LMFDB - Embedded newform 1920.1.db.a.1469.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1920,1,Mod(29,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1920.29"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 27, 16, 16])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1920.db (of order $32$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$2$ over $\Q(\zeta_{32})$
Coefficient field:	$\Q(\zeta_{64})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{32} + 1 $ x^32 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{32}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{32} + \cdots)$

Embedding invariants

Embedding label			1469.2
Root			$0.0980171 + 0.995185i$ of defining polynomial
Character	$\chi$	$=$	1920.1469
Dual form			1920.1.db.a.149.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.471397 - 0.881921i) q^{2} +(0.773010 - 0.634393i) q^{3} +(-0.555570 - 0.831470i) q^{4} +(0.290285 - 0.956940i) q^{5} +(-0.195090 - 0.980785i) q^{6} +(-0.995185 + 0.0980171i) q^{8} +(0.195090 - 0.980785i) q^{9} +(-0.707107 - 0.707107i) q^{10} +(-0.956940 - 0.290285i) q^{12} +(-0.382683 - 0.923880i) q^{15} +(-0.382683 + 0.923880i) q^{16} +(-0.732410 + 1.76820i) q^{17} +(-0.773010 - 0.634393i) q^{18} +(0.938254 - 1.75535i) q^{19} +(-0.956940 + 0.290285i) q^{20} +(0.979938 + 1.46658i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-0.831470 - 0.555570i) q^{25} +(-0.471397 - 0.881921i) q^{27} +(-0.995185 - 0.0980171i) q^{30} +(-0.785695 + 0.785695i) q^{31} +(0.634393 + 0.773010i) q^{32} +(1.21415 + 1.47945i) q^{34} +(-0.923880 + 0.382683i) q^{36} +(-1.10579 - 1.65493i) q^{38} +(-0.195090 + 0.980785i) q^{40} +(-0.881921 - 0.471397i) q^{45} +(1.75535 - 0.172887i) q^{46} +(1.17221 + 0.485544i) q^{47} +(0.290285 + 0.956940i) q^{48} +(0.923880 - 0.382683i) q^{49} +(-0.881921 + 0.471397i) q^{50} +(0.555570 + 1.83147i) q^{51} +(-1.95213 + 0.192268i) q^{53} -1.00000 q^{54} +(-0.388302 - 1.95213i) q^{57} +(-0.555570 + 0.831470i) q^{60} +(-0.124363 - 0.151537i) q^{61} +(0.322547 + 1.06330i) q^{62} +(0.980785 - 0.195090i) q^{64} +(1.87711 - 0.373380i) q^{68} +(1.68789 + 0.512016i) q^{69} +(-0.0980171 + 0.995185i) q^{72} +(-0.995185 + 0.0980171i) q^{75} +(-1.98079 + 0.195090i) q^{76} +(0.707107 - 0.292893i) q^{79} +(0.773010 + 0.634393i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(0.344109 + 0.183930i) q^{83} +(1.47945 + 1.21415i) q^{85} +(-0.831470 + 0.555570i) q^{90} +(0.674993 - 1.62958i) q^{92} +(-0.108911 + 1.10579i) q^{93} +(0.980785 - 0.804910i) q^{94} +(-1.40740 - 1.40740i) q^{95} +(0.980785 + 0.195090i) q^{96} +(0.0980171 - 0.995185i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{54} - 32 q^{76}+O(q^{100}) $ 32 * q - 32 * q^54 - 32 * q^76

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{32}\right)$	$-1$

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 $

$2$	0.471397	−	0.881921i	0.471397	−	0.881921i
$2$	0.471397	−	0.881921i	0.471397	−	0.881921i
$3$	0.773010	−	0.634393i	0.773010	−	0.634393i
$3$	0.773010	−	0.634393i	0.773010	−	0.634393i
$4$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$5$	0.290285	−	0.956940i	0.290285	−	0.956940i
$5$	0.290285	−	0.956940i	0.290285	−	0.956940i
$6$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$7$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$7$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$8$	−0.995185	+	0.0980171i	−0.995185	+	0.0980171i
$9$	0.195090	−	0.980785i	0.195090	−	0.980785i
$10$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$11$		0			0		−0.0980171	−	0.995185i	$-0.531250\pi$
$11$		0			0		0.0980171	+	0.995185i	$0.468750\pi$
$12$	−0.956940	−	0.290285i	−0.956940	−	0.290285i
$13$		0			0		0.956940	−	0.290285i	$-0.0937500\pi$
$13$		0			0		−0.956940	+	0.290285i	$0.906250\pi$
$14$		0			0
$15$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$16$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$17$	−0.732410	+	1.76820i	−0.732410	+	1.76820i	−0.0980171	+	0.995185i	$0.531250\pi$
$17$	−0.732410	+	1.76820i	−0.732410	+	1.76820i	−0.634393	+	0.773010i	$0.718750\pi$
$18$	−0.773010	−	0.634393i	−0.773010	−	0.634393i
$19$	0.938254	−	1.75535i	0.938254	−	1.75535i	0.382683	−	0.923880i	$-0.375000\pi$
$19$	0.938254	−	1.75535i	0.938254	−	1.75535i	0.555570	−	0.831470i	$-0.312500\pi$
$20$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$21$		0			0
$22$		0			0
$23$	0.979938	+	1.46658i	0.979938	+	1.46658i	0.881921	+	0.471397i	$0.156250\pi$
$23$	0.979938	+	1.46658i	0.979938	+	1.46658i	0.0980171	+	0.995185i	$0.468750\pi$
$24$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$25$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$26$		0			0
$27$	−0.471397	−	0.881921i	−0.471397	−	0.881921i
$28$		0			0
$29$		0			0		−0.995185	−	0.0980171i	$-0.968750\pi$
$29$		0			0		0.995185	+	0.0980171i	$0.0312500\pi$
$30$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$31$	−0.785695	+	0.785695i	−0.785695	+	0.785695i	−0.980785	−	0.195090i	$-0.937500\pi$
$31$	−0.785695	+	0.785695i	−0.785695	+	0.785695i	0.195090	+	0.980785i	$0.437500\pi$
$32$	0.634393	+	0.773010i	0.634393	+	0.773010i
$33$		0			0
$34$	1.21415	+	1.47945i	1.21415	+	1.47945i
$35$		0			0
$36$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$37$		0			0		0.881921	−	0.471397i	$-0.156250\pi$
$37$		0			0		−0.881921	+	0.471397i	$0.843750\pi$
$38$	−1.10579	−	1.65493i	−1.10579	−	1.65493i
$39$		0			0
$40$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$41$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$41$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$42$		0			0
$43$		0			0		−0.773010	−	0.634393i	$-0.781250\pi$
$43$		0			0		0.773010	+	0.634393i	$0.218750\pi$
$44$		0			0
$45$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$46$	1.75535	−	0.172887i	1.75535	−	0.172887i
$47$	1.17221	+	0.485544i	1.17221	+	0.485544i	0.881921	−	0.471397i	$-0.156250\pi$
$47$	1.17221	+	0.485544i	1.17221	+	0.485544i	0.290285	+	0.956940i	$0.406250\pi$
$48$	0.290285	+	0.956940i	0.290285	+	0.956940i
$49$	0.923880	−	0.382683i	0.923880	−	0.382683i
$50$	−0.881921	+	0.471397i	−0.881921	+	0.471397i
$51$	0.555570	+	1.83147i	0.555570	+	1.83147i
$52$		0			0
$53$	−1.95213	+	0.192268i	−1.95213	+	0.192268i	−0.995185	−	0.0980171i	$-0.968750\pi$
$53$	−1.95213	+	0.192268i	−1.95213	+	0.192268i	−0.956940	+	0.290285i	$0.906250\pi$
