LMFDB - Embedded newform 1078.2.e.g.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.60787333789$
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 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.g.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(2.00000 + 3.46410i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.50000 + 2.59808i) q^{12} +1.00000 q^{13} +12.0000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(3.00000 + 5.19615i) q^{18} +(3.00000 - 5.19615i) q^{19} +4.00000 q^{20} +1.00000 q^{22} +(1.00000 - 1.73205i) q^{23} +(1.50000 + 2.59808i) q^{24} +(-5.50000 - 9.52628i) q^{25} +(0.500000 - 0.866025i) q^{26} +9.00000 q^{27} +1.00000 q^{29} +(6.00000 - 10.3923i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +2.00000 q^{34} +6.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-1.50000 - 2.59808i) q^{39} +(2.00000 - 3.46410i) q^{40} +2.00000 q^{41} +4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-12.0000 - 20.7846i) q^{45} +(-1.00000 - 1.73205i) q^{46} +(1.00000 - 1.73205i) q^{47} +3.00000 q^{48} -11.0000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(6.00000 + 10.3923i) q^{53} +(4.50000 - 7.79423i) q^{54} -4.00000 q^{55} -18.0000 q^{57} +(0.500000 - 0.866025i) q^{58} +(4.50000 + 7.79423i) q^{59} +(-6.00000 - 10.3923i) q^{60} +(-2.50000 + 4.33013i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(4.50000 + 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} -6.00000 q^{69} +4.00000 q^{71} +(3.00000 - 5.19615i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-16.5000 + 28.5788i) q^{75} -6.00000 q^{76} -3.00000 q^{78} +(7.50000 - 12.9904i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.00000 - 1.73205i) q^{82} +6.00000 q^{83} -8.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} -24.0000 q^{90} -2.00000 q^{92} +(6.00000 - 10.3923i) q^{93} +(-1.00000 - 1.73205i) q^{94} +(12.0000 + 20.7846i) q^{95} +(1.50000 - 2.59808i) q^{96} +5.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} - q^{4} - 4 q^{5} - 6 q^{6} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + q^2 - 3 * q^3 - q^4 - 4 * q^5 - 6 * q^6 - 2 * q^8 - 6 * q^9	$ 2 q + q^{2} - 3 q^{3} - q^{4} - 4 q^{5} - 6 q^{6} - 2 q^{8} - 6 q^{9} + 4 q^{10} + q^{11} - 3 q^{12} + 2 q^{13} + 24 q^{15} - q^{16} + 2 q^{17} + 6 q^{18} + 6 q^{19} + 8 q^{20} + 2 q^{22} + 2 q^{23} + 3 q^{24} - 11 q^{25} + q^{26} + 18 q^{27} + 2 q^{29} + 12 q^{30} + 4 q^{31} + q^{32} + 3 q^{33} + 4 q^{34} + 12 q^{36} + 2 q^{37} - 6 q^{38} - 3 q^{39} + 4 q^{40} + 4 q^{41} + 8 q^{43} + q^{44} - 24 q^{45} - 2 q^{46} + 2 q^{47} + 6 q^{48} - 22 q^{50} + 6 q^{51} - q^{52} + 12 q^{53} + 9 q^{54} - 8 q^{55} - 36 q^{57} + q^{58} + 9 q^{59} - 12 q^{60} - 5 q^{61} + 8 q^{62} + 2 q^{64} - 4 q^{65} - 3 q^{66} + 9 q^{67} + 2 q^{68} - 12 q^{69} + 8 q^{71} + 6 q^{72} - 2 q^{73} - 2 q^{74} - 33 q^{75} - 12 q^{76} - 6 q^{78} + 15 q^{79} - 4 q^{80} - 9 q^{81} + 2 q^{82} + 12 q^{83} - 16 q^{85} + 4 q^{86} - 3 q^{87} - q^{88} + 6 q^{89} - 48 q^{90} - 4 q^{92} + 12 q^{93} - 2 q^{94} + 24 q^{95} + 3 q^{96} + 10 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 - q^4 - 4 * q^5 - 6 * q^6 - 2 * q^8 - 6 * q^9 + 4 * q^10 + q^11 - 3 * q^12 + 2 * q^13 + 24 * q^15 - q^16 + 2 * q^17 + 6 * q^18 + 6 * q^19 + 8 * q^20 + 2 * q^22 + 2 * q^23 + 3 * q^24 - 11 * q^25 + q^26 + 18 * q^27 + 2 * q^29 + 12 * q^30 + 4 * q^31 + q^32 + 3 * q^33 + 4 * q^34 + 12 * q^36 + 2 * q^37 - 6 * q^38 - 3 * q^39 + 4 * q^40 + 4 * q^41 + 8 * q^43 + q^44 - 24 * q^45 - 2 * q^46 + 2 * q^47 + 6 * q^48 - 22 * q^50 + 6 * q^51 - q^52 + 12 * q^53 + 9 * q^54 - 8 * q^55 - 36 * q^57 + q^58 + 9 * q^59 - 12 * q^60 - 5 * q^61 + 8 * q^62 + 2 * q^64 - 4 * q^65 - 3 * q^66 + 9 * q^67 + 2 * q^68 - 12 * q^69 + 8 * q^71 + 6 * q^72 - 2 * q^73 - 2 * q^74 - 33 * q^75 - 12 * q^76 - 6 * q^78 + 15 * q^79 - 4 * q^80 - 9 * q^81 + 2 * q^82 + 12 * q^83 - 16 * q^85 + 4 * q^86 - 3 * q^87 - q^88 + 6 * q^89 - 48 * q^90 - 4 * q^92 + 12 * q^93 - 2 * q^94 + 24 * q^95 + 3 * q^96 + 10 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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	−	2.59808i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.0599153	+	0.998203i	$0.519083\pi$
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.834512	+	0.550990i	$0.814250\pi$
$6$	−3.00000			−1.22474
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	2.00000	+	3.46410i	0.632456	+	1.09545i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.50000	+	2.59808i	−0.433013	+	0.750000i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$	12.0000			3.09839
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	3.00000	+	5.19615i	0.707107	+	1.22474i
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$	4.00000			0.894427
$21$		0			0
$22$	1.00000			0.213201
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	−0.742732	−	0.669588i	$-0.766471\pi$
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	0.951247	+	0.308431i	$0.0998038\pi$
$24$	1.50000	+	2.59808i	0.306186	+	0.530330i
$25$	−5.50000	−	9.52628i	−1.10000	−	1.90526i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	9.00000			1.73205
$28$		0			0
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$	6.00000	−	10.3923i	1.09545	−	1.89737i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	2.00000			0.342997
$35$		0			0
$36$	6.00000			1.00000
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	−3.00000	−	5.19615i	−0.486664	−	0.842927i
$39$	−1.50000	−	2.59808i	−0.240192	−	0.416025i
$40$	2.00000	−	3.46410i	0.316228	−	0.547723i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	−12.0000	−	20.7846i	−1.78885	−	3.09839i
$46$	−1.00000	−	1.73205i	−0.147442	−	0.255377i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$	3.00000			0.433013
$49$		0			0
$50$	−11.0000			−1.55563
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$	4.50000	−	7.79423i	0.612372	−	1.06066i
$55$	−4.00000			−0.539360
$56$		0			0
$57$	−18.0000			−2.38416
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$	−6.00000	−	10.3923i	−0.774597	−	1.34164i
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	−1.50000	−	2.59808i	−0.184637	−	0.319801i
$67$	4.50000	+	7.79423i	0.549762	+	0.952217i	0.998290	+	0.0584478i	$0.0186151\pi$
$67$	4.50000	+	7.79423i	0.549762	+	0.952217i	−0.448528	+	0.893769i	$0.648052\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	−6.00000			−0.722315
$70$		0			0
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$	3.00000	−	5.19615i	0.353553	−	0.612372i
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−16.5000	+	28.5788i	−1.90526	+	3.30000i
$76$	−6.00000			−0.688247
$77$		0			0
$78$	−3.00000			−0.339683
$79$	7.50000	−	12.9904i	0.843816	−	1.46153i	−0.0428296	−	0.999082i	$-0.513637\pi$
$79$	7.50000	−	12.9904i	0.843816	−	1.46153i	0.886646	−	0.462450i	$-0.153029\pi$
$80$	−2.00000	−	3.46410i	−0.223607	−	0.387298i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$	−8.00000			−0.867722
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	−24.0000			−2.52982
$91$		0			0
