LMFDB - Embedded newform 583.1.n.a.494.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [583,1,Mod(43,583)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(583, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([13, 11]))

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

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

chi := DirichletCharacter("583.43");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 583 = 11 \cdot 53 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	583.n (of order $26$, degree $12$, 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:	$0.290954902365$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{26})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{26}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{26} - \cdots)$

Embedding invariants

Embedding label			494.1
Root			$0.354605 + 0.935016i$ of defining polynomial
Character	$\chi$	$=$	583.494
Dual form			583.1.n.a.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31658 - 1.48611i) q^{3} +(0.354605 + 0.935016i) q^{4} +(1.31658 + 0.159861i) q^{5} +(-0.354605 + 2.92043i) q^{9} +O(q^{10})$	\(q+(-1.31658 - 1.48611i) q^{3} +(0.354605 + 0.935016i) q^{4} +(1.31658 + 0.159861i) q^{5} +(-0.354605 + 2.92043i) q^{9} +(0.885456 + 0.464723i) q^{11} +(0.922670 - 1.75800i) q^{12} +(-1.49580 - 2.16704i) q^{15} +(-0.748511 + 0.663123i) q^{16} +(0.317391 + 1.28771i) q^{20} -0.929446i q^{23} +(0.736874 + 0.181623i) q^{25} +(3.17297 - 2.19015i) q^{27} +(-0.869047 - 1.65583i) q^{31} +(-0.475142 - 1.92773i) q^{33} +(-2.85640 + 0.704039i) q^{36} +(0.180446 - 0.159861i) q^{37} +(-0.120537 + 0.992709i) q^{44} +(-0.933728 + 3.78828i) q^{45} +(0.180446 + 1.48611i) q^{47} +(1.97094 + 0.239316i) q^{48} +(-0.354605 - 0.935016i) q^{49} +(-0.970942 + 0.239316i) q^{53} +(1.09148 + 0.753393i) q^{55} +(0.0854858 + 0.704039i) q^{59} +(1.49580 - 2.16704i) q^{60} +(-0.885456 - 0.464723i) q^{64} +(-1.53901 + 0.583668i) q^{67} +(-1.38126 + 1.22369i) q^{69} +(-0.317391 + 0.358261i) q^{71} +(-0.700239 - 1.33419i) q^{75} +(-1.09148 + 0.753393i) q^{80} +(-4.57585 - 1.12785i) q^{81} +(1.71945 - 0.423807i) q^{89} +(0.869047 - 0.329586i) q^{92} +(-1.31658 + 3.47152i) q^{93} +(0.213460 - 1.75800i) q^{97} +(-1.67118 + 2.42112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{4} - q^{9}+O(q^{10}) $ 12 * q + q^4 - q^9	$ 12 q + q^{4} - q^{9} - q^{11} - 13 q^{15} - q^{16} - q^{25} - 12 q^{36} + 2 q^{37} + q^{44} + 2 q^{47} + 13 q^{48} - q^{49} - q^{53} + 2 q^{59} + 13 q^{60} + q^{64} - 14 q^{81} + 2 q^{89} - 2 q^{97} - q^{99}+O(q^{100}) $ 12 * q + q^4 - q^9 - q^11 - 13 * q^15 - q^16 - q^25 - 12 * q^36 + 2 * q^37 + q^44 + 2 * q^47 + 13 * q^48 - q^49 - q^53 + 2 * q^59 + 13 * q^60 + q^64 - 14 * q^81 + 2 * q^89 - 2 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/583\mathbb{Z}\right)^\times$.

$n$	$266$	$320$
$\chi(n)$	$-1$	$e\left(\frac{5}{26}\right)$

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			0		−0.822984	−	0.568065i	$-0.807692\pi$
$2$		0			0		0.822984	+	0.568065i	$0.192308\pi$
$3$	−1.31658	−	1.48611i	−1.31658	−	1.48611i	−0.748511	−	0.663123i	$-0.769231\pi$
$3$	−1.31658	−	1.48611i	−1.31658	−	1.48611i	−0.568065	−	0.822984i	$-0.692308\pi$
$4$	0.354605	+	0.935016i	0.354605	+	0.935016i
$5$	1.31658	+	0.159861i	1.31658	+	0.159861i	0.748511	−	0.663123i	$-0.230769\pi$
$5$	1.31658	+	0.159861i	1.31658	+	0.159861i	0.568065	+	0.822984i	$0.307692\pi$
$6$		0			0
$7$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$7$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$8$		0			0
$9$	−0.354605	+	2.92043i	−0.354605	+	2.92043i
$10$		0			0
$11$	0.885456	+	0.464723i	0.885456	+	0.464723i
$11$	0.885456	+	0.464723i	0.885456	+	0.464723i
$12$	0.922670	−	1.75800i	0.922670	−	1.75800i
$13$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$13$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$14$		0			0
$15$	−1.49580	−	2.16704i	−1.49580	−	2.16704i
$16$	−0.748511	+	0.663123i	−0.748511	+	0.663123i
$17$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$17$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$18$		0			0
$19$		0			0		−0.935016	−	0.354605i	$-0.884615\pi$
$19$		0			0		0.935016	+	0.354605i	$0.115385\pi$
$20$	0.317391	+	1.28771i	0.317391	+	1.28771i
$21$		0			0
$22$		0			0
$23$		−	0.929446i		−	0.929446i	−0.885456	−	0.464723i	$-0.846154\pi$
$23$		−	0.929446i		−	0.929446i	0.885456	−	0.464723i	$-0.153846\pi$
$24$		0			0
$25$	0.736874	+	0.181623i	0.736874	+	0.181623i
$26$		0			0
$27$	3.17297	−	2.19015i	3.17297	−	2.19015i
$28$		0			0
$29$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$29$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$30$		0			0
$31$	−0.869047	−	1.65583i	−0.869047	−	1.65583i	−0.748511	−	0.663123i	$-0.769231\pi$
$31$	−0.869047	−	1.65583i	−0.869047	−	1.65583i	−0.120537	−	0.992709i	$-0.538462\pi$
$32$		0			0
$33$	−0.475142	−	1.92773i	−0.475142	−	1.92773i
$34$		0			0
$35$		0			0
$36$	−2.85640	+	0.704039i	−2.85640	+	0.704039i
$37$	0.180446	−	0.159861i	0.180446	−	0.159861i	−0.568065	−	0.822984i	$-0.692308\pi$
$37$	0.180446	−	0.159861i	0.180446	−	0.159861i	0.748511	+	0.663123i	$0.230769\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.464723	−	0.885456i	$-0.346154\pi$
$41$		0			0		−0.464723	+	0.885456i	$0.653846\pi$
$42$		0			0
