LMFDB - Embedded newform 1564.1.w.c.611.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1564,1,Mod(271,1564)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1564, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("1564.271");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1564 = 2^{2} \cdot 17 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1564.w (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:	$0.780537679758$
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:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{22}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{22} - \cdots)$

Embedding invariants

Embedding label			611.2
Root			$0.755750 + 0.654861i$ of defining polynomial
Character	$\chi$	$=$	1564.611
Dual form			1564.1.w.c.407.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.654861 + 0.755750i) q^{2} +(0.474017 + 0.304632i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.0801894 + 0.557730i) q^{6} +(1.89945 + 0.557730i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.283524 - 0.620830i) q^{9} +(-0.708089 + 0.817178i) q^{11} +(-0.368991 + 0.425839i) q^{12} +(-0.273100 + 0.0801894i) q^{13} +(0.822373 + 1.80075i) q^{14} +(-0.959493 - 0.281733i) q^{16} +(-0.142315 - 0.989821i) q^{17} +(0.283524 - 0.620830i) q^{18} +(0.730471 + 0.843008i) q^{21} -1.08128 q^{22} +(0.989821 - 0.142315i) q^{23} -0.563465 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-0.239446 - 0.153882i) q^{26} +(0.134919 - 0.938384i) q^{27} +(-0.822373 + 1.80075i) q^{28} +(-0.909632 + 0.584585i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(-0.584585 + 0.171650i) q^{33} +(0.654861 - 0.755750i) q^{34} +(0.654861 - 0.192284i) q^{36} +(-0.153882 - 0.0451840i) q^{39} +(-0.158746 + 1.10411i) q^{42} +(-0.708089 - 0.817178i) q^{44} +(0.755750 + 0.654861i) q^{46} +(-0.368991 - 0.425839i) q^{48} +(2.45561 + 1.57812i) q^{49} +(0.142315 - 0.989821i) q^{50} +(0.234072 - 0.512546i) q^{51} +(-0.0405070 - 0.281733i) q^{52} +(-1.61435 - 0.474017i) q^{53} +(0.797537 - 0.512546i) q^{54} +(-1.89945 + 0.557730i) q^{56} +(-1.03748 - 0.304632i) q^{62} +(-0.192284 - 1.33737i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.512546 - 0.329393i) q^{66} +1.00000 q^{68} +(0.512546 + 0.234072i) q^{69} +(0.574161 + 0.368991i) q^{72} +(-0.0801894 - 0.557730i) q^{75} +(-1.80075 + 1.15727i) q^{77} +(-0.0666238 - 0.145886i) q^{78} +(1.45027 - 0.425839i) q^{79} +(-0.0971309 + 0.112095i) q^{81} +(-0.938384 + 0.603063i) q^{84} +(0.153882 - 1.07028i) q^{88} +(-1.41542 - 0.909632i) q^{89} -0.563465 q^{91} +1.00000i q^{92} -0.609264 q^{93} +(0.0801894 - 0.557730i) q^{96} +(0.415415 + 2.88927i) q^{98} +(0.708089 + 0.207914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9} + 4 q^{13} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 22 q^{33} + 2 q^{34} + 2 q^{36} - 22 q^{42} + 2 q^{49} + 2 q^{50} - 18 q^{52}+ \cdots - 2 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 + 2 * q^9 + 4 * q^13 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^25 - 4 * q^26 + 2 * q^32 - 22 * q^33 + 2 * q^34 + 2 * q^36 - 22 * q^42 + 2 * q^49 + 2 * q^50 - 18 * q^52 - 4 * q^53 - 2 * q^64 + 20 * q^68 + 20 * q^72 - 2 * q^81 - 18 * q^89 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1564\mathbb{Z}\right)^\times$.

$n$	$783$	$921$	$1293$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{11}\right)$

Coefficient data

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

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

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

$2$	0.654861	+	0.755750i	0.654861	+	0.755750i
$2$	0.654861	+	0.755750i	0.654861	+	0.755750i
$3$	0.474017	+	0.304632i	0.474017	+	0.304632i	0.755750	−	0.654861i	$-0.227273\pi$
$3$	0.474017	+	0.304632i	0.474017	+	0.304632i	−0.281733	+	0.959493i	$0.590909\pi$
$4$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$5$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$5$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$6$	0.0801894	+	0.557730i	0.0801894	+	0.557730i
$7$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.989821	+	0.142315i	$0.0454545\pi$
$7$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.909632	+	0.415415i	$0.136364\pi$
$8$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$9$	−0.283524	−	0.620830i	−0.283524	−	0.620830i
$10$		0			0
$11$	−0.708089	+	0.817178i	−0.708089	+	0.817178i	−0.989821	−	0.142315i	$-0.954545\pi$
$11$	−0.708089	+	0.817178i	−0.708089	+	0.817178i	0.281733	+	0.959493i	$0.409091\pi$
$12$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$13$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$13$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	0.142315	+	0.989821i	$0.454545\pi$
$14$	0.822373	+	1.80075i	0.822373	+	1.80075i
$15$		0			0
$16$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$17$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$17$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$18$	0.283524	−	0.620830i	0.283524	−	0.620830i
$19$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$19$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$20$		0			0
$21$	0.730471	+	0.843008i	0.730471	+	0.843008i
$22$	−1.08128			−1.08128
$23$	0.989821	−	0.142315i	0.989821	−	0.142315i
$23$	0.989821	−	0.142315i	0.989821	−	0.142315i
$24$	−0.563465			−0.563465
$25$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$26$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$27$	0.134919	−	0.938384i	0.134919	−	0.938384i
$28$	−0.822373	+	1.80075i	−0.822373	+	1.80075i
$29$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$29$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$30$		0			0
$31$	−0.909632	+	0.584585i	−0.909632	+	0.584585i	−0.909632	−	0.415415i	$-0.863636\pi$
$31$	−0.909632	+	0.584585i	−0.909632	+	0.584585i			1.00000i	$0.5\pi$
$32$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$33$	−0.584585	+	0.171650i	−0.584585	+	0.171650i
$34$	0.654861	−	0.755750i	0.654861	−	0.755750i
$35$		0			0
$36$	0.654861	−	0.192284i	0.654861	−	0.192284i
$37$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$37$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$38$		0			0
$39$	−0.153882	−	0.0451840i	−0.153882	−	0.0451840i
$40$		0			0
