LMFDB - Embedded newform 3840.1.dy.a.389.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3840,1,Mod(29,3840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3840, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 59, 32, 32]))

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

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

chi := DirichletCharacter("3840.29");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3840 = 2^{8} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3840.dy (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$2$ over $\Q(\zeta_{64})$
Coefficient field:	$\Q(\zeta_{128})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{64} + 1 $ x^64 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{64}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{64} + \cdots)$

Embedding invariants

Embedding label			389.2
Root			$0.989177 + 0.146730i$ of defining polynomial
Character	$\chi$	$=$	3840.389
Dual form			3840.1.dy.a.3149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.427555 + 0.903989i) q^{2} +(-0.989177 - 0.146730i) q^{3} +(-0.634393 + 0.773010i) q^{4} +(0.0490677 - 0.998795i) q^{5} +(-0.290285 - 0.956940i) q^{6} +(-0.970031 - 0.242980i) q^{8} +(0.956940 + 0.290285i) q^{9} +O(q^{10})$	\(q+(0.427555 + 0.903989i) q^{2} +(-0.989177 - 0.146730i) q^{3} +(-0.634393 + 0.773010i) q^{4} +(0.0490677 - 0.998795i) q^{5} +(-0.290285 - 0.956940i) q^{6} +(-0.970031 - 0.242980i) q^{8} +(0.956940 + 0.290285i) q^{9} +(0.923880 - 0.382683i) q^{10} +(0.740951 - 0.671559i) q^{12} +(-0.195090 + 0.980785i) q^{15} +(-0.195090 - 0.980785i) q^{16} +(0.262029 + 1.31731i) q^{17} +(0.146730 + 0.989177i) q^{18} +(1.75380 - 0.829484i) q^{19} +(0.740951 + 0.671559i) q^{20} +(-1.45565 - 1.19462i) q^{23} +(0.923880 + 0.382683i) q^{24} +(-0.995185 - 0.0980171i) q^{25} +(-0.903989 - 0.427555i) q^{27} +(-0.970031 + 0.242980i) q^{30} +(-1.42834 - 0.591637i) q^{31} +(0.803208 - 0.595699i) q^{32} +(-1.07880 + 0.800094i) q^{34} +(-0.831470 + 0.555570i) q^{36} +(1.49969 + 1.23076i) q^{38} +(-0.290285 + 0.956940i) q^{40} +(0.336890 - 0.941544i) q^{45} +(0.457553 - 1.82665i) q^{46} +(0.892476 - 1.33569i) q^{47} +(0.0490677 + 0.998795i) q^{48} +(0.555570 + 0.831470i) q^{49} +(-0.336890 - 0.941544i) q^{50} +(-0.0659037 - 1.34150i) q^{51} +(0.229080 - 0.914539i) q^{53} -1.00000i q^{54} +(-1.85652 + 0.563170i) q^{57} +(-0.634393 - 0.773010i) q^{60} +(1.37787 - 1.02190i) q^{61} +(-0.0758597 - 1.54416i) q^{62} +(0.881921 + 0.471397i) q^{64} +(-1.18452 - 0.633141i) q^{68} +(1.26460 + 1.39528i) q^{69} +(-0.857729 - 0.514103i) q^{72} +(0.970031 + 0.242980i) q^{75} +(-0.471397 + 1.88192i) q^{76} +(0.324423 - 0.216773i) q^{79} +(-0.989177 + 0.146730i) q^{80} +(0.831470 + 0.555570i) q^{81} +(1.80200 + 0.644767i) q^{83} +(1.32858 - 0.197076i) q^{85} +(0.995185 - 0.0980171i) q^{90} +(1.84691 - 0.367372i) q^{92} +(1.32607 + 0.794814i) q^{93} +(1.58903 + 0.235710i) q^{94} +(-0.742430 - 1.79238i) q^{95} +(-0.881921 + 0.471397i) q^{96} +(-0.514103 + 0.857729i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q+O(q^{100}) $ 64 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3840\mathbb{Z}\right)^\times$.

$n$	$511$	$1537$	$2561$	$2821$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{33}{64}\right)$

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 $

$2$	0.427555	+	0.903989i	0.427555	+	0.903989i
$2$	0.427555	+	0.903989i	0.427555	+	0.903989i
$3$	−0.989177	−	0.146730i	−0.989177	−	0.146730i
$3$	−0.989177	−	0.146730i	−0.989177	−	0.146730i
$4$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$5$	0.0490677	−	0.998795i	0.0490677	−	0.998795i
$5$	0.0490677	−	0.998795i	0.0490677	−	0.998795i
$6$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$7$		0			0		−0.881921	−	0.471397i	$-0.843750\pi$
$7$		0			0		0.881921	+	0.471397i	$0.156250\pi$
$8$	−0.970031	−	0.242980i	−0.970031	−	0.242980i
$9$	0.956940	+	0.290285i	0.956940	+	0.290285i
$10$	0.923880	−	0.382683i	0.923880	−	0.382683i
$11$		0			0		0.857729	−	0.514103i	$-0.171875\pi$
$11$		0			0		−0.857729	+	0.514103i	$0.828125\pi$
$12$	0.740951	−	0.671559i	0.740951	−	0.671559i
$13$		0			0		−0.740951	−	0.671559i	$-0.765625\pi$
$13$		0			0		0.740951	+	0.671559i	$0.234375\pi$
$14$		0			0
$15$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$16$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$17$	0.262029	+	1.31731i	0.262029	+	1.31731i	0.857729	+	0.514103i	$0.171875\pi$
$17$	0.262029	+	1.31731i	0.262029	+	1.31731i	−0.595699	+	0.803208i	$0.703125\pi$
$18$	0.146730	+	0.989177i	0.146730	+	0.989177i
$19$	1.75380	−	0.829484i	1.75380	−	0.829484i	0.773010	−	0.634393i	$-0.218750\pi$
$19$	1.75380	−	0.829484i	1.75380	−	0.829484i	0.980785	−	0.195090i	$-0.0625000\pi$
$20$	0.740951	+	0.671559i	0.740951	+	0.671559i
$21$		0			0
$22$		0			0
$23$	−1.45565	−	1.19462i	−1.45565	−	1.19462i	−0.941544	−	0.336890i	$-0.890625\pi$
$23$	−1.45565	−	1.19462i	−1.45565	−	1.19462i	−0.514103	−	0.857729i	$-0.671875\pi$
$24$	0.923880	+	0.382683i	0.923880	+	0.382683i
$25$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$26$		0			0
$27$	−0.903989	−	0.427555i	−0.903989	−	0.427555i
$28$		0			0
$29$		0			0		−0.242980	−	0.970031i	$-0.578125\pi$
$29$		0			0		0.242980	+	0.970031i	$0.421875\pi$
$30$	−0.970031	+	0.242980i	−0.970031	+	0.242980i
$31$	−1.42834	−	0.591637i	−1.42834	−	0.591637i	−0.471397	−	0.881921i	$-0.656250\pi$
$31$	−1.42834	−	0.591637i	−1.42834	−	0.591637i	−0.956940	+	0.290285i	$0.906250\pi$
$32$	0.803208	−	0.595699i	0.803208	−	0.595699i
$33$		0			0
$34$	−1.07880	+	0.800094i	−1.07880	+	0.800094i
$35$		0			0
$36$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$37$		0			0		0.941544	−	0.336890i	$-0.109375\pi$
$37$		0			0		−0.941544	+	0.336890i	$0.890625\pi$
$38$	1.49969	+	1.23076i	1.49969	+	1.23076i
$39$		0			0
$40$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$41$		0			0		0.995185	−	0.0980171i	$-0.0312500\pi$
$41$		0			0		−0.995185	+	0.0980171i	$0.968750\pi$
$42$		0			0
$43$		0			0		−0.146730	−	0.989177i	$-0.546875\pi$
$43$		0			0		0.146730	+	0.989177i	$0.453125\pi$
$44$		0			0
$45$	0.336890	−	0.941544i	0.336890	−	0.941544i
$46$	0.457553	−	1.82665i	0.457553	−	1.82665i
$47$	0.892476	−	1.33569i	0.892476	−	1.33569i	−0.0490677	−	0.998795i	$-0.515625\pi$
$47$	0.892476	−	1.33569i	0.892476	−	1.33569i	0.941544	−	0.336890i	$-0.109375\pi$
$48$	0.0490677	+	0.998795i	0.0490677	+	0.998795i
$49$	0.555570	+	0.831470i	0.555570	+	0.831470i