$54$	−1.00000			−1.00000
$55$		0			0
$56$		0			0
$57$	−0.388302	−	1.95213i	−0.388302	−	1.95213i
$58$		0			0
$59$		0			0		−0.956940	−	0.290285i	$-0.906250\pi$
$59$		0			0		0.956940	+	0.290285i	$0.0937500\pi$
$60$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$61$	−0.124363	−	0.151537i	−0.124363	−	0.151537i	0.707107	−	0.707107i	$-0.250000\pi$
$61$	−0.124363	−	0.151537i	−0.124363	−	0.151537i	−0.831470	+	0.555570i	$0.812500\pi$
$62$	0.322547	+	1.06330i	0.322547	+	1.06330i
$63$		0			0
$64$	0.980785	−	0.195090i	0.980785	−	0.195090i
$65$		0			0
$66$		0			0
$67$		0			0		−0.634393	−	0.773010i	$-0.718750\pi$
$67$		0			0		0.634393	+	0.773010i	$0.281250\pi$
$68$	1.87711	−	0.373380i	1.87711	−	0.373380i
$69$	1.68789	+	0.512016i	1.68789	+	0.512016i
$70$		0			0
$71$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$71$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$72$	−0.0980171	+	0.995185i	−0.0980171	+	0.995185i
$73$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$73$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$74$		0			0
$75$	−0.995185	+	0.0980171i	−0.995185	+	0.0980171i
$76$	−1.98079	+	0.195090i	−1.98079	+	0.195090i
$77$		0			0
$78$		0			0
$79$	0.707107	−	0.292893i	0.707107	−	0.292893i		−	1.00000i	$-0.5\pi$
$79$	0.707107	−	0.292893i	0.707107	−	0.292893i	0.707107	+	0.707107i	$0.250000\pi$
$80$	0.773010	+	0.634393i	0.773010	+	0.634393i
$81$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$82$		0			0
$83$	0.344109	+	0.183930i	0.344109	+	0.183930i	0.634393	−	0.773010i	$-0.281250\pi$
$83$	0.344109	+	0.183930i	0.344109	+	0.183930i	−0.290285	+	0.956940i	$0.593750\pi$
$84$		0			0
$85$	1.47945	+	1.21415i	1.47945	+	1.21415i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$89$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$90$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$91$		0			0
$92$	0.674993	−	1.62958i	0.674993	−	1.62958i
$93$	−0.108911	+	1.10579i	−0.108911	+	1.10579i
$94$	0.980785	−	0.804910i	0.980785	−	0.804910i
$95$	−1.40740	−	1.40740i	−1.40740	−	1.40740i
$96$	0.980785	+	0.195090i	0.980785	+	0.195090i
$97$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$97$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$98$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$99$		0			0
$100$			1.00000i			1.00000i
$101$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$101$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$102$	1.87711	+	0.373380i	1.87711	+	0.373380i
$103$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$103$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$104$		0			0
$105$		0			0
$106$	−0.750661	+	1.81225i	−0.750661	+	1.81225i
$107$	1.05496	−	1.28547i	1.05496	−	1.28547i	0.0980171	−	0.995185i	$-0.468750\pi$
$107$	1.05496	−	1.28547i	1.05496	−	1.28547i	0.956940	−	0.290285i	$-0.0937500\pi$
$108$	−0.471397	+	0.881921i	−0.471397	+	0.881921i
$109$	−0.728789	+	1.36347i	−0.728789	+	1.36347i	0.195090	+	0.980785i	$0.437500\pi$
$109$	−0.728789	+	1.36347i	−0.728789	+	1.36347i	−0.923880	+	0.382683i	$0.875000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.485544	−	1.17221i	−0.485544	−	1.17221i	−0.956940	−	0.290285i	$-0.906250\pi$
$113$	−0.485544	−	1.17221i	−0.485544	−	1.17221i	0.471397	−	0.881921i	$-0.343750\pi$
$114$	−1.90466	−	0.577774i	−1.90466	−	0.577774i
$115$	1.68789	−	0.512016i	1.68789	−	0.512016i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.471397	+	0.881921i	0.471397	+	0.881921i
$121$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$122$	−0.192268	+	0.0382444i	−0.192268	+	0.0382444i
$123$		0			0
$124$	1.08979	+	0.216773i	1.08979	+	0.216773i
$125$	−0.773010	+	0.634393i	−0.773010	+	0.634393i
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	0.290285	−	0.956940i	0.290285	−	0.956940i
$129$		0			0
$130$		0			0
$131$		0			0		0.773010	−	0.634393i	$-0.218750\pi$
$131$		0			0		−0.773010	+	0.634393i	$0.781250\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$136$	0.555570	−	1.83147i	0.555570	−	1.83147i
$137$	−0.301614	+	1.51631i	−0.301614	+	1.51631i	0.471397	+	0.881921i	$0.343750\pi$
$137$	−0.301614	+	1.51631i	−0.301614	+	1.51631i	−0.773010	+	0.634393i	$0.781250\pi$
$138$	1.24723	−	1.24723i	1.24723	−	1.24723i
$139$	−0.0924099	−	0.938254i	−0.0924099	−	0.938254i	−0.923880	−	0.382683i	$-0.875000\pi$
$139$	−0.0924099	−	0.938254i	−0.0924099	−	0.938254i	0.831470	−	0.555570i	$-0.187500\pi$
$140$		0			0
$141$	1.21415	−	0.368309i	1.21415	−	0.368309i
$142$		0			0
$143$		0			0
$144$	0.831470	+	0.555570i	0.831470	+	0.555570i
$145$		0			0
$146$		0			0
$147$	0.471397	−	0.881921i	0.471397	−	0.881921i
$148$		0			0
$149$		0			0		0.634393	−	0.773010i	$-0.281250\pi$
$149$		0			0		−0.634393	+	0.773010i	$0.718750\pi$
$150$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$151$	0.216773	+	0.324423i	0.216773	+	0.324423i	0.923880	−	0.382683i	$-0.125000\pi$
$151$	0.216773	+	0.324423i	0.216773	+	0.324423i	−0.707107	+	0.707107i	$0.750000\pi$
$152$	−0.761681	+	1.83886i	−0.761681	+	1.83886i
$153$	1.59133	+	1.06330i	1.59133	+	1.06330i
$154$		0			0
$155$	0.523788	+	0.979938i	0.523788	+	0.979938i
$156$		0			0
$157$		0			0		−0.995185	−	0.0980171i	$-0.968750\pi$
$157$		0			0		0.995185	+	0.0980171i	$0.0312500\pi$
$158$	0.0750191	−	0.761681i	0.0750191	−	0.761681i
$159$	−1.38704	+	1.38704i	−1.38704	+	1.38704i
$160$	0.923880	−	0.382683i	0.923880	−	0.382683i
$161$		0			0
$162$	−0.773010	+	0.634393i	−0.773010	+	0.634393i
$163$		0			0		0.0980171	−	0.995185i	$-0.468750\pi$
$163$		0			0		−0.0980171	+	0.995185i	$0.531250\pi$
$164$		0			0
$165$		0			0
$166$	0.324423	−	0.216773i	0.324423	−	0.216773i
$167$	−0.322547	+	0.482726i	−0.322547	+	0.482726i	−0.956940	−	0.290285i	$-0.906250\pi$
$167$	−0.322547	+	0.482726i	−0.322547	+	0.482726i	0.634393	+	0.773010i	$0.281250\pi$
$168$		0			0
$169$	0.831470	−	0.555570i	0.831470	−	0.555570i
$170$	1.76820	−	0.732410i	1.76820	−	0.732410i
$171$	−1.53858	−	1.26268i	−1.53858	−	1.26268i
$172$		0			0
$173$	1.46658	+	0.783904i	1.46658	+	0.783904i	0.995185	−	0.0980171i	$-0.0312500\pi$
$173$	1.46658	+	0.783904i	1.46658	+	0.783904i	0.471397	+	0.881921i	$0.343750\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$179$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$180$	0.0980171	+	0.995185i	0.0980171	+	0.995185i
