LMFDB - Embedded newform 3267.1.bf.a.2581.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3267,1,Mod(40,3267)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3267, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([40, 63]))

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

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

chi := DirichletCharacter("3267.40");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3267 = 3^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3267.bf (of order $90$, degree $24$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.63044539627$
Analytic rank:	$0$
Dimension:	$24$
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:	no (minimal twist has level 297)
Projective image:	$D_{9}$
Projective field:	Galois closure of 9.1.459450093735369.1

Embedding invariants

Embedding label			2581.1
Root			$0.0348995 - 0.999391i$ of defining polynomial
Character	$\chi$	$=$	3267.2581
Dual form			3267.1.bf.a.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374607 - 0.927184i) q^{3} +(-0.882948 + 0.469472i) q^{4} +(0.333843 - 0.0957278i) q^{5} +(-0.719340 + 0.694658i) q^{9} +O(q^{10})$	$q+(-0.374607 - 0.927184i) q^{3} +(-0.882948 + 0.469472i) q^{4} +(0.333843 - 0.0957278i) q^{5} +(-0.719340 + 0.694658i) q^{9} +(0.766044 + 0.642788i) q^{12} +(-0.213817 - 0.273673i) q^{15} +(0.559193 - 0.829038i) q^{16} +(-0.249824 + 0.241252i) q^{20} +(-0.173648 - 0.984808i) q^{23} +(-0.745761 + 0.466003i) q^{25} +(0.913545 + 0.406737i) q^{27} +(0.671624 - 1.37703i) q^{31} +(0.309017 - 0.951057i) q^{36} +(0.232387 - 0.258091i) q^{37} +(-0.173648 + 0.300767i) q^{45} +(1.65940 + 0.882318i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(0.961262 - 0.275637i) q^{49} +(-1.23949 - 0.900539i) q^{53} +(0.0534691 - 1.53116i) q^{59} +(0.317271 + 0.141258i) q^{60} +(-0.104528 + 0.994522i) q^{64} +(1.17365 - 0.984808i) q^{67} +(-0.848048 + 0.529919i) q^{69} +(-1.71690 - 0.764415i) q^{71} +(0.711438 + 0.516890i) q^{75} +(0.107320 - 0.330298i) q^{80} +(0.0348995 - 0.999391i) q^{81} +(0.500000 - 0.866025i) q^{89} +(0.615661 + 0.788011i) q^{92} +(-1.52836 - 0.106873i) q^{93} +(-1.80658 - 0.518029i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5}+O(q^{10}) $ 24 * q + 3 * q^5	$ 24 q + 3 q^{5} + 3 q^{15} - 6 q^{20} + 3 q^{25} + 3 q^{27} + 3 q^{31} - 6 q^{36} + 3 q^{47} + 3 q^{48} + 3 q^{59} + 3 q^{64} + 24 q^{67} - 6 q^{75} + 12 q^{89} - 6 q^{93} - 6 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 + 3 * q^15 - 6 * q^20 + 3 * q^25 + 3 * q^27 + 3 * q^31 - 6 * q^36 + 3 * q^47 + 3 * q^48 + 3 * q^59 + 3 * q^64 + 24 * q^67 - 6 * q^75 + 12 * q^89 - 6 * q^93 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3267\mathbb{Z}\right)^\times$.

$n$	$244$	$3026$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{9}\right)$

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			0		−0.241922	−	0.970296i	$-0.577778\pi$
$2$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$3$	−0.374607	−	0.927184i	−0.374607	−	0.927184i
$3$	−0.374607	−	0.927184i	−0.374607	−	0.927184i
$4$	−0.882948	+	0.469472i	−0.882948	+	0.469472i
$5$	0.333843	−	0.0957278i	0.333843	−	0.0957278i	−0.104528	−	0.994522i	$-0.533333\pi$
$5$	0.333843	−	0.0957278i	0.333843	−	0.0957278i	0.438371	+	0.898794i	$0.355556\pi$
$6$		0			0
$7$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$7$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$8$		0			0
$9$	−0.719340	+	0.694658i	−0.719340	+	0.694658i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	0.766044	+	0.642788i	0.766044	+	0.642788i
$13$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$13$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$14$		0			0
$15$	−0.213817	−	0.273673i	−0.213817	−	0.273673i
$16$	0.559193	−	0.829038i	0.559193	−	0.829038i
$17$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$17$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$18$		0			0
$19$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$19$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$20$	−0.249824	+	0.241252i	−0.249824	+	0.241252i
$21$		0			0
$22$		0			0
$23$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$23$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$24$		0			0
$25$	−0.745761	+	0.466003i	−0.745761	+	0.466003i
$26$		0			0
$27$	0.913545	+	0.406737i	0.913545	+	0.406737i
$28$		0			0
$29$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$29$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$30$		0			0
$31$	0.671624	−	1.37703i	0.671624	−	1.37703i	−0.241922	−	0.970296i	$-0.577778\pi$
$31$	0.671624	−	1.37703i	0.671624	−	1.37703i	0.913545	−	0.406737i	$-0.133333\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.309017	−	0.951057i	0.309017	−	0.951057i
$37$	0.232387	−	0.258091i	0.232387	−	0.258091i	−0.615661	−	0.788011i	$-0.711111\pi$
$37$	0.232387	−	0.258091i	0.232387	−	0.258091i	0.848048	+	0.529919i	$0.177778\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$41$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$42$		0			0
$43$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$43$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$44$		0			0
$45$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$46$		0			0
