LMFDB - Embedded newform 1920.2.y.j.1567.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(223,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("1920.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.y (of order $4$, degree $2$, not 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:	$15.3312771881$
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:	$\Z[a_1, \ldots, a_{17}]$
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			1567.4
Root			$1.38194 + 0.300388i$ of defining polynomial
Character	$\chi$	$=$	1920.1567
Dual form			1920.2.y.j.223.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(-0.311968 + 2.21420i) q^{5} +(1.96597 + 1.96597i) q^{7} +1.00000 q^{9} +(0.870396 - 0.870396i) q^{11} +5.88276i q^{13} +(-0.311968 + 2.21420i) q^{15} +(2.69398 + 2.69398i) q^{17} +(-2.40037 + 2.40037i) q^{19} +(1.96597 + 1.96597i) q^{21} +(-2.63907 + 2.63907i) q^{23} +(-4.80535 - 1.38152i) q^{25} +1.00000 q^{27} +(-7.43646 - 7.43646i) q^{29} -7.72239i q^{31} +(0.870396 - 0.870396i) q^{33} +(-4.96636 + 3.73972i) q^{35} +4.49007i q^{37} +5.88276i q^{39} -4.84873i q^{41} +0.461098i q^{43} +(-0.311968 + 2.21420i) q^{45} +(4.66693 - 4.66693i) q^{47} +0.730041i q^{49} +(2.69398 + 2.69398i) q^{51} +2.41272 q^{53} +(1.65569 + 2.19876i) q^{55} +(-2.40037 + 2.40037i) q^{57} +(6.47458 + 6.47458i) q^{59} +(-8.50808 + 8.50808i) q^{61} +(1.96597 + 1.96597i) q^{63} +(-13.0256 - 1.83523i) q^{65} +6.40870i q^{67} +(-2.63907 + 2.63907i) q^{69} +13.3214 q^{71} +(-1.62933 - 1.62933i) q^{73} +(-4.80535 - 1.38152i) q^{75} +3.42234 q^{77} +4.14482 q^{79} +1.00000 q^{81} -0.241277 q^{83} +(-6.80545 + 5.12458i) q^{85} +(-7.43646 - 7.43646i) q^{87} +2.86287 q^{89} +(-11.5653 + 11.5653i) q^{91} -7.72239i q^{93} +(-4.56605 - 6.06373i) q^{95} +(3.18909 + 3.18909i) q^{97} +(0.870396 - 0.870396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 4 q^{5} + 4 q^{7} + 16 q^{9} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} + 32 q^{25} + 16 q^{27} - 12 q^{29} - 20 q^{35} + 4 q^{45} + 32 q^{47} - 8 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) $ 16 * q + 16 * q^3 + 4 * q^5 + 4 * q^7 + 16 * q^9 + 4 * q^15 - 8 * q^17 + 8 * q^19 + 4 * q^21 + 32 * q^25 + 16 * q^27 - 12 * q^29 - 20 * q^35 + 4 * q^45 + 32 * q^47 - 8 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 24 * q^59 - 40 * q^61 + 4 * q^63 - 4 * q^65 + 8 * q^73 + 32 * q^75 + 72 * q^77 + 48 * q^79 + 16 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^87 - 40 * q^91 - 8 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−0.311968	+	2.21420i	−0.139516	+	0.990220i
$5$	−0.311968	+	2.21420i	−0.139516	+	0.990220i
$6$		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	$-0.690587\pi$
$11$	0.870396	−	0.870396i	0.262434	−	0.262434i	0.826042	+	0.563608i	$0.190587\pi$
$12$		0			0
$13$			5.88276i			1.63158i	0.578345	+	0.815792i	$0.303699\pi$
$13$			5.88276i			1.63158i	−0.578345	+	0.815792i	$0.696301\pi$
$14$		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	−0.926638	−	0.375956i	$-0.877314\pi$
$19$	−2.40037	+	2.40037i	−0.550682	+	0.550682i	0.375956	+	0.926638i	$0.377314\pi$
$20$		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
$27$	1.00000			0.192450
$28$		0			0
$29$	−7.43646	−	7.43646i	−1.38092	−	1.38092i	−0.842996	−	0.537919i	$-0.819210\pi$
$29$	−7.43646	−	7.43646i	−1.38092	−	1.38092i	−0.537919	−	0.842996i	$-0.680790\pi$
$30$		0			0
$31$		−	7.72239i		−	1.38698i	−0.720465	−	0.693491i	$-0.756072\pi$
$31$		−	7.72239i		−	1.38698i	0.720465	−	0.693491i	$-0.243928\pi$
$32$		0			0
$33$	0.870396	−	0.870396i	0.151516	−	0.151516i
$34$		0			0
$35$	−4.96636	+	3.73972i	−0.839467	+	0.632128i
$36$		0			0
$37$			4.49007i			0.738163i	0.929397	+	0.369081i	$0.120328\pi$
$37$			4.49007i			0.738163i	−0.929397	+	0.369081i	$0.879672\pi$
$38$		0			0
$39$			5.88276i			0.941996i
$40$		0			0
$41$		−	4.84873i		−	0.757244i	−0.925551	−	0.378622i	$-0.876398\pi$
$41$		−	4.84873i		−	0.757244i	0.925551	−	0.378622i	$-0.123602\pi$
$42$		0			0
$43$			0.461098i			0.0703168i	0.999382	+	0.0351584i	$0.0111936\pi$
$43$			0.461098i			0.0703168i	−0.999382	+	0.0351584i	$0.988806\pi$
$44$		0			0
$45$	−0.311968	+	2.21420i	−0.0465054	+	0.330073i
$46$		0			0
$47$	4.66693	−	4.66693i	0.680742	−	0.680742i	−0.279425	−	0.960167i	$-0.590144\pi$
$47$	4.66693	−	4.66693i	0.680742	−	0.680742i	0.960167	+	0.279425i	$0.0901439\pi$
$48$		0			0
$49$			0.730041i			0.104292i
$50$		0			0
$51$	2.69398	+	2.69398i	0.377233	+	0.377233i
$52$		0			0
$53$	2.41272			0.331413			0.165706	−	0.986175i	$-0.447010\pi$