$43$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$43$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$44$	−0.120537	+	0.992709i	−0.120537	+	0.992709i
$45$	−0.933728	+	3.78828i	−0.933728	+	3.78828i
$46$		0			0
$47$	0.180446	+	1.48611i	0.180446	+	1.48611i	0.748511	+	0.663123i	$0.230769\pi$
$47$	0.180446	+	1.48611i	0.180446	+	1.48611i	−0.568065	+	0.822984i	$0.692308\pi$
$48$	1.97094	+	0.239316i	1.97094	+	0.239316i
$49$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$53$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$54$		0			0
$55$	1.09148	+	0.753393i	1.09148	+	0.753393i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.0854858	+	0.704039i	0.0854858	+	0.704039i	0.970942	+	0.239316i	$0.0769231\pi$
$59$	0.0854858	+	0.704039i	0.0854858	+	0.704039i	−0.885456	+	0.464723i	$0.846154\pi$
$60$	1.49580	−	2.16704i	1.49580	−	2.16704i
$61$		0			0		0.239316	−	0.970942i	$-0.423077\pi$
$61$		0			0		−0.239316	+	0.970942i	$0.576923\pi$
$62$		0			0
$63$		0			0
$64$	−0.885456	−	0.464723i	−0.885456	−	0.464723i
$65$		0			0
$66$		0			0
$67$	−1.53901	+	0.583668i	−1.53901	+	0.583668i	−0.970942	−	0.239316i	$-0.923077\pi$
$67$	−1.53901	+	0.583668i	−1.53901	+	0.583668i	−0.568065	+	0.822984i	$0.692308\pi$
$68$		0			0
$69$	−1.38126	+	1.22369i	−1.38126	+	1.22369i
$70$		0			0
$71$	−0.317391	+	0.358261i	−0.317391	+	0.358261i	−0.885456	−	0.464723i	$-0.846154\pi$
$71$	−0.317391	+	0.358261i	−0.317391	+	0.358261i	0.568065	+	0.822984i	$0.307692\pi$
$72$		0			0
$73$		0			0		−0.239316	−	0.970942i	$-0.576923\pi$
$73$		0			0		0.239316	+	0.970942i	$0.423077\pi$
$74$		0			0
$75$	−0.700239	−	1.33419i	−0.700239	−	1.33419i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.822984	−	0.568065i	$-0.192308\pi$
$79$		0			0		−0.822984	+	0.568065i	$0.807692\pi$
$80$	−1.09148	+	0.753393i	−1.09148	+	0.753393i
$81$	−4.57585	−	1.12785i	−4.57585	−	1.12785i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.71945	−	0.423807i	1.71945	−	0.423807i	0.748511	−	0.663123i	$-0.230769\pi$
$89$	1.71945	−	0.423807i	1.71945	−	0.423807i	0.970942	+	0.239316i	$0.0769231\pi$
$90$		0			0
$91$		0			0
$92$	0.869047	−	0.329586i	0.869047	−	0.329586i
$93$	−1.31658	+	3.47152i	−1.31658	+	3.47152i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.213460	−	1.75800i	0.213460	−	1.75800i	−0.354605	−	0.935016i	$-0.615385\pi$
$97$	0.213460	−	1.75800i	0.213460	−	1.75800i	0.568065	−	0.822984i	$-0.307692\pi$
$98$		0			0
$99$	−1.67118	+	2.42112i	−1.67118	+	2.42112i
$100$	0.0914785	+	0.753393i	0.0914785	+	0.753393i
$101$		0			0		−0.992709	−	0.120537i	$-0.961538\pi$
$101$		0			0		0.992709	+	0.120537i	$0.0384615\pi$
$102$		0			0
$103$	−0.317391	−	0.358261i	−0.317391	−	0.358261i	0.568065	−	0.822984i	$-0.307692\pi$
$103$	−0.317391	−	0.358261i	−0.317391	−	0.358261i	−0.885456	+	0.464723i	$0.846154\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	3.17297	+	2.19015i	3.17297	+	2.19015i
$109$		0			0		−0.663123	−	0.748511i	$-0.730769\pi$
$109$		0			0		0.663123	+	0.748511i	$0.269231\pi$
$110$		0			0
$111$	−0.475142	−	0.0576926i	−0.475142	−	0.0576926i
$112$		0			0
$113$	−0.645395	+	0.935016i	−0.645395	+	0.935016i	0.354605	+	0.935016i	$0.384615\pi$
$113$	−0.645395	+	0.935016i	−0.645395	+	0.935016i	−1.00000			$\pi$
$114$		0			0
$115$	0.148582	−	1.22369i	0.148582	−	1.22369i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.568065	+	0.822984i	0.568065	+	0.822984i
$122$		0			0
$123$		0			0
$124$	1.24006	−	1.39974i	1.24006	−	1.39974i
$125$	−0.298946	−	0.113375i	−0.298946	−	0.113375i
$126$		0			0
$127$		0			0		0.992709	−	0.120537i	$-0.0384615\pi$
$127$		0			0		−0.992709	+	0.120537i	$0.961538\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$131$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$132$	1.63397	−	1.12785i	1.63397	−	1.12785i
$133$		0			0
$134$		0			0
$135$	4.52758	−	2.37626i	4.52758	−	2.37626i
$136$		0			0
$137$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$137$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$138$		0			0
$139$		0			0		−0.239316	−	0.970942i	$-0.576923\pi$
$139$		0			0		0.239316	+	0.970942i	$0.423077\pi$
$140$		0			0
$141$	1.97094	−	2.22473i	1.97094	−	2.22473i
$142$		0			0
$143$		0			0
$144$	−1.67118	−	2.42112i	−1.67118	−	2.42112i
$145$		0			0
$146$		0			0
$147$	−0.922670	+	1.75800i	−0.922670	+	1.75800i
$148$	0.213460	+	0.112032i	0.213460	+	0.112032i
$149$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$149$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$150$		0			0
$151$		0			0		0.239316	−	0.970942i	$-0.423077\pi$
$151$		0			0		−0.239316	+	0.970942i	$0.576923\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.879463	−	2.31895i	−0.879463	−	2.31895i
$156$		0			0
$157$	−0.393906	−	0.271894i	−0.393906	−	0.271894i	0.354605	−	0.935016i	$-0.384615\pi$
$157$	−0.393906	−	0.271894i	−0.393906	−	0.271894i	−0.748511	+	0.663123i	$0.769231\pi$
$158$		0			0
$159$	1.63397	+	1.12785i	1.63397	+	1.12785i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−0.251489	−	0.663123i	−0.251489	−	0.663123i	0.748511	−	0.663123i	$-0.230769\pi$
$163$	−0.251489	−	0.663123i	−0.251489	−	0.663123i	−1.00000			$\pi$
$164$		0			0
$165$	−0.317391	−	2.61395i	−0.317391	−	2.61395i
$166$		0			0
$167$		0			0		0.239316	−	0.970942i	$-0.423077\pi$
$167$		0			0		−0.239316	+	0.970942i	$0.576923\pi$
$168$		0			0
$169$	−0.748511	−	0.663123i	−0.748511	−	0.663123i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.935016	−	0.354605i	$-0.115385\pi$
