LMFDB - Embedded newform 2151.1.f.b.1672.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2151,1,Mod(238,2151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2151, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2151.238");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2151 = 3^{2} \cdot 239 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2151.f (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:	$1.07348884217$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{45})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 $ x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{45}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{45} - \cdots)$

Embedding invariants

Embedding label			1672.5
Root			$0.990268 + 0.139173i$ of defining polynomial
Character	$\chi$	$=$	2151.1672
Dual form			2151.1.f.b.238.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438371 + 0.759281i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.115661 + 0.200332i) q^{4} +(0.241922 + 0.419021i) q^{5} +(-0.709299 + 0.515336i) q^{6} -1.07955 q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.438371 + 0.759281i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.115661 + 0.200332i) q^{4} +(0.241922 + 0.419021i) q^{5} +(-0.709299 + 0.515336i) q^{6} -1.07955 q^{8} +(0.669131 + 0.743145i) q^{9} -0.424206 q^{10} +(-0.848048 + 1.46886i) q^{11} +(0.0241798 + 0.230056i) q^{12} +(0.0505754 + 0.481193i) q^{15} +(0.357583 - 0.619353i) q^{16} +0.347296 q^{17} +(-0.857583 + 0.182285i) q^{18} +(-0.0559621 + 0.0969292i) q^{20} +(-0.743520 - 1.28781i) q^{22} +(-0.986221 - 0.439094i) q^{24} +(0.382948 - 0.663285i) q^{25} +(0.309017 + 0.951057i) q^{27} +(0.374607 - 0.648838i) q^{29} +(-0.387532 - 0.172540i) q^{30} +(-0.559193 - 0.968551i) q^{31} +(-0.226268 - 0.391908i) q^{32} +(-1.37217 + 0.996940i) q^{33} +(-0.152245 + 0.263696i) q^{34} +(-0.0714827 + 0.220001i) q^{36} +(-0.261167 - 0.452355i) q^{40} -0.392346 q^{44} +(-0.149516 + 0.460163i) q^{45} +(0.578582 - 0.420364i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.335746 + 0.581530i) q^{50} +(0.317271 + 0.141258i) q^{51} +(-0.857583 - 0.182285i) q^{54} -0.820646 q^{55} +(0.328433 + 0.568863i) q^{58} +(-0.0905486 + 0.0657874i) q^{60} +(-0.173648 + 0.300767i) q^{61} +0.980536 q^{62} +1.11192 q^{64} +(-0.155438 - 1.47889i) q^{66} +(0.939693 + 1.62760i) q^{67} +(0.0401688 + 0.0695744i) q^{68} +0.618034 q^{71} +(-0.722362 - 0.802264i) q^{72} +(0.619622 - 0.450182i) q^{75} +0.346029 q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.990268 + 1.71519i) q^{83} +(0.0840186 + 0.145524i) q^{85} +(0.606126 - 0.440376i) q^{87} +(0.915513 - 1.58571i) q^{88} +(-0.283849 - 0.315247i) q^{90} +(-0.116903 - 1.11226i) q^{93} +(-0.0473029 - 0.450057i) q^{96} +0.876742 q^{98} +(-1.65903 + 0.352638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 12 q^{4} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 12 * q^4 + 6 * q^8 + 3 * q^9	$ 24 q + 3 q^{3} - 12 q^{4} + 6 q^{8} + 3 q^{9} + 6 q^{10} + 3 q^{12} - 12 q^{16} - 3 q^{20} - 3 q^{22} - 3 q^{24} - 12 q^{25} - 6 q^{27} - 3 q^{30} - 3 q^{32} + 6 q^{34} - 6 q^{36} - 3 q^{40} + 6 q^{44} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 12 q^{55} - 3 q^{58} - 9 q^{60} - 24 q^{62} + 30 q^{64} + 27 q^{66} - 3 q^{68} - 12 q^{71} - 18 q^{72} - 6 q^{75} + 54 q^{80} + 3 q^{81} - 3 q^{85} - 3 q^{88} - 18 q^{90} - 3 q^{96}+O(q^{100}) $ 24 * q + 3 * q^3 - 12 * q^4 + 6 * q^8 + 3 * q^9 + 6 * q^10 + 3 * q^12 - 12 * q^16 - 3 * q^20 - 3 * q^22 - 3 * q^24 - 12 * q^25 - 6 * q^27 - 3 * q^30 - 3 * q^32 + 6 * q^34 - 6 * q^36 - 3 * q^40 + 6 * q^44 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 12 * q^55 - 3 * q^58 - 9 * q^60 - 24 * q^62 + 30 * q^64 + 27 * q^66 - 3 * q^68 - 12 * q^71 - 18 * q^72 - 6 * q^75 + 54 * q^80 + 3 * q^81 - 3 * q^85 - 3 * q^88 - 18 * q^90 - 3 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2151\mathbb{Z}\right)^\times$.

