LMFDB - Embedded newform 2900.1.bj.b.2751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2900,1,Mod(451,2900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2900, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 2]))

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

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

chi := DirichletCharacter("2900.451");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$2900 = 2^{2} \cdot 5^{2} \cdot 29$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2900.bj (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:	$1.44728853664$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 580)
Projective image:	$D_{7}$
Projective field:	Galois closure of 7.1.4758586568000.1

Embedding invariants

Embedding label			2751.1
Root			$-0.433884 + 0.900969i$ of defining polynomial
Character	$\chi$	$=$	2900.2751
Dual form			2900.1.bj.b.1051.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.974928 - 0.222521i) q^{2} +(-0.193096 - 0.400969i) q^{3} +(0.900969 + 0.433884i) q^{4} +(0.0990311 + 0.433884i) q^{6} +(0.781831 + 1.62349i) q^{7} +(-0.781831 - 0.623490i) q^{8} +(0.500000 - 0.626980i) q^{9} -0.445042i q^{12} +(-0.400969 - 1.75676i) q^{14} +(0.623490 + 0.781831i) q^{16} +(-0.626980 + 0.500000i) q^{18} +(0.500000 - 0.626980i) q^{21} +(0.433884 - 0.0990311i) q^{23} +(-0.0990311 + 0.433884i) q^{24} +(-0.781831 - 0.178448i) q^{27} +1.80194i q^{28} +(0.900969 - 0.433884i) q^{29} +(-0.433884 - 0.900969i) q^{32} +(0.722521 - 0.347948i) q^{36} +1.24698 q^{41} +(-0.626980 + 0.500000i) q^{42} +(-1.21572 + 0.277479i) q^{43} -0.445042 q^{46} +(1.40881 - 1.12349i) q^{47} +(0.193096 - 0.400969i) q^{48} +(-1.40097 + 1.75676i) q^{49} +(0.722521 + 0.347948i) q^{54} +(0.400969 - 1.75676i) q^{56} +(-0.974928 + 0.222521i) q^{58} +(-1.80194 + 0.867767i) q^{61} +(1.40881 + 0.321552i) q^{63} +(0.222521 + 0.974928i) q^{64} +(1.56366 + 1.24698i) q^{67} +(-0.123490 - 0.154851i) q^{69} +(-0.781831 + 0.178448i) q^{72} +(-0.0990311 - 0.433884i) q^{81} +(-1.21572 - 0.277479i) q^{82} +(-0.541044 + 1.12349i) q^{83} +(0.722521 - 0.347948i) q^{84} +1.24698 q^{86} +(-0.347948 - 0.277479i) q^{87} +(-0.400969 + 1.75676i) q^{89} +(0.433884 + 0.0990311i) q^{92} +(-1.62349 + 0.781831i) q^{94} +(-0.277479 + 0.347948i) q^{96} +(1.75676 - 1.40097i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 2 q^{4} + 10 q^{6} + 6 q^{9} + 4 q^{14} - 2 q^{16} + 6 q^{21} - 10 q^{24} + 2 q^{29} + 8 q^{36} - 4 q^{41} - 4 q^{46} - 8 q^{49} + 8 q^{54} - 4 q^{56} - 4 q^{61} + 2 q^{64} + 8 q^{69} - 10 q^{81}+ \cdots - 4 q^{96}+O(q^{100})$ 12 * q + 2 * q^4 + 10 * q^6 + 6 * q^9 + 4 * q^14 - 2 * q^16 + 6 * q^21 - 10 * q^24 + 2 * q^29 + 8 * q^36 - 4 * q^41 - 4 * q^46 - 8 * q^49 + 8 * q^54 - 4 * q^56 - 4 * q^61 + 2 * q^64 + 8 * q^69 - 10 * q^81 + 8 * q^84 - 4 * q^86 + 4 * q^89 - 10 * q^94 - 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times$ .

