LMFDB - Embedded newform 2695.1.bi.b.2199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,1,Mod(274,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 6, 7]))

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

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

chi := DirichletCharacter("2695.274");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$2695 = 5 \cdot 7^{2} \cdot 11$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2695.bi (of order $14$ , degree $6$ , 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:	$1.34498020905$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{7}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{7} + \cdots)$

Embedding invariants

Embedding label			2199.1
Root			$-0.623490 + 0.781831i$ of defining polynomial
Character	$\chi$	$=$	2695.2199
Dual form			2695.1.bi.b.1429.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.277479 - 0.347948i) q^{2} +(0.178448 + 0.781831i) q^{4} +(-0.900969 - 0.433884i) q^{5} +(-0.623490 - 0.781831i) q^{7} +(0.722521 + 0.347948i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.400969 + 0.193096i) q^{10} +(0.623490 - 0.781831i) q^{11} +(-0.777479 + 0.974928i) q^{13} -0.445042 q^{14} +(-0.400969 + 0.193096i) q^{16} +(-0.400969 + 1.75676i) q^{17} +0.445042 q^{18} +(0.178448 - 0.781831i) q^{20} +(-0.0990311 - 0.433884i) q^{22} +(0.623490 + 0.781831i) q^{25} +(0.123490 + 0.541044i) q^{26} +(0.500000 - 0.626980i) q^{28} +2.00000 q^{31} +(-0.222521 + 0.974928i) q^{32} +(0.500000 + 0.626980i) q^{34} +(0.222521 + 0.974928i) q^{35} +(-0.500000 + 0.626980i) q^{36} +(-0.500000 - 0.626980i) q^{40} +(1.12349 - 0.541044i) q^{43} +(0.722521 + 0.347948i) q^{44} +(-0.222521 - 0.974928i) q^{45} +(-0.222521 + 0.974928i) q^{49} +0.445042 q^{50} +(-0.900969 - 0.433884i) q^{52} +(-0.900969 + 0.433884i) q^{55} +(-0.178448 - 0.781831i) q^{56} +(-1.12349 + 0.541044i) q^{59} +(0.554958 - 0.695895i) q^{62} +(0.222521 - 0.974928i) q^{63} +(1.12349 - 0.541044i) q^{65} -1.44504 q^{68} +(0.400969 + 0.193096i) q^{70} +(0.0990311 + 0.433884i) q^{71} +(0.178448 + 0.781831i) q^{72} +(1.12349 + 1.40881i) q^{73} -1.00000 q^{77} +0.445042 q^{80} +(-0.222521 + 0.974928i) q^{81} +(-1.24698 - 1.56366i) q^{83} +(1.12349 - 1.40881i) q^{85} +(0.123490 - 0.541044i) q^{86} +(0.722521 - 0.347948i) q^{88} +(0.777479 + 0.974928i) q^{89} +(-0.400969 - 0.193096i) q^{90} +1.24698 q^{91} +(0.277479 + 0.347948i) q^{98} +1.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q + 2 q^{2} - 3 q^{4} - q^{5} + q^{7} + 4 q^{8} - q^{9} + 2 q^{10} - q^{11} - 5 q^{13} - 2 q^{14} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{20} - 5 q^{22} - q^{25} - 4 q^{26} + 3 q^{28} + 12 q^{31}+ \cdots + 6 q^{99}+O(q^{100})$ 6 * q + 2 * q^2 - 3 * q^4 - q^5 + q^7 + 4 * q^8 - q^9 + 2 * q^10 - q^11 - 5 * q^13 - 2 * q^14 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^20 - 5 * q^22 - q^25 - 4 * q^26 + 3 * q^28 + 12 * q^31 - q^32 + 3 * q^34 + q^35 - 3 * q^36 - 3 * q^40 + 2 * q^43 + 4 * q^44 - q^45 - q^49 + 2 * q^50 - q^52 - q^55 + 3 * q^56 - 2 * q^59 + 4 * q^62 + q^63 + 2 * q^65 - 8 * q^68 - 2 * q^70 + 5 * q^71 - 3 * q^72 + 2 * q^73 - 6 * q^77 + 2 * q^80 - q^81 + 2 * q^83 + 2 * q^85 - 4 * q^86 + 4 * q^88 + 5 * q^89 + 2 * q^90 - 2 * q^91 + 2 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times$ .

