LMFDB - Embedded newform 896.2.ba.f.417.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(289,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,-4,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			417.7
Character	$\chi$	$=$	896.417
Dual form			896.2.ba.f.737.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0543752 - 0.0145698i) q^{3} +(-1.25781 - 0.337028i) q^{5} +(0.230738 - 2.63567i) q^{7} +(-2.59533 + 1.49842i) q^{9} +(0.402875 + 1.50355i) q^{11} +(-1.59615 - 1.59615i) q^{13} -0.0733039 q^{15} +(1.46910 - 2.54455i) q^{17} +(-2.05021 + 7.65147i) q^{19} +(-0.0258547 - 0.146677i) q^{21} +(-3.91784 + 2.26197i) q^{23} +(-2.86164 - 1.65217i) q^{25} +(-0.238706 + 0.238706i) q^{27} +(-2.06234 - 2.06234i) q^{29} +(-3.14025 + 5.43908i) q^{31} +(0.0438128 + 0.0758861i) q^{33} +(-1.17852 + 3.23740i) q^{35} +(-5.24787 - 1.40616i) q^{37} +(-0.110046 - 0.0635352i) q^{39} +7.34101i q^{41} +(1.99391 - 1.99391i) q^{43} +(3.76943 - 1.01002i) q^{45} +(0.979430 + 1.69642i) q^{47} +(-6.89352 - 1.21630i) q^{49} +(0.0428089 - 0.159765i) q^{51} +(-3.00493 - 11.2146i) q^{53} -2.02696i q^{55} +0.445921i q^{57} +(-0.793411 - 2.96105i) q^{59} +(-2.60480 + 9.72123i) q^{61} +(3.35049 + 7.18618i) q^{63} +(1.46970 + 2.54559i) q^{65} +(2.11517 - 0.566758i) q^{67} +(-0.180077 + 0.180077i) q^{69} +7.26378i q^{71} +(-12.2392 - 7.06631i) q^{73} +(-0.179674 - 0.0481435i) q^{75} +(4.05583 - 0.714920i) q^{77} +(-0.961559 - 1.66547i) q^{79} +(4.48574 - 7.76954i) q^{81} +(-8.82731 - 8.82731i) q^{83} +(-2.70543 + 2.70543i) q^{85} +(-0.142188 - 0.0820924i) q^{87} +(11.5526 - 6.66987i) q^{89} +(-4.57521 + 3.83862i) q^{91} +(-0.0915056 + 0.341503i) q^{93} +(5.15752 - 8.93309i) q^{95} -9.69578 q^{97} +(-3.29854 - 3.29854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{5} + 4 q^{11} + 24 q^{13} - 40 q^{15} + 8 q^{17} + 4 q^{19} + 8 q^{21} + 24 q^{27} - 24 q^{29} + 28 q^{31} + 16 q^{33} - 28 q^{35} + 24 q^{37} + 40 q^{43} + 28 q^{45} - 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^5 + 4 * q^11 + 24 * q^13 - 40 * q^15 + 8 * q^17 + 4 * q^19 + 8 * q^21 + 24 * q^27 - 24 * q^29 + 28 * q^31 + 16 * q^33 - 28 * q^35 + 24 * q^37 + 40 * q^43 + 28 * q^45 - 20 * q^47 - 24 * q^51 + 16 * q^53 + 20 * q^59 - 8 * q^61 - 16 * q^63 + 8 * q^65 - 48 * q^67 + 40 * q^69 + 4 * q^75 + 20 * q^77 - 36 * q^79 + 8 * q^83 - 64 * q^91 - 8 * q^93 - 4 * q^95 - 48 * q^97 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0543752	−	0.0145698i	0.0313935	−	0.00841187i	−0.243088	−	0.970004i	$-0.578160\pi$
$3$	0.0543752	−	0.0145698i	0.0313935	−	0.00841187i	0.274482	+	0.961592i	$0.411494\pi$
$4$		0			0
$5$	−1.25781	−	0.337028i	−0.562508	−	0.150724i	−0.0336497	−	0.999434i	$-0.510713\pi$
$5$	−1.25781	−	0.337028i	−0.562508	−	0.150724i	−0.528858	+	0.848710i	$0.677380\pi$
$6$		0			0
$7$	0.230738	−	2.63567i	0.0872109	−	0.996190i
$7$	0.230738	−	2.63567i	0.0872109	−	0.996190i
$8$		0			0
$9$	−2.59533	+	1.49842i	−0.865111	+	0.499472i
$10$		0			0
$11$	0.402875	+	1.50355i	0.121472	+	0.453338i	0.999689	−	0.0249229i	$-0.00793403\pi$
$11$	0.402875	+	1.50355i	0.121472	+	0.453338i	−0.878218	+	0.478261i	$0.841267\pi$
$12$		0			0
$13$	−1.59615	−	1.59615i	−0.442691	−	0.442691i	0.450224	−	0.892916i	$-0.351344\pi$
$13$	−1.59615	−	1.59615i	−0.442691	−	0.442691i	−0.892916	+	0.450224i	$0.851344\pi$
$14$		0			0
$15$	−0.0733039			−0.0189270
$16$		0			0
$17$	1.46910	−	2.54455i	0.356309	−	0.617145i	−0.631032	−	0.775757i	$-0.717368\pi$
$17$	1.46910	−	2.54455i	0.356309	−	0.617145i	0.987341	+	0.158612i	$0.0507018\pi$
$18$		0			0
$19$	−2.05021	+	7.65147i	−0.470350	+	1.75537i	0.168165	+	0.985759i	$0.446216\pi$
$19$	−2.05021	+	7.65147i	−0.470350	+	1.75537i	−0.638514	+	0.769610i	$0.720451\pi$
$20$		0			0
$21$	−0.0258547	−	0.146677i	−0.00564196	−	0.0320075i
$22$		0			0
$23$	−3.91784	+	2.26197i	−0.816927	+	0.471653i	−0.849356	−	0.527821i	$-0.823009\pi$
$23$	−3.91784	+	2.26197i	−0.816927	+	0.471653i	0.0324286	+	0.999474i	$0.489676\pi$
$24$		0			0
$25$	−2.86164	−	1.65217i	−0.572328	−	0.330434i
$26$		0			0
$27$	−0.238706	+	0.238706i	−0.0459390	+	0.0459390i
$28$		0			0
$29$	−2.06234	−	2.06234i	−0.382968	−	0.382968i	0.489203	−	0.872170i	$-0.337288\pi$
$29$	−2.06234	−	2.06234i	−0.382968	−	0.382968i	−0.872170	+	0.489203i	$0.837288\pi$
$30$		0			0
$31$	−3.14025	+	5.43908i	−0.564006	+	0.976887i	0.433136	+	0.901329i	$0.357407\pi$
$31$	−3.14025	+	5.43908i	−0.564006	+	0.976887i	−0.997141	+	0.0755580i	$0.975926\pi$
$32$		0			0
$33$	0.0438128	+	0.0758861i	0.00762684	+	0.0132101i
$34$		0			0
$35$	−1.17852	+	3.23740i	−0.199206	+	0.547220i
$36$		0			0
$37$	−5.24787	−	1.40616i	−0.862745	−	0.231172i	−0.199797	−	0.979837i	$-0.564028\pi$
$37$	−5.24787	−	1.40616i	−0.862745	−	0.231172i	−0.662948	+	0.748666i	$0.730695\pi$
$38$		0			0
$39$	−0.110046	−	0.0635352i	−0.0176215	−	0.0101738i
$40$		0			0
$41$			7.34101i			1.14647i	0.819390	+	0.573236i	$0.194312\pi$
$41$			7.34101i			1.14647i	−0.819390	+	0.573236i	$0.805688\pi$
$42$		0			0
$43$	1.99391	−	1.99391i	0.304068	−	0.304068i	−0.538535	−	0.842603i	$-0.681022\pi$
$43$	1.99391	−	1.99391i	0.304068	−	0.304068i	0.842603	+	0.538535i	$0.181022\pi$
$44$		0			0
$45$	3.76943	−	1.01002i	0.561914	−	0.150564i
$46$		0			0
$47$	0.979430	+	1.69642i	0.142865	+	0.247449i	0.928574	−	0.371147i	$-0.121035\pi$
$47$	0.979430	+	1.69642i	0.142865	+	0.247449i	−0.785710	+	0.618596i	$0.787702\pi$
$48$		0			0
$49$	−6.89352	−	1.21630i	−0.984789	−	0.173757i
$50$		0			0
$51$	0.0428089	−	0.159765i	0.00599444	−	0.0223716i
$52$		0			0
$53$	−3.00493	−	11.2146i	−0.412759	−	1.54044i	−0.789282	−	0.614031i	$-0.789547\pi$
$53$	−3.00493	−	11.2146i	−0.412759	−	1.54044i	0.376522	−	0.926408i	$-0.377120\pi$
$54$		0			0
$55$		−	2.02696i		−	0.273315i
$56$		0			0
$57$			0.445921i			0.0590637i
$58$		0			0
$59$	−0.793411	−	2.96105i	−0.103293	−	0.385496i	0.894853	−	0.446362i	$-0.147281\pi$
$59$	−0.793411	−	2.96105i	−0.103293	−	0.385496i	−0.998146	+	0.0608657i	$0.980614\pi$
$60$		0			0
$61$	−2.60480	+	9.72123i	−0.333510	+	1.24468i	0.571966	+	0.820277i	$0.306181\pi$
$61$	−2.60480	+	9.72123i	−0.333510	+	1.24468i	−0.905476	+	0.424398i	$0.860486\pi$
$62$		0			0
$63$	3.35049	+	7.18618i	0.422122	+	0.905374i
$64$		0			0
$65$	1.46970	+	2.54559i	0.182293	+	0.315742i
$66$		0			0
$67$	2.11517	−	0.566758i	0.258409	−	0.0692405i	−0.127289	−	0.991866i	$-0.540627\pi$
$67$	2.11517	−	0.566758i	0.258409	−	0.0692405i	0.385698	+	0.922625i	$0.373961\pi$
$68$		0			0
$69$	−0.180077	+	0.180077i	−0.0216787	+	0.0216787i
$70$		0			0
$71$			7.26378i			0.862052i	0.902340	+	0.431026i	$0.141848\pi$
$71$			7.26378i			0.862052i	−0.902340	+	0.431026i	$0.858152\pi$
$72$		0			0
$73$	−12.2392	−	7.06631i	−1.43249	−	0.827049i	−0.435181	−	0.900343i	$-0.643316\pi$
$73$	−12.2392	−	7.06631i	−1.43249	−	0.827049i	−0.997310	+	0.0732936i	$0.976649\pi$
$74$		0			0
$75$	−0.179674	−	0.0481435i	−0.0207469	−	0.00555913i
$76$		0			0
$77$	4.05583	−	0.714920i	0.462204	−	0.0814727i
$78$		0			0