$n$	$901$	$1277$	$1451$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$	$-1$

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

)

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

$2$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$2$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$3$	−0.193096	−	0.400969i	−0.193096	−	0.400969i	0.781831	−	0.623490i	$-0.214286\pi$
$3$	−0.193096	−	0.400969i	−0.193096	−	0.400969i	−0.974928	+	0.222521i	$0.928571\pi$
$4$	0.900969	+	0.433884i	0.900969	+	0.433884i
$5$		0			0
$5$		0			0
$6$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$7$	0.781831	+	1.62349i	0.781831	+	1.62349i	0.781831	+	0.623490i	$0.214286\pi$
$7$	0.781831	+	1.62349i	0.781831	+	1.62349i			1.00000i	$0.5\pi$
$8$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$9$	0.500000	−	0.626980i	0.500000	−	0.626980i
$10$		0			0
$11$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$11$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$12$		−	0.445042i		−	0.445042i
$13$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$13$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$14$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$15$		0			0
$16$	0.623490	+	0.781831i	0.623490	+	0.781831i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−0.626980	+	0.500000i	−0.626980	+	0.500000i
$19$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$19$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$20$		0			0
$21$	0.500000	−	0.626980i	0.500000	−	0.626980i
$22$		0			0
$23$	0.433884	−	0.0990311i	0.433884	−	0.0990311i		−	1.00000i	$-0.5\pi$
$23$	0.433884	−	0.0990311i	0.433884	−	0.0990311i	0.433884	+	0.900969i	$0.357143\pi$
$24$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$25$		0			0
$26$		0			0
$27$	−0.781831	−	0.178448i	−0.781831	−	0.178448i
$28$			1.80194i			1.80194i
$29$	0.900969	−	0.433884i	0.900969	−	0.433884i
$29$	0.900969	−	0.433884i	0.900969	−	0.433884i
$30$		0			0
$31$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$31$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$32$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.722521	−	0.347948i	0.722521	−	0.347948i
$37$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$37$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$41$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$42$	−0.626980	+	0.500000i	−0.626980	+	0.500000i
$43$	−1.21572	+	0.277479i	−1.21572	+	0.277479i	−0.781831	−	0.623490i	$-0.785714\pi$
$43$	−1.21572	+	0.277479i	−1.21572	+	0.277479i	−0.433884	+	0.900969i	$0.642857\pi$
$44$		0			0
$45$		0			0
$46$	−0.445042			−0.445042
$47$	1.40881	−	1.12349i	1.40881	−	1.12349i	0.433884	−	0.900969i	$-0.357143\pi$
$47$	1.40881	−	1.12349i	1.40881	−	1.12349i	0.974928	−	0.222521i	$-0.0714286\pi$
$48$	0.193096	−	0.400969i	0.193096	−	0.400969i
$49$	−1.40097	+	1.75676i	−1.40097	+	1.75676i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$53$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$54$	0.722521	+	0.347948i	0.722521	+	0.347948i
$55$		0			0
$56$	0.400969	−	1.75676i	0.400969	−	1.75676i
$57$		0			0
$58$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$61$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$62$		0			0
$63$	1.40881	+	0.321552i	1.40881	+	0.321552i
$64$	0.222521	+	0.974928i	0.222521	+	0.974928i
$65$		0			0
$66$		0			0
$67$	1.56366	+	1.24698i	1.56366	+	1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$67$	1.56366	+	1.24698i	1.56366	+	1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$68$		0			0
$69$	−0.123490	−	0.154851i	−0.123490	−	0.154851i
$70$		0			0
$71$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$71$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$72$	−0.781831	+	0.178448i	−0.781831	+	0.178448i
$73$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$73$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$79$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$80$		0			0
$81$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$82$	−1.21572	−	0.277479i	−1.21572	−	0.277479i
$83$	−0.541044	+	1.12349i	−0.541044	+	1.12349i	0.433884	+	0.900969i	$0.357143\pi$
$83$	−0.541044	+	1.12349i	−0.541044	+	1.12349i	−0.974928	+	0.222521i	$0.928571\pi$
$84$	0.722521	−	0.347948i	0.722521	−	0.347948i
$85$		0			0
$86$	1.24698			1.24698
$87$	−0.347948	−	0.277479i	−0.347948	−	0.277479i
$88$		0			0
$89$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$89$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$90$		0			0
$91$		0			0
$92$	0.433884	+	0.0990311i	0.433884	+	0.0990311i
$93$		0			0
$94$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$95$		0			0
$96$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$97$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$97$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$98$	1.75676	−	1.40097i	1.75676	−	1.40097i
$99$		0			0
$100$		0			0
$101$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$101$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$102$		0			0
$103$	0.974928	−	0.777479i	0.974928	−	0.777479i		−	1.00000i	$-0.5\pi$
$103$	0.974928	−	0.777479i	0.974928	−	0.777479i	0.974928	+	0.222521i	$0.0714286\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.347948	−	0.277479i	−0.347948	−	0.277479i	0.433884	−	0.900969i	$-0.357143\pi$
$107$	−0.347948	−	0.277479i	−0.347948	−	0.277479i	−0.781831	+	0.623490i	$0.785714\pi$
$108$	−0.626980	−	0.500000i	−0.626980	−	0.500000i
$109$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$109$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$110$		0			0
