LMFDB - Embedded newform 1096.1.u.a.563.1

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			563.1
Root			$0.273663 - 0.961826i$ of defining polynomial
Character	$\chi$	$=$	1096.563
Dual form			1096.1.u.a.475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.273663 - 0.961826i) q^{2} +(-0.247582 + 1.32445i) q^{3} +(-0.850217 - 0.526432i) q^{4} +(1.20614 + 0.600584i) q^{6} +(-0.739009 + 0.673696i) q^{8} +(-0.760397 - 0.294579i) q^{9} +O(q^{10})$	\(q+(0.273663 - 0.961826i) q^{2} +(-0.247582 + 1.32445i) q^{3} +(-0.850217 - 0.526432i) q^{4} +(1.20614 + 0.600584i) q^{6} +(-0.739009 + 0.673696i) q^{8} +(-0.760397 - 0.294579i) q^{9} +(0.757949 + 0.469302i) q^{11} +(0.907732 - 0.995734i) q^{12} +(0.445738 + 0.895163i) q^{16} +(0.658809 + 0.600584i) q^{17} +(-0.491426 + 0.650754i) q^{18} +(-0.890705 + 1.17948i) q^{19} +(0.658809 - 0.600584i) q^{22} +(-0.709310 - 1.14558i) q^{24} +(0.850217 - 0.526432i) q^{25} +(-0.130894 + 0.211401i) q^{27} +(0.982973 - 0.183750i) q^{32} +(-0.809222 + 0.887674i) q^{33} +(0.757949 - 0.469302i) q^{34} +(0.491426 + 0.650754i) q^{36} +(0.890705 + 1.17948i) q^{38} -0.367499i q^{41} +(1.42871 + 1.07891i) q^{43} +(-0.397365 - 0.798017i) q^{44} +(-1.29596 + 0.368731i) q^{48} +(-0.982973 + 0.183750i) q^{49} +(-0.273663 - 0.961826i) q^{50} +(-0.958553 + 0.723865i) q^{51} +(0.167510 + 0.183750i) q^{54} +(-1.34164 - 1.47171i) q^{57} +(-0.510366 - 0.197717i) q^{59} +(0.0922684 - 0.995734i) q^{64} +(0.632333 + 1.02125i) q^{66} +(1.34164 - 0.124322i) q^{67} +(-0.243964 - 0.857445i) q^{68} +(0.760397 - 0.294579i) q^{72} +(0.181395 - 1.95756i) q^{73} +(0.486734 + 1.25640i) q^{75} +(1.37821 - 0.533922i) q^{76} +(-0.850217 - 0.775075i) q^{81} +(-0.353470 - 0.100571i) q^{82} +(-1.34164 - 1.47171i) q^{83} +(1.42871 - 1.07891i) q^{86} +(-0.876298 + 0.163808i) q^{88} +(-1.53511 + 0.436776i) q^{89} +1.34739i q^{96} +(0.554262 - 0.895163i) q^{97} +(-0.0922684 + 0.995734i) q^{98} +(-0.438095 - 0.580132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1096\mathbb{Z}\right)^\times$.

$n$	$549$	$823$	$825$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{19}{34}\right)$

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 $

$2$	0.273663	−	0.961826i	0.273663	−	0.961826i
$2$	0.273663	−	0.961826i	0.273663	−	0.961826i
$3$	−0.247582	+	1.32445i	−0.247582	+	1.32445i	0.602635	+	0.798017i	$0.294118\pi$
$3$	−0.247582	+	1.32445i	−0.247582	+	1.32445i	−0.850217	+	0.526432i	$0.823529\pi$
$4$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$5$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$5$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$6$	1.20614	+	0.600584i	1.20614	+	0.600584i
$7$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$7$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$8$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$9$	−0.760397	−	0.294579i	−0.760397	−	0.294579i
$10$		0			0
$11$	0.757949	+	0.469302i	0.757949	+	0.469302i	0.850217	−	0.526432i	$-0.176471\pi$
$11$	0.757949	+	0.469302i	0.757949	+	0.469302i	−0.0922684	+	0.995734i	$0.529412\pi$
$12$	0.907732	−	0.995734i	0.907732	−	0.995734i
$13$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$13$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$14$		0			0
$15$		0			0
$16$	0.445738	+	0.895163i	0.445738	+	0.895163i
$17$	0.658809	+	0.600584i	0.658809	+	0.600584i	0.932472	−	0.361242i	$-0.117647\pi$
$17$	0.658809	+	0.600584i	0.658809	+	0.600584i	−0.273663	+	0.961826i	$0.588235\pi$
$18$	−0.491426	+	0.650754i	−0.491426	+	0.650754i
$19$	−0.890705	+	1.17948i	−0.890705	+	1.17948i	0.0922684	+	0.995734i	$0.470588\pi$
$19$	−0.890705	+	1.17948i	−0.890705	+	1.17948i	−0.982973	+	0.183750i	$0.941176\pi$
$20$		0			0
$21$		0			0
$22$	0.658809	−	0.600584i	0.658809	−	0.600584i
$23$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$23$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$24$	−0.709310	−	1.14558i	−0.709310	−	1.14558i
$25$	0.850217	−	0.526432i	0.850217	−	0.526432i
$26$		0			0
$27$	−0.130894	+	0.211401i	−0.130894	+	0.211401i
$28$		0			0
$29$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$29$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$30$		0			0
$31$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$31$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$32$	0.982973	−	0.183750i	0.982973	−	0.183750i
$33$	−0.809222	+	0.887674i	−0.809222	+	0.887674i
$34$	0.757949	−	0.469302i	0.757949	−	0.469302i
$35$		0			0
$36$	0.491426	+	0.650754i	0.491426	+	0.650754i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.890705	+	1.17948i	0.890705	+	1.17948i
$39$		0			0
$40$		0			0
$41$		−	0.367499i		−	0.367499i	−0.982973	−	0.183750i	$-0.941176\pi$
$41$		−	0.367499i		−	0.367499i	0.982973	−	0.183750i	$-0.0588235\pi$
$42$		0			0
$43$	1.42871	+	1.07891i	1.42871	+	1.07891i	0.982973	+	0.183750i	$0.0588235\pi$
$43$	1.42871	+	1.07891i	1.42871	+	1.07891i	0.445738	+	0.895163i	$0.352941\pi$
$44$	−0.397365	−	0.798017i	−0.397365	−	0.798017i
$45$		0			0
$46$		0			0
$47$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$47$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$48$	−1.29596	+	0.368731i	−1.29596	+	0.368731i
$49$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$50$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$51$	−0.958553	+	0.723865i	−0.958553	+	0.723865i
$52$		0			0
$53$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$53$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$54$	0.167510	+	0.183750i	0.167510	+	0.183750i
$55$		0			0
$56$		0			0
$57$	−1.34164	−	1.47171i	−1.34164	−	1.47171i
$58$		0			0
$59$	−0.510366	−	0.197717i	−0.510366	−	0.197717i	0.0922684	−	0.995734i	$-0.470588\pi$
$59$	−0.510366	−	0.197717i	−0.510366	−	0.197717i	−0.602635	+	0.798017i	$0.705882\pi$
