LMFDB - Embedded newform 3840.1.dy.a.869.2

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			869.2
Root			$-0.970031 + 0.242980i$ of defining polynomial
Character	$\chi$	$=$	3840.869
Dual form			3840.1.dy.a.2669.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.671559 - 0.740951i) q^{2} +(0.970031 - 0.242980i) q^{3} +(-0.0980171 - 0.995185i) q^{4} +(-0.903989 - 0.427555i) q^{5} +(0.471397 - 0.881921i) q^{6} +(-0.803208 - 0.595699i) q^{8} +(0.881921 - 0.471397i) q^{9} +O(q^{10})$	\(q+(0.671559 - 0.740951i) q^{2} +(0.970031 - 0.242980i) q^{3} +(-0.0980171 - 0.995185i) q^{4} +(-0.903989 - 0.427555i) q^{5} +(0.471397 - 0.881921i) q^{6} +(-0.803208 - 0.595699i) q^{8} +(0.881921 - 0.471397i) q^{9} +(-0.923880 + 0.382683i) q^{10} +(-0.336890 - 0.941544i) q^{12} +(-0.980785 - 0.195090i) q^{15} +(-0.980785 + 0.195090i) q^{16} +(1.84691 - 0.367372i) q^{17} +(0.242980 - 0.970031i) q^{18} +(-1.19028 - 1.07880i) q^{19} +(-0.336890 + 0.941544i) q^{20} +(-0.0976628 + 0.00961895i) q^{23} +(-0.923880 - 0.382683i) q^{24} +(0.634393 + 0.773010i) q^{25} +(0.740951 - 0.671559i) q^{27} +(-0.803208 + 0.595699i) q^{30} +(-1.83886 - 0.761681i) q^{31} +(-0.514103 + 0.857729i) q^{32} +(0.968101 - 1.61518i) q^{34} +(-0.555570 - 0.831470i) q^{36} +(-1.59868 + 0.157456i) q^{38} +(0.471397 + 0.881921i) q^{40} +(-0.998795 + 0.0490677i) q^{45} +(-0.0584592 + 0.0788231i) q^{46} +(0.854922 + 0.571240i) q^{47} +(-0.903989 + 0.427555i) q^{48} +(-0.831470 + 0.555570i) q^{49} +(0.998795 + 0.0490677i) q^{50} +(1.70229 - 0.805124i) q^{51} +(1.14010 - 1.53724i) q^{53} -1.00000i q^{54} +(-1.41673 - 0.757259i) q^{57} +(-0.0980171 + 0.995185i) q^{60} +(-1.01708 + 1.69689i) q^{61} +(-1.79927 + 0.850993i) q^{62} +(0.290285 + 0.956940i) q^{64} +(-0.546632 - 1.80200i) q^{68} +(-0.0923988 + 0.0330608i) q^{69} +(-0.989177 - 0.146730i) q^{72} +(0.803208 + 0.595699i) q^{75} +(-0.956940 + 1.29028i) q^{76} +(1.08979 + 1.63099i) q^{79} +(0.970031 + 0.242980i) q^{80} +(0.555570 - 0.831470i) q^{81} +(-0.0865477 - 1.76172i) q^{83} +(-1.82665 - 0.457553i) q^{85} +(-0.634393 + 0.773010i) q^{90} +(0.0191453 + 0.0962497i) q^{92} +(-1.96883 - 0.292048i) q^{93} +(0.997391 - 0.249834i) q^{94} +(0.614748 + 1.48413i) q^{95} +(-0.290285 + 0.956940i) q^{96} +(-0.146730 + 0.989177i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3840\mathbb{Z}\right)^\times$.

$n$	$511$	$1537$	$2561$	$2821$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{9}{64}\right)$

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 $

$2$	0.671559	−	0.740951i	0.671559	−	0.740951i
$2$	0.671559	−	0.740951i	0.671559	−	0.740951i
$3$	0.970031	−	0.242980i	0.970031	−	0.242980i
$3$	0.970031	−	0.242980i	0.970031	−	0.242980i
$4$	−0.0980171	−	0.995185i	−0.0980171	−	0.995185i
$5$	−0.903989	−	0.427555i	−0.903989	−	0.427555i
$5$	−0.903989	−	0.427555i	−0.903989	−	0.427555i
$6$	0.471397	−	0.881921i	0.471397	−	0.881921i
$7$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$7$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$8$	−0.803208	−	0.595699i	−0.803208	−	0.595699i
$9$	0.881921	−	0.471397i	0.881921	−	0.471397i
$10$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$11$		0			0		0.989177	−	0.146730i	$-0.0468750\pi$
$11$		0			0		−0.989177	+	0.146730i	$0.953125\pi$
$12$	−0.336890	−	0.941544i	−0.336890	−	0.941544i
$13$		0			0		0.336890	−	0.941544i	$-0.390625\pi$
$13$		0			0		−0.336890	+	0.941544i	$0.609375\pi$
$14$		0			0
$15$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$16$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$17$	1.84691	−	0.367372i	1.84691	−	0.367372i	0.857729	−	0.514103i	$-0.171875\pi$
$17$	1.84691	−	0.367372i	1.84691	−	0.367372i	0.989177	+	0.146730i	$0.0468750\pi$
$18$	0.242980	−	0.970031i	0.242980	−	0.970031i
$19$	−1.19028	−	1.07880i	−1.19028	−	1.07880i	−0.995185	−	0.0980171i	$-0.968750\pi$
$19$	−1.19028	−	1.07880i	−1.19028	−	1.07880i	−0.195090	−	0.980785i	$-0.562500\pi$
$20$	−0.336890	+	0.941544i	−0.336890	+	0.941544i
$21$		0			0
$22$		0			0
$23$	−0.0976628	+	0.00961895i	−0.0976628	+	0.00961895i	−0.146730	−	0.989177i	$-0.546875\pi$
$23$	−0.0976628	+	0.00961895i	−0.0976628	+	0.00961895i	0.0490677	+	0.998795i	$0.484375\pi$
$24$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$25$	0.634393	+	0.773010i	0.634393	+	0.773010i
$26$		0			0
$27$	0.740951	−	0.671559i	0.740951	−	0.671559i
$28$		0			0
$29$		0			0		−0.595699	−	0.803208i	$-0.703125\pi$
$29$		0			0		0.595699	+	0.803208i	$0.296875\pi$
$30$	−0.803208	+	0.595699i	−0.803208	+	0.595699i
$31$	−1.83886	−	0.761681i	−1.83886	−	0.761681i	−0.956940	−	0.290285i	$-0.906250\pi$
$31$	−1.83886	−	0.761681i	−1.83886	−	0.761681i	−0.881921	−	0.471397i	$-0.843750\pi$
$32$	−0.514103	+	0.857729i	−0.514103	+	0.857729i
$33$		0			0
$34$	0.968101	−	1.61518i	0.968101	−	1.61518i
$35$		0			0
$36$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$37$		0			0		0.0490677	−	0.998795i	$-0.484375\pi$
$37$		0			0		−0.0490677	+	0.998795i	$0.515625\pi$
$38$	−1.59868	+	0.157456i	−1.59868	+	0.157456i
$39$		0			0
$40$	0.471397	+	0.881921i	0.471397	+	0.881921i
$41$		0			0		0.634393	−	0.773010i	$-0.281250\pi$
$41$		0			0		−0.634393	+	0.773010i	$0.718750\pi$
$42$		0			0
$43$		0			0		0.242980	−	0.970031i	$-0.421875\pi$
$43$		0			0		−0.242980	+	0.970031i	$0.578125\pi$
$44$		0			0
$45$	−0.998795	+	0.0490677i	−0.998795	+	0.0490677i
$46$	−0.0584592	+	0.0788231i	−0.0584592	+	0.0788231i
$47$	0.854922	+	0.571240i	0.854922	+	0.571240i	0.903989	−	0.427555i	$-0.140625\pi$
$47$	0.854922	+	0.571240i	0.854922	+	0.571240i	−0.0490677	+	0.998795i	$0.515625\pi$
$48$	−0.903989	+	0.427555i	−0.903989	+	0.427555i
$49$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$50$	0.998795	+	0.0490677i	0.998795	+	0.0490677i
$51$	1.70229	−	0.805124i	1.70229	−	0.805124i
$52$		0			0
$53$	1.14010	−	1.53724i	1.14010	−	1.53724i	0.336890	−	0.941544i	$-0.390625\pi$
$53$	1.14010	−	1.53724i	1.14010	−	1.53724i	0.803208	−	0.595699i	$-0.203125\pi$
$54$		−	1.00000i		−	1.00000i
$55$		0			0
$56$		0			0
$57$	−1.41673	−	0.757259i	−1.41673	−	0.757259i
$58$		0			0
$59$		0			0		−0.336890	−	0.941544i	$-0.609375\pi$
$59$		0			0		0.336890	+	0.941544i	$0.390625\pi$
$60$	−0.0980171	+	0.995185i	−0.0980171	+	0.995185i
$61$	−1.01708	+	1.69689i	−1.01708	+	1.69689i	−0.382683	+	0.923880i	$0.625000\pi$
