LMFDB - Embedded newform 1096.1.s.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1096,1,Mod(59,1096)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1096, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([17, 17, 26]))

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

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

chi := DirichletCharacter("1096.59");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1096 = 2^{3} \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1096.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:	$0.546975253846$
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:	$\Z[a_1, a_2]$
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			59.1
Root			$-0.739009 - 0.673696i$ of defining polynomial
Character	$\chi$	$=$	1096.59
Dual form			1096.1.s.a.483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.445738 - 0.895163i) q^{2} +(-1.45285 + 1.32445i) q^{3} +(-0.602635 - 0.798017i) q^{4} +(0.538007 + 1.89090i) q^{6} +(-0.982973 + 0.183750i) q^{8} +(0.264344 - 2.85272i) q^{9} +O(q^{10})$	\(q+(0.445738 - 0.895163i) q^{2} +(-1.45285 + 1.32445i) q^{3} +(-0.602635 - 0.798017i) q^{4} +(0.538007 + 1.89090i) q^{6} +(-0.982973 + 0.183750i) q^{8} +(0.264344 - 2.85272i) q^{9} +(0.329838 + 0.436776i) q^{11} +(1.93247 + 0.361242i) q^{12} +(-0.273663 + 0.961826i) q^{16} +(0.538007 + 0.100571i) q^{17} +(-2.43582 - 1.50820i) q^{18} +(1.67148 + 1.03494i) q^{19} +(0.538007 - 0.100571i) q^{22} +(1.18475 - 1.56886i) q^{24} +(-0.602635 + 0.798017i) q^{25} +(2.20949 + 2.92583i) q^{27} +(0.739009 + 0.673696i) q^{32} +(-1.05769 - 0.197717i) q^{33} +(0.329838 - 0.436776i) q^{34} +(-2.43582 + 1.50820i) q^{36} +(1.67148 - 1.03494i) q^{38} +1.47802 q^{41} +(0.465346 + 0.288130i) q^{43} +(0.149783 - 0.526432i) q^{44} +(-0.876298 - 1.75984i) q^{48} +(0.739009 + 0.673696i) q^{49} +(0.445738 + 0.895163i) q^{50} +(-0.914845 + 0.566448i) q^{51} +(3.60395 - 0.673696i) q^{54} +(-3.79914 + 0.710182i) q^{57} +(0.0822551 - 0.887674i) q^{59} +(0.932472 - 0.361242i) q^{64} +(-0.648443 + 0.858677i) q^{66} +(-1.83319 - 0.710182i) q^{67} +(-0.243964 - 0.489946i) q^{68} +(0.264344 + 2.85272i) q^{72} +(1.37821 - 0.533922i) q^{73} +(-0.181395 - 1.95756i) q^{75} +(-0.181395 - 1.95756i) q^{76} +(-4.26902 - 0.798017i) q^{81} +(0.658809 - 1.32307i) q^{82} +(-1.83319 + 0.342683i) q^{83} +(0.465346 - 0.288130i) q^{86} +(-0.404479 - 0.368731i) q^{88} +(-0.757949 - 1.52217i) q^{89} -1.96595 q^{96} +(0.726337 + 0.961826i) q^{97} +(0.932472 - 0.361242i) q^{98} +(1.33319 - 0.825476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) $ 16 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9	$ 16 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} + 15 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{22} - 2 q^{24} - q^{25} - 4 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} - 2 q^{38} - 2 q^{41} - 2 q^{43} + 15 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} + 13 q^{54} - 4 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - 2 q^{76} - 5 q^{81} - 2 q^{82} - 2 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} + 15 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) $ 16 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9 - 2 * q^11 + 15 * q^12 - q^16 - 2 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^22 - 2 * q^24 - q^25 - 4 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 - 2 * q^38 - 2 * q^41 - 2 * q^43 + 15 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 + 13 * q^54 - 4 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 - 2 * q^75 - 2 * q^76 - 5 * q^81 - 2 * q^82 - 2 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 + 15 * q^97 - q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1096\mathbb{Z}\right)^\times$.

$n$	$549$	$823$	$825$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{17}\right)$

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 $

$2$	0.445738	−	0.895163i	0.445738	−	0.895163i
$2$	0.445738	−	0.895163i	0.445738	−	0.895163i
$3$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.602635	+	0.798017i	$0.705882\pi$
$3$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.850217	+	0.526432i	$0.823529\pi$
$4$	−0.602635	−	0.798017i	−0.602635	−	0.798017i
$5$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$5$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$6$	0.538007	+	1.89090i	0.538007	+	1.89090i
$7$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$7$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$8$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$9$	0.264344	−	2.85272i	0.264344	−	2.85272i
$10$		0			0
$11$	0.329838	+	0.436776i	0.329838	+	0.436776i	0.932472	−	0.361242i	$-0.117647\pi$
$11$	0.329838	+	0.436776i	0.329838	+	0.436776i	−0.602635	+	0.798017i	$0.705882\pi$
$12$	1.93247	+	0.361242i	1.93247	+	0.361242i
$13$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$13$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$14$		0			0
$15$		0			0
$16$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$17$	0.538007	+	0.100571i	0.538007	+	0.100571i	0.445738	−	0.895163i	$-0.352941\pi$
$17$	0.538007	+	0.100571i	0.538007	+	0.100571i	0.0922684	+	0.995734i	$0.470588\pi$
$18$	−2.43582	−	1.50820i	−2.43582	−	1.50820i
$19$	1.67148	+	1.03494i	1.67148	+	1.03494i	0.932472	+	0.361242i	$0.117647\pi$
$19$	1.67148	+	1.03494i	1.67148	+	1.03494i	0.739009	+	0.673696i	$0.235294\pi$
$20$		0			0
$21$		0			0
$22$	0.538007	−	0.100571i	0.538007	−	0.100571i
$23$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$23$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$24$	1.18475	−	1.56886i	1.18475	−	1.56886i
$25$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$26$		0			0
$27$	2.20949	+	2.92583i	2.20949	+	2.92583i
$28$		0			0
$29$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$29$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$30$		0			0
$31$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$31$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$32$	0.739009	+	0.673696i	0.739009	+	0.673696i
$33$	−1.05769	−	0.197717i	−1.05769	−	0.197717i
