LMFDB - Embedded newform 1156.1.o.a.319.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1156,1,Mod(47,1156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1156, base_ring=CyclotomicField(68))

chi = DirichletCharacter(H, H._module([34, 25]))

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

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

chi := DirichletCharacter("1156.47");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$1156 = 2^{2} \cdot 17^{2}$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	1156.o (of order $68$ , degree $32$ , 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:	$0.576919154604$
Analytic rank:	$0$
Dimension:	$32$
Coefficient field:	$\Q(\zeta_{68})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} + \cdots + 1$ x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{68}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{68} - \cdots)$

Embedding invariants

Embedding label			319.1
Root			$-0.183750 + 0.982973i$ of defining polynomial
Character	$\chi$	$=$	1156.319
Dual form			1156.1.o.a.395.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.361242 + 0.932472i) q^{2} +(-0.739009 + 0.673696i) q^{4} +(0.602635 - 1.79802i) q^{5} +(-0.895163 - 0.445738i) q^{8} +(-0.961826 - 0.273663i) q^{9} +(1.89430 - 0.0875787i) q^{10} +(0.857445 - 1.72198i) q^{13} +(0.0922684 - 0.995734i) q^{16} +(-0.0922684 + 0.995734i) q^{17} +(-0.0922684 - 0.995734i) q^{18} +(0.765964 + 1.73474i) q^{20} +(-2.07168 - 1.56446i) q^{25} +(1.91545 + 0.177492i) q^{26} +(0.972171 + 0.0449462i) q^{29} +(0.961826 - 0.273663i) q^{32} +(-0.961826 + 0.273663i) q^{34} +(0.895163 - 0.445738i) q^{36} +(0.666468 + 0.456541i) q^{37} +(-1.34090 + 1.34090i) q^{40} +(0.629488 + 0.0878098i) q^{41} +(-1.07168 + 1.56446i) q^{45} +(-0.526432 + 0.850217i) q^{49} +(0.710439 - 2.49693i) q^{50} +(0.526432 + 1.85022i) q^{52} +(1.01267 + 0.288130i) q^{53} +(0.309277 + 0.922758i) q^{58} +(-1.92821 + 0.453510i) q^{61} +(0.602635 + 0.798017i) q^{64} +(-2.57943 - 2.57943i) q^{65} +(-0.602635 - 0.798017i) q^{68} +(0.739009 + 0.673696i) q^{72} +(-1.34421 + 1.11622i) q^{73} +(-0.184956 + 0.786384i) q^{74} +(-1.73474 - 0.765964i) q^{80} +(0.850217 + 0.526432i) q^{81} +(0.145517 + 0.618701i) q^{82} +(1.73474 + 0.765964i) q^{85} +(0.322039 + 0.646741i) q^{89} +(-1.84595 - 0.434164i) q^{90} +(0.0806938 - 0.0449462i) q^{97} +(-0.982973 - 0.183750i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 2 q^{4} + 2 q^{5} - 2 q^{10} - 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 34 q^{25} - 2 q^{29} + 2 q^{37} + 2 q^{40} - 2 q^{41} - 2 q^{45} + 2 q^{50} + 2 q^{58} + 2 q^{61} + 2 q^{64} - 2 q^{68}+ \cdots - 2 q^{98}+O(q^{100})$ 32 * q + 2 * q^4 + 2 * q^5 - 2 * q^10 - 2 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^20 - 34 * q^25 - 2 * q^29 + 2 * q^37 + 2 * q^40 - 2 * q^41 - 2 * q^45 + 2 * q^50 + 2 * q^58 + 2 * q^61 + 2 * q^64 - 2 * q^68 - 2 * q^72 - 2 * q^73 - 2 * q^74 + 2 * q^80 + 2 * q^81 - 2 * q^82 - 2 * q^85 - 2 * q^90 + 2 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$ .

$n$	$579$	$581$
$\chi(n)$	$-1$	$e\left(\frac{37}{68}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.361242	+	0.932472i	0.361242	+	0.932472i
$2$	0.361242	+	0.932472i	0.361242	+	0.932472i
$3$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$3$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$4$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$5$	0.602635	−	1.79802i	0.602635	−	1.79802i		−	1.00000i	$-0.5\pi$
$5$	0.602635	−	1.79802i	0.602635	−	1.79802i	0.602635	−	0.798017i	$-0.294118\pi$
$6$		0			0
$7$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$7$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$8$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$9$	−0.961826	−	0.273663i	−0.961826	−	0.273663i
$10$	1.89430	−	0.0875787i	1.89430	−	0.0875787i
$11$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$11$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$12$		0			0
$13$	0.857445	−	1.72198i	0.857445	−	1.72198i	0.183750	−	0.982973i	$-0.441176\pi$
$13$	0.857445	−	1.72198i	0.857445	−	1.72198i	0.673696	−	0.739009i	$-0.264706\pi$
$14$		0			0
$15$		0			0
$16$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$17$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$17$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$18$	−0.0922684	−	0.995734i	−0.0922684	−	0.995734i
$19$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$19$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$20$	0.765964	+	1.73474i	0.765964	+	1.73474i
$21$		0			0
$22$		0			0
$23$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$23$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$24$		0			0
$25$	−2.07168	−	1.56446i	−2.07168	−	1.56446i
$26$	1.91545	+	0.177492i	1.91545	+	0.177492i
$27$		0			0
$28$		0			0
$29$	0.972171	+	0.0449462i	0.972171	+	0.0449462i	0.526432	−	0.850217i	$-0.323529\pi$
$29$	0.972171	+	0.0449462i	0.972171	+	0.0449462i	0.445738	+	0.895163i	$0.352941\pi$
$30$		0			0
$31$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$31$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$32$	0.961826	−	0.273663i	0.961826	−	0.273663i
$33$		0			0
$34$	−0.961826	+	0.273663i	−0.961826	+	0.273663i
$35$		0			0
$36$	0.895163	−	0.445738i	0.895163	−	0.445738i
$37$	0.666468	+	0.456541i	0.666468	+	0.456541i	0.850217	−	0.526432i	$-0.176471\pi$
$37$	0.666468	+	0.456541i	0.666468	+	0.456541i	−0.183750	+	0.982973i	$0.558824\pi$
$38$		0			0
