LMFDB - Embedded newform 1932.1.bi.a.1175.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1932,1,Mod(167,1932)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1932, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 11, 18]))

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

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

chi := DirichletCharacter("1932.167");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1932.bi (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:	$0.964193604407$
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			1175.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	1932.1175
Dual form			1932.1.bi.a.587.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.797176 - 0.234072i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.797176 - 0.234072i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.544078 - 0.627899i) q^{10} +(-1.10181 + 0.708089i) q^{11} +(0.841254 - 0.540641i) q^{12} +(-0.959493 + 0.281733i) q^{14} +(-0.118239 + 0.822373i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.118239 + 0.258908i) q^{17} +(-0.959493 - 0.281733i) q^{18} +(0.698939 + 1.53046i) q^{19} +(-0.118239 - 0.822373i) q^{20} +(0.841254 + 0.540641i) q^{21} -1.30972 q^{22} +(0.415415 + 0.909632i) q^{23} +1.00000 q^{24} +(-0.260554 - 0.167448i) q^{25} +(0.415415 + 0.909632i) q^{27} +(-0.959493 - 0.281733i) q^{28} +(-0.544078 + 0.627899i) q^{30} +(0.0405070 - 0.281733i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(0.857685 + 0.989821i) q^{33} +(-0.239446 + 0.153882i) q^{34} +(0.698939 - 0.449181i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(1.84125 - 0.540641i) q^{37} +(-0.239446 + 1.66538i) q^{38} +(0.345139 - 0.755750i) q^{40} +(-1.61435 - 0.474017i) q^{41} +(0.415415 + 0.909632i) q^{42} +(-1.10181 - 0.708089i) q^{44} +0.830830 q^{45} +(-0.142315 + 0.989821i) q^{46} +(0.841254 + 0.540641i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.128663 - 0.281733i) q^{50} +(0.273100 + 0.0801894i) q^{51} +(-0.142315 + 0.989821i) q^{54} +(1.04408 - 0.306569i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(1.41542 - 0.909632i) q^{57} +(-0.797176 + 0.234072i) q^{60} +(0.186393 - 0.215109i) q^{62} +(0.415415 - 0.909632i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.186393 + 1.29639i) q^{66} -0.284630 q^{68} +(0.841254 - 0.540641i) q^{69} +0.830830 q^{70} +(-1.61435 - 1.03748i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(1.84125 + 0.540641i) q^{74} +(-0.128663 + 0.281733i) q^{75} +(-1.10181 + 1.27155i) q^{76} +(0.186393 - 1.29639i) q^{77} +(0.698939 - 0.449181i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-1.10181 - 1.27155i) q^{82} +(-0.142315 + 0.989821i) q^{84} +(0.154861 - 0.178719i) q^{85} +(-0.544078 - 1.19136i) q^{88} +(0.273100 + 1.89945i) q^{89} +(0.698939 + 0.449181i) q^{90} +(-0.654861 + 0.755750i) q^{92} -0.284630 q^{93} +(-0.198939 - 1.38365i) q^{95} +(0.415415 + 0.909632i) q^{96} +(0.415415 - 0.909632i) q^{98} +(0.857685 - 0.989821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} - q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 - 2 * q^5 - q^6 - q^7 - q^8 - q^9	$ 10 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} - q^{7} - q^{8} - q^{9} - 2 q^{10} - 2 q^{11} - q^{12} - q^{14} - 2 q^{15} - q^{16} - 2 q^{17} - q^{18} - 2 q^{19} - 2 q^{20} - q^{21} - 2 q^{22} - q^{23} + 10 q^{24} - 3 q^{25} - q^{27} - q^{28} - 2 q^{30} + 9 q^{31} - q^{32} + 9 q^{33} - 2 q^{34} - 2 q^{35} - q^{36} + 9 q^{37} - 2 q^{38} + 9 q^{40} - 2 q^{41} - q^{42} - 2 q^{44} - 2 q^{45} - q^{46} - q^{48} - q^{49} - 3 q^{50} - 2 q^{51} - q^{54} + 7 q^{55} - q^{56} + 9 q^{57} - 2 q^{60} - 2 q^{62} - q^{63} - q^{64} - 2 q^{66} - 2 q^{68} - q^{69} - 2 q^{70} - 2 q^{71} - q^{72} + 9 q^{74} - 3 q^{75} - 2 q^{76} - 2 q^{77} - 2 q^{80} - q^{81} - 2 q^{82} - q^{84} - 4 q^{85} - 2 q^{88} - 2 q^{89} - 2 q^{90} - q^{92} - 2 q^{93} + 7 q^{95} - q^{96} - q^{98} + 9 q^{99}+O(q^{100}) $ 10 * q - q^2 - q^3 - q^4 - 2 * q^5 - q^6 - q^7 - q^8 - q^9 - 2 * q^10 - 2 * q^11 - q^12 - q^14 - 2 * q^15 - q^16 - 2 * q^17 - q^18 - 2 * q^19 - 2 * q^20 - q^21 - 2 * q^22 - q^23 + 10 * q^24 - 3 * q^25 - q^27 - q^28 - 2 * q^30 + 9 * q^31 - q^32 + 9 * q^33 - 2 * q^34 - 2 * q^35 - q^36 + 9 * q^37 - 2 * q^38 + 9 * q^40 - 2 * q^41 - q^42 - 2 * q^44 - 2 * q^45 - q^46 - q^48 - q^49 - 3 * q^50 - 2 * q^51 - q^54 + 7 * q^55 - q^56 + 9 * q^57 - 2 * q^60 - 2 * q^62 - q^63 - q^64 - 2 * q^66 - 2 * q^68 - q^69 - 2 * q^70 - 2 * q^71 - q^72 + 9 * q^74 - 3 * q^75 - 2 * q^76 - 2 * q^77 - 2 * q^80 - q^81 - 2 * q^82 - q^84 - 4 * q^85 - 2 * q^88 - 2 * q^89 - 2 * q^90 - q^92 - 2 * q^93 + 7 * q^95 - q^96 - q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1932\mathbb{Z}\right)^\times$.

