LMFDB - Embedded newform 1564.1.w.a.1223.1

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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{11}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{11} - \cdots)$

Embedding invariants

Embedding label			1223.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	1564.1223
Dual form			1564.1.w.a.1087.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.415415 + 0.909632i) q^{2} +(0.273100 - 0.0801894i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.186393 + 0.215109i) q^{6} +(0.186393 + 1.29639i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.773100 + 0.496841i) q^{9} +(-0.797176 + 1.74557i) q^{11} +(-0.118239 + 0.258908i) q^{12} +(0.186393 - 1.29639i) q^{13} +(-1.10181 + 0.708089i) q^{14} +(-0.142315 - 0.989821i) q^{16} +(-0.654861 - 0.755750i) q^{17} +(-0.773100 - 0.496841i) q^{18} +(0.154861 + 0.339098i) q^{21} -1.91899 q^{22} +(-0.654861 - 0.755750i) q^{23} -0.284630 q^{24} +(0.415415 + 0.909632i) q^{25} +(1.25667 - 0.368991i) q^{26} +(-0.357685 + 0.412791i) q^{27} +(-1.10181 - 0.708089i) q^{28} +(1.84125 + 0.540641i) q^{31} +(0.841254 - 0.540641i) q^{32} +(-0.0777324 + 0.540641i) q^{33} +(0.415415 - 0.909632i) q^{34} +(0.130785 - 0.909632i) q^{36} +(-0.0530529 - 0.368991i) q^{39} +(-0.244123 + 0.281733i) q^{42} +(-0.797176 - 1.74557i) q^{44} +(0.415415 - 0.909632i) q^{46} +(-0.118239 - 0.258908i) q^{48} +(-0.686393 + 0.201543i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-0.239446 - 0.153882i) q^{51} +(0.857685 + 0.989821i) q^{52} +(0.273100 + 1.89945i) q^{53} +(-0.524075 - 0.153882i) q^{54} +(0.186393 - 1.29639i) q^{56} +(0.273100 + 1.89945i) q^{62} +(-0.788201 - 0.909632i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.524075 + 0.153882i) q^{66} +1.00000 q^{68} +(-0.239446 - 0.153882i) q^{69} +(0.830830 + 1.81926i) q^{71} +(0.881761 - 0.258908i) q^{72} +(0.186393 + 0.215109i) q^{75} +(-2.41153 - 0.708089i) q^{77} +(0.313607 - 0.201543i) q^{78} +(-0.118239 + 0.822373i) q^{79} +(0.317178 - 0.694523i) q^{81} +(-0.357685 - 0.105026i) q^{84} +(1.25667 - 1.45027i) q^{88} +(1.84125 - 0.540641i) q^{89} +1.71537 q^{91} +1.00000 q^{92} +0.546200 q^{93} +(0.186393 - 0.215109i) q^{96} +(-0.468468 - 0.540641i) q^{98} +(-0.250975 - 1.74557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - 2 q^{7} - q^{8} - 3 q^{9} - 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - q^{16} - q^{17} - 3 q^{18} - 4 q^{21} - 2 q^{22} - q^{23} - 2 q^{24} - q^{25} - 2 q^{26}+ \cdots - 6 q^{99}+O(q^{100}) $ 10 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - 2 * q^7 - q^8 - 3 * q^9 - 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - q^16 - q^17 - 3 * q^18 - 4 * q^21 - 2 * q^22 - q^23 - 2 * q^24 - q^25 - 2 * q^26 - 4 * q^27 - 2 * q^28 + 9 * q^31 - q^32 + 7 * q^33 - q^34 - 3 * q^36 - 4 * q^39 + 7 * q^42 - 2 * q^44 - q^46 - 2 * q^48 - 3 * q^49 - q^50 - 2 * q^51 + 9 * q^52 - 2 * q^53 - 4 * q^54 - 2 * q^56 - 2 * q^62 + 5 * q^63 - q^64 - 4 * q^66 + 10 * q^68 - 2 * q^69 - 2 * q^71 + 8 * q^72 - 2 * q^75 - 4 * q^77 + 7 * q^78 - 2 * q^79 - 5 * q^81 - 4 * q^84 - 2 * q^88 + 9 * q^89 + 18 * q^91 + 10 * q^92 - 4 * q^93 - 2 * q^96 - 3 * q^98 - 6 * q^99

Character values

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

$n$	$783$	$921$	$1293$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	0.415415	+	0.909632i	0.415415	+	0.909632i
$2$	0.415415	+	0.909632i	0.415415	+	0.909632i
$3$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$3$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$4$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$5$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$5$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$6$	0.186393	+	0.215109i	0.186393	+	0.215109i
$7$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$7$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$8$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$9$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$10$		0			0
$11$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$11$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$12$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$13$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$13$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$14$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$15$		0			0
$16$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$17$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$17$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$18$	−0.773100	−	0.496841i	−0.773100	−	0.496841i
$19$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$19$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$20$		0			0
$21$	0.154861	+	0.339098i	0.154861	+	0.339098i
$22$	−1.91899			−1.91899
$23$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$23$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$24$	−0.284630			−0.284630
$25$	0.415415	+	0.909632i	0.415415	+	0.909632i
$26$	1.25667	−	0.368991i	1.25667	−	0.368991i
$27$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$28$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$29$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$29$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$30$		0			0
$31$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$31$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$32$	0.841254	−	0.540641i	0.841254	−	0.540641i
$33$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$34$	0.415415	−	0.909632i	0.415415	−	0.909632i
$35$		0			0
$36$	0.130785	−	0.909632i	0.130785	−	0.909632i
$37$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$37$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$38$		0			0
$39$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$40$		0			0
