LMFDB - Embedded newform 1340.1.bb.a.1179.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1340,1,Mod(59,1340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1340, 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("1340.59");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1340 = 2^{2} \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1340.bb (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:	$0.668747116928$
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			1179.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	1340.1179
Dual form			1340.1.bb.a.799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{2} +(-0.118239 + 0.258908i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.273100 - 0.0801894i) q^{6} +(-0.544078 - 0.627899i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.601808 + 0.694523i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.118239 + 0.258908i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.273100 - 0.0801894i) q^{6} +(-0.544078 - 0.627899i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.601808 + 0.694523i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-0.239446 - 0.153882i) q^{12} +(-0.118239 + 0.822373i) q^{14} +(0.186393 - 0.215109i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.130785 - 0.909632i) q^{18} +(0.415415 - 0.909632i) q^{20} +(0.226900 - 0.0666238i) q^{21} +(0.830830 - 1.81926i) q^{23} +(0.0405070 + 0.281733i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.524075 + 0.153882i) q^{27} +(0.698939 - 0.449181i) q^{28} +0.830830 q^{29} -0.284630 q^{30} +(0.415415 + 0.909632i) q^{32} +(0.345139 + 0.755750i) q^{35} +(-0.773100 + 0.496841i) q^{36} +(-0.959493 + 0.281733i) q^{40} +(-0.239446 - 1.66538i) q^{41} +(-0.198939 - 0.127850i) q^{42} +(0.0405070 + 0.281733i) q^{43} +(-0.381761 - 0.835939i) q^{45} +(-1.91899 + 0.563465i) q^{46} +(0.698939 - 1.53046i) q^{47} +(0.186393 - 0.215109i) q^{48} +(0.0440780 - 0.306569i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(0.459493 + 0.295298i) q^{54} +(-0.797176 - 0.234072i) q^{56} +(-0.544078 - 0.627899i) q^{58} +(0.186393 + 0.215109i) q^{60} +(1.84125 - 0.540641i) q^{61} +(0.108660 - 0.755750i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.142315 + 0.989821i) q^{67} +(0.372786 + 0.430218i) q^{69} +(0.345139 - 0.755750i) q^{70} +(0.881761 + 0.258908i) q^{72} +(-0.239446 + 0.153882i) q^{75} +(0.841254 + 0.540641i) q^{80} +(-0.108660 + 0.755750i) q^{81} +(-1.10181 + 1.27155i) q^{82} +(1.25667 + 0.368991i) q^{83} +(0.0336545 + 0.234072i) q^{84} +(0.186393 - 0.215109i) q^{86} +(-0.0982369 + 0.215109i) q^{87} +(-0.544078 - 1.19136i) q^{89} +(-0.381761 + 0.835939i) q^{90} +(1.68251 + 1.08128i) q^{92} +(-1.61435 + 0.474017i) q^{94} -0.284630 q^{96} +(-0.260554 + 0.167448i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^7 - q^8 - 3 * q^9	$ 10 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{7} - q^{8} - 3 q^{9} - q^{10} - 2 q^{12} - 2 q^{14} - 2 q^{15} - q^{16} - 3 q^{18} - q^{20} + 7 q^{21} - 2 q^{23} + 9 q^{24} - q^{25} - 4 q^{27} - 2 q^{28} - 2 q^{29} - 2 q^{30} - q^{32} + 9 q^{35} - 3 q^{36} - q^{40} - 2 q^{41} + 7 q^{42} + 9 q^{43} - 3 q^{45} - 2 q^{46} - 2 q^{47} - 2 q^{48} - 3 q^{49} - q^{50} - 4 q^{54} - 2 q^{56} - 2 q^{58} - 2 q^{60} + 9 q^{61} + 5 q^{63} - q^{64} - q^{67} - 4 q^{69} + 9 q^{70} + 8 q^{72} - 2 q^{75} - q^{80} - 5 q^{81} - 2 q^{82} - 2 q^{83} - 4 q^{84} - 2 q^{86} - 4 q^{87} - 2 q^{89} - 3 q^{90} - 2 q^{92} - 2 q^{94} - 2 q^{96} - 3 q^{98}+O(q^{100}) $ 10 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^7 - q^8 - 3 * q^9 - q^10 - 2 * q^12 - 2 * q^14 - 2 * q^15 - q^16 - 3 * q^18 - q^20 + 7 * q^21 - 2 * q^23 + 9 * q^24 - q^25 - 4 * q^27 - 2 * q^28 - 2 * q^29 - 2 * q^30 - q^32 + 9 * q^35 - 3 * q^36 - q^40 - 2 * q^41 + 7 * q^42 + 9 * q^43 - 3 * q^45 - 2 * q^46 - 2 * q^47 - 2 * q^48 - 3 * q^49 - q^50 - 4 * q^54 - 2 * q^56 - 2 * q^58 - 2 * q^60 + 9 * q^61 + 5 * q^63 - q^64 - q^67 - 4 * q^69 + 9 * q^70 + 8 * q^72 - 2 * q^75 - q^80 - 5 * q^81 - 2 * q^82 - 2 * q^83 - 4 * q^84 - 2 * q^86 - 4 * q^87 - 2 * q^89 - 3 * q^90 - 2 * q^92 - 2 * q^94 - 2 * q^96 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times$.

