LMFDB - Embedded newform 1380.1.bn.d.539.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,1,Mod(359,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 11, 21]))

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

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

chi := DirichletCharacter("1380.359");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1380.bn (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:	$0.688709717434$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{44})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
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			539.1
Root			$0.755750 + 0.654861i$ of defining polynomial
Character	$\chi$	$=$	1380.539
Dual form			1380.1.bn.d.1019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.755750 + 0.654861i) q^{2} +(0.281733 + 0.959493i) q^{3} +(0.142315 - 0.989821i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.540641 + 1.84125i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.755750 + 0.654861i) q^{2} +(0.281733 + 0.959493i) q^{3} +(0.142315 - 0.989821i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.540641 + 1.84125i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-0.281733 - 0.959493i) q^{10} +(0.989821 - 0.142315i) q^{12} +(-0.797176 - 1.74557i) q^{14} +(-0.989821 - 0.142315i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.281733 - 0.959493i) q^{18} +(0.841254 + 0.540641i) q^{20} -1.91899 q^{21} +(0.755750 - 0.654861i) q^{23} +(-0.654861 + 0.755750i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(-0.755750 - 0.654861i) q^{27} +(1.74557 + 0.797176i) q^{28} +(1.80075 - 0.258908i) q^{29} +(0.841254 - 0.540641i) q^{30} +(0.909632 - 0.415415i) q^{32} +(-1.45027 - 1.25667i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.989821 + 0.142315i) q^{40} +(-0.512546 - 0.234072i) q^{41} +(1.45027 - 1.25667i) q^{42} +(0.153882 - 0.239446i) q^{43} +(-0.142315 - 0.989821i) q^{45} +(-0.142315 + 0.989821i) q^{46} +0.830830i q^{47} -1.00000i q^{48} +(-2.25667 - 1.45027i) q^{49} +(0.989821 + 0.142315i) q^{50} +1.00000 q^{54} +(-1.84125 + 0.540641i) q^{56} +(-1.19136 + 1.37491i) q^{58} +(-0.281733 + 0.959493i) q^{60} +(1.07028 + 1.66538i) q^{61} +(-0.540641 - 1.84125i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-1.27155 + 1.10181i) q^{67} +(0.841254 + 0.540641i) q^{69} +1.91899 q^{70} +(-0.909632 - 0.415415i) q^{72} +(0.540641 - 0.841254i) q^{75} +(0.654861 - 0.755750i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.540641 - 0.158746i) q^{82} +(-0.449181 - 0.983568i) q^{83} +(-0.273100 + 1.89945i) q^{84} +(0.0405070 + 0.281733i) q^{86} +(0.755750 + 1.65486i) q^{87} +(1.10181 + 0.708089i) q^{89} +(0.755750 + 0.654861i) q^{90} +(-0.540641 - 0.841254i) q^{92} +(-0.544078 - 0.627899i) q^{94} +(0.654861 + 0.755750i) q^{96} +(2.65520 - 0.381761i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^9	$ 20 q + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{9} - 4 q^{14} - 2 q^{16} - 2 q^{20} - 4 q^{21} - 2 q^{24} - 2 q^{25} - 2 q^{30} - 2 q^{36} - 2 q^{45} - 2 q^{46} - 16 q^{49} + 20 q^{54} - 18 q^{56} + 2 q^{64} - 2 q^{69} + 4 q^{70} + 2 q^{80} - 2 q^{81} + 4 q^{84} + 18 q^{86} + 4 q^{89} - 4 q^{94} + 2 q^{96}+O(q^{100}) $ 20 * q + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^9 - 4 * q^14 - 2 * q^16 - 2 * q^20 - 4 * q^21 - 2 * q^24 - 2 * q^25 - 2 * q^30 - 2 * q^36 - 2 * q^45 - 2 * q^46 - 16 * q^49 + 20 * q^54 - 18 * q^56 + 2 * q^64 - 2 * q^69 + 4 * q^70 + 2 * q^80 - 2 * q^81 + 4 * q^84 + 18 * q^86 + 4 * q^89 - 4 * q^94 + 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$2$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$3$	0.281733	+	0.959493i	0.281733	+	0.959493i
$3$	0.281733	+	0.959493i	0.281733	+	0.959493i
$4$	0.142315	−	0.989821i	0.142315	−	0.989821i
$5$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$5$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$6$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$7$	−0.540641	+	1.84125i	−0.540641	+	1.84125i			1.00000i	$0.5\pi$
$7$	−0.540641	+	1.84125i	−0.540641	+	1.84125i	−0.540641	+	0.841254i	$0.681818\pi$
$8$	0.540641	+	0.841254i	0.540641	+	0.841254i
$9$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$10$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$11$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$11$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$12$	0.989821	−	0.142315i	0.989821	−	0.142315i
$13$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$13$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$14$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$15$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$16$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$17$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$17$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$18$	0.281733	−	0.959493i	0.281733	−	0.959493i
$19$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$19$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$20$	0.841254	+	0.540641i	0.841254	+	0.540641i
$21$	−1.91899			−1.91899
$22$		0			0
$23$	0.755750	−	0.654861i	0.755750	−	0.654861i
$23$	0.755750	−	0.654861i	0.755750	−	0.654861i
$24$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$25$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$26$		0			0
$27$	−0.755750	−	0.654861i	−0.755750	−	0.654861i
$28$	1.74557	+	0.797176i	1.74557	+	0.797176i
$29$	1.80075	−	0.258908i	1.80075	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$29$	1.80075	−	0.258908i	1.80075	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$30$	0.841254	−	0.540641i	0.841254	−	0.540641i
$31$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$31$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$32$	0.909632	−	0.415415i	0.909632	−	0.415415i
$33$		0			0
$34$		0			0
$35$	−1.45027	−	1.25667i	−1.45027	−	1.25667i
$36$	0.415415	+	0.909632i	0.415415	+	0.909632i
$37$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$37$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$38$		0			0
$39$		0			0
$40$	−0.989821	+	0.142315i	−0.989821	+	0.142315i
$41$	−0.512546	−	0.234072i	−0.512546	−	0.234072i	0.142315	−	0.989821i	$-0.454545\pi$
$41$	−0.512546	−	0.234072i	−0.512546	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$42$	1.45027	−	1.25667i	1.45027	−	1.25667i
$43$	0.153882	−	0.239446i	0.153882	−	0.239446i	−0.755750	−	0.654861i	$-0.772727\pi$
$43$	0.153882	−	0.239446i	0.153882	−	0.239446i	0.909632	+	0.415415i	$0.136364\pi$