$39$		0			0
$40$	−1.34090	+	1.34090i	−1.34090	+	1.34090i
$41$	0.629488	+	0.0878098i	0.629488	+	0.0878098i	0.445738	−	0.895163i	$-0.352941\pi$
$41$	0.629488	+	0.0878098i	0.629488	+	0.0878098i	0.183750	+	0.982973i	$0.441176\pi$
$42$		0			0
$43$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$43$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$44$		0			0
$45$	−1.07168	+	1.56446i	−1.07168	+	1.56446i
$46$		0			0
$47$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$47$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$48$		0			0
$49$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$50$	0.710439	−	2.49693i	0.710439	−	2.49693i
$51$		0			0
$52$	0.526432	+	1.85022i	0.526432	+	1.85022i
$53$	1.01267	+	0.288130i	1.01267	+	0.288130i	0.739009	−	0.673696i	$-0.235294\pi$
$53$	1.01267	+	0.288130i	1.01267	+	0.288130i	0.273663	+	0.961826i	$0.411765\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.309277	+	0.922758i	0.309277	+	0.922758i
$59$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$59$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$60$		0			0
$61$	−1.92821	+	0.453510i	−1.92821	+	0.453510i	−0.932472	+	0.361242i	$0.882353\pi$
$61$	−1.92821	+	0.453510i	−1.92821	+	0.453510i	−0.995734	+	0.0922684i	$0.970588\pi$
$62$		0			0
$63$		0			0
$64$	0.602635	+	0.798017i	0.602635	+	0.798017i
$65$	−2.57943	−	2.57943i	−2.57943	−	2.57943i
$66$		0			0
$67$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$67$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$68$	−0.602635	−	0.798017i	−0.602635	−	0.798017i
$69$		0			0
$70$		0			0
$71$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$71$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$72$	0.739009	+	0.673696i	0.739009	+	0.673696i
$73$	−1.34421	+	1.11622i	−1.34421	+	1.11622i	−0.361242	+	0.932472i	$0.617647\pi$
$73$	−1.34421	+	1.11622i	−1.34421	+	1.11622i	−0.982973	+	0.183750i	$0.941176\pi$
$74$	−0.184956	+	0.786384i	−0.184956	+	0.786384i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$79$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$80$	−1.73474	−	0.765964i	−1.73474	−	0.765964i
$81$	0.850217	+	0.526432i	0.850217	+	0.526432i
$82$	0.145517	+	0.618701i	0.145517	+	0.618701i
$83$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$83$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$84$		0			0
$85$	1.73474	+	0.765964i	1.73474	+	0.765964i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.322039	+	0.646741i	0.322039	+	0.646741i	0.995734	−	0.0922684i	$-0.0294118\pi$
$89$	0.322039	+	0.646741i	0.322039	+	0.646741i	−0.673696	+	0.739009i	$0.735294\pi$
$90$	−1.84595	−	0.434164i	−1.84595	−	0.434164i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.0806938	−	0.0449462i	0.0806938	−	0.0449462i	−0.445738	−	0.895163i	$-0.647059\pi$
$97$	0.0806938	−	0.0449462i	0.0806938	−	0.0449462i	0.526432	+	0.850217i	$0.323529\pi$
$98$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$99$		0			0
$100$	2.58496	−	0.239532i	2.58496	−	0.239532i
$101$	1.69318	+	1.04837i	1.69318	+	1.04837i	0.895163	+	0.445738i	$0.147059\pi$
$101$	1.69318	+	1.04837i	1.69318	+	1.04837i	0.798017	+	0.602635i	$0.205882\pi$
$102$		0			0
$103$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$103$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$104$	−1.53511	+	1.15926i	−1.53511	+	1.15926i
$105$		0			0
$106$	0.0971461	+	1.04837i	0.0971461	+	1.04837i
$107$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$107$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$108$		0			0
$109$	−0.252769	−	1.81204i	−0.252769	−	1.81204i	−0.526432	−	0.850217i	$-0.676471\pi$
$109$	−0.252769	−	1.81204i	−0.252769	−	1.81204i	0.273663	−	0.961826i	$-0.411765\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.40065	+	0.195383i	1.40065	+	0.195383i	0.798017	−	0.602635i	$-0.205882\pi$
$113$	1.40065	+	0.195383i	1.40065	+	0.195383i	0.602635	+	0.798017i	$0.294118\pi$
$114$		0			0
$115$		0			0
$116$	−0.748723	+	0.621731i	−0.748723	+	0.621731i
$117$	−1.29596	+	1.42160i	−1.29596	+	1.42160i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$122$	−1.11943	−	1.63417i	−1.11943	−	1.63417i
$123$		0			0
$124$		0			0
$125$	−2.49693	+	1.71044i	−2.49693	+	1.71044i
$126$		0			0
$127$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$127$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$128$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$129$		0			0
$130$	1.47345	−	3.33704i	1.47345	−	3.33704i
$131$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$131$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.526432	−	0.850217i	0.526432	−	0.850217i
$137$	1.32307	−	1.20614i	1.32307	−	1.20614i	0.361242	−	0.932472i	$-0.382353\pi$
$137$	1.32307	−	1.20614i	1.32307	−	1.20614i	0.961826	−	0.273663i	$-0.0882353\pi$
$138$		0			0
$139$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$139$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.361242	+	0.932472i	−0.361242	+	0.932472i
$145$	0.666678	−	1.72089i	0.666678	−	1.72089i
$146$	−1.52643	−	0.850217i	−1.52643	−	0.850217i
$147$		0			0
$148$	−0.800095	+	0.111609i	−0.800095	+	0.111609i
$149$	0.329838	−	0.436776i	0.329838	−	0.436776i	−0.602635	−	0.798017i	$-0.705882\pi$
$149$	0.329838	−	0.436776i	0.329838	−	0.436776i	0.932472	+	0.361242i	$0.117647\pi$
$150$		0			0
$151$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$151$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$152$		0			0