$n$	$479$	$1441$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.438371	+	0.759281i	−0.438371	+	0.759281i	−0.997564	−	0.0697565i	$-0.977778\pi$
$2$	−0.438371	+	0.759281i	−0.438371	+	0.759281i	0.559193	+	0.829038i	$0.311111\pi$
$3$	0.913545	+	0.406737i	0.913545	+	0.406737i
$3$	0.913545	+	0.406737i	0.913545	+	0.406737i
$4$	0.115661	+	0.200332i	0.115661	+	0.200332i
$5$	0.241922	+	0.419021i	0.241922	+	0.419021i	0.961262	−	0.275637i	$-0.0888889\pi$
$5$	0.241922	+	0.419021i	0.241922	+	0.419021i	−0.719340	+	0.694658i	$0.755556\pi$
$6$	−0.709299	+	0.515336i	−0.709299	+	0.515336i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$	−1.07955			−1.07955
$9$	0.669131	+	0.743145i	0.669131	+	0.743145i
$10$	−0.424206			−0.424206
$11$	−0.848048	+	1.46886i	−0.848048	+	1.46886i	0.0348995	+	0.999391i	$0.488889\pi$
$11$	−0.848048	+	1.46886i	−0.848048	+	1.46886i	−0.882948	+	0.469472i	$0.844444\pi$
$12$	0.0241798	+	0.230056i	0.0241798	+	0.230056i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$		0			0
$15$	0.0505754	+	0.481193i	0.0505754	+	0.481193i
$16$	0.357583	−	0.619353i	0.357583	−	0.619353i
$17$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$17$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$18$	−0.857583	+	0.182285i	−0.857583	+	0.182285i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−0.0559621	+	0.0969292i	−0.0559621	+	0.0969292i
$21$		0			0
$22$	−0.743520	−	1.28781i	−0.743520	−	1.28781i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−0.986221	−	0.439094i	−0.986221	−	0.439094i
$25$	0.382948	−	0.663285i	0.382948	−	0.663285i
$26$		0			0
$27$	0.309017	+	0.951057i	0.309017	+	0.951057i
$28$		0			0
$29$	0.374607	−	0.648838i	0.374607	−	0.648838i	−0.615661	−	0.788011i	$-0.711111\pi$
$29$	0.374607	−	0.648838i	0.374607	−	0.648838i	0.990268	+	0.139173i	$0.0444444\pi$
$30$	−0.387532	−	0.172540i	−0.387532	−	0.172540i
$31$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	−0.997564	−	0.0697565i	$-0.977778\pi$
$31$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	0.438371	−	0.898794i	$-0.355556\pi$
$32$	−0.226268	−	0.391908i	−0.226268	−	0.391908i
$33$	−1.37217	+	0.996940i	−1.37217	+	0.996940i
$34$	−0.152245	+	0.263696i	−0.152245	+	0.263696i
$35$		0			0
$36$	−0.0714827	+	0.220001i	−0.0714827	+	0.220001i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$	−0.261167	−	0.452355i	−0.261167	−	0.452355i
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$		0			0
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	−0.392346			−0.392346
$45$	−0.149516	+	0.460163i	−0.149516	+	0.460163i
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	0.578582	−	0.420364i	0.578582	−	0.420364i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	0.335746	+	0.581530i	0.335746	+	0.581530i
$51$	0.317271	+	0.141258i	0.317271	+	0.141258i
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−0.857583	−	0.182285i	−0.857583	−	0.182285i
$55$	−0.820646			−0.820646
$56$		0			0
$57$		0			0
$58$	0.328433	+	0.568863i	0.328433	+	0.568863i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$	−0.0905486	+	0.0657874i	−0.0905486	+	0.0657874i
$61$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$61$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$62$	0.980536			0.980536
$63$		0			0
$64$	1.11192			1.11192
$65$		0			0
$66$	−0.155438	−	1.47889i	−0.155438	−	1.47889i
$67$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$67$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$68$	0.0401688	+	0.0695744i	0.0401688	+	0.0695744i
$69$		0			0
$70$		0			0
$71$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$71$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$72$	−0.722362	−	0.802264i	−0.722362	−	0.802264i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	0.619622	−	0.450182i	0.619622	−	0.450182i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	0.346029			0.346029
$81$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$82$		0			0
$83$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.374607	+	0.927184i	$0.622222\pi$
$83$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.615661	+	0.788011i	$0.711111\pi$
$84$		0			0
$85$	0.0840186	+	0.145524i	0.0840186	+	0.145524i
$86$		0			0
$87$	0.606126	−	0.440376i	0.606126	−	0.440376i
$88$	0.915513	−	1.58571i	0.915513	−	1.58571i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−0.283849	−	0.315247i	−0.283849	−	0.315247i
$91$		0			0
$92$		0			0
$93$	−0.116903	−	1.11226i	−0.116903	−	1.11226i
$94$		0			0
$95$		0			0
$96$	−0.0473029	−	0.450057i	−0.0473029	−	0.450057i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	0.876742			0.876742
$99$	−1.65903	+	0.352638i	−1.65903	+	0.352638i
$100$	0.177169			0.177169
$101$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$101$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$102$	−0.246337	+	0.178974i	−0.246337	+	0.178974i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	−0.154785	+	0.171906i	−0.154785	+	0.171906i
$109$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$109$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$110$	0.359747	−	0.623101i	0.359747	−	0.623101i
$111$		0			0
$112$		0			0
$113$	0.104528	+	0.181049i	0.104528	+	0.181049i	0.913545	−	0.406737i	$-0.133333\pi$
$113$	0.104528	+	0.181049i	0.104528	+	0.181049i	−0.809017	+	0.587785i	$0.800000\pi$
$114$		0			0
$115$		0			0
$116$	0.173310			0.173310
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.0545989	−	0.519474i	−0.0545989	−	0.519474i
$121$	−0.938371	−	1.62531i	−0.938371	−	1.62531i
$122$	−0.152245	−	0.263696i	−0.152245	−	0.263696i
$123$		0			0
$124$	0.129354	−	0.224048i	0.129354	−	0.224048i
$125$	0.854417			0.854417
$126$		0			0
$127$	0.0697990			0.0697990			0.0348995	−	0.999391i	$-0.488889\pi$
$127$	0.0697990			0.0697990			0.0348995	+	0.999391i	$0.488889\pi$