$44$		0			0
$45$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$46$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$47$			0.830830i			0.830830i	0.909632	+	0.415415i	$0.136364\pi$
$47$			0.830830i			0.830830i	−0.909632	+	0.415415i	$0.863636\pi$
$48$		−	1.00000i		−	1.00000i
$49$	−2.25667	−	1.45027i	−2.25667	−	1.45027i
$50$	0.989821	+	0.142315i	0.989821	+	0.142315i
$51$		0			0
$52$		0			0
$53$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$53$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$54$	1.00000			1.00000
$55$		0			0
$56$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$57$		0			0
$58$	−1.19136	+	1.37491i	−1.19136	+	1.37491i
$59$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$59$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$60$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$61$	1.07028	+	1.66538i	1.07028	+	1.66538i	0.654861	+	0.755750i	$0.272727\pi$
$61$	1.07028	+	1.66538i	1.07028	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$62$		0			0
$63$	−0.540641	−	1.84125i	−0.540641	−	1.84125i
$64$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$65$		0			0
$66$		0			0
$67$	−1.27155	+	1.10181i	−1.27155	+	1.10181i	−0.281733	+	0.959493i	$0.590909\pi$
$67$	−1.27155	+	1.10181i	−1.27155	+	1.10181i	−0.989821	+	0.142315i	$0.954545\pi$
$68$		0			0
$69$	0.841254	+	0.540641i	0.841254	+	0.540641i
$70$	1.91899			1.91899
$71$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$71$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$72$	−0.909632	−	0.415415i	−0.909632	−	0.415415i
$73$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$73$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$74$		0			0
$75$	0.540641	−	0.841254i	0.540641	−	0.841254i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$79$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$80$	0.654861	−	0.755750i	0.654861	−	0.755750i
$81$	0.415415	−	0.909632i	0.415415	−	0.909632i
$82$	0.540641	−	0.158746i	0.540641	−	0.158746i
$83$	−0.449181	−	0.983568i	−0.449181	−	0.983568i	−0.989821	−	0.142315i	$-0.954545\pi$
$83$	−0.449181	−	0.983568i	−0.449181	−	0.983568i	0.540641	−	0.841254i	$-0.318182\pi$
$84$	−0.273100	+	1.89945i	−0.273100	+	1.89945i
$85$		0			0
$86$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$87$	0.755750	+	1.65486i	0.755750	+	1.65486i
$88$		0			0
$89$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.959493	−	0.281733i	$-0.0909091\pi$
$89$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.142315	+	0.989821i	$0.454545\pi$
$90$	0.755750	+	0.654861i	0.755750	+	0.654861i
$91$		0			0
$92$	−0.540641	−	0.841254i	−0.540641	−	0.841254i
$93$		0			0
$94$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$95$		0			0
$96$	0.654861	+	0.755750i	0.654861	+	0.755750i
$97$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$97$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$98$	2.65520	−	0.381761i	2.65520	−	0.381761i
$99$		0			0
$100$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$101$	−0.983568	+	0.449181i	−0.983568	+	0.449181i	−0.841254	−	0.540641i	$-0.818182\pi$
$101$	−0.983568	+	0.449181i	−0.983568	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$102$		0			0
$103$	−0.627899	−	0.544078i	−0.627899	−	0.544078i	0.281733	−	0.959493i	$-0.409091\pi$
$103$	−0.627899	−	0.544078i	−0.627899	−	0.544078i	−0.909632	+	0.415415i	$0.863636\pi$
$104$		0			0
$105$	0.797176	−	1.74557i	0.797176	−	1.74557i
$106$		0			0
$107$	−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	$0.954545\pi$
$108$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$109$	1.49611	−	0.215109i	1.49611	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$109$	1.49611	−	0.215109i	1.49611	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$110$		0			0
$111$		0			0
$112$	1.03748	−	1.61435i	1.03748	−	1.61435i
$113$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$113$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$114$		0			0
$115$	0.281733	+	0.959493i	0.281733	+	0.959493i
$116$		−	1.81926i		−	1.81926i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$121$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$122$	−1.89945	−	0.557730i	−1.89945	−	0.557730i
$123$	0.0801894	−	0.557730i	0.0801894	−	0.557730i
$124$		0			0
$125$	0.959493	−	0.281733i	0.959493	−	0.281733i
$126$	1.61435	+	1.03748i	1.61435	+	1.03748i
$127$	0.708089	−	0.817178i	0.708089	−	0.817178i	−0.281733	−	0.959493i	$-0.590909\pi$
$127$	0.708089	−	0.817178i	0.708089	−	0.817178i	0.989821	+	0.142315i	$0.0454545\pi$
$128$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$129$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$130$		0			0
$131$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$131$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$132$		0			0
$133$		0			0
$134$	0.239446	−	1.66538i	0.239446	−	1.66538i
$135$	0.909632	−	0.415415i	0.909632	−	0.415415i
$136$		0			0
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	−0.989821	+	0.142315i	−0.989821	+	0.142315i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	−1.45027	+	1.25667i	−1.45027	+	1.25667i
$141$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$142$		0			0
$143$		0			0
$144$	0.959493	−	0.281733i	0.959493	−	0.281733i
$145$	−0.512546	+	1.74557i	−0.512546	+	1.74557i
$146$		0			0
$147$	0.755750	−	2.57385i	0.755750	−	2.57385i
$148$		0			0
$149$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$149$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$150$	0.142315	+	0.989821i	0.142315	+	0.989821i
$151$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$151$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$157$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$158$		0			0
$159$		0			0
$160$			1.00000i			1.00000i
$161$	0.797176	+	1.74557i	0.797176	+	1.74557i
$162$	0.281733	+	0.959493i	0.281733	+	0.959493i
$163$	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	$0.318182\pi$
$164$	−0.304632	+	0.474017i	−0.304632	+	0.474017i
$165$		0			0
$166$	0.983568	+	0.449181i	0.983568	+	0.449181i
$167$	0.281733	−	0.0405070i	0.281733	−	0.0405070i		−	1.00000i	$-0.5\pi$
$167$	0.281733	−	0.0405070i	0.281733	−	0.0405070i	0.281733	+	0.959493i	$0.409091\pi$
$168$	−1.03748	−	1.61435i	−1.03748	−	1.61435i
$169$	0.841254	−	0.540641i	0.841254	−	0.540641i
$170$		0			0
$171$		0			0
$172$	−0.215109	−	0.186393i	−0.215109	−	0.186393i
$173$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$173$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$174$	−1.65486	−	0.755750i	−1.65486	−	0.755750i
