LMFDB - Embedded newform 560.2.x.a.463.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(127,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.x (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.1
Root			$1.19252 + 0.760198i$ of defining polynomial
Character	$\chi$	$=$	560.463
Dual form			560.2.x.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95272 + 1.95272i) q^{3} +(0.432320 - 2.19388i) q^{5} +(-0.707107 - 0.707107i) q^{7} -4.62620i q^{9} +O(q^{10})$	\(q+(-1.95272 + 1.95272i) q^{3} +(0.432320 - 2.19388i) q^{5} +(-0.707107 - 0.707107i) q^{7} -4.62620i q^{9} +1.68840i q^{11} +(4.19388 + 4.19388i) q^{13} +(3.43982 + 5.12822i) q^{15} +(-1.32924 + 1.32924i) q^{17} +6.35101 q^{19} +2.76156 q^{21} +(-5.12822 + 5.12822i) q^{23} +(-4.62620 - 1.89692i) q^{25} +(3.17550 + 3.17550i) q^{27} +5.35548i q^{29} -0.528636i q^{31} +(-3.29696 - 3.29696i) q^{33} +(-1.85700 + 1.24561i) q^{35} +(-5.76156 + 5.76156i) q^{37} -16.3789 q^{39} +0.658473 q^{41} +(2.91118 - 2.91118i) q^{43} +(-10.1493 - 2.00000i) q^{45} +(8.83236 + 8.83236i) q^{47} +1.00000i q^{49} -5.19124i q^{51} +(7.38776 + 7.38776i) q^{53} +(3.70414 + 0.729929i) q^{55} +(-12.4017 + 12.4017i) q^{57} -2.97421 q^{59} +8.77551 q^{61} +(-3.27122 + 3.27122i) q^{63} +(11.0140 - 7.38776i) q^{65} +(4.37104 + 4.37104i) q^{67} -20.0279i q^{69} -7.81086i q^{71} +(-0.896916 - 0.896916i) q^{73} +(12.7378 - 5.32951i) q^{75} +(1.19388 - 1.19388i) q^{77} -13.0021 q^{79} +1.47689 q^{81} +(-5.65685 + 5.65685i) q^{83} +(2.34153 + 3.49084i) q^{85} +(-10.4577 - 10.4577i) q^{87} +6.27072i q^{89} -5.93104i q^{91} +(1.03228 + 1.03228i) q^{93} +(2.74567 - 13.9333i) q^{95} +(10.3109 - 10.3109i) q^{97} +7.81086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 20 q^{13} + 4 q^{17} + 8 q^{21} - 20 q^{25} - 24 q^{33} - 44 q^{37} - 32 q^{41} - 36 q^{45} + 28 q^{53} + 8 q^{57} - 16 q^{61} + 36 q^{65} + 4 q^{73} - 16 q^{77} + 68 q^{81} + 68 q^{85} + 8 q^{93} + 12 q^{97}+O(q^{100}) $ 12 * q + 20 * q^13 + 4 * q^17 + 8 * q^21 - 20 * q^25 - 24 * q^33 - 44 * q^37 - 32 * q^41 - 36 * q^45 + 28 * q^53 + 8 * q^57 - 16 * q^61 + 36 * q^65 + 4 * q^73 - 16 * q^77 + 68 * q^81 + 68 * q^85 + 8 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.95272	+	1.95272i	−1.12740	+	1.12740i	−0.136803	+	0.990598i	$0.543683\pi$
$3$	−1.95272	+	1.95272i	−1.12740	+	1.12740i	−0.990598	+	0.136803i	$0.956317\pi$
$4$		0			0
$5$	0.432320	−	2.19388i	0.193340	−	0.981132i
$5$	0.432320	−	2.19388i	0.193340	−	0.981132i
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$		−	4.62620i		−	1.54207i
$10$		0			0
$11$			1.68840i			0.509071i	0.967063	+	0.254536i	$0.0819226\pi$
$11$			1.68840i			0.509071i	−0.967063	+	0.254536i	$0.918077\pi$
$12$		0			0
$13$	4.19388	+	4.19388i	1.16317	+	1.16317i	0.983777	+	0.179395i	$0.0574141\pi$
$13$	4.19388	+	4.19388i	1.16317	+	1.16317i	0.179395	+	0.983777i	$0.442586\pi$
$14$		0			0
$15$	3.43982	+	5.12822i	0.888158	+	1.32410i
$16$		0			0
$17$	−1.32924	+	1.32924i	−0.322387	+	0.322387i	−0.849682	−	0.527295i	$-0.823206\pi$
$17$	−1.32924	+	1.32924i	−0.322387	+	0.322387i	0.527295	+	0.849682i	$0.323206\pi$
$18$		0			0
$19$	6.35101			1.45702			0.728510	−	0.685035i	$-0.240213\pi$
$19$	6.35101			1.45702			0.728510	+	0.685035i	$0.240213\pi$
$20$		0			0
$21$	2.76156			0.602621
$22$		0			0
$23$	−5.12822	+	5.12822i	−1.06931	+	1.06931i	−0.0718953	+	0.997412i	$0.522905\pi$
$23$	−5.12822	+	5.12822i	−1.06931	+	1.06931i	−0.997412	+	0.0718953i	$0.977095\pi$
$24$		0			0
$25$	−4.62620	−	1.89692i	−0.925240	−	0.379383i
$26$		0			0
$27$	3.17550	+	3.17550i	0.611126	+	0.611126i
$28$		0			0
$29$			5.35548i			0.994488i	0.867611	+	0.497244i	$0.165655\pi$
$29$			5.35548i			0.994488i	−0.867611	+	0.497244i	$0.834345\pi$
$30$		0			0
$31$		−	0.528636i		−	0.0949458i	−0.998873	−	0.0474729i	$-0.984883\pi$
$31$		−	0.528636i		−	0.0949458i	0.998873	−	0.0474729i	$-0.0151168\pi$
$32$		0			0
$33$	−3.29696	−	3.29696i	−0.573927	−	0.573927i
$34$		0			0
$35$	−1.85700	+	1.24561i	−0.313891	+	0.210546i
$36$		0			0
$37$	−5.76156	+	5.76156i	−0.947194	+	0.947194i	−0.998674	−	0.0514799i	$-0.983606\pi$
$37$	−5.76156	+	5.76156i	−0.947194	+	0.947194i	0.0514799	+	0.998674i	$0.483606\pi$
$38$		0			0
$39$	−16.3789			−2.62272
$40$		0			0
$41$	0.658473			0.102836			0.0514181	−	0.998677i	$-0.483626\pi$
$41$	0.658473			0.102836			0.0514181	+	0.998677i	$0.483626\pi$
$42$		0			0
$43$	2.91118	−	2.91118i	0.443952	−	0.443952i	−0.449386	−	0.893338i	$-0.648357\pi$
$43$	2.91118	−	2.91118i	0.443952	−	0.443952i	0.893338	+	0.449386i	$0.148357\pi$
$44$		0			0
$45$	−10.1493	−	2.00000i	−1.51297	−	0.298142i
$46$		0			0
$47$	8.83236	+	8.83236i	1.28833	+	1.28833i	0.935800	+	0.352532i	$0.114679\pi$
$47$	8.83236	+	8.83236i	1.28833	+	1.28833i	0.352532	+	0.935800i	$0.385321\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		−	5.19124i		−	0.726919i
$52$		0			0
$53$	7.38776	+	7.38776i	1.01479	+	1.01479i	0.999889	+	0.0148972i	$0.00474210\pi$
$53$	7.38776	+	7.38776i	1.01479	+	1.01479i	0.0148972	+	0.999889i	$0.495258\pi$
$54$		0			0
$55$	3.70414	+	0.729929i	0.499466	+	0.0984236i
$56$		0			0
$57$	−12.4017	+	12.4017i	−1.64265	+	1.64265i
$58$		0			0
$59$	−2.97421			−0.387209			−0.193605	−	0.981080i	$-0.562018\pi$
$59$	−2.97421			−0.387209			−0.193605	+	0.981080i	$0.562018\pi$
$60$		0			0
$61$	8.77551			1.12359			0.561794	−	0.827277i	$-0.310111\pi$
$61$	8.77551			1.12359			0.561794	+	0.827277i	$0.310111\pi$
$62$		0			0
$63$	−3.27122	+	3.27122i	−0.412134	+	0.412134i
$64$		0			0
$65$	11.0140	−	7.38776i	1.36611	−	0.916338i
$66$		0			0
$67$	4.37104	+	4.37104i	0.534008	+	0.534008i	0.921763	−	0.387755i	$-0.126749\pi$
$67$	4.37104	+	4.37104i	0.534008	+	0.534008i	−0.387755	+	0.921763i	$0.626749\pi$
$68$		0			0
$69$		−	20.0279i		−	2.41108i
$70$		0			0
$71$		−	7.81086i		−	0.926979i	−0.886102	−	0.463489i	$-0.846597\pi$
$71$		−	7.81086i		−	0.926979i	0.886102	−	0.463489i	$-0.153403\pi$
$72$		0			0
$73$	−0.896916	−	0.896916i	−0.104976	−	0.104976i	0.652668	−	0.757644i	$-0.273650\pi$
$73$	−0.896916	−	0.896916i	−0.104976	−	0.104976i	−0.757644	+	0.652668i	$0.773650\pi$
$74$		0			0
$75$	12.7378	−	5.32951i	1.47083	−	0.615399i
$76$		0			0
$77$	1.19388	−	1.19388i	0.136055	−	0.136055i
