LMFDB - Embedded newform 3288.1.cj.b.971.1

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			971.1
Root			$-0.990410 + 0.138156i$ of defining polynomial
Character	$\chi$	$=$	3288.971
Dual form			3288.1.cj.b.491.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.990410 + 0.138156i) q^{2} +(-0.948161 + 0.317791i) q^{3} +(0.961826 + 0.273663i) q^{4} +(-0.982973 + 0.183750i) q^{6} +(0.914794 + 0.403921i) q^{8} +(0.798017 - 0.602635i) q^{9} +O(q^{10})$	\(q+(0.990410 + 0.138156i) q^{2} +(-0.948161 + 0.317791i) q^{3} +(0.961826 + 0.273663i) q^{4} +(-0.982973 + 0.183750i) q^{6} +(0.914794 + 0.403921i) q^{8} +(0.798017 - 0.602635i) q^{9} +(0.512328 + 0.919806i) q^{11} +(-0.998933 + 0.0461835i) q^{12} +(0.850217 + 0.526432i) q^{16} +(-0.786384 - 1.78099i) q^{17} +(0.873622 - 0.486604i) q^{18} +(0.765964 + 0.256725i) q^{19} +(0.380338 + 0.981767i) q^{22} +(-0.995734 - 0.0922684i) q^{24} +(0.873622 + 0.486604i) q^{25} +(-0.565136 + 0.824997i) q^{27} +(0.769334 + 0.638847i) q^{32} +(-0.778076 - 0.709310i) q^{33} +(-0.532788 - 1.87256i) q^{34} +(0.932472 - 0.361242i) q^{36} +(0.723151 + 0.360086i) q^{38} +(-0.861602 + 0.356887i) q^{41} +(1.16528 - 0.0808832i) q^{43} +(0.241054 + 1.02490i) q^{44} +(-0.973438 - 0.228951i) q^{48} +(-0.995734 + 0.0922684i) q^{49} +(0.798017 + 0.602635i) q^{50} +(1.31160 + 1.43876i) q^{51} +(-0.673696 + 0.739009i) q^{54} -0.807842 q^{57} +(-0.293271 + 1.56886i) q^{59} +(0.673696 + 0.739009i) q^{64} +(-0.672619 - 0.810004i) q^{66} +(0.0434502 + 0.0156884i) q^{67} +(-0.268973 - 1.92821i) q^{68} +(0.973438 - 0.228951i) q^{72} +(1.13709 - 1.03659i) q^{73} +(-0.982973 - 0.183750i) q^{75} +(0.666468 + 0.456541i) q^{76} +(0.273663 - 0.961826i) q^{81} +(-0.902646 + 0.234429i) q^{82} +(0.849659 + 0.0196306i) q^{83} +(1.16528 + 0.0808832i) q^{86} +(0.0971461 + 1.04837i) q^{88} +(0.0701658 + 0.119398i) q^{89} +(-0.932472 - 0.361242i) q^{96} +(-0.973438 + 1.22895i) q^{97} +(-0.998933 - 0.0461835i) q^{98} +(0.963154 + 0.425274i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3288\mathbb{Z}\right)^\times$.

$n$	$823$	$1097$	$1645$	$1921$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{21}{136}\right)$

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 $

$2$	0.990410	+	0.138156i	0.990410	+	0.138156i
$2$	0.990410	+	0.138156i	0.990410	+	0.138156i
$3$	−0.948161	+	0.317791i	−0.948161	+	0.317791i
$3$	−0.948161	+	0.317791i	−0.948161	+	0.317791i
$4$	0.961826	+	0.273663i	0.961826	+	0.273663i
$5$		0			0		−0.967890	−	0.251374i	$-0.919118\pi$
$5$		0			0		0.967890	+	0.251374i	$0.0808824\pi$
$6$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$7$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$7$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$8$	0.914794	+	0.403921i	0.914794	+	0.403921i
$9$	0.798017	−	0.602635i	0.798017	−	0.602635i
$10$		0			0
$11$	0.512328	+	0.919806i	0.512328	+	0.919806i	0.998933	+	0.0461835i	$0.0147059\pi$
$11$	0.512328	+	0.919806i	0.512328	+	0.919806i	−0.486604	+	0.873622i	$0.661765\pi$
$12$	−0.998933	+	0.0461835i	−0.998933	+	0.0461835i
$13$		0			0		0.905220	−	0.424943i	$-0.139706\pi$
$13$		0			0		−0.905220	+	0.424943i	$0.860294\pi$
$14$		0			0
$15$		0			0
$16$	0.850217	+	0.526432i	0.850217	+	0.526432i
$17$	−0.786384	−	1.78099i	−0.786384	−	1.78099i	−0.602635	−	0.798017i	$-0.705882\pi$
$17$	−0.786384	−	1.78099i	−0.786384	−	1.78099i	−0.183750	−	0.982973i	$-0.558824\pi$
$18$	0.873622	−	0.486604i	0.873622	−	0.486604i
$19$	0.765964	+	0.256725i	0.765964	+	0.256725i	0.673696	−	0.739009i	$-0.264706\pi$
$19$	0.765964	+	0.256725i	0.765964	+	0.256725i	0.0922684	+	0.995734i	$0.470588\pi$
$20$		0			0
$21$		0			0
$22$	0.380338	+	0.981767i	0.380338	+	0.981767i
$23$		0			0		0.811724	−	0.584041i	$-0.198529\pi$
$23$		0			0		−0.811724	+	0.584041i	$0.801471\pi$
$24$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$25$	0.873622	+	0.486604i	0.873622	+	0.486604i
$26$		0			0
$27$	−0.565136	+	0.824997i	−0.565136	+	0.824997i
$28$		0			0
$29$		0			0		0.160996	−	0.986955i	$-0.448529\pi$
$29$		0			0		−0.160996	+	0.986955i	$0.551471\pi$
$30$		0			0
$31$		0			0		−0.656446	−	0.754373i	$-0.727941\pi$
$31$		0			0		0.656446	+	0.754373i	$0.272059\pi$
$32$	0.769334	+	0.638847i	0.769334	+	0.638847i
$33$	−0.778076	−	0.709310i	−0.778076	−	0.709310i
$34$	−0.532788	−	1.87256i	−0.532788	−	1.87256i
$35$		0			0
$36$	0.932472	−	0.361242i	0.932472	−	0.361242i
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	0.723151	+	0.360086i	0.723151	+	0.360086i
$39$		0			0
$40$		0			0
$41$	−0.861602	+	0.356887i	−0.861602	+	0.356887i	−0.769334	−	0.638847i	$-0.779412\pi$
$41$	−0.861602	+	0.356887i	−0.861602	+	0.356887i	−0.0922684	+	0.995734i	$0.529412\pi$
$42$		0			0
$43$	1.16528	−	0.0808832i	1.16528	−	0.0808832i	0.526432	−	0.850217i	$-0.323529\pi$
$43$	1.16528	−	0.0808832i	1.16528	−	0.0808832i	0.638847	+	0.769334i	$0.279412\pi$
$44$	0.241054	+	1.02490i	0.241054	+	1.02490i
$45$		0			0
$46$		0			0
$47$		0			0		−0.206405	−	0.978467i	$-0.566176\pi$
$47$		0			0		0.206405	+	0.978467i	$0.433824\pi$
$48$	−0.973438	−	0.228951i	−0.973438	−	0.228951i
$49$	−0.995734	+	0.0922684i	−0.995734	+	0.0922684i
$50$	0.798017	+	0.602635i	0.798017	+	0.602635i
$51$	1.31160	+	1.43876i	1.31160	+	1.43876i
$52$		0			0
$53$		0			0		0.656446	−	0.754373i	$-0.272059\pi$
$53$		0			0		−0.656446	+	0.754373i	$0.727941\pi$
$54$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$55$		0			0
$56$		0			0
$57$	−0.807842			−0.807842
$58$		0			0
$59$	−0.293271	+	1.56886i	−0.293271	+	1.56886i	0.445738	+	0.895163i	$0.352941\pi$
$59$	−0.293271	+	1.56886i	−0.293271	+	1.56886i	−0.739009	+	0.673696i	$0.764706\pi$
$60$		0			0
$61$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$61$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$62$		0			0
$63$		0			0
$64$	0.673696	+	0.739009i	0.673696	+	0.739009i
$65$		0			0
$66$	−0.672619	−	0.810004i	−0.672619	−	0.810004i
$67$	0.0434502	+	0.0156884i	0.0434502	+	0.0156884i	0.361242	−	0.932472i	$-0.382353\pi$