$60$		0			0
$61$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$61$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$62$		0			0
$63$		0			0
$64$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$65$		0			0
$66$	0.632333	+	1.02125i	0.632333	+	1.02125i
$67$	1.34164	−	0.124322i	1.34164	−	0.124322i	0.602635	−	0.798017i	$-0.294118\pi$
$67$	1.34164	−	0.124322i	1.34164	−	0.124322i	0.739009	+	0.673696i	$0.235294\pi$
$68$	−0.243964	−	0.857445i	−0.243964	−	0.857445i
$69$		0			0
$70$		0			0
$71$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$71$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$72$	0.760397	−	0.294579i	0.760397	−	0.294579i
$73$	0.181395	−	1.95756i	0.181395	−	1.95756i	−0.0922684	−	0.995734i	$-0.529412\pi$
$73$	0.181395	−	1.95756i	0.181395	−	1.95756i	0.273663	−	0.961826i	$-0.411765\pi$
$74$		0			0
$75$	0.486734	+	1.25640i	0.486734	+	1.25640i
$76$	1.37821	−	0.533922i	1.37821	−	0.533922i
$77$		0			0
$78$		0			0
$79$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$79$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$80$		0			0
$81$	−0.850217	−	0.775075i	−0.850217	−	0.775075i
$82$	−0.353470	−	0.100571i	−0.353470	−	0.100571i
$83$	−1.34164	−	1.47171i	−1.34164	−	1.47171i	−0.739009	−	0.673696i	$-0.764706\pi$
$83$	−1.34164	−	1.47171i	−1.34164	−	1.47171i	−0.602635	−	0.798017i	$-0.705882\pi$
$84$		0			0
$85$		0			0
$86$	1.42871	−	1.07891i	1.42871	−	1.07891i
$87$		0			0
$88$	−0.876298	+	0.163808i	−0.876298	+	0.163808i
$89$	−1.53511	+	0.436776i	−1.53511	+	0.436776i	−0.932472	−	0.361242i	$-0.882353\pi$
$89$	−1.53511	+	0.436776i	−1.53511	+	0.436776i	−0.602635	+	0.798017i	$0.705882\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$			1.34739i			1.34739i
$97$	0.554262	−	0.895163i	0.554262	−	0.895163i	−0.445738	−	0.895163i	$-0.647059\pi$
$97$	0.554262	−	0.895163i	0.554262	−	0.895163i	1.00000			$0$
$98$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$99$	−0.438095	−	0.580132i	−0.438095	−	0.580132i
$100$	−1.00000			−1.00000
$101$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$101$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$102$	0.433912	+	1.12006i	0.433912	+	1.12006i
$103$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$103$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.181395	+	0.0339085i	0.181395	+	0.0339085i	0.273663	−	0.961826i	$-0.411765\pi$
$107$	0.181395	+	0.0339085i	0.181395	+	0.0339085i	−0.0922684	+	0.995734i	$0.529412\pi$
$108$	0.222576	−	0.110830i	0.222576	−	0.110830i
$109$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$109$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.193463	−	0.312454i	−0.193463	−	0.312454i	0.739009	−	0.673696i	$-0.235294\pi$
$113$	−0.193463	−	0.312454i	−0.193463	−	0.312454i	−0.932472	+	0.361242i	$0.882353\pi$
$114$	−1.78269	+	0.887674i	−1.78269	+	0.887674i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.329838	+	0.436776i	−0.329838	+	0.436776i
$119$		0			0
$120$		0			0
$121$	−0.0914964	−	0.183750i	−0.0914964	−	0.183750i
$122$		0			0
$123$	0.486734	+	0.0909863i	0.486734	+	0.0909863i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$129$	−1.78269	+	1.62514i	−1.78269	+	1.62514i
$130$		0			0
$131$	−1.60263	−	0.798017i	−1.60263	−	0.798017i	−0.602635	−	0.798017i	$-0.705882\pi$
$131$	−1.60263	−	0.798017i	−1.60263	−	0.798017i	−1.00000			$\pi$
$132$	1.15531	−	0.328715i	1.15531	−	0.328715i
$133$		0			0
$134$	0.247582	−	1.32445i	0.247582	−	1.32445i
$135$		0			0
$136$	−0.891477			−0.891477
$137$	0.602635	+	0.798017i	0.602635	+	0.798017i
$137$	0.602635	+	0.798017i	0.602635	+	0.798017i
$138$		0			0
$139$	0.404479	−	1.42160i	0.404479	−	1.42160i	−0.445738	−	0.895163i	$-0.647059\pi$
$139$	0.404479	−	1.42160i	0.404479	−	1.42160i	0.850217	−	0.526432i	$-0.176471\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.0752415	−	0.811985i	−0.0752415	−	0.811985i
$145$		0			0
$146$	−1.83319	−	0.710182i	−1.83319	−	0.710182i
$147$		−	1.34739i		−	1.34739i
$148$		0			0
$149$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$149$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$150$	1.34164	−	0.124322i	1.34164	−	0.124322i
$151$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$151$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$152$	−0.136374	−	1.47171i	−0.136374	−	1.47171i
$153$	−0.324037	−	0.650754i	−0.324037	−	0.650754i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$157$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.978160	+	0.605651i	−0.978160	+	0.605651i
$163$	0.193463	−	1.03494i	0.193463	−	1.03494i	−0.739009	−	0.673696i	$-0.764706\pi$
$163$	0.193463	−	1.03494i	0.193463	−	1.03494i	0.932472	−	0.361242i	$-0.117647\pi$
$164$	−0.193463	+	0.312454i	−0.193463	+	0.312454i
$165$		0			0
$166$	−1.78269	+	0.887674i	−1.78269	+	0.887674i
$167$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$167$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$168$		0			0
$169$	0.982973	−	0.183750i	0.982973	−	0.183750i
$170$		0			0
$171$	1.02474	−	0.634493i	1.02474	−	0.634493i
$172$	−0.646741	−	1.66943i	−0.646741	−	1.66943i
$173$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$173$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$174$		0			0
$175$		0			0
$176$	−0.0822551	+	0.887674i	−0.0822551	+	0.887674i
$177$	0.388224	−	0.627003i	0.388224	−	0.627003i
$178$			1.59603i			1.59603i
$179$	0.132756	−	0.342683i	0.132756	−	0.342683i	−0.850217	−	0.526432i	$-0.823529\pi$
$179$	0.132756	−	0.342683i	0.132756	−	0.342683i	0.982973	+	0.183750i	$0.0588235\pi$
$180$		0			0
$181$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$181$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.217488	+	0.764392i	0.217488	+	0.764392i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$191$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$192$	1.29596	+	0.368731i	1.29596	+	0.368731i