$181$	−0.577774	+	0.0569057i	−0.577774	+	0.0569057i	−0.382683	−	0.923880i	$-0.625000\pi$
$181$	−0.577774	+	0.0569057i	−0.577774	+	0.0569057i	−0.195090	+	0.980785i	$0.562500\pi$
$182$		0			0
$183$	−0.192268	−	0.0382444i	−0.192268	−	0.0382444i
$184$	−1.11897	−	1.36347i	−1.11897	−	1.36347i
$185$		0			0
$186$	0.923880	+	0.617317i	0.923880	+	0.617317i
$187$		0			0
$188$	−0.247528	−	1.24441i	−0.247528	−	1.24441i
$189$		0			0
$190$	−1.90466	+	0.577774i	−1.90466	+	0.577774i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	0.634393	−	0.773010i	0.634393	−	0.773010i
$193$		0			0			−	1.00000i	$-0.5\pi$
$193$		0			0				1.00000i	$0.5\pi$
$194$		0			0
$195$		0			0
$196$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$197$	−1.76820	−	0.536376i	−1.76820	−	0.536376i	−0.773010	−	0.634393i	$-0.781250\pi$
$197$	−1.76820	−	0.536376i	−1.76820	−	0.536376i	−0.995185	+	0.0980171i	$0.968750\pi$
$198$		0			0
$199$	−0.360480	−	1.81225i	−0.360480	−	1.81225i	−0.555570	−	0.831470i	$-0.687500\pi$
$199$	−0.360480	−	1.81225i	−0.360480	−	1.81225i	0.195090	−	0.980785i	$-0.437500\pi$
$200$	0.881921	+	0.471397i	0.881921	+	0.471397i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	1.21415	−	1.47945i	1.21415	−	1.47945i
$205$		0			0
$206$		0			0
$207$	1.62958	−	0.674993i	1.62958	−	0.674993i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.36347	+	0.728789i	1.36347	+	0.728789i	0.980785	−	0.195090i	$-0.0625000\pi$
$211$	1.36347	+	0.728789i	1.36347	+	0.728789i	0.382683	+	0.923880i	$0.375000\pi$
$212$	1.24441	+	1.51631i	1.24441	+	1.51631i
$213$		0			0
$214$	−0.636379	−	1.53636i	−0.636379	−	1.53636i
$215$		0			0
$216$	0.555570	+	0.831470i	0.555570	+	0.831470i
$217$		0			0
$218$	0.858923	+	1.28547i	0.858923	+	1.28547i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$		0			0
$225$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$226$	−1.26268	−	0.124363i	−1.26268	−	0.124363i
$227$	1.95213	+	0.192268i	1.95213	+	0.192268i	0.995185	−	0.0980171i	$-0.0312500\pi$
$227$	1.95213	+	0.192268i	1.95213	+	0.192268i	0.956940	+	0.290285i	$0.0937500\pi$
$228$	−1.40740	+	1.40740i	−1.40740	+	1.40740i
$229$	−0.444430	−	0.831470i	−0.444430	−	0.831470i	0.555570	−	0.831470i	$-0.312500\pi$
$229$	−0.444430	−	0.831470i	−0.444430	−	0.831470i	−1.00000			$\pi$
$230$	0.344109	−	1.72995i	0.344109	−	1.72995i
$231$		0			0
$232$		0			0
$233$	0.523788	+	0.783904i	0.523788	+	0.783904i	0.995185	−	0.0980171i	$-0.0312500\pi$
$233$	0.523788	+	0.783904i	0.523788	+	0.783904i	−0.471397	+	0.881921i	$0.656250\pi$
$234$		0			0
$235$	0.804910	−	0.980785i	0.804910	−	0.980785i
$236$		0			0
$237$	0.360791	−	0.674993i	0.360791	−	0.674993i
$238$		0			0
$239$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$239$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$240$	1.00000			1.00000
$241$	0.425215	+	1.02656i	0.425215	+	1.02656i	0.980785	+	0.195090i	$0.0625000\pi$
$241$	0.425215	+	1.02656i	0.425215	+	1.02656i	−0.555570	+	0.831470i	$0.687500\pi$
$242$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$243$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$244$	−0.0569057	+	0.187593i	−0.0569057	+	0.187593i
$245$	−0.0980171	−	0.995185i	−0.0980171	−	0.995185i
$246$		0			0
$247$		0			0
$248$	0.704900	−	0.858923i	0.704900	−	0.858923i
$249$	0.382683	−	0.0761205i	0.382683	−	0.0761205i
$250$	0.195090	+	0.980785i	0.195090	+	0.980785i
$251$		0			0		0.290285	−	0.956940i	$-0.406250\pi$
$251$		0			0		−0.290285	+	0.956940i	$0.593750\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	1.91388			1.91388
$256$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$257$	−1.76384			−1.76384			−0.881921	−	0.471397i	$-0.843750\pi$
$257$	−1.76384			−1.76384			−0.881921	+	0.471397i	$0.843750\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.87711	+	0.373380i	−1.87711	+	0.373380i	−0.995185	−	0.0980171i	$-0.968750\pi$
$263$	−1.87711	+	0.373380i	−1.87711	+	0.373380i	−0.881921	+	0.471397i	$0.843750\pi$
$264$		0			0
$265$	−0.382683	+	1.92388i	−0.382683	+	1.92388i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.956940	−	0.290285i	$-0.0937500\pi$
$269$		0			0		−0.956940	+	0.290285i	$0.906250\pi$
$270$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$271$	0.541196	+	1.30656i	0.541196	+	1.30656i	0.923880	+	0.382683i	$0.125000\pi$
$271$	0.541196	+	1.30656i	0.541196	+	1.30656i	−0.382683	+	0.923880i	$0.625000\pi$
$272$	−1.35332	−	1.35332i	−1.35332	−	1.35332i
$273$		0			0
$274$	1.19509	+	0.980785i	1.19509	+	0.980785i
$275$		0			0
$276$	−0.512016	−	1.68789i	−0.512016	−	1.68789i
$277$		0			0		0.634393	−	0.773010i	$-0.281250\pi$
$277$		0			0		−0.634393	+	0.773010i	$0.718750\pi$
$278$	−0.871028	−	0.360791i	−0.871028	−	0.360791i
$279$	0.617317	+	0.923880i	0.617317	+	0.923880i
$280$		0			0
$281$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$281$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$282$	0.247528	−	1.24441i	0.247528	−	1.24441i
$283$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$283$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$284$		0			0
$285$	−1.98079	−	0.195090i	−1.98079	−	0.195090i
$286$		0			0
$287$		0			0
$288$	0.881921	−	0.471397i	0.881921	−	0.471397i
$289$	−1.88298	−	1.88298i	−1.88298	−	1.88298i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.344109	−	0.183930i	0.344109	−	0.183930i	−0.290285	−	0.956940i	$-0.593750\pi$
$293$	0.344109	−	0.183930i	0.344109	−	0.183930i	0.634393	+	0.773010i	$0.281250\pi$
$294$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.634393	+	0.773010i	0.634393	+	0.773010i
$301$		0			0
$302$	0.388302	−	0.0382444i	0.388302	−	0.0382444i
$303$		0			0
$304$	1.26268	+	1.53858i	1.26268	+	1.53858i
$305$	−0.181112	+	0.0750191i	−0.181112	+	0.0750191i
$306$	1.68789	−	0.902197i	1.68789	−	0.902197i
$307$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$307$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$308$		0			0
$309$		0			0
$310$	1.11114			1.11114
$311$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$311$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$312$		0			0
$313$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$313$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$314$		0			0
$315$		0			0
$316$	−0.636379	−	0.425215i	−0.636379	−	0.425215i
$317$	0.485544	+	0.591637i	0.485544	+	0.591637i	0.956940	−	0.290285i	$-0.0937500\pi$