$79$	−0.961559	−	1.66547i	−0.108184	−	0.187380i	0.806851	−	0.590755i	$-0.201170\pi$
$79$	−0.961559	−	1.66547i	−0.108184	−	0.187380i	−0.915035	+	0.403376i	$0.867837\pi$
$80$		0			0
$81$	4.48574	−	7.76954i	0.498416	−	0.863282i
$82$		0			0
$83$	−8.82731	−	8.82731i	−0.968923	−	0.968923i	0.0306086	−	0.999531i	$-0.490255\pi$
$83$	−8.82731	−	8.82731i	−0.968923	−	0.968923i	−0.999531	+	0.0306086i	$0.990255\pi$
$84$		0			0
$85$	−2.70543	+	2.70543i	−0.293445	+	0.293445i
$86$		0			0
$87$	−0.142188	−	0.0820924i	−0.0152442	−	0.00880123i
$88$		0			0
$89$	11.5526	−	6.66987i	1.22457	−	0.707005i	0.258680	−	0.965963i	$-0.416713\pi$
$89$	11.5526	−	6.66987i	1.22457	−	0.707005i	0.965888	+	0.258959i	$0.0833793\pi$
$90$		0			0
$91$	−4.57521	+	3.83862i	−0.479612	+	0.402397i
$92$		0			0
$93$	−0.0915056	+	0.341503i	−0.00948869	+	0.0354123i
$94$		0			0
$95$	5.15752	−	8.93309i	0.529151	−	0.916516i
$96$		0			0
$97$	−9.69578			−0.984458			−0.492229	−	0.870466i	$-0.663818\pi$
$97$	−9.69578			−0.984458			−0.492229	+	0.870466i	$0.663818\pi$
$98$		0			0
$99$	−3.29854	−	3.29854i	−0.331516	−	0.331516i
$100$		0			0
$101$	2.73526	+	10.2081i	0.272168	+	1.01575i	0.957715	+	0.287718i	$0.0928966\pi$
$101$	2.73526	+	10.2081i	0.272168	+	1.01575i	−0.685547	+	0.728029i	$0.740437\pi$
$102$		0			0
$103$	−2.96542	+	1.71209i	−0.292192	+	0.168697i	−0.638930	−	0.769265i	$-0.720623\pi$
$103$	−2.96542	+	1.71209i	−0.292192	+	0.168697i	0.346738	+	0.937962i	$0.387289\pi$
$104$		0			0
$105$	−0.0169140	+	0.193205i	−0.00165064	+	0.0188549i
$106$		0			0
$107$	11.0668	+	2.96534i	1.06987	+	0.286670i	0.750439	−	0.660940i	$-0.229842\pi$
$107$	11.0668	+	2.96534i	1.06987	+	0.286670i	0.319429	+	0.947610i	$0.396509\pi$
$108$		0			0
$109$	−3.02860	+	0.811511i	−0.290087	+	0.0777287i	−0.400928	−	0.916110i	$-0.631312\pi$
$109$	−3.02860	+	0.811511i	−0.290087	+	0.0777287i	0.110841	+	0.993838i	$0.464646\pi$
$110$		0			0
$111$	−0.305841			−0.0290292
$112$		0			0
$113$	4.67963			0.440223			0.220111	−	0.975475i	$-0.429358\pi$
$113$	4.67963			0.440223			0.220111	+	0.975475i	$0.429358\pi$
$114$		0			0
$115$	5.69024	−	1.52469i	0.530617	−	0.142178i
$116$		0			0
$117$	6.53422	+	1.75084i	0.604089	+	0.161865i
$118$		0			0
$119$	−6.36763	−	4.45919i	−0.583719	−	0.408773i
$120$		0			0
$121$	7.42792	−	4.28851i	0.675265	−	0.389865i
$122$		0			0
$123$	0.106957	+	0.399168i	0.00964398	+	0.0359918i
$124$		0			0
$125$	7.64645	+	7.64645i	0.683919	+	0.683919i
$126$		0			0
$127$	5.63308			0.499855			0.249928	−	0.968265i	$-0.419593\pi$
$127$	5.63308			0.499855			0.249928	+	0.968265i	$0.419593\pi$
$128$		0			0
$129$	0.0793683	−	0.137470i	0.00698799	−	0.0121035i
$130$		0			0
$131$	−0.537304	+	2.00524i	−0.0469444	+	0.175199i	−0.985418	−	0.170153i	$-0.945574\pi$
$131$	−0.537304	+	2.00524i	−0.0469444	+	0.175199i	0.938473	+	0.345352i	$0.112240\pi$
$132$		0			0
$133$	19.6937	+	7.16916i	1.70766	+	0.621645i
$134$		0			0
$135$	0.380697	−	0.219795i	0.0327652	−	0.0189170i
$136$		0			0
$137$	2.68685	+	1.55125i	0.229553	+	0.132532i	0.610366	−	0.792120i	$-0.291022\pi$
$137$	2.68685	+	1.55125i	0.229553	+	0.132532i	−0.380813	+	0.924652i	$0.624356\pi$
$138$		0			0
$139$	−12.7451	+	12.7451i	−1.08103	+	1.08103i	−0.0846114	+	0.996414i	$0.526965\pi$
$139$	−12.7451	+	12.7451i	−1.08103	+	1.08103i	−0.996414	+	0.0846114i	$0.973035\pi$
$140$		0			0
$141$	0.0779732	+	0.0779732i	0.00656653	+	0.00656653i
$142$		0			0
$143$	1.75684	−	3.04294i	0.146914	−	0.254463i
$144$		0			0
$145$	1.89896	+	3.28910i	0.157700	+	0.273145i
$146$		0			0
$147$	−0.392558	+	0.0343005i	−0.0323776	+	0.00282906i
$148$		0			0
$149$	−14.5303	−	3.89339i	−1.19037	−	0.318959i	−0.391338	−	0.920247i	$-0.627988\pi$
$149$	−14.5303	−	3.89339i	−1.19037	−	0.318959i	−0.799032	+	0.601288i	$0.794654\pi$
$150$		0			0
$151$	15.7545	+	9.09588i	1.28209	+	0.740212i	0.977229	−	0.212186i	$-0.0680584\pi$
$151$	15.7545	+	9.09588i	1.28209	+	0.740212i	0.304856	+	0.952398i	$0.401392\pi$
$152$		0			0
$153$			8.80528i			0.711865i
$154$		0			0
$155$	5.78295	−	5.78295i	0.464498	−	0.464498i
$156$		0			0
$157$	−9.39175	+	2.51651i	−0.749544	+	0.200840i	−0.613316	−	0.789838i	$-0.710165\pi$
$157$	−9.39175	+	2.51651i	−0.749544	+	0.200840i	−0.136228	+	0.990678i	$0.543498\pi$
$158$		0			0
$159$	−0.326788	−	0.566013i	−0.0259159	−	0.0448877i
$160$		0			0
$161$	5.05781	+	10.8481i	0.398611	+	0.854948i
$162$		0			0
$163$	3.36548	−	12.5602i	0.263605	−	0.983787i	−0.699494	−	0.714639i	$-0.746591\pi$
$163$	3.36548	−	12.5602i	0.263605	−	0.983787i	0.963099	−	0.269148i	$-0.0867422\pi$
$164$		0			0
$165$	−0.0295323	−	0.110216i	−0.00229909	−	0.00858031i
$166$		0			0
$167$		−	16.5417i		−	1.28004i	−0.768360	−	0.640018i	$-0.778927\pi$
$167$		−	16.5417i		−	1.28004i	0.768360	−	0.640018i	$-0.221073\pi$
$168$		0			0
$169$		−	7.90463i		−	0.608049i
$170$		0			0
$171$	−6.14412	−	22.9302i	−0.469853	−	1.75351i
$172$		0			0
$173$	5.59219	−	20.8703i	0.425166	−	1.58674i	−0.338393	−	0.941005i	$-0.609883\pi$
$173$	5.59219	−	20.8703i	0.425166	−	1.58674i	0.763559	−	0.645738i	$-0.223450\pi$
$174$		0			0
$175$	−5.01486	+	7.16112i	−0.379088	+	0.541330i
$176$		0			0
$177$	−0.0862837	−	0.149448i	−0.00648548	−	0.0112332i
$178$		0			0
$179$	18.3264	−	4.91053i	1.36978	−	0.367031i	0.502379	−	0.864647i	$-0.332458\pi$
$179$	18.3264	−	4.91053i	1.36978	−	0.367031i	0.867397	+	0.497617i	$0.165791\pi$
$180$		0			0
$181$	−6.44222	+	6.44222i	−0.478846	+	0.478846i	−0.904763	−	0.425916i	$-0.859952\pi$
$181$	−6.44222	+	6.44222i	−0.478846	+	0.478846i	0.425916	+	0.904763i	$0.359952\pi$
$182$		0			0
$183$			0.566545i			0.0418802i
$184$		0			0
$185$	6.12689	+	3.53736i	0.450458	+	0.260072i
$186$		0			0
$187$	4.41773	+	1.18373i	0.323057	+	0.0865627i
$188$		0			0
$189$	0.574072	+	0.684230i	0.0417576	+	0.0497704i
$190$		0			0
$191$	−12.9567	−	22.4417i	−0.937515	−	1.62382i	−0.770086	−	0.637940i	$-0.779787\pi$
$191$	−12.9567	−	22.4417i	−0.937515	−	1.62382i	−0.167429	−	0.985884i	$-0.553546\pi$
$192$		0			0
$193$	−6.27389	+	10.8667i	−0.451604	+	0.782202i	−0.998486	−	0.0550082i	$-0.982481\pi$
$193$	−6.27389	+	10.8667i	−0.451604	+	0.782202i	0.546881	+	0.837210i	$0.315815\pi$
$194$		0			0
$195$	0.117004	+	0.117004i	0.00837881	+	0.00837881i
$196$		0			0
$197$	8.31651	−	8.31651i	0.592527	−	0.592527i	−0.345786	−	0.938313i	$-0.612388\pi$
$197$	8.31651	−	8.31651i	0.592527	−	0.592527i	0.938313	+	0.345786i	$0.112388\pi$
$198$		0			0
$199$	16.6783	+	9.62922i	1.18229	+	0.682597i	0.956544	−	0.291589i	$-0.0941838\pi$
$199$	16.6783	+	9.62922i	1.18229	+	0.682597i	0.225749	+	0.974186i	$0.427517\pi$
$200$		0			0
$201$	0.106755	−	0.0616352i	0.00752993	−	0.00434741i
$202$		0			0
$203$	−5.91152	+	4.95980i	−0.414907	+	0.348109i
$204$		0			0
$205$	2.47413	−	9.23356i	0.172800	−	0.644900i
$206$		0			0
$207$	6.77874	−	11.7411i	0.471155	−	0.816064i
$208$		0			0
$209$	−12.3304			−0.852909
$210$		0			0
$211$	8.62222	+	8.62222i	0.593578	+	0.593578i	0.938596	−	0.345018i	$-0.112127\pi$
