224i	0.929272	+	0.536515i
$754$		0			0
$755$	−48.0000			−1.74690
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	12.5000	−	21.6506i	0.454020	−	0.786386i
$759$	9.00000	+	5.19615i	0.326679	+	0.188608i
$760$	2.00000	+	3.46410i	0.0725476	+	0.125656i
$761$	−13.0000	−	22.5167i	−0.471250	−	0.816228i	0.528209	−	0.849114i	$-0.322864\pi$
$761$	−13.0000	−	22.5167i	−0.471250	−	0.816228i	−0.999459	+	0.0328858i	$0.989530\pi$
$762$	−3.00000	+	1.73205i	−0.108679	+	0.0627456i
$763$		0			0
$764$	22.0000			0.795932
$765$	−18.0000	+	31.1769i	−0.650791	+	1.12720i
$766$	28.0000			1.01168
$767$	−33.0000	+	57.1577i	−1.19156	+	2.06384i
$768$		−	1.73205i		−	0.0625000i
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$		−	22.5167i		−	0.810918i
$772$	−5.50000	+	9.52628i	−0.197949	+	0.342858i
$773$	14.0000			0.503545			0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000			0.503545			0.251773	+	0.967786i	$0.418987\pi$
$774$	7.50000	−	12.9904i	0.269582	−	0.466930i
$775$	−22.0000			−0.790263
$776$	1.50000	−	2.59808i	0.0538469	−	0.0932655i
$777$		0			0
$778$	16.0000	+	27.7128i	0.573628	+	0.993552i
$779$	4.50000	+	7.79423i	0.161229	+	0.279257i
$780$	−36.0000	−	20.7846i	−1.28901	−	0.744208i
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$	18.0000			0.643679
$783$		0			0
$784$	−7.00000			−0.250000
$785$	20.0000	−	34.6410i	0.713831	−	1.23639i
$786$	6.00000	+	3.46410i	0.214013	+	0.123560i
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	6.00000	+	10.3923i	0.213741	+	0.370211i
$789$	−45.0000	+	25.9808i	−1.60204	+	0.924940i
$790$	12.0000	−	20.7846i	0.426941	−	0.739483i
$791$		0			0
$792$	−3.00000			−0.106600
$793$	−12.0000			−0.426132
$794$	19.0000	−	32.9090i	0.674285	−	1.16790i
$795$		−	83.1384i		−	2.94862i
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	0.992492	+	0.122312i	$0.0390308\pi$
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	−0.390321	+	0.920679i	$0.627636\pi$
$798$		0			0
$799$	6.00000	−	10.3923i	0.212265	−	0.367653i
$800$	−11.0000			−0.388909
$801$	−15.0000	−	25.9808i	−0.529999	−	0.917985i
$802$	33.0000			1.16527
$803$	−2.50000	+	4.33013i	−0.0882231	+	0.152807i
$804$	−22.5000	+	12.9904i	−0.793514	+	0.458135i
$805$		0			0
$806$	−6.00000	−	10.3923i	−0.211341	−	0.366053i
$807$	39.0000	+	22.5167i	1.37287	+	0.792624i
$808$	−7.00000	+	12.1244i	−0.246259	+	0.426533i
$809$	27.0000			0.949269			0.474635	−	0.880183i	$-0.342580\pi$
$809$	27.0000			0.949269			0.474635	+	0.880183i	$0.342580\pi$
$810$	−18.0000	+	31.1769i	−0.632456	+	1.09545i
$811$	15.0000			0.526721			0.263361	−	0.964697i	$-0.415169\pi$
$811$	15.0000			0.526721			0.263361	+	0.964697i	$0.415169\pi$
$812$		0			0
$813$	−9.00000	−	5.19615i	−0.315644	−	0.182237i
$814$	−0.500000	−	0.866025i	−0.0175250	−	0.0303542i
$815$	8.00000	+	13.8564i	0.280228	+	0.485369i
$816$	−4.50000	+	2.59808i	−0.157532	+	0.0909509i
$817$	−2.50000	+	4.33013i	−0.0874639	+	0.151492i
$818$	−3.00000			−0.104893
$819$		0			0
$820$	−36.0000			−1.25717
$821$	8.00000	−	13.8564i	0.279202	−	0.483592i	−0.691985	−	0.721912i	$-0.743263\pi$
