LMFDB - Embedded newform 3864.1.dl.d.3443.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3864,1,Mod(587,3864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3864, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 11, 11, 20]))

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

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

chi := DirichletCharacter("3864.587");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3864.dl (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:	$1.92838720881$
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			3443.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	3864.3443
Dual form			3864.1.dl.d.2267.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.142315 + 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.142315 + 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.654861 + 0.755750i) q^{12} +(1.25667 + 0.368991i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.118239 - 0.822373i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.654861 - 0.755750i) q^{21} +(-0.841254 - 0.540641i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(1.10181 - 0.708089i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.415415 + 0.909632i) q^{28} +(0.239446 - 1.66538i) q^{29} +(-0.239446 - 0.153882i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-0.544078 - 0.627899i) q^{34} +(-0.959493 - 0.281733i) q^{36} +(-1.25667 + 0.368991i) q^{39} +(-0.345139 - 0.755750i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(1.41542 - 0.909632i) q^{43} +(-0.959493 + 0.281733i) q^{46} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.142315 + 0.989821i) q^{50} +(0.345139 + 0.755750i) q^{51} +(0.186393 - 1.29639i) q^{52} +(-0.273100 + 0.0801894i) q^{53} +(0.841254 + 0.540641i) q^{54} +(0.959493 + 0.281733i) q^{56} +(-1.10181 - 1.27155i) q^{58} +(-1.84125 - 0.540641i) q^{59} +(-1.61435 - 1.03748i) q^{61} +(-0.273100 + 0.0801894i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.25667 - 1.45027i) q^{67} -0.830830 q^{68} +1.00000 q^{69} +(-1.25667 + 1.45027i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(0.142315 - 0.989821i) q^{75} +(-0.544078 + 1.19136i) q^{78} +(-0.654861 - 0.755750i) q^{81} +(-0.797176 - 0.234072i) q^{82} +(0.544078 - 1.19136i) q^{83} +(-0.841254 - 0.540641i) q^{84} +(0.239446 - 1.66538i) q^{86} +(0.698939 + 1.53046i) q^{87} +(0.239446 - 0.153882i) q^{89} -1.30972 q^{91} +(-0.415415 + 0.909632i) q^{92} +0.284630 q^{93} +(-0.142315 - 0.989821i) q^{96} +(0.142315 - 0.989821i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + q^{3} - q^{4} - q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 + q^3 - q^4 - q^6 - q^7 + q^8 - q^9	$ 10 q + q^{2} + q^{3} - q^{4} - q^{6} - q^{7} + q^{8} - q^{9} + q^{12} - 2 q^{13} + q^{14} - q^{16} + 2 q^{17} + q^{18} + q^{21} + q^{23} + 10 q^{24} - q^{25} + 2 q^{26} + q^{27} - q^{28} + 2 q^{29} - 2 q^{31} + q^{32} - 2 q^{34} - q^{36} + 2 q^{39} - 9 q^{41} - q^{42} + 9 q^{43} - q^{46} + q^{48} - q^{49} + q^{50} + 9 q^{51} - 2 q^{52} + 2 q^{53} - q^{54} + q^{56} - 2 q^{58} - 9 q^{59} - 2 q^{61} + 2 q^{62} - q^{63} - q^{64} - 2 q^{67} + 2 q^{68} + 10 q^{69} + 2 q^{71} + q^{72} + q^{75} - 2 q^{78} - q^{81} - 2 q^{82} + 2 q^{83} + q^{84} + 2 q^{86} - 2 q^{87} + 2 q^{89} - 2 q^{91} + q^{92} + 2 q^{93} - q^{96} + q^{98}+O(q^{100}) $ 10 * q + q^2 + q^3 - q^4 - q^6 - q^7 + q^8 - q^9 + q^12 - 2 * q^13 + q^14 - q^16 + 2 * q^17 + q^18 + q^21 + q^23 + 10 * q^24 - q^25 + 2 * q^26 + q^27 - q^28 + 2 * q^29 - 2 * q^31 + q^32 - 2 * q^34 - q^36 + 2 * q^39 - 9 * q^41 - q^42 + 9 * q^43 - q^46 + q^48 - q^49 + q^50 + 9 * q^51 - 2 * q^52 + 2 * q^53 - q^54 + q^56 - 2 * q^58 - 9 * q^59 - 2 * q^61 + 2 * q^62 - q^63 - q^64 - 2 * q^67 + 2 * q^68 + 10 * q^69 + 2 * q^71 + q^72 + q^75 - 2 * q^78 - q^81 - 2 * q^82 + 2 * q^83 + q^84 + 2 * q^86 - 2 * q^87 + 2 * q^89 - 2 * q^91 + q^92 + 2 * q^93 - q^96 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3864\mathbb{Z}\right)^\times$.