$128$	−0.261167	+	0.452355i	−0.261167	+	0.452355i
$129$		0			0
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$	−0.358426	−	0.159581i	−0.358426	−	0.159581i
$133$		0			0
$134$	−1.64774			−1.64774
$135$	−0.323755	+	0.359566i	−0.323755	+	0.359566i
$136$	−0.374925			−0.374925
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$		0			0
$141$		0			0
$142$	−0.270928	+	0.469262i	−0.270928	+	0.469262i
$143$		0			0
$144$	0.699539	−	0.148692i	0.699539	−	0.148692i
$145$	0.362502			0.362502
$146$		0			0
$147$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	0.0701901	+	0.667814i	0.0701901	+	0.667814i
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$		0			0
$153$	0.232387	+	0.258091i	0.232387	+	0.258091i
$154$		0			0
$155$	0.270562	−	0.468627i	0.270562	−	0.468627i
$156$		0			0
$157$	0.374607	+	0.648838i	0.374607	+	0.648838i	0.990268	−	0.139173i	$-0.0444444\pi$
$157$	0.374607	+	0.648838i	0.374607	+	0.648838i	−0.615661	+	0.788011i	$0.711111\pi$
$158$		0			0
$159$		0			0
$160$	0.109478	−	0.189622i	0.109478	−	0.189622i
$161$		0			0
$162$	−0.709299	−	0.515336i	−0.709299	−	0.515336i
$163$	1.92252			1.92252			0.961262	−	0.275637i	$-0.0888889\pi$
$163$	1.92252			1.92252			0.961262	+	0.275637i	$0.0888889\pi$
$164$		0			0
$165$	−0.749697	−	0.333787i	−0.749697	−	0.333787i
$166$	−0.868210	−	1.50378i	−0.868210	−	1.50378i
$167$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$167$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$	−0.147325			−0.147325
$171$		0			0
$172$		0			0
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$	0.0686613	+	0.653269i	0.0686613	+	0.653269i
$175$		0			0
$176$	0.606496	+	1.05048i	0.606496	+	1.05048i
$177$		0			0
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−0.109478	+	0.0232703i	−0.109478	+	0.0232703i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	−0.280969	+	0.204136i	−0.280969	+	0.204136i
$184$		0			0
$185$		0			0
$186$	0.895764	+	0.398820i	0.895764	+	0.398820i
$187$	−0.294524	+	0.510131i	−0.294524	+	0.510131i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	1.01579	+	0.452260i	1.01579	+	0.452260i
$193$	−0.961262	−	1.66495i	−0.961262	−	1.66495i	−0.719340	−	0.694658i	$-0.755556\pi$
$193$	−0.961262	−	1.66495i	−0.961262	−	1.66495i	−0.241922	−	0.970296i	$-0.577778\pi$
$194$		0			0
$195$		0			0
$196$	0.115661	−	0.200332i	0.115661	−	0.200332i
$197$	−1.76590			−1.76590			−0.882948	−	0.469472i	$-0.844444\pi$
$197$	−1.76590			−1.76590			−0.882948	+	0.469472i	$0.844444\pi$
$198$	0.459520	−	1.41426i	0.459520	−	1.41426i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−0.413412	+	0.716051i	−0.413412	+	0.716051i
$201$	0.196449	+	1.86909i	0.196449	+	1.86909i
$202$	0.709299	+	1.22854i	0.709299	+	1.22854i
$203$		0			0
$204$	0.00839757	+	0.0798975i	0.00839757	+	0.0798975i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.990268	−	1.71519i	−0.990268	−	1.71519i	−0.615661	−	0.788011i	$-0.711111\pi$
$211$	−0.990268	−	1.71519i	−0.990268	−	1.71519i	−0.374607	−	0.927184i	$-0.622222\pi$
$212$		0			0
$213$	0.564602	+	0.251377i	0.564602	+	0.251377i
$214$		0			0
$215$		0			0
$216$	−0.333600	−	1.02672i	−0.333600	−	1.02672i
$217$		0			0
$218$	−0.586655	+	1.01612i	−0.586655	+	1.01612i
$219$		0			0
$220$	−0.0949171	−	0.164401i	−0.0949171	−	0.164401i
$221$		0			0
$222$		0			0
$223$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$223$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$224$		0			0
$225$	0.749159	−	0.159239i	0.749159	−	0.159239i
$226$	−0.183289			−0.183289
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$		0			0
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$		0			0
$232$	−0.404408	+	0.700455i	−0.404408	+	0.700455i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$239$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$240$	0.316113	+	0.140743i	0.316113	+	0.140743i
$241$	0.104528	−	0.181049i	0.104528	−	0.181049i	−0.809017	−	0.587785i	$-0.800000\pi$
$241$	0.104528	−	0.181049i	0.104528	−	0.181049i	0.913545	+	0.406737i	$0.133333\pi$
$242$	1.64542			1.64542
$243$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$244$	−0.0803376			−0.0803376
$245$	0.241922	−	0.419021i	0.241922	−	0.419021i
$246$		0			0
$247$		0			0
$248$	0.603678	+	1.04560i	0.603678	+	1.04560i
$249$	−1.60229	+	1.16413i	−1.60229	+	1.16413i
$250$	−0.374552	+	0.648743i	−0.374552	+	0.648743i
$251$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$251$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$252$		0			0
$253$		0			0
$254$	−0.0305979	+	0.0529971i	−0.0305979	+	0.0529971i
$255$	0.0175647	+	0.167117i	0.0175647	+	0.167117i
$256$	0.326986	+	0.566356i	0.326986	+	0.566356i
$257$	−0.0348995	−	0.0604477i	−0.0348995	−	0.0604477i	0.848048	−	0.529919i	$-0.177778\pi$
$257$	−0.0348995	−	0.0604477i	−0.0348995	−	0.0604477i	−0.882948	+	0.469472i	$0.844444\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.732841	−	0.155770i	0.732841	−	0.155770i
$262$		0			0
$263$	0.615661	−	1.06636i	0.615661	−	1.06636i	−0.374607	−	0.927184i	$-0.622222\pi$
$263$	0.615661	−	1.06636i	0.615661	−	1.06636i	0.990268	−	0.139173i	$-0.0444444\pi$
$264$	1.48133	−	1.07625i	1.48133	−	1.07625i
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.217372	+	0.376500i	−0.217372	+	0.376500i
$269$	1.11839			1.11839			0.559193	−	0.829038i	$-0.311111\pi$
$269$	1.11839			1.11839			0.559193	+	0.829038i	$0.311111\pi$
$270$	−0.131087	−	0.403444i	−0.131087	−	0.403444i
$271$	1.69610			1.69610			0.848048	−	0.529919i	$-0.177778\pi$
$271$	1.69610			1.69610			0.848048	+	0.529919i	$0.177778\pi$
$272$	0.124187	−	0.215099i	0.124187	−	0.215099i
$273$		0			0
$274$		0			0
$275$	0.649516	+	1.12499i	0.649516	+	1.12499i
$276$		0			0
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$	0.345600	−	1.06365i	0.345600	−	1.06365i
$280$		0			0
