LMFDB - Embedded newform 816.2.bf.c.191.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,2,Mod(47,816)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 2, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("816.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.bf (of order $4$, degree $2$, 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:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 $ x^8 - 3x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.4
Root			$-1.40126 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	816.191
Dual form			816.2.bf.c.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 + 0.618034i) q^{3} +(1.73205 + 1.73205i) q^{5} +(-1.73205 + 1.73205i) q^{7} +(2.23607 + 2.00000i) q^{9} +O(q^{10})$	\(q+(1.61803 + 0.618034i) q^{3} +(1.73205 + 1.73205i) q^{5} +(-1.73205 + 1.73205i) q^{7} +(2.23607 + 2.00000i) q^{9} +(-1.00000 - 1.00000i) q^{11} -2.00000 q^{13} +(1.73205 + 3.87298i) q^{15} +(2.23607 + 3.46410i) q^{17} +1.00803 q^{19} +(-3.87298 + 1.73205i) q^{21} +(1.87298 + 1.87298i) q^{23} +1.00000i q^{25} +(2.38197 + 4.61803i) q^{27} +(2.74009 + 2.74009i) q^{29} +(-6.20419 - 6.20419i) q^{31} +(-1.00000 - 2.23607i) q^{33} -6.00000 q^{35} +(-3.87298 + 3.87298i) q^{37} +(-3.23607 - 1.23607i) q^{39} +(6.70820 - 6.70820i) q^{41} -1.00803 q^{43} +(0.408882 + 7.33708i) q^{45} -4.00000 q^{47} +1.00000i q^{49} +(1.47710 + 6.98700i) q^{51} +11.4003 q^{53} -3.46410i q^{55} +(1.63103 + 0.622999i) q^{57} -11.7460i q^{59} +(0.127017 + 0.127017i) q^{61} +(-7.33708 + 0.408882i) q^{63} +(-3.46410 - 3.46410i) q^{65} +3.46410i q^{67} +(1.87298 + 4.18812i) q^{69} +(-5.87298 + 5.87298i) q^{71} +(10.7460 - 10.7460i) q^{73} +(-0.618034 + 1.61803i) q^{75} +3.46410 q^{77} +(6.20419 - 6.20419i) q^{79} +(1.00000 + 8.94427i) q^{81} -3.74597i q^{83} +(-2.12702 + 9.87298i) q^{85} +(2.74009 + 6.12702i) q^{87} +2.01607i q^{89} +(3.46410 - 3.46410i) q^{91} +(-6.20419 - 13.8730i) q^{93} +(1.74597 + 1.74597i) q^{95} +(-3.00000 + 3.00000i) q^{97} +(-0.236068 - 4.23607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3}+O(q^{10}) $ 8 * q + 4 * q^3	$ 8 q + 4 q^{3} - 8 q^{11} - 16 q^{13} - 16 q^{23} + 28 q^{27} - 8 q^{33} - 48 q^{35} - 8 q^{39} - 32 q^{47} + 20 q^{51} + 40 q^{57} + 32 q^{61} - 16 q^{69} - 16 q^{71} + 24 q^{73} + 4 q^{75} + 8 q^{81} - 48 q^{85} - 48 q^{95} - 24 q^{97} + 16 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 8 * q^11 - 16 * q^13 - 16 * q^23 + 28 * q^27 - 8 * q^33 - 48 * q^35 - 8 * q^39 - 32 * q^47 + 20 * q^51 + 40 * q^57 + 32 * q^61 - 16 * q^69 - 16 * q^71 + 24 * q^73 + 4 * q^75 + 8 * q^81 - 48 * q^85 - 48 * q^95 - 24 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.61803	+	0.618034i	0.934172	+	0.356822i
$3$	1.61803	+	0.618034i	0.934172	+	0.356822i
$4$		0			0
$5$	1.73205	+	1.73205i	0.774597	+	0.774597i	0.978906	−	0.204310i	$-0.0654949\pi$
$5$	1.73205	+	1.73205i	0.774597	+	0.774597i	−0.204310	+	0.978906i	$0.565495\pi$
$6$		0			0
$7$	−1.73205	+	1.73205i	−0.654654	+	0.654654i	−0.954110	−	0.299456i	$-0.903195\pi$
$7$	−1.73205	+	1.73205i	−0.654654	+	0.654654i	0.299456	+	0.954110i	$0.403195\pi$
$8$		0			0
$9$	2.23607	+	2.00000i	0.745356	+	0.666667i
$10$		0			0
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	1.73205	+	3.87298i	0.447214	+	1.00000i
$16$		0			0
$17$	2.23607	+	3.46410i	0.542326	+	0.840168i
$17$	2.23607	+	3.46410i	0.542326	+	0.840168i
$18$		0			0
$19$	1.00803			0.231259			0.115629	−	0.993292i	$-0.463111\pi$
$19$	1.00803			0.231259			0.115629	+	0.993292i	$0.463111\pi$
$20$		0			0
$21$	−3.87298	+	1.73205i	−0.845154	+	0.377964i
$22$		0			0
$23$	1.87298	+	1.87298i	0.390544	+	0.390544i	0.874881	−	0.484337i	$-0.160939\pi$
$23$	1.87298	+	1.87298i	0.390544	+	0.390544i	−0.484337	+	0.874881i	$0.660939\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	2.38197	+	4.61803i	0.458410	+	0.888741i
$28$		0			0
$29$	2.74009	+	2.74009i	0.508821	+	0.508821i	0.914164	−	0.405343i	$-0.132848\pi$
$29$	2.74009	+	2.74009i	0.508821	+	0.508821i	−0.405343	+	0.914164i	$0.632848\pi$
$30$		0			0
$31$	−6.20419	−	6.20419i	−1.11430	−	1.11430i	−0.992562	−	0.121743i	$-0.961152\pi$
$31$	−6.20419	−	6.20419i	−1.11430	−	1.11430i	−0.121743	−	0.992562i	$-0.538848\pi$
$32$		0			0
$33$	−1.00000	−	2.23607i	−0.174078	−	0.389249i
$34$		0			0
$35$	−6.00000			−1.01419
$36$		0			0
$37$	−3.87298	+	3.87298i	−0.636715	+	0.636715i	−0.949744	−	0.313029i	$-0.898656\pi$
$37$	−3.87298	+	3.87298i	−0.636715	+	0.636715i	0.313029	+	0.949744i	$0.398656\pi$
$38$		0			0
$39$	−3.23607	−	1.23607i	−0.518186	−	0.197929i
$40$		0			0
$41$	6.70820	−	6.70820i	1.04765	−	1.04765i	0.0488388	−	0.998807i	$-0.484448\pi$
$41$	6.70820	−	6.70820i	1.04765	−	1.04765i	0.998807	−	0.0488388i	$-0.0155520\pi$
$42$		0			0
$43$	−1.00803			−0.153724			−0.0768619	−	0.997042i	$-0.524490\pi$
$43$	−1.00803			−0.153724			−0.0768619	+	0.997042i	$0.524490\pi$
$44$		0			0
$45$	0.408882	+	7.33708i	0.0609525	+	1.09375i
$46$		0			0
$47$	−4.00000			−0.583460			−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000			−0.583460			−0.291730	+	0.956501i	$0.594231\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	1.47710	+	6.98700i	0.206836	+	0.978376i
$52$		0			0
$53$	11.4003			1.56596			0.782979	−	0.622049i	$-0.213699\pi$
$53$	11.4003			1.56596			0.782979	+	0.622049i	$0.213699\pi$
$54$		0			0
$55$		−	3.46410i		−	0.467099i
$56$		0			0
$57$	1.63103	+	0.622999i	0.216036	+	0.0825183i
$58$		0			0
$59$		−	11.7460i		−	1.52919i	−0.644508	−	0.764597i	$-0.722938\pi$
$59$		−	11.7460i		−	1.52919i	0.644508	−	0.764597i	$-0.277062\pi$
$60$		0			0
$61$	0.127017	+	0.127017i	0.0162628	+	0.0162628i	0.715191	−	0.698929i	$-0.246339\pi$
$61$	0.127017	+	0.127017i	0.0162628	+	0.0162628i	−0.698929	+	0.715191i	$0.746339\pi$
$62$		0			0
$63$	−7.33708	+	0.408882i	−0.924386	+	0.0515143i
$64$		0			0
$65$	−3.46410	−	3.46410i	−0.429669	−	0.429669i
$66$		0			0
$67$			3.46410i			0.423207i	0.977356	+	0.211604i	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$		0			0
$69$	1.87298	+	4.18812i	0.225481	+	0.504190i
$70$		0			0
$71$	−5.87298	+	5.87298i	−0.696995	+	0.696995i	−0.963761	−	0.266766i	$-0.914045\pi$
$71$	−5.87298	+	5.87298i	−0.696995	+	0.696995i	0.266766	+	0.963761i	$0.414045\pi$
$72$		0			0
$73$	10.7460	−	10.7460i	1.25772	−	1.25772i	0.305542	−	0.952179i	$-0.401163\pi$
