LMFDB - Embedded newform 390.2.y.d.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(139,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("390.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.y (of order $6$, degree $2$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	390.139
Dual form			390.2.y.d.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.133975 - 2.23205i) q^{10} +(-1.50000 + 2.59808i) q^{11} -1.00000i q^{12} +(-3.46410 - 1.00000i) q^{13} +(0.133975 - 2.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 + 3.00000i) q^{17} -1.00000i q^{18} +(-1.23205 + 1.86603i) q^{20} +(2.59808 - 1.50000i) q^{22} +(7.79423 + 4.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(2.50000 + 2.59808i) q^{26} -1.00000i q^{27} +(-3.50000 + 6.06218i) q^{29} +(-1.23205 + 1.86603i) q^{30} +1.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(2.59808 - 1.50000i) q^{33} +6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.866025 - 0.500000i) q^{37} +(2.50000 + 2.59808i) q^{39} +(2.00000 - 1.00000i) q^{40} +(11.2583 - 6.50000i) q^{43} -3.00000 q^{44} +(-1.23205 + 1.86603i) q^{45} +(-4.50000 - 7.79423i) q^{46} +11.0000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(4.59808 - 1.96410i) q^{50} +6.00000 q^{51} +(-0.866025 - 3.50000i) q^{52} +6.00000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(-6.69615 - 0.401924i) q^{55} +(6.06218 - 3.50000i) q^{58} +(-5.50000 - 9.52628i) q^{59} +(2.00000 - 1.00000i) q^{60} +(-0.866025 - 0.500000i) q^{62} -1.00000 q^{64} +(-1.46410 - 7.92820i) q^{65} -3.00000 q^{66} +(-3.46410 - 2.00000i) q^{67} +(-5.19615 - 3.00000i) q^{68} +(-4.50000 - 7.79423i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(0.866025 - 0.500000i) q^{72} +(0.500000 + 0.866025i) q^{74} +(4.59808 - 1.96410i) q^{75} +(-0.866025 - 3.50000i) q^{78} -1.00000 q^{79} +(-2.23205 - 0.133975i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.00000i q^{83} +(-11.1962 - 7.39230i) q^{85} -13.0000 q^{86} +(6.06218 - 3.50000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(-2.00000 + 3.46410i) q^{89} +(2.00000 - 1.00000i) q^{90} +9.00000i q^{92} +(-0.866025 - 0.500000i) q^{93} +(5.50000 - 9.52628i) q^{94} -1.00000 q^{96} +(-3.46410 + 2.00000i) q^{97} +(6.06218 - 3.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{9} + 4 q^{10} - 6 q^{11} + 4 q^{15} - 2 q^{16} + 2 q^{20} - 2 q^{24} - 12 q^{25} + 10 q^{26} - 14 q^{29} + 2 q^{30} + 4 q^{31} + 24 q^{34} - 2 q^{36} + 10 q^{39} + 8 q^{40} - 12 q^{44} + 2 q^{45} - 18 q^{46} - 14 q^{49} + 8 q^{50} + 24 q^{51} - 2 q^{54} - 6 q^{55} - 22 q^{59} + 8 q^{60} - 4 q^{64} + 8 q^{65} - 12 q^{66} - 18 q^{69} - 8 q^{71} + 2 q^{74} + 8 q^{75} - 4 q^{79} - 2 q^{80} - 2 q^{81} - 24 q^{85} - 52 q^{86} - 8 q^{89} + 8 q^{90} + 22 q^{94} - 4 q^{96} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^9 + 4 * q^10 - 6 * q^11 + 4 * q^15 - 2 * q^16 + 2 * q^20 - 2 * q^24 - 12 * q^25 + 10 * q^26 - 14 * q^29 + 2 * q^30 + 4 * q^31 + 24 * q^34 - 2 * q^36 + 10 * q^39 + 8 * q^40 - 12 * q^44 + 2 * q^45 - 18 * q^46 - 14 * q^49 + 8 * q^50 + 24 * q^51 - 2 * q^54 - 6 * q^55 - 22 * q^59 + 8 * q^60 - 4 * q^64 + 8 * q^65 - 12 * q^66 - 18 * q^69 - 8 * q^71 + 2 * q^74 + 8 * q^75 - 4 * q^79 - 2 * q^80 - 2 * q^81 - 24 * q^85 - 52 * q^86 - 8 * q^89 + 8 * q^90 + 22 * q^94 - 4 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.133975	−	2.23205i	0.0423665	−	0.705836i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$14$		0			0
$15$	0.133975	−	2.23205i	0.0345921	−	0.576313i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.973123	−	0.230285i	$-0.926034\pi$
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.287129	+	0.957892i	$0.592701\pi$
$18$		−	1.00000i		−	0.235702i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−1.23205	+	1.86603i	−0.275495	+	0.417256i
$21$		0			0
$22$	2.59808	−	1.50000i	0.553912	−	0.319801i
$23$	7.79423	+	4.50000i	1.62521	+	0.938315i	0.985496	+	0.169701i	$0.0542803\pi$
$23$	7.79423	+	4.50000i	1.62521	+	0.938315i	0.639713	+	0.768613i	$0.279053\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	2.50000	+	2.59808i	0.490290	+	0.509525i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	0.333205	+	0.942855i	$0.391870\pi$
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	−0.983138	+	0.182864i	$0.941463\pi$
$30$	−1.23205	+	1.86603i	−0.224941	+	0.340688i
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.59808	−	1.50000i	0.452267	−	0.261116i
$34$	6.00000			1.02899
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	0.427121	−	0.904194i	$-0.359528\pi$
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	−0.569495	+	0.821995i	$0.692861\pi$
$38$		0			0
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	11.2583	−	6.50000i	1.71688	−	0.991241i	0.792406	−	0.609994i	$-0.208828\pi$
$43$	11.2583	−	6.50000i	1.71688	−	0.991241i	0.924473	−	0.381246i	$-0.124505\pi$
$44$	−3.00000			−0.452267
$45$	−1.23205	+	1.86603i	−0.183663	+	0.278171i
$46$	−4.50000	−	7.79423i	−0.663489	−	1.14920i
$47$			11.0000i			1.60451i	0.596978	+	0.802257i	$0.296368\pi$
$47$			11.0000i			1.60451i	−0.596978	+	0.802257i	$0.703632\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	4.59808	−	1.96410i	0.650266	−	0.277766i
$51$	6.00000			0.840168
$52$	−0.866025	−	3.50000i	−0.120096	−	0.485363i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−6.69615	−	0.401924i	−0.902909	−	0.0541954i
$56$		0			0
$57$		0			0
$58$	6.06218	−	3.50000i	0.796003	−	0.459573i
$59$	−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	$-0.420713\pi$
$60$	2.00000	−	1.00000i	0.258199	−	0.129099i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	−0.866025	−	0.500000i	−0.109985	−	0.0635001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.46410	−	7.92820i	−0.181599	−	0.983373i
$66$	−3.00000			−0.369274
$67$	−3.46410	−	2.00000i	−0.423207	−	0.244339i	0.273241	−	0.961946i	$-0.411904\pi$
$67$	−3.46410	−	2.00000i	−0.423207	−	0.244339i	−0.696449	+	0.717607i	$0.745238\pi$
$68$	−5.19615	−	3.00000i	−0.630126	−	0.363803i
$69$	−4.50000	−	7.79423i	−0.541736	−	0.938315i
$70$		0			0
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	0.722599	−	0.691268i	$-0.242948\pi$
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	−0.959955	+	0.280155i	$0.909614\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	0.500000	+	0.866025i	0.0581238	+	0.100673i
$75$	4.59808	−	1.96410i	0.530940	−	0.226795i
$76$		0			0
$77$		0			0
$78$	−0.866025	−	3.50000i	−0.0980581	−	0.396297i
$79$	−1.00000			−0.112509			−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000			−0.112509			−0.0562544	+	0.998416i	$0.517916\pi$
$80$	−2.23205	−	0.133975i	−0.249551	−	0.0149788i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$		0			0
$85$	−11.1962	−	7.39230i	−1.21439	−	0.801808i
$86$	−13.0000			−1.40183
$87$	6.06218	−	3.50000i	0.649934	−	0.375239i
$88$	2.59808	+	1.50000i	0.276956	+	0.159901i
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	−0.952340	−	0.305038i	$-0.901331\pi$
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	0.740341	+	0.672232i	$0.234664\pi$
$90$	2.00000	−	1.00000i	0.210819	−	0.105409i
$91$		0			0
$92$			9.00000i			0.938315i
$93$	−0.866025	−	0.500000i	−0.0898027	−	0.0518476i
$94$	5.50000	−	9.52628i	0.567282	−	0.982561i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−3.46410	+	2.00000i	−0.351726	+	0.203069i	−0.665445	−	0.746447i	$-0.731758\pi$
