LMFDB - Embedded newform 3040.1.cn.a.1709.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3040,1,Mod(189,3040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3040, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

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

//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);

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

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

Self dual:	no
Analytic conductor:	$1.51715763840$
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			1709.8
Root			$0.290285 - 0.956940i$ of defining polynomial
Character	$\chi$	$=$	3040.1709
Dual form			3040.1.cn.a.2469.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.995185 + 0.0980171i) q^{2} +(-0.591637 + 1.42834i) q^{3} +(0.980785 + 0.195090i) q^{4} +(0.923880 - 0.382683i) q^{5} +(-0.728789 + 1.36347i) q^{6} +(0.956940 + 0.290285i) q^{8} +(-0.983006 - 0.983006i) q^{9} +(0.956940 - 0.290285i) q^{10} +(0.636379 + 1.53636i) q^{11} +(-0.858923 + 1.28547i) q^{12} +(-0.871028 - 0.360791i) q^{13} +1.54602i q^{15} +(0.923880 + 0.382683i) q^{16} +(-0.881921 - 1.07462i) q^{18} +(-0.923880 - 0.382683i) q^{19} +(0.980785 - 0.195090i) q^{20} +(0.482726 + 1.59133i) q^{22} +(-0.980785 + 1.19509i) q^{24} +(0.707107 - 0.707107i) q^{25} +(-0.831470 - 0.444430i) q^{26} +(0.557309 - 0.230845i) q^{27} +(-0.151537 + 1.53858i) q^{30} +(0.881921 + 0.471397i) q^{32} -2.57094 q^{33} +(-0.772343 - 1.15589i) q^{36} +(0.181112 - 0.0750191i) q^{37} +(-0.881921 - 0.471397i) q^{38} +(1.03066 - 1.03066i) q^{39} +(0.995185 - 0.0980171i) q^{40} +(0.324423 + 1.63099i) q^{44} +(-1.28436 - 0.531999i) q^{45} +(-1.09320 + 1.09320i) q^{48} -1.00000i q^{49} +(0.773010 - 0.634393i) q^{50} +(-0.783904 - 0.523788i) q^{52} +(0.485544 + 1.17221i) q^{53} +(0.577253 - 0.175108i) q^{54} +(1.17588 + 1.17588i) q^{55} +(1.09320 - 1.09320i) q^{57} +(-0.301614 + 1.51631i) q^{60} +(0.425215 - 1.02656i) q^{61} +(0.831470 + 0.555570i) q^{64} -0.942793 q^{65} +(-2.55856 - 0.251996i) q^{66} +(-0.222174 + 0.536376i) q^{67} +(-0.655327 - 1.22603i) q^{72} +(0.187593 - 0.0569057i) q^{74} +(0.591637 + 1.42834i) q^{75} +(-0.831470 - 0.555570i) q^{76} +(1.12672 - 0.924678i) q^{78} +1.00000 q^{80} -0.457578i q^{81} +(0.162997 + 1.65493i) q^{88} +(-1.22603 - 0.655327i) q^{90} -1.00000 q^{95} +(-1.19509 + 0.980785i) q^{96} -1.76384 q^{97} +(0.0980171 - 0.995185i) q^{98} +(0.884682 - 2.13581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3040\mathbb{Z}\right)^\times$.

$n$	$191$	$1217$	$1921$	$2661$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.995185	+	0.0980171i	0.995185	+	0.0980171i
$2$	0.995185	+	0.0980171i	0.995185	+	0.0980171i
$3$	−0.591637	+	1.42834i	−0.591637	+	1.42834i	0.290285	+	0.956940i	$0.406250\pi$
$3$	−0.591637	+	1.42834i	−0.591637	+	1.42834i	−0.881921	+	0.471397i	$0.843750\pi$
$4$	0.980785	+	0.195090i	0.980785	+	0.195090i
$5$	0.923880	−	0.382683i	0.923880	−	0.382683i
$5$	0.923880	−	0.382683i	0.923880	−	0.382683i
$6$	−0.728789	+	1.36347i	−0.728789	+	1.36347i
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	0.956940	+	0.290285i	0.956940	+	0.290285i
$9$	−0.983006	−	0.983006i	−0.983006	−	0.983006i
$10$	0.956940	−	0.290285i	0.956940	−	0.290285i
$11$	0.636379	+	1.53636i	0.636379	+	1.53636i	0.831470	+	0.555570i	$0.187500\pi$
$11$	0.636379	+	1.53636i	0.636379	+	1.53636i	−0.195090	+	0.980785i	$0.562500\pi$
$12$	−0.858923	+	1.28547i	−0.858923	+	1.28547i
$13$	−0.871028	−	0.360791i	−0.871028	−	0.360791i	−0.0980171	−	0.995185i	$-0.531250\pi$
$13$	−0.871028	−	0.360791i	−0.871028	−	0.360791i	−0.773010	+	0.634393i	$0.781250\pi$
$14$		0			0
$15$			1.54602i			1.54602i
$16$	0.923880	+	0.382683i	0.923880	+	0.382683i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−0.881921	−	1.07462i	−0.881921	−	1.07462i
$19$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$19$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$20$	0.980785	−	0.195090i	0.980785	−	0.195090i
$21$		0			0
$22$	0.482726	+	1.59133i	0.482726	+	1.59133i
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$	−0.980785	+	1.19509i	−0.980785	+	1.19509i
$25$	0.707107	−	0.707107i	0.707107	−	0.707107i
$26$	−0.831470	−	0.444430i	−0.831470	−	0.444430i
$27$	0.557309	−	0.230845i	0.557309	−	0.230845i
$28$		0			0
$29$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$29$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$30$	−0.151537	+	1.53858i	−0.151537	+	1.53858i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	0.881921	+	0.471397i	0.881921	+	0.471397i
$33$	−2.57094			−2.57094
$34$		0			0
$35$		0			0
$36$	−0.772343	−	1.15589i	−0.772343	−	1.15589i
$37$	0.181112	−	0.0750191i	0.181112	−	0.0750191i	−0.290285	−	0.956940i	$-0.593750\pi$
$37$	0.181112	−	0.0750191i	0.181112	−	0.0750191i	0.471397	+	0.881921i	$0.343750\pi$
$38$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$39$	1.03066	−	1.03066i	1.03066	−	1.03066i
$40$	0.995185	−	0.0980171i	0.995185	−	0.0980171i
$41$		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		−0.382683	−	0.923880i	$-0.625000\pi$
$43$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$44$	0.324423	+	1.63099i	0.324423	+	1.63099i
$45$	−1.28436	−	0.531999i	−1.28436	−	0.531999i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−1.09320	+	1.09320i	−1.09320	+	1.09320i
$49$		−	1.00000i		−	1.00000i
$50$	0.773010	−	0.634393i	0.773010	−	0.634393i
$51$		0			0
$52$	−0.783904	−	0.523788i	−0.783904	−	0.523788i
$53$	0.485544	+	1.17221i	0.485544	+	1.17221i	0.956940	+	0.290285i	$0.0937500\pi$
$53$	0.485544	+	1.17221i	0.485544	+	1.17221i	−0.471397	+	0.881921i	$0.656250\pi$
$54$	0.577253	−	0.175108i	0.577253	−	0.175108i
$55$	1.17588	+	1.17588i	1.17588	+	1.17588i
$56$		0			0
$57$	1.09320	−	1.09320i	1.09320	−	1.09320i
$58$		0			0
$59$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$59$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$60$	−0.301614	+	1.51631i	−0.301614	+	1.51631i
$61$	0.425215	−	1.02656i	0.425215	−	1.02656i	−0.555570	−	0.831470i	$-0.687500\pi$
