LMFDB - Embedded newform 800.2.be.a.209.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(209,800)] 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("800.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			209.5
Character	$\chi$	$=$	800.209
Dual form			800.2.be.a.689.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.732250 - 2.25363i) q^{3} +(-2.17427 + 0.522052i) q^{5} +3.97385i q^{7} +(-2.11562 + 1.53709i) q^{9} +(-0.0901459 + 0.124075i) q^{11} +(3.44230 - 2.50098i) q^{13} +(2.76862 + 4.51774i) q^{15} +(0.405955 + 0.131903i) q^{17} +(3.05129 + 0.991424i) q^{19} +(8.95560 - 2.90985i) q^{21} +(4.00689 - 5.51501i) q^{23} +(4.45492 - 2.27017i) q^{25} +(-0.737967 - 0.536164i) q^{27} +(3.12579 - 1.01563i) q^{29} +(-2.29653 + 7.06798i) q^{31} +(0.345629 + 0.112302i) q^{33} +(-2.07456 - 8.64023i) q^{35} +(-7.19328 + 5.22623i) q^{37} +(-8.15691 - 5.92634i) q^{39} +(7.02219 - 5.10192i) q^{41} +7.17438 q^{43} +(3.79750 - 4.44652i) q^{45} +(6.23420 - 2.02562i) q^{47} -8.79147 q^{49} -1.01146i q^{51} +(-2.46974 - 7.60109i) q^{53} +(0.131228 - 0.316834i) q^{55} -7.60246i q^{57} +(6.95639 + 9.57464i) q^{59} +(2.24292 - 3.08711i) q^{61} +(-6.10816 - 8.40716i) q^{63} +(-6.17886 + 7.23487i) q^{65} +(1.80462 - 5.55404i) q^{67} +(-15.3628 - 4.99169i) q^{69} +(-1.49867 - 4.61242i) q^{71} +(-0.112318 + 0.154592i) q^{73} +(-8.37824 - 8.37743i) q^{75} +(-0.493056 - 0.358226i) q^{77} +(2.30104 + 7.08187i) q^{79} +(-3.09223 + 9.51690i) q^{81} +(1.97729 - 6.08548i) q^{83} +(-0.951517 - 0.0748629i) q^{85} +(-4.57771 - 6.30068i) q^{87} +(5.37406 + 3.90448i) q^{89} +(9.93851 + 13.6792i) q^{91} +17.6103 q^{93} +(-7.15191 - 0.562694i) q^{95} +(11.2199 - 3.64557i) q^{97} -0.401058i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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
$3$	−0.732250	−	2.25363i	−0.422765	−	1.30114i	−0.905119	−	0.425159i	$-0.860218\pi$
$3$	−0.732250	−	2.25363i	−0.422765	−	1.30114i	0.482354	−	0.875976i	$-0.339782\pi$
$4$		0			0
$5$	−2.17427	+	0.522052i	−0.972364	+	0.233469i
$5$	−2.17427	+	0.522052i	−0.972364	+	0.233469i
$6$		0			0
$7$			3.97385i			1.50197i	0.660317	+	0.750987i	$0.270422\pi$
$7$			3.97385i			1.50197i	−0.660317	+	0.750987i	$0.729578\pi$
$8$		0			0
$9$	−2.11562	+	1.53709i	−0.705207	+	0.512363i
$10$		0			0
$11$	−0.0901459	+	0.124075i	−0.0271800	+	0.0374101i	−0.822391	−	0.568923i	$-0.807360\pi$
$11$	−0.0901459	+	0.124075i	−0.0271800	+	0.0374101i	0.795211	+	0.606333i	$0.207360\pi$
$12$		0			0
$13$	3.44230	−	2.50098i	0.954723	−	0.693647i	0.00280360	−	0.999996i	$-0.499108\pi$
$13$	3.44230	−	2.50098i	0.954723	−	0.693647i	0.951919	+	0.306349i	$0.0991076\pi$
$14$		0			0
$15$	2.76862	+	4.51774i	0.714856	+	1.16648i
$16$		0			0
$17$	0.405955	+	0.131903i	0.0984586	+	0.0319911i	0.357832	−	0.933786i	$-0.383516\pi$
$17$	0.405955	+	0.131903i	0.0984586	+	0.0319911i	−0.259373	+	0.965777i	$0.583516\pi$
$18$		0			0
$19$	3.05129	+	0.991424i	0.700014	+	0.227448i	0.637337	−	0.770586i	$-0.280036\pi$
$19$	3.05129	+	0.991424i	0.700014	+	0.227448i	0.0626774	+	0.998034i	$0.480036\pi$
$20$		0			0
$21$	8.95560	−	2.90985i	1.95427	−	0.634981i
$22$		0			0
$23$	4.00689	−	5.51501i	0.835494	−	1.14996i	−0.151382	−	0.988475i	$-0.548372\pi$
$23$	4.00689	−	5.51501i	0.835494	−	1.14996i	0.986876	−	0.161483i	$-0.0516277\pi$
$24$		0			0
$25$	4.45492	−	2.27017i	0.890985	−	0.454034i
$26$		0			0
$27$	−0.737967	−	0.536164i	−0.142022	−	0.103185i
$28$		0			0
$29$	3.12579	−	1.01563i	0.580444	−	0.188598i	−0.00405557	−	0.999992i	$-0.501291\pi$
$29$	3.12579	−	1.01563i	0.580444	−	0.188598i	0.584499	+	0.811394i	$0.301291\pi$
$30$		0			0
$31$	−2.29653	+	7.06798i	−0.412468	+	1.26945i	0.502028	+	0.864852i	$0.332588\pi$
$31$	−2.29653	+	7.06798i	−0.412468	+	1.26945i	−0.914496	+	0.404595i	$0.867412\pi$
$32$		0			0
$33$	0.345629	+	0.112302i	0.0601663	+	0.0195492i
$34$		0			0
$35$	−2.07456	−	8.64023i	−0.350664	−	1.46047i
$36$		0			0
$37$	−7.19328	+	5.22623i	−1.18257	+	0.859186i	−0.992459	−	0.122577i	$-0.960884\pi$
$37$	−7.19328	+	5.22623i	−1.18257	+	0.859186i	−0.190109	+	0.981763i	$0.560884\pi$
$38$		0			0
$39$	−8.15691	−	5.92634i	−1.30615	−	0.948975i
$40$		0			0
$41$	7.02219	−	5.10192i	1.09668	−	0.796786i	0.116166	−	0.993230i	$-0.462939\pi$
$41$	7.02219	−	5.10192i	1.09668	−	0.796786i	0.980515	+	0.196444i	$0.0629395\pi$
$42$		0			0
$43$	7.17438			1.09408			0.547042	−	0.837105i	$-0.315754\pi$
$43$	7.17438			1.09408			0.547042	+	0.837105i	$0.315754\pi$
$44$		0			0
$45$	3.79750	−	4.44652i	0.566097	−	0.662847i
$46$		0			0
$47$	6.23420	−	2.02562i	0.909352	−	0.295466i	0.183260	−	0.983064i	$-0.441335\pi$
$47$	6.23420	−	2.02562i	0.909352	−	0.295466i	0.726092	+	0.687598i	$0.241335\pi$
$48$		0			0
$49$	−8.79147			−1.25592
$50$		0			0
$51$		−	1.01146i		−	0.141633i
$52$		0			0
$53$	−2.46974	−	7.60109i	−0.339245	−	1.04409i	−0.964593	−	0.263743i	$-0.915043\pi$
$53$	−2.46974	−	7.60109i	−0.339245	−	1.04409i	0.625348	−	0.780346i	$-0.284957\pi$
$54$		0			0
$55$	0.131228	−	0.316834i	0.0176948	−	0.0427219i
$56$		0			0
$57$		−	7.60246i		−	1.00697i
$58$		0			0
$59$	6.95639	+	9.57464i	0.905644	+	1.24651i	0.968632	+	0.248498i	$0.0799370\pi$
$59$	6.95639	+	9.57464i	0.905644	+	1.24651i	−0.0629880	+	0.998014i	$0.520063\pi$
$60$		0			0
$61$	2.24292	−	3.08711i	0.287176	−	0.395264i	−0.640918	−	0.767609i	$-0.721446\pi$
$61$	2.24292	−	3.08711i	0.287176	−	0.395264i	0.928094	+	0.372345i	$0.121446\pi$
$62$		0			0
$63$	−6.10816	−	8.40716i	−0.769556	−	1.05920i
$64$		0			0
$65$	−6.17886	+	7.23487i	−0.766393	+	0.897375i
$66$		0			0
$67$	1.80462	−	5.55404i	0.220469	−	0.678533i	−0.778251	−	0.627953i	$-0.783893\pi$
$67$	1.80462	−	5.55404i	0.220469	−	0.678533i	0.998720	−	0.0505802i	$-0.0161071\pi$
$68$		0			0
$69$	−15.3628	−	4.99169i	−1.84947	−	0.600929i
$70$		0			0
$71$	−1.49867	−	4.61242i	−0.177859	−	0.547394i	0.821894	−	0.569641i	$-0.192918\pi$
$71$	−1.49867	−	4.61242i	−0.177859	−	0.547394i	−0.999752	+	0.0222475i	$0.992918\pi$
$72$		0			0
$73$	−0.112318	+	0.154592i	−0.0131458	+	0.0180936i	−0.815539	−	0.578702i	$-0.803560\pi$
$73$	−0.112318	+	0.154592i	−0.0131458	+	0.0180936i	0.802394	+	0.596795i	$0.203560\pi$
$74$		0			0
$75$	−8.37824	−	8.37743i	−0.967436	−	0.967342i
$76$		0			0
$77$	−0.493056	−	0.358226i	−0.0561890	−	0.0408237i
$78$		0			0
$79$	2.30104	+	7.08187i	0.258887	+	0.796773i	0.993039	+	0.117787i	$0.0375802\pi$
$79$	2.30104	+	7.08187i	0.258887	+	0.796773i	−0.734152	+	0.678986i	$0.762420\pi$
$80$		0			0
$81$	−3.09223	+	9.51690i	−0.343581	+	1.05743i
$82$		0			0
$83$	1.97729	−	6.08548i	0.217036	−	0.667968i	−0.781967	−	0.623320i	$-0.785783\pi$
$83$	1.97729	−	6.08548i	0.217036	−	0.667968i	0.999003	−	0.0446478i	$-0.0142166\pi$