$211$	8.62222	+	8.62222i	0.593578	+	0.593578i	−0.345018	+	0.938596i	$0.612127\pi$
$212$		0			0
$213$	0.105832	+	0.394969i	0.00725147	+	0.0270628i
$214$		0			0
$215$	−3.17995	+	1.83595i	−0.216871	+	0.125211i
$216$		0			0
$217$	13.6110	+	9.53167i	0.923977	+	0.647052i
$218$		0			0
$219$	−0.768464	−	0.205909i	−0.0519280	−	0.0139141i
$220$		0			0
$221$	−6.40638	+	1.71658i	−0.430940	+	0.115470i
$222$		0			0
$223$	−22.4402			−1.50271			−0.751354	−	0.659899i	$-0.770599\pi$
$223$	−22.4402			−1.50271			−0.751354	+	0.659899i	$0.770599\pi$
$224$		0			0
$225$	9.90254			0.660169
$226$		0			0
$227$	2.25930	−	0.605377i	0.149955	−	0.0401803i	−0.183061	−	0.983102i	$-0.558600\pi$
$227$	2.25930	−	0.605377i	0.149955	−	0.0401803i	0.333016	+	0.942921i	$0.391934\pi$
$228$		0			0
$229$	18.9832	+	5.08653i	1.25444	+	0.336127i	0.824052	−	0.566514i	$-0.191708\pi$
$229$	18.9832	+	5.08653i	1.25444	+	0.336127i	0.430393	+	0.902642i	$0.358375\pi$
$230$		0			0
$231$	0.210120	−	0.0979664i	0.0138249	−	0.00644572i
$232$		0			0
$233$	−3.35515	+	1.93710i	−0.219803	+	0.126903i	−0.605859	−	0.795572i	$-0.707171\pi$
$233$	−3.35515	+	1.93710i	−0.219803	+	0.126903i	0.386056	+	0.922475i	$0.373837\pi$
$234$		0			0
$235$	−0.660191	−	2.46387i	−0.0430661	−	0.160725i
$236$		0			0
$237$	−0.0765505	−	0.0765505i	−0.00497249	−	0.00497249i
$238$		0			0
$239$	−6.56774			−0.424832			−0.212416	−	0.977179i	$-0.568133\pi$
$239$	−6.56774			−0.424832			−0.212416	+	0.977179i	$0.568133\pi$
$240$		0			0
$241$	6.62647	−	11.4774i	0.426849	−	0.739323i	−0.569742	−	0.821823i	$-0.692957\pi$
$241$	6.62647	−	11.4774i	0.426849	−	0.739323i	0.996591	+	0.0824998i	$0.0262904\pi$
$242$		0			0
$243$	0.392830	−	1.46606i	0.0252001	−	0.0940479i
$244$		0			0
$245$	8.26078	+	3.85318i	0.527762	+	0.246171i
$246$		0			0
$247$	15.4853	−	8.94045i	0.985306	−	0.568867i
$248$		0			0
$249$	−0.608598	−	0.351374i	−0.0385683	−	0.0222674i
$250$		0			0
$251$	3.80916	−	3.80916i	0.240432	−	0.240432i	−0.576597	−	0.817029i	$-0.695620\pi$
$251$	3.80916	−	3.80916i	0.240432	−	0.240432i	0.817029	+	0.576597i	$0.195620\pi$
$252$		0			0
$253$	−4.97939	−	4.97939i	−0.313052	−	0.313052i
$254$		0			0
$255$	−0.107691	+	0.186526i	−0.00674385	+	0.0116807i
$256$		0			0
$257$	11.8190	+	20.4712i	0.737251	+	1.27696i	0.953729	+	0.300669i	$0.0972099\pi$
$257$	11.8190	+	20.4712i	0.737251	+	1.27696i	−0.216477	+	0.976288i	$0.569457\pi$
$258$		0			0
$259$	−4.91707	+	13.5072i	−0.305532	+	0.839297i
$260$		0			0
$261$	8.44271	+	2.26222i	0.522591	+	0.140028i
$262$		0			0
$263$	−15.4301	−	8.90857i	−0.951460	−	0.549326i	−0.0579260	−	0.998321i	$-0.518449\pi$
$263$	−15.4301	−	8.90857i	−0.951460	−	0.549326i	−0.893534	+	0.448995i	$0.851782\pi$
$264$		0			0
$265$			15.1185i			0.928722i
$266$		0			0
$267$	0.530993	−	0.530993i	0.0324963	−	0.0324963i
$268$		0			0
$269$	6.16728	−	1.65252i	0.376026	−	0.100756i	−0.0658559	−	0.997829i	$-0.520978\pi$
$269$	6.16728	−	1.65252i	0.376026	−	0.100756i	0.441882	+	0.897073i	$0.354311\pi$
$270$		0			0
$271$	3.98703	+	6.90574i	0.242195	+	0.419494i	0.961339	−	0.275367i	$-0.0887993\pi$
$271$	3.98703	+	6.90574i	0.242195	+	0.419494i	−0.719144	+	0.694861i	$0.755466\pi$
$272$		0			0
$273$	−0.192850	+	0.275386i	−0.0116718	+	0.0166671i
$274$		0			0
$275$	1.33124	−	4.96824i	0.0802765	−	0.299596i
$276$		0			0
$277$	−3.31607	−	12.3757i	−0.199243	−	0.743586i	−0.991127	−	0.132915i	$-0.957566\pi$
$277$	−3.31607	−	12.3757i	−0.199243	−	0.743586i	0.791884	−	0.610671i	$-0.209100\pi$
$278$		0			0
$279$		−	18.8216i		−	1.12682i
$280$		0			0
$281$		−	13.0438i		−	0.778126i	−0.921211	−	0.389063i	$-0.872799\pi$
$281$		−	13.0438i		−	0.778126i	0.921211	−	0.389063i	$-0.127201\pi$
$282$		0			0
$283$	4.98843	+	18.6171i	0.296531	+	1.10667i	0.939994	+	0.341192i	$0.110831\pi$
$283$	4.98843	+	18.6171i	0.296531	+	1.10667i	−0.643462	+	0.765478i	$0.722503\pi$
$284$		0			0
$285$	0.150288	−	0.560883i	0.00890229	−	0.0332238i
$286$		0			0
$287$	19.3485	+	1.69385i	1.14210	+	0.0999850i
$288$		0			0
$289$	4.18350	+	7.24603i	0.246088	+	0.426237i
$290$		0			0
$291$	−0.527210	+	0.141265i	−0.0309056	+	0.00828113i
$292$		0			0
$293$	−12.7021	+	12.7021i	−0.742067	+	0.742067i	−0.972975	−	0.230908i	$-0.925830\pi$
$293$	−12.7021	+	12.7021i	−0.742067	+	0.742067i	0.230908	+	0.972975i	$0.425830\pi$
$294$		0			0
$295$			3.99183i			0.232413i
$296$		0			0
$297$	−0.455076	−	0.262738i	−0.0264062	−	0.0152456i
$298$		0			0
$299$	9.86389	+	2.64302i	0.570443	+	0.152850i
$300$		0			0
$301$	−4.79521	−	5.71536i	−0.276391	−	0.329428i
$302$		0			0
$303$	0.297460	+	0.515217i	0.0170887	+	0.0295984i
$304$		0			0
$305$	6.55265	−	11.3495i	0.375204	−	0.649872i
$306$		0			0
$307$	−15.5180	−	15.5180i	−0.885657	−	0.885657i	0.108446	−	0.994102i	$-0.465413\pi$
$307$	−15.5180	−	15.5180i	−0.885657	−	0.885657i	−0.994102	+	0.108446i	$0.965413\pi$
$308$		0			0
$309$	−0.136300	+	0.136300i	−0.00775386	+	0.00775386i
$310$		0			0
$311$	3.14576	+	1.81621i	0.178380	+	0.102988i	0.586531	−	0.809927i	$-0.300493\pi$
$311$	3.14576	+	1.81621i	0.178380	+	0.102988i	−0.408151	+	0.912914i	$0.633826\pi$
$312$		0			0
$313$	3.24479	−	1.87338i	0.183406	−	0.105890i	−0.405486	−	0.914101i	$-0.632898\pi$
$313$	3.24479	−	1.87338i	0.183406	−	0.105890i	0.588892	+	0.808212i	$0.299564\pi$
$314$		0			0
$315$	−1.79232	−	10.1680i	−0.100986	−	0.572904i
$316$		0			0
$317$	−6.36774	+	23.7647i	−0.357648	+	1.33476i	0.519472	+	0.854488i	$0.326129\pi$
$317$	−6.36774	+	23.7647i	−0.357648	+	1.33476i	−0.877119	+	0.480272i	$0.840538\pi$
$318$		0			0
$319$	2.26997	−	3.93171i	0.127094	−	0.220133i
$320$		0			0
$321$	0.644963			0.0359983
$322$		0			0
$323$	16.4576	+	16.4576i	0.915727	+	0.915727i
$324$		0			0
$325$	1.93049	+	7.20470i	0.107084	+	0.399645i
$326$		0			0
$327$	−0.152857	+	0.0882521i	−0.00845302	+	0.00488035i
$328$		0			0
$329$	4.69721	−	2.19003i	0.258965	−	0.120740i
$330$		0			0
$331$	−9.79479	−	2.62451i	−0.538370	−	0.144256i	−0.0206195	−	0.999787i	$-0.506564\pi$
$331$	−9.79479	−	2.62451i	−0.538370	−	0.144256i	−0.517751	+	0.855532i	$0.673231\pi$
$332$		0			0
$333$	15.7270	−	4.21403i	0.861833	−	0.230928i
$334$		0			0
$335$	−2.85149			−0.155793
$336$		0			0
$337$	−5.30745			−0.289115			−0.144558	−	0.989496i	$-0.546176\pi$
$337$	−5.30745			−0.289115			−0.144558	+	0.989496i	$0.546176\pi$
$338$		0			0
$339$	0.254456	−	0.0681812i	0.0138201	−	0.00370309i
$340$		0			0
$341$	−9.44306	−	2.53026i	−0.511370	−	0.137021i
$342$		0			0
$343$	−4.79637	+	17.8884i	−0.258980	+	0.965883i
$344$		0			0
$345$	0.287193	−	0.165811i	0.0154620	−	0.00892696i
$346$		0			0
$347$	−1.06753	−	3.98409i	−0.0573082	−	0.213877i	0.931334	−	0.364166i	$-0.118646\pi$
$347$	−1.06753	−	3.98409i	−0.0573082	−	0.213877i	−0.988642	+	0.150290i	$0.951979\pi$
$348$		0			0
$349$	−11.4637	−	11.4637i	−0.613639	−	0.613639i	0.330253	−	0.943892i	$-0.392866\pi$
$349$	−11.4637	−	11.4637i	−0.613639	−	0.613639i	−0.943892	+	0.330253i	$0.892866\pi$
$350$		0			0
$351$	0.762020			0.0406736
$352$		0			0
