LMFDB - Embedded newform 3288.1.cj.b.1187.1

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			1187.1
Root			$-0.228951 + 0.973438i$ of defining polynomial
Character	$\chi$	$=$	3288.1187
Dual form			3288.1.cj.b.3011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.228951 + 0.973438i) q^{2} +(-0.486604 - 0.873622i) q^{3} +(-0.895163 + 0.445738i) q^{4} +(0.739009 - 0.673696i) q^{6} +(-0.638847 - 0.769334i) q^{8} +(-0.526432 + 0.850217i) q^{9} +O(q^{10})$	\(q+(0.228951 + 0.973438i) q^{2} +(-0.486604 - 0.873622i) q^{3} +(-0.895163 + 0.445738i) q^{4} +(0.739009 - 0.673696i) q^{6} +(-0.638847 - 0.769334i) q^{8} +(-0.526432 + 0.850217i) q^{9} +(-0.507206 + 1.51330i) q^{11} +(0.824997 + 0.565136i) q^{12} +(0.602635 - 0.798017i) q^{16} +(-1.52391 - 1.26544i) q^{17} +(-0.948161 - 0.317791i) q^{18} +(0.748723 - 1.34421i) q^{19} +(-1.58923 - 0.147263i) q^{22} +(-0.361242 + 0.932472i) q^{24} +(-0.948161 + 0.317791i) q^{25} +(0.998933 + 0.0461835i) q^{27} +(0.914794 + 0.403921i) q^{32} +(1.56886 - 0.293271i) q^{33} +(0.882928 - 1.77316i) q^{34} +(0.0922684 - 0.995734i) q^{36} +(1.47993 + 0.421076i) q^{38} +(-1.84727 - 0.765163i) q^{41} +(0.394096 - 0.312159i) q^{43} +(-0.220502 - 1.58073i) q^{44} +(-0.990410 - 0.138156i) q^{48} +(-0.361242 - 0.932472i) q^{49} +(-0.526432 - 0.850217i) q^{50} +(-0.363975 + 1.94709i) q^{51} +(0.183750 + 0.982973i) q^{54} -1.53867 q^{57} +(0.709310 - 0.778076i) q^{59} +(-0.183750 + 0.982973i) q^{64} +(0.644672 + 1.46004i) q^{66} +(-1.86936 - 0.394336i) q^{67} +(1.92821 + 0.453510i) q^{68} +(0.990410 - 0.138156i) q^{72} +(-1.79844 - 0.336186i) q^{73} +(0.739009 + 0.673696i) q^{75} +(-0.0710610 + 1.53703i) q^{76} +(-0.445738 - 0.895163i) q^{81} +(0.321906 - 1.97338i) q^{82} +(0.495671 + 1.60067i) q^{83} +(0.394096 + 0.312159i) q^{86} +(1.48826 - 0.576554i) q^{88} +(1.00801 + 0.725270i) q^{89} +(-0.0922684 - 0.995734i) q^{96} +(-0.990410 - 0.861844i) q^{97} +(0.824997 - 0.565136i) q^{98} +(-1.01962 - 1.22788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3288\mathbb{Z}\right)^\times$.

$n$	$823$	$1097$	$1645$	$1921$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{67}{136}\right)$

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 $

$2$	0.228951	+	0.973438i	0.228951	+	0.973438i
$2$	0.228951	+	0.973438i	0.228951	+	0.973438i
$3$	−0.486604	−	0.873622i	−0.486604	−	0.873622i
$3$	−0.486604	−	0.873622i	−0.486604	−	0.873622i
$4$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$5$		0			0		−0.160996	−	0.986955i	$-0.551471\pi$
$5$		0			0		0.160996	+	0.986955i	$0.448529\pi$
$6$	0.739009	−	0.673696i	0.739009	−	0.673696i
$7$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$7$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$8$	−0.638847	−	0.769334i	−0.638847	−	0.769334i
$9$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$10$		0			0
$11$	−0.507206	+	1.51330i	−0.507206	+	1.51330i	0.317791	+	0.948161i	$0.397059\pi$
$11$	−0.507206	+	1.51330i	−0.507206	+	1.51330i	−0.824997	+	0.565136i	$0.808824\pi$
$12$	0.824997	+	0.565136i	0.824997	+	0.565136i
$13$		0			0		−0.545930	−	0.837831i	$-0.683824\pi$
$13$		0			0		0.545930	+	0.837831i	$0.316176\pi$
$14$		0			0
$15$		0			0
$16$	0.602635	−	0.798017i	0.602635	−	0.798017i
$17$	−1.52391	−	1.26544i	−1.52391	−	1.26544i	−0.850217	−	0.526432i	$-0.823529\pi$
$17$	−1.52391	−	1.26544i	−1.52391	−	1.26544i	−0.673696	−	0.739009i	$-0.735294\pi$
$18$	−0.948161	−	0.317791i	−0.948161	−	0.317791i
$19$	0.748723	−	1.34421i	0.748723	−	1.34421i	−0.183750	−	0.982973i	$-0.558824\pi$
$19$	0.748723	−	1.34421i	0.748723	−	1.34421i	0.932472	−	0.361242i	$-0.117647\pi$
$20$		0			0
$21$		0			0
$22$	−1.58923	−	0.147263i	−1.58923	−	0.147263i
$23$		0			0		−0.967890	−	0.251374i	$-0.919118\pi$
$23$		0			0		0.967890	+	0.251374i	$0.0808824\pi$
$24$	−0.361242	+	0.932472i	−0.361242	+	0.932472i
$25$	−0.948161	+	0.317791i	−0.948161	+	0.317791i
$26$		0			0
$27$	0.998933	+	0.0461835i	0.998933	+	0.0461835i
$28$		0			0
$29$		0			0		−0.506653	−	0.862150i	$-0.669118\pi$
$29$		0			0		0.506653	+	0.862150i	$0.330882\pi$
$30$		0			0
$31$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$31$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$32$	0.914794	+	0.403921i	0.914794	+	0.403921i
$33$	1.56886	−	0.293271i	1.56886	−	0.293271i
$34$	0.882928	−	1.77316i	0.882928	−	1.77316i
$35$		0			0
$36$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$	1.47993	+	0.421076i	1.47993	+	0.421076i
$39$		0			0
$40$		0			0
$41$	−1.84727	−	0.765163i	−1.84727	−	0.765163i	−0.932472	−	0.361242i	$-0.882353\pi$
$41$	−1.84727	−	0.765163i	−1.84727	−	0.765163i	−0.914794	−	0.403921i	$-0.867647\pi$
$42$		0			0
$43$	0.394096	−	0.312159i	0.394096	−	0.312159i	−0.403921	−	0.914794i	$-0.632353\pi$
$43$	0.394096	−	0.312159i	0.394096	−	0.312159i	0.798017	+	0.602635i	$0.205882\pi$
$44$	−0.220502	−	1.58073i	−0.220502	−	1.58073i
$45$		0			0
$46$		0			0
$47$		0			0		0.905220	−	0.424943i	$-0.139706\pi$
$47$		0			0		−0.905220	+	0.424943i	$0.860294\pi$
$48$	−0.990410	−	0.138156i	−0.990410	−	0.138156i
$49$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$50$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$51$	−0.363975	+	1.94709i	−0.363975	+	1.94709i
$52$		0			0
$53$		0			0		−0.993337	−	0.115243i	$-0.963235\pi$
$53$		0			0		0.993337	+	0.115243i	$0.0367647\pi$
$54$	0.183750	+	0.982973i	0.183750	+	0.982973i
$55$		0			0
$56$		0			0
$57$	−1.53867			−1.53867
$58$		0			0
$59$	0.709310	−	0.778076i	0.709310	−	0.778076i	−0.273663	−	0.961826i	$-0.588235\pi$
$59$	0.709310	−	0.778076i	0.709310	−	0.778076i	0.982973	+	0.183750i	$0.0588235\pi$
$60$		0			0
$61$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$61$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$62$		0			0
$63$		0			0
$64$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$65$		0			0
$66$	0.644672	+	1.46004i	0.644672	+	1.46004i
$67$	−1.86936	−	0.394336i	−1.86936	−	0.394336i	−0.873622	−	0.486604i	$-0.838235\pi$
