LMFDB - Embedded newform 880.2.bo.k.641.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(81,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,3,0,-4,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 141 x^{12} - 220 x^{11} + 1105 x^{10} - 1935 x^{9} + \cdots + 10000 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 141x^12 - 220x^11 + 1105x^10 - 1935x^9 + 9865x^8 - 18475x^7 + 34075x^6 - 18400x^5 + 23025x^4 + 26000x^3 + 41000x^2 + 25000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			641.2
Root			$-0.220438 - 0.678438i$ of defining polynomial
Character	$\chi$	$=$	880.641
Dual form			880.2.bo.k.81.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.220438 - 0.678438i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.116244 + 0.357761i) q^{7} +(2.01537 - 1.46425i) q^{9} +(0.107091 + 3.31490i) q^{11} +(2.28815 - 1.66244i) q^{13} +(-0.220438 + 0.678438i) q^{15} +(3.91377 + 2.84352i) q^{17} +(-0.905388 - 2.78650i) q^{19} +0.268343 q^{21} -3.77226 q^{23} +(0.309017 + 0.951057i) q^{25} +(-3.16901 - 2.30242i) q^{27} +(2.60933 - 8.03068i) q^{29} +(6.50458 - 4.72586i) q^{31} +(2.22534 - 0.803383i) q^{33} +(0.304330 - 0.221108i) q^{35} +(0.877578 - 2.70091i) q^{37} +(-1.63226 - 1.18590i) q^{39} +(-1.14965 - 3.53825i) q^{41} +6.48484 q^{43} -2.49113 q^{45} +(-0.800034 - 2.46225i) q^{47} +(5.54864 + 4.03132i) q^{49} +(1.06641 - 3.28207i) q^{51} +(0.0394497 - 0.0286619i) q^{53} +(1.86181 - 2.74475i) q^{55} +(-1.69089 + 1.22850i) q^{57} +(0.509660 - 1.56857i) q^{59} +(-7.03606 - 5.11200i) q^{61} +(0.289578 + 0.891229i) q^{63} -2.82831 q^{65} -11.4395 q^{67} +(0.831550 + 2.55925i) q^{69} +(11.4246 + 8.30046i) q^{71} +(0.158595 - 0.488106i) q^{73} +(0.577114 - 0.419298i) q^{75} +(-1.19839 - 0.347022i) q^{77} +(10.5029 - 7.63082i) q^{79} +(1.44592 - 4.45010i) q^{81} +(2.21418 + 1.60869i) q^{83} +(-1.49493 - 4.60091i) q^{85} -6.02351 q^{87} +12.0195 q^{89} +(0.328773 + 1.01186i) q^{91} +(-4.64006 - 3.37120i) q^{93} +(-0.905388 + 2.78650i) q^{95} +(-13.0046 + 9.44836i) q^{97} +(5.06966 + 6.52392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9} + 7 q^{11} - 11 q^{13} + 3 q^{15} + 9 q^{17} + 2 q^{19} + 12 q^{21} - 20 q^{23} - 4 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 32 q^{33} + 2 q^{35} - 16 q^{37}+ \cdots + 10 q^{99}+O(q^{100}) $ 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9 + 7 * q^11 - 11 * q^13 + 3 * q^15 + 9 * q^17 + 2 * q^19 + 12 * q^21 - 20 * q^23 - 4 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 32 * q^33 + 2 * q^35 - 16 * q^37 - 3 * q^39 - 11 * q^41 + 16 * q^43 + 38 * q^45 + 10 * q^47 + 4 * q^49 - 26 * q^51 - 9 * q^53 - 3 * q^55 - 50 * q^57 + 60 * q^59 + 30 * q^61 - 52 * q^63 + 24 * q^65 + 4 * q^67 + 41 * q^69 + 10 * q^71 + q^73 - 2 * q^75 - 4 * q^77 - 19 * q^79 - 31 * q^81 - 64 * q^83 - 11 * q^85 - 30 * q^87 + 24 * q^89 + 9 * q^91 + 45 * q^93 + 2 * q^95 - 3 * q^97 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	−0.220438	−	0.678438i	−0.127270	−	0.391696i	0.867038	−	0.498242i	$-0.166021\pi$
$3$	−0.220438	−	0.678438i	−0.127270	−	0.391696i	−0.994308	+	0.106546i	$0.966021\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−0.116244	+	0.357761i	−0.0439359	+	0.135221i	−0.970618	−	0.240625i	$-0.922648\pi$
$7$	−0.116244	+	0.357761i	−0.0439359	+	0.135221i	0.926682	+	0.375846i	$0.122648\pi$
$8$		0			0
$9$	2.01537	−	1.46425i	0.671789	−	0.488083i
$10$		0			0
$11$	0.107091	+	3.31490i	0.0322892	+	0.999479i
$11$	0.107091	+	3.31490i	0.0322892	+	0.999479i
$12$		0			0
$13$	2.28815	−	1.66244i	0.634619	−	0.461077i	−0.223379	−	0.974732i	$-0.571709\pi$
$13$	2.28815	−	1.66244i	0.634619	−	0.461077i	0.857997	+	0.513654i	$0.171709\pi$
$14$		0			0
$15$	−0.220438	+	0.678438i	−0.0569168	+	0.175172i
$16$		0			0
$17$	3.91377	+	2.84352i	0.949228	+	0.689655i	0.950624	−	0.310344i	$-0.100444\pi$
$17$	3.91377	+	2.84352i	0.949228	+	0.689655i	−0.00139602	+	0.999999i	$0.500444\pi$
$18$		0			0
$19$	−0.905388	−	2.78650i	−0.207710	−	0.639267i	−0.999591	−	0.0285910i	$-0.990898\pi$
$19$	−0.905388	−	2.78650i	−0.207710	−	0.639267i	0.791881	−	0.610676i	$-0.209102\pi$
$20$		0			0
$21$	0.268343			0.0585573
$22$		0			0
$23$	−3.77226			−0.786571			−0.393285	−	0.919416i	$-0.628662\pi$
$23$	−3.77226			−0.786571			−0.393285	+	0.919416i	$0.628662\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−3.16901	−	2.30242i	−0.609876	−	0.443101i
$28$		0			0
$29$	2.60933	−	8.03068i	0.484540	−	1.49126i	−0.348107	−	0.937455i	$-0.613175\pi$
$29$	2.60933	−	8.03068i	0.484540	−	1.49126i	0.832646	−	0.553805i	$-0.186825\pi$
$30$		0			0
$31$	6.50458	−	4.72586i	1.16826	−	0.848789i	0.177458	−	0.984128i	$-0.443213\pi$
$31$	6.50458	−	4.72586i	1.16826	−	0.848789i	0.990799	+	0.135340i	$0.0432126\pi$
$32$		0			0
$33$	2.22534	−	0.803383i	0.387383	−	0.139851i
$34$		0			0
$35$	0.304330	−	0.221108i	0.0514411	−	0.0373742i
$36$		0			0
$37$	0.877578	−	2.70091i	0.144273	−	0.444026i	−0.852644	−	0.522492i	$-0.825002\pi$
$37$	0.877578	−	2.70091i	0.144273	−	0.444026i	0.996917	+	0.0784662i	$0.0250023\pi$
$38$		0			0
$39$	−1.63226	−	1.18590i	−0.261370	−	0.189897i
$40$		0			0
$41$	−1.14965	−	3.53825i	−0.179545	−	0.552583i	0.820267	−	0.571981i	$-0.193825\pi$
$41$	−1.14965	−	3.53825i	−0.179545	−	0.552583i	−0.999812	+	0.0193984i	$0.993825\pi$
$42$		0			0
$43$	6.48484			0.988929			0.494465	−	0.869198i	$-0.335364\pi$
$43$	6.48484			0.988929			0.494465	+	0.869198i	$0.335364\pi$
$44$		0			0
$45$	−2.49113			−0.371356
$46$		0			0
$47$	−0.800034	−	2.46225i	−0.116697	−	0.359157i	0.875600	−	0.483037i	$-0.160466\pi$
$47$	−0.800034	−	2.46225i	−0.116697	−	0.359157i	−0.992297	+	0.123880i	$0.960466\pi$
$48$		0			0
$49$	5.54864	+	4.03132i	0.792663	+	0.575903i
$50$		0			0
$51$	1.06641	−	3.28207i	0.149327	−	0.459582i
$52$		0			0
$53$	0.0394497	−	0.0286619i	0.00541884	−	0.00393702i	−0.585073	−	0.810981i	$-0.698934\pi$
$53$	0.0394497	−	0.0286619i	0.00541884	−	0.00393702i	0.590491	+	0.807044i	$0.298934\pi$
$54$		0			0
$55$	1.86181	−	2.74475i	0.251046	−	0.370102i
$56$		0			0
$57$	−1.69089	+	1.22850i	−0.223963	+	0.162719i
$58$		0			0
$59$	0.509660	−	1.56857i	0.0663521	−	0.204211i	−0.912384	−	0.409336i	$-0.865760\pi$
$59$	0.509660	−	1.56857i	0.0663521	−	0.204211i	0.978736	+	0.205126i	$0.0657603\pi$
$60$		0			0
$61$	−7.03606	−	5.11200i	−0.900875	−	0.654524i	0.0378153	−	0.999285i	$-0.487960\pi$
$61$	−7.03606	−	5.11200i	−0.900875	−	0.654524i	−0.938691	+	0.344760i	$0.887960\pi$
$62$		0			0
$63$	0.289578	+	0.891229i	0.0364834	+	0.112284i
$64$		0			0
$65$	−2.82831			−0.350809
$66$		0			0
$67$	−11.4395			−1.39756			−0.698779	−	0.715338i	$-0.746273\pi$
$67$	−11.4395			−1.39756			−0.698779	+	0.715338i	$0.746273\pi$
$68$		0			0
$69$	0.831550	+	2.55925i	0.100107	+	0.308097i