$111$		0			0
$112$	−0.781831	+	1.62349i	−0.781831	+	1.62349i
$113$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$113$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$114$		0			0
$115$		0			0
$116$	1.00000			1.00000
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$122$	1.94986	−	0.445042i	1.94986	−	0.445042i
$123$	−0.240787	−	0.500000i	−0.240787	−	0.500000i
$124$		0			0
$125$		0			0
$126$	−1.30194	−	0.626980i	−1.30194	−	0.626980i
$127$	1.40881	−	1.12349i	1.40881	−	1.12349i	0.433884	−	0.900969i	$-0.357143\pi$
$127$	1.40881	−	1.12349i	1.40881	−	1.12349i	0.974928	−	0.222521i	$-0.0714286\pi$
$128$		−	1.00000i		−	1.00000i
$129$	0.346011	+	0.433884i	0.346011	+	0.433884i
$130$		0			0
$131$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$131$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$132$		0			0
$133$		0			0
$134$	−1.24698	−	1.56366i	−1.24698	−	1.56366i
$135$		0			0
$136$		0			0
$137$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$137$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$138$	0.0859360	+	0.178448i	0.0859360	+	0.178448i
$139$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$139$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$140$		0			0
$141$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$142$		0			0
$143$		0			0
$144$	0.801938			0.801938
$145$		0			0
$146$		0			0
$147$	0.974928	+	0.222521i	0.974928	+	0.222521i
$148$		0			0
$149$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$149$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$150$		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
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.500000	+	0.626980i	0.500000	+	0.626980i
$162$			0.445042i			0.445042i
$163$	0.974928	−	0.777479i	0.974928	−	0.777479i		−	1.00000i	$-0.5\pi$
$163$	0.974928	−	0.777479i	0.974928	−	0.777479i	0.974928	+	0.222521i	$0.0714286\pi$
$164$	1.12349	+	0.541044i	1.12349	+	0.541044i
$165$		0			0
$166$	0.777479	−	0.974928i	0.777479	−	0.974928i
$167$	−0.541044	−	1.12349i	−0.541044	−	1.12349i	−0.974928	−	0.222521i	$-0.928571\pi$
$167$	−0.541044	−	1.12349i	−0.541044	−	1.12349i	0.433884	−	0.900969i	$-0.357143\pi$
$168$	−0.781831	+	0.178448i	−0.781831	+	0.178448i
$169$	0.222521	−	0.974928i	0.222521	−	0.974928i
$170$		0			0
$171$		0			0
$172$	−1.21572	−	0.277479i	−1.21572	−	0.277479i
$173$		0			0			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$	0.277479	+	0.347948i	0.277479	+	0.347948i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.781831	−	1.62349i	0.781831	−	1.62349i
$179$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$179$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$180$		0			0
$181$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$181$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$182$		0			0
$183$	0.695895	+	0.554958i	0.695895	+	0.554958i
$184$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.75676	−	0.400969i	1.75676	−	0.400969i
$189$	−0.321552	−	1.40881i	−0.321552	−	1.40881i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	0.347948	−	0.277479i	0.347948	−	0.277479i
$193$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$193$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$194$		0			0
$195$		0			0
$196$	−2.02446	+	0.974928i	−2.02446	+	0.974928i
$197$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$197$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$198$		0			0
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$		0			0
$201$	0.198062	−	0.867767i	0.198062	−	0.867767i
$202$		−	0.445042i		−	0.445042i
$203$	1.40881	+	1.12349i	1.40881	+	1.12349i
$204$		0			0
$205$		0			0
$206$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$207$	0.154851	−	0.321552i	0.154851	−	0.321552i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$211$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$212$		0			0
$213$		0			0
$214$	0.277479	+	0.347948i	0.277479	+	0.347948i
$215$		0			0
$216$	0.500000	+	0.626980i	0.500000	+	0.626980i
$217$		0			0
$218$	−1.21572	+	0.277479i	−1.21572	+	0.277479i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.974928	+	0.222521i	$0.0714286\pi$
$223$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.433884	+	0.900969i	$0.357143\pi$
$224$	1.12349	−	1.40881i	1.12349	−	1.40881i
$225$		0			0
$226$		0			0
$227$	−1.21572	−	0.277479i	−1.21572	−	0.277479i	−0.433884	−	0.900969i	$-0.642857\pi$
$227$	−1.21572	−	0.277479i	−1.21572	−	0.277479i	−0.781831	+	0.623490i	$0.785714\pi$
$228$		0			0
$229$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$229$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$230$		0			0
$231$		0			0
$232$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$239$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$240$		0			0
$241$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$241$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$242$	0.433884	−	0.900969i	0.433884	−	0.900969i
$243$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$244$	−2.00000			−2.00000
$245$		0			0
$246$	0.123490	+	0.541044i	0.123490	+	0.541044i
$247$		0			0
$248$		0			0
$249$	0.554958			0.554958
$250$		0			0
$251$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$251$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$252$	1.12978	+	0.900969i	1.12978	+	0.900969i
$253$		0			0
$254$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$255$		0			0
$256$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$257$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$257$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$258$	−0.240787	−	0.500000i	−0.240787	−	0.500000i
