LMFDB - Embedded newform 3840.1.dy.a.1709.2

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			1709.2
Root			$-0.514103 - 0.857729i$ of defining polynomial
Character	$\chi$	$=$	3840.1709
Dual form			3840.1.dy.a.1829.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0490677 - 0.998795i) q^{2} +(0.514103 + 0.857729i) q^{3} +(-0.995185 - 0.0980171i) q^{4} +(0.336890 - 0.941544i) q^{5} +(0.881921 - 0.471397i) q^{6} +(-0.146730 + 0.989177i) q^{8} +(-0.471397 + 0.881921i) q^{9} +O(q^{10})$	\(q+(0.0490677 - 0.998795i) q^{2} +(0.514103 + 0.857729i) q^{3} +(-0.995185 - 0.0980171i) q^{4} +(0.336890 - 0.941544i) q^{5} +(0.881921 - 0.471397i) q^{6} +(-0.146730 + 0.989177i) q^{8} +(-0.471397 + 0.881921i) q^{9} +(-0.923880 - 0.382683i) q^{10} +(-0.427555 - 0.903989i) q^{12} +(0.980785 - 0.195090i) q^{15} +(0.980785 + 0.195090i) q^{16} +(1.77324 + 0.352719i) q^{17} +(0.857729 + 0.514103i) q^{18} +(0.293107 + 0.0143994i) q^{19} +(-0.427555 + 0.903989i) q^{20} +(-0.145252 + 1.47477i) q^{23} +(-0.923880 + 0.382683i) q^{24} +(-0.773010 - 0.634393i) q^{25} +(-0.998795 + 0.0490677i) q^{27} +(-0.146730 - 0.989177i) q^{30} +(0.181112 - 0.0750191i) q^{31} +(0.242980 - 0.970031i) q^{32} +(0.439303 - 1.75380i) q^{34} +(0.555570 - 0.831470i) q^{36} +(0.0287642 - 0.292048i) q^{38} +(0.881921 + 0.471397i) q^{40} +(0.671559 + 0.740951i) q^{45} +(1.46586 + 0.217440i) q^{46} +(0.404061 - 0.269985i) q^{47} +(0.336890 + 0.941544i) q^{48} +(0.831470 + 0.555570i) q^{49} +(-0.671559 + 0.740951i) q^{50} +(0.609090 + 1.70229i) q^{51} +(0.574286 + 0.0851872i) q^{53} +1.00000i q^{54} +(0.138337 + 0.258809i) q^{57} +(-0.995185 + 0.0980171i) q^{60} +(0.390327 - 1.55827i) q^{61} +(-0.0660420 - 0.184575i) q^{62} +(-0.956940 - 0.290285i) q^{64} +(-1.73013 - 0.524828i) q^{68} +(-1.33962 + 0.633595i) q^{69} +(-0.803208 - 0.595699i) q^{72} +(0.146730 - 0.989177i) q^{75} +(-0.290285 - 0.0430597i) q^{76} +(1.08979 - 1.63099i) q^{79} +(0.514103 - 0.857729i) q^{80} +(-0.555570 - 0.831470i) q^{81} +(-0.698564 + 0.633141i) q^{83} +(0.929487 - 1.55075i) q^{85} +(0.773010 - 0.634393i) q^{90} +(0.289105 - 1.45343i) q^{92} +(0.157456 + 0.116777i) q^{93} +(-0.249834 - 0.416822i) q^{94} +(0.112303 - 0.271123i) q^{95} +(0.956940 - 0.290285i) q^{96} +(0.595699 - 0.803208i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3840\mathbb{Z}\right)^\times$.

$n$	$511$	$1537$	$2561$	$2821$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{39}{64}\right)$

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 $

$2$	0.0490677	−	0.998795i	0.0490677	−	0.998795i
$2$	0.0490677	−	0.998795i	0.0490677	−	0.998795i
$3$	0.514103	+	0.857729i	0.514103	+	0.857729i
$3$	0.514103	+	0.857729i	0.514103	+	0.857729i
$4$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$5$	0.336890	−	0.941544i	0.336890	−	0.941544i
$5$	0.336890	−	0.941544i	0.336890	−	0.941544i
$6$	0.881921	−	0.471397i	0.881921	−	0.471397i
$7$		0			0		−0.956940	−	0.290285i	$-0.906250\pi$
$7$		0			0		0.956940	+	0.290285i	$0.0937500\pi$
$8$	−0.146730	+	0.989177i	−0.146730	+	0.989177i
$9$	−0.471397	+	0.881921i	−0.471397	+	0.881921i
$10$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$11$		0			0		0.803208	−	0.595699i	$-0.203125\pi$
$11$		0			0		−0.803208	+	0.595699i	$0.796875\pi$
$12$	−0.427555	−	0.903989i	−0.427555	−	0.903989i
$13$		0			0		0.427555	−	0.903989i	$-0.359375\pi$
$13$		0			0		−0.427555	+	0.903989i	$0.640625\pi$
$14$		0			0
$15$	0.980785	−	0.195090i	0.980785	−	0.195090i
$16$	0.980785	+	0.195090i	0.980785	+	0.195090i
$17$	1.77324	+	0.352719i	1.77324	+	0.352719i	0.970031	−	0.242980i	$-0.0781250\pi$
$17$	1.77324	+	0.352719i	1.77324	+	0.352719i	0.803208	+	0.595699i	$0.203125\pi$
$18$	0.857729	+	0.514103i	0.857729	+	0.514103i
$19$	0.293107	+	0.0143994i	0.293107	+	0.0143994i	0.195090	−	0.980785i	$-0.437500\pi$
$19$	0.293107	+	0.0143994i	0.293107	+	0.0143994i	0.0980171	+	0.995185i	$0.468750\pi$
$20$	−0.427555	+	0.903989i	−0.427555	+	0.903989i
$21$		0			0
$22$		0			0
$23$	−0.145252	+	1.47477i	−0.145252	+	1.47477i	0.595699	+	0.803208i	$0.296875\pi$
$23$	−0.145252	+	1.47477i	−0.145252	+	1.47477i	−0.740951	+	0.671559i	$0.765625\pi$
$24$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$25$	−0.773010	−	0.634393i	−0.773010	−	0.634393i
$26$		0			0
$27$	−0.998795	+	0.0490677i	−0.998795	+	0.0490677i
$28$		0			0
$29$		0			0		0.989177	−	0.146730i	$-0.0468750\pi$
$29$		0			0		−0.989177	+	0.146730i	$0.953125\pi$
$30$	−0.146730	−	0.989177i	−0.146730	−	0.989177i
$31$	0.181112	−	0.0750191i	0.181112	−	0.0750191i	−0.290285	−	0.956940i	$-0.593750\pi$
$31$	0.181112	−	0.0750191i	0.181112	−	0.0750191i	0.471397	+	0.881921i	$0.343750\pi$
$32$	0.242980	−	0.970031i	0.242980	−	0.970031i
$33$		0			0
$34$	0.439303	−	1.75380i	0.439303	−	1.75380i
$35$		0			0
$36$	0.555570	−	0.831470i	0.555570	−	0.831470i
$37$		0			0		−0.740951	−	0.671559i	$-0.765625\pi$
$37$		0			0		0.740951	+	0.671559i	$0.234375\pi$
$38$	0.0287642	−	0.292048i	0.0287642	−	0.292048i
$39$		0			0
$40$	0.881921	+	0.471397i	0.881921	+	0.471397i
$41$		0			0		0.773010	−	0.634393i	$-0.218750\pi$
$41$		0			0		−0.773010	+	0.634393i	$0.781250\pi$
$42$		0			0
$43$		0			0		−0.857729	−	0.514103i	$-0.828125\pi$
$43$		0			0		0.857729	+	0.514103i	$0.171875\pi$
$44$		0			0
$45$	0.671559	+	0.740951i	0.671559	+	0.740951i
$46$	1.46586	+	0.217440i	1.46586	+	0.217440i
$47$	0.404061	−	0.269985i	0.404061	−	0.269985i	−0.336890	−	0.941544i	$-0.609375\pi$
$47$	0.404061	−	0.269985i	0.404061	−	0.269985i	0.740951	+	0.671559i	$0.234375\pi$
$48$	0.336890	+	0.941544i	0.336890	+	0.941544i
$49$	0.831470	+	0.555570i	0.831470	+	0.555570i
$50$	−0.671559	+	0.740951i	−0.671559	+	0.740951i
$51$	0.609090	+	1.70229i	0.609090	+	1.70229i
$52$		0			0
$53$	0.574286	+	0.0851872i	0.574286	+	0.0851872i	0.427555	−	0.903989i	$-0.359375\pi$
$53$	0.574286	+	0.0851872i	0.574286	+	0.0851872i	0.146730	+	0.989177i	$0.453125\pi$
$54$			1.00000i			1.00000i
$55$		0			0
$56$		0			0
$57$	0.138337	+	0.258809i	0.138337	+	0.258809i
$58$		0			0
$59$		0			0		−0.427555	−	0.903989i	$-0.640625\pi$
$59$		0			0		0.427555	+	0.903989i	$0.359375\pi$
$60$	−0.995185	+	0.0980171i	−0.995185	+	0.0980171i
$61$	0.390327	−	1.55827i	0.390327	−	1.55827i	−0.382683	−	0.923880i	$-0.625000\pi$
$61$	0.390327	−	1.55827i	0.390327	−	1.55827i	0.773010	−	0.634393i	$-0.218750\pi$
$62$	−0.0660420	−	0.184575i	−0.0660420	−	0.184575i