$n$	$829$	$925$	$967$	$1289$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$	$-1$	$-1$

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 $

$2$	0.841254	+	0.540641i	0.841254	+	0.540641i
$2$	0.841254	+	0.540641i	0.841254	+	0.540641i
$3$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$3$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$4$	0.415415	+	0.909632i	0.415415	+	0.909632i
$5$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$5$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$6$	0.415415	−	0.909632i	0.415415	−	0.909632i
$7$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$7$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$8$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$9$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$10$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$11$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$11$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$12$	0.841254	−	0.540641i	0.841254	−	0.540641i
$13$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$13$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$14$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$15$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$16$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$17$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$17$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$18$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$19$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$19$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$20$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$21$	0.841254	+	0.540641i	0.841254	+	0.540641i
$22$	−1.30972			−1.30972
$23$	0.415415	+	0.909632i	0.415415	+	0.909632i
$23$	0.415415	+	0.909632i	0.415415	+	0.909632i
$24$	1.00000			1.00000
$25$	−0.260554	−	0.167448i	−0.260554	−	0.167448i
$26$		0			0
$27$	0.415415	+	0.909632i	0.415415	+	0.909632i
$28$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$29$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$29$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$30$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$31$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$31$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$32$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$33$	0.857685	+	0.989821i	0.857685	+	0.989821i
$34$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$35$	0.698939	−	0.449181i	0.698939	−	0.449181i
$36$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$37$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$37$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$38$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$39$		0			0
$40$	0.345139	−	0.755750i	0.345139	−	0.755750i
$41$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$41$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$42$	0.415415	+	0.909632i	0.415415	+	0.909632i
$43$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$43$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$44$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$45$	0.830830			0.830830
$46$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	0.841254	+	0.540641i	0.841254	+	0.540641i
$49$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$50$	−0.128663	−	0.281733i	−0.128663	−	0.281733i
$51$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$52$		0			0
$53$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$53$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$54$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$55$	1.04408	−	0.306569i	1.04408	−	0.306569i
$56$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$57$	1.41542	−	0.909632i	1.41542	−	0.909632i
$58$		0			0
$59$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$59$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$60$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$61$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$61$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$62$	0.186393	−	0.215109i	0.186393	−	0.215109i
$63$	0.415415	−	0.909632i	0.415415	−	0.909632i
$64$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$65$		0			0
$66$	0.186393	+	1.29639i	0.186393	+	1.29639i
$67$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$67$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$68$	−0.284630			−0.284630
$69$	0.841254	−	0.540641i	0.841254	−	0.540641i
$70$	0.830830			0.830830
$71$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$71$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$72$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$73$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$73$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$74$	1.84125	+	0.540641i	1.84125	+	0.540641i
$75$	−0.128663	+	0.281733i	−0.128663	+	0.281733i
$76$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$77$	0.186393	−	1.29639i	0.186393	−	1.29639i
$78$		0			0
$79$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$79$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$80$	0.698939	−	0.449181i	0.698939	−	0.449181i
$81$	0.841254	−	0.540641i	0.841254	−	0.540641i
$82$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$83$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$83$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$84$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$85$	0.154861	−	0.178719i	0.154861	−	0.178719i
$86$		0			0
$87$		0			0
$88$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$89$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$89$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$90$	0.698939	+	0.449181i	0.698939	+	0.449181i
$91$		0			0
$92$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$93$	−0.284630			−0.284630
$94$		0			0
$95$	−0.198939	−	1.38365i	−0.198939	−	1.38365i
$96$	0.415415	+	0.909632i	0.415415	+	0.909632i
$97$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$97$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$98$	0.415415	−	0.909632i	0.415415	−	0.909632i
$99$	0.857685	−	0.989821i	0.857685	−	0.989821i
$100$	0.0440780	−	0.306569i	0.0440780	−	0.306569i
$101$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$101$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$102$	0.186393	+	0.215109i	0.186393	+	0.215109i
$103$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$103$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$104$		0			0
$105$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$106$		0			0
$107$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$107$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$108$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$109$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$109$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$110$	1.04408	+	0.306569i	1.04408	+	0.306569i
$111$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$112$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$113$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$113$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$114$	1.68251			1.68251
$115$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$120$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$121$	0.297176	−	0.650724i	0.297176	−	0.650724i
$122$		0			0
$123$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$124$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$125$	0.712591	+	0.822373i	0.712591	+	0.822373i