$259$		0			0
$260$		0			0
$261$	0.178448	−	0.781831i	0.178448	−	0.781831i
$262$		0			0
$263$	−1.75676	−	0.400969i	−1.75676	−	0.400969i	−0.781831	−	0.623490i	$-0.785714\pi$
$263$	−1.75676	−	0.400969i	−1.75676	−	0.400969i	−0.974928	+	0.222521i	$0.928571\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.781831	−	0.178448i	0.781831	−	0.178448i
$268$	0.867767	+	1.80194i	0.867767	+	1.80194i
$269$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$269$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$270$		0			0
$271$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$271$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.0440730	−	0.193096i	−0.0440730	−	0.193096i
$277$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$277$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$281$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$282$	0.626980	+	0.500000i	0.626980	+	0.500000i
$283$	−0.193096	−	0.400969i	−0.193096	−	0.400969i	0.781831	−	0.623490i	$-0.214286\pi$
$283$	−0.193096	−	0.400969i	−0.193096	−	0.400969i	−0.974928	+	0.222521i	$0.928571\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.974928	+	2.02446i	0.974928	+	2.02446i
$288$	−0.781831	−	0.178448i	−0.781831	−	0.178448i
$289$	−1.00000			−1.00000
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$293$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$294$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	1.40881	+	1.12349i	1.40881	+	1.12349i
$299$		0			0
$300$		0			0
$301$	−1.40097	−	1.75676i	−1.40097	−	1.75676i
$302$		0			0
$303$	0.154851	−	0.123490i	0.154851	−	0.123490i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	0.445042i		−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$307$		−	0.445042i		−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$308$		0			0
$309$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$310$		0			0
$311$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$311$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$312$		0			0
$313$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$313$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$317$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.0440730	+	0.193096i	−0.0440730	+	0.193096i
$322$	−0.347948	−	0.722521i	−0.347948	−	0.722521i
$323$		0			0
$324$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$325$		0			0
$326$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$327$	−0.433884	−	0.346011i	−0.433884	−	0.346011i
$328$	−0.974928	−	0.777479i	−0.974928	−	0.777479i
$329$	2.92543	+	1.40881i	2.92543	+	1.40881i
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−0.974928	+	0.777479i	−0.974928	+	0.777479i
$333$		0			0
$334$	0.277479	+	1.21572i	0.277479	+	1.21572i
$335$		0			0
$336$	0.801938			0.801938
$337$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$337$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$338$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−2.19064	−	0.500000i	−2.19064	−	0.500000i
$344$	1.12349	+	0.541044i	1.12349	+	0.541044i
$345$		0			0
$346$		0			0
$347$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$347$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$348$	−0.193096	−	0.400969i	−0.193096	−	0.400969i
$349$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$349$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$353$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$354$		0			0
$355$		0			0
$356$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$357$		0			0
$358$		0			0
$359$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$359$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$360$		0			0
$361$	0.623490	+	0.781831i	0.623490	+	0.781831i
$362$	−0.433884	+	0.0990311i	−0.433884	+	0.0990311i
$363$	0.433884	−	0.0990311i	0.433884	−	0.0990311i
$364$		0			0
$365$		0			0
$366$	−0.554958	−	0.695895i	−0.554958	−	0.695895i
$367$	−0.781831	+	1.62349i	−0.781831	+	1.62349i			1.00000i	$0.5\pi$
$367$	−0.781831	+	1.62349i	−0.781831	+	1.62349i	−0.781831	+	0.623490i	$0.785714\pi$
$368$	0.347948	+	0.277479i	0.347948	+	0.277479i
$369$	0.623490	−	0.781831i	0.623490	−	0.781831i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$373$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$374$		0			0
$375$		0			0
$376$	−1.80194			−1.80194
$377$		0			0
$378$			1.44504i			1.44504i
$379$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$379$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$380$		0			0
$381$	−0.722521	−	0.347948i	−0.722521	−	0.347948i
$382$		0			0
$383$	0.433884	−	0.0990311i	0.433884	−	0.0990311i		−	1.00000i	$-0.5\pi$
$383$	0.433884	−	0.0990311i	0.433884	−	0.0990311i	0.433884	+	0.900969i	$0.357143\pi$
$384$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$385$		0			0
$386$		0			0
$387$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$388$		0			0
$389$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$389$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$390$		0			0
$391$		0			0
$392$	2.19064	−	0.500000i	2.19064	−	0.500000i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$397$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$401$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$402$	−0.386193	+	0.801938i	−0.386193	+	0.801938i
$403$		0			0
$404$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$405$		0			0
$406$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$407$		0			0
$408$		0			0
$409$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$409$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−1.00000			$1.00000\pi$