$281$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$281$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$	−0.438371	−	0.759281i	−0.438371	−	0.759281i	0.559193	−	0.829038i	$-0.311111\pi$
$283$	−0.438371	−	0.759281i	−0.438371	−	0.759281i	−0.997564	+	0.0697565i	$0.977778\pi$
$284$	0.0714827	+	0.123812i	0.0714827	+	0.123812i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.139841	−	0.430387i	0.139841	−	0.430387i
$289$	−0.879385			−0.879385
$290$	−0.158910	+	0.275241i	−0.158910	+	0.275241i
$291$		0			0
$292$		0			0
$293$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$293$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$294$	0.800944	+	0.356603i	0.800944	+	0.356603i
$295$		0			0
$296$		0			0
$297$	−1.65903	−	0.352638i	−1.65903	−	0.352638i
$298$		0			0
$299$		0			0
$300$	0.161852	+	0.0720612i	0.161852	+	0.0720612i
$301$		0			0
$302$		0			0
$303$	1.30902	−	0.951057i	1.30902	−	0.951057i
$304$		0			0
$305$	−0.168037			−0.168037
$306$	−0.297836	+	0.0633069i	−0.297836	+	0.0633069i
$307$	−0.483844			−0.483844			−0.241922	−	0.970296i	$-0.577778\pi$
$307$	−0.483844			−0.483844			−0.241922	+	0.970296i	$0.577778\pi$
$308$		0			0
$309$		0			0
$310$	0.237213	+	0.410865i	0.237213	+	0.410865i
$311$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$311$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	−0.656867			−0.656867
$315$		0			0
$316$		0			0
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$	0.635369	+	1.10049i	0.635369	+	1.10049i
$320$	0.268999	+	0.465920i	0.268999	+	0.465920i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.211324	+	0.0940875i	−0.211324	+	0.0940875i
$325$		0			0
$326$	−0.842779	+	1.45974i	−0.842779	+	1.45974i
$327$	1.22256	+	0.544320i	1.22256	+	0.544320i
$328$		0			0
$329$		0			0
$330$	0.582083	−	0.422908i	0.582083	−	0.422908i
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−0.458143			−0.458143
$333$		0			0
$334$		0			0
$335$	−0.454664	+	0.787502i	−0.454664	+	0.787502i
$336$		0			0
$337$	0.241922	+	0.419021i	0.241922	+	0.419021i	0.961262	−	0.275637i	$-0.0888889\pi$
$337$	0.241922	+	0.419021i	0.241922	+	0.419021i	−0.719340	+	0.694658i	$0.755556\pi$
$338$	−0.438371	−	0.759281i	−0.438371	−	0.759281i
$339$	0.0218524	+	0.207912i	0.0218524	+	0.207912i
$340$	−0.0194354	+	0.0336632i	−0.0194354	+	0.0336632i
$341$	1.89689			1.89689
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	−0.997564	−	0.0697565i	$-0.977778\pi$
$347$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	0.438371	−	0.898794i	$-0.355556\pi$
$348$	0.158327	+	0.0704916i	0.158327	+	0.0704916i
$349$	−0.0348995	+	0.0604477i	−0.0348995	+	0.0604477i	−0.882948	−	0.469472i	$-0.844444\pi$
$349$	−0.0348995	+	0.0604477i	−0.0348995	+	0.0604477i	0.848048	+	0.529919i	$0.177778\pi$
$350$		0			0
$351$		0			0
$352$	0.767545			0.767545
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$	0.149516	+	0.258969i	0.149516	+	0.258969i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$359$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$360$	0.161410	−	0.496770i	0.161410	−	0.496770i
$361$	1.00000			1.00000
$362$		0			0
$363$	−0.196173	−	1.86646i	−0.196173	−	1.86646i
$364$		0			0
$365$		0			0
$366$	−0.0318278	−	0.302821i	−0.0318278	−	0.302821i
$367$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.374607	+	0.927184i	$0.622222\pi$
$367$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.615661	+	0.788011i	$0.711111\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.209299	−	0.152065i	0.209299	−	0.152065i
$373$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$373$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$374$	−0.258222	−	0.447253i	−0.258222	−	0.447253i
$375$	0.780549	+	0.347523i	0.780549	+	0.347523i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.0637646	+	0.0283898i	0.0637646	+	0.0283898i
$382$		0			0
$383$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$383$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$384$	−0.422578	+	0.307021i	−0.422578	+	0.307021i
$385$		0			0
$386$	1.68556			1.68556
$387$		0			0
$388$		0			0
$389$	0.997564	−	1.72783i	0.997564	−	1.72783i	0.438371	−	0.898794i	$-0.355556\pi$
$389$	0.997564	−	1.72783i	0.997564	−	1.72783i	0.559193	−	0.829038i	$-0.311111\pi$
$390$		0			0
$391$		0			0
$392$	0.539776	+	0.934920i	0.539776	+	0.934920i
$393$		0			0
$394$	0.774117	−	1.34081i	0.774117	−	1.34081i
$395$		0			0
$396$	−0.262531	−	0.291570i	−0.262531	−	0.291570i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	−0.273871	−	0.474359i	−0.273871	−	0.474359i
$401$	−0.990268	−	1.71519i	−0.990268	−	1.71519i	−0.615661	−	0.788011i	$-0.711111\pi$
$401$	−0.990268	−	1.71519i	−0.990268	−	1.71519i	−0.374607	−	0.927184i	$-0.622222\pi$
$402$	−1.50528	−	0.670195i	−1.50528	−	0.670195i
$403$		0			0
$404$	0.374288			0.374288
$405$	−0.442013	+	0.196797i	−0.442013	+	0.196797i
$406$		0			0
$407$		0			0
$408$	−0.342511	−	0.152496i	−0.342511	−	0.152496i
$409$	0.719340	+	1.24593i	0.719340	+	1.24593i	0.961262	+	0.275637i	$0.0888889\pi$
$409$	0.719340	+	1.24593i	0.719340	+	1.24593i	−0.241922	+	0.970296i	$0.577778\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.958270			−0.958270
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.615661	+	1.06636i	0.615661	+	1.06636i	0.990268	+	0.139173i	$0.0444444\pi$
$419$	0.615661	+	1.06636i	0.615661	+	1.06636i	−0.374607	+	0.927184i	$0.622222\pi$
$420$		0			0
$421$	0.104528	−	0.181049i	0.104528	−	0.181049i	−0.809017	−	0.587785i	$-0.800000\pi$
$421$	0.104528	−	0.181049i	0.104528	−	0.181049i	0.913545	+	0.406737i	$0.133333\pi$
$422$	1.73642			1.73642
$423$		0			0
$424$		0			0
$425$	0.132996	−	0.230356i	0.132996	−	0.230356i
$426$	−0.438371	+	0.318495i	−0.438371	+	0.318495i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.92252			1.92252			0.961262	−	0.275637i	$-0.0888889\pi$
$431$	1.92252			1.92252			0.961262	+	0.275637i	$0.0888889\pi$
