LMFDB - Embedded newform 960.2.bc.e.367.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(367,960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("960.367"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bc (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-8,0,4,0,-16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			367.1
Root			$1.38194 + 0.300388i$ of defining polynomial
Character	$\chi$	$=$	960.367
Dual form			960.2.bc.e.463.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{3} +(-2.21420 - 0.311968i) q^{5} +(1.96597 + 1.96597i) q^{7} -1.00000 q^{9} +(-0.870396 - 0.870396i) q^{11} +5.88276 q^{13} +(0.311968 - 2.21420i) q^{15} +(2.69398 + 2.69398i) q^{17} +(-2.40037 - 2.40037i) q^{19} +(-1.96597 + 1.96597i) q^{21} +(-2.63907 + 2.63907i) q^{23} +(4.80535 + 1.38152i) q^{25} -1.00000i q^{27} +(-7.43646 + 7.43646i) q^{29} +7.72239i q^{31} +(0.870396 - 0.870396i) q^{33} +(-3.73972 - 4.96636i) q^{35} -4.49007 q^{37} +5.88276i q^{39} +4.84873i q^{41} +0.461098 q^{43} +(2.21420 + 0.311968i) q^{45} +(-4.66693 + 4.66693i) q^{47} +0.730041i q^{49} +(-2.69398 + 2.69398i) q^{51} +2.41272i q^{53} +(1.65569 + 2.19876i) q^{55} +(2.40037 - 2.40037i) q^{57} +(6.47458 - 6.47458i) q^{59} +(8.50808 + 8.50808i) q^{61} +(-1.96597 - 1.96597i) q^{63} +(-13.0256 - 1.83523i) q^{65} -6.40870 q^{67} +(-2.63907 - 2.63907i) q^{69} +13.3214 q^{71} +(1.62933 + 1.62933i) q^{73} +(-1.38152 + 4.80535i) q^{75} -3.42234i q^{77} -4.14482 q^{79} +1.00000 q^{81} -0.241277i q^{83} +(-5.12458 - 6.80545i) q^{85} +(-7.43646 - 7.43646i) q^{87} -2.86287 q^{89} +(11.5653 + 11.5653i) q^{91} -7.72239 q^{93} +(4.56605 + 6.06373i) q^{95} +(3.18909 + 3.18909i) q^{97} +(0.870396 + 0.870396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5} + 4 q^{7} - 16 q^{9} - 8 q^{13} - 4 q^{15} - 8 q^{17} + 8 q^{19} - 4 q^{21} - 32 q^{25} - 12 q^{29} - 12 q^{35} - 24 q^{37} - 24 q^{43} + 8 q^{45} - 32 q^{47} + 8 q^{51} + 4 q^{55} - 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 + 4 * q^7 - 16 * q^9 - 8 * q^13 - 4 * q^15 - 8 * q^17 + 8 * q^19 - 4 * q^21 - 32 * q^25 - 12 * q^29 - 12 * q^35 - 24 * q^37 - 24 * q^43 + 8 * q^45 - 32 * q^47 + 8 * q^51 + 4 * q^55 - 8 * q^57 - 24 * q^59 + 40 * q^61 - 4 * q^63 - 4 * q^65 - 16 * q^67 - 8 * q^73 - 24 * q^75 - 48 * q^79 + 16 * q^81 - 8 * q^85 - 12 * q^87 + 40 * q^91 - 32 * q^93 + 8 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		0			0
$5$	−2.21420	−	0.311968i	−0.990220	−	0.139516i
$5$	−2.21420	−	0.311968i	−0.990220	−	0.139516i
$6$		0			0
$7$	1.96597	+	1.96597i	0.743065	+	0.743065i	0.973167	−	0.230101i	$-0.0739058\pi$
$7$	1.96597	+	1.96597i	0.743065	+	0.743065i	−0.230101	+	0.973167i	$0.573906\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	−0.870396	−	0.870396i	−0.262434	−	0.262434i	0.563608	−	0.826042i	$-0.309413\pi$
$11$	−0.870396	−	0.870396i	−0.262434	−	0.262434i	−0.826042	+	0.563608i	$0.809413\pi$
$12$		0			0
$13$	5.88276			1.63158			0.815792	−	0.578345i	$-0.196301\pi$
$13$	5.88276			1.63158			0.815792	+	0.578345i	$0.196301\pi$
$14$		0			0
$15$	0.311968	−	2.21420i	0.0805497	−	0.571704i
$16$		0			0
$17$	2.69398	+	2.69398i	0.653387	+	0.653387i	0.953807	−	0.300420i	$-0.0971268\pi$
$17$	2.69398	+	2.69398i	0.653387	+	0.653387i	−0.300420	+	0.953807i	$0.597127\pi$
$18$		0			0
$19$	−2.40037	−	2.40037i	−0.550682	−	0.550682i	0.375956	−	0.926638i	$-0.377314\pi$
$19$	−2.40037	−	2.40037i	−0.550682	−	0.550682i	−0.926638	+	0.375956i	$0.877314\pi$
$20$		0			0
$21$	−1.96597	+	1.96597i	−0.429009	+	0.429009i
$22$		0			0
$23$	−2.63907	+	2.63907i	−0.550284	+	0.550284i	−0.926523	−	0.376239i	$-0.877217\pi$
$23$	−2.63907	+	2.63907i	−0.550284	+	0.550284i	0.376239	+	0.926523i	$0.377217\pi$
$24$		0			0
$25$	4.80535	+	1.38152i	0.961070	+	0.276303i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−7.43646	+	7.43646i	−1.38092	+	1.38092i	−0.537919	+	0.842996i	$0.680790\pi$
$29$	−7.43646	+	7.43646i	−1.38092	+	1.38092i	−0.842996	+	0.537919i	$0.819210\pi$
$30$		0			0
$31$			7.72239i			1.38698i	0.720465	+	0.693491i	$0.243928\pi$
$31$			7.72239i			1.38698i	−0.720465	+	0.693491i	$0.756072\pi$
$32$		0			0
$33$	0.870396	−	0.870396i	0.151516	−	0.151516i
$34$		0			0
$35$	−3.73972	−	4.96636i	−0.632128	−	0.839467i
$36$		0			0
$37$	−4.49007			−0.738163			−0.369081	−	0.929397i	$-0.620328\pi$
$37$	−4.49007			−0.738163			−0.369081	+	0.929397i	$0.620328\pi$
$38$		0			0
$39$			5.88276i			0.941996i
$40$		0			0
$41$			4.84873i			0.757244i	0.925551	+	0.378622i	$0.123602\pi$
$41$			4.84873i			0.757244i	−0.925551	+	0.378622i	$0.876398\pi$
$42$		0			0
$43$	0.461098			0.0703168			0.0351584	−	0.999382i	$-0.488806\pi$
$43$	0.461098			0.0703168			0.0351584	+	0.999382i	$0.488806\pi$
$44$		0			0
$45$	2.21420	+	0.311968i	0.330073	+	0.0465054i
$46$		0			0
$47$	−4.66693	+	4.66693i	−0.680742	+	0.680742i	−0.960167	−	0.279425i	$-0.909856\pi$
$47$	−4.66693	+	4.66693i	−0.680742	+	0.680742i	0.279425	+	0.960167i	$0.409856\pi$
$48$		0			0
$49$			0.730041i			0.104292i
$50$		0			0
$51$	−2.69398	+	2.69398i	−0.377233	+	0.377233i
$52$		0			0
$53$			2.41272i			0.331413i	0.986175	+	0.165706i	$0.0529904\pi$
$53$			2.41272i			0.331413i	−0.986175	+	0.165706i	$0.947010\pi$
$54$		0			0
$55$	1.65569	+	2.19876i	0.223254	+	0.296481i
$56$		0			0
$57$	2.40037	−	2.40037i	0.317936	−	0.317936i
$58$		0			0
$59$	6.47458	−	6.47458i	0.842919	−	0.842919i	−0.146318	−	0.989238i	$-0.546742\pi$
$59$	6.47458	−	6.47458i	0.842919	−	0.842919i	0.989238	+	0.146318i	$0.0467424\pi$
$60$		0			0
$61$	8.50808	+	8.50808i	1.08935	+	1.08935i	0.995596	+	0.0937523i	$0.0298862\pi$
$61$	8.50808	+	8.50808i	1.08935	+	1.08935i	0.0937523	+	0.995596i	$0.470114\pi$
$62$		0			0
$63$	−1.96597	−	1.96597i	−0.247688	−	0.247688i
$64$		0			0
$65$	−13.0256	−	1.83523i	−1.61563	−	0.227632i
$66$		0			0
$67$	−6.40870			−0.782948			−0.391474	−	0.920189i	$-0.628035\pi$
$67$	−6.40870			−0.782948			−0.391474	+	0.920189i	$0.628035\pi$
$68$		0			0
$69$	−2.63907	−	2.63907i	−0.317706	−	0.317706i
$70$		0			0
$71$	13.3214			1.58096			0.790482	−	0.612486i	$-0.209830\pi$
$71$	13.3214			1.58096			0.790482	+	0.612486i	$0.209830\pi$
$72$		0			0
$73$	1.62933	+	1.62933i	0.190699	+	0.190699i	0.795998	−	0.605299i	$-0.206947\pi$
$73$	1.62933	+	1.62933i	0.190699	+	0.190699i	−0.605299	+	0.795998i	$0.706947\pi$
$74$		0			0
$75$	−1.38152	+	4.80535i	−0.159524	+	0.554874i
$76$		0			0
$77$		−	3.42234i		−	0.390011i