$73$	10.7460	−	10.7460i	1.25772	−	1.25772i	0.952179	−	0.305542i	$-0.0988375\pi$
$74$		0			0
$75$	−0.618034	+	1.61803i	−0.0713644	+	0.186834i
$76$		0			0
$77$	3.46410			0.394771
$78$		0			0
$79$	6.20419	−	6.20419i	0.698026	−	0.698026i	−0.265959	−	0.963984i	$-0.585689\pi$
$79$	6.20419	−	6.20419i	0.698026	−	0.698026i	0.963984	+	0.265959i	$0.0856885\pi$
$80$		0			0
$81$	1.00000	+	8.94427i	0.111111	+	0.993808i
$82$		0			0
$83$		−	3.74597i		−	0.411173i	−0.978639	−	0.205587i	$-0.934090\pi$
$83$		−	3.74597i		−	0.411173i	0.978639	−	0.205587i	$-0.0659102\pi$
$84$		0			0
$85$	−2.12702	+	9.87298i	−0.230707	+	1.07088i
$86$		0			0
$87$	2.74009	+	6.12702i	0.293768	+	0.656885i
$88$		0			0
$89$			2.01607i			0.213703i	0.994275	+	0.106851i	$0.0340769\pi$
$89$			2.01607i			0.213703i	−0.994275	+	0.106851i	$0.965923\pi$
$90$		0			0
$91$	3.46410	−	3.46410i	0.363137	−	0.363137i
$92$		0			0
$93$	−6.20419	−	13.8730i	−0.643344	−	1.43856i
$94$		0			0
$95$	1.74597	+	1.74597i	0.179132	+	0.179132i
$96$		0			0
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	−0.842812	−	0.538208i	$-0.819101\pi$
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	0.538208	+	0.842812i	$0.319101\pi$
$98$		0			0
$99$	−0.236068	−	4.23607i	−0.0237257	−	0.425741i
$100$		0			0
$101$		−	7.93624i		−	0.789685i	−0.918749	−	0.394843i	$-0.870799\pi$
$101$		−	7.93624i		−	0.789685i	0.918749	−	0.394843i	$-0.129201\pi$
$102$		0			0
$103$			19.3366i			1.90529i	0.304085	+	0.952645i	$0.401649\pi$
$103$			19.3366i			1.90529i	−0.304085	+	0.952645i	$0.598351\pi$
$104$		0			0
$105$	−9.70820	−	3.70820i	−0.947424	−	0.361884i
$106$		0			0
$107$	10.7460	−	10.7460i	1.03885	−	1.03885i	0.0396377	−	0.999214i	$-0.487380\pi$
$107$	10.7460	−	10.7460i	1.03885	−	1.03885i	0.999214	−	0.0396377i	$-0.0126204\pi$
$108$		0			0
$109$	0.127017	+	0.127017i	0.0121660	+	0.0121660i	0.713164	−	0.700998i	$-0.247262\pi$
$109$	0.127017	+	0.127017i	0.0121660	+	0.0121660i	−0.700998	+	0.713164i	$0.747262\pi$
$110$		0			0
$111$	−8.66025	+	3.87298i	−0.821995	+	0.367607i
$112$		0			0
$113$	−10.1723	+	10.1723i	−0.956930	+	0.956930i	−0.999110	−	0.0421800i	$-0.986570\pi$
$113$	−10.1723	+	10.1723i	−0.956930	+	0.956930i	0.0421800	+	0.999110i	$0.486570\pi$
$114$		0			0
$115$			6.48820i			0.605028i
$116$		0			0
$117$	−4.47214	−	4.00000i	−0.413449	−	0.369800i
$118$		0			0
$119$	−9.87298	−	2.12702i	−0.905055	−	0.194983i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		0			0
$123$	15.0000	−	6.70820i	1.35250	−	0.604858i
$124$		0			0
$125$	6.92820	−	6.92820i	0.619677	−	0.619677i
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$	−1.63103	−	0.622999i	−0.143605	−	0.0548520i
$130$		0			0
$131$	5.00000	−	5.00000i	0.436852	−	0.436852i	−0.454099	−	0.890951i	$-0.650039\pi$
$131$	5.00000	−	5.00000i	0.436852	−	0.436852i	0.890951	+	0.454099i	$0.150039\pi$
$132$		0			0
$133$	−1.74597	+	1.74597i	−0.151395	+	0.151395i
$134$		0			0
$135$	−3.87298	+	12.1244i	−0.333333	+	1.04350i
$136$		0			0
$137$		−	8.94427i		−	0.764161i	−0.924129	−	0.382080i	$-0.875208\pi$
$137$		−	8.94427i		−	0.764161i	0.924129	−	0.382080i	$-0.124792\pi$
$138$		0			0
$139$	8.15624	+	8.15624i	0.691803	+	0.691803i	0.962628	−	0.270825i	$-0.0872966\pi$
$139$	8.15624	+	8.15624i	0.691803	+	0.691803i	−0.270825	+	0.962628i	$0.587297\pi$
$140$		0			0
$141$	−6.47214	−	2.47214i	−0.545052	−	0.208191i
$142$		0			0
$143$	2.00000	+	2.00000i	0.167248	+	0.167248i
$144$		0			0
$145$			9.49193i			0.788262i
$146$		0			0
$147$	−0.618034	+	1.61803i	−0.0509746	+	0.133453i
$148$		0			0
$149$			9.95231i			0.815325i	0.913133	+	0.407662i	$0.133656\pi$
$149$			9.95231i			0.815325i	−0.913133	+	0.407662i	$0.866344\pi$
$150$		0			0
$151$	2.01607			0.164065			0.0820327	−	0.996630i	$-0.473859\pi$
$151$	2.01607			0.164065			0.0820327	+	0.996630i	$0.473859\pi$
$152$		0			0
$153$	−1.92820	+	12.2181i	−0.155886	+	0.987775i
$154$		0			0
$155$		−	21.4919i		−	1.72627i
$156$		0			0
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$		0			0
$159$	18.4461	+	7.04580i	1.46287	+	0.558768i
$160$		0			0
$161$	−6.48820			−0.511342
$162$		0			0
$163$	12.6284	−	12.6284i	0.989130	−	0.989130i	−0.0108111	−	0.999942i	$-0.503441\pi$
$163$	12.6284	−	12.6284i	0.989130	−	0.989130i	0.999942	+	0.0108111i	$0.00344133\pi$
$164$		0			0
$165$	2.14093	−	5.60503i	0.166671	−	0.436351i
$166$		0			0
$167$	17.6190	−	17.6190i	1.36340	−	1.36340i	0.493846	−	0.869550i	$-0.335591\pi$
$167$	17.6190	−	17.6190i	1.36340	−	1.36340i	0.869550	−	0.493846i	$-0.164409\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	2.25403	+	2.01607i	0.172370	+	0.154173i
$172$		0			0
$173$	−13.1324	−	13.1324i	−0.998437	−	0.998437i	0.00156166	−	0.999999i	$-0.499503\pi$
$173$	−13.1324	−	13.1324i	−0.998437	−	0.998437i	−0.999999	+	0.00156166i	$0.999503\pi$
$174$		0			0
$175$	−1.73205	−	1.73205i	−0.130931	−	0.130931i
$176$		0			0
$177$	7.25941	−	19.0054i	0.545650	−	1.42853i
$178$		0			0
$179$		−	11.7460i		−	0.877935i	−0.898503	−	0.438967i	$-0.855344\pi$
$179$		−	11.7460i		−	0.877935i	0.898503	−	0.438967i	$-0.144656\pi$
$180$		0			0
$181$	−2.12702	−	2.12702i	−0.158100	−	0.158100i	0.623624	−	0.781724i	$-0.285660\pi$
$181$	−2.12702	−	2.12702i	−0.158100	−	0.158100i	−0.781724	+	0.623624i	$0.785660\pi$
$182$		0			0
$183$	0.127017	+	0.284018i	0.00938934	+	0.0209952i
$184$		0			0
$185$	−13.4164			−0.986394
$186$		0			0
$187$	1.22803	−	5.70017i	0.0898027	−	0.416838i
$188$		0			0
$189$	−12.1244	−	3.87298i	−0.881917	−	0.281718i
$190$		0			0
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$		0			0
$193$	−18.4919	−	18.4919i	−1.33108	−	1.33108i	−0.904406	−	0.426672i	$-0.859686\pi$
$193$	−18.4919	−	18.4919i	−1.33108	−	1.33108i	−0.426672	−	0.904406i	$-0.640314\pi$
$194$		0			0
$195$	−3.46410	−	7.74597i	−0.248069	−	0.554700i
$196$		0			0
$197$	0.724016	−	0.724016i	0.0515840	−	0.0515840i	−0.680844	−	0.732428i	$-0.738387\pi$
$197$	0.724016	−	0.724016i	0.0515840	−	0.0515840i	0.732428	+	0.680844i	$0.238387\pi$
$198$		0			0
$199$	1.73205	+	1.73205i	0.122782	+	0.122782i	0.765828	−	0.643046i	$-0.222330\pi$
$199$	1.73205	+	1.73205i	0.122782	+	0.122782i	−0.643046	+	0.765828i	$0.722330\pi$
$200$		0			0
$201$	−2.14093	+	5.60503i	−0.151010	+	0.395349i
$202$		0			0
$203$	−9.49193			−0.666203
$204$		0			0
$205$	23.2379			1.62301
$206$		0			0
$207$	0.442151	+	7.93408i	0.0307316	+	0.551457i
$208$		0			0
$209$	−1.00803	−	1.00803i	−0.0697272	−	0.0697272i