$78$		0			0
$79$	−13.0021			−1.46285			−0.731426	−	0.681921i	$-0.761145\pi$
$79$	−13.0021			−1.46285			−0.731426	+	0.681921i	$0.761145\pi$
$80$		0			0
$81$	1.47689			0.164098
$82$		0			0
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	−0.945767	−	0.324846i	$-0.894687\pi$
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	0.324846	+	0.945767i	$0.394687\pi$
$84$		0			0
$85$	2.34153	+	3.49084i	0.253974	+	0.378635i
$86$		0			0
$87$	−10.4577	−	10.4577i	−1.12119	−	1.12119i
$88$		0			0
$89$			6.27072i			0.664695i	0.943157	+	0.332347i	$0.107841\pi$
$89$			6.27072i			0.664695i	−0.943157	+	0.332347i	$0.892159\pi$
$90$		0			0
$91$		−	5.93104i		−	0.621742i
$92$		0			0
$93$	1.03228	+	1.03228i	0.107042	+	0.107042i
$94$		0			0
$95$	2.74567	−	13.9333i	0.281700	−	1.42953i
$96$		0			0
$97$	10.3109	−	10.3109i	1.04691	−	1.04691i	0.0480708	−	0.998844i	$-0.484693\pi$
$97$	10.3109	−	10.3109i	1.04691	−	1.04691i	0.998844	−	0.0480708i	$-0.0153073\pi$
$98$		0			0
$99$	7.81086			0.785021
$100$		0			0
$101$	−0.387755			−0.0385831			−0.0192915	−	0.999814i	$-0.506141\pi$
$101$	−0.387755			−0.0385831			−0.0192915	+	0.999814i	$0.506141\pi$
$102$		0			0
$103$	5.32951	−	5.32951i	0.525132	−	0.525132i	−0.393985	−	0.919117i	$-0.628904\pi$
$103$	5.32951	−	5.32951i	0.525132	−	0.525132i	0.919117	+	0.393985i	$0.128904\pi$
$104$		0			0
$105$	1.19388	−	6.05852i	0.116511	−	0.591251i
$106$		0			0
$107$	−2.91118	−	2.91118i	−0.281435	−	0.281435i	0.552246	−	0.833681i	$-0.313771\pi$
$107$	−2.91118	−	2.91118i	−0.281435	−	0.281435i	−0.833681	+	0.552246i	$0.813771\pi$
$108$		0			0
$109$			3.14931i			0.301649i	0.988561	+	0.150825i	$0.0481929\pi$
$109$			3.14931i			0.301649i	−0.988561	+	0.150825i	$0.951807\pi$
$110$		0			0
$111$		−	22.5014i		−	2.13574i
$112$		0			0
$113$	−7.55539	−	7.55539i	−0.710751	−	0.710751i	0.255941	−	0.966692i	$-0.417615\pi$
$113$	−7.55539	−	7.55539i	−0.710751	−	0.710751i	−0.966692	+	0.255941i	$0.917615\pi$
$114$		0			0
$115$	9.03365	+	13.4677i	0.842392	+	1.25587i
$116$		0			0
$117$	19.4017	−	19.4017i	1.79369	−	1.79369i
$118$		0			0
$119$	1.87982			0.172323
$120$		0			0
$121$	8.14931			0.740847
$122$		0			0
$123$	−1.28581	+	1.28581i	−0.115938	+	0.115938i
$124$		0			0
$125$	−6.16160	+	9.32924i	−0.551110	+	0.834432i
$126$		0			0
$127$	3.43982	+	3.43982i	0.305235	+	0.305235i	0.843058	−	0.537823i	$-0.180753\pi$
$127$	3.43982	+	3.43982i	0.305235	+	0.305235i	−0.537823	+	0.843058i	$0.680753\pi$
$128$		0			0
$129$			11.3694i			1.00102i
$130$		0			0
$131$		−	6.87964i		−	0.601077i	−0.953770	−	0.300539i	$-0.902834\pi$
$131$		−	6.87964i		−	0.601077i	0.953770	−	0.300539i	$-0.0971664\pi$
$132$		0			0
$133$	−4.49084	−	4.49084i	−0.389405	−	0.389405i
$134$		0			0
$135$	8.33950	−	5.59383i	0.717750	−	0.481440i
$136$		0			0
$137$	−6.62620	+	6.62620i	−0.566114	+	0.566114i	−0.931038	−	0.364923i	$-0.881095\pi$
$137$	−6.62620	+	6.62620i	−0.566114	+	0.566114i	0.364923	+	0.931038i	$0.381095\pi$
$138$		0			0
$139$	18.9985			1.61143			0.805717	−	0.592301i	$-0.201780\pi$
$139$	18.9985			1.61143			0.805717	+	0.592301i	$0.201780\pi$
$140$		0			0
$141$	−34.4942			−2.90493
$142$		0			0
$143$	−7.08093	+	7.08093i	−0.592137	+	0.592137i
$144$		0			0
$145$	11.7493	+	2.31528i	0.975724	+	0.192274i
$146$		0			0
$147$	−1.95272	−	1.95272i	−0.161057	−	0.161057i
$148$		0			0
$149$		−	3.52311i		−	0.288625i	−0.989532	−	0.144312i	$-0.953903\pi$
$149$		−	3.52311i		−	0.288625i	0.989532	−	0.144312i	$-0.0460970\pi$
$150$		0			0
$151$		−	3.20275i		−	0.260636i	−0.991472	−	0.130318i	$-0.958400\pi$
$151$		−	3.20275i		−	0.260636i	0.991472	−	0.130318i	$-0.0415998\pi$
$152$		0			0
$153$	6.14931	+	6.14931i	0.497142	+	0.497142i
$154$		0			0
$155$	−1.15976	−	0.228540i	−0.0931543	−	0.0183568i
$156$		0			0
$157$	−8.08476	+	8.08476i	−0.645234	+	0.645234i	−0.951837	−	0.306603i	$-0.900808\pi$
$157$	−8.08476	+	8.08476i	−0.645234	+	0.645234i	0.306603	+	0.951837i	$0.400808\pi$
$158$		0			0
$159$	−28.8524			−2.28814
$160$		0			0
$161$	7.25240			0.571569
$162$		0			0
$163$	8.50501	−	8.50501i	0.666164	−	0.666164i	−0.290662	−	0.956826i	$-0.593875\pi$
$163$	8.50501	−	8.50501i	0.666164	−	0.666164i	0.956826	+	0.290662i	$0.0938754\pi$
$164$		0			0
$165$	−8.65847	+	5.80779i	−0.674061	+	0.452136i
$166$		0			0
$167$	−15.5859	−	15.5859i	−1.20608	−	1.20608i	−0.972287	−	0.233790i	$-0.924887\pi$
$167$	−15.5859	−	15.5859i	−1.20608	−	1.20608i	−0.233790	−	0.972287i	$-0.575113\pi$
$168$		0			0
$169$			22.1772i			1.70594i
$170$		0			0
$171$		−	29.3810i		−	2.24682i
$172$		0			0
$173$	−5.80612	−	5.80612i	−0.441431	−	0.441431i	0.451062	−	0.892493i	$-0.351045\pi$
$173$	−5.80612	−	5.80612i	−0.441431	−	0.441431i	−0.892493	+	0.451062i	$0.851045\pi$
$174$		0			0
$175$	1.92989	+	4.61254i	0.145886	+	0.348675i
$176$		0			0
$177$	5.80779	−	5.80779i	0.436540	−	0.436540i
$178$		0			0
$179$	−20.9870			−1.56864			−0.784322	−	0.620354i	$-0.786989\pi$
$179$	−20.9870			−1.56864			−0.784322	+	0.620354i	$0.786989\pi$
$180$		0			0
$181$	−5.13536			−0.381708			−0.190854	−	0.981618i	$-0.561126\pi$
$181$	−5.13536			−0.381708			−0.190854	+	0.981618i	$0.561126\pi$
$182$		0			0
$183$	−17.1361	+	17.1361i	−1.26674	+	1.26674i
$184$		0			0
$185$	10.1493	+	15.1310i	0.746192	+	1.11245i
$186$		0			0
$187$	−2.24428	−	2.24428i	−0.164118	−	0.164118i
$188$		0			0
$189$		−	4.49084i		−	0.326660i
$190$		0			0
$191$			11.0136i			0.796917i	0.917186	+	0.398459i	$0.130455\pi$
$191$			11.0136i			0.796917i	−0.917186	+	0.398459i	$0.869545\pi$
$192$		0			0
$193$	−13.1955	−	13.1955i	−0.949836	−	0.949836i	0.0489647	−	0.998801i	$-0.484408\pi$
$193$	−13.1955	−	13.1955i	−0.949836	−	0.949836i	−0.998801	+	0.0489647i	$0.984408\pi$
$194$		0			0
$195$	−7.08093	+	35.9333i	−0.507076	+	2.57324i
$196$		0			0
$197$	−0.640151	+	0.640151i	−0.0456089	+	0.0456089i	−0.729543	−	0.683935i	$-0.760267\pi$
$197$	−0.640151	+	0.640151i	−0.0456089	+	0.0456089i	0.683935	+	0.729543i	$0.260267\pi$
$198$		0			0
$199$	25.3495			1.79698			0.898490	−	0.438994i	$-0.144665\pi$
$199$	25.3495			1.79698			0.898490	+	0.438994i	$0.144665\pi$
$200$		0			0
$201$	−17.0708			−1.20408
$202$		0			0
$203$	3.78690	−	3.78690i	0.265788	−	0.265788i
$204$		0			0
$205$	0.284672	−	1.44461i	0.0198823	−	0.100896i