$173$		0			0		−0.935016	+	0.354605i	$0.884615\pi$
$174$		0			0
$175$		0			0
$176$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$177$	0.933728	−	1.05396i	0.933728	−	1.05396i
$178$		0			0
$179$	0.114544	+	0.464723i	0.114544	+	0.464723i	1.00000			$0$
$179$	0.114544	+	0.464723i	0.114544	+	0.464723i	−0.885456	+	0.464723i	$0.846154\pi$
$180$	−3.87321	+	0.470293i	−3.87321	+	0.470293i
$181$	0.764919	+	1.45743i	0.764919	+	1.45743i	0.885456	+	0.464723i	$0.153846\pi$
$181$	0.764919	+	1.45743i	0.764919	+	1.45743i	−0.120537	+	0.992709i	$0.538462\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.263126	−	0.181623i	0.263126	−	0.181623i
$186$		0			0
$187$		0			0
$188$	−1.32555	+	0.695701i	−1.32555	+	0.695701i
$189$		0			0
$190$		0			0
$191$	0.922670	−	0.112032i	0.922670	−	0.112032i	0.354605	−	0.935016i	$-0.384615\pi$
$191$	0.922670	−	0.112032i	0.922670	−	0.112032i	0.568065	+	0.822984i	$0.307692\pi$
$192$	0.475142	+	1.92773i	0.475142	+	1.92773i
$193$		0			0		−0.935016	−	0.354605i	$-0.884615\pi$
$193$		0			0		0.935016	+	0.354605i	$0.115385\pi$
$194$		0			0
$195$		0			0
$196$	0.748511	−	0.663123i	0.748511	−	0.663123i
$197$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$197$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$198$		0			0
$199$	0.402877	−	1.06230i	0.402877	−	1.06230i	−0.568065	−	0.822984i	$-0.692308\pi$
$199$	0.402877	−	1.06230i	0.402877	−	1.06230i	0.970942	−	0.239316i	$-0.0769231\pi$
$200$		0			0
$201$	2.89361	+	1.51868i	2.89361	+	1.51868i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.71439	+	0.329586i	2.71439	+	0.329586i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$	−0.568065	−	0.822984i	−0.568065	−	0.822984i
$213$	0.950283			0.950283
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.317391	+	1.28771i	−0.317391	+	1.28771i
$221$		0			0
$222$		0			0
$223$	−1.32555	−	0.695701i	−1.32555	−	0.695701i	−0.354605	−	0.935016i	$-0.615385\pi$
$223$	−1.32555	−	0.695701i	−1.32555	−	0.695701i	−0.970942	+	0.239316i	$0.923077\pi$
$224$		0			0
$225$	−0.791717	+	2.08759i	−0.791717	+	2.08759i
$226$		0			0
$227$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$227$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$228$		0			0
$229$	−1.71945	+	0.423807i	−1.71945	+	0.423807i	−0.970942	−	0.239316i	$-0.923077\pi$
$229$	−1.71945	+	0.423807i	−1.71945	+	0.423807i	−0.748511	+	0.663123i	$0.769231\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.992709	−	0.120537i	$-0.0384615\pi$
$233$		0			0		−0.992709	+	0.120537i	$0.961538\pi$
$234$		0			0
$235$			1.98542i			1.98542i
$236$	−0.627974	+	0.329586i	−0.627974	+	0.329586i
$237$		0			0
$238$		0			0
$239$		0			0		0.822984	−	0.568065i	$-0.192308\pi$
$239$		0			0		−0.822984	+	0.568065i	$0.807692\pi$
$240$	2.55664	+	0.630154i	2.55664	+	0.630154i
$241$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$241$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$242$		0			0
$243$	2.55664	+	4.87126i	2.55664	+	4.87126i
$244$		0			0
$245$	−0.317391	−	1.28771i	−0.317391	−	1.28771i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.74851	+	0.663123i	−1.74851	+	0.663123i	−0.748511	+	0.663123i	$0.769231\pi$
$251$	−1.74851	+	0.663123i	−1.74851	+	0.663123i	−1.00000			$1.00000\pi$
$252$		0			0
$253$	0.431935	−	0.822984i	0.431935	−	0.822984i
$254$		0			0
$255$		0			0
$256$	0.120537	−	0.992709i	0.120537	−	0.992709i
$257$	−0.475142	+	1.92773i	−0.475142	+	1.92773i	−0.120537	+	0.992709i	$0.538462\pi$
$257$	−0.475142	+	1.92773i	−0.475142	+	1.92773i	−0.354605	+	0.935016i	$0.615385\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.822984	−	0.568065i	$-0.807692\pi$
$263$		0			0		0.822984	+	0.568065i	$0.192308\pi$
$264$		0			0
$265$	−1.31658	+	0.159861i	−1.31658	+	0.159861i
$266$		0			0
$267$	−2.89361	−	1.99732i	−2.89361	−	1.99732i
$268$	−1.09148	−	1.23202i	−1.09148	−	1.23202i
$269$	−0.688601	−	1.81569i	−0.688601	−	1.81569i	−0.568065	−	0.822984i	$-0.692308\pi$
$269$	−0.688601	−	1.81569i	−0.688601	−	1.81569i	−0.120537	−	0.992709i	$-0.538462\pi$
$270$		0			0
$271$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$271$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.568065	+	0.503261i	0.568065	+	0.503261i
$276$	−1.63397	−	0.857572i	−1.63397	−	0.857572i
$277$		0			0		0.464723	−	0.885456i	$-0.346154\pi$
$277$		0			0		−0.464723	+	0.885456i	$0.653846\pi$
$278$		0			0
$279$	5.14392	−	1.95083i	5.14392	−	1.95083i
$280$		0			0
$281$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$281$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$282$		0			0
$283$		0			0		0.663123	−	0.748511i	$-0.269231\pi$
$283$		0			0		−0.663123	+	0.748511i	$0.730769\pi$
$284$	−0.447528	−	0.169725i	−0.447528	−	0.169725i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.885456	−	0.464723i	0.885456	−	0.464723i
$290$		0			0
$291$	−2.89361	+	1.99732i	−2.89361	+	1.99732i
$292$		0			0
$293$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$293$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$294$		0			0
$295$			0.940586i			0.940586i
$296$		0			0
$297$	3.82734	−	0.464723i	3.82734	−	0.464723i
$298$		0			0
$299$		0			0
$300$	0.999184	−	1.12785i	0.999184	−	1.12785i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$307$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$308$		0			0
$309$	−0.114544	+	0.943355i	−0.114544	+	0.943355i