$41$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$41$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$42$	−0.158746	+	1.10411i	−0.158746	+	1.10411i
$43$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$43$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$44$	−0.708089	−	0.817178i	−0.708089	−	0.817178i
$45$		0			0
$46$	0.755750	+	0.654861i	0.755750	+	0.654861i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−0.368991	−	0.425839i	−0.368991	−	0.425839i
$49$	2.45561	+	1.57812i	2.45561	+	1.57812i
$50$	0.142315	−	0.989821i	0.142315	−	0.989821i
$51$	0.234072	−	0.512546i	0.234072	−	0.512546i
$52$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$53$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$53$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$54$	0.797537	−	0.512546i	0.797537	−	0.512546i
$55$		0			0
$56$	−1.89945	+	0.557730i	−1.89945	+	0.557730i
$57$		0			0
$58$		0			0
$59$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$59$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$60$		0			0
$61$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$61$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$62$	−1.03748	−	0.304632i	−1.03748	−	0.304632i
$63$	−0.192284	−	1.33737i	−0.192284	−	1.33737i
$64$	0.415415	−	0.909632i	0.415415	−	0.909632i
$65$		0			0
$66$	−0.512546	−	0.329393i	−0.512546	−	0.329393i
$67$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$67$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$68$	1.00000			1.00000
$69$	0.512546	+	0.234072i	0.512546	+	0.234072i
$70$		0			0
$71$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$71$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$72$	0.574161	+	0.368991i	0.574161	+	0.368991i
$73$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$73$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$74$		0			0
$75$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i
$76$		0			0
$77$	−1.80075	+	1.15727i	−1.80075	+	1.15727i
$78$	−0.0666238	−	0.145886i	−0.0666238	−	0.145886i
$79$	1.45027	−	0.425839i	1.45027	−	0.425839i	0.540641	−	0.841254i	$-0.318182\pi$
$79$	1.45027	−	0.425839i	1.45027	−	0.425839i	0.909632	+	0.415415i	$0.136364\pi$
$80$		0			0
$81$	−0.0971309	+	0.112095i	−0.0971309	+	0.112095i
$82$		0			0
$83$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$83$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$84$	−0.938384	+	0.603063i	−0.938384	+	0.603063i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.153882	−	1.07028i	0.153882	−	1.07028i
$89$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−0.415415	−	0.909632i	$-0.636364\pi$
$89$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−1.00000			$\pi$
$90$		0			0
$91$	−0.563465			−0.563465
$92$			1.00000i			1.00000i
$93$	−0.609264			−0.609264
$94$		0			0
$95$		0			0
$96$	0.0801894	−	0.557730i	0.0801894	−	0.557730i
$97$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$97$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$98$	0.415415	+	2.88927i	0.415415	+	2.88927i
$99$	0.708089	+	0.207914i	0.708089	+	0.207914i
$100$	0.841254	−	0.540641i	0.841254	−	0.540641i
$101$	0.544078	+	1.19136i	0.544078	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$101$	0.544078	+	1.19136i	0.544078	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$102$	0.540641	−	0.158746i	0.540641	−	0.158746i
$103$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$103$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$104$	0.186393	−	0.215109i	0.186393	−	0.215109i
$105$		0			0
$106$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$107$	−1.53046	+	0.983568i	−1.53046	+	0.983568i	−0.540641	+	0.841254i	$0.681818\pi$
$107$	−1.53046	+	0.983568i	−1.53046	+	0.983568i	−0.989821	+	0.142315i	$0.954545\pi$
$108$	0.909632	+	0.267092i	0.909632	+	0.267092i
$109$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$109$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$110$		0			0
$111$		0			0
$112$	−1.66538	−	1.07028i	−1.66538	−	1.07028i
$113$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$113$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.127214	+	0.146813i	0.127214	+	0.146813i
$118$		0			0
$119$	0.281733	−	1.95949i	0.281733	−	1.95949i
$120$		0			0
$121$	−0.0240754	−	0.167448i	−0.0240754	−	0.167448i
$122$		0			0
$123$		0			0
$124$	−0.449181	−	0.983568i	−0.449181	−	0.983568i
$125$		0			0
$126$	0.884796	−	1.02111i	0.884796	−	1.02111i
$127$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$127$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$128$	0.959493	−	0.281733i	0.959493	−	0.281733i
$129$		0			0
$130$		0			0
$131$	−1.74557	−	0.512546i	−1.74557	−	0.512546i	−0.755750	−	0.654861i	$-0.772727\pi$
$131$	−1.74557	−	0.512546i	−1.74557	−	0.512546i	−0.989821	+	0.142315i	$0.954545\pi$
$132$	−0.0867074	−	0.603063i	−0.0867074	−	0.603063i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.654861	+	0.755750i	0.654861	+	0.755750i
$137$	1.30972			1.30972			0.654861	−	0.755750i	$-0.272727\pi$
$137$	1.30972			1.30972			0.654861	+	0.755750i	$0.272727\pi$
$138$	0.158746	+	0.540641i	0.158746	+	0.540641i
$139$	1.81926			1.81926			0.909632	−	0.415415i	$-0.136364\pi$
$139$	1.81926			1.81926			0.909632	+	0.415415i	$0.136364\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.127850	−	0.279953i	0.127850	−	0.279953i
$144$	0.0971309	+	0.675560i	0.0971309	+	0.675560i
$145$		0			0
$146$		0			0
$147$	0.683252	+	1.49611i	0.683252	+	1.49611i
$148$		0			0
$149$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$149$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$150$	0.368991	−	0.425839i	0.368991	−	0.425839i
$151$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$151$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$152$		0			0
$153$	−0.574161	+	0.368991i	−0.574161	+	0.368991i
$154$	−2.05384	−	0.603063i	−2.05384	−	0.603063i
$155$		0			0
$156$	0.0666238	−	0.145886i	0.0666238	−	0.145886i
$157$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$157$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$158$	1.27155	+	0.817178i	1.27155	+	0.817178i
$159$	−0.620830	−	0.716476i	−0.620830	−	0.716476i
$160$		0			0
$161$	1.95949	+	0.281733i	1.95949	+	0.281733i
$162$	−0.148323			−0.148323
$163$	1.29639	+	1.49611i	1.29639	+	1.49611i	0.755750	+	0.654861i	$0.227273\pi$
