LMFDB - Embedded newform 1096.1.z.a.419.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1096,1,Mod(11,1096)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1096, base_ring=CyclotomicField(68))

chi = DirichletCharacter(H, H._module([34, 34, 61]))

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

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

chi := DirichletCharacter("1096.11");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1096 = 2^{3} \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1096.z (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:	$0.546975253846$
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			419.1
Root			$0.526432 + 0.850217i$ of defining polynomial
Character	$\chi$	$=$	1096.419
Dual form			1096.1.z.a.531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.798017 - 0.602635i) q^{2} +(0.621500 + 0.516087i) q^{3} +(0.273663 + 0.961826i) q^{4} +(-0.184956 - 0.786384i) q^{6} +(0.361242 - 0.932472i) q^{8} +(-0.0638330 - 0.341476i) q^{9} +O(q^{10})$	\(q+(-0.798017 - 0.602635i) q^{2} +(0.621500 + 0.516087i) q^{3} +(0.273663 + 0.961826i) q^{4} +(-0.184956 - 0.786384i) q^{6} +(0.361242 - 0.932472i) q^{8} +(-0.0638330 - 0.341476i) q^{9} +(1.63552 - 0.465346i) q^{11} +(-0.326304 + 0.739009i) q^{12} +(-0.850217 + 0.526432i) q^{16} +(0.380338 + 0.981767i) q^{17} +(-0.154846 + 0.310972i) q^{18} +(-0.646741 - 0.322039i) q^{19} +(-1.58561 - 0.614268i) q^{22} +(0.705749 - 0.393100i) q^{24} +(-0.961826 - 0.273663i) q^{25} +(0.529659 - 0.950920i) q^{27} +(0.995734 + 0.0922684i) q^{32} +(1.25664 + 0.554859i) q^{33} +(0.288130 - 1.01267i) q^{34} +(0.310972 - 0.154846i) q^{36} +(0.322039 + 0.646741i) q^{38} +(1.08800 + 1.08800i) q^{41} +(-0.145517 - 0.434164i) q^{43} +(0.895163 + 1.44574i) q^{44} +(-0.800095 - 0.111609i) q^{48} +(-0.0922684 + 0.995734i) q^{49} +(0.602635 + 0.798017i) q^{50} +(-0.270297 + 0.806456i) q^{51} +(-0.995734 + 0.439660i) q^{54} +(-0.235749 - 0.533922i) q^{57} +(1.18475 - 0.221468i) q^{59} +(-0.739009 - 0.673696i) q^{64} +(-0.668440 - 1.20008i) q^{66} +(-1.82764 - 0.0844967i) q^{67} +(-0.840204 + 0.634493i) q^{68} +(-0.341476 - 0.0638330i) q^{72} +(1.47171 + 1.34164i) q^{73} +(-0.456541 - 0.666468i) q^{75} +(0.132756 - 0.710182i) q^{76} +(0.496008 - 0.192155i) q^{81} +(-0.212577 - 1.52391i) q^{82} +(0.0844967 - 0.0373089i) q^{83} +(-0.145517 + 0.434164i) q^{86} +(0.156896 - 1.69318i) q^{88} +(-0.629488 - 0.0878098i) q^{89} +(0.571231 + 0.571231i) q^{96} +(-1.52643 - 0.850217i) q^{97} +(0.673696 - 0.739009i) q^{98} +(-0.263305 - 0.528787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6}+O(q^{10}) $ 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6	$ 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6} - 32 q^{12} - 2 q^{16} - 2 q^{18} - 4 q^{22} + 2 q^{24} + 4 q^{33} - 2 q^{41} + 2 q^{43} - 2 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{59} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 2 q^{72} - 2 q^{75} - 2 q^{81} + 2 q^{82} - 2 q^{83} + 2 q^{86} + 4 q^{88} + 2 q^{89} - 2 q^{96} - 32 q^{97} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6 - 32 * q^12 - 2 * q^16 - 2 * q^18 - 4 * q^22 + 2 * q^24 + 4 * q^33 - 2 * q^41 + 2 * q^43 - 2 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^59 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 2 * q^72 - 2 * q^75 - 2 * q^81 + 2 * q^82 - 2 * q^83 + 2 * q^86 + 4 * q^88 + 2 * q^89 - 2 * q^96 - 32 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$549$	$823$	$825$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{68}\right)$

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 $

$2$	−0.798017	−	0.602635i	−0.798017	−	0.602635i
$2$	−0.798017	−	0.602635i	−0.798017	−	0.602635i
$3$	0.621500	+	0.516087i	0.621500	+	0.516087i	0.895163	−	0.445738i	$-0.147059\pi$
$3$	0.621500	+	0.516087i	0.621500	+	0.516087i	−0.273663	+	0.961826i	$0.588235\pi$
$4$	0.273663	+	0.961826i	0.273663	+	0.961826i
$5$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$5$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$6$	−0.184956	−	0.786384i	−0.184956	−	0.786384i
$7$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$7$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$8$	0.361242	−	0.932472i	0.361242	−	0.932472i
$9$	−0.0638330	−	0.341476i	−0.0638330	−	0.341476i
$10$		0			0
$11$	1.63552	−	0.465346i	1.63552	−	0.465346i	0.673696	−	0.739009i	$-0.264706\pi$
$11$	1.63552	−	0.465346i	1.63552	−	0.465346i	0.961826	+	0.273663i	$0.0882353\pi$
$12$	−0.326304	+	0.739009i	−0.326304	+	0.739009i
$13$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$13$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$14$		0			0
$15$		0			0
$16$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$17$	0.380338	+	0.981767i	0.380338	+	0.981767i	0.982973	+	0.183750i	$0.0588235\pi$
$17$	0.380338	+	0.981767i	0.380338	+	0.981767i	−0.602635	+	0.798017i	$0.705882\pi$
$18$	−0.154846	+	0.310972i	−0.154846	+	0.310972i
$19$	−0.646741	−	0.322039i	−0.646741	−	0.322039i	0.0922684	−	0.995734i	$-0.470588\pi$
$19$	−0.646741	−	0.322039i	−0.646741	−	0.322039i	−0.739009	+	0.673696i	$0.764706\pi$
$20$		0			0
$21$		0			0
$22$	−1.58561	−	0.614268i	−1.58561	−	0.614268i
$23$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$23$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$24$	0.705749	−	0.393100i	0.705749	−	0.393100i
$25$	−0.961826	−	0.273663i	−0.961826	−	0.273663i
$26$		0			0
$27$	0.529659	−	0.950920i	0.529659	−	0.950920i
$28$		0			0
$29$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$29$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$30$		0			0
$31$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$31$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$32$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$33$	1.25664	+	0.554859i	1.25664	+	0.554859i
$34$	0.288130	−	1.01267i	0.288130	−	1.01267i
$35$		0			0
$36$	0.310972	−	0.154846i	0.310972	−	0.154846i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	0.322039	+	0.646741i	0.322039	+	0.646741i
$39$		0			0
$40$		0			0
$41$	1.08800	+	1.08800i	1.08800	+	1.08800i	0.995734	+	0.0922684i	$0.0294118\pi$
