LMFDB - Embedded newform 2695.1.bi.c.2584.2

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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{14}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{14} - \cdots)$

Embedding invariants

Embedding label			2584.2
Root			$-0.781831 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	2695.2584
Dual form			2695.1.bi.c.1044.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.193096 + 0.846011i) q^{2} +(0.222521 - 0.107160i) q^{4} +(-0.623490 - 0.781831i) q^{5} +(0.974928 + 0.222521i) q^{7} +(0.674671 + 0.846011i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(0.541044 - 0.678448i) q^{10} +(0.222521 + 0.974928i) q^{11} +(-0.433884 - 1.90097i) q^{13} +0.867767i q^{14} +(-0.431468 + 0.541044i) q^{16} +(1.40881 + 0.678448i) q^{17} -0.867767 q^{18} +(-0.222521 - 0.107160i) q^{20} +(-0.781831 + 0.376510i) q^{22} +(-0.222521 + 0.974928i) q^{25} +(1.52446 - 0.734141i) q^{26} +(0.240787 - 0.0549581i) q^{28} -2.00000 q^{31} +(0.433884 + 0.208947i) q^{32} +(-0.301938 + 1.32288i) q^{34} +(-0.433884 - 0.900969i) q^{35} +(0.0549581 + 0.240787i) q^{36} +(0.240787 - 1.05496i) q^{40} +(1.21572 - 1.52446i) q^{43} +(0.153989 + 0.193096i) q^{44} +(0.900969 - 0.433884i) q^{45} +(0.900969 + 0.433884i) q^{49} -0.867767 q^{50} +(-0.300257 - 0.376510i) q^{52} +(0.623490 - 0.781831i) q^{55} +(0.469501 + 0.974928i) q^{56} +(-0.277479 + 0.347948i) q^{59} +(-0.386193 - 1.69202i) q^{62} +(-0.433884 + 0.900969i) q^{63} +(-0.246980 + 1.08209i) q^{64} +(-1.21572 + 1.52446i) q^{65} +0.386193 q^{68} +(0.678448 - 0.541044i) q^{70} +(1.62349 - 0.781831i) q^{71} +(-0.974928 + 0.469501i) q^{72} +(-0.347948 + 1.52446i) q^{73} +1.00000i q^{77} +0.692021 q^{80} +(-0.900969 - 0.433884i) q^{81} +(-0.347948 - 1.52446i) q^{85} +(1.52446 + 0.734141i) q^{86} +(-0.674671 + 0.846011i) q^{88} +(-0.0990311 + 0.433884i) q^{89} +(0.541044 + 0.678448i) q^{90} -1.94986i q^{91} +(-0.193096 + 0.846011i) q^{98} -1.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 2 q^{4} + 2 q^{5} - 2 q^{9} + 2 q^{11} - 16 q^{16} - 2 q^{20} - 2 q^{25} - 24 q^{31} + 14 q^{34} + 2 q^{36} + 12 q^{44} + 2 q^{45} + 2 q^{49} - 2 q^{55} - 14 q^{56} - 4 q^{59} + 16 q^{64} + 10 q^{71}+ \cdots - 12 q^{99}+O(q^{100})$ 12 * q + 2 * q^4 + 2 * q^5 - 2 * q^9 + 2 * q^11 - 16 * q^16 - 2 * q^20 - 2 * q^25 - 24 * q^31 + 14 * q^34 + 2 * q^36 + 12 * q^44 + 2 * q^45 + 2 * q^49 - 2 * q^55 - 14 * q^56 - 4 * q^59 + 16 * q^64 + 10 * q^71 - 12 * q^80 - 2 * q^81 - 10 * q^89 - 12 * q^99

Character values

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

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$e\left(\frac{2}{7}\right)$	$-1$

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

)

