LMFDB - Embedded newform 1932.1.bi.c.1511.1

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			1511.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	1932.1511
Dual form			1932.1.bi.c.335.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.118239 + 0.258908i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.118239 + 0.258908i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.273100 + 0.0801894i) q^{10} +(-1.25667 - 1.45027i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(-0.415415 + 0.909632i) q^{14} +(0.239446 + 0.153882i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.239446 - 1.66538i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.186393 + 1.29639i) q^{19} +(0.239446 - 0.153882i) q^{20} +(-0.654861 + 0.755750i) q^{21} -1.91899 q^{22} +(0.142315 + 0.989821i) q^{23} -1.00000 q^{24} +(0.601808 - 0.694523i) q^{25} +(-0.142315 - 0.989821i) q^{27} +(0.415415 + 0.909632i) q^{28} +(0.273100 - 0.0801894i) q^{30} +(1.41542 + 0.909632i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-1.84125 - 0.540641i) q^{33} +(-1.10181 - 1.27155i) q^{34} +(-0.186393 - 0.215109i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.345139 - 0.755750i) q^{37} +(1.10181 + 0.708089i) q^{38} +(0.0405070 - 0.281733i) q^{40} +(0.544078 + 1.19136i) q^{41} +(0.142315 + 0.989821i) q^{42} +(-1.25667 + 1.45027i) q^{44} +0.284630 q^{45} +(0.841254 + 0.540641i) q^{46} +(-0.654861 + 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.130785 - 0.909632i) q^{50} +(-0.698939 - 1.53046i) q^{51} +(-0.841254 - 0.540641i) q^{54} +(0.226900 - 0.496841i) q^{55} +(0.959493 + 0.281733i) q^{56} +(0.857685 + 0.989821i) q^{57} +(0.118239 - 0.258908i) q^{60} +(1.61435 - 0.474017i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-1.61435 + 1.03748i) q^{66} -1.68251 q^{68} +(0.654861 + 0.755750i) q^{69} -0.284630 q^{70} +(0.544078 - 0.627899i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(-0.345139 - 0.755750i) q^{74} +(0.130785 - 0.909632i) q^{75} +(1.25667 - 0.368991i) q^{76} +(1.61435 + 1.03748i) q^{77} +(-0.186393 - 0.215109i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(1.25667 + 0.368991i) q^{82} +(0.841254 + 0.540641i) q^{84} +(0.459493 - 0.134919i) q^{85} +(0.273100 + 1.89945i) q^{88} +(-0.698939 + 0.449181i) q^{89} +(0.186393 - 0.215109i) q^{90} +(0.959493 - 0.281733i) q^{92} +1.68251 q^{93} +(-0.313607 + 0.201543i) q^{95} +(0.142315 + 0.989821i) q^{96} +(0.142315 - 0.989821i) q^{98} +(-1.84125 + 0.540641i) 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 $\left(\mathbb{Z}/1932\mathbb{Z}\right)^\times$.

$n$	$829$	$925$	$967$	$1289$
$\chi(n)$	$-1$	$e\left(\frac{4}{11}\right)$	$-1$	$-1$

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 $

$2$	0.654861	−	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
$5$	0.118239	+	0.258908i	0.118239	+	0.258908i	0.959493	−	0.281733i	$-0.0909091\pi$
$5$	0.118239	+	0.258908i	0.118239	+	0.258908i	−0.841254	+	0.540641i	$0.818182\pi$
$6$	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
$10$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$11$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.841254	−	0.540641i	$-0.818182\pi$
$11$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.415415	−	0.909632i	$-0.636364\pi$
$12$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$13$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$13$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$14$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$15$	0.239446	+	0.153882i	0.239446	+	0.153882i
$16$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$17$	0.239446	−	1.66538i	0.239446	−	1.66538i	−0.415415	−	0.909632i	$-0.636364\pi$
$17$	0.239446	−	1.66538i	0.239446	−	1.66538i	0.654861	−	0.755750i	$-0.272727\pi$
$18$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$19$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$19$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$20$	0.239446	−	0.153882i	0.239446	−	0.153882i
$21$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$22$	−1.91899			−1.91899
$23$	0.142315	+	0.989821i	0.142315	+	0.989821i
$23$	0.142315	+	0.989821i	0.142315	+	0.989821i
$24$	−1.00000			−1.00000
$25$	0.601808	−	0.694523i	0.601808	−	0.694523i
$26$		0			0
$27$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$28$	0.415415	+	0.909632i	0.415415	+	0.909632i
$29$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$29$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$30$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$31$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$31$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$32$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$33$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$34$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$35$	−0.186393	−	0.215109i	−0.186393	−	0.215109i
$36$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$37$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$37$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$38$	1.10181	+	0.708089i	1.10181	+	0.708089i
$39$		0			0
$40$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$41$	0.544078	+	1.19136i	0.544078	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$41$	0.544078	+	1.19136i	0.544078	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$42$	0.142315	+	0.989821i	0.142315	+	0.989821i
$43$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$43$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$44$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$45$	0.284630			0.284630
$46$	0.841254	+	0.540641i	0.841254	+	0.540641i
$47$		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
$50$	−0.130785	−	0.909632i	−0.130785	−	0.909632i
$51$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$52$		0			0
$53$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$53$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$54$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$55$	0.226900	−	0.496841i	0.226900	−	0.496841i
$56$	0.959493	+	0.281733i	0.959493	+	0.281733i
$57$	0.857685	+	0.989821i	0.857685	+	0.989821i
$58$		0			0
$59$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$59$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$60$	0.118239	−	0.258908i	0.118239	−	0.258908i
$61$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$61$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$62$	1.61435	−	0.474017i	1.61435	−	0.474017i
$63$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$64$	0.415415	+	0.909632i	0.415415	+	0.909632i
