LMFDB - Embedded newform 3288.1.cj.b.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3288,1,Mod(35,3288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3288, base_ring=CyclotomicField(136))

chi = DirichletCharacter(H, H._module([68, 68, 68, 117]))

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

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

chi := DirichletCharacter("3288.35");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3288 = 2^{3} \cdot 3 \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3288.cj (of order $136$, degree $64$, 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:	$1.64092576154$
Analytic rank:	$0$
Dimension:	$64$
Coefficient field:	$\Q(\zeta_{136})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{64} - x^{60} + x^{56} - x^{52} + x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} + \cdots + 1 $ x^64 - x^60 + x^56 - x^52 + x^48 - x^44 + x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{136}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{136} - \cdots)$

Embedding invariants

Embedding label			35.1
Root			$0.948161 - 0.317791i$ of defining polynomial
Character	$\chi$	$=$	3288.35
Dual form			3288.1.cj.b.1691.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.948161 - 0.317791i) q^{2} +(0.228951 + 0.973438i) q^{3} +(0.798017 + 0.602635i) q^{4} +(0.0922684 - 0.995734i) q^{6} +(-0.565136 - 0.824997i) q^{8} +(-0.895163 + 0.445738i) q^{9} +O(q^{10})$	\(q+(-0.948161 - 0.317791i) q^{2} +(0.228951 + 0.973438i) q^{3} +(0.798017 + 0.602635i) q^{4} +(0.0922684 - 0.995734i) q^{6} +(-0.565136 - 0.824997i) q^{8} +(-0.895163 + 0.445738i) q^{9} +(0.265765 + 1.90520i) q^{11} +(-0.403921 + 0.914794i) q^{12} +(0.273663 + 0.961826i) q^{16} +(1.44147 + 0.987432i) q^{17} +(0.990410 - 0.138156i) q^{18} +(0.377767 - 1.60617i) q^{19} +(0.353470 - 1.89090i) q^{22} +(0.673696 - 0.739009i) q^{24} +(0.990410 + 0.138156i) q^{25} +(-0.638847 - 0.769334i) q^{27} +(0.0461835 - 0.998933i) q^{32} +(-1.79375 + 0.694903i) q^{33} +(-1.05295 - 1.39433i) q^{34} +(-0.982973 - 0.183750i) q^{36} +(-0.868610 + 1.40285i) q^{38} +(-0.785192 + 0.325237i) q^{41} +(-0.0371073 - 0.227480i) q^{43} +(-0.936057 + 1.68054i) q^{44} +(-0.873622 + 0.486604i) q^{48} +(0.673696 + 0.739009i) q^{49} +(-0.895163 - 0.445738i) q^{50} +(-0.631178 + 1.62926i) q^{51} +(0.361242 + 0.932472i) q^{54} +1.64999 q^{57} +(-1.78269 + 0.165190i) q^{59} +(-0.361242 + 0.932472i) q^{64} +(1.92160 - 0.0888409i) q^{66} +(-0.789689 + 0.754023i) q^{67} +(0.555259 + 1.65667i) q^{68} +(0.873622 + 0.486604i) q^{72} +(0.0861296 + 0.0333668i) q^{73} +(0.0922684 + 0.995734i) q^{75} +(1.26940 - 1.05409i) q^{76} +(0.602635 - 0.798017i) q^{81} +(0.847846 - 0.0588498i) q^{82} +(-1.67521 - 1.09157i) q^{83} +(-0.0371073 + 0.227480i) q^{86} +(1.42160 - 1.29596i) q^{88} +(1.29577 + 1.48906i) q^{89} +(0.982973 - 0.183750i) q^{96} +(-0.873622 + 0.513396i) q^{97} +(-0.403921 - 0.914794i) q^{98} +(-1.08713 - 1.58701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{6}+O(q^{10}) $ 64 * q - 4 * q^6	$ 64 q - 4 q^{6} + 4 q^{16} - 4 q^{17} - 4 q^{19} - 4 q^{36} + 4 q^{41} - 4 q^{68} - 4 q^{75} + 4 q^{76} + 4 q^{81} - 4 q^{83} + 4 q^{96}+O(q^{100}) $ 64 * q - 4 * q^6 + 4 * q^16 - 4 * q^17 - 4 * q^19 - 4 * q^36 + 4 * q^41 - 4 * q^68 - 4 * q^75 + 4 * q^76 + 4 * q^81 - 4 * q^83 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3288\mathbb{Z}\right)^\times$.

$n$	$823$	$1097$	$1645$	$1921$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{117}{136}\right)$

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 $

$2$	−0.948161	−	0.317791i	−0.948161	−	0.317791i
$2$	−0.948161	−	0.317791i	−0.948161	−	0.317791i
$3$	0.228951	+	0.973438i	0.228951	+	0.973438i
$3$	0.228951	+	0.973438i	0.228951	+	0.973438i
$4$	0.798017	+	0.602635i	0.798017	+	0.602635i
$5$		0			0		−0.997600	−	0.0692444i	$-0.977941\pi$
$5$		0			0		0.997600	+	0.0692444i	$0.0220588\pi$
$6$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$7$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$7$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$8$	−0.565136	−	0.824997i	−0.565136	−	0.824997i
$9$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$10$		0			0
$11$	0.265765	+	1.90520i	0.265765	+	1.90520i	0.403921	+	0.914794i	$0.367647\pi$
$11$	0.265765	+	1.90520i	0.265765	+	1.90520i	−0.138156	+	0.990410i	$0.544118\pi$
$12$	−0.403921	+	0.914794i	−0.403921	+	0.914794i
$13$		0			0		0.0230979	−	0.999733i	$-0.492647\pi$
$13$		0			0		−0.0230979	+	0.999733i	$0.507353\pi$
$14$		0			0
$15$		0			0
$16$	0.273663	+	0.961826i	0.273663	+	0.961826i
$17$	1.44147	+	0.987432i	1.44147	+	0.987432i	0.995734	+	0.0922684i	$0.0294118\pi$
$17$	1.44147	+	0.987432i	1.44147	+	0.987432i	0.445738	+	0.895163i	$0.352941\pi$
$18$	0.990410	−	0.138156i	0.990410	−	0.138156i
$19$	0.377767	−	1.60617i	0.377767	−	1.60617i	−0.361242	−	0.932472i	$-0.617647\pi$
$19$	0.377767	−	1.60617i	0.377767	−	1.60617i	0.739009	−	0.673696i	$-0.235294\pi$
$20$		0			0
$21$		0			0
$22$	0.353470	−	1.89090i	0.353470	−	1.89090i
$23$		0			0		−0.993337	−	0.115243i	$-0.963235\pi$
$23$		0			0		0.993337	+	0.115243i	$0.0367647\pi$
$24$	0.673696	−	0.739009i	0.673696	−	0.739009i
$25$	0.990410	+	0.138156i	0.990410	+	0.138156i
$26$		0			0
$27$	−0.638847	−	0.769334i	−0.638847	−	0.769334i
$28$		0			0
$29$		0			0		0.783885	−	0.620906i	$-0.213235\pi$
$29$		0			0		−0.783885	+	0.620906i	$0.786765\pi$
$30$		0			0
$31$		0			0		0.811724	−	0.584041i	$-0.198529\pi$
$31$		0			0		−0.811724	+	0.584041i	$0.801471\pi$
$32$	0.0461835	−	0.998933i	0.0461835	−	0.998933i
$33$	−1.79375	+	0.694903i	−1.79375	+	0.694903i
$34$	−1.05295	−	1.39433i	−1.05295	−	1.39433i
$35$		0			0
$36$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	−0.868610	+	1.40285i	−0.868610	+	1.40285i
$39$		0			0
$40$		0			0
$41$	−0.785192	+	0.325237i	−0.785192	+	0.325237i	−0.739009	−	0.673696i	$-0.764706\pi$
$41$	−0.785192	+	0.325237i	−0.785192	+	0.325237i	−0.0461835	+	0.998933i	$0.514706\pi$
$42$		0			0
$43$	−0.0371073	−	0.227480i	−0.0371073	−	0.227480i	0.961826	−	0.273663i	$-0.0882353\pi$