$193$	1.25664	+	1.14558i	1.25664	+	1.14558i	0.982973	+	0.183750i	$0.0588235\pi$
$193$	1.25664	+	1.14558i	1.25664	+	1.14558i	0.273663	+	0.961826i	$0.411765\pi$
$194$	−0.709310	−	0.778076i	−0.709310	−	0.778076i
$195$		0			0
$196$	0.932472	+	0.361242i	0.932472	+	0.361242i
$197$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$197$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$198$	−0.677876	+	0.262611i	−0.677876	+	0.262611i
$199$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$199$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$200$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$201$	−0.167510	+	1.80772i	−0.167510	+	1.80772i
$202$		0			0
$203$		0			0
$204$	1.19604	−	0.110830i	1.19604	−	0.110830i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.22864	+	0.475979i	−1.22864	+	0.475979i
$210$		0			0
$211$	−0.149783	+	0.526432i	−0.149783	+	0.526432i	0.850217	+	0.526432i	$0.176471\pi$
$211$	−0.149783	+	0.526432i	−0.149783	+	0.526432i	−1.00000			$\pi$
$212$		0			0
$213$		0			0
$214$	0.0822551	−	0.165190i	0.0822551	−	0.165190i
$215$		0			0
$216$	−0.0456881	−	0.244410i	−0.0456881	−	0.244410i
$217$		0			0
$218$		0			0
$219$	2.54778	+	0.724906i	2.54778	+	0.724906i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$223$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$224$		0			0
$225$	−0.801578	+	0.149841i	−0.801578	+	0.149841i
$226$	−0.353470	+	0.100571i	−0.353470	+	0.100571i
$227$	−0.719401	+	1.85699i	−0.719401	+	1.85699i	−0.273663	+	0.961826i	$0.588235\pi$
$227$	−0.719401	+	1.85699i	−0.719401	+	1.85699i	−0.445738	+	0.895163i	$0.647059\pi$
$228$	0.365931	+	1.95756i	0.365931	+	1.95756i
$229$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$229$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			1.05286i			1.05286i	0.850217	+	0.526432i	$0.176471\pi$
$233$			1.05286i			1.05286i	−0.850217	+	0.526432i	$0.823529\pi$
$234$		0			0
$235$		0			0
$236$	0.329838	+	0.436776i	0.329838	+	0.436776i
$237$		0			0
$238$		0			0
$239$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$239$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$240$		0			0
$241$	0.709310	−	0.778076i	0.709310	−	0.778076i	−0.273663	−	0.961826i	$-0.588235\pi$
$241$	0.709310	−	0.778076i	0.709310	−	0.778076i	0.982973	+	0.183750i	$0.0588235\pi$
$242$	−0.201774	+	0.0377181i	−0.201774	+	0.0377181i
$243$	1.03863	−	0.784333i	1.03863	−	0.784333i
$244$		0			0
$245$		0			0
$246$	0.220714	−	0.443254i	0.220714	−	0.443254i
$247$		0			0
$248$		0			0
$249$	2.28138	−	1.41257i	2.28138	−	1.41257i
$250$		0			0
$251$	−1.60263	+	0.798017i	−1.60263	+	0.798017i	−0.602635	+	0.798017i	$0.705882\pi$
$251$	−1.60263	+	0.798017i	−1.60263	+	0.798017i	−1.00000			$1.00000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$257$	1.45285	+	1.32445i	1.45285	+	1.32445i	0.850217	+	0.526432i	$0.176471\pi$
$257$	1.45285	+	1.32445i	1.45285	+	1.32445i	0.602635	+	0.798017i	$0.294118\pi$
$258$	1.07524	+	2.15938i	1.07524	+	2.15938i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.20614	+	1.32307i	−1.20614	+	1.32307i
$263$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$263$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$264$		−	1.20117i		−	1.20117i
$265$		0			0
$266$		0			0
$267$	−0.198422	−	2.14131i	−0.198422	−	2.14131i
$268$	−1.20614	−	0.600584i	−1.20614	−	0.600584i
$269$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$269$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$270$		0			0
$271$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$271$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$272$	−0.243964	+	0.857445i	−0.243964	+	0.857445i
$273$		0			0
$274$	0.932472	−	0.361242i	0.932472	−	0.361242i
$275$	0.891477			0.891477
$276$		0			0
$277$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$277$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$278$	−1.25664	−	0.778076i	−1.25664	−	0.778076i
$279$		0			0
$280$		0			0
$281$	−0.136374	−	1.47171i	−0.136374	−	1.47171i	−0.739009	−	0.673696i	$-0.764706\pi$
$281$	−0.136374	−	1.47171i	−0.136374	−	1.47171i	0.602635	−	0.798017i	$-0.294118\pi$
$282$		0			0
$283$	1.73901	+	0.673696i	1.73901	+	0.673696i	1.00000			$0$
$283$	1.73901	+	0.673696i	1.73901	+	0.673696i	0.739009	+	0.673696i	$0.235294\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.801578	−	0.149841i	−0.801578	−	0.149841i
$289$	−0.0189399	−	0.204394i	−0.0189399	−	0.204394i
$290$		0			0
$291$	1.04837	+	0.955718i	1.04837	+	0.955718i
$292$	−1.18475	+	1.56886i	−1.18475	+	1.56886i
$293$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$293$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$294$	−1.29596	−	0.368731i	−1.29596	−	0.368731i
$295$		0			0
$296$		0			0
$297$	−0.198422	+	0.0988022i	−0.198422	+	0.0988022i
$298$		0			0
$299$		0			0
$300$	0.247582	−	1.32445i	0.247582	−	1.32445i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.45285	−	0.271585i	−1.45285	−	0.271585i
$305$		0			0
$306$	−0.714589	+	0.133580i	−0.714589	+	0.133580i
$307$	0.907732	−	0.995734i	0.907732	−	0.995734i	−0.0922684	−	0.995734i	$-0.529412\pi$
$307$	0.907732	−	0.995734i	0.907732	−	0.995734i	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
$313$	−0.111208	+	1.20013i	−0.111208	+	1.20013i	0.739009	+	0.673696i	$0.235294\pi$
$313$	−0.111208	+	1.20013i	−0.111208	+	1.20013i	−0.850217	+	0.526432i	$0.823529\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$317$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.0898203	+	0.231853i	−0.0898203	+	0.231853i
$322$		0			0
$323$	−1.29518	+	0.242112i	−1.29518	+	0.242112i
$324$	0.314845	+	1.10656i	0.314845	+	1.10656i
$325$		0			0