$410$		0			0
$411$		0			0
$412$	1.21572	−	0.277479i	1.21572	−	0.277479i
$413$		0			0
$414$	−0.222521	+	0.279032i	−0.222521	+	0.279032i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$419$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$420$		0			0
$421$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$421$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$422$		0			0
$423$		−	1.44504i		−	1.44504i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−2.81762	−	2.24698i	−2.81762	−	2.24698i
$428$	−0.193096	−	0.400969i	−0.193096	−	0.400969i
$429$		0			0
$430$		0			0
$431$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$431$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$432$	−0.347948	−	0.722521i	−0.347948	−	0.722521i
$433$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$433$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$434$		0			0
$435$		0			0
$436$	1.24698			1.24698
$437$		0			0
$438$		0			0
$439$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$439$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$440$		0			0
$441$	0.400969	+	1.75676i	0.400969	+	1.75676i
$442$		0			0
$443$	−1.56366	−	1.24698i	−1.56366	−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$443$	−1.56366	−	1.24698i	−1.56366	−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$444$		0			0
$445$		0			0
$446$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$447$			0.801938i			0.801938i
$448$	−1.40881	+	1.12349i	−1.40881	+	1.12349i
$449$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$449$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.12349	+	0.541044i	1.12349	+	0.541044i
$455$		0			0
$456$		0			0
$457$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$457$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$458$	−1.21572	+	0.277479i	−1.21572	+	0.277479i
$459$		0			0
$460$		0			0
$461$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$461$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$462$		0			0
$463$		−	1.24698i		−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$463$		−	1.24698i		−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$464$	0.900969	+	0.433884i	0.900969	+	0.433884i
$465$		0			0
$466$		0			0
$467$	−0.541044	−	1.12349i	−0.541044	−	1.12349i	−0.974928	−	0.222521i	$-0.928571\pi$
$467$	−0.541044	−	1.12349i	−0.541044	−	1.12349i	0.433884	−	0.900969i	$-0.357143\pi$
$468$		0			0
$469$	−0.801938	+	3.51352i	−0.801938	+	3.51352i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$479$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$480$		0			0
$481$		0			0
$482$	0.347948	−	0.277479i	0.347948	−	0.277479i
$483$	0.154851	−	0.321552i	0.154851	−	0.321552i
$484$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$485$		0			0
$486$	0.900969	−	0.433884i	0.900969	−	0.433884i
$487$	−1.75676	+	0.400969i	−1.75676	+	0.400969i	−0.974928	−	0.222521i	$-0.928571\pi$
$487$	−1.75676	+	0.400969i	−1.75676	+	0.400969i	−0.781831	+	0.623490i	$0.785714\pi$
$488$	1.94986	+	0.445042i	1.94986	+	0.445042i
$489$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$490$		0			0
$491$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$491$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$492$		−	0.554958i		−	0.554958i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.541044	−	0.123490i	−0.541044	−	0.123490i
$499$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$499$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$500$		0			0
$501$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$502$		0			0
$503$	−0.541044	+	1.12349i	−0.541044	+	1.12349i	0.433884	+	0.900969i	$0.357143\pi$
$503$	−0.541044	+	1.12349i	−0.541044	+	1.12349i	−0.974928	+	0.222521i	$0.928571\pi$
$504$	−0.900969	−	1.12978i	−0.900969	−	1.12978i
$505$		0			0
$506$		0			0
$507$	−0.433884	+	0.0990311i	−0.433884	+	0.0990311i
$508$	1.75676	−	0.400969i	1.75676	−	0.400969i
$509$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	0.222521	−	0.974928i	$-0.428571\pi$
$509$	−0.777479	−	0.974928i	−0.777479	−	0.974928i	−1.00000			$\pi$
$510$		0			0
$511$		0			0
$512$	0.433884	−	0.900969i	0.433884	−	0.900969i
$513$		0			0
$514$		0			0
$515$		0			0
$516$	0.123490	+	0.541044i	0.123490	+	0.541044i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$521$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$522$	−0.347948	+	0.722521i	−0.347948	+	0.722521i
$523$		−	1.24698i		−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$523$		−	1.24698i		−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$524$		0			0
$525$		0			0
$526$	1.62349	+	0.781831i	1.62349	+	0.781831i
$527$		0			0
$528$		0			0
$529$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.801938			−0.801938
$535$		0			0
$536$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$537$		0			0
$538$	−0.347948	+	0.277479i	−0.347948	+	0.277479i
$539$		0			0
$540$		0			0
$541$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$541$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$542$		0			0
$543$	−0.154851	−	0.123490i	−0.154851	−	0.123490i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.541044	−	1.12349i	0.541044	−	1.12349i	−0.433884	−	0.900969i	$-0.642857\pi$
$547$	0.541044	−	1.12349i	0.541044	−	1.12349i	0.974928	−	0.222521i	$-0.0714286\pi$
$548$		0			0
$549$	−0.356896	+	1.56366i	−0.356896	+	1.56366i
$550$		0			0
$551$		0			0
$552$			0.198062i			0.198062i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$557$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.347948	−	0.277479i	0.347948	−	0.277479i
