LMFDB - Embedded newform 3040.1.cn.a.189.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3040.189");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{64})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{32} + 1 $ x^32 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{32}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{32} + \cdots)$

Embedding invariants

Embedding label			189.4
Root			$0.634393 - 0.773010i$ of defining polynomial
Character	$\chi$	$=$	3040.189
Dual form			3040.1.cn.a.949.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.290285 - 0.956940i) q^{2} +(1.62958 + 0.674993i) q^{3} +(-0.831470 + 0.555570i) q^{4} +(0.382683 + 0.923880i) q^{5} +(0.172887 - 1.75535i) q^{6} +(0.773010 + 0.634393i) q^{8} +(1.49280 + 1.49280i) q^{9} +(0.773010 - 0.634393i) q^{10} +(-0.360480 + 0.149316i) q^{11} +(-1.72995 + 0.344109i) q^{12} +(0.0750191 - 0.181112i) q^{13} +1.76384i q^{15} +(0.382683 - 0.923880i) q^{16} +(0.995185 - 1.86186i) q^{18} +(-0.382683 + 0.923880i) q^{19} +(-0.831470 - 0.555570i) q^{20} +(0.247528 + 0.301614i) q^{22} +(0.831470 + 1.55557i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(-0.195090 - 0.0192147i) q^{26} +(0.750012 + 1.81069i) q^{27} +(1.68789 - 0.512016i) q^{30} +(-0.995185 - 0.0980171i) q^{32} -0.688217 q^{33} +(-2.07058 - 0.411863i) q^{36} +(-0.732410 - 1.76820i) q^{37} +(0.995185 + 0.0980171i) q^{38} +(0.244499 - 0.244499i) q^{39} +(-0.290285 + 0.956940i) q^{40} +(0.216773 - 0.324423i) q^{44} +(-0.807898 + 1.95044i) q^{45} +(1.24723 - 1.24723i) q^{48} -1.00000i q^{49} +(0.881921 + 0.471397i) q^{50} +(0.0382444 + 0.192268i) q^{52} +(0.871028 - 0.360791i) q^{53} +(1.51501 - 1.24333i) q^{54} +(-0.275899 - 0.275899i) q^{55} +(-1.24723 + 1.24723i) q^{57} +(-0.979938 - 1.46658i) q^{60} +(-1.81225 - 0.750661i) q^{61} +(0.195090 + 0.980785i) q^{64} +0.196034 q^{65} +(0.199779 + 0.658583i) q^{66} +(1.17221 + 0.485544i) q^{67} +(0.206928 + 2.10097i) q^{72} +(-1.47945 + 1.21415i) q^{74} +(-1.62958 + 0.674993i) q^{75} +(-0.195090 - 0.980785i) q^{76} +(-0.304945 - 0.162997i) q^{78} +1.00000 q^{80} +1.34577i q^{81} +(-0.373380 - 0.113263i) q^{88} +(2.10097 + 0.206928i) q^{90} -1.00000 q^{95} +(-1.55557 - 0.831470i) q^{96} +1.99037 q^{97} +(-0.956940 + 0.290285i) q^{98} +(-0.761024 - 0.315226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{66} + 32 q^{80} - 32 q^{95} - 32 q^{96} - 32 q^{99}+O(q^{100}) $ 32 * q - 32 * q^66 + 32 * q^80 - 32 * q^95 - 32 * q^96 - 32 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$2$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$3$	1.62958	+	0.674993i	1.62958	+	0.674993i	0.995185	−	0.0980171i	$-0.0312500\pi$
$3$	1.62958	+	0.674993i	1.62958	+	0.674993i	0.634393	+	0.773010i	$0.281250\pi$
$4$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$5$	0.382683	+	0.923880i	0.382683	+	0.923880i
$5$	0.382683	+	0.923880i	0.382683	+	0.923880i
$6$	0.172887	−	1.75535i	0.172887	−	1.75535i
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	0.773010	+	0.634393i	0.773010	+	0.634393i
$9$	1.49280	+	1.49280i	1.49280	+	1.49280i
$10$	0.773010	−	0.634393i	0.773010	−	0.634393i
$11$	−0.360480	+	0.149316i	−0.360480	+	0.149316i	−0.555570	−	0.831470i	$-0.687500\pi$
$11$	−0.360480	+	0.149316i	−0.360480	+	0.149316i	0.195090	+	0.980785i	$0.437500\pi$
$12$	−1.72995	+	0.344109i	−1.72995	+	0.344109i
$13$	0.0750191	−	0.181112i	0.0750191	−	0.181112i	−0.881921	−	0.471397i	$-0.843750\pi$
$13$	0.0750191	−	0.181112i	0.0750191	−	0.181112i	0.956940	+	0.290285i	$0.0937500\pi$
$14$		0			0
$15$			1.76384i			1.76384i
$16$	0.382683	−	0.923880i	0.382683	−	0.923880i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	0.995185	−	1.86186i	0.995185	−	1.86186i
$19$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$19$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$20$	−0.831470	−	0.555570i	−0.831470	−	0.555570i
$21$		0			0
$22$	0.247528	+	0.301614i	0.247528	+	0.301614i
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$	0.831470	+	1.55557i	0.831470	+	1.55557i
$25$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$26$	−0.195090	−	0.0192147i	−0.195090	−	0.0192147i
$27$	0.750012	+	1.81069i	0.750012	+	1.81069i
$28$		0			0
$29$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$29$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$30$	1.68789	−	0.512016i	1.68789	−	0.512016i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−0.995185	−	0.0980171i	−0.995185	−	0.0980171i
$33$	−0.688217			−0.688217
$34$		0			0
$35$		0			0
$36$	−2.07058	−	0.411863i	−2.07058	−	0.411863i
$37$	−0.732410	−	1.76820i	−0.732410	−	1.76820i	−0.634393	−	0.773010i	$-0.718750\pi$
$37$	−0.732410	−	1.76820i	−0.732410	−	1.76820i	−0.0980171	−	0.995185i	$-0.531250\pi$
$38$	0.995185	+	0.0980171i	0.995185	+	0.0980171i
$39$	0.244499	−	0.244499i	0.244499	−	0.244499i
$40$	−0.290285	+	0.956940i	−0.290285	+	0.956940i
$41$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$41$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$42$		0			0
$43$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$43$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$44$	0.216773	−	0.324423i	0.216773	−	0.324423i
$45$	−0.807898	+	1.95044i	−0.807898	+	1.95044i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	1.24723	−	1.24723i	1.24723	−	1.24723i
$49$		−	1.00000i		−	1.00000i
$50$	0.881921	+	0.471397i	0.881921	+	0.471397i
$51$		0			0
$52$	0.0382444	+	0.192268i	0.0382444	+	0.192268i
$53$	0.871028	−	0.360791i	0.871028	−	0.360791i	0.0980171	−	0.995185i	$-0.468750\pi$
$53$	0.871028	−	0.360791i	0.871028	−	0.360791i	0.773010	+	0.634393i	$0.218750\pi$
$54$	1.51501	−	1.24333i	1.51501	−	1.24333i
$55$	−0.275899	−	0.275899i	−0.275899	−	0.275899i
$56$		0			0
$57$	−1.24723	+	1.24723i	−1.24723	+	1.24723i
$58$		0			0
$59$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$59$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$60$	−0.979938	−	1.46658i	−0.979938	−	1.46658i
$61$	−1.81225	−	0.750661i	−1.81225	−	0.750661i	−0.980785	−	0.195090i	$-0.937500\pi$