$50$	−0.336890	−	0.941544i	−0.336890	−	0.941544i
$51$	−0.0659037	−	1.34150i	−0.0659037	−	1.34150i
$52$		0			0
$53$	0.229080	−	0.914539i	0.229080	−	0.914539i	−0.740951	−	0.671559i	$-0.765625\pi$
$53$	0.229080	−	0.914539i	0.229080	−	0.914539i	0.970031	−	0.242980i	$-0.0781250\pi$
$54$		−	1.00000i		−	1.00000i
$55$		0			0
$56$		0			0
$57$	−1.85652	+	0.563170i	−1.85652	+	0.563170i
$58$		0			0
$59$		0			0		0.740951	−	0.671559i	$-0.234375\pi$
$59$		0			0		−0.740951	+	0.671559i	$0.765625\pi$
$60$	−0.634393	−	0.773010i	−0.634393	−	0.773010i
$61$	1.37787	−	1.02190i	1.37787	−	1.02190i	0.382683	−	0.923880i	$-0.375000\pi$
$61$	1.37787	−	1.02190i	1.37787	−	1.02190i	0.995185	−	0.0980171i	$-0.0312500\pi$
$62$	−0.0758597	−	1.54416i	−0.0758597	−	1.54416i
$63$		0			0
$64$	0.881921	+	0.471397i	0.881921	+	0.471397i
$65$		0			0
$66$		0			0
$67$		0			0		−0.595699	−	0.803208i	$-0.703125\pi$
$67$		0			0		0.595699	+	0.803208i	$0.296875\pi$
$68$	−1.18452	−	0.633141i	−1.18452	−	0.633141i
$69$	1.26460	+	1.39528i	1.26460	+	1.39528i
$70$		0			0
$71$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$71$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$72$	−0.857729	−	0.514103i	−0.857729	−	0.514103i
$73$		0			0		0.881921	−	0.471397i	$-0.156250\pi$
$73$		0			0		−0.881921	+	0.471397i	$0.843750\pi$
$74$		0			0
$75$	0.970031	+	0.242980i	0.970031	+	0.242980i
$76$	−0.471397	+	1.88192i	−0.471397	+	1.88192i
$77$		0			0
$78$		0			0
$79$	0.324423	−	0.216773i	0.324423	−	0.216773i	−0.382683	−	0.923880i	$-0.625000\pi$
$79$	0.324423	−	0.216773i	0.324423	−	0.216773i	0.707107	+	0.707107i	$0.250000\pi$
$80$	−0.989177	+	0.146730i	−0.989177	+	0.146730i
$81$	0.831470	+	0.555570i	0.831470	+	0.555570i
$82$		0			0
$83$	1.80200	+	0.644767i	1.80200	+	0.644767i	0.998795	+	0.0490677i	$0.0156250\pi$
$83$	1.80200	+	0.644767i	1.80200	+	0.644767i	0.803208	+	0.595699i	$0.203125\pi$
$84$		0			0
$85$	1.32858	−	0.197076i	1.32858	−	0.197076i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.773010	−	0.634393i	$-0.218750\pi$
$89$		0			0		−0.773010	+	0.634393i	$0.781250\pi$
$90$	0.995185	−	0.0980171i	0.995185	−	0.0980171i
$91$		0			0
$92$	1.84691	−	0.367372i	1.84691	−	0.367372i
$93$	1.32607	+	0.794814i	1.32607	+	0.794814i
$94$	1.58903	+	0.235710i	1.58903	+	0.235710i
$95$	−0.742430	−	1.79238i	−0.742430	−	1.79238i
$96$	−0.881921	+	0.471397i	−0.881921	+	0.471397i
$97$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$97$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$98$	−0.514103	+	0.857729i	−0.514103	+	0.857729i
$99$		0			0
$100$	0.707107	−	0.707107i	0.707107	−	0.707107i
$101$		0			0		0.427555	−	0.903989i	$-0.359375\pi$
$101$		0			0		−0.427555	+	0.903989i	$0.640625\pi$
$102$	1.18452	−	0.633141i	1.18452	−	0.633141i
$103$		0			0		0.0980171	−	0.995185i	$-0.468750\pi$
$103$		0			0		−0.0980171	+	0.995185i	$0.531250\pi$
$104$		0			0
$105$		0			0
$106$	0.924678	−	0.183930i	0.924678	−	0.183930i
$107$	1.18566	−	1.59868i	1.18566	−	1.59868i	0.514103	−	0.857729i	$-0.328125\pi$
$107$	1.18566	−	1.59868i	1.18566	−	1.59868i	0.671559	−	0.740951i	$-0.265625\pi$
$108$	0.903989	−	0.427555i	0.903989	−	0.427555i
$109$	0.125471	+	0.265286i	0.125471	+	0.265286i	0.956940	−	0.290285i	$-0.0937500\pi$
$109$	0.125471	+	0.265286i	0.125471	+	0.265286i	−0.831470	+	0.555570i	$0.812500\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.16851	−	0.232430i	−1.16851	−	0.232430i	−0.427555	−	0.903989i	$-0.640625\pi$
$113$	−1.16851	−	0.232430i	−1.16851	−	0.232430i	−0.740951	+	0.671559i	$0.765625\pi$
$114$	−1.30287	−	1.43749i	−1.30287	−	1.43749i
$115$	−1.26460	+	1.39528i	−1.26460	+	1.39528i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.427555	−	0.903989i	0.427555	−	0.903989i
$121$	0.471397	−	0.881921i	0.471397	−	0.881921i
$122$	1.51290	+	0.808661i	1.51290	+	0.808661i
$123$		0			0
$124$	1.36347	−	0.728789i	1.36347	−	0.728789i
$125$	−0.146730	+	0.989177i	−0.146730	+	0.989177i
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−0.0490677	+	0.998795i	−0.0490677	+	0.998795i
$129$		0			0
$130$		0			0
$131$		0			0		0.146730	−	0.989177i	$-0.453125\pi$
$131$		0			0		−0.146730	+	0.989177i	$0.546875\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.471397	+	0.881921i	−0.471397	+	0.881921i
$136$	0.0659037	−	1.34150i	0.0659037	−	1.34150i
$137$	0.574286	−	1.89317i	0.574286	−	1.89317i	0.146730	−	0.989177i	$-0.453125\pi$
$137$	0.574286	−	1.89317i	0.574286	−	1.89317i	0.427555	−	0.903989i	$-0.359375\pi$
$138$	−0.720627	+	1.73975i	−0.720627	+	1.73975i
$139$	−0.929487	−	1.55075i	−0.929487	−	1.55075i	−0.831470	−	0.555570i	$-0.812500\pi$
$139$	−0.929487	−	1.55075i	−0.929487	−	1.55075i	−0.0980171	−	0.995185i	$-0.531250\pi$
$140$		0			0
$141$	−1.07880	+	1.19028i	−1.07880	+	1.19028i
$142$		0			0
$143$		0			0
$144$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$145$		0			0
$146$		0			0
$147$	−0.427555	−	0.903989i	−0.427555	−	0.903989i
$148$		0			0
$149$		0			0		0.595699	−	0.803208i	$-0.296875\pi$
$149$		0			0		−0.595699	+	0.803208i	$0.703125\pi$
$150$	0.195090	+	0.980785i	0.195090	+	0.980785i
$151$	0.368309	−	0.448786i	0.368309	−	0.448786i	−0.555570	−	0.831470i	$-0.687500\pi$
$151$	0.368309	−	0.448786i	0.368309	−	0.448786i	0.923880	+	0.382683i	$0.125000\pi$
$152$	−1.90278	+	0.378487i	−1.90278	+	0.378487i
$153$	−0.131649	+	1.33665i	−0.131649	+	1.33665i
$154$		0			0
$155$	−0.661009	+	1.39759i	−0.661009	+	1.39759i
$156$		0			0
$157$		0			0		0.970031	−	0.242980i	$-0.0781250\pi$
$157$		0			0		−0.970031	+	0.242980i	$0.921875\pi$
$158$	0.334669	+	0.200593i	0.334669	+	0.200593i
$159$	−0.360791	+	0.871028i	−0.360791	+	0.871028i
$160$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$161$		0			0
$162$	−0.146730	+	0.989177i	−0.146730	+	0.989177i
$163$		0			0		−0.857729	−	0.514103i	$-0.828125\pi$
$163$		0			0		0.857729	+	0.514103i	$0.171875\pi$
$164$		0			0
$165$		0			0
$166$	0.187593	+	1.90466i	0.187593	+	1.90466i
$167$	−1.54416	+	1.26726i	−1.54416	+	1.26726i	−0.740951	+	0.671559i	$0.765625\pi$
$167$	−1.54416	+	1.26726i	−1.54416	+	1.26726i	−0.803208	+	0.595699i	$0.796875\pi$
$168$		0			0
$169$	0.0980171	+	0.995185i	0.0980171	+	0.995185i
$170$	0.746196	+	1.11676i	0.746196	+	1.11676i
$171$	1.91906	−	0.284666i	1.91906	−	0.284666i
$172$		0			0
$173$	−0.184575	−	0.0660420i	−0.184575	−	0.0660420i	0.242980	−	0.970031i	$-0.421875\pi$
$173$	−0.184575	−	0.0660420i	−0.184575	−	0.0660420i	−0.427555	+	0.903989i	$0.640625\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.998795	−	0.0490677i	$-0.0156250\pi$
