LMFDB - Embedded newform 2904.1.t.e.245.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2904,1,Mod(245,2904)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2904, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 8]))

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

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

chi := DirichletCharacter("2904.245");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2904 = 2^{3} \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2904.t (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:	$1.44928479669$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 264)
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.8433216.2

Embedding invariants

Embedding label			245.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	2904.245
Dual form			2904.1.t.e.2501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.190983 + 0.587785i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.190983 + 0.587785i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.61803 q^{10} +1.00000 q^{12} +(0.190983 + 0.587785i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.309017 + 0.951057i) q^{18} +(1.30902 - 0.951057i) q^{20} -0.618034 q^{21} +(0.809017 - 0.587785i) q^{24} +(0.500000 + 1.53884i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.500000 + 0.363271i) q^{28} +(0.500000 - 1.53884i) q^{29} +(0.500000 + 1.53884i) q^{30} +(-0.500000 + 0.363271i) q^{31} -1.00000 q^{32} +(-0.809017 + 0.587785i) q^{35} +(0.309017 + 0.951057i) q^{36} +(0.500000 - 1.53884i) q^{40} +(-0.500000 + 0.363271i) q^{42} -1.61803 q^{45} +(0.309017 - 0.951057i) q^{48} +(0.500000 + 0.363271i) q^{49} +(1.30902 + 0.951057i) q^{50} +(-0.500000 + 0.363271i) q^{53} -1.00000 q^{54} +0.618034 q^{56} +(-0.500000 - 1.53884i) q^{58} +(0.190983 - 0.587785i) q^{59} +(1.30902 + 0.951057i) q^{60} +(-0.190983 + 0.587785i) q^{62} +(-0.190983 - 0.587785i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.309017 + 0.951057i) q^{70} +(0.809017 + 0.587785i) q^{72} +(0.500000 - 1.53884i) q^{73} +(-1.30902 + 0.951057i) q^{75} +(-1.30902 + 0.951057i) q^{79} +(-0.500000 - 1.53884i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.30902 - 0.951057i) q^{83} +(-0.190983 + 0.587785i) q^{84} +1.61803 q^{87} +(-1.30902 + 0.951057i) q^{90} +(-0.500000 - 0.363271i) q^{93} +(-0.309017 - 0.951057i) q^{96} +(1.30902 - 0.951057i) q^{97} +0.618034 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - q^4 + 3 * q^5 + q^6 - 3 * q^7 + q^8 - q^9	$ 4 q + q^{2} - q^{3} - q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + q^{8} - q^{9} + 2 q^{10} + 4 q^{12} + 3 q^{14} - 2 q^{15} - q^{16} + q^{18} + 3 q^{20} + 2 q^{21} + q^{24} + 2 q^{25} - q^{27} + 2 q^{28} + 2 q^{29} + 2 q^{30} - 2 q^{31} - 4 q^{32} - q^{35} - q^{36} + 2 q^{40} - 2 q^{42} - 2 q^{45} - q^{48} + 2 q^{49} + 3 q^{50} - 2 q^{53} - 4 q^{54} - 2 q^{56} - 2 q^{58} + 3 q^{59} + 3 q^{60} - 3 q^{62} - 3 q^{63} - q^{64} + q^{70} + q^{72} + 2 q^{73} - 3 q^{75} - 3 q^{79} - 2 q^{80} - q^{81} - 3 q^{83} - 3 q^{84} + 2 q^{87} - 3 q^{90} - 2 q^{93} + q^{96} + 3 q^{97} - 2 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^3 - q^4 + 3 * q^5 + q^6 - 3 * q^7 + q^8 - q^9 + 2 * q^10 + 4 * q^12 + 3 * q^14 - 2 * q^15 - q^16 + q^18 + 3 * q^20 + 2 * q^21 + q^24 + 2 * q^25 - q^27 + 2 * q^28 + 2 * q^29 + 2 * q^30 - 2 * q^31 - 4 * q^32 - q^35 - q^36 + 2 * q^40 - 2 * q^42 - 2 * q^45 - q^48 + 2 * q^49 + 3 * q^50 - 2 * q^53 - 4 * q^54 - 2 * q^56 - 2 * q^58 + 3 * q^59 + 3 * q^60 - 3 * q^62 - 3 * q^63 - q^64 + q^70 + q^72 + 2 * q^73 - 3 * q^75 - 3 * q^79 - 2 * q^80 - q^81 - 3 * q^83 - 3 * q^84 + 2 * q^87 - 3 * q^90 - 2 * q^93 + q^96 + 3 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2904\mathbb{Z}\right)^\times$.

