LMFDB - Embedded newform 1288.1.bi.e.685.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1288,1,Mod(13,1288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1288, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 14]))

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

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

chi := DirichletCharacter("1288.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1288 = 2^{3} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1288.bi (of order $22$, degree $10$, 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:	$0.642795736271$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{44})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 11 $
Twist minimal:	yes
Projective image:	$D_{22}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{22} - \cdots)$

Embedding invariants

Embedding label			685.2
Root			$-0.755750 - 0.654861i$ of defining polynomial
Character	$\chi$	$=$	1288.685
Dual form			1288.1.bi.e.1021.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.959493 + 0.281733i) q^{2} +(0.989821 - 1.14231i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.258908 + 1.80075i) q^{5} +(1.27155 - 0.817178i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.182822 - 1.27155i) q^{9} +(-0.755750 + 1.65486i) q^{10} +(1.45027 - 0.425839i) q^{12} +(-0.234072 + 0.512546i) q^{13} +(-0.142315 - 0.989821i) q^{14} +(1.80075 + 2.07817i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.182822 - 1.27155i) q^{18} +(-1.66538 - 1.07028i) q^{19} +(-1.19136 + 1.37491i) q^{20} +(-1.45027 - 0.425839i) q^{21} +(0.415415 - 0.909632i) q^{23} +1.51150 q^{24} +(-2.21616 - 0.650724i) q^{25} +(-0.368991 + 0.425839i) q^{26} +(-0.361922 - 0.232593i) q^{27} +(0.142315 - 0.989821i) q^{28} +(1.14231 + 2.50132i) q^{30} +(0.142315 + 0.989821i) q^{32} +(1.74557 - 0.512546i) q^{35} +(0.533654 - 1.16854i) q^{36} +(-1.29639 - 1.49611i) q^{38} +(0.353799 + 0.774713i) q^{39} +(-1.53046 + 0.983568i) q^{40} +(-1.27155 - 0.817178i) q^{42} +2.33708 q^{45} +(0.654861 - 0.755750i) q^{46} +(1.45027 + 0.425839i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-1.94306 - 1.24873i) q^{50} +(-0.474017 + 0.304632i) q^{52} +(-0.281733 - 0.325137i) q^{54} +(0.415415 - 0.909632i) q^{56} +(-2.87102 + 0.843008i) q^{57} +(0.822373 - 1.80075i) q^{59} +(0.391340 + 2.72183i) q^{60} +(-1.08070 + 0.694523i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.862362 - 0.554206i) q^{65} +(-0.627899 - 1.37491i) q^{69} +1.81926 q^{70} +(-1.84125 - 0.540641i) q^{71} +(0.841254 - 0.970858i) q^{72} +(-2.93694 + 1.88745i) q^{75} +(-0.822373 - 1.80075i) q^{76} +(0.121206 + 0.843008i) q^{78} +(-0.698939 + 1.53046i) q^{79} +(-1.74557 + 0.512546i) q^{80} +(0.608660 - 0.178719i) q^{81} +(0.153882 + 1.07028i) q^{83} +(-0.989821 - 1.14231i) q^{84} +(2.24241 + 0.658432i) q^{90} +0.563465 q^{91} +(0.841254 - 0.540641i) q^{92} +(2.35848 - 2.72183i) q^{95} +(1.27155 + 0.817178i) q^{96} +(-0.841254 + 0.540641i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9} - 2 q^{14} - 2 q^{16} + 20 q^{18} - 2 q^{23} + 2 q^{25} + 2 q^{28} + 22 q^{30} + 2 q^{32} + 2 q^{36} - 22 q^{39} + 2 q^{46} - 2 q^{49} - 2 q^{50}+ \cdots + 2 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 2 * q^8 - 20 * q^9 - 2 * q^14 - 2 * q^16 + 20 * q^18 - 2 * q^23 + 2 * q^25 + 2 * q^28 + 22 * q^30 + 2 * q^32 + 2 * q^36 - 22 * q^39 + 2 * q^46 - 2 * q^49 - 2 * q^50 - 2 * q^56 - 2 * q^63 - 2 * q^64 - 18 * q^71 - 2 * q^72 + 4 * q^79 + 20 * q^81 - 2 * q^92 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1288\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$645$	$967$
$\chi(n)$	$-1$	$e\left(\frac{6}{11}\right)$	$-1$	$1$

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 $

$2$	0.959493	+	0.281733i	0.959493	+	0.281733i
$2$	0.959493	+	0.281733i	0.959493	+	0.281733i
$3$	0.989821	−	1.14231i	0.989821	−	1.14231i		−	1.00000i	$-0.5\pi$
$3$	0.989821	−	1.14231i	0.989821	−	1.14231i	0.989821	−	0.142315i	$-0.0454545\pi$
$4$	0.841254	+	0.540641i	0.841254	+	0.540641i
$5$	−0.258908	+	1.80075i	−0.258908	+	1.80075i	0.281733	+	0.959493i	$0.409091\pi$
$5$	−0.258908	+	1.80075i	−0.258908	+	1.80075i	−0.540641	+	0.841254i	$0.681818\pi$
$6$	1.27155	−	0.817178i	1.27155	−	0.817178i
$7$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$7$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$8$	0.654861	+	0.755750i	0.654861	+	0.755750i
$9$	−0.182822	−	1.27155i	−0.182822	−	1.27155i
$10$	−0.755750	+	1.65486i	−0.755750	+	1.65486i
$11$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$11$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$12$	1.45027	−	0.425839i	1.45027	−	0.425839i
$13$	−0.234072	+	0.512546i	−0.234072	+	0.512546i	−0.989821	−	0.142315i	$-0.954545\pi$
$13$	−0.234072	+	0.512546i	−0.234072	+	0.512546i	0.755750	+	0.654861i	$0.227273\pi$
$14$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$15$	1.80075	+	2.07817i	1.80075	+	2.07817i
$16$	0.415415	+	0.909632i	0.415415	+	0.909632i
$17$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$17$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$18$	0.182822	−	1.27155i	0.182822	−	1.27155i
$19$	−1.66538	−	1.07028i	−1.66538	−	1.07028i	−0.909632	−	0.415415i	$-0.863636\pi$
$19$	−1.66538	−	1.07028i	−1.66538	−	1.07028i	−0.755750	−	0.654861i	$-0.772727\pi$
$20$	−1.19136	+	1.37491i	−1.19136	+	1.37491i
$21$	−1.45027	−	0.425839i	−1.45027	−	0.425839i
$22$		0			0
$23$	0.415415	−	0.909632i	0.415415	−	0.909632i
$23$	0.415415	−	0.909632i	0.415415	−	0.909632i
$24$	1.51150			1.51150
$25$	−2.21616	−	0.650724i	−2.21616	−	0.650724i
$26$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$27$	−0.361922	−	0.232593i	−0.361922	−	0.232593i
$28$	0.142315	−	0.989821i	0.142315	−	0.989821i
$29$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$29$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$30$	1.14231	+	2.50132i	1.14231	+	2.50132i
$31$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$31$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$32$	0.142315	+	0.989821i	0.142315	+	0.989821i
$33$		0			0
$34$		0			0
$35$	1.74557	−	0.512546i	1.74557	−	0.512546i
$36$	0.533654	−	1.16854i	0.533654	−	1.16854i
$37$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$37$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$38$	−1.29639	−	1.49611i	−1.29639	−	1.49611i
$39$	0.353799	+	0.774713i	0.353799	+	0.774713i
$40$	−1.53046	+	0.983568i	−1.53046	+	0.983568i