$84$		0			0
$85$	−0.951517	−	0.0748629i	−0.103207	−	0.00812002i
$86$		0			0
$87$	−4.57771	−	6.30068i	−0.490782	−	0.675504i
$88$		0			0
$89$	5.37406	+	3.90448i	0.569649	+	0.413874i	0.834978	−	0.550284i	$-0.185480\pi$
$89$	5.37406	+	3.90448i	0.569649	+	0.413874i	−0.265329	+	0.964158i	$0.585480\pi$
$90$		0			0
$91$	9.93851	+	13.6792i	1.04184	+	1.43397i
$92$		0			0
$93$	17.6103			1.82610
$94$		0			0
$95$	−7.15191	−	0.562694i	−0.733771	−	0.0577311i
$96$		0			0
$97$	11.2199	−	3.64557i	1.13921	−	0.370151i	0.322140	−	0.946692i	$-0.395598\pi$
$97$	11.2199	−	3.64557i	1.13921	−	0.370151i	0.817068	+	0.576541i	$0.195598\pi$
$98$		0			0
$99$		−	0.401058i		−	0.0403079i
$100$		0			0
$101$			11.2177i			1.11620i	0.829774	+	0.558100i	$0.188470\pi$
$101$			11.2177i			1.11620i	−0.829774	+	0.558100i	$0.811530\pi$
$102$		0			0
$103$	2.59950	−	0.844629i	0.256136	−	0.0832238i	−0.178134	−	0.984006i	$-0.557006\pi$
$103$	2.59950	−	0.844629i	0.256136	−	0.0832238i	0.434271	+	0.900782i	$0.357006\pi$
$104$		0			0
$105$	−17.9528	+	11.0021i	−1.75202	+	1.07369i
$106$		0			0
$107$	0.836926			0.0809087			0.0404544	−	0.999181i	$-0.487119\pi$
$107$	0.836926			0.0809087			0.0404544	+	0.999181i	$0.487119\pi$
$108$		0			0
$109$	7.22454	+	9.94372i	0.691985	+	0.952436i	0.999999	+	0.00105409i	$0.000335528\pi$
$109$	7.22454	+	9.94372i	0.691985	+	0.952436i	−0.308014	+	0.951382i	$0.599664\pi$
$110$		0			0
$111$	17.0453	+	12.3841i	1.61787	+	1.17545i
$112$		0			0
$113$	−0.733589	−	1.00970i	−0.0690103	−	0.0949845i	0.773117	−	0.634264i	$-0.218697\pi$
$113$	−0.733589	−	1.00970i	−0.0690103	−	0.0949845i	−0.842127	+	0.539279i	$0.818697\pi$
$114$		0			0
$115$	−5.83294	+	14.0829i	−0.543925	+	1.31324i
$116$		0			0
$117$	−3.43838	+	10.5822i	−0.317878	+	0.978329i
$118$		0			0
$119$	−0.524162	+	1.61320i	−0.0480498	+	0.147882i
$120$		0			0
$121$	3.39192	+	10.4393i	0.308356	+	0.949023i
$122$		0			0
$123$	−16.6398	−	12.0896i	−1.50036	−	1.09008i
$124$		0			0
$125$	−8.50107	+	7.26167i	−0.760359	+	0.649503i
$126$		0			0
$127$	12.4049	−	17.0738i	1.10075	−	1.51506i	0.266370	−	0.963871i	$-0.414176\pi$
$127$	12.4049	−	17.0738i	1.10075	−	1.51506i	0.834383	−	0.551185i	$-0.185824\pi$
$128$		0			0
$129$	−5.25344	−	16.1684i	−0.462540	−	1.42355i
$130$		0			0
$131$	−6.85047	−	2.22585i	−0.598528	−	0.194474i	−0.00594432	−	0.999982i	$-0.501892\pi$
$131$	−6.85047	−	2.22585i	−0.598528	−	0.194474i	−0.592584	+	0.805509i	$0.701892\pi$
$132$		0			0
$133$	−3.93977	+	12.1254i	−0.341621	+	1.05140i
$134$		0			0
$135$	1.88445	+	0.780510i	0.162187	+	0.0671756i
$136$		0			0
$137$	6.72690	+	9.25878i	0.574718	+	0.791031i	0.993104	−	0.117238i	$-0.0374041\pi$
$137$	6.72690	+	9.25878i	0.574718	+	0.791031i	−0.418386	+	0.908269i	$0.637404\pi$
$138$		0			0
$139$	−2.93724	+	4.04276i	−0.249133	+	0.342903i	−0.915208	−	0.402983i	$-0.867973\pi$
$139$	−2.93724	+	4.04276i	−0.249133	+	0.342903i	0.666074	+	0.745886i	$0.267973\pi$
$140$		0			0
$141$	−9.12999	−	12.5663i	−0.768884	−	1.05828i
$142$		0			0
$143$			0.652557i			0.0545696i
$144$		0			0
$145$	−6.26610	+	3.84008i	−0.520371	+	0.318901i
$146$		0			0
$147$	6.43755	+	19.8128i	0.530961	+	1.63413i
$148$		0			0
$149$		−	6.44210i		−	0.527758i	−0.964556	−	0.263879i	$-0.914998\pi$
$149$		−	6.44210i		−	0.527758i	0.964556	−	0.263879i	$-0.0850019\pi$
$150$		0			0
$151$	−4.73935			−0.385683			−0.192842	−	0.981230i	$-0.561770\pi$
$151$	−4.73935			−0.385683			−0.192842	+	0.981230i	$0.561770\pi$
$152$		0			0
$153$	−1.06159	+	0.344933i	−0.0858248	+	0.0278862i
$154$		0			0
$155$	1.30342	−	16.5666i	0.104693	−	1.33066i
$156$		0			0
$157$	−6.30768			−0.503408			−0.251704	−	0.967804i	$-0.580991\pi$
$157$	−6.30768			−0.503408			−0.251704	+	0.967804i	$0.580991\pi$
$158$		0			0
$159$	−15.3216	+	11.1318i	−1.21508	+	0.882808i
$160$		0			0
$161$	21.9158	+	15.9228i	1.72721	+	1.25489i
$162$		0			0
$163$	−15.8677	+	11.5286i	−1.24286	+	0.902988i	−0.997785	−	0.0665173i	$-0.978811\pi$
$163$	−15.8677	+	11.5286i	−1.24286	+	0.902988i	−0.245071	+	0.969505i	$0.578811\pi$
$164$		0			0
$165$	−0.810120	−	0.0637381i	−0.0630677	−	0.00496200i
$166$		0			0
$167$	−1.38399	−	0.449686i	−0.107096	−	0.0347978i	0.254979	−	0.966947i	$-0.417932\pi$
$167$	−1.38399	−	0.449686i	−0.107096	−	0.0347978i	−0.362075	+	0.932149i	$0.617932\pi$
$168$		0			0
$169$	1.57733	−	4.85451i	0.121333	−	0.373424i
$170$		0			0
$171$	−7.97928	+	2.59263i	−0.610191	+	0.198263i
$172$		0			0
$173$	3.50839	+	2.54899i	0.266738	+	0.193796i	0.713112	−	0.701050i	$-0.247285\pi$
$173$	3.50839	+	2.54899i	0.266738	+	0.193796i	−0.446374	+	0.894846i	$0.647285\pi$
$174$		0			0
$175$	9.02130	+	17.7032i	0.681947	+	1.33824i
$176$		0			0
$177$	16.4839	−	22.6882i	1.23901	−	1.70535i
$178$		0			0
$179$	−1.61587	+	0.525029i	−0.120776	+	0.0392425i	−0.368781	−	0.929516i	$-0.620225\pi$
$179$	−1.61587	+	0.525029i	−0.120776	+	0.0392425i	0.248005	+	0.968759i	$0.420225\pi$
$180$		0			0
$181$	−10.8590	−	3.52830i	−0.807143	−	0.262257i	−0.123756	−	0.992313i	$-0.539494\pi$
$181$	−10.8590	−	3.52830i	−0.807143	−	0.262257i	−0.683387	+	0.730056i	$0.739494\pi$
$182$		0			0
$183$	−8.59960	−	2.79418i	−0.635701	−	0.206552i
$184$		0			0
$185$	12.9118	−	15.1185i	0.949294	−	1.11154i
$186$		0			0
$187$	−0.0529611	+	0.0384785i	−0.00387290	+	0.00281382i
$188$		0			0
$189$	2.13064	−	2.93257i	0.154981	−	0.213313i
$190$		0			0
$191$	12.7176	−	9.23991i	0.920216	−	0.668576i	−0.0233618	−	0.999727i	$-0.507437\pi$
$191$	12.7176	−	9.23991i	0.920216	−	0.668576i	0.943578	+	0.331151i	$0.107437\pi$
$192$		0			0
$193$		−	25.2391i		−	1.81675i	−0.418153	−	0.908377i	$-0.637322\pi$
$193$		−	25.2391i		−	1.81675i	0.418153	−	0.908377i	$-0.362678\pi$
$194$		0			0
$195$	20.8292	+	8.62715i	1.49161	+	0.617803i
$196$		0			0
$197$	−0.983987	−	3.02840i	−0.0701062	−	0.215765i	0.909865	−	0.414905i	$-0.136185\pi$
$197$	−0.983987	−	3.02840i	−0.0701062	−	0.215765i	−0.979971	+	0.199140i	$0.936185\pi$
$198$		0			0
$199$	−2.67148			−0.189376			−0.0946880	−	0.995507i	$-0.530185\pi$
$199$	−2.67148			−0.189376			−0.0946880	+	0.995507i	$0.530185\pi$
$200$		0			0
$201$	−13.8382			−0.976070
$202$		0			0
$203$	4.03596	+	12.4214i	0.283269	+	0.871811i
$204$		0			0
$205$	−12.6047	+	14.7589i	−0.880349	+	1.03081i
$206$		0			0
$207$			17.8266i			1.23903i
$208$		0			0
$209$	−0.398073	+	0.289217i	−0.0275353	+	0.0200055i
$210$		0			0
$211$	−4.80758	+	6.61706i	−0.330967	+	0.455537i	−0.941776	−	0.336241i	$-0.890844\pi$
$211$	−4.80758	+	6.61706i	−0.330967	+	0.455537i	0.610809	+	0.791778i	$0.290844\pi$
$212$		0			0
$213$	−9.29731	+	6.75489i	−0.637041	+	0.462837i
$214$		0			0
$215$	−15.5991	+	3.74540i	−1.06385	+	0.255434i
$216$		0			0
$217$	−28.0871	−	9.12605i	−1.90668	−	0.619516i
$218$		0			0