$65$		0			0
$66$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$67$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$67$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$68$	−1.68251			−1.68251
$69$	0.654861	+	0.755750i	0.654861	+	0.755750i
$70$	−0.284630			−0.284630
$71$	0.544078	−	0.627899i	0.544078	−	0.627899i	−0.415415	−	0.909632i	$-0.636364\pi$
$71$	0.544078	−	0.627899i	0.544078	−	0.627899i	0.959493	+	0.281733i	$0.0909091\pi$
$72$	−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	$0.454545\pi$
$74$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$75$	0.130785	−	0.909632i	0.130785	−	0.909632i
$76$	1.25667	−	0.368991i	1.25667	−	0.368991i
$77$	1.61435	+	1.03748i	1.61435	+	1.03748i
$78$		0			0
$79$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$79$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$80$	−0.186393	−	0.215109i	−0.186393	−	0.215109i
$81$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$82$	1.25667	+	0.368991i	1.25667	+	0.368991i
$83$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$83$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$84$	0.841254	+	0.540641i	0.841254	+	0.540641i
$85$	0.459493	−	0.134919i	0.459493	−	0.134919i
$86$		0			0
$87$		0			0
$88$	0.273100	+	1.89945i	0.273100	+	1.89945i
$89$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	−0.841254	−	0.540641i	$-0.818182\pi$
$89$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	0.142315	+	0.989821i	$0.454545\pi$
$90$	0.186393	−	0.215109i	0.186393	−	0.215109i
$91$		0			0
$92$	0.959493	−	0.281733i	0.959493	−	0.281733i
$93$	1.68251			1.68251
$94$		0			0
$95$	−0.313607	+	0.201543i	−0.313607	+	0.201543i
$96$	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
$99$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$100$	−0.773100	−	0.496841i	−0.773100	−	0.496841i
$101$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	0.654861	+	0.755750i	$0.272727\pi$
$101$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	−1.00000			$\pi$
$102$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$103$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$103$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$104$		0			0
$105$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$106$		0			0
$107$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.959493	−	0.281733i	$-0.0909091\pi$
$107$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.142315	+	0.989821i	$0.454545\pi$
$108$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$109$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$109$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$110$	−0.226900	−	0.496841i	−0.226900	−	0.496841i
$111$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$112$	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	$0.727273\pi$
$114$	1.30972			1.30972
$115$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.239446	+	1.66538i	0.239446	+	1.66538i
$120$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$121$	−0.381761	+	2.65520i	−0.381761	+	2.65520i
$122$		0			0
$123$	1.10181	+	0.708089i	1.10181	+	0.708089i
$124$	0.698939	−	1.53046i	0.698939	−	1.53046i
$125$	0.524075	+	0.153882i	0.524075	+	0.153882i
$126$	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			0
$130$		0			0
$131$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$131$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$132$	−0.273100	+	1.89945i	−0.273100	+	1.89945i
$133$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$134$		0			0
$135$	0.239446	−	0.153882i	0.239446	−	0.153882i
$136$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	1.00000			1.00000
$139$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$139$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$140$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$141$		0			0
$142$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$143$		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
$148$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$149$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$149$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$150$	−0.601808	−	0.694523i	−0.601808	−	0.694523i
$151$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$151$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$152$	0.544078	−	1.19136i	0.544078	−	1.19136i
$153$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$154$	1.84125	−	0.540641i	1.84125	−	0.540641i
$155$	−0.0681534	+	0.474017i	−0.0681534	+	0.474017i
$156$		0			0
$157$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$157$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$158$		0			0
$159$		0			0
$160$	−0.284630			−0.284630
$161$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$162$	−1.00000			−1.00000
$163$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$163$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$164$	1.10181	−	0.708089i	1.10181	−	0.708089i
$165$	−0.0777324	−	0.540641i	−0.0777324	−	0.540641i
$166$		0			0
$167$		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
$169$	0.841254	+	0.540641i	0.841254	+	0.540641i
$170$	0.198939	−	0.435615i	0.198939	−	0.435615i
$171$	1.25667	+	0.368991i	1.25667	+	0.368991i
$172$		0			0
$173$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$173$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$174$		0			0
$175$	−0.381761	+	0.835939i	−0.381761	+	0.835939i
$176$	1.61435	+	1.03748i	1.61435	+	1.03748i
$177$		0			0
$178$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$179$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$179$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	−1.00000			$\pi$
$180$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$181$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$181$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$182$		0			0
$183$		0			0
$184$	0.415415	−	0.909632i	0.415415	−	0.909632i
$185$	0.236479			0.236479
$186$	1.10181	−	1.27155i	1.10181	−	1.27155i
$187$	−2.71616	+	1.74557i	−2.71616	+	1.74557i
$188$		0			0
$189$	0.415415	+	0.909632i	0.415415	+	0.909632i
$190$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$191$	0.797176	−	0.234072i	0.797176	−	0.234072i	0.142315	−	0.989821i	$-0.454545\pi$
$191$	0.797176	−	0.234072i	0.797176	−	0.234072i	0.654861	+	0.755750i	$0.272727\pi$
$192$	0.841254	+	0.540641i	0.841254	+	0.540641i
$193$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$193$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$194$		0			0
$195$		0			0