$353$	1.93371	−	3.34929i	0.102921	−	0.178265i	−0.809966	−	0.586477i	$-0.800514\pi$
$353$	1.93371	−	3.34929i	0.102921	−	0.178265i	0.912887	+	0.408212i	$0.133848\pi$
$354$		0			0
$355$	2.44810	−	9.13642i	0.129932	−	0.484911i
$356$		0			0
$357$	−0.411210	−	0.149694i	−0.0217636	−	0.00792265i
$358$		0			0
$359$	−13.6977	+	7.90839i	−0.722938	+	0.417389i	−0.815833	−	0.578287i	$-0.803721\pi$
$359$	−13.6977	+	7.90839i	−0.722938	+	0.417389i	0.0928949	+	0.995676i	$0.470388\pi$
$360$		0			0
$361$	−37.8872	−	21.8742i	−1.99407	−	1.15127i
$362$		0			0
$363$	0.341412	−	0.341412i	0.0179195	−	0.0179195i
$364$		0			0
$365$	13.0130	+	13.0130i	0.681132	+	0.681132i
$366$		0			0
$367$	2.37345	−	4.11093i	0.123893	−	0.214589i	−0.797407	−	0.603442i	$-0.793795\pi$
$367$	2.37345	−	4.11093i	0.123893	−	0.214589i	0.921300	+	0.388853i	$0.127129\pi$
$368$		0			0
$369$	−10.9999	−	19.0523i	−0.572631	−	0.991826i
$370$		0			0
$371$	−30.2513	+	5.33238i	−1.57057	+	0.276844i
$372$		0			0
$373$	−22.0083	−	5.89711i	−1.13955	−	0.305341i	−0.360779	−	0.932651i	$-0.617489\pi$
$373$	−22.0083	−	5.89711i	−1.13955	−	0.305341i	−0.778769	+	0.627310i	$0.784156\pi$
$374$		0			0
$375$	0.527184	+	0.304370i	0.0272237	+	0.0157176i
$376$		0			0
$377$			6.58360i			0.339073i
$378$		0			0
$379$	−20.1030	+	20.1030i	−1.03262	+	1.03262i	−0.0331705	+	0.999450i	$0.510560\pi$
$379$	−20.1030	+	20.1030i	−1.03262	+	1.03262i	−0.999450	+	0.0331705i	$0.989440\pi$
$380$		0			0
$381$	0.306300	−	0.0820728i	0.0156922	−	0.00420472i
$382$		0			0
$383$	11.7252	+	20.3087i	0.599131	+	1.03773i	0.992950	+	0.118537i	$0.0378204\pi$
$383$	11.7252	+	20.3087i	0.599131	+	1.03773i	−0.393819	+	0.919188i	$0.628846\pi$
$384$		0			0
$385$	−5.34239	−	0.467697i	−0.272273	−	0.0238360i
$386$		0			0
$387$	−2.18715	+	8.16255i	−0.111179	+	0.414926i
$388$		0			0
$389$	−2.77356	−	10.3510i	−0.140625	−	0.524819i	−0.999911	−	0.0133242i	$-0.995759\pi$
$389$	−2.77356	−	10.3510i	−0.140625	−	0.524819i	0.859286	−	0.511495i	$-0.170908\pi$
$390$		0			0
$391$			13.2922i			0.672216i
$392$		0			0
$393$			0.116864i			0.00589500i
$394$		0			0
$395$	0.648145	+	2.41891i	0.0326117	+	0.121709i
$396$		0			0
$397$	−1.71548	+	6.40226i	−0.0860975	+	0.321320i	−0.995520	−	0.0945536i	$-0.969858\pi$
$397$	−1.71548	+	6.40226i	−0.0860975	+	0.321320i	0.909422	+	0.415874i	$0.136524\pi$
$398$		0			0
$399$	1.17530	+	0.102891i	0.0588387	+	0.00515100i
$400$		0			0
$401$	−15.8657	−	27.4802i	−0.792294	−	1.37229i	−0.924543	−	0.381077i	$-0.875553\pi$
$401$	−15.8657	−	27.4802i	−0.792294	−	1.37229i	0.132250	−	0.991216i	$-0.457780\pi$
$402$		0			0
$403$	13.6939	−	3.66926i	0.682140	−	0.182779i
$404$		0			0
$405$	−8.26075	+	8.26075i	−0.410480	+	0.410480i
$406$		0			0
$407$		−	8.45695i		−	0.419196i
$408$		0			0
$409$	−1.11952	−	0.646353i	−0.0553565	−	0.0319601i	0.472066	−	0.881563i	$-0.343508\pi$
$409$	−1.11952	−	0.646353i	−0.0553565	−	0.0319601i	−0.527423	+	0.849603i	$0.676842\pi$
$410$		0			0
$411$	0.168699	+	0.0452028i	0.00832131	+	0.00222969i
$412$		0			0
$413$	−7.98742	+	1.40794i	−0.393035	+	0.0692803i
$414$		0			0
$415$	8.12799	+	14.0781i	0.398987	+	0.691066i
$416$		0			0
$417$	−0.507324	+	0.878710i	−0.0248437	+	0.0430306i
$418$		0			0
$419$	−17.2788	−	17.2788i	−0.844124	−	0.844124i	0.145269	−	0.989392i	$-0.453595\pi$
$419$	−17.2788	−	17.2788i	−0.844124	−	0.844124i	−0.989392	+	0.145269i	$0.953595\pi$
$420$		0			0
$421$	−3.36245	+	3.36245i	−0.163876	+	0.163876i	−0.784281	−	0.620405i	$-0.786968\pi$
$421$	−3.36245	+	3.36245i	−0.163876	+	0.163876i	0.620405	+	0.784281i	$0.286968\pi$
$422$		0			0
$423$	−5.08389	−	2.93519i	−0.247187	−	0.142714i
$424$		0			0
$425$	−8.40806	+	4.85440i	−0.407851	+	0.235473i
$426$		0			0
$427$	25.0209	+	9.10844i	1.21085	+	0.440788i
$428$		0			0
$429$	0.0511936	−	0.191057i	0.00247165	−	0.00922432i
$430$		0			0
$431$	−5.58722	+	9.67735i	−0.269127	+	0.466141i	−0.968637	−	0.248482i	$-0.920068\pi$
$431$	−5.58722	+	9.67735i	−0.269127	+	0.466141i	0.699510	+	0.714623i	$0.253402\pi$
$432$		0			0
$433$	−17.3943			−0.835916			−0.417958	−	0.908466i	$-0.637254\pi$
$433$	−17.3943			−0.835916			−0.417958	+	0.908466i	$0.637254\pi$
$434$		0			0
$435$	0.151178	+	0.151178i	0.00724842	+	0.00724842i
$436$		0			0
$437$	−9.27500	−	34.6148i	−0.443684	−	1.65585i
$438$		0			0
$439$	−32.5115	+	18.7705i	−1.55169	+	0.895867i	−0.553683	+	0.832727i	$0.686778\pi$
$439$	−32.5115	+	18.7705i	−1.55169	+	0.895867i	−0.998005	+	0.0631399i	$0.979889\pi$
$440$		0			0
$441$	19.7135	−	7.17265i	0.938738	−	0.341555i
$442$		0			0
$443$	−6.88186	−	1.84399i	−0.326967	−	0.0876106i	0.0916015	−	0.995796i	$-0.470801\pi$
$443$	−6.88186	−	1.84399i	−0.326967	−	0.0876106i	−0.418569	+	0.908185i	$0.637468\pi$
$444$		0			0
$445$	−16.7788	+	4.49587i	−0.795392	+	0.213125i
$446$		0			0
$447$	−0.846815			−0.0400530
$448$		0			0
$449$	−7.84005			−0.369995			−0.184997	−	0.982739i	$-0.559228\pi$
$449$	−7.84005			−0.369995			−0.184997	+	0.982739i	$0.559228\pi$
$450$		0			0
$451$	−11.0376	+	2.95751i	−0.519739	+	0.139264i
$452$		0			0
$453$	0.989180	+	0.265050i	0.0464757	+	0.0124531i
$454$		0			0
$455$	7.04845	−	3.28627i	0.330436	−	0.154063i
$456$		0			0
$457$	−22.2821	+	12.8646i	−1.04231	+	0.601780i	−0.920488	−	0.390771i	$-0.872208\pi$
$457$	−22.2821	+	12.8646i	−1.04231	+	0.601780i	−0.121826	+	0.992551i	$0.538875\pi$
$458$		0			0
$459$	0.256718	+	0.958084i	0.0119826	+	0.0447195i
$460$		0			0
$461$	13.1661	+	13.1661i	0.613207	+	0.613207i	0.943780	−	0.330573i	$-0.107242\pi$
$461$	13.1661	+	13.1661i	0.613207	+	0.613207i	−0.330573	+	0.943780i	$0.607242\pi$
$462$		0			0
$463$	6.88821			0.320122			0.160061	−	0.987107i	$-0.448831\pi$
$463$	6.88821			0.320122			0.160061	+	0.987107i	$0.448831\pi$
$464$		0			0
$465$	0.230193	−	0.398705i	0.0106749	−	0.0184895i
$466$		0			0
$467$	−10.2399	+	38.2159i	−0.473847	+	1.76842i	0.151902	+	0.988396i	$0.451460\pi$
$467$	−10.2399	+	38.2159i	−0.473847	+	1.76842i	−0.625749	+	0.780025i	$0.715206\pi$
$468$		0			0
$469$	−1.00574	−	5.70567i	−0.0464406	−	0.263463i
$470$		0			0
$471$	−0.474013	+	0.273672i	−0.0218414	+	0.0126101i
$472$		0			0
$473$	3.80124	+	2.19465i	0.174781	+	0.100910i
$474$		0			0
$475$	18.5085	−	18.5085i	0.849227	−	0.849227i
$476$		0			0
$477$	24.6029	+	24.6029i	1.12649	+	1.12649i
$478$		0			0
$479$	0.261991	−	0.453782i	0.0119707	−	0.0207338i	−0.859978	−	0.510331i	$-0.829523\pi$
$479$	0.261991	−	0.453782i	0.0119707	−	0.0207338i	0.871949	+	0.489597i	$0.162856\pi$
$480$		0			0
$481$	6.13193	+	10.6208i	0.279592	+	0.484267i
$482$		0			0
$483$	0.433073	+	0.516175i	0.0197055	+	0.0234868i
$484$		0			0
$485$	12.1954	+	3.26775i	0.553765	+	0.148381i
$486$		0			0
$487$	2.46586	+	1.42366i	0.111739	+	0.0645124i	0.554828	−	0.831965i	$-0.312784\pi$
$487$	2.46586	+	1.42366i	0.111739	+	0.0645124i	−0.443089	+	0.896478i	$0.646117\pi$
$488$		0			0
$489$		−	0.731995i		−	0.0331019i
$490$		0			0
$491$	17.4826	−	17.4826i	0.788977	−	0.788977i	−0.192349	−	0.981327i	$-0.561611\pi$
