LMFDB - Embedded newform 1133.1.s.a.648.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1133,1,Mod(76,1133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1133, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([17, 22]))

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

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

chi := DirichletCharacter("1133.76");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1133 = 11 \cdot 103 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1133.s (of order $34$, degree $16$, 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:	$0.565440659313$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\Q(\zeta_{34})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + \cdots + 1 $ x^16 - x^15 + x^14 - x^13 + 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:	$D_{17}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{17} - \cdots)$

Embedding invariants

Embedding label			648.1
Root			$0.273663 - 0.961826i$ of defining polynomial
Character	$\chi$	$=$	1133.648
Dual form			1133.1.s.a.285.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58561 - 0.614268i) q^{3} +(0.0922684 + 0.995734i) q^{4} +(1.67148 - 1.03494i) q^{5} +(1.39782 + 1.27428i) q^{9} +O(q^{10})$	\(q+(-1.58561 - 0.614268i) q^{3} +(0.0922684 + 0.995734i) q^{4} +(1.67148 - 1.03494i) q^{5} +(1.39782 + 1.27428i) q^{9} +(0.739009 + 0.673696i) q^{11} +(0.465346 - 1.63552i) q^{12} +(-3.28604 + 0.614268i) q^{15} +(-0.982973 + 0.183750i) q^{16} +(1.18475 + 1.56886i) q^{20} +(-1.25664 + 1.14558i) q^{23} +(1.27702 - 2.56459i) q^{25} +(-0.675694 - 1.35698i) q^{27} +(1.67148 - 0.312454i) q^{31} +(-0.757949 - 1.52217i) q^{33} +(-1.13987 + 1.50943i) q^{36} +(0.149783 - 0.526432i) q^{37} +(-0.602635 + 0.798017i) q^{44} +(3.65523 + 0.683280i) q^{45} +0.891477 q^{47} +(1.67148 + 0.312454i) q^{48} +(-0.273663 + 0.961826i) q^{49} +(0.172075 - 0.0666624i) q^{53} +(1.93247 + 0.361242i) q^{55} +(0.329838 - 0.436776i) q^{59} +(-0.914845 - 3.21535i) q^{60} +(-0.273663 - 0.961826i) q^{64} +(0.726337 - 0.961826i) q^{67} +(2.69622 - 1.04452i) q^{69} +(-1.58561 - 0.981767i) q^{71} +(-3.60019 + 3.28201i) q^{75} +(-1.45285 + 1.32445i) q^{80} +(0.0633152 + 0.683280i) q^{81} +(-0.181395 + 1.95756i) q^{89} +(-1.25664 - 1.14558i) q^{92} +(-2.84224 - 0.531307i) q^{93} +(-0.876298 - 1.75984i) q^{97} +(0.174523 + 1.88341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^9	$ 16 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9} - q^{11} - 2 q^{12} - 4 q^{15} - q^{16} - 2 q^{20} - 2 q^{23} - 3 q^{25} - 4 q^{27} - 2 q^{31} - 2 q^{33} - 3 q^{36} + 15 q^{37} - q^{44} + 11 q^{45} - 2 q^{47} - 2 q^{48} - q^{49} - 2 q^{53} + 15 q^{55} - 2 q^{59} - 4 q^{60} - q^{64} + 15 q^{67} - 4 q^{69} - 2 q^{71} - 6 q^{75} - 2 q^{80} - 5 q^{81} - 2 q^{89} - 2 q^{92} - 4 q^{93} - 2 q^{97} - 3 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^9 - q^11 - 2 * q^12 - 4 * q^15 - q^16 - 2 * q^20 - 2 * q^23 - 3 * q^25 - 4 * q^27 - 2 * q^31 - 2 * q^33 - 3 * q^36 + 15 * q^37 - q^44 + 11 * q^45 - 2 * q^47 - 2 * q^48 - q^49 - 2 * q^53 + 15 * q^55 - 2 * q^59 - 4 * q^60 - q^64 + 15 * q^67 - 4 * q^69 - 2 * q^71 - 6 * q^75 - 2 * q^80 - 5 * q^81 - 2 * q^89 - 2 * q^92 - 4 * q^93 - 2 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1133\mathbb{Z}\right)^\times$.

$n$	$310$	$1035$
$\chi(n)$	$-1$	$e\left(\frac{14}{17}\right)$

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		−0.739009	−	0.673696i	$-0.764706\pi$
$2$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$3$	−1.58561	−	0.614268i	−1.58561	−	0.614268i	−0.602635	−	0.798017i	$-0.705882\pi$
$3$	−1.58561	−	0.614268i	−1.58561	−	0.614268i	−0.982973	+	0.183750i	$0.941176\pi$
$4$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$5$	1.67148	−	1.03494i	1.67148	−	1.03494i	0.739009	−	0.673696i	$-0.235294\pi$
$5$	1.67148	−	1.03494i	1.67148	−	1.03494i	0.932472	−	0.361242i	$-0.117647\pi$
$6$		0			0
$7$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$7$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$8$		0			0
$9$	1.39782	+	1.27428i	1.39782	+	1.27428i
$10$		0			0
$11$	0.739009	+	0.673696i	0.739009	+	0.673696i
$11$	0.739009	+	0.673696i	0.739009	+	0.673696i
$12$	0.465346	−	1.63552i	0.465346	−	1.63552i
$13$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$13$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$14$		0			0
$15$	−3.28604	+	0.614268i	−3.28604	+	0.614268i
$16$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$17$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$17$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$18$		0			0
$19$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$19$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$20$	1.18475	+	1.56886i	1.18475	+	1.56886i
$21$		0			0
$22$		0			0
$23$	−1.25664	+	1.14558i	−1.25664	+	1.14558i	−0.273663	+	0.961826i	$0.588235\pi$
$23$	−1.25664	+	1.14558i	−1.25664	+	1.14558i	−0.982973	+	0.183750i	$0.941176\pi$
$24$		0			0
$25$	1.27702	−	2.56459i	1.27702	−	2.56459i
$26$		0			0
$27$	−0.675694	−	1.35698i	−0.675694	−	1.35698i
$28$		0			0
$29$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$29$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$30$		0			0
$31$	1.67148	−	0.312454i	1.67148	−	0.312454i	0.739009	−	0.673696i	$-0.235294\pi$
$31$	1.67148	−	0.312454i	1.67148	−	0.312454i	0.932472	+	0.361242i	$0.117647\pi$
$32$		0			0
$33$	−0.757949	−	1.52217i	−0.757949	−	1.52217i
$34$		0			0
$35$		0			0
$36$	−1.13987	+	1.50943i	−1.13987	+	1.50943i