$61$	0.425215	−	1.02656i	0.425215	−	1.02656i	0.980785	−	0.195090i	$-0.0625000\pi$
$62$		0			0
$63$		0			0
$64$	0.831470	+	0.555570i	0.831470	+	0.555570i
$65$	−0.942793			−0.942793
$66$	−2.55856	−	0.251996i	−2.55856	−	0.251996i
$67$	−0.222174	+	0.536376i	−0.222174	+	0.536376i	−0.995185	−	0.0980171i	$-0.968750\pi$
$67$	−0.222174	+	0.536376i	−0.222174	+	0.536376i	0.773010	+	0.634393i	$0.218750\pi$
$68$		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	$0.750000\pi$
$72$	−0.655327	−	1.22603i	−0.655327	−	1.22603i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$	0.187593	−	0.0569057i	0.187593	−	0.0569057i
$75$	0.591637	+	1.42834i	0.591637	+	1.42834i
$76$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$77$		0			0
$78$	1.12672	−	0.924678i	1.12672	−	0.924678i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	1.00000			1.00000
$81$		−	0.457578i		−	0.457578i
$82$		0			0
$83$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$83$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.162997	+	1.65493i	0.162997	+	1.65493i
$89$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$89$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$90$	−1.22603	−	0.655327i	−1.22603	−	0.655327i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.00000			−1.00000
$96$	−1.19509	+	0.980785i	−1.19509	+	0.980785i
$97$	−1.76384			−1.76384			−0.881921	−	0.471397i	$-0.843750\pi$
$97$	−1.76384			−1.76384			−0.881921	+	0.471397i	$0.843750\pi$
$98$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$99$	0.884682	−	2.13581i	0.884682	−	2.13581i
$100$	0.831470	−	0.555570i	0.831470	−	0.555570i
$101$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.980785	−	0.195090i	$-0.937500\pi$
$101$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.555570	+	0.831470i	$0.687500\pi$
$102$		0			0
$103$	1.40740	−	1.40740i	1.40740	−	1.40740i	0.634393	−	0.773010i	$-0.281250\pi$
$103$	1.40740	−	1.40740i	1.40740	−	1.40740i	0.773010	−	0.634393i	$-0.218750\pi$
$104$	−0.728789	−	0.598102i	−0.728789	−	0.598102i
$105$		0			0
$106$	0.368309	+	1.21415i	0.368309	+	1.21415i
$107$	−0.732410	−	1.76820i	−0.732410	−	1.76820i	−0.634393	−	0.773010i	$-0.718750\pi$
$107$	−0.732410	−	1.76820i	−0.732410	−	1.76820i	−0.0980171	−	0.995185i	$-0.531250\pi$
$108$	0.591637	−	0.117684i	0.591637	−	0.117684i
$109$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$109$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$110$	1.05496	+	1.28547i	1.05496	+	1.28547i
$111$			0.303073i			0.303073i
$112$		0			0
$113$		−	1.26879i		−	1.26879i	−0.773010	−	0.634393i	$-0.781250\pi$
$113$		−	1.26879i		−	1.26879i	0.773010	−	0.634393i	$-0.218750\pi$
$114$	1.19509	−	0.980785i	1.19509	−	0.980785i
$115$		0			0
$116$		0			0
$117$	0.501565	+	1.21089i	0.501565	+	1.21089i
$118$		0			0
$119$		0			0
$120$	−0.448786	+	1.47945i	−0.448786	+	1.47945i
$121$	−1.24830	+	1.24830i	−1.24830	+	1.24830i
$122$	0.523788	−	0.979938i	0.523788	−	0.979938i
$123$		0			0
$124$		0			0
$125$	0.382683	−	0.923880i	0.382683	−	0.923880i
$126$		0			0
$127$	0.580569			0.580569			0.290285	−	0.956940i	$-0.406250\pi$
$127$	0.580569			0.580569			0.290285	+	0.956940i	$0.406250\pi$
$128$	0.773010	+	0.634393i	0.773010	+	0.634393i
$129$		0			0
$130$	−0.938254	−	0.0924099i	−0.938254	−	0.0924099i
$131$	−0.707107	+	1.70711i	−0.707107	+	1.70711i			1.00000i	$0.5\pi$
$131$	−0.707107	+	1.70711i	−0.707107	+	1.70711i	−0.707107	+	0.707107i	$0.750000\pi$
$132$	−2.52154	−	0.501565i	−2.52154	−	0.501565i
$133$		0			0
$134$	−0.273678	+	0.512016i	−0.273678	+	0.512016i
$135$	0.426546	−	0.426546i	0.426546	−	0.426546i
$136$		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
$139$	−0.750661	−	1.81225i	−0.750661	−	1.81225i	−0.555570	−	0.831470i	$-0.687500\pi$
$139$	−0.750661	−	1.81225i	−0.750661	−	1.81225i	−0.195090	−	0.980785i	$-0.562500\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	1.56781i		−	1.56781i
$144$	−0.531999	−	1.28436i	−0.531999	−	1.28436i
$145$		0			0
$146$		0			0
$147$	1.42834	+	0.591637i	1.42834	+	0.591637i
$148$	0.192268	−	0.0382444i	0.192268	−	0.0382444i
$149$	0.750661	+	1.81225i	0.750661	+	1.81225i	0.555570	+	0.831470i	$0.312500\pi$
$149$	0.750661	+	1.81225i	0.750661	+	1.81225i	0.195090	+	0.980785i	$0.437500\pi$
$150$	0.448786	+	1.47945i	0.448786	+	1.47945i
$151$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$151$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$152$	−0.773010	−	0.634393i	−0.773010	−	0.634393i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	1.21193	−	0.809787i	1.21193	−	0.809787i
$157$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$157$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$158$		0			0
$159$	−1.96157			−1.96157
$160$	0.995185	+	0.0980171i	0.995185	+	0.0980171i
$161$		0			0
$162$	0.0448505	−	0.455375i	0.0448505	−	0.455375i
$163$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$163$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$164$		0			0
$165$	−2.37524	+	0.983856i	−2.37524	+	0.983856i
$166$		0			0
$167$	1.35332	−	1.35332i	1.35332	−	1.35332i	0.471397	−	0.881921i	$-0.343750\pi$
$167$	1.35332	−	1.35332i	1.35332	−	1.35332i	0.881921	−	0.471397i	$-0.156250\pi$
$168$		0			0
$169$	−0.0785882	−	0.0785882i	−0.0785882	−	0.0785882i
$170$		0			0
$171$	0.531999	+	1.28436i	0.531999	+	1.28436i
$172$		0			0
$173$	0.536376	+	0.222174i	0.536376	+	0.222174i	0.634393	−	0.773010i	$-0.281250\pi$
$173$	0.536376	+	0.222174i	0.536376	+	0.222174i	−0.0980171	+	0.995185i	$0.531250\pi$
$174$		0			0
$175$		0			0
$176$			1.66294i			1.66294i
$177$		0			0
$178$		0			0
$179$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$179$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$180$	−1.15589	−	0.772343i	−1.15589	−	0.772343i
$181$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$181$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$182$		0			0
$183$	1.21470	+	1.21470i	1.21470	+	1.21470i
$184$		0			0