$n$	$967$	$1289$	$1933$	$2761$	$2857$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$	$e\left(\frac{4}{11}\right)$

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
$3$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$3$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$4$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$5$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$5$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$6$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$7$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$7$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$8$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$9$	0.415415	−	0.909632i	0.415415	−	0.909632i
$10$		0			0
$11$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$11$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$12$	0.654861	+	0.755750i	0.654861	+	0.755750i
$13$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$13$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$14$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$15$		0			0
$16$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$17$	0.118239	−	0.822373i	0.118239	−	0.822373i	−0.841254	−	0.540641i	$-0.818182\pi$
$17$	0.118239	−	0.822373i	0.118239	−	0.822373i	0.959493	−	0.281733i	$-0.0909091\pi$
$18$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$19$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$19$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$20$		0			0
$21$	0.654861	−	0.755750i	0.654861	−	0.755750i
$22$		0			0
$23$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$23$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$24$	1.00000			1.00000
$25$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$26$	1.10181	−	0.708089i	1.10181	−	0.708089i
$27$	0.142315	+	0.989821i	0.142315	+	0.989821i
$28$	0.415415	+	0.909632i	0.415415	+	0.909632i
$29$	0.239446	−	1.66538i	0.239446	−	1.66538i	−0.415415	−	0.909632i	$-0.636364\pi$
$29$	0.239446	−	1.66538i	0.239446	−	1.66538i	0.654861	−	0.755750i	$-0.272727\pi$
$30$		0			0
$31$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$31$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$32$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$33$		0			0
$34$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$35$		0			0
$36$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$37$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$37$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$38$		0			0
$39$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$40$		0			0
$41$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$41$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	−1.00000			$\pi$
$42$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$43$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$43$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$44$		0			0
$45$		0			0
$46$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	0.654861	−	0.755750i	0.654861	−	0.755750i
$49$	0.841254	−	0.540641i	0.841254	−	0.540641i
$50$	0.142315	+	0.989821i	0.142315	+	0.989821i
$51$	0.345139	+	0.755750i	0.345139	+	0.755750i
$52$	0.186393	−	1.29639i	0.186393	−	1.29639i
$53$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$53$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	0.142315	+	0.989821i	$0.454545\pi$
$54$	0.841254	+	0.540641i	0.841254	+	0.540641i
$55$		0			0
$56$	0.959493	+	0.281733i	0.959493	+	0.281733i
$57$		0			0
$58$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$59$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−0.841254	−	0.540641i	$-0.818182\pi$
$59$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−1.00000			$\pi$
$60$		0			0
$61$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$61$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$62$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$63$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$64$	0.415415	+	0.909632i	0.415415	+	0.909632i
$65$		0			0
$66$		0			0
$67$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$67$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$68$	−0.830830			−0.830830
$69$	1.00000			1.00000
$70$		0			0
$71$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$71$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$72$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$73$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$73$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$74$		0			0
$75$	0.142315	−	0.989821i	0.142315	−	0.989821i
$76$		0			0
$77$		0			0
$78$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$79$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$79$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$80$		0			0
$81$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$82$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$83$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$83$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$84$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$85$		0			0
$86$	0.239446	−	1.66538i	0.239446	−	1.66538i
$87$	0.698939	+	1.53046i	0.698939	+	1.53046i
$88$		0			0
$89$	0.239446	−	0.153882i	0.239446	−	0.153882i	−0.415415	−	0.909632i	$-0.636364\pi$
$89$	0.239446	−	0.153882i	0.239446	−	0.153882i	0.654861	+	0.755750i	$0.272727\pi$
$90$		0			0
$91$	−1.30972			−1.30972
$92$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$93$	0.284630			0.284630
$94$		0			0
$95$		0			0
$96$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$97$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$97$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$98$	0.142315	−	0.989821i	0.142315	−	0.989821i
$99$		0			0
$100$	0.841254	+	0.540641i	0.841254	+	0.540641i
$101$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$101$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$102$	0.797176	+	0.234072i	0.797176	+	0.234072i
$103$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$103$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$104$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$105$		0			0
$106$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$107$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$107$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$108$	0.959493	−	0.281733i	0.959493	−	0.281733i
$109$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$109$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$110$		0			0
$111$		0			0
$112$	0.841254	−	0.540641i	0.841254	−	0.540641i
$113$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$113$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$114$		0			0
$115$		0			0
$116$	−1.68251			−1.68251
$117$	0.857685	−	0.989821i	0.857685	−	0.989821i
$118$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$119$	0.118239	+	0.822373i	0.118239	+	0.822373i
$120$		0			0
$121$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$122$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$123$	0.698939	+	0.449181i	0.698939	+	0.449181i