$175$	1.74557	−	0.797176i	1.74557	−	0.797176i
$176$		0			0
$177$		0			0
$178$	−1.29639	+	0.186393i	−1.29639	+	0.186393i
$179$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$179$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$180$	−1.00000			−1.00000
$181$	−0.584585	+	0.909632i	−0.584585	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$181$	−0.584585	+	0.909632i	−0.584585	+	0.909632i	−1.00000			$1.00000\pi$
$182$		0			0
$183$	−1.29639	+	1.49611i	−1.29639	+	1.49611i
$184$	0.959493	+	0.281733i	0.959493	+	0.281733i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.822373	+	0.118239i	0.822373	+	0.118239i
$189$	1.61435	−	1.03748i	1.61435	−	1.03748i
$190$		0			0
$191$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$191$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$192$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$193$		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
$196$	−1.75667	+	2.02730i	−1.75667	+	2.02730i
$197$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$197$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$198$		0			0
$199$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$199$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$200$	0.281733	−	0.959493i	0.281733	−	0.959493i
$201$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$202$	0.449181	−	0.983568i	0.449181	−	0.983568i
$203$	−0.496841	+	3.45561i	−0.496841	+	3.45561i
$204$		0			0
$205$	0.425839	−	0.368991i	0.425839	−	0.368991i
$206$	0.830830			0.830830
$207$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$208$		0			0
$209$		0			0
$210$	0.540641	+	1.84125i	0.540641	+	1.84125i
$211$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$211$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$212$		0			0
$213$		0			0
$214$	0.512546	−	1.74557i	0.512546	−	1.74557i
$215$	0.153882	+	0.239446i	0.153882	+	0.239446i
$216$	0.142315	−	0.989821i	0.142315	−	0.989821i
$217$		0			0
$218$	−0.989821	+	1.14231i	−0.989821	+	1.14231i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.89945	−	0.557730i	−1.89945	−	0.557730i	−0.989821	−	0.142315i	$-0.954545\pi$
$223$	−1.89945	−	0.557730i	−1.89945	−	0.557730i	−0.909632	−	0.415415i	$-0.863636\pi$
$224$	0.273100	+	1.89945i	0.273100	+	1.89945i
$225$	0.959493	+	0.281733i	0.959493	+	0.281733i
$226$		0			0
$227$	1.53046	+	0.983568i	1.53046	+	0.983568i	0.989821	+	0.142315i	$0.0454545\pi$
$227$	1.53046	+	0.983568i	1.53046	+	0.983568i	0.540641	+	0.841254i	$0.318182\pi$
$228$		0			0
$229$			1.51150i			1.51150i	0.654861	+	0.755750i	$0.272727\pi$
$229$			1.51150i			1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$230$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$231$		0			0
$232$	1.19136	+	1.37491i	1.19136	+	1.37491i
$233$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$233$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$234$		0			0
$235$	−0.755750	−	0.345139i	−0.755750	−	0.345139i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$239$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$240$	0.909632	+	0.415415i	0.909632	+	0.415415i
$241$	−0.425839	−	0.368991i	−0.425839	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$241$	−0.425839	−	0.368991i	−0.425839	−	0.368991i	−0.841254	+	0.540641i	$0.818182\pi$
$242$	0.755750	+	0.654861i	0.755750	+	0.654861i
$243$	0.989821	+	0.142315i	0.989821	+	0.142315i
$244$	1.80075	−	0.822373i	1.80075	−	0.822373i
$245$	2.25667	−	1.45027i	2.25667	−	1.45027i
$246$	0.304632	+	0.474017i	0.304632	+	0.474017i
$247$		0			0
$248$		0			0
$249$	0.817178	−	0.708089i	0.817178	−	0.708089i
$250$	−0.540641	+	0.841254i	−0.540641	+	0.841254i
$251$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$251$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$252$	−1.89945	+	0.273100i	−1.89945	+	0.273100i
$253$		0			0
$254$			1.08128i			1.08128i
$255$		0			0
$256$	0.841254	+	0.540641i	0.841254	+	0.540641i
$257$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$257$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$258$	−0.258908	+	0.118239i	−0.258908	+	0.118239i
$259$		0			0
$260$		0			0
$261$	−1.37491	+	1.19136i	−1.37491	+	1.19136i
$262$		0			0
$263$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.909632	−	0.415415i	$-0.136364\pi$
$263$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.989821	−	0.142315i	$-0.0454545\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.368991	+	1.25667i	−0.368991	+	1.25667i
$268$	0.909632	+	1.41542i	0.909632	+	1.41542i
$269$	−0.304632	+	1.03748i	−0.304632	+	1.03748i	0.654861	+	0.755750i	$0.272727\pi$
$269$	−0.304632	+	1.03748i	−0.304632	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$270$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$271$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$271$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.654861	−	0.755750i	0.654861	−	0.755750i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$	0.273100	−	1.89945i	0.273100	−	1.89945i
$281$	0.118239	−	0.258908i	0.118239	−	0.258908i	−0.841254	−	0.540641i	$-0.818182\pi$
$281$	0.118239	−	0.258908i	0.118239	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$282$	0.449181	−	0.698939i	0.449181	−	0.698939i
$283$	0.368991	−	1.25667i	0.368991	−	1.25667i	−0.540641	−	0.841254i	$-0.681818\pi$
$283$	0.368991	−	1.25667i	0.368991	−	1.25667i	0.909632	−	0.415415i	$-0.136364\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.708089	−	0.817178i	0.708089	−	0.817178i
$288$	−0.540641	+	0.841254i	−0.540641	+	0.841254i
$289$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$290$	−0.755750	−	1.65486i	−0.755750	−	1.65486i
$291$		0			0
$292$		0			0
$293$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$293$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$294$	1.11435	+	2.44009i	1.11435	+	2.44009i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		−	0.830830i		−	0.830830i
$299$		0			0
$300$	−0.755750	−	0.654861i	−0.755750	−	0.654861i
$301$	0.357685	+	0.412791i	0.357685	+	0.412791i
$302$		0			0
$303$	−0.708089	−	0.817178i	−0.708089	−	0.817178i
$304$		0			0
$305$	−1.95949	+	0.281733i	−1.95949	+	0.281733i
$306$		0			0
$307$	0.474017	−	0.304632i	0.474017	−	0.304632i	−0.281733	−	0.959493i	$-0.590909\pi$
$307$	0.474017	−	0.304632i	0.474017	−	0.304632i	0.755750	+	0.654861i	$0.227273\pi$
$308$		0			0
$309$	0.345139	−	0.755750i	0.345139	−	0.755750i
$310$		0			0
