LMFDB - Embedded newform 320.2.j.b.143.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,2,Mod(47,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 1]))

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

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

chi := DirichletCharacter("320.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.j (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:	$2.55521286468$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.3
Root			$1.41323 + 0.0526497i$ of defining polynomial
Character	$\chi$	$=$	320.143
Dual form			320.2.j.b.47.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28110i q^{3} +(-0.841703 + 2.07160i) q^{5} +(1.13975 - 1.13975i) q^{7} +1.35879 q^{9} +O(q^{10})$	\(q-1.28110i q^{3} +(-0.841703 + 2.07160i) q^{5} +(1.13975 - 1.13975i) q^{7} +1.35879 q^{9} +(2.32204 - 2.32204i) q^{11} +1.36502 q^{13} +(2.65392 + 1.07830i) q^{15} +(5.25380 - 5.25380i) q^{17} +(-3.69752 + 3.69752i) q^{19} +(-1.46013 - 1.46013i) q^{21} +(0.911118 + 0.911118i) q^{23} +(-3.58307 - 3.48735i) q^{25} -5.58403i q^{27} +(2.37343 + 2.37343i) q^{29} -0.242577i q^{31} +(-2.97475 - 2.97475i) q^{33} +(1.40178 + 3.32044i) q^{35} -3.34494 q^{37} -1.74872i q^{39} +2.66956i q^{41} -9.04874 q^{43} +(-1.14370 + 2.81488i) q^{45} +(7.87820 + 7.87820i) q^{47} +4.40194i q^{49} +(-6.73063 - 6.73063i) q^{51} -5.80113i q^{53} +(2.85587 + 6.76480i) q^{55} +(4.73688 + 4.73688i) q^{57} +(5.91474 + 5.91474i) q^{59} +(-6.67404 + 6.67404i) q^{61} +(1.54868 - 1.54868i) q^{63} +(-1.14894 + 2.82778i) q^{65} +4.54673 q^{67} +(1.16723 - 1.16723i) q^{69} -15.4389 q^{71} +(1.49307 - 1.49307i) q^{73} +(-4.46763 + 4.59026i) q^{75} -5.29308i q^{77} -10.3024 q^{79} -3.07731 q^{81} -3.26589i q^{83} +(6.46165 + 15.3059i) q^{85} +(3.04060 - 3.04060i) q^{87} -9.77206 q^{89} +(1.55578 - 1.55578i) q^{91} -0.310765 q^{93} +(-4.54758 - 10.7720i) q^{95} +(-1.63587 + 1.63587i) q^{97} +(3.15516 - 3.15516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) $ 18 * q - 4 * q^5 - 2 * q^7 - 10 * q^9	$ 18 q - 4 q^{5} - 2 q^{7} - 10 q^{9} + 2 q^{11} - 20 q^{15} - 6 q^{17} - 2 q^{19} - 16 q^{21} + 2 q^{23} + 6 q^{25} - 14 q^{29} - 8 q^{33} + 6 q^{35} + 8 q^{37} + 44 q^{43} - 4 q^{45} + 38 q^{47} - 8 q^{51} + 6 q^{55} + 24 q^{57} + 10 q^{59} + 14 q^{61} - 6 q^{63} - 12 q^{67} + 32 q^{69} - 24 q^{71} + 14 q^{73} - 64 q^{75} - 16 q^{79} + 2 q^{81} - 10 q^{85} - 24 q^{87} - 12 q^{89} + 16 q^{93} + 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) $ 18 * q - 4 * q^5 - 2 * q^7 - 10 * q^9 + 2 * q^11 - 20 * q^15 - 6 * q^17 - 2 * q^19 - 16 * q^21 + 2 * q^23 + 6 * q^25 - 14 * q^29 - 8 * q^33 + 6 * q^35 + 8 * q^37 + 44 * q^43 - 4 * q^45 + 38 * q^47 - 8 * q^51 + 6 * q^55 + 24 * q^57 + 10 * q^59 + 14 * q^61 - 6 * q^63 - 12 * q^67 + 32 * q^69 - 24 * q^71 + 14 * q^73 - 64 * q^75 - 16 * q^79 + 2 * q^81 - 10 * q^85 - 24 * q^87 - 12 * q^89 + 16 * q^93 + 34 * q^95 + 18 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$		−	1.28110i		−	0.739642i	−0.929103	−	0.369821i	$-0.879419\pi$
$3$		−	1.28110i		−	0.739642i	0.929103	−	0.369821i	$-0.120581\pi$
$4$		0			0
$5$	−0.841703	+	2.07160i	−0.376421	+	0.926449i
$5$	−0.841703	+	2.07160i	−0.376421	+	0.926449i
$6$		0			0
$7$	1.13975	−	1.13975i	0.430785	−	0.430785i	−0.458111	−	0.888895i	$-0.651474\pi$
$7$	1.13975	−	1.13975i	0.430785	−	0.430785i	0.888895	+	0.458111i	$0.151474\pi$
$8$		0			0
$9$	1.35879			0.452930
$10$		0			0
$11$	2.32204	−	2.32204i	0.700120	−	0.700120i	−0.264316	−	0.964436i	$-0.585146\pi$
$11$	2.32204	−	2.32204i	0.700120	−	0.700120i	0.964436	+	0.264316i	$0.0851462\pi$
$12$		0			0
$13$	1.36502			0.378589			0.189294	−	0.981920i	$-0.439380\pi$
$13$	1.36502			0.378589			0.189294	+	0.981920i	$0.439380\pi$
$14$		0			0
$15$	2.65392	+	1.07830i	0.685240	+	0.278416i
$16$		0			0
$17$	5.25380	−	5.25380i	1.27423	−	1.27423i	0.330389	−	0.943845i	$-0.392820\pi$
$17$	5.25380	−	5.25380i	1.27423	−	1.27423i	0.943845	−	0.330389i	$-0.107180\pi$
$18$		0			0
$19$	−3.69752	+	3.69752i	−0.848269	+	0.848269i	−0.989917	−	0.141648i	$-0.954760\pi$
$19$	−3.69752	+	3.69752i	−0.848269	+	0.848269i	0.141648	+	0.989917i	$0.454760\pi$
$20$		0			0
$21$	−1.46013	−	1.46013i	−0.318626	−	0.318626i
$22$		0			0
$23$	0.911118	+	0.911118i	0.189981	+	0.189981i	0.795688	−	0.605707i	$-0.207110\pi$
$23$	0.911118	+	0.911118i	0.189981	+	0.189981i	−0.605707	+	0.795688i	$0.707110\pi$
$24$		0			0
$25$	−3.58307	−	3.48735i	−0.716615	−	0.697469i
$26$		0			0
$27$		−	5.58403i		−	1.07465i
$28$		0			0
$29$	2.37343	+	2.37343i	0.440736	+	0.440736i	0.892259	−	0.451524i	$-0.149119\pi$
$29$	2.37343	+	2.37343i	0.440736	+	0.440736i	−0.451524	+	0.892259i	$0.649119\pi$
$30$		0			0
$31$		−	0.242577i		−	0.0435681i	−0.999763	−	0.0217841i	$-0.993065\pi$
$31$		−	0.242577i		−	0.0435681i	0.999763	−	0.0217841i	$-0.00693463\pi$
$32$		0			0
$33$	−2.97475	−	2.97475i	−0.517838	−	0.517838i
$34$		0			0
$35$	1.40178	+	3.32044i	0.236944	+	0.561256i
$36$		0			0
$37$	−3.34494			−0.549905			−0.274953	−	0.961458i	$-0.588662\pi$
$37$	−3.34494			−0.549905			−0.274953	+	0.961458i	$0.588662\pi$
$38$		0			0
$39$		−	1.74872i		−	0.280020i
$40$		0			0
$41$			2.66956i			0.416915i	0.978031	+	0.208457i	$0.0668442\pi$
$41$			2.66956i			0.416915i	−0.978031	+	0.208457i	$0.933156\pi$
$42$		0			0
$43$	−9.04874			−1.37992			−0.689960	−	0.723847i	$-0.742372\pi$
$43$	−9.04874			−1.37992			−0.689960	+	0.723847i	$0.742372\pi$
$44$		0			0
$45$	−1.14370	+	2.81488i	−0.170492	+	0.419617i
$46$		0			0
$47$	7.87820	+	7.87820i	1.14915	+	1.14915i	0.986719	+	0.162435i	$0.0519348\pi$
$47$	7.87820	+	7.87820i	1.14915	+	1.14915i	0.162435	+	0.986719i	$0.448065\pi$
$48$		0			0
$49$			4.40194i			0.628849i
$50$		0			0
$51$	−6.73063	−	6.73063i	−0.942476	−	0.942476i
$52$		0			0
$53$		−	5.80113i		−	0.796846i	−0.917202	−	0.398423i	$-0.869558\pi$
$53$		−	5.80113i		−	0.796846i	0.917202	−	0.398423i	$-0.130442\pi$
$54$		0			0
$55$	2.85587	+	6.76480i	0.385086	+	0.912165i
$56$		0			0
$57$	4.73688	+	4.73688i	0.627415	+	0.627415i
$58$		0			0
$59$	5.91474	+	5.91474i	0.770033	+	0.770033i	0.978112	−	0.208079i	$-0.0667210\pi$
$59$	5.91474	+	5.91474i	0.770033	+	0.770033i	−0.208079	+	0.978112i	$0.566721\pi$
$60$		0			0
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	−0.990686	−	0.136163i	$-0.956523\pi$
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	0.136163	+	0.990686i	$0.456523\pi$
$62$		0			0
$63$	1.54868	−	1.54868i	0.195116	−	0.195116i
$64$		0			0
$65$	−1.14894	+	2.82778i	−0.142509	+	0.350743i
$66$		0			0
$67$	4.54673			0.555471			0.277736	−	0.960658i	$-0.410416\pi$