$210$		0			0
$211$	−8.15624	+	8.15624i	−0.561499	+	0.561499i	−0.929733	−	0.368234i	$-0.879962\pi$
$211$	−8.15624	+	8.15624i	−0.561499	+	0.561499i	0.368234	+	0.929733i	$0.379962\pi$
$212$		0			0
$213$	−13.1324	+	5.87298i	−0.899817	+	0.402410i
$214$		0			0
$215$	−1.74597	−	1.74597i	−0.119074	−	0.119074i
$216$		0			0
$217$	21.4919			1.45897
$218$		0			0
$219$	24.0287	−	10.7460i	1.62371	−	0.726145i
$220$		0			0
$221$	−4.47214	−	6.92820i	−0.300828	−	0.466041i
$222$		0			0
$223$	−22.8007			−1.52685			−0.763423	−	0.645899i	$-0.776483\pi$
$223$	−22.8007			−1.52685			−0.763423	+	0.645899i	$0.776483\pi$
$224$		0			0
$225$	−2.00000	+	2.23607i	−0.133333	+	0.149071i
$226$		0			0
$227$	12.7460	+	12.7460i	0.845980	+	0.845980i	0.989629	−	0.143649i	$-0.0458837\pi$
$227$	12.7460	+	12.7460i	0.845980	+	0.845980i	−0.143649	+	0.989629i	$0.545884\pi$
$228$		0			0
$229$		−	25.2379i		−	1.66777i	−0.551940	−	0.833884i	$-0.686112\pi$
$229$		−	25.2379i		−	1.66777i	0.551940	−	0.833884i	$-0.313888\pi$
$230$		0			0
$231$	5.60503	+	2.14093i	0.368784	+	0.140863i
$232$		0			0
$233$	13.6364	+	13.6364i	0.893351	+	0.893351i	0.994837	−	0.101486i	$-0.0323598\pi$
$233$	13.6364	+	13.6364i	0.893351	+	0.893351i	−0.101486	+	0.994837i	$0.532360\pi$
$234$		0			0
$235$	−6.92820	−	6.92820i	−0.451946	−	0.451946i
$236$		0			0
$237$	13.8730	−	6.20419i	0.901147	−	0.403005i
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	−0.674165	−	0.738581i	$-0.735496\pi$
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	0.738581	+	0.674165i	$0.235496\pi$
$242$		0			0
$243$	−3.90983	+	15.0902i	−0.250816	+	0.968035i
$244$		0			0
$245$	−1.73205	+	1.73205i	−0.110657	+	0.110657i
$246$		0			0
$247$	−2.01607			−0.128279
$248$		0			0
$249$	2.31513	−	6.06110i	0.146716	−	0.384107i
$250$		0			0
$251$	1.74597			0.110204			0.0551022	−	0.998481i	$-0.482452\pi$
$251$	1.74597			0.110204			0.0551022	+	0.998481i	$0.482452\pi$
$252$		0			0
$253$		−	3.74597i		−	0.235507i
$254$		0			0
$255$	−9.54342	+	14.6603i	−0.597632	+	0.918061i
$256$		0			0
$257$	4.47214			0.278964			0.139482	−	0.990225i	$-0.455456\pi$
$257$	4.47214			0.278964			0.139482	+	0.990225i	$0.455456\pi$
$258$		0			0
$259$		−	13.4164i		−	0.833655i
$260$		0			0
$261$	0.646846	+	11.6072i	0.0400388	+	0.718467i
$262$		0			0
$263$			16.2540i			1.00227i	0.865370	+	0.501133i	$0.167083\pi$
$263$			16.2540i			1.00227i	−0.865370	+	0.501133i	$0.832917\pi$
$264$		0			0
$265$	19.7460	+	19.7460i	1.21299	+	1.21299i
$266$		0			0
$267$	−1.24600	+	3.26207i	−0.0762539	+	0.199635i
$268$		0			0
$269$	−4.18812	−	4.18812i	−0.255354	−	0.255354i	0.567807	−	0.823161i	$-0.307792\pi$
$269$	−4.18812	−	4.18812i	−0.255354	−	0.255354i	−0.823161	+	0.567807i	$0.807792\pi$
$270$		0			0
$271$		−	3.46410i		−	0.210429i	−0.994450	−	0.105215i	$-0.966447\pi$
$271$		−	3.46410i		−	0.210429i	0.994450	−	0.105215i	$-0.0335529\pi$
$272$		0			0
$273$	7.74597	−	3.46410i	0.468807	−	0.209657i
$274$		0			0
$275$	1.00000	−	1.00000i	0.0603023	−	0.0603023i
$276$		0			0
$277$	12.1270	−	12.1270i	0.728642	−	0.728642i	−0.241707	−	0.970349i	$-0.577707\pi$
$277$	12.1270	−	12.1270i	0.728642	−	0.728642i	0.970349	+	0.241707i	$0.0777074\pi$
$278$		0			0
$279$	−1.46461	−	26.2814i	−0.0876839	−	1.57342i
$280$		0			0
$281$	−23.2407			−1.38642			−0.693211	−	0.720734i	$-0.743805\pi$
$281$	−23.2407			−1.38642			−0.693211	+	0.720734i	$0.743805\pi$
$282$		0			0
$283$	−11.1803	+	11.1803i	−0.664602	+	0.664602i	−0.956461	−	0.291859i	$-0.905726\pi$
$283$	−11.1803	+	11.1803i	−0.664602	+	0.664602i	0.291859	+	0.956461i	$0.405726\pi$
$284$		0			0
$285$	1.74597	+	3.90410i	0.103422	+	0.231259i
$286$		0			0
$287$			23.2379i			1.37169i
$288$		0			0
$289$	−7.00000	+	15.4919i	−0.411765	+	0.911290i
$290$		0			0
$291$	−6.70820	+	3.00000i	−0.393242	+	0.175863i
$292$		0			0
$293$		−	7.93624i		−	0.463640i	−0.972759	−	0.231820i	$-0.925532\pi$
$293$		−	7.93624i		−	0.463640i	0.972759	−	0.231820i	$-0.0744680\pi$
$294$		0			0
$295$	20.3446	−	20.3446i	1.18451	−	1.18451i
$296$		0			0
$297$	2.23607	−	7.00000i	0.129750	−	0.406181i
$298$		0			0
$299$	−3.74597	−	3.74597i	−0.216635	−	0.216635i
$300$		0			0
$301$	1.74597	−	1.74597i	0.100636	−	0.100636i
$302$		0			0
$303$	4.90486	−	12.8411i	0.281777	−	0.737702i
$304$		0			0
$305$			0.439999i			0.0251942i
$306$		0			0
$307$			17.3205i			0.988534i	0.869310	+	0.494267i	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$		0			0
$309$	−11.9507	+	31.2872i	−0.679849	+	1.77987i
$310$		0			0
$311$	10.1270	−	10.1270i	0.574250	−	0.574250i	−0.359063	−	0.933313i	$-0.616904\pi$
$311$	10.1270	−	10.1270i	0.574250	−	0.574250i	0.933313	+	0.359063i	$0.116904\pi$
$312$		0			0
$313$	−16.7460	−	16.7460i	−0.946538	−	0.946538i	0.0521037	−	0.998642i	$-0.483407\pi$
$313$	−16.7460	−	16.7460i	−0.946538	−	0.946538i	−0.998642	+	0.0521037i	$0.983407\pi$
$314$		0			0
$315$	−13.4164	−	12.0000i	−0.755929	−	0.676123i
$316$		0			0
$317$	17.6045	−	17.6045i	0.988769	−	0.988769i	−0.0111689	−	0.999938i	$-0.503555\pi$
$317$	17.6045	−	17.6045i	0.988769	−	0.988769i	0.999938	+	0.0111689i	$0.00355526\pi$
$318$		0			0
$319$		−	5.48017i		−	0.306831i
$320$		0			0
$321$	24.0287	−	10.7460i	1.34115	−	0.599781i
$322$		0			0
$323$	2.25403	+	3.49193i	0.125418	+	0.194296i
$324$		0			0
$325$		−	2.00000i		−	0.110940i
$326$		0			0
$327$	0.127017	+	0.284018i	0.00702404	+	0.0157062i
$328$		0			0
$329$	6.92820	−	6.92820i	0.381964	−	0.381964i
$330$		0			0
$331$	16.8805			0.927837			0.463918	−	0.885878i	$-0.346443\pi$
$331$	16.8805			0.927837			0.463918	+	0.885878i	$0.346443\pi$
$332$		0			0
$333$	−16.4062	+	0.914287i	−0.899055	+	0.0501026i
$334$		0			0
$335$	−6.00000	+	6.00000i	−0.327815	+	0.327815i
$336$		0			0
$337$	−18.4919	+	18.4919i	−1.00732	+	1.00732i	−0.00734679	+	0.999973i	$0.502339\pi$
$337$	−18.4919	+	18.4919i	−1.00732	+	1.00732i	−0.999973	+	0.00734679i	$0.997661\pi$
$338$		0			0
$339$	−22.7460	+	10.1723i	−1.23539	+	0.552484i
$340$		0			0
$341$			12.4084i			0.671951i
$342$		0			0
$343$	−13.8564	−	13.8564i	−0.748176	−	0.748176i
$344$		0			0
$345$	−4.00993	+	10.4981i	−0.215887	+	0.565201i
$346$		0			0
$347$	15.0000	+	15.0000i	0.805242	+	0.805242i	0.983910	−	0.178667i	$-0.0571786\pi$
$347$	15.0000	+	15.0000i	0.805242	+	0.805242i	−0.178667	+	0.983910i	$0.557179\pi$
$348$		0			0
$349$			33.2379i			1.77918i	0.456756	+	0.889592i	$0.349011\pi$
