LMFDB - Embedded newform 390.2.y.d.289.2

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			289.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	390.289
Dual form			390.2.y.d.139.2

$q$-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} +(1.86603 + 1.23205i) q^{10} +(-1.50000 - 2.59808i) q^{11} -1.00000i q^{12} +(3.46410 - 1.00000i) q^{13} +(1.86603 + 1.23205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(5.19615 + 3.00000i) q^{17} -1.00000i q^{18} +(2.23205 + 0.133975i) 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} +(2.23205 + 0.133975i) 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} +(2.23205 + 0.133975i) q^{45} +(-4.50000 + 7.79423i) q^{46} +11.0000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(-0.598076 + 4.96410i) q^{50} +6.00000 q^{51} +(0.866025 - 3.50000i) q^{52} +6.00000i q^{53} +(-0.500000 - 0.866025i) q^{54} +(3.69615 - 5.59808i) 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} +(5.46410 + 5.92820i) 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} +(-0.598076 + 4.96410i) q^{75} +(0.866025 - 3.50000i) q^{78} -1.00000 q^{79} +(1.23205 - 1.86603i) q^{80} +(-0.500000 - 0.866025i) q^{81} -4.00000i q^{83} +(-0.803848 + 13.3923i) 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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.866025	−	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	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.86603	+	1.23205i	0.590089	+	0.389609i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		−	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
$15$	1.86603	+	1.23205i	0.481806	+	0.318114i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.973123	−	0.230285i	$-0.0739659\pi$
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.287129	+	0.957892i	$0.407299\pi$
$18$		−	1.00000i		−	0.235702i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	2.23205	+	0.133975i	0.499102	+	0.0299576i
$21$		0			0
$22$	−2.59808	−	1.50000i	−0.553912	−	0.319801i
$23$	−7.79423	+	4.50000i	−1.62521	+	0.938315i	−0.639713	+	0.768613i	$0.720947\pi$
$23$	−7.79423	+	4.50000i	−1.62521	+	0.938315i	−0.985496	+	0.169701i	$0.945720\pi$
$24$	−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	−0.983138	−	0.182864i	$-0.941463\pi$
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	0.333205	−	0.942855i	$-0.391870\pi$
$30$	2.23205	+	0.133975i	0.407515	+	0.0244603i
$31$	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	$-0.640472\pi$
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	0.569495	+	0.821995i	$0.307139\pi$
$38$		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	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−11.2583	−	6.50000i	−1.71688	−	0.991241i	−0.924473	−	0.381246i	$-0.875495\pi$
$43$	−11.2583	−	6.50000i	−1.71688	−	0.991241i	−0.792406	−	0.609994i	$-0.791172\pi$
$44$	−3.00000			−0.452267
$45$	2.23205	+	0.133975i	0.332734	+	0.0199718i
$46$	−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
$50$	−0.598076	+	4.96410i	−0.0845807	+	0.702030i
$51$	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
$55$	3.69615	−	5.59808i	0.498389	−	0.754844i
$56$		0			0
$57$		0			0
$58$	−6.06218	−	3.50000i	−0.796003	−	0.459573i
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$	2.00000	−	1.00000i	0.258199	−	0.129099i
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	0.866025	−	0.500000i	0.109985	−	0.0635001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	5.46410	+	5.92820i	0.677738	+	0.735303i
$66$	−3.00000			−0.369274
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	−0.273241	−	0.961946i	$-0.588096\pi$
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	0.696449	+	0.717607i	$0.254762\pi$
$68$	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	−0.959955	−	0.280155i	$-0.909614\pi$
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	0.722599	+	0.691268i	$0.242948\pi$
$72$	−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
$75$	−0.598076	+	4.96410i	−0.0690599	+	0.573205i
$76$		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	$0.517916\pi$
$80$	1.23205	−	1.86603i	0.137747	−	0.208628i
$81$	−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
$85$	−0.803848	+	13.3923i	−0.0871895	+	1.45260i
