LMFDB - Embedded newform 2496.1.eh.a.77.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2496,1,Mod(77,2496)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2496, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 8, 8]))

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

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2496.77");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2496 = 2^{6} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2496.eh (of order $16$, degree $8$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
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			77.2
Root			$-0.0980171 + 0.995185i$ of defining polynomial
Character	$\chi$	$=$	2496.77
Dual form			2496.1.eh.a.389.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.471397 - 0.881921i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.555570 + 0.831470i) q^{4} +(-1.72995 + 0.344109i) q^{5} +(0.881921 + 0.471397i) q^{6} +(0.995185 + 0.0980171i) q^{8} +(0.382683 - 0.923880i) q^{9} +(1.11897 + 1.36347i) q^{10} +(-0.108911 + 0.162997i) q^{11} -1.00000i q^{12} +(0.980785 + 0.195090i) q^{13} +(1.24723 - 1.24723i) q^{15} +(-0.382683 - 0.923880i) q^{16} +(-0.995185 + 0.0980171i) q^{18} +(0.674993 - 1.62958i) q^{20} +(0.195090 + 0.0192147i) q^{22} +(-0.881921 + 0.471397i) q^{24} +(1.95044 - 0.807898i) q^{25} +(-0.290285 - 0.956940i) q^{26} +(0.195090 + 0.980785i) q^{27} +(-1.68789 - 0.512016i) q^{30} +(-0.634393 + 0.773010i) q^{32} -0.196034i q^{33} +(0.555570 + 0.831470i) q^{36} +(-0.923880 + 0.382683i) q^{39} +(-1.75535 + 0.172887i) q^{40} +(0.536376 + 0.222174i) q^{41} +(0.324423 + 0.216773i) q^{43} +(-0.0750191 - 0.181112i) q^{44} +(-0.344109 + 1.72995i) q^{45} +(-1.09320 - 1.09320i) q^{47} +(0.831470 + 0.555570i) q^{48} +(-0.707107 + 0.707107i) q^{49} +(-1.63193 - 1.33929i) q^{50} +(-0.707107 + 0.707107i) q^{52} +(0.773010 - 0.634393i) q^{54} +(0.132322 - 0.319453i) q^{55} +(-0.924678 + 0.183930i) q^{59} +(0.344109 + 1.72995i) q^{60} +(-1.53636 + 1.02656i) q^{61} +(0.980785 + 0.195090i) q^{64} -1.76384 q^{65} +(-0.172887 + 0.0924099i) q^{66} +(0.761681 + 1.83886i) q^{71} +(0.471397 - 0.881921i) q^{72} +(-1.17289 + 1.75535i) q^{75} +(0.773010 + 0.634393i) q^{78} +(-0.275899 + 0.275899i) q^{79} +(0.979938 + 1.46658i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(-0.0569057 - 0.577774i) q^{82} +(-0.373380 + 1.87711i) q^{83} +(0.0382444 - 0.388302i) q^{86} +(-0.124363 + 0.151537i) q^{88} +(1.42834 - 0.591637i) q^{89} +(1.68789 - 0.512016i) q^{90} +(-0.448786 + 1.47945i) q^{94} +(0.0980171 - 0.995185i) q^{96} +(0.956940 + 0.290285i) q^{98} +(0.108911 + 0.162997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{55} - 32 q^{75}+O(q^{100}) $ 32 * q - 32 * q^55 - 32 * q^75

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2496\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{15}{16}\right)$

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 $

$2$	−0.471397	−	0.881921i	−0.471397	−	0.881921i
$2$	−0.471397	−	0.881921i	−0.471397	−	0.881921i
$3$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$3$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$4$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$5$	−1.72995	+	0.344109i	−1.72995	+	0.344109i	−0.956940	−	0.290285i	$-0.906250\pi$
$5$	−1.72995	+	0.344109i	−1.72995	+	0.344109i	−0.773010	+	0.634393i	$0.781250\pi$
$6$	0.881921	+	0.471397i	0.881921	+	0.471397i
$7$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$7$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$8$	0.995185	+	0.0980171i	0.995185	+	0.0980171i
$9$	0.382683	−	0.923880i	0.382683	−	0.923880i
$10$	1.11897	+	1.36347i	1.11897	+	1.36347i
$11$	−0.108911	+	0.162997i	−0.108911	+	0.162997i	−0.881921	−	0.471397i	$-0.843750\pi$
$11$	−0.108911	+	0.162997i	−0.108911	+	0.162997i	0.773010	+	0.634393i	$0.218750\pi$
$12$		−	1.00000i		−	1.00000i
$13$	0.980785	+	0.195090i	0.980785	+	0.195090i
$13$	0.980785	+	0.195090i	0.980785	+	0.195090i
$14$		0			0
$15$	1.24723	−	1.24723i	1.24723	−	1.24723i
$16$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	−0.995185	+	0.0980171i	−0.995185	+	0.0980171i
$19$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$19$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$20$	0.674993	−	1.62958i	0.674993	−	1.62958i
$21$		0			0
$22$	0.195090	+	0.0192147i	0.195090	+	0.0192147i
$23$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$23$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$24$	−0.881921	+	0.471397i	−0.881921	+	0.471397i
$25$	1.95044	−	0.807898i	1.95044	−	0.807898i
$26$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$27$	0.195090	+	0.980785i	0.195090	+	0.980785i
$28$		0			0
$29$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$29$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$30$	−1.68789	−	0.512016i	−1.68789	−	0.512016i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$33$		−	0.196034i		−	0.196034i
$34$		0			0
$35$		0			0
$36$	0.555570	+	0.831470i	0.555570	+	0.831470i
$37$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$37$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$38$		0			0
$39$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$40$	−1.75535	+	0.172887i	−1.75535	+	0.172887i
$41$	0.536376	+	0.222174i	0.536376	+	0.222174i	0.634393	−	0.773010i	$-0.281250\pi$
$41$	0.536376	+	0.222174i	0.536376	+	0.222174i	−0.0980171	+	0.995185i	$0.531250\pi$
$42$		0			0
$43$	0.324423	+	0.216773i	0.324423	+	0.216773i	0.707107	−	0.707107i	$-0.250000\pi$
$43$	0.324423	+	0.216773i	0.324423	+	0.216773i	−0.382683	+	0.923880i	$0.625000\pi$
$44$	−0.0750191	−	0.181112i	−0.0750191	−	0.181112i
$45$	−0.344109	+	1.72995i	−0.344109	+	1.72995i
$46$		0			0
$47$	−1.09320	−	1.09320i	−1.09320	−	1.09320i	−0.995185	−	0.0980171i	$-0.968750\pi$
$47$	−1.09320	−	1.09320i	−1.09320	−	1.09320i	−0.0980171	−	0.995185i	$-0.531250\pi$
$48$	0.831470	+	0.555570i	0.831470	+	0.555570i
$49$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$50$	−1.63193	−	1.33929i	−1.63193	−	1.33929i
$51$		0			0
$52$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$53$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$53$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$54$	0.773010	−	0.634393i	0.773010	−	0.634393i