$317$	0.485544	+	0.591637i	0.485544	+	0.591637i	−0.471397	+	0.881921i	$0.656250\pi$
$318$	0.569414	+	1.87711i	0.569414	+	1.87711i
$319$		0			0
$320$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$321$		−	1.66294i		−	1.66294i
$322$		0			0
$323$	2.41661	+	2.94465i	2.41661	+	2.94465i
$324$	0.195090	+	0.980785i	0.195090	+	0.980785i
$325$		0			0
$326$		0			0
$327$	0.301614	+	1.51631i	0.301614	+	1.51631i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.577774	−	0.0569057i	0.577774	−	0.0569057i	0.195090	−	0.980785i	$-0.437500\pi$
$331$	0.577774	−	0.0569057i	0.577774	−	0.0569057i	0.382683	+	0.923880i	$0.375000\pi$
$332$	−0.0382444	−	0.388302i	−0.0382444	−	0.388302i
$333$		0			0
$334$	0.273678	+	0.512016i	0.273678	+	0.512016i
$335$		0			0
$336$		0			0
$337$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$337$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$338$	−0.0980171	−	0.995185i	−0.0980171	−	0.995185i
$339$	−1.11897	−	0.598102i	−1.11897	−	0.598102i
$340$	0.187593	−	1.90466i	0.187593	−	1.90466i
$341$		0			0
$342$	−1.83886	+	0.761681i	−1.83886	+	0.761681i
$343$		0			0
$344$		0			0
$345$	0.979938	−	1.46658i	0.979938	−	1.46658i
$346$	1.38268	−	0.923880i	1.38268	−	0.923880i
$347$	−0.674993	+	0.360791i	−0.674993	+	0.360791i	−0.773010	−	0.634393i	$-0.781250\pi$
$347$	−0.674993	+	0.360791i	−0.674993	+	0.360791i	0.0980171	+	0.995185i	$0.468750\pi$
$348$		0			0
$349$	−0.195090	+	1.98079i	−0.195090	+	1.98079i			1.00000i	$0.5\pi$
$349$	−0.195090	+	1.98079i	−0.195090	+	1.98079i	−0.195090	+	0.980785i	$0.562500\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.138617	−	0.138617i	0.138617	−	0.138617i	−0.634393	−	0.773010i	$-0.718750\pi$
$353$	0.138617	−	0.138617i	0.138617	−	0.138617i	0.773010	+	0.634393i	$0.218750\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$359$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$360$	0.923880	+	0.382683i	0.923880	+	0.382683i
$361$	−1.64536	−	2.46246i	−1.64536	−	2.46246i
$362$	−0.222174	+	0.536376i	−0.222174	+	0.536376i
$363$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$364$		0			0
$365$		0			0
$366$	−0.124363	+	0.151537i	−0.124363	+	0.151537i
$367$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$367$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$368$	−1.72995	+	0.344109i	−1.72995	+	0.344109i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.979938	−	0.523788i	0.979938	−	0.523788i
$373$		0			0		−0.0980171	−	0.995185i	$-0.531250\pi$
$373$		0			0		0.0980171	+	0.995185i	$0.468750\pi$
$374$		0			0
$375$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$376$	−1.21415	−	0.368309i	−1.21415	−	0.368309i
$377$		0			0
$378$		0			0
$379$	−0.168530	+	0.555570i	−0.168530	+	0.555570i	0.831470	+	0.555570i	$0.187500\pi$
$379$	−0.168530	+	0.555570i	−0.168530	+	0.555570i	−1.00000			$\pi$
$380$	−0.388302	+	1.95213i	−0.388302	+	1.95213i
$381$		0			0
$382$		0			0
$383$	−0.196034			−0.196034			−0.0980171	−	0.995185i	$-0.531250\pi$
$383$	−0.196034			−0.196034			−0.0980171	+	0.995185i	$0.531250\pi$
$384$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.290285	−	0.956940i	$-0.406250\pi$
$389$		0			0		−0.290285	+	0.956940i	$0.593750\pi$
$390$		0			0
$391$	−3.31092	+	0.658583i	−3.31092	+	0.658583i
$392$	−0.881921	+	0.471397i	−0.881921	+	0.471397i
$393$		0			0
$394$	−1.30656	+	1.30656i	−1.30656	+	1.30656i
$395$	−0.0750191	−	0.761681i	−0.0750191	−	0.761681i
$396$		0			0
$397$		0			0		0.956940	−	0.290285i	$-0.0937500\pi$
$397$		0			0		−0.956940	+	0.290285i	$0.906250\pi$
$398$	−1.76820	−	0.536376i	−1.76820	−	0.536376i
$399$		0			0
$400$	0.831470	−	0.555570i	0.831470	−	0.555570i
$401$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$401$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$406$		0			0
$407$		0			0
$408$	−0.732410	−	1.76820i	−0.732410	−	1.76820i
$409$	−0.324423	−	0.216773i	−0.324423	−	0.216773i	0.382683	−	0.923880i	$-0.375000\pi$
$409$	−0.324423	−	0.216773i	−0.324423	−	0.216773i	−0.707107	+	0.707107i	$0.750000\pi$
$410$		0			0
$411$	0.728789	+	1.36347i	0.728789	+	1.36347i
$412$		0			0
$413$		0			0
$414$	0.172887	−	1.75535i	0.172887	−	1.75535i
$415$	0.275899	−	0.275899i	0.275899	−	0.275899i
$416$		0			0
$417$	−0.666656	−	0.666656i	−0.666656	−	0.666656i
$418$		0			0
$419$		0			0		0.0980171	−	0.995185i	$-0.468750\pi$
$419$		0			0		−0.0980171	+	0.995185i	$0.531250\pi$
$420$		0			0
$421$	0.831470	−	0.444430i	0.831470	−	0.444430i		−	1.00000i	$-0.5\pi$
$421$	0.831470	−	0.444430i	0.831470	−	0.444430i	0.831470	+	0.555570i	$0.187500\pi$
$422$	1.28547	−	0.858923i	1.28547	−	0.858923i
$423$	0.704900	−	1.05496i	0.704900	−	1.05496i
$424$	1.92388	−	0.382683i	1.92388	−	0.382683i
$425$	1.59133	−	1.06330i	1.59133	−	1.06330i
$426$		0			0
$427$		0			0
$428$	−1.65493	−	0.162997i	−1.65493	−	0.162997i
$429$		0			0
$430$		0			0
$431$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$431$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$432$	0.995185	−	0.0980171i	0.995185	−	0.0980171i
$433$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$433$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$434$		0			0
$435$		0			0
$436$	1.53858	−	0.151537i	1.53858	−	0.151537i
$437$	3.49379	−	0.344109i	3.49379	−	0.344109i
$438$		0			0
$439$	1.81225	+	0.360480i	1.81225	+	0.360480i	0.980785	−	0.195090i	$-0.0625000\pi$
$439$	1.81225	+	0.360480i	1.81225	+	0.360480i	0.831470	+	0.555570i	$0.187500\pi$
$440$		0			0
$441$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$442$		0			0
$443$	−1.06330	−	0.322547i	−1.06330	−	0.322547i	−0.290285	−	0.956940i	$-0.593750\pi$
$443$	−1.06330	−	0.322547i	−1.06330	−	0.322547i	−0.773010	+	0.634393i	$0.781250\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	0.290285	+	0.956940i	0.290285	+	0.956940i
$451$		0			0
$452$	−0.704900	+	1.05496i	−0.704900	+	1.05496i
$453$	0.373380	+	0.113263i	0.373380	+	0.113263i
$454$	1.08979	−	1.63099i	1.08979	−	1.63099i
$455$		0			0
$456$	0.577774	+	1.90466i	0.577774	+	1.90466i
$457$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$457$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$458$	−0.942793			−0.942793
$459$	1.90466	−	0.187593i	1.90466	−	0.187593i
$460$	−1.36347	−	1.11897i	−1.36347	−	1.11897i
$461$		0			0		−0.290285	−	0.956940i	$-0.593750\pi$
