LMFDB - Embedded newform 529.1.d.a.359.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,1,Mod(28,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("529.28");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$529 = 23^{2}$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	529.d (of order $22$ , degree $10$ , not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.264005391683$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 23)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.23.1
Artin image:	$S_3\times C_{11}$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{33} - \cdots)$

Embedding invariants

Embedding label			359.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	529.359
Dual form			529.1.d.a.28.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-0.415415 - 0.909632i) q^{13} +(-0.415415 + 0.909632i) q^{16} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(-0.654861 - 0.755750i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.841254 - 0.540641i) q^{29} +(0.654861 - 0.755750i) q^{31} +(0.415415 - 0.909632i) q^{39} +(0.142315 + 0.989821i) q^{41} -1.00000 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(0.654861 - 0.755750i) q^{54} +(-0.959493 - 0.281733i) q^{58} +(0.830830 + 1.81926i) q^{59} +(0.415415 - 0.909632i) q^{62} +(-0.142315 - 0.989821i) q^{64} +(0.959493 - 0.281733i) q^{71} +(-0.841254 + 0.540641i) q^{73} +(-0.841254 - 0.540641i) q^{75} +(0.142315 - 0.989821i) q^{78} +(0.959493 + 0.281733i) q^{81} +(0.415415 + 0.909632i) q^{82} +(-0.142315 - 0.989821i) q^{87} +1.00000 q^{93} +(-0.959493 + 0.281733i) q^{94} +(-0.841254 - 0.540641i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q + q^{2} + q^{3} - q^{6} - q^{8} + q^{13} + q^{16} - 10 q^{24} - q^{25} - q^{26} - q^{27} + q^{29} + q^{31} - q^{39} + q^{41} - 10 q^{47} - q^{48} - q^{49} + q^{50} + q^{54} - q^{58}+ \cdots + q^{98}+O(q^{100})$ 10 * q + q^2 + q^3 - q^6 - q^8 + q^13 + q^16 - 10 * q^24 - q^25 - q^26 - q^27 + q^29 + q^31 - q^39 + q^41 - 10 * q^47 - q^48 - q^49 + q^50 + q^54 - q^58 - 2 * q^59 - q^62 - q^64 + q^71 + q^73 + q^75 + q^78 + q^81 - q^82 - q^87 + 10 * q^93 - q^94 + q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$ .

$n$	$5$
$\chi(n)$	$e\left(\frac{21}{22}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.235759	−	0.971812i	$-0.424242\pi$
$2$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.723734	+	0.690079i	$0.242424\pi$
$3$	0.654861	+	0.755750i	0.654861	+	0.755750i	0.981929	−	0.189251i	$-0.0606061\pi$
$3$	0.654861	+	0.755750i	0.654861	+	0.755750i	−0.327068	+	0.945001i	$0.606061\pi$
$4$		0			0
$5$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$5$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$6$	0.841254	+	0.540641i	0.841254	+	0.540641i
$7$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$7$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$8$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$9$		0			0
$10$		0			0
$11$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$11$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$12$		0			0
$13$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	−0.995472	−	0.0950560i	$-0.969697\pi$
$13$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	0.580057	−	0.814576i	$-0.303030\pi$
$14$		0			0
$15$		0			0
$16$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$17$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$17$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$18$		0			0
$19$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$19$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0
$23$		0			0
$24$	−1.00000			−1.00000
$25$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$26$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$27$	0.841254	−	0.540641i	0.841254	−	0.540641i
$28$		0			0
$29$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	0.0475819	−	0.998867i	$-0.484848\pi$
$29$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	−0.888835	+	0.458227i	$0.848485\pi$
$30$		0			0
$31$	0.654861	−	0.755750i	0.654861	−	0.755750i	−0.327068	−	0.945001i	$-0.606061\pi$
$31$	0.654861	−	0.755750i	0.654861	−	0.755750i	0.981929	+	0.189251i	$0.0606061\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$37$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$38$		0			0
$39$	0.415415	−	0.909632i	0.415415	−	0.909632i
$40$		0			0
$41$	0.142315	+	0.989821i	0.142315	+	0.989821i	0.928368	+	0.371662i	$0.121212\pi$
$41$	0.142315	+	0.989821i	0.142315	+	0.989821i	−0.786053	+	0.618159i	$0.787879\pi$
$42$		0			0
$43$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$43$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$47$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$48$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$49$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$50$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$51$		0			0
$52$		0			0
$53$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$53$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$54$	0.654861	−	0.755750i	0.654861	−	0.755750i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$59$	0.830830	+	1.81926i	0.830830	+	1.81926i	0.415415	+	0.909632i	$0.363636\pi$