$563$			1.80194i			1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$563$			1.80194i			1.80194i	−0.433884	+	0.900969i	$0.642857\pi$
$564$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$565$		0			0
$566$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$567$	0.626980	−	0.500000i	0.626980	−	0.500000i
$568$		0			0
$569$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$569$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$570$		0			0
$571$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$571$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$572$		0			0
$573$		0			0
$574$	−0.500000	−	2.19064i	−0.500000	−	2.19064i
$575$		0			0
$576$	0.722521	+	0.347948i	0.722521	+	0.347948i
$577$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$577$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$578$	0.974928	+	0.222521i	0.974928	+	0.222521i
$579$		0			0
$580$		0			0
$581$	−2.24698			−2.24698
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.193096	+	0.400969i	0.193096	+	0.400969i	0.974928	−	0.222521i	$-0.0714286\pi$
$587$	0.193096	+	0.400969i	0.193096	+	0.400969i	−0.781831	+	0.623490i	$0.785714\pi$
$588$	0.781831	+	0.623490i	0.781831	+	0.623490i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$593$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$594$		0			0
$595$		0			0
$596$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$597$		0			0
$598$		0			0
$599$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$599$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$600$		0			0
$601$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$601$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$602$	0.974928	+	2.02446i	0.974928	+	2.02446i
$603$	1.56366	−	0.356896i	1.56366	−	0.356896i
$604$		0			0
$605$		0			0
$606$	−0.178448	+	0.0859360i	−0.178448	+	0.0859360i
$607$	0.433884	+	0.0990311i	0.433884	+	0.0990311i	0.433884	−	0.900969i	$-0.357143\pi$
$607$	0.433884	+	0.0990311i	0.433884	+	0.0990311i			1.00000i	$0.5\pi$
$608$		0			0
$609$	0.178448	−	0.781831i	0.178448	−	0.781831i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$613$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$614$	−0.0990311	+	0.433884i	−0.0990311	+	0.433884i
$615$		0			0
$616$		0			0
$617$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$617$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$618$	0.433884	+	0.346011i	0.433884	+	0.346011i
$619$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$619$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$620$		0			0
$621$	−0.356896			−0.356896
$622$		0			0
$623$	−3.16557	+	0.722521i	−3.16557	+	0.722521i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$631$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$641$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$642$	0.0859360	−	0.178448i	0.0859360	−	0.178448i
$643$	−0.433884	−	0.0990311i	−0.433884	−	0.0990311i		−	1.00000i	$-0.5\pi$
$643$	−0.433884	−	0.0990311i	−0.433884	−	0.0990311i	−0.433884	+	0.900969i	$0.642857\pi$
$644$	0.178448	+	0.781831i	0.178448	+	0.781831i
$645$		0			0
$646$		0			0
$647$	−1.40881	−	1.12349i	−1.40881	−	1.12349i	−0.974928	−	0.222521i	$-0.928571\pi$
$647$	−1.40881	−	1.12349i	−1.40881	−	1.12349i	−0.433884	−	0.900969i	$-0.642857\pi$
$648$	−0.193096	+	0.400969i	−0.193096	+	0.400969i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.21572	−	0.277479i	1.21572	−	0.277479i
$653$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$653$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$654$	0.346011	+	0.433884i	0.346011	+	0.433884i
$655$		0			0
$656$	0.777479	+	0.974928i	0.777479	+	0.974928i
$657$		0			0
$658$	−2.53859	−	2.02446i	−2.53859	−	2.02446i
$659$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$659$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$660$		0			0
$661$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$661$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$662$		0			0
$663$		0			0
$664$	1.12349	−	0.541044i	1.12349	−	0.541044i
$665$		0			0
$666$		0			0
$667$	0.347948	−	0.277479i	0.347948	−	0.277479i
$668$		−	1.24698i		−	1.24698i
$669$	0.178448	−	0.781831i	0.178448	−	0.781831i
$670$		0			0
$671$		0			0
$672$	−0.781831	−	0.178448i	−0.781831	−	0.178448i
$673$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$673$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$674$		0			0
$675$		0			0
$676$	0.623490	−	0.781831i	0.623490	−	0.781831i
$677$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$677$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.123490	+	0.541044i	0.123490	+	0.541044i
$682$		0			0
$683$	−1.40881	+	1.12349i	−1.40881	+	1.12349i	−0.433884	+	0.900969i	$0.642857\pi$
$683$	−1.40881	+	1.12349i	−1.40881	+	1.12349i	−0.974928	+	0.222521i	$0.928571\pi$
$684$		0			0
$685$		0			0
$686$	2.02446	+	0.974928i	2.02446	+	0.974928i
$687$	−0.433884	−	0.346011i	−0.433884	−	0.346011i
$688$	−0.974928	−	0.777479i	−0.974928	−	0.777479i
$689$		0			0
$690$		0			0
$691$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$691$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$692$		0			0
$693$		0			0
$694$	0.445042	−	1.94986i	0.445042	−	1.94986i
$695$		0			0
$696$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$697$		0			0
$698$	1.21572	+	0.277479i	1.21572	+	0.277479i
$699$		0			0
$700$		0			0
$701$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$701$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.626980	+	0.500000i	−0.626980	+	0.500000i
$708$		0			0