$179$		0			0		−0.998795	+	0.0490677i	$0.984375\pi$
$180$	0.514103	+	0.857729i	0.514103	+	0.857729i
$181$	−0.0951944	−	0.0238449i	−0.0951944	−	0.0238449i	0.195090	−	0.980785i	$-0.437500\pi$
$181$	−0.0951944	−	0.0238449i	−0.0951944	−	0.0238449i	−0.290285	+	0.956940i	$0.593750\pi$
$182$		0			0
$183$	−1.51290	+	0.808661i	−1.51290	+	0.808661i
$184$	1.12175	+	1.51251i	1.12175	+	1.51251i
$185$		0			0
$186$	−0.151537	+	1.53858i	−0.151537	+	1.53858i
$187$		0			0
$188$	0.466318	+	1.53724i	0.466318	+	1.53724i
$189$		0			0
$190$	1.30287	−	1.43749i	1.30287	−	1.43749i
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	−0.803208	−	0.595699i	−0.803208	−	0.595699i
$193$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$193$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$194$		0			0
$195$		0			0
$196$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$197$	0.823301	−	0.746196i	0.823301	−	0.746196i	−0.146730	−	0.989177i	$-0.546875\pi$
$197$	0.823301	−	0.746196i	0.823301	−	0.746196i	0.970031	+	0.242980i	$0.0781250\pi$
$198$		0			0
$199$	−1.59133	+	0.482726i	−1.59133	+	0.482726i	−0.956940	−	0.290285i	$-0.906250\pi$
$199$	−1.59133	+	0.482726i	−1.59133	+	0.482726i	−0.634393	+	0.773010i	$0.718750\pi$
$200$	0.941544	+	0.336890i	0.941544	+	0.336890i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	1.07880	+	0.800094i	1.07880	+	0.800094i
$205$		0			0
$206$		0			0
$207$	−1.04619	−	1.56573i	−1.04619	−	1.56573i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.0988640	−	0.276306i	0.0988640	−	0.276306i	−0.881921	−	0.471397i	$-0.843750\pi$
$211$	0.0988640	−	0.276306i	0.0988640	−	0.276306i	0.980785	+	0.195090i	$0.0625000\pi$
$212$	0.561621	+	0.757259i	0.561621	+	0.757259i
$213$		0			0
$214$	1.95213	+	0.388302i	1.95213	+	0.388302i
$215$		0			0
$216$	0.773010	+	0.634393i	0.773010	+	0.634393i
$217$		0			0
$218$	−0.186170	+	0.226848i	−0.186170	+	0.226848i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$223$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$224$		0			0
$225$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$226$	−0.289486	−	1.15569i	−0.289486	−	1.15569i
$227$	0.428579	+	1.71098i	0.428579	+	1.71098i	0.671559	+	0.740951i	$0.265625\pi$
$227$	0.428579	+	1.71098i	0.428579	+	1.71098i	−0.242980	+	0.970031i	$0.578125\pi$
$228$	0.742430	−	1.79238i	0.742430	−	1.79238i
$229$	−0.773010	−	0.365607i	−0.773010	−	0.365607i		−	1.00000i	$-0.5\pi$
$229$	−0.773010	−	0.365607i	−0.773010	−	0.365607i	−0.773010	+	0.634393i	$0.781250\pi$
$230$	−1.80200	−	0.546632i	−1.80200	−	0.546632i
$231$		0			0
$232$		0			0
$233$	0.661009	+	0.542476i	0.661009	+	0.542476i	0.903989	−	0.427555i	$-0.140625\pi$
$233$	0.661009	+	0.542476i	0.661009	+	0.542476i	−0.242980	+	0.970031i	$0.578125\pi$
$234$		0			0
$235$	−1.29028	−	0.956940i	−1.29028	−	0.956940i
$236$		0			0
$237$	−0.352719	+	0.166824i	−0.352719	+	0.166824i
$238$		0			0
$239$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$239$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$240$	1.00000			1.00000
$241$	0.247528	−	1.24441i	0.247528	−	1.24441i	−0.634393	−	0.773010i	$-0.718750\pi$
$241$	0.247528	−	1.24441i	0.247528	−	1.24441i	0.881921	−	0.471397i	$-0.156250\pi$
$242$	0.998795	+	0.0490677i	0.998795	+	0.0490677i
$243$	−0.740951	−	0.671559i	−0.740951	−	0.671559i
$244$	−0.0841735	+	1.71339i	−0.0841735	+	1.71339i
$245$	0.857729	−	0.514103i	0.857729	−	0.514103i
$246$		0			0
$247$		0			0
$248$	1.24178	+	0.920964i	1.24178	+	0.920964i
$249$	−1.68789	−	0.902197i	−1.68789	−	0.902197i
$250$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$251$		0			0		0.0490677	−	0.998795i	$-0.484375\pi$
$251$		0			0		−0.0490677	+	0.998795i	$0.515625\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−1.34312			−1.34312
$256$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$257$	−0.673780			−0.673780			−0.336890	−	0.941544i	$-0.609375\pi$
$257$	−0.673780			−0.673780			−0.336890	+	0.941544i	$0.609375\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.30692	+	0.698564i	1.30692	+	0.698564i	0.970031	−	0.242980i	$-0.0781250\pi$
$263$	1.30692	+	0.698564i	1.30692	+	0.698564i	0.336890	+	0.941544i	$0.390625\pi$
$264$		0			0
$265$	−0.902197	−	0.273678i	−0.902197	−	0.273678i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.740951	−	0.671559i	$-0.765625\pi$
$269$		0			0		0.740951	+	0.671559i	$0.234375\pi$
$270$	−0.998795	−	0.0490677i	−0.998795	−	0.0490677i
$271$	−0.360480	+	1.81225i	−0.360480	+	1.81225i	0.195090	+	0.980785i	$0.437500\pi$
$271$	−0.360480	+	1.81225i	−0.360480	+	1.81225i	−0.555570	+	0.831470i	$0.687500\pi$
$272$	1.24088	−	0.513989i	1.24088	−	0.513989i
$273$		0			0
$274$	1.95694	−	0.290285i	1.95694	−	0.290285i
$275$		0			0
$276$	−1.88082	+	0.0923988i	−1.88082	+	0.0923988i
$277$		0			0		−0.803208	−	0.595699i	$-0.796875\pi$
$277$		0			0		0.803208	+	0.595699i	$0.203125\pi$
$278$	1.00446	−	1.50328i	1.00446	−	1.50328i
$279$	−1.19509	−	0.980785i	−1.19509	−	0.980785i
$280$		0			0
$281$		0			0		−0.995185	−	0.0980171i	$-0.968750\pi$
$281$		0			0		0.995185	+	0.0980171i	$0.0312500\pi$
$282$	−1.53724	−	0.466318i	−1.53724	−	0.466318i
$283$		0			0		−0.903989	−	0.427555i	$-0.859375\pi$
$283$		0			0		0.903989	+	0.427555i	$0.140625\pi$
$284$		0			0
$285$	0.471397	+	1.88192i	0.471397	+	1.88192i
$286$		0			0
$287$		0			0
$288$	0.941544	−	0.336890i	0.941544	−	0.336890i
$289$	−0.742767	+	0.307664i	−0.742767	+	0.307664i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.80200	−	0.644767i	1.80200	−	0.644767i	0.803208	−	0.595699i	$-0.203125\pi$
$293$	1.80200	−	0.644767i	1.80200	−	0.644767i	0.998795	−	0.0490677i	$-0.0156250\pi$
$294$	0.634393	−	0.773010i	0.634393	−	0.773010i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.803208	+	0.595699i	−0.803208	+	0.595699i
$301$		0			0
$302$	0.563170	+	0.141067i	0.563170	+	0.141067i
$303$		0			0
$304$	−1.15569	−	1.55827i	−1.15569	−	1.55827i
$305$	−0.953057	−	1.42635i	−0.953057	−	1.42635i
$306$	−1.26460	+	0.452483i	−1.26460	+	0.452483i
$307$		0			0		−0.0490677	−	0.998795i	$-0.515625\pi$
$307$		0			0		0.0490677	+	0.998795i	$0.484375\pi$
$308$		0			0
$309$		0			0
$310$	−1.54602			−1.54602
$311$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$311$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$312$		0			0
$313$		0			0		0.956940	−	0.290285i	$-0.0937500\pi$
$313$		0			0		−0.956940	+	0.290285i	$0.906250\pi$
$314$		0			0
$315$		0			0
$316$	−0.0382444	+	0.388302i	−0.0382444	+	0.388302i
