LMFDB - Embedded newform 3380.1.v.d.2219.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3380,1,Mod(2219,3380)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3380.2219"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3380, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 3380 = 2^{2} \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3380.v (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,-1,-3,-6,-1,1,6,-2,3,0,2,0,-2,1,-3,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$1.68683974270$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.64827.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{7}$
Projective field:	Galois closure of 7.1.38614472000.1

Embedding invariants

Embedding label			2219.3
Root			$0.900969 + 1.56052i$ of defining polynomial
Character	$\chi$	$=$	3380.2219
Dual form			3380.1.v.d.3019.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.623490 - 1.07992i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.623490 + 1.07992i) q^{6} +(0.900969 + 1.56052i) q^{7} +1.00000 q^{8} +(-0.277479 - 0.480608i) q^{9} +(0.500000 - 0.866025i) q^{10} -1.24698 q^{12} -1.80194 q^{14} +(-0.623490 + 1.07992i) q^{15} +(-0.500000 + 0.866025i) q^{16} +0.554958 q^{18} +(0.500000 + 0.866025i) q^{20} +2.24698 q^{21} +(-0.222521 + 0.385418i) q^{23} +(0.623490 - 1.07992i) q^{24} +1.00000 q^{25} +0.554958 q^{27} +(0.900969 - 1.56052i) q^{28} +(-0.623490 + 1.07992i) q^{29} +(-0.623490 - 1.07992i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(-0.900969 - 1.56052i) q^{35} +(-0.277479 + 0.480608i) q^{36} -1.00000 q^{40} +(-0.900969 + 1.56052i) q^{41} +(-1.12349 + 1.94594i) q^{42} +(-0.222521 - 0.385418i) q^{43} +(0.277479 + 0.480608i) q^{45} +(-0.222521 - 0.385418i) q^{46} -0.445042 q^{47} +(0.623490 + 1.07992i) q^{48} +(-1.12349 + 1.94594i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.277479 + 0.480608i) q^{54} +(0.900969 + 1.56052i) q^{56} +(-0.623490 - 1.07992i) q^{58} +1.24698 q^{60} +(0.900969 + 1.56052i) q^{61} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(0.222521 - 0.385418i) q^{67} +(0.277479 + 0.480608i) q^{69} +1.80194 q^{70} +(-0.277479 - 0.480608i) q^{72} +(0.623490 - 1.07992i) q^{75} +(0.500000 - 0.866025i) q^{80} +(0.623490 - 1.07992i) q^{81} +(-0.900969 - 1.56052i) q^{82} +1.24698 q^{83} +(-1.12349 - 1.94594i) q^{84} +0.445042 q^{86} +(0.777479 + 1.34663i) q^{87} +(-0.222521 + 0.385418i) q^{89} -0.554958 q^{90} +0.445042 q^{92} +(0.222521 - 0.385418i) q^{94} -1.24698 q^{96} +(-1.12349 - 1.94594i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + q^{7} + 6 q^{8} - 2 q^{9} + 3 q^{10} + 2 q^{12} - 2 q^{14} + q^{15} - 3 q^{16} + 4 q^{18} + 3 q^{20} + 4 q^{21} - q^{23} - q^{24} + 6 q^{25} + 4 q^{27}+ \cdots - 2 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - q^3 - 3 * q^4 - 6 * q^5 - q^6 + q^7 + 6 * q^8 - 2 * q^9 + 3 * q^10 + 2 * q^12 - 2 * q^14 + q^15 - 3 * q^16 + 4 * q^18 + 3 * q^20 + 4 * q^21 - q^23 - q^24 + 6 * q^25 + 4 * q^27 + q^28 + q^29 + q^30 - 3 * q^32 - q^35 - 2 * q^36 - 6 * q^40 - q^41 - 2 * q^42 - q^43 + 2 * q^45 - q^46 - 2 * q^47 - q^48 - 2 * q^49 - 3 * q^50 - 2 * q^54 + q^56 + q^58 - 2 * q^60 + q^61 + 3 * q^63 + 6 * q^64 + q^67 + 2 * q^69 + 2 * q^70 - 2 * q^72 - q^75 + 3 * q^80 - q^81 - q^82 - 2 * q^83 - 2 * q^84 + 2 * q^86 + 5 * q^87 - q^89 - 4 * q^90 + 2 * q^92 + q^94 + 2 * q^96 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3380\mathbb{Z}\right)^\times$.