$78$		0			0
$79$	−4.14482			−0.466328			−0.233164	−	0.972437i	$-0.574908\pi$
$79$	−4.14482			−0.466328			−0.233164	+	0.972437i	$0.574908\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$		−	0.241277i		−	0.0264836i	−0.999912	−	0.0132418i	$-0.995785\pi$
$83$		−	0.241277i		−	0.0264836i	0.999912	−	0.0132418i	$-0.00421511\pi$
$84$		0			0
$85$	−5.12458	−	6.80545i	−0.555839	−	0.738155i
$86$		0			0
$87$	−7.43646	−	7.43646i	−0.797272	−	0.797272i
$88$		0			0
$89$	−2.86287			−0.303464			−0.151732	−	0.988422i	$-0.548485\pi$
$89$	−2.86287			−0.303464			−0.151732	+	0.988422i	$0.548485\pi$
$90$		0			0
$91$	11.5653	+	11.5653i	1.21237	+	1.21237i
$92$		0			0
$93$	−7.72239			−0.800775
$94$		0			0
$95$	4.56605	+	6.06373i	0.468467	+	0.622125i
$96$		0			0
$97$	3.18909	+	3.18909i	0.323803	+	0.323803i	0.850224	−	0.526421i	$-0.176466\pi$
$97$	3.18909	+	3.18909i	0.323803	+	0.323803i	−0.526421	+	0.850224i	$0.676466\pi$
$98$		0			0
$99$	0.870396	+	0.870396i	0.0874781	+	0.0874781i
$100$		0			0
$101$	6.90372	−	6.90372i	0.686946	−	0.686946i	−0.274610	−	0.961556i	$-0.588549\pi$
$101$	6.90372	−	6.90372i	0.686946	−	0.686946i	0.961556	+	0.274610i	$0.0885487\pi$
$102$		0			0
$103$	−4.09832	+	4.09832i	−0.403819	+	0.403819i	−0.879577	−	0.475757i	$-0.842174\pi$
$103$	−4.09832	+	4.09832i	−0.403819	+	0.403819i	0.475757	+	0.879577i	$0.342174\pi$
$104$		0			0
$105$	4.96636	−	3.73972i	0.484667	−	0.364959i
$106$		0			0
$107$		−	10.0579i		−	0.972333i	−0.873866	−	0.486166i	$-0.838395\pi$
$107$		−	10.0579i		−	0.972333i	0.873866	−	0.486166i	$-0.161605\pi$
$108$		0			0
$109$	−11.2123	+	11.2123i	−1.07394	+	1.07394i	−0.0769025	+	0.997039i	$0.524503\pi$
$109$	−11.2123	+	11.2123i	−1.07394	+	1.07394i	−0.997039	+	0.0769025i	$0.975497\pi$
$110$		0			0
$111$		−	4.49007i		−	0.426178i
$112$		0			0
$113$	−0.420404	+	0.420404i	−0.0395483	+	0.0395483i	−0.726604	−	0.687056i	$-0.758903\pi$
$113$	−0.420404	+	0.420404i	−0.0395483	+	0.0395483i	0.687056	+	0.726604i	$0.258903\pi$
$114$		0			0
$115$	6.66672	−	5.02012i	0.621675	−	0.468128i
$116$		0			0
$117$	−5.88276			−0.543861
$118$		0			0
$119$			10.5926i			0.971018i
$120$		0			0
$121$		−	9.48482i		−	0.862257i
$122$		0			0
$123$	−4.84873			−0.437195
$124$		0			0
$125$	−10.2090	−	4.55807i	−0.913122	−	0.407686i
$126$		0			0
$127$	12.1223	−	12.1223i	1.07568	−	1.07568i	0.0787895	−	0.996891i	$-0.474894\pi$
$127$	12.1223	−	12.1223i	1.07568	−	1.07568i	0.996891	−	0.0787895i	$-0.0251055\pi$
$128$		0			0
$129$			0.461098i			0.0405974i
$130$		0			0
$131$	−9.02309	+	9.02309i	−0.788351	+	0.788351i	−0.981224	−	0.192873i	$-0.938220\pi$
$131$	−9.02309	+	9.02309i	−0.788351	+	0.788351i	0.192873	+	0.981224i	$0.438220\pi$
$132$		0			0
$133$		−	9.43808i		−	0.818385i
$134$		0			0
$135$	−0.311968	+	2.21420i	−0.0268499	+	0.190568i
$136$		0			0
$137$	8.12950	−	8.12950i	0.694550	−	0.694550i	−0.268679	−	0.963230i	$-0.586587\pi$
$137$	8.12950	−	8.12950i	0.694550	−	0.694550i	0.963230	+	0.268679i	$0.0865872\pi$
$138$		0			0
$139$	2.98593	−	2.98593i	0.253263	−	0.253263i	−0.569044	−	0.822307i	$-0.692687\pi$
$139$	2.98593	−	2.98593i	0.253263	−	0.253263i	0.822307	+	0.569044i	$0.192687\pi$
$140$		0			0
$141$	−4.66693	−	4.66693i	−0.393027	−	0.393027i
$142$		0			0
$143$	−5.12033	−	5.12033i	−0.428184	−	0.428184i
$144$		0			0
$145$	18.7857	−	14.1459i	1.56007	−	1.17475i
$146$		0			0
$147$	−0.730041			−0.0602128
$148$		0			0
$149$	0.994977	+	0.994977i	0.0815117	+	0.0815117i	0.746687	−	0.665175i	$-0.231643\pi$
$149$	0.994977	+	0.994977i	0.0815117	+	0.0815117i	−0.665175	+	0.746687i	$0.731643\pi$
$150$		0			0
$151$	18.1365			1.47592			0.737962	−	0.674842i	$-0.235788\pi$
$151$	18.1365			1.47592			0.737962	+	0.674842i	$0.235788\pi$
$152$		0			0
$153$	−2.69398	−	2.69398i	−0.217796	−	0.217796i
$154$		0			0
$155$	2.40914	−	17.0989i	0.193506	−	1.37342i
$156$		0			0
$157$		−	10.3489i		−	0.825932i	−0.910746	−	0.412966i	$-0.864493\pi$
$157$		−	10.3489i		−	0.825932i	0.910746	−	0.412966i	$-0.135507\pi$
$158$		0			0
$159$	−2.41272			−0.191341
$160$		0			0
$161$	−10.3766			−0.817793
$162$		0			0
$163$			13.2079i			1.03453i	0.855827	+	0.517263i	$0.173049\pi$
$163$			13.2079i			1.03453i	−0.855827	+	0.517263i	$0.826951\pi$
$164$		0			0
$165$	−2.19876	+	1.65569i	−0.171174	+	0.128896i
$166$		0			0
$167$	−0.0169530	−	0.0169530i	−0.00131186	−	0.00131186i	0.706451	−	0.707762i	$-0.250295\pi$
$167$	−0.0169530	−	0.0169530i	−0.00131186	−	0.00131186i	−0.707762	+	0.706451i	$0.750295\pi$
$168$		0			0
$169$	21.6069			1.66207
$170$		0			0
$171$	2.40037	+	2.40037i	0.183561	+	0.183561i
$172$		0			0
$173$	3.43931			0.261486			0.130743	−	0.991416i	$-0.458264\pi$
$173$	3.43931			0.261486			0.130743	+	0.991416i	$0.458264\pi$
$174$		0			0
$175$	6.73114	+	12.1632i	0.508827	+	0.919449i
$176$		0			0
$177$	6.47458	+	6.47458i	0.486660	+	0.486660i
$178$		0			0
$179$	0.816756	+	0.816756i	0.0610472	+	0.0610472i	0.736971	−	0.675924i	$-0.236255\pi$
$179$	0.816756	+	0.816756i	0.0610472	+	0.0610472i	−0.675924	+	0.736971i	$0.736255\pi$
$180$		0			0
$181$	−15.2070	+	15.2070i	−1.13032	+	1.13032i	−0.140201	+	0.990123i	$0.544775\pi$
$181$	−15.2070	+	15.2070i	−1.13032	+	1.13032i	−0.990123	+	0.140201i	$0.955225\pi$
$182$		0			0
$183$	−8.50808	+	8.50808i	−0.628935	+	0.628935i
$184$		0			0
$185$	9.94190	+	1.40076i	0.730943	+	0.102986i
$186$		0			0
$187$		−	4.68966i		−	0.342942i
$188$		0			0
$189$	1.96597	−	1.96597i	0.143003	−	0.143003i
$190$		0			0
$191$		−	0.536269i		−	0.0388031i	−0.999812	−	0.0194015i	$-0.993824\pi$
$191$		−	0.536269i		−	0.0388031i	0.999812	−	0.0194015i	$-0.00617609\pi$
$192$		0			0
$193$	−7.70962	+	7.70962i	−0.554951	+	0.554951i	−0.927866	−	0.372915i	$-0.878358\pi$
$193$	−7.70962	+	7.70962i	−0.554951	+	0.554951i	0.372915	+	0.927866i	$0.378358\pi$
$194$		0			0
$195$	1.83523	−	13.0256i	0.131424	−	0.932783i
$196$		0			0
$197$	19.6564			1.40046			0.700231	−	0.713916i	$-0.253080\pi$
$197$	19.6564			1.40046			0.700231	+	0.713916i	$0.253080\pi$
$198$		0			0
$199$		−	9.32963i		−	0.661360i	−0.943743	−	0.330680i	$-0.892722\pi$
$199$		−	9.32963i		−	0.661360i	0.943743	−	0.330680i	$-0.107278\pi$
$200$		0			0
$201$		−	6.40870i		−	0.452035i
$202$		0			0
$203$	−29.2396			−2.05222
$204$		0			0
$205$	1.51265	−	10.7361i	0.105648	−	0.749838i
$206$		0			0
$207$	2.63907	−	2.63907i	0.183428	−	0.183428i
$208$		0			0
$209$			4.17854i			0.289036i
$210$		0			0