$34$	0.329838	−	0.436776i	0.329838	−	0.436776i
$35$		0			0
$36$	−2.43582	+	1.50820i	−2.43582	+	1.50820i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	1.67148	−	1.03494i	1.67148	−	1.03494i
$39$		0			0
$40$		0			0
$41$	1.47802			1.47802			0.739009	−	0.673696i	$-0.235294\pi$
$41$	1.47802			1.47802			0.739009	+	0.673696i	$0.235294\pi$
$42$		0			0
$43$	0.465346	+	0.288130i	0.465346	+	0.288130i	0.739009	−	0.673696i	$-0.235294\pi$
$43$	0.465346	+	0.288130i	0.465346	+	0.288130i	−0.273663	+	0.961826i	$0.588235\pi$
$44$	0.149783	−	0.526432i	0.149783	−	0.526432i
$45$		0			0
$46$		0			0
$47$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$47$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$48$	−0.876298	−	1.75984i	−0.876298	−	1.75984i
$49$	0.739009	+	0.673696i	0.739009	+	0.673696i
$50$	0.445738	+	0.895163i	0.445738	+	0.895163i
$51$	−0.914845	+	0.566448i	−0.914845	+	0.566448i
$52$		0			0
$53$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$53$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$54$	3.60395	−	0.673696i	3.60395	−	0.673696i
$55$		0			0
$56$		0			0
$57$	−3.79914	+	0.710182i	−3.79914	+	0.710182i
$58$		0			0
$59$	0.0822551	−	0.887674i	0.0822551	−	0.887674i	−0.850217	−	0.526432i	$-0.823529\pi$
$59$	0.0822551	−	0.887674i	0.0822551	−	0.887674i	0.932472	−	0.361242i	$-0.117647\pi$
$60$		0			0
$61$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$61$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$62$		0			0
$63$		0			0
$64$	0.932472	−	0.361242i	0.932472	−	0.361242i
$65$		0			0
$66$	−0.648443	+	0.858677i	−0.648443	+	0.858677i
$67$	−1.83319	−	0.710182i	−1.83319	−	0.710182i	−0.982973	−	0.183750i	$-0.941176\pi$
$67$	−1.83319	−	0.710182i	−1.83319	−	0.710182i	−0.850217	−	0.526432i	$-0.823529\pi$
$68$	−0.243964	−	0.489946i	−0.243964	−	0.489946i
$69$		0			0
$70$		0			0
$71$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$71$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$72$	0.264344	+	2.85272i	0.264344	+	2.85272i
$73$	1.37821	−	0.533922i	1.37821	−	0.533922i	0.445738	−	0.895163i	$-0.352941\pi$
$73$	1.37821	−	0.533922i	1.37821	−	0.533922i	0.932472	+	0.361242i	$0.117647\pi$
$74$		0			0
$75$	−0.181395	−	1.95756i	−0.181395	−	1.95756i
$76$	−0.181395	−	1.95756i	−0.181395	−	1.95756i
$77$		0			0
$78$		0			0
$79$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$79$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$80$		0			0
$81$	−4.26902	−	0.798017i	−4.26902	−	0.798017i
$82$	0.658809	−	1.32307i	0.658809	−	1.32307i
$83$	−1.83319	+	0.342683i	−1.83319	+	0.342683i	−0.982973	−	0.183750i	$-0.941176\pi$
$83$	−1.83319	+	0.342683i	−1.83319	+	0.342683i	−0.850217	+	0.526432i	$0.823529\pi$
$84$		0			0
$85$		0			0
$86$	0.465346	−	0.288130i	0.465346	−	0.288130i
$87$		0			0
$88$	−0.404479	−	0.368731i	−0.404479	−	0.368731i
$89$	−0.757949	−	1.52217i	−0.757949	−	1.52217i	−0.850217	−	0.526432i	$-0.823529\pi$
$89$	−0.757949	−	1.52217i	−0.757949	−	1.52217i	0.0922684	−	0.995734i	$-0.470588\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.96595			−1.96595
$97$	0.726337	+	0.961826i	0.726337	+	0.961826i	1.00000			$0$
$97$	0.726337	+	0.961826i	0.726337	+	0.961826i	−0.273663	+	0.961826i	$0.588235\pi$
$98$	0.932472	−	0.361242i	0.932472	−	0.361242i
$99$	1.33319	−	0.825476i	1.33319	−	0.825476i
$100$	1.00000			1.00000
$101$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$101$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$102$	0.0992820	+	1.07142i	0.0992820	+	1.07142i
$103$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$103$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.37821	−	1.25640i	1.37821	−	1.25640i	0.445738	−	0.895163i	$-0.352941\pi$
$107$	1.37821	−	1.25640i	1.37821	−	1.25640i	0.932472	−	0.361242i	$-0.117647\pi$
$108$	1.00335	−	3.52642i	1.00335	−	3.52642i
$109$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$109$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.890705	+	1.17948i	−0.890705	+	1.17948i	0.0922684	+	0.995734i	$0.470588\pi$
$113$	−0.890705	+	1.17948i	−0.890705	+	1.17948i	−0.982973	+	0.183750i	$0.941176\pi$
$114$	−1.05769	+	3.71740i	−1.05769	+	3.71740i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.757949	−	0.469302i	−0.757949	−	0.469302i
$119$		0			0
$120$		0			0
$121$	0.191683	−	0.673696i	0.191683	−	0.673696i
$122$		0			0
$123$	−2.14734	+	1.95756i	−2.14734	+	1.95756i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$129$	−1.05769	+	0.197717i	−1.05769	+	0.197717i
$130$		0			0
$131$	0.149783	+	0.526432i	0.149783	+	0.526432i	1.00000			$0$
$131$	0.149783	+	0.526432i	0.149783	+	0.526432i	−0.850217	+	0.526432i	$0.823529\pi$
$132$	0.479620	+	0.963208i	0.479620	+	0.963208i
$133$		0			0
$134$	−1.45285	+	1.32445i	−1.45285	+	1.32445i
$135$		0			0
$136$	−0.547326			−0.547326
$137$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$137$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$138$		0			0
$139$	−0.876298	+	1.75984i	−0.876298	+	1.75984i	−0.273663	+	0.961826i	$0.588235\pi$
$139$	−0.876298	+	1.75984i	−0.876298	+	1.75984i	−0.602635	+	0.798017i	$0.705882\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	2.67148	+	1.03494i	2.67148	+	1.03494i
$145$		0			0
$146$	0.136374	−	1.47171i	0.136374	−	1.47171i
$147$	−1.96595			−1.96595
$148$		0			0
$149$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$149$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$150$	−1.83319	−	0.710182i	−1.83319	−	0.710182i
$151$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$151$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$152$	−1.83319	−	0.710182i	−1.83319	−	0.710182i
$153$	0.429120	−	1.50820i	0.429120	−	1.50820i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$157$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−2.61722	+	3.46576i	−2.61722	+	3.46576i
$163$	−0.890705	+	0.811985i	−0.890705	+	0.811985i	−0.982973	−	0.183750i	$-0.941176\pi$
$163$	−0.890705	+	0.811985i	−0.890705	+	0.811985i	0.0922684	+	0.995734i	$0.470588\pi$
$164$	−0.890705	−	1.17948i	−0.890705	−	1.17948i
$165$		0			0
$166$	−0.510366	+	1.79375i	−0.510366	+	1.79375i