$n$	$677$	$1691$	$1861$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$2$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$3$	0.623490	−	1.07992i	0.623490	−	1.07992i	−0.365341	−	0.930874i	$-0.619048\pi$
$3$	0.623490	−	1.07992i	0.623490	−	1.07992i	0.988831	−	0.149042i	$-0.0476190\pi$
$4$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$	−1.00000			−1.00000
$5$	−1.00000			−1.00000
$6$	0.623490	+	1.07992i	0.623490	+	1.07992i
$7$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.826239	+	0.563320i	$0.190476\pi$
$7$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.0747301	+	0.997204i	$0.476190\pi$
$8$	1.00000			1.00000
$9$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$10$	0.500000	−	0.866025i	0.500000	−	0.866025i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−1.24698			−1.24698
$13$		0			0
$13$		0			0
$14$	−1.80194			−1.80194
$15$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$	0.554958			0.554958
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	0.500000	+	0.866025i	0.500000	+	0.866025i
$21$	2.24698			2.24698
$22$		0			0
$23$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	−0.955573	−	0.294755i	$-0.904762\pi$
$23$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	0.733052	+	0.680173i	$0.238095\pi$
$24$	0.623490	−	1.07992i	0.623490	−	1.07992i
$25$	1.00000			1.00000
$26$		0			0
$27$	0.554958			0.554958
$28$	0.900969	−	1.56052i	0.900969	−	1.56052i
$29$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	0.365341	+	0.930874i	$0.380952\pi$
$29$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	−0.988831	+	0.149042i	$0.952381\pi$
$30$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$33$		0			0
$34$		0			0
$35$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$36$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$		0			0
$39$		0			0
$40$	−1.00000			−1.00000
$41$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$41$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.826239	+	0.563320i	$0.809524\pi$
$42$	−1.12349	+	1.94594i	−1.12349	+	1.94594i
$43$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	0.733052	−	0.680173i	$-0.238095\pi$
$43$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	−0.955573	+	0.294755i	$0.904762\pi$
$44$		0			0
$45$	0.277479	+	0.480608i	0.277479	+	0.480608i
$46$	−0.222521	−	0.385418i	−0.222521	−	0.385418i
$47$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$47$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$48$	0.623490	+	1.07992i	0.623490	+	1.07992i
$49$	−1.12349	+	1.94594i	−1.12349	+	1.94594i
$50$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$55$		0			0
$56$	0.900969	+	1.56052i	0.900969	+	1.56052i
$57$		0			0
$58$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$	1.24698			1.24698
$61$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.826239	+	0.563320i	$0.190476\pi$
$61$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.0747301	+	0.997204i	$0.476190\pi$
$62$		0			0
$63$	0.500000	−	0.866025i	0.500000	−	0.866025i
$64$	1.00000			1.00000
$65$		0			0
$66$		0			0
$67$	0.222521	−	0.385418i	0.222521	−	0.385418i	−0.733052	−	0.680173i	$-0.761905\pi$
$67$	0.222521	−	0.385418i	0.222521	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$68$		0			0
$69$	0.277479	+	0.480608i	0.277479	+	0.480608i
$70$	1.80194			1.80194
$71$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$71$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$72$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	0.623490	−	1.07992i	0.623490	−	1.07992i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	0.500000	−	0.866025i	0.500000	−	0.866025i
$81$	0.623490	−	1.07992i	0.623490	−	1.07992i
$82$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$83$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$83$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$84$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$85$		0			0
$86$	0.445042			0.445042
$87$	0.777479	+	1.34663i	0.777479	+	1.34663i
$88$		0			0
$89$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	−0.955573	−	0.294755i	$-0.904762\pi$
$89$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	0.733052	+	0.680173i	$0.238095\pi$
$90$	−0.554958			−0.554958
$91$		0			0
$92$	0.445042			0.445042
$93$		0			0
$94$	0.222521	−	0.385418i	0.222521	−	0.385418i
$95$		0			0
$96$	−1.24698			−1.24698
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$101$	0.222521	−	0.385418i	0.222521	−	0.385418i	−0.733052	−	0.680173i	$-0.761905\pi$
$101$	0.222521	−	0.385418i	0.222521	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$102$		0			0
$103$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$103$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$104$		0			0
$105$	−2.24698			−2.24698
$106$		0			0
$107$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$107$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$108$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$109$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$109$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$110$		0			0
$111$		0			0
$112$	−1.80194			−1.80194
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$		0			0
$115$	0.222521	−	0.385418i	0.222521	−	0.385418i
$116$	1.24698			1.24698
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$	−1.80194			−1.80194
$123$	1.12349	+	1.94594i	1.12349	+	1.94594i
$124$		0			0
$125$	−1.00000			−1.00000
$126$	0.500000	+	0.866025i	0.500000	+	0.866025i
$127$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$127$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.826239	+	0.563320i	$0.809524\pi$
$128$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$129$	−0.554958			−0.554958
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$	0.222521	+	0.385418i	0.222521	+	0.385418i