$n$	$727$	$1453$	$1937$	$2785$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.809017	−	0.587785i
$2$	0.809017	−	0.587785i	0.809017	−	0.587785i
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$4$	0.309017	−	0.951057i	0.309017	−	0.951057i
$5$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$5$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$6$	0.809017	+	0.587785i	0.809017	+	0.587785i
$7$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$7$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$8$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$9$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$10$	1.61803			1.61803
$11$		0			0
$11$		0			0
$12$	1.00000			1.00000
$13$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$13$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$14$	0.190983	+	0.587785i	0.190983	+	0.587785i
$15$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$16$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$17$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$17$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$18$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$19$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$19$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$20$	1.30902	−	0.951057i	1.30902	−	0.951057i
$21$	−0.618034			−0.618034
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	0.809017	−	0.587785i	0.809017	−	0.587785i
$25$	0.500000	+	1.53884i	0.500000	+	1.53884i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$28$	0.500000	+	0.363271i	0.500000	+	0.363271i
$29$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$29$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$30$	0.500000	+	1.53884i	0.500000	+	1.53884i
$31$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$31$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$32$	−1.00000			−1.00000
$33$		0			0
$34$		0			0
$35$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$36$	0.309017	+	0.951057i	0.309017	+	0.951057i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$		0			0
$39$		0			0
$40$	0.500000	−	1.53884i	0.500000	−	1.53884i
$41$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$41$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$42$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$	−1.61803			−1.61803
$46$		0			0
$47$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$47$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$48$	0.309017	−	0.951057i	0.309017	−	0.951057i
$49$	0.500000	+	0.363271i	0.500000	+	0.363271i
$50$	1.30902	+	0.951057i	1.30902	+	0.951057i
$51$		0			0
$52$		0			0
$53$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$53$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$54$	−1.00000			−1.00000
$55$		0			0
$56$	0.618034			0.618034
$57$		0			0
$58$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$59$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$59$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$60$	1.30902	+	0.951057i	1.30902	+	0.951057i
$61$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$61$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$62$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$63$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$64$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$65$		0			0
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$71$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$71$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$72$	0.809017	+	0.587785i	0.809017	+	0.587785i
$73$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$73$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$74$		0			0
$75$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$79$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$80$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$81$	0.309017	−	0.951057i	0.309017	−	0.951057i
$82$		0			0
$83$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$83$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$84$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$85$		0			0
$86$		0			0
$87$	1.61803			1.61803
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$91$		0			0
$92$		0			0
$93$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$94$		0			0
$95$		0			0
$96$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$97$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$97$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$98$	0.618034			0.618034
$99$		0			0
$100$	1.61803			1.61803
$101$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$101$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$102$		0			0
$103$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$103$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$104$		0			0
$105$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$106$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$107$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$107$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$108$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	0.500000	−	0.363271i	0.500000	−	0.363271i
$113$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$113$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$114$		0			0
$115$		0			0
$116$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$117$		0			0
$118$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$119$		0			0
$120$	1.61803			1.61803
$121$		0			0
$122$		0			0
$123$		0			0
$124$	0.190983	+	0.587785i	0.190983	+	0.587785i
$125$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$126$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$127$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$127$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$128$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$129$		0			0
$130$		0			0
$131$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$131$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$136$		0			0