$86$	−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	0.740341	−	0.672232i	$-0.234664\pi$
$89$	−2.00000	−	3.46410i	−0.212000	−	0.367194i	−0.952340	+	0.305038i	$0.901331\pi$
$90$	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	$-0.268242\pi$
$97$	3.46410	+	2.00000i	0.351726	+	0.203069i	−0.313719	+	0.949516i	$0.601575\pi$
$98$	−6.06218	−	3.50000i	−0.612372	−	0.353553i
$99$	−3.00000			−0.301511
$100$	1.96410	+	4.59808i	0.196410	+	0.459808i
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	0.969664	+	0.244443i	$0.0786053\pi$
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	−0.273138	+	0.961975i	$0.588061\pi$
$102$	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	$-0.604732\pi$
$107$	3.46410	−	2.00000i	0.334887	−	0.193347i	0.658009	+	0.753010i	$0.271399\pi$
$108$	−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	$0.222115\pi$
$110$	0.401924	−	6.69615i	0.0383219	−	0.638453i
$111$	0.500000	−	0.866025i	0.0474579	−	0.0821995i
$112$		0			0
$113$	−16.4545	−	9.50000i	−1.54791	−	0.893685i	−0.998301	−	0.0582609i	$-0.981444\pi$
$113$	−16.4545	−	9.50000i	−1.54791	−	0.893685i	−0.549606	−	0.835424i	$-0.685222\pi$
$114$		0			0
$115$	−16.7942	−	11.0885i	−1.56607	−	1.03400i
$116$	−7.00000			−0.649934
$117$	0.866025	−	3.50000i	0.0800641	−	0.323575i
$118$			11.0000i			1.01263i
$119$		0			0
$120$	1.23205	−	1.86603i	0.112470	−	0.170344i
$121$	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	$-0.752437\pi$
$127$	−5.19615	+	3.00000i	−0.461084	+	0.266207i	0.251416	+	0.967879i	$0.419104\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−13.0000			−1.14459
$130$	7.69615	+	2.40192i	0.674997	+	0.210663i
$131$	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	$-0.145924\pi$
$137$	11.2583	+	6.50000i	0.961864	+	0.555332i	0.0651178	+	0.997878i	$0.479258\pi$
$138$			9.00000i			0.766131i
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	−0.645021	−	0.764165i	$-0.723151\pi$
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	0.984297	+	0.176522i	$0.0564848\pi$
$140$		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
$145$	8.62436	−	13.0622i	0.716214	−	1.08475i
$146$		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	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$	1.96410	+	4.59808i	0.160368	+	0.375431i
$151$	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
$160$	0.133975	−	2.23205i	0.0105916	−	0.176459i
$161$		0			0
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	12.9904	+	7.50000i	1.01749	+	0.587445i	0.913375	−	0.407120i	$-0.133467\pi$
$163$	12.9904	+	7.50000i	1.01749	+	0.587445i	0.104111	+	0.994566i	$0.466800\pi$
$164$		0			0
$165$	0.401924	−	6.69615i	0.0312897	−	0.521295i
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	4.33013	−	2.50000i	0.335075	−	0.193456i	−0.323017	−	0.946393i	$-0.604697\pi$
$167$	4.33013	−	2.50000i	0.335075	−	0.193456i	0.658092	+	0.752937i	$0.271364\pi$
$168$		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	$-0.484113\pi$
$173$	−10.3923	−	6.00000i	−0.790112	−	0.456172i	−0.840002	+	0.542583i	$0.817446\pi$
$174$	−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	0.647397	−	0.762153i	$-0.275858\pi$
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	−0.983742	+	0.179585i	$0.942524\pi$
$180$	1.23205	−	1.86603i	0.0918316	−	0.139085i
$181$	−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
$185$	1.86603	+	1.23205i	0.137193	+	0.0905822i
$186$	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	0.176406	−	0.984317i	$-0.443553\pi$
$191$	13.0000	−	22.5167i	0.940647	−	1.62925i	0.764241	−	0.644931i	$-0.223114\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−13.8564	+	8.00000i	−0.997406	+	0.575853i	−0.907480	−	0.420096i	$-0.861996\pi$
$193$	−13.8564	+	8.00000i	−0.997406	+	0.575853i	−0.0899262	+	0.995948i	$0.528663\pi$
$194$	4.00000			0.287183
$195$	7.69615	+	2.40192i	0.551133	+	0.172005i
$196$	−7.00000			−0.500000
$197$	22.5167	−	13.0000i	1.60425	−	0.926212i	0.613621	−	0.789601i	$-0.289712\pi$
$197$	22.5167	−	13.0000i	1.60425	−	0.926212i	0.990625	−	0.136611i	$-0.0436210\pi$
$198$	−2.59808	+	1.50000i	−0.184637	+	0.106600i
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	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	0.640996	−	0.767544i	$-0.278521\pi$