$311$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$311$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$312$		0			0
$313$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$313$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$314$		0			0
$315$	1.89945	+	0.273100i	1.89945	+	0.273100i
$316$		0			0
$317$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$317$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$318$		0			0
$319$		0			0
$320$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$321$	−1.37491	−	1.19136i	−1.37491	−	1.19136i
$322$	−1.74557	−	0.797176i	−1.74557	−	0.797176i
$323$		0			0
$324$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$325$		0			0
$326$	−1.95949	−	0.281733i	−1.95949	−	0.281733i
$327$	0.627899	+	1.37491i	0.627899	+	1.37491i
$328$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i
$329$	−1.52977	−	0.449181i	−1.52977	−	0.449181i
$330$		0			0
$331$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$331$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$332$	−1.03748	+	0.304632i	−1.03748	+	0.304632i
$333$		0			0
$334$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$335$	−0.474017	−	1.61435i	−0.474017	−	1.61435i
$336$	1.84125	+	0.540641i	1.84125	+	0.540641i
$337$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$337$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$338$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	2.44009	−	2.11435i	2.44009	−	2.11435i
$344$	0.284630			0.284630
$345$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$346$		0			0
$347$	1.27155	−	1.10181i	1.27155	−	1.10181i	0.281733	−	0.959493i	$-0.409091\pi$
$347$	1.27155	−	1.10181i	1.27155	−	1.10181i	0.989821	−	0.142315i	$-0.0454545\pi$
$348$	1.74557	−	0.512546i	1.74557	−	0.512546i
$349$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	0.142315	+	0.989821i	$0.454545\pi$
$349$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	−0.415415	+	0.909632i	$0.636364\pi$
$350$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$351$		0			0
$352$		0			0
$353$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$353$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$354$		0			0
$355$		0			0
$356$	0.857685	−	0.989821i	0.857685	−	0.989821i
$357$		0			0
$358$		0			0
$359$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$359$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$360$	0.755750	−	0.654861i	0.755750	−	0.654861i
$361$	0.959493	+	0.281733i	0.959493	+	0.281733i
$362$	−0.153882	−	1.07028i	−0.153882	−	1.07028i
$363$	0.909632	−	0.415415i	0.909632	−	0.415415i
$364$		0			0
$365$		0			0
$366$		−	1.97964i		−	1.97964i
$367$		−	1.68251i		−	1.68251i	−0.540641	−	0.841254i	$-0.681818\pi$
$367$		−	1.68251i		−	1.68251i	0.540641	−	0.841254i	$-0.318182\pi$
$368$	−0.909632	+	0.415415i	−0.909632	+	0.415415i
$369$	0.557730	−	0.0801894i	0.557730	−	0.0801894i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$373$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$374$		0			0
$375$	0.540641	+	0.841254i	0.540641	+	0.841254i
$376$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$377$		0			0
$378$	−0.540641	+	1.84125i	−0.540641	+	1.84125i
$379$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$379$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$380$		0			0
$381$	0.983568	+	0.449181i	0.983568	+	0.449181i
$382$		0			0
$383$	0.474017	−	0.304632i	0.474017	−	0.304632i	−0.281733	−	0.959493i	$-0.590909\pi$
$383$	0.474017	−	0.304632i	0.474017	−	0.304632i	0.755750	+	0.654861i	$0.227273\pi$
$384$	0.841254	−	0.540641i	0.841254	−	0.540641i
$385$		0			0
$386$		0			0
$387$			0.284630i			0.284630i
$388$		0			0
$389$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$389$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$390$		0			0
$391$		0			0
$392$		−	2.68251i		−	2.68251i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$397$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$398$		0			0
$399$		0			0
$400$	0.415415	+	0.909632i	0.415415	+	0.909632i
$401$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$401$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$402$	1.66538	−	0.239446i	1.66538	−	0.239446i
$403$		0			0
$404$	0.304632	+	1.03748i	0.304632	+	1.03748i
$405$	0.654861	+	0.755750i	0.654861	+	0.755750i
$406$	−1.88745	−	2.93694i	−1.88745	−	2.93694i
$407$		0			0
$408$		0			0
$409$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$409$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$410$	−0.0801894	+	0.557730i	−0.0801894	+	0.557730i
$411$		0			0
$412$	−0.627899	+	0.544078i	−0.627899	+	0.544078i
$413$		0			0
$414$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$415$	1.08128			1.08128
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$419$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$420$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$421$	0.158746	−	0.540641i	0.158746	−	0.540641i	−0.841254	−	0.540641i	$-0.818182\pi$
$421$	0.158746	−	0.540641i	0.158746	−	0.540641i	1.00000			$0$
$422$		0			0
$423$	−0.449181	−	0.698939i	−0.449181	−	0.698939i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.64502	+	1.07028i	−3.64502	+	1.07028i
$428$	0.755750	+	1.65486i	0.755750	+	1.65486i
$429$		0			0
$430$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$431$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$431$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$432$	0.540641	+	0.841254i	0.540641	+	0.841254i
$433$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$433$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$434$		0			0
$435$	−1.81926			−1.81926
$436$		−	1.51150i		−	1.51150i
$437$		0			0
$438$		0			0
$439$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$439$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$440$		0			0
$441$	2.68251			2.68251
$442$		0			0
$443$	−0.281733	+	0.0405070i	−0.281733	+	0.0405070i	−0.281733	−	0.959493i	$-0.590909\pi$
$443$	−0.281733	+	0.0405070i	−0.281733	+	0.0405070i			1.00000i	$0.5\pi$
$444$		0			0
$445$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$446$	1.80075	−	0.822373i	1.80075	−	0.822373i
$447$	−0.755750	−	0.345139i	−0.755750	−	0.345139i
$448$	−1.45027	−	1.25667i	−1.45027	−	1.25667i
$449$	−1.14231	−	0.989821i	−1.14231	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$449$	−1.14231	−	0.989821i	−1.14231	−	0.989821i	−1.00000			$\pi$
$450$	−0.909632	+	0.415415i	−0.909632	+	0.415415i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−1.80075	+	0.258908i	−1.80075	+	0.258908i