$41$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$41$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$42$	−1.27155	−	0.817178i	−1.27155	−	0.817178i
$43$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$43$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$44$		0			0
$45$	2.33708			2.33708
$46$	0.654861	−	0.755750i	0.654861	−	0.755750i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	1.45027	+	0.425839i	1.45027	+	0.425839i
$49$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$50$	−1.94306	−	1.24873i	−1.94306	−	1.24873i
$51$		0			0
$52$	−0.474017	+	0.304632i	−0.474017	+	0.304632i
$53$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$53$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$54$	−0.281733	−	0.325137i	−0.281733	−	0.325137i
$55$		0			0
$56$	0.415415	−	0.909632i	0.415415	−	0.909632i
$57$	−2.87102	+	0.843008i	−2.87102	+	0.843008i
$58$		0			0
$59$	0.822373	−	1.80075i	0.822373	−	1.80075i	0.281733	−	0.959493i	$-0.409091\pi$
$59$	0.822373	−	1.80075i	0.822373	−	1.80075i	0.540641	−	0.841254i	$-0.318182\pi$
$60$	0.391340	+	2.72183i	0.391340	+	2.72183i
$61$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$61$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$62$		0			0
$63$	−1.08070	+	0.694523i	−1.08070	+	0.694523i
$64$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$65$	−0.862362	−	0.554206i	−0.862362	−	0.554206i
$66$		0			0
$67$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$67$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$68$		0			0
$69$	−0.627899	−	1.37491i	−0.627899	−	1.37491i
$70$	1.81926			1.81926
$71$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−0.841254	−	0.540641i	$-0.818182\pi$
$71$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−1.00000			$\pi$
$72$	0.841254	−	0.970858i	0.841254	−	0.970858i
$73$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$73$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$74$		0			0
$75$	−2.93694	+	1.88745i	−2.93694	+	1.88745i
$76$	−0.822373	−	1.80075i	−0.822373	−	1.80075i
$77$		0			0
$78$	0.121206	+	0.843008i	0.121206	+	0.843008i
$79$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$79$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	−0.841254	+	0.540641i	$0.818182\pi$
$80$	−1.74557	+	0.512546i	−1.74557	+	0.512546i
$81$	0.608660	−	0.178719i	0.608660	−	0.178719i
$82$		0			0
$83$	0.153882	+	1.07028i	0.153882	+	1.07028i	0.909632	+	0.415415i	$0.136364\pi$
$83$	0.153882	+	1.07028i	0.153882	+	1.07028i	−0.755750	+	0.654861i	$0.772727\pi$
$84$	−0.989821	−	1.14231i	−0.989821	−	1.14231i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$89$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$90$	2.24241	+	0.658432i	2.24241	+	0.658432i
$91$	0.563465			0.563465
$92$	0.841254	−	0.540641i	0.841254	−	0.540641i
$93$		0			0
$94$		0			0
$95$	2.35848	−	2.72183i	2.35848	−	2.72183i
$96$	1.27155	+	0.817178i	1.27155	+	0.817178i
$97$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$97$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$98$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$99$		0			0
$100$	−1.51255	−	1.74557i	−1.51255	−	1.74557i
$101$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$101$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$102$		0			0
$103$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$103$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$104$	−0.540641	+	0.158746i	−0.540641	+	0.158746i
$105$	1.14231	−	2.50132i	1.14231	−	2.50132i
$106$		0			0
$107$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$107$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$108$	−0.178719	−	0.391340i	−0.178719	−	0.391340i
$109$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$109$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$110$		0			0
$111$		0			0
$112$	0.654861	−	0.755750i	0.654861	−	0.755750i
$113$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.959493	−	0.281733i	$-0.0909091\pi$
$113$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.654861	+	0.755750i	$0.272727\pi$
$114$	−2.99223			−2.99223
$115$	1.53046	+	0.983568i	1.53046	+	0.983568i
$116$		0			0
$117$	0.694523	+	0.203930i	0.694523	+	0.203930i
$118$	1.29639	−	1.49611i	1.29639	−	1.49611i
$119$		0			0
$120$	−0.391340	+	2.72183i	−0.391340	+	2.72183i
$121$	0.841254	−	0.540641i	0.841254	−	0.540641i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.989821	−	2.16741i	0.989821	−	2.16741i
$126$	−1.23259	+	0.361922i	−1.23259	+	0.361922i
$127$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$127$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$128$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$129$		0			0
$130$	−0.671292	−	0.774713i	−0.671292	−	0.774713i
$131$	0.755750	+	1.65486i	0.755750	+	1.65486i	0.755750	+	0.654861i	$0.227273\pi$
$131$	0.755750	+	1.65486i	0.755750	+	1.65486i			1.00000i	$0.5\pi$
$132$		0			0
$133$	−0.281733	+	1.95949i	−0.281733	+	1.95949i
$134$		0			0
$135$	0.512546	−	0.591509i	0.512546	−	0.591509i
$136$		0			0
$137$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$137$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$138$	−0.215109	−	1.49611i	−0.215109	−	1.49611i
$139$	−1.08128			−1.08128			−0.540641	−	0.841254i	$-0.681818\pi$
$139$	−1.08128			−1.08128			−0.540641	+	0.841254i	$0.681818\pi$
$140$	1.74557	+	0.512546i	1.74557	+	0.512546i
$141$		0			0
$142$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$143$		0			0
$144$	1.08070	−	0.694523i	1.08070	−	0.694523i
$145$		0			0
$146$		0			0
$147$	0.215109	+	1.49611i	0.215109	+	1.49611i
$148$		0			0
$149$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$149$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$150$	−3.34973	+	0.983568i	−3.34973	+	0.983568i
$151$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$151$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$152$	−0.281733	−	1.95949i	−0.281733	−	1.95949i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.121206	+	0.843008i	−0.121206	+	0.843008i
$157$	−0.909632	−	0.584585i	−0.909632	−	0.584585i		−	1.00000i	$-0.5\pi$
$157$	−0.909632	−	0.584585i	−0.909632	−	0.584585i	−0.909632	+	0.415415i	$0.863636\pi$
$158$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$159$		0			0
$160$	−1.81926			−1.81926
$161$	−1.00000			−1.00000
$162$	0.634356			0.634356
$163$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$163$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$164$		0			0
$165$		0			0
$166$	−0.153882	+	1.07028i	−0.153882	+	1.07028i
$167$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$167$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$168$	−0.627899	−	1.37491i	−0.627899	−	1.37491i
