LMFDB - Embedded newform 3864.1.cx.b.125.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3864,1,Mod(125,3864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 11, 11, 11, 3]))

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

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

chi := DirichletCharacter("3864.125");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.92838720881$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{88})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{44}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{44} - \cdots)$

Embedding invariants

Embedding label			125.2
Root			$-0.800541 + 0.599278i$ of defining polynomial
Character	$\chi$	$=$	3864.125
Dual form			3864.1.cx.b.2813.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.755750 + 0.654861i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.142315 - 0.989821i) q^{4} +(-0.729202 + 1.59673i) q^{5} +(-0.0713392 + 0.997452i) q^{6} +(-0.281733 + 0.959493i) q^{7} +(0.540641 + 0.841254i) q^{8} -1.00000i q^{9} +(-0.494541 - 1.68425i) q^{10} +(-0.599278 - 0.800541i) q^{12} +(1.91410 - 0.562029i) q^{13} +(-0.415415 - 0.909632i) q^{14} +(0.613435 + 1.64468i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.654861 + 0.755750i) q^{18} +(0.691814 + 0.0994679i) q^{19} +(1.47670 + 0.949018i) q^{20} +(0.479249 + 0.877679i) q^{21} +(0.959493 - 0.281733i) q^{23} +(0.977147 + 0.212565i) q^{24} +(-1.36295 - 1.57293i) q^{25} +(-1.07853 + 1.67822i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.909632 + 0.415415i) q^{28} +(-1.54064 - 0.841254i) q^{30} +(0.909632 - 0.415415i) q^{32} +(-1.32661 - 1.14952i) q^{35} +(-0.989821 - 0.142315i) q^{36} +(-0.587976 + 0.377869i) q^{38} +(0.956056 - 1.75089i) q^{39} +(-1.73749 + 0.249813i) q^{40} +(-0.936950 - 0.349464i) q^{42} +(1.59673 + 0.729202i) q^{45} +(-0.540641 + 0.841254i) q^{46} +(-0.877679 + 0.479249i) q^{48} +(-0.841254 - 0.540641i) q^{49} +(2.06010 + 0.296197i) q^{50} +(-0.283904 - 1.97460i) q^{52} +(0.997452 + 0.0713392i) q^{54} +(-0.959493 + 0.281733i) q^{56} +(0.559521 - 0.418852i) q^{57} +(0.527938 + 1.79799i) q^{59} +(1.71524 - 0.373128i) q^{60} +(0.764582 + 1.18971i) q^{61} +(0.959493 + 0.281733i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-0.498354 + 3.46613i) q^{65} +(0.479249 - 0.877679i) q^{69} +1.75536 q^{70} +(-0.989821 + 0.857685i) q^{71} +(0.841254 - 0.540641i) q^{72} +(-2.07598 - 0.148477i) q^{75} +(0.196911 - 0.670617i) q^{76} +(0.424047 + 1.94931i) q^{78} +(0.0801894 + 0.273100i) q^{79} +(1.14952 - 1.32661i) q^{80} -1.00000 q^{81} +(0.665114 + 1.45640i) q^{83} +(0.936950 - 0.349464i) q^{84} +(-1.68425 + 0.494541i) q^{90} +1.99490i q^{91} +(-0.142315 - 0.989821i) q^{92} +(-0.663296 + 1.03211i) q^{95} +(0.349464 - 0.936950i) q^{96} +(0.989821 - 0.142315i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{4} + 4 q^{14} - 4 q^{15} - 4 q^{16} + 4 q^{18} + 4 q^{23} - 4 q^{25} - 40 q^{30} - 4 q^{39} + 4 q^{49} - 4 q^{56} - 4 q^{57} + 4 q^{60} + 4 q^{63} + 4 q^{64} - 8 q^{65} - 4 q^{72} + 4 q^{78}+ \cdots - 4 q^{92}+O(q^{100}) $ 40 * q + 4 * q^4 + 4 * q^14 - 4 * q^15 - 4 * q^16 + 4 * q^18 + 4 * q^23 - 4 * q^25 - 40 * q^30 - 4 * q^39 + 4 * q^49 - 4 * q^56 - 4 * q^57 + 4 * q^60 + 4 * q^63 + 4 * q^64 - 8 * q^65 - 4 * q^72 + 4 * q^78 - 40 * q^81 - 4 * q^92

Character values

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

$n$	$967$	$1289$	$1933$	$2761$	$2857$
$\chi(n)$	$1$	$-1$	$-1$	$-1$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$2$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$3$	0.707107	−	0.707107i	0.707107	−	0.707107i
$3$	0.707107	−	0.707107i	0.707107	−	0.707107i
$4$	0.142315	−	0.989821i	0.142315	−	0.989821i
$5$	−0.729202	+	1.59673i	−0.729202	+	1.59673i	0.0713392	+	0.997452i	$0.477273\pi$
$5$	−0.729202	+	1.59673i	−0.729202	+	1.59673i	−0.800541	+	0.599278i	$0.795455\pi$
$6$	−0.0713392	+	0.997452i	−0.0713392	+	0.997452i
$7$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$7$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$8$	0.540641	+	0.841254i	0.540641	+	0.841254i
$9$		−	1.00000i		−	1.00000i
$10$	−0.494541	−	1.68425i	−0.494541	−	1.68425i
$11$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$11$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$12$	−0.599278	−	0.800541i	−0.599278	−	0.800541i
$13$	1.91410	−	0.562029i	1.91410	−	0.562029i	0.936950	−	0.349464i	$-0.113636\pi$
$13$	1.91410	−	0.562029i	1.91410	−	0.562029i	0.977147	−	0.212565i	$-0.0681818\pi$
$14$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$15$	0.613435	+	1.64468i	0.613435	+	1.64468i
$16$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$17$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$17$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$18$	0.654861	+	0.755750i	0.654861	+	0.755750i
$19$	0.691814	+	0.0994679i	0.691814	+	0.0994679i	0.479249	−	0.877679i	$-0.340909\pi$
$19$	0.691814	+	0.0994679i	0.691814	+	0.0994679i	0.212565	+	0.977147i	$0.431818\pi$
$20$	1.47670	+	0.949018i	1.47670	+	0.949018i
$21$	0.479249	+	0.877679i	0.479249	+	0.877679i
$22$		0			0
$23$	0.959493	−	0.281733i	0.959493	−	0.281733i
$23$	0.959493	−	0.281733i	0.959493	−	0.281733i
$24$	0.977147	+	0.212565i	0.977147	+	0.212565i
$25$	−1.36295	−	1.57293i	−1.36295	−	1.57293i
$26$	−1.07853	+	1.67822i	−1.07853	+	1.67822i
$27$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$28$	0.909632	+	0.415415i	0.909632	+	0.415415i
$29$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$29$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$30$	−1.54064	−	0.841254i	−1.54064	−	0.841254i
$31$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$31$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$32$	0.909632	−	0.415415i	0.909632	−	0.415415i
$33$		0			0
$34$		0			0
$35$	−1.32661	−	1.14952i	−1.32661	−	1.14952i
$36$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$37$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$37$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$38$	−0.587976	+	0.377869i	−0.587976	+	0.377869i
$39$	0.956056	−	1.75089i	0.956056	−	1.75089i
$40$	−1.73749	+	0.249813i	−1.73749	+	0.249813i
$41$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$41$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$42$	−0.936950	−	0.349464i	−0.936950	−	0.349464i
$43$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$43$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$44$		0			0
$45$	1.59673	+	0.729202i	1.59673	+	0.729202i
$46$	−0.540641	+	0.841254i	−0.540641	+	0.841254i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−0.877679	+	0.479249i	−0.877679	+	0.479249i
$49$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$50$	2.06010	+	0.296197i	2.06010	+	0.296197i
$51$		0			0
$52$	−0.283904	−	1.97460i	−0.283904	−	1.97460i