$70$		0			0
$71$	11.4246	+	8.30046i	1.35585	+	0.985084i	0.998697	+	0.0510383i	$0.0162530\pi$
$71$	11.4246	+	8.30046i	1.35585	+	0.985084i	0.357155	+	0.934045i	$0.383747\pi$
$72$		0			0
$73$	0.158595	−	0.488106i	0.0185622	−	0.0571284i	−0.941346	−	0.337442i	$-0.890438\pi$
$73$	0.158595	−	0.488106i	0.0185622	−	0.0571284i	0.959909	+	0.280313i	$0.0904384\pi$
$74$		0			0
$75$	0.577114	−	0.419298i	0.0666394	−	0.0484163i
$76$		0			0
$77$	−1.19839	−	0.347022i	−0.136569	−	0.0395469i
$78$		0			0
$79$	10.5029	−	7.63082i	1.18167	−	0.858534i	0.189312	−	0.981917i	$-0.439374\pi$
$79$	10.5029	−	7.63082i	1.18167	−	0.858534i	0.992359	+	0.123383i	$0.0393743\pi$
$80$		0			0
$81$	1.44592	−	4.45010i	0.160658	−	0.494455i
$82$		0			0
$83$	2.21418	+	1.60869i	0.243037	+	0.176577i	0.702635	−	0.711550i	$-0.252007\pi$
$83$	2.21418	+	1.60869i	0.243037	+	0.176577i	−0.459598	+	0.888127i	$0.652007\pi$
$84$		0			0
$85$	−1.49493	−	4.60091i	−0.162148	−	0.499039i
$86$		0			0
$87$	−6.02351			−0.645789
$88$		0			0
$89$	12.0195			1.27407			0.637034	−	0.770835i	$-0.280161\pi$
$89$	12.0195			1.27407			0.637034	+	0.770835i	$0.280161\pi$
$90$		0			0
$91$	0.328773	+	1.01186i	0.0344648	+	0.106072i
$92$		0			0
$93$	−4.64006	−	3.37120i	−0.481152	−	0.349577i
$94$		0			0
$95$	−0.905388	+	2.78650i	−0.0928909	+	0.285889i
$96$		0			0
$97$	−13.0046	+	9.44836i	−1.32041	+	0.959336i	−0.320486	+	0.947253i	$0.603846\pi$
$97$	−13.0046	+	9.44836i	−1.32041	+	0.959336i	−0.999927	+	0.0120825i	$0.996154\pi$
$98$		0			0
$99$	5.06966	+	6.52392i	0.509520	+	0.655678i
$100$		0			0
$101$	−12.6112	+	9.16257i	−1.25486	+	0.911709i	−0.998493	−	0.0548702i	$-0.982525\pi$
$101$	−12.6112	+	9.16257i	−1.25486	+	0.911709i	−0.256367	+	0.966580i	$0.582525\pi$
$102$		0			0
$103$	2.86121	−	8.80590i	0.281923	−	0.867671i	−0.705381	−	0.708829i	$-0.749224\pi$
$103$	2.86121	−	8.80590i	0.281923	−	0.867671i	0.987304	−	0.158842i	$-0.0507761\pi$
$104$		0			0
$105$	−0.217094	−	0.157728i	−0.0211862	−	0.0153927i
$106$		0			0
$107$	0.667222	+	2.05350i	0.0645027	+	0.198519i	0.978114	−	0.208070i	$-0.0667181\pi$
$107$	0.667222	+	2.05350i	0.0645027	+	0.198519i	−0.913611	+	0.406589i	$0.866718\pi$
$108$		0			0
$109$	−5.79052			−0.554631			−0.277315	−	0.960779i	$-0.589445\pi$
$109$	−5.79052			−0.554631			−0.277315	+	0.960779i	$0.589445\pi$
$110$		0			0
$111$	−2.02585			−0.192285
$112$		0			0
$113$	5.87590	+	18.0842i	0.552758	+	1.70121i	0.701792	+	0.712382i	$0.252384\pi$
$113$	5.87590	+	18.0842i	0.552758	+	1.70121i	−0.149034	+	0.988832i	$0.547616\pi$
$114$		0			0
$115$	3.05182	+	2.21728i	0.284584	+	0.206762i
$116$		0			0
$117$	2.17724	−	6.70084i	0.201285	−	0.619493i
$118$		0			0
$119$	−1.47225	+	1.06965i	−0.134961	+	0.0980549i
$120$		0			0
$121$	−10.9771	+	0.709993i	−0.997915	+	0.0645448i
$122$		0			0
$123$	−2.14706	+	1.55993i	−0.193594	+	0.140654i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−8.16891	−	5.93506i	−0.724873	−	0.526651i	0.163064	−	0.986615i	$-0.447862\pi$
$127$	−8.16891	−	5.93506i	−0.724873	−	0.526651i	−0.887937	+	0.459964i	$0.847862\pi$
$128$		0			0
$129$	−1.42950	−	4.39956i	−0.125861	−	0.387360i
$130$		0			0
$131$	6.29651			0.550128			0.275064	−	0.961426i	$-0.411301\pi$
$131$	6.29651			0.550128			0.275064	+	0.961426i	$0.411301\pi$
$132$		0			0
$133$	1.10215			0.0955682
$134$		0			0
$135$	1.21045	+	3.72539i	0.104179	+	0.320631i
$136$		0			0
$137$	6.69323	+	4.86292i	0.571842	+	0.415467i	0.835774	−	0.549074i	$-0.185019\pi$
$137$	6.69323	+	4.86292i	0.571842	+	0.415467i	−0.263932	+	0.964541i	$0.585019\pi$
$138$		0			0
$139$	3.17270	−	9.76458i	0.269105	−	0.828221i	−0.721614	−	0.692296i	$-0.756599\pi$
$139$	3.17270	−	9.76458i	0.269105	−	0.828221i	0.990719	−	0.135925i	$-0.0434007\pi$
$140$		0			0
$141$	−1.49413	+	1.08555i	−0.125828	+	0.0914196i
$142$		0			0
$143$	5.75585	+	7.40694i	0.481328	+	0.619400i
$144$		0			0
$145$	−6.83130	+	4.96323i	−0.567309	+	0.412174i
$146$		0			0
$147$	1.51187	−	4.65306i	0.124697	−	0.383778i
$148$		0			0
$149$	3.96547	+	2.88109i	0.324864	+	0.236028i	0.738248	−	0.674529i	$-0.235653\pi$
$149$	3.96547	+	2.88109i	0.324864	+	0.236028i	−0.413384	+	0.910557i	$0.635653\pi$
$150$		0			0
$151$	2.89124	+	8.89833i	0.235286	+	0.724136i	0.997083	+	0.0763203i	$0.0243171\pi$
$151$	2.89124	+	8.89833i	0.235286	+	0.724136i	−0.761797	+	0.647815i	$0.775683\pi$
$152$		0			0
$153$	12.0513			0.974289
$154$		0			0
$155$	−8.04011			−0.645797
$156$		0			0
$157$	2.98454	+	9.18547i	0.238192	+	0.733080i	0.996682	+	0.0813952i	$0.0259376\pi$
$157$	2.98454	+	9.18547i	0.238192	+	0.733080i	−0.758490	+	0.651685i	$0.774062\pi$
$158$		0			0
$159$	−0.0281416	−	0.0204460i	−0.00223177	−	0.00162148i
$160$		0			0
$161$	0.438501	−	1.34957i	0.0345587	−	0.106361i
$162$		0			0
$163$	3.63088	−	2.63799i	0.284393	−	0.206623i	−0.436438	−	0.899734i	$-0.643760\pi$
$163$	3.63088	−	2.63799i	0.284393	−	0.206623i	0.720831	+	0.693111i	$0.243760\pi$
$164$		0			0
$165$	−2.27256	−	0.658074i	−0.176918	−	0.0512310i
$166$		0			0
$167$	−18.9889	+	13.7962i	−1.46940	+	1.06759i	−0.488619	+	0.872497i	$0.662499\pi$
$167$	−18.9889	+	13.7962i	−1.46940	+	1.06759i	−0.980786	+	0.195088i	$0.937501\pi$
$168$		0			0
$169$	−1.54529	+	4.75592i	−0.118869	+	0.365840i
$170$		0			0
$171$	−5.90482	−	4.29010i	−0.451553	−	0.328072i
$172$		0			0
$173$	−4.00204	−	12.3170i	−0.304270	−	0.936445i	−0.979949	−	0.199250i	$-0.936150\pi$
$173$	−4.00204	−	12.3170i	−0.304270	−	0.936445i	0.675679	−	0.737196i	$-0.263850\pi$
$174$		0			0
$175$	−0.376172			−0.0284359
$176$		0			0
$177$	−1.17653			−0.0884332
$178$		0			0
$179$	1.09062	+	3.35659i	0.0815170	+	0.250884i	0.983506	−	0.180875i	$-0.0578931\pi$
$179$	1.09062	+	3.35659i	0.0815170	+	0.250884i	−0.901989	+	0.431759i	$0.857893\pi$
$180$		0			0
$181$	−1.44958	−	1.05318i	−0.107746	−	0.0782824i	0.532607	−	0.846362i	$-0.321212\pi$
$181$	−1.44958	−	1.05318i	−0.107746	−	0.0782824i	−0.640354	+	0.768080i	$0.721212\pi$
$182$		0			0
$183$	−1.91716	+	5.90041i	−0.141721	+	0.436171i
$184$		0			0
$185$	−2.29753	+	1.66925i	−0.168918	+	0.122726i
$186$		0			0
$187$	−9.00684	+	13.2782i	−0.658645	+	0.971002i
$188$		0			0
$189$	1.19209	−	0.866106i	0.0867120	−	0.0629999i
$190$		0			0
$191$	−1.05101	+	3.23466i	−0.0760481	+	0.234052i	−0.981853	−	0.189643i	$-0.939267\pi$
$191$	−1.05101	+	3.23466i	−0.0760481	+	0.234052i	0.905805	+	0.423695i	$0.139267\pi$
$192$		0			0
$193$	6.29046	+	4.57028i	0.452797	+	0.328976i	0.790699	−	0.612205i	$-0.209717\pi$
$193$	6.29046	+	4.57028i	0.452797	+	0.328976i	−0.337902	+	0.941181i	$0.609717\pi$
$194$		0			0
$195$	0.623466	+	1.91883i	0.0446474	+	0.137410i
$196$		0			0
$197$	−7.09410			−0.505434			−0.252717	−	0.967540i	$-0.581324\pi$
$197$	−7.09410			−0.505434			−0.252717	+	0.967540i	$0.581324\pi$
$198$		0			0