$92$	−2.00000			−0.208514
$93$	6.00000	−	10.3923i	0.622171	−	1.07763i
$94$	−1.00000	−	1.73205i	−0.103142	−	0.178647i
$95$	12.0000	+	20.7846i	1.23117	+	2.13246i
$96$	1.50000	−	2.59808i	0.153093	−	0.265165i
$97$	5.00000			0.507673			0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000			0.507673			0.253837	+	0.967247i	$0.418307\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$	−5.50000	+	9.52628i	−0.550000	+	0.952628i
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	6.00000	−	10.3923i	0.591198	−	1.02398i	−0.402874	−	0.915255i	$-0.631989\pi$
$103$	6.00000	−	10.3923i	0.591198	−	1.02398i	0.994071	−	0.108729i	$-0.0346780\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	12.0000			1.16554
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	−0.992003	−	0.126217i	$-0.959717\pi$
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	0.605308	+	0.795991i	$0.293050\pi$
$108$	−4.50000	−	7.79423i	−0.433013	−	0.750000i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$	−2.00000	+	3.46410i	−0.190693	+	0.330289i
$111$	−6.00000			−0.569495
$112$		0			0
$113$	17.0000			1.59923			0.799613	−	0.600516i	$-0.205038\pi$
$113$	17.0000			1.59923			0.799613	+	0.600516i	$0.205038\pi$
$114$	−9.00000	+	15.5885i	−0.842927	+	1.45999i
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$	−0.500000	−	0.866025i	−0.0464238	−	0.0804084i
$117$	−3.00000	+	5.19615i	−0.277350	+	0.480384i
$118$	9.00000			0.828517
$119$		0			0
$120$	−12.0000			−1.09545
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	2.50000	+	4.33013i	0.226339	+	0.392031i
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	24.0000			2.14663
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−6.00000	−	10.3923i	−0.528271	−	0.914991i
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$	−3.00000			−0.261116
$133$		0			0
$134$	9.00000			0.777482
$135$	−18.0000	+	31.1769i	−1.54919	+	2.68328i
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	2.00000	−	3.46410i	0.167836	−	0.290701i
$143$	0.500000	+	0.866025i	0.0418121	+	0.0724207i
$144$	−3.00000	−	5.19615i	−0.250000	−	0.433013i
$145$	−2.00000	+	3.46410i	−0.166091	+	0.287678i
$146$	−2.00000			−0.165521
$147$		0			0
$148$	−2.00000			−0.164399
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	16.5000	+	28.5788i	1.34722	+	2.33345i
$151$	−4.50000	−	7.79423i	−0.366205	−	0.634285i	0.622764	−	0.782410i	$-0.286010\pi$
$151$	−4.50000	−	7.79423i	−0.366205	−	0.634285i	−0.988969	+	0.148124i	$0.952676\pi$
$152$	−3.00000	+	5.19615i	−0.243332	+	0.421464i
$153$	−12.0000			−0.970143
$154$		0			0
$155$	−16.0000			−1.28515
$156$	−1.50000	+	2.59808i	−0.120096	+	0.208013i
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	−7.50000	−	12.9904i	−0.596668	−	1.03346i
$159$	18.0000	−	31.1769i	1.42749	−	2.47249i
$160$	−4.00000			−0.316228
$161$		0			0
$162$	−9.00000			−0.707107
$163$	−6.50000	+	11.2583i	−0.509119	+	0.881820i	0.490825	+	0.871258i	$0.336695\pi$
$163$	−6.50000	+	11.2583i	−0.509119	+	0.881820i	−0.999944	+	0.0105623i	$0.996638\pi$
$164$	−1.00000	−	1.73205i	−0.0780869	−	0.135250i
$165$	6.00000	+	10.3923i	0.467099	+	0.809040i
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	17.0000			1.31550			0.657750	−	0.753237i	$-0.271508\pi$
$167$	17.0000			1.31550			0.657750	+	0.753237i	$0.271508\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$	18.0000	+	31.1769i	1.37649	+	2.38416i
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	−2.50000	+	4.33013i	−0.190071	+	0.329213i	−0.945274	−	0.326278i	$-0.894205\pi$
$173$	−2.50000	+	4.33013i	−0.190071	+	0.329213i	0.755202	+	0.655492i	$0.227539\pi$
$174$	−3.00000			−0.227429
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	13.5000	−	23.3827i	1.01472	−	1.75755i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	0.514035	−	0.857769i	$-0.328150\pi$
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	−0.999867	+	0.0162823i	$0.994817\pi$
$180$	−12.0000	+	20.7846i	−0.894427	+	1.54919i
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$	15.0000			1.10883
$184$	−1.00000	+	1.73205i	−0.0737210	+	0.127688i
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$	−6.00000	−	10.3923i	−0.439941	−	0.762001i
$187$	−1.00000	+	1.73205i	−0.0731272	+	0.126660i
$188$	−2.00000			−0.145865
$189$		0			0
$190$	24.0000			1.74114
$191$	−7.00000	+	12.1244i	−0.506502	+	0.877288i	0.493469	+	0.869763i	$0.335728\pi$
$191$	−7.00000	+	12.1244i	−0.506502	+	0.877288i	−0.999972	+	0.00752447i	$0.997605\pi$
$192$	−1.50000	−	2.59808i	−0.108253	−	0.187500i
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	0.924853	+	0.380325i	$0.124188\pi$
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	−0.133056	+	0.991109i	$0.542479\pi$
$194$	2.50000	−	4.33013i	0.179490	−	0.310885i
$195$	12.0000			0.859338
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	5.50000	+	9.52628i	0.388909	+	0.673610i
$201$	13.5000	−	23.3827i	0.952217	−	1.64929i
$202$	−15.0000			−1.05540
$203$		0			0
$204$	−6.00000			−0.420084
$205$	−4.00000	+	6.92820i	−0.279372	+	0.483887i
$206$	−6.00000	−	10.3923i	−0.418040	−	0.724066i
$207$	6.00000	+	10.3923i	0.417029	+	0.722315i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	6.00000			0.415029
$210$		0			0
$211$	−14.0000			−0.963800			−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000			−0.963800			−0.481900	+	0.876226i	$0.660053\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$	−6.00000	−	10.3923i	−0.411113	−	0.712069i
$214$	4.00000	+	6.92820i	0.273434	+	0.473602i
$215$	−8.00000	+	13.8564i	−0.545595	+	0.944999i
$216$	−9.00000			−0.612372
$217$		0			0
$218$	−10.0000			−0.677285
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$	2.00000	+	3.46410i	0.134840	+	0.233550i
$221$	1.00000	+	1.73205i	0.0672673	+	0.116510i
$222$	−3.00000	+	5.19615i	−0.201347	+	0.348743i
$223$	26.0000			1.74109			0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000			1.74109			0.870544	+	0.492090i	$0.163767\pi$
$224$		0			0
$225$	66.0000			4.40000
$226$	8.50000	−	14.7224i	0.565412	−	0.979322i
$227$	5.00000	+	8.66025i	0.331862	+	0.574801i	0.982877	−	0.184263i	$-0.0589899\pi$
$227$	5.00000	+	8.66025i	0.331862	+	0.574801i	−0.651015	+	0.759065i	$0.725657\pi$
$228$	9.00000	+	15.5885i	0.596040	+	1.03237i
$229$	−8.00000	+	13.8564i	−0.528655	+	0.915657i	0.470787	+	0.882247i	$0.343970\pi$
$229$	−8.00000	+	13.8564i	−0.528655	+	0.915657i	−0.999442	+	0.0334101i	$0.989363\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$	−1.00000			−0.0656532
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$	4.00000	+	6.92820i	0.260931	+	0.451946i
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	−45.0000			−2.92306
$238$		0			0
$239$	19.0000			1.22901			0.614504	−	0.788914i	$-0.289356\pi$
$239$	19.0000			1.22901			0.614504	+	0.788914i	$0.289356\pi$
$240$	−6.00000	+	10.3923i	−0.387298	+	0.670820i
$241$	15.0000	+	25.9808i	0.966235	+	1.67357i	0.706260	+	0.707953i	$0.250381\pi$
$241$	15.0000	+	25.9808i	0.966235	+	1.67357i	0.259975	+	0.965615i	$0.416286\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$		0			0