$317$	−1.57555	+	1.16851i	−1.57555	+	1.16851i	−0.671559	+	0.740951i	$0.734375\pi$
$317$	−1.57555	+	1.16851i	−1.57555	+	1.16851i	−0.903989	+	0.427555i	$0.859375\pi$
$318$	−0.941658	+	0.0462607i	−0.941658	+	0.0462607i
$319$		0			0
$320$	0.514103	−	0.857729i	0.514103	−	0.857729i
$321$	−1.40740	+	1.40740i	−1.40740	+	1.40740i
$322$		0			0
$323$	1.55223	+	2.09294i	1.55223	+	2.09294i
$324$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$325$		0			0
$326$		0			0
$327$	−0.0851872	−	0.280825i	−0.0851872	−	0.280825i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.93773	−	0.485375i	−1.93773	−	0.485375i	−0.980785	−	0.195090i	$-0.937500\pi$
$331$	−1.93773	−	0.485375i	−1.93773	−	0.485375i	−0.956940	−	0.290285i	$-0.906250\pi$
$332$	−1.64159	+	0.983931i	−1.64159	+	0.983931i
$333$		0			0
$334$	−1.80580	−	0.854080i	−1.80580	−	0.854080i
$335$		0			0
$336$		0			0
$337$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$337$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$338$	−0.857729	+	0.514103i	−0.857729	+	0.514103i
$339$	1.12175	+	0.401370i	1.12175	+	0.401370i
$340$	−0.690501	+	1.15203i	−0.690501	+	1.15203i
$341$		0			0
$342$	1.07784	+	1.61310i	1.07784	+	1.61310i
$343$		0			0
$344$		0			0
$345$	1.45565	−	1.19462i	1.45565	−	1.19462i
$346$	−0.0192147	−	0.195090i	−0.0192147	−	0.195090i
$347$	0.660833	+	1.84691i	0.660833	+	1.84691i	0.514103	+	0.857729i	$0.328125\pi$
$347$	0.660833	+	1.84691i	0.660833	+	1.84691i	0.146730	+	0.989177i	$0.453125\pi$
$348$		0			0
$349$	−0.416822	−	0.249834i	−0.416822	−	0.249834i	0.290285	−	0.956940i	$-0.406250\pi$
$349$	−0.416822	−	0.249834i	−0.416822	−	0.249834i	−0.707107	+	0.707107i	$0.750000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.393477	+	0.949938i	−0.393477	+	0.949938i	0.595699	+	0.803208i	$0.296875\pi$
$353$	−0.393477	+	0.949938i	−0.393477	+	0.949938i	−0.989177	+	0.146730i	$0.953125\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.0980171	−	0.995185i	$-0.468750\pi$
$359$		0			0		−0.0980171	+	0.995185i	$0.531250\pi$
$360$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$361$	1.75336	−	2.13648i	1.75336	−	2.13648i
$362$	−0.0191453	−	0.0962497i	−0.0191453	−	0.0962497i
$363$	−0.595699	+	0.803208i	−0.595699	+	0.803208i
$364$		0			0
$365$		0			0
$366$	−1.37787	−	1.02190i	−1.37787	−	1.02190i
$367$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$367$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$368$	−0.887682	+	1.66074i	−0.887682	+	1.66074i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−1.45565	+	0.520839i	−1.45565	+	0.520839i
$373$		0			0		−0.514103	−	0.857729i	$-0.671875\pi$
$373$		0			0		0.514103	+	0.857729i	$0.328125\pi$
$374$		0			0
$375$	0.290285	−	0.956940i	0.290285	−	0.956940i
$376$	−1.19028	+	1.07880i	−1.19028	+	1.07880i
$377$		0			0
$378$		0			0
$379$	0.0980171	+	0.00481527i	0.0980171	+	0.00481527i	0.0980171	−	0.995185i	$-0.468750\pi$
$379$	0.0980171	+	0.00481527i	0.0980171	+	0.00481527i			1.00000i	$0.5\pi$
$380$	1.85652	+	0.563170i	1.85652	+	0.563170i
$381$		0			0
$382$		0			0
$383$			1.02821i			1.02821i	0.857729	+	0.514103i	$0.171875\pi$
$383$			1.02821i			1.02821i	−0.857729	+	0.514103i	$0.828125\pi$
$384$	0.195090	−	0.980785i	0.195090	−	0.980785i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.998795	−	0.0490677i	$-0.984375\pi$
$389$		0			0		0.998795	+	0.0490677i	$0.0156250\pi$
$390$		0			0
$391$	1.19226	−	2.23056i	1.19226	−	2.23056i
$392$	−0.336890	−	0.941544i	−0.336890	−	0.941544i
$393$		0			0
$394$	1.02656	+	0.425215i	1.02656	+	0.425215i
$395$	−0.200593	−	0.334669i	−0.200593	−	0.334669i
$396$		0			0
$397$		0			0		0.671559	−	0.740951i	$-0.265625\pi$
$397$		0			0		−0.671559	+	0.740951i	$0.734375\pi$
$398$	−1.11676	−	1.23216i	−1.11676	−	1.23216i
$399$		0			0
$400$	0.0980171	+	0.995185i	0.0980171	+	0.995185i
$401$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$401$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.595699	−	0.803208i	0.595699	−	0.803208i
$406$		0			0
$407$		0			0
$408$	−0.262029	+	1.31731i	−0.262029	+	1.31731i
$409$	−0.0569057	+	0.577774i	−0.0569057	+	0.577774i	0.923880	+	0.382683i	$0.125000\pi$
$409$	−0.0569057	+	0.577774i	−0.0569057	+	0.577774i	−0.980785	+	0.195090i	$0.937500\pi$
$410$		0			0
$411$	−0.845855	+	1.78841i	−0.845855	+	1.78841i
$412$		0			0
$413$		0			0
$414$	0.968101	−	1.61518i	0.968101	−	1.61518i
$415$	0.732410	−	1.76820i	0.732410	−	1.76820i
$416$		0			0
$417$	0.691883	+	1.67035i	0.691883	+	1.67035i
$418$		0			0
$419$		0			0		−0.857729	−	0.514103i	$-0.828125\pi$
$419$		0			0		0.857729	+	0.514103i	$0.171875\pi$
$420$		0			0
$421$	−0.609090	−	1.70229i	−0.609090	−	1.70229i	−0.707107	−	0.707107i	$-0.750000\pi$
$421$	−0.609090	−	1.70229i	−0.609090	−	1.70229i	0.0980171	−	0.995185i	$-0.468750\pi$
$422$	0.292048	−	0.0287642i	0.292048	−	0.0287642i
$423$	1.24178	−	1.01910i	1.24178	−	1.01910i
$424$	−0.444430	+	0.831470i	−0.444430	+	0.831470i
$425$	−0.131649	−	1.33665i	−0.131649	−	1.33665i
$426$		0			0
$427$		0			0
$428$	0.483620	+	1.93072i	0.483620	+	1.93072i
$429$		0			0
$430$		0			0
$431$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$431$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$432$	−0.242980	+	0.970031i	−0.242980	+	0.970031i
$433$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$433$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$434$		0			0
$435$		0			0
$436$	−0.284666	−	0.0713052i	−0.284666	−	0.0713052i
$437$	−3.54382	−	0.887682i	−3.54382	−	0.887682i
$438$		0			0
$439$	−0.979938	+	0.523788i	−0.979938	+	0.523788i	−0.881921	−	0.471397i	$-0.843750\pi$
$439$	−0.979938	+	0.523788i	−0.979938	+	0.523788i	−0.0980171	+	0.995185i	$0.531250\pi$
$440$		0			0
$441$	0.290285	+	0.956940i	0.290285	+	0.956940i
$442$		0			0
$443$	−0.852065	−	0.940109i	−0.852065	−	0.940109i	0.146730	−	0.989177i	$-0.453125\pi$
$443$	−0.852065	−	0.940109i	−0.852065	−	0.940109i	−0.998795	+	0.0490677i	$0.984375\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$449$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$450$	−0.0490677	−	0.998795i	−0.0490677	−	0.998795i
$451$		0			0
$452$	0.920964	−	0.755815i	0.920964	−	0.755815i
$453$	−0.430174	+	0.389887i	−0.430174	+	0.389887i
$454$	−1.36347	+	1.11897i	−1.36347	+	1.11897i
$455$		0			0
$456$	1.93773	−	0.0951944i	1.93773	−	0.0951944i
$457$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$457$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$458$		−	0.855110i		−	0.855110i
$459$	0.326351	−	1.30287i	0.326351	−	1.30287i