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

$2$	0.193096	+	0.846011i	0.193096	+	0.846011i	0.974928	+	0.222521i	$0.0714286\pi$
$2$	0.193096	+	0.846011i	0.193096	+	0.846011i	−0.781831	+	0.623490i	$0.785714\pi$
$3$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$3$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$4$	0.222521	−	0.107160i	0.222521	−	0.107160i
$5$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$5$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$6$		0			0
$7$	0.974928	+	0.222521i	0.974928	+	0.222521i
$7$	0.974928	+	0.222521i	0.974928	+	0.222521i
$8$	0.674671	+	0.846011i	0.674671	+	0.846011i
$9$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$10$	0.541044	−	0.678448i	0.541044	−	0.678448i
$11$	0.222521	+	0.974928i	0.222521	+	0.974928i
$11$	0.222521	+	0.974928i	0.222521	+	0.974928i
$12$		0			0
$13$	−0.433884	−	1.90097i	−0.433884	−	1.90097i	−0.433884	−	0.900969i	$-0.642857\pi$
$13$	−0.433884	−	1.90097i	−0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$14$			0.867767i			0.867767i
$15$		0			0
$16$	−0.431468	+	0.541044i	−0.431468	+	0.541044i
$17$	1.40881	+	0.678448i	1.40881	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$17$	1.40881	+	0.678448i	1.40881	+	0.678448i	0.433884	+	0.900969i	$0.357143\pi$
$18$	−0.867767			−0.867767
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−0.222521	−	0.107160i	−0.222521	−	0.107160i
$21$		0			0
$22$	−0.781831	+	0.376510i	−0.781831	+	0.376510i
$23$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$23$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$24$		0			0
$25$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$26$	1.52446	−	0.734141i	1.52446	−	0.734141i
$27$		0			0
$28$	0.240787	−	0.0549581i	0.240787	−	0.0549581i
$29$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$29$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$30$		0			0
$31$	−2.00000			−2.00000			−1.00000			$\pi$
$31$	−2.00000			−2.00000			−1.00000			$\pi$
$32$	0.433884	+	0.208947i	0.433884	+	0.208947i
$33$		0			0
$34$	−0.301938	+	1.32288i	−0.301938	+	1.32288i
$35$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$36$	0.0549581	+	0.240787i	0.0549581	+	0.240787i
$37$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$37$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$38$		0			0
$39$		0			0
$40$	0.240787	−	1.05496i	0.240787	−	1.05496i
$41$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$41$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$42$		0			0
$43$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.433884	−	0.900969i	$-0.357143\pi$
$43$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$44$	0.153989	+	0.193096i	0.153989	+	0.193096i
$45$	0.900969	−	0.433884i	0.900969	−	0.433884i
$46$		0			0
$47$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$47$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$48$		0			0
$49$	0.900969	+	0.433884i	0.900969	+	0.433884i
$50$	−0.867767			−0.867767
$51$		0			0
$52$	−0.300257	−	0.376510i	−0.300257	−	0.376510i
$53$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$53$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$54$		0			0
$55$	0.623490	−	0.781831i	0.623490	−	0.781831i
$56$	0.469501	+	0.974928i	0.469501	+	0.974928i
$57$		0			0
$58$		0			0
$59$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$59$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$60$		0			0
$61$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$61$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$62$	−0.386193	−	1.69202i	−0.386193	−	1.69202i
$63$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$64$	−0.246980	+	1.08209i	−0.246980	+	1.08209i
$65$	−1.21572	+	1.52446i	−1.21572	+	1.52446i
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	0.386193			0.386193
$69$		0			0
$70$	0.678448	−	0.541044i	0.678448	−	0.541044i
$71$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$71$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$72$	−0.974928	+	0.469501i	−0.974928	+	0.469501i
$73$	−0.347948	+	1.52446i	−0.347948	+	1.52446i	0.433884	+	0.900969i	$0.357143\pi$
$73$	−0.347948	+	1.52446i	−0.347948	+	1.52446i	−0.781831	+	0.623490i	$0.785714\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			1.00000i			1.00000i
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	0.692021			0.692021
$81$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$82$		0			0
$83$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$83$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$84$		0			0
$85$	−0.347948	−	1.52446i	−0.347948	−	1.52446i
$86$	1.52446	+	0.734141i	1.52446	+	0.734141i
$87$		0			0
$88$	−0.674671	+	0.846011i	−0.674671	+	0.846011i
$89$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$89$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$90$	0.541044	+	0.678448i	0.541044	+	0.678448i
$91$		−	1.94986i		−	1.94986i
$92$		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			$\pi$
$98$	−0.193096	+	0.846011i	−0.193096	+	0.846011i
$99$	−1.00000			−1.00000
$100$	0.0549581	+	0.240787i	0.0549581	+	0.240787i
$101$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$101$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$102$		0			0
$103$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$103$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$104$	1.31551	−	1.64960i	1.31551	−	1.64960i
$105$		0			0
$106$		0			0
$107$	0.193096	−	0.846011i	0.193096	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$107$	0.193096	−	0.846011i	0.193096	−	0.846011i	0.974928	−	0.222521i	$-0.0714286\pi$
$108$		0			0
$109$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$109$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$110$	0.781831	+	0.376510i	0.781831	+	0.376510i