$455$		0			0
$456$		0			0
$457$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$457$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$458$	−0.989821	−	1.14231i	−0.989821	−	1.14231i
$459$		0			0
$460$	0.989821	−	0.142315i	0.989821	−	0.142315i
$461$		−	1.51150i		−	1.51150i	−0.654861	−	0.755750i	$-0.727273\pi$
$461$		−	1.51150i		−	1.51150i	0.654861	−	0.755750i	$-0.272727\pi$
$462$		0			0
$463$	0.474017	+	0.304632i	0.474017	+	0.304632i	0.755750	−	0.654861i	$-0.227273\pi$
$463$	0.474017	+	0.304632i	0.474017	+	0.304632i	−0.281733	+	0.959493i	$0.590909\pi$
$464$	−1.80075	−	0.258908i	−1.80075	−	0.258908i
$465$		0			0
$466$		0			0
$467$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$467$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$468$		0			0
$469$	−1.34125	−	2.93694i	−1.34125	−	2.93694i
$470$	0.797176	−	0.234072i	0.797176	−	0.234072i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$479$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$480$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$481$		0			0
$482$	0.563465			0.563465
$483$	−1.45027	+	1.25667i	−1.45027	+	1.25667i
$484$	−1.00000			−1.00000
$485$		0			0
$486$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$487$	0.0801894	−	0.557730i	0.0801894	−	0.557730i	−0.909632	−	0.415415i	$-0.863636\pi$
$487$	0.0801894	−	0.557730i	0.0801894	−	0.557730i	0.989821	−	0.142315i	$-0.0454545\pi$
$488$	−0.822373	+	1.80075i	−0.822373	+	1.80075i
$489$	−1.07028	+	1.66538i	−1.07028	+	1.66538i
$490$	−0.755750	+	2.57385i	−0.755750	+	2.57385i
$491$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$491$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$492$	−0.540641	−	0.158746i	−0.540641	−	0.158746i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.153882	+	1.07028i	−0.153882	+	1.07028i
$499$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$499$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$500$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$501$	0.118239	+	0.258908i	0.118239	+	0.258908i
$502$		0			0
$503$	1.27155	+	0.817178i	1.27155	+	0.817178i	0.989821	−	0.142315i	$-0.0454545\pi$
$503$	1.27155	+	0.817178i	1.27155	+	0.817178i	0.281733	+	0.959493i	$0.409091\pi$
$504$	1.25667	−	1.45027i	1.25667	−	1.45027i
$505$		−	1.08128i		−	1.08128i
$506$		0			0
$507$	0.755750	+	0.654861i	0.755750	+	0.654861i
$508$	−0.708089	−	0.817178i	−0.708089	−	0.817178i
$509$	−1.07028	+	1.66538i	−1.07028	+	1.66538i	−0.415415	+	0.909632i	$0.636364\pi$
$509$	−1.07028	+	1.66538i	−1.07028	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$510$		0			0
$511$		0			0
$512$	−0.989821	+	0.142315i	−0.989821	+	0.142315i
$513$		0			0
$514$		0			0
$515$	0.755750	−	0.345139i	0.755750	−	0.345139i
$516$	0.118239	−	0.258908i	0.118239	−	0.258908i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$521$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$522$	0.258908	−	1.80075i	0.258908	−	1.80075i
$523$	−1.66538	+	0.239446i	−1.66538	+	0.239446i	−0.909632	−	0.415415i	$-0.863636\pi$
$523$	−1.66538	+	0.239446i	−1.66538	+	0.239446i	−0.755750	+	0.654861i	$0.772727\pi$
$524$		0			0
$525$	1.25667	+	1.45027i	1.25667	+	1.45027i
$526$	−1.07028	+	1.66538i	−1.07028	+	1.66538i
$527$		0			0
$528$		0			0
$529$	0.142315	−	0.989821i	0.142315	−	0.989821i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$535$	−0.258908	−	1.80075i	−0.258908	−	1.80075i
$536$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$537$		0			0
$538$	−0.449181	−	0.983568i	−0.449181	−	0.983568i
$539$		0			0
$540$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$541$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.142315	−	0.989821i	$-0.454545\pi$
$541$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.959493	−	0.281733i	$-0.0909091\pi$
$542$		0			0
$543$	−1.03748	−	0.304632i	−1.03748	−	0.304632i
$544$		0			0
$545$	−0.425839	+	1.45027i	−0.425839	+	1.45027i
$546$		0			0
$547$	0.755750	−	1.65486i	0.755750	−	1.65486i		−	1.00000i	$-0.5\pi$
$547$	0.755750	−	1.65486i	0.755750	−	1.65486i	0.755750	−	0.654861i	$-0.227273\pi$
$548$		0			0
$549$	−1.80075	−	0.822373i	−1.80075	−	0.822373i
$550$		0			0
$551$		0			0
$552$			1.00000i			1.00000i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$557$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$558$		0			0
$559$		0			0
$560$	1.03748	+	1.61435i	1.03748	+	1.61435i
$561$		0			0
$562$	0.0801894	+	0.273100i	0.0801894	+	0.273100i
$563$	0.368991	−	0.425839i	0.368991	−	0.425839i	−0.540641	−	0.841254i	$-0.681818\pi$
$563$	0.368991	−	0.425839i	0.368991	−	0.425839i	0.909632	+	0.415415i	$0.136364\pi$
$564$	0.118239	+	0.822373i	0.118239	+	0.822373i
$565$		0			0
$566$	0.544078	+	1.19136i	0.544078	+	1.19136i
$567$	1.45027	+	1.25667i	1.45027	+	1.25667i
$568$		0			0
$569$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$569$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$570$		0			0
$571$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$571$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$572$		0			0
$573$		0			0
$574$			1.08128i			1.08128i
$575$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$576$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$577$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$577$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$578$	0.540641	−	0.841254i	0.540641	−	0.841254i
$579$		0			0
$580$	1.65486	+	0.755750i	1.65486	+	0.755750i
$581$	2.05384	−	0.295298i	2.05384	−	0.295298i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.215109	+	0.186393i	0.215109	+	0.186393i	0.755750	−	0.654861i	$-0.227273\pi$
$587$	0.215109	+	0.186393i	0.215109	+	0.186393i	−0.540641	+	0.841254i	$0.681818\pi$
$588$	−2.44009	−	1.11435i	−2.44009	−	1.11435i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$593$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$594$		0			0
$595$		0			0
$596$	0.544078	+	0.627899i	0.544078	+	0.627899i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	1.00000			1.00000
$601$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$601$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$602$	−0.540641	−	0.0777324i	−0.540641	−	0.0777324i
$603$	0.474017	−	1.61435i	0.474017	−	1.61435i
$604$		0			0
$605$	0.959493	+	0.281733i	0.959493	+	0.281733i
$606$	1.07028	+	0.153882i	1.07028	+	0.153882i
$607$	0.822373	+	1.80075i	0.822373	+	1.80075i	0.540641	+	0.841254i	$0.318182\pi$
$607$	0.822373	+	1.80075i	0.822373	+	1.80075i	0.281733	+	0.959493i	$0.409091\pi$
$608$		0			0