$135$	−0.554958			−0.554958
$136$		0			0
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$	−0.554958			−0.554958
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$141$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$142$		0			0
$143$		0			0
$144$	0.554958			0.554958
$145$	0.623490	−	1.07992i	0.623490	−	1.07992i
$146$		0			0
$147$	1.40097	+	2.42655i	1.40097	+	2.42655i
$148$		0			0
$149$	0.623490	+	1.07992i	0.623490	+	1.07992i	0.988831	+	0.149042i	$0.0476190\pi$
$149$	0.623490	+	1.07992i	0.623490	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$150$	0.623490	+	1.07992i	0.623490	+	1.07992i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$		0			0
$159$		0			0
$160$	0.500000	+	0.866025i	0.500000	+	0.866025i
$161$	−0.801938			−0.801938
$162$	0.623490	+	1.07992i	0.623490	+	1.07992i
$163$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$163$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$164$	1.80194			1.80194
$165$		0			0
$166$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$167$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$167$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$168$	2.24698			2.24698
$169$		0			0
$170$		0			0
$171$		0			0
$172$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$173$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$173$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$174$	−1.55496			−1.55496
$175$	0.900969	+	1.56052i	0.900969	+	1.56052i
$176$		0			0
$177$		0			0
$178$	−0.222521	−	0.385418i	−0.222521	−	0.385418i
$179$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$179$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$180$	0.277479	−	0.480608i	0.277479	−	0.480608i
$181$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$181$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$182$		0			0
$183$	2.24698			2.24698
$184$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.222521	+	0.385418i	0.222521	+	0.385418i
$189$	0.500000	+	0.866025i	0.500000	+	0.866025i
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	0.623490	−	1.07992i	0.623490	−	1.07992i
$193$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$193$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$		0			0
$196$	2.24698			2.24698
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	1.00000			1.00000
$201$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$202$	0.222521	+	0.385418i	0.222521	+	0.385418i
$203$	−2.24698			−2.24698
$204$		0			0
$205$	0.900969	−	1.56052i	0.900969	−	1.56052i
$206$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$207$	0.246980			0.246980
$208$		0			0
$209$		0			0
$210$	1.12349	−	1.94594i	1.12349	−	1.94594i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$		0			0
$214$	1.00000	+	1.73205i	1.00000	+	1.73205i
$215$	0.222521	+	0.385418i	0.222521	+	0.385418i
$216$	0.554958			0.554958
$217$		0			0
$218$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	0.365341	+	0.930874i	$0.380952\pi$
$223$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	−0.988831	+	0.149042i	$0.952381\pi$
$224$	0.900969	−	1.56052i	0.900969	−	1.56052i
$225$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$226$		0			0
$227$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$227$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$228$		0			0
$229$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$229$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$230$	0.222521	+	0.385418i	0.222521	+	0.385418i
$231$		0			0
$232$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$	0.445042			0.445042
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$241$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	0.733052	−	0.680173i	$-0.238095\pi$
$241$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	−0.955573	+	0.294755i	$0.904762\pi$
$242$	1.00000			1.00000
$243$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$244$	0.900969	−	1.56052i	0.900969	−	1.56052i
$245$	1.12349	−	1.94594i	1.12349	−	1.94594i
$246$	−2.24698			−2.24698
$247$		0			0
$248$		0			0
$249$	0.777479	−	1.34663i	0.777479	−	1.34663i
$250$	0.500000	−	0.866025i	0.500000	−	0.866025i
$251$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$251$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$252$	−1.00000			−1.00000
$253$		0			0
$254$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$	0.277479	−	0.480608i	0.277479	−	0.480608i
$259$		0			0
$260$		0			0
$261$	0.692021			0.692021
$262$		0			0
$263$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$263$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.826239	+	0.563320i	$0.809524\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.277479	+	0.480608i	0.277479	+	0.480608i
$268$	−0.445042			−0.445042
$269$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$269$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$270$	0.277479	−	0.480608i	0.277479	−	0.480608i
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.277479	−	0.480608i	0.277479	−	0.480608i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$281$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$281$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$282$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$283$	0.623490	−	1.07992i	0.623490	−	1.07992i	−0.365341	−	0.930874i	$-0.619048\pi$
$283$	0.623490	−	1.07992i	0.623490	−	1.07992i	0.988831	−	0.149042i	$-0.0476190\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.24698			−3.24698
$288$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$289$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$290$	0.623490	+	1.07992i	0.623490	+	1.07992i
$291$		0			0
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	−2.80194			−2.80194