$111$		0			0
$112$	−0.541044	+	0.431468i	−0.541044	+	0.431468i
$113$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$113$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.94986			1.94986
$118$	−0.347948	−	0.167563i	−0.347948	−	0.167563i
$119$	1.22252	+	0.974928i	1.22252	+	0.974928i
$120$		0			0
$121$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$122$		0			0
$123$		0			0
$124$	−0.445042	+	0.214321i	−0.445042	+	0.214321i
$125$	0.900969	−	0.433884i	0.900969	−	0.433884i
$126$	−0.846011	−	0.193096i	−0.846011	−	0.193096i
$127$	−0.781831	−	0.376510i	−0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$127$	−0.781831	−	0.376510i	−0.781831	−	0.376510i	−0.781831	+	0.623490i	$0.785714\pi$
$128$	−0.481575			−0.481575
$129$		0			0
$130$	−1.52446	−	0.734141i	−1.52446	−	0.734141i
$131$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$131$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.376510	+	1.64960i	0.376510	+	1.64960i
$137$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$137$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$138$		0			0
$139$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$139$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$140$	−0.193096	−	0.153989i	−0.193096	−	0.153989i
$141$		0			0
$142$	0.974928	+	1.22252i	0.974928	+	1.22252i
$143$	1.75676	−	0.846011i	1.75676	−	0.846011i
$144$	−0.431468	−	0.541044i	−0.431468	−	0.541044i
$145$		0			0
$146$	−1.35690			−1.35690
$147$		0			0
$148$		0			0
$149$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$149$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$150$		0			0
$151$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$151$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$152$		0			0
$153$	−0.974928	+	1.22252i	−0.974928	+	1.22252i
$154$	−0.846011	+	0.193096i	−0.846011	+	0.193096i
$155$	1.24698	+	1.56366i	1.24698	+	1.56366i
$156$		0			0
$157$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$157$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$158$		0			0
$159$		0			0
$160$	−0.107160	−	0.469501i	−0.107160	−	0.469501i
$161$		0			0
$162$	0.193096	−	0.846011i	0.193096	−	0.846011i
$163$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$163$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$167$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$168$		0			0
$169$	−2.52446	+	1.21572i	−2.52446	+	1.21572i
$170$	1.22252	−	0.588735i	1.22252	−	0.588735i
$171$		0			0
$172$	0.107160	−	0.469501i	0.107160	−	0.469501i
$173$	0.781831	−	0.376510i	0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$173$	0.781831	−	0.376510i	0.781831	−	0.376510i	0.781831	+	0.623490i	$0.214286\pi$
$174$		0			0
$175$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$176$	−0.623490	−	0.300257i	−0.623490	−	0.300257i
$177$		0			0
$178$	−0.386193			−0.386193
$179$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$179$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$180$	0.153989	−	0.193096i	0.153989	−	0.193096i
$181$	0.277479	−	1.21572i	0.277479	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$181$	0.277479	−	1.21572i	0.277479	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$182$	1.64960	−	0.376510i	1.64960	−	0.376510i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.347948	+	1.52446i	−0.347948	+	1.52446i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$191$	−1.24698	−	1.56366i	−1.24698	−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$192$		0			0
$193$	−0.974928	−	1.22252i	−0.974928	−	1.22252i	−0.974928	−	0.222521i	$-0.928571\pi$
$193$	−0.974928	−	1.22252i	−0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$194$		0			0
$195$		0			0
$196$	0.246980			0.246980
$197$	−0.867767			−0.867767			−0.433884	−	0.900969i	$-0.642857\pi$
$197$	−0.867767			−0.867767			−0.433884	+	0.900969i	$0.642857\pi$
$198$	−0.193096	−	0.846011i	−0.193096	−	0.846011i
$199$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$199$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$200$	−0.974928	+	0.469501i	−0.974928	+	0.469501i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	1.21572	+	0.585458i	1.21572	+	0.585458i
$209$		0			0
$210$		0			0
$211$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$211$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$212$		0			0
$213$		0			0
$214$	0.753020			0.753020
$215$	−1.94986			−1.94986
$216$		0			0
$217$	−1.94986	−	0.445042i	−1.94986	−	0.445042i
$218$		0			0
$219$		0			0
$220$	0.0549581	−	0.240787i	0.0549581	−	0.240787i
$221$	0.678448	−	2.97247i	0.678448	−	2.97247i
$222$		0			0
$223$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$223$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$224$	0.376510	+	0.300257i	0.376510	+	0.300257i
$225$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$226$		0			0
$227$	1.56366			1.56366			0.781831	−	0.623490i	$-0.214286\pi$
$227$	1.56366			1.56366			0.781831	+	0.623490i	$0.214286\pi$
$228$		0			0
$229$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$229$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$233$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$234$	0.376510	+	1.64960i	0.376510	+	1.64960i
$235$		0			0
$236$	−0.0244587	+	0.107160i	−0.0244587	+	0.107160i
$237$		0			0
$238$	−0.588735	+	1.22252i	−0.588735	+	1.22252i
$239$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$239$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$240$		0			0
$241$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$241$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$242$	−0.541044	−	0.678448i	−0.541044	−	0.678448i
$243$		0			0