$491$	17.4826	−	17.4826i	0.788977	−	0.788977i	0.981327	+	0.192349i	$0.0616106\pi$
$492$		0			0
$493$	−8.27753	+	2.21796i	−0.372801	+	0.0998918i
$494$		0			0
$495$	3.03722	+	5.26063i	0.136513	+	0.236448i
$496$		0			0
$497$	19.1449	+	1.67603i	0.858767	+	0.0751803i
$498$		0			0
$499$	−0.350599	+	1.30845i	−0.0156949	+	0.0585743i	−0.973329	−	0.229413i	$-0.926319\pi$
$499$	−0.350599	+	1.30845i	−0.0156949	+	0.0585743i	0.957634	+	0.287987i	$0.0929861\pi$
$500$		0			0
$501$	−0.241009	−	0.899458i	−0.0107675	−	0.0401848i
$502$		0			0
$503$			15.4389i			0.688388i	0.938899	+	0.344194i	$0.111848\pi$
$503$			15.4389i			0.688388i	−0.938899	+	0.344194i	$0.888152\pi$
$504$		0			0
$505$		−	13.7617i		−	0.612388i
$506$		0			0
$507$	−0.115169	−	0.429816i	−0.00511482	−	0.0190888i
$508$		0			0
$509$	2.23550	−	8.34301i	0.0990869	−	0.369797i	−0.898520	−	0.438932i	$-0.855357\pi$
$509$	2.23550	−	8.34301i	0.0990869	−	0.369797i	0.997607	+	0.0691342i	$0.0220237\pi$
$510$		0			0
$511$	−21.4485	+	30.6281i	−0.948827	+	1.35491i
$512$		0			0
$513$	−1.33706	−	2.31585i	−0.0590325	−	0.102247i
$514$		0			0
$515$	4.30694	−	1.15404i	0.189787	−	0.0508532i
$516$		0			0
$517$	−2.15607	+	2.15607i	−0.0948239	+	0.0948239i
$518$		0			0
$519$		−	1.21631i		−	0.0533899i
$520$		0			0
$521$	3.08690	+	1.78222i	0.135240	+	0.0780807i	0.566093	−	0.824341i	$-0.308454\pi$
$521$	3.08690	+	1.78222i	0.135240	+	0.0780807i	−0.430854	+	0.902422i	$0.641787\pi$
$522$		0			0
$523$	−19.5332	−	5.23389i	−0.854125	−	0.228862i	−0.194914	−	0.980820i	$-0.562443\pi$
$523$	−19.5332	−	5.23389i	−0.854125	−	0.228862i	−0.659211	+	0.751958i	$0.729110\pi$
$524$		0			0
$525$	−0.168348	+	0.462452i	−0.00734731	+	0.0201831i
$526$		0			0
$527$	9.22668	+	15.9811i	0.401920	+	0.696147i
$528$		0			0
$529$	−1.26700	+	2.19451i	−0.0550869	+	0.0954133i
$530$		0			0
$531$	6.49605	+	6.49605i	0.281905	+	0.281905i
$532$		0			0
$533$	11.7173	−	11.7173i	0.507534	−	0.507534i
$534$		0			0
$535$	−12.9205	−	7.45964i	−0.558601	−	0.322508i
$536$		0			0
$537$	0.924954	−	0.534022i	0.0399147	−	0.0230448i
$538$		0			0
$539$	−0.948458	−	10.8548i	−0.0408530	−	0.467549i
$540$		0			0
$541$	1.90773	−	7.11973i	0.0820195	−	0.306101i	−0.912714	−	0.408600i	$-0.866017\pi$
$541$	1.90773	−	7.11973i	0.0820195	−	0.306101i	0.994733	+	0.102499i	$0.0326838\pi$
$542$		0			0
$543$	−0.256435	+	0.444159i	−0.0110047	+	0.0190607i
$544$		0			0
$545$	4.08289			0.174892
$546$		0			0
$547$	−17.8464	−	17.8464i	−0.763058	−	0.763058i	0.213816	−	0.976874i	$-0.431411\pi$
$547$	−17.8464	−	17.8464i	−0.763058	−	0.763058i	−0.976874	+	0.213816i	$0.931411\pi$
$548$		0			0
$549$	−7.80613	−	29.1329i	−0.333158	−	1.24336i
$550$		0			0
$551$	20.0082	−	11.5517i	0.852378	−	0.492121i
$552$		0			0
$553$	−4.61150	+	2.15006i	−0.196101	+	0.0914301i
$554$		0			0
$555$	0.384689	+	0.103077i	0.0163291	+	0.00437538i
$556$		0			0
$557$	14.4174	−	3.86313i	0.610884	−	0.163686i	0.0599038	−	0.998204i	$-0.480921\pi$
$557$	14.4174	−	3.86313i	0.610884	−	0.163686i	0.550980	+	0.834518i	$0.314254\pi$
$558$		0			0
$559$	−6.36514			−0.269217
$560$		0			0
$561$	0.257462			0.0108700
$562$		0			0
$563$	−7.71786	+	2.06799i	−0.325269	+	0.0871556i	−0.417759	−	0.908558i	$-0.637184\pi$
$563$	−7.71786	+	2.06799i	−0.325269	+	0.0871556i	0.0924895	+	0.995714i	$0.470518\pi$
$564$		0			0
$565$	−5.88607	−	1.57717i	−0.247629	−	0.0663519i
$566$		0			0
$567$	−19.4429	−	13.6157i	−0.816525	−	0.571805i
$568$		0			0
$569$	−12.1275	+	7.00179i	−0.508409	+	0.293530i	−0.732180	−	0.681112i	$-0.761497\pi$
$569$	−12.1275	+	7.00179i	−0.508409	+	0.293530i	0.223770	+	0.974642i	$0.428163\pi$
$570$		0			0
$571$	0.488992	+	1.82494i	0.0204637	+	0.0763715i	0.975403	−	0.220431i	$-0.0707464\pi$
$571$	0.488992	+	1.82494i	0.0204637	+	0.0763715i	−0.954939	+	0.296802i	$0.904080\pi$
$572$		0			0
$573$	−1.03149	−	1.03149i	−0.0430913	−	0.0430913i
$574$		0			0
$575$	14.9486			0.623400
$576$		0			0
$577$	−8.81809	+	15.2734i	−0.367102	+	0.635839i	−0.989111	−	0.147171i	$-0.952983\pi$
$577$	−8.81809	+	15.2734i	−0.367102	+	0.635839i	0.622009	+	0.783010i	$0.286317\pi$
$578$		0			0
$579$	−0.182818	+	0.682288i	−0.00759767	+	0.0283549i
$580$		0			0
$581$	−25.3027	+	21.2291i	−1.04973	+	0.880730i
$582$		0			0
$583$	15.6511	−	9.03615i	0.648201	−	0.374239i
$584$		0			0
$585$	−7.62870	−	4.40443i	−0.315408	−	0.182101i
$586$		0			0
$587$	−18.5150	+	18.5150i	−0.764194	+	0.764194i	−0.977078	−	0.212883i	$-0.931715\pi$
$587$	−18.5150	+	18.5150i	−0.764194	+	0.764194i	0.212883	+	0.977078i	$0.431715\pi$
$588$		0			0
$589$	−35.1788	−	35.1788i	−1.44952	−	1.44952i
$590$		0			0
$591$	0.331042	−	0.573382i	0.0136172	−	0.0235858i
$592$		0			0
$593$	−3.95463	−	6.84963i	−0.162397	−	0.281281i	0.773331	−	0.634003i	$-0.218589\pi$
$593$	−3.95463	−	6.84963i	−0.162397	−	0.281281i	−0.935728	+	0.352722i	$0.885256\pi$
$594$		0			0
$595$	6.50637	+	7.75486i	0.266735	+	0.317918i
$596$		0			0
$597$	1.04718	+	0.280591i	0.0428582	+	0.0114838i
$598$		0			0
$599$	18.5333	+	10.7002i	0.757251	+	0.437199i	0.828308	−	0.560273i	$-0.189304\pi$
$599$	18.5333	+	10.7002i	0.757251	+	0.437199i	−0.0710572	+	0.997472i	$0.522637\pi$
$600$		0			0
$601$		−	0.974684i		−	0.0397582i	−0.999802	−	0.0198791i	$-0.993672\pi$
$601$		−	0.974684i		−	0.0397582i	0.999802	−	0.0198791i	$-0.00632813\pi$
$602$		0			0
$603$	−4.64033	+	4.64033i	−0.188969	+	0.188969i
$604$		0			0
$605$	−10.7882	+	2.89070i	−0.438604	+	0.117524i
$606$		0			0
$607$	−3.01261	−	5.21800i	−0.122278	−	0.211792i	0.798388	−	0.602144i	$-0.205687\pi$
$607$	−3.01261	−	5.21800i	−0.122278	−	0.211792i	−0.920666	+	0.390352i	$0.872353\pi$
$608$		0			0
$609$	−0.249177	+	0.355819i	−0.0100972	+	0.0144185i
$610$		0			0
$611$	1.14443	−	4.27106i	0.0462985	−	0.172788i
$612$		0			0
$613$	0.426012	+	1.58990i	0.0172065	+	0.0642155i	0.973995	−	0.226568i	$-0.0727506\pi$
$613$	0.426012	+	1.58990i	0.0172065	+	0.0642155i	−0.956789	+	0.290784i	$0.906084\pi$
$614$		0			0
$615$		−	0.538124i		−	0.0216993i
$616$		0			0
$617$			34.0864i			1.37227i	0.727476	+	0.686134i	$0.240693\pi$
$617$			34.0864i			1.37227i	−0.727476	+	0.686134i	$0.759307\pi$
$618$		0			0
$619$	8.65485	+	32.3004i	0.347868	+	1.29826i	0.889226	+	0.457469i	$0.151244\pi$
$619$	8.65485	+	32.3004i	0.347868	+	1.29826i	−0.541358	+	0.840792i	$0.682090\pi$
$620$		0			0
$621$	0.395268	−	1.47516i	0.0158615	−	0.0591961i
$622$		0			0
$623$	−14.9140	−	31.9877i	−0.597515	−	1.28156i
$624$		0			0
$625$	1.22016	+	2.11337i	0.0488063	+	0.0845349i
$626$		0			0
$627$	−0.670466	+	0.179651i	−0.0267758	+	0.00717456i
$628$		0			0
$629$	−11.2877	+	11.2877i	−0.450070	+	0.450070i
$630$		0			0
$631$		−	4.58799i		−	0.182645i	−0.995821	−	0.0913225i	$-0.970891\pi$
$631$		−	4.58799i		−	0.182645i	0.995821	−	0.0913225i	$-0.0291094\pi$
$632$		0			0
$633$	0.594458	+	0.343211i	0.0236276	+	0.0136414i
$634$		0			0
$635$	−7.08533	−	1.89851i	−0.281173	−	0.0753400i
$636$		0			0
$637$	9.06167	+	12.9445i	0.359037	+	0.512878i
$638$		0			0
$639$	−10.8842	−	18.8519i	−0.430571	−	0.745770i
$640$		0			0