$53$	2.41272			0.331413			0.165706	+	0.986175i	$0.447010\pi$
$54$		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	0.989238	−	0.146318i	$-0.0467424\pi$
$59$	6.47458	+	6.47458i	0.842919	+	0.842919i	−0.146318	+	0.989238i	$0.546742\pi$
$60$		0			0
$61$	−8.50808	+	8.50808i	−1.08935	+	1.08935i	−0.0937523	+	0.995596i	$0.529886\pi$
$61$	−8.50808	+	8.50808i	−1.08935	+	1.08935i	−0.995596	+	0.0937523i	$0.970114\pi$
$62$		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
$67$			6.40870i			0.782948i	0.920189	+	0.391474i	$0.128035\pi$
$67$			6.40870i			0.782948i	−0.920189	+	0.391474i	$0.871965\pi$
$68$		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	0.605299	−	0.795998i	$-0.293053\pi$
$73$	−1.62933	−	1.62933i	−0.190699	−	0.190699i	−0.795998	+	0.605299i	$0.793053\pi$
$74$		0			0
$75$	−4.80535	−	1.38152i	−0.554874	−	0.159524i
$76$		0			0
$77$	3.42234			0.390011
$78$		0			0
$79$	4.14482			0.466328			0.233164	−	0.972437i	$-0.425092\pi$
$79$	4.14482			0.466328			0.233164	+	0.972437i	$0.425092\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−0.241277			−0.0264836			−0.0132418	−	0.999912i	$-0.504215\pi$
$83$	−0.241277			−0.0264836			−0.0132418	+	0.999912i	$0.504215\pi$
$84$		0			0
$85$	−6.80545	+	5.12458i	−0.738155	+	0.555839i
$86$		0			0
$87$	−7.43646	−	7.43646i	−0.797272	−	0.797272i
$88$		0			0
$89$	2.86287			0.303464			0.151732	−	0.988422i	$-0.451515\pi$
$89$	2.86287			0.303464			0.151732	+	0.988422i	$0.451515\pi$
$90$		0			0
$91$	−11.5653	+	11.5653i	−1.21237	+	1.21237i
$92$		0			0
$93$		−	7.72239i		−	0.800775i
$94$		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	$-0.411451\pi$
$101$	−6.90372	−	6.90372i	−0.686946	−	0.686946i	−0.961556	+	0.274610i	$0.911451\pi$
$102$		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
$107$	10.0579			0.972333			0.486166	−	0.873866i	$-0.338395\pi$
$107$	10.0579			0.972333			0.486166	+	0.873866i	$0.338395\pi$
$108$		0			0
$109$	−11.2123	−	11.2123i	−1.07394	−	1.07394i	−0.997039	−	0.0769025i	$-0.975497\pi$
$109$	−11.2123	−	11.2123i	−1.07394	−	1.07394i	−0.0769025	−	0.997039i	$-0.524503\pi$
$110$		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
$115$	−5.02012	−	6.66672i	−0.468128	−	0.621675i
$116$		0			0
$117$			5.88276i			0.543861i
$118$		0			0
$119$			10.5926i			0.971018i
$120$		0			0
$121$			9.48482i			0.862257i
$122$		0			0
$123$		−	4.84873i		−	0.437195i
$124$		0			0
$125$	4.55807	−	10.2090i	0.407686	−	0.913122i
$126$		0			0
$127$	−12.1223	+	12.1223i	−1.07568	+	1.07568i	−0.0787895	+	0.996891i	$0.525106\pi$
$127$	−12.1223	+	12.1223i	−1.07568	+	1.07568i	−0.996891	+	0.0787895i	$0.974894\pi$
$128$		0			0
$129$			0.461098i			0.0405974i
$130$		0			0
$131$	9.02309	+	9.02309i	0.788351	+	0.788351i	0.981224	−	0.192873i	$-0.0617804\pi$
$131$	9.02309	+	9.02309i	0.788351	+	0.788351i	−0.192873	+	0.981224i	$0.561780\pi$
$132$		0			0
$133$	−9.43808			−0.818385
$134$		0			0
$135$	−0.311968	+	2.21420i	−0.0268499	+	0.190568i
$136$		0			0
$137$	−8.12950	+	8.12950i	−0.694550	+	0.694550i	−0.963230	−	0.268679i	$-0.913413\pi$
$137$	−8.12950	+	8.12950i	−0.694550	+	0.694550i	0.268679	+	0.963230i	$0.413413\pi$
$138$		0			0
$139$	2.98593	+	2.98593i	0.253263	+	0.253263i	0.822307	−	0.569044i	$-0.192687\pi$
$139$	2.98593	+	2.98593i	0.253263	+	0.253263i	−0.569044	+	0.822307i	$0.692687\pi$
$140$		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
$147$			0.730041i			0.0602128i
$148$		0			0
$149$	0.994977	−	0.994977i	0.0815117	−	0.0815117i	−0.665175	−	0.746687i	$-0.731643\pi$
$149$	0.994977	−	0.994977i	0.0815117	−	0.0815117i	0.746687	+	0.665175i	$0.231643\pi$
$150$		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
$155$	17.0989	+	2.40914i	1.37342	+	0.193506i
$156$		0			0
$157$	10.3489			0.825932			0.412966	−	0.910746i	$-0.364493\pi$
$157$	10.3489			0.825932			0.412966	+	0.910746i	$0.364493\pi$
$158$		0			0
$159$	2.41272			0.191341
$160$		0			0
$161$	−10.3766			−0.817793
$162$		0			0
$163$	13.2079			1.03453			0.517263	−	0.855827i	$-0.326951\pi$
$163$	13.2079			1.03453			0.517263	+	0.855827i	$0.326951\pi$
$164$		0			0
$165$	1.65569	+	2.19876i	0.128896	+	0.171174i
$166$		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
$173$			3.43931i			0.261486i	0.991416	+	0.130743i	$0.0417363\pi$
$173$			3.43931i			0.261486i	−0.991416	+	0.130743i	$0.958264\pi$
$174$		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	−0.675924	−	0.736971i	$-0.736255\pi$
$179$	0.816756	−	0.816756i	0.0610472	−	0.0610472i	0.736971	+	0.675924i	$0.236255\pi$