$67$	0.0434502	+	0.0156884i	0.0434502	+	0.0156884i	−0.317791	+	0.948161i	$0.602941\pi$
$68$	−0.268973	−	1.92821i	−0.268973	−	1.92821i
$69$		0			0
$70$		0			0
$71$		0			0		0.115243	−	0.993337i	$-0.463235\pi$
$71$		0			0		−0.115243	+	0.993337i	$0.536765\pi$
$72$	0.973438	−	0.228951i	0.973438	−	0.228951i
$73$	1.13709	−	1.03659i	1.13709	−	1.03659i	0.138156	−	0.990410i	$-0.455882\pi$
$73$	1.13709	−	1.03659i	1.13709	−	1.03659i	0.998933	−	0.0461835i	$-0.0147059\pi$
$74$		0			0
$75$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$76$	0.666468	+	0.456541i	0.666468	+	0.456541i
$77$		0			0
$78$		0			0
$79$		0			0		−0.955248	−	0.295806i	$-0.904412\pi$
$79$		0			0		0.955248	+	0.295806i	$0.0955882\pi$
$80$		0			0
$81$	0.273663	−	0.961826i	0.273663	−	0.961826i
$82$	−0.902646	+	0.234429i	−0.902646	+	0.234429i
$83$	0.849659	+	0.0196306i	0.849659	+	0.0196306i	0.445738	−	0.895163i	$-0.352941\pi$
$83$	0.849659	+	0.0196306i	0.849659	+	0.0196306i	0.403921	+	0.914794i	$0.367647\pi$
$84$		0			0
$85$		0			0
$86$	1.16528	+	0.0808832i	1.16528	+	0.0808832i
$87$		0			0
$88$	0.0971461	+	1.04837i	0.0971461	+	1.04837i
$89$	0.0701658	+	0.119398i	0.0701658	+	0.119398i	0.895163	−	0.445738i	$-0.147059\pi$
$89$	0.0701658	+	0.119398i	0.0701658	+	0.119398i	−0.824997	+	0.565136i	$0.808824\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$97$	−0.973438	+	1.22895i	−0.973438	+	1.22895i			1.00000i	$0.5\pi$
$97$	−0.973438	+	1.22895i	−0.973438	+	1.22895i	−0.973438	+	0.228951i	$0.926471\pi$
$98$	−0.998933	−	0.0461835i	−0.998933	−	0.0461835i
$99$	0.963154	+	0.425274i	0.963154	+	0.425274i
$100$	0.707107	+	0.707107i	0.707107	+	0.707107i
$101$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$101$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$102$	1.10025	+	1.60617i	1.10025	+	1.60617i
$103$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$103$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.944227	−	1.13709i	−0.944227	−	1.13709i	−0.990410	−	0.138156i	$-0.955882\pi$
$107$	−0.944227	−	1.13709i	−0.944227	−	1.13709i	0.0461835	−	0.998933i	$-0.485294\pi$
$108$	−0.769334	+	0.638847i	−0.769334	+	0.638847i
$109$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$109$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.463756	+	0.367336i	−0.463756	+	0.367336i	−0.824997	−	0.565136i	$-0.808824\pi$
$113$	−0.463756	+	0.367336i	−0.463756	+	0.367336i	0.361242	+	0.932472i	$0.382353\pi$
$114$	−0.800095	−	0.111609i	−0.800095	−	0.111609i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.507206	+	1.51330i	−0.507206	+	1.51330i
$119$		0			0
$120$		0			0
$121$	−0.0571301	+	0.0922684i	−0.0571301	+	0.0922684i
$122$		0			0
$123$	0.703522	−	0.612196i	0.703522	−	0.612196i
$124$		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	$0.625000\pi$
$128$	0.565136	+	0.824997i	0.565136	+	0.824997i
$129$	−1.07917	+	0.447006i	−1.07917	+	0.447006i
$130$		0			0
$131$	−0.188057	+	0.261368i	−0.188057	+	0.261368i	−0.895163	−	0.445738i	$-0.852941\pi$
$131$	−0.188057	+	0.261368i	−0.188057	+	0.261368i	0.707107	+	0.707107i	$0.250000\pi$
$132$	−0.554262	−	0.895163i	−0.554262	−	0.895163i
$133$		0			0
$134$	0.0408661	+	0.0215409i	0.0408661	+	0.0215409i
$135$		0			0
$136$		−	1.94688i		−	1.94688i
$137$	−0.317791	−	0.948161i	−0.317791	−	0.948161i
$137$	−0.317791	−	0.948161i	−0.317791	−	0.948161i
$138$		0			0
$139$	0.0998157	−	0.715555i	0.0998157	−	0.715555i	−0.873622	−	0.486604i	$-0.838235\pi$
$139$	0.0998157	−	0.715555i	0.0998157	−	0.715555i	0.973438	−	0.228951i	$-0.0735294\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.995734	−	0.0922684i	0.995734	−	0.0922684i
$145$		0			0
$146$	1.26940	−	0.869557i	1.26940	−	0.869557i
$147$	0.914794	−	0.403921i	0.914794	−	0.403921i
$148$		0			0
$149$		0			0		0.690585	−	0.723251i	$-0.257353\pi$
$149$		0			0		−0.690585	+	0.723251i	$0.742647\pi$
$150$	−0.948161	−	0.317791i	−0.948161	−	0.317791i
$151$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$151$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$152$	0.597002	+	0.544240i	0.597002	+	0.544240i
$153$	−1.70083	−	0.947359i	−1.70083	−	0.947359i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.506653	−	0.862150i	$-0.330882\pi$
$157$		0			0		−0.506653	+	0.862150i	$0.669118\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.403921	−	0.914794i	0.403921	−	0.914794i
$163$	0.0681792	+	0.220171i	0.0681792	+	0.220171i	0.982973	−	0.183750i	$-0.0588235\pi$
$163$	0.0681792	+	0.220171i	0.0681792	+	0.220171i	−0.914794	+	0.403921i	$0.867647\pi$
$164$	−0.926378	+	0.107475i	−0.926378	+	0.107475i
$165$		0			0
$166$	0.838799	+	0.136828i	0.838799	+	0.136828i
$167$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$167$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$168$		0			0
$169$	0.638847	−	0.769334i	0.638847	−	0.769334i
$170$		0			0
$171$	0.765964	−	0.256725i	0.765964	−	0.256725i
$172$	1.14293	+	0.241098i	1.14293	+	0.241098i
$173$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$173$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$174$		0			0
$175$		0			0
$176$	−0.0486249	+	1.05174i	−0.0486249	+	1.05174i
$177$	−0.220502	−	1.58073i	−0.220502	−	1.58073i
$178$	0.0529974	+	0.127947i	0.0529974	+	0.127947i
$179$	−1.04300	+	1.60067i	−1.04300	+	1.60067i	−0.273663	+	0.961826i	$0.588235\pi$
$179$	−1.04300	+	1.60067i	−1.04300	+	1.60067i	−0.769334	+	0.638847i	$0.779412\pi$
$180$		0			0
$181$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$181$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.23528	−	1.63577i	1.23528	−	1.63577i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.0230979	−	0.999733i	$-0.492647\pi$
$191$		0			0		−0.0230979	+	0.999733i	$0.507353\pi$
$192$	−0.873622	−	0.486604i	−0.873622	−	0.486604i
$193$	−1.62926	−	0.631178i	−1.62926	−	0.631178i	−0.638847	−	0.769334i	$-0.720588\pi$
$193$	−1.62926	−	0.631178i	−1.62926	−	0.631178i	−0.990410	+	0.138156i	$0.955882\pi$