$43$	−0.0371073	−	0.227480i	−0.0371073	−	0.227480i	−0.998933	+	0.0461835i	$0.985294\pi$
$44$	−0.936057	+	1.68054i	−0.936057	+	1.68054i
$45$		0			0
$46$		0			0
$47$		0			0		0.884629	−	0.466296i	$-0.154412\pi$
$47$		0			0		−0.884629	+	0.466296i	$0.845588\pi$
$48$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$49$	0.673696	+	0.739009i	0.673696	+	0.739009i
$50$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$51$	−0.631178	+	1.62926i	−0.631178	+	1.62926i
$52$		0			0
$53$		0			0		−0.811724	−	0.584041i	$-0.801471\pi$
$53$		0			0		0.811724	+	0.584041i	$0.198529\pi$
$54$	0.361242	+	0.932472i	0.361242	+	0.932472i
$55$		0			0
$56$		0			0
$57$	1.64999			1.64999
$58$		0			0
$59$	−1.78269	+	0.165190i	−1.78269	+	0.165190i	−0.932472	−	0.361242i	$-0.882353\pi$
$59$	−1.78269	+	0.165190i	−1.78269	+	0.165190i	−0.850217	+	0.526432i	$0.823529\pi$
$60$		0			0
$61$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$61$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$62$		0			0
$63$		0			0
$64$	−0.361242	+	0.932472i	−0.361242	+	0.932472i
$65$		0			0
$66$	1.92160	−	0.0888409i	1.92160	−	0.0888409i
$67$	−0.789689	+	0.754023i	−0.789689	+	0.754023i	−0.973438	−	0.228951i	$-0.926471\pi$
$67$	−0.789689	+	0.754023i	−0.789689	+	0.754023i	0.183750	+	0.982973i	$0.441176\pi$
$68$	0.555259	+	1.65667i	0.555259	+	1.65667i
$69$		0			0
$70$		0			0
$71$		0			0		−0.251374	−	0.967890i	$-0.580882\pi$
$71$		0			0		0.251374	+	0.967890i	$0.419118\pi$
$72$	0.873622	+	0.486604i	0.873622	+	0.486604i
$73$	0.0861296	+	0.0333668i	0.0861296	+	0.0333668i	0.403921	−	0.914794i	$-0.367647\pi$
$73$	0.0861296	+	0.0333668i	0.0861296	+	0.0333668i	−0.317791	+	0.948161i	$0.602941\pi$
$74$		0			0
$75$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$76$	1.26940	−	1.05409i	1.26940	−	1.05409i
$77$		0			0
$78$		0			0
$79$		0			0		−0.339607	−	0.940567i	$-0.610294\pi$
$79$		0			0		0.339607	+	0.940567i	$0.389706\pi$
$80$		0			0
$81$	0.602635	−	0.798017i	0.602635	−	0.798017i
$82$	0.847846	−	0.0588498i	0.847846	−	0.0588498i
$83$	−1.67521	−	1.09157i	−1.67521	−	1.09157i	−0.850217	−	0.526432i	$-0.823529\pi$
$83$	−1.67521	−	1.09157i	−1.67521	−	1.09157i	−0.824997	−	0.565136i	$-0.808824\pi$
$84$		0			0
$85$		0			0
$86$	−0.0371073	+	0.227480i	−0.0371073	+	0.227480i
$87$		0			0
$88$	1.42160	−	1.29596i	1.42160	−	1.29596i
$89$	1.29577	+	1.48906i	1.29577	+	1.48906i	0.769334	+	0.638847i	$0.220588\pi$
$89$	1.29577	+	1.48906i	1.29577	+	1.48906i	0.526432	+	0.850217i	$0.323529\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.982973	−	0.183750i	0.982973	−	0.183750i
$97$	−0.873622	+	0.513396i	−0.873622	+	0.513396i	−0.873622	−	0.486604i	$-0.838235\pi$
$97$	−0.873622	+	0.513396i	−0.873622	+	0.513396i			1.00000i	$0.5\pi$
$98$	−0.403921	−	0.914794i	−0.403921	−	0.914794i
$99$	−1.08713	−	1.58701i	−1.08713	−	1.58701i
$100$	0.707107	+	0.707107i	0.707107	+	0.707107i
$101$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$101$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$102$	1.11622	−	1.34421i	1.11622	−	1.34421i
$103$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$103$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.86295	−	0.0861296i	1.86295	−	0.0861296i	0.914794	−	0.403921i	$-0.132353\pi$
$107$	1.86295	−	0.0861296i	1.86295	−	0.0861296i	0.948161	+	0.317791i	$0.102941\pi$
$108$	−0.0461835	−	0.998933i	−0.0461835	−	0.998933i
$109$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$109$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.953083	−	1.62182i	0.953083	−	1.62182i	0.183750	−	0.982973i	$-0.441176\pi$
$113$	0.953083	−	1.62182i	0.953083	−	1.62182i	0.769334	−	0.638847i	$-0.220588\pi$
$114$	−1.56446	−	0.524354i	−1.56446	−	0.524354i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.74277	+	0.409896i	1.74277	+	0.409896i
$119$		0			0
$120$		0			0
$121$	−2.59735	+	0.739009i	−2.59735	+	0.739009i
$122$		0			0
$123$	−0.496369	−	0.689873i	−0.496369	−	0.689873i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$127$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$128$	0.638847	−	0.769334i	0.638847	−	0.769334i
$129$	0.212941	−	0.0882033i	0.212941	−	0.0882033i
$130$		0			0
$131$	0.180675	+	1.55732i	0.180675	+	1.55732i	0.707107	+	0.707107i	$0.250000\pi$
$131$	0.180675	+	1.55732i	0.180675	+	1.55732i	−0.526432	+	0.850217i	$0.676471\pi$
$132$	−1.85022	−	0.526432i	−1.85022	−	0.526432i
$133$		0			0
$134$	0.988373	−	0.463978i	0.988373	−	0.463978i
$135$		0			0
$136$		−	1.74724i		−	1.74724i
$137$	−0.973438	+	0.228951i	−0.973438	+	0.228951i
$137$	−0.973438	+	0.228951i	−0.973438	+	0.228951i
$138$		0			0
$139$	−0.116788	+	0.348448i	−0.116788	+	0.348448i	−0.990410	−	0.138156i	$-0.955882\pi$
$139$	−0.116788	+	0.348448i	−0.116788	+	0.348448i	0.873622	+	0.486604i	$0.161765\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$145$		0			0
$146$	−0.0710610	−	0.0590083i	−0.0710610	−	0.0590083i
$147$	−0.565136	+	0.824997i	−0.565136	+	0.824997i
$148$		0			0
$149$		0			0		0.206405	−	0.978467i	$-0.433824\pi$
$149$		0			0		−0.206405	+	0.978467i	$0.566176\pi$
$150$	0.228951	−	0.973438i	0.228951	−	0.973438i
$151$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$151$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$152$	−1.53857	+	0.596047i	−1.53857	+	0.596047i
$153$	−1.73049	−	0.241393i	−1.73049	−	0.241393i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.656446	−	0.754373i	$-0.272059\pi$
$157$		0			0		−0.656446	+	0.754373i	$0.727941\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.824997	+	0.565136i	−0.824997	+	0.565136i
$163$	0.472868	+	0.170737i	0.472868	+	0.170737i	0.565136	−	0.824997i	$-0.308824\pi$
$163$	0.472868	+	0.170737i	0.472868	+	0.170737i	−0.0922684	+	0.995734i	$0.529412\pi$
$164$	−0.822596	−	0.213639i	−0.822596	−	0.213639i
$165$		0			0
$166$	1.24148	+	1.56735i	1.24148	+	1.56735i
$167$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$167$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$168$		0			0
$169$	−0.998933	−	0.0461835i	−0.998933	−	0.0461835i
$170$		0			0
$171$	0.377767	+	1.60617i	0.377767	+	1.60617i
$172$	0.107475	−	0.203895i	0.107475	−	0.203895i
$173$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$173$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$174$		0			0