$37$	0.149783	−	0.526432i	0.149783	−	0.526432i	−0.850217	−	0.526432i	$-0.823529\pi$
$37$	0.149783	−	0.526432i	0.149783	−	0.526432i	1.00000			$0$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$41$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$42$		0			0
$43$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$43$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$44$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$45$	3.65523	+	0.683280i	3.65523	+	0.683280i
$46$		0			0
$47$	0.891477			0.891477			0.445738	−	0.895163i	$-0.352941\pi$
$47$	0.891477			0.891477			0.445738	+	0.895163i	$0.352941\pi$
$48$	1.67148	+	0.312454i	1.67148	+	0.312454i
$49$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.172075	−	0.0666624i	0.172075	−	0.0666624i	−0.273663	−	0.961826i	$-0.588235\pi$
$53$	0.172075	−	0.0666624i	0.172075	−	0.0666624i	0.445738	+	0.895163i	$0.352941\pi$
$54$		0			0
$55$	1.93247	+	0.361242i	1.93247	+	0.361242i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.329838	−	0.436776i	0.329838	−	0.436776i	−0.602635	−	0.798017i	$-0.705882\pi$
$59$	0.329838	−	0.436776i	0.329838	−	0.436776i	0.932472	+	0.361242i	$0.117647\pi$
$60$	−0.914845	−	3.21535i	−0.914845	−	3.21535i
$61$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$61$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$62$		0			0
$63$		0			0
$64$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$65$		0			0
$66$		0			0
$67$	0.726337	−	0.961826i	0.726337	−	0.961826i	−0.273663	−	0.961826i	$-0.588235\pi$
$67$	0.726337	−	0.961826i	0.726337	−	0.961826i	1.00000			$0$
$68$		0			0
$69$	2.69622	−	1.04452i	2.69622	−	1.04452i
$70$		0			0
$71$	−1.58561	−	0.981767i	−1.58561	−	0.981767i	−0.982973	−	0.183750i	$-0.941176\pi$
$71$	−1.58561	−	0.981767i	−1.58561	−	0.981767i	−0.602635	−	0.798017i	$-0.705882\pi$
$72$		0			0
$73$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$73$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$74$		0			0
$75$	−3.60019	+	3.28201i	−3.60019	+	3.28201i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$79$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$80$	−1.45285	+	1.32445i	−1.45285	+	1.32445i
$81$	0.0633152	+	0.683280i	0.0633152	+	0.683280i
$82$		0			0
$83$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$83$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.181395	+	1.95756i	−0.181395	+	1.95756i	0.0922684	+	0.995734i	$0.470588\pi$
$89$	−0.181395	+	1.95756i	−0.181395	+	1.95756i	−0.273663	+	0.961826i	$0.588235\pi$
$90$		0			0
$91$		0			0
$92$	−1.25664	−	1.14558i	−1.25664	−	1.14558i
$93$	−2.84224	−	0.531307i	−2.84224	−	0.531307i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.876298	−	1.75984i	−0.876298	−	1.75984i	−0.602635	−	0.798017i	$-0.705882\pi$
$97$	−0.876298	−	1.75984i	−0.876298	−	1.75984i	−0.273663	−	0.961826i	$-0.588235\pi$
$98$		0			0
$99$	0.174523	+	1.88341i	0.174523	+	1.88341i
$100$	2.67148	+	1.03494i	2.67148	+	1.03494i
$101$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$101$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$102$		0			0
$103$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$103$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$107$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$108$	1.28884	−	0.798017i	1.28884	−	0.798017i
$109$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$109$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$110$		0			0
$111$	−0.560867	+	0.742708i	−0.560867	+	0.742708i
$112$		0			0
$113$	−0.181395	−	0.0339085i	−0.181395	−	0.0339085i	0.0922684	−	0.995734i	$-0.470588\pi$
$113$	−0.181395	−	0.0339085i	−0.181395	−	0.0339085i	−0.273663	+	0.961826i	$0.588235\pi$
$114$		0			0
$115$	−0.914845	+	3.21535i	−0.914845	+	3.21535i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$122$		0			0
$123$		0			0
$124$	0.465346	+	1.63552i	0.465346	+	1.63552i
$125$	−0.338291	−	3.65074i	−0.338291	−	3.65074i
$126$		0			0
$127$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$127$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$131$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$132$	1.44574	−	0.895163i	1.44574	−	0.895163i
$133$		0			0
$134$		0			0
$135$	−2.53379	−	1.56886i	−2.53379	−	1.56886i
$136$		0			0
$137$	−1.83319	+	0.710182i	−1.83319	+	0.710182i	−0.850217	+	0.526432i	$0.823529\pi$
$137$	−1.83319	+	0.710182i	−1.83319	+	0.710182i	−0.982973	+	0.183750i	$0.941176\pi$
$138$		0			0
$139$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$139$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$140$		0			0
$141$	−1.41353	−	0.547605i	−1.41353	−	0.547605i
$142$		0			0
$143$		0			0
$144$	−1.60817	−	0.995734i	−1.60817	−	0.995734i
$145$		0			0
$146$		0			0
$147$	1.02474	−	1.35698i	1.02474	−	1.35698i
$148$	0.538007	+	0.100571i	0.538007	+	0.100571i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$		0			0
$151$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$151$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.47048	−	2.25214i	2.47048	−	2.25214i
$156$		0			0
$157$	−0.404479	+	1.42160i	−0.404479	+	1.42160i	0.445738	+	0.895163i	$0.352941\pi$
$157$	−0.404479	+	1.42160i	−0.404479	+	1.42160i	−0.850217	+	0.526432i	$0.823529\pi$
$158$		0			0
$159$	−0.313793			−0.313793
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.329838	+	1.15926i	0.329838	+	1.15926i	0.932472	+	0.361242i	$0.117647\pi$
$163$	0.329838	+	1.15926i	0.329838	+	1.15926i	−0.602635	+	0.798017i	$0.705882\pi$
$164$		0			0
$165$	−2.84224	−	1.75984i	−2.84224	−	1.75984i
$166$		0			0