$63$		0			0
$64$	−0.956940	−	0.290285i	−0.956940	−	0.290285i
$65$		0			0
$66$		0			0
$67$		0			0		−0.970031	−	0.242980i	$-0.921875\pi$
$67$		0			0		0.970031	+	0.242980i	$0.0781250\pi$
$68$	−1.73013	−	0.524828i	−1.73013	−	0.524828i
$69$	−1.33962	+	0.633595i	−1.33962	+	0.633595i
$70$		0			0
$71$		0			0		0.881921	−	0.471397i	$-0.156250\pi$
$71$		0			0		−0.881921	+	0.471397i	$0.843750\pi$
$72$	−0.803208	−	0.595699i	−0.803208	−	0.595699i
$73$		0			0		0.956940	−	0.290285i	$-0.0937500\pi$
$73$		0			0		−0.956940	+	0.290285i	$0.906250\pi$
$74$		0			0
$75$	0.146730	−	0.989177i	0.146730	−	0.989177i
$76$	−0.290285	−	0.0430597i	−0.290285	−	0.0430597i
$77$		0			0
$78$		0			0
$79$	1.08979	−	1.63099i	1.08979	−	1.63099i	0.382683	−	0.923880i	$-0.375000\pi$
$79$	1.08979	−	1.63099i	1.08979	−	1.63099i	0.707107	−	0.707107i	$-0.250000\pi$
$80$	0.514103	−	0.857729i	0.514103	−	0.857729i
$81$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$82$		0			0
$83$	−0.698564	+	0.633141i	−0.698564	+	0.633141i	−0.941544	−	0.336890i	$-0.890625\pi$
$83$	−0.698564	+	0.633141i	−0.698564	+	0.633141i	0.242980	+	0.970031i	$0.421875\pi$
$84$		0			0
$85$	0.929487	−	1.55075i	0.929487	−	1.55075i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.0980171	−	0.995185i	$-0.531250\pi$
$89$		0			0		0.0980171	+	0.995185i	$0.468750\pi$
$90$	0.773010	−	0.634393i	0.773010	−	0.634393i
$91$		0			0
$92$	0.289105	−	1.45343i	0.289105	−	1.45343i
$93$	0.157456	+	0.116777i	0.157456	+	0.116777i
$94$	−0.249834	−	0.416822i	−0.249834	−	0.416822i
$95$	0.112303	−	0.271123i	0.112303	−	0.271123i
$96$	0.956940	−	0.290285i	0.956940	−	0.290285i
$97$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$97$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$98$	0.595699	−	0.803208i	0.595699	−	0.803208i
$99$		0			0
$100$	0.707107	+	0.707107i	0.707107	+	0.707107i
$101$		0			0		−0.0490677	−	0.998795i	$-0.515625\pi$
$101$		0			0		0.0490677	+	0.998795i	$0.484375\pi$
$102$	1.73013	−	0.524828i	1.73013	−	0.524828i
$103$		0			0		0.634393	−	0.773010i	$-0.281250\pi$
$103$		0			0		−0.634393	+	0.773010i	$0.718750\pi$
$104$		0			0
$105$		0			0
$106$	0.113263	−	0.569414i	0.113263	−	0.569414i
$107$	−1.49969	+	0.375652i	−1.49969	+	0.375652i	−0.903989	−	0.427555i	$-0.859375\pi$
$107$	−1.49969	+	0.375652i	−1.49969	+	0.375652i	−0.595699	+	0.803208i	$0.703125\pi$
$108$	0.998795	+	0.0490677i	0.998795	+	0.0490677i
$109$	0.0841735	−	1.71339i	0.0841735	−	1.71339i	−0.471397	−	0.881921i	$-0.656250\pi$
$109$	0.0841735	−	1.71339i	0.0841735	−	1.71339i	0.555570	−	0.831470i	$-0.312500\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.378487	+	1.90278i	0.378487	+	1.90278i	0.427555	+	0.903989i	$0.359375\pi$
$113$	0.378487	+	1.90278i	0.378487	+	1.90278i	−0.0490677	+	0.998795i	$0.515625\pi$
$114$	0.265286	−	0.125471i	0.265286	−	0.125471i
$115$	1.33962	+	0.633595i	1.33962	+	0.633595i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.0490677	+	0.998795i	0.0490677	+	0.998795i
$121$	0.290285	−	0.956940i	0.290285	−	0.956940i
$122$	−1.53724	−	0.466318i	−1.53724	−	0.466318i
$123$		0			0
$124$	−0.187593	+	0.0569057i	−0.187593	+	0.0569057i
$125$	−0.857729	+	0.514103i	−0.857729	+	0.514103i
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−0.336890	+	0.941544i	−0.336890	+	0.941544i
$129$		0			0
$130$		0			0
$131$		0			0		0.857729	−	0.514103i	$-0.171875\pi$
$131$		0			0		−0.857729	+	0.514103i	$0.828125\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$136$	−0.609090	+	1.70229i	−0.609090	+	1.70229i
$137$	0.906796	+	0.484693i	0.906796	+	0.484693i	0.857729	−	0.514103i	$-0.171875\pi$
$137$	0.906796	+	0.484693i	0.906796	+	0.484693i	0.0490677	+	0.998795i	$0.484375\pi$
$138$	0.567099	+	1.36910i	0.567099	+	1.36910i
$139$	1.18996	+	1.60448i	1.18996	+	1.60448i	0.634393	+	0.773010i	$0.281250\pi$
$139$	1.18996	+	1.60448i	1.18996	+	1.60448i	0.555570	+	0.831470i	$0.312500\pi$
$140$		0			0
$141$	0.439303	+	0.207775i	0.439303	+	0.207775i
$142$		0			0
$143$		0			0
$144$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$145$		0			0
$146$		0			0
$147$	−0.0490677	+	0.998795i	−0.0490677	+	0.998795i
$148$		0			0
$149$		0			0		0.970031	−	0.242980i	$-0.0781250\pi$
$149$		0			0		−0.970031	+	0.242980i	$0.921875\pi$
$150$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$151$	−1.75535	−	0.172887i	−1.75535	−	0.172887i	−0.831470	−	0.555570i	$-0.812500\pi$
$151$	−1.75535	−	0.172887i	−1.75535	−	0.172887i	−0.923880	+	0.382683i	$0.875000\pi$
$152$	−0.0572514	+	0.287822i	−0.0572514	+	0.287822i
$153$	−1.14697	+	1.39759i	−1.14697	+	1.39759i
$154$		0			0
$155$	−0.00961895	−	0.195798i	−0.00961895	−	0.195798i
$156$		0			0
$157$		0			0		−0.146730	−	0.989177i	$-0.546875\pi$
$157$		0			0		0.146730	+	0.989177i	$0.453125\pi$
$158$	−1.57555	−	1.16851i	−1.57555	−	1.16851i
$159$	0.222174	+	0.536376i	0.222174	+	0.536376i
$160$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$161$		0			0
$162$	−0.857729	+	0.514103i	−0.857729	+	0.514103i
$163$		0			0		−0.803208	−	0.595699i	$-0.796875\pi$
$163$		0			0		0.803208	+	0.595699i	$0.203125\pi$
$164$		0			0
$165$		0			0
$166$	0.598102	+	0.728789i	0.598102	+	0.728789i
$167$	0.184575	+	1.87402i	0.184575	+	1.87402i	0.427555	+	0.903989i	$0.359375\pi$
$167$	0.184575	+	1.87402i	0.184575	+	1.87402i	−0.242980	+	0.970031i	$0.578125\pi$
$168$		0			0
$169$	−0.634393	−	0.773010i	−0.634393	−	0.773010i
$170$	−1.50328	−	1.00446i	−1.50328	−	1.00446i
$171$	−0.150869	+	0.251710i	−0.150869	+	0.251710i
$172$		0			0
$173$	0.940109	−	0.852065i	0.940109	−	0.852065i	−0.0490677	−	0.998795i	$-0.515625\pi$
$173$	0.940109	−	0.852065i	0.940109	−	0.852065i	0.989177	+	0.146730i	$0.0468750\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.941544	−	0.336890i	$-0.109375\pi$
$179$		0			0		−0.941544	+	0.336890i	$0.890625\pi$
$180$	−0.595699	−	0.803208i	−0.595699	−	0.803208i
$181$	−0.0988640	+	0.666487i	−0.0988640	+	0.666487i	0.881921	+	0.471397i	$0.156250\pi$
$181$	−0.0988640	+	0.666487i	−0.0988640	+	0.666487i	−0.980785	+	0.195090i	$0.937500\pi$
$182$		0			0
$183$	1.53724	−	0.466318i	1.53724	−	0.466318i
$184$	−1.43749	−	0.360073i	−1.43749	−	0.360073i
$185$		0			0
$186$	0.124363	−	0.151537i	0.124363	−	0.151537i
$187$		0			0
$188$	−0.428579	+	0.229080i	−0.428579	+	0.229080i
$189$		0			0
$190$	−0.265286	−	0.125471i	−0.265286	−	0.125471i