$59$	0.830830	+	1.81926i	0.830830	+	1.81926i	0.415415	+	0.909632i	$0.363636\pi$
$60$		0			0
$61$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$61$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$62$	0.415415	−	0.909632i	0.415415	−	0.909632i
$63$		0			0
$64$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$65$		0			0
$66$		0			0
$67$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$67$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.235759	−	0.971812i	$-0.424242\pi$
$71$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.723734	+	0.690079i	$0.242424\pi$
$72$		0			0
$73$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	−0.888835	−	0.458227i	$-0.848485\pi$
$73$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	0.0475819	+	0.998867i	$0.484848\pi$
$74$		0			0
$75$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$76$		0			0
$77$		0			0
$78$	0.142315	−	0.989821i	0.142315	−	0.989821i
$79$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$79$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$80$		0			0
$81$	0.959493	+	0.281733i	0.959493	+	0.281733i
$82$	0.415415	+	0.909632i	0.415415	+	0.909632i
$83$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$83$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$88$		0			0
$89$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$89$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.00000			1.00000
$94$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$95$		0			0
$96$		0			0
$97$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$97$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$98$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$99$		0			0
$100$		0			0
$101$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$101$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$102$		0			0
$103$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$103$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$104$	0.959493	+	0.281733i	0.959493	+	0.281733i
$105$		0			0
$106$		0			0
$107$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$107$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$108$		0			0
$109$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$109$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$113$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.30972	+	1.51150i	1.30972	+	1.51150i
$119$		0			0
$120$		0			0
$121$	0.841254	+	0.540641i	0.841254	+	0.540641i
$122$		0			0
$123$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.723734	−	0.690079i	$-0.242424\pi$
$127$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.235759	+	0.971812i	$0.424242\pi$
$128$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$129$		0			0
$130$		0			0
$131$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	0.580057	+	0.814576i	$0.303030\pi$
$131$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	−0.995472	+	0.0950560i	$0.969697\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$139$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$140$		0			0
$141$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$142$	0.841254	−	0.540641i	0.841254	−	0.540641i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$147$	0.142315	−	0.989821i	0.142315	−	0.989821i
$148$		0			0
$149$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$149$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$150$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$151$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	−0.995472	−	0.0950560i	$-0.969697\pi$
$151$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	0.580057	−	0.814576i	$-0.303030\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$157$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	1.00000			1.00000
$163$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.235759	−	0.971812i	$-0.424242\pi$
$163$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.723734	+	0.690079i	$0.242424\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$167$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$173$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$174$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$175$		0			0
$176$		0			0
$177$	−0.830830	+	1.81926i	−0.830830	+	1.81926i
$178$		0			0
$179$	0.142315	+	0.989821i	0.142315	+	0.989821i	0.928368	+	0.371662i	$0.121212\pi$
$179$	0.142315	+	0.989821i	0.142315	+	0.989821i	−0.786053	+	0.618159i	$0.787879\pi$
$180$		0			0
$181$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$181$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	0.959493	−	0.281733i	0.959493	−	0.281733i
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$191$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$192$	0.654861	−	0.755750i	0.654861	−	0.755750i
$193$	0.142315	−	0.989821i	0.142315	−	0.989821i	−0.786053	−	0.618159i	$-0.787879\pi$
$193$	0.142315	−	0.989821i	0.142315	−	0.989821i	0.928368	−	0.371662i	$-0.121212\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	−0.995472	−	0.0950560i	$-0.969697\pi$
$197$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	0.580057	−	0.814576i	$-0.303030\pi$
$198$		0			0
$199$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$199$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$200$	0.415415	−	0.909632i	0.415415	−	0.909632i