$67$	−1.86936	−	0.394336i	−1.86936	−	0.394336i	−0.995734	+	0.0922684i	$0.970588\pi$
$68$	1.92821	+	0.453510i	1.92821	+	0.453510i
$69$		0			0
$70$		0			0
$71$		0			0		0.0692444	−	0.997600i	$-0.477941\pi$
$71$		0			0		−0.0692444	+	0.997600i	$0.522059\pi$
$72$	0.990410	−	0.138156i	0.990410	−	0.138156i
$73$	−1.79844	−	0.336186i	−1.79844	−	0.336186i	−0.824997	−	0.565136i	$-0.808824\pi$
$73$	−1.79844	−	0.336186i	−1.79844	−	0.336186i	−0.973438	+	0.228951i	$0.926471\pi$
$74$		0			0
$75$	0.739009	+	0.673696i	0.739009	+	0.673696i
$76$	−0.0710610	+	1.53703i	−0.0710610	+	1.53703i
$77$		0			0
$78$		0			0
$79$		0			0		−0.690585	−	0.723251i	$-0.742647\pi$
$79$		0			0		0.690585	+	0.723251i	$0.257353\pi$
$80$		0			0
$81$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$82$	0.321906	−	1.97338i	0.321906	−	1.97338i
$83$	0.495671	+	1.60067i	0.495671	+	1.60067i	0.769334	+	0.638847i	$0.220588\pi$
$83$	0.495671	+	1.60067i	0.495671	+	1.60067i	−0.273663	+	0.961826i	$0.588235\pi$
$84$		0			0
$85$		0			0
$86$	0.394096	+	0.312159i	0.394096	+	0.312159i
$87$		0			0
$88$	1.48826	−	0.576554i	1.48826	−	0.576554i
$89$	1.00801	+	0.725270i	1.00801	+	0.725270i	0.961826	−	0.273663i	$-0.0882353\pi$
$89$	1.00801	+	0.725270i	1.00801	+	0.725270i	0.0461835	+	0.998933i	$0.485294\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.0922684	−	0.995734i	−0.0922684	−	0.995734i
$97$	−0.990410	−	0.861844i	−0.990410	−	0.861844i		−	1.00000i	$-0.5\pi$
$97$	−0.990410	−	0.861844i	−0.990410	−	0.861844i	−0.990410	+	0.138156i	$0.955882\pi$
$98$	0.824997	−	0.565136i	0.824997	−	0.565136i
$99$	−1.01962	−	1.22788i	−1.01962	−	1.22788i
$100$	0.707107	−	0.707107i	0.707107	−	0.707107i
$101$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$101$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$102$	−1.97871	+	0.0914812i	−1.97871	+	0.0914812i
$103$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$103$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.794087	−	1.79844i	−0.794087	−	1.79844i	−0.565136	−	0.824997i	$-0.691176\pi$
$107$	−0.794087	−	1.79844i	−0.794087	−	1.79844i	−0.228951	−	0.973438i	$-0.573529\pi$
$108$	−0.914794	+	0.403921i	−0.914794	+	0.403921i
$109$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$109$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.949551	−	1.09120i	−0.949551	−	1.09120i	−0.995734	−	0.0922684i	$-0.970588\pi$
$113$	−0.949551	−	1.09120i	−0.949551	−	1.09120i	0.0461835	−	0.998933i	$-0.485294\pi$
$114$	−0.352279	−	1.49780i	−0.352279	−	1.49780i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.919806	+	0.512328i	0.919806	+	0.512328i
$119$		0			0
$120$		0			0
$121$	−1.23479	−	0.932472i	−1.23479	−	0.932472i
$122$		0			0
$123$	0.230425	+	1.98614i	0.230425	+	1.98614i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$127$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$128$	−0.998933	+	0.0461835i	−0.998933	+	0.0461835i
$129$	−0.464478	−	0.192393i	−0.464478	−	0.192393i
$130$		0			0
$131$	−0.254719	−	0.980770i	−0.254719	−	0.980770i	−0.961826	−	0.273663i	$-0.911765\pi$
$131$	−0.254719	−	0.980770i	−0.254719	−	0.980770i	0.707107	−	0.707107i	$-0.250000\pi$
$132$	−1.27366	+	0.961826i	−1.27366	+	0.961826i
$133$		0			0
$134$	−0.0441284	−	1.90999i	−0.0441284	−	1.90999i
$135$		0			0
$136$			1.98082i			1.98082i
$137$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$137$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$138$		0			0
$139$	1.93857	−	0.455948i	1.93857	−	0.455948i	0.948161	−	0.317791i	$-0.102941\pi$
$139$	1.93857	−	0.455948i	1.93857	−	0.455948i	0.990410	−	0.138156i	$-0.0441176\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.361242	+	0.932472i	0.361242	+	0.932472i
$145$		0			0
$146$	−0.0844967	−	1.82764i	−0.0844967	−	1.82764i
$147$	−0.638847	+	0.769334i	−0.638847	+	0.769334i
$148$		0			0
$149$		0			0		0.884629	−	0.466296i	$-0.154412\pi$
$149$		0			0		−0.884629	+	0.466296i	$0.845588\pi$
$150$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$151$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$151$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$152$	−1.51247	+	0.282729i	−1.51247	+	0.282729i
$153$	1.87814	−	0.629488i	1.87814	−	0.629488i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.811724	−	0.584041i	$-0.198529\pi$
$157$		0			0		−0.811724	+	0.584041i	$0.801471\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.769334	−	0.638847i	0.769334	−	0.638847i
$163$	−0.100162	−	0.0956383i	−0.100162	−	0.0956383i	0.638847	−	0.769334i	$-0.279412\pi$
$163$	−0.100162	−	0.0956383i	−0.100162	−	0.0956383i	−0.739009	+	0.673696i	$0.764706\pi$
$164$	1.99467	−	0.138452i	1.99467	−	0.138452i
$165$		0			0
$166$	−1.44467	+	0.848980i	−1.44467	+	0.848980i
$167$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$167$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$168$		0			0
$169$	−0.403921	+	0.914794i	−0.403921	+	0.914794i
$170$		0			0
$171$	0.748723	+	1.34421i	0.748723	+	1.34421i
$172$	−0.213639	+	0.455097i	−0.213639	+	0.455097i
$173$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$173$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$174$		0			0
$175$		0			0
$176$	0.901977	+	1.31672i	0.901977	+	1.31672i
$177$	−1.02490	−	0.241054i	−1.02490	−	0.241054i
$178$	−0.475221	+	1.14729i	−0.475221	+	1.14729i
$179$	−0.469056	+	1.29908i	−0.469056	+	1.29908i	0.445738	+	0.895163i	$0.352941\pi$
$179$	−0.469056	+	1.29908i	−0.469056	+	1.29908i	−0.914794	+	0.403921i	$0.867647\pi$
$180$		0			0
$181$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$181$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.68793	−	1.66429i	2.68793	−	1.66429i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.955248	−	0.295806i	$-0.0955882\pi$
$191$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$192$	0.948161	−	0.317791i	0.948161	−	0.317791i
$193$	0.174970	+	1.88823i	0.174970	+	1.88823i	0.403921	+	0.914794i	$0.367647\pi$
$193$	0.174970	+	1.88823i	0.174970	+	1.88823i	−0.228951	+	0.973438i	$0.573529\pi$