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$e\left(\frac{1}{7}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$2$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$3$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$3$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$4$	0.178448	+	0.781831i	0.178448	+	0.781831i
$5$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$5$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$6$		0			0
$7$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$7$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$8$	0.722521	+	0.347948i	0.722521	+	0.347948i
$9$	0.623490	+	0.781831i	0.623490	+	0.781831i
$10$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$11$	0.623490	−	0.781831i	0.623490	−	0.781831i
$11$	0.623490	−	0.781831i	0.623490	−	0.781831i
$12$		0			0
$13$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$13$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$14$	−0.445042			−0.445042
$15$		0			0
$16$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$17$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$17$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$18$	0.445042			0.445042
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	0.178448	−	0.781831i	0.178448	−	0.781831i
$21$		0			0
$22$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$23$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$23$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$24$		0			0
$25$	0.623490	+	0.781831i	0.623490	+	0.781831i
$26$	0.123490	+	0.541044i	0.123490	+	0.541044i
$27$		0			0
$28$	0.500000	−	0.626980i	0.500000	−	0.626980i
$29$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$29$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$30$		0			0
$31$	2.00000			2.00000			1.00000			$0$
$31$	2.00000			2.00000			1.00000			$0$
$32$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$33$		0			0
$34$	0.500000	+	0.626980i	0.500000	+	0.626980i
$35$	0.222521	+	0.974928i	0.222521	+	0.974928i
$36$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$37$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$37$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$38$		0			0
$39$		0			0
$40$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$41$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$41$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$42$		0			0
$43$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$43$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$44$	0.722521	+	0.347948i	0.722521	+	0.347948i
$45$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$46$		0			0
$47$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$47$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$48$		0			0
$49$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$50$	0.445042			0.445042
$51$		0			0
$52$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$53$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$53$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$54$		0			0
$55$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$56$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$57$		0			0
$58$		0			0
$59$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$59$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$60$		0			0
$61$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$61$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$62$	0.554958	−	0.695895i	0.554958	−	0.695895i
$63$	0.222521	−	0.974928i	0.222521	−	0.974928i
$64$		0			0
$65$	1.12349	−	0.541044i	1.12349	−	0.541044i
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	−1.44504			−1.44504
$69$		0			0
$70$	0.400969	+	0.193096i	0.400969	+	0.193096i
$71$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$71$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$72$	0.178448	+	0.781831i	0.178448	+	0.781831i
$73$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$73$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.00000			−1.00000
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	0.445042			0.445042
$81$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$82$		0			0
$83$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$83$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$84$		0			0
$85$	1.12349	−	1.40881i	1.12349	−	1.40881i
$86$	0.123490	−	0.541044i	0.123490	−	0.541044i
$87$		0			0
$88$	0.722521	−	0.347948i	0.722521	−	0.347948i
$89$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$89$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$90$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$91$	1.24698			1.24698
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	0.277479	+	0.347948i	0.277479	+	0.347948i
$99$	1.00000			1.00000
$100$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$101$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$101$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$102$		0			0
$103$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$103$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$104$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$105$		0			0
$106$		0			0
$107$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$107$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$108$		0			0
$109$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$109$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$110$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$111$		0			0
$112$	0.400969	+	0.193096i	0.400969	+	0.193096i
$113$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$113$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.24698			−1.24698
$118$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$119$	1.62349	−	0.781831i	1.62349	−	0.781831i
$120$		0			0
$121$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$122$		0			0
$123$		0			0
$124$	0.356896	+	1.56366i	0.356896	+	1.56366i
$125$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$126$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$127$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$127$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$128$	−1.00000			−1.00000
$129$		0			0
$130$	0.123490	−	0.541044i	0.123490	−	0.541044i
$131$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$131$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.900969	+	1.12978i	−0.900969	+	1.12978i
$137$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$137$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$138$		0			0