$163$	1.29639	+	1.49611i	1.29639	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.215109	−	1.49611i	−0.215109	−	1.49611i	−0.755750	−	0.654861i	$-0.772727\pi$
$167$	−0.215109	−	1.49611i	−0.215109	−	1.49611i	0.540641	−	0.841254i	$-0.318182\pi$
$168$	−1.07028	−	0.314261i	−1.07028	−	0.314261i
$169$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$173$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$174$		0			0
$175$	−0.822373	−	1.80075i	−0.822373	−	1.80075i
$176$	0.909632	−	0.584585i	0.909632	−	0.584585i
$177$		0			0
$178$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$179$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$179$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$180$		0			0
$181$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$181$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$182$	−0.368991	−	0.425839i	−0.368991	−	0.425839i
$183$		0			0
$184$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$185$		0			0
$186$	−0.398983	−	0.460451i	−0.398983	−	0.460451i
$187$	0.909632	+	0.584585i	0.909632	+	0.584585i
$188$		0			0
$189$	0.779638	−	1.70717i	0.779638	−	1.70717i
$190$		0			0
$191$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$191$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$192$	0.474017	−	0.304632i	0.474017	−	0.304632i
$193$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$193$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$194$		0			0
$195$		0			0
$196$	−1.91153	+	2.20602i	−1.91153	+	2.20602i
$197$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$197$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$198$	0.306569	+	0.671292i	0.306569	+	0.671292i
$199$	0.474017	−	0.304632i	0.474017	−	0.304632i	−0.281733	−	0.959493i	$-0.590909\pi$
$199$	0.474017	−	0.304632i	0.474017	−	0.304632i	0.755750	+	0.654861i	$0.227273\pi$
$200$	0.959493	+	0.281733i	0.959493	+	0.281733i
$201$		0			0
$202$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$203$		0			0
$204$	0.474017	+	0.304632i	0.474017	+	0.304632i
$205$		0			0
$206$		0			0
$207$	−0.368991	−	0.574161i	−0.368991	−	0.574161i
$208$	0.284630			0.284630
$209$		0			0
$210$		0			0
$211$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$211$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	−0.755750	+	0.654861i	$0.772727\pi$
$212$	0.698939	−	1.53046i	0.698939	−	1.53046i
$213$		0			0
$214$	−1.74557	−	0.512546i	−1.74557	−	0.512546i
$215$		0			0
$216$	0.393828	+	0.862362i	0.393828	+	0.862362i
$217$	−2.05384	+	0.603063i	−2.05384	+	0.603063i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.118239	+	0.258908i	0.118239	+	0.258908i
$222$		0			0
$223$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$223$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$224$	−0.281733	−	1.95949i	−0.281733	−	1.95949i
$225$	−0.283524	+	0.620830i	−0.283524	+	0.620830i
$226$		0			0
$227$	−0.474017	−	0.304632i	−0.474017	−	0.304632i	0.281733	−	0.959493i	$-0.409091\pi$
$227$	−0.474017	−	0.304632i	−0.474017	−	0.304632i	−0.755750	+	0.654861i	$0.772727\pi$
$228$		0			0
$229$	0.284630			0.284630			0.142315	−	0.989821i	$-0.454545\pi$
$229$	0.284630			0.284630			0.142315	+	0.989821i	$0.454545\pi$
$230$		0			0
$231$	−1.20613			−1.20613
$232$		0			0
$233$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$233$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$234$	−0.0276463	+	0.192284i	−0.0276463	+	0.192284i
$235$		0			0
$236$		0			0
$237$	0.817178	+	0.239945i	0.817178	+	0.239945i
$238$	1.66538	−	1.07028i	1.66538	−	1.07028i
$239$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$239$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$240$		0			0
$241$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$241$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$242$	0.110783	−	0.127850i	0.110783	−	0.127850i
$243$	−0.989821	+	0.290638i	−0.989821	+	0.290638i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.449181	−	0.983568i	0.449181	−	0.983568i
$249$		0			0
$250$		0			0
$251$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$251$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$252$	1.35112			1.35112
$253$	−0.584585	+	0.909632i	−0.584585	+	0.909632i
$254$		0			0
$255$		0			0
$256$	0.841254	+	0.540641i	0.841254	+	0.540641i
$257$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	0.142315	+	0.989821i	$0.454545\pi$
$257$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	−0.415415	+	0.909632i	$0.636364\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.755750	−	1.65486i	−0.755750	−	1.65486i
$263$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$263$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$264$	0.398983	−	0.460451i	0.398983	−	0.460451i
$265$		0			0
$266$		0			0
$267$	−0.393828	−	0.862362i	−0.393828	−	0.862362i
$268$		0			0
$269$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$269$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$270$		0			0
$271$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$271$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$272$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$273$	−0.267092	−	0.171650i	−0.267092	−	0.171650i
$274$	0.857685	+	0.989821i	0.857685	+	0.989821i
$275$	1.08128			1.08128
$276$	−0.304632	+	0.474017i	−0.304632	+	0.474017i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	1.19136	+	1.37491i	1.19136	+	1.37491i
$279$	0.620830	+	0.398983i	0.620830	+	0.398983i
$280$		0			0
$281$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$281$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$282$		0			0
$283$	−1.45027	−	0.425839i	−1.45027	−	0.425839i	−0.540641	−	0.841254i	$-0.681818\pi$
$283$	−1.45027	−	0.425839i	−1.45027	−	0.425839i	−0.909632	+	0.415415i	$0.863636\pi$
$284$		0			0
$285$		0			0
$286$	0.295298	−	0.0867074i	0.295298	−	0.0867074i
$287$		0			0
$288$	−0.446947	+	0.515804i	−0.446947	+	0.515804i
$289$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$293$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$294$	−0.683252	+	1.49611i	−0.683252	+	1.49611i
$295$		0			0
$296$		0			0
$297$	0.671292	+	0.774713i	0.671292	+	0.774713i
$298$	1.91899			1.91899
$299$	−0.258908	+	0.118239i	−0.258908	+	0.118239i
$300$	0.563465			0.563465
$301$		0			0
$302$		0			0
$303$	−0.105026	+	0.730471i	−0.105026	+	0.730471i
$304$		0			0
$305$		0			0