$41$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$41$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$42$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$43$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$43$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$44$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$45$		0			0
$46$	0.415415	−	0.909632i	0.415415	−	0.909632i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$49$	−0.686393	+	0.201543i	−0.686393	+	0.201543i
$50$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$51$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$52$	0.857685	+	0.989821i	0.857685	+	0.989821i
$53$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$53$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$54$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$55$		0			0
$56$	0.186393	−	1.29639i	0.186393	−	1.29639i
$57$		0			0
$58$		0			0
$59$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$59$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$60$		0			0
$61$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$61$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$62$	0.273100	+	1.89945i	0.273100	+	1.89945i
$63$	−0.788201	−	0.909632i	−0.788201	−	0.909632i
$64$	0.841254	+	0.540641i	0.841254	+	0.540641i
$65$		0			0
$66$	−0.524075	+	0.153882i	−0.524075	+	0.153882i
$67$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$67$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$68$	1.00000			1.00000
$69$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$70$		0			0
$71$	0.830830	+	1.81926i	0.830830	+	1.81926i	0.415415	+	0.909632i	$0.363636\pi$
$71$	0.830830	+	1.81926i	0.830830	+	1.81926i	0.415415	+	0.909632i	$0.363636\pi$
$72$	0.881761	−	0.258908i	0.881761	−	0.258908i
$73$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$73$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$74$		0			0
$75$	0.186393	+	0.215109i	0.186393	+	0.215109i
$76$		0			0
$77$	−2.41153	−	0.708089i	−2.41153	−	0.708089i
$78$	0.313607	−	0.201543i	0.313607	−	0.201543i
$79$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$79$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$80$		0			0
$81$	0.317178	−	0.694523i	0.317178	−	0.694523i
$82$		0			0
$83$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$83$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$84$	−0.357685	−	0.105026i	−0.357685	−	0.105026i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	1.25667	−	1.45027i	1.25667	−	1.45027i
$89$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$89$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$90$		0			0
$91$	1.71537			1.71537
$92$	1.00000			1.00000
$93$	0.546200			0.546200
$94$		0			0
$95$		0			0
$96$	0.186393	−	0.215109i	0.186393	−	0.215109i
$97$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$97$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$98$	−0.468468	−	0.540641i	−0.468468	−	0.540641i
$99$	−0.250975	−	1.74557i	−0.250975	−	1.74557i
$100$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$101$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$101$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$102$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$103$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$103$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$104$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$105$		0			0
$106$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$107$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$107$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$108$	−0.0777324	−	0.540641i	−0.0777324	−	0.540641i
$109$		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
$112$	1.25667	−	0.368991i	1.25667	−	0.368991i
$113$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$113$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.500000	+	1.09485i	0.500000	+	1.09485i
$118$		0			0
$119$	0.857685	−	0.989821i	0.857685	−	0.989821i
$120$		0			0
$121$	−1.75667	−	2.02730i	−1.75667	−	2.02730i
$122$		0			0
$123$		0			0
$124$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$125$		0			0
$126$	0.500000	−	1.09485i	0.500000	−	1.09485i
$127$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$127$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$128$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$129$		0			0
$130$		0			0
$131$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$131$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$132$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.415415	+	0.909632i	0.415415	+	0.909632i
$137$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$137$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$138$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$139$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$139$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$140$		0			0
$141$		0			0
$142$	−1.30972	+	1.51150i	−1.30972	+	1.51150i
$143$	2.11435	+	1.35881i	2.11435	+	1.35881i
$144$	0.601808	+	0.694523i	0.601808	+	0.694523i
$145$		0			0
$146$		0			0
$147$	−0.171292	+	0.110083i	−0.171292	+	0.110083i
$148$		0			0
$149$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$149$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$150$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$151$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$151$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$152$		0			0
$153$	0.881761	+	0.258908i	0.881761	+	0.258908i
$154$	−0.357685	−	2.48775i	−0.357685	−	2.48775i
$155$		0			0
$156$	0.313607	+	0.201543i	0.313607	+	0.201543i
$157$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$157$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$158$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$159$	0.226900	+	0.496841i	0.226900	+	0.496841i
$160$		0			0
$161$	0.857685	−	0.989821i	0.857685	−	0.989821i
$162$	0.763521			0.763521