$211$	−5.00000	−	8.66025i	−0.344214	−	0.596196i	−0.985211	+	0.171347i	$0.945188\pi$
$212$	5.19615	+	3.00000i	0.356873	+	0.206041i
$213$			4.00000i			0.274075i
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	1.74167	−	29.0167i	0.118781	−	1.97892i
$216$	−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	$-0.511370\pi$
$223$	12.1244	−	7.00000i	0.811907	−	0.468755i	0.847618	+	0.530607i	$0.178036\pi$
$224$		0			0
$225$	1.96410	+	4.59808i	0.130940	+	0.306538i
$226$	−19.0000			−1.26386
$227$	−19.0526	−	11.0000i	−1.26456	−	0.730096i	−0.290609	−	0.956842i	$-0.593858\pi$
$227$	−19.0526	−	11.0000i	−1.26456	−	0.730096i	−0.973954	+	0.226746i	$0.927191\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$	−20.0885	−	1.20577i	−1.32459	−	0.0795062i
$231$		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	$0.326871\pi$
$240$	0.133975	−	2.23205i	0.00864802	−	0.144078i
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$		−	2.00000i		−	0.128565i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	8.62436	−	13.0622i	0.550990	−	0.834512i
$246$		0			0
$247$		0			0
$248$		−	1.00000i		−	0.0635001i
$249$	−2.00000	−	3.46410i	−0.126745	−	0.219529i
$250$	−10.5263	+	3.76795i	−0.665740	+	0.238306i
$251$	−2.50000	+	4.33013i	−0.157799	+	0.273315i	−0.934075	−	0.357078i	$-0.883773\pi$
$251$	−2.50000	+	4.33013i	−0.157799	+	0.273315i	0.776276	+	0.630393i	$0.217106\pi$
$252$		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	$-0.821633\pi$
$257$	−12.9904	+	7.50000i	−0.810318	+	0.467837i	0.0367485	+	0.999325i	$0.488300\pi$
$258$	−11.2583	+	6.50000i	−0.700913	+	0.404672i
$259$		0			0
$260$	7.86603	−	1.76795i	0.487830	−	0.109644i
$261$	−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	$-0.577167\pi$
$263$	7.79423	−	4.50000i	0.480613	−	0.277482i	0.720672	+	0.693276i	$0.243833\pi$
$264$	−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	−0.569789	−	0.821791i	$-0.692975\pi$
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	0.996586	+	0.0825561i	$0.0263084\pi$
$270$	1.23205	−	1.86603i	0.0749802	−	0.113563i
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$		−	6.00000i		−	0.363803i
$273$		0			0
$274$	13.0000			0.785359
$275$	14.8923	+	1.79423i	0.898040	+	0.108196i
$276$	4.50000	+	7.79423i	0.270868	+	0.469157i
$277$	−19.9186	−	11.5000i	−1.19679	−	0.690968i	−0.236953	−	0.971521i	$-0.576149\pi$
$277$	−19.9186	−	11.5000i	−1.19679	−	0.690968i	−0.959839	+	0.280553i	$0.909482\pi$
$278$		−	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	$-0.714146\pi$
$283$	−4.33013	+	2.50000i	−0.257399	+	0.148610i	0.365748	+	0.930714i	$0.380813\pi$
$284$	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
$290$	0.937822	−	15.6244i	0.0550708	−	0.917494i
$291$	4.00000			0.234484
$292$		0			0
$293$	24.2487	+	14.0000i	1.41662	+	0.817889i	0.996001	−	0.0893462i	$-0.0284778\pi$
$293$	24.2487	+	14.0000i	1.41662	+	0.817889i	0.420624	+	0.907235i	$0.361811\pi$
$294$	−7.00000			−0.408248
$295$	−24.5526	−	1.47372i	−1.42951	−	0.0858033i
$296$	−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
$310$	1.86603	+	1.23205i	0.105983	+	0.0699758i
$311$	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
$325$	−6.39230	+	16.8564i	−0.354581	+	0.935025i
$326$	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	−0.837234	−	0.546845i	$-0.815829\pi$
$331$	1.00000	−	1.73205i	0.0549650	−	0.0952021i	0.892199	+	0.451643i	$0.149162\pi$
$332$	−3.46410	−	2.00000i	−0.190117	−	0.109764i
$333$		−	1.00000i		−	0.0547997i
$334$	2.50000	−	4.33013i	0.136794	−	0.236934i
$335$	7.46410	+	4.92820i	0.407807	+	0.269257i
$336$		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
$340$	11.1962	+	7.39230i	0.607197	+	0.400904i
$341$	−1.50000	−	2.59808i	−0.0812296	−	0.140694i
$342$		0			0
$343$		0			0
$344$	−6.50000	+	11.2583i	−0.350457	+	0.607008i
$345$	−20.0885	−	1.20577i	−1.08153	−	0.0649165i
$346$	−12.0000			−0.645124
$347$	8.66025	+	5.00000i	0.464907	+	0.268414i	0.714105	−	0.700038i	$-0.246834\pi$
$347$	8.66025	+	5.00000i	0.464907	+	0.268414i	−0.249198	+	0.968452i	$0.580167\pi$
$348$	−6.06218	+	3.50000i	−0.324967	+	0.187620i
$349$	4.00000	+	6.92820i	0.214115	+	0.370858i	0.952998	−	0.302975i	$-0.0979799\pi$