$167$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$167$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$168$		0			0
$169$	0.739009	+	0.673696i	0.739009	+	0.673696i
$170$		0			0
$171$	3.39424	−	4.49469i	3.39424	−	4.49469i
$172$	−0.0505009	−	0.544991i	−0.0505009	−	0.544991i
$173$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$173$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$174$		0			0
$175$		0			0
$176$	−0.510366	+	0.197717i	−0.510366	+	0.197717i
$177$	1.05617	+	1.39860i	1.05617	+	1.39860i
$178$	−1.70043			−1.70043
$179$	0.136374	−	1.47171i	0.136374	−	1.47171i	−0.602635	−	0.798017i	$-0.705882\pi$
$179$	0.136374	−	1.47171i	0.136374	−	1.47171i	0.739009	−	0.673696i	$-0.235294\pi$
$180$		0			0
$181$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$181$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.133528	+	0.268160i	0.133528	+	0.268160i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$191$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$192$	−0.876298	+	1.75984i	−0.876298	+	1.75984i
$193$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.739009	−	0.673696i	$-0.235294\pi$
$193$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.445738	+	0.895163i	$0.352941\pi$
$194$	1.18475	−	0.221468i	1.18475	−	0.221468i
$195$		0			0
$196$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$197$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$197$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$198$	−0.144682	−	1.56137i	−0.144682	−	1.56137i
$199$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$199$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$200$	0.445738	−	0.895163i	0.445738	−	0.895163i
$201$	3.60395	−	1.39618i	3.60395	−	1.39618i
$202$		0			0
$203$		0			0
$204$	1.00335	+	0.388701i	1.00335	+	0.388701i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.0992820	+	1.07142i	0.0992820	+	1.07142i
$210$		0			0
$211$	0.397365	−	0.798017i	0.397365	−	0.798017i	−0.602635	−	0.798017i	$-0.705882\pi$
$211$	0.397365	−	0.798017i	0.397365	−	0.798017i	1.00000			$0$
$212$		0			0
$213$		0			0
$214$	−0.510366	−	1.79375i	−0.510366	−	1.79375i
$215$		0			0
$216$	−2.70949	−	2.47002i	−2.70949	−	2.47002i
$217$		0			0
$218$		0			0
$219$	−1.29518	+	2.60108i	−1.29518	+	2.60108i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$223$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$224$		0			0
$225$	2.11722	+	1.93010i	2.11722	+	1.93010i
$226$	0.658809	+	1.32307i	0.658809	+	1.32307i
$227$	0.172075	−	1.85699i	0.172075	−	1.85699i	−0.273663	−	0.961826i	$-0.588235\pi$
$227$	0.172075	−	1.85699i	0.172075	−	1.85699i	0.445738	−	0.895163i	$-0.352941\pi$
$228$	2.85623	+	2.60380i	2.85623	+	2.60380i
$229$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$229$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.20527			−1.20527			−0.602635	−	0.798017i	$-0.705882\pi$
$233$	−1.20527			−1.20527			−0.602635	+	0.798017i	$0.705882\pi$
$234$		0			0
$235$		0			0
$236$	−0.757949	+	0.469302i	−0.757949	+	0.469302i
$237$		0			0
$238$		0			0
$239$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$239$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$240$		0			0
$241$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.739009	−	0.673696i	$-0.235294\pi$
$241$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.445738	+	0.895163i	$0.352941\pi$
$242$	−0.517627	−	0.471880i	−0.517627	−	0.471880i
$243$	4.14196	−	2.56459i	4.14196	−	2.56459i
$244$		0			0
$245$		0			0
$246$	0.795184	+	2.79478i	0.795184	+	2.79478i
$247$		0			0
$248$		0			0
$249$	2.20949	−	2.92583i	2.20949	−	2.92583i
$250$		0			0
$251$	0.149783	−	0.526432i	0.149783	−	0.526432i	−0.850217	−	0.526432i	$-0.823529\pi$
$251$	0.149783	−	0.526432i	0.149783	−	0.526432i	1.00000			$0$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$257$	−1.45285	−	0.271585i	−1.45285	−	0.271585i	−0.602635	−	0.798017i	$-0.705882\pi$
$257$	−1.45285	−	0.271585i	−1.45285	−	0.271585i	−0.850217	+	0.526432i	$0.823529\pi$
$258$	−0.294465	+	1.03494i	−0.294465	+	1.03494i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.538007	+	0.100571i	0.538007	+	0.100571i
$263$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$263$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$264$	1.07601			1.07601
$265$		0			0
$266$		0			0
$267$	3.11722	+	1.20762i	3.11722	+	1.20762i
$268$	0.538007	+	1.89090i	0.538007	+	1.89090i
$269$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$269$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$270$		0			0
$271$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$271$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$272$	−0.243964	+	0.489946i	−0.243964	+	0.489946i
$273$		0			0
$274$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$275$	−0.547326			−0.547326
$276$		0			0
$277$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$277$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$278$	1.18475	+	1.56886i	1.18475	+	1.56886i
$279$		0			0
$280$		0			0
$281$	−1.83319	−	0.710182i	−1.83319	−	0.710182i	−0.982973	−	0.183750i	$-0.941176\pi$
$281$	−1.83319	−	0.710182i	−1.83319	−	0.710182i	−0.850217	−	0.526432i	$-0.823529\pi$
$282$		0			0
$283$	0.0170269	−	0.183750i	0.0170269	−	0.183750i	−0.982973	−	0.183750i	$-0.941176\pi$
$283$	0.0170269	−	0.183750i	0.0170269	−	0.183750i	1.00000			$0$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.11722	−	1.93010i	2.11722	−	1.93010i
$289$	−0.653136	−	0.253026i	−0.653136	−	0.253026i
$290$		0			0
$291$	−2.32915	−	0.435393i	−2.32915	−	0.435393i
$292$	−1.25664	−	0.778076i	−1.25664	−	0.778076i
$293$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$293$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$294$	−0.876298	+	1.75984i	−0.876298	+	1.75984i
$295$		0			0
$296$		0			0
$297$	−0.549161	+	1.93010i	−0.549161	+	1.93010i
$298$		0			0
$299$		0			0
$300$	−1.45285	+	1.32445i	−1.45285	+	1.32445i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.45285	+	1.32445i	−1.45285	+	1.32445i
$305$		0			0
$306$	−1.15881	−	1.05639i	−1.15881	−	1.05639i
$307$	1.93247	+	0.361242i	1.93247	+	0.361242i	1.00000			$0$