$199$	−12.7734			−0.905481			−0.452740	−	0.891642i	$-0.649554\pi$
$199$	−12.7734			−0.905481			−0.452740	+	0.891642i	$0.649554\pi$
$200$		0			0
$201$	2.52170	+	7.76100i	0.177867	+	0.547418i
$202$		0			0
$203$	2.56975	+	1.86703i	0.180361	+	0.131040i
$204$		0			0
$205$	−1.14965	+	3.53825i	−0.0802949	+	0.247122i
$206$		0			0
$207$	−7.60249	+	5.52353i	−0.528409	+	0.383912i
$208$		0			0
$209$	9.13999	−	3.29968i	0.632227	−	0.228243i
$210$		0			0
$211$	5.93856	−	4.31462i	0.408828	−	0.297031i	−0.364299	−	0.931282i	$-0.618692\pi$
$211$	5.93856	−	4.31462i	0.408828	−	0.297031i	0.773127	+	0.634251i	$0.218692\pi$
$212$		0			0
$213$	3.11293	−	9.58062i	0.213295	−	0.656454i
$214$		0			0
$215$	−5.24635	−	3.81169i	−0.357798	−	0.259955i
$216$		0			0
$217$	0.934611	+	2.87644i	0.0634455	+	0.195265i
$218$		0			0
$219$	−0.366110			−0.0247394
$220$		0			0
$221$	13.6825			0.920382
$222$		0			0
$223$	−2.02059	−	6.21872i	−0.135308	−	0.416436i	0.860329	−	0.509738i	$-0.170258\pi$
$223$	−2.02059	−	6.21872i	−0.135308	−	0.416436i	−0.995638	+	0.0933019i	$0.970258\pi$
$224$		0			0
$225$	2.01537	+	1.46425i	0.134358	+	0.0976166i
$226$		0			0
$227$	−6.34910	+	19.5405i	−0.421405	+	1.29695i	0.484990	+	0.874520i	$0.338823\pi$
$227$	−6.34910	+	19.5405i	−0.421405	+	1.29695i	−0.906395	+	0.422431i	$0.861177\pi$
$228$		0			0
$229$	3.50380	−	2.54566i	0.231538	−	0.168222i	−0.465967	−	0.884802i	$-0.654294\pi$
$229$	3.50380	−	2.54566i	0.231538	−	0.168222i	0.697505	+	0.716580i	$0.254294\pi$
$230$		0			0
$231$	0.0287372	+	0.889530i	0.00189077	+	0.0585268i
$232$		0			0
$233$	−23.1860	+	16.8456i	−1.51897	+	1.10360i	−0.556973	+	0.830531i	$0.688037\pi$
$233$	−23.1860	+	16.8456i	−1.51897	+	1.10360i	−0.961996	+	0.273064i	$0.911963\pi$
$234$		0			0
$235$	−0.800034	+	2.46225i	−0.0521885	+	0.160620i
$236$		0			0
$237$	−7.49228	−	5.44346i	−0.486676	−	0.353591i
$238$		0			0
$239$	3.23746	+	9.96387i	0.209414	+	0.644509i	0.999503	+	0.0315175i	$0.0100340\pi$
$239$	3.23746	+	9.96387i	0.209414	+	0.644509i	−0.790090	+	0.612991i	$0.789966\pi$
$240$		0			0
$241$	15.5202			0.999745			0.499873	−	0.866099i	$-0.333380\pi$
$241$	15.5202			0.999745			0.499873	+	0.866099i	$0.333380\pi$
$242$		0			0
$243$	−15.0892			−0.967971
$244$		0			0
$245$	−2.11939	−	6.52282i	−0.135403	−	0.416727i
$246$		0			0
$247$	−6.70405	−	4.87077i	−0.426568	−	0.309920i
$248$		0			0
$249$	0.603310	−	1.85680i	0.0382332	−	0.117670i
$250$		0			0
$251$	−9.68403	+	7.03586i	−0.611251	+	0.444100i	−0.849854	−	0.527017i	$-0.823310\pi$
$251$	−9.68403	+	7.03586i	−0.611251	+	0.444100i	0.238604	+	0.971117i	$0.423310\pi$
$252$		0			0
$253$	−0.403976	−	12.5047i	−0.0253978	−	0.786161i
$254$		0			0
$255$	−2.79189	+	2.02843i	−0.174835	+	0.127025i
$256$		0			0
$257$	−2.61843	+	8.05870i	−0.163333	+	0.502688i	−0.998910	−	0.0466864i	$-0.985134\pi$
$257$	−2.61843	+	8.05870i	−0.163333	+	0.502688i	0.835576	+	0.549374i	$0.185134\pi$
$258$		0			0
$259$	0.864266	+	0.627926i	0.0537029	+	0.0390174i
$260$		0			0
$261$	−6.50017	−	20.0055i	−0.402350	−	1.23831i
$262$		0			0
$263$	−12.5189			−0.771950			−0.385975	−	0.922509i	$-0.626135\pi$
$263$	−12.5189			−0.771950			−0.385975	+	0.922509i	$0.626135\pi$
$264$		0			0
$265$	−0.0487626			−0.00299546
$266$		0			0
$267$	−2.64956	−	8.15451i	−0.162151	−	0.499048i
$268$		0			0
$269$	19.4689	+	14.1450i	1.18704	+	0.862434i	0.992948	−	0.118549i	$-0.0378244\pi$
$269$	19.4689	+	14.1450i	1.18704	+	0.862434i	0.194091	+	0.980984i	$0.437824\pi$
$270$		0			0
$271$	2.91162	−	8.96105i	0.176868	−	0.544345i	−0.822845	−	0.568265i	$-0.807615\pi$
$271$	2.91162	−	8.96105i	0.176868	−	0.544345i	0.999714	+	0.0239201i	$0.00761474\pi$
$272$		0			0
$273$	0.614009	−	0.446104i	0.0371615	−	0.0269994i
$274$		0			0
$275$	−3.11956	+	1.12621i	−0.188117	+	0.0679129i
$276$		0			0
$277$	−19.2393	+	13.9782i	−1.15598	+	0.839867i	−0.989264	−	0.146138i	$-0.953316\pi$
$277$	−19.2393	+	13.9782i	−1.15598	+	0.839867i	−0.166714	+	0.986005i	$0.553316\pi$
$278$		0			0
$279$	6.18928	−	19.0487i	0.370543	−	1.14041i
$280$		0			0
$281$	−0.402004	−	0.292073i	−0.0239815	−	0.0174236i	0.575730	−	0.817640i	$-0.304718\pi$
$281$	−0.402004	−	0.292073i	−0.0239815	−	0.0174236i	−0.599711	+	0.800216i	$0.704718\pi$
$282$		0			0
$283$	−1.44629	−	4.45123i	−0.0859732	−	0.264598i	0.898823	−	0.438312i	$-0.144423\pi$
$283$	−1.44629	−	4.45123i	−0.0859732	−	0.264598i	−0.984796	+	0.173713i	$0.944423\pi$
$284$		0			0
$285$	2.09005			0.123804
$286$		0			0
$287$	1.39949			0.0826092
$288$		0			0
$289$	1.97869	+	6.08979i	0.116394	+	0.358223i
$290$		0			0
$291$	9.27683	+	6.74001i	0.543817	+	0.395106i
$292$		0			0
$293$	5.22865	−	16.0921i	0.305461	−	0.940112i	−0.674044	−	0.738691i	$-0.735444\pi$
$293$	5.22865	−	16.0921i	0.305461	−	0.940112i	0.979505	−	0.201421i	$-0.0645559\pi$
$294$		0			0
$295$	−1.33431	+	0.969431i	−0.0776864	+	0.0564424i
$296$		0			0
$297$	7.29290	−	10.7515i	0.423177	−	0.623865i
$298$		0			0
$299$	−8.63150	+	6.27115i	−0.499173	+	0.362670i
$300$		0			0
$301$	−0.753821	+	2.32002i	−0.0434495	+	0.133724i
$302$		0			0
$303$	8.99622	+	6.53614i	0.516819	+	0.375491i
$304$		0			0
$305$	2.68754	+	8.27139i	0.153888	+	0.473618i
$306$		0			0
$307$	34.3667			1.96141			0.980707	−	0.195486i	$-0.0626283\pi$
$307$	34.3667			1.96141			0.980707	+	0.195486i	$0.0626283\pi$
$308$		0			0
$309$	−6.60497			−0.375744
$310$		0			0
$311$	−2.27681	−	7.00729i	−0.129106	−	0.397347i	0.865521	−	0.500873i	$-0.166988\pi$
$311$	−2.27681	−	7.00729i	−0.129106	−	0.397347i	−0.994627	+	0.103526i	$0.966988\pi$
$312$		0			0
$313$	20.2744	+	14.7302i	1.14598	+	0.832602i	0.987941	−	0.154831i	$-0.0494834\pi$
$313$	20.2744	+	14.7302i	1.14598	+	0.832602i	0.158037	+	0.987433i	$0.449483\pi$
$314$		0			0
$315$	0.289578	−	0.891229i	0.0163159	−	0.0502150i
$316$		0			0
$317$	−22.7114	+	16.5008i	−1.27560	+	0.926777i	−0.999411	−	0.0343263i	$-0.989071\pi$
$317$	−22.7114	+	16.5008i	−1.27560	+	0.926777i	−0.276189	+	0.961103i	$0.589071\pi$
$318$		0			0
$319$	26.9003	+	7.78963i	1.50613	+	0.436135i
$320$		0			0
$321$	1.24609	−	0.905337i	0.0695499	−	0.0505310i
$322$		0			0
$323$	4.37998	−	13.4802i	0.243709	−	0.750058i
$324$		0			0
$325$	2.28815	+	1.66244i	0.126924	+	0.0922155i
$326$		0			0
$327$	1.27645	+	3.92851i	0.0705878	+	0.217247i
$328$		0			0
$329$	0.973897			0.0536927
$330$		0			0
$331$	−21.9644			−1.20727			−0.603637	−	0.797259i	$-0.706282\pi$
$331$	−21.9644			−1.20727			−0.603637	+	0.797259i	$0.706282\pi$
$332$		0			0
$333$	−2.18616	−	6.72830i	−0.119801	−	0.368709i
$334$		0			0
$335$	9.25475	+	6.72397i	0.505641	+	0.367370i
$336$		0			0
$337$	6.91576	−	21.2845i	0.376726	−	1.15944i	−0.565581	−	0.824693i	$-0.691348\pi$
$337$	6.91576	−	21.2845i	0.376726	−	1.15944i	0.942307	−	0.334750i	$-0.108652\pi$
$338$		0			0