$432$	0.699539	+	0.148692i	0.699539	+	0.148692i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$	0.331162	+	0.147443i	0.331162	+	0.147443i
$436$	0.154785	+	0.268096i	0.154785	+	0.268096i
$437$		0			0
$438$		0			0
$439$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.104528	+	0.994522i	$0.533333\pi$
$439$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.809017	+	0.587785i	$0.800000\pi$
$440$	0.885930			0.885930
$441$	0.309017	−	0.951057i	0.309017	−	0.951057i
$442$		0			0
$443$	0.719340	−	1.24593i	0.719340	−	1.24593i	−0.241922	−	0.970296i	$-0.577778\pi$
$443$	0.719340	−	1.24593i	0.719340	−	1.24593i	0.961262	−	0.275637i	$-0.0888889\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−0.207503	+	0.638628i	−0.207503	+	0.638628i
$451$		0			0
$452$	−0.0241798	+	0.0418807i	−0.0241798	+	0.0418807i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$457$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$458$		0			0
$459$	0.107320	+	0.330298i	0.107320	+	0.330298i
$460$		0			0
$461$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$461$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$	−0.267906	−	0.464027i	−0.267906	−	0.464027i
$465$	0.437779	−	0.318065i	0.437779	−	0.318065i
$466$		0			0
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.0783141	+	0.745109i	0.0783141	+	0.745109i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.876742			0.876742
$479$	0.997564	−	1.72783i	0.997564	−	1.72783i	0.438371	−	0.898794i	$-0.355556\pi$
$479$	0.997564	−	1.72783i	0.997564	−	1.72783i	0.559193	−	0.829038i	$-0.311111\pi$
$480$	0.177140	−	0.128700i	0.177140	−	0.128700i
$481$		0			0
$482$	0.0916445	+	0.158733i	0.0916445	+	0.158733i
$483$		0			0
$484$	0.217067	−	0.375971i	0.217067	−	0.375971i
$485$		0			0
$486$	−0.438371	−	0.759281i	−0.438371	−	0.759281i
$487$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$487$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$488$	0.187462	−	0.324694i	0.187462	−	0.324694i
$489$	1.75631	+	0.781961i	1.75631	+	0.781961i
$490$	0.212103	+	0.367373i	0.212103	+	0.367373i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$	0.130100	−	0.225339i	0.130100	−	0.225339i
$494$		0			0
$495$	−0.549119	−	0.609859i	−0.549119	−	0.609859i
$496$	−0.799832			−0.799832
$497$		0			0
$498$	−0.181505	−	1.72691i	−0.181505	−	1.72691i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	0.0988232	+	0.171167i	0.0988232	+	0.171167i
$501$		0			0
$502$	−0.671624	+	1.16329i	−0.671624	+	1.16329i
$503$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$503$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$504$		0			0
$505$	0.782876			0.782876
$506$		0			0
$507$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$508$	0.00807305	+	0.0139829i	0.00807305	+	0.0139829i
$509$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$509$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$510$	−0.134588	−	0.0599226i	−0.134588	−	0.0599226i
$511$		0			0
$512$	−1.09570			−1.09570
$513$		0			0
$514$	0.0611957			0.0611957
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.202983	+	0.624718i	−0.202983	+	0.624718i
$523$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$523$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$524$		0			0
$525$		0			0
$526$	0.539776	+	0.934920i	0.539776	+	0.934920i
$527$	−0.194206	−	0.336374i	−0.194206	−	0.336374i
$528$	0.126792	+	1.20635i	0.126792	+	1.20635i
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−1.01445	−	1.75708i	−1.01445	−	1.75708i
$537$		0			0
$538$	−0.490268	+	0.849169i	−0.490268	+	0.849169i
$539$	1.69610			1.69610
$540$	−0.109478	−	0.0232703i	−0.109478	−	0.0232703i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$	−0.743520	+	1.28781i	−0.743520	+	1.28781i
$543$		0			0
$544$	−0.0785820	−	0.136108i	−0.0785820	−	0.136108i
$545$	0.323755	+	0.560760i	0.323755	+	0.560760i
$546$		0			0
$547$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$547$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$548$		0			0
$549$	−0.339707	+	0.0722070i	−0.339707	+	0.0722070i
$550$	−1.13892			−1.13892
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$	0.656107	+	0.728680i	0.656107	+	0.728680i
$559$		0			0
$560$		0			0
$561$	−0.476550	+	0.346234i	−0.476550	+	0.346234i
$562$		0			0
$563$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$563$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$564$		0			0
$565$	−0.0505754	+	0.0875992i	−0.0505754	+	0.0875992i
$566$	0.768677			0.768677
$567$		0			0
$568$	−0.667200			−0.667200
$569$	−0.559193	+	0.968551i	−0.559193	+	0.968551i	0.438371	+	0.898794i	$0.355556\pi$
$569$	−0.559193	+	0.968551i	−0.559193	+	0.968551i	−0.997564	+	0.0697565i	$0.977778\pi$
$570$		0			0
$571$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.669131	+	0.743145i	$0.266667\pi$
$571$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.309017	+	0.951057i	$0.400000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.744022	+	0.826321i	0.744022	+	0.826321i
$577$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$577$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$578$	0.385497	−	0.667701i	0.385497	−	0.667701i
$579$	−0.200958	−	1.91199i	−0.200958	−	1.91199i
$580$	0.0419275	+	0.0726206i	0.0419275	+	0.0726206i
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	0.541857			0.541857
$587$	−0.961262	+	1.66495i	−0.961262	+	1.66495i	−0.241922	+	0.970296i	$0.577778\pi$
$587$	−0.961262	+	1.66495i	−0.961262	+	1.66495i	−0.719340	+	0.694658i	$0.755556\pi$
$588$	0.187144	−	0.135968i	0.187144	−	0.135968i
$589$		0			0
$590$		0			0
$591$	−1.61323	−	0.718254i	−1.61323	−	0.718254i
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	0.995023	−	1.10509i	0.995023	−	1.10509i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.809017	−	0.587785i	$-0.800000\pi$