$307$	1.93247	+	0.361242i	1.93247	+	0.361242i	0.932472	+	0.361242i	$0.117647\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$	−1.58561	+	0.614268i	−1.58561	+	0.614268i	−0.982973	−	0.183750i	$-0.941176\pi$
$313$	−1.58561	+	0.614268i	−1.58561	+	0.614268i	−0.602635	+	0.798017i	$0.705882\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$317$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.338291	+	3.65074i	−0.338291	+	3.65074i
$322$		0			0
$323$	0.795184	+	0.724906i	0.795184	+	0.724906i
$324$	1.93582	+	3.88766i	1.93582	+	3.88766i
$325$		0			0
$326$	0.329838	+	1.15926i	0.329838	+	1.15926i
$327$		0			0
$328$	−1.45285	+	0.271585i	−1.45285	+	0.271585i
$329$		0			0
$330$		0			0
$331$	−1.96595	+	0.367499i	−1.96595	+	0.367499i	−0.982973	+	0.183750i	$0.941176\pi$
$331$	−1.96595	+	0.367499i	−1.96595	+	0.367499i	−0.982973	+	0.183750i	$0.941176\pi$
$332$	1.37821	+	1.25640i	1.37821	+	1.25640i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.658809	−	1.32307i	0.658809	−	1.32307i	−0.273663	−	0.961826i	$-0.588235\pi$
$337$	0.658809	−	1.32307i	0.658809	−	1.32307i	0.932472	−	0.361242i	$-0.117647\pi$
$338$	0.932472	−	0.361242i	0.932472	−	0.361242i
$339$	−0.268104	−	2.89331i	−0.268104	−	2.89331i
$340$		0			0
$341$		0			0
$342$	−2.51054	−	5.04185i	−2.51054	−	5.04185i
$343$		0			0
$344$	−0.510366	−	0.197717i	−0.510366	−	0.197717i
$345$		0			0
$346$		0			0
$347$	0.172075	−	0.0666624i	0.172075	−	0.0666624i	−0.273663	−	0.961826i	$-0.588235\pi$
$347$	0.172075	−	0.0666624i	0.172075	−	0.0666624i	0.445738	+	0.895163i	$0.352941\pi$
$348$		0			0
$349$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$349$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$350$		0			0
$351$		0			0
$352$	−0.0505009	+	0.544991i	−0.0505009	+	0.544991i
$353$	1.37821	+	1.25640i	1.37821	+	1.25640i	0.932472	+	0.361242i	$0.117647\pi$
$353$	1.37821	+	1.25640i	1.37821	+	1.25640i	0.445738	+	0.895163i	$0.352941\pi$
$354$	1.72275	−	0.322039i	1.72275	−	0.322039i
$355$		0			0
$356$	−0.757949	+	1.52217i	−0.757949	+	1.52217i
$357$		0			0
$358$	−1.25664	−	0.778076i	−1.25664	−	0.778076i
$359$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$359$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$360$		0			0
$361$	1.27702	+	2.56459i	1.27702	+	2.56459i
$362$		0			0
$363$	0.613789	+	1.23265i	0.613789	+	1.23265i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$367$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$368$		0			0
$369$	0.390705	−	4.21638i	0.390705	−	4.21638i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$373$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$374$	0.299566			0.299566
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.890705	−	0.811985i	−0.890705	−	0.811985i	0.0922684	−	0.995734i	$-0.470588\pi$
$379$	−0.890705	−	0.811985i	−0.890705	−	0.811985i	−0.982973	+	0.183750i	$0.941176\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$383$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$384$	1.18475	+	1.56886i	1.18475	+	1.56886i
$385$		0			0
$386$	0.726337	−	0.961826i	0.726337	−	0.961826i
$387$	0.944966	−	1.25134i	0.944966	−	1.25134i
$388$	0.329838	−	1.15926i	0.329838	−	1.15926i
$389$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$389$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$390$		0			0
$391$		0			0
$392$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$393$	−0.914845	−	0.566448i	−0.914845	−	0.566448i
$394$		0			0
$395$		0			0
$396$	−1.46217	−	0.566448i	−1.46217	−	0.566448i
$397$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$397$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$398$		0			0
$399$		0			0
$400$	−0.602635	−	0.798017i	−0.602635	−	0.798017i
$401$	0.184537			0.184537			0.0922684	−	0.995734i	$-0.470588\pi$
$401$	0.184537			0.184537			0.0922684	+	0.995734i	$0.470588\pi$
$402$	0.356612	−	3.84846i	0.356612	−	3.84846i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.795184	−	0.724906i	0.795184	−	0.724906i
$409$	−0.537235	+	1.07891i	−0.537235	+	1.07891i	0.445738	+	0.895163i	$0.352941\pi$
$409$	−0.537235	+	1.07891i	−0.537235	+	1.07891i	−0.982973	+	0.183750i	$0.941176\pi$
$410$		0			0
$411$	0.538007	−	1.89090i	0.538007	−	1.89090i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.05769	−	3.71740i	−1.05769	−	3.71740i
$418$	1.00335	+	0.388701i	1.00335	+	0.388701i
$419$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.445738	−	0.895163i	$-0.352941\pi$
$419$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.739009	+	0.673696i	$0.235294\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	−0.537235	−	0.711414i	−0.537235	−	0.711414i
$423$		0			0
$424$		0			0
$425$	−0.404479	+	0.368731i	−0.404479	+	0.368731i
$426$		0			0
$427$		0			0
$428$	−1.83319	−	0.342683i	−1.83319	−	0.342683i
$429$		0			0
$430$		0			0
$431$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$431$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$432$	−3.41880	+	1.32445i	−3.41880	+	1.32445i
$433$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.445738	−	0.895163i	$-0.352941\pi$
$433$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.739009	+	0.673696i	$0.235294\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.75108	+	2.31880i	1.75108	+	2.31880i
$439$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$439$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$440$		0			0
$441$	2.11722	−	1.93010i	2.11722	−	1.93010i
$442$		0			0
$443$	−0.890705	−	0.811985i	−0.890705	−	0.811985i	0.0922684	−	0.995734i	$-0.470588\pi$
$443$	−0.890705	−	0.811985i	−0.890705	−	0.811985i	−0.982973	+	0.183750i	$0.941176\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.02474	−	0.634493i	1.02474	−	0.634493i	0.0922684	−	0.995734i	$-0.470588\pi$
$449$	1.02474	−	0.634493i	1.02474	−	0.634493i	0.932472	+	0.361242i	$0.117647\pi$
$450$	2.67148	−	1.03494i	2.67148	−	1.03494i
$451$	0.487506	+	0.645562i	0.487506	+	0.645562i
$452$	1.47802			1.47802
$453$		0			0
$454$	−1.58561	−	0.981767i	−1.58561	−	0.981767i
$455$		0			0
$456$	3.60395	−	1.39618i	3.60395	−	1.39618i
$457$	−0.404479	−	0.368731i	−0.404479	−	0.368731i	0.445738	−	0.895163i	$-0.352941\pi$