$211$	7.58277	−	7.58277i	0.522019	−	0.522019i	−0.396162	−	0.918181i	$-0.629658\pi$
$211$	7.58277	−	7.58277i	0.522019	−	0.522019i	0.918181	+	0.396162i	$0.129658\pi$
$212$		0			0
$213$			13.3214i			0.912769i
$214$		0			0
$215$	−1.02096	−	0.143848i	−0.0696291	−	0.00981033i
$216$		0			0
$217$	−15.1820	+	15.1820i	−1.03062	+	1.03062i
$218$		0			0
$219$	−1.62933	+	1.62933i	−0.110100	+	0.110100i
$220$		0			0
$221$	15.8481	+	15.8481i	1.06606	+	1.06606i
$222$		0			0
$223$	−8.76331	−	8.76331i	−0.586835	−	0.586835i	0.349938	−	0.936773i	$-0.386203\pi$
$223$	−8.76331	−	8.76331i	−0.586835	−	0.586835i	−0.936773	+	0.349938i	$0.886203\pi$
$224$		0			0
$225$	−4.80535	−	1.38152i	−0.320357	−	0.0921011i
$226$		0			0
$227$	25.0028			1.65949			0.829746	−	0.558141i	$-0.188485\pi$
$227$	25.0028			1.65949			0.829746	+	0.558141i	$0.188485\pi$
$228$		0			0
$229$	7.89911	+	7.89911i	0.521988	+	0.521988i	0.918171	−	0.396183i	$-0.129666\pi$
$229$	7.89911	+	7.89911i	0.521988	+	0.521988i	−0.396183	+	0.918171i	$0.629666\pi$
$230$		0			0
$231$	3.42234			0.225173
$232$		0			0
$233$	−7.91066	−	7.91066i	−0.518245	−	0.518245i	0.398795	−	0.917040i	$-0.369428\pi$
$233$	−7.91066	−	7.91066i	−0.518245	−	0.518245i	−0.917040	+	0.398795i	$0.869428\pi$
$234$		0			0
$235$	11.7895	−	8.87759i	0.769059	−	0.579110i
$236$		0			0
$237$		−	4.14482i		−	0.269235i
$238$		0			0
$239$	−11.4515			−0.740735			−0.370368	−	0.928885i	$-0.620768\pi$
$239$	−11.4515			−0.740735			−0.370368	+	0.928885i	$0.620768\pi$
$240$		0			0
$241$	20.9793			1.35139			0.675697	−	0.737180i	$-0.263843\pi$
$241$	20.9793			1.35139			0.675697	+	0.737180i	$0.263843\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	0.227749	−	1.61646i	0.0145504	−	0.103272i
$246$		0			0
$247$	−14.1208	−	14.1208i	−0.898484	−	0.898484i
$248$		0			0
$249$	0.241277			0.0152903
$250$		0			0
$251$	−15.6566	−	15.6566i	−0.988233	−	0.988233i	0.0116985	−	0.999932i	$-0.496276\pi$
$251$	−15.6566	−	15.6566i	−0.988233	−	0.988233i	−0.999932	+	0.0116985i	$0.996276\pi$
$252$		0			0
$253$	4.59407			0.288826
$254$		0			0
$255$	6.80545	−	5.12458i	0.426174	−	0.320914i
$256$		0			0
$257$	−8.44246	−	8.44246i	−0.526626	−	0.526626i	0.392939	−	0.919565i	$-0.371459\pi$
$257$	−8.44246	−	8.44246i	−0.526626	−	0.526626i	−0.919565	+	0.392939i	$0.871459\pi$
$258$		0			0
$259$	−8.82732	−	8.82732i	−0.548503	−	0.548503i
$260$		0			0
$261$	7.43646	−	7.43646i	0.460305	−	0.460305i
$262$		0			0
$263$	10.4796	−	10.4796i	0.646200	−	0.646200i	−0.305872	−	0.952073i	$-0.598948\pi$
$263$	10.4796	−	10.4796i	0.646200	−	0.646200i	0.952073	+	0.305872i	$0.0989480\pi$
$264$		0			0
$265$	0.752691	−	5.34225i	0.0462375	−	0.328172i
$266$		0			0
$267$		−	2.86287i		−	0.175205i
$268$		0			0
$269$	5.49337	−	5.49337i	0.334937	−	0.334937i	−0.519521	−	0.854458i	$-0.673890\pi$
$269$	5.49337	−	5.49337i	0.334937	−	0.334937i	0.854458	+	0.519521i	$0.173890\pi$
$270$		0			0
$271$		−	29.9569i		−	1.81975i	−0.414883	−	0.909875i	$-0.636178\pi$
$271$		−	29.9569i		−	1.81975i	0.414883	−	0.909875i	$-0.363822\pi$
$272$		0			0
$273$	−11.5653	+	11.5653i	−0.699964	+	0.699964i
$274$		0			0
$275$	−2.98009	−	5.38502i	−0.179706	−	0.324729i
$276$		0			0
$277$	−7.29980			−0.438602			−0.219301	−	0.975657i	$-0.570378\pi$
$277$	−7.29980			−0.438602			−0.219301	+	0.975657i	$0.570378\pi$
$278$		0			0
$279$		−	7.72239i		−	0.462328i
$280$		0			0
$281$			9.84488i			0.587296i	0.955914	+	0.293648i	$0.0948694\pi$
$281$			9.84488i			0.587296i	−0.955914	+	0.293648i	$0.905131\pi$
$282$		0			0
$283$	−2.84482			−0.169107			−0.0845535	−	0.996419i	$-0.526946\pi$
$283$	−2.84482			−0.169107			−0.0845535	+	0.996419i	$0.526946\pi$
$284$		0			0
$285$	−6.06373	+	4.56605i	−0.359184	+	0.270470i
$286$		0			0
$287$	−9.53244	+	9.53244i	−0.562682	+	0.562682i
$288$		0			0
$289$		−	2.48490i		−	0.146171i
$290$		0			0
$291$	−3.18909	+	3.18909i	−0.186948	+	0.186948i
$292$		0			0
$293$		−	27.6123i		−	1.61313i	−0.591149	−	0.806563i	$-0.701325\pi$
$293$		−	27.6123i		−	1.61313i	0.591149	−	0.806563i	$-0.298675\pi$
$294$		0			0
$295$	−16.3559	+	12.3162i	−0.952276	+	0.717074i
$296$		0			0
$297$	−0.870396	+	0.870396i	−0.0505055	+	0.0505055i
$298$		0			0
$299$	−15.5250	+	15.5250i	−0.897834	+	0.897834i
$300$		0			0
$301$	0.906503	+	0.906503i	0.0522500	+	0.0522500i
$302$		0			0
$303$	6.90372	+	6.90372i	0.396608	+	0.396608i
$304$		0			0
$305$	−16.1843	−	21.4928i	−0.926712	−	1.23068i
$306$		0			0
$307$	23.7612			1.35612			0.678061	−	0.735006i	$-0.262820\pi$
$307$	23.7612			1.35612			0.678061	+	0.735006i	$0.262820\pi$
$308$		0			0
$309$	−4.09832	−	4.09832i	−0.233145	−	0.233145i
$310$		0			0
$311$	−12.2337			−0.693707			−0.346854	−	0.937919i	$-0.612750\pi$
$311$	−12.2337			−0.693707			−0.346854	+	0.937919i	$0.612750\pi$
$312$		0			0
$313$	−10.9229	−	10.9229i	−0.617400	−	0.617400i	0.327464	−	0.944864i	$-0.393806\pi$
$313$	−10.9229	−	10.9229i	−0.617400	−	0.617400i	−0.944864	+	0.327464i	$0.893806\pi$
$314$		0			0
$315$	3.73972	+	4.96636i	0.210709	+	0.279822i
$316$		0			0
$317$		−	21.5403i		−	1.20982i	−0.796293	−	0.604911i	$-0.793209\pi$
$317$		−	21.5403i		−	1.20982i	0.796293	−	0.604911i	$-0.206791\pi$
$318$		0			0
$319$	12.9453			0.724799
$320$		0			0
$321$	10.0579			0.561377
$322$		0			0
$323$		−	12.9331i		−	0.719617i
$324$		0			0
$325$	28.2687	+	8.12713i	1.56807	+	0.450812i
$326$		0			0
$327$	−11.2123	−	11.2123i	−0.620040	−	0.620040i
$328$		0			0
$329$	−18.3501			−1.01167
$330$		0			0
$331$	21.2143	+	21.2143i	1.16604	+	1.16604i	0.983129	+	0.182914i	$0.0585530\pi$
$331$	21.2143	+	21.2143i	1.16604	+	1.16604i	0.182914	+	0.983129i	$0.441447\pi$
$332$		0			0
$333$	4.49007			0.246054
$334$		0			0
$335$	14.1901	+	1.99931i	0.775290	+	0.109234i
$336$		0			0
$337$	1.41673	+	1.41673i	0.0771744	+	0.0771744i	0.744640	−	0.667466i	$-0.232621\pi$
$337$	1.41673	+	1.41673i	0.0771744	+	0.0771744i	−0.667466	+	0.744640i	$0.732621\pi$
$338$		0			0
$339$	−0.420404	−	0.420404i	−0.0228332	−	0.0228332i
$340$		0			0
$341$	6.72154	−	6.72154i	0.363992	−	0.363992i
$342$		0			0
$343$	12.3265	−	12.3265i	0.665570	−	0.665570i
$344$		0			0
$345$	5.02012	+	6.66672i	0.270274	+	0.358924i
$346$		0			0
$347$			6.70115i			0.359736i	0.983691	+	0.179868i	$0.0575671\pi$
$347$			6.70115i			0.359736i	−0.983691	+	0.179868i	$0.942433\pi$
$348$		0			0
$349$	−7.28479	+	7.28479i	−0.389946	+	0.389946i	−0.874668	−	0.484722i	$-0.838921\pi$
