LMFDB - Embedded newform 3040.1.cn.a.189.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3040,1,Mod(189,3040)] 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("3040.189"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3040, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 3, 4, 4])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 3040 = 2^{5} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3040.cn (of order $8$, degree $4$, 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:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
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			189.8
Root			$-0.773010 - 0.634393i$ of defining polynomial
Character	$\chi$	$=$	3040.189
Dual form			3040.1.cn.a.949.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.956940 - 0.290285i) q^{2} +(-0.871028 - 0.360791i) q^{3} +(0.831470 - 0.555570i) q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.938254 - 0.0924099i) q^{6} +(0.634393 - 0.773010i) q^{8} +(-0.0785882 - 0.0785882i) q^{9} +(0.634393 + 0.773010i) q^{10} +(0.360480 - 0.149316i) q^{11} +(-0.924678 + 0.183930i) q^{12} +(0.761681 - 1.83886i) q^{13} -0.942793i q^{15} +(0.382683 - 0.923880i) q^{16} +(-0.0980171 - 0.0523913i) q^{18} +(-0.382683 + 0.923880i) q^{19} +(0.831470 + 0.555570i) q^{20} +(0.301614 - 0.247528i) q^{22} +(-0.831470 + 0.444430i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(0.195090 - 1.98079i) q^{26} +(0.400890 + 0.967834i) q^{27} +(-0.273678 - 0.902197i) q^{30} +(0.0980171 - 0.995185i) q^{32} -0.367860 q^{33} +(-0.109005 - 0.0216824i) q^{36} +(-0.222174 - 0.536376i) q^{37} +(-0.0980171 + 0.995185i) q^{38} +(-1.32689 + 1.32689i) q^{39} +(0.956940 + 0.290285i) q^{40} +(0.216773 - 0.324423i) q^{44} +(0.0425316 - 0.102680i) q^{45} +(-0.666656 + 0.666656i) q^{48} -1.00000i q^{49} +(-0.471397 + 0.881921i) q^{50} +(-0.388302 - 1.95213i) q^{52} +(1.62958 - 0.674993i) q^{53} +(0.664575 + 0.809787i) q^{54} +(0.275899 + 0.275899i) q^{55} +(0.666656 - 0.666656i) q^{57} +(-0.523788 - 0.783904i) q^{60} +(1.81225 + 0.750661i) q^{61} +(-0.195090 - 0.980785i) q^{64} +1.99037 q^{65} +(-0.352020 + 0.106784i) q^{66} +(-1.42834 - 0.591637i) q^{67} +(-0.110605 + 0.0108937i) q^{72} +(-0.368309 - 0.448786i) q^{74} +(0.871028 - 0.360791i) q^{75} +(0.195090 + 0.980785i) q^{76} +(-0.884579 + 1.65493i) q^{78} +1.00000 q^{80} -0.876507i q^{81} +(0.113263 - 0.373380i) q^{88} +(0.0108937 - 0.110605i) q^{90} -1.00000 q^{95} +(-0.444430 + 0.831470i) q^{96} -0.196034 q^{97} +(-0.290285 - 0.956940i) q^{98} +(-0.0400639 - 0.0165950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{66} + 32 q^{80} - 32 q^{95} - 32 q^{96} - 32 q^{99}+O(q^{100}) $ 32 * q - 32 * q^66 + 32 * q^80 - 32 * q^95 - 32 * q^96 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3040\mathbb{Z}\right)^\times$.

$n$	$191$	$1217$	$1921$	$2661$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.956940	−	0.290285i	0.956940	−	0.290285i
$2$	0.956940	−	0.290285i	0.956940	−	0.290285i
$3$	−0.871028	−	0.360791i	−0.871028	−	0.360791i	−0.0980171	−	0.995185i	$-0.531250\pi$
$3$	−0.871028	−	0.360791i	−0.871028	−	0.360791i	−0.773010	+	0.634393i	$0.781250\pi$
$4$	0.831470	−	0.555570i	0.831470	−	0.555570i
$5$	0.382683	+	0.923880i	0.382683	+	0.923880i
$5$	0.382683	+	0.923880i	0.382683	+	0.923880i
$6$	−0.938254	−	0.0924099i	−0.938254	−	0.0924099i
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	0.634393	−	0.773010i	0.634393	−	0.773010i
$9$	−0.0785882	−	0.0785882i	−0.0785882	−	0.0785882i
$10$	0.634393	+	0.773010i	0.634393	+	0.773010i
$11$	0.360480	−	0.149316i	0.360480	−	0.149316i	−0.195090	−	0.980785i	$-0.562500\pi$
$11$	0.360480	−	0.149316i	0.360480	−	0.149316i	0.555570	+	0.831470i	$0.312500\pi$
$12$	−0.924678	+	0.183930i	−0.924678	+	0.183930i
$13$	0.761681	−	1.83886i	0.761681	−	1.83886i	0.290285	−	0.956940i	$-0.406250\pi$
$13$	0.761681	−	1.83886i	0.761681	−	1.83886i	0.471397	−	0.881921i	$-0.343750\pi$
$14$		0			0
$15$		−	0.942793i		−	0.942793i
$16$	0.382683	−	0.923880i	0.382683	−	0.923880i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−0.0980171	−	0.0523913i	−0.0980171	−	0.0523913i
$19$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$19$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$20$	0.831470	+	0.555570i	0.831470	+	0.555570i
$21$		0			0
$22$	0.301614	−	0.247528i	0.301614	−	0.247528i
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$	−0.831470	+	0.444430i	−0.831470	+	0.444430i
$25$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$26$	0.195090	−	1.98079i	0.195090	−	1.98079i
$27$	0.400890	+	0.967834i	0.400890	+	0.967834i
$28$		0			0
$29$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$29$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$30$	−0.273678	−	0.902197i	−0.273678	−	0.902197i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$33$	−0.367860			−0.367860
$34$		0			0
$35$		0			0
$36$	−0.109005	−	0.0216824i	−0.109005	−	0.0216824i
$37$	−0.222174	−	0.536376i	−0.222174	−	0.536376i	0.773010	−	0.634393i	$-0.218750\pi$
$37$	−0.222174	−	0.536376i	−0.222174	−	0.536376i	−0.995185	+	0.0980171i	$0.968750\pi$
$38$	−0.0980171	+	0.995185i	−0.0980171	+	0.995185i
$39$	−1.32689	+	1.32689i	−1.32689	+	1.32689i
$40$	0.956940	+	0.290285i	0.956940	+	0.290285i
$41$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$41$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$42$		0			0
$43$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$43$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$44$	0.216773	−	0.324423i	0.216773	−	0.324423i
$45$	0.0425316	−	0.102680i	0.0425316	−	0.102680i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−0.666656	+	0.666656i	−0.666656	+	0.666656i
$49$		−	1.00000i		−	1.00000i
$50$	−0.471397	+	0.881921i	−0.471397	+	0.881921i
$51$		0			0
$52$	−0.388302	−	1.95213i	−0.388302	−	1.95213i
$53$	1.62958	−	0.674993i	1.62958	−	0.674993i	0.634393	−	0.773010i	$-0.281250\pi$
$53$	1.62958	−	0.674993i	1.62958	−	0.674993i	0.995185	+	0.0980171i	$0.0312500\pi$
$54$	0.664575	+	0.809787i	0.664575	+	0.809787i
$55$	0.275899	+	0.275899i	0.275899	+	0.275899i
$56$		0			0
$57$	0.666656	−	0.666656i	0.666656	−	0.666656i