$n$	$537$	$671$	$1141$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$2$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$3$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$3$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$4$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$5$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$5$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$6$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$7$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$7$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$8$	0.841254	−	0.540641i	0.841254	−	0.540641i
$9$	0.601808	+	0.694523i	0.601808	+	0.694523i
$10$	0.415415	+	0.909632i	0.415415	+	0.909632i
$11$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$11$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$12$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$13$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$13$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$14$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$15$	0.186393	−	0.215109i	0.186393	−	0.215109i
$16$	−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	$0.454545\pi$
$18$	0.130785	−	0.909632i	0.130785	−	0.909632i
$19$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$19$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$20$	0.415415	−	0.909632i	0.415415	−	0.909632i
$21$	0.226900	−	0.0666238i	0.226900	−	0.0666238i
$22$		0			0
$23$	0.830830	−	1.81926i	0.830830	−	1.81926i	0.415415	−	0.909632i	$-0.363636\pi$
$23$	0.830830	−	1.81926i	0.830830	−	1.81926i	0.415415	−	0.909632i	$-0.363636\pi$
$24$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$25$	0.841254	+	0.540641i	0.841254	+	0.540641i
$26$		0			0
$27$	−0.524075	+	0.153882i	−0.524075	+	0.153882i
$28$	0.698939	−	0.449181i	0.698939	−	0.449181i
$29$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$29$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$30$	−0.284630			−0.284630
$31$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$31$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$32$	0.415415	+	0.909632i	0.415415	+	0.909632i
$33$		0			0
$34$		0			0
$35$	0.345139	+	0.755750i	0.345139	+	0.755750i
$36$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$41$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$41$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$42$	−0.198939	−	0.127850i	−0.198939	−	0.127850i
$43$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$43$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$44$		0			0
$45$	−0.381761	−	0.835939i	−0.381761	−	0.835939i
$46$	−1.91899	+	0.563465i	−1.91899	+	0.563465i
$47$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$47$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$48$	0.186393	−	0.215109i	0.186393	−	0.215109i
$49$	0.0440780	−	0.306569i	0.0440780	−	0.306569i
$50$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$51$		0			0
$52$		0			0
$53$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$53$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$54$	0.459493	+	0.295298i	0.459493	+	0.295298i
$55$		0			0
$56$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$57$		0			0
$58$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$59$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$59$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$60$	0.186393	+	0.215109i	0.186393	+	0.215109i
$61$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$61$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$62$		0			0
$63$	0.108660	−	0.755750i	0.108660	−	0.755750i
$64$	0.415415	−	0.909632i	0.415415	−	0.909632i
$65$		0			0
$66$		0			0
$67$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$67$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$68$		0			0
$69$	0.372786	+	0.430218i	0.372786	+	0.430218i
$70$	0.345139	−	0.755750i	0.345139	−	0.755750i
$71$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$71$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$72$	0.881761	+	0.258908i	0.881761	+	0.258908i
$73$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$73$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$74$		0			0
$75$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$79$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$80$	0.841254	+	0.540641i	0.841254	+	0.540641i
$81$	−0.108660	+	0.755750i	−0.108660	+	0.755750i
$82$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$83$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$83$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$84$	0.0336545	+	0.234072i	0.0336545	+	0.234072i
$85$		0			0
$86$	0.186393	−	0.215109i	0.186393	−	0.215109i
$87$	−0.0982369	+	0.215109i	−0.0982369	+	0.215109i
$88$		0			0
$89$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$89$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$90$	−0.381761	+	0.835939i	−0.381761	+	0.835939i
$91$		0			0
$92$	1.68251	+	1.08128i	1.68251	+	1.08128i
$93$		0			0
$94$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$95$		0			0
$96$	−0.284630			−0.284630
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	−0.260554	+	0.167448i	−0.260554	+	0.167448i
$99$		0			0
$100$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$101$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$101$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$102$		0			0
$103$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$103$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$104$		0			0
$105$	−0.236479			−0.236479
$106$		0			0
$107$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$107$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$108$	−0.0777324	−	0.540641i	−0.0777324	−	0.540641i
$109$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$109$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$110$		0			0
$111$		0			0
$112$	0.345139	+	0.755750i	0.345139	+	0.755750i
$113$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$113$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$114$		0			0
$115$	−1.30972	+	1.51150i	−1.30972	+	1.51150i
$116$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$121$	0.841254	+	0.540641i	0.841254	+	0.540641i
$122$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$123$	0.459493	+	0.134919i	0.459493	+	0.134919i
$124$		0			0
$125$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$126$	−0.642315	+	0.412791i	−0.642315	+	0.412791i