$641$	24.9135	−	43.1515i	0.984025	−	1.70438i	0.337835	−	0.941205i	$-0.390305\pi$
$641$	24.9135	−	43.1515i	0.984025	−	1.70438i	0.646190	−	0.763177i	$-0.276361\pi$
$642$		0			0
$643$	31.1050	+	31.1050i	1.22666	+	1.22666i	0.965219	+	0.261443i	$0.0841985\pi$
$643$	31.1050	+	31.1050i	1.22666	+	1.22666i	0.261443	+	0.965219i	$0.415802\pi$
$644$		0			0
$645$	−0.146161	+	0.146161i	−0.00575509	+	0.00575509i
$646$		0			0
$647$	−25.4255	−	14.6794i	−0.999579	−	0.577107i	−0.0914555	−	0.995809i	$-0.529152\pi$
$647$	−25.4255	−	14.6794i	−0.999579	−	0.577107i	−0.908124	+	0.418702i	$0.862485\pi$
$648$		0			0
$649$	4.13245	−	2.38587i	0.162213	−	0.0936536i
$650$		0			0
$651$	0.878977	+	0.319977i	0.0344498	+	0.0125409i
$652$		0			0
$653$	3.93761	−	14.6954i	0.154091	−	0.575075i	−0.845091	−	0.534623i	$-0.820454\pi$
$653$	3.93761	−	14.6954i	0.154091	−	0.575075i	0.999181	−	0.0404516i	$-0.0128797\pi$
$654$		0			0
$655$	1.35165	−	2.34112i	0.0528132	−	0.0914752i
$656$		0			0
$657$	42.3531			1.65235
$658$		0			0
$659$	8.45620	+	8.45620i	0.329407	+	0.329407i	0.852361	−	0.522954i	$-0.175170\pi$
$659$	8.45620	+	8.45620i	0.329407	+	0.329407i	−0.522954	+	0.852361i	$0.675170\pi$
$660$		0			0
$661$	3.50720	+	13.0890i	0.136414	+	0.509105i	0.999988	+	0.00488232i	$0.00155410\pi$
$661$	3.50720	+	13.0890i	0.136414	+	0.509105i	−0.863574	+	0.504222i	$0.831779\pi$
$662$		0			0
$663$	−0.323338	+	0.186679i	−0.0125574	+	0.00725001i
$664$		0			0
$665$	−22.3547	−	15.6547i	−0.866876	−	0.607065i
$666$		0			0
$667$	12.7449	+	3.41498i	0.493484	+	0.132229i
$668$		0			0
$669$	−1.22019	+	0.326949i	−0.0471753	+	0.0126406i
$670$		0			0
$671$	−15.6658			−0.604771
$672$		0			0
$673$	−15.5552			−0.599610			−0.299805	−	0.954000i	$-0.596922\pi$
$673$	−15.5552			−0.599610			−0.299805	+	0.954000i	$0.596922\pi$
$674$		0			0
$675$	1.07747	−	0.288708i	0.0414720	−	0.0111124i
$676$		0			0
$677$	39.5868	+	10.6072i	1.52144	+	0.407669i	0.920217	−	0.391410i	$-0.128012\pi$
$677$	39.5868	+	10.6072i	1.52144	+	0.407669i	0.601226	+	0.799079i	$0.294679\pi$
$678$		0			0
$679$	−2.23719	+	25.5549i	−0.0858555	+	0.980707i
$680$		0			0
$681$	0.114030	−	0.0658350i	0.00436962	−	0.00252280i
$682$		0			0
$683$	−3.19786	−	11.9346i	−0.122363	−	0.456664i	0.877369	−	0.479816i	$-0.159296\pi$
$683$	−3.19786	−	11.9346i	−0.122363	−	0.456664i	−0.999732	+	0.0231521i	$0.992630\pi$
$684$		0			0
$685$	−2.85672	−	2.85672i	−0.109150	−	0.109150i
$686$		0			0
$687$	1.10632			0.0422089
$688$		0			0
$689$	−13.1038	+	22.6964i	−0.499214	+	0.864664i
$690$		0			0
$691$	1.44023	−	5.37500i	0.0547888	−	0.204475i	−0.933106	−	0.359603i	$-0.882912\pi$
$691$	1.44023	−	5.37500i	0.0547888	−	0.204475i	0.987894	+	0.155128i	$0.0495789\pi$
$692$		0			0
$693$	−9.45497	+	7.93277i	−0.359165	+	0.301341i
$694$		0			0
$695$	20.3263	−	11.7354i	0.771021	−	0.445149i
$696$		0			0
$697$	18.6796	+	10.7847i	0.707540	+	0.408498i
$698$		0			0
$699$	−0.154214	+	0.154214i	−0.00583290	+	0.00583290i
$700$		0			0
$701$	−22.0458	−	22.0458i	−0.832657	−	0.832657i	0.155223	−	0.987880i	$-0.450391\pi$
$701$	−22.0458	−	22.0458i	−0.832657	−	0.832657i	−0.987880	+	0.155223i	$0.950391\pi$
$702$		0			0
$703$	21.5184	−	37.2710i	0.811583	−	1.40570i
$704$		0			0
$705$	−0.0717960	−	0.124354i	−0.00270399	−	0.00468346i
$706$		0			0
$707$	27.5364	−	4.85384i	1.03561	−	0.182547i
$708$		0			0
$709$	11.9661	+	3.20632i	0.449398	+	0.120416i	0.476417	−	0.879219i	$-0.341935\pi$
$709$	11.9661	+	3.20632i	0.449398	+	0.120416i	−0.0270200	+	0.999635i	$0.508602\pi$
$710$		0			0
$711$	4.99113	+	2.88163i	0.187182	+	0.108070i
$712$		0			0
$713$		−	28.4126i		−	1.06406i
$714$		0			0
$715$	−3.23532	+	3.23532i	−0.120994	+	0.120994i
$716$		0			0
$717$	−0.357122	+	0.0956906i	−0.0133370	+	0.00357363i
$718$		0			0
$719$	−7.64439	−	13.2405i	−0.285088	−	0.493786i	0.687543	−	0.726144i	$-0.258689\pi$
$719$	−7.64439	−	13.2405i	−0.285088	−	0.493786i	−0.972630	+	0.232358i	$0.925356\pi$
$720$		0			0
$721$	3.82826	+	8.21091i	0.142572	+	0.305790i
$722$		0			0
$723$	0.193093	−	0.720631i	0.00718119	−	0.0268006i
$724$		0			0
$725$	2.49434	+	9.30902i	0.0926376	+	0.345728i
$726$		0			0
$727$		−	23.7860i		−	0.882173i	−0.897465	−	0.441086i	$-0.854593\pi$
$727$		−	23.7860i		−	0.882173i	0.897465	−	0.441086i	$-0.145407\pi$
$728$		0			0
$729$			26.8290i			0.993668i
$730$		0			0
$731$	−2.14436	−	8.00285i	−0.0793119	−	0.295996i
$732$		0			0
$733$	−5.32874	+	19.8871i	−0.196822	+	0.734548i	0.794966	+	0.606654i	$0.207489\pi$
$733$	−5.32874	+	19.8871i	−0.196822	+	0.734548i	−0.991788	+	0.127894i	$0.959178\pi$
$734$		0			0
$735$	0.505322	+	0.0891596i	0.0186391	+	0.00328870i
$736$		0			0
$737$	1.70430	+	2.95194i	0.0627787	+	0.108736i
$738$		0			0
$739$	−26.3224	+	7.05306i	−0.968284	+	0.259451i	−0.708103	−	0.706109i	$-0.750449\pi$
$739$	−26.3224	+	7.05306i	−0.968284	+	0.259451i	−0.260181	+	0.965560i	$0.583782\pi$
$740$		0			0
$741$	0.711756	−	0.711756i	0.0261470	−	0.0261470i
$742$		0			0
$743$		−	12.8386i		−	0.471002i	−0.971874	−	0.235501i	$-0.924327\pi$
$743$		−	12.8386i		−	0.471002i	0.971874	−	0.235501i	$-0.0756731\pi$
$744$		0			0
$745$	16.9641	+	9.79426i	0.621518	+	0.358834i
$746$		0			0
$747$	36.1368	+	9.68282i	1.32218	+	0.354276i
$748$		0			0
$749$	10.3692	−	28.4842i	0.378882	−	1.04079i
$750$		0			0
$751$	7.23318	+	12.5282i	0.263942	+	0.457162i	0.967286	−	0.253688i	$-0.0816438\pi$
$751$	7.23318	+	12.5282i	0.263942	+	0.457162i	−0.703344	+	0.710850i	$0.748310\pi$
$752$		0			0
$753$	0.151625	−	0.262622i	0.00552552	−	0.00957048i
$754$		0			0
$755$	−16.7506	−	16.7506i	−0.609616	−	0.609616i
$756$		0			0
$757$	2.16062	−	2.16062i	0.0785291	−	0.0785291i	−0.666751	−	0.745280i	$-0.732316\pi$
$757$	2.16062	−	2.16062i	0.0785291	−	0.0785291i	0.745280	+	0.666751i	$0.232316\pi$
$758$		0			0
$759$	−0.343304	−	0.198207i	−0.0124611	−	0.00719444i
$760$		0			0
$761$	2.04136	−	1.17858i	0.0739994	−	0.0427236i	−0.462544	−	0.886596i	$-0.653063\pi$
$761$	2.04136	−	1.17858i	0.0739994	−	0.0427236i	0.536543	+	0.843873i	$0.319730\pi$
$762$		0			0
$763$	1.44006	+	8.16964i	0.0521337	+	0.295761i
$764$		0			0
$765$	2.96763	−	11.0753i	0.107295	−	0.400430i
$766$		0			0
$767$	−3.45987	+	5.99267i	−0.124929	+	0.216383i
$768$		0			0
$769$	7.96868			0.287358			0.143679	−	0.989624i	$-0.454107\pi$
$769$	7.96868			0.287358			0.143679	+	0.989624i	$0.454107\pi$
$770$		0			0
$771$	0.940923	+	0.940923i	0.0338865	+	0.0338865i
$772$		0			0
$773$	5.69575	+	21.2568i	0.204862	+	0.764555i	0.989492	+	0.144590i	$0.0461865\pi$
$773$	5.69575	+	21.2568i	0.204862	+	0.764555i	−0.784630	+	0.619965i	$0.787147\pi$
$774$		0			0
$775$	17.9725	−	10.3764i	0.645592	−	0.372733i
$776$		0			0
$777$	−0.0705694	+	0.806097i	−0.00253166	+	0.0289186i
$778$		0			0
$779$	−56.1695	−	15.0506i	−2.01248	−	0.539243i
$780$		0			0
$781$	−10.9215	+	2.92640i	−0.390801	+	0.104715i
$782$		0			0
$783$	0.984588			0.0351863
$784$		0			0
$785$	12.6611			0.451896
$786$		0			0
$787$	27.7816	−	7.44405i	0.990306	−	0.265352i	0.272927	−	0.962035i	$-0.412008\pi$