$244$		0			0
$245$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$246$		0			0
$247$		0			0
$248$	−1.34934	−	1.69202i	−1.34934	−	1.69202i
$249$		0			0
$250$	0.541044	+	0.678448i	0.541044	+	0.678448i
$251$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$251$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$252$			0.246980i			0.246980i
$253$		0			0
$254$	0.167563	−	0.734141i	0.167563	−	0.734141i
$255$		0			0
$256$	0.153989	+	0.674671i	0.153989	+	0.674671i
$257$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$257$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$258$		0			0
$259$		0			0
$260$	−0.107160	+	0.469501i	−0.107160	+	0.469501i
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$269$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$270$		0			0
$271$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$271$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$272$	−0.974928	+	0.469501i	−0.974928	+	0.469501i
$273$		0			0
$274$		0			0
$275$	−1.00000			−1.00000
$276$		0			0
$277$	−1.40881	−	0.678448i	−1.40881	−	0.678448i	−0.433884	−	0.900969i	$-0.642857\pi$
$277$	−1.40881	−	0.678448i	−1.40881	−	0.678448i	−0.974928	+	0.222521i	$0.928571\pi$
$278$		0			0
$279$	0.445042	−	1.94986i	0.445042	−	1.94986i
$280$	0.469501	−	0.974928i	0.469501	−	0.974928i
$281$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$281$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$282$		0			0
$283$	−0.433884	−	1.90097i	−0.433884	−	1.90097i	−0.433884	−	0.900969i	$-0.642857\pi$
$283$	−0.433884	−	1.90097i	−0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$284$	0.277479	−	0.347948i	0.277479	−	0.347948i
$285$		0			0
$286$	1.05496	+	1.32288i	1.05496	+	1.32288i
$287$		0			0
$288$	−0.300257	+	0.376510i	−0.300257	+	0.376510i
$289$	0.900969	+	1.12978i	0.900969	+	1.12978i
$290$		0			0
$291$		0			0
$292$	0.0859360	+	0.376510i	0.0859360	+	0.376510i
$293$	−1.56366			−1.56366			−0.781831	−	0.623490i	$-0.785714\pi$
$293$	−1.56366			−1.56366			−0.781831	+	0.623490i	$0.785714\pi$
$294$		0			0
$295$	0.445042			0.445042
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	1.52446	−	1.21572i	1.52446	−	1.21572i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−1.22252	−	0.588735i	−1.22252	−	0.588735i
$307$	0.193096	+	0.846011i	0.193096	+	0.846011i	0.974928	+	0.222521i	$0.0714286\pi$
$307$	0.193096	+	0.846011i	0.193096	+	0.846011i	−0.781831	+	0.623490i	$0.785714\pi$
$308$	0.107160	+	0.222521i	0.107160	+	0.222521i
$309$		0			0
$310$	−1.08209	+	1.35690i	−1.08209	+	1.35690i
$311$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$311$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$		0			0
$315$	0.974928	−	0.222521i	0.974928	−	0.222521i
$316$		0			0
$317$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$317$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$318$		0			0
$319$		0			0
$320$	1.00000	−	0.481575i	1.00000	−	0.481575i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.246980			−0.246980
$325$	1.94986			1.94986
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	0.222521	−	0.974928i	$-0.428571\pi$
$331$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.433884	−	0.900969i	$-0.357143\pi$
$337$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$338$	−1.51597	−	1.90097i	−1.51597	−	1.90097i
$339$		0			0
$340$	−0.240787	−	0.301938i	−0.240787	−	0.301938i
$341$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$342$		0			0
$343$	0.781831	+	0.623490i	0.781831	+	0.623490i
$344$	2.10992			2.10992
$345$		0			0
$346$	0.469501	+	0.588735i	0.469501	+	0.588735i
$347$	−0.781831	+	0.376510i	−0.781831	+	0.376510i	−0.781831	−	0.623490i	$-0.785714\pi$
$347$	−0.781831	+	0.376510i	−0.781831	+	0.376510i			1.00000i	$0.5\pi$
$348$		0			0
$349$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$349$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$350$	−0.846011	−	0.193096i	−0.846011	−	0.193096i
$351$		0			0
$352$	−0.107160	+	0.469501i	−0.107160	+	0.469501i
$353$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$353$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$354$		0			0
$355$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$356$	0.0244587	+	0.107160i	0.0244587	+	0.107160i
$357$		0			0
$358$	0.347948	−	1.52446i	0.347948	−	1.52446i
$359$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$359$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$360$	0.974928	+	0.469501i	0.974928	+	0.469501i
$361$	1.00000			1.00000
$362$	1.08209			1.08209
$363$		0			0
$364$	−0.208947	−	0.433884i	−0.208947	−	0.433884i
$365$	1.40881	−	0.678448i	1.40881	−	0.678448i
$366$		0			0
$367$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$367$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.56366			1.56366			0.781831	−	0.623490i	$-0.214286\pi$
$373$	1.56366			1.56366			0.781831	+	0.623490i	$0.214286\pi$
$374$	−1.35690			−1.35690
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$379$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$380$		0			0
$381$		0			0
$382$	1.08209	−	1.35690i	1.08209	−	1.35690i
$383$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$383$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$384$		0			0
$385$	0.781831	−	0.623490i	0.781831	−	0.623490i
$386$	0.846011	−	1.06086i	0.846011	−	1.06086i
$387$	1.21572	+	1.52446i	1.21572	+	1.52446i
$388$		0			0
$389$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$389$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$390$		0			0
$391$		0			0
$392$	0.240787	+	1.05496i	0.240787	+	1.05496i
$393$		0			0
$394$	−0.167563	−	0.734141i	−0.167563	−	0.734141i
$395$		0			0
$396$	−0.222521	+	0.107160i	−0.222521	+	0.107160i