$191$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$191$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$192$	−0.242980	−	0.970031i	−0.242980	−	0.970031i
$193$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$193$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$194$		0			0
$195$		0			0
$196$	−0.773010	−	0.634393i	−0.773010	−	0.634393i
$197$	−0.710998	−	1.50328i	−0.710998	−	1.50328i	−0.857729	−	0.514103i	$-0.828125\pi$
$197$	−0.710998	−	1.50328i	−0.710998	−	1.50328i	0.146730	−	0.989177i	$-0.453125\pi$
$198$		0			0
$199$	−0.523788	−	0.979938i	−0.523788	−	0.979938i	−0.995185	−	0.0980171i	$-0.968750\pi$
$199$	−0.523788	−	0.979938i	−0.523788	−	0.979938i	0.471397	−	0.881921i	$-0.343750\pi$
$200$	0.740951	−	0.671559i	0.740951	−	0.671559i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.439303	−	1.75380i	−0.439303	−	1.75380i
$205$		0			0
$206$		0			0
$207$	−1.23216	−	0.823301i	−1.23216	−	0.823301i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.15203	+	1.27107i	1.15203	+	1.27107i	0.956940	+	0.290285i	$0.0937500\pi$
$211$	1.15203	+	1.27107i	1.15203	+	1.27107i	0.195090	+	0.980785i	$0.437500\pi$
$212$	−0.563170	−	0.141067i	−0.563170	−	0.141067i
$213$		0			0
$214$	0.301614	+	1.51631i	0.301614	+	1.51631i
$215$		0			0
$216$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$217$		0			0
$218$	−1.70720	−	0.168144i	−1.70720	−	0.168144i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$223$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$224$		0			0
$225$	0.923880	−	0.382683i	0.923880	−	0.382683i
$226$	1.91906	−	0.284666i	1.91906	−	0.284666i
$227$	−1.89317	+	0.280825i	−1.89317	+	0.280825i	−0.989177	−	0.146730i	$-0.953125\pi$
$227$	−1.89317	+	0.280825i	−1.89317	+	0.280825i	−0.903989	+	0.427555i	$0.859375\pi$
$228$	−0.112303	−	0.271123i	−0.112303	−	0.271123i
$229$	−0.0980171	+	0.00481527i	−0.0980171	+	0.00481527i	−0.0980171	−	0.995185i	$-0.531250\pi$
$229$	−0.0980171	+	0.00481527i	−0.0980171	+	0.00481527i			1.00000i	$0.5\pi$
$230$	0.698564	−	1.30692i	0.698564	−	1.30692i
$231$		0			0
$232$		0			0
$233$	0.00961895	−	0.0976628i	0.00961895	−	0.0976628i	−0.989177	−	0.146730i	$-0.953125\pi$
$233$	0.00961895	−	0.0976628i	0.00961895	−	0.0976628i	0.998795	+	0.0490677i	$0.0156250\pi$
$234$		0			0
$235$	−0.118079	−	0.471397i	−0.118079	−	0.471397i
$236$		0			0
$237$	1.95921	+	0.0962497i	1.95921	+	0.0962497i
$238$		0			0
$239$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$239$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$240$	1.00000			1.00000
$241$	−1.95213	+	0.388302i	−1.95213	+	0.388302i	−0.956940	+	0.290285i	$0.906250\pi$
$241$	−1.95213	+	0.388302i	−1.95213	+	0.388302i	−0.995185	+	0.0980171i	$0.968750\pi$
$242$	−0.941544	−	0.336890i	−0.941544	−	0.336890i
$243$	0.427555	−	0.903989i	0.427555	−	0.903989i
$244$	−0.541185	+	1.51251i	−0.541185	+	1.51251i
$245$	0.803208	−	0.595699i	0.803208	−	0.595699i
$246$		0			0
$247$		0			0
$248$	0.0476324	+	0.190159i	0.0476324	+	0.190159i
$249$	−0.902197	−	0.273678i	−0.902197	−	0.273678i
$250$	0.471397	+	0.881921i	0.471397	+	0.881921i
$251$		0			0		0.336890	−	0.941544i	$-0.390625\pi$
$251$		0			0		−0.336890	+	0.941544i	$0.609375\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	1.80798			1.80798
$256$	0.923880	+	0.382683i	0.923880	+	0.382683i
$257$	−1.34312			−1.34312			−0.671559	−	0.740951i	$-0.734375\pi$
$257$	−1.34312			−1.34312			−0.671559	+	0.740951i	$0.734375\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.818289	+	0.248225i	0.818289	+	0.248225i	0.671559	−	0.740951i	$-0.265625\pi$
$263$	0.818289	+	0.248225i	0.818289	+	0.248225i	0.146730	+	0.989177i	$0.453125\pi$
$264$		0			0
$265$	0.273678	−	0.512016i	0.273678	−	0.512016i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.427555	−	0.903989i	$-0.359375\pi$
$269$		0			0		−0.427555	+	0.903989i	$0.640625\pi$
$270$	0.941544	+	0.336890i	0.941544	+	0.336890i
$271$	−1.81225	+	0.360480i	−1.81225	+	0.360480i	−0.980785	−	0.195090i	$-0.937500\pi$
$271$	−1.81225	+	0.360480i	−1.81225	+	0.360480i	−0.831470	+	0.555570i	$0.812500\pi$
$272$	1.67035	+	0.691883i	1.67035	+	0.691883i
$273$		0			0
$274$	0.528603	−	0.881921i	0.528603	−	0.881921i
$275$		0			0
$276$	1.39528	−	0.499238i	1.39528	−	0.499238i
$277$		0			0		−0.242980	−	0.970031i	$-0.578125\pi$
$277$		0			0		0.242980	+	0.970031i	$0.421875\pi$
$278$	1.66094	−	1.10980i	1.66094	−	1.10980i
$279$	−0.0192147	+	0.195090i	−0.0192147	+	0.195090i
$280$		0			0
$281$		0			0		−0.773010	−	0.634393i	$-0.781250\pi$
$281$		0			0		0.773010	+	0.634393i	$0.218750\pi$
$282$	0.229080	−	0.428579i	0.229080	−	0.428579i
$283$		0			0		0.998795	−	0.0490677i	$-0.0156250\pi$
$283$		0			0		−0.998795	+	0.0490677i	$0.984375\pi$
$284$		0			0
$285$	0.290285	−	0.0430597i	0.290285	−	0.0430597i
$286$		0			0
$287$		0			0
$288$	0.740951	+	0.671559i	0.740951	+	0.671559i
$289$	2.09609	+	0.868227i	2.09609	+	0.868227i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.698564	−	0.633141i	−0.698564	−	0.633141i	0.242980	−	0.970031i	$-0.421875\pi$
$293$	−0.698564	−	0.633141i	−0.698564	−	0.633141i	−0.941544	+	0.336890i	$0.890625\pi$
$294$	0.995185	+	0.0980171i	0.995185	+	0.0980171i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.242980	+	0.970031i	−0.242980	+	0.970031i
$301$		0			0
$302$	−0.258809	+	1.74475i	−0.258809	+	1.74475i
$303$		0			0
$304$	0.284666	+	0.0713052i	0.284666	+	0.0713052i
$305$	−1.33569	−	0.892476i	−1.33569	−	0.892476i
$306$	1.33962	+	1.21416i	1.33962	+	1.21416i
$307$		0			0		−0.336890	−	0.941544i	$-0.609375\pi$
$307$		0			0		0.336890	+	0.941544i	$0.390625\pi$
$308$		0			0
$309$		0			0
$310$	−0.196034			−0.196034
$311$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$311$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$312$		0			0
$313$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$313$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$314$		0			0
$315$		0			0
$316$	−1.24441	+	1.51631i	−1.24441	+	1.51631i
$317$	−0.0948062	+	0.378487i	−0.0948062	+	0.378487i	−0.998795	−	0.0490677i	$-0.984375\pi$
$317$	−0.0948062	+	0.378487i	−0.0948062	+	0.378487i	0.903989	+	0.427555i	$0.140625\pi$
$318$	0.546632	−	0.195588i	0.546632	−	0.195588i
$319$		0			0
$320$	−0.595699	+	0.803208i	−0.595699	+	0.803208i
$321$	−1.09320	−	1.09320i	−1.09320	−	1.09320i
$322$		0			0
$323$	0.514671	+	0.128918i	0.514671	+	0.128918i
$324$	0.471397	+	0.881921i	0.471397	+	0.881921i
