LMFDB - Embedded newform 1288.1.bi.e.349.2

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			349.2
Root			$-0.281733 - 0.959493i$ of defining polynomial
Character	$\chi$	$=$	1288.349
Dual form			1288.1.bi.e.1133.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.415415 - 0.909632i) q^{2} +(0.540641 - 0.158746i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-1.66538 - 1.07028i) q^{5} +(-0.368991 - 0.425839i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.574161 + 0.368991i) q^{9} +(-0.281733 + 1.95949i) q^{10} +(-0.234072 + 0.512546i) q^{12} +(-0.258908 + 1.80075i) q^{13} +(0.841254 - 0.540641i) q^{14} +(-1.07028 - 0.314261i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.574161 + 0.368991i) q^{18} +(0.708089 - 0.817178i) q^{19} +(1.89945 - 0.557730i) q^{20} +(0.234072 + 0.512546i) q^{21} +(-0.142315 + 0.989821i) q^{23} +0.563465 q^{24} +(1.21259 + 2.65520i) q^{25} +(1.74557 - 0.512546i) q^{26} +(-0.620830 + 0.716476i) q^{27} +(-0.841254 - 0.540641i) q^{28} +(0.158746 + 1.10411i) q^{30} +(-0.841254 + 0.540641i) q^{32} +(0.822373 - 1.80075i) q^{35} +(0.0971309 - 0.675560i) q^{36} +(-1.03748 - 0.304632i) q^{38} +(0.145886 + 1.01466i) q^{39} +(-1.29639 - 1.49611i) q^{40} +(0.368991 - 0.425839i) q^{42} +1.35112 q^{45} +(0.959493 - 0.281733i) q^{46} +(-0.234072 - 0.512546i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(1.91153 - 2.20602i) q^{50} +(-1.19136 - 1.37491i) q^{52} +(0.909632 + 0.267092i) q^{54} +(-0.142315 + 0.989821i) q^{56} +(0.253098 - 0.554206i) q^{57} +(-0.153882 + 1.07028i) q^{59} +(0.938384 - 0.603063i) q^{60} +(-0.446947 - 0.515804i) q^{63} +(0.841254 + 0.540641i) q^{64} +(2.35848 - 2.72183i) q^{65} +(0.0801894 + 0.557730i) q^{69} -1.97964 q^{70} +(-0.345139 - 0.755750i) q^{71} +(-0.654861 + 0.192284i) q^{72} +(1.07708 + 1.24302i) q^{75} +(0.153882 + 1.07028i) q^{76} +(0.862362 - 0.554206i) q^{78} +(-0.186393 + 1.29639i) q^{79} +(-0.822373 + 1.80075i) q^{80} +(0.0616156 - 0.134919i) q^{81} +(-1.27155 + 0.817178i) q^{83} +(-0.540641 - 0.158746i) q^{84} +(-0.561276 - 1.22902i) q^{90} -1.81926 q^{91} +(-0.654861 - 0.755750i) q^{92} +(-2.05384 + 0.603063i) q^{95} +(-0.368991 + 0.425839i) q^{96} +(0.654861 + 0.755750i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1288\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$645$	$967$
$\chi(n)$	$-1$	$e\left(\frac{2}{11}\right)$	$-1$	$1$

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 $

$2$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$2$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$3$	0.540641	−	0.158746i	0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$3$	0.540641	−	0.158746i	0.540641	−	0.158746i	0.540641	+	0.841254i	$0.318182\pi$
$4$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$5$	−1.66538	−	1.07028i	−1.66538	−	1.07028i	−0.909632	−	0.415415i	$-0.863636\pi$
$5$	−1.66538	−	1.07028i	−1.66538	−	1.07028i	−0.755750	−	0.654861i	$-0.772727\pi$
$6$	−0.368991	−	0.425839i	−0.368991	−	0.425839i
$7$	0.142315	+	0.989821i	0.142315	+	0.989821i
$7$	0.142315	+	0.989821i	0.142315	+	0.989821i
$8$	0.959493	+	0.281733i	0.959493	+	0.281733i
$9$	−0.574161	+	0.368991i	−0.574161	+	0.368991i
$10$	−0.281733	+	1.95949i	−0.281733	+	1.95949i
$11$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$11$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$12$	−0.234072	+	0.512546i	−0.234072	+	0.512546i
$13$	−0.258908	+	1.80075i	−0.258908	+	1.80075i	0.281733	+	0.959493i	$0.409091\pi$
$13$	−0.258908	+	1.80075i	−0.258908	+	1.80075i	−0.540641	+	0.841254i	$0.681818\pi$
$14$	0.841254	−	0.540641i	0.841254	−	0.540641i
$15$	−1.07028	−	0.314261i	−1.07028	−	0.314261i
$16$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$17$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$17$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$18$	0.574161	+	0.368991i	0.574161	+	0.368991i
$19$	0.708089	−	0.817178i	0.708089	−	0.817178i	−0.281733	−	0.959493i	$-0.590909\pi$
$19$	0.708089	−	0.817178i	0.708089	−	0.817178i	0.989821	+	0.142315i	$0.0454545\pi$
$20$	1.89945	−	0.557730i	1.89945	−	0.557730i
$21$	0.234072	+	0.512546i	0.234072	+	0.512546i
$22$		0			0
$23$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$23$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$24$	0.563465			0.563465
$25$	1.21259	+	2.65520i	1.21259	+	2.65520i
$26$	1.74557	−	0.512546i	1.74557	−	0.512546i
$27$	−0.620830	+	0.716476i	−0.620830	+	0.716476i
$28$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$29$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$29$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$30$	0.158746	+	1.10411i	0.158746	+	1.10411i
$31$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$31$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$32$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$33$		0			0
$34$		0			0
$35$	0.822373	−	1.80075i	0.822373	−	1.80075i
$36$	0.0971309	−	0.675560i	0.0971309	−	0.675560i
$37$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$37$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$38$	−1.03748	−	0.304632i	−1.03748	−	0.304632i
$39$	0.145886	+	1.01466i	0.145886	+	1.01466i
$40$	−1.29639	−	1.49611i	−1.29639	−	1.49611i
$41$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$41$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$42$	0.368991	−	0.425839i	0.368991	−	0.425839i
$43$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$43$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$44$		0			0
$45$	1.35112			1.35112
$46$	0.959493	−	0.281733i	0.959493	−	0.281733i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−0.234072	−	0.512546i	−0.234072	−	0.512546i
$49$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$50$	1.91153	−	2.20602i	1.91153	−	2.20602i
$51$		0			0
$52$	−1.19136	−	1.37491i	−1.19136	−	1.37491i
$53$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$53$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$54$	0.909632	+	0.267092i	0.909632	+	0.267092i
$55$		0			0
$56$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$57$	0.253098	−	0.554206i	0.253098	−	0.554206i
$58$		0			0
$59$	−0.153882	+	1.07028i	−0.153882	+	1.07028i	0.755750	+	0.654861i	$0.227273\pi$
$59$	−0.153882	+	1.07028i	−0.153882	+	1.07028i	−0.909632	+	0.415415i	$0.863636\pi$
$60$	0.938384	−	0.603063i	0.938384	−	0.603063i