$175$		0			0
$176$	−1.75974	+	0.777003i	−1.75974	+	0.777003i
$177$	−0.568950	−	1.69752i	−0.568950	−	1.69752i
$178$	−0.755383	−	1.82366i	−0.755383	−	1.82366i
$179$	−0.648818	−	0.200916i	−0.648818	−	0.200916i	−0.0461835	−	0.998933i	$-0.514706\pi$
$179$	−0.648818	−	0.200916i	−0.648818	−	0.200916i	−0.602635	+	0.798017i	$0.705882\pi$
$180$		0			0
$181$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$181$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.49817	+	3.00872i	−1.49817	+	3.00872i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.545930	−	0.837831i	$-0.316176\pi$
$191$		0			0		−0.545930	+	0.837831i	$0.683824\pi$
$192$	−0.990410	−	0.138156i	−0.990410	−	0.138156i
$193$	1.94709	−	0.363975i	1.94709	−	0.363975i	0.948161	−	0.317791i	$-0.102941\pi$
$193$	1.94709	−	0.363975i	1.94709	−	0.363975i	0.998933	−	0.0461835i	$-0.0147059\pi$
$194$	0.991487	−	0.209152i	0.991487	−	0.209152i
$195$		0			0
$196$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$197$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$197$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$198$	0.526432	+	1.85022i	0.526432	+	1.85022i
$199$		0			0		−0.295806	−	0.955248i	$-0.595588\pi$
$199$		0			0		0.295806	+	0.955248i	$0.404412\pi$
$200$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$201$	−0.914794	−	0.596079i	−0.914794	−	0.596079i
$202$		0			0
$203$		0			0
$204$	−1.48554	+	0.919806i	−1.48554	+	0.919806i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.16048	+	0.292861i	3.16048	+	0.292861i
$210$		0			0
$211$	−0.283304	−	0.568950i	−0.283304	−	0.568950i	0.707107	−	0.707107i	$-0.250000\pi$
$211$	−0.283304	−	0.568950i	−0.283304	−	0.568950i	−0.990410	+	0.138156i	$0.955882\pi$
$212$		0			0
$213$		0			0
$214$	−1.79375	−	0.510366i	−1.79375	−	0.510366i
$215$		0			0
$216$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$217$		0			0
$218$		0			0
$219$	−0.0127611	+	0.0914812i	−0.0127611	+	0.0914812i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.986955	−	0.160996i	$-0.948529\pi$
$223$		0			0		0.986955	+	0.160996i	$0.0514706\pi$
$224$		0			0
$225$	−0.948161	+	0.317791i	−0.948161	+	0.317791i
$226$	−1.41908	+	1.23486i	−1.41908	+	1.23486i
$227$	0.0215409	+	0.0408661i	0.0215409	+	0.0408661i	0.895163	−	0.445738i	$-0.147059\pi$
$227$	0.0215409	+	0.0408661i	0.0215409	+	0.0408661i	−0.873622	+	0.486604i	$0.838235\pi$
$228$	1.31672	+	0.994344i	1.31672	+	0.994344i
$229$		0			0		0.690585	−	0.723251i	$-0.257353\pi$
$229$		0			0		−0.690585	+	0.723251i	$0.742647\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.740791	−	1.78843i	−0.740791	−	1.78843i	−0.602635	−	0.798017i	$-0.705882\pi$
$233$	−0.740791	−	1.78843i	−0.740791	−	1.78843i	−0.138156	−	0.990410i	$-0.544118\pi$
$234$		0			0
$235$		0			0
$236$	−1.52217	−	0.942485i	−1.52217	−	0.942485i
$237$		0			0
$238$		0			0
$239$		0			0		0.466296	−	0.884629i	$-0.345588\pi$
$239$		0			0		−0.466296	+	0.884629i	$0.654412\pi$
$240$		0			0
$241$	0.941347	+	1.44467i	0.941347	+	1.44467i	0.895163	+	0.445738i	$0.147059\pi$
$241$	0.941347	+	1.44467i	0.941347	+	1.44467i	0.0461835	+	0.998933i	$0.485294\pi$
$242$	2.69755	+	0.124715i	2.69755	+	0.124715i
$243$	0.914794	+	0.403921i	0.914794	+	0.403921i
$244$		0			0
$245$		0			0
$246$	0.251402	+	0.811852i	0.251402	+	0.811852i
$247$		0			0
$248$		0			0
$249$	0.679033	−	1.88063i	0.679033	−	1.88063i
$250$		0			0
$251$	0.143110	−	1.23354i	0.143110	−	1.23354i	−0.707107	−	0.707107i	$-0.750000\pi$
$251$	0.143110	−	1.23354i	0.143110	−	1.23354i	0.850217	−	0.526432i	$-0.176471\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$257$	0.761460	−	1.11159i	0.761460	−	1.11159i	−0.228951	−	0.973438i	$-0.573529\pi$
$257$	0.761460	−	1.11159i	0.761460	−	1.11159i	0.990410	−	0.138156i	$-0.0441176\pi$
$258$	−0.229933	+	0.0159599i	−0.229933	+	0.0159599i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.323596	−	1.53401i	0.323596	−	1.53401i
$263$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$263$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$264$	1.58701	+	1.08713i	1.58701	+	1.08713i
$265$		0			0
$266$		0			0
$267$	−1.15285	+	1.60227i	−1.15285	+	1.60227i
$268$	−1.08459	+	0.125829i	−1.08459	+	0.125829i
$269$		0			0		0.0692444	−	0.997600i	$-0.477941\pi$
$269$		0			0		−0.0692444	+	0.997600i	$0.522059\pi$
$270$		0			0
$271$		0			0		−0.424943	−	0.905220i	$-0.639706\pi$
$271$		0			0		0.424943	+	0.905220i	$0.360294\pi$
$272$	−0.555259	+	1.65667i	−0.555259	+	1.65667i
$273$		0			0
$274$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$275$			1.92365i			1.92365i
$276$		0			0
$277$		0			0		0.905220	−	0.424943i	$-0.139706\pi$
$277$		0			0		−0.905220	+	0.424943i	$0.860294\pi$
$278$	0.221468	−	0.293271i	0.221468	−	0.293271i
$279$		0			0
$280$		0			0
$281$	0.794087	−	1.79844i	0.794087	−	1.79844i	0.228951	−	0.973438i	$-0.426471\pi$
$281$	0.794087	−	1.79844i	0.794087	−	1.79844i	0.565136	−	0.824997i	$-0.308824\pi$
$282$		0			0
$283$	0.982973	−	1.18375i	0.982973	−	1.18375i		−	1.00000i	$-0.5\pi$
$283$	0.982973	−	1.18375i	0.982973	−	1.18375i	0.982973	−	0.183750i	$-0.0588235\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.403921	+	0.914794i	0.403921	+	0.914794i
$289$	0.741580	+	1.91424i	0.741580	+	1.91424i
$290$		0			0
$291$	−0.699775	−	0.732875i	−0.699775	−	0.732875i
$292$	0.0486249	+	0.0785319i	0.0486249	+	0.0785319i
$293$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$293$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$294$	0.798017	−	0.602635i	0.798017	−	0.602635i
$295$		0			0
$296$		0			0
$297$	1.29596	−	1.42160i	1.29596	−	1.42160i
$298$		0			0
$299$		0			0
$300$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.64823	−	0.0762025i	1.64823	−	0.0762025i
$305$		0			0
$306$	1.56407	+	0.778814i	1.56407	+	0.778814i
$307$	−1.40392	+	0.914794i	−1.40392	+	0.914794i	−0.403921	+	0.914794i	$0.632353\pi$
$307$	−1.40392	+	0.914794i	−1.40392	+	0.914794i	−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$311$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$312$		0			0
$313$	−0.184956	−	0.418885i	−0.184956	−	0.418885i	0.798017	−	0.602635i	$-0.205882\pi$
