LMFDB - Embedded newform 3375.1.m.b.2699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3375,1,Mod(674,3375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("3375.674");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$3375 = 3^{3} \cdot 5^{3}$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	3375.m (of order $10$ , degree $4$ , 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:	$1.68434441764$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{6} + x^{4} - x^{2} + 1$ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 675)
Projective image:	$A_{5}$
Projective field:	Galois closure of 5.1.31640625.2

Embedding invariants

Embedding label			2699.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	3375.2699
Dual form			3375.1.m.b.674.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 - 0.951057i) q^{2} +(0.500000 - 1.53884i) q^{4} -1.61803i q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.587785 - 0.809017i) q^{11} +(-1.53884 - 2.11803i) q^{14} +(-0.309017 - 0.951057i) q^{17} +(0.309017 + 0.951057i) q^{19} +(-1.53884 - 0.500000i) q^{22} +(-0.809017 + 0.587785i) q^{23} +(-2.48990 - 0.809017i) q^{28} +(0.587785 + 0.190983i) q^{29} +1.00000 q^{32} +(-1.30902 - 0.951057i) q^{34} +(-0.363271 + 0.500000i) q^{37} +(1.30902 + 0.951057i) q^{38} +(-0.587785 + 0.809017i) q^{41} +(-1.53884 + 0.500000i) q^{44} +(-0.500000 + 1.53884i) q^{46} +(-0.190983 + 0.587785i) q^{47} -1.61803 q^{49} +(0.500000 - 1.53884i) q^{53} +(-1.53884 + 0.500000i) q^{56} +(0.951057 - 0.309017i) q^{58} +(0.809017 - 0.587785i) q^{61} +(1.30902 - 0.951057i) q^{64} +(1.53884 - 0.500000i) q^{67} -1.61803 q^{68} +(-0.587785 - 0.190983i) q^{71} +1.00000i q^{74} +1.61803 q^{76} +(-1.30902 + 0.951057i) q^{77} +(0.190983 - 0.587785i) q^{79} +1.61803i q^{82} +(-0.500000 - 1.53884i) q^{83} +(-0.587785 + 0.809017i) q^{88} +(0.587785 + 0.809017i) q^{89} +(0.500000 + 1.53884i) q^{92} +(0.309017 + 0.951057i) q^{94} +(0.951057 + 0.309017i) q^{97} +(-2.11803 + 1.53884i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 6 q^{2} + 4 q^{4} + 2 q^{8} + 2 q^{17} - 2 q^{19} - 2 q^{23} + 8 q^{32} - 6 q^{34} + 6 q^{38} - 4 q^{46} - 6 q^{47} - 4 q^{49} + 4 q^{53} + 2 q^{61} + 6 q^{64} - 4 q^{68} + 4 q^{76} - 6 q^{77} + 6 q^{79}+ \cdots - 8 q^{98}+O(q^{100})$ 8 * q + 6 * q^2 + 4 * q^4 + 2 * q^8 + 2 * q^17 - 2 * q^19 - 2 * q^23 + 8 * q^32 - 6 * q^34 + 6 * q^38 - 4 * q^46 - 6 * q^47 - 4 * q^49 + 4 * q^53 + 2 * q^61 + 6 * q^64 - 4 * q^68 + 4 * q^76 - 6 * q^77 + 6 * q^79 - 4 * q^83 + 4 * q^92 - 2 * q^94 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3375\mathbb{Z}\right)^\times$ .