$457$	−0.404479	−	0.368731i	−0.404479	−	0.368731i	−0.850217	+	0.526432i	$0.823529\pi$
$458$		0			0
$459$	0.894466	+	1.79633i	0.894466	+	1.79633i
$460$		0			0
$461$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$461$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$462$		0			0
$463$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$463$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$464$		0			0
$465$		0			0
$466$	−0.537235	+	1.07891i	−0.537235	+	1.07891i
$467$	−1.45285	−	0.271585i	−1.45285	−	0.271585i	−0.602635	−	0.798017i	$-0.705882\pi$
$467$	−1.45285	−	0.271585i	−1.45285	−	0.271585i	−0.850217	+	0.526432i	$0.823529\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.0822551	+	0.887674i	0.0822551	+	0.887674i
$473$	0.0276404	+	0.298288i	0.0276404	+	0.298288i
$474$		0			0
$475$	−1.83319	+	0.710182i	−1.83319	+	0.710182i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$479$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$480$		0			0
$481$		0			0
$482$	0.726337	−	0.961826i	0.726337	−	0.961826i
$483$		0			0
$484$	−0.653136	+	0.253026i	−0.653136	+	0.253026i
$485$		0			0
$486$	−0.449499	−	4.85087i	−0.449499	−	4.85087i
$487$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$487$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$488$		0			0
$489$	0.218629	−	2.35939i	0.218629	−	2.35939i
$490$		0			0
$491$	−0.876298	+	0.163808i	−0.876298	+	0.163808i	−0.602635	−	0.798017i	$-0.705882\pi$
$491$	−0.876298	+	0.163808i	−0.876298	+	0.163808i	−0.273663	+	0.961826i	$0.588235\pi$
$492$	2.85623	+	0.533922i	2.85623	+	0.533922i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.63425	−	3.28201i	−1.63425	−	3.28201i
$499$	0.136374	+	0.124322i	0.136374	+	0.124322i	0.739009	−	0.673696i	$-0.235294\pi$
$499$	0.136374	+	0.124322i	0.136374	+	0.124322i	−0.602635	+	0.798017i	$0.705882\pi$
$500$		0			0
$501$		0			0
$502$	−0.404479	−	0.368731i	−0.404479	−	0.368731i
$503$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$503$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.96595			−1.96595
$508$		0			0
$509$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$509$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$510$		0			0
$511$		0			0
$512$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$513$	0.665062	+	7.17716i	0.665062	+	7.17716i
$514$	−0.890705	+	1.17948i	−0.890705	+	1.17948i
$515$		0			0
$516$	0.795184	+	0.724906i	0.795184	+	0.724906i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.890705	−	1.17948i	−0.890705	−	1.17948i	−0.982973	−	0.183750i	$-0.941176\pi$
$521$	−0.890705	−	1.17948i	−0.890705	−	1.17948i	0.0922684	−	0.995734i	$-0.470588\pi$
$522$		0			0
$523$	−0.111208	+	0.147263i	−0.111208	+	0.147263i	−0.850217	−	0.526432i	$-0.823529\pi$
$523$	−0.111208	+	0.147263i	−0.111208	+	0.147263i	0.739009	+	0.673696i	$0.235294\pi$
$524$	0.329838	−	0.436776i	0.329838	−	0.436776i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.479620	−	0.963208i	0.479620	−	0.963208i
$529$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$530$		0			0
$531$	−2.51054	−	0.469302i	−2.51054	−	0.469302i
$532$		0			0
$533$		0			0
$534$	2.47048	−	2.25214i	2.47048	−	2.25214i
$535$		0			0
$536$	1.93247	+	0.361242i	1.93247	+	0.361242i
$537$	1.75108	+	2.31880i	1.75108	+	2.31880i
$538$		0			0
$539$	−0.0505009	+	0.544991i	−0.0505009	+	0.544991i
$540$		0			0
$541$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$541$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$542$		0			0
$543$		0			0
$544$	0.329838	+	0.436776i	0.329838	+	0.436776i
$545$		0			0
$546$		0			0
$547$	1.47802			1.47802			0.739009	−	0.673696i	$-0.235294\pi$
$547$	1.47802			1.47802			0.739009	+	0.673696i	$0.235294\pi$
$548$	0.932472	+	0.361242i	0.932472	+	0.361242i
$549$		0			0
$550$	−0.243964	+	0.489946i	−0.243964	+	0.489946i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.93247	−	0.361242i	1.93247	−	0.361242i
$557$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$557$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.549161	−	0.212746i	−0.549161	−	0.212746i
$562$	−1.45285	+	1.32445i	−1.45285	+	1.32445i
$563$	1.73901	+	0.673696i	1.73901	+	0.673696i	1.00000			$0$
$563$	1.73901	+	0.673696i	1.73901	+	0.673696i	0.739009	+	0.673696i	$0.235294\pi$
$564$		0			0
$565$		0			0
$566$	−0.156896	−	0.0971461i	−0.156896	−	0.0971461i
$567$		0			0
$568$		0			0
$569$	0.172075	−	0.0666624i	0.172075	−	0.0666624i	−0.273663	−	0.961826i	$-0.588235\pi$
$569$	0.172075	−	0.0666624i	0.172075	−	0.0666624i	0.445738	+	0.895163i	$0.352941\pi$
$570$		0			0
$571$	−0.510366	+	1.79375i	−0.510366	+	1.79375i	0.0922684	+	0.995734i	$0.470588\pi$
$571$	−0.510366	+	1.79375i	−0.510366	+	1.79375i	−0.602635	+	0.798017i	$0.705882\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.784029	−	2.75558i	−0.784029	−	2.75558i
$577$	−0.0505009	+	0.177492i	−0.0505009	+	0.177492i	−0.982973	−	0.183750i	$-0.941176\pi$
$577$	−0.0505009	+	0.177492i	−0.0505009	+	0.177492i	0.932472	+	0.361242i	$0.117647\pi$
$578$	−0.517627	+	0.471880i	−0.517627	+	0.471880i
$579$	−2.01458	+	1.24738i	−2.01458	+	1.24738i
$580$		0			0
$581$		0			0
$582$	−1.42794	+	1.89090i	−1.42794	+	1.89090i
$583$		0			0
$584$	−1.25664	+	0.778076i	−1.25664	+	0.778076i
$585$		0			0
$586$		0			0
$587$	−1.58561	+	0.614268i	−1.58561	+	0.614268i	−0.982973	−	0.183750i	$-0.941176\pi$
$587$	−1.58561	+	0.614268i	−1.58561	+	0.614268i	−0.602635	+	0.798017i	$0.705882\pi$
$588$	1.18475	+	1.56886i	1.18475	+	1.56886i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.831277	−	0.322039i	0.831277	−	0.322039i	0.0922684	−	0.995734i	$-0.470588\pi$
$593$	0.831277	−	0.322039i	0.831277	−	0.322039i	0.739009	+	0.673696i	$0.235294\pi$
$594$	1.48297	+	1.35191i	1.48297	+	1.35191i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$599$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$600$	0.538007	+	1.89090i	0.538007	+	1.89090i
$601$	−1.58561	−	0.981767i	−1.58561	−	0.981767i	−0.982973	−	0.183750i	$-0.941176\pi$
$601$	−1.58561	−	0.981767i	−1.58561	−	0.981767i	−0.602635	−	0.798017i	$-0.705882\pi$
$602$		0			0