$67$	4.54673			0.555471			0.277736	+	0.960658i	$0.410416\pi$
$68$		0			0
$69$	1.16723	−	1.16723i	0.140518	−	0.140518i
$70$		0			0
$71$	−15.4389			−1.83226			−0.916128	−	0.400885i	$-0.868703\pi$
$71$	−15.4389			−1.83226			−0.916128	+	0.400885i	$0.868703\pi$
$72$		0			0
$73$	1.49307	−	1.49307i	0.174750	−	0.174750i	−0.614313	−	0.789063i	$-0.710567\pi$
$73$	1.49307	−	1.49307i	0.174750	−	0.174750i	0.789063	+	0.614313i	$0.210567\pi$
$74$		0			0
$75$	−4.46763	+	4.59026i	−0.515877	+	0.530038i
$76$		0			0
$77$		−	5.29308i		−	0.603202i
$78$		0			0
$79$	−10.3024			−1.15911			−0.579556	−	0.814932i	$-0.696774\pi$
$79$	−10.3024			−1.15911			−0.579556	+	0.814932i	$0.696774\pi$
$80$		0			0
$81$	−3.07731			−0.341924
$82$		0			0
$83$		−	3.26589i		−	0.358478i	−0.983806	−	0.179239i	$-0.942636\pi$
$83$		−	3.26589i		−	0.358478i	0.983806	−	0.179239i	$-0.0573636\pi$
$84$		0			0
$85$	6.46165	+	15.3059i	0.700864	+	1.66016i
$86$		0			0
$87$	3.04060	−	3.04060i	0.325986	−	0.325986i
$88$		0			0
$89$	−9.77206			−1.03584			−0.517918	−	0.855430i	$-0.673293\pi$
$89$	−9.77206			−1.03584			−0.517918	+	0.855430i	$0.673293\pi$
$90$		0			0
$91$	1.55578	−	1.55578i	0.163090	−	0.163090i
$92$		0			0
$93$	−0.310765			−0.0322248
$94$		0			0
$95$	−4.54758	−	10.7720i	−0.466571	−	1.10518i
$96$		0			0
$97$	−1.63587	+	1.63587i	−0.166097	+	0.166097i	−0.785262	−	0.619164i	$-0.787472\pi$
$97$	−1.63587	+	1.63587i	−0.166097	+	0.166097i	0.619164	+	0.785262i	$0.287472\pi$
$98$		0			0
$99$	3.15516	−	3.15516i	0.317106	−	0.317106i
$100$		0			0
$101$	−6.63953	−	6.63953i	−0.660658	−	0.660658i	0.294877	−	0.955535i	$-0.404721\pi$
$101$	−6.63953	−	6.63953i	−0.660658	−	0.660658i	−0.955535	+	0.294877i	$0.904721\pi$
$102$		0			0
$103$	−1.62219	−	1.62219i	−0.159839	−	0.159839i	0.622656	−	0.782496i	$-0.286054\pi$
$103$	−1.62219	−	1.62219i	−0.159839	−	0.159839i	−0.782496	+	0.622656i	$0.786054\pi$
$104$		0			0
$105$	4.25380	−	1.79581i	0.415129	−	0.175253i
$106$		0			0
$107$			3.65206i			0.353058i	0.984295	+	0.176529i	$0.0564869\pi$
$107$			3.65206i			0.353058i	−0.984295	+	0.176529i	$0.943513\pi$
$108$		0			0
$109$	−5.20757	−	5.20757i	−0.498795	−	0.498795i	0.412268	−	0.911063i	$-0.364737\pi$
$109$	−5.20757	−	5.20757i	−0.498795	−	0.498795i	−0.911063	+	0.412268i	$0.864737\pi$
$110$		0			0
$111$			4.28519i			0.406733i
$112$		0			0
$113$	−4.27905	−	4.27905i	−0.402539	−	0.402539i	0.476588	−	0.879127i	$-0.341873\pi$
$113$	−4.27905	−	4.27905i	−0.402539	−	0.402539i	−0.879127	+	0.476588i	$0.841873\pi$
$114$		0			0
$115$	−2.65437	+	1.12058i	−0.247521	+	0.104495i
$116$		0			0
$117$	1.85478			0.171474
$118$		0			0
$119$		−	11.9760i		−	1.09784i
$120$		0			0
$121$			0.216302i			0.0196639i
$122$		0			0
$123$	3.41996			0.308367
$124$		0			0
$125$	10.2403	−	4.48739i	0.915918	−	0.401365i
$126$		0			0
$127$	−7.29257	−	7.29257i	−0.647111	−	0.647111i	0.305183	−	0.952294i	$-0.401282\pi$
$127$	−7.29257	−	7.29257i	−0.647111	−	0.647111i	−0.952294	+	0.305183i	$0.901282\pi$
$128$		0			0
$129$			11.5923i			1.02065i
$130$		0			0
$131$	11.9793	+	11.9793i	1.04664	+	1.04664i	0.998858	+	0.0477778i	$0.0152139\pi$
$131$	11.9793	+	11.9793i	1.04664	+	1.04664i	0.0477778	+	0.998858i	$0.484786\pi$
$132$		0			0
$133$			8.42848i			0.730842i
$134$		0			0
$135$	11.5679	+	4.70010i	0.995606	+	0.404520i
$136$		0			0
$137$	4.92762	+	4.92762i	0.420995	+	0.420995i	0.885546	−	0.464551i	$-0.153784\pi$
$137$	4.92762	+	4.92762i	0.420995	+	0.420995i	−0.464551	+	0.885546i	$0.653784\pi$
$138$		0			0
$139$	10.3015	+	10.3015i	0.873761	+	0.873761i	0.992880	−	0.119119i	$-0.0380071\pi$
$139$	10.3015	+	10.3015i	0.873761	+	0.873761i	−0.119119	+	0.992880i	$0.538007\pi$
$140$		0			0
$141$	10.0927	−	10.0927i	0.849962	−	0.849962i
$142$		0			0
$143$	3.16963	−	3.16963i	0.265058	−	0.265058i
$144$		0			0
$145$	−6.91454	+	2.91909i	−0.574221	+	0.242417i
$146$		0			0
$147$	5.63931			0.465123
$148$		0			0
$149$	15.2040	−	15.2040i	1.24556	−	1.24556i	0.287896	−	0.957662i	$-0.407044\pi$
$149$	15.2040	−	15.2040i	1.24556	−	1.24556i	0.957662	−	0.287896i	$-0.0929557\pi$
$150$		0			0
$151$	10.7055			0.871204			0.435602	−	0.900139i	$-0.356536\pi$
$151$	10.7055			0.871204			0.435602	+	0.900139i	$0.356536\pi$
$152$		0			0
$153$	7.13882	−	7.13882i	0.577139	−	0.577139i
$154$		0			0
$155$	0.502523	+	0.204178i	0.0403636	+	0.0164000i
$156$		0			0
$157$		−	2.34588i		−	0.187222i	−0.995609	−	0.0936108i	$-0.970159\pi$
$157$		−	2.34588i		−	0.187222i	0.995609	−	0.0936108i	$-0.0298409\pi$
$158$		0			0
$159$	−7.43180			−0.589380
$160$		0			0
$161$	2.07689			0.163682
$162$		0			0
$163$			2.73625i			0.214319i	0.994242	+	0.107160i	$0.0341756\pi$
$163$			2.73625i			0.214319i	−0.994242	+	0.107160i	$0.965824\pi$
$164$		0			0
$165$	8.66636	−	3.65865i	0.674675	−	0.284825i
$166$		0			0
$167$	−10.1328	+	10.1328i	−0.784097	+	0.784097i	−0.980519	−	0.196423i	$-0.937068\pi$
$167$	−10.1328	+	10.1328i	−0.784097	+	0.784097i	0.196423	+	0.980519i	$0.437068\pi$
$168$		0			0
$169$	−11.1367			−0.856670
$170$		0			0
$171$	−5.02415	+	5.02415i	−0.384207	+	0.384207i
$172$		0			0
$173$	−8.79590			−0.668740			−0.334370	−	0.942442i	$-0.608523\pi$
$173$	−8.79590			−0.668740			−0.334370	+	0.942442i	$0.608523\pi$
$174$		0			0
$175$	−8.05851	+	0.109105i	−0.609166	+	0.00824753i
$176$		0			0
$177$	7.57735	−	7.57735i	0.569549	−	0.569549i
$178$		0			0
$179$	6.62071	−	6.62071i	0.494855	−	0.494855i	−0.414977	−	0.909832i	$-0.636210\pi$
$179$	6.62071	−	6.62071i	0.494855	−	0.494855i	0.909832	+	0.414977i	$0.136210\pi$
$180$		0			0
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	0.455765	−	0.890100i	$-0.349366\pi$
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	−0.890100	+	0.455765i	$0.849366\pi$
$182$		0			0
$183$	8.55009	+	8.55009i	0.632041	+	0.632041i
$184$		0			0
$185$	2.81545	−	6.92939i	0.206996	−	0.509459i
$186$		0			0
$187$		−	24.3990i		−	1.78423i
$188$		0			0
$189$	−6.36440	−	6.36440i	−0.462942	−	0.462942i
$190$		0			0
$191$		−	1.83906i		−	0.133070i	−0.997784	−	0.0665349i	$-0.978806\pi$
$191$		−	1.83906i		−	0.133070i	0.997784	−	0.0665349i	$-0.0211944\pi$
$192$		0			0
$193$	6.18343	+	6.18343i	0.445093	+	0.445093i	0.893719	−	0.448626i	$-0.148087\pi$
$193$	6.18343	+	6.18343i	0.445093	+	0.445093i	−0.448626	+	0.893719i	$0.648087\pi$
$194$		0			0
$195$	3.62266	+	1.47191i	0.259424	+	0.105405i
$196$		0			0
$197$	5.55669			0.395898			0.197949	−	0.980212i	$-0.436572\pi$
$197$	5.55669			0.395898			0.197949	+	0.980212i	$0.436572\pi$
$198$		0			0
$199$			6.96413i			0.493674i	0.969057	+	0.246837i	$0.0793912\pi$
$199$			6.96413i			0.493674i	−0.969057	+	0.246837i	$0.920609\pi$