$97$	−3.46410	+	2.00000i	−0.351726	+	0.203069i	0.313719	+	0.949516i	$0.398425\pi$
$98$	6.06218	−	3.50000i	0.612372	−	0.353553i
$99$	−3.00000			−0.301511
$100$	−4.96410	−	0.598076i	−0.496410	−	0.0598076i
$101$	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	$-0.0786053\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$		−	14.0000i		−	1.37946i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$		−	14.0000i		−	1.37946i	0.724066	−	0.689730i	$-0.242271\pi$
$104$	−1.00000	+	3.46410i	−0.0980581	+	0.339683i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	−3.46410	−	2.00000i	−0.334887	−	0.193347i	0.323122	−	0.946357i	$-0.395268\pi$
$107$	−3.46410	−	2.00000i	−0.334887	−	0.193347i	−0.658009	+	0.753010i	$0.728601\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	16.0000			1.53252			0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000			1.53252			0.766261	+	0.642529i	$0.222115\pi$
$110$	5.59808	+	3.69615i	0.533756	+	0.352414i
$111$	0.500000	+	0.866025i	0.0474579	+	0.0821995i
$112$		0			0
$113$	16.4545	−	9.50000i	1.54791	−	0.893685i	0.549606	−	0.835424i	$-0.314778\pi$
$113$	16.4545	−	9.50000i	1.54791	−	0.893685i	0.998301	−	0.0582609i	$-0.0185555\pi$
$114$		0			0
$115$	−1.20577	+	20.0885i	−0.112439	+	1.87326i
$116$	−7.00000			−0.649934
$117$	−0.866025	−	3.50000i	−0.0800641	−	0.323575i
$118$			11.0000i			1.01263i
$119$		0			0
$120$	−2.23205	−	0.133975i	−0.203757	−	0.0122302i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$		0			0
$124$	0.500000	+	0.866025i	0.0449013	+	0.0777714i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$	5.19615	+	3.00000i	0.461084	+	0.266207i	0.712500	−	0.701672i	$-0.247563\pi$
$127$	5.19615	+	3.00000i	0.461084	+	0.266207i	−0.251416	+	0.967879i	$0.580896\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−13.0000			−1.14459
$130$	−2.69615	+	7.59808i	−0.236468	+	0.666395i
$131$	15.0000			1.31056			0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000			1.31056			0.655278	+	0.755388i	$0.272551\pi$
$132$	2.59808	+	1.50000i	0.226134	+	0.130558i
$133$		0			0
$134$	2.00000	+	3.46410i	0.172774	+	0.299253i
$135$	2.00000	−	1.00000i	0.172133	−	0.0860663i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−11.2583	+	6.50000i	−0.961864	+	0.555332i	−0.896746	−	0.442545i	$-0.854076\pi$
$137$	−11.2583	+	6.50000i	−0.961864	+	0.555332i	−0.0651178	+	0.997878i	$0.520742\pi$
$138$			9.00000i			0.766131i
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$	5.50000	−	9.52628i	0.463184	−	0.802257i
$142$			4.00000i			0.335673i
$143$	7.79423	−	7.50000i	0.651786	−	0.627182i
$144$	−1.00000			−0.0833333
$145$	−15.6244	−	0.937822i	−1.29753	−	0.0778819i
$146$		0			0
$147$	6.06218	−	3.50000i	0.500000	−	0.288675i
$148$		−	1.00000i		−	0.0821995i
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	−0.990485	−	0.137619i	$-0.956055\pi$
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	0.376061	−	0.926595i	$-0.377278\pi$
$150$	−4.96410	−	0.598076i	−0.405317	−	0.0488327i
$151$	4.00000			0.325515			0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000			0.325515			0.162758	+	0.986666i	$0.447961\pi$
$152$		0			0
$153$	−5.19615	−	3.00000i	−0.420084	−	0.242536i
$154$		0			0
$155$	1.00000	+	2.00000i	0.0803219	+	0.160644i
$156$	−1.00000	+	3.46410i	−0.0800641	+	0.277350i
$157$			7.00000i			0.558661i	0.960195	+	0.279330i	$0.0901125\pi$
$157$			7.00000i			0.558661i	−0.960195	+	0.279330i	$0.909888\pi$
$158$	0.866025	+	0.500000i	0.0688973	+	0.0397779i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	1.86603	+	1.23205i	0.147522	+	0.0974022i
$161$		0			0
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−12.9904	+	7.50000i	−1.01749	+	0.587445i	−0.913375	−	0.407120i	$-0.866533\pi$
$163$	−12.9904	+	7.50000i	−1.01749	+	0.587445i	−0.104111	+	0.994566i	$0.533200\pi$
$164$		0			0
$165$	5.59808	+	3.69615i	0.435810	+	0.287745i
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	−4.33013	−	2.50000i	−0.335075	−	0.193456i	0.323017	−	0.946393i	$-0.395303\pi$
$167$	−4.33013	−	2.50000i	−0.335075	−	0.193456i	−0.658092	+	0.752937i	$0.728636\pi$
$168$		0			0
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$	6.00000	+	12.0000i	0.460179	+	0.920358i
$171$		0			0
$172$	11.2583	+	6.50000i	0.858440	+	0.495620i
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	−0.0498898	−	0.998755i	$-0.515887\pi$
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	0.840002	+	0.542583i	$0.182554\pi$
$174$	−7.00000			−0.530669
$175$		0			0
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$			11.0000i			0.826811i
$178$	3.46410	−	2.00000i	0.259645	−	0.149906i
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	−0.983742	−	0.179585i	$-0.942524\pi$
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	0.647397	+	0.762153i	$0.275858\pi$
$180$	−2.23205	−	0.133975i	−0.166367	−	0.00998588i
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$		0			0
$183$		0			0
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	0.133975	−	2.23205i	0.00985001	−	0.164104i
$186$	0.500000	+	0.866025i	0.0366618	+	0.0635001i
$187$		−	18.0000i		−	1.31629i
$188$	−9.52628	+	5.50000i	−0.694775	+	0.401129i
$189$		0			0
$190$		0			0
$191$	13.0000	+	22.5167i	0.940647	+	1.62925i	0.764241	+	0.644931i	$0.223114\pi$
$191$	13.0000	+	22.5167i	0.940647	+	1.62925i	0.176406	+	0.984317i	$0.443553\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	13.8564	+	8.00000i	0.997406	+	0.575853i	0.907480	−	0.420096i	$-0.138004\pi$
$193$	13.8564	+	8.00000i	0.997406	+	0.575853i	0.0899262	+	0.995948i	$0.471337\pi$
$194$	4.00000			0.287183
$195$	−2.69615	+	7.59808i	−0.193075	+	0.544110i
$196$	−7.00000			−0.500000
$197$	−22.5167	−	13.0000i	−1.60425	−	0.926212i	−0.990625	−	0.136611i	$-0.956379\pi$
$197$	−22.5167	−	13.0000i	−1.60425	−	0.926212i	−0.613621	−	0.789601i	$-0.710288\pi$
$198$	2.59808	+	1.50000i	0.184637	+	0.106600i
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$	−12.1244	+	7.00000i	−0.853067	+	0.492518i
$203$		0			0
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$		0			0
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$			9.00000i			0.625543i
$208$	2.59808	−	2.50000i	0.180144	−	0.173344i
$209$		0			0
$210$		0			0
$211$	−5.00000	+	8.66025i	−0.344214	+	0.596196i	−0.985211	−	0.171347i	$-0.945188\pi$
$211$	−5.00000	+	8.66025i	−0.344214	+	0.596196i	0.640996	+	0.767544i	$0.278521\pi$
$212$	−5.19615	+	3.00000i	−0.356873	+	0.206041i
$213$			4.00000i			0.274075i
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	24.2583	+	16.0167i	1.65440	+	1.09233i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−13.8564	−	8.00000i	−0.938474	−	0.541828i
$219$		0			0
$220$	−3.00000	−	6.00000i	−0.202260	−	0.404520i
$221$	21.0000	−	5.19615i	1.41261	−	0.349531i
$222$		−	1.00000i		−	0.0671156i
$223$	−12.1244	−	7.00000i	−0.811907	−	0.468755i	0.0357107	−	0.999362i	$-0.488630\pi$
$223$	−12.1244	−	7.00000i	−0.811907	−	0.468755i	−0.847618	+	0.530607i	$0.821964\pi$
$224$		0			0
$225$	−4.96410	−	0.598076i	−0.330940	−	0.0398717i
$226$	−19.0000			−1.26386
$227$	19.0526	−	11.0000i	1.26456	−	0.730096i	0.290609	−	0.956842i	$-0.406142\pi$
$227$	19.0526	−	11.0000i	1.26456	−	0.730096i	0.973954	+	0.226746i	$0.0728088\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$	11.0885	−	16.7942i	0.731151	−	1.10738i
$231$		0			0
$232$	6.06218	+	3.50000i	0.398001	+	0.229786i