$326$	−0.942485	−	0.469302i	−0.942485	−	0.469302i
$327$		0			0
$328$	0.247582	+	0.271585i	0.247582	+	0.271585i
$329$		0			0
$330$		0			0
$331$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$331$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$332$	0.365931	+	1.95756i	0.365931	+	1.95756i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.538007	+	1.89090i	−0.538007	+	1.89090i	−0.0922684	+	0.995734i	$0.529412\pi$
$337$	−0.538007	+	1.89090i	−0.538007	+	1.89090i	−0.445738	+	0.895163i	$0.647059\pi$
$338$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$339$	0.461728	−	0.178874i	0.461728	−	0.178874i
$340$		0			0
$341$		0			0
$342$	−0.329838	−	1.15926i	−0.329838	−	1.15926i
$343$		0			0
$344$	−1.78269	+	0.165190i	−1.78269	+	0.165190i
$345$		0			0
$346$		0			0
$347$	0.172075	−	1.85699i	0.172075	−	1.85699i	−0.273663	−	0.961826i	$-0.588235\pi$
$347$	0.172075	−	1.85699i	0.172075	−	1.85699i	0.445738	−	0.895163i	$-0.352941\pi$
$348$		0			0
$349$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$349$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$350$		0			0
$351$		0			0
$352$	0.831277	+	0.322039i	0.831277	+	0.322039i
$353$	−0.365931	−	1.95756i	−0.365931	−	1.95756i	−0.273663	−	0.961826i	$-0.588235\pi$
$353$	−0.365931	−	1.95756i	−0.365931	−	1.95756i	−0.0922684	−	0.995734i	$-0.529412\pi$
$354$	−0.496825	−	0.544991i	−0.496825	−	0.544991i
$355$		0			0
$356$	1.53511	+	0.436776i	1.53511	+	0.436776i
$357$		0			0
$358$	−0.293271	−	0.221468i	−0.293271	−	0.221468i
$359$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$359$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$360$		0			0
$361$	−0.324164	−	1.13932i	−0.324164	−	1.13932i
$362$		0			0
$363$	0.266020	−	0.0756892i	0.266020	−	0.0756892i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$367$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$368$		0			0
$369$	−0.108258	+	0.279445i	−0.108258	+	0.279445i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$373$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$374$	0.794731			0.794731
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.67148	+	0.312454i	−1.67148	+	0.312454i	−0.932472	−	0.361242i	$-0.882353\pi$
$379$	−1.67148	+	0.312454i	−1.67148	+	0.312454i	−0.739009	+	0.673696i	$0.764706\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$383$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$384$	0.709310	−	1.14558i	0.709310	−	1.14558i
$385$		0			0
$386$	1.44574	−	0.895163i	1.44574	−	0.895163i
$387$	−0.768562	−	1.24127i	−0.768562	−	1.24127i
$388$	−0.942485	+	0.469302i	−0.942485	+	0.469302i
$389$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$389$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$390$		0			0
$391$		0			0
$392$	0.602635	−	0.798017i	0.602635	−	0.798017i
$393$	1.45372	−	1.92503i	1.45372	−	1.92503i
$394$		0			0
$395$		0			0
$396$	0.0670760	+	0.723865i	0.0670760	+	0.723865i
$397$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$397$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$398$		0			0
$399$		0			0
$400$	0.850217	+	0.526432i	0.850217	+	0.526432i
$401$		−	0.722483i		−	0.722483i	−0.932472	−	0.361242i	$-0.882353\pi$
$401$		−	0.722483i		−	0.722483i	0.932472	−	0.361242i	$-0.117647\pi$
$402$	1.69287	+	0.655821i	1.69287	+	0.655821i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.220714	−	1.18072i	0.220714	−	1.18072i
$409$	−0.465346	+	1.63552i	−0.465346	+	1.63552i	0.273663	+	0.961826i	$0.411765\pi$
$409$	−0.465346	+	1.63552i	−0.465346	+	1.63552i	−0.739009	+	0.673696i	$0.764706\pi$
$410$		0			0
$411$	−1.20614	+	0.600584i	−1.20614	+	0.600584i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.78269	+	0.887674i	1.78269	+	0.887674i
$418$	0.121574	+	1.31200i	0.121574	+	1.31200i
$419$	1.25664	−	1.14558i	1.25664	−	1.14558i	0.273663	−	0.961826i	$-0.411765\pi$
$419$	1.25664	−	1.14558i	1.25664	−	1.14558i	0.982973	−	0.183750i	$-0.0588235\pi$
$420$		0			0
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$	0.465346	+	0.288130i	0.465346	+	0.288130i
$423$		0			0
$424$		0			0
$425$	0.876298	+	0.163808i	0.876298	+	0.163808i
$426$		0			0
$427$		0			0
$428$	−0.136374	−	0.124322i	−0.136374	−	0.124322i
$429$		0			0
$430$		0			0
$431$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$431$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$432$	−0.247582	−	0.0229419i	−0.247582	−	0.0229419i
$433$	1.25664	−	1.14558i	1.25664	−	1.14558i	0.273663	−	0.961826i	$-0.411765\pi$
$433$	1.25664	−	1.14558i	1.25664	−	1.14558i	0.982973	−	0.183750i	$-0.0588235\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.39447	−	2.25214i	1.39447	−	2.25214i
$439$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$439$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$440$		0			0
$441$	0.801578	+	0.149841i	0.801578	+	0.149841i
$442$		0			0
$443$	1.67148	−	0.312454i	1.67148	−	0.312454i	0.739009	−	0.673696i	$-0.235294\pi$
$443$	1.67148	−	0.312454i	1.67148	−	0.312454i	0.932472	+	0.361242i	$0.117647\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.02474	+	1.35698i	1.02474	+	1.35698i	0.932472	+	0.361242i	$0.117647\pi$
$449$	1.02474	+	1.35698i	1.02474	+	1.35698i	0.0922684	+	0.995734i	$0.470588\pi$
$450$	−0.0752415	+	0.811985i	−0.0752415	+	0.811985i
$451$	0.172468	−	0.278545i	0.172468	−	0.278545i
$452$			0.367499i			0.367499i
$453$		0			0
$454$	1.58923	+	1.20013i	1.58923	+	1.20013i
$455$		0			0
$456$	1.98297	+	0.183750i	1.98297	+	0.183750i
$457$	−0.328972	−	1.75984i	−0.328972	−	1.75984i	−0.602635	−	0.798017i	$-0.705882\pi$
$457$	−0.328972	−	1.75984i	−0.328972	−	1.75984i	0.273663	−	0.961826i	$-0.411765\pi$
$458$		0			0
$459$	−0.213198	+	0.0606600i	−0.213198	+	0.0606600i
$460$		0			0
$461$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$461$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$462$		0			0
