LMFDB - Embedded newform 2496.1.eh.a.1949.4

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			1949.4
Root			$-0.881921 - 0.471397i$ of defining polynomial
Character	$\chi$	$=$	2496.1949
Dual form			2496.1.eh.a.1013.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.773010 + 0.634393i) q^{2} +(-0.980785 - 0.195090i) q^{3} +(0.195090 + 0.980785i) q^{4} +(-0.704900 + 1.05496i) q^{5} +(-0.634393 - 0.773010i) q^{6} +(-0.471397 + 0.881921i) q^{8} +(0.923880 + 0.382683i) q^{9} +(-1.21415 + 0.368309i) q^{10} +(0.344109 + 1.72995i) q^{11} -1.00000i q^{12} +(-0.555570 - 0.831470i) q^{13} +(0.897168 - 0.897168i) q^{15} +(-0.923880 + 0.382683i) q^{16} +(0.471397 + 0.881921i) q^{18} +(-1.17221 - 0.485544i) q^{20} +(-0.831470 + 1.55557i) q^{22} +(0.634393 - 0.773010i) q^{24} +(-0.233368 - 0.563400i) q^{25} +(0.0980171 - 0.995185i) q^{26} +(-0.831470 - 0.555570i) q^{27} +(1.26268 - 0.124363i) q^{30} +(-0.956940 - 0.290285i) q^{32} -1.76384i q^{33} +(-0.195090 + 0.980785i) q^{36} +(0.382683 + 0.923880i) q^{39} +(-0.598102 - 1.11897i) q^{40} +(0.0750191 - 0.181112i) q^{41} +(-1.63099 + 0.324423i) q^{43} +(-1.62958 + 0.674993i) q^{44} +(-1.05496 + 0.704900i) q^{45} +(-0.410525 - 0.410525i) q^{47} +(0.980785 - 0.195090i) q^{48} +(0.707107 - 0.707107i) q^{49} +(0.177021 - 0.583561i) q^{50} +(0.707107 - 0.707107i) q^{52} +(-0.290285 - 0.956940i) q^{54} +(-2.06759 - 0.856422i) q^{55} +(-0.858923 + 1.28547i) q^{59} +(1.05496 + 0.704900i) q^{60} +(0.750661 + 0.149316i) q^{61} +(-0.555570 - 0.831470i) q^{64} +1.26879 q^{65} +(1.11897 - 1.36347i) q^{66} +(-0.871028 + 0.360791i) q^{71} +(-0.773010 + 0.634393i) q^{72} +(0.118970 + 0.598102i) q^{75} +(-0.290285 + 0.956940i) q^{78} +(-1.17588 + 1.17588i) q^{79} +(0.247528 - 1.24441i) q^{80} +(0.707107 + 0.707107i) q^{81} +(0.172887 - 0.0924099i) q^{82} +(1.65493 - 1.10579i) q^{83} +(-1.46658 - 0.783904i) q^{86} +(-1.68789 - 0.512016i) q^{88} +(0.222174 + 0.536376i) q^{89} +(-1.26268 - 0.124363i) q^{90} +(-0.0569057 - 0.577774i) q^{94} +(0.881921 + 0.471397i) q^{96} +(0.995185 - 0.0980171i) q^{98} +(-0.344109 + 1.72995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2496\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	0.773010	+	0.634393i	0.773010	+	0.634393i
$2$	0.773010	+	0.634393i	0.773010	+	0.634393i
$3$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$3$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$4$	0.195090	+	0.980785i	0.195090	+	0.980785i
$5$	−0.704900	+	1.05496i	−0.704900	+	1.05496i	0.290285	+	0.956940i	$0.406250\pi$
$5$	−0.704900	+	1.05496i	−0.704900	+	1.05496i	−0.995185	+	0.0980171i	$0.968750\pi$
$6$	−0.634393	−	0.773010i	−0.634393	−	0.773010i
$7$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$7$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$8$	−0.471397	+	0.881921i	−0.471397	+	0.881921i
$9$	0.923880	+	0.382683i	0.923880	+	0.382683i
$10$	−1.21415	+	0.368309i	−1.21415	+	0.368309i
$11$	0.344109	+	1.72995i	0.344109	+	1.72995i	0.634393	+	0.773010i	$0.281250\pi$
$11$	0.344109	+	1.72995i	0.344109	+	1.72995i	−0.290285	+	0.956940i	$0.593750\pi$
$12$		−	1.00000i		−	1.00000i
$13$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$13$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$14$		0			0
$15$	0.897168	−	0.897168i	0.897168	−	0.897168i
$16$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	0.471397	+	0.881921i	0.471397	+	0.881921i
$19$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$19$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$20$	−1.17221	−	0.485544i	−1.17221	−	0.485544i
$21$		0			0
$22$	−0.831470	+	1.55557i	−0.831470	+	1.55557i
$23$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$23$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$24$	0.634393	−	0.773010i	0.634393	−	0.773010i
$25$	−0.233368	−	0.563400i	−0.233368	−	0.563400i
$26$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$27$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$28$		0			0
$29$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$29$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$30$	1.26268	−	0.124363i	1.26268	−	0.124363i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.956940	−	0.290285i	−0.956940	−	0.290285i
$33$		−	1.76384i		−	1.76384i
$34$		0			0
$35$		0			0
$36$	−0.195090	+	0.980785i	−0.195090	+	0.980785i
$37$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$37$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$38$		0			0
$39$	0.382683	+	0.923880i	0.382683	+	0.923880i
$40$	−0.598102	−	1.11897i	−0.598102	−	1.11897i
$41$	0.0750191	−	0.181112i	0.0750191	−	0.181112i	−0.881921	−	0.471397i	$-0.843750\pi$
$41$	0.0750191	−	0.181112i	0.0750191	−	0.181112i	0.956940	+	0.290285i	$0.0937500\pi$
$42$		0			0
$43$	−1.63099	+	0.324423i	−1.63099	+	0.324423i	−0.923880	−	0.382683i	$-0.875000\pi$
$43$	−1.63099	+	0.324423i	−1.63099	+	0.324423i	−0.707107	+	0.707107i	$0.750000\pi$
$44$	−1.62958	+	0.674993i	−1.62958	+	0.674993i
$45$	−1.05496	+	0.704900i	−1.05496	+	0.704900i
$46$		0			0
$47$	−0.410525	−	0.410525i	−0.410525	−	0.410525i	0.471397	−	0.881921i	$-0.343750\pi$
$47$	−0.410525	−	0.410525i	−0.410525	−	0.410525i	−0.881921	+	0.471397i	$0.843750\pi$
$48$	0.980785	−	0.195090i	0.980785	−	0.195090i
$49$	0.707107	−	0.707107i	0.707107	−	0.707107i
$50$	0.177021	−	0.583561i	0.177021	−	0.583561i
$51$		0			0
$52$	0.707107	−	0.707107i	0.707107	−	0.707107i
$53$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$53$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$54$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$55$	−2.06759	−	0.856422i	−2.06759	−	0.856422i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.858923	+	1.28547i	−0.858923	+	1.28547i	0.0980171	+	0.995185i	$0.468750\pi$
$59$	−0.858923	+	1.28547i	−0.858923	+	1.28547i	−0.956940	+	0.290285i	$0.906250\pi$
$60$	1.05496	+	0.704900i	1.05496	+	0.704900i
$61$	0.750661	+	0.149316i	0.750661	+	0.149316i	0.555570	−	0.831470i	$-0.312500\pi$
$61$	0.750661	+	0.149316i	0.750661	+	0.149316i	0.195090	+	0.980785i	$0.437500\pi$
$62$		0			0
$63$		0			0
$64$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$65$	1.26879			1.26879