$127$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$127$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$128$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$129$	−0.0777324	−	0.0228243i	−0.0777324	−	0.0228243i
$130$		0			0
$131$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$131$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$132$		0			0
$133$		0			0
$134$	0.841254	−	0.540641i	0.841254	−	0.540641i
$135$	0.546200			0.546200
$136$		0			0
$137$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$137$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$138$	0.0810141	−	0.563465i	0.0810141	−	0.563465i
$139$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$139$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$140$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$141$	0.313607	+	0.361922i	0.313607	+	0.361922i
$142$		0			0
$143$		0			0
$144$	−0.381761	−	0.835939i	−0.381761	−	0.835939i
$145$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$146$		0			0
$147$	0.0741615	+	0.0476607i	0.0741615	+	0.0476607i
$148$		0			0
$149$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$149$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$150$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$151$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$151$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$157$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$158$		0			0
$159$		0			0
$160$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$161$	−1.59435	+	0.468144i	−1.59435	+	0.468144i
$162$	0.642315	−	0.412791i	0.642315	−	0.412791i
$163$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$163$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$164$	1.68251			1.68251
$165$		0			0
$166$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$167$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$167$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$168$	0.154861	−	0.178719i	0.154861	−	0.178719i
$169$	0.415415	+	0.909632i	0.415415	+	0.909632i
$170$		0			0
$171$		0			0
$172$	−0.284630			−0.284630
$173$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$173$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$174$	0.226900	−	0.0666238i	0.226900	−	0.0666238i
$175$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$176$		0			0
$177$		0			0
$178$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$179$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$179$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$180$	0.881761	−	0.258908i	0.881761	−	0.258908i
$181$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$181$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$182$		0			0
$183$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$184$	−0.284630	−	1.97964i	−0.284630	−	1.97964i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.41542	+	0.909632i	1.41542	+	0.909632i
$189$	0.381761	+	0.245343i	0.381761	+	0.245343i
$190$		0			0
$191$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$191$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$192$	0.186393	+	0.215109i	0.186393	+	0.215109i
$193$		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	+	0.0872586i	0.297176	+	0.0872586i
$197$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$197$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$198$		0			0
$199$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$199$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$200$	1.00000			1.00000
$201$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$202$	−1.30972			−1.30972
$203$	−0.452036	−	0.521678i	−0.452036	−	0.521678i
$204$		0			0
$205$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$206$	1.25667	+	0.368991i	1.25667	+	0.368991i
$207$	1.76352	−	0.517817i	1.76352	−	0.517817i
$208$		0			0
$209$		0			0
$210$	0.154861	+	0.178719i	0.154861	+	0.178719i
$211$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$211$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$212$		0			0
$213$		0			0
$214$	1.41542	+	0.909632i	1.41542	+	0.909632i
$215$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$216$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$217$		0			0
$218$	0.186393	+	1.29639i	0.186393	+	1.29639i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$223$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$224$	0.345139	−	0.755750i	0.345139	−	0.755750i
$225$	0.130785	+	0.909632i	0.130785	+	0.909632i
$226$		0			0
$227$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$227$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$228$		0			0
$229$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$229$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$230$	2.00000			2.00000
$231$		0			0
$232$	0.698939	−	0.449181i	0.698939	−	0.449181i
$233$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$233$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$234$		0			0
$235$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$241$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$241$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$242$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$243$	−0.642315	−	0.412791i	−0.642315	−	0.412791i
$244$	0.273100	+	1.89945i	0.273100	+	1.89945i
$245$	−0.128663	+	0.281733i	−0.128663	+	0.281733i
$246$	−0.198939	−	0.435615i	−0.198939	−	0.435615i
$247$		0			0
$248$		0			0
$249$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$250$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$251$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$251$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$252$	0.732593	+	0.215109i	0.732593	+	0.215109i
$253$		0			0
$254$	0.273100	−	1.89945i	0.273100	−	1.89945i
$255$		0			0
$256$	0.841254	+	0.540641i	0.841254	+	0.540641i
$257$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$257$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$258$	0.0336545	+	0.0736930i	0.0336545	+	0.0736930i
$259$		0			0
$260$		0			0
$261$	0.500000	+	0.577031i	0.500000	+	0.577031i
$262$		0			0
$263$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$263$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.372786			0.372786
$268$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$269$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$269$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$270$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$271$		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