$55$	0.132322	−	0.319453i	0.132322	−	0.319453i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.924678	+	0.183930i	−0.924678	+	0.183930i	−0.634393	−	0.773010i	$-0.718750\pi$
$59$	−0.924678	+	0.183930i	−0.924678	+	0.183930i	−0.290285	+	0.956940i	$0.593750\pi$
$60$	0.344109	+	1.72995i	0.344109	+	1.72995i
$61$	−1.53636	+	1.02656i	−1.53636	+	1.02656i	−0.555570	+	0.831470i	$0.687500\pi$
$61$	−1.53636	+	1.02656i	−1.53636	+	1.02656i	−0.980785	+	0.195090i	$0.937500\pi$
$62$		0			0
$63$		0			0
$64$	0.980785	+	0.195090i	0.980785	+	0.195090i
$65$	−1.76384			−1.76384
$66$	−0.172887	+	0.0924099i	−0.172887	+	0.0924099i
$67$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$67$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.471397	+	0.881921i	$0.343750\pi$
$71$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.290285	+	0.956940i	$0.406250\pi$
$72$	0.471397	−	0.881921i	0.471397	−	0.881921i
$73$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$73$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$74$		0			0
$75$	−1.17289	+	1.75535i	−1.17289	+	1.75535i
$76$		0			0
$77$		0			0
$78$	0.773010	+	0.634393i	0.773010	+	0.634393i
$79$	−0.275899	+	0.275899i	−0.275899	+	0.275899i	−0.831470	−	0.555570i	$-0.812500\pi$
$79$	−0.275899	+	0.275899i	−0.275899	+	0.275899i	0.555570	+	0.831470i	$0.312500\pi$
$80$	0.979938	+	1.46658i	0.979938	+	1.46658i
$81$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$82$	−0.0569057	−	0.577774i	−0.0569057	−	0.577774i
$83$	−0.373380	+	1.87711i	−0.373380	+	1.87711i	0.0980171	+	0.995185i	$0.468750\pi$
$83$	−0.373380	+	1.87711i	−0.373380	+	1.87711i	−0.471397	+	0.881921i	$0.656250\pi$
$84$		0			0
$85$		0			0
$86$	0.0382444	−	0.388302i	0.0382444	−	0.388302i
$87$		0			0
$88$	−0.124363	+	0.151537i	−0.124363	+	0.151537i
$89$	1.42834	−	0.591637i	1.42834	−	0.591637i	0.471397	−	0.881921i	$-0.343750\pi$
$89$	1.42834	−	0.591637i	1.42834	−	0.591637i	0.956940	+	0.290285i	$0.0937500\pi$
$90$	1.68789	−	0.512016i	1.68789	−	0.512016i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−0.448786	+	1.47945i	−0.448786	+	1.47945i
$95$		0			0
$96$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	0.956940	+	0.290285i	0.956940	+	0.290285i
$99$	0.108911	+	0.162997i	0.108911	+	0.162997i
$100$	−0.411863	+	2.07058i	−0.411863	+	2.07058i
$101$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$101$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$102$		0			0
$103$	−1.30656	+	0.541196i	−1.30656	+	0.541196i	−0.923880	−	0.382683i	$-0.875000\pi$
$103$	−1.30656	+	0.541196i	−1.30656	+	0.541196i	−0.382683	+	0.923880i	$0.625000\pi$
$104$	0.956940	+	0.290285i	0.956940	+	0.290285i
$105$		0			0
$106$		0			0
$107$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$107$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$108$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$109$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$109$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$110$	−0.344109	+	0.0338917i	−0.344109	+	0.0338917i
$111$		0			0
$112$		0			0
$113$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$113$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.555570	−	0.831470i	0.555570	−	0.831470i
$118$	0.598102	+	0.728789i	0.598102	+	0.728789i
$119$		0			0
$120$	1.36347	−	1.11897i	1.36347	−	1.11897i
$121$	0.367977	+	0.888375i	0.367977	+	0.888375i
$122$	1.62958	+	0.871028i	1.62958	+	0.871028i
$123$	−0.569414	+	0.113263i	−0.569414	+	0.113263i
$124$		0			0
$125$	−1.62958	+	1.08885i	−1.62958	+	1.08885i
$126$		0			0
$127$	−1.96157			−1.96157			−0.980785	−	0.195090i	$-0.937500\pi$
$127$	−1.96157			−1.96157			−0.980785	+	0.195090i	$0.937500\pi$
$128$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$129$	−0.390181			−0.390181
$130$	0.831470	+	1.55557i	0.831470	+	1.55557i
$131$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$131$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$132$	0.162997	+	0.108911i	0.162997	+	0.108911i
$133$		0			0
$134$		0			0
$135$	−0.674993	−	1.62958i	−0.674993	−	1.62958i
$136$		0			0
$137$	0.485544	−	1.17221i	0.485544	−	1.17221i	−0.471397	−	0.881921i	$-0.656250\pi$
$137$	0.485544	−	1.17221i	0.485544	−	1.17221i	0.956940	−	0.290285i	$-0.0937500\pi$
$138$		0			0
$139$	−0.923880	+	1.38268i	−0.923880	+	1.38268i			1.00000i	$0.5\pi$
$139$	−0.923880	+	1.38268i	−0.923880	+	1.38268i	−0.923880	+	0.382683i	$0.875000\pi$
$140$		0			0
$141$	1.51631	+	0.301614i	1.51631	+	0.301614i
$142$	1.26268	−	1.53858i	1.26268	−	1.53858i
$143$	−0.138617	+	0.138617i	−0.138617	+	0.138617i
$144$	−1.00000			−1.00000
$145$		0			0
$146$		0			0
$147$	0.195090	−	0.980785i	0.195090	−	0.980785i
$148$		0			0
$149$	1.05496	+	0.704900i	1.05496	+	0.704900i	0.956940	−	0.290285i	$-0.0937500\pi$
$149$	1.05496	+	0.704900i	1.05496	+	0.704900i	0.0980171	+	0.995185i	$0.468750\pi$
$150$	2.10097	+	0.206928i	2.10097	+	0.206928i
$151$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$151$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	0.195090	−	0.980785i	0.195090	−	0.980785i
$157$	−1.08979	−	1.63099i	−1.08979	−	1.63099i	−0.707107	−	0.707107i	$-0.750000\pi$
$157$	−1.08979	−	1.63099i	−1.08979	−	1.63099i	−0.382683	−	0.923880i	$-0.625000\pi$
$158$	0.373380	+	0.113263i	0.373380	+	0.113263i
$159$		0			0
$160$	0.831470	−	1.55557i	0.831470	−	1.55557i
$161$		0			0
$162$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$163$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$163$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$164$	−0.482726	+	0.322547i	−0.482726	+	0.322547i
$165$	0.0674571	+	0.339130i	0.0674571	+	0.339130i
$166$	1.83147	−	0.555570i	1.83147	−	0.555570i
$167$	−1.76820	+	0.732410i	−1.76820	+	0.732410i	−0.773010	+	0.634393i	$0.781250\pi$
$167$	−1.76820	+	0.732410i	−1.76820	+	0.732410i	−0.995185	+	0.0980171i	$0.968750\pi$
$168$		0			0
$169$	0.923880	+	0.382683i	0.923880	+	0.382683i
$170$		0			0
$171$		0			0
$172$	−0.360480	+	0.149316i	−0.360480	+	0.149316i
$173$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$173$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$174$		0			0
$175$		0			0
$176$	0.192268	+	0.0382444i	0.192268	+	0.0382444i
$177$	0.666656	−	0.666656i	0.666656	−	0.666656i
$178$	−1.19509	−	0.980785i	−1.19509	−	0.980785i
$179$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$179$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$180$	−1.24723	−	1.24723i	−1.24723	−	1.24723i