$200$		0			0
$201$		−	5.82480i		−	0.410850i
$202$		0			0
$203$	5.41024			0.379724
$204$		0			0
$205$	−5.53026	−	2.24697i	−0.386250	−	0.156935i
$206$		0			0
$207$	1.23802	+	1.23802i	0.0860483	+	0.0860483i
$208$		0			0
$209$			17.1715i			1.18778i
$210$		0			0
$211$	−5.43389	−	5.43389i	−0.374084	−	0.374084i	0.494878	−	0.868962i	$-0.335213\pi$
$211$	−5.43389	−	5.43389i	−0.374084	−	0.374084i	−0.868962	+	0.494878i	$0.835213\pi$
$212$		0			0
$213$			19.7787i			1.35521i
$214$		0			0
$215$	7.61635	−	18.7454i	0.519431	−	1.27843i
$216$		0			0
$217$	−0.276477	−	0.276477i	−0.0187685	−	0.0187685i
$218$		0			0
$219$	−1.91276	−	1.91276i	−0.129253	−	0.129253i
$220$		0			0
$221$	7.17155	−	7.17155i	0.482411	−	0.482411i
$222$		0			0
$223$	8.61776	−	8.61776i	0.577088	−	0.577088i	−0.357012	−	0.934100i	$-0.616204\pi$
$223$	8.61776	−	8.61776i	0.577088	−	0.577088i	0.934100	+	0.357012i	$0.116204\pi$
$224$		0			0
$225$	−4.86865	−	4.73858i	−0.324577	−	0.315905i
$226$		0			0
$227$	−6.01977			−0.399546			−0.199773	−	0.979842i	$-0.564020\pi$
$227$	−6.01977			−0.399546			−0.199773	+	0.979842i	$0.564020\pi$
$228$		0			0
$229$	0.568504	−	0.568504i	0.0375678	−	0.0375678i	−0.688073	−	0.725641i	$-0.741543\pi$
$229$	0.568504	−	0.568504i	0.0375678	−	0.0375678i	0.725641	+	0.688073i	$0.241543\pi$
$230$		0			0
$231$	−6.78094			−0.446153
$232$		0			0
$233$	−12.6979	+	12.6979i	−0.831869	+	0.831869i	−0.987772	−	0.155904i	$-0.950171\pi$
$233$	−12.6979	+	12.6979i	−0.831869	+	0.831869i	0.155904	+	0.987772i	$0.450171\pi$
$234$		0			0
$235$	−22.9516	+	9.68940i	−1.49720	+	0.632067i
$236$		0			0
$237$			13.1984i			0.857327i
$238$		0			0
$239$	1.78306			0.115336			0.0576682	−	0.998336i	$-0.481633\pi$
$239$	1.78306			0.115336			0.0576682	+	0.998336i	$0.481633\pi$
$240$		0			0
$241$	10.4440			0.672754			0.336377	−	0.941727i	$-0.390798\pi$
$241$	10.4440			0.672754			0.336377	+	0.941727i	$0.390798\pi$
$242$		0			0
$243$		−	12.8098i		−	0.821747i
$244$		0			0
$245$	−9.11908	−	3.70513i	−0.582596	−	0.236712i
$246$		0			0
$247$	−5.04719	+	5.04719i	−0.321145	+	0.321145i
$248$		0			0
$249$	−4.18392			−0.265145
$250$		0			0
$251$	12.6497	−	12.6497i	0.798445	−	0.798445i	−0.184406	−	0.982850i	$-0.559036\pi$
$251$	12.6497	−	12.6497i	0.798445	−	0.798445i	0.982850	+	0.184406i	$0.0590360\pi$
$252$		0			0
$253$	4.23130			0.266019
$254$		0			0
$255$	19.6084	−	8.27800i	1.22792	−	0.518388i
$256$		0			0
$257$	−4.13062	+	4.13062i	−0.257661	+	0.257661i	−0.824102	−	0.566441i	$-0.808320\pi$
$257$	−4.13062	+	4.13062i	−0.257661	+	0.257661i	0.566441	+	0.824102i	$0.308320\pi$
$258$		0			0
$259$	−3.81240	+	3.81240i	−0.236891	+	0.236891i
$260$		0			0
$261$	3.22500	+	3.22500i	0.199623	+	0.199623i
$262$		0			0
$263$	−17.1303	−	17.1303i	−1.05630	−	1.05630i	−0.998318	−	0.0579798i	$-0.981534\pi$
$263$	−17.1303	−	17.1303i	−1.05630	−	1.05630i	−0.0579798	−	0.998318i	$-0.518466\pi$
$264$		0			0
$265$	12.0176	+	4.88282i	0.738237	+	0.299949i
$266$		0			0
$267$			12.5190i			0.766147i
$268$		0			0
$269$	19.8075	+	19.8075i	1.20768	+	1.20768i	0.971775	+	0.235910i	$0.0758070\pi$
$269$	19.8075	+	19.8075i	1.20768	+	1.20768i	0.235910	+	0.971775i	$0.424193\pi$
$270$		0			0
$271$			27.9542i			1.69810i	0.528316	+	0.849048i	$0.322824\pi$
$271$			27.9542i			1.69810i	−0.528316	+	0.849048i	$0.677176\pi$
$272$		0			0
$273$	−1.99311	−	1.99311i	−0.120628	−	0.120628i
$274$		0			0
$275$	−16.4178	+	0.222281i	−0.990029	+	0.0134041i
$276$		0			0
$277$	−26.0257			−1.56373			−0.781866	−	0.623447i	$-0.785732\pi$
$277$	−26.0257			−1.56373			−0.781866	+	0.623447i	$0.785732\pi$
$278$		0			0
$279$		−	0.329612i		−	0.0197333i
$280$		0			0
$281$			24.1001i			1.43769i	0.695170	+	0.718846i	$0.255329\pi$
$281$			24.1001i			1.43769i	−0.695170	+	0.718846i	$0.744671\pi$
$282$		0			0
$283$	−4.73708			−0.281590			−0.140795	−	0.990039i	$-0.544966\pi$
$283$	−4.73708			−0.281590			−0.140795	+	0.990039i	$0.544966\pi$
$284$		0			0
$285$	−13.8000	+	5.82588i	−0.817439	+	0.345096i
$286$		0			0
$287$	3.04262	+	3.04262i	0.179600	+	0.179600i
$288$		0			0
$289$		−	38.2049i		−	2.24734i
$290$		0			0
$291$	2.09571	+	2.09571i	0.122852	+	0.122852i
$292$		0			0
$293$		−	3.11001i		−	0.181689i	−0.995865	−	0.0908445i	$-0.971043\pi$
$293$		−	3.11001i		−	0.181689i	0.995865	−	0.0908445i	$-0.0289566\pi$
$294$		0			0
$295$	−17.2314	+	7.27454i	−1.00325	+	0.423540i
$296$		0			0
$297$	−12.9663	−	12.9663i	−0.752382	−	0.752382i
$298$		0			0
$299$	1.24370	+	1.24370i	0.0719248	+	0.0719248i
$300$		0			0
$301$	−10.3133	+	10.3133i	−0.594449	+	0.594449i
$302$		0			0
$303$	−8.50588	+	8.50588i	−0.488650	+	0.488650i
$304$		0			0
$305$	−8.20840	−	19.4435i	−0.470012	−	1.11333i
$306$		0			0
$307$	−14.5670			−0.831382			−0.415691	−	0.909506i	$-0.636460\pi$
$307$	−14.5670			−0.831382			−0.415691	+	0.909506i	$0.636460\pi$
$308$		0			0
$309$	−2.07819	+	2.07819i	−0.118224	+	0.118224i
$310$		0			0
$311$	14.4572			0.819791			0.409896	−	0.912132i	$-0.365565\pi$
$311$	14.4572			0.819791			0.409896	+	0.912132i	$0.365565\pi$
$312$		0			0
$313$	10.1273	−	10.1273i	0.572429	−	0.572429i	−0.360377	−	0.932807i	$-0.617352\pi$
$313$	10.1273	−	10.1273i	0.572429	−	0.572429i	0.932807	+	0.360377i	$0.117352\pi$
$314$		0			0
$315$	1.90472	+	4.51178i	0.107319	+	0.254210i
$316$		0			0
$317$			13.8750i			0.779295i	0.920964	+	0.389648i	$0.127403\pi$
$317$			13.8750i			0.779295i	−0.920964	+	0.389648i	$0.872597\pi$
$318$		0			0
$319$	11.0224			0.617136
$320$		0			0
$321$	4.67864			0.261136
$322$		0			0
$323$			38.8520i			2.16179i
$324$		0			0
$325$	−4.89097	−	4.76030i	−0.271302	−	0.264054i
$326$		0			0
$327$	−6.67140	+	6.67140i	−0.368930	+	0.368930i
$328$		0			0
$329$	17.9584			0.990076
$330$		0			0
$331$	−1.69458	+	1.69458i	−0.0931425	+	0.0931425i	−0.752143	−	0.659000i	$-0.770980\pi$
$331$	−1.69458	+	1.69458i	−0.0931425	+	0.0931425i	0.659000	+	0.752143i	$0.270980\pi$
$332$		0			0
$333$	−4.54508			−0.249069
$334$		0			0
$335$	−3.82699	+	9.41902i	−0.209091	+	0.514616i
$336$		0			0
$337$	−9.53338	+	9.53338i	−0.519316	+	0.519316i	−0.917364	−	0.398048i	$-0.869688\pi$
$337$	−9.53338	+	9.53338i	−0.519316	+	0.519316i	0.398048	+	0.917364i	$0.369688\pi$
$338$		0			0
$339$	−5.48188	+	5.48188i	−0.297735	+	0.297735i
$340$		0			0
$341$	−0.563273	−	0.563273i	−0.0305029	−	0.0305029i
$342$		0			0
$343$	12.9954	+	12.9954i	0.701683	+	0.701683i
$344$		0			0
$345$	1.43558	+	3.40050i	0.0772888	+	0.183077i
$346$		0			0
$347$		−	6.67273i		−	0.358211i	−0.983830	−	0.179105i	$-0.942680\pi$
$347$		−	6.67273i		−	0.358211i	0.983830	−	0.179105i	$-0.0573203\pi$
$348$		0			0