$349$			33.2379i			1.77918i	−0.456756	+	0.889592i	$0.650989\pi$
$350$		0			0
$351$	−4.76393	−	9.23607i	−0.254280	−	0.492985i
$352$		0			0
$353$			20.7846i			1.10625i	0.833097	+	0.553127i	$0.186565\pi$
$353$			20.7846i			1.10625i	−0.833097	+	0.553127i	$0.813435\pi$
$354$		0			0
$355$	−20.3446			−1.07978
$356$		0			0
$357$	−14.6603	−	9.54342i	−0.775903	−	0.505092i
$358$		0			0
$359$		−	27.7460i		−	1.46438i	−0.681103	−	0.732188i	$-0.738499\pi$
$359$		−	27.7460i		−	1.46438i	0.681103	−	0.732188i	$-0.261501\pi$
$360$		0			0
$361$	−17.9839			−0.946519
$362$		0			0
$363$	5.56231	−	14.5623i	0.291945	−	0.764323i
$364$		0			0
$365$	37.2251			1.94845
$366$		0			0
$367$	−2.74009	+	2.74009i	−0.143031	+	0.143031i	−0.774997	−	0.631965i	$-0.782248\pi$
$367$	−2.74009	+	2.74009i	−0.143031	+	0.143031i	0.631965	+	0.774997i	$0.282248\pi$
$368$		0			0
$369$	28.4164	−	1.58359i	1.47930	−	0.0824385i
$370$		0			0
$371$	−19.7460	+	19.7460i	−1.02516	+	1.02516i
$372$		0			0
$373$	−18.0000			−0.932005			−0.466002	−	0.884783i	$-0.654306\pi$
$373$	−18.0000			−0.932005			−0.466002	+	0.884783i	$0.654306\pi$
$374$		0			0
$375$	15.4919	−	6.92820i	0.800000	−	0.357771i
$376$		0			0
$377$	−5.48017	−	5.48017i	−0.282243	−	0.282243i
$378$		0			0
$379$	12.1884	+	12.1884i	0.626075	+	0.626075i	0.947078	−	0.321003i	$-0.104020\pi$
$379$	12.1884	+	12.1884i	0.626075	+	0.626075i	−0.321003	+	0.947078i	$0.604020\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$			23.2379i			1.18740i	0.804686	+	0.593701i	$0.202334\pi$
$383$			23.2379i			1.18740i	−0.804686	+	0.593701i	$0.797666\pi$
$384$		0			0
$385$	6.00000	+	6.00000i	0.305788	+	0.305788i
$386$		0			0
$387$	−2.25403	−	2.01607i	−0.114579	−	0.102483i
$388$		0			0
$389$	15.4325			0.782458			0.391229	−	0.920293i	$-0.372050\pi$
$389$	15.4325			0.782458			0.391229	+	0.920293i	$0.372050\pi$
$390$		0			0
$391$	−2.30009	+	10.6763i	−0.116320	+	0.539925i
$392$		0			0
$393$	11.1803	−	5.00000i	0.563974	−	0.252217i
$394$		0			0
$395$	21.4919			1.08138
$396$		0			0
$397$	−15.3649	−	15.3649i	−0.771143	−	0.771143i	0.207163	−	0.978306i	$-0.433577\pi$
$397$	−15.3649	−	15.3649i	−0.771143	−	0.771143i	−0.978306	+	0.207163i	$0.933577\pi$
$398$		0			0
$399$	−3.90410	+	1.74597i	−0.195449	+	0.0874077i
$400$		0			0
$401$	−15.0844	+	15.0844i	−0.753281	+	0.753281i	−0.975090	−	0.221809i	$-0.928804\pi$
$401$	−15.0844	+	15.0844i	−0.753281	+	0.753281i	0.221809	+	0.975090i	$0.428804\pi$
$402$		0			0
$403$	12.4084	+	12.4084i	0.618105	+	0.618105i
$404$		0			0
$405$	−13.7599	+	17.2240i	−0.683734	+	0.855867i
$406$		0			0
$407$	7.74597			0.383953
$408$		0			0
$409$	1.49193			0.0737714			0.0368857	−	0.999319i	$-0.488256\pi$
$409$	1.49193			0.0737714			0.0368857	+	0.999319i	$0.488256\pi$
$410$		0			0
$411$	5.52786	−	14.4721i	0.272669	−	0.713858i
$412$		0			0
$413$	20.3446	+	20.3446i	1.00109	+	1.00109i
$414$		0			0
$415$	6.48820	−	6.48820i	0.318493	−	0.318493i
$416$		0			0
$417$	8.15624	+	18.2379i	0.399413	+	0.893114i
$418$		0			0
$419$	20.2379	+	20.2379i	0.988686	+	0.988686i	0.999937	−	0.0112506i	$-0.00358125\pi$
$419$	20.2379	+	20.2379i	0.988686	+	0.988686i	−0.0112506	+	0.999937i	$0.503581\pi$
$420$		0			0
$421$	28.9839			1.41259			0.706294	−	0.707919i	$-0.250366\pi$
$421$	28.9839			1.41259			0.706294	+	0.707919i	$0.250366\pi$
$422$		0			0
$423$	−8.94427	−	8.00000i	−0.434885	−	0.388973i
$424$		0			0
$425$	−3.46410	+	2.23607i	−0.168034	+	0.108465i
$426$		0			0
$427$	−0.439999			−0.0212930
$428$		0			0
$429$	2.00000	+	4.47214i	0.0965609	+	0.215917i
$430$		0			0
$431$	12.1270	+	12.1270i	0.584138	+	0.584138i	0.936038	−	0.351900i	$-0.114464\pi$
$431$	12.1270	+	12.1270i	0.584138	+	0.584138i	−0.351900	+	0.936038i	$0.614464\pi$
$432$		0			0
$433$			32.0000i			1.53782i	0.639356	+	0.768911i	$0.279201\pi$
$433$			32.0000i			1.53782i	−0.639356	+	0.768911i	$0.720799\pi$
$434$		0			0
$435$	−5.86634	+	15.3583i	−0.281269	+	0.736373i
$436$		0			0
$437$	1.88803	+	1.88803i	0.0903168	+	0.0903168i
$438$		0			0
$439$	−0.284018	−	0.284018i	−0.0135554	−	0.0135554i	0.700297	−	0.713852i	$-0.253051\pi$
$439$	−0.284018	−	0.284018i	−0.0135554	−	0.0135554i	−0.713852	+	0.700297i	$0.753051\pi$
$440$		0			0
$441$	−2.00000	+	2.23607i	−0.0952381	+	0.106479i
$442$		0			0
$443$	−29.2379			−1.38913			−0.694567	−	0.719428i	$-0.744404\pi$
$443$	−29.2379			−1.38913			−0.694567	+	0.719428i	$0.744404\pi$
$444$		0			0
$445$	−3.49193	+	3.49193i	−0.165534	+	0.165534i
$446$		0			0
$447$	−6.15086	+	16.1032i	−0.290926	+	0.761654i
$448$		0			0
$449$	−17.1005	+	17.1005i	−0.807023	+	0.807023i	−0.984182	−	0.177159i	$-0.943309\pi$
$449$	−17.1005	+	17.1005i	−0.807023	+	0.807023i	0.177159	+	0.984182i	$0.443309\pi$
$450$		0			0
$451$	−13.4164			−0.631754
$452$		0			0
$453$	3.26207	+	1.24600i	0.153265	+	0.0585421i
$454$		0			0
$455$	12.0000			0.562569
$456$		0			0
$457$		−	3.49193i		−	0.163346i	−0.996659	−	0.0816729i	$-0.973974\pi$
$457$		−	3.49193i		−	0.163346i	0.996659	−	0.0816729i	$-0.0260263\pi$
$458$		0			0
$459$	−10.6711	+	18.5776i	−0.498084	+	0.867129i
$460$		0			0
$461$	11.4003			0.530967			0.265483	−	0.964115i	$-0.414468\pi$
$461$	11.4003			0.530967			0.265483	+	0.964115i	$0.414468\pi$
$462$		0			0
$463$			19.3366i			0.898647i	0.893369	+	0.449323i	$0.148335\pi$
$463$			19.3366i			0.898647i	−0.893369	+	0.449323i	$0.851665\pi$
$464$		0			0
$465$	13.2827	−	34.7747i	0.615973	−	1.61264i
$466$		0			0
$467$			19.2379i			0.890224i	0.895475	+	0.445112i	$0.146836\pi$
$467$			19.2379i			0.890224i	−0.895475	+	0.445112i	$0.853164\pi$
$468$		0			0
$469$	−6.00000	−	6.00000i	−0.277054	−	0.277054i
$470$		0			0
$471$	−3.23607	−	1.23607i	−0.149110	−	0.0569550i
$472$		0			0
$473$	1.00803	+	1.00803i	0.0463495	+	0.0463495i
$474$		0			0
$475$			1.00803i			0.0462518i
$476$		0			0
$477$	25.4919	+	22.8007i	1.16720	+	1.04397i
$478$		0			0
$479$	−19.6190	+	19.6190i	−0.896413	+	0.896413i	−0.995117	−	0.0987041i	$-0.968530\pi$
$479$	−19.6190	+	19.6190i	−0.896413	+	0.896413i	0.0987041	+	0.995117i	$0.468530\pi$
$480$		0			0
$481$	7.74597	−	7.74597i	0.353186	−	0.353186i
$482$		0			0
$483$	−10.4981	−	4.00993i	−0.477682	−	0.182458i
$484$		0			0
$485$	−10.3923			−0.471890
$486$		0			0
$487$	−3.74812	+	3.74812i	−0.169844	+	0.169844i	−0.786911	−	0.617067i	$-0.788321\pi$
$487$	−3.74812	+	3.74812i	−0.169844	+	0.169844i	0.617067	+	0.786911i	$0.288321\pi$
$488$		0			0