$169$	0.446947	+	0.515804i	0.446947	+	0.515804i
$170$		0			0
$171$	−1.05645	+	2.31329i	−1.05645	+	2.31329i
$172$		0			0
$173$	1.03748	−	0.304632i	1.03748	−	0.304632i	0.281733	−	0.959493i	$-0.409091\pi$
$173$	1.03748	−	0.304632i	1.03748	−	0.304632i	0.755750	+	0.654861i	$0.227273\pi$
$174$		0			0
$175$	0.328708	+	2.28621i	0.328708	+	2.28621i
$176$		0			0
$177$	−1.24302	−	2.72183i	−1.24302	−	2.72183i
$178$		0			0
$179$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$179$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$180$	1.96608	+	1.26352i	1.96608	+	1.26352i
$181$	0.989821	−	1.14231i	0.989821	−	1.14231i		−	1.00000i	$-0.5\pi$
$181$	0.989821	−	1.14231i	0.989821	−	1.14231i	0.989821	−	0.142315i	$-0.0454545\pi$
$182$	0.540641	+	0.158746i	0.540641	+	0.158746i
$183$		0			0
$184$	0.959493	−	0.281733i	0.959493	−	0.281733i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.0612263	+	0.425839i	−0.0612263	+	0.425839i
$190$	3.02977	−	1.94711i	3.02977	−	1.94711i
$191$	0.544078	+	1.19136i	0.544078	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$191$	0.544078	+	1.19136i	0.544078	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$192$	0.989821	+	1.14231i	0.989821	+	1.14231i
$193$	0.118239	+	0.822373i	0.118239	+	0.822373i	0.959493	+	0.281733i	$0.0909091\pi$
$193$	0.118239	+	0.822373i	0.118239	+	0.822373i	−0.841254	+	0.540641i	$0.818182\pi$
$194$		0			0
$195$	−1.48666	+	0.436524i	−1.48666	+	0.436524i
$196$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$197$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$197$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$198$		0			0
$199$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$199$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$200$	−0.959493	−	2.10100i	−0.959493	−	2.10100i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.23259	−	0.361922i	−1.23259	−	0.361922i
$208$	−0.563465			−0.563465
$209$		0			0
$210$	1.80075	−	2.07817i	1.80075	−	2.07817i
$211$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$211$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$212$		0			0
$213$	−2.44009	+	1.56815i	−2.44009	+	1.56815i
$214$		0			0
$215$		0			0
$216$	−0.0612263	−	0.425839i	−0.0612263	−	0.425839i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$223$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$224$	0.841254	−	0.540641i	0.841254	−	0.540641i
$225$	−0.422268	+	2.93694i	−0.422268	+	2.93694i
$226$	1.41542	+	0.909632i	1.41542	+	0.909632i
$227$	−0.708089	+	0.817178i	−0.708089	+	0.817178i	−0.989821	−	0.142315i	$-0.954545\pi$
$227$	−0.708089	+	0.817178i	−0.708089	+	0.817178i	0.281733	+	0.959493i	$0.409091\pi$
$228$	−2.87102	−	0.843008i	−2.87102	−	0.843008i
$229$	1.97964			1.97964			0.989821	−	0.142315i	$-0.0454545\pi$
$229$	1.97964			1.97964			0.989821	+	0.142315i	$0.0454545\pi$
$230$	1.19136	+	1.37491i	1.19136	+	1.37491i
$231$		0			0
$232$		0			0
$233$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$233$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$234$	0.608936	+	0.391340i	0.608936	+	0.391340i
$235$		0			0
$236$	1.66538	−	1.07028i	1.66538	−	1.07028i
$237$	1.05645	+	2.31329i	1.05645	+	2.31329i
$238$		0			0
$239$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$239$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$240$	−1.14231	+	2.50132i	−1.14231	+	2.50132i
$241$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$241$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$242$	0.959493	−	0.281733i	0.959493	−	0.281733i
$243$	0.577031	−	1.26352i	0.577031	−	1.26352i
$244$		0			0
$245$	−1.19136	−	1.37491i	−1.19136	−	1.37491i
$246$		0			0
$247$	0.938384	−	0.603063i	0.938384	−	0.603063i
$248$		0			0
$249$	1.37491	+	0.883600i	1.37491	+	0.883600i
$250$	1.56036	−	1.80075i	1.56036	−	1.80075i
$251$	1.45027	+	0.425839i	1.45027	+	0.425839i	0.909632	−	0.415415i	$-0.136364\pi$
$251$	1.45027	+	0.425839i	1.45027	+	0.425839i	0.540641	+	0.841254i	$0.318182\pi$
$252$	−1.28463			−1.28463
$253$		0			0
$254$	−0.830830			−0.830830
$255$		0			0
$256$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$257$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$257$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$258$		0			0
$259$		0			0
$260$	−0.425839	−	0.932456i	−0.425839	−	0.932456i
$261$		0			0
$262$	0.258908	+	1.80075i	0.258908	+	1.80075i
$263$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$263$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$264$		0			0
$265$		0			0
$266$	−0.822373	+	1.80075i	−0.822373	+	1.80075i
$267$		0			0
$268$		0			0
$269$	−0.822373	−	1.80075i	−0.822373	−	1.80075i	−0.540641	−	0.841254i	$-0.681818\pi$
$269$	−0.822373	−	1.80075i	−0.822373	−	1.80075i	−0.281733	−	0.959493i	$-0.590909\pi$
$270$	0.658432	−	0.423148i	0.658432	−	0.423148i
$271$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$271$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$272$		0			0
$273$	0.557730	−	0.643655i	0.557730	−	0.643655i
$274$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$275$		0			0
$276$	0.215109	−	1.49611i	0.215109	−	1.49611i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	−1.03748	−	0.304632i	−1.03748	−	0.304632i
$279$		0			0
$280$	1.53046	+	0.983568i	1.53046	+	0.983568i
$281$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$281$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$282$		0			0
$283$	−0.234072	−	0.512546i	−0.234072	−	0.512546i	0.755750	−	0.654861i	$-0.227273\pi$
$283$	−0.234072	−	0.512546i	−0.234072	−	0.512546i	−0.989821	+	0.142315i	$0.954545\pi$
$284$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$285$	−0.774713	−	5.38825i	−0.774713	−	5.38825i
$286$		0			0
$287$		0			0
$288$	1.23259	−	0.361922i	1.23259	−	0.361922i
$289$	0.415415	−	0.909632i	0.415415	−	0.909632i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.27155	+	0.817178i	−1.27155	+	0.817178i	−0.989821	−	0.142315i	$-0.954545\pi$
$293$	−1.27155	+	0.817178i	−1.27155	+	0.817178i	−0.281733	+	0.959493i	$0.590909\pi$
$294$	−0.215109	+	1.49611i	−0.215109	+	1.49611i
$295$	3.02977	+	1.94711i	3.02977	+	1.94711i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.368991	+	0.425839i	0.368991	+	0.425839i
$300$	−3.49114			−3.49114
$301$		0			0
$302$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$303$		0			0
$304$	0.281733	−	1.95949i	0.281733	−	1.95949i
$305$		0			0
$306$		0			0
$307$	−0.368991	−	0.425839i	−0.368991	−	0.425839i	0.540641	−	0.841254i	$-0.318182\pi$