$196$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$197$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$197$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$198$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$199$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$199$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$200$	−0.881761	+	0.258908i	−0.881761	+	0.258908i
$201$		0			0
$202$	0.345139	+	0.755750i	0.345139	+	0.755750i
$203$		0			0
$204$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$205$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$206$	−0.830830			−0.830830
$207$	0.959493	+	0.281733i	0.959493	+	0.281733i
$208$		0			0
$209$	1.64589	−	1.89945i	1.64589	−	1.89945i
$210$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$211$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$211$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$212$		0			0
$213$	0.118239	−	0.822373i	0.118239	−	0.822373i
$214$	1.25667	−	0.368991i	1.25667	−	0.368991i
$215$		0			0
$216$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$217$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$218$	1.10181	+	1.27155i	1.10181	+	1.27155i
$219$		0			0
$220$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$221$		0			0
$222$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$223$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$223$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$224$	0.142315	−	0.989821i	0.142315	−	0.989821i
$225$	−0.381761	−	0.835939i	−0.381761	−	0.835939i
$226$		0			0
$227$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$227$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$228$	0.857685	−	0.989821i	0.857685	−	0.989821i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$231$	1.91899			1.91899
$232$		0			0
$233$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$233$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	1.41542	+	0.909632i	1.41542	+	0.909632i
$239$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$239$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$240$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$241$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$241$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$242$	1.75667	+	2.02730i	1.75667	+	2.02730i
$243$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$244$		0			0
$245$	0.239446	+	0.153882i	0.239446	+	0.153882i
$246$	1.25667	−	0.368991i	1.25667	−	0.368991i
$247$		0			0
$248$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$249$		0			0
$250$	0.459493	−	0.295298i	0.459493	−	0.295298i
$251$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$251$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$252$	1.00000			1.00000
$253$	1.25667	−	1.45027i	1.25667	−	1.45027i
$254$		0			0
$255$	0.313607	−	0.361922i	0.313607	−	0.361922i
$256$	0.841254	−	0.540641i	0.841254	−	0.540641i
$257$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	0.959493	−	0.281733i	$-0.0909091\pi$
$257$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	−1.00000			$\pi$
$258$		0			0
$259$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	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	$0.272727\pi$
$264$	1.25667	+	1.45027i	1.25667	+	1.45027i
$265$		0			0
$266$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$267$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$268$		0			0
$269$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−0.841254	+	0.540641i	$0.818182\pi$
$269$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−1.00000			$1.00000\pi$
$270$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$271$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$271$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$272$	0.239446	+	1.66538i	0.239446	+	1.66538i
$273$		0			0
$274$		0			0
$275$	−1.76352			−1.76352
$276$	0.654861	−	0.755750i	0.654861	−	0.755750i
$277$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$277$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$278$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$279$	1.41542	−	0.909632i	1.41542	−	0.909632i
$280$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$281$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$281$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$282$		0			0
$283$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$283$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$284$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$285$	−0.154861	+	0.339098i	−0.154861	+	0.339098i
$286$		0			0
$287$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$288$	0.654861	+	0.755750i	0.654861	+	0.755750i
$289$	−1.75667	−	0.515804i	−1.75667	−	0.515804i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$293$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$294$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$295$		0			0
$296$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$297$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$298$		0			0
$299$		0			0
$300$	−0.918986			−0.918986
$301$		0			0
$302$		0			0
$303$	0.118239	+	0.822373i	0.118239	+	0.822373i
$304$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$305$		0			0
$306$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$307$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$307$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$308$	0.797176	−	1.74557i	0.797176	−	1.74557i
$309$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$310$	0.313607	+	0.361922i	0.313607	+	0.361922i
$311$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$311$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$312$		0			0
$313$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$313$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$314$		0			0
$315$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$316$		0			0
$317$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$317$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$318$		0			0
$319$		0			0
$320$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$321$	1.30972			1.30972
$322$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$323$	2.20362			2.20362
$324$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$325$		0			0
$326$		0			0
$327$	0.698939	+	1.53046i	0.698939	+	1.53046i
$328$	0.186393	−	1.29639i	0.186393	−	1.29639i
$329$		0			0
$330$	−0.459493	−	0.295298i	−0.459493	−	0.295298i
$331$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$331$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$332$		0			0