$126$	0.841254	−	0.540641i	0.841254	−	0.540641i
$127$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$127$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$128$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$129$		0			0
$130$		0			0
$131$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$131$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$132$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$133$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$134$		0			0
$135$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$136$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	1.00000			1.00000
$139$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$139$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$140$	0.698939	+	0.449181i	0.698939	+	0.449181i
$141$		0			0
$142$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$143$		0			0
$144$	0.415415	−	0.909632i	0.415415	−	0.909632i
$145$		0			0
$146$		0			0
$147$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$148$	1.25667	+	1.45027i	1.25667	+	1.45027i
$149$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$149$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$150$	−0.260554	+	0.167448i	−0.260554	+	0.167448i
$151$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$151$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$152$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$153$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$154$	0.857685	−	0.989821i	0.857685	−	0.989821i
$155$	−0.0982369	+	0.215109i	−0.0982369	+	0.215109i
$156$		0			0
$157$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$157$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$158$		0			0
$159$		0			0
$160$	0.830830			0.830830
$161$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$162$	1.00000			1.00000
$163$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$163$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$164$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$165$	−0.452036	−	0.989821i	−0.452036	−	0.989821i
$166$		0			0
$167$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$167$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$168$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$169$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$170$	0.226900	−	0.0666238i	0.226900	−	0.0666238i
$171$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$172$		0			0
$173$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$173$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$174$		0			0
$175$	0.297176	−	0.0872586i	0.297176	−	0.0872586i
$176$	0.186393	−	1.29639i	0.186393	−	1.29639i
$177$		0			0
$178$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$179$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$179$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$180$	0.345139	+	0.755750i	0.345139	+	0.755750i
$181$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$181$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$182$		0			0
$183$		0			0
$184$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$185$	−1.59435			−1.59435
$186$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$187$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$188$		0			0
$189$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$190$	0.580699	−	1.27155i	0.580699	−	1.27155i
$191$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$191$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$192$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$193$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$193$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$194$		0			0
$195$		0			0
$196$	0.841254	−	0.540641i	0.841254	−	0.540641i
$197$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$197$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$198$	1.25667	−	0.368991i	1.25667	−	0.368991i
$199$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$199$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$200$	0.202824	−	0.234072i	0.202824	−	0.234072i
$201$		0			0
$202$	1.84125	+	0.540641i	1.84125	+	0.540641i
$203$		0			0
$204$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$205$	1.17597	+	0.755750i	1.17597	+	0.755750i
$206$	−1.91899			−1.91899
$207$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$208$		0			0
$209$	−1.85380	−	1.19136i	−1.85380	−	1.19136i
$210$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$211$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$211$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$212$		0			0
$213$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$214$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$215$		0			0
$216$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$217$	0.186393	+	0.215109i	0.186393	+	0.215109i
$218$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$219$		0			0
$220$	0.712591	+	0.822373i	0.712591	+	0.822373i
$221$		0			0
$222$	0.273100	−	1.89945i	0.273100	−	1.89945i
$223$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$223$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$224$	0.415415	−	0.909632i	0.415415	−	0.909632i
$225$	0.297176	+	0.0872586i	0.297176	+	0.0872586i
$226$		0			0
$227$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$227$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$228$	1.41542	+	0.909632i	1.41542	+	0.909632i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	0.345139	−	0.755750i	0.345139	−	0.755750i
$231$	−1.30972			−1.30972
$232$		0			0
$233$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$233$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$239$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$239$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$240$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$241$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$241$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$242$	0.601808	−	0.386758i	0.601808	−	0.386758i
$243$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$244$		0			0
$245$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$246$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$247$		0			0
$248$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$249$		0			0
$250$	0.154861	+	1.07708i	0.154861	+	1.07708i
$251$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$251$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$252$	1.00000			1.00000
$253$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$254$		0			0
$255$	−0.198939	−	0.127850i	−0.198939	−	0.127850i
$256$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$257$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$257$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$258$		0			0
$259$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$263$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$264$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$265$		0			0
$266$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$267$	1.84125	−	0.540641i	1.84125	−	0.540641i
$268$		0			0
$269$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$269$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$270$	0.345139	−	0.755750i	0.345139	−	0.755750i
$271$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$271$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$272$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$273$		0			0