$180$		0			0
$181$	15.2070	+	15.2070i	1.13032	+	1.13032i	0.990123	+	0.140201i	$0.0447748\pi$
$181$	15.2070	+	15.2070i	1.13032	+	1.13032i	0.140201	+	0.990123i	$0.455225\pi$
$182$		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
$187$	4.68966			0.342942
$188$		0			0
$189$	1.96597	+	1.96597i	0.143003	+	0.143003i
$190$		0			0
$191$			0.536269i			0.0388031i	0.999812	+	0.0194015i	$0.00617609\pi$
$191$			0.536269i			0.0388031i	−0.999812	+	0.0194015i	$0.993824\pi$
$192$		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
$195$	−13.0256	−	1.83523i	−0.932783	−	0.131424i
$196$		0			0
$197$		−	19.6564i		−	1.40046i	−0.713916	−	0.700231i	$-0.753080\pi$
$197$		−	19.6564i		−	1.40046i	0.713916	−	0.700231i	$-0.246920\pi$
$198$		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
$203$		−	29.2396i		−	2.05222i
$204$		0			0
$205$	10.7361	+	1.51265i	0.749838	+	0.105648i
$206$		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	$-0.370342\pi$
$211$	−7.58277	−	7.58277i	−0.522019	−	0.522019i	−0.918181	+	0.396162i	$0.870342\pi$
$212$		0			0
$213$	13.3214			0.912769
$214$		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	0.936773	−	0.349938i	$-0.113797\pi$
$223$	8.76331	+	8.76331i	0.586835	+	0.586835i	−0.349938	+	0.936773i	$0.613797\pi$
$224$		0			0
$225$	−4.80535	−	1.38152i	−0.320357	−	0.0921011i
$226$		0			0
$227$		−	25.0028i		−	1.65949i	−0.558141	−	0.829746i	$-0.688485\pi$
$227$		−	25.0028i		−	1.65949i	0.558141	−	0.829746i	$-0.311515\pi$
$228$		0			0
$229$	7.89911	−	7.89911i	0.521988	−	0.521988i	−0.396183	−	0.918171i	$-0.629666\pi$
$229$	7.89911	−	7.89911i	0.521988	−	0.521988i	0.918171	+	0.396183i	$0.129666\pi$
$230$		0			0
$231$	3.42234			0.225173
$232$		0			0
$233$	7.91066	+	7.91066i	0.518245	+	0.518245i	0.917040	−	0.398795i	$-0.130572\pi$
$233$	7.91066	+	7.91066i	0.518245	+	0.518245i	−0.398795	+	0.917040i	$0.630572\pi$
$234$		0			0
$235$	8.87759	+	11.7895i	0.579110	+	0.769059i
$236$		0			0
$237$	4.14482			0.269235
$238$		0			0
$239$	11.4515			0.740735			0.370368	−	0.928885i	$-0.379232\pi$
$239$	11.4515			0.740735			0.370368	+	0.928885i	$0.379232\pi$
$240$		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
$243$	1.00000			0.0641500
$244$		0			0
$245$	−1.61646	−	0.227749i	−0.103272	−	0.0145504i
$246$		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	$-0.503724\pi$
$251$	15.6566	−	15.6566i	0.988233	−	0.988233i	0.999932	+	0.0116985i	$0.00372383\pi$
$252$		0			0
$253$			4.59407i			0.288826i
$254$		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
$267$	2.86287			0.175205
$268$		0			0
$269$	5.49337	+	5.49337i	0.334937	+	0.334937i	0.854458	−	0.519521i	$-0.173890\pi$
$269$	5.49337	+	5.49337i	0.334937	+	0.334937i	−0.519521	+	0.854458i	$0.673890\pi$
$270$		0			0
$271$			29.9569i			1.81975i	0.414883	+	0.909875i	$0.363822\pi$
$271$			29.9569i			1.81975i	−0.414883	+	0.909875i	$0.636178\pi$
$272$		0			0
$273$	−11.5653	+	11.5653i	−0.699964	+	0.699964i
$274$		0			0
$275$	−5.38502	+	2.98009i	−0.324729	+	0.179706i
$276$		0			0
$277$			7.29980i			0.438602i	0.975657	+	0.219301i	$0.0703777\pi$
$277$			7.29980i			0.438602i	−0.975657	+	0.219301i	$0.929622\pi$
$278$		0			0
$279$		−	7.72239i		−	0.462328i
$280$		0			0
$281$		−	9.84488i		−	0.587296i	−0.955914	−	0.293648i	$-0.905131\pi$
$281$		−	9.84488i		−	0.587296i	0.955914	−	0.293648i	$-0.0948694\pi$
$282$		0			0
$283$		−	2.84482i		−	0.169107i	−0.996419	−	0.0845535i	$-0.973054\pi$
$283$		−	2.84482i		−	0.169107i	0.996419	−	0.0845535i	$-0.0269464\pi$
$284$		0			0
$285$	−4.56605	−	6.06373i	−0.270470	−	0.359184i
$286$		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
$293$	−27.6123			−1.61313			−0.806563	−	0.591149i	$-0.798675\pi$
$293$	−27.6123			−1.61313			−0.806563	+	0.591149i	$0.798675\pi$
$294$		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
$307$		−	23.7612i		−	1.35612i	−0.735006	−	0.678061i	$-0.762820\pi$
$307$		−	23.7612i		−	1.35612i	0.735006	−	0.678061i	$-0.237180\pi$
$308$		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	0.944864	−	0.327464i	$-0.106194\pi$
$313$	10.9229	+	10.9229i	0.617400	+	0.617400i	−0.327464	+	0.944864i	$0.606194\pi$
$314$		0			0
$315$	−4.96636	+	3.73972i	−0.279822	+	0.210709i
$316$		0			0
$317$	21.5403			1.20982			0.604911	−	0.796293i	$-0.293209\pi$
$317$	21.5403			1.20982			0.604911	+	0.796293i	$0.293209\pi$
$318$		0			0
$319$	−12.9453			−0.724799
$320$		0			0
$321$	10.0579			0.561377
$322$		0			0
$323$	−12.9331			−0.719617
$324$		0			0
$325$	8.12713	−	28.2687i	0.450812	−	1.56807i