$206$		0			0
$207$	23.7242	+	23.7242i	1.64894	+	1.64894i
$208$		0			0
$209$			10.7230i			0.741727i
$210$		0			0
$211$		−	19.8817i		−	1.36872i	−0.729146	−	0.684358i	$-0.760083\pi$
$211$		−	19.8817i		−	1.36872i	0.729146	−	0.684358i	$-0.239917\pi$
$212$		0			0
$213$	15.2524	+	15.2524i	1.04508	+	1.04508i
$214$		0			0
$215$	−5.12822	−	7.64535i	−0.349742	−	0.521408i
$216$		0			0
$217$	−0.373802	+	0.373802i	−0.0253753	+	0.0253753i
$218$		0			0
$219$	3.50285			0.236700
$220$		0			0
$221$	−11.1493			−0.749984
$222$		0			0
$223$	−2.88394	+	2.88394i	−0.193123	+	0.193123i	−0.797044	−	0.603921i	$-0.793604\pi$
$223$	−2.88394	+	2.88394i	−0.193123	+	0.193123i	0.603921	+	0.797044i	$0.293604\pi$
$224$		0			0
$225$	−8.77551	+	21.4017i	−0.585034	+	1.42678i
$226$		0			0
$227$	10.7493	+	10.7493i	0.713456	+	0.713456i	0.967257	−	0.253801i	$-0.0816808\pi$
$227$	10.7493	+	10.7493i	0.713456	+	0.713456i	−0.253801	+	0.967257i	$0.581681\pi$
$228$		0			0
$229$		−	12.8925i		−	0.851964i	−0.904732	−	0.425982i	$-0.859929\pi$
$229$		−	12.8925i		−	0.851964i	0.904732	−	0.425982i	$-0.140071\pi$
$230$		0			0
$231$			4.66261i			0.306777i
$232$		0			0
$233$	−7.67243	−	7.67243i	−0.502637	−	0.502637i	0.409619	−	0.912257i	$-0.365662\pi$
$233$	−7.67243	−	7.67243i	−0.502637	−	0.502637i	−0.912257	+	0.409619i	$0.865662\pi$
$234$		0			0
$235$	23.1955	−	15.5587i	1.51311	−	1.01494i
$236$		0			0
$237$	25.3894	−	25.3894i	1.64922	−	1.64922i
$238$		0			0
$239$	−9.62531			−0.622610			−0.311305	−	0.950310i	$-0.600766\pi$
$239$	−9.62531			−0.622610			−0.311305	+	0.950310i	$0.600766\pi$
$240$		0			0
$241$	−8.56934			−0.552000			−0.276000	−	0.961158i	$-0.589009\pi$
$241$	−8.56934			−0.552000			−0.276000	+	0.961158i	$0.589009\pi$
$242$		0			0
$243$	−12.4104	+	12.4104i	−0.796130	+	0.796130i
$244$		0			0
$245$	2.19388	+	0.432320i	0.140162	+	0.0276199i
$246$		0			0
$247$	26.6353	+	26.6353i	1.69477	+	1.69477i
$248$		0			0
$249$		−	22.0925i		−	1.40005i
$250$		0			0
$251$			5.82237i			0.367505i	0.982973	+	0.183752i	$0.0588244\pi$
$251$			5.82237i			0.367505i	−0.982973	+	0.183752i	$0.941176\pi$
$252$		0			0
$253$	−8.65847	−	8.65847i	−0.544354	−	0.544354i
$254$		0			0
$255$	−11.3890	−	2.24428i	−0.713204	−	0.140542i
$256$		0			0
$257$	20.1493	−	20.1493i	1.25688	−	1.25688i	0.304305	−	0.952575i	$-0.401576\pi$
$257$	20.1493	−	20.1493i	1.25688	−	1.25688i	0.952575	−	0.304305i	$-0.0984242\pi$
$258$		0			0
$259$	8.14807			0.506297
$260$		0			0
$261$	24.7755			1.53357
$262$		0			0
$263$	22.0358	−	22.0358i	1.35878	−	1.35878i	0.483363	−	0.875420i	$-0.339415\pi$
$263$	22.0358	−	22.0358i	1.35878	−	1.35878i	0.875420	−	0.483363i	$-0.160585\pi$
$264$		0			0
$265$	19.4017	−	13.0140i	1.19184	−	0.799441i
$266$		0			0
$267$	−12.2449	−	12.2449i	−0.749378	−	0.749378i
$268$		0			0
$269$		−	6.00000i		−	0.365826i	−0.983129	−	0.182913i	$-0.941447\pi$
$269$		−	6.00000i		−	0.365826i	0.983129	−	0.182913i	$-0.0585527\pi$
$270$		0			0
$271$			32.6318i			1.98224i	0.132978	+	0.991119i	$0.457546\pi$
$271$			32.6318i			1.98224i	−0.132978	+	0.991119i	$0.542454\pi$
$272$		0			0
$273$	11.5816	+	11.5816i	0.700952	+	0.700952i
$274$		0			0
$275$	3.20275	−	7.81086i	0.193133	−	0.471013i
$276$		0			0
$277$	−6.03228	+	6.03228i	−0.362444	+	0.362444i	−0.864712	−	0.502268i	$-0.832499\pi$
$277$	−6.03228	+	6.03228i	−0.362444	+	0.362444i	0.502268	+	0.864712i	$0.332499\pi$
$278$		0			0
$279$	−2.44557			−0.146413
$280$		0			0
$281$	5.56165			0.331780			0.165890	−	0.986144i	$-0.446950\pi$
$281$	5.56165			0.331780			0.165890	+	0.986144i	$0.446950\pi$
$282$		0			0
$283$	−17.1719	+	17.1719i	−1.02076	+	1.02076i	−0.0209810	+	0.999780i	$0.506679\pi$
$283$	−17.1719	+	17.1719i	−1.02076	+	1.02076i	−0.999780	+	0.0209810i	$0.993321\pi$
$284$		0			0
$285$	21.8463	+	32.5693i	1.29406	+	1.92924i
$286$		0			0
$287$	−0.465611	−	0.465611i	−0.0274842	−	0.0274842i
$288$		0			0
$289$			13.4663i			0.792133i
$290$		0			0
$291$			40.2686i			2.36059i
$292$		0			0
$293$	−18.4280	−	18.4280i	−1.07657	−	1.07657i	−0.996814	−	0.0797582i	$-0.974585\pi$
$293$	−18.4280	−	18.4280i	−1.07657	−	1.07657i	−0.0797582	−	0.996814i	$-0.525415\pi$
$294$		0			0
$295$	−1.28581	+	6.52505i	−0.0748628	+	0.379903i
$296$		0			0
$297$	−5.36151	+	5.36151i	−0.311106	+	0.311106i
$298$		0			0
$299$	−43.0142			−2.48758
$300$		0			0
$301$	−4.11704			−0.237302
$302$		0			0
$303$	0.757176	−	0.757176i	0.0434986	−	0.0434986i
$304$		0			0
$305$	3.79383	−	19.2524i	0.217234	−	1.10239i
$306$		0			0
$307$	−10.8209	−	10.8209i	−0.617579	−	0.617579i	0.327331	−	0.944910i	$-0.393851\pi$
$307$	−10.8209	−	10.8209i	−0.617579	−	0.617579i	−0.944910	+	0.327331i	$0.893851\pi$
$308$		0			0
$309$			20.8140i			1.18407i
$310$		0			0
$311$			10.9111i			0.618713i	0.950946	+	0.309356i	$0.100114\pi$
$311$			10.9111i			0.618713i	−0.950946	+	0.309356i	$0.899886\pi$
$312$		0			0
$313$	−14.3109	−	14.3109i	−0.808901	−	0.808901i	0.175567	−	0.984468i	$-0.443824\pi$
$313$	−14.3109	−	14.3109i	−0.808901	−	0.808901i	−0.984468	+	0.175567i	$0.943824\pi$
$314$		0			0
$315$	5.76243	+	8.59086i	0.324676	+	0.484040i
$316$		0			0
$317$	5.50479	−	5.50479i	0.309180	−	0.309180i	−0.535411	−	0.844591i	$-0.679843\pi$
$317$	5.50479	−	5.50479i	0.309180	−	0.309180i	0.844591	+	0.535411i	$0.179843\pi$
$318$		0			0
$319$	−9.04218			−0.506265
$320$		0			0
$321$	11.3694			0.634580
$322$		0			0
$323$	−8.44199	+	8.44199i	−0.469725	+	0.469725i
$324$		0			0
$325$	−11.4463	−	27.3571i	−0.634925	−	1.51750i
$326$		0			0
$327$	−6.14971	−	6.14971i	−0.340080	−	0.340080i
$328$		0			0
$329$		−	12.4908i		−	0.688642i
$330$		0			0
$331$			2.91972i			0.160482i	0.996775	+	0.0802410i	$0.0255690\pi$
$331$			2.91972i			0.160482i	−0.996775	+	0.0802410i	$0.974431\pi$
$332$		0			0
$333$	26.6541	+	26.6541i	1.46064	+	1.46064i
$334$		0			0
$335$	11.4792	−	7.69984i	0.627177	−	0.420687i
$336$		0			0
$337$	−1.01395	+	1.01395i	−0.0552336	+	0.0552336i	−0.734184	−	0.678950i	$-0.762435\pi$
$337$	−1.01395	+	1.01395i	−0.0552336	+	0.0552336i	0.678950	+	0.734184i	$0.262435\pi$
$338$		0			0
$339$	29.5071			1.60260
$340$		0			0
$341$	0.892548			0.0483342
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	−43.9388	−	8.65847i	−2.36558	−	0.466157i