$163$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$163$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$167$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$168$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$169$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$173$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$174$		0			0
$175$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$176$	1.84125	+	0.540641i	1.84125	+	0.540641i
$177$		0			0
$178$	1.25667	+	1.45027i	1.25667	+	1.45027i
$179$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$179$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$180$		0			0
$181$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$181$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$182$	0.712591	+	1.56036i	0.712591	+	1.56036i
$183$		0			0
$184$	0.415415	+	0.909632i	0.415415	+	0.909632i
$185$		0			0
$186$	0.226900	+	0.496841i	0.226900	+	0.496841i
$187$	1.84125	−	0.540641i	1.84125	−	0.540641i
$188$		0			0
$189$	−0.601808	−	0.386758i	−0.601808	−	0.386758i
$190$		0			0
$191$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$191$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$192$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$193$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$193$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$194$		0			0
$195$		0			0
$196$	0.297176	−	0.650724i	0.297176	−	0.650724i
$197$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$197$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$198$	1.48357	−	0.953431i	1.48357	−	0.953431i
$199$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$199$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$200$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$201$		0			0
$202$	0.698939	+	0.449181i	0.698939	+	0.449181i
$203$		0			0
$204$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$205$		0			0
$206$		0			0
$207$	0.881761	+	0.258908i	0.881761	+	0.258908i
$208$	−1.30972			−1.30972
$209$		0			0
$210$		0			0
$211$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$211$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$212$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$213$	0.372786	+	0.430218i	0.372786	+	0.430218i
$214$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$215$		0			0
$216$	0.459493	−	0.295298i	0.459493	−	0.295298i
$217$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$222$		0			0
$223$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$223$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$224$	0.857685	+	0.989821i	0.857685	+	0.989821i
$225$	−0.773100	−	0.496841i	−0.773100	−	0.496841i
$226$		0			0
$227$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$227$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$228$		0			0
$229$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$229$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$230$		0			0
$231$	−0.715370			−0.715370
$232$		0			0
$233$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$233$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$234$	−0.788201	+	0.909632i	−0.788201	+	0.909632i
$235$		0			0
$236$		0			0
$237$	0.0336545	+	0.234072i	0.0336545	+	0.234072i
$238$	1.25667	+	0.368991i	1.25667	+	0.368991i
$239$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$239$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$240$		0			0
$241$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$241$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$242$	1.11435	−	2.44009i	1.11435	−	2.44009i
$243$	0.108660	−	0.755750i	0.108660	−	0.755750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$249$		0			0
$250$		0			0
$251$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$251$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$252$	1.20362			1.20362
$253$	1.84125	−	0.540641i	1.84125	−	0.540641i
$254$		0			0
$255$		0			0
$256$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$257$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$257$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.41542	−	0.909632i	1.41542	−	0.909632i
$263$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$263$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$264$	0.226900	−	0.496841i	0.226900	−	0.496841i
$265$		0			0
$266$		0			0
$267$	0.459493	−	0.295298i	0.459493	−	0.295298i
$268$		0			0
$269$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$269$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$270$		0			0
$271$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$271$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$272$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$273$	0.468468	−	0.137555i	0.468468	−	0.137555i
$274$	0.345139	+	0.755750i	0.345139	+	0.755750i
$275$	−1.91899			−1.91899
$276$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	0.698939	+	1.53046i	0.698939	+	1.53046i
$279$	−1.69209	+	0.496841i	−1.69209	+	0.496841i
$280$		0			0
$281$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$281$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$282$		0			0
$283$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$283$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$284$	−1.91899	−	0.563465i	−1.91899	−	0.563465i
$285$		0			0
$286$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$287$		0			0
$288$	−0.381761	+	0.835939i	−0.381761	+	0.835939i
$289$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$293$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$294$	−0.171292	−	0.110083i	−0.171292	−	0.110083i
$295$		0			0
$296$		0			0
$297$	−0.435418	−	0.953431i	−0.435418	−	0.953431i
$298$	−0.284630			−0.284630
$299$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$300$	−0.284630			−0.284630
$301$		0			0
$302$		0			0
$303$	0.154861	−	0.178719i	0.154861	−	0.178719i
$304$		0			0
$305$		0			0
$306$	0.130785	+	0.909632i	0.130785	+	0.909632i