$139$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$139$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$140$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$141$		0			0
$142$	0.178448	+	0.0859360i	0.178448	+	0.0859360i
$143$	0.277479	+	1.21572i	0.277479	+	1.21572i
$144$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$145$		0			0
$146$	0.801938			0.801938
$147$		0			0
$148$		0			0
$149$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$149$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$150$		0			0
$151$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$151$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$152$		0			0
$153$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$154$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$155$	−1.80194	−	0.867767i	−1.80194	−	0.867767i
$156$		0			0
$157$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$157$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$158$		0			0
$159$		0			0
$160$	0.623490	−	0.781831i	0.623490	−	0.781831i
$161$		0			0
$162$	0.277479	+	0.347948i	0.277479	+	0.347948i
$163$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$163$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$164$		0			0
$165$		0			0
$166$	−0.890084			−0.890084
$167$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$167$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$168$		0			0
$169$	−0.123490	−	0.541044i	−0.123490	−	0.541044i
$170$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$171$		0			0
$172$	0.623490	+	0.781831i	0.623490	+	0.781831i
$173$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$173$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	−1.00000			$\pi$
$174$		0			0
$175$	0.222521	−	0.974928i	0.222521	−	0.974928i
$176$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$177$		0			0
$178$	0.554958			0.554958
$179$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$179$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$180$	0.722521	−	0.347948i	0.722521	−	0.347948i
$181$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$181$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$182$	0.346011	−	0.433884i	0.346011	−	0.433884i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.12349	+	1.40881i	1.12349	+	1.40881i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$191$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$192$		0			0
$193$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$193$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$194$		0			0
$195$		0			0
$196$	−0.801938			−0.801938
$197$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$197$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$198$	0.277479	−	0.347948i	0.277479	−	0.347948i
$199$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$199$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$200$	0.178448	+	0.781831i	0.178448	+	0.781831i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	0.123490	−	0.541044i	0.123490	−	0.541044i
$209$		0			0
$210$		0			0
$211$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$211$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$212$		0			0
$213$		0			0
$214$	0.198062			0.198062
$215$	−1.24698			−1.24698
$216$		0			0
$217$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$218$		0			0
$219$		0			0
$220$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$221$	−1.40097	−	1.75676i	−1.40097	−	1.75676i
$222$		0			0
$223$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$223$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$224$	0.900969	−	0.433884i	0.900969	−	0.433884i
$225$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$226$		0			0
$227$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$227$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$228$		0			0
$229$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$229$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$233$	0.445042	−	1.94986i	0.445042	−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$234$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$235$		0			0
$236$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$237$		0			0
$238$	0.178448	−	0.781831i	0.178448	−	0.781831i
$239$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$239$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$240$		0			0
$241$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$241$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$242$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$243$		0			0
$244$		0			0
$245$	0.623490	−	0.781831i	0.623490	−	0.781831i
$246$		0			0
$247$		0			0
$248$	1.44504	+	0.695895i	1.44504	+	0.695895i
$249$		0			0
$250$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$251$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$251$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$252$	0.801938			0.801938
$253$		0			0
$254$	0.123490	+	0.154851i	0.123490	+	0.154851i
$255$		0			0
$256$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$257$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$257$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$258$		0			0
$259$		0			0
$260$	0.623490	+	0.781831i	0.623490	+	0.781831i
$261$		0			0
$262$		0			0
$263$	−2.00000			−2.00000			−1.00000			$\pi$
$263$	−2.00000			−2.00000			−1.00000			$\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$269$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$270$		0			0
$271$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$271$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$272$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$273$		0			0
$274$		0			0
$275$	1.00000			1.00000
$276$		0			0
$277$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$277$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$278$		0			0
$279$	1.24698	+	1.56366i	1.24698	+	1.56366i
$280$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$281$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$281$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$282$		0			0
$283$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$283$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$284$	−0.321552	+	0.154851i	−0.321552	+	0.154851i
$285$		0			0
$286$	0.500000	+	0.240787i	0.500000	+	0.240787i
$287$		0			0
$288$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$289$	−2.02446	−	0.974928i	−2.02446	−	0.974928i