$326$		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	−0.182914	+	0.983129i	$0.558553\pi$
$331$	−21.2143	+	21.2143i	−1.16604	+	1.16604i	−0.983129	+	0.182914i	$0.941447\pi$
$332$		0			0
$333$			4.49007i			0.246054i
$334$		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
$347$	−6.70115			−0.359736			−0.179868	−	0.983691i	$-0.557567\pi$
$347$	−6.70115			−0.359736			−0.179868	+	0.983691i	$0.557567\pi$
$348$		0			0
$349$	−7.28479	−	7.28479i	−0.389946	−	0.389946i	0.484722	−	0.874668i	$-0.338921\pi$
$349$	−7.28479	−	7.28479i	−0.389946	−	0.389946i	−0.874668	+	0.484722i	$0.838921\pi$
$350$		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
$355$	−4.15585	+	29.4963i	−0.220570	+	1.56550i
$356$		0			0
$357$			10.5926i			0.560618i
$358$		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
$363$			9.48482i			0.497824i
$364$		0			0
$365$	4.11596	−	3.09936i	0.215439	−	0.162228i
$366$		0			0
$367$	15.5759	−	15.5759i	0.813056	−	0.813056i	−0.172035	−	0.985091i	$-0.555034\pi$
$367$	15.5759	−	15.5759i	0.813056	−	0.813056i	0.985091	+	0.172035i	$0.0550341\pi$
$368$		0			0
$369$		−	4.84873i		−	0.252415i
$370$		0			0
$371$	4.74333	+	4.74333i	0.246261	+	0.246261i
$372$		0			0
$373$	6.11186			0.316460			0.158230	−	0.987402i	$-0.449421\pi$
$373$	6.11186			0.316460			0.158230	+	0.987402i	$0.449421\pi$
$374$		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	−0.917768	−	0.397116i	$-0.870011\pi$
$379$	−25.5981	−	25.5981i	−1.31488	−	1.31488i	−0.397116	−	0.917768i	$-0.629989\pi$
$380$		0			0
$381$	−12.1223	+	12.1223i	−0.621045	+	0.621045i
$382$		0			0
$383$	−2.46156	−	2.46156i	−0.125780	−	0.125780i	0.641415	−	0.767194i	$-0.278348\pi$
$383$	−2.46156	−	2.46156i	−0.125780	−	0.125780i	−0.767194	+	0.641415i	$0.778348\pi$
$384$		0			0
$385$	−1.06766	+	7.57773i	−0.0544129	+	0.386197i
$386$		0			0
$387$			0.461098i			0.0234389i
$388$		0			0
$389$	23.1160	−	23.1160i	1.17203	−	1.17203i	0.190302	−	0.981726i	$-0.439053\pi$
$389$	23.1160	−	23.1160i	1.17203	−	1.17203i	0.981726	−	0.190302i	$-0.0609468\pi$
$390$		0			0
$391$	−14.2192			−0.719096
$392$		0			0
$393$	9.02309	+	9.02309i	0.455155	+	0.455155i
$394$		0			0
$395$	−1.29305	+	9.17745i	−0.0650603	+	0.461768i
$396$		0			0
$397$	29.1851			1.46476			0.732379	−	0.680897i	$-0.238410\pi$
$397$	29.1851			1.46476			0.732379	+	0.680897i	$0.238410\pi$
$398$		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
$403$	45.4290			2.26298
$404$		0			0
$405$	−0.311968	+	2.21420i	−0.0155018	+	0.110024i
$406$		0			0
$407$	3.90814	+	3.90814i	0.193719	+	0.193719i
$408$		0			0
$409$	7.11999			0.352061			0.176030	−	0.984385i	$-0.443674\pi$
$409$	7.11999			0.352061			0.176030	+	0.984385i	$0.443674\pi$
$410$		0			0
$411$	−8.12950	+	8.12950i	−0.400999	+	0.400999i
$412$		0			0
$413$			25.4576i			1.25269i
$414$		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	−0.231194	−	0.972908i	$-0.574263\pi$
$419$	15.1825	−	15.1825i	0.741713	−	0.741713i	0.972908	+	0.231194i	$0.0742633\pi$
$420$		0			0
$421$	8.92932	+	8.92932i	0.435188	+	0.435188i	0.890389	−	0.455201i	$-0.150432\pi$
$421$	8.92932	+	8.92932i	0.435188	+	0.435188i	−0.455201	+	0.890389i	$0.650432\pi$
$422$		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
$427$	−33.4532			−1.61891
$428$		0			0
$429$	5.12033	+	5.12033i	0.247212	+	0.247212i
$430$		0			0
$431$		−	23.7988i		−	1.14635i	−0.819434	−	0.573173i	$-0.805712\pi$
$431$		−	23.7988i		−	1.14635i	0.819434	−	0.573173i	$-0.194288\pi$
$432$		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
$435$	18.7857	−	14.1459i	0.900707	−	0.678242i
$436$		0			0
$437$		−	12.6695i		−	0.606062i
$438$		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
$443$			38.7016i			1.83877i	0.393360	+	0.919384i	$0.371313\pi$
$443$			38.7016i			1.83877i	−0.393360	+	0.919384i	$0.628687\pi$
$444$		0			0
$445$	−0.893124	+	6.33897i	−0.0423381	+	0.300496i
$446$		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
$453$	18.1365			0.852126
$454$		0			0
$455$	−21.9999	−	29.2159i	−1.03137	−	1.36966i
$456$		0			0
$457$	−1.77907	+	1.77907i	−0.0832213	+	0.0832213i	−0.747492	−	0.664271i	$-0.768742\pi$
$457$	−1.77907	+	1.77907i	−0.0832213	+	0.0832213i	0.664271	+	0.747492i	$0.268742\pi$
$458$		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	$-0.659502\pi$
$461$	8.51698	−	8.51698i	0.396675	−	0.396675i	0.877059	+	0.480383i	$0.159502\pi$
$462$		0			0
$463$	0.964355	+	0.964355i	0.0448174	+	0.0448174i	0.729160	−	0.684343i	$-0.239911\pi$
$463$	0.964355	+	0.964355i	0.0448174	+	0.0448174i	−0.684343	+	0.729160i	$0.739911\pi$