$276$	−0.478891	+	0.307765i	−0.478891	+	0.307765i
$277$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$277$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$278$		0			0
$279$		0			0
$280$	0.698939	+	0.449181i	0.698939	+	0.449181i
$281$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$281$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$282$	0.0681534	−	0.474017i	0.0681534	−	0.474017i
$283$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$283$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.915415	+	1.05645i	−0.915415	+	1.05645i
$288$	−0.381761	+	0.835939i	−0.381761	+	0.835939i
$289$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$290$	0.345139	+	0.755750i	0.345139	+	0.755750i
$291$		0			0
$292$		0			0
$293$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$293$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$294$	−0.0125459	−	0.0872586i	−0.0125459	−	0.0872586i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	1.68251			1.68251
$299$		0			0
$300$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$301$	0.154861	−	0.178719i	0.154861	−	0.178719i
$302$		0			0
$303$	0.154861	+	0.339098i	0.154861	+	0.339098i
$304$		0			0
$305$	−1.91899			−1.91899
$306$		0			0
$307$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$307$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$308$		0			0
$309$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$310$		0			0
$311$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$311$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$312$		0			0
$313$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$313$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$314$		0			0
$315$	−0.317178	+	0.694523i	−0.317178	+	0.694523i
$316$		0			0
$317$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$317$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$318$		0			0
$319$		0			0
$320$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$321$	0.0681534	−	0.474017i	0.0681534	−	0.474017i
$322$	1.39788	+	0.898361i	1.39788	+	0.898361i
$323$		0			0
$324$	−0.732593	−	0.215109i	−0.732593	−	0.215109i
$325$		0			0
$326$	0.186393	+	0.215109i	0.186393	+	0.215109i
$327$	0.313607	−	0.201543i	0.313607	−	0.201543i
$328$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$329$	−1.34125	+	0.393828i	−1.34125	+	0.393828i
$330$		0			0
$331$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$331$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$332$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$333$		0			0
$334$	0.830830			0.830830
$335$	0.415415	−	0.909632i	0.415415	−	0.909632i
$336$	−0.236479			−0.236479
$337$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$337$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$338$	0.415415	−	0.909632i	0.415415	−	0.909632i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.915415	+	0.588302i	−0.915415	+	0.588302i
$344$	0.186393	+	0.215109i	0.186393	+	0.215109i
$345$	−0.236479	−	0.517817i	−0.236479	−	0.517817i
$346$		0			0
$347$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$347$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$348$	−0.198939	−	0.127850i	−0.198939	−	0.127850i
$349$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$349$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$350$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$351$		0			0
$352$		0			0
$353$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$353$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$354$		0			0
$355$		0			0
$356$	1.25667	−	0.368991i	1.25667	−	0.368991i
$357$		0			0
$358$		0			0
$359$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$359$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$360$	−0.773100	−	0.496841i	−0.773100	−	0.496841i
$361$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$362$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$363$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$364$		0			0
$365$		0			0
$366$	0.459493	−	0.295298i	0.459493	−	0.295298i
$367$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$367$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$368$	−1.30972	+	1.51150i	−1.30972	+	1.51150i
$369$	1.01255	−	1.16854i	1.01255	−	1.16854i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$376$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$377$		0			0
$378$	−0.0645824	−	0.449181i	−0.0645824	−	0.449181i
$379$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$379$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$380$		0			0
$381$	−0.524075	+	0.153882i	−0.524075	+	0.153882i
$382$		0			0
$383$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$383$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$384$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$385$		0			0
$386$		0			0
$387$	−0.171292	+	0.197682i	−0.171292	+	0.197682i
$388$		0			0
$389$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$389$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$390$		0			0
$391$		0			0
$392$	−0.128663	−	0.281733i	−0.128663	−	0.281733i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$397$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$398$		0			0
$399$		0			0
$400$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$401$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$401$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$402$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$403$		0			0
$404$	0.857685	+	0.989821i	0.857685	+	0.989821i
$405$	0.317178	−	0.694523i	0.317178	−	0.694523i
$406$	−0.0982369	+	0.683252i	−0.0982369	+	0.683252i
$407$		0			0
$408$		0			0
$409$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$409$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$410$	1.41542	−	0.909632i	1.41542	−	0.909632i
$411$		0			0
$412$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$413$		0			0
$414$	−1.54620	−	0.993683i	−1.54620	−	0.993683i
$415$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$419$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$420$	0.0336545	−	0.234072i	0.0336545	−	0.234072i
$421$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$421$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$422$		0			0
$423$	1.48357	−	0.435615i	1.48357	−	0.435615i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.34125	−	0.861971i	−1.34125	−	0.861971i
$428$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$429$		0			0
$430$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	0.546200			0.546200