$167$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$167$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$168$		0			0
$169$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$173$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$174$		0			0
$175$		0			0
$176$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$177$	−0.791290	+	0.489946i	−0.791290	+	0.489946i
$178$		0			0
$179$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	−0.982973	−	0.183750i	$-0.941176\pi$
$179$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	0.445738	−	0.895163i	$-0.352941\pi$
$180$	−0.343104	+	3.70268i	−0.343104	+	3.70268i
$181$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	−0.982973	−	0.183750i	$-0.941176\pi$
$181$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	0.739009	+	0.673696i	$0.235294\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.294465	−	1.03494i	−0.294465	−	1.03494i
$186$		0			0
$187$		0			0
$188$	0.0822551	+	0.887674i	0.0822551	+	0.887674i
$189$		0			0
$190$		0			0
$191$	−1.45285	+	0.271585i	−1.45285	+	0.271585i	−0.850217	−	0.526432i	$-0.823529\pi$
$191$	−1.45285	+	0.271585i	−1.45285	+	0.271585i	−0.602635	+	0.798017i	$0.705882\pi$
$192$	−0.156896	+	1.69318i	−0.156896	+	1.69318i
$193$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$193$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$194$		0			0
$195$		0			0
$196$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$197$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$197$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$198$		0			0
$199$	−1.12388	−	1.48826i	−1.12388	−	1.48826i	−0.850217	−	0.526432i	$-0.823529\pi$
$199$	−1.12388	−	1.48826i	−1.12388	−	1.48826i	−0.273663	−	0.961826i	$-0.588235\pi$
$200$		0			0
$201$	−1.74250	+	1.07891i	−1.74250	+	1.07891i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.21633			−3.21633
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$211$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$212$	0.0822551	+	0.165190i	0.0822551	+	0.165190i
$213$	1.91108	+	2.53068i	1.91108	+	2.53068i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.181395	+	1.95756i	−0.181395	+	1.95756i
$221$		0			0
$222$		0			0
$223$	0.0822551	−	0.165190i	0.0822551	−	0.165190i	−0.850217	−	0.526432i	$-0.823529\pi$
$223$	0.0822551	−	0.165190i	0.0822551	−	0.165190i	0.932472	+	0.361242i	$0.117647\pi$
$224$		0			0
$225$	5.05304	−	1.95756i	5.05304	−	1.95756i
$226$		0			0
$227$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$227$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$228$		0			0
$229$	1.09227	−	0.995734i	1.09227	−	0.995734i	0.0922684	−	0.995734i	$-0.470588\pi$
$229$	1.09227	−	0.995734i	1.09227	−	0.995734i	1.00000			$0$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$233$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$234$		0			0
$235$	1.49009	−	0.922623i	1.49009	−	0.922623i
$236$	0.465346	+	0.288130i	0.465346	+	0.288130i
$237$		0			0
$238$		0			0
$239$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$239$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$240$	3.11722	−	1.20762i	3.11722	−	1.20762i
$241$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$241$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$242$		0			0
$243$	−0.0955212	+	0.335722i	−0.0955212	+	0.335722i
$244$		0			0
$245$	0.538007	+	1.89090i	0.538007	+	1.89090i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.538007	+	0.100571i	0.538007	+	0.100571i	0.445738	−	0.895163i	$-0.352941\pi$
$251$	0.538007	+	0.100571i	0.538007	+	0.100571i	0.0922684	+	0.995734i	$0.470588\pi$
$252$		0			0
$253$	−1.70043			−1.70043
$254$		0			0
$255$		0			0
$256$	0.932472	−	0.361242i	0.932472	−	0.361242i
$257$	1.09227	−	0.995734i	1.09227	−	0.995734i	0.0922684	−	0.995734i	$-0.470588\pi$
$257$	1.09227	−	0.995734i	1.09227	−	0.995734i	1.00000			$0$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		0			0
$265$	0.218629	−	0.289512i	0.218629	−	0.289512i
$266$		0			0
$267$	1.49009	−	2.99250i	1.49009	−	2.99250i
$268$	1.02474	+	0.634493i	1.02474	+	0.634493i
$269$	−0.0505009	+	0.544991i	−0.0505009	+	0.544991i	0.932472	+	0.361242i	$0.117647\pi$
$269$	−0.0505009	+	0.544991i	−0.0505009	+	0.544991i	−0.982973	+	0.183750i	$0.941176\pi$
$270$		0			0
$271$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$271$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.67148	−	1.03494i	2.67148	−	1.03494i
$276$	1.28884	+	2.58834i	1.28884	+	2.58834i
$277$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$277$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$278$		0			0
$279$	2.73458	+	1.69318i	2.73458	+	1.69318i
$280$		0			0
$281$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$281$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$282$		0			0
$283$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$283$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$284$	0.831277	−	1.66943i	0.831277	−	1.66943i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.602635	−	0.798017i	−0.602635	−	0.798017i
$290$		0			0
$291$	0.308450	+	3.32870i	0.308450	+	3.32870i
$292$		0			0
$293$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$293$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$294$		0			0
$295$	0.0992820	−	1.07142i	0.0992820	−	1.07142i
$296$		0			0
$297$	0.414845	−	1.45803i	0.414845	−	1.45803i
$298$		0			0
$299$		0			0
$300$	−3.60019	−	3.28201i	−3.60019	−	3.28201i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$307$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$308$		0			0