$244$	5.00000			0.320092
$245$		0			0
$246$	−6.00000			−0.382546
$247$	3.00000	−	5.19615i	0.190885	−	0.330623i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	−9.00000	−	15.5885i	−0.570352	−	0.987878i
$250$	12.0000	−	20.7846i	0.758947	−	1.31453i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	2.00000			0.125739
$254$	2.50000	−	4.33013i	0.156864	−	0.271696i
$255$	12.0000	+	20.7846i	0.751469	+	1.30158i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	0.326929	+	0.945049i	$0.393986\pi$
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	−0.981901	+	0.189396i	$0.939347\pi$
$258$	−12.0000			−0.747087
$259$		0			0
$260$	4.00000			0.248069
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$	9.00000	+	15.5885i	0.556022	+	0.963058i
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	0.816066	−	0.577959i	$-0.196151\pi$
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	−0.908560	+	0.417755i	$0.862817\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$	−48.0000			−2.94862
$266$		0			0
$267$	−18.0000			−1.10158
$268$	4.50000	−	7.79423i	0.274881	−	0.476108i
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	0.988908	−	0.148527i	$-0.0474530\pi$
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	−0.623082	+	0.782157i	$0.714120\pi$
$270$	18.0000	+	31.1769i	1.09545	+	1.89737i
$271$	12.5000	−	21.6506i	0.759321	−	1.31518i	−0.183876	−	0.982949i	$-0.558865\pi$
$271$	12.5000	−	21.6506i	0.759321	−	1.31518i	0.943197	−	0.332233i	$-0.107802\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	9.00000			0.543710
$275$	5.50000	−	9.52628i	0.331662	−	0.574456i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	0.907564	−	0.419914i	$-0.137940\pi$
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	−0.817438	+	0.576017i	$0.804606\pi$
$278$	−4.00000	+	6.92820i	−0.239904	+	0.415526i
$279$	−24.0000			−1.43684
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	−3.00000	−	5.19615i	−0.178331	−	0.308879i	0.762978	−	0.646425i	$-0.223737\pi$
$283$	−3.00000	−	5.19615i	−0.178331	−	0.308879i	−0.941309	+	0.337546i	$0.890403\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$	36.0000	−	62.3538i	2.13246	−	3.69352i
$286$	1.00000			0.0591312
$287$		0			0
$288$	−6.00000			−0.353553
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	2.00000	+	3.46410i	0.117444	+	0.203419i
$291$	−7.50000	−	12.9904i	−0.439658	−	0.761510i
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$	−36.0000			−2.09600
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$	4.50000	+	7.79423i	0.261116	+	0.452267i
$298$	−5.00000	−	8.66025i	−0.289642	−	0.501675i
$299$	1.00000	−	1.73205i	0.0578315	−	0.100167i
$300$	33.0000			1.90526
$301$		0			0
$302$	−9.00000			−0.517892
$303$	−22.5000	+	38.9711i	−1.29259	+	2.23883i
$304$	3.00000	+	5.19615i	0.172062	+	0.298020i
$305$	−10.0000	−	17.3205i	−0.572598	−	0.991769i
$306$	−6.00000	+	10.3923i	−0.342997	+	0.594089i
$307$	−32.0000			−1.82634			−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000			−1.82634			−0.913168	+	0.407583i	$0.866372\pi$
$308$		0			0
$309$	−36.0000			−2.04797
$310$	−8.00000	+	13.8564i	−0.454369	+	0.786991i
$311$	−14.0000	−	24.2487i	−0.793867	−	1.37502i	−0.923556	−	0.383464i	$-0.874731\pi$
$311$	−14.0000	−	24.2487i	−0.793867	−	1.37502i	0.129689	−	0.991555i	$-0.458602\pi$
$312$	1.50000	+	2.59808i	0.0849208	+	0.147087i
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−15.0000			−0.843816
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	−0.646872	−	0.762598i	$-0.723923\pi$
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	0.983866	+	0.178908i	$0.0572566\pi$
$318$	−18.0000	−	31.1769i	−1.00939	−	1.74831i
$319$	0.500000	+	0.866025i	0.0279946	+	0.0484881i
$320$	−2.00000	+	3.46410i	−0.111803	+	0.193649i
$321$	24.0000			1.33955
$322$		0			0
$323$	12.0000			0.667698
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−5.50000	−	9.52628i	−0.305085	−	0.528423i
$326$	6.50000	+	11.2583i	0.360002	+	0.623541i
$327$	−15.0000	+	25.9808i	−0.829502	+	1.43674i
$328$	−2.00000			−0.110432
$329$		0			0
$330$	12.0000			0.660578
$331$	−3.50000	+	6.06218i	−0.192377	+	0.333207i	−0.946038	−	0.324057i	$-0.894953\pi$
$331$	−3.50000	+	6.06218i	−0.192377	+	0.333207i	0.753660	+	0.657264i	$0.228286\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	6.00000	+	10.3923i	0.328798	+	0.569495i
$334$	8.50000	−	14.7224i	0.465099	−	0.805576i
$335$	−36.0000			−1.96689
$336$		0			0
$337$	−30.0000			−1.63420			−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−30.0000			−1.63420			−0.817102	+	0.576493i	$0.804421\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	−25.5000	−	44.1673i	−1.38497	−	2.39884i
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$	−2.00000	+	3.46410i	−0.108306	+	0.187592i
$342$	36.0000			1.94666
$343$		0			0
$344$	−4.00000			−0.215666
$345$	12.0000	−	20.7846i	0.646058	−	1.11901i
$346$	2.50000	+	4.33013i	0.134401	+	0.232789i
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	0.947067	+	0.321037i	$0.104031\pi$
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	−0.195507	+	0.980702i	$0.562635\pi$
$348$	−1.50000	+	2.59808i	−0.0804084	+	0.139272i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	9.00000			0.480384
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$	−13.5000	−	23.3827i	−0.717517	−	1.24278i
$355$	−8.00000	+	13.8564i	−0.424596	+	0.735422i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−13.0000			−0.687071
$359$	15.5000	−	26.8468i	0.818059	−	1.41692i	−0.0890519	−	0.996027i	$-0.528384\pi$
$359$	15.5000	−	26.8468i	0.818059	−	1.41692i	0.907111	−	0.420892i	$-0.138283\pi$
$360$	12.0000	+	20.7846i	0.632456	+	1.09545i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	11.0000	−	19.0526i	0.578147	−	1.00138i
$363$	3.00000			0.157459
$364$		0			0
$365$	8.00000			0.418739
$366$	7.50000	−	12.9904i	0.392031	−	0.679018i
$367$	−7.00000	−	12.1244i	−0.365397	−	0.632886i	0.623443	−	0.781869i	$-0.285733\pi$
$367$	−7.00000	−	12.1244i	−0.365397	−	0.632886i	−0.988840	+	0.148983i	$0.952400\pi$
$368$	1.00000	+	1.73205i	0.0521286	+	0.0902894i
$369$	−6.00000	+	10.3923i	−0.312348	+	0.541002i
$370$	8.00000			0.415900
$371$		0			0
$372$	−12.0000			−0.622171
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	−0.761074	−	0.648665i	$-0.775328\pi$
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	0.942297	+	0.334777i	$0.108661\pi$
$374$	1.00000	+	1.73205i	0.0517088	+	0.0895622i
$375$	−36.0000	−	62.3538i	−1.85903	−	3.21994i
$376$	−1.00000	+	1.73205i	−0.0515711	+	0.0893237i
$377$	1.00000			0.0515026
$378$		0			0
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$	12.0000	−	20.7846i	0.615587	−	1.06623i
$381$	−7.50000	−	12.9904i	−0.384237	−	0.665517i
$382$	7.00000	+	12.1244i	0.358151	+	0.620336i
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	−0.745548	−	0.666452i	$-0.767812\pi$
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	0.949938	+	0.312437i	$0.101145\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	22.0000			1.11977
$387$	−12.0000	+	20.7846i	−0.609994	+	1.05654i
