LMFDB - Embedded newform 1096.1.u.a.355.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1096,1,Mod(99,1096)]

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, 31]))

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

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

chi := DirichletCharacter("1096.99");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1096 = 2^{3} \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1096.u (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:	$D_{34}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{34} - \cdots)$

Embedding invariants

Embedding label			355.1
Root			$0.602635 + 0.798017i$ of defining polynomial
Character	$\chi$	$=$	1096.355
Dual form			1096.1.u.a.707.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.602635 + 0.798017i) q^{2} +(-0.719401 - 0.0666624i) q^{3} +(-0.273663 + 0.961826i) q^{4} +(-0.380338 - 0.614268i) q^{6} +(-0.932472 + 0.361242i) q^{8} +(-0.469879 - 0.0878355i) q^{9} +O(q^{10})$	\(q+(0.602635 + 0.798017i) q^{2} +(-0.719401 - 0.0666624i) q^{3} +(-0.273663 + 0.961826i) q^{4} +(-0.380338 - 0.614268i) q^{6} +(-0.932472 + 0.361242i) q^{8} +(-0.469879 - 0.0878355i) q^{9} +(-0.465346 + 1.63552i) q^{11} +(0.260991 - 0.673696i) q^{12} +(-0.850217 - 0.526432i) q^{16} +(-1.58561 - 0.614268i) q^{17} +(-0.213071 - 0.427904i) q^{18} +(0.831277 + 1.66943i) q^{19} +(-1.58561 + 0.614268i) q^{22} +(0.694903 - 0.197717i) q^{24} +(0.273663 + 0.961826i) q^{25} +(1.02708 + 0.292229i) q^{27} +(-0.0922684 - 0.995734i) q^{32} +(0.443798 - 1.14558i) q^{33} +(-0.465346 - 1.63552i) q^{34} +(0.213071 - 0.427904i) q^{36} +(-0.831277 + 1.66943i) q^{38} -1.99147i q^{41} +(-0.942485 + 0.469302i) q^{43} +(-1.44574 - 0.895163i) q^{44} +(0.576554 + 0.435393i) q^{48} +(0.0922684 + 0.995734i) q^{49} +(-0.602635 + 0.798017i) q^{50} +(1.09974 + 0.547605i) q^{51} +(0.385749 + 0.995734i) q^{54} +(-0.486734 - 1.25640i) q^{57} +(1.18475 + 0.221468i) q^{59} +(0.739009 - 0.673696i) q^{64} +(1.18164 - 0.336205i) q^{66} +(0.486734 - 0.533922i) q^{67} +(1.02474 - 1.35698i) q^{68} +(0.469879 - 0.0878355i) q^{72} +(-0.136374 + 0.124322i) q^{73} +(-0.132756 - 0.710182i) q^{75} +(-1.83319 + 0.342683i) q^{76} +(-0.273663 - 0.106018i) q^{81} +(1.58923 - 1.20013i) q^{82} +(-0.486734 - 1.25640i) q^{83} +(-0.942485 - 0.469302i) q^{86} +(-0.156896 - 1.69318i) q^{88} +(1.42871 + 1.07891i) q^{89} +0.722483i q^{96} +(1.85022 + 0.526432i) q^{97} +(-0.739009 + 0.673696i) q^{98} +(0.362313 - 0.727623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - q^{4} + q^{8} - q^{9}+O(q^{10}) $ 16 * q + q^2 - q^4 + q^8 - q^9	$ 16 q + q^{2} - q^{4} + q^{8} - q^{9} + 2 q^{11} + 17 q^{12} - q^{16} - 2 q^{17} + q^{18} - 2 q^{19} - 2 q^{22} + q^{25} + q^{32} + 2 q^{34} - q^{36} + 2 q^{38} - 15 q^{44} - q^{49} - q^{50} - 17 q^{54} - 2 q^{59} - q^{64} - 2 q^{68} + q^{72} + 2 q^{73} - 2 q^{76} - q^{81} - 2 q^{88} + 17 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) $ 16 * q + q^2 - q^4 + q^8 - q^9 + 2 * q^11 + 17 * q^12 - q^16 - 2 * q^17 + q^18 - 2 * q^19 - 2 * q^22 + q^25 + q^32 + 2 * q^34 - q^36 + 2 * q^38 - 15 * q^44 - q^49 - q^50 - 17 * q^54 - 2 * q^59 - q^64 - 2 * q^68 + q^72 + 2 * q^73 - 2 * q^76 - q^81 - 2 * q^88 + 17 * q^97 + q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$549$	$823$	$825$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{34}\right)$

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 $

$2$	0.602635	+	0.798017i	0.602635	+	0.798017i
$2$	0.602635	+	0.798017i	0.602635	+	0.798017i
$3$	−0.719401	−	0.0666624i	−0.719401	−	0.0666624i	−0.273663	−	0.961826i	$-0.588235\pi$
$3$	−0.719401	−	0.0666624i	−0.719401	−	0.0666624i	−0.445738	+	0.895163i	$0.647059\pi$
$4$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$5$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$5$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$6$	−0.380338	−	0.614268i	−0.380338	−	0.614268i
$7$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$7$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$8$	−0.932472	+	0.361242i	−0.932472	+	0.361242i
$9$	−0.469879	−	0.0878355i	−0.469879	−	0.0878355i
$10$		0			0
$11$	−0.465346	+	1.63552i	−0.465346	+	1.63552i	0.273663	+	0.961826i	$0.411765\pi$
$11$	−0.465346	+	1.63552i	−0.465346	+	1.63552i	−0.739009	+	0.673696i	$0.764706\pi$
$12$	0.260991	−	0.673696i	0.260991	−	0.673696i
$13$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$13$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$14$		0			0
$15$		0			0
$16$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$17$	−1.58561	−	0.614268i	−1.58561	−	0.614268i	−0.602635	−	0.798017i	$-0.705882\pi$
$17$	−1.58561	−	0.614268i	−1.58561	−	0.614268i	−0.982973	+	0.183750i	$0.941176\pi$
$18$	−0.213071	−	0.427904i	−0.213071	−	0.427904i
$19$	0.831277	+	1.66943i	0.831277	+	1.66943i	0.739009	+	0.673696i	$0.235294\pi$
$19$	0.831277	+	1.66943i	0.831277	+	1.66943i	0.0922684	+	0.995734i	$0.470588\pi$
$20$		0			0
$21$		0			0
$22$	−1.58561	+	0.614268i	−1.58561	+	0.614268i
$23$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$23$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$24$	0.694903	−	0.197717i	0.694903	−	0.197717i
$25$	0.273663	+	0.961826i	0.273663	+	0.961826i
$26$		0			0
$27$	1.02708	+	0.292229i	1.02708	+	0.292229i
$28$		0			0
$29$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$29$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$30$		0			0
$31$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$31$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$32$	−0.0922684	−	0.995734i	−0.0922684	−	0.995734i
$33$	0.443798	−	1.14558i	0.443798	−	1.14558i
$34$	−0.465346	−	1.63552i	−0.465346	−	1.63552i
$35$		0			0
$36$	0.213071	−	0.427904i	0.213071	−	0.427904i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−0.831277	+	1.66943i	−0.831277	+	1.66943i
$39$		0			0
$40$		0			0
$41$		−	1.99147i		−	1.99147i	−0.0922684	−	0.995734i	$-0.529412\pi$
$41$		−	1.99147i		−	1.99147i	0.0922684	−	0.995734i	$-0.470588\pi$