$153$	0.361242	−	0.932472i	0.361242	−	0.932472i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.757949	+	0.469302i	−0.757949	+	0.469302i	−0.850217	−	0.526432i	$-0.823529\pi$
$157$	−0.757949	+	0.469302i	−0.757949	+	0.469302i	0.0922684	+	0.995734i	$0.470588\pi$
$158$		0			0
$159$		0			0
$160$	0.0875787	−	1.89430i	0.0875787	−	1.89430i
$161$		0			0
$162$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$163$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$163$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$164$	−0.524354	+	0.359191i	−0.524354	+	0.359191i
$165$		0			0
$166$		0			0
$167$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$167$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$168$		0			0
$169$	−1.62738	−	2.15499i	−1.62738	−	2.15499i
$170$	−0.0875787	+	1.89430i	−0.0875787	+	1.89430i
$171$		0			0
$172$		0			0
$173$	−1.49780	+	1.24376i	−1.49780	+	1.24376i	−0.602635	+	0.798017i	$0.705882\pi$
$173$	−1.49780	+	1.24376i	−1.49780	+	1.24376i	−0.895163	+	0.445738i	$0.852941\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−0.486734	+	0.533922i	−0.486734	+	0.533922i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−0.261989	−	1.87814i	−0.261989	−	1.87814i
$181$	0.0878098	+	0.261989i	0.0878098	+	0.261989i	0.982973	−	0.183750i	$-0.0588235\pi$
$181$	0.0878098	+	0.261989i	0.0878098	+	0.261989i	−0.895163	+	0.445738i	$0.852941\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.22250	−	0.923193i	1.22250	−	0.923193i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$191$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$192$		0			0
$193$	−0.0632619	−	0.453510i	−0.0632619	−	0.453510i	−0.995734	−	0.0922684i	$-0.970588\pi$
$193$	−0.0632619	−	0.453510i	−0.0632619	−	0.453510i	0.932472	−	0.361242i	$-0.117647\pi$
$194$	0.0710610	+	0.0590083i	0.0710610	+	0.0590083i
$195$		0			0
$196$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$197$	−1.21146	−	0.406040i	−1.21146	−	0.406040i	−0.361242	−	0.932472i	$-0.617647\pi$
$197$	−1.21146	−	0.406040i	−1.21146	−	0.406040i	−0.850217	+	0.526432i	$0.823529\pi$
$198$		0			0
$199$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$199$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$200$	1.15715	+	2.32387i	1.15715	+	2.32387i
$201$		0			0
$202$	−0.365931	+	1.95756i	−0.365931	+	1.95756i
$203$		0			0
$204$		0			0
$205$	0.537235	−	1.07891i	0.537235	−	1.07891i
$206$		0			0
$207$		0			0
$208$	−1.63552	−	1.01267i	−1.63552	−	1.01267i
$209$		0			0
$210$		0			0
$211$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$211$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$212$	−0.942485	+	0.469302i	−0.942485	+	0.469302i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.59837	−	0.890286i	1.59837	−	0.890286i
$219$		0			0
$220$		0			0
$221$	1.63552	+	1.01267i	1.63552	+	1.01267i
$222$		0			0
$223$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$223$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$224$		0			0
$225$	1.56446	+	2.07168i	1.56446	+	2.07168i
$226$	0.323785	+	1.37665i	0.323785	+	1.37665i
$227$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$227$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$228$		0			0
$229$	1.89090	−	0.538007i	1.89090	−	0.538007i	0.895163	−	0.445738i	$-0.147059\pi$
$229$	1.89090	−	0.538007i	1.89090	−	0.538007i	0.995734	−	0.0922684i	$-0.0294118\pi$
$230$		0			0
$231$		0			0
$232$	−0.850217	−	0.473568i	−0.850217	−	0.473568i
$233$	0.0590083	+	1.27633i	0.0590083	+	1.27633i	0.798017	+	0.602635i	$0.205882\pi$
$233$	0.0590083	+	1.27633i	0.0590083	+	1.27633i	−0.739009	+	0.673696i	$0.764706\pi$
$234$	−1.79375	−	0.694903i	−1.79375	−	0.694903i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$239$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$240$		0			0
$241$	−0.268973	−	0.0632619i	−0.268973	−	0.0632619i	0.0922684	−	0.995734i	$-0.470588\pi$
$241$	−0.268973	−	0.0632619i	−0.268973	−	0.0632619i	−0.361242	+	0.932472i	$0.617647\pi$
$242$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$243$		0			0
$244$	1.11943	−	1.63417i	1.11943	−	1.63417i
$245$	1.21146	+	1.45890i	1.21146	+	1.45890i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−2.49693	−	1.71044i	−2.49693	−	1.71044i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$257$	1.79375	−	0.510366i	1.79375	−	0.510366i	0.798017	−	0.602635i	$-0.205882\pi$
$257$	1.79375	−	0.510366i	1.79375	−	0.510366i	0.995734	+	0.0922684i	$0.0294118\pi$
$258$		0			0
$259$		0			0
$260$	3.64397	+	0.168471i	3.64397	+	0.168471i
$261$	−0.922758	−	0.309277i	−0.922758	−	0.309277i
$262$		0			0
$263$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$263$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$264$		0			0
$265$	1.12833	−	1.64716i	1.12833	−	1.64716i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.621500	−	1.40756i	−0.621500	−	1.40756i	−0.895163	−	0.445738i	$-0.852941\pi$
$269$	−0.621500	−	1.40756i	−0.621500	−	1.40756i	0.273663	−	0.961826i	$-0.411765\pi$
$270$		0			0
$271$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$271$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$272$	0.982973	+	0.183750i	0.982973	+	0.183750i
$273$		0			0
$274$	1.60263	+	0.798017i	1.60263	+	0.798017i
$275$		0			0
$276$		0			0
$277$	1.10025	+	1.60617i	1.10025	+	1.60617i	0.739009	+	0.673696i	$0.235294\pi$
$277$	1.10025	+	1.60617i	1.10025	+	1.60617i	0.361242	+	0.932472i	$0.382353\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.20614	+	0.600584i	1.20614	+	0.600584i	0.932472	−	0.361242i	$-0.117647\pi$