$194$	−1.13389	+	1.08268i	−1.13389	+	1.08268i
$195$		0			0
$196$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$197$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$197$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$198$	0.895163	+	0.554262i	0.895163	+	0.554262i
$199$		0			0		0.837831	−	0.545930i	$-0.183824\pi$
$199$		0			0		−0.837831	+	0.545930i	$0.816176\pi$
$200$	0.602635	+	0.798017i	0.602635	+	0.798017i
$201$	−0.0461835	−	0.00106703i	−0.0461835	−	0.00106703i
$202$		0			0
$203$		0			0
$204$	0.867797	+	1.74277i	0.867797	+	1.74277i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.156288	+	0.836066i	0.156288	+	0.836066i
$210$		0			0
$211$	−0.166516	−	0.220502i	−0.166516	−	0.220502i	0.707107	−	0.707107i	$-0.250000\pi$
$211$	−0.166516	−	0.220502i	−0.166516	−	0.220502i	−0.873622	+	0.486604i	$0.838235\pi$
$212$		0			0
$213$		0			0
$214$	−0.778076	−	1.25664i	−0.778076	−	1.25664i
$215$		0			0
$216$	−0.850217	+	0.526432i	−0.850217	+	0.526432i
$217$		0			0
$218$		0			0
$219$	−0.748723	+	1.34421i	−0.748723	+	1.34421i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.0692444	−	0.997600i	$-0.477941\pi$
$223$		0			0		−0.0692444	+	0.997600i	$0.522059\pi$
$224$		0			0
$225$	0.990410	−	0.138156i	0.990410	−	0.138156i
$226$	−0.510058	+	0.299742i	−0.510058	+	0.299742i
$227$	−1.77146	+	0.373684i	−1.77146	+	0.373684i	−0.973438	−	0.228951i	$-0.926471\pi$
$227$	−1.77146	+	0.373684i	−1.77146	+	0.373684i	−0.798017	+	0.602635i	$0.794118\pi$
$228$	−0.777003	−	0.221076i	−0.777003	−	0.221076i
$229$		0			0		−0.339607	−	0.940567i	$-0.610294\pi$
$229$		0			0		0.339607	+	0.940567i	$0.389706\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.760267	−	1.83545i	−0.760267	−	1.83545i	−0.486604	−	0.873622i	$-0.661765\pi$
$233$	−0.760267	−	1.83545i	−0.760267	−	1.83545i	−0.273663	−	0.961826i	$-0.588235\pi$
$234$		0			0
$235$		0			0
$236$	−0.711414	+	1.42871i	−0.711414	+	1.42871i
$237$		0			0
$238$		0			0
$239$		0			0		−0.978467	−	0.206405i	$-0.933824\pi$
$239$		0			0		0.978467	+	0.206405i	$0.0661765\pi$
$240$		0			0
$241$	−0.0286833	−	1.24148i	−0.0286833	−	1.24148i	−0.798017	−	0.602635i	$-0.794118\pi$
$241$	−0.0286833	−	1.24148i	−0.0286833	−	1.24148i	0.769334	−	0.638847i	$-0.220588\pi$
$242$	−0.0693298	+	0.0834907i	−0.0693298	+	0.0834907i
$243$	0.0461835	+	0.998933i	0.0461835	+	0.998933i
$244$		0			0
$245$		0			0
$246$	0.781354	−	0.509130i	0.781354	−	0.509130i
$247$		0			0
$248$		0			0
$249$	−0.811852	+	0.251402i	−0.811852	+	0.251402i
$250$		0			0
$251$	−1.15285	−	1.60227i	−1.15285	−	1.60227i	−0.707107	−	0.707107i	$-0.750000\pi$
$251$	−1.15285	−	1.60227i	−1.15285	−	1.60227i	−0.445738	−	0.895163i	$-0.647059\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.445738	+	0.895163i	0.445738	+	0.895163i
$257$	1.82178	−	0.804396i	1.82178	−	0.804396i	0.873622	−	0.486604i	$-0.161765\pi$
$257$	1.82178	−	0.804396i	1.82178	−	0.804396i	0.948161	−	0.317791i	$-0.102941\pi$
$258$	−1.13058	+	0.293625i	−1.13058	+	0.293625i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.222363	+	0.232881i	−0.222363	+	0.232881i
$263$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$263$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$264$	−0.425274	−	0.963154i	−0.425274	−	0.963154i
$265$		0			0
$266$		0			0
$267$	−0.104472	−	0.0909104i	−0.104472	−	0.0909104i
$268$	0.0374982	+	0.0269802i	0.0374982	+	0.0269802i
$269$		0			0		0.251374	−	0.967890i	$-0.419118\pi$
$269$		0			0		−0.251374	+	0.967890i	$0.580882\pi$
$270$		0			0
$271$		0			0		0.466296	−	0.884629i	$-0.345588\pi$
$271$		0			0		−0.466296	+	0.884629i	$0.654412\pi$
$272$	0.268973	−	1.92821i	0.268973	−	1.92821i
$273$		0			0
$274$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$275$			1.05286i			1.05286i
$276$		0			0
$277$		0			0		−0.884629	−	0.466296i	$-0.845588\pi$
$277$		0			0		0.884629	+	0.466296i	$0.154412\pi$
$278$	0.197717	−	0.694903i	0.197717	−	0.694903i
$279$		0			0
$280$		0			0
$281$	−1.86295	+	0.0861296i	−1.86295	+	0.0861296i	−0.948161	−	0.317791i	$-0.897059\pi$
$281$	−1.86295	+	0.0861296i	−1.86295	+	0.0861296i	−0.914794	+	0.403921i	$0.867647\pi$
$282$		0			0
$283$	−0.932472	−	1.36124i	−0.932472	−	1.36124i	−0.932472	−	0.361242i	$-0.882353\pi$
$283$	−0.932472	−	1.36124i	−0.932472	−	1.36124i		−	1.00000i	$-0.5\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.998933	+	0.0461835i	0.998933	+	0.0461835i
$289$	−1.87983	+	2.06208i	−1.87983	+	2.06208i
$290$		0			0
$291$	0.532426	−	1.47459i	0.532426	−	1.47459i
$292$	1.37736	−	0.685843i	1.37736	−	0.685843i
$293$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$293$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$294$	0.961826	−	0.273663i	0.961826	−	0.273663i
$295$		0			0
$296$		0			0
$297$	−1.04837	−	0.0971461i	−1.04837	−	0.0971461i
$298$		0			0
$299$		0			0
$300$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.516087	+	0.621500i	0.516087	+	0.621500i
$305$		0			0
$306$	−1.55364	−	1.17325i	−1.55364	−	1.17325i
$307$	−1.99893	+	0.0461835i	−1.99893	+	0.0461835i	−0.998933	+	0.0461835i	$0.985294\pi$
$307$	−1.99893	+	0.0461835i	−1.99893	+	0.0461835i	−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
$313$	1.89430	+	0.0875787i	1.89430	+	0.0875787i	0.961826	−	0.273663i	$-0.0882353\pi$
$313$	1.89430	+	0.0875787i	1.89430	+	0.0875787i	0.932472	+	0.361242i	$0.117647\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.0692444	−	0.997600i	$-0.522059\pi$
$317$		0			0		0.0692444	+	0.997600i	$0.477941\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	1.25664	+	0.778076i	1.25664	+	0.778076i
$322$		0			0
$323$	−0.145117	−	1.56606i	−0.145117	−	1.56606i
$324$	0.526432	−	0.850217i	0.526432	−	0.850217i
$325$		0			0
$326$	0.0371073	+	0.227480i	0.0371073	+	0.227480i
$327$		0			0
$328$	−0.932343	−	0.0215409i	−0.932343	−	0.0215409i
$329$		0			0
$330$		0			0
$331$	−1.27604	−	1.33639i	−1.27604	−	1.33639i	−0.914794	−	0.403921i	$-0.867647\pi$
$331$	−1.27604	−	1.33639i	−1.27604	−	1.33639i	−0.361242	−	0.932472i	$-0.617647\pi$