$609$	−3.45561	+	0.496841i	−3.45561	+	0.496841i
$610$	1.29639	−	1.49611i	1.29639	−	1.49611i
$611$		0			0
$612$		0			0
$613$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$613$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$614$	−0.158746	+	0.540641i	−0.158746	+	0.540641i
$615$	0.474017	+	0.304632i	0.474017	+	0.304632i
$616$		0			0
$617$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$617$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$618$	0.234072	+	0.797176i	0.234072	+	0.797176i
$619$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$619$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$620$		0			0
$621$	−1.00000			−1.00000
$622$		0			0
$623$	−1.89945	+	1.64589i	−1.89945	+	1.64589i
$624$		0			0
$625$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$631$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$631$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.449181	+	0.983568i	0.449181	+	0.983568i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.989821	+	0.142315i	0.989821	+	0.142315i
$641$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$641$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$642$	1.81926			1.81926
$643$		−	0.284630i		−	0.284630i	−0.989821	−	0.142315i	$-0.954545\pi$
$643$		−	0.284630i		−	0.284630i	0.989821	−	0.142315i	$-0.0454545\pi$
$644$	1.84125	−	0.540641i	1.84125	−	0.540641i
$645$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$646$		0			0
$647$	−0.909632	+	1.41542i	−0.909632	+	1.41542i			1.00000i	$0.5\pi$
$647$	−0.909632	+	1.41542i	−0.909632	+	1.41542i	−0.909632	+	0.415415i	$0.863636\pi$
$648$	0.989821	−	0.142315i	0.989821	−	0.142315i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.66538	−	1.07028i	1.66538	−	1.07028i
$653$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$653$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$654$	−1.37491	−	0.627899i	−1.37491	−	0.627899i
$655$		0			0
$656$	0.425839	+	0.368991i	0.425839	+	0.368991i
$657$		0			0
$658$	1.45027	−	0.662317i	1.45027	−	0.662317i
$659$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$659$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$660$		0			0
$661$	1.80075	−	0.258908i	1.80075	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$661$	1.80075	−	0.258908i	1.80075	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$662$		0			0
$663$		0			0
$664$	0.584585	−	0.909632i	0.584585	−	0.909632i
$665$		0			0
$666$		0			0
$667$	1.19136	−	1.37491i	1.19136	−	1.37491i
$668$		−	0.284630i		−	0.284630i
$669$		−	1.97964i		−	1.97964i
$670$	1.41542	+	0.909632i	1.41542	+	0.909632i
$671$		0			0
$672$	−1.74557	+	0.797176i	−1.74557	+	0.797176i
$673$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$673$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$674$		0			0
$675$			1.00000i			1.00000i
$676$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$677$		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
$681$	−0.512546	+	1.74557i	−0.512546	+	1.74557i
$682$		0			0
$683$	0.540641	−	1.84125i	0.540641	−	1.84125i		−	1.00000i	$-0.5\pi$
$683$	0.540641	−	1.84125i	0.540641	−	1.84125i	0.540641	−	0.841254i	$-0.318182\pi$
$684$		0			0
$685$		0			0
$686$	−0.459493	+	3.19584i	−0.459493	+	3.19584i
$687$	−1.45027	+	0.425839i	−1.45027	+	0.425839i
$688$	−0.215109	+	0.186393i	−0.215109	+	0.186393i
$689$		0			0
$690$	0.281733	−	0.959493i	0.281733	−	0.959493i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$695$		0			0
$696$	−0.983568	+	1.53046i	−0.983568	+	1.53046i
$697$		0			0
$698$	−1.03748	−	1.61435i	−1.03748	−	1.61435i
$699$		0			0
$700$	−0.540641	−	1.84125i	−0.540641	−	1.84125i
$701$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$701$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.118239	−	0.822373i	0.118239	−	0.822373i
$706$		0			0
$707$	−0.295298	−	2.05384i	−0.295298	−	2.05384i
$708$		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			0
$712$			1.30972i			1.30972i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$719$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$720$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$721$	1.34125	−	0.861971i	1.34125	−	0.861971i
$722$	−0.909632	+	0.415415i	−0.909632	+	0.415415i
$723$	0.234072	−	0.512546i	0.234072	−	0.512546i
$724$	0.817178	+	0.708089i	0.817178	+	0.708089i
$725$	−1.37491	−	1.19136i	−1.37491	−	1.19136i
$726$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$727$	−0.755750	+	0.345139i	−0.755750	+	0.345139i	−0.755750	−	0.654861i	$-0.772727\pi$
$727$	−0.755750	+	0.345139i	−0.755750	+	0.345139i			1.00000i	$0.5\pi$
$728$		0			0
$729$	0.142315	+	0.989821i	0.142315	+	0.989821i
$730$		0			0
$731$		0			0
$732$	1.29639	+	1.49611i	1.29639	+	1.49611i
$733$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$733$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$734$	1.10181	+	1.27155i	1.10181	+	1.27155i
$735$	2.02730	+	1.75667i	2.02730	+	1.75667i
$736$	0.415415	−	0.909632i	0.415415	−	0.909632i
$737$		0			0
$738$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$739$		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			0
$743$	−1.74557	−	0.512546i	−1.74557	−	0.512546i	−0.755750	−	0.654861i	$-0.772727\pi$
$743$	−1.74557	−	0.512546i	−1.74557	−	0.512546i	−0.989821	+	0.142315i	$0.954545\pi$
$744$		0			0
$745$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$746$		0			0
$747$	0.909632	+	0.584585i	0.909632	+	0.584585i
$748$		0			0
$749$	−0.983568	−	3.34973i	−0.983568	−	3.34973i
$750$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$751$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$751$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$752$	0.234072	−	0.797176i	0.234072	−	0.797176i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$757$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$757$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.425839	−	0.368991i	0.425839	−	0.368991i	−0.415415	−	0.909632i	$-0.636364\pi$
$761$	0.425839	−	0.368991i	0.425839	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$762$	−1.03748	+	0.304632i	−1.03748	+	0.304632i
$763$	−0.412791	+	2.87102i	−0.412791	+	2.87102i
$764$		0			0
$765$		0			0
$766$	−0.158746	+	0.540641i	−0.158746	+	0.540641i
$767$		0			0