$219$	0.430638	+	0.139923i	0.0290998	+	0.00945511i
$220$		0			0
$221$	1.72731	−	0.561236i	0.116191	−	0.0377528i
$222$		0			0
$223$	−6.83294	+	9.40473i	−0.457567	+	0.629788i	−0.974002	−	0.226539i	$-0.927259\pi$
$223$	−6.83294	+	9.40473i	−0.457567	+	0.629788i	0.516435	+	0.856327i	$0.327259\pi$
$224$		0			0
$225$	−5.93548	+	11.6504i	−0.395699	+	0.776695i
$226$		0			0
$227$	−2.98300	−	2.16728i	−0.197989	−	0.143847i	0.484374	−	0.874861i	$-0.339047\pi$
$227$	−2.98300	−	2.16728i	−0.197989	−	0.143847i	−0.682363	+	0.731014i	$0.739047\pi$
$228$		0			0
$229$	7.32499	−	2.38003i	0.484049	−	0.157277i	−0.0568191	−	0.998384i	$-0.518096\pi$
$229$	7.32499	−	2.38003i	0.484049	−	0.157277i	0.540868	+	0.841107i	$0.318096\pi$
$230$		0			0
$231$	−0.446270	+	1.37348i	−0.0293624	+	0.0903683i
$232$		0			0
$233$	−24.6979	−	8.02485i	−1.61802	−	0.525725i	−0.646543	−	0.762877i	$-0.723786\pi$
$233$	−24.6979	−	8.02485i	−1.61802	−	0.525725i	−0.971473	+	0.237152i	$0.923786\pi$
$234$		0			0
$235$	−12.4974	+	7.65882i	−0.815239	+	0.499606i
$236$		0			0
$237$	14.2750	−	10.3714i	0.927262	−	0.673695i
$238$		0			0
$239$	−14.1821	−	10.3039i	−0.917362	−	0.666503i	0.0255037	−	0.999675i	$-0.491881\pi$
$239$	−14.1821	−	10.3039i	−0.917362	−	0.666503i	−0.942866	+	0.333172i	$0.891881\pi$
$240$		0			0
$241$	−1.71555	+	1.24642i	−0.110508	+	0.0802891i	−0.641667	−	0.766983i	$-0.721757\pi$
$241$	−1.71555	+	1.24642i	−0.110508	+	0.0802891i	0.531159	+	0.847272i	$0.321757\pi$
$242$		0			0
$243$	20.9753			1.34557
$244$		0			0
$245$	19.1151	−	4.58961i	1.22122	−	0.293219i
$246$		0			0
$247$	12.9830	−	4.21843i	0.826088	−	0.268412i
$248$		0			0
$249$	−15.1623			−0.960872
$250$		0			0
$251$			11.9422i			0.753784i	0.926257	+	0.376892i	$0.123007\pi$
$251$			11.9422i			0.753784i	−0.926257	+	0.376892i	$0.876993\pi$
$252$		0			0
$253$	0.323071	+	0.994311i	0.0203113	+	0.0625118i
$254$		0			0
$255$	0.528035	+	2.19919i	0.0330668	+	0.137719i
$256$		0			0
$257$			28.6858i			1.78937i	0.446696	+	0.894686i	$0.352601\pi$
$257$			28.6858i			1.78937i	−0.446696	+	0.894686i	$0.647399\pi$
$258$		0			0
$259$	−20.7682	−	28.5850i	−1.29048	−	1.77619i
$260$		0			0
$261$	−5.05187	+	6.95330i	−0.312703	+	0.430398i
$262$		0			0
$263$	−15.6987	−	21.6075i	−0.968026	−	1.33237i	−0.943038	−	0.332685i	$-0.892045\pi$
$263$	−15.6987	−	21.6075i	−0.968026	−	1.33237i	−0.0249876	−	0.999688i	$-0.507955\pi$
$264$		0			0
$265$	9.33806	+	15.2375i	0.573632	+	0.936032i
$266$		0			0
$267$	4.86412	−	14.9702i	0.297679	−	0.916162i
$268$		0			0
$269$	−10.2389	−	3.32682i	−0.624276	−	0.202840i	−0.0202383	−	0.999795i	$-0.506442\pi$
$269$	−10.2389	−	3.32682i	−0.624276	−	0.202840i	−0.604038	+	0.796956i	$0.706442\pi$
$270$		0			0
$271$	−0.686274	−	2.11214i	−0.0416882	−	0.128303i	0.928046	−	0.372465i	$-0.121487\pi$
$271$	−0.686274	−	2.11214i	−0.0416882	−	0.128303i	−0.969735	+	0.244162i	$0.921487\pi$
$272$		0			0
$273$	23.5504	−	32.4143i	1.42533	−	1.96180i
$274$		0			0
$275$	−0.119922	+	0.757392i	−0.00723154	+	0.0456724i
$276$		0			0
$277$	16.4822	+	11.9750i	0.990317	+	0.719507i	0.959990	−	0.280033i	$-0.0903454\pi$
$277$	16.4822	+	11.9750i	0.990317	+	0.719507i	0.0303263	+	0.999540i	$0.490345\pi$
$278$		0			0
$279$	−6.00553	−	18.4831i	−0.359542	−	1.10656i
$280$		0			0
$281$	6.01789	−	18.5212i	0.358997	−	1.10488i	−0.594658	−	0.803979i	$-0.702712\pi$
$281$	6.01789	−	18.5212i	0.358997	−	1.10488i	0.953655	−	0.300902i	$-0.0972876\pi$
$282$		0			0
$283$	−7.53527	+	23.1912i	−0.447925	+	1.37857i	0.431318	+	0.902200i	$0.358049\pi$
$283$	−7.53527	+	23.1912i	−0.447925	+	1.37857i	−0.879243	+	0.476373i	$0.841951\pi$
$284$		0			0
$285$	3.96888	+	16.5298i	0.235096	+	0.979142i
$286$		0			0
$287$	20.2742	+	27.9051i	1.19675	+	1.64719i
$288$		0			0
$289$	−13.6059	−	9.88526i	−0.800346	−	0.581486i
$290$		0			0
$291$	−16.4315	−	22.6161i	−0.963234	−	1.32578i
$292$		0			0
$293$	−6.35974			−0.371540			−0.185770	−	0.982593i	$-0.559478\pi$
$293$	−6.35974			−0.371540			−0.185770	+	0.982593i	$0.559478\pi$
$294$		0			0
$295$	−20.1235	−	17.1863i	−1.17164	−	1.00062i
$296$		0			0
$297$	0.133049	−	0.0432304i	0.00772031	−	0.00250848i
$298$		0			0
$299$		−	29.0055i		−	1.67743i
$300$		0			0
$301$			28.5099i			1.64328i
$302$		0			0
$303$	25.2805	−	8.21414i	1.45233	−	0.471890i
$304$		0			0
$305$	−3.26508	+	7.88315i	−0.186958	+	0.451388i
$306$		0			0
$307$	11.6407			0.664369			0.332184	−	0.943215i	$-0.392214\pi$
$307$	11.6407			0.664369			0.332184	+	0.943215i	$0.392214\pi$
$308$		0			0
$309$	−3.80697	−	5.23984i	−0.216571	−	0.298084i
$310$		0			0
$311$	3.35063	+	2.43438i	0.189997	+	0.138041i	0.678717	−	0.734400i	$-0.262536\pi$
$311$	3.35063	+	2.43438i	0.189997	+	0.138041i	−0.488720	+	0.872440i	$0.662536\pi$
$312$		0			0
$313$	11.9325	+	16.4236i	0.674463	+	0.928318i	0.999851	−	0.0172622i	$-0.00549501\pi$
$313$	11.9325	+	16.4236i	0.674463	+	0.928318i	−0.325388	+	0.945580i	$0.605495\pi$
$314$		0			0
$315$	17.6698	+	15.0907i	0.995579	+	0.850263i
$316$		0			0
$317$	7.88349	−	24.2629i	0.442781	−	1.36274i	−0.442118	−	0.896957i	$-0.645773\pi$
$317$	7.88349	−	24.2629i	0.442781	−	1.36274i	0.884899	−	0.465783i	$-0.154227\pi$
$318$		0			0
$319$	−0.155762	+	0.479387i	−0.00872102	+	0.0268405i
$320$		0			0
$321$	−0.612839	−	1.88613i	−0.0342053	−	0.105273i
$322$		0			0
$323$	1.10792	+	0.804948i	0.0616461	+	0.0447885i
$324$		0			0
$325$	9.65755	−	18.9563i	0.535704	−	1.05150i
$326$		0			0
$327$	17.1193	−	23.5627i	0.946701	−	1.30302i
$328$		0			0
$329$	8.04949	+	24.7738i	0.443783	+	1.36582i
$330$		0			0
$331$	−15.6015	−	5.06925i	−0.857538	−	0.278631i	−0.152938	−	0.988236i	$-0.548874\pi$
$331$	−15.6015	−	5.06925i	−0.857538	−	0.278631i	−0.704600	+	0.709605i	$0.748874\pi$
$332$		0			0
$333$	7.18509	−	22.1134i	0.393740	−	1.21181i
$334$		0			0
$335$	−1.02423	+	13.0181i	−0.0559596	+	0.711254i
$336$		0			0
$337$	4.30693	+	5.92798i	0.234613	+	0.322918i	0.910048	−	0.414502i	$-0.136044\pi$
$337$	4.30693	+	5.92798i	0.234613	+	0.322918i	−0.675435	+	0.737419i	$0.736044\pi$
$338$		0			0
$339$	−1.73832	+	2.39259i	−0.0944126	+	0.129948i
$340$		0			0
$341$	−0.669939	−	0.922091i	−0.0362792	−	0.0499340i
$342$		0			0
$343$		−	7.11905i		−	0.384392i
$344$		0			0
$345$	36.0089	+	2.83309i	1.93866	+	0.152528i
$346$		0			0
$347$	−5.02633	−	15.4695i	−0.269828	−	0.830444i	−0.990542	−	0.137212i	$-0.956186\pi$
$347$	−5.02633	−	15.4695i	−0.269828	−	0.830444i	0.720714	−	0.693232i	$-0.243814\pi$
$348$		0			0
$349$			8.49794i			0.454884i	0.973792	+	0.227442i	$0.0730363\pi$
$349$			8.49794i			0.454884i	−0.973792	+	0.227442i	$0.926964\pi$
$350$		0			0
$351$	−3.88124			−0.207165
$352$		0			0
$353$	−26.5350	+	8.62175i	−1.41232	+	0.458889i	−0.913152	−	0.407618i	$-0.866359\pi$