$397$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$397$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$398$	0.974928	−	1.22252i	0.974928	−	1.22252i
$399$		0			0
$400$	−0.431468	−	0.541044i	−0.431468	−	0.541044i
$401$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$401$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i	−1.00000			$\pi$
$402$		0			0
$403$	0.867767	+	3.80194i	0.867767	+	3.80194i
$404$		0			0
$405$	0.222521	+	0.974928i	0.222521	+	0.974928i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$409$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.347948	+	0.277479i	−0.347948	+	0.277479i
$414$		0			0
$415$		0			0
$416$	0.208947	−	0.915458i	0.208947	−	0.915458i
$417$		0			0
$418$		0			0
$419$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$419$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$420$		0			0
$421$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$421$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.974928	+	1.22252i	−0.974928	+	1.22252i
$426$		0			0
$427$		0			0
$428$	−0.0476909	−	0.208947i	−0.0476909	−	0.208947i
$429$		0			0
$430$	−0.376510	−	1.64960i	−0.376510	−	1.64960i
$431$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$431$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$432$		0			0
$433$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$433$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$434$		−	1.73553i		−	1.73553i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$439$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$440$	1.08209			1.08209
$441$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$442$	2.64575			2.64575
$443$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$443$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$444$		0			0
$445$	0.400969	−	0.193096i	0.400969	−	0.193096i
$446$		0			0
$447$		0			0
$448$	−0.481575	+	1.00000i	−0.481575	+	1.00000i
$449$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$449$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$450$	0.193096	−	0.846011i	0.193096	−	0.846011i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.301938	+	1.32288i	0.301938	+	1.32288i
$455$	−1.52446	+	1.21572i	−1.52446	+	1.21572i
$456$		0			0
$457$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$457$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$458$	−1.40881	−	0.678448i	−1.40881	−	0.678448i
$459$		0			0
$460$		0			0
$461$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$461$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$462$		0			0
$463$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$463$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$467$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$468$	0.433884	−	0.208947i	0.433884	−	0.208947i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.481575			−0.481575
$473$	1.75676	+	0.846011i	1.75676	+	0.846011i
$474$		0			0
$475$		0			0
$476$	0.376510	+	0.0859360i	0.376510	+	0.0859360i
$477$		0			0
$478$		0			0
$479$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$479$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.153989	+	0.193096i	−0.153989	+	0.193096i
$485$		0			0
$486$		0			0
$487$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$487$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$488$		0			0
$489$		0			0
$490$	0.781831	−	0.376510i	0.781831	−	0.376510i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.623490	+	0.781831i	0.623490	+	0.781831i
$496$	0.862937	−	1.08209i	0.862937	−	1.08209i
$497$	1.75676	−	0.400969i	1.75676	−	0.400969i
$498$		0			0
$499$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$499$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$500$	0.153989	−	0.193096i	0.153989	−	0.193096i
$501$		0			0
$502$	−1.40881	−	0.678448i	−1.40881	−	0.678448i
$503$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$503$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$504$	−1.05496	+	0.240787i	−1.05496	+	0.240787i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−0.214321			−0.214321
$509$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$509$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$510$		0			0
$511$	−0.678448	+	1.40881i	−0.678448	+	1.40881i
$512$	−0.974928	+	0.469501i	−0.974928	+	0.469501i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−2.10992			−2.10992
$521$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$521$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$522$		0			0
$523$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.433884	−	0.900969i	$-0.357143\pi$
$523$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.81762	−	1.35690i	−2.81762	−	1.35690i
$528$		0			0
$529$	0.623490	−	0.781831i	0.623490	−	0.781831i
$530$		0			0
$531$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.781831	+	0.376510i	−0.781831	+	0.376510i
$536$		0			0
$537$		0			0
$538$	−1.08209			−1.08209
$539$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$540$		0			0
$541$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$541$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$542$		0			0
$543$		0			0
$544$	0.469501	+	0.588735i	0.469501	+	0.588735i
$545$		0			0
$546$		0			0
$547$	−0.974928	−	1.22252i	−0.974928	−	1.22252i	−0.974928	−	0.222521i	$-0.928571\pi$
$547$	−0.974928	−	1.22252i	−0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$548$		0			0
$549$		0			0
$550$	−0.193096	−	0.846011i	−0.193096	−	0.846011i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.301938	−	1.32288i	0.301938	−	1.32288i
$555$		0			0
$556$		0			0
$557$	−1.94986			−1.94986			−0.974928	−	0.222521i	$-0.928571\pi$
$557$	−1.94986			−1.94986			−0.974928	+	0.222521i	$0.928571\pi$