$61$	−1.01708	+	1.69689i	−1.01708	+	1.69689i	−0.634393	+	0.773010i	$0.718750\pi$
$62$	−1.79927	+	0.850993i	−1.79927	+	0.850993i
$63$		0			0
$64$	0.290285	+	0.956940i	0.290285	+	0.956940i
$65$		0			0
$66$		0			0
$67$		0			0		−0.857729	−	0.514103i	$-0.828125\pi$
$67$		0			0		0.857729	+	0.514103i	$0.171875\pi$
$68$	−0.546632	−	1.80200i	−0.546632	−	1.80200i
$69$	−0.0923988	+	0.0330608i	−0.0923988	+	0.0330608i
$70$		0			0
$71$		0			0		0.471397	−	0.881921i	$-0.343750\pi$
$71$		0			0		−0.471397	+	0.881921i	$0.656250\pi$
$72$	−0.989177	−	0.146730i	−0.989177	−	0.146730i
$73$		0			0		0.290285	−	0.956940i	$-0.406250\pi$
$73$		0			0		−0.290285	+	0.956940i	$0.593750\pi$
$74$		0			0
$75$	0.803208	+	0.595699i	0.803208	+	0.595699i
$76$	−0.956940	+	1.29028i	−0.956940	+	1.29028i
$77$		0			0
$78$		0			0
$79$	1.08979	+	1.63099i	1.08979	+	1.63099i	0.707107	+	0.707107i	$0.250000\pi$
$79$	1.08979	+	1.63099i	1.08979	+	1.63099i	0.382683	+	0.923880i	$0.375000\pi$
$80$	0.970031	+	0.242980i	0.970031	+	0.242980i
$81$	0.555570	−	0.831470i	0.555570	−	0.831470i
$82$		0			0
$83$	−0.0865477	−	1.76172i	−0.0865477	−	1.76172i	−0.514103	−	0.857729i	$-0.671875\pi$
$83$	−0.0865477	−	1.76172i	−0.0865477	−	1.76172i	0.427555	−	0.903989i	$-0.359375\pi$
$84$		0			0
$85$	−1.82665	−	0.457553i	−1.82665	−	0.457553i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.995185	−	0.0980171i	$-0.968750\pi$
$89$		0			0		0.995185	+	0.0980171i	$0.0312500\pi$
$90$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$91$		0			0
$92$	0.0191453	+	0.0962497i	0.0191453	+	0.0962497i
$93$	−1.96883	−	0.292048i	−1.96883	−	0.292048i
$94$	0.997391	−	0.249834i	0.997391	−	0.249834i
$95$	0.614748	+	1.48413i	0.614748	+	1.48413i
$96$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$97$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$97$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$98$	−0.146730	+	0.989177i	−0.146730	+	0.989177i
$99$		0			0
$100$	0.707107	−	0.707107i	0.707107	−	0.707107i
$101$		0			0		−0.671559	−	0.740951i	$-0.734375\pi$
$101$		0			0		0.671559	+	0.740951i	$0.265625\pi$
$102$	0.546632	−	1.80200i	0.546632	−	1.80200i
$103$		0			0		0.773010	−	0.634393i	$-0.218750\pi$
$103$		0			0		−0.773010	+	0.634393i	$0.781250\pi$
$104$		0			0
$105$		0			0
$106$	−0.373380	−	1.87711i	−0.373380	−	1.87711i
$107$	1.08827	−	0.652287i	1.08827	−	0.652287i	0.146730	−	0.989177i	$-0.453125\pi$
$107$	1.08827	−	0.652287i	1.08827	−	0.652287i	0.941544	+	0.336890i	$0.109375\pi$
$108$	−0.740951	−	0.671559i	−0.740951	−	0.671559i
$109$	0.326351	−	0.360073i	0.326351	−	0.360073i	−0.555570	−	0.831470i	$-0.687500\pi$
$109$	0.326351	−	0.360073i	0.326351	−	0.360073i	0.881921	+	0.471397i	$0.156250\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.334669	+	1.68250i	−0.334669	+	1.68250i	0.336890	+	0.941544i	$0.390625\pi$
$113$	−0.334669	+	1.68250i	−0.334669	+	1.68250i	−0.671559	+	0.740951i	$0.734375\pi$
$114$	−1.51251	+	0.541185i	−1.51251	+	0.541185i
$115$	0.0923988	+	0.0330608i	0.0923988	+	0.0330608i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.671559	+	0.740951i	0.671559	+	0.740951i
$121$	0.956940	−	0.290285i	0.956940	−	0.290285i
$122$	0.574286	+	1.89317i	0.574286	+	1.89317i
$123$		0			0
$124$	−0.577774	+	1.90466i	−0.577774	+	1.90466i
$125$	−0.242980	−	0.970031i	−0.242980	−	0.970031i
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	0.903989	+	0.427555i	0.903989	+	0.427555i
$129$		0			0
$130$		0			0
$131$		0			0		−0.242980	−	0.970031i	$-0.578125\pi$
$131$		0			0		0.242980	+	0.970031i	$0.421875\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$136$	−1.70229	−	0.805124i	−1.70229	−	0.805124i
$137$	0.914539	+	1.71098i	0.914539	+	1.71098i	0.671559	+	0.740951i	$0.265625\pi$
$137$	0.914539	+	1.71098i	0.914539	+	1.71098i	0.242980	+	0.970031i	$0.421875\pi$
$138$	−0.0375548	+	0.0906652i	−0.0375548	+	0.0906652i
$139$	0.217440	+	1.46586i	0.217440	+	1.46586i	0.773010	+	0.634393i	$0.218750\pi$
$139$	0.217440	+	1.46586i	0.217440	+	1.46586i	−0.555570	+	0.831470i	$0.687500\pi$
$140$		0			0
$141$	0.968101	+	0.346392i	0.968101	+	0.346392i
$142$		0			0
$143$		0			0
$144$	−0.773010	+	0.634393i	−0.773010	+	0.634393i
$145$		0			0
$146$		0			0
$147$	−0.671559	+	0.740951i	−0.671559	+	0.740951i
$148$		0			0
$149$		0			0		0.857729	−	0.514103i	$-0.171875\pi$
$149$		0			0		−0.857729	+	0.514103i	$0.828125\pi$
$150$	0.980785	−	0.195090i	0.980785	−	0.195090i
$151$	−0.0924099	−	0.938254i	−0.0924099	−	0.938254i	−0.923880	−	0.382683i	$-0.875000\pi$
$151$	−0.0924099	−	0.938254i	−0.0924099	−	0.938254i	0.831470	−	0.555570i	$-0.187500\pi$
$152$	0.313396	+	1.57555i	0.313396	+	1.57555i
$153$	1.45565	−	1.19462i	1.45565	−	1.19462i
$154$		0			0
$155$	1.33665	+	1.47477i	1.33665	+	1.47477i
$156$		0			0
$157$		0			0		0.803208	−	0.595699i	$-0.203125\pi$
$157$		0			0		−0.803208	+	0.595699i	$0.796875\pi$
$158$	1.94034	+	0.287822i	1.94034	+	0.287822i
$159$	0.732410	−	1.76820i	0.732410	−	1.76820i
$160$	0.831470	−	0.555570i	0.831470	−	0.555570i
$161$		0			0
$162$	−0.242980	−	0.970031i	−0.242980	−	0.970031i
$163$		0			0		−0.989177	−	0.146730i	$-0.953125\pi$
$163$		0			0		0.989177	+	0.146730i	$0.0468750\pi$
$164$		0			0
$165$		0			0
$166$	−1.36347	−	1.11897i	−1.36347	−	1.11897i
$167$	0.850993	+	0.0838155i	0.850993	+	0.0838155i	0.514103	−	0.857729i	$-0.328125\pi$
$167$	0.850993	+	0.0838155i	0.850993	+	0.0838155i	0.336890	+	0.941544i	$0.390625\pi$
$168$		0			0
$169$	−0.773010	−	0.634393i	−0.773010	−	0.634393i
$170$	−1.56573	+	1.04619i	−1.56573	+	1.04619i
$171$	−1.55827	−	0.390327i	−1.55827	−	0.390327i
$172$		0			0
$173$	−0.0758597	−	1.54416i	−0.0758597	−	1.54416i	−0.671559	−	0.740951i	$-0.734375\pi$
$173$	−0.0758597	−	1.54416i	−0.0758597	−	1.54416i	0.595699	−	0.803208i	$-0.296875\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.427555	−	0.903989i	$-0.640625\pi$
$179$		0			0		0.427555	+	0.903989i	$0.359375\pi$
$180$	0.146730	+	0.989177i	0.146730	+	0.989177i
$181$	1.45218	+	1.07701i	1.45218	+	1.07701i	0.980785	+	0.195090i	$0.0625000\pi$
$181$	1.45218	+	1.07701i	1.45218	+	1.07701i	0.471397	+	0.881921i	$0.343750\pi$
$182$		0			0
$183$	−0.574286	+	1.89317i	−0.574286	+	1.89317i
$184$	0.0841735	+	0.0504517i	0.0841735	+	0.0504517i
$185$		0			0
$186$	−1.53858	+	1.26268i	−1.53858	+	1.26268i