$603$	−2.51054	+	5.04185i	−2.51054	+	5.04185i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$607$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$608$	0.538007	+	1.89090i	0.538007	+	1.89090i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.46217	+	0.566448i	−1.46217	+	0.566448i
$613$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$613$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$614$	1.18475	−	1.56886i	1.18475	−	1.56886i
$615$		0			0
$616$		0			0
$617$	−0.757949	−	1.52217i	−0.757949	−	1.52217i	−0.850217	−	0.526432i	$-0.823529\pi$
$617$	−0.757949	−	1.52217i	−0.757949	−	1.52217i	0.0922684	−	0.995734i	$-0.470588\pi$
$618$		0			0
$619$	−0.111208	+	0.147263i	−0.111208	+	0.147263i	−0.850217	−	0.526432i	$-0.823529\pi$
$619$	−0.111208	+	0.147263i	−0.111208	+	0.147263i	0.739009	+	0.673696i	$0.235294\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$626$	−0.156896	+	1.69318i	−0.156896	+	1.69318i
$627$	−1.56329	−	1.42513i	−1.56329	−	1.42513i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$631$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$632$		0			0
$633$	0.479620	+	1.68569i	0.479620	+	1.68569i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.0505009	+	0.177492i	−0.0505009	+	0.177492i	−0.982973	−	0.183750i	$-0.941176\pi$
$641$	−0.0505009	+	0.177492i	−0.0505009	+	0.177492i	0.932472	+	0.361242i	$0.117647\pi$
$642$	3.11722	+	1.93010i	3.11722	+	1.93010i
$643$	0.0170269	−	0.183750i	0.0170269	−	0.183750i	−0.982973	−	0.183750i	$-0.941176\pi$
$643$	0.0170269	−	0.183750i	0.0170269	−	0.183750i	1.00000			$0$
$644$		0			0
$645$		0			0
$646$	1.00335	−	0.388701i	1.00335	−	0.388701i
$647$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$647$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$648$	4.34296			4.34296
$649$	0.414845	−	0.256861i	0.414845	−	0.256861i
$650$		0			0
$651$		0			0
$652$	1.18475	+	0.221468i	1.18475	+	0.221468i
$653$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$653$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$654$		0			0
$655$		0			0
$656$	−0.404479	+	1.42160i	−0.404479	+	1.42160i
$657$	−1.15881	−	4.07279i	−1.15881	−	4.07279i
$658$		0			0
$659$	1.37821	−	1.25640i	1.37821	−	1.25640i	0.445738	−	0.895163i	$-0.352941\pi$
$659$	1.37821	−	1.25640i	1.37821	−	1.25640i	0.932472	−	0.361242i	$-0.117647\pi$
$660$		0			0
$661$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$661$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$662$	−0.547326	+	1.92365i	−0.547326	+	1.92365i
$663$		0			0
$664$	1.73901	−	0.673696i	1.73901	−	0.673696i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.538007	+	0.100571i	0.538007	+	0.100571i	0.445738	−	0.895163i	$-0.352941\pi$
$673$	0.538007	+	0.100571i	0.538007	+	0.100571i	0.0922684	+	0.995734i	$0.470588\pi$
$674$	−0.890705	−	1.17948i	−0.890705	−	1.17948i
$675$	−3.66638			−3.66638
$676$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$677$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$677$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$678$	−2.70949	−	1.04966i	−2.70949	−	1.04966i
$679$		0			0
$680$		0			0
$681$	2.20949	+	2.92583i	2.20949	+	2.92583i
$682$		0			0
$683$	0.658809	−	1.32307i	0.658809	−	1.32307i	−0.273663	−	0.961826i	$-0.588235\pi$
$683$	0.658809	−	1.32307i	0.658809	−	1.32307i	0.932472	−	0.361242i	$-0.117647\pi$
$684$	−5.63233			−5.63233
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.404479	+	0.368731i	−0.404479	+	0.368731i
$689$		0			0
$690$		0			0
$691$	−0.547326	−	1.92365i	−0.547326	−	1.92365i	−0.273663	−	0.961826i	$-0.588235\pi$
$691$	−0.547326	−	1.92365i	−0.547326	−	1.92365i	−0.273663	−	0.961826i	$-0.588235\pi$
$692$		0			0
$693$		0			0
$694$	0.0170269	−	0.183750i	0.0170269	−	0.183750i
$695$		0			0
$696$		0			0
$697$	0.795184	+	0.148646i	0.795184	+	0.148646i
$698$		0			0
$699$	1.75108	−	1.59632i	1.75108	−	1.59632i
$700$		0			0
$701$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$701$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$702$		0			0
$703$		0			0
$704$	0.465346	+	0.288130i	0.465346	+	0.288130i
$705$		0			0
$706$	1.73901	−	0.673696i	1.73901	−	0.673696i
$707$		0			0
$708$	0.479620	−	1.68569i	0.479620	−	1.68569i
$709$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$709$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$710$		0			0
$711$		0			0
$712$	1.02474	+	1.35698i	1.02474	+	1.35698i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.25664	+	0.778076i	−1.25664	+	0.778076i
$717$		0			0
$718$		0			0
$719$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$719$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$720$		0			0
$721$		0			0
$722$	2.86494			2.86494
$723$	−2.01458	+	1.24738i	−2.01458	+	1.24738i
$724$		0			0
$725$		0			0
$726$	1.37702			1.37702
$727$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$727$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$728$		0			0
$729$	−1.43247	+	5.03462i	−1.43247	+	5.03462i
$730$		0			0
$731$	0.221382	+	0.201816i	0.221382	+	0.201816i
$732$		0			0
$733$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$733$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.294465	−	1.03494i	−0.294465	−	1.03494i
$738$	−3.60019	−	2.22914i	−3.60019	−	2.22914i
$739$	−0.876298	+	0.163808i	−0.876298	+	0.163808i	−0.602635	−	0.798017i	$-0.705882\pi$
$739$	−0.876298	+	0.163808i	−0.876298	+	0.163808i	−0.273663	+	0.961826i	$0.588235\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$743$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.492986	+	5.32017i	0.492986	+	5.32017i
$748$	0.133528	−	0.268160i	0.133528	−	0.268160i
$749$		0			0
$750$		0			0
$751$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$751$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$752$		0			0
$753$	0.479620	+	0.963208i	0.479620	+	0.963208i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$757$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$758$	−1.12388	+	0.435393i	−1.12388	+	0.435393i
$759$		0			0
$760$		0			0
$761$	0.172075	+	1.85699i	0.172075	+	1.85699i	0.445738	+	0.895163i	$0.352941\pi$