$349$	−2.02618	−	2.02618i	−0.108459	−	0.108459i	0.650795	−	0.759254i	$-0.274436\pi$
$349$	−2.02618	−	2.02618i	−0.108459	−	0.108459i	−0.759254	+	0.650795i	$0.774436\pi$
$350$		0			0
$351$		−	7.62233i		−	0.406850i
$352$		0			0
$353$	−5.36542	−	5.36542i	−0.285572	−	0.285572i	0.549754	−	0.835327i	$-0.314721\pi$
$353$	−5.36542	−	5.36542i	−0.285572	−	0.285572i	−0.835327	+	0.549754i	$0.814721\pi$
$354$		0			0
$355$	12.9949	−	31.9832i	0.689700	−	1.69749i
$356$		0			0
$357$	−15.3425			−0.812009
$358$		0			0
$359$		−	7.76117i		−	0.409619i	−0.978802	−	0.204809i	$-0.934343\pi$
$359$		−	7.76117i		−	0.409619i	0.978802	−	0.204809i	$-0.0656574\pi$
$360$		0			0
$361$		−	8.34326i		−	0.439119i
$362$		0			0
$363$	0.277104			0.0145442
$364$		0			0
$365$	1.83632	+	4.34976i	0.0961175	+	0.227677i
$366$		0			0
$367$	18.0536	+	18.0536i	0.942389	+	0.942389i	0.998429	−	0.0560392i	$-0.0178472\pi$
$367$	18.0536	+	18.0536i	0.942389	+	0.942389i	−0.0560392	+	0.998429i	$0.517847\pi$
$368$		0			0
$369$			3.62737i			0.188833i
$370$		0			0
$371$	−6.61183	−	6.61183i	−0.343269	−	0.343269i
$372$		0			0
$373$		−	4.36197i		−	0.225854i	−0.993603	−	0.112927i	$-0.963977\pi$
$373$		−	4.36197i		−	0.225854i	0.993603	−	0.112927i	$-0.0360226\pi$
$374$		0			0
$375$	−5.74879	−	13.1188i	−0.296866	−	0.677451i
$376$		0			0
$377$	3.23979	+	3.23979i	0.166858	+	0.166858i
$378$		0			0
$379$	−5.93072	−	5.93072i	−0.304641	−	0.304641i	0.538186	−	0.842826i	$-0.319110\pi$
$379$	−5.93072	−	5.93072i	−0.304641	−	0.304641i	−0.842826	+	0.538186i	$0.819110\pi$
$380$		0			0
$381$	−9.34249	+	9.34249i	−0.478630	+	0.478630i
$382$		0			0
$383$	−19.3340	+	19.3340i	−0.987922	+	0.987922i	−0.999928	−	0.0120057i	$-0.996178\pi$
$383$	−19.3340	+	19.3340i	−0.987922	+	0.987922i	0.0120057	+	0.999928i	$0.496178\pi$
$384$		0			0
$385$	10.9652	+	4.45520i	0.558836	+	0.227058i
$386$		0			0
$387$	−12.2954			−0.625008
$388$		0			0
$389$	−6.28607	+	6.28607i	−0.318716	+	0.318716i	−0.848274	−	0.529558i	$-0.822358\pi$
$389$	−6.28607	+	6.28607i	−0.318716	+	0.318716i	0.529558	+	0.848274i	$0.322358\pi$
$390$		0			0
$391$	9.57367			0.484161
$392$		0			0
$393$	15.3466	−	15.3466i	0.774135	−	0.774135i
$394$		0			0
$395$	8.67157	−	21.3425i	0.436314	−	1.07386i
$396$		0			0
$397$		−	6.58413i		−	0.330448i	−0.986256	−	0.165224i	$-0.947165\pi$
$397$		−	6.58413i		−	0.330448i	0.986256	−	0.165224i	$-0.0528347\pi$
$398$		0			0
$399$	10.7977			0.540561
$400$		0			0
$401$	19.7951			0.988522			0.494261	−	0.869313i	$-0.335439\pi$
$401$	19.7951			0.988522			0.494261	+	0.869313i	$0.335439\pi$
$402$		0			0
$403$		−	0.331123i		−	0.0164944i
$404$		0			0
$405$	2.59018	−	6.37497i	0.128707	−	0.316775i
$406$		0			0
$407$	−7.76707	+	7.76707i	−0.385000	+	0.385000i
$408$		0			0
$409$	−5.76937			−0.285277			−0.142638	−	0.989775i	$-0.545559\pi$
$409$	−5.76937			−0.285277			−0.142638	+	0.989775i	$0.545559\pi$
$410$		0			0
$411$	6.31276	−	6.31276i	0.311385	−	0.311385i
$412$		0			0
$413$	13.4826			0.663437
$414$		0			0
$415$	6.76563	+	2.74891i	0.332112	+	0.134939i
$416$		0			0
$417$	13.1972	−	13.1972i	0.646270	−	0.646270i
$418$		0			0
$419$	8.68932	−	8.68932i	0.424501	−	0.424501i	−0.462249	−	0.886750i	$-0.652957\pi$
$419$	8.68932	−	8.68932i	0.424501	−	0.424501i	0.886750	+	0.462249i	$0.152957\pi$
$420$		0			0
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	0.999815	−	0.0192594i	$-0.00613083\pi$
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	−0.0192594	+	0.999815i	$0.506131\pi$
$422$		0			0
$423$	10.7048	+	10.7048i	0.520487	+	0.520487i
$424$		0			0
$425$	−37.1466	+	0.502930i	−1.80187	+	0.0243957i
$426$		0			0
$427$			15.2135i			0.736231i
$428$		0			0
$429$	−4.06060	−	4.06060i	−0.196048	−	0.196048i
$430$		0			0
$431$		−	33.6247i		−	1.61965i	−0.586675	−	0.809823i	$-0.699563\pi$
$431$		−	33.6247i		−	1.61965i	0.586675	−	0.809823i	$-0.300437\pi$
$432$		0			0
$433$	7.46558	+	7.46558i	0.358773	+	0.358773i	0.863361	−	0.504588i	$-0.168355\pi$
$433$	7.46558	+	7.46558i	0.358773	+	0.358773i	−0.504588	+	0.863361i	$0.668355\pi$
$434$		0			0
$435$	3.73963	+	8.85819i	0.179302	+	0.424718i
$436$		0			0
$437$	−6.73775			−0.322310
$438$		0			0
$439$		−	7.91929i		−	0.377967i	−0.981980	−	0.188984i	$-0.939481\pi$
$439$		−	7.91929i		−	0.377967i	0.981980	−	0.188984i	$-0.0605193\pi$
$440$		0			0
$441$			5.98132i			0.284825i
$442$		0			0
$443$	−10.6463			−0.505823			−0.252911	−	0.967489i	$-0.581388\pi$
$443$	−10.6463			−0.505823			−0.252911	+	0.967489i	$0.581388\pi$
$444$		0			0
$445$	8.22517	−	20.2438i	0.389910	−	0.959649i
$446$		0			0
$447$	−19.4778	−	19.4778i	−0.921266	−	0.921266i
$448$		0			0
$449$			6.08115i			0.286987i	0.989651	+	0.143494i	$0.0458336\pi$
$449$			6.08115i			0.286987i	−0.989651	+	0.143494i	$0.954166\pi$
$450$		0			0
$451$	6.19880	+	6.19880i	0.291890	+	0.291890i
$452$		0			0
$453$		−	13.7148i		−	0.644379i
$454$		0			0
$455$	1.91346	+	4.53247i	0.0897042	+	0.212485i
$456$		0			0
$457$	−0.313815	−	0.313815i	−0.0146796	−	0.0146796i	0.699729	−	0.714409i	$-0.253304\pi$
$457$	−0.313815	−	0.313815i	−0.0146796	−	0.0146796i	−0.714409	+	0.699729i	$0.753304\pi$
$458$		0			0
$459$	−29.3374	−	29.3374i	−1.36935	−	1.36935i
$460$		0			0
$461$	9.90949	−	9.90949i	0.461531	−	0.461531i	−0.437626	−	0.899157i	$-0.644181\pi$
$461$	9.90949	−	9.90949i	0.461531	−	0.461531i	0.899157	+	0.437626i	$0.144181\pi$
$462$		0			0
$463$	17.3430	−	17.3430i	0.805999	−	0.805999i	−0.178027	−	0.984026i	$-0.556971\pi$
$463$	17.3430	−	17.3430i	0.805999	−	0.805999i	0.984026	+	0.178027i	$0.0569714\pi$
$464$		0			0
$465$	0.261571	−	0.643781i	0.0121301	−	0.0298546i
$466$		0			0
$467$	−1.52267			−0.0704606			−0.0352303	−	0.999379i	$-0.511216\pi$
$467$	−1.52267			−0.0704606			−0.0352303	+	0.999379i	$0.511216\pi$
$468$		0			0
$469$	5.18213	−	5.18213i	0.239289	−	0.239289i
$470$		0			0
$471$	−3.00530			−0.138477
$472$		0			0
$473$	−21.0115	+	21.0115i	−0.966110	+	0.966110i
$474$		0			0
$475$	26.1430	−	0.353952i	1.19952	−	0.0162404i
$476$		0			0
$477$		−	7.88252i		−	0.360916i
$478$		0			0
$479$	0.507657			0.0231955			0.0115977	−	0.999933i	$-0.496308\pi$
$479$	0.507657			0.0231955			0.0115977	+	0.999933i	$0.496308\pi$
$480$		0			0
$481$	−4.56592			−0.208188
$482$		0			0
$483$		−	2.66070i		−	0.121066i
$484$		0			0
$485$	−2.01195	−	4.76578i	−0.0913581	−	0.216403i
$486$		0			0
$487$	25.9809	−	25.9809i	1.17730	−	1.17730i	0.196876	−	0.980428i	$-0.436920\pi$
$487$	25.9809	−	25.9809i	1.17730	−	1.17730i	0.980428	−	0.196876i	$-0.0630798\pi$
$488$		0			0
$489$	3.50539			0.158519
$490$		0			0
$491$	3.28208	−	3.28208i	0.148118	−	0.148118i	−0.629159	−	0.777277i	$-0.716600\pi$