$709$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$709$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$710$		0			0
$711$		0			0
$712$	1.40881	−	1.12349i	1.40881	−	1.12349i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$719$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$720$		0			0
$721$	2.02446	+	0.974928i	2.02446	+	0.974928i
$722$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$723$	0.193096	+	0.0440730i	0.193096	+	0.0440730i
$724$	0.445042			0.445042
$725$		0			0
$726$	−0.445042			−0.445042
$727$	−1.21572	−	0.277479i	−1.21572	−	0.277479i	−0.433884	−	0.900969i	$-0.642857\pi$
$727$	−1.21572	−	0.277479i	−1.21572	−	0.277479i	−0.781831	+	0.623490i	$0.785714\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$	0.386193	+	0.801938i	0.386193	+	0.801938i
$733$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$733$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$734$	1.12349	−	1.40881i	1.12349	−	1.40881i
$735$		0			0
$736$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$737$		0			0
$738$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$739$		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
$743$	0.974928	−	0.777479i	0.974928	−	0.777479i		−	1.00000i	$-0.5\pi$
$743$	0.974928	−	0.777479i	0.974928	−	0.777479i	0.974928	+	0.222521i	$0.0714286\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.433884	+	0.900969i	0.433884	+	0.900969i
$748$		0			0
$749$	0.178448	−	0.781831i	0.178448	−	0.781831i
$750$		0			0
$751$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$751$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$752$	1.75676	+	0.400969i	1.75676	+	0.400969i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.321552	−	1.40881i	0.321552	−	1.40881i
$757$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$757$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$761$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$762$	0.626980	+	0.500000i	0.626980	+	0.500000i
$763$	1.75676	+	1.40097i	1.75676	+	1.40097i
$764$		0			0
$765$		0			0
$766$	−0.445042			−0.445042
$767$		0			0
$768$	0.433884	−	0.0990311i	0.433884	−	0.0990311i
$769$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$769$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$773$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$774$	0.623490	−	0.781831i	0.623490	−	0.781831i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.433884	−	0.0990311i	−0.433884	−	0.0990311i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.781831	+	0.178448i	−0.781831	+	0.178448i
$784$	−2.24698			−2.24698
$785$		0			0
$786$		0			0
$787$	0.867767	−	1.80194i	0.867767	−	1.80194i	0.433884	−	0.900969i	$-0.357143\pi$
$787$	0.867767	−	1.80194i	0.867767	−	1.80194i	0.433884	−	0.900969i	$-0.357143\pi$
$788$		0			0
$789$	0.178448	+	0.781831i	0.178448	+	0.781831i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$797$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	0.900969	+	1.12978i	0.900969	+	1.12978i
$802$	−0.781831	+	1.62349i	−0.781831	+	1.62349i
$803$		0			0
$804$	0.554958	−	0.695895i	0.554958	−	0.695895i
$805$		0			0
$806$		0			0
$807$	−0.193096	−	0.0440730i	−0.193096	−	0.0440730i
$808$	0.193096	−	0.400969i	0.193096	−	0.400969i
$809$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$809$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	0.781831	+	1.62349i	0.781831	+	1.62349i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.75676	−	0.400969i	1.75676	−	0.400969i
$819$		0			0
$820$		0			0
$821$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$821$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$822$		0			0
$823$	−1.40881	+	1.12349i	−1.40881	+	1.12349i	−0.433884	+	0.900969i	$0.642857\pi$
$823$	−1.40881	+	1.12349i	−1.40881	+	1.12349i	−0.974928	+	0.222521i	$0.928571\pi$
$824$	−1.24698			−1.24698
$825$		0			0
$826$		0			0
$827$	−1.75676	+	0.400969i	−1.75676	+	0.400969i	−0.974928	−	0.222521i	$-0.928571\pi$
$827$	−1.75676	+	0.400969i	−1.75676	+	0.400969i	−0.781831	+	0.623490i	$0.785714\pi$
$828$	0.279032	−	0.222521i	0.279032	−	0.222521i
$829$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$829$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$839$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$840$		0			0
$841$	0.623490	−	0.781831i	0.623490	−	0.781831i
$842$			1.24698i			1.24698i
$843$	0.193096	+	0.0440730i	0.193096	+	0.0440730i
$844$		0			0
$845$		0			0
$846$	−0.321552	+	1.40881i	−0.321552	+	1.40881i
$847$	−1.75676	+	0.400969i	−1.75676	+	0.400969i
$848$		0			0
$849$	−0.123490	+	0.154851i	−0.123490	+	0.154851i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$	2.24698	+	2.81762i	2.24698	+	2.81762i
$855$		0			0
$856$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$857$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$857$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$858$		0			0
$859$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$859$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$860$		0			0
$861$	0.623490	−	0.781831i	0.623490	−	0.781831i
$862$		0			0
$863$	0.541044	+	1.12349i	0.541044	+	1.12349i	0.974928	+	0.222521i	$0.0714286\pi$
$863$	0.541044	+	1.12349i	0.541044	+	1.12349i	−0.433884	+	0.900969i	$0.642857\pi$
$864$	0.178448	+	0.781831i	0.178448	+	0.781831i
$865$		0			0
$866$		0			0
$867$	0.193096	+	0.400969i	0.193096	+	0.400969i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1.21572	−	0.277479i	−1.21572	−	0.277479i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$877$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$881$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$882$		−	1.80194i		−	1.80194i