$346$		0			0
$347$	13.9964	+	13.9964i	0.751364	+	0.751364i	0.974734	−	0.223370i	$-0.0717058\pi$
$347$	13.9964	+	13.9964i	0.751364	+	0.751364i	−0.223370	+	0.974734i	$0.571706\pi$
$348$		0			0
$349$			12.3232i			0.659646i	0.944043	+	0.329823i	$0.106989\pi$
$349$			12.3232i			0.659646i	−0.944043	+	0.329823i	$0.893011\pi$
$350$		0			0
$351$			26.6353i			1.42169i
$352$		0			0
$353$	−13.0585	−	13.0585i	−0.695035	−	0.695035i	0.268300	−	0.963335i	$-0.413538\pi$
$353$	−13.0585	−	13.0585i	−0.695035	−	0.695035i	−0.963335	+	0.268300i	$0.913538\pi$
$354$		0			0
$355$	−17.1361	−	3.37680i	−0.909489	−	0.179222i
$356$		0			0
$357$	−3.67076	+	3.67076i	−0.194277	+	0.194277i
$358$		0			0
$359$	−6.42256			−0.338970			−0.169485	−	0.985533i	$-0.554210\pi$
$359$	−6.42256			−0.338970			−0.169485	+	0.985533i	$0.554210\pi$
$360$		0			0
$361$	21.3353			1.12291
$362$		0			0
$363$	−15.9133	+	15.9133i	−0.835231	+	0.835231i
$364$		0			0
$365$	−2.35548	+	1.57997i	−0.123291	+	0.0826994i
$366$		0			0
$367$	0.895444	+	0.895444i	0.0467418	+	0.0467418i	0.730091	−	0.683350i	$-0.239477\pi$
$367$	0.895444	+	0.895444i	0.0467418	+	0.0467418i	−0.683350	+	0.730091i	$0.739477\pi$
$368$		0			0
$369$		−	3.04623i		−	0.158580i
$370$		0			0
$371$		−	10.4479i		−	0.542426i
$372$		0			0
$373$	20.6541	+	20.6541i	1.06943	+	1.06943i	0.997403	+	0.0720263i	$0.0229465\pi$
$373$	20.6541	+	20.6541i	1.06943	+	1.06943i	0.0720263	+	0.997403i	$0.477053\pi$
$374$		0			0
$375$	−6.18549	−	30.2492i	−0.319417	−	1.56206i
$376$		0			0
$377$	−22.4602	+	22.4602i	−1.15676	+	1.15676i
$378$		0			0
$379$	23.5586			1.21013			0.605063	−	0.796178i	$-0.293148\pi$
$379$	23.5586			1.21013			0.605063	+	0.796178i	$0.293148\pi$
$380$		0			0
$381$	−13.4340			−0.688244
$382$		0			0
$383$	6.58808	−	6.58808i	0.336635	−	0.336635i	−0.518464	−	0.855099i	$-0.673496\pi$
$383$	6.58808	−	6.58808i	0.336635	−	0.336635i	0.855099	+	0.518464i	$0.173496\pi$
$384$		0			0
$385$	−2.10308	−	3.13536i	−0.107183	−	0.159793i
$386$		0			0
$387$	−13.4677	−	13.4677i	−0.684603	−	0.684603i
$388$		0			0
$389$			26.2234i			1.32958i	0.747030	+	0.664791i	$0.231479\pi$
$389$			26.2234i			1.32958i	−0.747030	+	0.664791i	$0.768521\pi$
$390$		0			0
$391$		−	13.6332i		−	0.689462i
$392$		0			0
$393$	13.4340	+	13.4340i	0.677655	+	0.677655i
$394$		0			0
$395$	−5.62108	+	28.5250i	−0.282827	+	1.43525i
$396$		0			0
$397$	−7.35714	+	7.35714i	−0.369244	+	0.369244i	−0.867202	−	0.497957i	$-0.834084\pi$
$397$	−7.35714	+	7.35714i	−0.369244	+	0.369244i	0.497957	+	0.867202i	$0.334084\pi$
$398$		0			0
$399$	17.5387			0.878031
$400$		0			0
$401$	−8.33716			−0.416338			−0.208169	−	0.978093i	$-0.566750\pi$
$401$	−8.33716			−0.416338			−0.208169	+	0.978093i	$0.566750\pi$
$402$		0			0
$403$	2.21703	−	2.21703i	0.110438	−	0.110438i
$404$		0			0
$405$	0.638488	−	3.24011i	0.0317267	−	0.161002i
$406$		0			0
$407$	−9.72780	−	9.72780i	−0.482189	−	0.482189i
$408$		0			0
$409$		−	15.8463i		−	0.783550i	−0.920061	−	0.391775i	$-0.871861\pi$
$409$		−	15.8463i		−	0.783550i	0.920061	−	0.391775i	$-0.128139\pi$
$410$		0			0
$411$		−	25.8782i		−	1.27648i
$412$		0			0
$413$	2.10308	+	2.10308i	0.103486	+	0.103486i
$414$		0			0
$415$	9.96487	+	14.8560i	0.489156	+	0.729253i
$416$		0			0
$417$	−37.0987	+	37.0987i	−1.81673	+	1.81673i
$418$		0			0
$419$	13.7048			0.669523			0.334761	−	0.942303i	$-0.391344\pi$
$419$	13.7048			0.669523			0.334761	+	0.942303i	$0.391344\pi$
$420$		0			0
$421$	−13.7678			−0.671002			−0.335501	−	0.942040i	$-0.608906\pi$
$421$	−13.7678			−0.671002			−0.335501	+	0.942040i	$0.608906\pi$
$422$		0			0
$423$	40.8602	−	40.8602i	1.98669	−	1.98669i
$424$		0			0
$425$	8.67076	−	3.62786i	0.420594	−	0.175977i
$426$		0			0
$427$	−6.20522	−	6.20522i	−0.300292	−	0.300292i
$428$		0			0
$429$		−	27.6541i		−	1.33515i
$430$		0			0
$431$			22.8015i			1.09831i	0.835721	+	0.549154i	$0.185050\pi$
$431$			22.8015i			1.09831i	−0.835721	+	0.549154i	$0.814950\pi$
$432$		0			0
$433$	−8.98605	−	8.98605i	−0.431842	−	0.431842i	0.457413	−	0.889255i	$-0.348776\pi$
$433$	−8.98605	−	8.98605i	−0.431842	−	0.431842i	−0.889255	+	0.457413i	$0.848776\pi$
$434$		0			0
$435$	−27.4641	+	18.4219i	−1.31680	+	0.883262i
$436$		0			0
$437$	−32.5693	+	32.5693i	−1.55800	+	1.55800i
$438$		0			0
$439$	17.1361			0.817860			0.408930	−	0.912566i	$-0.365902\pi$
$439$	17.1361			0.817860			0.408930	+	0.912566i	$0.365902\pi$
$440$		0			0
$441$	4.62620			0.220295
$442$		0			0
$443$	10.2650	−	10.2650i	0.487703	−	0.487703i	−0.419877	−	0.907581i	$-0.637927\pi$
$443$	10.2650	−	10.2650i	0.487703	−	0.487703i	0.907581	+	0.419877i	$0.137927\pi$
$444$		0			0
$445$	13.7572	+	2.71096i	0.652153	+	0.128512i
$446$		0			0
$447$	6.87964	+	6.87964i	0.325396	+	0.325396i
$448$		0			0
$449$		−	31.1772i		−	1.47134i	−0.677338	−	0.735672i	$-0.736867\pi$
$449$		−	31.1772i		−	1.47134i	0.677338	−	0.735672i	$-0.263133\pi$
$450$		0			0
$451$			1.11177i			0.0523510i
$452$		0			0
$453$	6.25406	+	6.25406i	0.293841	+	0.293841i
$454$		0			0
$455$	−13.0120	−	2.56411i	−0.610011	−	0.120207i
$456$		0			0
$457$	−3.72302	+	3.72302i	−0.174156	+	0.174156i	−0.788802	−	0.614647i	$-0.789299\pi$
$457$	−3.72302	+	3.72302i	−0.174156	+	0.174156i	0.614647	+	0.788802i	$0.289299\pi$
$458$		0			0
$459$	−8.44199			−0.394038
$460$		0			0
$461$	13.3815			0.623238			0.311619	−	0.950207i	$-0.399129\pi$
$461$	13.3815			0.623238			0.311619	+	0.950207i	$0.399129\pi$
$462$		0			0
$463$	13.9248	−	13.9248i	0.647140	−	0.647140i	−0.305161	−	0.952301i	$-0.598710\pi$
$463$	13.9248	−	13.9248i	0.647140	−	0.647140i	0.952301	+	0.305161i	$0.0987102\pi$
$464$		0			0
$465$	2.71096	−	1.81841i	0.125718	−	0.0843268i
$466$		0			0
$467$	11.6805	+	11.6805i	0.540510	+	0.540510i	0.923678	−	0.383169i	$-0.125167\pi$
$467$	11.6805	+	11.6805i	0.540510	+	0.540510i	−0.383169	+	0.923678i	$0.625167\pi$
$468$		0			0
$469$		−	6.18159i		−	0.285439i
$470$		0			0
$471$		−	31.5745i		−	1.45488i
$472$		0			0
$473$	4.91524	+	4.91524i	0.226003	+	0.226003i
$474$		0			0
$475$	−29.3810	−	12.0473i	−1.34809	−	0.552769i
$476$		0			0
$477$	34.1772	−	34.1772i	1.56487	−	1.56487i
$478$		0			0
$479$	−23.0845			−1.05476			−0.527379	−	0.849630i	$-0.676825\pi$
$479$	−23.0845			−1.05476			−0.527379	+	0.849630i	$0.676825\pi$