$58$		0			0
$59$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$59$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$60$	−0.523788	−	0.783904i	−0.523788	−	0.783904i
$61$	1.81225	+	0.750661i	1.81225	+	0.750661i	0.980785	+	0.195090i	$0.0625000\pi$
$61$	1.81225	+	0.750661i	1.81225	+	0.750661i	0.831470	+	0.555570i	$0.187500\pi$
$62$		0			0
$63$		0			0
$64$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$65$	1.99037			1.99037
$66$	−0.352020	+	0.106784i	−0.352020	+	0.106784i
$67$	−1.42834	−	0.591637i	−1.42834	−	0.591637i	−0.471397	−	0.881921i	$-0.656250\pi$
$67$	−1.42834	−	0.591637i	−1.42834	−	0.591637i	−0.956940	+	0.290285i	$0.906250\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$71$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$72$	−0.110605	+	0.0108937i	−0.110605	+	0.0108937i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$	−0.368309	−	0.448786i	−0.368309	−	0.448786i
$75$	0.871028	−	0.360791i	0.871028	−	0.360791i
$76$	0.195090	+	0.980785i	0.195090	+	0.980785i
$77$		0			0
$78$	−0.884579	+	1.65493i	−0.884579	+	1.65493i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	1.00000			1.00000
$81$		−	0.876507i		−	0.876507i
$82$		0			0
$83$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$83$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.113263	−	0.373380i	0.113263	−	0.373380i
$89$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$89$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$90$	0.0108937	−	0.110605i	0.0108937	−	0.110605i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.00000			−1.00000
$96$	−0.444430	+	0.831470i	−0.444430	+	0.831470i
$97$	−0.196034			−0.196034			−0.0980171	−	0.995185i	$-0.531250\pi$
$97$	−0.196034			−0.196034			−0.0980171	+	0.995185i	$0.531250\pi$
$98$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$99$	−0.0400639	−	0.0165950i	−0.0400639	−	0.0165950i
$100$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$101$	0.149316	+	0.360480i	0.149316	+	0.360480i	0.980785	−	0.195090i	$-0.0625000\pi$
$101$	0.149316	+	0.360480i	0.149316	+	0.360480i	−0.831470	+	0.555570i	$0.812500\pi$
$102$		0			0
$103$	−1.35332	+	1.35332i	−1.35332	+	1.35332i	−0.471397	+	0.881921i	$0.656250\pi$
$103$	−1.35332	+	1.35332i	−1.35332	+	1.35332i	−0.881921	+	0.471397i	$0.843750\pi$
$104$	−0.938254	−	1.75535i	−0.938254	−	1.75535i
$105$		0			0
$106$	1.36347	−	1.11897i	1.36347	−	1.11897i
$107$	1.17221	−	0.485544i	1.17221	−	0.485544i	0.290285	−	0.956940i	$-0.406250\pi$
$107$	1.17221	−	0.485544i	1.17221	−	0.485544i	0.881921	+	0.471397i	$0.156250\pi$
$108$	0.871028	+	0.582002i	0.871028	+	0.582002i
$109$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$109$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$110$	0.344109	+	0.183930i	0.344109	+	0.183930i
$111$			0.547357i			0.547357i
$112$		0			0
$113$			1.76384i			1.76384i	0.471397	+	0.881921i	$0.343750\pi$
$113$			1.76384i			1.76384i	−0.471397	+	0.881921i	$0.656250\pi$
$114$	0.444430	−	0.831470i	0.444430	−	0.831470i
$115$		0			0
$116$		0			0
$117$	−0.204372	+	0.0846536i	−0.204372	+	0.0846536i
$118$		0			0
$119$		0			0
$120$	−0.728789	−	0.598102i	−0.728789	−	0.598102i
$121$	−0.599456	+	0.599456i	−0.599456	+	0.599456i
$122$	1.95213	+	0.192268i	1.95213	+	0.192268i
$123$		0			0
$124$		0			0
$125$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$126$		0			0
$127$	−1.54602			−1.54602			−0.773010	−	0.634393i	$-0.781250\pi$
$127$	−1.54602			−1.54602			−0.773010	+	0.634393i	$0.781250\pi$
$128$	−0.471397	−	0.881921i	−0.471397	−	0.881921i
$129$		0			0
$130$	1.90466	−	0.577774i	1.90466	−	0.577774i
$131$	0.707107	+	0.292893i	0.707107	+	0.292893i	0.707107	−	0.707107i	$-0.250000\pi$
$131$	0.707107	+	0.292893i	0.707107	+	0.292893i			1.00000i	$0.5\pi$
$132$	−0.305864	+	0.204372i	−0.305864	+	0.204372i
$133$		0			0
$134$	−1.53858	−	0.151537i	−1.53858	−	0.151537i
$135$	−0.740748	+	0.740748i	−0.740748	+	0.740748i
$136$		0			0
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$		0			0
$139$	1.53636	−	0.636379i	1.53636	−	0.636379i	0.555570	−	0.831470i	$-0.312500\pi$
$139$	1.53636	−	0.636379i	1.53636	−	0.636379i	0.980785	+	0.195090i	$0.0625000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	0.776604i		−	0.776604i
$144$	−0.102680	+	0.0425316i	−0.102680	+	0.0425316i
$145$		0			0
$146$		0			0
$147$	−0.360791	+	0.871028i	−0.360791	+	0.871028i
$148$	−0.482726	−	0.322547i	−0.482726	−	0.322547i
$149$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.980785	−	0.195090i	$-0.937500\pi$
$149$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.555570	+	0.831470i	$0.687500\pi$
$150$	0.728789	−	0.598102i	0.728789	−	0.598102i
$151$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$151$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$152$	0.471397	+	0.881921i	0.471397	+	0.881921i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.366088	+	1.84045i	−0.366088	+	1.84045i
$157$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$157$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$158$		0			0
$159$	−1.66294			−1.66294
$160$	0.956940	−	0.290285i	0.956940	−	0.290285i
$161$		0			0
$162$	−0.254437	−	0.838765i	−0.254437	−	0.838765i
$163$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$163$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$164$		0			0
$165$	−0.140774	−	0.339858i	−0.140774	−	0.339858i
$166$		0			0
$167$	−0.897168	+	0.897168i	−0.897168	+	0.897168i	−0.995185	−	0.0980171i	$-0.968750\pi$
$167$	−0.897168	+	0.897168i	−0.897168	+	0.897168i	0.0980171	+	0.995185i	$0.468750\pi$
$168$		0			0
$169$	−2.09415	−	2.09415i	−2.09415	−	2.09415i
$170$		0			0
$171$	0.102680	−	0.0425316i	0.102680	−	0.0425316i
$172$		0			0
$173$	−0.591637	+	1.42834i	−0.591637	+	1.42834i	0.290285	+	0.956940i	$0.406250\pi$
$173$	−0.591637	+	1.42834i	−0.591637	+	1.42834i	−0.881921	+	0.471397i	$0.843750\pi$
$174$		0			0
$175$		0			0
$176$		−	0.390181i		−	0.390181i
$177$		0			0
$178$		0			0
$179$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$179$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$180$	−0.0216824	−	0.109005i	−0.0216824	−	0.109005i