$306$	−0.654861	−	0.192284i	−0.654861	−	0.192284i
$307$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$307$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$308$	−0.889217	−	1.94711i	−0.889217	−	1.94711i
$309$		0			0
$310$		0			0
$311$	−1.29639	+	1.49611i	−1.29639	+	1.49611i	−0.540641	+	0.841254i	$0.681818\pi$
$311$	−1.29639	+	1.49611i	−1.29639	+	1.49611i	−0.755750	+	0.654861i	$0.772727\pi$
$312$	0.153882	−	0.0451840i	0.153882	−	0.0451840i
$313$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$313$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$314$	1.61435	−	1.03748i	1.61435	−	1.03748i
$315$		0			0
$316$	0.215109	+	1.49611i	0.215109	+	1.49611i
$317$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$317$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$318$	0.134919	−	0.938384i	0.134919	−	0.938384i
$319$		0			0
$320$		0			0
$321$	−1.02509			−1.02509
$322$	1.07028	+	1.66538i	1.07028	+	1.66538i
$323$		0			0
$324$	−0.0971309	−	0.112095i	−0.0971309	−	0.112095i
$325$	0.239446	+	0.153882i	0.239446	+	0.153882i
$326$	−0.281733	+	1.95949i	−0.281733	+	1.95949i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$331$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$332$		0			0
$333$		0			0
$334$	0.989821	−	1.14231i	0.989821	−	1.14231i
$335$		0			0
$336$	−0.463379	−	1.01466i	−0.463379	−	1.01466i
$337$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$337$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$338$	−0.881761	−	0.258908i	−0.881761	−	0.258908i
$339$		0			0
$340$		0			0
$341$	0.166390	−	1.15727i	0.166390	−	1.15727i
$342$		0			0
$343$	2.48775	+	2.87102i	2.48775	+	2.87102i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.708089	+	0.817178i	0.708089	+	0.817178i	0.989821	−	0.142315i	$-0.0454545\pi$
$347$	0.708089	+	0.817178i	0.708089	+	0.817178i	−0.281733	+	0.959493i	$0.590909\pi$
$348$		0			0
$349$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$349$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$350$	0.822373	−	1.80075i	0.822373	−	1.80075i
$351$	0.0384020	+	0.267092i	0.0384020	+	0.267092i
$352$	1.03748	+	0.304632i	1.03748	+	0.304632i
$353$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$353$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$354$		0			0
$355$		0			0
$356$	1.10181	−	1.27155i	1.10181	−	1.27155i
$357$	0.730471	−	0.843008i	0.730471	−	0.843008i
$358$		0			0
$359$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$359$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$360$		0			0
$361$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$362$		0			0
$363$	0.0395979	−	0.0867074i	0.0395979	−	0.0867074i
$364$	0.0801894	−	0.557730i	0.0801894	−	0.557730i
$365$		0			0
$366$		0			0
$367$	−1.81926			−1.81926			−0.909632	−	0.415415i	$-0.863636\pi$
$367$	−1.81926			−1.81926			−0.909632	+	0.415415i	$0.863636\pi$
$368$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$369$		0			0
$370$		0			0
$371$	−2.80202	−	1.80075i	−2.80202	−	1.80075i
$372$	0.0867074	−	0.603063i	0.0867074	−	0.603063i
$373$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$373$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$374$	0.153882	+	1.07028i	0.153882	+	1.07028i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	1.80075	−	0.528747i	1.80075	−	0.528747i
$379$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$379$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.909632	+	0.415415i	$0.863636\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$383$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$384$	0.540641	+	0.158746i	0.540641	+	0.158746i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.841254	−	0.540641i	$-0.818182\pi$
$389$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.415415	−	0.909632i	$-0.636364\pi$
$390$		0			0
$391$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$392$	−2.91899			−2.91899
$393$	−0.671292	−	0.774713i	−0.671292	−	0.774713i
$394$		0			0
$395$		0			0
$396$	−0.306569	+	0.671292i	−0.306569	+	0.671292i
$397$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$397$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$398$	0.540641	+	0.158746i	0.540641	+	0.158746i
$399$		0			0
$400$	0.415415	+	0.909632i	0.415415	+	0.909632i
$401$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$401$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$402$		0			0
$403$	0.201543	−	0.232593i	0.201543	−	0.232593i
$404$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.0801894	+	0.557730i	0.0801894	+	0.557730i
$409$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$409$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$410$		0			0
$411$	0.620830	+	0.398983i	0.620830	+	0.398983i
$412$		0			0
$413$		0			0
$414$	0.192284	−	0.654861i	0.192284	−	0.654861i
$415$		0			0
$416$	0.186393	+	0.215109i	0.186393	+	0.215109i
$417$	0.862362	+	0.554206i	0.862362	+	0.554206i
$418$		0			0
$419$	−0.449181	+	0.983568i	−0.449181	+	0.983568i	0.540641	+	0.841254i	$0.318182\pi$
$419$	−0.449181	+	0.983568i	−0.449181	+	0.983568i	−0.989821	+	0.142315i	$0.954545\pi$
$420$		0			0
$421$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−0.841254	−	0.540641i	$-0.818182\pi$
$421$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−1.00000			$\pi$
$422$	−1.27155	+	0.817178i	−1.27155	+	0.817178i
$423$		0			0
$424$	1.61435	−	0.474017i	1.61435	−	0.474017i
$425$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$426$		0			0
$427$		0			0
$428$	−0.755750	−	1.65486i	−0.755750	−	1.65486i
$429$	0.145886	−	0.0937551i	0.145886	−	0.0937551i
$430$		0			0
$431$	0.0801894	+	0.557730i	0.0801894	+	0.557730i	0.989821	+	0.142315i	$0.0454545\pi$
$431$	0.0801894	+	0.557730i	0.0801894	+	0.557730i	−0.909632	+	0.415415i	$0.863636\pi$
$432$	−0.393828	+	0.862362i	−0.393828	+	0.862362i
$433$	0.118239	−	0.822373i	0.118239	−	0.822373i	−0.841254	−	0.540641i	$-0.818182\pi$
$433$	0.118239	−	0.822373i	0.118239	−	0.822373i	0.959493	−	0.281733i	$-0.0909091\pi$
$434$	−1.80075	−	1.15727i	−1.80075	−	1.15727i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.708089	−	0.817178i	−0.708089	−	0.817178i	0.281733	−	0.959493i	$-0.409091\pi$
$439$	−0.708089	−	0.817178i	−0.708089	−	0.817178i	−0.989821	+	0.142315i	$0.954545\pi$
$440$		0			0
$441$	0.283524	−	1.97195i	0.283524	−	1.97195i