$332$	0.811852	+	0.251402i	0.811852	+	0.251402i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.01962	−	0.769982i	1.01962	−	0.769982i	0.0461835	−	0.998933i	$-0.485294\pi$
$337$	1.01962	−	0.769982i	1.01962	−	0.769982i	0.973438	+	0.228951i	$0.0735294\pi$
$338$	0.739009	−	0.673696i	0.739009	−	0.673696i
$339$	0.322979	−	0.495671i	0.322979	−	0.495671i
$340$		0			0
$341$		0			0
$342$	0.794087	−	0.148441i	0.794087	−	0.148441i
$343$		0			0
$344$	1.09866	+	0.396689i	1.09866	+	0.396689i
$345$		0			0
$346$		0			0
$347$	−1.32445	−	1.45285i	−1.32445	−	1.45285i	−0.798017	−	0.602635i	$-0.794118\pi$
$347$	−1.32445	−	1.45285i	−1.32445	−	1.45285i	−0.526432	−	0.850217i	$-0.676471\pi$
$348$		0			0
$349$		0			0		−0.545930	−	0.837831i	$-0.683824\pi$
$349$		0			0		0.545930	+	0.837831i	$0.316176\pi$
$350$		0			0
$351$		0			0
$352$	−0.193463	+	1.03494i	−0.193463	+	1.03494i
$353$	0.556451	−	1.79695i	0.556451	−	1.79695i	−0.0461835	−	0.998933i	$-0.514706\pi$
$353$	0.556451	−	1.79695i	0.556451	−	1.79695i	0.602635	−	0.798017i	$-0.294118\pi$
$354$		−	1.59603i		−	1.59603i
$355$		0			0
$356$	0.0348125	+	0.134042i	0.0348125	+	0.134042i
$357$		0			0
$358$	−1.25414	+	1.44123i	−1.25414	+	1.44123i
$359$		0			0		0.986955	−	0.160996i	$-0.0514706\pi$
$359$		0			0		−0.986955	+	0.160996i	$0.948529\pi$
$360$		0			0
$361$	−0.277224	−	0.209350i	−0.277224	−	0.209350i
$362$		0			0
$363$	0.0248465	−	0.105641i	0.0248465	−	0.105641i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$367$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$368$		0			0
$369$	−0.472501	+	0.804034i	−0.472501	+	0.804034i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$373$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$374$	1.44942	−	1.44942i	1.44942	−	1.44942i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.47993	+	1.22892i	1.47993	+	1.22892i	0.914794	+	0.403921i	$0.132353\pi$
$379$	1.47993	+	1.22892i	1.47993	+	1.22892i	0.565136	+	0.824997i	$0.308824\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$383$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$384$	−0.798017	−	0.602635i	−0.798017	−	0.602635i
$385$		0			0
$386$	−1.52643	−	0.850217i	−1.52643	−	0.850217i
$387$	0.881170	−	0.766784i	0.881170	−	0.766784i
$388$	−1.27260	+	0.915642i	−1.27260	+	0.915642i
$389$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$389$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$390$		0			0
$391$		0			0
$392$	−0.948161	−	0.317791i	−0.948161	−	0.317791i
$393$	0.0952471	−	0.307582i	0.0952471	−	0.307582i
$394$		0			0
$395$		0			0
$396$	0.810004	+	0.672619i	0.810004	+	0.672619i
$397$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$397$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$398$		0			0
$399$		0			0
$400$	0.486604	+	0.873622i	0.486604	+	0.873622i
$401$	1.00875	+	0.417837i	1.00875	+	0.417837i	0.824997	−	0.565136i	$-0.191176\pi$
$401$	1.00875	+	0.417837i	1.00875	+	0.417837i	0.183750	+	0.982973i	$0.441176\pi$
$402$	−0.0455932	−	0.00743733i	−0.0455932	−	0.00743733i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.618701	+	1.84595i	0.618701	+	1.84595i
$409$	0.542077	+	0.0756166i	0.542077	+	0.0756166i	0.403921	−	0.914794i	$-0.367647\pi$
$409$	0.542077	+	0.0756166i	0.542077	+	0.0756166i	0.138156	+	0.990410i	$0.455882\pi$
$410$		0			0
$411$	0.602635	+	0.798017i	0.602635	+	0.798017i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.132756	+	0.710182i	0.132756	+	0.710182i
$418$	0.0392812	+	0.849640i	0.0392812	+	0.849640i
$419$	−0.500690	−	0.221076i	−0.500690	−	0.221076i	0.138156	−	0.990410i	$-0.455882\pi$
$419$	−0.500690	−	0.221076i	−0.500690	−	0.221076i	−0.638847	+	0.769334i	$0.720588\pi$
$420$		0			0
$421$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$421$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$422$	−0.134455	−	0.241393i	−0.134455	−	0.241393i
$423$		0			0
$424$		0			0
$425$	0.179635	−	1.93857i	0.179635	−	1.93857i
$426$		0			0
$427$		0			0
$428$	−0.597002	−	1.35208i	−0.597002	−	1.35208i
$429$		0			0
$430$		0			0
$431$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$431$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$432$	−0.914794	+	0.403921i	−0.914794	+	0.403921i
$433$	0.351564	+	0.907490i	0.351564	+	0.907490i	0.990410	+	0.138156i	$0.0441176\pi$
$433$	0.351564	+	0.907490i	0.351564	+	0.907490i	−0.638847	+	0.769334i	$0.720588\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.927255	+	1.22788i	−0.927255	+	1.22788i
$439$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$439$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$440$		0			0
$441$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$442$		0			0
$443$	0.748723	+	0.621731i	0.748723	+	0.621731i	0.932472	−	0.361242i	$-0.117647\pi$
$443$	0.748723	+	0.621731i	0.748723	+	0.621731i	−0.183750	+	0.982973i	$0.558824\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.72198	+	0.857445i	1.72198	+	0.857445i	0.982973	+	0.183750i	$0.0588235\pi$
$449$	1.72198	+	0.857445i	1.72198	+	0.857445i	0.739009	+	0.673696i	$0.235294\pi$
$450$	1.00000			1.00000
$451$	−0.769691	−	0.609663i	−0.769691	−	0.609663i
$452$	−0.546578	+	0.226400i	−0.546578	+	0.226400i
$453$		0			0
$454$	−1.80609	+	0.125363i	−1.80609	+	0.125363i
$455$		0			0
$456$	−0.739009	−	0.326304i	−0.739009	−	0.326304i
$457$	−1.43615	+	0.757007i	−1.43615	+	0.757007i	−0.990410	−	0.138156i	$-0.955882\pi$
$457$	−1.43615	+	0.757007i	−1.43615	+	0.757007i	−0.445738	+	0.895163i	$0.647059\pi$
$458$		0			0
$459$	1.91373	+	0.357738i	1.91373	+	0.357738i
$460$		0			0
$461$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$461$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$462$		0			0
$463$		0			0		0.986955	−	0.160996i	$-0.0514706\pi$
$463$		0			0		−0.986955	+	0.160996i	$0.948529\pi$
$464$		0			0
$465$		0			0
$466$	−0.499398	−	1.92288i	−0.499398	−	1.92288i
$467$	−0.0666624	+	0.172075i	−0.0666624	+	0.172075i	−0.961826	−	0.273663i	$-0.911765\pi$