$307$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$307$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$308$	2.11435	−	1.35881i	2.11435	−	1.35881i
$309$		0			0
$310$		0			0
$311$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$311$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$312$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$313$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$313$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$314$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$315$		0			0
$316$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$317$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$317$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$318$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$319$		0			0
$320$		0			0
$321$	−0.478891			−0.478891
$322$	1.25667	+	0.368991i	1.25667	+	0.368991i
$323$		0			0
$324$	0.317178	+	0.694523i	0.317178	+	0.694523i
$325$	1.25667	−	0.368991i	1.25667	−	0.368991i
$326$	0.857685	−	0.989821i	0.857685	−	0.989821i
$327$		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			0
$333$		0			0
$334$	0.345139	−	0.755750i	0.345139	−	0.755750i
$335$		0			0
$336$	0.313607	−	0.201543i	0.313607	−	0.201543i
$337$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$337$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$338$	−0.101808	−	0.708089i	−0.101808	−	0.708089i
$339$		0			0
$340$		0			0
$341$	−2.41153	+	2.78305i	−2.41153	+	2.78305i
$342$		0			0
$343$	0.154861	+	0.339098i	0.154861	+	0.339098i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$347$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$348$		0			0
$349$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$349$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$350$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$351$	0.468468	+	0.540641i	0.468468	+	0.540641i
$352$	0.273100	+	1.89945i	0.273100	+	1.89945i
$353$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$353$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$354$		0			0
$355$		0			0
$356$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$357$	0.154861	−	0.339098i	0.154861	−	0.339098i
$358$		0			0
$359$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$359$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$360$		0			0
$361$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$362$		0			0
$363$	−0.642315	−	0.412791i	−0.642315	−	0.412791i
$364$	−1.12333	+	1.29639i	−1.12333	+	1.29639i
$365$		0			0
$366$		0			0
$367$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$367$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$368$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$369$		0			0
$370$		0			0
$371$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$372$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$373$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$373$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$374$	1.25667	+	1.45027i	1.25667	+	1.45027i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	0.101808	−	0.708089i	0.101808	−	0.708089i
$379$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$379$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$383$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$384$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$389$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$390$		0			0
$391$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$392$	0.715370			0.715370
$393$	−0.198939	−	0.435615i	−0.198939	−	0.435615i
$394$		0			0
$395$		0			0
$396$	1.48357	+	0.953431i	1.48357	+	0.953431i
$397$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$397$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$398$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$399$		0			0
$400$	0.841254	−	0.540641i	0.841254	−	0.540641i
$401$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$401$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$402$		0			0
$403$	1.04408	−	2.28621i	1.04408	−	2.28621i
$404$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.186393	+	0.215109i	0.186393	+	0.215109i
$409$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$409$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$410$		0			0
$411$	0.226900	−	0.0666238i	0.226900	−	0.0666238i
$412$		0			0
$413$		0			0
$414$	0.130785	+	0.909632i	0.130785	+	0.909632i
$415$		0			0
$416$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$417$	0.459493	−	0.134919i	0.459493	−	0.134919i
$418$		0			0
$419$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$419$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$420$		0			0
$421$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$421$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$422$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$423$		0			0
$424$	0.273100	−	1.89945i	0.273100	−	1.89945i
$425$	0.415415	−	0.909632i	0.415415	−	0.909632i
$426$	−0.236479	+	0.517817i	−0.236479	+	0.517817i
$427$		0			0
$428$	1.41542	−	0.909632i	1.41542	−	0.909632i
$429$	0.686393	+	0.201543i	0.686393	+	0.201543i
$430$		0			0
$431$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$431$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$432$	0.459493	+	0.295298i	0.459493	+	0.295298i
$433$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$433$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$434$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$439$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$440$		0			0
$441$	0.430515	−	0.496841i	0.430515	−	0.496841i
$442$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$443$		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
$447$	−0.0115295	+	0.0801894i	−0.0115295	+	0.0801894i
$448$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$449$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$449$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$450$	0.130785	−	0.909632i	0.130785	−	0.909632i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.186393	+	0.215109i	0.186393	+	0.215109i