$290$		0			0
$291$		0			0
$292$	−0.900969	+	1.12978i	−0.900969	+	1.12978i
$293$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$293$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$294$		0			0
$295$	1.24698			1.24698
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$307$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$307$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$308$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$309$		0			0
$310$	−0.801938	+	0.386193i	−0.801938	+	0.386193i
$311$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$311$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$		0			0
$315$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$316$		0			0
$317$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$317$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.801938			−0.801938
$325$	−1.24698			−1.24698
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$331$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$332$	1.00000	−	1.25396i	1.00000	−	1.25396i
$333$		0			0
$334$	−0.554958	−	0.695895i	−0.554958	−	0.695895i
$335$		0			0
$336$		0			0
$337$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$337$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$338$	−0.222521	−	0.107160i	−0.222521	−	0.107160i
$339$		0			0
$340$	1.30194	+	0.626980i	1.30194	+	0.626980i
$341$	1.24698	−	1.56366i	1.24698	−	1.56366i
$342$		0			0
$343$	0.900969	−	0.433884i	0.900969	−	0.433884i
$344$	1.00000			1.00000
$345$		0			0
$346$	−0.178448	−	0.0859360i	−0.178448	−	0.0859360i
$347$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$347$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	−1.00000			$\pi$
$348$		0			0
$349$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$349$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$350$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$351$		0			0
$352$	0.623490	+	0.781831i	0.623490	+	0.781831i
$353$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$353$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$354$		0			0
$355$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$356$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$357$		0			0
$358$	−0.123490	−	0.154851i	−0.123490	−	0.154851i
$359$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$359$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$360$	0.178448	−	0.781831i	0.178448	−	0.781831i
$361$	1.00000			1.00000
$362$	−0.801938			−0.801938
$363$		0			0
$364$	0.222521	+	0.974928i	0.222521	+	0.974928i
$365$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$366$		0			0
$367$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$367$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$373$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$374$	0.801938			0.801938
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$379$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$380$		0			0
$381$		0			0
$382$	−0.801938	+	0.386193i	−0.801938	+	0.386193i
$383$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$383$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$384$		0			0
$385$	0.900969	+	0.433884i	0.900969	+	0.433884i
$386$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$387$	1.12349	+	0.541044i	1.12349	+	0.541044i
$388$		0			0
$389$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$389$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$390$		0			0
$391$		0			0
$392$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$393$		0			0
$394$	0.123490	−	0.154851i	0.123490	−	0.154851i
$395$		0			0
$396$	0.178448	+	0.781831i	0.178448	+	0.781831i
$397$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$397$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$398$	0.178448	−	0.0859360i	0.178448	−	0.0859360i
$399$		0			0
$400$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$401$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$401$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$402$		0			0
$403$	−1.55496	+	1.94986i	−1.55496	+	1.94986i
$404$		0			0
$405$	0.623490	−	0.781831i	0.623490	−	0.781831i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$409$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.12349	+	0.541044i	1.12349	+	0.541044i
$414$		0			0
$415$	0.445042	+	1.94986i	0.445042	+	1.94986i
$416$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$417$		0			0
$418$		0			0
$419$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$419$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$420$		0			0
$421$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$421$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$426$		0			0
$427$		0			0
$428$	−0.222521	+	0.279032i	−0.222521	+	0.279032i
$429$		0			0
$430$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$431$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$431$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$432$		0			0
$433$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$433$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$434$	−0.890084			−0.890084
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$439$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$440$	−0.801938			−0.801938
$441$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$442$	−1.00000			−1.00000
$443$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$443$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$444$		0			0
$445$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$449$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$450$	0.277479	+	0.347948i	0.277479	+	0.347948i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.500000	−	0.626980i	0.500000	−	0.626980i
$455$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$456$		0			0
$457$	1.80194	−	0.867767i	1.80194	−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$457$	1.80194	−	0.867767i	1.80194	−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$458$	0.0440730	−	0.193096i	0.0440730	−	0.193096i
$459$		0			0
$460$		0			0
$461$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$461$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$462$		0			0
$463$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$463$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$464$		0			0
$465$		0			0
$466$	−0.554958	−	0.695895i	−0.554958	−	0.695895i