$181$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$181$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$182$		0			0
$183$	−1.30769	−	1.30769i	−1.30769	−	1.30769i
$184$		0			0
$185$	0.410525	−	0.410525i	0.410525	−	0.410525i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$191$	1.84776			1.84776			0.923880	−	0.382683i	$-0.125000\pi$
$191$	1.84776			1.84776			0.923880	+	0.382683i	$0.125000\pi$
$192$	−0.183930	+	0.924678i	−0.183930	+	0.924678i
$193$	−1.26879			−1.26879			−0.634393	−	0.773010i	$-0.718750\pi$
$193$	−1.26879			−1.26879			−0.634393	+	0.773010i	$0.718750\pi$
$194$	−0.187593	+	0.0569057i	−0.187593	+	0.0569057i
$195$	−1.73367	−	0.718108i	−1.73367	−	0.718108i
$196$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$197$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$197$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$198$	−0.0431560	−	0.00425050i	−0.0431560	−	0.00425050i
$199$	−1.30656	+	1.30656i	−1.30656	+	1.30656i	−0.382683	+	0.923880i	$0.625000\pi$
$199$	−1.30656	+	1.30656i	−1.30656	+	1.30656i	−0.923880	+	0.382683i	$0.875000\pi$
$200$	0.0980171	+	0.995185i	0.0980171	+	0.995185i
$201$	1.03066	+	1.03066i	1.03066	+	1.03066i
$202$	0.247528	+	0.301614i	0.247528	+	0.301614i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.902197	+	1.68789i	−0.902197	+	1.68789i
$207$		0			0
$208$	−1.40740	−	1.40740i	−1.40740	−	1.40740i
$209$			0.390181i			0.390181i
$210$		0			0
$211$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$211$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$212$	0.979938	−	1.46658i	0.979938	−	1.46658i
$213$		0			0
$214$	0.980785	−	0.804910i	0.980785	−	0.804910i
$215$		0			0
$216$	1.00247	+	0.304095i	1.00247	+	0.304095i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.382683	+	0.0761205i	0.382683	+	0.0761205i
$221$		0			0
$222$	0.158889	+	0.523788i	0.158889	+	0.523788i
$223$	0.196034			0.196034			0.0980171	−	0.995185i	$-0.468750\pi$
$223$	0.196034			0.196034			0.0980171	+	0.995185i	$0.468750\pi$
$224$		0			0
$225$	0.111140			0.111140
$226$	0.512016	+	1.68789i	0.512016	+	1.68789i
$227$	0.181112	+	0.0750191i	0.181112	+	0.0750191i	0.471397	−	0.881921i	$-0.343750\pi$
$227$	0.181112	+	0.0750191i	0.181112	+	0.0750191i	−0.290285	+	0.956940i	$0.593750\pi$
$228$	0.183930	−	0.924678i	0.183930	−	0.924678i
$229$	0.636379	+	1.53636i	0.636379	+	1.53636i	0.831470	+	0.555570i	$0.187500\pi$
$229$	0.636379	+	1.53636i	0.636379	+	1.53636i	−0.195090	+	0.980785i	$0.562500\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$233$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$234$	−0.170998	+	0.140335i	−0.170998	+	0.140335i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$239$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$240$	−0.871028	−	0.360791i	−0.871028	−	0.360791i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−0.399631	+	0.747657i	−0.399631	+	0.747657i
$243$	0.0846536	−	0.204372i	0.0846536	−	0.204372i
$244$	1.92388	−	0.382683i	1.92388	−	0.382683i
$245$	0.923880	−	0.382683i	0.923880	−	0.382683i
$246$		0			0
$247$	1.40740	+	1.40740i	1.40740	+	1.40740i
$248$		0			0
$249$		0			0
$250$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$251$	−0.541196	−	1.30656i	−0.541196	−	1.30656i	−0.923880	−	0.382683i	$-0.875000\pi$
$251$	−0.541196	−	1.30656i	−0.541196	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$252$		0			0
$253$		0			0
$254$	−1.47945	+	0.448786i	−1.47945	+	0.448786i
$255$		0			0
$256$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$257$	1.26879			1.26879			0.634393	−	0.773010i	$-0.281250\pi$
$257$	1.26879			1.26879			0.634393	+	0.773010i	$0.281250\pi$
$258$		0			0
$259$		0			0
$260$	1.65493	−	1.10579i	1.65493	−	1.10579i
$261$		0			0
$262$	0.761681	+	0.0750191i	0.761681	+	0.0750191i
$263$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$263$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$264$	−0.233368	+	0.284359i	−0.233368	+	0.284359i
$265$	1.24723	+	1.24723i	1.24723	+	1.24723i
$266$		0			0
$267$		0			0
$268$	−1.51631	+	0.301614i	−1.51631	+	0.301614i
$269$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$269$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$270$	−0.493824	+	0.923880i	−0.493824	+	0.923880i
$271$			1.66294i			1.66294i	0.555570	+	0.831470i	$0.312500\pi$
$271$			1.66294i			1.66294i	−0.555570	+	0.831470i	$0.687500\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.149316	+	0.360480i	−0.149316	+	0.360480i
$276$		0			0
$277$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$277$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$278$	1.28547	−	1.05496i	1.28547	−	1.05496i
$279$		0			0
$280$		0			0
$281$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$281$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$282$		0			0
$283$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$283$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$284$		0			0
$285$	0.871028	+	0.360791i	0.871028	+	0.360791i
$286$	−0.225436	−	0.743163i	−0.225436	−	0.743163i
$287$		0			0
$288$	−0.0859127	+	0.0705068i	−0.0859127	+	0.0705068i
$289$	−1.00000			−1.00000
$290$		0			0
$291$	0.170751	+	0.0707275i	0.170751	+	0.0707275i
$292$		0			0
$293$	0.732410	+	1.76820i	0.732410	+	1.76820i	0.634393	+	0.773010i	$0.281250\pi$
$293$	0.732410	+	1.76820i	0.732410	+	1.76820i	0.0980171	+	0.995185i	$0.468750\pi$
$294$	−0.0924099	+	0.938254i	−0.0924099	+	0.938254i
$295$		0			0
$296$	−0.555570	−	0.168530i	−0.555570	−	0.168530i
$297$	0.289026	+	0.289026i	0.289026	+	0.289026i
$298$	−1.28547	+	1.05496i	−1.28547	+	1.05496i
$299$		0			0
$300$	0.523788	−	0.783904i	0.523788	−	0.783904i
$301$		0			0
$302$		0			0
$303$		−	0.367860i		−	0.367860i
$304$	0.707107	+	0.707107i	0.707107	+	0.707107i
$305$			1.96157i			1.96157i
$306$		0			0
$307$	−0.0750191	+	0.181112i	−0.0750191	+	0.181112i	−0.956940	−	0.290285i	$-0.906250\pi$
$307$	−0.0750191	+	0.181112i	−0.0750191	+	0.181112i	0.881921	+	0.471397i	$0.156250\pi$
$308$		0			0
$309$	1.66704	−	0.690512i	1.66704	−	0.690512i
$310$		0			0
$311$	−1.38704	−	1.38704i	−1.38704	−	1.38704i	−0.831470	−	0.555570i	$-0.812500\pi$
$311$	−1.38704	−	1.38704i	−1.38704	−	1.38704i	−0.555570	−	0.831470i	$-0.687500\pi$