$187$		0			0
$188$	0.484693	−	0.906796i	0.484693	−	0.906796i
$189$		0			0
$190$	1.51251	+	0.541185i	1.51251	+	0.541185i
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	0.514103	+	0.857729i	0.514103	+	0.857729i
$193$		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
$196$	0.634393	+	0.773010i	0.634393	+	0.773010i
$197$	0.560227	+	1.56573i	0.560227	+	1.56573i	0.803208	+	0.595699i	$0.203125\pi$
$197$	0.560227	+	1.56573i	0.560227	+	1.56573i	−0.242980	+	0.970031i	$0.578125\pi$
$198$		0			0
$199$	−0.979938	−	0.523788i	−0.979938	−	0.523788i	−0.0980171	−	0.995185i	$-0.531250\pi$
$199$	−0.979938	−	0.523788i	−0.979938	−	0.523788i	−0.881921	+	0.471397i	$0.843750\pi$
$200$	−0.0490677	−	0.998795i	−0.0490677	−	0.998795i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.968101	−	1.61518i	−0.968101	−	1.61518i
$205$		0			0
$206$		0			0
$207$	−0.0815966	+	0.0545211i	−0.0815966	+	0.0545211i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.485375	+	0.0238449i	−0.485375	+	0.0238449i	−0.290285	−	0.956940i	$-0.593750\pi$
$211$	−0.485375	+	0.0238449i	−0.485375	+	0.0238449i	−0.195090	+	0.980785i	$0.562500\pi$
$212$	−1.64159	−	0.983931i	−1.64159	−	0.983931i
$213$		0			0
$214$	0.247528	−	1.24441i	0.247528	−	1.24441i
$215$		0			0
$216$	−0.995185	+	0.0980171i	−0.995185	+	0.0980171i
$217$		0			0
$218$	−0.0476324	−	0.483620i	−0.0476324	−	0.483620i
$219$		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
$226$	1.02190	+	1.37787i	1.02190	+	1.37787i
$227$	0.345845	+	0.466318i	0.345845	+	0.466318i	0.941544	−	0.336890i	$-0.109375\pi$
$227$	0.345845	+	0.466318i	0.345845	+	0.466318i	−0.595699	+	0.803208i	$0.703125\pi$
$228$	−0.614748	+	1.48413i	−0.614748	+	1.48413i
$229$	0.995185	−	0.901983i	0.995185	−	0.901983i		−	1.00000i	$-0.5\pi$
$229$	0.995185	−	0.901983i	0.995185	−	0.901983i	0.995185	+	0.0980171i	$0.0312500\pi$
$230$	0.0865477	−	0.0462607i	0.0865477	−	0.0462607i
$231$		0			0
$232$		0			0
$233$	−1.33665	+	0.131649i	−1.33665	+	0.131649i	−0.740951	−	0.671559i	$-0.765625\pi$
$233$	−1.33665	+	0.131649i	−1.33665	+	0.131649i	−0.595699	+	0.803208i	$0.703125\pi$
$234$		0			0
$235$	−0.528603	−	0.881921i	−0.528603	−	0.881921i
$236$		0			0
$237$	1.45343	+	1.31731i	1.45343	+	1.31731i
$238$		0			0
$239$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$239$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$240$	1.00000			1.00000
$241$	0.192268	+	0.0382444i	0.192268	+	0.0382444i	0.290285	−	0.956940i	$-0.406250\pi$
$241$	0.192268	+	0.0382444i	0.192268	+	0.0382444i	−0.0980171	+	0.995185i	$0.531250\pi$
$242$	0.427555	−	0.903989i	0.427555	−	0.903989i
$243$	0.336890	−	0.941544i	0.336890	−	0.941544i
$244$	1.78841	+	0.845855i	1.78841	+	0.845855i
$245$	0.989177	−	0.146730i	0.989177	−	0.146730i
$246$		0			0
$247$		0			0
$248$	1.02325	+	1.70720i	1.02325	+	1.70720i
$249$	−0.512016	−	1.68789i	−0.512016	−	1.68789i
$250$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$251$		0			0		−0.903989	−	0.427555i	$-0.859375\pi$
$251$		0			0		0.903989	+	0.427555i	$0.140625\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−1.88309			−1.88309
$256$	0.923880	−	0.382683i	0.923880	−	0.382683i
$257$	1.99759			1.99759			0.998795	−	0.0490677i	$-0.0156250\pi$
$257$	1.99759			1.99759			0.998795	+	0.0490677i	$0.0156250\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.195588	−	0.644767i	−0.195588	−	0.644767i	−0.998795	−	0.0490677i	$-0.984375\pi$
$263$	−0.195588	−	0.644767i	−0.195588	−	0.644767i	0.803208	−	0.595699i	$-0.203125\pi$
$264$		0			0
$265$	−1.68789	+	0.902197i	−1.68789	+	0.902197i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.336890	−	0.941544i	$-0.390625\pi$
$269$		0			0		−0.336890	+	0.941544i	$0.609375\pi$
$270$	−0.427555	+	0.903989i	−0.427555	+	0.903989i
$271$	1.81225	+	0.360480i	1.81225	+	0.360480i	0.980785	−	0.195090i	$-0.0625000\pi$
$271$	1.81225	+	0.360480i	1.81225	+	0.360480i	0.831470	+	0.555570i	$0.187500\pi$
$272$	−1.73975	+	0.720627i	−1.73975	+	0.720627i
$273$		0			0
$274$	1.88192	+	0.471397i	1.88192	+	0.471397i
$275$		0			0
$276$	0.0419583	+	0.0887133i	0.0419583	+	0.0887133i
$277$		0			0		−0.514103	−	0.857729i	$-0.671875\pi$
$277$		0			0		0.514103	+	0.857729i	$0.328125\pi$
$278$	1.23216	+	0.823301i	1.23216	+	0.823301i
$279$	−1.98079	+	0.195090i	−1.98079	+	0.195090i
$280$		0			0
$281$		0			0		−0.634393	−	0.773010i	$-0.718750\pi$
$281$		0			0		0.634393	+	0.773010i	$0.281250\pi$
$282$	0.906796	−	0.484693i	0.906796	−	0.484693i
$283$		0			0		0.740951	−	0.671559i	$-0.234375\pi$
$283$		0			0		−0.740951	+	0.671559i	$0.765625\pi$
$284$		0			0
$285$	0.956940	+	1.29028i	0.956940	+	1.29028i
$286$		0			0
$287$		0			0
$288$	−0.0490677	+	0.998795i	−0.0490677	+	0.998795i
$289$	2.35222	−	0.974320i	2.35222	−	0.974320i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.0865477	+	1.76172i	−0.0865477	+	1.76172i	0.427555	+	0.903989i	$0.359375\pi$
$293$	−0.0865477	+	1.76172i	−0.0865477	+	1.76172i	−0.514103	+	0.857729i	$0.671875\pi$
$294$	0.0980171	+	0.995185i	0.0980171	+	0.995185i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.514103	−	0.857729i	0.514103	−	0.857729i
$301$		0			0
$302$	−0.757259	−	0.561621i	−0.757259	−	0.561621i
$303$		0			0
$304$	1.37787	+	0.825862i	1.37787	+	0.825862i
$305$	1.64494	−	1.09911i	1.64494	−	1.09911i
$306$	0.0923988	−	1.88082i	0.0923988	−	1.88082i
$307$		0			0		0.903989	−	0.427555i	$-0.140625\pi$
$307$		0			0		−0.903989	+	0.427555i	$0.859375\pi$
$308$		0			0
$309$		0			0
$310$	1.99037			1.99037
$311$		0			0		−0.956940	−	0.290285i	$-0.906250\pi$
$311$		0			0		0.956940	+	0.290285i	$0.0937500\pi$
$312$		0			0
$313$		0			0		−0.881921	−	0.471397i	$-0.843750\pi$
$313$		0			0		0.881921	+	0.471397i	$0.156250\pi$
$314$		0			0
$315$		0			0
$316$	1.51631	−	1.24441i	1.51631	−	1.24441i
$317$	−0.200593	+	0.334669i	−0.200593	+	0.334669i	−0.941544	−	0.336890i	$-0.890625\pi$
$317$	−0.200593	+	0.334669i	−0.200593	+	0.334669i	0.740951	+	0.671559i	$0.234375\pi$
$318$	−0.818289	−	1.73013i	−0.818289	−	1.73013i
$319$		0			0
$320$	0.146730	−	0.989177i	0.146730	−	0.989177i
$321$	0.897168	−	0.897168i	0.897168	−	0.897168i
$322$		0			0
$323$	−2.59465	−	1.55517i	−2.59465	−	1.55517i
$324$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$325$		0			0
$326$		0			0