$463$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$463$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$464$		0			0
$465$		0			0
$466$	1.01267	+	0.288130i	1.01267	+	0.288130i
$467$	−1.45285	−	1.32445i	−1.45285	−	1.32445i	−0.850217	−	0.526432i	$-0.823529\pi$
$467$	−1.45285	−	1.32445i	−1.45285	−	1.32445i	−0.602635	−	0.798017i	$-0.705882\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.510366	−	0.197717i	0.510366	−	0.197717i
$473$	0.576554	+	1.48826i	0.576554	+	1.48826i
$474$		0			0
$475$	−0.136374	+	1.47171i	−0.136374	+	1.47171i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$479$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$480$		0			0
$481$		0			0
$482$	−0.554262	−	0.895163i	−0.554262	−	0.895163i
$483$		0			0
$484$	−0.0189399	+	0.204394i	−0.0189399	+	0.204394i
$485$		0			0
$486$	−0.470159	−	1.21362i	−0.470159	−	1.21362i
$487$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$487$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$488$		0			0
$489$	1.32282	+	0.512465i	1.32282	+	0.512465i
$490$		0			0
$491$	−1.29596	−	1.42160i	−1.29596	−	1.42160i	−0.850217	−	0.526432i	$-0.823529\pi$
$491$	−1.29596	−	1.42160i	−1.29596	−	1.42160i	−0.445738	−	0.895163i	$-0.647059\pi$
$492$	−0.365931	−	0.333591i	−0.365931	−	0.333591i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.734316	−	2.58085i	−0.734316	−	2.58085i
$499$	−1.83319	+	0.342683i	−1.83319	+	0.342683i	−0.982973	−	0.183750i	$-0.941176\pi$
$499$	−1.83319	+	0.342683i	−1.83319	+	0.342683i	−0.850217	+	0.526432i	$0.823529\pi$
$500$		0			0
$501$		0			0
$502$	0.328972	+	1.75984i	0.328972	+	1.75984i
$503$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$503$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			1.34739i			1.34739i
$508$		0			0
$509$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$509$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$510$		0			0
$511$		0			0
$512$	0.602635	+	0.798017i	0.602635	+	0.798017i
$513$	−0.132756	−	0.342683i	−0.132756	−	0.342683i
$514$	1.67148	−	1.03494i	1.67148	−	1.03494i
$515$		0			0
$516$	2.37120	−	0.443254i	2.37120	−	0.443254i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.193463	+	0.312454i	−0.193463	+	0.312454i	−0.932472	−	0.361242i	$-0.882353\pi$
$521$	−0.193463	+	0.312454i	−0.193463	+	0.312454i	0.739009	+	0.673696i	$0.235294\pi$
$522$		0			0
$523$	1.58561	−	0.981767i	1.58561	−	0.981767i	0.602635	−	0.798017i	$-0.294118\pi$
$523$	1.58561	−	0.981767i	1.58561	−	0.981767i	0.982973	−	0.183750i	$-0.0588235\pi$
$524$	0.942485	+	1.52217i	0.942485	+	1.52217i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.15531	−	0.328715i	−1.15531	−	0.328715i
$529$	0.602635	−	0.798017i	0.602635	−	0.798017i
$530$		0			0
$531$	0.329838	+	0.300687i	0.329838	+	0.300687i
$532$		0			0
$533$		0			0
$534$	−2.11387	−	0.395150i	−2.11387	−	0.395150i
$535$		0			0
$536$	−0.907732	+	0.995734i	−0.907732	+	0.995734i
$537$	0.420998	+	0.260671i	0.420998	+	0.260671i
$538$		0			0
$539$	−0.831277	−	0.322039i	−0.831277	−	0.322039i
$540$		0			0
$541$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$541$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$542$		0			0
$543$		0			0
$544$	0.757949	+	0.469302i	0.757949	+	0.469302i
$545$		0			0
$546$		0			0
$547$	−1.96595			−1.96595			−0.982973	−	0.183750i	$-0.941176\pi$
$547$	−1.96595			−1.96595			−0.982973	+	0.183750i	$0.941176\pi$
$548$	−0.0922684	−	0.995734i	−0.0922684	−	0.995734i
$549$		0			0
$550$	0.243964	−	0.857445i	0.243964	−	0.857445i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.09227	+	0.995734i	−1.09227	+	0.995734i
$557$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$557$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1.06625	+	0.0988022i	−1.06625	+	0.0988022i
$562$	−1.45285	−	0.271585i	−1.45285	−	0.271585i
$563$	0.0170269	+	0.183750i	0.0170269	+	0.183750i	1.00000			$0$
$563$	0.0170269	+	0.183750i	0.0170269	+	0.183750i	−0.982973	+	0.183750i	$0.941176\pi$
$564$		0			0
$565$		0			0
$566$	1.12388	−	1.48826i	1.12388	−	1.48826i
$567$		0			0
$568$		0			0
$569$	−0.719401	−	0.0666624i	−0.719401	−	0.0666624i	−0.273663	−	0.961826i	$-0.588235\pi$
$569$	−0.719401	−	0.0666624i	−0.719401	−	0.0666624i	−0.445738	+	0.895163i	$0.647059\pi$
$570$		0			0
$571$	−1.78269	+	0.887674i	−1.78269	+	0.887674i	−0.850217	+	0.526432i	$0.823529\pi$
$571$	−1.78269	+	0.887674i	−1.78269	+	0.887674i	−0.932472	+	0.361242i	$0.882353\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.363483	+	0.729973i	−0.363483	+	0.729973i
$577$	−0.646741	+	0.322039i	−0.646741	+	0.322039i	−0.739009	−	0.673696i	$-0.764706\pi$
$577$	−0.646741	+	0.322039i	−0.646741	+	0.322039i	0.0922684	+	0.995734i	$0.470588\pi$
$578$	−0.201774	−	0.0377181i	−0.201774	−	0.0377181i
$579$	−1.82838	+	1.38073i	−1.82838	+	1.38073i
$580$		0			0
$581$		0			0
$582$	1.20614	−	0.746807i	1.20614	−	0.746807i
$583$		0			0
$584$	1.18475	+	1.56886i	1.18475	+	1.56886i
$585$		0			0
$586$		0			0
$587$	0.111208	−	1.20013i	0.111208	−	1.20013i	−0.739009	−	0.673696i	$-0.764706\pi$
$587$	0.111208	−	1.20013i	0.111208	−	1.20013i	0.850217	−	0.526432i	$-0.176471\pi$
$588$	−0.709310	+	1.14558i	−0.709310	+	1.14558i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.91545	−	0.177492i	−1.91545	−	0.177492i	−0.932472	−	0.361242i	$-0.882353\pi$
$593$	−1.91545	−	0.177492i	−1.91545	−	0.177492i	−0.982973	+	0.183750i	$0.941176\pi$
$594$	0.0407298	+	0.217885i	0.0407298	+	0.217885i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$599$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$600$	−1.20614	−	0.600584i	−1.20614	−	0.600584i
$601$	1.58923	+	1.20013i	1.58923	+	1.20013i	0.850217	+	0.526432i	$0.176471\pi$
$601$	1.58923	+	1.20013i	1.58923	+	1.20013i	0.739009	+	0.673696i	$0.235294\pi$