$66$	1.11897	−	1.36347i	1.11897	−	1.36347i
$67$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$67$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.871028	+	0.360791i	−0.871028	+	0.360791i	−0.773010	−	0.634393i	$-0.781250\pi$
$71$	−0.871028	+	0.360791i	−0.871028	+	0.360791i	−0.0980171	+	0.995185i	$0.531250\pi$
$72$	−0.773010	+	0.634393i	−0.773010	+	0.634393i
$73$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$73$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$74$		0			0
$75$	0.118970	+	0.598102i	0.118970	+	0.598102i
$76$		0			0
$77$		0			0
$78$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$79$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$79$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$80$	0.247528	−	1.24441i	0.247528	−	1.24441i
$81$	0.707107	+	0.707107i	0.707107	+	0.707107i
$82$	0.172887	−	0.0924099i	0.172887	−	0.0924099i
$83$	1.65493	−	1.10579i	1.65493	−	1.10579i	0.773010	−	0.634393i	$-0.218750\pi$
$83$	1.65493	−	1.10579i	1.65493	−	1.10579i	0.881921	−	0.471397i	$-0.156250\pi$
$84$		0			0
$85$		0			0
$86$	−1.46658	−	0.783904i	−1.46658	−	0.783904i
$87$		0			0
$88$	−1.68789	−	0.512016i	−1.68789	−	0.512016i
$89$	0.222174	+	0.536376i	0.222174	+	0.536376i	0.995185	−	0.0980171i	$-0.0312500\pi$
$89$	0.222174	+	0.536376i	0.222174	+	0.536376i	−0.773010	+	0.634393i	$0.781250\pi$
$90$	−1.26268	−	0.124363i	−1.26268	−	0.124363i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−0.0569057	−	0.577774i	−0.0569057	−	0.577774i
$95$		0			0
$96$	0.881921	+	0.471397i	0.881921	+	0.471397i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	0.995185	−	0.0980171i	0.995185	−	0.0980171i
$99$	−0.344109	+	1.72995i	−0.344109	+	1.72995i
$100$	0.507046	−	0.338797i	0.507046	−	0.338797i
$101$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$101$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$102$		0			0
$103$	−0.541196	−	1.30656i	−0.541196	−	1.30656i	−0.923880	−	0.382683i	$-0.875000\pi$
$103$	−0.541196	−	1.30656i	−0.541196	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$104$	0.995185	−	0.0980171i	0.995185	−	0.0980171i
$105$		0			0
$106$		0			0
$107$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$107$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$108$	0.382683	−	0.923880i	0.382683	−	0.923880i
$109$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$109$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$110$	−1.05496	−	1.97369i	−1.05496	−	1.97369i
$111$		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
$117$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$118$	−1.47945	+	0.448786i	−1.47945	+	0.448786i
$119$		0			0
$120$	0.368309	+	1.21415i	0.368309	+	1.21415i
$121$	−1.95044	+	0.807898i	−1.95044	+	0.807898i
$122$	0.485544	+	0.591637i	0.485544	+	0.591637i
$123$	−0.108911	+	0.162997i	−0.108911	+	0.162997i
$124$		0			0
$125$	−0.485544	−	0.0965806i	−0.485544	−	0.0965806i
$126$		0			0
$127$	1.11114			1.11114			0.555570	−	0.831470i	$-0.312500\pi$
$127$	1.11114			1.11114			0.555570	+	0.831470i	$0.312500\pi$
$128$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$129$	1.66294			1.66294
$130$	0.980785	+	0.804910i	0.980785	+	0.804910i
$131$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$131$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$132$	1.72995	−	0.344109i	1.72995	−	0.344109i
$133$		0			0
$134$		0			0
$135$	1.17221	−	0.485544i	1.17221	−	0.485544i
$136$		0			0
$137$	1.76820	+	0.732410i	1.76820	+	0.732410i	0.995185	+	0.0980171i	$0.0312500\pi$
$137$	1.76820	+	0.732410i	1.76820	+	0.732410i	0.773010	+	0.634393i	$0.218750\pi$
$138$		0			0
$139$	0.382683	+	1.92388i	0.382683	+	1.92388i	0.382683	+	0.923880i	$0.375000\pi$
$139$	0.382683	+	1.92388i	0.382683	+	1.92388i			1.00000i	$0.5\pi$
$140$		0			0
$141$	0.322547	+	0.482726i	0.322547	+	0.482726i
$142$	−0.902197	−	0.273678i	−0.902197	−	0.273678i
$143$	1.24723	−	1.24723i	1.24723	−	1.24723i
$144$	−1.00000			−1.00000
$145$		0			0
$146$		0			0
$147$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$148$		0			0
$149$	1.87711	−	0.373380i	1.87711	−	0.373380i	0.881921	−	0.471397i	$-0.156250\pi$
$149$	1.87711	−	0.373380i	1.87711	−	0.373380i	0.995185	+	0.0980171i	$0.0312500\pi$
$150$	−0.287467	+	0.537813i	−0.287467	+	0.537813i
$151$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$151$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$157$	−0.216773	+	1.08979i	−0.216773	+	1.08979i	0.707107	+	0.707107i	$0.250000\pi$
$157$	−0.216773	+	1.08979i	−0.216773	+	1.08979i	−0.923880	+	0.382683i	$0.875000\pi$
$158$	−1.65493	+	0.162997i	−1.65493	+	0.162997i
$159$		0			0
$160$	0.980785	−	0.804910i	0.980785	−	0.804910i
$161$		0			0
$162$	0.0980171	+	0.995185i	0.0980171	+	0.995185i
$163$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$163$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$164$	0.192268	+	0.0382444i	0.192268	+	0.0382444i
$165$	1.86078	+	1.24333i	1.86078	+	1.24333i
$166$	1.98079	+	0.195090i	1.98079	+	0.195090i
$167$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.471397	+	0.881921i	$0.343750\pi$
$167$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.290285	+	0.956940i	$0.406250\pi$
$168$		0			0
$169$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$170$		0			0
$171$		0			0
$172$	−0.636379	−	1.53636i	−0.636379	−	1.53636i
$173$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$173$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$174$		0			0
$175$		0			0
$176$	−0.979938	−	1.46658i	−0.979938	−	1.46658i
$177$	1.09320	−	1.09320i	1.09320	−	1.09320i
$178$	−0.168530	+	0.555570i	−0.168530	+	0.555570i
$179$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$179$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$180$	−0.897168	−	0.897168i	−0.897168	−	0.897168i
$181$	−0.382683	−	1.92388i	−0.382683	−	1.92388i	−0.382683	−	0.923880i	$-0.625000\pi$
$181$	−0.382683	−	1.92388i	−0.382683	−	1.92388i		−	1.00000i	$-0.5\pi$
$182$		0			0
$183$	−0.707107	−	0.292893i	−0.707107	−	0.292893i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.322547	−	0.482726i	0.322547	−	0.482726i
$189$		0			0