$47$	1.65940	+	0.882318i	1.65940	+	0.882318i	0.990268	+	0.139173i	$0.0444444\pi$
$47$	1.65940	+	0.882318i	1.65940	+	0.882318i	0.669131	+	0.743145i	$0.266667\pi$
$48$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$49$	0.961262	−	0.275637i	0.961262	−	0.275637i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.23949	−	0.900539i	−1.23949	−	0.900539i	−0.241922	−	0.970296i	$-0.577778\pi$
$53$	−1.23949	−	0.900539i	−1.23949	−	0.900539i	−0.997564	+	0.0697565i	$0.977778\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.0534691	−	1.53116i	0.0534691	−	1.53116i	−0.615661	−	0.788011i	$-0.711111\pi$
$59$	0.0534691	−	1.53116i	0.0534691	−	1.53116i	0.669131	−	0.743145i	$-0.266667\pi$
$60$	0.317271	+	0.141258i	0.317271	+	0.141258i
$61$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$61$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$62$		0			0
$63$		0			0
$64$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$65$		0			0
$66$		0			0
$67$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$67$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$68$		0			0
$69$	−0.848048	+	0.529919i	−0.848048	+	0.529919i
$70$		0			0
$71$	−1.71690	−	0.764415i	−1.71690	−	0.764415i	−0.997564	−	0.0697565i	$-0.977778\pi$
$71$	−1.71690	−	0.764415i	−1.71690	−	0.764415i	−0.719340	−	0.694658i	$-0.755556\pi$
$72$		0			0
$73$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$73$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$74$		0			0
$75$	0.711438	+	0.516890i	0.711438	+	0.516890i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$79$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$80$	0.107320	−	0.330298i	0.107320	−	0.330298i
$81$	0.0348995	−	0.999391i	0.0348995	−	0.999391i
$82$		0			0
$83$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$83$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$89$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$90$		0			0
$91$		0			0
$92$	0.615661	+	0.788011i	0.615661	+	0.788011i
$93$	−1.52836	−	0.106873i	−1.52836	−	0.106873i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.80658	−	0.518029i	−1.80658	−	0.518029i	−0.809017	−	0.587785i	$-0.800000\pi$
$97$	−1.80658	−	0.518029i	−1.80658	−	0.518029i	−0.997564	+	0.0697565i	$0.977778\pi$
$98$		0			0
$99$		0			0
$100$	0.439693	−	0.761570i	0.439693	−	0.761570i
$101$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$101$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$102$		0			0
$103$	0.0121205	−	0.347085i	0.0121205	−	0.347085i	−0.978148	−	0.207912i	$-0.933333\pi$
$103$	0.0121205	−	0.347085i	0.0121205	−	0.347085i	0.990268	−	0.139173i	$-0.0444444\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$107$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$108$	−0.997564	+	0.0697565i	−0.997564	+	0.0697565i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$112$		0			0
$113$	1.15707	−	1.48098i	1.15707	−	1.48098i	0.309017	−	0.951057i	$-0.400000\pi$
$113$	1.15707	−	1.48098i	1.15707	−	1.48098i	0.848048	−	0.529919i	$-0.177778\pi$
$114$		0			0
$115$	−0.152245	−	0.312148i	−0.152245	−	0.312148i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$	0.0534691	+	1.53116i	0.0534691	+	1.53116i
$125$	−0.436744	+	0.485053i	−0.436744	+	0.485053i
$126$		0			0
$127$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$127$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$131$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.343916	+	0.0483343i	0.343916	+	0.0483343i
$136$		0			0
$137$	−1.52836	−	0.106873i	−1.52836	−	0.106873i	−0.719340	−	0.694658i	$-0.755556\pi$
$137$	−1.52836	−	0.106873i	−1.52836	−	0.106873i	−0.809017	+	0.587785i	$0.800000\pi$
$138$		0			0
$139$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$139$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$140$		0			0
$141$	0.196449	−	1.86909i	0.196449	−	1.86909i
$142$		0			0
$143$		0			0
$144$	0.173648	+	0.984808i	0.173648	+	0.984808i
$145$		0			0
$146$		0			0
$147$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$148$	−0.0840186	+	0.336980i	−0.0840186	+	0.336980i
$149$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$149$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$150$		0			0
$151$		0			0		−0.0348995	−	0.999391i	$-0.511111\pi$
$151$		0			0		0.0348995	+	0.999391i	$0.488889\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$156$		0			0
$157$	−0.943248	+	1.20730i	−0.943248	+	1.20730i	0.0348995	+	0.999391i	$0.488889\pi$
$157$	−0.943248	+	1.20730i	−0.943248	+	1.20730i	−0.978148	+	0.207912i	$0.933333\pi$
$158$		0			0
$159$	−0.370646	+	1.48658i	−0.370646	+	1.48658i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.52045	+	1.10467i	1.52045	+	1.10467i	0.961262	+	0.275637i	$0.0888889\pi$
$163$	1.52045	+	1.10467i	1.52045	+	1.10467i	0.559193	+	0.829038i	$0.311111\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$167$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$168$		0			0
$169$	0.990268	−	0.139173i	0.990268	−	0.139173i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.0348995	−	0.999391i	$-0.511111\pi$
$173$		0			0		0.0348995	+	0.999391i	$0.488889\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$178$		0			0
$179$	−1.49861	+	0.318539i	−1.49861	+	0.318539i	−0.882948	−	0.469472i	$-0.844444\pi$
$179$	−1.49861	+	0.318539i	−1.49861	+	0.318539i	−0.615661	+	0.788011i	$0.711111\pi$