$339$	10.9737	−	7.97287i	0.596010	−	0.433027i
$340$		0			0
$341$	16.3623	+	21.0559i	0.886068	+	1.14024i
$342$		0			0
$343$	−4.21755	+	3.06423i	−0.227726	+	0.165453i
$344$		0			0
$345$	0.831550	−	2.55925i	0.0447691	−	0.137785i
$346$		0			0
$347$	−20.0465	−	14.5646i	−1.07615	−	0.781869i	−0.0991431	−	0.995073i	$-0.531610\pi$
$347$	−20.0465	−	14.5646i	−1.07615	−	0.781869i	−0.977008	+	0.213204i	$0.931610\pi$
$348$		0			0
$349$	−6.89978	−	21.2354i	−0.369337	−	1.13670i	−0.947220	−	0.320583i	$-0.896121\pi$
$349$	−6.89978	−	21.2354i	−0.369337	−	1.13670i	0.577883	−	0.816119i	$-0.303879\pi$
$350$		0			0
$351$	−11.0788			−0.591342
$352$		0			0
$353$	−5.79232			−0.308294			−0.154147	−	0.988048i	$-0.549263\pi$
$353$	−5.79232			−0.308294			−0.154147	+	0.988048i	$0.549263\pi$
$354$		0			0
$355$	−4.36381	−	13.4304i	−0.231607	−	0.712813i
$356$		0			0
$357$	1.05023	+	0.763039i	0.0555842	+	0.0403843i
$358$		0			0
$359$	−6.50069	+	20.0071i	−0.343094	+	1.05593i	0.619503	+	0.784994i	$0.287334\pi$
$359$	−6.50069	+	20.0071i	−0.343094	+	1.05593i	−0.962597	+	0.270939i	$0.912666\pi$
$360$		0			0
$361$	8.42648	−	6.12219i	0.443499	−	0.322221i
$362$		0			0
$363$	2.90145	+	7.29075i	0.152286	+	0.382665i
$364$		0			0
$365$	−0.415207	+	0.301666i	−0.0217330	+	0.0157899i
$366$		0			0
$367$	7.30007	−	22.4673i	0.381061	−	1.17278i	−0.558237	−	0.829681i	$-0.688522\pi$
$367$	7.30007	−	22.4673i	0.381061	−	1.17278i	0.939298	−	0.343103i	$-0.111478\pi$
$368$		0			0
$369$	−7.49785	−	5.44750i	−0.390322	−	0.283586i
$370$		0			0
$371$	0.00566834	+	0.0174453i	0.000294285	+	0.000905717i
$372$		0			0
$373$	−12.7740			−0.661411			−0.330705	−	0.943734i	$-0.607287\pi$
$373$	−12.7740			−0.661411			−0.330705	+	0.943734i	$0.607287\pi$
$374$		0			0
$375$	−0.713352			−0.0368373
$376$		0			0
$377$	−7.37998	−	22.7132i	−0.380088	−	1.16979i
$378$		0			0
$379$	20.0453	+	14.5637i	1.02966	+	0.748089i	0.968240	−	0.250023i	$-0.0804381\pi$
$379$	20.0453	+	14.5637i	1.02966	+	0.748089i	0.0614167	+	0.998112i	$0.480438\pi$
$380$		0			0
$381$	−2.22583	+	6.85041i	−0.114033	+	0.350957i
$382$		0			0
$383$	30.8810	−	22.4363i	1.57794	−	1.14644i	0.658941	−	0.752195i	$-0.271005\pi$
$383$	30.8810	−	22.4363i	1.57794	−	1.14644i	0.919004	−	0.394249i	$-0.128995\pi$
$384$		0			0
$385$	0.765542	+	0.985142i	0.0390157	+	0.0502075i
$386$		0			0
$387$	13.0693	−	9.49542i	0.664351	−	0.482679i
$388$		0			0
$389$	0.744648	−	2.29179i	0.0377551	−	0.116198i	−0.930403	−	0.366539i	$-0.880543\pi$
$389$	0.744648	−	2.29179i	0.0377551	−	0.116198i	0.968158	+	0.250341i	$0.0805426\pi$
$390$		0			0
$391$	−14.7638	−	10.7265i	−0.746635	−	0.542462i
$392$		0			0
$393$	−1.38799	−	4.27179i	−0.0700148	−	0.215483i
$394$		0			0
$395$	−12.9823			−0.653212
$396$		0			0
$397$	−11.5456			−0.579459			−0.289729	−	0.957109i	$-0.593565\pi$
$397$	−11.5456			−0.579459			−0.289729	+	0.957109i	$0.593565\pi$
$398$		0			0
$399$	−0.242955	−	0.747738i	−0.0121630	−	0.0374337i
$400$		0			0
$401$	−20.7114	−	15.0477i	−1.03428	−	0.751445i	−0.0651157	−	0.997878i	$-0.520742\pi$
$401$	−20.7114	−	15.0477i	−1.03428	−	0.751445i	−0.969160	+	0.246432i	$0.920742\pi$
$402$		0			0
$403$	7.02702	−	21.6269i	0.350041	−	1.07731i
$404$		0			0
$405$	−3.78548	+	2.75031i	−0.188102	+	0.136664i
$406$		0			0
$407$	9.04720	+	2.61983i	0.448453	+	0.129860i
$408$		0			0
$409$	−7.57539	+	5.50384i	−0.374579	+	0.272147i	−0.759107	−	0.650966i	$-0.774364\pi$
$409$	−7.57539	+	5.50384i	−0.374579	+	0.272147i	0.384528	+	0.923113i	$0.374364\pi$
$410$		0			0
$411$	1.82375	−	5.61292i	0.0899588	−	0.276865i
$412$		0			0
$413$	0.501929	+	0.364673i	0.0246983	+	0.0179444i
$414$		0			0
$415$	−0.845740	−	2.60292i	−0.0415157	−	0.127772i
$416$		0			0
$417$	−7.32405			−0.358660
$418$		0			0
$419$	21.3716			1.04407			0.522035	−	0.852924i	$-0.325173\pi$
$419$	21.3716			1.04407			0.522035	+	0.852924i	$0.325173\pi$
$420$		0			0
$421$	8.50429	+	26.1735i	0.414474	+	1.27562i	0.912721	+	0.408584i	$0.133977\pi$
$421$	8.50429	+	26.1735i	0.414474	+	1.27562i	−0.498247	+	0.867035i	$0.666023\pi$
$422$		0			0
$423$	−5.21771	−	3.79089i	−0.253694	−	0.184319i
$424$		0			0
$425$	−1.49493	+	4.60091i	−0.0725146	+	0.223177i
$426$		0			0
$427$	2.64677	−	1.92299i	0.128086	−	0.0930601i
$428$		0			0
$429$	3.75635	−	5.53776i	0.181358	−	0.267366i
$430$		0			0
$431$	2.12962	−	1.54726i	0.102580	−	0.0745290i	−0.535313	−	0.844654i	$-0.679806\pi$
$431$	2.12962	−	1.54726i	0.102580	−	0.0745290i	0.637893	+	0.770125i	$0.279806\pi$
$432$		0			0
$433$	3.08722	−	9.50147i	0.148362	−	0.456612i	−0.849066	−	0.528287i	$-0.822835\pi$
$433$	3.08722	−	9.50147i	0.148362	−	0.456612i	0.997428	+	0.0716753i	$0.0228345\pi$
$434$		0			0
$435$	4.87313	+	3.54053i	0.233648	+	0.169756i
$436$		0			0
$437$	3.41536	+	10.5114i	0.163379	+	0.502829i
$438$		0			0
$439$	−2.85957			−0.136480			−0.0682400	−	0.997669i	$-0.521738\pi$
$439$	−2.85957			−0.136480			−0.0682400	+	0.997669i	$0.521738\pi$
$440$		0			0
$441$	17.0854			0.813590
$442$		0			0
$443$	12.4551	+	38.3329i	0.591761	+	1.82125i	0.570232	+	0.821484i	$0.306853\pi$
$443$	12.4551	+	38.3329i	0.591761	+	1.82125i	0.0215292	+	0.999768i	$0.493147\pi$
$444$		0			0
$445$	−9.72401	−	7.06491i	−0.460962	−	0.334909i
$446$		0			0
$447$	1.08050	−	3.32543i	0.0511058	−	0.157287i
$448$		0			0
$449$	1.57792	−	1.14642i	0.0744665	−	0.0541031i	−0.549929	−	0.835211i	$-0.685345\pi$
$449$	1.57792	−	1.14642i	0.0744665	−	0.0541031i	0.624396	+	0.781108i	$0.285345\pi$
$450$		0			0
$451$	11.6058	−	4.18988i	0.546497	−	0.197294i
$452$		0			0
$453$	5.39963	−	3.92306i	0.253697	−	0.184321i
$454$		0			0
$455$	0.328773	−	1.01186i	0.0154131	−	0.0474367i
$456$		0			0
$457$	−28.9438	−	21.0289i	−1.35393	−	0.983691i	−0.998805	−	0.0488733i	$-0.984437\pi$
$457$	−28.9438	−	21.0289i	−1.35393	−	0.983691i	−0.355129	−	0.934817i	$-0.615563\pi$
$458$		0			0
$459$	−5.85579	−	18.0223i	−0.273325	−	0.841207i
$460$		0			0
$461$	15.1433			0.705295			0.352648	−	0.935756i	$-0.385281\pi$
$461$	15.1433			0.705295			0.352648	+	0.935756i	$0.385281\pi$
$462$		0			0
$463$	12.6301			0.586972			0.293486	−	0.955963i	$-0.405185\pi$
$463$	12.6301			0.586972			0.293486	+	0.955963i	$0.405185\pi$
$464$		0			0
$465$	1.77234	+	5.45471i	0.0821905	+	0.252956i
$466$		0			0
$467$	25.3664	+	18.4298i	1.17382	+	0.852829i	0.991461	−	0.130403i	$-0.0416271\pi$
$467$	25.3664	+	18.4298i	1.17382	+	0.852829i	0.182358	+	0.983232i	$0.441627\pi$
$468$		0			0
$469$	1.32977	−	4.09261i	0.0614030	−	0.188979i
$470$		0			0
$471$	5.57387	−	4.04965i	0.256830	−	0.186598i
$472$		0			0
$473$	0.694470	+	21.4966i	0.0319318	+	0.988413i
$474$		0			0
$475$	2.37034	−	1.72215i	0.108759	−	0.0790177i
$476$		0			0
$477$	0.0375375	−	0.115528i	0.00171872	−	0.00528969i
$478$		0			0
$479$	−9.97966	−	7.25064i	−0.455982	−	0.331290i	0.335971	−	0.941872i	$-0.390936\pi$