$310$		0			0
$311$	0.136945	−	0.198399i	0.136945	−	0.198399i	−0.748511	−	0.663123i	$-0.769231\pi$
$311$	0.136945	−	0.198399i	0.136945	−	0.198399i	0.885456	+	0.464723i	$0.153846\pi$
$312$		0			0
$313$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$313$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.94188			1.94188			0.970942	−	0.239316i	$-0.0769231\pi$
$317$	1.94188			1.94188			0.970942	+	0.239316i	$0.0769231\pi$
$318$		0			0
$319$		0			0
$320$	−1.09148	−	0.753393i	−1.09148	−	0.753393i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.568065	−	4.67843i	−0.568065	−	4.67843i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.530851	+	1.39974i	−0.530851	+	1.39974i	0.354605	+	0.935016i	$0.384615\pi$
$331$	−0.530851	+	1.39974i	−0.530851	+	1.39974i	−0.885456	+	0.464723i	$0.846154\pi$
$332$		0			0
$333$	0.402877	+	0.583668i	0.402877	+	0.583668i
$334$		0			0
$335$	−2.11952	+	0.522416i	−2.11952	+	0.522416i
$336$		0			0
$337$		0			0		−0.935016	−	0.354605i	$-0.884615\pi$
$337$		0			0		0.935016	+	0.354605i	$0.115385\pi$
$338$		0			0
$339$	2.23925	−	0.271894i	2.23925	−	0.271894i
$340$		0			0
$341$		−	1.87003i		−	1.87003i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.01415	+	1.39027i	−2.01415	+	1.39027i
$346$		0			0
$347$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$347$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$348$		0			0
$349$		0			0		−0.464723	−	0.885456i	$-0.653846\pi$
$349$		0			0		0.464723	+	0.885456i	$0.346154\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.24006	−	1.39974i	1.24006	−	1.39974i	0.354605	−	0.935016i	$-0.384615\pi$
$353$	1.24006	−	1.39974i	1.24006	−	1.39974i	0.885456	−	0.464723i	$-0.153846\pi$
$354$		0			0
$355$	−0.475142	+	0.420939i	−0.475142	+	0.420939i
$356$	1.00599	+	1.45743i	1.00599	+	1.45743i
$357$		0			0
$358$		0			0
$359$		0			0		0.464723	−	0.885456i	$-0.346154\pi$
$359$		0			0		−0.464723	+	0.885456i	$0.653846\pi$
$360$		0			0
$361$	0.748511	+	0.663123i	0.748511	+	0.663123i
$362$		0			0
$363$	0.475142	−	1.92773i	0.475142	−	1.92773i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.627974	+	1.65583i	0.627974	+	1.65583i	0.748511	+	0.663123i	$0.230769\pi$
$367$	0.627974	+	1.65583i	0.627974	+	1.65583i	−0.120537	+	0.992709i	$0.538462\pi$
$368$	0.616337	+	0.695701i	0.616337	+	0.695701i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−3.71280			−3.71280
$373$		0			0		−0.822984	−	0.568065i	$-0.807692\pi$
$373$		0			0		0.822984	+	0.568065i	$0.192308\pi$
$374$		0			0
$375$	0.225097	+	0.593532i	0.225097	+	0.593532i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.222431	+	0.902438i	−0.222431	+	0.902438i	0.748511	+	0.663123i	$0.230769\pi$
$379$	−0.222431	+	0.902438i	−0.222431	+	0.902438i	−0.970942	+	0.239316i	$0.923077\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.616337	−	1.17433i	0.616337	−	1.17433i	−0.354605	−	0.935016i	$-0.615385\pi$
$383$	0.616337	−	1.17433i	0.616337	−	1.17433i	0.970942	−	0.239316i	$-0.0769231\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	1.71945	−	0.423807i	1.71945	−	0.423807i
$389$	1.31658	−	1.48611i	1.31658	−	1.48611i	0.568065	−	0.822984i	$-0.307692\pi$
$389$	1.31658	−	1.48611i	1.31658	−	1.48611i	0.748511	−	0.663123i	$-0.230769\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−2.85640	−	0.704039i	−2.85640	−	0.704039i
$397$	−0.764919	+	0.527986i	−0.764919	+	0.527986i	−0.885456	−	0.464723i	$-0.846154\pi$
$397$	−0.764919	+	0.527986i	−0.764919	+	0.527986i	0.120537	+	0.992709i	$0.461538\pi$
$398$		0			0
$399$		0			0
$400$	−0.671996	+	0.352691i	−0.671996	+	0.352691i
$401$		−	0.478631i		−	0.478631i	−0.970942	−	0.239316i	$-0.923077\pi$
$401$		−	0.478631i		−	0.478631i	0.970942	−	0.239316i	$-0.0769231\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−5.84415	−	2.21640i	−5.84415	−	2.21640i
$406$		0			0
$407$	0.234068	−	0.0576926i	0.234068	−	0.0576926i
$408$		0			0
$409$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$409$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$410$		0			0
$411$		0			0
$412$	0.222431	−	0.423807i	0.222431	−	0.423807i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.922670	−	0.112032i	−0.922670	−	0.112032i	−0.354605	−	0.935016i	$-0.615385\pi$
$419$	−0.922670	−	0.112032i	−0.922670	−	0.112032i	−0.568065	+	0.822984i	$0.692308\pi$
$420$		0			0
$421$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$421$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$422$		0			0
$423$	−4.40406			−4.40406
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$431$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$432$	−0.922670	+	3.74342i	−0.922670	+	3.74342i
$433$	0.0854858	−	0.704039i	0.0854858	−	0.704039i	−0.885456	−	0.464723i	$-0.846154\pi$
$433$	0.0854858	−	0.704039i	0.0854858	−	0.704039i	0.970942	−	0.239316i	$-0.0769231\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$439$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$440$		0			0
$441$	2.85640	−	0.704039i	2.85640	−	0.704039i
$442$		0			0
$443$	1.53901	+	0.583668i	1.53901	+	0.583668i	0.970942	−	0.239316i	$-0.0769231\pi$
$443$	1.53901	+	0.583668i	1.53901	+	0.583668i	0.568065	+	0.822984i	$0.307692\pi$
$444$	−0.114544	−	0.464723i	−0.114544	−	0.464723i
$445$	2.33154	−	0.283100i	2.33154	−	0.283100i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.568065	−	0.822984i	$-0.307692\pi$