$185$	0.138617	−	0.138617i	0.138617	−	0.138617i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$191$	−0.765367			−0.765367			−0.382683	−	0.923880i	$-0.625000\pi$
$191$	−0.765367			−0.765367			−0.382683	+	0.923880i	$0.625000\pi$
$192$	−1.28547	+	0.858923i	−1.28547	+	0.858923i
$193$	−1.91388			−1.91388			−0.956940	−	0.290285i	$-0.906250\pi$
$193$	−1.91388			−1.91388			−0.956940	+	0.290285i	$0.906250\pi$
$194$	−1.75535	−	0.172887i	−1.75535	−	0.172887i
$195$	0.557791	−	1.34663i	0.557791	−	1.34663i
$196$	0.195090	−	0.980785i	0.195090	−	0.980785i
$197$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$197$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$198$	1.08977	−	2.03881i	1.08977	−	2.03881i
$199$	−0.541196	+	0.541196i	−0.541196	+	0.541196i	−0.923880	−	0.382683i	$-0.875000\pi$
$199$	−0.541196	+	0.541196i	−0.541196	+	0.541196i	0.382683	+	0.923880i	$0.375000\pi$
$200$	0.881921	−	0.471397i	0.881921	−	0.471397i
$201$	−0.634680	−	0.634680i	−0.634680	−	0.634680i
$202$	−1.59133	+	0.482726i	−1.59133	+	0.482726i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	1.53858	−	1.26268i	1.53858	−	1.26268i
$207$		0			0
$208$	−0.666656	−	0.666656i	−0.666656	−	0.666656i
$209$		−	1.66294i		−	1.66294i
$210$		0			0
$211$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$211$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$212$	0.247528	+	1.24441i	0.247528	+	1.24441i
$213$		0			0
$214$	−0.555570	−	1.83147i	−0.555570	−	1.83147i
$215$		0			0
$216$	0.600323	−	0.0591266i	0.600323	−	0.0591266i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.923880	+	1.38268i	0.923880	+	1.38268i
$221$		0			0
$222$	−0.0297064	+	0.301614i	−0.0297064	+	0.301614i
$223$	1.76384			1.76384			0.881921	−	0.471397i	$-0.156250\pi$
$223$	1.76384			1.76384			0.881921	+	0.471397i	$0.156250\pi$
$224$		0			0
$225$	−1.39018			−1.39018
$226$	0.124363	−	1.26268i	0.124363	−	1.26268i
$227$	−0.674993	+	1.62958i	−0.674993	+	1.62958i	0.0980171	+	0.995185i	$0.468750\pi$
$227$	−0.674993	+	1.62958i	−0.674993	+	1.62958i	−0.773010	+	0.634393i	$0.781250\pi$
$228$	1.28547	−	0.858923i	1.28547	−	0.858923i
$229$	1.81225	−	0.750661i	1.81225	−	0.750661i	0.831470	−	0.555570i	$-0.187500\pi$
$229$	1.81225	−	0.750661i	1.81225	−	0.750661i	0.980785	−	0.195090i	$-0.0625000\pi$
$230$		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	$0.250000\pi$
$234$	0.380463	+	1.25422i	0.380463	+	1.25422i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$239$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$240$	−0.591637	+	1.42834i	−0.591637	+	1.42834i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−1.36465	+	1.11994i	−1.36465	+	1.11994i
$243$	1.21089	+	0.501565i	1.21089	+	0.501565i
$244$	0.617317	−	0.923880i	0.617317	−	0.923880i
$245$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$246$		0			0
$247$	0.666656	+	0.666656i	0.666656	+	0.666656i
$248$		0			0
$249$		0			0
$250$	0.471397	−	0.881921i	0.471397	−	0.881921i
$251$	1.30656	−	0.541196i	1.30656	−	0.541196i	0.382683	−	0.923880i	$-0.375000\pi$
$251$	1.30656	−	0.541196i	1.30656	−	0.541196i	0.923880	+	0.382683i	$0.125000\pi$
$252$		0			0
$253$		0			0
$254$	0.577774	+	0.0569057i	0.577774	+	0.0569057i
$255$		0			0
$256$	0.707107	+	0.707107i	0.707107	+	0.707107i
$257$	1.91388			1.91388			0.956940	−	0.290285i	$-0.0937500\pi$
$257$	1.91388			1.91388			0.956940	+	0.290285i	$0.0937500\pi$
$258$		0			0
$259$		0			0
$260$	−0.924678	−	0.183930i	−0.924678	−	0.183930i
$261$		0			0
$262$	−0.871028	+	1.62958i	−0.871028	+	1.62958i
$263$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$263$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$264$	−2.46024	−	0.746304i	−2.46024	−	0.746304i
$265$	0.897168	+	0.897168i	0.897168	+	0.897168i
$266$		0			0
$267$		0			0
$268$	−0.322547	+	0.482726i	−0.322547	+	0.482726i
$269$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$269$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$270$	0.466301	−	0.382683i	0.466301	−	0.382683i
$271$			1.96157i			1.96157i	0.195090	+	0.980785i	$0.437500\pi$
$271$			1.96157i			1.96157i	−0.195090	+	0.980785i	$0.562500\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.53636	+	0.636379i	1.53636	+	0.636379i
$276$		0			0
$277$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$277$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$278$	−0.569414	−	1.87711i	−0.569414	−	1.87711i
$279$		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		0.923880	−	0.382683i	$-0.125000\pi$
$283$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$284$		0			0
$285$	0.591637	−	1.42834i	0.591637	−	1.42834i
$286$	0.153672	−	1.56026i	0.153672	−	1.56026i
$287$		0			0
$288$	−0.403548	−	1.33032i	−0.403548	−	1.33032i
$289$	−1.00000			−1.00000
$290$		0			0
$291$	1.04355	−	2.51936i	1.04355	−	2.51936i
$292$		0			0
$293$	1.83886	−	0.761681i	1.83886	−	0.761681i	0.881921	−	0.471397i	$-0.156250\pi$
$293$	1.83886	−	0.761681i	1.83886	−	0.761681i	0.956940	−	0.290285i	$-0.0937500\pi$
$294$	1.36347	+	0.728789i	1.36347	+	0.728789i
$295$		0			0
$296$	0.195090	−	0.0192147i	0.195090	−	0.0192147i
$297$	0.709320	+	0.709320i	0.709320	+	0.709320i
$298$	0.569414	+	1.87711i	0.569414	+	1.87711i
$299$		0			0
$300$	0.301614	+	1.51631i	0.301614	+	1.51631i
$301$		0			0
$302$		0			0
$303$		−	2.57094i		−	2.57094i
$304$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$305$		−	1.11114i		−	1.11114i
$306$		0			0
$307$	−1.62958	−	0.674993i	−1.62958	−	0.674993i	−0.634393	−	0.773010i	$-0.718750\pi$
$307$	−1.62958	−	0.674993i	−1.62958	−	0.674993i	−0.995185	+	0.0980171i	$0.968750\pi$
$308$		0			0
$309$	1.17758	+	2.84292i	1.17758	+	2.84292i
$310$		0			0
$311$	−0.785695	−	0.785695i	−0.785695	−	0.785695i	0.195090	−	0.980785i	$-0.437500\pi$
$311$	−0.785695	−	0.785695i	−0.785695	−	0.785695i	−0.980785	+	0.195090i	$0.937500\pi$
$312$	1.28547	−	0.687098i	1.28547	−	0.687098i
$313$		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
$317$	0.732410	−	1.76820i	0.732410	−	1.76820i	0.0980171	−	0.995185i	$-0.468750\pi$
$317$	0.732410	−	1.76820i	0.732410	−	1.76820i	0.634393	−	0.773010i	$-0.281250\pi$