$461$		0			0		0.290285	+	0.956940i	$0.406250\pi$
$462$		0			0
$463$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$463$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$464$		0			0
$465$	1.02656	+	0.425215i	1.02656	+	0.425215i
$466$	0.938254	−	0.0924099i	0.938254	−	0.0924099i
$467$	−1.62958	−	0.871028i	−1.62958	−	0.871028i	−0.995185	−	0.0980171i	$-0.968750\pi$
$467$	−1.62958	−	0.871028i	−1.62958	−	0.871028i	−0.634393	−	0.773010i	$-0.718750\pi$
$468$		0			0
$469$		0			0
$470$	−0.485544	−	1.17221i	−0.485544	−	1.17221i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−0.425215	−	0.636379i	−0.425215	−	0.636379i
$475$	−1.75535	+	0.938254i	−1.75535	+	0.938254i
$476$		0			0
$477$	−0.192268	+	1.95213i	−0.192268	+	1.95213i
$478$		0			0
$479$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$479$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$480$	0.471397	−	0.881921i	0.471397	−	0.881921i
$481$		0			0
$482$	1.10579	+	0.108911i	1.10579	+	0.108911i
$483$		0			0
$484$	0.707107	+	0.707107i	0.707107	+	0.707107i
$485$		0			0
$486$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$487$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$487$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$488$	0.138617	+	0.138617i	0.138617	+	0.138617i
$489$		0			0
$490$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$491$		0			0		0.634393	−	0.773010i	$-0.281250\pi$
$491$		0			0		−0.634393	+	0.773010i	$0.718750\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.425215	−	1.02656i	−0.425215	−	1.02656i
$497$		0			0
$498$	0.113263	−	0.373380i	0.113263	−	0.373380i
$499$	−0.902197	+	0.273678i	−0.902197	+	0.273678i	−0.707107	−	0.707107i	$-0.750000\pi$
$499$	−0.902197	+	0.273678i	−0.902197	+	0.273678i	−0.195090	+	0.980785i	$0.562500\pi$
$500$	0.956940	+	0.290285i	0.956940	+	0.290285i
$501$	0.0569057	+	0.577774i	0.0569057	+	0.577774i
$502$		0			0
$503$	0.301614	−	1.51631i	0.301614	−	1.51631i	−0.471397	−	0.881921i	$-0.656250\pi$
$503$	0.301614	−	1.51631i	0.301614	−	1.51631i	0.773010	−	0.634393i	$-0.218750\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.290285	−	0.956940i	0.290285	−	0.956940i
$508$		0			0
$509$		0			0		0.773010	−	0.634393i	$-0.218750\pi$
$509$		0			0		−0.773010	+	0.634393i	$0.781250\pi$
$510$	0.902197	−	1.68789i	0.902197	−	1.68789i
$511$		0			0
$512$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$513$	−1.99037			−1.99037
$514$	−0.831470	+	1.55557i	−0.831470	+	1.55557i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.63099	−	0.324423i	1.63099	−	0.324423i
$520$		0			0
$521$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$521$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$522$		0			0
$523$		0			0		−0.0980171	−	0.995185i	$-0.531250\pi$
$523$		0			0		0.0980171	+	0.995185i	$0.468750\pi$
$524$		0			0
$525$		0			0
$526$	−0.555570	+	1.83147i	−0.555570	+	1.83147i
$527$	−0.813811	−	1.96471i	−0.813811	−	1.96471i
$528$		0			0
$529$	−0.807898	+	1.95044i	−0.807898	+	1.95044i
$530$	1.51631	+	1.24441i	1.51631	+	1.24441i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.923880	−	1.38268i	−0.923880	−	1.38268i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	0.707107	+	0.707107i	0.707107	+	0.707107i
$541$	−0.577774	−	0.0569057i	−0.577774	−	0.0569057i	−0.195090	−	0.980785i	$-0.562500\pi$
$541$	−0.577774	−	0.0569057i	−0.577774	−	0.0569057i	−0.382683	+	0.923880i	$0.625000\pi$
$542$	1.40740	+	0.138617i	1.40740	+	0.138617i
$543$	−0.410525	+	0.410525i	−0.410525	+	0.410525i
$544$	−1.83147	+	0.555570i	−1.83147	+	0.555570i
$545$	1.09320	+	1.09320i	1.09320	+	1.09320i
$546$		0			0
$547$		0			0		0.0980171	−	0.995185i	$-0.468750\pi$
$547$		0			0		−0.0980171	+	0.995185i	$0.531250\pi$
$548$	1.42834	−	0.591637i	1.42834	−	0.591637i
$549$	−0.172887	+	0.0924099i	−0.172887	+	0.0924099i
$550$		0			0
$551$		0			0
$552$	−1.72995	−	0.344109i	−1.72995	−	0.344109i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.728789	+	0.598102i	−0.728789	+	0.598102i
$557$	0.344109	+	0.183930i	0.344109	+	0.183930i	0.634393	−	0.773010i	$-0.281250\pi$
$557$	0.344109	+	0.183930i	0.344109	+	0.183930i	−0.290285	+	0.956940i	$0.593750\pi$
$558$	1.10579	−	0.108911i	1.10579	−	0.108911i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.536376	+	1.76820i	0.536376	+	1.76820i	0.634393	+	0.773010i	$0.281250\pi$
$563$	0.536376	+	1.76820i	0.536376	+	1.76820i	−0.0980171	+	0.995185i	$0.531250\pi$
$564$	−0.980785	−	0.804910i	−0.980785	−	0.804910i
$565$	−1.26268	+	0.124363i	−1.26268	+	0.124363i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$569$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$570$	−1.10579	+	1.65493i	−1.10579	+	1.65493i
$571$	1.68789	+	0.512016i	1.68789	+	0.512016i	0.980785	−	0.195090i	$-0.0625000\pi$
$571$	1.68789	+	0.512016i	1.68789	+	0.512016i	0.707107	+	0.707107i	$0.250000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	1.76384i		−	1.76384i
$576$		−	1.00000i		−	1.00000i
$577$		0			0			−	1.00000i	$-0.5\pi$
$577$		0			0				1.00000i	$0.5\pi$
$578$	−2.54827	+	0.773010i	−2.54827	+	0.773010i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		−	0.390181i		−	0.390181i
$587$	−1.65493	+	0.162997i	−1.65493	+	0.162997i	−0.881921	−	0.471397i	$-0.843750\pi$
$587$	−1.65493	+	0.162997i	−1.65493	+	0.162997i	−0.773010	+	0.634393i	$0.781250\pi$
$588$	−0.995185	+	0.0980171i	−0.995185	+	0.0980171i
$589$	0.641988	+	2.11635i	0.641988	+	2.11635i
$590$		0			0
$591$	−1.70711	+	0.707107i	−1.70711	+	0.707107i
$592$		0			0
$593$	0.871028	+	0.360791i	0.871028	+	0.360791i	0.773010	−	0.634393i	$-0.218750\pi$
$593$	0.871028	+	0.360791i	0.871028	+	0.360791i	0.0980171	+	0.995185i	$0.468750\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.42834	−	1.17221i	−1.42834	−	1.17221i
$598$		0			0
$599$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$599$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$600$	0.980785	−	0.195090i	0.980785	−	0.195090i
$601$	−0.216773	+	0.324423i	−0.216773	+	0.324423i	−0.923880	−	0.382683i	$-0.875000\pi$
$601$	−0.216773	+	0.324423i	−0.216773	+	0.324423i	0.707107	+	0.707107i	$0.250000\pi$
$602$		0			0
$603$		0			0
$604$	0.149316	−	0.360480i	0.149316	−	0.360480i
$605$	−0.0980171	+	0.995185i	−0.0980171	+	0.995185i
$606$		0			0