$233$			5.00000i			0.327561i	0.986497	+	0.163780i	$0.0523689\pi$
$233$			5.00000i			0.327561i	−0.986497	+	0.163780i	$0.947631\pi$
$234$	−1.00000	+	3.46410i	−0.0653720	+	0.226455i
$235$	−22.0000	+	11.0000i	−1.43512	+	0.717561i
$236$	5.50000	−	9.52628i	0.358020	−	0.620108i
$237$	0.866025	+	0.500000i	0.0562544	+	0.0324785i
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$	1.86603	+	1.23205i	0.120451	+	0.0795285i
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$		−	2.00000i		−	0.128565i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−15.6244	−	0.937822i	−0.998203	−	0.0599153i
$246$		0			0
$247$		0			0
$248$		−	1.00000i		−	0.0635001i
$249$	−2.00000	+	3.46410i	−0.126745	+	0.219529i
$250$	8.52628	+	7.23205i	0.539249	+	0.457395i
$251$	−2.50000	−	4.33013i	−0.157799	−	0.273315i	0.776276	−	0.630393i	$-0.217106\pi$
$251$	−2.50000	−	4.33013i	−0.157799	−	0.273315i	−0.934075	+	0.357078i	$0.883773\pi$
$252$		0			0
$253$	−23.3827	+	13.5000i	−1.47006	+	0.848738i
$254$	−3.00000	−	5.19615i	−0.188237	−	0.326036i
$255$	6.00000	+	12.0000i	0.375735	+	0.751469i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.9904	+	7.50000i	0.810318	+	0.467837i	0.847066	−	0.531487i	$-0.178367\pi$
$257$	12.9904	+	7.50000i	0.810318	+	0.467837i	−0.0367485	+	0.999325i	$0.511700\pi$
$258$	11.2583	+	6.50000i	0.700913	+	0.404672i
$259$		0			0
$260$	6.13397	−	5.23205i	0.380413	−	0.324478i
$261$	−7.00000			−0.433289
$262$	−12.9904	−	7.50000i	−0.802548	−	0.463352i
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	0.240059	−	0.970758i	$-0.422833\pi$
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	−0.720672	+	0.693276i	$0.756167\pi$
$264$	−1.50000	−	2.59808i	−0.0923186	−	0.159901i
$265$	−12.0000	+	6.00000i	−0.737154	+	0.368577i
$266$		0			0
$267$	3.46410	−	2.00000i	0.212000	−	0.122398i
$268$		−	4.00000i		−	0.244339i
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$	−2.23205	−	0.133975i	−0.135838	−	0.00815343i
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$		−	6.00000i		−	0.363803i
$273$		0			0
$274$	13.0000			0.785359
$275$	−5.89230	−	13.7942i	−0.355319	−	0.831823i
$276$	4.50000	−	7.79423i	0.270868	−	0.469157i
$277$	19.9186	−	11.5000i	1.19679	−	0.690968i	0.236953	−	0.971521i	$-0.423851\pi$
$277$	19.9186	−	11.5000i	1.19679	−	0.690968i	0.959839	+	0.280553i	$0.0905179\pi$
$278$		−	8.00000i		−	0.479808i
$279$	0.500000	+	0.866025i	0.0299342	+	0.0518476i
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$	−9.52628	+	5.50000i	−0.567282	+	0.327520i
$283$	4.33013	+	2.50000i	0.257399	+	0.148610i	0.623148	−	0.782104i	$-0.285854\pi$
$283$	4.33013	+	2.50000i	0.257399	+	0.148610i	−0.365748	+	0.930714i	$0.619187\pi$
$284$	2.00000	−	3.46410i	0.118678	−	0.205557i
$285$		0			0
$286$	−10.5000	+	2.59808i	−0.620878	+	0.153627i
$287$		0			0
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	9.50000	−	16.4545i	0.558824	−	0.967911i
$290$	13.0622	+	8.62436i	0.767037	+	0.506440i
$291$	4.00000			0.234484
$292$		0			0
$293$	−24.2487	+	14.0000i	−1.41662	+	0.817889i	−0.996001	−	0.0893462i	$-0.971522\pi$
$293$	−24.2487	+	14.0000i	−1.41662	+	0.817889i	−0.420624	+	0.907235i	$0.638189\pi$
$294$	−7.00000			−0.408248
$295$	13.5526	−	20.5263i	0.789060	−	1.19509i
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$	2.59808	+	1.50000i	0.150756	+	0.0870388i
$298$			15.0000i			0.868927i
$299$	−22.5000	−	23.3827i	−1.30121	−	1.35226i
$300$	4.00000	+	3.00000i	0.230940	+	0.173205i
$301$		0			0
$302$	−3.46410	−	2.00000i	−0.199337	−	0.115087i
$303$	−12.1244	+	7.00000i	−0.696526	+	0.402139i
$304$		0			0
$305$		0			0
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	−7.00000	+	12.1244i	−0.398216	+	0.689730i
$310$	0.133975	−	2.23205i	0.00760925	−	0.126772i
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$	2.59808	−	2.50000i	0.147087	−	0.141535i
$313$			10.0000i			0.565233i	0.959233	+	0.282617i	$0.0912024\pi$
$313$			10.0000i			0.565233i	−0.959233	+	0.282617i	$0.908798\pi$
$314$	3.50000	−	6.06218i	0.197516	−	0.342108i
$315$		0			0
$316$	−0.500000	−	0.866025i	−0.0281272	−	0.0487177i
$317$		−	24.0000i		−	1.34797i	−0.738743	−	0.673987i	$-0.764580\pi$
$317$		−	24.0000i		−	1.34797i	0.738743	−	0.673987i	$-0.235420\pi$
$318$	−5.19615	+	3.00000i	−0.291386	+	0.168232i
$319$	−10.5000	−	18.1865i	−0.587887	−	1.01825i
$320$	−1.00000	−	2.00000i	−0.0559017	−	0.111803i
$321$	2.00000	+	3.46410i	0.111629	+	0.193347i
$322$		0			0
$323$		0			0
$324$	−1.00000			−0.0555556
$325$	14.3923	−	10.8564i	0.798341	−	0.602205i
$326$	15.0000			0.830773
$327$	−13.8564	−	8.00000i	−0.766261	−	0.442401i
$328$		0			0
$329$		0			0
$330$	−3.00000	−	6.00000i	−0.165145	−	0.330289i
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	0.892199	−	0.451643i	$-0.149162\pi$
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	−0.837234	+	0.546845i	$0.815829\pi$
$332$	3.46410	−	2.00000i	0.190117	−	0.109764i
$333$		−	1.00000i		−	0.0547997i
$334$	2.50000	+	4.33013i	0.136794	+	0.236934i
$335$	0.535898	−	8.92820i	0.0292793	−	0.487800i
$336$		0			0
$337$			14.0000i			0.762629i	0.924445	+	0.381314i	$0.124528\pi$
$337$			14.0000i			0.762629i	−0.924445	+	0.381314i	$0.875472\pi$
$338$	−6.06218	−	11.5000i	−0.329739	−	0.625518i
$339$	−19.0000			−1.03194
$340$	0.803848	−	13.3923i	0.0435948	−	0.726300i
$341$	−1.50000	+	2.59808i	−0.0812296	+	0.140694i
$342$		0			0
$343$		0			0
$344$	−6.50000	−	11.2583i	−0.350457	−	0.607008i
$345$	11.0885	−	16.7942i	0.596982	−	0.904171i
$346$	−12.0000			−0.645124
$347$	−8.66025	+	5.00000i	−0.464907	+	0.268414i	−0.714105	−	0.700038i	$-0.753166\pi$
$347$	−8.66025	+	5.00000i	−0.464907	+	0.268414i	0.249198	+	0.968452i	$0.419833\pi$
$348$	6.06218	+	3.50000i	0.324967	+	0.187620i
$349$	4.00000	−	6.92820i	0.214115	−	0.370858i	−0.738883	−	0.673833i	$-0.764647\pi$
$349$	4.00000	−	6.92820i	0.214115	−	0.370858i	0.952998	+	0.302975i	$0.0979799\pi$
$350$		0			0
$351$	−1.00000	+	3.46410i	−0.0533761	+	0.184900i
$352$			3.00000i			0.159901i
$353$	12.1244	+	7.00000i	0.645314	+	0.372572i	0.786659	−	0.617388i	$-0.211809\pi$
$353$	12.1244	+	7.00000i	0.645314	+	0.372572i	−0.141344	+	0.989960i	$0.545142\pi$
$354$	5.50000	−	9.52628i	0.292322	−	0.506316i
$355$	4.92820	−	7.46410i	0.261562	−	0.396153i
$356$	−4.00000			−0.212000
$357$		0			0
$358$	7.79423	−	4.50000i	0.411938	−	0.237832i
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$	1.86603	+	1.23205i	0.0983482	+	0.0649348i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	6.92820	+	4.00000i	0.364138	+	0.210235i
$363$		−	2.00000i		−	0.104973i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	20.7846	+	12.0000i	1.08495	+	0.626395i	0.932227	−	0.361874i	$-0.117863\pi$
$367$	20.7846	+	12.0000i	1.08495	+	0.626395i	0.152721	+	0.988269i	$0.451196\pi$
$368$	−7.79423	+	4.50000i	−0.406302	+	0.234579i
$369$		0			0
$370$	−1.23205	+	1.86603i	−0.0640513	+	0.0970100i
$371$		0			0
$372$		−	1.00000i		−	0.0518476i
$373$	−9.52628	+	5.50000i	−0.493252	+	0.284779i	−0.725923	−	0.687776i	$-0.758587\pi$
$373$	−9.52628	+	5.50000i	−0.493252	+	0.284779i	0.232671	+	0.972556i	$0.425254\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$	8.52628	+	7.23205i	0.440295	+	0.373461i
$376$	11.0000			0.567282
$377$	18.1865	−	17.5000i	0.936654	−	0.901296i
$378$		0			0
$379$	−4.00000	+	6.92820i	−0.205466	+	0.355878i	−0.950281	−	0.311393i	$-0.899204\pi$
$379$	−4.00000	+	6.92820i	−0.205466	+	0.355878i	0.744815	+	0.667271i	$0.232538\pi$