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$		0			0
$139$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$139$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$140$	0.309017	+	0.951057i	0.309017	+	0.951057i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.00000			1.00000
$145$	2.11803	−	1.53884i	2.11803	−	1.53884i
$146$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$147$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$148$		0			0
$149$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$149$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$150$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$151$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$151$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.00000			−1.00000
$156$		0			0
$157$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$157$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$158$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$159$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$160$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$161$		0			0
$162$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$163$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$163$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$164$		0			0
$165$		0			0
$166$	−1.61803			−1.61803
$167$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$167$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$168$	0.190983	+	0.587785i	0.190983	+	0.587785i
$169$	0.309017	−	0.951057i	0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$173$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$174$	1.30902	−	0.951057i	1.30902	−	0.951057i
$175$	−1.00000			−1.00000
$176$		0			0
$177$	0.618034			0.618034
$178$		0			0
$179$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$179$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$180$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	−0.618034			−0.618034
$187$		0			0
$188$		0			0
$189$	0.500000	−	0.363271i	0.500000	−	0.363271i
$190$		0			0
$191$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$191$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$192$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$193$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$193$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$194$	0.500000	−	1.53884i	0.500000	−	1.53884i
$195$		0			0
$196$	0.500000	−	0.363271i	0.500000	−	0.363271i
$197$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$197$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$198$		0			0
$199$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$199$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$200$	1.30902	−	0.951057i	1.30902	−	0.951057i
$201$		0			0
$202$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$203$	0.809017	+	0.587785i	0.809017	+	0.587785i
$204$		0			0
$205$		0			0
$206$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−1.00000			−1.00000
$211$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$211$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$212$	0.190983	+	0.587785i	0.190983	+	0.587785i
$213$		0			0
$214$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$215$		0			0
$216$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$217$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$218$		0			0
$219$	1.61803			1.61803
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$223$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$224$	0.190983	−	0.587785i	0.190983	−	0.587785i
$225$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$226$		0			0
$227$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$227$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$228$		0			0
$229$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$229$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$230$		0			0
$231$		0			0
$232$	−1.61803			−1.61803
$233$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$233$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$234$		0			0
$235$		0			0
$236$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$237$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$238$		0			0
$239$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$239$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$240$	1.30902	−	0.951057i	1.30902	−	0.951057i
$241$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$241$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$242$		0			0
$243$	1.00000			1.00000
$244$		0			0
$245$	0.309017	+	0.951057i	0.309017	+	0.951057i
$246$		0			0
$247$		0			0
$248$	0.500000	+	0.363271i	0.500000	+	0.363271i
$249$	0.500000	−	1.53884i	0.500000	−	1.53884i
$250$	0.309017	+	0.951057i	0.309017	+	0.951057i
$251$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$251$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$252$	−0.618034			−0.618034
$253$		0			0
$254$	2.00000			2.00000
$255$		0			0
$256$	0.309017	+	0.951057i	0.309017	+	0.951057i
$257$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$257$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.500000	+	1.53884i	0.500000	+	1.53884i
$262$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		0			0
$265$	−1.00000			−1.00000
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$269$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$270$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$271$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$271$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		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			0
$279$	0.190983	−	0.587785i	0.190983	−	0.587785i
$280$	0.809017	+	0.587785i	0.809017	+	0.587785i
$281$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$281$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$282$		0			0