$480$		0			0
$481$	−48.3265			−2.20350
$482$		0			0
$483$	−14.1619	+	14.1619i	−0.644387	+	0.644387i
$484$		0			0
$485$	−18.1633	−	27.0785i	−0.824751	−	1.22957i
$486$		0			0
$487$	−4.19700	−	4.19700i	−0.190184	−	0.190184i	0.605592	−	0.795776i	$-0.292937\pi$
$487$	−4.19700	−	4.19700i	−0.190184	−	0.190184i	−0.795776	+	0.605592i	$0.792937\pi$
$488$		0			0
$489$			33.2158i			1.50207i
$490$		0			0
$491$		−	16.2529i		−	0.733481i	−0.930323	−	0.366740i	$-0.880474\pi$
$491$		−	16.2529i		−	0.733481i	0.930323	−	0.366740i	$-0.119526\pi$
$492$		0			0
$493$	−7.11870	−	7.11870i	−0.320610	−	0.320610i
$494$		0			0
$495$	3.37680	−	17.1361i	0.151776	−	0.770209i
$496$		0			0
$497$	−5.52311	+	5.52311i	−0.247746	+	0.247746i
$498$		0			0
$499$	26.3043			1.17754			0.588771	−	0.808300i	$-0.299612\pi$
$499$	26.3043			1.17754			0.588771	+	0.808300i	$0.299612\pi$
$500$		0			0
$501$	60.8699			2.71946
$502$		0			0
$503$	13.2664	−	13.2664i	0.591521	−	0.591521i	−0.346521	−	0.938042i	$-0.612637\pi$
$503$	13.2664	−	13.2664i	0.591521	−	0.591521i	0.938042	+	0.346521i	$0.112637\pi$
$504$		0			0
$505$	−0.167635	+	0.850688i	−0.00745964	+	0.0378551i
$506$		0			0
$507$	−43.3058	−	43.3058i	−1.92328	−	1.92328i
$508$		0			0
$509$			33.3449i			1.47798i	0.673714	+	0.738992i	$0.264698\pi$
$509$			33.3449i			1.47798i	−0.673714	+	0.738992i	$0.735302\pi$
$510$		0			0
$511$			1.26843i			0.0561121i
$512$		0			0
$513$	20.1676	+	20.1676i	0.890423	+	0.890423i
$514$		0			0
$515$	−9.38824	−	13.9964i	−0.413695	−	0.616753i
$516$		0			0
$517$	−14.9125	+	14.9125i	−0.655852	+	0.655852i
$518$		0			0
$519$	22.6754			0.995340
$520$		0			0
$521$	44.9850			1.97083			0.985414	−	0.170172i	$-0.0544322\pi$
$521$	44.9850			1.97083			0.985414	+	0.170172i	$0.0544322\pi$
$522$		0			0
$523$	12.9391	−	12.9391i	0.565787	−	0.565787i	−0.365159	−	0.930945i	$-0.618985\pi$
$523$	12.9391	−	12.9391i	0.565787	−	0.565787i	0.930945	+	0.365159i	$0.118985\pi$
$524$		0			0
$525$	−12.7755	−	5.23844i	−0.557569	−	0.228624i
$526$		0			0
$527$	0.702682	+	0.702682i	0.0306093	+	0.0306093i
$528$		0			0
$529$		−	29.5972i		−	1.28684i
$530$		0			0
$531$			13.7593i			0.597102i
$532$		0			0
$533$	2.76156	+	2.76156i	0.119616	+	0.119616i
$534$		0			0
$535$	−7.64535	+	5.12822i	−0.330537	+	0.221712i
$536$		0			0
$537$	40.9817	−	40.9817i	1.76849	−	1.76849i
$538$		0			0
$539$	−1.68840			−0.0727244
$540$		0			0
$541$	29.3188			1.26052			0.630258	−	0.776386i	$-0.282949\pi$
$541$	29.3188			1.26052			0.630258	+	0.776386i	$0.282949\pi$
$542$		0			0
$543$	10.0279	−	10.0279i	0.430338	−	0.430338i
$544$		0			0
$545$	6.90921	+	1.36151i	0.295958	+	0.0583208i
$546$		0			0
$547$	−21.7357	−	21.7357i	−0.929350	−	0.929350i	0.0683141	−	0.997664i	$-0.478238\pi$
$547$	−21.7357	−	21.7357i	−0.929350	−	0.929350i	−0.997664	+	0.0683141i	$0.978238\pi$
$548$		0			0
$549$		−	40.5972i		−	1.73265i
$550$		0			0
$551$			34.0127i			1.44899i
$552$		0			0
$553$	9.19388	+	9.19388i	0.390963	+	0.390963i
$554$		0			0
$555$	−49.3652	−	9.72780i	−2.09544	−	0.412922i
$556$		0			0
$557$	0.0847616	−	0.0847616i	0.00359146	−	0.00359146i	−0.705309	−	0.708900i	$-0.749192\pi$
$557$	0.0847616	−	0.0847616i	0.00359146	−	0.00359146i	0.708900	+	0.705309i	$0.249192\pi$
$558$		0			0
$559$	24.4183			1.03278
$560$		0			0
$561$	8.76488			0.370054
$562$		0			0
$563$	1.22279	−	1.22279i	0.0515343	−	0.0515343i	−0.680870	−	0.732404i	$-0.738398\pi$
$563$	1.22279	−	1.22279i	0.0515343	−	0.0515343i	0.732404	+	0.680870i	$0.238398\pi$
$564$		0			0
$565$	−19.8420	+	13.3093i	−0.834757	+	0.559924i
$566$		0			0
$567$	−1.04432	−	1.04432i	−0.0438571	−	0.0438571i
$568$		0			0
$569$		−	19.1108i		−	0.801166i	−0.916261	−	0.400583i	$-0.868808\pi$
$569$		−	19.1108i		−	0.801166i	0.916261	−	0.400583i	$-0.131192\pi$
$570$		0			0
$571$		−	28.3237i		−	1.18531i	−0.805456	−	0.592656i	$-0.798079\pi$
$571$		−	28.3237i		−	1.18531i	0.805456	−	0.592656i	$-0.201921\pi$
$572$		0			0
$573$	−21.5065	−	21.5065i	−0.898445	−	0.898445i
$574$		0			0
$575$	33.4520	−	13.9964i	1.39504	−	0.583688i
$576$		0			0
$577$	8.10475	−	8.10475i	0.337405	−	0.337405i	−0.517985	−	0.855390i	$-0.673318\pi$
$577$	8.10475	−	8.10475i	0.337405	−	0.337405i	0.855390	+	0.517985i	$0.173318\pi$
$578$		0			0
$579$	51.5343			2.14169
$580$		0			0
$581$	8.00000			0.331896
$582$		0			0
$583$	−12.4735	+	12.4735i	−0.516598	+	0.516598i
$584$		0			0
$585$	−34.1772	−	50.9527i	−1.41305	−	2.10664i
$586$		0			0
$587$	−5.53080	−	5.53080i	−0.228281	−	0.228281i	0.583693	−	0.811974i	$-0.301607\pi$
$587$	−5.53080	−	5.53080i	−0.228281	−	0.228281i	−0.811974	+	0.583693i	$0.801607\pi$
$588$		0			0
$589$		−	3.35737i		−	0.138338i
$590$		0			0
$591$		−	2.50007i		−	0.102839i
$592$		0			0
$593$	4.24636	+	4.24636i	0.174377	+	0.174377i	0.788899	−	0.614522i	$-0.210651\pi$
$593$	4.24636	+	4.24636i	0.174377	+	0.174377i	−0.614522	+	0.788899i	$0.710651\pi$
$594$		0			0
$595$	0.812687	−	4.12411i	0.0333169	−	0.169072i
$596$		0			0
$597$	−49.5004	+	49.5004i	−2.02592	+	2.02592i
$598$		0			0
$599$	−35.0293			−1.43126			−0.715630	−	0.698480i	$-0.753860\pi$
$599$	−35.0293			−1.43126			−0.715630	+	0.698480i	$0.753860\pi$
$600$		0			0
$601$	24.5573			1.00171			0.500856	−	0.865531i	$-0.333019\pi$
$601$	24.5573			1.00171			0.500856	+	0.865531i	$0.333019\pi$
$602$		0			0
$603$	20.2213	−	20.2213i	0.823475	−	0.823475i
$604$		0			0
$605$	3.52311	−	17.8786i	0.143235	−	0.726868i
$606$		0			0
$607$	3.99570	+	3.99570i	0.162181	+	0.162181i	0.783532	−	0.621351i	$-0.213416\pi$
$607$	3.99570	+	3.99570i	0.162181	+	0.162181i	−0.621351	+	0.783532i	$0.713416\pi$
$608$		0			0
$609$			14.7895i			0.599299i
$610$		0			0
$611$			74.0836i			2.99710i
$612$		0			0
$613$	−15.7110	−	15.7110i	−0.634560	−	0.634560i	0.314649	−	0.949208i	$-0.398113\pi$
$613$	−15.7110	−	15.7110i	−0.634560	−	0.634560i	−0.949208	+	0.314649i	$0.898113\pi$
$614$		0			0
$615$	2.26503	+	3.37680i	0.0913348	+	0.136166i
$616$		0			0
$617$	16.4725	−	16.4725i	0.663159	−	0.663159i	−0.292965	−	0.956123i	$-0.594642\pi$
$617$	16.4725	−	16.4725i	0.663159	−	0.663159i	0.956123	+	0.292965i	$0.0946418\pi$
$618$		0			0
$619$	−16.0788			−0.646262			−0.323131	−	0.946354i	$-0.604735\pi$