$313$	−0.184956	−	0.418885i	−0.184956	−	0.418885i	−0.982973	+	0.183750i	$0.941176\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.986955	−	0.160996i	$-0.0514706\pi$
$317$		0			0		−0.986955	+	0.160996i	$0.948529\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.510366	+	1.79375i	0.510366	+	1.79375i
$322$		0			0
$323$	2.13052	−	1.94223i	2.13052	−	1.94223i
$324$	0.961826	−	0.273663i	0.961826	−	0.273663i
$325$		0			0
$326$	−0.394096	−	0.312159i	−0.394096	−	0.312159i
$327$		0			0
$328$	0.712061	+	0.463978i	0.712061	+	0.463978i
$329$		0			0
$330$		0			0
$331$	0.381387	+	1.80797i	0.381387	+	1.80797i	0.565136	+	0.824997i	$0.308824\pi$
$331$	0.381387	+	1.80797i	0.381387	+	1.80797i	−0.183750	+	0.982973i	$0.558824\pi$
$332$	−0.679033	−	1.88063i	−0.679033	−	1.88063i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.78842	−	0.890525i	1.78842	−	0.890525i	0.873622	−	0.486604i	$-0.161765\pi$
$337$	1.78842	−	0.890525i	1.78842	−	0.890525i	0.914794	−	0.403921i	$-0.132353\pi$
$338$	0.932472	+	0.361242i	0.932472	+	0.361242i
$339$	1.79695	+	0.556451i	1.79695	+	0.556451i
$340$		0			0
$341$		0			0
$342$	0.152242	−	1.64296i	0.152242	−	1.64296i
$343$		0			0
$344$	−0.166699	+	0.159170i	−0.166699	+	0.159170i
$345$		0			0
$346$		0			0
$347$	−0.0666624	+	0.172075i	−0.0666624	+	0.172075i	−0.961826	−	0.273663i	$-0.911765\pi$
$347$	−0.0666624	+	0.172075i	−0.0666624	+	0.172075i	0.895163	+	0.445738i	$0.147059\pi$
$348$		0			0
$349$		0			0		0.955248	−	0.295806i	$-0.0955882\pi$
$349$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$350$		0			0
$351$		0			0
$352$	1.91545	−	0.177492i	1.91545	−	0.177492i
$353$	−1.36053	+	0.491242i	−1.36053	+	0.491242i	−0.914794	−	0.403921i	$-0.867647\pi$
$353$	−1.36053	+	0.491242i	−1.36053	+	0.491242i	−0.445738	+	0.895163i	$0.647059\pi$
$354$			1.79033i			1.79033i
$355$		0			0
$356$	0.136682	+	1.96917i	0.136682	+	1.96917i
$357$		0			0
$358$	0.551334	+	0.396689i	0.551334	+	0.396689i
$359$		0			0		0.620906	−	0.783885i	$-0.286765\pi$
$359$		0			0		−0.620906	+	0.783885i	$0.713235\pi$
$360$		0			0
$361$	−1.54190	−	0.767777i	−1.54190	−	0.767777i
$362$		0			0
$363$	−1.31404	−	2.35916i	−1.31404	−	2.35916i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$367$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$368$		0			0
$369$	0.557905	−	0.641131i	0.557905	−	0.641131i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$373$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$374$	2.37665	−	2.37665i	2.37665	−	2.37665i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0737104	−	1.59433i	0.0737104	−	1.59433i	−0.565136	−	0.824997i	$-0.691176\pi$
$379$	0.0737104	−	1.59433i	0.0737104	−	1.59433i	0.638847	−	0.769334i	$-0.279412\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$383$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$384$	0.895163	+	0.445738i	0.895163	+	0.445738i
$385$		0			0
$386$	−1.96183	−	0.273663i	−1.96183	−	0.273663i
$387$	0.134613	+	0.187091i	0.134613	+	0.187091i
$388$	−1.00656	−	0.116777i	−1.00656	−	0.116777i
$389$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$389$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$390$		0			0
$391$		0			0
$392$	0.228951	−	0.973438i	0.228951	−	0.973438i
$393$	−1.47459	+	0.532426i	−1.47459	+	0.532426i
$394$		0			0
$395$		0			0
$396$	0.0888409	−	1.92160i	0.0888409	−	1.92160i
$397$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$397$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$398$		0			0
$399$		0			0
$400$	0.138156	+	0.990410i	0.138156	+	0.990410i
$401$	−1.76507	−	0.731115i	−1.76507	−	0.731115i	−0.995734	−	0.0922684i	$-0.970588\pi$
$401$	−1.76507	−	0.731115i	−1.76507	−	0.731115i	−0.769334	−	0.638847i	$-0.779412\pi$
$402$	0.677943	+	0.855892i	0.677943	+	0.855892i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.70083	−	0.400033i	1.70083	−	0.400033i
$409$	−1.14279	−	0.383024i	−1.14279	−	0.383024i	−0.317791	−	0.948161i	$-0.602941\pi$
$409$	−1.14279	−	0.383024i	−1.14279	−	0.383024i	−0.824997	+	0.565136i	$0.808824\pi$
$410$		0			0
$411$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.365931	−	0.0339085i	−0.365931	−	0.0339085i
$418$	−2.90357	−	1.28205i	−2.90357	−	1.28205i
$419$	0.681142	+	0.994344i	0.681142	+	0.994344i	0.998933	+	0.0461835i	$0.0147059\pi$
$419$	0.681142	+	0.994344i	0.681142	+	0.994344i	−0.317791	+	0.948161i	$0.602941\pi$
$420$		0			0
$421$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$421$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$422$	0.0878098	+	0.629488i	0.0878098	+	0.629488i
$423$		0			0
$424$		0			0
$425$	1.29123	+	1.17711i	1.29123	+	1.17711i
$426$		0			0
$427$		0			0
$428$	1.53857	+	1.05395i	1.53857	+	1.05395i
$429$		0			0
$430$		0			0
$431$		0			0		−0.754373	−	0.656446i	$-0.772059\pi$
$431$		0			0		0.754373	+	0.656446i	$0.227941\pi$
$432$	0.565136	−	0.824997i	0.565136	−	0.824997i
$433$	0.0507723	−	0.271608i	0.0507723	−	0.271608i	−0.948161	−	0.317791i	$-0.897059\pi$
$433$	0.0507723	−	0.271608i	0.0507723	−	0.271608i	0.998933	+	0.0461835i	$0.0147059\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.0411715	−	0.0826835i	0.0411715	−	0.0826835i
$439$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$439$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$440$		0			0
$441$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$442$		0			0
$443$	0.0127611	−	0.276018i	0.0127611	−	0.276018i	−0.982973	−	0.183750i	$-0.941176\pi$
$443$	0.0127611	−	0.276018i	0.0127611	−	0.276018i	0.995734	−	0.0922684i	$-0.0294118\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.840204	−	1.35698i	0.840204	−	1.35698i	−0.0922684	−	0.995734i	$-0.529412\pi$
$449$	0.840204	−	1.35698i	0.840204	−	1.35698i	0.932472	−	0.361242i	$-0.117647\pi$
$450$	1.00000			1.00000
$451$	−0.828320	−	1.40952i	−0.828320	−	1.40952i
$452$	1.73794	−	0.719879i	1.73794	−	0.719879i
$453$		0			0
$454$	−0.00743733	−	0.0455932i	−0.00743733	−	0.0455932i
$455$		0			0
$456$	−0.932472	−	1.36124i	−0.932472	−	1.36124i
$457$	1.79838	+	0.844224i	1.79838	+	0.844224i	0.948161	+	0.317791i	$0.102941\pi$
$457$	1.79838	+	0.844224i	1.79838	+	0.844224i	0.850217	+	0.526432i	$0.176471\pi$