$283$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$283$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.809017	−	0.587785i	0.809017	−	0.587785i
$289$	0.309017	+	0.951057i	0.309017	+	0.951057i
$290$	0.809017	−	2.48990i	0.809017	−	2.48990i
$291$	1.30902	+	0.951057i	1.30902	+	0.951057i
$292$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$293$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$293$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$294$	0.190983	+	0.587785i	0.190983	+	0.587785i
$295$	0.809017	−	0.587785i	0.809017	−	0.587785i
$296$		0			0
$297$		0			0
$298$	0.618034			0.618034
$299$		0			0
$300$	0.500000	+	1.53884i	0.500000	+	1.53884i
$301$		0			0
$302$	1.30902	+	0.951057i	1.30902	+	0.951057i
$303$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	0.618034			0.618034
$310$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$311$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$311$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$312$		0			0
$313$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$313$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$314$		0			0
$315$	0.309017	−	0.951057i	0.309017	−	0.951057i
$316$	0.500000	+	1.53884i	0.500000	+	1.53884i
$317$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$317$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$318$	−0.618034			−0.618034
$319$		0			0
$320$	−1.61803			−1.61803
$321$	0.500000	−	0.363271i	0.500000	−	0.363271i
$322$		0			0
$323$		0			0
$324$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.500000	+	0.363271i	0.500000	+	0.363271i
$337$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$337$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$338$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$344$		0			0
$345$		0			0
$346$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$347$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$347$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$348$	0.500000	−	1.53884i	0.500000	−	1.53884i
$349$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$349$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$350$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$351$		0			0
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$	0.500000	−	0.363271i	0.500000	−	0.363271i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$359$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$359$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$360$	0.500000	+	1.53884i	0.500000	+	1.53884i
$361$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.11803	−	1.53884i	2.11803	−	1.53884i
$366$		0			0
$367$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$367$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$372$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$	−1.00000			−1.00000
$376$		0			0
$377$		0			0
$378$	0.190983	−	0.587785i	0.190983	−	0.587785i
$379$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$379$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$380$		0			0
$381$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$382$		0			0
$383$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$383$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$384$	−1.00000			−1.00000
$385$		0			0
$386$	0.618034			0.618034
$387$		0			0
$388$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$389$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$389$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$390$		0			0
$391$		0			0
$392$	0.190983	−	0.587785i	0.190983	−	0.587785i
$393$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$394$	1.30902	−	0.951057i	1.30902	−	0.951057i
$395$	−2.61803			−2.61803
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$399$		0			0
$400$	0.500000	−	1.53884i	0.500000	−	1.53884i
$401$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$401$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$402$		0			0
$403$		0			0
$404$	0.500000	+	1.53884i	0.500000	+	1.53884i
$405$	1.30902	−	0.951057i	1.30902	−	0.951057i
$406$	1.00000			1.00000
$407$		0			0
$408$		0			0
$409$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$409$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$413$	0.309017	+	0.224514i	0.309017	+	0.224514i
$414$		0			0
$415$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$419$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$420$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$421$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$421$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$422$		0			0
$423$		0			0
$424$	0.500000	+	0.363271i	0.500000	+	0.363271i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.618034			−0.618034
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$	0.309017	+	0.951057i	0.309017	+	0.951057i
$433$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$433$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$434$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$435$	2.11803	+	1.53884i	2.11803	+	1.53884i
$436$		0			0
$437$		0			0
$438$	1.30902	−	0.951057i	1.30902	−	0.951057i
$439$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$439$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$440$		0			0
$441$	−0.618034			−0.618034
$442$		0			0
$443$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$443$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$444$		0			0
$445$		0			0
$446$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$447$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$448$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$449$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$449$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$450$	−1.61803			−1.61803
$451$		0			0
$452$		0			0
$453$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$454$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$455$		0			0
$456$		0			0