$309$	1.67148	+	0.312454i	1.67148	+	0.312454i
$310$		0			0
$311$	−1.45285	−	1.32445i	−1.45285	−	1.32445i	−0.850217	−	0.526432i	$-0.823529\pi$
$311$	−1.45285	−	1.32445i	−1.45285	−	1.32445i	−0.602635	−	0.798017i	$-0.705882\pi$
$312$		0			0
$313$	0.0822551	+	0.887674i	0.0822551	+	0.887674i	0.932472	+	0.361242i	$0.117647\pi$
$313$	0.0822551	+	0.887674i	0.0822551	+	0.887674i	−0.850217	+	0.526432i	$0.823529\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.20527	+	1.59603i	−1.20527	+	1.59603i	−0.602635	+	0.798017i	$0.705882\pi$
$317$	−1.20527	+	1.59603i	−1.20527	+	1.59603i	−0.602635	+	0.798017i	$0.705882\pi$
$318$		0			0
$319$		0			0
$320$	−1.45285	−	1.32445i	−1.45285	−	1.32445i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.674523	+	0.126090i	−0.674523	+	0.126090i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.136374	+	1.47171i	0.136374	+	1.47171i	0.739009	+	0.673696i	$0.235294\pi$
$331$	0.136374	+	1.47171i	0.136374	+	1.47171i	−0.602635	+	0.798017i	$0.705882\pi$
$332$		0			0
$333$	0.880191	−	0.544991i	0.880191	−	0.544991i
$334$		0			0
$335$	0.218629	−	2.35939i	0.218629	−	2.35939i
$336$		0			0
$337$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$337$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$338$		0			0
$339$	0.266792	+	0.165190i	0.266792	+	0.165190i
$340$		0			0
$341$	1.44574	+	0.895163i	1.44574	+	0.895163i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3.42567	−	4.53632i	3.42567	−	4.53632i
$346$		0			0
$347$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$347$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$348$		0			0
$349$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$349$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.890705	+	1.17948i	−0.890705	+	1.17948i	0.0922684	+	0.995734i	$0.470588\pi$
$353$	−0.890705	+	1.17948i	−0.890705	+	1.17948i	−0.982973	+	0.183750i	$0.941176\pi$
$354$		0			0
$355$	−3.66638			−3.66638
$356$	−1.96595			−1.96595
$357$		0			0
$358$		0			0
$359$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$359$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$360$		0			0
$361$	0.739009	−	0.673696i	0.739009	−	0.673696i
$362$		0			0
$363$	0.465346	−	1.63552i	0.465346	−	1.63552i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.739009	−	0.673696i	$-0.235294\pi$
$367$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.445738	+	0.895163i	$0.352941\pi$
$368$	1.02474	−	1.35698i	1.02474	−	1.35698i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.266792	−	2.87914i	0.266792	−	2.87914i
$373$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$373$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$374$		0			0
$375$	−1.70614	+	5.99644i	−1.70614	+	5.99644i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.876298	−	1.75984i	−0.876298	−	1.75984i	−0.602635	−	0.798017i	$-0.705882\pi$
$379$	−0.876298	−	1.75984i	−0.876298	−	1.75984i	−0.273663	−	0.961826i	$-0.588235\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.757949	+	0.469302i	−0.757949	+	0.469302i	−0.850217	−	0.526432i	$-0.823529\pi$
$383$	−0.757949	+	0.469302i	−0.757949	+	0.469302i	0.0922684	+	0.995734i	$0.470588\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	1.67148	−	1.03494i	1.67148	−	1.03494i
$389$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.602635	+	0.798017i	$0.705882\pi$
$389$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.850217	+	0.526432i	$0.823529\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−1.85927	+	0.347558i	−1.85927	+	0.347558i
$397$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.445738	−	0.895163i	$-0.352941\pi$
$397$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.739009	+	0.673696i	$0.235294\pi$
$398$		0			0
$399$		0			0
$400$	−0.784029	+	2.75558i	−0.784029	+	2.75558i
$401$	−0.890705	−	0.811985i	−0.890705	−	0.811985i	0.0922684	−	0.995734i	$-0.470588\pi$
$401$	−0.890705	−	0.811985i	−0.890705	−	0.811985i	−0.982973	+	0.183750i	$0.941176\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.812982	+	1.07656i	0.812982	+	1.07656i
$406$		0			0
$407$	0.465346	−	0.288130i	0.465346	−	0.288130i
$408$		0			0
$409$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$409$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$410$		0			0
$411$	3.34296			3.34296
$412$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.111208	−	0.147263i	−0.111208	−	0.147263i	0.739009	−	0.673696i	$-0.235294\pi$
$419$	−0.111208	−	0.147263i	−0.111208	−	0.147263i	−0.850217	+	0.526432i	$0.823529\pi$
$420$		0			0
$421$	1.09227	+	0.995734i	1.09227	+	0.995734i	1.00000			$0$
$421$	1.09227	+	0.995734i	1.09227	+	0.995734i	0.0922684	+	0.995734i	$0.470588\pi$
$422$		0			0
$423$	1.24612	+	1.13599i	1.24612	+	1.13599i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$431$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$432$	0.913532	+	1.20971i	0.913532	+	1.20971i
$433$	−0.243964	−	0.857445i	−0.243964	−	0.857445i	−0.982973	−	0.183750i	$-0.941176\pi$
$433$	−0.243964	−	0.857445i	−0.243964	−	0.857445i	0.739009	−	0.673696i	$-0.235294\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$439$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$440$		0			0
$441$	−1.60817	+	0.995734i	−1.60817	+	0.995734i
$442$		0			0
$443$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.445738	−	0.895163i	$-0.352941\pi$
$443$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.739009	+	0.673696i	$0.235294\pi$
$444$	−0.791290	−	0.489946i	−0.791290	−	0.489946i