$449$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.120537	+	0.992709i	$0.461538\pi$
$450$		0			0
$451$		0			0
$452$	−1.10312	−	0.271894i	−1.10312	−	0.271894i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.239316	−	0.970942i	$-0.576923\pi$
$457$		0			0		0.239316	+	0.970942i	$0.423077\pi$
$458$		0			0
$459$		0			0
$460$	1.19685	−	0.294998i	1.19685	−	0.294998i
$461$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$461$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$462$		0			0
$463$	−1.53901	+	0.583668i	−1.53901	+	0.583668i	−0.970942	−	0.239316i	$-0.923077\pi$
$463$	−1.53901	+	0.583668i	−1.53901	+	0.583668i	−0.568065	+	0.822984i	$0.692308\pi$
$464$		0			0
$465$	−2.28833	+	4.36005i	−2.28833	+	4.36005i
$466$		0			0
$467$	1.32555	+	1.17433i	1.32555	+	1.17433i	0.970942	+	0.239316i	$0.0769231\pi$
$467$	1.32555	+	1.17433i	1.32555	+	1.17433i	0.354605	+	0.935016i	$0.384615\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.114544	+	0.943355i	0.114544	+	0.943355i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.354605	−	2.92043i	−0.354605	−	2.92043i
$478$		0			0
$479$		0			0		−0.822984	−	0.568065i	$-0.807692\pi$
$479$		0			0		0.822984	+	0.568065i	$0.192308\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.568065	+	0.822984i	−0.568065	+	0.822984i
$485$	0.562072	−	2.28042i	0.562072	−	2.28042i
$486$		0			0
$487$	−0.850405	−	0.753393i	−0.850405	−	0.753393i	0.120537	−	0.992709i	$-0.461538\pi$
$487$	−0.850405	−	0.753393i	−0.850405	−	0.753393i	−0.970942	+	0.239316i	$0.923077\pi$
$488$		0			0
$489$	−0.654366	+	1.24679i	−0.654366	+	1.24679i
$490$		0			0
$491$		0			0		0.935016	−	0.354605i	$-0.115385\pi$
$491$		0			0		−0.935016	+	0.354605i	$0.884615\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−2.58728	+	2.92043i	−2.58728	+	2.92043i
$496$	1.74851	+	0.663123i	1.74851	+	0.663123i
$497$		0			0
$498$		0			0
$499$	0.922670	+	1.75800i	0.922670	+	1.75800i	0.568065	+	0.822984i	$0.307692\pi$
$499$	0.922670	+	1.75800i	0.922670	+	1.75800i	0.354605	+	0.935016i	$0.384615\pi$
$500$		−	0.319722i		−	0.319722i
$501$		0			0
$502$		0			0
$503$		0			0		0.822984	−	0.568065i	$-0.192308\pi$
$503$		0			0		−0.822984	+	0.568065i	$0.807692\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			1.98542i			1.98542i
$508$		0			0
$509$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$509$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.360598	−	0.522416i	−0.360598	−	0.522416i
$516$		0			0
$517$	−0.530851	+	1.39974i	−0.530851	+	1.39974i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	0.568065	+	0.822984i	$0.307692\pi$
$521$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	−0.748511	+	0.663123i	$0.769231\pi$
$522$		0			0
$523$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$523$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.63397	+	1.12785i	1.63397	+	1.12785i
$529$	0.136129			0.136129
$530$		0			0
$531$	−2.08641			−2.08641
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.539822	−	0.782068i	0.539822	−	0.782068i
$538$		0			0
$539$	0.120537	−	0.992709i	0.120537	−	0.992709i
$540$	3.82734	+	3.39073i	3.82734	+	3.39073i
$541$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$541$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$542$		0			0
$543$	1.15883	−	3.05557i	1.15883	−	3.05557i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$547$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.616337	−	0.151913i	−0.616337	−	0.151913i
$556$		0			0
$557$		0			0		0.822984	−	0.568065i	$-0.192308\pi$
$557$		0			0		−0.822984	+	0.568065i	$0.807692\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.239316	−	0.970942i	$-0.576923\pi$
$563$		0			0		0.239316	+	0.970942i	$0.423077\pi$
$564$	2.77907	+	1.05396i	2.77907	+	1.05396i
$565$	−0.999184	+	1.12785i	−0.999184	+	1.12785i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.935016	−	0.354605i	$-0.115385\pi$
$569$		0			0		−0.935016	+	0.354605i	$0.884615\pi$
$570$		0			0
$571$		0			0		0.464723	−	0.885456i	$-0.346154\pi$
$571$		0			0		−0.464723	+	0.885456i	$0.653846\pi$
$572$		0			0
$573$	−1.38126	−	1.22369i	−1.38126	−	1.22369i
$574$		0			0
$575$	0.168809	−	0.684884i	0.168809	−	0.684884i
$576$	1.67118	−	2.42112i	1.67118	−	2.42112i
$577$	−0.136945	−	1.12785i	−0.136945	−	1.12785i	−0.885456	−	0.464723i	$-0.846154\pi$
$577$	−0.136945	−	1.12785i	−0.136945	−	1.12785i	0.748511	−	0.663123i	$-0.230769\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.970942	−	0.239316i	−0.970942	−	0.239316i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.251489	+	0.663123i	0.251489	+	0.663123i	1.00000			$0$
$587$	0.251489	+	0.663123i	0.251489	+	0.663123i	−0.748511	+	0.663123i	$0.769231\pi$
$588$	−1.97094	−	0.239316i	−1.97094	−	0.239316i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.0290582	+	0.239316i	−0.0290582	+	0.239316i
$593$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$593$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.10911	+	0.799879i	−2.10911	+	0.799879i
$598$		0			0
$599$	1.12054	−	0.992709i	1.12054	−	0.992709i	0.120537	−	0.992709i	$-0.461538\pi$
$599$	1.12054	−	0.992709i	1.12054	−	0.992709i	1.00000			$0$
$600$		0			0
$601$		0			0		0.663123	−	0.748511i	$-0.269231\pi$
$601$		0			0		−0.663123	+	0.748511i	$0.730769\pi$
$602$		0			0
$603$	−1.15883	−	4.70154i	−1.15883	−	4.70154i
$604$		0			0