$42$		0			0
$43$	−0.942485	+	0.469302i	−0.942485	+	0.469302i	−0.850217	−	0.526432i	$-0.823529\pi$
$43$	−0.942485	+	0.469302i	−0.942485	+	0.469302i	−0.0922684	+	0.995734i	$0.529412\pi$
$44$	−1.44574	−	0.895163i	−1.44574	−	0.895163i
$45$		0			0
$46$		0			0
$47$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$47$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$48$	0.576554	+	0.435393i	0.576554	+	0.435393i
$49$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$50$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$51$	1.09974	+	0.547605i	1.09974	+	0.547605i
$52$		0			0
$53$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$53$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$54$	0.385749	+	0.995734i	0.385749	+	0.995734i
$55$		0			0
$56$		0			0
$57$	−0.486734	−	1.25640i	−0.486734	−	1.25640i
$58$		0			0
$59$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.739009	−	0.673696i	$-0.235294\pi$
$59$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.445738	+	0.895163i	$0.352941\pi$
$60$		0			0
$61$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$61$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$62$		0			0
$63$		0			0
$64$	0.739009	−	0.673696i	0.739009	−	0.673696i
$65$		0			0
$66$	1.18164	−	0.336205i	1.18164	−	0.336205i
$67$	0.486734	−	0.533922i	0.486734	−	0.533922i	−0.445738	−	0.895163i	$-0.647059\pi$
$67$	0.486734	−	0.533922i	0.486734	−	0.533922i	0.932472	+	0.361242i	$0.117647\pi$
$68$	1.02474	−	1.35698i	1.02474	−	1.35698i
$69$		0			0
$70$		0			0
$71$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$71$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$72$	0.469879	−	0.0878355i	0.469879	−	0.0878355i
$73$	−0.136374	+	0.124322i	−0.136374	+	0.124322i	−0.739009	−	0.673696i	$-0.764706\pi$
$73$	−0.136374	+	0.124322i	−0.136374	+	0.124322i	0.602635	+	0.798017i	$0.294118\pi$
$74$		0			0
$75$	−0.132756	−	0.710182i	−0.132756	−	0.710182i
$76$	−1.83319	+	0.342683i	−1.83319	+	0.342683i
$77$		0			0
$78$		0			0
$79$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$79$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$80$		0			0
$81$	−0.273663	−	0.106018i	−0.273663	−	0.106018i
$82$	1.58923	−	1.20013i	1.58923	−	1.20013i
$83$	−0.486734	−	1.25640i	−0.486734	−	1.25640i	−0.932472	−	0.361242i	$-0.882353\pi$
$83$	−0.486734	−	1.25640i	−0.486734	−	1.25640i	0.445738	−	0.895163i	$-0.352941\pi$
$84$		0			0
$85$		0			0
$86$	−0.942485	−	0.469302i	−0.942485	−	0.469302i
$87$		0			0
$88$	−0.156896	−	1.69318i	−0.156896	−	1.69318i
$89$	1.42871	+	1.07891i	1.42871	+	1.07891i	0.982973	+	0.183750i	$0.0588235\pi$
$89$	1.42871	+	1.07891i	1.42871	+	1.07891i	0.445738	+	0.895163i	$0.352941\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$			0.722483i			0.722483i
$97$	1.85022	+	0.526432i	1.85022	+	0.526432i	1.00000			$0$
$97$	1.85022	+	0.526432i	1.85022	+	0.526432i	0.850217	+	0.526432i	$0.176471\pi$
$98$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$99$	0.362313	−	0.727623i	0.362313	−	0.727623i
$100$	−1.00000			−1.00000
$101$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$101$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$102$	0.225743	+	1.20762i	0.225743	+	1.20762i
$103$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$103$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.136374	+	1.47171i	−0.136374	+	1.47171i	0.602635	+	0.798017i	$0.294118\pi$
$107$	−0.136374	+	1.47171i	−0.136374	+	1.47171i	−0.739009	+	0.673696i	$0.764706\pi$
$108$	−0.562147	+	0.907899i	−0.562147	+	0.907899i
$109$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$109$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.91545	−	0.544991i	1.91545	−	0.544991i	0.932472	−	0.361242i	$-0.117647\pi$
$113$	1.91545	−	0.544991i	1.91545	−	0.544991i	0.982973	−	0.183750i	$-0.0588235\pi$
$114$	0.709310	−	1.14558i	0.709310	−	1.14558i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.537235	+	1.07891i	0.537235	+	1.07891i
$119$		0			0
$120$		0			0
$121$	−1.60817	−	0.995734i	−1.60817	−	0.995734i
$122$		0			0
$123$	−0.132756	+	1.43267i	−0.132756	+	1.43267i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	0.982973	+	0.183750i	0.982973	+	0.183750i
$129$	0.709310	−	0.274788i	0.709310	−	0.274788i
$130$		0			0
$131$	−0.554262	−	0.895163i	−0.554262	−	0.895163i	0.445738	−	0.895163i	$-0.352941\pi$
$131$	−0.554262	−	0.895163i	−0.554262	−	0.895163i	−1.00000			$\pi$
$132$	0.980392	+	0.740358i	0.980392	+	0.740358i
$133$		0			0
$134$	0.719401	+	0.0666624i	0.719401	+	0.0666624i
$135$		0			0
$136$	1.70043			1.70043
$137$	−0.445738	+	0.895163i	−0.445738	+	0.895163i
$137$	−0.445738	+	0.895163i	−0.445738	+	0.895163i
$138$		0			0
$139$	1.12388	+	1.48826i	1.12388	+	1.48826i	0.850217	+	0.526432i	$0.176471\pi$
$139$	1.12388	+	1.48826i	1.12388	+	1.48826i	0.273663	+	0.961826i	$0.411765\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.353259	+	0.322039i	0.353259	+	0.322039i
$145$		0			0
$146$	−0.181395	−	0.0339085i	−0.181395	−	0.0339085i
$147$		−	0.722483i		−	0.722483i
$148$		0			0
$149$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$149$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$150$	0.486734	−	0.533922i	0.486734	−	0.533922i
$151$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$151$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$152$	−1.37821	−	1.25640i	−1.37821	−	1.25640i
$153$	0.691089	+	0.427904i	0.691089	+	0.427904i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$157$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.0803149	−	0.282278i	−0.0803149	−	0.282278i
$163$	−1.91545	−	0.177492i	−1.91545	−	0.177492i	−0.932472	−	0.361242i	$-0.882353\pi$
$163$	−1.91545	−	0.177492i	−1.91545	−	0.177492i	−0.982973	+	0.183750i	$0.941176\pi$
$164$	1.91545	+	0.544991i	1.91545	+	0.544991i
$165$		0			0
$166$	0.709310	−	1.14558i	0.709310	−	1.14558i
$167$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$167$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$168$		0			0
$169$	−0.0922684	−	0.995734i	−0.0922684	−	0.995734i