$61$	−1.81225	−	0.750661i	−1.81225	−	0.750661i	−0.831470	−	0.555570i	$-0.812500\pi$
$62$		0			0
$63$		0			0
$64$	0.195090	+	0.980785i	0.195090	+	0.980785i
$65$	0.196034			0.196034
$66$	0.199779	+	0.658583i	0.199779	+	0.658583i
$67$	1.17221	+	0.485544i	1.17221	+	0.485544i	0.881921	−	0.471397i	$-0.156250\pi$
$67$	1.17221	+	0.485544i	1.17221	+	0.485544i	0.290285	+	0.956940i	$0.406250\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$71$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$72$	0.206928	+	2.10097i	0.206928	+	2.10097i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$	−1.47945	+	1.21415i	−1.47945	+	1.21415i
$75$	−1.62958	+	0.674993i	−1.62958	+	0.674993i
$76$	−0.195090	−	0.980785i	−0.195090	−	0.980785i
$77$		0			0
$78$	−0.304945	−	0.162997i	−0.304945	−	0.162997i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	1.00000			1.00000
$81$			1.34577i			1.34577i
$82$		0			0
$83$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$83$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.373380	−	0.113263i	−0.373380	−	0.113263i
$89$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$89$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$90$	2.10097	+	0.206928i	2.10097	+	0.206928i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.00000			−1.00000
$96$	−1.55557	−	0.831470i	−1.55557	−	0.831470i
$97$	1.99037			1.99037			0.995185	−	0.0980171i	$-0.0312500\pi$
$97$	1.99037			1.99037			0.995185	+	0.0980171i	$0.0312500\pi$
$98$	−0.956940	+	0.290285i	−0.956940	+	0.290285i
$99$	−0.761024	−	0.315226i	−0.761024	−	0.315226i
$100$	0.195090	−	0.980785i	0.195090	−	0.980785i
$101$	−0.149316	−	0.360480i	−0.149316	−	0.360480i	0.831470	−	0.555570i	$-0.187500\pi$
$101$	−0.149316	−	0.360480i	−0.149316	−	0.360480i	−0.980785	+	0.195090i	$0.937500\pi$
$102$		0			0
$103$	0.410525	−	0.410525i	0.410525	−	0.410525i	−0.471397	−	0.881921i	$-0.656250\pi$
$103$	0.410525	−	0.410525i	0.410525	−	0.410525i	0.881921	+	0.471397i	$0.156250\pi$
$104$	0.172887	−	0.0924099i	0.172887	−	0.0924099i
$105$		0			0
$106$	−0.598102	−	0.728789i	−0.598102	−	0.728789i
$107$	1.42834	−	0.591637i	1.42834	−	0.591637i	0.471397	−	0.881921i	$-0.343750\pi$
$107$	1.42834	−	0.591637i	1.42834	−	0.591637i	0.956940	+	0.290285i	$0.0937500\pi$
$108$	−1.62958	−	1.08885i	−1.62958	−	1.08885i
$109$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$109$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$110$	−0.183930	+	0.344109i	−0.183930	+	0.344109i
$111$		−	3.37578i		−	3.37578i
$112$		0			0
$113$			0.942793i			0.942793i	0.881921	+	0.471397i	$0.156250\pi$
$113$			0.942793i			0.942793i	−0.881921	+	0.471397i	$0.843750\pi$
$114$	1.55557	+	0.831470i	1.55557	+	0.831470i
$115$		0			0
$116$		0			0
$117$	0.382353	−	0.158376i	0.382353	−	0.158376i
$118$		0			0
$119$		0			0
$120$	−1.11897	+	1.36347i	−1.11897	+	1.36347i
$121$	−0.599456	+	0.599456i	−0.599456	+	0.599456i
$122$	−0.192268	+	1.95213i	−0.192268	+	1.95213i
$123$		0			0
$124$		0			0
$125$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$126$		0			0
$127$	1.26879			1.26879			0.634393	−	0.773010i	$-0.281250\pi$
$127$	1.26879			1.26879			0.634393	+	0.773010i	$0.281250\pi$
$128$	0.881921	−	0.471397i	0.881921	−	0.471397i
$129$		0			0
$130$	−0.0569057	−	0.187593i	−0.0569057	−	0.187593i
$131$	0.707107	+	0.292893i	0.707107	+	0.292893i	0.707107	−	0.707107i	$-0.250000\pi$
$131$	0.707107	+	0.292893i	0.707107	+	0.292893i			1.00000i	$0.5\pi$
$132$	0.572232	−	0.382353i	0.572232	−	0.382353i
$133$		0			0
$134$	0.124363	−	1.26268i	0.124363	−	1.26268i
$135$	−1.38584	+	1.38584i	−1.38584	+	1.38584i
$136$		0			0
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$		0			0
$139$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.980785	−	0.195090i	$-0.937500\pi$
$139$	−1.53636	+	0.636379i	−1.53636	+	0.636379i	−0.555570	+	0.831470i	$0.687500\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			0.0764888i			0.0764888i
$144$	1.95044	−	0.807898i	1.95044	−	0.807898i
$145$		0			0
$146$		0			0
$147$	0.674993	−	1.62958i	0.674993	−	1.62958i
$148$	1.59133	+	1.06330i	1.59133	+	1.06330i
$149$	1.53636	−	0.636379i	1.53636	−	0.636379i	0.555570	−	0.831470i	$-0.312500\pi$
$149$	1.53636	−	0.636379i	1.53636	−	0.636379i	0.980785	+	0.195090i	$0.0625000\pi$
$150$	1.11897	+	1.36347i	1.11897	+	1.36347i
$151$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$151$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$152$	−0.881921	+	0.471397i	−0.881921	+	0.471397i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.0674571	+	0.339130i	−0.0674571	+	0.339130i
$157$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$157$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$158$		0			0
$159$	1.66294			1.66294
$160$	−0.290285	−	0.956940i	−0.290285	−	0.956940i
$161$		0			0
$162$	1.28783	−	0.390657i	1.28783	−	0.390657i
$163$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$163$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$164$		0			0
$165$	−0.263369	−	0.635830i	−0.263369	−	0.635830i
$166$		0			0
$167$	−1.09320	+	1.09320i	−1.09320	+	1.09320i	−0.0980171	+	0.995185i	$0.531250\pi$
$167$	−1.09320	+	1.09320i	−1.09320	+	1.09320i	−0.995185	+	0.0980171i	$0.968750\pi$
$168$		0			0
$169$	0.679933	+	0.679933i	0.679933	+	0.679933i
$170$		0			0
$171$	−1.95044	+	0.807898i	−1.95044	+	0.807898i
$172$		0			0
$173$	0.485544	−	1.17221i	0.485544	−	1.17221i	−0.471397	−	0.881921i	$-0.656250\pi$
$173$	0.485544	−	1.17221i	0.485544	−	1.17221i	0.956940	−	0.290285i	$-0.0937500\pi$
$174$		0			0
$175$		0			0
$176$			0.390181i			0.390181i
$177$		0			0
$178$		0			0
$179$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$179$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$180$	−0.411863	−	2.07058i	−0.411863	−	2.07058i
$181$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$181$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$182$		0			0
$183$	−2.44652	−	2.44652i	−2.44652	−	2.44652i
$184$		0			0
$185$	1.35332	−	1.35332i	1.35332	−	1.35332i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	0.290285	+	0.956940i	0.290285	+	0.956940i