$602$		0			0
$603$	−1.05680	−	0.300687i	−1.05680	−	0.300687i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$607$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$608$	−0.658809	+	1.32307i	−0.658809	+	1.32307i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.0670760	+	0.723865i	−0.0670760	+	0.723865i
$613$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$613$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$614$	−0.709310	−	1.14558i	−0.709310	−	1.14558i
$615$		0			0
$616$		0			0
$617$	0.329838	+	1.15926i	0.329838	+	1.15926i	0.932472	+	0.361242i	$0.117647\pi$
$617$	0.329838	+	1.15926i	0.329838	+	1.15926i	−0.602635	+	0.798017i	$0.705882\pi$
$618$		0			0
$619$	0.380338	+	0.614268i	0.380338	+	0.614268i	0.982973	−	0.183750i	$-0.0588235\pi$
$619$	0.380338	+	0.614268i	0.380338	+	0.614268i	−0.602635	+	0.798017i	$0.705882\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.445738	−	0.895163i	0.445738	−	0.895163i
$626$	1.12388	+	0.435393i	1.12388	+	0.435393i
$627$	−0.326219	−	1.74512i	−0.326219	−	1.74512i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$631$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$632$		0			0
$633$	−0.660149	−	0.328715i	−0.660149	−	0.328715i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.831277	+	1.66943i	0.831277	+	1.66943i	0.739009	+	0.673696i	$0.235294\pi$
$641$	0.831277	+	1.66943i	0.831277	+	1.66943i	0.0922684	+	0.995734i	$0.470588\pi$
$642$	0.198422	+	0.149841i	0.198422	+	0.149841i
$643$	−0.260991	+	0.673696i	−0.260991	+	0.673696i	0.739009	+	0.673696i	$0.235294\pi$
$643$	−0.260991	+	0.673696i	−0.260991	+	0.673696i	−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$	−0.121574	+	1.31200i	−0.121574	+	1.31200i
$647$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$647$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$648$	1.15048			1.15048
$649$	−0.294043	−	0.389375i	−0.294043	−	0.389375i
$650$		0			0
$651$		0			0
$652$	−0.709310	+	0.778076i	−0.709310	+	0.778076i
$653$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$653$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$654$		0			0
$655$		0			0
$656$	0.328972	−	0.163808i	0.328972	−	0.163808i
$657$	−0.714589	+	1.43509i	−0.714589	+	1.43509i
$658$		0			0
$659$	−0.365931	+	1.95756i	−0.365931	+	1.95756i	−0.0922684	+	0.995734i	$0.529412\pi$
$659$	−0.365931	+	1.95756i	−0.365931	+	1.95756i	−0.273663	+	0.961826i	$0.588235\pi$
$660$		0			0
$661$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$661$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$662$		0			0
$663$		0			0
$664$	1.98297	+	0.183750i	1.98297	+	0.183750i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.20614	+	1.32307i	−1.20614	+	1.32307i	−0.273663	+	0.961826i	$0.588235\pi$
$673$	−1.20614	+	1.32307i	−1.20614	+	1.32307i	−0.932472	+	0.361242i	$0.882353\pi$
$674$	1.67148	+	1.03494i	1.67148	+	1.03494i
$675$			0.248643i			0.248643i
$676$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$677$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$677$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$678$	−0.0456881	−	0.493053i	−0.0456881	−	0.493053i
$679$		0			0
$680$		0			0
$681$	−2.28138	−	1.41257i	−2.28138	−	1.41257i
$682$		0			0
$683$	0.538007	−	1.89090i	0.538007	−	1.89090i	0.0922684	−	0.995734i	$-0.470588\pi$
$683$	0.538007	−	1.89090i	0.538007	−	1.89090i	0.445738	−	0.895163i	$-0.352941\pi$
$684$	−1.20527			−1.20527
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.328972	+	1.75984i	−0.328972	+	1.75984i
$689$		0			0
$690$		0			0
$691$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$691$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$692$		0			0
$693$		0			0
$694$	−1.73901	−	0.673696i	−1.73901	−	0.673696i
$695$		0			0
$696$		0			0
$697$	0.220714	−	0.242112i	0.220714	−	0.242112i
$698$		0			0
$699$	−1.39447	−	0.260671i	−1.39447	−	0.260671i
$700$		0			0
$701$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$701$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$702$		0			0
$703$		0			0
$704$	0.537235	−	0.711414i	0.537235	−	0.711414i
$705$		0			0
$706$	−1.98297	−	0.183750i	−1.98297	−	0.183750i
$707$		0			0
$708$	−0.660149	+	0.328715i	−0.660149	+	0.328715i
$709$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$709$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$710$		0			0
$711$		0			0
$712$	0.840204	−	1.35698i	0.840204	−	1.35698i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.293271	+	0.221468i	−0.293271	+	0.221468i
$717$		0			0
$718$		0			0
$719$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$719$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$720$		0			0
$721$		0			0
$722$	−1.18454			−1.18454
$723$	0.854910	+	1.13208i	0.854910	+	1.13208i
$724$		0			0
$725$		0			0
$726$		−	0.276578i		−	0.276578i
$727$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$727$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$728$		0			0
$729$	0.268850	+	0.539924i	0.268850	+	0.539924i
$730$		0			0
$731$	0.293271	+	1.56886i	0.293271	+	1.56886i
$732$		0			0
$733$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$733$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.07524	+	0.535407i	1.07524	+	0.535407i
$738$	0.239151	+	0.180599i	0.239151	+	0.180599i
$739$	−1.29596	−	1.42160i	−1.29596	−	1.42160i	−0.850217	−	0.526432i	$-0.823529\pi$
$739$	−1.29596	−	1.42160i	−1.29596	−	1.42160i	−0.445738	−	0.895163i	$-0.647059\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$743$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.586645	+	1.51431i	0.586645	+	1.51431i
$748$	0.217488	−	0.764392i	0.217488	−	0.764392i
$749$		0			0
$750$		0			0
$751$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$751$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$752$		0			0