$605$	0.616337	+	1.17433i	0.616337	+	1.17433i
$606$		0			0
$607$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$607$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0			−	1.00000i	$-0.5\pi$
$613$		0			0				1.00000i	$0.5\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$617$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$618$		0			0
$619$	1.45352	−	0.358261i	1.45352	−	0.358261i	0.568065	−	0.822984i	$-0.307692\pi$
$619$	1.45352	−	0.358261i	1.45352	−	0.358261i	0.885456	+	0.464723i	$0.153846\pi$
$620$	1.85640	−	1.64462i	1.85640	−	1.64462i
$621$	−2.03562	−	2.94911i	−2.03562	−	2.94911i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1.04746	−	0.549748i	−1.04746	−	0.549748i
$626$		0			0
$627$		0			0
$628$	0.114544	−	0.464723i	0.114544	−	0.464723i
$629$		0			0
$630$		0			0
$631$	1.85640	+	0.225408i	1.85640	+	0.225408i	0.970942	−	0.239316i	$-0.0769231\pi$
$631$	1.85640	+	0.225408i	1.85640	+	0.225408i	0.885456	+	0.464723i	$0.153846\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.475142	+	1.92773i	−0.475142	+	1.92773i
$637$		0			0
$638$		0			0
$639$	−0.933728	−	1.05396i	−0.933728	−	1.05396i
$640$		0			0
$641$	−1.31658	−	0.159861i	−1.31658	−	0.159861i	−0.568065	−	0.822984i	$-0.692308\pi$
$641$	−1.31658	−	0.159861i	−1.31658	−	0.159861i	−0.748511	+	0.663123i	$0.769231\pi$
$642$		0			0
$643$	1.10312	−	1.59814i	1.10312	−	1.59814i	0.354605	−	0.935016i	$-0.384615\pi$
$643$	1.10312	−	1.59814i	1.10312	−	1.59814i	0.748511	−	0.663123i	$-0.230769\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.00599	+	0.527986i	1.00599	+	0.527986i	0.885456	−	0.464723i	$-0.153846\pi$
$647$	1.00599	+	0.527986i	1.00599	+	0.527986i	0.120537	+	0.992709i	$0.461538\pi$
$648$		0			0
$649$	−0.251489	+	0.663123i	−0.251489	+	0.663123i
$650$		0			0
$651$		0			0
$652$	0.530851	−	0.470293i	0.530851	−	0.470293i
$653$	−1.10312	+	0.271894i	−1.10312	+	0.271894i	−0.748511	−	0.663123i	$-0.769231\pi$
$653$	−1.10312	+	0.271894i	−1.10312	+	0.271894i	−0.354605	+	0.935016i	$0.615385\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	2.33154	−	1.22369i	2.33154	−	1.22369i
$661$	−0.688601	−	0.169725i	−0.688601	−	0.169725i	−0.120537	−	0.992709i	$-0.538462\pi$
$661$	−0.688601	−	0.169725i	−0.688601	−	0.169725i	−0.568065	+	0.822984i	$0.692308\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	0.711297	+	2.88585i	0.711297	+	2.88585i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$673$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$674$		0			0
$675$	2.73586	−	1.03758i	2.73586	−	1.03758i
$676$	0.354605	−	0.935016i	0.354605	−	0.935016i
$677$		0			0		0.464723	−	0.885456i	$-0.346154\pi$
$677$		0			0		−0.464723	+	0.885456i	$0.653846\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.136945	+	1.12785i	0.136945	+	1.12785i	0.885456	+	0.464723i	$0.153846\pi$
$683$	0.136945	+	1.12785i	0.136945	+	1.12785i	−0.748511	+	0.663123i	$0.769231\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	2.89361	+	1.99732i	2.89361	+	1.99732i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.764919	−	0.527986i	−0.764919	−	0.527986i	0.120537	−	0.992709i	$-0.461538\pi$
$691$	−0.764919	−	0.527986i	−0.764919	−	0.527986i	−0.885456	+	0.464723i	$0.846154\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.464723	−	0.885456i	$-0.346154\pi$
$701$		0			0		−0.464723	+	0.885456i	$0.653846\pi$
$702$		0			0
$703$		0			0
$704$	−0.568065	−	0.822984i	−0.568065	−	0.822984i
$705$	2.95054	−	2.61395i	2.95054	−	2.61395i
$706$		0			0
$707$		0			0
$708$	1.31658	+	0.499311i	1.31658	+	0.499311i
$709$	0.393906	+	1.59814i	0.393906	+	1.59814i	0.748511	+	0.663123i	$0.230769\pi$
$709$	0.393906	+	1.59814i	0.393906	+	1.59814i	−0.354605	+	0.935016i	$0.615385\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.53901	+	0.807733i	−1.53901	+	0.807733i
$714$		0			0
$715$		0			0
$716$	−0.393906	+	0.271894i	−0.393906	+	0.271894i
$717$		0			0
$718$		0			0
$719$		−	1.98542i		−	1.98542i	−0.120537	−	0.992709i	$-0.538462\pi$
$719$		−	1.98542i		−	1.98542i	0.120537	−	0.992709i	$-0.461538\pi$
$720$	−1.81319	−	3.45475i	−1.81319	−	3.45475i
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−1.09148	+	1.23202i	−1.09148	+	1.23202i
$725$		0			0
$726$		0			0
$727$	1.13613	+	1.64597i	1.13613	+	1.64597i	0.568065	+	0.822984i	$0.307692\pi$
$727$	1.13613	+	1.64597i	1.13613	+	1.64597i	0.568065	+	0.822984i	$0.307692\pi$
$728$		0			0
$729$	2.20203	−	5.80628i	2.20203	−	5.80628i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$733$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$734$		0			0
$735$	−1.49580	+	2.16704i	−1.49580	+	2.16704i
$736$		0			0
$737$	−1.63397	−	0.198399i	−1.63397	−	0.198399i
$738$		0			0
$739$		0			0		−0.663123	−	0.748511i	$-0.730769\pi$
$739$		0			0		0.663123	+	0.748511i	$0.269231\pi$
$740$	0.263126	+	0.181623i	0.263126	+	0.181623i
$741$		0			0
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.136945	−	1.12785i	0.136945	−	1.12785i	−0.748511	−	0.663123i	$-0.769231\pi$
$751$	0.136945	−	1.12785i	0.136945	−	1.12785i	0.885456	−	0.464723i	$-0.153846\pi$
$752$	−1.12054	−	0.992709i	−1.12054	−	0.992709i
$753$	3.28752	+	1.72542i	3.28752	+	1.72542i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.00599	+	1.45743i	1.00599	+	1.45743i	0.885456	+	0.464723i	$0.153846\pi$
$757$	1.00599	+	1.45743i	1.00599	+	1.45743i	0.120537	+	0.992709i	$0.461538\pi$
$758$		0			0