$388$	−2.50000	−	4.33013i	−0.126918	−	0.219829i
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$	6.00000	−	10.3923i	0.303822	−	0.526235i
$391$	4.00000			0.202289
$392$		0			0
$393$	54.0000			2.72394
$394$	−1.50000	+	2.59808i	−0.0755689	+	0.130889i
$395$	30.0000	+	51.9615i	1.50946	+	2.61447i
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	−15.0000	+	25.9808i	−0.752828	+	1.30394i	0.193618	+	0.981077i	$0.437978\pi$
$397$	−15.0000	+	25.9808i	−0.752828	+	1.30394i	−0.946447	+	0.322860i	$0.895356\pi$
$398$	10.0000			0.501255
$399$		0			0
$400$	11.0000			0.550000
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$	−13.5000	−	23.3827i	−0.673319	−	1.16622i
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$	−7.50000	+	12.9904i	−0.373139	+	0.646296i
$405$	36.0000			1.78885
$406$		0			0
$407$	2.00000			0.0991363
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	−0.925256	−	0.379344i	$-0.876150\pi$
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	0.134107	−	0.990967i	$-0.457183\pi$
$410$	4.00000	+	6.92820i	0.197546	+	0.342160i
$411$	13.5000	−	23.3827i	0.665906	−	1.15338i
$412$	−12.0000			−0.591198
$413$		0			0
$414$	12.0000			0.589768
$415$	−12.0000	+	20.7846i	−0.589057	+	1.02028i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	12.0000	+	20.7846i	0.587643	+	1.01783i
$418$	3.00000	−	5.19615i	0.146735	−	0.254152i
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	−7.00000	+	12.1244i	−0.340755	+	0.590204i
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$	−6.00000	−	10.3923i	−0.291386	−	0.504695i
$425$	11.0000	−	19.0526i	0.533578	−	0.924185i
$426$	−12.0000			−0.581402
$427$		0			0
$428$	8.00000			0.386695
$429$	1.50000	−	2.59808i	0.0724207	−	0.125436i
$430$	8.00000	+	13.8564i	0.385794	+	0.668215i
$431$	−0.500000	−	0.866025i	−0.0240842	−	0.0417150i	0.853732	−	0.520712i	$-0.174334\pi$
$431$	−0.500000	−	0.866025i	−0.0240842	−	0.0417150i	−0.877816	+	0.478997i	$0.841000\pi$
$432$	−4.50000	+	7.79423i	−0.216506	+	0.375000i
$433$	10.0000			0.480569			0.240285	−	0.970702i	$-0.422759\pi$
$433$	10.0000			0.480569			0.240285	+	0.970702i	$0.422759\pi$
$434$		0			0
$435$	12.0000			0.575356
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	−6.00000	−	10.3923i	−0.287019	−	0.497131i
$438$	3.00000	+	5.19615i	0.143346	+	0.248282i
$439$	−2.50000	+	4.33013i	−0.119318	+	0.206666i	−0.919498	−	0.393095i	$-0.871404\pi$
$439$	−2.50000	+	4.33013i	−0.119318	+	0.206666i	0.800179	+	0.599761i	$0.204738\pi$
$440$	4.00000			0.190693
$441$		0			0
$442$	2.00000			0.0951303
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$	3.00000	+	5.19615i	0.142374	+	0.246598i
$445$	12.0000	+	20.7846i	0.568855	+	0.985285i
$446$	13.0000	−	22.5167i	0.615568	−	1.06619i
$447$	−30.0000			−1.41895
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	33.0000	−	57.1577i	1.55563	−	2.69444i
$451$	1.00000	+	1.73205i	0.0470882	+	0.0815591i
$452$	−8.50000	−	14.7224i	−0.399806	−	0.692485i
$453$	−13.5000	+	23.3827i	−0.634285	+	1.09861i
$454$	10.0000			0.469323
$455$		0			0
$456$	18.0000			0.842927
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	−0.888466	−	0.458942i	$-0.848229\pi$
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	0.841688	+	0.539964i	$0.181562\pi$
$458$	8.00000	+	13.8564i	0.373815	+	0.647467i
$459$	9.00000	+	15.5885i	0.420084	+	0.727607i
$460$	4.00000	−	6.92820i	0.186501	−	0.323029i
$461$	3.00000			0.139724			0.0698620	−	0.997557i	$-0.477744\pi$
$461$	3.00000			0.139724			0.0698620	+	0.997557i	$0.477744\pi$
$462$		0			0
$463$	−14.0000			−0.650635			−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000			−0.650635			−0.325318	+	0.945605i	$0.605471\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	24.0000	+	41.5692i	1.11297	+	1.92773i
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$	6.00000			0.277350
$469$		0			0
$470$	8.00000			0.369012
$471$	6.00000	−	10.3923i	0.276465	−	0.478852i
$472$	−4.50000	−	7.79423i	−0.207129	−	0.358758i
$473$	2.00000	+	3.46410i	0.0919601	+	0.159280i
$474$	−22.5000	+	38.9711i	−1.03346	+	1.79000i
$475$	−66.0000			−3.02829
$476$		0			0
$477$	−72.0000			−3.29665
$478$	9.50000	−	16.4545i	0.434520	−	0.752611i
$479$	−18.5000	−	32.0429i	−0.845287	−	1.46408i	−0.885372	−	0.464883i	$-0.846096\pi$
$479$	−18.5000	−	32.0429i	−0.845287	−	1.46408i	0.0400855	−	0.999196i	$-0.487237\pi$
$480$	6.00000	+	10.3923i	0.273861	+	0.474342i
$481$	1.00000	−	1.73205i	0.0455961	−	0.0789747i
$482$	30.0000			1.36646
$483$		0			0
$484$	1.00000			0.0454545
$485$	−10.0000	+	17.3205i	−0.454077	+	0.786484i
$486$		0			0
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	0.907776	−	0.419456i	$-0.137779\pi$
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	−0.817147	+	0.576429i	$0.804446\pi$
$488$	2.50000	−	4.33013i	0.113170	−	0.196016i
$489$	39.0000			1.76364
$490$		0			0
$491$	18.0000			0.812329			0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000			0.812329			0.406164	+	0.913800i	$0.366866\pi$
$492$	−3.00000	+	5.19615i	−0.135250	+	0.234261i
$493$	1.00000	+	1.73205i	0.0450377	+	0.0780076i
$494$	−3.00000	−	5.19615i	−0.134976	−	0.233786i
$495$	12.0000	−	20.7846i	0.539360	−	0.934199i
$496$	−4.00000			−0.179605
$497$		0			0
$498$	−18.0000			−0.806599
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	−0.629519	−	0.776985i	$-0.716748\pi$
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	0.987648	+	0.156687i	$0.0500814\pi$
$500$	−12.0000	−	20.7846i	−0.536656	−	0.929516i
$501$	−25.5000	−	44.1673i	−1.13926	−	1.97325i
$502$	−6.00000	+	10.3923i	−0.267793	+	0.463831i
$503$	21.0000			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$504$		0			0
$505$	60.0000			2.66996
$506$	1.00000	−	1.73205i	0.0444554	−	0.0769991i
$507$	18.0000	+	31.1769i	0.799408	+	1.38462i
$508$	−2.50000	−	4.33013i	−0.110920	−	0.192118i
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	−0.843012	−	0.537895i	$-0.819220\pi$
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	0.887336	+	0.461123i	$0.152553\pi$
$510$	24.0000			1.06274
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	27.0000	−	46.7654i	1.19208	−	2.06474i
$514$	10.5000	+	18.1865i	0.463135	+	0.802174i
$515$	24.0000	+	41.5692i	1.05757	+	1.83176i
$516$	−6.00000	+	10.3923i	−0.264135	+	0.457496i
$517$	2.00000			0.0879599
$518$		0			0
$519$	15.0000			0.658427
$520$	2.00000	−	3.46410i	0.0877058	−	0.151911i
$521$	−13.0000	−	22.5167i	−0.569540	−	0.986473i	−0.996611	−	0.0822547i	$-0.973788\pi$
$521$	−13.0000	−	22.5167i	−0.569540	−	0.986473i	0.427071	−	0.904218i	$-0.359545\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	−0.560208	−	0.828352i	$-0.689279\pi$
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	0.997478	+	0.0709788i	$0.0226123\pi$
$524$	18.0000			0.786334
$525$		0			0
$526$	−3.00000			−0.130806
$527$	−4.00000	+	6.92820i	−0.174243	+	0.301797i
$528$	1.50000	+	2.59808i	0.0652791	+	0.113067i
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$	−24.0000	+	41.5692i	−1.04249	+	1.80565i
$531$	−54.0000			−2.34340
$532$		0			0
$533$	2.00000			0.0866296