$457$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$457$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.00000			−2.00000			−1.00000			$\pi$
$461$	−2.00000			−2.00000			−1.00000			$\pi$
$462$		0			0
$463$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$463$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$464$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$465$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$466$		0			0
$467$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$467$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.618034			−0.618034
$473$		0			0
$474$	−1.61803			−1.61803
$475$		0			0
$476$		0			0
$477$	0.190983	−	0.587785i	0.190983	−	0.587785i
$478$		0			0
$479$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$479$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$480$	0.500000	−	1.53884i	0.500000	−	1.53884i
$481$		0			0
$482$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$483$		0			0
$484$		0			0
$485$	2.61803			2.61803
$486$	0.809017	−	0.587785i	0.809017	−	0.587785i
$487$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$487$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$488$		0			0
$489$		0			0
$490$	0.809017	+	0.587785i	0.809017	+	0.587785i
$491$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$491$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.618034			0.618034
$497$		0			0
$498$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$499$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$499$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$500$	0.809017	+	0.587785i	0.809017	+	0.587785i
$501$		0			0
$502$	0.500000	−	1.53884i	0.500000	−	1.53884i
$503$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$503$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$504$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$505$	−2.61803			−2.61803
$506$		0			0
$507$	1.00000			1.00000
$508$	1.61803	−	1.17557i	1.61803	−	1.17557i
$509$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$509$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$	0.809017	+	0.587785i	0.809017	+	0.587785i
$512$	0.809017	+	0.587785i	0.809017	+	0.587785i
$513$		0			0
$514$		0			0
$515$	0.809017	−	0.587785i	0.809017	−	0.587785i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.500000	−	0.363271i	0.500000	−	0.363271i
$520$		0			0
$521$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$	1.30902	+	0.951057i	1.30902	+	0.951057i
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$525$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	1.00000			1.00000
$530$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$531$	0.190983	+	0.587785i	0.190983	+	0.587785i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.309017	−	0.951057i	0.309017	−	0.951057i
$536$		0			0
$537$	1.30902	−	0.951057i	1.30902	−	0.951057i
$538$	−2.00000			−2.00000
$539$		0			0
$540$	−1.61803			−1.61803
$541$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$541$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$542$	0.618034	+	1.90211i	0.618034	+	1.90211i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$547$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$557$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$558$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$559$		0			0
$560$	1.00000			1.00000
$561$		0			0
$562$		0			0
$563$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$563$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.500000	+	0.363271i	0.500000	+	0.363271i
$568$		0			0
$569$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$569$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.309017	−	0.951057i	0.309017	−	0.951057i
$577$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$577$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$578$	0.809017	+	0.587785i	0.809017	+	0.587785i
$579$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$580$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$581$	0.809017	−	0.587785i	0.809017	−	0.587785i
$582$	1.61803			1.61803
$583$		0			0
$584$	−1.61803			−1.61803
$585$		0			0
$586$	0.190983	+	0.587785i	0.190983	+	0.587785i
$587$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$587$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$588$	0.500000	+	0.363271i	0.500000	+	0.363271i
$589$		0			0
$590$	0.309017	−	0.951057i	0.309017	−	0.951057i
$591$	0.500000	+	1.53884i	0.500000	+	1.53884i
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$	0.500000	−	0.363271i	0.500000	−	0.363271i
$597$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$598$		0			0
$599$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$599$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$600$	1.30902	+	0.951057i	1.30902	+	0.951057i
$601$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$601$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	1.61803			1.61803
$605$		0			0
$606$	−1.61803			−1.61803
$607$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$607$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$608$		0			0
$609$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$613$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$	0.500000	−	0.363271i	0.500000	−	0.363271i
$619$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$619$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$620$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$	1.61803			1.61803
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$631$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$631$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$632$	1.30902	+	0.951057i	1.30902	+	0.951057i
$633$		0			0
$634$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$635$	1.00000	+	3.07768i	1.00000	+	3.07768i
$636$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$641$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$641$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$642$	0.190983	−	0.587785i	0.190983	−	0.587785i