$433$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$433$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$434$		0			0
$435$	0.154861	−	0.178719i	0.154861	−	0.178719i
$436$	0.857685	−	0.989821i	0.857685	−	0.989821i
$437$		0			0
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$	0.239446	−	0.153882i	0.239446	−	0.153882i
$442$		0			0
$443$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$443$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$444$		0			0
$445$	0.186393	+	1.29639i	0.186393	+	1.29639i
$446$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$447$	−0.198939	−	0.435615i	−0.198939	−	0.435615i
$448$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$449$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$449$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$450$	0.601808	−	0.694523i	0.601808	−	0.694523i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.857685	−	0.989821i	0.857685	−	0.989821i
$455$		0			0
$456$		0			0
$457$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$457$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$458$	1.84125	+	0.540641i	1.84125	+	0.540641i
$459$		0			0
$460$	−1.30972	−	1.51150i	−1.30972	−	1.51150i
$461$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$461$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$462$		0			0
$463$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$463$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$464$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$465$		0			0
$466$		0			0
$467$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$467$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$468$		0			0
$469$	0.698939	−	0.449181i	0.698939	−	0.449181i
$470$	1.68251			1.68251
$471$		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		−0.415415	−	0.909632i	$-0.636364\pi$
$479$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$480$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$481$		0			0
$482$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$483$	0.0673089	−	0.468144i	0.0673089	−	0.468144i
$484$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$485$		0			0
$486$	0.108660	+	0.755750i	0.108660	+	0.755750i
$487$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$487$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$488$	1.25667	−	1.45027i	1.25667	−	1.45027i
$489$	0.0336545	−	0.0736930i	0.0336545	−	0.0736930i
$490$	0.297176	−	0.0872586i	0.297176	−	0.0872586i
$491$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$491$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$492$	−0.198939	+	0.435615i	−0.198939	+	0.435615i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.372786			0.372786
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	0.841254	−	0.540641i	0.841254	−	0.540641i
$501$	−0.0982369	−	0.215109i	−0.0982369	−	0.215109i
$502$		0			0
$503$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$503$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$504$	−0.317178	−	0.694523i	−0.317178	−	0.694523i
$505$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$506$		0			0
$507$	−0.284630			−0.284630
$508$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$509$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$509$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$510$		0			0
$511$		0			0
$512$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$513$		0			0
$514$		0			0
$515$	1.25667	−	0.368991i	1.25667	−	0.368991i
$516$	0.0336545	−	0.0736930i	0.0336545	−	0.0736930i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$521$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$522$	0.108660	−	0.755750i	0.108660	−	0.755750i
$523$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$523$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$524$		0			0
$525$	0.226900	+	0.0666238i	0.226900	+	0.0666238i
$526$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$527$		0			0
$528$		0			0
$529$	−1.96458	−	2.26725i	−1.96458	−	2.26725i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$535$	1.68251			1.68251
$536$	0.415415	+	0.909632i	0.415415	+	0.909632i
$537$		0			0
$538$	0.186393	+	0.215109i	0.186393	+	0.215109i
$539$		0			0
$540$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$541$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$541$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$542$		0			0
$543$	−0.0530529	−	0.0612263i	−0.0530529	−	0.0612263i
$544$		0			0
$545$	0.857685	+	0.989821i	0.857685	+	0.989821i
$546$		0			0
$547$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$547$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$548$		0			0
$549$	1.48357	+	0.953431i	1.48357	+	0.953431i
$550$		0			0
$551$		0			0
$552$	0.546200	+	0.160379i	0.546200	+	0.160379i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$557$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$558$		0			0
$559$		0			0
$560$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$561$		0			0
$562$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$563$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$563$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$564$	−0.402869	+	0.258908i	−0.402869	+	0.258908i
$565$		0			0
$566$	−1.91899			−1.91899
$567$	0.533654	−	0.342959i	0.533654	−	0.342959i
$568$		0			0
$569$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$569$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$570$		0			0
$571$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$571$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$572$		0			0
$573$		0			0
$574$	1.39788			1.39788
$575$	1.68251	−	1.08128i	1.68251	−	1.08128i
$576$	0.881761	−	0.258908i	0.881761	−	0.258908i
$577$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$577$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$578$	0.841254	+	0.540641i	0.841254	+	0.540641i
$579$		0			0
$580$	0.345139	−	0.755750i	0.345139	−	0.755750i
$581$	−0.452036	−	0.989821i	−0.452036	−	0.989821i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$587$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$588$	−0.0577299	+	0.0666238i	−0.0577299	+	0.0666238i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$593$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$594$		0			0
$595$		0			0
$596$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$597$		0			0
$598$		0			0
