LMFDB - Embedded newform 3864.1.cx.b.1805.2

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			1805.2
Root			$0.936950 - 0.349464i$ of defining polynomial
Character	$\chi$	$=$	3864.1805
Dual form			3864.1.cx.b.3149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.540641 - 0.841254i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.91410 - 0.562029i) q^{5} +(-0.977147 - 0.212565i) q^{6} +(-0.755750 + 0.654861i) q^{7} +(0.989821 - 0.142315i) q^{8} -1.00000i q^{9} +(-1.50765 - 1.30638i) q^{10} +(0.349464 + 0.936950i) q^{12} +(-0.278401 + 0.321292i) q^{13} +(0.959493 + 0.281733i) q^{14} +(0.956056 - 1.75089i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.841254 + 0.540641i) q^{18} +(-0.871880 - 0.398174i) q^{19} +(-0.283904 + 1.97460i) q^{20} +(-0.0713392 + 0.997452i) q^{21} +(0.654861 - 0.755750i) q^{23} +(0.599278 - 0.800541i) q^{24} +(2.50664 - 1.61092i) q^{25} +(0.420803 + 0.0605024i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.281733 - 0.959493i) q^{28} +(-1.98982 + 0.142315i) q^{30} +(-0.281733 + 0.959493i) q^{32} +(-1.07853 + 1.67822i) q^{35} +(0.909632 + 0.415415i) q^{36} +(0.136408 + 0.948742i) q^{38} +(0.0303285 + 0.424047i) q^{39} +(1.81463 - 0.828713i) q^{40} +(0.877679 - 0.479249i) q^{42} +(-0.562029 - 1.91410i) q^{45} +(-0.989821 - 0.142315i) q^{46} +(-0.997452 - 0.0713392i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-2.71038 - 1.23779i) q^{50} +(-0.176606 - 0.386712i) q^{52} +(-0.212565 + 0.977147i) q^{54} +(-0.654861 + 0.755750i) q^{56} +(-0.898064 + 0.334961i) q^{57} +(-1.32661 - 1.14952i) q^{59} +(1.19550 + 1.59700i) q^{60} +(1.39982 - 0.201264i) q^{61} +(0.654861 + 0.755750i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.352311 + 0.771454i) q^{65} +(-0.0713392 - 0.997452i) q^{69} +1.99490 q^{70} +(0.909632 + 1.41542i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(0.633369 - 2.91155i) q^{75} +(0.724384 - 0.627683i) q^{76} +(0.340335 - 0.254771i) q^{78} +(-0.627899 - 0.544078i) q^{79} +(-1.67822 - 1.07853i) q^{80} -1.00000 q^{81} +(1.79799 + 0.527938i) q^{83} +(-0.877679 - 0.479249i) q^{84} +(-1.30638 + 1.50765i) q^{90} -0.425131i q^{91} +(0.415415 + 0.909632i) q^{92} +(-1.89265 - 0.272122i) q^{95} +(0.479249 + 0.877679i) q^{96} +(-0.909632 + 0.415415i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3864\mathbb{Z}\right)^\times$.

$n$	$967$	$1289$	$1933$	$2761$	$2857$
$\chi(n)$	$1$	$-1$	$-1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.540641	−	0.841254i	−0.540641	−	0.841254i
$2$	−0.540641	−	0.841254i	−0.540641	−	0.841254i
$3$	0.707107	−	0.707107i	0.707107	−	0.707107i
$3$	0.707107	−	0.707107i	0.707107	−	0.707107i
$4$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$5$	1.91410	−	0.562029i	1.91410	−	0.562029i	0.936950	−	0.349464i	$-0.113636\pi$
$5$	1.91410	−	0.562029i	1.91410	−	0.562029i	0.977147	−	0.212565i	$-0.0681818\pi$
$6$	−0.977147	−	0.212565i	−0.977147	−	0.212565i
$7$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$7$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$8$	0.989821	−	0.142315i	0.989821	−	0.142315i
$9$		−	1.00000i		−	1.00000i
$10$	−1.50765	−	1.30638i	−1.50765	−	1.30638i
$11$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$11$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$12$	0.349464	+	0.936950i	0.349464	+	0.936950i
$13$	−0.278401	+	0.321292i	−0.278401	+	0.321292i	−0.877679	−	0.479249i	$-0.840909\pi$
$13$	−0.278401	+	0.321292i	−0.278401	+	0.321292i	0.599278	+	0.800541i	$0.295455\pi$
$14$	0.959493	+	0.281733i	0.959493	+	0.281733i
$15$	0.956056	−	1.75089i	0.956056	−	1.75089i
$16$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$17$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$17$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$18$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$19$	−0.871880	−	0.398174i	−0.871880	−	0.398174i	−0.0713392	−	0.997452i	$-0.522727\pi$
$19$	−0.871880	−	0.398174i	−0.871880	−	0.398174i	−0.800541	+	0.599278i	$0.795455\pi$
$20$	−0.283904	+	1.97460i	−0.283904	+	1.97460i
$21$	−0.0713392	+	0.997452i	−0.0713392	+	0.997452i
$22$		0			0
$23$	0.654861	−	0.755750i	0.654861	−	0.755750i
$23$	0.654861	−	0.755750i	0.654861	−	0.755750i
$24$	0.599278	−	0.800541i	0.599278	−	0.800541i
$25$	2.50664	−	1.61092i	2.50664	−	1.61092i
$26$	0.420803	+	0.0605024i	0.420803	+	0.0605024i
$27$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$28$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$29$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$29$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$30$	−1.98982	+	0.142315i	−1.98982	+	0.142315i
$31$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$31$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$32$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$33$		0			0
$34$		0			0
$35$	−1.07853	+	1.67822i	−1.07853	+	1.67822i
$36$	0.909632	+	0.415415i	0.909632	+	0.415415i
$37$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$37$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$38$	0.136408	+	0.948742i	0.136408	+	0.948742i
$39$	0.0303285	+	0.424047i	0.0303285	+	0.424047i
$40$	1.81463	−	0.828713i	1.81463	−	0.828713i
$41$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$41$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$42$	0.877679	−	0.479249i	0.877679	−	0.479249i
$43$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$43$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$44$		0			0
$45$	−0.562029	−	1.91410i	−0.562029	−	1.91410i
$46$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−0.997452	−	0.0713392i	−0.997452	−	0.0713392i
$49$	0.142315	−	0.989821i	0.142315	−	0.989821i
$50$	−2.71038	−	1.23779i	−2.71038	−	1.23779i
$51$		0			0
$52$	−0.176606	−	0.386712i	−0.176606	−	0.386712i
$53$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$53$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$54$	−0.212565	+	0.977147i	−0.212565	+	0.977147i
$55$		0			0
$56$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$57$	−0.898064	+	0.334961i	−0.898064	+	0.334961i
$58$		0			0
$59$	−1.32661	−	1.14952i	−1.32661	−	1.14952i	−0.977147	−	0.212565i	$-0.931818\pi$
$59$	−1.32661	−	1.14952i	−1.32661	−	1.14952i	−0.349464	−	0.936950i	$-0.613636\pi$
$60$	1.19550	+	1.59700i	1.19550	+	1.59700i
$61$	1.39982	−	0.201264i	1.39982	−	0.201264i	0.599278	−	0.800541i	$-0.295455\pi$
$61$	1.39982	−	0.201264i	1.39982	−	0.201264i	0.800541	+	0.599278i	$0.204545\pi$
$62$		0			0
$63$	0.654861	+	0.755750i	0.654861	+	0.755750i
$64$	0.959493	−	0.281733i	0.959493	−	0.281733i
$65$	−0.352311	+	0.771454i	−0.352311	+	0.771454i
$66$		0			0