$312$	0.183930	+	1.86747i	0.183930	+	1.86747i
$313$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$313$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.17221	−	0.485544i	−1.17221	−	0.485544i	−0.290285	−	0.956940i	$-0.593750\pi$
$317$	−1.17221	−	0.485544i	−1.17221	−	0.485544i	−0.881921	+	0.471397i	$0.843750\pi$
$318$	−1.59133	+	0.482726i	−1.59133	+	0.482726i
$319$		0			0
$320$	0.831470	−	0.555570i	0.831470	−	0.555570i
$321$	−1.19620			−1.19620
$322$		0			0
$323$		0			0
$324$	−0.486961	−	0.728789i	−0.486961	−	0.728789i
$325$	0.761681	+	1.83886i	0.761681	+	1.83886i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−0.233368	−	0.284359i	−0.233368	−	0.284359i
$331$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$331$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$332$		0			0
$333$	−0.0246926	+	0.0596131i	−0.0246926	+	0.0596131i
$334$	−0.598102	+	1.11897i	−0.598102	+	1.11897i
$335$		−	1.54602i		−	1.54602i
$336$		0			0
$337$		−	0.580569i		−	0.580569i	−0.956940	−	0.290285i	$-0.906250\pi$
$337$		−	0.580569i		−	0.580569i	0.956940	−	0.290285i	$-0.0937500\pi$
$338$	−2.61187	−	1.39607i	−2.61187	−	1.39607i
$339$	0.636379	−	1.53636i	0.636379	−	1.53636i
$340$		0			0
$341$		0			0
$342$	0.0859127	−	0.0705068i	0.0859127	−	0.0705068i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.151537	+	1.53858i	−0.151537	+	1.53858i
$347$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$347$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$348$		0			0
$349$	−1.30656	−	0.541196i	−1.30656	−	0.541196i	−0.382683	−	0.923880i	$-0.625000\pi$
$349$	−1.30656	−	0.541196i	−1.30656	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$350$		0			0
$351$	2.08506			2.08506
$352$	−0.113263	−	0.373380i	−0.113263	−	0.373380i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.17588	−	1.17588i	1.17588	−	1.17588i	0.195090	−	0.980785i	$-0.437500\pi$
$359$	1.17588	−	1.17588i	1.17588	−	1.17588i	0.980785	−	0.195090i	$-0.0625000\pi$
$360$	−0.0523913	−	0.0980171i	−0.0523913	−	0.0980171i
$361$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$362$		0			0
$363$	0.738422	−	0.305864i	0.738422	−	0.305864i
$364$		0			0
$365$		0			0
$366$	−1.63099	−	0.871780i	−1.63099	−	0.871780i
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$		0			0
$369$		0			0
$370$	0.273678	−	0.512016i	0.273678	−	0.512016i
$371$		0			0
$372$		0			0
$373$	0.871028	−	0.360791i	0.871028	−	0.360791i	0.0980171	−	0.995185i	$-0.468750\pi$
$373$	0.871028	−	0.360791i	0.871028	−	0.360791i	0.773010	+	0.634393i	$0.218750\pi$
$374$		0			0
$375$	0.666656	+	0.666656i	0.666656	+	0.666656i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$379$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$380$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$381$	1.34663	+	0.557791i	1.34663	+	0.557791i
$382$	1.76820	−	0.536376i	1.76820	−	0.536376i
$383$	−1.91388			−1.91388			−0.956940	−	0.290285i	$-0.906250\pi$
$383$	−1.91388			−1.91388			−0.956940	+	0.290285i	$0.906250\pi$
$384$	0.0924099	+	0.938254i	0.0924099	+	0.938254i
$385$		0			0
$386$	−1.21415	+	0.368309i	−1.21415	+	0.368309i
$387$		0			0
$388$	−0.162997	+	0.108911i	−0.162997	+	0.108911i
$389$	0.292893	+	0.707107i	0.292893	+	0.707107i	1.00000			$0$
$389$	0.292893	+	0.707107i	0.292893	+	0.707107i	−0.707107	+	0.707107i	$0.750000\pi$
$390$	−1.86747	−	0.183930i	−1.86747	−	0.183930i
$391$		0			0
$392$	−0.773010	−	0.634393i	−0.773010	−	0.634393i
$393$	−0.510236	−	0.510236i	−0.510236	−	0.510236i
$394$		0			0
$395$		0			0
$396$	−0.0425316	+	0.00846006i	−0.0425316	+	0.00846006i
$397$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$397$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$398$	−0.871028	+	1.62958i	−0.871028	+	1.62958i
$399$		0			0
$400$	0.382683	+	0.923880i	0.382683	+	0.923880i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$	1.28547	+	0.687098i	1.28547	+	0.687098i
$403$		0			0
$404$	0.324423	+	0.216773i	0.324423	+	0.216773i
$405$	0.809787	−	0.335425i	0.809787	−	0.335425i
$406$		0			0
$407$	−0.160179	−	0.160179i	−0.160179	−	0.160179i
$408$		0			0
$409$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$409$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$410$		0			0
$411$		0			0
$412$	−0.373380	+	1.87711i	−0.373380	+	1.87711i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−1.75535	−	0.938254i	−1.75535	−	0.938254i
$417$	−1.56781			−1.56781
$418$	0.113263	+	0.373380i	0.113263	+	0.373380i
$419$	1.70711	+	0.707107i	1.70711	+	0.707107i	1.00000			$0$
$419$	1.70711	+	0.707107i	1.70711	+	0.707107i	0.707107	+	0.707107i	$0.250000\pi$
$420$		0			0
$421$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$421$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$422$		0			0
$423$		0			0
$424$	0.512016	−	1.68789i	0.512016	−	1.68789i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.704900	−	1.05496i	0.704900	−	1.05496i
$429$	−0.280192	+	0.676443i	−0.280192	+	0.676443i
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	1.04758			1.04758
$433$			0.942793i			0.942793i	0.881921	+	0.471397i	$0.156250\pi$
$433$			0.942793i			0.942793i	−0.881921	+	0.471397i	$0.843750\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$439$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$440$	0.388302	−	0.0382444i	0.388302	−	0.0382444i
$441$	−0.0785882	+	0.0785882i	−0.0785882	+	0.0785882i
$442$		0			0
$443$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$443$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$444$	0.304095	+	0.455111i	0.304095	+	0.455111i
$445$		0			0
$446$	0.187593	−	0.0569057i	0.187593	−	0.0569057i
$447$	1.56781			1.56781
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	0.106355	−	0.0322624i	0.106355	−	0.0322624i
$451$		0			0
$452$	0.979938	+	1.46658i	0.979938	+	1.46658i
$453$		0			0
$454$	0.195090	+	0.0192147i	0.195090	+	0.0192147i
$455$		0			0
$456$	−0.0924099	−	0.938254i	−0.0924099	−	0.938254i
$457$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$457$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$458$	1.05496	+	1.28547i	1.05496	+	1.28547i
$459$		0			0
$460$		0			0
$461$	0.707107	−	1.70711i	0.707107	−	1.70711i		−	1.00000i	$-0.5\pi$
