LMFDB - Embedded newform 1932.1.bi.d.671.1

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			671.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	1932.671
Dual form			1932.1.bi.d.167.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-1.10181 - 0.708089i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-1.10181 - 0.708089i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.186393 + 1.29639i) q^{10} +(0.118239 - 0.258908i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(0.841254 - 0.540641i) q^{14} +(-1.25667 - 0.368991i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(1.25667 + 1.45027i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(0.544078 - 0.627899i) q^{19} +(1.25667 - 0.368991i) q^{20} +(0.415415 + 0.909632i) q^{21} -0.284630 q^{22} +(0.654861 - 0.755750i) q^{23} +1.00000 q^{24} +(0.297176 + 0.650724i) q^{25} +(0.654861 - 0.755750i) q^{27} +(-0.841254 - 0.540641i) q^{28} +(0.186393 + 1.29639i) q^{30} +(-1.84125 - 0.540641i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(0.0405070 - 0.281733i) q^{33} +(0.797176 - 1.74557i) q^{34} +(0.544078 - 1.19136i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(1.41542 - 0.909632i) q^{37} +(-0.797176 - 0.234072i) q^{38} +(-0.857685 - 0.989821i) q^{40} +(0.698939 + 0.449181i) q^{41} +(0.654861 - 0.755750i) q^{42} +(0.118239 + 0.258908i) q^{44} -1.30972 q^{45} +(-0.959493 - 0.281733i) q^{46} +(-0.415415 - 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(0.468468 - 0.540641i) q^{50} +(1.61435 + 1.03748i) q^{51} +(-0.959493 - 0.281733i) q^{54} +(-0.313607 + 0.201543i) q^{55} +(-0.142315 + 0.989821i) q^{56} +(0.345139 - 0.755750i) q^{57} +(1.10181 - 0.708089i) q^{60} +(0.273100 + 1.89945i) q^{62} +(0.654861 + 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.273100 + 0.0801894i) q^{66} -1.91899 q^{68} +(0.415415 - 0.909632i) q^{69} -1.30972 q^{70} +(-0.698939 - 1.53046i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-1.41542 - 0.909632i) q^{74} +(0.468468 + 0.540641i) q^{75} +(0.118239 + 0.822373i) q^{76} +(0.273100 + 0.0801894i) q^{77} +(-0.544078 + 1.19136i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.118239 - 0.822373i) q^{82} +(-0.959493 - 0.281733i) q^{84} +(-0.357685 - 2.48775i) q^{85} +(0.186393 - 0.215109i) q^{88} +(-1.61435 + 0.474017i) q^{89} +(0.544078 + 1.19136i) q^{90} +(0.142315 + 0.989821i) q^{92} -1.91899 q^{93} +(-1.04408 + 0.306569i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(0.654861 + 0.755750i) q^{98} +(-0.0405070 - 0.281733i) 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 $\left(\mathbb{Z}/1932\mathbb{Z}\right)^\times$.

$n$	$829$	$925$	$967$	$1289$
$\chi(n)$	$-1$	$e\left(\frac{2}{11}\right)$	$-1$	$-1$

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 $

$2$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$2$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$3$	0.959493	−	0.281733i	0.959493	−	0.281733i
$3$	0.959493	−	0.281733i	0.959493	−	0.281733i
$4$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$5$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$5$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$6$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$7$	0.142315	+	0.989821i	0.142315	+	0.989821i
$7$	0.142315	+	0.989821i	0.142315	+	0.989821i
$8$	0.959493	+	0.281733i	0.959493	+	0.281733i
$9$	0.841254	−	0.540641i	0.841254	−	0.540641i
$10$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$11$	0.118239	−	0.258908i	0.118239	−	0.258908i	−0.841254	−	0.540641i	$-0.818182\pi$
$11$	0.118239	−	0.258908i	0.118239	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$12$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$13$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$13$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$14$	0.841254	−	0.540641i	0.841254	−	0.540641i
$15$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$16$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$17$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$17$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$18$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$19$	0.544078	−	0.627899i	0.544078	−	0.627899i	−0.415415	−	0.909632i	$-0.636364\pi$
$19$	0.544078	−	0.627899i	0.544078	−	0.627899i	0.959493	+	0.281733i	$0.0909091\pi$
$20$	1.25667	−	0.368991i	1.25667	−	0.368991i
$21$	0.415415	+	0.909632i	0.415415	+	0.909632i
$22$	−0.284630			−0.284630
$23$	0.654861	−	0.755750i	0.654861	−	0.755750i
$23$	0.654861	−	0.755750i	0.654861	−	0.755750i
$24$	1.00000			1.00000
$25$	0.297176	+	0.650724i	0.297176	+	0.650724i
$26$		0			0
$27$	0.654861	−	0.755750i	0.654861	−	0.755750i
$28$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$29$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$29$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$30$	0.186393	+	1.29639i	0.186393	+	1.29639i
$31$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−0.841254	−	0.540641i	$-0.818182\pi$
$31$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−1.00000			$\pi$
$32$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$33$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$34$	0.797176	−	1.74557i	0.797176	−	1.74557i
$35$	0.544078	−	1.19136i	0.544078	−	1.19136i
$36$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$37$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$37$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$38$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$39$		0			0
$40$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$41$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$41$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$42$	0.654861	−	0.755750i	0.654861	−	0.755750i
$43$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$43$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$44$	0.118239	+	0.258908i	0.118239	+	0.258908i
$45$	−1.30972			−1.30972
$46$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$49$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$50$	0.468468	−	0.540641i	0.468468	−	0.540641i
$51$	1.61435	+	1.03748i	1.61435	+	1.03748i
$52$		0			0
$53$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$53$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$54$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$55$	−0.313607	+	0.201543i	−0.313607	+	0.201543i
$56$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$57$	0.345139	−	0.755750i	0.345139	−	0.755750i
$58$		0			0
$59$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$59$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$60$	1.10181	−	0.708089i	1.10181	−	0.708089i
$61$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$61$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$62$	0.273100	+	1.89945i	0.273100	+	1.89945i
$63$	0.654861	+	0.755750i	0.654861	+	0.755750i