$201$		0			0
$202$	0.284630	+	1.97964i	0.284630	+	1.97964i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	1.00000			1.00000
$209$		0			0
$210$		0			0
$211$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$211$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$212$		0			0
$213$	0.841254	+	0.540641i	0.841254	+	0.540641i
$214$		0			0
$215$		0			0
$216$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$217$		0			0
$218$		0			0
$219$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.830830	−	1.81926i	0.830830	−	1.81926i	0.415415	−	0.909632i	$-0.363636\pi$
$223$	0.830830	−	1.81926i	0.830830	−	1.81926i	0.415415	−	0.909632i	$-0.363636\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$227$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$	0.959493	−	0.281733i	0.959493	−	0.281733i
$233$	0.654861	+	0.755750i	0.654861	+	0.755750i	0.981929	−	0.189251i	$-0.0606061\pi$
$233$	0.654861	+	0.755750i	0.654861	+	0.755750i	−0.327068	+	0.945001i	$0.606061\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.142315	−	0.989821i	0.142315	−	0.989821i	−0.786053	−	0.618159i	$-0.787879\pi$
$239$	0.142315	−	0.989821i	0.142315	−	0.989821i	0.928368	−	0.371662i	$-0.121212\pi$
$240$		0			0
$241$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$241$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$242$	0.959493	+	0.281733i	0.959493	+	0.281733i
$243$		0			0
$244$		0			0
$245$		0			0
$246$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$247$		0			0
$248$	0.142315	+	0.989821i	0.142315	+	0.989821i
$249$		0			0
$250$		0			0
$251$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$251$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$252$		0			0
$253$		0			0
$254$	1.00000			1.00000
$255$		0			0
$256$		0			0
$257$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	−0.888835	−	0.458227i	$-0.848485\pi$
$257$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	0.0475819	+	0.998867i	$0.484848\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$263$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$263$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	0.580057	+	0.814576i	$0.303030\pi$
$269$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	−0.995472	+	0.0950560i	$0.969697\pi$
$270$		0			0
$271$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$271$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$277$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$278$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$279$		0			0
$280$		0			0
$281$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$281$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$282$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$283$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$283$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.415415	+	0.909632i	0.415415	+	0.909632i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$293$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$294$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$303$	−1.68251	+	1.08128i	−1.68251	+	1.08128i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$307$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.723734	−	0.690079i	$-0.242424\pi$
$311$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.235759	+	0.971812i	$0.424242\pi$
$312$	0.415415	+	0.909632i	0.415415	+	0.909632i
$313$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$313$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$317$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	0.654861	+	0.755750i	0.654861	+	0.755750i
$326$	0.841254	−	0.540641i	0.841254	−	0.540641i
$327$		0			0
$328$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$329$		0			0
$330$		0			0
$331$	0.142315	−	0.989821i	0.142315	−	0.989821i	−0.786053	−	0.618159i	$-0.787879\pi$
$331$	0.142315	−	0.989821i	0.142315	−	0.989821i	0.928368	−	0.371662i	$-0.121212\pi$
$332$		0			0
$333$		0			0
$334$	1.91899	+	0.563465i	1.91899	+	0.563465i
$335$		0			0
$336$		0			0
$337$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$337$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−2.00000			−2.00000
$347$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$347$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$348$		0			0
$349$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	−0.888835	−	0.458227i	$-0.848485\pi$
$349$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	0.0475819	+	0.998867i	$0.484848\pi$
$350$		0			0
$351$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$352$		0			0
$353$	0.654861	−	0.755750i	0.654861	−	0.755750i	−0.327068	−	0.945001i	$-0.606061\pi$
$353$	0.654861	−	0.755750i	0.654861	−	0.755750i	0.981929	+	0.189251i	$0.0606061\pi$
$354$	−0.284630	+	1.97964i	−0.284630	+	1.97964i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.415415	+	0.909632i	0.415415	+	0.909632i
$359$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$359$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$360$		0			0
$361$	0.415415	−	0.909632i	0.415415	−	0.909632i
$362$		0			0
$363$	0.142315	+	0.989821i	0.142315	+	0.989821i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$373$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$374$		0			0