$124$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$125$		0			0
$126$	0.654861	+	0.755750i	0.654861	+	0.755750i
$127$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$127$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$128$	0.959493	+	0.281733i	0.959493	+	0.281733i
$129$	−0.698939	+	1.53046i	−0.698939	+	1.53046i
$130$		0			0
$131$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$131$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$132$		0			0
$133$		0			0
$134$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$135$		0			0
$136$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	0.654861	−	0.755750i	0.654861	−	0.755750i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$		0			0
$141$		0			0
$142$	0.273100	+	1.89945i	0.273100	+	1.89945i
$143$		0			0
$144$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$145$		0			0
$146$		0			0
$147$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$148$		0			0
$149$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	0.142315	−	0.989821i	$-0.454545\pi$
$149$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	−1.00000			$\pi$
$150$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$151$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$151$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$152$		0			0
$153$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$154$		0			0
$155$		0			0
$156$	0.544078	+	1.19136i	0.544078	+	1.19136i
$157$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$157$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$158$		0			0
$159$	0.186393	−	0.215109i	0.186393	−	0.215109i
$160$		0			0
$161$	0.959493	+	0.281733i	0.959493	+	0.281733i
$162$	−1.00000			−1.00000
$163$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$163$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$164$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$165$		0			0
$166$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$167$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$167$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$168$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$169$	0.601808	+	0.386758i	0.601808	+	0.386758i
$170$		0			0
$171$		0			0
$172$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$173$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$173$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$174$	1.61435	+	0.474017i	1.61435	+	0.474017i
$175$	0.415415	−	0.909632i	0.415415	−	0.909632i
$176$		0			0
$177$	1.84125	−	0.540641i	1.84125	−	0.540641i
$178$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$179$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$179$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$180$		0			0
$181$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$181$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$182$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$183$	1.91899			1.91899
$184$	0.415415	+	0.909632i	0.415415	+	0.909632i
$185$		0			0
$186$	0.186393	−	0.215109i	0.186393	−	0.215109i
$187$		0			0
$188$		0			0
$189$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$190$		0			0
$191$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$191$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$192$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$193$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$193$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$194$		0			0
$195$		0			0
$196$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$197$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.654861	−	0.755750i	$-0.272727\pi$
$197$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.142315	+	0.989821i	$0.454545\pi$
$198$		0			0
$199$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$199$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$200$	0.959493	−	0.281733i	0.959493	−	0.281733i
$201$	−0.273100	+	1.89945i	−0.273100	+	1.89945i
$202$		0			0
$203$	0.239446	+	1.66538i	0.239446	+	1.66538i
$204$	0.698939	−	0.449181i	0.698939	−	0.449181i
$205$		0			0
$206$	−1.68251			−1.68251
$207$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$208$	−1.30972			−1.30972
$209$		0			0
$210$		0			0
$211$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$211$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$212$	0.118239	+	0.258908i	0.118239	+	0.258908i
$213$	0.273100	−	1.89945i	0.273100	−	1.89945i
$214$		0			0
$215$		0			0
$216$	0.415415	−	0.909632i	0.415415	−	0.909632i
$217$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.452036	−	0.989821i	0.452036	−	0.989821i
$222$		0			0
$223$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$223$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$224$	0.142315	−	0.989821i	0.142315	−	0.989821i
$225$	0.415415	+	0.909632i	0.415415	+	0.909632i
$226$		0			0
$227$	1.61435	−	1.03748i	1.61435	−	1.03748i	0.654861	−	0.755750i	$-0.272727\pi$
$227$	1.61435	−	1.03748i	1.61435	−	1.03748i	0.959493	−	0.281733i	$-0.0909091\pi$
$228$		0			0
$229$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$229$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$230$		0			0
$231$		0			0
$232$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$233$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$233$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$234$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$235$		0			0
$236$	−0.273100	+	1.89945i	−0.273100	+	1.89945i
$237$		0			0
$238$	0.698939	+	0.449181i	0.698939	+	0.449181i
$239$	0.118239	−	0.258908i	0.118239	−	0.258908i	−0.841254	−	0.540641i	$-0.818182\pi$
$239$	0.118239	−	0.258908i	0.118239	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$240$		0			0
$241$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$241$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$242$	0.654861	+	0.755750i	0.654861	+	0.755750i
$243$	0.959493	+	0.281733i	0.959493	+	0.281733i
$244$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$245$		0			0
$246$	0.797176	−	0.234072i	0.797176	−	0.234072i
$247$		0			0
$248$	0.118239	+	0.258908i	0.118239	+	0.258908i
$249$	0.186393	+	1.29639i	0.186393	+	1.29639i
$250$		0			0
$251$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$251$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$252$	1.00000			1.00000
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.841254	−	0.540641i	0.841254	−	0.540641i
$257$	0.239446	+	1.66538i	0.239446	+	1.66538i	0.654861	+	0.755750i	$0.272727\pi$
$257$	0.239446	+	1.66538i	0.239446	+	1.66538i	−0.415415	+	0.909632i	$0.636364\pi$
$258$	0.698939	+	1.53046i	0.698939	+	1.53046i
$259$		0			0
$260$		0			0
$261$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$262$	0.698939	−	1.53046i	0.698939	−	1.53046i
$263$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.959493	−	0.281733i	$-0.0909091\pi$