$761$	0.172075	+	1.85699i	0.172075	+	1.85699i	−0.273663	+	0.961826i	$0.588235\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.93247	−	0.361242i	1.93247	−	0.361242i
$769$	−0.757949	−	0.469302i	−0.757949	−	0.469302i	0.0922684	−	0.995734i	$-0.470588\pi$
$769$	−0.757949	−	0.469302i	−0.757949	−	0.469302i	−0.850217	+	0.526432i	$0.823529\pi$
$770$		0			0
$771$	2.47048	−	1.52966i	2.47048	−	1.52966i
$772$	−0.537235	−	1.07891i	−0.537235	−	1.07891i
$773$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$773$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$774$	−0.698944	−	1.40367i	−0.698944	−	1.40367i
$775$		0			0
$776$	−0.890705	−	0.811985i	−0.890705	−	0.811985i
$777$		0			0
$778$		0			0
$779$	2.47048	+	1.52966i	2.47048	+	1.52966i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$785$		0			0
$786$	−0.914845	+	0.566448i	−0.914845	+	0.566448i
$787$	−0.111208	−	1.20013i	−0.111208	−	1.20013i	−0.850217	−	0.526432i	$-0.823529\pi$
$787$	−0.111208	−	1.20013i	−0.111208	−	1.20013i	0.739009	−	0.673696i	$-0.235294\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−1.15881	+	1.05639i	−1.15881	+	1.05639i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$797$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$798$		0			0
$799$		0			0
$800$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$801$	−4.54268	+	1.75984i	−4.54268	+	1.75984i
$802$	0.0822551	−	0.165190i	0.0822551	−	0.165190i
$803$	0.687790	+	0.425861i	0.687790	+	0.425861i
$804$	−3.28604	−	2.03463i	−3.28604	−	2.03463i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.831277	+	0.322039i	0.831277	+	0.322039i	0.739009	−	0.673696i	$-0.235294\pi$
$809$	0.831277	+	0.322039i	0.831277	+	0.322039i	0.0922684	+	0.995734i	$0.470588\pi$
$810$		0			0
$811$	−0.537235	−	0.711414i	−0.537235	−	0.711414i	0.445738	−	0.895163i	$-0.352941\pi$
$811$	−0.537235	−	0.711414i	−0.537235	−	0.711414i	−0.982973	+	0.183750i	$0.941176\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.294465	−	1.03494i	−0.294465	−	1.03494i
$817$	0.479620	+	0.963208i	0.479620	+	0.963208i
$818$	0.726337	+	0.961826i	0.726337	+	0.961826i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	−1.45285	−	1.32445i	−1.45285	−	1.32445i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	0.795184	−	0.724906i	0.795184	−	0.724906i
$826$		0			0
$827$	0.658809	+	1.32307i	0.658809	+	1.32307i	0.932472	+	0.361242i	$0.117647\pi$
$827$	0.658809	+	1.32307i	0.658809	+	1.32307i	−0.273663	+	0.961826i	$0.588235\pi$
$828$		0			0
$829$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$829$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.329838	+	0.436776i	0.329838	+	0.436776i
$834$	−3.79914	−	0.710182i	−3.79914	−	0.710182i
$835$		0			0
$836$	0.795184	−	0.724906i	0.795184	−	0.724906i
$837$		0			0
$838$	0.329838	−	1.15926i	0.329838	−	1.15926i
$839$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$839$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$840$		0			0
$841$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$842$		0			0
$843$	3.60395	−	1.39618i	3.60395	−	1.39618i
$844$	−0.876298	+	0.163808i	−0.876298	+	0.163808i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.218629	+	0.289512i	0.218629	+	0.289512i
$850$	0.149783	+	0.526432i	0.149783	+	0.526432i
$851$		0			0
$852$		0			0
$853$		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
$856$	−1.12388	+	1.48826i	−1.12388	+	1.48826i
$857$	−0.181395	−	1.95756i	−0.181395	−	1.95756i	−0.273663	−	0.961826i	$-0.588235\pi$
$857$	−0.181395	−	1.95756i	−0.181395	−	1.95756i	0.0922684	−	0.995734i	$-0.470588\pi$
$858$		0			0
$859$	1.47802			1.47802			0.739009	−	0.673696i	$-0.235294\pi$
$859$	1.47802			1.47802			0.739009	+	0.673696i	$0.235294\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	−0.338291	+	3.65074i	−0.338291	+	3.65074i
$865$		0			0
$866$	0.329838	−	1.15926i	0.329838	−	1.15926i
$867$	1.28403	−	0.497436i	1.28403	−	0.497436i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	2.93582	−	1.81779i	2.93582	−	1.81779i
$874$		0			0
$875$		0			0
$876$	2.85623	−	0.533922i	2.85623	−	0.533922i
$877$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$877$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.111208	+	1.20013i	−0.111208	+	1.20013i	0.739009	+	0.673696i	$0.235294\pi$
$881$	−0.111208	+	1.20013i	−0.111208	+	1.20013i	−0.850217	+	0.526432i	$0.823529\pi$
$882$	−0.784029	−	2.75558i	−0.784029	−	2.75558i
$883$	−0.181395	−	1.95756i	−0.181395	−	1.95756i	−0.273663	−	0.961826i	$-0.588235\pi$
$883$	−0.181395	−	1.95756i	−0.181395	−	1.95756i	0.0922684	−	0.995734i	$-0.470588\pi$
$884$		0			0
$885$		0			0
$886$	−1.12388	+	0.435393i	−1.12388	+	0.435393i
$887$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$887$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.05953	−	2.12782i	−1.05953	−	2.12782i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.111208	−	1.20013i	−0.111208	−	1.20013i
$899$		0			0
$900$	0.264344	−	2.85272i	0.264344	−	2.85272i
$901$		0			0
$902$	0.795184	−	0.148646i	0.795184	−	0.148646i
$903$		0			0
$904$	0.658809	−	1.32307i	0.658809	−	1.32307i
$905$		0			0
$906$		0			0
$907$	−0.510366	−	1.79375i	−0.510366	−	1.79375i	−0.602635	−	0.798017i	$-0.705882\pi$
$907$	−0.510366	−	1.79375i	−0.510366	−	1.79375i	0.0922684	−	0.995734i	$-0.470588\pi$
$908$	−1.58561	+	0.981767i	−1.58561	+	0.981767i
$909$		0			0
$910$		0			0
$911$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$911$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$912$	0.356612	−	3.84846i	0.356612	−	3.84846i
$913$	−0.754330	−	0.687663i	−0.754330	−	0.687663i
$914$	−0.510366	+	0.197717i	−0.510366	+	0.197717i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	2.00671			2.00671
$919$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$919$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$920$		0			0
$921$	−3.28604	+	2.03463i	−3.28604	+	2.03463i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.25664	+	1.14558i	−1.25664	+	1.14558i	−0.273663	+	0.961826i	$0.588235\pi$
$929$	−1.25664	+	1.14558i	−1.25664	+	1.14558i	−0.982973	+	0.183750i	$0.941176\pi$
$930$		0			0
$931$	0.538007	+	1.89090i	0.538007	+	1.89090i
$932$	0.726337	+	0.961826i	0.726337	+	0.961826i