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.24698			−1.24698
$299$		0			0
$300$	−1.24698			−1.24698
$301$	0.400969	−	0.694498i	0.400969	−	0.694498i
$302$		0			0
$303$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$304$		0			0
$305$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$306$		0			0
$307$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$307$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$308$		0			0
$309$	1.12349	−	1.94594i	1.12349	−	1.94594i
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$		0			0
$315$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$316$		0			0
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$	−1.00000			−1.00000
$321$	−1.24698	−	2.15983i	−1.24698	−	2.15983i
$322$	0.400969	−	0.694498i	0.400969	−	0.694498i
$323$		0			0
$324$	−1.24698			−1.24698
$325$		0			0
$326$	1.24698			1.24698
$327$	1.12349	−	1.94594i	1.12349	−	1.94594i
$328$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$329$	−0.400969	−	0.694498i	−0.400969	−	0.694498i
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$333$		0			0
$334$	0.900969	+	1.56052i	0.900969	+	1.56052i
$335$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$336$	−1.12349	+	1.94594i	−1.12349	+	1.94594i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−2.24698			−2.24698
$344$	−0.222521	−	0.385418i	−0.222521	−	0.385418i
$345$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$346$		0			0
$347$	0.623490	+	1.07992i	0.623490	+	1.07992i	0.988831	+	0.149042i	$0.0476190\pi$
$347$	0.623490	+	1.07992i	0.623490	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$348$	0.777479	−	1.34663i	0.777479	−	1.34663i
$349$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$349$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$350$	−1.80194			−1.80194
$351$		0			0
$352$		0			0
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$	0.445042			0.445042
$357$		0			0
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	0.277479	+	0.480608i	0.277479	+	0.480608i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$	0.222521	−	0.385418i	0.222521	−	0.385418i
$363$	−1.24698			−1.24698
$364$		0			0
$365$		0			0
$366$	−1.12349	+	1.94594i	−1.12349	+	1.94594i
$367$	0.623490	−	1.07992i	0.623490	−	1.07992i	−0.365341	−	0.930874i	$-0.619048\pi$
$367$	0.623490	−	1.07992i	0.623490	−	1.07992i	0.988831	−	0.149042i	$-0.0476190\pi$
$368$	−0.222521	−	0.385418i	−0.222521	−	0.385418i
$369$	1.00000			1.00000
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$376$	−0.445042			−0.445042
$377$		0			0
$378$	−1.00000			−1.00000
$379$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$379$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$380$		0			0
$381$	1.12349	+	1.94594i	1.12349	+	1.94594i
$382$		0			0
$383$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$383$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$384$	0.623490	+	1.07992i	0.623490	+	1.07992i
$385$		0			0
$386$		0			0
$387$	−0.123490	+	0.213891i	−0.123490	+	0.213891i
$388$		0			0
$389$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$389$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$390$		0			0
$391$		0			0
$392$	−1.12349	+	1.94594i	−1.12349	+	1.94594i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$		0			0
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$401$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$401$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.826239	+	0.563320i	$0.809524\pi$
$402$	0.554958			0.554958
$403$		0			0
$404$	−0.445042			−0.445042
$405$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$406$	1.12349	−	1.94594i	1.12349	−	1.94594i
$407$		0			0
$408$		0			0
$409$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.826239	−	0.563320i	$-0.809524\pi$
$409$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.0747301	−	0.997204i	$-0.523810\pi$
$410$	0.900969	+	1.56052i	0.900969	+	1.56052i
$411$		0			0
$412$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$413$		0			0
$414$	−0.123490	+	0.213891i	−0.123490	+	0.213891i
$415$	−1.24698			−1.24698
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$419$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$420$	1.12349	+	1.94594i	1.12349	+	1.94594i
$421$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$421$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$422$		0			0
$423$	0.123490	+	0.213891i	0.123490	+	0.213891i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.62349	+	2.81197i	−1.62349	+	2.81197i
$428$	−2.00000			−2.00000
$429$		0			0
$430$	−0.445042			−0.445042
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$433$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$433$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$434$		0			0
$435$	−0.777479	−	1.34663i	−0.777479	−	1.34663i
$436$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$437$		0			0
$438$		0			0
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	1.24698			1.24698
$442$		0			0
$443$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$443$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$444$		0			0
$445$	0.222521	−	0.385418i	0.222521	−	0.385418i
$446$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$447$	1.55496			1.55496
$448$	0.900969	+	1.56052i	0.900969	+	1.56052i
$449$	0.623490	+	1.07992i	0.623490	+	1.07992i	0.988831	+	0.149042i	$0.0476190\pi$
$449$	0.623490	+	1.07992i	0.623490	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$450$	0.554958			0.554958
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.24698			1.24698
$455$		0			0
$456$		0			0
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	0.623490	−	1.07992i	0.623490	−	1.07992i
$459$		0			0
$460$	−0.445042			−0.445042
$461$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	0.733052	−	0.680173i	$-0.238095\pi$