$353$	−26.5350	+	8.62175i	−1.41232	+	0.458889i	−0.499164	+	0.866508i	$0.666359\pi$
$354$		0			0
$355$	5.66643	+	9.24628i	0.300743	+	0.490741i
$356$		0			0
$357$	4.01939			0.212729
$358$		0			0
$359$	−3.88920	+	2.82567i	−0.205264	+	0.149133i	−0.685668	−	0.727914i	$-0.740490\pi$
$359$	−3.88920	+	2.82567i	−0.205264	+	0.149133i	0.480404	+	0.877047i	$0.340490\pi$
$360$		0			0
$361$	−7.04387	−	5.11767i	−0.370730	−	0.269351i
$362$		0			0
$363$	21.0425	−	15.2883i	1.10445	−	0.802427i
$364$		0			0
$365$	0.163504	−	0.394761i	0.00855820	−	0.0206627i
$366$		0			0
$367$	−25.0194	−	8.12928i	−1.30600	−	0.424345i	−0.428335	−	0.903620i	$-0.640900\pi$
$367$	−25.0194	−	8.12928i	−1.30600	−	0.424345i	−0.877665	+	0.479275i	$0.840900\pi$
$368$		0			0
$369$	−7.01419	+	21.5874i	−0.365144	+	1.12380i
$370$		0			0
$371$	30.2056	−	9.81438i	1.56819	−	0.509537i
$372$		0			0
$373$	0.602132	+	0.437474i	0.0311772	+	0.0226516i	0.603265	−	0.797541i	$-0.293866\pi$
$373$	0.602132	+	0.437474i	0.0311772	+	0.0226516i	−0.572088	+	0.820193i	$0.693866\pi$
$374$		0			0
$375$	22.5900	+	13.8409i	1.16654	+	0.714743i
$376$		0			0
$377$	8.21983	−	11.3136i	0.423343	−	0.582681i
$378$		0			0
$379$	12.9975	−	4.22314i	0.667636	−	0.216928i	0.0444617	−	0.999011i	$-0.485843\pi$
$379$	12.9975	−	4.22314i	0.667636	−	0.216928i	0.623174	+	0.782083i	$0.285843\pi$
$380$		0			0
$381$	−47.5616	−	15.4537i	−2.43665	−	0.791716i
$382$		0			0
$383$	29.3793	+	9.54593i	1.50121	+	0.487774i	0.940372	−	0.340148i	$-0.110477\pi$
$383$	29.3793	+	9.54593i	1.50121	+	0.487774i	0.560843	+	0.827922i	$0.310477\pi$
$384$		0			0
$385$	1.25905	+	0.521480i	0.0641672	+	0.0265771i
$386$		0			0
$387$	−15.1783	+	11.0277i	−0.771555	+	0.560568i
$388$		0			0
$389$	11.9671	−	16.4713i	0.606757	−	0.835129i	−0.389549	−	0.921006i	$-0.627369\pi$
$389$	11.9671	−	16.4713i	0.606757	−	0.835129i	0.996306	+	0.0858769i	$0.0273692\pi$
$390$		0			0
$391$	2.35406	−	1.71033i	0.119050	−	0.0864949i
$392$		0			0
$393$			17.0683i			0.860983i
$394$		0			0
$395$	−8.70020	−	14.1967i	−0.437754	−	0.714312i
$396$		0			0
$397$	−2.98890	−	9.19889i	−0.150009	−	0.461679i	0.847612	−	0.530616i	$-0.178039\pi$
$397$	−2.98890	−	9.19889i	−0.150009	−	0.461679i	−0.997621	+	0.0689367i	$0.978039\pi$
$398$		0			0
$399$	30.2110			1.51244
$400$		0			0
$401$	2.73446			0.136553			0.0682763	−	0.997666i	$-0.478250\pi$
$401$	2.73446			0.136553			0.0682763	+	0.997666i	$0.478250\pi$
$402$		0			0
$403$	9.77153	+	30.0737i	0.486755	+	1.49808i
$404$		0			0
$405$	1.75503	−	22.3066i	0.0872080	−	1.10843i
$406$		0			0
$407$		−	1.36363i		−	0.0675927i
$408$		0			0
$409$	4.63848	−	3.37005i	0.229358	−	0.166638i	−0.467171	−	0.884167i	$-0.654727\pi$
$409$	4.63848	−	3.37005i	0.229358	−	0.166638i	0.696529	+	0.717529i	$0.254727\pi$
$410$		0			0
$411$	15.9401	−	21.9397i	0.786268	−	1.08221i
$412$		0			0
$413$	−38.0482	+	27.6436i	−1.87223	+	1.36025i
$414$		0			0
$415$	−1.12223	+	14.2637i	−0.0550882	+	0.700179i
$416$		0			0
$417$	11.2617	+	3.65915i	0.551488	+	0.179189i
$418$		0			0
$419$	12.1575	+	3.95021i	0.593932	+	0.192980i	0.590532	−	0.807014i	$-0.298918\pi$
$419$	12.1575	+	3.95021i	0.593932	+	0.192980i	0.00339993	+	0.999994i	$0.498918\pi$
$420$		0			0
$421$	31.0541	−	10.0901i	1.51348	−	0.491761i	0.569568	−	0.821945i	$-0.307111\pi$
$421$	31.0541	−	10.0901i	1.51348	−	0.491761i	0.943917	+	0.330184i	$0.107111\pi$
$422$		0			0
$423$	−10.0757	+	13.8680i	−0.489895	+	0.674283i
$424$		0			0
$425$	2.10794	−	0.333969i	0.102250	−	0.0161999i
$426$		0			0
$427$	12.2677	+	8.91302i	0.593677	+	0.431331i
$428$		0			0
$429$	1.47062	−	0.477835i	0.0710024	−	0.0230701i
$430$		0			0
$431$	−6.17275	+	18.9978i	−0.297331	+	0.915090i	0.685098	+	0.728451i	$0.259759\pi$
$431$	−6.17275	+	18.9978i	−0.297331	+	0.915090i	−0.982429	+	0.186639i	$0.940241\pi$
$432$		0			0
$433$	17.8084	+	5.78629i	0.855815	+	0.278071i	0.703880	−	0.710319i	$-0.251449\pi$
$433$	17.8084	+	5.78629i	0.855815	+	0.278071i	0.151936	+	0.988390i	$0.451449\pi$
$434$		0			0
$435$	13.2425	+	11.3096i	0.634928	+	0.542253i
$436$		0			0
$437$	17.6939	−	12.8554i	0.846413	−	0.614955i
$438$		0			0
$439$	3.05596	+	2.22028i	0.145853	+	0.105968i	0.658319	−	0.752739i	$-0.271268\pi$
$439$	3.05596	+	2.22028i	0.145853	+	0.105968i	−0.512466	+	0.858708i	$0.671268\pi$
$440$		0			0
$441$	18.5994	−	13.5133i	0.885687	−	0.643489i
$442$		0			0
$443$	−18.1857			−0.864027			−0.432014	−	0.901867i	$-0.642197\pi$
$443$	−18.1857			−0.864027			−0.432014	+	0.901867i	$0.642197\pi$
$444$		0			0
$445$	−13.7230	−	5.68387i	−0.650533	−	0.269441i
$446$		0			0
$447$	−14.5181	+	4.71723i	−0.686684	+	0.223117i
$448$		0			0
$449$	−14.3619			−0.677782			−0.338891	−	0.940826i	$-0.610052\pi$
$449$	−14.3619			−0.677782			−0.338891	+	0.940826i	$0.610052\pi$
$450$		0			0
$451$			1.33120i			0.0626836i
$452$		0			0
$453$	3.47039	+	10.6808i	0.163053	+	0.501826i
$454$		0			0
$455$	−28.7503	−	24.5539i	−1.34783	−	1.15110i
$456$		0			0
$457$			6.53654i			0.305767i	0.988244	+	0.152883i	$0.0488558\pi$
$457$			6.53654i			0.305767i	−0.988244	+	0.152883i	$0.951144\pi$
$458$		0			0
$459$	−0.228860	−	0.314999i	−0.0106823	−	0.0147029i
$460$		0			0
$461$	7.47611	−	10.2900i	0.348197	−	0.479252i	−0.598616	−	0.801036i	$-0.704282\pi$
$461$	7.47611	−	10.2900i	0.348197	−	0.479252i	0.946813	+	0.321784i	$0.104282\pi$
$462$		0			0
$463$	−9.95183	−	13.6975i	−0.462501	−	0.636578i	0.512524	−	0.858673i	$-0.328710\pi$
$463$	−9.95183	−	13.6975i	−0.462501	−	0.636578i	−0.975025	+	0.222095i	$0.928710\pi$
$464$		0			0
$465$	−38.2895	+	9.19348i	−1.77563	+	0.426337i
$466$		0			0
$467$	−9.20560	+	28.3319i	−0.425985	+	1.31105i	0.476064	+	0.879411i	$0.342063\pi$
$467$	−9.20560	+	28.3319i	−0.425985	+	1.31105i	−0.902048	+	0.431635i	$0.857937\pi$
$468$		0			0
$469$	22.0709	+	7.17127i	1.01914	+	0.331138i
$470$		0			0
$471$	4.61880	+	14.2152i	0.212823	+	0.655002i
$472$		0			0
$473$	−0.646741	+	0.890163i	−0.0297372	+	0.0409297i
$474$		0			0
$475$	15.8440	−	2.51022i	0.726971	−	0.115177i
$476$		0			0
$477$	16.9086	+	12.2848i	0.774191	+	0.562483i
$478$		0			0
$479$	3.43557	+	10.5736i	0.156975	+	0.483120i	0.998356	−	0.0573232i	$-0.0182566\pi$
$479$	3.43557	+	10.5736i	0.156975	+	0.483120i	−0.841380	+	0.540443i	$0.818257\pi$
$480$		0			0
$481$	−11.6908	+	35.9805i	−0.533053	+	1.64057i
$482$		0			0
$483$	19.8362	−	61.0496i	0.902579	−	2.77785i
$484$		0			0
$485$	−22.4920	+	13.7838i	−1.02131	+	0.625892i
$486$		0			0
$487$	−7.50918	−	10.3355i	−0.340273	−	0.468346i	0.604248	−	0.796796i	$-0.293474\pi$
$487$	−7.50918	−	10.3355i	−0.340273	−	0.468346i	−0.944521	+	0.328450i	$0.893474\pi$
$488$		0			0
$489$	37.6003	+	27.3182i	1.70035	+	1.23537i
$490$		0			0