$534$	−9.00000	+	15.5885i	−0.389468	+	0.674579i
$535$	−16.0000	−	27.7128i	−0.691740	−	1.19813i
$536$	−4.50000	−	7.79423i	−0.194370	−	0.336659i
$537$	−19.5000	+	33.7750i	−0.841487	+	1.45750i
$538$	12.0000			0.517357
$539$		0			0
$540$	36.0000			1.54919
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$	−12.5000	−	21.6506i	−0.536921	−	0.929974i
$543$	−33.0000	−	57.1577i	−1.41617	−	2.45287i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	40.0000			1.71341
$546$		0			0
$547$		0			0			−	1.00000i	$-0.5\pi$
$547$		0			0				1.00000i	$0.5\pi$
$548$	4.50000	−	7.79423i	0.192230	−	0.332953i
$549$	−15.0000	−	25.9808i	−0.640184	−	1.10883i
$550$	−5.50000	−	9.52628i	−0.234521	−	0.406202i
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$	6.00000			0.255377
$553$		0			0
$554$	3.00000			0.127458
$555$	12.0000	−	20.7846i	0.509372	−	0.882258i
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	−19.0000	−	32.9090i	−0.805056	−	1.39440i	−0.916253	−	0.400599i	$-0.868802\pi$
$557$	−19.0000	−	32.9090i	−0.805056	−	1.39440i	0.111198	−	0.993798i	$-0.464531\pi$
$558$	−12.0000	+	20.7846i	−0.508001	+	0.879883i
$559$	4.00000			0.169182
$560$		0			0
$561$	6.00000			0.253320
$562$	−5.00000	+	8.66025i	−0.210912	+	0.365311i
$563$	13.0000	+	22.5167i	0.547885	+	0.948964i	0.998419	+	0.0562051i	$0.0179001\pi$
$563$	13.0000	+	22.5167i	0.547885	+	0.948964i	−0.450535	+	0.892759i	$0.648767\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$	−34.0000	+	58.8897i	−1.43039	+	2.47751i
$566$	−6.00000			−0.252199
$567$		0			0
$568$	−4.00000			−0.167836
$569$	−18.0000	+	31.1769i	−0.754599	+	1.30700i	0.190974	+	0.981595i	$0.438835\pi$
$569$	−18.0000	+	31.1769i	−0.754599	+	1.30700i	−0.945573	+	0.325409i	$0.894498\pi$
$570$	−36.0000	−	62.3538i	−1.50787	−	2.61171i
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	0.995788	−	0.0916910i	$-0.0292272\pi$
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	−0.577301	+	0.816532i	$0.695894\pi$
$572$	0.500000	−	0.866025i	0.0209061	−	0.0362103i
$573$	42.0000			1.75458
$574$		0			0
$575$	−22.0000			−0.917463
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	0.783930	−	0.620850i	$-0.213212\pi$
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	−0.929636	+	0.368478i	$0.879879\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	33.0000	−	57.1577i	1.37143	−	2.37539i
$580$	4.00000			0.166091
$581$		0			0
$582$	−15.0000			−0.621770
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$	−12.0000	−	20.7846i	−0.496139	−	0.859338i
$586$	3.00000	−	5.19615i	0.123929	−	0.214651i
$587$	3.00000			0.123823			0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000			0.123823			0.0619116	+	0.998082i	$0.480280\pi$
$588$		0			0
$589$	24.0000			0.988903
$590$	−18.0000	+	31.1769i	−0.741048	+	1.28353i
$591$	4.50000	+	7.79423i	0.185105	+	0.320612i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$	9.00000			0.369274
$595$		0			0
$596$	−10.0000			−0.409616
$597$	15.0000	−	25.9808i	0.613909	−	1.06332i
$598$	−1.00000	−	1.73205i	−0.0408930	−	0.0708288i
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$	16.5000	−	28.5788i	0.673610	−	1.16673i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	−54.0000			−2.19905
$604$	−4.50000	+	7.79423i	−0.183102	+	0.317143i
$605$	−2.00000	−	3.46410i	−0.0813116	−	0.140836i
$606$	22.5000	+	38.9711i	0.914000	+	1.58309i
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	−0.981454	−	0.191700i	$-0.938600\pi$
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	0.656744	+	0.754114i	$0.271933\pi$
$608$	6.00000			0.243332
$609$		0			0
$610$	−20.0000			−0.809776
$611$	1.00000	−	1.73205i	0.0404557	−	0.0700713i
$612$	6.00000	+	10.3923i	0.242536	+	0.420084i
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	0.553716	−	0.832705i	$-0.313209\pi$
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	−0.998002	+	0.0631797i	$0.979876\pi$
$614$	−16.0000	+	27.7128i	−0.645707	+	1.11840i
$615$	24.0000			0.967773
$616$		0			0
$617$	−27.0000			−1.08698			−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000			−1.08698			−0.543490	+	0.839416i	$0.682897\pi$
$618$	−18.0000	+	31.1769i	−0.724066	+	1.25412i
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$	8.00000	+	13.8564i	0.321288	+	0.556487i
$621$	9.00000	−	15.5885i	0.361158	−	0.625543i
$622$	−28.0000			−1.12270
$623$		0			0
$624$	3.00000			0.120096
$625$	−20.5000	+	35.5070i	−0.820000	+	1.42028i
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$	−9.00000	−	15.5885i	−0.359425	−	0.622543i
$628$	2.00000	−	3.46410i	0.0798087	−	0.138233i
$629$	4.00000			0.159490
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$	−7.50000	+	12.9904i	−0.298334	+	0.516730i
$633$	21.0000	+	36.3731i	0.834675	+	1.44570i
$634$	−6.00000	−	10.3923i	−0.238290	−	0.412731i
$635$	−10.0000	+	17.3205i	−0.396838	+	0.687343i
$636$	−36.0000			−1.42749
$637$		0			0
$638$	1.00000			0.0395904
$639$	−12.0000	+	20.7846i	−0.474713	+	0.822226i
$640$	2.00000	+	3.46410i	0.0790569	+	0.136931i
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	0.763367	−	0.645966i	$-0.223545\pi$
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	−0.941106	+	0.338112i	$0.890212\pi$
$642$	12.0000	−	20.7846i	0.473602	−	0.820303i
$643$	−1.00000			−0.0394362			−0.0197181	−	0.999806i	$-0.506277\pi$
$643$	−1.00000			−0.0394362			−0.0197181	+	0.999806i	$0.506277\pi$
$644$		0			0
$645$	48.0000			1.89000
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$	−11.0000			−0.431455
$651$		0			0
$652$	13.0000			0.509119
$653$	−11.0000	+	19.0526i	−0.430463	+	0.745584i	−0.996913	−	0.0785119i	$-0.974983\pi$
$653$	−11.0000	+	19.0526i	−0.430463	+	0.745584i	0.566450	+	0.824096i	$0.308316\pi$
$654$	15.0000	+	25.9808i	0.586546	+	1.01593i
$655$	−36.0000	−	62.3538i	−1.40664	−	2.43637i
$656$	−1.00000	+	1.73205i	−0.0390434	+	0.0676252i
$657$	12.0000			0.468165
$658$		0			0
$659$	−32.0000			−1.24654			−0.623272	−	0.782006i	$-0.714197\pi$
$659$	−32.0000			−1.24654			−0.623272	+	0.782006i	$0.714197\pi$
$660$	6.00000	−	10.3923i	0.233550	−	0.404520i
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	0.752252	−	0.658876i	$-0.228968\pi$
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	−0.946729	+	0.322031i	$0.895634\pi$
$662$	3.50000	+	6.06218i	0.136031	+	0.235613i
$663$	3.00000	−	5.19615i	0.116510	−	0.201802i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	12.0000			0.464991
$667$	1.00000	−	1.73205i	0.0387202	−	0.0670653i
$668$	−8.50000	−	14.7224i	−0.328875	−	0.569628i
$669$	−39.0000	−	67.5500i	−1.50783	−	2.61163i
$670$	−18.0000	+	31.1769i	−0.695401	+	1.20447i
$671$	−5.00000			−0.193023
$672$		0			0
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$	−15.0000	+	25.9808i	−0.577778	+	1.00074i
$675$	−49.5000	−	85.7365i	−1.90526	−	3.30000i
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	19.0000	−	32.9090i	0.730229	−	1.26479i	−0.226556	−	0.973998i	$-0.572747\pi$
$677$	19.0000	−	32.9090i	0.730229	−	1.26479i	0.956785	−	0.290796i	$-0.0939201\pi$
$678$	−51.0000			−1.95864
$679$		0			0
$680$	8.00000			0.306786