$380$		0			0
$381$	−3.00000	−	5.19615i	−0.153695	−	0.266207i
$382$		−	26.0000i		−	1.33028i
$383$	9.52628	−	5.50000i	0.486770	−	0.281037i	−0.236463	−	0.971640i	$-0.575988\pi$
$383$	9.52628	−	5.50000i	0.486770	−	0.281037i	0.723234	+	0.690604i	$0.242655\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	−8.00000	−	13.8564i	−0.407189	−	0.705273i
$387$	11.2583	+	6.50000i	0.572293	+	0.330414i
$388$	−3.46410	−	2.00000i	−0.175863	−	0.101535i
$389$	−13.0000			−0.659126			−0.329563	−	0.944134i	$-0.606901\pi$
$389$	−13.0000			−0.659126			−0.329563	+	0.944134i	$0.606901\pi$
$390$	6.13397	−	5.23205i	0.310606	−	0.264935i
$391$	−54.0000			−2.73090
$392$	6.06218	+	3.50000i	0.306186	+	0.176777i
$393$	−12.9904	−	7.50000i	−0.655278	−	0.378325i
$394$	13.0000	+	22.5167i	0.654931	+	1.13437i
$395$	−1.00000	−	2.00000i	−0.0503155	−	0.100631i
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	−23.3827	+	13.5000i	−1.17354	+	0.677546i	−0.954512	−	0.298172i	$-0.903623\pi$
$397$	−23.3827	+	13.5000i	−1.17354	+	0.677546i	−0.219031	+	0.975718i	$0.570290\pi$
$398$			8.00000i			0.401004i
$399$		0			0
$400$	−1.96410	−	4.59808i	−0.0982051	−	0.229904i
$401$	−10.0000	+	17.3205i	−0.499376	+	0.864945i	−1.00000		0.000720188i	$-0.999771\pi$
$401$	−10.0000	+	17.3205i	−0.499376	+	0.864945i	0.500624	+	0.865665i	$0.333104\pi$
$402$		−	4.00000i		−	0.199502i
$403$	−3.46410	−	1.00000i	−0.172559	−	0.0498135i
$404$	14.0000			0.696526
$405$	−2.23205	−	0.133975i	−0.110911	−	0.00665725i
$406$		0			0
$407$	2.59808	−	1.50000i	0.128782	−	0.0743522i
$408$		−	6.00000i		−	0.297044i
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	0.782274	−	0.622935i	$-0.214060\pi$
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	−0.930614	+	0.366002i	$0.880726\pi$
$410$		0			0
$411$	13.0000			0.641243
$412$	12.1244	−	7.00000i	0.597324	−	0.344865i
$413$		0			0
$414$	4.50000	−	7.79423i	0.221163	−	0.383065i
$415$	8.00000	−	4.00000i	0.392705	−	0.196352i
$416$	−3.50000	+	0.866025i	−0.171602	+	0.0424604i
$417$		−	8.00000i		−	0.391762i
$418$		0			0
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	−0.813029	−	0.582224i	$-0.802183\pi$
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	0.910735	+	0.412991i	$0.135516\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	8.66025	−	5.00000i	0.421575	−	0.243396i
$423$	−9.52628	+	5.50000i	−0.463184	+	0.267419i
$424$	6.00000			0.291386
$425$	3.58846	−	29.7846i	0.174066	−	1.44477i
$426$	2.00000	−	3.46410i	0.0969003	−	0.167836i
$427$		0			0
$428$		−	4.00000i		−	0.193347i
$429$	−10.5000	+	2.59808i	−0.506945	+	0.125436i
$430$	−13.0000	−	26.0000i	−0.626916	−	1.25383i
$431$	10.0000	−	17.3205i	0.481683	−	0.834300i	−0.518096	−	0.855323i	$-0.673359\pi$
$431$	10.0000	−	17.3205i	0.481683	−	0.834300i	0.999779	+	0.0210230i	$0.00669232\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	10.3923	−	6.00000i	0.499422	−	0.288342i	−0.229053	−	0.973414i	$-0.573563\pi$
$433$	10.3923	−	6.00000i	0.499422	−	0.288342i	0.728475	+	0.685072i	$0.240229\pi$
$434$		0			0
$435$	13.0622	+	8.62436i	0.626283	+	0.413506i
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$		0			0
$438$		0			0
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$	−0.401924	+	6.69615i	−0.0191610	+	0.319227i
$441$	−7.00000			−0.333333
$442$	−20.7846	−	6.00000i	−0.988623	−	0.285391i
$443$			26.0000i			1.23530i	0.786454	+	0.617649i	$0.211915\pi$
$443$			26.0000i			1.23530i	−0.786454	+	0.617649i	$0.788085\pi$
$444$	−0.500000	+	0.866025i	−0.0237289	+	0.0410997i
$445$	−8.92820	−	0.535898i	−0.423237	−	0.0254040i
$446$	7.00000	+	12.1244i	0.331460	+	0.574105i
$447$			15.0000i			0.709476i
$448$		0			0
$449$	16.0000	+	27.7128i	0.755087	+	1.30785i	0.945331	+	0.326112i	$0.105739\pi$
$449$	16.0000	+	27.7128i	0.755087	+	1.30785i	−0.190245	+	0.981737i	$0.560928\pi$
$450$	4.00000	+	3.00000i	0.188562	+	0.141421i
$451$		0			0
$452$	16.4545	+	9.50000i	0.773954	+	0.446842i
$453$	−3.46410	−	2.00000i	−0.162758	−	0.0939682i
$454$	−22.0000			−1.03251
$455$		0			0
$456$		0			0
$457$	36.3731	+	21.0000i	1.70146	+	0.982339i	0.944286	+	0.329125i	$0.106754\pi$
$457$	36.3731	+	21.0000i	1.70146	+	0.982339i	0.757174	+	0.653213i	$0.226579\pi$
$458$	−19.0526	−	11.0000i	−0.890268	−	0.513996i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$	−18.0000	+	9.00000i	−0.839254	+	0.419627i
$461$	−10.5000	−	18.1865i	−0.489034	−	0.847031i	0.510887	−	0.859648i	$-0.329317\pi$
$461$	−10.5000	−	18.1865i	−0.489034	−	0.847031i	−0.999920	+	0.0126168i	$0.995984\pi$
$462$		0			0
$463$			34.0000i			1.58011i	0.613033	+	0.790057i	$0.289949\pi$
$463$			34.0000i			1.58011i	−0.613033	+	0.790057i	$0.710051\pi$
$464$	−3.50000	−	6.06218i	−0.162483	−	0.281430i
$465$	0.133975	−	2.23205i	0.00621292	−	0.103509i
$466$	2.50000	−	4.33013i	0.115810	−	0.200589i
$467$			38.0000i			1.75843i	0.476425	+	0.879215i	$0.341932\pi$
$467$			38.0000i			1.75843i	−0.476425	+	0.879215i	$0.658068\pi$
$468$	2.59808	−	2.50000i	0.120096	−	0.115563i
$469$		0			0
$470$	24.5526	+	1.47372i	1.13253	+	0.0679777i
$471$	3.50000	−	6.06218i	0.161271	−	0.279330i
$472$	−9.52628	+	5.50000i	−0.438483	+	0.253158i
$473$			39.0000i			1.79322i
$474$	−0.500000	−	0.866025i	−0.0229658	−	0.0397779i
$475$		0			0
$476$		0			0
$477$	−5.19615	+	3.00000i	−0.237915	+	0.137361i
$478$	−13.8564	−	8.00000i	−0.633777	−	0.365911i
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	−0.957351	−	0.288929i	$-0.906701\pi$
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	0.728895	+	0.684626i	$0.240034\pi$
$480$	−1.00000	−	2.00000i	−0.0456435	−	0.0912871i
$481$	2.50000	+	2.59808i	0.113990	+	0.118462i
$482$		−	7.00000i		−	0.318841i
$483$		0			0
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$	−7.46410	−	4.92820i	−0.338927	−	0.223778i
$486$	−1.00000			−0.0453609
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$	15.0000			0.678323
$490$	13.0622	+	8.62436i	0.590089	+	0.389609i
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	−0.969061	−	0.246822i	$-0.920614\pi$
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$492$		0			0
$493$		−	42.0000i		−	1.89158i
$494$		0			0
$495$	−3.00000	−	6.00000i	−0.134840	−	0.269680i
$496$	−0.500000	+	0.866025i	−0.0224507	+	0.0388857i
$497$		0			0
$498$	3.46410	−	2.00000i	0.155230	−	0.0896221i
$499$	36.0000			1.61158			0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000			1.61158			0.805791	+	0.592200i	$0.201741\pi$
$500$	−3.76795	−	10.5263i	−0.168508	−	0.470750i
$501$	2.50000	+	4.33013i	0.111692	+	0.193456i
$502$			5.00000i			0.223161i
$503$	−13.8564	+	8.00000i	−0.617827	+	0.356702i	−0.776022	−	0.630705i	$-0.782766\pi$
$503$	−13.8564	+	8.00000i	−0.617827	+	0.356702i	0.158196	+	0.987408i	$0.449432\pi$
$504$		0			0
$505$	31.2487	+	1.87564i	1.39055	+	0.0834651i
$506$	27.0000			1.20030
$507$	−6.06218	−	11.5000i	−0.269231	−	0.510733i
$508$			6.00000i			0.266207i
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	0.394684	+	0.918817i	$0.370854\pi$
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	−0.993061	+	0.117602i	$0.962479\pi$
$510$	0.803848	−	13.3923i	0.0355950	−	0.593021i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−7.50000	−	12.9904i	−0.330811	−	0.572981i
$515$	28.0000	−	14.0000i	1.23383	−	0.616914i
$516$	−6.50000	−	11.2583i	−0.286147	−	0.495620i
$517$	−28.5788	−	16.5000i	−1.25690	−	0.725669i
$518$		0			0
$519$	−12.0000			−0.526742