$263$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.654861	+	0.755750i	$0.272727\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$268$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$269$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$269$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$270$		0			0
$271$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$271$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$272$	0.118239	+	0.822373i	0.118239	+	0.822373i
$273$	1.10181	−	0.708089i	1.10181	−	0.708089i
$274$		0			0
$275$		0			0
$276$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$280$		0			0
$281$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$281$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$282$		0			0
$283$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$283$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$284$	1.61435	+	1.03748i	1.61435	+	1.03748i
$285$		0			0
$286$		0			0
$287$	0.544078	+	0.627899i	0.544078	+	0.627899i
$288$	0.654861	+	0.755750i	0.654861	+	0.755750i
$289$	0.297176	+	0.0872586i	0.297176	+	0.0872586i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$293$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$294$	0.415415	+	0.909632i	0.415415	+	0.909632i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.30972			−1.30972
$299$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$300$	−1.00000			−1.00000
$301$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$307$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$307$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$308$		0			0
$309$	1.61435	+	0.474017i	1.61435	+	0.474017i
$310$		0			0
$311$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$311$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$312$	1.25667	+	0.368991i	1.25667	+	0.368991i
$313$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$313$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$314$	1.10181	+	0.708089i	1.10181	+	0.708089i
$315$		0			0
$316$		0			0
$317$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.654861	+	0.755750i	$0.272727\pi$
$317$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.142315	+	0.989821i	$0.454545\pi$
$318$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	0.841254	−	0.540641i	0.841254	−	0.540641i
$323$		0			0
$324$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$325$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$326$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$327$		0			0
$328$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$329$		0			0
$330$		0			0
$331$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$331$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$332$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$337$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$337$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$338$	0.686393	−	0.201543i	0.686393	−	0.201543i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$344$	−1.68251			−1.68251
$345$		0			0
$346$		0			0
$347$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$347$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$348$	1.41542	−	0.909632i	1.41542	−	0.909632i
$349$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$349$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$350$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$351$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$352$		0			0
$353$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−0.415415	−	0.909632i	$-0.636364\pi$
$353$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−1.00000			$\pi$
$354$	0.797176	−	1.74557i	0.797176	−	1.74557i
$355$		0			0
$356$	−0.186393	−	0.215109i	−0.186393	−	0.215109i
$357$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$358$		0			0
$359$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	0.654861	+	0.755750i	$0.272727\pi$
$359$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	−1.00000			$\pi$
$360$		0			0
$361$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$362$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$363$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$364$	0.186393	+	1.29639i	0.186393	+	1.29639i
$365$		0			0
$366$	1.25667	−	1.45027i	1.25667	−	1.45027i
$367$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$367$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$368$	0.959493	+	0.281733i	0.959493	+	0.281733i
$369$	−0.830830			−0.830830
$370$		0			0
$371$	0.239446	−	0.153882i	0.239446	−	0.153882i
$372$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$373$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$373$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.915415	−	2.00448i	0.915415	−	2.00448i
$378$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$379$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$379$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$380$		0			0
$381$		0			0
$382$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$383$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$383$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$384$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$385$		0			0
$386$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$387$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$388$		0			0
$389$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.142315	−	0.989821i	$-0.454545\pi$
$389$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.959493	−	0.281733i	$-0.0909091\pi$
$390$		0			0
$391$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$392$	−1.00000			−1.00000
$393$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$394$	0.698939	−	0.449181i	0.698939	−	0.449181i
$395$		0			0
$396$		0			0
$397$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$397$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$398$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$399$		0			0
$400$	0.415415	−	0.909632i	0.415415	−	0.909632i
$401$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$401$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$402$	1.25667	+	1.45027i	1.25667	+	1.45027i
$403$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$404$		0			0
$405$		0			0
$406$	1.41542	+	0.909632i	1.41542	+	0.909632i
$407$		0			0
$408$	0.118239	−	0.822373i	0.118239	−	0.822373i
$409$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$409$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$410$		0			0
$411$		0			0
$412$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$413$	1.91899			1.91899
$414$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$415$		0			0
$416$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$417$		0			0
$418$		0			0
$419$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.654861	+	0.755750i	$0.272727\pi$
$419$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.142315	+	0.989821i	$0.454545\pi$
$420$		0			0
$421$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$421$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$422$	1.61435	+	1.03748i	1.61435	+	1.03748i