$464$		0			0
$465$	17.0989	+	2.40914i	0.792943	+	0.111721i
$466$		0			0
$467$			4.65741i			0.215519i	0.994177	+	0.107760i	$0.0343677\pi$
$467$			4.65741i			0.215519i	−0.994177	+	0.107760i	$0.965632\pi$
$468$		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
$475$	14.8508	−	8.21846i	0.681399	−	0.377089i
$476$		0			0
$477$	2.41272			0.110471
$478$		0			0
$479$	−22.6790			−1.03623			−0.518114	−	0.855311i	$-0.673366\pi$
$479$	−22.6790			−1.03623			−0.518114	+	0.855311i	$0.673366\pi$
$480$		0			0
$481$	−26.4140			−1.20437
$482$		0			0
$483$	−10.3766			−0.472153
$484$		0			0
$485$	−8.05618	+	6.06639i	−0.365812	+	0.275461i
$486$		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	$-0.747783\pi$
$491$	0.218295	−	0.218295i	0.00985151	−	0.00985151i	0.712015	+	0.702164i	$0.247783\pi$
$492$		0			0
$493$		−	40.0674i		−	1.80455i
$494$		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	−0.957686	−	0.287815i	$-0.907071\pi$
$499$	−14.9638	+	14.9638i	−0.669871	+	0.669871i	0.287815	+	0.957686i	$0.407071\pi$
$500$		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
$507$	−21.6069			−0.959595
$508$		0			0
$509$	−18.0574	−	18.0574i	−0.800381	−	0.800381i	0.182774	−	0.983155i	$-0.441492\pi$
$509$	−18.0574	−	18.0574i	−0.800381	−	0.800381i	−0.983155	+	0.182774i	$0.941492\pi$
$510$		0			0
$511$		−	6.40641i		−	0.283403i
$512$		0			0
$513$	−2.40037	+	2.40037i	−0.105979	+	0.105979i
$514$		0			0
$515$	−7.79595	−	10.3530i	−0.343531	−	0.456209i
$516$		0			0
$517$		−	8.12416i		−	0.357300i
$518$		0			0
$519$			3.43931i			0.150969i
$520$		0			0
$521$			3.75389i			0.164461i	0.996613	+	0.0822305i	$0.0262044\pi$
$521$			3.75389i			0.164461i	−0.996613	+	0.0822305i	$0.973796\pi$
$522$		0			0
$523$		−	30.3429i		−	1.32680i	−0.748263	−	0.663402i	$-0.769112\pi$
$523$		−	30.3429i		−	1.32680i	0.748263	−	0.663402i	$-0.230888\pi$
$524$		0			0
$525$	−6.73114	−	12.1632i	−0.293771	−	0.530844i
$526$		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
$533$	28.5239			1.23551
$534$		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	−0.0790451	+	0.996871i	$0.525187\pi$
$541$	−25.0252	+	25.0252i	−1.07592	+	1.07592i	−0.996871	+	0.0790451i	$0.974813\pi$
$542$		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
$547$		−	31.6172i		−	1.35185i	−0.736969	−	0.675927i	$-0.763744\pi$
$547$		−	31.6172i		−	1.35185i	0.736969	−	0.675927i	$-0.236256\pi$
$548$		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
$555$	−9.94190	−	1.40076i	−0.422010	−	0.0594588i
$556$		0			0
$557$	5.06043			0.214418			0.107209	−	0.994237i	$-0.465809\pi$
$557$	5.06043			0.214418			0.107209	+	0.994237i	$0.465809\pi$
$558$		0			0
$559$	−2.71253			−0.114728
$560$		0			0
$561$	4.68966			0.197998
$562$		0			0
$563$	−10.2694			−0.432804			−0.216402	−	0.976304i	$-0.569432\pi$
$563$	−10.2694			−0.432804			−0.216402	+	0.976304i	$0.569432\pi$
$564$		0			0
$565$	−0.799706	−	1.06201i	−0.0336439	−	0.0446791i
$566$		0			0
$567$	1.96597	+	1.96597i	0.0825628	+	0.0825628i
$568$		0			0
$569$	−30.5352			−1.28010			−0.640052	−	0.768332i	$-0.721087\pi$
$569$	−30.5352			−1.28010			−0.640052	+	0.768332i	$0.721087\pi$
$570$		0			0
$571$	15.6507	−	15.6507i	0.654962	−	0.654962i	−0.299222	−	0.954184i	$-0.596727\pi$
$571$	15.6507	−	15.6507i	0.654962	−	0.654962i	0.954184	+	0.299222i	$0.0967271\pi$
$572$		0			0
$573$			0.536269i			0.0224030i
$574$		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
$587$	−4.75989			−0.196461			−0.0982307	−	0.995164i	$-0.531318\pi$
$587$	−4.75989			−0.196461			−0.0982307	+	0.995164i	$0.531318\pi$
$588$		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
$595$	−23.4540	−	3.30454i	−0.961522	−	0.135473i
$596$		0			0
$597$		−	9.32963i		−	0.381836i
$598$		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	$0.0145698\pi$
$601$			2.24346i			0.0915126i	−0.998953	+	0.0457563i	$0.985430\pi$
$602$		0			0
$603$			6.40870i			0.260983i
$604$		0			0
$605$	−21.0013	−	2.95896i	−0.853824	−	0.120299i
$606$		0			0
$607$	20.2716	−	20.2716i	0.822800	−	0.822800i	−0.163709	−	0.986509i	$-0.552346\pi$
$607$	20.2716	−	20.2716i	0.822800	−	0.822800i	0.986509	+	0.163709i	$0.0523457\pi$
$608$		0			0
$609$		−	29.2396i		−	1.18485i
$610$		0			0
$611$	27.4545	+	27.4545i	1.11069	+	1.11069i
$612$		0			0
$613$	10.2599			0.414392			0.207196	−	0.978299i	$-0.433566\pi$
$613$	10.2599			0.414392			0.207196	+	0.978299i	$0.433566\pi$
$614$		0			0
$615$	10.7361	+	1.51265i	0.432919	+	0.0609958i
$616$		0			0
$617$	−16.5590	+	16.5590i	−0.666640	+	0.666640i	−0.956937	−	0.290297i	$-0.906246\pi$