$281$	1.20614	+	0.600584i	1.20614	+	0.600584i	0.273663	+	0.961826i	$0.411765\pi$
$282$		0			0
$283$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$283$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.00000			−1.00000
$289$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$290$	1.84552			1.84552
$291$		0			0
$292$	0.241393	−	1.73049i	0.241393	−	1.73049i
$293$	−1.37821	+	1.25640i	−1.37821	+	1.25640i	−0.445738	+	0.895163i	$0.647059\pi$
$293$	−1.37821	+	1.25640i	−1.37821	+	1.25640i	−0.932472	+	0.361242i	$0.882353\pi$
$294$		0			0
$295$		0			0
$296$	−0.393100	−	0.705749i	−0.393100	−	0.705749i
$297$		0			0
$298$	0.526432	+	0.149783i	0.526432	+	0.149783i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.346585	+	3.74025i	−0.346585	+	3.74025i
$306$	1.00000			1.00000
$307$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$307$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$311$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$312$		0			0
$313$	−0.869557	+	1.26940i	−0.869557	+	1.26940i	0.0922684	+	0.995734i	$0.470588\pi$
$313$	−0.869557	+	1.26940i	−0.869557	+	1.26940i	−0.961826	+	0.273663i	$0.911765\pi$
$314$	−0.711414	−	0.537235i	−0.711414	−	0.537235i
$315$		0			0
$316$		0			0
$317$	1.45890	+	0.488975i	1.45890	+	0.488975i	0.932472	−	0.361242i	$-0.117647\pi$
$317$	1.45890	+	0.488975i	1.45890	+	0.488975i	0.526432	+	0.850217i	$0.323529\pi$
$318$		0			0
$319$		0			0
$320$	1.79802	−	0.602635i	1.79802	−	0.602635i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$325$	−4.47032	+	2.22596i	−4.47032	+	2.22596i
$326$		0			0
$327$		0			0
$328$	−0.524354	−	0.359191i	−0.524354	−	0.359191i
$329$		0			0
$330$		0			0
$331$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$331$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$332$		0			0
$333$	−0.516087	−	0.621500i	−0.516087	−	0.621500i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.10025	+	0.258777i	1.10025	+	0.258777i	0.739009	−	0.673696i	$-0.235294\pi$
$337$	1.10025	+	0.258777i	1.10025	+	0.258777i	0.361242	+	0.932472i	$0.382353\pi$
$338$	1.42160	−	2.29596i	1.42160	−	2.29596i
$339$		0			0
$340$	−1.79802	+	0.602635i	−1.79802	+	0.602635i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.70083	−	0.947359i	−1.70083	−	0.947359i
$347$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$347$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$348$		0			0
$349$	0.353470	−	0.100571i	0.353470	−	0.100571i	−0.0922684	−	0.995734i	$-0.529412\pi$
$349$	0.353470	−	0.100571i	0.353470	−	0.100571i	0.445738	+	0.895163i	$0.352941\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.111208	+	0.147263i	0.111208	+	0.147263i	0.850217	−	0.526432i	$-0.176471\pi$
$353$	0.111208	+	0.147263i	0.111208	+	0.147263i	−0.739009	+	0.673696i	$0.764706\pi$
$354$		0			0
$355$		0			0
$356$	−0.673696	−	0.260991i	−0.673696	−	0.260991i
$357$		0			0
$358$		0			0
$359$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$359$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$360$	1.65667	−	0.922758i	1.65667	−	0.922758i
$361$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$362$	−0.212577	+	0.176521i	−0.212577	+	0.176521i
$363$		0			0
$364$		0			0
$365$	1.19692	+	3.08960i	1.19692	+	3.08960i
$366$		0			0
$367$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$367$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$368$		0			0
$369$	−0.581427	−	0.256725i	−0.581427	−	0.256725i
$370$	1.30247	+	0.806456i	1.30247	+	0.806456i
$371$		0			0
$372$		0			0
$373$	0.163808	−	0.328972i	0.163808	−	0.328972i	−0.798017	−	0.602635i	$-0.794118\pi$
$373$	0.163808	−	0.328972i	0.163808	−	0.328972i	0.961826	+	0.273663i	$0.0882353\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.910979	−	1.63552i	0.910979	−	1.63552i
$378$		0			0
$379$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$379$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$383$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$384$		0			0
$385$		0			0
$386$	0.400033	−	0.222817i	0.400033	−	0.222817i
$387$		0			0
$388$	−0.0293534	+	0.0875787i	−0.0293534	+	0.0875787i
$389$	−1.69318	+	0.156896i	−1.69318	+	0.156896i	−0.895163	−	0.445738i	$-0.852941\pi$
$389$	−1.69318	+	0.156896i	−1.69318	+	0.156896i	−0.798017	+	0.602635i	$0.794118\pi$
$390$		0			0
$391$		0			0
$392$	0.850217	−	0.526432i	0.850217	−	0.526432i
$393$		0			0
$394$	−0.0590083	−	1.27633i	−0.0590083	−	1.27633i
$395$		0			0
$396$		0			0
$397$	0.581427	+	1.73474i	0.581427	+	1.73474i	0.673696	+	0.739009i	$0.264706\pi$
$397$	0.581427	+	1.73474i	0.581427	+	1.73474i	−0.0922684	+	0.995734i	$0.529412\pi$
$398$		0			0
$399$		0			0
$400$	−1.74894	+	1.91849i	−1.74894	+	1.91849i
$401$	−1.78099	+	0.786384i	−1.78099	+	0.786384i	−0.798017	+	0.602635i	$0.794118\pi$
$401$	−1.78099	+	0.786384i	−1.78099	+	0.786384i	−0.982973	+	0.183750i	$0.941176\pi$
$402$		0			0
$403$		0			0
$404$	−1.95756	+	0.365931i	−1.95756	+	0.365931i
$405$	1.45890	−	1.21146i	1.45890	−	1.21146i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.726337	−	0.961826i	−0.726337	−	0.961826i	0.273663	−	0.961826i	$-0.411765\pi$
$409$	−0.726337	−	0.961826i	−0.726337	−	0.961826i	−1.00000			$\pi$
$410$	1.20013	+	0.111208i	1.20013	+	0.111208i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.353470	−	1.89090i	0.353470	−	1.89090i
$417$		0			0
$418$		0			0
$419$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$419$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$420$		0			0
$421$	1.69318	−	1.04837i	1.69318	−	1.04837i	0.798017	−	0.602635i	$-0.205882\pi$