$191$	1.84776			1.84776			0.923880	−	0.382683i	$-0.125000\pi$
$191$	1.84776			1.84776			0.923880	+	0.382683i	$0.125000\pi$
$192$	−0.344109	+	1.72995i	−0.344109	+	1.72995i
$193$	−1.54602			−1.54602			−0.773010	−	0.634393i	$-0.781250\pi$
$193$	−1.54602			−1.54602			−0.773010	+	0.634393i	$0.781250\pi$
$194$	−0.577774	−	1.90466i	−0.577774	−	1.90466i
$195$	0.319453	+	0.132322i	0.319453	+	0.132322i
$196$	0.555570	+	0.831470i	0.555570	+	0.831470i
$197$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$197$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$198$	−0.0807393	+	0.819760i	−0.0807393	+	0.819760i
$199$	−1.30656	+	1.30656i	−1.30656	+	1.30656i	−0.382683	+	0.923880i	$0.625000\pi$
$199$	−1.30656	+	1.30656i	−1.30656	+	1.30656i	−0.923880	+	0.382683i	$0.875000\pi$
$200$	−0.995185	+	0.0980171i	−0.995185	+	0.0980171i
$201$	1.58246	+	1.58246i	1.58246	+	1.58246i
$202$	−0.301614	+	0.247528i	−0.301614	+	0.247528i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.512016	−	0.273678i	−0.512016	−	0.273678i
$207$		0			0
$208$	−0.138617	−	0.138617i	−0.138617	−	0.138617i
$209$		−	0.390181i		−	0.390181i
$210$		0			0
$211$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$211$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$212$	−0.523788	+	0.783904i	−0.523788	+	0.783904i
$213$		0			0
$214$	−0.980785	−	1.19509i	−0.980785	−	1.19509i
$215$		0			0
$216$	−0.568922	+	1.87549i	−0.568922	+	1.87549i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.382683	+	0.0761205i	0.382683	+	0.0761205i
$221$		0			0
$222$	−3.23042	+	0.979938i	−3.23042	+	0.979938i
$223$	−1.99037			−1.99037			−0.995185	−	0.0980171i	$-0.968750\pi$
$223$	−1.99037			−1.99037			−0.995185	+	0.0980171i	$0.968750\pi$
$224$		0			0
$225$	−2.11114			−2.11114
$226$	0.902197	−	0.273678i	0.902197	−	0.273678i
$227$	−1.83886	−	0.761681i	−1.83886	−	0.761681i	−0.956940	−	0.290285i	$-0.906250\pi$
$227$	−1.83886	−	0.761681i	−1.83886	−	0.761681i	−0.881921	−	0.471397i	$-0.843750\pi$
$228$	0.344109	−	1.72995i	0.344109	−	1.72995i
$229$	−0.636379	−	1.53636i	−0.636379	−	1.53636i	−0.831470	−	0.555570i	$-0.812500\pi$
$229$	−0.636379	−	1.53636i	−0.636379	−	1.53636i	0.195090	−	0.980785i	$-0.437500\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$233$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$234$	−0.262547	−	0.319915i	−0.262547	−	0.319915i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$239$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$240$	1.62958	+	0.674993i	1.62958	+	0.674993i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	0.747657	+	0.399631i	0.747657	+	0.399631i
$243$	−0.158376	+	0.382353i	−0.158376	+	0.382353i
$244$	1.92388	−	0.382683i	1.92388	−	0.382683i
$245$	0.923880	−	0.382683i	0.923880	−	0.382683i
$246$		0			0
$247$	0.138617	+	0.138617i	0.138617	+	0.138617i
$248$		0			0
$249$		0			0
$250$	−0.0980171	+	0.995185i	−0.0980171	+	0.995185i
$251$	−0.541196	−	1.30656i	−0.541196	−	1.30656i	−0.923880	−	0.382683i	$-0.875000\pi$
$251$	−0.541196	−	1.30656i	−0.541196	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$252$		0			0
$253$		0			0
$254$	−0.368309	−	1.21415i	−0.368309	−	1.21415i
$255$		0			0
$256$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$257$	1.54602			1.54602			0.773010	−	0.634393i	$-0.218750\pi$
$257$	1.54602			1.54602			0.773010	+	0.634393i	$0.218750\pi$
$258$		0			0
$259$		0			0
$260$	−0.162997	+	0.108911i	−0.162997	+	0.108911i
$261$		0			0
$262$	0.0750191	−	0.761681i	0.0750191	−	0.761681i
$263$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$263$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$264$	−0.531999	−	0.436600i	−0.531999	−	0.436600i
$265$	0.666656	+	0.666656i	0.666656	+	0.666656i
$266$		0			0
$267$		0			0
$268$	−1.24441	+	0.247528i	−1.24441	+	0.247528i
$269$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$269$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$270$	1.72846	+	0.923880i	1.72846	+	0.923880i
$271$		−	1.66294i		−	1.66294i	−0.555570	−	0.831470i	$-0.687500\pi$
$271$		−	1.66294i		−	1.66294i	0.555570	−	0.831470i	$-0.312500\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.149316	−	0.360480i	0.149316	−	0.360480i
$276$		0			0
$277$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$277$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$278$	1.05496	+	1.28547i	1.05496	+	1.28547i
$279$		0			0
$280$		0			0
$281$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$281$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$282$		0			0
$283$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$283$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$284$		0			0
$285$	−1.62958	−	0.674993i	−1.62958	−	0.674993i
$286$	0.0731952	−	0.0222035i	0.0731952	−	0.0222035i
$287$		0			0
$288$	−1.33929	−	1.63193i	−1.33929	−	1.63193i
$289$	−1.00000			−1.00000
$290$		0			0
$291$	3.24346	+	1.34349i	3.24346	+	1.34349i
$292$		0			0
$293$	−0.222174	−	0.536376i	−0.222174	−	0.536376i	0.773010	−	0.634393i	$-0.218750\pi$
$293$	−0.222174	−	0.536376i	−0.222174	−	0.536376i	−0.995185	+	0.0980171i	$0.968750\pi$
$294$	−1.75535	−	0.172887i	−1.75535	−	0.172887i
$295$		0			0
$296$	0.555570	−	1.83147i	0.555570	−	1.83147i
$297$	−0.540729	−	0.540729i	−0.540729	−	0.540729i
$298$	−1.05496	−	1.28547i	−1.05496	−	1.28547i
$299$		0			0
$300$	0.979938	−	1.46658i	0.979938	−	1.46658i
$301$		0			0
$302$		0			0
$303$		−	0.688217i		−	0.688217i
$304$	0.707107	+	0.707107i	0.707107	+	0.707107i
$305$		−	1.96157i		−	1.96157i
$306$		0			0
$307$	0.761681	−	1.83886i	0.761681	−	1.83886i	0.290285	−	0.956940i	$-0.406250\pi$
$307$	0.761681	−	1.83886i	0.761681	−	1.83886i	0.471397	−	0.881921i	$-0.343750\pi$
$308$		0			0
$309$	0.946083	−	0.391880i	0.946083	−	0.391880i
$310$		0			0
$311$	1.38704	+	1.38704i	1.38704	+	1.38704i	0.831470	+	0.555570i	$0.187500\pi$
$311$	1.38704	+	1.38704i	1.38704	+	1.38704i	0.555570	+	0.831470i	$0.312500\pi$
$312$	0.344109	−	0.0338917i	0.344109	−	0.0338917i
$313$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$313$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.42834	−	0.591637i	−1.42834	−	0.591637i	−0.471397	−	0.881921i	$-0.656250\pi$