$180$	0.0121205	−	0.347085i	0.0121205	−	0.347085i
$181$	−0.0363024	−	0.345394i	−0.0363024	−	0.345394i	−0.997564	−	0.0697565i	$-0.977778\pi$
$181$	−0.0363024	−	0.345394i	−0.0363024	−	0.345394i	0.961262	−	0.275637i	$-0.0888889\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.0528740	−	0.108408i	0.0528740	−	0.108408i
$186$		0			0
$187$		0			0
$188$	−1.87939			−1.87939
$189$		0			0
$190$		0			0
$191$	0.704030	−	1.74254i	0.704030	−	1.74254i	0.0348995	−	0.999391i	$-0.488889\pi$
$191$	0.704030	−	1.74254i	0.704030	−	1.74254i	0.669131	−	0.743145i	$-0.266667\pi$
$192$	0.961262	−	0.275637i	0.961262	−	0.275637i
$193$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$193$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$194$		0			0
$195$		0			0
$196$	−0.719340	+	0.694658i	−0.719340	+	0.694658i
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$		0			0
$199$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$199$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$200$		0			0
$201$	−1.35275	−	0.719272i	−1.35275	−	0.719272i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.809017	+	0.587785i	0.809017	+	0.587785i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$211$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$212$	1.51718	+	0.213226i	1.51718	+	0.213226i
$213$	−0.0655896	+	1.87824i	−0.0655896	+	1.87824i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.882948	+	0.469472i	0.882948	+	0.469472i	0.848048	−	0.529919i	$-0.177778\pi$
$223$	0.882948	+	0.469472i	0.882948	+	0.469472i	0.0348995	+	0.999391i	$0.488889\pi$
$224$		0			0
$225$	0.212743	−	0.853264i	0.212743	−	0.853264i
$226$		0			0
$227$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$227$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$228$		0			0
$229$	0.997564	−	0.0697565i	0.997564	−	0.0697565i	0.438371	−	0.898794i	$-0.355556\pi$
$229$	0.997564	−	0.0697565i	0.997564	−	0.0697565i	0.559193	+	0.829038i	$0.311111\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$233$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$234$		0			0
$235$	0.638441	+	0.135705i	0.638441	+	0.135705i
$236$	0.671624	+	1.37703i	0.671624	+	1.37703i
$237$		0			0
$238$		0			0
$239$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$239$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$240$	−0.346450	+	0.0242262i	−0.346450	+	0.0242262i
$241$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$241$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$242$		0			0
$243$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$244$		0			0
$245$	0.294524	−	0.184039i	0.294524	−	0.184039i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.82709	−	0.813473i	1.82709	−	0.813473i	0.913545	−	0.406737i	$-0.133333\pi$
$251$	1.82709	−	0.813473i	1.82709	−	0.813473i	0.913545	−	0.406737i	$-0.133333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.374607	−	0.927184i	−0.374607	−	0.927184i
$257$	−0.848048	−	0.529919i	−0.848048	−	0.529919i	0.0348995	−	0.999391i	$-0.488889\pi$
$257$	−0.848048	−	0.529919i	−0.848048	−	0.529919i	−0.882948	+	0.469472i	$0.844444\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$263$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$264$		0			0
$265$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$266$		0			0
$267$	−0.990268	−	0.139173i	−0.990268	−	0.139173i
$268$	−0.573931	+	1.42053i	−0.573931	+	1.42053i
$269$	1.52045	−	1.10467i	1.52045	−	1.10467i	0.559193	−	0.829038i	$-0.311111\pi$
$269$	1.52045	−	1.10467i	1.52045	−	1.10467i	0.961262	−	0.275637i	$-0.0888889\pi$
$270$		0			0
$271$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$271$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.500000	−	0.866025i	0.500000	−	0.866025i
$277$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$277$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$278$		0			0
$279$	0.473442	+	1.45710i	0.473442	+	1.45710i
$280$		0			0
$281$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$281$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$282$		0			0
$283$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$283$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$284$	1.87481	−	0.131099i	1.87481	−	0.131099i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.669131	+	0.743145i	0.669131	+	0.743145i
$290$		0			0
$291$	0.196449	+	1.86909i	0.196449	+	1.86909i
$292$		0			0
$293$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$293$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$294$		0			0
$295$	−0.128724	−	0.516284i	−0.128724	−	0.516284i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.870827	−	0.122387i	−0.870827	−	0.122387i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$307$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$308$		0			0
$309$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$310$		0			0
$311$	−0.573931	−	1.42053i	−0.573931	−	1.42053i	−0.882948	−	0.469472i	$-0.844444\pi$
$311$	−0.573931	−	1.42053i	−0.573931	−	1.42053i	0.309017	−	0.951057i	$-0.400000\pi$
$312$		0			0
$313$	−0.559193	+	0.829038i	−0.559193	+	0.829038i	−0.997564	−	0.0697565i	$-0.977778\pi$
$313$	−0.559193	+	0.829038i	−0.559193	+	0.829038i	0.438371	+	0.898794i	$0.355556\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.43868	+	1.38932i	−1.43868	+	1.38932i	−0.719340	+	0.694658i	$0.755556\pi$