$421$	1.69318	−	1.04837i	1.69318	−	1.04837i	0.895163	−	0.445738i	$-0.147059\pi$
$422$		0			0
$423$		0			0
$424$	−0.778076	−	0.709310i	−0.778076	−	0.709310i
$425$	1.74894	−	1.91849i	1.74894	−	1.91849i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$431$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$432$		0			0
$433$	−0.322039	+	0.831277i	−0.322039	+	0.831277i	0.673696	+	0.739009i	$0.264706\pi$
$433$	−0.322039	+	0.831277i	−0.322039	+	0.831277i	−0.995734	+	0.0922684i	$0.970588\pi$
$434$		0			0
$435$		0			0
$436$	1.40756	+	1.16883i	1.40756	+	1.16883i
$437$		0			0
$438$		0			0
$439$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$439$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$440$		0			0
$441$	0.739009	−	0.673696i	0.739009	−	0.673696i
$442$	−0.353470	+	1.89090i	−0.353470	+	1.89090i
$443$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$443$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$444$		0			0
$445$	1.35692	−	0.189283i	1.35692	−	0.189283i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.0211475	−	0.457413i	0.0211475	−	0.457413i	−0.961826	−	0.273663i	$-0.911765\pi$
$449$	0.0211475	−	0.457413i	0.0211475	−	0.457413i	0.982973	−	0.183750i	$-0.0588235\pi$
$450$	−1.36664	+	2.20719i	−1.36664	+	2.20719i
$451$		0			0
$452$	−1.16672	+	0.799224i	−1.16672	+	0.799224i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.183750	+	0.0170269i	0.183750	+	0.0170269i	0.183750	−	0.982973i	$-0.441176\pi$
$457$	0.183750	+	0.0170269i	0.183750	+	0.0170269i			1.00000i	$0.5\pi$
$458$	1.18475	+	1.56886i	1.18475	+	1.56886i
$459$		0			0
$460$		0			0
$461$	−0.907732	+	0.995734i	−0.907732	+	0.995734i	0.0922684	+	0.995734i	$0.470588\pi$
$461$	−0.907732	+	0.995734i	−0.907732	+	0.995734i	−1.00000			$\pi$
$462$		0			0
$463$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$463$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$464$	0.134455	−	0.963876i	0.134455	−	0.963876i
$465$		0			0
$466$	−1.16883	+	0.516087i	−1.16883	+	0.516087i
$467$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$467$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$468$		−	1.92365i		−	1.92365i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.895163	−	0.554262i	−0.895163	−	0.554262i
$478$		0			0
$479$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$479$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$480$		0			0
$481$	1.35761	−	0.756186i	1.35761	−	0.756186i
$482$	−0.0381744	−	0.273663i	−0.0381744	−	0.273663i
$483$		0			0
$484$	0.798017	−	0.602635i	0.798017	−	0.602635i
$485$	−0.0321851	−	0.172175i	−0.0321851	−	0.172175i
$486$		0			0
$487$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$487$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$488$	1.92821	+	0.453510i	1.92821	+	0.453510i
$489$		0			0
$490$	−0.922758	+	1.65667i	−0.922758	+	1.65667i
$491$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$491$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$492$		0			0
$493$	−0.134455	+	0.963876i	−0.134455	+	0.963876i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$499$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$500$	0.692940	−	2.94620i	0.692940	−	2.94620i
$501$		0			0
$502$		0			0
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$		0			0
$505$	2.90536	−	2.41258i	2.90536	−	2.41258i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.58561	−	0.614268i	1.58561	−	0.614268i	0.602635	−	0.798017i	$-0.294118\pi$
$509$	1.58561	−	0.614268i	1.58561	−	0.614268i	0.982973	+	0.183750i	$0.0588235\pi$
$510$		0			0
$511$		0			0
$512$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$513$		0			0
$514$	1.12388	+	1.48826i	1.12388	+	1.48826i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	1.15926	+	3.45876i	1.15926	+	3.45876i
$521$	−1.23549	−	0.688163i	−1.23549	−	0.688163i	−0.273663	−	0.961826i	$-0.588235\pi$
$521$	−1.23549	−	0.688163i	−1.23549	−	0.688163i	−0.961826	+	0.273663i	$0.911765\pi$
$522$	−0.0449462	−	0.972171i	−0.0449462	−	0.972171i
$523$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$523$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$530$	1.94354	+	0.457116i	1.94354	+	0.457116i
$531$		0			0
$532$		0			0
$533$	0.690958	−	1.00867i	0.690958	−	1.00867i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	1.08800	−	1.08800i	1.08800	−	1.08800i
$539$		0			0
$540$		0			0
$541$	0.227957	+	0.156154i	0.227957	+	0.156154i	0.673696	−	0.739009i	$-0.264706\pi$
$541$	0.227957	+	0.156154i	0.227957	+	0.156154i	−0.445738	+	0.895163i	$0.647059\pi$
$542$		0			0
$543$		0			0
$544$	0.183750	+	0.982973i	0.183750	+	0.982973i
$545$	−3.41041	−	0.637516i	−3.41041	−	0.637516i
$546$		0			0
$547$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$547$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$548$	−0.165190	+	1.78269i	−0.165190	+	1.78269i
$549$	1.97871	+	0.0914812i	1.97871	+	0.0914812i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−1.10025	+	1.60617i	−1.10025	+	1.60617i
$555$		0			0
$556$		0			0
$557$	−0.673696	+	0.260991i	−0.673696	+	0.260991i	−0.673696	−	0.739009i	$-0.735294\pi$
$557$	−0.673696	+	0.260991i	−0.673696	+	0.260991i			1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.124322	+	1.34164i	−0.124322	+	1.34164i
$563$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$563$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$564$		0			0
$565$	1.19538	−	2.40065i	1.19538	−	2.40065i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$569$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$570$		0			0