$194$	0.612196	−	1.16142i	0.612196	−	1.16142i
$195$		0			0
$196$	0.739009	+	0.673696i	0.739009	+	0.673696i
$197$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$197$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$198$	0.961826	−	1.27366i	0.961826	−	1.27366i
$199$		0			0		0.940567	−	0.339607i	$-0.110294\pi$
$199$		0			0		−0.940567	+	0.339607i	$0.889706\pi$
$200$	0.850217	+	0.526432i	0.850217	+	0.526432i
$201$	0.565136	+	1.82500i	0.565136	+	1.82500i
$202$		0			0
$203$		0			0
$204$	−0.542077	−	1.90520i	−0.542077	−	1.90520i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.65444	+	1.81483i	1.65444	+	1.81483i
$210$		0			0
$211$	1.65527	+	1.02490i	1.65527	+	1.02490i	0.948161	+	0.317791i	$0.102941\pi$
$211$	1.65527	+	1.02490i	1.65527	+	1.02490i	0.707107	+	0.707107i	$0.250000\pi$
$212$		0			0
$213$		0			0
$214$	1.56886	−	1.18475i	1.56886	−	1.18475i
$215$		0			0
$216$	−0.602635	−	0.798017i	−0.602635	−	0.798017i
$217$		0			0
$218$		0			0
$219$	0.581427	+	1.73474i	0.581427	+	1.73474i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.620906	−	0.783885i	$-0.286765\pi$
$223$		0			0		−0.620906	+	0.783885i	$0.713235\pi$
$224$		0			0
$225$	0.228951	−	0.973438i	0.228951	−	0.973438i
$226$	0.844817	−	1.17416i	0.844817	−	1.17416i
$227$	−0.463978	−	0.988373i	−0.463978	−	0.988373i	−0.990410	−	0.138156i	$-0.955882\pi$
$227$	−0.463978	−	0.988373i	−0.463978	−	0.988373i	0.526432	−	0.850217i	$-0.323529\pi$
$228$	1.37736	−	0.685843i	1.37736	−	0.685843i
$229$		0			0		−0.206405	−	0.978467i	$-0.566176\pi$
$229$		0			0		0.206405	+	0.978467i	$0.433824\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.763530	−	1.84332i	0.763530	−	1.84332i	0.317791	−	0.948161i	$-0.397059\pi$
$233$	0.763530	−	1.84332i	0.763530	−	1.84332i	0.445738	−	0.895163i	$-0.352941\pi$
$234$		0			0
$235$		0			0
$236$	−0.288130	+	1.01267i	−0.288130	+	1.01267i
$237$		0			0
$238$		0			0
$239$		0			0		0.424943	−	0.905220i	$-0.360294\pi$
$239$		0			0		−0.424943	+	0.905220i	$0.639706\pi$
$240$		0			0
$241$	1.44123	+	0.446296i	1.44123	+	0.446296i	0.914794	−	0.403921i	$-0.132353\pi$
$241$	1.44123	+	0.446296i	1.44123	+	0.446296i	0.526432	+	0.850217i	$0.323529\pi$
$242$	0.624997	−	1.41548i	0.624997	−	1.41548i
$243$	−0.565136	+	0.824997i	−0.565136	+	0.824997i
$244$		0			0
$245$		0			0
$246$	−1.88063	+	0.679033i	−1.88063	+	0.679033i
$247$		0			0
$248$		0			0
$249$	1.15719	−	1.21192i	1.15719	−	1.21192i
$250$		0			0
$251$	−0.433444	+	1.66893i	−0.433444	+	1.66893i	0.273663	+	0.961826i	$0.411765\pi$
$251$	−0.433444	+	1.66893i	−0.433444	+	1.66893i	−0.707107	+	0.707107i	$0.750000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$257$	−0.461556	+	0.555831i	−0.461556	+	0.555831i	−0.948161	−	0.317791i	$-0.897059\pi$
$257$	−0.461556	+	0.555831i	−0.461556	+	0.555831i	0.486604	+	0.873622i	$0.338235\pi$
$258$	0.0809403	−	0.496189i	0.0809403	−	0.496189i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.896401	−	0.472501i	0.896401	−	0.472501i
$263$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$263$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$264$	−1.22788	−	1.01962i	−1.22788	−	1.01962i
$265$		0			0
$266$		0			0
$267$	0.143110	−	1.23354i	0.143110	−	1.23354i
$268$	1.84915	−	0.480249i	1.84915	−	0.480249i
$269$		0			0		0.986955	−	0.160996i	$-0.0514706\pi$
$269$		0			0		−0.986955	+	0.160996i	$0.948529\pi$
$270$		0			0
$271$		0			0		0.999733	−	0.0230979i	$-0.00735294\pi$
$271$		0			0		−0.999733	+	0.0230979i	$0.992647\pi$
$272$	−1.92821	+	0.453510i	−1.92821	+	0.453510i
$273$		0			0
$274$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$275$		−	1.59603i		−	1.59603i
$276$		0			0
$277$		0			0		−0.0230979	−	0.999733i	$-0.507353\pi$
$277$		0			0		0.0230979	+	0.999733i	$0.492647\pi$
$278$	0.887674	+	1.78269i	0.887674	+	1.78269i
$279$		0			0
$280$		0			0
$281$	0.152242	+	0.104288i	0.152242	+	0.104288i	0.638847	−	0.769334i	$-0.279412\pi$
$281$	0.152242	+	0.104288i	0.152242	+	0.104288i	−0.486604	+	0.873622i	$0.661765\pi$
$282$		0			0
$283$	−0.0922684	+	0.00426582i	−0.0922684	+	0.00426582i	−0.0922684	−	0.995734i	$-0.529412\pi$
$283$	−0.0922684	+	0.00426582i	−0.0922684	+	0.00426582i			1.00000i	$0.5\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.824997	+	0.565136i	−0.824997	+	0.565136i
$289$	0.537220	+	2.87387i	0.537220	+	2.87387i
$290$		0			0
$291$	−0.270988	+	1.28462i	−0.270988	+	1.28462i
$292$	1.75974	−	0.500690i	1.75974	−	0.500690i
$293$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$293$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$294$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$295$		0			0
$296$		0			0
$297$	−0.576554	+	1.48826i	−0.576554	+	1.48826i
$298$		0			0
$299$		0			0
$300$	−0.961826	−	0.273663i	−0.961826	−	0.273663i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.621500	−	1.40756i	−0.621500	−	1.40756i
$305$		0			0
$306$	1.04277	+	1.68413i	1.04277	+	1.68413i
$307$	−0.175003	+	0.565136i	−0.175003	+	0.565136i	0.824997	+	0.565136i	$0.191176\pi$
$307$	−0.175003	+	0.565136i	−0.175003	+	0.565136i	−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$311$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$312$		0			0
$313$	−0.802895	+	0.549996i	−0.802895	+	0.549996i	−0.895163	−	0.445738i	$-0.852941\pi$
$313$	−0.802895	+	0.549996i	−0.802895	+	0.549996i	0.0922684	+	0.995734i	$0.470588\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.620906	−	0.783885i	$-0.713235\pi$
$317$		0			0		0.620906	+	0.783885i	$0.286765\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.18475	+	1.56886i	−1.18475	+	1.56886i
$322$		0			0
$323$	−2.84201	+	1.10100i	−2.84201	+	1.10100i
$324$	0.798017	+	0.602635i	0.798017	+	0.602635i
$325$		0			0
$326$	0.0701658	−	0.119398i	0.0701658	−	0.119398i
$327$		0			0
$328$	0.591454	+	1.90999i	0.591454	+	1.90999i
$329$		0			0
$330$		0			0
$331$	1.63458	+	0.861602i	1.63458	+	0.861602i	0.995734	+	0.0922684i	$0.0294118\pi$