$753$	−0.660149	−	2.32018i	−0.660149	−	2.32018i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$757$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$758$	−0.156896	+	1.69318i	−0.156896	+	1.69318i
$759$		0			0
$760$		0			0
$761$	−0.172075	+	0.0666624i	−0.172075	+	0.0666624i	−0.445738	−	0.895163i	$-0.647059\pi$
$761$	−0.172075	+	0.0666624i	−0.172075	+	0.0666624i	0.273663	+	0.961826i	$0.411765\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.907732	−	0.995734i	−0.907732	−	0.995734i
$769$	1.53511	+	1.15926i	1.53511	+	1.15926i	0.932472	+	0.361242i	$0.117647\pi$
$769$	1.53511	+	1.15926i	1.53511	+	1.15926i	0.602635	+	0.798017i	$0.294118\pi$
$770$		0			0
$771$	−2.11387	+	1.59632i	−2.11387	+	1.59632i
$772$	−0.465346	−	1.63552i	−0.465346	−	1.63552i
$773$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$773$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$774$	−1.40421	+	0.399533i	−1.40421	+	0.399533i
$775$		0			0
$776$	0.193463	+	1.03494i	0.193463	+	1.03494i
$777$		0			0
$778$		0			0
$779$	0.433459	+	0.327333i	0.433459	+	0.327333i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.602635	−	0.798017i	−0.602635	−	0.798017i
$785$		0			0
$786$	−1.45372	−	1.92503i	−1.45372	−	1.92503i
$787$	−0.380338	−	0.981767i	−0.380338	−	0.981767i	−0.982973	−	0.183750i	$-0.941176\pi$
$787$	−0.380338	−	0.981767i	−0.380338	−	0.981767i	0.602635	−	0.798017i	$-0.294118\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.714589	+	0.133580i	0.714589	+	0.133580i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$797$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$798$		0			0
$799$		0			0
$800$	0.739009	−	0.673696i	0.739009	−	0.673696i
$801$	1.29596	+	0.120088i	1.29596	+	0.120088i
$802$	−0.694903	−	0.197717i	−0.694903	−	0.197717i
$803$	1.05617	−	1.39860i	1.05617	−	1.39860i
$804$	1.09406	−	1.44877i	1.09406	−	1.44877i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.91545	+	0.177492i	−1.91545	+	0.177492i	−0.982973	−	0.183750i	$-0.941176\pi$
$809$	−1.91545	+	0.177492i	−1.91545	+	0.177492i	−0.932472	+	0.361242i	$0.882353\pi$
$810$		0			0
$811$	0.465346	+	0.288130i	0.465346	+	0.288130i	0.739009	−	0.673696i	$-0.235294\pi$
$811$	0.465346	+	0.288130i	0.465346	+	0.288130i	−0.273663	+	0.961826i	$0.588235\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.07524	−	0.535407i	−1.07524	−	0.535407i
$817$	−2.54512	+	0.724149i	−2.54512	+	0.724149i
$818$	1.44574	+	0.895163i	1.44574	+	0.895163i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	0.247582	+	1.32445i	0.247582	+	1.32445i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	−0.220714	+	1.18072i	−0.220714	+	1.18072i
$826$		0			0
$827$	−0.353470	+	0.100571i	−0.353470	+	0.100571i	−0.445738	−	0.895163i	$-0.647059\pi$
$827$	−0.353470	+	0.100571i	−0.353470	+	0.100571i	0.0922684	+	0.995734i	$0.470588\pi$
$828$		0			0
$829$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$829$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.757949	−	0.469302i	−0.757949	−	0.469302i
$834$	1.34164	−	1.47171i	1.34164	−	1.47171i
$835$		0			0
$836$	1.29518	+	0.242112i	1.29518	+	0.242112i
$837$		0			0
$838$	−0.757949	−	1.52217i	−0.757949	−	1.52217i
$839$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$839$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$840$		0			0
$841$	0.602635	−	0.798017i	0.602635	−	0.798017i
$842$		0			0
$843$	1.98297	+	0.183750i	1.98297	+	0.183750i
$844$	0.404479	−	0.368731i	0.404479	−	0.368731i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.32282	+	2.13643i	−1.32282	+	2.13643i
$850$	0.397365	−	0.798017i	0.397365	−	0.798017i
$851$		0			0
$852$		0			0
$853$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$853$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$854$		0			0
$855$		0			0
$856$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i
$857$	0.486734	+	1.25640i	0.486734	+	1.25640i	0.932472	+	0.361242i	$0.117647\pi$
$857$	0.486734	+	1.25640i	0.486734	+	1.25640i	−0.445738	+	0.895163i	$0.647059\pi$
$858$		0			0
$859$	1.96595			1.96595			0.982973	−	0.183750i	$-0.0588235\pi$
$859$	1.96595			1.96595			0.982973	+	0.183750i	$0.0588235\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	−0.0898203	+	0.231853i	−0.0898203	+	0.231853i
$865$		0			0
$866$	−0.757949	−	1.52217i	−0.757949	−	1.52217i
$867$	0.275398	+	0.0255194i	0.275398	+	0.0255194i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.685155	+	0.517405i	−0.685155	+	0.517405i
$874$		0			0
$875$		0			0
$876$	−1.78455	−	1.95756i	−1.78455	−	1.95756i
$877$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$877$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.58561	+	0.614268i	1.58561	+	0.614268i	0.982973	−	0.183750i	$-0.0588235\pi$
$881$	1.58561	+	0.614268i	1.58561	+	0.614268i	0.602635	+	0.798017i	$0.294118\pi$
$882$	0.363483	−	0.729973i	0.363483	−	0.729973i
$883$	−1.37821	+	0.533922i	−1.37821	+	0.533922i	−0.932472	−	0.361242i	$-0.882353\pi$
$883$	−1.37821	+	0.533922i	−1.37821	+	0.533922i	−0.445738	+	0.895163i	$0.647059\pi$
$884$		0			0
$885$		0			0
$886$	0.156896	−	1.69318i	0.156896	−	1.69318i
$887$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$887$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.280677	−	0.986476i	−0.280677	−	0.986476i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.58561	−	0.614268i	1.58561	−	0.614268i
$899$		0			0
$900$	0.760397	+	0.294579i	0.760397	+	0.294579i
$901$		0			0
$902$	−0.220714	−	0.242112i	−0.220714	−	0.242112i
$903$		0			0
$904$	0.353470	+	0.100571i	0.353470	+	0.100571i
$905$		0			0
$906$		0			0
$907$	1.78269	+	0.887674i	1.78269	+	0.887674i	0.932472	+	0.361242i	$0.117647\pi$
$907$	1.78269	+	0.887674i	1.78269	+	0.887674i	0.850217	+	0.526432i	$0.176471\pi$