$181$	0.923880	−	1.38268i	0.923880	−	1.38268i		−	1.00000i	$-0.5\pi$
$181$	0.923880	−	1.38268i	0.923880	−	1.38268i	0.923880	−	0.382683i	$-0.125000\pi$
$182$		0			0
$183$	0.707107	−	1.70711i	0.707107	−	1.70711i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.51631	−	0.301614i	1.51631	−	0.301614i
$189$		0			0
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$	1.46658	−	0.979938i	1.46658	−	0.979938i
$196$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$197$	−1.95213	+	0.388302i	−1.95213	+	0.388302i	−0.956940	+	0.290285i	$0.906250\pi$
$197$	−1.95213	+	0.388302i	−1.95213	+	0.388302i	−0.995185	+	0.0980171i	$0.968750\pi$
$198$	0.0924099	−	0.172887i	0.0924099	−	0.172887i
$199$	0.636379	+	1.53636i	0.636379	+	1.53636i	0.831470	+	0.555570i	$0.187500\pi$
$199$	0.636379	+	1.53636i	0.636379	+	1.53636i	−0.195090	+	0.980785i	$0.562500\pi$
$200$	2.02024	−	0.612832i	2.02024	−	0.612832i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1.00436	−	0.199779i	−1.00436	−	0.199779i
$206$	1.09320	+	0.897168i	1.09320	+	0.897168i
$207$		0			0
$208$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$209$		0			0
$210$		0			0
$211$	0.360480	−	1.81225i	0.360480	−	1.81225i	−0.195090	−	0.980785i	$-0.562500\pi$
$211$	0.360480	−	1.81225i	0.360480	−	1.81225i	0.555570	−	0.831470i	$-0.312500\pi$
$212$		0			0
$213$	−1.65493	−	1.10579i	−1.65493	−	1.10579i
$214$		0			0
$215$	−0.635830	−	0.263369i	−0.635830	−	0.263369i
$216$	0.0980171	+	0.995185i	0.0980171	+	0.995185i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.192102	+	0.287500i	0.192102	+	0.287500i
$221$		0			0
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$		−	2.11114i		−	2.11114i
$226$		0			0
$227$	0.704900	+	1.05496i	0.704900	+	1.05496i	0.995185	+	0.0980171i	$0.0312500\pi$
$227$	0.704900	+	1.05496i	0.704900	+	1.05496i	−0.290285	+	0.956940i	$0.593750\pi$
$228$		0			0
$229$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$229$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$233$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$234$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$235$	2.26737	+	1.51501i	2.26737	+	1.51501i
$236$	0.360791	−	0.871028i	0.360791	−	0.871028i
$237$	0.0761205	−	0.382683i	0.0761205	−	0.382683i
$238$		0			0
$239$	−0.410525	−	0.410525i	−0.410525	−	0.410525i	0.471397	−	0.881921i	$-0.343750\pi$
$239$	−0.410525	−	0.410525i	−0.410525	−	0.410525i	−0.881921	+	0.471397i	$0.843750\pi$
$240$	−1.62958	−	0.674993i	−1.62958	−	0.674993i
$241$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$241$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$242$	0.610014	−	0.743304i	0.610014	−	0.743304i
$243$	0.980785	+	0.195090i	0.980785	+	0.195090i
$244$		−	1.84776i		−	1.84776i
$245$	0.979938	−	1.46658i	0.979938	−	1.46658i
$246$	0.368309	+	0.448786i	0.368309	+	0.448786i
$247$		0			0
$248$		0			0
$249$	−0.732410	−	1.76820i	−0.732410	−	1.76820i
$250$	1.72846	+	0.923880i	1.72846	+	0.923880i
$251$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$251$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$252$		0			0
$253$		0			0
$254$	0.924678	+	1.72995i	0.924678	+	1.72995i
$255$		0			0
$256$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$	0.183930	+	0.344109i	0.183930	+	0.344109i
$259$		0			0
$260$	0.979938	−	1.46658i	0.979938	−	1.46658i
$261$		0			0
$262$		0			0
$263$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$263$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$264$	0.0192147	−	0.195090i	0.0192147	−	0.195090i
$265$		0			0
$266$		0			0
$267$	−0.858923	+	1.28547i	−0.858923	+	1.28547i
$268$		0			0
$269$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$269$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$270$	−1.11897	+	1.36347i	−1.11897	+	1.36347i
$271$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$271$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$272$		0			0
$273$		0			0
$274$	−1.26268	+	0.124363i	−1.26268	+	0.124363i
$275$	−0.0807393	+	0.405904i	−0.0807393	+	0.405904i
$276$		0			0
$277$	1.38268	+	0.923880i	1.38268	+	0.923880i	1.00000			$0$
$277$	1.38268	+	0.923880i	1.38268	+	0.923880i	0.382683	+	0.923880i	$0.375000\pi$
$278$	1.65493	+	0.162997i	1.65493	+	0.162997i
$279$		0			0
$280$		0			0
$281$	0.871028	−	0.360791i	0.871028	−	0.360791i	0.0980171	−	0.995185i	$-0.468750\pi$
$281$	0.871028	−	0.360791i	0.871028	−	0.360791i	0.773010	+	0.634393i	$0.218750\pi$
$282$	−0.448786	−	1.47945i	−0.448786	−	1.47945i
$283$	−0.149316	−	0.750661i	−0.149316	−	0.750661i	−0.980785	−	0.195090i	$-0.937500\pi$
$283$	−0.149316	−	0.750661i	−0.149316	−	0.750661i	0.831470	−	0.555570i	$-0.187500\pi$
$284$	−1.95213	−	0.388302i	−1.95213	−	0.388302i
$285$		0			0
$286$	0.187593	+	0.0569057i	0.187593	+	0.0569057i
$287$		0			0
$288$	0.471397	+	0.881921i	0.471397	+	0.881921i
$289$			1.00000i			1.00000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.247528	+	1.24441i	0.247528	+	1.24441i	0.881921	+	0.471397i	$0.156250\pi$
$293$	0.247528	+	1.24441i	0.247528	+	1.24441i	−0.634393	+	0.773010i	$0.718750\pi$
$294$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$295$	1.53636	−	0.636379i	1.53636	−	0.636379i
$296$		0			0
$297$	−0.181112	−	0.0750191i	−0.181112	−	0.0750191i
$298$	0.124363	−	1.26268i	0.124363	−	1.26268i
$299$		0			0
$300$	−0.807898	−	1.95044i	−0.807898	−	1.95044i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.30457	−	2.30457i	2.30457	−	2.30457i
$306$		0			0
$307$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$307$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$308$		0			0
$309$	0.785695	−	1.17588i	0.785695	−	1.17588i
$310$		0			0
$311$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$311$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$312$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$313$	0.149316	+	0.360480i	0.149316	+	0.360480i	0.980785	−	0.195090i	$-0.0625000\pi$
$313$	0.149316	+	0.360480i	0.149316	+	0.360480i	−0.831470	+	0.555570i	$0.812500\pi$
$314$	−0.924678	+	1.72995i	−0.924678	+	1.72995i
$315$		0			0
$316$	−0.0761205	−	0.382683i	−0.0761205	−	0.382683i
$317$	−1.28547	+	0.858923i	−1.28547	+	0.858923i	−0.995185	−	0.0980171i	$-0.968750\pi$
$317$	−1.28547	+	0.858923i	−1.28547	+	0.858923i	−0.290285	+	0.956940i	$0.593750\pi$