$458$		0			0
$459$	−0.161215	−	1.73979i	−0.161215	−	1.73979i
$460$		0			0
$461$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$461$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$462$		0			0
$463$		0			0		0.620906	−	0.783885i	$-0.286765\pi$
$463$		0			0		−0.620906	+	0.783885i	$0.713235\pi$
$464$		0			0
$465$		0			0
$466$	0.134042	+	1.93113i	0.134042	+	1.93113i
$467$	−0.271585	−	1.45285i	−0.271585	−	1.45285i	−0.798017	−	0.602635i	$-0.794118\pi$
$467$	−0.271585	−	1.45285i	−0.271585	−	1.45285i	0.526432	−	0.850217i	$-0.323529\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.14374	+	1.37736i	1.14374	+	1.37736i
$473$	0.423533	−	0.131153i	0.423533	−	0.131153i
$474$		0			0
$475$	0.596047	−	1.53857i	0.596047	−	1.53857i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$479$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$480$		0			0
$481$		0			0
$482$	−0.433444	−	1.66893i	−0.433444	−	1.66893i
$483$		0			0
$484$	−2.51808	−	0.975509i	−2.51808	−	0.975509i
$485$		0			0
$486$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$487$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$487$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$488$		0			0
$489$	−0.0579382	+	0.499398i	−0.0579382	+	0.499398i
$490$		0			0
$491$	0.311413	+	1.47626i	0.311413	+	1.47626i	0.798017	+	0.602635i	$0.205882\pi$
$491$	0.311413	+	1.47626i	0.311413	+	1.47626i	−0.486604	+	0.873622i	$0.661765\pi$
$492$	0.0196306	−	0.849659i	0.0196306	−	0.849659i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.24148	+	1.56735i	−1.24148	+	1.56735i
$499$	−0.136374	+	0.124322i	−0.136374	+	0.124322i	−0.739009	−	0.673696i	$-0.764706\pi$
$499$	−0.136374	+	0.124322i	−0.136374	+	0.124322i	0.602635	+	0.798017i	$0.294118\pi$
$500$		0			0
$501$		0			0
$502$	−0.527700	+	1.12411i	−0.527700	+	1.12411i
$503$		0			0		−0.723251	−	0.690585i	$-0.757353\pi$
$503$		0			0		0.723251	+	0.690585i	$0.242647\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$508$		0			0
$509$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$509$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$510$		0			0
$511$		0			0
$512$	0.973438	−	0.228951i	0.973438	−	0.228951i
$513$	−1.47701	+	0.735466i	−1.47701	+	0.735466i
$514$	−1.07524	+	0.811985i	−1.07524	+	0.811985i
$515$		0			0
$516$	0.223085	+	0.0579382i	0.223085	+	0.0579382i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.455097	+	1.75231i	−0.455097	+	1.75231i	0.183750	+	0.982973i	$0.441176\pi$
$521$	−0.455097	+	1.75231i	−0.455097	+	1.75231i	−0.638847	+	0.769334i	$0.720588\pi$
$522$		0			0
$523$	0.275134	−	1.97237i	0.275134	−	1.97237i	0.0461835	−	0.998933i	$-0.485294\pi$
$523$	0.275134	−	1.97237i	0.275134	−	1.97237i	0.228951	−	0.973438i	$-0.426471\pi$
$524$	−0.794316	+	1.35165i	−0.794316	+	1.35165i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.15926	−	1.53511i	−1.15926	−	1.53511i
$529$	0.973438	+	0.228951i	0.973438	+	0.228951i
$530$		0			0
$531$	1.52217	−	0.942485i	1.52217	−	0.942485i
$532$		0			0
$533$		0			0
$534$	1.60227	−	1.15285i	1.60227	−	1.15285i
$535$		0			0
$536$	1.06835	+	0.225365i	1.06835	+	0.225365i
$537$	0.0470318	−	0.677584i	0.0470318	−	0.677584i
$538$		0			0
$539$	−1.22892	+	1.47993i	−1.22892	+	1.47993i
$540$		0			0
$541$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$541$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$542$		0			0
$543$		0			0
$544$	1.05295	−	1.39433i	1.05295	−	1.39433i
$545$		0			0
$546$		0			0
$547$		−	1.47802i		−	1.47802i	−0.673696	−	0.739009i	$-0.735294\pi$
$547$		−	1.47802i		−	1.47802i	0.673696	−	0.739009i	$-0.264706\pi$
$548$	−0.914794	−	0.403921i	−0.914794	−	0.403921i
$549$		0			0
$550$	0.611320	−	1.82393i	0.611320	−	1.82393i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.303186	+	0.207687i	−0.303186	+	0.207687i
$557$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$557$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−3.27181	−	0.769523i	−3.27181	−	0.769523i
$562$	−1.32445	+	1.45285i	−1.32445	+	1.45285i
$563$	−0.673696	+	0.260991i	−0.673696	+	0.260991i	−0.673696	−	0.739009i	$-0.735294\pi$
$563$	−0.673696	+	0.260991i	−0.673696	+	0.260991i			1.00000i	$0.5\pi$
$564$		0			0
$565$		0			0
$566$	−1.30820	+	0.810004i	−1.30820	+	0.810004i
$567$		0			0
$568$		0			0
$569$	−0.0408661	−	1.76879i	−0.0408661	−	1.76879i	−0.486604	−	0.873622i	$-0.661765\pi$
$569$	−0.0408661	−	1.76879i	−0.0408661	−	1.76879i	0.445738	−	0.895163i	$-0.352941\pi$
$570$		0			0
$571$	−0.159170	+	1.37197i	−0.159170	+	1.37197i	0.638847	+	0.769334i	$0.279412\pi$
$571$	−0.159170	+	1.37197i	−0.159170	+	1.37197i	−0.798017	+	0.602635i	$0.794118\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.0922684	−	0.995734i	−0.0922684	−	0.995734i
$577$	0.367336	+	0.463756i	0.367336	+	0.463756i	0.932472	−	0.361242i	$-0.117647\pi$
$577$	0.367336	+	0.463756i	0.367336	+	0.463756i	−0.565136	+	0.824997i	$0.691176\pi$
$578$	−0.0948084	−	2.05067i	−0.0948084	−	2.05067i
$579$	0.800095	+	1.81204i	0.800095	+	1.81204i
$580$		0			0
$581$		0			0
$582$	0.430598	+	0.917266i	0.430598	+	0.917266i
$583$		0			0
$584$	−0.0211475	−	0.0899135i	−0.0211475	−	0.0899135i
$585$		0			0
$586$		0			0
$587$	0.963154	−	0.425274i	0.963154	−	0.425274i	0.138156	−	0.990410i	$-0.455882\pi$
$587$	0.963154	−	0.425274i	0.963154	−	0.425274i	0.824997	+	0.565136i	$0.191176\pi$
$588$	−0.948161	+	0.317791i	−0.948161	+	0.317791i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.37786	−	1.44303i	1.37786	−	1.44303i	0.638847	−	0.769334i	$-0.279412\pi$
$593$	1.37786	−	1.44303i	1.37786	−	1.44303i	0.739009	−	0.673696i	$-0.235294\pi$
$594$	−1.68054	+	0.936057i	−1.68054	+	0.936057i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.986955	−	0.160996i	$-0.948529\pi$
$599$		0			0		0.986955	+	0.160996i	$0.0514706\pi$
$600$	0.769334	−	0.638847i	0.769334	−	0.638847i
$601$	0.806661	−	1.12113i	0.806661	−	1.12113i	−0.183750	−	0.982973i	$-0.558824\pi$
$601$	0.806661	−	1.12113i	0.806661	−	1.12113i	0.990410	−	0.138156i	$-0.0441176\pi$
$602$		0			0