$307$	−0.368991	−	0.425839i	−0.368991	−	0.425839i	−0.909632	+	0.415415i	$0.863636\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$311$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$312$	−0.353799	+	0.774713i	−0.353799	+	0.774713i
$313$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$313$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$314$	−0.708089	−	0.817178i	−0.708089	−	0.817178i
$315$	−0.970858	−	2.12588i	−0.970858	−	2.12588i
$316$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$317$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$317$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$318$		0			0
$319$		0			0
$320$	−1.74557	−	0.512546i	−1.74557	−	0.512546i
$321$		0			0
$322$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$323$		0			0
$324$	0.608660	+	0.178719i	0.608660	+	0.178719i
$325$	0.852267	−	0.983568i	0.852267	−	0.983568i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$331$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$332$	−0.449181	+	0.983568i	−0.449181	+	0.983568i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−0.215109	−	1.49611i	−0.215109	−	1.49611i
$337$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.841254	−	0.540641i	$-0.818182\pi$
$337$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.415415	−	0.909632i	$-0.636364\pi$
$338$	0.283524	+	0.620830i	0.283524	+	0.620830i
$339$	2.13940	−	1.37491i	2.13940	−	1.37491i
$340$		0			0
$341$		0			0
$342$	−1.66538	+	1.92195i	−1.66538	+	1.92195i
$343$	0.959493	+	0.281733i	0.959493	+	0.281733i
$344$		0			0
$345$	2.63843	−	0.774713i	2.63843	−	0.774713i
$346$	1.08128			1.08128
$347$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$347$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$348$		0			0
$349$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$349$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$350$	−0.328708	+	2.28621i	−0.328708	+	2.28621i
$351$	0.203930	−	0.131058i	0.203930	−	0.131058i
$352$		0			0
$353$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$353$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$354$	−0.425839	−	2.96177i	−0.425839	−	2.96177i
$355$	1.45027	−	3.17565i	1.45027	−	3.17565i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$359$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$360$	1.53046	+	1.76625i	1.53046	+	1.76625i
$361$	1.21259	+	2.65520i	1.21259	+	2.65520i
$362$	1.27155	−	0.817178i	1.27155	−	0.817178i
$363$	0.215109	−	1.49611i	0.215109	−	1.49611i
$364$	0.474017	+	0.304632i	0.474017	+	0.304632i
$365$		0			0
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	1.00000			1.00000
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$373$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$374$		0			0
$375$	−1.49611	−	3.27603i	−1.49611	−	3.27603i
$376$		0			0
$377$		0			0
$378$	−0.178719	+	0.391340i	−0.178719	+	0.391340i
$379$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$379$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$380$	3.45561	−	1.01466i	3.45561	−	1.01466i
$381$	−0.521678	+	1.14231i	−0.521678	+	1.14231i
$382$	0.186393	+	1.29639i	0.186393	+	1.29639i
$383$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$383$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$384$	0.627899	+	1.37491i	0.627899	+	1.37491i
$385$		0			0
$386$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$387$		0			0
$388$		0			0
$389$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$389$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$390$	−1.54943			−1.54943
$391$		0			0
$392$	−1.00000			−1.00000
$393$	2.63843	+	0.774713i	2.63843	+	0.774713i
$394$		0			0
$395$	−2.57501	−	1.65486i	−2.57501	−	1.65486i
$396$		0			0
$397$	0.474017	−	0.304632i	0.474017	−	0.304632i	−0.281733	−	0.959493i	$-0.590909\pi$
$397$	0.474017	−	0.304632i	0.474017	−	0.304632i	0.755750	+	0.654861i	$0.227273\pi$
$398$		0			0
$399$	1.95949	+	2.26138i	1.95949	+	2.26138i
$400$	−0.328708	−	2.28621i	−0.328708	−	2.28621i
$401$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$401$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.164240	+	1.14231i	0.164240	+	1.14231i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$409$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$410$		0			0
$411$	−0.281733	+	0.325137i	−0.281733	+	0.325137i
$412$		0			0
$413$	−1.97964			−1.97964
$414$	−1.08070	−	0.694523i	−1.08070	−	0.694523i
$415$	−1.96714			−1.96714
$416$	−0.540641	−	0.158746i	−0.540641	−	0.158746i
$417$	−1.07028	+	1.23516i	−1.07028	+	1.23516i
$418$		0			0
$419$	0.0801894	−	0.557730i	0.0801894	−	0.557730i	−0.909632	−	0.415415i	$-0.863636\pi$
$419$	0.0801894	−	0.557730i	0.0801894	−	0.557730i	0.989821	−	0.142315i	$-0.0454545\pi$
$420$	2.31329	−	1.48666i	2.31329	−	1.48666i
$421$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$421$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−2.78305	+	0.817178i	−2.78305	+	0.817178i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$431$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$432$	0.0612263	−	0.425839i	0.0612263	−	0.425839i
$433$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$433$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.66538	+	1.07028i	−1.66538	+	1.07028i
$438$		0			0
$439$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$439$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$440$		0			0
$441$	1.08070	+	0.694523i	1.08070	+	0.694523i
$442$		0			0
$443$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$443$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.959493	−	0.281733i	0.959493	−	0.281733i
$449$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$449$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$450$	−1.23259	+	2.69900i	−1.23259	+	2.69900i
$451$		0			0
$452$	1.10181	+	1.27155i	1.10181	+	1.27155i
$453$	0.822373	+	1.80075i	0.822373	+	1.80075i
$454$	−0.909632	+	0.584585i	−0.909632	+	0.584585i
$455$	−0.145886	+	1.01466i	−0.145886	+	1.01466i
$456$	−2.51722	−	1.61772i	−2.51722	−	1.61772i
$457$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$457$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$458$	1.89945	+	0.557730i	1.89945	+	0.557730i
$459$		0			0
$460$	0.755750	+	1.65486i	0.755750	+	1.65486i
$461$	1.08128			1.08128			0.540641	−	0.841254i	$-0.318182\pi$
$461$	1.08128			1.08128			0.540641	+	0.841254i	$0.318182\pi$
$462$		0			0
$463$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$463$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$464$		0			0