$599$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$600$	−0.668915	+	0.485995i	−0.668915	+	0.485995i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$	−0.580762	+	1.78740i	−0.580762	+	1.78740i
$604$		0			0
$605$	0.454025	−	0.786394i	0.454025	−	0.786394i
$606$	0.148284	+	1.41083i	0.148284	+	1.41083i
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$		0			0
$609$		0			0
$610$	0.0736627	−	0.127587i	0.0736627	−	0.127587i
$611$		0			0
$612$	−0.0248257	+	0.0764056i	−0.0248257	+	0.0764056i
$613$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$613$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$614$	0.212103	−	0.367373i	0.212103	−	0.367373i
$615$		0			0
$616$		0			0
$617$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$617$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$	0.125174			0.125174
$621$		0			0
$622$	1.34325			1.34325
$623$		0			0
$624$		0			0
$625$	−0.176245	−	0.305266i	−0.176245	−	0.305266i
$626$		0			0
$627$		0			0
$628$	−0.0866551	+	0.150091i	−0.0866551	+	0.150091i
$629$		0			0
$630$		0			0
$631$	−0.483844			−0.483844			−0.241922	−	0.970296i	$-0.577778\pi$
$631$	−0.483844			−0.483844			−0.241922	+	0.970296i	$0.577778\pi$
$632$		0			0
$633$	−0.207022	−	1.96969i	−0.207022	−	1.96969i
$634$		0			0
$635$	0.0168859	+	0.0292472i	0.0168859	+	0.0292472i
$636$		0			0
$637$		0			0
$638$	−1.11411			−1.11411
$639$	0.413545	+	0.459289i	0.413545	+	0.459289i
$640$	−0.252729			−0.252729
$641$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.0348995	−	0.999391i	$-0.488889\pi$
$641$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.848048	−	0.529919i	$-0.177778\pi$
$642$		0			0
$643$	−0.0348995	−	0.0604477i	−0.0348995	−	0.0604477i	0.848048	−	0.529919i	$-0.177778\pi$
$643$	−0.0348995	−	0.0604477i	−0.0348995	−	0.0604477i	−0.882948	+	0.469472i	$0.844444\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.99513			−1.99513			−0.997564	−	0.0697565i	$-0.977778\pi$
$647$	−1.99513			−1.99513			−0.997564	+	0.0697565i	$0.977778\pi$
$648$	0.112844	−	1.07364i	0.112844	−	1.07364i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.222362	+	0.385142i	0.222362	+	0.385142i
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	−0.949228	+	0.689654i	−0.949228	+	0.689654i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$659$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$660$	−0.0198431	−	0.188794i	−0.0198431	−	0.188794i
$661$	−0.848048	−	1.46886i	−0.848048	−	1.46886i	−0.882948	−	0.469472i	$-0.844444\pi$
$661$	−0.848048	−	1.46886i	−0.848048	−	1.46886i	0.0348995	−	0.999391i	$-0.488889\pi$
$662$		0			0
$663$		0			0
$664$	1.06905	−	1.85164i	1.06905	−	1.85164i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	−0.398624	−	0.690436i	−0.398624	−	0.690436i
$671$	−0.294524	−	0.510131i	−0.294524	−	0.510131i
$672$		0			0
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$	−0.424206			−0.424206
$675$	0.749159	+	0.159239i	0.749159	+	0.159239i
$676$	−0.231323			−0.231323
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	−0.167443	−	0.0745504i	−0.167443	−	0.0745504i
$679$		0			0
$680$	−0.0907025	−	0.157101i	−0.0907025	−	0.157101i
$681$		0			0
$682$	−0.831542	+	1.44027i	−0.831542	+	1.44027i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$691$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$692$		0			0
$693$		0			0
$694$	0.980536			0.980536
$695$		0			0
$696$	−0.654345	+	0.475410i	−0.654345	+	0.475410i
$697$		0			0
$698$	−0.0305979	−	0.0529971i	−0.0305979	−	0.0529971i
$699$		0			0
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$	−0.942965	+	1.63326i	−0.942965	+	1.63326i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$	−0.262174			−0.262174
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$718$	0.709299	−	1.22854i	0.709299	−	1.22854i
$719$	−1.43868			−1.43868			−0.719340	−	0.694658i	$-0.755556\pi$
$719$	−1.43868			−1.43868			−0.719340	+	0.694658i	$0.755556\pi$
$720$	0.231539	+	0.257150i	0.231539	+	0.257150i
$721$		0			0
$722$	−0.438371	+	0.759281i	−0.438371	+	0.759281i
$723$	0.169131	−	0.122881i	0.169131	−	0.122881i
$724$		0			0
$725$	−0.286909	−	0.496942i	−0.286909	−	0.496942i
$726$	1.50317	+	0.669252i	1.50317	+	0.669252i
$727$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.104528	+	0.994522i	$0.533333\pi$
$727$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.809017	+	0.587785i	$0.800000\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$730$		0			0
$731$		0			0
$732$	−0.0733921	−	0.0326763i	−0.0733921	−	0.0326763i
$733$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	−0.997564	−	0.0697565i	$-0.977778\pi$
$733$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	0.438371	−	0.898794i	$-0.355556\pi$
$734$	−0.868210	−	1.50378i	−0.868210	−	1.50378i
$735$	0.391438	−	0.284396i	0.391438	−	0.284396i
$736$		0			0
$737$	−3.18762			−3.18762
$738$		0			0
$739$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$739$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$743$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$744$	0.126203	+	1.20074i	0.126203	+	1.20074i
$745$		0			0
$746$	0.541857			0.541857
$747$	−1.93726	+	0.411777i	−1.93726	+	0.411777i
$748$	−0.136260			−0.136260
$749$		0			0
$750$	−0.606038	+	0.440312i	−0.606038	+	0.440312i
$751$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$751$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	0.309017	−	0.951057i	$-0.400000\pi$
$752$		0			0
$753$	1.39963	+	0.623157i	1.39963	+	0.623157i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.876742			0.876742			0.438371	−	0.898794i	$-0.355556\pi$
$757$	0.876742			0.876742			0.438371	+	0.898794i	$0.355556\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$761$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	0.309017	−	0.951057i	$-0.400000\pi$
$762$	−0.0495084	+	0.0359699i	−0.0495084	+	0.0359699i
$763$		0			0
$764$		0			0