$327$	0.229080	−	0.428579i	0.229080	−	0.428579i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.686831	−	0.509389i	−0.686831	−	0.509389i	0.195090	−	0.980785i	$-0.437500\pi$
$331$	−0.686831	−	0.509389i	−0.686831	−	0.509389i	−0.881921	+	0.471397i	$0.843750\pi$
$332$	−1.74475	+	0.258809i	−1.74475	+	0.258809i
$333$		0			0
$334$	0.633595	−	0.574257i	0.633595	−	0.574257i
$335$		0			0
$336$		0			0
$337$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$337$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$338$	−0.989177	+	0.146730i	−0.989177	+	0.146730i
$339$	0.0841735	+	1.71339i	0.0841735	+	1.71339i
$340$	−0.276306	+	1.86271i	−0.276306	+	1.86271i
$341$		0			0
$342$	−1.33569	+	0.892476i	−1.33569	+	0.892476i
$343$		0			0
$344$		0			0
$345$	0.0976628	+	0.00961895i	0.0976628	+	0.00961895i
$346$	−1.19509	−	0.980785i	−1.19509	−	0.980785i
$347$	0.389711	+	0.0191453i	0.389711	+	0.0191453i	0.242980	−	0.970031i	$-0.421875\pi$
$347$	0.389711	+	0.0191453i	0.389711	+	0.0191453i	0.146730	+	0.989177i	$0.453125\pi$
$348$		0			0
$349$	−1.17850	−	0.174814i	−1.17850	−	0.174814i	−0.471397	−	0.881921i	$-0.656250\pi$
$349$	−1.17850	−	0.174814i	−1.17850	−	0.174814i	−0.707107	+	0.707107i	$0.750000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.112303	−	0.271123i	0.112303	−	0.271123i	−0.857729	−	0.514103i	$-0.828125\pi$
$353$	0.112303	−	0.271123i	0.112303	−	0.271123i	0.970031	+	0.242980i	$0.0781250\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.773010	−	0.634393i	$-0.218750\pi$
$359$		0			0		−0.773010	+	0.634393i	$0.781250\pi$
$360$	0.831470	+	0.555570i	0.831470	+	0.555570i
$361$	0.154923	+	1.57296i	0.154923	+	1.57296i
$362$	1.77324	−	0.352719i	1.77324	−	0.352719i
$363$	0.857729	−	0.514103i	0.857729	−	0.514103i
$364$		0			0
$365$		0			0
$366$	1.01708	+	1.69689i	1.01708	+	1.69689i
$367$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$367$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$368$	0.0939097	−	0.0284872i	0.0939097	−	0.0284872i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.0976628	+	1.98797i	−0.0976628	+	1.98797i
$373$		0			0		−0.146730	−	0.989177i	$-0.546875\pi$
$373$		0			0		0.146730	+	0.989177i	$0.453125\pi$
$374$		0			0
$375$	−0.471397	−	0.881921i	−0.471397	−	0.881921i
$376$	−0.346392	−	0.968101i	−0.346392	−	0.968101i
$377$		0			0
$378$		0			0
$379$	−0.773010	+	1.63439i	−0.773010	+	1.63439i			1.00000i	$0.5\pi$
$379$	−0.773010	+	1.63439i	−0.773010	+	1.63439i	−0.773010	+	0.634393i	$0.781250\pi$
$380$	1.41673	−	0.757259i	1.41673	−	0.757259i
$381$		0			0
$382$		0			0
$383$			0.293461i			0.293461i	0.989177	+	0.146730i	$0.0468750\pi$
$383$			0.293461i			0.293461i	−0.989177	+	0.146730i	$0.953125\pi$
$384$	0.980785	+	0.195090i	0.980785	+	0.195090i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.427555	−	0.903989i	$-0.359375\pi$
$389$		0			0		−0.427555	+	0.903989i	$0.640625\pi$
$390$		0			0
$391$	−0.176840	+	0.0536439i	−0.176840	+	0.0536439i
$392$	0.998795	+	0.0490677i	0.998795	+	0.0490677i
$393$		0			0
$394$	1.53636	+	0.636379i	1.53636	+	0.636379i
$395$	−0.287822	−	1.94034i	−0.287822	−	1.94034i
$396$		0			0
$397$		0			0		−0.941544	−	0.336890i	$-0.890625\pi$
$397$		0			0		0.941544	+	0.336890i	$0.109375\pi$
$398$	−1.04619	+	0.374332i	−1.04619	+	0.374332i
$399$		0			0
$400$	−0.773010	−	0.634393i	−0.773010	−	0.634393i
$401$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$401$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.857729	+	0.514103i	−0.857729	+	0.514103i
$406$		0			0
$407$		0			0
$408$	−1.84691	−	0.367372i	−1.84691	−	0.367372i
$409$	−0.728789	+	0.598102i	−0.728789	+	0.598102i	−0.923880	−	0.382683i	$-0.875000\pi$
$409$	−0.728789	+	0.598102i	−0.728789	+	0.598102i	0.195090	+	0.980785i	$0.437500\pi$
$410$		0			0
$411$	1.30287	+	1.43749i	1.30287	+	1.43749i
$412$		0			0
$413$		0			0
$414$	−0.0143994	+	0.0970732i	−0.0143994	+	0.0970732i
$415$	−0.674993	+	1.62958i	−0.674993	+	1.62958i
$416$		0			0
$417$	0.567099	+	1.36910i	0.567099	+	1.36910i
$418$		0			0
$419$		0			0		−0.989177	−	0.146730i	$-0.953125\pi$
$419$		0			0		0.989177	+	0.146730i	$0.0468750\pi$
$420$		0			0
$421$	−1.48012	−	0.0727135i	−1.48012	−	0.0727135i	−0.707107	−	0.707107i	$-0.750000\pi$
$421$	−1.48012	−	0.0727135i	−1.48012	−	0.0727135i	−0.773010	+	0.634393i	$0.781250\pi$
$422$	−0.308290	+	0.375652i	−0.308290	+	0.375652i
$423$	1.02325	+	0.100782i	1.02325	+	0.100782i
$424$	−1.83147	+	0.555570i	−1.83147	+	0.555570i
$425$	1.45565	+	1.19462i	1.45565	+	1.19462i
$426$		0			0
$427$		0			0
$428$	−0.755815	−	1.01910i	−0.755815	−	1.01910i
$429$		0			0
$430$		0			0
$431$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$431$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$432$	−0.595699	+	0.803208i	−0.595699	+	0.803208i
$433$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$433$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$434$		0			0
$435$		0			0
$436$	−0.390327	−	0.289486i	−0.390327	−	0.289486i
$437$	0.126623	+	0.0939097i	0.126623	+	0.0939097i
$438$		0			0
$439$	0.482726	−	1.59133i	0.482726	−	1.59133i	−0.290285	−	0.956940i	$-0.593750\pi$
$439$	0.482726	−	1.59133i	0.482726	−	1.59133i	0.773010	−	0.634393i	$-0.218750\pi$
$440$		0			0
$441$	−0.471397	+	0.881921i	−0.471397	+	0.881921i
$442$		0			0
$443$	−0.184575	+	0.0660420i	−0.184575	+	0.0660420i	−0.427555	−	0.903989i	$-0.640625\pi$
$443$	−0.184575	+	0.0660420i	−0.184575	+	0.0660420i	0.242980	+	0.970031i	$0.421875\pi$
$444$		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	$0.250000\pi$
$450$	0.903989	−	0.427555i	0.903989	−	0.427555i
$451$		0			0
$452$	1.70720	+	0.168144i	1.70720	+	0.168144i
$453$	−0.317618	−	0.887682i	−0.317618	−	0.887682i
$454$	0.577774	+	0.0569057i	0.577774	+	0.0569057i
$455$		0			0
$456$	0.686831	+	1.45218i	0.686831	+	1.45218i
$457$		0			0		−0.956940	−	0.290285i	$-0.906250\pi$
$457$		0			0		0.956940	+	0.290285i	$0.0937500\pi$
$458$		−	1.34312i		−	1.34312i
$459$	1.12175	−	1.51251i	1.12175	−	1.51251i
$460$	0.0238449	−	0.0951944i	0.0238449	−	0.0951944i
$461$		0			0		0.903989	−	0.427555i	$-0.140625\pi$
$461$		0			0		−0.903989	+	0.427555i	$0.859375\pi$
$462$		0			0
$463$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$463$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$464$		0			0
$465$	1.65493	+	1.10579i	1.65493	+	1.10579i
$466$	−0.800094	+	1.07880i	−0.800094	+	1.07880i