$491$	3.28208	−	3.28208i	0.148118	−	0.148118i	0.777277	+	0.629159i	$0.216600\pi$
$492$		0			0
$493$	24.9391			1.12320
$494$		0			0
$495$	3.88053	+	9.19195i	0.174417	+	0.413147i
$496$		0			0
$497$	−17.5964	+	17.5964i	−0.789308	+	0.789308i
$498$		0			0
$499$	−6.73907	+	6.73907i	−0.301682	+	0.301682i	−0.841672	−	0.539990i	$-0.818428\pi$
$499$	−6.73907	+	6.73907i	−0.301682	+	0.301682i	0.539990	+	0.841672i	$0.318428\pi$
$500$		0			0
$501$	12.9810	+	12.9810i	0.579950	+	0.579950i
$502$		0			0
$503$	6.12090	+	6.12090i	0.272918	+	0.272918i	0.830274	−	0.557356i	$-0.188184\pi$
$503$	6.12090	+	6.12090i	0.272918	+	0.272918i	−0.557356	+	0.830274i	$0.688184\pi$
$504$		0			0
$505$	19.3430	−	8.16596i	0.860752	−	0.363380i
$506$		0			0
$507$			14.2672i			0.633629i
$508$		0			0
$509$	−13.8727	−	13.8727i	−0.614894	−	0.614894i	0.329323	−	0.944217i	$-0.393180\pi$
$509$	−13.8727	−	13.8727i	−0.614894	−	0.614894i	−0.944217	+	0.329323i	$0.893180\pi$
$510$		0			0
$511$		−	3.40344i		−	0.150559i
$512$		0			0
$513$	20.6471	+	20.6471i	0.911590	+	0.911590i
$514$		0			0
$515$	4.72594	−	1.99514i	0.208250	−	0.0879162i
$516$		0			0
$517$	36.5869			1.60909
$518$		0			0
$519$			11.2684i			0.494628i
$520$		0			0
$521$		−	5.87686i		−	0.257470i	−0.991679	−	0.128735i	$-0.958908\pi$
$521$		−	5.87686i		−	0.257470i	0.991679	−	0.128735i	$-0.0410917\pi$
$522$		0			0
$523$	26.0176			1.13767			0.568834	−	0.822452i	$-0.307395\pi$
$523$	26.0176			1.13767			0.568834	+	0.822452i	$0.307395\pi$
$524$		0			0
$525$	0.139774	+	10.3237i	0.00610022	+	0.450564i
$526$		0			0
$527$	−1.27445	−	1.27445i	−0.0555160	−	0.0555160i
$528$		0			0
$529$		−	21.3397i		−	0.927814i
$530$		0			0
$531$	8.03690	+	8.03690i	0.348772	+	0.348772i
$532$		0			0
$533$			3.64400i			0.157839i
$534$		0			0
$535$	−7.56561	−	3.07394i	−0.327090	−	0.132898i
$536$		0			0
$537$	−8.48177	−	8.48177i	−0.366016	−	0.366016i
$538$		0			0
$539$	10.2215	+	10.2215i	0.440270	+	0.440270i
$540$		0			0
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	−0.834210	−	0.551447i	$-0.814076\pi$
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	0.551447	+	0.834210i	$0.314076\pi$
$542$		0			0
$543$	−7.48594	+	7.48594i	−0.321253	+	0.321253i
$544$		0			0
$545$	15.1712	−	6.40479i	0.649865	−	0.274351i
$546$		0			0
$547$	10.6170			0.453951			0.226976	−	0.973900i	$-0.427116\pi$
$547$	10.6170			0.453951			0.226976	+	0.973900i	$0.427116\pi$
$548$		0			0
$549$	−9.06863	+	9.06863i	−0.387040	+	0.387040i
$550$		0			0
$551$	−17.5516			−0.747724
$552$		0			0
$553$	−11.7422	+	11.7422i	−0.499328	+	0.499328i
$554$		0			0
$555$	−8.87722	−	3.60686i	−0.376817	−	0.153103i
$556$		0			0
$557$		−	20.9610i		−	0.888146i	−0.895991	−	0.444073i	$-0.853533\pi$
$557$		−	20.9610i		−	0.888146i	0.895991	−	0.444073i	$-0.146467\pi$
$558$		0			0
$559$	−12.3517			−0.522422
$560$		0			0
$561$	−31.2575			−1.31969
$562$		0			0
$563$		−	16.5598i		−	0.697911i	−0.937139	−	0.348955i	$-0.886536\pi$
$563$		−	16.5598i		−	0.697911i	0.937139	−	0.348955i	$-0.113464\pi$
$564$		0			0
$565$	12.4662	−	5.26280i	0.524456	−	0.221408i
$566$		0			0
$567$	−3.50736	+	3.50736i	−0.147295	+	0.147295i
$568$		0			0
$569$	39.6751			1.66327			0.831634	−	0.555325i	$-0.187406\pi$
$569$	39.6751			1.66327			0.831634	+	0.555325i	$0.187406\pi$
$570$		0			0
$571$	−24.0292	+	24.0292i	−1.00559	+	1.00559i	−0.00560819	+	0.999984i	$0.501785\pi$
$571$	−24.0292	+	24.0292i	−1.00559	+	1.00559i	−0.999984	+	0.00560819i	$0.998215\pi$
$572$		0			0
$573$	−2.35602			−0.0984240
$574$		0			0
$575$	−0.0872185	−	6.44199i	−0.00363726	−	0.268649i
$576$		0			0
$577$	−28.7705	+	28.7705i	−1.19773	+	1.19773i	−0.222888	+	0.974844i	$0.571549\pi$
$577$	−28.7705	+	28.7705i	−1.19773	+	1.19773i	−0.974844	+	0.222888i	$0.928451\pi$
$578$		0			0
$579$	7.92157	−	7.92157i	0.329209	−	0.329209i
$580$		0			0
$581$	−3.72230	−	3.72230i	−0.154427	−	0.154427i
$582$		0			0
$583$	−13.4704	−	13.4704i	−0.557888	−	0.557888i
$584$		0			0
$585$	−1.56117	+	3.84237i	−0.0645466	+	0.158862i
$586$		0			0
$587$			33.4854i			1.38209i	0.722811	+	0.691046i	$0.242850\pi$
$587$			33.4854i			1.38209i	−0.722811	+	0.691046i	$0.757150\pi$
$588$		0			0
$589$	0.896933	+	0.896933i	0.0369575	+	0.0369575i
$590$		0			0
$591$		−	7.11866i		−	0.292822i
$592$		0			0
$593$	11.5298	+	11.5298i	0.473472	+	0.473472i	0.903036	−	0.429564i	$-0.141333\pi$
$593$	11.5298	+	11.5298i	0.473472	+	0.473472i	−0.429564	+	0.903036i	$0.641333\pi$
$594$		0			0
$595$	24.8096	+	10.0803i	1.01709	+	0.413250i
$596$		0			0
$597$	8.92172			0.365142
$598$		0			0
$599$			20.0148i			0.817781i	0.912583	+	0.408891i	$0.134084\pi$
$599$			20.0148i			0.817781i	−0.912583	+	0.408891i	$0.865916\pi$
$600$		0			0
$601$		−	27.5924i		−	1.12552i	−0.826621	−	0.562759i	$-0.809740\pi$
$601$		−	27.5924i		−	1.12552i	0.826621	−	0.562759i	$-0.190260\pi$
$602$		0			0
$603$	6.17806			0.251590
$604$		0			0
$605$	−0.448093	−	0.182062i	−0.0182176	−	0.00740188i
$606$		0			0
$607$	−30.4850	−	30.4850i	−1.23735	−	1.23735i	−0.961081	−	0.276265i	$-0.910903\pi$
$607$	−30.4850	−	30.4850i	−1.23735	−	1.23735i	−0.276265	−	0.961081i	$-0.589097\pi$
$608$		0			0
$609$		−	6.93104i		−	0.280860i
$610$		0			0
$611$	10.7539	+	10.7539i	0.435057	+	0.435057i
$612$		0			0
$613$		−	20.2657i		−	0.818523i	−0.912417	−	0.409261i	$-0.865786\pi$
$613$		−	20.2657i		−	0.818523i	0.912417	−	0.409261i	$-0.134214\pi$
$614$		0			0
$615$	−2.87859	+	7.08480i	−0.116076	+	0.285687i
$616$		0			0
$617$	−1.61302	−	1.61302i	−0.0649378	−	0.0649378i	0.673892	−	0.738830i	$-0.264621\pi$
$617$	−1.61302	−	1.61302i	−0.0649378	−	0.0649378i	−0.738830	+	0.673892i	$0.764621\pi$
$618$		0			0
$619$	−2.46756	−	2.46756i	−0.0991797	−	0.0991797i	0.655776	−	0.754956i	$-0.272342\pi$
$619$	−2.46756	−	2.46756i	−0.0991797	−	0.0991797i	−0.754956	+	0.655776i	$0.772342\pi$
$620$		0			0
$621$	5.08771	−	5.08771i	0.204163	−	0.204163i
$622$		0			0
$623$	−11.1377	+	11.1377i	−0.446222	+	0.446222i
$624$		0			0
$625$	0.676829	+	24.9908i	0.0270732	+	0.999633i
$626$		0			0
$627$	21.9984			0.878531
$628$		0			0
$629$	−17.5737	+	17.5737i	−0.700708	+	0.700708i
$630$		0			0
$631$	29.9602			1.19270			0.596348	−	0.802726i	$-0.296618\pi$
$631$	29.9602			1.19270			0.596348	+	0.802726i	$0.296618\pi$
$632$		0			0
$633$	−6.96133	+	6.96133i	−0.276688	+	0.276688i
$634$		0			0
$635$	21.2455	−	8.96913i	0.843101	−	0.355929i
$636$		0			0
$637$			6.00875i			0.238075i
$638$		0			0
$639$	−20.9782			−0.829885
$640$		0			0
$641$	−37.3386			−1.47478			−0.737392	−	0.675465i	$-0.763943\pi$
$641$	−37.3386			−1.47478			−0.737392	+	0.675465i	$0.763943\pi$
$642$		0			0