$520$	−7.92820	+	1.46410i	−0.347675	+	0.0642051i
$521$	−28.0000			−1.22670			−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000			−1.22670			−0.613351	+	0.789810i	$0.710179\pi$
$522$	6.06218	+	3.50000i	0.265334	+	0.153191i
$523$	−25.1147	−	14.5000i	−1.09819	−	0.634041i	−0.162446	−	0.986718i	$-0.551938\pi$
$523$	−25.1147	−	14.5000i	−1.09819	−	0.634041i	−0.935745	+	0.352677i	$0.885272\pi$
$524$	7.50000	+	12.9904i	0.327639	+	0.567487i
$525$		0			0
$526$	4.50000	+	7.79423i	0.196209	+	0.339845i
$527$	−5.19615	+	3.00000i	−0.226348	+	0.130682i
$528$			3.00000i			0.130558i
$529$	29.0000	+	50.2295i	1.26087	+	2.18389i
$530$	13.3923	+	0.803848i	0.581725	+	0.0349169i
$531$	5.50000	−	9.52628i	0.238680	−	0.413405i
$532$		0			0
$533$		0			0
$534$	−4.00000			−0.173097
$535$	0.535898	−	8.92820i	0.0231689	−	0.386000i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	7.79423	−	4.50000i	0.336346	−	0.194189i
$538$		−	14.0000i		−	0.603583i
$539$	−10.5000	−	18.1865i	−0.452267	−	0.783349i
$540$	1.86603	+	1.23205i	0.0803009	+	0.0530190i
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$	−0.866025	+	0.500000i	−0.0371990	+	0.0214768i
$543$	6.92820	+	4.00000i	0.297318	+	0.171656i
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$	16.0000	+	32.0000i	0.685365	+	1.37073i
$546$		0			0
$547$		−	12.0000i		−	0.513083i	−0.966533	−	0.256541i	$-0.917417\pi$
$547$		−	12.0000i		−	0.513083i	0.966533	−	0.256541i	$-0.0825830\pi$
$548$	−11.2583	−	6.50000i	−0.480932	−	0.277666i
$549$		0			0
$550$	−1.79423	+	14.8923i	−0.0765062	+	0.635010i
$551$		0			0
$552$	−7.79423	+	4.50000i	−0.331744	+	0.191533i
$553$		0			0
$554$	−23.0000			−0.977176
$555$	−1.23205	+	1.86603i	−0.0522976	+	0.0792084i
$556$	−4.00000	+	6.92820i	−0.169638	+	0.293821i
$557$	−8.66025	−	5.00000i	−0.366947	−	0.211857i	0.305177	−	0.952296i	$-0.401284\pi$
$557$	−8.66025	−	5.00000i	−0.366947	−	0.211857i	−0.672124	+	0.740439i	$0.734618\pi$
$558$		−	1.00000i		−	0.0423334i
$559$	−45.5000	+	11.2583i	−1.92444	+	0.476177i
$560$		0			0
$561$	−9.00000	+	15.5885i	−0.379980	+	0.658145i
$562$	19.0526	+	11.0000i	0.803684	+	0.464007i
$563$	−25.9808	+	15.0000i	−1.09496	+	0.632175i	−0.934892	−	0.354932i	$-0.884504\pi$
$563$	−25.9808	+	15.0000i	−1.09496	+	0.632175i	−0.160066	+	0.987106i	$0.551171\pi$
$564$	11.0000			0.463184
$565$	35.4545	+	23.4090i	1.49158	+	0.984823i
$566$	−2.50000	−	4.33013i	−0.105083	−	0.182009i
$567$		0			0
$568$	−3.46410	+	2.00000i	−0.145350	+	0.0839181i
$569$	−19.0000	+	32.9090i	−0.796521	+	1.37962i	0.125347	+	0.992113i	$0.459996\pi$
$569$	−19.0000	+	32.9090i	−0.796521	+	1.37962i	−0.921869	+	0.387503i	$0.873338\pi$
$570$		0			0
$571$	34.0000			1.42286			0.711428	−	0.702759i	$-0.248049\pi$
$571$	34.0000			1.42286			0.711428	+	0.702759i	$0.248049\pi$
$572$	10.3923	+	3.00000i	0.434524	+	0.125436i
$573$		−	26.0000i		−	1.08617i
$574$		0			0
$575$	−41.3827	+	17.6769i	−1.72578	+	0.737178i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	2.00000i		−	0.0832611i	−0.999133	−	0.0416305i	$-0.986745\pi$
$577$		−	2.00000i		−	0.0832611i	0.999133	−	0.0416305i	$-0.0132552\pi$
$578$	−16.4545	+	9.50000i	−0.684416	+	0.395148i
$579$	−8.00000	−	13.8564i	−0.332469	−	0.575853i
$580$	−7.00000	−	14.0000i	−0.290659	−	0.581318i
$581$		0			0
$582$	−3.46410	−	2.00000i	−0.143592	−	0.0829027i
$583$	−15.5885	−	9.00000i	−0.645608	−	0.372742i
$584$		0			0
$585$	6.13397	−	5.23205i	0.253609	−	0.216319i
$586$	28.0000			1.15667
$587$	−5.19615	−	3.00000i	−0.214468	−	0.123823i	0.388918	−	0.921272i	$-0.372849\pi$
$587$	−5.19615	−	3.00000i	−0.214468	−	0.123823i	−0.603386	+	0.797449i	$0.706182\pi$
$588$	6.06218	+	3.50000i	0.250000	+	0.144338i
$589$		0			0
$590$	−22.0000	+	11.0000i	−0.905726	+	0.452863i
$591$	13.0000	+	22.5167i	0.534749	+	0.926212i
$592$	0.866025	−	0.500000i	0.0355934	−	0.0205499i
$593$			3.00000i			0.123195i	0.998101	+	0.0615976i	$0.0196196\pi$
$593$			3.00000i			0.123195i	−0.998101	+	0.0615976i	$0.980380\pi$
$594$	−1.50000	−	2.59808i	−0.0615457	−	0.106600i
$595$		0			0
$596$	7.50000	−	12.9904i	0.307212	−	0.532107i
$597$			8.00000i			0.327418i
$598$	7.79423	+	31.5000i	0.318730	+	1.28813i
$599$	38.0000			1.55264			0.776319	−	0.630340i	$-0.217085\pi$
$599$	38.0000			1.55264			0.776319	+	0.630340i	$0.217085\pi$
$600$	−1.96410	−	4.59808i	−0.0801841	−	0.187716i
$601$	3.50000	−	6.06218i	0.142768	−	0.247281i	−0.785770	−	0.618519i	$-0.787733\pi$
$601$	3.50000	−	6.06218i	0.142768	−	0.247281i	0.928538	+	0.371237i	$0.121066\pi$
$602$		0			0
$603$		−	4.00000i		−	0.162893i
$604$	2.00000	+	3.46410i	0.0813788	+	0.140952i
$605$	−2.46410	+	3.73205i	−0.100180	+	0.151729i
$606$	14.0000			0.568711
$607$	−8.66025	+	5.00000i	−0.351509	+	0.202944i	−0.665350	−	0.746532i	$-0.731718\pi$
$607$	−8.66025	+	5.00000i	−0.351509	+	0.202944i	0.313841	+	0.949476i	$0.398384\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	11.0000	−	38.1051i	0.445012	−	1.54157i
$612$		−	6.00000i		−	0.242536i
$613$	−9.52628	−	5.50000i	−0.384763	−	0.222143i	0.295126	−	0.955458i	$-0.404638\pi$
$613$	−9.52628	−	5.50000i	−0.384763	−	0.222143i	−0.679888	+	0.733316i	$0.737972\pi$
$614$	−2.00000	+	3.46410i	−0.0807134	+	0.139800i
$615$		0			0
$616$		0			0
$617$	23.3827	−	13.5000i	0.941351	−	0.543490i	0.0509678	−	0.998700i	$-0.483769\pi$
$617$	23.3827	−	13.5000i	0.941351	−	0.543490i	0.890384	+	0.455211i	$0.150436\pi$
$618$	12.1244	−	7.00000i	0.487713	−	0.281581i
$619$	−8.00000			−0.321547			−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000			−0.321547			−0.160774	+	0.986991i	$0.551399\pi$
$620$	−1.23205	+	1.86603i	−0.0494804	+	0.0749414i
$621$	4.50000	−	7.79423i	0.180579	−	0.312772i
$622$	−15.5885	−	9.00000i	−0.625040	−	0.360867i
$623$		0			0
$624$	−3.50000	+	0.866025i	−0.140112	+	0.0346688i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	5.00000	−	8.66025i	0.199840	−	0.346133i
$627$		0			0
$628$	−6.06218	+	3.50000i	−0.241907	+	0.139665i
$629$	6.00000			0.239236
$630$		0			0
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	0.595397	−	0.803432i	$-0.296995\pi$
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	−0.993491	+	0.113913i	$0.963661\pi$
$632$			1.00000i			0.0397779i
$633$	8.66025	−	5.00000i	0.344214	−	0.198732i
$634$	−12.0000	+	20.7846i	−0.476581	+	0.825462i
$635$	−0.803848	+	13.3923i	−0.0318997	+	0.531457i
$636$	6.00000			0.237915
$637$	18.1865	−	17.5000i	0.720577	−	0.693375i
$638$			21.0000i			0.831398i
$639$	2.00000	−	3.46410i	0.0791188	−	0.137038i
$640$	−0.133975	+	2.23205i	−0.00529581	+	0.0882296i
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	0.959848	−	0.280521i	$-0.0905072\pi$
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	−0.722862	+	0.690992i	$0.757174\pi$
$642$		−	4.00000i		−	0.157867i
$643$	−6.92820	+	4.00000i	−0.273222	+	0.157745i	−0.630351	−	0.776310i	$-0.717089\pi$
$643$	−6.92820	+	4.00000i	−0.273222	+	0.157745i	0.357129	+	0.934055i	$0.383756\pi$
$644$		0			0
$645$	−13.0000	−	26.0000i	−0.511875	−	1.02375i
$646$		0			0
$647$	−6.92820	−	4.00000i	−0.272376	−	0.157256i	0.357591	−	0.933878i	$-0.383598\pi$
$647$	−6.92820	−	4.00000i	−0.272376	−	0.157256i	−0.629967	+	0.776622i	$0.716932\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	33.0000			1.29536
$650$	−17.8923	+	2.20577i	−0.701794	+	0.0865175i
$651$		0			0
$652$	−12.9904	−	7.50000i	−0.508743	−	0.293723i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$	8.00000	+	13.8564i	0.312825	+	0.541828i