$603$	0.370803	−	1.02697i	0.370803	−	1.02697i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$607$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$608$	−1.58701	−	0.451543i	−1.58701	−	0.451543i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.23549	−	1.23549i	−1.23549	−	1.23549i
$613$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$613$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$614$	1.62186	−	0.421217i	1.62186	−	0.421217i
$615$		0			0
$616$		0			0
$617$	−0.434164	+	0.145517i	−0.434164	+	0.145517i	−0.526432	−	0.850217i	$-0.676471\pi$
$617$	−0.434164	+	0.145517i	−0.434164	+	0.145517i	0.0922684	+	0.995734i	$0.470588\pi$
$618$		0			0
$619$	−0.572616	+	0.148716i	−0.572616	+	0.148716i	−0.526432	−	0.850217i	$-0.676471\pi$
$619$	−0.572616	+	0.148716i	−0.572616	+	0.148716i	−0.0461835	+	0.998933i	$0.514706\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.961826	+	0.273663i	0.961826	+	0.273663i
$626$	0.0422498	+	0.455948i	0.0422498	+	0.455948i
$627$	0.438510	+	3.14358i	0.438510	+	3.14358i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.545930	−	0.837831i	$-0.316176\pi$
$631$		0			0		−0.545930	+	0.837831i	$0.683824\pi$
$632$		0			0
$633$	0.488975	−	0.406040i	0.488975	−	0.406040i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.34421	+	0.748723i	1.34421	+	0.748723i	0.982973	−	0.183750i	$-0.0588235\pi$
$641$	1.34421	+	0.748723i	1.34421	+	0.748723i	0.361242	+	0.932472i	$0.382353\pi$
$642$	0.0861296	−	1.86295i	0.0861296	−	1.86295i
$643$	−0.890856	−	0.275866i	−0.890856	−	0.275866i	−0.183750	−	0.982973i	$-0.558824\pi$
$643$	−0.890856	−	0.275866i	−0.890856	−	0.275866i	−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$		0			0
$646$	−2.63730	+	1.16448i	−2.63730	+	1.16448i
$647$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$647$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$648$	−0.998933	−	0.0461835i	−0.998933	−	0.0461835i
$649$	−0.788497	−	3.35249i	−0.788497	−	3.35249i
$650$		0			0
$651$		0			0
$652$	0.274465	+	0.421217i	0.274465	+	0.421217i
$653$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$653$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$654$		0			0
$655$		0			0
$656$	−0.527700	−	0.666213i	−0.527700	−	0.666213i
$657$	−0.0919729	+	0.00852254i	−0.0919729	+	0.00852254i
$658$		0			0
$659$	−1.29908	−	0.469056i	−1.29908	−	0.469056i	−0.403921	−	0.914794i	$-0.632353\pi$
$659$	−1.29908	−	0.469056i	−1.29908	−	0.469056i	−0.895163	+	0.445738i	$0.852941\pi$
$660$		0			0
$661$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$661$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$662$	0.212941	−	1.83545i	0.212941	−	1.83545i
$663$		0			0
$664$	0.0461835	+	1.99893i	0.0461835	+	1.99893i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.256316	−	1.21507i	0.256316	−	1.21507i	−0.638847	−	0.769334i	$-0.720588\pi$
$673$	0.256316	−	1.21507i	0.256316	−	1.21507i	0.895163	−	0.445738i	$-0.147059\pi$
$674$	−1.97871	+	0.276018i	−1.97871	+	0.276018i
$675$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$676$	−0.769334	−	0.638847i	−0.769334	−	0.638847i
$677$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$677$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$678$	−1.52696	−	1.09866i	−1.52696	−	1.09866i
$679$		0			0
$680$		0			0
$681$	−0.0348488	+	0.0303251i	−0.0348488	+	0.0303251i
$682$		0			0
$683$	0.634905	−	1.89430i	0.634905	−	1.89430i	0.273663	−	0.961826i	$-0.411765\pi$
$683$	0.634905	−	1.89430i	0.634905	−	1.89430i	0.361242	−	0.932472i	$-0.382353\pi$
$684$	−0.666468	+	1.50941i	−0.666468	+	1.50941i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.208641	−	0.0979435i	0.208641	−	0.0979435i
$689$		0			0
$690$		0			0
$691$	0.0882033	+	0.760267i	0.0882033	+	0.760267i	0.961826	+	0.273663i	$0.0882353\pi$
$691$	0.0882033	+	0.760267i	0.0882033	+	0.760267i	−0.873622	+	0.486604i	$0.838235\pi$
$692$		0			0
$693$		0			0
$694$	0.117891	−	0.141970i	0.117891	−	0.141970i
$695$		0			0
$696$		0			0
$697$	−1.45298	−	0.306503i	−1.45298	−	0.306503i
$698$		0			0
$699$	1.57132	−	1.13058i	1.57132	−	1.13058i
$700$		0			0
$701$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$701$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$702$		0			0
$703$		0			0
$704$	−1.87256	−	0.440421i	−1.87256	−	0.440421i
$705$		0			0
$706$	1.44612	−	0.0334111i	1.44612	−	0.0334111i
$707$		0			0
$708$	0.568950	−	1.69752i	0.568950	−	1.69752i
$709$		0			0		0.506653	−	0.862150i	$-0.330882\pi$
$709$		0			0		−0.506653	+	0.862150i	$0.669118\pi$
$710$		0			0
$711$		0			0
$712$	0.496189	−	1.91053i	0.496189	−	1.91053i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.396689	−	0.551334i	−0.396689	−	0.551334i
$717$		0			0
$718$		0			0
$719$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$719$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$720$		0			0
$721$		0			0
$722$	1.21798	+	1.21798i	1.21798	+	1.21798i
$723$	−1.19078	+	1.24710i	−1.19078	+	1.24710i
$724$		0			0
$725$		0			0
$726$	0.496203	+	2.65445i	0.496203	+	2.65445i
$727$		0			0		0.295806	−	0.955248i	$-0.404412\pi$
$727$		0			0		−0.295806	+	0.955248i	$0.595588\pi$
$728$		0			0
$729$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$730$		0			0
$731$	0.171131	−	0.364546i	0.171131	−	0.364546i
$732$		0			0
$733$		0			0		−0.656446	−	0.754373i	$-0.727941\pi$
$733$		0			0		0.656446	+	0.754373i	$0.272059\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.64644	−	1.30413i	−1.64644	−	1.30413i
$738$	−0.732729	+	0.430598i	−0.732729	+	0.430598i
$739$	0.116030	+	0.0756052i	0.116030	+	0.0756052i	0.602635	−	0.798017i	$-0.294118\pi$
$739$	0.116030	+	0.0756052i	0.116030	+	0.0756052i	−0.486604	+	0.873622i	$0.661765\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.339607	−	0.940567i	$-0.610294\pi$
$743$		0			0		0.339607	+	0.940567i	$0.389706\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.98614	+	0.230425i	1.98614	+	0.230425i
$748$	−3.00872	+	1.49817i	−3.00872	+	1.49817i
$749$		0			0
$750$		0			0
$751$		0			0		−0.251374	−	0.967890i	$-0.580882\pi$
$751$		0			0		0.251374	+	0.967890i	$0.419118\pi$
$752$		0			0
$753$	1.23354	−	0.143110i	1.23354	−	0.143110i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$757$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$758$	−0.576554	+	1.48826i	−0.576554	+	1.48826i