$274$		0			0
$275$	0.405649			0.405649
$276$	0.841254	+	0.540641i	0.841254	+	0.540641i
$277$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$277$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$278$	1.41542	+	0.909632i	1.41542	+	0.909632i
$279$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$280$	0.345139	+	0.755750i	0.345139	+	0.755750i
$281$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$281$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$282$		0			0
$283$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$283$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$284$	0.273100	−	1.89945i	0.273100	−	1.89945i
$285$	−1.34125	+	0.393828i	−1.34125	+	0.393828i
$286$		0			0
$287$	1.41542	−	0.909632i	1.41542	−	0.909632i
$288$	0.841254	−	0.540641i	0.841254	−	0.540641i
$289$	0.601808	+	0.694523i	0.601808	+	0.694523i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$293$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$294$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$295$		0			0
$296$	0.273100	+	1.89945i	0.273100	+	1.89945i
$297$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$298$		0			0
$299$		0			0
$300$	−0.309721			−0.309721
$301$		0			0
$302$		0			0
$303$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$304$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$305$		0			0
$306$	0.186393	−	0.215109i	0.186393	−	0.215109i
$307$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$307$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$308$	1.25667	−	0.368991i	1.25667	−	0.368991i
$309$	1.25667	+	1.45027i	1.25667	+	1.45027i
$310$	−0.198939	+	0.127850i	−0.198939	+	0.127850i
$311$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$311$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$312$		0			0
$313$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$313$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$314$		0			0
$315$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$316$		0			0
$317$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$317$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$318$		0			0
$319$		0			0
$320$	0.698939	+	0.449181i	0.698939	+	0.449181i
$321$	1.68251			1.68251
$322$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$323$	−0.478891			−0.478891
$324$	0.841254	+	0.540641i	0.841254	+	0.540641i
$325$		0			0
$326$		0			0
$327$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$328$	0.698939	−	1.53046i	0.698939	−	1.53046i
$329$		0			0
$330$	0.154861	−	1.07708i	0.154861	−	1.07708i
$331$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$331$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$332$		0			0
$333$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$334$		0			0
$335$		0			0
$336$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$337$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$337$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$338$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$339$		0			0
$340$	0.226900	+	0.0666238i	0.226900	+	0.0666238i
$341$	0.154861	+	0.339098i	0.154861	+	0.339098i
$342$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$343$	0.841254	+	0.540641i	0.841254	+	0.540641i
$344$		0			0
$345$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$346$	0.830830			0.830830
$347$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$347$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$348$		0			0
$349$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$349$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$350$	0.297176	+	0.0872586i	0.297176	+	0.0872586i
$351$		0			0
$352$	0.857685	−	0.989821i	0.857685	−	0.989821i
$353$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$353$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$354$		0			0
$355$	1.04408	+	1.20493i	1.04408	+	1.20493i
$356$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$357$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$358$	1.25667	+	1.45027i	1.25667	+	1.45027i
$359$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$359$	−1.91899	+	0.563465i	−1.91899	+	0.563465i	−0.959493	+	0.281733i	$0.909091\pi$
$360$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$361$	−1.19894	+	1.38365i	−1.19894	+	1.38365i
$362$		0			0
$363$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$367$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$368$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$369$	1.68251			1.68251
$370$	−1.34125	−	0.861971i	−1.34125	−	0.861971i
$371$		0			0
$372$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$373$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$373$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$374$	0.154861	−	0.339098i	0.154861	−	0.339098i
$375$	0.712591	−	0.822373i	0.712591	−	0.822373i
$376$		0			0
$377$		0			0
$378$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$379$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$379$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$380$	1.17597	−	0.755750i	1.17597	−	0.755750i
$381$		0			0
$382$	1.84125	−	0.540641i	1.84125	−	0.540641i
$383$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$383$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$384$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$385$	−0.452036	+	0.989821i	−0.452036	+	0.989821i
$386$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$387$		0			0
$388$		0			0
$389$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$389$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$390$		0			0
$391$	−0.284630			−0.284630
$392$	1.00000			1.00000
$393$		0			0
$394$		0			0
$395$		0			0
$396$	1.25667	+	0.368991i	1.25667	+	0.368991i
$397$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$397$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$398$	0.857685	−	0.989821i	0.857685	−	0.989821i
$399$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$400$	0.297176	−	0.0872586i	0.297176	−	0.0872586i
$401$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$401$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$402$		0			0
$403$		0			0
$404$	1.25667	+	1.45027i	1.25667	+	1.45027i
$405$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$406$		0			0
$407$	−1.64589	+	1.89945i	−1.64589	+	1.89945i
$408$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$409$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$409$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$410$	0.580699	+	1.27155i	0.580699	+	1.27155i
$411$		0			0
$412$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$413$		0			0
$414$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$415$		0			0
$416$		0			0
$417$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$418$	−0.915415	−	2.00448i	−0.915415	−	2.00448i
$419$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$419$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$420$	0.345139	−	0.755750i	0.345139	−	0.755750i
$421$	−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
$423$		0			0
$424$		0			0
$425$	0.0741615	−	0.0476607i	0.0741615	−	0.0476607i
$426$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$427$		0			0
$428$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$429$		0			0
$430$		0			0
$431$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$431$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$432$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$433$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$433$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$434$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$435$		0			0