$681$	15.0000	−	25.9808i	0.574801	−	0.995585i
$682$	2.00000	+	3.46410i	0.0765840	+	0.132647i
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	0.987275	+	0.159022i	$0.0508342\pi$
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	−0.355920	+	0.934516i	$0.615832\pi$
$684$	18.0000	−	31.1769i	0.688247	−	1.19208i
$685$	−36.0000			−1.37549
$686$		0			0
$687$	48.0000			1.83131
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$	−12.0000	−	20.7846i	−0.456832	−	0.791257i
$691$	7.50000	−	12.9904i	0.285313	−	0.494177i	−0.687372	−	0.726306i	$-0.741236\pi$
$691$	7.50000	−	12.9904i	0.285313	−	0.494177i	0.972685	+	0.232128i	$0.0745690\pi$
$692$	5.00000			0.190071
$693$		0			0
$694$	28.0000			1.06287
$695$	16.0000	−	27.7128i	0.606915	−	1.05121i
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$	2.00000	+	3.46410i	0.0757554	+	0.131212i
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$	18.0000			0.680823
$700$		0			0
$701$	39.0000			1.47301			0.736505	−	0.676432i	$-0.236475\pi$
$701$	39.0000			1.47301			0.736505	+	0.676432i	$0.236475\pi$
$702$	4.50000	−	7.79423i	0.169842	−	0.294174i
$703$	−6.00000	−	10.3923i	−0.226294	−	0.391953i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	12.0000	−	20.7846i	0.451946	−	0.782794i
$706$	−18.0000			−0.677439
$707$		0			0
$708$	−27.0000			−1.01472
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$	8.00000	+	13.8564i	0.300235	+	0.520022i
$711$	45.0000	+	77.9423i	1.68763	+	2.92306i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	8.00000			0.299602
$714$		0			0
$715$	−4.00000			−0.149592
$716$	−6.50000	+	11.2583i	−0.242916	+	0.420744i
$717$	−28.5000	−	49.3634i	−1.06435	−	1.84351i
$718$	−15.5000	−	26.8468i	−0.578455	−	1.00191i
$719$	−13.0000	+	22.5167i	−0.484818	+	0.839730i	−0.999848	−	0.0174426i	$-0.994448\pi$
$719$	−13.0000	+	22.5167i	−0.484818	+	0.839730i	0.515030	+	0.857172i	$0.327781\pi$
$720$	24.0000			0.894427
$721$		0			0
$722$	−17.0000			−0.632674
$723$	45.0000	−	77.9423i	1.67357	−	2.89870i
$724$	−11.0000	−	19.0526i	−0.408812	−	0.708083i
$725$	−5.50000	−	9.52628i	−0.204265	−	0.353797i
$726$	1.50000	−	2.59808i	0.0556702	−	0.0964237i
$727$	34.0000			1.26099			0.630495	−	0.776193i	$-0.282852\pi$
$727$	34.0000			1.26099			0.630495	+	0.776193i	$0.282852\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	4.00000	−	6.92820i	0.148047	−	0.256424i
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$	−7.50000	−	12.9904i	−0.277208	−	0.480138i
$733$	−0.500000	+	0.866025i	−0.0184679	+	0.0319874i	−0.875112	−	0.483921i	$-0.839212\pi$
$733$	−0.500000	+	0.866025i	−0.0184679	+	0.0319874i	0.856644	+	0.515908i	$0.172546\pi$
$734$	−14.0000			−0.516749
$735$		0			0
$736$	2.00000			0.0737210
$737$	−4.50000	+	7.79423i	−0.165760	+	0.287104i
$738$	6.00000	+	10.3923i	0.220863	+	0.382546i
$739$	−9.00000	−	15.5885i	−0.331070	−	0.573431i	0.651652	−	0.758518i	$-0.274076\pi$
$739$	−9.00000	−	15.5885i	−0.331070	−	0.573431i	−0.982722	+	0.185088i	$0.940743\pi$
$740$	4.00000	−	6.92820i	0.147043	−	0.254686i
$741$	−18.0000			−0.661247
$742$		0			0
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$	20.0000	+	34.6410i	0.732743	+	1.26915i
$746$	−3.50000	−	6.06218i	−0.128144	−	0.221952i
$747$	−18.0000	+	31.1769i	−0.658586	+	1.14070i
$748$	2.00000			0.0731272
$749$		0			0
$750$	−72.0000			−2.62907
$751$	22.0000	−	38.1051i	0.802791	−	1.39048i	−0.114981	−	0.993368i	$-0.536681\pi$
$751$	22.0000	−	38.1051i	0.802791	−	1.39048i	0.917772	−	0.397108i	$-0.129986\pi$
$752$	1.00000	+	1.73205i	0.0364662	+	0.0631614i
$753$	18.0000	+	31.1769i	0.655956	+	1.13615i
$754$	0.500000	−	0.866025i	0.0182089	−	0.0315388i
$755$	36.0000			1.31017
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	−14.5000	+	25.1147i	−0.526664	+	0.912208i
$759$	−3.00000	−	5.19615i	−0.108893	−	0.188608i
$760$	−12.0000	−	20.7846i	−0.435286	−	0.753937i
$761$	27.0000	−	46.7654i	0.978749	−	1.69524i	0.311787	−	0.950152i	$-0.399073\pi$
$761$	27.0000	−	46.7654i	0.978749	−	1.69524i	0.666962	−	0.745091i	$-0.267594\pi$
$762$	−15.0000			−0.543393
$763$		0			0
$764$	14.0000			0.506502
$765$	24.0000	−	41.5692i	0.867722	−	1.50294i
$766$	−4.00000	−	6.92820i	−0.144526	−	0.250326i
$767$	4.50000	+	7.79423i	0.162486	+	0.281433i
$768$	−1.50000	+	2.59808i	−0.0541266	+	0.0937500i
$769$	38.0000			1.37032			0.685158	−	0.728395i	$-0.259733\pi$
$769$	38.0000			1.37032			0.685158	+	0.728395i	$0.259733\pi$
$770$		0			0
$771$	63.0000			2.26889
$772$	11.0000	−	19.0526i	0.395899	−	0.685717i
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	0.565402	−	0.824815i	$-0.308721\pi$
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	−0.997012	+	0.0772449i	$0.975388\pi$
$774$	12.0000	+	20.7846i	0.431331	+	0.747087i
$775$	22.0000	−	38.1051i	0.790263	−	1.36878i
$776$	−5.00000			−0.179490
$777$		0			0
$778$		0			0
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$	−6.00000	−	10.3923i	−0.214834	−	0.372104i
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	2.00000	−	3.46410i	0.0715199	−	0.123876i
$783$	9.00000			0.321634
$784$		0			0
$785$	−16.0000			−0.571064
$786$	27.0000	−	46.7654i	0.963058	−	1.66807i
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	0.600620	−	0.799535i	$-0.294921\pi$
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	−0.992727	+	0.120384i	$0.961587\pi$
$788$	1.50000	+	2.59808i	0.0534353	+	0.0925526i
$789$	−4.50000	+	7.79423i	−0.160204	+	0.277482i
$790$	60.0000			2.13470
$791$		0			0
$792$	6.00000			0.213201
$793$	−2.50000	+	4.33013i	−0.0887776	+	0.153767i
$794$	15.0000	+	25.9808i	0.532330	+	0.922023i
$795$	72.0000	+	124.708i	2.55358	+	4.42292i
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	−38.0000			−1.34603			−0.673015	−	0.739629i	$-0.735001\pi$
$797$	−38.0000			−1.34603			−0.673015	+	0.739629i	$0.735001\pi$
$798$		0			0
$799$	4.00000			0.141510
$800$	5.50000	−	9.52628i	0.194454	−	0.336805i
$801$	18.0000	+	31.1769i	0.635999	+	1.10158i
$802$	7.50000	+	12.9904i	0.264834	+	0.458706i
$803$	1.00000	−	1.73205i	0.0352892	−	0.0611227i
$804$	−27.0000			−0.952217
$805$		0			0
$806$	4.00000			0.140894
$807$	18.0000	−	31.1769i	0.633630	−	1.09748i
$808$	7.50000	+	12.9904i	0.263849	+	0.457000i
$809$	24.0000	+	41.5692i	0.843795	+	1.46150i	0.886664	+	0.462415i	$0.153017\pi$
$809$	24.0000	+	41.5692i	0.843795	+	1.46150i	−0.0428684	+	0.999081i	$0.513650\pi$
$810$	18.0000	−	31.1769i	0.632456	−	1.09545i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	−75.0000			−2.63036
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	−26.0000	−	45.0333i	−0.910740	−	1.57745i
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	12.0000	−	20.7846i	0.419827	−	0.727161i
$818$	−32.0000			−1.11885
$819$		0			0
$820$	8.00000			0.279372
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	−0.704956	−	0.709251i	$-0.749033\pi$
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	0.966708	+	0.255884i	$0.0823665\pi$
$822$	−13.5000	−	23.3827i	−0.470867	−	0.815565i
$823$	−19.0000	−	32.9090i	−0.662298	−	1.14713i	−0.980010	−	0.198947i	$-0.936248\pi$