$455$		0			0
$456$		0			0
$457$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$457$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$458$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$459$	0.546200			0.546200
$460$		0			0
$461$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$461$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$462$	−0.297176	−	0.650724i	−0.297176	−	0.650724i
$463$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$463$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$467$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$468$	−1.15486	−	0.339098i	−1.15486	−	0.339098i
$469$		0			0
$470$		0			0
$471$	0.0336545	−	0.0736930i	0.0336545	−	0.0736930i
$472$		0			0
$473$		0			0
$474$	−0.198939	+	0.127850i	−0.198939	+	0.127850i
$475$		0			0
$476$	0.186393	+	1.29639i	0.186393	+	1.29639i
$477$	−1.15486	−	1.33278i	−1.15486	−	1.33278i
$478$		0			0
$479$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$479$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	0.154861	−	0.339098i	0.154861	−	0.339098i
$484$	2.68251			2.68251
$485$		0			0
$486$	0.732593	−	0.215109i	0.732593	−	0.215109i
$487$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$487$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$488$		0			0
$489$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$490$		0			0
$491$		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			0
$495$		0			0
$496$	0.273100	−	1.89945i	0.273100	−	1.89945i
$497$	−2.20362	+	1.41618i	−2.20362	+	1.41618i
$498$		0			0
$499$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$499$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$500$		0			0
$501$	−0.198939	−	0.127850i	−0.198939	−	0.127850i
$502$		0			0
$503$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$503$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$504$	0.500000	+	1.09485i	0.500000	+	1.09485i
$505$		0			0
$506$	1.25667	+	1.45027i	1.25667	+	1.45027i
$507$	−0.203616			−0.203616
$508$		0			0
$509$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$509$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$510$		0			0
$511$		0			0
$512$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$513$		0			0
$514$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$521$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$522$		0			0
$523$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$523$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$524$	1.41542	+	0.909632i	1.41542	+	0.909632i
$525$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$526$		0			0
$527$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$528$	0.546200			0.546200
$529$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.459493	+	0.295298i	0.459493	+	0.295298i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.195368	−	1.35881i	0.195368	−	1.35881i
$540$		0			0
$541$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$541$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$542$		0			0
$543$		0			0
$544$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$545$		0			0
$546$	0.319733	+	0.368991i	0.319733	+	0.368991i
$547$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$547$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$548$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$549$		0			0
$550$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$551$		0			0
$552$	0.186393	+	0.215109i	0.186393	+	0.215109i
$553$	−1.08816			−1.08816
$554$		0			0
$555$		0			0
$556$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$557$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$557$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$558$	−1.15486	−	1.33278i	−1.15486	−	1.33278i
$559$		0			0
$560$		0			0
$561$	0.459493	−	0.295298i	0.459493	−	0.295298i
$562$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$563$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$563$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$564$		0			0
$565$		0			0
$566$	0.698939	−	0.449181i	0.698939	−	0.449181i
$567$	0.959493	+	0.281733i	0.959493	+	0.281733i
$568$	−0.284630	−	1.97964i	−0.284630	−	1.97964i
$569$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$569$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$570$		0			0
$571$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$571$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$572$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$573$		0			0
$574$		0			0
$575$	0.415415	−	0.909632i	0.415415	−	0.909632i
$576$	−0.918986			−0.918986
$577$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$577$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$578$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.53334	−	1.03748i	−3.53334	−	1.03748i
$584$		0			0
$585$		0			0
$586$	0.345139	−	0.755750i	0.345139	−	0.755750i
$587$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$587$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$588$	0.0289775	−	0.201543i	0.0289775	−	0.201543i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$593$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$594$	0.686393	−	0.792140i	0.686393	−	0.792140i
$595$		0			0
$596$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$597$	0.0810141			0.0810141
$598$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$601$		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
$604$		0			0
$605$		0			0
$606$	0.226900	+	0.0666238i	0.226900	+	0.0666238i
$607$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$607$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$613$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$613$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$614$		0			0
$615$		0			0