$349$	−7.28479	+	7.28479i	−0.389946	+	0.389946i	0.484722	+	0.874668i	$0.338921\pi$
$350$		0			0
$351$		−	5.88276i		−	0.313999i
$352$		0			0
$353$	1.08305	−	1.08305i	0.0576448	−	0.0576448i	−0.677697	−	0.735342i	$-0.737022\pi$
$353$	1.08305	−	1.08305i	0.0576448	−	0.0576448i	0.735342	+	0.677697i	$0.237022\pi$
$354$		0			0
$355$	−29.4963	−	4.15585i	−1.56550	−	0.220570i
$356$		0			0
$357$	−10.5926			−0.560618
$358$		0			0
$359$			35.6985i			1.88409i	0.335483	+	0.942046i	$0.391101\pi$
$359$			35.6985i			1.88409i	−0.335483	+	0.942046i	$0.608899\pi$
$360$		0			0
$361$		−	7.47647i		−	0.393499i
$362$		0			0
$363$	9.48482			0.497824
$364$		0			0
$365$	−3.09936	−	4.11596i	−0.162228	−	0.215439i
$366$		0			0
$367$	−15.5759	+	15.5759i	−0.813056	+	0.813056i	−0.985091	−	0.172035i	$-0.944966\pi$
$367$	−15.5759	+	15.5759i	−0.813056	+	0.813056i	0.172035	+	0.985091i	$0.444966\pi$
$368$		0			0
$369$		−	4.84873i		−	0.252415i
$370$		0			0
$371$	−4.74333	+	4.74333i	−0.246261	+	0.246261i
$372$		0			0
$373$			6.11186i			0.316460i	0.987402	+	0.158230i	$0.0505788\pi$
$373$			6.11186i			0.316460i	−0.987402	+	0.158230i	$0.949421\pi$
$374$		0			0
$375$	4.55807	−	10.2090i	0.235378	−	0.527191i
$376$		0			0
$377$	−43.7469	+	43.7469i	−2.25308	+	2.25308i
$378$		0			0
$379$	−25.5981	+	25.5981i	−1.31488	+	1.31488i	−0.397116	+	0.917768i	$0.629989\pi$
$379$	−25.5981	+	25.5981i	−1.31488	+	1.31488i	−0.917768	+	0.397116i	$0.870011\pi$
$380$		0			0
$381$	12.1223	+	12.1223i	0.621045	+	0.621045i
$382$		0			0
$383$	2.46156	+	2.46156i	0.125780	+	0.125780i	0.767194	−	0.641415i	$-0.221652\pi$
$383$	2.46156	+	2.46156i	0.125780	+	0.125780i	−0.641415	+	0.767194i	$0.721652\pi$
$384$		0			0
$385$	−1.06766	+	7.57773i	−0.0544129	+	0.386197i
$386$		0			0
$387$	−0.461098			−0.0234389
$388$		0			0
$389$	23.1160	+	23.1160i	1.17203	+	1.17203i	0.981726	+	0.190302i	$0.0609468\pi$
$389$	23.1160	+	23.1160i	1.17203	+	1.17203i	0.190302	+	0.981726i	$0.439053\pi$
$390$		0			0
$391$	−14.2192			−0.719096
$392$		0			0
$393$	−9.02309	−	9.02309i	−0.455155	−	0.455155i
$394$		0			0
$395$	9.17745	+	1.29305i	0.461768	+	0.0650603i
$396$		0			0
$397$		−	29.1851i		−	1.46476i	−0.680897	−	0.732379i	$-0.738410\pi$
$397$		−	29.1851i		−	1.46476i	0.680897	−	0.732379i	$-0.261590\pi$
$398$		0			0
$399$	9.43808			0.472495
$400$		0			0
$401$	1.70478			0.0851329			0.0425664	−	0.999094i	$-0.486447\pi$
$401$	1.70478			0.0851329			0.0425664	+	0.999094i	$0.486447\pi$
$402$		0			0
$403$			45.4290i			2.26298i
$404$		0			0
$405$	−2.21420	−	0.311968i	−0.110024	−	0.0155018i
$406$		0			0
$407$	3.90814	+	3.90814i	0.193719	+	0.193719i
$408$		0			0
$409$	−7.11999			−0.352061			−0.176030	−	0.984385i	$-0.556326\pi$
$409$	−7.11999			−0.352061			−0.176030	+	0.984385i	$0.556326\pi$
$410$		0			0
$411$	8.12950	+	8.12950i	0.400999	+	0.400999i
$412$		0			0
$413$	25.4576			1.25269
$414$		0			0
$415$	−0.0752705	+	0.534235i	−0.00369488	+	0.0262245i
$416$		0			0
$417$	2.98593	+	2.98593i	0.146222	+	0.146222i
$418$		0			0
$419$	15.1825	+	15.1825i	0.741713	+	0.741713i	0.972908	−	0.231194i	$-0.0742633\pi$
$419$	15.1825	+	15.1825i	0.741713	+	0.741713i	−0.231194	+	0.972908i	$0.574263\pi$
$420$		0			0
$421$	−8.92932	+	8.92932i	−0.435188	+	0.435188i	−0.890389	−	0.455201i	$-0.849568\pi$
$421$	−8.92932	+	8.92932i	−0.435188	+	0.435188i	0.455201	+	0.890389i	$0.349568\pi$
$422$		0			0
$423$	4.66693	−	4.66693i	0.226914	−	0.226914i
$424$		0			0
$425$	9.22376	+	16.6673i	0.447418	+	0.808484i
$426$		0			0
$427$			33.4532i			1.61891i
$428$		0			0
$429$	5.12033	−	5.12033i	0.247212	−	0.247212i
$430$		0			0
$431$			23.7988i			1.14635i	0.819434	+	0.573173i	$0.194288\pi$
$431$			23.7988i			1.14635i	−0.819434	+	0.573173i	$0.805712\pi$
$432$		0			0
$433$	−18.7878	+	18.7878i	−0.902886	+	0.902886i	−0.995685	−	0.0927987i	$-0.970419\pi$
$433$	−18.7878	+	18.7878i	−0.902886	+	0.902886i	0.0927987	+	0.995685i	$0.470419\pi$
$434$		0			0
$435$	14.1459	+	18.7857i	0.678242	+	0.900707i
$436$		0			0
$437$	12.6695			0.606062
$438$		0			0
$439$		−	29.1333i		−	1.39046i	−0.718789	−	0.695229i	$-0.755303\pi$
$439$		−	29.1333i		−	1.39046i	0.718789	−	0.695229i	$-0.244697\pi$
$440$		0			0
$441$		−	0.730041i		−	0.0347639i
$442$		0			0
$443$	38.7016			1.83877			0.919384	−	0.393360i	$-0.128687\pi$
$443$	38.7016			1.83877			0.919384	+	0.393360i	$0.128687\pi$
$444$		0			0
$445$	6.33897	+	0.893124i	0.300496	+	0.0423381i
$446$		0			0
$447$	−0.994977	+	0.994977i	−0.0470608	+	0.0470608i
$448$		0			0
$449$		−	9.96141i		−	0.470108i	−0.971982	−	0.235054i	$-0.924473\pi$
$449$		−	9.96141i		−	0.470108i	0.971982	−	0.235054i	$-0.0755267\pi$
$450$		0			0
$451$	4.22031	−	4.22031i	0.198727	−	0.198727i
$452$		0			0
$453$			18.1365i			0.852126i
$454$		0			0
$455$	−21.9999	−	29.2159i	−1.03137	−	1.36966i
$456$		0			0
$457$	1.77907	−	1.77907i	0.0832213	−	0.0832213i	−0.664271	−	0.747492i	$-0.731258\pi$
$457$	1.77907	−	1.77907i	0.0832213	−	0.0832213i	0.747492	+	0.664271i	$0.231258\pi$
$458$		0			0
$459$	2.69398	−	2.69398i	0.125744	−	0.125744i
$460$		0			0
$461$	−8.51698	−	8.51698i	−0.396675	−	0.396675i	0.480383	−	0.877059i	$-0.340498\pi$
$461$	−8.51698	−	8.51698i	−0.396675	−	0.396675i	−0.877059	+	0.480383i	$0.840498\pi$
$462$		0			0
$463$	−0.964355	−	0.964355i	−0.0448174	−	0.0448174i	0.684343	−	0.729160i	$-0.260089\pi$
$463$	−0.964355	−	0.964355i	−0.0448174	−	0.0448174i	−0.729160	+	0.684343i	$0.760089\pi$
$464$		0			0
$465$	17.0989	+	2.40914i	0.792943	+	0.111721i
$466$		0			0
$467$	−4.65741			−0.215519			−0.107760	−	0.994177i	$-0.534368\pi$
$467$	−4.65741			−0.215519			−0.107760	+	0.994177i	$0.534368\pi$
$468$		0			0
$469$	−12.5993	−	12.5993i	−0.581781	−	0.581781i
$470$		0			0
$471$	10.3489			0.476852
$472$		0			0
$473$	−0.401338	−	0.401338i	−0.0184535	−	0.0184535i
$474$		0			0
$475$	−8.21846	−	14.8508i	−0.377089	−	0.681399i
$476$		0			0
$477$		−	2.41272i		−	0.110471i
$478$		0			0
$479$	22.6790			1.03623			0.518114	−	0.855311i	$-0.326634\pi$
$479$	22.6790			1.03623			0.518114	+	0.855311i	$0.326634\pi$
$480$		0			0
$481$	−26.4140			−1.20437
$482$		0			0
$483$		−	10.3766i		−	0.472153i
$484$		0			0
$485$	−6.06639	−	8.05618i	−0.275461	−	0.365812i
$486$		0			0
$487$	−4.16034	−	4.16034i	−0.188523	−	0.188523i	0.606534	−	0.795057i	$-0.292559\pi$
$487$	−4.16034	−	4.16034i	−0.188523	−	0.188523i	−0.795057	+	0.606534i	$0.792559\pi$
$488$		0			0
$489$	−13.2079			−0.597283
$490$		0			0