$442$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$443$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$443$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.03748	−	0.304632i	1.03748	−	0.304632i
$448$	1.29639	−	1.49611i	1.29639	−	1.49611i
$449$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$449$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$450$	−0.654861	+	0.192284i	−0.654861	+	0.192284i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i
$455$		0			0
$456$		0			0
$457$	0.239446	+	0.153882i	0.239446	+	0.153882i	0.654861	−	0.755750i	$-0.272727\pi$
$457$	0.239446	+	0.153882i	0.239446	+	0.153882i	−0.415415	+	0.909632i	$0.636364\pi$
$458$	0.186393	+	0.215109i	0.186393	+	0.215109i
$459$	−0.948034			−0.948034
$460$		0			0
$461$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$461$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$462$	−0.789845	−	0.911529i	−0.789845	−	0.911529i
$463$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$463$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$467$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$468$	−0.163423	+	0.105026i	−0.163423	+	0.105026i
$469$		0			0
$470$		0			0
$471$	0.708089	−	0.817178i	0.708089	−	0.817178i
$472$		0			0
$473$		0			0
$474$	0.353799	+	0.774713i	0.353799	+	0.774713i
$475$		0			0
$476$	1.89945	+	0.557730i	1.89945	+	0.557730i
$477$	0.163423	+	1.13663i	0.163423	+	1.13663i
$478$		0			0
$479$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$479$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	0.843008	+	0.730471i	0.843008	+	0.730471i
$484$	0.169170			0.169170
$485$		0			0
$486$	−0.867845	−	0.557730i	−0.867845	−	0.557730i
$487$	−0.281733	+	1.95949i	−0.281733	+	1.95949i			1.00000i	$0.5\pi$
$487$	−0.281733	+	1.95949i	−0.281733	+	1.95949i	−0.281733	+	0.959493i	$0.590909\pi$
$488$		0			0
$489$	0.158746	+	1.10411i	0.158746	+	1.10411i
$490$		0			0
$491$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$491$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	1.03748	−	0.304632i	1.03748	−	0.304632i
$497$		0			0
$498$		0			0
$499$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.989821	+	0.142315i	$0.0454545\pi$
$499$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.909632	+	0.415415i	$0.136364\pi$
$500$		0			0
$501$	0.353799	−	0.774713i	0.353799	−	0.774713i
$502$		0			0
$503$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$503$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$504$	0.884796	+	1.02111i	0.884796	+	1.02111i
$505$		0			0
$506$	−1.07028	+	0.153882i	−1.07028	+	0.153882i
$507$	−0.517817			−0.517817
$508$		0			0
$509$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$509$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$510$		0			0
$511$		0			0
$512$	0.142315	+	0.989821i	0.142315	+	0.989821i
$513$		0			0
$514$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$521$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$522$		0			0
$523$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$523$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$524$	0.755750	−	1.65486i	0.755750	−	1.65486i
$525$	0.158746	−	1.10411i	0.158746	−	1.10411i
$526$		0			0
$527$	0.708089	+	0.817178i	0.708089	+	0.817178i
$528$	0.609264			0.609264
$529$	0.959493	−	0.281733i	0.959493	−	0.281733i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.393828	−	0.862362i	0.393828	−	0.862362i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.02840	+	0.889217i	−3.02840	+	0.889217i
$540$		0			0
$541$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$541$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$542$		0			0
$543$		0			0
$544$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$545$		0			0
$546$	−0.0451840	−	0.314261i	−0.0451840	−	0.314261i
$547$	−0.627899	+	1.37491i	−0.627899	+	1.37491i	0.281733	+	0.959493i	$0.409091\pi$
$547$	−0.627899	+	1.37491i	−0.627899	+	1.37491i	−0.909632	+	0.415415i	$0.863636\pi$
$548$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$549$		0			0
$550$	0.708089	+	0.817178i	0.708089	+	0.817178i
$551$		0			0
$552$	−0.557730	+	0.0801894i	−0.557730	+	0.0801894i
$553$	2.99223			2.99223
$554$		0			0
$555$		0			0
$556$	−0.258908	+	1.80075i	−0.258908	+	1.80075i
$557$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	0.654861	+	0.755750i	$0.272727\pi$
$557$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	−1.00000			$\pi$
$558$	0.105026	+	0.730471i	0.105026	+	0.730471i
$559$		0			0
$560$		0			0
$561$	0.253098	+	0.554206i	0.253098	+	0.554206i
$562$	0.797176	−	0.234072i	0.797176	−	0.234072i
$563$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$563$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$564$		0			0
$565$		0			0
$566$	−0.627899	−	1.37491i	−0.627899	−	1.37491i
$567$	−0.247014	+	0.158746i	−0.247014	+	0.158746i
$568$		0			0
$569$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$569$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$570$		0			0
$571$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$571$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	−0.755750	+	0.654861i	$0.772727\pi$
$572$	0.258908	+	0.166390i	0.258908	+	0.166390i
$573$		0			0
$574$		0			0
$575$	−0.755750	−	0.654861i	−0.755750	−	0.654861i
$576$	−0.682507			−0.682507
$577$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	0.142315	−	0.989821i	$-0.454545\pi$
$577$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	−1.00000			$\pi$
$578$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.53046	−	0.983568i	1.53046	−	0.983568i
$584$		0			0
$585$		0			0
$586$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$587$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$587$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$588$	−1.57812	+	0.463379i	−1.57812	+	0.463379i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$593$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$594$	−0.145886	+	1.01466i	−0.145886	+	1.01466i
$595$		0			0
$596$	1.25667	+	1.45027i	1.25667	+	1.45027i
$597$	0.317493			0.317493
$598$	−0.258908	−	0.118239i	−0.258908	−	0.118239i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	0.368991	+	0.425839i	0.368991	+	0.425839i
$601$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$601$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−0.620830	+	0.398983i	−0.620830	+	0.398983i