$461$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	−0.955573	+	0.294755i	$0.904762\pi$
$462$		0			0
$463$	2.00000			2.00000			1.00000			$0$
$463$	2.00000			2.00000			1.00000			$0$
$464$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$465$		0			0
$466$		0			0
$467$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$467$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$468$		0			0
$469$	0.801938			0.801938
$470$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$	1.24698			1.24698
$481$		0			0
$482$	0.445042			0.445042
$483$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$484$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$485$		0			0
$486$	1.00000			1.00000
$487$	0.222521	+	0.385418i	0.222521	+	0.385418i	0.955573	−	0.294755i	$-0.0952381\pi$
$487$	0.222521	+	0.385418i	0.222521	+	0.385418i	−0.733052	+	0.680173i	$0.761905\pi$
$488$	0.900969	+	1.56052i	0.900969	+	1.56052i
$489$	−1.55496			−1.55496
$490$	1.12349	+	1.94594i	1.12349	+	1.94594i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$	1.12349	−	1.94594i	1.12349	−	1.94594i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.777479	+	1.34663i	0.777479	+	1.34663i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	0.500000	+	0.866025i	0.500000	+	0.866025i
$501$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$502$		0			0
$503$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.826239	−	0.563320i	$-0.809524\pi$
$503$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.0747301	−	0.997204i	$-0.523810\pi$
$504$	0.500000	−	0.866025i	0.500000	−	0.866025i
$505$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$506$		0			0
$507$		0			0
$508$	1.80194			1.80194
$509$	0.623490	−	1.07992i	0.623490	−	1.07992i	−0.365341	−	0.930874i	$-0.619048\pi$
$509$	0.623490	−	1.07992i	0.623490	−	1.07992i	0.988831	−	0.149042i	$-0.0476190\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			1.00000
$513$		0			0
$514$		0			0
$515$	−1.80194			−1.80194
$516$	0.277479	+	0.480608i	0.277479	+	0.480608i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$521$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$522$	−0.346011	+	0.599308i	−0.346011	+	0.599308i
$523$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	−0.955573	−	0.294755i	$-0.904762\pi$
$523$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	0.733052	+	0.680173i	$0.238095\pi$
$524$		0			0
$525$	2.24698			2.24698
$526$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$527$		0			0
$528$		0			0
$529$	0.400969	+	0.694498i	0.400969	+	0.694498i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.554958			−0.554958
$535$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$536$	0.222521	−	0.385418i	0.222521	−	0.385418i
$537$		0			0
$538$	1.24698			1.24698
$539$		0			0
$540$	0.277479	+	0.480608i	0.277479	+	0.480608i
$541$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$541$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$542$		0			0
$543$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$544$		0			0
$545$	−1.80194			−1.80194
$546$		0			0
$547$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$547$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$548$		0			0
$549$	0.500000	−	0.866025i	0.500000	−	0.866025i
$550$		0			0
$551$		0			0
$552$	0.277479	+	0.480608i	0.277479	+	0.480608i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$	1.80194			1.80194
$561$		0			0
$562$	0.623490	−	1.07992i	0.623490	−	1.07992i
$563$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.826239	−	0.563320i	$-0.809524\pi$
$563$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.0747301	−	0.997204i	$-0.523810\pi$
$564$	0.554958			0.554958
$565$		0			0
$566$	0.623490	+	1.07992i	0.623490	+	1.07992i
$567$	2.24698			2.24698
$568$		0			0
$569$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$569$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$	1.62349	−	2.81197i	1.62349	−	2.81197i
$575$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$576$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$579$		0			0
$580$	−1.24698			−1.24698
$581$	1.12349	+	1.94594i	1.12349	+	1.94594i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$587$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$588$	1.40097	−	2.42655i	1.40097	−	2.42655i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$	0.623490	−	1.07992i	0.623490	−	1.07992i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	0.623490	−	1.07992i	0.623490	−	1.07992i
$601$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$601$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$602$	0.400969	+	0.694498i	0.400969	+	0.694498i
$603$	−0.246980			−0.246980
$604$		0			0
$605$	0.500000	+	0.866025i	0.500000	+	0.866025i
$606$	0.554958			0.554958
$607$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	0.733052	−	0.680173i	$-0.238095\pi$
$607$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	−0.955573	+	0.294755i	$0.904762\pi$
$608$		0			0
$609$	−1.40097	+	2.42655i	−1.40097	+	2.42655i
$610$	1.80194			1.80194
$611$		0			0
$612$		0			0
$613$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$613$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$614$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$615$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$616$		0			0
$617$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$617$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$618$	1.12349	+	1.94594i	1.12349	+	1.94594i
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$		0			0
$621$	−0.123490	+	0.213891i	−0.123490	+	0.213891i
$622$		0			0
$623$	−0.801938			−0.801938
$624$		0			0
$625$	1.00000			1.00000