$467$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$467$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$468$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.00000			−1.00000
$473$	0.277479	−	1.21572i	0.277479	−	1.21572i
$474$		0			0
$475$		0			0
$476$	0.900969	+	1.12978i	0.900969	+	1.12978i
$477$		0			0
$478$		0			0
$479$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$479$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.722521	−	0.347948i	0.722521	−	0.347948i
$485$		0			0
$486$		0			0
$487$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$487$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$488$		0			0
$489$		0			0
$490$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$496$	−0.801938	+	0.386193i	−0.801938	+	0.386193i
$497$	0.277479	−	0.347948i	0.277479	−	0.347948i
$498$		0			0
$499$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$499$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$500$	0.722521	−	0.347948i	0.722521	−	0.347948i
$501$		0			0
$502$	0.0440730	−	0.193096i	0.0440730	−	0.193096i
$503$	−1.24698	+	1.56366i	−1.24698	+	1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$503$	−1.24698	+	1.56366i	−1.24698	+	1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$504$	0.500000	−	0.626980i	0.500000	−	0.626980i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−0.356896			−0.356896
$509$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$509$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$510$		0			0
$511$	0.400969	−	1.75676i	0.400969	−	1.75676i
$512$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	1.00000			1.00000
$521$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$521$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$522$		0			0
$523$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$523$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$524$		0			0
$525$		0			0
$526$	−0.554958	+	0.695895i	−0.554958	+	0.695895i
$527$	−0.801938	+	3.51352i	−0.801938	+	3.51352i
$528$		0			0
$529$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$530$		0			0
$531$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$536$		0			0
$537$		0			0
$538$	−0.801938			−0.801938
$539$	0.623490	+	0.781831i	0.623490	+	0.781831i
$540$		0			0
$541$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$541$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$542$		0			0
$543$		0			0
$544$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$545$		0			0
$546$		0			0
$547$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$547$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$548$		0			0
$549$		0			0
$550$	0.277479	−	0.347948i	0.277479	−	0.347948i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.500000	+	0.626980i	0.500000	+	0.626980i
$555$		0			0
$556$		0			0
$557$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$557$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$558$	0.890084			0.890084
$559$	−0.346011	+	1.51597i	−0.346011	+	1.51597i
$560$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$561$		0			0
$562$		0			0
$563$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$563$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$564$		0			0
$565$		0			0
$566$	0.123490	+	0.541044i	0.123490	+	0.541044i
$567$	0.900969	−	0.433884i	0.900969	−	0.433884i
$568$	−0.0794168	+	0.347948i	−0.0794168	+	0.347948i
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$571$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$572$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$577$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$578$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$579$		0			0
$580$		0			0
$581$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$582$		0			0
$583$		0			0
$584$	0.321552	+	1.40881i	0.321552	+	1.40881i
$585$	1.12349	+	0.541044i	1.12349	+	0.541044i
$586$	0.500000	−	0.626980i	0.500000	−	0.626980i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	0.346011	−	0.433884i	0.346011	−	0.433884i
$591$		0			0
$592$		0			0
$593$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$593$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$594$		0			0
$595$	−1.80194			−1.80194
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$599$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$600$		0			0
$601$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$601$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$602$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$603$		0			0
$604$		0			0
$605$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$606$		0			0
$607$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$607$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.900969	−	1.12978i	−0.900969	−	1.12978i
$613$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$613$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$614$	−0.0440730	−	0.193096i	−0.0440730	−	0.193096i
$615$		0			0
$616$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$617$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$617$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$618$		0			0
$619$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$619$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$620$	0.356896	−	1.56366i	0.356896	−	1.56366i
$621$		0			0
$622$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$623$	0.277479	−	1.21572i	0.277479	−	1.21572i
$624$		0			0
$625$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$631$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$631$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.277479	−	0.347948i	0.277479	−	0.347948i
$636$		0			0
$637$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$638$		0			0
$639$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$640$	0.900969	+	0.433884i	0.900969	+	0.433884i
$641$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$641$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$642$		0			0
$643$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$643$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$647$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$648$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$649$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$650$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$651$		0			0
$652$		0			0
$653$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$653$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$658$		0			0