$599$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$599$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$600$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$601$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$601$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$602$	−0.236479			−0.236479
$603$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$604$		0			0
$605$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$606$	0.154861	−	0.339098i	0.154861	−	0.339098i
$607$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$607$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$608$		0			0
$609$	0.188515	−	0.0553531i	0.188515	−	0.0553531i
$610$	1.25667	+	1.45027i	1.25667	+	1.45027i
$611$		0			0
$612$		0			0
$613$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$613$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$614$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$615$	−0.402869	−	0.258908i	−0.402869	−	0.258908i
$616$		0			0
$617$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$617$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$618$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$619$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$619$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$620$		0			0
$621$	−0.155465	+	1.08128i	−0.155465	+	1.08128i
$622$		0			0
$623$	−0.452036	+	0.989821i	−0.452036	+	0.989821i
$624$		0			0
$625$	0.415415	+	0.909632i	0.415415	+	0.909632i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.732593	−	0.215109i	0.732593	−	0.215109i
$631$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$631$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	1.00000			1.00000
$641$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$641$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$642$	−0.402869	+	0.258908i	−0.402869	+	0.258908i
$643$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$643$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$644$	−0.236479	−	1.64475i	−0.236479	−	1.64475i
$645$	0.0681534	+	0.0437995i	0.0681534	+	0.0437995i
$646$		0			0
$647$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$647$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$648$	0.317178	+	0.694523i	0.317178	+	0.694523i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$653$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$653$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$654$	−0.357685	−	0.105026i	−0.357685	−	0.105026i
$655$		0			0
$656$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$657$		0			0
$658$	1.17597	+	0.755750i	1.17597	+	0.755750i
$659$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$659$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$660$		0			0
$661$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$661$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$662$		0			0
$663$		0			0
$664$	1.25667	−	0.368991i	1.25667	−	0.368991i
$665$		0			0
$666$		0			0
$667$	0.690279	−	1.51150i	0.690279	−	1.51150i
$668$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$669$	0.546200			0.546200
$670$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$671$		0			0
$672$	0.154861	+	0.178719i	0.154861	+	0.178719i
$673$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$673$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$674$		0			0
$675$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$676$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$677$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$677$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.357685	−	0.105026i	−0.357685	−	0.105026i
$682$		0			0
$683$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$683$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$684$		0			0
$685$		0			0
$686$	1.04408	+	0.306569i	1.04408	+	0.306569i
$687$	−0.0777324	−	0.540641i	−0.0777324	−	0.540641i
$688$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$689$		0			0
$690$	−0.236479	+	0.517817i	−0.236479	+	0.517817i
$691$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$691$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$692$		0			0
$693$		0			0
$694$	0.273100	+	1.89945i	0.273100	+	1.89945i
$695$		0			0
$696$	0.0336545	+	0.234072i	0.0336545	+	0.234072i
$697$		0			0
$698$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$699$		0			0
$700$	0.830830			0.830830
$701$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$701$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.198939	−	0.435615i	−0.198939	−	0.435615i
$706$		0			0
$707$	−1.08816			−1.08816
$708$		0			0
$709$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$709$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$710$		0			0
$711$		0			0
$712$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$719$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$720$	0.130785	+	0.909632i	0.130785	+	0.909632i
$721$	1.04408	+	0.306569i	1.04408	+	0.306569i
$722$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$723$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$724$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$725$	0.698939	+	0.449181i	0.698939	+	0.449181i
$726$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$727$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$727$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$728$		0			0
$729$	−0.459493	+	0.295298i	−0.459493	+	0.295298i
$730$		0			0
$731$		0			0
$732$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$733$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$733$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$734$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$735$	−0.0577299	−	0.0666238i	−0.0577299	−	0.0666238i
$736$	2.00000			2.00000
$737$		0			0
$738$	−1.54620			−1.54620
$739$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$739$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$743$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$744$		0			0
$745$	1.41542	−	0.909632i	1.41542	−	0.909632i
$746$		0			0
$747$	0.500000	+	1.09485i	0.500000	+	1.09485i
$748$		0			0
$749$	1.17597	+	0.755750i	1.17597	+	0.755750i
$750$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$751$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$751$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$752$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.297176	+	0.342959i	−0.297176	+	0.342959i
$757$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$757$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$761$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$762$	0.459493	+	0.295298i	0.459493	+	0.295298i