$467$	−1.66094	+	0.0815966i	−1.66094	+	0.0815966i	−0.857729	−	0.514103i	$-0.828125\pi$
$467$	−1.66094	+	0.0815966i	−1.66094	+	0.0815966i	−0.803208	+	0.595699i	$0.796875\pi$
$468$		0			0
$469$		0			0
$470$	−1.00845	−	0.200593i	−1.00845	−	0.200593i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	1.95213	−	0.192268i	1.95213	−	0.192268i
$475$	0.0788231	−	1.60448i	0.0788231	−	1.60448i
$476$		0			0
$477$	0.280825	−	1.89317i	0.280825	−	1.89317i
$478$		0			0
$479$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$479$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$480$	0.671559	−	0.740951i	0.671559	−	0.740951i
$481$		0			0
$482$	0.157456	−	0.116777i	0.157456	−	0.116777i
$483$		0			0
$484$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$485$		0			0
$486$	−0.471397	−	0.881921i	−0.471397	−	0.881921i
$487$		0			0		−0.634393	−	0.773010i	$-0.718750\pi$
$487$		0			0		0.634393	+	0.773010i	$0.281250\pi$
$488$	1.82776	−	0.757083i	1.82776	−	0.757083i
$489$		0			0
$490$	0.555570	−	0.831470i	0.555570	−	0.831470i
$491$		0			0		−0.514103	−	0.857729i	$-0.671875\pi$
$491$		0			0		0.514103	+	0.857729i	$0.328125\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	1.95213	+	0.388302i	1.95213	+	0.388302i
$497$		0			0
$498$	−1.59449	−	0.754140i	−1.59449	−	0.754140i
$499$	0.452483	−	1.26460i	0.452483	−	1.26460i	−0.471397	−	0.881921i	$-0.656250\pi$
$499$	0.452483	−	1.26460i	0.452483	−	1.26460i	0.923880	−	0.382683i	$-0.125000\pi$
$500$	−0.941544	+	0.336890i	−0.941544	+	0.336890i
$501$	0.845855	−	0.125471i	0.845855	−	0.125471i
$502$		0			0
$503$	−1.71098	+	0.914539i	−1.71098	+	0.914539i	−0.740951	+	0.671559i	$0.765625\pi$
$503$	−1.71098	+	0.914539i	−1.71098	+	0.914539i	−0.970031	+	0.242980i	$0.921875\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.903989	−	0.427555i	−0.903989	−	0.427555i
$508$		0			0
$509$		0			0		0.970031	−	0.242980i	$-0.0781250\pi$
$509$		0			0		−0.970031	+	0.242980i	$0.921875\pi$
$510$	−1.26460	+	1.39528i	−1.26460	+	1.39528i
$511$		0			0
$512$	0.336890	−	0.941544i	0.336890	−	0.941544i
$513$	−1.60642			−1.60642
$514$	1.34150	−	1.48012i	1.34150	−	1.48012i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.448786	−	1.47945i	−0.448786	−	1.47945i
$520$		0			0
$521$		0			0		0.881921	−	0.471397i	$-0.156250\pi$
$521$		0			0		−0.881921	+	0.471397i	$0.843750\pi$
$522$		0			0
$523$		0			0		0.989177	−	0.146730i	$-0.0468750\pi$
$523$		0			0		−0.989177	+	0.146730i	$0.953125\pi$
$524$		0			0
$525$		0			0
$526$	−0.609090	−	0.288078i	−0.609090	−	0.288078i
$527$	−3.67602	−	0.731207i	−3.67602	−	0.731207i
$528$		0			0
$529$	−0.971340	+	0.193211i	−0.971340	+	0.193211i
$530$	−0.465035	+	1.85652i	−0.465035	+	1.85652i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−1.26268	+	0.124363i	−1.26268	+	0.124363i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	0.382683	+	0.923880i	0.382683	+	0.923880i
$541$	0.509389	+	0.686831i	0.509389	+	0.686831i	0.980785	−	0.195090i	$-0.0625000\pi$
$541$	0.509389	+	0.686831i	0.509389	+	0.686831i	−0.471397	+	0.881921i	$0.656250\pi$
$542$	1.48413	−	1.10071i	1.48413	−	1.10071i
$543$	1.67035	+	0.691883i	1.67035	+	0.691883i
$544$	−0.634393	+	1.77301i	−0.634393	+	1.77301i
$545$	−0.448969	+	0.185969i	−0.448969	+	0.185969i
$546$		0			0
$547$		0			0		0.146730	−	0.989177i	$-0.453125\pi$
$547$		0			0		−0.146730	+	0.989177i	$0.546875\pi$
$548$	1.61310	−	1.07784i	1.61310	−	1.07784i
$549$	−0.0970732	+	1.97597i	−0.0970732	+	1.97597i
$550$		0			0
$551$		0			0
$552$	0.0939097	+	0.0284872i	0.0939097	+	0.0284872i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.43749	−	0.360073i	1.43749	−	0.360073i
$557$	−0.941658	+	0.0462607i	−0.941658	+	0.0462607i	−0.514103	−	0.857729i	$-0.671875\pi$
$557$	−0.941658	+	0.0462607i	−0.941658	+	0.0462607i	−0.427555	+	0.903989i	$0.640625\pi$
$558$	−1.18566	+	1.59868i	−1.18566	+	1.59868i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.50328	+	0.710998i	−1.50328	+	0.710998i	−0.989177	−	0.146730i	$-0.953125\pi$
$563$	−1.50328	+	0.710998i	−1.50328	+	0.710998i	−0.514103	+	0.857729i	$0.671875\pi$
$564$	0.249834	−	0.997391i	0.249834	−	0.997391i
$565$	1.02190	−	1.37787i	1.02190	−	1.37787i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.881921	−	0.471397i	$-0.843750\pi$
$569$		0			0		0.881921	+	0.471397i	$0.156250\pi$
$570$	1.59868	+	0.157456i	1.59868	+	0.157456i
$571$	0.672968	+	1.88082i	0.672968	+	1.88082i	0.382683	+	0.923880i	$0.375000\pi$
$571$	0.672968	+	1.88082i	0.672968	+	1.88082i	0.290285	+	0.956940i	$0.406250\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.0693922	−	0.0693922i	−0.0693922	−	0.0693922i
$576$	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	$0.750000\pi$
$578$	0.857729	−	2.39719i	0.857729	−	2.39719i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	1.24723	+	1.24723i	1.24723	+	1.24723i
$587$	−1.24178	−	0.920964i	−1.24178	−	0.920964i	−0.242980	−	0.970031i	$-0.578125\pi$
$587$	−1.24178	−	0.920964i	−1.24178	−	0.920964i	−0.998795	+	0.0490677i	$0.984375\pi$
$588$	0.803208	+	0.595699i	0.803208	+	0.595699i
$589$	1.36705	+	2.89038i	1.36705	+	2.89038i
$590$		0			0
$591$	0.923880	+	1.38268i	0.923880	+	1.38268i
$592$		0			0
$593$	0.823301	−	1.23216i	0.823301	−	1.23216i	−0.146730	−	0.989177i	$-0.546875\pi$
$593$	0.823301	−	1.23216i	0.823301	−	1.23216i	0.970031	−	0.242980i	$-0.0781250\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.07784	−	0.269985i	−1.07784	−	0.269985i
$598$		0			0
$599$		0			0		−0.773010	−	0.634393i	$-0.781250\pi$
$599$		0			0		0.773010	+	0.634393i	$0.218750\pi$
$600$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$601$	−0.938254	−	0.0924099i	−0.938254	−	0.0924099i	−0.382683	−	0.923880i	$-0.625000\pi$
$601$	−0.938254	−	0.0924099i	−0.938254	−	0.0924099i	−0.555570	+	0.831470i	$0.687500\pi$
$602$		0			0
$603$		0			0
$604$	−0.924678	+	0.183930i	−0.924678	+	0.183930i
$605$	−0.989177	−	0.146730i	−0.989177	−	0.146730i
$606$		0			0
$607$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$607$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$608$	1.53724	−	0.466318i	1.53724	−	0.466318i
$609$		0			0
$610$	0.290285	−	1.95694i	0.290285	−	1.95694i
$611$		0			0
$612$	−1.33154	−	1.33154i	−1.33154	−	1.33154i
$613$		0			0		−0.671559	−	0.740951i	$-0.734375\pi$