$571$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$571$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$577$	−0.367499			−0.367499			−0.183750	−	0.982973i	$-0.558824\pi$
$577$	−0.367499			−0.367499			−0.183750	+	0.982973i	$0.558824\pi$
$578$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$579$		0			0
$580$	0.666678	+	1.72089i	0.666678	+	1.72089i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	1.70083	−	0.400033i	1.70083	−	0.400033i
$585$	1.77507	+	3.18685i	1.77507	+	3.18685i
$586$	−1.66943	−	0.831277i	−1.66943	−	0.831277i
$587$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$587$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.516087	−	0.621500i	0.516087	−	0.621500i
$593$	1.60263	+	0.798017i	1.60263	+	0.798017i	1.00000			$0$
$593$	1.60263	+	0.798017i	1.60263	+	0.798017i	0.602635	+	0.798017i	$0.294118\pi$
$594$		0			0
$595$		0			0
$596$	0.0505009	+	0.544991i	0.0505009	+	0.544991i
$597$		0			0
$598$		0			0
$599$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$599$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$600$		0			0
$601$	−0.850217	−	1.52643i	−0.850217	−	1.52643i	−0.850217	−	0.526432i	$-0.823529\pi$
$601$	−0.850217	−	1.52643i	−0.850217	−	1.52643i		−	1.00000i	$-0.5\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.765964	+	1.73474i	−0.765964	+	1.73474i
$606$		0			0
$607$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$607$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$608$		0			0
$609$		0			0
$610$	−3.61288	+	1.02795i	−3.61288	+	1.02795i
$611$		0			0
$612$	0.361242	+	0.932472i	0.361242	+	0.932472i
$613$	−1.45285	+	0.271585i	−1.45285	+	0.271585i	−0.850217	−	0.526432i	$-0.823529\pi$
$613$	−1.45285	+	0.271585i	−1.45285	+	0.271585i	−0.602635	+	0.798017i	$0.705882\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.44147	−	0.987432i	−1.44147	−	0.987432i	−0.995734	−	0.0922684i	$-0.970588\pi$
$617$	−1.44147	−	0.987432i	−1.44147	−	0.987432i	−0.445738	−	0.895163i	$-0.647059\pi$
$618$		0			0
$619$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$619$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.860221	+	3.02336i	0.860221	+	3.02336i
$626$	−1.49780	−	0.352279i	−1.49780	−	0.352279i
$627$		0			0
$628$	0.243964	−	0.857445i	0.243964	−	0.857445i
$629$	−0.516087	+	0.621500i	−0.516087	+	0.621500i
$630$		0			0
$631$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$631$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$632$		0			0
$633$		0			0
$634$	0.0710610	+	1.53703i	0.0710610	+	1.53703i
$635$		0			0
$636$		0			0
$637$	1.01267	+	1.63552i	1.01267	+	1.63552i
$638$		0			0
$639$		0			0
$640$	1.21146	+	1.45890i	1.21146	+	1.45890i
$641$	−0.258777	−	1.10025i	−0.258777	−	1.10025i	−0.932472	−	0.361242i	$-0.882353\pi$
$641$	−0.258777	−	1.10025i	−0.258777	−	1.10025i	0.673696	−	0.739009i	$-0.264706\pi$
$642$		0			0
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$647$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$648$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$649$		0			0
$650$	−3.69051	−	3.36435i	−3.69051	−	3.36435i
$651$		0			0
$652$		0			0
$653$	−1.16672	+	1.16672i	−1.16672	+	1.16672i	−0.183750	+	0.982973i	$0.558824\pi$
$653$	−1.16672	+	1.16672i	−1.16672	+	1.16672i	−0.982973	+	0.183750i	$0.941176\pi$
$654$		0			0
$655$		0			0
$656$	0.145517	−	0.618701i	0.145517	−	0.618701i
$657$	1.59837	−	0.705749i	1.59837	−	0.705749i
$658$		0			0
$659$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$659$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$660$		0			0
$661$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$661$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.393100	−	0.705749i	0.393100	−	0.705749i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.53703	−	1.27633i	−1.53703	−	1.27633i	−0.798017	−	0.602635i	$-0.794118\pi$
$673$	−1.53703	−	1.27633i	−1.53703	−	1.27633i	−0.739009	−	0.673696i	$-0.764706\pi$
$674$	0.156154	+	1.11943i	0.156154	+	1.11943i
$675$		0			0
$676$	2.65445	+	0.496203i	2.65445	+	0.496203i
$677$	−0.634905	+	1.89430i	−0.634905	+	1.89430i	−0.273663	+	0.961826i	$0.588235\pi$
$677$	−0.634905	+	1.89430i	−0.634905	+	1.89430i	−0.361242	+	0.932472i	$0.617647\pi$
$678$		0			0
$679$		0			0
$680$	−1.21146	−	1.45890i	−1.21146	−	1.45890i
$681$		0			0
$682$		0			0
$683$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$683$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$684$		0			0
$685$	−1.37133	−	3.10576i	−1.37133	−	3.10576i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.36447	−	1.49675i	1.36447	−	1.49675i
$690$		0			0
$691$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$691$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$692$	0.268973	−	1.92821i	0.268973	−	1.92821i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.145517	+	0.618701i	−0.145517	+	0.618701i
$698$	0.221468	+	0.293271i	0.221468	+	0.293271i
$699$		0			0
$700$		0			0
$701$	0.544991	−	1.91545i	0.544991	−	1.91545i	0.183750	−	0.982973i	$-0.441176\pi$
$701$	0.544991	−	1.91545i	0.544991	−	1.91545i	0.361242	−	0.932472i	$-0.382353\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.0971461	+	0.156896i	−0.0971461	+	0.156896i
$707$		0			0
$708$		0			0
$709$	−1.16672	−	1.16672i	−1.16672	−	1.16672i	−0.982973	−	0.183750i	$-0.941176\pi$
$709$	−1.16672	−	1.16672i	−1.16672	−	1.16672i	−0.183750	−	0.982973i	$-0.558824\pi$
$710$		0			0
$711$		0			0