$436$	−0.284630			−0.284630
$437$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$438$		0			0
$439$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$439$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$440$	0.154861	+	1.07708i	0.154861	+	1.07708i
$441$	0.415415	+	0.909632i	0.415415	+	0.909632i
$442$		0			0
$443$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$443$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$444$	1.25667	−	1.45027i	1.25667	−	1.45027i
$445$	0.226900	−	1.57812i	0.226900	−	1.57812i
$446$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$447$		0			0
$448$	0.841254	−	0.540641i	0.841254	−	0.540641i
$449$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$449$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$450$	0.202824	+	0.234072i	0.202824	+	0.234072i
$451$	2.11435	−	0.620830i	2.11435	−	0.620830i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	0.698939	+	1.53046i	0.698939	+	1.53046i
$457$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$457$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$458$		0			0
$459$	−0.284630			−0.284630
$460$	0.698939	−	0.449181i	0.698939	−	0.449181i
$461$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$461$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$462$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$463$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$463$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$464$		0			0
$465$	0.226900	+	0.0666238i	0.226900	+	0.0666238i
$466$		0			0
$467$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$467$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.0741615	−	0.515804i	0.0741615	−	0.515804i
$476$	0.186393	−	0.215109i	0.186393	−	0.215109i
$477$		0			0
$478$	1.25667	+	0.368991i	1.25667	+	0.368991i
$479$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$479$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$480$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$481$		0			0
$482$		0			0
$483$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$484$	0.715370			0.715370
$485$		0			0
$486$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$487$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$487$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$488$		0			0
$489$		0			0
$490$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$491$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$491$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$492$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$493$		0			0
$494$		0			0
$495$	−0.915415	+	0.588302i	−0.915415	+	0.588302i
$496$	0.186393	+	0.215109i	0.186393	+	0.215109i
$497$	1.84125	−	0.540641i	1.84125	−	0.540641i
$498$		0			0
$499$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$499$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$500$	−0.452036	+	0.989821i	−0.452036	+	0.989821i
$501$		0			0
$502$		0			0
$503$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$503$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$504$	0.841254	+	0.540641i	0.841254	+	0.540641i
$505$	−1.59435			−1.59435
$506$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$507$	1.00000			1.00000
$508$		0			0
$509$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$509$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$510$	−0.0982369	−	0.215109i	−0.0982369	−	0.215109i
$511$		0			0
$512$	0.415415	−	0.909632i	0.415415	−	0.909632i
$513$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$514$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$515$	1.52977	−	0.449181i	1.52977	−	0.449181i
$516$		0			0
$517$		0			0
$518$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$519$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$520$		0			0
$521$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$521$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$522$		0			0
$523$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$523$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$524$		0			0
$525$	−0.128663	−	0.281733i	−0.128663	−	0.281733i
$526$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$527$	0.0681534	+	0.0437995i	0.0681534	+	0.0437995i
$528$	−1.30972			−1.30972
$529$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$530$		0			0
$531$		0			0
$532$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$533$		0			0
$534$	1.84125	+	0.540641i	1.84125	+	0.540641i
$535$	0.580699	−	1.27155i	0.580699	−	1.27155i
$536$		0			0
$537$	0.273100	−	1.89945i	0.273100	−	1.89945i
$538$	1.25667	−	0.368991i	1.25667	−	0.368991i
$539$	0.857685	+	0.989821i	0.857685	+	0.989821i
$540$	0.698939	−	0.449181i	0.698939	−	0.449181i
$541$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$541$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$542$	0.857685	+	0.989821i	0.857685	+	0.989821i
$543$		0			0
$544$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$545$	0.154861	−	0.178719i	0.154861	−	0.178719i
$546$		0			0
$547$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$547$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$548$		0			0
$549$		0			0
$550$	0.341254	+	0.219310i	0.341254	+	0.219310i
$551$		0			0
$552$	0.415415	+	0.909632i	0.415415	+	0.909632i
$553$		0			0
$554$	0.698939	+	0.449181i	0.698939	+	0.449181i
$555$	0.226900	+	1.57812i	0.226900	+	1.57812i
$556$	0.698939	+	1.53046i	0.698939	+	1.53046i
$557$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$557$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$558$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$559$		0			0
$560$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$561$	−0.357685	+	0.105026i	−0.357685	+	0.105026i
$562$		0			0
$563$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$563$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$564$		0			0
$565$		0			0
$566$	1.25667	−	0.368991i	1.25667	−	0.368991i
$567$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$568$	1.25667	−	1.45027i	1.25667	−	1.45027i
$569$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$569$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$570$	−1.34125	−	0.393828i	−1.34125	−	0.393828i
$571$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$571$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$572$		0			0
$573$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$574$	1.68251			1.68251
$575$	0.0440780	−	0.306569i	0.0440780	−	0.306569i
$576$	1.00000			1.00000
$577$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$577$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$578$	0.130785	+	0.909632i	0.130785	+	0.909632i
$579$	0.345139	+	0.755750i	0.345139	+	0.755750i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	1.41542	−	0.909632i	1.41542	−	0.909632i
$587$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$587$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$588$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$589$	0.459493	−	0.134919i	0.459493	−	0.134919i
$590$		0			0
$591$		0			0
$592$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$593$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$593$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$594$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$595$	0.0336545	+	0.234072i	0.0336545	+	0.234072i
$596$		0			0