$333$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$334$		0			0
$335$		0			0
$336$	0.415415	−	0.909632i	0.415415	−	0.909632i
$337$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$337$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$338$	0.959493	−	0.281733i	0.959493	−	0.281733i
$339$		0			0
$340$	−0.198939	−	0.435615i	−0.198939	−	0.435615i
$341$	−0.459493	−	3.19584i	−0.459493	−	3.19584i
$342$	1.10181	−	0.708089i	1.10181	−	0.708089i
$343$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$344$		0			0
$345$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$346$	−0.284630			−0.284630
$347$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$347$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$348$		0			0
$349$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$349$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$350$	0.381761	+	0.835939i	0.381761	+	0.835939i
$351$		0			0
$352$	1.84125	−	0.540641i	1.84125	−	0.540641i
$353$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.959493	−	0.281733i	$-0.0909091\pi$
$353$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.142315	+	0.989821i	$0.454545\pi$
$354$		0			0
$355$	0.226900	+	0.0666238i	0.226900	+	0.0666238i
$356$	0.544078	+	0.627899i	0.544078	+	0.627899i
$357$	1.10181	+	1.27155i	1.10181	+	1.27155i
$358$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$359$	−0.830830	+	1.81926i	−0.830830	+	1.81926i	−0.415415	+	0.909632i	$0.636364\pi$
$359$	−0.830830	+	1.81926i	−0.830830	+	1.81926i	−0.415415	+	0.909632i	$0.636364\pi$
$360$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$361$	−0.686393	+	0.201543i	−0.686393	+	0.201543i
$362$		0			0
$363$	1.11435	+	2.44009i	1.11435	+	2.44009i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$367$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$368$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$369$	1.30972			1.30972
$370$	0.154861	−	0.178719i	0.154861	−	0.178719i
$371$		0			0
$372$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$373$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$373$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$374$	−0.459493	+	3.19584i	−0.459493	+	3.19584i
$375$	0.524075	−	0.153882i	0.524075	−	0.153882i
$376$		0			0
$377$		0			0
$378$	0.959493	+	0.281733i	0.959493	+	0.281733i
$379$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$379$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$380$	0.244123	+	0.281733i	0.244123	+	0.281733i
$381$		0			0
$382$	0.345139	−	0.755750i	0.345139	−	0.755750i
$383$		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
$385$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$386$	0.118239	+	0.258908i	0.118239	+	0.258908i
$387$		0			0
$388$		0			0
$389$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$389$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$390$		0			0
$391$	1.68251			1.68251
$392$	−1.00000			−1.00000
$393$		0			0
$394$		0			0
$395$		0			0
$396$	0.797176	+	1.74557i	0.797176	+	1.74557i
$397$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$397$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$398$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$399$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$400$	−0.381761	+	0.835939i	−0.381761	+	0.835939i
$401$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$401$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$402$		0			0
$403$		0			0
$404$	0.797176	+	0.234072i	0.797176	+	0.234072i
$405$	0.118239	−	0.258908i	0.118239	−	0.258908i
$406$		0			0
$407$	−1.52977	+	0.449181i	−1.52977	+	0.449181i
$408$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$409$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$409$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$410$	0.0530529	+	0.368991i	0.0530529	+	0.368991i
$411$		0			0
$412$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$413$		0			0
$414$	0.841254	−	0.540641i	0.841254	−	0.540641i
$415$		0			0
$416$		0			0
$417$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$418$	−0.357685	−	2.48775i	−0.357685	−	2.48775i
$419$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$419$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$420$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$421$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$421$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.01255	−	1.16854i	−1.01255	−	1.16854i
$426$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$427$		0			0
$428$	0.544078	−	1.19136i	0.544078	−	1.19136i
$429$		0			0
$430$		0			0
$431$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$431$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$432$	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	$0.454545\pi$
$434$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$435$		0			0
$436$	1.68251			1.68251
$437$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$438$		0			0
$439$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$439$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$440$	−0.459493	+	0.295298i	−0.459493	+	0.295298i
$441$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$442$		0			0
$443$	0.239446	−	1.66538i	0.239446	−	1.66538i	−0.415415	−	0.909632i	$-0.636364\pi$
$443$	0.239446	−	1.66538i	0.239446	−	1.66538i	0.654861	−	0.755750i	$-0.272727\pi$
$444$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$445$	−0.198939	−	0.127850i	−0.198939	−	0.127850i
$446$	0.118239	−	0.258908i	0.118239	−	0.258908i
$447$		0			0
$448$	−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	$0.272727\pi$
$450$	−0.881761	−	0.258908i	−0.881761	−	0.258908i
$451$	1.04408	−	2.28621i	1.04408	−	2.28621i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$457$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$457$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$458$		0			0
$459$	−1.68251			−1.68251
$460$	0.186393	+	0.215109i	0.186393	+	0.215109i
$461$	0.284630			0.284630			0.142315	−	0.989821i	$-0.454545\pi$
$461$	0.284630			0.284630			0.142315	+	0.989821i	$0.454545\pi$
$462$	1.25667	−	1.45027i	1.25667	−	1.45027i
$463$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$463$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$464$		0			0
$465$	0.198939	+	0.435615i	0.198939	+	0.435615i
$466$		0			0
$467$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$467$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	1.01255	+	0.650724i	1.01255	+	0.650724i
$476$	1.61435	−	0.474017i	1.61435	−	0.474017i
$477$		0			0