$491$	−0.218295	−	0.218295i	−0.00985151	−	0.00985151i	0.702164	−	0.712015i	$-0.252217\pi$
$491$	−0.218295	−	0.218295i	−0.00985151	−	0.00985151i	−0.712015	+	0.702164i	$0.752217\pi$
$492$		0			0
$493$	−40.0674			−1.80455
$494$		0			0
$495$	−1.65569	−	2.19876i	−0.0744179	−	0.0988271i
$496$		0			0
$497$	26.1895	+	26.1895i	1.17476	+	1.17476i
$498$		0			0
$499$	−14.9638	−	14.9638i	−0.669871	−	0.669871i	0.287815	−	0.957686i	$-0.407071\pi$
$499$	−14.9638	−	14.9638i	−0.669871	−	0.669871i	−0.957686	+	0.287815i	$0.907071\pi$
$500$		0			0
$501$	0.0169530	−	0.0169530i	0.000757405	−	0.000757405i
$502$		0			0
$503$	20.3166	−	20.3166i	0.905872	−	0.905872i	−0.0900637	−	0.995936i	$-0.528707\pi$
$503$	20.3166	−	20.3166i	0.905872	−	0.905872i	0.995936	+	0.0900637i	$0.0287071\pi$
$504$		0			0
$505$	−17.4399	+	13.1325i	−0.776067	+	0.584387i
$506$		0			0
$507$			21.6069i			0.959595i
$508$		0			0
$509$	−18.0574	+	18.0574i	−0.800381	+	0.800381i	−0.983155	−	0.182774i	$-0.941492\pi$
$509$	−18.0574	+	18.0574i	−0.800381	+	0.800381i	0.182774	+	0.983155i	$0.441492\pi$
$510$		0			0
$511$			6.40641i			0.283403i
$512$		0			0
$513$	−2.40037	+	2.40037i	−0.105979	+	0.105979i
$514$		0			0
$515$	10.3530	−	7.79595i	0.456209	−	0.343531i
$516$		0			0
$517$	8.12416			0.357300
$518$		0			0
$519$			3.43931i			0.150969i
$520$		0			0
$521$		−	3.75389i		−	0.164461i	−0.996613	−	0.0822305i	$-0.973796\pi$
$521$		−	3.75389i		−	0.164461i	0.996613	−	0.0822305i	$-0.0262044\pi$
$522$		0			0
$523$	−30.3429			−1.32680			−0.663402	−	0.748263i	$-0.730888\pi$
$523$	−30.3429			−1.32680			−0.663402	+	0.748263i	$0.730888\pi$
$524$		0			0
$525$	−12.1632	+	6.73114i	−0.530844	+	0.293771i
$526$		0			0
$527$	−20.8040	+	20.8040i	−0.906237	+	0.906237i
$528$		0			0
$529$			9.07065i			0.394376i
$530$		0			0
$531$	−6.47458	+	6.47458i	−0.280973	+	0.280973i
$532$		0			0
$533$			28.5239i			1.23551i
$534$		0			0
$535$	−3.13773	+	22.2702i	−0.135656	+	0.962823i
$536$		0			0
$537$	−0.816756	+	0.816756i	−0.0352456	+	0.0352456i
$538$		0			0
$539$	0.635425	−	0.635425i	0.0273697	−	0.0273697i
$540$		0			0
$541$	25.0252	+	25.0252i	1.07592	+	1.07592i	0.996871	+	0.0790451i	$0.0251871\pi$
$541$	25.0252	+	25.0252i	1.07592	+	1.07592i	0.0790451	+	0.996871i	$0.474813\pi$
$542$		0			0
$543$	−15.2070	−	15.2070i	−0.652593	−	0.652593i
$544$		0			0
$545$	28.3241	−	21.3283i	1.21327	−	0.913606i
$546$		0			0
$547$	31.6172			1.35185			0.675927	−	0.736969i	$-0.263744\pi$
$547$	31.6172			1.35185			0.675927	+	0.736969i	$0.263744\pi$
$548$		0			0
$549$	−8.50808	−	8.50808i	−0.363116	−	0.363116i
$550$		0			0
$551$	35.7005			1.52089
$552$		0			0
$553$	−8.14857	−	8.14857i	−0.346512	−	0.346512i
$554$		0			0
$555$	−1.40076	+	9.94190i	−0.0594588	+	0.422010i
$556$		0			0
$557$		−	5.06043i		−	0.214418i	−0.994237	−	0.107209i	$-0.965809\pi$
$557$		−	5.06043i		−	0.214418i	0.994237	−	0.107209i	$-0.0341913\pi$
$558$		0			0
$559$	2.71253			0.114728
$560$		0			0
$561$	4.68966			0.197998
$562$		0			0
$563$		−	10.2694i		−	0.432804i	−0.976304	−	0.216402i	$-0.930568\pi$
$563$		−	10.2694i		−	0.432804i	0.976304	−	0.216402i	$-0.0694321\pi$
$564$		0			0
$565$	1.06201	−	0.799706i	0.0446791	−	0.0336439i
$566$		0			0
$567$	1.96597	+	1.96597i	0.0825628	+	0.0825628i
$568$		0			0
$569$	30.5352			1.28010			0.640052	−	0.768332i	$-0.278913\pi$
$569$	30.5352			1.28010			0.640052	+	0.768332i	$0.278913\pi$
$570$		0			0
$571$	−15.6507	−	15.6507i	−0.654962	−	0.654962i	0.299222	−	0.954184i	$-0.403273\pi$
$571$	−15.6507	−	15.6507i	−0.654962	−	0.654962i	−0.954184	+	0.299222i	$0.903273\pi$
$572$		0			0
$573$	0.536269			0.0224030
$574$		0			0
$575$	−16.3276	+	9.03573i	−0.680906	+	0.376816i
$576$		0			0
$577$	−24.2221	−	24.2221i	−1.00838	−	1.00838i	−0.999965	−	0.00841548i	$-0.997321\pi$
$577$	−24.2221	−	24.2221i	−1.00838	−	1.00838i	−0.00841548	−	0.999965i	$-0.502679\pi$
$578$		0			0
$579$	−7.70962	−	7.70962i	−0.320401	−	0.320401i
$580$		0			0
$581$	0.474342	−	0.474342i	0.0196790	−	0.0196790i
$582$		0			0
$583$	2.10002	−	2.10002i	0.0869741	−	0.0869741i
$584$		0			0
$585$	13.0256	+	1.83523i	0.538542	+	0.0758775i
$586$		0			0
$587$			4.75989i			0.196461i	0.995164	+	0.0982307i	$0.0313183\pi$
$587$			4.75989i			0.196461i	−0.995164	+	0.0982307i	$0.968682\pi$
$588$		0			0
$589$	18.5366	−	18.5366i	0.763786	−	0.763786i
$590$		0			0
$591$			19.6564i			0.808557i
$592$		0			0
$593$	4.52357	−	4.52357i	0.185761	−	0.185761i	−0.608100	−	0.793861i	$-0.708068\pi$
$593$	4.52357	−	4.52357i	0.185761	−	0.185761i	0.793861	+	0.608100i	$0.208068\pi$
$594$		0			0
$595$	3.30454	−	23.4540i	0.135473	−	0.961522i
$596$		0			0
$597$	9.32963			0.381836
$598$		0			0
$599$			4.69105i			0.191671i	0.995397	+	0.0958356i	$0.0305523\pi$
$599$			4.69105i			0.191671i	−0.995397	+	0.0958356i	$0.969448\pi$
$600$		0			0
$601$		−	2.24346i		−	0.0915126i	−0.998953	−	0.0457563i	$-0.985430\pi$
$601$		−	2.24346i		−	0.0915126i	0.998953	−	0.0457563i	$-0.0145698\pi$
$602$		0			0
$603$	6.40870			0.260983
$604$		0			0
$605$	−2.95896	+	21.0013i	−0.120299	+	0.853824i
$606$		0			0
$607$	−20.2716	+	20.2716i	−0.822800	+	0.822800i	−0.986509	−	0.163709i	$-0.947654\pi$
$607$	−20.2716	+	20.2716i	−0.822800	+	0.822800i	0.163709	+	0.986509i	$0.447654\pi$
$608$		0			0
$609$		−	29.2396i		−	1.18485i
$610$		0			0
$611$	−27.4545	+	27.4545i	−1.11069	+	1.11069i
$612$		0			0
$613$			10.2599i			0.414392i	0.978299	+	0.207196i	$0.0664338\pi$
$613$			10.2599i			0.414392i	−0.978299	+	0.207196i	$0.933566\pi$
$614$		0			0
$615$	10.7361	+	1.51265i	0.432919	+	0.0609958i
$616$		0			0
$617$	16.5590	−	16.5590i	0.666640	−	0.666640i	−0.290297	−	0.956937i	$-0.593754\pi$
$617$	16.5590	−	16.5590i	0.666640	−	0.666640i	0.956937	+	0.290297i	$0.0937539\pi$
$618$		0			0
$619$	14.3984	−	14.3984i	0.578720	−	0.578720i	−0.355831	−	0.934550i	$-0.615802\pi$
$619$	14.3984	−	14.3984i	0.578720	−	0.578720i	0.934550	+	0.355831i	$0.115802\pi$
$620$		0			0
$621$	2.63907	+	2.63907i	0.105902	+	0.105902i
$622$		0			0
$623$	−5.62831	−	5.62831i	−0.225493	−	0.225493i
$624$		0			0
$625$	21.1828	+	13.2773i	0.847313	+	0.531094i
$626$		0			0
$627$	−4.17854			−0.166875
$628$		0			0
$629$	−12.0962	−	12.0962i	−0.482306	−	0.482306i
$630$		0			0
$631$	−14.9606			−0.595571			−0.297785	−	0.954633i	$-0.596248\pi$
$631$	−14.9606			−0.595571			−0.297785	+	0.954633i	$0.596248\pi$
$632$		0			0
$633$	7.58277	+	7.58277i	0.301388	+	0.301388i
$634$		0			0