$461$	0.707107	−	1.70711i	0.707107	−	1.70711i	0.707107	−	0.707107i	$-0.250000\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$467$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$468$	−0.122898	+	0.183930i	−0.122898	+	0.183930i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$476$		0			0
$477$	−0.181112	−	0.0750191i	−0.181112	−	0.0750191i
$478$	0.410525	+	1.35332i	0.410525	+	1.35332i
$479$	0.390181			0.390181			0.195090	−	0.980785i	$-0.437500\pi$
$479$	0.390181			0.390181			0.195090	+	0.980785i	$0.437500\pi$
$480$	−0.938254	−	0.0924099i	−0.938254	−	0.0924099i
$481$	−1.15555			−1.15555
$482$		0			0
$483$		0			0
$484$	−0.165390	+	0.831470i	−0.165390	+	0.831470i
$485$	−0.0750191	−	0.181112i	−0.0750191	−	0.181112i
$486$	0.0216824	−	0.220145i	0.0216824	−	0.220145i
$487$	−1.24723	+	1.24723i	−1.24723	+	1.24723i	−0.290285	+	0.956940i	$0.593750\pi$
$487$	−1.24723	+	1.24723i	−1.24723	+	1.24723i	−0.956940	+	0.290285i	$0.906250\pi$
$488$	1.72995	−	0.924678i	1.72995	−	0.924678i
$489$		0			0
$490$	0.773010	−	0.634393i	0.773010	−	0.634393i
$491$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$491$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$492$		0			0
$493$		0			0
$494$	1.75535	+	0.938254i	1.75535	+	0.938254i
$495$		−	0.0433649i		−	0.0433649i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.425215	−	1.02656i	0.425215	−	1.02656i	−0.555570	−	0.831470i	$-0.687500\pi$
$499$	0.425215	−	1.02656i	0.425215	−	1.02656i	0.980785	−	0.195090i	$-0.0625000\pi$
$500$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$501$	1.10515	−	0.457767i	1.10515	−	0.457767i
$502$	−0.897168	−	1.09320i	−0.897168	−	1.09320i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$		0			0
$505$	−0.275899	+	0.275899i	−0.275899	+	0.275899i
$506$		0			0
$507$	1.06851	+	2.57961i	1.06851	+	2.57961i
$508$	−1.28547	+	0.858923i	−1.28547	+	0.858923i
$509$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$509$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$510$		0			0
$511$		0			0
$512$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$513$	−1.04758			−1.04758
$514$	1.21415	−	0.368309i	1.21415	−	0.368309i
$515$	−1.76820	−	0.732410i	−1.76820	−	0.732410i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.03066	−	1.03066i	1.03066	−	1.03066i
$520$	1.26268	−	1.53858i	1.26268	−	1.53858i
$521$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$521$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$522$		0			0
$523$	−1.76820	+	0.732410i	−1.76820	+	0.732410i	−0.773010	+	0.634393i	$0.781250\pi$
$523$	−1.76820	+	0.732410i	−1.76820	+	0.732410i	−0.995185	+	0.0980171i	$0.968750\pi$
$524$	0.750661	−	0.149316i	0.750661	−	0.149316i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.140774	+	0.339858i	−0.140774	+	0.339858i
$529$			1.00000i			1.00000i
$530$	1.55557	+	0.831470i	1.55557	+	0.831470i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.897168	+	0.897168i	0.897168	+	0.897168i
$536$	−1.36347	+	0.728789i	−1.36347	+	0.728789i
$537$		0			0
$538$		0			0
$539$	−0.149316	−	0.360480i	−0.149316	−	0.360480i
$540$	−0.204372	+	1.02745i	−0.204372	+	1.02745i
$541$	1.02656	+	0.425215i	1.02656	+	0.425215i	0.831470	−	0.555570i	$-0.187500\pi$
$541$	1.02656	+	0.425215i	1.02656	+	0.425215i	0.195090	+	0.980785i	$0.437500\pi$
$542$	0.482726	+	1.59133i	0.482726	+	1.59133i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.536376	−	0.222174i	−0.536376	−	0.222174i	0.0980171	−	0.995185i	$-0.468750\pi$
$547$	−0.536376	−	0.222174i	−0.536376	−	0.222174i	−0.634393	+	0.773010i	$0.718750\pi$
$548$		0			0
$549$	−0.0834288	−	0.201415i	−0.0834288	−	0.201415i
$550$	−0.0382444	+	0.388302i	−0.0382444	+	0.388302i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.505692	+	0.209464i	−0.505692	+	0.209464i
$556$	0.923880	−	1.38268i	0.923880	−	1.38268i
$557$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$557$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.222174	+	0.536376i	−0.222174	+	0.536376i	−0.995185	−	0.0980171i	$-0.968750\pi$
$563$	−0.222174	+	0.536376i	−0.222174	+	0.536376i	0.773010	+	0.634393i	$0.218750\pi$
$564$		0			0
$565$	−1.62958	+	0.674993i	−1.62958	+	0.674993i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$569$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$570$	0.938254	+	0.0924099i	0.938254	+	0.0924099i
$571$	−0.425215	−	1.02656i	−0.425215	−	1.02656i	−0.980785	−	0.195090i	$-0.937500\pi$
$571$	−0.425215	−	1.02656i	−0.425215	−	1.02656i	0.555570	−	0.831470i	$-0.312500\pi$
$572$	−0.431458	−	0.645722i	−0.431458	−	0.645722i
$573$	−1.60945	−	0.666656i	−1.60945	−	0.666656i
$574$		0			0
$575$		0			0
$576$	−0.0617463	+	0.0924099i	−0.0617463	+	0.0924099i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$579$	1.10515	+	0.457767i	1.10515	+	0.457767i
$580$		0			0
$581$		0			0
$582$	0.183930	+	0.0181155i	0.183930	+	0.0181155i
$583$	0.486643	−	0.486643i	0.486643	−	0.486643i
$584$		0			0
$585$	−0.156420	−	0.156420i	−0.156420	−	0.156420i
$586$	1.21415	+	1.47945i	1.21415	+	1.47945i
$587$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$587$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$588$	0.183930	+	0.924678i	0.183930	+	0.924678i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.580569			−0.580569
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	0.360480	+	0.192681i	0.360480	+	0.192681i
$595$		0			0
$596$	−0.923880	+	1.38268i	−0.923880	+	1.38268i
$597$	1.60945	−	0.666656i	1.60945	−	0.666656i
$598$		0			0
$599$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$599$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$600$	0.273678	−	0.902197i	0.273678	−	0.902197i
$601$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$601$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$602$		0			0
$603$	0.0657548	+	0.158746i	0.0657548	+	0.158746i
$604$		0			0
$605$	−0.783227	−	0.324423i	−0.783227	−	0.324423i
$606$	−0.106784	−	0.352020i	−0.106784	−	0.352020i
$607$	1.76384			1.76384			0.881921	−	0.471397i	$-0.156250\pi$
$607$	1.76384			1.76384			0.881921	+	0.471397i	$0.156250\pi$
$608$	0.881921	+	0.471397i	0.881921	+	0.471397i
$609$		0			0
$610$	0.569414	+	1.87711i	0.569414	+	1.87711i