$n$	$1001$	$2377$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

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

)

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

$2$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$2$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$3$		0			0
$3$		0			0
$4$	0.500000	−	1.53884i	0.500000	−	1.53884i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$7$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$8$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$9$		0			0
$10$		0			0
$11$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$11$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$12$		0			0
$13$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$13$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$14$	−1.53884	−	2.11803i	−1.53884	−	2.11803i
$15$		0			0
$16$		0			0
$17$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$17$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$18$		0			0
$19$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$19$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$20$		0			0
$21$		0			0
$22$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$23$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$23$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$29$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$29$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$30$		0			0
$31$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$31$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$32$	1.00000			1.00000
$33$		0			0
$34$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$35$		0			0
$36$		0			0
$37$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$37$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$38$	1.30902	+	0.951057i	1.30902	+	0.951057i
$39$		0			0
$40$		0			0
$41$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$41$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$45$		0			0
$46$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$47$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$47$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$48$		0			0
$49$	−1.61803			−1.61803
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$53$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$54$		0			0
$55$		0			0
$56$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$57$		0			0
$58$	0.951057	−	0.309017i	0.951057	−	0.309017i
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$		0			0
$61$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$61$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$62$		0			0
$63$		0			0
$64$	1.30902	−	0.951057i	1.30902	−	0.951057i
$65$		0			0
$66$		0			0
$67$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$67$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$68$	−1.61803			−1.61803
$69$		0			0
$70$		0			0
$71$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$71$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$72$		0			0
$73$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$73$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$74$			1.00000i			1.00000i
$75$		0			0
$76$	1.61803			1.61803
$77$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$78$		0			0
$79$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$79$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$80$		0			0
$81$		0			0
$82$			1.61803i			1.61803i
$83$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$83$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$89$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$89$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$90$		0			0
$91$		0			0
$92$	0.500000	+	1.53884i	0.500000	+	1.53884i
$93$		0			0
$94$	0.309017	+	0.951057i	0.309017	+	0.951057i
$95$		0			0
$96$		0			0
$97$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$97$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$98$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$99$		0			0
$100$		0			0
$101$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$101$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$		0			0
$105$		0			0
$106$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$109$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$113$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$114$		0			0
$115$		0			0
$116$	0.587785	−	0.809017i	0.587785	−	0.809017i
$117$		0			0
$118$		0			0
$119$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$120$		0			0
$121$		0			0
$122$	0.500000	−	1.53884i	0.500000	−	1.53884i
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$127$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$128$	0.500000	−	1.53884i	0.500000	−	1.53884i
$129$		0			0
$130$		0			0
$131$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$131$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$132$		0			0
$133$	1.53884	−	0.500000i	1.53884	−	0.500000i
$134$	1.53884	−	2.11803i	1.53884	−	2.11803i
$135$		0			0
$136$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$137$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$137$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$138$		0			0
$139$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$139$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$140$		0			0
$141$		0			0
$142$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.587785	+	0.809017i	0.587785	+	0.809017i
$149$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$149$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	0.809017	−	0.587785i	0.809017	−	0.587785i
$153$		0			0
$154$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$155$		0			0
$156$		0			0
$157$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$157$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$158$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$159$		0			0
$160$		0			0
$161$	0.951057	+	1.30902i	0.951057	+	1.30902i
$162$		0			0
$163$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$163$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$164$	0.951057	+	1.30902i	0.951057	+	1.30902i
$165$		0			0
$166$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$167$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$167$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$168$		0			0
$169$	0.309017	+	0.951057i	0.309017	+	0.951057i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$173$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	1.53884	+	0.500000i	1.53884	+	0.500000i
$179$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$179$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$180$		0			0
$181$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$181$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$182$		0			0
$183$		0			0
$184$	0.809017	+	0.587785i	0.809017	+	0.587785i
$185$		0			0
$186$		0			0
$187$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$188$	0.809017	+	0.587785i	0.809017	+	0.587785i