$643$		−	24.5635i		−	0.968691i	−0.874877	−	0.484345i	$-0.839058\pi$
$643$		−	24.5635i		−	0.968691i	0.874877	−	0.484345i	$-0.160942\pi$
$644$		0			0
$645$	−24.0147	−	9.75728i	−0.945577	−	0.384193i
$646$		0			0
$647$	23.1347	−	23.1347i	0.909519	−	0.909519i	−0.0867142	−	0.996233i	$-0.527637\pi$
$647$	23.1347	−	23.1347i	0.909519	−	0.909519i	0.996233	+	0.0867142i	$0.0276367\pi$
$648$		0			0
$649$	27.4685			1.07823
$650$		0			0
$651$	−0.354194	+	0.354194i	−0.0138820	+	0.0138820i
$652$		0			0
$653$	−50.8060			−1.98819			−0.994097	−	0.108496i	$-0.965397\pi$
$653$	−50.8060			−1.98819			−0.994097	+	0.108496i	$0.965397\pi$
$654$		0			0
$655$	−34.8993	+	14.7333i	−1.36363	+	0.575679i
$656$		0			0
$657$	2.02877	−	2.02877i	0.0791497	−	0.0791497i
$658$		0			0
$659$	−9.97780	+	9.97780i	−0.388680	+	0.388680i	−0.874216	−	0.485537i	$-0.838624\pi$
$659$	−9.97780	+	9.97780i	−0.388680	+	0.388680i	0.485537	+	0.874216i	$0.338624\pi$
$660$		0			0
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	0.601012	−	0.799240i	$-0.294764\pi$
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	−0.799240	+	0.601012i	$0.794764\pi$
$662$		0			0
$663$	−9.18745	−	9.18745i	−0.356811	−	0.356811i
$664$		0			0
$665$	−17.4605	−	7.09428i	−0.677088	−	0.275104i
$666$		0			0
$667$			4.32496i			0.167463i
$668$		0			0
$669$	−11.0402	−	11.0402i	−0.426838	−	0.426838i
$670$		0			0
$671$			30.9947i			1.19654i
$672$		0			0
$673$	−31.6322	−	31.6322i	−1.21933	−	1.21933i	−0.967867	−	0.251464i	$-0.919088\pi$
$673$	−31.6322	−	31.6322i	−1.21933	−	1.21933i	−0.251464	−	0.967867i	$-0.580912\pi$
$674$		0			0
$675$	−19.4735	+	20.0080i	−0.749534	+	0.770108i
$676$		0			0
$677$	25.6600			0.986196			0.493098	−	0.869974i	$-0.335864\pi$
$677$	25.6600			0.986196			0.493098	+	0.869974i	$0.335864\pi$
$678$		0			0
$679$			3.72896i			0.143104i
$680$		0			0
$681$			7.71190i			0.295521i
$682$		0			0
$683$	−12.3536			−0.472698			−0.236349	−	0.971668i	$-0.575951\pi$
$683$	−12.3536			−0.472698			−0.236349	+	0.971668i	$0.575951\pi$
$684$		0			0
$685$	−14.3557	+	6.06048i	−0.548501	+	0.231559i
$686$		0			0
$687$	−0.728309	−	0.728309i	−0.0277867	−	0.0277867i
$688$		0			0
$689$		−	7.91866i		−	0.301677i
$690$		0			0
$691$	−22.5426	−	22.5426i	−0.857561	−	0.857561i	0.133489	−	0.991050i	$-0.457382\pi$
$691$	−22.5426	−	22.5426i	−0.857561	−	0.857561i	−0.991050	+	0.133489i	$0.957382\pi$
$692$		0			0
$693$		−	7.19219i		−	0.273209i
$694$		0			0
$695$	−30.0114	+	12.6698i	−1.13840	+	0.480593i
$696$		0			0
$697$	14.0253	+	14.0253i	0.531247	+	0.531247i
$698$		0			0
$699$	16.2673	+	16.2673i	0.615285	+	0.615285i
$700$		0			0
$701$	26.9530	−	26.9530i	1.01800	−	1.01800i	0.0181663	−	0.999835i	$-0.494217\pi$
$701$	26.9530	−	26.9530i	1.01800	−	1.01800i	0.999835	−	0.0181663i	$-0.00578284\pi$
$702$		0			0
$703$	12.3680	−	12.3680i	0.466467	−	0.466467i
$704$		0			0
$705$	12.4131	+	29.4032i	0.467503	+	1.10739i
$706$		0			0
$707$	−15.1348			−0.569203
$708$		0			0
$709$	−7.78615	+	7.78615i	−0.292415	+	0.292415i	−0.838034	−	0.545619i	$-0.816295\pi$
$709$	−7.78615	+	7.78615i	−0.292415	+	0.292415i	0.545619	+	0.838034i	$0.316295\pi$
$710$		0			0
$711$	−13.9988			−0.524997
$712$		0			0
$713$	0.221016	−	0.221016i	0.00827713	−	0.00827713i
$714$		0			0
$715$	3.89833	+	9.23410i	0.145789	+	0.345336i
$716$		0			0
$717$		−	2.28427i		−	0.0853076i
$718$		0			0
$719$	20.6777			0.771150			0.385575	−	0.922677i	$-0.374003\pi$
$719$	20.6777			0.771150			0.385575	+	0.922677i	$0.374003\pi$
$720$		0			0
$721$	−3.69779			−0.137713
$722$		0			0
$723$		−	13.3797i		−	0.497597i
$724$		0			0
$725$	−0.227201	−	16.7812i	−0.00843805	−	0.623237i
$726$		0			0
$727$	−20.4994	+	20.4994i	−0.760280	+	0.760280i	−0.976373	−	0.216093i	$-0.930669\pi$
$727$	−20.4994	+	20.4994i	−0.760280	+	0.760280i	0.216093	+	0.976373i	$0.430669\pi$
$728$		0			0
$729$	−25.6425			−0.949722
$730$		0			0
$731$	−47.5403	+	47.5403i	−1.75834	+	1.75834i
$732$		0			0
$733$	10.7306			0.396344			0.198172	−	0.980167i	$-0.436500\pi$
$733$	10.7306			0.396344			0.198172	+	0.980167i	$0.436500\pi$
$734$		0			0
$735$	−4.74663	+	11.6824i	−0.175082	+	0.430912i
$736$		0			0
$737$	10.5577	−	10.5577i	0.388897	−	0.388897i
$738$		0			0
$739$	2.93837	−	2.93837i	0.108090	−	0.108090i	−0.650994	−	0.759083i	$-0.725648\pi$
$739$	2.93837	−	2.93837i	0.108090	−	0.108090i	0.759083	+	0.650994i	$0.225648\pi$
$740$		0			0
$741$	6.46594	+	6.46594i	0.237532	+	0.237532i
$742$		0			0
$743$	0.223404	+	0.223404i	0.00819590	+	0.00819590i	0.711193	−	0.702997i	$-0.248155\pi$
$743$	0.223404	+	0.223404i	0.00819590	+	0.00819590i	−0.702997	+	0.711193i	$0.748155\pi$
$744$		0			0
$745$	18.6994	+	44.2938i	0.685091	+	1.62280i
$746$		0			0
$747$		−	4.43766i		−	0.162366i
$748$		0			0
$749$	4.16243	+	4.16243i	0.152092	+	0.152092i
$750$		0			0
$751$		−	39.9939i		−	1.45940i	−0.683769	−	0.729699i	$-0.739660\pi$
$751$		−	39.9939i		−	1.45940i	0.683769	−	0.729699i	$-0.260340\pi$
$752$		0			0
$753$	−16.2055	−	16.2055i	−0.590563	−	0.590563i
$754$		0			0
$755$	−9.01088	+	22.1776i	−0.327939	+	0.807126i
$756$		0			0
$757$	32.9120			1.19621			0.598103	−	0.801419i	$-0.295921\pi$
$757$	32.9120			1.19621			0.598103	+	0.801419i	$0.295921\pi$
$758$		0			0
$759$		−	5.42070i		−	0.196759i
$760$		0			0
$761$		−	33.9591i		−	1.23102i	−0.788130	−	0.615509i	$-0.788951\pi$
$761$		−	33.9591i		−	1.23102i	0.788130	−	0.615509i	$-0.211049\pi$
$762$		0			0
$763$	−11.8707			−0.429747
$764$		0			0
$765$	8.78003	+	20.7976i	0.317443	+	0.751937i
$766$		0			0
$767$	8.07375	+	8.07375i	0.291526	+	0.291526i
$768$		0			0
$769$			40.2535i			1.45158i	0.687917	+	0.725789i	$0.258525\pi$
$769$			40.2535i			1.45158i	−0.687917	+	0.725789i	$0.741475\pi$
$770$		0			0
$771$	5.29172	+	5.29172i	0.190577	+	0.190577i
$772$		0			0
$773$			9.47175i			0.340675i	0.985386	+	0.170338i	$0.0544858\pi$
$773$			9.47175i			0.340675i	−0.985386	+	0.170338i	$0.945514\pi$
$774$		0			0
$775$	−0.845950	+	0.869172i	−0.0303874	+	0.0312216i
$776$		0			0
$777$	4.88405	+	4.88405i	0.175214	+	0.175214i
$778$		0			0
$779$	−9.87073	−	9.87073i	−0.353656	−	0.353656i
$780$		0			0
$781$	−35.8496	+	35.8496i	−1.28280	+	1.28280i
$782$		0			0
$783$	13.2533	−	13.2533i	0.473636	−	0.473636i
$784$		0			0
$785$	4.85973	+	1.97453i	0.173451	+	0.0704741i
$786$		0			0
$787$	48.1367			1.71589			0.857945	−	0.513742i	$-0.171741\pi$
$787$	48.1367			1.71589			0.857945	+	0.513742i	$0.171741\pi$
$788$		0			0
$789$	−21.9455	+	21.9455i	−0.781282	+	0.781282i
$790$		0			0
$791$	−9.75409			−0.346815
$792$		0			0
$793$	−9.11021	+	9.11021i	−0.323513	+	0.323513i
$794$		0			0