$64$	0.841254	+	0.540641i	0.841254	+	0.540641i
$65$		0			0
$66$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$67$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$67$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$68$	−1.91899			−1.91899
$69$	0.415415	−	0.909632i	0.415415	−	0.909632i
$70$	−1.30972			−1.30972
$71$	−0.698939	−	1.53046i	−0.698939	−	1.53046i	−0.841254	−	0.540641i	$-0.818182\pi$
$71$	−0.698939	−	1.53046i	−0.698939	−	1.53046i	0.142315	−	0.989821i	$-0.454545\pi$
$72$	0.959493	−	0.281733i	0.959493	−	0.281733i
$73$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$73$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$74$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$75$	0.468468	+	0.540641i	0.468468	+	0.540641i
$76$	0.118239	+	0.822373i	0.118239	+	0.822373i
$77$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$78$		0			0
$79$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$79$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$80$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$81$	0.415415	−	0.909632i	0.415415	−	0.909632i
$82$	0.118239	−	0.822373i	0.118239	−	0.822373i
$83$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$83$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$84$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$85$	−0.357685	−	2.48775i	−0.357685	−	2.48775i
$86$		0			0
$87$		0			0
$88$	0.186393	−	0.215109i	0.186393	−	0.215109i
$89$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$89$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$90$	0.544078	+	1.19136i	0.544078	+	1.19136i
$91$		0			0
$92$	0.142315	+	0.989821i	0.142315	+	0.989821i
$93$	−1.91899			−1.91899
$94$		0			0
$95$	−1.04408	+	0.306569i	−1.04408	+	0.306569i
$96$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$97$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$97$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$98$	0.654861	+	0.755750i	0.654861	+	0.755750i
$99$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$100$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$101$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$101$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$102$	0.273100	−	1.89945i	0.273100	−	1.89945i
$103$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$103$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	−0.841254	+	0.540641i	$0.818182\pi$
$104$		0			0
$105$	0.186393	−	1.29639i	0.186393	−	1.29639i
$106$		0			0
$107$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.654861	−	0.755750i	$-0.272727\pi$
$107$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.142315	+	0.989821i	$0.454545\pi$
$108$	0.142315	+	0.989821i	0.142315	+	0.989821i
$109$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$109$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$110$	0.313607	+	0.201543i	0.313607	+	0.201543i
$111$	1.10181	−	1.27155i	1.10181	−	1.27155i
$112$	0.959493	−	0.281733i	0.959493	−	0.281733i
$113$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$113$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$114$	−0.830830			−0.830830
$115$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$120$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$121$	0.601808	+	0.694523i	0.601808	+	0.694523i
$122$		0			0
$123$	0.797176	+	0.234072i	0.797176	+	0.234072i
$124$	1.61435	−	1.03748i	1.61435	−	1.03748i
$125$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$126$	0.415415	−	0.909632i	0.415415	−	0.909632i
$127$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$127$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$128$	0.142315	−	0.989821i	0.142315	−	0.989821i
$129$		0			0
$130$		0			0
$131$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$131$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$132$	0.186393	+	0.215109i	0.186393	+	0.215109i
$133$	0.698939	+	0.449181i	0.698939	+	0.449181i
$134$		0			0
$135$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$136$	0.797176	+	1.74557i	0.797176	+	1.74557i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	−1.00000			−1.00000
$139$	−0.830830			−0.830830			−0.415415	−	0.909632i	$-0.636364\pi$
$139$	−0.830830			−0.830830			−0.415415	+	0.909632i	$0.636364\pi$
$140$	0.544078	+	1.19136i	0.544078	+	1.19136i
$141$		0			0
$142$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$143$		0			0
$144$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$145$		0			0
$146$		0			0
$147$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$148$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$149$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$149$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$150$	0.297176	−	0.650724i	0.297176	−	0.650724i
$151$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$151$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$152$	0.698939	−	0.449181i	0.698939	−	0.449181i
$153$	1.84125	+	0.540641i	1.84125	+	0.540641i
$154$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$155$	1.64589	+	1.89945i	1.64589	+	1.89945i
$156$		0			0
$157$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$157$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$158$		0			0
$159$		0			0
$160$	1.30972			1.30972
$161$	0.841254	+	0.540641i	0.841254	+	0.540641i
$162$	−1.00000			−1.00000
$163$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$163$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$164$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$165$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$166$		0			0
$167$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$167$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$168$	0.142315	+	0.989821i	0.142315	+	0.989821i
$169$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$170$	−2.11435	+	1.35881i	−2.11435	+	1.35881i
$171$	0.118239	−	0.822373i	0.118239	−	0.822373i
$172$		0			0
$173$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$173$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$174$		0			0
$175$	−0.601808	+	0.386758i	−0.601808	+	0.386758i
$176$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$177$		0			0
$178$	1.10181	+	1.27155i	1.10181	+	1.27155i
$179$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−0.415415	−	0.909632i	$-0.636364\pi$
$179$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−1.00000			$\pi$
$180$	0.857685	−	0.989821i	0.857685	−	0.989821i
$181$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$181$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$182$		0			0
$183$		0			0
$184$	0.841254	−	0.540641i	0.841254	−	0.540641i
$185$	−2.20362			−2.20362
$186$	0.797176	+	1.74557i	0.797176	+	1.74557i
$187$	0.524075	−	0.153882i	0.524075	−	0.153882i
$188$		0			0
$189$	0.841254	+	0.540641i	0.841254	+	0.540641i
$190$	0.712591	+	0.822373i	0.712591	+	0.822373i