$67$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$67$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$68$		0			0
$69$	−0.0713392	−	0.997452i	−0.0713392	−	0.997452i
$70$	1.99490			1.99490
$71$	0.909632	+	1.41542i	0.909632	+	1.41542i	0.909632	+	0.415415i	$0.136364\pi$
$71$	0.909632	+	1.41542i	0.909632	+	1.41542i			1.00000i	$0.5\pi$
$72$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$73$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$73$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$74$		0			0
$75$	0.633369	−	2.91155i	0.633369	−	2.91155i
$76$	0.724384	−	0.627683i	0.724384	−	0.627683i
$77$		0			0
$78$	0.340335	−	0.254771i	0.340335	−	0.254771i
$79$	−0.627899	−	0.544078i	−0.627899	−	0.544078i	0.281733	−	0.959493i	$-0.409091\pi$
$79$	−0.627899	−	0.544078i	−0.627899	−	0.544078i	−0.909632	+	0.415415i	$0.863636\pi$
$80$	−1.67822	−	1.07853i	−1.67822	−	1.07853i
$81$	−1.00000			−1.00000
$82$		0			0
$83$	1.79799	+	0.527938i	1.79799	+	0.527938i	0.997452	−	0.0713392i	$-0.0227273\pi$
$83$	1.79799	+	0.527938i	1.79799	+	0.527938i	0.800541	+	0.599278i	$0.204545\pi$
$84$	−0.877679	−	0.479249i	−0.877679	−	0.479249i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$89$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$90$	−1.30638	+	1.50765i	−1.30638	+	1.50765i
$91$		−	0.425131i		−	0.425131i
$92$	0.415415	+	0.909632i	0.415415	+	0.909632i
$93$		0			0
$94$		0			0
$95$	−1.89265	−	0.272122i	−1.89265	−	0.272122i
$96$	0.479249	+	0.877679i	0.479249	+	0.877679i
$97$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$97$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$98$	−0.909632	+	0.415415i	−0.909632	+	0.415415i
$99$		0			0
$100$	0.424047	+	2.94931i	0.424047	+	2.94931i
$101$	−0.398430	+	1.35693i	−0.398430	+	1.35693i	0.479249	+	0.877679i	$0.340909\pi$
$101$	−0.398430	+	1.35693i	−0.398430	+	1.35693i	−0.877679	+	0.479249i	$0.840909\pi$
$102$		0			0
$103$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$103$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$104$	−0.229843	+	0.357643i	−0.229843	+	0.357643i
$105$	0.424047	+	1.94931i	0.424047	+	1.94931i
$106$		0			0
$107$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$107$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$108$	0.936950	−	0.349464i	0.936950	−	0.349464i
$109$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$109$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$110$		0			0
$111$		0			0
$112$	0.989821	+	0.142315i	0.989821	+	0.142315i
$113$	−1.53046	+	0.983568i	−1.53046	+	0.983568i	−0.540641	+	0.841254i	$0.681818\pi$
$113$	−1.53046	+	0.983568i	−1.53046	+	0.983568i	−0.989821	+	0.142315i	$0.954545\pi$
$114$	0.767317	+	0.574406i	0.767317	+	0.574406i
$115$	0.828713	−	1.81463i	0.828713	−	1.81463i
$116$		0			0
$117$	0.321292	+	0.278401i	0.321292	+	0.278401i
$118$	−0.249813	+	1.73749i	−0.249813	+	1.73749i
$119$		0			0
$120$	0.697148	−	1.86912i	0.697148	−	1.86912i
$121$	0.415415	+	0.909632i	0.415415	+	0.909632i
$122$	−0.926113	−	1.06879i	−0.926113	−	1.06879i
$123$		0			0
$124$		0			0
$125$	2.58617	−	2.98460i	2.58617	−	2.98460i
$126$	0.281733	−	0.959493i	0.281733	−	0.959493i
$127$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.959493	−	0.281733i	$-0.0909091\pi$
$127$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.142315	+	0.989821i	$0.454545\pi$
$128$	−0.755750	−	0.654861i	−0.755750	−	0.654861i
$129$		0			0
$130$	0.839462	−	0.120696i	0.839462	−	0.120696i
$131$	−0.107829	+	0.0934345i	−0.107829	+	0.0934345i	−0.707107	−	0.707107i	$-0.750000\pi$
$131$	−0.107829	+	0.0934345i	−0.107829	+	0.0934345i	0.599278	+	0.800541i	$0.295455\pi$
$132$		0			0
$133$	0.919672	−	0.270040i	0.919672	−	0.270040i
$134$		0			0
$135$	−1.75089	−	0.956056i	−1.75089	−	0.956056i
$136$		0			0
$137$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$137$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$138$	−0.800541	+	0.599278i	−0.800541	+	0.599278i
$139$	−1.87390			−1.87390			−0.936950	−	0.349464i	$-0.886364\pi$
$139$	−1.87390			−1.87390			−0.936950	+	0.349464i	$0.886364\pi$
$140$	−1.07853	−	1.67822i	−1.07853	−	1.67822i
$141$		0			0
$142$	0.698939	−	1.53046i	0.698939	−	1.53046i
$143$		0			0
$144$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$145$		0			0
$146$		0			0
$147$	−0.599278	−	0.800541i	−0.599278	−	0.800541i
$148$		0			0
$149$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$149$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$150$	−2.79178	+	1.04128i	−2.79178	+	1.04128i
$151$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$151$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$152$	−0.919672	−	0.270040i	−0.919672	−	0.270040i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.398326	−	0.148568i	−0.398326	−	0.148568i
$157$	0.635768	+	0.290345i	0.635768	+	0.290345i	0.707107	−	0.707107i	$-0.250000\pi$
$157$	0.635768	+	0.290345i	0.635768	+	0.290345i	−0.0713392	+	0.997452i	$0.522727\pi$
$158$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$159$		0			0
$160$			1.99490i			1.99490i
$161$			1.00000i			1.00000i
$162$	0.540641	+	0.841254i	0.540641	+	0.841254i
$163$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$163$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$164$		0			0
$165$		0			0
$166$	−0.527938	−	1.79799i	−0.527938	−	1.79799i
$167$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$167$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$168$	0.0713392	+	0.997452i	0.0713392	+	0.997452i
$169$	0.116593	+	0.810925i	0.116593	+	0.810925i
$170$		0			0
$171$	−0.398174	+	0.871880i	−0.398174	+	0.871880i
$172$		0			0
$173$	0.377869	−	0.587976i	0.377869	−	0.587976i	−0.599278	−	0.800541i	$-0.704545\pi$
$173$	0.377869	−	0.587976i	0.377869	−	0.587976i	0.977147	+	0.212565i	$0.0681818\pi$
$174$		0			0
$175$	−0.839462	+	2.85895i	−0.839462	+	2.85895i
$176$		0			0
$177$	−1.75089	+	0.125226i	−1.75089	+	0.125226i
$178$		0			0
$179$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$179$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$180$	1.97460	+	0.283904i	1.97460	+	0.283904i
$181$	−1.18636	−	0.170572i	−1.18636	−	0.170572i	−0.479249	−	0.877679i	$-0.659091\pi$
$181$	−1.18636	−	0.170572i	−1.18636	−	0.170572i	−0.707107	+	0.707107i	$0.750000\pi$
$182$	−0.357643	+	0.229843i	−0.357643	+	0.229843i
$183$	0.847507	−	1.13214i	0.847507	−	1.13214i
$184$	0.540641	−	0.841254i	0.540641	−	0.841254i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.997452	+	0.0713392i	0.997452	+	0.0713392i
$190$	0.794320	+	1.73932i	0.794320	+	1.73932i
$191$	1.29639	+	1.49611i	1.29639	+	1.49611i	0.755750	+	0.654861i	$0.227273\pi$
$191$	1.29639	+	1.49611i	1.29639	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$192$	0.479249	−	0.877679i	0.479249	−	0.877679i