$607$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$607$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$608$	1.95213	−	0.388302i	1.95213	−	0.388302i
$609$		0			0
$610$	−0.0192147	+	0.195090i	−0.0192147	+	0.195090i
$611$		0			0
$612$		−	1.91388i		−	1.91388i
$613$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$613$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.704900	−	1.05496i	−0.704900	−	1.05496i	−0.995185	−	0.0980171i	$-0.968750\pi$
$617$	−0.704900	−	1.05496i	−0.704900	−	1.05496i	0.290285	−	0.956940i	$-0.406250\pi$
$618$		0			0
$619$	−0.980785	+	1.19509i	−0.980785	+	1.19509i			1.00000i	$0.5\pi$
$619$	−0.980785	+	1.19509i	−0.980785	+	1.19509i	−0.980785	+	0.195090i	$0.937500\pi$
$620$	0.523788	−	0.979938i	0.523788	−	0.979938i
$621$	0.831470	−	1.55557i	0.831470	−	1.55557i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.382683	+	0.923880i	0.382683	+	0.923880i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.275899	+	1.38704i	−0.275899	+	1.38704i	0.555570	+	0.831470i	$0.312500\pi$
$631$	−0.275899	+	1.38704i	−0.275899	+	1.38704i	−0.831470	+	0.555570i	$0.812500\pi$
$632$	−0.674993	+	0.360791i	−0.674993	+	0.360791i
$633$	1.51631	−	0.301614i	1.51631	−	0.301614i
$634$	0.750661	−	0.149316i	0.750661	−	0.149316i
$635$		0			0
$636$	1.92388	+	0.382683i	1.92388	+	0.382683i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	−1.46658	−	0.783904i	−1.46658	−	0.783904i
$643$		0			0		0.773010	−	0.634393i	$-0.218750\pi$
$643$		0			0		−0.773010	+	0.634393i	$0.781250\pi$
$644$		0			0
$645$		0			0
$646$	3.73613	−	0.743163i	3.73613	−	0.743163i
$647$	−1.95213	+	0.388302i	−1.95213	+	0.388302i	−0.956940	+	0.290285i	$0.906250\pi$
$647$	−1.95213	+	0.388302i	−1.95213	+	0.388302i	−0.995185	+	0.0980171i	$0.968750\pi$
$648$	0.956940	+	0.290285i	0.956940	+	0.290285i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.59133	+	0.482726i	−1.59133	+	0.482726i	−0.956940	−	0.290285i	$-0.906250\pi$
$653$	−1.59133	+	0.482726i	−1.59133	+	0.482726i	−0.634393	+	0.773010i	$0.718750\pi$
$654$	1.47945	+	0.448786i	1.47945	+	0.448786i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.471397	−	0.881921i	$-0.343750\pi$
$659$		0			0		−0.471397	+	0.881921i	$0.656250\pi$
$660$		0			0
$661$	−0.980785	+	1.19509i	−0.980785	+	1.19509i			1.00000i	$0.5\pi$
$661$	−0.980785	+	1.19509i	−0.980785	+	1.19509i	−0.980785	+	0.195090i	$0.937500\pi$
$662$	0.222174	−	0.536376i	0.222174	−	0.536376i
$663$		0			0
$664$	−0.360480	−	0.149316i	−0.360480	−	0.149316i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.580569			0.580569
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$673$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$674$		0			0
$675$	−0.0980171	+	0.995185i	−0.0980171	+	0.995185i
$676$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$677$	0.979938	−	0.523788i	0.979938	−	0.523788i	0.0980171	−	0.995185i	$-0.468750\pi$
$677$	0.979938	−	0.523788i	0.979938	−	0.523788i	0.881921	+	0.471397i	$0.156250\pi$
$678$	−1.05496	+	0.704900i	−1.05496	+	0.704900i
$679$		0			0
$680$	−1.59133	−	1.06330i	−1.59133	−	1.06330i
$681$	1.63099	−	1.08979i	1.63099	−	1.08979i
$682$		0			0
$683$	−0.591637	−	0.485544i	−0.591637	−	0.485544i	0.290285	−	0.956940i	$-0.406250\pi$
$683$	−0.591637	−	0.485544i	−0.591637	−	0.485544i	−0.881921	+	0.471397i	$0.843750\pi$
$684$	−0.195090	+	1.98079i	−0.195090	+	1.98079i
$685$	1.36347	+	0.728789i	1.36347	+	0.728789i
$686$		0			0
$687$	−0.871028	−	0.360791i	−0.871028	−	0.360791i
$688$		0			0
$689$		0			0
$690$	−0.831470	−	1.55557i	−0.831470	−	1.55557i
$691$	−0.168530	−	0.555570i	−0.168530	−	0.555570i	0.831470	−	0.555570i	$-0.187500\pi$
$691$	−0.168530	−	0.555570i	−0.168530	−	0.555570i	−1.00000			$\pi$
$692$	−0.162997	−	1.65493i	−0.162997	−	1.65493i
$693$		0			0
$694$			0.765367i			0.765367i
$695$	−0.924678	−	0.183930i	−0.924678	−	0.183930i
$696$		0			0
$697$		0			0
$698$	1.65493	+	1.10579i	1.65493	+	1.10579i
$699$	0.902197	+	0.273678i	0.902197	+	0.273678i
$700$		0			0
$701$		0			0		−0.634393	−	0.773010i	$-0.718750\pi$
$701$		0			0		0.634393	+	0.773010i	$0.281250\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		−	1.26879i		−	1.26879i
$706$	−0.0569057	−	0.187593i	−0.0569057	−	0.187593i
$707$		0			0
$708$		0			0
$709$	−1.90466	−	0.577774i	−1.90466	−	0.577774i	−0.980785	−	0.195090i	$-0.937500\pi$
$709$	−1.90466	−	0.577774i	−1.90466	−	0.577774i	−0.923880	−	0.382683i	$-0.875000\pi$
$710$		0			0
$711$	−0.149316	−	0.750661i	−0.149316	−	0.750661i
$712$		0			0
$713$	−1.92222	−	0.382353i	−1.92222	−	0.382353i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$719$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$720$	0.773010	−	0.634393i	0.773010	−	0.634393i
$721$		0			0
$722$	−2.94731	+	0.290285i	−2.94731	+	0.290285i
$723$	0.979938	+	0.523788i	0.979938	+	0.523788i
$724$	0.368309	+	0.448786i	0.368309	+	0.448786i
$725$		0			0
$726$	0.382683	+	0.923880i	0.382683	+	0.923880i
$727$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$727$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$728$		0			0
$729$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$730$		0			0
$731$		0			0
$732$	0.0750191	+	0.181112i	0.0750191	+	0.181112i
$733$		0			0		0.0980171	−	0.995185i	$-0.468750\pi$
$733$		0			0		−0.0980171	+	0.995185i	$0.531250\pi$
$734$		0			0
$735$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$736$	−0.512016	+	1.68789i	−0.512016	+	1.68789i
$737$		0			0
$738$		0			0
$739$	−1.26268	−	0.124363i	−1.26268	−	0.124363i	−0.555570	−	0.831470i	$-0.687500\pi$
$739$	−1.26268	−	0.124363i	−1.26268	−	0.124363i	−0.707107	+	0.707107i	$0.750000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.162997	−	0.108911i	−0.162997	−	0.108911i	0.471397	−	0.881921i	$-0.343750\pi$
$743$	−0.162997	−	0.108911i	−0.162997	−	0.108911i	−0.634393	+	0.773010i	$0.718750\pi$
$744$		−	1.11114i		−	1.11114i
$745$		0			0
$746$		0			0
$747$	0.247528	−	0.301614i	0.247528	−	0.301614i
$748$		0			0
$749$		0			0
$750$	0.773010	+	0.634393i	0.773010	+	0.634393i
$751$	0.636379	−	1.53636i	0.636379	−	1.53636i	−0.195090	−	0.980785i	$-0.562500\pi$
$751$	0.636379	−	1.53636i	0.636379	−	1.53636i	0.831470	−	0.555570i	$-0.187500\pi$
$752$	−0.897168	+	0.897168i	−0.897168	+	0.897168i
$753$		0			0
$754$		0			0
$755$	0.373380	−	0.113263i	0.373380	−	0.113263i
$756$		0			0
$757$		0			0		−0.0980171	−	0.995185i	$-0.531250\pi$