$655$	15.0000	+	30.0000i	0.586098	+	1.17220i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	0.682161	−	0.731202i	$-0.261040\pi$
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	−0.974320	+	0.225168i	$0.927707\pi$
$660$	−0.401924	+	6.69615i	−0.0156449	+	0.260647i
$661$	17.0000	−	29.4449i	0.661223	−	1.14527i	−0.319071	−	0.947731i	$-0.603371\pi$
$661$	17.0000	−	29.4449i	0.661223	−	1.14527i	0.980294	−	0.197542i	$-0.0632958\pi$
$662$		−	2.00000i		−	0.0777322i
$663$	−20.7846	−	6.00000i	−0.807207	−	0.233021i
$664$	−4.00000			−0.155230
$665$		0			0
$666$	−0.500000	+	0.866025i	−0.0193746	+	0.0335578i
$667$	−54.5596	+	31.5000i	−2.11256	+	1.21968i
$668$		−	5.00000i		−	0.193456i
$669$	7.00000	+	12.1244i	0.270636	+	0.468755i
$670$	−4.92820	+	7.46410i	−0.190393	+	0.288363i
$671$		0			0
$672$		0			0
$673$	22.5167	+	13.0000i	0.867953	+	0.501113i	0.866668	−	0.498886i	$-0.166257\pi$
$673$	22.5167	+	13.0000i	0.867953	+	0.501113i	0.00128586	+	0.999999i	$0.499591\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$	4.00000	+	3.00000i	0.153960	+	0.115470i
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$		−	10.0000i		−	0.384331i	−0.981363	−	0.192166i	$-0.938449\pi$
$677$		−	10.0000i		−	0.384331i	0.981363	−	0.192166i	$-0.0615511\pi$
$678$	16.4545	+	9.50000i	0.631931	+	0.364845i
$679$		0			0
$680$	−7.39230	+	11.1962i	−0.283482	+	0.429353i
$681$	−22.0000			−0.843042
$682$	2.59808	−	1.50000i	0.0994855	−	0.0574380i
$683$	20.7846	−	12.0000i	0.795301	−	0.459167i	−0.0465244	−	0.998917i	$-0.514815\pi$
$683$	20.7846	−	12.0000i	0.795301	−	0.459167i	0.841825	+	0.539750i	$0.181481\pi$
$684$		0			0
$685$	−24.2583	−	16.0167i	−0.926863	−	0.611965i
$686$		0			0
$687$	−19.0526	−	11.0000i	−0.726900	−	0.419676i
$688$			13.0000i			0.495620i
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$	−18.0000	+	9.00000i	−0.685248	+	0.342624i
$691$	−17.0000	+	29.4449i	−0.646710	+	1.12014i	0.337193	+	0.941435i	$0.390522\pi$
$691$	−17.0000	+	29.4449i	−0.646710	+	1.12014i	−0.983904	+	0.178700i	$0.942811\pi$
$692$	10.3923	+	6.00000i	0.395056	+	0.228086i
$693$		0			0
$694$	10.0000			0.379595
$695$	−9.85641	+	14.9282i	−0.373875	+	0.566259i
$696$	−3.50000	−	6.06218i	−0.132667	−	0.229786i
$697$		0			0
$698$	−6.92820	+	4.00000i	−0.262236	+	0.151402i
$699$	2.50000	−	4.33013i	0.0945587	−	0.163780i
$700$		0			0
$701$	−39.0000			−1.47301			−0.736505	−	0.676432i	$-0.763525\pi$
$701$	−39.0000			−1.47301			−0.736505	+	0.676432i	$0.763525\pi$
$702$	2.59808	−	2.50000i	0.0980581	−	0.0943564i
$703$		0			0
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$	24.5526	+	1.47372i	0.924703	+	0.0555035i
$706$	−7.00000	−	12.1244i	−0.263448	−	0.456306i
$707$		0			0
$708$	−9.52628	+	5.50000i	−0.358020	+	0.206703i
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	0.976237	−	0.216705i	$-0.0695310\pi$
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	−0.675791	+	0.737093i	$0.736198\pi$
$710$	−8.00000	+	4.00000i	−0.300235	+	0.150117i
$711$	−0.500000	−	0.866025i	−0.0187515	−	0.0324785i
$712$	3.46410	+	2.00000i	0.129823	+	0.0749532i
$713$	7.79423	+	4.50000i	0.291896	+	0.168526i
$714$		0			0
$715$	22.7942	+	8.08846i	0.852456	+	0.302491i
$716$	−9.00000			−0.336346
$717$	−13.8564	−	8.00000i	−0.517477	−	0.298765i
$718$	15.5885	+	9.00000i	0.581756	+	0.335877i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$	−1.00000	−	2.00000i	−0.0372678	−	0.0745356i
$721$		0			0
$722$	−16.4545	+	9.50000i	−0.612372	+	0.353553i
$723$		−	7.00000i		−	0.260333i
$724$	−4.00000	−	6.92820i	−0.148659	−	0.257485i
$725$	−13.7487	−	32.1865i	−0.510614	−	1.19538i
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$		−	46.0000i		−	1.70605i	−0.521874	−	0.853023i	$-0.674767\pi$
$727$		−	46.0000i		−	1.70605i	0.521874	−	0.853023i	$-0.325233\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−39.0000	+	67.5500i	−1.44247	+	2.49843i
$732$		0			0
$733$			14.0000i			0.517102i	0.965998	+	0.258551i	$0.0832450\pi$
$733$			14.0000i			0.517102i	−0.965998	+	0.258551i	$0.916755\pi$
$734$	−12.0000	−	20.7846i	−0.442928	−	0.767174i
$735$	13.0622	+	8.62436i	0.481806	+	0.318114i
$736$	9.00000			0.331744
$737$	10.3923	−	6.00000i	0.382805	−	0.221013i
$738$		0			0
$739$	22.0000	−	38.1051i	0.809283	−	1.40172i	−0.104078	−	0.994569i	$-0.533189\pi$
$739$	22.0000	−	38.1051i	0.809283	−	1.40172i	0.913361	−	0.407150i	$-0.133477\pi$
$740$	2.00000	−	1.00000i	0.0735215	−	0.0367607i
$741$		0			0
$742$		0			0
$743$	32.0429	+	18.5000i	1.17554	+	0.678699i	0.954979	−	0.296674i	$-0.0958774\pi$
$743$	32.0429	+	18.5000i	1.17554	+	0.678699i	0.220563	+	0.975373i	$0.429211\pi$
$744$	−0.500000	+	0.866025i	−0.0183309	+	0.0317500i
$745$	18.4808	−	27.9904i	0.677083	−	1.02549i
$746$	11.0000			0.402739
$747$	3.46410	−	2.00000i	0.126745	−	0.0731762i
$748$	15.5885	−	9.00000i	0.569970	−	0.329073i
$749$		0			0
$750$	−3.76795	−	10.5263i	−0.137586	−	0.384365i
$751$	9.50000	−	16.4545i	0.346660	−	0.600433i	−0.638994	−	0.769212i	$-0.720649\pi$
$751$	9.50000	−	16.4545i	0.346660	−	0.600433i	0.985654	+	0.168779i	$0.0539825\pi$
$752$	−9.52628	−	5.50000i	−0.347388	−	0.200564i
$753$			5.00000i			0.182210i
$754$	−24.5000	+	6.06218i	−0.892237	+	0.220771i
$755$	4.00000	+	8.00000i	0.145575	+	0.291150i
$756$		0			0
$757$	32.9090	+	19.0000i	1.19610	+	0.690567i	0.959683	−	0.281086i	$-0.0906945\pi$
$757$	32.9090	+	19.0000i	1.19610	+	0.690567i	0.236414	+	0.971652i	$0.424028\pi$
$758$	6.92820	−	4.00000i	0.251644	−	0.145287i
$759$	27.0000			0.980038
$760$		0			0
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.861996	+	0.506915i	$0.169214\pi$
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.00800331	+	0.999968i	$0.497452\pi$
$762$			6.00000i			0.217357i
$763$		0			0
$764$	−13.0000	+	22.5167i	−0.470323	+	0.814624i
$765$	0.803848	−	13.3923i	0.0290632	−	0.484200i
$766$	−11.0000			−0.397446
$767$	9.52628	+	38.5000i	0.343974	+	1.39015i
$768$			1.00000i			0.0360844i
$769$	−4.50000	+	7.79423i	−0.162274	+	0.281067i	−0.935684	−	0.352839i	$-0.885216\pi$
$769$	−4.50000	+	7.79423i	−0.162274	+	0.281067i	0.773410	+	0.633906i	$0.218550\pi$
$770$		0			0
$771$	−7.50000	−	12.9904i	−0.270106	−	0.467837i
$772$			16.0000i			0.575853i
$773$	41.5692	−	24.0000i	1.49514	−	0.863220i	0.495156	−	0.868804i	$-0.335111\pi$
$773$	41.5692	−	24.0000i	1.49514	−	0.863220i	0.999984	+	0.00558380i	$0.00177739\pi$
$774$	−6.50000	−	11.2583i	−0.233638	−	0.404672i
$775$	−3.00000	+	4.00000i	−0.107763	+	0.143684i
$776$	2.00000	+	3.46410i	0.0717958	+	0.124354i
$777$		0			0
$778$	11.2583	+	6.50000i	0.403631	+	0.233036i
$779$		0			0
$780$	−7.92820	+	1.46410i	−0.283875	+	0.0524232i
$781$	12.0000			0.429394
$782$	46.7654	+	27.0000i	1.67233	+	0.965518i
$783$	6.06218	+	3.50000i	0.216645	+	0.125080i
$784$	−3.50000	−	6.06218i	−0.125000	−	0.216506i
$785$	−14.0000	+	7.00000i	−0.499681	+	0.249841i
$786$	7.50000	+	12.9904i	0.267516	+	0.463352i
$787$	33.7750	−	19.5000i	1.20395	−	0.695100i	0.242518	−	0.970147i	$-0.422027\pi$
$787$	33.7750	−	19.5000i	1.20395	−	0.695100i	0.961431	+	0.275047i	$0.0886934\pi$
$788$		−	26.0000i		−	0.926212i
$789$	4.50000	+	7.79423i	0.160204	+	0.277482i
$790$	−0.133975	+	2.23205i	−0.00476660	+	0.0794128i
$791$		0			0
$792$			3.00000i			0.106600i
$793$		0			0
$794$	27.0000			0.958194
$795$	13.3923	+	0.803848i	0.474976	+	0.0285095i
$796$	4.00000	−	6.92820i	0.141776	−	0.245564i