$616$	2.11435	+	1.35881i	2.11435	+	1.35881i
$617$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$617$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$618$		0			0
$619$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$619$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$620$		0			0
$621$	0.546200			0.546200
$622$	−1.30972			−1.30972
$623$	1.04408	+	2.28621i	1.04408	+	2.28621i
$624$	−0.357685	+	0.105026i	−0.357685	+	0.105026i
$625$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$626$		0			0
$627$		0			0
$628$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$629$		0			0
$630$		0			0
$631$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$631$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$632$	0.345139	−	0.755750i	0.345139	−	0.755750i
$633$	−0.0982369	+	0.215109i	−0.0982369	+	0.215109i
$634$		0			0
$635$		0			0
$636$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$637$	0.133340	+	0.927399i	0.133340	+	0.927399i
$638$		0			0
$639$	−1.54620	−	0.993683i	−1.54620	−	0.993683i
$640$		0			0
$641$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$641$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$642$	−0.198939	−	0.435615i	−0.198939	−	0.435615i
$643$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$643$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$644$	0.186393	+	1.29639i	0.186393	+	1.29639i
$645$		0			0
$646$		0			0
$647$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$647$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$648$	−0.500000	+	0.577031i	−0.500000	+	0.577031i
$649$		0			0
$650$	0.857685	+	0.989821i	0.857685	+	0.989821i
$651$	0.101808	+	0.708089i	0.101808	+	0.708089i
$652$	1.25667	+	0.368991i	1.25667	+	0.368991i
$653$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$653$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$654$		0			0
$655$		0			0
$656$		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
$661$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$661$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$662$		0			0
$663$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.830830			0.830830
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.313607	+	0.201543i	0.313607	+	0.201543i
$673$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$673$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$674$		0			0
$675$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$676$	0.601808	−	0.386758i	0.601808	−	0.386758i
$677$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$677$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.0681534	−	0.0437995i	0.0681534	−	0.0437995i
$682$	−3.53334	−	1.03748i	−3.53334	−	1.03748i
$683$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$683$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$684$		0			0
$685$		0			0
$686$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$687$	−0.357685	+	0.105026i	−0.357685	+	0.105026i
$688$		0			0
$689$	2.51334			2.51334
$690$		0			0
$691$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$691$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$692$		0			0
$693$	2.21616	−	0.650724i	2.21616	−	0.650724i
$694$	1.25667	−	1.45027i	1.25667	−	1.45027i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	1.25667	+	0.368991i	1.25667	+	0.368991i
$699$		0			0
$700$	0.186393	−	1.29639i	0.186393	−	1.29639i
$701$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$701$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$702$	−0.297176	+	0.650724i	−0.297176	+	0.650724i
$703$		0			0
$704$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$705$		0			0
$706$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$707$	0.712591	+	0.822373i	0.712591	+	0.822373i
$708$		0			0
$709$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$709$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$710$		0			0
$711$	−0.317178	−	0.694523i	−0.317178	−	0.694523i
$712$	−1.91899			−1.91899
$713$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$714$	0.372786			0.372786
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$719$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$720$		0			0
$721$		0			0
$722$	0.841254	−	0.540641i	0.841254	−	0.540641i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.108660	−	0.755750i	0.108660	−	0.755750i
$727$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$727$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$728$	−1.64589	−	0.483276i	−1.64589	−	0.483276i
$729$	0.0777324	+	0.540641i	0.0777324	+	0.540641i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$733$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$734$	0.698939	+	1.53046i	0.698939	+	1.53046i
$735$		0			0
$736$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$737$		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			0
$742$	−1.64589	−	1.89945i	−1.64589	−	1.89945i
$743$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$743$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$744$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$745$		0			0
$746$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$747$		0			0
$748$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$749$	0.313607	−	2.18119i	0.313607	−	2.18119i
$750$		0			0
$751$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$751$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.686393	−	0.201543i	0.686393	−	0.201543i
$757$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$757$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$758$	1.68251			1.68251
$759$	0.459493	−	0.295298i	0.459493	−	0.295298i
$760$		0			0
$761$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$761$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$769$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$769$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$770$		0			0
$771$	0.0336545	−	0.0736930i	0.0336545	−	0.0736930i