$465$		0			0
$466$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$467$	0.627899	+	1.37491i	0.627899	+	1.37491i	0.909632	+	0.415415i	$0.136364\pi$
$467$	0.627899	+	1.37491i	0.627899	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$468$	0.474017	+	0.547045i	0.474017	+	0.547045i
$469$		0			0
$470$		0			0
$471$	−1.56815	+	0.460451i	−1.56815	+	0.460451i
$472$	1.89945	−	0.557730i	1.89945	−	0.557730i
$473$		0			0
$474$	0.361922	+	2.51722i	0.361922	+	2.51722i
$475$	2.99430	+	3.45561i	2.99430	+	3.45561i
$476$		0			0
$477$		0			0
$478$	0.118239	−	0.822373i	0.118239	−	0.822373i
$479$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$479$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$480$	−1.80075	+	2.07817i	−1.80075	+	2.07817i
$481$		0			0
$482$		0			0
$483$	−0.989821	+	1.14231i	−0.989821	+	1.14231i
$484$	1.00000			1.00000
$485$		0			0
$486$	0.909632	−	1.04977i	0.909632	−	1.04977i
$487$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$487$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$488$		0			0
$489$		0			0
$490$	−0.755750	−	1.65486i	−0.755750	−	1.65486i
$491$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$491$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$492$		0			0
$493$		0			0
$494$	1.07028	−	0.314261i	1.07028	−	0.314261i
$495$		0			0
$496$		0			0
$497$	0.273100	+	1.89945i	0.273100	+	1.89945i
$498$	1.07028	+	1.23516i	1.07028	+	1.23516i
$499$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$499$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$500$	2.00448	−	1.28820i	2.00448	−	1.28820i
$501$		0			0
$502$	1.27155	+	0.817178i	1.27155	+	0.817178i
$503$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$503$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$504$	−1.23259	−	0.361922i	−1.23259	−	0.361922i
$505$		0			0
$506$		0			0
$507$	1.03161			1.03161
$508$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$509$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$509$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.909632	+	0.415415i	$0.863636\pi$
$510$		0			0
$511$		0			0
$512$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$513$	0.353799	+	0.774713i	0.353799	+	0.774713i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.678936	−	1.48666i	0.678936	−	1.48666i
$520$	−0.145886	−	1.01466i	−0.145886	−	1.01466i
$521$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$521$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$522$		0			0
$523$	0.909632	−	0.584585i	0.909632	−	0.584585i		−	1.00000i	$-0.5\pi$
$523$	0.909632	−	0.584585i	0.909632	−	0.584585i	0.909632	+	0.415415i	$0.136364\pi$
$524$	−0.258908	+	1.80075i	−0.258908	+	1.80075i
$525$	2.93694	+	1.88745i	2.93694	+	1.88745i
$526$	1.25667	−	1.45027i	1.25667	−	1.45027i
$527$		0			0
$528$		0			0
$529$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$530$		0			0
$531$	−2.44009	−	0.716476i	−2.44009	−	0.716476i
$532$	−1.29639	+	1.49611i	−1.29639	+	1.49611i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.281733	−	1.95949i	−0.281733	−	1.95949i
$539$		0			0
$540$	0.750975	−	0.220506i	0.750975	−	0.220506i
$541$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$541$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$542$		0			0
$543$	−0.325137	−	2.26138i	−0.325137	−	2.26138i
$544$		0			0
$545$		0			0
$546$	0.716476	−	0.460451i	0.716476	−	0.460451i
$547$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$547$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$548$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	0.627899	−	1.37491i	0.627899	−	1.37491i
$553$	1.68251			1.68251
$554$		0			0
$555$		0			0
$556$	−0.909632	−	0.584585i	−0.909632	−	0.584585i
$557$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$557$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$558$		0			0
$559$		0			0
$560$	1.19136	+	1.37491i	1.19136	+	1.37491i
$561$		0			0
$562$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$563$	−0.540641	+	0.158746i	−0.540641	+	0.158746i	−0.540641	−	0.841254i	$-0.681818\pi$
$563$	−0.540641	+	0.158746i	−0.540641	+	0.158746i			1.00000i	$0.5\pi$
$564$		0			0
$565$	−1.27155	+	2.78431i	−1.27155	+	2.78431i
$566$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i
$567$	−0.415415	−	0.479414i	−0.415415	−	0.479414i
$568$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$569$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.142315	−	0.989821i	$-0.454545\pi$
$569$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.959493	+	0.281733i	$0.0909091\pi$
$570$	0.774713	−	5.38825i	0.774713	−	5.38825i
$571$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$571$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$572$		0			0
$573$	1.89945	+	0.557730i	1.89945	+	0.557730i
$574$		0			0
$575$	−1.51255	+	1.74557i	−1.51255	+	1.74557i
$576$	1.28463			1.28463
$577$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$577$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$578$	0.654861	−	0.755750i	0.654861	−	0.755750i
$579$	1.05645	+	0.678936i	1.05645	+	0.678936i
$580$		0			0
$581$	0.909632	−	0.584585i	0.909632	−	0.584585i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.547045	+	1.19786i	−0.547045	+	1.19786i
$586$	−1.45027	+	0.425839i	−1.45027	+	0.425839i
$587$	0.540641	−	0.158746i	0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$587$	0.540641	−	0.158746i	0.540641	−	0.158746i	0.540641	+	0.841254i	$0.318182\pi$
$588$	−0.627899	+	1.37491i	−0.627899	+	1.37491i
$589$		0			0
$590$	2.35848	+	2.72183i	2.35848	+	2.72183i
$591$		0			0
$592$		0			0
$593$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$593$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.234072	+	0.512546i	0.234072	+	0.512546i
$599$	1.30972			1.30972			0.654861	−	0.755750i	$-0.272727\pi$
$599$	1.30972			1.30972			0.654861	+	0.755750i	$0.272727\pi$
$600$	−3.34973	−	0.983568i	−3.34973	−	0.983568i
$601$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$601$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$602$		0			0
$603$		0			0
$604$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$605$	0.755750	+	1.65486i	0.755750	+	1.65486i
$606$		0			0
$607$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$607$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$608$	0.822373	−	1.80075i	0.822373	−	1.80075i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$613$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$614$	−0.234072	−	0.512546i	−0.234072	−	0.512546i
$615$		0			0
$616$		0			0