$607$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	−0.909632	−	0.415415i	$-0.863636\pi$
$607$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	0.281733	−	0.959493i	$-0.409091\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.283524	−	0.620830i	−0.283524	−	0.620830i
$613$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$613$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$614$		0			0
$615$		0			0
$616$	0.889217	−	1.94711i	0.889217	−	1.94711i
$617$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$617$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$618$		0			0
$619$	−1.19136	−	1.37491i	−1.19136	−	1.37491i	−0.909632	−	0.415415i	$-0.863636\pi$
$619$	−1.19136	−	1.37491i	−1.19136	−	1.37491i	−0.281733	−	0.959493i	$-0.590909\pi$
$620$		0			0
$621$		−	0.948034i		−	0.948034i
$622$	−1.97964			−1.97964
$623$	−2.18119	−	2.51722i	−2.18119	−	2.51722i
$624$	0.134919	+	0.0867074i	0.134919	+	0.0867074i
$625$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$626$		0			0
$627$		0			0
$628$	1.84125	+	0.540641i	1.84125	+	0.540641i
$629$		0			0
$630$		0			0
$631$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$631$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$632$	−0.989821	+	1.14231i	−0.989821	+	1.14231i
$633$	−0.557730	+	0.643655i	−0.557730	+	0.643655i
$634$		0			0
$635$		0			0
$636$	0.797537	−	0.512546i	0.797537	−	0.512546i
$637$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$641$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$642$	−0.671292	−	0.774713i	−0.671292	−	0.774713i
$643$	1.97964			1.97964			0.989821	−	0.142315i	$-0.0454545\pi$
$643$	1.97964			1.97964			0.989821	+	0.142315i	$0.0454545\pi$
$644$	−0.557730	+	1.89945i	−0.557730	+	1.89945i
$645$		0			0
$646$		0			0
$647$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$647$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$648$	0.0211086	−	0.146813i	0.0211086	−	0.146813i
$649$		0			0
$650$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$651$	−1.15727	−	0.339805i	−1.15727	−	0.339805i
$652$	−1.66538	+	1.07028i	−1.66538	+	1.07028i
$653$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$653$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$659$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$660$		0			0
$661$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$661$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$662$		0			0
$663$	−0.0228243	+	0.158746i	−0.0228243	+	0.158746i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.51150			1.51150
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.463379	−	1.01466i	0.463379	−	1.01466i
$673$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$673$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$674$		0			0
$675$	−0.797537	+	0.512546i	−0.797537	+	0.512546i
$676$	−0.381761	−	0.835939i	−0.381761	−	0.835939i
$677$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$677$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.131891	−	0.288802i	−0.131891	−	0.288802i
$682$	0.983568	−	0.632101i	0.983568	−	0.632101i
$683$	−1.45027	−	0.425839i	−1.45027	−	0.425839i	−0.540641	−	0.841254i	$-0.681818\pi$
$683$	−1.45027	−	0.425839i	−1.45027	−	0.425839i	−0.909632	+	0.415415i	$0.863636\pi$
$684$		0			0
$685$		0			0
$686$	−0.540641	+	3.76024i	−0.540641	+	3.76024i
$687$	0.134919	+	0.0867074i	0.134919	+	0.0867074i
$688$		0			0
$689$	0.478891			0.478891
$690$		0			0
$691$	1.97964			1.97964			0.989821	−	0.142315i	$-0.0454545\pi$
$691$	1.97964			1.97964			0.989821	+	0.142315i	$0.0454545\pi$
$692$		0			0
$693$	1.22902	+	0.789845i	1.22902	+	0.789845i
$694$	−0.153882	+	1.07028i	−0.153882	+	1.07028i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.239446	−	0.153882i	0.239446	−	0.153882i
$699$		0			0
$700$	1.89945	−	0.557730i	1.89945	−	0.557730i
$701$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$701$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$702$	−0.176707	+	0.203930i	−0.176707	+	0.203930i
$703$		0			0
$704$	0.449181	+	0.983568i	0.449181	+	0.983568i
$705$		0			0
$706$	0.797176	+	0.234072i	0.797176	+	0.234072i
$707$	0.368991	+	2.56639i	0.368991	+	2.56639i
$708$		0			0
$709$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$709$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$710$		0			0
$711$	−0.675560	−	0.779638i	−0.675560	−	0.779638i
$712$	1.68251			1.68251
$713$	−0.817178	+	0.708089i	−0.817178	+	0.708089i
$714$	1.11546			1.11546
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.281733	+	1.95949i	0.281733	+	1.95949i	0.281733	+	0.959493i	$0.409091\pi$
$719$	0.281733	+	1.95949i	0.281733	+	1.95949i			1.00000i	$0.500000\pi$
$720$		0			0
$721$		0			0
$722$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.0914602	−	0.0268551i	0.0914602	−	0.0268551i
$727$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$727$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$728$	0.474017	−	0.304632i	0.474017	−	0.304632i
$729$	−0.415415	−	0.121977i	−0.415415	−	0.121977i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$733$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$734$	−1.19136	−	1.37491i	−1.19136	−	1.37491i
$735$		0			0
$736$	−0.540641	−	0.841254i	−0.540641	−	0.841254i
$737$		0			0
$738$		0			0
$739$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$739$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$740$		0			0
$741$		0			0
$742$	−0.474017	−	3.29686i	−0.474017	−	3.29686i
$743$	−0.540641	−	0.158746i	−0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$743$	−0.540641	−	0.158746i	−0.540641	−	0.158746i	−0.540641	+	0.841254i	$0.681818\pi$
$744$	0.512546	−	0.329393i	0.512546	−	0.329393i
$745$		0			0
$746$	1.25667	−	0.368991i	1.25667	−	0.368991i
$747$		0			0
$748$	−0.708089	+	0.817178i	−0.708089	+	0.817178i
$749$	−3.45561	+	1.01466i	−3.45561	+	1.01466i
$750$		0			0
$751$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.755750	−	0.654861i	$-0.227273\pi$
$751$	1.66538	−	1.07028i	1.66538	−	1.07028i	0.909632	−	0.415415i	$-0.136364\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	1.57884	+	1.01466i	1.57884	+	1.01466i
$757$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$757$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$758$	−1.81926			−1.81926