$318$		0			0
$319$		0			0
$320$	−1.76384			−1.76384
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.980785	−	0.195090i	0.980785	−	0.195090i
$325$	2.07058	−	0.411863i	2.07058	−	0.411863i
$326$		0			0
$327$		0			0
$328$	0.512016	+	0.273678i	0.512016	+	0.273678i
$329$		0			0
$330$	0.267287	−	0.219356i	0.267287	−	0.219356i
$331$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$331$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$332$	−1.35332	−	1.35332i	−1.35332	−	1.35332i
$333$		0			0
$334$	1.47945	+	1.21415i	1.47945	+	1.21415i
$335$		0			0
$336$		0			0
$337$	−1.38704	−	1.38704i	−1.38704	−	1.38704i	−0.831470	−	0.555570i	$-0.812500\pi$
$337$	−1.38704	−	1.38704i	−1.38704	−	1.38704i	−0.555570	−	0.831470i	$-0.687500\pi$
$338$	−0.0980171	−	0.995185i	−0.0980171	−	0.995185i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	0.301614	+	0.247528i	0.301614	+	0.247528i
$345$		0			0
$346$		0			0
$347$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$347$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$348$		0			0
$349$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$349$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$350$		0			0
$351$			1.00000i			1.00000i
$352$	−0.0569057	−	0.187593i	−0.0569057	−	0.187593i
$353$			1.91388i			1.91388i	0.290285	+	0.956940i	$0.406250\pi$
$353$			1.91388i			1.91388i	−0.290285	+	0.956940i	$0.593750\pi$
$354$	−0.902197	−	0.273678i	−0.902197	−	0.273678i
$355$	−1.95044	−	2.91904i	−1.95044	−	2.91904i
$356$	−0.301614	+	1.51631i	−0.301614	+	1.51631i
$357$		0			0
$358$		0			0
$359$	1.17221	−	0.485544i	1.17221	−	0.485544i	0.290285	−	0.956940i	$-0.406250\pi$
$359$	1.17221	−	0.485544i	1.17221	−	0.485544i	0.881921	+	0.471397i	$0.156250\pi$
$360$	−0.512016	+	1.68789i	−0.512016	+	1.68789i
$361$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$362$	−1.65493	−	0.162997i	−1.65493	−	0.162997i
$363$	−0.799517	−	0.534220i	−0.799517	−	0.534220i
$364$		0			0
$365$		0			0
$366$	−1.83886	+	0.181112i	−1.83886	+	0.181112i
$367$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.923880	+	0.382683i	$0.125000\pi$
$367$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.382683	+	0.923880i	$0.375000\pi$
$368$		0			0
$369$	0.410525	−	0.410525i	0.410525	−	0.410525i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−0.425215	+	0.636379i	−0.425215	+	0.636379i	−0.980785	−	0.195090i	$-0.937500\pi$
$373$	−0.425215	+	0.636379i	−0.425215	+	0.636379i	0.555570	+	0.831470i	$0.312500\pi$
$374$		0			0
$375$	0.750012	−	1.81069i	0.750012	−	1.81069i
$376$	−0.980785	−	1.19509i	−0.980785	−	1.19509i
$377$		0			0
$378$		0			0
$379$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$379$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$380$		0			0
$381$	1.63099	−	1.08979i	1.63099	−	1.08979i
$382$		0			0
$383$	−1.91388			−1.91388			−0.956940	−	0.290285i	$-0.906250\pi$
$383$	−1.91388			−1.91388			−0.956940	+	0.290285i	$0.906250\pi$
$384$	0.773010	+	0.634393i	0.773010	+	0.634393i
$385$		0			0
$386$		0			0
$387$	0.324423	−	0.216773i	0.324423	−	0.216773i
$388$		0			0
$389$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$389$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$390$	−1.55557	−	0.831470i	−1.55557	−	0.831470i
$391$		0			0
$392$	−0.773010	+	0.634393i	−0.773010	+	0.634393i
$393$		0			0
$394$	1.26268	+	1.53858i	1.26268	+	1.53858i
$395$	0.382353	−	0.572232i	0.382353	−	0.572232i
$396$	−0.196034			−0.196034
$397$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$397$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$398$	1.05496	−	1.28547i	1.05496	−	1.28547i
$399$		0			0
$400$	−1.49280	−	1.49280i	−1.49280	−	1.49280i
$401$	1.40740	+	1.40740i	1.40740	+	1.40740i	0.773010	+	0.634393i	$0.218750\pi$
$401$	1.40740	+	1.40740i	1.40740	+	1.40740i	0.634393	+	0.773010i	$0.281250\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	1.46658	+	0.979938i	1.46658	+	0.979938i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$409$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$410$	0.297261	+	0.979938i	0.297261	+	0.979938i
$411$	0.247528	+	1.24441i	0.247528	+	1.24441i
$412$	0.275899	−	1.38704i	0.275899	−	1.38704i
$413$		0			0
$414$		0			0
$415$		−	3.37578i		−	3.37578i
$416$	−0.773010	+	0.634393i	−0.773010	+	0.634393i
$417$		−	1.66294i		−	1.66294i
$418$		0			0
$419$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$419$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$420$		0			0
$421$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$421$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$422$	−1.76820	+	0.536376i	−1.76820	+	0.536376i
$423$	−1.42834	+	0.591637i	−1.42834	+	0.591637i
$424$		0			0
$425$		0			0
$426$	−0.195090	+	1.98079i	−0.195090	+	1.98079i
$427$		0			0
$428$		0			0
$429$	0.0382444	−	0.192268i	0.0382444	−	0.192268i
$430$	0.0674571	+	0.684903i	0.0674571	+	0.684903i
$431$	1.35332	+	1.35332i	1.35332	+	1.35332i	0.881921	+	0.471397i	$0.156250\pi$
$431$	1.35332	+	1.35332i	1.35332	+	1.35332i	0.471397	+	0.881921i	$0.343750\pi$
$432$	0.831470	−	0.555570i	0.831470	−	0.555570i
$433$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$433$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.707107	+	1.70711i	−0.707107	+	1.70711i			1.00000i	$0.5\pi$
$439$	−0.707107	+	1.70711i	−0.707107	+	1.70711i	−0.707107	+	0.707107i	$0.750000\pi$
$440$	0.162997	−	0.304945i	0.162997	−	0.304945i
$441$	0.382683	+	0.923880i	0.382683	+	0.923880i
$442$		0			0
$443$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$443$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$444$		0			0
$445$	−2.26737	+	1.51501i	−2.26737	+	1.51501i
$446$		0			0
$447$	−1.26879			−1.26879
$448$		0			0
$449$	−1.54602			−1.54602			−0.773010	−	0.634393i	$-0.781250\pi$
$449$	−1.54602			−1.54602			−0.773010	+	0.634393i	$0.781250\pi$
$450$	−1.86186	+	0.995185i	−1.86186	+	0.995185i
$451$	−0.0946308	+	0.0632303i	−0.0946308	+	0.0632303i
$452$		0			0
$453$		0			0
$454$	0.598102	−	1.11897i	0.598102	−	1.11897i
$455$		0			0
$456$		0			0
$457$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$457$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.192268	+	0.0382444i	0.192268	+	0.0382444i	0.290285	−	0.956940i	$-0.406250\pi$
$461$	0.192268	+	0.0382444i	0.192268	+	0.0382444i	−0.0980171	+	0.995185i	$0.531250\pi$