$467$	−0.0666624	+	0.172075i	−0.0666624	+	0.172075i	0.895163	+	0.445738i	$0.147059\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.901977	+	1.31672i	−0.901977	+	1.31672i
$473$	0.671402	+	1.03039i	0.671402	+	1.03039i
$474$		0			0
$475$	0.544240	+	0.597002i	0.544240	+	0.597002i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$479$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$480$		0			0
$481$		0			0
$482$	0.143110	−	1.23354i	0.143110	−	1.23354i
$483$		0			0
$484$	−0.0801997	+	0.0731117i	−0.0801997	+	0.0731117i
$485$		0			0
$486$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$487$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$487$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$488$		0			0
$489$	−0.134613	−	0.187091i	−0.134613	−	0.187091i
$490$		0			0
$491$	1.19078	+	1.24710i	1.19078	+	1.24710i	0.961826	+	0.273663i	$0.0882353\pi$
$491$	1.19078	+	1.24710i	1.19078	+	1.24710i	0.228951	+	0.973438i	$0.426471\pi$
$492$	0.844201	−	0.396298i	0.844201	−	0.396298i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.838799	+	0.136828i	−0.838799	+	0.136828i
$499$	0.181395	+	1.95756i	0.181395	+	1.95756i	0.273663	+	0.961826i	$0.411765\pi$
$499$	0.181395	+	1.95756i	0.181395	+	1.95756i	−0.0922684	+	0.995734i	$0.529412\pi$
$500$		0			0
$501$		0			0
$502$	−0.920426	−	1.74618i	−0.920426	−	1.74618i
$503$		0			0		0.940567	−	0.339607i	$-0.110294\pi$
$503$		0			0		−0.940567	+	0.339607i	$0.889706\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.361242	+	0.932472i	−0.361242	+	0.932472i
$508$		0			0
$509$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$509$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$510$		0			0
$511$		0			0
$512$	0.317791	+	0.948161i	0.317791	+	0.948161i
$513$	−0.644672	+	0.486834i	−0.644672	+	0.486834i
$514$	1.91545	−	0.544991i	1.91545	−	0.544991i
$515$		0			0
$516$	−1.16030	+	0.134613i	−1.16030	+	0.134613i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.203895	−	1.75747i	−0.203895	−	1.75747i	−0.565136	−	0.824997i	$-0.691176\pi$
$521$	−0.203895	−	1.75747i	−0.203895	−	1.75747i	0.361242	−	0.932472i	$-0.382353\pi$
$522$		0			0
$523$	−0.178827	+	0.321055i	−0.178827	+	0.321055i	−0.948161	−	0.317791i	$-0.897059\pi$
$523$	−0.178827	+	0.321055i	−0.178827	+	0.321055i	0.769334	+	0.638847i	$0.220588\pi$
$524$	−0.252404	+	0.199927i	−0.252404	+	0.199927i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.288130	−	1.01267i	−0.288130	−	1.01267i
$529$	0.317791	−	0.948161i	0.317791	−	0.948161i
$530$		0			0
$531$	0.711414	+	1.42871i	0.711414	+	1.42871i
$532$		0			0
$533$		0			0
$534$	−0.0909104	−	0.104472i	−0.0909104	−	0.104472i
$535$		0			0
$536$	0.0334111	+	0.0319021i	0.0334111	+	0.0319021i
$537$	0.480249	−	1.84915i	0.480249	−	1.84915i
$538$		0			0
$539$	−0.595012	−	0.868610i	−0.595012	−	0.868610i
$540$		0			0
$541$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$541$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$542$		0			0
$543$		0			0
$544$	0.532788	−	1.87256i	0.532788	−	1.87256i
$545$		0			0
$546$		0			0
$547$		−	0.184537i		−	0.184537i	−0.995734	−	0.0922684i	$-0.970588\pi$
$547$		−	0.184537i		−	0.184537i	0.995734	−	0.0922684i	$-0.0294118\pi$
$548$	−0.0461835	−	0.998933i	−0.0461835	−	0.998933i
$549$		0			0
$550$	−0.145460	+	1.04277i	−0.145460	+	1.04277i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.291826	−	0.660923i	0.291826	−	0.660923i
$557$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$557$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.651408	+	1.94354i	−0.651408	+	1.94354i
$562$	−1.85699	−	0.172075i	−1.85699	−	0.172075i
$563$	0.995734	+	0.907732i	0.995734	+	0.907732i	0.995734	−	0.0922684i	$-0.0294118\pi$
$563$	0.995734	+	0.907732i	0.995734	+	0.907732i			1.00000i	$0.5\pi$
$564$		0			0
$565$		0			0
$566$	−0.735466	−	1.47701i	−0.735466	−	1.47701i
$567$		0			0
$568$		0			0
$569$	−0.373684	−	0.175421i	−0.373684	−	0.175421i	0.228951	−	0.973438i	$-0.426471\pi$
$569$	−0.373684	−	0.175421i	−0.373684	−	0.175421i	−0.602635	+	0.798017i	$0.705882\pi$
$570$		0			0
$571$	−0.396689	−	0.551334i	−0.396689	−	0.551334i	0.565136	−	0.824997i	$-0.308824\pi$
$571$	−0.396689	−	0.551334i	−0.396689	−	0.551334i	−0.961826	+	0.273663i	$0.911765\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.982973	+	0.183750i	0.982973	+	0.183750i
$577$	1.65380	+	0.269775i	1.65380	+	0.269775i	0.914794	−	0.403921i	$-0.132353\pi$
$577$	1.65380	+	0.269775i	1.65380	+	0.269775i	0.739009	+	0.673696i	$0.235294\pi$
$578$	−2.14669	+	1.78259i	−2.14669	+	1.78259i
$579$	1.74538	+	0.0806938i	1.74538	+	0.0806938i
$580$		0			0
$581$		0			0
$582$	0.731044	−	1.38689i	0.731044	−	1.38689i
$583$		0			0
$584$	1.45890	−	0.488975i	1.45890	−	0.488975i
$585$		0			0
$586$		0			0
$587$	0.0826835	−	1.78842i	0.0826835	−	1.78842i	−0.403921	−	0.914794i	$-0.632353\pi$
$587$	0.0826835	−	1.78842i	0.0826835	−	1.78842i	0.486604	−	0.873622i	$-0.338235\pi$
$588$	0.990410	−	0.138156i	0.990410	−	0.138156i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.657405	+	1.82073i	0.657405	+	1.82073i	0.565136	+	0.824997i	$0.308824\pi$
$593$	0.657405	+	1.82073i	0.657405	+	1.82073i	0.0922684	+	0.995734i	$0.470588\pi$
$594$	−1.02490	−	0.241054i	−1.02490	−	0.241054i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.0692444	−	0.997600i	$-0.477941\pi$
$599$		0			0		−0.0692444	+	0.997600i	$0.522059\pi$
$600$	−0.824997	−	0.565136i	−0.824997	−	0.565136i
$601$	0.512381	+	0.445868i	0.512381	+	0.445868i	0.873622	−	0.486604i	$-0.161765\pi$
$601$	0.512381	+	0.445868i	0.512381	+	0.445868i	−0.361242	+	0.932472i	$0.617647\pi$
$602$		0			0
$603$	0.0441284	−	0.0136650i	0.0441284	−	0.0136650i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$607$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$608$	0.425274	+	0.686841i	0.425274	+	0.686841i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.37665	−	1.37665i	−1.37665	−	1.37665i