$597$	−1.30972			−1.30972
$598$		0			0
$599$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$599$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$600$	−0.260554	−	0.167448i	−0.260554	−	0.167448i
$601$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$601$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.389217	+	0.449181i	−0.389217	+	0.449181i
$606$	0.273100	−	1.89945i	0.273100	−	1.89945i
$607$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$607$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$608$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$613$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$613$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$614$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$615$	0.580699	−	1.27155i	0.580699	−	1.27155i
$616$	1.25667	+	0.368991i	1.25667	+	0.368991i
$617$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$617$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$618$	0.273100	+	1.89945i	0.273100	+	1.89945i
$619$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$619$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$620$	−0.236479			−0.236479
$621$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$622$		0			0
$623$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$624$		0			0
$625$	−0.246902	−	0.540641i	−0.246902	−	0.540641i
$626$		0			0
$627$	−0.915415	+	2.00448i	−0.915415	+	2.00448i
$628$		0			0
$629$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$630$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$631$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$631$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.84125	+	0.540641i	1.84125	+	0.540641i
$640$	0.345139	+	0.755750i	0.345139	+	0.755750i
$641$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$641$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$642$	1.41542	+	0.909632i	1.41542	+	0.909632i
$643$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$643$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$644$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$645$		0			0
$646$	−0.402869	−	0.258908i	−0.402869	−	0.258908i
$647$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$647$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$648$	0.415415	+	0.909632i	0.415415	+	0.909632i
$649$		0			0
$650$		0			0
$651$	0.186393	−	0.215109i	0.186393	−	0.215109i
$652$		0			0
$653$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$653$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$654$	0.186393	+	0.215109i	0.186393	+	0.215109i
$655$		0			0
$656$	1.41542	−	0.909632i	1.41542	−	0.909632i
$657$		0			0
$658$		0			0
$659$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$659$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$660$	0.712591	−	0.822373i	0.712591	−	0.822373i
$661$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$661$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.17597	+	0.755750i	1.17597	+	0.755750i
$666$	−1.91899			−1.91899
$667$		0			0
$668$		0			0
$669$	0.698939	+	0.449181i	0.698939	+	0.449181i
$670$		0			0
$671$		0			0
$672$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$673$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$673$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$674$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$675$	0.0440780	−	0.306569i	0.0440780	−	0.306569i
$676$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$677$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$677$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$678$		0			0
$679$		0			0
$680$	0.154861	+	0.178719i	0.154861	+	0.178719i
$681$		0			0
$682$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$683$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$683$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$684$	0.698939	−	1.53046i	0.698939	−	1.53046i
$685$		0			0
$686$	0.415415	+	0.909632i	0.415415	+	0.909632i
$687$		0			0
$688$		0			0
$689$		0			0
$690$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$691$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$691$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$692$	0.698939	+	0.449181i	0.698939	+	0.449181i
$693$	0.186393	+	1.29639i	0.186393	+	1.29639i
$694$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$695$	−1.34125	−	0.393828i	−1.34125	−	0.393828i
$696$		0			0
$697$	0.313607	−	0.361922i	0.313607	−	0.361922i
$698$		0			0
$699$		0			0
$700$	0.202824	+	0.234072i	0.202824	+	0.234072i
$701$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$701$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$702$		0			0
$703$	2.11435	+	2.44009i	2.11435	+	2.44009i
$704$	1.25667	−	0.368991i	1.25667	−	0.368991i
$705$		0			0
$706$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$707$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$708$		0			0
$709$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$709$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$710$	0.226900	+	1.57812i	0.226900	+	1.57812i
$711$		0			0
$712$	−1.91899			−1.91899
$713$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$714$	−0.284630			−0.284630
$715$		0			0
$716$	0.273100	+	1.89945i	0.273100	+	1.89945i
$717$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$718$	−1.91899	−	0.563465i	−1.91899	−	0.563465i
$719$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$719$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$720$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$721$	0.273100	−	1.89945i	0.273100	−	1.89945i
$722$	−1.75667	+	0.515804i	−1.75667	+	0.515804i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−0.468468	−	0.540641i	−0.468468	−	0.540641i
$727$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$727$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$733$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$734$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$735$	0.830830			0.830830
$736$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$737$		0			0
$738$	1.41542	+	0.909632i	1.41542	+	0.909632i
$739$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$739$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$740$	−0.662317	−	1.45027i	−0.662317	−	1.45027i
$741$		0			0
$742$		0			0
$743$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$743$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$744$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$745$		0			0
$746$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$747$		0			0
$748$	0.313607	−	0.201543i	0.313607	−	0.201543i
$749$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$750$	1.04408	−	0.306569i	1.04408	−	0.306569i
$751$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$751$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$757$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$757$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$758$		0			0
$759$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$760$	1.39788			1.39788
$761$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$761$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$762$		0			0
$763$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$764$	1.84125	+	0.540641i	1.84125	+	0.540641i
$765$	−0.0982369	+	0.215109i	−0.0982369	+	0.215109i
$766$		0			0
$767$		0			0
$768$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$769$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$769$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$770$	−0.915415	+	0.588302i	−0.915415	+	0.588302i