$460$	−0.276306	−	1.86271i	−0.276306	−	1.86271i
$461$		0			0		−0.0490677	−	0.998795i	$-0.515625\pi$
$461$		0			0		0.0490677	+	0.998795i	$0.484375\pi$
$462$		0			0
$463$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$463$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$464$		0			0
$465$	0.858923	−	1.28547i	0.858923	−	1.28547i
$466$	−0.207775	+	0.829484i	−0.207775	+	0.829484i
$467$	−0.374332	+	1.04619i	−0.374332	+	1.04619i	0.595699	+	0.803208i	$0.296875\pi$
$467$	−0.374332	+	1.04619i	−0.374332	+	1.04619i	−0.970031	+	0.242980i	$0.921875\pi$
$468$		0			0
$469$		0			0
$470$	0.313396	−	1.57555i	0.313396	−	1.57555i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−0.301614	−	0.247528i	−0.301614	−	0.247528i
$475$	−1.82665	+	0.653587i	−1.82665	+	0.653587i
$476$		0			0
$477$	0.484693	−	0.808661i	0.484693	−	0.808661i
$478$		0			0
$479$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$479$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$480$	0.427555	+	0.903989i	0.427555	+	0.903989i
$481$		0			0
$482$	1.23076	−	0.308290i	1.23076	−	0.308290i
$483$		0			0
$484$	0.382683	+	0.923880i	0.382683	+	0.923880i
$485$		0			0
$486$	0.290285	−	0.956940i	0.290285	−	0.956940i
$487$		0			0		−0.995185	−	0.0980171i	$-0.968750\pi$
$487$		0			0		0.995185	+	0.0980171i	$0.0312500\pi$
$488$	−1.58488	+	0.656477i	−1.58488	+	0.656477i
$489$		0			0
$490$	0.831470	+	0.555570i	0.831470	+	0.555570i
$491$		0			0		−0.803208	−	0.595699i	$-0.796875\pi$
$491$		0			0		0.803208	+	0.595699i	$0.203125\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.301614	+	1.51631i	−0.301614	+	1.51631i
$497$		0			0
$498$	0.0939097	−	1.91158i	0.0939097	−	1.91158i
$499$	−0.633595	−	0.574257i	−0.633595	−	0.574257i	0.290285	−	0.956940i	$-0.406250\pi$
$499$	−0.633595	−	0.574257i	−0.633595	−	0.574257i	−0.923880	+	0.382683i	$0.875000\pi$
$500$	−0.671559	−	0.740951i	−0.671559	−	0.740951i
$501$	1.71339	−	1.02697i	1.71339	−	1.02697i
$502$		0			0
$503$	1.89317	+	0.574286i	1.89317	+	0.574286i	0.989177	+	0.146730i	$0.0468750\pi$
$503$	1.89317	+	0.574286i	1.89317	+	0.574286i	0.903989	+	0.427555i	$0.140625\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.0490677	−	0.998795i	0.0490677	−	0.998795i
$508$		0			0
$509$		0			0		−0.989177	−	0.146730i	$-0.953125\pi$
$509$		0			0		0.989177	+	0.146730i	$0.0468750\pi$
$510$	−0.574257	−	1.21416i	−0.574257	−	1.21416i
$511$		0			0
$512$	−0.740951	−	0.671559i	−0.740951	−	0.671559i
$513$	−1.94006			−1.94006
$514$	−0.288078	−	0.609090i	−0.288078	−	0.609090i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.172887	+	0.0924099i	0.172887	+	0.0924099i
$520$		0			0
$521$		0			0		−0.956940	−	0.290285i	$-0.906250\pi$
$521$		0			0		0.956940	+	0.290285i	$0.0937500\pi$
$522$		0			0
$523$		0			0		0.857729	−	0.514103i	$-0.171875\pi$
$523$		0			0		−0.857729	+	0.514103i	$0.828125\pi$
$524$		0			0
$525$		0			0
$526$	−0.0727135	+	1.48012i	−0.0727135	+	1.48012i
$527$	0.405103	−	2.03659i	0.405103	−	2.03659i
$528$		0			0
$529$	0.496704	+	2.49710i	0.496704	+	2.49710i
$530$	−0.138337	−	0.932589i	−0.138337	−	0.932589i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−1.53858	−	1.26268i	−1.53858	−	1.26268i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$541$	0.485375	+	1.93773i	0.485375	+	1.93773i	0.290285	+	0.956940i	$0.406250\pi$
$541$	0.485375	+	1.93773i	0.485375	+	1.93773i	0.195090	+	0.980785i	$0.437500\pi$
$542$	−1.79238	+	0.448969i	−1.79238	+	0.448969i
$543$	0.0906652	+	0.0375548i	0.0906652	+	0.0375548i
$544$	0.995185	+	0.901983i	0.995185	+	0.901983i
$545$	0.271123	−	0.112303i	0.271123	−	0.112303i
$546$		0			0
$547$		0			0		0.514103	−	0.857729i	$-0.328125\pi$
$547$		0			0		−0.514103	+	0.857729i	$0.671875\pi$
$548$	1.09911	+	1.64494i	1.09911	+	1.64494i
$549$	1.61518	−	0.577920i	1.61518	−	0.577920i
$550$		0			0
$551$		0			0
$552$	−0.887682	−	1.66074i	−0.887682	−	1.66074i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.78841	+	0.265286i	1.78841	+	0.265286i
$557$	−0.195588	+	0.546632i	−0.195588	+	0.546632i	−0.998795	−	0.0490677i	$-0.984375\pi$
$557$	−0.195588	+	0.546632i	−0.195588	+	0.546632i	0.803208	+	0.595699i	$0.203125\pi$
$558$	0.375652	−	1.49969i	0.375652	−	1.49969i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.0545211	−	1.10980i	−0.0545211	−	1.10980i	−0.857729	−	0.514103i	$-0.828125\pi$
$563$	−0.0545211	−	1.10980i	−0.0545211	−	1.10980i	0.803208	−	0.595699i	$-0.203125\pi$
$564$	−0.235710	−	1.58903i	−0.235710	−	1.58903i
$565$	−0.289486	+	1.15569i	−0.289486	+	1.15569i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.956940	−	0.290285i	$-0.0937500\pi$
$569$		0			0		−0.956940	+	0.290285i	$0.906250\pi$
$570$	−1.49969	+	1.23076i	−1.49969	+	1.23076i
$571$	0.499238	−	0.452483i	0.499238	−	0.452483i	−0.382683	−	0.923880i	$-0.625000\pi$
$571$	0.499238	−	0.452483i	0.499238	−	0.452483i	0.881921	+	0.471397i	$0.156250\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.33154	+	1.33154i	1.33154	+	1.33154i
$576$	0.707107	+	0.707107i	0.707107	+	0.707107i
$577$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$577$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$578$	−0.595699	−	0.539910i	−0.595699	−	0.539910i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	1.35332	+	1.35332i	1.35332	+	1.35332i
$587$	0.190159	+	0.0476324i	0.190159	+	0.0476324i	0.336890	−	0.941544i	$-0.390625\pi$
$587$	0.190159	+	0.0476324i	0.190159	+	0.0476324i	−0.146730	+	0.989177i	$0.546875\pi$
$588$	0.970031	+	0.242980i	0.970031	+	0.242980i
$589$	−2.99576	+	0.147172i	−2.99576	+	0.147172i
$590$		0			0
$591$	−0.923880	+	0.617317i	−0.923880	+	0.617317i
$592$		0			0
$593$	−1.50328	−	1.00446i	−1.50328	−	1.00446i	−0.989177	−	0.146730i	$-0.953125\pi$
$593$	−1.50328	−	1.00446i	−1.50328	−	1.00446i	−0.514103	−	0.857729i	$-0.671875\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.64494	−	0.244004i	1.64494	−	0.244004i
$598$		0			0
$599$		0			0		−0.0980171	−	0.995185i	$-0.531250\pi$
$599$		0			0		0.0980171	+	0.995185i	$0.468750\pi$
$600$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$601$	−0.448786	+	0.368309i	−0.448786	+	0.368309i	−0.831470	−	0.555570i	$-0.812500\pi$
$601$	−0.448786	+	0.368309i	−0.448786	+	0.368309i	0.382683	+	0.923880i	$0.375000\pi$
$602$		0			0
$603$		0			0
$604$	0.113263	+	0.569414i	0.113263	+	0.569414i
$605$	−0.857729	−	0.514103i	−0.857729	−	0.514103i
$606$		0			0
$607$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$607$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$608$	0.914539	−	1.71098i	0.914539	−	1.71098i