$349$	4.00000	+	6.92820i	0.214115	+	0.370858i	−0.738883	+	0.673833i	$0.764647\pi$
$350$		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	$-0.788191\pi$
$353$	−12.1244	+	7.00000i	−0.645314	+	0.372572i	0.141344	+	0.989960i	$0.454858\pi$
$354$	5.50000	+	9.52628i	0.292322	+	0.506316i
$355$	−8.92820	−	0.535898i	−0.473860	−	0.0284425i
$356$	−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	$0.657553\pi$
$360$	0.133975	−	2.23205i	0.00706108	−	0.117639i
$361$	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	$-0.882137\pi$
$367$	−20.7846	+	12.0000i	−1.08495	+	0.626395i	−0.152721	+	0.988269i	$0.548804\pi$
$368$	7.79423	+	4.50000i	0.406302	+	0.234579i
$369$		0			0
$370$	2.23205	+	0.133975i	0.116039	+	0.00696501i
$371$		0			0
$372$		−	1.00000i		−	0.0518476i
$373$	9.52628	+	5.50000i	0.493252	+	0.284779i	0.725923	−	0.687776i	$-0.241413\pi$
$373$	9.52628	+	5.50000i	0.493252	+	0.284779i	−0.232671	+	0.972556i	$0.574746\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$	−10.5263	+	3.76795i	−0.543575	+	0.194576i
$376$	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	0.744815	−	0.667271i	$-0.232538\pi$
$379$	−4.00000	−	6.92820i	−0.205466	−	0.355878i	−0.950281	+	0.311393i	$0.899204\pi$
$380$		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	$-0.424012\pi$
$383$	−9.52628	−	5.50000i	−0.486770	−	0.281037i	−0.723234	+	0.690604i	$0.757345\pi$
$384$	−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	$0.606901\pi$
$390$	7.86603	−	1.76795i	0.398312	−	0.0895236i
$391$	−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	$-0.0963770\pi$
$397$	23.3827	+	13.5000i	1.17354	+	0.677546i	0.219031	+	0.975718i	$0.429710\pi$
$398$			8.00000i			0.401004i
$399$		0			0
$400$	4.96410	+	0.598076i	0.248205	+	0.0299038i
$401$	−10.0000	−	17.3205i	−0.499376	−	0.864945i	0.500624	−	0.865665i	$-0.333104\pi$
$401$	−10.0000	−	17.3205i	−0.499376	−	0.864945i	−1.00000		0.000720188i	$0.999771\pi$
$402$		−	4.00000i		−	0.199502i
$403$	3.46410	−	1.00000i	0.172559	−	0.0498135i
$404$	14.0000			0.696526
$405$	1.23205	−	1.86603i	0.0612211	−	0.0927235i
$406$		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	−0.930614	−	0.366002i	$-0.880726\pi$
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	0.782274	+	0.622935i	$0.214060\pi$
$410$		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	0.910735	−	0.412991i	$-0.135516\pi$
$419$	2.00000	+	3.46410i	0.0977064	+	0.169232i	−0.813029	+	0.582224i	$0.802183\pi$
$420$		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
$425$	−27.5885	+	11.7846i	−1.33824	+	0.571638i
$426$	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	0.999779	−	0.0210230i	$-0.00669232\pi$
$431$	10.0000	+	17.3205i	0.481683	+	0.834300i	−0.518096	+	0.855323i	$0.673359\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−10.3923	−	6.00000i	−0.499422	−	0.288342i	0.229053	−	0.973414i	$-0.426437\pi$
$433$	−10.3923	−	6.00000i	−0.499422	−	0.288342i	−0.728475	+	0.685072i	$0.759771\pi$
$434$		0			0
$435$	0.937822	−	15.6244i	0.0449651	−	0.749131i
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$		0			0
$438$		0			0
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	−5.59808	−	3.69615i	−0.266878	−	0.176207i
$441$	−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
$445$	4.92820	−	7.46410i	0.233619	−	0.353832i
$446$	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	−0.190245	−	0.981737i	$-0.560928\pi$
$449$	16.0000	−	27.7128i	0.755087	−	1.30785i	0.945331	−	0.326112i	$-0.105739\pi$
$450$	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	−0.757174	+	0.653213i	$0.773421\pi$
$457$	−36.3731	+	21.0000i	−1.70146	+	0.982339i	−0.944286	+	0.329125i	$0.893246\pi$
$458$	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	−0.999920	−	0.0126168i	$-0.995984\pi$
$461$	−10.5000	+	18.1865i	−0.489034	+	0.847031i	0.510887	+	0.859648i	$0.329317\pi$
$462$		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
$465$	1.86603	+	1.23205i	0.0865349	+	0.0571350i
$466$	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
$470$	−13.5526	+	20.5263i	−0.625133	+	0.946807i
$471$	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	0.728895	−	0.684626i	$-0.240034\pi$
$479$	−5.00000	−	8.66025i	−0.228456	−	0.395697i	−0.957351	+	0.288929i	$0.906701\pi$