$318$	−1.95213	−	0.192268i	−1.95213	−	0.192268i
$319$		0			0
$320$	0.980785	+	0.195090i	0.980785	+	0.195090i
$321$	2.95890			2.95890
$322$		0			0
$323$		0			0
$324$	0.0892691	−	0.448786i	0.0892691	−	0.448786i
$325$	−0.871028	+	0.360791i	−0.871028	+	0.360791i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−2.46024	+	0.746304i	−2.46024	+	0.746304i
$331$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$331$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$332$		0			0
$333$	−0.251778	−	0.104290i	−0.251778	−	0.104290i
$334$	1.47945	−	1.21415i	1.47945	−	1.21415i
$335$			0.580569i			0.580569i
$336$		0			0
$337$			0.196034i			0.196034i	0.995185	+	0.0980171i	$0.0312500\pi$
$337$			0.196034i			0.196034i	−0.995185	+	0.0980171i	$0.968750\pi$
$338$	−0.0705068	−	0.0859127i	−0.0705068	−	0.0859127i
$339$	1.81225	+	0.750661i	1.81225	+	0.750661i
$340$		0			0
$341$		0			0
$342$	0.403548	+	1.33032i	0.403548	+	1.33032i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.512016	+	0.273678i	0.512016	+	0.273678i
$347$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$347$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$348$		0			0
$349$	−0.541196	+	1.30656i	−0.541196	+	1.30656i	0.382683	+	0.923880i	$0.375000\pi$
$349$	−0.541196	+	1.30656i	−0.541196	+	1.30656i	−0.923880	+	0.382683i	$0.875000\pi$
$350$		0			0
$351$	−0.568719			−0.568719
$352$	−0.162997	+	1.65493i	−0.162997	+	1.65493i
$353$		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
$359$	−1.38704	+	1.38704i	−1.38704	+	1.38704i	−0.555570	+	0.831470i	$0.687500\pi$
$359$	−1.38704	+	1.38704i	−1.38704	+	1.38704i	−0.831470	+	0.555570i	$0.812500\pi$
$360$	−1.07462	−	0.881921i	−1.07462	−	0.881921i
$361$	0.707107	+	0.707107i	0.707107	+	0.707107i
$362$		0			0
$363$	−1.04446	−	2.52154i	−1.04446	−	2.52154i
$364$		0			0
$365$		0			0
$366$	1.08979	+	1.32791i	1.08979	+	1.32791i
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$		0			0
$369$		0			0
$370$	0.151537	−	0.124363i	0.151537	−	0.124363i
$371$		0			0
$372$		0			0
$373$	0.591637	+	1.42834i	0.591637	+	1.42834i	0.881921	+	0.471397i	$0.156250\pi$
$373$	0.591637	+	1.42834i	0.591637	+	1.42834i	−0.290285	+	0.956940i	$0.593750\pi$
$374$		0			0
$375$	1.09320	+	1.09320i	1.09320	+	1.09320i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$379$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$380$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$381$	−0.343486	+	0.829249i	−0.343486	+	0.829249i
$382$	−0.761681	−	0.0750191i	−0.761681	−	0.0750191i
$383$	−1.99037			−1.99037			−0.995185	−	0.0980171i	$-0.968750\pi$
$383$	−1.99037			−1.99037			−0.995185	+	0.0980171i	$0.968750\pi$
$384$	−1.36347	+	0.728789i	−1.36347	+	0.728789i
$385$		0			0
$386$	−1.90466	−	0.187593i	−1.90466	−	0.187593i
$387$		0			0
$388$	−1.72995	−	0.344109i	−1.72995	−	0.344109i
$389$	1.70711	−	0.707107i	1.70711	−	0.707107i	0.707107	−	0.707107i	$-0.250000\pi$
$389$	1.70711	−	0.707107i	1.70711	−	0.707107i	1.00000			$0$
$390$	0.687098	−	1.28547i	0.687098	−	1.28547i
$391$		0			0
$392$	0.290285	−	0.956940i	0.290285	−	0.956940i
$393$	−2.01997	−	2.01997i	−2.01997	−	2.01997i
$394$		0			0
$395$		0			0
$396$	1.28436	−	1.92218i	1.28436	−	1.92218i
$397$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$397$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$398$	−0.591637	+	0.485544i	−0.591637	+	0.485544i
$399$		0			0
$400$	0.923880	−	0.382683i	0.923880	−	0.382683i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$	−0.569414	−	0.693833i	−0.569414	−	0.693833i
$403$		0			0
$404$	−1.63099	+	0.324423i	−1.63099	+	0.324423i
$405$	−0.175108	−	0.422747i	−0.175108	−	0.422747i
$406$		0			0
$407$	0.230512	+	0.230512i	0.230512	+	0.230512i
$408$		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
$412$	1.65493	−	1.10579i	1.65493	−	1.10579i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.598102	−	0.728789i	−0.598102	−	0.728789i
$417$	3.03263			3.03263
$418$	0.162997	−	1.65493i	0.162997	−	1.65493i
$419$	0.292893	−	0.707107i	0.292893	−	0.707107i	−0.707107	−	0.707107i	$-0.750000\pi$
$419$	0.292893	−	0.707107i	0.292893	−	0.707107i	1.00000			$0$
$420$		0			0
$421$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$421$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$422$		0			0
$423$		0			0
$424$	0.124363	+	1.26268i	0.124363	+	1.26268i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.373380	−	1.87711i	−0.373380	−	1.87711i
$429$	2.23936	+	0.927573i	2.23936	+	0.927573i
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	0.603227			0.603227
$433$		−	1.54602i		−	1.54602i	−0.634393	−	0.773010i	$-0.718750\pi$
$433$		−	1.54602i		−	1.54602i	0.634393	−	0.773010i	$-0.281250\pi$
$434$		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	$0.250000\pi$
$440$	0.783904	+	1.46658i	0.783904	+	1.46658i
$441$	−0.983006	+	0.983006i	−0.983006	+	0.983006i
$442$		0			0
$443$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$443$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$444$	−0.0591266	+	0.297250i	−0.0591266	+	0.297250i
$445$		0			0
$446$	1.75535	+	0.172887i	1.75535	+	0.172887i
$447$	−3.03263			−3.03263
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−1.38349	−	0.136262i	−1.38349	−	0.136262i
$451$		0			0
$452$	0.247528	−	1.24441i	0.247528	−	1.24441i
$453$		0			0
$454$	−0.831470	+	1.55557i	−0.831470	+	1.55557i
$455$		0			0
$456$	1.36347	−	0.728789i	1.36347	−	0.728789i
$457$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$457$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$458$	1.87711	−	0.569414i	1.87711	−	0.569414i
$459$		0			0
$460$		0			0
$461$	−0.707107	−	0.292893i	−0.707107	−	0.292893i		−	1.00000i	$-0.5\pi$
$461$	−0.707107	−	0.292893i	−0.707107	−	0.292893i	−0.707107	+	0.707107i	$0.750000\pi$
$462$		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		−0.923880	−	0.382683i	$-0.875000\pi$
$467$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$468$	0.255696	+	1.28547i	0.255696	+	1.28547i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$476$		0			0