$317$	−1.42834	−	0.591637i	−1.42834	−	0.591637i	−0.956940	+	0.290285i	$0.906250\pi$
$318$	−0.482726	−	1.59133i	−0.482726	−	1.59133i
$319$		0			0
$320$	−0.831470	+	0.555570i	−0.831470	+	0.555570i
$321$	2.72694			2.72694
$322$		0			0
$323$		0			0
$324$	−0.747672	−	1.11897i	−0.747672	−	1.11897i
$325$	0.0750191	+	0.181112i	0.0750191	+	0.181112i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−0.531999	+	0.436600i	−0.531999	+	0.436600i
$331$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$331$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$332$		0			0
$333$	1.54622	−	3.73291i	1.54622	−	3.73291i
$334$	1.36347	+	0.728789i	1.36347	+	0.728789i
$335$			1.26879i			1.26879i
$336$		0			0
$337$		−	1.91388i		−	1.91388i	−0.290285	−	0.956940i	$-0.593750\pi$
$337$		−	1.91388i		−	1.91388i	0.290285	−	0.956940i	$-0.406250\pi$
$338$	0.453281	−	0.848030i	0.453281	−	0.848030i
$339$	−0.636379	+	1.53636i	−0.636379	+	1.53636i
$340$		0			0
$341$		0			0
$342$	1.33929	+	1.63193i	1.33929	+	1.63193i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.26268	−	0.124363i	−1.26268	−	0.124363i
$347$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$347$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$348$		0			0
$349$	−1.30656	−	0.541196i	−1.30656	−	0.541196i	−0.382683	−	0.923880i	$-0.625000\pi$
$349$	−1.30656	−	0.541196i	−1.30656	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$350$		0			0
$351$	0.384203			0.384203
$352$	0.373380	−	0.113263i	0.373380	−	0.113263i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$359$	−1.17588	+	1.17588i	−1.17588	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$360$	−1.86186	+	0.995185i	−1.86186	+	0.995185i
$361$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$362$		0			0
$363$	−1.38149	+	0.572232i	−1.38149	+	0.572232i
$364$		0			0
$365$		0			0
$366$	−1.63099	+	3.05136i	−1.63099	+	3.05136i
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$		0			0
$369$		0			0
$370$	−1.68789	−	0.902197i	−1.68789	−	0.902197i
$371$		0			0
$372$		0			0
$373$	−1.62958	+	0.674993i	−1.62958	+	0.674993i	−0.995185	−	0.0980171i	$-0.968750\pi$
$373$	−1.62958	+	0.674993i	−1.62958	+	0.674993i	−0.634393	+	0.773010i	$0.718750\pi$
$374$		0			0
$375$	−1.24723	−	1.24723i	−1.24723	−	1.24723i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$379$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$380$	0.831470	−	0.555570i	0.831470	−	0.555570i
$381$	2.06759	+	0.856422i	2.06759	+	0.856422i
$382$	−0.536376	−	1.76820i	−0.536376	−	1.76820i
$383$	0.580569			0.580569			0.290285	−	0.956940i	$-0.406250\pi$
$383$	0.580569			0.580569			0.290285	+	0.956940i	$0.406250\pi$
$384$	1.75535	−	0.172887i	1.75535	−	0.172887i
$385$		0			0
$386$	0.448786	+	1.47945i	0.448786	+	1.47945i
$387$		0			0
$388$	−1.65493	+	1.10579i	−1.65493	+	1.10579i
$389$	0.292893	+	0.707107i	0.292893	+	0.707107i	1.00000			$0$
$389$	0.292893	+	0.707107i	0.292893	+	0.707107i	−0.707107	+	0.707107i	$0.750000\pi$
$390$	0.0338917	−	0.344109i	0.0338917	−	0.344109i
$391$		0			0
$392$	0.634393	−	0.773010i	0.634393	−	0.773010i
$393$	0.954585	+	0.954585i	0.954585	+	0.954585i
$394$		0			0
$395$		0			0
$396$	0.807898	−	0.160701i	0.807898	−	0.160701i
$397$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$397$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$398$	1.62958	+	0.871028i	1.62958	+	0.871028i
$399$		0			0
$400$	0.382683	+	0.923880i	0.382683	+	0.923880i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$	1.05496	−	1.97369i	1.05496	−	1.97369i
$403$		0			0
$404$	0.324423	+	0.216773i	0.324423	+	0.216773i
$405$	−1.24333	+	0.515005i	−1.24333	+	0.515005i
$406$		0			0
$407$	0.528038	+	0.528038i	0.528038	+	0.528038i
$408$		0			0
$409$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$409$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$410$		0			0
$411$		0			0
$412$	−0.113263	+	0.569414i	−0.113263	+	0.569414i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.0924099	+	0.172887i	−0.0924099	+	0.172887i
$417$	−2.93316			−2.93316
$418$	−0.373380	+	0.113263i	−0.373380	+	0.113263i
$419$	1.70711	+	0.707107i	1.70711	+	0.707107i	1.00000			$0$
$419$	1.70711	+	0.707107i	1.70711	+	0.707107i	0.707107	+	0.707107i	$0.250000\pi$
$420$		0			0
$421$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$421$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$422$		0			0
$423$		0			0
$424$	0.902197	+	0.273678i	0.902197	+	0.273678i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.858923	+	1.28547i	−0.858923	+	1.28547i
$429$	−0.0516294	+	0.124644i	−0.0516294	+	0.124644i
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	1.95988			1.95988
$433$		−	1.76384i		−	1.76384i	−0.471397	−	0.881921i	$-0.656250\pi$
$433$		−	1.76384i		−	1.76384i	0.471397	−	0.881921i	$-0.343750\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$439$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$440$	−0.0382444	−	0.388302i	−0.0382444	−	0.388302i
$441$	1.49280	−	1.49280i	1.49280	−	1.49280i
$442$		0			0
$443$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$443$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$444$	1.87549	+	2.80686i	1.87549	+	2.80686i
$445$		0			0
$446$	0.577774	+	1.90466i	0.577774	+	1.90466i
$447$	2.93316			2.93316
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	0.612832	+	2.02024i	0.612832	+	2.02024i
$451$		0			0
$452$	−0.523788	−	0.783904i	−0.523788	−	0.783904i
$453$		0			0
$454$	−0.195090	+	1.98079i	−0.195090	+	1.98079i
$455$		0			0
$456$	−1.75535	+	0.172887i	−1.75535	+	0.172887i
$457$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$457$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$458$	−1.28547	+	1.05496i	−1.28547	+	1.05496i
$459$		0			0
$460$		0			0
$461$	0.707107	−	1.70711i	0.707107	−	1.70711i		−	1.00000i	$-0.5\pi$
$461$	0.707107	−	1.70711i	0.707107	−	1.70711i	0.707107	−	0.707107i	$-0.250000\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$467$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$468$	−0.229926	+	0.344109i	−0.229926	+	0.344109i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$476$		0			0