$619$	−16.0788			−0.646262			−0.323131	+	0.946354i	$0.604735\pi$
$620$		0			0
$621$	−32.5693			−1.30696
$622$		0			0
$623$	4.43407	−	4.43407i	0.177647	−	0.177647i
$624$		0			0
$625$	17.8034	+	17.5510i	0.712137	+	0.702041i
$626$		0			0
$627$	−20.9390	−	20.9390i	−0.836224	−	0.836224i
$628$		0			0
$629$		−	15.3169i		−	0.610727i
$630$		0			0
$631$		−	3.55084i		−	0.141357i	−0.997499	−	0.0706784i	$-0.977484\pi$
$631$		−	3.55084i		−	0.141357i	0.997499	−	0.0706784i	$-0.0225164\pi$
$632$		0			0
$633$	38.8234	+	38.8234i	1.54309	+	1.54309i
$634$		0			0
$635$	9.03365	−	6.05944i	0.358489	−	0.240462i
$636$		0			0
$637$	−4.19388	+	4.19388i	−0.166167	+	0.166167i
$638$		0			0
$639$	−36.1346			−1.42946
$640$		0			0
$641$	−43.1020			−1.70243			−0.851214	−	0.524819i	$-0.824133\pi$
$641$	−43.1020			−1.70243			−0.851214	+	0.524819i	$0.824133\pi$
$642$		0			0
$643$	17.7005	−	17.7005i	0.698039	−	0.698039i	−0.265948	−	0.963987i	$-0.585685\pi$
$643$	17.7005	−	17.7005i	0.698039	−	0.698039i	0.963987	+	0.265948i	$0.0856850\pi$
$644$		0			0
$645$	24.9431	+	4.91524i	0.982135	+	0.193537i
$646$		0			0
$647$	18.8875	+	18.8875i	0.742544	+	0.742544i	0.973067	−	0.230523i	$-0.0740436\pi$
$647$	18.8875	+	18.8875i	0.742544	+	0.742544i	−0.230523	+	0.973067i	$0.574044\pi$
$648$		0			0
$649$		−	5.02165i		−	0.197117i
$650$		0			0
$651$		−	1.45986i		−	0.0572163i
$652$		0			0
$653$	−4.31695	−	4.31695i	−0.168935	−	0.168935i	0.617576	−	0.786511i	$-0.288115\pi$
$653$	−4.31695	−	4.31695i	−0.168935	−	0.168935i	−0.786511	+	0.617576i	$0.788115\pi$
$654$		0			0
$655$	−15.0931	−	2.97421i	−0.589736	−	0.116212i
$656$		0			0
$657$	−4.14931	+	4.14931i	−0.161880	+	0.161880i
$658$		0			0
$659$	−7.05369			−0.274773			−0.137386	−	0.990518i	$-0.543870\pi$
$659$	−7.05369			−0.274773			−0.137386	+	0.990518i	$0.543870\pi$
$660$		0			0
$661$	30.2216			1.17548			0.587741	−	0.809049i	$-0.300017\pi$
$661$	30.2216			1.17548			0.587741	+	0.809049i	$0.300017\pi$
$662$		0			0
$663$	21.7714	−	21.7714i	0.845533	−	0.845533i
$664$		0			0
$665$	−11.7938	+	7.91087i	−0.457345	+	0.306770i
$666$		0			0
$667$	−27.4641	−	27.4641i	−1.06341	−	1.06341i
$668$		0			0
$669$		−	11.2630i		−	0.435454i
$670$		0			0
$671$			14.8166i			0.571987i
$672$		0			0
$673$	14.9248	+	14.9248i	0.575310	+	0.575310i	0.933607	−	0.358298i	$-0.116643\pi$
$673$	14.9248	+	14.9248i	0.575310	+	0.575310i	−0.358298	+	0.933607i	$0.616643\pi$
$674$		0			0
$675$	−8.66684	−	20.7142i	−0.333587	−	0.797289i
$676$		0			0
$677$	2.37214	−	2.37214i	0.0911687	−	0.0911687i	−0.660052	−	0.751220i	$-0.729466\pi$
$677$	2.37214	−	2.37214i	0.0911687	−	0.0911687i	0.751220	+	0.660052i	$0.229466\pi$
$678$		0			0
$679$	−14.5818			−0.559599
$680$		0			0
$681$	−41.9806			−1.60870
$682$		0			0
$683$	−6.58808	+	6.58808i	−0.252086	+	0.252086i	−0.821825	−	0.569740i	$-0.807044\pi$
$683$	−6.58808	+	6.58808i	−0.252086	+	0.252086i	0.569740	+	0.821825i	$0.307044\pi$
$684$		0			0
$685$	11.6724	+	17.4017i	0.445981	+	0.664885i
$686$		0			0
$687$	25.1755	+	25.1755i	0.960505	+	0.960505i
$688$		0			0
$689$			61.9667i			2.36074i
$690$		0			0
$691$			9.45126i			0.359543i	0.983708	+	0.179772i	$0.0575358\pi$
$691$			9.45126i			0.359543i	−0.983708	+	0.179772i	$0.942464\pi$
$692$		0			0
$693$	−5.52311	−	5.52311i	−0.209806	−	0.209806i
$694$		0			0
$695$	8.21345	−	41.6804i	0.311554	−	1.58103i
$696$		0			0
$697$	−0.875267	+	0.875267i	−0.0331531	+	0.0331531i
$698$		0			0
$699$	29.9641			1.13335
$700$		0			0
$701$	9.71866			0.367069			0.183534	−	0.983013i	$-0.441246\pi$
$701$	9.71866			0.367069			0.183534	+	0.983013i	$0.441246\pi$
$702$		0			0
$703$	−36.5917	+	36.5917i	−1.38008	+	1.38008i
$704$		0			0
$705$	−14.9125	+	75.6760i	−0.561638	+	2.85012i
$706$		0			0
$707$	0.274184	+	0.274184i	0.0103118	+	0.0103118i
$708$		0			0
$709$			28.2514i			1.06100i	0.847684	+	0.530501i	$0.177996\pi$
$709$			28.2514i			1.06100i	−0.847684	+	0.530501i	$0.822004\pi$
$710$		0			0
$711$			60.1503i			2.25581i
$712$		0			0
$713$	2.71096	+	2.71096i	0.101526	+	0.101526i
$714$		0			0
$715$	12.4735	+	18.5959i	0.466481	+	0.695449i
$716$		0			0
$717$	18.7955	−	18.7955i	0.701931	−	0.701931i
$718$		0			0
$719$	38.4541			1.43410			0.717048	−	0.697023i	$-0.245493\pi$
$719$	38.4541			1.43410			0.717048	+	0.697023i	$0.245493\pi$
$720$		0			0
$721$	−7.53707			−0.280695
$722$		0			0
$723$	16.7335	−	16.7335i	0.622325	−	0.622325i
$724$		0			0
$725$	10.1589	−	24.7755i	0.377292	−	0.920139i
$726$		0			0
$727$	5.53080	+	5.53080i	0.205126	+	0.205126i	0.802192	−	0.597066i	$-0.203667\pi$
$727$	5.53080	+	5.53080i	0.205126	+	0.205126i	−0.597066	+	0.802192i	$0.703667\pi$
$728$		0			0
$729$		−	44.0375i		−	1.63102i
$730$		0			0
$731$			7.73931i			0.286249i
$732$		0			0
$733$	−35.8986	−	35.8986i	−1.32594	−	1.32594i	−0.908874	−	0.417070i	$-0.863057\pi$
$733$	−35.8986	−	35.8986i	−1.32594	−	1.32594i	−0.417070	−	0.908874i	$-0.636943\pi$
$734$		0			0
$735$	−5.12822	+	3.43982i	−0.189157	+	0.126880i
$736$		0			0
$737$	−7.38006	+	7.38006i	−0.271848	+	0.271848i
$738$		0			0
$739$	−9.83029			−0.361613			−0.180807	−	0.983519i	$-0.557871\pi$
$739$	−9.83029			−0.361613			−0.180807	+	0.983519i	$0.557871\pi$
$740$		0			0
$741$	−104.022			−3.82136
$742$		0			0
$743$	24.0787	−	24.0787i	0.883363	−	0.883363i	−0.110511	−	0.993875i	$-0.535249\pi$
$743$	24.0787	−	24.0787i	0.883363	−	0.883363i	0.993875	+	0.110511i	$0.0352489\pi$
$744$		0			0
$745$	−7.72928	−	1.52311i	−0.283179	−	0.0558026i
$746$		0			0
$747$	26.1697	+	26.1697i	0.957500	+	0.957500i
$748$		0			0
$749$			4.11704i			0.150433i
$750$		0			0
$751$		−	16.0479i		−	0.585595i	−0.956174	−	0.292798i	$-0.905414\pi$
$751$		−	16.0479i		−	0.585595i	0.956174	−	0.292798i	$-0.0945862\pi$
$752$		0			0
$753$	−11.3694	−	11.3694i	−0.414325	−	0.414325i
$754$		0			0
$755$	−7.02644	−	1.38461i	−0.255718	−	0.0503913i
$756$		0			0
$757$	14.6541	−	14.6541i	0.532612	−	0.532612i	−0.388736	−	0.921349i	$-0.627088\pi$
$757$	14.6541	−	14.6541i	0.532612	−	0.532612i	0.921349	+	0.388736i	$0.127088\pi$
$758$		0			0
$759$	33.8151			1.22741
$760$		0			0
$761$	−12.2707			−0.444813			−0.222407	−	0.974954i	$-0.571391\pi$
$761$	−12.2707			−0.444813			−0.222407	+	0.974954i	$0.571391\pi$
$762$		0			0
$763$	2.22690	−	2.22690i	0.0806192	−	0.0806192i