$558$	1.73553			1.73553
$559$	−3.42543	−	1.64960i	−3.42543	−	1.64960i
$560$	0.674671	+	0.153989i	0.674671	+	0.153989i
$561$		0			0
$562$		0			0
$563$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	0.781831	+	0.623490i	$0.214286\pi$
$563$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$564$		0			0
$565$		0			0
$566$	1.52446	−	0.734141i	1.52446	−	0.734141i
$567$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$568$	1.75676	+	0.846011i	1.75676	+	0.846011i
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$571$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$572$	0.300257	−	0.376510i	0.300257	−	0.376510i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1.00000	−	0.481575i	−1.00000	−	0.481575i
$577$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$577$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$578$	−0.781831	+	0.980386i	−0.781831	+	0.980386i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.52446	+	0.734141i	−1.52446	+	0.734141i
$585$	−1.21572	−	1.52446i	−1.21572	−	1.52446i
$586$	−0.301938	−	1.32288i	−0.301938	−	1.32288i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	0.0859360	+	0.376510i	0.0859360	+	0.376510i
$591$		0			0
$592$		0			0
$593$	1.21572	+	1.52446i	1.21572	+	1.52446i	0.781831	+	0.623490i	$0.214286\pi$
$593$	1.21572	+	1.52446i	1.21572	+	1.52446i	0.433884	+	0.900969i	$0.357143\pi$
$594$		0			0
$595$		−	1.56366i		−	1.56366i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$599$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$600$		0			0
$601$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$601$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$602$	1.32288	+	1.05496i	1.32288	+	1.05496i
$603$		0			0
$604$		0			0
$605$	0.900969	+	0.433884i	0.900969	+	0.433884i
$606$		0			0
$607$	−1.56366			−1.56366			−0.781831	−	0.623490i	$-0.785714\pi$
$607$	−1.56366			−1.56366			−0.781831	+	0.623490i	$0.785714\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.0859360	+	0.376510i	−0.0859360	+	0.376510i
$613$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	0.781831	+	0.623490i	$0.214286\pi$
$613$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$614$	−0.678448	+	0.326723i	−0.678448	+	0.326723i
$615$		0			0
$616$	−0.846011	+	0.674671i	−0.846011	+	0.674671i
$617$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$617$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$618$		0			0
$619$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$619$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$620$	0.445042	+	0.214321i	0.445042	+	0.214321i
$621$		0			0
$622$	0.240787	−	1.05496i	0.240787	−	1.05496i
$623$	−0.193096	+	0.400969i	−0.193096	+	0.400969i
$624$		0			0
$625$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.376510	+	0.781831i	0.376510	+	0.781831i
$631$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$631$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.193096	+	0.846011i	0.193096	+	0.846011i
$636$		0			0
$637$	0.433884	−	1.90097i	0.433884	−	1.90097i
$638$		0			0
$639$	0.400969	+	1.75676i	0.400969	+	1.75676i
$640$	0.300257	+	0.376510i	0.300257	+	0.376510i
$641$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$641$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−1.00000			$1.00000\pi$
$642$		0			0
$643$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$643$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$647$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$648$	−0.240787	−	1.05496i	−0.240787	−	1.05496i
$649$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$650$	0.376510	+	1.64960i	0.376510	+	1.64960i
$651$		0			0
$652$		0			0
$653$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$653$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.40881	−	0.678448i	−1.40881	−	0.678448i
$658$		0			0
$659$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$659$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$660$		0			0
$661$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$661$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$662$	0.0859360	−	0.376510i	0.0859360	−	0.376510i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$673$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$674$	1.52446	+	0.734141i	1.52446	+	0.734141i
$675$		0			0
$676$	−0.431468	+	0.541044i	−0.431468	+	0.541044i
$677$	−0.433884	+	1.90097i	−0.433884	+	1.90097i			1.00000i	$0.5\pi$
$677$	−0.433884	+	1.90097i	−0.433884	+	1.90097i	−0.433884	+	0.900969i	$0.642857\pi$
$678$		0			0
$679$		0			0
$680$	1.05496	−	1.32288i	1.05496	−	1.32288i
$681$		0			0
$682$	1.56366	−	0.753020i	1.56366	−	0.753020i
$683$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$683$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$684$		0			0
$685$		0			0
$686$	−0.376510	+	0.781831i	−0.376510	+	0.781831i
$687$		0			0
$688$	0.300257	+	1.31551i	0.300257	+	1.31551i
$689$		0			0
$690$		0			0
$691$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$691$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$692$	0.133627	−	0.167563i	0.133627	−	0.167563i
$693$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$694$	−0.469501	−	0.588735i	−0.469501	−	0.588735i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$			0.246980i			0.246980i
$701$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$701$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$702$		0			0
$703$		0			0
$704$	−1.10992			−1.10992
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.80194	−	0.867767i	1.80194	−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$709$	1.80194	−	0.867767i	1.80194	−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$710$	0.347948	−	1.52446i	0.347948	−	1.52446i