$795$	6.25537	−	15.3957i	0.221855	−	0.546031i
$796$		0			0
$797$			33.8962i			1.20066i	0.799751	+	0.600332i	$0.204965\pi$
$797$			33.8962i			1.20066i	−0.799751	+	0.600332i	$0.795035\pi$
$798$		0			0
$799$	82.7810			2.92858
$800$		0			0
$801$	−13.2782			−0.469162
$802$		0			0
$803$		−	6.93391i		−	0.244692i
$804$		0			0
$805$	−1.74813	+	4.30250i	−0.0616133	+	0.151643i
$806$		0			0
$807$	25.3753	−	25.3753i	0.893254	−	0.893254i
$808$		0			0
$809$	−27.5625			−0.969047			−0.484523	−	0.874778i	$-0.661007\pi$
$809$	−27.5625			−0.969047			−0.484523	+	0.874778i	$0.661007\pi$
$810$		0			0
$811$	24.1817	−	24.1817i	0.849133	−	0.849133i	−0.140892	−	0.990025i	$-0.544997\pi$
$811$	24.1817	−	24.1817i	0.849133	−	0.849133i	0.990025	+	0.140892i	$0.0449970\pi$
$812$		0			0
$813$	35.8120			1.25598
$814$		0			0
$815$	−5.66841	−	2.30310i	−0.198556	−	0.0806742i
$816$		0			0
$817$	33.4579	−	33.4579i	1.17054	−	1.17054i
$818$		0			0
$819$	2.11398	−	2.11398i	0.0738686	−	0.0738686i
$820$		0			0
$821$	0.0575735	+	0.0575735i	0.00200933	+	0.00200933i	0.708111	−	0.706101i	$-0.249548\pi$
$821$	0.0575735	+	0.0575735i	0.00200933	+	0.00200933i	−0.706101	+	0.708111i	$0.749548\pi$
$822$		0			0
$823$	−28.5594	−	28.5594i	−0.995518	−	0.995518i	0.00447159	−	0.999990i	$-0.498577\pi$
$823$	−28.5594	−	28.5594i	−0.995518	−	0.995518i	−0.999990	+	0.00447159i	$0.998577\pi$
$824$		0			0
$825$	0.284764	+	21.0327i	0.00991420	+	0.732266i
$826$		0			0
$827$		−	23.0863i		−	0.802788i	−0.915905	−	0.401394i	$-0.868526\pi$
$827$		−	23.0863i		−	0.802788i	0.915905	−	0.401394i	$-0.131474\pi$
$828$		0			0
$829$	33.3543	+	33.3543i	1.15844	+	1.15844i	0.984811	+	0.173631i	$0.0555499\pi$
$829$	33.3543	+	33.3543i	1.15844	+	1.15844i	0.173631	+	0.984811i	$0.444450\pi$
$830$		0			0
$831$			33.3414i			1.15660i
$832$		0			0
$833$	23.1269	+	23.1269i	0.801301	+	0.801301i
$834$		0			0
$835$	−12.4623	−	29.5198i	−0.431275	−	1.02158i
$836$		0			0
$837$	−1.35456			−0.0468204
$838$		0			0
$839$			49.4524i			1.70729i	0.520859	+	0.853643i	$0.325612\pi$
$839$			49.4524i			1.70729i	−0.520859	+	0.853643i	$0.674388\pi$
$840$		0			0
$841$		−	17.7336i		−	0.611504i
$842$		0			0
$843$	30.8746			1.06338
$844$		0			0
$845$	9.37380	−	23.0708i	0.322469	−	0.793661i
$846$		0			0
$847$	0.246530	+	0.246530i	0.00847089	+	0.00847089i
$848$		0			0
$849$			6.06865i			0.208276i
$850$		0			0
$851$	−3.04764	−	3.04764i	−0.104472	−	0.104472i
$852$		0			0
$853$		−	31.3639i		−	1.07388i	−0.843621	−	0.536939i	$-0.819581\pi$
$853$		−	31.3639i		−	1.07388i	0.843621	−	0.536939i	$-0.180419\pi$
$854$		0			0
$855$	−6.17921	−	14.6369i	−0.211324	−	0.500571i
$856$		0			0
$857$	−16.1594	−	16.1594i	−0.551996	−	0.551996i	0.375021	−	0.927016i	$-0.377636\pi$
$857$	−16.1594	−	16.1594i	−0.551996	−	0.551996i	−0.927016	+	0.375021i	$0.877636\pi$
$858$		0			0
$859$	−30.7369	−	30.7369i	−1.04873	−	1.04873i	−0.998750	−	0.0499792i	$-0.984085\pi$
$859$	−30.7369	−	30.7369i	−1.04873	−	1.04873i	−0.0499792	−	0.998750i	$-0.515915\pi$
$860$		0			0
$861$	3.89790	−	3.89790i	0.132840	−	0.132840i
$862$		0			0
$863$	−18.9353	+	18.9353i	−0.644565	+	0.644565i	−0.951674	−	0.307109i	$-0.900638\pi$
$863$	−18.9353	+	18.9353i	−0.644565	+	0.644565i	0.307109	+	0.951674i	$0.400638\pi$
$864$		0			0
$865$	7.40353	−	18.2216i	0.251728	−	0.619553i
$866$		0			0
$867$	−48.9441			−1.66223
$868$		0			0
$869$	−23.9226	+	23.9226i	−0.811517	+	0.811517i
$870$		0			0
$871$	6.20638			0.210295
$872$		0			0
$873$	−2.22280	+	2.22280i	−0.0752305	+	0.0752305i
$874$		0			0
$875$	6.55684	−	16.7859i	0.221662	−	0.567465i
$876$		0			0
$877$		−	49.7461i		−	1.67981i	−0.542737	−	0.839903i	$-0.682612\pi$
$877$		−	49.7461i		−	1.67981i	0.542737	−	0.839903i	$-0.317388\pi$
$878$		0			0
$879$	−3.98423			−0.134385
$880$		0			0
$881$	27.7694			0.935574			0.467787	−	0.883841i	$-0.345051\pi$
$881$	27.7694			0.935574			0.467787	+	0.883841i	$0.345051\pi$
$882$		0			0
$883$			42.4602i			1.42890i	0.699686	+	0.714450i	$0.253323\pi$
$883$			42.4602i			1.42890i	−0.699686	+	0.714450i	$0.746677\pi$
$884$		0			0
$885$	9.31938	+	22.0751i	0.313268	+	0.742048i
$886$		0			0
$887$	16.1076	−	16.1076i	0.540842	−	0.540842i	−0.382934	−	0.923776i	$-0.625086\pi$
$887$	16.1076	−	16.1076i	0.540842	−	0.540842i	0.923776	+	0.382934i	$0.125086\pi$
$888$		0			0
$889$	−16.6234			−0.557531
$890$		0			0
$891$	−7.14563	+	7.14563i	−0.239388	+	0.239388i
$892$		0			0
$893$	−58.2596			−1.94958
$894$		0			0
$895$	8.14281	+	19.2882i	0.272184	+	0.644732i
$896$		0			0
$897$	1.59329	−	1.59329i	0.0531986	−	0.0531986i
$898$		0			0
$899$	0.575741	−	0.575741i	0.0192020	−	0.0192020i
$900$		0			0
$901$	−30.4780	−	30.4780i	−1.01537	−	1.01537i
$902$		0			0
$903$	13.2123	+	13.2123i	0.439679	+	0.439679i
$904$		0			0
$905$	17.0236	−	7.18678i	0.565883	−	0.238897i
$906$		0			0
$907$		−	9.20991i		−	0.305810i	−0.988241	−	0.152905i	$-0.951137\pi$
$907$		−	9.20991i		−	0.305810i	0.988241	−	0.152905i	$-0.0488628\pi$
$908$		0			0
$909$	−9.02174	−	9.02174i	−0.299232	−	0.299232i
$910$		0			0
$911$		−	45.8065i		−	1.51764i	−0.651302	−	0.758819i	$-0.725777\pi$
$911$		−	45.8065i		−	1.51764i	0.651302	−	0.758819i	$-0.274223\pi$
$912$		0			0
$913$	−7.58351	−	7.58351i	−0.250978	−	0.250978i
$914$		0			0
$915$	−24.9090	+	10.5158i	−0.823467	+	0.347640i
$916$		0			0
$917$	27.3068			0.901749
$918$		0			0
$919$			5.52468i			0.182242i	0.995840	+	0.0911211i	$0.0290450\pi$
$919$			5.52468i			0.182242i	−0.995840	+	0.0911211i	$0.970955\pi$
$920$		0			0
$921$			18.6617i			0.614924i
$922$		0			0
$923$	−21.0744			−0.693672
$924$		0			0
$925$	11.9852	+	11.6650i	0.394070	+	0.383542i
$926$		0			0
$927$	−2.20422	−	2.20422i	−0.0723961	−	0.0723961i
$928$		0			0
$929$		−	43.4288i		−	1.42485i	−0.701746	−	0.712427i	$-0.747596\pi$
$929$		−	43.4288i		−	1.42485i	0.701746	−	0.712427i	$-0.252404\pi$
$930$		0			0
$931$	−16.2763	−	16.2763i	−0.533433	−	0.533433i
$932$		0			0
$933$		−	18.5210i		−	0.606352i
$934$		0			0
$935$	50.5451	+	20.5367i	1.65300	+	0.671623i
$936$		0			0
$937$	−20.7275	−	20.7275i	−0.677138	−	0.677138i	0.282213	−	0.959352i	$-0.408931\pi$
$937$	−20.7275	−	20.7275i	−0.677138	−	0.677138i	−0.959352	+	0.282213i	$0.908931\pi$
$938$		0			0
$939$	−12.9741	−	12.9741i	−0.423392	−	0.423392i
$940$		0			0
$941$	12.3393	−	12.3393i	0.402251	−	0.402251i	−0.476775	−	0.879026i	$-0.658194\pi$
$941$	12.3393	−	12.3393i	0.402251	−	0.402251i	0.879026	+	0.476775i	$0.158194\pi$
$942$		0			0
$943$	−2.43228	+	2.43228i	−0.0792060	+	0.0792060i
$944$		0			0
$945$	18.5414	−	7.82757i	0.603153	−	0.254631i
$946$		0			0
$947$	48.3611			1.57152			0.785762	−	0.618529i	$-0.212271\pi$