$477$	0.674993	−	1.62958i	0.674993	−	1.62958i
$478$	0.138617	−	1.40740i	0.138617	−	1.40740i
$479$	−1.66294			−1.66294			−0.831470	−	0.555570i	$-0.812500\pi$
$479$	−1.66294			−1.66294			−0.831470	+	0.555570i	$0.812500\pi$
$480$	−0.728789	+	1.36347i	−0.728789	+	1.36347i
$481$	−0.184820			−0.184820
$482$		0			0
$483$		0			0
$484$	−1.46785	+	0.980785i	−1.46785	+	0.980785i
$485$	−1.62958	+	0.674993i	−1.62958	+	0.674993i
$486$	1.15589	+	0.617838i	1.15589	+	0.617838i
$487$	−0.897168	+	0.897168i	−0.897168	+	0.897168i	−0.995185	−	0.0980171i	$-0.968750\pi$
$487$	−0.897168	+	0.897168i	−0.897168	+	0.897168i	0.0980171	+	0.995185i	$0.468750\pi$
$488$	0.704900	−	0.858923i	0.704900	−	0.858923i
$489$		0			0
$490$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$491$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$491$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$492$		0			0
$493$		0			0
$494$	0.598102	+	0.728789i	0.598102	+	0.728789i
$495$		−	2.31179i		−	2.31179i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.360480	−	0.149316i	−0.360480	−	0.149316i	0.195090	−	0.980785i	$-0.437500\pi$
$499$	−0.360480	−	0.149316i	−0.360480	−	0.149316i	−0.555570	+	0.831470i	$0.687500\pi$
$500$	0.555570	−	0.831470i	0.555570	−	0.831470i
$501$	1.13232	+	2.73367i	1.13232	+	2.73367i
$502$	1.35332	−	0.410525i	1.35332	−	0.410525i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$		0			0
$505$	−1.17588	+	1.17588i	−1.17588	+	1.17588i
$506$		0			0
$507$	0.158746	−	0.0657548i	0.158746	−	0.0657548i
$508$	0.569414	+	0.113263i	0.569414	+	0.113263i
$509$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$509$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$510$		0			0
$511$		0			0
$512$	0.634393	+	0.773010i	0.634393	+	0.773010i
$513$	−0.603227			−0.603227
$514$	1.90466	+	0.187593i	1.90466	+	0.187593i
$515$	0.761681	−	1.83886i	0.761681	−	1.83886i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.634680	+	0.634680i	−0.634680	+	0.634680i
$520$	−0.902197	−	0.273678i	−0.902197	−	0.273678i
$521$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$521$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$522$		0			0
$523$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.471397	+	0.881921i	$0.343750\pi$
$523$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.290285	+	0.956940i	$0.406250\pi$
$524$	−1.02656	+	1.53636i	−1.02656	+	1.53636i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−2.37524	−	0.983856i	−2.37524	−	0.983856i
$529$			1.00000i			1.00000i
$530$	0.804910	+	0.980785i	0.804910	+	0.980785i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−1.35332	−	1.35332i	−1.35332	−	1.35332i
$536$	−0.368309	+	0.448786i	−0.368309	+	0.448786i
$537$		0			0
$538$		0			0
$539$	1.53636	−	0.636379i	1.53636	−	0.636379i
$540$	0.501565	−	0.335135i	0.501565	−	0.335135i
$541$	0.149316	−	0.360480i	0.149316	−	0.360480i	−0.831470	−	0.555570i	$-0.812500\pi$
$541$	0.149316	−	0.360480i	0.149316	−	0.360480i	0.980785	+	0.195090i	$0.0625000\pi$
$542$	−0.192268	+	1.95213i	−0.192268	+	1.95213i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.0750191	+	0.181112i	−0.0750191	+	0.181112i	−0.956940	−	0.290285i	$-0.906250\pi$
$547$	−0.0750191	+	0.181112i	−0.0750191	+	0.181112i	0.881921	+	0.471397i	$0.156250\pi$
$548$		0			0
$549$	−1.42710	+	0.591126i	−1.42710	+	0.591126i
$550$	1.46658	+	0.783904i	1.46658	+	0.783904i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.115981	+	0.280003i	0.115981	+	0.280003i
$556$	−0.382683	−	1.92388i	−0.382683	−	1.92388i
$557$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$557$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.181112	+	0.0750191i	0.181112	+	0.0750191i	0.471397	−	0.881921i	$-0.343750\pi$
$563$	0.181112	+	0.0750191i	0.181112	+	0.0750191i	−0.290285	+	0.956940i	$0.593750\pi$
$564$		0			0
$565$	−0.485544	−	1.17221i	−0.485544	−	1.17221i
$566$		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	$0.750000\pi$
$570$	0.728789	−	1.36347i	0.728789	−	1.36347i
$571$	0.360480	−	0.149316i	0.360480	−	0.149316i	−0.195090	−	0.980785i	$-0.562500\pi$
$571$	0.360480	−	0.149316i	0.360480	−	0.149316i	0.555570	+	0.831470i	$0.312500\pi$
$572$	0.305864	−	1.53768i	0.305864	−	1.53768i
$573$	0.452819	−	1.09320i	0.452819	−	1.09320i
$574$		0			0
$575$		0			0
$576$	−0.271211	−	1.36347i	−0.271211	−	1.36347i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$579$	1.13232	−	2.73367i	1.13232	−	2.73367i
$580$		0			0
$581$		0			0
$582$	1.28547	−	2.40494i	1.28547	−	2.40494i
$583$	−1.49194	+	1.49194i	−1.49194	+	1.49194i
$584$		0			0
$585$	0.926772	+	0.926772i	0.926772	+	0.926772i
$586$	1.90466	−	0.577774i	1.90466	−	0.577774i
$587$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$587$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$588$	1.28547	+	0.858923i	1.28547	+	0.858923i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.196034			0.196034
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	0.636379	+	0.775430i	0.636379	+	0.775430i
$595$		0			0
$596$	0.382683	+	1.92388i	0.382683	+	1.92388i
$597$	−0.452819	−	1.09320i	−0.452819	−	1.09320i
$598$		0			0
$599$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$599$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$600$	0.151537	+	1.53858i	0.151537	+	1.53858i
$601$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$601$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$602$		0			0
$603$	0.745660	−	0.308862i	0.745660	−	0.308862i
$604$		0			0
$605$	−0.675577	+	1.63099i	−0.675577	+	1.63099i
$606$	0.251996	−	2.55856i	0.251996	−	2.55856i
$607$	−1.26879			−1.26879			−0.634393	−	0.773010i	$-0.718750\pi$
$607$	−1.26879			−1.26879			−0.634393	+	0.773010i	$0.718750\pi$
$608$	−0.634393	−	0.773010i	−0.634393	−	0.773010i
$609$		0			0
$610$	0.108911	−	1.10579i	0.108911	−	1.10579i
$611$		0			0
$612$		0			0
$613$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$613$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$614$	−1.55557	−	0.831470i	−1.55557	−	0.831470i