$170$		0			0
$171$	−0.243964	−	0.857445i	−0.243964	−	0.857445i
$172$	−0.193463	−	1.03494i	−0.193463	−	1.03494i
$173$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$173$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$174$		0			0
$175$		0			0
$176$	1.25664	−	1.14558i	1.25664	−	1.14558i
$177$	−0.837545	−	0.238302i	−0.837545	−	0.238302i
$178$			1.79033i			1.79033i
$179$	−0.365931	+	1.95756i	−0.365931	+	1.95756i	−0.0922684	+	0.995734i	$0.529412\pi$
$179$	−0.365931	+	1.95756i	−0.365931	+	1.95756i	−0.273663	+	0.961826i	$0.588235\pi$
$180$		0			0
$181$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$181$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.74250	−	2.30745i	1.74250	−	2.30745i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$191$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$192$	−0.576554	+	0.435393i	−0.576554	+	0.435393i
$193$	0.510366	+	0.197717i	0.510366	+	0.197717i	0.602635	−	0.798017i	$-0.294118\pi$
$193$	0.510366	+	0.197717i	0.510366	+	0.197717i	−0.0922684	+	0.995734i	$0.529412\pi$
$194$	0.694903	+	1.79375i	0.694903	+	1.79375i
$195$		0			0
$196$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$197$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$197$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$198$	0.798998	−	0.149359i	0.798998	−	0.149359i
$199$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$199$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$200$	−0.602635	−	0.798017i	−0.602635	−	0.798017i
$201$	−0.385749	+	0.351657i	−0.385749	+	0.351657i
$202$		0			0
$203$		0			0
$204$	−0.827659	+	0.907899i	−0.827659	+	0.907899i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.11722	+	0.582709i	−3.11722	+	0.582709i
$210$		0			0
$211$	−0.726337	−	0.961826i	−0.726337	−	0.961826i	0.273663	−	0.961826i	$-0.411765\pi$
$211$	−0.726337	−	0.961826i	−0.726337	−	0.961826i	−1.00000			$\pi$
$212$		0			0
$213$		0			0
$214$	−1.25664	+	0.778076i	−1.25664	+	0.778076i
$215$		0			0
$216$	−1.06329	+	0.0985281i	−1.06329	+	0.0985281i
$217$		0			0
$218$		0			0
$219$	0.106395	−	0.0803461i	0.106395	−	0.0803461i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$223$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$224$		0			0
$225$	−0.0441059	−	0.475979i	−0.0441059	−	0.475979i
$226$	1.58923	+	1.20013i	1.58923	+	1.20013i
$227$	0.247582	−	1.32445i	0.247582	−	1.32445i	−0.602635	−	0.798017i	$-0.705882\pi$
$227$	0.247582	−	1.32445i	0.247582	−	1.32445i	0.850217	−	0.526432i	$-0.176471\pi$
$228$	1.34164	−	0.124322i	1.34164	−	0.124322i
$229$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$229$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	1.92365i		−	1.92365i	−0.273663	−	0.961826i	$-0.588235\pi$
$233$		−	1.92365i		−	1.92365i	0.273663	−	0.961826i	$-0.411765\pi$
$234$		0			0
$235$		0			0
$236$	−0.537235	+	1.07891i	−0.537235	+	1.07891i
$237$		0			0
$238$		0			0
$239$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$239$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$240$		0			0
$241$	−0.694903	+	1.79375i	−0.694903	+	1.79375i	−0.0922684	+	0.995734i	$0.529412\pi$
$241$	−0.694903	+	1.79375i	−0.694903	+	1.79375i	−0.602635	+	0.798017i	$0.705882\pi$
$242$	−0.174523	−	1.88341i	−0.174523	−	1.88341i
$243$	−0.766088	−	0.381466i	−0.766088	−	0.381466i
$244$		0			0
$245$		0			0
$246$	−1.22329	+	0.757432i	−1.22329	+	0.757432i
$247$		0			0
$248$		0			0
$249$	0.266402	+	0.936306i	0.266402	+	0.936306i
$250$		0			0
$251$	−0.554262	+	0.895163i	−0.554262	+	0.895163i	0.445738	+	0.895163i	$0.352941\pi$
$251$	−0.554262	+	0.895163i	−0.554262	+	0.895163i	−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.445738	+	0.895163i	0.445738	+	0.895163i
$257$	−0.172075	−	0.0666624i	−0.172075	−	0.0666624i	0.273663	−	0.961826i	$-0.411765\pi$
$257$	−0.172075	−	0.0666624i	−0.172075	−	0.0666624i	−0.445738	+	0.895163i	$0.647059\pi$
$258$	0.646741	+	0.400445i	0.646741	+	0.400445i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.380338	−	0.981767i	0.380338	−	0.981767i
$263$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$263$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$264$			1.22854i			1.22854i
$265$		0			0
$266$		0			0
$267$	−0.955894	−	0.871413i	−0.955894	−	0.871413i
$268$	0.380338	+	0.614268i	0.380338	+	0.614268i
$269$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$269$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$270$		0			0
$271$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$271$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$272$	1.02474	+	1.35698i	1.02474	+	1.35698i
$273$		0			0
$274$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$275$	−1.70043			−1.70043
$276$		0			0
$277$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$277$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$278$	−0.510366	+	1.79375i	−0.510366	+	1.79375i
$279$		0			0
$280$		0			0
$281$	−1.37821	−	1.25640i	−1.37821	−	1.25640i	−0.932472	−	0.361242i	$-0.882353\pi$
$281$	−1.37821	−	1.25640i	−1.37821	−	1.25640i	−0.445738	−	0.895163i	$-0.647059\pi$
$282$		0			0
$283$	1.93247	+	0.361242i	1.93247	+	0.361242i	1.00000			$0$
$283$	1.93247	+	0.361242i	1.93247	+	0.361242i	0.932472	+	0.361242i	$0.117647\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0441059	+	0.475979i	−0.0441059	+	0.475979i
$289$	1.39782	+	1.27428i	1.39782	+	1.27428i
$290$		0			0
$291$	−1.29596	−	0.502056i	−1.29596	−	0.502056i
$292$	−0.0822551	−	0.165190i	−0.0822551	−	0.165190i
$293$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$293$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$294$	0.576554	−	0.435393i	0.576554	−	0.435393i
$295$		0			0
$296$		0			0
$297$	−0.955894	+	1.54382i	−0.955894	+	1.54382i
$298$		0			0
$299$		0			0
$300$	0.719401	+	0.0666624i	0.719401	+	0.0666624i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.172075	−	1.85699i	0.172075	−	1.85699i
$305$		0			0
$306$	0.0749992	+	0.809370i	0.0749992	+	0.809370i
$307$	0.260991	−	0.673696i	0.260991	−	0.673696i	−0.739009	−	0.673696i	$-0.764706\pi$