$478$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$479$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$479$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$480$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$481$		0			0
$482$		0			0
$483$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$484$	2.68251			2.68251
$485$		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			0
$489$		0			0
$490$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$491$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.959493	−	0.281733i	$-0.0909091\pi$
$491$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.142315	+	0.989821i	$0.454545\pi$
$492$	0.544078	−	1.19136i	0.544078	−	1.19136i
$493$		0			0
$494$		0			0
$495$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$496$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$497$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$498$		0			0
$499$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$499$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$500$	0.0777324	−	0.540641i	0.0777324	−	0.540641i
$501$		0			0
$502$		0			0
$503$		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
$505$	−0.236479			−0.236479
$506$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$507$	1.00000			1.00000
$508$		0			0
$509$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−0.415415	+	0.909632i	$0.636364\pi$
$509$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−1.00000			$\pi$
$510$	−0.0681534	−	0.474017i	−0.0681534	−	0.474017i
$511$		0			0
$512$	0.142315	−	0.989821i	0.142315	−	0.989821i
$513$	1.25667	−	0.368991i	1.25667	−	0.368991i
$514$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$515$	0.0982369	−	0.215109i	0.0982369	−	0.215109i
$516$		0			0
$517$		0			0
$518$	0.544078	+	0.627899i	0.544078	+	0.627899i
$519$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$520$		0			0
$521$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.959493	+	0.281733i	$0.0909091\pi$
$521$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.654861	+	0.755750i	$0.272727\pi$
$522$		0			0
$523$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$523$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$524$		0			0
$525$	0.130785	+	0.909632i	0.130785	+	0.909632i
$526$	1.41542	−	0.909632i	1.41542	−	0.909632i
$527$	1.85380	−	2.13940i	1.85380	−	2.13940i
$528$	1.91899			1.91899
$529$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$530$		0			0
$531$		0			0
$532$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$533$		0			0
$534$	0.345139	+	0.755750i	0.345139	+	0.755750i
$535$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$536$		0			0
$537$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$538$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$539$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$540$	−0.186393	−	0.215109i	−0.186393	−	0.215109i
$541$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$541$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$542$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$543$		0			0
$544$	1.41542	+	0.909632i	1.41542	+	0.909632i
$545$	−0.459493	+	0.134919i	−0.459493	+	0.134919i
$546$		0			0
$547$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$547$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$548$		0			0
$549$		0			0
$550$	−1.15486	+	1.33278i	−1.15486	+	1.33278i
$551$		0			0
$552$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$553$		0			0
$554$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$555$	0.198939	−	0.127850i	0.198939	−	0.127850i
$556$	0.186393	+	1.29639i	0.186393	+	1.29639i
$557$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$557$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$558$	0.239446	−	1.66538i	0.239446	−	1.66538i
$559$		0			0
$560$	0.239446	+	0.153882i	0.239446	+	0.153882i
$561$	−1.34125	+	2.93694i	−1.34125	+	2.93694i
$562$		0			0
$563$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$563$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$564$		0			0
$565$		0			0
$566$	0.797176	−	1.74557i	0.797176	−	1.74557i
$567$	0.841254	+	0.540641i	0.841254	+	0.540641i
$568$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$569$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$569$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$570$	0.154861	+	0.339098i	0.154861	+	0.339098i
$571$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$571$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$572$		0			0
$573$	0.544078	−	0.627899i	0.544078	−	0.627899i
$574$	−1.30972			−1.30972
$575$	0.773100	+	0.496841i	0.773100	+	0.496841i
$576$	1.00000			1.00000
$577$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$577$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$578$	−1.54019	+	0.989821i	−1.54019	+	0.989821i
$579$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	0.857685	+	0.989821i	0.857685	+	0.989821i
$587$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$587$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$588$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$589$	−0.915415	+	2.00448i	−0.915415	+	2.00448i
$590$		0			0
$591$		0			0
$592$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$593$	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	$0.454545\pi$
$594$	0.273100	+	1.89945i	0.273100	+	1.89945i
$595$	−0.402869	+	0.258908i	−0.402869	+	0.258908i
$596$		0			0
$597$	−1.91899			−1.91899
$598$		0			0
$599$	1.30972			1.30972			0.654861	−	0.755750i	$-0.272727\pi$
$599$	1.30972			1.30972			0.654861	+	0.755750i	$0.272727\pi$
$600$	−0.601808	+	0.694523i	−0.601808	+	0.694523i
$601$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$601$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.732593	+	0.215109i	−0.732593	+	0.215109i
$606$	0.698939	+	0.449181i	0.698939	+	0.449181i
$607$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$607$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$608$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.698939	+	1.53046i	−0.698939	+	1.53046i
$613$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$613$	1.68251	+	1.08128i	1.68251	+	1.08128i	0.841254	+	0.540641i	$0.181818\pi$
$614$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$615$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$616$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$617$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$617$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$618$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$619$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$619$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$620$	0.478891			0.478891