$477$	1.83886	+	0.761681i	1.83886	+	0.761681i
$478$	1.35332	−	0.410525i	1.35332	−	0.410525i
$479$	−0.390181			−0.390181			−0.195090	−	0.980785i	$-0.562500\pi$
$479$	−0.390181			−0.390181			−0.195090	+	0.980785i	$0.562500\pi$
$480$	0.172887	−	1.75535i	0.172887	−	1.75535i
$481$	−0.375186			−0.375186
$482$		0			0
$483$		0			0
$484$	0.165390	−	0.831470i	0.165390	−	0.831470i
$485$	0.761681	+	1.83886i	0.761681	+	1.83886i
$486$	0.411863	+	0.0405650i	0.411863	+	0.0405650i
$487$	−0.666656	+	0.666656i	−0.666656	+	0.666656i	−0.956940	−	0.290285i	$-0.906250\pi$
$487$	−0.666656	+	0.666656i	−0.666656	+	0.666656i	0.290285	+	0.956940i	$0.406250\pi$
$488$	−0.924678	−	1.72995i	−0.924678	−	1.72995i
$489$		0			0
$490$	−0.634393	−	0.773010i	−0.634393	−	0.773010i
$491$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$491$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$492$		0			0
$493$		0			0
$494$	0.0924099	−	0.172887i	0.0924099	−	0.172887i
$495$		−	0.823726i		−	0.823726i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.425215	+	1.02656i	−0.425215	+	1.02656i	0.555570	+	0.831470i	$0.312500\pi$
$499$	−0.425215	+	1.02656i	−0.425215	+	1.02656i	−0.980785	+	0.195090i	$0.937500\pi$
$500$	0.980785	−	0.195090i	0.980785	−	0.195090i
$501$	−2.51936	+	1.04355i	−2.51936	+	1.04355i
$502$	−1.09320	+	0.897168i	−1.09320	+	0.897168i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$		0			0
$505$	0.275899	−	0.275899i	0.275899	−	0.275899i
$506$		0			0
$507$	0.649054	+	1.56695i	0.649054	+	1.56695i
$508$	−1.05496	+	0.704900i	−1.05496	+	0.704900i
$509$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$509$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$510$		0			0
$511$		0			0
$512$	−0.471397	+	0.881921i	−0.471397	+	0.881921i
$513$	−1.95988			−1.95988
$514$	−0.448786	−	1.47945i	−0.448786	−	1.47945i
$515$	0.536376	+	0.222174i	0.536376	+	0.222174i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.58246	−	1.58246i	1.58246	−	1.58246i
$520$	0.151537	+	0.124363i	0.151537	+	0.124363i
$521$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$521$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$522$		0			0
$523$	0.536376	−	0.222174i	0.536376	−	0.222174i	−0.0980171	−	0.995185i	$-0.531250\pi$
$523$	0.536376	−	0.222174i	0.536376	−	0.222174i	0.634393	+	0.773010i	$0.281250\pi$
$524$	−0.750661	+	0.149316i	−0.750661	+	0.149316i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.263369	+	0.635830i	−0.263369	+	0.635830i
$529$			1.00000i			1.00000i
$530$	0.444430	−	0.831470i	0.444430	−	0.831470i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.09320	+	1.09320i	1.09320	+	1.09320i
$536$	0.598102	+	1.11897i	0.598102	+	1.11897i
$537$		0			0
$538$		0			0
$539$	0.149316	+	0.360480i	0.149316	+	0.360480i
$540$	0.382353	−	1.92222i	0.382353	−	1.92222i
$541$	−1.02656	−	0.425215i	−1.02656	−	0.425215i	−0.195090	−	0.980785i	$-0.562500\pi$
$541$	−1.02656	−	0.425215i	−1.02656	−	0.425215i	−0.831470	+	0.555570i	$0.812500\pi$
$542$	−1.59133	+	0.482726i	−1.59133	+	0.482726i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.76820	−	0.732410i	−1.76820	−	0.732410i	−0.995185	−	0.0980171i	$-0.968750\pi$
$547$	−1.76820	−	0.732410i	−1.76820	−	0.732410i	−0.773010	−	0.634393i	$-0.781250\pi$
$548$		0			0
$549$	−1.58475	−	3.82592i	−1.58475	−	3.82592i
$550$	−0.388302	−	0.0382444i	−0.388302	−	0.0382444i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.11882	−	1.29186i	3.11882	−	1.29186i
$556$	0.923880	−	1.38268i	0.923880	−	1.38268i
$557$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$557$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.732410	+	1.76820i	−0.732410	+	1.76820i	−0.0980171	+	0.995185i	$0.531250\pi$
$563$	−0.732410	+	1.76820i	−0.732410	+	1.76820i	−0.634393	+	0.773010i	$0.718750\pi$
$564$		0			0
$565$	−0.871028	+	0.360791i	−0.871028	+	0.360791i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$569$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$570$	−0.172887	+	1.75535i	−0.172887	+	1.75535i
$571$	0.425215	+	1.02656i	0.425215	+	1.02656i	0.980785	+	0.195090i	$0.0625000\pi$
$571$	0.425215	+	1.02656i	0.425215	+	1.02656i	−0.555570	+	0.831470i	$0.687500\pi$
$572$	−0.0424949	−	0.0635981i	−0.0424949	−	0.0635981i
$573$	3.01107	+	1.24723i	3.01107	+	1.24723i
$574$		0			0
$575$		0			0
$576$	−1.17289	+	1.75535i	−1.17289	+	1.75535i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	0.290285	+	0.956940i	0.290285	+	0.956940i
$579$	−2.51936	−	1.04355i	−2.51936	−	1.04355i
$580$		0			0
$581$		0			0
$582$	0.344109	−	3.49379i	0.344109	−	3.49379i
$583$	−0.260116	+	0.260116i	−0.260116	+	0.260116i
$584$		0			0
$585$	0.292640	+	0.292640i	0.292640	+	0.292640i
$586$	−0.448786	+	0.368309i	−0.448786	+	0.368309i
$587$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$587$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$588$	0.344109	+	1.72995i	0.344109	+	1.72995i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.91388			−1.91388
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	−0.360480	+	0.674410i	−0.360480	+	0.674410i
$595$		0			0
$596$	−0.923880	+	1.38268i	−0.923880	+	1.38268i
$597$	−3.01107	+	1.24723i	−3.01107	+	1.24723i
$598$		0			0
$599$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$599$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$600$	−1.68789	−	0.512016i	−1.68789	−	0.512016i
$601$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$601$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$602$		0			0
$603$	1.02505	+	2.47469i	1.02505	+	2.47469i
$604$		0			0
$605$	−0.783227	−	0.324423i	−0.783227	−	0.324423i
$606$	−0.658583	+	0.199779i	−0.658583	+	0.199779i
$607$	0.942793			0.942793			0.471397	−	0.881921i	$-0.343750\pi$
$607$	0.942793			0.942793			0.471397	+	0.881921i	$0.343750\pi$
$608$	0.471397	−	0.881921i	0.471397	−	0.881921i
$609$		0			0
$610$	−1.87711	+	0.569414i	−1.87711	+	0.569414i
$611$		0			0
$612$		0			0
$613$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$613$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$614$	−1.98079	−	0.195090i	−1.98079	−	0.195090i