$787$	27.7816	−	7.44405i	0.990306	−	0.265352i	0.717379	+	0.696683i	$0.245342\pi$
$788$		0			0
$789$	−0.968810	−	0.259592i	−0.0344905	−	0.00924171i
$790$		0			0
$791$	1.07977	−	12.3340i	0.0383922	−	0.438545i
$792$		0			0
$793$	19.6741	−	11.3589i	0.698649	−	0.403365i
$794$		0			0
$795$	0.220273	+	0.822071i	0.00781229	+	0.0291558i
$796$		0			0
$797$	22.0411	+	22.0411i	0.780736	+	0.780736i	0.979955	−	0.199219i	$-0.0638405\pi$
$797$	22.0411	+	22.0411i	0.780736	+	0.780736i	−0.199219	+	0.979955i	$0.563840\pi$
$798$		0			0
$799$	5.75552			0.203616
$800$		0			0
$801$	−19.9885	+	34.6210i	−0.706258	+	1.22327i
$802$		0			0
$803$	5.69369	−	21.2491i	0.200926	−	0.749866i
$804$		0			0
$805$	−2.70563	−	15.3494i	−0.0953611	−	0.540995i
$806$		0			0
$807$	0.311270	−	0.179712i	0.0109572	−	0.00632616i
$808$		0			0
$809$	25.9855	+	15.0027i	0.913600	+	0.527467i	0.881588	−	0.472020i	$-0.156475\pi$
$809$	25.9855	+	15.0027i	0.913600	+	0.527467i	0.0320125	+	0.999487i	$0.489808\pi$
$810$		0			0
$811$	20.2976	−	20.2976i	0.712746	−	0.712746i	−0.254363	−	0.967109i	$-0.581866\pi$
$811$	20.2976	−	20.2976i	0.712746	−	0.712746i	0.967109	+	0.254363i	$0.0818658\pi$
$812$		0			0
$813$	0.317411	+	0.317411i	0.0111321	+	0.0111321i
$814$		0			0
$815$	−8.46625	+	14.6640i	−0.296560	+	0.513657i
$816$		0			0
$817$	11.1684	+	19.3443i	0.390733	+	0.676770i
$818$		0			0
$819$	6.12233	−	16.8181i	0.213932	−	0.587671i
$820$		0			0
$821$	53.0609	+	14.2176i	1.85184	+	0.496199i	0.999635	−	0.0270111i	$-0.00859894\pi$
$821$	53.0609	+	14.2176i	1.85184	+	0.496199i	0.852204	+	0.523210i	$0.175266\pi$
$822$		0			0
$823$	20.1906	+	11.6571i	0.703800	+	0.406339i	0.808761	−	0.588137i	$-0.200138\pi$
$823$	20.1906	+	11.6571i	0.703800	+	0.406339i	−0.104961	+	0.994476i	$0.533472\pi$
$824$		0			0
$825$		−	0.289545i		−	0.0100807i
$826$		0			0
$827$	−4.26358	+	4.26358i	−0.148259	+	0.148259i	−0.777340	−	0.629081i	$-0.783432\pi$
$827$	−4.26358	+	4.26358i	−0.148259	+	0.148259i	0.629081	+	0.777340i	$0.283432\pi$
$828$		0			0
$829$	40.5325	−	10.8606i	1.40775	−	0.377206i	0.526630	−	0.850095i	$-0.323455\pi$
$829$	40.5325	−	10.8606i	1.40775	−	0.377206i	0.881122	+	0.472889i	$0.156789\pi$
$830$		0			0
$831$	−0.360624	−	0.624619i	−0.0125099	−	0.0216678i
$832$		0			0
$833$	−13.2222	+	15.7541i	−0.458122	+	0.545846i
$834$		0			0
$835$	−5.57502	+	20.8063i	−0.192932	+	0.720030i
$836$		0			0
$837$	−0.548743	−	2.04794i	−0.0189673	−	0.0707871i
$838$		0			0
$839$			46.6970i			1.61216i	0.591806	+	0.806081i	$0.298415\pi$
$839$			46.6970i			1.61216i	−0.591806	+	0.806081i	$0.701585\pi$
$840$		0			0
$841$		−	20.4935i		−	0.706672i
$842$		0			0
$843$	−0.190045	−	0.709257i	−0.00654549	−	0.0244281i
$844$		0			0
$845$	−2.66408	+	9.94249i	−0.0916472	+	0.342032i
$846$		0			0
$847$	−9.58920	−	20.5671i	−0.329489	−	0.706693i
$848$		0			0
$849$	0.542493	+	0.939626i	0.0186183	+	0.0322479i
$850$		0			0
$851$	23.7410	−	6.36139i	0.813832	−	0.218066i
$852$		0			0
$853$	14.9036	−	14.9036i	0.510289	−	0.510289i	−0.404326	−	0.914615i	$-0.632494\pi$
$853$	14.9036	−	14.9036i	0.510289	−	0.510289i	0.914615	+	0.404326i	$0.132494\pi$
$854$		0			0
$855$			30.9125i			1.05718i
$856$		0			0
$857$	12.5881	+	7.26772i	0.430000	+	0.248261i	0.699347	−	0.714783i	$-0.253474\pi$
$857$	12.5881	+	7.26772i	0.430000	+	0.248261i	−0.269347	+	0.963043i	$0.586808\pi$
$858$		0			0
$859$	−37.9861	−	10.1784i	−1.29607	−	0.347281i	−0.456107	−	0.889925i	$-0.650757\pi$
$859$	−37.9861	−	10.1784i	−1.29607	−	0.347281i	−0.839963	+	0.542644i	$0.817423\pi$
$860$		0			0
$861$	1.07676	−	0.189800i	0.0366957	−	0.00646835i
$862$		0			0
$863$	6.49230	+	11.2450i	0.221000	+	0.382784i	0.955112	−	0.296245i	$-0.0957345\pi$
$863$	6.49230	+	11.2450i	0.221000	+	0.382784i	−0.734112	+	0.679029i	$0.762401\pi$
$864$		0			0
$865$	−14.0678	+	24.3661i	−0.478319	+	0.828473i
$866$		0			0
$867$	0.333052	+	0.333052i	0.0113110	+	0.0113110i
$868$		0			0
$869$	2.11673	−	2.11673i	0.0718052	−	0.0718052i
$870$		0			0
$871$	−4.28075	−	2.47149i	−0.145048	−	0.0837434i
$872$		0			0
$873$	25.1638	−	14.5283i	0.851665	−	0.491709i
$874$		0			0
$875$	21.9179	−	18.3892i	0.740959	−	0.621668i
$876$		0			0
$877$	−5.80637	+	21.6697i	−0.196067	+	0.731733i	0.795921	+	0.605401i	$0.206987\pi$
$877$	−5.80637	+	21.6697i	−0.196067	+	0.731733i	−0.991988	+	0.126332i	$0.959679\pi$
$878$		0			0
$879$	−0.505614	+	0.875749i	−0.0170539	+	0.0295383i
$880$		0			0
$881$	−8.65332			−0.291538			−0.145769	−	0.989319i	$-0.546566\pi$
$881$	−8.65332			−0.291538			−0.145769	+	0.989319i	$0.546566\pi$
$882$		0			0
$883$	−30.6837	−	30.6837i	−1.03259	−	1.03259i	−0.999451	−	0.0331374i	$-0.989450\pi$
$883$	−30.6837	−	30.6837i	−1.03259	−	1.03259i	−0.0331374	−	0.999451i	$-0.510550\pi$
$884$		0			0
$885$	0.0581601	+	0.217056i	0.00195503	+	0.00729627i
$886$		0			0
$887$	24.7803	−	14.3069i	0.832042	−	0.480380i	−0.0225091	−	0.999747i	$-0.507165\pi$
$887$	24.7803	−	14.3069i	0.832042	−	0.480380i	0.854551	+	0.519367i	$0.173832\pi$
$888$		0			0
$889$	1.29977	−	14.8470i	0.0435929	−	0.497951i
$890$		0			0
$891$	13.4891	+	3.61439i	0.451902	+	0.121087i
$892$		0			0
$893$	−14.9882	+	4.01607i	−0.501560	+	0.134393i
$894$		0			0
$895$	−24.7060			−0.825830
$896$		0			0
$897$	0.574859			0.0191940
$898$		0			0
$899$	17.6935	−	4.74096i	0.590112	−	0.158120i
$900$		0			0
$901$	−32.9506	−	8.82909i	−1.09774	−	0.294140i
$902$		0			0
$903$	−0.344012	−	0.240908i	−0.0114480	−	0.00801692i
$904$		0			0
$905$	10.2743	−	5.93185i	0.341528	−	0.197182i
$906$		0			0
$907$	−4.82227	−	17.9969i	−0.160121	−	0.597579i	−0.998612	−	0.0526640i	$-0.983229\pi$
$907$	−4.82227	−	17.9969i	−0.160121	−	0.597579i	0.838492	−	0.544915i	$-0.183438\pi$
$908$		0			0
$909$	−22.3949	−	22.3949i	−0.742793	−	0.742793i
$910$		0			0
$911$	−12.2041			−0.404341			−0.202170	−	0.979350i	$-0.564799\pi$
$911$	−12.2041			−0.404341			−0.202170	+	0.979350i	$0.564799\pi$
$912$		0			0
$913$	9.71601	−	16.8286i	0.321553	−	0.556946i
$914$		0			0
$915$	0.190942	−	0.712603i	0.00631233	−	0.0235579i
$916$		0			0
$917$	5.16119	+	1.87884i	0.170437	+	0.0620448i
$918$		0			0
$919$	−3.57056	+	2.06146i	−0.117782	+	0.0680014i	−0.557734	−	0.830020i	$-0.688329\pi$
$919$	−3.57056	+	2.06146i	−0.117782	+	0.0680014i	0.439952	+	0.898021i	$0.354996\pi$
$920$		0			0
$921$	−1.06989	−	0.617699i	−0.0352539	−	0.0203539i
$922$		0			0
$923$	11.5941	−	11.5941i	0.381623	−	0.381623i
$924$		0			0
$925$	12.6943	+	12.6943i	0.417386	+	0.417386i
$926$		0			0
$927$	5.13083	−	8.88686i	0.168519	−	0.291883i
$928$		0			0
$929$	−22.7002	−	39.3180i	−0.744771	−	1.28998i	−0.950302	−	0.311330i	$-0.899225\pi$
$929$	−22.7002	−	39.3180i	−0.744771	−	1.28998i	0.205531	−	0.978651i	$-0.434108\pi$
$930$		0			0
$931$	23.4396	−	50.2519i	0.768203	−	1.64694i
$932$		0			0
$933$	0.197513	+	0.0529235i	0.00646629	+	0.00173264i
$934$		0			0
$935$	−5.15770	−	2.97780i	−0.168675	−	0.0973845i
$936$		0			0
$937$		−	8.69727i		−	0.284127i	−0.989858	−	0.142064i	$-0.954626\pi$