$611$		0			0
$612$		0			0
$613$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$613$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$614$	−0.0192147	+	0.195090i	−0.0192147	+	0.195090i
$615$		0			0
$616$		0			0
$617$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$617$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$618$	1.39482	−	1.14470i	1.39482	−	1.14470i
$619$	1.81225	−	0.750661i	1.81225	−	0.750661i	0.831470	−	0.555570i	$-0.187500\pi$
$619$	1.81225	−	0.750661i	1.81225	−	0.750661i	0.980785	−	0.195090i	$-0.0625000\pi$
$620$		0			0
$621$		0			0
$622$	−1.72995	−	0.924678i	−1.72995	−	0.924678i
$623$		0			0
$624$	0.718108	+	1.73367i	0.718108	+	1.73367i
$625$		−	1.00000i		−	1.00000i
$626$		0			0
$627$	0.140774	−	0.339858i	0.140774	−	0.339858i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.785695	−	0.785695i	−0.785695	−	0.785695i	0.195090	−	0.980785i	$-0.437500\pi$
$631$	−0.785695	−	0.785695i	−0.785695	−	0.785695i	−0.980785	+	0.195090i	$0.937500\pi$
$632$		0			0
$633$		0			0
$634$	−1.26268	−	0.124363i	−1.26268	−	0.124363i
$635$	−0.591637	−	1.42834i	−0.591637	−	1.42834i
$636$	−1.38268	+	0.923880i	−1.38268	+	0.923880i
$637$	−1.83886	−	0.761681i	−1.83886	−	0.761681i
$638$		0			0
$639$		0			0
$640$	0.634393	−	0.773010i	0.634393	−	0.773010i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	−1.14470	+	0.347240i	−1.14470	+	0.347240i
$643$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$643$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	−0.677549	−	0.556050i	−0.677549	−	0.556050i
$649$		0			0
$650$	1.26268	+	1.53858i	1.26268	+	1.53858i
$651$		0			0
$652$		0			0
$653$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$653$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$654$		0			0
$655$			0.765367i			0.765367i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$659$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$660$	−0.305864	−	0.204372i	−0.305864	−	0.204372i
$661$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$661$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.00632453	+	0.0642140i	−0.00632453	+	0.0642140i
$667$		0			0
$668$	−0.247528	+	1.24441i	−0.247528	+	1.24441i
$669$	−0.170751	−	0.0707275i	−0.170751	−	0.0707275i
$670$	−0.448786	−	1.47945i	−0.448786	−	1.47945i
$671$	0.765367			0.765367
$672$		0			0
$673$	−0.580569			−0.580569			−0.290285	−	0.956940i	$-0.593750\pi$
$673$	−0.580569			−0.580569			−0.290285	+	0.956940i	$0.593750\pi$
$674$	−0.168530	−	0.555570i	−0.168530	−	0.555570i
$675$	−0.967834	−	0.400890i	−0.967834	−	0.400890i
$676$	−2.90466	−	0.577774i	−2.90466	−	0.577774i
$677$	0.222174	+	0.536376i	0.222174	+	0.536376i	0.995185	−	0.0980171i	$-0.0312500\pi$
$677$	0.222174	+	0.536376i	0.222174	+	0.536376i	−0.773010	+	0.634393i	$0.781250\pi$
$678$	0.162997	−	1.65493i	0.162997	−	1.65493i
$679$		0			0
$680$		0			0
$681$	−0.130687	−	0.130687i	−0.130687	−	0.130687i
$682$		0			0
$683$	−0.536376	+	0.222174i	−0.536376	+	0.222174i	−0.634393	−	0.773010i	$-0.718750\pi$
$683$	−0.536376	+	0.222174i	−0.536376	+	0.222174i	0.0980171	+	0.995185i	$0.468750\pi$
$684$	0.0617463	−	0.0924099i	0.0617463	−	0.0924099i
$685$		0			0
$686$		0			0
$687$		−	1.56781i		−	1.56781i
$688$		0			0
$689$		−	3.51070i		−	3.51070i
$690$		0			0
$691$	0.750661	−	1.81225i	0.750661	−	1.81225i	0.195090	−	0.980785i	$-0.437500\pi$
$691$	0.750661	−	1.81225i	0.750661	−	1.81225i	0.555570	−	0.831470i	$-0.312500\pi$
$692$	0.301614	+	1.51631i	0.301614	+	1.51631i
$693$		0			0
$694$		0			0
$695$	1.17588	+	1.17588i	1.17588	+	1.17588i
$696$		0			0
$697$		0			0
$698$	−1.40740	−	0.138617i	−1.40740	−	0.138617i
$699$		0			0
$700$		0			0
$701$	−1.02656	−	0.425215i	−1.02656	−	0.425215i	−0.195090	−	0.980785i	$-0.562500\pi$
$701$	−1.02656	−	0.425215i	−1.02656	−	0.425215i	−0.831470	+	0.555570i	$0.812500\pi$
$702$	1.99528	−	0.605262i	1.99528	−	0.605262i
$703$	0.580569			0.580569
$704$	−0.216773	−	0.324423i	−0.216773	−	0.324423i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.541196	+	1.30656i	0.541196	+	1.30656i	0.923880	+	0.382683i	$0.125000\pi$
$709$	0.541196	+	1.30656i	0.541196	+	1.30656i	−0.382683	+	0.923880i	$0.625000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	0.717488	−	0.297193i	0.717488	−	0.297193i
$716$		0			0
$717$	0.510236	−	1.23182i	0.510236	−	1.23182i
$718$	0.783904	−	1.46658i	0.783904	−	1.46658i
$719$			1.11114i			1.11114i	0.831470	+	0.555570i	$0.187500\pi$
$719$			1.11114i			1.11114i	−0.831470	+	0.555570i	$0.812500\pi$
$720$	−0.0785882	−	0.0785882i	−0.0785882	−	0.0785882i
$721$		0			0
$722$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.617838	−	0.507046i	0.617838	−	0.507046i
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$		0			0
$729$	−0.767256	+	0.767256i	−0.767256	+	0.767256i
$730$		0			0
$731$		0			0
$732$	−1.81382	−	0.360791i	−1.81382	−	0.360791i
$733$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$733$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$734$		0			0
$735$	−0.942793			−0.942793
$736$		0			0
$737$	−0.603227			−0.603227
$738$		0			0
$739$	−1.30656	−	0.541196i	−1.30656	−	0.541196i	−0.382683	−	0.923880i	$-0.625000\pi$
$739$	−1.30656	−	0.541196i	−1.30656	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$740$	0.113263	−	0.569414i	0.113263	−	0.569414i
$741$	−0.718108	−	1.73367i	−0.718108	−	1.73367i
$742$		0			0
$743$	1.40740	−	1.40740i	1.40740	−	1.40740i	0.634393	−	0.773010i	$-0.281250\pi$
$743$	1.40740	−	1.40740i	1.40740	−	1.40740i	0.773010	−	0.634393i	$-0.218750\pi$
$744$		0			0
$745$	−1.17588	−	1.17588i	−1.17588	−	1.17588i
$746$	0.728789	−	0.598102i	0.728789	−	0.598102i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.831470	+	0.444430i	0.831470	+	0.444430i
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$			1.33331i			1.33331i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$757$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$758$		0			0
$759$		0			0
$760$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$761$	1.38704	−	1.38704i	1.38704	−	1.38704i	0.555570	−	0.831470i	$-0.312500\pi$
$761$	1.38704	−	1.38704i	1.38704	−	1.38704i	0.831470	−	0.555570i	$-0.187500\pi$