$331$	1.63458	+	0.861602i	1.63458	+	0.861602i	0.638847	+	0.769334i	$0.279412\pi$
$332$	−1.15719	−	1.21192i	−1.15719	−	1.21192i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.425274	−	0.686841i	0.425274	−	0.686841i	−0.565136	−	0.824997i	$-0.691176\pi$
$337$	0.425274	−	0.686841i	0.425274	−	0.686841i	0.990410	+	0.138156i	$0.0441176\pi$
$338$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$339$	−0.491242	+	1.36053i	−0.491242	+	1.36053i
$340$		0			0
$341$		0			0
$342$	−1.13709	+	1.03659i	−1.13709	+	1.03659i
$343$		0			0
$344$	−0.491922	−	0.103770i	−0.491922	−	0.103770i
$345$		0			0
$346$		0			0
$347$	−0.271585	+	1.45285i	−0.271585	+	1.45285i	0.526432	+	0.850217i	$0.323529\pi$
$347$	−0.271585	+	1.45285i	−0.271585	+	1.45285i	−0.798017	+	0.602635i	$0.794118\pi$
$348$		0			0
$349$		0			0		−0.339607	−	0.940567i	$-0.610294\pi$
$349$		0			0		0.339607	+	0.940567i	$0.389706\pi$
$350$		0			0
$351$		0			0
$352$	−1.07524	+	1.17948i	−1.07524	+	1.17948i
$353$	1.41535	−	1.35143i	1.41535	−	1.35143i	0.565136	−	0.824997i	$-0.308824\pi$
$353$	1.41535	−	1.35143i	1.41535	−	1.35143i	0.850217	−	0.526432i	$-0.176471\pi$
$354$		−	1.05286i		−	1.05286i
$355$		0			0
$356$	−1.22561	−	0.199927i	−1.22561	−	0.199927i
$357$		0			0
$358$	−1.37197	−	0.159170i	−1.37197	−	0.159170i
$359$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$359$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$360$		0			0
$361$	−0.719895	−	1.16267i	−0.719895	−	1.16267i
$362$		0			0
$363$	−0.213773	+	1.53249i	−0.213773	+	1.53249i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$367$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$368$		0			0
$369$	1.62301	−	1.16777i	1.62301	−	1.16777i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$373$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$374$	2.23549	+	2.23549i	2.23549	+	2.23549i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.63778	−	0.723151i	−1.63778	−	0.723151i	−0.638847	−	0.769334i	$-0.720588\pi$
$379$	−1.63778	−	0.723151i	−1.63778	−	0.723151i	−0.998933	+	0.0461835i	$0.985294\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$383$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$384$	0.526432	+	0.850217i	0.526432	+	0.850217i
$385$		0			0
$386$	−1.79802	+	0.602635i	−1.79802	+	0.602635i
$387$	0.0579382	+	0.499398i	0.0579382	+	0.499398i
$388$	1.27074	+	0.330027i	1.27074	+	0.330027i
$389$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$389$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$390$		0			0
$391$		0			0
$392$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$393$	−0.732875	+	0.699775i	−0.732875	+	0.699775i
$394$		0			0
$395$		0			0
$396$	1.46004	+	0.644672i	1.46004	+	0.644672i
$397$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$397$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$398$		0			0
$399$		0			0
$400$	−0.317791	+	0.948161i	−0.317791	+	0.948161i
$401$	0.627512	−	0.259924i	0.627512	−	0.259924i	−0.0461835	−	0.998933i	$-0.514706\pi$
$401$	0.627512	−	0.259924i	0.627512	−	0.259924i	0.673696	+	0.739009i	$0.264706\pi$
$402$	−1.64713	+	0.967959i	−1.64713	+	0.967959i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.73049	−	0.963876i	1.73049	−	0.963876i
$409$	−0.204104	−	0.867797i	−0.204104	−	0.867797i	−0.973438	−	0.228951i	$-0.926471\pi$
$409$	−0.204104	−	0.867797i	−0.204104	−	0.867797i	0.769334	−	0.638847i	$-0.220588\pi$
$410$		0			0
$411$	0.850217	+	0.526432i	0.850217	+	0.526432i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.34164	−	1.47171i	−1.34164	−	1.47171i
$418$	−1.38784	+	2.02600i	−1.38784	+	2.02600i
$419$	−0.569517	−	0.685843i	−0.569517	−	0.685843i	0.403921	−	0.914794i	$-0.367647\pi$
$419$	−0.569517	−	0.685843i	−0.569517	−	0.685843i	−0.973438	+	0.228951i	$0.926471\pi$
$420$		0			0
$421$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$421$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$422$	−0.618701	+	1.84595i	−0.618701	+	1.84595i
$423$		0			0
$424$		0			0
$425$	1.84706	+	0.715555i	1.84706	+	0.715555i
$426$		0			0
$427$		0			0
$428$	1.51247	+	1.25594i	1.51247	+	1.25594i
$429$		0			0
$430$		0			0
$431$		0			0		−0.584041	−	0.811724i	$-0.698529\pi$
$431$		0			0		0.584041	+	0.811724i	$0.301471\pi$
$432$	0.638847	−	0.769334i	0.638847	−	0.769334i
$433$	0.632872	+	0.0586442i	0.632872	+	0.0586442i	0.403921	−	0.914794i	$-0.367647\pi$
$433$	0.632872	+	0.0586442i	0.632872	+	0.0586442i	0.228951	+	0.973438i	$0.426471\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−1.55555	+	0.963154i	−1.55555	+	0.963154i
$439$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$439$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$440$		0			0
$441$	0.982973	+	0.183750i	0.982973	+	0.183750i
$442$		0			0
$443$	−0.581427	−	0.256725i	−0.581427	−	0.256725i	0.0922684	−	0.995734i	$-0.470588\pi$
$443$	−0.581427	−	0.256725i	−0.581427	−	0.256725i	−0.673696	+	0.739009i	$0.735294\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.72198	−	0.489946i	−1.72198	−	0.489946i	−0.739009	−	0.673696i	$-0.764706\pi$
$449$	−1.72198	−	0.489946i	−1.72198	−	0.489946i	−0.982973	+	0.183750i	$0.941176\pi$
$450$	1.00000			1.00000
$451$	2.09486	−	2.40737i	2.09486	−	2.40737i
$452$	1.33639	+	0.553552i	1.33639	+	0.553552i
$453$		0			0
$454$	0.855892	−	0.677943i	0.855892	−	0.677943i
$455$		0			0
$456$	0.982973	+	1.18375i	0.982973	+	1.18375i
$457$	0.0447124	−	1.93526i	0.0447124	−	1.93526i	−0.228951	−	0.973438i	$-0.573529\pi$
$457$	0.0447124	−	1.93526i	0.0447124	−	1.93526i	0.273663	−	0.961826i	$-0.411765\pi$
$458$		0			0
$459$	−1.46384	−	1.33447i	−1.46384	−	1.33447i
$460$		0			0
$461$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$461$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$462$		0			0
$463$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$463$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$464$		0			0
$465$		0			0
$466$	1.96917	+	0.321219i	1.96917	+	0.321219i
$467$	1.85699	−	0.172075i	1.85699	−	0.172075i	0.895163	−	0.445738i	$-0.147059\pi$