$191$	0.239446	+	1.66538i	0.239446	+	1.66538i	0.654861	+	0.755750i	$0.272727\pi$
$191$	0.239446	+	1.66538i	0.239446	+	1.66538i	−0.415415	+	0.909632i	$0.636364\pi$
$192$	0.959493	+	0.281733i	0.959493	+	0.281733i
$193$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$193$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$194$		0			0
$195$		0			0
$196$	0.415415	−	0.909632i	0.415415	−	0.909632i
$197$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$197$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$198$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$199$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i	0.142315	−	0.989821i	$-0.454545\pi$
$199$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i	−0.415415	+	0.909632i	$0.636364\pi$
$200$	0.101808	+	0.708089i	0.101808	+	0.708089i
$201$		0			0
$202$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$203$		0			0
$204$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$205$	−0.452036	−	0.989821i	−0.452036	−	0.989821i
$206$	1.68251			1.68251
$207$	0.142315	−	0.989821i	0.142315	−	0.989821i
$208$		0			0
$209$	−0.0982369	−	0.215109i	−0.0982369	−	0.215109i
$210$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$211$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$211$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$212$		0			0
$213$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$214$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$215$		0			0
$216$	0.841254	−	0.540641i	0.841254	−	0.540641i
$217$	0.273100	−	1.89945i	0.273100	−	1.89945i
$218$	0.797176	−	1.74557i	0.797176	−	1.74557i
$219$		0			0
$220$	0.0530529	−	0.368991i	0.0530529	−	0.368991i
$221$		0			0
$222$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$223$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	−0.841254	−	0.540641i	$-0.818182\pi$
$223$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	0.654861	−	0.755750i	$-0.272727\pi$
$224$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$225$	0.601808	+	0.386758i	0.601808	+	0.386758i
$226$		0			0
$227$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$227$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$228$	0.345139	+	0.755750i	0.345139	+	0.755750i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	0.857685	+	0.989821i	0.857685	+	0.989821i
$231$	0.284630			0.284630
$232$		0			0
$233$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$233$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	1.84125	+	0.540641i	1.84125	+	0.540641i
$239$	0.239446	−	0.153882i	0.239446	−	0.153882i	−0.415415	−	0.909632i	$-0.636364\pi$
$239$	0.239446	−	0.153882i	0.239446	−	0.153882i	0.654861	+	0.755750i	$0.272727\pi$
$240$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$241$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$241$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$242$	0.381761	−	0.835939i	0.381761	−	0.835939i
$243$	0.142315	−	0.989821i	0.142315	−	0.989821i
$244$		0			0
$245$	1.25667	+	0.368991i	1.25667	+	0.368991i
$246$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$247$		0			0
$248$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$249$		0			0
$250$	0.357685	−	0.105026i	0.357685	−	0.105026i
$251$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$251$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$252$	−1.00000			−1.00000
$253$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$254$		0			0
$255$	−1.04408	−	2.28621i	−1.04408	−	2.28621i
$256$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$257$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$257$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$258$		0			0
$259$	1.10181	+	1.27155i	1.10181	+	1.27155i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	0.142315	+	0.989821i	$0.454545\pi$
$263$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	−0.415415	+	0.909632i	$0.636364\pi$
$264$	0.118239	−	0.258908i	0.118239	−	0.258908i
$265$		0			0
$266$	0.118239	−	0.822373i	0.118239	−	0.822373i
$267$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$268$		0			0
$269$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$269$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$270$	0.857685	+	0.989821i	0.857685	+	0.989821i
$271$	0.239446	+	0.153882i	0.239446	+	0.153882i	0.654861	−	0.755750i	$-0.272727\pi$
$271$	0.239446	+	0.153882i	0.239446	+	0.153882i	−0.415415	+	0.909632i	$0.636364\pi$
$272$	1.25667	−	1.45027i	1.25667	−	1.45027i
$273$		0			0
$274$		0			0
$275$	0.203616			0.203616
$276$	0.415415	+	0.909632i	0.415415	+	0.909632i
$277$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$277$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$278$	0.345139	+	0.755750i	0.345139	+	0.755750i
$279$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$280$	0.857685	−	0.989821i	0.857685	−	0.989821i
$281$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$281$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$282$		0			0
$283$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	0.959493	−	0.281733i	$-0.0909091\pi$
$283$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	−1.00000			$\pi$
$284$	1.61435	+	0.474017i	1.61435	+	0.474017i
$285$	−0.915415	+	0.588302i	−0.915415	+	0.588302i
$286$		0			0
$287$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$288$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$289$	−0.381761	+	2.65520i	−0.381761	+	2.65520i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$293$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$294$	0.841254	+	0.540641i	0.841254	+	0.540641i
$295$		0			0
$296$	1.61435	−	0.474017i	1.61435	−	0.474017i
$297$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$298$		0			0
$299$		0			0
$300$	−0.715370			−0.715370
$301$		0			0
$302$		0			0
$303$	1.10181	−	1.27155i	1.10181	−	1.27155i
$304$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$305$		0			0
$306$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$307$	−1.25667	−	0.368991i	−1.25667	−	0.368991i	−0.415415	−	0.909632i	$-0.636364\pi$
$307$	−1.25667	−	0.368991i	−1.25667	−	0.368991i	−0.841254	+	0.540641i	$0.818182\pi$
$308$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$309$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$310$	1.04408	−	2.28621i	1.04408	−	2.28621i
$311$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$311$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$312$		0			0
$313$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$313$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$314$		0			0
$315$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$316$		0			0
$317$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$317$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$318$		0			0
$319$		0			0
$320$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$321$	0.830830			0.830830