$771$	0.698939	−	0.449181i	0.698939	−	0.449181i
$772$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$773$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$773$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$774$		0			0
$775$	−0.0577299	+	0.0666238i	−0.0577299	+	0.0666238i
$776$		0			0
$777$	1.84125	+	0.540641i	1.84125	+	0.540641i
$778$		0			0
$779$	−0.402869	−	2.80202i	−0.402869	−	2.80202i
$780$		0			0
$781$	2.51334			2.51334
$782$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$783$		0			0
$784$	0.841254	+	0.540641i	0.841254	+	0.540641i
$785$		0			0
$786$		0			0
$787$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$787$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$788$		0			0
$789$	0.186393	−	0.215109i	0.186393	−	0.215109i
$790$		0			0
$791$		0			0
$792$	0.857685	+	0.989821i	0.857685	+	0.989821i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.25667	−	0.368991i	1.25667	−	0.368991i
$797$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$797$	−0.284630	+	1.97964i	−0.284630	+	1.97964i	−0.142315	+	0.989821i	$0.545455\pi$
$798$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$799$		0			0
$800$	0.297176	+	0.0872586i	0.297176	+	0.0872586i
$801$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	0.698939	+	0.449181i	0.698939	+	0.449181i
$806$		0			0
$807$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$808$	0.273100	+	1.89945i	0.273100	+	1.89945i
$809$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$809$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$810$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$811$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$811$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$812$		0			0
$813$	0.186393	−	1.29639i	0.186393	−	1.29639i
$814$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$815$		0			0
$816$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−0.198939	+	1.38365i	−0.198939	+	1.38365i
$821$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$821$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$822$		0			0
$823$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$823$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$824$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$825$	−0.0577299	−	0.401520i	−0.0577299	−	0.401520i
$826$		0			0
$827$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$827$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$828$	0.415415	−	0.909632i	0.415415	−	0.909632i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$832$		0			0
$833$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$834$	0.698939	−	1.53046i	0.698939	−	1.53046i
$835$		0			0
$836$	0.313607	−	2.18119i	0.313607	−	2.18119i
$837$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$838$		0			0
$839$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$839$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$840$	0.698939	−	0.449181i	0.698939	−	0.449181i
$841$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$842$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$843$		0			0
$844$		0			0
$845$	0.345139	−	0.755750i	0.345139	−	0.755750i
$846$		0			0
$847$	0.297176	+	0.650724i	0.297176	+	0.650724i
$848$		0			0
$849$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$850$	0.0881559			0.0881559
$851$	1.25667	+	1.45027i	1.25667	+	1.45027i
$852$	−1.91899			−1.91899
$853$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$853$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$854$		0			0
$855$	0.580699	+	1.27155i	0.580699	+	1.27155i
$856$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$857$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$857$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$858$		0			0
$859$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$859$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$860$		0			0
$861$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$862$	1.41542	−	0.909632i	1.41542	−	0.909632i
$863$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$863$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$864$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$865$	−0.662317	+	0.194474i	−0.662317	+	0.194474i
$866$		0			0
$867$	0.601808	−	0.694523i	0.601808	−	0.694523i
$868$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$873$		0			0
$874$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$875$	−1.08816			−1.08816
$876$		0			0
$877$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$877$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$878$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$879$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$880$	−0.452036	+	0.989821i	−0.452036	+	0.989821i
$881$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$881$	−1.30972	+	1.51150i	−1.30972	+	1.51150i	−0.654861	+	0.755750i	$0.727273\pi$
$882$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$883$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$883$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$884$		0			0
$885$		0			0
$886$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$887$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$887$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$888$	1.84125	−	0.540641i	1.84125	−	0.540641i
$889$		0			0
$890$	1.04408	−	1.20493i	1.04408	−	1.20493i
$891$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$892$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$893$		0			0
$894$		0			0
$895$	−1.34125	−	0.861971i	−1.34125	−	0.861971i
$896$	1.00000			1.00000
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.0440780	+	0.306569i	0.0440780	+	0.306569i
$901$		0			0
$902$	2.11435	+	0.620830i	2.11435	+	0.620830i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$907$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$908$		0			0
$909$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$910$		0			0
$911$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$911$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$912$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$913$		0			0
$914$	0.345139	−	0.755750i	0.345139	−	0.755750i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	0.830830			0.830830
$921$	0.830830			0.830830
$922$	0.698939	+	0.449181i	0.698939	+	0.449181i
$923$		0			0
$924$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$925$	−0.570276	−	0.167448i	−0.570276	−	0.167448i
$926$		0			0
$927$	1.25667	−	1.45027i	1.25667	−	1.45027i
$928$		0			0
$929$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$929$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$930$	0.154861	+	0.178719i	0.154861	+	0.178719i
$931$	1.41542	−	0.909632i	1.41542	−	0.909632i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.0440780	+	0.306569i	−0.0440780	+	0.306569i
$936$		0			0
$937$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$937$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$941$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$942$		0			0
$943$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$944$		0			0
$945$	0.698939	+	0.449181i	0.698939	+	0.449181i
$946$		0			0
$947$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$947$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$948$		0			0
$949$		0			0
$950$	0.341254	−	0.393828i	0.341254	−	0.393828i