$759$	−0.554206	+	0.253098i	−0.554206	+	0.253098i
$760$		0			0
$761$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$761$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.234072	+	0.512546i	0.234072	+	0.512546i
$769$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−0.841254	+	0.540641i	$0.818182\pi$
$769$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−1.00000			$1.00000\pi$
$770$		0			0
$771$	−0.708089	+	0.817178i	−0.708089	+	0.817178i
$772$		0			0
$773$	0.544078	+	1.19136i	0.544078	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$773$	0.544078	+	1.19136i	0.544078	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$774$		0			0
$775$	1.03748	+	0.304632i	1.03748	+	0.304632i
$776$		0			0
$777$		0			0
$778$	0.273100	−	1.89945i	0.273100	−	1.89945i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.540641	−	0.841254i	0.540641	−	0.841254i
$783$		0			0
$784$	−1.91153	−	2.20602i	−1.91153	−	2.20602i
$785$		0			0
$786$	0.145886	−	1.01466i	0.145886	−	1.01466i
$787$	0.822373	−	1.80075i	0.822373	−	1.80075i	0.281733	−	0.959493i	$-0.409091\pi$
$787$	0.822373	−	1.80075i	0.822373	−	1.80075i	0.540641	−	0.841254i	$-0.318182\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.708089	+	0.207914i	−0.708089	+	0.207914i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.234072	+	0.512546i	0.234072	+	0.512546i
$797$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$797$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$798$		0			0
$799$		0			0
$800$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$801$	−0.163423	+	1.13663i	−0.163423	+	1.13663i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	0.307765			0.307765
$807$		0			0
$808$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$809$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$809$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$810$		0			0
$811$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$811$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$817$		0			0
$818$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$819$	0.159756	+	0.349816i	0.159756	+	0.349816i
$820$		0			0
$821$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$821$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$822$	0.105026	+	0.730471i	0.105026	+	0.730471i
$823$	−0.755750	+	1.65486i	−0.755750	+	1.65486i			1.00000i	$0.5\pi$
$823$	−0.755750	+	1.65486i	−0.755750	+	1.65486i	−0.755750	+	0.654861i	$0.772727\pi$
$824$		0			0
$825$	0.512546	+	0.329393i	0.512546	+	0.329393i
$826$		0			0
$827$	1.51150			1.51150			0.755750	−	0.654861i	$-0.227273\pi$
$827$	1.51150			1.51150			0.755750	+	0.654861i	$0.227273\pi$
$828$	0.620830	−	0.283524i	0.620830	−	0.283524i
$829$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$829$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$830$		0			0
$831$		0			0
$832$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$833$	1.21259	−	2.65520i	1.21259	−	2.65520i
$834$	0.145886	+	1.01466i	0.145886	+	1.01466i
$835$		0			0
$836$		0			0
$837$	0.425839	+	0.932456i	0.425839	+	0.932456i
$838$	−1.03748	+	0.304632i	−1.03748	+	0.304632i
$839$	1.19136	−	1.37491i	1.19136	−	1.37491i	0.281733	−	0.959493i	$-0.409091\pi$
$839$	1.19136	−	1.37491i	1.19136	−	1.37491i	0.909632	−	0.415415i	$-0.136364\pi$
$840$		0			0
$841$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$842$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$843$	0.393828	−	0.253098i	0.393828	−	0.253098i
$844$	−1.45027	−	0.425839i	−1.45027	−	0.425839i
$845$		0			0
$846$		0			0
$847$	0.0476607	−	0.331487i	0.0476607	−	0.331487i
$848$	1.41542	+	0.909632i	1.41542	+	0.909632i
$849$	−0.557730	−	0.643655i	−0.557730	−	0.643655i
$850$	−1.00000			−1.00000
$851$		0			0
$852$		0			0
$853$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$853$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$854$		0			0
$855$		0			0
$856$	0.755750	−	1.65486i	0.755750	−	1.65486i
$857$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$857$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$858$	0.166390	+	0.0488566i	0.166390	+	0.0488566i
$859$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$859$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$860$		0			0
$861$		0			0
$862$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$863$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$863$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$864$	−0.909632	+	0.267092i	−0.909632	+	0.267092i
$865$		0			0
$866$	0.698939	−	0.449181i	0.698939	−	0.449181i
$867$	−0.540641	−	0.158746i	−0.540641	−	0.158746i
$868$	−0.304632	−	2.11876i	−0.304632	−	2.11876i
$869$	−0.678936	+	1.48666i	−0.678936	+	1.48666i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$877$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$878$	0.153882	−	1.07028i	0.153882	−	1.07028i
$879$	−0.306569	+	0.671292i	−0.306569	+	0.671292i
$880$		0			0
$881$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$881$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$882$	1.67597	−	1.07708i	1.67597	−	1.07708i
$883$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$883$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$884$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$885$		0			0
$886$		0			0
$887$	1.74557	−	0.512546i	1.74557	−	0.512546i	0.755750	−	0.654861i	$-0.227273\pi$
$887$	1.74557	−	0.512546i	1.74557	−	0.512546i	0.989821	+	0.142315i	$0.0454545\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.0228243	−	0.158746i	−0.0228243	−	0.158746i
$892$		0			0
$893$		0			0
$894$	0.909632	+	0.584585i	0.909632	+	0.584585i
$895$		0			0
$896$	1.97964			1.97964
$897$	−0.158746	−	0.0228243i	−0.158746	−	0.0228243i
$898$		0			0
$899$		0			0
$900$	−0.574161	−	0.368991i	−0.574161	−	0.368991i
$901$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.540641	−	0.158746i	0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$907$	0.540641	−	0.158746i	0.540641	−	0.158746i	0.540641	+	0.841254i	$0.318182\pi$
$908$	0.368991	−	0.425839i	0.368991	−	0.425839i
$909$	0.585376	−	0.675560i	0.585376	−	0.675560i
$910$		0			0
$911$	0.627899	+	1.37491i	0.627899	+	1.37491i	0.909632	+	0.415415i	$0.136364\pi$
$911$	0.627899	+	1.37491i	0.627899	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$912$		0			0
$913$		0			0