$491$	2.31718	+	3.18932i	0.104573	+	0.143932i	0.858096	−	0.513489i	$-0.171647\pi$
$491$	2.31718	+	3.18932i	0.104573	+	0.143932i	−0.753523	+	0.657421i	$0.771647\pi$
$492$		0			0
$493$	1.40289			0.0631831
$494$		0			0
$495$	0.209373	+	0.872010i	0.00941064	+	0.0391939i
$496$		0			0
$497$	18.3291	−	5.95547i	0.822171	−	0.267139i
$498$		0			0
$499$			11.9283i			0.533984i	0.963699	+	0.266992i	$0.0860297\pi$
$499$			11.9283i			0.533984i	−0.963699	+	0.266992i	$0.913970\pi$
$500$		0			0
$501$			3.44829i			0.154058i
$502$		0			0
$503$	−3.90940	+	1.27024i	−0.174312	+	0.0566373i	−0.394873	−	0.918736i	$-0.629211\pi$
$503$	−3.90940	+	1.27024i	−0.174312	+	0.0566373i	0.220561	+	0.975373i	$0.429211\pi$
$504$		0			0
$505$	−5.85621	−	24.3903i	−0.260598	−	1.08535i
$506$		0			0
$507$	−12.0953			−0.537170
$508$		0			0
$509$	−3.33050	−	4.58404i	−0.147622	−	0.203184i	0.728802	−	0.684724i	$-0.240077\pi$
$509$	−3.33050	−	4.58404i	−0.147622	−	0.203184i	−0.876424	+	0.481541i	$0.840077\pi$
$510$		0			0
$511$	−0.614325	−	0.446334i	−0.0271762	−	0.0197446i
$512$		0			0
$513$	−1.72019	−	2.36763i	−0.0759480	−	0.104533i
$514$		0			0
$515$	−5.21108	+	3.19353i	−0.229628	+	0.140724i
$516$		0			0
$517$	−0.310659	+	0.956111i	−0.0136628	+	0.0420497i
$518$		0			0
$519$	3.17548	−	9.77312i	0.139388	−	0.428992i
$520$		0			0
$521$	−12.0623	−	37.1240i	−0.528460	−	1.62643i	−0.757371	−	0.652985i	$-0.773516\pi$
$521$	−12.0623	−	37.1240i	−0.528460	−	1.62643i	0.228911	−	0.973447i	$-0.426484\pi$
$522$		0			0
$523$	−8.43650	−	6.12948i	−0.368903	−	0.268023i	0.387853	−	0.921721i	$-0.373217\pi$
$523$	−8.43650	−	6.12948i	−0.368903	−	0.268023i	−0.756756	+	0.653698i	$0.773217\pi$
$524$		0			0
$525$	33.2906	−	33.2939i	1.45292	−	1.45306i
$526$		0			0
$527$	−1.86457	+	2.56636i	−0.0812221	+	0.111793i
$528$		0			0
$529$	−7.25276	−	22.3217i	−0.315337	−	0.970509i
$530$		0			0
$531$	−29.4342	−	9.56374i	−1.27733	−	0.415031i
$532$		0			0
$533$	11.4127	−	35.1247i	0.494339	−	1.52142i
$534$		0			0
$535$	−1.81971	+	0.436919i	−0.0786728	+	0.0188897i
$536$		0			0
$537$	2.36644	+	3.25713i	0.102120	+	0.140556i
$538$		0			0
$539$	0.792515	−	1.09080i	0.0341361	−	0.0469843i
$540$		0			0
$541$	26.5512	+	36.5445i	1.14152	+	1.57117i	0.764056	+	0.645150i	$0.223205\pi$
$541$	26.5512	+	36.5445i	1.14152	+	1.57117i	0.377468	+	0.926023i	$0.376795\pi$
$542$		0			0
$543$			27.0558i			1.16108i
$544$		0			0
$545$	−20.8993	−	17.8488i	−0.895226	−	0.764558i
$546$		0			0
$547$	−7.26120	−	22.3477i	−0.310467	−	0.955518i	−0.977580	−	0.210562i	$-0.932471\pi$
$547$	−7.26120	−	22.3477i	−0.310467	−	0.955518i	0.667114	−	0.744956i	$-0.267529\pi$
$548$		0			0
$549$			9.97873i			0.425882i
$550$		0			0
$551$	10.5446			0.449215
$552$		0			0
$553$	−28.1423	+	9.14399i	−1.19673	+	0.388842i
$554$		0			0
$555$	−43.5262	−	18.0279i	−1.84759	−	0.765243i
$556$		0			0
$557$	−13.2964			−0.563387			−0.281693	−	0.959504i	$-0.590896\pi$
$557$	−13.2964			−0.563387			−0.281693	+	0.959504i	$0.590896\pi$
$558$		0			0
$559$	24.6964	−	17.9430i	1.04455	−	0.758907i
$560$		0			0
$561$	0.125497	+	0.0911790i	0.00529849	+	0.00384958i
$562$		0			0
$563$	18.8220	−	13.6750i	0.793254	−	0.576332i	−0.115674	−	0.993287i	$-0.536903\pi$
$563$	18.8220	−	13.6750i	0.793254	−	0.576332i	0.908927	+	0.416955i	$0.136903\pi$
$564$		0			0
$565$	2.12214	+	1.81239i	0.0892790	+	0.0762478i
$566$		0			0
$567$	−37.8187	−	12.2880i	−1.58824	−	0.516049i
$568$		0			0
$569$	5.82276	−	17.9206i	0.244103	−	0.751272i	−0.751680	−	0.659528i	$-0.770756\pi$
$569$	5.82276	−	17.9206i	0.244103	−	0.751272i	0.995783	−	0.0917433i	$-0.0292439\pi$
$570$		0			0
$571$	21.2548	−	6.90610i	0.889485	−	0.289011i	0.171595	−	0.985168i	$-0.445108\pi$
$571$	21.2548	−	6.90610i	0.889485	−	0.289011i	0.717890	+	0.696156i	$0.245108\pi$
$572$		0			0
$573$	−30.1358	−	21.8950i	−1.25894	−	0.914676i
$574$		0			0
$575$	5.33038	−	33.6652i	0.222292	−	1.40394i
$576$		0			0
$577$	−1.18138	+	1.62603i	−0.0491816	+	0.0676927i	−0.832899	−	0.553424i	$-0.813321\pi$
$577$	−1.18138	+	1.62603i	−0.0491816	+	0.0676927i	0.783718	+	0.621117i	$0.213321\pi$
$578$		0			0
$579$	−56.8798	+	18.4814i	−2.36384	+	0.768059i
$580$		0			0
$581$	24.1828	+	7.85746i	1.00327	+	0.325982i
$582$		0			0
$583$	1.16574	+	0.378773i	0.0482802	+	0.0156872i
$584$		0			0
$585$	1.95149	−	24.8037i	0.0806842	−	1.02551i
$586$		0			0
$587$	6.11054	−	4.43957i	0.252209	−	0.183241i	−0.454496	−	0.890749i	$-0.650181\pi$
$587$	6.11054	−	4.43957i	0.252209	−	0.183241i	0.706705	+	0.707508i	$0.250181\pi$
$588$		0			0
$589$	−14.0147	+	19.2896i	−0.577467	+	0.794815i
$590$		0			0
$591$	−6.10438	+	4.43509i	−0.251101	+	0.182435i
$592$		0			0
$593$			3.98822i			0.163777i	0.996642	+	0.0818883i	$0.0260951\pi$
$593$			3.98822i			0.163777i	−0.996642	+	0.0818883i	$0.973905\pi$
$594$		0			0
$595$	0.297494	−	3.78119i	0.0121961	−	0.155014i
$596$		0			0
$597$	1.95619	+	6.02053i	0.0800614	+	0.246404i
$598$		0			0
$599$	−5.40034			−0.220652			−0.110326	−	0.993895i	$-0.535190\pi$
$599$	−5.40034			−0.220652			−0.110326	+	0.993895i	$0.535190\pi$
$600$		0			0
$601$	−22.5630			−0.920364			−0.460182	−	0.887825i	$-0.652216\pi$
$601$	−22.5630			−0.920364			−0.460182	+	0.887825i	$0.652216\pi$
$602$		0			0
$603$	4.71916	+	14.5241i	0.192179	+	0.591467i
$604$		0			0
$605$	−12.8248	−	20.9270i	−0.521402	−	0.850804i
$606$		0			0
$607$		−	9.99712i		−	0.405771i	−0.979202	−	0.202885i	$-0.934968\pi$
$607$		−	9.99712i		−	0.405771i	0.979202	−	0.202885i	$-0.0650319\pi$
$608$		0			0
$609$	25.0379	−	18.1911i	1.01459	−	0.737142i
$610$		0			0
$611$	16.3940	−	22.5644i	0.663230	−	0.912857i
$612$		0			0
$613$	6.04756	−	4.39381i	0.244259	−	0.177464i	−0.458920	−	0.888478i	$-0.651763\pi$
$613$	6.04756	−	4.39381i	0.244259	−	0.177464i	0.703178	+	0.711013i	$0.251763\pi$
$614$		0			0
$615$	42.4909	+	17.5991i	1.71340	+	0.709665i
$616$		0			0
$617$	−38.2178	−	12.4177i	−1.53859	−	0.499919i	−0.587605	−	0.809148i	$-0.699929\pi$
$617$	−38.2178	−	12.4177i	−1.53859	−	0.499919i	−0.950988	+	0.309229i	$0.899929\pi$
$618$		0			0
$619$	31.9264	+	10.3735i	1.28323	+	0.416946i	0.869716	−	0.493552i	$-0.164302\pi$
$619$	31.9264	+	10.3735i	1.28323	+	0.416946i	0.413513	+	0.910498i	$0.364302\pi$
$620$		0			0
$621$	−5.91390	+	1.92154i	−0.237317	+	0.0771089i
$622$		0			0
$623$	−15.5158	+	21.3557i	−0.621628	+	0.855598i
$624$		0			0
$625$	14.6927	−	20.2268i	0.587707	−	0.809074i
$626$		0			0
$627$	0.943277	+	0.685331i	0.0376708	+	0.0273695i
$628$		0			0
$629$	−3.60950	+	1.17280i	−0.143920	+	0.0467626i
$630$		0			0
$631$	7.98445	−	24.5736i	0.317856	−	0.978260i	−0.656707	−	0.754146i	$-0.728051\pi$
$631$	7.98445	−	24.5736i	0.317856	−	0.978260i	0.974563	−	0.224114i	$-0.0719489\pi$
$632$		0			0
$633$	18.4328	+	5.98917i	0.732637	+	0.238048i