$821$	8.00000	−	13.8564i	0.279202	−	0.483592i	0.971187	+	0.238320i	$0.0765968\pi$
$822$		−	25.9808i		−	0.906183i
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$			19.0526i			0.663325i
$826$		0			0
$827$	32.0000			1.11275			0.556375	−	0.830932i	$-0.312192\pi$
$827$	32.0000			1.11275			0.556375	+	0.830932i	$0.312192\pi$
$828$	18.0000			0.625543
$829$	20.0000			0.694629			0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000			0.694629			0.347314	+	0.937749i	$0.387094\pi$
$830$	8.00000	−	13.8564i	0.277684	−	0.480963i
$831$	−36.0000	+	20.7846i	−1.24883	+	0.721010i
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$	10.5000	+	18.1865i	0.363803	+	0.630126i
$834$	1.50000	+	0.866025i	0.0519408	+	0.0299880i
$835$	−28.0000	+	48.4974i	−0.968980	+	1.67832i
$836$	1.00000			0.0345857
$837$	−9.00000	+	5.19615i	−0.311086	+	0.179605i
$838$	16.0000			0.552711
$839$	−5.00000	+	8.66025i	−0.172619	+	0.298985i	−0.939335	−	0.343002i	$-0.888556\pi$
$839$	−5.00000	+	8.66025i	−0.172619	+	0.298985i	0.766716	+	0.641987i	$0.221890\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−2.00000	−	3.46410i	−0.0689246	−	0.119381i
$843$	−27.0000	+	15.5885i	−0.929929	+	0.536895i
$844$		0			0
$845$	−92.0000			−3.16490
$846$	6.00000	−	10.3923i	0.206284	−	0.357295i
$847$		0			0
$848$	6.00000	−	10.3923i	0.206041	−	0.356873i
$849$			34.6410i			1.18888i
$850$	16.5000	+	28.5788i	0.565945	+	0.980246i
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$		−	20.7846i		−	0.712069i
$853$	8.00000	−	13.8564i	0.273915	−	0.474434i	−0.695946	−	0.718094i	$-0.745015\pi$
$853$	8.00000	−	13.8564i	0.273915	−	0.474434i	0.969861	+	0.243660i	$0.0783480\pi$
$854$		0			0
$855$	6.00000	−	10.3923i	0.205196	−	0.355409i
$856$	−17.0000			−0.581048
$857$	−11.0000	+	19.0526i	−0.375753	+	0.650823i	−0.990439	−	0.137948i	$-0.955949\pi$
$857$	−11.0000	+	19.0526i	−0.375753	+	0.650823i	0.614687	+	0.788771i	$0.289283\pi$
$858$	−9.00000	+	5.19615i	−0.307255	+	0.177394i
$859$	−9.50000	−	16.4545i	−0.324136	−	0.561420i	0.657201	−	0.753715i	$-0.271740\pi$
$859$	−9.50000	−	16.4545i	−0.324136	−	0.561420i	−0.981337	+	0.192295i	$0.938407\pi$
$860$	−10.0000	−	17.3205i	−0.340997	−	0.590624i
$861$		0			0
$862$	−4.00000	+	6.92820i	−0.136241	+	0.235976i
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	−64.0000			−2.17607
$866$	−7.50000	+	12.9904i	−0.254860	+	0.441431i
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$		0			0
$869$	−3.00000	−	5.19615i	−0.101768	−	0.176267i
$870$		0			0
$871$	−45.0000	+	77.9423i	−1.52477	+	2.64097i
$872$	16.0000			0.541828
$873$	−9.00000			−0.304604
$874$	−6.00000			−0.202953
$875$		0			0
$876$			8.66025i			0.292603i
$877$	7.00000	+	12.1244i	0.236373	+	0.409410i	0.959671	−	0.281126i	$-0.0907079\pi$
$877$	7.00000	+	12.1244i	0.236373	+	0.409410i	−0.723298	+	0.690536i	$0.757375\pi$
$878$	2.00000	+	3.46410i	0.0674967	+	0.116908i
$879$			24.2487i			0.817889i
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	10.5000	+	18.1865i	0.353553	+	0.612372i
$883$	25.0000			0.841317			0.420658	−	0.907219i	$-0.361799\pi$
$883$	25.0000			0.841317			0.420658	+	0.907219i	$0.361799\pi$