$643$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$643$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$	−1.00000			−1.00000
$649$		0			0
$650$		0			0
$651$	0.309017	−	0.224514i	0.309017	−	0.224514i
$652$		0			0
$653$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$653$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$654$		0			0
$655$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$656$		0			0
$657$	0.500000	+	1.53884i	0.500000	+	1.53884i
$658$		0			0
$659$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$659$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	1.30902	−	0.951057i	1.30902	−	0.951057i
$670$		0			0
$671$		0			0
$672$	0.618034			0.618034
$673$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$673$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$674$	0.618034	+	1.90211i	0.618034	+	1.90211i
$675$	0.500000	−	1.53884i	0.500000	−	1.53884i
$676$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$677$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$677$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$678$		0			0
$679$	0.309017	+	0.951057i	0.309017	+	0.951057i
$680$		0			0
$681$	1.61803			1.61803
$682$		0			0
$683$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$683$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$684$		0			0
$685$		0			0
$686$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$691$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$692$	−0.618034			−0.618034
$693$		0			0
$694$	0.618034			0.618034
$695$		0			0
$696$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$701$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$701$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$708$	0.190983	−	0.587785i	0.190983	−	0.587785i
$709$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$709$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$710$		0			0
$711$	0.500000	−	1.53884i	0.500000	−	1.53884i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.61803			−1.61803
$717$		0			0
$718$		0			0
$719$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$719$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$720$	1.30902	+	0.951057i	1.30902	+	0.951057i
$721$	0.309017	+	0.224514i	0.309017	+	0.224514i
$722$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$723$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$724$		0			0
$725$	2.61803			2.61803
$726$		0			0
$727$	2.00000			2.00000			1.00000			$0$
$727$	2.00000			2.00000			1.00000			$0$
$728$		0			0
$729$	0.309017	+	0.951057i	0.309017	+	0.951057i
$730$	0.809017	−	2.48990i	0.809017	−	2.48990i
$731$		0			0
$732$		0			0
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$	0.500000	+	1.53884i	0.500000	+	1.53884i
$735$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$739$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$		0			0
$742$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$743$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$743$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$744$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$745$	0.309017	+	0.951057i	0.309017	+	0.951057i
$746$		0			0
$747$	1.61803			1.61803
$748$		0			0
$749$	0.381966			0.381966
$750$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$751$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$751$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$752$		0			0
$753$	1.30902	+	0.951057i	1.30902	+	0.951057i
$754$		0			0
$755$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$756$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$757$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$757$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$761$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$762$	0.618034	+	1.90211i	0.618034	+	1.90211i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$769$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$769$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$770$		0			0
$771$		0			0
$772$	0.500000	−	0.363271i	0.500000	−	0.363271i
$773$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$773$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$774$		0			0
$775$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$776$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$777$		0			0
$778$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$784$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$785$		0			0
$786$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$787$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$787$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$788$	0.500000	−	1.53884i	0.500000	−	1.53884i
$789$		0			0
$790$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$796$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$797$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$797$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.618034	−	1.90211i	0.618034	−	1.90211i
$808$	1.30902	+	0.951057i	1.30902	+	0.951057i
$809$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$809$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$810$	0.500000	−	1.53884i	0.500000	−	1.53884i
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$	0.809017	−	0.587785i	0.809017	−	0.587785i
$813$	−2.00000			−2.00000
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$819$		0			0
$820$		0			0
$821$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$821$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$822$		0			0
$823$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$823$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$824$	−0.618034			−0.618034
$825$		0			0
$826$	0.381966			0.381966
$827$	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			0		0.309017	−	0.951057i	$-0.400000\pi$
$829$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$830$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.618034			0.618034