$445$	1.72275	+	3.45976i	1.72275	+	3.45976i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.243964	+	0.857445i	−0.243964	+	0.857445i	0.739009	+	0.673696i	$0.235294\pi$
$449$	−0.243964	+	0.857445i	−0.243964	+	0.857445i	−0.982973	+	0.183750i	$0.941176\pi$
$450$		0			0
$451$		0			0
$452$	0.0170269	−	0.183750i	0.0170269	−	0.183750i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$457$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$458$		0			0
$459$		0			0
$460$	−3.28604	−	0.614268i	−3.28604	−	0.614268i
$461$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$461$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$462$		0			0
$463$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.602635	+	0.798017i	$0.705882\pi$
$463$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.850217	+	0.526432i	$0.823529\pi$
$464$		0			0
$465$	−5.30063	+	2.05347i	−5.30063	+	2.05347i
$466$		0			0
$467$	−0.181395	−	0.0339085i	−0.181395	−	0.0339085i	0.0922684	−	0.995734i	$-0.470588\pi$
$467$	−0.181395	−	0.0339085i	−0.181395	−	0.0339085i	−0.273663	+	0.961826i	$0.588235\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.51458	−	2.00563i	1.51458	−	2.00563i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.325477	+	0.126090i	0.325477	+	0.126090i
$478$		0			0
$479$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$479$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$485$	−3.28604	−	2.03463i	−3.28604	−	2.03463i
$486$		0			0
$487$	1.37821	−	1.25640i	1.37821	−	1.25640i	0.445738	−	0.895163i	$-0.352941\pi$
$487$	1.37821	−	1.25640i	1.37821	−	1.25640i	0.932472	−	0.361242i	$-0.117647\pi$
$488$		0			0
$489$	0.189102	−	2.04074i	0.189102	−	2.04074i
$490$		0			0
$491$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$491$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	2.24092	+	2.96746i	2.24092	+	2.96746i
$496$	−1.58561	+	0.614268i	−1.58561	+	0.614268i
$497$		0			0
$498$		0			0
$499$	−1.96595	+	0.367499i	−1.96595	+	0.367499i	−0.982973	+	0.183750i	$0.941176\pi$
$499$	−1.96595	+	0.367499i	−1.96595	+	0.367499i	−0.982973	+	0.183750i	$0.941176\pi$
$500$	3.60395	−	0.673696i	3.60395	−	0.673696i
$501$		0			0
$502$		0			0
$503$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$503$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.02474	−	1.35698i	1.02474	−	1.35698i
$508$		0			0
$509$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	−0.982973	−	0.183750i	$-0.941176\pi$
$509$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	0.445738	−	0.895163i	$-0.352941\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.45285	+	1.32445i	−1.45285	+	1.32445i
$516$		0			0
$517$	0.658809	+	0.600584i	0.658809	+	0.600584i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	−0.982973	−	0.183750i	$-0.941176\pi$
$521$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	0.445738	−	0.895163i	$-0.352941\pi$
$522$		0			0
$523$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$523$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.02474	+	1.35698i	1.02474	+	1.35698i
$529$	0.174523	−	1.88341i	0.174523	−	1.88341i
$530$		0			0
$531$	1.01763	−	0.190227i	1.01763	−	0.190227i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.189102	+	2.04074i	0.189102	+	2.04074i
$538$		0			0
$539$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$540$	1.32838	−	2.66774i	1.32838	−	2.66774i
$541$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$541$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$542$		0			0
$543$	0.687790	−	0.627003i	0.687790	−	0.627003i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$547$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$548$	−0.876298	−	1.75984i	−0.876298	−	1.75984i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.168823	+	1.82188i	−0.168823	+	1.82188i
$556$		0			0
$557$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$557$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$563$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$564$	0.414845	−	1.45803i	0.414845	−	1.45803i
$565$	−0.338291	+	0.131055i	−0.338291	+	0.131055i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$569$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	2.47048	+	0.461813i	2.47048	+	0.461813i
$574$		0			0
$575$	1.33319	+	4.68568i	1.33319	+	4.68568i
$576$	0.843104	−	1.69318i	0.843104	−	1.69318i
$577$	−0.156896	−	0.0971461i	−0.156896	−	0.0971461i	0.445738	−	0.895163i	$-0.352941\pi$
$577$	−0.156896	−	0.0971461i	−0.156896	−	0.0971461i	−0.602635	+	0.798017i	$0.705882\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.172075	+	0.0666624i	0.172075	+	0.0666624i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.181395	+	0.0339085i	−0.181395	+	0.0339085i	−0.273663	−	0.961826i	$-0.588235\pi$
$587$	−0.181395	+	0.0339085i	−0.181395	+	0.0339085i	0.0922684	+	0.995734i	$0.470588\pi$
$588$	1.44574	+	0.895163i	1.44574	+	0.895163i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.0505009	+	0.544991i	−0.0505009	+	0.544991i
$593$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$593$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.867844	+	3.05016i	0.867844	+	3.05016i
$598$		0			0
$599$	−1.12388	+	0.435393i	−1.12388	+	0.435393i	−0.850217	−	0.526432i	$-0.823529\pi$
$599$	−1.12388	+	0.435393i	−1.12388	+	0.435393i	−0.273663	+	0.961826i	$0.588235\pi$
$600$		0			0
$601$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$601$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$602$		0			0
$603$	2.24092	−	0.418901i	2.24092	−	0.418901i
$604$		0			0