$53$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$53$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$54$	0.997452	+	0.0713392i	0.997452	+	0.0713392i
$55$		0			0
$56$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$57$	0.559521	−	0.418852i	0.559521	−	0.418852i
$58$		0			0
$59$	0.527938	+	1.79799i	0.527938	+	1.79799i	0.599278	+	0.800541i	$0.295455\pi$
$59$	0.527938	+	1.79799i	0.527938	+	1.79799i	−0.0713392	+	0.997452i	$0.522727\pi$
$60$	1.71524	−	0.373128i	1.71524	−	0.373128i
$61$	0.764582	+	1.18971i	0.764582	+	1.18971i	0.977147	+	0.212565i	$0.0681818\pi$
$61$	0.764582	+	1.18971i	0.764582	+	1.18971i	−0.212565	+	0.977147i	$0.568182\pi$
$62$		0			0
$63$	0.959493	+	0.281733i	0.959493	+	0.281733i
$64$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$65$	−0.498354	+	3.46613i	−0.498354	+	3.46613i
$66$		0			0
$67$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$67$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$68$		0			0
$69$	0.479249	−	0.877679i	0.479249	−	0.877679i
$70$	1.75536			1.75536
$71$	−0.989821	+	0.857685i	−0.989821	+	0.857685i	−0.989821	−	0.142315i	$-0.954545\pi$
$71$	−0.989821	+	0.857685i	−0.989821	+	0.857685i			1.00000i	$0.5\pi$
$72$	0.841254	−	0.540641i	0.841254	−	0.540641i
$73$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$73$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$74$		0			0
$75$	−2.07598	−	0.148477i	−2.07598	−	0.148477i
$76$	0.196911	−	0.670617i	0.196911	−	0.670617i
$77$		0			0
$78$	0.424047	+	1.94931i	0.424047	+	1.94931i
$79$	0.0801894	+	0.273100i	0.0801894	+	0.273100i	0.989821	−	0.142315i	$-0.0454545\pi$
$79$	0.0801894	+	0.273100i	0.0801894	+	0.273100i	−0.909632	+	0.415415i	$0.863636\pi$
$80$	1.14952	−	1.32661i	1.14952	−	1.32661i
$81$	−1.00000			−1.00000
$82$		0			0
$83$	0.665114	+	1.45640i	0.665114	+	1.45640i	0.877679	+	0.479249i	$0.159091\pi$
$83$	0.665114	+	1.45640i	0.665114	+	1.45640i	−0.212565	+	0.977147i	$0.568182\pi$
$84$	0.936950	−	0.349464i	0.936950	−	0.349464i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$89$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$90$	−1.68425	+	0.494541i	−1.68425	+	0.494541i
$91$			1.99490i			1.99490i
$92$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$93$		0			0
$94$		0			0
$95$	−0.663296	+	1.03211i	−0.663296	+	1.03211i
$96$	0.349464	−	0.936950i	0.349464	−	0.936950i
$97$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$97$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$98$	0.989821	−	0.142315i	0.989821	−	0.142315i
$99$		0			0
$100$	−1.75089	+	1.12523i	−1.75089	+	1.12523i
$101$	1.28641	−	0.587486i	1.28641	−	0.587486i	0.349464	−	0.936950i	$-0.386364\pi$
$101$	1.28641	−	0.587486i	1.28641	−	0.587486i	0.936950	+	0.349464i	$0.113636\pi$
$102$		0			0
$103$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$103$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$104$	1.50765	+	1.30638i	1.50765	+	1.30638i
$105$	−1.75089	+	0.125226i	−1.75089	+	0.125226i
$106$		0			0
$107$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$107$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$108$	−0.800541	+	0.599278i	−0.800541	+	0.599278i
$109$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$109$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$110$		0			0
$111$		0			0
$112$	0.540641	−	0.841254i	0.540641	−	0.841254i
$113$	−1.29639	−	1.49611i	−1.29639	−	1.49611i	−0.755750	−	0.654861i	$-0.772727\pi$
$113$	−1.29639	−	1.49611i	−1.29639	−	1.49611i	−0.540641	−	0.841254i	$-0.681818\pi$
$114$	−0.148568	+	0.682956i	−0.148568	+	0.682956i
$115$	−0.249813	+	1.73749i	−0.249813	+	1.73749i
$116$		0			0
$117$	−0.562029	−	1.91410i	−0.562029	−	1.91410i
$118$	−1.57642	−	1.01311i	−1.57642	−	1.01311i
$119$		0			0
$120$	−1.05195	+	1.40524i	−1.05195	+	1.40524i
$121$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$122$	−1.35693	−	0.398430i	−1.35693	−	0.398430i
$123$		0			0
$124$		0			0
$125$	1.82115	−	0.534739i	1.82115	−	0.534739i
$126$	−0.909632	+	0.415415i	−0.909632	+	0.415415i
$127$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$127$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$128$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$129$		0			0
$130$	−1.89320	−	2.94588i	−1.89320	−	2.94588i
$131$	0.270040	−	0.919672i	0.270040	−	0.919672i	−0.707107	−	0.707107i	$-0.750000\pi$
$131$	0.270040	−	0.919672i	0.270040	−	0.919672i	0.977147	−	0.212565i	$-0.0681818\pi$
$132$		0			0
$133$	−0.290345	+	0.635768i	−0.290345	+	0.635768i
$134$		0			0
$135$	1.64468	−	0.613435i	1.64468	−	0.613435i
$136$		0			0
$137$	−0.830830			−0.830830			−0.415415	−	0.909632i	$-0.636364\pi$
$137$	−0.830830			−0.830830			−0.415415	+	0.909632i	$0.636364\pi$
$138$	0.212565	+	0.977147i	0.212565	+	0.977147i
$139$	1.60108			1.60108			0.800541	−	0.599278i	$-0.204545\pi$
$139$	1.60108			1.60108			0.800541	+	0.599278i	$0.204545\pi$
$140$	−1.32661	+	1.14952i	−1.32661	+	1.14952i
$141$		0			0
$142$	0.186393	−	1.29639i	0.186393	−	1.29639i
$143$		0			0
$144$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$145$		0			0
$146$		0			0
$147$	−0.977147	+	0.212565i	−0.977147	+	0.212565i
$148$		0			0
$149$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$149$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$150$	1.66615	−	1.24727i	1.66615	−	1.24727i
$151$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$151$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$152$	0.290345	+	0.635768i	0.290345	+	0.635768i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−1.59700	−	1.19550i	−1.59700	−	1.19550i
$157$	1.18636	+	0.170572i	1.18636	+	0.170572i	0.707107	−	0.707107i	$-0.250000\pi$
$157$	1.18636	+	0.170572i	1.18636	+	0.170572i	0.479249	+	0.877679i	$0.340909\pi$
$158$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$159$		0			0
$160$			1.75536i			1.75536i
$161$			1.00000i			1.00000i
$162$	0.755750	−	0.654861i	0.755750	−	0.654861i
$163$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$163$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$164$		0			0
$165$		0			0
$166$	−1.45640	−	0.665114i	−1.45640	−	0.665114i
$167$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$167$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$168$	−0.479249	+	0.877679i	−0.479249	+	0.877679i
$169$	2.50664	−	1.61092i	2.50664	−	1.61092i
$170$		0			0
$171$	0.0994679	−	0.691814i	0.0994679	−	0.691814i
$172$		0			0
$173$	−0.905808	−	0.784887i	−0.905808	−	0.784887i	0.0713392	−	0.997452i	$-0.477273\pi$
$173$	−0.905808	−	0.784887i	−0.905808	−	0.784887i	−0.977147	+	0.212565i	$0.931818\pi$
$174$		0			0
$175$	1.89320	−	0.864596i	1.89320	−	0.864596i
$176$		0			0
$177$	1.64468	+	0.898064i	1.64468	+	0.898064i
$178$		0			0
$179$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$179$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$180$	0.949018	−	1.47670i	0.949018	−	1.47670i