$797$	5.19615	−	3.00000i	0.184057	−	0.106265i	−0.405140	−	0.914255i	$-0.632777\pi$
$797$	5.19615	−	3.00000i	0.184057	−	0.106265i	0.589197	+	0.807989i	$0.299444\pi$
$798$		0			0
$799$	−33.0000	−	57.1577i	−1.16746	−	2.02209i
$800$	−0.598076	+	4.96410i	−0.0211452	+	0.175507i
$801$	−4.00000			−0.141333
$802$	17.3205	−	10.0000i	0.611608	−	0.353112i
$803$		0			0
$804$	−2.00000	+	3.46410i	−0.0705346	+	0.122169i
$805$		0			0
$806$	2.50000	+	2.59808i	0.0880587	+	0.0915133i
$807$		−	14.0000i		−	0.492823i
$808$	−12.1244	−	7.00000i	−0.426533	−	0.246259i
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	−0.574228	−	0.818696i	$-0.694698\pi$
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	0.996125	+	0.0879478i	$0.0280309\pi$
$810$	1.86603	+	1.23205i	0.0655654	+	0.0432899i
$811$	−34.0000			−1.19390			−0.596951	−	0.802278i	$-0.703621\pi$
$811$	−34.0000			−1.19390			−0.596951	+	0.802278i	$0.703621\pi$
$812$		0			0
$813$	−0.866025	+	0.500000i	−0.0303728	+	0.0175358i
$814$	−3.00000			−0.105150
$815$	−27.9904	−	18.4808i	−0.980460	−	0.647353i
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$		0			0
$818$			6.00000i			0.209785i
$819$		0			0
$820$		0			0
$821$	23.5000	−	40.7032i	0.820156	−	1.42055i	−0.0854103	−	0.996346i	$-0.527220\pi$
$821$	23.5000	−	40.7032i	0.820156	−	1.42055i	0.905566	−	0.424205i	$-0.139447\pi$
$822$	−11.2583	−	6.50000i	−0.392679	−	0.226714i
$823$	36.3731	−	21.0000i	1.26789	−	0.732014i	0.293298	−	0.956021i	$-0.405247\pi$
$823$	36.3731	−	21.0000i	1.26789	−	0.732014i	0.974588	+	0.224007i	$0.0719139\pi$
$824$	−14.0000			−0.487713
$825$	−1.79423	+	14.8923i	−0.0624670	+	0.518484i
$826$		0			0
$827$			16.0000i			0.556375i	0.960527	+	0.278187i	$0.0897336\pi$
$827$			16.0000i			0.556375i	−0.960527	+	0.278187i	$0.910266\pi$
$828$	−7.79423	+	4.50000i	−0.270868	+	0.156386i
$829$	−23.0000	+	39.8372i	−0.798823	+	1.38360i	0.121560	+	0.992584i	$0.461210\pi$
$829$	−23.0000	+	39.8372i	−0.798823	+	1.38360i	−0.920383	+	0.391018i	$0.872123\pi$
$830$	−8.92820	−	0.535898i	−0.309902	−	0.0186013i
$831$	−23.0000			−0.797861
$832$	3.46410	+	1.00000i	0.120096	+	0.0346688i
$833$		−	42.0000i		−	1.45521i
$834$	−4.00000	+	6.92820i	−0.138509	+	0.239904i
$835$	0.669873	−	11.1603i	0.0231819	−	0.386217i
$836$		0			0
$837$		−	1.00000i		−	0.0345651i
$838$	−3.46410	+	2.00000i	−0.119665	+	0.0690889i
$839$	−8.00000	−	13.8564i	−0.276191	−	0.478376i	0.694244	−	0.719740i	$-0.255739\pi$
$839$	−8.00000	−	13.8564i	−0.276191	−	0.478376i	−0.970435	+	0.241363i	$0.922405\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	−8.66025	−	5.00000i	−0.298452	−	0.172311i
$843$	19.0526	+	11.0000i	0.656205	+	0.378860i
$844$	−10.0000			−0.344214
$845$	−2.85641	+	28.9282i	−0.0982634	+	0.995160i
$846$	11.0000			0.378188
$847$		0			0
$848$	−5.19615	−	3.00000i	−0.178437	−	0.103020i
$849$	−2.50000	−	4.33013i	−0.0857998	−	0.148610i
$850$	−18.0000	+	24.0000i	−0.617395	+	0.823193i
$851$	−4.50000	−	7.79423i	−0.154258	−	0.267183i
$852$	−3.46410	+	2.00000i	−0.118678	+	0.0685189i
$853$		−	41.0000i		−	1.40381i	−0.712269	−	0.701907i	$-0.752332\pi$
$853$		−	41.0000i		−	1.40381i	0.712269	−	0.701907i	$-0.247668\pi$
$854$		0			0
$855$		0			0
$856$	−2.00000	+	3.46410i	−0.0683586	+	0.118401i
$857$		−	43.0000i		−	1.46885i	−0.678689	−	0.734426i	$-0.737451\pi$
$857$		−	43.0000i		−	1.46885i	0.678689	−	0.734426i	$-0.262549\pi$
$858$	10.3923	+	3.00000i	0.354787	+	0.102418i
$859$	−18.0000			−0.614152			−0.307076	−	0.951685i	$-0.599351\pi$
$859$	−18.0000			−0.614152			−0.307076	+	0.951685i	$0.599351\pi$
$860$	−1.74167	+	29.0167i	−0.0593904	+	0.989460i
$861$		0			0
$862$	−17.3205	+	10.0000i	−0.589939	+	0.340601i
$863$			11.0000i			0.374444i	0.982318	+	0.187222i	$0.0599484\pi$
$863$			11.0000i			0.374444i	−0.982318	+	0.187222i	$0.940052\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	22.3923	+	14.7846i	0.761361	+	0.502692i
$866$	−12.0000			−0.407777
$867$	−16.4545	+	9.50000i	−0.558824	+	0.322637i
$868$		0			0
$869$	1.50000	−	2.59808i	0.0508840	−	0.0881337i
$870$	−7.00000	−	14.0000i	−0.237322	−	0.474644i
$871$	10.0000	+	10.3923i	0.338837	+	0.352130i
$872$		−	16.0000i		−	0.541828i
$873$	−3.46410	−	2.00000i	−0.117242	−	0.0676897i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−42.4352	+	24.5000i	−1.43294	+	0.827306i	−0.997344	−	0.0728377i	$-0.976794\pi$
$877$	−42.4352	+	24.5000i	−1.43294	+	0.827306i	−0.435593	+	0.900144i	$0.643461\pi$
$878$	−13.8564	+	8.00000i	−0.467631	+	0.269987i
$879$	28.0000			0.944417
$880$	3.69615	−	5.59808i	0.124597	−	0.188711i
$881$	−3.00000	+	5.19615i	−0.101073	+	0.175063i	−0.912127	−	0.409908i	$-0.865561\pi$
$881$	−3.00000	+	5.19615i	−0.101073	+	0.175063i	0.811054	+	0.584971i	$0.198894\pi$
$882$	6.06218	+	3.50000i	0.204124	+	0.117851i
$883$		−	41.0000i		−	1.37976i	−0.723924	−	0.689880i	$-0.757663\pi$
$883$		−	41.0000i		−	1.37976i	0.723924	−	0.689880i	$-0.242337\pi$
$884$	15.0000	+	15.5885i	0.504505	+	0.524297i
$885$	−22.0000	+	11.0000i	−0.739522	+	0.369761i
$886$	13.0000	−	22.5167i	0.436744	−	0.756462i
$887$	−0.866025	−	0.500000i	−0.0290783	−	0.0167884i	0.485390	−	0.874298i	$-0.338677\pi$
$887$	−0.866025	−	0.500000i	−0.0290783	−	0.0167884i	−0.514469	+	0.857509i	$0.672011\pi$
$888$	0.866025	−	0.500000i	0.0290619	−	0.0167789i
$889$		0			0
$890$	7.46410	+	4.92820i	0.250197	+	0.165194i
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$		−	14.0000i		−	0.468755i
$893$		0			0
$894$	7.50000	−	12.9904i	0.250838	−	0.434463i
$895$	−20.0885	−	1.20577i	−0.671483	−	0.0403045i
$896$		0			0
$897$	7.79423	+	31.5000i	0.260242	+	1.05175i
$898$		−	32.0000i		−	1.06785i
$899$	−3.50000	+	6.06218i	−0.116732	+	0.202185i
$900$	−1.96410	−	4.59808i	−0.0654701	−	0.153269i
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$	−9.50000	−	16.4545i	−0.315965	−	0.547268i
$905$	−8.00000	−	16.0000i	−0.265929	−	0.531858i
$906$	2.00000	+	3.46410i	0.0664455	+	0.115087i
$907$	−7.79423	−	4.50000i	−0.258803	−	0.149420i	0.364985	−	0.931013i	$-0.381074\pi$
$907$	−7.79423	−	4.50000i	−0.258803	−	0.149420i	−0.623788	+	0.781593i	$0.714407\pi$
$908$	19.0526	+	11.0000i	0.632281	+	0.365048i
$909$	14.0000			0.464351
$910$		0			0
$911$	−34.0000			−1.12647			−0.563235	−	0.826297i	$-0.690443\pi$
$911$	−34.0000			−1.12647			−0.563235	+	0.826297i	$0.690443\pi$
$912$		0			0
$913$	10.3923	+	6.00000i	0.343935	+	0.198571i
$914$	−21.0000	−	36.3731i	−0.694618	−	1.20311i
$915$		0			0
$916$	11.0000	+	19.0526i	0.363450	+	0.629514i
$917$		0			0
$918$		−	6.00000i		−	0.198030i
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$	20.0885	+	1.20577i	0.662297	+	0.0397531i
$921$	−2.00000	+	3.46410i	−0.0659022	+	0.114146i
$922$			21.0000i			0.691598i
$923$	3.46410	+	14.0000i	0.114022	+	0.460816i
$924$		0			0
$925$	4.59808	−	1.96410i	0.151184	−	0.0645793i
$926$	17.0000	−	29.4449i	0.558655	−	0.967618i
$927$	12.1244	−	7.00000i	0.398216	−	0.229910i
$928$			7.00000i			0.229786i
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	−0.972166	−	0.234294i	$-0.924722\pi$
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	0.283178	−	0.959067i	$-0.408611\pi$
$930$	−1.23205	+	1.86603i	−0.0404005	+	0.0611894i
$931$		0			0
$932$	−4.33013	+	2.50000i	−0.141838	+	0.0818902i
$933$	−15.5885	−	9.00000i	−0.510343	−	0.294647i
$934$	19.0000	−	32.9090i	0.621699	−	1.07681i
$935$	36.0000	−	18.0000i	1.17733	−	0.588663i