$193$	−1.45027	−	0.425839i	−1.45027	−	0.425839i	−0.540641	−	0.841254i	$-0.681818\pi$
$193$	−1.45027	−	0.425839i	−1.45027	−	0.425839i	−0.909632	+	0.415415i	$0.863636\pi$
$194$		0			0
$195$	0.296379	+	0.794622i	0.296379	+	0.794622i
$196$	0.841254	+	0.540641i	0.841254	+	0.540641i
$197$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$197$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$198$		0			0
$199$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$199$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$200$	2.25186	−	1.95125i	2.25186	−	1.95125i
$201$		0			0
$202$	1.35693	−	0.398430i	1.35693	−	0.398430i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.755750	−	0.654861i	−0.755750	−	0.654861i
$208$	0.425131			0.425131
$209$		0			0
$210$	1.41061	−	1.41061i	1.41061	−	1.41061i
$211$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$211$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$212$		0			0
$213$	1.64406	+	0.357643i	1.64406	+	0.357643i
$214$		0			0
$215$		0			0
$216$	−0.800541	−	0.599278i	−0.800541	−	0.599278i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$223$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$224$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$225$	−1.61092	−	2.50664i	−1.61092	−	2.50664i
$226$	1.65486	+	0.755750i	1.65486	+	0.755750i
$227$	−0.0994679	+	0.691814i	−0.0994679	+	0.691814i	0.877679	+	0.479249i	$0.159091\pi$
$227$	−0.0994679	+	0.691814i	−0.0994679	+	0.691814i	−0.977147	+	0.212565i	$0.931818\pi$
$228$	0.0683785	−	0.956056i	0.0683785	−	0.956056i
$229$			1.75536i			1.75536i	0.479249	+	0.877679i	$0.340909\pi$
$229$			1.75536i			1.75536i	−0.479249	+	0.877679i	$0.659091\pi$
$230$	−1.97460	+	0.283904i	−1.97460	+	0.283904i
$231$		0			0
$232$		0			0
$233$	−1.80075	−	0.258908i	−1.80075	−	0.258908i	−0.841254	−	0.540641i	$-0.818182\pi$
$233$	−1.80075	−	0.258908i	−1.80075	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$234$	0.0605024	−	0.420803i	0.0605024	−	0.420803i
$235$		0			0
$236$	1.59673	−	0.729202i	1.59673	−	0.729202i
$237$	−0.828713	+	0.0592707i	−0.828713	+	0.0592707i
$238$		0			0
$239$	−0.425839	+	1.45027i	−0.425839	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$239$	−0.425839	+	1.45027i	−0.425839	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$240$	−1.94931	+	0.424047i	−1.94931	+	0.424047i
$241$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$241$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$242$	0.540641	−	0.841254i	0.540641	−	0.841254i
$243$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$244$	−0.398430	+	1.35693i	−0.398430	+	1.35693i
$245$	−0.283904	−	1.97460i	−0.283904	−	1.97460i
$246$		0			0
$247$	0.370663	−	0.169276i	0.370663	−	0.169276i
$248$		0			0
$249$	1.64468	−	0.898064i	1.64468	−	0.898064i
$250$	−3.90900	−	0.562029i	−3.90900	−	0.562029i
$251$	−1.34692	+	0.865611i	−1.34692	+	0.865611i	−0.997452	−	0.0713392i	$-0.977273\pi$
$251$	−1.34692	+	0.865611i	−1.34692	+	0.865611i	−0.349464	+	0.936950i	$0.613636\pi$
$252$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$253$		0			0
$254$		−	1.30972i		−	1.30972i
$255$		0			0
$256$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$257$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$257$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$258$		0			0
$259$		0			0
$260$	−0.555384	−	0.640947i	−0.555384	−	0.640947i
$261$		0			0
$262$	0.136899	+	0.0401971i	0.136899	+	0.0401971i
$263$	−0.708089	+	0.817178i	−0.708089	+	0.817178i	−0.989821	−	0.142315i	$-0.954545\pi$
$263$	−0.708089	+	0.817178i	−0.708089	+	0.817178i	0.281733	+	0.959493i	$0.409091\pi$
$264$		0			0
$265$		0			0
$266$	−0.724384	−	0.627683i	−0.724384	−	0.627683i
$267$		0			0
$268$		0			0
$269$	−0.724384	+	0.627683i	−0.724384	+	0.627683i	−0.936950	−	0.349464i	$-0.886364\pi$
$269$	−0.724384	+	0.627683i	−0.724384	+	0.627683i	0.212565	+	0.977147i	$0.431818\pi$
$270$	0.142315	+	1.98982i	0.142315	+	1.98982i
$271$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$271$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$272$		0			0
$273$	−0.300613	−	0.300613i	−0.300613	−	0.300613i
$274$	−1.03748	−	1.61435i	−1.03748	−	1.61435i
$275$		0			0
$276$	0.936950	+	0.349464i	0.936950	+	0.349464i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	1.01311	+	1.57642i	1.01311	+	1.57642i
$279$		0			0
$280$	−0.828713	+	1.81463i	−0.828713	+	1.81463i
$281$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$281$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$282$		0			0
$283$	−1.47696	+	1.27979i	−1.47696	+	1.27979i	−0.599278	+	0.800541i	$0.704545\pi$
$283$	−1.47696	+	1.27979i	−1.47696	+	1.27979i	−0.877679	+	0.479249i	$0.840909\pi$
$284$	−1.66538	+	0.239446i	−1.66538	+	0.239446i
$285$	−1.53072	+	1.14589i	−1.53072	+	1.14589i
$286$		0			0
$287$		0			0
$288$	0.959493	+	0.281733i	0.959493	+	0.281733i
$289$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.665114	−	1.45640i	−0.665114	−	1.45640i	−0.877679	−	0.479249i	$-0.840909\pi$
$293$	−0.665114	−	1.45640i	−0.665114	−	1.45640i	0.212565	−	0.977147i	$-0.431818\pi$
$294$	−0.349464	+	0.936950i	−0.349464	+	0.936950i
$295$	−3.18532	−	1.45469i	−3.18532	−	1.45469i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.0605024	+	0.420803i	0.0605024	+	0.420803i
$300$	2.38533	+	1.78563i	2.38533	+	1.78563i
$301$		0			0
$302$	−0.281733	−	0.0405070i	−0.281733	−	0.0405070i
$303$	0.677760	+	1.24123i	0.677760	+	1.24123i
$304$	0.270040	+	0.919672i	0.270040	+	0.919672i
$305$	2.56627	−	1.17198i	2.56627	−	1.17198i
$306$		0			0
$307$	−0.278125	−	1.93440i	−0.278125	−	1.93440i	−0.349464	−	0.936950i	$-0.613636\pi$
$307$	−0.278125	−	1.93440i	−0.278125	−	1.93440i	0.0713392	−	0.997452i	$-0.477273\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$311$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$312$	0.0903680	+	0.415415i	0.0903680	+	0.415415i
$313$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$313$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$314$	−0.0994679	−	0.691814i	−0.0994679	−	0.691814i
$315$	1.67822	+	1.07853i	1.67822	+	1.07853i
$316$	0.755750	−	0.345139i	0.755750	−	0.345139i
$317$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$317$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$318$		0			0
$319$		0			0
$320$	1.67822	−	1.07853i	1.67822	−	1.07853i
$321$		0			0
$322$	0.841254	−	0.540641i	0.841254	−	0.540641i
$323$		0			0
$324$	0.415415	−	0.909632i	0.415415	−	0.909632i
$325$	−0.180276	+	1.25384i	−0.180276	+	1.25384i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$331$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$332$	−1.22714	+	1.41620i	−1.22714	+	1.41620i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.800541	−	0.599278i	0.800541	−	0.599278i