$317$	−1.43868	+	1.38932i	−1.43868	+	1.38932i	−0.719340	+	0.694658i	$0.755556\pi$
$318$		0			0
$319$		0			0
$320$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.438371	+	0.898794i	0.438371	+	0.898794i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$331$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$	0.0121205	+	0.347085i	0.0121205	+	0.347085i
$334$		0			0
$335$	0.297540	−	0.441122i	0.297540	−	0.441122i
$336$		0			0
$337$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$337$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$338$		0			0
$339$	−1.80658	−	0.518029i	−1.80658	−	0.518029i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.232387	+	0.258091i	−0.232387	+	0.258091i
$346$		0			0
$347$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$347$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$348$		0			0
$349$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$349$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$353$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$354$		0			0
$355$	−0.646352	−	0.0908388i	−0.646352	−	0.0908388i
$356$	−0.0348995	+	0.999391i	−0.0348995	+	0.999391i
$357$		0			0
$358$		0			0
$359$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$359$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$360$		0			0
$361$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.15707	+	1.48098i	1.15707	+	1.48098i	0.848048	+	0.529919i	$0.177778\pi$
$367$	1.15707	+	1.48098i	1.15707	+	1.48098i	0.309017	+	0.951057i	$0.400000\pi$
$368$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	1.39963	−	0.623157i	1.39963	−	0.623157i
$373$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$373$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$374$		0			0
$375$	0.613341	+	0.223238i	0.613341	+	0.223238i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$379$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.856733	+	1.27016i	0.856733	+	1.27016i	0.961262	+	0.275637i	$0.0888889\pi$
$383$	0.856733	+	1.27016i	0.856733	+	1.27016i	−0.104528	+	0.994522i	$0.533333\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	1.83832	−	0.390746i	1.83832	−	0.390746i
$389$	1.15707	+	1.48098i	1.15707	+	1.48098i	0.848048	+	0.529919i	$0.177778\pi$
$389$	1.15707	+	1.48098i	1.15707	+	1.48098i	0.309017	+	0.951057i	$0.400000\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$397$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$398$		0			0
$399$		0			0
$400$	−0.0306901	+	0.878850i	−0.0306901	+	0.878850i
$401$	−0.249824	−	0.241252i	−0.249824	−	0.241252i	0.559193	−	0.829038i	$-0.311111\pi$
$401$	−0.249824	−	0.241252i	−0.249824	−	0.241252i	−0.809017	+	0.587785i	$0.800000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.0840186	−	0.336980i	−0.0840186	−	0.336980i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$409$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$410$		0			0
$411$	0.473442	+	1.45710i	0.473442	+	1.45710i
$412$	0.152245	+	0.312148i	0.152245	+	0.312148i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$419$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$420$		0			0
$421$	0.0121205	+	0.347085i	0.0121205	+	0.347085i	0.990268	+	0.139173i	$0.0444444\pi$
$421$	0.0121205	+	0.347085i	0.0121205	+	0.347085i	−0.978148	+	0.207912i	$0.933333\pi$
$422$		0			0
$423$	−1.80658	+	0.518029i	−1.80658	+	0.518029i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$431$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$432$	0.848048	−	0.529919i	0.848048	−	0.529919i
$433$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$433$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$439$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$440$		0			0
$441$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$442$		0			0
$443$	0.0121205	+	0.347085i	0.0121205	+	0.347085i	0.990268	+	0.139173i	$0.0444444\pi$
$443$	0.0121205	+	0.347085i	0.0121205	+	0.347085i	−0.978148	+	0.207912i	$0.933333\pi$
$444$	0.343916	−	0.0483343i	0.343916	−	0.0483343i
$445$	0.0840186	−	0.336980i	0.0840186	−	0.336980i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.0363024	+	0.345394i	−0.0363024	+	0.345394i	0.961262	+	0.275637i	$0.0888889\pi$
$449$	−0.0363024	+	0.345394i	−0.0363024	+	0.345394i	−0.997564	+	0.0697565i	$0.977778\pi$
$450$		0			0
$451$		0			0
$452$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$457$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$458$		0			0
$459$		0			0
$460$	0.280969	+	0.204136i	0.280969	+	0.204136i
$461$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$461$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$462$		0			0
$463$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$463$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$464$		0			0
$465$	−0.520461	+	0.110628i	−0.520461	+	0.110628i
$466$		0			0
$467$	0.196449	+	1.86909i	0.196449	+	1.86909i	0.438371	+	0.898794i	$0.355556\pi$
$467$	0.196449	+	1.86909i	0.196449	+	1.86909i	−0.241922	+	0.970296i	$0.577778\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.47274	+	0.422301i	1.47274	+	0.422301i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.51718	−	0.213226i	1.51718	−	0.213226i
$478$		0			0