$936$	−3.50000	+	0.866025i	−0.114401	+	0.0283069i
$937$			22.0000i			0.718709i	0.933201	+	0.359354i	$0.117003\pi$
$937$			22.0000i			0.718709i	−0.933201	+	0.359354i	$0.882997\pi$
$938$		0			0
$939$	5.00000	−	8.66025i	0.163169	−	0.282617i
$940$	−20.5263	−	13.5526i	−0.669493	−	0.442036i
$941$	18.0000			0.586783			0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000			0.586783			0.293392	+	0.955992i	$0.405216\pi$
$942$	−6.06218	+	3.50000i	−0.197516	+	0.114036i
$943$		0			0
$944$	11.0000			0.358020
$945$		0			0
$946$	19.5000	−	33.7750i	0.634000	−	1.09812i
$947$	−34.6410	−	20.0000i	−1.12568	−	0.649913i	−0.182836	−	0.983143i	$-0.558528\pi$
$947$	−34.6410	−	20.0000i	−1.12568	−	0.649913i	−0.942845	+	0.333231i	$0.891861\pi$
$948$			1.00000i			0.0324785i
$949$		0			0
$950$		0			0
$951$	−12.0000	+	20.7846i	−0.389127	+	0.673987i
$952$		0			0
$953$	−9.52628	+	5.50000i	−0.308586	+	0.178162i	−0.646294	−	0.763089i	$-0.723682\pi$
$953$	−9.52628	+	5.50000i	−0.308586	+	0.178162i	0.337707	+	0.941251i	$0.390349\pi$
$954$	6.00000			0.194257
$955$	−32.0333	+	48.5167i	−1.03657	+	1.56996i
$956$	8.00000	+	13.8564i	0.258738	+	0.448148i
$957$			21.0000i			0.678834i
$958$	8.66025	−	5.00000i	0.279800	−	0.161543i
$959$		0			0
$960$	−0.133975	+	2.23205i	−0.00432401	+	0.0720391i
$961$	−30.0000			−0.967742
$962$	−0.866025	−	3.50000i	−0.0279218	−	0.112845i
$963$		−	4.00000i		−	0.128898i
$964$	−3.50000	+	6.06218i	−0.112727	+	0.195250i
$965$	−2.14359	+	35.7128i	−0.0690047	+	1.14964i
$966$		0			0
$967$		−	16.0000i		−	0.514525i	−0.966342	−	0.257263i	$-0.917179\pi$
$967$		−	16.0000i		−	0.514525i	0.966342	−	0.257263i	$-0.0828206\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$		0			0
$970$	4.00000	+	8.00000i	0.128432	+	0.256865i
$971$	−26.0000	−	45.0333i	−0.834380	−	1.44519i	−0.894534	−	0.446999i	$-0.852493\pi$
$971$	−26.0000	−	45.0333i	−0.834380	−	1.44519i	0.0601548	−	0.998189i	$-0.480841\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$		0			0
$974$		0			0
$975$	−17.8923	+	2.20577i	−0.573012	+	0.0706412i
$976$		0			0
$977$	−14.7224	−	8.50000i	−0.471012	−	0.271939i	0.245651	−	0.969358i	$-0.420998\pi$
$977$	−14.7224	−	8.50000i	−0.471012	−	0.271939i	−0.716663	+	0.697419i	$0.754332\pi$
$978$	−12.9904	−	7.50000i	−0.415387	−	0.239824i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$	−7.00000	−	14.0000i	−0.223607	−	0.447214i
$981$	8.00000	+	13.8564i	0.255420	+	0.442401i
$982$	10.3923	−	6.00000i	0.331632	−	0.191468i
$983$		−	51.0000i		−	1.62665i	−0.581811	−	0.813324i	$-0.697656\pi$
$983$		−	51.0000i		−	1.62665i	0.581811	−	0.813324i	$-0.302344\pi$
$984$		0			0
$985$	3.48334	−	58.0333i	0.110988	−	1.84910i
$986$	−21.0000	+	36.3731i	−0.668776	+	1.15835i
$987$		0			0
$988$		0			0
$989$	117.000			3.72038
$990$	−0.401924	+	6.69615i	−0.0127740	+	0.212818i
$991$	−5.50000	+	9.52628i	−0.174713	+	0.302612i	−0.940062	−	0.341004i	$-0.889233\pi$
$991$	−5.50000	+	9.52628i	−0.174713	+	0.302612i	0.765349	+	0.643616i	$0.222567\pi$
$992$	0.866025	−	0.500000i	0.0274963	−	0.0158750i
$993$		−	2.00000i		−	0.0634681i
$994$		0			0
$995$	9.85641	−	14.9282i	0.312469	−	0.473256i
$996$	−4.00000			−0.126745
$997$	−39.8372	+	23.0000i	−1.26166	+	0.728417i	−0.973395	−	0.229135i	$-0.926410\pi$
$997$	−39.8372	+	23.0000i	−1.26166	+	0.728417i	−0.288261	+	0.957552i	$0.593077\pi$
$998$	−31.1769	−	18.0000i	−0.986888	−	0.569780i
$999$	−0.500000	+	0.866025i	−0.0158193	+	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.y.d.139.1	✓	4
3.2	odd	2		1170.2.bp.c.919.2		4
5.2	odd	4		1950.2.i.p.451.1		2
5.3	odd	4		1950.2.i.l.451.1		2
5.4	even	2	inner	390.2.y.d.139.2	yes	4
13.3	even	3	inner	390.2.y.d.289.2	yes	4
15.14	odd	2		1170.2.bp.c.919.1		4
39.29	odd	6		1170.2.bp.c.289.1		4
65.3	odd	12		1950.2.i.l.601.1		2
65.29	even	6	inner	390.2.y.d.289.1	yes	4
65.42	odd	12		1950.2.i.p.601.1		2
195.29	odd	6		1170.2.bp.c.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.d.139.1	✓	4	1.1	even	1	trivial
390.2.y.d.139.2	yes	4	5.4	even	2	inner
390.2.y.d.289.1	yes	4	65.29	even	6	inner
390.2.y.d.289.2	yes	4	13.3	even	3	inner
1170.2.bp.c.289.1		4	39.29	odd	6
1170.2.bp.c.289.2		4	195.29	odd	6
1170.2.bp.c.919.1		4	15.14	odd	2
1170.2.bp.c.919.2		4	3.2	odd	2
1950.2.i.l.451.1		2	5.3	odd	4
1950.2.i.l.601.1		2	65.3	odd	12
1950.2.i.p.451.1		2	5.2	odd	4
1950.2.i.p.601.1		2	65.42	odd	12

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.133975 - 2.23205i) q^{10} +(-1.50000 + 2.59808i) q^{11} -1.00000i q^{12} +(-3.46410 - 1.00000i) q^{13} +(0.133975 - 2.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 + 3.00000i) q^{17} -1.00000i q^{18} +(-1.23205 + 1.86603i) q^{20} +(2.59808 - 1.50000i) q^{22} +(7.79423 + 4.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(2.50000 + 2.59808i) q^{26} -1.00000i q^{27} +(-3.50000 + 6.06218i) q^{29} +(-1.23205 + 1.86603i) q^{30} +1.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(2.59808 - 1.50000i) q^{33} +6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.866025 - 0.500000i) q^{37} +(2.50000 + 2.59808i) q^{39} +(2.00000 - 1.00000i) q^{40} +(11.2583 - 6.50000i) q^{43} -3.00000 q^{44} +(-1.23205 + 1.86603i) q^{45} +(-4.50000 - 7.79423i) q^{46} +11.0000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(4.59808 - 1.96410i) q^{50} +6.00000 q^{51} +(-0.866025 - 3.50000i) q^{52} +6.00000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(-6.69615 - 0.401924i) q^{55} +(6.06218 - 3.50000i) q^{58} +(-5.50000 - 9.52628i) q^{59} +(2.00000 - 1.00000i) q^{60} +(-0.866025 - 0.500000i) q^{62} -1.00000 q^{64} +(-1.46410 - 7.92820i) q^{65} -3.00000 q^{66} +(-3.46410 - 2.00000i) q^{67} +(-5.19615 - 3.00000i) q^{68} +(-4.50000 - 7.79423i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(0.866025 - 0.500000i) q^{72} +(0.500000 + 0.866025i) q^{74} +(4.59808 - 1.96410i) q^{75} +(-0.866025 - 3.50000i) q^{78} -1.00000 q^{79} +(-2.23205 - 0.133975i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.00000i q^{83} +(-11.1962 - 7.39230i) q^{85} -13.0000 q^{86} +(6.06218 - 3.50000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(-2.00000 + 3.46410i) q^{89} +(2.00000 - 1.00000i) q^{90} +9.00000i q^{92} +(-0.866025 - 0.500000i) q^{93} +(5.50000 - 9.52628i) q^{94} -1.00000 q^{96} +(-3.46410 + 2.00000i) q^{97} +(6.06218 - 3.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{9} + 4 q^{10} - 6 q^{11} + 4 q^{15} - 2 q^{16} + 2 q^{20} - 2 q^{24} - 12 q^{25} + 10 q^{26} - 14 q^{29} + 2 q^{30} + 4 q^{31} + 24 q^{34} - 2 q^{36} + 10 q^{39} + 8 q^{40} - 12 q^{44} + 2 q^{45} - 18 q^{46} - 14 q^{49} + 8 q^{50} + 24 q^{51} - 2 q^{54} - 6 q^{55} - 22 q^{59} + 8 q^{60} - 4 q^{64} + 8 q^{65} - 12 q^{66} - 18 q^{69} - 8 q^{71} + 2 q^{74} + 8 q^{75} - 4 q^{79} - 2 q^{80} - 2 q^{81} - 24 q^{85} - 52 q^{86} - 8 q^{89} + 8 q^{90} + 22 q^{94} - 4 q^{96} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^9 + 4 * q^10 - 6 * q^11 + 4 * q^15 - 2 * q^16 + 2 * q^20 - 2 * q^24 - 12 * q^25 + 10 * q^26 - 14 * q^29 + 2 * q^30 + 4 * q^31 + 24 * q^34 - 2 * q^36 + 10 * q^39 + 8 * q^40 - 12 * q^44 + 2 * q^45 - 18 * q^46 - 14 * q^49 + 8 * q^50 + 24 * q^51 - 2 * q^54 - 6 * q^55 - 22 * q^59 + 8 * q^60 - 4 * q^64 + 8 * q^65 - 12 * q^66 - 18 * q^69 - 8 * q^71 + 2 * q^74 + 8 * q^75 - 4 * q^79 - 2 * q^80 - 2 * q^81 - 24 * q^85 - 52 * q^86 - 8 * q^89 + 8 * q^90 + 22 * q^94 - 4 * q^96 - 12 * q^99

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