$613$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$613$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$614$	−1.98614	−	0.230425i	−1.98614	−	0.230425i
$615$		0			0
$616$		0			0
$617$	−1.87814	+	0.261989i	−1.87814	+	0.261989i	−0.982973	−	0.183750i	$-0.941176\pi$
$617$	−1.87814	+	0.261989i	−1.87814	+	0.261989i	−0.895163	+	0.445738i	$0.852941\pi$
$618$		0			0
$619$	−1.66450	−	0.193108i	−1.66450	−	0.193108i	−0.769334	−	0.638847i	$-0.779412\pi$
$619$	−1.66450	−	0.193108i	−1.66450	−	0.193108i	−0.895163	+	0.445738i	$0.852941\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.526432	+	0.850217i	0.526432	+	0.850217i
$626$	1.86403	+	0.348448i	1.86403	+	0.348448i
$627$	−0.413880	−	0.743058i	−0.413880	−	0.743058i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.0230979	−	0.999733i	$-0.492647\pi$
$631$		0			0		−0.0230979	+	0.999733i	$0.507353\pi$
$632$		0			0
$633$	0.227957	+	0.156154i	0.227957	+	0.156154i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.60617	+	0.377767i	−1.60617	+	0.377767i	−0.932472	−	0.361242i	$-0.882353\pi$
$641$	−1.60617	+	0.377767i	−1.60617	+	0.377767i	−0.673696	+	0.739009i	$0.735294\pi$
$642$	1.13709	+	0.944227i	1.13709	+	0.944227i
$643$	−1.06835	+	1.63958i	−1.06835	+	1.63958i	−0.361242	+	0.932472i	$0.617647\pi$
$643$	−1.06835	+	1.63958i	−1.06835	+	1.63958i	−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$		0			0
$646$	0.0726359	−	1.57109i	0.0726359	−	1.57109i
$647$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$647$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$648$	0.638847	−	0.769334i	0.638847	−	0.769334i
$649$	−1.59330	+	0.534019i	−1.59330	+	0.534019i
$650$		0			0
$651$		0			0
$652$	0.00532375	+	0.230425i	0.00532375	+	0.230425i
$653$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$653$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$654$		0			0
$655$		0			0
$656$	−0.920426	−	0.150143i	−0.920426	−	0.150143i
$657$	0.282729	−	1.51247i	0.282729	−	1.51247i
$658$		0			0
$659$	−0.200916	−	0.648818i	−0.200916	−	0.648818i	−0.998933	−	0.0461835i	$-0.985294\pi$
$659$	−0.200916	−	0.648818i	−0.200916	−	0.648818i	0.798017	−	0.602635i	$-0.205882\pi$
$660$		0			0
$661$		0			0		−0.620906	−	0.783885i	$-0.713235\pi$
$661$		0			0		0.620906	+	0.783885i	$0.286765\pi$
$662$	−1.07917	−	1.49987i	−1.07917	−	1.49987i
$663$		0			0
$664$	0.769334	+	0.361153i	0.769334	+	0.361153i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.36315	+	1.42763i	−1.36315	+	1.42763i	−0.565136	+	0.824997i	$0.691176\pi$
$673$	−1.36315	+	1.42763i	−1.36315	+	1.42763i	−0.798017	+	0.602635i	$0.794118\pi$
$674$	1.11622	−	0.621731i	1.11622	−	0.621731i
$675$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$676$	0.824997	−	0.565136i	0.824997	−	0.565136i
$677$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$677$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$678$	0.388362	−	0.446296i	0.388362	−	0.446296i
$679$		0			0
$680$		0			0
$681$	1.56087	−	0.917266i	1.56087	−	0.917266i
$682$		0			0
$683$	0.176521	−	1.26544i	0.176521	−	1.26544i	−0.673696	−	0.739009i	$-0.735294\pi$
$683$	0.176521	−	1.26544i	0.176521	−	1.26544i	0.850217	−	0.526432i	$-0.176471\pi$
$684$	0.806980	−	0.0373089i	0.806980	−	0.0373089i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.03332	+	0.544672i	1.03332	+	0.544672i
$689$		0			0
$690$		0			0
$691$	−0.447006	+	0.621267i	−0.447006	+	0.621267i	−0.973438	−	0.228951i	$-0.926471\pi$
$691$	−0.447006	+	0.621267i	−0.447006	+	0.621267i	0.526432	+	0.850217i	$0.323529\pi$
$692$		0			0
$693$		0			0
$694$	−1.11103	−	1.62190i	−1.11103	−	1.62190i
$695$		0			0
$696$		0			0
$697$	1.31316	+	1.25385i	1.31316	+	1.25385i
$698$		0			0
$699$	1.30415	+	1.49869i	1.30415	+	1.49869i
$700$		0			0
$701$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$701$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$702$		0			0
$703$		0			0
$704$	−0.334591	+	0.998285i	−0.334591	+	0.998285i
$705$		0			0
$706$	0.799375	−	1.70284i	0.799375	−	1.70284i
$707$		0			0
$708$	0.220502	−	1.58073i	0.220502	−	1.58073i
$709$		0			0		0.783885	−	0.620906i	$-0.213235\pi$
$709$		0			0		−0.783885	+	0.620906i	$0.786765\pi$
$710$		0			0
$711$		0			0
$712$	0.0159599	+	0.137566i	0.0159599	+	0.137566i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.44123	+	1.25414i	−1.44123	+	1.25414i
$717$		0			0
$718$		0			0
$719$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$719$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$720$		0			0
$721$		0			0
$722$	−0.245643	−	0.245643i	−0.245643	−	0.245643i
$723$	0.421728	+	1.16801i	0.421728	+	1.16801i
$724$		0			0
$725$		0			0
$726$	0.0392031	−	0.101195i	0.0392031	−	0.101195i
$727$		0			0		−0.837831	−	0.545930i	$-0.816176\pi$
$727$		0			0		0.837831	+	0.545930i	$0.183824\pi$
$728$		0			0
$729$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$730$		0			0
$731$	−1.06041	−	2.01175i	−1.06041	−	2.01175i
$732$		0			0
$733$		0			0		−0.506653	−	0.862150i	$-0.669118\pi$
$733$		0			0		0.506653	+	0.862150i	$0.330882\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.00783050	+	0.0480034i	0.00783050	+	0.0480034i
$738$	−0.579052	+	0.731044i	−0.579052	+	0.731044i
$739$	0.502614	+	0.0116124i	0.502614	+	0.0116124i	0.273663	−	0.961826i	$-0.411765\pi$
$739$	0.502614	+	0.0116124i	0.502614	+	0.0116124i	0.228951	+	0.973438i	$0.426471\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.955248	−	0.295806i	$-0.904412\pi$
$743$		0			0		0.955248	+	0.295806i	$0.0955882\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.689873	−	0.496369i	0.689873	−	0.496369i
$748$	1.63577	−	1.23528i	1.63577	−	1.23528i
$749$		0			0
$750$		0			0
$751$		0			0		0.115243	−	0.993337i	$-0.463235\pi$
$751$		0			0		−0.115243	+	0.993337i	$0.536765\pi$
$752$		0			0
$753$	1.60227	+	1.15285i	1.60227	+	1.15285i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$757$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$758$	1.29596	+	1.42160i	1.29596	+	1.42160i
$759$		0			0
$760$		0			0
$761$	−0.761460	+	1.11159i	−0.761460	+	1.11159i	0.228951	+	0.973438i	$0.426471\pi$