$711$		0			0
$712$	−0.433884	+	0.208947i	−0.433884	+	0.208947i
$713$		0			0
$714$		0			0
$715$	−1.75676	−	0.846011i	−1.75676	−	0.846011i
$716$	−0.445042			−0.445042
$717$		0			0
$718$		0			0
$719$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$719$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$720$	−0.153989	+	0.674671i	−0.153989	+	0.674671i
$721$		0			0
$722$	0.193096	+	0.846011i	0.193096	+	0.846011i
$723$		0			0
$724$	−0.0685317	−	0.300257i	−0.0685317	−	0.300257i
$725$		0			0
$726$		0			0
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$	1.64960	−	1.31551i	1.64960	−	1.31551i
$729$	0.623490	−	0.781831i	0.623490	−	0.781831i
$730$	0.846011	+	1.06086i	0.846011	+	1.06086i
$731$	2.74698	−	1.32288i	2.74698	−	1.32288i
$732$		0			0
$733$	−0.193096	−	0.846011i	−0.193096	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$733$	−0.193096	−	0.846011i	−0.193096	−	0.846011i	0.781831	−	0.623490i	$-0.214286\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$739$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.21572	+	1.52446i	1.21572	+	1.52446i	0.781831	+	0.623490i	$0.214286\pi$
$743$	1.21572	+	1.52446i	1.21572	+	1.52446i	0.433884	+	0.900969i	$0.357143\pi$
$744$		0			0
$745$		0			0
$746$	0.301938	+	1.32288i	0.301938	+	1.32288i
$747$		0			0
$748$	0.0859360	+	0.376510i	0.0859360	+	0.376510i
$749$	0.376510	−	0.781831i	0.376510	−	0.781831i
$750$		0			0
$751$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$751$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$757$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$758$	0.974928	−	0.469501i	0.974928	−	0.469501i
$759$		0			0
$760$		0			0
$761$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$761$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$762$		0			0
$763$		0			0
$764$	−0.445042	−	0.214321i	−0.445042	−	0.214321i
$765$	1.56366			1.56366
$766$		0			0
$767$	0.781831	+	0.376510i	0.781831	+	0.376510i
$768$		0			0
$769$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$769$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$770$	0.678448	+	0.541044i	0.678448	+	0.541044i
$771$		0			0
$772$	−0.347948	−	0.167563i	−0.347948	−	0.167563i
$773$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$773$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$774$	−1.05496	+	1.32288i	−1.05496	+	1.32288i
$775$	0.445042	−	1.94986i	0.445042	−	1.94986i
$776$		0			0
$777$		0			0
$778$	−0.674671	+	0.846011i	−0.674671	+	0.846011i
$779$		0			0
$780$		0			0
$781$	1.12349	+	1.40881i	1.12349	+	1.40881i
$782$		0			0
$783$		0			0
$784$	−0.623490	+	0.300257i	−0.623490	+	0.300257i
$785$		0			0
$786$		0			0
$787$	−0.541044	−	0.678448i	−0.541044	−	0.678448i	0.433884	−	0.900969i	$-0.357143\pi$
$787$	−0.541044	−	0.678448i	−0.541044	−	0.678448i	−0.974928	+	0.222521i	$0.928571\pi$
$788$	−0.193096	+	0.0929903i	−0.193096	+	0.0929903i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.674671	−	0.846011i	−0.674671	−	0.846011i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$797$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$797$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$798$		0			0
$799$		0			0
$800$	−0.300257	+	0.376510i	−0.300257	+	0.376510i
$801$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$802$	−0.386193			−0.386193
$803$	−1.56366			−1.56366
$804$		0			0
$805$		0			0
$806$	−3.04892	+	1.46828i	−3.04892	+	1.46828i
$807$		0			0
$808$		0			0
$809$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$809$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$810$	−0.781831	+	0.376510i	−0.781831	+	0.376510i
$811$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$811$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	1.90097	+	0.433884i	1.90097	+	0.433884i
$820$		0			0
$821$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$821$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$822$		0			0
$823$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$823$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$824$		0			0
$825$		0			0
$826$	−0.301938	−	0.240787i	−0.301938	−	0.240787i
$827$	−0.974928	+	1.22252i	−0.974928	+	1.22252i			1.00000i	$0.5\pi$
$827$	−0.974928	+	1.22252i	−0.974928	+	1.22252i	−0.974928	+	0.222521i	$0.928571\pi$
$828$		0			0
$829$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$829$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$830$		0			0
$831$		0			0
$832$	2.16418			2.16418
$833$	0.974928	+	1.22252i	0.974928	+	1.22252i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−0.240787	−	0.301938i	−0.240787	−	0.301938i
$839$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$839$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$840$		0			0
$841$	0.623490	+	0.781831i	0.623490	+	0.781831i
$842$	−0.240787	+	1.05496i	−0.240787	+	1.05496i
$843$		0			0
$844$		0			0
$845$	2.52446	+	1.21572i	2.52446	+	1.21572i
$846$		0			0
$847$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$848$		0			0
$849$		0			0
$850$	−1.22252	−	0.588735i	−1.22252	−	0.588735i
$851$		0			0
$852$		0			0
$853$	0.781831	+	0.376510i	0.781831	+	0.376510i	0.781831	−	0.623490i	$-0.214286\pi$
$853$	0.781831	+	0.376510i	0.781831	+	0.376510i			1.00000i	$0.5\pi$
$854$		0			0
$855$		0			0
$856$	0.846011	−	0.407417i	0.846011	−	0.407417i
$857$	0.193096	−	0.846011i	0.193096	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$857$	0.193096	−	0.846011i	0.193096	−	0.846011i	0.974928	−	0.222521i	$-0.0714286\pi$
$858$		0			0
$859$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$859$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$860$	−0.433884	+	0.208947i	−0.433884	+	0.208947i