$375$		0			0
$376$	0.654861	−	0.755750i	0.654861	−	0.755750i
$377$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$378$		0			0
$379$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$379$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$380$		0			0
$381$	0.415415	+	0.909632i	0.415415	+	0.909632i
$382$		0			0
$383$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$383$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$384$	0.415415	−	0.909632i	0.415415	−	0.909632i
$385$		0			0
$386$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$387$		0			0
$388$		0			0
$389$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$389$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$390$		0			0
$391$		0			0
$392$	1.00000			1.00000
$393$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$394$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$395$		0			0
$396$		0			0
$397$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	0.0475819	−	0.998867i	$-0.484848\pi$
$397$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	−0.888835	+	0.458227i	$0.848485\pi$
$398$		0			0
$399$		0			0
$400$	0.142315	−	0.989821i	0.142315	−	0.989821i
$401$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$401$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$402$		0			0
$403$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.142315	+	0.989821i	0.142315	+	0.989821i	0.928368	+	0.371662i	$0.121212\pi$
$409$	0.142315	+	0.989821i	0.142315	+	0.989821i	−0.786053	+	0.618159i	$0.787879\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$418$		0			0
$419$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$419$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$420$		0			0
$421$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$421$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$422$	1.30972	−	1.51150i	1.30972	−	1.51150i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	0.959493	+	0.281733i	0.959493	+	0.281733i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$431$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$432$	0.142315	+	0.989821i	0.142315	+	0.989821i
$433$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$433$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−1.00000			−1.00000
$439$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.235759	−	0.971812i	$-0.424242\pi$
$439$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.723734	+	0.690079i	$0.242424\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	0.0475819	−	0.998867i	$-0.484848\pi$
$443$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	−0.888835	+	0.458227i	$0.848485\pi$
$444$		0			0
$445$		0			0
$446$	0.284630	−	1.97964i	0.284630	−	1.97964i
$447$		0			0
$448$		0			0
$449$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$449$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	0.415415	−	0.909632i	0.415415	−	0.909632i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$457$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$461$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$	−1.30972	−	1.51150i	−1.30972	−	1.51150i	−0.654861	−	0.755750i	$-0.727273\pi$
$463$	−1.30972	−	1.51150i	−1.30972	−	1.51150i	−0.654861	−	0.755750i	$-0.727273\pi$
$464$	0.841254	−	0.540641i	0.841254	−	0.540641i
$465$		0			0
$466$	0.841254	+	0.540641i	0.841254	+	0.540641i
$467$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$467$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.91899	−	0.563465i	−1.91899	−	0.563465i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$479$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$479$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	−0.888835	−	0.458227i	$-0.848485\pi$
$487$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	0.0475819	+	0.998867i	$0.484848\pi$
$488$		0			0
$489$	0.841254	+	0.540641i	0.841254	+	0.540641i
$490$		0			0
$491$	0.654861	−	0.755750i	0.654861	−	0.755750i	−0.327068	−	0.945001i	$-0.606061\pi$
$491$	0.654861	−	0.755750i	0.654861	−	0.755750i	0.981929	+	0.189251i	$0.0606061\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.415415	+	0.909632i	0.415415	+	0.909632i
$497$		0			0
$498$		0			0
$499$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	0.580057	+	0.814576i	$0.303030\pi$
$499$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	−0.995472	+	0.0950560i	$0.969697\pi$
$500$		0			0
$501$	0.284630	+	1.97964i	0.284630	+	1.97964i
$502$		0			0
$503$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$503$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.654861	+	0.755750i	0.654861	+	0.755750i	0.981929	−	0.189251i	$-0.0606061\pi$
$509$	0.654861	+	0.755750i	0.654861	+	0.755750i	−0.327068	+	0.945001i	$0.606061\pi$
$510$		0			0
$511$		0			0
$512$	0.841254	+	0.540641i	0.841254	+	0.540641i
$513$		0			0
$514$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.830830	−	1.81926i	−0.830830	−	1.81926i
$520$		0			0
$521$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$521$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$522$		0			0
$523$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$523$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.841254	−	0.540641i	0.841254	−	0.540641i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$538$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$539$		0			0