$307$	0.260991	−	0.673696i	0.260991	−	0.673696i	1.00000			$0$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$	0.658809	−	0.600584i	0.658809	−	0.600584i	−0.273663	−	0.961826i	$-0.588235\pi$
$313$	0.658809	−	0.600584i	0.658809	−	0.600584i	0.932472	+	0.361242i	$0.117647\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$317$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.196216	−	1.04966i	0.196216	−	1.04966i
$322$		0			0
$323$	−0.292603	−	3.15769i	−0.292603	−	3.15769i
$324$	0.176862	−	0.234203i	0.176862	−	0.234203i
$325$		0			0
$326$	−1.01267	−	1.63552i	−1.01267	−	1.63552i
$327$		0			0
$328$	0.719401	+	1.85699i	0.719401	+	1.85699i
$329$		0			0
$330$		0			0
$331$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$331$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$332$	1.34164	−	0.124322i	1.34164	−	0.124322i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.111208	+	0.147263i	0.111208	+	0.147263i	0.850217	−	0.526432i	$-0.176471\pi$
$337$	0.111208	+	0.147263i	0.111208	+	0.147263i	−0.739009	+	0.673696i	$0.764706\pi$
$338$	0.739009	−	0.673696i	0.739009	−	0.673696i
$339$	−1.41430	+	0.264379i	−1.41430	+	0.264379i
$340$		0			0
$341$		0			0
$342$	0.537235	−	0.711414i	0.537235	−	0.711414i
$343$		0			0
$344$	0.709310	−	0.778076i	0.709310	−	0.778076i
$345$		0			0
$346$		0			0
$347$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.602635	+	0.798017i	$0.705882\pi$
$347$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.850217	+	0.526432i	$0.823529\pi$
$348$		0			0
$349$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$349$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$350$		0			0
$351$		0			0
$352$	1.67148	+	0.312454i	1.67148	+	0.312454i
$353$	−1.34164	+	0.124322i	−1.34164	+	0.124322i	−0.739009	−	0.673696i	$-0.764706\pi$
$353$	−1.34164	+	0.124322i	−1.34164	+	0.124322i	−0.602635	+	0.798017i	$0.705882\pi$
$354$	−0.314565	−	0.811985i	−0.314565	−	0.811985i
$355$		0			0
$356$	−1.42871	+	1.07891i	−1.42871	+	1.07891i
$357$		0			0
$358$	−1.78269	+	0.887674i	−1.78269	+	0.887674i
$359$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$359$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$360$		0			0
$361$	−1.49334	+	1.97750i	−1.49334	+	1.97750i
$362$		0			0
$363$	1.09054	+	0.823537i	1.09054	+	0.823537i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$367$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$368$		0			0
$369$	−0.174922	+	0.935749i	−0.174922	+	0.935749i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$373$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$374$	2.89148			2.89148
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0505009	+	0.544991i	0.0505009	+	0.544991i	0.982973	+	0.183750i	$0.0588235\pi$
$379$	0.0505009	+	0.544991i	0.0505009	+	0.544991i	−0.932472	+	0.361242i	$0.882353\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$383$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$384$	−0.694903	−	0.197717i	−0.694903	−	0.197717i
$385$		0			0
$386$	0.149783	+	0.526432i	0.149783	+	0.526432i
$387$	0.484075	−	0.137731i	0.484075	−	0.137731i
$388$	−1.01267	+	1.63552i	−1.01267	+	1.63552i
$389$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$389$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$390$		0			0
$391$		0			0
$392$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$393$	0.339063	+	0.680930i	0.339063	+	0.680930i
$394$		0			0
$395$		0			0
$396$	0.600694	+	0.547605i	0.600694	+	0.547605i
$397$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$397$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$398$		0			0
$399$		0			0
$400$	0.273663	−	0.961826i	0.273663	−	0.961826i
$401$			0.367499i			0.367499i	0.982973	+	0.183750i	$0.0588235\pi$
$401$			0.367499i			0.367499i	−0.982973	+	0.183750i	$0.941176\pi$
$402$	−0.513094	−	0.0959140i	−0.513094	−	0.0959140i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.22329	−	0.113355i	−1.22329	−	0.113355i
$409$	−0.329838	−	0.436776i	−0.329838	−	0.436776i	0.602635	−	0.798017i	$-0.294118\pi$
$409$	−0.329838	−	0.436776i	−0.329838	−	0.436776i	−0.932472	+	0.361242i	$0.882353\pi$
$410$		0			0
$411$	0.380338	−	0.614268i	0.380338	−	0.614268i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.709310	−	1.14558i	−0.709310	−	1.14558i
$418$	−2.34356	−	2.13643i	−2.34356	−	2.13643i
$419$	0.510366	−	0.197717i	0.510366	−	0.197717i	−0.0922684	−	0.995734i	$-0.529412\pi$
$419$	0.510366	−	0.197717i	0.510366	−	0.197717i	0.602635	+	0.798017i	$0.294118\pi$
$420$		0			0
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$	0.329838	−	1.15926i	0.329838	−	1.15926i
$423$		0			0
$424$		0			0
$425$	0.156896	−	1.69318i	0.156896	−	1.69318i
$426$		0			0
$427$		0			0
$428$	−1.37821	−	0.533922i	−1.37821	−	0.533922i
$429$		0			0
$430$		0			0
$431$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$431$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$432$	−0.719401	−	0.789146i	−0.719401	−	0.789146i
$433$	0.510366	−	0.197717i	0.510366	−	0.197717i	−0.0922684	−	0.995734i	$-0.529412\pi$
$433$	0.510366	−	0.197717i	0.510366	−	0.197717i	0.602635	+	0.798017i	$0.294118\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.128235	+	0.0364860i	0.128235	+	0.0364860i
$439$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$439$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$440$		0			0
$441$	0.0441059	−	0.475979i	0.0441059	−	0.475979i
$442$		0			0
$443$	−0.0505009	−	0.544991i	−0.0505009	−	0.544991i	−0.982973	−	0.183750i	$-0.941176\pi$
$443$	−0.0505009	−	0.544991i	−0.0505009	−	0.544991i	0.932472	−	0.361242i	$-0.117647\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	−0.982973	−	0.183750i	$-0.941176\pi$
$449$	−0.243964	+	0.489946i	−0.243964	+	0.489946i	0.739009	+	0.673696i	$0.235294\pi$
$450$	0.353259	−	0.322039i	0.353259	−	0.322039i
$451$	3.25709	+	0.926722i	3.25709	+	0.926722i
$452$			1.99147i			1.99147i
$453$		0			0
$454$	1.20614	−	0.600584i	1.20614	−	0.600584i
$455$		0			0
$456$	0.907732	+	0.995734i	0.907732	+	0.995734i