$763$	0.154861	+	1.07708i	0.154861	+	1.07708i
$764$		0			0
$765$		0			0
$766$	1.68251			1.68251
$767$		0			0
$768$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$769$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$769$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$773$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$774$	0.261571			0.261571
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.186393	+	1.29639i	0.186393	+	1.29639i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.435418	+	0.127850i	−0.435418	+	0.127850i
$784$	−0.128663	+	0.281733i	−0.128663	+	0.281733i
$785$		0			0
$786$		0			0
$787$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$787$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$788$		0			0
$789$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$797$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$798$		0			0
$799$		0			0
$800$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$801$	0.500000	−	1.09485i	0.500000	−	1.09485i
$802$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$803$		0			0
$804$	0.186393	−	0.215109i	0.186393	−	0.215109i
$805$	1.66166			1.66166
$806$		0			0
$807$	0.0336545	−	0.0736930i	0.0336545	−	0.0736930i
$808$	0.186393	−	1.29639i	0.186393	−	1.29639i
$809$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$809$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$810$	−0.732593	+	0.215109i	−0.732593	+	0.215109i
$811$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$811$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$812$	0.580699	−	0.373193i	0.580699	−	0.373193i
$813$		0			0
$814$		0			0
$815$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$816$		0			0
$817$		0			0
$818$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$819$		0			0
$820$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$821$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$821$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$822$		0			0
$823$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$823$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$824$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$825$		0			0
$826$		0			0
$827$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$827$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$828$	0.261571	+	1.81926i	0.261571	+	1.81926i
$829$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$829$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$830$	0.186393	+	1.29639i	0.186393	+	1.29639i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.698939	−	0.449181i	0.698939	−	0.449181i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$839$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$840$	−0.198939	+	0.127850i	−0.198939	+	0.127850i
$841$	−0.309721			−0.309721
$842$	0.830830			0.830830
$843$	−0.402869	+	0.258908i	−0.402869	+	0.258908i
$844$		0			0
$845$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$846$	−1.30075	−	0.835939i	−1.30075	−	0.835939i
$847$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$848$		0			0
$849$	0.226900	+	0.496841i	0.226900	+	0.496841i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$853$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$854$	0.226900	+	1.57812i	0.226900	+	1.57812i
$855$		0			0
$856$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$857$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$857$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$858$		0			0
$859$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$859$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$860$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$861$	−0.165284	−	0.361922i	−0.165284	−	0.361922i
$862$		0			0
$863$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$863$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$864$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$865$		0			0
$866$		0			0
$867$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$868$		0			0
$869$		0			0
$870$	−0.236479			−0.236479
$871$		0			0
$872$	−1.30972			−1.30972
$873$		0			0
$874$		0			0
$875$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$876$		0			0
$877$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$877$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.830830	+	1.81926i	0.830830	+	1.81926i	0.415415	+	0.909632i	$0.363636\pi$
$881$	0.830830	+	1.81926i	0.830830	+	1.81926i	0.415415	+	0.909632i	$0.363636\pi$
$882$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$883$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$883$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$884$		0			0
$885$		0			0
$886$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$887$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$887$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$888$		0			0
$889$	0.226900	−	1.57812i	0.226900	−	1.57812i
$890$	0.857685	−	0.989821i	0.857685	−	0.989821i
$891$		0			0
$892$	1.84125	−	0.540641i	1.84125	−	0.540641i
$893$		0			0
$894$	−0.198939	+	0.435615i	−0.198939	+	0.435615i
$895$		0			0
$896$	0.698939	+	0.449181i	0.698939	+	0.449181i
$897$		0			0
$898$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$899$		0			0
$900$	−0.918986			−0.918986
$901$		0			0
$902$		0			0
$903$	0.0279611	+	0.0612263i	0.0279611	+	0.0612263i
$904$		0			0
$905$	0.186393	−	0.215109i	0.186393	−	0.215109i
$906$		0			0
$907$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$907$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$908$	−1.30972			−1.30972
$909$	1.20362			1.20362
$910$		0			0
$911$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$911$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.226900	−	0.496841i	0.226900	−	0.496841i
$916$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$917$		0			0
$918$		0			0
$919$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$919$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$920$	−0.284630	+	1.97964i	−0.284630	+	1.97964i
$921$	0.0681534	+	0.474017i	0.0681534	+	0.474017i
$922$	1.25667	+	0.368991i	1.25667	+	0.368991i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$927$	−1.15486	−	0.339098i	−1.15486	−	0.339098i
$928$	0.345139	+	0.755750i	0.345139	+	0.755750i
$929$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$929$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.273100	−	1.89945i	0.273100	−	1.89945i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$939$		0			0