$540$		0			0
$541$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.723734	−	0.690079i	$-0.242424\pi$
$541$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.235759	+	0.971812i	$0.424242\pi$
$542$	−0.830830	−	1.81926i	−0.830830	−	1.81926i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.142315	+	0.989821i	0.142315	+	0.989821i	0.928368	+	0.371662i	$0.121212\pi$
$547$	0.142315	+	0.989821i	0.142315	+	0.989821i	−0.786053	+	0.618159i	$0.787879\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$555$		0			0
$556$		0			0
$557$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$557$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$563$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$569$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$569$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$570$		0			0
$571$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$571$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.235759	−	0.971812i	$-0.424242\pi$
$577$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.723734	+	0.690079i	$0.242424\pi$
$578$	0.654861	+	0.755750i	0.654861	+	0.755750i
$579$	0.841254	−	0.540641i	0.841254	−	0.540641i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.142315	−	0.989821i	0.142315	−	0.989821i
$585$		0			0
$586$		0			0
$587$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.723734	−	0.690079i	$-0.242424\pi$
$587$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.235759	+	0.971812i	$0.424242\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	0.415415	−	0.909632i	0.415415	−	0.909632i
$592$		0			0
$593$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$593$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.00000			2.00000			1.00000			$0$
$599$	2.00000			2.00000			1.00000			$0$
$600$	0.959493	−	0.281733i	0.959493	−	0.281733i
$601$	0.654861	+	0.755750i	0.654861	+	0.755750i	0.981929	−	0.189251i	$-0.0606061\pi$
$601$	0.654861	+	0.755750i	0.654861	+	0.755750i	−0.327068	+	0.945001i	$0.606061\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−1.30972	+	1.51150i	−1.30972	+	1.51150i
$607$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$607$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.415415	+	0.909632i	0.415415	+	0.909632i
$612$		0			0
$613$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$613$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$614$	−0.830830	+	1.81926i	−0.830830	+	1.81926i
$615$		0			0
$616$		0			0
$617$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$617$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$618$		0			0
$619$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$619$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$620$		0			0
$621$		0			0
$622$	1.00000			1.00000
$623$		0			0
$624$	0.654861	+	0.755750i	0.654861	+	0.755750i
$625$	0.841254	−	0.540641i	0.841254	−	0.540641i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$631$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$632$		0			0
$633$	1.91899	+	0.563465i	1.91899	+	0.563465i
$634$	−0.830830	−	1.81926i	−0.830830	−	1.81926i
$635$		0			0
$636$		0			0
$637$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$641$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$642$		0			0
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.654861	+	0.755750i	0.654861	+	0.755750i	0.981929	−	0.189251i	$-0.0606061\pi$
$647$	0.654861	+	0.755750i	0.654861	+	0.755750i	−0.327068	+	0.945001i	$0.606061\pi$
$648$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$649$		0			0
$650$	0.841254	+	0.540641i	0.841254	+	0.540641i
$651$		0			0
$652$		0			0
$653$	0.142315	−	0.989821i	0.142315	−	0.989821i	−0.786053	−	0.618159i	$-0.787879\pi$
$653$	0.142315	−	0.989821i	0.142315	−	0.989821i	0.928368	−	0.371662i	$-0.121212\pi$
$654$		0			0
$655$		0			0
$656$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$657$		0			0
$658$		0			0
$659$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$659$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$660$		0			0
$661$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$661$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$662$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	1.91899	−	0.563465i	1.91899	−	0.563465i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	0.0475819	−	0.998867i	$-0.484848\pi$
$673$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	−0.888835	+	0.458227i	$0.848485\pi$
$674$		0			0
$675$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$676$		0			0
$677$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$677$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	0.580057	+	0.814576i	$0.303030\pi$
$683$	−0.415415	+	0.909632i	−0.415415	+	0.909632i	−0.995472	+	0.0950560i	$0.969697\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	2.00000			2.00000			1.00000			$0$
$691$	2.00000			2.00000			1.00000			$0$
$692$		0			0
$693$		0			0
$694$	−1.68251	+	1.08128i	−1.68251	+	1.08128i
$695$		0			0
$696$	0.841254	+	0.540641i	0.841254	+	0.540641i
$697$		0			0
$698$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$699$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$700$		0			0