$41$	1.08800	+	1.08800i	1.08800	+	1.08800i	0.0922684	+	0.995734i	$0.470588\pi$
$42$		0			0
$43$	−0.145517	−	0.434164i	−0.145517	−	0.434164i	0.850217	−	0.526432i	$-0.176471\pi$
$43$	−0.145517	−	0.434164i	−0.145517	−	0.434164i	−0.995734	+	0.0922684i	$0.970588\pi$
$44$	0.895163	+	1.44574i	0.895163	+	1.44574i
$45$		0			0
$46$		0			0
$47$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$47$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$48$	−0.800095	−	0.111609i	−0.800095	−	0.111609i
$49$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$50$	0.602635	+	0.798017i	0.602635	+	0.798017i
$51$	−0.270297	+	0.806456i	−0.270297	+	0.806456i
$52$		0			0
$53$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$53$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$54$	−0.995734	+	0.439660i	−0.995734	+	0.439660i
$55$		0			0
$56$		0			0
$57$	−0.235749	−	0.533922i	−0.235749	−	0.533922i
$58$		0			0
$59$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.445738	−	0.895163i	$-0.352941\pi$
$59$	1.18475	−	0.221468i	1.18475	−	0.221468i	0.739009	+	0.673696i	$0.235294\pi$
$60$		0			0
$61$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$61$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$62$		0			0
$63$		0			0
$64$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$65$		0			0
$66$	−0.668440	−	1.20008i	−0.668440	−	1.20008i
$67$	−1.82764	−	0.0844967i	−1.82764	−	0.0844967i	−0.895163	−	0.445738i	$-0.852941\pi$
$67$	−1.82764	−	0.0844967i	−1.82764	−	0.0844967i	−0.932472	+	0.361242i	$0.882353\pi$
$68$	−0.840204	+	0.634493i	−0.840204	+	0.634493i
$69$		0			0
$70$		0			0
$71$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$71$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$72$	−0.341476	−	0.0638330i	−0.341476	−	0.0638330i
$73$	1.47171	+	1.34164i	1.47171	+	1.34164i	0.798017	+	0.602635i	$0.205882\pi$
$73$	1.47171	+	1.34164i	1.47171	+	1.34164i	0.673696	+	0.739009i	$0.264706\pi$
$74$		0			0
$75$	−0.456541	−	0.666468i	−0.456541	−	0.666468i
$76$	0.132756	−	0.710182i	0.132756	−	0.710182i
$77$		0			0
$78$		0			0
$79$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$79$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$80$		0			0
$81$	0.496008	−	0.192155i	0.496008	−	0.192155i
$82$	−0.212577	−	1.52391i	−0.212577	−	1.52391i
$83$	0.0844967	−	0.0373089i	0.0844967	−	0.0373089i	−0.361242	−	0.932472i	$-0.617647\pi$
$83$	0.0844967	−	0.0373089i	0.0844967	−	0.0373089i	0.445738	+	0.895163i	$0.352941\pi$
$84$		0			0
$85$		0			0
$86$	−0.145517	+	0.434164i	−0.145517	+	0.434164i
$87$		0			0
$88$	0.156896	−	1.69318i	0.156896	−	1.69318i
$89$	−0.629488	−	0.0878098i	−0.629488	−	0.0878098i	−0.183750	−	0.982973i	$-0.558824\pi$
$89$	−0.629488	−	0.0878098i	−0.629488	−	0.0878098i	−0.445738	+	0.895163i	$0.647059\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.571231	+	0.571231i	0.571231	+	0.571231i
$97$	−1.52643	−	0.850217i	−1.52643	−	0.850217i	−0.526432	−	0.850217i	$-0.676471\pi$
$97$	−1.52643	−	0.850217i	−1.52643	−	0.850217i	−1.00000			$\pi$
$98$	0.673696	−	0.739009i	0.673696	−	0.739009i
$99$	−0.263305	−	0.528787i	−0.263305	−	0.528787i
$100$		−	1.00000i		−	1.00000i
$101$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$101$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$102$	0.701700	−	0.480676i	0.701700	−	0.480676i
$103$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$103$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.47171	+	0.136374i	−1.47171	+	0.136374i	−0.798017	−	0.602635i	$-0.794118\pi$
$107$	−1.47171	+	0.136374i	−1.47171	+	0.136374i	−0.673696	+	0.739009i	$0.735294\pi$
$108$	1.05957	+	0.249208i	1.05957	+	0.249208i
$109$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$109$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.11622	+	0.621731i	−1.11622	+	0.621731i	−0.932472	−	0.361242i	$-0.882353\pi$
$113$	−1.11622	+	0.621731i	−1.11622	+	0.621731i	−0.183750	+	0.982973i	$0.558824\pi$
$114$	−0.133628	+	0.568149i	−0.133628	+	0.568149i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.07891	−	0.537235i	−1.07891	−	0.537235i
$119$		0			0
$120$		0			0
$121$	1.60817	−	0.995734i	1.60817	−	0.995734i
$122$		0			0
$123$	0.114690	+	1.23770i	0.114690	+	1.23770i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	0.183750	+	0.982973i	0.183750	+	0.982973i
$129$	0.133628	−	0.344932i	0.133628	−	0.344932i
$130$		0			0
$131$	−0.445738	−	1.89516i	−0.445738	−	1.89516i	−0.445738	−	0.895163i	$-0.647059\pi$
$131$	−0.445738	−	1.89516i	−0.445738	−	1.89516i		−	1.00000i	$-0.5\pi$
$132$	−0.189783	+	1.36051i	−0.189783	+	1.36051i
$133$		0			0
$134$	1.40756	+	1.16883i	1.40756	+	1.16883i
$135$		0			0
$136$	1.05286			1.05286
$137$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$137$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$138$		0			0
$139$	−1.48826	−	1.12388i	−1.48826	−	1.12388i	−0.961826	−	0.273663i	$-0.911765\pi$
$139$	−1.48826	−	1.12388i	−1.48826	−	1.12388i	−0.526432	−	0.850217i	$-0.676471\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.234036	+	0.256725i	0.234036	+	0.256725i
$145$		0			0
$146$	−0.365931	−	1.95756i	−0.365931	−	1.95756i
$147$	−0.571231	+	0.571231i	−0.571231	+	0.571231i
$148$		0			0
$149$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$149$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$150$	−0.0373089	+	0.806980i	−0.0373089	+	0.806980i
$151$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$151$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$152$	−0.533922	+	0.486734i	−0.533922	+	0.486734i
$153$	0.310972	−	0.192546i	0.310972	−	0.192546i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$157$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.511622	−	0.145569i	−0.511622	−	0.145569i
$163$	−0.621731	+	0.748723i	−0.621731	+	0.748723i	−0.982973	−	0.183750i	$-0.941176\pi$
$163$	−0.621731	+	0.748723i	−0.621731	+	0.748723i	0.361242	+	0.932472i	$0.382353\pi$
$164$	−0.748723	+	1.34421i	−0.748723	+	1.34421i
$165$		0			0
$166$	−0.0899135	−	0.0211475i	−0.0899135	−	0.0211475i
$167$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$167$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$168$		0			0
$169$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$170$		0			0