$489$	28.2379	−	12.6284i	1.27696	−	0.571075i
$490$		0			0
$491$			4.25403i			0.191982i	0.995382	+	0.0959909i	$0.0306020\pi$
$491$			4.25403i			0.191982i	−0.995382	+	0.0959909i	$0.969398\pi$
$492$		0			0
$493$	−3.36492	+	15.6190i	−0.151548	+	0.703442i
$494$		0			0
$495$	6.92820	−	7.74597i	0.311400	−	0.348155i
$496$		0			0
$497$		−	20.3446i		−	0.912581i
$498$		0			0
$499$	23.5887	−	23.5887i	1.05598	−	1.05598i	0.0576383	−	0.998338i	$-0.481643\pi$
$499$	23.5887	−	23.5887i	1.05598	−	1.05598i	0.998338	−	0.0576383i	$-0.0183570\pi$
$500$		0			0
$501$	39.3972	−	17.6190i	1.76014	−	0.787157i
$502$		0			0
$503$	5.87298	+	5.87298i	0.261863	+	0.261863i	0.825811	−	0.563947i	$-0.190718\pi$
$503$	5.87298	+	5.87298i	0.261863	+	0.261863i	−0.563947	+	0.825811i	$0.690718\pi$
$504$		0			0
$505$	13.7460	−	13.7460i	0.611687	−	0.611687i
$506$		0			0
$507$	−14.5623	−	5.56231i	−0.646735	−	0.247031i
$508$		0			0
$509$			39.6812i			1.75884i	0.476049	+	0.879419i	$0.342069\pi$
$509$			39.6812i			1.75884i	−0.476049	+	0.879419i	$0.657931\pi$
$510$		0			0
$511$			37.2251i			1.64674i
$512$		0			0
$513$	2.40110	+	4.65514i	0.106011	+	0.205529i
$514$		0			0
$515$	−33.4919	+	33.4919i	−1.47583	+	1.47583i
$516$		0			0
$517$	4.00000	+	4.00000i	0.175920	+	0.175920i
$518$		0			0
$519$	−13.1324	−	29.3649i	−0.576448	−	1.28898i
$520$		0			0
$521$	−14.0764	+	14.0764i	−0.616699	+	0.616699i	−0.944683	−	0.327985i	$-0.893631\pi$
$521$	−14.0764	+	14.0764i	−0.616699	+	0.616699i	0.327985	+	0.944683i	$0.393631\pi$
$522$		0			0
$523$			3.46410i			0.151475i	0.997128	+	0.0757373i	$0.0241310\pi$
$523$			3.46410i			0.151475i	−0.997128	+	0.0757373i	$0.975869\pi$
$524$		0			0
$525$	−1.73205	−	3.87298i	−0.0755929	−	0.169031i
$526$		0			0
$527$	7.61895	−	35.3649i	0.331887	−	1.54052i
$528$		0			0
$529$		−	15.9839i		−	0.694951i
$530$		0			0
$531$	23.4919	−	26.2648i	1.01946	−	1.13979i
$532$		0			0
$533$	−13.4164	+	13.4164i	−0.581129	+	0.581129i
$534$		0			0
$535$	37.2251			1.60938
$536$		0			0
$537$	7.25941	−	19.0054i	0.313267	−	0.820142i
$538$		0			0
$539$	1.00000	−	1.00000i	0.0430730	−	0.0430730i
$540$		0			0
$541$	−17.6190	+	17.6190i	−0.757498	+	0.757498i	−0.975866	−	0.218369i	$-0.929927\pi$
$541$	−17.6190	+	17.6190i	−0.757498	+	0.757498i	0.218369	+	0.975866i	$0.429927\pi$
$542$		0			0
$543$	−2.12702	−	4.75615i	−0.0912790	−	0.204106i
$544$		0			0
$545$			0.439999i			0.0188475i
$546$		0			0
$547$	−31.5250	−	31.5250i	−1.34791	−	1.34791i	−0.887929	−	0.459981i	$-0.847856\pi$
$547$	−31.5250	−	31.5250i	−1.34791	−	1.34791i	−0.459981	−	0.887929i	$-0.652144\pi$
$548$		0			0
$549$	0.0299846	+	0.538051i	0.00127971	+	0.0229635i
$550$		0			0
$551$	2.76210	+	2.76210i	0.117669	+	0.117669i
$552$		0			0
$553$			21.4919i			0.913930i
$554$		0			0
$555$	−21.7082	−	8.29180i	−0.921462	−	0.351967i
$556$		0			0
$557$		−	27.8409i		−	1.17965i	−0.807529	−	0.589827i	$-0.799196\pi$
$557$		−	27.8409i		−	1.17965i	0.807529	−	0.589827i	$-0.200804\pi$
$558$		0			0
$559$	2.01607			0.0852706
$560$		0			0
$561$	5.50990	−	8.46410i	0.232628	−	0.357355i
$562$		0			0
$563$			27.2379i			1.14794i	0.818876	+	0.573970i	$0.194598\pi$
$563$			27.2379i			1.14794i	−0.818876	+	0.573970i	$0.805402\pi$
$564$		0			0
$565$	−35.2379			−1.48247
$566$		0			0
$567$	−17.2240	−	13.7599i	−0.723339	−	0.577861i
$568$		0			0
$569$	−2.45607			−0.102964			−0.0514818	−	0.998674i	$-0.516394\pi$
$569$	−2.45607			−0.102964			−0.0514818	+	0.998674i	$0.516394\pi$
$570$		0			0
$571$	18.5485	−	18.5485i	0.776232	−	0.776232i	−0.202956	−	0.979188i	$-0.565055\pi$
$571$	18.5485	−	18.5485i	0.776232	−	0.776232i	0.979188	+	0.202956i	$0.0650547\pi$
$572$		0			0
$573$	−32.3607	−	12.3607i	−1.35189	−	0.516375i
$574$		0			0
$575$	−1.87298	+	1.87298i	−0.0781088	+	0.0781088i
$576$		0			0
$577$	33.4919			1.39429			0.697144	−	0.716931i	$-0.254454\pi$
$577$	33.4919			1.39429			0.697144	+	0.716931i	$0.254454\pi$
$578$		0			0
$579$	−18.4919	−	41.3492i	−0.768499	−	1.71841i
$580$		0			0
$581$	6.48820	+	6.48820i	0.269176	+	0.269176i
$582$		0			0
$583$	−11.4003	−	11.4003i	−0.472154	−	0.472154i
$584$		0			0
$585$	−0.817763	−	14.6742i	−0.0338104	−	0.606702i
$586$		0			0
$587$		−	3.74597i		−	0.154613i	−0.997007	−	0.0773063i	$-0.975368\pi$
$587$		−	3.74597i		−	0.154613i	0.997007	−	0.0773063i	$-0.0246319\pi$
$588$		0			0
$589$	−6.25403	−	6.25403i	−0.257693	−	0.257693i
$590$		0			0
$591$	1.61895	−	0.724016i	0.0665947	−	0.0297821i
$592$		0			0
$593$	−2.45607			−0.100859			−0.0504293	−	0.998728i	$-0.516059\pi$
$593$	−2.45607			−0.100859			−0.0504293	+	0.998728i	$0.516059\pi$
$594$		0			0
$595$	−13.4164	−	20.7846i	−0.550019	−	0.852086i
$596$		0			0
$597$	1.73205	+	3.87298i	0.0708881	+	0.158511i
$598$		0			0
$599$	−3.49193			−0.142677			−0.0713383	−	0.997452i	$-0.522727\pi$
$599$	−3.49193			−0.142677			−0.0713383	+	0.997452i	$0.522727\pi$
$600$		0			0
$601$	−28.7460	−	28.7460i	−1.17257	−	1.17257i	−0.981594	−	0.190978i	$-0.938834\pi$
$601$	−28.7460	−	28.7460i	−1.17257	−	1.17257i	−0.190978	−	0.981594i	$-0.561166\pi$
$602$		0			0
$603$	−6.92820	+	7.74597i	−0.282138	+	0.315440i
$604$		0			0
$605$	15.5885	−	15.5885i	0.633761	−	0.633761i
$606$		0			0
$607$	2.74009	+	2.74009i	0.111217	+	0.111217i	0.760525	−	0.649309i	$-0.224942\pi$
$607$	2.74009	+	2.74009i	0.111217	+	0.111217i	−0.649309	+	0.760525i	$0.724942\pi$
$608$		0			0
$609$	−15.3583	−	5.86634i	−0.622349	−	0.237716i
$610$		0			0
$611$	8.00000			0.323645
$612$		0			0
$613$	28.9839			1.17065			0.585324	−	0.810800i	$-0.300967\pi$
$613$	28.9839			1.17065			0.585324	+	0.810800i	$0.300967\pi$
$614$		0			0
$615$	37.5997	+	14.3618i	1.51617	+	0.579124i
$616$		0			0
$617$	2.67607	+	2.67607i	0.107734	+	0.107734i	0.758919	−	0.651185i	$-0.225728\pi$
$617$	2.67607	+	2.67607i	0.107734	+	0.107734i	−0.651185	+	0.758919i	$0.725728\pi$
$618$		0			0
$619$	−4.25214	+	4.25214i	−0.170908	+	0.170908i	−0.787378	−	0.616470i	$-0.788562\pi$
$619$	−4.25214	+	4.25214i	−0.170908	+	0.170908i	0.616470	+	0.787378i	$0.288562\pi$
$620$		0			0
$621$	−4.18812	+	13.1109i	−0.168063	+	0.526122i
$622$		0			0
$623$	−3.49193	−	3.49193i	−0.139901	−	0.139901i
$624$		0			0
$625$	29.0000			1.16000
$626$		0			0
$627$	−1.00803	−	2.25403i	−0.0402570	−	0.0900174i
$628$		0			0
$629$	−22.0767	−	4.75615i	−0.880254	−	0.189640i
$630$		0			0
$631$	2.89607			0.115291			0.0576453	−	0.998337i	$-0.481641\pi$