$701$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$701$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$702$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.415415	−	0.909632i	0.415415	−	0.909632i
$707$		0			0
$708$		0			0
$709$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$709$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.841254	−	0.540641i	0.841254	−	0.540641i
$718$		0			0
$719$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$719$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$720$		0			0
$721$		0			0
$722$	0.142315	−	0.989821i	0.142315	−	0.989821i
$723$		0			0
$724$		0			0
$725$	0.959493	+	0.281733i	0.959493	+	0.281733i
$726$	0.415415	+	0.909632i	0.415415	+	0.909632i
$727$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$727$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.415415	−	0.909632i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$733$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.654861	+	0.755750i	0.654861	+	0.755750i	0.981929	−	0.189251i	$-0.0606061\pi$
$739$	0.654861	+	0.755750i	0.654861	+	0.755750i	−0.327068	+	0.945001i	$0.606061\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$743$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$744$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$751$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$752$	0.415415	−	0.909632i	0.415415	−	0.909632i
$753$		0			0
$754$	0.142315	+	0.989821i	0.142315	+	0.989821i
$755$		0			0
$756$		0			0
$757$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$757$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.235759	−	0.971812i	$-0.424242\pi$
$761$	0.959493	−	0.281733i	0.959493	−	0.281733i	0.723734	+	0.690079i	$0.242424\pi$
$762$	0.654861	+	0.755750i	0.654861	+	0.755750i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.30972	−	1.51150i	1.30972	−	1.51150i
$768$		0			0
$769$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$769$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$770$		0			0
$771$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$772$		0			0
$773$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$773$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$774$		0			0
$775$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.00000			−1.00000
$784$	0.959493	−	0.281733i	0.959493	−	0.281733i
$785$		0			0
$786$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$787$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$787$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$795$		0			0
$796$		0			0
$797$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$797$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−1.00000			−1.00000
$807$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$808$	−1.30972	−	1.51150i	−1.30972	−	1.51150i
$809$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$809$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$810$		0			0
$811$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	0.0475819	−	0.998867i	$-0.484848\pi$
$811$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	−0.888835	+	0.458227i	$0.848485\pi$
$812$		0			0
$813$	1.30972	−	1.51150i	1.30972	−	1.51150i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.415415	+	0.909632i	0.415415	+	0.909632i
$819$		0			0
$820$		0			0
$821$	0.830830	−	1.81926i	0.830830	−	1.81926i	0.415415	−	0.909632i	$-0.363636\pi$
$821$	0.830830	−	1.81926i	0.830830	−	1.81926i	0.415415	−	0.909632i	$-0.363636\pi$
$822$		0			0
$823$	0.142315	+	0.989821i	0.142315	+	0.989821i	0.928368	+	0.371662i	$0.121212\pi$
$823$	0.142315	+	0.989821i	0.142315	+	0.989821i	−0.786053	+	0.618159i	$0.787879\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$	2.00000			2.00000			1.00000			$0$
$829$	2.00000			2.00000			1.00000			$0$
$830$		0			0
$831$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$832$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$833$		0			0
$834$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$835$		0			0
$836$		0			0
$837$	0.142315	−	0.989821i	0.142315	−	0.989821i
$838$		0			0
$839$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$839$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$840$		0			0
$841$		0			0
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$853$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	0.0475819	−	0.998867i	$-0.484848\pi$
$857$	−0.841254	−	0.540641i	−0.841254	−	0.540641i	−0.888835	+	0.458227i	$0.848485\pi$
$858$		0			0
$859$	0.654861	−	0.755750i	0.654861	−	0.755750i	−0.327068	−	0.945001i	$-0.606061\pi$
$859$	0.654861	−	0.755750i	0.654861	−	0.755750i	0.981929	+	0.189251i	$0.0606061\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.723734	−	0.690079i	$-0.242424\pi$
$863$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.235759	+	0.971812i	$0.424242\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.30972	−	1.51150i	−1.30972	−	1.51150i	−0.654861	−	0.755750i	$-0.727273\pi$
$877$	−1.30972	−	1.51150i	−1.30972	−	1.51150i	−0.654861	−	0.755750i	$-0.727273\pi$
$878$	0.841254	−	0.540641i	0.841254	−	0.540641i
$879$		0			0
$880$		0			0
$881$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$881$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$882$		0			0