$61$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$61$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$62$		0			0
$63$	−0.446947	−	0.515804i	−0.446947	−	0.515804i
$64$	0.841254	+	0.540641i	0.841254	+	0.540641i
$65$	2.35848	−	2.72183i	2.35848	−	2.72183i
$66$		0			0
$67$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$67$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$68$		0			0
$69$	0.0801894	+	0.557730i	0.0801894	+	0.557730i
$70$	−1.97964			−1.97964
$71$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$71$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	−1.00000			$\pi$
$72$	−0.654861	+	0.192284i	−0.654861	+	0.192284i
$73$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$73$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$74$		0			0
$75$	1.07708	+	1.24302i	1.07708	+	1.24302i
$76$	0.153882	+	1.07028i	0.153882	+	1.07028i
$77$		0			0
$78$	0.862362	−	0.554206i	0.862362	−	0.554206i
$79$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$79$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$80$	−0.822373	+	1.80075i	−0.822373	+	1.80075i
$81$	0.0616156	−	0.134919i	0.0616156	−	0.134919i
$82$		0			0
$83$	−1.27155	+	0.817178i	−1.27155	+	0.817178i	−0.989821	−	0.142315i	$-0.954545\pi$
$83$	−1.27155	+	0.817178i	−1.27155	+	0.817178i	−0.281733	+	0.959493i	$0.590909\pi$
$84$	−0.540641	−	0.158746i	−0.540641	−	0.158746i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$89$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$90$	−0.561276	−	1.22902i	−0.561276	−	1.22902i
$91$	−1.81926			−1.81926
$92$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$93$		0			0
$94$		0			0
$95$	−2.05384	+	0.603063i	−2.05384	+	0.603063i
$96$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$97$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$97$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$98$	0.654861	+	0.755750i	0.654861	+	0.755750i
$99$		0			0
$100$	−2.80075	−	0.822373i	−2.80075	−	0.822373i
$101$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$101$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$102$		0			0
$103$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$103$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$104$	−0.755750	+	1.65486i	−0.755750	+	1.65486i
$105$	0.158746	−	1.10411i	0.158746	−	1.10411i
$106$		0			0
$107$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$107$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$108$	−0.134919	−	0.938384i	−0.134919	−	0.938384i
$109$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$109$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$110$		0			0
$111$		0			0
$112$	0.959493	−	0.281733i	0.959493	−	0.281733i
$113$	0.544078	+	1.19136i	0.544078	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$113$	0.544078	+	1.19136i	0.544078	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$114$	−0.609264			−0.609264
$115$	1.29639	−	1.49611i	1.29639	−	1.49611i
$116$		0			0
$117$	−0.515804	−	1.12945i	−0.515804	−	1.12945i
$118$	1.03748	−	0.304632i	1.03748	−	0.304632i
$119$		0			0
$120$	−0.938384	−	0.603063i	−0.938384	−	0.603063i
$121$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.540641	−	3.76024i	0.540641	−	3.76024i
$126$	−0.283524	+	0.620830i	−0.283524	+	0.620830i
$127$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$127$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$128$	0.142315	−	0.989821i	0.142315	−	0.989821i
$129$		0			0
$130$	−3.45561	−	1.01466i	−3.45561	−	1.01466i
$131$	0.281733	+	1.95949i	0.281733	+	1.95949i	0.281733	+	0.959493i	$0.409091\pi$
$131$	0.281733	+	1.95949i	0.281733	+	1.95949i			1.00000i	$0.500000\pi$
$132$		0			0
$133$	0.909632	+	0.584585i	0.909632	+	0.584585i
$134$		0			0
$135$	1.80075	−	0.528747i	1.80075	−	0.528747i
$136$		0			0
$137$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$137$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$138$	0.474017	−	0.304632i	0.474017	−	0.304632i
$139$	−1.51150			−1.51150			−0.755750	−	0.654861i	$-0.772727\pi$
$139$	−1.51150			−1.51150			−0.755750	+	0.654861i	$0.772727\pi$
$140$	0.822373	+	1.80075i	0.822373	+	1.80075i
$141$		0			0
$142$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$143$		0			0
$144$	0.446947	+	0.515804i	0.446947	+	0.515804i
$145$		0			0
$146$		0			0
$147$	−0.474017	+	0.304632i	−0.474017	+	0.304632i
$148$		0			0
$149$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$149$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$150$	0.683252	−	1.49611i	0.683252	−	1.49611i
$151$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$151$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$152$	0.909632	−	0.584585i	0.909632	−	0.584585i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.862362	−	0.554206i	−0.862362	−	0.554206i
$157$	0.989821	−	1.14231i	0.989821	−	1.14231i		−	1.00000i	$-0.5\pi$
$157$	0.989821	−	1.14231i	0.989821	−	1.14231i	0.989821	−	0.142315i	$-0.0454545\pi$
$158$	1.25667	−	0.368991i	1.25667	−	0.368991i
$159$		0			0
$160$	1.97964			1.97964
$161$	−1.00000			−1.00000
$162$	−0.148323			−0.148323
$163$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$163$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$164$		0			0
$165$		0			0
$166$	1.27155	+	0.817178i	1.27155	+	0.817178i
$167$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$167$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$168$	0.0801894	+	0.557730i	0.0801894	+	0.557730i
$169$	−2.21616	−	0.650724i	−2.21616	−	0.650724i
$170$		0			0
$171$	−0.105026	+	0.730471i	−0.105026	+	0.730471i
$172$		0			0
$173$	−0.627899	+	1.37491i	−0.627899	+	1.37491i	0.281733	+	0.959493i	$0.409091\pi$
$173$	−0.627899	+	1.37491i	−0.627899	+	1.37491i	−0.909632	+	0.415415i	$0.863636\pi$
$174$		0			0
$175$	−2.45561	+	1.57812i	−2.45561	+	1.57812i
$176$		0			0
$177$	0.0867074	+	0.603063i	0.0867074	+	0.603063i
$178$		0			0
$179$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$179$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$180$	−0.884796	+	1.02111i	−0.884796	+	1.02111i
$181$	0.540641	−	0.158746i	0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$181$	0.540641	−	0.158746i	0.540641	−	0.158746i	0.540641	+	0.841254i	$0.318182\pi$
$182$	0.755750	+	1.65486i	0.755750	+	1.65486i
$183$		0			0
$184$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.797537	−	0.512546i	−0.797537	−	0.512546i