$322$	0.142315	−	0.989821i	0.142315	−	0.989821i
$323$	1.59435			1.59435
$324$	0.415415	+	0.909632i	0.415415	+	0.909632i
$325$		0			0
$326$		0			0
$327$	1.61435	+	1.03748i	1.61435	+	1.03748i
$328$	0.544078	+	0.627899i	0.544078	+	0.627899i
$329$		0			0
$330$	0.357685	+	0.105026i	0.357685	+	0.105026i
$331$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$331$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$332$		0			0
$333$	0.698939	−	1.53046i	0.698939	−	1.53046i
$334$		0			0
$335$		0			0
$336$	0.841254	−	0.540641i	0.841254	−	0.540641i
$337$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$337$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$338$	0.142315	+	0.989821i	0.142315	+	0.989821i
$339$		0			0
$340$	2.11435	+	1.35881i	2.11435	+	1.35881i
$341$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$342$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$343$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$344$		0			0
$345$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$346$	1.30972			1.30972
$347$	0.118239	+	0.258908i	0.118239	+	0.258908i	0.959493	−	0.281733i	$-0.0909091\pi$
$347$	0.118239	+	0.258908i	0.118239	+	0.258908i	−0.841254	+	0.540641i	$0.818182\pi$
$348$		0			0
$349$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$349$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$350$	0.601808	+	0.386758i	0.601808	+	0.386758i
$351$		0			0
$352$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$353$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$353$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$354$		0			0
$355$	−0.313607	+	2.18119i	−0.313607	+	2.18119i
$356$	0.698939	−	1.53046i	0.698939	−	1.53046i
$357$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$358$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$359$	−1.68251	+	1.08128i	−1.68251	+	1.08128i	−0.841254	+	0.540641i	$0.818182\pi$
$359$	−1.68251	+	1.08128i	−1.68251	+	1.08128i	−0.841254	+	0.540641i	$0.818182\pi$
$360$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$361$	0.0440780	+	0.306569i	0.0440780	+	0.306569i
$362$		0			0
$363$	0.773100	+	0.496841i	0.773100	+	0.496841i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$367$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$368$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$369$	0.830830			0.830830
$370$	0.915415	+	2.00448i	0.915415	+	2.00448i
$371$		0			0
$372$	1.25667	−	1.45027i	1.25667	−	1.45027i
$373$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$373$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$374$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$375$	0.0530529	+	0.368991i	0.0530529	+	0.368991i
$376$		0			0
$377$		0			0
$378$	0.142315	−	0.989821i	0.142315	−	0.989821i
$379$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$379$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$380$	0.452036	−	0.989821i	0.452036	−	0.989821i
$381$		0			0
$382$	1.41542	−	0.909632i	1.41542	−	0.909632i
$383$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$383$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$384$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$385$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$386$	1.10181	+	0.708089i	1.10181	+	0.708089i
$387$		0			0
$388$		0			0
$389$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$389$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$390$		0			0
$391$	1.91899			1.91899
$392$	−1.00000			−1.00000
$393$		0			0
$394$		0			0
$395$		0			0
$396$	0.239446	+	0.153882i	0.239446	+	0.153882i
$397$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$397$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$398$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$399$	0.797176	+	0.234072i	0.797176	+	0.234072i
$400$	0.601808	−	0.386758i	0.601808	−	0.386758i
$401$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$401$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$402$		0			0
$403$		0			0
$404$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$405$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$406$		0			0
$407$	−0.0681534	−	0.474017i	−0.0681534	−	0.474017i
$408$	1.25667	+	1.45027i	1.25667	+	1.45027i
$409$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$409$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$410$	−0.712591	+	0.822373i	−0.712591	+	0.822373i
$411$		0			0
$412$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$413$		0			0
$414$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$415$		0			0
$416$		0			0
$417$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$418$	−0.154861	+	0.178719i	−0.154861	+	0.178719i
$419$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$419$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$420$	0.857685	+	0.989821i	0.857685	+	0.989821i
$421$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$421$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.570276	+	1.24873i	−0.570276	+	1.24873i
$426$	−0.698939	+	1.53046i	−0.698939	+	1.53046i
$427$		0			0
$428$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$429$		0			0
$430$		0			0
$431$	0.544078	+	0.627899i	0.544078	+	0.627899i	0.959493	−	0.281733i	$-0.0909091\pi$
$431$	0.544078	+	0.627899i	0.544078	+	0.627899i	−0.415415	+	0.909632i	$0.636364\pi$
$432$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$433$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$433$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$434$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$435$		0			0
$436$	−1.91899			−1.91899
$437$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$438$		0			0
$439$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.654861	+	0.755750i	$0.272727\pi$
$439$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.142315	+	0.989821i	$0.454545\pi$
$440$	−0.357685	+	0.105026i	−0.357685	+	0.105026i
$441$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$442$		0			0
$443$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.841254	−	0.540641i	$-0.818182\pi$
$443$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.415415	−	0.909632i	$-0.636364\pi$
$444$	0.239446	+	1.66538i	0.239446	+	1.66538i
$445$	2.11435	+	0.620830i	2.11435	+	0.620830i
$446$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$447$		0			0
$448$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$449$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$449$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$450$	0.101808	−	0.708089i	0.101808	−	0.708089i
$451$	0.198939	−	0.127850i	0.198939	−	0.127850i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	0.544078	−	0.627899i	0.544078	−	0.627899i
$457$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$457$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$458$		0			0