$621$	0.959493	−	0.281733i	0.959493	−	0.281733i
$622$		0			0
$623$	0.544078	−	0.627899i	0.544078	−	0.627899i
$624$		0			0
$625$	−0.108660	−	0.755750i	−0.108660	−	0.755750i
$626$		0			0
$627$	0.357685	−	2.48775i	0.357685	−	2.48775i
$628$		0			0
$629$	−1.17597	−	0.755750i	−1.17597	−	0.755750i
$630$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$631$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$631$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$640$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$641$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$641$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$642$	0.857685	−	0.989821i	0.857685	−	0.989821i
$643$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$643$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$644$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$645$		0			0
$646$	1.44306	−	1.66538i	1.44306	−	1.66538i
$647$		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			0
$651$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$652$		0			0
$653$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$653$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$654$	1.61435	+	0.474017i	1.61435	+	0.474017i
$655$		0			0
$656$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$657$		0			0
$658$		0			0
$659$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−0.415415	−	0.909632i	$-0.636364\pi$
$659$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−1.00000			$\pi$
$660$	−0.524075	+	0.153882i	−0.524075	+	0.153882i
$661$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$661$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.244123	−	0.281733i	0.244123	−	0.281733i
$666$	−0.830830			−0.830830
$667$		0			0
$668$		0			0
$669$	0.186393	−	0.215109i	0.186393	−	0.215109i
$670$		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	$-0.181818\pi$
$674$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$675$	−0.773100	−	0.496841i	−0.773100	−	0.496841i
$676$	0.415415	−	0.909632i	0.415415	−	0.909632i
$677$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.959493	−	0.281733i	$-0.0909091\pi$
$677$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.654861	+	0.755750i	$0.272727\pi$
$678$		0			0
$679$		0			0
$680$	−0.459493	−	0.134919i	−0.459493	−	0.134919i
$681$		0			0
$682$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$683$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$683$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$684$	0.186393	−	1.29639i	0.186393	−	1.29639i
$685$		0			0
$686$	0.142315	+	0.989821i	0.142315	+	0.989821i
$687$		0			0
$688$		0			0
$689$		0			0
$690$	0.118239	+	0.258908i	0.118239	+	0.258908i
$691$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$691$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$692$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$693$	1.61435	−	1.03748i	1.61435	−	1.03748i
$694$	0.273100	+	1.89945i	0.273100	+	1.89945i
$695$	−0.154861	−	0.339098i	−0.154861	−	0.339098i
$696$		0			0
$697$	2.11435	−	0.620830i	2.11435	−	0.620830i
$698$		0			0
$699$		0			0
$700$	0.881761	+	0.258908i	0.881761	+	0.258908i
$701$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$701$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$702$		0			0
$703$	1.04408	+	0.306569i	1.04408	+	0.306569i
$704$	0.797176	−	1.74557i	0.797176	−	1.74557i
$705$		0			0
$706$	1.25667	−	0.368991i	1.25667	−	0.368991i
$707$	0.118239	−	0.822373i	0.118239	−	0.822373i
$708$		0			0
$709$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$709$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$710$	0.198939	−	0.127850i	0.198939	−	0.127850i
$711$		0			0
$712$	0.830830			0.830830
$713$	−0.698939	+	1.53046i	−0.698939	+	1.53046i
$714$	1.68251			1.68251
$715$		0			0
$716$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$717$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$718$	0.830830	+	1.81926i	0.830830	+	1.81926i
$719$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$719$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$720$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$721$	0.698939	+	0.449181i	0.698939	+	0.449181i
$722$	−0.297176	+	0.650724i	−0.297176	+	0.650724i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	2.57385	+	0.755750i	2.57385	+	0.755750i
$727$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$727$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$728$		0			0
$729$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$733$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$734$	1.10181	−	1.27155i	1.10181	−	1.27155i
$735$	0.284630			0.284630
$736$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$737$		0			0
$738$	0.857685	−	0.989821i	0.857685	−	0.989821i
$739$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$739$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$740$	−0.0336545	−	0.234072i	−0.0336545	−	0.234072i
$741$		0			0
$742$		0			0
$743$	−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	$0.454545\pi$
$744$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$745$		0			0
$746$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$747$		0			0
$748$	2.11435	+	2.44009i	2.11435	+	2.44009i
$749$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$750$	0.226900	−	0.496841i	0.226900	−	0.496841i
$751$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$751$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.841254	−	0.540641i	0.841254	−	0.540641i
$757$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$757$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$758$		0			0
$759$	0.273100	−	1.89945i	0.273100	−	1.89945i
$760$	0.372786			0.372786
$761$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$761$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$762$		0			0
$763$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$764$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$765$	0.0681534	−	0.474017i	0.0681534	−	0.474017i
$766$		0			0
$767$		0			0
$768$	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	$0.0909091\pi$
$770$	0.357685	+	0.412791i	0.357685	+	0.412791i
$771$	−0.186393	−	0.215109i	−0.186393	−	0.215109i
$772$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$773$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$773$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$774$		0			0
$775$	1.48357	−	0.435615i	1.48357	−	0.435615i