$479$	−9.97966	−	7.25064i	−0.455982	−	0.331290i	−0.791953	+	0.610582i	$0.790936\pi$
$480$		0			0
$481$	−2.48206	−	7.63900i	−0.113172	−	0.348308i
$482$		0			0
$483$	−1.01226			−0.0460595
$484$		0			0
$485$	16.0745			0.729906
$486$		0			0
$487$	6.77063	+	20.8379i	0.306807	+	0.944254i	0.978997	+	0.203875i	$0.0653537\pi$
$487$	6.77063	+	20.8379i	0.306807	+	0.944254i	−0.672190	+	0.740378i	$0.734646\pi$
$488$		0			0
$489$	−2.59010	−	1.88182i	−0.117128	−	0.0850987i
$490$		0			0
$491$	8.45266	−	26.0146i	0.381463	−	1.17402i	−0.557551	−	0.830143i	$-0.688259\pi$
$491$	8.45266	−	26.0146i	0.381463	−	1.17402i	0.939014	−	0.343880i	$-0.111741\pi$
$492$		0			0
$493$	33.0477	−	24.0106i	1.48839	−	1.08138i
$494$		0			0
$495$	−0.266778	−	8.25783i	−0.0119908	−	0.371162i
$496$		0			0
$497$	−4.29762	+	3.12240i	−0.192775	+	0.140059i
$498$		0			0
$499$	3.21316	−	9.88908i	0.143841	−	0.442696i	−0.853019	−	0.521879i	$-0.825231\pi$
$499$	3.21316	−	9.88908i	0.143841	−	0.442696i	0.996860	+	0.0791832i	$0.0252312\pi$
$500$		0			0
$501$	13.5458	+	9.84158i	0.605180	+	0.439689i
$502$		0			0
$503$	3.20969	+	9.87840i	0.143113	+	0.440456i	0.996763	−	0.0803900i	$-0.0256166\pi$
$503$	3.20969	+	9.87840i	0.143113	+	0.440456i	−0.853651	+	0.520846i	$0.825617\pi$
$504$		0			0
$505$	15.5883			0.693670
$506$		0			0
$507$	3.56724			0.158427
$508$		0			0
$509$	7.13139	+	21.9482i	0.316093	+	0.972835i	0.975302	+	0.220875i	$0.0708913\pi$
$509$	7.13139	+	21.9482i	0.316093	+	0.972835i	−0.659209	+	0.751960i	$0.729109\pi$
$510$		0			0
$511$	0.156189	+	0.113478i	0.00690942	+	0.00501998i
$512$		0			0
$513$	−3.54650	+	10.9150i	−0.156582	+	0.481910i
$514$		0			0
$515$	−7.49074	+	5.44234i	−0.330082	+	0.239818i
$516$		0			0
$517$	8.07643	−	2.91572i	0.355201	−	0.128233i
$518$		0			0
$519$	−7.47413	+	5.43027i	−0.328078	+	0.238363i
$520$		0			0
$521$	10.9451	−	33.6855i	0.479513	−	1.47579i	−0.360260	−	0.932852i	$-0.617312\pi$
$521$	10.9451	−	33.6855i	0.479513	−	1.47579i	0.839773	−	0.542938i	$-0.182688\pi$
$522$		0			0
$523$	−14.6855	−	10.6697i	−0.642153	−	0.466551i	0.218436	−	0.975851i	$-0.429904\pi$
$523$	−14.6855	−	10.6697i	−0.642153	−	0.466551i	−0.860589	+	0.509300i	$0.829904\pi$
$524$		0			0
$525$	0.0829226	+	0.255210i	0.00361904	+	0.0111383i
$526$		0			0
$527$	38.8955			1.69431
$528$		0			0
$529$	−8.77004			−0.381306
$530$		0			0
$531$	−1.26963	−	3.90751i	−0.0550972	−	0.169572i
$532$		0			0
$533$	−8.51270	−	6.18484i	−0.368726	−	0.267895i
$534$		0			0
$535$	0.667222	−	2.05350i	0.0288465	−	0.0887804i
$536$		0			0
$537$	2.03683	−	1.47984i	0.0878956	−	0.0638599i
$538$		0			0
$539$	−12.7692	+	18.8249i	−0.550008	+	0.810845i
$540$		0			0
$541$	−13.1542	+	9.55711i	−0.565545	+	0.410892i	−0.833484	−	0.552543i	$-0.813657\pi$
$541$	−13.1542	+	9.55711i	−0.565545	+	0.410892i	0.267939	+	0.963436i	$0.413657\pi$
$542$		0			0
$543$	−0.394976	+	1.21561i	−0.0169500	+	0.0521669i
$544$		0			0
$545$	4.68463	+	3.40358i	0.200667	+	0.145793i
$546$		0			0
$547$	−4.81979	−	14.8338i	−0.206079	−	0.634246i	−0.999667	−	0.0257912i	$-0.991790\pi$
$547$	−4.81979	−	14.8338i	−0.206079	−	0.634246i	0.793588	−	0.608455i	$-0.208210\pi$
$548$		0			0
$549$	−21.6655			−0.924660
$550$		0			0
$551$	−24.7399			−1.05396
$552$		0			0
$553$	1.50911	+	4.64457i	0.0641740	+	0.197507i
$554$		0			0
$555$	1.63895	+	1.19076i	0.0695694	+	0.0505451i
$556$		0			0
$557$	3.25243	−	10.0099i	0.137810	−	0.424135i	−0.858207	−	0.513304i	$-0.828421\pi$
$557$	3.25243	−	10.0099i	0.137810	−	0.424135i	0.996016	+	0.0891695i	$0.0284213\pi$
$558$		0			0
$559$	14.8383	−	10.7806i	0.627593	−	0.455973i
$560$		0			0
$561$	10.9939	+	3.18355i	0.464164	+	0.134410i
$562$		0			0
$563$	9.48416	−	6.89065i	0.399710	−	0.290406i	−0.369713	−	0.929146i	$-0.620544\pi$
$563$	9.48416	−	6.89065i	0.399710	−	0.290406i	0.769423	+	0.638740i	$0.220544\pi$
$564$		0			0
$565$	5.87590	−	18.0842i	0.247201	−	0.760806i
$566$		0			0
$567$	1.42399	+	1.03459i	0.0598020	+	0.0434487i
$568$		0			0
$569$	−2.95887	−	9.10646i	−0.124042	−	0.381763i	0.869683	−	0.493610i	$-0.164323\pi$
$569$	−2.95887	−	9.10646i	−0.124042	−	0.381763i	−0.993725	+	0.111848i	$0.964323\pi$
$570$		0			0
$571$	−44.0439			−1.84318			−0.921589	−	0.388166i	$-0.873109\pi$
$571$	−44.0439			−1.84318			−0.921589	+	0.388166i	$0.873109\pi$
$572$		0			0
$573$	2.42620			0.101356
$574$		0			0
$575$	−1.16569	−	3.58763i	−0.0486128	−	0.149615i
$576$		0			0
$577$	22.6902	+	16.4854i	0.944604	+	0.686295i	0.949525	−	0.313693i	$-0.101566\pi$
$577$	22.6902	+	16.4854i	0.944604	+	0.686295i	−0.00492032	+	0.999988i	$0.501566\pi$
$578$		0			0
$579$	1.71400	−	5.27515i	0.0712314	−	0.219228i
$580$		0			0
$581$	−0.832911	+	0.605145i	−0.0345550	+	0.0251057i
$582$		0			0
$583$	0.0992360	+	0.127702i	0.00410993	+	0.00528889i
$584$		0			0
$585$	−5.70008	+	4.14135i	−0.235669	+	0.171224i
$586$		0			0
$587$	0.837247	−	2.57678i	0.0345569	−	0.106355i	−0.932290	−	0.361711i	$-0.882193\pi$
$587$	0.837247	−	2.57678i	0.0345569	−	0.106355i	0.966847	+	0.255356i	$0.0821927\pi$
$588$		0			0
$589$	−19.0578	−	13.8463i	−0.785261	−	0.570526i
$590$		0			0
$591$	1.56381	+	4.81291i	0.0643265	+	0.197977i
$592$		0			0
$593$	−35.1817			−1.44474			−0.722369	−	0.691508i	$-0.756947\pi$
$593$	−35.1817			−1.44474			−0.722369	+	0.691508i	$0.756947\pi$
$594$		0			0
$595$	1.81980			0.0746046
$596$		0			0
$597$	2.81574	+	8.66595i	0.115240	+	0.354674i
$598$		0			0
$599$	−38.2343	−	27.7788i	−1.56221	−	1.13501i	−0.934167	−	0.356835i	$-0.883856\pi$
$599$	−38.2343	−	27.7788i	−1.56221	−	1.13501i	−0.628044	−	0.778178i	$-0.716144\pi$
$600$		0			0
$601$	3.59792	−	11.0733i	0.146762	−	0.451687i	−0.850471	−	0.526022i	$-0.823683\pi$
$601$	3.59792	−	11.0733i	0.146762	−	0.451687i	0.997233	+	0.0743341i	$0.0236831\pi$
$602$		0			0
$603$	−23.0548	+	16.7503i	−0.938863	+	0.682124i
$604$		0			0
$605$	9.29795	+	5.87776i	0.378016	+	0.238965i
$606$		0			0
$607$	−37.1632	+	27.0006i	−1.50841	+	1.09592i	−0.541528	+	0.840683i	$0.682154\pi$
$607$	−37.1632	+	27.0006i	−1.50841	+	1.09592i	−0.966878	+	0.255238i	$0.917846\pi$
$608$		0			0
$609$	0.700195	−	2.15498i	0.0283733	−	0.0873241i
$610$		0			0
$611$	−5.92394	−	4.30400i	−0.239657	−	0.174121i
$612$		0			0
$613$	1.03724	+	3.19229i	0.0418937	+	0.128935i	0.969816	−	0.243839i	$-0.0784067\pi$
$613$	1.03724	+	3.19229i	0.0418937	+	0.128935i	−0.927922	+	0.372774i	$0.878407\pi$
$614$		0			0
$615$	2.65391			0.107016
$616$		0			0
$617$	−16.4880			−0.663783			−0.331892	−	0.943318i	$-0.607687\pi$
$617$	−16.4880			−0.663783			−0.331892	+	0.943318i	$0.607687\pi$
$618$		0			0
$619$	−0.635849	−	1.95694i	−0.0255569	−	0.0786561i	0.937465	−	0.348081i	$-0.113166\pi$
$619$	−0.635849	−	1.95694i	−0.0255569	−	0.0786561i	−0.963021	+	0.269425i	$0.913166\pi$