$337$	−1.66538	+	0.239446i	−1.66538	+	0.239446i	−0.909632	−	0.415415i	$-0.863636\pi$
$337$	−1.66538	+	0.239446i	−1.66538	+	0.239446i	−0.755750	+	0.654861i	$0.772727\pi$
$338$	0.619158	−	0.536504i	0.619158	−	0.536504i
$339$	−0.386712	+	1.77769i	−0.386712	+	1.77769i
$340$		0			0
$341$		0			0
$342$	0.948742	−	0.136408i	0.948742	−	0.136408i
$343$	0.540641	+	0.841254i	0.540641	+	0.841254i
$344$		0			0
$345$	−0.697148	−	1.86912i	−0.697148	−	1.86912i
$346$	−0.698928			−0.698928
$347$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$347$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$348$		0			0
$349$	0.587486	−	1.28641i	0.587486	−	1.28641i	−0.349464	−	0.936950i	$-0.613636\pi$
$349$	0.587486	−	1.28641i	0.587486	−	1.28641i	0.936950	−	0.349464i	$-0.113636\pi$
$350$	2.85895	−	0.839462i	2.85895	−	0.839462i
$351$	0.424047	−	0.0303285i	0.424047	−	0.0303285i
$352$		0			0
$353$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$353$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$354$	1.05195	+	1.40524i	1.05195	+	1.40524i
$355$	2.53663	+	2.19800i	2.53663	+	2.19800i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$359$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$360$	−0.828713	−	1.81463i	−0.828713	−	1.81463i
$361$	−0.0532282	−	0.0614286i	−0.0532282	−	0.0614286i
$362$	0.497898	+	1.09024i	0.497898	+	1.09024i
$363$	0.936950	+	0.349464i	0.936950	+	0.349464i
$364$	0.386712	+	0.176606i	0.386712	+	0.176606i
$365$		0			0
$366$	−1.41061	−	0.100889i	−1.41061	−	0.100889i
$367$		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		−0.281733	−	0.959493i	$-0.590909\pi$
$373$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$374$		0			0
$375$	−0.281733	−	3.93914i	−0.281733	−	3.93914i
$376$		0			0
$377$		0			0
$378$	−0.479249	−	0.877679i	−0.479249	−	0.877679i
$379$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$379$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$380$	1.03377	−	1.60857i	1.03377	−	1.60857i
$381$	1.27979	−	0.278401i	1.27979	−	0.278401i
$382$	0.557730	−	1.89945i	0.557730	−	1.89945i
$383$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$383$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$384$	−0.997452	+	0.0713392i	−0.997452	+	0.0713392i
$385$		0			0
$386$	0.425839	+	1.45027i	0.425839	+	1.45027i
$387$		0			0
$388$		0			0
$389$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$389$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$390$	0.508244	−	0.678935i	0.508244	−	0.678935i
$391$		0			0
$392$		−	1.00000i		−	1.00000i
$393$	−0.0101786	+	0.142315i	−0.0101786	+	0.142315i
$394$		0			0
$395$	−1.50765	−	0.688520i	−1.50765	−	0.688520i
$396$		0			0
$397$	−0.811843	−	1.77769i	−0.811843	−	1.77769i	−0.599278	−	0.800541i	$-0.704545\pi$
$397$	−0.811843	−	1.77769i	−0.811843	−	1.77769i	−0.212565	−	0.977147i	$-0.568182\pi$
$398$		0			0
$399$	0.459359	−	0.841254i	0.459359	−	0.841254i
$400$	−2.85895	−	0.839462i	−2.85895	−	0.839462i
$401$	0.708089	−	0.817178i	0.708089	−	0.817178i	−0.281733	−	0.959493i	$-0.590909\pi$
$401$	0.708089	−	0.817178i	0.708089	−	0.817178i	0.989821	+	0.142315i	$0.0454545\pi$
$402$		0			0
$403$		0			0
$404$	−1.06879	−	0.926113i	−1.06879	−	0.926113i
$405$	−1.91410	+	0.562029i	−1.91410	+	0.562029i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$409$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$410$		0			0
$411$	1.35693	−	1.35693i	1.35693	−	1.35693i
$412$		0			0
$413$	1.75536			1.75536
$414$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$415$	3.73825			3.73825
$416$	−0.229843	−	0.357643i	−0.229843	−	0.357643i
$417$	−1.32505	+	1.32505i	−1.32505	+	1.32505i
$418$		0			0
$419$	−0.407910	+	0.119773i	−0.407910	+	0.119773i	−0.479249	−	0.877679i	$-0.659091\pi$
$419$	−0.407910	+	0.119773i	−0.407910	+	0.119773i	0.0713392	+	0.997452i	$0.477273\pi$
$420$	−1.94931	−	0.424047i	−1.94931	−	0.424047i
$421$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$421$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.587976	−	1.57642i	−0.587976	−	1.57642i
$427$	−0.926113	+	1.06879i	−0.926113	+	1.06879i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$431$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$432$	−0.0713392	+	0.997452i	−0.0713392	+	0.997452i
$433$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$433$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.871880	+	0.398174i	−0.871880	+	0.398174i
$438$		0			0
$439$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$439$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$440$		0			0
$441$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$442$		0			0
$443$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$443$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.540641	+	0.841254i	−0.540641	+	0.841254i
$449$	−0.304632	+	0.474017i	−0.304632	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$449$	−0.304632	+	0.474017i	−0.304632	+	0.474017i	0.654861	+	0.755750i	$0.272727\pi$
$450$	−1.23779	+	2.71038i	−1.23779	+	2.71038i
$451$		0			0
$452$	−0.258908	−	1.80075i	−0.258908	−	1.80075i
$453$	−0.0203052	−	0.283904i	−0.0203052	−	0.283904i
$454$	0.635768	−	0.290345i	0.635768	−	0.290345i
$455$	−0.238936	−	0.813741i	−0.238936	−	0.813741i
$456$	−0.841254	+	0.459359i	−0.841254	+	0.459359i
$457$	1.89945	+	0.273100i	1.89945	+	0.273100i	0.989821	−	0.142315i	$-0.0454545\pi$
$457$	1.89945	+	0.273100i	1.89945	+	0.273100i	0.909632	+	0.415415i	$0.136364\pi$
$458$	1.47670	−	0.949018i	1.47670	−	0.949018i
$459$		0			0
$460$	1.30638	+	1.50765i	1.30638	+	1.50765i
$461$			1.87390i			1.87390i	0.349464	+	0.936950i	$0.386364\pi$
$461$			1.87390i			1.87390i	−0.349464	+	0.936950i	$0.613636\pi$
$462$		0			0
$463$	0.153882	−	1.07028i	0.153882	−	1.07028i	−0.755750	−	0.654861i	$-0.772727\pi$
$463$	0.153882	−	1.07028i	0.153882	−	1.07028i	0.909632	−	0.415415i	$-0.136364\pi$
$464$		0			0
$465$		0			0
$466$	0.755750	+	1.65486i	0.755750	+	1.65486i
$467$	−0.784887	−	0.905808i	−0.784887	−	0.905808i	0.212565	−	0.977147i	$-0.431818\pi$
$467$	−0.784887	−	0.905808i	−0.784887	−	0.905808i	−0.997452	+	0.0713392i	$0.977273\pi$
$468$	−0.386712	+	0.176606i	−0.386712	+	0.176606i
$469$		0			0
$470$		0			0
$471$	0.654861	−	0.244250i	0.654861	−	0.244250i
$472$	−1.47670	−	0.949018i	−1.47670	−	0.949018i
$473$		0			0
$474$	0.497898	+	0.665114i	0.497898	+	0.665114i
$475$	−2.82691	+	0.406449i	−2.82691	+	0.406449i
$476$		0			0
$477$		0			0
$478$	1.45027	−	0.425839i	1.45027	−	0.425839i
$479$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$479$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$480$	1.41061	+	1.41061i	1.41061	+	1.41061i