$759$		0			0
$760$		0			0
$761$	0.461556	+	0.555831i	0.461556	+	0.555831i	0.948161	−	0.317791i	$-0.102941\pi$
$761$	0.461556	+	0.555831i	0.461556	+	0.555831i	−0.486604	+	0.873622i	$0.661765\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$769$	1.22468	+	0.881170i	1.22468	+	0.881170i	0.995734	−	0.0922684i	$-0.0294118\pi$
$769$	1.22468	+	0.881170i	1.22468	+	0.881170i	0.228951	+	0.973438i	$0.426471\pi$
$770$		0			0
$771$	1.25640	+	0.486734i	1.25640	+	0.486734i
$772$	1.77316	+	0.882928i	1.77316	+	0.882928i
$773$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$773$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$774$	−0.0681792	−	0.220171i	−0.0681792	−	0.220171i
$775$		0			0
$776$	0.917266	+	0.430598i	0.917266	+	0.430598i
$777$		0			0
$778$		0			0
$779$	0.225766	+	1.38401i	0.225766	+	1.38401i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$785$		0			0
$786$	1.56735	−	0.0362122i	1.56735	−	0.0362122i
$787$	1.71245	+	0.902646i	1.71245	+	0.902646i	0.973438	+	0.228951i	$0.0735294\pi$
$787$	1.71245	+	0.902646i	1.71245	+	0.902646i	0.739009	+	0.673696i	$0.235294\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.694903	+	1.79375i	−0.694903	+	1.79375i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$797$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$798$		0			0
$799$		0			0
$800$	0.183750	−	0.982973i	0.183750	−	0.982973i
$801$	−1.82366	−	0.755383i	−1.82366	−	0.755383i
$802$	1.44123	+	1.25414i	1.44123	+	1.25414i
$803$	−0.0406803	+	0.172962i	−0.0406803	+	0.172962i
$804$	−0.370803	−	1.02697i	−0.370803	−	1.02697i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.0303251	+	1.31254i	−0.0303251	+	1.31254i	0.739009	+	0.673696i	$0.235294\pi$
$809$	−0.0303251	+	1.31254i	−0.0303251	+	1.31254i	−0.769334	+	0.638847i	$0.779412\pi$
$810$		0			0
$811$	−0.261989	−	1.87814i	−0.261989	−	1.87814i	−0.445738	−	0.895163i	$-0.647059\pi$
$811$	−0.261989	−	1.87814i	−0.261989	−	1.87814i	0.183750	−	0.982973i	$-0.441176\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.73979	−	0.161215i	−1.73979	−	0.161215i
$817$	−0.379388	−	0.0263337i	−0.379388	−	0.0263337i
$818$	0.961826	+	0.726337i	0.961826	+	0.726337i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	0.138156	+	0.990410i	0.138156	+	0.990410i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	−1.87256	+	0.440421i	−1.87256	+	0.440421i
$826$		0			0
$827$	1.80609	+	0.125363i	1.80609	+	0.125363i	0.932472	−	0.361242i	$-0.117647\pi$
$827$	1.80609	+	0.125363i	1.80609	+	0.125363i	0.873622	+	0.486604i	$0.161765\pi$
$828$		0			0
$829$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$829$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.241393	+	1.73049i	0.241393	+	1.73049i
$834$	0.336186	+	0.148441i	0.336186	+	0.148441i
$835$		0			0
$836$	2.34563	+	2.13832i	2.34563	+	2.13832i
$837$		0			0
$838$	−0.329838	−	1.15926i	−0.329838	−	1.15926i
$839$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$839$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$840$		0			0
$841$	0.228951	−	0.973438i	0.228951	−	0.973438i
$842$		0			0
$843$	1.93247	+	0.361242i	1.93247	+	0.361242i
$844$	0.116788	−	0.624761i	0.116788	−	0.624761i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.37736	+	0.685843i	1.37736	+	0.685843i
$850$	−0.850217	−	1.52643i	−0.850217	−	1.52643i
$851$		0			0
$852$		0			0
$853$		0			0		0.811724	−	0.584041i	$-0.198529\pi$
$853$		0			0		−0.811724	+	0.584041i	$0.801471\pi$
$854$		0			0
$855$		0			0
$856$	−1.12388	−	1.48826i	−1.12388	−	1.48826i
$857$	1.48234	+	0.781354i	1.48234	+	0.781354i	0.995734	−	0.0922684i	$-0.0294118\pi$
$857$	1.48234	+	0.781354i	1.48234	+	0.781354i	0.486604	+	0.873622i	$0.338235\pi$
$858$		0			0
$859$	0.952750	−	0.952750i	0.952750	−	0.952750i	−0.0461835	−	0.998933i	$-0.514706\pi$
$859$	0.952750	−	0.952750i	0.952750	−	0.952750i	0.998933	+	0.0461835i	$0.0147059\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$863$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$864$	−0.798017	+	0.602635i	−0.798017	+	0.602635i
$865$		0			0
$866$	−0.134455	+	0.241393i	−0.134455	+	0.241393i
$867$	−1.69361	+	1.16015i	−1.69361	+	1.16015i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.553195	−	0.848980i	0.553195	−	0.848980i
$874$		0			0
$875$		0			0
$876$	−0.0653133	+	0.0653133i	−0.0653133	+	0.0653133i
$877$		0			0		−0.0692444	−	0.997600i	$-0.522059\pi$
$877$		0			0		0.0692444	+	0.997600i	$0.477941\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.275134	−	0.0254949i	0.275134	−	0.0254949i	0.0461835	−	0.998933i	$-0.485294\pi$
$881$	0.275134	−	0.0254949i	0.275134	−	0.0254949i	0.228951	+	0.973438i	$0.426471\pi$
$882$	0.769334	+	0.638847i	0.769334	+	0.638847i
$883$	1.25594	+	1.51247i	1.25594	+	1.51247i	0.769334	+	0.638847i	$0.220588\pi$
$883$	1.25594	+	1.51247i	1.25594	+	1.51247i	0.486604	+	0.873622i	$0.338235\pi$
$884$		0			0
$885$		0			0
$886$	−0.0998157	+	0.257654i	−0.0998157	+	0.257654i
$887$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$887$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.68054	+	0.936057i	1.68054	+	0.936057i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.22788	+	1.01962i	−1.22788	+	1.01962i
$899$		0			0
$900$	−0.948161	−	0.317791i	−0.948161	−	0.317791i
$901$		0			0
$902$	0.337448	+	1.59968i	0.337448	+	1.59968i
$903$		0			0
$904$	−1.87662	+	0.130258i	−1.87662	+	0.130258i
$905$		0			0
$906$		0			0
$907$	−1.13389	−	0.898142i	−1.13389	−	0.898142i	−0.138156	−	0.990410i	$-0.544118\pi$
$907$	−1.13389	−	0.898142i	−1.13389	−	0.898142i	−0.995734	+	0.0922684i	$0.970588\pi$
$908$	−0.00743733	+	0.0455932i	−0.00743733	+	0.0455932i
$909$		0			0
$910$		0			0
$911$		0			0		−0.656446	−	0.754373i	$-0.727941\pi$
$911$		0			0		0.656446	+	0.754373i	$0.272059\pi$
$912$	0.451543	+	1.58701i	0.451543	+	1.58701i
$913$	1.63445	−	3.48173i	1.63445	−	3.48173i
$914$	−1.43686	−	1.37197i	−1.43686	−	1.37197i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.400033	+	1.70083i	−0.400033	+	1.70083i
$919$		0			0		0.862150	−	0.506653i	$-0.169118\pi$
$919$		0			0		−0.862150	+	0.506653i	$0.830882\pi$
$920$		0			0