$189$		0			0
$190$		0			0
$191$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$191$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$192$		0			0
$193$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$193$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$194$	1.53884	−	0.500000i	1.53884	−	0.500000i
$195$		0			0
$196$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$197$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$197$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$		0			0
$202$	0.951057	+	1.30902i	0.951057	+	1.30902i
$203$	0.309017	−	0.951057i	0.309017	−	0.951057i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.587785	−	0.809017i	0.587785	−	0.809017i
$210$		0			0
$211$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$211$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$212$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.61803			1.61803
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$223$	0.951057	+	1.30902i	0.951057	+	1.30902i			1.00000i	$0.5\pi$
$224$		−	1.61803i		−	1.61803i
$225$		0			0
$226$		0			0
$227$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$227$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$228$		0			0
$229$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$229$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$230$		0			0
$231$		0			0
$232$		−	0.618034i		−	0.618034i
$233$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$233$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−1.53884	+	2.11803i	−1.53884	+	2.11803i
$239$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$239$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$240$		0			0
$241$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$241$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$242$		0			0
$243$		0			0
$244$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$251$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$252$		0			0
$253$	0.951057	+	0.309017i	0.951057	+	0.309017i
$254$	0.951057	+	0.309017i	0.951057	+	0.309017i
$255$		0			0
$256$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$		0			0
$259$	0.809017	+	0.587785i	0.809017	+	0.587785i
$260$		0			0
$261$		0			0
$262$	0.587785	−	0.809017i	0.587785	−	0.809017i
$263$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$263$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$264$		0			0
$265$		0			0
$266$	1.53884	−	2.11803i	1.53884	−	2.11803i
$267$		0			0
$268$		−	2.61803i		−	2.61803i
$269$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$269$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$270$		0			0
$271$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$271$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$272$		0			0
$273$		0			0
$274$	1.61803			1.61803
$275$		0			0
$276$		0			0
$277$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$277$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$278$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$279$		0			0
$280$		0			0
$281$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$281$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$282$		0			0
$283$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$283$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$284$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$285$		0			0
$286$		0			0
$287$	1.30902	+	0.951057i	1.30902	+	0.951057i
$288$		0			0
$289$		0			0
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$293$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$294$		0			0
$295$		0			0
$296$	0.587785	+	0.190983i	0.587785	+	0.190983i
$297$		0			0
$298$	1.53884	+	2.11803i	1.53884	+	2.11803i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$307$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$308$	0.809017	+	2.48990i	0.809017	+	2.48990i
$309$		0			0
$310$		0			0
$311$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$311$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$312$		0			0
$313$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$313$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$314$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$315$		0			0
$316$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$317$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$317$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$318$		0			0
$319$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$320$		0			0
$321$		0			0
$322$	2.48990	+	0.809017i	2.48990	+	0.809017i
$323$	0.809017	−	0.587785i	0.809017	−	0.587785i
$324$		0			0
$325$		0			0
$326$		−	1.61803i		−	1.61803i
$327$		0			0
$328$	0.951057	+	0.309017i	0.951057	+	0.309017i
$329$	0.951057	+	0.309017i	0.951057	+	0.309017i
$330$		0			0
$331$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$331$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$332$	−2.61803			−2.61803
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$337$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$338$	1.30902	+	0.951057i	1.30902	+	0.951057i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$			1.00000i			1.00000i
$344$		0			0
$345$		0			0
$346$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$347$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$347$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$		0			0
$352$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$353$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$353$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$354$		0			0
$355$		0			0
$356$	1.53884	−	0.500000i	1.53884	−	0.500000i
$357$		0			0
$358$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$359$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$359$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$360$		0			0
$361$		0			0
$362$	1.30902	+	0.951057i	1.30902	+	0.951057i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$367$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$372$		0			0
$373$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$373$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$374$			1.61803i			1.61803i
$375$		0			0
$376$	0.618034			0.618034
$377$		0			0
$378$		0			0
$379$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$379$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$380$		0			0
$381$		0			0
$382$			2.61803i			2.61803i
$383$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$383$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$384$		0			0
$385$		0			0
$386$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$387$		0			0
$388$	0.951057	−	1.30902i	0.951057	−	1.30902i
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$	0.809017	+	0.587785i	0.809017	+	0.587785i
$392$	0.500000	+	1.53884i	0.500000	+	1.53884i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$397$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$401$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$402$		0			0