$480$	−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
$485$	−0.535898	+	8.92820i	−0.0243339	+	0.405409i
$486$	−1.00000			−0.0453609
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$	15.0000			0.678323
$490$	0.937822	−	15.6244i	0.0423665	−	0.705836i
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$		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	$0.201741\pi$
$500$	−7.23205	+	8.52628i	−0.323427	+	0.381307i
$501$	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	$-0.217234\pi$
$503$	13.8564	+	8.00000i	0.617827	+	0.356702i	−0.158196	+	0.987408i	$0.550568\pi$
$504$		0			0
$505$	−17.2487	+	26.1244i	−0.767558	+	1.16252i
$506$	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	−0.993061	−	0.117602i	$-0.962479\pi$
$509$	−13.5000	−	23.3827i	−0.598377	−	1.03642i	0.394684	−	0.918817i	$-0.370854\pi$
$510$	11.1962	+	7.39230i	0.495774	+	0.327337i
$511$		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
$520$	5.92820	−	5.46410i	0.259969	−	0.239617i
$521$	−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	$-0.448062\pi$
$523$	25.1147	−	14.5000i	1.09819	−	0.634041i	0.935745	+	0.352677i	$0.114728\pi$
$524$	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
$530$	−7.39230	+	11.1962i	−0.321101	+	0.486330i
$531$	5.50000	+	9.52628i	0.238680	+	0.413405i
$532$		0			0
$533$		0			0
$534$	−4.00000			−0.173097
$535$	7.46410	+	4.92820i	0.322701	+	0.213065i
$536$	−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
$540$	0.133975	−	2.23205i	0.00576535	−	0.0960522i
$541$	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
$550$	13.7942	−	5.89230i	0.588188	−	0.251249i
$551$		0			0
$552$	7.79423	+	4.50000i	0.331744	+	0.191533i
$553$		0			0
$554$	−23.0000			−0.977176
$555$	2.23205	+	0.133975i	0.0947453	+	0.00568690i
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	8.66025	−	5.00000i	0.366947	−	0.211857i	−0.305177	−	0.952296i	$-0.598716\pi$
$557$	8.66025	−	5.00000i	0.366947	−	0.211857i	0.672124	+	0.740439i	$0.265382\pi$
$558$		−	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	$-0.115496\pi$
$563$	25.9808	+	15.0000i	1.09496	+	0.632175i	0.160066	+	0.987106i	$0.448829\pi$
$564$	11.0000			0.463184
$565$	2.54552	−	42.4090i	0.107091	−	1.78416i
$566$	−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	−0.921869	−	0.387503i	$-0.873338\pi$
$569$	−19.0000	−	32.9090i	−0.796521	−	1.37962i	0.125347	−	0.992113i	$-0.459996\pi$
$570$		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
$575$	5.38269	−	44.6769i	0.224474	−	1.86316i
$576$	−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
$585$	7.86603	−	1.76795i	0.325220	−	0.0730957i
$586$	28.0000			1.15667
$587$	5.19615	−	3.00000i	0.214468	−	0.123823i	−0.388918	−	0.921272i	$-0.627151\pi$
$587$	5.19615	−	3.00000i	0.214468	−	0.123823i	0.603386	+	0.797449i	$0.293818\pi$
$588$	−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	$0.217085\pi$
$600$	4.96410	+	0.598076i	0.202659	+	0.0244164i
$601$	3.50000	+	6.06218i	0.142768	+	0.247281i	0.928538	−	0.371237i	$-0.121066\pi$
$601$	3.50000	+	6.06218i	0.142768	+	0.247281i	−0.785770	+	0.618519i	$0.787733\pi$
$602$		0			0
$603$		−	4.00000i		−	0.162893i
$604$	2.00000	−	3.46410i	0.0813788	−	0.140952i
$605$	4.46410	+	0.267949i	0.181492	+	0.0108937i
$606$	14.0000			0.568711
$607$	8.66025	+	5.00000i	0.351509	+	0.202944i	0.665350	−	0.746532i	$-0.268282\pi$
$607$	8.66025	+	5.00000i	0.351509	+	0.202944i	−0.313841	+	0.949476i	$0.601616\pi$
$608$		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	$-0.595362\pi$
$613$	9.52628	−	5.50000i	0.384763	−	0.222143i	0.679888	+	0.733316i	$0.262028\pi$
$614$	−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	$-0.516231\pi$
$617$	−23.3827	−	13.5000i	−0.941351	−	0.543490i	−0.890384	+	0.455211i	$0.849564\pi$
$618$	−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	$0.551399\pi$
$620$	2.23205	+	0.133975i	0.0896413	+	0.00538055i
$621$	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	−0.993491	−	0.113913i	$-0.963661\pi$
$631$	−10.0000	+	17.3205i	−0.398094	+	0.689519i	0.595397	+	0.803432i	$0.296995\pi$
$632$			1.00000i			0.0397779i
$633$	−8.66025	−	5.00000i	−0.344214	−	0.198732i
$634$	−12.0000	−	20.7846i	−0.476581	−	0.825462i
$635$	−11.1962	−	7.39230i	−0.444306	−	0.293355i