$617$	−16.5590	+	16.5590i	−0.666640	+	0.666640i	0.290297	+	0.956937i	$0.406246\pi$
$618$		0			0
$619$	14.3984	+	14.3984i	0.578720	+	0.578720i	0.934550	−	0.355831i	$-0.115802\pi$
$619$	14.3984	+	14.3984i	0.578720	+	0.578720i	−0.355831	+	0.934550i	$0.615802\pi$
$620$		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
$627$			4.17854i			0.166875i
$628$		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
$635$	−23.0594	−	30.6230i	−0.915086	−	1.21524i
$636$		0			0
$637$	−4.29466			−0.170161
$638$		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
$643$	5.24582			0.206875			0.103437	−	0.994636i	$-0.467016\pi$
$643$	5.24582			0.206875			0.103437	+	0.994636i	$0.467016\pi$
$644$		0			0
$645$	−1.02096	−	0.143848i	−0.0402004	−	0.00566400i
$646$		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
$653$			9.14647i			0.357929i	0.983856	+	0.178965i	$0.0572747\pi$
$653$			9.14647i			0.357929i	−0.983856	+	0.178965i	$0.942725\pi$
$654$		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	−0.405042	−	0.914298i	$-0.632743\pi$
$659$	13.0731	−	13.0731i	0.509256	−	0.509256i	0.914298	+	0.405042i	$0.132743\pi$
$660$		0			0
$661$	−10.8969	−	10.8969i	−0.423839	−	0.423839i	0.462684	−	0.886523i	$-0.346886\pi$
$661$	−10.8969	−	10.8969i	−0.423839	−	0.423839i	−0.886523	+	0.462684i	$0.846886\pi$
$662$		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
$667$	39.2506			1.51979
$668$		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
$675$	−4.80535	−	1.38152i	−0.184958	−	0.0531746i
$676$		0			0
$677$		−	10.5396i		−	0.405070i	−0.979275	−	0.202535i	$-0.935082\pi$
$677$		−	10.5396i		−	0.405070i	0.979275	−	0.202535i	$-0.0649181\pi$
$678$		0			0
$679$			12.5393i			0.481214i
$680$		0			0
$681$		−	25.0028i		−	0.958108i
$682$		0			0
$683$			36.3666i			1.39153i	0.718270	+	0.695765i	$0.244934\pi$
$683$			36.3666i			1.39153i	−0.718270	+	0.695765i	$0.755066\pi$
$684$		0			0
$685$	−15.4642	−	20.5365i	−0.590856	−	0.784658i
$686$		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	$-0.183490\pi$
$691$	7.71130	+	7.71130i	0.293352	+	0.293352i	−0.545051	+	0.838403i	$0.683490\pi$
$692$		0			0
$693$	3.42234			0.130004
$694$		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	$-0.820905\pi$
$701$	−8.27188	+	8.27188i	−0.312425	+	0.312425i	0.533424	+	0.845848i	$0.320905\pi$
$702$		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
$707$		−	27.1450i		−	1.02089i
$708$		0			0
$709$	−24.1462	+	24.1462i	−0.906828	+	0.906828i	−0.996015	−	0.0891868i	$-0.971573\pi$
$709$	−24.1462	+	24.1462i	−0.906828	+	0.906828i	0.0891868	+	0.996015i	$0.471573\pi$
$710$		0			0
$711$	4.14482			0.155443
$712$		0			0
$713$	20.3799	+	20.3799i	0.763234	+	0.763234i
$714$		0			0
$715$	−12.9348	+	9.74005i	−0.483734	+	0.364257i
$716$		0			0
$717$	11.4515			0.427664
$718$		0			0
$719$	5.46091			0.203658			0.101829	−	0.994802i	$-0.467531\pi$
$719$	5.46091			0.203658			0.101829	+	0.994802i	$0.467531\pi$
$720$		0			0
$721$	−16.1143			−0.600128
$722$		0			0
$723$	20.9793			0.780227
$724$		0			0
$725$	25.4612	+	46.0084i	0.945606	+	1.70871i
$726$		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
$733$		−	3.99744i		−	0.147649i	−0.997271	−	0.0738245i	$-0.976480\pi$
$733$		−	3.99744i		−	0.147649i	0.997271	−	0.0738245i	$-0.0235205\pi$
$734$		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	−0.169084	−	0.985602i	$-0.554081\pi$
$739$	22.1967	−	22.1967i	0.816517	−	0.816517i	0.985602	+	0.169084i	$0.0540811\pi$
$740$		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
$747$	−0.241277			−0.00882785
$748$		0			0
$749$	19.7735	+	19.7735i	0.722506	+	0.722506i
$750$		0			0
$751$			33.6280i			1.22710i	0.789654	+	0.613552i	$0.210260\pi$
$751$			33.6280i			1.22710i	−0.789654	+	0.613552i	$0.789740\pi$
$752$		0			0
$753$	15.6566	−	15.6566i	0.570557	−	0.570557i
$754$		0			0
$755$	−5.65799	+	40.1577i	−0.205915	+	1.46149i
$756$		0			0
$757$			22.0813i			0.802560i	0.915955	+	0.401280i	$0.131435\pi$
$757$			22.0813i			0.802560i	−0.915955	+	0.401280i	$0.868565\pi$
$758$		0			0
$759$			4.59407i			0.166754i
$760$		0			0
$761$			0.186655i			0.00676626i	0.999994	+	0.00338313i	$0.00107689\pi$
$761$			0.186655i			0.00676626i	−0.999994	+	0.00338313i	$0.998923\pi$
$762$		0			0
$763$		−	44.0859i		−	1.59602i
$764$		0			0
$765$	−6.80545	+	5.12458i	−0.246052	+	0.185280i
$766$		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
$773$	−3.95359			−0.142201			−0.0711003	−	0.997469i	$-0.522651\pi$
$773$	−3.95359			−0.142201			−0.0711003	+	0.997469i	$0.522651\pi$