$462$		0			0
$463$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$463$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$467$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$468$	0.382683	+	0.923880i	0.382683	+	0.923880i
$469$		0			0
$470$	0.267287	−	2.71381i	0.267287	−	2.71381i
$471$	1.81225	+	0.750661i	1.81225	+	0.750661i
$472$	−0.938254	+	0.0924099i	−0.938254	+	0.0924099i
$473$	−0.0706664	+	0.0292710i	−0.0706664	+	0.0292710i
$474$	−0.373380	+	0.113263i	−0.373380	+	0.113263i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.168530	+	0.555570i	−0.168530	+	0.555570i
$479$			0.196034i			0.196034i	0.995185	+	0.0980171i	$0.0312500\pi$
$479$			0.196034i			0.196034i	−0.995185	+	0.0980171i	$0.968750\pi$
$480$	0.172887	+	1.75535i	0.172887	+	1.75535i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.943094	−	0.187593i	−0.943094	−	0.187593i
$485$		0			0
$486$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$487$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$487$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$488$	−1.62958	+	0.871028i	−1.62958	+	0.871028i
$489$		0			0
$490$	−1.75535	−	0.172887i	−1.75535	−	0.172887i
$491$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$491$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$492$	0.222174	−	0.536376i	0.222174	−	0.536376i
$493$		0			0
$494$		0			0
$495$	−0.244499	−	0.244499i	−0.244499	−	0.244499i
$496$		0			0
$497$		0			0
$498$	−1.21415	+	1.47945i	−1.21415	+	1.47945i
$499$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$499$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$500$		−	1.95988i		−	1.95988i
$501$	1.06330	−	1.59133i	1.06330	−	1.59133i
$502$		0			0
$503$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$503$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.980785	+	0.195090i	−0.980785	+	0.195090i
$508$	1.08979	−	1.63099i	1.08979	−	1.63099i
$509$	0.482726	−	0.322547i	0.482726	−	0.322547i	−0.290285	−	0.956940i	$-0.593750\pi$
$509$	0.482726	−	0.322547i	0.482726	−	0.322547i	0.773010	+	0.634393i	$0.218750\pi$
$510$		0			0
$511$		0			0
$512$	0.956940	+	0.290285i	0.956940	+	0.290285i
$513$		0			0
$514$		0			0
$515$	2.07406	−	1.38584i	2.07406	−	1.38584i
$516$	0.216773	−	0.324423i	0.216773	−	0.324423i
$517$	0.297250	−	0.0591266i	0.297250	−	0.0591266i
$518$		0			0
$519$		0			0
$520$	−1.75535	−	0.172887i	−1.75535	−	0.172887i
$521$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$521$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$522$		0			0
$523$	0.923880	−	1.38268i	0.923880	−	1.38268i		−	1.00000i	$-0.5\pi$
$523$	0.923880	−	1.38268i	0.923880	−	1.38268i	0.923880	−	0.382683i	$-0.125000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.181112	+	0.0750191i	−0.181112	+	0.0750191i
$529$	0.707107	+	0.707107i	0.707107	+	0.707107i
$530$		0			0
$531$	−0.183930	+	0.924678i	−0.183930	+	0.924678i
$532$		0			0
$533$	0.482726	+	0.322547i	0.482726	+	0.322547i
$534$	1.53858	+	0.151537i	1.53858	+	0.151537i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.0382444	−	0.192268i	−0.0382444	−	0.192268i
$540$	1.72995	+	0.344109i	1.72995	+	0.344109i
$541$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$541$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$542$		0			0
$543$			1.66294i			1.66294i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.617317	−	0.923880i	−0.617317	−	0.923880i	0.382683	−	0.923880i	$-0.375000\pi$
$547$	−0.617317	−	0.923880i	−0.617317	−	0.923880i	−1.00000			$\pi$
$548$	0.704900	+	1.05496i	0.704900	+	1.05496i
$549$	0.360480	+	1.81225i	0.360480	+	1.81225i
$550$	0.396035	−	0.120136i	0.396035	−	0.120136i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.162997	−	1.65493i	0.162997	−	1.65493i
$555$		0			0
$556$	−0.636379	−	1.53636i	−0.636379	−	1.53636i
$557$	0.373380	−	1.87711i	0.373380	−	1.87711i	−0.0980171	−	0.995185i	$-0.531250\pi$
$557$	0.373380	−	1.87711i	0.373380	−	1.87711i	0.471397	−	0.881921i	$-0.343750\pi$
$558$		0			0
$559$	0.275899	+	0.275899i	0.275899	+	0.275899i
$560$		0			0
$561$		0			0
$562$	−0.728789	−	0.598102i	−0.728789	−	0.598102i
$563$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$563$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$564$	−1.09320	+	1.09320i	−1.09320	+	1.09320i
$565$		0			0
$566$	−0.591637	+	0.485544i	−0.591637	+	0.485544i
$567$		0			0
$568$	0.577774	+	1.90466i	0.577774	+	1.90466i
$569$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$569$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$570$		0			0
$571$	−0.750661	+	0.149316i	−0.750661	+	0.149316i	−0.555570	−	0.831470i	$-0.687500\pi$
$571$	−0.750661	+	0.149316i	−0.750661	+	0.149316i	−0.195090	+	0.980785i	$0.562500\pi$
$572$	−0.0382444	−	0.192268i	−0.0382444	−	0.192268i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.555570	−	0.831470i	0.555570	−	0.831470i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	0.881921	−	0.471397i	0.881921	−	0.471397i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.674993	+	1.62958i	−0.674993	+	1.62958i
$586$	0.980785	−	0.804910i	0.980785	−	0.804910i
$587$	0.979938	−	1.46658i	0.979938	−	1.46658i	0.0980171	−	0.995185i	$-0.468750\pi$
$587$	0.979938	−	1.46658i	0.979938	−	1.46658i	0.881921	−	0.471397i	$-0.156250\pi$
$588$	0.707107	+	0.707107i	0.707107	+	0.707107i
$589$		0			0
$590$	−1.28547	−	1.05496i	−1.28547	−	1.05496i
$591$	1.40740	−	1.40740i	1.40740	−	1.40740i
$592$		0			0
$593$	−0.666656	−	0.666656i	−0.666656	−	0.666656i	0.290285	−	0.956940i	$-0.406250\pi$
$593$	−0.666656	−	0.666656i	−0.666656	−	0.666656i	−0.956940	+	0.290285i	$0.906250\pi$
$594$	0.0192147	+	0.195090i	0.0192147	+	0.195090i
$595$		0			0
$596$	−1.17221	+	0.485544i	−1.17221	+	0.485544i
$597$	−1.38268	−	0.923880i	−1.38268	−	0.923880i
$598$		0			0
$599$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$599$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$600$	−1.33929	+	1.63193i	−1.33929	+	1.63193i
$601$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.980785	−	0.195090i	$-0.937500\pi$
$601$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.555570	+	0.831470i	$0.687500\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.942280	−	1.41022i	−0.942280	−	1.41022i
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$	−3.11882	−	0.946083i	−3.11882	−	0.946083i