$181$	−1.05657	+	1.64406i	−1.05657	+	1.64406i	−0.349464	+	0.936950i	$0.613636\pi$
$181$	−1.05657	+	1.64406i	−1.05657	+	1.64406i	−0.707107	+	0.707107i	$0.750000\pi$
$182$	−1.30638	−	1.50765i	−1.30638	−	1.50765i
$183$	1.38189	+	0.300613i	1.38189	+	0.300613i
$184$	0.755750	+	0.654861i	0.755750	+	0.654861i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.877679	−	0.479249i	0.877679	−	0.479249i
$190$	−0.174602	−	1.21438i	−0.174602	−	1.21438i
$191$	1.03748	+	0.304632i	1.03748	+	0.304632i	0.755750	−	0.654861i	$-0.227273\pi$
$191$	1.03748	+	0.304632i	1.03748	+	0.304632i	0.281733	+	0.959493i	$0.409091\pi$
$192$	0.349464	+	0.936950i	0.349464	+	0.936950i
$193$	0.234072	+	0.512546i	0.234072	+	0.512546i	0.989821	−	0.142315i	$-0.0454545\pi$
$193$	0.234072	+	0.512546i	0.234072	+	0.512546i	−0.755750	+	0.654861i	$0.772727\pi$
$194$		0			0
$195$	2.09853	+	2.80331i	2.09853	+	2.80331i
$196$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$197$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$197$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$198$		0			0
$199$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$199$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$200$	0.586365	−	1.99698i	0.586365	−	1.99698i
$201$		0			0
$202$	−0.587486	+	1.28641i	−0.587486	+	1.28641i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$208$	−1.99490			−1.99490
$209$		0			0
$210$	1.24123	−	1.24123i	1.24123	−	1.24123i
$211$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$211$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$212$		0			0
$213$	−0.0934345	+	1.30638i	−0.0934345	+	1.30638i
$214$		0			0
$215$		0			0
$216$	0.212565	−	0.977147i	0.212565	−	0.977147i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$223$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$224$	0.142315	+	0.989821i	0.142315	+	0.989821i
$225$	−1.57293	+	1.36295i	−1.57293	+	1.36295i
$226$	1.95949	+	0.281733i	1.95949	+	0.281733i
$227$	−1.00829	−	0.647988i	−1.00829	−	0.647988i	−0.0713392	−	0.997452i	$-0.522727\pi$
$227$	−1.00829	−	0.647988i	−1.00829	−	0.647988i	−0.936950	+	0.349464i	$0.886364\pi$
$228$	−0.334961	−	0.613435i	−0.334961	−	0.613435i
$229$		−	1.87390i		−	1.87390i	−0.349464	−	0.936950i	$-0.613636\pi$
$229$		−	1.87390i		−	1.87390i	0.349464	−	0.936950i	$-0.386364\pi$
$230$	−0.949018	−	1.47670i	−0.949018	−	1.47670i
$231$		0			0
$232$		0			0
$233$	1.07028	−	1.66538i	1.07028	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$233$	1.07028	−	1.66538i	1.07028	−	1.66538i	0.654861	−	0.755750i	$-0.272727\pi$
$234$	1.67822	+	1.07853i	1.67822	+	1.07853i
$235$		0			0
$236$	1.85483	−	0.266684i	1.85483	−	0.266684i
$237$	0.249813	+	0.136408i	0.249813	+	0.136408i
$238$		0			0
$239$	0.512546	−	0.234072i	0.512546	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$239$	0.512546	−	0.234072i	0.512546	−	0.234072i	0.654861	+	0.755750i	$0.272727\pi$
$240$	−0.125226	−	1.75089i	−0.125226	−	1.75089i
$241$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$241$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$242$	0.755750	+	0.654861i	0.755750	+	0.654861i
$243$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$244$	1.28641	−	0.587486i	1.28641	−	0.587486i
$245$	1.47670	−	0.949018i	1.47670	−	0.949018i
$246$		0			0
$247$	1.38010	−	0.198429i	1.38010	−	0.198429i
$248$		0			0
$249$	1.50013	+	0.559521i	1.50013	+	0.559521i
$250$	−1.02616	+	1.59673i	−1.02616	+	1.59673i
$251$	−0.278401	−	0.321292i	−0.278401	−	0.321292i	0.599278	−	0.800541i	$-0.295455\pi$
$251$	−0.278401	−	0.321292i	−0.278401	−	0.321292i	−0.877679	+	0.479249i	$0.840909\pi$
$252$	0.415415	−	0.909632i	0.415415	−	0.909632i
$253$		0			0
$254$		−	1.91899i		−	1.91899i
$255$		0			0
$256$	0.841254	+	0.540641i	0.841254	+	0.540641i
$257$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$257$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$258$		0			0
$259$		0			0
$260$	3.35992	+	0.986563i	3.35992	+	0.986563i
$261$		0			0
$262$	0.398174	+	0.871880i	0.398174	+	0.871880i
$263$	−1.45027	+	0.425839i	−1.45027	+	0.425839i	−0.909632	−	0.415415i	$-0.863636\pi$
$263$	−1.45027	+	0.425839i	−1.45027	+	0.425839i	−0.540641	+	0.841254i	$0.681818\pi$
$264$		0			0
$265$		0			0
$266$	−0.196911	−	0.670617i	−0.196911	−	0.670617i
$267$		0			0
$268$		0			0
$269$	−0.196911	+	0.670617i	−0.196911	+	0.670617i	0.800541	+	0.599278i	$0.204545\pi$
$269$	−0.196911	+	0.670617i	−0.196911	+	0.670617i	−0.997452	+	0.0713392i	$0.977273\pi$
$270$	−0.841254	+	1.54064i	−0.841254	+	1.54064i
$271$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$271$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$272$		0			0
$273$	1.41061	+	1.41061i	1.41061	+	1.41061i
$274$	0.627899	−	0.544078i	0.627899	−	0.544078i
$275$		0			0
$276$	−0.800541	−	0.599278i	−0.800541	−	0.599278i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	−1.21002	+	1.04849i	−1.21002	+	1.04849i
$279$		0			0
$280$	0.249813	−	1.73749i	0.249813	−	1.73749i
$281$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$281$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$282$		0			0
$283$	−0.0401971	+	0.136899i	−0.0401971	+	0.136899i	−0.977147	−	0.212565i	$-0.931818\pi$
$283$	−0.0401971	+	0.136899i	−0.0401971	+	0.136899i	0.936950	+	0.349464i	$0.113636\pi$
$284$	0.708089	+	1.10181i	0.708089	+	1.10181i
$285$	0.260790	+	1.19883i	0.260790	+	1.19883i
$286$		0			0
$287$		0			0
$288$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$289$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.0605024	−	0.420803i	−0.0605024	−	0.420803i	−0.997452	−	0.0713392i	$-0.977273\pi$
$293$	−0.0605024	−	0.420803i	−0.0605024	−	0.420803i	0.936950	−	0.349464i	$-0.113636\pi$
$294$	0.599278	−	0.800541i	0.599278	−	0.800541i
$295$	−3.25588	−	0.468125i	−3.25588	−	0.468125i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.67822	−	1.07853i	1.67822	−	1.07853i
$300$	−0.442408	+	2.03372i	−0.442408	+	2.03372i
$301$		0			0
$302$	0.909632	−	1.41542i	0.909632	−	1.41542i
$303$	0.494217	−	1.32505i	0.494217	−	1.32505i
$304$	−0.635768	−	0.290345i	−0.635768	−	0.290345i
$305$	−2.45718	+	0.353290i	−2.45718	+	0.353290i
$306$		0			0
$307$	0.120029	−	0.0771377i	0.120029	−	0.0771377i	−0.479249	−	0.877679i	$-0.659091\pi$
$307$	0.120029	−	0.0771377i	0.120029	−	0.0771377i	0.599278	+	0.800541i	$0.295455\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$311$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$312$	1.98982	−	0.142315i	1.98982	−	0.142315i
$313$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$313$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$314$	−1.00829	+	0.647988i	−1.00829	+	0.647988i
$315$	−1.14952	+	1.32661i	−1.14952	+	1.32661i
$316$	0.281733	−	0.0405070i	0.281733	−	0.0405070i