$617$	−0.698939	−	0.449181i	−0.698939	−	0.449181i	0.142315	−	0.989821i	$-0.454545\pi$
$617$	−0.698939	−	0.449181i	−0.698939	−	0.449181i	−0.841254	+	0.540641i	$0.818182\pi$
$618$		0			0
$619$	−1.03748	−	0.304632i	−1.03748	−	0.304632i	−0.281733	−	0.959493i	$-0.590909\pi$
$619$	−1.03748	−	0.304632i	−1.03748	−	0.304632i	−0.755750	+	0.654861i	$0.772727\pi$
$620$		0			0
$621$	−0.361922	+	0.232593i	−0.361922	+	0.232593i
$622$		0			0
$623$		0			0
$624$	−0.557730	+	0.643655i	−0.557730	+	0.643655i
$625$	1.70362	+	1.09485i	1.70362	+	1.09485i
$626$		0			0
$627$		0			0
$628$	−0.449181	−	0.983568i	−0.449181	−	0.983568i
$629$		0			0
$630$	−0.332601	−	2.31329i	−0.332601	−	2.31329i
$631$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$631$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$632$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$633$		0			0
$634$		0			0
$635$	−0.215109	−	1.49611i	−0.215109	−	1.49611i
$636$		0			0
$637$	−0.234072	−	0.512546i	−0.234072	−	0.512546i
$638$		0			0
$639$	−0.350833	+	2.44009i	−0.350833	+	2.44009i
$640$	−1.53046	−	0.983568i	−1.53046	−	0.983568i
$641$	0.544078	−	0.627899i	0.544078	−	0.627899i	−0.415415	−	0.909632i	$-0.636364\pi$
$641$	0.544078	−	0.627899i	0.544078	−	0.627899i	0.959493	+	0.281733i	$0.0909091\pi$
$642$		0			0
$643$	−1.51150			−1.51150			−0.755750	−	0.654861i	$-0.772727\pi$
$643$	−1.51150			−1.51150			−0.755750	+	0.654861i	$0.772727\pi$
$644$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$645$		0			0
$646$		0			0
$647$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$647$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$648$	0.533654	+	0.342959i	0.533654	+	0.342959i
$649$		0			0
$650$	1.09485	−	0.703616i	1.09485	−	0.703616i
$651$		0			0
$652$		0			0
$653$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$653$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$654$		0			0
$655$	−3.17565	+	0.932456i	−3.17565	+	0.932456i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$659$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$660$		0			0
$661$	−0.474017	+	0.304632i	−0.474017	+	0.304632i	−0.755750	−	0.654861i	$-0.772727\pi$
$661$	−0.474017	+	0.304632i	−0.474017	+	0.304632i	0.281733	+	0.959493i	$0.409091\pi$
$662$		0			0
$663$		0			0
$664$	−0.708089	+	0.817178i	−0.708089	+	0.817178i
$665$	−3.45561	−	1.01466i	−3.45561	−	1.01466i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.215109	−	1.49611i	0.215109	−	1.49611i
$673$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$673$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$674$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$675$	0.650724	+	0.750975i	0.650724	+	0.750975i
$676$	0.0971309	+	0.675560i	0.0971309	+	0.675560i
$677$	0.449181	−	0.983568i	0.449181	−	0.983568i	−0.540641	−	0.841254i	$-0.681818\pi$
$677$	0.449181	−	0.983568i	0.449181	−	0.983568i	0.989821	−	0.142315i	$-0.0454545\pi$
$678$	2.44009	−	0.716476i	2.44009	−	0.716476i
$679$		0			0
$680$		0			0
$681$	0.232593	+	1.61772i	0.232593	+	1.61772i
$682$		0			0
$683$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$683$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$684$	−2.13940	+	1.37491i	−2.13940	+	1.37491i
$685$	0.0736930	−	0.512546i	0.0736930	−	0.512546i
$686$	0.841254	+	0.540641i	0.841254	+	0.540641i
$687$	1.95949	−	2.26138i	1.95949	−	2.26138i
$688$		0			0
$689$		0			0
$690$	2.74982			2.74982
$691$	−1.97964			−1.97964			−0.989821	−	0.142315i	$-0.954545\pi$
$691$	−1.97964			−1.97964			−0.989821	+	0.142315i	$0.954545\pi$
$692$	1.03748	+	0.304632i	1.03748	+	0.304632i
$693$		0			0
$694$		0			0
$695$	0.279953	−	1.94711i	0.279953	−	1.94711i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	0.361922	+	2.51722i	0.361922	+	2.51722i
$700$	−0.959493	+	2.10100i	−0.959493	+	2.10100i
$701$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$701$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$702$	0.232593	−	0.0682955i	0.232593	−	0.0682955i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$	0.425839	−	2.96177i	0.425839	−	2.96177i
$709$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$709$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$710$	2.28621	−	2.63843i	2.28621	−	2.63843i
$711$	2.07385	+	0.608936i	2.07385	+	0.608936i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.05645	−	0.678936i	−1.05645	−	0.678936i
$718$	0.118239	−	0.822373i	0.118239	−	0.822373i
$719$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$719$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$720$	0.970858	+	2.12588i	0.970858	+	2.12588i
$721$		0			0
$722$	0.415415	+	2.88927i	0.415415	+	2.88927i
$723$		0			0
$724$	1.45027	−	0.425839i	1.45027	−	0.425839i
$725$		0			0
$726$	0.627899	−	1.37491i	0.627899	−	1.37491i
$727$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$727$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$728$	0.368991	+	0.425839i	0.368991	+	0.425839i
$729$	−0.608660	−	1.33278i	−0.608660	−	1.33278i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.368991	+	0.425839i	−0.368991	+	0.425839i	−0.909632	−	0.415415i	$-0.863636\pi$
$733$	−0.368991	+	0.425839i	−0.368991	+	0.425839i	0.540641	+	0.841254i	$0.318182\pi$
$734$		0			0
$735$	−2.74982			−2.74982
$736$	0.959493	+	0.281733i	0.959493	+	0.281733i
$737$		0			0
$738$		0			0
$739$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$739$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$740$		0			0
$741$	0.239945	−	1.66886i	0.239945	−	1.66886i
$742$		0			0
$743$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$743$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.33278	−	0.391340i	1.33278	−	0.391340i
$748$		0			0
$749$		0			0
$750$	−0.512546	−	3.56484i	−0.512546	−	3.56484i
$751$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$751$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$752$		0			0
$753$	1.92195	−	1.23516i	1.92195	−	1.23516i
$754$		0			0
$755$	−2.00448	−	1.28820i	−2.00448	−	1.28820i
$756$	−0.281733	+	0.325137i	−0.281733	+	0.325137i
$757$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$757$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$758$		0			0
$759$		0			0
$760$	3.60149			3.60149
$761$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$761$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$762$	−0.822373	+	0.949069i	−0.822373	+	0.949069i
$763$		0			0
$764$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$765$		0			0
$766$		0			0
$767$	0.730471	+	0.843008i	0.730471	+	0.843008i
$768$	0.215109	+	1.49611i	0.215109	+	1.49611i