$914$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$915$		0			0
$916$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$917$	−3.02977	−	1.94711i	−3.02977	−	1.94711i
$918$	−0.620830	−	0.716476i	−0.620830	−	0.716476i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	0.544078	+	0.627899i	0.544078	+	0.627899i
$923$		0			0
$924$	0.171650	−	1.19385i	0.171650	−	1.19385i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$929$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.07028	+	0.314261i	−1.07028	+	0.314261i
$934$		0			0
$935$		0			0
$936$	−0.186393	−	0.0547299i	−0.186393	−	0.0547299i
$937$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$937$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$941$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$942$	1.08128			1.08128
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.258908	−	1.80075i	0.258908	−	1.80075i	−0.281733	−	0.959493i	$-0.590909\pi$
$947$	0.258908	−	1.80075i	0.258908	−	1.80075i	0.540641	−	0.841254i	$-0.318182\pi$
$948$	−0.353799	+	0.774713i	−0.353799	+	0.774713i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.822373	+	1.80075i	0.822373	+	1.80075i
$953$	1.91899	−	0.563465i	1.91899	−	0.563465i	0.959493	−	0.281733i	$-0.0909091\pi$
$953$	1.91899	−	0.563465i	1.91899	−	0.563465i	0.959493	−	0.281733i	$-0.0909091\pi$
$954$	−0.751992	+	0.867845i	−0.751992	+	0.867845i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.48775	+	0.730471i	2.48775	+	0.730471i
$960$		0			0
$961$	0.0702757	−	0.153882i	0.0702757	−	0.153882i
$962$		0			0
$963$	1.04455	+	0.671292i	1.04455	+	0.671292i
$964$		0			0
$965$		0			0
$966$			1.11546i			1.11546i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.110783	+	0.127850i	0.110783	+	0.127850i
$969$		0			0
$970$		0			0
$971$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$971$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$972$	−0.146813	−	1.02111i	−0.146813	−	1.02111i
$973$	3.45561	+	1.01466i	3.45561	+	1.01466i
$974$	−1.66538	+	1.07028i	−1.66538	+	1.07028i
$975$	0.0666238	+	0.145886i	0.0666238	+	0.145886i
$976$		0			0
$977$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$977$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$978$	−0.730471	+	0.843008i	−0.730471	+	0.843008i
$979$	1.74557	−	0.512546i	1.74557	−	0.512546i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i	−0.989821	−	0.142315i	$-0.954545\pi$
$983$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i	0.909632	−	0.415415i	$-0.136364\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.989821	−	1.14231i	−0.989821	−	1.14231i	−0.989821	−	0.142315i	$-0.954545\pi$
$991$	−0.989821	−	1.14231i	−0.989821	−	1.14231i		−	1.00000i	$-0.5\pi$
$992$	0.909632	+	0.584585i	0.909632	+	0.584585i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$997$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$998$	0.822373	+	1.80075i	0.822373	+	1.80075i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1564.1.w.c.611.2	yes	20
4.3	odd	2	inner	1564.1.w.c.611.1	yes	20
17.16	even	2	inner	1564.1.w.c.611.1	yes	20
23.16	even	11	inner	1564.1.w.c.407.2	yes	20
68.67	odd	2	CM	1564.1.w.c.611.2	yes	20
92.39	odd	22	inner	1564.1.w.c.407.1	✓	20
391.16	even	22	inner	1564.1.w.c.407.1	✓	20
1564.407	odd	22	inner	1564.1.w.c.407.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1564.1.w.c.407.1	✓	20	92.39	odd	22	inner
1564.1.w.c.407.1	✓	20	391.16	even	22	inner
1564.1.w.c.407.2	yes	20	23.16	even	11	inner
1564.1.w.c.407.2	yes	20	1564.407	odd	22	inner
1564.1.w.c.611.1	yes	20	4.3	odd	2	inner
1564.1.w.c.611.1	yes	20	17.16	even	2	inner
1564.1.w.c.611.2	yes	20	1.1	even	1	trivial
1564.1.w.c.611.2	yes	20	68.67	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1564 = 2^{2} \cdot 17 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1564.w (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{2} +(0.474017 + 0.304632i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.0801894 + 0.557730i) q^{6} +(1.89945 + 0.557730i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.283524 - 0.620830i) q^{9} +(-0.708089 + 0.817178i) q^{11} +(-0.368991 + 0.425839i) q^{12} +(-0.273100 + 0.0801894i) q^{13} +(0.822373 + 1.80075i) q^{14} +(-0.959493 - 0.281733i) q^{16} +(-0.142315 - 0.989821i) q^{17} +(0.283524 - 0.620830i) q^{18} +(0.730471 + 0.843008i) q^{21} -1.08128 q^{22} +(0.989821 - 0.142315i) q^{23} -0.563465 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-0.239446 - 0.153882i) q^{26} +(0.134919 - 0.938384i) q^{27} +(-0.822373 + 1.80075i) q^{28} +(-0.909632 + 0.584585i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(-0.584585 + 0.171650i) q^{33} +(0.654861 - 0.755750i) q^{34} +(0.654861 - 0.192284i) q^{36} +(-0.153882 - 0.0451840i) q^{39} +(-0.158746 + 1.10411i) q^{42} +(-0.708089 - 0.817178i) q^{44} +(0.755750 + 0.654861i) q^{46} +(-0.368991 - 0.425839i) q^{48} +(2.45561 + 1.57812i) q^{49} +(0.142315 - 0.989821i) q^{50} +(0.234072 - 0.512546i) q^{51} +(-0.0405070 - 0.281733i) q^{52} +(-1.61435 - 0.474017i) q^{53} +(0.797537 - 0.512546i) q^{54} +(-1.89945 + 0.557730i) q^{56} +(-1.03748 - 0.304632i) q^{62} +(-0.192284 - 1.33737i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.512546 - 0.329393i) q^{66} +1.00000 q^{68} +(0.512546 + 0.234072i) q^{69} +(0.574161 + 0.368991i) q^{72} +(-0.0801894 - 0.557730i) q^{75} +(-1.80075 + 1.15727i) q^{77} +(-0.0666238 - 0.145886i) q^{78} +(1.45027 - 0.425839i) q^{79} +(-0.0971309 + 0.112095i) q^{81} +(-0.938384 + 0.603063i) q^{84} +(0.153882 - 1.07028i) q^{88} +(-1.41542 - 0.909632i) q^{89} -0.563465 q^{91} +1.00000i q^{92} -0.609264 q^{93} +(0.0801894 - 0.557730i) q^{96} +(0.415415 + 2.88927i) q^{98} +(0.708089 + 0.207914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9} + 4 q^{13} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 22 q^{33} + 2 q^{34} + 2 q^{36} - 22 q^{42} + 2 q^{49} + 2 q^{50} - 18 q^{52}+ \cdots - 2 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 + 2 * q^9 + 4 * q^13 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^25 - 4 * q^26 + 2 * q^32 - 22 * q^33 + 2 * q^34 + 2 * q^36 - 22 * q^42 + 2 * q^49 + 2 * q^50 - 18 * q^52 - 4 * q^53 - 2 * q^64 + 20 * q^68 + 20 * q^72 - 2 * q^81 - 18 * q^89 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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