$190$	1.40176	+	1.61772i	1.40176	+	1.61772i
$191$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	−0.415415	−	0.909632i	$-0.636364\pi$
$191$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	0.142315	−	0.989821i	$-0.454545\pi$
$192$	0.540641	+	0.158746i	0.540641	+	0.158746i
$193$	0.239446	−	0.153882i	0.239446	−	0.153882i	−0.415415	−	0.909632i	$-0.636364\pi$
$193$	0.239446	−	0.153882i	0.239446	−	0.153882i	0.654861	+	0.755750i	$0.272727\pi$
$194$		0			0
$195$	0.843008	−	1.84593i	0.843008	−	1.84593i
$196$	0.415415	−	0.909632i	0.415415	−	0.909632i
$197$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$197$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$198$		0			0
$199$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$199$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$200$	0.415415	+	2.88927i	0.415415	+	2.88927i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.283524	−	0.620830i	−0.283524	−	0.620830i
$208$	1.81926			1.81926
$209$		0			0
$210$	−1.07028	+	0.314261i	−1.07028	+	0.314261i
$211$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$211$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$212$		0			0
$213$	−0.306569	−	0.353799i	−0.306569	−	0.353799i
$214$		0			0
$215$		0			0
$216$	−0.797537	+	0.512546i	−0.797537	+	0.512546i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$223$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$224$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$225$	−1.67597	−	1.07708i	−1.67597	−	1.07708i
$226$	0.857685	−	0.989821i	0.857685	−	0.989821i
$227$	−1.45027	+	0.425839i	−1.45027	+	0.425839i	−0.909632	−	0.415415i	$-0.863636\pi$
$227$	−1.45027	+	0.425839i	−1.45027	+	0.425839i	−0.540641	+	0.841254i	$0.681818\pi$
$228$	0.253098	+	0.554206i	0.253098	+	0.554206i
$229$	1.08128			1.08128			0.540641	−	0.841254i	$-0.318182\pi$
$229$	1.08128			1.08128			0.540641	+	0.841254i	$0.318182\pi$
$230$	−1.89945	−	0.557730i	−1.89945	−	0.557730i
$231$		0			0
$232$		0			0
$233$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$233$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$234$	−0.813115	+	0.938384i	−0.813115	+	0.938384i
$235$		0			0
$236$	−0.708089	−	0.817178i	−0.708089	−	0.817178i
$237$	0.105026	+	0.730471i	0.105026	+	0.730471i
$238$		0			0
$239$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$239$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$240$	−0.158746	+	1.10411i	−0.158746	+	1.10411i
$241$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$241$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$242$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$243$	0.146813	−	1.02111i	0.146813	−	1.02111i
$244$		0			0
$245$	1.89945	+	0.557730i	1.89945	+	0.557730i
$246$		0			0
$247$	1.28820	+	1.48666i	1.28820	+	1.48666i
$248$		0			0
$249$	−0.557730	+	0.643655i	−0.557730	+	0.643655i
$250$	−3.64502	+	1.07028i	−3.64502	+	1.07028i
$251$	−0.234072	−	0.512546i	−0.234072	−	0.512546i	0.755750	−	0.654861i	$-0.227273\pi$
$251$	−0.234072	−	0.512546i	−0.234072	−	0.512546i	−0.989821	+	0.142315i	$0.954545\pi$
$252$	0.682507			0.682507
$253$		0			0
$254$	0.284630			0.284630
$255$		0			0
$256$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$257$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$257$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$258$		0			0
$259$		0			0
$260$	0.512546	+	3.56484i	0.512546	+	3.56484i
$261$		0			0
$262$	1.66538	−	1.07028i	1.66538	−	1.07028i
$263$	0.118239	−	0.822373i	0.118239	−	0.822373i	−0.841254	−	0.540641i	$-0.818182\pi$
$263$	0.118239	−	0.822373i	0.118239	−	0.822373i	0.959493	−	0.281733i	$-0.0909091\pi$
$264$		0			0
$265$		0			0
$266$	0.153882	−	1.07028i	0.153882	−	1.07028i
$267$		0			0
$268$		0			0
$269$	0.153882	+	1.07028i	0.153882	+	1.07028i	0.909632	+	0.415415i	$0.136364\pi$
$269$	0.153882	+	1.07028i	0.153882	+	1.07028i	−0.755750	+	0.654861i	$0.772727\pi$
$270$	−1.22902	−	1.41837i	−1.22902	−	1.41837i
$271$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$271$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$272$		0			0
$273$	−0.983568	+	0.288802i	−0.983568	+	0.288802i
$274$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$275$		0			0
$276$	−0.474017	−	0.304632i	−0.474017	−	0.304632i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	0.627899	+	1.37491i	0.627899	+	1.37491i
$279$		0			0
$280$	1.29639	−	1.49611i	1.29639	−	1.49611i
$281$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$281$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$282$		0			0
$283$	−0.258908	−	1.80075i	−0.258908	−	1.80075i	−0.540641	−	0.841254i	$-0.681818\pi$
$283$	−0.258908	−	1.80075i	−0.258908	−	1.80075i	0.281733	−	0.959493i	$-0.409091\pi$
$284$	0.797176	+	0.234072i	0.797176	+	0.234072i
$285$	−1.01466	+	0.652081i	−1.01466	+	0.652081i
$286$		0			0
$287$		0			0
$288$	0.283524	−	0.620830i	0.283524	−	0.620830i
$289$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.368991	+	0.425839i	0.368991	+	0.425839i	0.909632	−	0.415415i	$-0.136364\pi$
$293$	0.368991	+	0.425839i	0.368991	+	0.425839i	−0.540641	+	0.841254i	$0.681818\pi$
$294$	0.474017	+	0.304632i	0.474017	+	0.304632i
$295$	1.40176	−	1.61772i	1.40176	−	1.61772i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.74557	−	0.512546i	−1.74557	−	0.512546i
$300$	−1.64475			−1.64475
$301$		0			0
$302$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$303$		0			0
$304$	−0.909632	−	0.584585i	−0.909632	−	0.584585i
$305$		0			0
$306$		0			0
$307$	1.74557	+	0.512546i	1.74557	+	0.512546i	0.989821	−	0.142315i	$-0.0454545\pi$
$307$	1.74557	+	0.512546i	1.74557	+	0.512546i	0.755750	+	0.654861i	$0.227273\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$311$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$312$	−0.145886	+	1.01466i	−0.145886	+	1.01466i
$313$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$313$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$314$	−1.45027	−	0.425839i	−1.45027	−	0.425839i
$315$	0.192284	+	1.33737i	0.192284	+	1.33737i
$316$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$317$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$317$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$318$		0			0
$319$		0			0
$320$	−0.822373	−	1.80075i	−0.822373	−	1.80075i
$321$		0			0
$322$	0.415415	+	0.909632i	0.415415	+	0.909632i
$323$		0			0