$883$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$883$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$884$		0			0
$885$		0			0
$886$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$887$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	−0.995472	−	0.0950560i	$-0.969697\pi$
$887$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	0.580057	−	0.814576i	$-0.303030\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−2.00000			−2.00000
$899$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.142315	−	0.989821i	0.142315	−	0.989821i
$907$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$907$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$911$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	−2.00000			−2.00000
$922$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$923$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$924$		0			0
$925$		0			0
$926$	−1.68251	−	1.08128i	−1.68251	−	1.08128i
$927$		0			0
$928$		0			0
$929$	0.142315	−	0.989821i	0.142315	−	0.989821i	−0.786053	−	0.618159i	$-0.787879\pi$
$929$	0.142315	−	0.989821i	0.142315	−	0.989821i	0.928368	−	0.371662i	$-0.121212\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	0.415415	+	0.909632i	0.415415	+	0.909632i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$937$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$941$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$942$		0			0
$943$		0			0
$944$	−2.00000			−2.00000
$945$		0			0
$946$		0			0
$947$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	−0.888835	−	0.458227i	$-0.848485\pi$
$947$	−0.841254	+	0.540641i	−0.841254	+	0.540641i	0.0475819	+	0.998867i	$0.484848\pi$
$948$		0			0
$949$	0.841254	+	0.540641i	0.841254	+	0.540641i
$950$		0			0
$951$	1.30972	−	1.51150i	1.30972	−	1.51150i
$952$		0			0
$953$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$953$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$967$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$968$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$969$		0			0
$970$		0			0
$971$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$971$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$972$		0			0
$973$		0			0
$974$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$975$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$976$		0			0
$977$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$977$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$978$	0.959493	+	0.281733i	0.959493	+	0.281733i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	0.415415	−	0.909632i	0.415415	−	0.909632i
$983$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$983$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$984$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$991$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$992$		0			0
$993$	0.841254	−	0.540641i	0.841254	−	0.540641i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$997$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$998$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$999$		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	529.1.d.a.359.1		10
23.2	even	11	inner	529.1.d.a.263.1		10
23.3	even	11	inner	529.1.d.a.195.1		10
23.4	even	11	inner	529.1.d.a.63.1		10
23.5	odd	22	inner	529.1.d.a.28.1		10
23.6	even	11	inner	529.1.d.a.274.1		10
23.7	odd	22	inner	529.1.d.a.42.1		10
23.8	even	11		23.1.b.a.22.1	✓	1
23.9	even	11	inner	529.1.d.a.352.1		10
23.10	odd	22	inner	529.1.d.a.411.1		10
23.11	odd	22	inner	529.1.d.a.130.1		10
23.12	even	11	inner	529.1.d.a.130.1		10
23.13	even	11	inner	529.1.d.a.411.1		10
23.14	odd	22	inner	529.1.d.a.352.1		10
23.15	odd	22		23.1.b.a.22.1	✓	1
23.16	even	11	inner	529.1.d.a.42.1		10
23.17	odd	22	inner	529.1.d.a.274.1		10
23.18	even	11	inner	529.1.d.a.28.1		10
23.19	odd	22	inner	529.1.d.a.63.1		10
23.20	odd	22	inner	529.1.d.a.195.1		10
23.21	odd	22	inner	529.1.d.a.263.1		10
23.22	odd	2	CM	529.1.d.a.359.1		10
69.8	odd	22		207.1.d.a.91.1		1
69.38	even	22		207.1.d.a.91.1		1
92.15	even	22		368.1.f.a.321.1		1
92.31	odd	22		368.1.f.a.321.1		1
115.8	odd	44		575.1.c.a.574.2		2
115.38	even	44		575.1.c.a.574.2		2
115.54	even	22		575.1.d.a.551.1		1
115.77	odd	44		575.1.c.a.574.1		2
115.84	odd	22		575.1.d.a.551.1		1
115.107	even	44		575.1.c.a.574.1		2
161.31	odd	66		1127.1.f.a.275.1		2
161.38	even	66		1127.1.f.a.275.1		2
161.54	odd	66		1127.1.f.a.459.1		2
161.61	even	66		1127.1.f.a.459.1		2
161.100	even	33		1127.1.f.b.459.1		2
161.107	odd	66		1127.1.f.b.459.1		2
161.123	even	33		1127.1.f.b.275.1		2
161.130	odd	66		1127.1.f.b.275.1		2
161.146	odd	22		1127.1.d.b.344.1		1
161.153	even	22		1127.1.d.b.344.1		1
184.61	odd	22		1472.1.f.b.321.1		1
184.77	even	22		1472.1.f.b.321.1		1
184.107	even	22		1472.1.f.a.321.1		1
184.123	odd	22		1472.1.f.a.321.1		1
207.31	even	33		1863.1.f.b.298.1		2
207.38	even	66		1863.1.f.a.919.1		2
207.61	odd	66		1863.1.f.b.919.1		2
207.77	odd	66		1863.1.f.a.298.1		2
207.130	odd	66		1863.1.f.b.298.1		2
207.146	odd	66		1863.1.f.a.919.1		2
207.169	even	33		1863.1.f.b.919.1		2
207.176	even	66		1863.1.f.a.298.1		2
253.8	odd	110		2783.1.f.a.735.1		4
253.15	odd	110		2783.1.f.c.390.1		4
253.31	even	55		2783.1.f.c.2138.1		4