$659$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$659$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$660$		0			0
$661$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$661$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$662$	0.346011	+	0.433884i	0.346011	+	0.433884i
$663$		0			0
$664$	−0.356896	−	1.56366i	−0.356896	−	1.56366i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.60388			1.60388
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.24698	+	1.56366i	−1.24698	+	1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$673$	−1.24698	+	1.56366i	−1.24698	+	1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$674$	0.123490	−	0.541044i	0.123490	−	0.541044i
$675$		0			0
$676$	0.400969	−	0.193096i	0.400969	−	0.193096i
$677$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	0.222521	−	0.974928i	$-0.428571\pi$
$677$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	−1.00000			$\pi$
$678$		0			0
$679$		0			0
$680$	1.30194	−	0.626980i	1.30194	−	0.626980i
$681$		0			0
$682$	−0.198062	−	0.867767i	−0.198062	−	0.867767i
$683$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$683$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$684$		0			0
$685$		0			0
$686$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$687$		0			0
$688$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$689$		0			0
$690$		0			0
$691$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$691$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$692$	0.321552	−	0.154851i	0.321552	−	0.154851i
$693$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$694$	−0.178448	−	0.0859360i	−0.178448	−	0.0859360i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.801938			0.801938
$701$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$701$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$709$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$710$	−0.123490	−	0.154851i	−0.123490	−	0.154851i
$711$		0			0
$712$	0.222521	+	0.974928i	0.222521	+	0.974928i
$713$		0			0
$714$		0			0
$715$	0.277479	−	1.21572i	0.277479	−	1.21572i
$716$	0.356896			0.356896
$717$		0			0
$718$		0			0
$719$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$719$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$720$	0.277479	+	0.347948i	0.277479	+	0.347948i
$721$		0			0
$722$	0.277479	−	0.347948i	0.277479	−	0.347948i
$723$		0			0
$724$	0.900969	−	1.12978i	0.900969	−	1.12978i
$725$		0			0
$726$		0			0
$727$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$727$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$728$	0.900969	+	0.433884i	0.900969	+	0.433884i
$729$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$730$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$731$	0.500000	+	2.19064i	0.500000	+	2.19064i
$732$		0			0
$733$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$733$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$739$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$743$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$744$		0			0
$745$		0			0
$746$	0.500000	−	0.626980i	0.500000	−	0.626980i
$747$	0.445042	−	1.94986i	0.445042	−	1.94986i
$748$	−0.900969	+	1.12978i	−0.900969	+	1.12978i
$749$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$750$		0			0
$751$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$751$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$757$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$758$	0.178448	+	0.781831i	0.178448	+	0.781831i
$759$		0			0
$760$		0			0
$761$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$761$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$762$		0			0
$763$		0			0
$764$	0.356896	−	1.56366i	0.356896	−	1.56366i
$765$	1.80194			1.80194
$766$		0			0
$767$	0.346011	−	1.51597i	0.346011	−	1.51597i
$768$		0			0
$769$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$769$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$770$	0.400969	−	0.193096i	0.400969	−	0.193096i
$771$		0			0
$772$	0.321552	−	1.40881i	0.321552	−	1.40881i
$773$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$773$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$774$	0.500000	−	0.240787i	0.500000	−	0.240787i
$775$	1.24698	+	1.56366i	1.24698	+	1.56366i
$776$		0			0
$777$		0			0
$778$	0.722521	−	0.347948i	0.722521	−	0.347948i
$779$		0			0
$780$		0			0
$781$	0.400969	+	0.193096i	0.400969	+	0.193096i
$782$		0			0
$783$		0			0
$784$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$785$		0			0
$786$		0			0
$787$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	0.222521	−	0.974928i	$-0.428571\pi$
$787$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$788$	0.0794168	+	0.347948i	0.0794168	+	0.347948i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.722521	+	0.347948i	0.722521	+	0.347948i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.0794168	+	0.347948i	−0.0794168	+	0.347948i
$797$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$797$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$798$		0			0
$799$		0			0
$800$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$801$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$802$	0.554958			0.554958
$803$	1.80194			1.80194
$804$		0			0
$805$		0			0
$806$	0.246980	+	1.08209i	0.246980	+	1.08209i
$807$		0			0
$808$		0			0
$809$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$809$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$810$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$811$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$811$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.777479	+	0.974928i	0.777479	+	0.974928i
$820$		0			0
$821$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$821$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$822$		0			0
$823$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$823$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$824$		0			0
$825$		0			0
$826$	0.500000	−	0.240787i	0.500000	−	0.240787i
$827$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$827$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−1.00000			$1.00000\pi$
$828$		0			0
$829$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$829$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$830$	0.801938	+	0.386193i	0.801938	+	0.386193i
$831$		0			0
$832$		0			0
$833$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$834$		0			0
$835$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$836$		0			0
$837$		0			0