$324$	0.0616156	+	0.134919i	0.0616156	+	0.134919i
$325$	−5.09530	+	1.49611i	−5.09530	+	1.49611i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$331$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$332$	0.215109	−	1.49611i	0.215109	−	1.49611i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.474017	−	0.304632i	0.474017	−	0.304632i
$337$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.654861	−	0.755750i	$-0.272727\pi$
$337$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.142315	+	0.989821i	$0.454545\pi$
$338$	0.328708	+	2.28621i	0.328708	+	2.28621i
$339$	0.483276	+	0.557730i	0.483276	+	0.557730i
$340$		0			0
$341$		0			0
$342$	0.708089	−	0.207914i	0.708089	−	0.207914i
$343$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$344$		0			0
$345$	0.463379	−	1.01466i	0.463379	−	1.01466i
$346$	1.51150			1.51150
$347$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$347$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$348$		0			0
$349$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$349$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$350$	2.45561	+	1.57812i	2.45561	+	1.57812i
$351$	−1.12945	−	1.30346i	−1.12945	−	1.30346i
$352$		0			0
$353$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$353$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$354$	0.512546	−	0.329393i	0.512546	−	0.329393i
$355$	−0.234072	+	1.62801i	−0.234072	+	1.62801i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$359$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$360$	1.29639	+	0.380655i	1.29639	+	0.380655i
$361$	−0.0240754	−	0.167448i	−0.0240754	−	0.167448i
$362$	−0.368991	−	0.425839i	−0.368991	−	0.425839i
$363$	−0.474017	−	0.304632i	−0.474017	−	0.304632i
$364$	1.19136	−	1.37491i	1.19136	−	1.37491i
$365$		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		−0.841254	−	0.540641i	$-0.818182\pi$
$373$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$374$		0			0
$375$	−0.304632	−	2.11876i	−0.304632	−	2.11876i
$376$		0			0
$377$		0			0
$378$	−0.134919	+	0.938384i	−0.134919	+	0.938384i
$379$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$379$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$380$	0.889217	−	1.94711i	0.889217	−	1.94711i
$381$	−0.0228243	+	0.158746i	−0.0228243	+	0.158746i
$382$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$383$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$383$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$384$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i
$385$		0			0
$386$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$387$		0			0
$388$		0			0
$389$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$389$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$390$	−2.02932			−2.02932
$391$		0			0
$392$	−1.00000			−1.00000
$393$	0.463379	+	1.01466i	0.463379	+	1.01466i
$394$		0			0
$395$	1.69791	−	1.95949i	1.69791	−	1.95949i
$396$		0			0
$397$	1.19136	+	1.37491i	1.19136	+	1.37491i	0.909632	+	0.415415i	$0.136364\pi$
$397$	1.19136	+	1.37491i	1.19136	+	1.37491i	0.281733	+	0.959493i	$0.409091\pi$
$398$		0			0
$399$	0.584585	+	0.171650i	0.584585	+	0.171650i
$400$	2.45561	−	1.57812i	2.45561	−	1.57812i
$401$	0.118239	−	0.822373i	0.118239	−	0.822373i	−0.841254	−	0.540641i	$-0.818182\pi$
$401$	0.118239	−	0.822373i	0.118239	−	0.822373i	0.959493	−	0.281733i	$-0.0909091\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.247014	+	0.158746i	−0.247014	+	0.158746i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$409$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$410$		0			0
$411$	0.909632	−	0.267092i	0.909632	−	0.267092i
$412$		0			0
$413$	−1.08128			−1.08128
$414$	−0.446947	+	0.515804i	−0.446947	+	0.515804i
$415$	2.99223			2.99223
$416$	−0.755750	−	1.65486i	−0.755750	−	1.65486i
$417$	−0.817178	+	0.239945i	−0.817178	+	0.239945i
$418$		0			0
$419$	1.53046	+	0.983568i	1.53046	+	0.983568i	0.989821	+	0.142315i	$0.0454545\pi$
$419$	1.53046	+	0.983568i	1.53046	+	0.983568i	0.540641	+	0.841254i	$0.318182\pi$
$420$	0.730471	+	0.843008i	0.730471	+	0.843008i
$421$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$421$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.194474	+	0.425839i	−0.194474	+	0.425839i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$431$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$432$	0.797537	+	0.512546i	0.797537	+	0.512546i
$433$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$433$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.708089	+	0.817178i	0.708089	+	0.817178i
$438$		0			0
$439$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$439$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$440$		0			0
$441$	0.446947	−	0.515804i	0.446947	−	0.515804i
$442$		0			0
$443$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$443$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$449$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$449$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$450$	−0.283524	+	1.97195i	−0.283524	+	1.97195i
$451$		0			0
$452$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$453$	−0.153882	−	1.07028i	−0.153882	−	1.07028i
$454$	0.989821	+	1.14231i	0.989821	+	1.14231i
$455$	3.02977	+	1.94711i	3.02977	+	1.94711i
$456$	0.398983	−	0.460451i	0.398983	−	0.460451i
$457$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$457$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$458$	−0.449181	−	0.983568i	−0.449181	−	0.983568i
$459$		0			0
$460$	0.281733	+	1.95949i	0.281733	+	1.95949i
$461$	1.51150			1.51150			0.755750	−	0.654861i	$-0.227273\pi$
$461$	1.51150			1.51150			0.755750	+	0.654861i	$0.227273\pi$
$462$		0			0
$463$	0.797176	−	0.234072i	0.797176	−	0.234072i	0.142315	−	0.989821i	$-0.454545\pi$
$463$	0.797176	−	0.234072i	0.797176	−	0.234072i	0.654861	+	0.755750i	$0.272727\pi$
$464$		0			0
$465$		0			0
$466$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$467$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i	−0.989821	−	0.142315i	$-0.954545\pi$
$467$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i	0.909632	−	0.415415i	$-0.136364\pi$
$468$	1.19136	+	0.349816i	1.19136	+	0.349816i
$469$		0			0
$470$		0			0
$471$	0.353799	−	0.774713i	0.353799	−	0.774713i
$472$	−0.449181	+	0.983568i	−0.449181	+	0.983568i
$473$		0			0
$474$	0.620830	−	0.398983i	0.620830	−	0.398983i