$947$	48.3611			1.57152			0.785762	+	0.618529i	$0.212271\pi$
$948$		0			0
$949$	2.03807	−	2.03807i	0.0661585	−	0.0661585i
$950$		0			0
$951$	17.7752			0.576399
$952$		0			0
$953$	34.0371	−	34.0371i	1.10257	−	1.10257i	0.108471	−	0.994100i	$-0.465405\pi$
$953$	34.0371	−	34.0371i	1.10257	−	1.10257i	0.994100	−	0.108471i	$-0.0345953\pi$
$954$		0			0
$955$	3.80980	+	1.54794i	0.123282	+	0.0500903i
$956$		0			0
$957$		−	14.1208i		−	0.456459i
$958$		0			0
$959$	11.2325			0.362716
$960$		0			0
$961$	30.9412			0.998102
$962$		0			0
$963$			4.96238i			0.159911i
$964$		0			0
$965$	−18.0142	+	7.60500i	−0.579898	+	0.244814i
$966$		0			0
$967$	18.9307	−	18.9307i	0.608770	−	0.608770i	−0.333855	−	0.942625i	$-0.608349\pi$
$967$	18.9307	−	18.9307i	0.608770	−	0.608770i	0.942625	+	0.333855i	$0.108349\pi$
$968$		0			0
$969$	49.7732			1.59895
$970$		0			0
$971$	21.2698	−	21.2698i	0.682580	−	0.682580i	−0.278001	−	0.960581i	$-0.589672\pi$
$971$	21.2698	−	21.2698i	0.682580	−	0.682580i	0.960581	+	0.278001i	$0.0896719\pi$
$972$		0			0
$973$	23.4822			0.752805
$974$		0			0
$975$	−6.09841	+	6.26581i	−0.195305	+	0.200666i
$976$		0			0
$977$	2.13884	−	2.13884i	0.0684275	−	0.0684275i	−0.672065	−	0.740492i	$-0.734592\pi$
$977$	2.13884	−	2.13884i	0.0684275	−	0.0684275i	0.740492	+	0.672065i	$0.234592\pi$
$978$		0			0
$979$	−22.6911	+	22.6911i	−0.725210	+	0.725210i
$980$		0			0
$981$	−7.07601	−	7.07601i	−0.225919	−	0.225919i
$982$		0			0
$983$	6.18193	+	6.18193i	0.197173	+	0.197173i	0.798787	−	0.601614i	$-0.205475\pi$
$983$	6.18193	+	6.18193i	0.197173	+	0.197173i	−0.601614	+	0.798787i	$0.705475\pi$
$984$		0			0
$985$	−4.67708	+	11.5113i	−0.149024	+	0.366779i
$986$		0			0
$987$		−	23.0064i		−	0.732302i
$988$		0			0
$989$	−8.24447	−	8.24447i	−0.262159	−	0.262159i
$990$		0			0
$991$			43.4847i			1.38134i	0.723172	+	0.690668i	$0.242683\pi$
$991$			43.4847i			1.38134i	−0.723172	+	0.690668i	$0.757317\pi$
$992$		0			0
$993$	2.17092	+	2.17092i	0.0688921	+	0.0688921i
$994$		0			0
$995$	−14.4269	−	5.86173i	−0.457364	−	0.185829i
$996$		0			0
$997$	−33.4043			−1.05793			−0.528963	−	0.848645i	$-0.677419\pi$
$997$	−33.4043			−1.05793			−0.528963	+	0.848645i	$0.677419\pi$
$998$		0			0
$999$			18.6783i			0.590954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.2.j.b.143.3		18
4.3	odd	2		80.2.j.b.43.2	✓	18
5.2	odd	4		320.2.s.b.207.3		18
5.3	odd	4		1600.2.s.d.207.7		18
5.4	even	2		1600.2.j.d.143.7		18
8.3	odd	2		640.2.j.d.543.3		18
8.5	even	2		640.2.j.c.543.7		18
12.11	even	2		720.2.bd.g.523.8		18
16.3	odd	4		320.2.s.b.303.3		18
16.5	even	4		640.2.s.d.223.3		18
16.11	odd	4		640.2.s.c.223.7		18
16.13	even	4		80.2.s.b.3.4	yes	18
20.3	even	4		400.2.s.d.107.6		18
20.7	even	4		80.2.s.b.27.4	yes	18
20.19	odd	2		400.2.j.d.43.8		18
40.27	even	4		640.2.s.d.287.3		18
40.37	odd	4		640.2.s.c.287.7		18
48.29	odd	4		720.2.z.g.163.6		18
60.47	odd	4		720.2.z.g.667.6		18
80.3	even	4		1600.2.j.d.1007.3		18
80.13	odd	4		400.2.j.d.307.8		18
80.19	odd	4		1600.2.s.d.943.7		18
80.27	even	4		640.2.j.c.607.3		18
80.29	even	4		400.2.s.d.243.6		18
80.37	odd	4		640.2.j.d.607.7		18
80.67	even	4	inner	320.2.j.b.47.7		18
80.77	odd	4		80.2.j.b.67.2	yes	18
240.77	even	4		720.2.bd.g.307.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.2	✓	18	4.3	odd	2
80.2.j.b.67.2	yes	18	80.77	odd	4
80.2.s.b.3.4	yes	18	16.13	even	4
80.2.s.b.27.4	yes	18	20.7	even	4
320.2.j.b.47.7		18	80.67	even	4	inner
320.2.j.b.143.3		18	1.1	even	1	trivial
320.2.s.b.207.3		18	5.2	odd	4
320.2.s.b.303.3		18	16.3	odd	4
400.2.j.d.43.8		18	20.19	odd	2
400.2.j.d.307.8		18	80.13	odd	4
400.2.s.d.107.6		18	20.3	even	4
400.2.s.d.243.6		18	80.29	even	4
640.2.j.c.543.7		18	8.5	even	2
640.2.j.c.607.3		18	80.27	even	4
640.2.j.d.543.3		18	8.3	odd	2
640.2.j.d.607.7		18	80.37	odd	4
640.2.s.c.223.7		18	16.11	odd	4
640.2.s.c.287.7		18	40.37	odd	4
640.2.s.d.223.3		18	16.5	even	4
640.2.s.d.287.3		18	40.27	even	4
720.2.z.g.163.6		18	48.29	odd	4
720.2.z.g.667.6		18	60.47	odd	4
720.2.bd.g.307.8		18	240.77	even	4
720.2.bd.g.523.8		18	12.11	even	2
1600.2.j.d.143.7		18	5.4	even	2
1600.2.j.d.1007.3		18	80.3	even	4
1600.2.s.d.207.7		18	5.3	odd	4
1600.2.s.d.943.7		18	80.19	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.28110i q^{3} +(-0.841703 + 2.07160i) q^{5} +(1.13975 - 1.13975i) q^{7} +1.35879 q^{9} +O(q^{10})\)	\(q-1.28110i q^{3} +(-0.841703 + 2.07160i) q^{5} +(1.13975 - 1.13975i) q^{7} +1.35879 q^{9} +(2.32204 - 2.32204i) q^{11} +1.36502 q^{13} +(2.65392 + 1.07830i) q^{15} +(5.25380 - 5.25380i) q^{17} +(-3.69752 + 3.69752i) q^{19} +(-1.46013 - 1.46013i) q^{21} +(0.911118 + 0.911118i) q^{23} +(-3.58307 - 3.48735i) q^{25} -5.58403i q^{27} +(2.37343 + 2.37343i) q^{29} -0.242577i q^{31} +(-2.97475 - 2.97475i) q^{33} +(1.40178 + 3.32044i) q^{35} -3.34494 q^{37} -1.74872i q^{39} +2.66956i q^{41} -9.04874 q^{43} +(-1.14370 + 2.81488i) q^{45} +(7.87820 + 7.87820i) q^{47} +4.40194i q^{49} +(-6.73063 - 6.73063i) q^{51} -5.80113i q^{53} +(2.85587 + 6.76480i) q^{55} +(4.73688 + 4.73688i) q^{57} +(5.91474 + 5.91474i) q^{59} +(-6.67404 + 6.67404i) q^{61} +(1.54868 - 1.54868i) q^{63} +(-1.14894 + 2.82778i) q^{65} +4.54673 q^{67} +(1.16723 - 1.16723i) q^{69} -15.4389 q^{71} +(1.49307 - 1.49307i) q^{73} +(-4.46763 + 4.59026i) q^{75} -5.29308i q^{77} -10.3024 q^{79} -3.07731 q^{81} -3.26589i q^{83} +(6.46165 + 15.3059i) q^{85} +(3.04060 - 3.04060i) q^{87} -9.77206 q^{89} +(1.55578 - 1.55578i) q^{91} -0.310765 q^{93} +(-4.54758 - 10.7720i) q^{95} +(-1.63587 + 1.63587i) q^{97} +(3.15516 - 3.15516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) \) 18 * q - 4 * q^5 - 2 * q^7 - 10 * q^9	\( 18 q - 4 q^{5} - 2 q^{7} - 10 q^{9} + 2 q^{11} - 20 q^{15} - 6 q^{17} - 2 q^{19} - 16 q^{21} + 2 q^{23} + 6 q^{25} - 14 q^{29} - 8 q^{33} + 6 q^{35} + 8 q^{37} + 44 q^{43} - 4 q^{45} + 38 q^{47} - 8 q^{51} + 6 q^{55} + 24 q^{57} + 10 q^{59} + 14 q^{61} - 6 q^{63} - 12 q^{67} + 32 q^{69} - 24 q^{71} + 14 q^{73} - 64 q^{75} - 16 q^{79} + 2 q^{81} - 10 q^{85} - 24 q^{87} - 12 q^{89} + 16 q^{93} + 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) \) 18 * q - 4 * q^5 - 2 * q^7 - 10 * q^9 + 2 * q^11 - 20 * q^15 - 6 * q^17 - 2 * q^19 - 16 * q^21 + 2 * q^23 + 6 * q^25 - 14 * q^29 - 8 * q^33 + 6 * q^35 + 8 * q^37 + 44 * q^43 - 4 * q^45 + 38 * q^47 - 8 * q^51 + 6 * q^55 + 24 * q^57 + 10 * q^59 + 14 * q^61 - 6 * q^63 - 12 * q^67 + 32 * q^69 - 24 * q^71 + 14 * q^73 - 64 * q^75 - 16 * q^79 + 2 * q^81 - 10 * q^85 - 24 * q^87 - 12 * q^89 + 16 * q^93 + 34 * q^95 + 18 * q^97 + 22 * q^99

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