$467$	1.85699	−	0.172075i	1.85699	−	0.172075i	0.961826	+	0.273663i	$0.0882353\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.05174	−	0.0486249i	−1.05174	−	0.0486249i
$473$	0.272502	+	0.754714i	0.272502	+	0.754714i
$474$		0			0
$475$	−0.282729	+	1.51247i	−0.282729	+	1.51247i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$479$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$480$		0			0
$481$		0			0
$482$	−0.104472	+	1.50512i	−0.104472	+	1.50512i
$483$		0			0
$484$	1.52098	+	0.284320i	1.52098	+	0.284320i
$485$		0			0
$486$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$487$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$487$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$488$		0			0
$489$	−0.0348125	+	0.134042i	−0.0348125	+	0.134042i
$490$		0			0
$491$	−1.03332	−	0.544672i	−1.03332	−	0.544672i	−0.138156	−	0.990410i	$-0.544118\pi$
$491$	−1.03332	−	0.544672i	−1.03332	−	0.544672i	−0.895163	+	0.445738i	$0.852941\pi$
$492$	−1.09157	−	1.67521i	−1.09157	−	1.67521i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.44467	+	0.848980i	1.44467	+	0.848980i
$499$	−1.37821	+	0.533922i	−1.37821	+	0.533922i	−0.932472	−	0.361242i	$-0.882353\pi$
$499$	−1.37821	+	0.533922i	−1.37821	+	0.533922i	−0.445738	+	0.895163i	$0.647059\pi$
$500$		0			0
$501$		0			0
$502$	−1.72384	−	0.0398277i	−1.72384	−	0.0398277i
$503$		0			0		0.978467	−	0.206405i	$-0.0661765\pi$
$503$		0			0		−0.978467	+	0.206405i	$0.933824\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.995734	−	0.0922684i	0.995734	−	0.0922684i
$508$		0			0
$509$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$509$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$510$		0			0
$511$		0			0
$512$	0.873622	−	0.486604i	0.873622	−	0.486604i
$513$	0.810004	−	1.30820i	0.810004	−	1.30820i
$514$	−0.646741	−	0.322039i	−0.646741	−	0.322039i
$515$		0			0
$516$	0.501541	−	0.0348125i	0.501541	−	0.0348125i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.00319880	+	0.0460849i	0.00319880	+	0.0460849i	0.998933	−	0.0461835i	$-0.0147059\pi$
$521$	0.00319880	+	0.0460849i	0.00319880	+	0.0460849i	−0.995734	+	0.0922684i	$0.970588\pi$
$522$		0			0
$523$	0.428189	+	1.27754i	0.428189	+	1.27754i	0.914794	+	0.403921i	$0.132353\pi$
$523$	0.428189	+	1.27754i	0.428189	+	1.27754i	−0.486604	+	0.873622i	$0.661765\pi$
$524$	0.665182	+	0.764411i	0.665182	+	0.764411i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.711414	−	1.42871i	0.711414	−	1.42871i
$529$	0.873622	+	0.486604i	0.873622	+	0.486604i
$530$		0			0
$531$	0.288130	+	1.01267i	0.288130	+	1.01267i
$532$		0			0
$533$		0			0
$534$	1.23354	−	0.143110i	1.23354	−	0.143110i
$535$		0			0
$536$	0.890856	+	1.69008i	0.890856	+	1.69008i
$537$	1.36315	−	0.222363i	1.36315	−	0.222363i
$538$		0			0
$539$	1.59433	−	0.0737104i	1.59433	−	0.0737104i
$540$		0			0
$541$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$541$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$542$		0			0
$543$		0			0
$544$	−0.882928	−	1.77316i	−0.882928	−	1.77316i
$545$		0			0
$546$		0			0
$547$			1.86494i			1.86494i	0.361242	+	0.932472i	$0.382353\pi$
$547$			1.86494i			1.86494i	−0.361242	+	0.932472i	$0.617647\pi$
$548$	0.565136	−	0.824997i	0.565136	−	0.824997i
$549$		0			0
$550$	1.55364	−	0.365413i	1.55364	−	0.365413i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.53210	+	1.27224i	−1.53210	+	1.27224i
$557$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$557$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−2.76192	−	1.53838i	−2.76192	−	1.53838i
$562$	−0.0666624	+	0.172075i	−0.0666624	+	0.172075i
$563$	0.361242	−	0.0675278i	0.361242	−	0.0675278i		−	1.00000i	$-0.5\pi$
$563$	0.361242	−	0.0675278i	0.361242	−	0.0675278i	0.361242	+	0.932472i	$0.382353\pi$
$564$		0			0
$565$		0			0
$566$	−0.0252774	−	0.0888409i	−0.0252774	−	0.0888409i
$567$		0			0
$568$		0			0
$569$	−0.988373	+	1.51684i	−0.988373	+	1.51684i	−0.138156	+	0.990410i	$0.544118\pi$
$569$	−0.988373	+	1.51684i	−0.988373	+	1.51684i	−0.850217	+	0.526432i	$0.823529\pi$
$570$		0			0
$571$	−0.103770	+	0.399555i	−0.103770	+	0.399555i	−0.998933	−	0.0461835i	$-0.985294\pi$
$571$	−0.103770	+	0.399555i	−0.103770	+	0.399555i	0.895163	+	0.445738i	$0.147059\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$577$	−1.62182	+	0.953083i	−1.62182	+	0.953083i	−0.638847	+	0.769334i	$0.720588\pi$
$577$	−1.62182	+	0.953083i	−1.62182	+	0.953083i	−0.982973	+	0.183750i	$0.941176\pi$
$578$	−2.67454	+	1.18092i	−2.67454	+	1.18092i
$579$	1.56446	−	1.07168i	1.56446	−	1.07168i
$580$		0			0
$581$		0			0
$582$	−1.31254	+	0.0303251i	−1.31254	+	0.0303251i
$583$		0			0
$584$	0.890286	+	1.59837i	0.890286	+	1.59837i
$585$		0			0
$586$		0			0
$587$	−1.08713	−	1.58701i	−1.08713	−	1.58701i	−0.769334	−	0.638847i	$-0.779412\pi$
$587$	−1.08713	−	1.58701i	−1.08713	−	1.58701i	−0.317791	−	0.948161i	$-0.602941\pi$
$588$	0.228951	−	0.973438i	0.228951	−	0.973438i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.0664607	−	0.315058i	−0.0664607	−	0.315058i	0.932472	−	0.361242i	$-0.117647\pi$
$593$	−0.0664607	−	0.315058i	−0.0664607	−	0.315058i	−0.998933	+	0.0461835i	$0.985294\pi$
$594$	−1.58073	−	0.220502i	−1.58073	−	0.220502i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.620906	−	0.783885i	$-0.286765\pi$
$599$		0			0		−0.620906	+	0.783885i	$0.713235\pi$
$600$	0.0461835	−	0.998933i	0.0461835	−	0.998933i
$601$	0.0475735	−	0.410060i	0.0475735	−	0.410060i	−0.948161	−	0.317791i	$-0.897059\pi$
$601$	0.0475735	−	0.410060i	0.0475735	−	0.410060i	0.995734	−	0.0922684i	$-0.0294118\pi$
$602$		0			0
$603$	1.31936	−	1.38177i	1.31936	−	1.38177i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$607$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$608$	1.22788	−	0.927255i	1.22788	−	0.927255i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.40065	+	1.40065i	−1.40065	+	1.40065i