$620$		0			0
$621$	11.9543	+	8.68533i	0.479711	+	0.348530i
$622$		0			0
$623$	−1.39719	+	4.30012i	−0.0559774	+	0.172281i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−4.25343	−	5.47355i	−0.169866	−	0.218592i
$628$		0			0
$629$	11.1147	−	8.07531i	0.443173	−	0.321984i
$630$		0			0
$631$	−10.8822	+	33.4918i	−0.433212	+	1.33329i	0.461696	+	0.887038i	$0.347241\pi$
$631$	−10.8822	+	33.4918i	−0.433212	+	1.33329i	−0.894908	+	0.446251i	$0.852759\pi$
$632$		0			0
$633$	−4.23629	−	3.07784i	−0.168377	−	0.122333i
$634$		0			0
$635$	3.12025	+	9.60313i	0.123823	+	0.381088i
$636$		0			0
$637$	19.3979			0.768574
$638$		0			0
$639$	35.1787			1.39165
$640$		0			0
$641$	−10.4016	−	32.0128i	−0.410838	−	1.26443i	−0.915921	−	0.401359i	$-0.868538\pi$
$641$	−10.4016	−	32.0128i	−0.410838	−	1.26443i	0.505083	−	0.863071i	$-0.331462\pi$
$642$		0			0
$643$	−1.62876	−	1.18336i	−0.0642320	−	0.0466673i	0.555206	−	0.831713i	$-0.312639\pi$
$643$	−1.62876	−	1.18336i	−0.0642320	−	0.0466673i	−0.619438	+	0.785046i	$0.712639\pi$
$644$		0			0
$645$	−1.42950	+	4.39956i	−0.0562867	+	0.173233i
$646$		0			0
$647$	27.5398	−	20.0088i	1.08270	−	0.786628i	0.104548	−	0.994520i	$-0.466660\pi$
$647$	27.5398	−	20.0088i	1.08270	−	0.786628i	0.978152	+	0.207892i	$0.0666603\pi$
$648$		0			0
$649$	5.25423	+	1.52149i	0.206247	+	0.0597237i
$650$		0			0
$651$	1.74546	−	1.26815i	0.0684100	−	0.0497028i
$652$		0			0
$653$	−6.53960	+	20.1268i	−0.255914	+	0.787623i	0.737734	+	0.675091i	$0.235896\pi$
$653$	−6.53960	+	20.1268i	−0.255914	+	0.787623i	−0.993648	+	0.112531i	$0.964104\pi$
$654$		0			0
$655$	−5.09398	−	3.70099i	−0.199038	−	0.144610i
$656$		0			0
$657$	−0.395081	−	1.21593i	−0.0154136	−	0.0474381i
$658$		0			0
$659$	−21.3464			−0.831539			−0.415770	−	0.909470i	$-0.636488\pi$
$659$	−21.3464			−0.831539			−0.415770	+	0.909470i	$0.636488\pi$
$660$		0			0
$661$	11.3318			0.440757			0.220379	−	0.975414i	$-0.429271\pi$
$661$	11.3318			0.440757			0.220379	+	0.975414i	$0.429271\pi$
$662$		0			0
$663$	−3.01613	−	9.28270i	−0.117137	−	0.360510i
$664$		0			0
$665$	−0.891655	−	0.647825i	−0.0345769	−	0.0251216i
$666$		0			0
$667$	−9.84306	+	30.2938i	−0.381125	+	1.17298i
$668$		0			0
$669$	−3.77360	+	2.74168i	−0.145896	+	0.106000i
$670$		0			0
$671$	16.1922	−	23.8713i	0.625094	−	0.921540i
$672$		0			0
$673$	15.7639	−	11.4531i	0.607653	−	0.441486i	−0.240934	−	0.970541i	$-0.577454\pi$
$673$	15.7639	−	11.4531i	0.607653	−	0.441486i	0.848587	+	0.529056i	$0.177454\pi$
$674$		0			0
$675$	1.21045	−	3.72539i	0.0465904	−	0.143390i
$676$		0			0
$677$	20.8399	+	15.1411i	0.800944	+	0.581920i	0.911191	−	0.411985i	$-0.135164\pi$
$677$	20.8399	+	15.1411i	0.800944	+	0.581920i	−0.110247	+	0.993904i	$0.535164\pi$
$678$		0			0
$679$	−1.86856	−	5.75083i	−0.0717087	−	0.220697i
$680$		0			0
$681$	14.6566			0.561643
$682$		0			0
$683$	−13.0179			−0.498117			−0.249059	−	0.968488i	$-0.580121\pi$
$683$	−13.0179			−0.498117			−0.249059	+	0.968488i	$0.580121\pi$
$684$		0			0
$685$	−2.55659	−	7.86837i	−0.0976822	−	0.300635i
$686$		0			0
$687$	−2.49945	−	1.81595i	−0.0953598	−	0.0692829i
$688$		0			0
$689$	0.0426183	−	0.131166i	0.00162363	−	0.00499701i
$690$		0			0
$691$	−39.4366	+	28.6523i	−1.50024	+	1.08999i	−0.529950	+	0.848029i	$0.677789\pi$
$691$	−39.4366	+	28.6523i	−1.50024	+	1.08999i	−0.970287	+	0.241957i	$0.922211\pi$
$692$		0			0
$693$	−2.92332	+	1.05536i	−0.111048	+	0.0400899i
$694$		0			0
$695$	−8.30625	+	6.03484i	−0.315074	+	0.228915i
$696$		0			0
$697$	5.56164	−	17.1170i	0.210662	−	0.648351i
$698$		0			0
$699$	16.5398	+	12.0169i	0.625593	+	0.454520i
$700$		0			0
$701$	13.9531	+	42.9432i	0.527001	+	1.62194i	0.760324	+	0.649544i	$0.225040\pi$
$701$	13.9531	+	42.9432i	0.527001	+	1.62194i	−0.233322	+	0.972399i	$0.574960\pi$
$702$		0			0
$703$	−8.32062			−0.313818
$704$		0			0
$705$	1.84684			0.0695562
$706$		0			0
$707$	−1.81204	−	5.57688i	−0.0681487	−	0.209740i
$708$		0			0
$709$	6.34695	+	4.61133i	0.238365	+	0.173182i	0.700554	−	0.713599i	$-0.252936\pi$
$709$	6.34695	+	4.61133i	0.238365	+	0.173182i	−0.462190	+	0.886781i	$0.652936\pi$
$710$		0			0
$711$	9.99381	−	30.7578i	0.374797	−	1.15351i
$712$		0			0
$713$	−24.5370	+	17.8272i	−0.918917	+	0.667633i
$714$		0			0
$715$	−0.302887	−	9.37555i	−0.0113273	−	0.350626i
$716$		0			0
$717$	6.04621	−	4.39283i	0.225800	−	0.164053i
$718$		0			0
$719$	−11.2597	+	34.6538i	−0.419916	+	1.29237i	0.487864	+	0.872920i	$0.337776\pi$
$719$	−11.2597	+	34.6538i	−0.419916	+	1.29237i	−0.907780	+	0.419447i	$0.862224\pi$
$720$		0			0
$721$	2.81781	+	2.04726i	0.104941	+	0.0762439i
$722$		0			0
$723$	−3.42124	−	10.5295i	−0.127237	−	0.391597i
$724$		0			0
$725$	8.44396			0.313601
$726$		0			0
$727$	15.4970			0.574753			0.287376	−	0.957818i	$-0.407217\pi$
$727$	15.4970			0.574753			0.287376	+	0.957818i	$0.407217\pi$
$728$		0			0
$729$	−1.01155	−	3.11322i	−0.0374647	−	0.115304i
$730$		0			0
$731$	25.3802	+	18.4398i	0.938719	+	0.682020i
$732$		0			0
$733$	13.0999	−	40.3172i	0.483854	−	1.48915i	−0.349779	−	0.936832i	$-0.613743\pi$
$733$	13.0999	−	40.3172i	0.483854	−	1.48915i	0.833633	−	0.552318i	$-0.186257\pi$
$734$		0			0
$735$	−3.95813	+	2.87575i	−0.145998	+	0.106074i
$736$		0			0
$737$	−1.22507	−	37.9208i	−0.0451261	−	1.39683i
$738$		0			0
$739$	−24.5290	+	17.8214i	−0.902315	+	0.655570i	−0.939060	−	0.343754i	$-0.888301\pi$
$739$	−24.5290	+	17.8214i	−0.902315	+	0.655570i	0.0367444	+	0.999325i	$0.488301\pi$
$740$		0			0
$741$	−1.82669	+	5.62198i	−0.0671053	+	0.206529i
$742$		0			0
$743$	−16.8518	−	12.2436i	−0.618234	−	0.449173i	0.234070	−	0.972220i	$-0.424795\pi$
$743$	−16.8518	−	12.2436i	−0.618234	−	0.449173i	−0.852304	+	0.523047i	$0.824795\pi$
$744$		0			0
$745$	−1.51468	−	4.66169i	−0.0554934	−	0.170791i
$746$		0			0
$747$	6.81790			0.249454
$748$		0			0
$749$	−0.812221			−0.0296779
$750$		0			0
$751$	9.50988	+	29.2684i	0.347020	+	1.06802i	0.960493	+	0.278303i	$0.0897720\pi$
$751$	9.50988	+	29.2684i	0.347020	+	1.06802i	−0.613473	+	0.789716i	$0.710228\pi$
$752$		0			0
$753$	6.90812	+	5.01905i	0.251746	+	0.182904i
$754$		0			0
$755$	2.89124	−	8.89833i	0.105223	−	0.323843i
$756$		0			0
$757$	20.5370	−	14.9210i	0.746429	−	0.542312i	−0.148289	−	0.988944i	$-0.547377\pi$
$757$	20.5370	−	14.9210i	0.746429	−	0.542312i	0.894718	+	0.446632i	$0.147377\pi$
$758$		0			0
$759$	−8.39458	+	3.03057i	−0.304704	+	0.110003i
$760$		0			0
$761$	−27.2145	+	19.7725i	−0.986526	+	0.716753i	−0.959158	−	0.282872i	$-0.908713\pi$
$761$	−27.2145	+	19.7725i	−0.986526	+	0.716753i	−0.0273686	+	0.999625i	$0.508713\pi$
$762$		0			0
$763$	0.673110	−	2.07162i	0.0243682	−	0.0749977i
$764$		0			0
$765$	−9.74970	−	7.08357i	−0.352501	−	0.256107i
$766$		0			0
$767$	−1.44148	−	4.43641i	−0.0520487	−	0.160189i
$768$		0			0