253.38	odd	110		2783.1.f.c.850.1		4
253.54	odd	22		2783.1.d.b.1816.1		1
253.61	even	110		2783.1.f.a.850.1		4
253.84	even	110		2783.1.f.a.390.1		4
253.107	even	110		2783.1.f.a.735.1		4
253.123	odd	110		2783.1.f.a.2138.1		4
253.130	odd	110		2783.1.f.c.2138.1		4
253.146	even	55		2783.1.f.c.735.1		4
253.153	even	22		2783.1.d.b.1816.1		1
253.169	even	55		2783.1.f.c.390.1		4
253.192	even	55		2783.1.f.c.850.1		4
253.215	odd	110		2783.1.f.a.850.1		4
253.222	even	110		2783.1.f.a.2138.1		4
253.238	odd	110		2783.1.f.a.390.1		4
253.245	odd	110		2783.1.f.c.735.1		4
276.107	odd	22		3312.1.c.a.2161.1		1
276.215	even	22		3312.1.c.a.2161.1		1
299.8	odd	44		3887.1.c.a.3886.1		2
299.15	even	132		3887.1.j.e.2851.1		4
299.31	odd	44		3887.1.c.a.3886.2		2
299.38	odd	22		3887.1.d.b.2874.1		1
299.54	odd	132		3887.1.j.e.2851.1		4
299.61	odd	66		3887.1.h.c.3357.1		2
299.77	even	22		3887.1.d.b.2874.1		1
299.84	even	132		3887.1.j.e.3403.2		4
299.100	even	33		3887.1.h.c.3357.1		2
299.107	odd	66		3887.1.h.c.22.1		2
299.123	odd	132		3887.1.j.e.3403.2		4
299.146	even	33		3887.1.h.c.22.1		2
299.153	odd	66		3887.1.h.a.22.1		2
299.176	even	132		3887.1.j.e.3403.1		4
299.192	even	66		3887.1.h.a.22.1		2
299.199	odd	66		3887.1.h.a.3357.1		2
299.215	odd	132		3887.1.j.e.3403.1		4
299.238	even	66		3887.1.h.a.3357.1		2
299.245	even	132		3887.1.j.e.2851.2		4
299.268	even	44		3887.1.c.a.3886.1		2
299.284	odd	132		3887.1.j.e.2851.2		4
299.291	even	44		3887.1.c.a.3886.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.1.b.a.22.1	✓	1	23.8	even	11
23.1.b.a.22.1	✓	1	23.15	odd	22
207.1.d.a.91.1		1	69.8	odd	22
207.1.d.a.91.1		1	69.38	even	22
368.1.f.a.321.1		1	92.15	even	22
368.1.f.a.321.1		1	92.31	odd	22
529.1.d.a.28.1		10	23.5	odd	22	inner
529.1.d.a.28.1		10	23.18	even	11	inner
529.1.d.a.42.1		10	23.7	odd	22	inner
529.1.d.a.42.1		10	23.16	even	11	inner
529.1.d.a.63.1		10	23.4	even	11	inner
529.1.d.a.63.1		10	23.19	odd	22	inner
529.1.d.a.130.1		10	23.11	odd	22	inner
529.1.d.a.130.1		10	23.12	even	11	inner
529.1.d.a.195.1		10	23.3	even	11	inner
529.1.d.a.195.1		10	23.20	odd	22	inner
529.1.d.a.263.1		10	23.2	even	11	inner
529.1.d.a.263.1		10	23.21	odd	22	inner
529.1.d.a.274.1		10	23.6	even	11	inner
529.1.d.a.274.1		10	23.17	odd	22	inner
529.1.d.a.352.1		10	23.9	even	11	inner
529.1.d.a.352.1		10	23.14	odd	22	inner
529.1.d.a.359.1		10	1.1	even	1	trivial
529.1.d.a.359.1		10	23.22	odd	2	CM
529.1.d.a.411.1		10	23.10	odd	22	inner
529.1.d.a.411.1		10	23.13	even	11	inner
575.1.c.a.574.1		2	115.77	odd	44
575.1.c.a.574.1		2	115.107	even	44
575.1.c.a.574.2		2	115.8	odd	44
575.1.c.a.574.2		2	115.38	even	44
575.1.d.a.551.1		1	115.54	even	22
575.1.d.a.551.1		1	115.84	odd	22
1127.1.d.b.344.1		1	161.146	odd	22
1127.1.d.b.344.1		1	161.153	even	22
1127.1.f.a.275.1		2	161.31	odd	66
1127.1.f.a.275.1		2	161.38	even	66
1127.1.f.a.459.1		2	161.54	odd	66
1127.1.f.a.459.1		2	161.61	even	66
1127.1.f.b.275.1		2	161.123	even	33
1127.1.f.b.275.1		2	161.130	odd	66
1127.1.f.b.459.1		2	161.100	even	33
1127.1.f.b.459.1		2	161.107	odd	66
1472.1.f.a.321.1		1	184.107	even	22
1472.1.f.a.321.1		1	184.123	odd	22
1472.1.f.b.321.1		1	184.61	odd	22
1472.1.f.b.321.1		1	184.77	even	22
1863.1.f.a.298.1		2	207.77	odd	66
1863.1.f.a.298.1		2	207.176	even	66
1863.1.f.a.919.1		2	207.38	even	66
1863.1.f.a.919.1		2	207.146	odd	66
1863.1.f.b.298.1		2	207.31	even	33
1863.1.f.b.298.1		2	207.130	odd	66
1863.1.f.b.919.1		2	207.61	odd	66
1863.1.f.b.919.1		2	207.169	even	33
2783.1.d.b.1816.1		1	253.54	odd	22
2783.1.d.b.1816.1		1	253.153	even	22
2783.1.f.a.390.1		4	253.84	even	110
2783.1.f.a.390.1		4	253.238	odd	110
2783.1.f.a.735.1		4	253.8	odd	110
2783.1.f.a.735.1		4	253.107	even	110
2783.1.f.a.850.1		4	253.61	even	110
2783.1.f.a.850.1		4	253.215	odd	110
2783.1.f.a.2138.1		4	253.123	odd	110
2783.1.f.a.2138.1		4	253.222	even	110
2783.1.f.c.390.1		4	253.15	odd	110
2783.1.f.c.390.1		4	253.169	even	55
2783.1.f.c.735.1		4	253.146	even	55
2783.1.f.c.735.1		4	253.245	odd	110
2783.1.f.c.850.1		4	253.38	odd	110
2783.1.f.c.850.1		4	253.192	even	55
2783.1.f.c.2138.1		4	253.31	even	55
2783.1.f.c.2138.1		4	253.130	odd	110
3312.1.c.a.2161.1		1	276.107	odd	22
3312.1.c.a.2161.1		1	276.215	even	22
3887.1.c.a.3886.1		2	299.8	odd	44
3887.1.c.a.3886.1		2	299.268	even	44
3887.1.c.a.3886.2		2	299.31	odd	44
3887.1.c.a.3886.2		2	299.291	even	44
3887.1.d.b.2874.1		1	299.38	odd	22
3887.1.d.b.2874.1		1	299.77	even	22
3887.1.h.a.22.1		2	299.153	odd	66
3887.1.h.a.22.1		2	299.192	even	66
3887.1.h.a.3357.1		2	299.199	odd	66
3887.1.h.a.3357.1		2	299.238	even	66
3887.1.h.c.22.1		2	299.107	odd	66
3887.1.h.c.22.1		2	299.146	even	33
3887.1.h.c.3357.1		2	299.61	odd	66
3887.1.h.c.3357.1		2	299.100	even	33
3887.1.j.e.2851.1		4	299.15	even	132
3887.1.j.e.2851.1		4	299.54	odd	132
3887.1.j.e.2851.2		4	299.245	even	132
3887.1.j.e.2851.2		4	299.284	odd	132
3887.1.j.e.3403.1		4	299.176	even	132
3887.1.j.e.3403.1		4	299.215	odd	132
3887.1.j.e.3403.2		4	299.84	even	132
3887.1.j.e.3403.2		4	299.123	odd	132

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	529.1.d.a.359.1

Level	$529$
Weight	$1$
Character	529.359
Analytic conductor	$0.264$
Analytic rank	$0$
Dimension	$10$
Projective image	$D_{3}$
CM discriminant	-23
Inner twists	$20$