$615$		0			0
$616$		0			0
$617$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$617$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$618$	0.893250	+	2.94465i	0.893250	+	2.94465i
$619$	0.425215	+	1.02656i	0.425215	+	1.02656i	0.980785	+	0.195090i	$0.0625000\pi$
$619$	0.425215	+	1.02656i	0.425215	+	1.02656i	−0.555570	+	0.831470i	$0.687500\pi$
$620$		0			0
$621$		0			0
$622$	−0.704900	−	0.858923i	−0.704900	−	0.858923i
$623$		0			0
$624$	1.34663	−	0.557791i	1.34663	−	0.557791i
$625$		−	1.00000i		−	1.00000i
$626$		0			0
$627$	2.37524	+	0.983856i	2.37524	+	0.983856i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.275899	−	0.275899i	−0.275899	−	0.275899i	0.555570	−	0.831470i	$-0.312500\pi$
$631$	−0.275899	−	0.275899i	−0.275899	−	0.275899i	−0.831470	+	0.555570i	$0.812500\pi$
$632$		0			0
$633$		0			0
$634$	0.902197	−	1.68789i	0.902197	−	1.68789i
$635$	0.536376	−	0.222174i	0.536376	−	0.222174i
$636$	−1.92388	−	0.382683i	−1.92388	−	0.382683i
$637$	−0.360791	+	0.871028i	−0.360791	+	0.871028i
$638$		0			0
$639$		0			0
$640$	0.956940	+	0.290285i	0.956940	+	0.290285i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	2.94465	+	0.290023i	2.94465	+	0.290023i
$643$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$643$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$644$		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	$0.750000\pi$
$648$	0.132828	−	0.437875i	0.132828	−	0.437875i
$649$		0			0
$650$	−0.902197	+	0.273678i	−0.902197	+	0.273678i
$651$		0			0
$652$		0			0
$653$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$653$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$654$		0			0
$655$			1.84776i			1.84776i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$659$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$660$	−2.52154	+	0.501565i	−2.52154	+	0.501565i
$661$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$661$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.240344	−	0.128466i	−0.240344	−	0.128466i
$667$		0			0
$668$	1.59133	−	1.06330i	1.59133	−	1.06330i
$669$	−1.04355	+	2.51936i	−1.04355	+	2.51936i
$670$	−0.0569057	+	0.577774i	−0.0569057	+	0.577774i
$671$	1.84776			1.84776
$672$		0			0
$673$	0.196034			0.196034			0.0980171	−	0.995185i	$-0.468750\pi$
$673$	0.196034			0.196034			0.0980171	+	0.995185i	$0.468750\pi$
$674$	−0.0192147	+	0.195090i	−0.0192147	+	0.195090i
$675$	0.230845	−	0.557309i	0.230845	−	0.557309i
$676$	−0.0617463	−	0.0924099i	−0.0617463	−	0.0924099i
$677$	−0.181112	+	0.0750191i	−0.181112	+	0.0750191i	−0.471397	−	0.881921i	$-0.656250\pi$
$677$	−0.181112	+	0.0750191i	−0.181112	+	0.0750191i	0.290285	+	0.956940i	$0.406250\pi$
$678$	1.72995	+	0.924678i	1.72995	+	0.924678i
$679$		0			0
$680$		0			0
$681$	−1.92824	−	1.92824i	−1.92824	−	1.92824i
$682$		0			0
$683$	−0.0750191	−	0.181112i	−0.0750191	−	0.181112i	0.881921	−	0.471397i	$-0.156250\pi$
$683$	−0.0750191	−	0.181112i	−0.0750191	−	0.181112i	−0.956940	+	0.290285i	$0.906250\pi$
$684$	0.271211	+	1.36347i	0.271211	+	1.36347i
$685$		0			0
$686$		0			0
$687$			3.03263i			3.03263i
$688$		0			0
$689$		−	1.19620i		−	1.19620i
$690$		0			0
$691$	−1.02656	−	0.425215i	−1.02656	−	0.425215i	−0.195090	−	0.980785i	$-0.562500\pi$
$691$	−1.02656	−	0.425215i	−1.02656	−	0.425215i	−0.831470	+	0.555570i	$0.812500\pi$
$692$	0.482726	+	0.322547i	0.482726	+	0.322547i
$693$		0			0
$694$		0			0
$695$	−1.38704	−	1.38704i	−1.38704	−	1.38704i
$696$		0			0
$697$		0			0
$698$	−0.666656	+	1.24723i	−0.666656	+	1.24723i
$699$		0			0
$700$		0			0
$701$	−0.149316	+	0.360480i	−0.149316	+	0.360480i	−0.980785	−	0.195090i	$-0.937500\pi$
$701$	−0.149316	+	0.360480i	−0.149316	+	0.360480i	0.831470	+	0.555570i	$0.187500\pi$
$702$	−0.565980	−	0.0557442i	−0.565980	−	0.0557442i
$703$	−0.196034			−0.196034
$704$	−0.324423	+	1.63099i	−0.324423	+	1.63099i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.30656	+	0.541196i	−1.30656	+	0.541196i	−0.923880	−	0.382683i	$-0.875000\pi$
$709$	−1.30656	+	0.541196i	−1.30656	+	0.541196i	−0.382683	+	0.923880i	$0.625000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−0.599974	−	1.44847i	−0.599974	−	1.44847i
$716$		0			0
$717$	2.01997	+	0.836700i	2.01997	+	0.836700i
$718$	−1.51631	+	1.24441i	−1.51631	+	1.24441i
$719$		−	0.390181i		−	0.390181i	−0.980785	−	0.195090i	$-0.937500\pi$
$719$		−	0.390181i		−	0.390181i	0.980785	−	0.195090i	$-0.0625000\pi$
$720$	−0.983006	−	0.983006i	−0.983006	−	0.983006i
$721$		0			0
$722$	0.634393	+	0.773010i	0.634393	+	0.773010i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−0.792272	−	2.61177i	−0.792272	−	2.61177i
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$		0			0
$729$	−1.10925	+	1.10925i	−1.10925	+	1.10925i
$730$		0			0
$731$		0			0
$732$	0.954384	+	1.42834i	0.954384	+	1.42834i
$733$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$733$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$734$		0			0
$735$	1.54602			1.54602
$736$		0			0
$737$	−0.965452			−0.965452
$738$		0			0
$739$	−0.541196	+	1.30656i	−0.541196	+	1.30656i	0.382683	+	0.923880i	$0.375000\pi$
$739$	−0.541196	+	1.30656i	−0.541196	+	1.30656i	−0.923880	+	0.382683i	$0.875000\pi$
$740$	0.162997	−	0.108911i	0.162997	−	0.108911i
$741$	−1.34663	+	0.557791i	−1.34663	+	0.557791i
$742$		0			0
$743$	0.666656	−	0.666656i	0.666656	−	0.666656i	−0.290285	−	0.956940i	$-0.593750\pi$
$743$	0.666656	−	0.666656i	0.666656	−	0.666656i	0.956940	+	0.290285i	$0.0937500\pi$
$744$		0			0
$745$	1.38704	+	1.38704i	1.38704	+	1.38704i
$746$	0.448786	+	1.47945i	0.448786	+	1.47945i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.980785	+	1.19509i	0.980785	+	1.19509i
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$			2.18640i			2.18640i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$757$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$758$		0			0
$759$		0			0
$760$	−0.956940	−	0.290285i	−0.956940	−	0.290285i
$761$	0.785695	−	0.785695i	0.785695	−	0.785695i	−0.195090	−	0.980785i	$-0.562500\pi$