$762$	1.45056	+	0.142868i	1.45056	+	0.142868i
$763$		0			0
$764$	1.53636	−	1.02656i	1.53636	−	1.02656i
$765$		0			0
$766$	−1.83147	+	0.555570i	−1.83147	+	0.555570i
$767$		0			0
$768$	0.360791	+	0.871028i	0.360791	+	0.871028i
$769$	−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
$771$	−1.10515	−	0.457767i	−1.10515	−	0.457767i
$772$	−1.05496	+	0.704900i	−1.05496	+	0.704900i
$773$	−0.0750191	−	0.181112i	−0.0750191	−	0.181112i	0.881921	−	0.471397i	$-0.156250\pi$
$773$	−0.0750191	−	0.181112i	−0.0750191	−	0.181112i	−0.956940	+	0.290285i	$0.906250\pi$
$774$		0			0
$775$		0			0
$776$	−0.124363	+	0.151537i	−0.124363	+	0.151537i
$777$		0			0
$778$	0.485544	+	0.591637i	0.485544	+	0.591637i
$779$		0			0
$780$	−1.84045	+	0.366088i	−1.84045	+	0.366088i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$785$		0			0
$786$	−0.636379	−	0.340152i	−0.636379	−	0.340152i
$787$	−0.732410	+	1.76820i	−0.732410	+	1.76820i	−0.0980171	+	0.995185i	$0.531250\pi$
$787$	−0.732410	+	1.76820i	−0.732410	+	1.76820i	−0.634393	+	0.773010i	$0.718750\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.0382444	+	0.0204421i	−0.0382444	+	0.0204421i
$793$	2.76072	−	2.76072i	2.76072	−	2.76072i
$794$		0			0
$795$	−0.636379	−	1.53636i	−0.636379	−	1.53636i
$796$	−0.360480	+	1.81225i	−0.360480	+	1.81225i
$797$	1.76820	+	0.732410i	1.76820	+	0.732410i	0.995185	+	0.0980171i	$0.0312500\pi$
$797$	1.76820	+	0.732410i	1.76820	+	0.732410i	0.773010	+	0.634393i	$0.218750\pi$
$798$		0			0
$799$		0			0
$800$	0.634393	+	0.773010i	0.634393	+	0.773010i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	1.42957	+	0.284359i	1.42957	+	0.284359i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.373380	+	0.113263i	0.373380	+	0.113263i
$809$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	0.382683	−	0.923880i	$-0.375000\pi$
$809$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$810$	0.677549	−	0.556050i	0.677549	−	0.556050i
$811$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$811$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$812$		0			0
$813$	0.599974	−	1.44847i	0.599974	−	1.44847i
$814$	−0.199779	−	0.106784i	−0.199779	−	0.106784i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.707107	+	0.292893i	−0.707107	+	0.292893i	−0.707107	−	0.707107i	$-0.750000\pi$
$821$	−0.707107	+	0.292893i	−0.707107	+	0.292893i			1.00000i	$0.5\pi$
$822$		0			0
$823$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$823$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$824$	0.187593	+	1.90466i	0.187593	+	1.90466i
$825$	0.260116	−	0.260116i	0.260116	−	0.260116i
$826$		0			0
$827$	−0.732410	−	1.76820i	−0.732410	−	1.76820i	−0.634393	−	0.773010i	$-0.718750\pi$
$827$	−0.732410	−	1.76820i	−0.732410	−	1.76820i	−0.0980171	−	0.995185i	$-0.531250\pi$
$828$		0			0
$829$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$829$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$830$		0			0
$831$		0			0
$832$	−1.95213	−	0.388302i	−1.95213	−	0.388302i
$833$		0			0
$834$	−1.50030	+	0.455111i	−1.50030	+	0.455111i
$835$	−1.17221	−	0.485544i	−1.17221	−	0.485544i
$836$	0.216773	+	0.324423i	0.216773	+	0.324423i
$837$		0			0
$838$	1.83886	+	0.181112i	1.83886	+	0.181112i
$839$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$839$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$840$		0			0
$841$	0.707107	+	0.707107i	0.707107	+	0.707107i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.13334	−	2.73613i	1.13334	−	2.73613i
$846$		0			0
$847$		0			0
$848$		−	1.76384i		−	1.76384i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$853$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$854$		0			0
$855$	0.0785882	+	0.0785882i	0.0785882	+	0.0785882i
$856$	0.368309	−	1.21415i	0.368309	−	1.21415i
$857$	0.897168	−	0.897168i	0.897168	−	0.897168i	−0.0980171	−	0.995185i	$-0.531250\pi$
$857$	0.897168	−	0.897168i	0.897168	−	0.897168i	0.995185	+	0.0980171i	$0.0312500\pi$
$858$	−0.0717659	+	0.728651i	−0.0717659	+	0.728651i
$859$	−0.292893	−	0.707107i	−0.292893	−	0.707107i	0.707107	−	0.707107i	$-0.250000\pi$
$859$	−0.292893	−	0.707107i	−0.292893	−	0.707107i	−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.54602			1.54602			0.773010	−	0.634393i	$-0.218750\pi$
$863$	1.54602			1.54602			0.773010	+	0.634393i	$0.218750\pi$
$864$	1.00247	−	0.304095i	1.00247	−	0.304095i
$865$	−1.54602			−1.54602
$866$	0.273678	+	0.902197i	0.273678	+	0.902197i
$867$	0.871028	+	0.360791i	0.871028	+	0.360791i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−2.17588	+	2.17588i	−2.17588	+	2.17588i
$872$		0			0
$873$	0.0154060	+	0.0154060i	0.0154060	+	0.0154060i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.360791	−	0.871028i	0.360791	−	0.871028i	−0.634393	−	0.773010i	$-0.718750\pi$
$877$	0.360791	−	0.871028i	0.360791	−	0.871028i	0.995185	−	0.0980171i	$-0.0312500\pi$
$878$		0			0
$879$		−	1.80439i		−	1.80439i
$880$	0.360480	−	0.149316i	0.360480	−	0.149316i
$881$			1.66294i			1.66294i	0.555570	+	0.831470i	$0.312500\pi$
$881$			1.66294i			1.66294i	−0.555570	+	0.831470i	$0.687500\pi$
$882$	−0.0523913	+	0.0980171i	−0.0523913	+	0.0980171i
$883$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$883$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.24723	+	1.24723i	1.24723	+	1.24723i	0.956940	+	0.290285i	$0.0937500\pi$
$887$	1.24723	+	1.24723i	1.24723	+	1.24723i	0.290285	+	0.956940i	$0.406250\pi$
$888$	0.423113	+	0.347240i	0.423113	+	0.347240i
$889$		0			0
$890$		0			0
$891$	−0.130876	−	0.315963i	−0.130876	−	0.315963i
$892$	0.162997	−	0.108911i	0.162997	−	0.108911i
$893$		0			0
$894$	1.50030	−	0.455111i	1.50030	−	0.455111i
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.0924099	−	0.0617463i	0.0924099	−	0.0617463i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	1.36347	+	1.11897i	1.36347	+	1.11897i
$905$		0			0
$906$		0			0
$907$	1.83886	−	0.761681i	1.83886	−	0.761681i	0.881921	−	0.471397i	$-0.156250\pi$
$907$	1.83886	−	0.761681i	1.83886	−	0.761681i	0.956940	−	0.290285i	$-0.0937500\pi$
$908$	0.192268	−	0.0382444i	0.192268	−	0.0382444i
$909$	0.0165950	−	0.0400639i	0.0165950	−	0.0400639i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−0.360791	−	0.871028i	−0.360791	−	0.871028i