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$631$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$631$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.900969	−	1.56052i	0.900969	−	1.56052i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.500000	−	0.866025i	0.500000	−	0.866025i
$641$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.826239	+	0.563320i	$0.190476\pi$
$641$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.0747301	+	0.997204i	$0.476190\pi$
$642$	2.49396			2.49396
$643$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$643$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$644$	0.400969	+	0.694498i	0.400969	+	0.694498i
$645$	0.554958			0.554958
$646$		0			0
$647$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$647$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$648$	0.623490	−	1.07992i	0.623490	−	1.07992i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$	1.12349	+	1.94594i	1.12349	+	1.94594i
$655$		0			0
$656$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$657$		0			0
$658$	0.801938			0.801938
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	−0.955573	−	0.294755i	$-0.904762\pi$
$661$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	0.733052	+	0.680173i	$0.238095\pi$
$662$		0			0
$663$		0			0
$664$	1.24698			1.24698
$665$		0			0
$666$		0			0
$667$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$668$	−1.80194			−1.80194
$669$	0.777479	+	1.34663i	0.777479	+	1.34663i
$670$	−0.222521	−	0.385418i	−0.222521	−	0.385418i
$671$		0			0
$672$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	0.554958			0.554958
$676$		0			0
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.55496			−1.55496
$682$		0			0
$683$	0.222521	+	0.385418i	0.222521	+	0.385418i	0.955573	−	0.294755i	$-0.0952381\pi$
$683$	0.222521	+	0.385418i	0.222521	+	0.385418i	−0.733052	+	0.680173i	$0.761905\pi$
$684$		0			0
$685$		0			0
$686$	1.12349	−	1.94594i	1.12349	−	1.94594i
$687$	−0.777479	+	1.34663i	−0.777479	+	1.34663i
$688$	0.445042			0.445042
$689$		0			0
$690$	0.554958			0.554958
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$		0			0
$694$	−1.24698			−1.24698
$695$		0			0
$696$	0.777479	+	1.34663i	0.777479	+	1.34663i
$697$		0			0
$698$	1.00000	+	1.73205i	1.00000	+	1.73205i
$699$		0			0
$700$	0.900969	−	1.56052i	0.900969	−	1.56052i
$701$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$701$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.277479	−	0.480608i	0.277479	−	0.480608i
$706$		0			0
$707$	0.801938			0.801938
$708$		0			0
$709$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.826239	−	0.563320i	$-0.809524\pi$
$709$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.0747301	−	0.997204i	$-0.523810\pi$
$710$		0			0
$711$		0			0
$712$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	−0.554958			−0.554958
$721$	1.62349	+	2.81197i	1.62349	+	2.81197i
$722$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$723$	−0.554958			−0.554958
$724$	0.222521	+	0.385418i	0.222521	+	0.385418i
$725$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$726$	0.623490	−	1.07992i	0.623490	−	1.07992i
$727$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$727$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$	0.623490	+	1.07992i	0.623490	+	1.07992i
$735$	−1.40097	−	2.42655i	−1.40097	−	2.42655i
$736$	0.445042			0.445042
$737$		0			0
$738$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$743$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$744$		0			0
$745$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$746$		0			0
$747$	−0.346011	−	0.599308i	−0.346011	−	0.599308i
$748$		0			0
$749$	3.60388			3.60388
$750$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$	0.222521	−	0.385418i	0.222521	−	0.385418i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.500000	−	0.866025i	0.500000	−	0.866025i
$757$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$757$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.623490	+	1.07992i	0.623490	+	1.07992i	0.988831	+	0.149042i	$0.0476190\pi$
$761$	0.623490	+	1.07992i	0.623490	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$762$	−2.24698			−2.24698
$763$	1.62349	+	2.81197i	1.62349	+	2.81197i
$764$		0			0
$765$		0			0
$766$	1.24698			1.24698
$767$		0			0
$768$	−1.24698			−1.24698
$769$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$769$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.826239	+	0.563320i	$0.809524\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$	−0.123490	−	0.213891i	−0.123490	−	0.213891i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.222521	−	0.385418i	0.222521	−	0.385418i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.346011	+	0.599308i	−0.346011	+	0.599308i
$784$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$785$		0			0
$786$		0			0
$787$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$787$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$788$		0			0
$789$	1.12349	+	1.94594i	1.12349	+	1.94594i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$797$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$801$	0.246980			0.246980
$802$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$803$		0			0
$804$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$805$	0.801938			0.801938
$806$		0			0
$807$	−1.55496			−1.55496
$808$	0.222521	−	0.385418i	0.222521	−	0.385418i
$809$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$809$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$810$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	1.12349	+	1.94594i	1.12349	+	1.94594i
$813$		0			0
$814$		0			0
$815$	0.623490	+	1.07992i	0.623490	+	1.07992i
$816$		0			0
$817$		0			0
$818$	1.80194			1.80194
$819$		0			0
$820$	−1.80194			−1.80194
$821$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	−0.955573	−	0.294755i	$-0.904762\pi$