$884$	−9.00000	+	15.5885i	−0.302703	+	0.524297i
$885$	66.0000	−	38.1051i	2.21857	−	1.28089i
$886$	4.50000	+	7.79423i	0.151180	+	0.261852i
$887$	−8.00000	−	13.8564i	−0.268614	−	0.465253i	0.699890	−	0.714250i	$-0.253232\pi$
$887$	−8.00000	−	13.8564i	−0.268614	−	0.465253i	−0.968504	+	0.248998i	$0.919899\pi$
$888$	−1.50000	−	0.866025i	−0.0503367	−	0.0290619i
$889$		0			0
$890$	−40.0000			−1.34080
$891$	4.50000	+	7.79423i	0.150756	+	0.261116i
$892$	14.0000			0.468755
$893$	−2.00000	+	3.46410i	−0.0669274	+	0.115922i
$894$	9.00000	+	5.19615i	0.301005	+	0.173785i
$895$	24.0000	+	41.5692i	0.802232	+	1.38951i
$896$		0			0
$897$	54.0000	−	31.1769i	1.80301	−	1.04097i
$898$	−12.5000	+	21.6506i	−0.417130	+	0.722491i
$899$		0			0
$900$	16.5000	+	28.5788i	0.550000	+	0.952628i
$901$	−36.0000			−1.19933
$902$	−4.50000	+	7.79423i	−0.149834	+	0.259519i
$903$		0			0
$904$	7.00000	+	12.1244i	0.232817	+	0.403250i
$905$	28.0000	+	48.4974i	0.930751	+	1.61211i
$906$			20.7846i			0.690522i
$907$	15.5000	−	26.8468i	0.514669	−	0.891433i	−0.485186	−	0.874411i	$-0.661248\pi$
$907$	15.5000	−	26.8468i	0.514669	−	0.891433i	0.999855	−	0.0170220i	$-0.00541854\pi$
$908$	−3.00000			−0.0995585
$909$	42.0000			1.39305
$910$		0			0
$911$	20.0000	−	34.6410i	0.662630	−	1.14771i	−0.317293	−	0.948328i	$-0.602774\pi$
$911$	20.0000	−	34.6410i	0.662630	−	1.14771i	0.979922	−	0.199380i	$-0.0638929\pi$
$912$	1.50000	−	0.866025i	0.0496700	−	0.0286770i
$913$	−2.00000	−	3.46410i	−0.0661903	−	0.114645i
$914$	−4.50000	−	7.79423i	−0.148847	−	0.257810i
$915$	12.0000	+	6.92820i	0.396708	+	0.229039i
$916$	1.00000	−	1.73205i	0.0330409	−	0.0572286i
$917$		0			0
$918$	13.5000	+	7.79423i	0.445566	+	0.257248i
$919$	−50.0000			−1.64935			−0.824674	−	0.565608i	$-0.808641\pi$
$919$	−50.0000			−1.64935			−0.824674	+	0.565608i	$0.808641\pi$
$920$	12.0000	−	20.7846i	0.395628	−	0.685248i
$921$	52.5000	+	30.3109i	1.72993	+	0.998778i
$922$	−8.00000	−	13.8564i	−0.263466	−	0.456336i
$923$	−36.0000	−	62.3538i	−1.18495	−	2.05240i
$924$		0			0
$925$	−5.50000	+	9.52628i	−0.180839	+	0.313222i
$926$	14.0000			0.460069
$927$	−12.0000	+	20.7846i	−0.394132	+	0.682656i
$928$		0			0
$929$	−13.0000	+	22.5167i	−0.426516	+	0.738748i	−0.996561	−	0.0828661i	$-0.973593\pi$
$929$	−13.0000	+	22.5167i	−0.426516	+	0.738748i	0.570045	+	0.821614i	$0.306926\pi$
$930$			13.8564i			0.454369i
$931$	−3.50000	−	6.06218i	−0.114708	−	0.198680i
$932$	0.500000	+	0.866025i	0.0163780	+	0.0283676i
$933$		−	31.1769i		−	1.02069i
$934$	4.50000	−	7.79423i	0.147244	−	0.255035i
$935$	12.0000			0.392442
$936$	−9.00000	+	15.5885i	−0.294174	+	0.509525i
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$		0			0
$939$	−28.5000	+	16.4545i	−0.930062	+	0.536972i
$940$	−8.00000	−	13.8564i	−0.260931	−	0.451946i
$941$	6.00000	+	10.3923i	0.195594	+	0.338779i	0.947095	−	0.320953i	$-0.104003\pi$
$941$	6.00000	+	10.3923i	0.195594	+	0.338779i	−0.751501	+	0.659732i	$0.770670\pi$
$942$	−15.0000	−	8.66025i	−0.488726	−	0.282166i
$943$	27.0000	−	46.7654i	0.879241	−	1.52289i
$944$	11.0000			0.358020
$945$		0			0
$946$	−5.00000			−0.162564