$423$		0			0
$424$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$425$	0.544078	+	0.627899i	0.544078	+	0.627899i
$426$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$427$	1.84125	+	0.540641i	1.84125	+	0.540641i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i	0.959493	+	0.281733i	$0.0909091\pi$
$431$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i	−1.00000			$1.00000\pi$
$432$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$433$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$433$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$434$	0.239446	−	0.153882i	0.239446	−	0.153882i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$439$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$440$		0			0
$441$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$442$	−0.452036	−	0.989821i	−0.452036	−	0.989821i
$443$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$443$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$444$		0			0
$445$		0			0
$446$	0.797176	−	1.74557i	0.797176	−	1.74557i
$447$	1.25667	+	0.368991i	1.25667	+	0.368991i
$448$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$449$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$449$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$450$	0.959493	+	0.281733i	0.959493	+	0.281733i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.273100	−	1.89945i	0.273100	−	1.89945i
$455$		0			0
$456$		0			0
$457$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$457$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$458$	1.10181	−	1.27155i	1.10181	−	1.27155i
$459$	0.830830			0.830830
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$463$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$464$	0.239446	+	1.66538i	0.239446	+	1.66538i
$465$		0			0
$466$		0			0
$467$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$467$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$468$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$469$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$470$		0			0
$471$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$472$	1.25667	+	1.45027i	1.25667	+	1.45027i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	0.797176	−	0.234072i	0.797176	−	0.234072i
$477$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$478$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$479$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$479$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$484$	1.00000			1.00000
$485$		0			0
$486$	0.841254	−	0.540641i	0.841254	−	0.540641i
$487$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$487$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$488$	0.797176	+	1.74557i	0.797176	+	1.74557i
$489$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$490$		0			0
$491$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$491$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$492$	0.345139	−	0.755750i	0.345139	−	0.755750i
$493$	−1.34125	−	0.393828i	−1.34125	−	0.393828i
$494$		0			0
$495$		0			0
$496$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$497$	0.797176	−	1.74557i	0.797176	−	1.74557i
$498$	1.10181	+	0.708089i	1.10181	+	0.708089i
$499$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$499$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$500$		0			0
$501$		0			0
$502$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$503$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$503$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$504$	0.654861	−	0.755750i	0.654861	−	0.755750i
$505$		0			0
$506$		0			0
$507$	−0.715370			−0.715370
$508$		0			0
$509$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$509$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$510$		0			0
$511$		0			0
$512$	0.142315	−	0.989821i	0.142315	−	0.989821i
$513$		0			0
$514$	1.41542	+	0.909632i	1.41542	+	0.909632i
$515$		0			0
$516$	1.61435	+	0.474017i	1.61435	+	0.474017i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.959493	−	0.281733i	$-0.0909091\pi$
$521$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.142315	+	0.989821i	$0.454545\pi$
$522$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$523$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$523$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$524$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$525$	0.142315	+	0.989821i	0.142315	+	0.989821i
$526$	1.41542	−	0.909632i	1.41542	−	0.909632i
$527$	−0.154861	+	0.178719i	−0.154861	+	0.178719i
$528$		0			0
$529$	0.415415	+	0.909632i	0.415415	+	0.909632i
$530$		0			0
$531$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$532$		0			0
$533$	−0.154861	−	1.07708i	−0.154861	−	1.07708i
$534$	0.118239	+	0.258908i	0.118239	+	0.258908i
$535$		0			0
$536$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$541$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$542$	0.797176	+	0.234072i	0.797176	+	0.234072i
$543$	0.118239	−	0.258908i	0.118239	−	0.258908i
$544$	0.698939	+	0.449181i	0.698939	+	0.449181i
$545$		0			0
$546$	0.186393	−	1.29639i	0.186393	−	1.29639i
$547$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$547$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$548$		0			0
$549$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$550$		0			0
$551$		0			0
$552$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$557$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	−1.00000			$\pi$
$558$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$559$	2.11435	−	0.620830i	2.11435	−	0.620830i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$563$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.841254	+	0.540641i	0.841254	+	0.540641i
$568$	1.84125	−	0.540641i	1.84125	−	0.540641i
$569$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$569$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$570$		0			0
$571$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$571$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$572$		0			0
$573$	0.857685	−	0.989821i	0.857685	−	0.989821i
$574$	0.830830			0.830830
$575$	0.959493	−	0.281733i	0.959493	−	0.281733i
$576$	1.00000			1.00000
$577$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$577$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$578$	0.260554	−	0.167448i	0.260554	−	0.167448i
$579$	0.118239	+	0.822373i	0.118239	+	0.822373i
$580$		0			0
$581$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.544078	+	0.627899i	0.544078	+	0.627899i	0.959493	−	0.281733i	$-0.0909091\pi$
$587$	0.544078	+	0.627899i	0.544078	+	0.627899i	−0.415415	+	0.909632i	$0.636364\pi$
$588$	0.959493	+	0.281733i	0.959493	+	0.281733i
$589$		0			0
$590$		0			0
$591$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$592$		0			0
$593$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.654861	+	0.755750i	$0.272727\pi$
$593$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.142315	+	0.989821i	$0.454545\pi$