$757$		0			0		0.0980171	+	0.995185i	$0.468750\pi$
$758$	0.410525	+	0.410525i	0.410525	+	0.410525i
$759$		0			0
$760$	1.53858	+	1.26268i	1.53858	+	1.26268i
$761$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$761$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.47945	−	1.21415i	1.47945	−	1.21415i
$766$	−0.0924099	+	0.172887i	−0.0924099	+	0.172887i
$767$		0			0
$768$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$769$	−1.66294			−1.66294			−0.831470	−	0.555570i	$-0.812500\pi$
$769$	−1.66294			−1.66294			−0.831470	+	0.555570i	$0.812500\pi$
$770$		0			0
$771$	−1.36347	+	1.11897i	−1.36347	+	1.11897i
$772$		0			0
$773$	0.410525	−	1.35332i	0.410525	−	1.35332i	−0.471397	−	0.881921i	$-0.656250\pi$
$773$	0.410525	−	1.35332i	0.410525	−	1.35332i	0.881921	−	0.471397i	$-0.156250\pi$
$774$		0			0
$775$	1.08979	−	0.216773i	1.08979	−	0.216773i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.979938	+	3.23042i	−0.979938	+	3.23042i
$783$		0			0
$784$			1.00000i			1.00000i
$785$		0			0
$786$		0			0
$787$		0			0		0.471397	−	0.881921i	$-0.343750\pi$
$787$		0			0		−0.471397	+	0.881921i	$0.656250\pi$
$788$	0.536376	+	1.76820i	0.536376	+	1.76820i
$789$	−1.21415	+	1.47945i	−1.21415	+	1.47945i
$790$	−0.707107	−	0.292893i	−0.707107	−	0.292893i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.924678	+	1.72995i	0.924678	+	1.72995i
$796$	−1.30656	+	1.30656i	−1.30656	+	1.30656i
$797$	0.761681	+	0.0750191i	0.761681	+	0.0750191i	0.471397	−	0.881921i	$-0.343750\pi$
$797$	0.761681	+	0.0750191i	0.761681	+	0.0750191i	0.290285	+	0.956940i	$0.406250\pi$
$798$		0			0
$799$	−1.71707	+	1.71707i	−1.71707	+	1.71707i
$800$	−0.0980171	−	0.995185i	−0.0980171	−	0.995185i
$801$		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		0.831470	−	0.555570i	$-0.187500\pi$
$809$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$810$	0.382683	+	0.923880i	0.382683	+	0.923880i
$811$	−0.151537	−	0.124363i	−0.151537	−	0.124363i	0.555570	−	0.831470i	$-0.312500\pi$
$811$	−0.151537	−	0.124363i	−0.151537	−	0.124363i	−0.707107	+	0.707107i	$0.750000\pi$
$812$		0			0
$813$	1.24723	+	0.666656i	1.24723	+	0.666656i
$814$		0			0
$815$		0			0
$816$	−1.90466	−	0.187593i	−1.90466	−	0.187593i
$817$		0			0
$818$	−0.344109	+	0.183930i	−0.344109	+	0.183930i
$819$		0			0
$820$		0			0
$821$		0			0		0.995185	−	0.0980171i	$-0.0312500\pi$
$821$		0			0		−0.995185	+	0.0980171i	$0.968750\pi$
$822$	1.54602			1.54602
$823$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$823$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.732410	−	0.222174i	−0.732410	−	0.222174i	−0.0980171	−	0.995185i	$-0.531250\pi$
$827$	−0.732410	−	0.222174i	−0.732410	−	0.222174i	−0.634393	+	0.773010i	$0.718750\pi$
$828$	−1.46658	−	0.979938i	−1.46658	−	0.979938i
$829$	−1.21415	−	1.47945i	−1.21415	−	1.47945i	−0.831470	−	0.555570i	$-0.812500\pi$
$829$	−1.21415	−	1.47945i	−1.21415	−	1.47945i	−0.382683	−	0.923880i	$-0.625000\pi$
$830$	−0.113263	−	0.373380i	−0.113263	−	0.373380i
$831$		0			0
$832$		0			0
$833$			1.91388i			1.91388i
$834$	−0.902197	+	0.273678i	−0.902197	+	0.273678i
$835$	0.368309	+	0.448786i	0.368309	+	0.448786i
$836$		0			0
$837$	1.06330	+	0.322547i	1.06330	+	0.322547i
$838$		0			0
$839$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$839$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$840$		0			0
$841$	0.980785	+	0.195090i	0.980785	+	0.195090i
$842$		−	0.942793i		−	0.942793i
$843$		0			0
$844$	−0.151537	−	1.53858i	−0.151537	−	1.53858i
$845$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$846$	−0.598102	−	1.11897i	−0.598102	−	1.11897i
$847$		0			0
$848$	0.569414	−	1.87711i	0.569414	−	1.87711i
$849$		0			0
$850$	−0.187593	−	1.90466i	−0.187593	−	1.90466i
$851$		0			0
$852$		0			0
$853$		0			0		−0.773010	−	0.634393i	$-0.781250\pi$
$853$		0			0		0.773010	+	0.634393i	$0.218750\pi$
$854$		0			0
$855$	−1.65493	+	1.10579i	−1.65493	+	1.10579i
$856$	−0.923880	+	1.38268i	−0.923880	+	1.38268i
$857$	−0.108911	+	0.162997i	−0.108911	+	0.162997i	−0.881921	−	0.471397i	$-0.843750\pi$
$857$	−0.108911	+	0.162997i	−0.108911	+	0.162997i	0.773010	+	0.634393i	$0.218750\pi$
$858$		0			0
$859$	0.172887	−	0.0924099i	0.172887	−	0.0924099i	−0.382683	−	0.923880i	$-0.625000\pi$
$859$	0.172887	−	0.0924099i	0.172887	−	0.0924099i	0.555570	+	0.831470i	$0.312500\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.666656	−	0.666656i	−0.666656	−	0.666656i	0.290285	−	0.956940i	$-0.406250\pi$
$863$	−0.666656	−	0.666656i	−0.666656	−	0.666656i	−0.956940	+	0.290285i	$0.906250\pi$
$864$	0.382683	−	0.923880i	0.382683	−	0.923880i
$865$	1.17588	−	1.17588i	1.17588	−	1.17588i
$866$		0			0
$867$	−2.65012	−	0.261014i	−2.65012	−	0.261014i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.591637	−	1.42834i	0.591637	−	1.42834i
$873$		0			0
$874$	1.34349	−	3.24346i	1.34349	−	3.24346i
$875$		0			0
$876$		0			0
$877$		0			0		0.471397	−	0.881921i	$-0.343750\pi$
$877$		0			0		−0.471397	+	0.881921i	$0.656250\pi$
$878$	1.17221	−	1.42834i	1.17221	−	1.42834i
$879$	0.149316	−	0.360480i	0.149316	−	0.360480i
$880$		0			0
$881$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$881$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$882$	−0.956940	−	0.290285i	−0.956940	−	0.290285i
$883$		0			0		0.956940	−	0.290285i	$-0.0937500\pi$
$883$		0			0		−0.956940	+	0.290285i	$0.906250\pi$
$884$		0			0
$885$		0			0
$886$	−0.785695	+	0.785695i	−0.785695	+	0.785695i
$887$	−0.183930	+	0.924678i	−0.183930	+	0.924678i	0.773010	+	0.634393i	$0.218750\pi$
$887$	−0.183930	+	0.924678i	−0.183930	+	0.924678i	−0.956940	+	0.290285i	$0.906250\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.95213	−	1.60207i	1.95213	−	1.60207i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.980785	+	0.195090i	0.980785	+	0.195090i
$901$	1.08979	−	3.59256i	1.08979	−	3.59256i
$902$		0			0
$903$		0			0
$904$	0.598102	+	1.11897i	0.598102	+	1.11897i
$905$	−0.113263	+	0.569414i	−0.113263	+	0.569414i
$906$	0.275899	−	0.275899i	0.275899	−	0.275899i
$907$		0			0		−0.0980171	−	0.995185i	$-0.531250\pi$
$907$		0			0		0.0980171	+	0.995185i	$0.468750\pi$
$908$	−0.924678	−	1.72995i	−0.924678	−	1.72995i
$909$		0			0
$910$		0			0
$911$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$911$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$912$	1.95213	+	0.388302i	1.95213	+	0.388302i