$459$	1.91899			1.91899
$460$	0.544078	−	1.19136i	0.544078	−	1.19136i
$461$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$461$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$462$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$463$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$463$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$464$		0			0
$465$	2.11435	+	1.35881i	2.11435	+	1.35881i
$466$		0			0
$467$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$467$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.570276	+	0.167448i	0.570276	+	0.167448i
$476$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$477$		0			0
$478$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$479$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$479$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$480$	1.25667	−	0.368991i	1.25667	−	0.368991i
$481$		0			0
$482$		0			0
$483$	0.959493	+	0.281733i	0.959493	+	0.281733i
$484$	−0.918986			−0.918986
$485$		0			0
$486$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$487$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$487$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$488$		0			0
$489$		0			0
$490$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$491$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.654861	−	0.755750i	$-0.272727\pi$
$491$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.142315	+	0.989821i	$0.454545\pi$
$492$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$493$		0			0
$494$		0			0
$495$	−0.154861	+	0.339098i	−0.154861	+	0.339098i
$496$	−0.273100	+	1.89945i	−0.273100	+	1.89945i
$497$	1.41542	−	0.909632i	1.41542	−	0.909632i
$498$		0			0
$499$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$499$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$500$	−0.244123	−	0.281733i	−0.244123	−	0.281733i
$501$		0			0
$502$		0			0
$503$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$503$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$504$	0.415415	+	0.909632i	0.415415	+	0.909632i
$505$	−2.20362			−2.20362
$506$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$507$	−1.00000			−1.00000
$508$		0			0
$509$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$509$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$510$	−1.64589	+	1.89945i	−1.64589	+	1.89945i
$511$		0			0
$512$	0.654861	+	0.755750i	0.654861	+	0.755750i
$513$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$514$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$515$	1.85380	−	1.19136i	1.85380	−	1.19136i
$516$		0			0
$517$		0			0
$518$	0.698939	−	1.53046i	0.698939	−	1.53046i
$519$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$520$		0			0
$521$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$521$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$522$		0			0
$523$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$523$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$524$		0			0
$525$	−0.468468	+	0.540641i	−0.468468	+	0.540641i
$526$	1.84125	−	0.540641i	1.84125	−	0.540641i
$527$	−1.52977	−	3.34973i	−1.52977	−	3.34973i
$528$	−0.284630			−0.284630
$529$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$530$		0			0
$531$		0			0
$532$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$533$		0			0
$534$	1.41542	+	0.909632i	1.41542	+	0.909632i
$535$	−0.712591	−	0.822373i	−0.712591	−	0.822373i
$536$		0			0
$537$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$538$	0.239446	−	0.153882i	0.239446	−	0.153882i
$539$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$540$	0.544078	−	1.19136i	0.544078	−	1.19136i
$541$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$541$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$542$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$543$		0			0
$544$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$545$	−0.357685	−	2.48775i	−0.357685	−	2.48775i
$546$		0			0
$547$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$547$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$548$		0			0
$549$		0			0
$550$	−0.0845850	−	0.185215i	−0.0845850	−	0.185215i
$551$		0			0
$552$	0.654861	−	0.755750i	0.654861	−	0.755750i
$553$		0			0
$554$	0.544078	+	1.19136i	0.544078	+	1.19136i
$555$	−2.11435	+	0.620830i	−2.11435	+	0.620830i
$556$	0.544078	−	0.627899i	0.544078	−	0.627899i
$557$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$557$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$558$	1.25667	+	1.45027i	1.25667	+	1.45027i
$559$		0			0
$560$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$561$	0.459493	−	0.295298i	0.459493	−	0.295298i
$562$		0			0
$563$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$563$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$564$		0			0
$565$		0			0
$566$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$567$	0.959493	+	0.281733i	0.959493	+	0.281733i
$568$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$569$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$569$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$570$	0.915415	+	0.588302i	0.915415	+	0.588302i
$571$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$571$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$572$		0			0
$573$	0.698939	+	1.53046i	0.698939	+	1.53046i
$574$	0.830830			0.830830
$575$	0.686393	+	0.201543i	0.686393	+	0.201543i
$576$	1.00000			1.00000
$577$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$577$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$578$	2.57385	−	0.755750i	2.57385	−	0.755750i
$579$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$587$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$587$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$588$	0.142315	−	0.989821i	0.142315	−	0.989821i
$589$	−1.34125	+	0.861971i	−1.34125	+	0.861971i
$590$		0			0
$591$		0			0
$592$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$593$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$593$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$594$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$595$	2.41153	−	0.708089i	2.41153	−	0.708089i
$596$		0			0
$597$	−0.284630			−0.284630
$598$		0			0
$599$	−0.830830			−0.830830			−0.415415	−	0.909632i	$-0.636364\pi$
$599$	−0.830830			−0.830830			−0.415415	+	0.909632i	$0.636364\pi$
$600$	0.297176	+	0.650724i	0.297176	+	0.650724i
$601$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$601$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.171292	−	1.19136i	−0.171292	−	1.19136i
$606$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$607$	0.239446	−	0.153882i	0.239446	−	0.153882i	−0.415415	−	0.909632i	$-0.636364\pi$
$607$	0.239446	−	0.153882i	0.239446	−	0.153882i	0.654861	+	0.755750i	$0.272727\pi$