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	0.382683	+	0.923880i	0.382683	+	0.923880i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$	−1.24441	−	0.247528i	−1.24441	−	0.247528i
$196$	0.831470	+	0.555570i	0.831470	+	0.555570i
$197$	−0.523788	+	0.783904i	−0.523788	+	0.783904i	−0.995185	−	0.0980171i	$-0.968750\pi$
$197$	−0.523788	+	0.783904i	−0.523788	+	0.783904i	0.471397	+	0.881921i	$0.343750\pi$
$198$	−1.36347	+	1.11897i	−1.36347	+	1.11897i
$199$	1.81225	−	0.750661i	1.81225	−	0.750661i	0.831470	−	0.555570i	$-0.187500\pi$
$199$	1.81225	−	0.750661i	1.81225	−	0.750661i	0.980785	−	0.195090i	$-0.0625000\pi$
$200$	0.606883	+	0.0597727i	0.606883	+	0.0597727i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.138185	+	0.206808i	0.138185	+	0.206808i
$206$	0.410525	−	1.35332i	0.410525	−	1.35332i
$207$		0			0
$208$	0.831470	+	0.555570i	0.831470	+	0.555570i
$209$		0			0
$210$		0			0
$211$	0.636379	−	0.425215i	0.636379	−	0.425215i	−0.195090	−	0.980785i	$-0.562500\pi$
$211$	0.636379	−	0.425215i	0.636379	−	0.425215i	0.831470	+	0.555570i	$0.187500\pi$
$212$		0			0
$213$	0.924678	−	0.183930i	0.924678	−	0.183930i
$214$		0			0
$215$	0.807429	−	1.94931i	0.807429	−	1.94931i
$216$	0.881921	−	0.471397i	0.881921	−	0.471397i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.436600	−	2.19494i	0.436600	−	2.19494i
$221$		0			0
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$		−	0.609819i		−	0.609819i
$226$		0			0
$227$	−0.373380	+	1.87711i	−0.373380	+	1.87711i	0.0980171	+	0.995185i	$0.468750\pi$
$227$	−0.373380	+	1.87711i	−0.373380	+	1.87711i	−0.471397	+	0.881921i	$0.656250\pi$
$228$		0			0
$229$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$229$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$233$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$234$	0.471397	−	0.881921i	0.471397	−	0.881921i
$235$	0.722465	−	0.143707i	0.722465	−	0.143707i
$236$	−1.42834	−	0.591637i	−1.42834	−	0.591637i
$237$	1.38268	−	0.923880i	1.38268	−	0.923880i
$238$		0			0
$239$	−0.138617	−	0.138617i	−0.138617	−	0.138617i	0.634393	−	0.773010i	$-0.281250\pi$
$239$	−0.138617	−	0.138617i	−0.138617	−	0.138617i	−0.773010	+	0.634393i	$0.781250\pi$
$240$	−0.485544	+	1.17221i	−0.485544	+	1.17221i
$241$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$241$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$242$	−2.02024	−	0.612832i	−2.02024	−	0.612832i
$243$	−0.555570	−	0.831470i	−0.555570	−	0.831470i
$244$			0.765367i			0.765367i
$245$	0.247528	+	1.24441i	0.247528	+	1.24441i
$246$	−0.187593	+	0.0569057i	−0.187593	+	0.0569057i
$247$		0			0
$248$		0			0
$249$	−1.83886	+	0.761681i	−1.83886	+	0.761681i
$250$	−0.314060	−	0.382683i	−0.314060	−	0.382683i
$251$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$251$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$252$		0			0
$253$		0			0
$254$	0.858923	+	0.704900i	0.858923	+	0.704900i
$255$		0			0
$256$	0.707107	−	0.707107i	0.707107	−	0.707107i
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$	1.28547	+	1.05496i	1.28547	+	1.05496i
$259$		0			0
$260$	0.247528	+	1.24441i	0.247528	+	1.24441i
$261$		0			0
$262$		0			0
$263$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$263$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$264$	1.55557	+	0.831470i	1.55557	+	0.831470i
$265$		0			0
$266$		0			0
$267$	−0.113263	−	0.569414i	−0.113263	−	0.569414i
$268$		0			0
$269$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$269$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$270$	1.21415	+	0.368309i	1.21415	+	0.368309i
$271$		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
$274$	0.902197	+	1.68789i	0.902197	+	1.68789i
$275$	0.894350	−	0.597585i	0.894350	−	0.597585i
$276$		0			0
$277$	1.92388	−	0.382683i	1.92388	−	0.382683i	0.923880	−	0.382683i	$-0.125000\pi$
$277$	1.92388	−	0.382683i	1.92388	−	0.382683i	1.00000			$0$
$278$	−0.924678	+	1.72995i	−0.924678	+	1.72995i
$279$		0			0
$280$		0			0
$281$	0.591637	+	1.42834i	0.591637	+	1.42834i	0.881921	+	0.471397i	$0.156250\pi$
$281$	0.591637	+	1.42834i	0.591637	+	1.42834i	−0.290285	+	0.956940i	$0.593750\pi$
$282$	−0.0569057	+	0.577774i	−0.0569057	+	0.577774i
$283$	1.53636	+	1.02656i	1.53636	+	1.02656i	0.980785	+	0.195090i	$0.0625000\pi$
$283$	1.53636	+	1.02656i	1.53636	+	1.02656i	0.555570	+	0.831470i	$0.312500\pi$
$284$	−0.523788	−	0.783904i	−0.523788	−	0.783904i
$285$		0			0
$286$	1.75535	−	0.172887i	1.75535	−	0.172887i
$287$		0			0
$288$	−0.773010	−	0.634393i	−0.773010	−	0.634393i
$289$			1.00000i			1.00000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.59133	−	1.06330i	−1.59133	−	1.06330i	−0.956940	−	0.290285i	$-0.906250\pi$
$293$	−1.59133	−	1.06330i	−1.59133	−	1.06330i	−0.634393	−	0.773010i	$-0.718750\pi$
$294$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$295$	−0.750661	−	1.81225i	−0.750661	−	1.81225i
$296$		0			0
$297$	0.674993	−	1.62958i	0.674993	−	1.62958i
$298$	1.68789	+	0.902197i	1.68789	+	0.902197i
$299$		0			0
$300$	−0.563400	+	0.233368i	−0.563400	+	0.233368i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.686662	+	0.686662i	−0.686662	+	0.686662i
$306$		0			0
$307$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$307$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$308$		0			0
$309$	0.275899	+	1.38704i	0.275899	+	1.38704i
$310$		0			0
$311$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$311$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$312$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$313$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.980785	−	0.195090i	$-0.937500\pi$
$313$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.555570	+	0.831470i	$0.687500\pi$
$314$	−0.858923	+	0.704900i	−0.858923	+	0.704900i
$315$		0			0
$316$	−1.38268	−	0.923880i	−1.38268	−	0.923880i
$317$	0.569414	+	0.113263i	0.569414	+	0.113263i	0.471397	−	0.881921i	$-0.343750\pi$
$317$	0.569414	+	0.113263i	0.569414	+	0.113263i	0.0980171	+	0.995185i	$0.468750\pi$
$318$		0			0
$319$		0			0
$320$	1.26879			1.26879
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$325$	−0.338797	+	0.507046i	−0.338797	+	0.507046i
$326$		0			0
$327$		0			0
$328$	0.124363	+	0.151537i	0.124363	+	0.151537i
$329$		0			0
$330$	0.649640	+	2.14157i	0.649640	+	2.14157i