$403$		0			0
$404$	1.53884	+	0.500000i	1.53884	+	0.500000i
$405$		0			0
$406$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$407$	0.618034			0.618034
$408$		0			0
$409$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$409$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		−	1.61803i		−	1.61803i
$419$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$419$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$420$		0			0
$421$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$421$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$422$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$423$		0			0
$424$	−1.61803			−1.61803
$425$		0			0
$426$		0			0
$427$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$431$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$432$		0			0
$433$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$433$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$434$		0			0
$435$		0			0
$436$	1.30902	−	0.951057i	1.30902	−	0.951057i
$437$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$438$		0			0
$439$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$439$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$443$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$444$		0			0
$445$		0			0
$446$	2.48990	+	0.809017i	2.48990	+	0.809017i
$447$		0			0
$448$	−1.53884	−	2.11803i	−1.53884	−	2.11803i
$449$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$449$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$450$		0			0
$451$	1.00000			1.00000
$452$		0			0
$453$		0			0
$454$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$455$		0			0
$456$		0			0
$457$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$457$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$461$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$462$		0			0
$463$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$463$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$464$		0			0
$465$		0			0
$466$	1.30902	+	0.951057i	1.30902	+	0.951057i
$467$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$467$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$468$		0			0
$469$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$			2.61803i			2.61803i
$477$		0			0
$478$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$479$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$479$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$480$		0			0
$481$		0			0
$482$	−1.00000			−1.00000
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$487$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$488$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$489$		0			0
$490$		0			0
$491$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$491$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$492$		0			0
$493$		−	0.618034i		−	0.618034i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$498$		0			0
$499$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$499$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$500$		0			0
$501$		0			0
$502$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$503$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$503$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$504$		0			0
$505$		0			0
$506$	1.53884	−	0.500000i	1.53884	−	0.500000i
$507$		0			0
$508$	0.951057	−	0.309017i	0.951057	−	0.309017i
$509$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$509$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.587785	−	0.190983i	0.587785	−	0.190983i
$518$	1.61803			1.61803
$519$		0			0
$520$		0			0
$521$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$521$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$522$		0			0
$523$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$523$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$524$		−	1.00000i		−	1.00000i
$525$		0			0
$526$	1.61803			1.61803
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		−	2.61803i		−	2.61803i
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$537$		0			0
$538$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$539$	0.951057	+	1.30902i	0.951057	+	1.30902i
$540$		0			0
$541$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$541$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$542$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$543$		0			0
$544$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$545$		0			0
$546$		0			0
$547$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$547$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$548$	1.30902	−	0.951057i	1.30902	−	0.951057i
$549$		0			0
$550$		0			0
$551$			0.618034i			0.618034i
$552$		0			0
$553$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$554$		0			0
$555$		0			0
$556$	0.500000	+	1.53884i	0.500000	+	1.53884i
$557$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$557$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.951057	−	1.30902i	0.951057	−	1.30902i
$563$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$563$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$564$		0			0
$565$		0			0
$566$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$567$		0			0
$568$			0.618034i			0.618034i
$569$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$569$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$570$		0			0
$571$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$571$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$572$		0			0
$573$		0			0
$574$	2.61803			2.61803
$575$		0			0
$576$		0			0
$577$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$577$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$582$		0			0
$583$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$584$		0			0
$585$		0			0
$586$	1.30902	−	0.951057i	1.30902	−	0.951057i
$587$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$587$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$593$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$594$		0			0
$595$		0			0
$596$	2.48990	+	0.809017i	2.48990	+	0.809017i
$597$		0			0
$598$		0			0
$599$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$599$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$600$		0			0
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	0.309017	+	0.951057i	0.309017	+	0.951057i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$613$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$614$	0.587785	+	0.809017i	0.587785	+	0.809017i
$615$		0			0
$616$	1.30902	+	0.951057i	1.30902	+	0.951057i
$617$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$617$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$618$		0			0
$619$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$619$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$620$		0			0
$621$		0			0
$622$	1.53884	+	0.500000i	1.53884	+	0.500000i
$623$	1.30902	−	0.951057i	1.30902	−	0.951057i