$613$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$613$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$614$	−0.590192	−	0.0409658i	−0.590192	−	0.0409658i
$615$		0			0
$616$		0			0
$617$	−0.222817	+	0.947359i	−0.222817	+	0.947359i	0.739009	+	0.673696i	$0.235294\pi$
$617$	−0.222817	+	0.947359i	−0.222817	+	0.947359i	−0.961826	+	0.273663i	$0.911765\pi$
$618$		0			0
$619$	−1.87662	−	0.130258i	−1.87662	−	0.130258i	−0.914794	−	0.403921i	$-0.867647\pi$
$619$	−1.87662	−	0.130258i	−1.87662	−	0.130258i	−0.961826	+	0.273663i	$0.911765\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.798017	−	0.602635i	0.798017	−	0.602635i
$626$	−0.719210	−	0.655647i	−0.719210	−	0.655647i
$627$	0.780422	−	2.32846i	0.780422	−	2.32846i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.955248	−	0.295806i	$-0.0955882\pi$
$631$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$632$		0			0
$633$	0.0899135	−	1.94480i	0.0899135	−	1.94480i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.0914812	−	0.0127611i	0.0914812	−	0.0127611i	−0.0922684	−	0.995734i	$-0.529412\pi$
$641$	0.0914812	−	0.0127611i	0.0914812	−	0.0127611i	0.183750	+	0.982973i	$0.441176\pi$
$642$	−1.79844	−	0.794087i	−1.79844	−	0.794087i
$643$	0.288627	−	0.799375i	0.288627	−	0.799375i	−0.707107	−	0.707107i	$-0.750000\pi$
$643$	0.288627	−	0.799375i	0.288627	−	0.799375i	0.995734	−	0.0922684i	$-0.0294118\pi$
$644$		0			0
$645$		0			0
$646$	−1.72244	−	2.51445i	−1.72244	−	2.51445i
$647$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$647$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$648$	−0.403921	+	0.914794i	−0.403921	+	0.914794i
$649$	0.817694	+	1.46804i	0.817694	+	1.46804i
$650$		0			0
$651$		0			0
$652$	0.132291	+	0.0409658i	0.132291	+	0.0409658i
$653$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$653$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$654$		0			0
$655$		0			0
$656$	−1.72384	+	1.01304i	−1.72384	+	1.01304i
$657$	1.23259	−	1.35208i	1.23259	−	1.35208i
$658$		0			0
$659$	0.298565	+	0.285081i	0.298565	+	0.285081i	0.824997	−	0.565136i	$-0.191176\pi$
$659$	0.298565	+	0.285081i	0.298565	+	0.285081i	−0.526432	+	0.850217i	$0.676471\pi$
$660$		0			0
$661$		0			0		0.754373	−	0.656446i	$-0.227941\pi$
$661$		0			0		−0.754373	+	0.656446i	$0.772059\pi$
$662$	−0.464478	+	1.78843i	−0.464478	+	1.78843i
$663$		0			0
$664$	0.914794	−	1.40392i	0.914794	−	1.40392i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.52537	−	0.804034i	1.52537	−	0.804034i	0.526432	−	0.850217i	$-0.323529\pi$
$673$	1.52537	−	0.804034i	1.52537	−	0.804034i	0.998933	+	0.0461835i	$0.0147059\pi$
$674$	0.765964	+	0.256725i	0.765964	+	0.256725i
$675$	−0.961826	+	0.273663i	−0.961826	+	0.273663i
$676$	−0.0461835	−	0.998933i	−0.0461835	−	0.998933i
$677$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$677$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$678$	−1.43686	−	0.166699i	−1.43686	−	0.166699i
$679$		0			0
$680$		0			0
$681$	−0.637691	+	0.886289i	−0.637691	+	0.886289i
$682$		0			0
$683$	0.786384	−	0.184956i	0.786384	−	0.184956i	0.183750	−	0.982973i	$-0.441176\pi$
$683$	0.786384	−	0.184956i	0.786384	−	0.184956i	0.602635	+	0.798017i	$0.294118\pi$
$684$	−1.26940	−	0.869557i	−1.26940	−	0.869557i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.0116124	−	0.502614i	−0.0116124	−	0.502614i
$689$		0			0
$690$		0			0
$691$	−0.192393	−	0.740791i	−0.192393	−	0.740791i	−0.990410	−	0.138156i	$-0.955882\pi$
$691$	−0.192393	−	0.740791i	−0.192393	−	0.740791i	0.798017	−	0.602635i	$-0.205882\pi$
$692$		0			0
$693$		0			0
$694$	−1.47644	+	0.0682600i	−1.47644	+	0.0682600i
$695$		0			0
$696$		0			0
$697$	1.84680	+	3.50365i	1.84680	+	3.50365i
$698$		0			0
$699$	−1.98191	+	0.229933i	−1.98191	+	0.229933i
$700$		0			0
$701$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$701$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$702$		0			0
$703$		0			0
$704$	−1.39433	−	0.776638i	−1.39433	−	0.776638i
$705$		0			0
$706$	1.63958	+	1.06835i	1.63958	+	1.06835i
$707$		0			0
$708$	1.02490	−	0.241054i	1.02490	−	0.241054i
$709$		0			0		−0.656446	−	0.754373i	$-0.727941\pi$
$709$		0			0		0.656446	+	0.754373i	$0.272059\pi$
$710$		0			0
$711$		0			0
$712$	−0.0859886	−	1.23883i	−0.0859886	−	1.23883i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.159170	−	1.37197i	−0.159170	−	1.37197i
$717$		0			0
$718$		0			0
$719$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$719$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$720$		0			0
$721$		0			0
$722$	0.966968	−	0.966968i	0.966968	−	0.966968i
$723$	−0.311413	−	1.47626i	−0.311413	−	1.47626i
$724$		0			0
$725$		0			0
$726$	−1.54073	+	0.142769i	−1.54073	+	0.142769i
$727$		0			0		−0.940567	−	0.339607i	$-0.889706\pi$
$727$		0			0		0.940567	+	0.339607i	$0.110294\pi$
$728$		0			0
$729$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$730$		0			0
$731$	−0.995587	−	0.0230021i	−0.995587	−	0.0230021i
$732$		0			0
$733$		0			0		−0.811724	−	0.584041i	$-0.801471\pi$
$733$		0			0		0.811724	+	0.584041i	$0.198529\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.54490	−	2.62888i	1.54490	−	2.62888i
$738$	1.50834	+	1.31254i	1.50834	+	1.31254i
$739$	−0.583895	−	1.88557i	−0.583895	−	1.88557i	−0.445738	−	0.895163i	$-0.647059\pi$
$739$	−0.583895	−	1.88557i	−0.583895	−	1.88557i	−0.138156	−	0.990410i	$-0.544118\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.690585	−	0.723251i	$-0.742647\pi$
$743$		0			0		0.690585	+	0.723251i	$0.257353\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.62186	−	0.421217i	−1.62186	−	0.421217i
$748$	−1.66429	+	2.68793i	−1.66429	+	2.68793i
$749$		0			0
$750$		0			0
$751$		0			0		0.0692444	−	0.997600i	$-0.477941\pi$
$751$		0			0		−0.0692444	+	0.997600i	$0.522059\pi$
$752$		0			0
$753$	1.66893	−	0.433444i	1.66893	−	0.433444i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$757$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$758$	0.328972	−	1.75984i	0.328972	−	1.75984i
$759$		0			0
$760$		0			0