$457$	1.04837	−	0.0971461i	1.04837	−	0.0971461i	0.445738	−	0.895163i	$-0.352941\pi$
$457$	1.04837	−	0.0971461i	1.04837	−	0.0971461i	0.602635	+	0.798017i	$0.294118\pi$
$458$		0			0
$459$	−1.44904	−	1.09426i	−1.44904	−	1.09426i
$460$		0			0
$461$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$461$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$462$		0			0
$463$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$463$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$464$		0			0
$465$		0			0
$466$	1.53511	−	1.15926i	1.53511	−	1.15926i
$467$	0.172075	+	0.0666624i	0.172075	+	0.0666624i	0.445738	−	0.895163i	$-0.352941\pi$
$467$	0.172075	+	0.0666624i	0.172075	+	0.0666624i	−0.273663	+	0.961826i	$0.588235\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.18475	+	0.221468i	−1.18475	+	0.221468i
$473$	−0.328972	−	1.75984i	−0.328972	−	1.75984i
$474$		0			0
$475$	−1.37821	+	1.25640i	−1.37821	+	1.25640i
$476$		0			0
$477$		0			0
$478$		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
$482$	−1.85022	+	0.526432i	−1.85022	+	0.526432i
$483$		0			0
$484$	1.39782	−	1.27428i	1.39782	−	1.27428i
$485$		0			0
$486$	−0.157254	−	0.841236i	−0.157254	−	0.841236i
$487$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$487$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$488$		0			0
$489$	1.36614	+	0.255376i	1.36614	+	0.255376i
$490$		0			0
$491$	0.576554	+	1.48826i	0.576554	+	1.48826i	0.850217	+	0.526432i	$0.176471\pi$
$491$	0.576554	+	1.48826i	0.576554	+	1.48826i	−0.273663	+	0.961826i	$0.588235\pi$
$492$	−1.34164	−	0.519755i	−1.34164	−	0.519755i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.586645	+	0.776844i	−0.586645	+	0.776844i
$499$	−0.181395	−	1.95756i	−0.181395	−	1.95756i	−0.273663	−	0.961826i	$-0.588235\pi$
$499$	−0.181395	−	1.95756i	−0.181395	−	1.95756i	0.0922684	−	0.995734i	$-0.470588\pi$
$500$		0			0
$501$		0			0
$502$	−1.04837	+	0.0971461i	−1.04837	+	0.0971461i
$503$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$503$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			0.722483i			0.722483i
$508$		0			0
$509$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$509$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$510$		0			0
$511$		0			0
$512$	−0.445738	+	0.895163i	−0.445738	+	0.895163i
$513$	0.365931	+	1.95756i	0.365931	+	1.95756i
$514$	−0.0505009	−	0.177492i	−0.0505009	−	0.177492i
$515$		0			0
$516$	0.0701864	+	0.757432i	0.0701864	+	0.757432i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.91545	+	0.544991i	1.91545	+	0.544991i	0.982973	+	0.183750i	$0.0588235\pi$
$521$	1.91545	+	0.544991i	1.91545	+	0.544991i	0.932472	+	0.361242i	$0.117647\pi$
$522$		0			0
$523$	−0.538007	−	1.89090i	−0.538007	−	1.89090i	−0.445738	−	0.895163i	$-0.647059\pi$
$523$	−0.538007	−	1.89090i	−0.538007	−	1.89090i	−0.0922684	−	0.995734i	$-0.529412\pi$
$524$	1.01267	−	0.288130i	1.01267	−	0.288130i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.980392	+	0.740358i	−0.980392	+	0.740358i
$529$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$530$		0			0
$531$	−0.537235	−	0.208126i	−0.537235	−	0.208126i
$532$		0			0
$533$		0			0
$534$	0.119347	−	1.28796i	0.119347	−	1.28796i
$535$		0			0
$536$	−0.260991	+	0.673696i	−0.260991	+	0.673696i
$537$	0.393747	−	1.38388i	0.393747	−	1.38388i
$538$		0			0
$539$	−1.67148	−	0.312454i	−1.67148	−	0.312454i
$540$		0			0
$541$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$541$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$542$		0			0
$543$		0			0
$544$	−0.465346	+	1.63552i	−0.465346	+	1.63552i
$545$		0			0
$546$		0			0
$547$	0.184537			0.184537			0.0922684	−	0.995734i	$-0.470588\pi$
$547$	0.184537			0.184537			0.0922684	+	0.995734i	$0.470588\pi$
$548$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$549$		0			0
$550$	−1.02474	−	1.35698i	−1.02474	−	1.35698i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.73901	+	0.673696i	−1.73901	+	0.673696i
$557$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$557$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1.40738	+	1.54382i	−1.40738	+	1.54382i
$562$	0.172075	−	1.85699i	0.172075	−	1.85699i
$563$	1.09227	+	0.995734i	1.09227	+	0.995734i	1.00000			$0$
$563$	1.09227	+	0.995734i	1.09227	+	0.995734i	0.0922684	+	0.995734i	$0.470588\pi$
$564$		0			0
$565$		0			0
$566$	0.876298	+	1.75984i	0.876298	+	1.75984i
$567$		0			0
$568$		0			0
$569$	0.247582	+	0.271585i	0.247582	+	0.271585i	0.850217	−	0.526432i	$-0.176471\pi$
$569$	0.247582	+	0.271585i	0.247582	+	0.271585i	−0.602635	+	0.798017i	$0.705882\pi$
$570$		0			0
$571$	0.709310	−	1.14558i	0.709310	−	1.14558i	−0.273663	−	0.961826i	$-0.588235\pi$
$571$	0.709310	−	1.14558i	0.709310	−	1.14558i	0.982973	−	0.183750i	$-0.0588235\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.406419	+	0.251644i	−0.406419	+	0.251644i
$577$	−0.193463	+	0.312454i	−0.193463	+	0.312454i	−0.932472	−	0.361242i	$-0.882353\pi$
$577$	−0.193463	+	0.312454i	−0.193463	+	0.312454i	0.739009	+	0.673696i	$0.235294\pi$
$578$	−0.174523	+	1.88341i	−0.174523	+	1.88341i
$579$	−0.353978	−	0.176260i	−0.353978	−	0.176260i
$580$		0			0
$581$		0			0
$582$	−0.380338	−	1.33675i	−0.380338	−	1.33675i
$583$		0			0
$584$	0.0822551	−	0.165190i	0.0822551	−	0.165190i
$585$		0			0
$586$		0			0
$587$	−0.658809	+	0.600584i	−0.658809	+	0.600584i	−0.932472	−	0.361242i	$-0.882353\pi$
$587$	−0.658809	+	0.600584i	−0.658809	+	0.600584i	0.273663	+	0.961826i	$0.411765\pi$
$588$	0.694903	+	0.197717i	0.694903	+	0.197717i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.07524	+	1.17948i	1.07524	+	1.17948i	0.982973	+	0.183750i	$0.0588235\pi$
$593$	1.07524	+	1.17948i	1.07524	+	1.17948i	0.0922684	+	0.995734i	$0.470588\pi$
$594$	−1.80805	+	0.167541i	−1.80805	+	0.167541i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$599$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$600$	0.380338	+	0.614268i	0.380338	+	0.614268i
$601$	1.20614	−	0.600584i	1.20614	−	0.600584i	0.273663	−	0.961826i	$-0.411765\pi$