$171$	−0.0686851	+	0.241403i	−0.0686851	+	0.241403i
$172$	0.377767	−	0.258777i	0.377767	−	0.258777i
$173$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$173$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$174$		0			0
$175$		0			0
$176$	−1.14558	+	1.25664i	−1.14558	+	1.25664i
$177$	0.850617	+	0.473791i	0.850617	+	0.473791i
$178$	0.449425	+	0.449425i	0.449425	+	0.449425i
$179$	0.722071	−	1.05409i	0.722071	−	1.05409i	−0.273663	−	0.961826i	$-0.588235\pi$
$179$	0.722071	−	1.05409i	0.722071	−	1.05409i	0.995734	−	0.0922684i	$-0.0294118\pi$
$180$		0			0
$181$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$181$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.07891	+	1.42871i	1.07891	+	1.42871i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$191$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$192$	−0.111609	−	0.800095i	−0.111609	−	0.800095i
$193$	−1.79375	+	0.694903i	−1.79375	+	0.694903i	−0.798017	+	0.602635i	$0.794118\pi$
$193$	−1.79375	+	0.694903i	−1.79375	+	0.694903i	−0.995734	+	0.0922684i	$0.970588\pi$
$194$	0.705749	+	1.59837i	0.705749	+	1.59837i
$195$		0			0
$196$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$197$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$197$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$198$	−0.108544	+	0.580658i	−0.108544	+	0.580658i
$199$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$199$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$200$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$201$	−1.09227	−	0.995734i	−1.09227	−	0.995734i
$202$		0			0
$203$		0			0
$204$	−0.849640	−	0.0392812i	−0.849640	−	0.0392812i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.20762	−	0.225743i	−1.20762	−	0.225743i
$210$		0			0
$211$	−0.961826	+	1.27366i	−0.961826	+	1.27366i			1.00000i	$0.5\pi$
$211$	−0.961826	+	1.27366i	−0.961826	+	1.27366i	−0.961826	+	0.273663i	$0.911765\pi$
$212$		0			0
$213$		0			0
$214$	1.25664	+	0.778076i	1.25664	+	0.778076i
$215$		0			0
$216$	−0.695372	−	0.837404i	−0.695372	−	0.837404i
$217$		0			0
$218$		0			0
$219$	0.222265	+	1.59336i	0.222265	+	1.59336i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$223$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$224$		0			0
$225$	−0.0320532	+	0.345909i	−0.0320532	+	0.345909i
$226$	1.26544	+	0.176521i	1.26544	+	0.176521i
$227$	0.0762025	+	0.0521999i	0.0762025	+	0.0521999i	0.602635	−	0.798017i	$-0.294118\pi$
$227$	0.0762025	+	0.0521999i	0.0762025	+	0.0521999i	−0.526432	+	0.850217i	$0.676471\pi$
$228$	0.449024	−	0.372864i	0.449024	−	0.372864i
$229$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$229$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.688163	+	0.688163i	0.688163	+	0.688163i	0.961826	−	0.273663i	$-0.0882353\pi$
$233$	0.688163	+	0.688163i	0.688163	+	0.688163i	−0.273663	+	0.961826i	$0.588235\pi$
$234$		0			0
$235$		0			0
$236$	0.537235	+	1.07891i	0.537235	+	1.07891i
$237$		0			0
$238$		0			0
$239$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$239$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$240$		0			0
$241$	1.59837	+	0.705749i	1.59837	+	0.705749i	0.995734	−	0.0922684i	$-0.0294118\pi$
$241$	1.59837	+	0.705749i	1.59837	+	0.705749i	0.602635	+	0.798017i	$0.294118\pi$
$242$	−1.88341	−	0.174523i	−1.88341	−	0.174523i
$243$	−0.624616	−	0.209350i	−0.624616	−	0.209350i
$244$		0			0
$245$		0			0
$246$	0.654355	−	1.05682i	0.654355	−	1.05682i
$247$		0			0
$248$		0			0
$249$	0.0717694	+	0.0204202i	0.0717694	+	0.0204202i
$250$		0			0
$251$	0.445738	−	1.89516i	0.445738	−	1.89516i		−	1.00000i	$-0.5\pi$
$251$	0.445738	−	1.89516i	0.445738	−	1.89516i	0.445738	−	0.895163i	$-0.352941\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.445738	−	0.895163i	0.445738	−	0.895163i
$257$	−0.0666624	−	0.172075i	−0.0666624	−	0.172075i	0.895163	−	0.445738i	$-0.147059\pi$
$257$	−0.0666624	−	0.172075i	−0.0666624	−	0.172075i	−0.961826	+	0.273663i	$0.911765\pi$
$258$	−0.314505	+	0.194733i	−0.314505	+	0.194733i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.786384	+	1.78099i	−0.786384	+	1.78099i
$263$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$263$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$264$	0.971340	−	0.971340i	0.971340	−	0.971340i
$265$		0			0
$266$		0			0
$267$	−0.345909	−	0.379445i	−0.345909	−	0.379445i
$268$	−0.418885	−	1.78099i	−0.418885	−	1.78099i
$269$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$269$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$270$		0			0
$271$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$271$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$272$	−0.840204	−	0.634493i	−0.840204	−	0.634493i
$273$		0			0
$274$	0.982973	+	0.183750i	0.982973	+	0.183750i
$275$	−1.70043			−1.70043
$276$		0			0
$277$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$277$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$278$	0.510366	+	1.79375i	0.510366	+	1.79375i
$279$		0			0
$280$		0			0
$281$	1.25640	+	1.37821i	1.25640	+	1.37821i	0.895163	+	0.445738i	$0.147059\pi$
$281$	1.25640	+	1.37821i	1.25640	+	1.37821i	0.361242	+	0.932472i	$0.382353\pi$
$282$		0			0
$283$	−0.0675278	−	0.361242i	−0.0675278	−	0.361242i	0.932472	−	0.361242i	$-0.117647\pi$
$283$	−0.0675278	−	0.361242i	−0.0675278	−	0.361242i	−1.00000			$\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0320532	−	0.345909i	−0.0320532	−	0.345909i
$289$	−0.0801997	+	0.0731117i	−0.0801997	+	0.0731117i
$290$		0			0
$291$	−0.509892	−	1.31618i	−0.509892	−	1.31618i
$292$	−0.887674	+	1.78269i	−0.887674	+	1.78269i
$293$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$293$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$294$	0.800095	−	0.111609i	0.800095	−	0.111609i
$295$		0			0
$296$		0			0
$297$	0.423762	−	1.80172i	0.423762	−	1.80172i
$298$		0			0
$299$		0			0
$300$	0.516087	−	0.621500i	0.516087	−	0.621500i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.719401	−	0.0666624i	0.719401	−	0.0666624i
$305$		0			0
$306$	−0.364196	−	0.0337477i	−0.364196	−	0.0337477i
$307$	1.67370	+	0.739009i	1.67370	+	0.739009i	1.00000			$0$