$761$	−0.367107	−	0.0169724i	−0.367107	−	0.0169724i	−0.138156	−	0.990410i	$-0.544118\pi$
$761$	−0.367107	−	0.0169724i	−0.367107	−	0.0169724i	−0.228951	+	0.973438i	$0.573529\pi$
$762$		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
$769$	−1.16030	−	0.134613i	−1.16030	−	0.134613i	−0.486604	−	0.873622i	$-0.661765\pi$
$769$	−1.16030	−	0.134613i	−1.16030	−	0.134613i	−0.673696	+	0.739009i	$0.735294\pi$
$770$		0			0
$771$	0.710182	+	0.132756i	0.710182	+	0.132756i
$772$	−0.998285	−	1.61228i	−0.998285	−	1.61228i
$773$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$773$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$774$	−0.472868	+	0.170737i	−0.472868	+	0.170737i
$775$		0			0
$776$	−0.0303251	+	1.31254i	−0.0303251	+	1.31254i
$777$		0			0
$778$		0			0
$779$	−2.41163	+	1.91023i	−2.41163	+	1.91023i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.961826	−	0.273663i	−0.961826	−	0.273663i
$785$		0			0
$786$	−0.848980	−	0.553195i	−0.848980	−	0.553195i
$787$	1.80609	+	0.847846i	1.80609	+	0.847846i	0.932472	+	0.361242i	$0.117647\pi$
$787$	1.80609	+	0.847846i	1.80609	+	0.847846i	0.873622	+	0.486604i	$0.161765\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.293271	+	1.56886i	−0.293271	+	1.56886i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$797$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$798$		0			0
$799$		0			0
$800$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$801$	−1.14729	+	0.475221i	−1.14729	+	0.475221i
$802$	0.396689	+	0.551334i	0.396689	+	0.551334i
$803$	1.42093	−	2.55105i	1.42093	−	2.55105i
$804$	−1.31936	−	1.38177i	−1.31936	−	1.38177i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.886289	+	1.36017i	0.886289	+	1.36017i	0.932472	+	0.361242i	$0.117647\pi$
$809$	0.886289	+	1.36017i	0.886289	+	1.36017i	−0.0461835	+	0.998933i	$0.514706\pi$
$810$		0			0
$811$	−0.145517	+	0.434164i	−0.145517	+	0.434164i	−0.995734	−	0.0922684i	$-0.970588\pi$
$811$	−0.145517	+	0.434164i	−0.145517	+	0.434164i	0.850217	+	0.526432i	$0.176471\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.33447	+	1.46384i	1.33447	+	1.46384i
$817$	−0.124540	−	0.763471i	−0.124540	−	0.763471i
$818$	0.798017	−	0.397365i	0.798017	−	0.397365i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	−0.317791	+	0.948161i	−0.317791	+	0.948161i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	−1.39433	+	0.776638i	−1.39433	+	0.776638i
$826$		0			0
$827$	0.00743733	+	0.0455932i	0.00743733	+	0.0455932i	0.990410	−	0.138156i	$-0.0441176\pi$
$827$	0.00743733	+	0.0455932i	0.00743733	+	0.0455932i	−0.982973	+	0.183750i	$0.941176\pi$
$828$		0			0
$829$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$829$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.629488	+	1.87814i	−0.629488	+	1.87814i
$834$	1.12545	−	1.64296i	1.12545	−	1.64296i
$835$		0			0
$836$	−2.28993	−	0.887125i	−2.28993	−	0.887125i
$837$		0			0
$838$	0.537235	−	0.711414i	0.537235	−	0.711414i
$839$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$839$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$840$		0			0
$841$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$842$		0			0
$843$	0.0170269	−	0.183750i	0.0170269	−	0.183750i
$844$	−1.93857	−	0.179635i	−1.93857	−	0.179635i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.0486249	+	0.0785319i	0.0486249	+	0.0785319i
$850$	−0.273663	+	1.96183i	−0.273663	+	1.96183i
$851$		0			0
$852$		0			0
$853$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$853$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$854$		0			0
$855$		0			0
$856$	−0.876298	+	1.75984i	−0.876298	+	1.75984i
$857$	−0.535539	−	0.251402i	−0.535539	−	0.251402i	0.138156	−	0.990410i	$-0.455882\pi$
$857$	−0.535539	−	0.251402i	−0.535539	−	0.251402i	−0.673696	+	0.739009i	$0.735294\pi$
$858$		0			0
$859$	−0.510873	−	0.510873i	−0.510873	−	0.510873i	0.403921	−	0.914794i	$-0.367647\pi$
$859$	−0.510873	−	0.510873i	−0.510873	−	0.510873i	−0.914794	+	0.403921i	$0.867647\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$863$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$864$	0.895163	+	0.445738i	0.895163	+	0.445738i
$865$		0			0
$866$	0.0878098	+	0.629488i	0.0878098	+	0.629488i
$867$	2.24926	−	1.86777i	2.24926	−	1.86777i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.25414	−	0.388362i	1.25414	−	0.388362i
$874$		0			0
$875$		0			0
$876$	−1.29371	−	1.29371i	−1.29371	−	1.29371i
$877$		0			0		−0.986955	−	0.160996i	$-0.948529\pi$
$877$		0			0		0.986955	+	0.160996i	$0.0514706\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.428189	−	0.469701i	0.428189	−	0.469701i	−0.486604	−	0.873622i	$-0.661765\pi$
$881$	0.428189	−	0.469701i	0.428189	−	0.469701i	0.914794	+	0.403921i	$0.132353\pi$
$882$	0.0461835	+	0.998933i	0.0461835	+	0.998933i
$883$	0.184340	+	0.00852254i	0.184340	+	0.00852254i	0.138156	−	0.990410i	$-0.455882\pi$
$883$	0.184340	+	0.00852254i	0.184340	+	0.00852254i	0.0461835	+	0.998933i	$0.485294\pi$
$884$		0			0
$885$		0			0
$886$	0.116788	−	0.624761i	0.116788	−	0.624761i
$887$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$887$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.58073	−	0.220502i	1.58073	−	0.220502i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.0826835	−	1.78842i	0.0826835	−	1.78842i
$899$		0			0
$900$	0.228951	+	0.973438i	0.228951	+	0.973438i
$901$		0			0
$902$	2.82304	+	1.48805i	2.82304	+	1.48805i
$903$		0			0
$904$	−0.232881	+	1.42763i	−0.232881	+	1.42763i
$905$		0			0
$906$		0			0
$907$	0.991487	−	1.68717i	0.991487	−	1.68717i	0.317791	−	0.948161i	$-0.397059\pi$
$907$	0.991487	−	1.68717i	0.991487	−	1.68717i	0.673696	−	0.739009i	$-0.264706\pi$
$908$	0.855892	+	0.677943i	0.855892	+	0.677943i
$909$		0			0
$910$		0			0
$911$		0			0		−0.811724	−	0.584041i	$-0.801471\pi$
$911$		0			0		0.811724	+	0.584041i	$0.198529\pi$
$912$	−0.927255	+	1.22788i	−0.927255	+	1.22788i
$913$	−2.67370	−	0.0617733i	−2.67370	−	0.0617733i