$479$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$479$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.652704			−0.652704
$486$		0			0
$487$	0.107320	−	0.330298i	0.107320	−	0.330298i	−0.882948	−	0.469472i	$-0.844444\pi$
$487$	0.107320	−	0.330298i	0.107320	−	0.330298i	0.990268	+	0.139173i	$0.0444444\pi$
$488$		0			0
$489$	0.454664	−	1.82356i	0.454664	−	1.82356i
$490$		0			0
$491$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$491$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$497$		0			0
$498$		0			0
$499$	0.294524	+	0.184039i	0.294524	+	0.184039i	0.669131	−	0.743145i	$-0.266667\pi$
$499$	0.294524	+	0.184039i	0.294524	+	0.184039i	−0.374607	+	0.927184i	$0.622222\pi$
$500$	0.157903	−	0.633316i	0.157903	−	0.633316i
$501$		0			0
$502$		0			0
$503$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$503$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$508$		0			0
$509$	−0.990268	−	0.139173i	−0.990268	−	0.139173i	−0.374607	−	0.927184i	$-0.622222\pi$
$509$	−0.990268	−	0.139173i	−0.990268	−	0.139173i	−0.615661	+	0.788011i	$0.711111\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.0291794	−	0.117032i	−0.0291794	−	0.117032i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.339707	−	0.0722070i	−0.339707	−	0.0722070i	0.0348995	−	0.999391i	$-0.488889\pi$
$521$	−0.339707	−	0.0722070i	−0.339707	−	0.0722070i	−0.374607	+	0.927184i	$0.622222\pi$
$522$		0			0
$523$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$523$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$	1.02517	+	1.13856i	1.02517	+	1.13856i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.856733	+	1.27016i	0.856733	+	1.27016i
$538$		0			0
$539$		0			0
$540$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$541$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$541$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$542$		0			0
$543$	−0.306644	+	0.163046i	−0.306644	+	0.163046i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$547$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$548$	1.39963	−	0.623157i	1.39963	−	0.623157i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.120321	−	0.00841366i	−0.120321	−	0.00841366i
$556$		0			0
$557$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$557$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$563$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$564$	0.704030	+	1.74254i	0.704030	+	1.74254i
$565$	0.244507	−	0.605176i	0.244507	−	0.605176i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$569$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$570$		0			0
$571$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$571$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$572$		0			0
$573$	−1.87939			−1.87939
$574$		0			0
$575$	0.588424	+	0.653511i	0.588424	+	0.653511i
$576$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$577$	0.317271	+	0.141258i	0.317271	+	0.141258i	0.559193	−	0.829038i	$-0.311111\pi$
$577$	0.317271	+	0.141258i	0.317271	+	0.141258i	−0.241922	+	0.970296i	$0.577778\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.343916	−	0.0483343i	0.343916	−	0.0483343i	0.0348995	−	0.999391i	$-0.488889\pi$
$587$	0.343916	−	0.0483343i	0.343916	−	0.0483343i	0.309017	+	0.951057i	$0.400000\pi$
$588$	0.913545	+	0.406737i	0.913545	+	0.406737i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.0840186	−	0.336980i	−0.0840186	−	0.336980i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.15707	−	1.48098i	1.15707	−	1.48098i
$598$		0			0
$599$	−0.961262	+	0.275637i	−0.961262	+	0.275637i	−0.719340	−	0.694658i	$-0.755556\pi$
$599$	−0.961262	+	0.275637i	−0.961262	+	0.275637i	−0.241922	+	0.970296i	$0.577778\pi$
$600$		0			0
$601$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$601$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$602$		0			0
$603$	−0.160147	+	1.52370i	−0.160147	+	1.52370i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$607$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$613$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$617$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$618$		0			0
$619$	0.294524	−	0.184039i	0.294524	−	0.184039i	−0.374607	−	0.927184i	$-0.622222\pi$
$619$	0.294524	−	0.184039i	0.294524	−	0.184039i	0.669131	+	0.743145i	$0.266667\pi$
$620$	0.164425	+	0.506047i	0.164425	+	0.506047i
$621$	0.241922	−	0.970296i	0.241922	−	0.970296i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.286126	−	0.586646i	0.286126	−	0.586646i
$626$		0			0
$627$		0			0
$628$	0.266044	−	1.50881i	0.266044	−	1.50881i
$629$		0			0
$630$		0			0
$631$	1.02517	−	1.13856i	1.02517	−	1.13856i	0.0348995	−	0.999391i	$-0.488889\pi$
$631$	1.02517	−	1.13856i	1.02517	−	1.13856i	0.990268	−	0.139173i	$-0.0444444\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.370646	−	1.48658i	−0.370646	−	1.48658i
$637$		0			0
$638$		0			0
$639$	1.76604	−	0.642788i	1.76604	−	0.642788i
$640$		0			0
$641$	0.882948	+	0.469472i	0.882948	+	0.469472i	0.848048	−	0.529919i	$-0.177778\pi$
$641$	0.882948	+	0.469472i	0.882948	+	0.469472i	0.0348995	+	0.999391i	$0.488889\pi$
$642$		0			0
$643$	−0.961262	+	0.275637i	−0.961262	+	0.275637i	−0.719340	−	0.694658i	$-0.755556\pi$