$611$	−0.858923	−	1.28547i	−0.858923	−	1.28547i
$612$		0			0
$613$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$613$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$614$		0			0
$615$	0.946083	−	0.391880i	0.946083	−	0.391880i
$616$		0			0
$617$	1.62958	+	0.674993i	1.62958	+	0.674993i	0.995185	−	0.0980171i	$-0.0312500\pi$
$617$	1.62958	+	0.674993i	1.62958	+	0.674993i	0.634393	+	0.773010i	$0.281250\pi$
$618$	−1.40740	−	0.138617i	−1.40740	−	0.138617i
$619$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$619$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	0.707107	+	0.707107i	0.707107	+	0.707107i
$625$	0.951606	−	0.951606i	0.951606	−	0.951606i
$626$	0.247528	−	0.301614i	0.247528	−	0.301614i
$627$		0			0
$628$	1.96157			1.96157
$629$		0			0
$630$		0			0
$631$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$631$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$632$	−0.301614	+	0.247528i	−0.301614	+	0.247528i
$633$	0.707107	+	1.70711i	0.707107	+	1.70711i
$634$	1.36347	+	0.728789i	1.36347	+	0.728789i
$635$	3.39342	−	0.674993i	3.39342	−	0.674993i
$636$		0			0
$637$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$638$		0			0
$639$	1.99037			1.99037
$640$	0.831470	+	1.55557i	0.831470	+	1.55557i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		0			0
$643$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$643$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$644$		0			0
$645$	0.674993	−	0.134265i	0.674993	−	0.134265i
$646$		0			0
$647$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$647$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$648$	−0.634393	−	0.773010i	−0.634393	−	0.773010i
$649$	0.0707275	−	0.170751i	0.0707275	−	0.170751i
$650$	−1.33929	−	1.63193i	−1.33929	−	1.63193i
$651$		0			0
$652$		0			0
$653$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$653$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$654$		0			0
$655$		0			0
$656$		−	0.580569i		−	0.580569i
$657$		0			0
$658$		0			0
$659$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$659$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$660$	−0.319453	−	0.132322i	−0.319453	−	0.132322i
$661$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$661$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$662$		0			0
$663$		0			0
$664$	−0.555570	+	1.83147i	−0.555570	+	1.83147i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.373380	−	1.87711i	0.373380	−	1.87711i
$669$		0			0
$670$		0			0
$671$		−	0.362224i		−	0.362224i
$672$		0			0
$673$			0.765367i			0.765367i	0.923880	+	0.382683i	$0.125000\pi$
$673$			0.765367i			0.765367i	−0.923880	+	0.382683i	$0.875000\pi$
$674$	−0.569414	+	1.87711i	−0.569414	+	1.87711i
$675$	1.17289	+	1.75535i	1.17289	+	1.75535i
$676$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$677$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$677$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.17221	−	0.485544i	−1.17221	−	0.485544i
$682$		0			0
$683$	−0.783904	−	0.523788i	−0.783904	−	0.523788i	0.0980171	−	0.995185i	$-0.468750\pi$
$683$	−0.783904	−	0.523788i	−0.783904	−	0.523788i	−0.881921	+	0.471397i	$0.843750\pi$
$684$		0			0
$685$	−0.436600	+	2.19494i	−0.436600	+	2.19494i
$686$		0			0
$687$		0			0
$688$	0.0761205	−	0.382683i	0.0761205	−	0.382683i
$689$		0			0
$690$		0			0
$691$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$691$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.12247	−	2.70989i	1.12247	−	2.70989i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$701$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$702$	0.881921	−	0.471397i	0.881921	−	0.471397i
$703$		0			0
$704$	−0.138617	+	0.138617i	−0.138617	+	0.138617i
$705$	−2.72694			−2.72694
$706$	1.68789	−	0.902197i	1.68789	−	0.902197i
$707$		0			0
$708$	0.183930	+	0.924678i	0.183930	+	0.924678i
$709$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$709$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$710$	−1.65493	+	3.09616i	−1.65493	+	3.09616i
$711$	0.149316	+	0.360480i	0.149316	+	0.360480i
$712$	1.47945	−	0.448786i	1.47945	−	0.448786i
$713$		0			0
$714$		0			0
$715$	0.192102	−	0.287500i	0.192102	−	0.287500i
$716$		0			0
$717$	0.569414	+	0.113263i	0.569414	+	0.113263i
$718$	−0.980785	−	0.804910i	−0.980785	−	0.804910i
$719$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$719$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$720$	1.72995	−	0.344109i	1.72995	−	0.344109i
$721$		0			0
$722$	0.0980171	+	0.995185i	0.0980171	+	0.995185i
$723$		0			0
$724$	0.636379	+	1.53636i	0.636379	+	1.53636i
$725$		0			0
$726$	−0.0942504	+	0.956940i	−0.0942504	+	0.956940i
$727$	1.02656	+	0.425215i	1.02656	+	0.425215i	0.831470	−	0.555570i	$-0.187500\pi$
$727$	1.02656	+	0.425215i	1.02656	+	0.425215i	0.195090	+	0.980785i	$0.437500\pi$
$728$		0			0
$729$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$730$		0			0
$731$		0			0
$732$	1.02656	+	1.53636i	1.02656	+	1.53636i
$733$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$733$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$734$	0.536376	−	1.76820i	0.536376	−	1.76820i
$735$			1.76384i			1.76384i
$736$		0			0
$737$		0			0
$738$	−0.555570	−	0.168530i	−0.555570	−	0.168530i
$739$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$739$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.536376	−	0.222174i	0.536376	−	0.222174i	−0.0980171	−	0.995185i	$-0.531250\pi$
$743$	0.536376	−	0.222174i	0.536376	−	0.222174i	0.634393	+	0.773010i	$0.281250\pi$
$744$		0			0
$745$	−2.06759	−	0.856422i	−2.06759	−	0.856422i
$746$	0.761681	+	0.0750191i	0.761681	+	0.0750191i
$747$	1.59133	+	1.06330i	1.59133	+	1.06330i
$748$		0			0
$749$		0			0
$750$	−1.95044	+	0.192102i	−1.95044	+	0.192102i
$751$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	0.382683	−	0.923880i	$-0.375000\pi$
$751$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$752$	−0.591637	+	1.42834i	−0.591637	+	1.42834i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.02656	−	1.53636i	1.02656	−	1.53636i	0.195090	−	0.980785i	$-0.437500\pi$
$757$	1.02656	−	1.53636i	1.02656	−	1.53636i	0.831470	−	0.555570i	$-0.187500\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.471397	+	0.881921i	$0.343750\pi$
$761$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.290285	+	0.956940i	$0.406250\pi$