$636$	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
$640$	−1.86603	−	1.23205i	−0.0737611	−	0.0487011i
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	−0.722862	−	0.690992i	$-0.757174\pi$
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	0.959848	+	0.280521i	$0.0905072\pi$
$642$		−	4.00000i		−	0.157867i
$643$	6.92820	+	4.00000i	0.273222	+	0.157745i	0.630351	−	0.776310i	$-0.282911\pi$
$643$	6.92820	+	4.00000i	0.273222	+	0.157745i	−0.357129	+	0.934055i	$0.616244\pi$
$644$		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	$-0.616402\pi$
$647$	6.92820	−	4.00000i	0.272376	−	0.157256i	0.629967	+	0.776622i	$0.283068\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	33.0000			1.29536
$650$	2.89230	+	17.7942i	0.113446	+	0.697947i
$651$		0			0
$652$	12.9904	−	7.50000i	0.508743	−	0.293723i
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	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	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$	−5.59808	−	3.69615i	−0.217905	−	0.143873i
$661$	17.0000	+	29.4449i	0.661223	+	1.14527i	0.980294	+	0.197542i	$0.0632958\pi$
$661$	17.0000	+	29.4449i	0.661223	+	1.14527i	−0.319071	+	0.947731i	$0.603371\pi$
$662$		−	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
$670$	8.92820	+	0.535898i	0.344927	+	0.0207036i
$671$		0			0
$672$		0			0
$673$	−22.5167	+	13.0000i	−0.867953	+	0.501113i	−0.866668	−	0.498886i	$-0.833743\pi$
$673$	−22.5167	+	13.0000i	−0.867953	+	0.501113i	−0.00128586	+	0.999999i	$0.500409\pi$
$674$	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
$680$	13.3923	+	0.803848i	0.513571	+	0.0308261i
$681$	−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	$-0.485185\pi$
$683$	−20.7846	−	12.0000i	−0.795301	−	0.459167i	−0.841825	+	0.539750i	$0.818519\pi$
$684$		0			0
$685$	−1.74167	+	29.0167i	−0.0665458	+	1.10867i
$686$		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	−0.983904	−	0.178700i	$-0.942811\pi$
$691$	−17.0000	−	29.4449i	−0.646710	−	1.12014i	0.337193	−	0.941435i	$-0.390522\pi$
$692$	−10.3923	+	6.00000i	−0.395056	+	0.228086i
$693$		0			0
$694$	10.0000			0.379595
$695$	17.8564	+	1.07180i	0.677332	+	0.0406556i
$696$	−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
$705$	−13.5526	+	20.5263i	−0.510419	+	0.773064i
$706$	−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	−0.675791	−	0.737093i	$-0.736198\pi$
$709$	8.00000	−	13.8564i	0.300446	−	0.520388i	0.976237	+	0.216705i	$0.0695310\pi$
$710$	−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
$715$	7.20577	−	23.0885i	0.269481	−	0.863459i
$716$	−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	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$	−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
$725$	34.7487	+	4.18653i	1.29053	+	0.155484i
$726$	−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
$735$	0.937822	−	15.6244i	0.0345921	−	0.576313i
$736$	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	0.913361	+	0.407150i	$0.133477\pi$
$739$	22.0000	+	38.1051i	0.809283	+	1.40172i	−0.104078	+	0.994569i	$0.533189\pi$
$740$	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	$-0.904123\pi$
$743$	−32.0429	+	18.5000i	−1.17554	+	0.678699i	−0.220563	+	0.975373i	$0.570789\pi$
$744$	−0.500000	−	0.866025i	−0.0183309	−	0.0317500i
$745$	−33.4808	−	2.00962i	−1.22664	−	0.0736267i
$746$	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
$750$	−7.23205	+	8.52628i	−0.264077	+	0.311336i
$751$	9.50000	+	16.4545i	0.346660	+	0.600433i	0.985654	−	0.168779i	$-0.0539825\pi$
$751$	9.50000	+	16.4545i	0.346660	+	0.600433i	−0.638994	+	0.769212i	$0.720649\pi$
$752$	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	$-0.909305\pi$
$757$	−32.9090	+	19.0000i	−1.19610	+	0.690567i	−0.236414	+	0.971652i	$0.575972\pi$
$758$	−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	0.00800331	−	0.999968i	$-0.497452\pi$
$761$	24.0000	−	41.5692i	0.869999	−	1.50688i	0.861996	−	0.506915i	$-0.169214\pi$
$762$			6.00000i			0.217357i
$763$		0			0
$764$	−13.0000	−	22.5167i	−0.470323	−	0.814624i
$765$	11.1962	+	7.39230i	0.404798	+	0.267269i
$766$	−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	0.773410	−	0.633906i	$-0.218550\pi$