$774$		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
$787$			25.3395i			0.903255i	0.892207	+	0.451628i	$0.149156\pi$
$787$			25.3395i			0.903255i	−0.892207	+	0.451628i	$0.850844\pi$
$788$		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
$795$	−0.752691	+	5.34225i	−0.0266952	+	0.189470i
$796$		0			0
$797$	−40.2492			−1.42570			−0.712849	−	0.701317i	$-0.752596\pi$
$797$	−40.2492			−1.42570			−0.712849	+	0.701317i	$0.752596\pi$
$798$		0			0
$799$	25.1453			0.889576
$800$		0			0
$801$	2.86287			0.101155
$802$		0			0
$803$	−2.83632			−0.100092
$804$		0			0
$805$	3.23717	−	22.9759i	0.114095	−	0.809795i
$806$		0			0
$807$	5.49337	+	5.49337i	0.193376	+	0.193376i
$808$		0			0
$809$	10.5847			0.372137			0.186069	−	0.982537i	$-0.440425\pi$
$809$	10.5847			0.372137			0.186069	+	0.982537i	$0.440425\pi$
$810$		0			0
$811$	14.0997	−	14.0997i	0.495109	−	0.495109i	−0.414803	−	0.909911i	$-0.636149\pi$
$811$	14.0997	−	14.0997i	0.495109	−	0.495109i	0.909911	+	0.414803i	$0.136149\pi$
$812$		0			0
$813$			29.9569i			1.05063i
$814$		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	$-0.341008\pi$
$821$	−11.4283	−	11.4283i	−0.398851	−	0.398851i	−0.877828	+	0.478977i	$0.841008\pi$
$822$		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
$827$	−24.8187			−0.863032			−0.431516	−	0.902105i	$-0.642021\pi$
$827$	−24.8187			−0.863032			−0.431516	+	0.902105i	$0.642021\pi$
$828$		0			0
$829$	−7.79087	−	7.79087i	−0.270588	−	0.270588i	0.558749	−	0.829337i	$-0.311282\pi$
$829$	−7.79087	−	7.79087i	−0.270588	−	0.270588i	−0.829337	+	0.558749i	$0.811282\pi$
$830$		0			0
$831$			7.29980i			0.253227i
$832$		0			0
$833$	−1.96672	+	1.96672i	−0.0681428	+	0.0681428i
$834$		0			0
$835$	0.0428261	−	0.0322485i	0.00148206	−	0.00111601i
$836$		0			0
$837$		−	7.72239i		−	0.266925i
$838$		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
$843$		−	9.84488i		−	0.339076i
$844$		0			0
$845$	6.74065	−	47.8419i	0.231885	−	1.64581i
$846$		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
$853$	−5.84193			−0.200024			−0.100012	−	0.994986i	$-0.531888\pi$
$853$	−5.84193			−0.200024			−0.100012	+	0.994986i	$0.531888\pi$
$854$		0			0
$855$	−4.56605	−	6.06373i	−0.156156	−	0.207375i
$856$		0			0
$857$	−26.9251	+	26.9251i	−0.919745	+	0.919745i	−0.997011	−	0.0772652i	$-0.975381\pi$
$857$	−26.9251	+	26.9251i	−0.919745	+	0.919745i	0.0772652	+	0.997011i	$0.475381\pi$
$858$		0			0
$859$	2.05019	+	2.05019i	0.0699516	+	0.0699516i	0.741217	−	0.671265i	$-0.234249\pi$
$859$	2.05019	+	2.05019i	0.0699516	+	0.0699516i	−0.671265	+	0.741217i	$0.734249\pi$
$860$		0			0
$861$	9.53244	−	9.53244i	0.324865	−	0.324865i
$862$		0			0
$863$	18.1091	+	18.1091i	0.616443	+	0.616443i	0.944617	−	0.328175i	$-0.106433\pi$
$863$	18.1091	+	18.1091i	0.616443	+	0.616443i	−0.328175	+	0.944617i	$0.606433\pi$
$864$		0			0
$865$	−7.61532	−	1.07295i	−0.258929	−	0.0364815i
$866$		0			0
$867$		−	2.48490i		−	0.0843916i
$868$		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
$875$	29.0316	−	11.1096i	0.981446	−	0.375572i
$876$		0			0
$877$	47.2518			1.59558			0.797791	−	0.602934i	$-0.206002\pi$
$877$	47.2518			1.59558			0.797791	+	0.602934i	$0.206002\pi$
$878$		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
$883$	−46.1246			−1.55222			−0.776109	−	0.630599i	$-0.782809\pi$
$883$	−46.1246			−1.55222			−0.776109	+	0.630599i	$0.782809\pi$
$884$		0			0
$885$	−16.3559	+	12.3162i	−0.549797	+	0.414003i
$886$		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
$893$			22.4047i			0.749745i
$894$		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
$907$	25.0169			0.830671			0.415336	−	0.909668i	$-0.363664\pi$
$907$	25.0169			0.830671			0.415336	+	0.909668i	$0.363664\pi$
$908$		0			0
$909$	−6.90372	−	6.90372i	−0.228982	−	0.228982i
$910$		0			0
$911$		−	5.76809i		−	0.191105i	−0.995424	−	0.0955527i	$-0.969538\pi$
$911$		−	5.76809i		−	0.191105i	0.995424	−	0.0955527i	$-0.0304618\pi$
$912$		0			0
$913$	−0.210006	+	0.210006i	−0.00695019	+	0.00695019i
$914$		0			0
$915$	−16.1843	−	21.4928i	−0.535038	−	0.710531i
$916$		0			0
$917$			35.4782i			1.17159i
$918$		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
$923$			78.3668i			2.57947i
$924$		0			0
$925$	6.20310	−	21.5764i	0.203957	−	0.709426i
$926$		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
$933$	−12.2337			−0.400512
$934$		0			0
$935$	−1.46302	+	10.3839i	−0.0478460	+	0.339588i
$936$		0			0
$937$	−7.20557	+	7.20557i	−0.235396	+	0.235396i	−0.814940	−	0.579545i	$-0.803230\pi$