$821$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	0.733052	+	0.680173i	$0.238095\pi$
$822$		0			0
$823$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$823$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$824$	1.80194			1.80194
$825$		0			0
$826$		0			0
$827$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$827$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$828$	−0.123490	−	0.213891i	−0.123490	−	0.213891i
$829$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	0.365341	+	0.930874i	$0.380952\pi$
$829$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	−0.988831	+	0.149042i	$0.952381\pi$
$830$	0.623490	−	1.07992i	0.623490	−	1.07992i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$839$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$840$	−2.24698			−2.24698
$841$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$842$	0.623490	−	1.07992i	0.623490	−	1.07992i
$843$	−0.777479	+	1.34663i	−0.777479	+	1.34663i
$844$		0			0
$845$		0			0
$846$	−0.246980			−0.246980
$847$	0.900969	−	1.56052i	0.900969	−	1.56052i
$848$		0			0
$849$	−0.777479	−	1.34663i	−0.777479	−	1.34663i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	−1.62349	−	2.81197i	−1.62349	−	2.81197i
$855$		0			0
$856$	1.00000	−	1.73205i	1.00000	−	1.73205i
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$	0.222521	−	0.385418i	0.222521	−	0.385418i
$861$	−2.02446	+	3.50647i	−2.02446	+	3.50647i
$862$		0			0
$863$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$863$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$864$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$865$		0			0
$866$		0			0
$867$	0.623490	+	1.07992i	0.623490	+	1.07992i
$868$		0			0
$869$		0			0
$870$	1.55496			1.55496
$871$		0			0
$872$	1.80194			1.80194
$873$		0			0
$874$		0			0
$875$	−0.900969	−	1.56052i	−0.900969	−	1.56052i
$876$		0			0
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$881$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$882$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$883$	−2.00000			−2.00000			−1.00000			$\pi$
$883$	−2.00000			−2.00000			−1.00000			$\pi$
$884$		0			0
$885$		0			0
$886$	0.623490	−	1.07992i	0.623490	−	1.07992i
$887$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$887$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.826239	+	0.563320i	$0.809524\pi$
$888$		0			0
$889$	−3.24698			−3.24698
$890$	0.222521	+	0.385418i	0.222521	+	0.385418i
$891$		0			0
$892$	1.24698			1.24698
$893$		0			0
$894$	−0.777479	+	1.34663i	−0.777479	+	1.34663i
$895$		0			0
$896$	−1.80194			−1.80194
$897$		0			0
$898$	−1.24698			−1.24698
$899$		0			0
$900$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$901$		0			0
$902$		0			0
$903$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$904$		0			0
$905$	0.445042			0.445042
$906$		0			0
$907$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$907$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.826239	+	0.563320i	$0.809524\pi$
$908$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$909$	−0.246980			−0.246980
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−2.24698			−2.24698
$916$	0.623490	+	1.07992i	0.623490	+	1.07992i
$917$		0			0
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$	0.222521	−	0.385418i	0.222521	−	0.385418i
$921$	0.777479	−	1.34663i	0.777479	−	1.34663i
$922$	0.445042			0.445042
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$927$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$928$	1.24698			1.24698
$929$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	0.733052	−	0.680173i	$-0.238095\pi$
$929$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	−0.955573	+	0.294755i	$0.904762\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−0.400969	+	0.694498i	−0.400969	+	0.694498i
$939$		0			0
$940$	−0.222521	−	0.385418i	−0.222521	−	0.385418i
$941$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$941$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$942$		0			0
$943$	−0.400969	−	0.694498i	−0.400969	−	0.694498i
$944$		0			0
$945$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$946$		0			0
$947$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$947$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$953$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$961$	1.00000			1.00000
$962$		0			0
$963$	−1.10992			−1.10992
$964$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$965$		0			0
$966$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$967$	2.00000			2.00000			1.00000			$0$
$967$	2.00000			2.00000			1.00000			$0$
$968$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$971$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$972$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$973$		0			0
$974$	−0.445042			−0.445042
$975$		0			0
$976$	−1.80194			−1.80194
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$	0.777479	−	1.34663i	0.777479	−	1.34663i
$979$		0			0
$980$	−2.24698			−2.24698
$981$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$982$		0			0
$983$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$983$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$984$	1.12349	+	1.94594i	1.12349	+	1.94594i
$985$		0			0
$986$		0			0
$987$	−1.00000			−1.00000
$988$		0			0
$989$	0.198062			0.198062
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−1.55496			−1.55496
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3380.1.v.d.2219.3		6
4.3	odd	2		3380.1.v.g.2219.1		6
5.4	even	2		3380.1.v.g.2219.1		6
13.2	odd	12		3380.1.w.e.699.3		12
13.3	even	3	inner	3380.1.v.d.3019.3		6
13.4	even	6		3380.1.h.c.339.1	yes	3
13.5	odd	4		3380.1.w.e.1499.6		12
13.6	odd	12		3380.1.g.d.3379.1		6
13.7	odd	12		3380.1.g.d.3379.4		6