$475$	3.02840	+	0.889217i	3.02840	+	0.889217i
$476$		0			0
$477$		0			0
$478$	0.239446	+	0.153882i	0.239446	+	0.153882i
$479$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$479$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$480$	1.07028	−	0.314261i	1.07028	−	0.314261i
$481$		0			0
$482$		0			0
$483$	−0.540641	+	0.158746i	−0.540641	+	0.158746i
$484$	1.00000			1.00000
$485$		0			0
$486$	−0.989821	+	0.290638i	−0.989821	+	0.290638i
$487$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$487$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$488$		0			0
$489$		0			0
$490$	−0.281733	−	1.95949i	−0.281733	−	1.95949i
$491$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$491$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$492$		0			0
$493$		0			0
$494$	0.817178	−	1.78937i	0.817178	−	1.78937i
$495$		0			0
$496$		0			0
$497$	0.698939	−	0.449181i	0.698939	−	0.449181i
$498$	0.817178	+	0.239945i	0.817178	+	0.239945i
$499$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$499$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$500$	2.48775	+	2.87102i	2.48775	+	2.87102i
$501$		0			0
$502$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$503$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$503$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$504$	−0.283524	−	0.620830i	−0.283524	−	0.620830i
$505$		0			0
$506$		0			0
$507$	−1.30145			−1.30145
$508$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$509$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.909632	−	0.415415i	$-0.136364\pi$
$509$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.989821	−	0.142315i	$-0.0454545\pi$
$510$		0			0
$511$		0			0
$512$	0.654861	+	0.755750i	0.654861	+	0.755750i
$513$	0.145886	+	1.01466i	0.145886	+	1.01466i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.121206	+	0.843008i	−0.121206	+	0.843008i
$520$	3.02977	−	1.94711i	3.02977	−	1.94711i
$521$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$521$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$522$		0			0
$523$	−0.989821	−	1.14231i	−0.989821	−	1.14231i	−0.989821	−	0.142315i	$-0.954545\pi$
$523$	−0.989821	−	1.14231i	−0.989821	−	1.14231i		−	1.00000i	$-0.5\pi$
$524$	−1.66538	−	1.07028i	−1.66538	−	1.07028i
$525$	−1.07708	+	1.24302i	−1.07708	+	1.24302i
$526$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$527$		0			0
$528$		0			0
$529$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$530$		0			0
$531$	−0.306569	−	0.671292i	−0.306569	−	0.671292i
$532$	−1.03748	+	0.304632i	−1.03748	+	0.304632i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.909632	−	0.584585i	0.909632	−	0.584585i
$539$		0			0
$540$	−0.779638	+	1.70717i	−0.779638	+	1.70717i
$541$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$541$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$542$		0			0
$543$	0.267092	−	0.171650i	0.267092	−	0.171650i
$544$		0			0
$545$		0			0
$546$	0.671292	+	0.774713i	0.671292	+	0.774713i
$547$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$547$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$548$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−0.0801894	+	0.557730i	−0.0801894	+	0.557730i
$553$	−1.30972			−1.30972
$554$		0			0
$555$		0			0
$556$	0.989821	−	1.14231i	0.989821	−	1.14231i
$557$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$557$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$558$		0			0
$559$		0			0
$560$	−1.89945	−	0.557730i	−1.89945	−	0.557730i
$561$		0			0
$562$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$563$	−0.755750	+	1.65486i	−0.755750	+	1.65486i			1.00000i	$0.5\pi$
$563$	−0.755750	+	1.65486i	−0.755750	+	1.65486i	−0.755750	+	0.654861i	$0.772727\pi$
$564$		0			0
$565$	0.368991	−	2.56639i	0.368991	−	2.56639i
$566$	−1.53046	+	0.983568i	−1.53046	+	0.983568i
$567$	0.142315	+	0.0417874i	0.142315	+	0.0417874i
$568$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$569$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.841254	−	0.540641i	$-0.818182\pi$
$569$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.415415	−	0.909632i	$-0.636364\pi$
$570$	1.01466	+	0.652081i	1.01466	+	0.652081i
$571$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$571$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$572$		0			0
$573$	−0.449181	−	0.983568i	−0.449181	−	0.983568i
$574$		0			0
$575$	−2.80075	+	0.822373i	−2.80075	+	0.822373i
$576$	−0.682507			−0.682507
$577$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$577$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$578$	0.959493	−	0.281733i	0.959493	−	0.281733i
$579$	0.105026	−	0.121206i	0.105026	−	0.121206i
$580$		0			0
$581$	−0.989821	−	1.14231i	−0.989821	−	1.14231i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.349816	+	2.43303i	−0.349816	+	2.43303i
$586$	0.234072	−	0.512546i	0.234072	−	0.512546i
$587$	0.755750	−	1.65486i	0.755750	−	1.65486i		−	1.00000i	$-0.5\pi$
$587$	0.755750	−	1.65486i	0.755750	−	1.65486i	0.755750	−	0.654861i	$-0.227273\pi$
$588$	0.0801894	−	0.557730i	0.0801894	−	0.557730i
$589$		0			0
$590$	−2.05384	−	0.603063i	−2.05384	−	0.603063i
$591$		0			0
$592$		0			0
$593$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$593$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.258908	+	1.80075i	0.258908	+	1.80075i
$599$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$599$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$600$	0.683252	+	1.49611i	0.683252	+	1.49611i
$601$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$601$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$602$		0			0
$603$		0			0
$604$	1.25667	+	1.45027i	1.25667	+	1.45027i
$605$	0.281733	+	1.95949i	0.281733	+	1.95949i
$606$		0			0
$607$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$607$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$608$	−0.153882	+	1.07028i	−0.153882	+	1.07028i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$613$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$614$	−0.258908	−	1.80075i	−0.258908	−	1.80075i
$615$		0			0
$616$		0			0
$617$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$617$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$618$		0			0
$619$	0.627899	+	1.37491i	0.627899	+	1.37491i	0.909632	+	0.415415i	$0.136364\pi$
$619$	0.627899	+	1.37491i	0.627899	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$620$		0			0