$634$		0			0
$635$	−18.0581	+	43.5991i	−0.716614	+	1.73018i
$636$		0			0
$637$	−30.2629	+	21.9873i	−1.19906	+	0.871168i
$638$		0			0
$639$	10.2603	+	7.45455i	0.405892	+	0.294898i
$640$		0			0
$641$	0.412927	−	0.300009i	0.0163096	−	0.0118496i	−0.579601	−	0.814901i	$-0.696791\pi$
$641$	0.412927	−	0.300009i	0.0163096	−	0.0118496i	0.595910	+	0.803051i	$0.296791\pi$
$642$		0			0
$643$	10.5308			0.415295			0.207648	−	0.978204i	$-0.433419\pi$
$643$	10.5308			0.415295			0.207648	+	0.978204i	$0.433419\pi$
$644$		0			0
$645$	19.8632	+	32.4120i	0.782112	+	1.27622i
$646$		0			0
$647$	−3.99881	+	1.29929i	−0.157209	+	0.0510804i	−0.386564	−	0.922262i	$-0.626338\pi$
$647$	−3.99881	+	1.29929i	−0.157209	+	0.0510804i	0.229355	+	0.973343i	$0.426338\pi$
$648$		0			0
$649$	−1.81507			−0.0712476
$650$		0			0
$651$			69.9805i			2.74275i
$652$		0			0
$653$	11.3948	+	35.0696i	0.445913	+	1.37238i	0.881479	+	0.472223i	$0.156548\pi$
$653$	11.3948	+	35.0696i	0.445913	+	1.37238i	−0.435566	+	0.900157i	$0.643452\pi$
$654$		0			0
$655$	16.0568	+	1.26331i	0.627391	+	0.0493615i
$656$		0			0
$657$		−	0.499700i		−	0.0194952i
$658$		0			0
$659$	−3.74222	−	5.15073i	−0.145776	−	0.200644i	0.729885	−	0.683570i	$-0.239574\pi$
$659$	−3.74222	−	5.15073i	−0.145776	−	0.200644i	−0.875661	+	0.482927i	$0.839574\pi$
$660$		0			0
$661$	−11.2489	+	15.4828i	−0.437533	+	0.602213i	−0.969662	−	0.244451i	$-0.921392\pi$
$661$	−11.2489	+	15.4828i	−0.437533	+	0.602213i	0.532128	+	0.846664i	$0.321392\pi$
$662$		0			0
$663$	−2.52964	−	3.48175i	−0.0982430	−	0.135220i
$664$		0			0
$665$	2.23606	−	28.4206i	0.0867107	−	1.10210i
$666$		0			0
$667$	6.92347	−	21.3082i	0.268078	−	0.825058i
$668$		0			0
$669$	26.1982	+	8.51232i	1.01288	+	0.329105i
$670$		0			0
$671$	0.180844	+	0.556581i	0.00698142	+	0.0214866i
$672$		0			0
$673$	6.67094	−	9.18177i	0.257146	−	0.353931i	−0.660852	−	0.750516i	$-0.729805\pi$
$673$	6.67094	−	9.18177i	0.257146	−	0.353931i	0.917998	+	0.396585i	$0.129805\pi$
$674$		0			0
$675$	−4.50477	−	0.713262i	−0.173389	−	0.0274535i
$676$		0			0
$677$	−36.4526	−	26.4844i	−1.40099	−	1.01788i	−0.994557	−	0.104197i	$-0.966773\pi$
$677$	−36.4526	−	26.4844i	−1.40099	−	1.01788i	−0.406432	−	0.913681i	$-0.633227\pi$
$678$		0			0
$679$	14.4869	+	44.5862i	0.555957	+	1.71106i
$680$		0			0
$681$	−2.69995	+	8.30958i	−0.103462	+	0.318424i
$682$		0			0
$683$	−1.81402	+	5.58297i	−0.0694114	+	0.213626i	−0.979745	−	0.200249i	$-0.935825\pi$
$683$	−1.81402	+	5.58297i	−0.0694114	+	0.213626i	0.910334	+	0.413875i	$0.135825\pi$
$684$		0			0
$685$	−19.4597	−	16.6193i	−0.743516	−	0.634992i
$686$		0			0
$687$	−10.7274	−	14.7651i	−0.409278	−	0.563322i
$688$		0			0
$689$	−27.5118	−	19.9885i	−1.04811	−	0.761500i
$690$		0			0
$691$	−15.1834	−	20.8982i	−0.577604	−	0.795004i	0.415826	−	0.909444i	$-0.363493\pi$
$691$	−15.1834	−	20.8982i	−0.577604	−	0.795004i	−0.993430	+	0.114440i	$0.963493\pi$
$692$		0			0
$693$	1.59375			0.0605414
$694$		0			0
$695$	4.27583	−	10.3235i	0.162191	−	0.391591i
$696$		0			0
$697$	3.52365	−	1.14490i	0.133468	−	0.0433663i
$698$		0			0
$699$			61.5363i			2.32752i
$700$		0			0
$701$			1.13715i			0.0429497i	0.999769	+	0.0214749i	$0.00683619\pi$
$701$			1.13715i			0.0429497i	−0.999769	+	0.0214749i	$0.993164\pi$
$702$		0			0
$703$	−27.1302	+	8.81514i	−1.02323	+	0.332469i
$704$		0			0
$705$	26.4114	+	22.5563i	0.994710	+	0.849521i
$706$		0			0
$707$	−44.5773			−1.67650
$708$		0			0
$709$	10.2367	+	14.0896i	0.384447	+	0.529147i	0.956756	−	0.290892i	$-0.0939520\pi$
$709$	10.2367	+	14.0896i	0.384447	+	0.529147i	−0.572308	+	0.820038i	$0.693952\pi$
$710$		0			0
$711$	−15.7536	−	11.4457i	−0.590806	−	0.429246i
$712$		0			0
$713$	29.7780	+	40.9859i	1.11520	+	1.53494i
$714$		0			0
$715$	−0.340669	−	1.41884i	−0.0127403	−	0.0530615i
$716$		0			0
$717$	−12.8363	+	39.5062i	−0.479382	+	1.47539i
$718$		0			0
$719$	5.78813	−	17.8140i	0.215861	−	0.664351i	−0.783231	−	0.621731i	$-0.786430\pi$
$719$	5.78813	−	17.8140i	0.215861	−	0.664351i	0.999091	−	0.0426199i	$-0.0135704\pi$
$720$		0			0
$721$	3.35643	+	10.3300i	0.125000	+	0.384710i
$722$		0			0
$723$	4.06519	+	2.95353i	0.151186	+	0.109843i
$724$		0			0
$725$	11.6195	−	11.6206i	0.431537	−	0.431579i
$726$		0			0
$727$	−26.4822	+	36.4497i	−0.982172	+	1.35184i	−0.0465209	+	0.998917i	$0.514813\pi$
$727$	−26.4822	+	36.4497i	−0.982172	+	1.35184i	−0.935651	+	0.352926i	$0.885187\pi$
$728$		0			0
$729$	−6.08251	−	18.7200i	−0.225278	−	0.693335i
$730$		0			0
$731$	2.91248	+	0.946322i	0.107722	+	0.0350010i
$732$		0			0
$733$	9.67831	−	29.7868i	0.357476	−	1.10020i	−0.597083	−	0.802179i	$-0.703674\pi$
$733$	9.67831	−	29.7868i	0.357476	−	1.10020i	0.954560	−	0.298020i	$-0.0963262\pi$
$734$		0			0
$735$	−24.3403	−	39.7176i	−0.897805	−	1.46501i
$736$		0			0
$737$	0.526439	+	0.724582i	0.0193916	+	0.0266903i
$738$		0			0
$739$	3.68173	−	5.06746i	0.135435	−	0.186410i	−0.735913	−	0.677076i	$-0.763247\pi$
$739$	3.68173	−	5.06746i	0.135435	−	0.186410i	0.871347	+	0.490667i	$0.163247\pi$
$740$		0			0
$741$	−19.0136	−	26.1700i	−0.698482	−	0.961377i
$742$		0			0
$743$			38.8347i			1.42471i	0.701820	+	0.712354i	$0.252371\pi$
$743$			38.8347i			1.42471i	−0.701820	+	0.712354i	$0.747629\pi$
$744$		0			0
$745$	3.36312	+	14.0069i	0.123215	+	0.513173i
$746$		0			0
$747$	5.17072	+	15.9138i	0.189187	+	0.582257i
$748$		0			0
$749$			3.32582i			0.121523i
$750$		0			0
$751$	−51.9829			−1.89688			−0.948441	−	0.316953i	$-0.897340\pi$
$751$	−51.9829			−1.89688			−0.948441	+	0.316953i	$0.897340\pi$
$752$		0			0
$753$	26.9133	−	8.74466i	0.980775	−	0.318673i
$754$		0			0
$755$	10.3046	−	2.47419i	0.375025	−	0.0900450i
$756$		0			0
$757$	−8.96987			−0.326015			−0.163008	−	0.986625i	$-0.552120\pi$
$757$	−8.96987			−0.326015			−0.163008	+	0.986625i	$0.552120\pi$
$758$		0			0
$759$	2.00424	−	1.45617i	0.0727494	−	0.0528555i
$760$		0			0
$761$	2.35324	+	1.70973i	0.0853050	+	0.0619777i	0.629620	−	0.776903i	$-0.283210\pi$
$761$	2.35324	+	1.70973i	0.0853050	+	0.0619777i	−0.544315	+	0.838881i	$0.683210\pi$
$762$		0			0
$763$	−39.5148	+	28.7092i	−1.43053	+	1.03934i
$764$		0			0
$765$	2.12812	−	1.30419i	0.0769424	−	0.0471529i
$766$		0			0
$767$	47.8920	+	15.5610i	1.72928	+	0.561877i
$768$		0			0
$769$	−13.6554	+	42.0269i	−0.492425	+	1.51553i	0.328507	+	0.944502i	$0.393455\pi$
$769$	−13.6554	+	42.0269i	−0.492425	+	1.51553i	−0.820932	+	0.571026i	$0.806545\pi$
$770$		0			0
$771$	64.6473	−	21.0052i	2.32822	−	0.756483i
$772$		0			0
$773$	6.38549	+	4.63933i	0.229670	+	0.166865i	0.696669	−	0.717393i	$-0.254665\pi$
$773$	6.38549	+	4.63933i	0.229670	+	0.166865i	−0.466999	+	0.884258i	$0.654665\pi$
$774$		0			0
$775$	5.81466	+	36.7008i	0.208869	+	1.31833i