$608$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$613$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$613$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$614$	0.186393	+	1.29639i	0.186393	+	1.29639i
$615$	−0.712591	−	0.822373i	−0.712591	−	0.822373i
$616$	0.239446	+	0.153882i	0.239446	+	0.153882i
$617$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$617$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$618$	1.61435	−	0.474017i	1.61435	−	0.474017i
$619$	−0.698939	−	1.53046i	−0.698939	−	1.53046i	−0.841254	−	0.540641i	$-0.818182\pi$
$619$	−0.698939	−	1.53046i	−0.698939	−	1.53046i	0.142315	−	0.989821i	$-0.454545\pi$
$620$	−2.51334			−2.51334
$621$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$622$		0			0
$623$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$624$		0			0
$625$	0.788201	−	0.909632i	0.788201	−	0.909632i
$626$		0			0
$627$	−0.154861	−	0.178719i	−0.154861	−	0.178719i
$628$		0			0
$629$	3.09792	+	0.909632i	3.09792	+	0.909632i
$630$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$631$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$631$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$640$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$641$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$641$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$642$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$643$	0.284630			0.284630			0.142315	−	0.989821i	$-0.454545\pi$
$643$	0.284630			0.284630			0.142315	+	0.989821i	$0.454545\pi$
$644$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$645$		0			0
$646$	−0.662317	−	1.45027i	−0.662317	−	1.45027i
$647$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$647$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$648$	0.654861	−	0.755750i	0.654861	−	0.755750i
$649$		0			0
$650$		0			0
$651$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$652$		0			0
$653$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$653$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$654$	0.273100	−	1.89945i	0.273100	−	1.89945i
$655$		0			0
$656$	0.345139	−	0.755750i	0.345139	−	0.755750i
$657$		0			0
$658$		0			0
$659$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−0.841254	−	0.540641i	$-0.818182\pi$
$659$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−1.00000			$\pi$
$660$	−0.0530529	−	0.368991i	−0.0530529	−	0.368991i
$661$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$661$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.452036	−	0.989821i	−0.452036	−	0.989821i
$666$	−1.68251			−1.68251
$667$		0			0
$668$		0			0
$669$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$670$		0			0
$671$		0			0
$672$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$673$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$673$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$674$	0.118239	+	0.822373i	0.118239	+	0.822373i
$675$	0.686393	+	0.201543i	0.686393	+	0.201543i
$676$	0.841254	−	0.540641i	0.841254	−	0.540641i
$677$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$677$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$678$		0			0
$679$		0			0
$680$	0.357685	−	2.48775i	0.357685	−	2.48775i
$681$		0			0
$682$	0.524075	+	0.153882i	0.524075	+	0.153882i
$683$	0.118239	+	0.822373i	0.118239	+	0.822373i	0.959493	+	0.281733i	$0.0909091\pi$
$683$	0.118239	+	0.822373i	0.118239	+	0.822373i	−0.841254	+	0.540641i	$0.818182\pi$
$684$	0.544078	+	0.627899i	0.544078	+	0.627899i
$685$		0			0
$686$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$687$		0			0
$688$		0			0
$689$		0			0
$690$	1.10181	+	0.708089i	1.10181	+	0.708089i
$691$	−1.68251			−1.68251			−0.841254	−	0.540641i	$-0.818182\pi$
$691$	−1.68251			−1.68251			−0.841254	+	0.540641i	$0.818182\pi$
$692$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$693$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$694$	0.186393	−	0.215109i	0.186393	−	0.215109i
$695$	0.915415	+	0.588302i	0.915415	+	0.588302i
$696$		0			0
$697$	0.226900	+	1.57812i	0.226900	+	1.57812i
$698$		0			0
$699$		0			0
$700$	0.101808	−	0.708089i	0.101808	−	0.708089i
$701$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$701$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$702$		0			0
$703$	0.198939	−	1.38365i	0.198939	−	1.38365i
$704$	0.239446	−	0.153882i	0.239446	−	0.153882i
$705$		0			0
$706$	0.118239	+	0.822373i	0.118239	+	0.822373i
$707$	1.10181	+	1.27155i	1.10181	+	1.27155i
$708$		0			0
$709$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$709$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$710$	2.11435	−	0.620830i	2.11435	−	0.620830i
$711$		0			0
$712$	−1.68251			−1.68251
$713$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$714$	1.91899			1.91899
$715$		0			0
$716$	1.61435	−	0.474017i	1.61435	−	0.474017i
$717$	0.186393	−	0.215109i	0.186393	−	0.215109i
$718$	1.68251	+	1.08128i	1.68251	+	1.08128i
$719$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$719$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$720$	0.186393	+	1.29639i	0.186393	+	1.29639i
$721$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$722$	0.260554	−	0.167448i	0.260554	−	0.167448i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.130785	−	0.909632i	0.130785	−	0.909632i
$727$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	−0.841254	−	0.540641i	$-0.818182\pi$
$727$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	0.142315	+	0.989821i	$0.454545\pi$
$728$		0			0
$729$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$733$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$734$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$735$	1.30972			1.30972
$736$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$737$		0			0
$738$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$739$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$739$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$740$	1.44306	−	1.66538i	1.44306	−	1.66538i
$741$		0			0
$742$		0			0
$743$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	−0.841254	−	0.540641i	$-0.818182\pi$
$743$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	0.654861	−	0.755750i	$-0.272727\pi$
$744$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$745$		0			0
$746$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$747$		0			0
$748$	−0.226900	+	0.496841i	−0.226900	+	0.496841i
$749$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$750$	0.313607	−	0.201543i	0.313607	−	0.201543i
$751$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$751$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$757$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$757$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$758$		0			0
$759$	−0.186393	−	0.215109i	−0.186393	−	0.215109i
$760$	−1.08816			−1.08816
$761$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$761$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$762$		0			0