$317$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$317$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$318$		0			0
$319$		0			0
$320$	−1.14952	−	1.32661i	−1.14952	−	1.32661i
$321$		0			0
$322$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$323$		0			0
$324$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$325$	−3.49285	−	2.24472i	−3.49285	−	2.24472i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$331$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$332$	1.53623	−	0.451077i	1.53623	−	0.451077i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−0.212565	−	0.977147i	−0.212565	−	0.977147i
$337$	0.708089	+	1.10181i	0.708089	+	1.10181i	0.989821	+	0.142315i	$0.0454545\pi$
$337$	0.708089	+	1.10181i	0.708089	+	1.10181i	−0.281733	+	0.959493i	$0.590909\pi$
$338$	−0.839462	+	2.85895i	−0.839462	+	2.85895i
$339$	−1.97460	−	0.141226i	−1.97460	−	0.141226i
$340$		0			0
$341$		0			0
$342$	0.377869	+	0.587976i	0.377869	+	0.587976i
$343$	0.755750	−	0.654861i	0.755750	−	0.654861i
$344$		0			0
$345$	1.05195	+	1.40524i	1.05195	+	1.40524i
$346$	1.19856			1.19856
$347$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$347$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$348$		0			0
$349$	−0.201264	+	1.39982i	−0.201264	+	1.39982i	0.599278	+	0.800541i	$0.295455\pi$
$349$	−0.201264	+	1.39982i	−0.201264	+	1.39982i	−0.800541	+	0.599278i	$0.795455\pi$
$350$	−0.864596	+	1.89320i	−0.864596	+	1.89320i
$351$	−1.75089	−	0.956056i	−1.75089	−	0.956056i
$352$		0			0
$353$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$353$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$354$	−1.83107	+	0.398326i	−1.83107	+	0.398326i
$355$	−0.647712	−	2.20590i	−0.647712	−	2.20590i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$359$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$360$	0.249813	+	1.73749i	0.249813	+	1.73749i
$361$	−0.490780	−	0.144106i	−0.490780	−	0.144106i
$362$	−0.278125	−	1.93440i	−0.278125	−	1.93440i
$363$	−0.800541	−	0.599278i	−0.800541	−	0.599278i
$364$	1.97460	+	0.283904i	1.97460	+	0.283904i
$365$		0			0
$366$	−1.24123	+	0.677760i	−1.24123	+	0.677760i
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$	−1.00000			−1.00000
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$373$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$374$		0			0
$375$	0.909632	−	1.66587i	0.909632	−	1.66587i
$376$		0			0
$377$		0			0
$378$	−0.349464	+	0.936950i	−0.349464	+	0.936950i
$379$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$379$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$380$	0.927206	+	0.803429i	0.927206	+	0.803429i
$381$	0.136899	+	1.91410i	0.136899	+	1.91410i
$382$	−0.983568	+	0.449181i	−0.983568	+	0.449181i
$383$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$383$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$384$	−0.877679	−	0.479249i	−0.877679	−	0.479249i
$385$		0			0
$386$	−0.512546	−	0.234072i	−0.512546	−	0.234072i
$387$		0			0
$388$		0			0
$389$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$389$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$390$	−3.42174	−	0.744355i	−3.42174	−	0.744355i
$391$		0			0
$392$		−	1.00000i		−	1.00000i
$393$	−0.459359	−	0.841254i	−0.459359	−	0.841254i
$394$		0			0
$395$	−0.494541	−	0.0711043i	−0.494541	−	0.0711043i
$396$		0			0
$397$	0.0203052	+	0.141226i	0.0203052	+	0.141226i	0.997452	−	0.0713392i	$-0.0227273\pi$
$397$	0.0203052	+	0.141226i	0.0203052	+	0.141226i	−0.977147	+	0.212565i	$0.931818\pi$
$398$		0			0
$399$	0.244250	+	0.654861i	0.244250	+	0.654861i
$400$	0.864596	+	1.89320i	0.864596	+	1.89320i
$401$	1.45027	−	0.425839i	1.45027	−	0.425839i	0.540641	−	0.841254i	$-0.318182\pi$
$401$	1.45027	−	0.425839i	1.45027	−	0.425839i	0.909632	+	0.415415i	$0.136364\pi$
$402$		0			0
$403$		0			0
$404$	−0.398430	−	1.35693i	−0.398430	−	1.35693i
$405$	0.729202	−	1.59673i	0.729202	−	1.59673i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$409$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$410$		0			0
$411$	−0.587486	+	0.587486i	−0.587486	+	0.587486i
$412$		0			0
$413$	−1.87390			−1.87390
$414$	0.841254	+	0.540641i	0.841254	+	0.540641i
$415$	−2.81047			−2.81047
$416$	1.50765	−	1.30638i	1.50765	−	1.30638i
$417$	1.13214	−	1.13214i	1.13214	−	1.13214i
$418$		0			0
$419$	−0.828713	+	1.81463i	−0.828713	+	1.81463i	−0.349464	+	0.936950i	$0.613636\pi$
$419$	−0.828713	+	1.81463i	−0.828713	+	1.81463i	−0.479249	+	0.877679i	$0.659091\pi$
$420$	−0.125226	+	1.75089i	−0.125226	+	1.75089i
$421$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$421$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.784887	−	1.04849i	−0.784887	−	1.04849i
$427$	−1.35693	+	0.398430i	−1.35693	+	0.398430i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$431$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$432$	0.479249	+	0.877679i	0.479249	+	0.877679i
$433$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$433$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.691814	−	0.0994679i	0.691814	−	0.0994679i
$438$		0			0
$439$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$439$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$440$		0			0
$441$	−0.540641	+	0.841254i	−0.540641	+	0.841254i
$442$		0			0
$443$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$443$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.755750	−	0.654861i	−0.755750	−	0.654861i
$449$	1.37491	+	1.19136i	1.37491	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$449$	1.37491	+	1.19136i	1.37491	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$450$	0.296197	−	2.06010i	0.296197	−	2.06010i
$451$		0			0
$452$	−1.66538	+	1.07028i	−1.66538	+	1.07028i
$453$	−0.806340	+	1.47670i	−0.806340	+	1.47670i
$454$	1.18636	−	0.170572i	1.18636	−	0.170572i
$455$	−3.18532	−	1.45469i	−3.18532	−	1.45469i
$456$	0.654861	+	0.244250i	0.654861	+	0.244250i
$457$	−0.449181	+	0.698939i	−0.449181	+	0.698939i	−0.989821	−	0.142315i	$-0.954545\pi$
$457$	−0.449181	+	0.698939i	−0.449181	+	0.698939i	0.540641	+	0.841254i	$0.318182\pi$
$458$	1.22714	+	1.41620i	1.22714	+	1.41620i
$459$		0			0
$460$	1.68425	+	0.494541i	1.68425	+	0.494541i
$461$		−	1.60108i		−	1.60108i	−0.599278	−	0.800541i	$-0.704545\pi$
$461$		−	1.60108i		−	1.60108i	0.599278	−	0.800541i	$-0.295455\pi$
$462$		0			0
$463$	−1.27155	−	0.817178i	−1.27155	−	0.817178i	−0.281733	−	0.959493i	$-0.590909\pi$
$463$	−1.27155	−	0.817178i	−1.27155	−	0.817178i	−0.989821	+	0.142315i	$0.954545\pi$
$464$		0			0
$465$		0			0
$466$	0.281733	+	1.95949i	0.281733	+	1.95949i
$467$	−1.87513	−	0.550588i	−1.87513	−	0.550588i	−0.997452	−	0.0713392i	$-0.977273\pi$
$467$	−1.87513	−	0.550588i	−1.87513	−	0.550588i	−0.877679	−	0.479249i	$-0.840909\pi$
$468$	−1.97460	+	0.283904i	−1.97460	+	0.283904i
$469$		0			0
$470$		0			0
$471$	0.959493	−	0.718267i	0.959493	−	0.718267i