$605$	1.18475	+	1.56886i	1.18475	+	1.56886i
$606$		0			0
$607$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$607$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$613$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.86494			1.86494			0.932472	−	0.361242i	$-0.117647\pi$
$617$	1.86494			1.86494			0.932472	+	0.361242i	$0.117647\pi$
$618$		0			0
$619$	2.00000			2.00000			1.00000			$0$
$619$	2.00000			2.00000			1.00000			$0$
$620$	2.47048	+	2.25214i	2.47048	+	2.25214i
$621$	2.40362	+	0.931167i	2.40362	+	0.931167i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−2.61722	−	3.46576i	−2.61722	−	3.46576i
$626$		0			0
$627$		0			0
$628$	−1.45285	−	0.271585i	−1.45285	−	0.271585i
$629$		0			0
$630$		0			0
$631$	−0.111208	−	0.147263i	−0.111208	−	0.147263i	0.739009	−	0.673696i	$-0.235294\pi$
$631$	−0.111208	−	0.147263i	−0.111208	−	0.147263i	−0.850217	+	0.526432i	$0.823529\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.0289531	−	0.312454i	−0.0289531	−	0.312454i
$637$		0			0
$638$		0			0
$639$	−0.965346	−	3.39284i	−0.965346	−	3.39284i
$640$		0			0
$641$	0.136374	−	0.124322i	0.136374	−	0.124322i	−0.602635	−	0.798017i	$-0.705882\pi$
$641$	0.136374	−	0.124322i	0.136374	−	0.124322i	0.739009	+	0.673696i	$0.235294\pi$
$642$		0			0
$643$	0.831277	−	1.66943i	0.831277	−	1.66943i	0.0922684	−	0.995734i	$-0.470588\pi$
$643$	0.831277	−	1.66943i	0.831277	−	1.66943i	0.739009	−	0.673696i	$-0.235294\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.465346	−	0.288130i	0.465346	−	0.288130i	−0.273663	−	0.961826i	$-0.588235\pi$
$647$	0.465346	−	0.288130i	0.465346	−	0.288130i	0.739009	+	0.673696i	$0.235294\pi$
$648$		0			0
$649$	0.538007	−	0.100571i	0.538007	−	0.100571i
$650$		0			0
$651$		0			0
$652$	−1.12388	+	0.435393i	−1.12388	+	0.435393i
$653$	−1.12388	−	0.435393i	−1.12388	−	0.435393i	−0.273663	−	0.961826i	$-0.588235\pi$
$653$	−1.12388	−	0.435393i	−1.12388	−	0.435393i	−0.850217	+	0.526432i	$0.823529\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$659$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$660$	1.49009	−	2.99250i	1.49009	−	2.99250i
$661$	−0.243964	−	0.857445i	−0.243964	−	0.857445i	−0.982973	−	0.183750i	$-0.941176\pi$
$661$	−0.243964	−	0.857445i	−0.243964	−	0.857445i	0.739009	−	0.673696i	$-0.235294\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.231896	+	0.211401i	−0.231896	+	0.211401i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$673$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$674$		0			0
$675$	−4.34296			−4.34296
$676$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$677$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$677$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.510366	−	0.197717i	−0.510366	−	0.197717i	0.0922684	−	0.995734i	$-0.470588\pi$
$683$	−0.510366	−	0.197717i	−0.510366	−	0.197717i	−0.602635	+	0.798017i	$0.705882\pi$
$684$		0			0
$685$	−2.32915	+	3.08429i	−2.32915	+	3.08429i
$686$		0			0
$687$	−2.34356	+	0.907899i	−2.34356	+	0.907899i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	1.67148	+	1.03494i	1.67148	+	1.03494i	0.932472	+	0.361242i	$0.117647\pi$
$691$	1.67148	+	1.03494i	1.67148	+	1.03494i	0.739009	+	0.673696i	$0.235294\pi$
$692$		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		−0.602635	−	0.798017i	$-0.705882\pi$
$701$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$702$		0			0
$703$		0			0
$704$	0.445738	−	0.895163i	0.445738	−	0.895163i
$705$	−2.92943	+	0.547605i	−2.92943	+	0.547605i
$706$		0			0
$707$		0			0
$708$	−0.560867	−	0.742708i	−0.560867	−	0.742708i
$709$	0.149783	−	0.526432i	0.149783	−	0.526432i	−0.850217	−	0.526432i	$-0.823529\pi$
$709$	0.149783	−	0.526432i	0.149783	−	0.526432i	1.00000			$0$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.74250	+	2.30745i	−1.74250	+	2.30745i
$714$		0			0
$715$		0			0
$716$	1.02474	−	0.634493i	1.02474	−	0.634493i
$717$		0			0
$718$		0			0
$719$	1.37821	+	1.25640i	1.37821	+	1.25640i	0.932472	+	0.361242i	$0.117647\pi$
$719$	1.37821	+	1.25640i	1.37821	+	1.25640i	0.445738	+	0.895163i	$0.352941\pi$
$720$	−3.71854			−3.71854
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−0.510366	−	0.197717i	−0.510366	−	0.197717i
$725$		0			0
$726$		0			0
$727$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	−0.982973	−	0.183750i	$-0.941176\pi$
$727$	−0.537235	−	1.07891i	−0.537235	−	1.07891i	0.445738	−	0.895163i	$-0.352941\pi$
$728$		0			0
$729$	0.771215	−	1.02125i	0.771215	−	1.02125i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$733$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$734$		0			0
$735$	0.308450	−	3.32870i	0.308450	−	3.32870i
$736$		0			0
$737$	1.18475	−	0.221468i	1.18475	−	0.221468i
$738$		0			0
$739$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$739$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$740$	1.00335	−	0.388701i	1.00335	−	0.388701i
$741$		0			0
$742$		0			0
$743$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$743$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.67148	+	1.03494i	1.67148	+	1.03494i	0.932472	+	0.361242i	$0.117647\pi$
$751$	1.67148	+	1.03494i	1.67148	+	1.03494i	0.739009	+	0.673696i	$0.235294\pi$
$752$	−0.876298	+	0.163808i	−0.876298	+	0.163808i
$753$	−0.791290	−	0.489946i	−0.791290	−	0.489946i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.02474	−	1.35698i	1.02474	−	1.35698i	0.0922684	−	0.995734i	$-0.470588\pi$
$757$	1.02474	−	1.35698i	1.02474	−	1.35698i	0.932472	−	0.361242i	$-0.117647\pi$
$758$		0			0
$759$	2.69622	+	1.04452i	2.69622	+	1.04452i