$764$		0			0
$765$	16.1493	−	10.8324i	0.583880	−	0.391645i
$766$		0			0
$767$	−12.4735	−	12.4735i	−0.450391	−	0.450391i
$768$		0			0
$769$			17.2278i			0.621251i	0.950532	+	0.310625i	$0.100538\pi$
$769$			17.2278i			0.621251i	−0.950532	+	0.310625i	$0.899462\pi$
$770$		0			0
$771$			78.6918i			2.83401i
$772$		0			0
$773$	−13.4463	−	13.4463i	−0.483629	−	0.483629i	0.422660	−	0.906288i	$-0.361097\pi$
$773$	−13.4463	−	13.4463i	−0.483629	−	0.483629i	−0.906288	+	0.422660i	$0.861097\pi$
$774$		0			0
$775$	−1.00278	+	2.44557i	−0.0360208	+	0.0878476i
$776$		0			0
$777$	−15.9109	+	15.9109i	−0.570799	+	0.570799i
$778$		0			0
$779$	4.18197			0.149835
$780$		0			0
$781$	13.1878			0.471898
$782$		0			0
$783$	−17.0063	+	17.0063i	−0.607757	+	0.607757i
$784$		0			0
$785$	14.2418	+	21.2322i	0.508311	+	0.757809i
$786$		0			0
$787$	13.6690	+	13.6690i	0.487248	+	0.487248i	0.907437	−	0.420189i	$-0.138036\pi$
$787$	13.6690	+	13.6690i	0.487248	+	0.487248i	−0.420189	+	0.907437i	$0.638036\pi$
$788$		0			0
$789$			86.0591i			3.06379i
$790$		0			0
$791$			10.6849i			0.379913i
$792$		0			0
$793$	36.8034	+	36.8034i	1.30693	+	1.30693i
$794$		0			0
$795$	−12.4735	+	63.2986i	−0.442388	+	2.24497i
$796$		0			0
$797$	5.48292	−	5.48292i	0.194215	−	0.194215i	−0.603300	−	0.797515i	$-0.706148\pi$
$797$	5.48292	−	5.48292i	0.194215	−	0.194215i	0.797515	+	0.603300i	$0.206148\pi$
$798$		0			0
$799$	−23.4806			−0.830683
$800$		0			0
$801$	29.0096			1.02500
$802$		0			0
$803$	1.51435	−	1.51435i	0.0534403	−	0.0534403i
$804$		0			0
$805$	3.13536	−	15.9109i	0.110507	−	0.560784i
$806$		0			0
$807$	11.7163	+	11.7163i	0.412433	+	0.412433i
$808$		0			0
$809$			17.6907i			0.621974i	0.950414	+	0.310987i	$0.100659\pi$
$809$			17.6907i			0.621974i	−0.950414	+	0.310987i	$0.899341\pi$
$810$		0			0
$811$		−	3.95993i		−	0.139052i	−0.997580	−	0.0695259i	$-0.977851\pi$
$811$		−	3.95993i		−	0.139052i	0.997580	−	0.0695259i	$-0.0221486\pi$
$812$		0			0
$813$	−63.7205	−	63.7205i	−2.23478	−	2.23478i
$814$		0			0
$815$	−14.9821	−	22.3359i	−0.524799	−	0.782391i
$816$		0			0
$817$	18.4890	−	18.4890i	0.646846	−	0.646846i
$818$		0			0
$819$	−27.4382			−0.958767
$820$		0			0
$821$	−4.42962			−0.154595			−0.0772973	−	0.997008i	$-0.524629\pi$
$821$	−4.42962			−0.154595			−0.0772973	+	0.997008i	$0.524629\pi$
$822$		0			0
$823$	−16.0158	+	16.0158i	−0.558275	+	0.558275i	−0.928816	−	0.370541i	$-0.879172\pi$
$823$	−16.0158	+	16.0158i	−0.558275	+	0.558275i	0.370541	+	0.928816i	$0.379172\pi$
$824$		0			0
$825$	8.99834	+	21.5065i	0.313282	+	0.748759i
$826$		0			0
$827$	29.0179	+	29.0179i	1.00905	+	1.00905i	0.999959	+	0.00909218i	$0.00289417\pi$
$827$	29.0179	+	29.0179i	1.00905	+	1.00905i	0.00909218	+	0.999959i	$0.497106\pi$
$828$		0			0
$829$			5.54769i			0.192679i	0.995349	+	0.0963397i	$0.0307135\pi$
$829$			5.54769i			0.192679i	−0.995349	+	0.0963397i	$0.969286\pi$
$830$		0			0
$831$		−	23.5586i		−	0.817240i
$832$		0			0
$833$	−1.32924	−	1.32924i	−0.0460553	−	0.0460553i
$834$		0			0
$835$	−40.9318	+	27.4555i	−1.41650	+	0.950138i
$836$		0			0
$837$	1.67868	−	1.67868i	0.0580238	−	0.0580238i
$838$		0			0
$839$	−28.9239			−0.998565			−0.499282	−	0.866439i	$-0.666403\pi$
$839$	−28.9239			−0.998565			−0.499282	+	0.866439i	$0.666403\pi$
$840$		0			0
$841$	0.318836			0.0109943
$842$		0			0
$843$	−10.8603	+	10.8603i	−0.374049	+	0.374049i
$844$		0			0
$845$	48.6541	+	9.58767i	1.67375	+	0.329826i
$846$		0			0
$847$	−5.76243	−	5.76243i	−0.198000	−	0.198000i
$848$		0			0
$849$		−	67.0635i		−	2.30161i
$850$		0			0
$851$		−	59.0930i		−	2.02568i
$852$		0			0
$853$	23.8140	+	23.8140i	0.815377	+	0.815377i	0.985434	−	0.170057i	$-0.0543952\pi$
$853$	23.8140	+	23.8140i	0.815377	+	0.815377i	−0.170057	+	0.985434i	$0.554395\pi$
$854$		0			0
$855$	−64.4583	−	12.7020i	−2.20443	−	0.434400i
$856$		0			0
$857$	22.9527	−	22.9527i	0.784050	−	0.784050i	−0.196461	−	0.980512i	$-0.562945\pi$
$857$	22.9527	−	22.9527i	0.784050	−	0.784050i	0.980512	+	0.196461i	$0.0629450\pi$
$858$		0			0
$859$	−11.6447			−0.397313			−0.198657	−	0.980069i	$-0.563658\pi$
$859$	−11.6447			−0.397313			−0.198657	+	0.980069i	$0.563658\pi$
$860$		0			0
$861$	1.81841			0.0619713
$862$		0			0
$863$	−26.7464	+	26.7464i	−0.910457	+	0.910457i	−0.996308	−	0.0858513i	$-0.972639\pi$
$863$	−26.7464	+	26.7464i	−0.910457	+	0.910457i	0.0858513	+	0.996308i	$0.472639\pi$
$864$		0			0
$865$	−15.2480	+	10.2278i	−0.518448	+	0.347756i
$866$		0			0
$867$	−26.2958	−	26.2958i	−0.893051	−	0.893051i
$868$		0			0
$869$		−	21.9527i		−	0.744695i
$870$		0			0
$871$			36.6632i			1.24229i
$872$		0			0
$873$	−47.7003	−	47.7003i	−1.61441	−	1.61441i
$874$		0			0
$875$	10.9537	−	2.23986i	0.370302	−	0.0757209i
$876$		0			0
$877$	−15.0646	+	15.0646i	−0.508694	+	0.508694i	−0.914125	−	0.405432i	$-0.867121\pi$
$877$	−15.0646	+	15.0646i	−0.508694	+	0.508694i	0.405432	+	0.914125i	$0.367121\pi$
$878$		0			0
$879$	71.9691			2.42746
$880$		0			0
$881$	−29.6801			−0.999949			−0.499974	−	0.866040i	$-0.666657\pi$
$881$	−29.6801			−0.999949			−0.499974	+	0.866040i	$0.666657\pi$
$882$		0			0
$883$	−25.2385	+	25.2385i	−0.849343	+	0.849343i	−0.990051	−	0.140708i	$-0.955062\pi$
$883$	−25.2385	+	25.2385i	−0.849343	+	0.849343i	0.140708	+	0.990051i	$0.455062\pi$
$884$		0			0
$885$	−10.2307	−	15.2524i	−0.343903	−	0.512704i
$886$		0			0
$887$	2.28006	+	2.28006i	0.0765569	+	0.0765569i	0.744348	−	0.667792i	$-0.232760\pi$
$887$	2.28006	+	2.28006i	0.0765569	+	0.0765569i	−0.667792	+	0.744348i	$0.732760\pi$
$888$		0			0
$889$		−	4.86464i		−	0.163155i
$890$		0			0
$891$			2.49357i			0.0835378i
$892$		0			0
$893$	56.0943	+	56.0943i	1.87713	+	1.87713i
$894$		0			0
$895$	−9.07312	+	46.0429i	−0.303281	+	1.53905i
$896$		0			0
$897$	83.9946	−	83.9946i	2.80450	−	2.80450i
$898$		0			0
$899$	2.83110			0.0944224
$900$		0			0
$901$	−19.6402			−0.654308
$902$		0			0
$903$	8.03940	−	8.03940i	0.267535	−	0.267535i
$904$		0			0
$905$	−2.22012	+	11.2663i	−0.0737993	+	0.374506i
$906$		0			0
$907$	−0.237071	−	0.237071i	−0.00787181	−	0.00787181i	0.703160	−	0.711032i	$-0.251772\pi$
$907$	−0.237071	−	0.237071i	−0.00787181	−	0.00787181i	−0.711032	+	0.703160i	$0.751772\pi$
$908$		0			0
$909$			1.79383i			0.0594977i