$613$		0			0		0.671559	+	0.740951i	$0.265625\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.100782	+	1.02325i	0.100782	+	1.02325i	0.903989	+	0.427555i	$0.140625\pi$
$617$	0.100782	+	1.02325i	0.100782	+	1.02325i	−0.803208	+	0.595699i	$0.796875\pi$
$618$		0			0
$619$	−1.66405	+	0.997391i	−1.66405	+	0.997391i	−0.707107	+	0.707107i	$0.750000\pi$
$619$	−1.66405	+	0.997391i	−1.66405	+	0.997391i	−0.956940	+	0.290285i	$0.906250\pi$
$620$	1.33665	−	1.47477i	1.33665	−	1.47477i
$621$	−0.0659037	+	0.0727135i	−0.0659037	+	0.0727135i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.360791	+	0.674993i	0.360791	+	0.674993i	0.995185	−	0.0980171i	$-0.0312500\pi$
$631$	0.360791	+	0.674993i	0.360791	+	0.674993i	−0.634393	+	0.773010i	$0.718750\pi$
$632$	0.0962497	−	1.95921i	0.0962497	−	1.95921i
$633$	−0.465035	+	0.141067i	−0.465035	+	0.141067i
$634$	0.113263	+	0.373380i	0.113263	+	0.373380i
$635$		0			0
$636$	−1.83147	−	0.555570i	−1.83147	−	0.555570i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.634393	−	0.773010i	−0.634393	−	0.773010i
$641$		0			0			−	1.00000i	$-0.5\pi$
$641$		0			0				1.00000i	$0.5\pi$
$642$	−0.0622564	−	1.26726i	−0.0622564	−	1.26726i
$643$		0			0		−0.242980	−	0.970031i	$-0.578125\pi$
$643$		0			0		0.242980	+	0.970031i	$0.421875\pi$
$644$		0			0
$645$		0			0
$646$	−2.89476	+	0.878117i	−2.89476	+	0.878117i
$647$	−1.14010	+	0.345845i	−1.14010	+	0.345845i	−0.803208	−	0.595699i	$-0.796875\pi$
$647$	−1.14010	+	0.345845i	−1.14010	+	0.345845i	−0.336890	+	0.941544i	$0.609375\pi$
$648$	−0.941544	+	0.336890i	−0.941544	+	0.336890i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.19462	−	0.427441i	−1.19462	−	0.427441i	−0.336890	−	0.941544i	$-0.609375\pi$
$653$	−1.19462	−	0.427441i	−1.19462	−	0.427441i	−0.857729	+	0.514103i	$0.828125\pi$
$654$	−0.163715	−	0.457553i	−0.163715	−	0.457553i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.671559	−	0.740951i	$-0.265625\pi$
$659$		0			0		−0.671559	+	0.740951i	$0.734375\pi$
$660$		0			0
$661$	1.66405	−	0.997391i	1.66405	−	0.997391i	0.707107	−	0.707107i	$-0.250000\pi$
$661$	1.66405	−	0.997391i	1.66405	−	0.997391i	0.956940	−	0.290285i	$-0.0937500\pi$
$662$	−0.838679	+	0.166824i	−0.838679	+	0.166824i
$663$		0			0
$664$	−0.979938	+	1.46658i	−0.979938	+	1.46658i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		−	0.855110i		−	0.855110i
$669$		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
$675$	0.989177	+	0.146730i	0.989177	+	0.146730i
$676$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$677$	−0.195798	−	0.00961895i	−0.195798	−	0.00961895i	−0.0490677	−	0.998795i	$-0.515625\pi$
$677$	−0.195798	−	0.00961895i	−0.195798	−	0.00961895i	−0.146730	+	0.989177i	$0.546875\pi$
$678$	1.32607	+	1.08827i	1.32607	+	1.08827i
$679$		0			0
$680$	1.19462	+	1.45565i	1.19462	+	1.45565i
$681$	0.448786	+	0.368309i	0.448786	+	0.368309i
$682$		0			0
$683$	1.90278	+	0.476623i	1.90278	+	0.476623i	0.998795	+	0.0490677i	$0.0156250\pi$
$683$	1.90278	+	0.476623i	1.90278	+	0.476623i	0.903989	+	0.427555i	$0.140625\pi$
$684$	−0.235710	+	1.58903i	−0.235710	+	1.58903i
$685$	−0.0951944	−	1.93773i	−0.0951944	−	1.93773i
$686$		0			0
$687$	0.746196	−	1.11676i	0.746196	−	1.11676i
$688$		0			0
$689$		0			0
$690$	0.0727135	−	0.0659037i	0.0727135	−	0.0659037i
$691$	−0.773010	−	1.63439i	−0.773010	−	1.63439i	−0.773010	−	0.634393i	$-0.781250\pi$
$691$	−0.773010	−	1.63439i	−0.773010	−	1.63439i		−	1.00000i	$-0.5\pi$
$692$	−1.52929	+	0.226848i	−1.52929	+	0.226848i
$693$		0			0
$694$	0.275899	−	0.275899i	0.275899	−	0.275899i
$695$	0.430174	−	1.41809i	0.430174	−	1.41809i
$696$		0			0
$697$		0			0
$698$	−0.920964	+	0.755815i	−0.920964	+	0.755815i
$699$	−1.26460	+	0.452483i	−1.26460	+	0.452483i
$700$		0			0
$701$		0			0		−0.857729	−	0.514103i	$-0.828125\pi$
$701$		0			0		0.857729	+	0.514103i	$0.171875\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.727051	−	0.727051i	−0.727051	−	0.727051i
$706$	−0.125471	−	0.265286i	−0.125471	−	0.265286i
$707$		0			0
$708$		0			0
$709$	−0.401370	−	1.12175i	−0.401370	−	1.12175i	−0.956940	−	0.290285i	$-0.906250\pi$
$709$	−0.401370	−	1.12175i	−0.401370	−	1.12175i	0.555570	−	0.831470i	$-0.312500\pi$
$710$		0			0
$711$	1.72995	+	0.924678i	1.72995	+	0.924678i
$712$		0			0
$713$	0.186915	+	0.0567000i	0.186915	+	0.0567000i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$719$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$720$	0.970031	−	0.242980i	0.970031	−	0.242980i
$721$		0			0
$722$	1.26953	+	0.941544i	1.26953	+	0.941544i
$723$	0.195798	−	0.00961895i	0.195798	−	0.00961895i
$724$	0.929487	−	1.55075i	0.929487	−	1.55075i
$725$		0			0
$726$	0.195090	−	0.980785i	0.195090	−	0.980785i
$727$		0			0		0.634393	−	0.773010i	$-0.281250\pi$
$727$		0			0		−0.634393	+	0.773010i	$0.718750\pi$
$728$		0			0
$729$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$730$		0			0
$731$		0			0
$732$	1.94034	+	0.385958i	1.94034	+	0.385958i
$733$		0			0		0.146730	−	0.989177i	$-0.453125\pi$
$733$		0			0		−0.146730	+	0.989177i	$0.546875\pi$
$734$		0			0
$735$	0.923880	−	0.382683i	0.923880	−	0.382683i
$736$	0.0419583	−	0.0887133i	0.0419583	−	0.0887133i
$737$		0			0
$738$		0			0
$739$	1.02190	+	1.37787i	1.02190	+	1.37787i	0.923880	+	0.382683i	$0.125000\pi$
$739$	1.02190	+	1.37787i	1.02190	+	1.37787i	0.0980171	+	0.995185i	$0.468750\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.186170	−	0.226848i	−0.186170	−	0.226848i	0.671559	−	0.740951i	$-0.265625\pi$
$743$	−0.186170	−	0.226848i	−0.186170	−	0.226848i	−0.857729	+	0.514103i	$0.828125\pi$
$744$	1.40740	+	1.40740i	1.40740	+	1.40740i
$745$		0			0
$746$		0			0
$747$	−0.906796	−	1.51290i	−0.906796	−	1.51290i
$748$		0			0
$749$		0			0
$750$	−0.970031	−	0.242980i	−0.970031	−	0.242980i
$751$	−1.24441	+	0.247528i	−1.24441	+	0.247528i	−0.773010	−	0.634393i	$-0.781250\pi$
$751$	−1.24441	+	0.247528i	−1.24441	+	0.247528i	−0.471397	+	0.881921i	$0.656250\pi$
$752$	−0.949938	−	0.393477i	−0.949938	−	0.393477i
$753$		0			0
$754$		0			0
$755$	−0.317618	+	0.887682i	−0.317618	+	0.887682i
$756$		0			0
$757$		0			0		0.989177	−	0.146730i	$-0.0468750\pi$
$757$		0			0		−0.989177	+	0.146730i	$0.953125\pi$
$758$	0.691883	+	1.67035i	0.691883	+	1.67035i
$759$		0			0
$760$	0.390327	−	1.55827i	0.390327	−	1.55827i