$601$	1.20614	−	0.600584i	1.20614	−	0.600584i	0.932472	+	0.361242i	$0.117647\pi$
$602$		0			0
$603$	−0.275603	+	0.208126i	−0.275603	+	0.208126i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$607$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$608$	1.58561	−	0.981767i	1.58561	−	0.981767i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.600694	+	0.547605i	−0.600694	+	0.547605i
$613$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$613$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$614$	0.694903	−	0.197717i	0.694903	−	0.197717i
$615$		0			0
$616$		0			0
$617$	−0.537235	+	0.711414i	−0.537235	+	0.711414i	−0.982973	−	0.183750i	$-0.941176\pi$
$617$	−0.537235	+	0.711414i	−0.537235	+	0.711414i	0.445738	+	0.895163i	$0.352941\pi$
$618$		0			0
$619$	0.353470	−	0.100571i	0.353470	−	0.100571i	−0.0922684	−	0.995734i	$-0.529412\pi$
$619$	0.353470	−	0.100571i	0.353470	−	0.100571i	0.445738	+	0.895163i	$0.352941\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$626$	0.876298	+	0.163808i	0.876298	+	0.163808i
$627$	2.28138	−	0.211401i	2.28138	−	0.211401i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$631$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$632$		0			0
$633$	0.458410	+	0.740358i	0.458410	+	0.740358i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.67148	+	1.03494i	1.67148	+	1.03494i	0.932472	+	0.361242i	$0.117647\pi$
$641$	1.67148	+	1.03494i	1.67148	+	1.03494i	0.739009	+	0.673696i	$0.235294\pi$
$642$	0.955894	−	0.475979i	0.955894	−	0.475979i
$643$	−0.0675278	+	0.361242i	−0.0675278	+	0.361242i	0.932472	+	0.361242i	$0.117647\pi$
$643$	−0.0675278	+	0.361242i	−0.0675278	+	0.361242i	−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$	2.34356	−	2.13643i	2.34356	−	2.13643i
$647$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$647$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$648$	0.293481			0.293481
$649$	−0.913532	+	1.83462i	−0.913532	+	1.83462i
$650$		0			0
$651$		0			0
$652$	0.694903	−	1.79375i	0.694903	−	1.79375i
$653$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$653$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$654$		0			0
$655$		0			0
$656$	−1.04837	+	1.69318i	−1.04837	+	1.69318i
$657$	0.0749992	−	0.0464376i	0.0749992	−	0.0464376i
$658$		0			0
$659$	−1.34164	−	0.124322i	−1.34164	−	0.124322i	−0.602635	−	0.798017i	$-0.705882\pi$
$659$	−1.34164	−	0.124322i	−1.34164	−	0.124322i	−0.739009	+	0.673696i	$0.764706\pi$
$660$		0			0
$661$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$661$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$662$		0			0
$663$		0			0
$664$	0.907732	+	0.995734i	0.907732	+	0.995734i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.380338	−	0.981767i	0.380338	−	0.981767i	−0.602635	−	0.798017i	$-0.705882\pi$
$673$	0.380338	−	0.981767i	0.380338	−	0.981767i	0.982973	−	0.183750i	$-0.0588235\pi$
$674$	−0.0505009	+	0.177492i	−0.0505009	+	0.177492i
$675$			1.06784i			1.06784i
$676$	0.982973	+	0.183750i	0.982973	+	0.183750i
$677$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$677$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$678$	−1.06329	−	0.969315i	−1.06329	−	0.969315i
$679$		0			0
$680$		0			0
$681$	−0.266402	+	0.936306i	−0.266402	+	0.936306i
$682$		0			0
$683$	−0.111208	−	0.147263i	−0.111208	−	0.147263i	0.739009	−	0.673696i	$-0.235294\pi$
$683$	−0.111208	−	0.147263i	−0.111208	−	0.147263i	−0.850217	+	0.526432i	$0.823529\pi$
$684$	0.891477			0.891477
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.04837	+	0.0971461i	1.04837	+	0.0971461i
$689$		0			0
$690$		0			0
$691$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$691$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$692$		0			0
$693$		0			0
$694$	−1.93247	−	0.361242i	−1.93247	−	0.361242i
$695$		0			0
$696$		0			0
$697$	−1.22329	+	3.15769i	−1.22329	+	3.15769i
$698$		0			0
$699$	−0.128235	+	1.38388i	−0.128235	+	1.38388i
$700$		0			0
$701$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$701$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$702$		0			0
$703$		0			0
$704$	0.757949	+	1.52217i	0.757949	+	1.52217i
$705$		0			0
$706$	−0.907732	−	0.995734i	−0.907732	−	0.995734i
$707$		0			0
$708$	0.458410	−	0.740358i	0.458410	−	0.740358i
$709$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$709$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$710$		0			0
$711$		0			0
$712$	−1.72198	−	0.489946i	−1.72198	−	0.489946i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.78269	−	0.887674i	−1.78269	−	0.887674i
$717$		0			0
$718$		0			0
$719$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$719$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$720$		0			0
$721$		0			0
$722$	−2.47802			−2.47802
$723$	0.619490	−	1.24410i	0.619490	−	1.24410i
$724$		0			0
$725$		0			0
$726$			1.36656i			1.36656i
$727$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$727$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$728$		0			0
$729$	0.775218	+	0.479995i	0.775218	+	0.479995i
$730$		0			0
$731$	1.78269	−	0.165190i	1.78269	−	0.165190i
$732$		0			0
$733$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$733$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.646741	+	1.04452i	0.646741	+	1.04452i
$738$	−0.852157	+	0.424324i	−0.852157	+	0.424324i
$739$	0.576554	+	1.48826i	0.576554	+	1.48826i	0.850217	+	0.526432i	$0.176471\pi$
$739$	0.576554	+	1.48826i	0.576554	+	1.48826i	−0.273663	+	0.961826i	$0.588235\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$743$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.118349	+	0.633110i	0.118349	+	0.633110i
$748$	1.74250	+	2.30745i	1.74250	+	2.30745i
$749$		0			0
$750$		0			0
$751$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$751$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$752$		0			0
$753$	0.458410	−	0.607033i	0.458410	−	0.607033i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$757$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$758$	−0.404479	+	0.368731i	−0.404479	+	0.368731i
$759$		0			0
$760$		0			0