$609$		0			0
$610$	0.881921	−	1.47140i	0.881921	−	1.47140i
$611$		0			0
$612$	−0.949728	−	0.949728i	−0.949728	−	0.949728i
$613$		0			0		0.427555	−	0.903989i	$-0.359375\pi$
$613$		0			0		−0.427555	+	0.903989i	$0.640625\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.01910	+	1.24178i	−1.01910	+	1.24178i	−0.0490677	+	0.998795i	$0.515625\pi$
$617$	−1.01910	+	1.24178i	−1.01910	+	1.24178i	−0.970031	+	0.242980i	$0.921875\pi$
$618$		0			0
$619$	−1.17850	+	1.58903i	−1.17850	+	1.58903i	−0.471397	+	0.881921i	$0.656250\pi$
$619$	−1.17850	+	1.58903i	−1.17850	+	1.58903i	−0.707107	+	0.707107i	$0.750000\pi$
$620$	−0.661009	−	1.39759i	−0.661009	−	1.39759i
$621$	0.805124	+	1.70229i	0.805124	+	1.70229i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.980785	+	0.195090i	0.980785	+	0.195090i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.222174	−	0.732410i	0.222174	−	0.732410i	−0.773010	−	0.634393i	$-0.781250\pi$
$631$	0.222174	−	0.732410i	0.222174	−	0.732410i	0.995185	−	0.0980171i	$-0.0312500\pi$
$632$	−0.367372	+	0.131448i	−0.367372	+	0.131448i
$633$	−0.138337	+	0.258809i	−0.138337	+	0.258809i
$634$	−1.72995	−	0.924678i	−1.72995	−	0.924678i
$635$		0			0
$636$	−0.444430	−	0.831470i	−0.444430	−	0.831470i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.995185	+	0.0980171i	0.995185	+	0.0980171i
$641$		0			0			−	1.00000i	$-0.5\pi$
$641$		0			0				1.00000i	$0.5\pi$
$642$	−1.87402	−	0.670535i	−1.87402	−	0.670535i
$643$		0			0		0.146730	−	0.989177i	$-0.453125\pi$
$643$		0			0		−0.146730	+	0.989177i	$0.546875\pi$
$644$		0			0
$645$		0			0
$646$	−1.22833	+	2.29805i	−1.22833	+	2.29805i
$647$	−0.229080	+	0.428579i	−0.229080	+	0.428579i	−0.970031	−	0.242980i	$-0.921875\pi$
$647$	−0.229080	+	0.428579i	−0.229080	+	0.428579i	0.740951	+	0.671559i	$0.234375\pi$
$648$	−0.671559	−	0.740951i	−0.671559	−	0.740951i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.33665	−	1.47477i	1.33665	−	1.47477i	0.595699	−	0.803208i	$-0.296875\pi$
$653$	1.33665	−	1.47477i	1.33665	−	1.47477i	0.740951	−	0.671559i	$-0.234375\pi$
$654$	0.217440	−	0.197076i	0.217440	−	0.197076i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.427555	−	0.903989i	$-0.640625\pi$
$659$		0			0		0.427555	+	0.903989i	$0.359375\pi$
$660$		0			0
$661$	1.17850	−	1.58903i	1.17850	−	1.58903i	0.471397	−	0.881921i	$-0.343750\pi$
$661$	1.17850	−	1.58903i	1.17850	−	1.58903i	0.707107	−	0.707107i	$-0.250000\pi$
$662$	−0.389711	−	1.95921i	−0.389711	−	1.95921i
$663$		0			0
$664$	−1.59133	−	1.06330i	−1.59133	−	1.06330i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		−	1.99759i		−	1.99759i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$673$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$674$		0			0
$675$	0.857729	+	0.514103i	0.857729	+	0.514103i
$676$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$677$	0.427441	+	1.19462i	0.427441	+	1.19462i	0.941544	+	0.336890i	$0.109375\pi$
$677$	0.427441	+	1.19462i	0.427441	+	1.19462i	−0.514103	+	0.857729i	$0.671875\pi$
$678$	0.116777	+	1.18566i	0.116777	+	1.18566i
$679$		0			0
$680$	−1.33665	−	0.131649i	−1.33665	−	0.131649i
$681$	−0.172887	−	1.75535i	−0.172887	−	1.75535i
$682$		0			0
$683$	−0.385958	+	0.0572514i	−0.385958	+	0.0572514i	−0.336890	−	0.941544i	$-0.609375\pi$
$683$	−0.385958	+	0.0572514i	−0.385958	+	0.0572514i	−0.0490677	+	0.998795i	$0.515625\pi$
$684$	−0.997391	+	1.66405i	−0.997391	+	1.66405i
$685$	−1.86271	−	0.666487i	−1.86271	−	0.666487i
$686$		0			0
$687$	0.710998	+	0.475074i	0.710998	+	0.475074i
$688$		0			0
$689$		0			0
$690$	1.70229	+	0.805124i	1.70229	+	0.805124i
$691$	0.0980171	−	0.00481527i	0.0980171	−	0.00481527i		−	1.00000i	$-0.5\pi$
$691$	0.0980171	−	0.00481527i	0.0980171	−	0.00481527i	0.0980171	+	0.995185i	$0.468750\pi$
$692$	0.168144	−	0.100782i	0.168144	−	0.100782i
$693$		0			0
$694$	−1.38704	+	1.38704i	−1.38704	+	1.38704i
$695$	−1.59449	+	0.852275i	−1.59449	+	0.852275i
$696$		0			0
$697$		0			0
$698$	0.0476324	−	0.483620i	0.0476324	−	0.483620i
$699$	−0.574257	−	0.633595i	−0.574257	−	0.633595i
$700$		0			0
$701$		0			0		−0.595699	−	0.803208i	$-0.703125\pi$
$701$		0			0		0.595699	+	0.803208i	$0.296875\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	1.13591	+	1.13591i	1.13591	+	1.13591i
$706$	−1.02697	+	0.0504517i	−1.02697	+	0.0504517i
$707$		0			0
$708$		0			0
$709$	0.360073	−	0.326351i	0.360073	−	0.326351i	−0.471397	−	0.881921i	$-0.656250\pi$
$709$	0.360073	−	0.326351i	0.360073	−	0.326351i	0.831470	+	0.555570i	$0.187500\pi$
$710$		0			0
$711$	0.373380	−	0.113263i	0.373380	−	0.113263i
$712$		0			0
$713$	1.37237	+	2.56753i	1.37237	+	2.56753i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$719$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$720$	−0.989177	−	0.146730i	−0.989177	−	0.146730i
$721$		0			0
$722$	2.68101	+	0.671559i	2.68101	+	0.671559i
$723$	−0.427441	+	1.19462i	−0.427441	+	1.19462i
$724$	0.0788231	−	0.0584592i	0.0788231	−	0.0584592i
$725$		0			0
$726$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$727$		0			0		0.995185	−	0.0980171i	$-0.0312500\pi$
$727$		0			0		−0.995185	+	0.0980171i	$0.968750\pi$
$728$		0			0
$729$	0.634393	+	0.773010i	0.634393	+	0.773010i
$730$		0			0
$731$		0			0
$732$	0.334669	−	1.68250i	0.334669	−	1.68250i
$733$		0			0		0.514103	−	0.857729i	$-0.328125\pi$
$733$		0			0		−0.514103	+	0.857729i	$0.671875\pi$
$734$		0			0
$735$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$736$	−1.88082	−	0.0923988i	−1.88082	−	0.0923988i
$737$		0			0
$738$		0			0
$739$	−0.289486	−	1.15569i	−0.289486	−	1.15569i	−0.923880	−	0.382683i	$-0.875000\pi$
$739$	−0.289486	−	1.15569i	−0.289486	−	1.15569i	0.634393	−	0.773010i	$-0.281250\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.02325	+	0.100782i	1.02325	+	0.100782i	0.595699	−	0.803208i	$-0.296875\pi$
$743$	1.02325	+	0.100782i	1.02325	+	0.100782i	0.427555	+	0.903989i	$0.359375\pi$
$744$	−1.09320	−	1.09320i	−1.09320	−	1.09320i
$745$		0			0
$746$		0			0
$747$	1.53724	+	1.14010i	1.53724	+	1.14010i
$748$		0			0
$749$		0			0
$750$	0.989177	−	0.146730i	0.989177	−	0.146730i
$751$	0.388302	+	1.95213i	0.388302	+	1.95213i	0.290285	+	0.956940i	$0.406250\pi$
$751$	0.388302	+	1.95213i	0.388302	+	1.95213i	0.0980171	+	0.995185i	$0.468750\pi$
$752$	−1.48413	−	0.614748i	−1.48413	−	0.614748i
$753$		0			0
$754$		0			0
$755$	−0.430174	−	0.389887i	−0.430174	−	0.389887i
$756$		0			0
$757$		0			0		0.857729	−	0.514103i	$-0.171875\pi$