$759$	−1.79172	+	0.441619i	−1.79172	+	0.441619i
$760$		0			0
$761$		0			0		−0.935016	−	0.354605i	$-0.884615\pi$
$761$		0			0		0.935016	+	0.354605i	$0.115385\pi$
$762$		0			0
$763$		0			0
$764$	0.431935	+	0.822984i	0.431935	+	0.822984i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.63397	+	1.12785i	−1.63397	+	1.12785i
$769$		0			0		0.822984	−	0.568065i	$-0.192308\pi$
$769$		0			0		−0.822984	+	0.568065i	$0.807692\pi$
$770$		0			0
$771$	3.49036	−	1.83188i	3.49036	−	1.83188i
$772$		0			0
$773$	−0.431935	−	0.822984i	−0.431935	−	0.822984i	0.568065	−	0.822984i	$-0.307692\pi$
$773$	−0.431935	−	0.822984i	−0.431935	−	0.822984i	−1.00000			$\pi$
$774$		0			0
$775$	−0.339641	−	1.37798i	−0.339641	−	1.37798i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−0.447528	+	0.169725i	−0.447528	+	0.169725i
$782$		0			0
$783$		0			0
$784$	0.885456	+	0.464723i	0.885456	+	0.464723i
$785$	−0.475142	−	0.420939i	−0.475142	−	0.420939i
$786$		0			0
$787$		0			0		0.239316	−	0.970942i	$-0.423077\pi$
$787$		0			0		−0.239316	+	0.970942i	$0.576923\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	1.97094	+	1.74610i	1.97094	+	1.74610i
$796$	1.13613			1.13613
$797$	1.35460	+	0.935016i	1.35460	+	0.935016i	1.00000			$0$
$797$	1.35460	+	0.935016i	1.35460	+	0.935016i	0.354605	+	0.935016i	$0.384615\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	0.627974	+	5.17183i	0.627974	+	5.17183i
$802$		0			0
$803$		0			0
$804$	−0.393906	+	3.24411i	−0.393906	+	3.24411i
$805$		0			0
$806$		0			0
$807$	−1.79172	+	3.41383i	−1.79172	+	3.41383i
$808$		0			0
$809$		0			0		0.935016	−	0.354605i	$-0.115385\pi$
$809$		0			0		−0.935016	+	0.354605i	$0.884615\pi$
$810$		0			0
$811$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$811$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.225097	−	0.913254i	−0.225097	−	0.913254i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.822984	−	0.568065i	$-0.192308\pi$
$821$		0			0		−0.822984	+	0.568065i	$0.807692\pi$
$822$		0			0
$823$	−0.688601	−	0.169725i	−0.688601	−	0.169725i	−0.120537	−	0.992709i	$-0.538462\pi$
$823$	−0.688601	−	0.169725i	−0.688601	−	0.169725i	−0.568065	+	0.822984i	$0.692308\pi$
$824$		0			0
$825$		−	1.50679i		−	1.50679i
$826$		0			0
$827$		0			0		0.992709	−	0.120537i	$-0.0384615\pi$
$827$		0			0		−0.992709	+	0.120537i	$0.961538\pi$
$828$	0.654366	+	2.65487i	0.654366	+	2.65487i
$829$	0.869047	+	0.329586i	0.869047	+	0.329586i	0.748511	−	0.663123i	$-0.230769\pi$
$829$	0.869047	+	0.329586i	0.869047	+	0.329586i	0.120537	+	0.992709i	$0.461538\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−6.38398	−	3.35057i	−6.38398	−	3.35057i
$838$		0			0
$839$	0.0290582	−	0.239316i	0.0290582	−	0.239316i	−0.970942	−	0.239316i	$-0.923077\pi$
$839$	0.0290582	−	0.239316i	0.0290582	−	0.239316i	1.00000			$0$
$840$		0			0
$841$	0.568065	−	0.822984i	0.568065	−	0.822984i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.879463	−	0.992709i	−0.879463	−	0.992709i
$846$		0			0
$847$		0			0
$848$	0.568065	−	0.822984i	0.568065	−	0.822984i
$849$		0			0
$850$		0			0
$851$	−0.148582	−	0.167715i	−0.148582	−	0.167715i
$852$	0.336975	+	0.888530i	0.336975	+	0.888530i
$853$		0			0		−0.992709	−	0.120537i	$-0.961538\pi$
$853$		0			0		0.992709	+	0.120537i	$0.0384615\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$857$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$858$		0			0
$859$	−1.71945	−	0.902438i	−1.71945	−	0.902438i	−0.970942	−	0.239316i	$-0.923077\pi$
$859$	−1.71945	−	0.902438i	−1.71945	−	0.902438i	−0.748511	−	0.663123i	$-0.769231\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.10312	+	1.59814i	1.10312	+	1.59814i	0.748511	+	0.663123i	$0.230769\pi$
$863$	1.10312	+	1.59814i	1.10312	+	1.59814i	0.354605	+	0.935016i	$0.384615\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.85640	−	0.704039i	−1.85640	−	0.704039i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	5.05843	+	1.24679i	5.05843	+	1.24679i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$877$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$878$		0			0
$879$		0			0
$880$	−1.31658	+	0.159861i	−1.31658	+	0.159861i
$881$	0.393906	+	1.59814i	0.393906	+	1.59814i	0.748511	+	0.663123i	$0.230769\pi$
$881$	0.393906	+	1.59814i	0.393906	+	1.59814i	−0.354605	+	0.935016i	$0.615385\pi$
$882$		0			0
$883$	−1.09148	+	1.23202i	−1.09148	+	1.23202i	−0.120537	+	0.992709i	$0.538462\pi$
$883$	−1.09148	+	1.23202i	−1.09148	+	1.23202i	−0.970942	+	0.239316i	$0.923077\pi$
$884$		0			0
$885$	1.39781	−	1.23835i	1.39781	−	1.23835i
$886$		0			0
$887$		0			0		0.935016	−	0.354605i	$-0.115385\pi$
$887$		0			0		−0.935016	+	0.354605i	$0.884615\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−3.52758	−	3.12516i	−3.52758	−	3.12516i
$892$	0.180446	−	1.48611i	0.180446	−	1.48611i
$893$		0			0
$894$		0			0
$895$	0.0765146	+	0.630154i	0.0765146	+	0.630154i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−2.23267			−2.23267
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.774087	+	2.04110i	0.774087	+	2.04110i
$906$		0			0
$907$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	−0.970942	−	0.239316i	$-0.923077\pi$
$907$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	0.885456	−	0.464723i	$-0.153846\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.32555	+	1.17433i	1.32555	+	1.17433i	0.970942	+	0.239316i	$0.0769231\pi$