$481$		0			0
$482$		0			0
$483$	0.707107	+	0.707107i	0.707107	+	0.707107i
$484$	−1.00000			−1.00000
$485$		0			0
$486$	0.977147	+	0.212565i	0.977147	+	0.212565i
$487$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$487$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	−0.841254	+	0.540641i	$0.818182\pi$
$488$	1.35693	−	0.398430i	1.35693	−	0.398430i
$489$		0			0
$490$	−1.50765	+	1.30638i	−1.50765	+	1.30638i
$491$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$491$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$492$		0			0
$493$		0			0
$494$	−0.342800	−	0.220304i	−0.342800	−	0.220304i
$495$		0			0
$496$		0			0
$497$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$498$	−1.64468	−	0.898064i	−1.64468	−	0.898064i
$499$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$499$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$500$	1.64056	+	3.59232i	1.64056	+	3.59232i
$501$		0			0
$502$	1.45640	+	0.665114i	1.45640	+	0.665114i
$503$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$503$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$504$	0.755750	+	0.654861i	0.755750	+	0.654861i
$505$			2.82122i			2.82122i
$506$		0			0
$507$	0.655855	+	0.490967i	0.655855	+	0.490967i
$508$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$509$	−0.141226	−	0.0203052i	−0.141226	−	0.0203052i	0.0713392	−	0.997452i	$-0.477273\pi$
$509$	−0.141226	−	0.0203052i	−0.141226	−	0.0203052i	−0.212565	+	0.977147i	$0.568182\pi$
$510$		0			0
$511$		0			0
$512$	0.909632	−	0.415415i	0.909632	−	0.415415i
$513$	0.334961	+	0.898064i	0.334961	+	0.898064i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.148568	−	0.682956i	−0.148568	−	0.682956i
$520$	−0.238936	+	0.813741i	−0.238936	+	0.813741i
$521$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$521$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$522$		0			0
$523$	1.70456	−	0.778446i	1.70456	−	0.778446i	0.707107	−	0.707107i	$-0.250000\pi$
$523$	1.70456	−	0.778446i	1.70456	−	0.778446i	0.997452	−	0.0713392i	$-0.0227273\pi$
$524$	−0.0401971	−	0.136899i	−0.0401971	−	0.136899i
$525$	1.42799	+	2.61517i	1.42799	+	2.61517i
$526$	1.07028	+	0.153882i	1.07028	+	0.153882i
$527$		0			0
$528$		0			0
$529$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$530$		0			0
$531$	−1.14952	+	1.32661i	−1.14952	+	1.32661i
$532$	−0.136408	+	0.948742i	−0.136408	+	0.948742i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.919672	+	0.270040i	0.919672	+	0.270040i
$539$		0			0
$540$	1.59700	−	1.19550i	1.59700	−	1.19550i
$541$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$541$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$542$		0			0
$543$	−0.959493	+	0.718267i	−0.959493	+	0.718267i
$544$		0			0
$545$		0			0
$546$	−0.0903680	+	0.415415i	−0.0903680	+	0.415415i
$547$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$547$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$548$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$549$	−0.201264	−	1.39982i	−0.201264	−	1.39982i
$550$		0			0
$551$		0			0
$552$	−0.212565	−	0.977147i	−0.212565	−	0.977147i
$553$	0.830830			0.830830
$554$		0			0
$555$		0			0
$556$	0.778446	−	1.70456i	0.778446	−	1.70456i
$557$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$557$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$558$		0			0
$559$		0			0
$560$	1.97460	−	0.283904i	1.97460	−	0.283904i
$561$		0			0
$562$	0.989821	+	0.857685i	0.989821	+	0.857685i
$563$	1.64406	+	1.05657i	1.64406	+	1.05657i	0.936950	+	0.349464i	$0.113636\pi$
$563$	1.64406	+	1.05657i	1.64406	+	1.05657i	0.707107	+	0.707107i	$0.250000\pi$
$564$		0			0
$565$	−2.37666	+	2.74281i	−2.37666	+	2.74281i
$566$	1.87513	+	0.550588i	1.87513	+	0.550588i
$567$	0.755750	−	0.654861i	0.755750	−	0.654861i
$568$	1.10181	+	1.27155i	1.10181	+	1.27155i
$569$	0.822373	+	1.80075i	0.822373	+	1.80075i	0.540641	+	0.841254i	$0.318182\pi$
$569$	0.822373	+	1.80075i	0.822373	+	1.80075i	0.281733	+	0.959493i	$0.409091\pi$
$570$	1.79155	+	0.668215i	1.79155	+	0.668215i
$571$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$571$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$572$		0			0
$573$	1.97460	+	0.141226i	1.97460	+	0.141226i
$574$		0			0
$575$	0.424047	−	2.94931i	0.424047	−	2.94931i
$576$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$577$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$577$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$578$	0.989821	+	0.142315i	0.989821	+	0.142315i
$579$	−1.32661	+	0.724384i	−1.32661	+	0.724384i
$580$		0			0
$581$	−1.70456	+	0.778446i	−1.70456	+	0.778446i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.771454	+	0.352311i	0.771454	+	0.352311i
$586$	−0.865611	+	1.34692i	−0.865611	+	1.34692i
$587$	1.05657	−	1.64406i	1.05657	−	1.64406i	0.349464	−	0.936950i	$-0.386364\pi$
$587$	1.05657	−	1.64406i	1.05657	−	1.64406i	0.707107	−	0.707107i	$-0.250000\pi$
$588$	0.977147	−	0.212565i	0.977147	−	0.212565i
$589$		0			0
$590$	0.498354	+	3.46613i	0.498354	+	3.46613i
$591$		0			0
$592$		0			0
$593$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$593$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.321292	−	0.278401i	0.321292	−	0.278401i
$599$			0.284630i			0.284630i	0.989821	+	0.142315i	$0.0454545\pi$
$599$			0.284630i			0.284630i	−0.989821	+	0.142315i	$0.954545\pi$
$600$	0.212565	−	2.97205i	0.212565	−	2.97205i
$601$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$601$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$602$		0			0
$603$		0			0
$604$	0.118239	+	0.258908i	0.118239	+	0.258908i
$605$	1.30638	+	1.50765i	1.30638	+	1.50765i
$606$	0.677760	−	1.24123i	0.677760	−	1.24123i
$607$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$607$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$608$	0.627683	−	0.724384i	0.627683	−	0.724384i
$609$		0			0
$610$	−2.37336	−	1.52527i	−2.37336	−	1.52527i
$611$		0			0
$612$		0			0
$613$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$613$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$614$	−1.47696	+	1.27979i	−1.47696	+	1.27979i
$615$		0			0
$616$		0			0
$617$	0.627899	−	1.37491i	0.627899	−	1.37491i	−0.281733	−	0.959493i	$-0.590909\pi$
$617$	0.627899	−	1.37491i	0.627899	−	1.37491i	0.909632	−	0.415415i	$-0.136364\pi$
$618$		0			0
$619$	−1.01311	−	1.57642i	−1.01311	−	1.57642i	−0.800541	−	0.599278i	$-0.795455\pi$
$619$	−1.01311	−	1.57642i	−1.01311	−	1.57642i	−0.212565	−	0.977147i	$-0.568182\pi$
$620$		0			0
$621$	−0.997452	+	0.0713392i	−0.997452	+	0.0713392i
$622$		0			0
$623$		0			0
$624$	0.300613	−	0.300613i	0.300613	−	0.300613i
$625$	2.03496	−	4.45595i	2.03496	−	4.45595i