$472$	−1.22714	+	1.41620i	−1.22714	+	1.41620i
$473$		0			0
$474$	−0.278125	+	0.0605024i	−0.278125	+	0.0605024i
$475$	−0.786452	−	1.22374i	−0.786452	−	1.22374i
$476$		0			0
$477$		0			0
$478$	−0.234072	+	0.512546i	−0.234072	+	0.512546i
$479$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$479$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$480$	1.24123	+	1.24123i	1.24123	+	1.24123i
$481$		0			0
$482$		0			0
$483$	0.707107	+	0.707107i	0.707107	+	0.707107i
$484$	−1.00000			−1.00000
$485$		0			0
$486$	0.0713392	−	0.997452i	0.0713392	−	0.997452i
$487$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$487$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$488$	−0.587486	+	1.28641i	−0.587486	+	1.28641i
$489$		0			0
$490$	−0.494541	+	1.68425i	−0.494541	+	1.68425i
$491$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$491$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$492$		0			0
$493$		0			0
$494$	−0.913069	+	1.05374i	−0.913069	+	1.05374i
$495$		0			0
$496$		0			0
$497$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$498$	−1.50013	+	0.559521i	−1.50013	+	0.559521i
$499$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$499$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$500$	−0.270119	−	1.87872i	−0.270119	−	1.87872i
$501$		0			0
$502$	0.420803	+	0.0605024i	0.420803	+	0.0605024i
$503$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$503$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$504$	0.281733	+	0.959493i	0.281733	+	0.959493i
$505$			2.48245i			2.48245i
$506$		0			0
$507$	0.633369	−	2.91155i	0.633369	−	2.91155i
$508$	1.25667	+	1.45027i	1.25667	+	1.45027i
$509$	0.518203	−	0.806340i	0.518203	−	0.806340i	−0.479249	−	0.877679i	$-0.659091\pi$
$509$	0.518203	−	0.806340i	0.518203	−	0.806340i	0.997452	+	0.0713392i	$0.0227273\pi$
$510$		0			0
$511$		0			0
$512$	−0.989821	+	0.142315i	−0.989821	+	0.142315i
$513$	−0.418852	−	0.559521i	−0.418852	−	0.559521i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.19550	+	0.0855040i	−1.19550	+	0.0855040i
$520$	−3.18532	+	1.45469i	−3.18532	+	1.45469i
$521$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$521$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$522$		0			0
$523$	1.58479	−	0.227858i	1.58479	−	0.227858i	0.707107	−	0.707107i	$-0.250000\pi$
$523$	1.58479	−	0.227858i	1.58479	−	0.227858i	0.877679	+	0.479249i	$0.159091\pi$
$524$	−0.871880	−	0.398174i	−0.871880	−	0.398174i
$525$	0.727333	−	1.95006i	0.727333	−	1.95006i
$526$	0.817178	−	1.27155i	0.817178	−	1.27155i
$527$		0			0
$528$		0			0
$529$	0.841254	−	0.540641i	0.841254	−	0.540641i
$530$		0			0
$531$	1.79799	−	0.527938i	1.79799	−	0.527938i
$532$	0.587976	+	0.377869i	0.587976	+	0.377869i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.290345	−	0.635768i	−0.290345	−	0.635768i
$539$		0			0
$540$	−0.373128	−	1.71524i	−0.373128	−	1.71524i
$541$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$541$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$542$		0			0
$543$	0.415415	+	1.90963i	0.415415	+	1.90963i
$544$		0			0
$545$		0			0
$546$	−1.98982	−	0.142315i	−1.98982	−	0.142315i
$547$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$547$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$548$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$549$	1.18971	−	0.764582i	1.18971	−	0.764582i
$550$		0			0
$551$		0			0
$552$	0.997452	−	0.0713392i	0.997452	−	0.0713392i
$553$	−0.284630			−0.284630
$554$		0			0
$555$		0			0
$556$	0.227858	−	1.58479i	0.227858	−	1.58479i
$557$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$557$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$558$		0			0
$559$		0			0
$560$	0.949018	+	1.47670i	0.949018	+	1.47670i
$561$		0			0
$562$	0.540641	+	1.84125i	0.540641	+	1.84125i
$563$	−0.0934345	+	0.107829i	−0.0934345	+	0.107829i	−0.800541	−	0.599278i	$-0.795455\pi$
$563$	−0.0934345	+	0.107829i	−0.0934345	+	0.107829i	0.707107	+	0.707107i	$0.250000\pi$
$564$		0			0
$565$	3.33422	−	0.979016i	3.33422	−	0.979016i
$566$	−0.0592707	−	0.129785i	−0.0592707	−	0.129785i
$567$	0.281733	−	0.959493i	0.281733	−	0.959493i
$568$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$569$	−0.153882	−	1.07028i	−0.153882	−	1.07028i	−0.909632	−	0.415415i	$-0.863636\pi$
$569$	−0.153882	−	1.07028i	−0.153882	−	1.07028i	0.755750	−	0.654861i	$-0.227273\pi$
$570$	−0.982160	−	0.735235i	−0.982160	−	0.735235i
$571$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$571$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$572$		0			0
$573$	0.949018	−	0.518203i	0.949018	−	0.518203i
$574$		0			0
$575$	−1.75089	−	1.12523i	−1.75089	−	1.12523i
$576$	0.909632	+	0.415415i	0.909632	+	0.415415i
$577$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$577$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$578$	0.540641	−	0.841254i	0.540641	−	0.841254i
$579$	0.527938	+	0.196911i	0.527938	+	0.196911i
$580$		0			0
$581$	−1.58479	+	0.227858i	−1.58479	+	0.227858i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	3.46613	+	0.498354i	3.46613	+	0.498354i
$586$	0.321292	+	0.278401i	0.321292	+	0.278401i
$587$	0.107829	+	0.0934345i	0.107829	+	0.0934345i	0.707107	−	0.707107i	$-0.250000\pi$
$587$	0.107829	+	0.0934345i	0.107829	+	0.0934345i	−0.599278	+	0.800541i	$0.704545\pi$
$588$	0.0713392	+	0.997452i	0.0713392	+	0.997452i
$589$		0			0
$590$	2.76719	−	1.77836i	2.76719	−	1.77836i
$591$		0			0
$592$		0			0
$593$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$593$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.562029	+	1.91410i	−0.562029	+	1.91410i
$599$		−	1.68251i		−	1.68251i	−0.540641	−	0.841254i	$-0.681818\pi$
$599$		−	1.68251i		−	1.68251i	0.540641	−	0.841254i	$-0.318182\pi$
$600$	−0.997452	−	1.82670i	−0.997452	−	1.82670i
$601$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$601$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$602$		0			0
$603$		0			0
$604$	0.239446	+	1.66538i	0.239446	+	1.66538i
$605$	1.68425	+	0.494541i	1.68425	+	0.494541i
$606$	0.494217	+	1.32505i	0.494217	+	1.32505i
$607$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$607$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$608$	0.670617	−	0.196911i	0.670617	−	0.196911i
$609$		0			0
$610$	1.62566	−	1.87611i	1.62566	−	1.87611i
$611$		0			0
$612$		0			0
$613$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$613$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$614$	−0.0401971	+	0.136899i	−0.0401971	+	0.136899i
$615$		0			0
$616$		0			0
$617$	−0.0801894	+	0.557730i	−0.0801894	+	0.557730i	0.909632	+	0.415415i	$0.136364\pi$
$617$	−0.0801894	+	0.557730i	−0.0801894	+	0.557730i	−0.989821	+	0.142315i	$0.954545\pi$
$618$		0			0
$619$	1.21002	−	1.04849i	1.21002	−	1.04849i	0.212565	−	0.977147i	$-0.431818\pi$