$763$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$764$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$765$	−1.64589	−	1.89945i	−1.64589	−	1.89945i
$766$		0			0
$767$		0			0
$768$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$769$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$769$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$770$	−0.154861	+	0.339098i	−0.154861	+	0.339098i
$771$	0.544078	−	1.19136i	0.544078	−	1.19136i
$772$	0.186393	−	1.29639i	0.186393	−	1.29639i
$773$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$773$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$774$		0			0
$775$	−0.195368	−	1.35881i	−0.195368	−	1.35881i
$776$		0			0
$777$	1.41542	+	0.909632i	1.41542	+	0.909632i
$778$		0			0
$779$	0.662317	−	0.194474i	0.662317	−	0.194474i
$780$		0			0
$781$	−0.478891			−0.478891
$782$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$783$		0			0
$784$	0.415415	+	0.909632i	0.415415	+	0.909632i
$785$		0			0
$786$		0			0
$787$	−0.698939	−	0.449181i	−0.698939	−	0.449181i	0.142315	−	0.989821i	$-0.454545\pi$
$787$	−0.698939	−	0.449181i	−0.698939	−	0.449181i	−0.841254	+	0.540641i	$0.818182\pi$
$788$		0			0
$789$	0.273100	+	1.89945i	0.273100	+	1.89945i
$790$		0			0
$791$		0			0
$792$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.239446	−	0.153882i	0.239446	−	0.153882i
$797$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$797$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$798$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$799$		0			0
$800$	−0.601808	−	0.386758i	−0.601808	−	0.386758i
$801$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$806$		0			0
$807$	0.118239	+	0.258908i	0.118239	+	0.258908i
$808$	1.61435	−	0.474017i	1.61435	−	0.474017i
$809$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$809$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$810$	1.10181	+	0.708089i	1.10181	+	0.708089i
$811$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	0.142315	−	0.989821i	$-0.454545\pi$
$811$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	−1.00000			$\pi$
$812$		0			0
$813$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$814$	−0.402869	+	0.258908i	−0.402869	+	0.258908i
$815$		0			0
$816$	0.797176	−	1.74557i	0.797176	−	1.74557i
$817$		0			0
$818$		0			0
$819$		0			0
$820$	1.04408	+	0.306569i	1.04408	+	0.306569i
$821$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$821$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$822$		0			0
$823$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$823$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$824$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$825$	0.195368	−	0.0573652i	0.195368	−	0.0573652i
$826$		0			0
$827$	1.30972			1.30972			0.654861	−	0.755750i	$-0.272727\pi$
$827$	1.30972			1.30972			0.654861	+	0.755750i	$0.272727\pi$
$828$	0.654861	+	0.755750i	0.654861	+	0.755750i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$832$		0			0
$833$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$834$	0.544078	+	0.627899i	0.544078	+	0.627899i
$835$		0			0
$836$	0.226900	+	0.0666238i	0.226900	+	0.0666238i
$837$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$838$		0			0
$839$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$839$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$840$	0.544078	−	1.19136i	0.544078	−	1.19136i
$841$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$842$	1.10181	−	0.708089i	1.10181	−	0.708089i
$843$		0			0
$844$		0			0
$845$	0.857685	+	0.989821i	0.857685	+	0.989821i
$846$		0			0
$847$	−0.601808	+	0.694523i	−0.601808	+	0.694523i
$848$		0			0
$849$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$850$	1.37279			1.37279
$851$	0.239446	−	1.66538i	0.239446	−	1.66538i
$852$	1.68251			1.68251
$853$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$853$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$854$		0			0
$855$	−0.712591	+	0.822373i	−0.712591	+	0.822373i
$856$	0.698939	+	0.449181i	0.698939	+	0.449181i
$857$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$857$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$858$		0			0
$859$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.959493	−	0.281733i	$-0.0909091\pi$
$859$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.654861	+	0.755750i	$0.272727\pi$
$860$		0			0
$861$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$862$	0.345139	−	0.755750i	0.345139	−	0.755750i
$863$	0.118239	−	0.258908i	0.118239	−	0.258908i	−0.841254	−	0.540641i	$-0.818182\pi$
$863$	0.118239	−	0.258908i	0.118239	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$864$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$865$	1.44306	−	0.927399i	1.44306	−	0.927399i
$866$		0			0
$867$	0.381761	+	2.65520i	0.381761	+	2.65520i
$868$	1.25667	+	1.45027i	1.25667	+	1.45027i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.797176	+	1.74557i	0.797176	+	1.74557i
$873$		0			0
$874$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$875$	−0.372786			−0.372786
$876$		0			0
$877$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$877$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$878$	1.25667	−	1.45027i	1.25667	−	1.45027i
$879$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$880$	0.244123	+	0.281733i	0.244123	+	0.281733i
$881$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$881$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$882$	0.959493	+	0.281733i	0.959493	+	0.281733i
$883$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$883$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$884$		0			0
$885$		0			0
$886$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$887$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$887$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$888$	1.41542	−	0.909632i	1.41542	−	0.909632i
$889$		0			0
$890$	−0.313607	−	2.18119i	−0.313607	−	2.18119i
$891$	−0.186393	−	0.215109i	−0.186393	−	0.215109i
$892$	1.10181	+	0.708089i	1.10181	+	0.708089i
$893$		0			0
$894$		0			0
$895$	0.915415	+	2.00448i	0.915415	+	2.00448i
$896$	1.00000			1.00000
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.686393	+	0.201543i	−0.686393	+	0.201543i
$901$		0			0
$902$	−0.198939	−	0.127850i	−0.198939	−	0.127850i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$907$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$908$		0			0
$909$	0.698939	−	1.53046i	0.698939	−	1.53046i
$910$		0			0
$911$	1.61435	−	1.03748i	1.61435	−	1.03748i	0.654861	−	0.755750i	$-0.272727\pi$
$911$	1.61435	−	1.03748i	1.61435	−	1.03748i	0.959493	−	0.281733i	$-0.0909091\pi$
$912$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$913$		0			0
$914$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	−1.30972			−1.30972