$631$	2.89607			0.115291			0.0576453	+	0.998337i	$0.481641\pi$
$632$		0			0
$633$	−18.2379	+	8.15624i	−0.724891	+	0.324181i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		−	2.00000i		−	0.0792429i
$638$		0			0
$639$	−24.8784	+	1.38642i	−0.984173	+	0.0548461i
$640$		0			0
$641$	−30.9569	−	30.9569i	−1.22272	−	1.22272i	−0.966660	−	0.256065i	$-0.917574\pi$
$641$	−30.9569	−	30.9569i	−1.22272	−	1.22272i	−0.256065	−	0.966660i	$-0.582426\pi$
$642$		0			0
$643$	−29.5089	−	29.5089i	−1.16372	−	1.16372i	−0.983655	−	0.180061i	$-0.942370\pi$
$643$	−29.5089	−	29.5089i	−1.16372	−	1.16372i	−0.180061	−	0.983655i	$-0.557630\pi$
$644$		0			0
$645$	−1.74597	−	3.90410i	−0.0687474	−	0.153724i
$646$		0			0
$647$	23.4919			0.923563			0.461782	−	0.886994i	$-0.347210\pi$
$647$	23.4919			0.923563			0.461782	+	0.886994i	$0.347210\pi$
$648$		0			0
$649$	−11.7460	+	11.7460i	−0.461070	+	0.461070i
$650$		0			0
$651$	34.7747	+	13.2827i	1.36293	+	0.520592i
$652$		0			0
$653$	−18.1726	+	18.1726i	−0.711147	+	0.711147i	−0.966775	−	0.255628i	$-0.917718\pi$
$653$	−18.1726	+	18.1726i	−0.711147	+	0.711147i	0.255628	+	0.966775i	$0.417718\pi$
$654$		0			0
$655$	17.3205			0.676768
$656$		0			0
$657$	45.5206	−	2.53678i	1.77593	−	0.0989692i
$658$		0			0
$659$	−17.7460			−0.691285			−0.345642	−	0.938366i	$-0.612339\pi$
$659$	−17.7460			−0.691285			−0.345642	+	0.938366i	$0.612339\pi$
$660$		0			0
$661$		−	2.25403i		−	0.0876717i	−0.999039	−	0.0438359i	$-0.986042\pi$
$661$		−	2.25403i		−	0.0876717i	0.999039	−	0.0438359i	$-0.0139579\pi$
$662$		0			0
$663$	−2.95420	−	13.9740i	−0.114732	−	0.542705i
$664$		0			0
$665$	−6.04821			−0.234539
$666$		0			0
$667$			10.2643i			0.397434i
$668$		0			0
$669$	−36.8923	−	14.0916i	−1.42634	−	0.544813i
$670$		0			0
$671$		−	0.254033i		−	0.00980685i
$672$		0			0
$673$	−3.00000	−	3.00000i	−0.115642	−	0.115642i	0.646918	−	0.762560i	$-0.276058\pi$
$673$	−3.00000	−	3.00000i	−0.115642	−	0.115642i	−0.762560	+	0.646918i	$0.776058\pi$
$674$		0			0
$675$	−4.61803	+	2.38197i	−0.177748	+	0.0916819i
$676$		0			0
$677$	−27.9968	−	27.9968i	−1.07601	−	1.07601i	−0.996863	−	0.0791423i	$-0.974782\pi$
$677$	−27.9968	−	27.9968i	−1.07601	−	1.07601i	−0.0791423	−	0.996863i	$-0.525218\pi$
$678$		0			0
$679$		−	10.3923i		−	0.398820i
$680$		0			0
$681$	12.7460	+	28.5008i	0.488427	+	1.09215i
$682$		0			0
$683$	14.7460	−	14.7460i	0.564239	−	0.564239i	−0.366270	−	0.930509i	$-0.619365\pi$
$683$	14.7460	−	14.7460i	0.564239	−	0.564239i	0.930509	+	0.366270i	$0.119365\pi$
$684$		0			0
$685$	15.4919	−	15.4919i	0.591916	−	0.591916i
$686$		0			0
$687$	15.5979	−	40.8358i	0.595096	−	1.55798i
$688$		0			0
$689$	−22.8007			−0.868637
$690$		0			0
$691$	−28.9408	+	28.9408i	−1.10096	+	1.10096i	−0.106667	+	0.994295i	$0.534018\pi$
$691$	−28.9408	+	28.9408i	−1.10096	+	1.10096i	−0.994295	+	0.106667i	$0.965982\pi$
$692$		0			0
$693$	7.74597	+	6.92820i	0.294245	+	0.263181i
$694$		0			0
$695$			28.2540i			1.07174i
$696$		0			0
$697$	38.2379	+	8.23790i	1.44836	+	0.312033i
$698$		0			0
$699$	13.6364	+	30.4919i	0.515776	+	1.15331i
$700$		0			0
$701$		−	37.6651i		−	1.42259i	−0.702893	−	0.711296i	$-0.748109\pi$
$701$		−	37.6651i		−	1.42259i	0.702893	−	0.711296i	$-0.251891\pi$
$702$		0			0
$703$	−3.90410	+	3.90410i	−0.147246	+	0.147246i
$704$		0			0
$705$	−6.92820	−	15.4919i	−0.260931	−	0.583460i
$706$		0			0
$707$	13.7460	+	13.7460i	0.516970	+	0.516970i
$708$		0			0
$709$	7.61895	−	7.61895i	0.286136	−	0.286136i	−0.549414	−	0.835550i	$-0.685149\pi$
$709$	7.61895	−	7.61895i	0.286136	−	0.286136i	0.835550	+	0.549414i	$0.185149\pi$
$710$		0			0
$711$	26.2814	−	1.46461i	0.985628	−	0.0549272i
$712$		0			0
$713$		−	23.2407i		−	0.870370i
$714$		0			0
$715$			6.92820i			0.259100i
$716$		0			0
$717$	−19.4164	−	7.41641i	−0.725119	−	0.276971i
$718$		0			0
$719$	11.8730	−	11.8730i	0.442788	−	0.442788i	−0.450160	−	0.892948i	$-0.648633\pi$
$719$	11.8730	−	11.8730i	0.442788	−	0.442788i	0.892948	+	0.450160i	$0.148633\pi$
$720$		0			0
$721$	−33.4919	−	33.4919i	−1.24730	−	1.24730i
$722$		0			0
$723$	2.23607	−	1.00000i	0.0831603	−	0.0371904i
$724$		0			0
$725$	−2.74009	+	2.74009i	−0.101764	+	0.101764i
$726$		0			0
$727$			46.1694i			1.71233i	0.516704	+	0.856164i	$0.327159\pi$
$727$			46.1694i			1.71233i	−0.516704	+	0.856164i	$0.672841\pi$
$728$		0			0
$729$	−15.6525	+	22.0000i	−0.579721	+	0.814815i
$730$		0			0
$731$	−2.25403	−	3.49193i	−0.0833684	−	0.129154i
$732$		0			0
$733$		−	21.7460i		−	0.803206i	−0.915814	−	0.401603i	$-0.868453\pi$
$733$		−	21.7460i		−	0.803206i	0.915814	−	0.401603i	$-0.131547\pi$
$734$		0			0
$735$	−3.87298	+	1.73205i	−0.142857	+	0.0638877i
$736$		0			0
$737$	3.46410	−	3.46410i	0.127602	−	0.127602i
$738$		0			0
$739$	−3.02410			−0.111243			−0.0556217	−	0.998452i	$-0.517714\pi$
$739$	−3.02410			−0.111243			−0.0556217	+	0.998452i	$0.517714\pi$
$740$		0			0
$741$	−3.26207	−	1.24600i	−0.119835	−	0.0457729i
$742$		0			0
$743$	37.6190	−	37.6190i	1.38011	−	1.38011i	0.535692	−	0.844414i	$-0.320051\pi$
$743$	37.6190	−	37.6190i	1.38011	−	1.38011i	0.844414	−	0.535692i	$-0.179949\pi$
$744$		0			0
$745$	−17.2379	+	17.2379i	−0.631548	+	0.631548i
$746$		0			0
$747$	7.49193	−	8.37624i	0.274116	−	0.306470i
$748$		0			0
$749$			37.2251i			1.36018i
$750$		0			0
$751$	−24.9727	−	24.9727i	−0.911268	−	0.911268i	0.0851043	−	0.996372i	$-0.472878\pi$
$751$	−24.9727	−	24.9727i	−0.911268	−	0.911268i	−0.996372	+	0.0851043i	$0.972878\pi$
$752$		0			0
$753$	2.82503	+	1.07907i	0.102950	+	0.0393234i
$754$		0			0
$755$	3.49193	+	3.49193i	0.127084	+	0.127084i
$756$		0			0
$757$		−	2.25403i		−	0.0819242i	−0.999161	−	0.0409621i	$-0.986958\pi$
$757$		−	2.25403i		−	0.0819242i	0.999161	−	0.0409621i	$-0.0130423\pi$
$758$		0			0
$759$	2.31513	−	6.06110i	0.0840341	−	0.220004i
$760$		0			0
$761$			22.8007i			0.826524i	0.910612	+	0.413262i	$0.135611\pi$
$761$			22.8007i			0.826524i	−0.910612	+	0.413262i	$0.864389\pi$
$762$		0			0
$763$	−0.439999			−0.0159290
$764$		0			0
$765$	−24.5021	+	17.8226i	−0.885876	+	0.644378i
$766$		0			0
$767$			23.4919i			0.848245i
$768$		0			0
$769$	17.4919			0.630775			0.315388	−	0.948963i	$-0.397865\pi$
$769$	17.4919			0.630775			0.315388	+	0.948963i	$0.397865\pi$
$770$		0			0
$771$	7.23607	+	2.76393i	0.260601	+	0.0995406i
$772$		0			0
$773$	−16.3125			−0.586719			−0.293359	−	0.956002i	$-0.594773\pi$