$643$	−0.961262	+	0.275637i	−0.961262	+	0.275637i	−0.241922	+	0.970296i	$0.577778\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$647$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.86110	−	0.261560i	−1.86110	−	0.261560i
$653$	0.0121205	−	0.347085i	0.0121205	−	0.347085i	−0.978148	−	0.207912i	$-0.933333\pi$
$653$	0.0121205	−	0.347085i	0.0121205	−	0.347085i	0.990268	−	0.139173i	$-0.0444444\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$659$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$660$		0			0
$661$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$661$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	0.104528	−	0.994522i	0.104528	−	0.994522i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$673$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$674$		0			0
$675$	−0.870827	+	0.122387i	−0.870827	+	0.122387i
$676$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$677$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$677$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$683$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$684$		0			0
$685$	−0.520461	+	0.110628i	−0.520461	+	0.110628i
$686$		0			0
$687$	−0.438371	−	0.898794i	−0.438371	−	0.898794i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.333843	+	0.0957278i	0.333843	+	0.0957278i	0.438371	−	0.898794i	$-0.355556\pi$
$691$	0.333843	+	0.0957278i	0.333843	+	0.0957278i	−0.104528	+	0.994522i	$0.533333\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$701$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.113341	−	0.642788i	−0.113341	−	0.642788i
$706$		0			0
$707$		0			0
$708$	1.02517	−	1.13856i	1.02517	−	1.13856i
$709$	0.152245	+	0.312148i	0.152245	+	0.312148i	0.961262	−	0.275637i	$-0.0888889\pi$
$709$	0.152245	+	0.312148i	0.152245	+	0.312148i	−0.809017	+	0.587785i	$0.800000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.47274	−	0.422301i	−1.47274	−	0.422301i
$714$		0			0
$715$		0			0
$716$	1.17365	−	0.984808i	1.17365	−	0.984808i
$717$		0			0
$718$		0			0
$719$	−1.25755	+	1.39666i	−1.25755	+	1.39666i	−0.374607	+	0.927184i	$0.622222\pi$
$719$	−1.25755	+	1.39666i	−1.25755	+	1.39666i	−0.882948	+	0.469472i	$0.844444\pi$
$720$	0.152245	+	0.312148i	0.152245	+	0.312148i
$721$		0			0
$722$		0			0
$723$		0			0
$724$	0.194206	+	0.287922i	0.194206	+	0.287922i
$725$		0			0
$726$		0			0
$727$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$727$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$728$		0			0
$729$	0.669131	+	0.743145i	0.669131	+	0.743145i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$733$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$734$		0			0
$735$	−0.280969	−	0.204136i	−0.280969	−	0.204136i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$739$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$740$	0.00420939	+	0.120541i	0.00420939	+	0.120541i
$741$		0			0
$742$		0			0
$743$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$743$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.15707	−	1.48098i	1.15707	−	1.48098i	0.309017	−	0.951057i	$-0.400000\pi$
$751$	1.15707	−	1.48098i	1.15707	−	1.48098i	0.848048	−	0.529919i	$-0.177778\pi$
$752$	1.65940	−	0.882318i	1.65940	−	0.882318i
$753$	−1.43868	−	1.38932i	−1.43868	−	1.38932i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.23949	−	0.900539i	−1.23949	−	0.900539i	−0.241922	−	0.970296i	$-0.577778\pi$
$757$	−1.23949	−	0.900539i	−1.23949	−	0.900539i	−0.997564	+	0.0697565i	$0.977778\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$761$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$762$		0			0
$763$		0			0
$764$	0.196449	+	1.86909i	0.196449	+	1.86909i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.719340	+	0.694658i	−0.719340	+	0.694658i
$769$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$769$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$770$		0			0
$771$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$772$		0			0
$773$	−1.95630	+	0.415823i	−1.95630	+	0.415823i	−0.978148	+	0.207912i	$0.933333\pi$
$773$	−1.95630	+	0.415823i	−1.95630	+	0.415823i	−0.978148	+	0.207912i	$0.933333\pi$
$774$		0			0
$775$	0.140831	+	1.33992i	0.140831	+	1.33992i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.309017	−	0.951057i	0.309017	−	0.951057i
$785$	−0.199324	+	0.493344i	−0.199324	+	0.493344i
$786$		0			0
$787$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$787$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.0185696	+	0.531765i	0.0185696	+	0.531765i
$796$	−1.59381	−	0.995922i	−1.59381	−	0.995922i
$797$	−0.0840186	+	0.336980i	−0.0840186	+	0.336980i	−0.997564	−	0.0697565i	$-0.977778\pi$
$797$	−0.0840186	+	0.336980i	−0.0840186	+	0.336980i	0.913545	+	0.406737i	$0.133333\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	0.241922	+	0.970296i	0.241922	+	0.970296i
$802$		0			0
$803$		0			0
$804$	1.53209			1.53209
$805$		0			0
$806$		0			0
$807$	−1.59381	−	0.995922i	−1.59381	−	0.995922i
$808$		0			0
$809$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$809$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$810$		0			0
$811$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$811$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.613341	+	0.223238i	0.613341	+	0.223238i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$821$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$822$		0			0