$619$	1.21002	−	1.04849i	1.21002	−	1.04849i	0.997452	−	0.0713392i	$-0.0227273\pi$
$620$		0			0
$621$	−0.877679	−	0.479249i	−0.877679	−	0.479249i
$622$		0			0
$623$		0			0
$624$	−1.41061	+	1.41061i	−1.41061	+	1.41061i
$625$	−0.177958	+	1.23772i	−0.177958	+	1.23772i
$626$		0			0
$627$		0			0
$628$	0.337672	−	1.15001i	0.337672	−	1.15001i
$629$		0			0
$630$		−	1.75536i		−	1.75536i
$631$	−0.474017	−	1.61435i	−0.474017	−	1.61435i	−0.755750	−	0.654861i	$-0.772727\pi$
$631$	−0.474017	−	1.61435i	−0.474017	−	1.61435i	0.281733	−	0.959493i	$-0.409091\pi$
$632$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$633$		0			0
$634$		0			0
$635$	−1.39933	−	3.06410i	−1.39933	−	3.06410i
$636$		0			0
$637$	−1.91410	−	0.562029i	−1.91410	−	0.562029i
$638$		0			0
$639$	0.857685	+	0.989821i	0.857685	+	0.989821i
$640$	1.73749	+	0.249813i	1.73749	+	0.249813i
$641$	0.474017	+	0.304632i	0.474017	+	0.304632i	0.755750	−	0.654861i	$-0.227273\pi$
$641$	0.474017	+	0.304632i	0.474017	+	0.304632i	−0.281733	+	0.959493i	$0.590909\pi$
$642$		0			0
$643$		−	1.95429i		−	1.95429i	−0.212565	−	0.977147i	$-0.568182\pi$
$643$		−	1.95429i		−	1.95429i	0.212565	−	0.977147i	$-0.431818\pi$
$644$	0.989821	+	0.142315i	0.989821	+	0.142315i
$645$		0			0
$646$		0			0
$647$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$647$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$648$	−0.540641	−	0.841254i	−0.540641	−	0.841254i
$649$		0			0
$650$	4.10970	−	0.590885i	4.10970	−	0.590885i
$651$		0			0
$652$		0			0
$653$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$653$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$654$		0			0
$655$	1.27155	+	1.10181i	1.27155	+	1.10181i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$659$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$660$		0			0
$661$	−0.141226	+	0.0203052i	−0.141226	+	0.0203052i	−0.212565	−	0.977147i	$-0.568182\pi$
$661$	−0.141226	+	0.0203052i	−0.141226	+	0.0203052i	0.0713392	+	0.997452i	$0.477273\pi$
$662$		0			0
$663$		0			0
$664$	−0.865611	+	1.34692i	−0.865611	+	1.34692i
$665$	−0.803429	−	0.927206i	−0.803429	−	0.927206i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.800541	+	0.599278i	0.800541	+	0.599278i
$673$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$673$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$674$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$675$	−0.148477	+	2.07598i	−0.148477	+	2.07598i
$676$	−1.23779	−	2.71038i	−1.23779	−	2.71038i
$677$	−1.15001	+	0.337672i	−1.15001	+	0.337672i	−0.800541	−	0.599278i	$-0.795455\pi$
$677$	−1.15001	+	0.337672i	−1.15001	+	0.337672i	−0.349464	+	0.936950i	$0.613636\pi$
$678$	1.58479	−	1.18636i	1.58479	−	1.18636i
$679$		0			0
$680$		0			0
$681$	−1.17116	+	0.254771i	−1.17116	+	0.254771i
$682$		0			0
$683$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$683$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$684$	−0.670617	−	0.196911i	−0.670617	−	0.196911i
$685$	0.605843	−	1.32661i	0.605843	−	1.32661i
$686$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$687$	−1.32505	−	1.32505i	−1.32505	−	1.32505i
$688$		0			0
$689$		0			0
$690$	−1.71524	−	0.373128i	−1.71524	−	0.373128i
$691$	−1.87390			−1.87390			−0.936950	−	0.349464i	$-0.886364\pi$
$691$	−1.87390			−1.87390			−0.936950	+	0.349464i	$0.886364\pi$
$692$	−0.905808	+	0.784887i	−0.905808	+	0.784887i
$693$		0			0
$694$		0			0
$695$	−1.16751	+	2.55650i	−1.16751	+	2.55650i
$696$		0			0
$697$		0			0
$698$	−0.764582	−	1.18971i	−0.764582	−	1.18971i
$699$	−0.420803	−	1.93440i	−0.420803	−	1.93440i
$700$	−0.586365	−	1.99698i	−0.586365	−	1.99698i
$701$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$701$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$702$	1.94931	−	0.424047i	1.94931	−	0.424047i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.201264	+	1.39982i	0.201264	+	1.39982i
$708$	1.12299	−	1.50013i	1.12299	−	1.50013i
$709$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$709$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$710$	1.93407	+	1.24295i	1.93407	+	1.24295i
$711$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.196911	−	0.527938i	0.196911	−	0.527938i
$718$	1.74557	+	0.797176i	1.74557	+	0.797176i
$719$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$719$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$720$	−1.32661	−	1.14952i	−1.32661	−	1.14952i
$721$		0			0
$722$	0.465276	−	0.212484i	0.465276	−	0.212484i
$723$		0			0
$724$	1.47696	+	1.27979i	1.47696	+	1.27979i
$725$		0			0
$726$	0.997452	−	0.0713392i	0.997452	−	0.0713392i
$727$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$727$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$728$	−1.67822	+	1.07853i	−1.67822	+	1.07853i
$729$			1.00000i			1.00000i
$730$		0			0
$731$		0			0
$732$	0.494217	−	1.32505i	0.494217	−	1.32505i
$733$	−1.07853	+	1.67822i	−1.07853	+	1.67822i	−0.479249	+	0.877679i	$0.659091\pi$
$733$	−1.07853	+	1.67822i	−1.07853	+	1.67822i	−0.599278	+	0.800541i	$0.704545\pi$
$734$		0			0
$735$	0.373128	−	1.71524i	0.373128	−	1.71524i
$736$	0.755750	−	0.654861i	0.755750	−	0.654861i
$737$		0			0
$738$		0			0
$739$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$739$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$740$		0			0
$741$	0.835570	−	1.11619i	0.835570	−	1.11619i
$742$		0			0
$743$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$743$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.45640	−	0.665114i	1.45640	−	0.665114i
$748$		0			0
$749$		0			0
$750$	0.403457	+	1.85466i	0.403457	+	1.85466i
$751$	0.983568	+	1.53046i	0.983568	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$751$	0.983568	+	1.53046i	0.983568	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$752$		0			0
$753$	−0.424047	−	0.0303285i	−0.424047	−	0.0303285i
$754$		0			0
$755$	0.420313	−	2.92334i	0.420313	−	2.92334i
$756$	−0.349464	−	0.936950i	−0.349464	−	0.936950i
$757$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$757$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$758$		0			0
$759$		0			0
$760$	−1.22687			−1.22687
$761$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$761$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$762$	−1.35693	−	1.35693i	−1.35693	−	1.35693i
$763$		0			0
$764$	0.449181	−	0.983568i	0.449181	−	0.983568i
$765$		0			0
$766$		0			0
$767$	2.02105	+	3.14482i	2.02105	+	3.14482i
$768$	0.977147	−	0.212565i	0.977147	−	0.212565i
$769$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$769$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$770$		0			0
$771$		0			0
$772$	0.540641	−	0.158746i	0.540641	−	0.158746i
$773$	0.398174	+	0.871880i	0.398174	+	0.871880i	0.997452	+	0.0713392i	$0.0227273\pi$