$914$	1.89410	−	0.399555i	1.89410	−	0.399555i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.963876	−	1.73049i	0.963876	−	1.73049i
$919$		0			0		−0.754373	−	0.656446i	$-0.772059\pi$
$919$		0			0		0.754373	+	0.656446i	$0.227941\pi$
$920$		0			0
$921$	0.578873	−	0.122112i	0.578873	−	0.122112i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.705749	−	1.59837i	−0.705749	−	1.59837i	−0.798017	−	0.602635i	$-0.794118\pi$
$929$	−0.705749	−	1.59837i	−0.705749	−	1.59837i	0.0922684	−	0.995734i	$-0.470588\pi$
$930$		0			0
$931$	−1.52391	−	0.212577i	−1.52391	−	0.212577i
$932$	0.138156	+	1.99041i	0.138156	+	1.99041i
$933$		0			0
$934$	0.592663	+	1.76827i	0.592663	+	1.76827i
$935$		0			0
$936$		0			0
$937$	−0.184340	+	1.98934i	−0.184340	+	1.98934i	−0.0461835	+	0.998933i	$0.514706\pi$
$937$	−0.184340	+	1.98934i	−0.184340	+	1.98934i	−0.138156	+	0.990410i	$0.544118\pi$
$938$		0			0
$939$	0.871181	+	0.433797i	0.871181	+	0.433797i
$940$		0			0
$941$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$941$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$942$		0			0
$943$		0			0
$944$	−0.193463	−	1.03494i	−0.193463	−	1.03494i
$945$		0			0
$946$	−0.672278	+	0.438056i	−0.672278	+	0.438056i
$947$	−0.150143	−	0.284843i	−0.150143	−	0.284843i	0.798017	−	0.602635i	$-0.205882\pi$
$947$	−0.150143	−	0.284843i	−0.150143	−	0.284843i	−0.948161	+	0.317791i	$0.897059\pi$
$948$		0			0
$949$		0			0
$950$	−1.53703	+	0.0710610i	−1.53703	+	0.0710610i
$951$		0			0
$952$		0			0
$953$	0.0579382	+	0.223085i	0.0579382	+	0.223085i	0.990410	−	0.138156i	$-0.0441176\pi$
$953$	0.0579382	+	0.223085i	0.0579382	+	0.223085i	−0.932472	+	0.361242i	$0.882353\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.973438	−	0.228951i	0.973438	−	0.228951i
$962$		0			0
$963$	1.94709	+	0.271608i	1.94709	+	0.271608i
$964$	−1.48906	+	0.242902i	−1.48906	+	0.242902i
$965$		0			0
$966$		0			0
$967$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$967$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$968$	0.0714609	+	1.54567i	0.0714609	+	1.54567i
$969$	2.34480	+	1.94709i	2.34480	+	1.94709i
$970$		0			0
$971$	−0.600853	+	0.316715i	−0.600853	+	0.316715i	−0.739009	−	0.673696i	$-0.764706\pi$
$971$	−0.600853	+	0.316715i	−0.600853	+	0.316715i	0.138156	+	0.990410i	$0.455882\pi$
$972$	0.138156	−	0.990410i	0.138156	−	0.990410i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.387018	−	1.36023i	−0.387018	−	1.36023i	−0.873622	−	0.486604i	$-0.838235\pi$
$977$	−0.387018	−	1.36023i	−0.387018	−	1.36023i	0.486604	−	0.873622i	$-0.338235\pi$
$978$	−0.138452	−	0.00319880i	−0.138452	−	0.00319880i
$979$	−1.60882	+	1.15756i	−1.60882	+	1.15756i
$980$		0			0
$981$		0			0
$982$	0.293625	−	1.13058i	0.293625	−	1.13058i
$983$		0			0		0.754373	−	0.656446i	$-0.227941\pi$
$983$		0			0		−0.754373	+	0.656446i	$0.772059\pi$
$984$	1.38080	−	1.44612i	1.38080	−	1.44612i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$991$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$992$		0			0
$993$	−0.0426793	−	1.84727i	−0.0426793	−	1.84727i
$994$		0			0
$995$		0			0
$996$	−0.495671	+	1.60067i	−0.495671	+	1.60067i
$997$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$997$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$998$	−0.835282	−	1.21936i	−0.835282	−	1.21936i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3288.1.cj.b.1187.1	yes	64
3.2	odd	2		3288.1.cj.a.1187.1	✓	64
8.3	odd	2	CM	3288.1.cj.b.1187.1	yes	64
24.11	even	2		3288.1.cj.a.1187.1	✓	64
137.134	odd	136		3288.1.cj.a.3011.1	yes	64
411.134	even	136	inner	3288.1.cj.b.3011.1	yes	64
1096.819	even	136		3288.1.cj.a.3011.1	yes	64
3288.3011	odd	136	inner	3288.1.cj.b.3011.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3288.1.cj.a.1187.1	✓	64	3.2	odd	2
3288.1.cj.a.1187.1	✓	64	24.11	even	2
3288.1.cj.a.3011.1	yes	64	137.134	odd	136
3288.1.cj.a.3011.1	yes	64	1096.819	even	136
3288.1.cj.b.1187.1	yes	64	1.1	even	1	trivial
3288.1.cj.b.1187.1	yes	64	8.3	odd	2	CM
3288.1.cj.b.3011.1	yes	64	411.134	even	136	inner
3288.1.cj.b.3011.1	yes	64	3288.3011	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)

\(f(q)\)	\(=\)	\(q+(0.228951 + 0.973438i) q^{2} +(-0.486604 - 0.873622i) q^{3} +(-0.895163 + 0.445738i) q^{4} +(0.739009 - 0.673696i) q^{6} +(-0.638847 - 0.769334i) q^{8} +(-0.526432 + 0.850217i) q^{9} +O(q^{10})\)	\(q+(0.228951 + 0.973438i) q^{2} +(-0.486604 - 0.873622i) q^{3} +(-0.895163 + 0.445738i) q^{4} +(0.739009 - 0.673696i) q^{6} +(-0.638847 - 0.769334i) q^{8} +(-0.526432 + 0.850217i) q^{9} +(-0.507206 + 1.51330i) q^{11} +(0.824997 + 0.565136i) q^{12} +(0.602635 - 0.798017i) q^{16} +(-1.52391 - 1.26544i) q^{17} +(-0.948161 - 0.317791i) q^{18} +(0.748723 - 1.34421i) q^{19} +(-1.58923 - 0.147263i) q^{22} +(-0.361242 + 0.932472i) q^{24} +(-0.948161 + 0.317791i) q^{25} +(0.998933 + 0.0461835i) q^{27} +(0.914794 + 0.403921i) q^{32} +(1.56886 - 0.293271i) q^{33} +(0.882928 - 1.77316i) q^{34} +(0.0922684 - 0.995734i) q^{36} +(1.47993 + 0.421076i) q^{38} +(-1.84727 - 0.765163i) q^{41} +(0.394096 - 0.312159i) q^{43} +(-0.220502 - 1.58073i) q^{44} +(-0.990410 - 0.138156i) q^{48} +(-0.361242 - 0.932472i) q^{49} +(-0.526432 - 0.850217i) q^{50} +(-0.363975 + 1.94709i) q^{51} +(0.183750 + 0.982973i) q^{54} -1.53867 q^{57} +(0.709310 - 0.778076i) q^{59} +(-0.183750 + 0.982973i) q^{64} +(0.644672 + 1.46004i) q^{66} +(-1.86936 - 0.394336i) q^{67} +(1.92821 + 0.453510i) q^{68} +(0.990410 - 0.138156i) q^{72} +(-1.79844 - 0.336186i) q^{73} +(0.739009 + 0.673696i) q^{75} +(-0.0710610 + 1.53703i) q^{76} +(-0.445738 - 0.895163i) q^{81} +(0.321906 - 1.97338i) q^{82} +(0.495671 + 1.60067i) q^{83} +(0.394096 + 0.312159i) q^{86} +(1.48826 - 0.576554i) q^{88} +(1.00801 + 0.725270i) q^{89} +(-0.0922684 - 0.995734i) q^{96} +(-0.990410 - 0.861844i) q^{97} +(0.824997 - 0.565136i) q^{98} +(-1.01962 - 1.22788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{6}+O(q^{10}) \) 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

Related objects

Downloads

Learn more