$761$	1.45285	−	0.271585i	1.45285	−	0.271585i	0.602635	−	0.798017i	$-0.294118\pi$
$761$	1.45285	−	0.271585i	1.45285	−	0.271585i	0.850217	+	0.526432i	$0.176471\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.260991	−	0.673696i	−0.260991	−	0.673696i
$769$	−1.42871	+	0.711414i	−1.42871	+	0.711414i	−0.982973	−	0.183750i	$-0.941176\pi$
$769$	−1.42871	+	0.711414i	−1.42871	+	0.711414i	−0.445738	+	0.895163i	$0.647059\pi$
$770$		0			0
$771$	0.119347	+	0.0594279i	0.119347	+	0.0594279i
$772$	−0.329838	+	0.436776i	−0.329838	+	0.436776i
$773$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$773$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$774$	0.401632	+	0.303299i	0.401632	+	0.303299i
$775$		0			0
$776$	−1.91545	+	0.177492i	−1.91545	+	0.177492i
$777$		0			0
$778$		0			0
$779$	3.32462	−	1.65546i	3.32462	−	1.65546i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.445738	−	0.895163i	0.445738	−	0.895163i
$785$		0			0
$786$	−0.339063	+	0.680930i	−0.339063	+	0.680930i
$787$	−0.353470	−	1.89090i	−0.353470	−	1.89090i	−0.445738	−	0.895163i	$-0.647059\pi$
$787$	−0.353470	−	1.89090i	−0.353470	−	1.89090i	0.0922684	−	0.995734i	$-0.470588\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.0749992	+	0.809370i	−0.0749992	+	0.809370i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$797$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$798$		0			0
$799$		0			0
$800$	0.932472	−	0.361242i	0.932472	−	0.361242i
$801$	−0.576554	−	0.632450i	−0.576554	−	0.632450i
$802$	−0.293271	+	0.221468i	−0.293271	+	0.221468i
$803$	−0.139869	−	0.280896i	−0.139869	−	0.280896i
$804$	−0.232667	−	0.467259i	−0.232667	−	0.467259i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.07524	−	1.17948i	1.07524	−	1.17948i	0.0922684	−	0.995734i	$-0.470588\pi$
$809$	1.07524	−	1.17948i	1.07524	−	1.17948i	0.982973	−	0.183750i	$-0.0588235\pi$
$810$		0			0
$811$	0.329838	−	1.15926i	0.329838	−	1.15926i	−0.602635	−	0.798017i	$-0.705882\pi$
$811$	0.329838	−	1.15926i	0.329838	−	1.15926i	0.932472	−	0.361242i	$-0.117647\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.646741	−	1.04452i	−0.646741	−	1.04452i
$817$	−1.56693	−	1.18329i	−1.56693	−	1.18329i
$818$	0.149783	−	0.526432i	0.149783	−	0.526432i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	0.719401	−	0.0666624i	0.719401	−	0.0666624i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	1.22329	+	0.113355i	1.22329	+	0.113355i
$826$		0			0
$827$	1.58923	+	1.20013i	1.58923	+	1.20013i	0.850217	+	0.526432i	$0.176471\pi$
$827$	1.58923	+	1.20013i	1.58923	+	1.20013i	0.739009	+	0.673696i	$0.235294\pi$
$828$		0			0
$829$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$829$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.465346	−	1.63552i	0.465346	−	1.63552i
$834$	0.486734	−	1.25640i	0.486734	−	1.25640i
$835$		0			0
$836$	0.292603	−	3.15769i	0.292603	−	3.15769i
$837$		0			0
$838$	0.465346	+	0.288130i	0.465346	+	0.288130i
$839$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$839$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$840$		0			0
$841$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$842$		0			0
$843$	0.907732	+	0.995734i	0.907732	+	0.995734i
$844$	1.12388	−	0.435393i	1.12388	−	0.435393i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.36614	−	0.388701i	−1.36614	−	0.388701i
$850$	1.44574	−	0.895163i	1.44574	−	0.895163i
$851$		0			0
$852$		0			0
$853$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$853$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$854$		0			0
$855$		0			0
$856$	−0.404479	−	1.42160i	−0.404479	−	1.42160i
$857$	−0.132756	−	0.710182i	−0.132756	−	0.710182i	−0.982973	−	0.183750i	$-0.941176\pi$
$857$	−0.132756	−	0.710182i	−0.132756	−	0.710182i	0.850217	−	0.526432i	$-0.176471\pi$
$858$		0			0
$859$	−0.184537			−0.184537			−0.0922684	−	0.995734i	$-0.529412\pi$
$859$	−0.184537			−0.184537			−0.0922684	+	0.995734i	$0.529412\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	0.196216	−	1.04966i	0.196216	−	1.04966i
$865$		0			0
$866$	0.465346	+	0.288130i	0.465346	+	0.288130i
$867$	−0.920646	−	1.00990i	−0.920646	−	1.00990i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.823138	−	0.409874i	−0.823138	−	0.409874i
$874$		0			0
$875$		0			0
$876$	0.0481624	+	0.124322i	0.0481624	+	0.124322i
$877$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$877$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.538007	−	0.100571i	−0.538007	−	0.100571i	−0.0922684	−	0.995734i	$-0.529412\pi$
$881$	−0.538007	−	0.100571i	−0.538007	−	0.100571i	−0.445738	+	0.895163i	$0.647059\pi$
$882$	0.406419	−	0.251644i	0.406419	−	0.251644i
$883$	1.83319	−	0.342683i	1.83319	−	0.342683i	0.850217	−	0.526432i	$-0.176471\pi$
$883$	1.83319	−	0.342683i	1.83319	−	0.342683i	0.982973	+	0.183750i	$0.0588235\pi$
$884$		0			0
$885$		0			0
$886$	0.404479	−	0.368731i	0.404479	−	0.368731i
$887$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$887$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.300742	−	0.398247i	0.300742	−	0.398247i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.538007	+	0.100571i	−0.538007	+	0.100571i
$899$		0			0
$900$	0.469879	+	0.0878355i	0.469879	+	0.0878355i
$901$		0			0
$902$	1.22329	+	3.15769i	1.22329	+	3.15769i
$903$		0			0
$904$	−1.58923	+	1.20013i	−1.58923	+	1.20013i
$905$		0			0
$906$		0			0
$907$	−0.709310	−	1.14558i	−0.709310	−	1.14558i	−0.982973	−	0.183750i	$-0.941176\pi$
$907$	−0.709310	−	1.14558i	−0.709310	−	1.14558i	0.273663	−	0.961826i	$-0.411765\pi$
$908$	1.20614	+	0.600584i	1.20614	+	0.600584i
$909$		0			0
$910$		0			0
$911$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$911$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$912$	−0.247582	+	1.32445i	−0.247582	+	1.32445i
$913$	2.28138	−	0.211401i	2.28138	−	0.211401i
$914$	0.709310	+	0.778076i	0.709310	+	0.778076i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		−	1.81580i		−	1.81580i
$919$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$919$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$920$		0			0