$823$	−19.0000	−	32.9090i	−0.662298	−	1.14713i	0.317712	−	0.948187i	$-0.397086\pi$
$824$	−6.00000	+	10.3923i	−0.209020	+	0.362033i
$825$	−33.0000			−1.14891
$826$		0			0
$827$	−22.0000			−0.765015			−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000			−0.765015			−0.382507	+	0.923952i	$0.624939\pi$
$828$	6.00000	−	10.3923i	0.208514	−	0.361158i
$829$	8.00000	+	13.8564i	0.277851	+	0.481253i	0.970851	−	0.239686i	$-0.0770444\pi$
$829$	8.00000	+	13.8564i	0.277851	+	0.481253i	−0.692999	+	0.720938i	$0.743711\pi$
$830$	12.0000	+	20.7846i	0.416526	+	0.721444i
$831$	4.50000	−	7.79423i	0.156103	−	0.270379i
$832$	1.00000			0.0346688
$833$		0			0
$834$	24.0000			0.831052
$835$	−34.0000	+	58.8897i	−1.17662	+	2.03796i
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$	18.0000	+	31.1769i	0.622171	+	1.07763i
$838$	10.0000	−	17.3205i	0.345444	−	0.598327i
$839$	−54.0000			−1.86429			−0.932144	−	0.362089i	$-0.882064\pi$
$839$	−54.0000			−1.86429			−0.932144	+	0.362089i	$0.882064\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	−10.0000	+	17.3205i	−0.344623	+	0.596904i
$843$	15.0000	+	25.9808i	0.516627	+	0.894825i
$844$	7.00000	+	12.1244i	0.240950	+	0.417338i
$845$	24.0000	−	41.5692i	0.825625	−	1.43002i
$846$	12.0000			0.412568
$847$		0			0
$848$	−12.0000			−0.412082
$849$	−9.00000	+	15.5885i	−0.308879	+	0.534994i
$850$	−11.0000	−	19.0526i	−0.377297	−	0.653497i
$851$	−2.00000	−	3.46410i	−0.0685591	−	0.118748i
$852$	−6.00000	+	10.3923i	−0.205557	+	0.356034i
$853$	−50.0000			−1.71197			−0.855984	−	0.517003i	$-0.827048\pi$
$853$	−50.0000			−1.71197			−0.855984	+	0.517003i	$0.827048\pi$
$854$		0			0
$855$	−144.000			−4.92470
$856$	4.00000	−	6.92820i	0.136717	−	0.236801i
$857$	−2.00000	−	3.46410i	−0.0683187	−	0.118331i	0.829843	−	0.557998i	$-0.188430\pi$
$857$	−2.00000	−	3.46410i	−0.0683187	−	0.118331i	−0.898161	+	0.439666i	$0.855097\pi$
$858$	−1.50000	−	2.59808i	−0.0512092	−	0.0886969i
$859$	−8.50000	+	14.7224i	−0.290016	+	0.502323i	−0.973813	−	0.227349i	$-0.926994\pi$
$859$	−8.50000	+	14.7224i	−0.290016	+	0.502323i	0.683797	+	0.729672i	$0.260327\pi$
$860$	16.0000			0.545595
$861$		0			0
$862$	−1.00000			−0.0340601
$863$	−5.00000	+	8.66025i	−0.170202	+	0.294798i	−0.938490	−	0.345305i	$-0.887775\pi$
$863$	−5.00000	+	8.66025i	−0.170202	+	0.294798i	0.768288	+	0.640104i	$0.221109\pi$
$864$	4.50000	+	7.79423i	0.153093	+	0.265165i
$865$	−10.0000	−	17.3205i	−0.340010	−	0.588915i
$866$	5.00000	−	8.66025i	0.169907	−	0.294287i
$867$	−39.0000			−1.32451
$868$		0			0
$869$	15.0000			0.508840
$870$	6.00000	−	10.3923i	0.203419	−	0.352332i
$871$	4.50000	+	7.79423i	0.152477	+	0.264097i
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$	−15.0000	+	25.9808i	−0.507673	+	0.879316i
$874$	−12.0000			−0.405906
$875$		0			0
$876$	6.00000			0.202721
$877$	−12.5000	+	21.6506i	−0.422095	+	0.731090i	−0.996144	−	0.0877308i	$-0.972038\pi$
$877$	−12.5000	+	21.6506i	−0.422095	+	0.731090i	0.574049	+	0.818821i	$0.305372\pi$
$878$	2.50000	+	4.33013i	0.0843709	+	0.146135i
$879$	−9.00000	−	15.5885i	−0.303562	−	0.525786i
$880$	2.00000	−	3.46410i	0.0674200	−	0.116775i
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$		0			0
$883$	1.00000			0.0336527			0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000			0.0336527			0.0168263	+	0.999858i	$0.494644\pi$
$884$	1.00000	−	1.73205i	0.0336336	−	0.0582552i
$885$	54.0000	+	93.5307i	1.81519	+	3.14400i
$886$	−6.00000	−	10.3923i	−0.201574	−	0.349136i
$887$	−8.50000	+	14.7224i	−0.285402	+	0.494331i	−0.972707	−	0.232038i	$-0.925460\pi$
$887$	−8.50000	+	14.7224i	−0.285402	+	0.494331i	0.687305	+	0.726369i	$0.258794\pi$
$888$	6.00000			0.201347
$889$		0			0
$890$	24.0000			0.804482
$891$	4.50000	−	7.79423i	0.150756	−	0.261116i
$892$	−13.0000	−	22.5167i	−0.435272	−	0.753914i
$893$	−6.00000	−	10.3923i	−0.200782	−	0.347765i
$894$	−15.0000	+	25.9808i	−0.501675	+	0.868927i
$895$	52.0000			1.73817
$896$		0			0
$897$	−6.00000			−0.200334
$898$	15.0000	−	25.9808i	0.500556	−	0.866989i
$899$	2.00000	+	3.46410i	0.0667037	+	0.115534i
$900$	−33.0000	−	57.1577i	−1.10000	−	1.90526i
$901$	−12.0000	+	20.7846i	−0.399778	+	0.692436i
$902$	2.00000			0.0665927
$903$		0			0
$904$	−17.0000			−0.565412
$905$	−44.0000	+	76.2102i	−1.46261	+	2.53331i
$906$	13.5000	+	23.3827i	0.448507	+	0.776838i
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	−0.956671	−	0.291172i	$-0.905955\pi$
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	0.226173	−	0.974087i	$-0.427379\pi$
$908$	5.00000	−	8.66025i	0.165931	−	0.287401i
$909$	90.0000			2.98511
$910$		0			0
$911$	−54.0000			−1.78910			−0.894550	−	0.446968i	$-0.852504\pi$
$911$	−54.0000			−1.78910			−0.894550	+	0.446968i	$0.852504\pi$
$912$	9.00000	−	15.5885i	0.298020	−	0.516185i
$913$	3.00000	+	5.19615i	0.0992855	+	0.171968i
$914$	1.00000	+	1.73205i	0.0330771	+	0.0572911i
$915$	−30.0000	+	51.9615i	−0.991769	+	1.71780i
$916$	16.0000			0.528655
$917$		0			0
$918$	18.0000			0.594089
$919$	12.0000	−	20.7846i	0.395843	−	0.685621i	−0.597365	−	0.801970i	$-0.703786\pi$
$919$	12.0000	−	20.7846i	0.395843	−	0.685621i	0.993208	+	0.116348i	$0.0371189\pi$
$920$	−4.00000	−	6.92820i	−0.131876	−	0.228416i
$921$	48.0000	+	83.1384i	1.58165	+	2.73950i
$922$	1.50000	−	2.59808i	0.0493999	−	0.0855631i
$923$	4.00000			0.131662
$924$		0			0
$925$	−22.0000			−0.723356
$926$	−7.00000	+	12.1244i	−0.230034	+	0.398431i
$927$	36.0000	+	62.3538i	1.18240	+	2.04797i
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	0.457480	+	0.889220i	$0.348752\pi$
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	−0.998827	+	0.0484211i	$0.984581\pi$
$930$	48.0000			1.57398
$931$		0			0
$932$	6.00000			0.196537
$933$	−42.0000	+	72.7461i	−1.37502	+	2.38160i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$	−4.00000	−	6.92820i	−0.130814	−	0.226576i
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$	12.0000			0.392023			0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000			0.392023			0.196011	+	0.980602i	$0.437201\pi$
$938$		0			0
$939$	−3.00000			−0.0979013
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$	27.5000	+	47.6314i	0.896474	+	1.55274i	0.831969	+	0.554822i	$0.187214\pi$
$941$	27.5000	+	47.6314i	0.896474	+	1.55274i	0.0645052	+	0.997917i	$0.479453\pi$
$942$	−6.00000	−	10.3923i	−0.195491	−	0.338600i
$943$	2.00000	−	3.46410i	0.0651290	−	0.112807i
$944$	−9.00000			−0.292925
$945$		0			0
$946$	4.00000			0.130051
$947$	8.00000	−	13.8564i	0.259965	−	0.450273i	−0.706267	−	0.707945i	$-0.749622\pi$
$947$	8.00000	−	13.8564i	0.259965	−	0.450273i	0.966232	+	0.257673i	$0.0829556\pi$
$948$	22.5000	+	38.9711i	0.730766	+	1.26572i
$949$	−1.00000	−	1.73205i	−0.0324614	−	0.0562247i
$950$	−33.0000	+	57.1577i	−1.07066	+	1.85444i
$951$	−36.0000			−1.16738
$952$		0			0
$953$	56.0000			1.81402			0.907009	−	0.421111i	$-0.138360\pi$
$953$	56.0000			1.81402			0.907009	+	0.421111i	$0.138360\pi$
$954$	−36.0000	+	62.3538i	−1.16554	+	2.01878i
$955$	−28.0000	−	48.4974i	−0.906059	−	1.56934i
$956$	−9.50000	−	16.4545i	−0.307252	−	0.532176i
$957$	1.50000	−	2.59808i	0.0484881	−	0.0839839i