$757$		0			0		−0.857729	+	0.514103i	$0.828125\pi$
$758$	0.0375548	+	0.0906652i	0.0375548	+	0.0906652i
$759$		0			0
$760$	0.284666	+	1.91906i	0.284666	+	1.91906i
$761$		0			0		−0.881921	−	0.471397i	$-0.843750\pi$
$761$		0			0		0.881921	+	0.471397i	$0.156250\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.32858	+	0.197076i	1.32858	+	0.197076i
$766$	−0.929487	+	0.439614i	−0.929487	+	0.439614i
$767$		0			0
$768$	0.970031	−	0.242980i	0.970031	−	0.242980i
$769$	1.99037			1.99037			0.995185	−	0.0980171i	$-0.0312500\pi$
$769$	1.99037			1.99037			0.995185	+	0.0980171i	$0.0312500\pi$
$770$		0			0
$771$	0.666487	+	0.0988640i	0.666487	+	0.0988640i
$772$		0			0
$773$	0.0375548	−	0.764445i	0.0375548	−	0.764445i	−0.903989	−	0.427555i	$-0.859375\pi$
$773$	0.0375548	−	0.764445i	0.0375548	−	0.764445i	0.941544	−	0.336890i	$-0.109375\pi$
$774$		0			0
$775$	1.36347	+	0.728789i	1.36347	+	0.728789i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	2.52616	+	0.124102i	2.52616	+	0.124102i
$783$		0			0
$784$	0.707107	−	0.707107i	0.707107	−	0.707107i
$785$		0			0
$786$		0			0
$787$		0			0		0.903989	−	0.427555i	$-0.140625\pi$
$787$		0			0		−0.903989	+	0.427555i	$0.859375\pi$
$788$	0.0545211	+	1.10980i	0.0545211	+	1.10980i
$789$	−1.19028	−	0.882768i	−1.19028	−	0.882768i
$790$	0.216773	−	0.324423i	0.216773	−	0.324423i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.852275	+	0.403096i	0.852275	+	0.403096i
$796$	0.636379	−	1.53636i	0.636379	−	1.53636i
$797$	0.476623	+	1.90278i	0.476623	+	1.90278i	0.427555	+	0.903989i	$0.359375\pi$
$797$	0.476623	+	1.90278i	0.476623	+	1.90278i	0.0490677	+	0.998795i	$0.484375\pi$
$798$		0			0
$799$	1.99337	+	0.825680i	1.99337	+	0.825680i
$800$	−0.857729	+	0.514103i	−0.857729	+	0.514103i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.995185	−	0.0980171i	$-0.0312500\pi$
$809$		0			0		−0.995185	+	0.0980171i	$0.968750\pi$
$810$	0.980785	+	0.195090i	0.980785	+	0.195090i
$811$	0.150869	+	1.01708i	0.150869	+	1.01708i	0.923880	+	0.382683i	$0.125000\pi$
$811$	0.150869	+	1.01708i	0.150869	+	1.01708i	−0.773010	+	0.634393i	$0.781250\pi$
$812$		0			0
$813$	0.622491	−	1.73975i	0.622491	−	1.73975i
$814$		0			0
$815$		0			0
$816$	−1.30287	+	0.326351i	−1.30287	+	0.326351i
$817$		0			0
$818$	−0.546632	+	0.195588i	−0.546632	+	0.195588i
$819$		0			0
$820$		0			0
$821$		0			0		0.242980	−	0.970031i	$-0.421875\pi$
$821$		0			0		−0.242980	+	0.970031i	$0.578125\pi$
$822$	−1.97835			−1.97835
$823$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$823$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.45343	−	1.31731i	1.45343	−	1.31731i	0.595699	−	0.803208i	$-0.296875\pi$
$827$	1.45343	−	1.31731i	1.45343	−	1.31731i	0.857729	−	0.514103i	$-0.171875\pi$
$828$	1.87402	+	0.184575i	1.87402	+	0.184575i
$829$	−1.19028	+	0.882768i	−1.19028	+	0.882768i	−0.995185	−	0.0980171i	$-0.968750\pi$
$829$	−1.19028	+	0.882768i	−1.19028	+	0.882768i	−0.195090	+	0.980785i	$0.562500\pi$
$830$	1.91158	−	0.0939097i	1.91158	−	0.0939097i
$831$		0			0
$832$		0			0
$833$	−0.949728	+	0.949728i	−0.949728	+	0.949728i
$834$	−1.21416	+	1.33962i	−1.21416	+	1.33962i
$835$	1.18996	+	1.60448i	1.18996	+	1.60448i
$836$		0			0
$837$	1.03824	+	1.14553i	1.03824	+	1.14553i
$838$		0			0
$839$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$839$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$840$		0			0
$841$	−0.881921	+	0.471397i	−0.881921	+	0.471397i
$842$	1.27843	−	1.27843i	1.27843	−	1.27843i
$843$		0			0
$844$	0.150869	+	0.251710i	0.150869	+	0.251710i
$845$	0.998795	−	0.0490677i	0.998795	−	0.0490677i
$846$	1.45218	+	0.686831i	1.45218	+	0.686831i
$847$		0			0
$848$	−0.941658	−	0.0462607i	−0.941658	−	0.0462607i
$849$		0			0
$850$	1.15203	−	0.690501i	1.15203	−	0.690501i
$851$		0			0
$852$		0			0
$853$		0			0		0.989177	−	0.146730i	$-0.0468750\pi$
$853$		0			0		−0.989177	+	0.146730i	$0.953125\pi$
$854$		0			0
$855$	−0.190159	−	1.93072i	−0.190159	−	1.93072i
$856$	−1.53858	+	1.26268i	−1.53858	+	1.26268i
$857$	−1.32607	+	1.08827i	−1.32607	+	1.08827i	−0.336890	+	0.941544i	$0.609375\pi$
$857$	−1.32607	+	1.08827i	−1.32607	+	1.08827i	−0.989177	+	0.146730i	$0.953125\pi$
$858$		0			0
$859$	0.577920	+	1.61518i	0.577920	+	1.61518i	0.773010	+	0.634393i	$0.218750\pi$
$859$	0.577920	+	1.61518i	0.577920	+	1.61518i	−0.195090	+	0.980785i	$0.562500\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.691883	+	1.67035i	0.691883	+	1.67035i	0.740951	+	0.671559i	$0.234375\pi$
$863$	0.691883	+	1.67035i	0.691883	+	1.67035i	−0.0490677	+	0.998795i	$0.515625\pi$
$864$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$865$	−0.0750191	+	0.181112i	−0.0750191	+	0.181112i
$866$		0			0
$867$	0.779872	−	0.195348i	0.779872	−	0.195348i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.0572514	−	0.287822i	−0.0572514	−	0.287822i
$873$		0			0
$874$	−0.712725	−	3.58311i	−0.712725	−	3.58311i
$875$		0			0
$876$		0			0
$877$		0			0		−0.427555	−	0.903989i	$-0.640625\pi$
$877$		0			0		0.427555	+	0.903989i	$0.359375\pi$
$878$	−0.892476	−	0.661906i	−0.892476	−	0.661906i
$879$	−1.87711	+	0.373380i	−1.87711	+	0.373380i
$880$		0			0
$881$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$881$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$882$	−0.740951	+	0.671559i	−0.740951	+	0.671559i
$883$		0			0		0.671559	−	0.740951i	$-0.265625\pi$
$883$		0			0		−0.671559	+	0.740951i	$0.734375\pi$
$884$		0			0
$885$		0			0
$886$	0.485544	−	1.17221i	0.485544	−	1.17221i
$887$	0.248225	−	0.818289i	0.248225	−	0.818289i	−0.740951	−	0.671559i	$-0.765625\pi$
$887$	0.248225	−	0.818289i	0.248225	−	0.818289i	0.989177	−	0.146730i	$-0.0468750\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.457292	−	3.08281i	0.457292	−	3.08281i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.881921	−	0.471397i	0.881921	−	0.471397i
$901$	1.26476	+	0.0621336i	1.26476	+	0.0621336i
$902$		0			0
$903$		0			0
$904$	1.07701	+	0.509389i	1.07701	+	0.509389i
$905$	−0.0284872	+	0.0939097i	−0.0284872	+	0.0939097i
$906$	−0.536376	−	0.222174i	−0.536376	−	0.222174i
$907$		0			0		−0.514103	−	0.857729i	$-0.671875\pi$
$907$		0			0		0.514103	+	0.857729i	$0.328125\pi$
$908$	−1.59449	−	0.754140i	−1.59449	−	0.754140i
$909$		0			0
$910$		0			0
$911$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$911$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$912$	0.914539	+	1.71098i	0.914539	+	1.71098i
$913$		0			0
$914$		0			0
$915$	0.733452	+	1.55075i	0.733452	+	1.55075i