$712$		−	0.722483i		−	0.722483i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$719$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$720$	1.45890	+	1.21146i	1.45890	+	1.21146i
$721$		0			0
$722$	0.361242	−	0.932472i	0.361242	−	0.932472i
$723$		0			0
$724$	−0.241393	−	0.134455i	−0.241393	−	0.134455i
$725$	−1.94371	−	1.61404i	−1.94371	−	1.61404i
$726$		0			0
$727$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$727$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$728$		0			0
$729$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$730$	−2.44859	+	2.23218i	−2.44859	+	2.23218i
$731$		0			0
$732$		0			0
$733$		−	1.79033i		−	1.79033i	−0.445738	−	0.895163i	$-0.647059\pi$
$733$		−	1.79033i		−	1.79033i	0.445738	−	0.895163i	$-0.352941\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.0293534	−	0.634905i	0.0293534	−	0.634905i
$739$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$739$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$740$	−0.281491	+	1.50584i	−0.281491	+	1.50584i
$741$		0			0
$742$		0			0
$743$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$743$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$744$		0			0
$745$	−0.586558	−	0.856270i	−0.586558	−	0.856270i
$746$	0.365931	+	0.0339085i	0.365931	+	0.0339085i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$751$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$752$		0			0
$753$		0			0
$754$	1.85416	+	0.258645i	1.85416	+	0.258645i
$755$		0			0
$756$		0			0
$757$		−	1.47802i		−	1.47802i	−0.673696	−	0.739009i	$-0.735294\pi$
$757$		−	1.47802i		−	1.47802i	0.673696	−	0.739009i	$-0.264706\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.165190	−	1.78269i	−0.165190	−	1.78269i	−0.526432	−	0.850217i	$-0.676471\pi$
$761$	−0.165190	−	1.78269i	−0.165190	−	1.78269i	0.361242	−	0.932472i	$-0.382353\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.45890	−	1.21146i	−1.45890	−	1.21146i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.710182	+	0.132756i	0.710182	+	0.132756i	0.526432	−	0.850217i	$-0.323529\pi$
$769$	0.710182	+	0.132756i	0.710182	+	0.132756i	0.183750	+	0.982973i	$0.441176\pi$
$770$		0			0
$771$		0			0
$772$	0.352279	+	0.292529i	0.352279	+	0.292529i
$773$	0.711414	−	0.537235i	0.711414	−	0.537235i	−0.183750	−	0.982973i	$-0.558824\pi$
$773$	0.711414	−	0.537235i	0.711414	−	0.537235i	0.895163	+	0.445738i	$0.147059\pi$
$774$		0			0
$775$		0			0
$776$	−0.0922684	+	0.00426582i	−0.0922684	+	0.00426582i
$777$		0			0
$778$	−0.757949	−	1.52217i	−0.757949	−	1.52217i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.798017	+	0.602635i	0.798017	+	0.602635i
$785$	0.387047	+	1.64562i	0.387047	+	1.64562i
$786$		0			0
$787$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$787$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$788$	1.16883	−	0.516087i	1.16883	−	0.516087i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.872395	+	3.70920i	−0.872395	+	3.70920i
$794$	−1.40756	+	1.16883i	−1.40756	+	1.16883i
$795$		0			0
$796$		0			0
$797$	−0.554262	−	0.895163i	−0.554262	−	0.895163i	0.445738	−	0.895163i	$-0.352941\pi$
$797$	−0.554262	−	0.895163i	−0.554262	−	0.895163i	−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$	−2.42073	−	0.937796i	−2.42073	−	0.937796i
$801$	−0.132756	−	0.710182i	−0.132756	−	0.710182i
$802$	−1.37665	−	1.37665i	−1.37665	−	1.37665i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.04837	−	1.69318i	−1.04837	−	1.69318i
$809$	−0.406040	−	1.21146i	−0.406040	−	1.21146i	−0.932472	−	0.361242i	$-0.882353\pi$
$809$	−0.406040	−	1.21146i	−0.406040	−	1.21146i	0.526432	−	0.850217i	$-0.323529\pi$
$810$	1.65667	+	0.922758i	1.65667	+	0.922758i
$811$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$811$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.634493	−	1.02474i	0.634493	−	1.02474i
$819$		0			0
$820$	0.329838	+	1.15926i	0.329838	+	1.15926i
$821$	1.26544	−	1.52391i	1.26544	−	1.52391i	0.526432	−	0.850217i	$-0.323529\pi$
$821$	1.26544	−	1.52391i	1.26544	−	1.52391i	0.739009	−	0.673696i	$-0.235294\pi$
$822$		0			0
$823$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$823$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$	−0.547326			−0.547326			−0.273663	−	0.961826i	$-0.588235\pi$
$829$	−0.547326			−0.547326			−0.273663	+	0.961826i	$0.588235\pi$
$830$		0			0
$831$		0			0
$832$	1.89090	−	0.353470i	1.89090	−	0.353470i
$833$	−0.798017	−	0.602635i	−0.798017	−	0.602635i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$839$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$840$		0			0
$841$	−0.0526388	−	0.00487770i	−0.0526388	−	0.00487770i
$842$	1.58923	+	1.20013i	1.58923	+	1.20013i
$843$		0			0
$844$		0			0
$845$	−4.85543	+	1.62738i	−4.85543	+	1.62738i
$846$		0			0
$847$		0			0
$848$	0.380338	−	0.981767i	0.380338	−	0.981767i
$849$		0			0
$850$	2.42073	+	0.937796i	2.42073	+	0.937796i
$851$		0			0
$852$		0			0
$853$	−0.722071	+	0.869557i	−0.722071	+	0.869557i	−0.995734	−	0.0922684i	$-0.970588\pi$
$853$	−0.722071	+	0.869557i	−0.722071	+	0.869557i	0.273663	+	0.961826i	$0.411765\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.64823	+	0.0762025i	−1.64823	+	0.0762025i	−0.850217	−	0.526432i	$-0.823529\pi$
$857$	−1.64823	+	0.0762025i	−1.64823	+	0.0762025i	−0.798017	+	0.602635i	$0.794118\pi$
$858$		0			0
$859$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$859$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$863$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$864$		0			0
$865$	1.33367	+	3.44260i	1.33367	+	3.44260i