13.8	odd	4		3380.1.w.e.1499.3		12
13.9	even	3		3380.1.h.e.339.1	yes	3
13.10	even	6		3380.1.v.f.3019.3		6
13.11	odd	12		3380.1.w.e.699.6		12
13.12	even	2		3380.1.v.f.2219.3		6
20.19	odd	2	CM	3380.1.v.d.2219.3		6
52.3	odd	6		3380.1.v.g.3019.1		6
52.7	even	12		3380.1.g.c.3379.3		6
52.11	even	12		3380.1.w.f.699.1		12
52.15	even	12		3380.1.w.f.699.4		12
52.19	even	12		3380.1.g.c.3379.6		6
52.23	odd	6		3380.1.v.e.3019.1		6
52.31	even	4		3380.1.w.f.1499.1		12
52.35	odd	6		3380.1.h.b.339.3	✓	3
52.43	odd	6		3380.1.h.d.339.3	yes	3
52.47	even	4		3380.1.w.f.1499.4		12
52.51	odd	2		3380.1.v.e.2219.1		6
65.4	even	6		3380.1.h.d.339.3	yes	3
65.9	even	6		3380.1.h.b.339.3	✓	3
65.19	odd	12		3380.1.g.c.3379.6		6
65.24	odd	12		3380.1.w.f.699.1		12
65.29	even	6		3380.1.v.g.3019.1		6
65.34	odd	4		3380.1.w.f.1499.4		12
65.44	odd	4		3380.1.w.f.1499.1		12
65.49	even	6		3380.1.v.e.3019.1		6
65.54	odd	12		3380.1.w.f.699.4		12
65.59	odd	12		3380.1.g.c.3379.3		6
65.64	even	2		3380.1.v.e.2219.1		6
260.19	even	12		3380.1.g.d.3379.1		6
260.59	even	12		3380.1.g.d.3379.4		6
260.99	even	4		3380.1.w.e.1499.3		12
260.119	even	12		3380.1.w.e.699.3		12
260.139	odd	6		3380.1.h.e.339.1	yes	3
260.159	odd	6	inner	3380.1.v.d.3019.3		6
260.179	odd	6		3380.1.v.f.3019.3		6
260.199	odd	6		3380.1.h.c.339.1	yes	3
260.219	even	12		3380.1.w.e.699.6		12
260.239	even	4		3380.1.w.e.1499.6		12
260.259	odd	2		3380.1.v.f.2219.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3380.1.g.c.3379.3		6	52.7	even	12
3380.1.g.c.3379.3		6	65.59	odd	12
3380.1.g.c.3379.6		6	52.19	even	12
3380.1.g.c.3379.6		6	65.19	odd	12
3380.1.g.d.3379.1		6	13.6	odd	12
3380.1.g.d.3379.1		6	260.19	even	12
3380.1.g.d.3379.4		6	13.7	odd	12
3380.1.g.d.3379.4		6	260.59	even	12
3380.1.h.b.339.3	✓	3	52.35	odd	6
3380.1.h.b.339.3	✓	3	65.9	even	6
3380.1.h.c.339.1	yes	3	13.4	even	6
3380.1.h.c.339.1	yes	3	260.199	odd	6
3380.1.h.d.339.3	yes	3	52.43	odd	6
3380.1.h.d.339.3	yes	3	65.4	even	6
3380.1.h.e.339.1	yes	3	13.9	even	3
3380.1.h.e.339.1	yes	3	260.139	odd	6
3380.1.v.d.2219.3		6	1.1	even	1	trivial
3380.1.v.d.2219.3		6	20.19	odd	2	CM
3380.1.v.d.3019.3		6	13.3	even	3	inner
3380.1.v.d.3019.3		6	260.159	odd	6	inner
3380.1.v.e.2219.1		6	52.51	odd	2
3380.1.v.e.2219.1		6	65.64	even	2
3380.1.v.e.3019.1		6	52.23	odd	6
3380.1.v.e.3019.1		6	65.49	even	6
3380.1.v.f.2219.3		6	13.12	even	2
3380.1.v.f.2219.3		6	260.259	odd	2
3380.1.v.f.3019.3		6	13.10	even	6
3380.1.v.f.3019.3		6	260.179	odd	6
3380.1.v.g.2219.1		6	4.3	odd	2
3380.1.v.g.2219.1		6	5.4	even	2
3380.1.v.g.3019.1		6	52.3	odd	6
3380.1.v.g.3019.1		6	65.29	even	6
3380.1.w.e.699.3		12	13.2	odd	12
3380.1.w.e.699.3		12	260.119	even	12
3380.1.w.e.699.6		12	13.11	odd	12
3380.1.w.e.699.6		12	260.219	even	12
3380.1.w.e.1499.3		12	13.8	odd	4
3380.1.w.e.1499.3		12	260.99	even	4
3380.1.w.e.1499.6		12	13.5	odd	4
3380.1.w.e.1499.6		12	260.239	even	4
3380.1.w.f.699.1		12	52.11	even	12
3380.1.w.f.699.1		12	65.24	odd	12
3380.1.w.f.699.4		12	52.15	even	12
3380.1.w.f.699.4		12	65.54	odd	12
3380.1.w.f.1499.1		12	52.31	even	4
3380.1.w.f.1499.1		12	65.44	odd	4
3380.1.w.f.1499.4		12	52.47	even	4
3380.1.w.f.1499.4		12	65.34	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3380.v (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.623490 - 1.07992i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.623490 + 1.07992i) q^{6} +(0.900969 + 1.56052i) q^{7} +1.00000 q^{8} +(-0.277479 - 0.480608i) q^{9} +(0.500000 - 0.866025i) q^{10} -1.24698 q^{12} -1.80194 q^{14} +(-0.623490 + 1.07992i) q^{15} +(-0.500000 + 0.866025i) q^{16} +0.554958 q^{18} +(0.500000 + 0.866025i) q^{20} +2.24698 q^{21} +(-0.222521 + 0.385418i) q^{23} +(0.623490 - 1.07992i) q^{24} +1.00000 q^{25} +0.554958 q^{27} +(0.900969 - 1.56052i) q^{28} +(-0.623490 + 1.07992i) q^{29} +(-0.623490 - 1.07992i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(-0.900969 - 1.56052i) q^{35} +(-0.277479 + 0.480608i) q^{36} -1.00000 q^{40} +(-0.900969 + 1.56052i) q^{41} +(-1.12349 + 1.94594i) q^{42} +(-0.222521 - 0.385418i) q^{43} +(0.277479 + 0.480608i) q^{45} +(-0.222521 - 0.385418i) q^{46} -0.445042 q^{47} +(0.623490 + 1.07992i) q^{48} +(-1.12349 + 1.94594i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.277479 + 0.480608i) q^{54} +(0.900969 + 1.56052i) q^{56} +(-0.623490 - 1.07992i) q^{58} +1.24698 q^{60} +(0.900969 + 1.56052i) q^{61} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(0.222521 - 0.385418i) q^{67} +(0.277479 + 0.480608i) q^{69} +1.80194 q^{70} +(-0.277479 - 0.480608i) q^{72} +(0.623490 - 1.07992i) q^{75} +(0.500000 - 0.866025i) q^{80} +(0.623490 - 1.07992i) q^{81} +(-0.900969 - 1.56052i) q^{82} +1.24698 q^{83} +(-1.12349 - 1.94594i) q^{84} +0.445042 q^{86} +(0.777479 + 1.34663i) q^{87} +(-0.222521 + 0.385418i) q^{89} -0.554958 q^{90} +0.445042 q^{92} +(0.222521 - 0.385418i) q^{94} -1.24698 q^{96} +(-1.12349 - 1.94594i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + q^{7} + 6 q^{8} - 2 q^{9} + 3 q^{10} + 2 q^{12} - 2 q^{14} + q^{15} - 3 q^{16} + 4 q^{18} + 3 q^{20} + 4 q^{21} - q^{23} - q^{24} + 6 q^{25} + 4 q^{27}+ \cdots - 2 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - q^3 - 3 * q^4 - 6 * q^5 - q^6 + q^7 + 6 * q^8 - 2 * q^9 + 3 * q^10 + 2 * q^12 - 2 * q^14 + q^15 - 3 * q^16 + 4 * q^18 + 3 * q^20 + 4 * q^21 - q^23 - q^24 + 6 * q^25 + 4 * q^27 + q^28 + q^29 + q^30 - 3 * q^32 - q^35 - 2 * q^36 - 6 * q^40 - q^41 - 2 * q^42 - q^43 + 2 * q^45 - q^46 - 2 * q^47 - q^48 - 2 * q^49 - 3 * q^50 - 2 * q^54 + q^56 + q^58 - 2 * q^60 + q^61 + 3 * q^63 + 6 * q^64 + q^67 + 2 * q^69 + 2 * q^70 - 2 * q^72 - q^75 + 3 * q^80 - q^81 - q^82 - 2 * q^83 - 2 * q^84 + 2 * q^86 + 5 * q^87 - q^89 - 4 * q^90 + 2 * q^92 + q^94 + 2 * q^96 - 2 * q^98

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