$769$	−4.50000	−	7.79423i	−0.162274	−	0.281067i	−0.935684	+	0.352839i	$0.885216\pi$
$770$		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	$-0.664889\pi$
$773$	−41.5692	−	24.0000i	−1.49514	−	0.863220i	−0.999984	+	0.00558380i	$0.998223\pi$
$774$	−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
$780$	5.92820	−	5.46410i	0.212264	−	0.195646i
$781$	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	$-0.577973\pi$
$787$	−33.7750	−	19.5000i	−1.20395	−	0.695100i	−0.961431	+	0.275047i	$0.911307\pi$
$788$		−	26.0000i		−	0.926212i
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$	−1.86603	−	1.23205i	−0.0663902	−	0.0438344i
$791$		0			0
$792$			3.00000i			0.106600i
$793$		0			0
$794$	27.0000			0.958194
$795$	−7.39230	+	11.1962i	−0.262178	+	0.397087i
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	−5.19615	−	3.00000i	−0.184057	−	0.106265i	0.405140	−	0.914255i	$-0.367223\pi$
$797$	−5.19615	−	3.00000i	−0.184057	−	0.106265i	−0.589197	+	0.807989i	$0.700556\pi$
$798$		0			0
$799$	−33.0000	+	57.1577i	−1.16746	+	2.02209i
$800$	4.59808	−	1.96410i	0.162567	−	0.0694415i
$801$	−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	0.996125	−	0.0879478i	$-0.0280309\pi$
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	−0.574228	+	0.818696i	$0.694698\pi$
$810$	0.133975	−	2.23205i	0.00470739	−	0.0784263i
$811$	−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
$815$	−2.00962	+	33.4808i	−0.0703939	+	1.17278i
$816$	−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	0.905566	+	0.424205i	$0.139447\pi$
$821$	23.5000	+	40.7032i	0.820156	+	1.42055i	−0.0854103	+	0.996346i	$0.527220\pi$
$822$	11.2583	−	6.50000i	0.392679	−	0.226714i
$823$	−36.3731	−	21.0000i	−1.26789	−	0.732014i	−0.293298	−	0.956021i	$-0.594753\pi$
$823$	−36.3731	−	21.0000i	−1.26789	−	0.732014i	−0.974588	+	0.224007i	$0.928086\pi$
$824$	−14.0000			−0.487713
$825$	13.7942	−	5.89230i	0.480253	−	0.205144i
$826$		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	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	0.121560	−	0.992584i	$-0.461210\pi$
$830$	4.92820	−	7.46410i	0.171060	−	0.259083i
$831$	−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
$835$	9.33013	+	6.16025i	0.322882	+	0.213184i
$836$		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	−0.970435	−	0.241363i	$-0.922405\pi$
$839$	−8.00000	+	13.8564i	−0.276191	+	0.478376i	0.694244	+	0.719740i	$0.255739\pi$
$840$		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
$845$	24.8564	+	15.0718i	0.855086	+	0.518486i
$846$	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	$0.599351\pi$
$860$	−24.2583	−	16.0167i	−0.827202	−	0.546164i
$861$		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
$865$	1.60770	−	26.7846i	0.0546633	−	0.910704i
$866$	−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	$-0.0232055\pi$
$877$	42.4352	+	24.5000i	1.43294	+	0.827306i	0.435593	+	0.900144i	$0.356539\pi$
$878$	13.8564	+	8.00000i	0.467631	+	0.269987i
$879$	28.0000			0.944417
$880$	−6.69615	−	0.401924i	−0.225727	−	0.0135488i
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	0.811054	−	0.584971i	$-0.198894\pi$
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	−0.912127	+	0.409908i	$0.865561\pi$
$882$	−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	$-0.661323\pi$
$887$	0.866025	−	0.500000i	0.0290783	−	0.0167884i	0.514469	+	0.857509i	$0.327989\pi$
$888$	−0.866025	−	0.500000i	−0.0290619	−	0.0167789i
$889$		0			0
$890$	0.535898	−	8.92820i	0.0179634	−	0.299274i
$891$	−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
$895$	11.0885	−	16.7942i	0.370646	−	0.561369i
$896$		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
$900$	4.96410	+	0.598076i	0.165470	+	0.0199359i
$901$	−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	$-0.618926\pi$
$907$	7.79423	−	4.50000i	0.258803	−	0.149420i	0.623788	+	0.781593i	$0.285593\pi$
$908$	−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	−0.993208	−	0.116348i	$-0.962881\pi$
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	0.597365	+	0.801970i	$0.296214\pi$
$920$	−11.0885	+	16.7942i	−0.365576	+	0.553689i
$921$	−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
$925$	−0.598076	+	4.96410i	−0.0196646	+	0.163219i