$913$		0			0
$914$		0			0
$915$	0.707718	−	1.70858i	0.707718	−	1.70858i
$916$	1.38268	+	0.923880i	1.38268	+	0.923880i
$917$		0			0
$918$		0			0
$919$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$919$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$920$		0			0
$921$	0.130687	−	0.130687i	0.130687	−	0.130687i
$922$	0.181112	−	1.83886i	0.181112	−	1.83886i
$923$		0			0
$924$		0			0
$925$	0.536376	+	0.222174i	0.536376	+	0.222174i
$926$		0			0
$927$	0.212710			0.212710
$928$		0			0
$929$	1.84776			1.84776			0.923880	−	0.382683i	$-0.125000\pi$
$929$	1.84776			1.84776			0.923880	+	0.382683i	$0.125000\pi$
$930$		0			0
$931$	0.923880	+	0.382683i	0.923880	+	0.382683i
$932$		0			0
$933$	0.707718	+	1.70858i	0.707718	+	1.70858i
$934$		0			0
$935$		0			0
$936$	−0.0642140	+	0.211685i	−0.0642140	+	0.211685i
$937$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$937$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$941$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$947$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$948$		0			0
$949$		0			0
$950$	−0.634393	−	0.773010i	−0.634393	−	0.773010i
$951$	0.845844	+	0.845844i	0.845844	+	0.845844i
$952$		0			0
$953$	−0.138617	+	0.138617i	−0.138617	+	0.138617i	−0.773010	−	0.634393i	$-0.781250\pi$
$953$	−0.138617	+	0.138617i	−0.138617	+	0.138617i	0.634393	+	0.773010i	$0.281250\pi$
$954$	−0.195090	−	0.0192147i	−0.195090	−	0.0192147i
$955$	0.707107	+	1.70711i	0.707107	+	1.70711i
$956$	0.785695	+	1.17588i	0.785695	+	1.17588i
$957$		0			0
$958$	0.373380	−	0.113263i	0.373380	−	0.113263i
$959$		0			0
$960$	−0.924678	+	0.183930i	−0.924678	+	0.183930i
$961$	1.00000			1.00000
$962$	−1.10579	+	0.335438i	−1.10579	+	0.335438i
$963$	−0.130280	−	0.0539635i	−0.130280	−	0.0539635i
$964$		0			0
$965$	−0.485544	−	1.17221i	−0.485544	−	1.17221i
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	0.0830949	+	0.843677i	0.0830949	+	0.843677i
$969$		0			0
$970$	−0.124363	−	0.151537i	−0.124363	−	0.151537i
$971$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$971$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$972$	−0.0431560	−	0.216960i	−0.0431560	−	0.216960i
$973$		0			0
$974$	−0.831470	+	1.55557i	−0.831470	+	1.55557i
$975$		−	1.87651i		−	1.87651i
$976$	1.38704	−	1.38704i	1.38704	−	1.38704i
$977$		−	1.91388i		−	1.91388i	−0.290285	−	0.956940i	$-0.593750\pi$
$977$		−	1.91388i		−	1.91388i	0.290285	−	0.956940i	$-0.406250\pi$
$978$		0			0
$979$		0			0
$980$	0.555570	−	0.831470i	0.555570	−	0.831470i
$981$		0			0
$982$		0			0
$983$	−1.35332	−	1.35332i	−1.35332	−	1.35332i	−0.881921	−	0.471397i	$-0.843750\pi$
$983$	−1.35332	−	1.35332i	−1.35332	−	1.35332i	−0.471397	−	0.881921i	$-0.656250\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	1.95213	+	0.388302i	1.95213	+	0.388302i
$989$		0			0
$990$	−0.0125882	−	0.0414976i	−0.0125882	−	0.0414976i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.70711	−	0.707107i	−1.70711	−	0.707107i
$996$		0			0
$997$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$997$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$998$	0.108911	−	1.10579i	0.108911	−	1.10579i
$999$	0.430056	−	0.430056i	0.430056	−	0.430056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3040.1.cn.a.189.8	yes	32
5.4	even	2	inner	3040.1.cn.a.189.1	✓	32
19.18	odd	2	inner	3040.1.cn.a.189.1	✓	32
32.21	even	8	inner	3040.1.cn.a.949.8	yes	32
95.94	odd	2	CM	3040.1.cn.a.189.8	yes	32
160.149	even	8	inner	3040.1.cn.a.949.1	yes	32
608.341	odd	8	inner	3040.1.cn.a.949.1	yes	32
3040.949	odd	8	inner	3040.1.cn.a.949.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3040.1.cn.a.189.1	✓	32	5.4	even	2	inner
3040.1.cn.a.189.1	✓	32	19.18	odd	2	inner
3040.1.cn.a.189.8	yes	32	1.1	even	1	trivial
3040.1.cn.a.189.8	yes	32	95.94	odd	2	CM
3040.1.cn.a.949.1	yes	32	160.149	even	8	inner
3040.1.cn.a.949.1	yes	32	608.341	odd	8	inner
3040.1.cn.a.949.8	yes	32	32.21	even	8	inner
3040.1.cn.a.949.8	yes	32	3040.949	odd	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3040.cn (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.956940 - 0.290285i) q^{2} +(-0.871028 - 0.360791i) q^{3} +(0.831470 - 0.555570i) q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.938254 - 0.0924099i) q^{6} +(0.634393 - 0.773010i) q^{8} +(-0.0785882 - 0.0785882i) q^{9} +(0.634393 + 0.773010i) q^{10} +(0.360480 - 0.149316i) q^{11} +(-0.924678 + 0.183930i) q^{12} +(0.761681 - 1.83886i) q^{13} -0.942793i q^{15} +(0.382683 - 0.923880i) q^{16} +(-0.0980171 - 0.0523913i) q^{18} +(-0.382683 + 0.923880i) q^{19} +(0.831470 + 0.555570i) q^{20} +(0.301614 - 0.247528i) q^{22} +(-0.831470 + 0.444430i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(0.195090 - 1.98079i) q^{26} +(0.400890 + 0.967834i) q^{27} +(-0.273678 - 0.902197i) q^{30} +(0.0980171 - 0.995185i) q^{32} -0.367860 q^{33} +(-0.109005 - 0.0216824i) q^{36} +(-0.222174 - 0.536376i) q^{37} +(-0.0980171 + 0.995185i) q^{38} +(-1.32689 + 1.32689i) q^{39} +(0.956940 + 0.290285i) q^{40} +(0.216773 - 0.324423i) q^{44} +(0.0425316 - 0.102680i) q^{45} +(-0.666656 + 0.666656i) q^{48} -1.00000i q^{49} +(-0.471397 + 0.881921i) q^{50} +(-0.388302 - 1.95213i) q^{52} +(1.62958 - 0.674993i) q^{53} +(0.664575 + 0.809787i) q^{54} +(0.275899 + 0.275899i) q^{55} +(0.666656 - 0.666656i) q^{57} +(-0.523788 - 0.783904i) q^{60} +(1.81225 + 0.750661i) q^{61} +(-0.195090 - 0.980785i) q^{64} +1.99037 q^{65} +(-0.352020 + 0.106784i) q^{66} +(-1.42834 - 0.591637i) q^{67} +(-0.110605 + 0.0108937i) q^{72} +(-0.368309 - 0.448786i) q^{74} +(0.871028 - 0.360791i) q^{75} +(0.195090 + 0.980785i) q^{76} +(-0.884579 + 1.65493i) q^{78} +1.00000 q^{80} -0.876507i q^{81} +(0.113263 - 0.373380i) q^{88} +(0.0108937 - 0.110605i) q^{90} -1.00000 q^{95} +(-0.444430 + 0.831470i) q^{96} -0.196034 q^{97} +(-0.290285 - 0.956940i) q^{98} +(-0.0400639 - 0.0165950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{66} + 32 q^{80} - 32 q^{95} - 32 q^{96} - 32 q^{99}+O(q^{100}) \) 32 * q - 32 * q^66 + 32 * q^80 - 32 * q^95 - 32 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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