$621$	−0.620830	−	0.716476i	−0.620830	−	0.716476i
$622$		0			0
$623$		0			0
$624$	0.983568	−	0.288802i	0.983568	−	0.288802i
$625$	−3.01334	+	3.47758i	−3.01334	+	3.47758i
$626$		0			0
$627$		0			0
$628$	0.215109	+	1.49611i	0.215109	+	1.49611i
$629$		0			0
$630$	1.13663	−	0.730471i	1.13663	−	0.730471i
$631$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	0.142315	+	0.989821i	$0.454545\pi$
$631$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	−0.415415	+	0.909632i	$0.636364\pi$
$632$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$633$		0			0
$634$		0			0
$635$	0.474017	−	0.304632i	0.474017	−	0.304632i
$636$		0			0
$637$	−0.258908	−	1.80075i	−0.258908	−	1.80075i
$638$		0			0
$639$	0.477031	+	0.306569i	0.477031	+	0.306569i
$640$	−1.29639	+	1.49611i	−1.29639	+	1.49611i
$641$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$641$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	0.142315	+	0.989821i	$0.454545\pi$
$642$		0			0
$643$	−0.563465			−0.563465			−0.281733	−	0.959493i	$-0.590909\pi$
$643$	−0.563465			−0.563465			−0.281733	+	0.959493i	$0.590909\pi$
$644$	0.654861	−	0.755750i	0.654861	−	0.755750i
$645$		0			0
$646$		0			0
$647$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$647$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$648$	0.0971309	−	0.112095i	0.0971309	−	0.112095i
$649$		0			0
$650$	3.47758	+	4.01334i	3.47758	+	4.01334i
$651$		0			0
$652$		0			0
$653$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$653$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$654$		0			0
$655$	1.62801	−	3.56484i	1.62801	−	3.56484i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$659$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$660$		0			0
$661$	−1.19136	−	1.37491i	−1.19136	−	1.37491i	−0.909632	−	0.415415i	$-0.863636\pi$
$661$	−1.19136	−	1.37491i	−1.19136	−	1.37491i	−0.281733	−	0.959493i	$-0.590909\pi$
$662$		0			0
$663$		0			0
$664$	−1.45027	+	0.425839i	−1.45027	+	0.425839i
$665$	−0.889217	−	1.94711i	−0.889217	−	1.94711i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.474017	−	0.304632i	−0.474017	−	0.304632i
$673$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$673$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$674$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$675$	−2.65520	−	0.779638i	−2.65520	−	0.779638i
$676$	1.94306	−	1.24873i	1.94306	−	1.24873i
$677$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$677$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	−0.755750	+	0.654861i	$0.772727\pi$
$678$	0.306569	−	0.671292i	0.306569	−	0.671292i
$679$		0			0
$680$		0			0
$681$	−0.716476	+	0.460451i	−0.716476	+	0.460451i
$682$		0			0
$683$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$683$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$684$	−0.483276	−	0.557730i	−0.483276	−	0.557730i
$685$	−2.80202	−	1.80075i	−2.80202	−	1.80075i
$686$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$687$	0.584585	−	0.171650i	0.584585	−	0.171650i
$688$		0			0
$689$		0			0
$690$	−1.11546			−1.11546
$691$	−1.08128			−1.08128			−0.540641	−	0.841254i	$-0.681818\pi$
$691$	−1.08128			−1.08128			−0.540641	+	0.841254i	$0.681818\pi$
$692$	−0.627899	−	1.37491i	−0.627899	−	1.37491i
$693$		0			0
$694$		0			0
$695$	2.51722	+	1.61772i	2.51722	+	1.61772i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	0.620830	−	0.398983i	0.620830	−	0.398983i
$700$	0.415415	−	2.88927i	0.415415	−	2.88927i
$701$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$701$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$702$	−0.716476	+	1.56886i	−0.716476	+	1.56886i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$	−0.512546	−	0.329393i	−0.512546	−	0.329393i
$709$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$709$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$710$	1.57812	−	0.463379i	1.57812	−	0.463379i
$711$	−0.371337	−	0.813115i	−0.371337	−	0.813115i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.105026	+	0.121206i	−0.105026	+	0.121206i
$718$	0.239446	+	0.153882i	0.239446	+	0.153882i
$719$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$719$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$720$	−0.192284	−	1.33737i	−0.192284	−	1.33737i
$721$		0			0
$722$	−0.142315	+	0.0914602i	−0.142315	+	0.0914602i
$723$		0			0
$724$	−0.234072	+	0.512546i	−0.234072	+	0.512546i
$725$		0			0
$726$	−0.0801894	+	0.557730i	−0.0801894	+	0.557730i
$727$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$727$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$728$	−1.74557	−	0.512546i	−1.74557	−	0.512546i
$729$	−0.0616156	−	0.428546i	−0.0616156	−	0.428546i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	1.74557	−	0.512546i	1.74557	−	0.512546i	0.755750	−	0.654861i	$-0.227273\pi$
$733$	1.74557	−	0.512546i	1.74557	−	0.512546i	0.989821	+	0.142315i	$0.0454545\pi$
$734$		0			0
$735$	1.11546			1.11546
$736$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$737$		0			0
$738$		0			0
$739$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$739$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$740$		0			0
$741$	0.932456	+	0.599253i	0.932456	+	0.599253i
$742$		0			0
$743$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$743$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.428546	−	0.938384i	0.428546	−	0.938384i
$748$		0			0
$749$		0			0
$750$	−1.80075	+	1.15727i	−1.80075	+	1.15727i
$751$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$751$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$752$		0			0
$753$	−0.207914	−	0.239945i	−0.207914	−	0.239945i
$754$		0			0
$755$	−2.48775	+	2.87102i	−2.48775	+	2.87102i
$756$	0.909632	−	0.267092i	0.909632	−	0.267092i
$757$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$757$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$758$		0			0
$759$		0			0
$760$	−2.14055			−2.14055
$761$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$761$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$762$	0.153882	−	0.0451840i	0.153882	−	0.0451840i
$763$		0			0
$764$	1.61435	+	1.03748i	1.61435	+	1.03748i
$765$		0			0
$766$		0			0
$767$	−1.88745	−	0.554206i	−1.88745	−	0.554206i
$768$	−0.474017	+	0.304632i	−0.474017	+	0.304632i
$769$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$769$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$770$		0			0