$765$	−0.0519263	+	0.159813i	−0.0519263	+	0.159813i
$766$	−0.876742			−0.876742
$767$		0			0
$768$	0.0683586	+	0.650388i	0.0683586	+	0.650388i
$769$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$769$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$770$		0			0
$771$	−0.00729598	−	0.0694166i	−0.00729598	−	0.0694166i
$772$	0.222362	−	0.385142i	0.222362	−	0.385142i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$	−0.856566			−0.856566
$776$		0			0
$777$		0			0
$778$	0.874607	+	1.51486i	0.874607	+	1.51486i
$779$		0			0
$780$		0			0
$781$	−0.524123	+	0.907807i	−0.524123	+	0.907807i
$782$		0			0
$783$	0.732841	+	0.155770i	0.732841	+	0.155770i
$784$	−0.715167			−0.715167
$785$	−0.181251	+	0.313936i	−0.181251	+	0.313936i
$786$		0			0
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$	−0.204246	−	0.353765i	−0.204246	−	0.353765i
$789$	0.996161	−	0.723753i	0.996161	−	0.723753i
$790$		0			0
$791$		0			0
$792$	1.79101	−	0.380692i	1.79101	−	0.380692i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.997564	+	1.72783i	0.997564	+	1.72783i	0.559193	+	0.829038i	$0.311111\pi$
$797$	0.997564	+	1.72783i	0.997564	+	1.72783i	0.438371	+	0.898794i	$0.355556\pi$
$798$		0			0
$799$		0			0
$800$	−0.346595			−0.346595
$801$		0			0
$802$	1.73642			1.73642
$803$		0			0
$804$	−0.351716	+	0.255537i	−0.351716	+	0.255537i
$805$		0			0
$806$		0			0
$807$	1.02170	+	0.454888i	1.02170	+	0.454888i
$808$	−0.873377	+	1.51273i	−0.873377	+	1.51273i
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$	0.0443416	−	0.421882i	0.0443416	−	0.421882i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	1.54946	+	0.689864i	1.54946	+	0.689864i
$814$		0			0
$815$	0.465101	+	0.805578i	0.465101	+	0.805578i
$816$	0.200939	−	0.145991i	0.200939	−	0.145991i
$817$		0			0
$818$	−1.26135			−1.26135
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	0.135786	+	1.29192i	0.135786	+	1.29192i
$826$		0			0
$827$	−0.749213			−0.749213			−0.374607	−	0.927184i	$-0.622222\pi$
$827$	−0.749213			−0.749213			−0.374607	+	0.927184i	$0.622222\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$	0.420078	−	0.727596i	0.420078	−	0.727596i
$831$		0			0
$832$		0			0
$833$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.748346	−	0.831123i	0.748346	−	0.831123i
$838$	−1.07955			−1.07955
$839$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.0348995	−	0.999391i	$-0.488889\pi$
$839$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.848048	−	0.529919i	$-0.177778\pi$
$840$		0			0
$841$	0.219340	+	0.379908i	0.219340	+	0.379908i
$842$	0.0916445	+	0.158733i	0.0916445	+	0.158733i
$843$		0			0
$844$	0.229072	−	0.396764i	0.229072	−	0.396764i
$845$	−0.483844			−0.483844
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.0916445	−	0.871939i	−0.0916445	−	0.871939i
$850$	0.116603	+	0.201963i	0.116603	+	0.201963i
$851$		0			0
$852$	0.0149440	+	0.142182i	0.0149440	+	0.142182i
$853$	0.719340	−	1.24593i	0.719340	−	1.24593i	−0.241922	−	0.970296i	$-0.577778\pi$
$853$	0.719340	−	1.24593i	0.719340	−	1.24593i	0.961262	−	0.275637i	$-0.0888889\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	0.882948	+	1.52931i	0.882948	+	1.52931i	0.848048	+	0.529919i	$0.177778\pi$
$859$	0.882948	+	1.52931i	0.882948	+	1.52931i	0.0348995	+	0.999391i	$0.488889\pi$
$860$		0			0
$861$		0			0
$862$	−0.842779	+	1.45974i	−0.842779	+	1.45974i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	0.302806	−	0.336300i	0.302806	−	0.336300i
$865$		0			0
$866$		0			0
$867$	−0.803358	−	0.357678i	−0.803358	−	0.357678i
$868$		0			0
$869$		0			0
$870$	−0.257123	+	0.186810i	−0.257123	+	0.186810i
$871$		0			0
$872$	−1.44472			−1.44472
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.990268	−	1.71519i	−0.990268	−	1.71519i	−0.615661	−	0.788011i	$-0.711111\pi$
$877$	−0.990268	−	1.71519i	−0.990268	−	1.71519i	−0.374607	−	0.927184i	$-0.622222\pi$
$878$	−0.800944	−	1.38728i	−0.800944	−	1.38728i
$879$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$880$	−0.293449	+	0.508269i	−0.293449	+	0.508269i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	0.586655	+	0.651546i	0.586655	+	0.651546i
$883$	−1.99513			−1.99513			−0.997564	−	0.0697565i	$-0.977778\pi$
$883$	−1.99513			−1.99513			−0.997564	+	0.0697565i	$0.977778\pi$
$884$		0			0
$885$		0			0
$886$	0.630676	+	1.09236i	0.630676	+	1.09236i
$887$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.669131	+	0.743145i	$0.266667\pi$
$887$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.309017	+	0.951057i	$0.400000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.37217	−	0.996940i	−1.37217	−	0.996940i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.837909			−0.837909
$900$	0.118549	+	0.131662i	0.118549	+	0.131662i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.112844	−	0.195452i	−0.112844	−	0.195452i
$905$		0			0
$906$		0			0
$907$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$907$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$908$		0			0
$909$	1.58268	−	0.336408i	1.58268	−	0.336408i
$910$		0			0
$911$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$911$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$912$		0			0
$913$	−1.67959	−	2.90914i	−1.67959	−	2.90914i
$914$	−0.270928	−	0.469262i	−0.270928	−	0.469262i
$915$	−0.153510	−	0.0683469i	−0.153510	−	0.0683469i
$916$		0			0
$917$		0			0
$918$	−0.297836	−	0.0633069i	−0.297836	−	0.0633069i
$919$	1.92252			1.92252			0.961262	−	0.275637i	$-0.0888889\pi$
$919$	1.92252			1.92252			0.961262	+	0.275637i	$0.0888889\pi$
$920$		0			0
$921$	−0.442013	−	0.196797i	−0.442013	−	0.196797i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$	−0.339046			−0.339046
$929$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$929$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$930$	0.0495911	+	0.471827i	0.0495911	+	0.471827i