$773$	−16.3125			−0.586719			−0.293359	+	0.956002i	$0.594773\pi$
$774$		0			0
$775$	6.20419	−	6.20419i	0.222861	−	0.222861i
$776$		0			0
$777$	8.29180	−	21.7082i	0.297467	−	0.778777i
$778$		0			0
$779$	6.76210	−	6.76210i	0.242277	−	0.242277i
$780$		0			0
$781$	11.7460			0.420304
$782$		0			0
$783$	−6.12702	+	19.1806i	−0.218962	+	0.685459i
$784$		0			0
$785$	−3.46410	−	3.46410i	−0.123639	−	0.123639i
$786$		0			0
$787$	6.26821	+	6.26821i	0.223437	+	0.223437i	0.809944	−	0.586507i	$-0.199497\pi$
$787$	6.26821	+	6.26821i	0.223437	+	0.223437i	−0.586507	+	0.809944i	$0.699497\pi$
$788$		0			0
$789$	−10.0455	+	26.2996i	−0.357631	+	0.936290i
$790$		0			0
$791$		−	35.2379i		−	1.25292i
$792$		0			0
$793$	−0.254033	−	0.254033i	−0.00902099	−	0.00902099i
$794$		0			0
$795$	19.7460	+	44.1533i	0.700317	+	1.56596i
$796$		0			0
$797$	21.2246			0.751814			0.375907	−	0.926657i	$-0.377331\pi$
$797$	21.2246			0.751814			0.375907	+	0.926657i	$0.377331\pi$
$798$		0			0
$799$	−8.94427	−	13.8564i	−0.316426	−	0.490204i
$800$		0			0
$801$	−4.03214	+	4.50807i	−0.142469	+	0.159285i
$802$		0			0
$803$	−21.4919			−0.758434
$804$		0			0
$805$	−11.2379	−	11.2379i	−0.396084	−	0.396084i
$806$		0			0
$807$	−4.18812	−	9.36492i	−0.147429	−	0.329661i
$808$		0			0
$809$	−4.25214	+	4.25214i	−0.149497	+	0.149497i	−0.777893	−	0.628396i	$-0.783712\pi$
$809$	−4.25214	+	4.25214i	−0.149497	+	0.149497i	0.628396	+	0.777893i	$0.283712\pi$
$810$		0			0
$811$	30.9569	+	30.9569i	1.08704	+	1.08704i	0.995831	+	0.0912129i	$0.0290744\pi$
$811$	30.9569	+	30.9569i	1.08704	+	1.08704i	0.0912129	+	0.995831i	$0.470926\pi$
$812$		0			0
$813$	2.14093	−	5.60503i	0.0750858	−	0.196577i
$814$		0			0
$815$	43.7460			1.53235
$816$		0			0
$817$	−1.01613			−0.0355500
$818$		0			0
$819$	14.6742	−	0.817763i	0.512757	−	0.0285750i
$820$		0			0
$821$	10.6763	+	10.6763i	0.372606	+	0.372606i	0.868426	−	0.495819i	$-0.165132\pi$
$821$	10.6763	+	10.6763i	0.372606	+	0.372606i	−0.495819	+	0.868426i	$0.665132\pi$
$822$		0			0
$823$	16.1565	−	16.1565i	0.563180	−	0.563180i	−0.367029	−	0.930209i	$-0.619625\pi$
$823$	16.1565	−	16.1565i	0.563180	−	0.563180i	0.930209	+	0.367029i	$0.119625\pi$
$824$		0			0
$825$	2.23607	−	1.00000i	0.0778499	−	0.0348155i
$826$		0			0
$827$	3.00000	+	3.00000i	0.104320	+	0.104320i	0.757340	−	0.653020i	$-0.226498\pi$
$827$	3.00000	+	3.00000i	0.104320	+	0.104320i	−0.653020	+	0.757340i	$0.726498\pi$
$828$		0			0
$829$	−26.0000			−0.903017			−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000			−0.903017			−0.451509	+	0.892267i	$0.649114\pi$
$830$		0			0
$831$	27.1168	−	12.1270i	0.940673	−	0.420682i
$832$		0			0
$833$	−3.46410	+	2.23607i	−0.120024	+	0.0774752i
$834$		0			0
$835$	61.0338			2.11216
$836$		0			0
$837$	13.8730	−	43.4293i	0.479520	−	1.50114i
$838$		0			0
$839$	−29.1109	−	29.1109i	−1.00502	−	1.00502i	−0.999987	−	0.00503197i	$-0.998398\pi$
$839$	−29.1109	−	29.1109i	−1.00502	−	1.00502i	−0.00503197	−	0.999987i	$-0.501602\pi$
$840$		0			0
$841$		−	13.9839i		−	0.482202i
$842$		0			0
$843$	−37.6042	−	14.3635i	−1.29516	−	0.494706i
$844$		0			0
$845$	−15.5885	−	15.5885i	−0.536259	−	0.536259i
$846$		0			0
$847$	15.5885	+	15.5885i	0.535626	+	0.535626i
$848$		0			0
$849$	−25.0000	+	11.1803i	−0.857998	+	0.383708i
$850$		0			0
$851$	−14.5081			−0.497330
$852$		0			0
$853$	20.1270	−	20.1270i	0.689136	−	0.689136i	−0.272905	−	0.962041i	$-0.587984\pi$
$853$	20.1270	−	20.1270i	0.689136	−	0.689136i	0.962041	+	0.272905i	$0.0879845\pi$
$854$		0			0
$855$	0.412167	+	7.39603i	0.0140958	+	0.252939i
$856$		0			0
$857$	29.5089	−	29.5089i	1.00800	−	1.00800i	0.00803651	−	0.999968i	$-0.497442\pi$
$857$	29.5089	−	29.5089i	1.00800	−	1.00800i	0.999968	−	0.00803651i	$-0.00255813\pi$
$858$		0			0
$859$	−32.7530			−1.11752			−0.558759	−	0.829330i	$-0.688722\pi$
$859$	−32.7530			−1.11752			−0.558759	+	0.829330i	$0.688722\pi$
$860$		0			0
$861$	−14.3618	+	37.5997i	−0.489449	+	1.28139i
$862$		0			0
$863$	−8.00000			−0.272323			−0.136162	−	0.990687i	$-0.543477\pi$
$863$	−8.00000			−0.272323			−0.136162	+	0.990687i	$0.543477\pi$
$864$		0			0
$865$		−	45.4919i		−	1.54677i
$866$		0			0
$867$	−20.9008	+	20.7402i	−0.709828	+	0.704375i
$868$		0			0
$869$	−12.4084			−0.420925
$870$		0			0
$871$		−	6.92820i		−	0.234753i
$872$		0			0
$873$	−12.7082	+	0.708204i	−0.430108	+	0.0239691i
$874$		0			0
$875$			24.0000i			0.811348i
$876$		0			0
$877$	12.1270	+	12.1270i	0.409500	+	0.409500i	0.881564	−	0.472064i	$-0.156491\pi$
$877$	12.1270	+	12.1270i	0.409500	+	0.409500i	−0.472064	+	0.881564i	$0.656491\pi$
$878$		0			0
$879$	4.90486	−	12.8411i	0.165437	−	0.433120i
$880$		0			0
$881$	−14.2044	−	14.2044i	−0.478560	−	0.478560i	0.426111	−	0.904671i	$-0.359883\pi$
$881$	−14.2044	−	14.2044i	−0.478560	−	0.478560i	−0.904671	+	0.426111i	$0.859883\pi$
$882$		0			0
$883$			7.49624i			0.252269i	0.992013	+	0.126134i	$0.0402570\pi$
$883$			7.49624i			0.252269i	−0.992013	+	0.126134i	$0.959743\pi$
$884$		0			0
$885$	45.4919	−	20.3446i	1.52919	−	0.683877i
$886$		0			0
$887$	29.6190	−	29.6190i	0.994507	−	0.994507i	−0.00547798	−	0.999985i	$-0.501744\pi$
$887$	29.6190	−	29.6190i	0.994507	−	0.994507i	0.999985	+	0.00547798i	$0.00174371\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	7.94427	−	9.94427i	0.266143	−	0.333146i
$892$		0			0
$893$	−4.03214			−0.134930
$894$		0			0
$895$	20.3446	−	20.3446i	0.680045	−	0.680045i
$896$		0			0
$897$	−3.74597	−	8.37624i	−0.125074	−	0.279674i
$898$		0			0
$899$		−	34.0000i		−	1.13396i
$900$		0			0
$901$	25.4919	+	39.4919i	0.849259	+	1.31567i
$902$		0			0
$903$	3.90410	−	1.74597i	0.129920	−	0.0581021i
$904$		0			0
$905$		−	7.36820i		−	0.244927i
$906$		0			0
$907$	−33.9810	+	33.9810i	−1.12832	+	1.12832i	−0.137871	+	0.990450i	$0.544026\pi$
$907$	−33.9810	+	33.9810i	−1.12832	+	1.12832i	−0.990450	+	0.137871i	$0.955974\pi$
$908$		0			0
$909$	15.8725	−	17.7460i	0.526457	−	0.588597i
$910$		0			0
$911$	−19.3649	−	19.3649i	−0.641588	−	0.641588i	0.309357	−	0.950946i	$-0.399886\pi$
$911$	−19.3649	−	19.3649i	−0.641588	−	0.641588i	−0.950946	+	0.309357i	$0.899886\pi$
$912$		0			0
$913$	−3.74597	+	3.74597i	−0.123973	+	0.123973i
$914$		0			0
$915$	−0.271934	+	0.711933i	−0.00898986	+	0.0235358i
$916$		0			0
$917$			17.3205i			0.571974i
$918$		0			0
$919$			46.1694i			1.52299i	0.648172	+	0.761494i	$0.275534\pi$
$919$			46.1694i			1.52299i	−0.648172	+	0.761494i	$0.724466\pi$