$911$	1.32555	+	1.17433i	1.32555	+	1.17433i	0.354605	+	0.935016i	$0.384615\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.00599	−	1.45743i	−1.00599	−	1.45743i
$917$		0			0
$918$		0			0
$919$		0			0		0.663123	−	0.748511i	$-0.269231\pi$
$919$		0			0		−0.663123	+	0.748511i	$0.730769\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.162000	−	0.0850244i	0.162000	−	0.0850244i
$926$		0			0
$927$	1.15883	−	0.799879i	1.15883	−	0.799879i
$928$		0			0
$929$	0.234068	+	0.0576926i	0.234068	+	0.0576926i	0.354605	−	0.935016i	$-0.384615\pi$
$929$	0.234068	+	0.0576926i	0.234068	+	0.0576926i	−0.120537	+	0.992709i	$0.538462\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.475142	+	0.0576926i	−0.475142	+	0.0576926i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$937$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$938$		0			0
$939$		0			0
$940$	−1.85640	+	0.704039i	−1.85640	+	0.704039i
$941$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$941$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$942$		0			0
$943$		0			0
$944$	−0.530851	−	0.470293i	−0.530851	−	0.470293i
$945$		0			0
$946$		0			0
$947$	−0.850405	+	1.23202i	−0.850405	+	1.23202i	0.120537	+	0.992709i	$0.461538\pi$
$947$	−0.850405	+	1.23202i	−0.850405	+	1.23202i	−0.970942	+	0.239316i	$0.923077\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−2.55664	−	2.88585i	−2.55664	−	2.88585i
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$	1.23267			1.23267
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.317391	+	2.61395i	0.317391	+	2.61395i
$961$	−1.41847	+	2.05501i	−1.41847	+	2.05501i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$967$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.10312	−	0.271894i	1.10312	−	0.271894i	0.354605	−	0.935016i	$-0.384615\pi$
$971$	1.10312	−	0.271894i	1.10312	−	0.271894i	0.748511	+	0.663123i	$0.230769\pi$
$972$	−3.64811	+	4.11787i	−3.64811	+	4.11787i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	1.32625i		−	1.32625i	−0.748511	−	0.663123i	$-0.769231\pi$
$977$		−	1.32625i		−	1.32625i	0.748511	−	0.663123i	$-0.230769\pi$
$978$		0			0
$979$	1.71945	+	0.423807i	1.71945	+	0.423807i
$980$	1.09148	−	0.753393i	1.09148	−	0.753393i
$981$		0			0
$982$		0			0
$983$	−1.71945	+	0.902438i	−1.71945	+	0.902438i	−0.748511	+	0.663123i	$0.769231\pi$
$983$	−1.71945	+	0.902438i	−1.71945	+	0.902438i	−0.970942	+	0.239316i	$0.923077\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.12054	+	0.992709i	−1.12054	+	0.992709i	−0.120537	+	0.992709i	$0.538462\pi$
$991$	−1.12054	+	0.992709i	−1.12054	+	0.992709i	−1.00000			$\pi$
$992$		0			0
$993$	2.77907	−	1.05396i	2.77907	−	1.05396i
$994$		0			0
$995$	0.700239	−	1.33419i	0.700239	−	1.33419i
$996$		0			0
$997$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$997$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$998$		0			0
$999$	0.222431	−	0.902438i	0.222431	−	0.902438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	583.1.n.a.494.1	yes	12
11.10	odd	2	CM	583.1.n.a.494.1	yes	12
53.25	even	26	inner	583.1.n.a.131.1	✓	12
583.131	odd	26	inner	583.1.n.a.131.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
583.1.n.a.131.1	✓	12	53.25	even	26	inner
583.1.n.a.131.1	✓	12	583.131	odd	26	inner
583.1.n.a.494.1	yes	12	1.1	even	1	trivial
583.1.n.a.494.1	yes	12	11.10	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 583 = 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	583.n (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31658 - 1.48611i) q^{3} +(0.354605 + 0.935016i) q^{4} +(1.31658 + 0.159861i) q^{5} +(-0.354605 + 2.92043i) q^{9} +O(q^{10})\)	\(q+(-1.31658 - 1.48611i) q^{3} +(0.354605 + 0.935016i) q^{4} +(1.31658 + 0.159861i) q^{5} +(-0.354605 + 2.92043i) q^{9} +(0.885456 + 0.464723i) q^{11} +(0.922670 - 1.75800i) q^{12} +(-1.49580 - 2.16704i) q^{15} +(-0.748511 + 0.663123i) q^{16} +(0.317391 + 1.28771i) q^{20} -0.929446i q^{23} +(0.736874 + 0.181623i) q^{25} +(3.17297 - 2.19015i) q^{27} +(-0.869047 - 1.65583i) q^{31} +(-0.475142 - 1.92773i) q^{33} +(-2.85640 + 0.704039i) q^{36} +(0.180446 - 0.159861i) q^{37} +(-0.120537 + 0.992709i) q^{44} +(-0.933728 + 3.78828i) q^{45} +(0.180446 + 1.48611i) q^{47} +(1.97094 + 0.239316i) q^{48} +(-0.354605 - 0.935016i) q^{49} +(-0.970942 + 0.239316i) q^{53} +(1.09148 + 0.753393i) q^{55} +(0.0854858 + 0.704039i) q^{59} +(1.49580 - 2.16704i) q^{60} +(-0.885456 - 0.464723i) q^{64} +(-1.53901 + 0.583668i) q^{67} +(-1.38126 + 1.22369i) q^{69} +(-0.317391 + 0.358261i) q^{71} +(-0.700239 - 1.33419i) q^{75} +(-1.09148 + 0.753393i) q^{80} +(-4.57585 - 1.12785i) q^{81} +(1.71945 - 0.423807i) q^{89} +(0.869047 - 0.329586i) q^{92} +(-1.31658 + 3.47152i) q^{93} +(0.213460 - 1.75800i) q^{97} +(-1.67118 + 2.42112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{4} - q^{9}+O(q^{10}) \) 12 * q + q^4 - q^9	\( 12 q + q^{4} - q^{9} - q^{11} - 13 q^{15} - q^{16} - q^{25} - 12 q^{36} + 2 q^{37} + q^{44} + 2 q^{47} + 13 q^{48} - q^{49} - q^{53} + 2 q^{59} + 13 q^{60} + q^{64} - 14 q^{81} + 2 q^{89} - 2 q^{97} - q^{99}+O(q^{100}) \) 12 * q + q^4 - q^9 - q^11 - 13 * q^15 - q^16 - q^25 - 12 * q^36 + 2 * q^37 + q^44 + 2 * q^47 + 13 * q^48 - q^49 - q^53 + 2 * q^59 + 13 * q^60 + q^64 - 14 * q^81 + 2 * q^89 - 2 * q^97 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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