$325$		0			0
$326$		0			0
$327$	1.51290	−	0.808661i	1.51290	−	0.808661i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.276306	−	1.86271i	0.276306	−	1.86271i	−0.195090	−	0.980785i	$-0.562500\pi$
$331$	0.276306	−	1.86271i	0.276306	−	1.86271i	0.471397	−	0.881921i	$-0.343750\pi$
$332$	0.757259	−	0.561621i	0.757259	−	0.561621i
$333$		0			0
$334$	1.88082	−	0.0923988i	1.88082	−	0.0923988i
$335$		0			0
$336$		0			0
$337$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$337$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$338$	−0.803208	+	0.595699i	−0.803208	+	0.595699i
$339$	−1.43749	+	1.30287i	−1.43749	+	1.30287i
$340$	−1.07701	+	1.45218i	−1.07701	+	1.45218i
$341$		0			0
$342$	0.244004	+	0.163038i	0.244004	+	0.163038i
$343$		0			0
$344$		0			0
$345$	0.145252	+	1.47477i	0.145252	+	1.47477i
$346$	−0.804910	−	0.980785i	−0.804910	−	0.980785i
$347$	0.262029	−	0.289105i	0.262029	−	0.289105i	−0.595699	−	0.803208i	$-0.703125\pi$
$347$	0.262029	−	0.289105i	0.262029	−	0.289105i	0.857729	+	0.514103i	$0.171875\pi$
$348$		0			0
$349$	−1.58903	−	1.17850i	−1.58903	−	1.17850i	−0.881921	−	0.471397i	$-0.843750\pi$
$349$	−1.58903	−	1.17850i	−1.58903	−	1.17850i	−0.707107	−	0.707107i	$-0.750000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.455929	−	1.10071i	−0.455929	−	1.10071i	−0.970031	−	0.242980i	$-0.921875\pi$
$353$	−0.455929	−	1.10071i	−0.455929	−	1.10071i	0.514103	−	0.857729i	$-0.328125\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.634393	−	0.773010i	$-0.281250\pi$
$359$		0			0		−0.634393	+	0.773010i	$0.718750\pi$
$360$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$361$	−0.909480	−	0.0895760i	−0.909480	−	0.0895760i
$362$	0.660833	+	0.131448i	0.660833	+	0.131448i
$363$	0.970031	−	0.242980i	0.970031	−	0.242980i
$364$		0			0
$365$		0			0
$366$	−0.390327	−	1.55827i	−0.390327	−	1.55827i
$367$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$367$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$368$	−0.430174	+	1.41809i	−0.430174	+	1.41809i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.145252	−	0.131649i	−0.145252	−	0.131649i
$373$		0			0		−0.595699	−	0.803208i	$-0.703125\pi$
$373$		0			0		0.595699	+	0.803208i	$0.296875\pi$
$374$		0			0
$375$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$376$	0.207775	+	0.439303i	0.207775	+	0.439303i
$377$		0			0
$378$		0			0
$379$	−0.634393	−	0.226990i	−0.634393	−	0.226990i		−	1.00000i	$-0.5\pi$
$379$	−0.634393	−	0.226990i	−0.634393	−	0.226990i	−0.634393	+	0.773010i	$0.718750\pi$
$380$	−0.138337	+	0.258809i	−0.138337	+	0.258809i
$381$		0			0
$382$		0			0
$383$			1.19140i			1.19140i	0.803208	+	0.595699i	$0.203125\pi$
$383$			1.19140i			1.19140i	−0.803208	+	0.595699i	$0.796875\pi$
$384$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.941544	−	0.336890i	$-0.890625\pi$
$389$		0			0		0.941544	+	0.336890i	$0.109375\pi$
$390$		0			0
$391$	−0.777745	+	2.56388i	−0.777745	+	2.56388i
$392$	−0.671559	+	0.740951i	−0.671559	+	0.740951i
$393$		0			0
$394$	−1.53636	+	0.636379i	−1.53636	+	0.636379i
$395$	−1.16851	−	1.57555i	−1.16851	−	1.57555i
$396$		0			0
$397$		0			0		−0.903989	−	0.427555i	$-0.859375\pi$
$397$		0			0		0.903989	+	0.427555i	$0.140625\pi$
$398$	−1.00446	+	0.475074i	−1.00446	+	0.475074i
$399$		0			0
$400$	−0.634393	−	0.773010i	−0.634393	−	0.773010i
$401$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$401$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.970031	+	0.242980i	−0.970031	+	0.242980i
$406$		0			0
$407$		0			0
$408$	−1.77324	+	0.352719i	−1.77324	+	0.352719i
$409$	−1.11897	+	1.36347i	−1.11897	+	1.36347i	−0.195090	+	0.980785i	$0.562500\pi$
$409$	−1.11897	+	1.36347i	−1.11897	+	1.36347i	−0.923880	+	0.382683i	$0.875000\pi$
$410$		0			0
$411$	0.0504517	+	1.02697i	0.0504517	+	1.02697i
$412$		0			0
$413$		0			0
$414$	−0.882768	+	1.19028i	−0.882768	+	1.19028i
$415$	0.360791	+	0.871028i	0.360791	+	0.871028i
$416$		0			0
$417$	−0.764445	+	1.84553i	−0.764445	+	1.84553i
$418$		0			0
$419$		0			0		−0.803208	−	0.595699i	$-0.796875\pi$
$419$		0			0		0.803208	+	0.595699i	$0.203125\pi$
$420$		0			0
$421$	−1.34150	+	1.48012i	−1.34150	+	1.48012i	−0.634393	+	0.773010i	$0.718750\pi$
$421$	−1.34150	+	1.48012i	−1.34150	+	1.48012i	−0.707107	+	0.707107i	$0.750000\pi$
$422$	1.32607	−	1.08827i	1.32607	−	1.08827i
$423$	0.0476324	+	0.483620i	0.0476324	+	0.483620i
$424$	−0.168530	+	0.555570i	−0.168530	+	0.555570i
$425$	−1.14697	−	1.39759i	−1.14697	−	1.39759i
$426$		0			0
$427$		0			0
$428$	1.52929	−	0.226848i	1.52929	−	0.226848i
$429$		0			0
$430$		0			0
$431$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$431$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$432$	−0.989177	−	0.146730i	−0.989177	−	0.146730i
$433$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$433$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$434$		0			0
$435$		0			0
$436$	−0.251710	+	1.69689i	−0.251710	+	1.69689i
$437$	−0.0638102	+	0.430174i	−0.0638102	+	0.430174i
$438$		0			0
$439$	1.59133	−	0.482726i	1.59133	−	0.482726i	0.634393	−	0.773010i	$-0.281250\pi$
$439$	1.59133	−	0.482726i	1.59133	−	0.482726i	0.956940	+	0.290285i	$0.0937500\pi$
$440$		0			0
$441$	−0.881921	+	0.471397i	−0.881921	+	0.471397i
$442$		0			0
$443$	1.79927	−	0.850993i	1.79927	−	0.850993i	0.857729	−	0.514103i	$-0.171875\pi$
$443$	1.79927	−	0.850993i	1.79927	−	0.850993i	0.941544	−	0.336890i	$-0.109375\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$449$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$450$	−0.336890	−	0.941544i	−0.336890	−	0.941544i
$451$		0			0
$452$	−0.190159	−	1.93072i	−0.190159	−	1.93072i
$453$	−0.754140	−	1.59449i	−0.754140	−	1.59449i
$454$	0.187593	+	1.90466i	0.187593	+	1.90466i
$455$		0			0
$456$	−0.276306	+	0.0988640i	−0.276306	+	0.0988640i
$457$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$457$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$458$			0.0981353i			0.0981353i
$459$	−1.78841	−	0.265286i	−1.78841	−	0.265286i
$460$	−1.27107	−	0.761850i	−1.27107	−	0.761850i
$461$		0			0		−0.336890	−	0.941544i	$-0.609375\pi$
$461$		0			0		0.336890	+	0.941544i	$0.390625\pi$
$462$		0			0
$463$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$463$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$464$		0			0
$465$	0.162997	−	0.108911i	0.162997	−	0.108911i
$466$	−0.0970732	−	0.0143994i	−0.0970732	−	0.0143994i