$307$	1.67370	+	0.739009i	1.67370	+	0.739009i	0.673696	+	0.739009i	$0.264706\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	1.20614	−	1.32307i	1.20614	−	1.32307i	0.273663	−	0.961826i	$-0.411765\pi$
$313$	1.20614	−	1.32307i	1.20614	−	1.32307i	0.932472	−	0.361242i	$-0.117647\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$317$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.985051	−	0.674776i	−0.985051	−	0.674776i
$322$		0			0
$323$	0.0701864	−	0.757432i	0.0701864	−	0.757432i
$324$	0.320558	+	0.424488i	0.320558	+	0.424488i
$325$		0			0
$326$	0.947359	−	0.222817i	0.947359	−	0.222817i
$327$		0			0
$328$	1.40756	−	0.621500i	1.40756	−	0.621500i
$329$		0			0
$330$		0			0
$331$	−0.571231	−	1.29371i	−0.571231	−	1.29371i	−0.932472	−	0.361242i	$-0.882353\pi$
$331$	−0.571231	−	1.29371i	−0.571231	−	1.29371i	0.361242	−	0.932472i	$-0.382353\pi$
$332$	0.0590083	+	0.0710610i	0.0590083	+	0.0710610i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.20013	+	1.58923i	−1.20013	+	1.58923i	−0.526432	+	0.850217i	$0.676471\pi$
$337$	−1.20013	+	1.58923i	−1.20013	+	1.58923i	−0.673696	+	0.739009i	$0.735294\pi$
$338$	0.739009	+	0.673696i	0.739009	+	0.673696i
$339$	−1.01460	−	0.189662i	−1.01460	−	0.189662i
$340$		0			0
$341$		0			0
$342$	0.200290	−	0.151252i	0.200290	−	0.151252i
$343$		0			0
$344$	−0.457413	−	0.0211475i	−0.457413	−	0.0211475i
$345$		0			0
$346$		0			0
$347$	1.45285	+	1.32445i	1.45285	+	1.32445i	0.850217	+	0.526432i	$0.176471\pi$
$347$	1.45285	+	1.32445i	1.45285	+	1.32445i	0.602635	+	0.798017i	$0.294118\pi$
$348$		0			0
$349$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$349$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$350$		0			0
$351$		0			0
$352$	1.67148	−	0.312454i	1.67148	−	0.312454i
$353$	−1.27633	−	1.53703i	−1.27633	−	1.53703i	−0.673696	−	0.739009i	$-0.735294\pi$
$353$	−1.27633	−	1.53703i	−1.27633	−	1.53703i	−0.602635	−	0.798017i	$-0.705882\pi$
$354$	−0.393285	−	0.890705i	−0.393285	−	0.890705i
$355$		0			0
$356$	−0.0878098	−	0.629488i	−0.0878098	−	0.629488i
$357$		0			0
$358$	−1.21146	+	0.406040i	−1.21146	+	0.406040i
$359$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$359$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$360$		0			0
$361$	−0.288070	−	0.381466i	−0.288070	−	0.381466i
$362$		0			0
$363$	1.51336	+	0.211105i	1.51336	+	0.211105i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$367$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$368$		0			0
$369$	0.302077	−	0.440978i	0.302077	−	0.440978i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$373$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$374$		−	1.79033i		−	1.79033i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.544991	+	0.0505009i	0.544991	+	0.0505009i	0.361242	−	0.932472i	$-0.382353\pi$
$379$	0.544991	+	0.0505009i	0.544991	+	0.0505009i	0.183750	+	0.982973i	$0.441176\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$383$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$384$	−0.393100	+	0.705749i	−0.393100	+	0.705749i
$385$		0			0
$386$	1.85022	+	0.526432i	1.85022	+	0.526432i
$387$	−0.138968	+	0.0774046i	−0.138968	+	0.0774046i
$388$	0.400033	−	1.70083i	0.400033	−	1.70083i
$389$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$389$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$390$		0			0
$391$		0			0
$392$	0.895163	+	0.445738i	0.895163	+	0.445738i
$393$	0.701043	−	1.40788i	0.701043	−	1.40788i
$394$		0			0
$395$		0			0
$396$	0.436544	−	0.397963i	0.436544	−	0.397963i
$397$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$397$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$398$		0			0
$399$		0			0
$400$	0.961826	−	0.273663i	0.961826	−	0.273663i
$401$	0.799224	−	0.799224i	0.799224	−	0.799224i	−0.183750	−	0.982973i	$-0.558824\pi$
$401$	0.799224	−	0.799224i	0.799224	−	0.799224i	0.982973	+	0.183750i	$0.0588235\pi$
$402$	0.271585	+	1.45285i	0.271585	+	1.45285i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.654355	+	0.543370i	0.654355	+	0.543370i
$409$	0.436776	+	0.329838i	0.436776	+	0.329838i	0.798017	−	0.602635i	$-0.205882\pi$
$409$	0.436776	+	0.329838i	0.436776	+	0.329838i	−0.361242	+	0.932472i	$0.617647\pi$
$410$		0			0
$411$	−0.786384	−	0.184956i	−0.786384	−	0.184956i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.344932	−	1.46656i	−0.344932	−	1.46656i
$418$	0.827659	+	0.907899i	0.827659	+	0.907899i
$419$	−0.197717	+	0.510366i	−0.197717	+	0.510366i	−0.995734	−	0.0922684i	$-0.970588\pi$
$419$	−0.197717	+	0.510366i	−0.197717	+	0.510366i	0.798017	+	0.602635i	$0.205882\pi$
$420$		0			0
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$	1.53511	−	0.436776i	1.53511	−	0.436776i
$423$		0			0
$424$		0			0
$425$	−0.0971461	−	1.04837i	−0.0971461	−	1.04837i
$426$		0			0
$427$		0			0
$428$	−0.533922	−	1.37821i	−0.533922	−	1.37821i
$429$		0			0
$430$		0			0
$431$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$431$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$432$	0.0502697	+	1.08732i	0.0502697	+	1.08732i
$433$	−1.79375	−	0.694903i	−1.79375	−	0.694903i	−0.995734	−	0.0922684i	$-0.970588\pi$
$433$	−1.79375	−	0.694903i	−1.79375	−	0.694903i	−0.798017	−	0.602635i	$-0.794118\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.782845	−	1.40548i	0.782845	−	1.40548i
$439$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$439$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$440$		0			0
$441$	0.345909	−	0.0320532i	0.345909	−	0.0320532i
$442$		0			0
$443$	1.91545	+	0.177492i	1.91545	+	0.177492i	0.982973	−	0.183750i	$-0.0588235\pi$
$443$	1.91545	+	0.177492i	1.91545	+	0.177492i	0.932472	+	0.361242i	$0.117647\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.243964	−	0.489946i	−0.243964	−	0.489946i	0.739009	−	0.673696i	$-0.235294\pi$
$449$	−0.243964	−	0.489946i	−0.243964	−	0.489946i	−0.982973	+	0.183750i	$0.941176\pi$
$450$	0.234036	−	0.256725i	0.234036	−	0.256725i
$451$	2.28575	+	1.27315i	2.28575	+	1.27315i
$452$	−0.903466	−	0.903466i	−0.903466	−	0.903466i
$453$		0			0
$454$	−0.0293534	−	0.0875787i	−0.0293534	−	0.0875787i
$455$		0			0
$456$	−0.583030	+	0.0269551i	−0.583030	+	0.0269551i
$457$	−0.352279	+	0.292529i	−0.352279	+	0.292529i	−0.798017	−	0.602635i	$-0.794118\pi$