$635$	−30.6230	+	23.0594i	−1.21524	+	0.915086i
$636$		0			0
$637$			4.29466i			0.170161i
$638$		0			0
$639$	−13.3214			−0.526988
$640$		0			0
$641$	−36.0219			−1.42278			−0.711390	−	0.702797i	$-0.751934\pi$
$641$	−36.0219			−1.42278			−0.711390	+	0.702797i	$0.751934\pi$
$642$		0			0
$643$			5.24582i			0.206875i	0.994636	+	0.103437i	$0.0329842\pi$
$643$			5.24582i			0.206875i	−0.994636	+	0.103437i	$0.967016\pi$
$644$		0			0
$645$	0.143848	−	1.02096i	0.00566400	−	0.0402004i
$646$		0			0
$647$	−28.2923	−	28.2923i	−1.11229	−	1.11229i	−0.992841	−	0.119445i	$-0.961888\pi$
$647$	−28.2923	−	28.2923i	−1.11229	−	1.11229i	−0.119445	−	0.992841i	$-0.538112\pi$
$648$		0			0
$649$	−11.2709			−0.442422
$650$		0			0
$651$	−15.1820	−	15.1820i	−0.595028	−	0.595028i
$652$		0			0
$653$	9.14647			0.357929			0.178965	−	0.983856i	$-0.442725\pi$
$653$	9.14647			0.357929			0.178965	+	0.983856i	$0.442725\pi$
$654$		0			0
$655$	22.7938	−	17.1640i	0.890629	−	0.670653i
$656$		0			0
$657$	−1.62933	−	1.62933i	−0.0635662	−	0.0635662i
$658$		0			0
$659$	13.0731	+	13.0731i	0.509256	+	0.509256i	0.914298	−	0.405042i	$-0.132743\pi$
$659$	13.0731	+	13.0731i	0.509256	+	0.509256i	−0.405042	+	0.914298i	$0.632743\pi$
$660$		0			0
$661$	10.8969	−	10.8969i	0.423839	−	0.423839i	−0.462684	−	0.886523i	$-0.653114\pi$
$661$	10.8969	−	10.8969i	0.423839	−	0.423839i	0.886523	+	0.462684i	$0.153114\pi$
$662$		0			0
$663$	−15.8481	+	15.8481i	−0.615488	+	0.615488i
$664$		0			0
$665$	−2.94437	+	20.8978i	−0.114178	+	0.810381i
$666$		0			0
$667$		−	39.2506i		−	1.51979i
$668$		0			0
$669$	8.76331	−	8.76331i	0.338809	−	0.338809i
$670$		0			0
$671$		−	14.8108i		−	0.571764i
$672$		0			0
$673$	13.7432	−	13.7432i	0.529762	−	0.529762i	−0.390740	−	0.920501i	$-0.627781\pi$
$673$	13.7432	−	13.7432i	0.529762	−	0.529762i	0.920501	+	0.390740i	$0.127781\pi$
$674$		0			0
$675$	1.38152	−	4.80535i	0.0531746	−	0.184958i
$676$		0			0
$677$	10.5396			0.405070			0.202535	−	0.979275i	$-0.435082\pi$
$677$	10.5396			0.405070			0.202535	+	0.979275i	$0.435082\pi$
$678$		0			0
$679$			12.5393i			0.481214i
$680$		0			0
$681$			25.0028i			0.958108i
$682$		0			0
$683$	36.3666			1.39153			0.695765	−	0.718270i	$-0.255066\pi$
$683$	36.3666			1.39153			0.695765	+	0.718270i	$0.255066\pi$
$684$		0			0
$685$	−20.5365	+	15.4642i	−0.784658	+	0.590856i
$686$		0			0
$687$	−7.89911	+	7.89911i	−0.301370	+	0.301370i
$688$		0			0
$689$			14.1935i			0.540728i
$690$		0			0
$691$	−7.71130	+	7.71130i	−0.293352	+	0.293352i	−0.838403	−	0.545051i	$-0.816510\pi$
$691$	−7.71130	+	7.71130i	−0.293352	+	0.293352i	0.545051	+	0.838403i	$0.316510\pi$
$692$		0			0
$693$			3.42234i			0.130004i
$694$		0			0
$695$	−7.54295	+	5.67992i	−0.286120	+	0.215452i
$696$		0			0
$697$	−13.0624	+	13.0624i	−0.494774	+	0.494774i
$698$		0			0
$699$	7.91066	−	7.91066i	0.299209	−	0.299209i
$700$		0			0
$701$	8.27188	+	8.27188i	0.312425	+	0.312425i	0.845848	−	0.533424i	$-0.179095\pi$
$701$	8.27188	+	8.27188i	0.312425	+	0.312425i	−0.533424	+	0.845848i	$0.679095\pi$
$702$		0			0
$703$	10.7778	+	10.7778i	0.406493	+	0.406493i
$704$		0			0
$705$	8.87759	+	11.7895i	0.334349	+	0.444016i
$706$		0			0
$707$	27.1450			1.02089
$708$		0			0
$709$	−24.1462	−	24.1462i	−0.906828	−	0.906828i	0.0891868	−	0.996015i	$-0.471573\pi$
$709$	−24.1462	−	24.1462i	−0.906828	−	0.906828i	−0.996015	+	0.0891868i	$0.971573\pi$
$710$		0			0
$711$	4.14482			0.155443
$712$		0			0
$713$	−20.3799	−	20.3799i	−0.763234	−	0.763234i
$714$		0			0
$715$	9.74005	+	12.9348i	0.364257	+	0.483734i
$716$		0			0
$717$		−	11.4515i		−	0.427664i
$718$		0			0
$719$	−5.46091			−0.203658			−0.101829	−	0.994802i	$-0.532469\pi$
$719$	−5.46091			−0.203658			−0.101829	+	0.994802i	$0.532469\pi$
$720$		0			0
$721$	−16.1143			−0.600128
$722$		0			0
$723$			20.9793i			0.780227i
$724$		0			0
$725$	−46.0084	+	25.4612i	−1.70871	+	0.945606i
$726$		0			0
$727$	0.818679	+	0.818679i	0.0303631	+	0.0303631i	0.722125	−	0.691762i	$-0.243165\pi$
$727$	0.818679	+	0.818679i	0.0303631	+	0.0303631i	−0.691762	+	0.722125i	$0.743165\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	1.24219	+	1.24219i	0.0459441	+	0.0459441i
$732$		0			0
$733$	−3.99744			−0.147649			−0.0738245	−	0.997271i	$-0.523520\pi$
$733$	−3.99744			−0.147649			−0.0738245	+	0.997271i	$0.523520\pi$
$734$		0			0
$735$	1.61646	+	0.227749i	0.0596239	+	0.00840066i
$736$		0			0
$737$	5.57811	+	5.57811i	0.205472	+	0.205472i
$738$		0			0
$739$	22.1967	+	22.1967i	0.816517	+	0.816517i	0.985602	−	0.169084i	$-0.0540811\pi$
$739$	22.1967	+	22.1967i	0.816517	+	0.816517i	−0.169084	+	0.985602i	$0.554081\pi$
$740$		0			0
$741$	14.1208	−	14.1208i	0.518740	−	0.518740i
$742$		0			0
$743$	29.4601	−	29.4601i	1.08078	−	1.08078i	0.0843481	−	0.996436i	$-0.473119\pi$
$743$	29.4601	−	29.4601i	1.08078	−	1.08078i	0.996436	−	0.0843481i	$-0.0268808\pi$
$744$		0			0
$745$	−1.89268	−	2.51348i	−0.0693423	−	0.0920867i
$746$		0			0
$747$			0.241277i			0.00882785i
$748$		0			0
$749$	19.7735	−	19.7735i	0.722506	−	0.722506i
$750$		0			0
$751$		−	33.6280i		−	1.22710i	−0.789654	−	0.613552i	$-0.789740\pi$
$751$		−	33.6280i		−	1.22710i	0.789654	−	0.613552i	$-0.210260\pi$
$752$		0			0
$753$	15.6566	−	15.6566i	0.570557	−	0.570557i
$754$		0			0
$755$	−40.1577	−	5.65799i	−1.46149	−	0.205915i
$756$		0			0
$757$	−22.0813			−0.802560			−0.401280	−	0.915955i	$-0.631435\pi$
$757$	−22.0813			−0.802560			−0.401280	+	0.915955i	$0.631435\pi$
$758$		0			0
$759$			4.59407i			0.166754i
$760$		0			0
$761$		−	0.186655i		−	0.00676626i	−0.999994	−	0.00338313i	$-0.998923\pi$
$761$		−	0.186655i		−	0.00676626i	0.999994	−	0.00338313i	$-0.00107689\pi$
$762$		0			0
$763$	−44.0859			−1.59602
$764$		0			0
$765$	5.12458	+	6.80545i	0.185280	+	0.246052i
$766$		0			0
$767$	38.0884	−	38.0884i	1.37529	−	1.37529i
$768$		0			0
$769$		−	2.52000i		−	0.0908734i	−0.998967	−	0.0454367i	$-0.985532\pi$
$769$		−	2.52000i		−	0.0908734i	0.998967	−	0.0454367i	$-0.0144679\pi$
$770$		0			0
$771$	8.44246	−	8.44246i	0.304048	−	0.304048i
$772$		0			0
$773$		−	3.95359i		−	0.142201i	−0.997469	−	0.0711003i	$-0.977349\pi$
$773$		−	3.95359i		−	0.142201i	0.997469	−	0.0711003i	$-0.0226511\pi$
$774$		0			0
$775$	−10.6686	+	37.1088i	−0.383228	+	1.33299i
$776$		0			0
$777$	8.82732	−	8.82732i	0.316678	−	0.316678i
$778$		0			0
$779$	11.6387	−	11.6387i	0.417001	−	0.417001i
$780$		0			0
$781$	−11.5949	−	11.5949i	−0.414899	−	0.414899i
$782$		0			0