$331$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$331$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$332$	1.40740	+	1.40740i	1.40740	+	1.40740i
$333$		0			0
$334$	−0.577774	+	1.90466i	−0.577774	+	1.90466i
$335$		0			0
$336$		0			0
$337$	−0.785695	−	0.785695i	−0.785695	−	0.785695i	0.195090	−	0.980785i	$-0.437500\pi$
$337$	−0.785695	−	0.785695i	−0.785695	−	0.785695i	−0.980785	+	0.195090i	$0.937500\pi$
$338$	−0.881921	+	0.471397i	−0.881921	+	0.471397i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	0.482726	−	1.59133i	0.482726	−	1.59133i
$345$		0			0
$346$		0			0
$347$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$347$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$348$		0			0
$349$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$349$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$350$		0			0
$351$			1.00000i			1.00000i
$352$	0.172887	−	1.75535i	0.172887	−	1.75535i
$353$			1.99037i			1.99037i	0.0980171	+	0.995185i	$0.468750\pi$
$353$			1.99037i			1.99037i	−0.0980171	+	0.995185i	$0.531250\pi$
$354$	1.53858	−	0.151537i	1.53858	−	0.151537i
$355$	0.233368	−	1.17322i	0.233368	−	1.17322i
$356$	−0.482726	+	0.322547i	−0.482726	+	0.322547i
$357$		0			0
$358$		0			0
$359$	−0.732410	−	1.76820i	−0.732410	−	1.76820i	−0.634393	−	0.773010i	$-0.718750\pi$
$359$	−0.732410	−	1.76820i	−0.732410	−	1.76820i	−0.0980171	−	0.995185i	$-0.531250\pi$
$360$	−0.124363	−	1.26268i	−0.124363	−	1.26268i
$361$	0.382683	−	0.923880i	0.382683	−	0.923880i
$362$	0.924678	−	1.72995i	0.924678	−	1.72995i
$363$	2.07058	−	0.411863i	2.07058	−	0.411863i
$364$		0			0
$365$		0			0
$366$	−0.360791	−	0.674993i	−0.360791	−	0.674993i
$367$	0.541196	+	0.541196i	0.541196	+	0.541196i	0.923880	−	0.382683i	$-0.125000\pi$
$367$	0.541196	+	0.541196i	0.541196	+	0.541196i	−0.382683	+	0.923880i	$0.625000\pi$
$368$		0			0
$369$	0.138617	−	0.138617i	0.138617	−	0.138617i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.360480	+	1.81225i	0.360480	+	1.81225i	0.555570	+	0.831470i	$0.312500\pi$
$373$	0.360480	+	1.81225i	0.360480	+	1.81225i	−0.195090	+	0.980785i	$0.562500\pi$
$374$		0			0
$375$	0.457372	+	0.189450i	0.457372	+	0.189450i
$376$	0.555570	−	0.168530i	0.555570	−	0.168530i
$377$		0			0
$378$		0			0
$379$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$379$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$380$		0			0
$381$	−1.08979	−	0.216773i	−1.08979	−	0.216773i
$382$		0			0
$383$	−1.99037			−1.99037			−0.995185	−	0.0980171i	$-0.968750\pi$
$383$	−1.99037			−1.99037			−0.995185	+	0.0980171i	$0.968750\pi$
$384$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$385$		0			0
$386$		0			0
$387$	−1.63099	−	0.324423i	−1.63099	−	0.324423i
$388$		0			0
$389$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$389$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$390$	−0.804910	−	0.980785i	−0.804910	−	0.980785i
$391$		0			0
$392$	0.290285	+	0.956940i	0.290285	+	0.956940i
$393$		0			0
$394$	−0.902197	+	0.273678i	−0.902197	+	0.273678i
$395$	−0.411624	−	2.06937i	−0.411624	−	2.06937i
$396$	−1.76384			−1.76384
$397$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$397$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$398$	1.87711	+	0.569414i	1.87711	+	0.569414i
$399$		0			0
$400$	0.431207	+	0.431207i	0.431207	+	0.431207i
$401$	0.666656	+	0.666656i	0.666656	+	0.666656i	0.956940	−	0.290285i	$-0.0937500\pi$
$401$	0.666656	+	0.666656i	0.666656	+	0.666656i	−0.290285	+	0.956940i	$0.593750\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.24441	+	0.247528i	−1.24441	+	0.247528i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$409$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$410$	−0.0243794	+	0.247528i	−0.0243794	+	0.247528i
$411$	−1.59133	−	1.06330i	−1.59133	−	1.06330i
$412$	1.17588	−	0.785695i	1.17588	−	0.785695i
$413$		0			0
$414$		0			0
$415$			2.52535i			2.52535i
$416$	0.290285	+	0.956940i	0.290285	+	0.956940i
$417$		−	1.96157i		−	1.96157i
$418$		0			0
$419$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$419$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$420$		0			0
$421$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$421$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$422$	0.761681	+	0.0750191i	0.761681	+	0.0750191i
$423$	−0.222174	−	0.536376i	−0.222174	−	0.536376i
$424$		0			0
$425$		0			0
$426$	0.831470	+	0.444430i	0.831470	+	0.444430i
$427$		0			0
$428$		0			0
$429$	−1.46658	+	0.979938i	−1.46658	+	0.979938i
$430$	1.86078	−	0.994607i	1.86078	−	0.994607i
$431$	−1.40740	−	1.40740i	−1.40740	−	1.40740i	−0.773010	−	0.634393i	$-0.781250\pi$
$431$	−1.40740	−	1.40740i	−1.40740	−	1.40740i	−0.634393	−	0.773010i	$-0.718750\pi$
$432$	0.980785	+	0.195090i	0.980785	+	0.195090i
$433$	1.38704	−	1.38704i	1.38704	−	1.38704i	0.555570	−	0.831470i	$-0.312500\pi$
$433$	1.38704	−	1.38704i	1.38704	−	1.38704i	0.831470	−	0.555570i	$-0.187500\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.707107	+	0.292893i	0.707107	+	0.292893i	0.707107	−	0.707107i	$-0.250000\pi$
$439$	0.707107	+	0.292893i	0.707107	+	0.292893i			1.00000i	$0.5\pi$
$440$	1.72995	−	1.41973i	1.72995	−	1.41973i
$441$	0.923880	−	0.382683i	0.923880	−	0.382683i
$442$		0			0
$443$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$443$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$444$		0			0
$445$	−0.722465	−	0.143707i	−0.722465	−	0.143707i
$446$		0			0
$447$	−1.91388			−1.91388
$448$		0			0
$449$	0.580569			0.580569			0.290285	−	0.956940i	$-0.406250\pi$
$449$	0.580569			0.580569			0.290285	+	0.956940i	$0.406250\pi$
$450$	0.386865	−	0.471397i	0.386865	−	0.471397i
$451$	0.339130	+	0.0674571i	0.339130	+	0.0674571i
$452$		0			0
$453$		0			0
$454$	−1.47945	+	1.21415i	−1.47945	+	1.21415i
$455$		0			0
$456$		0			0
$457$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$457$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.979938	−	1.46658i	−0.979938	−	1.46658i	−0.881921	−	0.471397i	$-0.843750\pi$
$461$	−0.979938	−	1.46658i	−0.979938	−	1.46658i	−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		0.831470	−	0.555570i	$-0.187500\pi$