$908$	1.58923	−	1.20013i	1.58923	−	1.20013i
$909$		0			0
$910$		0			0
$911$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$911$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$912$	0.719401	−	1.85699i	0.719401	−	1.85699i
$913$	−0.326219	−	1.74512i	−0.326219	−	1.74512i
$914$	−1.78269	−	0.165190i	−1.78269	−	0.165190i
$915$		0			0
$916$		0			0
$917$		0			0
$918$			0.221660i			0.221660i
$919$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$919$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$920$		0			0
$921$	1.09406	+	1.44877i	1.09406	+	1.44877i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.739009	−	0.673696i	$-0.235294\pi$
$929$	1.18475	+	0.221468i	1.18475	+	0.221468i	0.445738	+	0.895163i	$0.352941\pi$
$930$		0			0
$931$	0.658809	−	1.32307i	0.658809	−	1.32307i
$932$	0.554262	−	0.895163i	0.554262	−	0.895163i
$933$		0			0
$934$	−1.67148	+	1.03494i	−1.67148	+	1.03494i
$935$		0			0
$936$		0			0
$937$	−1.37821	+	1.25640i	−1.37821	+	1.25640i	−0.445738	+	0.895163i	$0.647059\pi$
$937$	−1.37821	+	1.25640i	−1.37821	+	1.25640i	−0.932472	+	0.361242i	$0.882353\pi$
$938$		0			0
$939$	−1.56198	−	0.444420i	−1.56198	−	0.444420i
$940$		0			0
$941$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$941$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$942$		0			0
$943$		0			0
$944$	−0.0505009	−	0.544991i	−0.0505009	−	0.544991i
$945$		0			0
$946$	1.58923	−	0.147263i	1.58923	−	0.147263i
$947$	1.29596	−	1.42160i	1.29596	−	1.42160i	0.445738	−	0.895163i	$-0.352941\pi$
$947$	1.29596	−	1.42160i	1.29596	−	1.42160i	0.850217	−	0.526432i	$-0.176471\pi$
$948$		0			0
$949$		0			0
$950$	1.37821	+	0.533922i	1.37821	+	0.533922i
$951$		0			0
$952$		0			0
$953$	−1.42871	−	0.711414i	−1.42871	−	0.711414i	−0.445738	−	0.895163i	$-0.647059\pi$
$953$	−1.42871	−	0.711414i	−1.42871	−	0.711414i	−0.982973	+	0.183750i	$0.941176\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.273663	−	0.961826i	0.273663	−	0.961826i
$962$		0			0
$963$	−0.127943	−	0.0792190i	−0.127943	−	0.0792190i
$964$	−1.01267	+	0.288130i	−1.01267	+	0.288130i
$965$		0			0
$966$		0			0
$967$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$967$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$968$	0.191408	+	0.0741518i	0.191408	+	0.0741518i
$969$		−	1.77535i		−	1.77535i
$970$		0			0
$971$	0.486734	−	0.533922i	0.486734	−	0.533922i	−0.445738	−	0.895163i	$-0.647059\pi$
$971$	0.486734	−	0.533922i	0.486734	−	0.533922i	0.932472	+	0.361242i	$0.117647\pi$
$972$	−1.29596	+	0.120088i	−1.29596	+	0.120088i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.20527	−	1.59603i	1.20527	−	1.59603i	0.602635	−	0.798017i	$-0.294118\pi$
$977$	1.20527	−	1.59603i	1.20527	−	1.59603i	0.602635	−	0.798017i	$-0.294118\pi$
$978$	0.854910	−	1.13208i	0.854910	−	1.13208i
$979$	−1.36851	−	0.389375i	−1.36851	−	0.389375i
$980$		0			0
$981$		0			0
$982$	−1.72198	+	0.857445i	−1.72198	+	0.857445i
$983$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$983$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$984$	−0.420998	+	0.260671i	−0.420998	+	0.260671i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$991$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−2.68329			−2.68329
$997$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$997$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$998$	−0.172075	+	1.85699i	−0.172075	+	1.85699i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1096.1.u.a.563.1	yes	16
8.3	odd	2	CM	1096.1.u.a.563.1	yes	16
137.64	even	34	inner	1096.1.u.a.475.1	✓	16
1096.475	odd	34	inner	1096.1.u.a.475.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1096.1.u.a.475.1	✓	16	137.64	even	34	inner
1096.1.u.a.475.1	✓	16	1096.475	odd	34	inner
1096.1.u.a.563.1	yes	16	1.1	even	1	trivial
1096.1.u.a.563.1	yes	16	8.3	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.273663 - 0.961826i) q^{2} +(-0.247582 + 1.32445i) q^{3} +(-0.850217 - 0.526432i) q^{4} +(1.20614 + 0.600584i) q^{6} +(-0.739009 + 0.673696i) q^{8} +(-0.760397 - 0.294579i) q^{9} +O(q^{10})\)	\(q+(0.273663 - 0.961826i) q^{2} +(-0.247582 + 1.32445i) q^{3} +(-0.850217 - 0.526432i) q^{4} +(1.20614 + 0.600584i) q^{6} +(-0.739009 + 0.673696i) q^{8} +(-0.760397 - 0.294579i) q^{9} +(0.757949 + 0.469302i) q^{11} +(0.907732 - 0.995734i) q^{12} +(0.445738 + 0.895163i) q^{16} +(0.658809 + 0.600584i) q^{17} +(-0.491426 + 0.650754i) q^{18} +(-0.890705 + 1.17948i) q^{19} +(0.658809 - 0.600584i) q^{22} +(-0.709310 - 1.14558i) q^{24} +(0.850217 - 0.526432i) q^{25} +(-0.130894 + 0.211401i) q^{27} +(0.982973 - 0.183750i) q^{32} +(-0.809222 + 0.887674i) q^{33} +(0.757949 - 0.469302i) q^{34} +(0.491426 + 0.650754i) q^{36} +(0.890705 + 1.17948i) q^{38} -0.367499i q^{41} +(1.42871 + 1.07891i) q^{43} +(-0.397365 - 0.798017i) q^{44} +(-1.29596 + 0.368731i) q^{48} +(-0.982973 + 0.183750i) q^{49} +(-0.273663 - 0.961826i) q^{50} +(-0.958553 + 0.723865i) q^{51} +(0.167510 + 0.183750i) q^{54} +(-1.34164 - 1.47171i) q^{57} +(-0.510366 - 0.197717i) q^{59} +(0.0922684 - 0.995734i) q^{64} +(0.632333 + 1.02125i) q^{66} +(1.34164 - 0.124322i) q^{67} +(-0.243964 - 0.857445i) q^{68} +(0.760397 - 0.294579i) q^{72} +(0.181395 - 1.95756i) q^{73} +(0.486734 + 1.25640i) q^{75} +(1.37821 - 0.533922i) q^{76} +(-0.850217 - 0.775075i) q^{81} +(-0.353470 - 0.100571i) q^{82} +(-1.34164 - 1.47171i) q^{83} +(1.42871 - 1.07891i) q^{86} +(-0.876298 + 0.163808i) q^{88} +(-1.53511 + 0.436776i) q^{89} +1.34739i q^{96} +(0.554262 - 0.895163i) q^{97} +(-0.0922684 + 0.995734i) q^{98} +(-0.438095 - 0.580132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - q^{4} + q^{8} - q^{9}+O(q^{10}) \) 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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