$594$		0			0
$595$		0			0
$596$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$597$	1.30972			1.30972
$598$	−1.30972			−1.30972
$599$	0.284630			0.284630			0.142315	−	0.989821i	$-0.454545\pi$
$599$	0.284630			0.284630			0.142315	+	0.989821i	$0.454545\pi$
$600$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$601$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$601$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$602$	0.239446	+	1.66538i	0.239446	+	1.66538i
$603$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$607$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$608$		0			0
$609$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$610$		0			0
$611$		0			0
$612$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$613$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$613$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$617$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$618$	1.41542	−	0.909632i	1.41542	−	0.909632i
$619$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$619$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$620$		0			0
$621$	0.415415	−	0.909632i	0.415415	−	0.909632i
$622$		0			0
$623$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$624$	1.10181	−	0.708089i	1.10181	−	0.708089i
$625$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$626$		0			0
$627$		0			0
$628$	1.25667	−	0.368991i	1.25667	−	0.368991i
$629$		0			0
$630$		0			0
$631$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$631$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$632$		0			0
$633$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$634$	1.84125	+	0.540641i	1.84125	+	0.540641i
$635$		0			0
$636$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$637$	1.25667	−	0.368991i	1.25667	−	0.368991i
$638$		0			0
$639$	0.797176	+	1.74557i	0.797176	+	1.74557i
$640$		0			0
$641$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$641$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$642$		0			0
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$	0.142315	−	0.989821i	0.142315	−	0.989821i
$645$		0			0
$646$		0			0
$647$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$647$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$648$	0.142315	+	0.989821i	0.142315	+	0.989821i
$649$		0			0
$650$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$651$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$652$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$653$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$653$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$654$		0			0
$655$		0			0
$656$	0.544078	+	0.627899i	0.544078	+	0.627899i
$657$		0			0
$658$		0			0
$659$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$659$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$660$		0			0
$661$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$661$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$662$	0.544078	+	1.19136i	0.544078	+	1.19136i
$663$	0.154861	+	1.07708i	0.154861	+	1.07708i
$664$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$665$		0			0
$666$		0			0
$667$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$668$		0			0
$669$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$670$		0			0
$671$		0			0
$672$	0.415415	+	0.909632i	0.415415	+	0.909632i
$673$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$673$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$674$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$675$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$676$	0.297176	−	0.650724i	0.297176	−	0.650724i
$677$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$677$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$682$		0			0
$683$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$683$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$684$		0			0
$685$		0			0
$686$	0.142315	+	0.989821i	0.142315	+	0.989821i
$687$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$688$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$689$	−0.372786			−0.372786
$690$		0			0
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	0.239446	−	1.66538i	0.239446	−	1.66538i
$697$	−0.662317	+	0.194474i	−0.662317	+	0.194474i
$698$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$699$		0			0
$700$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$701$	0.544078	+	0.627899i	0.544078	+	0.627899i	0.959493	−	0.281733i	$-0.0909091\pi$
$701$	0.544078	+	0.627899i	0.544078	+	0.627899i	−0.415415	+	0.909632i	$0.636364\pi$
$702$	0.857685	+	0.989821i	0.857685	+	0.989821i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$707$		0			0
$708$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$709$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$709$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$710$		0			0
$711$		0			0
$712$	−0.284630			−0.284630
$713$	0.118239	+	0.258908i	0.118239	+	0.258908i
$714$	−0.830830			−0.830830
$715$		0			0
$716$		0			0
$717$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$718$	0.345139	+	0.755750i	0.345139	+	0.755750i
$719$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$719$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$720$		0			0
$721$	1.41542	+	0.909632i	1.41542	+	0.909632i
$722$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$723$		0			0
$724$	0.186393	+	0.215109i	0.186393	+	0.215109i
$725$	1.10181	+	1.27155i	1.10181	+	1.27155i
$726$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$727$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$727$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$728$	1.10181	+	0.708089i	1.10181	+	0.708089i
$729$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$730$		0			0
$731$	−0.580699	−	1.27155i	−0.580699	−	1.27155i
$732$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$733$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$733$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$734$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$735$		0			0
$736$	0.841254	−	0.540641i	0.841254	−	0.540641i
$737$		0			0
$738$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$739$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$739$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$740$		0			0
$741$		0			0
$742$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$743$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$743$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	0.142315	+	0.989821i	$0.454545\pi$
$744$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$745$		0			0
$746$		0			0
$747$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$751$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$752$		0			0
$753$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$754$	−0.915415	−	2.00448i	−0.915415	−	2.00448i
$755$		0			0