$920$		0			0
$921$	−10.7047	+	28.0252i	−0.352731	+	0.923461i
$922$		0			0
$923$	11.7460	−	11.7460i	0.386623	−	0.386623i
$924$		0			0
$925$	−3.87298	−	3.87298i	−0.127343	−	0.127343i
$926$		0			0
$927$	−38.6732	+	43.2379i	−1.27019	+	1.42012i
$928$		0			0
$929$	−24.0287	+	24.0287i	−0.788356	+	0.788356i	−0.981225	−	0.192868i	$-0.938221\pi$
$929$	−24.0287	+	24.0287i	−0.788356	+	0.788356i	0.192868	+	0.981225i	$0.438221\pi$
$930$		0			0
$931$			1.00803i			0.0330370i
$932$		0			0
$933$	22.6447	−	10.1270i	0.741354	−	0.331544i
$934$		0			0
$935$	12.0000	−	7.74597i	0.392442	−	0.253320i
$936$		0			0
$937$			26.9839i			0.881525i	0.897624	+	0.440762i	$0.145292\pi$
$937$			26.9839i			0.881525i	−0.897624	+	0.440762i	$0.854708\pi$
$938$		0			0
$939$	−16.7460	−	37.4451i	−0.546484	−	1.22198i
$940$		0			0
$941$	15.5885	−	15.5885i	0.508169	−	0.508169i	−0.405795	−	0.913964i	$-0.633005\pi$
$941$	15.5885	−	15.5885i	0.508169	−	0.508169i	0.913964	+	0.405795i	$0.133005\pi$
$942$		0			0
$943$	25.1287			0.818303
$944$		0			0
$945$	−14.2918	−	27.7082i	−0.464912	−	0.901348i
$946$		0			0
$947$	−23.0000	+	23.0000i	−0.747400	+	0.747400i	−0.973990	−	0.226591i	$-0.927242\pi$
$947$	−23.0000	+	23.0000i	−0.747400	+	0.747400i	0.226591	+	0.973990i	$0.427242\pi$
$948$		0			0
$949$	−21.4919	+	21.4919i	−0.697658	+	0.697658i
$950$		0			0
$951$	39.3649	−	17.6045i	1.27649	−	0.570866i
$952$		0			0
$953$			47.6174i			1.54248i	0.636545	+	0.771240i	$0.280363\pi$
$953$			47.6174i			1.54248i	−0.636545	+	0.771240i	$0.719637\pi$
$954$		0			0
$955$	−34.6410	−	34.6410i	−1.12096	−	1.12096i
$956$		0			0
$957$	3.38693	−	8.86710i	0.109484	−	0.286633i
$958$		0			0
$959$	15.4919	+	15.4919i	0.500261	+	0.500261i
$960$		0			0
$961$			45.9839i			1.48335i
$962$		0			0
$963$	45.5206	−	2.53678i	1.46688	−	0.0817465i
$964$		0			0
$965$		−	64.0579i		−	2.06210i
$966$		0			0
$967$	24.8167			0.798053			0.399026	−	0.916939i	$-0.369348\pi$
$967$	24.8167			0.798053			0.399026	+	0.916939i	$0.369348\pi$
$968$		0			0
$969$	1.48897	+	7.04314i	0.0478326	+	0.226258i
$970$		0			0
$971$			35.2379i			1.13084i	0.824804	+	0.565419i	$0.191286\pi$
$971$			35.2379i			1.13084i	−0.824804	+	0.565419i	$0.808714\pi$
$972$		0			0
$973$	−28.2540			−0.905783
$974$		0			0
$975$	1.23607	−	3.23607i	0.0395859	−	0.103637i
$976$		0			0
$977$	−10.5203			−0.336576			−0.168288	−	0.985738i	$-0.553824\pi$
$977$	−10.5203			−0.336576			−0.168288	+	0.985738i	$0.553824\pi$
$978$		0			0
$979$	2.01607	−	2.01607i	0.0644338	−	0.0644338i
$980$		0			0
$981$	0.0299846	+	0.538051i	0.000957333	+	0.0171787i
$982$		0			0
$983$	−6.38105	+	6.38105i	−0.203524	+	0.203524i	−0.801508	−	0.597984i	$-0.795969\pi$
$983$	−6.38105	+	6.38105i	−0.203524	+	0.203524i	0.597984	+	0.801508i	$0.295969\pi$
$984$		0			0
$985$	2.50807			0.0799136
$986$		0			0
$987$	15.4919	−	6.92820i	0.493114	−	0.220527i
$988$		0			0
$989$	−1.88803	−	1.88803i	−0.0600359	−	0.0600359i
$990$		0			0
$991$	−31.0209	−	31.0209i	−0.985412	−	0.985412i	0.0144827	−	0.999895i	$-0.495390\pi$
$991$	−31.0209	−	31.0209i	−0.985412	−	0.985412i	−0.999895	+	0.0144827i	$0.995390\pi$
$992$		0			0
$993$	27.3132	+	10.4327i	0.866759	+	0.331073i
$994$		0			0
$995$			6.00000i			0.190213i
$996$		0			0
$997$	6.38105	+	6.38105i	0.202090	+	0.202090i	0.800895	−	0.598805i	$-0.204358\pi$
$997$	6.38105	+	6.38105i	0.202090	+	0.202090i	−0.598805	+	0.800895i	$0.704358\pi$
$998$		0			0
$999$	−27.1109	−	8.66025i	−0.857750	−	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.bf.c.191.4	yes	8
3.2	odd	2		816.2.bf.a.191.3	yes	8
4.3	odd	2		816.2.bf.a.191.2	yes	8
12.11	even	2	inner	816.2.bf.c.191.1	yes	8
17.13	even	4	inner	816.2.bf.c.47.1	yes	8
51.47	odd	4		816.2.bf.a.47.2	✓	8
68.47	odd	4		816.2.bf.a.47.3	yes	8
204.47	even	4	inner	816.2.bf.c.47.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
816.2.bf.a.47.2	✓	8	51.47	odd	4
816.2.bf.a.47.3	yes	8	68.47	odd	4
816.2.bf.a.191.2	yes	8	4.3	odd	2
816.2.bf.a.191.3	yes	8	3.2	odd	2
816.2.bf.c.47.1	yes	8	17.13	even	4	inner
816.2.bf.c.47.4	yes	8	204.47	even	4	inner
816.2.bf.c.191.1	yes	8	12.11	even	2	inner
816.2.bf.c.191.4	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.bf (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61803 + 0.618034i) q^{3} +(1.73205 + 1.73205i) q^{5} +(-1.73205 + 1.73205i) q^{7} +(2.23607 + 2.00000i) q^{9} +O(q^{10})\)	\(q+(1.61803 + 0.618034i) q^{3} +(1.73205 + 1.73205i) q^{5} +(-1.73205 + 1.73205i) q^{7} +(2.23607 + 2.00000i) q^{9} +(-1.00000 - 1.00000i) q^{11} -2.00000 q^{13} +(1.73205 + 3.87298i) q^{15} +(2.23607 + 3.46410i) q^{17} +1.00803 q^{19} +(-3.87298 + 1.73205i) q^{21} +(1.87298 + 1.87298i) q^{23} +1.00000i q^{25} +(2.38197 + 4.61803i) q^{27} +(2.74009 + 2.74009i) q^{29} +(-6.20419 - 6.20419i) q^{31} +(-1.00000 - 2.23607i) q^{33} -6.00000 q^{35} +(-3.87298 + 3.87298i) q^{37} +(-3.23607 - 1.23607i) q^{39} +(6.70820 - 6.70820i) q^{41} -1.00803 q^{43} +(0.408882 + 7.33708i) q^{45} -4.00000 q^{47} +1.00000i q^{49} +(1.47710 + 6.98700i) q^{51} +11.4003 q^{53} -3.46410i q^{55} +(1.63103 + 0.622999i) q^{57} -11.7460i q^{59} +(0.127017 + 0.127017i) q^{61} +(-7.33708 + 0.408882i) q^{63} +(-3.46410 - 3.46410i) q^{65} +3.46410i q^{67} +(1.87298 + 4.18812i) q^{69} +(-5.87298 + 5.87298i) q^{71} +(10.7460 - 10.7460i) q^{73} +(-0.618034 + 1.61803i) q^{75} +3.46410 q^{77} +(6.20419 - 6.20419i) q^{79} +(1.00000 + 8.94427i) q^{81} -3.74597i q^{83} +(-2.12702 + 9.87298i) q^{85} +(2.74009 + 6.12702i) q^{87} +2.01607i q^{89} +(3.46410 - 3.46410i) q^{91} +(-6.20419 - 13.8730i) q^{93} +(1.74597 + 1.74597i) q^{95} +(-3.00000 + 3.00000i) q^{97} +(-0.236068 - 4.23607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3}+O(q^{10}) \) 8 * q + 4 * q^3	\( 8 q + 4 q^{3} - 8 q^{11} - 16 q^{13} - 16 q^{23} + 28 q^{27} - 8 q^{33} - 48 q^{35} - 8 q^{39} - 32 q^{47} + 20 q^{51} + 40 q^{57} + 32 q^{61} - 16 q^{69} - 16 q^{71} + 24 q^{73} + 4 q^{75} + 8 q^{81} - 48 q^{85} - 48 q^{95} - 24 q^{97} + 16 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 8 * q^11 - 16 * q^13 - 16 * q^23 + 28 * q^27 - 8 * q^33 - 48 * q^35 - 8 * q^39 - 32 * q^47 + 20 * q^51 + 40 * q^57 + 32 * q^61 - 16 * q^69 - 16 * q^71 + 24 * q^73 + 4 * q^75 + 8 * q^81 - 48 * q^85 - 48 * q^95 - 24 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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