$457$	−0.352279	+	0.292529i	−0.352279	+	0.292529i	0.445738	+	0.895163i	$0.352941\pi$
$458$		0			0
$459$	1.13503	+	0.158330i	1.13503	+	0.158330i
$460$		0			0
$461$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$461$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$462$		0			0
$463$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$463$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$464$		0			0
$465$		0			0
$466$	−0.134455	−	0.963876i	−0.134455	−	0.963876i
$467$	−0.172075	+	0.0666624i	−0.172075	+	0.0666624i	−0.445738	−	0.895163i	$-0.647059\pi$
$467$	−0.172075	+	0.0666624i	−0.172075	+	0.0666624i	0.273663	+	0.961826i	$0.411765\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.221468	−	1.18475i	0.221468	−	1.18475i
$473$	−0.440033	−	0.642368i	−0.440033	−	0.642368i
$474$		0			0
$475$	0.533922	+	0.486734i	0.533922	+	0.486734i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$479$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$480$		0			0
$481$		0			0
$482$	−0.850217	−	1.52643i	−0.850217	−	1.52643i
$483$		0			0
$484$	1.39782	+	1.27428i	1.39782	+	1.27428i
$485$		0			0
$486$	0.372292	+	0.543480i	0.372292	+	0.543480i
$487$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$487$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$488$		0			0
$489$	−0.772813	+	0.144464i	−0.772813	+	0.144464i
$490$		0			0
$491$	0.800095	+	1.81204i	0.800095	+	1.81204i	0.526432	+	0.850217i	$0.323529\pi$
$491$	0.800095	+	1.81204i	0.800095	+	1.81204i	0.273663	+	0.961826i	$0.411765\pi$
$492$	−1.15906	+	0.449024i	−1.15906	+	0.449024i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.0449673	−	0.0595464i	−0.0449673	−	0.0595464i
$499$	−0.181395	+	1.95756i	−0.181395	+	1.95756i	0.0922684	+	0.995734i	$0.470588\pi$
$499$	−0.181395	+	1.95756i	−0.181395	+	1.95756i	−0.273663	+	0.961826i	$0.588235\pi$
$500$		0			0
$501$		0			0
$502$	−1.49780	+	1.24376i	−1.49780	+	1.24376i
$503$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$503$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.571231	−	0.571231i	−0.571231	−	0.571231i
$508$		0			0
$509$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$509$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$510$		0			0
$511$		0			0
$512$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$513$	−0.648785	+	0.444428i	−0.648785	+	0.444428i
$514$	−0.0505009	+	0.177492i	−0.0505009	+	0.177492i
$515$		0			0
$516$	0.368334	+	0.0341311i	0.368334	+	0.0341311i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.748723	+	1.34421i	−0.748723	+	1.34421i	0.183750	+	0.982973i	$0.441176\pi$
$521$	−0.748723	+	1.34421i	−0.748723	+	1.34421i	−0.932472	+	0.361242i	$0.882353\pi$
$522$		0			0
$523$	1.89090	+	0.538007i	1.89090	+	0.538007i	0.995734	+	0.0922684i	$0.0294118\pi$
$523$	1.89090	+	0.538007i	1.89090	+	0.538007i	0.895163	+	0.445738i	$0.147059\pi$
$524$	1.70083	−	0.947359i	1.70083	−	0.947359i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.36051	+	0.189783i	−1.36051	+	0.189783i
$529$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$530$		0			0
$531$	−0.151252	−	0.390426i	−0.151252	−	0.390426i
$532$		0			0
$533$		0			0
$534$	0.0473752	+	0.511260i	0.0473752	+	0.511260i
$535$		0			0
$536$	−0.739009	+	1.67370i	−0.739009	+	1.67370i
$537$	0.992772	−	0.282468i	0.992772	−	0.282468i
$538$		0			0
$539$	0.312454	+	1.67148i	0.312454	+	1.67148i
$540$		0			0
$541$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$541$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$542$		0			0
$543$		0			0
$544$	0.288130	+	1.01267i	0.288130	+	1.01267i
$545$		0			0
$546$		0			0
$547$	−0.184537			−0.184537			−0.0922684	−	0.995734i	$-0.529412\pi$
$547$	−0.184537			−0.184537			−0.0922684	+	0.995734i	$0.529412\pi$
$548$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$549$		0			0
$550$	1.35698	+	1.02474i	1.35698	+	1.02474i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.673696	−	1.73901i	0.673696	−	1.73901i
$557$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$557$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.0667952	+	1.44476i	−0.0667952	+	1.44476i
$562$	−0.172075	−	1.85699i	−0.172075	−	1.85699i
$563$	−1.09227	+	0.995734i	−1.09227	+	0.995734i	−0.0922684	+	0.995734i	$0.529412\pi$
$563$	−1.09227	+	0.995734i	−1.09227	+	0.995734i	−1.00000			$1.00000\pi$
$564$		0			0
$565$		0			0
$566$	−0.163808	+	0.328972i	−0.163808	+	0.328972i
$567$		0			0
$568$		0			0
$569$	−0.0762025	−	1.64823i	−0.0762025	−	1.64823i	−0.602635	−	0.798017i	$-0.705882\pi$
$569$	−0.0762025	−	1.64823i	−0.0762025	−	1.64823i	0.526432	−	0.850217i	$-0.323529\pi$
$570$		0			0
$571$	0.457413	−	1.94480i	0.457413	−	1.94480i	0.183750	−	0.982973i	$-0.441176\pi$
$571$	0.457413	−	1.94480i	0.457413	−	1.94480i	0.273663	−	0.961826i	$-0.411765\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.182878	+	0.295358i	−0.182878	+	0.295358i
$577$	1.10025	+	0.258777i	1.10025	+	0.258777i	0.739009	−	0.673696i	$-0.235294\pi$
$577$	1.10025	+	0.258777i	1.10025	+	0.258777i	0.361242	+	0.932472i	$0.382353\pi$
$578$	0.108060	−	0.0100133i	0.108060	−	0.0100133i
$579$	−1.47345	−	0.493850i	−1.47345	−	0.493850i
$580$		0			0
$581$		0			0
$582$	−0.386275	+	1.35761i	−0.386275	+	1.35761i
$583$		0			0
$584$	1.78269	−	0.887674i	1.78269	−	0.887674i
$585$		0			0
$586$		0			0
$587$	0.600584	−	0.658809i	0.600584	−	0.658809i	−0.361242	−	0.932472i	$-0.617647\pi$
$587$	0.600584	−	0.658809i	0.600584	−	0.658809i	0.961826	+	0.273663i	$0.0882353\pi$
$588$	−0.705749	−	0.393100i	−0.705749	−	0.393100i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.276018	−	0.0127611i	0.276018	−	0.0127611i	0.0922684	−	0.995734i	$-0.470588\pi$
$593$	0.276018	−	0.0127611i	0.276018	−	0.0127611i	0.183750	+	0.982973i	$0.441176\pi$
$594$	−1.42395	+	1.18243i	−1.42395	+	1.18243i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$599$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$600$	−0.786384	+	0.184956i	−0.786384	+	0.184956i
$601$	−1.89430	+	0.634905i	−1.89430	+	0.634905i	−0.932472	+	0.361242i	$0.882353\pi$
$601$	−1.89430	+	0.634905i	−1.89430	+	0.634905i	−0.961826	+	0.273663i	$0.911765\pi$
$602$		0			0