$467$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$468$	0.923880	−	0.382683i	0.923880	−	0.382683i
$469$		0			0
$470$	0.649640	+	0.347240i	0.649640	+	0.347240i
$471$	0.425215	−	1.02656i	0.425215	−	1.02656i
$472$	−0.728789	−	1.36347i	−0.728789	−	1.36347i
$473$	−1.12247	−	2.70989i	−1.12247	−	2.70989i
$474$	1.65493	+	0.162997i	1.65493	+	0.162997i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.0192147	−	0.195090i	−0.0192147	−	0.195090i
$479$			1.76384i			1.76384i	0.471397	+	0.881921i	$0.343750\pi$
$479$			1.76384i			1.76384i	−0.471397	+	0.881921i	$0.656250\pi$
$480$	−1.11897	+	0.598102i	−1.11897	+	0.598102i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.17289	−	1.75535i	−1.17289	−	1.75535i
$485$		0			0
$486$	0.0980171	−	0.995185i	0.0980171	−	0.995185i
$487$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$487$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$488$	−0.485544	+	0.591637i	−0.485544	+	0.591637i
$489$		0			0
$490$	−0.598102	+	1.11897i	−0.598102	+	1.11897i
$491$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$491$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$492$	−0.181112	−	0.0750191i	−0.181112	−	0.0750191i
$493$		0			0
$494$		0			0
$495$	−1.58246	−	1.58246i	−1.58246	−	1.58246i
$496$		0			0
$497$		0			0
$498$	−1.90466	−	0.577774i	−1.90466	−	0.577774i
$499$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$499$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$500$		−	0.495056i		−	0.495056i
$501$	−0.388302	−	1.95213i	−0.388302	−	1.95213i
$502$		0			0
$503$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$503$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.555570	−	0.831470i	0.555570	−	0.831470i
$508$	0.216773	+	1.08979i	0.216773	+	1.08979i
$509$	−0.192268	−	0.0382444i	−0.192268	−	0.0382444i	0.0980171	−	0.995185i	$-0.468750\pi$
$509$	−0.192268	−	0.0382444i	−0.192268	−	0.0382444i	−0.290285	+	0.956940i	$0.593750\pi$
$510$		0			0
$511$		0			0
$512$	0.995185	−	0.0980171i	0.995185	−	0.0980171i
$513$		0			0
$514$		0			0
$515$	1.75986	+	0.350057i	1.75986	+	0.350057i
$516$	0.324423	+	1.63099i	0.324423	+	1.63099i
$517$	0.568922	−	0.851452i	0.568922	−	0.851452i
$518$		0			0
$519$		0			0
$520$	−0.598102	+	1.11897i	−0.598102	+	1.11897i
$521$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$521$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$522$		0			0
$523$	−0.382683	−	1.92388i	−0.382683	−	1.92388i	−0.382683	−	0.923880i	$-0.625000\pi$
$523$	−0.382683	−	1.92388i	−0.382683	−	1.92388i		−	1.00000i	$-0.5\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.674993	+	1.62958i	0.674993	+	1.62958i
$529$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$530$		0			0
$531$	−1.28547	+	0.858923i	−1.28547	+	0.858923i
$532$		0			0
$533$	−0.192268	+	0.0382444i	−0.192268	+	0.0382444i
$534$	0.273678	−	0.512016i	0.273678	−	0.512016i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.46658	+	0.979938i	1.46658	+	0.979938i
$540$	0.704900	+	1.05496i	0.704900	+	1.05496i
$541$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$541$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$542$		0			0
$543$			1.96157i			1.96157i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.0761205	+	0.382683i	−0.0761205	+	0.382683i	0.923880	+	0.382683i	$0.125000\pi$
$547$	−0.0761205	+	0.382683i	−0.0761205	+	0.382683i	−1.00000			$\pi$
$548$	−0.373380	+	1.87711i	−0.373380	+	1.87711i
$549$	0.636379	+	0.425215i	0.636379	+	0.425215i
$550$	1.07045	+	0.105430i	1.07045	+	0.105430i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	1.72995	+	0.924678i	1.72995	+	0.924678i
$555$		0			0
$556$	−1.81225	+	0.750661i	−1.81225	+	0.750661i
$557$	−1.65493	+	1.10579i	−1.65493	+	1.10579i	−0.773010	+	0.634393i	$0.781250\pi$
$557$	−1.65493	+	1.10579i	−1.65493	+	1.10579i	−0.881921	+	0.471397i	$0.843750\pi$
$558$		0			0
$559$	1.17588	+	1.17588i	1.17588	+	1.17588i
$560$		0			0
$561$		0			0
$562$	−0.448786	+	1.47945i	−0.448786	+	1.47945i
$563$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$563$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$564$	−0.410525	+	0.410525i	−0.410525	+	0.410525i
$565$		0			0
$566$	0.536376	+	1.76820i	0.536376	+	1.76820i
$567$		0			0
$568$	0.0924099	−	0.938254i	0.0924099	−	0.938254i
$569$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$569$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$570$		0			0
$571$	1.02656	−	1.53636i	1.02656	−	1.53636i	0.195090	−	0.980785i	$-0.437500\pi$
$571$	1.02656	−	1.53636i	1.02656	−	1.53636i	0.831470	−	0.555570i	$-0.187500\pi$
$572$	1.46658	+	0.979938i	1.46658	+	0.979938i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.17221	+	0.485544i	1.17221	+	0.485544i
$586$	−0.555570	−	1.83147i	−0.555570	−	1.83147i
$587$	0.247528	+	1.24441i	0.247528	+	1.24441i	0.881921	+	0.471397i	$0.156250\pi$
$587$	0.247528	+	1.24441i	0.247528	+	1.24441i	−0.634393	+	0.773010i	$0.718750\pi$
$588$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$589$		0			0
$590$	0.569414	−	1.87711i	0.569414	−	1.87711i
$591$	0.666656	−	0.666656i	0.666656	−	0.666656i
$592$		0			0
$593$	−1.09320	−	1.09320i	−1.09320	−	1.09320i	−0.995185	−	0.0980171i	$-0.968750\pi$
$593$	−1.09320	−	1.09320i	−1.09320	−	1.09320i	−0.0980171	−	0.995185i	$-0.531250\pi$
$594$	1.55557	−	0.831470i	1.55557	−	0.831470i
$595$		0			0
$596$	0.732410	+	1.76820i	0.732410	+	1.76820i
$597$	−1.92388	+	0.382683i	−1.92388	+	0.382683i
$598$		0			0
$599$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$599$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$600$	−0.583561	−	0.177021i	−0.583561	−	0.177021i
$601$	0.750661	+	1.81225i	0.750661	+	1.81225i	0.555570	+	0.831470i	$0.312500\pi$
$601$	0.750661	+	1.81225i	0.750661	+	1.81225i	0.195090	+	0.980785i	$0.437500\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.522566	−	2.62712i	0.522566	−	2.62712i
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$	−0.966411	+	0.0951832i	−0.966411	+	0.0951832i
$611$	−0.113263	+	0.569414i	−0.113263	+	0.569414i
$612$		0			0
$613$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$613$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$614$		0			0
$615$	−0.0951832	−	0.229793i	−0.0951832	−	0.229793i