$771$		0			0
$772$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$773$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.755750	−	0.654861i	$-0.227273\pi$
$773$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.909632	−	0.415415i	$-0.136364\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	0.843008	+	1.84593i	0.843008	+	1.84593i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.415415	+	0.909632i	0.415415	+	0.909632i
$785$	−2.87102	+	0.843008i	−2.87102	+	0.843008i
$786$	0.730471	−	0.843008i	0.730471	−	0.843008i
$787$	0.909632	+	0.584585i	0.909632	+	0.584585i	0.909632	−	0.415415i	$-0.136364\pi$
$787$	0.909632	+	0.584585i	0.909632	+	0.584585i			1.00000i	$0.5\pi$
$788$		0			0
$789$	−0.0666238	−	0.463379i	−0.0666238	−	0.463379i
$790$	−2.48775	−	0.730471i	−2.48775	−	0.730471i
$791$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$792$		0			0
$793$		0			0
$794$	0.755750	−	1.65486i	0.755750	−	1.65486i
$795$		0			0
$796$		0			0
$797$	−1.74557	−	0.512546i	−1.74557	−	0.512546i	−0.755750	−	0.654861i	$-0.772727\pi$
$797$	−1.74557	−	0.512546i	−1.74557	−	0.512546i	−0.989821	+	0.142315i	$0.954545\pi$
$798$	−0.0867074	−	0.603063i	−0.0867074	−	0.603063i
$799$		0			0
$800$	−2.45561	−	1.57812i	−2.45561	−	1.57812i
$801$		0			0
$802$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$803$		0			0
$804$		0			0
$805$	1.66538	+	1.07028i	1.66538	+	1.07028i
$806$		0			0
$807$	0.253098	+	0.554206i	0.253098	+	0.554206i
$808$		0			0
$809$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	0.142315	+	0.989821i	$0.454545\pi$
$809$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	−1.00000			$\pi$
$810$	0.247014	+	0.158746i	0.247014	+	0.158746i
$811$	−0.708089	−	0.817178i	−0.708089	−	0.817178i	0.281733	−	0.959493i	$-0.409091\pi$
$811$	−0.708089	−	0.817178i	−0.708089	−	0.817178i	−0.989821	+	0.142315i	$0.954545\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	1.04455	−	0.671292i	1.04455	−	0.671292i
$820$		0			0
$821$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$821$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$822$	−0.620830	−	0.716476i	−0.620830	−	0.716476i
$823$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−0.415415	−	0.909632i	$-0.636364\pi$
$823$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−1.00000			$\pi$
$824$		0			0
$825$		0			0
$826$	0.449181	+	0.983568i	0.449181	+	0.983568i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	0.654861	+	0.192284i	0.654861	+	0.192284i
$829$	1.97964			1.97964			0.989821	−	0.142315i	$-0.0454545\pi$
$829$	1.97964			1.97964			0.989821	+	0.142315i	$0.0454545\pi$
$830$	−1.24302	−	2.72183i	−1.24302	−	2.72183i
$831$		0			0
$832$	−1.19136	+	1.37491i	−1.19136	+	1.37491i
$833$		0			0
$834$	0.557730	+	0.643655i	0.557730	+	0.643655i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.258908	−	1.80075i	0.258908	−	1.80075i
$839$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$839$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$840$	0.463379	−	1.01466i	0.463379	−	1.01466i
$841$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$842$		0			0
$843$	−0.153882	−	0.0451840i	−0.153882	−	0.0451840i
$844$		0			0
$845$	2.99430	+	3.45561i	2.99430	+	3.45561i
$846$		0			0
$847$	0.654861	−	0.755750i	0.654861	−	0.755750i
$848$		0			0
$849$	−0.425839	−	0.932456i	−0.425839	−	0.932456i
$850$		0			0
$851$		0			0
$852$	0.468144			0.468144
$853$	0.627899	+	1.37491i	0.627899	+	1.37491i	0.909632	+	0.415415i	$0.136364\pi$
$853$	0.627899	+	1.37491i	0.627899	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$854$		0			0
$855$	0.956713	−	1.10411i	0.956713	−	1.10411i
$856$		0			0
$857$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$857$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$858$		0			0
$859$	−1.89945	−	0.557730i	−1.89945	−	0.557730i	−0.989821	−	0.142315i	$-0.954545\pi$
$859$	−1.89945	−	0.557730i	−1.89945	−	0.557730i	−0.909632	−	0.415415i	$-0.863636\pi$
$860$		0			0
$861$		0			0
$862$	0.544078	−	1.19136i	0.544078	−	1.19136i
$863$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$863$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	−0.841254	+	0.540641i	$0.818182\pi$
$864$	0.134919	−	0.938384i	0.134919	−	0.938384i
$865$	2.51722	−	1.61772i	2.51722	−	1.61772i
$866$		0			0
$867$	0.0801894	+	0.557730i	0.0801894	+	0.557730i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	0.449181	−	0.983568i	0.449181	−	0.983568i
$875$	3.79891			3.79891
$876$		0			0
$877$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$877$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$878$		0			0
$879$	0.267092	+	0.171650i	0.267092	+	0.171650i
$880$		0			0
$881$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$881$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$882$	−0.654861	−	0.192284i	−0.654861	−	0.192284i
$883$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$883$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$884$		0			0
$885$	0.501043	−	1.09713i	0.501043	−	1.09713i
$886$		0			0
$887$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$887$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$888$		0			0
$889$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.00000			1.00000
$897$	−1.02509			−1.02509
$898$	−1.68251			−1.68251
$899$		0			0
$900$	1.91153	−	0.561276i	1.91153	−	0.561276i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.186393	+	1.29639i	0.186393	+	1.29639i
$905$	−1.07028	−	0.314261i	−1.07028	−	0.314261i
$906$	−0.909632	+	0.584585i	−0.909632	+	0.584585i
$907$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$907$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$908$	0.627899	−	1.37491i	0.627899	−	1.37491i
$909$		0			0
$910$	0.512546	−	3.56484i	0.512546	−	3.56484i
$911$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$911$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$912$	−0.584585	−	0.171650i	−0.584585	−	0.171650i
$913$		0			0
$914$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$915$		0			0
$916$	−0.708089	+	0.817178i	−0.708089	+	0.817178i
$917$	−1.89945	+	0.557730i	−1.89945	+	0.557730i
$918$		0			0
$919$	−0.830830			−0.830830			−0.415415	−	0.909632i	$-0.636364\pi$
$919$	−0.830830			−0.830830			−0.415415	+	0.909632i	$0.636364\pi$
$920$	1.66538	−	1.07028i	1.66538	−	1.07028i