$913$		0			0
$914$		0			0
$915$	−0.0924099	+	0.172887i	−0.0924099	+	0.172887i
$916$	−0.444430	+	0.831470i	−0.444430	+	0.831470i
$917$		0			0
$918$	0.732410	−	1.76820i	0.732410	−	1.76820i
$919$	−1.08979	−	1.63099i	−1.08979	−	1.63099i	−0.707107	−	0.707107i	$-0.750000\pi$
$919$	−1.08979	−	1.63099i	−1.08979	−	1.63099i	−0.382683	−	0.923880i	$-0.625000\pi$
$920$	−1.62958	+	0.674993i	−1.62958	+	0.674993i
$921$		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		−0.707107	−	0.707107i	$-0.750000\pi$
$929$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$930$	0.858923	−	0.704900i	0.858923	−	0.704900i
$931$	0.195090	−	1.98079i	0.195090	−	1.98079i
$932$	0.360791	−	0.871028i	0.360791	−	0.871028i
$933$		0			0
$934$	−1.53636	+	1.02656i	−1.53636	+	1.02656i
$935$		0			0
$936$		0			0
$937$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$937$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$938$		0			0
$939$		0			0
$940$	−1.26268	−	0.124363i	−1.26268	−	0.124363i
$941$		0			0		−0.881921	−	0.471397i	$-0.843750\pi$
$941$		0			0		0.881921	+	0.471397i	$0.156250\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.113263	+	0.373380i	0.113263	+	0.373380i	0.995185	−	0.0980171i	$-0.0312500\pi$
$947$	0.113263	+	0.373380i	0.113263	+	0.373380i	−0.881921	+	0.471397i	$0.843750\pi$
$948$	−0.761681	+	0.0750191i	−0.761681	+	0.0750191i
$949$		0			0
$950$			1.99037i			1.99037i
$951$	0.750661	+	0.149316i	0.750661	+	0.149316i
$952$		0			0
$953$	0.113263	+	0.569414i	0.113263	+	0.569414i	0.995185	+	0.0980171i	$0.0312500\pi$
$953$	0.113263	+	0.569414i	0.113263	+	0.569414i	−0.881921	+	0.471397i	$0.843750\pi$
$954$	1.63099	+	1.08979i	1.63099	+	1.08979i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$961$		−	0.234633i		−	0.234633i
$962$		0			0
$963$	−1.05496	−	1.28547i	−1.05496	−	1.28547i
$964$	0.617317	−	0.923880i	0.617317	−	0.923880i
$965$		0			0
$966$		0			0
$967$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$967$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$968$	0.956940	−	0.290285i	0.956940	−	0.290285i
$969$	3.73613	+	0.743163i	3.73613	+	0.743163i
$970$		0			0
$971$		0			0		0.995185	−	0.0980171i	$-0.0312500\pi$
$971$		0			0		−0.995185	+	0.0980171i	$0.968750\pi$
$972$	0.773010	+	0.634393i	0.773010	+	0.634393i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.187593	−	0.0569057i	0.187593	−	0.0569057i
$977$	−1.62958	−	0.674993i	−1.62958	−	0.674993i	−0.634393	−	0.773010i	$-0.718750\pi$
$977$	−1.62958	−	0.674993i	−1.62958	−	0.674993i	−0.995185	+	0.0980171i	$0.968750\pi$
$978$		0			0
$979$		0			0
$980$	−0.773010	+	0.634393i	−0.773010	+	0.634393i
$981$	1.19509	+	0.980785i	1.19509	+	0.980785i
$982$		0			0
$983$	1.59133	−	1.06330i	1.59133	−	1.06330i	0.634393	−	0.773010i	$-0.281250\pi$
$983$	1.59133	−	1.06330i	1.59133	−	1.06330i	0.956940	−	0.290285i	$-0.0937500\pi$
$984$		0			0
$985$	−1.02656	+	1.53636i	−1.02656	+	1.53636i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$991$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$992$	−1.10579	−	0.108911i	−1.10579	−	0.108911i
$993$	0.410525	−	0.410525i	0.410525	−	0.410525i
$994$		0			0
$995$	−1.83886	−	0.181112i	−1.83886	−	0.181112i
$996$	−0.275899	−	0.275899i	−0.275899	−	0.275899i
$997$		0			0		−0.471397	−	0.881921i	$-0.656250\pi$
$997$		0			0		0.471397	+	0.881921i	$0.343750\pi$
$998$	−0.183930	+	0.924678i	−0.183930	+	0.924678i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.1.db.a.1469.2	yes	32
3.2	odd	2	inner	1920.1.db.a.1469.1	yes	32
5.4	even	2	inner	1920.1.db.a.1469.1	yes	32
15.14	odd	2	CM	1920.1.db.a.1469.2	yes	32
128.21	even	32	inner	1920.1.db.a.149.2	yes	32
384.149	odd	32	inner	1920.1.db.a.149.1	✓	32
640.149	even	32	inner	1920.1.db.a.149.1	✓	32
1920.149	odd	32	inner	1920.1.db.a.149.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.1.db.a.149.1	✓	32	384.149	odd	32	inner
1920.1.db.a.149.1	✓	32	640.149	even	32	inner
1920.1.db.a.149.2	yes	32	128.21	even	32	inner
1920.1.db.a.149.2	yes	32	1920.149	odd	32	inner
1920.1.db.a.1469.1	yes	32	3.2	odd	2	inner
1920.1.db.a.1469.1	yes	32	5.4	even	2	inner
1920.1.db.a.1469.2	yes	32	1.1	even	1	trivial
1920.1.db.a.1469.2	yes	32	15.14	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1920.db (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.471397 - 0.881921i) q^{2} +(0.773010 - 0.634393i) q^{3} +(-0.555570 - 0.831470i) q^{4} +(0.290285 - 0.956940i) q^{5} +(-0.195090 - 0.980785i) q^{6} +(-0.995185 + 0.0980171i) q^{8} +(0.195090 - 0.980785i) q^{9} +(-0.707107 - 0.707107i) q^{10} +(-0.956940 - 0.290285i) q^{12} +(-0.382683 - 0.923880i) q^{15} +(-0.382683 + 0.923880i) q^{16} +(-0.732410 + 1.76820i) q^{17} +(-0.773010 - 0.634393i) q^{18} +(0.938254 - 1.75535i) q^{19} +(-0.956940 + 0.290285i) q^{20} +(0.979938 + 1.46658i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-0.831470 - 0.555570i) q^{25} +(-0.471397 - 0.881921i) q^{27} +(-0.995185 - 0.0980171i) q^{30} +(-0.785695 + 0.785695i) q^{31} +(0.634393 + 0.773010i) q^{32} +(1.21415 + 1.47945i) q^{34} +(-0.923880 + 0.382683i) q^{36} +(-1.10579 - 1.65493i) q^{38} +(-0.195090 + 0.980785i) q^{40} +(-0.881921 - 0.471397i) q^{45} +(1.75535 - 0.172887i) q^{46} +(1.17221 + 0.485544i) q^{47} +(0.290285 + 0.956940i) q^{48} +(0.923880 - 0.382683i) q^{49} +(-0.881921 + 0.471397i) q^{50} +(0.555570 + 1.83147i) q^{51} +(-1.95213 + 0.192268i) q^{53} -1.00000 q^{54} +(-0.388302 - 1.95213i) q^{57} +(-0.555570 + 0.831470i) q^{60} +(-0.124363 - 0.151537i) q^{61} +(0.322547 + 1.06330i) q^{62} +(0.980785 - 0.195090i) q^{64} +(1.87711 - 0.373380i) q^{68} +(1.68789 + 0.512016i) q^{69} +(-0.0980171 + 0.995185i) q^{72} +(-0.995185 + 0.0980171i) q^{75} +(-1.98079 + 0.195090i) q^{76} +(0.707107 - 0.292893i) q^{79} +(0.773010 + 0.634393i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(0.344109 + 0.183930i) q^{83} +(1.47945 + 1.21415i) q^{85} +(-0.831470 + 0.555570i) q^{90} +(0.674993 - 1.62958i) q^{92} +(-0.108911 + 1.10579i) q^{93} +(0.980785 - 0.804910i) q^{94} +(-1.40740 - 1.40740i) q^{95} +(0.980785 + 0.195090i) q^{96} +(0.0980171 - 0.995185i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{54} - 32 q^{76}+O(q^{100}) \) 32 * q - 32 * q^54 - 32 * q^76

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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