$776$		0			0
$777$	0.345139	+	0.755750i	0.345139	+	0.755750i
$778$		0			0
$779$	−1.44306	+	0.927399i	−1.44306	+	0.927399i
$780$		0			0
$781$	−1.59435			−1.59435
$782$	1.10181	−	1.27155i	1.10181	−	1.27155i
$783$		0			0
$784$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$785$		0			0
$786$		0			0
$787$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$787$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$788$		0			0
$789$	1.61435	−	0.474017i	1.61435	−	0.474017i
$790$		0			0
$791$		0			0
$792$	1.84125	+	0.540641i	1.84125	+	0.540641i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$797$	−1.68251	−	1.08128i	−1.68251	−	1.08128i	−0.841254	−	0.540641i	$-0.818182\pi$
$797$	−1.68251	−	1.08128i	−1.68251	−	1.08128i	−0.841254	−	0.540641i	$-0.818182\pi$
$798$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$799$		0			0
$800$	0.381761	+	0.835939i	0.381761	+	0.835939i
$801$	0.118239	+	0.822373i	0.118239	+	0.822373i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	0.186393	−	0.215109i	0.186393	−	0.215109i
$806$		0			0
$807$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$808$	0.698939	−	0.449181i	0.698939	−	0.449181i
$809$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$809$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$810$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$811$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$811$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$812$		0			0
$813$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$814$	−0.662317	+	1.45027i	−0.662317	+	1.45027i
$815$		0			0
$816$	1.10181	+	1.27155i	1.10181	+	1.27155i
$817$		0			0
$818$		0			0
$819$		0			0
$820$	0.313607	+	0.201543i	0.313607	+	0.201543i
$821$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$821$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$822$		0			0
$823$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$823$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$824$	0.118239	+	0.822373i	0.118239	+	0.822373i
$825$	−1.48357	+	0.953431i	−1.48357	+	0.953431i
$826$		0			0
$827$	0.284630			0.284630			0.142315	−	0.989821i	$-0.454545\pi$
$827$	0.284630			0.284630			0.142315	+	0.989821i	$0.454545\pi$
$828$	0.142315	−	0.989821i	0.142315	−	0.989821i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$832$		0			0
$833$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$834$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$835$		0			0
$836$	−2.11435	−	1.35881i	−2.11435	−	1.35881i
$837$	0.698939	−	1.53046i	0.698939	−	1.53046i
$838$		0			0
$839$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$839$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$840$	0.186393	+	0.215109i	0.186393	+	0.215109i
$841$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$842$	0.118239	−	0.258908i	0.118239	−	0.258908i
$843$		0			0
$844$		0			0
$845$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$846$		0			0
$847$	−0.381761	−	2.65520i	−0.381761	−	2.65520i
$848$		0			0
$849$	1.25667	−	1.45027i	1.25667	−	1.45027i
$850$	−1.54620			−1.54620
$851$	0.797176	+	0.234072i	0.797176	+	0.234072i
$852$	−0.830830			−0.830830
$853$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$853$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$854$		0			0
$855$	0.0530529	+	0.368991i	0.0530529	+	0.368991i
$856$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$857$	0.239446	−	1.66538i	0.239446	−	1.66538i	−0.415415	−	0.909632i	$-0.636364\pi$
$857$	0.239446	−	1.66538i	0.239446	−	1.66538i	0.654861	−	0.755750i	$-0.272727\pi$
$858$		0			0
$859$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$859$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$860$		0			0
$861$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$862$	0.857685	+	0.989821i	0.857685	+	0.989821i
$863$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.841254	−	0.540641i	$-0.818182\pi$
$863$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.415415	−	0.909632i	$-0.636364\pi$
$864$	0.959493	+	0.281733i	0.959493	+	0.281733i
$865$	0.0336545	−	0.0736930i	0.0336545	−	0.0736930i
$866$		0			0
$867$	−1.75667	+	0.515804i	−1.75667	+	0.515804i
$868$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	1.10181	−	1.27155i	1.10181	−	1.27155i
$873$		0			0
$874$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$875$	−0.546200			−0.546200
$876$		0			0
$877$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$877$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$878$	0.239446	+	1.66538i	0.239446	+	1.66538i
$879$	0.544078	+	1.19136i	0.544078	+	1.19136i
$880$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$881$	1.91899	−	0.563465i	1.91899	−	0.563465i	0.959493	−	0.281733i	$-0.0909091\pi$
$881$	1.91899	−	0.563465i	1.91899	−	0.563465i	0.959493	−	0.281733i	$-0.0909091\pi$
$882$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$883$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$883$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$884$		0			0
$885$		0			0
$886$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$887$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$887$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$888$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$889$		0			0
$890$	−0.226900	+	0.0666238i	−0.226900	+	0.0666238i
$891$	−0.273100	+	1.89945i	−0.273100	+	1.89945i
$892$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$893$		0			0
$894$		0			0
$895$	0.154861	−	0.178719i	0.154861	−	0.178719i
$896$	−1.00000			−1.00000
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$901$		0			0
$902$	−1.04408	−	2.28621i	−1.04408	−	2.28621i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$907$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$908$		0			0
$909$	0.544078	+	0.627899i	0.544078	+	0.627899i
$910$		0			0
$911$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$911$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	−0.841254	+	0.540641i	$0.818182\pi$
$912$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$913$		0			0
$914$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	0.284630			0.284630
$921$	−0.284630			−0.284630
$922$	0.186393	−	0.215109i	0.186393	−	0.215109i
$923$		0			0
$924$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$925$	−0.317178	−	0.694523i	−0.317178	−	0.694523i
$926$		0			0
$927$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$928$		0			0
$929$	0.118239	−	0.258908i	0.118239	−	0.258908i	−0.841254	−	0.540641i	$-0.818182\pi$