$603$	0.0878098	+	0.629488i	0.0878098	+	0.629488i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$607$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$608$	−0.614268	−	0.380338i	−0.614268	−	0.380338i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.270297	+	0.246408i	0.270297	+	0.246408i
$613$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$613$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$614$	−0.890286	−	1.59837i	−0.890286	−	1.59837i
$615$		0			0
$616$		0			0
$617$	−1.42871	+	1.07891i	−1.42871	+	1.07891i	−0.445738	+	0.895163i	$0.647059\pi$
$617$	−1.42871	+	1.07891i	−1.42871	+	1.07891i	−0.982973	+	0.183750i	$0.941176\pi$
$618$		0			0
$619$	0.549996	+	0.987432i	0.549996	+	0.987432i	0.995734	+	0.0922684i	$0.0294118\pi$
$619$	0.549996	+	0.987432i	0.549996	+	0.987432i	−0.445738	+	0.895163i	$0.647059\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.850217	+	0.526432i	0.850217	+	0.526432i
$626$	−1.75984	+	0.328972i	−1.75984	+	0.328972i
$627$	−0.634032	−	0.763535i	−0.634032	−	0.763535i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$631$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$632$		0			0
$633$	−1.25510	+	0.295196i	−1.25510	+	0.295196i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.193463	+	0.312454i	0.193463	+	0.312454i	0.932472	−	0.361242i	$-0.117647\pi$
$641$	0.193463	+	0.312454i	0.193463	+	0.312454i	−0.739009	+	0.673696i	$0.764706\pi$
$642$	0.379445	+	1.13211i	0.379445	+	1.13211i
$643$	−0.932472	+	1.36124i	−0.932472	+	1.36124i			1.00000i	$0.5\pi$
$643$	−0.932472	+	1.36124i	−0.932472	+	1.36124i	−0.932472	+	0.361242i	$0.882353\pi$
$644$		0			0
$645$		0			0
$646$	−0.512465	+	0.562147i	−0.512465	+	0.562147i
$647$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$647$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$648$		−	0.531928i		−	0.531928i
$649$	1.83462	−	0.913532i	1.83462	−	0.913532i
$650$		0			0
$651$		0			0
$652$	−0.890286	−	0.393100i	−0.890286	−	0.393100i
$653$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$653$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$654$		0			0
$655$		0			0
$656$	−1.49780	−	0.352279i	−1.49780	−	0.352279i
$657$	0.364196	−	0.588196i	0.364196	−	0.588196i
$658$		0			0
$659$	1.27633	−	1.53703i	1.27633	−	1.53703i	0.602635	−	0.798017i	$-0.294118\pi$
$659$	1.27633	−	1.53703i	1.27633	−	1.53703i	0.673696	−	0.739009i	$-0.264706\pi$
$660$		0			0
$661$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$661$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$662$	−0.323785	+	1.37665i	−0.323785	+	1.37665i
$663$		0			0
$664$	−0.00426582	−	0.0922684i	−0.00426582	−	0.0922684i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.786384	−	1.78099i	0.786384	−	1.78099i	0.183750	−	0.982973i	$-0.441176\pi$
$673$	0.786384	−	1.78099i	0.786384	−	1.78099i	0.602635	−	0.798017i	$-0.294118\pi$
$674$	1.91545	−	0.544991i	1.91545	−	0.544991i
$675$	−0.769671	+	0.769671i	−0.769671	+	0.769671i
$676$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$677$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$677$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$678$	0.695372	+	0.762786i	0.695372	+	0.762786i
$679$		0			0
$680$		0			0
$681$	0.0204202	+	0.0717694i	0.0204202	+	0.0717694i
$682$		0			0
$683$	−1.58923	−	1.20013i	−1.58923	−	1.20013i	−0.850217	−	0.526432i	$-0.823529\pi$
$683$	−1.58923	−	1.20013i	−1.58923	−	1.20013i	−0.739009	−	0.673696i	$-0.764706\pi$
$684$	−0.250984			−0.250984
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.352279	+	0.292529i	0.352279	+	0.292529i
$689$		0			0
$690$		0			0
$691$	0.323785	+	1.37665i	0.323785	+	1.37665i	0.850217	+	0.526432i	$0.176471\pi$
$691$	0.323785	+	1.37665i	0.323785	+	1.37665i	−0.526432	+	0.850217i	$0.676471\pi$
$692$		0			0
$693$		0			0
$694$	−0.361242	−	1.93247i	−0.361242	−	1.93247i
$695$		0			0
$696$		0			0
$697$	−0.654355	+	1.48197i	−0.654355	+	1.48197i
$698$		0			0
$699$	0.0725413	+	0.782845i	0.0725413	+	0.782845i
$700$		0			0
$701$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$701$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$702$		0			0
$703$		0			0
$704$	−1.52217	−	0.757949i	−1.52217	−	0.757949i
$705$		0			0
$706$	0.0922684	+	1.99573i	0.0922684	+	1.99573i
$707$		0			0
$708$	−0.222922	+	0.947805i	−0.222922	+	0.947805i
$709$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$709$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$710$		0			0
$711$		0			0
$712$	−0.309277	+	0.555259i	−0.309277	+	0.555259i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.21146	+	0.406040i	1.21146	+	0.406040i
$717$		0			0
$718$		0			0
$719$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$719$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$720$		0			0
$721$		0			0
$722$			0.478018i			0.478018i
$723$	0.629159	+	1.26352i	0.629159	+	1.26352i
$724$		0			0
$725$		0			0
$726$	−1.08047	−	1.08047i	−1.08047	−	1.08047i
$727$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$727$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$728$		0			0
$729$	−0.560180	−	0.904722i	−0.560180	−	0.904722i
$730$		0			0
$731$	0.370902	−	0.307993i	0.370902	−	0.307993i
$732$		0			0
$733$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$733$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.02846	+	0.712287i	−3.02846	+	0.712287i
$738$	−0.506811	+	0.169866i	−0.506811	+	0.169866i
$739$	0.252769	−	0.111609i	0.252769	−	0.111609i	−0.273663	−	0.961826i	$-0.588235\pi$
$739$	0.252769	−	0.111609i	0.252769	−	0.111609i	0.526432	+	0.850217i	$0.323529\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$743$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.0181338	−	0.0264721i	−0.0181338	−	0.0264721i
$748$	−1.07891	+	1.42871i	−1.07891	+	1.42871i
$749$		0			0
$750$		0			0
$751$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$751$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$752$		0			0
$753$	1.25510	−	0.947805i	1.25510	−	0.947805i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$757$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$758$	−0.404479	−	0.368731i	−0.404479	−	0.368731i
$759$		0			0
$760$		0			0
$761$	−0.271585	+	1.45285i	−0.271585	+	1.45285i	0.526432	+	0.850217i	$0.323529\pi$