$761$	0.785695	−	0.785695i	0.785695	−	0.785695i	0.980785	+	0.195090i	$0.0625000\pi$
$762$	−0.423113	+	0.791588i	−0.423113	+	0.791588i
$763$		0			0
$764$	−0.750661	−	0.149316i	−0.750661	−	0.149316i
$765$		0			0
$766$	−1.98079	−	0.195090i	−1.98079	−	0.195090i
$767$		0			0
$768$	−1.42834	+	0.591637i	−1.42834	+	0.591637i
$769$	−1.96157			−1.96157			−0.980785	−	0.195090i	$-0.937500\pi$
$769$	−1.96157			−1.96157			−0.980785	+	0.195090i	$0.937500\pi$
$770$		0			0
$771$	−1.13232	+	2.73367i	−1.13232	+	2.73367i
$772$	−1.87711	−	0.373380i	−1.87711	−	0.373380i
$773$	−1.62958	+	0.674993i	−1.62958	+	0.674993i	−0.995185	−	0.0980171i	$-0.968750\pi$
$773$	−1.62958	+	0.674993i	−1.62958	+	0.674993i	−0.634393	+	0.773010i	$0.718750\pi$
$774$		0			0
$775$		0			0
$776$	−1.68789	−	0.512016i	−1.68789	−	0.512016i
$777$		0			0
$778$	1.76820	−	0.536376i	1.76820	−	0.536376i
$779$		0			0
$780$	0.809787	−	1.21193i	0.809787	−	1.21193i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.382683	−	0.923880i	0.382683	−	0.923880i
$785$		0			0
$786$	−1.81225	−	2.20824i	−1.81225	−	2.20824i
$787$	−1.83886	−	0.761681i	−1.83886	−	0.761681i	−0.956940	−	0.290285i	$-0.906250\pi$
$787$	−1.83886	−	0.761681i	−1.83886	−	0.761681i	−0.881921	−	0.471397i	$-0.843750\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1.46658	−	1.78703i	1.46658	−	1.78703i
$793$	−0.740748	+	0.740748i	−0.740748	+	0.740748i
$794$		0			0
$795$	−1.81225	+	0.750661i	−1.81225	+	0.750661i
$796$	−0.636379	+	0.425215i	−0.636379	+	0.425215i
$797$	−0.761681	+	1.83886i	−0.761681	+	1.83886i	−0.290285	+	0.956940i	$0.593750\pi$
$797$	−0.761681	+	1.83886i	−0.761681	+	1.83886i	−0.471397	+	0.881921i	$0.656250\pi$
$798$		0			0
$799$		0			0
$800$	0.956940	−	0.290285i	0.956940	−	0.290285i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−0.498664	−	0.746304i	−0.498664	−	0.746304i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.65493	+	0.162997i	−1.65493	+	0.162997i
$809$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.923880	+	0.382683i	$0.125000\pi$
$809$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.382683	+	0.923880i	$0.375000\pi$
$810$	−0.132828	−	0.437875i	−0.132828	−	0.437875i
$811$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$811$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$812$		0			0
$813$	−2.80178	−	1.16054i	−2.80178	−	1.16054i
$814$	0.206808	+	0.251996i	0.206808	+	0.251996i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.707107	+	1.70711i	0.707107	+	1.70711i	0.707107	+	0.707107i	$0.250000\pi$
$821$	0.707107	+	1.70711i	0.707107	+	1.70711i			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	$0.250000\pi$
$824$	1.75535	−	0.938254i	1.75535	−	0.938254i
$825$	−1.81793	+	1.81793i	−1.81793	+	1.81793i
$826$		0			0
$827$	−1.83886	+	0.761681i	−1.83886	+	0.761681i	−0.881921	+	0.471397i	$0.843750\pi$
$827$	−1.83886	+	0.761681i	−1.83886	+	0.761681i	−0.956940	+	0.290285i	$0.906250\pi$
$828$		0			0
$829$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$829$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$830$		0			0
$831$		0			0
$832$	−0.523788	−	0.783904i	−0.523788	−	0.783904i
$833$		0			0
$834$	3.01803	+	0.297250i	3.01803	+	0.297250i
$835$	0.732410	−	1.76820i	0.732410	−	1.76820i
$836$	0.324423	−	1.63099i	0.324423	−	1.63099i
$837$		0			0
$838$	0.360791	−	0.674993i	0.360791	−	0.674993i
$839$		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
$845$	−0.102680	−	0.0425316i	−0.102680	−	0.0425316i
$846$		0			0
$847$		0			0
$848$			1.26879i			1.26879i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$853$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$854$		0			0
$855$	0.983006	+	0.983006i	0.983006	+	0.983006i
$856$	−0.187593	−	1.90466i	−0.187593	−	1.90466i
$857$	−1.35332	+	1.35332i	−1.35332	+	1.35332i	−0.471397	+	0.881921i	$0.656250\pi$
$857$	−1.35332	+	1.35332i	−1.35332	+	1.35332i	−0.881921	+	0.471397i	$0.843750\pi$
$858$	2.13766	+	1.14260i	2.13766	+	1.14260i
$859$	−1.70711	+	0.707107i	−1.70711	+	0.707107i	−0.707107	+	0.707107i	$0.750000\pi$
$859$	−1.70711	+	0.707107i	−1.70711	+	0.707107i	−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.580569			−0.580569			−0.290285	−	0.956940i	$-0.593750\pi$
$863$	−0.580569			−0.580569			−0.290285	+	0.956940i	$0.593750\pi$
$864$	0.600323	+	0.0591266i	0.600323	+	0.0591266i
$865$	0.580569			0.580569
$866$	0.151537	−	1.53858i	0.151537	−	1.53858i
$867$	0.591637	−	1.42834i	0.591637	−	1.42834i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	0.387040	−	0.387040i	0.387040	−	0.387040i
$872$		0			0
$873$	1.73387	+	1.73387i	1.73387	+	1.73387i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.42834	−	0.591637i	−1.42834	−	0.591637i	−0.471397	−	0.881921i	$-0.656250\pi$
$877$	−1.42834	−	0.591637i	−1.42834	−	0.591637i	−0.956940	+	0.290285i	$0.906250\pi$
$878$		0			0
$879$			3.07715i			3.07715i
$880$	0.636379	+	1.53636i	0.636379	+	1.53636i
$881$			1.96157i			1.96157i	0.195090	+	0.980785i	$0.437500\pi$
$881$			1.96157i			1.96157i	−0.195090	+	0.980785i	$0.562500\pi$
$882$	−1.07462	+	0.881921i	−1.07462	+	0.881921i
$883$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$883$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.897168	+	0.897168i	0.897168	+	0.897168i	0.995185	−	0.0980171i	$-0.0312500\pi$
$887$	0.897168	+	0.897168i	0.897168	+	0.897168i	−0.0980171	+	0.995185i	$0.531250\pi$
$888$	−0.0879775	+	0.290023i	−0.0879775	+	0.290023i
$889$		0			0
$890$		0			0
$891$	0.703003	−	0.291193i	0.703003	−	0.291193i
$892$	1.72995	+	0.344109i	1.72995	+	0.344109i
$893$		0			0
$894$	−3.01803	−	0.297250i	−3.01803	−	0.297250i
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−1.36347	−	0.271211i	−1.36347	−	0.271211i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.368309	−	1.21415i	0.368309	−	1.21415i
$905$		0			0
$906$		0			0
$907$	0.360791	+	0.871028i	0.360791	+	0.871028i	0.995185	+	0.0980171i	$0.0312500\pi$
$907$	0.360791	+	0.871028i	0.360791	+	0.871028i	−0.634393	+	0.773010i	$0.718750\pi$
$908$	−0.979938	+	1.46658i	−0.979938	+	1.46658i