$883$	1.56366	−	1.24698i	1.56366	−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$883$	1.56366	−	1.24698i	1.56366	−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$884$		0			0
$885$		0			0
$886$	1.24698	+	1.56366i	1.24698	+	1.56366i
$887$		−	1.80194i		−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$887$		−	1.80194i		−	1.80194i	0.433884	−	0.900969i	$-0.357143\pi$
$888$		0			0
$889$	2.92543	+	1.40881i	2.92543	+	1.40881i
$890$		0			0
$891$		0			0
$892$	0.781831	+	1.62349i	0.781831	+	1.62349i
$893$		0			0
$894$	0.178448	−	0.781831i	0.178448	−	0.781831i
$895$		0			0
$896$	1.62349	−	0.781831i	1.62349	−	0.781831i
$897$		0			0
$898$			1.80194i			1.80194i
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.974928	+	0.777479i	0.974928	+	0.777479i	0.974928	−	0.222521i	$-0.0714286\pi$
$907$	0.974928	+	0.777479i	0.974928	+	0.777479i			1.00000i	$0.5\pi$
$908$	−0.974928	−	0.777479i	−0.974928	−	0.777479i
$909$	0.321552	+	0.154851i	0.321552	+	0.154851i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	1.24698			1.24698
$917$		0			0
$918$		0			0
$919$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$919$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$920$		0			0
$921$	−0.178448	+	0.0859360i	−0.178448	+	0.0859360i
$922$	1.21572	−	0.277479i	1.21572	−	0.277479i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$927$		−	1.00000i		−	1.00000i
$928$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$929$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$929$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.277479	+	1.21572i	0.277479	+	1.21572i
$935$		0			0
$936$		0			0
$937$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$937$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$938$	1.56366	−	3.24698i	1.56366	−	3.24698i
$939$		0			0
$940$		0			0
$941$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$941$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$942$		0			0
$943$	0.541044	−	0.123490i	0.541044	−	0.123490i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.193096	+	0.400969i	−0.193096	+	0.400969i	−0.974928	−	0.222521i	$-0.928571\pi$
$947$	−0.193096	+	0.400969i	−0.193096	+	0.400969i	0.781831	+	0.623490i	$0.214286\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$953$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$962$		0			0
$963$	−0.347948	+	0.0794168i	−0.347948	+	0.0794168i
$964$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$965$		0			0
$966$	−0.222521	+	0.279032i	−0.222521	+	0.279032i
$967$	0.541044	−	1.12349i	0.541044	−	1.12349i	−0.433884	−	0.900969i	$-0.642857\pi$
$967$	0.541044	−	1.12349i	0.541044	−	1.12349i	0.974928	−	0.222521i	$-0.0714286\pi$
$968$	0.781831	−	0.623490i	0.781831	−	0.623490i
$969$		0			0
$970$		0			0
$971$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$971$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$972$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$973$		0			0
$974$	1.80194			1.80194
$975$		0			0
$976$	−1.80194	−	0.867767i	−1.80194	−	0.867767i
$977$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$977$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$978$	0.433884	+	0.346011i	0.433884	+	0.346011i
$979$		0			0
$980$		0			0
$981$	0.222521	−	0.974928i	0.222521	−	0.974928i
$982$		0			0
$983$	0.867767	+	1.80194i	0.867767	+	1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$983$	0.867767	+	1.80194i	0.867767	+	1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$984$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$985$		0			0
$986$		0			0
$987$		−	1.44504i		−	1.44504i
$988$		0			0
$989$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$990$		0			0
$991$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$991$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.500000	+	0.240787i	0.500000	+	0.240787i
$997$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$997$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$998$		0			0
$999$		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	2900.1.bj.b.2751.1		12
4.3	odd	2	inner	2900.1.bj.b.2751.2		12
5.2	odd	4		580.1.v.b.199.1	yes	6
5.3	odd	4		580.1.v.a.199.1	✓	6
5.4	even	2	inner	2900.1.bj.b.2751.2		12
20.3	even	4		580.1.v.b.199.1	yes	6
20.7	even	4		580.1.v.a.199.1	✓	6
20.19	odd	2	CM	2900.1.bj.b.2751.1		12
29.7	even	7	inner	2900.1.bj.b.1051.2		12
116.7	odd	14	inner	2900.1.bj.b.1051.1		12
145.7	odd	28		580.1.v.b.239.1	yes	6
145.94	even	14	inner	2900.1.bj.b.1051.1		12
145.123	odd	28		580.1.v.a.239.1	yes	6
580.7	even	28		580.1.v.a.239.1	yes	6
580.123	even	28		580.1.v.b.239.1	yes	6
580.239	odd	14	inner	2900.1.bj.b.1051.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.1.v.a.199.1	✓	6	5.3	odd	4
580.1.v.a.199.1	✓	6	20.7	even	4
580.1.v.a.239.1	yes	6	145.123	odd	28
580.1.v.a.239.1	yes	6	580.7	even	28
580.1.v.b.199.1	yes	6	5.2	odd	4
580.1.v.b.199.1	yes	6	20.3	even	4
580.1.v.b.239.1	yes	6	145.7	odd	28
580.1.v.b.239.1	yes	6	580.123	even	28
2900.1.bj.b.1051.1		12	116.7	odd	14	inner
2900.1.bj.b.1051.1		12	145.94	even	14	inner
2900.1.bj.b.1051.2		12	29.7	even	7	inner
2900.1.bj.b.1051.2		12	580.239	odd	14	inner
2900.1.bj.b.2751.1		12	1.1	even	1	trivial
2900.1.bj.b.2751.1		12	20.19	odd	2	CM
2900.1.bj.b.2751.2		12	4.3	odd	2	inner
2900.1.bj.b.2751.2		12	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	2900.1.bj.b.2751.1

Level	$2900$
Weight	$1$
Character	2900.2751
Analytic conductor	$1.447$
Analytic rank	$0$
Dimension	$12$
Projective image	$D_{7}$
CM discriminant	-20
Inner twists	$8$