$937$		−	8.69727i		−	0.284127i	0.989858	−	0.142064i	$-0.0453738\pi$
$938$		0			0
$939$	0.149141	−	0.149141i	0.00486704	−	0.00486704i
$940$		0			0
$941$	11.6093	−	3.11071i	0.378454	−	0.101406i	−0.0645772	−	0.997913i	$-0.520570\pi$
$941$	11.6093	−	3.11071i	0.378454	−	0.101406i	0.443031	+	0.896506i	$0.353903\pi$
$942$		0			0
$943$	−16.6051	−	28.7609i	−0.540737	−	0.936584i
$944$		0			0
$945$	−0.491467	−	1.05411i	−0.0159874	−	0.0342901i
$946$		0			0
$947$	14.8879	−	55.5623i	0.483791	−	1.80553i	−0.101652	−	0.994820i	$-0.532413\pi$
$947$	14.8879	−	55.5623i	0.483791	−	1.80553i	0.585443	−	0.810713i	$-0.300920\pi$
$948$		0			0
$949$	8.25671	+	30.8145i	0.268024	+	1.00028i
$950$		0			0
$951$			1.38499i			0.0449113i
$952$		0			0
$953$			8.69133i			0.281540i	0.990042	+	0.140770i	$0.0449578\pi$
$953$			8.69133i			0.281540i	−0.990042	+	0.140770i	$0.955042\pi$
$954$		0			0
$955$	8.73356	+	32.5941i	0.282611	+	1.05472i
$956$		0			0
$957$	0.0661460	−	0.246860i	0.00213820	−	0.00797986i
$958$		0			0
$959$	4.70855	−	6.72371i	0.152047	−	0.217120i
$960$		0			0
$961$	−4.22236	−	7.31334i	−0.136205	−	0.235914i
$962$		0			0
$963$	−33.1653	+	8.88662i	−1.06874	+	0.286367i
$964$		0			0
$965$	11.5537	−	11.5537i	0.371927	−	0.371927i
$966$		0			0
$967$		−	28.1636i		−	0.905681i	−0.891592	−	0.452840i	$-0.850411\pi$
$967$		−	28.1636i		−	0.905681i	0.891592	−	0.452840i	$-0.149589\pi$
$968$		0			0
$969$	1.13467	+	0.655102i	0.0364509	+	0.0210449i
$970$		0			0
$971$	−10.1276	−	2.71368i	−0.325010	−	0.0870862i	0.0926248	−	0.995701i	$-0.470474\pi$
$971$	−10.1276	−	2.71368i	−0.325010	−	0.0870862i	−0.417635	+	0.908615i	$0.637141\pi$
$972$		0			0
$973$	30.6511	+	36.5327i	0.982629	+	1.17118i
$974$		0			0
$975$	0.209942	+	0.363630i	0.00672352	+	0.0116455i
$976$		0			0
$977$	−17.3812	+	30.1051i	−0.556073	+	0.963147i	0.441746	+	0.897140i	$0.354359\pi$
$977$	−17.3812	+	30.1051i	−0.556073	+	0.963147i	−0.997819	+	0.0660068i	$0.978974\pi$
$978$		0			0
$979$	14.6827	+	14.6827i	0.469262	+	0.469262i
$980$		0			0
$981$	6.64424	−	6.64424i	0.212134	−	0.212134i
$982$		0			0
$983$	2.48718	+	1.43597i	0.0793286	+	0.0458004i	0.539140	−	0.842216i	$-0.318750\pi$
$983$	2.48718	+	1.43597i	0.0793286	+	0.0458004i	−0.459811	+	0.888017i	$0.652083\pi$
$984$		0			0
$985$	−13.2635	+	7.65766i	−0.422609	+	0.243993i
$986$		0			0
$987$	0.223503	−	0.187520i	0.00711418	−	0.00596884i
$988$		0			0
$989$	−3.30166	+	12.3220i	−0.104987	+	0.391816i
$990$		0			0
$991$	15.8744	−	27.4952i	0.504266	−	0.873414i	−0.495722	−	0.868481i	$-0.665097\pi$
$991$	15.8744	−	27.4952i	0.504266	−	0.873414i	0.999988	−	0.00493273i	$-0.00157014\pi$
$992$		0			0
$993$	−0.570832			−0.0181148
$994$		0			0
$995$	−17.7327	−	17.7327i	−0.562166	−	0.562166i
$996$		0			0
$997$	−5.29788	−	19.7719i	−0.167785	−	0.626184i	−0.997668	−	0.0682464i	$-0.978260\pi$
$997$	−5.29788	−	19.7719i	−0.167785	−	0.626184i	0.829883	−	0.557937i	$-0.188407\pi$
$998$		0			0
$999$	1.58836	−	0.917039i	0.0502534	−	0.0290138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.ba.f.417.7		48
4.3	odd	2		896.2.ba.e.417.6		48
7.2	even	3	inner	896.2.ba.f.289.6		48
8.3	odd	2		448.2.ba.c.81.7		48
8.5	even	2		112.2.w.c.109.10	yes	48
16.3	odd	4		448.2.ba.c.305.6		48
16.5	even	4	inner	896.2.ba.f.865.6		48
16.11	odd	4		896.2.ba.e.865.7		48
16.13	even	4		112.2.w.c.53.8	yes	48
28.23	odd	6		896.2.ba.e.289.7		48
56.5	odd	6		784.2.x.o.765.8		48
56.13	odd	2		784.2.x.o.557.10		48
56.37	even	6		112.2.w.c.93.8	yes	48
56.45	odd	6		784.2.m.k.589.1		24
56.51	odd	6		448.2.ba.c.401.6		48
56.53	even	6		784.2.m.j.589.1		24
112.13	odd	4		784.2.x.o.165.8		48
112.37	even	12	inner	896.2.ba.f.737.7		48
112.45	odd	12		784.2.m.k.197.1		24
112.51	odd	12		448.2.ba.c.177.7		48
112.61	odd	12		784.2.x.o.373.10		48
112.93	even	12		112.2.w.c.37.10	✓	48
112.107	odd	12		896.2.ba.e.737.6		48
112.109	even	12		784.2.m.j.197.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.10	✓	48	112.93	even	12
112.2.w.c.53.8	yes	48	16.13	even	4
112.2.w.c.93.8	yes	48	56.37	even	6
112.2.w.c.109.10	yes	48	8.5	even	2
448.2.ba.c.81.7		48	8.3	odd	2
448.2.ba.c.177.7		48	112.51	odd	12
448.2.ba.c.305.6		48	16.3	odd	4
448.2.ba.c.401.6		48	56.51	odd	6
784.2.m.j.197.1		24	112.109	even	12
784.2.m.j.589.1		24	56.53	even	6
784.2.m.k.197.1		24	112.45	odd	12
784.2.m.k.589.1		24	56.45	odd	6
784.2.x.o.165.8		48	112.13	odd	4
784.2.x.o.373.10		48	112.61	odd	12
784.2.x.o.557.10		48	56.13	odd	2
784.2.x.o.765.8		48	56.5	odd	6
896.2.ba.e.289.7		48	28.23	odd	6
896.2.ba.e.417.6		48	4.3	odd	2
896.2.ba.e.737.6		48	112.107	odd	12
896.2.ba.e.865.7		48	16.11	odd	4
896.2.ba.f.289.6		48	7.2	even	3	inner
896.2.ba.f.417.7		48	1.1	even	1	trivial
896.2.ba.f.737.7		48	112.37	even	12	inner
896.2.ba.f.865.6		48	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0543752 - 0.0145698i) q^{3} +(-1.25781 - 0.337028i) q^{5} +(0.230738 - 2.63567i) q^{7} +(-2.59533 + 1.49842i) q^{9} +(0.402875 + 1.50355i) q^{11} +(-1.59615 - 1.59615i) q^{13} -0.0733039 q^{15} +(1.46910 - 2.54455i) q^{17} +(-2.05021 + 7.65147i) q^{19} +(-0.0258547 - 0.146677i) q^{21} +(-3.91784 + 2.26197i) q^{23} +(-2.86164 - 1.65217i) q^{25} +(-0.238706 + 0.238706i) q^{27} +(-2.06234 - 2.06234i) q^{29} +(-3.14025 + 5.43908i) q^{31} +(0.0438128 + 0.0758861i) q^{33} +(-1.17852 + 3.23740i) q^{35} +(-5.24787 - 1.40616i) q^{37} +(-0.110046 - 0.0635352i) q^{39} +7.34101i q^{41} +(1.99391 - 1.99391i) q^{43} +(3.76943 - 1.01002i) q^{45} +(0.979430 + 1.69642i) q^{47} +(-6.89352 - 1.21630i) q^{49} +(0.0428089 - 0.159765i) q^{51} +(-3.00493 - 11.2146i) q^{53} -2.02696i q^{55} +0.445921i q^{57} +(-0.793411 - 2.96105i) q^{59} +(-2.60480 + 9.72123i) q^{61} +(3.35049 + 7.18618i) q^{63} +(1.46970 + 2.54559i) q^{65} +(2.11517 - 0.566758i) q^{67} +(-0.180077 + 0.180077i) q^{69} +7.26378i q^{71} +(-12.2392 - 7.06631i) q^{73} +(-0.179674 - 0.0481435i) q^{75} +(4.05583 - 0.714920i) q^{77} +(-0.961559 - 1.66547i) q^{79} +(4.48574 - 7.76954i) q^{81} +(-8.82731 - 8.82731i) q^{83} +(-2.70543 + 2.70543i) q^{85} +(-0.142188 - 0.0820924i) q^{87} +(11.5526 - 6.66987i) q^{89} +(-4.57521 + 3.83862i) q^{91} +(-0.0915056 + 0.341503i) q^{93} +(5.15752 - 8.93309i) q^{95} -9.69578 q^{97} +(-3.29854 - 3.29854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{5} + 4 q^{11} + 24 q^{13} - 40 q^{15} + 8 q^{17} + 4 q^{19} + 8 q^{21} + 24 q^{27} - 24 q^{29} + 28 q^{31} + 16 q^{33} - 28 q^{35} + 24 q^{37} + 40 q^{43} + 28 q^{45} - 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^5 + 4 * q^11 + 24 * q^13 - 40 * q^15 + 8 * q^17 + 4 * q^19 + 8 * q^21 + 24 * q^27 - 24 * q^29 + 28 * q^31 + 16 * q^33 - 28 * q^35 + 24 * q^37 + 40 * q^43 + 28 * q^45 - 20 * q^47 - 24 * q^51 + 16 * q^53 + 20 * q^59 - 8 * q^61 - 16 * q^63 + 8 * q^65 - 48 * q^67 + 40 * q^69 + 4 * q^75 + 20 * q^77 - 36 * q^79 + 8 * q^83 - 64 * q^91 - 8 * q^93 - 4 * q^95 - 48 * q^97 + 24 * q^99

Introduction

L-functions

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