$467$	−1.11676	−	1.23216i	−1.11676	−	1.23216i	−0.970031	−	0.242980i	$-0.921875\pi$
$467$	−1.11676	−	1.23216i	−1.11676	−	1.23216i	−0.146730	−	0.989177i	$-0.546875\pi$
$468$		0			0
$469$		0			0
$470$	−0.476623	+	0.0948062i	−0.476623	+	0.0948062i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.192268	−	1.95213i	0.192268	−	1.95213i
$475$	−0.217440	−	0.197076i	−0.217440	−	0.197076i
$476$		0			0
$477$	−0.345845	+	0.466318i	−0.345845	+	0.466318i
$478$		0			0
$479$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$479$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$480$	0.0490677	−	0.998795i	0.0490677	−	0.998795i
$481$		0			0
$482$	0.292048	+	1.96883i	0.292048	+	1.96883i
$483$		0			0
$484$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$485$		0			0
$486$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$487$		0			0		−0.773010	−	0.634393i	$-0.781250\pi$
$487$		0			0		0.773010	+	0.634393i	$0.218750\pi$
$488$	1.48413	+	0.614748i	1.48413	+	0.614748i
$489$		0			0
$490$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$491$		0			0		−0.242980	−	0.970031i	$-0.578125\pi$
$491$		0			0		0.242980	+	0.970031i	$0.421875\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.192268	−	0.0382444i	0.192268	−	0.0382444i
$497$		0			0
$498$	−0.317618	+	0.887682i	−0.317618	+	0.887682i
$499$	0.0419583	−	0.0887133i	0.0419583	−	0.0887133i	−0.881921	−	0.471397i	$-0.843750\pi$
$499$	0.0419583	−	0.0887133i	0.0419583	−	0.0887133i	0.923880	+	0.382683i	$0.125000\pi$
$500$	0.903989	−	0.427555i	0.903989	−	0.427555i
$501$	−1.51251	+	1.12175i	−1.51251	+	1.12175i
$502$		0			0
$503$	0.484693	−	0.906796i	0.484693	−	0.906796i	−0.514103	−	0.857729i	$-0.671875\pi$
$503$	0.484693	−	0.906796i	0.484693	−	0.906796i	0.998795	−	0.0490677i	$-0.0156250\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.336890	−	0.941544i	0.336890	−	0.941544i
$508$		0			0
$509$		0			0		−0.514103	−	0.857729i	$-0.671875\pi$
$509$		0			0		0.514103	+	0.857729i	$0.328125\pi$
$510$	0.0887133	−	1.80580i	0.0887133	−	1.80580i
$511$		0			0
$512$	0.427555	−	0.903989i	0.427555	−	0.903989i
$513$	−0.293461			−0.293461
$514$	−0.0659037	+	1.34150i	−0.0659037	+	1.34150i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.21415	+	0.368309i	1.21415	+	0.368309i
$520$		0			0
$521$		0			0		0.471397	−	0.881921i	$-0.343750\pi$
$521$		0			0		−0.471397	+	0.881921i	$0.656250\pi$
$522$		0			0
$523$		0			0		0.803208	−	0.595699i	$-0.203125\pi$
$523$		0			0		−0.803208	+	0.595699i	$0.796875\pi$
$524$		0			0
$525$		0			0
$526$	0.288078	−	0.805124i	0.288078	−	0.805124i
$527$	0.347616	−	0.0691450i	0.347616	−	0.0691450i
$528$		0			0
$529$	−1.17305	−	0.233335i	−1.17305	−	0.233335i
$530$	−0.497971	−	0.298472i	−0.497971	−	0.298472i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.151537	+	1.53858i	−0.151537	+	1.53858i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	0.382683	−	0.923880i	0.382683	−	0.923880i
$541$	−1.86271	+	0.276306i	−1.86271	+	0.276306i	−0.980785	−	0.195090i	$-0.937500\pi$
$541$	−1.86271	+	0.276306i	−1.86271	+	0.276306i	−0.881921	+	0.471397i	$0.843750\pi$
$542$	0.271123	+	1.82776i	0.271123	+	1.82776i
$543$	−0.622491	+	0.257844i	−0.622491	+	0.257844i
$544$	0.773010	−	1.63439i	0.773010	−	1.63439i
$545$	−1.58488	−	0.656477i	−1.58488	−	0.656477i
$546$		0			0
$547$		0			0		0.595699	−	0.803208i	$-0.296875\pi$
$547$		0			0		−0.595699	+	0.803208i	$0.703125\pi$
$548$	−0.854922	−	0.571240i	−0.854922	−	0.571240i
$549$	1.19028	+	1.07880i	1.19028	+	1.07880i
$550$		0			0
$551$		0			0
$552$	−0.430174	−	1.41809i	−0.430174	−	1.41809i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.02697	−	1.71339i	−1.02697	−	1.71339i
$557$	1.18452	+	1.30692i	1.18452	+	1.30692i	0.941544	+	0.336890i	$0.109375\pi$
$557$	1.18452	+	1.30692i	1.18452	+	1.30692i	0.242980	+	0.970031i	$0.421875\pi$
$558$	0.193913	+	0.0287642i	0.193913	+	0.0287642i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.560227	−	1.56573i	−0.560227	−	1.56573i	−0.803208	−	0.595699i	$-0.796875\pi$
$563$	−0.560227	−	1.56573i	−0.560227	−	1.56573i	0.242980	−	0.970031i	$-0.421875\pi$
$564$	−0.416822	−	0.249834i	−0.416822	−	0.249834i
$565$	1.91906	+	0.284666i	1.91906	+	0.284666i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$569$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$570$	−0.0287642	−	0.292048i	−0.0287642	−	0.292048i
$571$	−0.574257	−	1.21416i	−0.574257	−	1.21416i	−0.956940	−	0.290285i	$-0.906250\pi$
$571$	−0.574257	−	1.21416i	−0.574257	−	1.21416i	0.382683	−	0.923880i	$-0.375000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.04786	−	1.04786i	1.04786	−	1.04786i
$576$	0.707107	−	0.707107i	0.707107	−	0.707107i
$577$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$577$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$578$	0.970031	−	2.05096i	0.970031	−	2.05096i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.666656	+	0.666656i	−0.666656	+	0.666656i
$587$	−0.186170	+	1.25505i	−0.186170	+	1.25505i	0.671559	+	0.740951i	$0.265625\pi$
$587$	−0.186170	+	1.25505i	−0.186170	+	1.25505i	−0.857729	+	0.514103i	$0.828125\pi$
$588$	0.146730	−	0.989177i	0.146730	−	0.989177i
$589$	0.0541655	−	0.0193807i	0.0541655	−	0.0193807i
$590$		0			0
$591$	0.923880	−	1.38268i	0.923880	−	1.38268i
$592$		0			0
$593$	1.10980	+	1.66094i	1.10980	+	1.66094i	0.595699	+	0.803208i	$0.296875\pi$
$593$	1.10980	+	1.66094i	1.10980	+	1.66094i	0.514103	+	0.857729i	$0.328125\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.571240	−	0.953057i	0.571240	−	0.953057i
$598$		0			0
$599$		0			0		−0.634393	−	0.773010i	$-0.718750\pi$
$599$		0			0		0.634393	+	0.773010i	$0.281250\pi$
$600$	0.956940	+	0.290285i	0.956940	+	0.290285i
$601$	0.172887	+	1.75535i	0.172887	+	1.75535i	0.555570	+	0.831470i	$0.312500\pi$
$601$	0.172887	+	1.75535i	0.172887	+	1.75535i	−0.382683	+	0.923880i	$0.625000\pi$
$602$		0			0
$603$		0			0
$604$	1.72995	+	0.344109i	1.72995	+	0.344109i
$605$	−0.803208	−	0.595699i	−0.803208	−	0.595699i
$606$		0			0
$607$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$607$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$608$	0.0851872	−	0.280825i	0.0851872	−	0.280825i
$609$		0			0
$610$	−0.956940	+	1.29028i	−0.956940	+	1.29028i
$611$		0			0
$612$	1.27843	−	1.27843i	1.27843	−	1.27843i
$613$		0			0		−0.0490677	−	0.998795i	$-0.515625\pi$