$756$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$757$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$757$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$758$	0.284630			0.284630
$759$		0			0
$760$		0			0
$761$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$761$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$762$		0			0
$763$		0			0
$764$	0.544078	+	1.19136i	0.544078	+	1.19136i
$765$		0			0
$766$		0			0
$767$	−2.11435	−	1.35881i	−2.11435	−	1.35881i
$768$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$769$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$769$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$770$		0			0
$771$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$772$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$773$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$773$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$774$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$775$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$776$		0			0
$777$		0			0
$778$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.118239	+	0.822373i	0.118239	+	0.822373i
$783$	1.68251			1.68251
$784$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$785$		0			0
$786$	0.239446	+	1.66538i	0.239446	+	1.66538i
$787$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$787$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$788$	0.118239	−	0.822373i	0.118239	−	0.822373i
$789$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.64589	−	1.89945i	−1.64589	−	1.89945i
$794$	1.10181	+	1.27155i	1.10181	+	1.27155i
$795$		0			0
$796$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$797$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$797$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$798$		0			0
$799$		0			0
$800$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$801$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$802$		0			0
$803$		0			0
$804$	1.91899			1.91899
$805$		0			0
$806$	−0.372786			−0.372786
$807$		0			0
$808$		0			0
$809$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$809$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$810$		0			0
$811$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$811$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$812$	1.61435	−	0.474017i	1.61435	−	0.474017i
$813$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$814$		0			0
$815$		0			0
$816$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$817$		0			0
$818$		0			0
$819$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$820$		0			0
$821$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$821$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$822$		0			0
$823$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$823$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$824$	0.239446	+	1.66538i	0.239446	+	1.66538i
$825$		0			0
$826$	1.25667	−	1.45027i	1.25667	−	1.45027i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	0.654861	+	0.755750i	0.654861	+	0.755750i
$829$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$829$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$830$		0			0
$831$		0			0
$832$	0.186393	+	1.29639i	0.186393	+	1.29639i
$833$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.118239	−	0.258908i	0.118239	−	0.258908i
$838$	1.84125	+	0.540641i	1.84125	+	0.540641i
$839$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$839$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$840$		0			0
$841$	−1.75667	−	0.515804i	−1.75667	−	0.515804i
$842$		0			0
$843$		0			0
$844$	1.84125	−	0.540641i	1.84125	−	0.540641i
$845$		0			0
$846$		0			0
$847$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$848$	0.239446	−	0.153882i	0.239446	−	0.153882i
$849$		0			0
$850$	0.830830			0.830830
$851$		0			0
$852$	−1.91899			−1.91899
$853$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$853$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$854$	1.61435	−	1.03748i	1.61435	−	1.03748i
$855$		0			0
$856$		0			0
$857$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$857$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$858$		0			0
$859$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$859$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$860$		0			0
$861$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$862$	0.186393	+	0.215109i	0.186393	+	0.215109i
$863$	1.10181	+	1.27155i	1.10181	+	1.27155i	0.959493	+	0.281733i	$0.0909091\pi$
$863$	1.10181	+	1.27155i	1.10181	+	1.27155i	0.142315	+	0.989821i	$0.454545\pi$
$864$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$865$		0			0
$866$		0			0
$867$	−0.297176	+	0.0872586i	−0.297176	+	0.0872586i
$868$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$869$		0			0
$870$		0			0
$871$	2.11435	−	1.35881i	2.11435	−	1.35881i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$877$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$878$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$879$		0			0
$880$		0			0
$881$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−0.841254	+	0.540641i	$0.818182\pi$
$881$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−1.00000			$1.00000\pi$
$882$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$883$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$883$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$884$	−1.04408	−	0.306569i	−1.04408	−	0.306569i
$885$		0			0
$886$		0			0
$887$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$887$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$893$		0			0
$894$	1.10181	−	0.708089i	1.10181	−	0.708089i
$895$		0			0
$896$	−1.00000			−1.00000
$897$	1.25667	+	0.368991i	1.25667	+	0.368991i
$898$		0			0
$899$	−0.313607	+	0.361922i	−0.313607	+	0.361922i
$900$	0.841254	−	0.540641i	0.841254	−	0.540641i
$901$	0.0336545	+	0.234072i	0.0336545	+	0.234072i
$902$		0			0
$903$	0.239446	−	1.66538i	0.239446	−	1.66538i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$907$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$908$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$909$		0			0
$910$		0			0
$911$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$911$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$912$		0			0
$913$		0			0
$914$	0.118239	−	0.822373i	0.118239	−	0.822373i
$915$		0			0
$916$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$917$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$918$	0.544078	−	0.627899i	0.544078	−	0.627899i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.11435	+	1.35881i	−2.11435	+	1.35881i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$928$	1.41542	+	0.909632i	1.41542	+	0.909632i
$929$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$929$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.698939	−	1.53046i	0.698939	−	1.53046i
$935$		0			0
$936$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$937$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$937$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$938$	0.797176	+	1.74557i	0.797176	+	1.74557i