$861$		0			0
$862$		0			0
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$		0			0
$865$	−0.781831	−	0.376510i	−0.781831	−	0.376510i
$866$		0			0
$867$		0			0
$868$	−0.481575	+	0.109916i	−0.481575	+	0.109916i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.974928	−	0.222521i	0.974928	−	0.222521i
$876$		0			0
$877$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$877$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$878$		0			0
$879$		0			0
$880$	0.153989	+	0.674671i	0.153989	+	0.674671i
$881$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$881$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$882$	−0.781831	−	0.376510i	−0.781831	−	0.376510i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−0.167563	−	0.734141i	−0.167563	−	0.734141i
$885$		0			0
$886$		0			0
$887$	−0.974928	−	1.22252i	−0.974928	−	1.22252i	−0.974928	−	0.222521i	$-0.928571\pi$
$887$	−0.974928	−	1.22252i	−0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$888$		0			0
$889$	−0.678448	−	0.541044i	−0.678448	−	0.541044i
$890$	0.240787	+	0.301938i	0.240787	+	0.301938i
$891$	0.222521	−	0.974928i	0.222521	−	0.974928i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	0.400969	+	1.75676i	0.400969	+	1.75676i
$896$	−0.469501	−	0.107160i	−0.469501	−	0.107160i
$897$		0			0
$898$	−0.240787	+	0.301938i	−0.240787	+	0.301938i
$899$		0			0
$900$	−0.246980			−0.246980
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$906$		0			0
$907$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$907$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$908$	0.347948	−	0.167563i	0.347948	−	0.167563i
$909$		0			0
$910$	−1.32288	−	1.05496i	−1.32288	−	1.05496i
$911$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$911$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$917$		0			0
$918$		0			0
$919$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$919$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.19064	−	2.74698i	−2.19064	−	2.74698i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$929$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.40881	−	0.678448i	1.40881	−	0.678448i
$936$	1.31551	+	1.64960i	1.31551	+	1.64960i
$937$	−1.21572	+	1.52446i	−1.21572	+	1.52446i	−0.433884	+	0.900969i	$0.642857\pi$
$937$	−1.21572	+	1.52446i	−1.21572	+	1.52446i	−0.781831	+	0.623490i	$0.785714\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$941$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$942$		0			0
$943$		0			0
$944$	−0.0685317	−	0.300257i	−0.0685317	−	0.300257i
$945$		0			0
$946$	−0.376510	+	1.64960i	−0.376510	+	1.64960i
$947$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$947$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$948$		0			0
$949$	3.04892			3.04892
$950$		0			0
$951$		0			0
$952$			1.69202i			1.69202i
$953$	1.75676	−	0.846011i	1.75676	−	0.846011i	0.781831	−	0.623490i	$-0.214286\pi$
$953$	1.75676	−	0.846011i	1.75676	−	0.846011i	0.974928	−	0.222521i	$-0.0714286\pi$
$954$		0			0
$955$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	3.00000			3.00000
$962$		0			0
$963$	0.781831	+	0.376510i	0.781831	+	0.376510i
$964$		0			0
$965$	−0.347948	+	1.52446i	−0.347948	+	1.52446i
$966$		0			0
$967$	0.347948	+	1.52446i	0.347948	+	1.52446i	0.781831	+	0.623490i	$0.214286\pi$
$967$	0.347948	+	1.52446i	0.347948	+	1.52446i	−0.433884	+	0.900969i	$0.642857\pi$
$968$	−0.974928	−	0.469501i	−0.974928	−	0.469501i
$969$		0			0
$970$		0			0
$971$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$971$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$977$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$978$		0			0
$979$	−0.445042			−0.445042
$980$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$981$		0			0
$982$		0			0
$983$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$983$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$984$		0			0
$985$	0.541044	+	0.678448i	0.541044	+	0.678448i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.541044	+	0.678448i	−0.541044	+	0.678448i
$991$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$991$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$992$	−0.867767	−	0.417895i	−0.867767	−	0.417895i
$993$		0			0
$994$	0.678448	+	1.40881i	0.678448	+	1.40881i
$995$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$996$		0			0
$997$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$997$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$998$	0.386193			0.386193
$999$		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.c.2584.2	yes	12
5.4	even	2	inner	2695.1.bi.c.2584.1	yes	12
11.10	odd	2	inner	2695.1.bi.c.2584.1	yes	12
49.15	even	7	inner	2695.1.bi.c.1044.2	yes	12
55.54	odd	2	CM	2695.1.bi.c.2584.2	yes	12
245.64	even	14	inner	2695.1.bi.c.1044.1	✓	12
539.505	odd	14	inner	2695.1.bi.c.1044.1	✓	12
2695.1044	odd	14	inner	2695.1.bi.c.1044.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.1.bi.c.1044.1	✓	12	245.64	even	14	inner
2695.1.bi.c.1044.1	✓	12	539.505	odd	14	inner
2695.1.bi.c.1044.2	yes	12	49.15	even	7	inner
2695.1.bi.c.1044.2	yes	12	2695.1044	odd	14	inner
2695.1.bi.c.2584.1	yes	12	5.4	even	2	inner
2695.1.bi.c.2584.1	yes	12	11.10	odd	2	inner
2695.1.bi.c.2584.2	yes	12	1.1	even	1	trivial
2695.1.bi.c.2584.2	yes	12	55.54	odd	2	CM

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

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$q$ -expansion

Character values

Coefficient data

Twists

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

Label	2695.1.bi.c.2584.2

Level	$2695$
Weight	$1$
Character	2695.2584
Analytic conductor	$1.345$
Analytic rank	$0$
Dimension	$12$
Projective image	$D_{14}$
CM discriminant	-55
Inner twists	$8$