$616$		0			0
$617$	0.485544	−	1.17221i	0.485544	−	1.17221i	−0.471397	−	0.881921i	$-0.656250\pi$
$617$	0.485544	−	1.17221i	0.485544	−	1.17221i	0.956940	−	0.290285i	$-0.0937500\pi$
$618$	−0.666656	+	1.24723i	−0.666656	+	1.24723i
$619$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$619$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$625$	0.875356	−	0.875356i	0.875356	−	0.875356i
$626$	−1.59133	−	0.482726i	−1.59133	−	0.482726i
$627$		0			0
$628$	−1.11114			−1.11114
$629$		0			0
$630$		0			0
$631$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$631$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$632$	−0.482726	−	1.59133i	−0.482726	−	1.59133i
$633$	−0.707107	+	0.292893i	−0.707107	+	0.292893i
$634$	0.368309	+	0.448786i	0.368309	+	0.448786i
$635$	−0.783243	+	1.17221i	−0.783243	+	1.17221i
$636$		0			0
$637$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$638$		0			0
$639$	−0.942793			−0.942793
$640$	0.980785	+	0.804910i	0.980785	+	0.804910i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		0			0
$643$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$643$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$644$		0			0
$645$	−1.17221	+	1.75433i	−1.17221	+	1.75433i
$646$		0			0
$647$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$647$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$648$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$649$	−2.51936	−	1.04355i	−2.51936	−	1.04355i
$650$	−0.583561	+	0.177021i	−0.583561	+	0.177021i
$651$		0			0
$652$		0			0
$653$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$653$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$654$		0			0
$655$		0			0
$656$			0.196034i			0.196034i
$657$		0			0
$658$		0			0
$659$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$659$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$660$	−0.856422	+	2.06759i	−0.856422	+	2.06759i
$661$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$661$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$662$		0			0
$663$		0			0
$664$	0.195090	+	1.98079i	0.195090	+	1.98079i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−1.65493	+	1.10579i	−1.65493	+	1.10579i
$669$		0			0
$670$		0			0
$671$			1.34999i			1.34999i
$672$		0			0
$673$			1.84776i			1.84776i	0.382683	+	0.923880i	$0.375000\pi$
$673$			1.84776i			1.84776i	−0.382683	+	0.923880i	$0.625000\pi$
$674$	−0.108911	−	1.10579i	−0.108911	−	1.10579i
$675$	−0.118970	+	0.598102i	−0.118970	+	0.598102i
$676$	−0.980785	−	0.195090i	−0.980785	−	0.195090i
$677$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$677$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.732410	−	1.76820i	0.732410	−	1.76820i
$682$		0			0
$683$	1.51631	−	0.301614i	1.51631	−	0.301614i	0.634393	−	0.773010i	$-0.281250\pi$
$683$	1.51631	−	0.301614i	1.51631	−	0.301614i	0.881921	+	0.471397i	$0.156250\pi$
$684$		0			0
$685$	−2.01906	+	1.34909i	−2.01906	+	1.34909i
$686$		0			0
$687$		0			0
$688$	1.38268	−	0.923880i	1.38268	−	0.923880i
$689$		0			0
$690$		0			0
$691$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$691$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.29936	−	0.952428i	−2.29936	−	0.952428i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$701$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$702$	−0.634393	+	0.773010i	−0.634393	+	0.773010i
$703$		0			0
$704$	1.24723	−	1.24723i	1.24723	−	1.24723i
$705$	−0.736619			−0.736619
$706$	−1.26268	+	1.53858i	−1.26268	+	1.53858i
$707$		0			0
$708$	1.28547	+	0.858923i	1.28547	+	0.858923i
$709$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$709$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$710$	0.924678	−	0.758864i	0.924678	−	0.758864i
$711$	−1.53636	+	0.636379i	−1.53636	+	0.636379i
$712$	−0.577774	−	0.0569057i	−0.577774	−	0.0569057i
$713$		0			0
$714$		0			0
$715$	0.436600	+	2.19494i	0.436600	+	2.19494i
$716$		0			0
$717$	0.108911	+	0.162997i	0.108911	+	0.162997i
$718$	0.555570	−	1.83147i	0.555570	−	1.83147i
$719$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$719$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$720$	0.704900	−	1.05496i	0.704900	−	1.05496i
$721$		0			0
$722$	0.881921	−	0.471397i	0.881921	−	0.471397i
$723$		0			0
$724$	1.81225	−	0.750661i	1.81225	−	0.750661i
$725$		0			0
$726$	1.86186	+	0.995185i	1.86186	+	0.995185i
$727$	0.149316	−	0.360480i	0.149316	−	0.360480i	−0.831470	−	0.555570i	$-0.812500\pi$
$727$	0.149316	−	0.360480i	0.149316	−	0.360480i	0.980785	+	0.195090i	$0.0625000\pi$
$728$		0			0
$729$	0.382683	+	0.923880i	0.382683	+	0.923880i
$730$		0			0
$731$		0			0
$732$	0.149316	−	0.750661i	0.149316	−	0.750661i
$733$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$733$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$734$	0.0750191	+	0.761681i	0.0750191	+	0.761681i
$735$		−	1.26879i		−	1.26879i
$736$		0			0
$737$		0			0
$738$	0.195090	−	0.0192147i	0.195090	−	0.0192147i
$739$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$739$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.0750191	+	0.181112i	0.0750191	+	0.181112i	0.956940	−	0.290285i	$-0.0937500\pi$
$743$	0.0750191	+	0.181112i	0.0750191	+	0.181112i	−0.881921	+	0.471397i	$0.843750\pi$
$744$		0			0
$745$	−0.929273	+	2.24346i	−0.929273	+	2.24346i
$746$	−0.871028	+	1.62958i	−0.871028	+	1.62958i
$747$	1.95213	−	0.388302i	1.95213	−	0.388302i
$748$		0			0
$749$		0			0
$750$	0.233368	+	0.436600i	0.233368	+	0.436600i
$751$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.923880	+	0.382683i	$0.125000\pi$
$751$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.382683	+	0.923880i	$0.375000\pi$
$752$	0.536376	+	0.222174i	0.536376	+	0.222174i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.149316	+	0.750661i	0.149316	+	0.750661i	0.980785	+	0.195090i	$0.0625000\pi$
$757$	0.149316	+	0.750661i	0.149316	+	0.750661i	−0.831470	+	0.555570i	$0.812500\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.871028	+	0.360791i	−0.871028	+	0.360791i	−0.773010	−	0.634393i	$-0.781250\pi$
$761$	−0.871028	+	0.360791i	−0.871028	+	0.360791i	−0.0980171	+	0.995185i	$0.531250\pi$