$615$		0			0
$616$		0			0
$617$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$617$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$618$	−0.649640	−	0.791588i	−0.649640	−	0.791588i
$619$	−1.81225	+	0.750661i	−1.81225	+	0.750661i	−0.831470	+	0.555570i	$0.812500\pi$
$619$	−1.81225	+	0.750661i	−1.81225	+	0.750661i	−0.980785	+	0.195090i	$0.937500\pi$
$620$		0			0
$621$		0			0
$622$	0.924678	−	1.72995i	0.924678	−	1.72995i
$623$		0			0
$624$	−0.132322	−	0.319453i	−0.132322	−	0.319453i
$625$		−	1.00000i		−	1.00000i
$626$		0			0
$627$	0.263369	−	0.635830i	0.263369	−	0.635830i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.785695	+	0.785695i	0.785695	+	0.785695i	0.980785	−	0.195090i	$-0.0625000\pi$
$631$	0.785695	+	0.785695i	0.785695	+	0.785695i	−0.195090	+	0.980785i	$0.562500\pi$
$632$		0			0
$633$		0			0
$634$	−0.151537	+	1.53858i	−0.151537	+	1.53858i
$635$	0.485544	+	1.17221i	0.485544	+	1.17221i
$636$	−1.38268	+	0.923880i	−1.38268	+	0.923880i
$637$	−0.181112	−	0.0750191i	−0.181112	−	0.0750191i
$638$		0			0
$639$		0			0
$640$	0.773010	+	0.634393i	0.773010	+	0.634393i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	−0.791588	−	2.60952i	−0.791588	−	2.60952i
$643$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$643$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	−0.853750	+	1.04030i	−0.853750	+	1.04030i
$649$		0			0
$650$	0.151537	−	0.124363i	0.151537	−	0.124363i
$651$		0			0
$652$		0			0
$653$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$653$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$654$		0			0
$655$			0.765367i			0.765367i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$659$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$660$	0.572232	+	0.382353i	0.572232	+	0.382353i
$661$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$661$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−4.02101	−	0.396035i	−4.02101	−	0.396035i
$667$		0			0
$668$	0.301614	−	1.51631i	0.301614	−	1.51631i
$669$	−3.24346	−	1.34349i	−3.24346	−	1.34349i
$670$	1.21415	−	0.368309i	1.21415	−	0.368309i
$671$	0.765367			0.765367
$672$		0			0
$673$	−1.91388			−1.91388			−0.956940	−	0.290285i	$-0.906250\pi$
$673$	−1.91388			−1.91388			−0.956940	+	0.290285i	$0.906250\pi$
$674$	−1.83147	+	0.555570i	−1.83147	+	0.555570i
$675$	−1.81069	−	0.750012i	−1.81069	−	0.750012i
$676$	−0.943094	−	0.187593i	−0.943094	−	0.187593i
$677$	0.732410	+	1.76820i	0.732410	+	1.76820i	0.634393	+	0.773010i	$0.281250\pi$
$677$	0.732410	+	1.76820i	0.732410	+	1.76820i	0.0980171	+	0.995185i	$0.468750\pi$
$678$	1.65493	+	0.162997i	1.65493	+	0.162997i
$679$		0			0
$680$		0			0
$681$	−2.48244	−	2.48244i	−2.48244	−	2.48244i
$682$		0			0
$683$	−1.76820	+	0.732410i	−1.76820	+	0.732410i	−0.773010	+	0.634393i	$0.781250\pi$
$683$	−1.76820	+	0.732410i	−1.76820	+	0.732410i	−0.995185	+	0.0980171i	$0.968750\pi$
$684$	1.17289	−	1.75535i	1.17289	−	1.75535i
$685$		0			0
$686$		0			0
$687$		−	2.93316i		−	2.93316i
$688$		0			0
$689$		−	0.184820i		−	0.184820i
$690$		0			0
$691$	−0.750661	+	1.81225i	−0.750661	+	1.81225i	−0.195090	+	0.980785i	$0.562500\pi$
$691$	−0.750661	+	1.81225i	−0.750661	+	1.81225i	−0.555570	+	0.831470i	$0.687500\pi$
$692$	0.247528	+	1.24441i	0.247528	+	1.24441i
$693$		0			0
$694$		0			0
$695$	−1.17588	−	1.17588i	−1.17588	−	1.17588i
$696$		0			0
$697$		0			0
$698$	−0.138617	+	1.40740i	−0.138617	+	1.40740i
$699$		0			0
$700$		0			0
$701$	1.02656	+	0.425215i	1.02656	+	0.425215i	0.831470	−	0.555570i	$-0.187500\pi$
$701$	1.02656	+	0.425215i	1.02656	+	0.425215i	0.195090	+	0.980785i	$0.437500\pi$
$702$	−0.111528	−	0.367659i	−0.111528	−	0.367659i
$703$	1.91388			1.91388
$704$	−0.216773	−	0.324423i	−0.216773	−	0.324423i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.541196	+	1.30656i	0.541196	+	1.30656i	0.923880	+	0.382683i	$0.125000\pi$
$709$	0.541196	+	1.30656i	0.541196	+	1.30656i	−0.382683	+	0.923880i	$0.625000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−0.0706664	+	0.0292710i	−0.0706664	+	0.0292710i
$716$		0			0
$717$	−0.954585	+	2.30457i	−0.954585	+	2.30457i
$718$	1.46658	+	0.783904i	1.46658	+	0.783904i
$719$		−	1.11114i		−	1.11114i	−0.831470	−	0.555570i	$-0.812500\pi$
$719$		−	1.11114i		−	1.11114i	0.831470	−	0.555570i	$-0.187500\pi$
$720$	1.49280	+	1.49280i	1.49280	+	1.49280i
$721$		0			0
$722$	−0.471397	+	0.881921i	−0.471397	+	0.881921i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.948617	+	1.15589i	0.948617	+	1.15589i
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$		0			0
$729$	0.435434	−	0.435434i	0.435434	−	0.435434i
$730$		0			0
$731$		0			0
$732$	3.39342	+	0.674993i	3.39342	+	0.674993i
$733$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$733$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$734$		0			0
$735$	1.76384			1.76384
$736$		0			0
$737$	−0.495056			−0.495056
$738$		0			0
$739$	−1.30656	−	0.541196i	−1.30656	−	0.541196i	−0.382683	−	0.923880i	$-0.625000\pi$
$739$	−1.30656	−	0.541196i	−1.30656	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$740$	−0.373380	+	1.87711i	−0.373380	+	1.87711i
$741$	0.132322	+	0.319453i	0.132322	+	0.319453i
$742$		0			0
$743$	0.138617	−	0.138617i	0.138617	−	0.138617i	−0.634393	−	0.773010i	$-0.718750\pi$
$743$	0.138617	−	0.138617i	0.138617	−	0.138617i	0.773010	+	0.634393i	$0.218750\pi$
$744$		0			0
$745$	1.17588	+	1.17588i	1.17588	+	1.17588i
$746$	1.11897	+	1.36347i	1.11897	+	1.36347i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−0.831470	+	1.55557i	−0.831470	+	1.55557i
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$		−	2.49445i		−	2.49445i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$757$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$758$		0			0
$759$		0			0
$760$	−0.773010	−	0.634393i	−0.773010	−	0.634393i
$761$	−1.38704	+	1.38704i	−1.38704	+	1.38704i	−0.555570	+	0.831470i	$0.687500\pi$
$761$	−1.38704	+	1.38704i	−1.38704	+	1.38704i	−0.831470	+	0.555570i	$0.812500\pi$
$762$	0.219356	−	2.22716i	0.219356	−	2.22716i
$763$		0			0
$764$	−1.53636	+	1.02656i	−1.53636	+	1.02656i