$937$	−7.20557	+	7.20557i	−0.235396	+	0.235396i	0.579545	+	0.814940i	$0.303230\pi$
$938$		0			0
$939$	10.9229	+	10.9229i	0.356456	+	0.356456i
$940$		0			0
$941$	36.0800	−	36.0800i	1.17617	−	1.17617i	0.195464	−	0.980711i	$-0.437379\pi$
$941$	36.0800	−	36.0800i	1.17617	−	1.17617i	0.980711	−	0.195464i	$-0.0626212\pi$
$942$		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
$947$		−	27.2599i		−	0.885828i	−0.896564	−	0.442914i	$-0.853945\pi$
$947$		−	27.2599i		−	0.885828i	0.896564	−	0.442914i	$-0.146055\pi$
$948$		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	0.930353	−	0.366666i	$-0.119501\pi$
$953$	17.4014	+	17.4014i	0.563687	+	0.563687i	−0.366666	+	0.930353i	$0.619501\pi$
$954$		0			0
$955$	−1.18741	−	0.167299i	−0.0384236	−	0.00541365i
$956$		0			0
$957$	−12.9453			−0.418463
$958$		0			0
$959$	−31.9646			−1.03219
$960$		0			0
$961$	−28.6353			−0.923721
$962$		0			0
$963$	10.0579			0.324111
$964$		0			0
$965$	−14.6655	−	19.4758i	−0.472099	−	0.626948i
$966$		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	$-0.555811\pi$
$971$	25.2474	−	25.2474i	0.810229	−	0.810229i	0.984668	+	0.174439i	$0.0558112\pi$
$972$		0			0
$973$			11.7405i			0.376382i
$974$		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
$987$	18.3501			0.584089
$988$		0			0
$989$	−1.21687	−	1.21687i	−0.0386942	−	0.0386942i
$990$		0			0
$991$		−	35.7662i		−	1.13615i	−0.822977	−	0.568075i	$-0.807688\pi$
$991$		−	35.7662i		−	1.13615i	0.822977	−	0.568075i	$-0.192312\pi$
$992$		0			0
$993$	−21.2143	+	21.2143i	−0.673215	+	0.673215i
$994$		0			0
$995$	20.6577	+	2.91054i	0.654892	+	0.0922704i
$996$		0			0
$997$		−	53.1029i		−	1.68178i	−0.541203	−	0.840892i	$-0.682031\pi$
$997$		−	53.1029i		−	1.68178i	0.541203	−	0.840892i	$-0.317969\pi$
$998$		0			0
$999$			4.49007i			0.142059i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.2	✓	16	80.53	odd	4
240.2.y.e.187.2	yes	16	8.3	odd	2
240.2.bc.e.43.6	yes	16	40.3	even	4
240.2.bc.e.67.6	yes	16	16.5	even	4
720.2.z.f.163.7		16	240.53	even	4
720.2.z.f.667.7		16	24.11	even	2
720.2.bd.f.307.3		16	48.5	odd	4
720.2.bd.f.523.3		16	120.83	odd	4
960.2.y.e.847.5		16	8.5	even	2
960.2.y.e.943.5		16	80.43	even	4
960.2.bc.e.367.1		16	16.11	odd	4
960.2.bc.e.463.1		16	40.13	odd	4
1920.2.y.i.223.4		16	80.13	odd	4
1920.2.y.i.1567.4		16	4.3	odd	2
1920.2.y.j.223.4		16	80.3	even	4	inner
1920.2.y.j.1567.4		16	1.1	even	1	trivial
1920.2.bc.i.607.8		16	16.13	even	4
1920.2.bc.i.1183.8		16	20.3	even	4
1920.2.bc.j.607.8		16	16.3	odd	4
1920.2.bc.j.1183.8		16	5.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-0.311968 + 2.21420i) q^{5} +(1.96597 + 1.96597i) q^{7} +1.00000 q^{9} +(0.870396 - 0.870396i) q^{11} +5.88276i q^{13} +(-0.311968 + 2.21420i) q^{15} +(2.69398 + 2.69398i) q^{17} +(-2.40037 + 2.40037i) q^{19} +(1.96597 + 1.96597i) q^{21} +(-2.63907 + 2.63907i) q^{23} +(-4.80535 - 1.38152i) q^{25} +1.00000 q^{27} +(-7.43646 - 7.43646i) q^{29} -7.72239i q^{31} +(0.870396 - 0.870396i) q^{33} +(-4.96636 + 3.73972i) q^{35} +4.49007i q^{37} +5.88276i q^{39} -4.84873i q^{41} +0.461098i q^{43} +(-0.311968 + 2.21420i) q^{45} +(4.66693 - 4.66693i) q^{47} +0.730041i q^{49} +(2.69398 + 2.69398i) q^{51} +2.41272 q^{53} +(1.65569 + 2.19876i) q^{55} +(-2.40037 + 2.40037i) q^{57} +(6.47458 + 6.47458i) q^{59} +(-8.50808 + 8.50808i) q^{61} +(1.96597 + 1.96597i) q^{63} +(-13.0256 - 1.83523i) q^{65} +6.40870i q^{67} +(-2.63907 + 2.63907i) q^{69} +13.3214 q^{71} +(-1.62933 - 1.62933i) q^{73} +(-4.80535 - 1.38152i) q^{75} +3.42234 q^{77} +4.14482 q^{79} +1.00000 q^{81} -0.241277 q^{83} +(-6.80545 + 5.12458i) q^{85} +(-7.43646 - 7.43646i) q^{87} +2.86287 q^{89} +(-11.5653 + 11.5653i) q^{91} -7.72239i q^{93} +(-4.56605 - 6.06373i) q^{95} +(3.18909 + 3.18909i) q^{97} +(0.870396 - 0.870396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 4 q^{5} + 4 q^{7} + 16 q^{9} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} + 32 q^{25} + 16 q^{27} - 12 q^{29} - 20 q^{35} + 4 q^{45} + 32 q^{47} - 8 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) \) 16 * q + 16 * q^3 + 4 * q^5 + 4 * q^7 + 16 * q^9 + 4 * q^15 - 8 * q^17 + 8 * q^19 + 4 * q^21 + 32 * q^25 + 16 * q^27 - 12 * q^29 - 20 * q^35 + 4 * q^45 + 32 * q^47 - 8 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 24 * q^59 - 40 * q^61 + 4 * q^63 - 4 * q^65 + 8 * q^73 + 32 * q^75 + 72 * q^77 + 48 * q^79 + 16 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^87 - 40 * q^91 - 8 * q^95 + 48 * q^97

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