$947$	10.5000	−	18.1865i	0.341204	−	0.590983i	−0.643452	−	0.765486i	$-0.722499\pi$
$947$	10.5000	−	18.1865i	0.341204	−	0.590983i	0.984657	+	0.174503i	$0.0558319\pi$
$948$	−9.00000	−	5.19615i	−0.292306	−	0.168763i
$949$	15.0000	+	25.9808i	0.486921	+	0.843371i
$950$	−5.50000	−	9.52628i	−0.178444	−	0.309073i
$951$	21.0000	−	12.1244i	0.680972	−	0.393159i
$952$		0			0
$953$	49.0000			1.58727			0.793633	−	0.608397i	$-0.208187\pi$
$953$	49.0000			1.58727			0.793633	+	0.608397i	$0.208187\pi$
$954$	−36.0000			−1.16554
$955$	−88.0000			−2.84761
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$		0			0
$958$	16.0000	+	27.7128i	0.516937	+	0.895360i
$959$		0			0
$960$			6.92820i			0.223607i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−6.00000			−0.193448
$963$	25.5000	+	44.1673i	0.821726	+	1.42327i
$964$	−1.00000			−0.0322078
$965$	22.0000	−	38.1051i	0.708205	−	1.22665i
$966$		0			0
$967$	26.0000	+	45.0333i	0.836104	+	1.44817i	0.893129	+	0.449801i	$0.148505\pi$
$967$	26.0000	+	45.0333i	0.836104	+	1.44817i	−0.0570251	+	0.998373i	$0.518161\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$	−4.50000	−	2.59808i	−0.144561	−	0.0834622i
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	48.0000			1.54039			0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000			1.54039			0.770197	+	0.637806i	$0.220158\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$		0			0
$974$	−1.00000	+	1.73205i	−0.0320421	+	0.0554985i
$975$	99.0000	+	57.1577i	3.17054	+	1.83051i
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	4.50000	+	7.79423i	0.143968	+	0.249359i	0.928987	−	0.370111i	$-0.120681\pi$
$977$	4.50000	+	7.79423i	0.143968	+	0.249359i	−0.785020	+	0.619471i	$0.787347\pi$
$978$	6.00000	−	3.46410i	0.191859	−	0.110770i
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$	28.0000			0.894427
$981$	−24.0000	−	41.5692i	−0.766261	−	1.32720i
$982$	−15.0000			−0.478669
$983$	30.0000	−	51.9615i	0.956851	−	1.65732i	0.226778	−	0.973946i	$-0.427181\pi$
$983$	30.0000	−	51.9615i	0.956851	−	1.65732i	0.730073	−	0.683369i	$-0.239486\pi$
$984$			15.5885i			0.496942i
$985$	−24.0000	−	41.5692i	−0.764704	−	1.32451i
$986$		0			0
$987$		0			0
$988$	3.00000	−	5.19615i	0.0954427	−	0.165312i
$989$	30.0000			0.953945
$990$	12.0000			0.381385
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$	−6.00000	+	3.46410i	−0.190404	+	0.109930i
$994$		0			0
$995$	−28.0000	−	48.4974i	−0.887660	−	1.53747i
$996$	−6.00000	−	3.46410i	−0.190117	−	0.109764i
$997$	6.00000	−	10.3923i	0.190022	−	0.329128i	−0.755235	−	0.655454i	$-0.772477\pi$
$997$	6.00000	−	10.3923i	0.190022	−	0.329128i	0.945257	+	0.326326i	$0.105811\pi$
$998$	−39.0000			−1.23452
$999$			5.19615i			0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.e.b.223.1	✓	2
3.2	odd	2		1998.2.e.a.667.1		2
9.2	odd	6		5994.2.a.h.1.1		1
9.4	even	3	inner	666.2.e.b.445.1	yes	2
9.5	odd	6		1998.2.e.a.1333.1		2
9.7	even	3		5994.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.e.b.223.1	✓	2	1.1	even	1	trivial
666.2.e.b.445.1	yes	2	9.4	even	3	inner
1998.2.e.a.667.1		2	3.2	odd	2