$776$		0			0
$777$	−49.2126	+	67.7354i	−1.76549	+	2.42999i
$778$		0			0
$779$	26.4849	−	8.60546i	0.948920	−	0.308323i
$780$		0			0
$781$	0.707386	+	0.229844i	0.0253122	+	0.00822445i
$782$		0			0
$783$	−2.85127	−	0.926434i	−0.101896	−	0.0331081i
$784$		0			0
$785$	13.7146	−	3.29294i	0.489496	−	0.117530i
$786$		0			0
$787$	−22.0945	+	16.0526i	−0.787585	+	0.572214i	−0.907246	−	0.420601i	$-0.861819\pi$
$787$	−22.0945	+	16.0526i	−0.787585	+	0.572214i	0.119661	+	0.992815i	$0.461819\pi$
$788$		0			0
$789$	−37.1999	+	51.2012i	−1.32435	+	1.82281i
$790$		0			0
$791$	4.01239	−	2.91517i	0.142664	−	0.103652i
$792$		0			0
$793$		−	16.2363i		−	0.576567i
$794$		0			0
$795$	27.5019	−	32.2022i	0.975393	−	1.14209i
$796$		0			0
$797$	13.7936	+	42.4524i	0.488596	+	1.50374i	0.826705	+	0.562636i	$0.190213\pi$
$797$	13.7936	+	42.4524i	0.488596	+	1.50374i	−0.338109	+	0.941107i	$0.609787\pi$
$798$		0			0
$799$	2.79799			0.0989858
$800$		0			0
$801$	−17.3710			−0.613775
$802$		0			0
$803$	−0.00905606	−	0.0278717i	−0.000319581	−	0.000983570i
$804$		0			0
$805$	−55.9634	−	23.1792i	−1.97245	−	0.816960i
$806$		0			0
$807$			25.5108i			0.898022i
$808$		0			0
$809$	−21.7506	+	15.8027i	−0.764710	+	0.555594i	−0.900351	−	0.435164i	$-0.856690\pi$
$809$	−21.7506	+	15.8027i	−0.764710	+	0.555594i	0.135641	+	0.990758i	$0.456690\pi$
$810$		0			0
$811$	−16.2026	+	22.3010i	−0.568951	+	0.783095i	−0.992430	−	0.122812i	$-0.960809\pi$
$811$	−16.2026	+	22.3010i	−0.568951	+	0.783095i	0.423479	+	0.905906i	$0.360809\pi$
$812$		0			0
$813$	−4.25745	+	3.09322i	−0.149315	+	0.108484i
$814$		0			0
$815$	28.4822	−	33.3501i	0.997689	−	1.16820i
$816$		0			0
$817$	21.8911	+	7.11286i	0.765874	+	0.248847i
$818$		0			0
$819$	−42.0522	−	13.6636i	−1.46942	−	0.477445i
$820$		0			0
$821$	−3.95039	+	1.28356i	−0.137869	+	0.0447965i	−0.377139	−	0.926157i	$-0.623092\pi$
$821$	−3.95039	+	1.28356i	−0.137869	+	0.0447965i	0.239269	+	0.970953i	$0.423092\pi$
$822$		0			0
$823$	15.2147	−	20.9412i	0.530350	−	0.729964i	−0.456834	−	0.889552i	$-0.651017\pi$
$823$	15.2147	−	20.9412i	0.530350	−	0.729964i	0.987184	+	0.159588i	$0.0510166\pi$
$824$		0			0
$825$	1.79470	−	0.284341i	0.0624833	−	0.00989948i
$826$		0			0
$827$	−23.9203	−	17.3791i	−0.831790	−	0.604330i	0.0882755	−	0.996096i	$-0.471864\pi$
$827$	−23.9203	−	17.3791i	−0.831790	−	0.604330i	−0.920065	+	0.391766i	$0.871864\pi$
$828$		0			0
$829$	−6.49796	+	2.11131i	−0.225683	+	0.0733290i	−0.419676	−	0.907674i	$-0.637856\pi$
$829$	−6.49796	+	2.11131i	−0.225683	+	0.0733290i	0.193993	+	0.981003i	$0.437856\pi$
$830$		0			0
$831$	14.9182	−	45.9134i	0.517506	−	1.59272i
$832$		0			0
$833$	−3.56894	−	1.15962i	−0.123657	−	0.0401785i
$834$		0			0
$835$	3.24393	+	0.255224i	0.112261	+	0.00883240i
$836$		0			0
$837$	5.48436	−	3.98462i	0.189567	−	0.137729i
$838$		0			0
$839$	−17.3783	−	12.6261i	−0.599964	−	0.435900i	0.245902	−	0.969295i	$-0.420916\pi$
$839$	−17.3783	−	12.6261i	−0.599964	−	0.435900i	−0.845866	+	0.533395i	$0.820916\pi$
$840$		0			0
$841$	−14.7225	+	10.6965i	−0.507671	+	0.368845i
$842$		0			0
$843$	−46.1465			−1.58937
$844$		0			0
$845$	−0.895229	+	11.3785i	−0.0307968	+	0.391432i
$846$		0			0
$847$	−41.4840	+	13.4790i	−1.42541	+	0.463143i
$848$		0			0
$849$	57.7821			1.98308
$850$		0			0
$851$			60.6119i			2.07775i
$852$		0			0
$853$	1.18714	+	3.65365i	0.0406469	+	0.125098i	0.969321	−	0.245799i	$-0.0790502\pi$
$853$	1.18714	+	3.65365i	0.0406469	+	0.125098i	−0.928674	+	0.370897i	$0.879050\pi$
$854$		0			0
$855$	15.9956	−	9.80268i	0.547040	−	0.335244i
$856$		0			0
$857$			0.293028i			0.0100096i	0.999987	+	0.00500482i	$0.00159309\pi$
$857$			0.293028i			0.0100096i	−0.999987	+	0.00500482i	$0.998407\pi$
$858$		0			0
$859$	3.58283	+	4.93135i	0.122245	+	0.168255i	0.865753	−	0.500471i	$-0.166840\pi$
$859$	3.58283	+	4.93135i	0.122245	+	0.168255i	−0.743509	+	0.668726i	$0.766840\pi$
$860$		0			0
$861$	48.0421	−	66.1242i	1.63727	−	2.25351i
$862$		0			0
$863$	29.9343	+	41.2010i	1.01897	+	1.40250i	0.912921	+	0.408137i	$0.133821\pi$
$863$	29.9343	+	41.2010i	1.01897	+	1.40250i	0.106053	+	0.994360i	$0.466179\pi$
$864$		0			0
$865$	−8.95890	−	3.71065i	−0.304612	−	0.126166i
$866$		0			0
$867$	−12.3148	+	37.9012i	−0.418234	+	1.28719i
$868$		0			0
$869$	−1.08611	−	0.352900i	−0.0368439	−	0.0119713i
$870$		0			0
$871$	−7.67849	−	23.6320i	−0.260176	−	0.800739i
$872$		0			0
$873$	−18.1335	+	24.9586i	−0.613726	+	0.844722i
$874$		0			0
$875$	−28.8568	−	33.7820i	−0.975537	−	1.14204i
$876$		0			0
$877$	−31.6298	−	22.9804i	−1.06806	−	0.775993i	−0.0924999	−	0.995713i	$-0.529486\pi$
$877$	−31.6298	−	22.9804i	−1.06806	−	0.775993i	−0.975563	+	0.219720i	$0.929486\pi$
$878$		0			0
$879$	4.65692	+	14.3325i	0.157074	+	0.483424i
$880$		0			0
$881$	14.7146	−	45.2868i	0.495746	−	1.52575i	−0.320045	−	0.947402i	$-0.603698\pi$
$881$	14.7146	−	45.2868i	0.495746	−	1.52575i	0.815791	−	0.578347i	$-0.196302\pi$
$882$		0			0
$883$	9.74973	−	30.0066i	0.328104	−	1.00980i	−0.641915	−	0.766775i	$-0.721860\pi$
$883$	9.74973	−	30.0066i	0.328104	−	1.00980i	0.970020	−	0.243026i	$-0.0781400\pi$
$884$		0			0
$885$	−23.9961	+	57.9357i	−0.806621	+	1.94749i
$886$		0			0
$887$	−2.02393	−	2.78570i	−0.0679570	−	0.0935348i	0.773686	−	0.633570i	$-0.218411\pi$
$887$	−2.02393	−	2.78570i	−0.0679570	−	0.0935348i	−0.841643	+	0.540035i	$0.818411\pi$
$888$		0			0
$889$	67.8488	+	49.2950i	2.27557	+	1.65330i
$890$		0			0
$891$	−0.902059	−	1.24158i	−0.0302201	−	0.0415944i
$892$		0			0
$893$	21.0306			0.703762
$894$		0			0
$895$	3.23925	−	1.98512i	0.108276	−	0.0663554i
$896$		0			0
$897$	−65.3676	+	21.2392i	−2.18256	+	0.709157i
$898$		0			0
$899$			24.4254i			0.814633i
$900$		0			0
$901$		−	3.41147i		−	0.113652i
$902$		0			0
$903$	64.2509	−	20.8764i	2.13814	−	0.694722i
$904$		0			0
$905$	25.4524	+	2.00253i	0.846066	+	0.0665662i
$906$		0			0
$907$	52.1263			1.73082			0.865412	−	0.501061i	$-0.167057\pi$
$907$	52.1263			1.73082			0.865412	+	0.501061i	$0.167057\pi$
$908$		0			0
$909$	−17.2426	−	23.7323i	−0.571900	−	0.787152i
$910$		0			0
$911$	−6.68942	−	4.86015i	−0.221630	−	0.161024i	0.471430	−	0.881904i	$-0.343738\pi$
$911$	−6.68942	−	4.86015i	−0.221630	−	0.161024i	−0.693060	+	0.720880i	$0.743738\pi$
$912$		0			0
$913$	0.576812	+	0.793914i	0.0190897	+	0.0262747i
$914$		0			0
$915$	20.1566	+	1.58587i	0.666356	+	0.0524271i
$916$		0			0
$917$	8.84520	−	27.2227i	0.292094	−	0.898974i
$918$		0			0
$919$	4.18616	−	12.8837i	0.138089	−	0.424993i	−0.857969	−	0.513702i	$-0.828274\pi$
$919$	4.18616	−	12.8837i	0.138089	−	0.424993i	0.996058	+	0.0887082i	$0.0282739\pi$
$920$		0			0
$921$	−8.52388	−	26.2338i	−0.280871	−	0.864434i
$922$		0			0
$923$	−16.6944	−	12.1292i	−0.549504	−	0.399238i