$761$	−0.761460	+	1.11159i	−0.761460	+	1.11159i	−0.990410	+	0.138156i	$0.955882\pi$
$762$		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
$769$	−1.13191	+	1.30076i	−1.13191	+	1.30076i	−0.183750	+	0.982973i	$0.558824\pi$
$769$	−1.13191	+	1.30076i	−1.13191	+	1.30076i	−0.948161	+	0.317791i	$0.897059\pi$
$770$		0			0
$771$	−1.47171	+	1.34164i	−1.47171	+	1.34164i
$772$	−1.39433	−	1.05295i	−1.39433	−	1.05295i
$773$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$773$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$774$	0.978656	−	0.637691i	0.978656	−	0.637691i
$775$		0			0
$776$	−1.38689	+	0.731044i	−1.38689	+	0.731044i
$777$		0			0
$778$		0			0
$779$	−0.751578	+	0.0521678i	−0.751578	+	0.0521678i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$785$		0			0
$786$	0.136828	−	0.291473i	0.136828	−	0.291473i
$787$	0.410060	−	1.94389i	0.410060	−	1.94389i	0.0922684	−	0.995734i	$-0.470588\pi$
$787$	0.410060	−	1.94389i	0.410060	−	1.94389i	0.317791	−	0.948161i	$-0.397059\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.709310	+	0.778076i	0.709310	+	0.778076i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$797$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$798$		0			0
$799$		0			0
$800$	0.361242	+	0.932472i	0.361242	+	0.932472i
$801$	0.127947	+	0.0529974i	0.127947	+	0.0529974i
$802$	0.941347	+	0.553195i	0.941347	+	0.553195i
$803$	1.53603	+	0.514825i	1.53603	+	0.514825i
$804$	−0.0441284	−	0.0136650i	−0.0441284	−	0.0136650i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.917266	−	0.430598i	0.917266	−	0.430598i	0.0922684	−	0.995734i	$-0.470588\pi$
$809$	0.917266	−	0.430598i	0.917266	−	0.430598i	0.824997	+	0.565136i	$0.191176\pi$
$810$		0			0
$811$	0.963876	+	1.73049i	0.963876	+	1.73049i	0.602635	+	0.798017i	$0.294118\pi$
$811$	0.963876	+	1.73049i	0.963876	+	1.73049i	0.361242	+	0.932472i	$0.382353\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.357738	+	1.91373i	0.357738	+	1.91373i
$817$	0.913326	+	0.237203i	0.913326	+	0.237203i
$818$	0.526432	+	0.149783i	0.526432	+	0.149783i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	0.486604	+	0.873622i	0.486604	+	0.873622i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	−0.334591	−	0.998285i	−0.334591	−	0.998285i
$826$		0			0
$827$	1.71245	+	0.444745i	1.71245	+	0.444745i	0.973438	−	0.228951i	$-0.0735294\pi$
$827$	1.71245	+	0.444745i	1.71245	+	0.444745i	0.739009	+	0.673696i	$0.235294\pi$
$828$		0			0
$829$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$829$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.947359	+	1.70083i	0.947359	+	1.70083i
$834$	0.0333668	+	0.721712i	0.0333668	+	0.721712i
$835$		0			0
$836$	−0.0784787	+	0.846920i	−0.0784787	+	0.846920i
$837$		0			0
$838$	−0.465346	−	0.288130i	−0.465346	−	0.288130i
$839$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$839$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$840$		0			0
$841$	−0.948161	−	0.317791i	−0.948161	−	0.317791i
$842$		0			0
$843$	1.73901	−	0.673696i	1.73901	−	0.673696i
$844$	−0.0998157	−	0.257654i	−0.0998157	−	0.257654i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.31672	+	0.994344i	1.31672	+	0.994344i
$850$	0.445738	−	1.89516i	0.445738	−	1.89516i
$851$		0			0
$852$		0			0
$853$		0			0		−0.656446	−	0.754373i	$-0.727941\pi$
$853$		0			0		0.656446	+	0.754373i	$0.272059\pi$
$854$		0			0
$855$		0			0
$856$	−0.404479	−	1.42160i	−0.404479	−	1.42160i
$857$	−0.412700	+	1.95641i	−0.412700	+	1.95641i	−0.183750	+	0.982973i	$0.558824\pi$
$857$	−0.412700	+	1.95641i	−0.412700	+	1.95641i	−0.228951	+	0.973438i	$0.573529\pi$
$858$		0			0
$859$	−1.40818	+	1.40818i	−1.40818	+	1.40818i	−0.638847	+	0.769334i	$0.720588\pi$
$859$	−1.40818	+	1.40818i	−1.40818	+	1.40818i	−0.769334	+	0.638847i	$0.779412\pi$
$860$		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	$0.875000\pi$
$864$	−0.961826	+	0.273663i	−0.961826	+	0.273663i
$865$		0			0
$866$	0.222817	+	0.947359i	0.222817	+	0.947359i
$867$	1.12707	−	2.55257i	1.12707	−	2.55257i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.0362122	+	1.56735i	−0.0362122	+	1.56735i
$874$		0			0
$875$		0			0
$876$	−1.08800	+	1.08800i	−1.08800	+	1.08800i
$877$		0			0		−0.251374	−	0.967890i	$-0.580882\pi$
$877$		0			0		0.251374	+	0.967890i	$0.419118\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.178827	+	0.956638i	−0.178827	+	0.956638i	0.769334	+	0.638847i	$0.220588\pi$
$881$	−0.178827	+	0.956638i	−0.178827	+	0.956638i	−0.948161	+	0.317791i	$0.897059\pi$
$882$	−0.824997	+	0.565136i	−0.824997	+	0.565136i
$883$	−1.05395	+	1.53857i	−1.05395	+	1.53857i	−0.228951	+	0.973438i	$0.573529\pi$
$883$	−1.05395	+	1.53857i	−1.05395	+	1.53857i	−0.824997	+	0.565136i	$0.808824\pi$
$884$		0			0
$885$		0			0
$886$	0.655647	+	0.719210i	0.655647	+	0.719210i
$887$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$887$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.02490	−	0.241054i	1.02490	−	0.241054i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.58701	+	1.08713i	1.58701	+	1.08713i
$899$		0			0
$900$	0.990410	+	0.138156i	0.990410	+	0.138156i
$901$		0			0
$902$	−0.678081	−	0.710155i	−0.678081	−	0.710155i
$903$		0			0
$904$	−0.572616	+	0.148716i	−0.572616	+	0.148716i
$905$		0			0
$906$		0			0
$907$	−0.302855	−	1.85660i	−0.302855	−	1.85660i	−0.486604	−	0.873622i	$-0.661765\pi$
$907$	−0.302855	−	1.85660i	−0.302855	−	1.85660i	0.183750	−	0.982973i	$-0.441176\pi$
$908$	−1.80609	−	0.125363i	−1.80609	−	0.125363i
$909$		0			0
$910$		0			0
$911$		0			0		−0.506653	−	0.862150i	$-0.669118\pi$
$911$		0			0		0.506653	+	0.862150i	$0.330882\pi$
$912$	−0.686841	−	0.425274i	−0.686841	−	0.425274i
$913$	0.417248	+	0.791579i	0.417248	+	0.791579i
$914$	−1.52696	+	0.551334i	−1.52696	+	0.551334i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1.84595	+	0.618701i	1.84595	+	0.618701i
$919$		0			0		0.620906	−	0.783885i	$-0.286765\pi$
$919$		0			0		−0.620906	+	0.783885i	$0.713235\pi$