$769$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$769$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$770$		0			0
$771$		0			0
$772$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$773$	0.258908	+	1.80075i	0.258908	+	1.80075i	0.540641	+	0.841254i	$0.318182\pi$
$773$	0.258908	+	1.80075i	0.258908	+	1.80075i	−0.281733	+	0.959493i	$0.590909\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−1.48666	−	0.436524i	−1.48666	−	0.436524i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$785$	1.28820	−	1.48666i	1.28820	−	1.48666i
$786$	2.31329	+	1.48666i	2.31329	+	1.48666i
$787$	−0.281733	+	1.95949i	−0.281733	+	1.95949i			1.00000i	$0.5\pi$
$787$	−0.281733	+	1.95949i	−0.281733	+	1.95949i	−0.281733	+	0.959493i	$0.590909\pi$
$788$		0			0
$789$	−1.20493	−	2.63843i	−1.20493	−	2.63843i
$790$	−2.00448	−	2.31329i	−2.00448	−	2.31329i
$791$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$792$		0			0
$793$		0			0
$794$	0.540641	−	0.158746i	0.540641	−	0.158746i
$795$		0			0
$796$		0			0
$797$	0.368991	+	0.425839i	0.368991	+	0.425839i	0.909632	−	0.415415i	$-0.136364\pi$
$797$	0.368991	+	0.425839i	0.368991	+	0.425839i	−0.540641	+	0.841254i	$0.681818\pi$
$798$	1.24302	+	2.72183i	1.24302	+	2.72183i
$799$		0			0
$800$	0.328708	−	2.28621i	0.328708	−	2.28621i
$801$		0			0
$802$	1.25667	−	1.45027i	1.25667	−	1.45027i
$803$		0			0
$804$		0			0
$805$	0.258908	−	1.80075i	0.258908	−	1.80075i
$806$		0			0
$807$	−2.87102	−	0.843008i	−2.87102	−	0.843008i
$808$		0			0
$809$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−0.415415	−	0.909632i	$-0.636364\pi$
$809$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−1.00000			$\pi$
$810$	−0.164240	+	1.14231i	−0.164240	+	1.14231i
$811$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.755750	−	0.654861i	$-0.227273\pi$
$811$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.909632	−	0.415415i	$-0.136364\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−0.103014	−	0.716476i	−0.103014	−	0.716476i
$820$		0			0
$821$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$821$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$822$	−0.361922	+	0.232593i	−0.361922	+	0.232593i
$823$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i	0.959493	+	0.281733i	$0.0909091\pi$
$823$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i	−1.00000			$1.00000\pi$
$824$		0			0
$825$		0			0
$826$	−1.89945	−	0.557730i	−1.89945	−	0.557730i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	−0.841254	−	0.970858i	−0.841254	−	0.970858i
$829$	−1.81926			−1.81926			−0.909632	−	0.415415i	$-0.863636\pi$
$829$	−1.81926			−1.81926			−0.909632	+	0.415415i	$0.863636\pi$
$830$	−1.88745	−	0.554206i	−1.88745	−	0.554206i
$831$		0			0
$832$	−0.474017	−	0.304632i	−0.474017	−	0.304632i
$833$		0			0
$834$	−1.37491	+	0.883600i	−1.37491	+	0.883600i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.234072	−	0.512546i	0.234072	−	0.512546i
$839$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$839$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$840$	2.63843	−	0.774713i	2.63843	−	0.774713i
$841$	0.415415	−	0.909632i	0.415415	−	0.909632i
$842$		0			0
$843$	0.822373	+	0.949069i	0.822373	+	0.949069i
$844$		0			0
$845$	−1.04455	+	0.671292i	−1.04455	+	0.671292i
$846$		0			0
$847$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$848$		0			0
$849$	−0.817178	−	0.239945i	−0.817178	−	0.239945i
$850$		0			0
$851$		0			0
$852$	−2.90055			−2.90055
$853$	−1.03748	−	0.304632i	−1.03748	−	0.304632i	−0.281733	−	0.959493i	$-0.590909\pi$
$853$	−1.03748	−	0.304632i	−1.03748	−	0.304632i	−0.755750	+	0.654861i	$0.772727\pi$
$854$		0			0
$855$	−3.89213	−	2.50132i	−3.89213	−	2.50132i
$856$		0			0
$857$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$857$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$858$		0			0
$859$	1.19136	+	1.37491i	1.19136	+	1.37491i	0.909632	+	0.415415i	$0.136364\pi$
$859$	1.19136	+	1.37491i	1.19136	+	1.37491i	0.281733	+	0.959493i	$0.409091\pi$
$860$		0			0
$861$		0			0
$862$	1.61435	−	0.474017i	1.61435	−	0.474017i
$863$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$863$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	0.142315	+	0.989821i	$0.454545\pi$
$864$	0.178719	−	0.391340i	0.178719	−	0.391340i
$865$	0.279953	+	1.94711i	0.279953	+	1.94711i
$866$		0			0
$867$	−0.627899	−	1.37491i	−0.627899	−	1.37491i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−1.89945	+	0.557730i	−1.89945	+	0.557730i
$875$	−2.38273			−2.38273
$876$		0			0
$877$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$877$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$878$		0			0
$879$	−0.325137	+	2.26138i	−0.325137	+	2.26138i
$880$		0			0
$881$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$881$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$882$	0.841254	+	0.970858i	0.841254	+	0.970858i
$883$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$883$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$884$		0			0
$885$	5.22315	−	1.53365i	5.22315	−	1.53365i
$886$		0			0
$887$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$887$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$888$		0			0
$889$	0.544078	+	0.627899i	0.544078	+	0.627899i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.00000			1.00000
$897$	0.851677			0.851677
$898$	0.284630			0.284630
$899$		0			0
$900$	−1.94306	+	2.24241i	−1.94306	+	2.24241i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.698939	+	1.53046i	0.698939	+	1.53046i
$905$	1.80075	+	2.07817i	1.80075	+	2.07817i
$906$	0.281733	+	1.95949i	0.281733	+	1.95949i
$907$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$907$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$908$	−1.03748	+	0.304632i	−1.03748	+	0.304632i
$909$		0			0
$910$	−0.425839	+	0.932456i	−0.425839	+	0.932456i
$911$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$911$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$912$	−1.95949	−	2.26138i	−1.95949	−	2.26138i
$913$		0			0
$914$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$915$		0			0
$916$	1.66538	+	1.07028i	1.66538	+	1.07028i
$917$	1.19136	−	1.37491i	1.19136	−	1.37491i
$918$		0			0
$919$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$919$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$920$	0.258908	+	1.80075i	0.258908	+	1.80075i
$921$	−0.851677			−0.851677
$922$	1.03748	+	0.304632i	1.03748	+	0.304632i
$923$	0.708089	−	0.817178i	0.708089	−	0.817178i
$924$		0			0
$925$		0			0