$933$		0			0
$934$	−0.890705	+	1.17948i	−0.890705	+	1.17948i
$935$		0			0
$936$		0			0
$937$	−0.181395	+	0.0339085i	−0.181395	+	0.0339085i	−0.273663	−	0.961826i	$-0.588235\pi$
$937$	−0.181395	+	0.0339085i	−0.181395	+	0.0339085i	0.0922684	+	0.995734i	$0.470588\pi$
$938$		0			0
$939$	1.49009	−	2.99250i	1.49009	−	2.99250i
$940$		0			0
$941$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$941$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$942$		0			0
$943$		0			0
$944$	0.831277	+	0.322039i	0.831277	+	0.322039i
$945$		0			0
$946$	0.279337	+	0.108216i	0.279337	+	0.108216i
$947$	−0.876298	−	0.163808i	−0.876298	−	0.163808i	−0.273663	−	0.961826i	$-0.588235\pi$
$947$	−0.876298	−	0.163808i	−0.876298	−	0.163808i	−0.602635	+	0.798017i	$0.705882\pi$
$948$		0			0
$949$		0			0
$950$	−0.181395	+	1.95756i	−0.181395	+	1.95756i
$951$		0			0
$952$		0			0
$953$	0.465346	+	1.63552i	0.465346	+	1.63552i	0.739009	+	0.673696i	$0.235294\pi$
$953$	0.465346	+	1.63552i	0.465346	+	1.63552i	−0.273663	+	0.961826i	$0.588235\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.445738	−	0.895163i	0.445738	−	0.895163i
$962$		0			0
$963$	−3.21985	−	4.26378i	−3.21985	−	4.26378i
$964$	−0.537235	−	1.07891i	−0.537235	−	1.07891i
$965$		0			0
$966$		0			0
$967$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$967$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$968$	−0.0646279	+	0.697446i	−0.0646279	+	0.697446i
$969$	−2.11538			−2.11538
$970$		0			0
$971$	−0.181395	−	0.0339085i	−0.181395	−	0.0339085i	0.0922684	−	0.995734i	$-0.470588\pi$
$971$	−0.181395	−	0.0339085i	−0.181395	−	0.0339085i	−0.273663	+	0.961826i	$0.588235\pi$
$972$	−4.54268	−	1.75984i	−4.54268	−	1.75984i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.70043	−	1.05286i	−1.70043	−	1.05286i	−0.850217	−	0.526432i	$-0.823529\pi$
$977$	−1.70043	−	1.05286i	−1.70043	−	1.05286i	−0.850217	−	0.526432i	$-0.823529\pi$
$978$	−2.01458	−	1.24738i	−2.01458	−	1.24738i
$979$	0.414845	−	0.833121i	0.414845	−	0.833121i
$980$		0			0
$981$		0			0
$982$	−0.243964	+	0.857445i	−0.243964	+	0.857445i
$983$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$983$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$984$	1.75108	−	2.31880i	1.75108	−	2.31880i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$991$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$992$		0			0
$993$	2.36949	−	3.13772i	2.36949	−	3.13772i
$994$		0			0
$995$		0			0
$996$	−3.66638			−3.66638
$997$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$997$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$998$	0.172075	−	0.0666624i	0.172075	−	0.0666624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1096.1.s.a.59.1	✓	16
8.3	odd	2	CM	1096.1.s.a.59.1	✓	16
137.72	even	17	inner	1096.1.s.a.483.1	yes	16
1096.483	odd	34	inner	1096.1.s.a.483.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1096.1.s.a.59.1	✓	16	1.1	even	1	trivial
1096.1.s.a.59.1	✓	16	8.3	odd	2	CM
1096.1.s.a.483.1	yes	16	137.72	even	17	inner
1096.1.s.a.483.1	yes	16	1096.483	odd	34	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1096 = 2^{3} \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1096.s (of order \(34\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.445738 - 0.895163i) q^{2} +(-1.45285 + 1.32445i) q^{3} +(-0.602635 - 0.798017i) q^{4} +(0.538007 + 1.89090i) q^{6} +(-0.982973 + 0.183750i) q^{8} +(0.264344 - 2.85272i) q^{9} +O(q^{10})\)	\(q+(0.445738 - 0.895163i) q^{2} +(-1.45285 + 1.32445i) q^{3} +(-0.602635 - 0.798017i) q^{4} +(0.538007 + 1.89090i) q^{6} +(-0.982973 + 0.183750i) q^{8} +(0.264344 - 2.85272i) q^{9} +(0.329838 + 0.436776i) q^{11} +(1.93247 + 0.361242i) q^{12} +(-0.273663 + 0.961826i) q^{16} +(0.538007 + 0.100571i) q^{17} +(-2.43582 - 1.50820i) q^{18} +(1.67148 + 1.03494i) q^{19} +(0.538007 - 0.100571i) q^{22} +(1.18475 - 1.56886i) q^{24} +(-0.602635 + 0.798017i) q^{25} +(2.20949 + 2.92583i) q^{27} +(0.739009 + 0.673696i) q^{32} +(-1.05769 - 0.197717i) q^{33} +(0.329838 - 0.436776i) q^{34} +(-2.43582 + 1.50820i) q^{36} +(1.67148 - 1.03494i) q^{38} +1.47802 q^{41} +(0.465346 + 0.288130i) q^{43} +(0.149783 - 0.526432i) q^{44} +(-0.876298 - 1.75984i) q^{48} +(0.739009 + 0.673696i) q^{49} +(0.445738 + 0.895163i) q^{50} +(-0.914845 + 0.566448i) q^{51} +(3.60395 - 0.673696i) q^{54} +(-3.79914 + 0.710182i) q^{57} +(0.0822551 - 0.887674i) q^{59} +(0.932472 - 0.361242i) q^{64} +(-0.648443 + 0.858677i) q^{66} +(-1.83319 - 0.710182i) q^{67} +(-0.243964 - 0.489946i) q^{68} +(0.264344 + 2.85272i) q^{72} +(1.37821 - 0.533922i) q^{73} +(-0.181395 - 1.95756i) q^{75} +(-0.181395 - 1.95756i) q^{76} +(-4.26902 - 0.798017i) q^{81} +(0.658809 - 1.32307i) q^{82} +(-1.83319 + 0.342683i) q^{83} +(0.465346 - 0.288130i) q^{86} +(-0.404479 - 0.368731i) q^{88} +(-0.757949 - 1.52217i) q^{89} -1.96595 q^{96} +(0.726337 + 0.961826i) q^{97} +(0.932472 - 0.361242i) q^{98} +(1.33319 - 0.825476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 16 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9	\( 16 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} + 15 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{22} - 2 q^{24} - q^{25} - 4 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} - 2 q^{38} - 2 q^{41} - 2 q^{43} + 15 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} + 13 q^{54} - 4 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - 2 q^{76} - 5 q^{81} - 2 q^{82} - 2 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} + 15 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9 - 2 * q^11 + 15 * q^12 - q^16 - 2 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^22 - 2 * q^24 - q^25 - 4 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 - 2 * q^38 - 2 * q^41 - 2 * q^43 + 15 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 + 13 * q^54 - 4 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 - 2 * q^75 - 2 * q^76 - 5 * q^81 - 2 * q^82 - 2 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 + 15 * q^97 - q^98 - 6 * q^99

Introduction

L-functions

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