$765$		0			0
$766$	−0.168530	−	0.555570i	−0.168530	−	0.555570i
$767$		0			0
$768$	−0.674993	−	1.62958i	−0.674993	−	1.62958i
$769$	1.66294			1.66294			0.831470	−	0.555570i	$-0.187500\pi$
$769$	1.66294			1.66294			0.831470	+	0.555570i	$0.187500\pi$
$770$		0			0
$771$	2.51936	+	1.04355i	2.51936	+	1.04355i
$772$	1.28547	−	0.858923i	1.28547	−	0.858923i
$773$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.471397	+	0.881921i	$0.343750\pi$
$773$	0.761681	+	1.83886i	0.761681	+	1.83886i	0.290285	+	0.956940i	$0.406250\pi$
$774$		0			0
$775$		0			0
$776$	1.53858	+	1.26268i	1.53858	+	1.26268i
$777$		0			0
$778$	0.591637	−	0.485544i	0.591637	−	0.485544i
$779$		0			0
$780$	−0.339130	+	0.0674571i	−0.339130	+	0.0674571i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$785$		0			0
$786$	0.636379	−	1.19058i	0.636379	−	1.19058i
$787$	0.222174	−	0.536376i	0.222174	−	0.536376i	−0.773010	−	0.634393i	$-0.781250\pi$
$787$	0.222174	−	0.536376i	0.222174	−	0.536376i	0.995185	+	0.0980171i	$0.0312500\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.388302	−	0.726462i	−0.388302	−	0.726462i
$793$	−0.271907	+	0.271907i	−0.271907	+	0.271907i
$794$		0			0
$795$	0.636379	+	1.53636i	0.636379	+	1.53636i
$796$	0.360480	−	1.81225i	0.360480	−	1.81225i
$797$	−0.536376	−	0.222174i	−0.536376	−	0.222174i	0.0980171	−	0.995185i	$-0.468750\pi$
$797$	−0.536376	−	0.222174i	−0.536376	−	0.222174i	−0.634393	+	0.773010i	$0.718750\pi$
$798$		0			0
$799$		0			0
$800$	0.773010	−	0.634393i	0.773010	−	0.634393i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−2.19494	−	0.436600i	−2.19494	−	0.436600i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.113263	−	0.373380i	0.113263	−	0.373380i
$809$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	0.382683	−	0.923880i	$-0.375000\pi$
$809$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$810$	0.853750	+	1.04030i	0.853750	+	1.04030i
$811$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$811$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$812$		0			0
$813$	1.12247	−	2.70989i	1.12247	−	2.70989i
$814$	0.352020	−	0.658583i	0.352020	−	0.658583i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.707107	+	0.292893i	−0.707107	+	0.292893i	−0.707107	−	0.707107i	$-0.750000\pi$
$821$	−0.707107	+	0.292893i	−0.707107	+	0.292893i			1.00000i	$0.5\pi$
$822$		0			0
$823$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$823$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$824$	0.577774	−	0.0569057i	0.577774	−	0.0569057i
$825$	0.486643	−	0.486643i	0.486643	−	0.486643i
$826$		0			0
$827$	0.222174	+	0.536376i	0.222174	+	0.536376i	0.995185	−	0.0980171i	$-0.0312500\pi$
$827$	0.222174	+	0.536376i	0.222174	+	0.536376i	−0.773010	+	0.634393i	$0.781250\pi$
$828$		0			0
$829$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$829$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$830$		0			0
$831$		0			0
$832$	0.192268	+	0.0382444i	0.192268	+	0.0382444i
$833$		0			0
$834$	0.851452	+	2.80686i	0.851452	+	2.80686i
$835$	−1.42834	−	0.591637i	−1.42834	−	0.591637i
$836$	0.216773	+	0.324423i	0.216773	+	0.324423i
$837$		0			0
$838$	0.181112	−	1.83886i	0.181112	−	1.83886i
$839$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$839$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$840$		0			0
$841$	0.707107	+	0.707107i	0.707107	+	0.707107i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.367977	+	0.888375i	−0.367977	+	0.888375i
$846$		0			0
$847$		0			0
$848$		−	0.942793i		−	0.942793i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$853$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$854$		0			0
$855$	−1.49280	−	1.49280i	−1.49280	−	1.49280i
$856$	1.47945	+	0.448786i	1.47945	+	0.448786i
$857$	1.09320	−	1.09320i	1.09320	−	1.09320i	0.0980171	−	0.995185i	$-0.468750\pi$
$857$	1.09320	−	1.09320i	1.09320	−	1.09320i	0.995185	−	0.0980171i	$-0.0312500\pi$
$858$	0.134265	+	0.0132239i	0.134265	+	0.0132239i
$859$	−0.292893	−	0.707107i	−0.292893	−	0.707107i	0.707107	−	0.707107i	$-0.250000\pi$
$859$	−0.292893	−	0.707107i	−0.292893	−	0.707107i	−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.26879			−1.26879			−0.634393	−	0.773010i	$-0.718750\pi$
$863$	−1.26879			−1.26879			−0.634393	+	0.773010i	$0.718750\pi$
$864$	−0.568922	−	1.87549i	−0.568922	−	1.87549i
$865$	1.26879			1.26879
$866$	−1.68789	+	0.512016i	−1.68789	+	0.512016i
$867$	−1.62958	−	0.674993i	−1.62958	−	0.674993i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	0.175876	−	0.175876i	0.175876	−	0.175876i
$872$		0			0
$873$	2.97123	+	2.97123i	2.97123	+	2.97123i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.674993	+	1.62958i	−0.674993	+	1.62958i	0.0980171	+	0.995185i	$0.468750\pi$
$877$	−0.674993	+	1.62958i	−0.674993	+	1.62958i	−0.773010	+	0.634393i	$0.781250\pi$
$878$		0			0
$879$		−	1.02403i		−	1.02403i
$880$	−0.360480	+	0.149316i	−0.360480	+	0.149316i
$881$		−	1.66294i		−	1.66294i	−0.555570	−	0.831470i	$-0.687500\pi$
$881$		−	1.66294i		−	1.66294i	0.555570	−	0.831470i	$-0.312500\pi$
$882$	−1.86186	−	0.995185i	−1.86186	−	0.995185i
$883$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$883$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.666656	+	0.666656i	0.666656	+	0.666656i	0.956940	−	0.290285i	$-0.0937500\pi$
$887$	0.666656	+	0.666656i	0.666656	+	0.666656i	−0.290285	+	0.956940i	$0.593750\pi$
$888$	2.14157	−	2.60952i	2.14157	−	2.60952i
$889$		0			0
$890$		0			0
$891$	−0.200945	−	0.485124i	−0.200945	−	0.485124i
$892$	1.65493	−	1.10579i	1.65493	−	1.10579i
$893$		0			0
$894$	−0.851452	−	2.80686i	−0.851452	−	2.80686i
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	1.75535	−	1.17289i	1.75535	−	1.17289i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.598102	+	0.728789i	−0.598102	+	0.728789i
$905$		0			0
$906$		0			0
$907$	0.181112	−	0.0750191i	0.181112	−	0.0750191i	−0.290285	−	0.956940i	$-0.593750\pi$
$907$	0.181112	−	0.0750191i	0.181112	−	0.0750191i	0.471397	+	0.881921i	$0.343750\pi$
$908$	1.95213	−	0.388302i	1.95213	−	0.388302i