$783$	7.43646	+	7.43646i	0.265757	+	0.265757i
$784$		0			0
$785$	−3.22852	+	22.9145i	−0.115231	+	0.817855i
$786$		0			0
$787$	−25.3395			−0.903255			−0.451628	−	0.892207i	$-0.649156\pi$
$787$	−25.3395			−0.903255			−0.451628	+	0.892207i	$0.649156\pi$
$788$		0			0
$789$	10.4796	+	10.4796i	0.373084	+	0.373084i
$790$		0			0
$791$	−1.65300			−0.0587739
$792$		0			0
$793$	50.0510	+	50.0510i	1.77736	+	1.77736i
$794$		0			0
$795$	5.34225	+	0.752691i	0.189470	+	0.0266952i
$796$		0			0
$797$			40.2492i			1.42570i	0.701317	+	0.712849i	$0.252596\pi$
$797$			40.2492i			1.42570i	−0.701317	+	0.712849i	$0.747404\pi$
$798$		0			0
$799$	−25.1453			−0.889576
$800$		0			0
$801$	2.86287			0.101155
$802$		0			0
$803$		−	2.83632i		−	0.100092i
$804$		0			0
$805$	22.9759	+	3.23717i	0.809795	+	0.114095i
$806$		0			0
$807$	5.49337	+	5.49337i	0.193376	+	0.193376i
$808$		0			0
$809$	−10.5847			−0.372137			−0.186069	−	0.982537i	$-0.559575\pi$
$809$	−10.5847			−0.372137			−0.186069	+	0.982537i	$0.559575\pi$
$810$		0			0
$811$	−14.0997	−	14.0997i	−0.495109	−	0.495109i	0.414803	−	0.909911i	$-0.363851\pi$
$811$	−14.0997	−	14.0997i	−0.495109	−	0.495109i	−0.909911	+	0.414803i	$0.863851\pi$
$812$		0			0
$813$	29.9569			1.05063
$814$		0			0
$815$	4.12045	−	29.2450i	0.144333	−	1.02441i
$816$		0			0
$817$	−1.10681	−	1.10681i	−0.0387222	−	0.0387222i
$818$		0			0
$819$	−11.5653	−	11.5653i	−0.404125	−	0.404125i
$820$		0			0
$821$	11.4283	−	11.4283i	0.398851	−	0.398851i	−0.478977	−	0.877828i	$-0.658992\pi$
$821$	11.4283	−	11.4283i	0.398851	−	0.398851i	0.877828	+	0.478977i	$0.158992\pi$
$822$		0			0
$823$	−10.9724	+	10.9724i	−0.382475	+	0.382475i	−0.871993	−	0.489518i	$-0.837173\pi$
$823$	−10.9724	+	10.9724i	−0.382475	+	0.382475i	0.489518	+	0.871993i	$0.337173\pi$
$824$		0			0
$825$	5.38502	−	2.98009i	0.187482	−	0.103753i
$826$		0			0
$827$			24.8187i			0.863032i	0.902105	+	0.431516i	$0.142021\pi$
$827$			24.8187i			0.863032i	−0.902105	+	0.431516i	$0.857979\pi$
$828$		0			0
$829$	−7.79087	+	7.79087i	−0.270588	+	0.270588i	−0.829337	−	0.558749i	$-0.811282\pi$
$829$	−7.79087	+	7.79087i	−0.270588	+	0.270588i	0.558749	+	0.829337i	$0.311282\pi$
$830$		0			0
$831$		−	7.29980i		−	0.253227i
$832$		0			0
$833$	−1.96672	+	1.96672i	−0.0681428	+	0.0681428i
$834$		0			0
$835$	0.0322485	+	0.0428261i	0.00111601	+	0.00148206i
$836$		0			0
$837$	7.72239			0.266925
$838$		0			0
$839$			12.7895i			0.441542i	0.975326	+	0.220771i	$0.0708573\pi$
$839$			12.7895i			0.441542i	−0.975326	+	0.220771i	$0.929143\pi$
$840$		0			0
$841$		−	81.6018i		−	2.81386i
$842$		0			0
$843$	−9.84488			−0.339076
$844$		0			0
$845$	−47.8419	−	6.74065i	−1.64581	−	0.231885i
$846$		0			0
$847$	18.6468	−	18.6468i	0.640713	−	0.640713i
$848$		0			0
$849$		−	2.84482i		−	0.0976340i
$850$		0			0
$851$	11.8496	−	11.8496i	0.406199	−	0.406199i
$852$		0			0
$853$		−	5.84193i		−	0.200024i	−0.994986	−	0.100012i	$-0.968112\pi$
$853$		−	5.84193i		−	0.200024i	0.994986	−	0.100012i	$-0.0318881\pi$
$854$		0			0
$855$	−4.56605	−	6.06373i	−0.156156	−	0.207375i
$856$		0			0
$857$	26.9251	−	26.9251i	0.919745	−	0.919745i	−0.0772652	−	0.997011i	$-0.524619\pi$
$857$	26.9251	−	26.9251i	0.919745	−	0.919745i	0.997011	+	0.0772652i	$0.0246188\pi$
$858$		0			0
$859$	2.05019	−	2.05019i	0.0699516	−	0.0699516i	−0.671265	−	0.741217i	$-0.734249\pi$
$859$	2.05019	−	2.05019i	0.0699516	−	0.0699516i	0.741217	+	0.671265i	$0.234249\pi$
$860$		0			0
$861$	−9.53244	−	9.53244i	−0.324865	−	0.324865i
$862$		0			0
$863$	−18.1091	−	18.1091i	−0.616443	−	0.616443i	0.328175	−	0.944617i	$-0.393567\pi$
$863$	−18.1091	−	18.1091i	−0.616443	−	0.616443i	−0.944617	+	0.328175i	$0.893567\pi$
$864$		0			0
$865$	−7.61532	−	1.07295i	−0.258929	−	0.0364815i
$866$		0			0
$867$	2.48490			0.0843916
$868$		0			0
$869$	3.60763	+	3.60763i	0.122381	+	0.122381i
$870$		0			0
$871$	−37.7009			−1.27745
$872$		0			0
$873$	−3.18909	−	3.18909i	−0.107934	−	0.107934i
$874$		0			0
$875$	−11.1096	−	29.0316i	−0.375572	−	0.981446i
$876$		0			0
$877$		−	47.2518i		−	1.59558i	−0.602934	−	0.797791i	$-0.706002\pi$
$877$		−	47.2518i		−	1.59558i	0.602934	−	0.797791i	$-0.293998\pi$
$878$		0			0
$879$	27.6123			0.931338
$880$		0			0
$881$	11.4431			0.385527			0.192763	−	0.981245i	$-0.438255\pi$
$881$	11.4431			0.385527			0.192763	+	0.981245i	$0.438255\pi$
$882$		0			0
$883$		−	46.1246i		−	1.55222i	−0.630599	−	0.776109i	$-0.717191\pi$
$883$		−	46.1246i		−	1.55222i	0.630599	−	0.776109i	$-0.282809\pi$
$884$		0			0
$885$	−12.3162	−	16.3559i	−0.414003	−	0.549797i
$886$		0			0
$887$	25.0305	+	25.0305i	0.840441	+	0.840441i	0.988916	−	0.148475i	$-0.0474365\pi$
$887$	25.0305	+	25.0305i	0.840441	+	0.840441i	−0.148475	+	0.988916i	$0.547436\pi$
$888$		0			0
$889$	47.6641			1.59860
$890$		0			0
$891$	−0.870396	−	0.870396i	−0.0291594	−	0.0291594i
$892$		0			0
$893$	22.4047			0.749745
$894$		0			0
$895$	−1.55366	−	2.06326i	−0.0519331	−	0.0689672i
$896$		0			0
$897$	−15.5250	−	15.5250i	−0.518365	−	0.518365i
$898$		0			0
$899$	−57.4272	−	57.4272i	−1.91531	−	1.91531i
$900$		0			0
$901$	−6.49984	+	6.49984i	−0.216541	+	0.216541i
$902$		0			0
$903$	−0.906503	+	0.906503i	−0.0301665	+	0.0301665i
$904$		0			0
$905$	38.4153	−	28.9271i	1.27697	−	0.961571i
$906$		0			0
$907$		−	25.0169i		−	0.830671i	−0.909668	−	0.415336i	$-0.863664\pi$
$907$		−	25.0169i		−	0.830671i	0.909668	−	0.415336i	$-0.136336\pi$
$908$		0			0
$909$	−6.90372	+	6.90372i	−0.228982	+	0.228982i
$910$		0			0
$911$			5.76809i			0.191105i	0.995424	+	0.0955527i	$0.0304618\pi$
$911$			5.76809i			0.191105i	−0.995424	+	0.0955527i	$0.969538\pi$
$912$		0			0
$913$	−0.210006	+	0.210006i	−0.00695019	+	0.00695019i
$914$		0			0
$915$	21.4928	−	16.1843i	0.710531	−	0.535038i
$916$		0			0
$917$	−35.4782			−1.17159
$918$		0			0
$919$			0.398221i			0.0131361i	0.999978	+	0.00656804i	$0.00209069\pi$
$919$			0.398221i			0.0131361i	−0.999978	+	0.00656804i	$0.997909\pi$
$920$		0			0
$921$			23.7612i			0.782958i
$922$		0			0
$923$	78.3668			2.57947
$924$		0			0
$925$	−21.5764	−	6.20310i	−0.709426	−	0.203957i
$926$		0			0
$927$	4.09832	−	4.09832i	0.134606	−	0.134606i
$928$		0			0
$929$			4.71373i			0.154653i	0.997006	+	0.0773263i	$0.0246383\pi$
$929$			4.71373i			0.154653i	−0.997006	+	0.0773263i	$0.975362\pi$
$930$		0			0
$931$	1.75237	−	1.75237i	0.0574315	−	0.0574315i
$932$		0			0
$933$		−	12.2337i		−	0.400512i
$934$		0			0