$939$		0			0
$940$		0			0
$941$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$941$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$942$	−1.30972			−1.30972
$943$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$944$	1.91899			1.91899
$945$		0			0
$946$		0			0
$947$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$947$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$952$	0.345139	−	0.755750i	0.345139	−	0.755750i
$953$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$953$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$954$	0.186393	+	0.215109i	0.186393	+	0.215109i
$955$		0			0
$956$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.381761	−	0.835939i	−0.381761	−	0.835939i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.654861	−	0.755750i	0.654861	−	0.755750i
$969$		0			0
$970$		0			0
$971$	−0.698939	−	1.53046i	−0.698939	−	1.53046i	−0.841254	−	0.540641i	$-0.818182\pi$
$971$	−0.698939	−	1.53046i	−0.698939	−	1.53046i	0.142315	−	0.989821i	$-0.454545\pi$
$972$	0.142315	−	0.989821i	0.142315	−	0.989821i
$973$		0			0
$974$		0			0
$975$	0.544078	−	1.19136i	0.544078	−	1.19136i
$976$	1.84125	+	0.540641i	1.84125	+	0.540641i
$977$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$977$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$978$	0.186393	+	0.215109i	0.186393	+	0.215109i
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$983$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$984$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$985$		0			0
$986$	−1.17597	+	0.755750i	−1.17597	+	0.755750i
$987$		0			0
$988$		0			0
$989$	−1.68251			−1.68251
$990$		0			0
$991$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$991$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$992$	0.239446	−	0.153882i	0.239446	−	0.153882i
$993$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$994$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$995$		0			0
$996$	1.25667	−	0.368991i	1.25667	−	0.368991i
$997$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$997$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$998$	−0.698939	+	1.53046i	−0.698939	+	1.53046i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3864.1.dl.d.3443.1	yes	10
3.2	odd	2		3864.1.dl.a.3443.1	yes	10
7.6	odd	2		3864.1.dl.c.3443.1	yes	10
8.3	odd	2		3864.1.dl.b.3443.1	yes	10
21.20	even	2		3864.1.dl.b.3443.1	yes	10
23.13	even	11	inner	3864.1.dl.d.2267.1	yes	10
24.11	even	2		3864.1.dl.c.3443.1	yes	10
56.27	even	2		3864.1.dl.a.3443.1	yes	10
69.59	odd	22		3864.1.dl.a.2267.1	✓	10
161.13	odd	22		3864.1.dl.c.2267.1	yes	10
168.83	odd	2	CM	3864.1.dl.d.3443.1	yes	10
184.59	odd	22		3864.1.dl.b.2267.1	yes	10
483.335	even	22		3864.1.dl.b.2267.1	yes	10
552.59	even	22		3864.1.dl.c.2267.1	yes	10
1288.979	even	22		3864.1.dl.a.2267.1	✓	10
3864.2267	odd	22	inner	3864.1.dl.d.2267.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3864.1.dl.a.2267.1	✓	10	69.59	odd	22
3864.1.dl.a.2267.1	✓	10	1288.979	even	22
3864.1.dl.a.3443.1	yes	10	3.2	odd	2
3864.1.dl.a.3443.1	yes	10	56.27	even	2
3864.1.dl.b.2267.1	yes	10	184.59	odd	22
3864.1.dl.b.2267.1	yes	10	483.335	even	22
3864.1.dl.b.3443.1	yes	10	8.3	odd	2
3864.1.dl.b.3443.1	yes	10	21.20	even	2
3864.1.dl.c.2267.1	yes	10	161.13	odd	22
3864.1.dl.c.2267.1	yes	10	552.59	even	22
3864.1.dl.c.3443.1	yes	10	7.6	odd	2
3864.1.dl.c.3443.1	yes	10	24.11	even	2
3864.1.dl.d.2267.1	yes	10	23.13	even	11	inner
3864.1.dl.d.2267.1	yes	10	3864.2267	odd	22	inner
3864.1.dl.d.3443.1	yes	10	1.1	even	1	trivial
3864.1.dl.d.3443.1	yes	10	168.83	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3864.dl (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.142315 + 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.142315 + 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.654861 + 0.755750i) q^{12} +(1.25667 + 0.368991i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.118239 - 0.822373i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.654861 - 0.755750i) q^{21} +(-0.841254 - 0.540641i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(1.10181 - 0.708089i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.415415 + 0.909632i) q^{28} +(0.239446 - 1.66538i) q^{29} +(-0.239446 - 0.153882i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-0.544078 - 0.627899i) q^{34} +(-0.959493 - 0.281733i) q^{36} +(-1.25667 + 0.368991i) q^{39} +(-0.345139 - 0.755750i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(1.41542 - 0.909632i) q^{43} +(-0.959493 + 0.281733i) q^{46} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.142315 + 0.989821i) q^{50} +(0.345139 + 0.755750i) q^{51} +(0.186393 - 1.29639i) q^{52} +(-0.273100 + 0.0801894i) q^{53} +(0.841254 + 0.540641i) q^{54} +(0.959493 + 0.281733i) q^{56} +(-1.10181 - 1.27155i) q^{58} +(-1.84125 - 0.540641i) q^{59} +(-1.61435 - 1.03748i) q^{61} +(-0.273100 + 0.0801894i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.25667 - 1.45027i) q^{67} -0.830830 q^{68} +1.00000 q^{69} +(-1.25667 + 1.45027i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(0.142315 - 0.989821i) q^{75} +(-0.544078 + 1.19136i) q^{78} +(-0.654861 - 0.755750i) q^{81} +(-0.797176 - 0.234072i) q^{82} +(0.544078 - 1.19136i) q^{83} +(-0.841254 - 0.540641i) q^{84} +(0.239446 - 1.66538i) q^{86} +(0.698939 + 1.53046i) q^{87} +(0.239446 - 0.153882i) q^{89} -1.30972 q^{91} +(-0.415415 + 0.909632i) q^{92} +0.284630 q^{93} +(-0.142315 - 0.989821i) q^{96} +(0.142315 - 0.989821i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + q^{3} - q^{4} - q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 + q^3 - q^4 - q^6 - q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} - q^{6} - q^{7} + q^{8} - q^{9} + q^{12} - 2 q^{13} + q^{14} - q^{16} + 2 q^{17} + q^{18} + q^{21} + q^{23} + 10 q^{24} - q^{25} + 2 q^{26} + q^{27} - q^{28} + 2 q^{29} - 2 q^{31} + q^{32} - 2 q^{34} - q^{36} + 2 q^{39} - 9 q^{41} - q^{42} + 9 q^{43} - q^{46} + q^{48} - q^{49} + q^{50} + 9 q^{51} - 2 q^{52} + 2 q^{53} - q^{54} + q^{56} - 2 q^{58} - 9 q^{59} - 2 q^{61} + 2 q^{62} - q^{63} - q^{64} - 2 q^{67} + 2 q^{68} + 10 q^{69} + 2 q^{71} + q^{72} + q^{75} - 2 q^{78} - q^{81} - 2 q^{82} + 2 q^{83} + q^{84} + 2 q^{86} - 2 q^{87} + 2 q^{89} - 2 q^{91} + q^{92} + 2 q^{93} - q^{96} + q^{98}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 - q^6 - q^7 + q^8 - q^9 + q^12 - 2 * q^13 + q^14 - q^16 + 2 * q^17 + q^18 + q^21 + q^23 + 10 * q^24 - q^25 + 2 * q^26 + q^27 - q^28 + 2 * q^29 - 2 * q^31 + q^32 - 2 * q^34 - q^36 + 2 * q^39 - 9 * q^41 - q^42 + 9 * q^43 - q^46 + q^48 - q^49 + q^50 + 9 * q^51 - 2 * q^52 + 2 * q^53 - q^54 + q^56 - 2 * q^58 - 9 * q^59 - 2 * q^61 + 2 * q^62 - q^63 - q^64 - 2 * q^67 + 2 * q^68 + 10 * q^69 + 2 * q^71 + q^72 + q^75 - 2 * q^78 - q^81 - 2 * q^82 + 2 * q^83 + q^84 + 2 * q^86 - 2 * q^87 + 2 * q^89 - 2 * q^91 + q^92 + 2 * q^93 - q^96 + q^98

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