$838$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$841$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.30902	−	0.951057i	1.30902	−	0.951057i
$846$		0			0
$847$		0			0
$848$	0.618034			0.618034
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$853$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$854$		0			0
$855$		0			0
$856$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$857$		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			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$863$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$864$	0.809017	+	0.587785i	0.809017	+	0.587785i
$865$	0.309017	−	0.951057i	0.309017	−	0.951057i
$866$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$867$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$868$	−0.381966			−0.381966
$869$		0			0
$870$	2.61803			2.61803
$871$		0			0
$872$		0			0
$873$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$874$		0			0
$875$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$876$	0.500000	−	1.53884i	0.500000	−	1.53884i
$877$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$877$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$878$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$879$	−0.618034			−0.618034
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$883$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$883$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$	0.809017	+	0.587785i	0.809017	+	0.587785i
$886$	0.500000	+	0.363271i	0.500000	+	0.363271i
$887$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$887$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$888$		0			0
$889$	−1.00000	+	0.726543i	−1.00000	+	0.726543i
$890$		0			0
$891$		0			0
$892$	−1.61803			−1.61803
$893$		0			0
$894$	0.190983	+	0.587785i	0.190983	+	0.587785i
$895$	0.809017	−	2.48990i	0.809017	−	2.48990i
$896$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$897$		0			0
$898$		0			0
$899$	0.309017	+	0.951057i	0.309017	+	0.951057i
$900$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$907$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$907$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$908$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$909$	0.500000	−	1.53884i	0.500000	−	1.53884i
$910$		0			0
$911$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$911$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$912$		0			0
$913$		0			0
$914$	−1.61803			−1.61803
$915$		0			0
$916$		0			0
$917$	0.118034	−	0.363271i	0.118034	−	0.363271i
$918$		0			0
$919$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$919$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.500000	−	0.363271i	0.500000	−	0.363271i
$927$	0.190983	+	0.587785i	0.190983	+	0.587785i
$928$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$929$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$929$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$930$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.618034			−0.618034
$935$		0			0
$936$		0			0
$937$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$937$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$938$		0			0
$939$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$940$		0			0
$941$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$941$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$942$		0			0
$943$		0			0
$944$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$945$	1.00000			1.00000
$946$		0			0
$947$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$947$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$948$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$949$		0			0
$950$		0			0
$951$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$952$		0			0
$953$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$953$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$954$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$961$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$962$		0			0
$963$	0.500000	+	0.363271i	0.500000	+	0.363271i
$964$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$965$	0.309017	+	0.951057i	0.309017	+	0.951057i
$966$		0			0
$967$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$967$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$968$		0			0
$969$		0			0
$970$	2.11803	−	1.53884i	2.11803	−	1.53884i
$971$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$971$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$972$	0.309017	−	0.951057i	0.309017	−	0.951057i
$973$		0			0
$974$	0.500000	+	0.363271i	0.500000	+	0.363271i
$975$		0			0
$976$		0			0
$977$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$977$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$978$		0			0
$979$		0			0
$980$	1.00000			1.00000
$981$		0			0
$982$	0.618034	+	1.90211i	0.618034	+	1.90211i
$983$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$983$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$984$		0			0
$985$	2.11803	+	1.53884i	2.11803	+	1.53884i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$991$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$992$	0.500000	−	0.363271i	0.500000	−	0.363271i
$993$		0			0
$994$		0			0
$995$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$996$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$997$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$997$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2904.1.t.e.245.1		4
3.2	odd	2		2904.1.t.b.245.1		4
8.5	even	2		2904.1.t.b.245.1		4
11.2	odd	10		2904.1.n.d.485.1		2
11.3	even	5		2904.1.t.d.269.1		4
11.4	even	5	inner	2904.1.t.e.2501.1		4
11.5	even	5		2904.1.t.d.2429.1		4
11.6	odd	10		264.1.t.a.53.1	yes	4
11.7	odd	10		2904.1.t.a.2501.1		4
11.8	odd	10		264.1.t.a.5.1	✓	4
11.9	even	5		2904.1.n.b.485.1		2
11.10	odd	2		2904.1.t.a.245.1		4
24.5	odd	2	CM	2904.1.t.e.245.1		4
33.2	even	10		2904.1.n.a.485.2		2