$772$		0			0
$773$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$773$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$774$		0			0
$775$	0.273100	+	1.89945i	0.273100	+	1.89945i
$776$		0			0
$777$		0			0
$778$	0.186393	−	0.215109i	0.186393	−	0.215109i
$779$		0			0
$780$		0			0
$781$	−3.83797			−3.83797
$782$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$783$		0			0
$784$	0.297176	+	0.650724i	0.297176	+	0.650724i
$785$		0			0
$786$	0.313607	−	0.361922i	0.313607	−	0.361922i
$787$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$787$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.250975	+	1.74557i	−0.250975	+	1.74557i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$797$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$797$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$798$		0			0
$799$		0			0
$800$	0.841254	+	0.540641i	0.841254	+	0.540641i
$801$	−1.15486	+	1.33278i	−1.15486	+	1.33278i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	2.51334			2.51334
$807$		0			0
$808$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$809$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$809$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$810$		0			0
$811$	−1.30972	−	1.51150i	−1.30972	−	1.51150i	−0.654861	−	0.755750i	$-0.727273\pi$
$811$	−1.30972	−	1.51150i	−1.30972	−	1.51150i	−0.654861	−	0.755750i	$-0.727273\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$817$		0			0
$818$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$819$	−1.32615	+	0.852267i	−1.32615	+	0.852267i
$820$		0			0
$821$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$821$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$822$	0.154861	+	0.178719i	0.154861	+	0.178719i
$823$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$823$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$824$		0			0
$825$	−0.524075	+	0.153882i	−0.524075	+	0.153882i
$826$		0			0
$827$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$827$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$828$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$829$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$829$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$830$		0			0
$831$		0			0
$832$	0.857685	−	0.989821i	0.857685	−	0.989821i
$833$	0.601808	+	0.386758i	0.601808	+	0.386758i
$834$	0.313607	+	0.361922i	0.313607	+	0.361922i
$835$		0			0
$836$		0			0
$837$	−0.881761	+	0.566673i	−0.881761	+	0.566673i
$838$	0.273100	−	1.89945i	0.273100	−	1.89945i
$839$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$839$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$840$		0			0
$841$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$842$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$843$	0.459493	+	0.134919i	0.459493	+	0.134919i
$844$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$845$		0			0
$846$		0			0
$847$	2.30075	−	2.65520i	2.30075	−	2.65520i
$848$	1.84125	−	0.540641i	1.84125	−	0.540641i
$849$	−0.0982369	−	0.215109i	−0.0982369	−	0.215109i
$850$	1.00000			1.00000
$851$		0			0
$852$	−0.569259			−0.569259
$853$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$853$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$854$		0			0
$855$		0			0
$856$	1.41542	+	0.909632i	1.41542	+	0.909632i
$857$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$857$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$858$	0.101808	+	0.708089i	0.101808	+	0.708089i
$859$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$859$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$860$		0			0
$861$		0			0
$862$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$863$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$863$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$864$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$865$		0			0
$866$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$867$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$868$	−1.64589	−	1.89945i	−1.64589	−	1.89945i
$869$	−1.34125	−	0.861971i	−1.34125	−	0.861971i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$877$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$878$	1.25667	−	1.45027i	1.25667	−	1.45027i
$879$	−0.198939	−	0.127850i	−0.198939	−	0.127850i
$880$		0			0
$881$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$881$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$882$	0.630785	+	0.185215i	0.630785	+	0.185215i
$883$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$883$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$884$	0.186393	−	1.29639i	0.186393	−	1.29639i
$885$		0			0
$886$		0			0
$887$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$887$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.959493	+	1.10731i	0.959493	+	1.10731i
$892$		0			0
$893$		0			0
$894$	−0.0777324	+	0.0228243i	−0.0777324	+	0.0228243i
$895$		0			0
$896$	−1.30972			−1.30972
$897$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$898$		0			0
$899$		0			0
$900$	0.881761	−	0.258908i	0.881761	−	0.258908i
$901$	1.25667	−	1.45027i	1.25667	−	1.45027i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$907$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$908$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$909$	−0.317178	+	0.694523i	−0.317178	+	0.694523i
$910$		0			0
$911$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$911$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$912$		0			0
$913$		0			0
$914$	0.857685	+	0.989821i	0.857685	+	0.989821i
$915$		0			0
$916$	0.857685	−	0.989821i	0.857685	−	0.989821i
$917$	2.11435	−	0.620830i	2.11435	−	0.620830i
$918$	0.226900	+	0.496841i	0.226900	+	0.496841i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	0.698939	+	1.53046i	0.698939	+	1.53046i
$923$	2.51334	−	0.737982i	2.51334	−	0.737982i
$924$	0.468468	−	0.540641i	0.468468	−	0.540641i