$761$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$761$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.82665	+	0.457553i	−1.82665	+	0.457553i
$766$	0.217440	+	0.197076i	0.217440	+	0.197076i
$767$		0			0
$768$	0.803208	−	0.595699i	0.803208	−	0.595699i
$769$	−1.26879			−1.26879			−0.634393	−	0.773010i	$-0.718750\pi$
$769$	−1.26879			−1.26879			−0.634393	+	0.773010i	$0.718750\pi$
$770$		0			0
$771$	1.93773	−	0.485375i	1.93773	−	0.485375i
$772$		0			0
$773$	0.691883	+	0.327237i	0.691883	+	0.327237i	0.740951	−	0.671559i	$-0.234375\pi$
$773$	0.691883	+	0.327237i	0.691883	+	0.327237i	−0.0490677	+	0.998795i	$0.515625\pi$
$774$		0			0
$775$	−0.577774	−	1.90466i	−0.577774	−	1.90466i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.0790111	+	0.167055i	−0.0790111	+	0.167055i
$783$		0			0
$784$	0.707107	−	0.707107i	0.707107	−	0.707107i
$785$		0			0
$786$		0			0
$787$		0			0		−0.740951	−	0.671559i	$-0.765625\pi$
$787$		0			0		0.740951	+	0.671559i	$0.234375\pi$
$788$	1.50328	−	0.710998i	1.50328	−	0.710998i
$789$	−0.346392	−	0.577920i	−0.346392	−	0.577920i
$790$	−1.63099	−	1.08979i	−1.63099	−	1.08979i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−1.41809	+	1.28528i	−1.41809	+	1.28528i
$796$	−0.425215	+	1.02656i	−0.425215	+	1.02656i
$797$	−0.232430	−	0.313396i	−0.232430	−	0.313396i	0.671559	−	0.740951i	$-0.265625\pi$
$797$	−0.232430	−	0.313396i	−0.232430	−	0.313396i	−0.903989	+	0.427555i	$0.859375\pi$
$798$		0			0
$799$	1.78882	+	0.740952i	1.78882	+	0.740952i
$800$	−0.989177	+	0.146730i	−0.989177	+	0.146730i
$801$		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		0.634393	−	0.773010i	$-0.281250\pi$
$809$		0			0		−0.634393	+	0.773010i	$0.718750\pi$
$810$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$811$	0.0713052	−	0.284666i	0.0713052	−	0.284666i	−0.923880	−	0.382683i	$-0.875000\pi$
$811$	0.0713052	−	0.284666i	0.0713052	−	0.284666i	0.995185	+	0.0980171i	$0.0312500\pi$
$812$		0			0
$813$	1.84553	−	0.0906652i	1.84553	−	0.0906652i
$814$		0			0
$815$		0			0
$816$	−1.51251	+	1.12175i	−1.51251	+	1.12175i
$817$		0			0
$818$	−0.0462607	+	0.941658i	−0.0462607	+	0.941658i
$819$		0			0
$820$		0			0
$821$		0			0		0.595699	−	0.803208i	$-0.296875\pi$
$821$		0			0		−0.595699	+	0.803208i	$0.703125\pi$
$822$	1.94006			1.94006
$823$		0			0		−0.956940	−	0.290285i	$-0.906250\pi$
$823$		0			0		0.956940	+	0.290285i	$0.0937500\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.131448	+	0.367372i	0.131448	+	0.367372i	0.989177	−	0.146730i	$-0.0468750\pi$
$827$	0.131448	+	0.367372i	0.131448	+	0.367372i	−0.857729	+	0.514103i	$0.828125\pi$
$828$	0.0622564	+	0.0758597i	0.0622564	+	0.0758597i
$829$	−0.346392	+	0.577920i	−0.346392	+	0.577920i	−0.980785	−	0.195090i	$-0.937500\pi$
$829$	−0.346392	+	0.577920i	−0.346392	+	0.577920i	0.634393	+	0.773010i	$0.281250\pi$
$830$	0.754140	+	1.59449i	0.754140	+	1.59449i
$831$		0			0
$832$		0			0
$833$	−1.33154	+	1.33154i	−1.33154	+	1.33154i
$834$	1.39528	+	0.499238i	1.39528	+	0.499238i
$835$	−0.733452	−	0.439614i	−0.733452	−	0.439614i
$836$		0			0
$837$	−1.87402	+	0.670535i	−1.87402	+	0.670535i
$838$		0			0
$839$		0			0		0.471397	−	0.881921i	$-0.343750\pi$
$839$		0			0		−0.471397	+	0.881921i	$0.656250\pi$
$840$		0			0
$841$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$842$	−1.04786	+	1.04786i	−1.04786	+	1.04786i
$843$		0			0
$844$	0.0713052	+	0.480701i	0.0713052	+	0.480701i
$845$	0.427555	+	0.903989i	0.427555	+	0.903989i
$846$	0.761850	−	0.690501i	0.761850	−	0.690501i
$847$		0			0
$848$	−0.818289	+	1.73013i	−0.818289	+	1.73013i
$849$		0			0
$850$	1.86271	−	0.276306i	1.86271	−	0.276306i
$851$		0			0
$852$		0			0
$853$		0			0		−0.970031	−	0.242980i	$-0.921875\pi$
$853$		0			0		0.970031	+	0.242980i	$0.0781250\pi$
$854$		0			0
$855$	1.24178	+	1.01910i	1.24178	+	1.01910i
$856$	−1.26268	−	0.124363i	−1.26268	−	0.124363i
$857$	1.96883	+	0.193913i	1.96883	+	0.193913i	0.998795	−	0.0490677i	$-0.0156250\pi$
$857$	1.96883	+	0.193913i	1.96883	+	0.193913i	0.970031	+	0.242980i	$0.0781250\pi$
$858$		0			0
$859$	−1.97597	−	0.0970732i	−1.97597	−	0.0970732i	−0.980785	−	0.195090i	$-0.937500\pi$
$859$	−1.97597	−	0.0970732i	−1.97597	−	0.0970732i	−0.995185	+	0.0980171i	$0.968750\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.567099	+	1.36910i	0.567099	+	1.36910i	0.903989	+	0.427555i	$0.140625\pi$
$863$	0.567099	+	1.36910i	0.567099	+	1.36910i	−0.336890	+	0.941544i	$0.609375\pi$
$864$	0.195090	+	0.980785i	0.195090	+	0.980785i
$865$	−0.591637	+	1.42834i	−0.591637	+	1.42834i
$866$		0			0
$867$	2.04498	−	1.51666i	2.04498	−	1.51666i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.476623	+	0.0948062i	−0.476623	+	0.0948062i
$873$		0			0
$874$	0.154617	−	0.0307552i	0.154617	−	0.0307552i
$875$		0			0
$876$		0			0
$877$		0			0		0.671559	−	0.740951i	$-0.265625\pi$
$877$		0			0		−0.671559	+	0.740951i	$0.734375\pi$
$878$	−0.854922	−	1.42635i	−0.854922	−	1.42635i
$879$	0.344109	+	1.72995i	0.344109	+	1.72995i
$880$		0			0
$881$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$881$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$882$	0.336890	+	0.941544i	0.336890	+	0.941544i
$883$		0			0		−0.941544	−	0.336890i	$-0.890625\pi$
$883$		0			0		0.941544	+	0.336890i	$0.109375\pi$
$884$		0			0
$885$		0			0
$886$	−0.0750191	+	0.181112i	−0.0750191	+	0.181112i
$887$	−0.633141	−	1.18452i	−0.633141	−	1.18452i	−0.970031	−	0.242980i	$-0.921875\pi$
$887$	−0.633141	−	1.18452i	−0.633141	−	1.18452i	0.336890	−	0.941544i	$-0.390625\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.401336	−	1.60222i	−0.401336	−	1.60222i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.290285	−	0.956940i	0.290285	−	0.956940i
$901$	1.54091	−	3.25798i	1.54091	−	3.25798i
$902$		0			0
$903$		0			0
$904$	1.27107	−	1.15203i	1.27107	−	1.15203i
$905$	−0.852275	−	1.59449i	−0.852275	−	1.59449i
$906$	−0.871028	−	0.360791i	−0.871028	−	0.360791i
$907$		0			0		−0.146730	−	0.989177i	$-0.546875\pi$
$907$		0			0		0.146730	+	0.989177i	$0.453125\pi$
$908$	0.430174	−	0.389887i	0.430174	−	0.389887i
$909$		0			0
$910$		0			0
$911$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$911$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$912$	1.53724	+	0.466318i	1.53724	+	0.466318i
$913$		0			0
$914$		0			0
$915$	1.32858	−	1.46586i	1.32858	−	1.46586i