$916$	0.773010	−	0.365607i	0.773010	−	0.365607i
$917$		0			0
$918$	1.31731	−	0.262029i	1.31731	−	0.262029i
$919$	1.11897	−	1.36347i	1.11897	−	1.36347i	0.195090	−	0.980785i	$-0.437500\pi$
$919$	1.11897	−	1.36347i	1.11897	−	1.36347i	0.923880	−	0.382683i	$-0.125000\pi$
$920$	1.56573	−	1.04619i	1.56573	−	1.04619i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$929$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$930$	1.52929	+	0.226848i	1.52929	+	0.226848i
$931$	1.66405	+	0.997391i	1.66405	+	0.997391i
$932$	−0.838679	+	0.166824i	−0.838679	+	0.166824i
$933$		0			0
$934$	−1.10579	+	0.108911i	−1.10579	+	0.108911i
$935$		0			0
$936$		0			0
$937$		0			0		−0.0980171	−	0.995185i	$-0.531250\pi$
$937$		0			0		0.0980171	+	0.995185i	$0.468750\pi$
$938$		0			0
$939$		0			0
$940$	1.55827	−	0.390327i	1.55827	−	0.390327i
$941$		0			0		−0.941544	−	0.336890i	$-0.890625\pi$
$941$		0			0		0.941544	+	0.336890i	$0.109375\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.579870	−	0.0284872i	0.579870	−	0.0284872i	0.242980	−	0.970031i	$-0.421875\pi$
$947$	0.579870	−	0.0284872i	0.579870	−	0.0284872i	0.336890	+	0.941544i	$0.390625\pi$
$948$	0.0948062	−	0.378487i	0.0948062	−	0.378487i
$949$		0			0
$950$	−1.37183	−	1.37183i	−1.37183	−	1.37183i
$951$	1.72995	−	0.924678i	1.72995	−	0.924678i
$952$		0			0
$953$	−0.579870	−	1.91158i	−0.579870	−	1.91158i	−0.336890	−	0.941544i	$-0.609375\pi$
$953$	−0.579870	−	1.91158i	−0.579870	−	1.91158i	−0.242980	−	0.970031i	$-0.578125\pi$
$954$	0.938254	+	0.0924099i	0.938254	+	0.0924099i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$961$	0.983006	+	0.983006i	0.983006	+	0.983006i
$962$		0			0
$963$	1.59868	−	1.18566i	1.59868	−	1.18566i
$964$	0.804910	+	0.980785i	0.804910	+	0.980785i
$965$		0			0
$966$		0			0
$967$		0			0		0.956940	−	0.290285i	$-0.0937500\pi$
$967$		0			0		−0.956940	+	0.290285i	$0.906250\pi$
$968$	−0.671559	+	0.740951i	−0.671559	+	0.740951i
$969$	−1.22833	−	2.29805i	−1.22833	−	2.29805i
$970$		0			0
$971$		0			0		0.242980	−	0.970031i	$-0.421875\pi$
$971$		0			0		−0.242980	+	0.970031i	$0.578125\pi$
$972$	0.989177	−	0.146730i	0.989177	−	0.146730i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−1.27107	−	1.15203i	−1.27107	−	1.15203i
$977$	0.374332	−	0.560227i	0.374332	−	0.560227i	−0.595699	−	0.803208i	$-0.703125\pi$
$977$	0.374332	−	0.560227i	0.374332	−	0.560227i	0.970031	+	0.242980i	$0.0781250\pi$
$978$		0			0
$979$		0			0
$980$	−0.146730	+	0.989177i	−0.146730	+	0.989177i
$981$	0.0430597	+	0.290285i	0.0430597	+	0.290285i
$982$		0			0
$983$	−1.47477	+	0.145252i	−1.47477	+	0.145252i	−0.803208	−	0.595699i	$-0.796875\pi$
$983$	−1.47477	+	0.145252i	−1.47477	+	0.145252i	−0.671559	+	0.740951i	$0.734375\pi$
$984$		0			0
$985$	−0.704900	−	0.858923i	−0.704900	−	0.858923i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.70711	−	0.707107i	1.70711	−	0.707107i	0.707107	−	0.707107i	$-0.250000\pi$
$991$	1.70711	−	0.707107i	1.70711	−	0.707107i	1.00000			$0$
$992$	−1.49969	+	0.375652i	−1.49969	+	0.375652i
$993$	1.84553	+	0.764445i	1.84553	+	0.764445i
$994$		0			0
$995$	0.404061	+	1.61310i	0.404061	+	1.61310i
$996$	1.76820	−	0.732410i	1.76820	−	0.732410i
$997$		0			0		−0.903989	−	0.427555i	$-0.859375\pi$
$997$		0			0		0.903989	+	0.427555i	$0.140625\pi$
$998$	0.248225	−	0.818289i	0.248225	−	0.818289i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3840.1.dy.a.389.2	yes	64
3.2	odd	2	inner	3840.1.dy.a.389.1	✓	64
5.4	even	2	inner	3840.1.dy.a.389.1	✓	64
15.14	odd	2	CM	3840.1.dy.a.389.2	yes	64
256.77	even	64	inner	3840.1.dy.a.3149.2	yes	64
768.77	odd	64	inner	3840.1.dy.a.3149.1	yes	64
1280.589	even	64	inner	3840.1.dy.a.3149.1	yes	64
3840.3149	odd	64	inner	3840.1.dy.a.3149.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3840.1.dy.a.389.1	✓	64	3.2	odd	2	inner
3840.1.dy.a.389.1	✓	64	5.4	even	2	inner
3840.1.dy.a.389.2	yes	64	1.1	even	1	trivial
3840.1.dy.a.389.2	yes	64	15.14	odd	2	CM
3840.1.dy.a.3149.1	yes	64	768.77	odd	64	inner
3840.1.dy.a.3149.1	yes	64	1280.589	even	64	inner
3840.1.dy.a.3149.2	yes	64	256.77	even	64	inner
3840.1.dy.a.3149.2	yes	64	3840.3149	odd	64	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:	\( N \)	\(=\)	\( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3840.dy (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.427555 + 0.903989i) q^{2} +(-0.989177 - 0.146730i) q^{3} +(-0.634393 + 0.773010i) q^{4} +(0.0490677 - 0.998795i) q^{5} +(-0.290285 - 0.956940i) q^{6} +(-0.970031 - 0.242980i) q^{8} +(0.956940 + 0.290285i) q^{9} +O(q^{10})\)	\(q+(0.427555 + 0.903989i) q^{2} +(-0.989177 - 0.146730i) q^{3} +(-0.634393 + 0.773010i) q^{4} +(0.0490677 - 0.998795i) q^{5} +(-0.290285 - 0.956940i) q^{6} +(-0.970031 - 0.242980i) q^{8} +(0.956940 + 0.290285i) q^{9} +(0.923880 - 0.382683i) q^{10} +(0.740951 - 0.671559i) q^{12} +(-0.195090 + 0.980785i) q^{15} +(-0.195090 - 0.980785i) q^{16} +(0.262029 + 1.31731i) q^{17} +(0.146730 + 0.989177i) q^{18} +(1.75380 - 0.829484i) q^{19} +(0.740951 + 0.671559i) q^{20} +(-1.45565 - 1.19462i) q^{23} +(0.923880 + 0.382683i) q^{24} +(-0.995185 - 0.0980171i) q^{25} +(-0.903989 - 0.427555i) q^{27} +(-0.970031 + 0.242980i) q^{30} +(-1.42834 - 0.591637i) q^{31} +(0.803208 - 0.595699i) q^{32} +(-1.07880 + 0.800094i) q^{34} +(-0.831470 + 0.555570i) q^{36} +(1.49969 + 1.23076i) q^{38} +(-0.290285 + 0.956940i) q^{40} +(0.336890 - 0.941544i) q^{45} +(0.457553 - 1.82665i) q^{46} +(0.892476 - 1.33569i) q^{47} +(0.0490677 + 0.998795i) q^{48} +(0.555570 + 0.831470i) q^{49} +(-0.336890 - 0.941544i) q^{50} +(-0.0659037 - 1.34150i) q^{51} +(0.229080 - 0.914539i) q^{53} -1.00000i q^{54} +(-1.85652 + 0.563170i) q^{57} +(-0.634393 - 0.773010i) q^{60} +(1.37787 - 1.02190i) q^{61} +(-0.0758597 - 1.54416i) q^{62} +(0.881921 + 0.471397i) q^{64} +(-1.18452 - 0.633141i) q^{68} +(1.26460 + 1.39528i) q^{69} +(-0.857729 - 0.514103i) q^{72} +(0.970031 + 0.242980i) q^{75} +(-0.471397 + 1.88192i) q^{76} +(0.324423 - 0.216773i) q^{79} +(-0.989177 + 0.146730i) q^{80} +(0.831470 + 0.555570i) q^{81} +(1.80200 + 0.644767i) q^{83} +(1.32858 - 0.197076i) q^{85} +(0.995185 - 0.0980171i) q^{90} +(1.84691 - 0.367372i) q^{92} +(1.32607 + 0.794814i) q^{93} +(1.58903 + 0.235710i) q^{94} +(-0.742430 - 1.79238i) q^{95} +(-0.881921 + 0.471397i) q^{96} +(-0.514103 + 0.857729i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q+O(q^{100}) \) 64 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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