$613$		0			0		0.0490677	+	0.998795i	$0.484375\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.483620	−	0.0476324i	−0.483620	−	0.0476324i	−0.146730	−	0.989177i	$-0.546875\pi$
$617$	−0.483620	−	0.0476324i	−0.483620	−	0.0476324i	−0.336890	+	0.941544i	$0.609375\pi$
$618$		0			0
$619$	−0.997391	+	0.249834i	−0.997391	+	0.249834i	−0.707107	−	0.707107i	$-0.750000\pi$
$619$	−0.997391	+	0.249834i	−0.997391	+	0.249834i	−0.290285	+	0.956940i	$0.593750\pi$
$620$	−0.00961895	+	0.195798i	−0.00961895	+	0.195798i
$621$	0.0727135	−	1.48012i	0.0727135	−	1.48012i
$622$		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
$631$	0.674993	+	0.360791i	0.674993	+	0.360791i	0.773010	−	0.634393i	$-0.218750\pi$
$631$	0.674993	+	0.360791i	0.674993	+	0.360791i	−0.0980171	+	0.995185i	$0.531250\pi$
$632$	1.45343	+	1.31731i	1.45343	+	1.31731i
$633$	−0.497971	+	1.64159i	−0.497971	+	1.64159i
$634$	0.373380	+	0.113263i	0.373380	+	0.113263i
$635$		0			0
$636$	−0.168530	−	0.555570i	−0.168530	−	0.555570i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.773010	+	0.634393i	0.773010	+	0.634393i
$641$		0			0			−	1.00000i	$-0.5\pi$
$641$		0			0				1.00000i	$0.5\pi$
$642$	−1.14553	+	1.03824i	−1.14553	+	1.03824i
$643$		0			0		0.857729	−	0.514103i	$-0.171875\pi$
$643$		0			0		−0.857729	+	0.514103i	$0.828125\pi$
$644$		0			0
$645$		0			0
$646$	0.154017	−	0.507725i	0.154017	−	0.507725i
$647$	−0.574286	+	1.89317i	−0.574286	+	1.89317i	−0.146730	+	0.989177i	$0.546875\pi$
$647$	−0.574286	+	1.89317i	−0.574286	+	1.89317i	−0.427555	+	0.903989i	$0.640625\pi$
$648$	0.903989	−	0.427555i	0.903989	−	0.427555i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.39759	−	0.661009i	−1.39759	−	0.661009i	−0.427555	−	0.903989i	$-0.640625\pi$
$653$	−1.39759	−	0.661009i	−1.39759	−	0.661009i	−0.970031	+	0.242980i	$0.921875\pi$
$654$	−0.733452	−	1.55075i	−0.733452	−	1.55075i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.0490677	−	0.998795i	$-0.484375\pi$
$659$		0			0		−0.0490677	+	0.998795i	$0.515625\pi$
$660$		0			0
$661$	0.997391	−	0.249834i	0.997391	−	0.249834i	0.290285	−	0.956940i	$-0.406250\pi$
$661$	0.997391	−	0.249834i	0.997391	−	0.249834i	0.707107	+	0.707107i	$0.250000\pi$
$662$	−1.84691	−	0.367372i	−1.84691	−	0.367372i
$663$		0			0
$664$	−0.523788	−	0.783904i	−0.523788	−	0.783904i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		−	1.88309i		−	1.88309i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$673$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$674$		0			0
$675$	0.803208	+	0.595699i	0.803208	+	0.595699i
$676$	0.555570	+	0.831470i	0.555570	+	0.831470i
$677$	1.33665	−	1.47477i	1.33665	−	1.47477i	0.595699	−	0.803208i	$-0.296875\pi$
$677$	1.33665	−	1.47477i	1.33665	−	1.47477i	0.740951	−	0.671559i	$-0.234375\pi$
$678$	1.23076	+	1.49969i	1.23076	+	1.49969i
$679$		0			0
$680$	1.39759	+	1.14697i	1.39759	+	1.14697i
$681$	−1.21415	−	1.47945i	−1.21415	−	1.47945i
$682$		0			0
$683$	−1.00845	+	1.68250i	−1.00845	+	1.68250i	−0.336890	+	0.941544i	$0.609375\pi$
$683$	−1.00845	+	1.68250i	−1.00845	+	1.68250i	−0.671559	+	0.740951i	$0.734375\pi$
$684$	0.174814	−	0.235710i	0.174814	−	0.235710i
$685$	0.761850	−	0.690501i	0.761850	−	0.690501i
$686$		0			0
$687$	−0.0545211	−	0.0815966i	−0.0545211	−	0.0815966i
$688$		0			0
$689$		0			0
$690$	1.48012	−	0.0727135i	1.48012	−	0.0727135i
$691$	−0.634393	+	0.226990i	−0.634393	+	0.226990i	−0.634393	−	0.773010i	$-0.718750\pi$
$691$	−0.634393	+	0.226990i	−0.634393	+	0.226990i			1.00000i	$0.5\pi$
$692$	−1.01910	+	0.755815i	−1.01910	+	0.755815i
$693$		0			0
$694$	−0.275899	−	0.275899i	−0.275899	−	0.275899i
$695$	1.91158	−	0.579870i	1.91158	−	0.579870i
$696$		0			0
$697$		0			0
$698$	−1.25505	+	1.52929i	−1.25505	+	1.52929i
$699$	0.0887133	−	0.0419583i	0.0887133	−	0.0419583i
$700$		0			0
$701$		0			0		−0.970031	−	0.242980i	$-0.921875\pi$
$701$		0			0		0.970031	+	0.242980i	$0.0781250\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.343626	−	0.343626i	0.343626	−	0.343626i
$706$	−1.12175	+	0.401370i	−1.12175	+	0.401370i
$707$		0			0
$708$		0			0
$709$	−0.845855	−	1.78841i	−0.845855	−	1.78841i	−0.555570	−	0.831470i	$-0.687500\pi$
$709$	−0.845855	−	1.78841i	−0.845855	−	1.78841i	−0.290285	−	0.956940i	$-0.593750\pi$
$710$		0			0
$711$	0.924678	+	1.72995i	0.924678	+	1.72995i
$712$		0			0
$713$	0.0843288	+	0.277995i	0.0843288	+	0.277995i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$719$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$720$	0.514103	+	0.857729i	0.514103	+	0.857729i
$721$		0			0
$722$	−0.134094	+	0.903989i	−0.134094	+	0.903989i
$723$	−1.33665	−	1.47477i	−1.33665	−	1.47477i
$724$	0.163715	−	0.653587i	0.163715	−	0.653587i
$725$		0			0
$726$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$727$		0			0		0.773010	−	0.634393i	$-0.218750\pi$
$727$		0			0		−0.773010	+	0.634393i	$0.781250\pi$
$728$		0			0
$729$	0.995185	−	0.0980171i	0.995185	−	0.0980171i
$730$		0			0
$731$		0			0
$732$	−1.57555	+	0.313396i	−1.57555	+	0.313396i
$733$		0			0		0.595699	−	0.803208i	$-0.296875\pi$
$733$		0			0		−0.595699	+	0.803208i	$0.703125\pi$
$734$		0			0
$735$	0.923880	+	0.382683i	0.923880	+	0.382683i
$736$	1.39528	+	0.499238i	1.39528	+	0.499238i
$737$		0			0
$738$		0			0
$739$	1.91906	−	0.284666i	1.91906	−	0.284666i	0.923880	−	0.382683i	$-0.125000\pi$
$739$	1.91906	−	0.284666i	1.91906	−	0.284666i	0.995185	+	0.0980171i	$0.0312500\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.920964	−	0.755815i	−0.920964	−	0.755815i	0.0490677	−	0.998795i	$-0.484375\pi$
$743$	−0.920964	−	0.755815i	−0.920964	−	0.755815i	−0.970031	+	0.242980i	$0.921875\pi$
$744$	−0.138617	+	0.138617i	−0.138617	+	0.138617i
$745$		0			0
$746$		0			0
$747$	−0.229080	−	0.914539i	−0.229080	−	0.914539i
$748$		0			0
$749$		0			0
$750$	−0.514103	+	0.857729i	−0.514103	+	0.857729i
$751$	−1.51631	−	0.301614i	−1.51631	−	0.301614i	−0.634393	−	0.773010i	$-0.718750\pi$
$751$	−1.51631	−	0.301614i	−1.51631	−	0.301614i	−0.881921	+	0.471397i	$0.843750\pi$
$752$	0.448969	−	0.185969i	0.448969	−	0.185969i
$753$		0			0
$754$		0			0
$755$	−0.754140	+	1.59449i	−0.754140	+	1.59449i
$756$		0			0
$757$		0			0		0.803208	−	0.595699i	$-0.203125\pi$
$757$		0			0		−0.803208	+	0.595699i	$0.796875\pi$
$758$	−0.257844	+	0.622491i	−0.257844	+	0.622491i
$759$		0			0
$760$	0.251710	+	0.150869i	0.251710	+	0.150869i
$761$		0			0		−0.956940	−	0.290285i	$-0.906250\pi$