$866$	−0.891477			−0.891477
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.581427	+	1.73474i	−0.581427	+	1.73474i
$873$	−0.0899135	+	0.0211475i	−0.0899135	+	0.0211475i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.74538	−	0.0806938i	1.74538	−	0.0806938i	0.850217	−	0.526432i	$-0.176471\pi$
$877$	1.74538	−	0.0806938i	1.74538	−	0.0806938i	0.895163	+	0.445738i	$0.147059\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.0590083	+	0.0710610i	−0.0590083	+	0.0710610i	−0.798017	−	0.602635i	$-0.794118\pi$
$881$	−0.0590083	+	0.0710610i	−0.0590083	+	0.0710610i	0.739009	+	0.673696i	$0.235294\pi$
$882$	0.895163	+	0.445738i	0.895163	+	0.445738i
$883$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$883$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$884$	−1.89090	+	0.353470i	−1.89090	+	0.353470i
$885$		0			0
$886$		0			0
$887$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$887$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$888$		0			0
$889$		0			0
$890$	0.666678	+	1.19692i	0.666678	+	1.19692i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.434164	−	0.145517i	0.434164	−	0.145517i
$899$		0			0
$900$	−2.55183	−	0.477020i	−2.55183	−	0.477020i
$901$	−0.380338	+	0.981767i	−0.380338	+	0.981767i
$902$		0			0
$903$		0			0
$904$	−1.16672	−	0.799224i	−1.16672	−	0.799224i
$905$	0.523978			0.523978
$906$		0			0
$907$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$907$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$908$		0			0
$909$	−1.34164	−	1.47171i	−1.34164	−	1.47171i
$910$		0			0
$911$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$911$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$912$		0			0
$913$		0			0
$914$	0.0505009	+	0.177492i	0.0505009	+	0.177492i
$915$		0			0
$916$	−1.03494	+	1.67148i	−1.03494	+	1.67148i
$917$		0			0
$918$		0			0
$919$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$919$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$920$		0			0
$921$		0			0
$922$	−1.25640	−	0.486734i	−1.25640	−	0.486734i
$923$		0			0
$924$		0			0
$925$	−0.666468	−	1.98847i	−0.666468	−	1.98847i
$926$		0			0
$927$		0			0
$928$	0.947359	−	0.222817i	0.947359	−	0.222817i
$929$	−1.27633	−	1.53703i	−1.27633	−	1.53703i	−0.673696	−	0.739009i	$-0.735294\pi$
$929$	−1.27633	−	1.53703i	−1.27633	−	1.53703i	−0.602635	−	0.798017i	$-0.705882\pi$
$930$		0			0
$931$		0			0
$932$	−0.903466	−	0.903466i	−0.903466	−	0.903466i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	1.79375	−	0.694903i	1.79375	−	0.694903i
$937$	0.709310	+	1.14558i	0.709310	+	1.14558i	0.982973	+	0.183750i	$0.0588235\pi$
$937$	0.709310	+	1.14558i	0.709310	+	1.14558i	−0.273663	+	0.961826i	$0.588235\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.457413	+	1.94480i	−0.457413	+	1.94480i	−0.183750	+	0.982973i	$0.558824\pi$
$941$	−0.457413	+	1.94480i	−0.457413	+	1.94480i	−0.273663	+	0.961826i	$0.588235\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$947$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$948$		0			0
$949$	0.769523	+	3.27181i	0.769523	+	3.27181i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.322039	−	0.646741i	−0.322039	−	0.646741i	0.673696	−	0.739009i	$-0.264706\pi$
$953$	−0.322039	−	0.646741i	−0.322039	−	0.646741i	−0.995734	+	0.0922684i	$0.970588\pi$
$954$	0.193463	−	1.03494i	0.193463	−	1.03494i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.798017	−	0.602635i	0.798017	−	0.602635i
$962$	1.19555	+	0.992772i	1.19555	+	0.992772i
$963$		0			0
$964$	0.241393	−	0.134455i	0.241393	−	0.134455i
$965$	−0.853543	−	0.159555i	−0.853543	−	0.159555i
$966$		0			0
$967$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$967$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$968$	0.850217	+	0.526432i	0.850217	+	0.526432i
$969$		0			0
$970$	0.148922	−	0.0922085i	0.148922	−	0.0922085i
$971$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$971$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.273663	+	1.96183i	0.273663	+	1.96183i
$977$			0.367499i			0.367499i	0.982973	+	0.183750i	$0.0588235\pi$
$977$			0.367499i			0.367499i	−0.982973	+	0.183750i	$0.941176\pi$
$978$		0			0
$979$		0			0
$980$	−1.87814	−	0.261989i	−1.87814	−	0.261989i
$981$	−0.252769	+	1.81204i	−0.252769	+	1.81204i
$982$		0			0
$983$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$983$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$984$		0			0
$985$	−1.46013	+	1.93353i	−1.46013	+	1.93353i
$986$	−0.947359	+	0.222817i	−0.947359	+	0.222817i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$991$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.184956	+	0.418885i	−0.184956	+	0.418885i	−0.982973	−	0.183750i	$-0.941176\pi$
$997$	−0.184956	+	0.418885i	−0.184956	+	0.418885i	0.798017	+	0.602635i	$0.205882\pi$
$998$		0			0
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1156.1.o.a.319.1	✓	32
4.3	odd	2	CM	1156.1.o.a.319.1	✓	32
289.106	even	68	inner	1156.1.o.a.395.1	yes	32
1156.395	odd	68	inner	1156.1.o.a.395.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1156.1.o.a.319.1	✓	32	1.1	even	1	trivial
1156.1.o.a.319.1	✓	32	4.3	odd	2	CM
1156.1.o.a.395.1	yes	32	289.106	even	68	inner
1156.1.o.a.395.1	yes	32	1156.395	odd	68	inner

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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1156.1.o.a.319.1

Level	$1156$
Weight	$1$
Character	1156.319
Analytic conductor	$0.577$
Analytic rank	$0$
Dimension	$32$
Projective image	$D_{68}$
CM discriminant	-4
Inner twists	$4$