$626$		0			0
$627$		0			0
$628$	−0.528215	+	0.457701i	−0.528215	+	0.457701i
$629$		0			0
$630$		−	1.99490i		−	1.99490i
$631$	0.215109	+	0.186393i	0.215109	+	0.186393i	0.755750	−	0.654861i	$-0.227273\pi$
$631$	0.215109	+	0.186393i	0.215109	+	0.186393i	−0.540641	+	0.841254i	$0.681818\pi$
$632$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$633$		0			0
$634$		0			0
$635$	2.50693	+	0.736102i	2.50693	+	0.736102i
$636$		0			0
$637$	0.278401	+	0.321292i	0.278401	+	0.321292i
$638$		0			0
$639$	1.41542	−	0.909632i	1.41542	−	0.909632i
$640$	−1.81463	−	0.828713i	−1.81463	−	0.828713i
$641$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$641$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	−0.755750	+	0.654861i	$0.772727\pi$
$642$		0			0
$643$		−	1.19856i		−	1.19856i	−0.800541	−	0.599278i	$-0.795455\pi$
$643$		−	1.19856i		−	1.19856i	0.800541	−	0.599278i	$-0.204545\pi$
$644$	−0.909632	−	0.415415i	−0.909632	−	0.415415i
$645$		0			0
$646$		0			0
$647$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$647$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$648$	−0.989821	+	0.142315i	−0.989821	+	0.142315i
$649$		0			0
$650$	1.15226	−	0.526222i	1.15226	−	0.526222i
$651$		0			0
$652$		0			0
$653$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$653$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$654$		0			0
$655$	−0.153882	+	0.239446i	−0.153882	+	0.239446i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$659$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$660$		0			0
$661$	1.77769	−	0.811843i	1.77769	−	0.811843i	0.800541	−	0.599278i	$-0.204545\pi$
$661$	1.77769	−	0.811843i	1.77769	−	0.811843i	0.977147	−	0.212565i	$-0.0681818\pi$
$662$		0			0
$663$		0			0
$664$	1.85483	+	0.266684i	1.85483	+	0.266684i
$665$	1.60857	−	1.03377i	1.60857	−	1.03377i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.936950	−	0.349464i	−0.936950	−	0.349464i
$673$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$673$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$674$	1.10181	+	1.27155i	1.10181	+	1.27155i
$675$	−2.91155	−	0.633369i	−2.91155	−	0.633369i
$676$	−0.786078	−	0.230813i	−0.786078	−	0.230813i
$677$	0.457701	−	0.528215i	0.457701	−	0.528215i	−0.479249	−	0.877679i	$-0.659091\pi$
$677$	0.457701	−	0.528215i	0.457701	−	0.528215i	0.936950	+	0.349464i	$0.113636\pi$
$678$	1.70456	−	0.635768i	1.70456	−	0.635768i
$679$		0			0
$680$		0			0
$681$	0.418852	+	0.559521i	0.418852	+	0.559521i
$682$		0			0
$683$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$683$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$684$	−0.627683	−	0.724384i	−0.627683	−	0.724384i
$685$	3.67312	−	1.07853i	3.67312	−	1.07853i
$686$	0.415415	−	0.909632i	0.415415	−	0.909632i
$687$	1.24123	+	1.24123i	1.24123	+	1.24123i
$688$		0			0
$689$		0			0
$690$	−1.19550	+	1.59700i	−1.19550	+	1.59700i
$691$	1.75536			1.75536			0.877679	−	0.479249i	$-0.159091\pi$
$691$	1.75536			1.75536			0.877679	+	0.479249i	$0.159091\pi$
$692$	0.377869	+	0.587976i	0.377869	+	0.587976i
$693$		0			0
$694$		0			0
$695$	−3.58682	+	1.05319i	−3.58682	+	1.05319i
$696$		0			0
$697$		0			0
$698$	−1.39982	+	0.201264i	−1.39982	+	0.201264i
$699$	−1.45640	+	1.09024i	−1.45640	+	1.09024i
$700$	−2.25186	−	1.95125i	−2.25186	−	1.95125i
$701$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$701$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$702$	−0.254771	−	0.340335i	−0.254771	−	0.340335i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.587486	−	1.28641i	−0.587486	−	1.28641i
$708$	0.613435	−	1.64468i	0.613435	−	1.64468i
$709$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$709$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$710$	0.477671	−	3.32228i	0.477671	−	3.32228i
$711$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.724384	+	1.32661i	0.724384	+	1.32661i
$718$	−0.368991	−	1.25667i	−0.368991	−	1.25667i
$719$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$719$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$720$	−1.07853	+	1.67822i	−1.07853	+	1.67822i
$721$		0			0
$722$	−0.0228997	+	0.0779892i	−0.0228997	+	0.0779892i
$723$		0			0
$724$	0.647988	−	1.00829i	0.647988	−	1.00829i
$725$		0			0
$726$	−0.212565	−	0.977147i	−0.212565	−	0.977147i
$727$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$727$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$728$	−0.0605024	−	0.420803i	−0.0605024	−	0.420803i
$729$			1.00000i			1.00000i
$730$		0			0
$731$		0			0
$732$	0.677760	+	1.24123i	0.677760	+	1.24123i
$733$	0.420803	+	0.0605024i	0.420803	+	0.0605024i	0.349464	−	0.936950i	$-0.386364\pi$
$733$	0.420803	+	0.0605024i	0.420803	+	0.0605024i	0.0713392	+	0.997452i	$0.477273\pi$
$734$		0			0
$735$	−1.59700	−	1.19550i	−1.59700	−	1.19550i
$736$	0.540641	+	0.841254i	0.540641	+	0.841254i
$737$		0			0
$738$		0			0
$739$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$739$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$740$		0			0
$741$	0.142402	−	0.381795i	0.142402	−	0.381795i
$742$		0			0
$743$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$743$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.527938	−	1.79799i	0.527938	−	1.79799i
$748$		0			0
$749$		0			0
$750$	−3.16150	+	2.36667i	−3.16150	+	2.36667i
$751$	−0.557730	+	0.0801894i	−0.557730	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$751$	−0.557730	+	0.0801894i	−0.557730	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$752$		0			0
$753$	−0.340335	+	1.56449i	−0.340335	+	1.56449i
$754$		0			0
$755$	0.235876	−	0.516497i	0.235876	−	0.516497i
$756$	−0.479249	+	0.877679i	−0.479249	+	0.877679i
$757$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$757$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$758$		0			0
$759$		0			0
$760$	−1.91211			−1.91211
$761$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$761$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$762$	−0.926113	−	0.926113i	−0.926113	−	0.926113i
$763$		0			0
$764$	−1.89945	+	0.557730i	−1.89945	+	0.557730i
$765$		0			0
$766$		0			0
$767$	0.738661	−	0.106203i	0.738661	−	0.106203i
$768$	0.599278	+	0.800541i	0.599278	+	0.800541i
$769$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$769$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$770$		0			0
$771$		0			0
$772$	0.989821	−	1.14231i	0.989821	−	1.14231i
$773$	0.136899	+	0.0401971i	0.136899	+	0.0401971i	0.349464	−	0.936950i	$-0.386364\pi$
$773$	0.136899	+	0.0401971i	0.136899	+	0.0401971i	−0.212565	+	0.977147i	$0.568182\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−0.845934	−	0.0605024i	−0.845934	−	0.0605024i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$785$	1.38010	+	0.198429i	1.38010	+	0.198429i