$909$	0.315226	−	0.761024i	0.315226	−	0.761024i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	0.674993	+	1.62958i	0.674993	+	1.62958i
$913$		0			0
$914$		0			0
$915$	1.32405	−	3.19653i	1.32405	−	3.19653i
$916$	1.38268	+	0.923880i	1.38268	+	0.923880i
$917$		0			0
$918$		0			0
$919$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$919$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$920$		0			0
$921$	2.48244	−	2.48244i	2.48244	−	2.48244i
$922$	−1.83886	−	0.181112i	−1.83886	−	0.181112i
$923$		0			0
$924$		0			0
$925$	1.76820	+	0.732410i	1.76820	+	0.732410i
$926$		0			0
$927$	1.22566			1.22566
$928$		0			0
$929$	1.84776			1.84776			0.923880	−	0.382683i	$-0.125000\pi$
$929$	1.84776			1.84776			0.923880	+	0.382683i	$0.125000\pi$
$930$		0			0
$931$	0.923880	+	0.382683i	0.923880	+	0.382683i
$932$		0			0
$933$	1.32405	+	3.19653i	1.32405	+	3.19653i
$934$		0			0
$935$		0			0
$936$	0.396035	+	0.120136i	0.396035	+	0.120136i
$937$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$937$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$941$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$947$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$948$		0			0
$949$		0			0
$950$	−0.773010	+	0.634393i	−0.773010	+	0.634393i
$951$	−1.92824	−	1.92824i	−1.92824	−	1.92824i
$952$		0			0
$953$	1.40740	−	1.40740i	1.40740	−	1.40740i	0.634393	−	0.773010i	$-0.281250\pi$
$953$	1.40740	−	1.40740i	1.40740	−	1.40740i	0.773010	−	0.634393i	$-0.218750\pi$
$954$	0.195090	−	1.98079i	0.195090	−	1.98079i
$955$	0.707107	+	1.70711i	0.707107	+	1.70711i
$956$	−0.785695	−	1.17588i	−0.785695	−	1.17588i
$957$		0			0
$958$	0.113263	+	0.373380i	0.113263	+	0.373380i
$959$		0			0
$960$	−1.72995	+	0.344109i	−1.72995	+	0.344109i
$961$	1.00000			1.00000
$962$	0.108911	+	0.359031i	0.108911	+	0.359031i
$963$	3.01542	+	1.24903i	3.01542	+	1.24903i
$964$		0			0
$965$	−0.591637	−	1.42834i	−0.591637	−	1.42834i
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	−0.843677	+	0.0830949i	−0.843677	+	0.0830949i
$969$		0			0
$970$	1.53858	−	1.26268i	1.53858	−	1.26268i
$971$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$971$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$972$	−0.0807393	−	0.405904i	−0.0807393	−	0.405904i
$973$		0			0
$974$	0.831470	+	0.444430i	0.831470	+	0.444430i
$975$			0.345774i			0.345774i
$976$	−1.38704	+	1.38704i	−1.38704	+	1.38704i
$977$			0.580569i			0.580569i	0.956940	+	0.290285i	$0.0937500\pi$
$977$			0.580569i			0.580569i	−0.956940	+	0.290285i	$0.906250\pi$
$978$		0			0
$979$		0			0
$980$	−0.555570	+	0.831470i	−0.555570	+	0.831470i
$981$		0			0
$982$		0			0
$983$	0.410525	+	0.410525i	0.410525	+	0.410525i	0.881921	−	0.471397i	$-0.156250\pi$
$983$	0.410525	+	0.410525i	0.410525	+	0.410525i	−0.471397	+	0.881921i	$0.656250\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.192268	−	0.0382444i	−0.192268	−	0.0382444i
$989$		0			0
$990$	−0.788257	+	0.239115i	−0.788257	+	0.239115i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.70711	−	0.707107i	−1.70711	−	0.707107i
$996$		0			0
$997$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$997$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$998$	1.10579	+	0.108911i	1.10579	+	0.108911i
$999$	2.65234	−	2.65234i	2.65234	−	2.65234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3040.1.cn.a.189.4	✓	32
5.4	even	2	inner	3040.1.cn.a.189.5	yes	32
19.18	odd	2	inner	3040.1.cn.a.189.5	yes	32
32.21	even	8	inner	3040.1.cn.a.949.4	yes	32
95.94	odd	2	CM	3040.1.cn.a.189.4	✓	32
160.149	even	8	inner	3040.1.cn.a.949.5	yes	32
608.341	odd	8	inner	3040.1.cn.a.949.5	yes	32
3040.949	odd	8	inner	3040.1.cn.a.949.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3040.1.cn.a.189.4	✓	32	1.1	even	1	trivial
3040.1.cn.a.189.4	✓	32	95.94	odd	2	CM
3040.1.cn.a.189.5	yes	32	5.4	even	2	inner
3040.1.cn.a.189.5	yes	32	19.18	odd	2	inner
3040.1.cn.a.949.4	yes	32	32.21	even	8	inner
3040.1.cn.a.949.4	yes	32	3040.949	odd	8	inner
3040.1.cn.a.949.5	yes	32	160.149	even	8	inner
3040.1.cn.a.949.5	yes	32	608.341	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.290285 - 0.956940i) q^{2} +(1.62958 + 0.674993i) q^{3} +(-0.831470 + 0.555570i) q^{4} +(0.382683 + 0.923880i) q^{5} +(0.172887 - 1.75535i) q^{6} +(0.773010 + 0.634393i) q^{8} +(1.49280 + 1.49280i) q^{9} +(0.773010 - 0.634393i) q^{10} +(-0.360480 + 0.149316i) q^{11} +(-1.72995 + 0.344109i) q^{12} +(0.0750191 - 0.181112i) q^{13} +1.76384i q^{15} +(0.382683 - 0.923880i) q^{16} +(0.995185 - 1.86186i) q^{18} +(-0.382683 + 0.923880i) q^{19} +(-0.831470 - 0.555570i) q^{20} +(0.247528 + 0.301614i) q^{22} +(0.831470 + 1.55557i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(-0.195090 - 0.0192147i) q^{26} +(0.750012 + 1.81069i) q^{27} +(1.68789 - 0.512016i) q^{30} +(-0.995185 - 0.0980171i) q^{32} -0.688217 q^{33} +(-2.07058 - 0.411863i) q^{36} +(-0.732410 - 1.76820i) q^{37} +(0.995185 + 0.0980171i) q^{38} +(0.244499 - 0.244499i) q^{39} +(-0.290285 + 0.956940i) q^{40} +(0.216773 - 0.324423i) q^{44} +(-0.807898 + 1.95044i) q^{45} +(1.24723 - 1.24723i) q^{48} -1.00000i q^{49} +(0.881921 + 0.471397i) q^{50} +(0.0382444 + 0.192268i) q^{52} +(0.871028 - 0.360791i) q^{53} +(1.51501 - 1.24333i) q^{54} +(-0.275899 - 0.275899i) q^{55} +(-1.24723 + 1.24723i) q^{57} +(-0.979938 - 1.46658i) q^{60} +(-1.81225 - 0.750661i) q^{61} +(0.195090 + 0.980785i) q^{64} +0.196034 q^{65} +(0.199779 + 0.658583i) q^{66} +(1.17221 + 0.485544i) q^{67} +(0.206928 + 2.10097i) q^{72} +(-1.47945 + 1.21415i) q^{74} +(-1.62958 + 0.674993i) q^{75} +(-0.195090 - 0.980785i) q^{76} +(-0.304945 - 0.162997i) q^{78} +1.00000 q^{80} +1.34577i q^{81} +(-0.373380 - 0.113263i) q^{88} +(2.10097 + 0.206928i) q^{90} -1.00000 q^{95} +(-1.55557 - 0.831470i) q^{96} +1.99037 q^{97} +(-0.956940 + 0.290285i) q^{98} +(-0.761024 - 0.315226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{66} + 32 q^{80} - 32 q^{95} - 32 q^{96} - 32 q^{99}+O(q^{100}) \) 32 * q - 32 * q^66 + 32 * q^80 - 32 * q^95 - 32 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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