$762$	−0.704900	−	0.858923i	−0.704900	−	0.858923i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−1.53858	−	1.26268i	−1.53858	−	1.26268i
$767$	1.54602			1.54602
$768$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.10579	−	1.65493i	1.10579	−	1.65493i	0.471397	−	0.881921i	$-0.343750\pi$
$773$	1.10579	−	1.65493i	1.10579	−	1.65493i	0.634393	−	0.773010i	$-0.281250\pi$
$774$	−1.05496	−	1.28547i	−1.05496	−	1.28547i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		−	1.26879i		−	1.26879i
$781$	−0.923880	−	1.38268i	−0.923880	−	1.38268i
$782$		0			0
$783$		0			0
$784$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$785$	−0.996879	−	0.996879i	−0.996879	−	0.996879i
$786$		0			0
$787$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$787$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$788$	−0.871028	−	0.360791i	−0.871028	−	0.360791i
$789$		0			0
$790$	0.994607	−	1.86078i	0.994607	−	1.86078i
$791$		0			0
$792$	−1.36347	−	1.11897i	−1.36347	−	1.11897i
$793$	−0.292893	−	0.707107i	−0.292893	−	0.707107i
$794$		0			0
$795$		0			0
$796$	1.08979	+	1.63099i	1.08979	+	1.63099i
$797$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$797$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$798$		0			0
$799$		0			0
$800$	0.0597727	+	0.606883i	0.0597727	+	0.606883i
$801$			0.580569i			0.580569i
$802$	0.0924099	+	0.938254i	0.0924099	+	0.938254i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$809$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$810$	−1.11897	−	0.598102i	−1.11897	−	0.598102i
$811$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$811$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−0.175876	+	0.175876i	−0.175876	+	0.175876i
$821$	−0.183930	−	0.924678i	−0.183930	−	0.924678i	−0.956940	−	0.290285i	$-0.906250\pi$
$821$	−0.183930	−	0.924678i	−0.183930	−	0.924678i	0.773010	−	0.634393i	$-0.218750\pi$
$822$	−0.555570	−	1.83147i	−0.555570	−	1.83147i
$823$	1.70711	+	0.707107i	1.70711	+	0.707107i	1.00000			$0$
$823$	1.70711	+	0.707107i	1.70711	+	0.707107i	0.707107	+	0.707107i	$0.250000\pi$
$824$	1.40740	+	0.138617i	1.40740	+	0.138617i
$825$	−0.993748	+	0.411624i	−0.993748	+	0.411624i
$826$		0			0
$827$	0.704900	−	1.05496i	0.704900	−	1.05496i	−0.290285	−	0.956940i	$-0.593750\pi$
$827$	0.704900	−	1.05496i	0.704900	−	1.05496i	0.995185	−	0.0980171i	$-0.0312500\pi$
$828$		0			0
$829$	−1.38704	−	0.275899i	−1.38704	−	0.275899i	−0.555570	−	0.831470i	$-0.687500\pi$
$829$	−1.38704	−	0.275899i	−1.38704	−	0.275899i	−0.831470	+	0.555570i	$0.812500\pi$
$830$	−1.60207	+	1.95213i	−1.60207	+	1.95213i
$831$	−1.96157			−1.96157
$832$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$833$		0			0
$834$	1.24441	−	1.51631i	1.24441	−	1.51631i
$835$	−2.47683	−	0.492672i	−2.47683	−	0.492672i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.42834	+	0.591637i	−1.42834	+	0.591637i	−0.956940	−	0.290285i	$-0.906250\pi$
$839$	−1.42834	+	0.591637i	−1.42834	+	0.591637i	−0.471397	+	0.881921i	$0.656250\pi$
$840$		0			0
$841$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$842$		0			0
$843$	−0.301614	−	1.51631i	−0.301614	−	1.51631i
$844$	0.541196	+	0.541196i	0.541196	+	0.541196i
$845$	−0.704900	−	1.05496i	−0.704900	−	1.05496i
$846$	0.168530	−	0.555570i	0.168530	−	0.555570i
$847$		0			0
$848$		0			0
$849$	−1.30656	−	1.30656i	−1.30656	−	1.30656i
$850$		0			0
$851$		0			0
$852$	0.360791	+	0.871028i	0.360791	+	0.871028i
$853$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$853$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$857$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$858$	−1.75535	−	0.172887i	−1.75535	−	0.172887i
$859$	1.17588	+	0.785695i	1.17588	+	0.785695i	0.980785	−	0.195090i	$-0.0625000\pi$
$859$	1.17588	+	0.785695i	1.17588	+	0.785695i	0.195090	+	0.980785i	$0.437500\pi$
$860$	2.06937	+	0.411624i	2.06937	+	0.411624i
$861$		0			0
$862$	−0.195090	−	1.98079i	−0.195090	−	1.98079i
$863$			0.580569i			0.580569i	0.956940	+	0.290285i	$0.0937500\pi$
$863$			0.580569i			0.580569i	−0.956940	+	0.290285i	$0.906250\pi$
$864$	0.634393	+	0.773010i	0.634393	+	0.773010i
$865$		0			0
$866$	1.95213	−	0.192268i	1.95213	−	0.192268i
$867$	0.195090	−	0.980785i	0.195090	−	0.980785i
$868$		0			0
$869$	−2.43884	−	1.62958i	−2.43884	−	1.62958i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$877$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$878$	0.360791	+	0.674993i	0.360791	+	0.674993i
$879$	1.35332	+	1.35332i	1.35332	+	1.35332i
$880$	2.23794			2.23794
$881$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$881$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$882$	0.956940	+	0.290285i	0.956940	+	0.290285i
$883$	−0.425215	−	0.636379i	−0.425215	−	0.636379i	0.555570	−	0.831470i	$-0.312500\pi$
$883$	−0.425215	−	0.636379i	−0.425215	−	0.636379i	−0.980785	+	0.195090i	$0.937500\pi$
$884$		0			0
$885$	0.382683	+	1.92388i	0.382683	+	1.92388i
$886$		0			0
$887$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$887$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$888$		0			0
$889$		0			0
$890$	−0.467306	−	0.569414i	−0.467306	−	0.569414i
$891$	−0.979938	+	1.46658i	−0.979938	+	1.46658i
$892$		0			0
$893$		0			0
$894$	−1.47945	−	1.21415i	−1.47945	−	1.21415i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.448786	+	0.368309i	0.448786	+	0.368309i
$899$		0			0
$900$	0.598102	−	0.118970i	0.598102	−	0.118970i
$901$		0			0
$902$	0.219356	+	0.267287i	0.219356	+	0.267287i
$903$		0			0
$904$		0			0
$905$	2.29936	+	0.952428i	2.29936	+	0.952428i
$906$		0			0
$907$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	−0.831470	−	0.555570i	$-0.812500\pi$
$907$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	0.555570	−	0.831470i	$-0.312500\pi$
$908$	−1.91388			−1.91388
$909$		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
$913$	2.48244	+	2.48244i	2.48244	+	2.48244i
$914$		0			0
$915$	0.807429	−	0.539507i	0.807429	−	0.539507i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.149316	+	0.360480i	−0.149316	+	0.360480i	−0.980785	−	0.195090i	$-0.937500\pi$
$919$	−0.149316	+	0.360480i	−0.149316	+	0.360480i	0.831470	+	0.555570i	$0.187500\pi$
$920$		0			0
$921$		0			0
$922$	0.172887	−	1.75535i	0.172887	−	1.75535i