$838$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$839$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$839$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$840$		0			0
$841$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$842$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$843$		0			0
$844$		0			0
$845$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$846$		0			0
$847$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$848$		0			0
$849$		0			0
$850$	−0.178448	+	0.781831i	−0.178448	+	0.781831i
$851$		0			0
$852$		0			0
$853$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$853$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$	0.0794168	+	0.347948i	0.0794168	+	0.347948i
$857$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$857$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$858$		0			0
$859$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$859$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$860$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$861$		0			0
$862$		0			0
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$		0			0
$865$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$866$		0			0
$867$		0			0
$868$	1.00000	−	1.25396i	1.00000	−	1.25396i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$876$		0			0
$877$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$877$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$878$		0			0
$879$		0			0
$880$	0.277479	−	0.347948i	0.277479	−	0.347948i
$881$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$881$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$882$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	1.12349	−	1.40881i	1.12349	−	1.40881i
$885$		0			0
$886$		0			0
$887$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$887$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$888$		0			0
$889$	0.400969	−	0.193096i	0.400969	−	0.193096i
$890$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$891$	0.623490	+	0.781831i	0.623490	+	0.781831i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$896$	0.623490	+	0.781831i	0.623490	+	0.781831i
$897$		0			0
$898$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$899$		0			0
$900$	−0.801938			−0.801938
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.400969	+	1.75676i	0.400969	+	1.75676i
$906$		0			0
$907$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$907$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$908$	0.321552	+	1.40881i	0.321552	+	1.40881i
$909$		0			0
$910$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$911$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$911$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$912$		0			0
$913$	−2.00000			−2.00000
$914$	0.198062	−	0.867767i	0.198062	−	0.867767i
$915$		0			0
$916$	0.222521	+	0.279032i	0.222521	+	0.279032i
$917$		0			0
$918$		0			0
$919$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$919$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$929$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$930$		0			0
$931$		0			0
$932$	1.60388			1.60388
$933$		0			0
$934$		0			0
$935$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$936$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$937$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$937$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$941$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$942$		0			0
$943$		0			0
$944$	0.346011	−	0.433884i	0.346011	−	0.433884i
$945$		0			0
$946$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$947$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$947$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$948$		0			0
$949$	−2.24698			−2.24698
$950$		0			0
$951$		0			0
$952$	1.44504			1.44504
$953$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$953$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$954$		0			0
$955$	1.24698	+	1.56366i	1.24698	+	1.56366i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	3.00000			3.00000
$962$		0			0
$963$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$964$		0			0
$965$	1.12349	+	1.40881i	1.12349	+	1.40881i
$966$		0			0
$967$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$967$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$968$	0.178448	−	0.781831i	0.178448	−	0.781831i
$969$		0			0
$970$		0			0
$971$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$971$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$977$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$978$		0			0
$979$	1.24698			1.24698
$980$	0.722521	+	0.347948i	0.722521	+	0.347948i
$981$		0			0
$982$		0			0
$983$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$983$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$984$		0			0
$985$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$991$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$991$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$992$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$993$		0			0
$994$	−0.0440730	−	0.193096i	−0.0440730	−	0.193096i
$995$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$996$		0			0
$997$	0.277479	−	1.21572i	0.277479	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$997$	0.277479	−	1.21572i	0.277479	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$998$	0.554958			0.554958
$999$		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	2695.1.bi.b.2199.1	yes	6
5.4	even	2		2695.1.bi.a.2199.1	yes	6
11.10	odd	2		2695.1.bi.a.2199.1	yes	6
49.8	even	7	inner	2695.1.bi.b.1429.1	yes	6
55.54	odd	2	CM	2695.1.bi.b.2199.1	yes	6
245.204	even	14		2695.1.bi.a.1429.1	✓	6
539.351	odd	14		2695.1.bi.a.1429.1	✓	6
2695.1429	odd	14	inner	2695.1.bi.b.1429.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.1.bi.a.1429.1	✓	6	245.204	even	14
2695.1.bi.a.1429.1	✓	6	539.351	odd	14
2695.1.bi.a.2199.1	yes	6	5.4	even	2
2695.1.bi.a.2199.1	yes	6	11.10	odd	2
2695.1.bi.b.1429.1	yes	6	49.8	even	7	inner
2695.1.bi.b.1429.1	yes	6	2695.1429	odd	14	inner
2695.1.bi.b.2199.1	yes	6	1.1	even	1	trivial
2695.1.bi.b.2199.1	yes	6	55.54	odd	2	CM

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

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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	2695.1.bi.b.2199.1

Level	$2695$
Weight	$1$
Character	2695.2199
Analytic conductor	$1.345$
Analytic rank	$0$
Dimension	$6$
Projective image	$D_{7}$
CM discriminant	-55
Inner twists	$4$