$940$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$941$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$941$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$942$		0			0
$943$	−3.22871	−	0.948034i	−3.22871	−	0.948034i
$944$		0			0
$945$	−0.297176	−	0.342959i	−0.297176	−	0.342959i
$946$		0			0
$947$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$947$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$953$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$961$	0.415415	−	0.909632i	0.415415	−	0.909632i
$962$		0			0
$963$	−1.30075	−	0.835939i	−1.30075	−	0.835939i
$964$	0.186393	+	1.29639i	0.186393	+	1.29639i
$965$		0			0
$966$	−0.397877	+	0.255700i	−0.397877	+	0.255700i
$967$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$967$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$968$	1.00000			1.00000
$969$		0			0
$970$		0			0
$971$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$971$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$972$	0.500000	−	0.577031i	0.500000	−	0.577031i
$973$		0			0
$974$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$975$		0			0
$976$	−1.91899			−1.91899
$977$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$977$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$978$	−0.0777324	+	0.0228243i	−0.0777324	+	0.0228243i
$979$		0			0
$980$	−0.260554	−	0.167448i	−0.260554	−	0.167448i
$981$	−0.171292	−	1.19136i	−0.171292	−	1.19136i
$982$		0			0
$983$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$983$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$984$	0.459493	−	0.134919i	0.459493	−	0.134919i
$985$		0			0
$986$		0			0
$987$	0.0566239	−	0.393828i	0.0566239	−	0.393828i
$988$		0			0
$989$	0.546200	+	0.160379i	0.546200	+	0.160379i
$990$		0			0
$991$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$991$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$997$		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	1340.1.bb.a.1179.1	yes	10
4.3	odd	2		1340.1.bb.b.1179.1	yes	10
5.4	even	2		1340.1.bb.b.1179.1	yes	10
20.19	odd	2	CM	1340.1.bb.a.1179.1	yes	10
67.62	even	11	inner	1340.1.bb.a.799.1	✓	10
268.263	odd	22		1340.1.bb.b.799.1	yes	10
335.129	even	22		1340.1.bb.b.799.1	yes	10
1340.799	odd	22	inner	1340.1.bb.a.799.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1340.1.bb.a.799.1	✓	10	67.62	even	11	inner
1340.1.bb.a.799.1	✓	10	1340.799	odd	22	inner
1340.1.bb.a.1179.1	yes	10	1.1	even	1	trivial
1340.1.bb.a.1179.1	yes	10	20.19	odd	2	CM
1340.1.bb.b.799.1	yes	10	268.263	odd	22
1340.1.bb.b.799.1	yes	10	335.129	even	22
1340.1.bb.b.1179.1	yes	10	4.3	odd	2
1340.1.bb.b.1179.1	yes	10	5.4	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:	\( N \)	\(=\)	\( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1340.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.118239 + 0.258908i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.273100 - 0.0801894i) q^{6} +(-0.544078 - 0.627899i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.601808 + 0.694523i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.118239 + 0.258908i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.273100 - 0.0801894i) q^{6} +(-0.544078 - 0.627899i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.601808 + 0.694523i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-0.239446 - 0.153882i) q^{12} +(-0.118239 + 0.822373i) q^{14} +(0.186393 - 0.215109i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.130785 - 0.909632i) q^{18} +(0.415415 - 0.909632i) q^{20} +(0.226900 - 0.0666238i) q^{21} +(0.830830 - 1.81926i) q^{23} +(0.0405070 + 0.281733i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.524075 + 0.153882i) q^{27} +(0.698939 - 0.449181i) q^{28} +0.830830 q^{29} -0.284630 q^{30} +(0.415415 + 0.909632i) q^{32} +(0.345139 + 0.755750i) q^{35} +(-0.773100 + 0.496841i) q^{36} +(-0.959493 + 0.281733i) q^{40} +(-0.239446 - 1.66538i) q^{41} +(-0.198939 - 0.127850i) q^{42} +(0.0405070 + 0.281733i) q^{43} +(-0.381761 - 0.835939i) q^{45} +(-1.91899 + 0.563465i) q^{46} +(0.698939 - 1.53046i) q^{47} +(0.186393 - 0.215109i) q^{48} +(0.0440780 - 0.306569i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(0.459493 + 0.295298i) q^{54} +(-0.797176 - 0.234072i) q^{56} +(-0.544078 - 0.627899i) q^{58} +(0.186393 + 0.215109i) q^{60} +(1.84125 - 0.540641i) q^{61} +(0.108660 - 0.755750i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.142315 + 0.989821i) q^{67} +(0.372786 + 0.430218i) q^{69} +(0.345139 - 0.755750i) q^{70} +(0.881761 + 0.258908i) q^{72} +(-0.239446 + 0.153882i) q^{75} +(0.841254 + 0.540641i) q^{80} +(-0.108660 + 0.755750i) q^{81} +(-1.10181 + 1.27155i) q^{82} +(1.25667 + 0.368991i) q^{83} +(0.0336545 + 0.234072i) q^{84} +(0.186393 - 0.215109i) q^{86} +(-0.0982369 + 0.215109i) q^{87} +(-0.544078 - 1.19136i) q^{89} +(-0.381761 + 0.835939i) q^{90} +(1.68251 + 1.08128i) q^{92} +(-1.61435 + 0.474017i) q^{94} -0.284630 q^{96} +(-0.260554 + 0.167448i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^7 - q^8 - 3 * q^9	\( 10 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{7} - q^{8} - 3 q^{9} - q^{10} - 2 q^{12} - 2 q^{14} - 2 q^{15} - q^{16} - 3 q^{18} - q^{20} + 7 q^{21} - 2 q^{23} + 9 q^{24} - q^{25} - 4 q^{27} - 2 q^{28} - 2 q^{29} - 2 q^{30} - q^{32} + 9 q^{35} - 3 q^{36} - q^{40} - 2 q^{41} + 7 q^{42} + 9 q^{43} - 3 q^{45} - 2 q^{46} - 2 q^{47} - 2 q^{48} - 3 q^{49} - q^{50} - 4 q^{54} - 2 q^{56} - 2 q^{58} - 2 q^{60} + 9 q^{61} + 5 q^{63} - q^{64} - q^{67} - 4 q^{69} + 9 q^{70} + 8 q^{72} - 2 q^{75} - q^{80} - 5 q^{81} - 2 q^{82} - 2 q^{83} - 4 q^{84} - 2 q^{86} - 4 q^{87} - 2 q^{89} - 3 q^{90} - 2 q^{92} - 2 q^{94} - 2 q^{96} - 3 q^{98}+O(q^{100}) \) 10 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^7 - q^8 - 3 * q^9 - q^10 - 2 * q^12 - 2 * q^14 - 2 * q^15 - q^16 - 3 * q^18 - q^20 + 7 * q^21 - 2 * q^23 + 9 * q^24 - q^25 - 4 * q^27 - 2 * q^28 - 2 * q^29 - 2 * q^30 - q^32 + 9 * q^35 - 3 * q^36 - q^40 - 2 * q^41 + 7 * q^42 + 9 * q^43 - 3 * q^45 - 2 * q^46 - 2 * q^47 - 2 * q^48 - 3 * q^49 - q^50 - 4 * q^54 - 2 * q^56 - 2 * q^58 - 2 * q^60 + 9 * q^61 + 5 * q^63 - q^64 - q^67 - 4 * q^69 + 9 * q^70 + 8 * q^72 - 2 * q^75 - q^80 - 5 * q^81 - 2 * q^82 - 2 * q^83 - 4 * q^84 - 2 * q^86 - 4 * q^87 - 2 * q^89 - 3 * q^90 - 2 * q^92 - 2 * q^94 - 2 * q^96 - 3 * q^98

Introduction

L-functions

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