$786$	0.125226	−	0.0683785i	0.125226	−	0.0683785i
$787$	−0.494541	−	1.68425i	−0.494541	−	1.68425i	−0.707107	−	0.707107i	$-0.750000\pi$
$787$	−0.494541	−	1.68425i	−0.494541	−	1.68425i	0.212565	−	0.977147i	$-0.431818\pi$
$788$		0			0
$789$	0.0771377	+	1.07853i	0.0771377	+	1.07853i
$790$	0.235876	+	1.64056i	0.235876	+	1.64056i
$791$	0.512546	−	1.74557i	0.512546	−	1.74557i
$792$		0			0
$793$	−0.325047	+	0.505783i	−0.325047	+	0.505783i
$794$	−1.05657	+	1.64406i	−1.05657	+	1.64406i
$795$		0			0
$796$		0			0
$797$	0.0605024	+	0.420803i	0.0605024	+	0.420803i	0.997452	+	0.0713392i	$0.0227273\pi$
$797$	0.0605024	+	0.420803i	0.0605024	+	0.420803i	−0.936950	+	0.349464i	$0.886364\pi$
$798$	−0.956056	+	0.0683785i	−0.956056	+	0.0683785i
$799$		0			0
$800$	0.839462	+	2.85895i	0.839462	+	2.85895i
$801$		0			0
$802$	−1.07028	−	0.153882i	−1.07028	−	0.153882i
$803$		0			0
$804$		0			0
$805$	0.562029	+	1.91410i	0.562029	+	1.91410i
$806$		0			0
$807$	−0.0683785	+	0.956056i	−0.0683785	+	0.956056i
$808$	−0.201264	+	1.39982i	−0.201264	+	1.39982i
$809$	0.755750	+	0.345139i	0.755750	+	0.345139i	0.755750	−	0.654861i	$-0.227273\pi$
$809$	0.755750	+	0.345139i	0.755750	+	0.345139i			1.00000i	$0.5\pi$
$810$	1.50765	+	1.30638i	1.50765	+	1.30638i
$811$	−0.398174	−	0.871880i	−0.398174	−	0.871880i	−0.997452	−	0.0713392i	$-0.977273\pi$
$811$	−0.398174	−	0.871880i	−0.398174	−	0.871880i	0.599278	−	0.800541i	$-0.295455\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−0.425131			−0.425131
$820$		0			0
$821$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$821$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$822$	−1.87513	−	0.407910i	−1.87513	−	0.407910i
$823$	0.540641	−	0.158746i	0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$823$	0.540641	−	0.158746i	0.540641	−	0.158746i	0.540641	+	0.841254i	$0.318182\pi$
$824$		0			0
$825$		0			0
$826$	−0.949018	−	1.47670i	−0.949018	−	1.47670i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	0.909632	−	0.415415i	0.909632	−	0.415415i
$829$	0.142678			0.142678			0.0713392	−	0.997452i	$-0.477273\pi$
$829$	0.142678			0.142678			0.0713392	+	0.997452i	$0.477273\pi$
$830$	−2.02105	−	3.14482i	−2.02105	−	3.14482i
$831$		0			0
$832$	−0.176606	+	0.386712i	−0.176606	+	0.386712i
$833$		0			0
$834$	1.83107	+	0.398326i	1.83107	+	0.398326i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.321292	+	0.278401i	0.321292	+	0.278401i
$839$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$839$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$840$	0.697148	+	1.86912i	0.697148	+	1.86912i
$841$	0.654861	−	0.755750i	0.654861	−	0.755750i
$842$		0			0
$843$	−0.627683	+	1.14952i	−0.627683	+	1.14952i
$844$		0			0
$845$	0.678935	+	1.48666i	0.678935	+	1.48666i
$846$		0			0
$847$	−0.909632	−	0.415415i	−0.909632	−	0.415415i
$848$		0			0
$849$	−0.139418	+	1.94931i	−0.139418	+	1.94931i
$850$		0			0
$851$		0			0
$852$	−1.00829	+	1.34692i	−1.00829	+	1.34692i
$853$	−0.587976	+	0.377869i	−0.587976	+	0.377869i	−0.800541	−	0.599278i	$-0.795455\pi$
$853$	−0.587976	+	0.377869i	−0.587976	+	0.377869i	0.212565	+	0.977147i	$0.431818\pi$
$854$	1.39982	+	0.201264i	1.39982	+	0.201264i
$855$	−0.272122	+	1.89265i	−0.272122	+	1.89265i
$856$		0			0
$857$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$857$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$858$		0			0
$859$	0.0203052	+	0.141226i	0.0203052	+	0.141226i	0.997452	−	0.0713392i	$-0.0227273\pi$
$859$	0.0203052	+	0.141226i	0.0203052	+	0.141226i	−0.977147	+	0.212565i	$0.931818\pi$
$860$		0			0
$861$		0			0
$862$	0.449181	−	0.698939i	0.449181	−	0.698939i
$863$	1.03748	−	1.61435i	1.03748	−	1.61435i	0.281733	−	0.959493i	$-0.409091\pi$
$863$	1.03748	−	1.61435i	1.03748	−	1.61435i	0.755750	−	0.654861i	$-0.227273\pi$
$864$	0.877679	−	0.479249i	0.877679	−	0.479249i
$865$	0.392818	−	1.33782i	0.392818	−	1.33782i
$866$		0			0
$867$	0.0713392	+	0.997452i	0.0713392	+	0.997452i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	0.806340	+	0.518203i	0.806340	+	0.518203i
$875$			3.94920i			3.94920i
$876$		0			0
$877$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$877$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$878$		0			0
$879$	−1.50013	−	0.559521i	−1.50013	−	0.559521i
$880$		0			0
$881$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$881$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$882$	0.415415	+	0.909632i	0.415415	+	0.909632i
$883$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$883$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$884$		0			0
$885$	−3.28098	+	1.22374i	−3.28098	+	1.22374i
$886$		0			0
$887$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$887$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$888$		0			0
$889$	−1.29639	+	0.186393i	−1.29639	+	0.186393i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.00000			1.00000
$897$	0.340335	+	0.254771i	0.340335	+	0.254771i
$898$	0.563465			0.563465
$899$		0			0
$900$	2.94931	−	0.424047i	2.94931	−	0.424047i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−1.37491	+	1.19136i	−1.37491	+	1.19136i
$905$	−2.36667	+	0.340275i	−2.36667	+	0.340275i
$906$	−0.227858	+	0.170572i	−0.227858	+	0.170572i
$907$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$907$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$908$	−0.587976	−	0.377869i	−0.587976	−	0.377869i
$909$	1.35693	+	0.398430i	1.35693	+	0.398430i
$910$	−0.555384	+	0.640947i	−0.555384	+	0.640947i
$911$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.654861	−	0.755750i	$-0.272727\pi$
$911$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.142315	+	0.989821i	$0.454545\pi$
$912$	0.841254	+	0.459359i	0.841254	+	0.459359i
$913$		0			0
$914$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$915$	0.985916	−	2.64334i	0.985916	−	2.64334i
$916$	−1.59673	−	0.729202i	−1.59673	−	0.729202i
$917$	0.0203052	−	0.141226i	0.0203052	−	0.141226i
$918$		0			0
$919$		−	1.68251i		−	1.68251i	−0.540641	−	0.841254i	$-0.681818\pi$
$919$		−	1.68251i		−	1.68251i	0.540641	−	0.841254i	$-0.318182\pi$
$920$	0.562029	−	1.91410i	0.562029	−	1.91410i
$921$	−1.56449	−	1.17116i	−1.56449	−	1.17116i
$922$	1.57642	−	1.01311i	1.57642	−	1.01311i
$923$	−0.708005	−	0.101796i	−0.708005	−	0.101796i
$924$		0			0
$925$		0			0
$926$	−0.983568	+	0.449181i	−0.983568	+	0.449181i
$927$		0			0
$928$		0			0
$929$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$929$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$930$		0			0
$931$	−0.518203	+	0.806340i	−0.518203	+	0.806340i
$932$	0.983568	−	1.53046i	0.983568	−	1.53046i
$933$		0			0
$934$	−0.337672	+	1.15001i	−0.337672	+	1.15001i