$926$	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	0.283178	+	0.959067i	$0.408611\pi$
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	−0.972166	+	0.234294i	$0.924722\pi$
$930$	2.23205	+	0.133975i	0.0731918	+	0.00439320i
$931$		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
$940$	−1.47372	+	24.5526i	−0.0480675	+	0.800816i
$941$	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	$-0.441472\pi$
$947$	34.6410	−	20.0000i	1.12568	−	0.649913i	0.942845	+	0.333231i	$0.108139\pi$
$948$			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	$-0.276318\pi$
$953$	9.52628	+	5.50000i	0.308586	+	0.178162i	−0.337707	+	0.941251i	$0.609651\pi$
$954$	6.00000			0.194257
$955$	58.0333	+	3.48334i	1.87791	+	0.112718i
$956$	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
$960$	−1.86603	−	1.23205i	−0.0602257	−	0.0397643i
$961$	−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
$965$	−29.8564	−	19.7128i	−0.961112	−	0.634578i
$966$		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	0.0601548	+	0.998189i	$0.480841\pi$
$971$	−26.0000	+	45.0333i	−0.834380	+	1.44519i	−0.894534	+	0.446999i	$0.852493\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$		0			0
$974$		0			0
$975$	2.89230	+	17.7942i	0.0926279	+	0.569871i
$976$		0			0
$977$	14.7224	−	8.50000i	0.471012	−	0.271939i	−0.245651	−	0.969358i	$-0.579002\pi$
$977$	14.7224	−	8.50000i	0.471012	−	0.271939i	0.716663	+	0.697419i	$0.245668\pi$
$978$	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
$985$	48.5167	+	32.0333i	1.54587	+	1.02067i
$986$	−21.0000	−	36.3731i	−0.668776	−	1.15835i
$987$		0			0
$988$		0			0
$989$	117.000			3.72038
$990$	−5.59808	−	3.69615i	−0.177919	−	0.117471i
$991$	−5.50000	−	9.52628i	−0.174713	−	0.302612i	0.765349	−	0.643616i	$-0.222567\pi$
$991$	−5.50000	−	9.52628i	−0.174713	−	0.302612i	−0.940062	+	0.341004i	$0.889233\pi$
$992$	−0.866025	−	0.500000i	−0.0274963	−	0.0158750i
$993$		−	2.00000i		−	0.0634681i
$994$		0			0
$995$	−17.8564	−	1.07180i	−0.566086	−	0.0339782i
$996$	−4.00000			−0.126745
$997$	39.8372	+	23.0000i	1.26166	+	0.728417i	0.973395	−	0.229135i	$-0.0735896\pi$
$997$	39.8372	+	23.0000i	1.26166	+	0.728417i	0.288261	+	0.957552i	$0.406923\pi$
$998$	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.289.2	yes	4
3.2	odd	2		1170.2.bp.c.289.1		4
5.2	odd	4		1950.2.i.p.601.1		2
5.3	odd	4		1950.2.i.l.601.1		2
5.4	even	2	inner	390.2.y.d.289.1	yes	4
13.9	even	3	inner	390.2.y.d.139.1	✓	4
15.14	odd	2		1170.2.bp.c.289.2		4
39.35	odd	6		1170.2.bp.c.919.2		4
65.9	even	6	inner	390.2.y.d.139.2	yes	4
65.22	odd	12		1950.2.i.p.451.1		2
65.48	odd	12		1950.2.i.l.451.1		2
195.74	odd	6		1170.2.bp.c.919.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.d.139.1	✓	4	13.9	even	3	inner
390.2.y.d.139.2	yes	4	65.9	even	6	inner
390.2.y.d.289.1	yes	4	5.4	even	2	inner
390.2.y.d.289.2	yes	4	1.1	even	1	trivial
1170.2.bp.c.289.1		4	3.2	odd	2
1170.2.bp.c.289.2		4	15.14	odd	2
1170.2.bp.c.919.1		4	195.74	odd	6
1170.2.bp.c.919.2		4	39.35	odd	6
1950.2.i.l.451.1		2	65.48	odd	12
1950.2.i.l.601.1		2	5.3	odd	4
1950.2.i.p.451.1		2	65.22	odd	12
1950.2.i.p.601.1		2	5.2	odd	4

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} +(1.86603 + 1.23205i) q^{10} +(-1.50000 - 2.59808i) q^{11} -1.00000i q^{12} +(3.46410 - 1.00000i) q^{13} +(1.86603 + 1.23205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(5.19615 + 3.00000i) q^{17} -1.00000i q^{18} +(2.23205 + 0.133975i) 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} +(2.23205 + 0.133975i) 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} +(2.23205 + 0.133975i) q^{45} +(-4.50000 + 7.79423i) q^{46} +11.0000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(-0.598076 + 4.96410i) q^{50} +6.00000 q^{51} +(0.866025 - 3.50000i) q^{52} +6.00000i q^{53} +(-0.500000 - 0.866025i) q^{54} +(3.69615 - 5.59808i) 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} +(5.46410 + 5.92820i) 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} +(-0.598076 + 4.96410i) q^{75} +(0.866025 - 3.50000i) q^{78} -1.00000 q^{79} +(1.23205 - 1.86603i) q^{80} +(-0.500000 - 0.866025i) q^{81} -4.00000i q^{83} +(-0.803848 + 13.3923i) 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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