$761$		0			0		0.956940	+	0.290285i	$0.0937500\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.929487	+	1.55075i	0.929487	+	1.55075i
$766$	1.18996	+	0.0584592i	1.18996	+	0.0584592i
$767$		0			0
$768$	0.146730	+	0.989177i	0.146730	+	0.989177i
$769$	1.54602			1.54602			0.773010	−	0.634393i	$-0.218750\pi$
$769$	1.54602			1.54602			0.773010	+	0.634393i	$0.218750\pi$
$770$		0			0
$771$	−0.690501	−	1.15203i	−0.690501	−	1.15203i
$772$		0			0
$773$	−0.257844	+	0.720627i	−0.257844	+	0.720627i	0.740951	+	0.671559i	$0.234375\pi$
$773$	−0.257844	+	0.720627i	−0.257844	+	0.720627i	−0.998795	+	0.0490677i	$0.984375\pi$
$774$		0			0
$775$	−0.187593	−	0.0569057i	−0.187593	−	0.0569057i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	2.52263	+	0.902611i	2.52263	+	0.902611i
$783$		0			0
$784$	0.707107	+	0.707107i	0.707107	+	0.707107i
$785$		0			0
$786$		0			0
$787$		0			0		−0.998795	−	0.0490677i	$-0.984375\pi$
$787$		0			0		0.998795	+	0.0490677i	$0.0156250\pi$
$788$	0.560227	+	1.56573i	0.560227	+	1.56573i
$789$	0.207775	+	0.829484i	0.207775	+	0.829484i
$790$	−1.63099	+	1.08979i	−1.63099	+	1.08979i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.579870	−	0.0284872i	0.579870	−	0.0284872i
$796$	0.425215	+	1.02656i	0.425215	+	1.02656i
$797$	0.385958	−	0.0572514i	0.385958	−	0.0572514i	0.0490677	−	0.998795i	$-0.484375\pi$
$797$	0.385958	−	0.0572514i	0.385958	−	0.0572514i	0.336890	+	0.941544i	$0.390625\pi$
$798$		0			0
$799$	0.811726	−	0.336228i	0.811726	−	0.336228i
$800$	−0.803208	+	0.595699i	−0.803208	+	0.595699i
$801$		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		0.773010	−	0.634393i	$-0.218750\pi$
$809$		0			0		−0.773010	+	0.634393i	$0.781250\pi$
$810$	0.195090	+	0.980785i	0.195090	+	0.980785i
$811$	−1.02190	−	0.612501i	−1.02190	−	0.612501i	−0.0980171	−	0.995185i	$-0.531250\pi$
$811$	−1.02190	−	0.612501i	−1.02190	−	0.612501i	−0.923880	+	0.382683i	$0.875000\pi$
$812$		0			0
$813$	−1.24088	−	1.36910i	−1.24088	−	1.36910i
$814$		0			0
$815$		0			0
$816$	0.265286	+	1.78841i	0.265286	+	1.78841i
$817$		0			0
$818$	1.30692	+	1.18452i	1.30692	+	1.18452i
$819$		0			0
$820$		0			0
$821$		0			0		−0.989177	−	0.146730i	$-0.953125\pi$
$821$		0			0		0.989177	+	0.146730i	$0.0468750\pi$
$822$	1.02821			1.02821
$823$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$823$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.166824	−	0.352719i	−0.166824	−	0.352719i	0.803208	−	0.595699i	$-0.203125\pi$
$827$	−0.166824	−	0.352719i	−0.166824	−	0.352719i	−0.970031	+	0.242980i	$0.921875\pi$
$828$	1.14553	+	0.940109i	1.14553	+	0.940109i
$829$	0.207775	−	0.829484i	0.207775	−	0.829484i	−0.773010	−	0.634393i	$-0.781250\pi$
$829$	0.207775	−	0.829484i	0.207775	−	0.829484i	0.980785	−	0.195090i	$-0.0625000\pi$
$830$	0.887682	−	0.317618i	0.887682	−	0.317618i
$831$		0			0
$832$		0			0
$833$	1.27843	+	1.27843i	1.27843	+	1.27843i
$834$	1.80580	+	0.854080i	1.80580	+	0.854080i
$835$	1.82665	+	0.457553i	1.82665	+	0.457553i
$836$		0			0
$837$	−0.177213	+	0.0838155i	−0.177213	+	0.0838155i
$838$		0			0
$839$		0			0		0.881921	−	0.471397i	$-0.156250\pi$
$839$		0			0		−0.881921	+	0.471397i	$0.843750\pi$
$840$		0			0
$841$	0.956940	−	0.290285i	0.956940	−	0.290285i
$842$	1.41251	+	1.41251i	1.41251	+	1.41251i
$843$		0			0
$844$	−1.02190	−	1.37787i	−1.02190	−	1.37787i
$845$	−0.941544	+	0.336890i	−0.941544	+	0.336890i
$846$	0.485375	−	0.0238449i	0.485375	−	0.0238449i
$847$		0			0
$848$	0.546632	+	0.195588i	0.546632	+	0.195588i
$849$		0			0
$850$	−1.45218	+	1.07701i	−1.45218	+	1.07701i
$851$		0			0
$852$		0			0
$853$		0			0		0.514103	−	0.857729i	$-0.328125\pi$
$853$		0			0		−0.514103	+	0.857729i	$0.671875\pi$
$854$		0			0
$855$	0.186170	+	0.226848i	0.186170	+	0.226848i
$856$	−0.151537	−	1.53858i	−0.151537	−	1.53858i
$857$	−0.157456	−	1.59868i	−0.157456	−	1.59868i	−0.671559	−	0.740951i	$-0.734375\pi$
$857$	−0.157456	−	1.59868i	−0.157456	−	1.59868i	0.514103	−	0.857729i	$-0.328125\pi$
$858$		0			0
$859$	1.07880	−	1.19028i	1.07880	−	1.19028i	0.0980171	−	0.995185i	$-0.468750\pi$
$859$	1.07880	−	1.19028i	1.07880	−	1.19028i	0.980785	−	0.195090i	$-0.0625000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.764445	+	1.84553i	−0.764445	+	1.84553i	−0.336890	+	0.941544i	$0.609375\pi$
$863$	−0.764445	+	1.84553i	−0.764445	+	1.84553i	−0.427555	+	0.903989i	$0.640625\pi$
$864$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$865$	−0.485544	−	1.17221i	−0.485544	−	1.17221i
$866$		0			0
$867$	0.332900	+	2.24423i	0.332900	+	2.24423i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	1.68250	+	0.334669i	1.68250	+	0.334669i
$873$		0			0
$874$	0.426524	+	0.0848410i	0.426524	+	0.0848410i
$875$		0			0
$876$		0			0
$877$		0			0		0.0490677	−	0.998795i	$-0.484375\pi$
$877$		0			0		−0.0490677	+	0.998795i	$0.515625\pi$
$878$	−0.404061	−	1.61310i	−0.404061	−	1.61310i
$879$	0.183930	−	0.924678i	0.183930	−	0.924678i
$880$		0			0
$881$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$881$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$882$	0.427555	+	0.903989i	0.427555	+	0.903989i
$883$		0			0		−0.903989	−	0.427555i	$-0.859375\pi$
$883$		0			0		0.903989	+	0.427555i	$0.140625\pi$
$884$		0			0
$885$		0			0
$886$	−0.761681	−	1.83886i	−0.761681	−	1.83886i
$887$	−0.0865477	−	0.0462607i	−0.0865477	−	0.0462607i	0.427555	−	0.903989i	$-0.359375\pi$
$887$	−0.0865477	−	0.0462607i	−0.0865477	−	0.0462607i	−0.514103	+	0.857729i	$0.671875\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.122321	−	0.0733164i	0.122321	−	0.0733164i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$901$	0.988298	+	0.353619i	0.988298	+	0.353619i
$902$		0			0
$903$		0			0
$904$	−1.93773	+	0.0951944i	−1.93773	+	0.0951944i
$905$	0.594221	+	0.317618i	0.594221	+	0.317618i
$906$	−1.62958	+	0.674993i	−1.62958	+	0.674993i
$907$		0			0		−0.595699	−	0.803208i	$-0.703125\pi$
$907$		0			0		0.595699	+	0.803208i	$0.296875\pi$
$908$	1.91158	−	0.0939097i	1.91158	−	0.0939097i
$909$		0			0
$910$		0			0
$911$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$911$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$912$	0.0851872	+	0.280825i	0.0851872	+	0.280825i
$913$		0			0
$914$		0			0
$915$	0.0788231	−	1.60448i	0.0788231	−	1.60448i
$916$	0.0980171	+	0.00481527i	0.0980171	+	0.00481527i
$917$		0			0
$918$	−0.352719	+	1.77324i	−0.352719	+	1.77324i