$931$		0			0
$932$		0			0
$933$	−0.160147	−	1.52370i	−0.160147	−	1.52370i
$934$		0			0
$935$	−0.285007			−0.285007
$936$		0			0
$937$	−1.99513			−1.99513			−0.997564	−	0.0697565i	$-0.977778\pi$
$937$	−1.99513			−1.99513			−0.997564	+	0.0697565i	$0.977778\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$941$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$942$	−0.600078	−	0.267172i	−0.600078	−	0.267172i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$	0.115661	−	0.200332i	0.115661	−	0.200332i
$957$	0.132828	+	1.26378i	0.132828	+	1.26378i
$958$	0.874607	+	1.51486i	0.874607	+	1.51486i
$959$		0			0
$960$	0.0562361	+	0.535050i	0.0562361	+	0.535050i
$961$	−0.125393	+	0.217188i	−0.125393	+	0.217188i
$962$		0			0
$963$		0			0
$964$	0.0483597			0.0483597
$965$	0.465101	−	0.805578i	0.465101	−	0.805578i
$966$		0			0
$967$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.669131	+	0.743145i	$0.266667\pi$
$967$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.309017	+	0.951057i	$0.400000\pi$
$968$	1.01302	+	1.75460i	1.01302	+	1.75460i
$969$		0			0
$970$		0			0
$971$	−1.43868			−1.43868			−0.719340	−	0.694658i	$-0.755556\pi$
$971$	−1.43868			−1.43868			−0.719340	+	0.694658i	$0.755556\pi$
$972$	−0.231323			−0.231323
$973$		0			0
$974$	−0.671624	+	1.16329i	−0.671624	+	1.16329i
$975$		0			0
$976$	0.124187	+	0.215099i	0.124187	+	0.215099i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$	−1.36364	+	0.990746i	−1.36364	+	0.990746i
$979$		0			0
$980$	0.111924			0.111924
$981$	0.895472	+	0.994522i	0.895472	+	0.994522i
$982$		0			0
$983$	−0.0348995	+	0.0604477i	−0.0348995	+	0.0604477i	−0.882948	−	0.469472i	$-0.844444\pi$
$983$	−0.0348995	+	0.0604477i	−0.0348995	+	0.0604477i	0.848048	+	0.529919i	$0.177778\pi$
$984$		0			0
$985$	−0.427209	−	0.739947i	−0.427209	−	0.739947i
$986$	0.114064	+	0.197564i	0.114064	+	0.197564i
$987$		0			0
$988$		0			0
$989$		0			0
$990$	0.703772	−	0.149591i	0.703772	−	0.149591i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	−0.253055	+	0.438304i	−0.253055	+	0.438304i
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.418535	−	0.186344i	−0.418535	−	0.186344i
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2151.1.f.b.1672.5	yes	24
9.4	even	3	inner	2151.1.f.b.238.5	✓	24
239.238	odd	2	CM	2151.1.f.b.1672.5	yes	24
2151.238	odd	6	inner	2151.1.f.b.238.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2151.1.f.b.238.5	✓	24	9.4	even	3	inner
2151.1.f.b.238.5	✓	24	2151.238	odd	6	inner
2151.1.f.b.1672.5	yes	24	1.1	even	1	trivial
2151.1.f.b.1672.5	yes	24	239.238	odd	2	CM

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:	\( N \)	\(=\)	\( 2151 = 3^{2} \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2151.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.438371 + 0.759281i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.115661 + 0.200332i) q^{4} +(0.241922 + 0.419021i) q^{5} +(-0.709299 + 0.515336i) q^{6} -1.07955 q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.438371 + 0.759281i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.115661 + 0.200332i) q^{4} +(0.241922 + 0.419021i) q^{5} +(-0.709299 + 0.515336i) q^{6} -1.07955 q^{8} +(0.669131 + 0.743145i) q^{9} -0.424206 q^{10} +(-0.848048 + 1.46886i) q^{11} +(0.0241798 + 0.230056i) q^{12} +(0.0505754 + 0.481193i) q^{15} +(0.357583 - 0.619353i) q^{16} +0.347296 q^{17} +(-0.857583 + 0.182285i) q^{18} +(-0.0559621 + 0.0969292i) q^{20} +(-0.743520 - 1.28781i) q^{22} +(-0.986221 - 0.439094i) q^{24} +(0.382948 - 0.663285i) q^{25} +(0.309017 + 0.951057i) q^{27} +(0.374607 - 0.648838i) q^{29} +(-0.387532 - 0.172540i) q^{30} +(-0.559193 - 0.968551i) q^{31} +(-0.226268 - 0.391908i) q^{32} +(-1.37217 + 0.996940i) q^{33} +(-0.152245 + 0.263696i) q^{34} +(-0.0714827 + 0.220001i) q^{36} +(-0.261167 - 0.452355i) q^{40} -0.392346 q^{44} +(-0.149516 + 0.460163i) q^{45} +(0.578582 - 0.420364i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.335746 + 0.581530i) q^{50} +(0.317271 + 0.141258i) q^{51} +(-0.857583 - 0.182285i) q^{54} -0.820646 q^{55} +(0.328433 + 0.568863i) q^{58} +(-0.0905486 + 0.0657874i) q^{60} +(-0.173648 + 0.300767i) q^{61} +0.980536 q^{62} +1.11192 q^{64} +(-0.155438 - 1.47889i) q^{66} +(0.939693 + 1.62760i) q^{67} +(0.0401688 + 0.0695744i) q^{68} +0.618034 q^{71} +(-0.722362 - 0.802264i) q^{72} +(0.619622 - 0.450182i) q^{75} +0.346029 q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.990268 + 1.71519i) q^{83} +(0.0840186 + 0.145524i) q^{85} +(0.606126 - 0.440376i) q^{87} +(0.915513 - 1.58571i) q^{88} +(-0.283849 - 0.315247i) q^{90} +(-0.116903 - 1.11226i) q^{93} +(-0.0473029 - 0.450057i) q^{96} +0.876742 q^{98} +(-1.65903 + 0.352638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 12 q^{4} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 12 * q^4 + 6 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 12 q^{4} + 6 q^{8} + 3 q^{9} + 6 q^{10} + 3 q^{12} - 12 q^{16} - 3 q^{20} - 3 q^{22} - 3 q^{24} - 12 q^{25} - 6 q^{27} - 3 q^{30} - 3 q^{32} + 6 q^{34} - 6 q^{36} - 3 q^{40} + 6 q^{44} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 12 q^{55} - 3 q^{58} - 9 q^{60} - 24 q^{62} + 30 q^{64} + 27 q^{66} - 3 q^{68} - 12 q^{71} - 18 q^{72} - 6 q^{75} + 54 q^{80} + 3 q^{81} - 3 q^{85} - 3 q^{88} - 18 q^{90} - 3 q^{96}+O(q^{100}) \) 24 * q + 3 * q^3 - 12 * q^4 + 6 * q^8 + 3 * q^9 + 6 * q^10 + 3 * q^12 - 12 * q^16 - 3 * q^20 - 3 * q^22 - 3 * q^24 - 12 * q^25 - 6 * q^27 - 3 * q^30 - 3 * q^32 + 6 * q^34 - 6 * q^36 - 3 * q^40 + 6 * q^44 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 12 * q^55 - 3 * q^58 - 9 * q^60 - 24 * q^62 + 30 * q^64 + 27 * q^66 - 3 * q^68 - 12 * q^71 - 18 * q^72 - 6 * q^75 + 54 * q^80 + 3 * q^81 - 3 * q^85 - 3 * q^88 - 18 * q^90 - 3 * q^96

Introduction

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