$958$	−37.0000			−1.19542
$959$		0			0
$960$	12.0000			0.387298
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−1.00000	−	1.73205i	−0.0322413	−	0.0558436i
$963$	−24.0000	−	41.5692i	−0.773389	−	1.33955i
$964$	15.0000	−	25.9808i	0.483117	−	0.836784i
$965$	−88.0000			−2.83282
$966$		0			0
$967$	56.0000			1.80084			0.900419	−	0.435023i	$-0.143260\pi$
$967$	56.0000			1.80084			0.900419	+	0.435023i	$0.143260\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	−18.0000	−	31.1769i	−0.578243	−	1.00155i
$970$	10.0000	+	17.3205i	0.321081	+	0.556128i
$971$	−6.50000	+	11.2583i	−0.208595	+	0.361297i	−0.951272	−	0.308353i	$-0.900222\pi$
$971$	−6.50000	+	11.2583i	−0.208595	+	0.361297i	0.742677	+	0.669650i	$0.233556\pi$
$972$		0			0
$973$		0			0
$974$	4.00000			0.128168
$975$	−16.5000	+	28.5788i	−0.528423	+	0.915255i
$976$	−2.50000	−	4.33013i	−0.0800230	−	0.138604i
$977$	−7.00000	−	12.1244i	−0.223950	−	0.387893i	0.732054	−	0.681247i	$-0.238562\pi$
$977$	−7.00000	−	12.1244i	−0.223950	−	0.387893i	−0.956004	+	0.293354i	$0.905229\pi$
$978$	19.5000	−	33.7750i	0.623541	−	1.08001i
$979$	6.00000			0.191761
$980$		0			0
$981$	60.0000			1.91565
$982$	9.00000	−	15.5885i	0.287202	−	0.497448i
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	0.973106	−	0.230360i	$-0.0739903\pi$
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	−0.686050	+	0.727554i	$0.740657\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$	2.00000			0.0636930
$987$		0			0
$988$	−6.00000			−0.190885
$989$	4.00000	−	6.92820i	0.127193	−	0.220304i
$990$	−12.0000	−	20.7846i	−0.381385	−	0.660578i
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	0.979999	−	0.199000i	$-0.0637695\pi$
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	−0.662339	+	0.749204i	$0.730436\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	21.0000			0.666415
$994$		0			0
$995$	−40.0000			−1.26809
$996$	−9.00000	+	15.5885i	−0.285176	+	0.493939i
$997$	−21.0000	−	36.3731i	−0.665077	−	1.15195i	−0.979265	−	0.202586i	$-0.935066\pi$
$997$	−21.0000	−	36.3731i	−0.665077	−	1.15195i	0.314188	−	0.949361i	$-0.398268\pi$
$998$	−8.00000	−	13.8564i	−0.253236	−	0.438617i
$999$	9.00000	−	15.5885i	0.284747	−	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.g.177.1		2
7.2	even	3		1078.2.a.f.1.1		1
7.3	odd	6		154.2.e.d.67.1	yes	2
7.4	even	3	inner	1078.2.e.g.67.1		2
7.5	odd	6		1078.2.a.a.1.1		1
7.6	odd	2		154.2.e.d.23.1	✓	2
21.2	odd	6		9702.2.a.bb.1.1		1
21.5	even	6		9702.2.a.cg.1.1		1
21.17	even	6		1386.2.k.a.991.1		2
21.20	even	2		1386.2.k.a.793.1		2
28.3	even	6		1232.2.q.a.529.1		2
28.19	even	6		8624.2.a.bd.1.1		1
28.23	odd	6		8624.2.a.d.1.1		1
28.27	even	2		1232.2.q.a.177.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.d.23.1	✓	2	7.6	odd	2
154.2.e.d.67.1	yes	2	7.3	odd	6
1078.2.a.a.1.1		1	7.5	odd	6
1078.2.a.f.1.1		1	7.2	even	3
1078.2.e.g.67.1		2	7.4	even	3	inner
1078.2.e.g.177.1		2	1.1	even	1	trivial
1232.2.q.a.177.1		2	28.27	even	2
1232.2.q.a.529.1		2	28.3	even	6
1386.2.k.a.793.1		2	21.20	even	2
1386.2.k.a.991.1		2	21.17	even	6
8624.2.a.d.1.1		1	28.23	odd	6
8624.2.a.bd.1.1		1	28.19	even	6
9702.2.a.bb.1.1		1	21.2	odd	6
9702.2.a.cg.1.1		1	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(2.00000 + 3.46410i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.50000 + 2.59808i) q^{12} +1.00000 q^{13} +12.0000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(3.00000 + 5.19615i) q^{18} +(3.00000 - 5.19615i) q^{19} +4.00000 q^{20} +1.00000 q^{22} +(1.00000 - 1.73205i) q^{23} +(1.50000 + 2.59808i) q^{24} +(-5.50000 - 9.52628i) q^{25} +(0.500000 - 0.866025i) q^{26} +9.00000 q^{27} +1.00000 q^{29} +(6.00000 - 10.3923i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +2.00000 q^{34} +6.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-1.50000 - 2.59808i) q^{39} +(2.00000 - 3.46410i) q^{40} +2.00000 q^{41} +4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-12.0000 - 20.7846i) q^{45} +(-1.00000 - 1.73205i) q^{46} +(1.00000 - 1.73205i) q^{47} +3.00000 q^{48} -11.0000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(6.00000 + 10.3923i) q^{53} +(4.50000 - 7.79423i) q^{54} -4.00000 q^{55} -18.0000 q^{57} +(0.500000 - 0.866025i) q^{58} +(4.50000 + 7.79423i) q^{59} +(-6.00000 - 10.3923i) q^{60} +(-2.50000 + 4.33013i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(4.50000 + 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} -6.00000 q^{69} +4.00000 q^{71} +(3.00000 - 5.19615i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-16.5000 + 28.5788i) q^{75} -6.00000 q^{76} -3.00000 q^{78} +(7.50000 - 12.9904i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.00000 - 1.73205i) q^{82} +6.00000 q^{83} -8.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} -24.0000 q^{90} -2.00000 q^{92} +(6.00000 - 10.3923i) q^{93} +(-1.00000 - 1.73205i) q^{94} +(12.0000 + 20.7846i) q^{95} +(1.50000 - 2.59808i) q^{96} +5.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} - q^{4} - 4 q^{5} - 6 q^{6} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + q^2 - 3 * q^3 - q^4 - 4 * q^5 - 6 * q^6 - 2 * q^8 - 6 * q^9	\( 2 q + q^{2} - 3 q^{3} - q^{4} - 4 q^{5} - 6 q^{6} - 2 q^{8} - 6 q^{9} + 4 q^{10} + q^{11} - 3 q^{12} + 2 q^{13} + 24 q^{15} - q^{16} + 2 q^{17} + 6 q^{18} + 6 q^{19} + 8 q^{20} + 2 q^{22} + 2 q^{23} + 3 q^{24} - 11 q^{25} + q^{26} + 18 q^{27} + 2 q^{29} + 12 q^{30} + 4 q^{31} + q^{32} + 3 q^{33} + 4 q^{34} + 12 q^{36} + 2 q^{37} - 6 q^{38} - 3 q^{39} + 4 q^{40} + 4 q^{41} + 8 q^{43} + q^{44} - 24 q^{45} - 2 q^{46} + 2 q^{47} + 6 q^{48} - 22 q^{50} + 6 q^{51} - q^{52} + 12 q^{53} + 9 q^{54} - 8 q^{55} - 36 q^{57} + q^{58} + 9 q^{59} - 12 q^{60} - 5 q^{61} + 8 q^{62} + 2 q^{64} - 4 q^{65} - 3 q^{66} + 9 q^{67} + 2 q^{68} - 12 q^{69} + 8 q^{71} + 6 q^{72} - 2 q^{73} - 2 q^{74} - 33 q^{75} - 12 q^{76} - 6 q^{78} + 15 q^{79} - 4 q^{80} - 9 q^{81} + 2 q^{82} + 12 q^{83} - 16 q^{85} + 4 q^{86} - 3 q^{87} - q^{88} + 6 q^{89} - 48 q^{90} - 4 q^{92} + 12 q^{93} - 2 q^{94} + 24 q^{95} + 3 q^{96} + 10 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 - q^4 - 4 * q^5 - 6 * q^6 - 2 * q^8 - 6 * q^9 + 4 * q^10 + q^11 - 3 * q^12 + 2 * q^13 + 24 * q^15 - q^16 + 2 * q^17 + 6 * q^18 + 6 * q^19 + 8 * q^20 + 2 * q^22 + 2 * q^23 + 3 * q^24 - 11 * q^25 + q^26 + 18 * q^27 + 2 * q^29 + 12 * q^30 + 4 * q^31 + q^32 + 3 * q^33 + 4 * q^34 + 12 * q^36 + 2 * q^37 - 6 * q^38 - 3 * q^39 + 4 * q^40 + 4 * q^41 + 8 * q^43 + q^44 - 24 * q^45 - 2 * q^46 + 2 * q^47 + 6 * q^48 - 22 * q^50 + 6 * q^51 - q^52 + 12 * q^53 + 9 * q^54 - 8 * q^55 - 36 * q^57 + q^58 + 9 * q^59 - 12 * q^60 - 5 * q^61 + 8 * q^62 + 2 * q^64 - 4 * q^65 - 3 * q^66 + 9 * q^67 + 2 * q^68 - 12 * q^69 + 8 * q^71 + 6 * q^72 - 2 * q^73 - 2 * q^74 - 33 * q^75 - 12 * q^76 - 6 * q^78 + 15 * q^79 - 4 * q^80 - 9 * q^81 + 2 * q^82 + 12 * q^83 - 16 * q^85 + 4 * q^86 - 3 * q^87 - q^88 + 6 * q^89 - 48 * q^90 - 4 * q^92 + 12 * q^93 - 2 * q^94 + 24 * q^95 + 3 * q^96 + 10 * q^97 - 12 * q^99

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