$919$	−1.90466	−	0.187593i	−1.90466	−	0.187593i	−0.923880	−	0.382683i	$-0.875000\pi$
$919$	−1.90466	−	0.187593i	−1.90466	−	0.187593i	−0.980785	+	0.195090i	$0.937500\pi$
$920$	−0.823301	+	1.23216i	−0.823301	+	1.23216i
$921$		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	$-0.375000\pi$
$929$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$930$	−0.100782	−	0.168144i	−0.100782	−	0.168144i
$931$	0.235710	+	0.174814i	0.235710	+	0.174814i
$932$	−0.0191453	+	0.0962497i	−0.0191453	+	0.0962497i
$933$		0			0
$934$	−1.28547	+	1.05496i	−1.28547	+	1.05496i
$935$		0			0
$936$		0			0
$937$		0			0		−0.634393	−	0.773010i	$-0.718750\pi$
$937$		0			0		0.634393	+	0.773010i	$0.281250\pi$
$938$		0			0
$939$		0			0
$940$	0.0713052	+	0.480701i	0.0713052	+	0.480701i
$941$		0			0		0.740951	−	0.671559i	$-0.234375\pi$
$941$		0			0		−0.740951	+	0.671559i	$0.765625\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.66074	−	0.594221i	1.66074	−	0.594221i	0.671559	−	0.740951i	$-0.265625\pi$
$947$	1.66074	−	0.594221i	1.66074	−	0.594221i	0.989177	+	0.146730i	$0.0468750\pi$
$948$	−1.94034	−	0.287822i	−1.94034	−	0.287822i
$949$		0			0
$950$	−0.207508	+	0.207508i	−0.207508	+	0.207508i
$951$	−0.373380	+	0.113263i	−0.373380	+	0.113263i
$952$		0			0
$953$	−1.66074	+	0.887682i	−1.66074	+	0.887682i	−0.671559	+	0.740951i	$0.734375\pi$
$953$	−1.66074	+	0.887682i	−1.66074	+	0.887682i	−0.989177	+	0.146730i	$0.953125\pi$
$954$	0.448786	+	0.368309i	0.448786	+	0.368309i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$961$	−0.679933	+	0.679933i	−0.679933	+	0.679933i
$962$		0			0
$963$	0.375652	−	1.49969i	0.375652	−	1.49969i
$964$	1.98079	−	0.195090i	1.98079	−	0.195090i
$965$		0			0
$966$		0			0
$967$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$967$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$968$	0.903989	+	0.427555i	0.903989	+	0.427555i
$969$	0.154017	+	0.507725i	0.154017	+	0.507725i
$970$		0			0
$971$		0			0		−0.989177	−	0.146730i	$-0.953125\pi$
$971$		0			0		0.989177	+	0.146730i	$0.0468750\pi$
$972$	−0.514103	+	0.857729i	−0.514103	+	0.857729i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.686831	−	1.45218i	0.686831	−	1.45218i
$977$	1.11676	−	0.746196i	1.11676	−	0.746196i	0.146730	−	0.989177i	$-0.453125\pi$
$977$	1.11676	−	0.746196i	1.11676	−	0.746196i	0.970031	+	0.242980i	$0.0781250\pi$
$978$		0			0
$979$		0			0
$980$	−0.857729	+	0.514103i	−0.857729	+	0.514103i
$981$	1.47140	+	0.881921i	1.47140	+	0.881921i
$982$		0			0
$983$	0.661009	−	0.542476i	0.661009	−	0.542476i	−0.242980	−	0.970031i	$-0.578125\pi$
$983$	0.661009	−	0.542476i	0.661009	−	0.542476i	0.903989	+	0.427555i	$0.140625\pi$
$984$		0			0
$985$	−1.65493	+	0.162997i	−1.65493	+	0.162997i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.70711	+	0.707107i	1.70711	+	0.707107i	1.00000			$0$
$991$	1.70711	+	0.707107i	1.70711	+	0.707107i	0.707107	+	0.707107i	$0.250000\pi$
$992$	−0.0287642	−	0.193913i	−0.0287642	−	0.193913i
$993$	1.73975	−	0.720627i	1.73975	−	0.720627i
$994$		0			0
$995$	−1.09911	+	0.163038i	−1.09911	+	0.163038i
$996$	0.871028	+	0.360791i	0.871028	+	0.360791i
$997$		0			0		0.998795	−	0.0490677i	$-0.0156250\pi$
$997$		0			0		−0.998795	+	0.0490677i	$0.984375\pi$
$998$	−0.0865477	−	0.0462607i	−0.0865477	−	0.0462607i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3840.1.dy.a.1709.2	yes	64
3.2	odd	2	inner	3840.1.dy.a.1709.1	✓	64
5.4	even	2	inner	3840.1.dy.a.1709.1	✓	64
15.14	odd	2	CM	3840.1.dy.a.1709.2	yes	64
256.37	even	64	inner	3840.1.dy.a.1829.2	yes	64
768.293	odd	64	inner	3840.1.dy.a.1829.1	yes	64
1280.549	even	64	inner	3840.1.dy.a.1829.1	yes	64
3840.1829	odd	64	inner	3840.1.dy.a.1829.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3840.1.dy.a.1709.1	✓	64	3.2	odd	2	inner
3840.1.dy.a.1709.1	✓	64	5.4	even	2	inner
3840.1.dy.a.1709.2	yes	64	1.1	even	1	trivial
3840.1.dy.a.1709.2	yes	64	15.14	odd	2	CM
3840.1.dy.a.1829.1	yes	64	768.293	odd	64	inner
3840.1.dy.a.1829.1	yes	64	1280.549	even	64	inner
3840.1.dy.a.1829.2	yes	64	256.37	even	64	inner
3840.1.dy.a.1829.2	yes	64	3840.1829	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)

\(f(q)\)	\(=\)	\(q+(0.0490677 - 0.998795i) q^{2} +(0.514103 + 0.857729i) q^{3} +(-0.995185 - 0.0980171i) q^{4} +(0.336890 - 0.941544i) q^{5} +(0.881921 - 0.471397i) q^{6} +(-0.146730 + 0.989177i) q^{8} +(-0.471397 + 0.881921i) q^{9} +O(q^{10})\)	\(q+(0.0490677 - 0.998795i) q^{2} +(0.514103 + 0.857729i) q^{3} +(-0.995185 - 0.0980171i) q^{4} +(0.336890 - 0.941544i) q^{5} +(0.881921 - 0.471397i) q^{6} +(-0.146730 + 0.989177i) q^{8} +(-0.471397 + 0.881921i) q^{9} +(-0.923880 - 0.382683i) q^{10} +(-0.427555 - 0.903989i) q^{12} +(0.980785 - 0.195090i) q^{15} +(0.980785 + 0.195090i) q^{16} +(1.77324 + 0.352719i) q^{17} +(0.857729 + 0.514103i) q^{18} +(0.293107 + 0.0143994i) q^{19} +(-0.427555 + 0.903989i) q^{20} +(-0.145252 + 1.47477i) q^{23} +(-0.923880 + 0.382683i) q^{24} +(-0.773010 - 0.634393i) q^{25} +(-0.998795 + 0.0490677i) q^{27} +(-0.146730 - 0.989177i) q^{30} +(0.181112 - 0.0750191i) q^{31} +(0.242980 - 0.970031i) q^{32} +(0.439303 - 1.75380i) q^{34} +(0.555570 - 0.831470i) q^{36} +(0.0287642 - 0.292048i) q^{38} +(0.881921 + 0.471397i) q^{40} +(0.671559 + 0.740951i) q^{45} +(1.46586 + 0.217440i) q^{46} +(0.404061 - 0.269985i) q^{47} +(0.336890 + 0.941544i) q^{48} +(0.831470 + 0.555570i) q^{49} +(-0.671559 + 0.740951i) q^{50} +(0.609090 + 1.70229i) q^{51} +(0.574286 + 0.0851872i) q^{53} +1.00000i q^{54} +(0.138337 + 0.258809i) q^{57} +(-0.995185 + 0.0980171i) q^{60} +(0.390327 - 1.55827i) q^{61} +(-0.0660420 - 0.184575i) q^{62} +(-0.956940 - 0.290285i) q^{64} +(-1.73013 - 0.524828i) q^{68} +(-1.33962 + 0.633595i) q^{69} +(-0.803208 - 0.595699i) q^{72} +(0.146730 - 0.989177i) q^{75} +(-0.290285 - 0.0430597i) q^{76} +(1.08979 - 1.63099i) q^{79} +(0.514103 - 0.857729i) q^{80} +(-0.555570 - 0.831470i) q^{81} +(-0.698564 + 0.633141i) q^{83} +(0.929487 - 1.55075i) q^{85} +(0.773010 - 0.634393i) q^{90} +(0.289105 - 1.45343i) q^{92} +(0.157456 + 0.116777i) q^{93} +(-0.249834 - 0.416822i) q^{94} +(0.112303 - 0.271123i) q^{95} +(0.956940 - 0.290285i) q^{96} +(0.595699 - 0.803208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q+O(q^{100}) \) 64 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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