$760$		0			0
$761$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$761$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$762$		0			0
$763$		0			0
$764$	−0.404479	−	1.42160i	−0.404479	−	1.42160i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.70043			−1.70043
$769$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$769$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$770$		0			0
$771$	−2.34356	+	0.907899i	−2.34356	+	0.907899i
$772$		0			0
$773$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.602635	+	0.798017i	$0.705882\pi$
$773$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.850217	+	0.526432i	$0.823529\pi$
$774$		0			0
$775$	1.33319	−	4.68568i	1.33319	−	4.68568i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−0.510366	−	1.79375i	−0.510366	−	1.79375i
$782$		0			0
$783$		0			0
$784$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$785$	0.795184	+	2.79478i	0.795184	+	2.79478i
$786$		0			0
$787$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$787$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−0.524498	+	0.324756i	−0.524498	+	0.324756i
$796$	1.37821	−	1.25640i	1.37821	−	1.25640i
$797$	0.658809	+	1.32307i	0.658809	+	1.32307i	0.932472	+	0.361242i	$0.117647\pi$
$797$	0.658809	+	1.32307i	0.658809	+	1.32307i	−0.273663	+	0.961826i	$0.588235\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−2.74804	+	2.50517i	−2.74804	+	2.50517i
$802$		0			0
$803$		0			0
$804$	−1.23509	−	1.63552i	−1.23509	−	1.63552i
$805$		0			0
$806$		0			0
$807$	0.414845	−	0.833121i	0.414845	−	0.833121i
$808$		0			0
$809$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$809$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$810$		0			0
$811$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$811$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.75108	+	1.59632i	1.75108	+	1.59632i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$821$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$822$		0			0
$823$	0.891477			0.891477			0.445738	−	0.895163i	$-0.352941\pi$
$823$	0.891477			0.891477			0.445738	+	0.895163i	$0.352941\pi$
$824$		0			0
$825$	−4.87165			−4.87165
$826$		0			0
$827$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$827$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$828$	−0.296766	−	3.20261i	−0.296766	−	3.20261i
$829$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i	−0.602635	−	0.798017i	$-0.705882\pi$
$829$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i	0.445738	+	0.895163i	$0.352941\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.55340	−	2.05704i	−1.55340	−	2.05704i
$838$		0			0
$839$	−0.181395	+	0.0339085i	−0.181395	+	0.0339085i	−0.273663	−	0.961826i	$-0.588235\pi$
$839$	−0.181395	+	0.0339085i	−0.181395	+	0.0339085i	0.0922684	+	0.995734i	$0.470588\pi$
$840$		0			0
$841$	0.445738	−	0.895163i	0.445738	−	0.895163i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.538007	+	1.89090i	0.538007	+	1.89090i
$846$		0			0
$847$		0			0
$848$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i
$849$		0			0
$850$		0			0
$851$	0.414845	+	0.833121i	0.414845	+	0.833121i
$852$	−2.34356	+	2.13643i	−2.34356	+	2.13643i
$853$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$853$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$857$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$858$		0			0
$859$	1.37821	+	0.533922i	1.37821	+	0.533922i	0.932472	−	0.361242i	$-0.117647\pi$
$859$	1.37821	+	0.533922i	1.37821	+	0.533922i	0.445738	+	0.895163i	$0.352941\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.149783	+	0.526432i	0.149783	+	0.526432i	1.00000			$0$
$863$	0.149783	+	0.526432i	0.149783	+	0.526432i	−0.850217	+	0.526432i	$0.823529\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.465346	+	1.63552i	0.465346	+	1.63552i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.01763	−	3.57659i	1.01763	−	3.57659i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$877$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$878$		0			0
$879$		0			0
$880$	−1.96595			−1.96595
$881$	−0.547326			−0.547326			−0.273663	−	0.961826i	$-0.588235\pi$
$881$	−0.547326			−0.547326			−0.273663	+	0.961826i	$0.588235\pi$
$882$		0			0
$883$	−0.537235	+	0.711414i	−0.537235	+	0.711414i	−0.982973	−	0.183750i	$-0.941176\pi$
$883$	−0.537235	+	0.711414i	−0.537235	+	0.711414i	0.445738	+	0.895163i	$0.352941\pi$
$884$		0			0
$885$	−0.815563	+	1.63787i	−0.815563	+	1.63787i
$886$		0			0
$887$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$887$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.413532	+	0.547605i	−0.413532	+	0.547605i
$892$	0.172075	+	0.0666624i	0.172075	+	0.0666624i
$893$		0			0
$894$		0			0
$895$	−2.01458	−	1.24738i	−2.01458	−	1.24738i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	2.41545	+	4.85087i	2.41545	+	4.85087i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.0992820	+	1.07142i	0.0992820	+	1.07142i
$906$		0			0
$907$	1.02474	+	1.35698i	1.02474	+	1.35698i	0.932472	+	0.361242i	$0.117647\pi$
$907$	1.02474	+	1.35698i	1.02474	+	1.35698i	0.0922684	+	0.995734i	$0.470588\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.445738	−	0.895163i	$-0.352941\pi$
$911$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.739009	+	0.673696i	$0.235294\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	1.09227	+	0.995734i	1.09227	+	0.995734i
$917$		0			0
$918$		0			0
$919$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$919$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.15881	−	1.05639i	−1.15881	−	1.05639i