$923$	0.783904	+	0.523788i	0.783904	+	0.523788i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		−	1.41421i		−	1.41421i
$928$		0			0
$929$			1.26879i			1.26879i	0.773010	+	0.634393i	$0.218750\pi$
$929$			1.26879i			1.26879i	−0.773010	+	0.634393i	$0.781250\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.956940	+	0.290285i	0.956940	+	0.290285i
$937$	0.425215	−	1.02656i	0.425215	−	1.02656i	−0.555570	−	0.831470i	$-0.687500\pi$
$937$	0.425215	−	1.02656i	0.425215	−	1.02656i	0.980785	−	0.195090i	$-0.0625000\pi$
$938$		0			0
$939$	1.63099	−	0.324423i	1.63099	−	0.324423i
$940$	0.281892	+	0.680547i	0.281892	+	0.680547i
$941$	0.162997	−	0.108911i	0.162997	−	0.108911i	−0.471397	−	0.881921i	$-0.656250\pi$
$941$	0.162997	−	0.108911i	0.162997	−	0.108911i	0.634393	+	0.773010i	$0.281250\pi$
$942$	0.979938	−	0.523788i	0.979938	−	0.523788i
$943$		0			0
$944$	0.301614	−	1.51631i	0.301614	−	1.51631i
$945$		0			0
$946$	0.851452	−	2.80686i	0.851452	−	2.80686i
$947$	−1.06330	−	1.59133i	−1.06330	−	1.59133i	−0.773010	−	0.634393i	$-0.781250\pi$
$947$	−1.06330	−	1.59133i	−1.06330	−	1.59133i	−0.290285	−	0.956940i	$-0.593750\pi$
$948$	1.17588	+	1.17588i	1.17588	+	1.17588i
$949$		0			0
$950$		0			0
$951$	−0.536376	−	0.222174i	−0.536376	−	0.222174i
$952$		0			0
$953$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$953$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$954$		0			0
$955$		0			0
$956$	0.108911	−	0.162997i	0.108911	−	0.162997i
$957$		0			0
$958$	−1.11897	+	1.36347i	−1.11897	+	1.36347i
$959$		0			0
$960$	−1.24441	−	0.247528i	−1.24441	−	0.247528i
$961$	−1.00000			−1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$967$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$968$	0.206928	−	2.10097i	0.206928	−	2.10097i
$969$		0			0
$970$		0			0
$971$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$971$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$972$	0.707107	−	0.707107i	0.707107	−	0.707107i
$973$		0			0
$974$		0			0
$975$	0.431207	−	0.431207i	0.431207	−	0.431207i
$976$	−0.750661	+	0.149316i	−0.750661	+	0.149316i
$977$	0.138617	+	0.138617i	0.138617	+	0.138617i	0.773010	−	0.634393i	$-0.218750\pi$
$977$	0.138617	+	0.138617i	0.138617	+	0.138617i	−0.634393	+	0.773010i	$0.718750\pi$
$978$		0			0
$979$	−0.851452	+	0.568922i	−0.851452	+	0.568922i
$980$	−1.17221	+	0.485544i	−1.17221	+	0.485544i
$981$		0			0
$982$		0			0
$983$	0.591637	−	1.42834i	0.591637	−	1.42834i	−0.290285	−	0.956940i	$-0.593750\pi$
$983$	0.591637	−	1.42834i	0.591637	−	1.42834i	0.881921	−	0.471397i	$-0.156250\pi$
$984$	−0.0924099	−	0.172887i	−0.0924099	−	0.172887i
$985$	−0.457767	−	1.10515i	−0.457767	−	1.10515i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.219356	−	2.22716i	−0.219356	−	2.22716i
$991$			0.765367i			0.765367i	0.923880	+	0.382683i	$0.125000\pi$
$991$			0.765367i			0.765367i	−0.923880	+	0.382683i	$0.875000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.485544	+	2.44099i	−0.485544	+	2.44099i
$996$	−1.10579	−	1.65493i	−1.10579	−	1.65493i
$997$	−0.324423	−	0.216773i	−0.324423	−	0.216773i	0.382683	−	0.923880i	$-0.375000\pi$
$997$	−0.324423	−	0.216773i	−0.324423	−	0.216773i	−0.707107	+	0.707107i	$0.750000\pi$
$998$		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.1949.4	yes	32
3.2	odd	2	inner	2496.1.eh.a.1949.1	yes	32
13.12	even	2	inner	2496.1.eh.a.1949.1	yes	32
39.38	odd	2	CM	2496.1.eh.a.1949.4	yes	32
64.53	even	16	inner	2496.1.eh.a.1013.4	yes	32
192.53	odd	16	inner	2496.1.eh.a.1013.1	✓	32
832.181	even	16	inner	2496.1.eh.a.1013.1	✓	32
2496.1013	odd	16	inner	2496.1.eh.a.1013.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2496.1.eh.a.1013.1	✓	32	192.53	odd	16	inner
2496.1.eh.a.1013.1	✓	32	832.181	even	16	inner
2496.1.eh.a.1013.4	yes	32	64.53	even	16	inner
2496.1.eh.a.1013.4	yes	32	2496.1013	odd	16	inner
2496.1.eh.a.1949.1	yes	32	3.2	odd	2	inner
2496.1.eh.a.1949.1	yes	32	13.12	even	2	inner
2496.1.eh.a.1949.4	yes	32	1.1	even	1	trivial
2496.1.eh.a.1949.4	yes	32	39.38	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2496.eh (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.773010 + 0.634393i) q^{2} +(-0.980785 - 0.195090i) q^{3} +(0.195090 + 0.980785i) q^{4} +(-0.704900 + 1.05496i) q^{5} +(-0.634393 - 0.773010i) q^{6} +(-0.471397 + 0.881921i) q^{8} +(0.923880 + 0.382683i) q^{9} +(-1.21415 + 0.368309i) q^{10} +(0.344109 + 1.72995i) q^{11} -1.00000i q^{12} +(-0.555570 - 0.831470i) q^{13} +(0.897168 - 0.897168i) q^{15} +(-0.923880 + 0.382683i) q^{16} +(0.471397 + 0.881921i) q^{18} +(-1.17221 - 0.485544i) q^{20} +(-0.831470 + 1.55557i) q^{22} +(0.634393 - 0.773010i) q^{24} +(-0.233368 - 0.563400i) q^{25} +(0.0980171 - 0.995185i) q^{26} +(-0.831470 - 0.555570i) q^{27} +(1.26268 - 0.124363i) q^{30} +(-0.956940 - 0.290285i) q^{32} -1.76384i q^{33} +(-0.195090 + 0.980785i) q^{36} +(0.382683 + 0.923880i) q^{39} +(-0.598102 - 1.11897i) q^{40} +(0.0750191 - 0.181112i) q^{41} +(-1.63099 + 0.324423i) q^{43} +(-1.62958 + 0.674993i) q^{44} +(-1.05496 + 0.704900i) q^{45} +(-0.410525 - 0.410525i) q^{47} +(0.980785 - 0.195090i) q^{48} +(0.707107 - 0.707107i) q^{49} +(0.177021 - 0.583561i) q^{50} +(0.707107 - 0.707107i) q^{52} +(-0.290285 - 0.956940i) q^{54} +(-2.06759 - 0.856422i) q^{55} +(-0.858923 + 1.28547i) q^{59} +(1.05496 + 0.704900i) q^{60} +(0.750661 + 0.149316i) q^{61} +(-0.555570 - 0.831470i) q^{64} +1.26879 q^{65} +(1.11897 - 1.36347i) q^{66} +(-0.871028 + 0.360791i) q^{71} +(-0.773010 + 0.634393i) q^{72} +(0.118970 + 0.598102i) q^{75} +(-0.290285 + 0.956940i) q^{78} +(-1.17588 + 1.17588i) q^{79} +(0.247528 - 1.24441i) q^{80} +(0.707107 + 0.707107i) q^{81} +(0.172887 - 0.0924099i) q^{82} +(1.65493 - 1.10579i) q^{83} +(-1.46658 - 0.783904i) q^{86} +(-1.68789 - 0.512016i) q^{88} +(0.222174 + 0.536376i) q^{89} +(-1.26268 - 0.124363i) q^{90} +(-0.0569057 - 0.577774i) q^{94} +(0.881921 + 0.471397i) q^{96} +(0.995185 - 0.0980171i) q^{98} +(-0.344109 + 1.72995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{55} - 32 q^{75}+O(q^{100}) \) 32 * q - 32 * q^55 - 32 * q^75

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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