$925$		0			0
$926$		0			0
$927$		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			0
$932$		0			0
$933$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$934$		0			0
$935$		0			0
$936$	−0.171292	−	1.19136i	−0.171292	−	1.19136i
$937$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$937$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$941$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$942$	0.0810141			0.0810141
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$947$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$948$	−0.198939	−	0.127850i	−0.198939	−	0.127850i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$953$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$953$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$954$	0.732593	−	1.60416i	0.732593	−	1.60416i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	−1.91899	−	0.563465i	−1.91899	−	0.563465i
$959$	0.154861	+	1.07708i	0.154861	+	1.07708i
$960$		0			0
$961$	2.25667	+	1.45027i	2.25667	+	1.45027i
$962$		0			0
$963$	1.48357	−	0.435615i	1.48357	−	0.435615i
$964$		0			0
$965$		0			0
$966$	0.372786			0.372786
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	1.11435	+	2.44009i	1.11435	+	2.44009i
$969$		0			0
$970$		0			0
$971$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$971$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$972$	0.500000	+	0.577031i	0.500000	+	0.577031i
$973$	0.313607	+	2.18119i	0.313607	+	2.18119i
$974$	1.25667	+	0.368991i	1.25667	+	0.368991i
$975$	0.313607	−	0.201543i	0.313607	−	0.201543i
$976$		0			0
$977$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$977$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$978$	0.154861	−	0.339098i	0.154861	−	0.339098i
$979$	−0.524075	+	3.64502i	−0.524075	+	3.64502i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$983$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$991$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$992$	1.84125	−	0.540641i	1.84125	−	0.540641i
$993$		0			0
$994$	−2.20362	−	1.41618i	−2.20362	−	1.41618i
$995$		0			0
$996$		0			0
$997$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$997$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$998$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1564.1.w.a.1223.1	yes	10
4.3	odd	2		1564.1.w.b.1223.1	yes	10
17.16	even	2		1564.1.w.b.1223.1	yes	10
23.6	even	11	inner	1564.1.w.a.1087.1	✓	10
68.67	odd	2	CM	1564.1.w.a.1223.1	yes	10
92.75	odd	22		1564.1.w.b.1087.1	yes	10
391.305	even	22		1564.1.w.b.1087.1	yes	10
1564.1087	odd	22	inner	1564.1.w.a.1087.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1564.1.w.a.1087.1	✓	10	23.6	even	11	inner
1564.1.w.a.1087.1	✓	10	1564.1087	odd	22	inner
1564.1.w.a.1223.1	yes	10	1.1	even	1	trivial
1564.1.w.a.1223.1	yes	10	68.67	odd	2	CM
1564.1.w.b.1087.1	yes	10	92.75	odd	22
1564.1.w.b.1087.1	yes	10	391.305	even	22
1564.1.w.b.1223.1	yes	10	4.3	odd	2
1564.1.w.b.1223.1	yes	10	17.16	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.415415 + 0.909632i) q^{2} +(0.273100 - 0.0801894i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.186393 + 0.215109i) q^{6} +(0.186393 + 1.29639i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.773100 + 0.496841i) q^{9} +(-0.797176 + 1.74557i) q^{11} +(-0.118239 + 0.258908i) q^{12} +(0.186393 - 1.29639i) q^{13} +(-1.10181 + 0.708089i) q^{14} +(-0.142315 - 0.989821i) q^{16} +(-0.654861 - 0.755750i) q^{17} +(-0.773100 - 0.496841i) q^{18} +(0.154861 + 0.339098i) q^{21} -1.91899 q^{22} +(-0.654861 - 0.755750i) q^{23} -0.284630 q^{24} +(0.415415 + 0.909632i) q^{25} +(1.25667 - 0.368991i) q^{26} +(-0.357685 + 0.412791i) q^{27} +(-1.10181 - 0.708089i) q^{28} +(1.84125 + 0.540641i) q^{31} +(0.841254 - 0.540641i) q^{32} +(-0.0777324 + 0.540641i) q^{33} +(0.415415 - 0.909632i) q^{34} +(0.130785 - 0.909632i) q^{36} +(-0.0530529 - 0.368991i) q^{39} +(-0.244123 + 0.281733i) q^{42} +(-0.797176 - 1.74557i) q^{44} +(0.415415 - 0.909632i) q^{46} +(-0.118239 - 0.258908i) q^{48} +(-0.686393 + 0.201543i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-0.239446 - 0.153882i) q^{51} +(0.857685 + 0.989821i) q^{52} +(0.273100 + 1.89945i) q^{53} +(-0.524075 - 0.153882i) q^{54} +(0.186393 - 1.29639i) q^{56} +(0.273100 + 1.89945i) q^{62} +(-0.788201 - 0.909632i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.524075 + 0.153882i) q^{66} +1.00000 q^{68} +(-0.239446 - 0.153882i) q^{69} +(0.830830 + 1.81926i) q^{71} +(0.881761 - 0.258908i) q^{72} +(0.186393 + 0.215109i) q^{75} +(-2.41153 - 0.708089i) q^{77} +(0.313607 - 0.201543i) q^{78} +(-0.118239 + 0.822373i) q^{79} +(0.317178 - 0.694523i) q^{81} +(-0.357685 - 0.105026i) q^{84} +(1.25667 - 1.45027i) q^{88} +(1.84125 - 0.540641i) q^{89} +1.71537 q^{91} +1.00000 q^{92} +0.546200 q^{93} +(0.186393 - 0.215109i) q^{96} +(-0.468468 - 0.540641i) q^{98} +(-0.250975 - 1.74557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - 2 q^{7} - q^{8} - 3 q^{9} - 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - q^{16} - q^{17} - 3 q^{18} - 4 q^{21} - 2 q^{22} - q^{23} - 2 q^{24} - q^{25} - 2 q^{26}+ \cdots - 6 q^{99}+O(q^{100}) \) 10 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - 2 * q^7 - q^8 - 3 * q^9 - 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - q^16 - q^17 - 3 * q^18 - 4 * q^21 - 2 * q^22 - q^23 - 2 * q^24 - q^25 - 2 * q^26 - 4 * q^27 - 2 * q^28 + 9 * q^31 - q^32 + 7 * q^33 - q^34 - 3 * q^36 - 4 * q^39 + 7 * q^42 - 2 * q^44 - q^46 - 2 * q^48 - 3 * q^49 - q^50 - 2 * q^51 + 9 * q^52 - 2 * q^53 - 4 * q^54 - 2 * q^56 - 2 * q^62 + 5 * q^63 - q^64 - 4 * q^66 + 10 * q^68 - 2 * q^69 - 2 * q^71 + 8 * q^72 - 2 * q^75 - 4 * q^77 + 7 * q^78 - 2 * q^79 - 5 * q^81 - 4 * q^84 - 2 * q^88 + 9 * q^89 + 18 * q^91 + 10 * q^92 - 4 * q^93 - 2 * q^96 - 3 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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