$935$	−1.46302	+	10.3839i	−0.0478460	+	0.339588i
$936$		0			0
$937$	7.20557	−	7.20557i	0.235396	−	0.235396i	−0.579545	−	0.814940i	$-0.696770\pi$
$937$	7.20557	−	7.20557i	0.235396	−	0.235396i	0.814940	+	0.579545i	$0.196770\pi$
$938$		0			0
$939$	10.9229	−	10.9229i	0.356456	−	0.356456i
$940$		0			0
$941$	−36.0800	−	36.0800i	−1.17617	−	1.17617i	−0.980711	−	0.195464i	$-0.937379\pi$
$941$	−36.0800	−	36.0800i	−1.17617	−	1.17617i	−0.195464	−	0.980711i	$-0.562621\pi$
$942$		0			0
$943$	−12.7961	−	12.7961i	−0.416699	−	0.416699i
$944$		0			0
$945$	−4.96636	+	3.73972i	−0.161556	+	0.121653i
$946$		0			0
$947$	27.2599			0.885828			0.442914	−	0.896564i	$-0.353945\pi$
$947$	27.2599			0.885828			0.442914	+	0.896564i	$0.353945\pi$
$948$		0			0
$949$	9.58495	+	9.58495i	0.311141	+	0.311141i
$950$		0			0
$951$	21.5403			0.698491
$952$		0			0
$953$	−17.4014	−	17.4014i	−0.563687	−	0.563687i	0.366666	−	0.930353i	$-0.380499\pi$
$953$	−17.4014	−	17.4014i	−0.563687	−	0.563687i	−0.930353	+	0.366666i	$0.880499\pi$
$954$		0			0
$955$	−0.167299	+	1.18741i	−0.00541365	+	0.0384236i
$956$		0			0
$957$			12.9453i			0.418463i
$958$		0			0
$959$	31.9646			1.03219
$960$		0			0
$961$	−28.6353			−0.923721
$962$		0			0
$963$			10.0579i			0.324111i
$964$		0			0
$965$	19.4758	−	14.6655i	0.626948	−	0.472099i
$966$		0			0
$967$	28.3082	+	28.3082i	0.910331	+	0.910331i	0.996298	−	0.0859674i	$-0.0273981\pi$
$967$	28.3082	+	28.3082i	0.910331	+	0.910331i	−0.0859674	+	0.996298i	$0.527398\pi$
$968$		0			0
$969$	12.9331			0.415471
$970$		0			0
$971$	−25.2474	−	25.2474i	−0.810229	−	0.810229i	0.174439	−	0.984668i	$-0.444189\pi$
$971$	−25.2474	−	25.2474i	−0.810229	−	0.810229i	−0.984668	+	0.174439i	$0.944189\pi$
$972$		0			0
$973$	11.7405			0.376382
$974$		0			0
$975$	−8.12713	+	28.2687i	−0.260277	+	0.905324i
$976$		0			0
$977$	15.1184	+	15.1184i	0.483680	+	0.483680i	0.906305	−	0.422625i	$-0.138891\pi$
$977$	15.1184	+	15.1184i	0.483680	+	0.483680i	−0.422625	+	0.906305i	$0.638891\pi$
$978$		0			0
$979$	2.49183	+	2.49183i	0.0796393	+	0.0796393i
$980$		0			0
$981$	11.2123	−	11.2123i	0.357980	−	0.357980i
$982$		0			0
$983$	−29.6618	+	29.6618i	−0.946063	+	0.946063i	−0.998618	−	0.0525548i	$-0.983264\pi$
$983$	−29.6618	+	29.6618i	−0.946063	+	0.946063i	0.0525548	+	0.998618i	$0.483264\pi$
$984$		0			0
$985$	−43.5232	−	6.13217i	−1.38677	−	0.195387i
$986$		0			0
$987$		−	18.3501i		−	0.584089i
$988$		0			0
$989$	−1.21687	+	1.21687i	−0.0386942	+	0.0386942i
$990$		0			0
$991$			35.7662i			1.13615i	0.822977	+	0.568075i	$0.192312\pi$
$991$			35.7662i			1.13615i	−0.822977	+	0.568075i	$0.807688\pi$
$992$		0			0
$993$	−21.2143	+	21.2143i	−0.673215	+	0.673215i
$994$		0			0
$995$	−2.91054	+	20.6577i	−0.0922704	+	0.654892i
$996$		0			0
$997$	53.1029			1.68178			0.840892	−	0.541203i	$-0.182031\pi$
$997$	53.1029			1.68178			0.840892	+	0.541203i	$0.182031\pi$
$998$		0			0
$999$			4.49007i			0.142059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bc.e.367.1		16
4.3	odd	2		240.2.bc.e.67.6	yes	16
5.3	odd	4		960.2.y.e.943.5		16
8.3	odd	2		1920.2.bc.i.607.8		16
8.5	even	2		1920.2.bc.j.607.8		16
12.11	even	2		720.2.bd.f.307.3		16
16.3	odd	4		1920.2.y.j.1567.4		16
16.5	even	4		240.2.y.e.187.2	yes	16
16.11	odd	4		960.2.y.e.847.5		16
16.13	even	4		1920.2.y.i.1567.4		16
20.3	even	4		240.2.y.e.163.2	✓	16
40.3	even	4		1920.2.y.i.223.4		16
40.13	odd	4		1920.2.y.j.223.4		16
48.5	odd	4		720.2.z.f.667.7		16
60.23	odd	4		720.2.z.f.163.7		16
80.3	even	4		1920.2.bc.j.1183.8		16
80.13	odd	4		1920.2.bc.i.1183.8		16
80.43	even	4	inner	960.2.bc.e.463.1		16
80.53	odd	4		240.2.bc.e.43.6	yes	16
240.53	even	4		720.2.bd.f.523.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.2	✓	16	20.3	even	4
240.2.y.e.187.2	yes	16	16.5	even	4
240.2.bc.e.43.6	yes	16	80.53	odd	4
240.2.bc.e.67.6	yes	16	4.3	odd	2
720.2.z.f.163.7		16	60.23	odd	4
720.2.z.f.667.7		16	48.5	odd	4
720.2.bd.f.307.3		16	12.11	even	2
720.2.bd.f.523.3		16	240.53	even	4
960.2.y.e.847.5		16	16.11	odd	4
960.2.y.e.943.5		16	5.3	odd	4
960.2.bc.e.367.1		16	1.1	even	1	trivial
960.2.bc.e.463.1		16	80.43	even	4	inner
1920.2.y.i.223.4		16	40.3	even	4
1920.2.y.i.1567.4		16	16.13	even	4
1920.2.y.j.223.4		16	40.13	odd	4
1920.2.y.j.1567.4		16	16.3	odd	4
1920.2.bc.i.607.8		16	8.3	odd	2
1920.2.bc.i.1183.8		16	80.13	odd	4
1920.2.bc.j.607.8		16	8.5	even	2
1920.2.bc.j.1183.8		16	80.3	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bc (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} +(-2.21420 - 0.311968i) q^{5} +(1.96597 + 1.96597i) q^{7} -1.00000 q^{9} +(-0.870396 - 0.870396i) q^{11} +5.88276 q^{13} +(0.311968 - 2.21420i) q^{15} +(2.69398 + 2.69398i) q^{17} +(-2.40037 - 2.40037i) q^{19} +(-1.96597 + 1.96597i) q^{21} +(-2.63907 + 2.63907i) q^{23} +(4.80535 + 1.38152i) q^{25} -1.00000i q^{27} +(-7.43646 + 7.43646i) q^{29} +7.72239i q^{31} +(0.870396 - 0.870396i) q^{33} +(-3.73972 - 4.96636i) q^{35} -4.49007 q^{37} +5.88276i q^{39} +4.84873i q^{41} +0.461098 q^{43} +(2.21420 + 0.311968i) q^{45} +(-4.66693 + 4.66693i) q^{47} +0.730041i q^{49} +(-2.69398 + 2.69398i) q^{51} +2.41272i q^{53} +(1.65569 + 2.19876i) q^{55} +(2.40037 - 2.40037i) q^{57} +(6.47458 - 6.47458i) q^{59} +(8.50808 + 8.50808i) q^{61} +(-1.96597 - 1.96597i) q^{63} +(-13.0256 - 1.83523i) q^{65} -6.40870 q^{67} +(-2.63907 - 2.63907i) q^{69} +13.3214 q^{71} +(1.62933 + 1.62933i) q^{73} +(-1.38152 + 4.80535i) q^{75} -3.42234i q^{77} -4.14482 q^{79} +1.00000 q^{81} -0.241277i q^{83} +(-5.12458 - 6.80545i) q^{85} +(-7.43646 - 7.43646i) q^{87} -2.86287 q^{89} +(11.5653 + 11.5653i) q^{91} -7.72239 q^{93} +(4.56605 + 6.06373i) q^{95} +(3.18909 + 3.18909i) q^{97} +(0.870396 + 0.870396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} + 4 q^{7} - 16 q^{9} - 8 q^{13} - 4 q^{15} - 8 q^{17} + 8 q^{19} - 4 q^{21} - 32 q^{25} - 12 q^{29} - 12 q^{35} - 24 q^{37} - 24 q^{43} + 8 q^{45} - 32 q^{47} + 8 q^{51} + 4 q^{55} - 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 + 4 * q^7 - 16 * q^9 - 8 * q^13 - 4 * q^15 - 8 * q^17 + 8 * q^19 - 4 * q^21 - 32 * q^25 - 12 * q^29 - 12 * q^35 - 24 * q^37 - 24 * q^43 + 8 * q^45 - 32 * q^47 + 8 * q^51 + 4 * q^55 - 8 * q^57 - 24 * q^59 + 40 * q^61 - 4 * q^63 - 4 * q^65 - 16 * q^67 - 8 * q^73 - 24 * q^75 - 48 * q^79 + 16 * q^81 - 8 * q^85 - 12 * q^87 + 40 * q^91 - 32 * q^93 + 8 * q^95 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more