$921$	−0.232667	+	0.467259i	−0.232667	+	0.467259i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.0822551	−	0.887674i	0.0822551	−	0.887674i	−0.850217	−	0.526432i	$-0.823529\pi$
$929$	0.0822551	−	0.887674i	0.0822551	−	0.887674i	0.932472	−	0.361242i	$-0.117647\pi$
$930$		0			0
$931$	−1.58561	+	0.981767i	−1.58561	+	0.981767i
$932$	1.85022	+	0.526432i	1.85022	+	0.526432i
$933$		0			0
$934$	0.0505009	+	0.177492i	0.0505009	+	0.177492i
$935$		0			0
$936$		0			0
$937$	1.83319	−	0.710182i	1.83319	−	0.710182i	0.850217	−	0.526432i	$-0.176471\pi$
$937$	1.83319	−	0.710182i	1.83319	−	0.710182i	0.982973	−	0.183750i	$-0.0588235\pi$
$938$		0			0
$939$	−0.513985	+	0.388143i	−0.513985	+	0.388143i
$940$		0			0
$941$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$941$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$942$		0			0
$943$		0			0
$944$	−0.890705	−	0.811985i	−0.890705	−	0.811985i
$945$		0			0
$946$	1.20614	−	1.32307i	1.20614	−	1.32307i
$947$	−0.576554	+	1.48826i	−0.576554	+	1.48826i	0.273663	+	0.961826i	$0.411765\pi$
$947$	−0.576554	+	1.48826i	−0.576554	+	1.48826i	−0.850217	+	0.526432i	$0.823529\pi$
$948$		0			0
$949$		0			0
$950$	−1.83319	−	0.342683i	−1.83319	−	0.342683i
$951$		0			0
$952$		0			0
$953$	0.942485	+	1.52217i	0.942485	+	1.52217i	0.850217	+	0.526432i	$0.176471\pi$
$953$	0.942485	+	1.52217i	0.942485	+	1.52217i	0.0922684	+	0.995734i	$0.470588\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.602635	+	0.798017i	0.602635	+	0.798017i
$962$		0			0
$963$	0.193348	−	0.679548i	0.193348	−	0.679548i
$964$	−1.53511	−	1.15926i	−1.53511	−	1.15926i
$965$		0			0
$966$		0			0
$967$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$967$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$968$	1.85927	+	0.347558i	1.85927	+	0.347558i
$969$			2.29115i			2.29115i
$970$		0			0
$971$	−0.132756	+	0.342683i	−0.132756	+	0.342683i	−0.982973	−	0.183750i	$-0.941176\pi$
$971$	−0.132756	+	0.342683i	−0.132756	+	0.342683i	0.850217	+	0.526432i	$0.176471\pi$
$972$	0.576554	−	0.632450i	0.576554	−	0.632450i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.891477	−	1.79033i	−0.891477	−	1.79033i	−0.445738	−	0.895163i	$-0.647059\pi$
$977$	−0.891477	−	1.79033i	−0.891477	−	1.79033i	−0.445738	−	0.895163i	$-0.647059\pi$
$978$	0.619490	+	1.24410i	0.619490	+	1.24410i
$979$	−2.42943	+	1.83462i	−2.42943	+	1.83462i
$980$		0			0
$981$		0			0
$982$	−0.840204	+	1.35698i	−0.840204	+	1.35698i
$983$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$983$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$984$	−0.393747	−	1.38388i	−0.393747	−	1.38388i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$991$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.973468			−0.973468
$997$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$997$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$998$	1.45285	−	1.32445i	1.45285	−	1.32445i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1096.1.u.a.355.1	✓	16
8.3	odd	2	CM	1096.1.u.a.355.1	✓	16
137.22	even	34	inner	1096.1.u.a.707.1	yes	16
1096.707	odd	34	inner	1096.1.u.a.707.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1096.1.u.a.355.1	✓	16	1.1	even	1	trivial
1096.1.u.a.355.1	✓	16	8.3	odd	2	CM
1096.1.u.a.707.1	yes	16	137.22	even	34	inner
1096.1.u.a.707.1	yes	16	1096.707	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.u (of order \(34\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.602635 + 0.798017i) q^{2} +(-0.719401 - 0.0666624i) q^{3} +(-0.273663 + 0.961826i) q^{4} +(-0.380338 - 0.614268i) q^{6} +(-0.932472 + 0.361242i) q^{8} +(-0.469879 - 0.0878355i) q^{9} +O(q^{10})\)	\(q+(0.602635 + 0.798017i) q^{2} +(-0.719401 - 0.0666624i) q^{3} +(-0.273663 + 0.961826i) q^{4} +(-0.380338 - 0.614268i) q^{6} +(-0.932472 + 0.361242i) q^{8} +(-0.469879 - 0.0878355i) q^{9} +(-0.465346 + 1.63552i) q^{11} +(0.260991 - 0.673696i) q^{12} +(-0.850217 - 0.526432i) q^{16} +(-1.58561 - 0.614268i) q^{17} +(-0.213071 - 0.427904i) q^{18} +(0.831277 + 1.66943i) q^{19} +(-1.58561 + 0.614268i) q^{22} +(0.694903 - 0.197717i) q^{24} +(0.273663 + 0.961826i) q^{25} +(1.02708 + 0.292229i) q^{27} +(-0.0922684 - 0.995734i) q^{32} +(0.443798 - 1.14558i) q^{33} +(-0.465346 - 1.63552i) q^{34} +(0.213071 - 0.427904i) q^{36} +(-0.831277 + 1.66943i) q^{38} -1.99147i q^{41} +(-0.942485 + 0.469302i) q^{43} +(-1.44574 - 0.895163i) q^{44} +(0.576554 + 0.435393i) q^{48} +(0.0922684 + 0.995734i) q^{49} +(-0.602635 + 0.798017i) q^{50} +(1.09974 + 0.547605i) q^{51} +(0.385749 + 0.995734i) q^{54} +(-0.486734 - 1.25640i) q^{57} +(1.18475 + 0.221468i) q^{59} +(0.739009 - 0.673696i) q^{64} +(1.18164 - 0.336205i) q^{66} +(0.486734 - 0.533922i) q^{67} +(1.02474 - 1.35698i) q^{68} +(0.469879 - 0.0878355i) q^{72} +(-0.136374 + 0.124322i) q^{73} +(-0.132756 - 0.710182i) q^{75} +(-1.83319 + 0.342683i) q^{76} +(-0.273663 - 0.106018i) q^{81} +(1.58923 - 1.20013i) q^{82} +(-0.486734 - 1.25640i) q^{83} +(-0.942485 - 0.469302i) q^{86} +(-0.156896 - 1.69318i) q^{88} +(1.42871 + 1.07891i) q^{89} +0.722483i q^{96} +(1.85022 + 0.526432i) q^{97} +(-0.739009 + 0.673696i) q^{98} +(0.362313 - 0.727623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - q^{4} + q^{8} - q^{9}+O(q^{10}) \) 16 * q + q^2 - q^4 + q^8 - q^9	\( 16 q + q^{2} - q^{4} + q^{8} - q^{9} + 2 q^{11} + 17 q^{12} - q^{16} - 2 q^{17} + q^{18} - 2 q^{19} - 2 q^{22} + q^{25} + q^{32} + 2 q^{34} - q^{36} + 2 q^{38} - 15 q^{44} - q^{49} - q^{50} - 17 q^{54} - 2 q^{59} - q^{64} - 2 q^{68} + q^{72} + 2 q^{73} - 2 q^{76} - q^{81} - 2 q^{88} + 17 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) \) 16 * q + q^2 - q^4 + q^8 - q^9 + 2 * q^11 + 17 * q^12 - q^16 - 2 * q^17 + q^18 - 2 * q^19 - 2 * q^22 + q^25 + q^32 + 2 * q^34 - q^36 + 2 * q^38 - 15 * q^44 - q^49 - q^50 - 17 * q^54 - 2 * q^59 - q^64 - 2 * q^68 + q^72 + 2 * q^73 - 2 * q^76 - q^81 - 2 * q^88 + 17 * q^97 + q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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