$761$	−0.271585	+	1.45285i	−0.271585	+	1.45285i	−0.798017	+	0.602635i	$0.794118\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.739009	−	0.326304i	0.739009	−	0.326304i
$769$	1.87814	−	0.629488i	1.87814	−	0.629488i	0.895163	−	0.445738i	$-0.147059\pi$
$769$	1.87814	−	0.629488i	1.87814	−	0.629488i	0.982973	−	0.183750i	$-0.0588235\pi$
$770$		0			0
$771$	0.0473752	−	0.141348i	0.0473752	−	0.141348i
$772$	−1.15926	−	1.53511i	−1.15926	−	1.53511i
$773$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$773$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$774$	0.157545	+	0.0219766i	0.157545	+	0.0219766i
$775$		0			0
$776$	−1.34421	+	1.11622i	−1.34421	+	1.11622i
$777$		0			0
$778$		0			0
$779$	−0.353277	−	1.05403i	−0.353277	−	1.05403i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$785$		0			0
$786$	−1.40788	+	0.701043i	−1.40788	+	0.701043i
$787$	−0.802895	+	0.549996i	−0.802895	+	0.549996i	−0.895163	−	0.445738i	$-0.852941\pi$
$787$	−0.802895	+	0.549996i	−0.802895	+	0.549996i	0.0922684	+	0.995734i	$0.470588\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.588196	+	0.0545044i	−0.588196	+	0.0545044i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$797$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$798$		0			0
$799$		0			0
$800$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$801$	0.0101971	+	0.220560i	0.0101971	+	0.220560i
$802$	−1.11943	+	0.156154i	−1.11943	+	0.156154i
$803$	3.03135	+	1.50943i	3.03135	+	1.50943i
$804$	0.658809	−	1.32307i	0.658809	−	1.32307i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.0914812	+	1.97871i	−0.0914812	+	1.97871i	0.0922684	+	0.995734i	$0.470588\pi$
$809$	−0.0914812	+	1.97871i	−0.0914812	+	1.97871i	−0.183750	+	0.982973i	$0.558824\pi$
$810$		0			0
$811$	−1.53511	+	0.436776i	−1.53511	+	0.436776i	−0.932472	−	0.361242i	$-0.882353\pi$
$811$	−1.53511	+	0.436776i	−1.53511	+	0.436776i	−0.602635	+	0.798017i	$0.705882\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.194733	−	0.827956i	−0.194733	−	0.827956i
$817$	−0.0457057	+	0.327653i	−0.0457057	+	0.327653i
$818$	−0.149783	−	0.526432i	−0.149783	−	0.526432i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	0.516087	+	0.621500i	0.516087	+	0.621500i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	−1.05682	−	0.877573i	−1.05682	−	0.877573i
$826$		0			0
$827$	0.212577	−	1.52391i	0.212577	−	1.52391i	−0.526432	−	0.850217i	$-0.676471\pi$
$827$	0.212577	−	1.52391i	0.212577	−	1.52391i	0.739009	−	0.673696i	$-0.235294\pi$
$828$		0			0
$829$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$829$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.01267	+	0.288130i	−1.01267	+	0.288130i
$834$	−0.608540	+	1.37821i	−0.608540	+	1.37821i
$835$		0			0
$836$	−0.113355	−	1.22329i	−0.113355	−	1.22329i
$837$		0			0
$838$	0.465346	−	0.288130i	0.465346	−	0.288130i
$839$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$839$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$840$		0			0
$841$	0.895163	+	0.445738i	0.895163	+	0.445738i
$842$		0			0
$843$	0.0695791	+	1.50497i	0.0695791	+	1.50497i
$844$	−1.48826	−	0.576554i	−1.48826	−	0.576554i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.144464	−	0.259362i	0.144464	−	0.259362i
$850$	−0.554262	+	0.895163i	−0.554262	+	0.895163i
$851$		0			0
$852$		0			0
$853$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$853$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$854$		0			0
$855$		0			0
$856$	−0.404479	+	1.42160i	−0.404479	+	1.42160i
$857$	1.50941	−	1.03397i	1.50941	−	1.03397i	0.526432	−	0.850217i	$-0.323529\pi$
$857$	1.50941	−	1.03397i	1.50941	−	1.03397i	0.982973	−	0.183750i	$-0.0588235\pi$
$858$		0			0
$859$		−	0.184537i		−	0.184537i	−0.995734	−	0.0922684i	$-0.970588\pi$
$859$		−	0.184537i		−	0.184537i	0.995734	−	0.0922684i	$-0.0294118\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$863$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$864$	0.615139	−	0.897993i	0.615139	−	0.897993i
$865$		0			0
$866$	1.01267	+	1.63552i	1.01267	+	1.63552i
$867$	−0.0875761	+	0.00404889i	−0.0875761	+	0.00404889i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.192892	+	0.575512i	−0.192892	+	0.575512i
$874$		0			0
$875$		0			0
$876$	−1.47171	+	0.649825i	−1.47171	+	0.649825i
$877$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$877$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.89090	−	0.353470i	1.89090	−	0.353470i	0.895163	−	0.445738i	$-0.147059\pi$
$881$	1.89090	−	0.353470i	1.89090	−	0.353470i	0.995734	+	0.0922684i	$0.0294118\pi$
$882$	−0.295358	−	0.182878i	−0.295358	−	0.182878i
$883$	0.342683	−	1.83319i	0.342683	−	1.83319i	−0.183750	−	0.982973i	$-0.558824\pi$
$883$	0.342683	−	1.83319i	0.342683	−	1.83319i	0.526432	−	0.850217i	$-0.323529\pi$
$884$		0			0
$885$		0			0
$886$	−1.42160	−	1.29596i	−1.42160	−	1.29596i
$887$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$887$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.721813	−	0.545088i	0.721813	−	0.545088i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.100571	+	0.538007i	−0.100571	+	0.538007i
$899$		0			0
$900$	−0.341476	+	0.0638330i	−0.341476	+	0.0638330i
$901$		0			0
$902$	−1.05682	−	2.39347i	−1.05682	−	2.39347i
$903$		0			0
$904$	0.176521	+	1.26544i	0.176521	+	1.26544i
$905$		0			0
$906$		0			0
$907$	1.94480	−	0.457413i	1.94480	−	0.457413i	0.961826	−	0.273663i	$-0.0882353\pi$
$907$	1.94480	−	0.457413i	1.94480	−	0.457413i	0.982973	−	0.183750i	$-0.0588235\pi$
$908$	−0.0293534	+	0.0875787i	−0.0293534	+	0.0875787i
$909$		0			0
$910$		0			0
$911$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$911$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$912$	0.481512	+	0.329843i	0.481512	+	0.329843i
$913$	0.120835	−	0.100340i	0.120835	−	0.100340i
$914$	0.457413	−	0.0211475i	0.457413	−	0.0211475i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.810359	−	0.810359i	−0.810359	−	0.810359i
$919$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$919$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$920$		0			0
$921$	0.658809	+	1.32307i	0.658809	+	1.32307i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.78269	−	0.165190i	1.78269	−	0.165190i	0.850217	−	0.526432i	$-0.176471\pi$