33.5	odd	10		2904.1.t.c.2429.1		4
33.8	even	10		264.1.t.b.5.1	yes	4
33.14	odd	10		2904.1.t.c.269.1		4
33.17	even	10		264.1.t.b.53.1	yes	4
33.20	odd	10		2904.1.n.c.485.2		2
33.26	odd	10		2904.1.t.b.2501.1		4
33.29	even	10		2904.1.t.f.2501.1		4
33.32	even	2		2904.1.t.f.245.1		4
44.19	even	10		1056.1.bj.b.401.1		4
44.39	even	10		1056.1.bj.b.977.1		4
88.5	even	10		2904.1.t.c.2429.1		4
88.13	odd	10		2904.1.n.a.485.2		2
88.19	even	10		1056.1.bj.a.401.1		4
88.21	odd	2		2904.1.t.f.245.1		4
88.29	odd	10		2904.1.t.f.2501.1		4
88.37	even	10		2904.1.t.b.2501.1		4
88.53	even	10		2904.1.n.c.485.2		2
88.61	odd	10		264.1.t.b.53.1	yes	4
88.69	even	10		2904.1.t.c.269.1		4
88.83	even	10		1056.1.bj.a.977.1		4
88.85	odd	10		264.1.t.b.5.1	yes	4
132.83	odd	10		1056.1.bj.a.977.1		4
132.107	odd	10		1056.1.bj.a.401.1		4
264.5	odd	10		2904.1.t.d.2429.1		4
264.29	even	10		2904.1.t.a.2501.1		4
264.53	odd	10		2904.1.n.b.485.1		2
264.83	odd	10		1056.1.bj.b.977.1		4
264.101	even	10		2904.1.n.d.485.1		2
264.107	odd	10		1056.1.bj.b.401.1		4
264.125	odd	10	inner	2904.1.t.e.2501.1		4
264.149	even	10		264.1.t.a.53.1	yes	4
264.173	even	10		264.1.t.a.5.1	✓	4
264.197	even	2		2904.1.t.a.245.1		4
264.245	odd	10		2904.1.t.d.269.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.1.t.a.5.1	✓	4	11.8	odd	10
264.1.t.a.5.1	✓	4	264.173	even	10
264.1.t.a.53.1	yes	4	11.6	odd	10
264.1.t.a.53.1	yes	4	264.149	even	10
264.1.t.b.5.1	yes	4	33.8	even	10
264.1.t.b.5.1	yes	4	88.85	odd	10
264.1.t.b.53.1	yes	4	33.17	even	10
264.1.t.b.53.1	yes	4	88.61	odd	10
1056.1.bj.a.401.1		4	88.19	even	10
1056.1.bj.a.401.1		4	132.107	odd	10
1056.1.bj.a.977.1		4	88.83	even	10
1056.1.bj.a.977.1		4	132.83	odd	10
1056.1.bj.b.401.1		4	44.19	even	10
1056.1.bj.b.401.1		4	264.107	odd	10
1056.1.bj.b.977.1		4	44.39	even	10
1056.1.bj.b.977.1		4	264.83	odd	10
2904.1.n.a.485.2		2	33.2	even	10
2904.1.n.a.485.2		2	88.13	odd	10
2904.1.n.b.485.1		2	11.9	even	5
2904.1.n.b.485.1		2	264.53	odd	10
2904.1.n.c.485.2		2	33.20	odd	10
2904.1.n.c.485.2		2	88.53	even	10
2904.1.n.d.485.1		2	11.2	odd	10
2904.1.n.d.485.1		2	264.101	even	10
2904.1.t.a.245.1		4	11.10	odd	2
2904.1.t.a.245.1		4	264.197	even	2
2904.1.t.a.2501.1		4	11.7	odd	10
2904.1.t.a.2501.1		4	264.29	even	10
2904.1.t.b.245.1		4	3.2	odd	2
2904.1.t.b.245.1		4	8.5	even	2
2904.1.t.b.2501.1		4	33.26	odd	10
2904.1.t.b.2501.1		4	88.37	even	10
2904.1.t.c.269.1		4	33.14	odd	10
2904.1.t.c.269.1		4	88.69	even	10
2904.1.t.c.2429.1		4	33.5	odd	10
2904.1.t.c.2429.1		4	88.5	even	10
2904.1.t.d.269.1		4	11.3	even	5
2904.1.t.d.269.1		4	264.245	odd	10
2904.1.t.d.2429.1		4	11.5	even	5
2904.1.t.d.2429.1		4	264.5	odd	10
2904.1.t.e.245.1		4	1.1	even	1	trivial
2904.1.t.e.245.1		4	24.5	odd	2	CM
2904.1.t.e.2501.1		4	11.4	even	5	inner
2904.1.t.e.2501.1		4	264.125	odd	10	inner
2904.1.t.f.245.1		4	33.32	even	2
2904.1.t.f.245.1		4	88.21	odd	2
2904.1.t.f.2501.1		4	33.29	even	10
2904.1.t.f.2501.1		4	88.29	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2904 = 2^{3} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2904.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.190983 + 0.587785i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.190983 + 0.587785i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.61803 q^{10} +1.00000 q^{12} +(0.190983 + 0.587785i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.309017 + 0.951057i) q^{18} +(1.30902 - 0.951057i) q^{20} -0.618034 q^{21} +(0.809017 - 0.587785i) q^{24} +(0.500000 + 1.53884i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.500000 + 0.363271i) q^{28} +(0.500000 - 1.53884i) q^{29} +(0.500000 + 1.53884i) q^{30} +(-0.500000 + 0.363271i) q^{31} -1.00000 q^{32} +(-0.809017 + 0.587785i) q^{35} +(0.309017 + 0.951057i) q^{36} +(0.500000 - 1.53884i) q^{40} +(-0.500000 + 0.363271i) q^{42} -1.61803 q^{45} +(0.309017 - 0.951057i) q^{48} +(0.500000 + 0.363271i) q^{49} +(1.30902 + 0.951057i) q^{50} +(-0.500000 + 0.363271i) q^{53} -1.00000 q^{54} +0.618034 q^{56} +(-0.500000 - 1.53884i) q^{58} +(0.190983 - 0.587785i) q^{59} +(1.30902 + 0.951057i) q^{60} +(-0.190983 + 0.587785i) q^{62} +(-0.190983 - 0.587785i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.309017 + 0.951057i) q^{70} +(0.809017 + 0.587785i) q^{72} +(0.500000 - 1.53884i) q^{73} +(-1.30902 + 0.951057i) q^{75} +(-1.30902 + 0.951057i) q^{79} +(-0.500000 - 1.53884i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.30902 - 0.951057i) q^{83} +(-0.190983 + 0.587785i) q^{84} +1.61803 q^{87} +(-1.30902 + 0.951057i) q^{90} +(-0.500000 - 0.363271i) q^{93} +(-0.309017 - 0.951057i) q^{96} +(1.30902 - 0.951057i) q^{97} +0.618034 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - q^4 + 3 * q^5 + q^6 - 3 * q^7 + q^8 - q^9	\( 4 q + q^{2} - q^{3} - q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + q^{8} - q^{9} + 2 q^{10} + 4 q^{12} + 3 q^{14} - 2 q^{15} - q^{16} + q^{18} + 3 q^{20} + 2 q^{21} + q^{24} + 2 q^{25} - q^{27} + 2 q^{28} + 2 q^{29} + 2 q^{30} - 2 q^{31} - 4 q^{32} - q^{35} - q^{36} + 2 q^{40} - 2 q^{42} - 2 q^{45} - q^{48} + 2 q^{49} + 3 q^{50} - 2 q^{53} - 4 q^{54} - 2 q^{56} - 2 q^{58} + 3 q^{59} + 3 q^{60} - 3 q^{62} - 3 q^{63} - q^{64} + q^{70} + q^{72} + 2 q^{73} - 3 q^{75} - 3 q^{79} - 2 q^{80} - q^{81} - 3 q^{83} - 3 q^{84} + 2 q^{87} - 3 q^{90} - 2 q^{93} + q^{96} + 3 q^{97} - 2 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + 3 * q^5 + q^6 - 3 * q^7 + q^8 - q^9 + 2 * q^10 + 4 * q^12 + 3 * q^14 - 2 * q^15 - q^16 + q^18 + 3 * q^20 + 2 * q^21 + q^24 + 2 * q^25 - q^27 + 2 * q^28 + 2 * q^29 + 2 * q^30 - 2 * q^31 - 4 * q^32 - q^35 - q^36 + 2 * q^40 - 2 * q^42 - 2 * q^45 - q^48 + 2 * q^49 + 3 * q^50 - 2 * q^53 - 4 * q^54 - 2 * q^56 - 2 * q^58 + 3 * q^59 + 3 * q^60 - 3 * q^62 - 3 * q^63 - q^64 + q^70 + q^72 + 2 * q^73 - 3 * q^75 - 3 * q^79 - 2 * q^80 - q^81 - 3 * q^83 - 3 * q^84 + 2 * q^87 - 3 * q^90 - 2 * q^93 + q^96 + 3 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more