$916$	−0.995185	−	0.901983i	−0.995185	−	0.901983i
$917$		0			0
$918$	−0.367372	−	1.84691i	−0.367372	−	1.84691i
$919$	0.0569057	+	0.577774i	0.0569057	+	0.577774i	0.980785	+	0.195090i	$0.0625000\pi$
$919$	0.0569057	+	0.577774i	0.0569057	+	0.577774i	−0.923880	+	0.382683i	$0.875000\pi$
$920$	−0.0545211	−	0.0815966i	−0.0545211	−	0.0815966i
$921$		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	$0.375000\pi$
$930$	1.93072	−	0.483620i	1.93072	−	0.483620i
$931$	1.58903	+	0.235710i	1.58903	+	0.235710i
$932$	0.262029	+	1.31731i	0.262029	+	1.31731i
$933$		0			0
$934$	−1.05496	+	1.28547i	−1.05496	+	1.28547i
$935$		0			0
$936$		0			0
$937$		0			0		−0.773010	−	0.634393i	$-0.781250\pi$
$937$		0			0		0.773010	+	0.634393i	$0.218750\pi$
$938$		0			0
$939$		0			0
$940$	−0.825862	+	0.612501i	−0.825862	+	0.612501i
$941$		0			0		−0.0490677	−	0.998795i	$-0.515625\pi$
$941$		0			0		0.0490677	+	0.998795i	$0.484375\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.403096	−	0.852275i	−0.403096	−	0.852275i	−0.998795	−	0.0490677i	$-0.984375\pi$
$947$	−0.403096	−	0.852275i	−0.403096	−	0.852275i	0.595699	−	0.803208i	$-0.296875\pi$
$948$	1.16851	−	1.57555i	1.16851	−	1.57555i
$949$		0			0
$950$	−1.13591	−	1.13591i	−1.13591	−	1.13591i
$951$	−0.113263	+	0.373380i	−0.113263	+	0.373380i
$952$		0			0
$953$	0.403096	−	0.754140i	0.403096	−	0.754140i	−0.595699	−	0.803208i	$-0.703125\pi$
$953$	0.403096	−	0.754140i	0.403096	−	0.754140i	0.998795	+	0.0490677i	$0.0156250\pi$
$954$	−1.21415	−	1.47945i	−1.21415	−	1.47945i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.0980171	−	0.995185i	−0.0980171	−	0.995185i
$961$	2.09415	+	2.09415i	2.09415	+	2.09415i
$962$		0			0
$963$	0.652287	−	1.08827i	0.652287	−	1.08827i
$964$	0.0192147	−	0.195090i	0.0192147	−	0.195090i
$965$		0			0
$966$		0			0
$967$		0			0		−0.881921	−	0.471397i	$-0.843750\pi$
$967$		0			0		0.881921	+	0.471397i	$0.156250\pi$
$968$	−0.941544	−	0.336890i	−0.941544	−	0.336890i
$969$	−2.89476	−	0.878117i	−2.89476	−	0.878117i
$970$		0			0
$971$		0			0		0.595699	−	0.803208i	$-0.296875\pi$
$971$		0			0		−0.595699	+	0.803208i	$0.703125\pi$
$972$	−0.970031	−	0.242980i	−0.970031	−	0.242980i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.666487	−	1.86271i	0.666487	−	1.86271i
$977$	1.66094	+	1.10980i	1.66094	+	1.10980i	0.857729	+	0.514103i	$0.171875\pi$
$977$	1.66094	+	1.10980i	1.66094	+	1.10980i	0.803208	+	0.595699i	$0.203125\pi$
$978$		0			0
$979$		0			0
$980$	−0.242980	−	0.970031i	−0.242980	−	0.970031i
$981$	0.118079	−	0.471397i	0.118079	−	0.471397i
$982$		0			0
$983$	−0.427441	+	0.520839i	−0.427441	+	0.520839i	−0.941544	−	0.336890i	$-0.890625\pi$
$983$	−0.427441	+	0.520839i	−0.427441	+	0.520839i	0.514103	+	0.857729i	$0.328125\pi$
$984$		0			0
$985$	0.162997	−	1.65493i	0.162997	−	1.65493i
$986$		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			$0$
$992$	1.59868	−	1.18566i	1.59868	−	1.18566i
$993$	−0.790019	−	0.327237i	−0.790019	−	0.327237i
$994$		0			0
$995$	0.661906	+	0.892476i	0.661906	+	0.892476i
$996$	−1.62958	+	0.674993i	−1.62958	+	0.674993i
$997$		0			0		0.740951	−	0.671559i	$-0.234375\pi$
$997$		0			0		−0.740951	+	0.671559i	$0.765625\pi$
$998$	−0.633141	−	1.18452i	−0.633141	−	1.18452i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3840.1.dy.a.869.2	yes	64
3.2	odd	2	inner	3840.1.dy.a.869.1	✓	64
5.4	even	2	inner	3840.1.dy.a.869.1	✓	64
15.14	odd	2	CM	3840.1.dy.a.869.2	yes	64
256.109	even	64	inner	3840.1.dy.a.2669.2	yes	64
768.365	odd	64	inner	3840.1.dy.a.2669.1	yes	64
1280.109	even	64	inner	3840.1.dy.a.2669.1	yes	64
3840.2669	odd	64	inner	3840.1.dy.a.2669.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3840.1.dy.a.869.1	✓	64	3.2	odd	2	inner
3840.1.dy.a.869.1	✓	64	5.4	even	2	inner
3840.1.dy.a.869.2	yes	64	1.1	even	1	trivial
3840.1.dy.a.869.2	yes	64	15.14	odd	2	CM
3840.1.dy.a.2669.1	yes	64	768.365	odd	64	inner
3840.1.dy.a.2669.1	yes	64	1280.109	even	64	inner
3840.1.dy.a.2669.2	yes	64	256.109	even	64	inner
3840.1.dy.a.2669.2	yes	64	3840.2669	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)

\(f(q)\)	\(=\)	\(q+(0.671559 - 0.740951i) q^{2} +(0.970031 - 0.242980i) q^{3} +(-0.0980171 - 0.995185i) q^{4} +(-0.903989 - 0.427555i) q^{5} +(0.471397 - 0.881921i) q^{6} +(-0.803208 - 0.595699i) q^{8} +(0.881921 - 0.471397i) q^{9} +O(q^{10})\)	\(q+(0.671559 - 0.740951i) q^{2} +(0.970031 - 0.242980i) q^{3} +(-0.0980171 - 0.995185i) q^{4} +(-0.903989 - 0.427555i) q^{5} +(0.471397 - 0.881921i) q^{6} +(-0.803208 - 0.595699i) q^{8} +(0.881921 - 0.471397i) q^{9} +(-0.923880 + 0.382683i) q^{10} +(-0.336890 - 0.941544i) q^{12} +(-0.980785 - 0.195090i) q^{15} +(-0.980785 + 0.195090i) q^{16} +(1.84691 - 0.367372i) q^{17} +(0.242980 - 0.970031i) q^{18} +(-1.19028 - 1.07880i) q^{19} +(-0.336890 + 0.941544i) q^{20} +(-0.0976628 + 0.00961895i) q^{23} +(-0.923880 - 0.382683i) q^{24} +(0.634393 + 0.773010i) q^{25} +(0.740951 - 0.671559i) q^{27} +(-0.803208 + 0.595699i) q^{30} +(-1.83886 - 0.761681i) q^{31} +(-0.514103 + 0.857729i) q^{32} +(0.968101 - 1.61518i) q^{34} +(-0.555570 - 0.831470i) q^{36} +(-1.59868 + 0.157456i) q^{38} +(0.471397 + 0.881921i) q^{40} +(-0.998795 + 0.0490677i) q^{45} +(-0.0584592 + 0.0788231i) q^{46} +(0.854922 + 0.571240i) q^{47} +(-0.903989 + 0.427555i) q^{48} +(-0.831470 + 0.555570i) q^{49} +(0.998795 + 0.0490677i) q^{50} +(1.70229 - 0.805124i) q^{51} +(1.14010 - 1.53724i) q^{53} -1.00000i q^{54} +(-1.41673 - 0.757259i) q^{57} +(-0.0980171 + 0.995185i) q^{60} +(-1.01708 + 1.69689i) q^{61} +(-1.79927 + 0.850993i) q^{62} +(0.290285 + 0.956940i) q^{64} +(-0.546632 - 1.80200i) q^{68} +(-0.0923988 + 0.0330608i) q^{69} +(-0.989177 - 0.146730i) q^{72} +(0.803208 + 0.595699i) q^{75} +(-0.956940 + 1.29028i) q^{76} +(1.08979 + 1.63099i) q^{79} +(0.970031 + 0.242980i) q^{80} +(0.555570 - 0.831470i) q^{81} +(-0.0865477 - 1.76172i) q^{83} +(-1.82665 - 0.457553i) q^{85} +(-0.634393 + 0.773010i) q^{90} +(0.0191453 + 0.0962497i) q^{92} +(-1.96883 - 0.292048i) q^{93} +(0.997391 - 0.249834i) q^{94} +(0.614748 + 1.48413i) q^{95} +(-0.290285 + 0.956940i) q^{96} +(-0.146730 + 0.989177i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q+O(q^{100}) \) 64 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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