$624$		0			0
$625$		0			0
$626$			2.61803i			2.61803i
$627$		0			0
$628$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$629$	0.587785	+	0.190983i	0.587785	+	0.190983i
$630$		0			0
$631$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$631$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$632$	−0.618034			−0.618034
$633$		0			0
$634$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$639$		0			0
$640$		0			0
$641$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$641$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$642$		0			0
$643$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$643$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$644$	2.48990	−	0.809017i	2.48990	−	0.809017i
$645$		0			0
$646$	0.500000	−	1.53884i	0.500000	−	1.53884i
$647$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$647$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$653$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$653$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	1.53884	−	0.500000i	1.53884	−	0.500000i
$659$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$659$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$660$		0			0
$661$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$661$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$662$		0			0
$663$		0			0
$664$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$665$		0			0
$666$		0			0
$667$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$672$		0			0
$673$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$673$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$674$		0			0
$675$		0			0
$676$	1.61803			1.61803
$677$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$677$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$678$		0			0
$679$	0.500000	−	1.53884i	0.500000	−	1.53884i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$683$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$684$		0			0
$685$		0			0
$686$	0.951057	+	1.30902i	0.951057	+	1.30902i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$691$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$692$	0.309017	+	0.951057i	0.309017	+	0.951057i
$693$		0			0
$694$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$695$		0			0
$696$		0			0
$697$	0.951057	+	0.309017i	0.951057	+	0.309017i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$701$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$702$		0			0
$703$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$704$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$705$		0			0
$706$	0.809017	+	2.48990i	0.809017	+	2.48990i
$707$	1.61803			1.61803
$708$		0			0
$709$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$709$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$710$		0			0
$711$		0			0
$712$	0.587785	−	0.809017i	0.587785	−	0.809017i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$717$		0			0
$718$			1.61803i			1.61803i
$719$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$719$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$	1.61803			1.61803
$725$		0			0
$726$		0			0
$727$	1.17557	+	1.61803i	1.17557	+	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$727$	1.17557	+	1.61803i	1.17557	+	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$733$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$734$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$735$		0			0
$736$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$737$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$738$		0			0
$739$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$739$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$740$		0			0
$741$		0			0
$742$	−4.02874	+	1.30902i	−4.02874	+	1.30902i
$743$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$743$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$		0			0
$746$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$747$		0			0
$748$	0.951057	+	1.30902i	0.951057	+	1.30902i
$749$		0			0
$750$		0			0
$751$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$751$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$757$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$758$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$759$		0			0
$760$		0			0
$761$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$761$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$762$		0			0
$763$	0.951057	−	1.30902i	0.951057	−	1.30902i
$764$	1.53884	+	2.11803i	1.53884	+	2.11803i
$765$		0			0
$766$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$767$		0			0
$768$		0			0
$769$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$769$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$770$		0			0
$771$		0			0
$772$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$773$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$773$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$774$		0			0
$775$		0			0
$776$		−	1.00000i		−	1.00000i
$777$		0			0
$778$		0			0
$779$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$780$		0			0
$781$	0.190983	+	0.587785i	0.190983	+	0.587785i
$782$	1.61803			1.61803
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$787$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$795$		0			0
$796$		0			0
$797$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$797$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$798$		0			0
$799$	0.618034			0.618034
$800$		0			0
$801$		0			0
$802$	−1.53884	−	2.11803i	−1.53884	−	2.11803i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.951057	−	0.309017i	0.951057	−	0.309017i
$809$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$809$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$810$		0			0
$811$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$811$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$812$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$813$		0			0
$814$	0.809017	−	0.587785i	0.809017	−	0.587785i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$821$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$822$		0			0
$823$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$823$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$827$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$828$		0			0
$829$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$829$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.500000	+	1.53884i	0.500000	+	1.53884i
$834$		0			0
$835$		0			0
$836$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$837$		0			0
$838$	1.53884	−	2.11803i	1.53884	−	2.11803i
$839$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$839$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$840$		0			0
$841$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$842$	0.500000	+	1.53884i	0.500000	+	1.53884i
$843$		0			0
$844$	0.809017	+	2.48990i	0.809017	+	2.48990i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	0.618034i		−	0.618034i