$769$	−29.4388			−1.06159			−0.530795	−	0.847500i	$-0.678107\pi$
$769$	−29.4388			−1.06159			−0.530795	+	0.847500i	$0.678107\pi$
$770$		0			0
$771$	6.04453			0.217688
$772$		0			0
$773$	7.65080	+	23.5467i	0.275180	+	0.846917i	0.989172	+	0.146763i	$0.0468855\pi$
$773$	7.65080	+	23.5467i	0.275180	+	0.846917i	−0.713992	+	0.700154i	$0.753115\pi$
$774$		0			0
$775$	6.50458	+	4.72586i	0.233651	+	0.169758i
$776$		0			0
$777$	0.235492	−	0.724770i	0.00844823	−	0.0260010i
$778$		0			0
$779$	−8.81846	+	6.40699i	−0.315954	+	0.229554i
$780$		0			0
$781$	−26.2917	+	38.7603i	−0.940791	+	1.38695i
$782$		0			0
$783$	−26.7590	+	19.4415i	−0.956287	+	0.694783i
$784$		0			0
$785$	2.98454	−	9.18547i	0.106523	−	0.327843i
$786$		0			0
$787$	30.3056	+	22.0183i	1.08028	+	0.784869i	0.977732	−	0.209860i	$-0.0673007\pi$
$787$	30.3056	+	22.0183i	1.08028	+	0.784869i	0.102547	+	0.994728i	$0.467301\pi$
$788$		0			0
$789$	2.75965	+	8.49332i	0.0982460	+	0.302370i
$790$		0			0
$791$	−7.15284			−0.254326
$792$		0			0
$793$	−24.5979			−0.873499
$794$		0			0
$795$	0.0107491	+	0.0330824i	0.000381232	+	0.00117331i
$796$		0			0
$797$	38.9506	+	28.2993i	1.37970	+	1.00241i	0.996908	+	0.0785781i	$0.0250380\pi$
$797$	38.9506	+	28.2993i	1.37970	+	1.00241i	0.382794	+	0.923834i	$0.374962\pi$
$798$		0			0
$799$	3.87031	−	11.9116i	0.136922	−	0.421402i
$800$		0			0
$801$	24.2238	−	17.5996i	0.855905	−	0.621851i
$802$		0			0
$803$	1.63500	+	0.473454i	0.0576980	+	0.0167078i
$804$		0			0
$805$	−1.14801	+	0.834079i	−0.0404621	+	0.0293974i
$806$		0			0
$807$	5.30481	−	16.3265i	0.186738	−	0.574721i
$808$		0			0
$809$	−30.1663	−	21.9171i	−1.06059	−	0.770564i	−0.0863934	−	0.996261i	$-0.527534\pi$
$809$	−30.1663	−	21.9171i	−1.06059	−	0.770564i	−0.974198	+	0.225697i	$0.927534\pi$
$810$		0			0
$811$	−2.74285	−	8.44162i	−0.0963145	−	0.296425i	0.891280	−	0.453454i	$-0.149808\pi$
$811$	−2.74285	−	8.44162i	−0.0963145	−	0.296425i	−0.987594	+	0.157029i	$0.949808\pi$
$812$		0			0
$813$	−6.72135			−0.235728
$814$		0			0
$815$	−4.48802			−0.157208
$816$		0			0
$817$	−5.87130	−	18.0700i	−0.205411	−	0.632189i
$818$		0			0
$819$	2.14421	+	1.55786i	0.0749248	+	0.0544360i
$820$		0			0
$821$	−9.62682	+	29.6283i	−0.335978	+	1.03403i	0.630260	+	0.776384i	$0.282948\pi$
$821$	−9.62682	+	29.6283i	−0.335978	+	1.03403i	−0.966238	+	0.257650i	$0.917052\pi$
$822$		0			0
$823$	−26.4022	+	19.1823i	−0.920321	+	0.668653i	−0.943604	−	0.331076i	$-0.892588\pi$
$823$	−26.4022	+	19.1823i	−0.920321	+	0.668653i	0.0232827	+	0.999729i	$0.492588\pi$
$824$		0			0
$825$	1.45173	+	1.86817i	0.0505428	+	0.0650413i
$826$		0			0
$827$	−23.2668	+	16.9043i	−0.809067	+	0.587822i	−0.913560	−	0.406704i	$-0.866678\pi$
$827$	−23.2668	+	16.9043i	−0.809067	+	0.587822i	0.104493	+	0.994526i	$0.466678\pi$
$828$		0			0
$829$	−13.2250	+	40.7023i	−0.459323	+	1.41365i	0.406661	+	0.913579i	$0.366693\pi$
$829$	−13.2250	+	40.7023i	−0.459323	+	1.41365i	−0.865984	+	0.500071i	$0.833307\pi$
$830$		0			0
$831$	13.7244	+	9.97136i	0.476094	+	0.345903i
$832$		0			0
$833$	10.2529	+	31.5553i	0.355243	+	1.09333i
$834$		0			0
$835$	23.4716			0.812267
$836$		0			0
$837$	−31.4940			−1.08859
$838$		0			0
$839$	8.81709	+	27.1362i	0.304400	+	0.936846i	0.979900	+	0.199487i	$0.0639276\pi$
$839$	8.81709	+	27.1362i	0.304400	+	0.936846i	−0.675501	+	0.737359i	$0.736072\pi$
$840$		0			0
$841$	−34.2218	−	24.8636i	−1.18006	−	0.857364i
$842$		0			0
$843$	−0.109536	+	0.337119i	−0.00377264	+	0.0116110i
$844$		0			0
$845$	4.04563	−	2.93932i	0.139174	−	0.101116i
$846$		0			0
$847$	1.02201	−	4.00970i	0.0351165	−	0.137775i
$848$		0			0
$849$	−2.70107	+	1.96244i	−0.0927004	+	0.0673508i
$850$		0			0
$851$	−3.31045	+	10.1885i	−0.113481	+	0.349258i
$852$		0			0
$853$	−27.0293	−	19.6380i	−0.925466	−	0.672391i	0.0194121	−	0.999812i	$-0.493821\pi$
$853$	−27.0293	−	19.6380i	−0.925466	−	0.672391i	−0.944879	+	0.327421i	$0.893821\pi$
$854$		0			0
$855$	2.25544	+	6.94153i	0.0771344	+	0.237395i
$856$		0			0
$857$	11.9632			0.408656			0.204328	−	0.978902i	$-0.434499\pi$
$857$	11.9632			0.408656			0.204328	+	0.978902i	$0.434499\pi$
$858$		0			0
$859$	−23.4984			−0.801755			−0.400878	−	0.916132i	$-0.631295\pi$
$859$	−23.4984			−0.801755			−0.400878	+	0.916132i	$0.631295\pi$
$860$		0			0
$861$	−0.308500	−	0.949467i	−0.0105137	−	0.0323577i
$862$		0			0
$863$	3.31223	+	2.40647i	0.112750	+	0.0819173i	0.642731	−	0.766092i	$-0.277801\pi$
$863$	3.31223	+	2.40647i	0.112750	+	0.0819173i	−0.529982	+	0.848009i	$0.677801\pi$
$864$		0			0
$865$	−4.00204	+	12.3170i	−0.136073	+	0.418791i
$866$		0			0
$867$	3.69536	−	2.68484i	0.125501	−	0.0911819i
$868$		0			0
$869$	26.4201	+	33.9989i	0.896242	+	1.15333i
$870$		0			0
$871$	−26.1753	+	19.0175i	−0.886916	+	0.644382i
$872$		0			0
$873$	−12.3742	+	38.0838i	−0.418803	+	1.28894i
$874$		0			0
$875$	0.304330	+	0.221108i	0.0102882	+	0.00747483i
$876$		0			0
$877$	13.7101	+	42.1952i	0.462956	+	1.42483i	0.861535	+	0.507698i	$0.169503\pi$
$877$	13.7101	+	42.1952i	0.462956	+	1.42483i	−0.398579	+	0.917134i	$0.630497\pi$
$878$		0			0
$879$	−12.0701			−0.407115
$880$		0			0
$881$	−43.0315			−1.44977			−0.724884	−	0.688871i	$-0.758107\pi$
$881$	−43.0315			−1.44977			−0.724884	+	0.688871i	$0.758107\pi$
$882$		0			0
$883$	11.2928	+	34.7558i	0.380034	+	1.16963i	0.940019	+	0.341122i	$0.110807\pi$
$883$	11.2928	+	34.7558i	0.380034	+	1.16963i	−0.559985	+	0.828503i	$0.689193\pi$
$884$		0			0
$885$	0.951831	+	0.691545i	0.0319954	+	0.0232460i
$886$		0			0
$887$	0.554496	−	1.70656i	0.0186181	−	0.0573008i	−0.941316	−	0.337527i	$-0.890410\pi$
$887$	0.554496	−	1.70656i	0.0186181	−	0.0573008i	0.959934	+	0.280226i	$0.0904095\pi$
$888$		0			0
$889$	3.07292	−	2.23260i	0.103062	−	0.0748791i
$890$		0			0
$891$	14.9065	+	4.31652i	0.499385	+	0.144609i
$892$		0			0
$893$	−6.13672	+	4.45859i	−0.205358	+	0.149201i
$894$		0			0
$895$	1.09062	−	3.35659i	0.0364555	−	0.112199i
$896$		0			0
$897$	6.15730	+	4.47354i	0.205586	+	0.149367i
$898$		0			0
$899$	−20.9793	−	64.5675i	−0.699697	−	2.15345i
$900$		0			0
$901$	0.235898			0.00785890
$902$		0			0
$903$	1.74016			0.0579090
$904$		0			0
$905$	0.553690	+	1.70408i	0.0184053	+	0.0566457i
$906$		0			0
$907$	−41.4760	−	30.1341i	−1.37719	−	1.00059i	−0.997137	−	0.0756199i	$-0.975906\pi$
$907$	−41.4760	−	30.1341i	−1.37719	−	1.00059i	−0.380051	−	0.924966i	$-0.624094\pi$
$908$		0			0
$909$	−11.9999	+	36.9318i	−0.398011	+	1.22495i
$910$		0			0
$911$	32.4256	−	23.5586i	1.07431	−	0.780531i	0.0976273	−	0.995223i	$-0.468875\pi$
$911$	32.4256	−	23.5586i	1.07431	−	0.780531i	0.976682	+	0.214692i	$0.0688747\pi$
$912$		0			0
$913$	−5.09553	+	7.51204i	−0.168637	+	0.248612i
$914$		0			0
$915$	5.01919	−	3.64665i	0.165929	−	0.120555i
$916$		0			0