$921$	1.02509			1.02509
$922$	−0.627899	−	1.37491i	−0.627899	−	1.37491i
$923$	1.45027	−	0.425839i	1.45027	−	0.425839i
$924$		0			0
$925$		0			0
$926$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$927$		0			0
$928$		0			0
$929$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$929$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$930$		0			0
$931$	−0.449181	+	0.983568i	−0.449181	+	0.983568i
$932$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$933$		0			0
$934$	−0.474017	+	0.304632i	−0.474017	+	0.304632i
$935$		0			0
$936$	−0.176707	−	1.22902i	−0.176707	−	1.22902i
$937$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$937$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	−0.909632	−	0.415415i	$-0.863636\pi$
$941$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	0.281733	−	0.959493i	$-0.409091\pi$
$942$	−0.851677			−0.851677
$943$		0			0
$944$	1.08128			1.08128
$945$	0.779638	+	1.70717i	0.779638	+	1.70717i
$946$		0			0
$947$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$947$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$948$	−0.620830	−	0.398983i	−0.620830	−	0.398983i
$949$		0			0
$950$	−0.449181	−	3.12412i	−0.449181	−	3.12412i
$951$		0			0
$952$		0			0
$953$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$953$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$954$		0			0
$955$	−1.57812	+	3.45561i	−1.57812	+	3.45561i
$956$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$957$		0			0
$958$		0			0
$959$	0.239446	+	1.66538i	0.239446	+	1.66538i
$960$	−0.730471	−	0.843008i	−0.730471	−	0.843008i
$961$	0.841254	+	0.540641i	0.841254	+	0.540641i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.563465			−0.563465
$966$	0.368991	+	0.425839i	0.368991	+	0.425839i
$967$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$967$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$968$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$969$		0			0
$970$		0			0
$971$	1.66538	+	1.07028i	1.66538	+	1.07028i	0.909632	+	0.415415i	$0.136364\pi$
$971$	1.66538	+	1.07028i	1.66538	+	1.07028i	0.755750	+	0.654861i	$0.227273\pi$
$972$	0.675560	+	0.779638i	0.675560	+	0.779638i
$973$	−0.215109	−	1.49611i	−0.215109	−	1.49611i
$974$	0.797176	+	0.234072i	0.797176	+	0.234072i
$975$	−2.51722	+	1.61772i	−2.51722	+	1.61772i
$976$		0			0
$977$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$977$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$978$		0			0
$979$		0			0
$980$	−1.66538	+	1.07028i	−1.66538	+	1.07028i
$981$		0			0
$982$		0			0
$983$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$983$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−1.96714			−1.96714
$989$		0			0
$990$		0			0
$991$	0.118239	+	0.258908i	0.118239	+	0.258908i	0.959493	−	0.281733i	$-0.0909091\pi$
$991$	0.118239	+	0.258908i	0.118239	+	0.258908i	−0.841254	+	0.540641i	$0.818182\pi$
$992$		0			0
$993$		0			0
$994$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$995$		0			0
$996$	−0.121206	−	0.843008i	−0.121206	−	0.843008i
$997$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.989821	+	0.142315i	$0.0454545\pi$
$997$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.909632	+	0.415415i	$0.136364\pi$
$998$		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.349.2	yes	20
7.6	odd	2	inner	1288.1.bi.e.349.1	✓	20
8.5	even	2	inner	1288.1.bi.e.349.1	✓	20
23.6	even	11	inner	1288.1.bi.e.1133.2	yes	20
56.13	odd	2	CM	1288.1.bi.e.349.2	yes	20
161.6	odd	22	inner	1288.1.bi.e.1133.1	yes	20
184.29	even	22	inner	1288.1.bi.e.1133.1	yes	20
1288.1133	odd	22	inner	1288.1.bi.e.1133.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.1.bi.e.349.1	✓	20	7.6	odd	2	inner
1288.1.bi.e.349.1	✓	20	8.5	even	2	inner
1288.1.bi.e.349.2	yes	20	1.1	even	1	trivial
1288.1.bi.e.349.2	yes	20	56.13	odd	2	CM
1288.1.bi.e.1133.1	yes	20	161.6	odd	22	inner
1288.1.bi.e.1133.1	yes	20	184.29	even	22	inner
1288.1.bi.e.1133.2	yes	20	23.6	even	11	inner
1288.1.bi.e.1133.2	yes	20	1288.1133	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)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.540641 - 0.158746i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-1.66538 - 1.07028i) q^{5} +(-0.368991 - 0.425839i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.574161 + 0.368991i) q^{9} +(-0.281733 + 1.95949i) q^{10} +(-0.234072 + 0.512546i) q^{12} +(-0.258908 + 1.80075i) q^{13} +(0.841254 - 0.540641i) q^{14} +(-1.07028 - 0.314261i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.574161 + 0.368991i) q^{18} +(0.708089 - 0.817178i) q^{19} +(1.89945 - 0.557730i) q^{20} +(0.234072 + 0.512546i) q^{21} +(-0.142315 + 0.989821i) q^{23} +0.563465 q^{24} +(1.21259 + 2.65520i) q^{25} +(1.74557 - 0.512546i) q^{26} +(-0.620830 + 0.716476i) q^{27} +(-0.841254 - 0.540641i) q^{28} +(0.158746 + 1.10411i) q^{30} +(-0.841254 + 0.540641i) q^{32} +(0.822373 - 1.80075i) q^{35} +(0.0971309 - 0.675560i) q^{36} +(-1.03748 - 0.304632i) q^{38} +(0.145886 + 1.01466i) q^{39} +(-1.29639 - 1.49611i) q^{40} +(0.368991 - 0.425839i) q^{42} +1.35112 q^{45} +(0.959493 - 0.281733i) q^{46} +(-0.234072 - 0.512546i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(1.91153 - 2.20602i) q^{50} +(-1.19136 - 1.37491i) q^{52} +(0.909632 + 0.267092i) q^{54} +(-0.142315 + 0.989821i) q^{56} +(0.253098 - 0.554206i) q^{57} +(-0.153882 + 1.07028i) q^{59} +(0.938384 - 0.603063i) q^{60} +(-0.446947 - 0.515804i) q^{63} +(0.841254 + 0.540641i) q^{64} +(2.35848 - 2.72183i) q^{65} +(0.0801894 + 0.557730i) q^{69} -1.97964 q^{70} +(-0.345139 - 0.755750i) q^{71} +(-0.654861 + 0.192284i) q^{72} +(1.07708 + 1.24302i) q^{75} +(0.153882 + 1.07028i) q^{76} +(0.862362 - 0.554206i) q^{78} +(-0.186393 + 1.29639i) q^{79} +(-0.822373 + 1.80075i) q^{80} +(0.0616156 - 0.134919i) q^{81} +(-1.27155 + 0.817178i) q^{83} +(-0.540641 - 0.158746i) q^{84} +(-0.561276 - 1.22902i) q^{90} -1.81926 q^{91} +(-0.654861 - 0.755750i) q^{92} +(-2.05384 + 0.603063i) q^{95} +(-0.368991 + 0.425839i) q^{96} +(0.654861 + 0.755750i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9} - 2 q^{14} - 2 q^{16} + 20 q^{18} - 2 q^{23} + 2 q^{25} + 2 q^{28} + 22 q^{30} + 2 q^{32} + 2 q^{36} - 22 q^{39} + 2 q^{46} - 2 q^{49} - 2 q^{50}+ \cdots + 2 q^{98}+O(q^{100}) \) 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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