$926$		0			0
$927$	−1.60817	−	0.995734i	−1.60817	−	0.995734i
$928$		0			0
$929$	−1.25664	−	1.14558i	−1.25664	−	1.14558i	−0.982973	−	0.183750i	$-0.941176\pi$
$929$	−1.25664	−	1.14558i	−1.25664	−	1.14558i	−0.273663	−	0.961826i	$-0.588235\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.49009	+	2.99250i	1.49009	+	2.99250i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$937$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$938$		0			0
$939$	0.414845	−	1.45803i	0.414845	−	1.45803i
$940$	1.05617	+	1.39860i	1.05617	+	1.39860i
$941$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$941$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$942$		0			0
$943$		0			0
$944$	−0.243964	+	0.489946i	−0.243964	+	0.489946i
$945$		0			0
$946$		0			0
$947$	1.02474	+	1.35698i	1.02474	+	1.35698i	0.932472	+	0.361242i	$0.117647\pi$
$947$	1.02474	+	1.35698i	1.02474	+	1.35698i	0.0922684	+	0.995734i	$0.470588\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	2.89148	−	1.79033i	2.89148	−	1.79033i
$952$		0			0
$953$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$953$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$954$		0			0
$955$	−2.14734	+	1.95756i	−2.14734	+	1.95756i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.49009	+	2.99250i	1.49009	+	2.99250i
$961$	1.76375	−	0.683280i	1.76375	−	0.683280i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$967$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.726337	−	0.961826i	0.726337	−	0.961826i	−0.273663	−	0.961826i	$-0.588235\pi$
$971$	0.726337	−	0.961826i	0.726337	−	0.961826i	1.00000			$0$
$972$	−0.343104	−	0.0641372i	−0.343104	−	0.0641372i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.510366	+	0.197717i	−0.510366	+	0.197717i	−0.602635	−	0.798017i	$-0.705882\pi$
$977$	−0.510366	+	0.197717i	−0.510366	+	0.197717i	0.0922684	+	0.995734i	$0.470588\pi$
$978$		0			0
$979$	−1.45285	+	1.32445i	−1.45285	+	1.32445i
$980$	−1.83319	+	0.710182i	−1.83319	+	0.710182i
$981$		0			0
$982$		0			0
$983$	−1.70043			−1.70043			−0.850217	−	0.526432i	$-0.823529\pi$
$983$	−1.70043			−1.70043			−0.850217	+	0.526432i	$0.823529\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.0505009	−	0.177492i	−0.0505009	−	0.177492i	0.932472	−	0.361242i	$-0.117647\pi$
$991$	−0.0505009	−	0.177492i	−0.0505009	−	0.177492i	−0.982973	+	0.183750i	$0.941176\pi$
$992$		0			0
$993$	0.687790	−	2.41733i	0.687790	−	2.41733i
$994$		0			0
$995$	−3.41880	−	1.32445i	−3.41880	−	1.32445i
$996$		0			0
$997$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$997$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$998$		0			0
$999$	−0.815563	+	0.152455i	−0.815563	+	0.152455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1133.1.s.a.648.1	yes	16
11.10	odd	2	CM	1133.1.s.a.648.1	yes	16
103.79	even	17	inner	1133.1.s.a.285.1	✓	16
1133.285	odd	34	inner	1133.1.s.a.285.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1133.1.s.a.285.1	✓	16	103.79	even	17	inner
1133.1.s.a.285.1	✓	16	1133.285	odd	34	inner
1133.1.s.a.648.1	yes	16	1.1	even	1	trivial
1133.1.s.a.648.1	yes	16	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:	\( N \)	\(=\)	\( 1133 = 11 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1133.s (of order \(34\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58561 - 0.614268i) q^{3} +(0.0922684 + 0.995734i) q^{4} +(1.67148 - 1.03494i) q^{5} +(1.39782 + 1.27428i) q^{9} +O(q^{10})\)	\(q+(-1.58561 - 0.614268i) q^{3} +(0.0922684 + 0.995734i) q^{4} +(1.67148 - 1.03494i) q^{5} +(1.39782 + 1.27428i) q^{9} +(0.739009 + 0.673696i) q^{11} +(0.465346 - 1.63552i) q^{12} +(-3.28604 + 0.614268i) q^{15} +(-0.982973 + 0.183750i) q^{16} +(1.18475 + 1.56886i) q^{20} +(-1.25664 + 1.14558i) q^{23} +(1.27702 - 2.56459i) q^{25} +(-0.675694 - 1.35698i) q^{27} +(1.67148 - 0.312454i) q^{31} +(-0.757949 - 1.52217i) q^{33} +(-1.13987 + 1.50943i) q^{36} +(0.149783 - 0.526432i) q^{37} +(-0.602635 + 0.798017i) q^{44} +(3.65523 + 0.683280i) q^{45} +0.891477 q^{47} +(1.67148 + 0.312454i) q^{48} +(-0.273663 + 0.961826i) q^{49} +(0.172075 - 0.0666624i) q^{53} +(1.93247 + 0.361242i) q^{55} +(0.329838 - 0.436776i) q^{59} +(-0.914845 - 3.21535i) q^{60} +(-0.273663 - 0.961826i) q^{64} +(0.726337 - 0.961826i) q^{67} +(2.69622 - 1.04452i) q^{69} +(-1.58561 - 0.981767i) q^{71} +(-3.60019 + 3.28201i) q^{75} +(-1.45285 + 1.32445i) q^{80} +(0.0633152 + 0.683280i) q^{81} +(-0.181395 + 1.95756i) q^{89} +(-1.25664 - 1.14558i) q^{92} +(-2.84224 - 0.531307i) q^{93} +(-0.876298 - 1.75984i) q^{97} +(0.174523 + 1.88341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^9	\( 16 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9} - q^{11} - 2 q^{12} - 4 q^{15} - q^{16} - 2 q^{20} - 2 q^{23} - 3 q^{25} - 4 q^{27} - 2 q^{31} - 2 q^{33} - 3 q^{36} + 15 q^{37} - q^{44} + 11 q^{45} - 2 q^{47} - 2 q^{48} - q^{49} - 2 q^{53} + 15 q^{55} - 2 q^{59} - 4 q^{60} - q^{64} + 15 q^{67} - 4 q^{69} - 2 q^{71} - 6 q^{75} - 2 q^{80} - 5 q^{81} - 2 q^{89} - 2 q^{92} - 4 q^{93} - 2 q^{97} - 3 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^9 - q^11 - 2 * q^12 - 4 * q^15 - q^16 - 2 * q^20 - 2 * q^23 - 3 * q^25 - 4 * q^27 - 2 * q^31 - 2 * q^33 - 3 * q^36 + 15 * q^37 - q^44 + 11 * q^45 - 2 * q^47 - 2 * q^48 - q^49 - 2 * q^53 + 15 * q^55 - 2 * q^59 - 4 * q^60 - q^64 + 15 * q^67 - 4 * q^69 - 2 * q^71 - 6 * q^75 - 2 * q^80 - 5 * q^81 - 2 * q^89 - 2 * q^92 - 4 * q^93 - 2 * q^97 - 3 * q^99

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