$823$	0.997564	−	0.0697565i	0.997564	−	0.0697565i	0.438371	−	0.898794i	$-0.355556\pi$
$823$	0.997564	−	0.0697565i	0.997564	−	0.0697565i	0.559193	+	0.829038i	$0.311111\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$827$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$828$	−0.990268	−	0.139173i	−0.990268	−	0.139173i
$829$	−1.49861	−	0.318539i	−1.49861	−	0.318539i	−0.615661	−	0.788011i	$-0.711111\pi$
$829$	−1.49861	−	0.318539i	−1.49861	−	0.318539i	−0.882948	+	0.469472i	$0.844444\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.17365	−	0.984808i	1.17365	−	0.984808i
$838$		0			0
$839$	−0.848048	+	0.529919i	−0.848048	+	0.529919i	−0.882948	−	0.469472i	$-0.844444\pi$
$839$	−0.848048	+	0.529919i	−0.848048	+	0.529919i	0.0348995	+	0.999391i	$0.488889\pi$
$840$		0			0
$841$	−0.719340	−	0.694658i	−0.719340	−	0.694658i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.317271	−	0.141258i	0.317271	−	0.141258i
$846$		0			0
$847$		0			0
$848$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$849$		0			0
$850$		0			0
$851$	−0.294524	−	0.184039i	−0.294524	−	0.184039i
$852$	−0.823868	−	1.68918i	−0.823868	−	1.68918i
$853$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$853$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$857$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$858$		0			0
$859$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$859$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$863$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.438371	−	0.898794i	0.438371	−	0.898794i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.65940	−	0.882318i	1.65940	−	0.882318i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$877$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$881$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$882$		0			0
$883$	−1.25755	−	1.39666i	−1.25755	−	1.39666i	−0.882948	−	0.469472i	$-0.844444\pi$
$883$	−1.25755	−	1.39666i	−1.25755	−	1.39666i	−0.374607	−	0.927184i	$-0.622222\pi$
$884$		0			0
$885$	−0.430469	+	0.312754i	−0.430469	+	0.312754i
$886$		0			0
$887$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$887$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−1.00000			−1.00000
$893$		0			0
$894$		0			0
$895$	−0.469807	+	0.249801i	−0.469807	+	0.249801i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.212743	+	0.853264i	0.212743	+	0.853264i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.0451831	−	0.111832i	−0.0451831	−	0.111832i
$906$		0			0
$907$	−0.559193	+	0.829038i	−0.559193	+	0.829038i	−0.997564	−	0.0697565i	$-0.977778\pi$
$907$	−0.559193	+	0.829038i	−0.559193	+	0.829038i	0.438371	+	0.898794i	$0.355556\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.249824	+	0.241252i	−0.249824	+	0.241252i	−0.809017	−	0.587785i	$-0.800000\pi$
$911$	−0.249824	+	0.241252i	−0.249824	+	0.241252i	0.559193	+	0.829038i	$0.311111\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.848048	+	0.529919i	−0.848048	+	0.529919i
$917$		0			0
$918$		0			0
$919$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$919$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.0530334	+	0.300767i	−0.0530334	+	0.300767i
$926$		0			0
$927$	0.232387	+	0.258091i	0.232387	+	0.258091i
$928$		0			0
$929$	0.856733	−	1.27016i	0.856733	−	1.27016i	−0.104528	−	0.994522i	$-0.533333\pi$
$929$	0.856733	−	1.27016i	0.856733	−	1.27016i	0.961262	−	0.275637i	$-0.0888889\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.10209	+	1.06428i	−1.10209	+	1.06428i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$937$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$938$		0			0
$939$	0.978148	+	0.207912i	0.978148	+	0.207912i
$940$	−0.627419	+	0.179910i	−0.627419	+	0.179910i
$941$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$941$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$942$		0			0
$943$		0			0
$944$	−1.23949	−	0.900539i	−1.23949	−	0.900539i
$945$		0			0
$946$		0			0
$947$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$947$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	1.82709	+	0.813473i	1.82709	+	0.813473i
$952$		0			0
$953$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$953$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$954$		0			0
$955$	0.0682261	−	0.649128i	0.0682261	−	0.649128i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.294524	−	0.184039i	0.294524	−	0.184039i
$961$	−0.829478	−	1.06168i	−0.829478	−	1.06168i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$967$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$971$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$972$	0.669131	−	0.743145i	0.669131	−	0.743145i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.11839	+	1.65808i	1.11839	+	1.65808i	0.559193	+	0.829038i	$0.311111\pi$
$977$	1.11839	+	1.65808i	1.11839	+	1.65808i	0.559193	+	0.829038i	$0.311111\pi$
$978$		0			0
$979$		0			0
$980$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$981$		0			0
$982$		0			0
$983$	−0.943248	−	1.20730i	−0.943248	−	1.20730i	−0.978148	−	0.207912i	$-0.933333\pi$
$983$	−0.943248	−	1.20730i	−0.943248	−	1.20730i	0.0348995	−	0.999391i	$-0.488889\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$992$		0			0
$993$	1.83832	−	0.390746i	1.83832	−	0.390746i
$994$		0			0