$920$		0			0
$921$	1.88063	−	0.679033i	1.88063	−	0.679033i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.406040	+	0.488975i	0.406040	+	0.488975i	0.932472	−	0.361242i	$-0.117647\pi$
$929$	0.406040	+	0.488975i	0.406040	+	0.488975i	−0.526432	+	0.850217i	$0.676471\pi$
$930$		0			0
$931$	−0.786384	−	0.184956i	−0.786384	−	0.184956i
$932$	−0.228951	−	1.97344i	−0.228951	−	1.97344i
$933$		0			0
$934$	−0.0897964	+	0.161215i	−0.0897964	+	0.161215i
$935$		0			0
$936$		0			0
$937$	1.05395	−	0.408302i	1.05395	−	0.408302i	0.228951	−	0.973438i	$-0.426471\pi$
$937$	1.05395	−	0.408302i	1.05395	−	0.408302i	0.824997	+	0.565136i	$0.191176\pi$
$938$		0			0
$939$	−1.82393	+	0.518953i	−1.82393	+	0.518953i
$940$		0			0
$941$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$941$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$942$		0			0
$943$		0			0
$944$	−1.07524	+	1.17948i	−1.07524	+	1.17948i
$945$		0			0
$946$	0.522609	+	1.11327i	0.522609	+	1.11327i
$947$	1.40005	+	1.33682i	1.40005	+	1.33682i	0.873622	+	0.486604i	$0.161765\pi$
$947$	1.40005	+	1.33682i	1.40005	+	1.33682i	0.526432	+	0.850217i	$0.323529\pi$
$948$		0			0
$949$		0			0
$950$	0.456541	+	0.666468i	0.456541	+	0.666468i
$951$		0			0
$952$		0			0
$953$	0.881170	−	1.22468i	0.881170	−	1.22468i	−0.0922684	−	0.995734i	$-0.529412\pi$
$953$	0.881170	−	1.22468i	0.881170	−	1.22468i	0.973438	−	0.228951i	$-0.0735294\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.138156	+	0.990410i	−0.138156	+	0.990410i
$962$		0			0
$963$	−1.43876	−	0.338393i	−1.43876	−	0.338393i
$964$	0.312159	−	1.20194i	0.312159	−	1.20194i
$965$		0			0
$966$		0			0
$967$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$967$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$968$	−0.0895314	+	0.0613305i	−0.0895314	+	0.0613305i
$969$	0.635274	+	1.43876i	0.635274	+	1.43876i
$970$		0			0
$971$	0.754023	−	0.789689i	0.754023	−	0.789689i	−0.228951	−	0.973438i	$-0.573529\pi$
$971$	0.754023	−	0.789689i	0.754023	−	0.789689i	0.982973	+	0.183750i	$0.0588235\pi$
$972$	−0.228951	+	0.973438i	−0.228951	+	0.973438i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.630369	+	1.26595i	0.630369	+	1.26595i	0.948161	+	0.317791i	$0.102941\pi$
$977$	0.630369	+	1.26595i	0.630369	+	1.26595i	−0.317791	+	0.948161i	$0.602941\pi$
$978$	−0.107475	−	0.203895i	−0.107475	−	0.203895i
$979$	−0.0738751	+	0.125710i	−0.0738751	+	0.125710i
$980$		0			0
$981$		0			0
$982$	1.00706	+	1.39966i	1.00706	+	1.39966i
$983$		0			0		−0.620906	−	0.783885i	$-0.713235\pi$
$983$		0			0		0.620906	+	0.783885i	$0.286765\pi$
$984$	0.890856	−	0.275866i	0.890856	−	0.275866i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$991$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$992$		0			0
$993$	1.63458	+	0.861602i	1.63458	+	0.861602i
$994$		0			0
$995$		0			0
$996$	−0.849659	+	0.0196306i	−0.849659	+	0.0196306i
$997$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$997$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$998$	−0.0907942	+	1.96385i	−0.0907942	+	1.96385i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3288.1.cj.b.971.1	yes	64
3.2	odd	2		3288.1.cj.a.971.1	yes	64
8.3	odd	2	CM	3288.1.cj.b.971.1	yes	64
24.11	even	2		3288.1.cj.a.971.1	yes	64
137.80	odd	136		3288.1.cj.a.491.1	✓	64
411.80	even	136	inner	3288.1.cj.b.491.1	yes	64
1096.491	even	136		3288.1.cj.a.491.1	✓	64
3288.491	odd	136	inner	3288.1.cj.b.491.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3288.1.cj.a.491.1	✓	64	137.80	odd	136
3288.1.cj.a.491.1	✓	64	1096.491	even	136
3288.1.cj.a.971.1	yes	64	3.2	odd	2
3288.1.cj.a.971.1	yes	64	24.11	even	2
3288.1.cj.b.491.1	yes	64	411.80	even	136	inner
3288.1.cj.b.491.1	yes	64	3288.491	odd	136	inner
3288.1.cj.b.971.1	yes	64	1.1	even	1	trivial
3288.1.cj.b.971.1	yes	64	8.3	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3288 = 2^{3} \cdot 3 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3288.cj (of order \(136\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(0.990410 + 0.138156i) q^{2} +(-0.948161 + 0.317791i) q^{3} +(0.961826 + 0.273663i) q^{4} +(-0.982973 + 0.183750i) q^{6} +(0.914794 + 0.403921i) q^{8} +(0.798017 - 0.602635i) q^{9} +O(q^{10})\)	\(q+(0.990410 + 0.138156i) q^{2} +(-0.948161 + 0.317791i) q^{3} +(0.961826 + 0.273663i) q^{4} +(-0.982973 + 0.183750i) q^{6} +(0.914794 + 0.403921i) q^{8} +(0.798017 - 0.602635i) q^{9} +(0.512328 + 0.919806i) q^{11} +(-0.998933 + 0.0461835i) q^{12} +(0.850217 + 0.526432i) q^{16} +(-0.786384 - 1.78099i) q^{17} +(0.873622 - 0.486604i) q^{18} +(0.765964 + 0.256725i) q^{19} +(0.380338 + 0.981767i) q^{22} +(-0.995734 - 0.0922684i) q^{24} +(0.873622 + 0.486604i) q^{25} +(-0.565136 + 0.824997i) q^{27} +(0.769334 + 0.638847i) q^{32} +(-0.778076 - 0.709310i) q^{33} +(-0.532788 - 1.87256i) q^{34} +(0.932472 - 0.361242i) q^{36} +(0.723151 + 0.360086i) q^{38} +(-0.861602 + 0.356887i) q^{41} +(1.16528 - 0.0808832i) q^{43} +(0.241054 + 1.02490i) q^{44} +(-0.973438 - 0.228951i) q^{48} +(-0.995734 + 0.0922684i) q^{49} +(0.798017 + 0.602635i) q^{50} +(1.31160 + 1.43876i) q^{51} +(-0.673696 + 0.739009i) q^{54} -0.807842 q^{57} +(-0.293271 + 1.56886i) q^{59} +(0.673696 + 0.739009i) q^{64} +(-0.672619 - 0.810004i) q^{66} +(0.0434502 + 0.0156884i) q^{67} +(-0.268973 - 1.92821i) q^{68} +(0.973438 - 0.228951i) q^{72} +(1.13709 - 1.03659i) q^{73} +(-0.982973 - 0.183750i) q^{75} +(0.666468 + 0.456541i) q^{76} +(0.273663 - 0.961826i) q^{81} +(-0.902646 + 0.234429i) q^{82} +(0.849659 + 0.0196306i) q^{83} +(1.16528 + 0.0808832i) q^{86} +(0.0971461 + 1.04837i) q^{88} +(0.0701658 + 0.119398i) q^{89} +(-0.932472 - 0.361242i) q^{96} +(-0.973438 + 1.22895i) q^{97} +(-0.998933 - 0.0461835i) q^{98} +(0.963154 + 0.425274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{6}+O(q^{10}) \) 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

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Database

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