$935$		0			0
$936$	0.357643	+	0.229843i	0.357643	+	0.229843i
$937$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$937$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.57642	+	1.01311i	−1.57642	+	1.01311i	−0.599278	+	0.800541i	$0.704545\pi$
$941$	−1.57642	+	1.01311i	−1.57642	+	1.01311i	−0.977147	+	0.212565i	$0.931818\pi$
$942$	−0.559521	−	0.418852i	−0.559521	−	0.418852i
$943$		0			0
$944$			1.75536i			1.75536i
$945$	1.94931	−	0.424047i	1.94931	−	0.424047i
$946$		0			0
$947$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$947$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$948$	0.290345	−	0.778446i	0.290345	−	0.778446i
$949$		0			0
$950$	1.87027	+	2.15841i	1.87027	+	2.15841i
$951$		0			0
$952$		0			0
$953$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.142315	−	0.989821i	$-0.454545\pi$
$953$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.959493	−	0.281733i	$-0.0909091\pi$
$954$		0			0
$955$	3.32228	+	2.13510i	3.32228	+	2.13510i
$956$	−1.14231	−	0.989821i	−1.14231	−	0.989821i
$957$		0			0
$958$		0			0
$959$	−1.45027	+	1.25667i	−1.45027	+	1.25667i
$960$	0.424047	−	1.94931i	0.424047	−	1.94931i
$961$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.01530			−3.01530
$966$	0.212565	−	0.977147i	0.212565	−	0.977147i
$967$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$967$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$968$	0.540641	+	0.841254i	0.540641	+	0.841254i
$969$		0			0
$970$		0			0
$971$	0.136899	−	0.0401971i	0.136899	−	0.0401971i	−0.212565	−	0.977147i	$-0.568182\pi$
$971$	0.136899	−	0.0401971i	0.136899	−	0.0401971i	0.349464	+	0.936950i	$0.386364\pi$
$972$	−0.349464	−	0.936950i	−0.349464	−	0.936950i
$973$	1.41620	−	1.22714i	1.41620	−	1.22714i
$974$	1.66538	−	0.239446i	1.66538	−	0.239446i
$975$	0.759127	+	1.01408i	0.759127	+	1.01408i
$976$	−1.06879	−	0.926113i	−1.06879	−	0.926113i
$977$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.959493	−	0.281733i	$-0.0909091\pi$
$977$	1.10181	+	0.708089i	1.10181	+	0.708089i	0.142315	+	0.989821i	$0.454545\pi$
$978$		0			0
$979$		0			0
$980$	1.91410	+	0.562029i	1.91410	+	0.562029i
$981$		0			0
$982$		0			0
$983$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$983$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$			0.407487i			0.407487i
$989$		0			0
$990$		0			0
$991$	−1.27155	+	0.817178i	−1.27155	+	0.817178i	−0.989821	−	0.142315i	$-0.954545\pi$
$991$	−1.27155	+	0.817178i	−1.27155	+	0.817178i	−0.281733	+	0.959493i	$0.590909\pi$
$992$		0			0
$993$		0			0
$994$	0.474017	+	1.61435i	0.474017	+	1.61435i
$995$		0			0
$996$	0.133682	+	1.86912i	0.133682	+	1.86912i
$997$	−0.283904	−	1.97460i	−0.283904	−	1.97460i	−0.212565	−	0.977147i	$-0.568182\pi$
$997$	−0.283904	−	1.97460i	−0.283904	−	1.97460i	−0.0713392	−	0.997452i	$-0.522727\pi$
$998$		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.1805.2	yes	40
3.2	odd	2		3864.1.cx.a.1805.3	✓	40
7.6	odd	2	inner	3864.1.cx.b.1805.1	yes	40
8.5	even	2	inner	3864.1.cx.b.1805.1	yes	40
21.20	even	2		3864.1.cx.a.1805.4	yes	40
23.21	odd	22		3864.1.cx.a.3149.3	yes	40
24.5	odd	2		3864.1.cx.a.1805.4	yes	40
56.13	odd	2	CM	3864.1.cx.b.1805.2	yes	40
69.44	even	22	inner	3864.1.cx.b.3149.2	yes	40
161.90	even	22		3864.1.cx.a.3149.4	yes	40
168.125	even	2		3864.1.cx.a.1805.3	✓	40
184.21	odd	22		3864.1.cx.a.3149.4	yes	40
483.251	odd	22	inner	3864.1.cx.b.3149.1	yes	40
552.389	even	22	inner	3864.1.cx.b.3149.1	yes	40
1288.573	even	22		3864.1.cx.a.3149.3	yes	40
3864.3149	odd	22	inner	3864.1.cx.b.3149.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3864.1.cx.a.1805.3	✓	40	3.2	odd	2
3864.1.cx.a.1805.3	✓	40	168.125	even	2
3864.1.cx.a.1805.4	yes	40	21.20	even	2
3864.1.cx.a.1805.4	yes	40	24.5	odd	2
3864.1.cx.a.3149.3	yes	40	23.21	odd	22
3864.1.cx.a.3149.3	yes	40	1288.573	even	22
3864.1.cx.a.3149.4	yes	40	161.90	even	22
3864.1.cx.a.3149.4	yes	40	184.21	odd	22
3864.1.cx.b.1805.1	yes	40	7.6	odd	2	inner
3864.1.cx.b.1805.1	yes	40	8.5	even	2	inner
3864.1.cx.b.1805.2	yes	40	1.1	even	1	trivial
3864.1.cx.b.1805.2	yes	40	56.13	odd	2	CM
3864.1.cx.b.3149.1	yes	40	483.251	odd	22	inner
3864.1.cx.b.3149.1	yes	40	552.389	even	22	inner
3864.1.cx.b.3149.2	yes	40	69.44	even	22	inner
3864.1.cx.b.3149.2	yes	40	3864.3149	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)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.91410 - 0.562029i) q^{5} +(-0.977147 - 0.212565i) q^{6} +(-0.755750 + 0.654861i) q^{7} +(0.989821 - 0.142315i) q^{8} -1.00000i q^{9} +(-1.50765 - 1.30638i) q^{10} +(0.349464 + 0.936950i) q^{12} +(-0.278401 + 0.321292i) q^{13} +(0.959493 + 0.281733i) q^{14} +(0.956056 - 1.75089i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.841254 + 0.540641i) q^{18} +(-0.871880 - 0.398174i) q^{19} +(-0.283904 + 1.97460i) q^{20} +(-0.0713392 + 0.997452i) q^{21} +(0.654861 - 0.755750i) q^{23} +(0.599278 - 0.800541i) q^{24} +(2.50664 - 1.61092i) q^{25} +(0.420803 + 0.0605024i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.281733 - 0.959493i) q^{28} +(-1.98982 + 0.142315i) q^{30} +(-0.281733 + 0.959493i) q^{32} +(-1.07853 + 1.67822i) q^{35} +(0.909632 + 0.415415i) q^{36} +(0.136408 + 0.948742i) q^{38} +(0.0303285 + 0.424047i) q^{39} +(1.81463 - 0.828713i) q^{40} +(0.877679 - 0.479249i) q^{42} +(-0.562029 - 1.91410i) q^{45} +(-0.989821 - 0.142315i) q^{46} +(-0.997452 - 0.0713392i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-2.71038 - 1.23779i) q^{50} +(-0.176606 - 0.386712i) q^{52} +(-0.212565 + 0.977147i) q^{54} +(-0.654861 + 0.755750i) q^{56} +(-0.898064 + 0.334961i) q^{57} +(-1.32661 - 1.14952i) q^{59} +(1.19550 + 1.59700i) q^{60} +(1.39982 - 0.201264i) q^{61} +(0.654861 + 0.755750i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.352311 + 0.771454i) q^{65} +(-0.0713392 - 0.997452i) q^{69} +1.99490 q^{70} +(0.909632 + 1.41542i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(0.633369 - 2.91155i) q^{75} +(0.724384 - 0.627683i) q^{76} +(0.340335 - 0.254771i) q^{78} +(-0.627899 - 0.544078i) q^{79} +(-1.67822 - 1.07853i) q^{80} -1.00000 q^{81} +(1.79799 + 0.527938i) q^{83} +(-0.877679 - 0.479249i) q^{84} +(-1.30638 + 1.50765i) q^{90} -0.425131i q^{91} +(0.415415 + 0.909632i) q^{92} +(-1.89265 - 0.272122i) q^{95} +(0.479249 + 0.877679i) q^{96} +(-0.909632 + 0.415415i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{4} + 4 q^{14} - 4 q^{15} - 4 q^{16} + 4 q^{18} + 4 q^{23} - 4 q^{25} - 40 q^{30} - 4 q^{39} + 4 q^{49} - 4 q^{56} - 4 q^{57} + 4 q^{60} + 4 q^{63} + 4 q^{64} - 8 q^{65} - 4 q^{72} + 4 q^{78}+ \cdots - 4 q^{92}+O(q^{100}) \) 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

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