$910$		0			0
$911$		−	27.2665i		−	0.903378i	−0.892175	−	0.451689i	$-0.850822\pi$
$911$		−	27.2665i		−	0.903378i	0.892175	−	0.451689i	$-0.149178\pi$
$912$		0			0
$913$	−9.55102	−	9.55102i	−0.316093	−	0.316093i
$914$		0			0
$915$	30.1862	+	45.0027i	0.997924	+	1.48774i
$916$		0			0
$917$	−4.86464	+	4.86464i	−0.160645	+	0.160645i
$918$		0			0
$919$	−12.7500			−0.420584			−0.210292	−	0.977639i	$-0.567441\pi$
$919$	−12.7500			−0.420584			−0.210292	+	0.977639i	$0.567441\pi$
$920$		0			0
$921$	42.2601			1.39252
$922$		0			0
$923$	32.7578	−	32.7578i	1.07824	−	1.07824i
$924$		0			0
$925$	37.5833	−	15.7249i	1.23573	−	0.517032i
$926$		0			0
$927$	−24.6554	−	24.6554i	−0.809789	−	0.809789i
$928$		0			0
$929$			23.8742i			0.783288i	0.920117	+	0.391644i	$0.128094\pi$
$929$			23.8742i			0.783288i	−0.920117	+	0.391644i	$0.871906\pi$
$930$		0			0
$931$			6.35101i			0.208146i
$932$		0			0
$933$	−21.3063	−	21.3063i	−0.697538	−	0.697538i
$934$		0			0
$935$	−5.89393	+	3.95343i	−0.192752	+	0.129291i
$936$		0			0
$937$	−3.71699	+	3.71699i	−0.121429	+	0.121429i	−0.765210	−	0.643781i	$-0.777365\pi$
$937$	−3.71699	+	3.71699i	−0.121429	+	0.121429i	0.643781	+	0.765210i	$0.277365\pi$
$938$		0			0
$939$	55.8903			1.82391
$940$		0			0
$941$	23.3940			0.762623			0.381312	−	0.924447i	$-0.375473\pi$
$941$	23.3940			0.762623			0.381312	+	0.924447i	$0.375473\pi$
$942$		0			0
$943$	−3.37680	+	3.37680i	−0.109964	+	0.109964i
$944$		0			0
$945$	−9.85235	−	1.94148i	−0.320497	−	0.0631564i
$946$		0			0
$947$	13.8223	+	13.8223i	0.449165	+	0.449165i	0.895077	−	0.445912i	$-0.147121\pi$
$947$	13.8223	+	13.8223i	0.449165	+	0.449165i	−0.445912	+	0.895077i	$0.647121\pi$
$948$		0			0
$949$		−	7.52311i		−	0.244211i
$950$		0			0
$951$			21.4986i			0.697140i
$952$		0			0
$953$	−4.78177	−	4.78177i	−0.154897	−	0.154897i	0.625404	−	0.780301i	$-0.284934\pi$
$953$	−4.78177	−	4.78177i	−0.154897	−	0.154897i	−0.780301	+	0.625404i	$0.784934\pi$
$954$		0			0
$955$	24.1625	+	4.76141i	0.781881	+	0.154076i
$956$		0			0
$957$	17.6568	−	17.6568i	0.570764	−	0.570764i
$958$		0			0
$959$	9.37086			0.302601
$960$		0			0
$961$	30.7205			0.990985
$962$		0			0
$963$	−13.4677	+	13.4677i	−0.433991	+	0.433991i
$964$		0			0
$965$	−34.6541	+	23.2447i	−1.11556	+	0.748273i
$966$		0			0
$967$	−5.02573	−	5.02573i	−0.161617	−	0.161617i	0.621666	−	0.783282i	$-0.286456\pi$
$967$	−5.02573	−	5.02573i	−0.161617	−	0.161617i	−0.783282	+	0.621666i	$0.786456\pi$
$968$		0			0
$969$		−	32.9696i		−	1.05914i
$970$		0			0
$971$			25.6806i			0.824128i	0.911155	+	0.412064i	$0.135192\pi$
$971$			25.6806i			0.824128i	−0.911155	+	0.412064i	$0.864808\pi$
$972$		0			0
$973$	−13.4340	−	13.4340i	−0.430674	−	0.430674i
$974$		0			0
$975$	75.7720	+	31.0694i	2.42665	+	0.995017i
$976$		0			0
$977$	22.5510	−	22.5510i	0.721471	−	0.721471i	−0.247434	−	0.968905i	$-0.579587\pi$
$977$	22.5510	−	22.5510i	0.721471	−	0.721471i	0.968905	+	0.247434i	$0.0795873\pi$
$978$		0			0
$979$	−10.5875			−0.338377
$980$		0			0
$981$	14.5693			0.465163
$982$		0			0
$983$	19.4914	−	19.4914i	0.621678	−	0.621678i	−0.324282	−	0.945960i	$-0.605123\pi$
$983$	19.4914	−	19.4914i	0.621678	−	0.621678i	0.945960	+	0.324282i	$0.105123\pi$
$984$		0			0
$985$	1.12766	+	1.68116i	0.0359303	+	0.0535663i
$986$		0			0
$987$	24.3911	+	24.3911i	0.776376	+	0.776376i
$988$		0			0
$989$			29.8584i			0.949441i
$990$		0			0
$991$		−	2.46264i		−	0.0782282i	−0.999235	−	0.0391141i	$-0.987546\pi$
$991$		−	2.46264i		−	0.0782282i	0.999235	−	0.0391141i	$-0.0124536\pi$
$992$		0			0
$993$	−5.70138	−	5.70138i	−0.180928	−	0.180928i
$994$		0			0
$995$	10.9591	−	55.6138i	0.347427	−	1.76307i
$996$		0			0
$997$	24.9973	−	24.9973i	0.791672	−	0.791672i	−0.190094	−	0.981766i	$-0.560879\pi$
$997$	24.9973	−	24.9973i	0.791672	−	0.791672i	0.981766	+	0.190094i	$0.0608792\pi$
$998$		0			0
$999$	−36.5917			−1.15771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.x.a.463.1	yes	12
4.3	odd	2	inner	560.2.x.a.463.6	yes	12
5.2	odd	4	inner	560.2.x.a.127.6	yes	12
20.7	even	4	inner	560.2.x.a.127.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.x.a.127.1	✓	12	20.7	even	4	inner
560.2.x.a.127.6	yes	12	5.2	odd	4	inner
560.2.x.a.463.1	yes	12	1.1	even	1	trivial
560.2.x.a.463.6	yes	12	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95272 + 1.95272i) q^{3} +(0.432320 - 2.19388i) q^{5} +(-0.707107 - 0.707107i) q^{7} -4.62620i q^{9} +O(q^{10})\)	\(q+(-1.95272 + 1.95272i) q^{3} +(0.432320 - 2.19388i) q^{5} +(-0.707107 - 0.707107i) q^{7} -4.62620i q^{9} +1.68840i q^{11} +(4.19388 + 4.19388i) q^{13} +(3.43982 + 5.12822i) q^{15} +(-1.32924 + 1.32924i) q^{17} +6.35101 q^{19} +2.76156 q^{21} +(-5.12822 + 5.12822i) q^{23} +(-4.62620 - 1.89692i) q^{25} +(3.17550 + 3.17550i) q^{27} +5.35548i q^{29} -0.528636i q^{31} +(-3.29696 - 3.29696i) q^{33} +(-1.85700 + 1.24561i) q^{35} +(-5.76156 + 5.76156i) q^{37} -16.3789 q^{39} +0.658473 q^{41} +(2.91118 - 2.91118i) q^{43} +(-10.1493 - 2.00000i) q^{45} +(8.83236 + 8.83236i) q^{47} +1.00000i q^{49} -5.19124i q^{51} +(7.38776 + 7.38776i) q^{53} +(3.70414 + 0.729929i) q^{55} +(-12.4017 + 12.4017i) q^{57} -2.97421 q^{59} +8.77551 q^{61} +(-3.27122 + 3.27122i) q^{63} +(11.0140 - 7.38776i) q^{65} +(4.37104 + 4.37104i) q^{67} -20.0279i q^{69} -7.81086i q^{71} +(-0.896916 - 0.896916i) q^{73} +(12.7378 - 5.32951i) q^{75} +(1.19388 - 1.19388i) q^{77} -13.0021 q^{79} +1.47689 q^{81} +(-5.65685 + 5.65685i) q^{83} +(2.34153 + 3.49084i) q^{85} +(-10.4577 - 10.4577i) q^{87} +6.27072i q^{89} -5.93104i q^{91} +(1.03228 + 1.03228i) q^{93} +(2.74567 - 13.9333i) q^{95} +(10.3109 - 10.3109i) q^{97} +7.81086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 20 q^{13} + 4 q^{17} + 8 q^{21} - 20 q^{25} - 24 q^{33} - 44 q^{37} - 32 q^{41} - 36 q^{45} + 28 q^{53} + 8 q^{57} - 16 q^{61} + 36 q^{65} + 4 q^{73} - 16 q^{77} + 68 q^{81} + 68 q^{85} + 8 q^{93} + 12 q^{97}+O(q^{100}) \) 12 * q + 20 * q^13 + 4 * q^17 + 8 * q^21 - 20 * q^25 - 24 * q^33 - 44 * q^37 - 32 * q^41 - 36 * q^45 + 28 * q^53 + 8 * q^57 - 16 * q^61 + 36 * q^65 + 4 * q^73 - 16 * q^77 + 68 * q^81 + 68 * q^85 + 8 * q^93 + 12 * q^97

Introduction

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