$768$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$769$	0.557730	+	1.89945i	0.557730	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$769$	0.557730	+	1.89945i	0.557730	+	1.89945i	0.142315	+	0.989821i	$0.454545\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$773$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$774$	−0.186393	−	0.215109i	−0.186393	−	0.215109i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.29639	−	0.186393i	−1.29639	−	0.186393i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.53046	−	0.983568i	−1.53046	−	0.983568i
$784$	1.75667	+	2.02730i	1.75667	+	2.02730i
$785$		0			0
$786$		0			0
$787$	1.19136	+	0.544078i	1.19136	+	0.544078i	0.909632	−	0.415415i	$-0.136364\pi$
$787$	1.19136	+	0.544078i	1.19136	+	0.544078i	0.281733	+	0.959493i	$0.409091\pi$
$788$		0			0
$789$	1.07028	+	1.66538i	1.07028	+	1.66538i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$797$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$798$		0			0
$799$		0			0
$800$	−0.909632	−	0.415415i	−0.909632	−	0.415415i
$801$	−1.30972			−1.30972
$802$	0.909632	−	1.41542i	0.909632	−	1.41542i
$803$		0			0
$804$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$805$	−1.91899			−1.91899
$806$		0			0
$807$	−1.08128			−1.08128
$808$	−0.909632	−	0.584585i	−0.909632	−	0.584585i
$809$	−1.49611	−	0.215109i	−1.49611	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$809$	−1.49611	−	0.215109i	−1.49611	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$810$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$811$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$811$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$812$	3.34973	+	0.983568i	3.34973	+	0.983568i
$813$		0			0
$814$		0			0
$815$	−1.89945	+	0.557730i	−1.89945	+	0.557730i
$816$		0			0
$817$		0			0
$818$	0.234072	+	0.797176i	0.234072	+	0.797176i
$819$		0			0
$820$	−0.304632	−	0.474017i	−0.304632	−	0.474017i
$821$	0.512546	−	1.74557i	0.512546	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$821$	0.512546	−	1.74557i	0.512546	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$822$		0			0
$823$	0.234072	−	0.512546i	0.234072	−	0.512546i	−0.755750	−	0.654861i	$-0.772727\pi$
$823$	0.234072	−	0.512546i	0.234072	−	0.512546i	0.989821	+	0.142315i	$0.0454545\pi$
$824$	0.118239	−	0.822373i	0.118239	−	0.822373i
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	0.909632	+	0.415415i	0.909632	+	0.415415i
$829$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$829$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$830$	−0.817178	+	0.708089i	−0.817178	+	0.708089i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.0801894	+	0.273100i	−0.0801894	+	0.273100i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$839$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$840$	1.89945	−	0.273100i	1.89945	−	0.273100i
$841$	2.21616	−	0.650724i	2.21616	−	0.650724i
$842$	0.234072	+	0.512546i	0.234072	+	0.512546i
$843$	0.281733	+	0.0405070i	0.281733	+	0.0405070i
$844$		0			0
$845$	0.142315	+	0.989821i	0.142315	+	0.989821i
$846$	0.797176	+	0.234072i	0.797176	+	0.234072i
$847$	1.89945	+	0.273100i	1.89945	+	0.273100i
$848$		0			0
$849$	1.30972			1.30972
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$853$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$854$	2.05384	−	3.19584i	2.05384	−	3.19584i
$855$		0			0
$856$	−1.65486	−	0.755750i	−1.65486	−	0.755750i
$857$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$857$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$858$		0			0
$859$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$859$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$860$	0.258908	−	0.118239i	0.258908	−	0.118239i
$861$	0.983568	+	0.449181i	0.983568	+	0.449181i
$862$		0			0
$863$	1.45027	+	1.25667i	1.45027	+	1.25667i	0.909632	+	0.415415i	$0.136364\pi$
$863$	1.45027	+	1.25667i	1.45027	+	1.25667i	0.540641	+	0.841254i	$0.318182\pi$
$864$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$865$		0			0
$866$		0			0
$867$	−0.540641	−	0.841254i	−0.540641	−	0.841254i
$868$		0			0
$869$		0			0
$870$	1.37491	−	1.19136i	1.37491	−	1.19136i
$871$		0			0
$872$	0.989821	+	1.14231i	0.989821	+	1.14231i
$873$		0			0
$874$		0			0
$875$			1.91899i			1.91899i
$876$		0			0
$877$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$877$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.959493	−	0.281733i	$-0.0909091\pi$
$881$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.654861	+	0.755750i	$0.272727\pi$
$882$	−2.02730	+	1.75667i	−2.02730	+	1.75667i
$883$	0.627899	+	1.37491i	0.627899	+	1.37491i	0.909632	+	0.415415i	$0.136364\pi$
$883$	0.627899	+	1.37491i	0.627899	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$884$		0			0
$885$		0			0
$886$	0.186393	−	0.215109i	0.186393	−	0.215109i
$887$	−0.368991	−	1.25667i	−0.368991	−	1.25667i	−0.909632	−	0.415415i	$-0.863636\pi$
$887$	−0.368991	−	1.25667i	−0.368991	−	1.25667i	0.540641	−	0.841254i	$-0.318182\pi$
$888$		0			0
$889$	1.12181	+	1.74557i	1.12181	+	1.74557i
$890$	0.368991	−	1.25667i	0.368991	−	1.25667i
$891$		0			0
$892$	−0.822373	+	1.80075i	−0.822373	+	1.80075i
$893$		0			0
$894$	0.797176	−	0.234072i	0.797176	−	0.234072i
$895$		0			0
$896$	1.91899			1.91899
$897$		0			0
$898$	1.51150			1.51150
$899$		0			0
$900$	0.415415	−	0.909632i	0.415415	−	0.909632i
$901$		0			0
$902$		0			0
$903$	−0.295298	+	0.459493i	−0.295298	+	0.459493i
$904$		0			0
$905$	−0.584585	−	0.909632i	−0.584585	−	0.909632i
$906$		0			0
$907$	0.368991	+	1.25667i	0.368991	+	1.25667i	0.909632	+	0.415415i	$0.136364\pi$
$907$	0.368991	+	1.25667i	0.368991	+	1.25667i	−0.540641	+	0.841254i	$0.681818\pi$
$908$	1.19136	−	1.37491i	1.19136	−	1.37491i
$909$	0.584585	−	0.909632i	0.584585	−	0.909632i
$910$		0			0
$911$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$911$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.822373	−	1.80075i	−0.822373	−	1.80075i
$916$	1.49611	+	0.215109i	1.49611	+	0.215109i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$921$	0.425839	+	0.368991i	0.425839	+	0.368991i
$922$	0.989821	+	1.14231i	0.989821	+	1.14231i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.557730	+	0.0801894i	−0.557730	+	0.0801894i
$927$	0.822373	+	0.118239i	0.822373	+	0.118239i
$928$	1.53046	−	0.983568i	1.53046	−	0.983568i
$929$	1.65486	−	0.755750i	1.65486	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$929$	1.65486	−	0.755750i	1.65486	−	0.755750i	1.00000			$0$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$937$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$938$	2.93694	+	1.34125i	2.93694	+	1.34125i
$939$		0			0
$940$	−0.449181	+	0.698939i	−0.449181	+	0.698939i