$921$	−1.21192	−	1.15719i	−1.21192	−	1.15719i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.94480	+	0.0899135i	−1.94480	+	0.0899135i	−0.982973	−	0.183750i	$-0.941176\pi$
$929$	−1.94480	+	0.0899135i	−1.94480	+	0.0899135i	−0.961826	+	0.273663i	$0.911765\pi$
$930$		0			0
$931$	1.44147	−	0.802895i	1.44147	−	0.802895i
$932$	0.486604	−	1.87362i	0.486604	−	1.87362i
$933$		0			0
$934$	−0.204198	+	1.46384i	−0.204198	+	1.46384i
$935$		0			0
$936$		0			0
$937$	−1.25594	−	0.234776i	−1.25594	−	0.234776i	−0.486604	−	0.873622i	$-0.661765\pi$
$937$	−1.25594	−	0.234776i	−1.25594	−	0.234776i	−0.769334	+	0.638847i	$0.779412\pi$
$938$		0			0
$939$	0.365413	−	0.275947i	0.365413	−	0.275947i
$940$		0			0
$941$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$941$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$942$		0			0
$943$		0			0
$944$	−0.646741	−	1.66943i	−0.646741	−	1.66943i
$945$		0			0
$946$	−0.443257	−	0.0102410i	−0.443257	−	0.0102410i
$947$	1.95224	+	0.411819i	1.95224	+	0.411819i	0.990410	+	0.138156i	$0.0441176\pi$
$947$	1.95224	+	0.411819i	1.95224	+	0.411819i	0.961826	+	0.273663i	$0.0882353\pi$
$948$		0			0
$949$		0			0
$950$	−1.05409	+	1.26940i	−1.05409	+	1.26940i
$951$		0			0
$952$		0			0
$953$	0.134613	+	1.16030i	0.134613	+	1.16030i	0.873622	+	0.486604i	$0.161765\pi$
$953$	0.134613	+	1.16030i	0.134613	+	1.16030i	−0.739009	+	0.673696i	$0.764706\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.317791	−	0.948161i	0.317791	−	0.948161i
$962$		0			0
$963$	−1.62926	+	0.907490i	−1.62926	+	0.907490i
$964$	−0.119398	+	1.72016i	−0.119398	+	1.72016i
$965$		0			0
$966$		0			0
$967$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$967$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$968$	2.07754	+	1.72516i	2.07754	+	1.72516i
$969$	2.37842	+	1.62926i	2.37842	+	1.62926i
$970$		0			0
$971$	0.394336	−	1.86936i	0.394336	−	1.86936i	−0.0922684	−	0.995734i	$-0.529412\pi$
$971$	0.394336	−	1.86936i	0.394336	−	1.86936i	0.486604	−	0.873622i	$-0.338235\pi$
$972$	0.486604	+	0.873622i	0.486604	+	0.873622i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.20239	+	0.744488i	−1.20239	+	0.744488i	−0.973438	−	0.228951i	$-0.926471\pi$
$977$	−1.20239	+	0.744488i	−1.20239	+	0.744488i	−0.228951	+	0.973438i	$0.573529\pi$
$978$	0.213639	−	0.455097i	0.213639	−	0.455097i
$979$	−2.49260	+	2.86444i	−2.49260	+	2.86444i
$980$		0			0
$981$		0			0
$982$	0.173873	−	1.49869i	0.173873	−	1.49869i
$983$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$983$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$984$	−0.288627	+	0.799375i	−0.288627	+	0.799375i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$991$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$992$		0			0
$993$	−1.67263	+	0.785192i	−1.67263	+	0.785192i
$994$		0			0
$995$		0			0
$996$	1.67521	−	1.09157i	1.67521	−	1.09157i
$997$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$997$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$998$	0.168813	−	0.0745383i	0.168813	−	0.0745383i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3288.1.cj.b.35.1	yes	64
3.2	odd	2		3288.1.cj.a.35.1	✓	64
8.3	odd	2	CM	3288.1.cj.b.35.1	yes	64
24.11	even	2		3288.1.cj.a.35.1	✓	64
137.47	odd	136		3288.1.cj.a.1691.1	yes	64
411.47	even	136	inner	3288.1.cj.b.1691.1	yes	64
1096.595	even	136		3288.1.cj.a.1691.1	yes	64
3288.1691	odd	136	inner	3288.1.cj.b.1691.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3288.1.cj.a.35.1	✓	64	3.2	odd	2
3288.1.cj.a.35.1	✓	64	24.11	even	2
3288.1.cj.a.1691.1	yes	64	137.47	odd	136
3288.1.cj.a.1691.1	yes	64	1096.595	even	136
3288.1.cj.b.35.1	yes	64	1.1	even	1	trivial
3288.1.cj.b.35.1	yes	64	8.3	odd	2	CM
3288.1.cj.b.1691.1	yes	64	411.47	even	136	inner
3288.1.cj.b.1691.1	yes	64	3288.1691	odd	136	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:	\( N \)	\(=\)	\( 3288 = 2^{3} \cdot 3 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3288.cj (of order \(136\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.948161 - 0.317791i) q^{2} +(0.228951 + 0.973438i) q^{3} +(0.798017 + 0.602635i) q^{4} +(0.0922684 - 0.995734i) q^{6} +(-0.565136 - 0.824997i) q^{8} +(-0.895163 + 0.445738i) q^{9} +O(q^{10})\)	\(q+(-0.948161 - 0.317791i) q^{2} +(0.228951 + 0.973438i) q^{3} +(0.798017 + 0.602635i) q^{4} +(0.0922684 - 0.995734i) q^{6} +(-0.565136 - 0.824997i) q^{8} +(-0.895163 + 0.445738i) q^{9} +(0.265765 + 1.90520i) q^{11} +(-0.403921 + 0.914794i) q^{12} +(0.273663 + 0.961826i) q^{16} +(1.44147 + 0.987432i) q^{17} +(0.990410 - 0.138156i) q^{18} +(0.377767 - 1.60617i) q^{19} +(0.353470 - 1.89090i) q^{22} +(0.673696 - 0.739009i) q^{24} +(0.990410 + 0.138156i) q^{25} +(-0.638847 - 0.769334i) q^{27} +(0.0461835 - 0.998933i) q^{32} +(-1.79375 + 0.694903i) q^{33} +(-1.05295 - 1.39433i) q^{34} +(-0.982973 - 0.183750i) q^{36} +(-0.868610 + 1.40285i) q^{38} +(-0.785192 + 0.325237i) q^{41} +(-0.0371073 - 0.227480i) q^{43} +(-0.936057 + 1.68054i) q^{44} +(-0.873622 + 0.486604i) q^{48} +(0.673696 + 0.739009i) q^{49} +(-0.895163 - 0.445738i) q^{50} +(-0.631178 + 1.62926i) q^{51} +(0.361242 + 0.932472i) q^{54} +1.64999 q^{57} +(-1.78269 + 0.165190i) q^{59} +(-0.361242 + 0.932472i) q^{64} +(1.92160 - 0.0888409i) q^{66} +(-0.789689 + 0.754023i) q^{67} +(0.555259 + 1.65667i) q^{68} +(0.873622 + 0.486604i) q^{72} +(0.0861296 + 0.0333668i) q^{73} +(0.0922684 + 0.995734i) q^{75} +(1.26940 - 1.05409i) q^{76} +(0.602635 - 0.798017i) q^{81} +(0.847846 - 0.0588498i) q^{82} +(-1.67521 - 1.09157i) q^{83} +(-0.0371073 + 0.227480i) q^{86} +(1.42160 - 1.29596i) q^{88} +(1.29577 + 1.48906i) q^{89} +(0.982973 - 0.183750i) q^{96} +(-0.873622 + 0.513396i) q^{97} +(-0.403921 - 0.914794i) q^{98} +(-1.08713 - 1.58701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{6}+O(q^{10}) \) 64 * q - 4 * q^6	\( 64 q - 4 q^{6} + 4 q^{16} - 4 q^{17} - 4 q^{19} - 4 q^{36} + 4 q^{41} - 4 q^{68} - 4 q^{75} + 4 q^{76} + 4 q^{81} - 4 q^{83} + 4 q^{96}+O(q^{100}) \) 64 * q - 4 * q^6 + 4 * q^16 - 4 * q^17 - 4 * q^19 - 4 * q^36 + 4 * q^41 - 4 * q^68 - 4 * q^75 + 4 * q^76 + 4 * q^81 - 4 * q^83 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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