$773$	0.398174	+	0.871880i	0.398174	+	0.871880i	−0.599278	+	0.800541i	$0.704545\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	3.07343	−	1.67822i	3.07343	−	1.67822i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.654861	+	0.755750i	0.654861	+	0.755750i
$785$	−1.13745	+	1.76991i	−1.13745	+	1.76991i
$786$	0.898064	+	0.334961i	0.898064	+	0.334961i
$787$	−1.70456	−	0.778446i	−1.70456	−	0.778446i	−0.997452	−	0.0713392i	$-0.977273\pi$
$787$	−1.70456	−	0.778446i	−1.70456	−	0.778446i	−0.707107	−	0.707107i	$-0.750000\pi$
$788$		0			0
$789$	−0.724384	+	1.32661i	−0.724384	+	1.32661i
$790$	0.420313	−	0.270119i	0.420313	−	0.270119i
$791$	1.80075	−	0.822373i	1.80075	−	0.822373i
$792$		0			0
$793$	2.13214	+	1.84751i	2.13214	+	1.84751i
$794$	−0.107829	−	0.0934345i	−0.107829	−	0.0934345i
$795$		0			0
$796$		0			0
$797$	1.67822	−	1.07853i	1.67822	−	1.07853i	0.800541	−	0.599278i	$-0.204545\pi$
$797$	1.67822	−	1.07853i	1.67822	−	1.07853i	0.877679	−	0.479249i	$-0.159091\pi$
$798$	−0.613435	−	0.334961i	−0.613435	−	0.334961i
$799$		0			0
$800$	−1.89320	−	0.864596i	−1.89320	−	0.864596i
$801$		0			0
$802$	−0.817178	+	1.27155i	−0.817178	+	1.27155i
$803$		0			0
$804$		0			0
$805$	−1.59673	−	0.729202i	−1.59673	−	0.729202i
$806$		0			0
$807$	0.334961	+	0.613435i	0.334961	+	0.613435i
$808$	1.18971	+	0.764582i	1.18971	+	0.764582i
$809$	0.281733	+	0.0405070i	0.281733	+	0.0405070i	0.281733	−	0.959493i	$-0.409091\pi$
$809$	0.281733	+	0.0405070i	0.281733	+	0.0405070i			1.00000i	$0.5\pi$
$810$	0.494541	+	1.68425i	0.494541	+	1.68425i
$811$	0.0994679	+	0.691814i	0.0994679	+	0.691814i	0.977147	+	0.212565i	$0.0681818\pi$
$811$	0.0994679	+	0.691814i	0.0994679	+	0.691814i	−0.877679	+	0.479249i	$0.840909\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	1.99490			1.99490
$820$		0			0
$821$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$821$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$822$	0.0592707	−	0.828713i	0.0592707	−	0.828713i
$823$	0.755750	−	1.65486i	0.755750	−	1.65486i		−	1.00000i	$-0.5\pi$
$823$	0.755750	−	1.65486i	0.755750	−	1.65486i	0.755750	−	0.654861i	$-0.227273\pi$
$824$		0			0
$825$		0			0
$826$	1.41620	−	1.22714i	1.41620	−	1.22714i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	−0.989821	+	0.142315i	−0.989821	+	0.142315i
$829$	−0.958498			−0.958498			−0.479249	−	0.877679i	$-0.659091\pi$
$829$	−0.958498			−0.958498			−0.479249	+	0.877679i	$0.659091\pi$
$830$	2.12401	−	1.84047i	2.12401	−	1.84047i
$831$		0			0
$832$	−0.283904	+	1.97460i	−0.283904	+	1.97460i
$833$		0			0
$834$	−0.114220	+	1.59700i	−0.114220	+	1.59700i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−0.562029	−	1.91410i	−0.562029	−	1.91410i
$839$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$839$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$840$	−1.05195	−	1.40524i	−1.05195	−	1.40524i
$841$	0.959493	−	0.281733i	0.959493	−	0.281733i
$842$		0			0
$843$	−0.670617	−	1.79799i	−0.670617	−	1.79799i
$844$		0			0
$845$	0.744355	+	5.17710i	0.744355	+	5.17710i
$846$		0			0
$847$	0.989821	+	0.142315i	0.989821	+	0.142315i
$848$		0			0
$849$	0.0683785	+	0.125226i	0.0683785	+	0.125226i
$850$		0			0
$851$		0			0
$852$	1.27979	+	0.278401i	1.27979	+	0.278401i
$853$	−0.784887	−	0.905808i	−0.784887	−	0.905808i	0.212565	−	0.977147i	$-0.431818\pi$
$853$	−0.784887	−	0.905808i	−0.784887	−	0.905808i	−0.997452	+	0.0713392i	$0.977273\pi$
$854$	0.764582	−	1.18971i	0.764582	−	1.18971i
$855$	1.03211	+	0.663296i	1.03211	+	0.663296i
$856$		0			0
$857$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$857$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$858$		0			0
$859$	0.806340	−	0.518203i	0.806340	−	0.518203i	−0.0713392	−	0.997452i	$-0.522727\pi$
$859$	0.806340	−	0.518203i	0.806340	−	0.518203i	0.877679	+	0.479249i	$0.159091\pi$
$860$		0			0
$861$		0			0
$862$	−0.215109	−	0.186393i	−0.215109	−	0.186393i
$863$	−0.627899	−	0.544078i	−0.627899	−	0.544078i	0.281733	−	0.959493i	$-0.409091\pi$
$863$	−0.627899	−	0.544078i	−0.627899	−	0.544078i	−0.909632	+	0.415415i	$0.863636\pi$
$864$	−0.936950	−	0.349464i	−0.936950	−	0.349464i
$865$	1.91377	−	0.873989i	1.91377	−	0.873989i
$866$		0			0
$867$	−0.479249	+	0.877679i	−0.479249	+	0.877679i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−0.457701	+	0.528215i	−0.457701	+	0.528215i
$875$			1.89804i			1.89804i
$876$		0			0
$877$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$877$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$878$		0			0
$879$	−0.340335	−	0.254771i	−0.340335	−	0.254771i
$880$		0			0
$881$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$881$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$882$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$883$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$883$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$884$		0			0
$885$	−2.63327	+	1.97124i	−2.63327	+	1.97124i
$886$		0			0
$887$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$887$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$888$		0			0
$889$	−1.03748	−	1.61435i	−1.03748	−	1.61435i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.00000			1.00000
$897$	0.424047	−	1.94931i	0.424047	−	1.94931i
$898$	−1.81926			−1.81926
$899$		0			0
$900$	1.12523	+	1.75089i	1.12523	+	1.75089i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.557730	−	1.89945i	0.557730	−	1.89945i
$905$	−1.85466	−	2.88591i	−1.85466	−	2.88591i
$906$	−0.357643	−	1.64406i	−0.357643	−	1.64406i
$907$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$907$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$908$	−0.784887	+	0.905808i	−0.784887	+	0.905808i
$909$	−0.587486	−	1.28641i	−0.587486	−	1.28641i
$910$	3.35992	−	0.986563i	3.35992	−	0.986563i
$911$	0.118239	+	0.258908i	0.118239	+	0.258908i	0.959493	−	0.281733i	$-0.0909091\pi$
$911$	0.118239	+	0.258908i	0.118239	+	0.258908i	−0.841254	+	0.540641i	$0.818182\pi$
$912$	−0.654861	+	0.244250i	−0.654861	+	0.244250i
$913$		0			0
$914$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$915$	−1.48768	+	1.98730i	−1.48768	+	1.98730i
$916$	−1.85483	−	0.266684i	−1.85483	−	0.266684i
$917$	0.806340	+	0.518203i	0.806340	+	0.518203i
$918$		0			0
$919$			1.30972i			1.30972i	0.755750	+	0.654861i	$0.227273\pi$
$919$			1.30972i			1.30972i	−0.755750	+	0.654861i	$0.772727\pi$
$920$	−1.59673	+	0.729202i	−1.59673	+	0.729202i
$921$	0.0303285	−	0.139418i	0.0303285	−	0.139418i
$922$	1.04849	+	1.21002i	1.04849	+	1.21002i
$923$	−1.41257	+	2.19800i	−1.41257	+	2.19800i
$924$		0			0
$925$		0			0
$926$	1.49611	−	0.215109i	1.49611	−	0.215109i
$927$		0			0
$928$		0			0
$929$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$929$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$930$		0			0
$931$	−0.528215	−	0.457701i	−0.528215	−	0.457701i
$932$	−1.49611	−	1.29639i	−1.49611	−	1.29639i
$933$		0			0
$934$	1.77769	−	0.811843i	1.77769	−	0.811843i
$935$		0			0