$941$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$941$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$942$		0			0
$943$	−0.540641	+	0.158746i	−0.540641	+	0.158746i
$944$		0			0
$945$	0.273100	+	1.89945i	0.273100	+	1.89945i
$946$		0			0
$947$	−1.29639	−	0.186393i	−1.29639	−	0.186393i	−0.540641	−	0.841254i	$-0.681818\pi$
$947$	−1.29639	−	0.186393i	−1.29639	−	0.186393i	−0.755750	+	0.654861i	$0.772727\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$953$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.540641	−	0.841254i	0.540641	−	0.841254i
$961$	0.415415	−	0.909632i	0.415415	−	0.909632i
$962$		0			0
$963$	0.755750	−	1.65486i	0.755750	−	1.65486i
$964$	−0.425839	+	0.368991i	−0.425839	+	0.368991i
$965$		0			0
$966$	0.273100	−	1.89945i	0.273100	−	1.89945i
$967$	−1.51150			−1.51150			−0.755750	−	0.654861i	$-0.772727\pi$
$967$	−1.51150			−1.51150			−0.755750	+	0.654861i	$0.772727\pi$
$968$	0.755750	−	0.654861i	0.755750	−	0.654861i
$969$		0			0
$970$		0			0
$971$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$971$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$972$	0.281733	−	0.959493i	0.281733	−	0.959493i
$973$		0			0
$974$	0.304632	+	0.474017i	0.304632	+	0.474017i
$975$		0			0
$976$	−0.557730	−	1.89945i	−0.557730	−	1.89945i
$977$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$977$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$978$	−0.281733	−	1.95949i	−0.281733	−	1.95949i
$979$		0			0
$980$	−1.11435	−	2.44009i	−1.11435	−	2.44009i
$981$	−1.14231	+	0.989821i	−1.14231	+	0.989821i
$982$		0			0
$983$	0.215109	+	1.49611i	0.215109	+	1.49611i	0.755750	+	0.654861i	$0.227273\pi$
$983$	0.215109	+	1.49611i	0.215109	+	1.49611i	−0.540641	+	0.841254i	$0.681818\pi$
$984$	0.512546	−	0.234072i	0.512546	−	0.234072i
$985$		0			0
$986$		0			0
$987$		−	1.59435i		−	1.59435i
$988$		0			0
$989$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$990$		0			0
$991$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$991$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.584585	−	0.909632i	−0.584585	−	0.909632i
$997$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$997$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.1.bn.d.539.1	yes	20
3.2	odd	2		1380.1.bn.a.539.2	yes	20
4.3	odd	2	inner	1380.1.bn.d.539.2	yes	20
5.4	even	2	inner	1380.1.bn.d.539.2	yes	20
12.11	even	2		1380.1.bn.a.539.1	✓	20
15.14	odd	2		1380.1.bn.a.539.1	✓	20
20.19	odd	2	CM	1380.1.bn.d.539.1	yes	20
23.7	odd	22		1380.1.bn.a.1019.2	yes	20
60.59	even	2		1380.1.bn.a.539.2	yes	20
69.53	even	22	inner	1380.1.bn.d.1019.1	yes	20
92.7	even	22		1380.1.bn.a.1019.1	yes	20
115.99	odd	22		1380.1.bn.a.1019.1	yes	20
276.191	odd	22	inner	1380.1.bn.d.1019.2	yes	20
345.329	even	22	inner	1380.1.bn.d.1019.2	yes	20
460.99	even	22		1380.1.bn.a.1019.2	yes	20
1380.1019	odd	22	inner	1380.1.bn.d.1019.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.1.bn.a.539.1	✓	20	12.11	even	2
1380.1.bn.a.539.1	✓	20	15.14	odd	2
1380.1.bn.a.539.2	yes	20	3.2	odd	2
1380.1.bn.a.539.2	yes	20	60.59	even	2
1380.1.bn.a.1019.1	yes	20	92.7	even	22
1380.1.bn.a.1019.1	yes	20	115.99	odd	22
1380.1.bn.a.1019.2	yes	20	23.7	odd	22
1380.1.bn.a.1019.2	yes	20	460.99	even	22
1380.1.bn.d.539.1	yes	20	1.1	even	1	trivial
1380.1.bn.d.539.1	yes	20	20.19	odd	2	CM
1380.1.bn.d.539.2	yes	20	4.3	odd	2	inner
1380.1.bn.d.539.2	yes	20	5.4	even	2	inner
1380.1.bn.d.1019.1	yes	20	69.53	even	22	inner
1380.1.bn.d.1019.1	yes	20	1380.1019	odd	22	inner
1380.1.bn.d.1019.2	yes	20	276.191	odd	22	inner
1380.1.bn.d.1019.2	yes	20	345.329	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1380.bn (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.755750 + 0.654861i) q^{2} +(0.281733 + 0.959493i) q^{3} +(0.142315 - 0.989821i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.540641 + 1.84125i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.755750 + 0.654861i) q^{2} +(0.281733 + 0.959493i) q^{3} +(0.142315 - 0.989821i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.540641 + 1.84125i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-0.281733 - 0.959493i) q^{10} +(0.989821 - 0.142315i) q^{12} +(-0.797176 - 1.74557i) q^{14} +(-0.989821 - 0.142315i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.281733 - 0.959493i) q^{18} +(0.841254 + 0.540641i) q^{20} -1.91899 q^{21} +(0.755750 - 0.654861i) q^{23} +(-0.654861 + 0.755750i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(-0.755750 - 0.654861i) q^{27} +(1.74557 + 0.797176i) q^{28} +(1.80075 - 0.258908i) q^{29} +(0.841254 - 0.540641i) q^{30} +(0.909632 - 0.415415i) q^{32} +(-1.45027 - 1.25667i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.989821 + 0.142315i) q^{40} +(-0.512546 - 0.234072i) q^{41} +(1.45027 - 1.25667i) q^{42} +(0.153882 - 0.239446i) q^{43} +(-0.142315 - 0.989821i) q^{45} +(-0.142315 + 0.989821i) q^{46} +0.830830i q^{47} -1.00000i q^{48} +(-2.25667 - 1.45027i) q^{49} +(0.989821 + 0.142315i) q^{50} +1.00000 q^{54} +(-1.84125 + 0.540641i) q^{56} +(-1.19136 + 1.37491i) q^{58} +(-0.281733 + 0.959493i) q^{60} +(1.07028 + 1.66538i) q^{61} +(-0.540641 - 1.84125i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-1.27155 + 1.10181i) q^{67} +(0.841254 + 0.540641i) q^{69} +1.91899 q^{70} +(-0.909632 - 0.415415i) q^{72} +(0.540641 - 0.841254i) q^{75} +(0.654861 - 0.755750i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.540641 - 0.158746i) q^{82} +(-0.449181 - 0.983568i) q^{83} +(-0.273100 + 1.89945i) q^{84} +(0.0405070 + 0.281733i) q^{86} +(0.755750 + 1.65486i) q^{87} +(1.10181 + 0.708089i) q^{89} +(0.755750 + 0.654861i) q^{90} +(-0.540641 - 0.841254i) q^{92} +(-0.544078 - 0.627899i) q^{94} +(0.654861 + 0.755750i) q^{96} +(2.65520 - 0.381761i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^9	\( 20 q + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{9} - 4 q^{14} - 2 q^{16} - 2 q^{20} - 4 q^{21} - 2 q^{24} - 2 q^{25} - 2 q^{30} - 2 q^{36} - 2 q^{45} - 2 q^{46} - 16 q^{49} + 20 q^{54} - 18 q^{56} + 2 q^{64} - 2 q^{69} + 4 q^{70} + 2 q^{80} - 2 q^{81} + 4 q^{84} + 18 q^{86} + 4 q^{89} - 4 q^{94} + 2 q^{96}+O(q^{100}) \) 20 * q + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^9 - 4 * q^14 - 2 * q^16 - 2 * q^20 - 4 * q^21 - 2 * q^24 - 2 * q^25 - 2 * q^30 - 2 * q^36 - 2 * q^45 - 2 * q^46 - 16 * q^49 + 20 * q^54 - 18 * q^56 + 2 * q^64 - 2 * q^69 + 4 * q^70 + 2 * q^80 - 2 * q^81 + 4 * q^84 + 18 * q^86 + 4 * q^89 - 4 * q^94 + 2 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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