$924$		0			0
$925$	−20.1811	+	39.6124i	−0.663551	+	1.30245i
$926$		0			0
$927$	−4.20129	+	5.78258i	−0.137988	+	0.189925i
$928$		0			0
$929$	−4.82136	−	14.8386i	−0.158184	−	0.486839i	0.840286	−	0.542144i	$-0.182387\pi$
$929$	−4.82136	−	14.8386i	−0.158184	−	0.486839i	−0.998470	+	0.0553044i	$0.982387\pi$
$930$		0			0
$931$	−26.8253	−	8.71608i	−0.879165	−	0.285658i
$932$		0			0
$933$	3.03269	−	9.33367i	0.0992859	−	0.305571i
$934$		0			0
$935$	0.0950640	−	0.111311i	0.00310893	−	0.00364026i
$936$		0			0
$937$	−34.3932	−	47.3382i	−1.12358	−	1.54647i	−0.799728	−	0.600363i	$-0.795023\pi$
$937$	−34.3932	−	47.3382i	−1.12358	−	1.54647i	−0.323849	−	0.946109i	$-0.604977\pi$
$938$		0			0
$939$	28.2753	−	38.9176i	0.922729	−	1.27003i
$940$		0			0
$941$	14.6909	+	20.2203i	0.478909	+	0.659162i	0.978295	−	0.207218i	$-0.0664410\pi$
$941$	14.6909	+	20.2203i	0.478909	+	0.659162i	−0.499386	+	0.866380i	$0.666441\pi$
$942$		0			0
$943$		−	59.1702i		−	1.92685i
$944$		0			0
$945$	−3.10163	+	7.48851i	−0.100896	+	0.243601i
$946$		0			0
$947$	5.61268	+	17.2740i	0.182388	+	0.561331i	0.999894	−	0.0145890i	$-0.00464397\pi$
$947$	5.61268	+	17.2740i	0.182388	+	0.561331i	−0.817506	+	0.575920i	$0.804644\pi$
$948$		0			0
$949$			0.813057i			0.0263929i
$950$		0			0
$951$	−60.4524			−1.96030
$952$		0			0
$953$	−28.0280	+	9.10684i	−0.907915	+	0.295000i	−0.725500	−	0.688222i	$-0.758391\pi$
$953$	−28.0280	+	9.10684i	−0.907915	+	0.295000i	−0.182415	+	0.983222i	$0.558391\pi$
$954$		0			0
$955$	−22.8279	+	26.7293i	−0.738693	+	0.864941i
$956$		0			0
$957$	1.19442			0.0386101
$958$		0			0
$959$	−36.7930	+	26.7317i	−1.18811	+	0.863211i
$960$		0			0
$961$	−19.6028	−	14.2422i	−0.632348	−	0.459427i
$962$		0			0
$963$	−1.77062	+	1.28643i	−0.0570574	+	0.0414546i
$964$		0			0
$965$	13.1762	+	54.8768i	0.424155	+	1.76655i
$966$		0			0
$967$	45.7969	+	14.8803i	1.47273	+	0.478518i	0.931931	−	0.362635i	$-0.118123\pi$
$967$	45.7969	+	14.8803i	1.47273	+	0.478518i	0.540797	+	0.841153i	$0.318123\pi$
$968$		0			0
$969$	1.00279	−	3.08626i	0.0322141	−	0.0991449i
$970$		0			0
$971$	6.19282	−	2.01217i	0.198737	−	0.0645736i	−0.207957	−	0.978138i	$-0.566681\pi$
$971$	6.19282	−	2.01217i	0.198737	−	0.0645736i	0.406694	+	0.913564i	$0.366681\pi$
$972$		0			0
$973$	−16.0653	−	11.6721i	−0.515031	−	0.374192i
$974$		0			0
$975$	−49.7922	−	7.88384i	−1.59463	−	0.252485i
$976$		0			0
$977$	12.3885	−	17.0513i	0.396342	−	0.545518i	−0.563479	−	0.826130i	$-0.690538\pi$
$977$	12.3885	−	17.0513i	0.396342	−	0.545518i	0.959821	+	0.280612i	$0.0905375\pi$
$978$		0			0
$979$	−0.968899	+	0.314814i	−0.0309662	+	0.0100615i
$980$		0			0
$981$	−30.5688	−	9.93239i	−0.975986	−	0.317117i
$982$		0			0
$983$	−2.23619	−	0.726581i	−0.0713232	−	0.0231743i	0.273138	−	0.961975i	$-0.411938\pi$
$983$	−2.23619	−	0.726581i	−0.0713232	−	0.0231743i	−0.344461	+	0.938801i	$0.611938\pi$
$984$		0			0
$985$	3.72044	+	6.07088i	0.118543	+	0.193434i
$986$		0			0
$987$	49.9368	−	36.2812i	1.58950	−	1.15484i
$988$		0			0
$989$	28.7469	−	39.5668i	0.914100	−	1.25815i
$990$		0			0
$991$	6.59439	−	4.79110i	0.209478	−	0.152194i	−0.478100	−	0.878306i	$-0.658674\pi$
$991$	6.59439	−	4.79110i	0.209478	−	0.152194i	0.687577	+	0.726111i	$0.258674\pi$
$992$		0			0
$993$			38.8721i			1.23357i
$994$		0			0
$995$	5.80852	−	1.39465i	0.184142	−	0.0442134i
$996$		0			0
$997$	−7.07471	−	21.7737i	−0.224058	−	0.689580i	−0.998386	−	0.0567955i	$-0.981912\pi$
$997$	−7.07471	−	21.7737i	−0.224058	−	0.689580i	0.774328	−	0.632785i	$-0.218088\pi$
$998$		0			0
$999$	8.11052			0.256606

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.209.5		112
4.3	odd	2		200.2.o.a.109.26	yes	112
8.3	odd	2		200.2.o.a.109.7	✓	112
8.5	even	2	inner	800.2.be.a.209.24		112
20.3	even	4		1000.2.t.b.701.35		224
20.7	even	4		1000.2.t.b.701.22		224
20.19	odd	2		1000.2.o.a.549.3		112
25.14	even	10	inner	800.2.be.a.689.24		112
40.3	even	4		1000.2.t.b.701.14		224
40.19	odd	2		1000.2.o.a.549.22		112
40.27	even	4		1000.2.t.b.701.43		224
100.11	odd	10		1000.2.o.a.949.22		112
100.23	even	20		1000.2.t.b.301.14		224
100.27	even	20		1000.2.t.b.301.43		224
100.39	odd	10		200.2.o.a.189.7	yes	112
200.11	odd	10		1000.2.o.a.949.3		112
200.27	even	20		1000.2.t.b.301.22		224
200.123	even	20		1000.2.t.b.301.35		224
200.139	odd	10		200.2.o.a.189.26	yes	112
200.189	even	10	inner	800.2.be.a.689.5		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.7	✓	112	8.3	odd	2
200.2.o.a.109.26	yes	112	4.3	odd	2
200.2.o.a.189.7	yes	112	100.39	odd	10
200.2.o.a.189.26	yes	112	200.139	odd	10
800.2.be.a.209.5		112	1.1	even	1	trivial
800.2.be.a.209.24		112	8.5	even	2	inner
800.2.be.a.689.5		112	200.189	even	10	inner
800.2.be.a.689.24		112	25.14	even	10	inner
1000.2.o.a.549.3		112	20.19	odd	2
1000.2.o.a.549.22		112	40.19	odd	2
1000.2.o.a.949.3		112	200.11	odd	10
1000.2.o.a.949.22		112	100.11	odd	10
1000.2.t.b.301.14		224	100.23	even	20
1000.2.t.b.301.22		224	200.27	even	20
1000.2.t.b.301.35		224	200.123	even	20
1000.2.t.b.301.43		224	100.27	even	20
1000.2.t.b.701.14		224	40.3	even	4
1000.2.t.b.701.22		224	20.7	even	4
1000.2.t.b.701.35		224	20.3	even	4
1000.2.t.b.701.43		224	40.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.732250 - 2.25363i) q^{3} +(-2.17427 + 0.522052i) q^{5} +3.97385i q^{7} +(-2.11562 + 1.53709i) q^{9} +(-0.0901459 + 0.124075i) q^{11} +(3.44230 - 2.50098i) q^{13} +(2.76862 + 4.51774i) q^{15} +(0.405955 + 0.131903i) q^{17} +(3.05129 + 0.991424i) q^{19} +(8.95560 - 2.90985i) q^{21} +(4.00689 - 5.51501i) q^{23} +(4.45492 - 2.27017i) q^{25} +(-0.737967 - 0.536164i) q^{27} +(3.12579 - 1.01563i) q^{29} +(-2.29653 + 7.06798i) q^{31} +(0.345629 + 0.112302i) q^{33} +(-2.07456 - 8.64023i) q^{35} +(-7.19328 + 5.22623i) q^{37} +(-8.15691 - 5.92634i) q^{39} +(7.02219 - 5.10192i) q^{41} +7.17438 q^{43} +(3.79750 - 4.44652i) q^{45} +(6.23420 - 2.02562i) q^{47} -8.79147 q^{49} -1.01146i q^{51} +(-2.46974 - 7.60109i) q^{53} +(0.131228 - 0.316834i) q^{55} -7.60246i q^{57} +(6.95639 + 9.57464i) q^{59} +(2.24292 - 3.08711i) q^{61} +(-6.10816 - 8.40716i) q^{63} +(-6.17886 + 7.23487i) q^{65} +(1.80462 - 5.55404i) q^{67} +(-15.3628 - 4.99169i) q^{69} +(-1.49867 - 4.61242i) q^{71} +(-0.112318 + 0.154592i) q^{73} +(-8.37824 - 8.37743i) q^{75} +(-0.493056 - 0.358226i) q^{77} +(2.30104 + 7.08187i) q^{79} +(-3.09223 + 9.51690i) q^{81} +(1.97729 - 6.08548i) q^{83} +(-0.951517 - 0.0748629i) q^{85} +(-4.57771 - 6.30068i) q^{87} +(5.37406 + 3.90448i) q^{89} +(9.93851 + 13.6792i) q^{91} +17.6103 q^{93} +(-7.15191 - 0.562694i) q^{95} +(11.2199 - 3.64557i) q^{97} -0.401058i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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