$936$	1.30638	−	1.50765i	1.30638	−	1.50765i
$937$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$937$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.04849	−	1.21002i	−1.04849	−	1.21002i	−0.977147	−	0.212565i	$-0.931818\pi$
$941$	−1.04849	−	1.21002i	−1.04849	−	1.21002i	−0.0713392	−	0.997452i	$-0.522727\pi$
$942$	−0.254771	+	1.17116i	−0.254771	+	1.17116i
$943$		0			0
$944$		−	1.87390i		−	1.87390i
$945$	0.125226	+	1.75089i	0.125226	+	1.75089i
$946$		0			0
$947$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$947$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$948$	0.170572	−	0.227858i	0.170572	−	0.227858i
$949$		0			0
$950$	1.39574	+	0.409827i	1.39574	+	0.409827i
$951$		0			0
$952$		0			0
$953$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$953$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$954$		0			0
$955$	−1.24295	+	1.43444i	−1.24295	+	1.43444i
$956$	−0.158746	−	0.540641i	−0.158746	−	0.540641i
$957$		0			0
$958$		0			0
$959$	0.234072	−	0.797176i	0.234072	−	0.797176i
$960$	−1.75089	−	0.125226i	−1.75089	−	0.125226i
$961$	0.415415	−	0.909632i	0.415415	−	0.909632i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.989083			−0.989083
$966$	−0.997452	−	0.0713392i	−0.997452	−	0.0713392i
$967$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$967$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$968$	0.755750	−	0.654861i	0.755750	−	0.654861i
$969$		0			0
$970$		0			0
$971$	0.398174	−	0.871880i	0.398174	−	0.871880i	−0.599278	−	0.800541i	$-0.704545\pi$
$971$	0.398174	−	0.871880i	0.398174	−	0.871880i	0.997452	−	0.0713392i	$-0.0227273\pi$
$972$	0.599278	+	0.800541i	0.599278	+	0.800541i
$973$	−0.451077	+	1.53623i	−0.451077	+	1.53623i
$974$	−0.708089	−	1.10181i	−0.708089	−	1.10181i
$975$	−4.05707	+	0.882562i	−4.05707	+	0.882562i
$976$	−0.398430	−	1.35693i	−0.398430	−	1.35693i
$977$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$977$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$978$		0			0
$979$		0			0
$980$	−0.729202	−	1.59673i	−0.729202	−	1.59673i
$981$		0			0
$982$		0			0
$983$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$983$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		−	1.39430i		−	1.39430i
$989$		0			0
$990$		0			0
$991$	0.368991	+	0.425839i	0.368991	+	0.425839i	0.909632	−	0.415415i	$-0.136364\pi$
$991$	0.368991	+	0.425839i	0.368991	+	0.425839i	−0.540641	+	0.841254i	$0.681818\pi$
$992$		0			0
$993$		0			0
$994$	1.19136	+	0.544078i	1.19136	+	0.544078i
$995$		0			0
$996$	0.767317	−	1.40524i	0.767317	−	1.40524i
$997$	1.47670	−	0.949018i	1.47670	−	0.949018i	0.479249	−	0.877679i	$-0.340909\pi$
$997$	1.47670	−	0.949018i	1.47670	−	0.949018i	0.997452	−	0.0713392i	$-0.0227273\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3864.1.cx.b.125.2	yes	40
3.2	odd	2		3864.1.cx.a.125.3	✓	40
7.6	odd	2	inner	3864.1.cx.b.125.1	yes	40
8.5	even	2	inner	3864.1.cx.b.125.1	yes	40
21.20	even	2		3864.1.cx.a.125.4	yes	40
23.7	odd	22		3864.1.cx.a.2813.3	yes	40
24.5	odd	2		3864.1.cx.a.125.4	yes	40
56.13	odd	2	CM	3864.1.cx.b.125.2	yes	40
69.53	even	22	inner	3864.1.cx.b.2813.2	yes	40
161.76	even	22		3864.1.cx.a.2813.4	yes	40
168.125	even	2		3864.1.cx.a.125.3	✓	40
184.53	odd	22		3864.1.cx.a.2813.4	yes	40
483.398	odd	22	inner	3864.1.cx.b.2813.1	yes	40
552.53	even	22	inner	3864.1.cx.b.2813.1	yes	40
1288.237	even	22		3864.1.cx.a.2813.3	yes	40
3864.2813	odd	22	inner	3864.1.cx.b.2813.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3864.1.cx.a.125.3	✓	40	3.2	odd	2
3864.1.cx.a.125.3	✓	40	168.125	even	2
3864.1.cx.a.125.4	yes	40	21.20	even	2
3864.1.cx.a.125.4	yes	40	24.5	odd	2
3864.1.cx.a.2813.3	yes	40	23.7	odd	22
3864.1.cx.a.2813.3	yes	40	1288.237	even	22
3864.1.cx.a.2813.4	yes	40	161.76	even	22
3864.1.cx.a.2813.4	yes	40	184.53	odd	22
3864.1.cx.b.125.1	yes	40	7.6	odd	2	inner
3864.1.cx.b.125.1	yes	40	8.5	even	2	inner
3864.1.cx.b.125.2	yes	40	1.1	even	1	trivial
3864.1.cx.b.125.2	yes	40	56.13	odd	2	CM
3864.1.cx.b.2813.1	yes	40	483.398	odd	22	inner
3864.1.cx.b.2813.1	yes	40	552.53	even	22	inner
3864.1.cx.b.2813.2	yes	40	69.53	even	22	inner
3864.1.cx.b.2813.2	yes	40	3864.2813	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.755750 + 0.654861i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.142315 - 0.989821i) q^{4} +(-0.729202 + 1.59673i) q^{5} +(-0.0713392 + 0.997452i) q^{6} +(-0.281733 + 0.959493i) q^{7} +(0.540641 + 0.841254i) q^{8} -1.00000i q^{9} +(-0.494541 - 1.68425i) q^{10} +(-0.599278 - 0.800541i) q^{12} +(1.91410 - 0.562029i) q^{13} +(-0.415415 - 0.909632i) q^{14} +(0.613435 + 1.64468i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.654861 + 0.755750i) q^{18} +(0.691814 + 0.0994679i) q^{19} +(1.47670 + 0.949018i) q^{20} +(0.479249 + 0.877679i) q^{21} +(0.959493 - 0.281733i) q^{23} +(0.977147 + 0.212565i) q^{24} +(-1.36295 - 1.57293i) q^{25} +(-1.07853 + 1.67822i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.909632 + 0.415415i) q^{28} +(-1.54064 - 0.841254i) q^{30} +(0.909632 - 0.415415i) q^{32} +(-1.32661 - 1.14952i) q^{35} +(-0.989821 - 0.142315i) q^{36} +(-0.587976 + 0.377869i) q^{38} +(0.956056 - 1.75089i) q^{39} +(-1.73749 + 0.249813i) q^{40} +(-0.936950 - 0.349464i) q^{42} +(1.59673 + 0.729202i) q^{45} +(-0.540641 + 0.841254i) q^{46} +(-0.877679 + 0.479249i) q^{48} +(-0.841254 - 0.540641i) q^{49} +(2.06010 + 0.296197i) q^{50} +(-0.283904 - 1.97460i) q^{52} +(0.997452 + 0.0713392i) q^{54} +(-0.959493 + 0.281733i) q^{56} +(0.559521 - 0.418852i) q^{57} +(0.527938 + 1.79799i) q^{59} +(1.71524 - 0.373128i) q^{60} +(0.764582 + 1.18971i) q^{61} +(0.959493 + 0.281733i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-0.498354 + 3.46613i) q^{65} +(0.479249 - 0.877679i) q^{69} +1.75536 q^{70} +(-0.989821 + 0.857685i) q^{71} +(0.841254 - 0.540641i) q^{72} +(-2.07598 - 0.148477i) q^{75} +(0.196911 - 0.670617i) q^{76} +(0.424047 + 1.94931i) q^{78} +(0.0801894 + 0.273100i) q^{79} +(1.14952 - 1.32661i) q^{80} -1.00000 q^{81} +(0.665114 + 1.45640i) q^{83} +(0.936950 - 0.349464i) q^{84} +(-1.68425 + 0.494541i) q^{90} +1.99490i q^{91} +(-0.142315 - 0.989821i) q^{92} +(-0.663296 + 1.03211i) q^{95} +(0.349464 - 0.936950i) q^{96} +(0.989821 - 0.142315i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{4} + 4 q^{14} - 4 q^{15} - 4 q^{16} + 4 q^{18} + 4 q^{23} - 4 q^{25} - 40 q^{30} - 4 q^{39} + 4 q^{49} - 4 q^{56} - 4 q^{57} + 4 q^{60} + 4 q^{63} + 4 q^{64} - 8 q^{65} - 4 q^{72} + 4 q^{78}+ \cdots - 4 q^{92}+O(q^{100}) \) 40 * q + 4 * q^4 + 4 * q^14 - 4 * q^15 - 4 * q^16 + 4 * q^18 + 4 * q^23 - 4 * q^25 - 40 * q^30 - 4 * q^39 + 4 * q^49 - 4 * q^56 - 4 * q^57 + 4 * q^60 + 4 * q^63 + 4 * q^64 - 8 * q^65 - 4 * q^72 + 4 * q^78 - 40 * q^81 - 4 * q^92

Introduction

L-functions

Modular forms

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