$929$	0.118239	−	0.258908i	0.118239	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$930$	0.459493	+	0.134919i	0.459493	+	0.134919i
$931$	0.857685	+	0.989821i	0.857685	+	0.989821i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.773100	−	0.496841i	−0.773100	−	0.496841i
$936$		0			0
$937$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$937$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	0.142315	+	0.989821i	$0.454545\pi$
$941$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	−1.00000			$\pi$
$942$		0			0
$943$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$944$		0			0
$945$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$946$		0			0
$947$	0.118239	+	0.822373i	0.118239	+	0.822373i	0.959493	+	0.281733i	$0.0909091\pi$
$947$	0.118239	+	0.822373i	0.118239	+	0.822373i	−0.841254	+	0.540641i	$0.818182\pi$
$948$		0			0
$949$		0			0
$950$	1.15486	−	0.339098i	1.15486	−	0.339098i
$951$		0			0
$952$	0.698939	−	1.53046i	0.698939	−	1.53046i
$953$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$953$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$954$		0			0
$955$	0.154861	+	0.178719i	0.154861	+	0.178719i
$956$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$961$	0.760554	+	1.66538i	0.760554	+	1.66538i
$962$		0			0
$963$	1.10181	−	0.708089i	1.10181	−	0.708089i
$964$		0			0
$965$	−0.0810141			−0.0810141
$966$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	1.75667	−	2.02730i	1.75667	−	2.02730i
$969$	1.85380	−	1.19136i	1.85380	−	1.19136i
$970$		0			0
$971$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$971$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$972$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$973$	1.25667	−	0.368991i	1.25667	−	0.368991i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$977$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$978$		0			0
$979$	1.52977	+	0.449181i	1.52977	+	0.449181i
$980$	0.118239	−	0.258908i	0.118239	−	0.258908i
$981$	1.41542	+	0.909632i	1.41542	+	0.909632i
$982$	1.25667	−	0.368991i	1.25667	−	0.368991i
$983$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$983$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$984$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.546200			−0.546200
$991$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$991$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$992$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$993$		0			0
$994$	0.345139	+	0.755750i	0.345139	+	0.755750i
$995$	0.0777324	−	0.540641i	0.0777324	−	0.540641i
$996$		0			0
$997$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$997$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$998$		0			0
$999$	−0.797176	−	0.234072i	−0.797176	−	0.234072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1932.1.bi.c.1511.1	yes	10
3.2	odd	2		1932.1.bi.a.1511.1	yes	10
4.3	odd	2		1932.1.bi.b.1511.1	yes	10
7.6	odd	2		1932.1.bi.d.1511.1	yes	10
12.11	even	2		1932.1.bi.d.1511.1	yes	10
21.20	even	2		1932.1.bi.b.1511.1	yes	10
23.13	even	11	inner	1932.1.bi.c.335.1	yes	10
28.27	even	2		1932.1.bi.a.1511.1	yes	10
69.59	odd	22		1932.1.bi.a.335.1	✓	10
84.83	odd	2	CM	1932.1.bi.c.1511.1	yes	10
92.59	odd	22		1932.1.bi.b.335.1	yes	10
161.13	odd	22		1932.1.bi.d.335.1	yes	10
276.59	even	22		1932.1.bi.d.335.1	yes	10
483.335	even	22		1932.1.bi.b.335.1	yes	10
644.335	even	22		1932.1.bi.a.335.1	✓	10
1932.335	odd	22	inner	1932.1.bi.c.335.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1932.1.bi.a.335.1	✓	10	69.59	odd	22
1932.1.bi.a.335.1	✓	10	644.335	even	22
1932.1.bi.a.1511.1	yes	10	3.2	odd	2
1932.1.bi.a.1511.1	yes	10	28.27	even	2
1932.1.bi.b.335.1	yes	10	92.59	odd	22
1932.1.bi.b.335.1	yes	10	483.335	even	22
1932.1.bi.b.1511.1	yes	10	4.3	odd	2
1932.1.bi.b.1511.1	yes	10	21.20	even	2
1932.1.bi.c.335.1	yes	10	23.13	even	11	inner
1932.1.bi.c.335.1	yes	10	1932.335	odd	22	inner
1932.1.bi.c.1511.1	yes	10	1.1	even	1	trivial
1932.1.bi.c.1511.1	yes	10	84.83	odd	2	CM
1932.1.bi.d.335.1	yes	10	161.13	odd	22
1932.1.bi.d.335.1	yes	10	276.59	even	22
1932.1.bi.d.1511.1	yes	10	7.6	odd	2
1932.1.bi.d.1511.1	yes	10	12.11	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)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.118239 + 0.258908i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.118239 + 0.258908i) q^{5} +(0.142315 - 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.273100 + 0.0801894i) q^{10} +(-1.25667 - 1.45027i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(-0.415415 + 0.909632i) q^{14} +(0.239446 + 0.153882i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.239446 - 1.66538i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.186393 + 1.29639i) q^{19} +(0.239446 - 0.153882i) q^{20} +(-0.654861 + 0.755750i) q^{21} -1.91899 q^{22} +(0.142315 + 0.989821i) q^{23} -1.00000 q^{24} +(0.601808 - 0.694523i) q^{25} +(-0.142315 - 0.989821i) q^{27} +(0.415415 + 0.909632i) q^{28} +(0.273100 - 0.0801894i) q^{30} +(1.41542 + 0.909632i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-1.84125 - 0.540641i) q^{33} +(-1.10181 - 1.27155i) q^{34} +(-0.186393 - 0.215109i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.345139 - 0.755750i) q^{37} +(1.10181 + 0.708089i) q^{38} +(0.0405070 - 0.281733i) q^{40} +(0.544078 + 1.19136i) q^{41} +(0.142315 + 0.989821i) q^{42} +(-1.25667 + 1.45027i) q^{44} +0.284630 q^{45} +(0.841254 + 0.540641i) q^{46} +(-0.654861 + 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.130785 - 0.909632i) q^{50} +(-0.698939 - 1.53046i) q^{51} +(-0.841254 - 0.540641i) q^{54} +(0.226900 - 0.496841i) q^{55} +(0.959493 + 0.281733i) q^{56} +(0.857685 + 0.989821i) q^{57} +(0.118239 - 0.258908i) q^{60} +(1.61435 - 0.474017i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-1.61435 + 1.03748i) q^{66} -1.68251 q^{68} +(0.654861 + 0.755750i) q^{69} -0.284630 q^{70} +(0.544078 - 0.627899i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(-0.345139 - 0.755750i) q^{74} +(0.130785 - 0.909632i) q^{75} +(1.25667 - 0.368991i) q^{76} +(1.61435 + 1.03748i) q^{77} +(-0.186393 - 0.215109i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(1.25667 + 0.368991i) q^{82} +(0.841254 + 0.540641i) q^{84} +(0.459493 - 0.134919i) q^{85} +(0.273100 + 1.89945i) q^{88} +(-0.698939 + 0.449181i) q^{89} +(0.186393 - 0.215109i) q^{90} +(0.959493 - 0.281733i) q^{92} +1.68251 q^{93} +(-0.313607 + 0.201543i) q^{95} +(0.142315 + 0.989821i) q^{96} +(0.142315 - 0.989821i) q^{98} +(-1.84125 + 0.540641i) 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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