$917$	−0.731929	+	2.25264i	−0.0241704	+	0.0743889i
$918$		0			0
$919$	0.876551	+	0.636852i	0.0289147	+	0.0210078i	0.602149	−	0.798384i	$-0.294311\pi$
$919$	0.876551	+	0.636852i	0.0289147	+	0.0210078i	−0.573234	+	0.819392i	$0.694311\pi$
$920$		0			0
$921$	−7.57573	−	23.3157i	−0.249629	−	0.768279i
$922$		0			0
$923$	39.9402			1.31465
$924$		0			0
$925$	2.83990			0.0933754
$926$		0			0
$927$	−7.12764	−	21.9366i	−0.234102	−	0.720493i
$928$		0			0
$929$	−11.5480	−	8.39015i	−0.378879	−	0.275272i	0.382004	−	0.924161i	$-0.375234\pi$
$929$	−11.5480	−	8.39015i	−0.378879	−	0.275272i	−0.760883	+	0.648889i	$0.775234\pi$
$930$		0			0
$931$	6.20960	−	19.1112i	0.203511	−	0.626344i
$932$		0			0
$933$	−4.25212	+	3.08935i	−0.139208	+	0.101141i
$934$		0			0
$935$	15.0914	−	5.44824i	0.493543	−	0.178177i
$936$		0			0
$937$	22.5636	−	16.3934i	0.737120	−	0.535549i	−0.154688	−	0.987963i	$-0.549437\pi$
$937$	22.5636	−	16.3934i	0.737120	−	0.535549i	0.891808	+	0.452415i	$0.149437\pi$
$938$		0			0
$939$	5.52430	−	17.0020i	0.180279	−	0.554841i
$940$		0			0
$941$	−2.93220	−	2.13037i	−0.0955869	−	0.0694480i	0.538965	−	0.842328i	$-0.318815\pi$
$941$	−2.93220	−	2.13037i	−0.0955869	−	0.0694480i	−0.634552	+	0.772880i	$0.718815\pi$
$942$		0			0
$943$	4.33678	+	13.3472i	0.141225	+	0.434645i
$944$		0			0
$945$	−1.47351			−0.0479332
$946$		0			0
$947$	54.9559			1.78583			0.892913	−	0.450230i	$-0.148658\pi$
$947$	54.9559			1.78583			0.892913	+	0.450230i	$0.148658\pi$
$948$		0			0
$949$	−0.448556	−	1.38051i	−0.0145607	−	0.0448134i
$950$		0			0
$951$	16.2012	+	11.7709i	0.525361	+	0.381697i
$952$		0			0
$953$	−2.79241	+	8.59415i	−0.0904550	+	0.278392i	−0.986043	−	0.166493i	$-0.946756\pi$
$953$	−2.79241	+	8.59415i	−0.0904550	+	0.278392i	0.895588	+	0.444885i	$0.146756\pi$
$954$		0			0
$955$	2.75157	−	1.99913i	0.0890387	−	0.0646904i
$956$		0			0
$957$	−0.645066	−	19.9673i	−0.0208520	−	0.645452i
$958$		0			0
$959$	−2.51781	+	1.82930i	−0.0813043	+	0.0590710i
$960$		0			0
$961$	10.3964	−	31.9967i	0.335366	−	1.03215i
$962$		0			0
$963$	4.35153	+	3.16157i	0.140226	+	0.101880i
$964$		0			0
$965$	−2.40274	−	7.39487i	−0.0773469	−	0.238049i
$966$		0			0
$967$	44.4619			1.42980			0.714900	−	0.699227i	$-0.246472\pi$
$967$	44.4619			1.42980			0.714900	+	0.699227i	$0.246472\pi$
$968$		0			0
$969$	−10.1110			−0.324812
$970$		0			0
$971$	−0.515647	−	1.58700i	−0.0165479	−	0.0509292i	0.942442	−	0.334371i	$-0.108524\pi$
$971$	−0.515647	−	1.58700i	−0.0165479	−	0.0509292i	−0.958990	+	0.283442i	$0.908524\pi$
$972$		0			0
$973$	3.12458	+	2.27014i	0.100169	+	0.0727773i
$974$		0			0
$975$	0.623466	−	1.91883i	0.0199669	−	0.0614518i
$976$		0			0
$977$	−18.3272	+	13.3155i	−0.586339	+	0.426000i	−0.841004	−	0.541029i	$-0.818035\pi$
$977$	−18.3272	+	13.3155i	−0.586339	+	0.426000i	0.254665	+	0.967029i	$0.418035\pi$
$978$		0			0
$979$	1.28719	+	39.8435i	0.0411387	+	1.27340i
$980$		0			0
$981$	−11.6700	+	8.47876i	−0.372595	+	0.270706i
$982$		0			0
$983$	−14.5087	+	44.6531i	−0.462754	+	1.42421i	0.399031	+	0.916938i	$0.369347\pi$
$983$	−14.5087	+	44.6531i	−0.462754	+	1.42421i	−0.861785	+	0.507274i	$0.830653\pi$
$984$		0			0
$985$	5.73925	+	4.16981i	0.182868	+	0.132861i
$986$		0			0
$987$	−0.214684	−	0.660729i	−0.00683346	−	0.0210312i
$988$		0			0
$989$	−24.4625			−0.777863
$990$		0			0
$991$	0.122612			0.00389489			0.00194745	−	0.999998i	$-0.499380\pi$
$991$	0.122612			0.00389489			0.00194745	+	0.999998i	$0.499380\pi$
$992$		0			0
$993$	4.84179	+	14.9015i	0.153650	+	0.472885i
$994$		0			0
$995$	10.3339	+	7.50800i	0.327606	+	0.238020i
$996$		0			0
$997$	−6.23692	+	19.1953i	−0.197525	+	0.607920i	0.802413	+	0.596770i	$0.203549\pi$
$997$	−6.23692	+	19.1953i	−0.197525	+	0.607920i	−0.999938	+	0.0111504i	$0.996451\pi$
$998$		0			0
$999$	−8.99967	+	6.53864i	−0.284737	+	0.206873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.k.641.2		16
4.3	odd	2		440.2.y.d.201.3	yes	16
11.2	odd	10		9680.2.a.de.1.4		8
11.4	even	5	inner	880.2.bo.k.81.2		16
11.9	even	5		9680.2.a.df.1.4		8
44.15	odd	10		440.2.y.d.81.3	✓	16
44.31	odd	10		4840.2.a.bg.1.5		8
44.35	even	10		4840.2.a.bh.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.d.81.3	✓	16	44.15	odd	10
440.2.y.d.201.3	yes	16	4.3	odd	2
880.2.bo.k.81.2		16	11.4	even	5	inner
880.2.bo.k.641.2		16	1.1	even	1	trivial
4840.2.a.bg.1.5		8	44.31	odd	10
4840.2.a.bh.1.5		8	44.35	even	10
9680.2.a.de.1.4		8	11.2	odd	10
9680.2.a.df.1.4		8	11.9	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.220438 - 0.678438i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.116244 + 0.357761i) q^{7} +(2.01537 - 1.46425i) q^{9} +(0.107091 + 3.31490i) q^{11} +(2.28815 - 1.66244i) q^{13} +(-0.220438 + 0.678438i) q^{15} +(3.91377 + 2.84352i) q^{17} +(-0.905388 - 2.78650i) q^{19} +0.268343 q^{21} -3.77226 q^{23} +(0.309017 + 0.951057i) q^{25} +(-3.16901 - 2.30242i) q^{27} +(2.60933 - 8.03068i) q^{29} +(6.50458 - 4.72586i) q^{31} +(2.22534 - 0.803383i) q^{33} +(0.304330 - 0.221108i) q^{35} +(0.877578 - 2.70091i) q^{37} +(-1.63226 - 1.18590i) q^{39} +(-1.14965 - 3.53825i) q^{41} +6.48484 q^{43} -2.49113 q^{45} +(-0.800034 - 2.46225i) q^{47} +(5.54864 + 4.03132i) q^{49} +(1.06641 - 3.28207i) q^{51} +(0.0394497 - 0.0286619i) q^{53} +(1.86181 - 2.74475i) q^{55} +(-1.69089 + 1.22850i) q^{57} +(0.509660 - 1.56857i) q^{59} +(-7.03606 - 5.11200i) q^{61} +(0.289578 + 0.891229i) q^{63} -2.82831 q^{65} -11.4395 q^{67} +(0.831550 + 2.55925i) q^{69} +(11.4246 + 8.30046i) q^{71} +(0.158595 - 0.488106i) q^{73} +(0.577114 - 0.419298i) q^{75} +(-1.19839 - 0.347022i) q^{77} +(10.5029 - 7.63082i) q^{79} +(1.44592 - 4.45010i) q^{81} +(2.21418 + 1.60869i) q^{83} +(-1.49493 - 4.60091i) q^{85} -6.02351 q^{87} +12.0195 q^{89} +(0.328773 + 1.01186i) q^{91} +(-4.64006 - 3.37120i) q^{93} +(-0.905388 + 2.78650i) q^{95} +(-13.0046 + 9.44836i) q^{97} +(5.06966 + 6.52392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9} + 7 q^{11} - 11 q^{13} + 3 q^{15} + 9 q^{17} + 2 q^{19} + 12 q^{21} - 20 q^{23} - 4 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 32 q^{33} + 2 q^{35} - 16 q^{37}+ \cdots + 10 q^{99}+O(q^{100}) \) 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9 + 7 * q^11 - 11 * q^13 + 3 * q^15 + 9 * q^17 + 2 * q^19 + 12 * q^21 - 20 * q^23 - 4 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 32 * q^33 + 2 * q^35 - 16 * q^37 - 3 * q^39 - 11 * q^41 + 16 * q^43 + 38 * q^45 + 10 * q^47 + 4 * q^49 - 26 * q^51 - 9 * q^53 - 3 * q^55 - 50 * q^57 + 60 * q^59 + 30 * q^61 - 52 * q^63 + 24 * q^65 + 4 * q^67 + 41 * q^69 + 10 * q^71 + q^73 - 2 * q^75 - 4 * q^77 - 19 * q^79 - 31 * q^81 - 64 * q^83 - 11 * q^85 - 30 * q^87 + 24 * q^89 + 9 * q^91 + 45 * q^93 + 2 * q^95 - 3 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more