$926$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$927$		0			0
$928$		0			0
$929$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$929$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$930$		0			0
$931$	1.89945	−	0.557730i	1.89945	−	0.557730i
$932$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$933$		0			0
$934$	0.215109	+	1.49611i	0.215109	+	1.49611i
$935$		0			0
$936$	0.300696	+	0.658432i	0.300696	+	0.658432i
$937$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$937$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.03748	+	0.304632i	1.03748	+	0.304632i	0.755750	−	0.654861i	$-0.227273\pi$
$941$	1.03748	+	0.304632i	1.03748	+	0.304632i	0.281733	+	0.959493i	$0.409091\pi$
$942$	−1.63436			−1.63436
$943$		0			0
$944$	1.97964			1.97964
$945$	−0.750975	−	0.220506i	−0.750975	−	0.220506i
$946$		0			0
$947$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$947$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$948$	−0.361922	+	2.51722i	−0.361922	+	2.51722i
$949$		0			0
$950$	1.89945	+	4.15922i	1.89945	+	4.15922i
$951$		0			0
$952$		0			0
$953$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$953$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$954$		0			0
$955$	−2.28621	+	0.671292i	−2.28621	+	0.671292i
$956$	0.345139	−	0.755750i	0.345139	−	0.755750i
$957$		0			0
$958$		0			0
$959$	0.118239	+	0.258908i	0.118239	+	0.258908i
$960$	−2.31329	+	1.48666i	−2.31329	+	1.48666i
$961$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.51150			−1.51150
$966$	−1.27155	+	0.817178i	−1.27155	+	0.817178i
$967$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$967$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$968$	0.959493	+	0.281733i	0.959493	+	0.281733i
$969$		0			0
$970$		0			0
$971$	0.258908	−	1.80075i	0.258908	−	1.80075i	−0.281733	−	0.959493i	$-0.590909\pi$
$971$	0.258908	−	1.80075i	0.258908	−	1.80075i	0.540641	−	0.841254i	$-0.318182\pi$
$972$	1.16854	−	0.750975i	1.16854	−	0.750975i
$973$	0.449181	+	0.983568i	0.449181	+	0.983568i
$974$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$975$	−0.279953	−	1.94711i	−0.279953	−	1.94711i
$976$		0			0
$977$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$977$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$978$		0			0
$979$		0			0
$980$	−0.258908	−	1.80075i	−0.258908	−	1.80075i
$981$		0			0
$982$		0			0
$983$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$983$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	1.11546			1.11546
$989$		0			0
$990$		0			0
$991$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.654861	−	0.755750i	$-0.272727\pi$
$991$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.142315	+	0.989821i	$0.454545\pi$
$992$		0			0
$993$		0			0
$994$	−0.273100	+	1.89945i	−0.273100	+	1.89945i
$995$		0			0
$996$	0.678936	+	1.48666i	0.678936	+	1.48666i
$997$	−1.19136	−	1.37491i	−1.19136	−	1.37491i	−0.909632	−	0.415415i	$-0.863636\pi$
$997$	−1.19136	−	1.37491i	−1.19136	−	1.37491i	−0.281733	−	0.959493i	$-0.590909\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1288.1.bi.e.685.2	yes	20
7.6	odd	2	inner	1288.1.bi.e.685.1	✓	20
8.5	even	2	inner	1288.1.bi.e.685.1	✓	20
23.9	even	11	inner	1288.1.bi.e.1021.2	yes	20
56.13	odd	2	CM	1288.1.bi.e.685.2	yes	20
161.55	odd	22	inner	1288.1.bi.e.1021.1	yes	20
184.101	even	22	inner	1288.1.bi.e.1021.1	yes	20
1288.1021	odd	22	inner	1288.1.bi.e.1021.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.1.bi.e.685.1	✓	20	7.6	odd	2	inner
1288.1.bi.e.685.1	✓	20	8.5	even	2	inner
1288.1.bi.e.685.2	yes	20	1.1	even	1	trivial
1288.1.bi.e.685.2	yes	20	56.13	odd	2	CM
1288.1.bi.e.1021.1	yes	20	161.55	odd	22	inner
1288.1.bi.e.1021.1	yes	20	184.101	even	22	inner
1288.1.bi.e.1021.2	yes	20	23.9	even	11	inner
1288.1.bi.e.1021.2	yes	20	1288.1021	odd	22	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:	\( N \)	\(=\)	\( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1288.bi (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.989821 - 1.14231i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.258908 + 1.80075i) q^{5} +(1.27155 - 0.817178i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.182822 - 1.27155i) q^{9} +(-0.755750 + 1.65486i) q^{10} +(1.45027 - 0.425839i) q^{12} +(-0.234072 + 0.512546i) q^{13} +(-0.142315 - 0.989821i) q^{14} +(1.80075 + 2.07817i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.182822 - 1.27155i) q^{18} +(-1.66538 - 1.07028i) q^{19} +(-1.19136 + 1.37491i) q^{20} +(-1.45027 - 0.425839i) q^{21} +(0.415415 - 0.909632i) q^{23} +1.51150 q^{24} +(-2.21616 - 0.650724i) q^{25} +(-0.368991 + 0.425839i) q^{26} +(-0.361922 - 0.232593i) q^{27} +(0.142315 - 0.989821i) q^{28} +(1.14231 + 2.50132i) q^{30} +(0.142315 + 0.989821i) q^{32} +(1.74557 - 0.512546i) q^{35} +(0.533654 - 1.16854i) q^{36} +(-1.29639 - 1.49611i) q^{38} +(0.353799 + 0.774713i) q^{39} +(-1.53046 + 0.983568i) q^{40} +(-1.27155 - 0.817178i) q^{42} +2.33708 q^{45} +(0.654861 - 0.755750i) q^{46} +(1.45027 + 0.425839i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-1.94306 - 1.24873i) q^{50} +(-0.474017 + 0.304632i) q^{52} +(-0.281733 - 0.325137i) q^{54} +(0.415415 - 0.909632i) q^{56} +(-2.87102 + 0.843008i) q^{57} +(0.822373 - 1.80075i) q^{59} +(0.391340 + 2.72183i) q^{60} +(-1.08070 + 0.694523i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.862362 - 0.554206i) q^{65} +(-0.627899 - 1.37491i) q^{69} +1.81926 q^{70} +(-1.84125 - 0.540641i) q^{71} +(0.841254 - 0.970858i) q^{72} +(-2.93694 + 1.88745i) q^{75} +(-0.822373 - 1.80075i) q^{76} +(0.121206 + 0.843008i) q^{78} +(-0.698939 + 1.53046i) q^{79} +(-1.74557 + 0.512546i) q^{80} +(0.608660 - 0.178719i) q^{81} +(0.153882 + 1.07028i) q^{83} +(-0.989821 - 1.14231i) q^{84} +(2.24241 + 0.658432i) q^{90} +0.563465 q^{91} +(0.841254 - 0.540641i) q^{92} +(2.35848 - 2.72183i) q^{95} +(1.27155 + 0.817178i) q^{96} +(-0.841254 + 0.540641i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9} - 2 q^{14} - 2 q^{16} + 20 q^{18} - 2 q^{23} + 2 q^{25} + 2 q^{28} + 22 q^{30} + 2 q^{32} + 2 q^{36} - 22 q^{39} + 2 q^{46} - 2 q^{49} - 2 q^{50}+ \cdots + 2 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 2 * q^8 - 20 * q^9 - 2 * q^14 - 2 * q^16 + 20 * q^18 - 2 * q^23 + 2 * q^25 + 2 * q^28 + 22 * q^30 + 2 * q^32 + 2 * q^36 - 22 * q^39 + 2 * q^46 - 2 * q^49 - 2 * q^50 - 2 * q^56 - 2 * q^63 - 2 * q^64 - 18 * q^71 - 2 * q^72 + 4 * q^79 + 20 * q^81 - 2 * q^92 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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