$852$		0			0
$853$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$853$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$854$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$859$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$863$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$864$		0			0
$865$		0			0
$866$	0.951057	−	1.30902i	0.951057	−	1.30902i
$867$		0			0
$868$		0			0
$869$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$870$		0			0
$871$		0			0
$872$	0.309017	−	0.951057i	0.309017	−	0.951057i
$873$		0			0
$874$	−1.61803			−1.61803
$875$		0			0
$876$		0			0
$877$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$877$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$878$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$879$		0			0
$880$		0			0
$881$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$881$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$882$		0			0
$883$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$883$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$884$		0			0
$885$		0			0
$886$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$887$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$887$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$888$		0			0
$889$	0.809017	−	0.587785i	0.809017	−	0.587785i
$890$		0			0
$891$		0			0
$892$	2.48990	−	0.809017i	2.48990	−	0.809017i
$893$	−0.618034			−0.618034
$894$		0			0
$895$		0			0
$896$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$897$		0			0
$898$	0.587785	+	0.809017i	0.587785	+	0.809017i
$899$		0			0
$900$		0			0
$901$	−1.61803			−1.61803
$902$	1.30902	−	0.951057i	1.30902	−	0.951057i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$907$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$908$	0.809017	+	2.48990i	0.809017	+	2.48990i
$909$		0			0
$910$		0			0
$911$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$911$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$912$		0			0
$913$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$914$	0.951057	+	1.30902i	0.951057	+	1.30902i
$915$		0			0
$916$		0			0
$917$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$918$		0			0
$919$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$919$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$920$		0			0
$921$		0			0
$922$	1.53884	+	0.500000i	1.53884	+	0.500000i
$923$		0			0
$924$		0			0
$925$		0			0
$926$		−	1.61803i		−	1.61803i
$927$		0			0
$928$	0.587785	+	0.190983i	0.587785	+	0.190983i
$929$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$929$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$930$		0			0
$931$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$932$	1.61803			1.61803
$933$		0			0
$934$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$935$		0			0
$936$		0			0
$937$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$937$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$938$	−3.42705	−	2.48990i	−3.42705	−	2.48990i
$939$		0			0
$940$		0			0
$941$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$941$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$942$		0			0
$943$		−	1.00000i		−	1.00000i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$947$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.951057	+	1.30902i	0.951057	+	1.30902i
$953$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$953$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$954$		0			0
$955$		0			0
$956$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$957$		0			0
$958$		0			0
$959$	0.951057	−	1.30902i	0.951057	−	1.30902i
$960$		0			0
$961$	0.809017	−	0.587785i	0.809017	−	0.587785i
$962$		0			0
$963$		0			0
$964$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$965$		0			0
$966$		0			0
$967$	−0.587785	+	0.190983i	−0.587785	+	0.190983i	−0.587785	−	0.809017i	$-0.700000\pi$
$967$	−0.587785	+	0.190983i	−0.587785	+	0.190983i			1.00000i	$0.5\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$971$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$972$		0			0
$973$	0.951057	+	1.30902i	0.951057	+	1.30902i
$974$		−	1.61803i		−	1.61803i
$975$		0			0
$976$		0			0
$977$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$977$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$978$		0			0
$979$	0.309017	−	0.951057i	0.309017	−	0.951057i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$983$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$984$		0			0
$985$		0			0
$986$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$991$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$992$		0			0
$993$		0			0
$994$	0.500000	+	1.53884i	0.500000	+	1.53884i
$995$		0			0
$996$		0			0
$997$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$997$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$998$	1.30902	−	0.951057i	1.30902	−	0.951057i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3375.1.m.b.2699.1		8
3.2	odd	2		3375.1.m.a.2699.1		8
5.2	odd	4		3375.1.o.a.2051.2		8
5.3	odd	4		675.1.o.a.161.1	✓	8
5.4	even	2		3375.1.m.a.2699.2		8
15.2	even	4		3375.1.o.a.2051.1		8
15.8	even	4		675.1.o.a.161.2	yes	8
15.14	odd	2	inner	3375.1.m.b.2699.2		8
25.9	even	10		3375.1.m.a.674.2		8
25.12	odd	20		3375.1.o.a.701.1		8
25.13	odd	20		675.1.o.a.566.2	yes	8
25.16	even	5	inner	3375.1.m.b.674.1		8
45.13	odd	12		2025.1.y.a.836.2		16
45.23	even	12		2025.1.y.a.836.1		16
45.38	even	12		2025.1.y.a.1511.2		16
45.43	odd	12		2025.1.y.a.1511.1		16
75.38	even	20		675.1.o.a.566.1	yes	8
75.41	odd	10		3375.1.m.a.674.1		8
75.59	odd	10	inner	3375.1.m.b.674.2		8
75.62	even	20		3375.1.o.a.701.2		8
225.13	odd	60		2025.1.y.a.1241.2		16
225.38	even	60		2025.1.y.a.1916.2		16
225.88	odd	60		2025.1.y.a.1916.1		16
225.113	even	60		2025.1.y.a.1241.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.1.o.a.161.1	✓	8	5.3	odd	4
675.1.o.a.161.2	yes	8	15.8	even	4
675.1.o.a.566.1	yes	8	75.38	even	20
675.1.o.a.566.2	yes	8	25.13	odd	20
2025.1.y.a.836.1		16	45.23	even	12
2025.1.y.a.836.2		16	45.13	odd	12
2025.1.y.a.1241.1		16	225.113	even	60
2025.1.y.a.1241.2		16	225.13	odd	60
2025.1.y.a.1511.1		16	45.43	odd	12
2025.1.y.a.1511.2		16	45.38	even	12
2025.1.y.a.1916.1		16	225.88	odd	60
2025.1.y.a.1916.2		16	225.38	even	60
3375.1.m.a.674.1		8	75.41	odd	10
3375.1.m.a.674.2		8	25.9	even	10
3375.1.m.a.2699.1		8	3.2	odd	2
3375.1.m.a.2699.2		8	5.4	even	2
3375.1.m.b.674.1		8	25.16	even	5	inner
3375.1.m.b.674.2		8	75.59	odd	10	inner
3375.1.m.b.2699.1		8	1.1	even	1	trivial
3375.1.m.b.2699.2		8	15.14	odd	2	inner
3375.1.o.a.701.1		8	25.12	odd	20
3375.1.o.a.701.2		8	75.62	even	20
3375.1.o.a.2051.1		8	15.2	even	4
3375.1.o.a.2051.2		8	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	3375.1.m.b.2699.1

Level	$3375$
Weight	$1$
Character	3375.2699
Analytic conductor	$1.684$
Analytic rank	$0$
Dimension	$8$
Projective image	$A_{5}$
CM/RM	no
Inner twists	$4$