$762$	−1.72995	−	0.924678i	−1.72995	−	0.924678i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.902197	+	1.68789i	0.902197	+	1.68789i
$767$	−0.942793			−0.942793
$768$	0.195090	−	0.980785i	0.195090	−	0.980785i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.87711	+	0.373380i	−1.87711	+	0.373380i	−0.995185	−	0.0980171i	$-0.968750\pi$
$773$	−1.87711	+	0.373380i	−1.87711	+	0.373380i	−0.881921	+	0.471397i	$0.843750\pi$
$774$	−0.344109	−	0.183930i	−0.344109	−	0.183930i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$			1.76384i			1.76384i
$781$	−0.382683	−	0.0761205i	−0.382683	−	0.0761205i
$782$		0			0
$783$		0			0
$784$	0.923880	+	0.382683i	0.923880	+	0.382683i
$785$	2.44652	+	2.44652i	2.44652	+	2.44652i
$786$		0			0
$787$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$787$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$788$	0.761681	−	1.83886i	0.761681	−	1.83886i
$789$		0			0
$790$	−0.684903	−	0.0674571i	−0.684903	−	0.0674571i
$791$		0			0
$792$	0.0924099	+	0.172887i	0.0924099	+	0.172887i
$793$	−1.70711	+	0.707107i	−1.70711	+	0.707107i
$794$		0			0
$795$		0			0
$796$	−1.63099	−	0.324423i	−1.63099	−	0.324423i
$797$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$797$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$798$		0			0
$799$		0			0
$800$	−0.612832	+	2.02024i	−0.612832	+	2.02024i
$801$		−	1.54602i		−	1.54602i
$802$	0.577774	−	1.90466i	0.577774	−	1.90466i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$809$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$810$	0.172887	−	1.75535i	0.172887	−	1.75535i
$811$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$811$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	0.724101	−	0.724101i	0.724101	−	0.724101i
$821$	−1.10579	+	1.65493i	−1.10579	+	1.65493i	−0.471397	+	0.881921i	$0.656250\pi$
$821$	−1.10579	+	1.65493i	−1.10579	+	1.65493i	−0.634393	+	0.773010i	$0.718750\pi$
$822$	0.980785	−	0.804910i	0.980785	−	0.804910i
$823$	0.292893	−	0.707107i	0.292893	−	0.707107i	−0.707107	−	0.707107i	$-0.750000\pi$
$823$	0.292893	−	0.707107i	0.292893	−	0.707107i	1.00000			$0$
$824$	−1.35332	+	0.410525i	−1.35332	+	0.410525i
$825$	−0.158376	−	0.382353i	−0.158376	−	0.382353i
$826$		0			0
$827$	1.72995	−	0.344109i	1.72995	−	0.344109i	0.773010	−	0.634393i	$-0.218750\pi$
$827$	1.72995	−	0.344109i	1.72995	−	0.344109i	0.956940	+	0.290285i	$0.0937500\pi$
$828$		0			0
$829$	1.17588	−	0.785695i	1.17588	−	0.785695i	0.195090	−	0.980785i	$-0.437500\pi$
$829$	1.17588	−	0.785695i	1.17588	−	0.785695i	0.980785	+	0.195090i	$0.0625000\pi$
$830$	−2.97718	+	1.59133i	−2.97718	+	1.59133i
$831$	−1.66294			−1.66294
$832$	0.923880	+	0.382683i	0.923880	+	0.382683i
$833$		0			0
$834$	−1.46658	+	0.783904i	−1.46658	+	0.783904i
$835$	2.80686	−	1.87549i	2.80686	−	1.87549i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.360791	+	0.871028i	0.360791	+	0.871028i	0.995185	+	0.0980171i	$0.0312500\pi$
$839$	0.360791	+	0.871028i	0.360791	+	0.871028i	−0.634393	+	0.773010i	$0.718750\pi$
$840$		0			0
$841$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$842$		0			0
$843$	−0.523788	+	0.783904i	−0.523788	+	0.783904i
$844$	1.30656	+	1.30656i	1.30656	+	1.30656i
$845$	−1.72995	−	0.344109i	−1.72995	−	0.344109i
$846$	1.19509	+	0.980785i	1.19509	+	0.980785i
$847$		0			0
$848$		0			0
$849$	0.541196	+	0.541196i	0.541196	+	0.541196i
$850$		0			0
$851$		0			0
$852$	1.83886	−	0.761681i	1.83886	−	0.761681i
$853$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$853$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$857$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$858$	−0.187593	+	0.0569057i	−0.187593	+	0.0569057i
$859$	0.275899	+	1.38704i	0.275899	+	1.38704i	0.831470	+	0.555570i	$0.187500\pi$
$859$	0.275899	+	1.38704i	0.275899	+	1.38704i	−0.555570	+	0.831470i	$0.687500\pi$
$860$	0.572232	−	0.382353i	0.572232	−	0.382353i
$861$		0			0
$862$	0.555570	−	1.83147i	0.555570	−	1.83147i
$863$		−	1.54602i		−	1.54602i	−0.634393	−	0.773010i	$-0.718750\pi$
$863$		−	1.54602i		−	1.54602i	0.634393	−	0.773010i	$-0.281250\pi$
$864$	−0.881921	−	0.471397i	−0.881921	−	0.471397i
$865$		0			0
$866$	1.59133	+	0.482726i	1.59133	+	0.482726i
$867$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$868$		0			0
$869$	−0.0149222	−	0.0750191i	−0.0149222	−	0.0750191i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$877$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$878$	1.83886	−	0.181112i	1.83886	−	0.181112i
$879$	−0.897168	−	0.897168i	−0.897168	−	0.897168i
$880$	−0.345774			−0.345774
$881$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$881$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$882$	0.634393	−	0.773010i	0.634393	−	0.773010i
$883$	−1.81225	−	0.360480i	−1.81225	−	0.360480i	−0.831470	−	0.555570i	$-0.812500\pi$
$883$	−1.81225	−	0.360480i	−1.81225	−	0.360480i	−0.980785	+	0.195090i	$0.937500\pi$
$884$		0			0
$885$	−0.923880	+	1.38268i	−0.923880	+	1.38268i
$886$		0			0
$887$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$887$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$888$		0			0
$889$		0			0
$890$	2.40494	+	1.28547i	2.40494	+	1.28547i
$891$	0.192268	−	0.0382444i	0.192268	−	0.0382444i
$892$		0			0
$893$		0			0
$894$	0.598102	+	1.11897i	0.598102	+	1.11897i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.728789	+	1.36347i	0.728789	+	1.36347i
$899$		0			0
$900$	1.75535	+	1.17289i	1.75535	+	1.17289i
$901$		0			0
$902$	0.100373	+	0.0536504i	0.100373	+	0.0536504i
$903$		0			0
$904$		0			0
$905$	−1.12247	+	2.70989i	−1.12247	+	2.70989i
$906$		0			0
$907$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	0.195090	+	0.980785i	$0.437500\pi$
$907$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$908$	−1.26879			−1.26879
$909$		0			0
$910$		0			0
$911$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$911$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$912$		0			0
$913$	−0.265297	−	0.265297i	−0.265297	−	0.265297i
$914$		0			0
$915$	−0.635830	+	3.19653i	−0.635830	+	3.19653i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.02656	−	0.425215i	−1.02656	−	0.425215i	−0.195090	−	0.980785i	$-0.562500\pi$
$919$	−1.02656	−	0.425215i	−1.02656	−	0.425215i	−0.831470	+	0.555570i	$0.812500\pi$
$920$		0			0