$929$	1.78269	−	0.165190i	1.78269	−	0.165190i	0.932472	+	0.361242i	$0.117647\pi$
$930$		0			0
$931$	0.380338	−	0.614268i	0.380338	−	0.614268i
$932$	−0.473568	+	0.850217i	−0.473568	+	0.850217i
$933$		0			0
$934$	0.177492	+	0.0505009i	0.177492	+	0.0505009i
$935$		0			0
$936$		0			0
$937$	0.342683	+	0.132756i	0.342683	+	0.132756i	0.526432	−	0.850217i	$-0.323529\pi$
$937$	0.342683	+	0.132756i	0.342683	+	0.132756i	−0.183750	+	0.982973i	$0.558824\pi$
$938$		0			0
$939$	1.43243	−	0.199816i	1.43243	−	0.199816i
$940$		0			0
$941$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$941$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$942$		0			0
$943$		0			0
$944$	−0.890705	+	0.811985i	−0.890705	+	0.811985i
$945$		0			0
$946$	−0.0359599	+	0.777800i	−0.0359599	+	0.777800i
$947$	−0.111609	+	0.252769i	−0.111609	+	0.252769i	−0.961826	−	0.273663i	$-0.911765\pi$
$947$	−0.111609	+	0.252769i	−0.111609	+	0.252769i	0.850217	+	0.526432i	$0.176471\pi$
$948$		0			0
$949$		0			0
$950$	−0.132756	−	0.710182i	−0.132756	−	0.710182i
$951$		0			0
$952$		0			0
$953$	−0.434164	−	1.84595i	−0.434164	−	1.84595i	−0.526432	−	0.850217i	$-0.676471\pi$
$953$	−0.434164	−	1.84595i	−0.434164	−	1.84595i	0.0922684	−	0.995734i	$-0.470588\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.798017	+	0.602635i	0.798017	+	0.602635i
$962$		0			0
$963$	0.140512	+	0.493850i	0.140512	+	0.493850i
$964$	−0.241393	+	1.73049i	−0.241393	+	1.73049i
$965$		0			0
$966$		0			0
$967$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$967$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$968$	−0.347558	−	1.85927i	−0.347558	−	1.85927i
$969$	0.434522	−	0.434522i	0.434522	−	0.434522i
$970$		0			0
$971$	−0.456541	+	1.03397i	−0.456541	+	1.03397i	0.526432	+	0.850217i	$0.323529\pi$
$971$	−0.456541	+	1.03397i	−0.456541	+	1.03397i	−0.982973	+	0.183750i	$0.941176\pi$
$972$	0.0304241	−	0.658063i	0.0304241	−	0.658063i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$977$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$978$	0.703777	+	0.350439i	0.703777	+	0.350439i
$979$	−1.07040	+	0.149315i	−1.07040	+	0.149315i
$980$		0			0
$981$		0			0
$982$	0.453510	−	1.92821i	0.453510	−	1.92821i
$983$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$983$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$984$	1.19555	+	0.340163i	1.19555	+	0.340163i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$991$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$992$		0			0
$993$	0.312649	−	1.09885i	0.312649	−	1.09885i
$994$		0			0
$995$		0			0
$996$			0.0746179i			0.0746179i
$997$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$997$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$998$	1.32445	−	1.45285i	1.32445	−	1.45285i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1096.1.z.a.419.1	✓	32
8.3	odd	2	CM	1096.1.z.a.419.1	✓	32
137.120	even	68	inner	1096.1.z.a.531.1	yes	32
1096.531	odd	68	inner	1096.1.z.a.531.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1096.1.z.a.419.1	✓	32	1.1	even	1	trivial
1096.1.z.a.419.1	✓	32	8.3	odd	2	CM
1096.1.z.a.531.1	yes	32	137.120	even	68	inner
1096.1.z.a.531.1	yes	32	1096.531	odd	68	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1096 = 2^{3} \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1096.z (of order \(68\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.798017 - 0.602635i) q^{2} +(0.621500 + 0.516087i) q^{3} +(0.273663 + 0.961826i) q^{4} +(-0.184956 - 0.786384i) q^{6} +(0.361242 - 0.932472i) q^{8} +(-0.0638330 - 0.341476i) q^{9} +O(q^{10})\)	\(q+(-0.798017 - 0.602635i) q^{2} +(0.621500 + 0.516087i) q^{3} +(0.273663 + 0.961826i) q^{4} +(-0.184956 - 0.786384i) q^{6} +(0.361242 - 0.932472i) q^{8} +(-0.0638330 - 0.341476i) q^{9} +(1.63552 - 0.465346i) q^{11} +(-0.326304 + 0.739009i) q^{12} +(-0.850217 + 0.526432i) q^{16} +(0.380338 + 0.981767i) q^{17} +(-0.154846 + 0.310972i) q^{18} +(-0.646741 - 0.322039i) q^{19} +(-1.58561 - 0.614268i) q^{22} +(0.705749 - 0.393100i) q^{24} +(-0.961826 - 0.273663i) q^{25} +(0.529659 - 0.950920i) q^{27} +(0.995734 + 0.0922684i) q^{32} +(1.25664 + 0.554859i) q^{33} +(0.288130 - 1.01267i) q^{34} +(0.310972 - 0.154846i) q^{36} +(0.322039 + 0.646741i) q^{38} +(1.08800 + 1.08800i) q^{41} +(-0.145517 - 0.434164i) q^{43} +(0.895163 + 1.44574i) q^{44} +(-0.800095 - 0.111609i) q^{48} +(-0.0922684 + 0.995734i) q^{49} +(0.602635 + 0.798017i) q^{50} +(-0.270297 + 0.806456i) q^{51} +(-0.995734 + 0.439660i) q^{54} +(-0.235749 - 0.533922i) q^{57} +(1.18475 - 0.221468i) q^{59} +(-0.739009 - 0.673696i) q^{64} +(-0.668440 - 1.20008i) q^{66} +(-1.82764 - 0.0844967i) q^{67} +(-0.840204 + 0.634493i) q^{68} +(-0.341476 - 0.0638330i) q^{72} +(1.47171 + 1.34164i) q^{73} +(-0.456541 - 0.666468i) q^{75} +(0.132756 - 0.710182i) q^{76} +(0.496008 - 0.192155i) q^{81} +(-0.212577 - 1.52391i) q^{82} +(0.0844967 - 0.0373089i) q^{83} +(-0.145517 + 0.434164i) q^{86} +(0.156896 - 1.69318i) q^{88} +(-0.629488 - 0.0878098i) q^{89} +(0.571231 + 0.571231i) q^{96} +(-1.52643 - 0.850217i) q^{97} +(0.673696 - 0.739009i) q^{98} +(-0.263305 - 0.528787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6}+O(q^{10}) \) 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6	\( 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6} - 32 q^{12} - 2 q^{16} - 2 q^{18} - 4 q^{22} + 2 q^{24} + 4 q^{33} - 2 q^{41} + 2 q^{43} - 2 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{59} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 2 q^{72} - 2 q^{75} - 2 q^{81} + 2 q^{82} - 2 q^{83} + 2 q^{86} + 4 q^{88} + 2 q^{89} - 2 q^{96} - 32 q^{97} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6 - 32 * q^12 - 2 * q^16 - 2 * q^18 - 4 * q^22 + 2 * q^24 + 4 * q^33 - 2 * q^41 + 2 * q^43 - 2 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^59 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 2 * q^72 - 2 * q^75 - 2 * q^81 + 2 * q^82 - 2 * q^83 + 2 * q^86 + 4 * q^88 + 2 * q^89 - 2 * q^96 - 32 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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