$995$	0.469516	+	0.453406i	0.469516	+	0.453406i
$996$		0			0
$997$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$997$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$998$		0			0
$999$	0.317271	−	0.141258i	0.317271	−	0.141258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3267.1.bf.a.2581.1		24
11.2	odd	10	inner	3267.1.bf.a.2635.1		24
11.3	even	5	inner	3267.1.bf.a.1933.1		24
11.4	even	5	inner	3267.1.bf.a.475.1		24
11.5	even	5		297.1.q.a.43.1	✓	6
11.6	odd	10		297.1.q.a.43.1	✓	6
11.7	odd	10	inner	3267.1.bf.a.475.1		24
11.8	odd	10	inner	3267.1.bf.a.1933.1		24
11.9	even	5	inner	3267.1.bf.a.2635.1		24
11.10	odd	2	CM	3267.1.bf.a.2581.1		24
27.22	even	9	inner	3267.1.bf.a.1129.1		24
33.5	odd	10		891.1.q.a.208.1		6
33.17	even	10		891.1.q.a.208.1		6
99.5	odd	30		2673.1.q.a.2485.1		6
99.16	even	15		2673.1.q.b.703.1		6
99.38	odd	30		2673.1.q.c.703.1		6
99.49	even	15		2673.1.q.d.2485.1		6
99.50	even	30		2673.1.q.a.2485.1		6
99.61	odd	30		2673.1.q.b.703.1		6
99.83	even	30		2673.1.q.c.703.1		6
99.94	odd	30		2673.1.q.d.2485.1		6
297.5	odd	90		891.1.q.a.604.1		6
297.49	even	45		297.1.q.a.76.1	yes	6
297.50	even	90		2673.1.q.c.1000.1		6
297.76	odd	18	inner	3267.1.bf.a.1129.1		24
297.94	odd	90		2673.1.q.d.1891.1		6
297.103	even	45	inner	3267.1.bf.a.2290.1		24
297.104	odd	90		2673.1.q.c.1000.1		6
297.130	even	45	inner	3267.1.bf.a.1183.1		24
297.148	even	45		2673.1.q.d.1891.1		6
297.149	even	90		2673.1.q.a.1891.1		6
297.157	even	45	inner	3267.1.bf.a.481.1		24
297.184	odd	90	inner	3267.1.bf.a.481.1		24
297.193	odd	90		2673.1.q.b.1000.1		6
297.203	odd	90		2673.1.q.a.1891.1		6
297.211	odd	90	inner	3267.1.bf.a.1183.1		24
297.238	odd	90	inner	3267.1.bf.a.2290.1		24
297.247	even	45		2673.1.q.b.1000.1		6
297.248	even	90		891.1.q.a.604.1		6
297.292	odd	90		297.1.q.a.76.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.1.q.a.43.1	✓	6	11.5	even	5
297.1.q.a.43.1	✓	6	11.6	odd	10
297.1.q.a.76.1	yes	6	297.49	even	45
297.1.q.a.76.1	yes	6	297.292	odd	90
891.1.q.a.208.1		6	33.5	odd	10
891.1.q.a.208.1		6	33.17	even	10
891.1.q.a.604.1		6	297.5	odd	90
891.1.q.a.604.1		6	297.248	even	90
2673.1.q.a.1891.1		6	297.149	even	90
2673.1.q.a.1891.1		6	297.203	odd	90
2673.1.q.a.2485.1		6	99.5	odd	30
2673.1.q.a.2485.1		6	99.50	even	30
2673.1.q.b.703.1		6	99.16	even	15
2673.1.q.b.703.1		6	99.61	odd	30
2673.1.q.b.1000.1		6	297.193	odd	90
2673.1.q.b.1000.1		6	297.247	even	45
2673.1.q.c.703.1		6	99.38	odd	30
2673.1.q.c.703.1		6	99.83	even	30
2673.1.q.c.1000.1		6	297.50	even	90
2673.1.q.c.1000.1		6	297.104	odd	90
2673.1.q.d.1891.1		6	297.94	odd	90
2673.1.q.d.1891.1		6	297.148	even	45
2673.1.q.d.2485.1		6	99.49	even	15
2673.1.q.d.2485.1		6	99.94	odd	30
3267.1.bf.a.475.1		24	11.4	even	5	inner
3267.1.bf.a.475.1		24	11.7	odd	10	inner
3267.1.bf.a.481.1		24	297.157	even	45	inner
3267.1.bf.a.481.1		24	297.184	odd	90	inner
3267.1.bf.a.1129.1		24	27.22	even	9	inner
3267.1.bf.a.1129.1		24	297.76	odd	18	inner
3267.1.bf.a.1183.1		24	297.130	even	45	inner
3267.1.bf.a.1183.1		24	297.211	odd	90	inner
3267.1.bf.a.1933.1		24	11.3	even	5	inner
3267.1.bf.a.1933.1		24	11.8	odd	10	inner
3267.1.bf.a.2290.1		24	297.103	even	45	inner
3267.1.bf.a.2290.1		24	297.238	odd	90	inner
3267.1.bf.a.2581.1		24	1.1	even	1	trivial
3267.1.bf.a.2581.1		24	11.10	odd	2	CM
3267.1.bf.a.2635.1		24	11.2	odd	10	inner
3267.1.bf.a.2635.1		24	11.9	even	5	inner

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:	\( N \)	\(=\)	\( 3267 = 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3267.bf (of order \(90\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.374607 - 0.927184i) q^{3} +(-0.882948 + 0.469472i) q^{4} +(0.333843 - 0.0957278i) q^{5} +(-0.719340 + 0.694658i) q^{9} +O(q^{10})\)	\(q+(-0.374607 - 0.927184i) q^{3} +(-0.882948 + 0.469472i) q^{4} +(0.333843 - 0.0957278i) q^{5} +(-0.719340 + 0.694658i) q^{9} +(0.766044 + 0.642788i) q^{12} +(-0.213817 - 0.273673i) q^{15} +(0.559193 - 0.829038i) q^{16} +(-0.249824 + 0.241252i) q^{20} +(-0.173648 - 0.984808i) q^{23} +(-0.745761 + 0.466003i) q^{25} +(0.913545 + 0.406737i) q^{27} +(0.671624 - 1.37703i) q^{31} +(0.309017 - 0.951057i) q^{36} +(0.232387 - 0.258091i) q^{37} +(-0.173648 + 0.300767i) q^{45} +(1.65940 + 0.882318i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(0.961262 - 0.275637i) q^{49} +(-1.23949 - 0.900539i) q^{53} +(0.0534691 - 1.53116i) q^{59} +(0.317271 + 0.141258i) q^{60} +(-0.104528 + 0.994522i) q^{64} +(1.17365 - 0.984808i) q^{67} +(-0.848048 + 0.529919i) q^{69} +(-1.71690 - 0.764415i) q^{71} +(0.711438 + 0.516890i) q^{75} +(0.107320 - 0.330298i) q^{80} +(0.0348995 - 0.999391i) q^{81} +(0.500000 - 0.866025i) q^{89} +(0.615661 + 0.788011i) q^{92} +(-1.52836 - 0.106873i) q^{93} +(-1.80658 - 0.518029i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5}+O(q^{10}) \) 24 * q + 3 * q^5	\( 24 q + 3 q^{5} + 3 q^{15} - 6 q^{20} + 3 q^{25} + 3 q^{27} + 3 q^{31} - 6 q^{36} + 3 q^{47} + 3 q^{48} + 3 q^{59} + 3 q^{64} + 24 q^{67} - 6 q^{75} + 12 q^{89} - 6 q^{93} - 6 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 + 3 * q^15 - 6 * q^20 + 3 * q^25 + 3 * q^27 + 3 * q^31 - 6 * q^36 + 3 * q^47 + 3 * q^48 + 3 * q^59 + 3 * q^64 + 24 * q^67 - 6 * q^75 + 12 * q^89 - 6 * q^93 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more