1998.2.e.a.1333.1		2	9.5	odd	6
5994.2.a.a.1.1		1	9.7	even	3
5994.2.a.h.1.1		1	9.2	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(1.50000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +4.00000 q^{10} +(0.500000 - 0.866025i) q^{11} -1.73205i q^{12} +(-3.00000 - 5.19615i) q^{13} +6.92820i q^{15} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +3.00000 q^{18} -1.00000 q^{19} +(2.00000 - 3.46410i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} -6.00000 q^{26} +5.19615i q^{27} +(6.00000 + 3.46410i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 0.866025i) q^{33} +(1.50000 - 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} +1.00000 q^{37} +(-0.500000 + 0.866025i) q^{38} -10.3923i q^{39} +(-2.00000 - 3.46410i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(2.50000 - 4.33013i) q^{43} -1.00000 q^{44} +(-6.00000 + 10.3923i) q^{45} +6.00000 q^{46} +(2.00000 - 3.46410i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(3.50000 + 6.06218i) q^{49} +(5.50000 + 9.52628i) q^{50} +(4.50000 + 2.59808i) q^{51} +(-3.00000 + 5.19615i) q^{52} -12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +4.00000 q^{55} +(-1.50000 - 0.866025i) q^{57} +(-5.50000 - 9.52628i) q^{59} +(6.00000 - 3.46410i) q^{60} +(1.00000 - 1.73205i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(12.0000 - 20.7846i) q^{65} -1.73205i q^{66} +(-7.50000 - 12.9904i) q^{67} +(-1.50000 - 2.59808i) q^{68} +10.3923i q^{69} +12.0000 q^{71} +(-1.50000 - 2.59808i) q^{72} -5.00000 q^{73} +(0.500000 - 0.866025i) q^{74} +(-16.5000 + 9.52628i) q^{75} +(0.500000 + 0.866025i) q^{76} +(-9.00000 - 5.19615i) q^{78} +(3.00000 - 5.19615i) q^{79} -4.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -9.00000 q^{82} +(2.00000 - 3.46410i) q^{83} +(6.00000 + 10.3923i) q^{85} +(-2.50000 - 4.33013i) q^{86} +(-0.500000 + 0.866025i) q^{88} -10.0000 q^{89} +(6.00000 + 10.3923i) q^{90} +(3.00000 - 5.19615i) q^{92} +3.46410i q^{93} +(-2.00000 - 3.46410i) q^{94} +(-2.00000 - 3.46410i) q^{95} +1.73205i q^{96} +(-1.50000 + 2.59808i) q^{97} +7.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9} + 8 q^{10} + q^{11} - 6 q^{13} - q^{16} + 6 q^{17} + 6 q^{18} - 2 q^{19} + 4 q^{20} - q^{22} + 6 q^{23} - 3 q^{24} - 11 q^{25}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9 + 8 * q^10 + q^11 - 6 * q^13 - q^16 + 6 * q^17 + 6 * q^18 - 2 * q^19 + 4 * q^20 - q^22 + 6 * q^23 - 3 * q^24 - 11 * q^25 - 12 * q^26 + 12 * q^30 + 2 * q^31 + q^32 + 3 * q^33 + 3 * q^34 + 3 * q^36 + 2 * q^37 - q^38 - 4 * q^40 - 9 * q^41 + 5 * q^43 - 2 * q^44 - 12 * q^45 + 12 * q^46 + 4 * q^47 - 3 * q^48 + 7 * q^49 + 11 * q^50 + 9 * q^51 - 6 * q^52 - 24 * q^53 + 9 * q^54 + 8 * q^55 - 3 * q^57 - 11 * q^59 + 12 * q^60 + 2 * q^61 + 4 * q^62 + 2 * q^64 + 24 * q^65 - 15 * q^67 - 3 * q^68 + 24 * q^71 - 3 * q^72 - 10 * q^73 + q^74 - 33 * q^75 + q^76 - 18 * q^78 + 6 * q^79 - 8 * q^80 - 9 * q^81 - 18 * q^82 + 4 * q^83 + 12 * q^85 - 5 * q^86 - q^88 - 20 * q^89 + 12 * q^90 + 6 * q^92 - 4 * q^94 - 4 * q^95 - 3 * q^97 + 14 * q^98 + 6 * q^99

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