$921$	−1.30972			−1.30972
$922$	0.544078	+	1.19136i	0.544078	+	1.19136i
$923$		0			0
$924$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$925$	1.01255	+	0.650724i	1.01255	+	0.650724i
$926$		0			0
$927$	0.239446	+	1.66538i	0.239446	+	1.66538i
$928$		0			0
$929$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.959493	−	0.281733i	$-0.909091\pi$
$929$	−1.10181	+	0.708089i	−1.10181	+	0.708089i	−0.142315	+	0.989821i	$0.545455\pi$
$930$	0.357685	−	2.48775i	0.357685	−	2.48775i
$931$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.686393	−	0.201543i	−0.686393	−	0.201543i
$936$		0			0
$937$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$937$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$941$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$942$		0			0
$943$	0.797176	−	0.234072i	0.797176	−	0.234072i
$944$		0			0
$945$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$946$		0			0
$947$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.142315	−	0.989821i	$-0.454545\pi$
$947$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.959493	−	0.281733i	$-0.0909091\pi$
$948$		0			0
$949$		0			0
$950$	−0.0845850	−	0.588302i	−0.0845850	−	0.588302i
$951$		0			0
$952$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$953$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$953$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$954$		0			0
$955$	0.915415	−	2.00448i	0.915415	−	2.00448i
$956$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$961$	2.25667	+	1.45027i	2.25667	+	1.45027i
$962$		0			0
$963$	0.797176	−	0.234072i	0.797176	−	0.234072i
$964$		0			0
$965$	1.71537			1.71537
$966$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.381761	+	0.835939i	0.381761	+	0.835939i
$969$	1.52977	−	0.449181i	1.52977	−	0.449181i
$970$		0			0
$971$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$971$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$972$	0.654861	+	0.755750i	0.654861	+	0.755750i
$973$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$977$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$978$		0			0
$979$	−0.0681534	+	0.474017i	−0.0681534	+	0.474017i
$980$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$981$	1.84125	+	0.540641i	1.84125	+	0.540641i
$982$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$983$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$983$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$984$	0.698939	+	0.449181i	0.698939	+	0.449181i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	0.372786			0.372786
$991$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$991$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$992$	1.84125	−	0.540641i	1.84125	−	0.540641i
$993$		0			0
$994$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$995$	0.244123	+	0.281733i	0.244123	+	0.281733i
$996$		0			0
$997$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$997$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$998$		0			0
$999$	0.239446	−	1.66538i	0.239446	−	1.66538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1932.1.bi.d.671.1	yes	10
3.2	odd	2		1932.1.bi.b.671.1	yes	10
4.3	odd	2		1932.1.bi.a.671.1	yes	10
7.6	odd	2		1932.1.bi.c.671.1	yes	10
12.11	even	2		1932.1.bi.c.671.1	yes	10
21.20	even	2		1932.1.bi.a.671.1	yes	10
23.6	even	11	inner	1932.1.bi.d.167.1	yes	10
28.27	even	2		1932.1.bi.b.671.1	yes	10
69.29	odd	22		1932.1.bi.b.167.1	yes	10
84.83	odd	2	CM	1932.1.bi.d.671.1	yes	10
92.75	odd	22		1932.1.bi.a.167.1	✓	10
161.6	odd	22		1932.1.bi.c.167.1	yes	10
276.167	even	22		1932.1.bi.c.167.1	yes	10
483.167	even	22		1932.1.bi.a.167.1	✓	10
644.167	even	22		1932.1.bi.b.167.1	yes	10
1932.167	odd	22	inner	1932.1.bi.d.167.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1932.1.bi.a.167.1	✓	10	92.75	odd	22
1932.1.bi.a.167.1	✓	10	483.167	even	22
1932.1.bi.a.671.1	yes	10	4.3	odd	2
1932.1.bi.a.671.1	yes	10	21.20	even	2
1932.1.bi.b.167.1	yes	10	69.29	odd	22
1932.1.bi.b.167.1	yes	10	644.167	even	22
1932.1.bi.b.671.1	yes	10	3.2	odd	2
1932.1.bi.b.671.1	yes	10	28.27	even	2
1932.1.bi.c.167.1	yes	10	161.6	odd	22
1932.1.bi.c.167.1	yes	10	276.167	even	22
1932.1.bi.c.671.1	yes	10	7.6	odd	2
1932.1.bi.c.671.1	yes	10	12.11	even	2
1932.1.bi.d.167.1	yes	10	23.6	even	11	inner
1932.1.bi.d.167.1	yes	10	1932.167	odd	22	inner
1932.1.bi.d.671.1	yes	10	1.1	even	1	trivial
1932.1.bi.d.671.1	yes	10	84.83	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1932.bi (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-1.10181 - 0.708089i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-1.10181 - 0.708089i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.186393 + 1.29639i) q^{10} +(0.118239 - 0.258908i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(0.841254 - 0.540641i) q^{14} +(-1.25667 - 0.368991i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(1.25667 + 1.45027i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(0.544078 - 0.627899i) q^{19} +(1.25667 - 0.368991i) q^{20} +(0.415415 + 0.909632i) q^{21} -0.284630 q^{22} +(0.654861 - 0.755750i) q^{23} +1.00000 q^{24} +(0.297176 + 0.650724i) q^{25} +(0.654861 - 0.755750i) q^{27} +(-0.841254 - 0.540641i) q^{28} +(0.186393 + 1.29639i) q^{30} +(-1.84125 - 0.540641i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(0.0405070 - 0.281733i) q^{33} +(0.797176 - 1.74557i) q^{34} +(0.544078 - 1.19136i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(1.41542 - 0.909632i) q^{37} +(-0.797176 - 0.234072i) q^{38} +(-0.857685 - 0.989821i) q^{40} +(0.698939 + 0.449181i) q^{41} +(0.654861 - 0.755750i) q^{42} +(0.118239 + 0.258908i) q^{44} -1.30972 q^{45} +(-0.959493 - 0.281733i) q^{46} +(-0.415415 - 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(0.468468 - 0.540641i) q^{50} +(1.61435 + 1.03748i) q^{51} +(-0.959493 - 0.281733i) q^{54} +(-0.313607 + 0.201543i) q^{55} +(-0.142315 + 0.989821i) q^{56} +(0.345139 - 0.755750i) q^{57} +(1.10181 - 0.708089i) q^{60} +(0.273100 + 1.89945i) q^{62} +(0.654861 + 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.273100 + 0.0801894i) q^{66} -1.91899 q^{68} +(0.415415 - 0.909632i) q^{69} -1.30972 q^{70} +(-0.698939 - 1.53046i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-1.41542 - 0.909632i) q^{74} +(0.468468 + 0.540641i) q^{75} +(0.118239 + 0.822373i) q^{76} +(0.273100 + 0.0801894i) q^{77} +(-0.544078 + 1.19136i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.118239 - 0.822373i) q^{82} +(-0.959493 - 0.281733i) q^{84} +(-0.357685 - 2.48775i) q^{85} +(0.186393 - 0.215109i) q^{88} +(-1.61435 + 0.474017i) q^{89} +(0.544078 + 1.19136i) q^{90} +(0.142315 + 0.989821i) q^{92} -1.91899 q^{93} +(-1.04408 + 0.306569i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(0.654861 + 0.755750i) q^{98} +(-0.0405070 - 0.281733i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more