$909$	2.13581	+	0.884682i	2.13581	+	0.884682i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	1.42834	−	0.591637i	1.42834	−	0.591637i
$913$		0			0
$914$		0			0
$915$	1.58708	+	0.657391i	1.58708	+	0.657391i
$916$	1.92388	−	0.382683i	1.92388	−	0.382683i
$917$		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
$921$	1.92824	−	1.92824i	1.92824	−	1.92824i
$922$	−0.674993	−	0.360791i	−0.674993	−	0.360791i
$923$		0			0
$924$		0			0
$925$	0.0750191	−	0.181112i	0.0750191	−	0.181112i
$926$		0			0
$927$	−2.76697			−2.76697
$928$		0			0
$929$	−0.765367			−0.765367			−0.382683	−	0.923880i	$-0.625000\pi$
$929$	−0.765367			−0.765367			−0.382683	+	0.923880i	$0.625000\pi$
$930$		0			0
$931$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$932$		0			0
$933$	1.58708	−	0.657391i	1.58708	−	0.657391i
$934$		0			0
$935$		0			0
$936$	0.128466	+	1.30434i	0.128466	+	1.30434i
$937$		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		−0.923880	−	0.382683i	$-0.875000\pi$
$941$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$947$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$948$		0			0
$949$		0			0
$950$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$951$	2.09226	+	2.09226i	2.09226	+	2.09226i
$952$		0			0
$953$	1.24723	−	1.24723i	1.24723	−	1.24723i	0.290285	−	0.956940i	$-0.406250\pi$
$953$	1.24723	−	1.24723i	1.24723	−	1.24723i	0.956940	−	0.290285i	$-0.0937500\pi$
$954$	0.831470	−	1.55557i	0.831470	−	1.55557i
$955$	−0.707107	+	0.292893i	−0.707107	+	0.292893i
$956$	0.275899	−	1.38704i	0.275899	−	1.38704i
$957$		0			0
$958$	−1.65493	−	0.162997i	−1.65493	−	0.162997i
$959$		0			0
$960$	−0.858923	+	1.28547i	−0.858923	+	1.28547i
$961$	1.00000			1.00000
$962$	−0.183930	−	0.0181155i	−0.183930	−	0.0181155i
$963$	−1.01818	+	2.45811i	−1.01818	+	2.45811i
$964$		0			0
$965$	−1.76820	+	0.732410i	−1.76820	+	0.732410i
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	−1.55691	+	0.832188i	−1.55691	+	0.832188i
$969$		0			0
$970$	−1.68789	+	0.512016i	−1.68789	+	0.512016i
$971$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$971$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$972$	1.08977	+	0.728160i	1.08977	+	0.728160i
$973$		0			0
$974$	−0.980785	+	0.804910i	−0.980785	+	0.804910i
$975$		−	1.45758i		−	1.45758i
$976$	0.785695	−	0.785695i	0.785695	−	0.785695i
$977$		−	1.99037i		−	1.99037i	−0.0980171	−	0.995185i	$-0.531250\pi$
$977$		−	1.99037i		−	1.99037i	0.0980171	−	0.995185i	$-0.468750\pi$
$978$		0			0
$979$		0			0
$980$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$981$		0			0
$982$		0			0
$983$	1.40740	+	1.40740i	1.40740	+	1.40740i	0.773010	+	0.634393i	$0.218750\pi$
$983$	1.40740	+	1.40740i	1.40740	+	1.40740i	0.634393	+	0.773010i	$0.281250\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.523788	+	0.783904i	0.523788	+	0.783904i
$989$		0			0
$990$	0.226595	−	2.30065i	0.226595	−	2.30065i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.292893	+	0.707107i	−0.292893	+	0.707107i
$996$		0			0
$997$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$997$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$998$	−0.344109	−	0.183930i	−0.344109	−	0.183930i
$999$	0.0836177	−	0.0836177i	0.0836177	−	0.0836177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3040.1.cn.a.1709.8	yes	32
5.4	even	2	inner	3040.1.cn.a.1709.1	✓	32
19.18	odd	2	inner	3040.1.cn.a.1709.1	✓	32
32.5	even	8	inner	3040.1.cn.a.2469.8	yes	32
95.94	odd	2	CM	3040.1.cn.a.1709.8	yes	32
160.69	even	8	inner	3040.1.cn.a.2469.1	yes	32
608.37	odd	8	inner	3040.1.cn.a.2469.1	yes	32
3040.2469	odd	8	inner	3040.1.cn.a.2469.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3040.1.cn.a.1709.1	✓	32	5.4	even	2	inner
3040.1.cn.a.1709.1	✓	32	19.18	odd	2	inner
3040.1.cn.a.1709.8	yes	32	1.1	even	1	trivial
3040.1.cn.a.1709.8	yes	32	95.94	odd	2	CM
3040.1.cn.a.2469.1	yes	32	160.69	even	8	inner
3040.1.cn.a.2469.1	yes	32	608.37	odd	8	inner
3040.1.cn.a.2469.8	yes	32	32.5	even	8	inner
3040.1.cn.a.2469.8	yes	32	3040.2469	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.995185 + 0.0980171i) q^{2} +(-0.591637 + 1.42834i) q^{3} +(0.980785 + 0.195090i) q^{4} +(0.923880 - 0.382683i) q^{5} +(-0.728789 + 1.36347i) q^{6} +(0.956940 + 0.290285i) q^{8} +(-0.983006 - 0.983006i) q^{9} +(0.956940 - 0.290285i) q^{10} +(0.636379 + 1.53636i) q^{11} +(-0.858923 + 1.28547i) q^{12} +(-0.871028 - 0.360791i) q^{13} +1.54602i q^{15} +(0.923880 + 0.382683i) q^{16} +(-0.881921 - 1.07462i) q^{18} +(-0.923880 - 0.382683i) q^{19} +(0.980785 - 0.195090i) q^{20} +(0.482726 + 1.59133i) q^{22} +(-0.980785 + 1.19509i) q^{24} +(0.707107 - 0.707107i) q^{25} +(-0.831470 - 0.444430i) q^{26} +(0.557309 - 0.230845i) q^{27} +(-0.151537 + 1.53858i) q^{30} +(0.881921 + 0.471397i) q^{32} -2.57094 q^{33} +(-0.772343 - 1.15589i) q^{36} +(0.181112 - 0.0750191i) q^{37} +(-0.881921 - 0.471397i) q^{38} +(1.03066 - 1.03066i) q^{39} +(0.995185 - 0.0980171i) q^{40} +(0.324423 + 1.63099i) q^{44} +(-1.28436 - 0.531999i) q^{45} +(-1.09320 + 1.09320i) q^{48} -1.00000i q^{49} +(0.773010 - 0.634393i) q^{50} +(-0.783904 - 0.523788i) q^{52} +(0.485544 + 1.17221i) q^{53} +(0.577253 - 0.175108i) q^{54} +(1.17588 + 1.17588i) q^{55} +(1.09320 - 1.09320i) q^{57} +(-0.301614 + 1.51631i) q^{60} +(0.425215 - 1.02656i) q^{61} +(0.831470 + 0.555570i) q^{64} -0.942793 q^{65} +(-2.55856 - 0.251996i) q^{66} +(-0.222174 + 0.536376i) q^{67} +(-0.655327 - 1.22603i) q^{72} +(0.187593 - 0.0569057i) q^{74} +(0.591637 + 1.42834i) q^{75} +(-0.831470 - 0.555570i) q^{76} +(1.12672 - 0.924678i) q^{78} +1.00000 q^{80} -0.457578i q^{81} +(0.162997 + 1.65493i) q^{88} +(-1.22603 - 0.655327i) q^{90} -1.00000 q^{95} +(-1.19509 + 0.980785i) q^{96} -1.76384 q^{97} +(0.0980171 - 0.995185i) q^{98} +(0.884682 - 2.13581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{66} + 32 q^{80} - 32 q^{95} - 32 q^{96} - 32 q^{99}+O(q^{100}) \) 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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