$921$		0			0
$922$	−0.0569057	−	0.187593i	−0.0569057	−	0.187593i
$923$	0.388302	+	1.95213i	0.388302	+	1.95213i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			1.41421i			1.41421i
$928$		0			0
$929$		−	1.76384i		−	1.76384i	−0.471397	−	0.881921i	$-0.656250\pi$
$929$		−	1.76384i		−	1.76384i	0.471397	−	0.881921i	$-0.343750\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.634393	−	0.773010i	0.634393	−	0.773010i
$937$	1.81225	+	0.750661i	1.81225	+	0.750661i	0.980785	+	0.195090i	$0.0625000\pi$
$937$	1.81225	+	0.750661i	1.81225	+	0.750661i	0.831470	+	0.555570i	$0.187500\pi$
$938$		0			0
$939$	−0.324423	−	0.216773i	−0.324423	−	0.216773i
$940$	−2.51936	+	1.04355i	−2.51936	+	1.04355i
$941$	0.113263	−	0.569414i	0.113263	−	0.569414i	−0.881921	−	0.471397i	$-0.843750\pi$
$941$	0.113263	−	0.569414i	0.113263	−	0.569414i	0.995185	−	0.0980171i	$-0.0312500\pi$
$942$	−0.192268	−	1.95213i	−0.192268	−	1.95213i
$943$		0			0
$944$	0.523788	+	0.783904i	0.523788	+	0.783904i
$945$		0			0
$946$	0.0591266	+	0.0485240i	0.0591266	+	0.0485240i
$947$	1.24441	+	0.247528i	1.24441	+	0.247528i	0.773010	−	0.634393i	$-0.218750\pi$
$947$	1.24441	+	0.247528i	1.24441	+	0.247528i	0.471397	+	0.881921i	$0.343750\pi$
$948$	0.275899	+	0.275899i	0.275899	+	0.275899i
$949$		0			0
$950$		0			0
$951$	0.591637	−	1.42834i	0.591637	−	1.42834i
$952$		0			0
$953$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$953$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$954$		0			0
$955$		0			0
$956$	0.569414	−	0.113263i	0.569414	−	0.113263i
$957$		0			0
$958$	0.172887	−	0.0924099i	0.172887	−	0.0924099i
$959$		0			0
$960$	1.46658	−	0.979938i	1.46658	−	0.979938i
$961$	−1.00000			−1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$967$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$968$	0.279129	+	0.920166i	0.279129	+	0.920166i
$969$		0			0
$970$		0			0
$971$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$971$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$972$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$973$		0			0
$974$		0			0
$975$	−1.49280	+	1.49280i	−1.49280	+	1.49280i
$976$	1.53636	+	1.02656i	1.53636	+	1.02656i
$977$	0.410525	+	0.410525i	0.410525	+	0.410525i	0.881921	−	0.471397i	$-0.156250\pi$
$977$	0.410525	+	0.410525i	0.410525	+	0.410525i	−0.471397	+	0.881921i	$0.656250\pi$
$978$		0			0
$979$	−0.0591266	+	0.297250i	−0.0591266	+	0.297250i
$980$	0.674993	+	1.62958i	0.674993	+	1.62958i
$981$		0			0
$982$		0			0
$983$	0.871028	+	0.360791i	0.871028	+	0.360791i	0.773010	−	0.634393i	$-0.218750\pi$
$983$	0.871028	+	0.360791i	0.871028	+	0.360791i	0.0980171	+	0.995185i	$0.468750\pi$
$984$	−0.577774	+	0.0569057i	−0.577774	+	0.0569057i
$985$	3.24346	−	1.34349i	3.24346	−	1.34349i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.100373	+	0.330885i	−0.100373	+	0.330885i
$991$		−	1.84776i		−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$991$		−	1.84776i		−	1.84776i	0.382683	−	0.923880i	$-0.375000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.62958	−	2.43884i	−1.62958	−	2.43884i
$996$	1.87711	+	0.373380i	1.87711	+	0.373380i
$997$	−0.216773	−	1.08979i	−0.216773	−	1.08979i	−0.923880	−	0.382683i	$-0.875000\pi$
$997$	−0.216773	−	1.08979i	−0.216773	−	1.08979i	0.707107	−	0.707107i	$-0.250000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2496.1.eh.a.77.2	✓	32
3.2	odd	2	inner	2496.1.eh.a.77.3	yes	32
13.12	even	2	inner	2496.1.eh.a.77.3	yes	32
39.38	odd	2	CM	2496.1.eh.a.77.2	✓	32
64.5	even	16	inner	2496.1.eh.a.389.2	yes	32
192.5	odd	16	inner	2496.1.eh.a.389.3	yes	32
832.389	even	16	inner	2496.1.eh.a.389.3	yes	32
2496.389	odd	16	inner	2496.1.eh.a.389.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2496.1.eh.a.77.2	✓	32	1.1	even	1	trivial
2496.1.eh.a.77.2	✓	32	39.38	odd	2	CM
2496.1.eh.a.77.3	yes	32	3.2	odd	2	inner
2496.1.eh.a.77.3	yes	32	13.12	even	2	inner
2496.1.eh.a.389.2	yes	32	64.5	even	16	inner
2496.1.eh.a.389.2	yes	32	2496.389	odd	16	inner
2496.1.eh.a.389.3	yes	32	192.5	odd	16	inner
2496.1.eh.a.389.3	yes	32	832.389	even	16	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:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2496.eh (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.471397 - 0.881921i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.555570 + 0.831470i) q^{4} +(-1.72995 + 0.344109i) q^{5} +(0.881921 + 0.471397i) q^{6} +(0.995185 + 0.0980171i) q^{8} +(0.382683 - 0.923880i) q^{9} +(1.11897 + 1.36347i) q^{10} +(-0.108911 + 0.162997i) q^{11} -1.00000i q^{12} +(0.980785 + 0.195090i) q^{13} +(1.24723 - 1.24723i) q^{15} +(-0.382683 - 0.923880i) q^{16} +(-0.995185 + 0.0980171i) q^{18} +(0.674993 - 1.62958i) q^{20} +(0.195090 + 0.0192147i) q^{22} +(-0.881921 + 0.471397i) q^{24} +(1.95044 - 0.807898i) q^{25} +(-0.290285 - 0.956940i) q^{26} +(0.195090 + 0.980785i) q^{27} +(-1.68789 - 0.512016i) q^{30} +(-0.634393 + 0.773010i) q^{32} -0.196034i q^{33} +(0.555570 + 0.831470i) q^{36} +(-0.923880 + 0.382683i) q^{39} +(-1.75535 + 0.172887i) q^{40} +(0.536376 + 0.222174i) q^{41} +(0.324423 + 0.216773i) q^{43} +(-0.0750191 - 0.181112i) q^{44} +(-0.344109 + 1.72995i) q^{45} +(-1.09320 - 1.09320i) q^{47} +(0.831470 + 0.555570i) q^{48} +(-0.707107 + 0.707107i) q^{49} +(-1.63193 - 1.33929i) q^{50} +(-0.707107 + 0.707107i) q^{52} +(0.773010 - 0.634393i) q^{54} +(0.132322 - 0.319453i) q^{55} +(-0.924678 + 0.183930i) q^{59} +(0.344109 + 1.72995i) q^{60} +(-1.53636 + 1.02656i) q^{61} +(0.980785 + 0.195090i) q^{64} -1.76384 q^{65} +(-0.172887 + 0.0924099i) q^{66} +(0.761681 + 1.83886i) q^{71} +(0.471397 - 0.881921i) q^{72} +(-1.17289 + 1.75535i) q^{75} +(0.773010 + 0.634393i) q^{78} +(-0.275899 + 0.275899i) q^{79} +(0.979938 + 1.46658i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(-0.0569057 - 0.577774i) q^{82} +(-0.373380 + 1.87711i) q^{83} +(0.0382444 - 0.388302i) q^{86} +(-0.124363 + 0.151537i) q^{88} +(1.42834 - 0.591637i) q^{89} +(1.68789 - 0.512016i) q^{90} +(-0.448786 + 1.47945i) q^{94} +(0.0980171 - 0.995185i) q^{96} +(0.956940 + 0.290285i) q^{98} +(0.108911 + 0.162997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{55} - 32 q^{75}+O(q^{100}) \) 32 * q - 32 * q^55 - 32 * q^75

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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