$951$		0			0
$952$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$953$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$953$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$954$		0			0
$955$	−1.34125	+	0.861971i	−1.34125	+	0.861971i
$956$	0.857685	+	0.989821i	0.857685	+	0.989821i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.345139	−	0.755750i	0.345139	−	0.755750i
$961$	0.881761	+	0.258908i	0.881761	+	0.258908i
$962$		0			0
$963$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$964$		0			0
$965$	0.690279			0.690279
$966$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.601808	+	0.386758i	0.601808	+	0.386758i
$969$	0.0681534	+	0.474017i	0.0681534	+	0.474017i
$970$		0			0
$971$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$971$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$972$	0.415415	−	0.909632i	0.415415	−	0.909632i
$973$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$977$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$978$		0			0
$979$	−1.64589	−	1.89945i	−1.64589	−	1.89945i
$980$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$981$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$982$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$983$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$983$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$984$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−1.08816			−1.08816
$991$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$991$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$992$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$993$		0			0
$994$	1.84125	+	0.540641i	1.84125	+	0.540641i
$995$	−0.452036	+	0.989821i	−0.452036	+	0.989821i
$996$		0			0
$997$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$997$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$998$		0			0
$999$	1.25667	+	1.45027i	1.25667	+	1.45027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1932.1.bi.a.1175.1	yes	10
3.2	odd	2		1932.1.bi.c.1175.1	yes	10
4.3	odd	2		1932.1.bi.d.1175.1	yes	10
7.6	odd	2		1932.1.bi.b.1175.1	yes	10
12.11	even	2		1932.1.bi.b.1175.1	yes	10
21.20	even	2		1932.1.bi.d.1175.1	yes	10
23.12	even	11	inner	1932.1.bi.a.587.1	✓	10
28.27	even	2		1932.1.bi.c.1175.1	yes	10
69.35	odd	22		1932.1.bi.c.587.1	yes	10
84.83	odd	2	CM	1932.1.bi.a.1175.1	yes	10
92.35	odd	22		1932.1.bi.d.587.1	yes	10
161.104	odd	22		1932.1.bi.b.587.1	yes	10
276.35	even	22		1932.1.bi.b.587.1	yes	10
483.104	even	22		1932.1.bi.d.587.1	yes	10
644.587	even	22		1932.1.bi.c.587.1	yes	10
1932.587	odd	22	inner	1932.1.bi.a.587.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1932.1.bi.a.587.1	✓	10	23.12	even	11	inner
1932.1.bi.a.587.1	✓	10	1932.587	odd	22	inner
1932.1.bi.a.1175.1	yes	10	1.1	even	1	trivial
1932.1.bi.a.1175.1	yes	10	84.83	odd	2	CM
1932.1.bi.b.587.1	yes	10	161.104	odd	22
1932.1.bi.b.587.1	yes	10	276.35	even	22
1932.1.bi.b.1175.1	yes	10	7.6	odd	2
1932.1.bi.b.1175.1	yes	10	12.11	even	2
1932.1.bi.c.587.1	yes	10	69.35	odd	22
1932.1.bi.c.587.1	yes	10	644.587	even	22
1932.1.bi.c.1175.1	yes	10	3.2	odd	2
1932.1.bi.c.1175.1	yes	10	28.27	even	2
1932.1.bi.d.587.1	yes	10	92.35	odd	22
1932.1.bi.d.587.1	yes	10	483.104	even	22
1932.1.bi.d.1175.1	yes	10	4.3	odd	2
1932.1.bi.d.1175.1	yes	10	21.20	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:	\( N \)	\(=\)	\( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1932.bi (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.797176 - 0.234072i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.797176 - 0.234072i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.544078 - 0.627899i) q^{10} +(-1.10181 + 0.708089i) q^{11} +(0.841254 - 0.540641i) q^{12} +(-0.959493 + 0.281733i) q^{14} +(-0.118239 + 0.822373i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.118239 + 0.258908i) q^{17} +(-0.959493 - 0.281733i) q^{18} +(0.698939 + 1.53046i) q^{19} +(-0.118239 - 0.822373i) q^{20} +(0.841254 + 0.540641i) q^{21} -1.30972 q^{22} +(0.415415 + 0.909632i) q^{23} +1.00000 q^{24} +(-0.260554 - 0.167448i) q^{25} +(0.415415 + 0.909632i) q^{27} +(-0.959493 - 0.281733i) q^{28} +(-0.544078 + 0.627899i) q^{30} +(0.0405070 - 0.281733i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(0.857685 + 0.989821i) q^{33} +(-0.239446 + 0.153882i) q^{34} +(0.698939 - 0.449181i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(1.84125 - 0.540641i) q^{37} +(-0.239446 + 1.66538i) q^{38} +(0.345139 - 0.755750i) q^{40} +(-1.61435 - 0.474017i) q^{41} +(0.415415 + 0.909632i) q^{42} +(-1.10181 - 0.708089i) q^{44} +0.830830 q^{45} +(-0.142315 + 0.989821i) q^{46} +(0.841254 + 0.540641i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.128663 - 0.281733i) q^{50} +(0.273100 + 0.0801894i) q^{51} +(-0.142315 + 0.989821i) q^{54} +(1.04408 - 0.306569i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(1.41542 - 0.909632i) q^{57} +(-0.797176 + 0.234072i) q^{60} +(0.186393 - 0.215109i) q^{62} +(0.415415 - 0.909632i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.186393 + 1.29639i) q^{66} -0.284630 q^{68} +(0.841254 - 0.540641i) q^{69} +0.830830 q^{70} +(-1.61435 - 1.03748i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(1.84125 + 0.540641i) q^{74} +(-0.128663 + 0.281733i) q^{75} +(-1.10181 + 1.27155i) q^{76} +(0.186393 - 1.29639i) q^{77} +(0.698939 - 0.449181i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-1.10181 - 1.27155i) q^{82} +(-0.142315 + 0.989821i) q^{84} +(0.154861 - 0.178719i) q^{85} +(-0.544078 - 1.19136i) q^{88} +(0.273100 + 1.89945i) q^{89} +(0.698939 + 0.449181i) q^{90} +(-0.654861 + 0.755750i) q^{92} -0.284630 q^{93} +(-0.198939 - 1.38365i) q^{95} +(0.415415 + 0.909632i) q^{96} +(0.415415 - 0.909632i) q^{98} +(0.857685 - 0.989821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} - q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 - 2 * q^5 - q^6 - q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} - q^{7} - q^{8} - q^{9} - 2 q^{10} - 2 q^{11} - q^{12} - q^{14} - 2 q^{15} - q^{16} - 2 q^{17} - q^{18} - 2 q^{19} - 2 q^{20} - q^{21} - 2 q^{22} - q^{23} + 10 q^{24} - 3 q^{25} - q^{27} - q^{28} - 2 q^{30} + 9 q^{31} - q^{32} + 9 q^{33} - 2 q^{34} - 2 q^{35} - q^{36} + 9 q^{37} - 2 q^{38} + 9 q^{40} - 2 q^{41} - q^{42} - 2 q^{44} - 2 q^{45} - q^{46} - q^{48} - q^{49} - 3 q^{50} - 2 q^{51} - q^{54} + 7 q^{55} - q^{56} + 9 q^{57} - 2 q^{60} - 2 q^{62} - q^{63} - q^{64} - 2 q^{66} - 2 q^{68} - q^{69} - 2 q^{70} - 2 q^{71} - q^{72} + 9 q^{74} - 3 q^{75} - 2 q^{76} - 2 q^{77} - 2 q^{80} - q^{81} - 2 q^{82} - q^{84} - 4 q^{85} - 2 q^{88} - 2 q^{89} - 2 q^{90} - q^{92} - 2 q^{93} + 7 q^{95} - q^{96} - q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 - 2 * q^5 - q^6 - q^7 - q^8 - q^9 - 2 * q^10 - 2 * q^11 - q^12 - q^14 - 2 * q^15 - q^16 - 2 * q^17 - q^18 - 2 * q^19 - 2 * q^20 - q^21 - 2 * q^22 - q^23 + 10 * q^24 - 3 * q^25 - q^27 - q^28 - 2 * q^30 + 9 * q^31 - q^32 + 9 * q^33 - 2 * q^34 - 2 * q^35 - q^36 + 9 * q^37 - 2 * q^38 + 9 * q^40 - 2 * q^41 - q^42 - 2 * q^44 - 2 * q^45 - q^46 - q^48 - q^49 - 3 * q^50 - 2 * q^51 - q^54 + 7 * q^55 - q^56 + 9 * q^57 - 2 * q^60 - 2 * q^62 - q^63 - q^64 - 2 * q^66 - 2 * q^68 - q^69 - 2 * q^70 - 2 * q^71 - q^72 + 9 * q^74 - 3 * q^75 - 2 * q^76 - 2 * q^77 - 2 * q^80 - q^81 - 2 * q^82 - q^84 - 4 * q^85 - 2 * q^88 - 2 * q^89 - 2 * q^90 - q^92 - 2 * q^93 + 7 * q^95 - q^96 - q^98 + 9 * q^99

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